Date: 2019-12-25 21:52:27 CET, cola version: 1.3.2
Document is loading...
All available functions which can be applied to this res_list object:
res_list
#> A 'ConsensusPartitionList' object with 24 methods.
#> On a matrix with 31632 rows and 73 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] 31632 73
The density distribution for each sample is visualized as in one column in the following heatmap. The clustering is based on the distance which is the Kolmogorov-Smirnov statistic between two distributions.
library(ComplexHeatmap)
densityHeatmap(mat, top_annotation = HeatmapAnnotation(df = get_anno(res_list),
col = get_anno_col(res_list)), ylab = "value", cluster_columns = TRUE, show_column_names = FALSE,
mc.cores = 4)
Folowing table shows the best k (number of partitions) for each combination
of top-value methods and partition methods. Clicking on the method name in
the table goes to the section for a single combination of methods.
The cola vignette explains the definition of the metrics used for determining the best number of partitions.
suggest_best_k(res_list)
| The best k | 1-PAC | Mean silhouette | Concordance | Optional k | ||
|---|---|---|---|---|---|---|
| SD:kmeans | 2 | 1.000 | 0.989 | 0.994 | ** | |
| SD:NMF | 2 | 1.000 | 0.973 | 0.989 | ** | |
| CV:kmeans | 2 | 1.000 | 0.996 | 0.998 | ** | |
| CV:NMF | 2 | 1.000 | 0.972 | 0.987 | ** | |
| MAD:kmeans | 2 | 1.000 | 0.984 | 0.993 | ** | |
| ATC:kmeans | 3 | 1.000 | 0.991 | 0.996 | ** | 2 |
| ATC:skmeans | 2 | 1.000 | 0.989 | 0.995 | ** | |
| ATC:mclust | 3 | 1.000 | 0.972 | 0.980 | ** | 2 |
| ATC:NMF | 2 | 1.000 | 0.957 | 0.983 | ** | |
| MAD:NMF | 2 | 1.000 | 0.967 | 0.984 | ** | |
| SD:skmeans | 2 | 0.968 | 0.964 | 0.983 | ** | |
| CV:skmeans | 2 | 0.968 | 0.957 | 0.980 | ** | |
| ATC:pam | 6 | 0.945 | 0.891 | 0.954 | * | 2,3,5 |
| MAD:pam | 3 | 0.908 | 0.901 | 0.956 | * | |
| MAD:skmeans | 3 | 0.870 | 0.909 | 0.959 | ||
| SD:mclust | 4 | 0.762 | 0.803 | 0.922 | ||
| SD:pam | 3 | 0.757 | 0.845 | 0.930 | ||
| MAD:mclust | 3 | 0.665 | 0.859 | 0.919 | ||
| CV:mclust | 4 | 0.581 | 0.727 | 0.873 | ||
| ATC:hclust | 3 | 0.575 | 0.789 | 0.879 | ||
| CV:pam | 3 | 0.555 | 0.788 | 0.890 | ||
| SD:hclust | 5 | 0.431 | 0.536 | 0.717 | ||
| MAD:hclust | 4 | 0.353 | 0.550 | 0.745 | ||
| CV:hclust | 3 | 0.330 | 0.645 | 0.815 |
**: 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 0.973 0.989 0.396 0.597 0.597
#> CV:NMF 2 1.000 0.972 0.987 0.387 0.610 0.610
#> MAD:NMF 2 1.000 0.967 0.984 0.415 0.597 0.597
#> ATC:NMF 2 1.000 0.957 0.983 0.457 0.543 0.543
#> SD:skmeans 2 0.968 0.964 0.983 0.482 0.521 0.521
#> CV:skmeans 2 0.968 0.957 0.980 0.487 0.521 0.521
#> MAD:skmeans 2 0.859 0.894 0.957 0.489 0.521 0.521
#> ATC:skmeans 2 1.000 0.989 0.995 0.487 0.514 0.514
#> SD:mclust 2 0.624 0.877 0.933 0.296 0.740 0.740
#> CV:mclust 2 0.556 0.865 0.912 0.351 0.686 0.686
#> MAD:mclust 2 0.835 0.903 0.949 0.291 0.703 0.703
#> ATC:mclust 2 0.941 0.954 0.977 0.475 0.521 0.521
#> SD:kmeans 2 1.000 0.989 0.994 0.386 0.610 0.610
#> CV:kmeans 2 1.000 0.996 0.998 0.393 0.610 0.610
#> MAD:kmeans 2 1.000 0.984 0.993 0.393 0.610 0.610
#> ATC:kmeans 2 1.000 0.985 0.994 0.442 0.562 0.562
#> SD:pam 2 0.829 0.913 0.948 0.282 0.740 0.740
#> CV:pam 2 0.757 0.833 0.935 0.324 0.703 0.703
#> MAD:pam 2 0.599 0.899 0.923 0.435 0.543 0.543
#> ATC:pam 2 1.000 0.998 0.999 0.298 0.703 0.703
#> SD:hclust 2 0.668 0.815 0.914 0.311 0.703 0.703
#> CV:hclust 2 0.658 0.839 0.917 0.339 0.686 0.686
#> MAD:hclust 2 0.640 0.810 0.908 0.332 0.703 0.703
#> ATC:hclust 2 0.789 0.838 0.927 0.389 0.562 0.562
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.839 0.848 0.934 0.4403 0.789 0.657
#> CV:NMF 3 0.761 0.816 0.919 0.4837 0.780 0.649
#> MAD:NMF 3 0.824 0.851 0.938 0.4364 0.770 0.627
#> ATC:NMF 3 0.732 0.823 0.912 0.2633 0.851 0.735
#> SD:skmeans 3 0.758 0.812 0.898 0.3828 0.718 0.500
#> CV:skmeans 3 0.556 0.678 0.840 0.3106 0.852 0.721
#> MAD:skmeans 3 0.870 0.909 0.959 0.3789 0.719 0.501
#> ATC:skmeans 3 0.872 0.918 0.959 0.2990 0.824 0.664
#> SD:mclust 3 0.440 0.715 0.750 0.7075 0.648 0.556
#> CV:mclust 3 0.305 0.635 0.754 0.3873 0.767 0.696
#> MAD:mclust 3 0.665 0.859 0.919 0.9081 0.653 0.538
#> ATC:mclust 3 1.000 0.972 0.980 -0.0892 0.747 0.624
#> SD:kmeans 3 0.470 0.752 0.867 0.5400 0.614 0.443
#> CV:kmeans 3 0.743 0.851 0.922 0.5642 0.607 0.432
#> MAD:kmeans 3 0.494 0.757 0.859 0.5951 0.675 0.496
#> ATC:kmeans 3 1.000 0.991 0.996 0.4348 0.622 0.421
#> SD:pam 3 0.757 0.845 0.930 1.0398 0.634 0.526
#> CV:pam 3 0.555 0.788 0.890 0.6767 0.635 0.524
#> MAD:pam 3 0.908 0.901 0.956 0.3416 0.866 0.754
#> ATC:pam 3 0.912 0.975 0.989 1.0349 0.663 0.530
#> SD:hclust 3 0.341 0.288 0.691 0.6633 0.858 0.811
#> CV:hclust 3 0.330 0.645 0.815 0.4021 0.897 0.850
#> MAD:hclust 3 0.289 0.259 0.638 0.6212 0.909 0.870
#> ATC:hclust 3 0.575 0.789 0.879 0.4432 0.885 0.800
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.668 0.752 0.873 0.1640 0.873 0.722
#> CV:NMF 4 0.505 0.547 0.756 0.1936 0.860 0.703
#> MAD:NMF 4 0.605 0.748 0.854 0.1573 0.859 0.671
#> ATC:NMF 4 0.645 0.693 0.846 0.1285 0.915 0.805
#> SD:skmeans 4 0.750 0.780 0.894 0.1183 0.828 0.539
#> CV:skmeans 4 0.622 0.697 0.845 0.1413 0.827 0.583
#> MAD:skmeans 4 0.763 0.777 0.893 0.1076 0.874 0.641
#> ATC:skmeans 4 0.897 0.868 0.938 0.0599 0.955 0.878
#> SD:mclust 4 0.762 0.803 0.922 0.2736 0.772 0.577
#> CV:mclust 4 0.581 0.727 0.873 0.3321 0.658 0.467
#> MAD:mclust 4 0.731 0.775 0.913 0.1947 0.782 0.576
#> ATC:mclust 4 0.694 0.849 0.898 0.2224 0.924 0.868
#> SD:kmeans 4 0.646 0.747 0.862 0.1928 0.716 0.411
#> CV:kmeans 4 0.627 0.750 0.857 0.1566 0.849 0.631
#> MAD:kmeans 4 0.667 0.705 0.845 0.1472 0.876 0.679
#> ATC:kmeans 4 0.857 0.917 0.961 0.1313 0.790 0.508
#> SD:pam 4 0.696 0.777 0.897 0.1656 0.876 0.721
#> CV:pam 4 0.549 0.371 0.661 0.1780 0.769 0.520
#> MAD:pam 4 0.760 0.854 0.894 0.1676 0.908 0.777
#> ATC:pam 4 0.710 0.882 0.923 0.1197 0.916 0.790
#> SD:hclust 4 0.422 0.517 0.739 0.1873 0.618 0.446
#> CV:hclust 4 0.343 0.419 0.618 0.3199 0.645 0.426
#> MAD:hclust 4 0.353 0.550 0.745 0.1916 0.628 0.447
#> ATC:hclust 4 0.551 0.693 0.793 0.1992 0.797 0.588
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.590 0.619 0.823 0.1118 0.884 0.689
#> CV:NMF 5 0.617 0.656 0.832 0.0766 0.799 0.515
#> MAD:NMF 5 0.611 0.661 0.820 0.0855 0.937 0.804
#> ATC:NMF 5 0.644 0.645 0.816 0.1485 0.846 0.596
#> SD:skmeans 5 0.707 0.660 0.831 0.0618 0.911 0.672
#> CV:skmeans 5 0.621 0.593 0.789 0.0624 0.941 0.785
#> MAD:skmeans 5 0.728 0.641 0.820 0.0612 0.899 0.634
#> ATC:skmeans 5 0.876 0.852 0.925 0.0682 0.938 0.822
#> SD:mclust 5 0.647 0.790 0.855 0.0987 0.839 0.603
#> CV:mclust 5 0.486 0.611 0.802 0.0645 0.837 0.591
#> MAD:mclust 5 0.653 0.760 0.861 0.0870 0.815 0.557
#> ATC:mclust 5 0.553 0.443 0.703 0.3003 0.759 0.519
#> SD:kmeans 5 0.629 0.535 0.750 0.0866 0.902 0.702
#> CV:kmeans 5 0.563 0.571 0.768 0.0738 0.935 0.788
#> MAD:kmeans 5 0.651 0.526 0.733 0.0786 0.930 0.778
#> ATC:kmeans 5 0.726 0.667 0.804 0.0704 0.839 0.500
#> SD:pam 5 0.621 0.741 0.836 0.1237 0.845 0.565
#> CV:pam 5 0.632 0.753 0.851 0.1641 0.747 0.337
#> MAD:pam 5 0.802 0.863 0.915 0.1296 0.881 0.650
#> ATC:pam 5 0.970 0.933 0.973 0.1283 0.821 0.512
#> SD:hclust 5 0.431 0.536 0.717 0.0805 0.844 0.616
#> CV:hclust 5 0.372 0.519 0.712 0.1225 0.822 0.514
#> MAD:hclust 5 0.481 0.598 0.755 0.1126 0.883 0.691
#> ATC:hclust 5 0.588 0.664 0.803 0.0317 0.995 0.984
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.558 0.522 0.747 0.0755 0.906 0.669
#> CV:NMF 6 0.574 0.537 0.754 0.0833 0.894 0.612
#> MAD:NMF 6 0.572 0.479 0.708 0.0678 0.947 0.806
#> ATC:NMF 6 0.604 0.555 0.761 0.0457 0.953 0.819
#> SD:skmeans 6 0.687 0.508 0.763 0.0362 0.979 0.903
#> CV:skmeans 6 0.616 0.487 0.730 0.0406 0.980 0.914
#> MAD:skmeans 6 0.693 0.482 0.755 0.0367 0.975 0.880
#> ATC:skmeans 6 0.774 0.743 0.873 0.0390 0.993 0.977
#> SD:mclust 6 0.650 0.737 0.818 0.0877 0.937 0.789
#> CV:mclust 6 0.507 0.474 0.718 0.0979 0.904 0.701
#> MAD:mclust 6 0.674 0.569 0.810 0.0661 0.918 0.738
#> ATC:mclust 6 0.535 0.574 0.724 0.0719 0.785 0.410
#> SD:kmeans 6 0.655 0.522 0.722 0.0469 0.944 0.797
#> CV:kmeans 6 0.594 0.484 0.720 0.0516 0.896 0.641
#> MAD:kmeans 6 0.663 0.492 0.707 0.0494 0.868 0.557
#> ATC:kmeans 6 0.700 0.749 0.799 0.0465 0.931 0.701
#> SD:pam 6 0.610 0.580 0.777 0.0450 0.935 0.745
#> CV:pam 6 0.644 0.609 0.798 0.0496 0.949 0.802
#> MAD:pam 6 0.760 0.770 0.871 0.0417 0.968 0.865
#> ATC:pam 6 0.945 0.891 0.954 0.0298 0.974 0.889
#> SD:hclust 6 0.479 0.582 0.745 0.0541 0.930 0.799
#> CV:hclust 6 0.461 0.562 0.747 0.0650 0.929 0.754
#> MAD:hclust 6 0.529 0.626 0.793 0.0454 0.989 0.961
#> ATC:hclust 6 0.648 0.719 0.817 0.0603 0.945 0.828
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) protocol(p) k
#> SD:NMF 72 0.0627 0.05971 2
#> CV:NMF 73 0.0820 0.08278 2
#> MAD:NMF 73 0.0373 0.03254 2
#> ATC:NMF 72 0.0301 0.22647 2
#> SD:skmeans 73 0.0195 0.41301 2
#> CV:skmeans 72 0.0509 0.45775 2
#> MAD:skmeans 68 0.0115 0.44976 2
#> ATC:skmeans 73 0.1251 0.53982 2
#> SD:mclust 72 0.2291 0.08225 2
#> CV:mclust 72 0.2222 0.06909 2
#> MAD:mclust 69 0.1245 0.14294 2
#> ATC:mclust 73 0.2023 0.15705 2
#> SD:kmeans 73 0.2001 0.28085 2
#> CV:kmeans 73 0.2001 0.28085 2
#> MAD:kmeans 73 0.2001 0.28085 2
#> ATC:kmeans 72 0.0539 0.10956 2
#> SD:pam 71 0.1167 0.17607 2
#> CV:pam 66 0.1941 0.12671 2
#> MAD:pam 70 0.4972 0.00524 2
#> ATC:pam 73 0.3086 0.01410 2
#> SD:hclust 67 0.4934 0.08373 2
#> CV:hclust 69 0.2592 0.15694 2
#> MAD:hclust 66 0.1968 0.05298 2
#> ATC:hclust 65 0.0203 0.01259 2
test_to_known_factors(res_list, k = 3)
#> n disease.state(p) protocol(p) k
#> SD:NMF 68 0.01004 0.020751 3
#> CV:NMF 66 0.01573 0.033820 3
#> MAD:NMF 68 0.01355 0.012173 3
#> ATC:NMF 69 0.05370 0.852822 3
#> SD:skmeans 66 0.26072 0.002246 3
#> CV:skmeans 59 0.13192 0.560464 3
#> MAD:skmeans 70 0.13711 0.003911 3
#> ATC:skmeans 70 0.12743 0.023240 3
#> SD:mclust 68 0.69430 0.000355 3
#> CV:mclust 56 0.43629 0.000475 3
#> MAD:mclust 71 0.56073 0.000356 3
#> ATC:mclust 73 0.00304 0.162811 3
#> SD:kmeans 68 0.03307 0.025074 3
#> CV:kmeans 69 0.16624 0.015692 3
#> MAD:kmeans 68 0.36611 0.000924 3
#> ATC:kmeans 73 0.16649 0.013746 3
#> SD:pam 69 0.52017 0.000720 3
#> CV:pam 68 0.64310 0.001341 3
#> MAD:pam 69 0.59151 0.000486 3
#> ATC:pam 73 0.26327 0.005017 3
#> SD:hclust 8 NA NA 3
#> CV:hclust 59 0.57916 0.245754 3
#> MAD:hclust 10 NA NA 3
#> ATC:hclust 69 0.07188 0.088634 3
test_to_known_factors(res_list, k = 4)
#> n disease.state(p) protocol(p) k
#> SD:NMF 65 0.003498 9.27e-03 4
#> CV:NMF 48 0.089534 1.15e-01 4
#> MAD:NMF 69 0.000541 3.74e-02 4
#> ATC:NMF 62 0.039027 8.39e-01 4
#> SD:skmeans 66 0.205023 4.00e-02 4
#> CV:skmeans 61 0.088656 2.66e-01 4
#> MAD:skmeans 63 0.129816 6.68e-03 4
#> ATC:skmeans 70 0.053090 6.39e-02 4
#> SD:mclust 67 0.018514 8.01e-07 4
#> CV:mclust 61 0.121983 1.00e-03 4
#> MAD:mclust 64 0.075376 5.16e-06 4
#> ATC:mclust 70 0.005686 2.41e-01 4
#> SD:kmeans 64 0.010572 6.67e-05 4
#> CV:kmeans 63 0.195758 2.92e-02 4
#> MAD:kmeans 60 0.045655 9.87e-04 4
#> ATC:kmeans 72 0.309004 1.14e-02 4
#> SD:pam 67 0.009047 3.38e-05 4
#> CV:pam 33 0.251837 5.04e-02 4
#> MAD:pam 70 0.008388 1.91e-05 4
#> ATC:pam 73 0.018556 1.89e-04 4
#> SD:hclust 47 0.363194 1.82e-02 4
#> CV:hclust 34 0.246008 1.87e-01 4
#> MAD:hclust 52 0.407948 1.20e-03 4
#> ATC:hclust 64 0.164468 8.71e-03 4
test_to_known_factors(res_list, k = 5)
#> n disease.state(p) protocol(p) k
#> SD:NMF 51 0.01064 4.49e-02 5
#> CV:NMF 59 0.05516 3.21e-02 5
#> MAD:NMF 57 0.04567 8.31e-02 5
#> ATC:NMF 56 0.05708 4.38e-01 5
#> SD:skmeans 56 0.02275 4.07e-03 5
#> CV:skmeans 48 0.10676 1.64e-01 5
#> MAD:skmeans 53 0.01050 6.49e-03 5
#> ATC:skmeans 67 0.03753 2.16e-01 5
#> SD:mclust 67 0.00532 3.10e-08 5
#> CV:mclust 57 0.12910 2.16e-07 5
#> MAD:mclust 66 0.00725 3.58e-07 5
#> ATC:mclust 35 0.00941 5.35e-01 5
#> SD:kmeans 42 0.01435 1.13e-03 5
#> CV:kmeans 54 0.12297 4.21e-03 5
#> MAD:kmeans 43 0.00835 4.63e-03 5
#> ATC:kmeans 60 0.24913 1.86e-03 5
#> SD:pam 63 0.00451 4.88e-06 5
#> CV:pam 64 0.01618 5.64e-04 5
#> MAD:pam 70 0.00663 1.96e-05 5
#> ATC:pam 73 0.01145 7.46e-06 5
#> SD:hclust 48 0.22484 2.16e-05 5
#> CV:hclust 50 0.10620 2.35e-02 5
#> MAD:hclust 53 0.27236 7.63e-05 5
#> ATC:hclust 62 0.11200 1.34e-02 5
test_to_known_factors(res_list, k = 6)
#> n disease.state(p) protocol(p) k
#> SD:NMF 44 0.06290 2.82e-02 6
#> CV:NMF 48 0.02428 1.06e-02 6
#> MAD:NMF 36 0.21603 5.32e-02 6
#> ATC:NMF 44 0.03977 5.07e-01 6
#> SD:skmeans 44 0.01196 4.88e-02 6
#> CV:skmeans 37 0.16028 1.48e-01 6
#> MAD:skmeans 41 0.04098 6.23e-02 6
#> ATC:skmeans 61 0.00625 2.84e-01 6
#> SD:mclust 68 0.00486 2.77e-06 6
#> CV:mclust 37 0.14550 1.15e-04 6
#> MAD:mclust 54 0.00439 2.15e-05 6
#> ATC:mclust 61 0.01540 6.29e-02 6
#> SD:kmeans 45 0.01031 5.89e-03 6
#> CV:kmeans 45 0.10855 2.26e-03 6
#> MAD:kmeans 45 0.03738 1.32e-02 6
#> ATC:kmeans 68 0.01203 7.98e-03 6
#> SD:pam 53 0.29199 8.43e-07 6
#> CV:pam 54 0.04573 8.61e-03 6
#> MAD:pam 66 0.01164 8.04e-06 6
#> ATC:pam 72 0.12091 2.05e-04 6
#> SD:hclust 51 0.14014 3.49e-05 6
#> CV:hclust 52 0.13924 3.51e-03 6
#> MAD:hclust 55 0.07985 1.45e-03 6
#> ATC:hclust 63 0.02188 9.13e-03 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 31632 rows and 73 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 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.668 0.815 0.914 0.3111 0.703 0.703
#> 3 3 0.341 0.288 0.691 0.6633 0.858 0.811
#> 4 4 0.422 0.517 0.739 0.1873 0.618 0.446
#> 5 5 0.431 0.536 0.717 0.0805 0.844 0.616
#> 6 6 0.479 0.582 0.745 0.0541 0.930 0.799
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM1178971 1 0.0938 0.919 0.988 0.012
#> GSM1178979 2 0.9996 0.100 0.488 0.512
#> GSM1179009 1 0.7056 0.767 0.808 0.192
#> GSM1179031 2 0.0376 0.807 0.004 0.996
#> GSM1178970 1 0.8081 0.682 0.752 0.248
#> GSM1178972 2 0.0376 0.807 0.004 0.996
#> GSM1178973 1 0.0376 0.916 0.996 0.004
#> GSM1178974 2 0.0376 0.807 0.004 0.996
#> GSM1178977 1 0.8081 0.682 0.752 0.248
#> GSM1178978 1 0.6801 0.780 0.820 0.180
#> GSM1178998 1 0.0376 0.916 0.996 0.004
#> GSM1179010 1 0.0376 0.916 0.996 0.004
#> GSM1179018 1 0.6247 0.814 0.844 0.156
#> GSM1179024 1 0.0376 0.916 0.996 0.004
#> GSM1178984 1 0.0938 0.918 0.988 0.012
#> GSM1178990 1 0.0672 0.918 0.992 0.008
#> GSM1178991 1 0.1843 0.912 0.972 0.028
#> GSM1178994 1 0.0938 0.918 0.988 0.012
#> GSM1178997 1 0.0376 0.918 0.996 0.004
#> GSM1179000 1 0.0376 0.918 0.996 0.004
#> GSM1179013 1 0.0376 0.916 0.996 0.004
#> GSM1179014 1 0.3584 0.893 0.932 0.068
#> GSM1179019 1 0.0376 0.918 0.996 0.004
#> GSM1179020 1 0.0376 0.916 0.996 0.004
#> GSM1179022 1 0.0376 0.916 0.996 0.004
#> GSM1179028 2 0.0376 0.807 0.004 0.996
#> GSM1179032 1 0.0376 0.916 0.996 0.004
#> GSM1179041 2 0.0376 0.807 0.004 0.996
#> GSM1179042 2 0.0376 0.807 0.004 0.996
#> GSM1178976 1 0.9754 0.277 0.592 0.408
#> GSM1178981 1 0.1633 0.918 0.976 0.024
#> GSM1178982 1 0.2236 0.915 0.964 0.036
#> GSM1178983 1 0.2236 0.915 0.964 0.036
#> GSM1178985 1 0.1843 0.917 0.972 0.028
#> GSM1178992 1 0.1843 0.916 0.972 0.028
#> GSM1179005 1 0.1843 0.916 0.972 0.028
#> GSM1179007 1 0.1633 0.917 0.976 0.024
#> GSM1179012 1 0.0376 0.916 0.996 0.004
#> GSM1179016 1 0.4431 0.874 0.908 0.092
#> GSM1179030 1 0.3274 0.904 0.940 0.060
#> GSM1179038 1 0.1184 0.918 0.984 0.016
#> GSM1178987 1 0.1633 0.918 0.976 0.024
#> GSM1179003 2 0.9815 0.344 0.420 0.580
#> GSM1179004 1 0.2236 0.914 0.964 0.036
#> GSM1179039 2 0.0376 0.807 0.004 0.996
#> GSM1178975 1 0.0376 0.916 0.996 0.004
#> GSM1178980 2 0.9850 0.326 0.428 0.572
#> GSM1178995 1 0.1843 0.916 0.972 0.028
#> GSM1178996 1 0.0938 0.919 0.988 0.012
#> GSM1179001 1 0.0376 0.916 0.996 0.004
#> GSM1179002 1 0.0376 0.916 0.996 0.004
#> GSM1179006 1 0.3114 0.907 0.944 0.056
#> GSM1179008 1 0.0376 0.916 0.996 0.004
#> GSM1179015 1 0.0376 0.916 0.996 0.004
#> GSM1179017 1 0.9754 0.255 0.592 0.408
#> GSM1179026 1 0.2603 0.912 0.956 0.044
#> GSM1179033 1 0.1843 0.916 0.972 0.028
#> GSM1179035 1 0.2778 0.910 0.952 0.048
#> GSM1179036 1 0.1414 0.919 0.980 0.020
#> GSM1178986 1 0.3274 0.902 0.940 0.060
#> GSM1178989 1 0.9732 0.290 0.596 0.404
#> GSM1178993 1 0.7299 0.750 0.796 0.204
#> GSM1178999 2 0.9248 0.522 0.340 0.660
#> GSM1179021 2 0.8763 0.586 0.296 0.704
#> GSM1179025 2 0.0376 0.807 0.004 0.996
#> GSM1179027 1 0.8909 0.557 0.692 0.308
#> GSM1179011 1 0.3274 0.895 0.940 0.060
#> GSM1179023 1 0.0376 0.916 0.996 0.004
#> GSM1179029 1 0.0376 0.916 0.996 0.004
#> GSM1179034 1 0.0376 0.916 0.996 0.004
#> GSM1179040 1 0.8909 0.557 0.692 0.308
#> GSM1178988 1 0.5059 0.862 0.888 0.112
#> GSM1179037 1 0.2778 0.910 0.952 0.048
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1178971 1 0.4702 0.28275 0.788 0.000 0.212
#> GSM1178979 1 0.9749 -0.05180 0.444 0.260 0.296
#> GSM1179009 1 0.6026 0.12757 0.624 0.000 0.376
#> GSM1179031 2 0.0000 0.87307 0.000 1.000 0.000
#> GSM1178970 1 0.7186 0.14349 0.624 0.040 0.336
#> GSM1178972 2 0.1031 0.86183 0.000 0.976 0.024
#> GSM1178973 3 0.6280 0.45490 0.460 0.000 0.540
#> GSM1178974 2 0.0000 0.87307 0.000 1.000 0.000
#> GSM1178977 1 0.7186 0.14349 0.624 0.040 0.336
#> GSM1178978 1 0.5678 0.18922 0.684 0.000 0.316
#> GSM1178998 1 0.6045 0.01731 0.620 0.000 0.380
#> GSM1179010 1 0.6026 0.02327 0.624 0.000 0.376
#> GSM1179018 1 0.5986 0.20992 0.704 0.012 0.284
#> GSM1179024 1 0.6111 0.00111 0.604 0.000 0.396
#> GSM1178984 1 0.2959 0.40103 0.900 0.000 0.100
#> GSM1178990 1 0.4555 0.28600 0.800 0.000 0.200
#> GSM1178991 3 0.6274 0.44691 0.456 0.000 0.544
#> GSM1178994 1 0.2625 0.41443 0.916 0.000 0.084
#> GSM1178997 1 0.5988 0.04998 0.632 0.000 0.368
#> GSM1179000 1 0.5988 0.04998 0.632 0.000 0.368
#> GSM1179013 1 0.6111 0.00111 0.604 0.000 0.396
#> GSM1179014 1 0.6095 0.04302 0.608 0.000 0.392
#> GSM1179019 1 0.5988 0.04998 0.632 0.000 0.368
#> GSM1179020 1 0.6095 0.00172 0.608 0.000 0.392
#> GSM1179022 1 0.6111 0.00111 0.604 0.000 0.396
#> GSM1179028 2 0.0000 0.87307 0.000 1.000 0.000
#> GSM1179032 1 0.6111 0.00111 0.604 0.000 0.396
#> GSM1179041 2 0.0000 0.87307 0.000 1.000 0.000
#> GSM1179042 2 0.0000 0.87307 0.000 1.000 0.000
#> GSM1178976 1 0.8845 0.08799 0.576 0.240 0.184
#> GSM1178981 1 0.1163 0.45390 0.972 0.000 0.028
#> GSM1178982 1 0.2537 0.43991 0.920 0.000 0.080
#> GSM1178983 1 0.2959 0.43137 0.900 0.000 0.100
#> GSM1178985 1 0.1031 0.45627 0.976 0.000 0.024
#> GSM1178992 1 0.0892 0.45763 0.980 0.000 0.020
#> GSM1179005 1 0.0892 0.45763 0.980 0.000 0.020
#> GSM1179007 1 0.1529 0.45387 0.960 0.000 0.040
#> GSM1179012 1 0.6026 0.02917 0.624 0.000 0.376
#> GSM1179016 1 0.5650 0.22362 0.688 0.000 0.312
#> GSM1179030 1 0.3910 0.42302 0.876 0.020 0.104
#> GSM1179038 1 0.1753 0.44494 0.952 0.000 0.048
#> GSM1178987 1 0.1163 0.45390 0.972 0.000 0.028
#> GSM1179003 1 0.9992 -0.24296 0.352 0.320 0.328
#> GSM1179004 1 0.1163 0.45150 0.972 0.000 0.028
#> GSM1179039 2 0.0000 0.87307 0.000 1.000 0.000
#> GSM1178975 3 0.6280 0.45490 0.460 0.000 0.540
#> GSM1178980 3 0.9817 -0.34602 0.272 0.300 0.428
#> GSM1178995 1 0.0892 0.45763 0.980 0.000 0.020
#> GSM1178996 1 0.4121 0.34343 0.832 0.000 0.168
#> GSM1179001 1 0.6095 0.00172 0.608 0.000 0.392
#> GSM1179002 1 0.6095 0.00172 0.608 0.000 0.392
#> GSM1179006 1 0.2339 0.45065 0.940 0.012 0.048
#> GSM1179008 1 0.6111 -0.00968 0.604 0.000 0.396
#> GSM1179015 1 0.6079 0.01087 0.612 0.000 0.388
#> GSM1179017 1 0.9544 -0.05008 0.420 0.192 0.388
#> GSM1179026 1 0.1411 0.44954 0.964 0.000 0.036
#> GSM1179033 1 0.1163 0.45688 0.972 0.000 0.028
#> GSM1179035 1 0.1411 0.44949 0.964 0.000 0.036
#> GSM1179036 1 0.2537 0.43460 0.920 0.000 0.080
#> GSM1178986 1 0.3896 0.39329 0.864 0.008 0.128
#> GSM1178989 1 0.8813 0.09222 0.580 0.236 0.184
#> GSM1178993 1 0.6079 0.11736 0.612 0.000 0.388
#> GSM1178999 2 0.9805 0.27147 0.240 0.396 0.364
#> GSM1179021 2 0.9684 0.34256 0.220 0.428 0.352
#> GSM1179025 2 0.0000 0.87307 0.000 1.000 0.000
#> GSM1179027 1 0.7784 0.06389 0.556 0.056 0.388
#> GSM1179011 3 0.6079 0.44732 0.388 0.000 0.612
#> GSM1179023 1 0.6111 0.00111 0.604 0.000 0.396
#> GSM1179029 1 0.6079 0.01087 0.612 0.000 0.388
#> GSM1179034 1 0.6111 0.00111 0.604 0.000 0.396
#> GSM1179040 1 0.7784 0.06389 0.556 0.056 0.388
#> GSM1178988 1 0.3850 0.39538 0.884 0.028 0.088
#> GSM1179037 1 0.1411 0.44949 0.964 0.000 0.036
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1178971 1 0.4477 0.2414 0.688 0.000 0.312 0.000
#> GSM1178979 3 0.7021 -0.3350 0.004 0.116 0.536 0.344
#> GSM1179009 3 0.4259 0.2488 0.056 0.000 0.816 0.128
#> GSM1179031 2 0.0000 0.9931 0.000 1.000 0.000 0.000
#> GSM1178970 3 0.2335 0.2678 0.008 0.020 0.928 0.044
#> GSM1178972 2 0.1411 0.9498 0.000 0.960 0.020 0.020
#> GSM1178973 1 0.5371 0.5703 0.732 0.000 0.188 0.080
#> GSM1178974 2 0.0000 0.9931 0.000 1.000 0.000 0.000
#> GSM1178977 3 0.2335 0.2678 0.008 0.020 0.928 0.044
#> GSM1178978 3 0.2773 0.3715 0.072 0.000 0.900 0.028
#> GSM1178998 1 0.1677 0.7645 0.948 0.000 0.040 0.012
#> GSM1179010 1 0.2670 0.7476 0.904 0.000 0.072 0.024
#> GSM1179018 3 0.5042 0.4012 0.136 0.000 0.768 0.096
#> GSM1179024 1 0.0000 0.7779 1.000 0.000 0.000 0.000
#> GSM1178984 1 0.5399 -0.3925 0.520 0.000 0.468 0.012
#> GSM1178990 1 0.4431 0.2287 0.696 0.000 0.304 0.000
#> GSM1178991 1 0.5496 0.5190 0.704 0.000 0.232 0.064
#> GSM1178994 1 0.5296 -0.4641 0.496 0.000 0.496 0.008
#> GSM1178997 1 0.1637 0.7539 0.940 0.000 0.060 0.000
#> GSM1179000 1 0.1637 0.7539 0.940 0.000 0.060 0.000
#> GSM1179013 1 0.0000 0.7779 1.000 0.000 0.000 0.000
#> GSM1179014 1 0.5882 0.3930 0.608 0.000 0.048 0.344
#> GSM1179019 1 0.1637 0.7539 0.940 0.000 0.060 0.000
#> GSM1179020 1 0.0376 0.7776 0.992 0.000 0.004 0.004
#> GSM1179022 1 0.0000 0.7779 1.000 0.000 0.000 0.000
#> GSM1179028 2 0.0000 0.9931 0.000 1.000 0.000 0.000
#> GSM1179032 1 0.0000 0.7779 1.000 0.000 0.000 0.000
#> GSM1179041 2 0.0000 0.9931 0.000 1.000 0.000 0.000
#> GSM1179042 2 0.0000 0.9931 0.000 1.000 0.000 0.000
#> GSM1178976 3 0.6464 0.1291 0.008 0.120 0.660 0.212
#> GSM1178981 3 0.4877 0.5919 0.408 0.000 0.592 0.000
#> GSM1178982 3 0.4977 0.5076 0.460 0.000 0.540 0.000
#> GSM1178983 3 0.5151 0.4858 0.464 0.000 0.532 0.004
#> GSM1178985 3 0.4916 0.5790 0.424 0.000 0.576 0.000
#> GSM1178992 3 0.4907 0.5846 0.420 0.000 0.580 0.000
#> GSM1179005 3 0.4907 0.5846 0.420 0.000 0.580 0.000
#> GSM1179007 3 0.4948 0.5572 0.440 0.000 0.560 0.000
#> GSM1179012 1 0.2670 0.7527 0.908 0.000 0.040 0.052
#> GSM1179016 4 0.7192 -0.1124 0.368 0.000 0.144 0.488
#> GSM1179030 3 0.5893 0.5006 0.444 0.012 0.528 0.016
#> GSM1179038 3 0.4994 0.4876 0.480 0.000 0.520 0.000
#> GSM1178987 3 0.4877 0.5919 0.408 0.000 0.592 0.000
#> GSM1179003 3 0.7492 -0.5203 0.000 0.180 0.432 0.388
#> GSM1179004 3 0.4817 0.6062 0.388 0.000 0.612 0.000
#> GSM1179039 2 0.0000 0.9931 0.000 1.000 0.000 0.000
#> GSM1178975 1 0.5371 0.5703 0.732 0.000 0.188 0.080
#> GSM1178980 4 0.7978 0.5017 0.012 0.196 0.388 0.404
#> GSM1178995 3 0.4907 0.5846 0.420 0.000 0.580 0.000
#> GSM1178996 1 0.4964 -0.0199 0.616 0.000 0.380 0.004
#> GSM1179001 1 0.0376 0.7776 0.992 0.000 0.004 0.004
#> GSM1179002 1 0.0376 0.7776 0.992 0.000 0.004 0.004
#> GSM1179006 3 0.5441 0.6003 0.396 0.012 0.588 0.004
#> GSM1179008 1 0.0524 0.7767 0.988 0.000 0.008 0.004
#> GSM1179015 1 0.2546 0.7519 0.912 0.000 0.028 0.060
#> GSM1179017 4 0.4452 0.3101 0.000 0.048 0.156 0.796
#> GSM1179026 3 0.5313 0.6107 0.376 0.000 0.608 0.016
#> GSM1179033 3 0.5060 0.5925 0.412 0.000 0.584 0.004
#> GSM1179035 3 0.5204 0.6108 0.376 0.000 0.612 0.012
#> GSM1179036 3 0.5295 0.4478 0.488 0.000 0.504 0.008
#> GSM1178986 3 0.5289 0.5598 0.344 0.000 0.636 0.020
#> GSM1178989 3 0.6415 0.1384 0.008 0.116 0.664 0.212
#> GSM1178993 3 0.4174 0.2129 0.044 0.000 0.816 0.140
#> GSM1178999 4 0.8165 0.4962 0.012 0.256 0.320 0.412
#> GSM1179021 4 0.7888 0.4424 0.000 0.320 0.300 0.380
#> GSM1179025 2 0.0000 0.9931 0.000 1.000 0.000 0.000
#> GSM1179027 3 0.5349 -0.0477 0.024 0.000 0.640 0.336
#> GSM1179011 1 0.6452 0.3649 0.620 0.000 0.268 0.112
#> GSM1179023 1 0.0000 0.7779 1.000 0.000 0.000 0.000
#> GSM1179029 1 0.2546 0.7519 0.912 0.000 0.028 0.060
#> GSM1179034 1 0.0000 0.7779 1.000 0.000 0.000 0.000
#> GSM1179040 3 0.5349 -0.0477 0.024 0.000 0.640 0.336
#> GSM1178988 3 0.6402 0.6100 0.296 0.016 0.628 0.060
#> GSM1179037 3 0.5204 0.6108 0.376 0.000 0.612 0.012
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1178971 3 0.4264 0.0142 0.376 0.000 0.620 0.004 0.000
#> GSM1178979 4 0.7971 0.5277 0.024 0.052 0.348 0.400 0.176
#> GSM1179009 3 0.6829 -0.1057 0.164 0.000 0.528 0.276 0.032
#> GSM1179031 2 0.0000 0.9923 0.000 1.000 0.000 0.000 0.000
#> GSM1178970 3 0.7070 0.0494 0.132 0.008 0.580 0.208 0.072
#> GSM1178972 2 0.1485 0.9441 0.000 0.948 0.000 0.020 0.032
#> GSM1178973 1 0.5888 0.3280 0.684 0.000 0.140 0.124 0.052
#> GSM1178974 2 0.0000 0.9923 0.000 1.000 0.000 0.000 0.000
#> GSM1178977 3 0.7070 0.0494 0.132 0.008 0.580 0.208 0.072
#> GSM1178978 3 0.6479 0.2021 0.156 0.000 0.616 0.180 0.048
#> GSM1178998 1 0.5305 0.6307 0.624 0.000 0.320 0.016 0.040
#> GSM1179010 1 0.7623 0.1865 0.396 0.000 0.348 0.192 0.064
#> GSM1179018 3 0.6384 0.0838 0.128 0.000 0.572 0.276 0.024
#> GSM1179024 1 0.3774 0.7149 0.704 0.000 0.296 0.000 0.000
#> GSM1178984 3 0.3599 0.6267 0.140 0.000 0.824 0.016 0.020
#> GSM1178990 3 0.3913 0.1632 0.324 0.000 0.676 0.000 0.000
#> GSM1178991 1 0.5783 0.2976 0.692 0.000 0.124 0.136 0.048
#> GSM1178994 3 0.3069 0.6684 0.104 0.000 0.864 0.016 0.016
#> GSM1178997 1 0.4151 0.6693 0.652 0.000 0.344 0.004 0.000
#> GSM1179000 1 0.4151 0.6693 0.652 0.000 0.344 0.004 0.000
#> GSM1179013 1 0.3774 0.7149 0.704 0.000 0.296 0.000 0.000
#> GSM1179014 5 0.6788 -0.1634 0.344 0.000 0.284 0.000 0.372
#> GSM1179019 1 0.4151 0.6693 0.652 0.000 0.344 0.004 0.000
#> GSM1179020 1 0.3928 0.7133 0.700 0.000 0.296 0.000 0.004
#> GSM1179022 1 0.3774 0.7149 0.704 0.000 0.296 0.000 0.000
#> GSM1179028 2 0.0000 0.9923 0.000 1.000 0.000 0.000 0.000
#> GSM1179032 1 0.3774 0.7149 0.704 0.000 0.296 0.000 0.000
#> GSM1179041 2 0.0000 0.9923 0.000 1.000 0.000 0.000 0.000
#> GSM1179042 2 0.0000 0.9923 0.000 1.000 0.000 0.000 0.000
#> GSM1178976 3 0.7166 -0.0257 0.016 0.080 0.576 0.100 0.228
#> GSM1178981 3 0.1205 0.7315 0.040 0.000 0.956 0.004 0.000
#> GSM1178982 3 0.2723 0.6716 0.124 0.000 0.864 0.012 0.000
#> GSM1178983 3 0.3154 0.6447 0.148 0.000 0.836 0.012 0.004
#> GSM1178985 3 0.1043 0.7281 0.040 0.000 0.960 0.000 0.000
#> GSM1178992 3 0.0880 0.7278 0.032 0.000 0.968 0.000 0.000
#> GSM1179005 3 0.0963 0.7283 0.036 0.000 0.964 0.000 0.000
#> GSM1179007 3 0.1478 0.7187 0.064 0.000 0.936 0.000 0.000
#> GSM1179012 1 0.7886 0.2326 0.368 0.000 0.352 0.188 0.092
#> GSM1179016 5 0.5901 0.3458 0.132 0.000 0.300 0.000 0.568
#> GSM1179030 3 0.3759 0.6489 0.148 0.000 0.812 0.012 0.028
#> GSM1179038 3 0.1965 0.6905 0.096 0.000 0.904 0.000 0.000
#> GSM1178987 3 0.1124 0.7316 0.036 0.000 0.960 0.004 0.000
#> GSM1179003 4 0.7518 0.5762 0.008 0.076 0.216 0.524 0.176
#> GSM1179004 3 0.0671 0.7276 0.016 0.000 0.980 0.004 0.000
#> GSM1179039 2 0.0000 0.9923 0.000 1.000 0.000 0.000 0.000
#> GSM1178975 1 0.5888 0.3280 0.684 0.000 0.140 0.124 0.052
#> GSM1178980 4 0.4858 0.5474 0.024 0.108 0.080 0.776 0.012
#> GSM1178995 3 0.0963 0.7283 0.036 0.000 0.964 0.000 0.000
#> GSM1178996 3 0.4102 0.2832 0.300 0.000 0.692 0.004 0.004
#> GSM1179001 1 0.4193 0.7101 0.684 0.000 0.304 0.000 0.012
#> GSM1179002 1 0.4193 0.7101 0.684 0.000 0.304 0.000 0.012
#> GSM1179006 3 0.1989 0.7269 0.032 0.004 0.932 0.028 0.004
#> GSM1179008 1 0.4173 0.7103 0.688 0.000 0.300 0.000 0.012
#> GSM1179015 1 0.7803 0.2471 0.392 0.000 0.336 0.188 0.084
#> GSM1179017 5 0.3389 -0.0851 0.000 0.000 0.048 0.116 0.836
#> GSM1179026 3 0.1074 0.7239 0.012 0.000 0.968 0.004 0.016
#> GSM1179033 3 0.0955 0.7306 0.028 0.000 0.968 0.000 0.004
#> GSM1179035 3 0.0854 0.7224 0.008 0.000 0.976 0.004 0.012
#> GSM1179036 3 0.2911 0.6545 0.136 0.000 0.852 0.004 0.008
#> GSM1178986 3 0.4267 0.6393 0.180 0.000 0.772 0.028 0.020
#> GSM1178989 3 0.7116 -0.0135 0.016 0.076 0.580 0.100 0.228
#> GSM1178993 3 0.6903 -0.1689 0.164 0.000 0.508 0.296 0.032
#> GSM1178999 4 0.6704 0.5269 0.008 0.144 0.068 0.628 0.152
#> GSM1179021 4 0.5393 0.4782 0.004 0.228 0.068 0.684 0.016
#> GSM1179025 2 0.0000 0.9923 0.000 1.000 0.000 0.000 0.000
#> GSM1179027 4 0.5883 0.4096 0.068 0.000 0.420 0.500 0.012
#> GSM1179011 1 0.5603 0.1335 0.688 0.000 0.060 0.200 0.052
#> GSM1179023 1 0.3774 0.7149 0.704 0.000 0.296 0.000 0.000
#> GSM1179029 1 0.7720 0.2837 0.408 0.000 0.332 0.180 0.080
#> GSM1179034 1 0.3774 0.7149 0.704 0.000 0.296 0.000 0.000
#> GSM1179040 4 0.5883 0.4096 0.068 0.000 0.420 0.500 0.012
#> GSM1178988 3 0.2847 0.6612 0.012 0.004 0.892 0.036 0.056
#> GSM1179037 3 0.0854 0.7224 0.008 0.000 0.976 0.004 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1178971 3 0.4301 0.00224 0.400 0.000 0.580 0.000 0.004 0.016
#> GSM1178979 3 0.8008 -0.27210 0.032 0.024 0.344 0.328 0.208 0.064
#> GSM1179009 3 0.7095 0.32376 0.172 0.000 0.512 0.152 0.012 0.152
#> GSM1179031 2 0.0000 0.99114 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178970 3 0.6921 0.41111 0.096 0.004 0.572 0.112 0.036 0.180
#> GSM1178972 2 0.1518 0.93522 0.000 0.944 0.000 0.024 0.024 0.008
#> GSM1178973 1 0.5161 0.34256 0.728 0.000 0.076 0.052 0.024 0.120
#> GSM1178974 2 0.0000 0.99114 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178977 3 0.6921 0.41111 0.096 0.004 0.572 0.112 0.036 0.180
#> GSM1178978 3 0.6474 0.46248 0.140 0.000 0.588 0.068 0.020 0.184
#> GSM1178998 1 0.5486 0.41514 0.568 0.000 0.208 0.000 0.000 0.224
#> GSM1179010 6 0.4641 0.67729 0.116 0.000 0.200 0.000 0.000 0.684
#> GSM1179018 3 0.6534 0.34726 0.124 0.000 0.548 0.252 0.016 0.060
#> GSM1179024 1 0.3101 0.76480 0.756 0.000 0.244 0.000 0.000 0.000
#> GSM1178984 3 0.3558 0.57346 0.088 0.000 0.800 0.000 0.000 0.112
#> GSM1178990 3 0.3620 0.19442 0.352 0.000 0.648 0.000 0.000 0.000
#> GSM1178991 1 0.5371 0.31238 0.716 0.000 0.072 0.088 0.024 0.100
#> GSM1178994 3 0.3032 0.61085 0.056 0.000 0.840 0.000 0.000 0.104
#> GSM1178997 1 0.3885 0.70421 0.684 0.000 0.300 0.000 0.004 0.012
#> GSM1179000 1 0.3885 0.70421 0.684 0.000 0.300 0.000 0.004 0.012
#> GSM1179013 1 0.3101 0.76722 0.756 0.000 0.244 0.000 0.000 0.000
#> GSM1179014 5 0.6014 -0.08296 0.368 0.000 0.240 0.000 0.392 0.000
#> GSM1179019 1 0.3867 0.70685 0.688 0.000 0.296 0.000 0.004 0.012
#> GSM1179020 1 0.3584 0.76249 0.740 0.000 0.244 0.000 0.004 0.012
#> GSM1179022 1 0.3101 0.76722 0.756 0.000 0.244 0.000 0.000 0.000
#> GSM1179028 2 0.0000 0.99114 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179032 1 0.3101 0.76722 0.756 0.000 0.244 0.000 0.000 0.000
#> GSM1179041 2 0.0000 0.99114 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179042 2 0.0000 0.99114 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178976 3 0.6645 0.35294 0.016 0.072 0.580 0.044 0.244 0.044
#> GSM1178981 3 0.1442 0.68249 0.040 0.000 0.944 0.004 0.000 0.012
#> GSM1178982 3 0.2790 0.63299 0.132 0.000 0.844 0.000 0.000 0.024
#> GSM1178983 3 0.2988 0.61175 0.152 0.000 0.824 0.000 0.000 0.024
#> GSM1178985 3 0.1152 0.67805 0.044 0.000 0.952 0.000 0.000 0.004
#> GSM1178992 3 0.0935 0.67726 0.032 0.000 0.964 0.000 0.004 0.000
#> GSM1179005 3 0.1010 0.67776 0.036 0.000 0.960 0.000 0.004 0.000
#> GSM1179007 3 0.1615 0.67046 0.064 0.000 0.928 0.000 0.004 0.004
#> GSM1179012 6 0.5931 0.80817 0.168 0.000 0.224 0.000 0.032 0.576
#> GSM1179016 5 0.5163 0.12437 0.140 0.000 0.252 0.000 0.608 0.000
#> GSM1179030 3 0.3594 0.61093 0.152 0.000 0.800 0.000 0.024 0.024
#> GSM1179038 3 0.1958 0.64985 0.100 0.000 0.896 0.000 0.004 0.000
#> GSM1178987 3 0.1370 0.68224 0.036 0.000 0.948 0.004 0.000 0.012
#> GSM1179003 4 0.6254 0.54538 0.004 0.020 0.176 0.572 0.212 0.016
#> GSM1179004 3 0.0964 0.68151 0.016 0.000 0.968 0.004 0.000 0.012
#> GSM1179039 2 0.0000 0.99114 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178975 1 0.5161 0.34256 0.728 0.000 0.076 0.052 0.024 0.120
#> GSM1178980 4 0.1528 0.71056 0.016 0.000 0.012 0.944 0.000 0.028
#> GSM1178995 3 0.1152 0.67843 0.044 0.000 0.952 0.000 0.004 0.000
#> GSM1178996 3 0.3819 0.27899 0.316 0.000 0.672 0.000 0.000 0.012
#> GSM1179001 1 0.3817 0.75233 0.720 0.000 0.252 0.000 0.000 0.028
#> GSM1179002 1 0.3817 0.75233 0.720 0.000 0.252 0.000 0.000 0.028
#> GSM1179006 3 0.2007 0.67637 0.036 0.000 0.920 0.032 0.000 0.012
#> GSM1179008 1 0.3794 0.75243 0.724 0.000 0.248 0.000 0.000 0.028
#> GSM1179015 6 0.6298 0.80350 0.192 0.000 0.244 0.000 0.040 0.524
#> GSM1179017 5 0.1225 -0.19532 0.000 0.000 0.012 0.036 0.952 0.000
#> GSM1179026 3 0.0725 0.67957 0.012 0.000 0.976 0.000 0.012 0.000
#> GSM1179033 3 0.0865 0.68039 0.036 0.000 0.964 0.000 0.000 0.000
#> GSM1179035 3 0.0767 0.67891 0.008 0.000 0.976 0.000 0.012 0.004
#> GSM1179036 3 0.2794 0.61674 0.144 0.000 0.840 0.000 0.004 0.012
#> GSM1178986 3 0.4113 0.62969 0.180 0.000 0.764 0.020 0.016 0.020
#> GSM1178989 3 0.6598 0.35982 0.016 0.068 0.584 0.044 0.244 0.044
#> GSM1178993 3 0.7171 0.30111 0.168 0.000 0.500 0.172 0.012 0.148
#> GSM1178999 4 0.3329 0.72001 0.000 0.020 0.004 0.792 0.184 0.000
#> GSM1179021 4 0.2306 0.71801 0.000 0.092 0.000 0.888 0.004 0.016
#> GSM1179025 2 0.0000 0.99114 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179027 3 0.6864 0.06386 0.072 0.000 0.412 0.384 0.012 0.120
#> GSM1179011 1 0.5379 0.20286 0.696 0.000 0.028 0.128 0.024 0.124
#> GSM1179023 1 0.3101 0.76722 0.756 0.000 0.244 0.000 0.000 0.000
#> GSM1179029 6 0.6553 0.72428 0.244 0.000 0.248 0.000 0.040 0.468
#> GSM1179034 1 0.3101 0.76722 0.756 0.000 0.244 0.000 0.000 0.000
#> GSM1179040 3 0.6864 0.06386 0.072 0.000 0.412 0.384 0.012 0.120
#> GSM1178988 3 0.2534 0.65535 0.008 0.000 0.896 0.024 0.056 0.016
#> GSM1179037 3 0.0767 0.67891 0.008 0.000 0.976 0.000 0.012 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) protocol(p) k
#> SD:hclust 67 0.493 8.37e-02 2
#> SD:hclust 8 NA NA 3
#> SD:hclust 47 0.363 1.82e-02 4
#> SD:hclust 48 0.225 2.16e-05 5
#> SD:hclust 51 0.140 3.49e-05 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 31632 rows and 73 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.989 0.994 0.3860 0.610 0.610
#> 3 3 0.470 0.752 0.867 0.5400 0.614 0.443
#> 4 4 0.646 0.747 0.862 0.1928 0.716 0.411
#> 5 5 0.629 0.535 0.750 0.0866 0.902 0.702
#> 6 6 0.655 0.522 0.722 0.0469 0.944 0.797
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
#> GSM1178971 1 0.000 0.999 1.000 0.000
#> GSM1178979 2 0.000 0.979 0.000 1.000
#> GSM1179009 1 0.000 0.999 1.000 0.000
#> GSM1179031 2 0.000 0.979 0.000 1.000
#> GSM1178970 2 0.000 0.979 0.000 1.000
#> GSM1178972 2 0.000 0.979 0.000 1.000
#> GSM1178973 1 0.000 0.999 1.000 0.000
#> GSM1178974 2 0.000 0.979 0.000 1.000
#> GSM1178977 2 0.000 0.979 0.000 1.000
#> GSM1178978 1 0.000 0.999 1.000 0.000
#> GSM1178998 1 0.000 0.999 1.000 0.000
#> GSM1179010 1 0.000 0.999 1.000 0.000
#> GSM1179018 1 0.000 0.999 1.000 0.000
#> GSM1179024 1 0.000 0.999 1.000 0.000
#> GSM1178984 1 0.000 0.999 1.000 0.000
#> GSM1178990 1 0.000 0.999 1.000 0.000
#> GSM1178991 1 0.000 0.999 1.000 0.000
#> GSM1178994 1 0.000 0.999 1.000 0.000
#> GSM1178997 1 0.000 0.999 1.000 0.000
#> GSM1179000 1 0.000 0.999 1.000 0.000
#> GSM1179013 1 0.000 0.999 1.000 0.000
#> GSM1179014 1 0.000 0.999 1.000 0.000
#> GSM1179019 1 0.000 0.999 1.000 0.000
#> GSM1179020 1 0.000 0.999 1.000 0.000
#> GSM1179022 1 0.000 0.999 1.000 0.000
#> GSM1179028 2 0.000 0.979 0.000 1.000
#> GSM1179032 1 0.000 0.999 1.000 0.000
#> GSM1179041 2 0.000 0.979 0.000 1.000
#> GSM1179042 2 0.000 0.979 0.000 1.000
#> GSM1178976 2 0.000 0.979 0.000 1.000
#> GSM1178981 1 0.000 0.999 1.000 0.000
#> GSM1178982 1 0.000 0.999 1.000 0.000
#> GSM1178983 1 0.000 0.999 1.000 0.000
#> GSM1178985 1 0.000 0.999 1.000 0.000
#> GSM1178992 1 0.000 0.999 1.000 0.000
#> GSM1179005 1 0.000 0.999 1.000 0.000
#> GSM1179007 1 0.000 0.999 1.000 0.000
#> GSM1179012 1 0.000 0.999 1.000 0.000
#> GSM1179016 1 0.000 0.999 1.000 0.000
#> GSM1179030 1 0.000 0.999 1.000 0.000
#> GSM1179038 1 0.000 0.999 1.000 0.000
#> GSM1178987 1 0.000 0.999 1.000 0.000
#> GSM1179003 2 0.000 0.979 0.000 1.000
#> GSM1179004 1 0.000 0.999 1.000 0.000
#> GSM1179039 2 0.000 0.979 0.000 1.000
#> GSM1178975 1 0.000 0.999 1.000 0.000
#> GSM1178980 2 0.443 0.903 0.092 0.908
#> GSM1178995 1 0.000 0.999 1.000 0.000
#> GSM1178996 1 0.000 0.999 1.000 0.000
#> GSM1179001 1 0.000 0.999 1.000 0.000
#> GSM1179002 1 0.000 0.999 1.000 0.000
#> GSM1179006 1 0.000 0.999 1.000 0.000
#> GSM1179008 1 0.000 0.999 1.000 0.000
#> GSM1179015 1 0.000 0.999 1.000 0.000
#> GSM1179017 2 0.745 0.746 0.212 0.788
#> GSM1179026 1 0.000 0.999 1.000 0.000
#> GSM1179033 1 0.000 0.999 1.000 0.000
#> GSM1179035 1 0.000 0.999 1.000 0.000
#> GSM1179036 1 0.000 0.999 1.000 0.000
#> GSM1178986 1 0.000 0.999 1.000 0.000
#> GSM1178989 2 0.242 0.952 0.040 0.960
#> GSM1178993 1 0.000 0.999 1.000 0.000
#> GSM1178999 2 0.242 0.952 0.040 0.960
#> GSM1179021 2 0.000 0.979 0.000 1.000
#> GSM1179025 2 0.000 0.979 0.000 1.000
#> GSM1179027 1 0.204 0.966 0.968 0.032
#> GSM1179011 1 0.000 0.999 1.000 0.000
#> GSM1179023 1 0.000 0.999 1.000 0.000
#> GSM1179029 1 0.000 0.999 1.000 0.000
#> GSM1179034 1 0.000 0.999 1.000 0.000
#> GSM1179040 2 0.000 0.979 0.000 1.000
#> GSM1178988 1 0.000 0.999 1.000 0.000
#> GSM1179037 1 0.000 0.999 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1178971 1 0.5560 0.605 0.700 0.000 0.300
#> GSM1178979 3 0.6045 0.337 0.000 0.380 0.620
#> GSM1179009 3 0.0237 0.791 0.004 0.000 0.996
#> GSM1179031 2 0.0000 0.950 0.000 1.000 0.000
#> GSM1178970 3 0.6140 0.297 0.000 0.404 0.596
#> GSM1178972 2 0.0237 0.949 0.000 0.996 0.004
#> GSM1178973 1 0.3551 0.736 0.868 0.000 0.132
#> GSM1178974 2 0.0237 0.949 0.000 0.996 0.004
#> GSM1178977 3 0.2537 0.746 0.000 0.080 0.920
#> GSM1178978 3 0.0747 0.795 0.016 0.000 0.984
#> GSM1178998 1 0.0424 0.840 0.992 0.000 0.008
#> GSM1179010 1 0.5098 0.689 0.752 0.000 0.248
#> GSM1179018 3 0.0424 0.793 0.008 0.000 0.992
#> GSM1179024 1 0.0000 0.841 1.000 0.000 0.000
#> GSM1178984 1 0.5363 0.655 0.724 0.000 0.276
#> GSM1178990 1 0.0000 0.841 1.000 0.000 0.000
#> GSM1178991 1 0.6302 0.128 0.520 0.000 0.480
#> GSM1178994 1 0.5254 0.673 0.736 0.000 0.264
#> GSM1178997 1 0.5397 0.505 0.720 0.000 0.280
#> GSM1179000 1 0.0000 0.841 1.000 0.000 0.000
#> GSM1179013 1 0.0000 0.841 1.000 0.000 0.000
#> GSM1179014 1 0.0000 0.841 1.000 0.000 0.000
#> GSM1179019 1 0.0000 0.841 1.000 0.000 0.000
#> GSM1179020 1 0.0000 0.841 1.000 0.000 0.000
#> GSM1179022 1 0.0000 0.841 1.000 0.000 0.000
#> GSM1179028 2 0.0000 0.950 0.000 1.000 0.000
#> GSM1179032 1 0.0000 0.841 1.000 0.000 0.000
#> GSM1179041 2 0.0000 0.950 0.000 1.000 0.000
#> GSM1179042 2 0.0000 0.950 0.000 1.000 0.000
#> GSM1178976 3 0.4974 0.663 0.000 0.236 0.764
#> GSM1178981 3 0.5591 0.642 0.304 0.000 0.696
#> GSM1178982 3 0.4178 0.783 0.172 0.000 0.828
#> GSM1178983 3 0.4002 0.787 0.160 0.000 0.840
#> GSM1178985 3 0.4931 0.750 0.232 0.000 0.768
#> GSM1178992 1 0.5216 0.677 0.740 0.000 0.260
#> GSM1179005 1 0.5291 0.668 0.732 0.000 0.268
#> GSM1179007 1 0.5016 0.696 0.760 0.000 0.240
#> GSM1179012 1 0.1860 0.824 0.948 0.000 0.052
#> GSM1179016 1 0.4654 0.728 0.792 0.000 0.208
#> GSM1179030 3 0.1411 0.803 0.036 0.000 0.964
#> GSM1179038 1 0.5291 0.668 0.732 0.000 0.268
#> GSM1178987 3 0.5016 0.743 0.240 0.000 0.760
#> GSM1179003 3 0.4399 0.701 0.000 0.188 0.812
#> GSM1179004 3 0.5016 0.743 0.240 0.000 0.760
#> GSM1179039 2 0.0000 0.950 0.000 1.000 0.000
#> GSM1178975 1 0.6140 0.345 0.596 0.000 0.404
#> GSM1178980 3 0.2448 0.749 0.000 0.076 0.924
#> GSM1178995 1 0.5216 0.677 0.740 0.000 0.260
#> GSM1178996 3 0.5058 0.738 0.244 0.000 0.756
#> GSM1179001 1 0.0000 0.841 1.000 0.000 0.000
#> GSM1179002 1 0.0424 0.840 0.992 0.000 0.008
#> GSM1179006 3 0.4931 0.751 0.232 0.000 0.768
#> GSM1179008 1 0.0000 0.841 1.000 0.000 0.000
#> GSM1179015 1 0.1031 0.835 0.976 0.000 0.024
#> GSM1179017 3 0.5710 0.780 0.080 0.116 0.804
#> GSM1179026 3 0.5016 0.743 0.240 0.000 0.760
#> GSM1179033 3 0.4178 0.788 0.172 0.000 0.828
#> GSM1179035 3 0.5560 0.650 0.300 0.000 0.700
#> GSM1179036 3 0.5138 0.727 0.252 0.000 0.748
#> GSM1178986 3 0.3551 0.802 0.132 0.000 0.868
#> GSM1178989 3 0.4569 0.801 0.072 0.068 0.860
#> GSM1178993 3 0.0237 0.791 0.004 0.000 0.996
#> GSM1178999 3 0.2448 0.749 0.000 0.076 0.924
#> GSM1179021 2 0.6095 0.421 0.000 0.608 0.392
#> GSM1179025 2 0.0237 0.949 0.000 0.996 0.004
#> GSM1179027 3 0.0237 0.788 0.000 0.004 0.996
#> GSM1179011 3 0.2261 0.766 0.068 0.000 0.932
#> GSM1179023 1 0.0000 0.841 1.000 0.000 0.000
#> GSM1179029 1 0.0000 0.841 1.000 0.000 0.000
#> GSM1179034 1 0.0000 0.841 1.000 0.000 0.000
#> GSM1179040 3 0.2537 0.746 0.000 0.080 0.920
#> GSM1178988 3 0.3816 0.797 0.148 0.000 0.852
#> GSM1179037 3 0.5016 0.743 0.240 0.000 0.760
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1178971 3 0.5440 0.4881 0.384 0.000 0.596 0.020
#> GSM1178979 4 0.4581 0.7048 0.000 0.120 0.080 0.800
#> GSM1179009 3 0.5000 -0.0652 0.000 0.000 0.504 0.496
#> GSM1179031 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM1178970 4 0.6475 0.6160 0.000 0.172 0.184 0.644
#> GSM1178972 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM1178973 1 0.3444 0.7685 0.816 0.000 0.000 0.184
#> GSM1178974 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM1178977 4 0.3047 0.7610 0.000 0.012 0.116 0.872
#> GSM1178978 4 0.5055 0.4606 0.008 0.000 0.368 0.624
#> GSM1178998 1 0.1820 0.9076 0.944 0.000 0.036 0.020
#> GSM1179010 3 0.5649 0.5256 0.344 0.000 0.620 0.036
#> GSM1179018 4 0.4746 0.4731 0.000 0.000 0.368 0.632
#> GSM1179024 1 0.0707 0.9216 0.980 0.000 0.000 0.020
#> GSM1178984 3 0.5085 0.6060 0.304 0.000 0.676 0.020
#> GSM1178990 1 0.0895 0.9238 0.976 0.000 0.004 0.020
#> GSM1178991 4 0.5750 0.1819 0.440 0.000 0.028 0.532
#> GSM1178994 3 0.5085 0.6060 0.304 0.000 0.676 0.020
#> GSM1178997 1 0.5085 0.5748 0.708 0.000 0.260 0.032
#> GSM1179000 1 0.1004 0.9213 0.972 0.000 0.004 0.024
#> GSM1179013 1 0.0657 0.9228 0.984 0.000 0.004 0.012
#> GSM1179014 1 0.1743 0.9114 0.940 0.000 0.004 0.056
#> GSM1179019 1 0.1004 0.9213 0.972 0.000 0.004 0.024
#> GSM1179020 1 0.0657 0.9242 0.984 0.000 0.004 0.012
#> GSM1179022 1 0.0524 0.9253 0.988 0.000 0.004 0.008
#> GSM1179028 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM1179032 1 0.0524 0.9253 0.988 0.000 0.004 0.008
#> GSM1179041 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM1179042 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM1178976 3 0.2483 0.7574 0.000 0.032 0.916 0.052
#> GSM1178981 3 0.1284 0.7962 0.024 0.000 0.964 0.012
#> GSM1178982 3 0.2662 0.7571 0.016 0.000 0.900 0.084
#> GSM1178983 3 0.4214 0.6329 0.016 0.000 0.780 0.204
#> GSM1178985 3 0.1042 0.7962 0.020 0.000 0.972 0.008
#> GSM1178992 3 0.2751 0.7793 0.056 0.000 0.904 0.040
#> GSM1179005 3 0.4882 0.6630 0.272 0.000 0.708 0.020
#> GSM1179007 3 0.5582 0.4467 0.400 0.000 0.576 0.024
#> GSM1179012 1 0.5056 0.6487 0.732 0.000 0.224 0.044
#> GSM1179016 3 0.3858 0.7540 0.100 0.000 0.844 0.056
#> GSM1179030 3 0.3688 0.5971 0.000 0.000 0.792 0.208
#> GSM1179038 3 0.5062 0.6446 0.284 0.000 0.692 0.024
#> GSM1178987 3 0.1042 0.7962 0.020 0.000 0.972 0.008
#> GSM1179003 4 0.5853 0.2848 0.000 0.032 0.460 0.508
#> GSM1179004 3 0.1042 0.7962 0.020 0.000 0.972 0.008
#> GSM1179039 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM1178975 4 0.4972 0.1000 0.456 0.000 0.000 0.544
#> GSM1178980 4 0.2124 0.7624 0.000 0.008 0.068 0.924
#> GSM1178995 3 0.5428 0.5003 0.380 0.000 0.600 0.020
#> GSM1178996 3 0.2313 0.7943 0.044 0.000 0.924 0.032
#> GSM1179001 1 0.1004 0.9244 0.972 0.000 0.004 0.024
#> GSM1179002 1 0.1284 0.9222 0.964 0.000 0.012 0.024
#> GSM1179006 3 0.1820 0.7910 0.020 0.000 0.944 0.036
#> GSM1179008 1 0.0895 0.9242 0.976 0.000 0.004 0.020
#> GSM1179015 1 0.4417 0.7533 0.796 0.000 0.160 0.044
#> GSM1179017 3 0.5009 0.4646 0.004 0.016 0.700 0.280
#> GSM1179026 3 0.1798 0.7902 0.016 0.000 0.944 0.040
#> GSM1179033 3 0.1820 0.7910 0.020 0.000 0.944 0.036
#> GSM1179035 3 0.0817 0.7968 0.024 0.000 0.976 0.000
#> GSM1179036 3 0.1938 0.7951 0.052 0.000 0.936 0.012
#> GSM1178986 3 0.2222 0.7860 0.016 0.000 0.924 0.060
#> GSM1178989 3 0.1302 0.7782 0.000 0.000 0.956 0.044
#> GSM1178993 4 0.2081 0.7615 0.000 0.000 0.084 0.916
#> GSM1178999 4 0.2976 0.7609 0.000 0.008 0.120 0.872
#> GSM1179021 4 0.3447 0.6787 0.000 0.128 0.020 0.852
#> GSM1179025 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM1179027 4 0.2081 0.7615 0.000 0.000 0.084 0.916
#> GSM1179011 4 0.2036 0.7357 0.032 0.000 0.032 0.936
#> GSM1179023 1 0.0524 0.9253 0.988 0.000 0.004 0.008
#> GSM1179029 1 0.1305 0.9127 0.960 0.000 0.004 0.036
#> GSM1179034 1 0.0524 0.9253 0.988 0.000 0.004 0.008
#> GSM1179040 4 0.2124 0.7624 0.000 0.008 0.068 0.924
#> GSM1178988 3 0.1305 0.7827 0.004 0.000 0.960 0.036
#> GSM1179037 3 0.0707 0.7960 0.020 0.000 0.980 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1178971 3 0.6368 -0.00303 0.332 0.000 0.488 0.000 0.180
#> GSM1178979 4 0.6314 0.65982 0.000 0.056 0.088 0.616 0.240
#> GSM1179009 4 0.6598 -0.24146 0.000 0.000 0.324 0.448 0.228
#> GSM1179031 2 0.0000 0.99501 0.000 1.000 0.000 0.000 0.000
#> GSM1178970 4 0.7785 0.48012 0.000 0.080 0.244 0.432 0.244
#> GSM1178972 2 0.0963 0.96428 0.000 0.964 0.000 0.000 0.036
#> GSM1178973 1 0.5135 0.57502 0.700 0.000 0.008 0.204 0.088
#> GSM1178974 2 0.0000 0.99501 0.000 1.000 0.000 0.000 0.000
#> GSM1178977 4 0.5264 0.67729 0.000 0.000 0.092 0.652 0.256
#> GSM1178978 5 0.7211 -0.05106 0.020 0.000 0.272 0.304 0.404
#> GSM1178998 5 0.5280 0.13939 0.440 0.000 0.048 0.000 0.512
#> GSM1179010 5 0.6163 0.22020 0.144 0.000 0.352 0.000 0.504
#> GSM1179018 3 0.5919 0.00727 0.000 0.000 0.480 0.416 0.104
#> GSM1179024 1 0.0880 0.75706 0.968 0.000 0.000 0.000 0.032
#> GSM1178984 3 0.5243 0.18668 0.048 0.000 0.540 0.000 0.412
#> GSM1178990 1 0.2583 0.72254 0.864 0.000 0.004 0.000 0.132
#> GSM1178991 1 0.5862 0.39558 0.560 0.000 0.004 0.336 0.100
#> GSM1178994 3 0.5243 0.18665 0.048 0.000 0.540 0.000 0.412
#> GSM1178997 1 0.5417 0.42171 0.648 0.000 0.236 0.000 0.116
#> GSM1179000 1 0.1628 0.74235 0.936 0.000 0.008 0.000 0.056
#> GSM1179013 1 0.1671 0.75357 0.924 0.000 0.000 0.000 0.076
#> GSM1179014 1 0.3320 0.69899 0.828 0.000 0.008 0.012 0.152
#> GSM1179019 1 0.1557 0.74327 0.940 0.000 0.008 0.000 0.052
#> GSM1179020 1 0.0000 0.75601 1.000 0.000 0.000 0.000 0.000
#> GSM1179022 1 0.1671 0.75357 0.924 0.000 0.000 0.000 0.076
#> GSM1179028 2 0.0000 0.99501 0.000 1.000 0.000 0.000 0.000
#> GSM1179032 1 0.1671 0.75357 0.924 0.000 0.000 0.000 0.076
#> GSM1179041 2 0.0000 0.99501 0.000 1.000 0.000 0.000 0.000
#> GSM1179042 2 0.0000 0.99501 0.000 1.000 0.000 0.000 0.000
#> GSM1178976 3 0.4169 0.44357 0.000 0.000 0.732 0.028 0.240
#> GSM1178981 3 0.4015 0.41660 0.000 0.000 0.652 0.000 0.348
#> GSM1178982 3 0.3885 0.49424 0.000 0.000 0.724 0.008 0.268
#> GSM1178983 3 0.4479 0.48603 0.004 0.000 0.704 0.028 0.264
#> GSM1178985 3 0.3586 0.49455 0.000 0.000 0.736 0.000 0.264
#> GSM1178992 3 0.3783 0.51021 0.004 0.000 0.768 0.012 0.216
#> GSM1179005 3 0.5442 0.36329 0.116 0.000 0.644 0.000 0.240
#> GSM1179007 3 0.6642 -0.28676 0.228 0.000 0.420 0.000 0.352
#> GSM1179012 5 0.5870 0.45688 0.276 0.000 0.140 0.000 0.584
#> GSM1179016 3 0.4773 0.41619 0.084 0.000 0.748 0.012 0.156
#> GSM1179030 3 0.3991 0.48486 0.000 0.000 0.780 0.048 0.172
#> GSM1179038 3 0.4819 0.44781 0.112 0.000 0.724 0.000 0.164
#> GSM1178987 3 0.3966 0.43084 0.000 0.000 0.664 0.000 0.336
#> GSM1179003 3 0.6586 -0.15901 0.000 0.000 0.464 0.292 0.244
#> GSM1179004 3 0.3949 0.43304 0.000 0.000 0.668 0.000 0.332
#> GSM1179039 2 0.0000 0.99501 0.000 1.000 0.000 0.000 0.000
#> GSM1178975 1 0.6154 0.43594 0.568 0.000 0.016 0.308 0.108
#> GSM1178980 4 0.0693 0.75265 0.000 0.000 0.012 0.980 0.008
#> GSM1178995 3 0.6309 0.08811 0.236 0.000 0.532 0.000 0.232
#> GSM1178996 3 0.1774 0.57024 0.016 0.000 0.932 0.000 0.052
#> GSM1179001 1 0.3476 0.68064 0.804 0.000 0.020 0.000 0.176
#> GSM1179002 1 0.4254 0.58544 0.740 0.000 0.040 0.000 0.220
#> GSM1179006 3 0.0451 0.58071 0.004 0.000 0.988 0.000 0.008
#> GSM1179008 1 0.3123 0.69931 0.828 0.000 0.012 0.000 0.160
#> GSM1179015 1 0.5697 -0.07187 0.480 0.000 0.068 0.004 0.448
#> GSM1179017 3 0.5996 0.15781 0.000 0.000 0.512 0.120 0.368
#> GSM1179026 3 0.1251 0.58064 0.000 0.000 0.956 0.008 0.036
#> GSM1179033 3 0.0451 0.58236 0.004 0.000 0.988 0.000 0.008
#> GSM1179035 3 0.3913 0.43402 0.000 0.000 0.676 0.000 0.324
#> GSM1179036 3 0.1117 0.57840 0.020 0.000 0.964 0.000 0.016
#> GSM1178986 3 0.1970 0.57205 0.004 0.000 0.924 0.012 0.060
#> GSM1178989 3 0.3789 0.46703 0.000 0.000 0.768 0.020 0.212
#> GSM1178993 4 0.0566 0.74940 0.000 0.000 0.012 0.984 0.004
#> GSM1178999 4 0.4960 0.69718 0.000 0.000 0.112 0.708 0.180
#> GSM1179021 4 0.2635 0.74577 0.000 0.016 0.008 0.888 0.088
#> GSM1179025 2 0.0000 0.99501 0.000 1.000 0.000 0.000 0.000
#> GSM1179027 4 0.0566 0.74940 0.000 0.000 0.012 0.984 0.004
#> GSM1179011 4 0.1965 0.70769 0.024 0.000 0.000 0.924 0.052
#> GSM1179023 1 0.1671 0.75357 0.924 0.000 0.000 0.000 0.076
#> GSM1179029 1 0.4039 0.62801 0.720 0.000 0.004 0.008 0.268
#> GSM1179034 1 0.1671 0.75357 0.924 0.000 0.000 0.000 0.076
#> GSM1179040 4 0.1364 0.75508 0.000 0.000 0.012 0.952 0.036
#> GSM1178988 3 0.2563 0.54096 0.000 0.000 0.872 0.008 0.120
#> GSM1179037 3 0.1965 0.56989 0.000 0.000 0.904 0.000 0.096
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1178971 3 0.6383 0.0714 0.208 0.000 0.508 0.000 0.040 0.244
#> GSM1178979 5 0.4265 0.5396 0.000 0.016 0.020 0.284 0.680 0.000
#> GSM1179009 4 0.6225 -0.1613 0.000 0.000 0.236 0.492 0.020 0.252
#> GSM1179031 2 0.0000 0.9659 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178970 5 0.5624 0.6164 0.000 0.044 0.092 0.132 0.692 0.040
#> GSM1178972 2 0.3344 0.8048 0.000 0.804 0.000 0.000 0.152 0.044
#> GSM1178973 1 0.6765 0.5103 0.552 0.000 0.016 0.196 0.092 0.144
#> GSM1178974 2 0.0993 0.9556 0.000 0.964 0.000 0.000 0.012 0.024
#> GSM1178977 5 0.4295 0.5357 0.000 0.000 0.012 0.264 0.692 0.032
#> GSM1178978 6 0.6934 0.1838 0.004 0.000 0.128 0.120 0.264 0.484
#> GSM1178998 6 0.4847 0.4993 0.280 0.000 0.080 0.000 0.004 0.636
#> GSM1179010 6 0.5271 0.3499 0.080 0.000 0.316 0.000 0.016 0.588
#> GSM1179018 3 0.7257 0.0466 0.000 0.000 0.412 0.276 0.160 0.152
#> GSM1179024 1 0.1492 0.7105 0.940 0.000 0.000 0.000 0.024 0.036
#> GSM1178984 3 0.4871 0.1505 0.020 0.000 0.496 0.000 0.024 0.460
#> GSM1178990 1 0.1779 0.6912 0.920 0.000 0.016 0.000 0.000 0.064
#> GSM1178991 1 0.7421 0.2398 0.392 0.000 0.008 0.308 0.136 0.156
#> GSM1178994 3 0.4871 0.1442 0.024 0.000 0.496 0.000 0.020 0.460
#> GSM1178997 1 0.6741 0.4020 0.508 0.000 0.228 0.000 0.100 0.164
#> GSM1179000 1 0.3538 0.6870 0.832 0.000 0.048 0.000 0.048 0.072
#> GSM1179013 1 0.0632 0.7142 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM1179014 1 0.5374 0.6075 0.672 0.000 0.048 0.000 0.148 0.132
#> GSM1179019 1 0.3474 0.6877 0.836 0.000 0.048 0.000 0.044 0.072
#> GSM1179020 1 0.0291 0.7155 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM1179022 1 0.0632 0.7142 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM1179028 2 0.0146 0.9647 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM1179032 1 0.0632 0.7142 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM1179041 2 0.0000 0.9659 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179042 2 0.0000 0.9659 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178976 5 0.4364 0.5907 0.000 0.000 0.308 0.012 0.656 0.024
#> GSM1178981 3 0.4576 0.2964 0.000 0.000 0.560 0.000 0.040 0.400
#> GSM1178982 3 0.4516 0.4655 0.000 0.000 0.668 0.000 0.072 0.260
#> GSM1178983 3 0.5170 0.3977 0.000 0.000 0.592 0.008 0.088 0.312
#> GSM1178985 3 0.4044 0.4765 0.000 0.000 0.704 0.000 0.040 0.256
#> GSM1178992 3 0.4200 0.4516 0.000 0.000 0.740 0.000 0.120 0.140
#> GSM1179005 3 0.3394 0.5049 0.012 0.000 0.788 0.000 0.012 0.188
#> GSM1179007 3 0.5255 0.1775 0.140 0.000 0.588 0.000 0.000 0.272
#> GSM1179012 6 0.5916 0.5630 0.196 0.000 0.180 0.000 0.036 0.588
#> GSM1179016 3 0.5875 0.2524 0.064 0.000 0.616 0.000 0.196 0.124
#> GSM1179030 3 0.4513 -0.1533 0.000 0.000 0.532 0.004 0.440 0.024
#> GSM1179038 3 0.2604 0.5480 0.020 0.000 0.872 0.000 0.008 0.100
#> GSM1178987 3 0.4561 0.3028 0.000 0.000 0.568 0.000 0.040 0.392
#> GSM1179003 5 0.5183 0.6478 0.000 0.000 0.264 0.120 0.612 0.004
#> GSM1179004 3 0.4500 0.3062 0.000 0.000 0.572 0.000 0.036 0.392
#> GSM1179039 2 0.0000 0.9659 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178975 1 0.7727 0.3683 0.428 0.000 0.044 0.260 0.108 0.160
#> GSM1178980 4 0.0777 0.7699 0.000 0.000 0.000 0.972 0.024 0.004
#> GSM1178995 3 0.4821 0.4035 0.112 0.000 0.700 0.000 0.016 0.172
#> GSM1178996 3 0.2688 0.5325 0.000 0.000 0.868 0.000 0.068 0.064
#> GSM1179001 1 0.5300 0.5145 0.604 0.000 0.048 0.000 0.044 0.304
#> GSM1179002 1 0.5835 0.4131 0.548 0.000 0.088 0.000 0.044 0.320
#> GSM1179006 3 0.1267 0.5633 0.000 0.000 0.940 0.000 0.060 0.000
#> GSM1179008 1 0.5037 0.5557 0.636 0.000 0.036 0.000 0.044 0.284
#> GSM1179015 1 0.6430 0.0439 0.456 0.000 0.076 0.000 0.100 0.368
#> GSM1179017 5 0.5092 0.5652 0.000 0.000 0.272 0.016 0.632 0.080
#> GSM1179026 3 0.1972 0.5656 0.000 0.000 0.916 0.004 0.056 0.024
#> GSM1179033 3 0.1141 0.5658 0.000 0.000 0.948 0.000 0.052 0.000
#> GSM1179035 3 0.3871 0.4392 0.000 0.000 0.676 0.000 0.016 0.308
#> GSM1179036 3 0.1349 0.5639 0.000 0.000 0.940 0.000 0.056 0.004
#> GSM1178986 3 0.3503 0.5204 0.000 0.000 0.816 0.008 0.108 0.068
#> GSM1178989 5 0.4222 0.3695 0.000 0.000 0.472 0.004 0.516 0.008
#> GSM1178993 4 0.0405 0.7715 0.000 0.000 0.004 0.988 0.000 0.008
#> GSM1178999 5 0.4931 0.2540 0.000 0.000 0.044 0.464 0.484 0.008
#> GSM1179021 4 0.3122 0.5943 0.000 0.020 0.000 0.804 0.176 0.000
#> GSM1179025 2 0.0993 0.9556 0.000 0.964 0.000 0.000 0.012 0.024
#> GSM1179027 4 0.0000 0.7736 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1179011 4 0.2209 0.7230 0.000 0.000 0.004 0.904 0.052 0.040
#> GSM1179023 1 0.0632 0.7142 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM1179029 1 0.5182 0.5288 0.624 0.000 0.004 0.000 0.136 0.236
#> GSM1179034 1 0.0632 0.7142 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM1179040 4 0.1714 0.7229 0.000 0.000 0.000 0.908 0.092 0.000
#> GSM1178988 3 0.3733 0.2557 0.000 0.000 0.700 0.004 0.288 0.008
#> GSM1179037 3 0.2006 0.5654 0.000 0.000 0.904 0.000 0.016 0.080
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) protocol(p) k
#> SD:kmeans 73 0.2001 2.81e-01 2
#> SD:kmeans 68 0.0331 2.51e-02 3
#> SD:kmeans 64 0.0106 6.67e-05 4
#> SD:kmeans 42 0.0144 1.13e-03 5
#> SD:kmeans 45 0.0103 5.89e-03 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 31632 rows and 73 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.968 0.964 0.983 0.4822 0.521 0.521
#> 3 3 0.758 0.812 0.898 0.3828 0.718 0.500
#> 4 4 0.750 0.780 0.894 0.1183 0.828 0.539
#> 5 5 0.707 0.660 0.831 0.0618 0.911 0.672
#> 6 6 0.687 0.508 0.763 0.0362 0.979 0.903
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
#> GSM1178971 1 0.0000 0.981 1.000 0.000
#> GSM1178979 2 0.0000 0.984 0.000 1.000
#> GSM1179009 1 0.4022 0.913 0.920 0.080
#> GSM1179031 2 0.0000 0.984 0.000 1.000
#> GSM1178970 2 0.0000 0.984 0.000 1.000
#> GSM1178972 2 0.0000 0.984 0.000 1.000
#> GSM1178973 1 0.0000 0.981 1.000 0.000
#> GSM1178974 2 0.0000 0.984 0.000 1.000
#> GSM1178977 2 0.0000 0.984 0.000 1.000
#> GSM1178978 2 0.2948 0.937 0.052 0.948
#> GSM1178998 1 0.0000 0.981 1.000 0.000
#> GSM1179010 1 0.0000 0.981 1.000 0.000
#> GSM1179018 2 0.1414 0.967 0.020 0.980
#> GSM1179024 1 0.0000 0.981 1.000 0.000
#> GSM1178984 1 0.0000 0.981 1.000 0.000
#> GSM1178990 1 0.0000 0.981 1.000 0.000
#> GSM1178991 1 0.7219 0.761 0.800 0.200
#> GSM1178994 1 0.0000 0.981 1.000 0.000
#> GSM1178997 2 0.7602 0.723 0.220 0.780
#> GSM1179000 1 0.0000 0.981 1.000 0.000
#> GSM1179013 1 0.0000 0.981 1.000 0.000
#> GSM1179014 1 0.0000 0.981 1.000 0.000
#> GSM1179019 1 0.0000 0.981 1.000 0.000
#> GSM1179020 1 0.0000 0.981 1.000 0.000
#> GSM1179022 1 0.0000 0.981 1.000 0.000
#> GSM1179028 2 0.0000 0.984 0.000 1.000
#> GSM1179032 1 0.0000 0.981 1.000 0.000
#> GSM1179041 2 0.0000 0.984 0.000 1.000
#> GSM1179042 2 0.0000 0.984 0.000 1.000
#> GSM1178976 2 0.0000 0.984 0.000 1.000
#> GSM1178981 1 0.0000 0.981 1.000 0.000
#> GSM1178982 1 0.3584 0.924 0.932 0.068
#> GSM1178983 1 0.1414 0.966 0.980 0.020
#> GSM1178985 1 0.3733 0.919 0.928 0.072
#> GSM1178992 1 0.0000 0.981 1.000 0.000
#> GSM1179005 1 0.0000 0.981 1.000 0.000
#> GSM1179007 1 0.0000 0.981 1.000 0.000
#> GSM1179012 1 0.0000 0.981 1.000 0.000
#> GSM1179016 1 0.0000 0.981 1.000 0.000
#> GSM1179030 2 0.0000 0.984 0.000 1.000
#> GSM1179038 1 0.0000 0.981 1.000 0.000
#> GSM1178987 1 0.0000 0.981 1.000 0.000
#> GSM1179003 2 0.0000 0.984 0.000 1.000
#> GSM1179004 1 0.0000 0.981 1.000 0.000
#> GSM1179039 2 0.0000 0.984 0.000 1.000
#> GSM1178975 1 0.6438 0.807 0.836 0.164
#> GSM1178980 2 0.0000 0.984 0.000 1.000
#> GSM1178995 1 0.0000 0.981 1.000 0.000
#> GSM1178996 1 0.0000 0.981 1.000 0.000
#> GSM1179001 1 0.0000 0.981 1.000 0.000
#> GSM1179002 1 0.0000 0.981 1.000 0.000
#> GSM1179006 1 0.0938 0.972 0.988 0.012
#> GSM1179008 1 0.0000 0.981 1.000 0.000
#> GSM1179015 1 0.0000 0.981 1.000 0.000
#> GSM1179017 2 0.0000 0.984 0.000 1.000
#> GSM1179026 1 0.0000 0.981 1.000 0.000
#> GSM1179033 2 0.5629 0.849 0.132 0.868
#> GSM1179035 1 0.0000 0.981 1.000 0.000
#> GSM1179036 1 0.0000 0.981 1.000 0.000
#> GSM1178986 1 0.7376 0.749 0.792 0.208
#> GSM1178989 2 0.0000 0.984 0.000 1.000
#> GSM1178993 2 0.0000 0.984 0.000 1.000
#> GSM1178999 2 0.0000 0.984 0.000 1.000
#> GSM1179021 2 0.0000 0.984 0.000 1.000
#> GSM1179025 2 0.0000 0.984 0.000 1.000
#> GSM1179027 2 0.0000 0.984 0.000 1.000
#> GSM1179011 2 0.0000 0.984 0.000 1.000
#> GSM1179023 1 0.0000 0.981 1.000 0.000
#> GSM1179029 1 0.0000 0.981 1.000 0.000
#> GSM1179034 1 0.0000 0.981 1.000 0.000
#> GSM1179040 2 0.0000 0.984 0.000 1.000
#> GSM1178988 2 0.0000 0.984 0.000 1.000
#> GSM1179037 1 0.0000 0.981 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1178971 1 0.0000 0.8869 1.000 0.000 0.000
#> GSM1178979 2 0.0000 0.9605 0.000 1.000 0.000
#> GSM1179009 3 0.0237 0.7996 0.004 0.000 0.996
#> GSM1179031 2 0.0000 0.9605 0.000 1.000 0.000
#> GSM1178970 2 0.0000 0.9605 0.000 1.000 0.000
#> GSM1178972 2 0.0000 0.9605 0.000 1.000 0.000
#> GSM1178973 1 0.2537 0.8334 0.920 0.000 0.080
#> GSM1178974 2 0.0000 0.9605 0.000 1.000 0.000
#> GSM1178977 2 0.0000 0.9605 0.000 1.000 0.000
#> GSM1178978 1 0.7958 0.3874 0.544 0.064 0.392
#> GSM1178998 1 0.5678 0.4958 0.684 0.000 0.316
#> GSM1179010 3 0.2625 0.8543 0.084 0.000 0.916
#> GSM1179018 3 0.1860 0.7710 0.000 0.052 0.948
#> GSM1179024 1 0.0000 0.8869 1.000 0.000 0.000
#> GSM1178984 3 0.2625 0.8543 0.084 0.000 0.916
#> GSM1178990 1 0.1529 0.8547 0.960 0.000 0.040
#> GSM1178991 1 0.4137 0.8064 0.872 0.032 0.096
#> GSM1178994 3 0.2625 0.8543 0.084 0.000 0.916
#> GSM1178997 1 0.1315 0.8711 0.972 0.020 0.008
#> GSM1179000 1 0.0000 0.8869 1.000 0.000 0.000
#> GSM1179013 1 0.0000 0.8869 1.000 0.000 0.000
#> GSM1179014 1 0.0000 0.8869 1.000 0.000 0.000
#> GSM1179019 1 0.0000 0.8869 1.000 0.000 0.000
#> GSM1179020 1 0.0000 0.8869 1.000 0.000 0.000
#> GSM1179022 1 0.0000 0.8869 1.000 0.000 0.000
#> GSM1179028 2 0.0000 0.9605 0.000 1.000 0.000
#> GSM1179032 1 0.0000 0.8869 1.000 0.000 0.000
#> GSM1179041 2 0.0000 0.9605 0.000 1.000 0.000
#> GSM1179042 2 0.0000 0.9605 0.000 1.000 0.000
#> GSM1178976 2 0.0000 0.9605 0.000 1.000 0.000
#> GSM1178981 3 0.2625 0.8543 0.084 0.000 0.916
#> GSM1178982 3 0.2537 0.8463 0.080 0.000 0.920
#> GSM1178983 1 0.6062 0.4330 0.616 0.000 0.384
#> GSM1178985 3 0.2537 0.8541 0.080 0.000 0.920
#> GSM1178992 3 0.2878 0.8503 0.096 0.000 0.904
#> GSM1179005 3 0.5785 0.6627 0.332 0.000 0.668
#> GSM1179007 3 0.5678 0.6815 0.316 0.000 0.684
#> GSM1179012 3 0.2625 0.8543 0.084 0.000 0.916
#> GSM1179016 1 0.5859 0.2445 0.656 0.000 0.344
#> GSM1179030 2 0.0000 0.9605 0.000 1.000 0.000
#> GSM1179038 3 0.6286 0.4112 0.464 0.000 0.536
#> GSM1178987 3 0.2537 0.8541 0.080 0.000 0.920
#> GSM1179003 2 0.0000 0.9605 0.000 1.000 0.000
#> GSM1179004 3 0.2537 0.8541 0.080 0.000 0.920
#> GSM1179039 2 0.0000 0.9605 0.000 1.000 0.000
#> GSM1178975 1 0.2537 0.8334 0.920 0.000 0.080
#> GSM1178980 2 0.2537 0.9111 0.000 0.920 0.080
#> GSM1178995 3 0.6309 0.3268 0.496 0.000 0.504
#> GSM1178996 1 0.5360 0.5946 0.768 0.012 0.220
#> GSM1179001 1 0.0000 0.8869 1.000 0.000 0.000
#> GSM1179002 1 0.0000 0.8869 1.000 0.000 0.000
#> GSM1179006 3 0.5835 0.7884 0.164 0.052 0.784
#> GSM1179008 1 0.0000 0.8869 1.000 0.000 0.000
#> GSM1179015 3 0.6062 0.5837 0.384 0.000 0.616
#> GSM1179017 2 0.0000 0.9605 0.000 1.000 0.000
#> GSM1179026 3 0.2682 0.8525 0.076 0.004 0.920
#> GSM1179033 3 0.6143 0.6094 0.024 0.256 0.720
#> GSM1179035 3 0.2537 0.8541 0.080 0.000 0.920
#> GSM1179036 3 0.6026 0.5937 0.376 0.000 0.624
#> GSM1178986 3 0.5627 0.6866 0.188 0.032 0.780
#> GSM1178989 2 0.2261 0.9019 0.000 0.932 0.068
#> GSM1178993 2 0.3551 0.8682 0.000 0.868 0.132
#> GSM1178999 2 0.0000 0.9605 0.000 1.000 0.000
#> GSM1179021 2 0.0000 0.9605 0.000 1.000 0.000
#> GSM1179025 2 0.0000 0.9605 0.000 1.000 0.000
#> GSM1179027 2 0.2711 0.9060 0.000 0.912 0.088
#> GSM1179011 1 0.6625 0.6685 0.744 0.176 0.080
#> GSM1179023 1 0.0000 0.8869 1.000 0.000 0.000
#> GSM1179029 1 0.0237 0.8844 0.996 0.000 0.004
#> GSM1179034 1 0.0000 0.8869 1.000 0.000 0.000
#> GSM1179040 2 0.1411 0.9406 0.000 0.964 0.036
#> GSM1178988 2 0.6280 0.0968 0.000 0.540 0.460
#> GSM1179037 3 0.2537 0.8541 0.080 0.000 0.920
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1178971 1 0.0000 0.903 1.000 0.000 0.000 0.000
#> GSM1178979 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM1179009 4 0.2469 0.750 0.000 0.000 0.108 0.892
#> GSM1179031 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM1178970 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM1178972 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM1178973 4 0.4985 0.201 0.468 0.000 0.000 0.532
#> GSM1178974 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM1178977 2 0.0188 0.928 0.000 0.996 0.000 0.004
#> GSM1178978 4 0.3102 0.777 0.024 0.016 0.064 0.896
#> GSM1178998 1 0.4375 0.708 0.788 0.000 0.180 0.032
#> GSM1179010 3 0.2623 0.835 0.064 0.000 0.908 0.028
#> GSM1179018 4 0.1022 0.784 0.000 0.000 0.032 0.968
#> GSM1179024 1 0.0000 0.903 1.000 0.000 0.000 0.000
#> GSM1178984 3 0.3144 0.826 0.072 0.000 0.884 0.044
#> GSM1178990 1 0.0336 0.900 0.992 0.000 0.008 0.000
#> GSM1178991 4 0.3837 0.688 0.224 0.000 0.000 0.776
#> GSM1178994 3 0.2816 0.833 0.064 0.000 0.900 0.036
#> GSM1178997 1 0.2466 0.814 0.900 0.096 0.000 0.004
#> GSM1179000 1 0.0000 0.903 1.000 0.000 0.000 0.000
#> GSM1179013 1 0.0000 0.903 1.000 0.000 0.000 0.000
#> GSM1179014 1 0.0188 0.902 0.996 0.000 0.000 0.004
#> GSM1179019 1 0.0000 0.903 1.000 0.000 0.000 0.000
#> GSM1179020 1 0.0000 0.903 1.000 0.000 0.000 0.000
#> GSM1179022 1 0.0000 0.903 1.000 0.000 0.000 0.000
#> GSM1179028 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM1179032 1 0.0000 0.903 1.000 0.000 0.000 0.000
#> GSM1179041 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM1179042 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM1178976 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM1178981 3 0.2174 0.835 0.020 0.000 0.928 0.052
#> GSM1178982 4 0.5158 0.181 0.004 0.000 0.472 0.524
#> GSM1178983 4 0.4881 0.675 0.048 0.000 0.196 0.756
#> GSM1178985 3 0.1118 0.839 0.000 0.000 0.964 0.036
#> GSM1178992 3 0.1406 0.838 0.024 0.000 0.960 0.016
#> GSM1179005 3 0.4837 0.505 0.348 0.000 0.648 0.004
#> GSM1179007 3 0.4920 0.467 0.368 0.000 0.628 0.004
#> GSM1179012 3 0.3598 0.798 0.124 0.000 0.848 0.028
#> GSM1179016 1 0.4290 0.717 0.772 0.000 0.212 0.016
#> GSM1179030 2 0.1635 0.900 0.000 0.948 0.008 0.044
#> GSM1179038 1 0.4123 0.694 0.772 0.000 0.220 0.008
#> GSM1178987 3 0.1118 0.839 0.000 0.000 0.964 0.036
#> GSM1179003 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM1179004 3 0.1118 0.839 0.000 0.000 0.964 0.036
#> GSM1179039 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM1178975 4 0.3649 0.711 0.204 0.000 0.000 0.796
#> GSM1178980 4 0.1474 0.783 0.000 0.052 0.000 0.948
#> GSM1178995 1 0.4877 0.226 0.592 0.000 0.408 0.000
#> GSM1178996 1 0.5830 0.580 0.672 0.036 0.276 0.016
#> GSM1179001 1 0.0000 0.903 1.000 0.000 0.000 0.000
#> GSM1179002 1 0.0000 0.903 1.000 0.000 0.000 0.000
#> GSM1179006 3 0.3167 0.805 0.040 0.048 0.896 0.016
#> GSM1179008 1 0.0000 0.903 1.000 0.000 0.000 0.000
#> GSM1179015 1 0.4769 0.532 0.684 0.000 0.308 0.008
#> GSM1179017 2 0.1610 0.900 0.000 0.952 0.032 0.016
#> GSM1179026 3 0.0592 0.837 0.000 0.000 0.984 0.016
#> GSM1179033 3 0.4774 0.719 0.020 0.116 0.808 0.056
#> GSM1179035 3 0.0592 0.841 0.000 0.000 0.984 0.016
#> GSM1179036 3 0.5220 0.440 0.352 0.000 0.632 0.016
#> GSM1178986 4 0.6356 0.411 0.088 0.000 0.308 0.604
#> GSM1178989 2 0.2179 0.877 0.000 0.924 0.064 0.012
#> GSM1178993 4 0.0707 0.787 0.000 0.020 0.000 0.980
#> GSM1178999 2 0.4500 0.541 0.000 0.684 0.000 0.316
#> GSM1179021 2 0.4134 0.641 0.000 0.740 0.000 0.260
#> GSM1179025 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM1179027 4 0.1302 0.785 0.000 0.044 0.000 0.956
#> GSM1179011 4 0.1488 0.788 0.032 0.012 0.000 0.956
#> GSM1179023 1 0.0000 0.903 1.000 0.000 0.000 0.000
#> GSM1179029 1 0.0524 0.898 0.988 0.000 0.008 0.004
#> GSM1179034 1 0.0000 0.903 1.000 0.000 0.000 0.000
#> GSM1179040 4 0.3873 0.612 0.000 0.228 0.000 0.772
#> GSM1178988 2 0.5298 0.410 0.000 0.612 0.372 0.016
#> GSM1179037 3 0.0469 0.838 0.000 0.000 0.988 0.012
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1178971 1 0.4459 0.731 0.744 0.000 0.200 0.004 0.052
#> GSM1178979 2 0.0000 0.899 0.000 1.000 0.000 0.000 0.000
#> GSM1179009 4 0.3774 0.536 0.000 0.000 0.000 0.704 0.296
#> GSM1179031 2 0.0000 0.899 0.000 1.000 0.000 0.000 0.000
#> GSM1178970 2 0.0162 0.897 0.000 0.996 0.004 0.000 0.000
#> GSM1178972 2 0.0000 0.899 0.000 1.000 0.000 0.000 0.000
#> GSM1178973 1 0.4874 0.301 0.600 0.000 0.032 0.368 0.000
#> GSM1178974 2 0.0000 0.899 0.000 1.000 0.000 0.000 0.000
#> GSM1178977 2 0.0912 0.887 0.000 0.972 0.012 0.016 0.000
#> GSM1178978 4 0.6571 0.209 0.028 0.032 0.040 0.456 0.444
#> GSM1178998 5 0.5111 0.209 0.408 0.000 0.040 0.000 0.552
#> GSM1179010 5 0.1168 0.712 0.008 0.000 0.032 0.000 0.960
#> GSM1179018 4 0.2782 0.698 0.000 0.000 0.048 0.880 0.072
#> GSM1179024 1 0.0404 0.850 0.988 0.000 0.012 0.000 0.000
#> GSM1178984 5 0.1012 0.711 0.020 0.000 0.012 0.000 0.968
#> GSM1178990 1 0.1965 0.842 0.924 0.000 0.024 0.000 0.052
#> GSM1178991 4 0.4775 0.572 0.256 0.000 0.040 0.696 0.008
#> GSM1178994 5 0.0807 0.714 0.012 0.000 0.012 0.000 0.976
#> GSM1178997 1 0.3216 0.788 0.868 0.048 0.068 0.016 0.000
#> GSM1179000 1 0.0609 0.849 0.980 0.000 0.020 0.000 0.000
#> GSM1179013 1 0.0290 0.855 0.992 0.000 0.000 0.000 0.008
#> GSM1179014 1 0.1608 0.835 0.928 0.000 0.072 0.000 0.000
#> GSM1179019 1 0.0703 0.849 0.976 0.000 0.024 0.000 0.000
#> GSM1179020 1 0.0404 0.855 0.988 0.000 0.000 0.000 0.012
#> GSM1179022 1 0.0404 0.855 0.988 0.000 0.000 0.000 0.012
#> GSM1179028 2 0.0000 0.899 0.000 1.000 0.000 0.000 0.000
#> GSM1179032 1 0.0404 0.855 0.988 0.000 0.000 0.000 0.012
#> GSM1179041 2 0.0000 0.899 0.000 1.000 0.000 0.000 0.000
#> GSM1179042 2 0.0000 0.899 0.000 1.000 0.000 0.000 0.000
#> GSM1178976 2 0.0290 0.896 0.000 0.992 0.008 0.000 0.000
#> GSM1178981 5 0.0798 0.707 0.000 0.000 0.016 0.008 0.976
#> GSM1178982 5 0.4329 0.408 0.000 0.000 0.032 0.252 0.716
#> GSM1178983 4 0.6619 0.310 0.072 0.000 0.056 0.500 0.372
#> GSM1178985 5 0.1792 0.679 0.000 0.000 0.084 0.000 0.916
#> GSM1178992 3 0.5080 0.529 0.056 0.000 0.628 0.000 0.316
#> GSM1179005 5 0.6589 0.113 0.364 0.000 0.212 0.000 0.424
#> GSM1179007 5 0.6188 0.233 0.364 0.000 0.144 0.000 0.492
#> GSM1179012 5 0.2756 0.664 0.092 0.000 0.024 0.004 0.880
#> GSM1179016 3 0.3999 0.555 0.240 0.000 0.740 0.000 0.020
#> GSM1179030 2 0.2875 0.834 0.000 0.884 0.052 0.056 0.008
#> GSM1179038 1 0.6178 0.224 0.484 0.000 0.376 0.000 0.140
#> GSM1178987 5 0.1205 0.701 0.000 0.000 0.040 0.004 0.956
#> GSM1179003 2 0.0880 0.883 0.000 0.968 0.032 0.000 0.000
#> GSM1179004 5 0.1430 0.694 0.000 0.000 0.052 0.004 0.944
#> GSM1179039 2 0.0000 0.899 0.000 1.000 0.000 0.000 0.000
#> GSM1178975 4 0.4594 0.528 0.284 0.000 0.036 0.680 0.000
#> GSM1178980 4 0.0404 0.719 0.000 0.012 0.000 0.988 0.000
#> GSM1178995 1 0.6148 0.399 0.568 0.000 0.160 0.004 0.268
#> GSM1178996 3 0.2786 0.653 0.084 0.012 0.884 0.000 0.020
#> GSM1179001 1 0.3133 0.821 0.864 0.000 0.080 0.004 0.052
#> GSM1179002 1 0.3449 0.809 0.844 0.000 0.088 0.004 0.064
#> GSM1179006 3 0.2911 0.695 0.008 0.000 0.852 0.004 0.136
#> GSM1179008 1 0.2728 0.830 0.888 0.000 0.068 0.004 0.040
#> GSM1179015 1 0.6044 0.424 0.584 0.000 0.152 0.004 0.260
#> GSM1179017 2 0.4211 0.449 0.004 0.636 0.360 0.000 0.000
#> GSM1179026 3 0.3109 0.672 0.000 0.000 0.800 0.000 0.200
#> GSM1179033 3 0.4418 0.646 0.004 0.024 0.756 0.016 0.200
#> GSM1179035 5 0.3366 0.488 0.000 0.000 0.232 0.000 0.768
#> GSM1179036 3 0.2871 0.688 0.040 0.000 0.872 0.000 0.088
#> GSM1178986 4 0.7929 0.174 0.128 0.004 0.316 0.424 0.128
#> GSM1178989 2 0.3586 0.706 0.000 0.792 0.188 0.000 0.020
#> GSM1178993 4 0.0162 0.721 0.000 0.004 0.000 0.996 0.000
#> GSM1178999 2 0.4702 0.282 0.000 0.552 0.016 0.432 0.000
#> GSM1179021 2 0.4182 0.386 0.000 0.600 0.000 0.400 0.000
#> GSM1179025 2 0.0000 0.899 0.000 1.000 0.000 0.000 0.000
#> GSM1179027 4 0.0162 0.721 0.000 0.004 0.000 0.996 0.000
#> GSM1179011 4 0.0579 0.720 0.008 0.000 0.008 0.984 0.000
#> GSM1179023 1 0.0404 0.855 0.988 0.000 0.000 0.000 0.012
#> GSM1179029 1 0.2775 0.815 0.876 0.000 0.100 0.004 0.020
#> GSM1179034 1 0.0404 0.855 0.988 0.000 0.000 0.000 0.012
#> GSM1179040 4 0.2813 0.621 0.000 0.168 0.000 0.832 0.000
#> GSM1178988 3 0.5906 0.166 0.000 0.404 0.492 0.000 0.104
#> GSM1179037 3 0.4306 0.200 0.000 0.000 0.508 0.000 0.492
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1178971 1 0.5683 0.44879 0.532 0.000 0.116 0.000 0.336 0.016
#> GSM1178979 2 0.0000 0.86508 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179009 4 0.3882 0.34126 0.000 0.000 0.012 0.716 0.012 0.260
#> GSM1179031 2 0.0000 0.86508 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178970 2 0.0713 0.85572 0.000 0.972 0.000 0.000 0.028 0.000
#> GSM1178972 2 0.0260 0.86302 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM1178973 1 0.5466 0.30879 0.596 0.000 0.008 0.240 0.156 0.000
#> GSM1178974 2 0.0000 0.86508 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178977 2 0.1461 0.84069 0.000 0.940 0.000 0.016 0.044 0.000
#> GSM1178978 6 0.6948 0.01468 0.044 0.008 0.008 0.264 0.204 0.472
#> GSM1178998 6 0.5599 0.26712 0.344 0.000 0.008 0.000 0.124 0.524
#> GSM1179010 6 0.2954 0.60829 0.044 0.000 0.028 0.000 0.060 0.868
#> GSM1179018 4 0.4163 0.49735 0.000 0.000 0.056 0.788 0.068 0.088
#> GSM1179024 1 0.0790 0.71769 0.968 0.000 0.000 0.000 0.032 0.000
#> GSM1178984 6 0.2307 0.62267 0.032 0.000 0.016 0.000 0.048 0.904
#> GSM1178990 1 0.3406 0.66852 0.840 0.000 0.036 0.000 0.068 0.056
#> GSM1178991 4 0.6117 -0.10579 0.288 0.000 0.004 0.472 0.232 0.004
#> GSM1178994 6 0.1232 0.62603 0.024 0.000 0.004 0.000 0.016 0.956
#> GSM1178997 1 0.4496 0.56421 0.700 0.028 0.024 0.004 0.244 0.000
#> GSM1179000 1 0.2092 0.68318 0.876 0.000 0.000 0.000 0.124 0.000
#> GSM1179013 1 0.0508 0.72193 0.984 0.000 0.004 0.000 0.012 0.000
#> GSM1179014 1 0.3736 0.62530 0.776 0.000 0.068 0.000 0.156 0.000
#> GSM1179019 1 0.2234 0.68643 0.872 0.000 0.004 0.000 0.124 0.000
#> GSM1179020 1 0.0458 0.72326 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM1179022 1 0.0000 0.72265 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179028 2 0.0000 0.86508 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179032 1 0.0000 0.72265 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179041 2 0.0000 0.86508 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179042 2 0.0000 0.86508 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178976 2 0.0692 0.85634 0.000 0.976 0.020 0.000 0.004 0.000
#> GSM1178981 6 0.1401 0.61666 0.004 0.000 0.020 0.000 0.028 0.948
#> GSM1178982 6 0.5415 0.39772 0.008 0.000 0.040 0.172 0.104 0.676
#> GSM1178983 6 0.7196 -0.07594 0.032 0.000 0.036 0.308 0.216 0.408
#> GSM1178985 6 0.2618 0.57168 0.000 0.000 0.116 0.000 0.024 0.860
#> GSM1178992 3 0.6061 0.31153 0.056 0.000 0.568 0.000 0.120 0.256
#> GSM1179005 6 0.7569 0.00581 0.264 0.000 0.212 0.000 0.180 0.344
#> GSM1179007 6 0.7365 0.09452 0.300 0.000 0.184 0.000 0.144 0.372
#> GSM1179012 6 0.4243 0.56503 0.112 0.000 0.040 0.000 0.072 0.776
#> GSM1179016 3 0.5953 -0.05847 0.196 0.000 0.520 0.000 0.272 0.012
#> GSM1179030 2 0.5058 0.67009 0.000 0.736 0.052 0.052 0.128 0.032
#> GSM1179038 1 0.7235 0.03098 0.400 0.000 0.292 0.000 0.184 0.124
#> GSM1178987 6 0.1794 0.60751 0.000 0.000 0.036 0.000 0.040 0.924
#> GSM1179003 2 0.1257 0.84484 0.000 0.952 0.028 0.000 0.020 0.000
#> GSM1179004 6 0.2112 0.58650 0.000 0.000 0.088 0.000 0.016 0.896
#> GSM1179039 2 0.0000 0.86508 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178975 4 0.6182 -0.04214 0.312 0.000 0.012 0.456 0.220 0.000
#> GSM1178980 4 0.0458 0.65401 0.000 0.000 0.000 0.984 0.016 0.000
#> GSM1178995 1 0.7211 0.20979 0.448 0.000 0.184 0.000 0.164 0.204
#> GSM1178996 3 0.4703 0.24906 0.028 0.008 0.616 0.000 0.340 0.008
#> GSM1179001 1 0.4898 0.53906 0.612 0.000 0.048 0.000 0.324 0.016
#> GSM1179002 1 0.5381 0.50103 0.568 0.000 0.064 0.000 0.340 0.028
#> GSM1179006 3 0.3123 0.47422 0.004 0.000 0.848 0.008 0.040 0.100
#> GSM1179008 1 0.4536 0.57911 0.652 0.000 0.036 0.000 0.300 0.012
#> GSM1179015 1 0.7054 0.15587 0.464 0.000 0.156 0.000 0.140 0.240
#> GSM1179017 2 0.5309 0.32201 0.000 0.560 0.312 0.000 0.128 0.000
#> GSM1179026 3 0.4106 0.46031 0.000 0.000 0.736 0.000 0.076 0.188
#> GSM1179033 3 0.5145 0.43869 0.000 0.016 0.720 0.048 0.080 0.136
#> GSM1179035 6 0.4050 0.39574 0.000 0.000 0.236 0.000 0.048 0.716
#> GSM1179036 3 0.4723 0.41419 0.036 0.000 0.716 0.000 0.184 0.064
#> GSM1178986 5 0.7891 0.00000 0.064 0.000 0.220 0.228 0.408 0.080
#> GSM1178989 2 0.4012 0.61204 0.000 0.724 0.240 0.000 0.024 0.012
#> GSM1178993 4 0.0146 0.65483 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM1178999 2 0.4876 0.17829 0.000 0.504 0.004 0.444 0.048 0.000
#> GSM1179021 2 0.3868 0.12726 0.000 0.504 0.000 0.496 0.000 0.000
#> GSM1179025 2 0.0000 0.86508 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179027 4 0.0000 0.65427 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1179011 4 0.1141 0.63964 0.000 0.000 0.000 0.948 0.052 0.000
#> GSM1179023 1 0.0146 0.72262 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM1179029 1 0.4024 0.60125 0.744 0.000 0.072 0.000 0.184 0.000
#> GSM1179034 1 0.0000 0.72265 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179040 4 0.1957 0.54821 0.000 0.112 0.000 0.888 0.000 0.000
#> GSM1178988 3 0.6480 0.12529 0.000 0.328 0.484 0.000 0.100 0.088
#> GSM1179037 3 0.4791 0.19602 0.000 0.000 0.512 0.000 0.052 0.436
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) protocol(p) k
#> SD:skmeans 73 0.0195 0.41301 2
#> SD:skmeans 66 0.2607 0.00225 3
#> SD:skmeans 66 0.2050 0.03999 4
#> SD:skmeans 56 0.0228 0.00407 5
#> SD:skmeans 44 0.0120 0.04878 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 31632 rows and 73 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 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 0.829 0.913 0.948 0.282 0.740 0.740
#> 3 3 0.757 0.845 0.930 1.040 0.634 0.526
#> 4 4 0.696 0.777 0.897 0.166 0.876 0.721
#> 5 5 0.621 0.741 0.836 0.124 0.845 0.565
#> 6 6 0.610 0.580 0.777 0.045 0.935 0.745
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM1178971 1 0.2043 0.951 0.968 0.032
#> GSM1178979 2 0.8661 0.620 0.288 0.712
#> GSM1179009 1 0.2043 0.951 0.968 0.032
#> GSM1179031 2 0.1184 0.931 0.016 0.984
#> GSM1178970 2 0.8813 0.595 0.300 0.700
#> GSM1178972 2 0.1184 0.931 0.016 0.984
#> GSM1178973 1 0.1184 0.944 0.984 0.016
#> GSM1178974 2 0.1184 0.931 0.016 0.984
#> GSM1178977 1 0.5946 0.859 0.856 0.144
#> GSM1178978 1 0.3733 0.906 0.928 0.072
#> GSM1178998 1 0.1184 0.944 0.984 0.016
#> GSM1179010 1 0.2043 0.951 0.968 0.032
#> GSM1179018 1 0.3431 0.933 0.936 0.064
#> GSM1179024 1 0.1184 0.944 0.984 0.016
#> GSM1178984 1 0.0000 0.947 1.000 0.000
#> GSM1178990 1 0.1184 0.944 0.984 0.016
#> GSM1178991 1 0.1184 0.944 0.984 0.016
#> GSM1178994 1 0.2043 0.951 0.968 0.032
#> GSM1178997 1 0.1184 0.944 0.984 0.016
#> GSM1179000 1 0.1184 0.944 0.984 0.016
#> GSM1179013 1 0.1184 0.944 0.984 0.016
#> GSM1179014 1 0.1184 0.944 0.984 0.016
#> GSM1179019 1 0.1184 0.944 0.984 0.016
#> GSM1179020 1 0.1184 0.944 0.984 0.016
#> GSM1179022 1 0.1184 0.944 0.984 0.016
#> GSM1179028 2 0.1184 0.931 0.016 0.984
#> GSM1179032 1 0.1184 0.944 0.984 0.016
#> GSM1179041 2 0.1184 0.931 0.016 0.984
#> GSM1179042 2 0.1184 0.931 0.016 0.984
#> GSM1178976 1 0.9491 0.450 0.632 0.368
#> GSM1178981 1 0.2043 0.951 0.968 0.032
#> GSM1178982 1 0.2043 0.951 0.968 0.032
#> GSM1178983 1 0.1633 0.950 0.976 0.024
#> GSM1178985 1 0.2043 0.951 0.968 0.032
#> GSM1178992 1 0.2043 0.951 0.968 0.032
#> GSM1179005 1 0.2043 0.951 0.968 0.032
#> GSM1179007 1 0.2043 0.951 0.968 0.032
#> GSM1179012 1 0.1184 0.944 0.984 0.016
#> GSM1179016 1 0.2043 0.951 0.968 0.032
#> GSM1179030 1 0.3879 0.924 0.924 0.076
#> GSM1179038 1 0.2043 0.951 0.968 0.032
#> GSM1178987 1 0.2043 0.951 0.968 0.032
#> GSM1179003 1 0.9491 0.450 0.632 0.368
#> GSM1179004 1 0.2043 0.951 0.968 0.032
#> GSM1179039 2 0.1184 0.931 0.016 0.984
#> GSM1178975 1 0.0000 0.947 1.000 0.000
#> GSM1178980 1 0.5946 0.859 0.856 0.144
#> GSM1178995 1 0.2043 0.951 0.968 0.032
#> GSM1178996 1 0.2043 0.951 0.968 0.032
#> GSM1179001 1 0.1184 0.944 0.984 0.016
#> GSM1179002 1 0.1184 0.944 0.984 0.016
#> GSM1179006 1 0.2043 0.951 0.968 0.032
#> GSM1179008 1 0.1184 0.944 0.984 0.016
#> GSM1179015 1 0.1184 0.944 0.984 0.016
#> GSM1179017 1 0.5946 0.859 0.856 0.144
#> GSM1179026 1 0.2043 0.951 0.968 0.032
#> GSM1179033 1 0.2043 0.951 0.968 0.032
#> GSM1179035 1 0.2043 0.951 0.968 0.032
#> GSM1179036 1 0.2043 0.951 0.968 0.032
#> GSM1178986 1 0.2043 0.951 0.968 0.032
#> GSM1178989 1 0.5842 0.864 0.860 0.140
#> GSM1178993 1 0.3114 0.938 0.944 0.056
#> GSM1178999 1 0.5946 0.859 0.856 0.144
#> GSM1179021 2 0.3733 0.893 0.072 0.928
#> GSM1179025 2 0.1184 0.931 0.016 0.984
#> GSM1179027 1 0.3274 0.936 0.940 0.060
#> GSM1179011 1 0.0376 0.946 0.996 0.004
#> GSM1179023 1 0.1184 0.944 0.984 0.016
#> GSM1179029 1 0.1184 0.944 0.984 0.016
#> GSM1179034 1 0.1184 0.944 0.984 0.016
#> GSM1179040 1 0.5946 0.859 0.856 0.144
#> GSM1178988 1 0.2043 0.951 0.968 0.032
#> GSM1179037 1 0.2043 0.951 0.968 0.032
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1178971 3 0.2448 0.8722 0.076 0.000 0.924
#> GSM1178979 3 0.0000 0.8918 0.000 0.000 1.000
#> GSM1179009 3 0.0747 0.8926 0.016 0.000 0.984
#> GSM1179031 2 0.0000 0.9243 0.000 1.000 0.000
#> GSM1178970 3 0.0000 0.8918 0.000 0.000 1.000
#> GSM1178972 2 0.0000 0.9243 0.000 1.000 0.000
#> GSM1178973 1 0.0000 0.9516 1.000 0.000 0.000
#> GSM1178974 2 0.0000 0.9243 0.000 1.000 0.000
#> GSM1178977 3 0.0000 0.8918 0.000 0.000 1.000
#> GSM1178978 3 0.5178 0.6497 0.256 0.000 0.744
#> GSM1178998 1 0.1529 0.9155 0.960 0.000 0.040
#> GSM1179010 3 0.6095 0.4737 0.392 0.000 0.608
#> GSM1179018 3 0.0000 0.8918 0.000 0.000 1.000
#> GSM1179024 1 0.0000 0.9516 1.000 0.000 0.000
#> GSM1178984 3 0.6095 0.4363 0.392 0.000 0.608
#> GSM1178990 1 0.0000 0.9516 1.000 0.000 0.000
#> GSM1178991 1 0.2796 0.8692 0.908 0.000 0.092
#> GSM1178994 3 0.5810 0.5866 0.336 0.000 0.664
#> GSM1178997 1 0.5859 0.4262 0.656 0.000 0.344
#> GSM1179000 1 0.0000 0.9516 1.000 0.000 0.000
#> GSM1179013 1 0.0000 0.9516 1.000 0.000 0.000
#> GSM1179014 1 0.0237 0.9494 0.996 0.000 0.004
#> GSM1179019 1 0.0237 0.9494 0.996 0.000 0.004
#> GSM1179020 1 0.0000 0.9516 1.000 0.000 0.000
#> GSM1179022 1 0.0000 0.9516 1.000 0.000 0.000
#> GSM1179028 2 0.0000 0.9243 0.000 1.000 0.000
#> GSM1179032 1 0.0000 0.9516 1.000 0.000 0.000
#> GSM1179041 2 0.0000 0.9243 0.000 1.000 0.000
#> GSM1179042 2 0.0000 0.9243 0.000 1.000 0.000
#> GSM1178976 3 0.0000 0.8918 0.000 0.000 1.000
#> GSM1178981 3 0.1964 0.8816 0.056 0.000 0.944
#> GSM1178982 3 0.1289 0.8895 0.032 0.000 0.968
#> GSM1178983 3 0.0892 0.8884 0.020 0.000 0.980
#> GSM1178985 3 0.0892 0.8921 0.020 0.000 0.980
#> GSM1178992 3 0.4291 0.7982 0.180 0.000 0.820
#> GSM1179005 3 0.2711 0.8662 0.088 0.000 0.912
#> GSM1179007 3 0.5988 0.5342 0.368 0.000 0.632
#> GSM1179012 1 0.1411 0.9249 0.964 0.000 0.036
#> GSM1179016 3 0.5178 0.6775 0.256 0.000 0.744
#> GSM1179030 3 0.0000 0.8918 0.000 0.000 1.000
#> GSM1179038 3 0.5327 0.6901 0.272 0.000 0.728
#> GSM1178987 3 0.2625 0.8601 0.084 0.000 0.916
#> GSM1179003 3 0.0000 0.8918 0.000 0.000 1.000
#> GSM1179004 3 0.0592 0.8924 0.012 0.000 0.988
#> GSM1179039 2 0.0000 0.9243 0.000 1.000 0.000
#> GSM1178975 3 0.5810 0.5628 0.336 0.000 0.664
#> GSM1178980 3 0.0000 0.8918 0.000 0.000 1.000
#> GSM1178995 3 0.4654 0.7756 0.208 0.000 0.792
#> GSM1178996 3 0.1860 0.8812 0.052 0.000 0.948
#> GSM1179001 1 0.0000 0.9516 1.000 0.000 0.000
#> GSM1179002 1 0.4121 0.7376 0.832 0.000 0.168
#> GSM1179006 3 0.0747 0.8924 0.016 0.000 0.984
#> GSM1179008 1 0.0592 0.9431 0.988 0.000 0.012
#> GSM1179015 1 0.0000 0.9516 1.000 0.000 0.000
#> GSM1179017 3 0.0000 0.8918 0.000 0.000 1.000
#> GSM1179026 3 0.0592 0.8924 0.012 0.000 0.988
#> GSM1179033 3 0.1860 0.8812 0.052 0.000 0.948
#> GSM1179035 3 0.0747 0.8924 0.016 0.000 0.984
#> GSM1179036 3 0.1860 0.8812 0.052 0.000 0.948
#> GSM1178986 3 0.0000 0.8918 0.000 0.000 1.000
#> GSM1178989 3 0.0000 0.8918 0.000 0.000 1.000
#> GSM1178993 3 0.0000 0.8918 0.000 0.000 1.000
#> GSM1178999 3 0.0000 0.8918 0.000 0.000 1.000
#> GSM1179021 2 0.6295 0.0301 0.000 0.528 0.472
#> GSM1179025 2 0.0000 0.9243 0.000 1.000 0.000
#> GSM1179027 3 0.0424 0.8923 0.008 0.000 0.992
#> GSM1179011 3 0.5621 0.5574 0.308 0.000 0.692
#> GSM1179023 1 0.0000 0.9516 1.000 0.000 0.000
#> GSM1179029 1 0.0000 0.9516 1.000 0.000 0.000
#> GSM1179034 1 0.0000 0.9516 1.000 0.000 0.000
#> GSM1179040 3 0.0000 0.8918 0.000 0.000 1.000
#> GSM1178988 3 0.0000 0.8918 0.000 0.000 1.000
#> GSM1179037 3 0.1964 0.8810 0.056 0.000 0.944
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1178971 3 0.2081 0.8375 0.084 0.000 0.916 0.000
#> GSM1178979 3 0.4898 0.1441 0.000 0.000 0.584 0.416
#> GSM1179009 4 0.5000 0.0485 0.000 0.000 0.496 0.504
#> GSM1179031 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM1178970 3 0.0592 0.8367 0.000 0.000 0.984 0.016
#> GSM1178972 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM1178973 1 0.0657 0.9326 0.984 0.000 0.004 0.012
#> GSM1178974 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM1178977 3 0.1867 0.8109 0.000 0.000 0.928 0.072
#> GSM1178978 4 0.7495 0.3047 0.184 0.000 0.368 0.448
#> GSM1178998 1 0.2644 0.8611 0.908 0.000 0.060 0.032
#> GSM1179010 3 0.5645 0.5224 0.364 0.000 0.604 0.032
#> GSM1179018 3 0.1940 0.8043 0.000 0.000 0.924 0.076
#> GSM1179024 1 0.0000 0.9357 1.000 0.000 0.000 0.000
#> GSM1178984 3 0.5492 0.5232 0.328 0.000 0.640 0.032
#> GSM1178990 1 0.0000 0.9357 1.000 0.000 0.000 0.000
#> GSM1178991 4 0.6965 0.0581 0.428 0.000 0.112 0.460
#> GSM1178994 3 0.5344 0.6097 0.300 0.000 0.668 0.032
#> GSM1178997 1 0.4679 0.3947 0.648 0.000 0.352 0.000
#> GSM1179000 1 0.0188 0.9347 0.996 0.000 0.004 0.000
#> GSM1179013 1 0.0000 0.9357 1.000 0.000 0.000 0.000
#> GSM1179014 1 0.0188 0.9351 0.996 0.000 0.004 0.000
#> GSM1179019 1 0.0336 0.9331 0.992 0.000 0.008 0.000
#> GSM1179020 1 0.0592 0.9316 0.984 0.000 0.000 0.016
#> GSM1179022 1 0.0000 0.9357 1.000 0.000 0.000 0.000
#> GSM1179028 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM1179032 1 0.0000 0.9357 1.000 0.000 0.000 0.000
#> GSM1179041 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM1179042 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM1178976 3 0.0000 0.8387 0.000 0.000 1.000 0.000
#> GSM1178981 3 0.2224 0.8386 0.040 0.000 0.928 0.032
#> GSM1178982 3 0.1833 0.8410 0.024 0.000 0.944 0.032
#> GSM1178983 3 0.1510 0.8354 0.016 0.000 0.956 0.028
#> GSM1178985 3 0.1624 0.8421 0.020 0.000 0.952 0.028
#> GSM1178992 3 0.3444 0.7773 0.184 0.000 0.816 0.000
#> GSM1179005 3 0.2530 0.8259 0.112 0.000 0.888 0.000
#> GSM1179007 3 0.5495 0.5657 0.348 0.000 0.624 0.028
#> GSM1179012 1 0.2565 0.8732 0.912 0.000 0.056 0.032
#> GSM1179016 3 0.3907 0.6700 0.232 0.000 0.768 0.000
#> GSM1179030 3 0.0000 0.8387 0.000 0.000 1.000 0.000
#> GSM1179038 3 0.4356 0.6579 0.292 0.000 0.708 0.000
#> GSM1178987 3 0.2483 0.8240 0.052 0.000 0.916 0.032
#> GSM1179003 3 0.2469 0.7836 0.000 0.000 0.892 0.108
#> GSM1179004 3 0.1724 0.8412 0.020 0.000 0.948 0.032
#> GSM1179039 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM1178975 3 0.4356 0.6138 0.292 0.000 0.708 0.000
#> GSM1178980 4 0.1022 0.6622 0.000 0.000 0.032 0.968
#> GSM1178995 3 0.3751 0.7672 0.196 0.000 0.800 0.004
#> GSM1178996 3 0.2081 0.8375 0.084 0.000 0.916 0.000
#> GSM1179001 1 0.0707 0.9298 0.980 0.000 0.000 0.020
#> GSM1179002 1 0.4867 0.5719 0.736 0.000 0.232 0.032
#> GSM1179006 3 0.0921 0.8464 0.028 0.000 0.972 0.000
#> GSM1179008 1 0.1388 0.9185 0.960 0.000 0.012 0.028
#> GSM1179015 1 0.0000 0.9357 1.000 0.000 0.000 0.000
#> GSM1179017 3 0.0000 0.8387 0.000 0.000 1.000 0.000
#> GSM1179026 3 0.0707 0.8445 0.020 0.000 0.980 0.000
#> GSM1179033 3 0.2081 0.8375 0.084 0.000 0.916 0.000
#> GSM1179035 3 0.1022 0.8468 0.032 0.000 0.968 0.000
#> GSM1179036 3 0.2081 0.8375 0.084 0.000 0.916 0.000
#> GSM1178986 3 0.0000 0.8387 0.000 0.000 1.000 0.000
#> GSM1178989 3 0.0000 0.8387 0.000 0.000 1.000 0.000
#> GSM1178993 4 0.0000 0.6406 0.000 0.000 0.000 1.000
#> GSM1178999 4 0.4998 0.0723 0.000 0.000 0.488 0.512
#> GSM1179021 4 0.2480 0.5928 0.000 0.088 0.008 0.904
#> GSM1179025 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM1179027 4 0.1022 0.6622 0.000 0.000 0.032 0.968
#> GSM1179011 4 0.1022 0.6622 0.000 0.000 0.032 0.968
#> GSM1179023 1 0.0000 0.9357 1.000 0.000 0.000 0.000
#> GSM1179029 1 0.0592 0.9319 0.984 0.000 0.000 0.016
#> GSM1179034 1 0.0000 0.9357 1.000 0.000 0.000 0.000
#> GSM1179040 4 0.1302 0.6607 0.000 0.000 0.044 0.956
#> GSM1178988 3 0.0000 0.8387 0.000 0.000 1.000 0.000
#> GSM1179037 3 0.1940 0.8402 0.076 0.000 0.924 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1178971 3 0.0000 0.8422 0.000 0.000 1.000 0.000 0.000
#> GSM1178979 4 0.5177 0.5930 0.000 0.000 0.220 0.676 0.104
#> GSM1179009 5 0.5750 0.5757 0.000 0.000 0.156 0.228 0.616
#> GSM1179031 2 0.0000 0.9964 0.000 1.000 0.000 0.000 0.000
#> GSM1178970 3 0.4639 0.7385 0.000 0.000 0.708 0.056 0.236
#> GSM1178972 2 0.0794 0.9742 0.000 0.972 0.000 0.000 0.028
#> GSM1178973 1 0.4183 0.7434 0.780 0.000 0.136 0.000 0.084
#> GSM1178974 2 0.0000 0.9964 0.000 1.000 0.000 0.000 0.000
#> GSM1178977 3 0.4845 0.7294 0.000 0.000 0.724 0.128 0.148
#> GSM1178978 5 0.3277 0.6908 0.072 0.000 0.068 0.004 0.856
#> GSM1178998 5 0.3796 0.4605 0.300 0.000 0.000 0.000 0.700
#> GSM1179010 5 0.4317 0.6329 0.076 0.000 0.160 0.000 0.764
#> GSM1179018 3 0.4021 0.7887 0.000 0.000 0.780 0.052 0.168
#> GSM1179024 1 0.0000 0.8003 1.000 0.000 0.000 0.000 0.000
#> GSM1178984 5 0.4808 0.6802 0.108 0.000 0.168 0.000 0.724
#> GSM1178990 1 0.2424 0.7855 0.868 0.000 0.132 0.000 0.000
#> GSM1178991 1 0.6341 0.4308 0.564 0.000 0.008 0.200 0.228
#> GSM1178994 5 0.4451 0.7139 0.040 0.000 0.248 0.000 0.712
#> GSM1178997 1 0.6080 0.3289 0.528 0.000 0.332 0.000 0.140
#> GSM1179000 1 0.2127 0.7964 0.892 0.000 0.108 0.000 0.000
#> GSM1179013 1 0.0000 0.8003 1.000 0.000 0.000 0.000 0.000
#> GSM1179014 1 0.2329 0.7900 0.876 0.000 0.124 0.000 0.000
#> GSM1179019 1 0.2230 0.7945 0.884 0.000 0.116 0.000 0.000
#> GSM1179020 1 0.3442 0.7546 0.836 0.000 0.060 0.000 0.104
#> GSM1179022 1 0.0000 0.8003 1.000 0.000 0.000 0.000 0.000
#> GSM1179028 2 0.0000 0.9964 0.000 1.000 0.000 0.000 0.000
#> GSM1179032 1 0.0000 0.8003 1.000 0.000 0.000 0.000 0.000
#> GSM1179041 2 0.0000 0.9964 0.000 1.000 0.000 0.000 0.000
#> GSM1179042 2 0.0000 0.9964 0.000 1.000 0.000 0.000 0.000
#> GSM1178976 3 0.2424 0.8375 0.000 0.000 0.868 0.000 0.132
#> GSM1178981 5 0.3508 0.6857 0.000 0.000 0.252 0.000 0.748
#> GSM1178982 5 0.4300 0.1441 0.000 0.000 0.476 0.000 0.524
#> GSM1178983 5 0.3109 0.6683 0.000 0.000 0.200 0.000 0.800
#> GSM1178985 3 0.4227 0.2303 0.000 0.000 0.580 0.000 0.420
#> GSM1178992 3 0.1082 0.8342 0.028 0.000 0.964 0.000 0.008
#> GSM1179005 3 0.0000 0.8422 0.000 0.000 1.000 0.000 0.000
#> GSM1179007 3 0.4581 0.4576 0.072 0.000 0.732 0.000 0.196
#> GSM1179012 5 0.3628 0.5475 0.216 0.000 0.012 0.000 0.772
#> GSM1179016 3 0.4036 0.8128 0.068 0.000 0.788 0.000 0.144
#> GSM1179030 3 0.3074 0.8074 0.000 0.000 0.804 0.000 0.196
#> GSM1179038 3 0.1608 0.7862 0.072 0.000 0.928 0.000 0.000
#> GSM1178987 5 0.3010 0.6893 0.004 0.000 0.172 0.000 0.824
#> GSM1179003 3 0.2962 0.8175 0.000 0.000 0.868 0.084 0.048
#> GSM1179004 5 0.3661 0.6744 0.000 0.000 0.276 0.000 0.724
#> GSM1179039 2 0.0000 0.9964 0.000 1.000 0.000 0.000 0.000
#> GSM1178975 3 0.3365 0.6725 0.120 0.000 0.836 0.000 0.044
#> GSM1178980 4 0.0510 0.8807 0.000 0.000 0.000 0.984 0.016
#> GSM1178995 3 0.1012 0.8289 0.012 0.000 0.968 0.000 0.020
#> GSM1178996 3 0.0000 0.8422 0.000 0.000 1.000 0.000 0.000
#> GSM1179001 5 0.6158 0.0822 0.416 0.000 0.132 0.000 0.452
#> GSM1179002 5 0.6439 0.4599 0.260 0.000 0.236 0.000 0.504
#> GSM1179006 3 0.1608 0.8497 0.000 0.000 0.928 0.000 0.072
#> GSM1179008 1 0.5783 0.4855 0.612 0.000 0.160 0.000 0.228
#> GSM1179015 1 0.4083 0.7421 0.788 0.000 0.080 0.000 0.132
#> GSM1179017 3 0.2561 0.8346 0.000 0.000 0.856 0.000 0.144
#> GSM1179026 3 0.1792 0.8469 0.000 0.000 0.916 0.000 0.084
#> GSM1179033 3 0.0000 0.8422 0.000 0.000 1.000 0.000 0.000
#> GSM1179035 3 0.1608 0.8498 0.000 0.000 0.928 0.000 0.072
#> GSM1179036 3 0.0000 0.8422 0.000 0.000 1.000 0.000 0.000
#> GSM1178986 3 0.2424 0.8388 0.000 0.000 0.868 0.000 0.132
#> GSM1178989 3 0.2561 0.8346 0.000 0.000 0.856 0.000 0.144
#> GSM1178993 4 0.0000 0.8826 0.000 0.000 0.000 1.000 0.000
#> GSM1178999 4 0.4693 0.6614 0.000 0.000 0.196 0.724 0.080
#> GSM1179021 4 0.0955 0.8684 0.000 0.028 0.000 0.968 0.004
#> GSM1179025 2 0.0000 0.9964 0.000 1.000 0.000 0.000 0.000
#> GSM1179027 4 0.0000 0.8826 0.000 0.000 0.000 1.000 0.000
#> GSM1179011 4 0.0510 0.8807 0.000 0.000 0.000 0.984 0.016
#> GSM1179023 1 0.0000 0.8003 1.000 0.000 0.000 0.000 0.000
#> GSM1179029 1 0.5953 0.1302 0.504 0.000 0.112 0.000 0.384
#> GSM1179034 1 0.0000 0.8003 1.000 0.000 0.000 0.000 0.000
#> GSM1179040 4 0.0290 0.8821 0.000 0.000 0.008 0.992 0.000
#> GSM1178988 3 0.2424 0.8375 0.000 0.000 0.868 0.000 0.132
#> GSM1179037 3 0.0162 0.8436 0.000 0.000 0.996 0.000 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1178971 3 0.2300 0.7668 0.000 0.000 0.856 0.000 0.000 0.144
#> GSM1178979 5 0.4591 0.5464 0.000 0.000 0.120 0.112 0.740 0.028
#> GSM1179009 4 0.5673 -0.1579 0.000 0.000 0.156 0.448 0.000 0.396
#> GSM1179031 2 0.0000 0.9459 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178970 3 0.4897 0.2704 0.000 0.000 0.492 0.000 0.448 0.060
#> GSM1178972 2 0.3684 0.4997 0.000 0.628 0.000 0.000 0.372 0.000
#> GSM1178973 4 0.6828 -0.1475 0.288 0.000 0.048 0.436 0.004 0.224
#> GSM1178974 2 0.0000 0.9459 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178977 3 0.4811 0.2931 0.000 0.000 0.508 0.008 0.448 0.036
#> GSM1178978 6 0.5947 0.4830 0.036 0.000 0.128 0.000 0.280 0.556
#> GSM1178998 6 0.4284 0.5330 0.256 0.000 0.000 0.000 0.056 0.688
#> GSM1179010 6 0.2796 0.6119 0.016 0.000 0.020 0.000 0.100 0.864
#> GSM1179018 3 0.3453 0.6916 0.000 0.000 0.824 0.064 0.012 0.100
#> GSM1179024 1 0.0000 0.7828 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1178984 6 0.2972 0.6801 0.036 0.000 0.128 0.000 0.000 0.836
#> GSM1178990 1 0.3734 0.7277 0.784 0.000 0.040 0.000 0.012 0.164
#> GSM1178991 4 0.4048 0.2287 0.016 0.000 0.088 0.788 0.004 0.104
#> GSM1178994 6 0.2805 0.6757 0.000 0.000 0.160 0.000 0.012 0.828
#> GSM1178997 1 0.8159 0.1619 0.360 0.000 0.244 0.132 0.052 0.212
#> GSM1179000 1 0.3302 0.7584 0.824 0.000 0.028 0.004 0.008 0.136
#> GSM1179013 1 0.0260 0.7819 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM1179014 1 0.3606 0.7463 0.800 0.000 0.024 0.004 0.016 0.156
#> GSM1179019 1 0.3271 0.7558 0.820 0.000 0.028 0.004 0.004 0.144
#> GSM1179020 1 0.3194 0.7145 0.808 0.000 0.012 0.004 0.004 0.172
#> GSM1179022 1 0.0000 0.7828 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179028 2 0.0000 0.9459 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179032 1 0.0000 0.7828 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179041 2 0.0000 0.9459 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179042 2 0.0000 0.9459 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178976 3 0.1444 0.7680 0.000 0.000 0.928 0.000 0.072 0.000
#> GSM1178981 6 0.3175 0.6623 0.000 0.000 0.256 0.000 0.000 0.744
#> GSM1178982 3 0.3854 -0.1170 0.000 0.000 0.536 0.000 0.000 0.464
#> GSM1178983 6 0.4215 0.6255 0.000 0.000 0.244 0.000 0.056 0.700
#> GSM1178985 3 0.3601 0.3630 0.000 0.000 0.684 0.000 0.004 0.312
#> GSM1178992 3 0.2673 0.7702 0.012 0.000 0.852 0.000 0.004 0.132
#> GSM1179005 3 0.2491 0.7544 0.000 0.000 0.836 0.000 0.000 0.164
#> GSM1179007 3 0.4174 0.5109 0.016 0.000 0.628 0.000 0.004 0.352
#> GSM1179012 6 0.4464 0.5608 0.136 0.000 0.020 0.000 0.100 0.744
#> GSM1179016 3 0.2307 0.7594 0.024 0.000 0.900 0.000 0.064 0.012
#> GSM1179030 3 0.2837 0.7159 0.000 0.000 0.856 0.000 0.056 0.088
#> GSM1179038 3 0.3147 0.7466 0.016 0.000 0.816 0.000 0.008 0.160
#> GSM1178987 6 0.3896 0.6517 0.000 0.000 0.196 0.000 0.056 0.748
#> GSM1179003 3 0.3835 0.6497 0.000 0.000 0.756 0.056 0.188 0.000
#> GSM1179004 6 0.3634 0.6035 0.000 0.000 0.356 0.000 0.000 0.644
#> GSM1179039 2 0.0000 0.9459 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178975 4 0.6371 0.0288 0.012 0.000 0.340 0.440 0.008 0.200
#> GSM1178980 4 0.2003 0.2053 0.000 0.000 0.000 0.884 0.116 0.000
#> GSM1178995 3 0.2915 0.7426 0.008 0.000 0.808 0.000 0.000 0.184
#> GSM1178996 3 0.1957 0.7787 0.000 0.000 0.888 0.000 0.000 0.112
#> GSM1179001 6 0.4605 0.4198 0.272 0.000 0.040 0.004 0.012 0.672
#> GSM1179002 6 0.5018 0.5815 0.104 0.000 0.180 0.004 0.020 0.692
#> GSM1179006 3 0.0547 0.7864 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM1179008 1 0.7433 0.1616 0.368 0.000 0.080 0.192 0.020 0.340
#> GSM1179015 1 0.4873 0.6564 0.676 0.000 0.004 0.004 0.104 0.212
#> GSM1179017 3 0.2883 0.6731 0.000 0.000 0.788 0.000 0.212 0.000
#> GSM1179026 3 0.0146 0.7821 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM1179033 3 0.1957 0.7787 0.000 0.000 0.888 0.000 0.000 0.112
#> GSM1179035 3 0.1007 0.7882 0.000 0.000 0.956 0.000 0.000 0.044
#> GSM1179036 3 0.1957 0.7787 0.000 0.000 0.888 0.000 0.000 0.112
#> GSM1178986 3 0.1196 0.7687 0.000 0.000 0.952 0.000 0.040 0.008
#> GSM1178989 3 0.1152 0.7686 0.000 0.000 0.952 0.000 0.044 0.004
#> GSM1178993 4 0.3828 -0.0995 0.000 0.000 0.000 0.560 0.440 0.000
#> GSM1178999 5 0.5449 0.5261 0.000 0.000 0.204 0.092 0.652 0.052
#> GSM1179021 5 0.4648 0.2631 0.000 0.056 0.000 0.340 0.604 0.000
#> GSM1179025 2 0.0000 0.9459 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179027 4 0.3828 -0.0995 0.000 0.000 0.000 0.560 0.440 0.000
#> GSM1179011 4 0.0146 0.2520 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM1179023 1 0.0000 0.7828 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179029 6 0.5562 0.2008 0.332 0.000 0.024 0.004 0.076 0.564
#> GSM1179034 1 0.0000 0.7828 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179040 4 0.4062 -0.1123 0.000 0.000 0.008 0.552 0.440 0.000
#> GSM1178988 3 0.1010 0.7699 0.000 0.000 0.960 0.000 0.036 0.004
#> GSM1179037 3 0.1910 0.7799 0.000 0.000 0.892 0.000 0.000 0.108
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) protocol(p) k
#> SD:pam 71 0.11669 1.76e-01 2
#> SD:pam 69 0.52017 7.20e-04 3
#> SD:pam 67 0.00905 3.38e-05 4
#> SD:pam 63 0.00451 4.88e-06 5
#> SD:pam 53 0.29199 8.43e-07 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "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 31632 rows and 73 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 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 0.624 0.877 0.933 0.2963 0.740 0.740
#> 3 3 0.440 0.715 0.750 0.7075 0.648 0.556
#> 4 4 0.762 0.803 0.922 0.2736 0.772 0.577
#> 5 5 0.647 0.790 0.855 0.0987 0.839 0.603
#> 6 6 0.650 0.737 0.818 0.0877 0.937 0.789
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
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
#> GSM1178971 1 0.0000 0.923 1.000 0.000
#> GSM1178979 2 0.6973 0.766 0.188 0.812
#> GSM1179009 1 0.7453 0.795 0.788 0.212
#> GSM1179031 2 0.0672 0.920 0.008 0.992
#> GSM1178970 2 0.9170 0.477 0.332 0.668
#> GSM1178972 2 0.0672 0.920 0.008 0.992
#> GSM1178973 1 0.7453 0.795 0.788 0.212
#> GSM1178974 2 0.0672 0.920 0.008 0.992
#> GSM1178977 1 0.7453 0.795 0.788 0.212
#> GSM1178978 1 0.7453 0.795 0.788 0.212
#> GSM1178998 1 0.0000 0.923 1.000 0.000
#> GSM1179010 1 0.0672 0.923 0.992 0.008
#> GSM1179018 1 0.7453 0.795 0.788 0.212
#> GSM1179024 1 0.0000 0.923 1.000 0.000
#> GSM1178984 1 0.0000 0.923 1.000 0.000
#> GSM1178990 1 0.0000 0.923 1.000 0.000
#> GSM1178991 1 0.7453 0.795 0.788 0.212
#> GSM1178994 1 0.0000 0.923 1.000 0.000
#> GSM1178997 1 0.0000 0.923 1.000 0.000
#> GSM1179000 1 0.0000 0.923 1.000 0.000
#> GSM1179013 1 0.0376 0.923 0.996 0.004
#> GSM1179014 1 0.0938 0.921 0.988 0.012
#> GSM1179019 1 0.0000 0.923 1.000 0.000
#> GSM1179020 1 0.0000 0.923 1.000 0.000
#> GSM1179022 1 0.0000 0.923 1.000 0.000
#> GSM1179028 2 0.0672 0.920 0.008 0.992
#> GSM1179032 1 0.0000 0.923 1.000 0.000
#> GSM1179041 2 0.0672 0.920 0.008 0.992
#> GSM1179042 2 0.0672 0.920 0.008 0.992
#> GSM1178976 1 0.7453 0.792 0.788 0.212
#> GSM1178981 1 0.0000 0.923 1.000 0.000
#> GSM1178982 1 0.0672 0.922 0.992 0.008
#> GSM1178983 1 0.0938 0.921 0.988 0.012
#> GSM1178985 1 0.0376 0.923 0.996 0.004
#> GSM1178992 1 0.0938 0.922 0.988 0.012
#> GSM1179005 1 0.0000 0.923 1.000 0.000
#> GSM1179007 1 0.0000 0.923 1.000 0.000
#> GSM1179012 1 0.0376 0.923 0.996 0.004
#> GSM1179016 1 0.4022 0.887 0.920 0.080
#> GSM1179030 1 0.3431 0.896 0.936 0.064
#> GSM1179038 1 0.0000 0.923 1.000 0.000
#> GSM1178987 1 0.0376 0.923 0.996 0.004
#> GSM1179003 1 0.9460 0.521 0.636 0.364
#> GSM1179004 1 0.0376 0.923 0.996 0.004
#> GSM1179039 2 0.0672 0.920 0.008 0.992
#> GSM1178975 1 0.7453 0.795 0.788 0.212
#> GSM1178980 1 0.7453 0.795 0.788 0.212
#> GSM1178995 1 0.0000 0.923 1.000 0.000
#> GSM1178996 1 0.0376 0.923 0.996 0.004
#> GSM1179001 1 0.0000 0.923 1.000 0.000
#> GSM1179002 1 0.0000 0.923 1.000 0.000
#> GSM1179006 1 0.0000 0.923 1.000 0.000
#> GSM1179008 1 0.0000 0.923 1.000 0.000
#> GSM1179015 1 0.0938 0.922 0.988 0.012
#> GSM1179017 1 0.6973 0.813 0.812 0.188
#> GSM1179026 1 0.0672 0.923 0.992 0.008
#> GSM1179033 1 0.0938 0.922 0.988 0.012
#> GSM1179035 1 0.0376 0.923 0.996 0.004
#> GSM1179036 1 0.0000 0.923 1.000 0.000
#> GSM1178986 1 0.6531 0.829 0.832 0.168
#> GSM1178989 1 0.6623 0.826 0.828 0.172
#> GSM1178993 1 0.7453 0.795 0.788 0.212
#> GSM1178999 1 0.7299 0.799 0.796 0.204
#> GSM1179021 2 0.6801 0.771 0.180 0.820
#> GSM1179025 2 0.0672 0.920 0.008 0.992
#> GSM1179027 1 0.7453 0.795 0.788 0.212
#> GSM1179011 1 0.7453 0.795 0.788 0.212
#> GSM1179023 1 0.0000 0.923 1.000 0.000
#> GSM1179029 1 0.0000 0.923 1.000 0.000
#> GSM1179034 1 0.0000 0.923 1.000 0.000
#> GSM1179040 1 0.7528 0.791 0.784 0.216
#> GSM1178988 1 0.1414 0.918 0.980 0.020
#> GSM1179037 1 0.0376 0.923 0.996 0.004
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1178971 3 0.2165 0.7251 0.064 0.000 0.936
#> GSM1178979 3 0.6336 0.6748 0.180 0.064 0.756
#> GSM1179009 3 0.6999 0.6050 0.268 0.052 0.680
#> GSM1179031 2 0.0475 0.9932 0.004 0.992 0.004
#> GSM1178970 3 0.5947 0.6882 0.172 0.052 0.776
#> GSM1178972 2 0.0424 0.9906 0.000 0.992 0.008
#> GSM1178973 1 0.6935 0.6236 0.652 0.036 0.312
#> GSM1178974 2 0.0424 0.9906 0.000 0.992 0.008
#> GSM1178977 3 0.6109 0.6753 0.192 0.048 0.760
#> GSM1178978 3 0.5618 0.6935 0.156 0.048 0.796
#> GSM1178998 1 0.6309 0.7667 0.504 0.000 0.496
#> GSM1179010 3 0.1878 0.7298 0.044 0.004 0.952
#> GSM1179018 3 0.6348 0.6608 0.212 0.048 0.740
#> GSM1179024 1 0.6008 0.8885 0.664 0.004 0.332
#> GSM1178984 3 0.1163 0.7423 0.028 0.000 0.972
#> GSM1178990 1 0.6140 0.9072 0.596 0.000 0.404
#> GSM1178991 3 0.7471 0.0338 0.448 0.036 0.516
#> GSM1178994 3 0.2682 0.6923 0.076 0.004 0.920
#> GSM1178997 3 0.3851 0.6187 0.136 0.004 0.860
#> GSM1179000 1 0.6345 0.9099 0.596 0.004 0.400
#> GSM1179013 1 0.5956 0.8843 0.672 0.004 0.324
#> GSM1179014 1 0.6345 0.9099 0.596 0.004 0.400
#> GSM1179019 1 0.6345 0.9099 0.596 0.004 0.400
#> GSM1179020 1 0.6345 0.9099 0.596 0.004 0.400
#> GSM1179022 1 0.5956 0.8843 0.672 0.004 0.324
#> GSM1179028 2 0.0475 0.9932 0.004 0.992 0.004
#> GSM1179032 1 0.5956 0.8843 0.672 0.004 0.324
#> GSM1179041 2 0.0475 0.9932 0.004 0.992 0.004
#> GSM1179042 2 0.0237 0.9921 0.004 0.996 0.000
#> GSM1178976 3 0.2860 0.7444 0.084 0.004 0.912
#> GSM1178981 3 0.0237 0.7577 0.004 0.000 0.996
#> GSM1178982 3 0.0237 0.7577 0.004 0.000 0.996
#> GSM1178983 3 0.0592 0.7608 0.012 0.000 0.988
#> GSM1178985 3 0.0237 0.7598 0.000 0.004 0.996
#> GSM1178992 3 0.2200 0.7221 0.056 0.004 0.940
#> GSM1179005 3 0.1289 0.7407 0.032 0.000 0.968
#> GSM1179007 3 0.3619 0.5846 0.136 0.000 0.864
#> GSM1179012 3 0.6521 -0.7665 0.496 0.004 0.500
#> GSM1179016 3 0.6451 -0.5386 0.436 0.004 0.560
#> GSM1179030 3 0.2261 0.7504 0.068 0.000 0.932
#> GSM1179038 3 0.2066 0.7135 0.060 0.000 0.940
#> GSM1178987 3 0.0237 0.7598 0.000 0.004 0.996
#> GSM1179003 3 0.4007 0.7377 0.084 0.036 0.880
#> GSM1179004 3 0.0237 0.7598 0.000 0.004 0.996
#> GSM1179039 2 0.0475 0.9932 0.004 0.992 0.004
#> GSM1178975 3 0.6124 0.6457 0.220 0.036 0.744
#> GSM1178980 3 0.7037 0.5769 0.328 0.036 0.636
#> GSM1178995 3 0.2878 0.6859 0.096 0.000 0.904
#> GSM1178996 3 0.0592 0.7556 0.012 0.000 0.988
#> GSM1179001 1 0.6140 0.9072 0.596 0.000 0.404
#> GSM1179002 3 0.5016 0.3385 0.240 0.000 0.760
#> GSM1179006 3 0.0000 0.7592 0.000 0.000 1.000
#> GSM1179008 1 0.6345 0.9099 0.596 0.004 0.400
#> GSM1179015 1 0.6451 0.8675 0.560 0.004 0.436
#> GSM1179017 3 0.3851 0.7206 0.136 0.004 0.860
#> GSM1179026 3 0.0237 0.7598 0.000 0.004 0.996
#> GSM1179033 3 0.0000 0.7592 0.000 0.000 1.000
#> GSM1179035 3 0.0475 0.7583 0.004 0.004 0.992
#> GSM1179036 3 0.0424 0.7568 0.008 0.000 0.992
#> GSM1178986 3 0.2918 0.7489 0.044 0.032 0.924
#> GSM1178989 3 0.2860 0.7444 0.084 0.004 0.912
#> GSM1178993 3 0.7037 0.5769 0.328 0.036 0.636
#> GSM1178999 3 0.5558 0.7005 0.152 0.048 0.800
#> GSM1179021 3 0.9972 0.1012 0.328 0.304 0.368
#> GSM1179025 2 0.0424 0.9906 0.000 0.992 0.008
#> GSM1179027 3 0.7037 0.5769 0.328 0.036 0.636
#> GSM1179011 3 0.7037 0.5769 0.328 0.036 0.636
#> GSM1179023 1 0.5956 0.8843 0.672 0.004 0.324
#> GSM1179029 1 0.6140 0.9072 0.596 0.000 0.404
#> GSM1179034 1 0.5956 0.8843 0.672 0.004 0.324
#> GSM1179040 3 0.7037 0.5769 0.328 0.036 0.636
#> GSM1178988 3 0.0475 0.7603 0.004 0.004 0.992
#> GSM1179037 3 0.0237 0.7598 0.000 0.004 0.996
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1178971 3 0.4746 0.424 0.368 0.000 0.632 0.000
#> GSM1178979 3 0.4678 0.638 0.000 0.232 0.744 0.024
#> GSM1179009 4 0.4103 0.527 0.000 0.000 0.256 0.744
#> GSM1179031 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM1178970 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1178972 2 0.2216 0.869 0.000 0.908 0.092 0.000
#> GSM1178973 4 0.7617 0.304 0.332 0.000 0.216 0.452
#> GSM1178974 2 0.0817 0.938 0.000 0.976 0.024 0.000
#> GSM1178977 3 0.3024 0.780 0.000 0.000 0.852 0.148
#> GSM1178978 3 0.1118 0.893 0.000 0.000 0.964 0.036
#> GSM1178998 3 0.1867 0.862 0.072 0.000 0.928 0.000
#> GSM1179010 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1179018 3 0.1211 0.891 0.000 0.000 0.960 0.040
#> GSM1179024 1 0.0000 0.875 1.000 0.000 0.000 0.000
#> GSM1178984 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1178990 1 0.2814 0.731 0.868 0.000 0.132 0.000
#> GSM1178991 1 0.7806 -0.258 0.392 0.000 0.252 0.356
#> GSM1178994 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1178997 1 0.0336 0.869 0.992 0.000 0.008 0.000
#> GSM1179000 1 0.0000 0.875 1.000 0.000 0.000 0.000
#> GSM1179013 1 0.0000 0.875 1.000 0.000 0.000 0.000
#> GSM1179014 1 0.0000 0.875 1.000 0.000 0.000 0.000
#> GSM1179019 1 0.0000 0.875 1.000 0.000 0.000 0.000
#> GSM1179020 1 0.0000 0.875 1.000 0.000 0.000 0.000
#> GSM1179022 1 0.0000 0.875 1.000 0.000 0.000 0.000
#> GSM1179028 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM1179032 1 0.0000 0.875 1.000 0.000 0.000 0.000
#> GSM1179041 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM1179042 2 0.0188 0.948 0.000 0.996 0.004 0.000
#> GSM1178976 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1178981 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1178982 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1178983 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1178985 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1178992 3 0.2011 0.856 0.080 0.000 0.920 0.000
#> GSM1179005 3 0.0707 0.905 0.020 0.000 0.980 0.000
#> GSM1179007 3 0.0817 0.902 0.024 0.000 0.976 0.000
#> GSM1179012 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1179016 1 0.4955 0.136 0.556 0.000 0.444 0.000
#> GSM1179030 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1179038 3 0.0188 0.913 0.004 0.000 0.996 0.000
#> GSM1178987 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1179003 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1179004 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1179039 2 0.0000 0.948 0.000 1.000 0.000 0.000
#> GSM1178975 4 0.7715 0.289 0.324 0.000 0.240 0.436
#> GSM1178980 4 0.0000 0.785 0.000 0.000 0.000 1.000
#> GSM1178995 3 0.3726 0.713 0.212 0.000 0.788 0.000
#> GSM1178996 3 0.4277 0.613 0.280 0.000 0.720 0.000
#> GSM1179001 1 0.3400 0.669 0.820 0.000 0.180 0.000
#> GSM1179002 3 0.4605 0.513 0.336 0.000 0.664 0.000
#> GSM1179006 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1179008 1 0.0000 0.875 1.000 0.000 0.000 0.000
#> GSM1179015 3 0.4661 0.486 0.348 0.000 0.652 0.000
#> GSM1179017 3 0.3873 0.689 0.228 0.000 0.772 0.000
#> GSM1179026 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1179033 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1179035 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1179036 3 0.0188 0.913 0.004 0.000 0.996 0.000
#> GSM1178986 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1178989 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1178993 4 0.0000 0.785 0.000 0.000 0.000 1.000
#> GSM1178999 3 0.4103 0.617 0.000 0.000 0.744 0.256
#> GSM1179021 4 0.0000 0.785 0.000 0.000 0.000 1.000
#> GSM1179025 2 0.2216 0.869 0.000 0.908 0.092 0.000
#> GSM1179027 4 0.0000 0.785 0.000 0.000 0.000 1.000
#> GSM1179011 4 0.0000 0.785 0.000 0.000 0.000 1.000
#> GSM1179023 1 0.0000 0.875 1.000 0.000 0.000 0.000
#> GSM1179029 1 0.0817 0.855 0.976 0.000 0.024 0.000
#> GSM1179034 1 0.0000 0.875 1.000 0.000 0.000 0.000
#> GSM1179040 4 0.0000 0.785 0.000 0.000 0.000 1.000
#> GSM1178988 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1179037 3 0.0000 0.915 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
#> GSM1178971 3 0.4850 0.602 0.232 0.000 0.696 0.000 0.072
#> GSM1178979 5 0.3992 0.903 0.004 0.004 0.280 0.000 0.712
#> GSM1179009 3 0.4464 0.341 0.000 0.000 0.584 0.408 0.008
#> GSM1179031 2 0.0000 0.839 0.000 1.000 0.000 0.000 0.000
#> GSM1178970 5 0.3707 0.906 0.000 0.000 0.284 0.000 0.716
#> GSM1178972 2 0.5389 0.619 0.004 0.680 0.160 0.000 0.156
#> GSM1178973 1 0.5812 0.308 0.540 0.000 0.048 0.388 0.024
#> GSM1178974 2 0.3649 0.729 0.000 0.808 0.152 0.000 0.040
#> GSM1178977 5 0.4440 0.891 0.004 0.000 0.324 0.012 0.660
#> GSM1178978 3 0.1741 0.817 0.000 0.000 0.936 0.024 0.040
#> GSM1178998 3 0.1831 0.820 0.004 0.000 0.920 0.000 0.076
#> GSM1179010 3 0.1671 0.819 0.000 0.000 0.924 0.000 0.076
#> GSM1179018 3 0.1648 0.819 0.000 0.000 0.940 0.020 0.040
#> GSM1179024 1 0.0162 0.868 0.996 0.000 0.004 0.000 0.000
#> GSM1178984 3 0.1124 0.838 0.004 0.000 0.960 0.000 0.036
#> GSM1178990 3 0.6330 0.277 0.364 0.000 0.472 0.000 0.164
#> GSM1178991 1 0.5724 0.479 0.620 0.000 0.064 0.292 0.024
#> GSM1178994 3 0.1544 0.824 0.000 0.000 0.932 0.000 0.068
#> GSM1178997 1 0.0510 0.861 0.984 0.000 0.016 0.000 0.000
#> GSM1179000 1 0.0162 0.868 0.996 0.000 0.004 0.000 0.000
#> GSM1179013 1 0.0000 0.867 1.000 0.000 0.000 0.000 0.000
#> GSM1179014 1 0.0566 0.863 0.984 0.000 0.012 0.000 0.004
#> GSM1179019 1 0.0162 0.868 0.996 0.000 0.004 0.000 0.000
#> GSM1179020 1 0.0162 0.868 0.996 0.000 0.004 0.000 0.000
#> GSM1179022 1 0.0000 0.867 1.000 0.000 0.000 0.000 0.000
#> GSM1179028 2 0.0000 0.839 0.000 1.000 0.000 0.000 0.000
#> GSM1179032 1 0.0000 0.867 1.000 0.000 0.000 0.000 0.000
#> GSM1179041 2 0.0000 0.839 0.000 1.000 0.000 0.000 0.000
#> GSM1179042 2 0.1661 0.834 0.000 0.940 0.024 0.000 0.036
#> GSM1178976 5 0.3895 0.916 0.000 0.000 0.320 0.000 0.680
#> GSM1178981 3 0.0000 0.841 0.000 0.000 1.000 0.000 0.000
#> GSM1178982 3 0.0000 0.841 0.000 0.000 1.000 0.000 0.000
#> GSM1178983 3 0.0771 0.842 0.004 0.000 0.976 0.000 0.020
#> GSM1178985 3 0.0000 0.841 0.000 0.000 1.000 0.000 0.000
#> GSM1178992 3 0.2409 0.808 0.068 0.000 0.900 0.000 0.032
#> GSM1179005 3 0.3875 0.720 0.048 0.000 0.792 0.000 0.160
#> GSM1179007 3 0.3731 0.760 0.040 0.000 0.800 0.000 0.160
#> GSM1179012 3 0.1671 0.819 0.000 0.000 0.924 0.000 0.076
#> GSM1179016 3 0.3745 0.689 0.196 0.000 0.780 0.000 0.024
#> GSM1179030 3 0.0955 0.828 0.004 0.000 0.968 0.000 0.028
#> GSM1179038 3 0.3695 0.727 0.036 0.000 0.800 0.000 0.164
#> GSM1178987 3 0.0000 0.841 0.000 0.000 1.000 0.000 0.000
#> GSM1179003 5 0.4047 0.916 0.004 0.000 0.320 0.000 0.676
#> GSM1179004 3 0.0162 0.841 0.000 0.000 0.996 0.000 0.004
#> GSM1179039 2 0.0000 0.839 0.000 1.000 0.000 0.000 0.000
#> GSM1178975 1 0.5943 0.123 0.472 0.000 0.052 0.452 0.024
#> GSM1178980 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM1178995 3 0.4916 0.640 0.124 0.000 0.716 0.000 0.160
#> GSM1178996 3 0.2771 0.772 0.128 0.000 0.860 0.000 0.012
#> GSM1179001 1 0.5783 0.458 0.612 0.000 0.228 0.000 0.160
#> GSM1179002 3 0.5476 0.596 0.160 0.000 0.656 0.000 0.184
#> GSM1179006 3 0.0671 0.843 0.004 0.000 0.980 0.000 0.016
#> GSM1179008 1 0.0451 0.865 0.988 0.000 0.004 0.000 0.008
#> GSM1179015 3 0.3476 0.768 0.088 0.000 0.836 0.000 0.076
#> GSM1179017 5 0.4946 0.881 0.052 0.000 0.300 0.000 0.648
#> GSM1179026 3 0.0162 0.840 0.000 0.000 0.996 0.000 0.004
#> GSM1179033 3 0.0324 0.842 0.004 0.000 0.992 0.000 0.004
#> GSM1179035 3 0.0290 0.842 0.000 0.000 0.992 0.000 0.008
#> GSM1179036 3 0.2879 0.786 0.032 0.000 0.868 0.000 0.100
#> GSM1178986 3 0.0798 0.840 0.016 0.000 0.976 0.000 0.008
#> GSM1178989 5 0.3895 0.916 0.000 0.000 0.320 0.000 0.680
#> GSM1178993 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM1178999 5 0.6808 0.680 0.004 0.000 0.328 0.244 0.424
#> GSM1179021 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM1179025 2 0.5658 0.584 0.004 0.648 0.160 0.000 0.188
#> GSM1179027 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM1179011 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM1179023 1 0.0000 0.867 1.000 0.000 0.000 0.000 0.000
#> GSM1179029 1 0.3449 0.748 0.812 0.000 0.024 0.000 0.164
#> GSM1179034 1 0.0000 0.867 1.000 0.000 0.000 0.000 0.000
#> GSM1179040 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM1178988 3 0.0404 0.839 0.000 0.000 0.988 0.000 0.012
#> GSM1179037 3 0.0000 0.841 0.000 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1178971 3 0.3263 0.647 0.116 0.000 0.832 0.000 0.012 0.040
#> GSM1178979 5 0.1327 0.841 0.000 0.000 0.064 0.000 0.936 0.000
#> GSM1179009 3 0.4267 0.270 0.000 0.000 0.564 0.420 0.008 0.008
#> GSM1179031 2 0.0000 0.830 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178970 5 0.2301 0.859 0.000 0.000 0.096 0.000 0.884 0.020
#> GSM1178972 2 0.4220 0.685 0.000 0.664 0.028 0.000 0.304 0.004
#> GSM1178973 1 0.5639 0.435 0.572 0.000 0.024 0.332 0.048 0.024
#> GSM1178974 2 0.3698 0.761 0.000 0.756 0.028 0.000 0.212 0.004
#> GSM1178977 5 0.2237 0.833 0.000 0.000 0.068 0.036 0.896 0.000
#> GSM1178978 3 0.5183 0.668 0.000 0.000 0.688 0.040 0.132 0.140
#> GSM1178998 6 0.3867 0.750 0.000 0.000 0.328 0.000 0.012 0.660
#> GSM1179010 6 0.3428 0.763 0.000 0.000 0.304 0.000 0.000 0.696
#> GSM1179018 3 0.4856 0.674 0.000 0.000 0.700 0.016 0.140 0.144
#> GSM1179024 1 0.0632 0.839 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM1178984 3 0.3394 0.665 0.000 0.000 0.752 0.000 0.012 0.236
#> GSM1178990 1 0.4777 0.614 0.676 0.000 0.244 0.000 0.020 0.060
#> GSM1178991 1 0.6089 0.459 0.552 0.000 0.112 0.292 0.008 0.036
#> GSM1178994 3 0.3175 0.650 0.000 0.000 0.744 0.000 0.000 0.256
#> GSM1178997 1 0.1644 0.811 0.932 0.000 0.040 0.000 0.000 0.028
#> GSM1179000 1 0.0458 0.837 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM1179013 1 0.1387 0.825 0.932 0.000 0.000 0.000 0.000 0.068
#> GSM1179014 1 0.1643 0.819 0.924 0.000 0.008 0.000 0.000 0.068
#> GSM1179019 1 0.0458 0.837 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM1179020 1 0.0000 0.838 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179022 1 0.0632 0.839 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM1179028 2 0.0000 0.830 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179032 1 0.0632 0.839 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM1179041 2 0.0000 0.830 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179042 2 0.2778 0.802 0.000 0.824 0.008 0.000 0.168 0.000
#> GSM1178976 5 0.3023 0.846 0.000 0.000 0.120 0.000 0.836 0.044
#> GSM1178981 3 0.3163 0.669 0.000 0.000 0.764 0.000 0.004 0.232
#> GSM1178982 3 0.3698 0.723 0.000 0.000 0.788 0.000 0.116 0.096
#> GSM1178983 3 0.2573 0.720 0.004 0.000 0.856 0.000 0.132 0.008
#> GSM1178985 3 0.3003 0.709 0.000 0.000 0.812 0.000 0.016 0.172
#> GSM1178992 3 0.4436 0.699 0.016 0.000 0.740 0.000 0.092 0.152
#> GSM1179005 3 0.2375 0.673 0.016 0.000 0.896 0.000 0.020 0.068
#> GSM1179007 3 0.2002 0.722 0.012 0.000 0.920 0.000 0.028 0.040
#> GSM1179012 6 0.3481 0.763 0.032 0.000 0.192 0.000 0.000 0.776
#> GSM1179016 3 0.5521 0.540 0.056 0.000 0.660 0.000 0.132 0.152
#> GSM1179030 3 0.2723 0.720 0.004 0.000 0.856 0.000 0.120 0.020
#> GSM1179038 3 0.2123 0.678 0.008 0.000 0.908 0.000 0.020 0.064
#> GSM1178987 3 0.3288 0.631 0.000 0.000 0.724 0.000 0.000 0.276
#> GSM1179003 5 0.2234 0.856 0.000 0.000 0.124 0.000 0.872 0.004
#> GSM1179004 3 0.3288 0.631 0.000 0.000 0.724 0.000 0.000 0.276
#> GSM1179039 2 0.0000 0.830 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178975 1 0.6025 0.289 0.500 0.000 0.028 0.388 0.048 0.036
#> GSM1178980 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1178995 3 0.2642 0.659 0.032 0.000 0.884 0.000 0.020 0.064
#> GSM1178996 3 0.4004 0.669 0.084 0.000 0.796 0.000 0.084 0.036
#> GSM1179001 1 0.4896 0.606 0.660 0.000 0.256 0.000 0.020 0.064
#> GSM1179002 3 0.3846 0.581 0.100 0.000 0.800 0.000 0.020 0.080
#> GSM1179006 3 0.1956 0.735 0.004 0.000 0.908 0.000 0.080 0.008
#> GSM1179008 1 0.0622 0.837 0.980 0.000 0.012 0.000 0.000 0.008
#> GSM1179015 6 0.5061 0.601 0.056 0.000 0.204 0.000 0.056 0.684
#> GSM1179017 5 0.3927 0.795 0.004 0.000 0.120 0.000 0.776 0.100
#> GSM1179026 3 0.3210 0.712 0.000 0.000 0.804 0.000 0.028 0.168
#> GSM1179033 3 0.1753 0.736 0.004 0.000 0.912 0.000 0.084 0.000
#> GSM1179035 3 0.3151 0.653 0.000 0.000 0.748 0.000 0.000 0.252
#> GSM1179036 3 0.1577 0.714 0.008 0.000 0.940 0.000 0.036 0.016
#> GSM1178986 3 0.2890 0.728 0.004 0.000 0.852 0.008 0.120 0.016
#> GSM1178989 5 0.3150 0.839 0.000 0.000 0.120 0.000 0.828 0.052
#> GSM1178993 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1178999 5 0.5016 0.491 0.000 0.000 0.092 0.324 0.584 0.000
#> GSM1179021 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1179025 2 0.4286 0.665 0.000 0.648 0.028 0.000 0.320 0.004
#> GSM1179027 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1179011 4 0.0363 0.989 0.000 0.000 0.000 0.988 0.000 0.012
#> GSM1179023 1 0.0632 0.839 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM1179029 1 0.5087 0.638 0.664 0.000 0.216 0.000 0.020 0.100
#> GSM1179034 1 0.0632 0.839 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM1179040 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1178988 3 0.3424 0.724 0.000 0.000 0.812 0.000 0.092 0.096
#> GSM1179037 3 0.3230 0.689 0.000 0.000 0.776 0.000 0.012 0.212
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) protocol(p) k
#> SD:mclust 72 0.22907 8.23e-02 2
#> SD:mclust 68 0.69430 3.55e-04 3
#> SD:mclust 67 0.01851 8.01e-07 4
#> SD:mclust 67 0.00532 3.10e-08 5
#> SD:mclust 68 0.00486 2.77e-06 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 31632 rows and 73 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.973 0.989 0.3962 0.597 0.597
#> 3 3 0.839 0.848 0.934 0.4403 0.789 0.657
#> 4 4 0.668 0.752 0.873 0.1640 0.873 0.722
#> 5 5 0.590 0.619 0.823 0.1118 0.884 0.689
#> 6 6 0.558 0.522 0.747 0.0755 0.906 0.669
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
#> GSM1178971 1 0.0000 0.998 1.000 0.000
#> GSM1178979 2 0.0000 0.963 0.000 1.000
#> GSM1179009 1 0.2236 0.963 0.964 0.036
#> GSM1179031 2 0.0000 0.963 0.000 1.000
#> GSM1178970 2 0.0000 0.963 0.000 1.000
#> GSM1178972 2 0.0000 0.963 0.000 1.000
#> GSM1178973 1 0.0000 0.998 1.000 0.000
#> GSM1178974 2 0.0000 0.963 0.000 1.000
#> GSM1178977 2 0.0000 0.963 0.000 1.000
#> GSM1178978 1 0.0376 0.994 0.996 0.004
#> GSM1178998 1 0.0000 0.998 1.000 0.000
#> GSM1179010 1 0.0000 0.998 1.000 0.000
#> GSM1179018 1 0.2778 0.950 0.952 0.048
#> GSM1179024 1 0.0000 0.998 1.000 0.000
#> GSM1178984 1 0.0000 0.998 1.000 0.000
#> GSM1178990 1 0.0000 0.998 1.000 0.000
#> GSM1178991 1 0.0000 0.998 1.000 0.000
#> GSM1178994 1 0.0000 0.998 1.000 0.000
#> GSM1178997 1 0.0000 0.998 1.000 0.000
#> GSM1179000 1 0.0000 0.998 1.000 0.000
#> GSM1179013 1 0.0000 0.998 1.000 0.000
#> GSM1179014 1 0.0000 0.998 1.000 0.000
#> GSM1179019 1 0.0000 0.998 1.000 0.000
#> GSM1179020 1 0.0000 0.998 1.000 0.000
#> GSM1179022 1 0.0000 0.998 1.000 0.000
#> GSM1179028 2 0.0000 0.963 0.000 1.000
#> GSM1179032 1 0.0000 0.998 1.000 0.000
#> GSM1179041 2 0.0000 0.963 0.000 1.000
#> GSM1179042 2 0.0000 0.963 0.000 1.000
#> GSM1178976 2 0.0000 0.963 0.000 1.000
#> GSM1178981 1 0.0000 0.998 1.000 0.000
#> GSM1178982 1 0.0000 0.998 1.000 0.000
#> GSM1178983 1 0.0000 0.998 1.000 0.000
#> GSM1178985 1 0.0000 0.998 1.000 0.000
#> GSM1178992 1 0.0000 0.998 1.000 0.000
#> GSM1179005 1 0.0000 0.998 1.000 0.000
#> GSM1179007 1 0.0000 0.998 1.000 0.000
#> GSM1179012 1 0.0000 0.998 1.000 0.000
#> GSM1179016 1 0.0000 0.998 1.000 0.000
#> GSM1179030 1 0.0000 0.998 1.000 0.000
#> GSM1179038 1 0.0000 0.998 1.000 0.000
#> GSM1178987 1 0.0000 0.998 1.000 0.000
#> GSM1179003 2 0.0000 0.963 0.000 1.000
#> GSM1179004 1 0.0000 0.998 1.000 0.000
#> GSM1179039 2 0.0000 0.963 0.000 1.000
#> GSM1178975 1 0.0000 0.998 1.000 0.000
#> GSM1178980 2 0.0000 0.963 0.000 1.000
#> GSM1178995 1 0.0000 0.998 1.000 0.000
#> GSM1178996 1 0.0000 0.998 1.000 0.000
#> GSM1179001 1 0.0000 0.998 1.000 0.000
#> GSM1179002 1 0.0000 0.998 1.000 0.000
#> GSM1179006 1 0.0000 0.998 1.000 0.000
#> GSM1179008 1 0.0000 0.998 1.000 0.000
#> GSM1179015 1 0.0000 0.998 1.000 0.000
#> GSM1179017 1 0.2043 0.967 0.968 0.032
#> GSM1179026 1 0.0000 0.998 1.000 0.000
#> GSM1179033 1 0.0000 0.998 1.000 0.000
#> GSM1179035 1 0.0000 0.998 1.000 0.000
#> GSM1179036 1 0.0000 0.998 1.000 0.000
#> GSM1178986 1 0.0000 0.998 1.000 0.000
#> GSM1178989 2 0.9896 0.238 0.440 0.560
#> GSM1178993 2 0.7815 0.699 0.232 0.768
#> GSM1178999 2 0.1843 0.940 0.028 0.972
#> GSM1179021 2 0.0000 0.963 0.000 1.000
#> GSM1179025 2 0.0000 0.963 0.000 1.000
#> GSM1179027 2 0.0000 0.963 0.000 1.000
#> GSM1179011 1 0.0376 0.994 0.996 0.004
#> GSM1179023 1 0.0000 0.998 1.000 0.000
#> GSM1179029 1 0.0000 0.998 1.000 0.000
#> GSM1179034 1 0.0000 0.998 1.000 0.000
#> GSM1179040 2 0.0000 0.963 0.000 1.000
#> GSM1178988 1 0.0000 0.998 1.000 0.000
#> GSM1179037 1 0.0000 0.998 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1178971 1 0.0000 0.95175 1.000 0.000 0.000
#> GSM1178979 2 0.0424 0.89209 0.000 0.992 0.008
#> GSM1179009 1 0.1860 0.93896 0.948 0.000 0.052
#> GSM1179031 2 0.0000 0.89540 0.000 1.000 0.000
#> GSM1178970 3 0.5650 0.39469 0.000 0.312 0.688
#> GSM1178972 2 0.5016 0.67163 0.000 0.760 0.240
#> GSM1178973 1 0.0237 0.94962 0.996 0.004 0.000
#> GSM1178974 2 0.6062 0.39265 0.000 0.616 0.384
#> GSM1178977 2 0.0000 0.89540 0.000 1.000 0.000
#> GSM1178978 1 0.1643 0.93359 0.956 0.000 0.044
#> GSM1178998 1 0.1163 0.94949 0.972 0.000 0.028
#> GSM1179010 3 0.4931 0.67845 0.232 0.000 0.768
#> GSM1179018 1 0.5760 0.51216 0.672 0.000 0.328
#> GSM1179024 1 0.0000 0.95175 1.000 0.000 0.000
#> GSM1178984 1 0.2261 0.92792 0.932 0.000 0.068
#> GSM1178990 1 0.0424 0.95196 0.992 0.000 0.008
#> GSM1178991 1 0.0000 0.95175 1.000 0.000 0.000
#> GSM1178994 1 0.1964 0.93682 0.944 0.000 0.056
#> GSM1178997 1 0.0000 0.95175 1.000 0.000 0.000
#> GSM1179000 1 0.0000 0.95175 1.000 0.000 0.000
#> GSM1179013 1 0.0000 0.95175 1.000 0.000 0.000
#> GSM1179014 1 0.0000 0.95175 1.000 0.000 0.000
#> GSM1179019 1 0.0000 0.95175 1.000 0.000 0.000
#> GSM1179020 1 0.0000 0.95175 1.000 0.000 0.000
#> GSM1179022 1 0.0000 0.95175 1.000 0.000 0.000
#> GSM1179028 2 0.0000 0.89540 0.000 1.000 0.000
#> GSM1179032 1 0.0000 0.95175 1.000 0.000 0.000
#> GSM1179041 2 0.0000 0.89540 0.000 1.000 0.000
#> GSM1179042 2 0.0000 0.89540 0.000 1.000 0.000
#> GSM1178976 3 0.0000 0.81239 0.000 0.000 1.000
#> GSM1178981 1 0.2625 0.91547 0.916 0.000 0.084
#> GSM1178982 1 0.1163 0.94901 0.972 0.000 0.028
#> GSM1178983 1 0.0000 0.95175 1.000 0.000 0.000
#> GSM1178985 3 0.6309 0.00599 0.496 0.000 0.504
#> GSM1178992 1 0.6180 0.25899 0.584 0.000 0.416
#> GSM1179005 1 0.1289 0.94773 0.968 0.000 0.032
#> GSM1179007 1 0.1529 0.94488 0.960 0.000 0.040
#> GSM1179012 1 0.2261 0.92792 0.932 0.000 0.068
#> GSM1179016 1 0.2066 0.93449 0.940 0.000 0.060
#> GSM1179030 1 0.1647 0.94580 0.960 0.004 0.036
#> GSM1179038 1 0.1031 0.94996 0.976 0.000 0.024
#> GSM1178987 3 0.4974 0.67443 0.236 0.000 0.764
#> GSM1179003 3 0.1860 0.78099 0.000 0.052 0.948
#> GSM1179004 3 0.0000 0.81239 0.000 0.000 1.000
#> GSM1179039 2 0.0000 0.89540 0.000 1.000 0.000
#> GSM1178975 1 0.0424 0.94731 0.992 0.008 0.000
#> GSM1178980 2 0.0237 0.89342 0.004 0.996 0.000
#> GSM1178995 1 0.0424 0.95196 0.992 0.000 0.008
#> GSM1178996 1 0.1643 0.94330 0.956 0.000 0.044
#> GSM1179001 1 0.0000 0.95175 1.000 0.000 0.000
#> GSM1179002 1 0.0592 0.95175 0.988 0.000 0.012
#> GSM1179006 1 0.3340 0.87672 0.880 0.000 0.120
#> GSM1179008 1 0.0000 0.95175 1.000 0.000 0.000
#> GSM1179015 1 0.2066 0.93393 0.940 0.000 0.060
#> GSM1179017 3 0.0000 0.81239 0.000 0.000 1.000
#> GSM1179026 3 0.0237 0.81346 0.004 0.000 0.996
#> GSM1179033 1 0.4291 0.79739 0.820 0.000 0.180
#> GSM1179035 3 0.1411 0.81336 0.036 0.000 0.964
#> GSM1179036 1 0.1753 0.94113 0.952 0.000 0.048
#> GSM1178986 1 0.1163 0.94902 0.972 0.000 0.028
#> GSM1178989 3 0.0000 0.81239 0.000 0.000 1.000
#> GSM1178993 2 0.1289 0.87358 0.032 0.968 0.000
#> GSM1178999 2 0.2229 0.85219 0.044 0.944 0.012
#> GSM1179021 2 0.0000 0.89540 0.000 1.000 0.000
#> GSM1179025 2 0.5016 0.67533 0.000 0.760 0.240
#> GSM1179027 2 0.0000 0.89540 0.000 1.000 0.000
#> GSM1179011 2 0.6204 0.27030 0.424 0.576 0.000
#> GSM1179023 1 0.0000 0.95175 1.000 0.000 0.000
#> GSM1179029 1 0.0424 0.95196 0.992 0.000 0.008
#> GSM1179034 1 0.0000 0.95175 1.000 0.000 0.000
#> GSM1179040 2 0.0000 0.89540 0.000 1.000 0.000
#> GSM1178988 3 0.2448 0.80126 0.076 0.000 0.924
#> GSM1179037 3 0.3038 0.78474 0.104 0.000 0.896
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1178971 1 0.1109 0.8861 0.968 0.004 0.000 0.028
#> GSM1178979 4 0.4699 0.5382 0.000 0.320 0.004 0.676
#> GSM1179009 4 0.5275 0.6678 0.172 0.016 0.052 0.760
#> GSM1179031 2 0.0592 0.8834 0.000 0.984 0.000 0.016
#> GSM1178970 3 0.5847 0.0856 0.000 0.404 0.560 0.036
#> GSM1178972 2 0.4012 0.7512 0.000 0.800 0.184 0.016
#> GSM1178973 1 0.4948 0.2358 0.560 0.000 0.000 0.440
#> GSM1178974 2 0.2623 0.8552 0.000 0.908 0.064 0.028
#> GSM1178977 2 0.4978 0.2727 0.000 0.612 0.004 0.384
#> GSM1178978 1 0.5256 0.5725 0.692 0.000 0.036 0.272
#> GSM1178998 1 0.1022 0.8813 0.968 0.000 0.000 0.032
#> GSM1179010 3 0.3982 0.6359 0.220 0.000 0.776 0.004
#> GSM1179018 4 0.2973 0.7327 0.020 0.000 0.096 0.884
#> GSM1179024 1 0.0469 0.8854 0.988 0.000 0.000 0.012
#> GSM1178984 1 0.2021 0.8746 0.936 0.000 0.024 0.040
#> GSM1178990 1 0.0000 0.8854 1.000 0.000 0.000 0.000
#> GSM1178991 4 0.3791 0.6652 0.200 0.000 0.004 0.796
#> GSM1178994 1 0.1724 0.8779 0.948 0.000 0.020 0.032
#> GSM1178997 1 0.1059 0.8852 0.972 0.016 0.000 0.012
#> GSM1179000 1 0.0469 0.8854 0.988 0.000 0.000 0.012
#> GSM1179013 1 0.0336 0.8852 0.992 0.000 0.000 0.008
#> GSM1179014 1 0.0921 0.8846 0.972 0.000 0.000 0.028
#> GSM1179019 1 0.0336 0.8858 0.992 0.000 0.000 0.008
#> GSM1179020 1 0.0336 0.8852 0.992 0.000 0.000 0.008
#> GSM1179022 1 0.0188 0.8852 0.996 0.000 0.000 0.004
#> GSM1179028 2 0.0592 0.8834 0.000 0.984 0.000 0.016
#> GSM1179032 1 0.0336 0.8853 0.992 0.000 0.000 0.008
#> GSM1179041 2 0.0188 0.8825 0.000 0.996 0.000 0.004
#> GSM1179042 2 0.0188 0.8826 0.000 0.996 0.000 0.004
#> GSM1178976 3 0.0188 0.8424 0.004 0.000 0.996 0.000
#> GSM1178981 1 0.4037 0.8129 0.832 0.000 0.112 0.056
#> GSM1178982 1 0.4121 0.7536 0.796 0.000 0.020 0.184
#> GSM1178983 1 0.3444 0.7687 0.816 0.000 0.000 0.184
#> GSM1178985 1 0.5163 0.1555 0.516 0.004 0.480 0.000
#> GSM1178992 1 0.5315 0.6613 0.724 0.004 0.224 0.048
#> GSM1179005 1 0.0524 0.8854 0.988 0.000 0.004 0.008
#> GSM1179007 1 0.1256 0.8842 0.964 0.000 0.008 0.028
#> GSM1179012 1 0.0921 0.8850 0.972 0.000 0.028 0.000
#> GSM1179016 1 0.2053 0.8702 0.924 0.000 0.004 0.072
#> GSM1179030 1 0.2673 0.8701 0.916 0.016 0.020 0.048
#> GSM1179038 1 0.1576 0.8815 0.948 0.000 0.004 0.048
#> GSM1178987 3 0.1716 0.8261 0.064 0.000 0.936 0.000
#> GSM1179003 4 0.6187 0.1631 0.004 0.052 0.360 0.584
#> GSM1179004 3 0.0000 0.8402 0.000 0.000 1.000 0.000
#> GSM1179039 2 0.0592 0.8834 0.000 0.984 0.000 0.016
#> GSM1178975 4 0.4790 0.3473 0.380 0.000 0.000 0.620
#> GSM1178980 4 0.2081 0.7615 0.000 0.084 0.000 0.916
#> GSM1178995 1 0.0707 0.8843 0.980 0.000 0.000 0.020
#> GSM1178996 1 0.2876 0.8524 0.892 0.008 0.008 0.092
#> GSM1179001 1 0.1743 0.8749 0.940 0.004 0.000 0.056
#> GSM1179002 1 0.1118 0.8838 0.964 0.000 0.000 0.036
#> GSM1179006 1 0.6783 0.2271 0.512 0.000 0.388 0.100
#> GSM1179008 1 0.1389 0.8815 0.952 0.000 0.000 0.048
#> GSM1179015 1 0.1042 0.8857 0.972 0.000 0.008 0.020
#> GSM1179017 3 0.5640 0.6336 0.052 0.004 0.688 0.256
#> GSM1179026 3 0.2382 0.8159 0.004 0.004 0.912 0.080
#> GSM1179033 1 0.5846 0.1926 0.516 0.000 0.452 0.032
#> GSM1179035 3 0.1610 0.8423 0.032 0.000 0.952 0.016
#> GSM1179036 1 0.2926 0.8602 0.888 0.004 0.012 0.096
#> GSM1178986 1 0.4295 0.6770 0.752 0.000 0.008 0.240
#> GSM1178989 3 0.0188 0.8424 0.004 0.000 0.996 0.000
#> GSM1178993 4 0.2944 0.7588 0.004 0.128 0.000 0.868
#> GSM1178999 4 0.2021 0.7605 0.012 0.056 0.000 0.932
#> GSM1179021 4 0.3649 0.7098 0.000 0.204 0.000 0.796
#> GSM1179025 2 0.2999 0.8096 0.000 0.864 0.132 0.004
#> GSM1179027 4 0.2921 0.7536 0.000 0.140 0.000 0.860
#> GSM1179011 4 0.3732 0.7582 0.056 0.092 0.000 0.852
#> GSM1179023 1 0.0188 0.8852 0.996 0.000 0.000 0.004
#> GSM1179029 1 0.3356 0.7924 0.824 0.000 0.000 0.176
#> GSM1179034 1 0.0336 0.8853 0.992 0.000 0.000 0.008
#> GSM1179040 4 0.3356 0.7334 0.000 0.176 0.000 0.824
#> GSM1178988 3 0.0469 0.8445 0.012 0.000 0.988 0.000
#> GSM1179037 3 0.2011 0.8120 0.080 0.000 0.920 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1178971 1 0.2419 0.7217 0.904 0.004 0.028 0.000 0.064
#> GSM1178979 4 0.1430 0.8673 0.000 0.052 0.004 0.944 0.000
#> GSM1179009 4 0.4350 0.6912 0.132 0.000 0.088 0.776 0.004
#> GSM1179031 2 0.0794 0.8960 0.000 0.972 0.000 0.028 0.000
#> GSM1178970 3 0.4832 0.2368 0.000 0.356 0.616 0.004 0.024
#> GSM1178972 2 0.3887 0.7765 0.000 0.804 0.148 0.008 0.040
#> GSM1178973 1 0.4604 0.1980 0.560 0.000 0.000 0.428 0.012
#> GSM1178974 2 0.2060 0.8751 0.000 0.924 0.016 0.008 0.052
#> GSM1178977 2 0.5588 0.4153 0.000 0.580 0.044 0.356 0.020
#> GSM1178978 1 0.5781 0.4197 0.652 0.000 0.208 0.124 0.016
#> GSM1178998 1 0.2005 0.7278 0.924 0.000 0.056 0.004 0.016
#> GSM1179010 3 0.4311 0.5313 0.264 0.000 0.712 0.004 0.020
#> GSM1179018 4 0.1605 0.8758 0.004 0.000 0.040 0.944 0.012
#> GSM1179024 1 0.2230 0.6979 0.884 0.000 0.000 0.000 0.116
#> GSM1178984 1 0.2818 0.6853 0.856 0.000 0.132 0.000 0.012
#> GSM1178990 1 0.1732 0.7189 0.920 0.000 0.000 0.000 0.080
#> GSM1178991 4 0.3749 0.7545 0.080 0.000 0.000 0.816 0.104
#> GSM1178994 1 0.2660 0.6913 0.864 0.000 0.128 0.000 0.008
#> GSM1178997 1 0.2825 0.6777 0.860 0.124 0.000 0.000 0.016
#> GSM1179000 1 0.1965 0.7117 0.904 0.000 0.000 0.000 0.096
#> GSM1179013 1 0.2813 0.6436 0.832 0.000 0.000 0.000 0.168
#> GSM1179014 1 0.3999 0.3537 0.656 0.000 0.000 0.000 0.344
#> GSM1179019 1 0.0798 0.7386 0.976 0.008 0.000 0.000 0.016
#> GSM1179020 1 0.1410 0.7264 0.940 0.000 0.000 0.000 0.060
#> GSM1179022 1 0.0510 0.7370 0.984 0.000 0.000 0.000 0.016
#> GSM1179028 2 0.0703 0.8962 0.000 0.976 0.000 0.024 0.000
#> GSM1179032 1 0.0000 0.7365 1.000 0.000 0.000 0.000 0.000
#> GSM1179041 2 0.0566 0.8949 0.000 0.984 0.000 0.012 0.004
#> GSM1179042 2 0.0671 0.8909 0.000 0.980 0.000 0.004 0.016
#> GSM1178976 3 0.0671 0.7407 0.000 0.004 0.980 0.000 0.016
#> GSM1178981 1 0.4464 0.2364 0.584 0.000 0.408 0.000 0.008
#> GSM1178982 1 0.4824 0.5949 0.744 0.000 0.124 0.124 0.008
#> GSM1178983 1 0.4171 0.6629 0.808 0.000 0.052 0.112 0.028
#> GSM1178985 3 0.4211 0.4049 0.360 0.000 0.636 0.000 0.004
#> GSM1178992 5 0.5381 0.2465 0.428 0.000 0.056 0.000 0.516
#> GSM1179005 1 0.1197 0.7334 0.952 0.000 0.048 0.000 0.000
#> GSM1179007 1 0.2208 0.7238 0.908 0.000 0.072 0.000 0.020
#> GSM1179012 1 0.2505 0.7184 0.888 0.000 0.092 0.000 0.020
#> GSM1179016 5 0.4331 0.3642 0.400 0.000 0.000 0.004 0.596
#> GSM1179030 1 0.6140 0.5262 0.680 0.008 0.064 0.096 0.152
#> GSM1179038 1 0.4166 0.3465 0.648 0.000 0.000 0.004 0.348
#> GSM1178987 3 0.1251 0.7405 0.036 0.000 0.956 0.000 0.008
#> GSM1179003 5 0.3919 0.3460 0.000 0.000 0.036 0.188 0.776
#> GSM1179004 3 0.0324 0.7402 0.000 0.000 0.992 0.004 0.004
#> GSM1179039 2 0.0880 0.8950 0.000 0.968 0.000 0.032 0.000
#> GSM1178975 4 0.4465 0.4072 0.304 0.000 0.000 0.672 0.024
#> GSM1178980 4 0.0703 0.8893 0.000 0.000 0.000 0.976 0.024
#> GSM1178995 1 0.0771 0.7354 0.976 0.000 0.020 0.000 0.004
#> GSM1178996 5 0.4858 0.2883 0.424 0.012 0.008 0.000 0.556
#> GSM1179001 1 0.5042 0.3674 0.652 0.008 0.020 0.012 0.308
#> GSM1179002 1 0.3631 0.6535 0.820 0.008 0.020 0.004 0.148
#> GSM1179006 5 0.7388 0.3917 0.292 0.000 0.232 0.040 0.436
#> GSM1179008 1 0.3243 0.6514 0.812 0.000 0.004 0.004 0.180
#> GSM1179015 1 0.3730 0.4771 0.712 0.000 0.000 0.000 0.288
#> GSM1179017 5 0.1547 0.4375 0.004 0.000 0.032 0.016 0.948
#> GSM1179026 5 0.4066 0.0827 0.000 0.000 0.324 0.004 0.672
#> GSM1179033 3 0.6368 0.1399 0.376 0.000 0.484 0.008 0.132
#> GSM1179035 3 0.2900 0.6952 0.028 0.000 0.864 0.000 0.108
#> GSM1179036 1 0.4849 0.0850 0.548 0.000 0.004 0.016 0.432
#> GSM1178986 1 0.6660 -0.0856 0.476 0.000 0.008 0.188 0.328
#> GSM1178989 3 0.0963 0.7287 0.000 0.000 0.964 0.000 0.036
#> GSM1178993 4 0.0162 0.8916 0.000 0.004 0.000 0.996 0.000
#> GSM1178999 4 0.1591 0.8753 0.004 0.000 0.004 0.940 0.052
#> GSM1179021 4 0.0510 0.8894 0.000 0.016 0.000 0.984 0.000
#> GSM1179025 2 0.2678 0.8476 0.000 0.880 0.100 0.016 0.004
#> GSM1179027 4 0.0162 0.8919 0.000 0.000 0.000 0.996 0.004
#> GSM1179011 4 0.0671 0.8906 0.004 0.016 0.000 0.980 0.000
#> GSM1179023 1 0.0000 0.7365 1.000 0.000 0.000 0.000 0.000
#> GSM1179029 5 0.4505 0.3815 0.384 0.000 0.000 0.012 0.604
#> GSM1179034 1 0.0880 0.7340 0.968 0.000 0.000 0.000 0.032
#> GSM1179040 4 0.0290 0.8912 0.000 0.008 0.000 0.992 0.000
#> GSM1178988 3 0.1410 0.7202 0.000 0.000 0.940 0.000 0.060
#> GSM1179037 3 0.2522 0.7182 0.052 0.000 0.896 0.000 0.052
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1178971 1 0.3830 0.4876 0.744 0.000 0.000 0.000 0.212 0.044
#> GSM1178979 4 0.2441 0.8195 0.000 0.056 0.024 0.900 0.008 0.012
#> GSM1179009 4 0.6163 0.4963 0.152 0.000 0.088 0.648 0.056 0.056
#> GSM1179031 2 0.0260 0.8631 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM1178970 3 0.5306 0.1885 0.000 0.304 0.596 0.000 0.080 0.020
#> GSM1178972 2 0.5356 0.5830 0.000 0.620 0.232 0.000 0.136 0.012
#> GSM1178973 1 0.4662 0.2126 0.560 0.000 0.000 0.404 0.020 0.016
#> GSM1178974 2 0.2623 0.8192 0.000 0.852 0.000 0.000 0.132 0.016
#> GSM1178977 2 0.7161 0.4608 0.004 0.524 0.156 0.204 0.084 0.028
#> GSM1178978 1 0.6656 0.0418 0.484 0.008 0.356 0.024 0.084 0.044
#> GSM1178998 1 0.4330 0.5489 0.756 0.000 0.040 0.000 0.156 0.048
#> GSM1179010 3 0.6218 0.2077 0.360 0.000 0.468 0.000 0.136 0.036
#> GSM1179018 4 0.2554 0.8238 0.004 0.000 0.044 0.896 0.032 0.024
#> GSM1179024 1 0.2854 0.4600 0.792 0.000 0.000 0.000 0.000 0.208
#> GSM1178984 1 0.5358 0.4965 0.680 0.000 0.144 0.000 0.116 0.060
#> GSM1178990 1 0.3023 0.4343 0.768 0.000 0.000 0.000 0.000 0.232
#> GSM1178991 4 0.4725 0.6027 0.084 0.000 0.008 0.708 0.008 0.192
#> GSM1178994 1 0.4139 0.4729 0.700 0.000 0.260 0.000 0.004 0.036
#> GSM1178997 1 0.2999 0.5687 0.840 0.112 0.000 0.000 0.000 0.048
#> GSM1179000 1 0.3240 0.4127 0.752 0.004 0.000 0.000 0.000 0.244
#> GSM1179013 1 0.3547 0.1909 0.668 0.000 0.000 0.000 0.000 0.332
#> GSM1179014 6 0.3774 0.5057 0.408 0.000 0.000 0.000 0.000 0.592
#> GSM1179019 1 0.2320 0.5723 0.864 0.004 0.000 0.000 0.000 0.132
#> GSM1179020 1 0.0820 0.6248 0.972 0.000 0.000 0.000 0.012 0.016
#> GSM1179022 1 0.1814 0.5880 0.900 0.000 0.000 0.000 0.000 0.100
#> GSM1179028 2 0.0291 0.8629 0.000 0.992 0.000 0.004 0.000 0.004
#> GSM1179032 1 0.0790 0.6214 0.968 0.000 0.000 0.000 0.000 0.032
#> GSM1179041 2 0.0291 0.8620 0.000 0.992 0.000 0.000 0.004 0.004
#> GSM1179042 2 0.1970 0.8350 0.000 0.900 0.000 0.000 0.092 0.008
#> GSM1178976 3 0.3663 0.6127 0.000 0.004 0.796 0.000 0.128 0.072
#> GSM1178981 3 0.4871 0.3940 0.324 0.000 0.616 0.000 0.024 0.036
#> GSM1178982 1 0.7012 0.3111 0.516 0.000 0.228 0.152 0.024 0.080
#> GSM1178983 1 0.5173 0.5160 0.716 0.000 0.032 0.108 0.020 0.124
#> GSM1178985 3 0.4970 0.5804 0.168 0.004 0.712 0.000 0.044 0.072
#> GSM1178992 6 0.4075 0.5940 0.240 0.000 0.048 0.000 0.000 0.712
#> GSM1179005 1 0.3054 0.6024 0.848 0.000 0.072 0.000 0.004 0.076
#> GSM1179007 1 0.3841 0.5910 0.812 0.000 0.052 0.000 0.072 0.064
#> GSM1179012 1 0.4916 0.5221 0.696 0.000 0.196 0.000 0.072 0.036
#> GSM1179016 6 0.3652 0.6029 0.264 0.000 0.000 0.000 0.016 0.720
#> GSM1179030 6 0.6468 0.4028 0.312 0.008 0.188 0.004 0.016 0.472
#> GSM1179038 1 0.4509 -0.0510 0.532 0.000 0.000 0.000 0.032 0.436
#> GSM1178987 3 0.2103 0.6249 0.024 0.000 0.916 0.000 0.040 0.020
#> GSM1179003 5 0.5100 0.3577 0.000 0.000 0.000 0.128 0.612 0.260
#> GSM1179004 3 0.0458 0.6323 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM1179039 2 0.0405 0.8629 0.000 0.988 0.000 0.008 0.000 0.004
#> GSM1178975 4 0.4200 0.5119 0.264 0.000 0.000 0.696 0.032 0.008
#> GSM1178980 4 0.0858 0.8588 0.000 0.000 0.000 0.968 0.028 0.004
#> GSM1178995 1 0.2555 0.6168 0.888 0.000 0.016 0.000 0.064 0.032
#> GSM1178996 5 0.5965 0.3492 0.232 0.000 0.004 0.000 0.484 0.280
#> GSM1179001 5 0.3953 0.4408 0.328 0.000 0.000 0.000 0.656 0.016
#> GSM1179002 5 0.4048 0.3985 0.340 0.000 0.004 0.000 0.644 0.012
#> GSM1179006 6 0.6726 0.1250 0.092 0.000 0.216 0.024 0.108 0.560
#> GSM1179008 1 0.4246 0.1258 0.580 0.000 0.000 0.000 0.400 0.020
#> GSM1179015 6 0.4300 0.3927 0.456 0.000 0.004 0.000 0.012 0.528
#> GSM1179017 6 0.4459 -0.3526 0.000 0.000 0.004 0.020 0.460 0.516
#> GSM1179026 5 0.6372 0.0872 0.000 0.000 0.272 0.012 0.376 0.340
#> GSM1179033 3 0.7507 0.2881 0.212 0.000 0.436 0.012 0.156 0.184
#> GSM1179035 3 0.5785 0.5322 0.064 0.000 0.620 0.000 0.212 0.104
#> GSM1179036 1 0.5848 -0.1749 0.452 0.000 0.028 0.000 0.424 0.096
#> GSM1178986 6 0.5193 0.5802 0.296 0.000 0.008 0.096 0.000 0.600
#> GSM1178989 3 0.1908 0.6355 0.000 0.000 0.916 0.000 0.028 0.056
#> GSM1178993 4 0.0260 0.8636 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM1178999 4 0.1327 0.8437 0.000 0.000 0.000 0.936 0.000 0.064
#> GSM1179021 4 0.0363 0.8634 0.000 0.012 0.000 0.988 0.000 0.000
#> GSM1179025 2 0.1628 0.8523 0.000 0.940 0.036 0.008 0.004 0.012
#> GSM1179027 4 0.0291 0.8641 0.000 0.004 0.000 0.992 0.004 0.000
#> GSM1179011 4 0.0665 0.8630 0.008 0.008 0.000 0.980 0.000 0.004
#> GSM1179023 1 0.1141 0.6141 0.948 0.000 0.000 0.000 0.000 0.052
#> GSM1179029 6 0.5391 0.4871 0.356 0.000 0.000 0.004 0.108 0.532
#> GSM1179034 1 0.0713 0.6196 0.972 0.000 0.000 0.000 0.000 0.028
#> GSM1179040 4 0.0000 0.8630 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1178988 3 0.3073 0.5749 0.016 0.000 0.824 0.000 0.008 0.152
#> GSM1179037 3 0.4750 0.5957 0.036 0.000 0.728 0.000 0.140 0.096
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) protocol(p) k
#> SD:NMF 72 0.0627 0.05971 2
#> SD:NMF 68 0.0100 0.02075 3
#> SD:NMF 65 0.0035 0.00927 4
#> SD:NMF 51 0.0106 0.04488 5
#> SD:NMF 44 0.0629 0.02820 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 31632 rows and 73 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.658 0.839 0.917 0.339 0.686 0.686
#> 3 3 0.330 0.645 0.815 0.402 0.897 0.850
#> 4 4 0.343 0.419 0.618 0.320 0.645 0.426
#> 5 5 0.372 0.519 0.712 0.123 0.822 0.514
#> 6 6 0.461 0.562 0.747 0.065 0.929 0.754
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM1178971 1 0.1843 0.919 0.972 0.028
#> GSM1178979 2 0.8661 0.642 0.288 0.712
#> GSM1179009 1 0.3431 0.899 0.936 0.064
#> GSM1179031 2 0.0000 0.859 0.000 1.000
#> GSM1178970 2 0.8861 0.610 0.304 0.696
#> GSM1178972 2 0.0000 0.859 0.000 1.000
#> GSM1178973 1 0.0000 0.917 1.000 0.000
#> GSM1178974 2 0.0000 0.859 0.000 1.000
#> GSM1178977 1 0.9686 0.333 0.604 0.396
#> GSM1178978 1 0.2423 0.915 0.960 0.040
#> GSM1178998 1 0.0000 0.917 1.000 0.000
#> GSM1179010 1 0.0000 0.917 1.000 0.000
#> GSM1179018 1 0.4562 0.889 0.904 0.096
#> GSM1179024 1 0.0000 0.917 1.000 0.000
#> GSM1178984 1 0.0000 0.917 1.000 0.000
#> GSM1178990 1 0.0000 0.917 1.000 0.000
#> GSM1178991 1 0.3114 0.903 0.944 0.056
#> GSM1178994 1 0.0938 0.919 0.988 0.012
#> GSM1178997 1 0.3114 0.913 0.944 0.056
#> GSM1179000 1 0.2236 0.918 0.964 0.036
#> GSM1179013 1 0.0000 0.917 1.000 0.000
#> GSM1179014 1 0.3584 0.908 0.932 0.068
#> GSM1179019 1 0.1633 0.919 0.976 0.024
#> GSM1179020 1 0.0938 0.919 0.988 0.012
#> GSM1179022 1 0.0000 0.917 1.000 0.000
#> GSM1179028 2 0.0000 0.859 0.000 1.000
#> GSM1179032 1 0.0000 0.917 1.000 0.000
#> GSM1179041 2 0.0000 0.859 0.000 1.000
#> GSM1179042 2 0.0000 0.859 0.000 1.000
#> GSM1178976 1 0.9922 0.194 0.552 0.448
#> GSM1178981 1 0.2236 0.918 0.964 0.036
#> GSM1178982 1 0.1843 0.919 0.972 0.028
#> GSM1178983 1 0.2236 0.918 0.964 0.036
#> GSM1178985 1 0.4939 0.881 0.892 0.108
#> GSM1178992 1 0.3879 0.902 0.924 0.076
#> GSM1179005 1 0.1184 0.919 0.984 0.016
#> GSM1179007 1 0.0000 0.917 1.000 0.000
#> GSM1179012 1 0.0000 0.917 1.000 0.000
#> GSM1179016 1 0.8207 0.701 0.744 0.256
#> GSM1179030 1 0.7883 0.717 0.764 0.236
#> GSM1179038 1 0.0938 0.919 0.988 0.012
#> GSM1178987 1 0.3114 0.911 0.944 0.056
#> GSM1179003 2 0.8955 0.599 0.312 0.688
#> GSM1179004 1 0.3114 0.911 0.944 0.056
#> GSM1179039 2 0.0000 0.859 0.000 1.000
#> GSM1178975 1 0.0000 0.917 1.000 0.000
#> GSM1178980 2 0.9427 0.524 0.360 0.640
#> GSM1178995 1 0.1843 0.919 0.972 0.028
#> GSM1178996 1 0.4022 0.902 0.920 0.080
#> GSM1179001 1 0.0000 0.917 1.000 0.000
#> GSM1179002 1 0.0000 0.917 1.000 0.000
#> GSM1179006 1 0.5408 0.867 0.876 0.124
#> GSM1179008 1 0.0000 0.917 1.000 0.000
#> GSM1179015 1 0.0000 0.917 1.000 0.000
#> GSM1179017 1 0.9710 0.377 0.600 0.400
#> GSM1179026 1 0.4298 0.896 0.912 0.088
#> GSM1179033 1 0.2603 0.917 0.956 0.044
#> GSM1179035 1 0.3879 0.903 0.924 0.076
#> GSM1179036 1 0.3114 0.914 0.944 0.056
#> GSM1178986 1 0.2603 0.916 0.956 0.044
#> GSM1178989 1 0.9710 0.362 0.600 0.400
#> GSM1178993 1 0.3584 0.897 0.932 0.068
#> GSM1178999 2 0.7602 0.730 0.220 0.780
#> GSM1179021 2 0.4815 0.817 0.104 0.896
#> GSM1179025 2 0.0000 0.859 0.000 1.000
#> GSM1179027 1 0.7602 0.720 0.780 0.220
#> GSM1179011 1 0.3431 0.899 0.936 0.064
#> GSM1179023 1 0.0000 0.917 1.000 0.000
#> GSM1179029 1 0.0000 0.917 1.000 0.000
#> GSM1179034 1 0.0000 0.917 1.000 0.000
#> GSM1179040 1 0.8081 0.677 0.752 0.248
#> GSM1178988 1 0.6712 0.810 0.824 0.176
#> GSM1179037 1 0.4022 0.901 0.920 0.080
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1178971 1 0.2878 0.781 0.904 0.000 0.096
#> GSM1178979 2 0.8842 0.386 0.144 0.548 0.308
#> GSM1179009 1 0.4399 0.639 0.812 0.000 0.188
#> GSM1179031 2 0.0000 0.780 0.000 1.000 0.000
#> GSM1178970 2 0.8953 0.311 0.180 0.560 0.260
#> GSM1178972 2 0.2959 0.752 0.000 0.900 0.100
#> GSM1178973 1 0.2959 0.720 0.900 0.000 0.100
#> GSM1178974 2 0.0000 0.780 0.000 1.000 0.000
#> GSM1178977 1 0.9498 -0.266 0.484 0.300 0.216
#> GSM1178978 1 0.3686 0.706 0.860 0.000 0.140
#> GSM1178998 1 0.0592 0.777 0.988 0.000 0.012
#> GSM1179010 1 0.0592 0.777 0.988 0.000 0.012
#> GSM1179018 1 0.6012 0.634 0.748 0.032 0.220
#> GSM1179024 1 0.0592 0.777 0.988 0.000 0.012
#> GSM1178984 1 0.1529 0.781 0.960 0.000 0.040
#> GSM1178990 1 0.2448 0.780 0.924 0.000 0.076
#> GSM1178991 1 0.3879 0.683 0.848 0.000 0.152
#> GSM1178994 1 0.2959 0.770 0.900 0.000 0.100
#> GSM1178997 1 0.4235 0.738 0.824 0.000 0.176
#> GSM1179000 1 0.3816 0.755 0.852 0.000 0.148
#> GSM1179013 1 0.0592 0.777 0.988 0.000 0.012
#> GSM1179014 3 0.6291 0.264 0.468 0.000 0.532
#> GSM1179019 1 0.2796 0.778 0.908 0.000 0.092
#> GSM1179020 1 0.2448 0.780 0.924 0.000 0.076
#> GSM1179022 1 0.0592 0.777 0.988 0.000 0.012
#> GSM1179028 2 0.0000 0.780 0.000 1.000 0.000
#> GSM1179032 1 0.0592 0.777 0.988 0.000 0.012
#> GSM1179041 2 0.0000 0.780 0.000 1.000 0.000
#> GSM1179042 2 0.0000 0.780 0.000 1.000 0.000
#> GSM1178976 3 0.9909 0.497 0.364 0.268 0.368
#> GSM1178981 1 0.4062 0.747 0.836 0.000 0.164
#> GSM1178982 1 0.4062 0.750 0.836 0.000 0.164
#> GSM1178983 1 0.4235 0.746 0.824 0.000 0.176
#> GSM1178985 1 0.5728 0.601 0.720 0.008 0.272
#> GSM1178992 1 0.5254 0.619 0.736 0.000 0.264
#> GSM1179005 1 0.3192 0.768 0.888 0.000 0.112
#> GSM1179007 1 0.2356 0.780 0.928 0.000 0.072
#> GSM1179012 1 0.0592 0.777 0.988 0.000 0.012
#> GSM1179016 3 0.4974 0.570 0.236 0.000 0.764
#> GSM1179030 1 0.8038 0.268 0.620 0.100 0.280
#> GSM1179038 1 0.3192 0.771 0.888 0.000 0.112
#> GSM1178987 1 0.4346 0.725 0.816 0.000 0.184
#> GSM1179003 2 0.9149 0.287 0.168 0.516 0.316
#> GSM1179004 1 0.4346 0.725 0.816 0.000 0.184
#> GSM1179039 2 0.0000 0.780 0.000 1.000 0.000
#> GSM1178975 1 0.2959 0.720 0.900 0.000 0.100
#> GSM1178980 2 0.9026 0.264 0.248 0.556 0.196
#> GSM1178995 1 0.3482 0.761 0.872 0.000 0.128
#> GSM1178996 1 0.4842 0.689 0.776 0.000 0.224
#> GSM1179001 1 0.0592 0.777 0.988 0.000 0.012
#> GSM1179002 1 0.1289 0.781 0.968 0.000 0.032
#> GSM1179006 1 0.6205 0.479 0.656 0.008 0.336
#> GSM1179008 1 0.0592 0.777 0.988 0.000 0.012
#> GSM1179015 1 0.0892 0.778 0.980 0.000 0.020
#> GSM1179017 3 0.4056 0.340 0.092 0.032 0.876
#> GSM1179026 1 0.5560 0.562 0.700 0.000 0.300
#> GSM1179033 1 0.3752 0.754 0.856 0.000 0.144
#> GSM1179035 1 0.5465 0.579 0.712 0.000 0.288
#> GSM1179036 1 0.4605 0.711 0.796 0.000 0.204
#> GSM1178986 1 0.4235 0.744 0.824 0.000 0.176
#> GSM1178989 3 0.9481 0.492 0.384 0.184 0.432
#> GSM1178993 1 0.4733 0.619 0.800 0.004 0.196
#> GSM1178999 2 0.7919 0.506 0.064 0.556 0.380
#> GSM1179021 2 0.4390 0.723 0.012 0.840 0.148
#> GSM1179025 2 0.0000 0.780 0.000 1.000 0.000
#> GSM1179027 1 0.7960 0.284 0.648 0.120 0.232
#> GSM1179011 1 0.4504 0.626 0.804 0.000 0.196
#> GSM1179023 1 0.0592 0.777 0.988 0.000 0.012
#> GSM1179029 1 0.0747 0.777 0.984 0.000 0.016
#> GSM1179034 1 0.0592 0.777 0.988 0.000 0.012
#> GSM1179040 1 0.8284 0.217 0.628 0.148 0.224
#> GSM1178988 1 0.7295 0.221 0.584 0.036 0.380
#> GSM1179037 1 0.5497 0.574 0.708 0.000 0.292
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1178971 1 0.5207 0.38650 0.680 0.000 0.292 0.028
#> GSM1178979 2 0.7551 0.46692 0.008 0.456 0.388 0.148
#> GSM1179009 4 0.7410 0.77367 0.184 0.000 0.328 0.488
#> GSM1179031 2 0.0000 0.77651 0.000 1.000 0.000 0.000
#> GSM1178970 2 0.7381 0.42209 0.008 0.472 0.392 0.128
#> GSM1178972 2 0.4100 0.74214 0.000 0.832 0.092 0.076
#> GSM1178973 1 0.7806 -0.33374 0.412 0.000 0.264 0.324
#> GSM1178974 2 0.0000 0.77651 0.000 1.000 0.000 0.000
#> GSM1178977 3 0.9050 -0.47317 0.068 0.228 0.364 0.340
#> GSM1178978 3 0.7863 -0.44565 0.276 0.000 0.380 0.344
#> GSM1178998 1 0.1182 0.64751 0.968 0.000 0.016 0.016
#> GSM1179010 1 0.1411 0.64317 0.960 0.000 0.020 0.020
#> GSM1179018 3 0.8001 -0.00657 0.304 0.016 0.472 0.208
#> GSM1179024 1 0.0000 0.65051 1.000 0.000 0.000 0.000
#> GSM1178984 1 0.3991 0.53869 0.808 0.000 0.172 0.020
#> GSM1178990 1 0.4436 0.51089 0.764 0.000 0.216 0.020
#> GSM1178991 4 0.7728 0.63621 0.236 0.000 0.340 0.424
#> GSM1178994 1 0.6280 0.06036 0.584 0.000 0.344 0.072
#> GSM1178997 1 0.6200 -0.10043 0.504 0.000 0.444 0.052
#> GSM1179000 1 0.6222 0.01364 0.532 0.000 0.412 0.056
#> GSM1179013 1 0.0000 0.65051 1.000 0.000 0.000 0.000
#> GSM1179014 3 0.7811 0.18097 0.336 0.000 0.404 0.260
#> GSM1179019 1 0.5256 0.42277 0.692 0.000 0.272 0.036
#> GSM1179020 1 0.4175 0.53039 0.784 0.000 0.200 0.016
#> GSM1179022 1 0.0000 0.65051 1.000 0.000 0.000 0.000
#> GSM1179028 2 0.0000 0.77651 0.000 1.000 0.000 0.000
#> GSM1179032 1 0.0000 0.65051 1.000 0.000 0.000 0.000
#> GSM1179041 2 0.0000 0.77651 0.000 1.000 0.000 0.000
#> GSM1179042 2 0.0000 0.77651 0.000 1.000 0.000 0.000
#> GSM1178976 3 0.7348 -0.03058 0.072 0.200 0.636 0.092
#> GSM1178981 3 0.6696 0.34776 0.428 0.000 0.484 0.088
#> GSM1178982 3 0.6445 0.30805 0.444 0.000 0.488 0.068
#> GSM1178983 3 0.6599 0.32978 0.432 0.000 0.488 0.080
#> GSM1178985 3 0.5968 0.49057 0.324 0.004 0.624 0.048
#> GSM1178992 3 0.5172 0.40909 0.404 0.000 0.588 0.008
#> GSM1179005 1 0.5835 0.19598 0.588 0.000 0.372 0.040
#> GSM1179007 1 0.5496 0.33992 0.652 0.000 0.312 0.036
#> GSM1179012 1 0.1411 0.64317 0.960 0.000 0.020 0.020
#> GSM1179016 3 0.6669 0.08328 0.104 0.000 0.564 0.332
#> GSM1179030 3 0.8351 0.34026 0.288 0.080 0.512 0.120
#> GSM1179038 1 0.5682 0.24775 0.612 0.000 0.352 0.036
#> GSM1178987 3 0.6627 0.38638 0.412 0.000 0.504 0.084
#> GSM1179003 2 0.7580 0.43687 0.016 0.432 0.428 0.124
#> GSM1179004 3 0.6633 0.38052 0.416 0.000 0.500 0.084
#> GSM1179039 2 0.0000 0.77651 0.000 1.000 0.000 0.000
#> GSM1178975 1 0.7806 -0.33374 0.412 0.000 0.264 0.324
#> GSM1178980 2 0.7838 0.32020 0.004 0.424 0.220 0.352
#> GSM1178995 1 0.5894 0.13628 0.568 0.000 0.392 0.040
#> GSM1178996 3 0.5576 0.27393 0.444 0.000 0.536 0.020
#> GSM1179001 1 0.0804 0.65231 0.980 0.000 0.012 0.008
#> GSM1179002 1 0.1975 0.64318 0.936 0.000 0.048 0.016
#> GSM1179006 3 0.5172 0.50001 0.284 0.008 0.692 0.016
#> GSM1179008 1 0.0937 0.65230 0.976 0.000 0.012 0.012
#> GSM1179015 1 0.1004 0.64559 0.972 0.000 0.024 0.004
#> GSM1179017 3 0.5290 -0.08606 0.000 0.012 0.584 0.404
#> GSM1179026 3 0.5018 0.48172 0.332 0.000 0.656 0.012
#> GSM1179033 1 0.5971 0.00658 0.532 0.000 0.428 0.040
#> GSM1179035 3 0.5143 0.46042 0.360 0.000 0.628 0.012
#> GSM1179036 3 0.5685 0.22209 0.460 0.000 0.516 0.024
#> GSM1178986 3 0.6600 0.39167 0.396 0.000 0.520 0.084
#> GSM1178989 3 0.6627 0.03144 0.076 0.124 0.708 0.092
#> GSM1178993 4 0.7205 0.79560 0.152 0.000 0.344 0.504
#> GSM1178999 2 0.7710 0.53220 0.004 0.456 0.340 0.200
#> GSM1179021 2 0.5585 0.68185 0.000 0.712 0.084 0.204
#> GSM1179025 2 0.0000 0.77651 0.000 1.000 0.000 0.000
#> GSM1179027 4 0.5693 0.70238 0.020 0.008 0.368 0.604
#> GSM1179011 4 0.7239 0.79318 0.156 0.000 0.344 0.500
#> GSM1179023 1 0.0000 0.65051 1.000 0.000 0.000 0.000
#> GSM1179029 1 0.0707 0.65095 0.980 0.000 0.020 0.000
#> GSM1179034 1 0.0000 0.65051 1.000 0.000 0.000 0.000
#> GSM1179040 4 0.6373 0.68839 0.020 0.036 0.368 0.576
#> GSM1178988 3 0.5770 0.40971 0.228 0.024 0.708 0.040
#> GSM1179037 3 0.5127 0.46523 0.356 0.000 0.632 0.012
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1178971 3 0.4980 0.1711 0.484 0.000 0.488 0.028 0.000
#> GSM1178979 2 0.8472 0.2507 0.000 0.320 0.280 0.184 0.216
#> GSM1179009 4 0.4830 0.6627 0.072 0.000 0.208 0.716 0.004
#> GSM1179031 2 0.0000 0.7031 0.000 1.000 0.000 0.000 0.000
#> GSM1178970 2 0.8196 0.2515 0.000 0.356 0.324 0.164 0.156
#> GSM1178972 2 0.4767 0.6238 0.000 0.776 0.044 0.096 0.084
#> GSM1178973 4 0.6354 0.4832 0.264 0.000 0.216 0.520 0.000
#> GSM1178974 2 0.0000 0.7031 0.000 1.000 0.000 0.000 0.000
#> GSM1178977 4 0.7534 0.3478 0.008 0.152 0.196 0.540 0.104
#> GSM1178978 4 0.5976 0.4604 0.092 0.000 0.368 0.532 0.008
#> GSM1178998 1 0.1904 0.7419 0.936 0.000 0.028 0.020 0.016
#> GSM1179010 1 0.2180 0.7280 0.924 0.000 0.024 0.032 0.020
#> GSM1179018 3 0.6670 0.2516 0.128 0.000 0.556 0.276 0.040
#> GSM1179024 1 0.0963 0.7750 0.964 0.000 0.036 0.000 0.000
#> GSM1178984 1 0.4153 0.5671 0.740 0.000 0.236 0.016 0.008
#> GSM1178990 1 0.4339 0.3696 0.652 0.000 0.336 0.012 0.000
#> GSM1178991 4 0.5576 0.6298 0.100 0.000 0.268 0.628 0.004
#> GSM1178994 1 0.5697 -0.1642 0.480 0.000 0.448 0.068 0.004
#> GSM1178997 3 0.5029 0.5790 0.292 0.000 0.648 0.060 0.000
#> GSM1179000 3 0.5172 0.5317 0.324 0.000 0.616 0.060 0.000
#> GSM1179013 1 0.0963 0.7750 0.964 0.000 0.036 0.000 0.000
#> GSM1179014 3 0.6683 -0.2647 0.180 0.000 0.444 0.008 0.368
#> GSM1179019 1 0.5230 -0.0877 0.504 0.000 0.452 0.044 0.000
#> GSM1179020 1 0.4165 0.4309 0.672 0.000 0.320 0.008 0.000
#> GSM1179022 1 0.0963 0.7750 0.964 0.000 0.036 0.000 0.000
#> GSM1179028 2 0.0000 0.7031 0.000 1.000 0.000 0.000 0.000
#> GSM1179032 1 0.0963 0.7750 0.964 0.000 0.036 0.000 0.000
#> GSM1179041 2 0.0000 0.7031 0.000 1.000 0.000 0.000 0.000
#> GSM1179042 2 0.0000 0.7031 0.000 1.000 0.000 0.000 0.000
#> GSM1178976 3 0.6743 -0.1098 0.000 0.132 0.616 0.108 0.144
#> GSM1178981 3 0.4959 0.6256 0.240 0.000 0.684 0.076 0.000
#> GSM1178982 3 0.4987 0.6498 0.236 0.000 0.684 0.080 0.000
#> GSM1178983 3 0.4914 0.6625 0.204 0.000 0.704 0.092 0.000
#> GSM1178985 3 0.4639 0.6613 0.132 0.000 0.776 0.040 0.052
#> GSM1178992 3 0.4148 0.6592 0.216 0.000 0.752 0.004 0.028
#> GSM1179005 3 0.5024 0.3224 0.440 0.000 0.532 0.024 0.004
#> GSM1179007 1 0.5002 0.0219 0.548 0.000 0.424 0.024 0.004
#> GSM1179012 1 0.2082 0.7319 0.928 0.000 0.024 0.032 0.016
#> GSM1179016 5 0.5236 0.5251 0.052 0.000 0.380 0.000 0.568
#> GSM1179030 3 0.7468 0.5005 0.136 0.056 0.604 0.112 0.092
#> GSM1179038 3 0.4803 0.3149 0.444 0.000 0.536 0.020 0.000
#> GSM1178987 3 0.4747 0.6454 0.196 0.000 0.720 0.084 0.000
#> GSM1179003 2 0.8375 0.1935 0.000 0.316 0.316 0.160 0.208
#> GSM1179004 3 0.4725 0.6446 0.200 0.000 0.720 0.080 0.000
#> GSM1179039 2 0.0000 0.7031 0.000 1.000 0.000 0.000 0.000
#> GSM1178975 4 0.6354 0.4832 0.264 0.000 0.216 0.520 0.000
#> GSM1178980 4 0.7600 -0.1980 0.000 0.292 0.128 0.468 0.112
#> GSM1178995 3 0.5024 0.4339 0.396 0.000 0.572 0.028 0.004
#> GSM1178996 3 0.4684 0.6474 0.244 0.000 0.712 0.024 0.020
#> GSM1179001 1 0.2574 0.7502 0.876 0.000 0.112 0.012 0.000
#> GSM1179002 1 0.3098 0.7192 0.836 0.000 0.148 0.016 0.000
#> GSM1179006 3 0.4605 0.6238 0.112 0.004 0.788 0.032 0.064
#> GSM1179008 1 0.2677 0.7484 0.872 0.000 0.112 0.016 0.000
#> GSM1179015 1 0.2857 0.7338 0.868 0.000 0.112 0.008 0.012
#> GSM1179017 5 0.2389 0.5319 0.000 0.004 0.116 0.000 0.880
#> GSM1179026 3 0.3745 0.6547 0.132 0.000 0.820 0.012 0.036
#> GSM1179033 3 0.4882 0.5455 0.328 0.000 0.636 0.032 0.004
#> GSM1179035 3 0.3730 0.6662 0.152 0.000 0.808 0.004 0.036
#> GSM1179036 3 0.4969 0.6341 0.264 0.000 0.684 0.032 0.020
#> GSM1178986 3 0.4797 0.6680 0.172 0.000 0.724 0.104 0.000
#> GSM1178989 3 0.6168 -0.0868 0.000 0.060 0.644 0.088 0.208
#> GSM1178993 4 0.4302 0.6680 0.048 0.000 0.208 0.744 0.000
#> GSM1178999 2 0.8524 0.2549 0.000 0.308 0.192 0.236 0.264
#> GSM1179021 2 0.6664 0.5104 0.000 0.580 0.068 0.256 0.096
#> GSM1179025 2 0.0000 0.7031 0.000 1.000 0.000 0.000 0.000
#> GSM1179027 4 0.3723 0.5812 0.000 0.000 0.152 0.804 0.044
#> GSM1179011 4 0.4302 0.6681 0.048 0.000 0.208 0.744 0.000
#> GSM1179023 1 0.0963 0.7750 0.964 0.000 0.036 0.000 0.000
#> GSM1179029 1 0.2570 0.7558 0.880 0.000 0.108 0.004 0.008
#> GSM1179034 1 0.0963 0.7750 0.964 0.000 0.036 0.000 0.000
#> GSM1179040 4 0.4478 0.5733 0.000 0.028 0.152 0.776 0.044
#> GSM1178988 3 0.4116 0.4919 0.056 0.000 0.816 0.032 0.096
#> GSM1179037 3 0.3688 0.6646 0.148 0.000 0.812 0.004 0.036
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1178971 3 0.4898 0.3253 0.352 0.000 0.588 0.052 0.004 0.004
#> GSM1178979 5 0.5054 0.6259 0.000 0.140 0.160 0.008 0.684 0.008
#> GSM1179009 4 0.2717 0.7152 0.020 0.000 0.068 0.884 0.020 0.008
#> GSM1179031 2 0.0000 0.9454 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178970 5 0.6213 0.5449 0.004 0.260 0.204 0.012 0.516 0.004
#> GSM1178972 2 0.3448 0.4759 0.004 0.716 0.000 0.000 0.280 0.000
#> GSM1178973 4 0.5378 0.5848 0.180 0.000 0.096 0.680 0.020 0.024
#> GSM1178974 2 0.0146 0.9427 0.004 0.996 0.000 0.000 0.000 0.000
#> GSM1178977 4 0.6348 0.0592 0.000 0.084 0.088 0.492 0.336 0.000
#> GSM1178978 4 0.4780 0.5256 0.028 0.000 0.284 0.656 0.028 0.004
#> GSM1178998 1 0.4086 0.6185 0.812 0.000 0.040 0.024 0.060 0.064
#> GSM1179010 1 0.4708 0.5459 0.764 0.000 0.028 0.032 0.084 0.092
#> GSM1179018 3 0.5590 0.2836 0.020 0.000 0.580 0.284 0.116 0.000
#> GSM1179024 1 0.2588 0.7732 0.860 0.000 0.124 0.012 0.004 0.000
#> GSM1178984 1 0.5852 0.4720 0.596 0.000 0.284 0.040 0.028 0.052
#> GSM1178990 1 0.5072 0.1937 0.524 0.000 0.424 0.028 0.012 0.012
#> GSM1178991 4 0.3731 0.6802 0.044 0.000 0.140 0.800 0.008 0.008
#> GSM1178994 3 0.6198 0.1834 0.356 0.000 0.492 0.112 0.008 0.032
#> GSM1178997 3 0.4424 0.6093 0.156 0.000 0.740 0.088 0.016 0.000
#> GSM1179000 3 0.4747 0.5792 0.184 0.000 0.708 0.092 0.012 0.004
#> GSM1179013 1 0.2588 0.7732 0.860 0.000 0.124 0.012 0.004 0.000
#> GSM1179014 3 0.6116 -0.2734 0.116 0.000 0.448 0.000 0.036 0.400
#> GSM1179019 3 0.5360 0.2579 0.360 0.000 0.552 0.072 0.012 0.004
#> GSM1179020 1 0.4897 0.2622 0.544 0.000 0.408 0.036 0.008 0.004
#> GSM1179022 1 0.2588 0.7732 0.860 0.000 0.124 0.012 0.004 0.000
#> GSM1179028 2 0.0146 0.9419 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM1179032 1 0.2588 0.7732 0.860 0.000 0.124 0.012 0.004 0.000
#> GSM1179041 2 0.0000 0.9454 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179042 2 0.0000 0.9454 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178976 3 0.6085 -0.2050 0.004 0.080 0.488 0.008 0.388 0.032
#> GSM1178981 3 0.4281 0.6398 0.084 0.000 0.760 0.140 0.004 0.012
#> GSM1178982 3 0.4076 0.6655 0.088 0.000 0.776 0.124 0.004 0.008
#> GSM1178983 3 0.3728 0.6624 0.068 0.000 0.788 0.140 0.000 0.004
#> GSM1178985 3 0.3767 0.6324 0.020 0.000 0.828 0.072 0.056 0.024
#> GSM1178992 3 0.2736 0.6398 0.072 0.000 0.880 0.004 0.016 0.028
#> GSM1179005 3 0.5278 0.4312 0.300 0.000 0.616 0.052 0.016 0.016
#> GSM1179007 3 0.5538 0.0858 0.428 0.000 0.492 0.044 0.012 0.024
#> GSM1179012 1 0.4506 0.5640 0.780 0.000 0.028 0.032 0.072 0.088
#> GSM1179016 6 0.5374 0.4021 0.028 0.000 0.356 0.000 0.060 0.556
#> GSM1179030 3 0.5475 0.4954 0.036 0.000 0.636 0.108 0.220 0.000
#> GSM1179038 3 0.5000 0.4531 0.296 0.000 0.632 0.052 0.012 0.008
#> GSM1178987 3 0.3621 0.6279 0.044 0.000 0.804 0.140 0.004 0.008
#> GSM1179003 5 0.5636 0.5803 0.000 0.136 0.188 0.008 0.640 0.028
#> GSM1179004 3 0.3744 0.6301 0.048 0.000 0.800 0.136 0.004 0.012
#> GSM1179039 2 0.0000 0.9454 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178975 4 0.5378 0.5848 0.180 0.000 0.096 0.680 0.020 0.024
#> GSM1178980 5 0.6138 0.3737 0.000 0.084 0.020 0.280 0.572 0.044
#> GSM1178995 3 0.4906 0.5083 0.264 0.000 0.660 0.056 0.012 0.008
#> GSM1178996 3 0.3383 0.6613 0.112 0.000 0.832 0.036 0.016 0.004
#> GSM1179001 1 0.4601 0.7163 0.732 0.000 0.192 0.024 0.024 0.028
#> GSM1179002 1 0.4486 0.6915 0.716 0.000 0.224 0.032 0.016 0.012
#> GSM1179006 3 0.2911 0.5990 0.008 0.000 0.872 0.024 0.076 0.020
#> GSM1179008 1 0.4705 0.7117 0.724 0.000 0.196 0.028 0.024 0.028
#> GSM1179015 1 0.5042 0.6550 0.704 0.000 0.176 0.004 0.068 0.048
#> GSM1179017 6 0.3361 0.3160 0.000 0.000 0.020 0.004 0.188 0.788
#> GSM1179026 3 0.1879 0.6230 0.016 0.000 0.932 0.008 0.016 0.028
#> GSM1179033 3 0.4471 0.5893 0.192 0.000 0.728 0.064 0.008 0.008
#> GSM1179035 3 0.1856 0.6303 0.024 0.000 0.932 0.008 0.008 0.028
#> GSM1179036 3 0.3721 0.6505 0.136 0.000 0.804 0.036 0.020 0.004
#> GSM1178986 3 0.3662 0.6543 0.036 0.000 0.800 0.148 0.012 0.004
#> GSM1178989 3 0.5092 -0.1121 0.004 0.000 0.512 0.008 0.428 0.048
#> GSM1178993 4 0.1829 0.7167 0.004 0.000 0.064 0.920 0.012 0.000
#> GSM1178999 5 0.4042 0.5766 0.000 0.060 0.068 0.044 0.812 0.016
#> GSM1179021 5 0.5369 0.3439 0.000 0.364 0.000 0.040 0.552 0.044
#> GSM1179025 2 0.0000 0.9454 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179027 4 0.3957 0.6054 0.000 0.000 0.028 0.780 0.152 0.040
#> GSM1179011 4 0.1429 0.7135 0.004 0.000 0.052 0.940 0.004 0.000
#> GSM1179023 1 0.2588 0.7732 0.860 0.000 0.124 0.012 0.004 0.000
#> GSM1179029 1 0.4546 0.7201 0.748 0.000 0.160 0.008 0.036 0.048
#> GSM1179034 1 0.2699 0.7722 0.856 0.000 0.124 0.012 0.008 0.000
#> GSM1179040 4 0.4591 0.5844 0.000 0.024 0.028 0.752 0.156 0.040
#> GSM1178988 3 0.3603 0.4846 0.000 0.000 0.804 0.012 0.136 0.048
#> GSM1179037 3 0.1957 0.6293 0.024 0.000 0.928 0.012 0.008 0.028
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) protocol(p) k
#> CV:hclust 69 0.259 0.15694 2
#> CV:hclust 59 0.579 0.24575 3
#> CV:hclust 34 0.246 0.18731 4
#> CV:hclust 50 0.106 0.02348 5
#> CV:hclust 52 0.139 0.00351 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 31632 rows and 73 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.996 0.998 0.3925 0.610 0.610
#> 3 3 0.743 0.851 0.922 0.5642 0.607 0.432
#> 4 4 0.627 0.750 0.857 0.1566 0.849 0.631
#> 5 5 0.563 0.571 0.768 0.0738 0.935 0.788
#> 6 6 0.594 0.484 0.720 0.0516 0.896 0.641
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM1178971 1 0.0000 0.998 1.000 0.000
#> GSM1178979 2 0.0000 1.000 0.000 1.000
#> GSM1179009 1 0.0000 0.998 1.000 0.000
#> GSM1179031 2 0.0000 1.000 0.000 1.000
#> GSM1178970 2 0.0000 1.000 0.000 1.000
#> GSM1178972 2 0.0000 1.000 0.000 1.000
#> GSM1178973 1 0.0000 0.998 1.000 0.000
#> GSM1178974 2 0.0000 1.000 0.000 1.000
#> GSM1178977 2 0.0000 1.000 0.000 1.000
#> GSM1178978 1 0.0000 0.998 1.000 0.000
#> GSM1178998 1 0.0000 0.998 1.000 0.000
#> GSM1179010 1 0.0000 0.998 1.000 0.000
#> GSM1179018 1 0.0000 0.998 1.000 0.000
#> GSM1179024 1 0.0000 0.998 1.000 0.000
#> GSM1178984 1 0.0000 0.998 1.000 0.000
#> GSM1178990 1 0.0000 0.998 1.000 0.000
#> GSM1178991 1 0.0000 0.998 1.000 0.000
#> GSM1178994 1 0.0000 0.998 1.000 0.000
#> GSM1178997 1 0.0000 0.998 1.000 0.000
#> GSM1179000 1 0.0000 0.998 1.000 0.000
#> GSM1179013 1 0.0000 0.998 1.000 0.000
#> GSM1179014 1 0.0000 0.998 1.000 0.000
#> GSM1179019 1 0.0000 0.998 1.000 0.000
#> GSM1179020 1 0.0000 0.998 1.000 0.000
#> GSM1179022 1 0.0000 0.998 1.000 0.000
#> GSM1179028 2 0.0000 1.000 0.000 1.000
#> GSM1179032 1 0.0000 0.998 1.000 0.000
#> GSM1179041 2 0.0000 1.000 0.000 1.000
#> GSM1179042 2 0.0000 1.000 0.000 1.000
#> GSM1178976 2 0.0000 1.000 0.000 1.000
#> GSM1178981 1 0.0000 0.998 1.000 0.000
#> GSM1178982 1 0.0000 0.998 1.000 0.000
#> GSM1178983 1 0.0000 0.998 1.000 0.000
#> GSM1178985 1 0.0000 0.998 1.000 0.000
#> GSM1178992 1 0.0000 0.998 1.000 0.000
#> GSM1179005 1 0.0000 0.998 1.000 0.000
#> GSM1179007 1 0.0000 0.998 1.000 0.000
#> GSM1179012 1 0.0000 0.998 1.000 0.000
#> GSM1179016 1 0.0000 0.998 1.000 0.000
#> GSM1179030 1 0.4431 0.900 0.908 0.092
#> GSM1179038 1 0.0000 0.998 1.000 0.000
#> GSM1178987 1 0.0000 0.998 1.000 0.000
#> GSM1179003 2 0.0000 1.000 0.000 1.000
#> GSM1179004 1 0.0000 0.998 1.000 0.000
#> GSM1179039 2 0.0000 1.000 0.000 1.000
#> GSM1178975 1 0.0000 0.998 1.000 0.000
#> GSM1178980 2 0.0000 1.000 0.000 1.000
#> GSM1178995 1 0.0000 0.998 1.000 0.000
#> GSM1178996 1 0.0000 0.998 1.000 0.000
#> GSM1179001 1 0.0000 0.998 1.000 0.000
#> GSM1179002 1 0.0000 0.998 1.000 0.000
#> GSM1179006 1 0.0000 0.998 1.000 0.000
#> GSM1179008 1 0.0000 0.998 1.000 0.000
#> GSM1179015 1 0.0000 0.998 1.000 0.000
#> GSM1179017 2 0.0672 0.992 0.008 0.992
#> GSM1179026 1 0.0000 0.998 1.000 0.000
#> GSM1179033 1 0.0000 0.998 1.000 0.000
#> GSM1179035 1 0.0000 0.998 1.000 0.000
#> GSM1179036 1 0.0000 0.998 1.000 0.000
#> GSM1178986 1 0.0000 0.998 1.000 0.000
#> GSM1178989 2 0.0000 1.000 0.000 1.000
#> GSM1178993 1 0.0000 0.998 1.000 0.000
#> GSM1178999 2 0.0000 1.000 0.000 1.000
#> GSM1179021 2 0.0000 1.000 0.000 1.000
#> GSM1179025 2 0.0000 1.000 0.000 1.000
#> GSM1179027 1 0.2043 0.967 0.968 0.032
#> GSM1179011 1 0.0000 0.998 1.000 0.000
#> GSM1179023 1 0.0000 0.998 1.000 0.000
#> GSM1179029 1 0.0000 0.998 1.000 0.000
#> GSM1179034 1 0.0000 0.998 1.000 0.000
#> GSM1179040 2 0.0000 1.000 0.000 1.000
#> GSM1178988 1 0.0376 0.994 0.996 0.004
#> GSM1179037 1 0.0000 0.998 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1178971 3 0.5254 0.7019 0.264 0.000 0.736
#> GSM1178979 2 0.4654 0.7180 0.000 0.792 0.208
#> GSM1179009 3 0.3879 0.8015 0.152 0.000 0.848
#> GSM1179031 2 0.0000 0.9286 0.000 1.000 0.000
#> GSM1178970 2 0.6204 0.2273 0.000 0.576 0.424
#> GSM1178972 2 0.0000 0.9286 0.000 1.000 0.000
#> GSM1178973 1 0.2356 0.8981 0.928 0.000 0.072
#> GSM1178974 2 0.0000 0.9286 0.000 1.000 0.000
#> GSM1178977 3 0.0592 0.8745 0.000 0.012 0.988
#> GSM1178978 3 0.1411 0.8910 0.036 0.000 0.964
#> GSM1178998 1 0.0237 0.9424 0.996 0.000 0.004
#> GSM1179010 1 0.0424 0.9408 0.992 0.000 0.008
#> GSM1179018 3 0.0237 0.8802 0.004 0.000 0.996
#> GSM1179024 1 0.0237 0.9424 0.996 0.000 0.004
#> GSM1178984 1 0.2448 0.8964 0.924 0.000 0.076
#> GSM1178990 1 0.0237 0.9424 0.996 0.000 0.004
#> GSM1178991 3 0.4062 0.8023 0.164 0.000 0.836
#> GSM1178994 1 0.2448 0.8981 0.924 0.000 0.076
#> GSM1178997 3 0.2625 0.8953 0.084 0.000 0.916
#> GSM1179000 1 0.0424 0.9409 0.992 0.000 0.008
#> GSM1179013 1 0.0000 0.9401 1.000 0.000 0.000
#> GSM1179014 1 0.4796 0.7054 0.780 0.000 0.220
#> GSM1179019 1 0.0237 0.9424 0.996 0.000 0.004
#> GSM1179020 1 0.0237 0.9424 0.996 0.000 0.004
#> GSM1179022 1 0.0237 0.9424 0.996 0.000 0.004
#> GSM1179028 2 0.0000 0.9286 0.000 1.000 0.000
#> GSM1179032 1 0.0237 0.9424 0.996 0.000 0.004
#> GSM1179041 2 0.0000 0.9286 0.000 1.000 0.000
#> GSM1179042 2 0.0000 0.9286 0.000 1.000 0.000
#> GSM1178976 3 0.3482 0.8135 0.000 0.128 0.872
#> GSM1178981 3 0.5016 0.7487 0.240 0.000 0.760
#> GSM1178982 3 0.1964 0.8960 0.056 0.000 0.944
#> GSM1178983 3 0.1643 0.8937 0.044 0.000 0.956
#> GSM1178985 3 0.2537 0.8954 0.080 0.000 0.920
#> GSM1178992 1 0.6192 0.1952 0.580 0.000 0.420
#> GSM1179005 1 0.2711 0.8874 0.912 0.000 0.088
#> GSM1179007 1 0.0237 0.9424 0.996 0.000 0.004
#> GSM1179012 1 0.0237 0.9391 0.996 0.000 0.004
#> GSM1179016 3 0.5497 0.6573 0.292 0.000 0.708
#> GSM1179030 3 0.1031 0.8894 0.024 0.000 0.976
#> GSM1179038 1 0.4346 0.7752 0.816 0.000 0.184
#> GSM1178987 3 0.2711 0.8931 0.088 0.000 0.912
#> GSM1179003 3 0.6307 0.0125 0.000 0.488 0.512
#> GSM1179004 3 0.2711 0.8931 0.088 0.000 0.912
#> GSM1179039 2 0.0000 0.9286 0.000 1.000 0.000
#> GSM1178975 3 0.1289 0.8875 0.032 0.000 0.968
#> GSM1178980 3 0.0592 0.8745 0.000 0.012 0.988
#> GSM1178995 1 0.2448 0.8964 0.924 0.000 0.076
#> GSM1178996 3 0.2625 0.8944 0.084 0.000 0.916
#> GSM1179001 1 0.0237 0.9424 0.996 0.000 0.004
#> GSM1179002 1 0.0237 0.9424 0.996 0.000 0.004
#> GSM1179006 3 0.2356 0.8963 0.072 0.000 0.928
#> GSM1179008 1 0.0237 0.9424 0.996 0.000 0.004
#> GSM1179015 1 0.0424 0.9364 0.992 0.000 0.008
#> GSM1179017 3 0.4349 0.8140 0.020 0.128 0.852
#> GSM1179026 3 0.2625 0.8944 0.084 0.000 0.916
#> GSM1179033 3 0.2356 0.8963 0.072 0.000 0.928
#> GSM1179035 3 0.2711 0.8931 0.088 0.000 0.912
#> GSM1179036 3 0.2625 0.8944 0.084 0.000 0.916
#> GSM1178986 3 0.2537 0.8954 0.080 0.000 0.920
#> GSM1178989 3 0.2486 0.8700 0.008 0.060 0.932
#> GSM1178993 3 0.0424 0.8803 0.008 0.000 0.992
#> GSM1178999 3 0.3340 0.8073 0.000 0.120 0.880
#> GSM1179021 2 0.1163 0.9155 0.000 0.972 0.028
#> GSM1179025 2 0.0000 0.9286 0.000 1.000 0.000
#> GSM1179027 3 0.0424 0.8803 0.008 0.000 0.992
#> GSM1179011 3 0.0424 0.8803 0.008 0.000 0.992
#> GSM1179023 1 0.0237 0.9424 0.996 0.000 0.004
#> GSM1179029 1 0.0424 0.9364 0.992 0.000 0.008
#> GSM1179034 1 0.0237 0.9424 0.996 0.000 0.004
#> GSM1179040 3 0.5859 0.3874 0.000 0.344 0.656
#> GSM1178988 3 0.2066 0.8947 0.060 0.000 0.940
#> GSM1179037 3 0.2625 0.8944 0.084 0.000 0.916
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1178971 3 0.3806 0.656 0.156 0.000 0.824 0.020
#> GSM1178979 2 0.6444 0.490 0.000 0.612 0.104 0.284
#> GSM1179009 4 0.5627 0.769 0.068 0.000 0.240 0.692
#> GSM1179031 2 0.0000 0.878 0.000 1.000 0.000 0.000
#> GSM1178970 2 0.7251 0.318 0.000 0.536 0.192 0.272
#> GSM1178972 2 0.0921 0.865 0.000 0.972 0.000 0.028
#> GSM1178973 1 0.5271 0.481 0.640 0.000 0.020 0.340
#> GSM1178974 2 0.0000 0.878 0.000 1.000 0.000 0.000
#> GSM1178977 4 0.4454 0.737 0.000 0.000 0.308 0.692
#> GSM1178978 4 0.4994 0.473 0.000 0.000 0.480 0.520
#> GSM1178998 1 0.1411 0.891 0.960 0.000 0.020 0.020
#> GSM1179010 1 0.3810 0.843 0.848 0.000 0.092 0.060
#> GSM1179018 3 0.4605 0.237 0.000 0.000 0.664 0.336
#> GSM1179024 1 0.0188 0.891 0.996 0.000 0.000 0.004
#> GSM1178984 1 0.4290 0.789 0.800 0.000 0.164 0.036
#> GSM1178990 1 0.0188 0.892 0.996 0.000 0.000 0.004
#> GSM1178991 4 0.6730 0.722 0.132 0.000 0.276 0.592
#> GSM1178994 1 0.5109 0.744 0.744 0.000 0.196 0.060
#> GSM1178997 3 0.1356 0.801 0.008 0.000 0.960 0.032
#> GSM1179000 1 0.2635 0.856 0.904 0.000 0.076 0.020
#> GSM1179013 1 0.0336 0.891 0.992 0.000 0.000 0.008
#> GSM1179014 3 0.6875 0.252 0.388 0.000 0.504 0.108
#> GSM1179019 1 0.2413 0.866 0.916 0.000 0.064 0.020
#> GSM1179020 1 0.0937 0.891 0.976 0.000 0.012 0.012
#> GSM1179022 1 0.0000 0.892 1.000 0.000 0.000 0.000
#> GSM1179028 2 0.0336 0.874 0.000 0.992 0.000 0.008
#> GSM1179032 1 0.0000 0.892 1.000 0.000 0.000 0.000
#> GSM1179041 2 0.0000 0.878 0.000 1.000 0.000 0.000
#> GSM1179042 2 0.0000 0.878 0.000 1.000 0.000 0.000
#> GSM1178976 3 0.4318 0.695 0.000 0.068 0.816 0.116
#> GSM1178981 3 0.3474 0.739 0.068 0.000 0.868 0.064
#> GSM1178982 3 0.1211 0.799 0.000 0.000 0.960 0.040
#> GSM1178983 3 0.1474 0.795 0.000 0.000 0.948 0.052
#> GSM1178985 3 0.1118 0.799 0.000 0.000 0.964 0.036
#> GSM1178992 3 0.4224 0.713 0.044 0.000 0.812 0.144
#> GSM1179005 1 0.5657 0.257 0.540 0.000 0.436 0.024
#> GSM1179007 1 0.2662 0.866 0.900 0.000 0.084 0.016
#> GSM1179012 1 0.2546 0.881 0.912 0.000 0.028 0.060
#> GSM1179016 3 0.2888 0.764 0.004 0.000 0.872 0.124
#> GSM1179030 3 0.1792 0.783 0.000 0.000 0.932 0.068
#> GSM1179038 3 0.5659 0.292 0.368 0.000 0.600 0.032
#> GSM1178987 3 0.1474 0.796 0.000 0.000 0.948 0.052
#> GSM1179003 3 0.7443 0.148 0.000 0.312 0.492 0.196
#> GSM1179004 3 0.1474 0.796 0.000 0.000 0.948 0.052
#> GSM1179039 2 0.0000 0.878 0.000 1.000 0.000 0.000
#> GSM1178975 4 0.4955 0.819 0.024 0.000 0.268 0.708
#> GSM1178980 4 0.3444 0.819 0.000 0.000 0.184 0.816
#> GSM1178995 1 0.4524 0.753 0.768 0.000 0.204 0.028
#> GSM1178996 3 0.0592 0.803 0.000 0.000 0.984 0.016
#> GSM1179001 1 0.2224 0.890 0.928 0.000 0.032 0.040
#> GSM1179002 1 0.2399 0.889 0.920 0.000 0.032 0.048
#> GSM1179006 3 0.1118 0.801 0.000 0.000 0.964 0.036
#> GSM1179008 1 0.1610 0.892 0.952 0.000 0.016 0.032
#> GSM1179015 1 0.2101 0.880 0.928 0.000 0.012 0.060
#> GSM1179017 3 0.4426 0.698 0.000 0.024 0.772 0.204
#> GSM1179026 3 0.2530 0.772 0.000 0.000 0.888 0.112
#> GSM1179033 3 0.0921 0.800 0.000 0.000 0.972 0.028
#> GSM1179035 3 0.1557 0.795 0.000 0.000 0.944 0.056
#> GSM1179036 3 0.0707 0.802 0.000 0.000 0.980 0.020
#> GSM1178986 3 0.0817 0.803 0.000 0.000 0.976 0.024
#> GSM1178989 3 0.2589 0.764 0.000 0.000 0.884 0.116
#> GSM1178993 4 0.3764 0.850 0.000 0.000 0.216 0.784
#> GSM1178999 3 0.5855 0.189 0.000 0.044 0.600 0.356
#> GSM1179021 2 0.4250 0.649 0.000 0.724 0.000 0.276
#> GSM1179025 2 0.0000 0.878 0.000 1.000 0.000 0.000
#> GSM1179027 4 0.3726 0.849 0.000 0.000 0.212 0.788
#> GSM1179011 4 0.3764 0.850 0.000 0.000 0.216 0.784
#> GSM1179023 1 0.0000 0.892 1.000 0.000 0.000 0.000
#> GSM1179029 1 0.1557 0.883 0.944 0.000 0.000 0.056
#> GSM1179034 1 0.0000 0.892 1.000 0.000 0.000 0.000
#> GSM1179040 4 0.4312 0.758 0.000 0.056 0.132 0.812
#> GSM1178988 3 0.1940 0.791 0.000 0.000 0.924 0.076
#> GSM1179037 3 0.1302 0.798 0.000 0.000 0.956 0.044
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1178971 3 0.5608 0.566 0.120 0.000 0.692 0.028 0.160
#> GSM1178979 2 0.7803 -0.356 0.000 0.380 0.072 0.220 0.328
#> GSM1179009 4 0.4768 0.618 0.028 0.000 0.148 0.760 0.064
#> GSM1179031 2 0.0000 0.838 0.000 1.000 0.000 0.000 0.000
#> GSM1178970 5 0.8360 0.415 0.000 0.312 0.168 0.192 0.328
#> GSM1178972 2 0.3492 0.637 0.000 0.796 0.000 0.016 0.188
#> GSM1178973 1 0.6252 0.142 0.484 0.000 0.012 0.400 0.104
#> GSM1178974 2 0.0000 0.838 0.000 1.000 0.000 0.000 0.000
#> GSM1178977 4 0.6418 -0.321 0.000 0.000 0.184 0.472 0.344
#> GSM1178978 3 0.5972 0.358 0.000 0.000 0.560 0.300 0.140
#> GSM1178998 1 0.2848 0.744 0.840 0.000 0.004 0.000 0.156
#> GSM1179010 1 0.6038 0.586 0.576 0.000 0.184 0.000 0.240
#> GSM1179018 3 0.4681 0.442 0.000 0.000 0.696 0.252 0.052
#> GSM1179024 1 0.0671 0.756 0.980 0.000 0.000 0.004 0.016
#> GSM1178984 1 0.6359 0.489 0.520 0.000 0.260 0.000 0.220
#> GSM1178990 1 0.0290 0.760 0.992 0.000 0.000 0.000 0.008
#> GSM1178991 4 0.7241 0.400 0.208 0.000 0.204 0.524 0.064
#> GSM1178994 1 0.6678 0.261 0.404 0.000 0.360 0.000 0.236
#> GSM1178997 3 0.4208 0.625 0.032 0.000 0.788 0.024 0.156
#> GSM1179000 1 0.5659 0.525 0.652 0.000 0.236 0.016 0.096
#> GSM1179013 1 0.0404 0.757 0.988 0.000 0.000 0.000 0.012
#> GSM1179014 3 0.6924 0.106 0.292 0.000 0.380 0.004 0.324
#> GSM1179019 1 0.5375 0.570 0.684 0.000 0.216 0.016 0.084
#> GSM1179020 1 0.1808 0.753 0.936 0.000 0.020 0.004 0.040
#> GSM1179022 1 0.0290 0.758 0.992 0.000 0.000 0.000 0.008
#> GSM1179028 2 0.0290 0.834 0.000 0.992 0.000 0.000 0.008
#> GSM1179032 1 0.0290 0.758 0.992 0.000 0.000 0.000 0.008
#> GSM1179041 2 0.0000 0.838 0.000 1.000 0.000 0.000 0.000
#> GSM1179042 2 0.0000 0.838 0.000 1.000 0.000 0.000 0.000
#> GSM1178976 3 0.6327 -0.391 0.000 0.040 0.540 0.072 0.348
#> GSM1178981 3 0.4130 0.639 0.020 0.000 0.776 0.020 0.184
#> GSM1178982 3 0.2450 0.684 0.000 0.000 0.896 0.028 0.076
#> GSM1178983 3 0.2676 0.681 0.000 0.000 0.884 0.036 0.080
#> GSM1178985 3 0.1845 0.689 0.000 0.000 0.928 0.016 0.056
#> GSM1178992 3 0.3575 0.649 0.016 0.000 0.800 0.004 0.180
#> GSM1179005 3 0.6484 0.173 0.316 0.000 0.520 0.012 0.152
#> GSM1179007 1 0.5430 0.628 0.660 0.000 0.192 0.000 0.148
#> GSM1179012 1 0.3728 0.710 0.748 0.000 0.008 0.000 0.244
#> GSM1179016 3 0.4270 0.364 0.004 0.000 0.656 0.004 0.336
#> GSM1179030 3 0.3897 0.459 0.000 0.000 0.768 0.028 0.204
#> GSM1179038 3 0.5372 0.527 0.184 0.000 0.692 0.012 0.112
#> GSM1178987 3 0.3022 0.668 0.004 0.000 0.848 0.012 0.136
#> GSM1179003 5 0.8205 0.671 0.000 0.184 0.276 0.152 0.388
#> GSM1179004 3 0.3067 0.666 0.004 0.000 0.844 0.012 0.140
#> GSM1179039 2 0.0000 0.838 0.000 1.000 0.000 0.000 0.000
#> GSM1178975 4 0.5177 0.634 0.044 0.000 0.108 0.744 0.104
#> GSM1178980 4 0.1012 0.722 0.000 0.000 0.012 0.968 0.020
#> GSM1178995 1 0.6773 0.139 0.412 0.000 0.412 0.016 0.160
#> GSM1178996 3 0.1697 0.671 0.000 0.000 0.932 0.008 0.060
#> GSM1179001 1 0.4652 0.727 0.736 0.000 0.048 0.012 0.204
#> GSM1179002 1 0.5055 0.716 0.708 0.000 0.072 0.012 0.208
#> GSM1179006 3 0.1830 0.665 0.000 0.000 0.924 0.008 0.068
#> GSM1179008 1 0.3742 0.740 0.792 0.000 0.012 0.012 0.184
#> GSM1179015 1 0.2813 0.728 0.832 0.000 0.000 0.000 0.168
#> GSM1179017 5 0.5163 0.466 0.000 0.004 0.368 0.040 0.588
#> GSM1179026 3 0.1965 0.669 0.000 0.000 0.904 0.000 0.096
#> GSM1179033 3 0.0671 0.684 0.000 0.000 0.980 0.016 0.004
#> GSM1179035 3 0.3022 0.672 0.004 0.000 0.848 0.012 0.136
#> GSM1179036 3 0.2069 0.681 0.000 0.000 0.912 0.012 0.076
#> GSM1178986 3 0.2773 0.664 0.000 0.000 0.868 0.020 0.112
#> GSM1178989 3 0.5113 -0.225 0.000 0.000 0.576 0.044 0.380
#> GSM1178993 4 0.1121 0.744 0.000 0.000 0.044 0.956 0.000
#> GSM1178999 5 0.7021 0.569 0.000 0.008 0.332 0.284 0.376
#> GSM1179021 2 0.5048 0.372 0.000 0.580 0.000 0.380 0.040
#> GSM1179025 2 0.0000 0.838 0.000 1.000 0.000 0.000 0.000
#> GSM1179027 4 0.1124 0.742 0.000 0.000 0.036 0.960 0.004
#> GSM1179011 4 0.1331 0.743 0.000 0.000 0.040 0.952 0.008
#> GSM1179023 1 0.0290 0.758 0.992 0.000 0.000 0.000 0.008
#> GSM1179029 1 0.3171 0.724 0.816 0.000 0.000 0.008 0.176
#> GSM1179034 1 0.0290 0.758 0.992 0.000 0.000 0.000 0.008
#> GSM1179040 4 0.1243 0.713 0.000 0.004 0.008 0.960 0.028
#> GSM1178988 3 0.3639 0.498 0.000 0.000 0.792 0.024 0.184
#> GSM1179037 3 0.1571 0.690 0.004 0.000 0.936 0.000 0.060
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1178971 3 0.4330 0.55221 0.036 0.000 0.680 0.000 0.008 0.276
#> GSM1178979 5 0.6153 0.56997 0.000 0.204 0.044 0.156 0.588 0.008
#> GSM1179009 4 0.3608 0.65094 0.000 0.000 0.128 0.800 0.004 0.068
#> GSM1179031 2 0.0000 0.86988 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178970 5 0.6459 0.66798 0.000 0.156 0.108 0.120 0.600 0.016
#> GSM1178972 2 0.4076 0.25234 0.000 0.592 0.000 0.000 0.396 0.012
#> GSM1178973 1 0.6802 -0.02502 0.376 0.000 0.020 0.356 0.016 0.232
#> GSM1178974 2 0.0000 0.86988 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178977 5 0.5486 0.57259 0.000 0.004 0.096 0.292 0.592 0.016
#> GSM1178978 3 0.6041 0.46369 0.000 0.000 0.592 0.188 0.056 0.164
#> GSM1178998 1 0.4482 0.12562 0.628 0.000 0.016 0.000 0.020 0.336
#> GSM1179010 6 0.6302 0.14624 0.364 0.000 0.148 0.000 0.036 0.452
#> GSM1179018 3 0.4822 0.55808 0.000 0.000 0.720 0.148 0.096 0.036
#> GSM1179024 1 0.0260 0.57648 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM1178984 6 0.6439 0.24238 0.284 0.000 0.272 0.000 0.020 0.424
#> GSM1178990 1 0.0891 0.56587 0.968 0.000 0.000 0.000 0.008 0.024
#> GSM1178991 4 0.7782 0.33149 0.176 0.000 0.212 0.428 0.032 0.152
#> GSM1178994 3 0.6349 -0.16876 0.188 0.000 0.396 0.000 0.024 0.392
#> GSM1178997 3 0.5246 0.55857 0.020 0.000 0.640 0.000 0.104 0.236
#> GSM1179000 1 0.5616 0.13770 0.584 0.000 0.164 0.000 0.012 0.240
#> GSM1179013 1 0.0000 0.57877 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179014 6 0.7805 -0.00706 0.212 0.000 0.180 0.008 0.296 0.304
#> GSM1179019 1 0.5411 0.18024 0.612 0.000 0.140 0.000 0.012 0.236
#> GSM1179020 1 0.2377 0.48917 0.868 0.000 0.004 0.000 0.004 0.124
#> GSM1179022 1 0.0146 0.57898 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM1179028 2 0.0458 0.86206 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM1179032 1 0.0146 0.57898 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM1179041 2 0.0000 0.86988 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179042 2 0.0000 0.86988 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178976 5 0.4670 0.57534 0.000 0.008 0.352 0.024 0.608 0.008
#> GSM1178981 3 0.3589 0.62840 0.004 0.000 0.768 0.008 0.012 0.208
#> GSM1178982 3 0.2213 0.67574 0.000 0.000 0.908 0.012 0.032 0.048
#> GSM1178983 3 0.2593 0.67595 0.000 0.000 0.884 0.012 0.036 0.068
#> GSM1178985 3 0.1841 0.67605 0.000 0.000 0.920 0.008 0.008 0.064
#> GSM1178992 3 0.4838 0.61749 0.000 0.000 0.680 0.004 0.148 0.168
#> GSM1179005 3 0.5639 0.19744 0.212 0.000 0.536 0.000 0.000 0.252
#> GSM1179007 1 0.6101 -0.24291 0.488 0.000 0.188 0.000 0.016 0.308
#> GSM1179012 1 0.5170 -0.04492 0.512 0.000 0.028 0.000 0.036 0.424
#> GSM1179016 3 0.6268 0.11869 0.000 0.000 0.376 0.008 0.360 0.256
#> GSM1179030 3 0.3907 0.47698 0.000 0.000 0.704 0.000 0.268 0.028
#> GSM1179038 3 0.5371 0.47157 0.108 0.000 0.620 0.000 0.020 0.252
#> GSM1178987 3 0.3539 0.62645 0.000 0.000 0.768 0.008 0.016 0.208
#> GSM1179003 5 0.5861 0.71143 0.000 0.092 0.156 0.104 0.644 0.004
#> GSM1179004 3 0.3596 0.62051 0.000 0.000 0.760 0.008 0.016 0.216
#> GSM1179039 2 0.0000 0.86988 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178975 4 0.6846 0.45415 0.104 0.000 0.096 0.536 0.024 0.240
#> GSM1178980 4 0.1938 0.72532 0.000 0.000 0.008 0.920 0.052 0.020
#> GSM1178995 3 0.5908 0.00334 0.248 0.000 0.468 0.000 0.000 0.284
#> GSM1178996 3 0.3372 0.65020 0.000 0.000 0.816 0.000 0.084 0.100
#> GSM1179001 6 0.4825 -0.01146 0.460 0.000 0.028 0.004 0.008 0.500
#> GSM1179002 6 0.5140 0.07469 0.424 0.000 0.052 0.004 0.008 0.512
#> GSM1179006 3 0.2968 0.64162 0.000 0.000 0.852 0.004 0.092 0.052
#> GSM1179008 1 0.4619 -0.12474 0.504 0.000 0.016 0.004 0.008 0.468
#> GSM1179015 1 0.4539 0.25619 0.644 0.000 0.004 0.000 0.048 0.304
#> GSM1179017 5 0.4599 0.47342 0.000 0.004 0.112 0.012 0.732 0.140
#> GSM1179026 3 0.3782 0.63230 0.000 0.000 0.784 0.004 0.140 0.072
#> GSM1179033 3 0.1995 0.66847 0.000 0.000 0.912 0.000 0.052 0.036
#> GSM1179035 3 0.3264 0.64278 0.000 0.000 0.796 0.008 0.012 0.184
#> GSM1179036 3 0.4075 0.63576 0.000 0.000 0.740 0.000 0.076 0.184
#> GSM1178986 3 0.4148 0.61707 0.000 0.000 0.744 0.000 0.108 0.148
#> GSM1178989 5 0.4047 0.46378 0.000 0.000 0.384 0.000 0.604 0.012
#> GSM1178993 4 0.0458 0.75626 0.000 0.000 0.016 0.984 0.000 0.000
#> GSM1178999 5 0.5528 0.67948 0.000 0.004 0.160 0.192 0.628 0.016
#> GSM1179021 2 0.5880 0.17084 0.000 0.476 0.000 0.384 0.120 0.020
#> GSM1179025 2 0.0000 0.86988 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179027 4 0.0767 0.75446 0.000 0.000 0.012 0.976 0.004 0.008
#> GSM1179011 4 0.1232 0.75469 0.000 0.000 0.024 0.956 0.004 0.016
#> GSM1179023 1 0.0000 0.57877 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179029 1 0.4705 0.30457 0.640 0.000 0.000 0.004 0.064 0.292
#> GSM1179034 1 0.0146 0.57898 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM1179040 4 0.2492 0.67788 0.000 0.000 0.004 0.876 0.100 0.020
#> GSM1178988 3 0.3867 0.53315 0.000 0.000 0.744 0.004 0.216 0.036
#> GSM1179037 3 0.2604 0.67811 0.000 0.000 0.872 0.008 0.020 0.100
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) protocol(p) k
#> CV:kmeans 73 0.200 0.28085 2
#> CV:kmeans 69 0.166 0.01569 3
#> CV:kmeans 63 0.196 0.02918 4
#> CV:kmeans 54 0.123 0.00421 5
#> CV:kmeans 45 0.109 0.00226 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 31632 rows and 73 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.968 0.957 0.980 0.4867 0.521 0.521
#> 3 3 0.556 0.678 0.840 0.3106 0.852 0.721
#> 4 4 0.622 0.697 0.845 0.1413 0.827 0.583
#> 5 5 0.621 0.593 0.789 0.0624 0.941 0.785
#> 6 6 0.616 0.487 0.730 0.0406 0.980 0.914
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
#> GSM1178971 1 0.0000 0.969 1.000 0.000
#> GSM1178979 2 0.0000 0.995 0.000 1.000
#> GSM1179009 1 0.1843 0.951 0.972 0.028
#> GSM1179031 2 0.0000 0.995 0.000 1.000
#> GSM1178970 2 0.0000 0.995 0.000 1.000
#> GSM1178972 2 0.0000 0.995 0.000 1.000
#> GSM1178973 1 0.0000 0.969 1.000 0.000
#> GSM1178974 2 0.0000 0.995 0.000 1.000
#> GSM1178977 2 0.0000 0.995 0.000 1.000
#> GSM1178978 1 0.7139 0.775 0.804 0.196
#> GSM1178998 1 0.0000 0.969 1.000 0.000
#> GSM1179010 1 0.0000 0.969 1.000 0.000
#> GSM1179018 2 0.0672 0.989 0.008 0.992
#> GSM1179024 1 0.0000 0.969 1.000 0.000
#> GSM1178984 1 0.0000 0.969 1.000 0.000
#> GSM1178990 1 0.0000 0.969 1.000 0.000
#> GSM1178991 1 0.0000 0.969 1.000 0.000
#> GSM1178994 1 0.0000 0.969 1.000 0.000
#> GSM1178997 2 0.1414 0.978 0.020 0.980
#> GSM1179000 1 0.0000 0.969 1.000 0.000
#> GSM1179013 1 0.0000 0.969 1.000 0.000
#> GSM1179014 1 0.0000 0.969 1.000 0.000
#> GSM1179019 1 0.0000 0.969 1.000 0.000
#> GSM1179020 1 0.0000 0.969 1.000 0.000
#> GSM1179022 1 0.0000 0.969 1.000 0.000
#> GSM1179028 2 0.0000 0.995 0.000 1.000
#> GSM1179032 1 0.0000 0.969 1.000 0.000
#> GSM1179041 2 0.0000 0.995 0.000 1.000
#> GSM1179042 2 0.0000 0.995 0.000 1.000
#> GSM1178976 2 0.0000 0.995 0.000 1.000
#> GSM1178981 1 0.0000 0.969 1.000 0.000
#> GSM1178982 1 0.6531 0.812 0.832 0.168
#> GSM1178983 1 0.3114 0.929 0.944 0.056
#> GSM1178985 1 0.6973 0.782 0.812 0.188
#> GSM1178992 1 0.0000 0.969 1.000 0.000
#> GSM1179005 1 0.0000 0.969 1.000 0.000
#> GSM1179007 1 0.0000 0.969 1.000 0.000
#> GSM1179012 1 0.0000 0.969 1.000 0.000
#> GSM1179016 1 0.6531 0.804 0.832 0.168
#> GSM1179030 2 0.0000 0.995 0.000 1.000
#> GSM1179038 1 0.0000 0.969 1.000 0.000
#> GSM1178987 1 0.0000 0.969 1.000 0.000
#> GSM1179003 2 0.0000 0.995 0.000 1.000
#> GSM1179004 1 0.0000 0.969 1.000 0.000
#> GSM1179039 2 0.0000 0.995 0.000 1.000
#> GSM1178975 1 0.4022 0.907 0.920 0.080
#> GSM1178980 2 0.0000 0.995 0.000 1.000
#> GSM1178995 1 0.0000 0.969 1.000 0.000
#> GSM1178996 1 0.9686 0.360 0.604 0.396
#> GSM1179001 1 0.0000 0.969 1.000 0.000
#> GSM1179002 1 0.0000 0.969 1.000 0.000
#> GSM1179006 2 0.4161 0.907 0.084 0.916
#> GSM1179008 1 0.0000 0.969 1.000 0.000
#> GSM1179015 1 0.0000 0.969 1.000 0.000
#> GSM1179017 2 0.0000 0.995 0.000 1.000
#> GSM1179026 1 0.1633 0.954 0.976 0.024
#> GSM1179033 2 0.1184 0.982 0.016 0.984
#> GSM1179035 1 0.0000 0.969 1.000 0.000
#> GSM1179036 1 0.0672 0.964 0.992 0.008
#> GSM1178986 1 0.1633 0.953 0.976 0.024
#> GSM1178989 2 0.0000 0.995 0.000 1.000
#> GSM1178993 2 0.0000 0.995 0.000 1.000
#> GSM1178999 2 0.0000 0.995 0.000 1.000
#> GSM1179021 2 0.0000 0.995 0.000 1.000
#> GSM1179025 2 0.0000 0.995 0.000 1.000
#> GSM1179027 2 0.0000 0.995 0.000 1.000
#> GSM1179011 2 0.0672 0.989 0.008 0.992
#> GSM1179023 1 0.0000 0.969 1.000 0.000
#> GSM1179029 1 0.0000 0.969 1.000 0.000
#> GSM1179034 1 0.0000 0.969 1.000 0.000
#> GSM1179040 2 0.0000 0.995 0.000 1.000
#> GSM1178988 2 0.0000 0.995 0.000 1.000
#> GSM1179037 1 0.0000 0.969 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1178971 1 0.4842 0.5448 0.776 0.000 0.224
#> GSM1178979 2 0.0000 0.8853 0.000 1.000 0.000
#> GSM1179009 3 0.4749 0.6610 0.172 0.012 0.816
#> GSM1179031 2 0.0000 0.8853 0.000 1.000 0.000
#> GSM1178970 2 0.0000 0.8853 0.000 1.000 0.000
#> GSM1178972 2 0.0000 0.8853 0.000 1.000 0.000
#> GSM1178973 1 0.6192 -0.0961 0.580 0.000 0.420
#> GSM1178974 2 0.0000 0.8853 0.000 1.000 0.000
#> GSM1178977 2 0.0424 0.8800 0.000 0.992 0.008
#> GSM1178978 3 0.6349 0.7087 0.140 0.092 0.768
#> GSM1178998 1 0.0747 0.7959 0.984 0.000 0.016
#> GSM1179010 1 0.4555 0.7186 0.800 0.000 0.200
#> GSM1179018 3 0.4399 0.5902 0.000 0.188 0.812
#> GSM1179024 1 0.0237 0.7947 0.996 0.000 0.004
#> GSM1178984 1 0.4750 0.7034 0.784 0.000 0.216
#> GSM1178990 1 0.0237 0.7947 0.996 0.000 0.004
#> GSM1178991 3 0.6359 0.4793 0.404 0.004 0.592
#> GSM1178994 1 0.4842 0.7043 0.776 0.000 0.224
#> GSM1178997 2 0.7979 0.3607 0.248 0.640 0.112
#> GSM1179000 1 0.0747 0.7894 0.984 0.000 0.016
#> GSM1179013 1 0.0237 0.7947 0.996 0.000 0.004
#> GSM1179014 1 0.0892 0.7928 0.980 0.000 0.020
#> GSM1179019 1 0.0237 0.7947 0.996 0.000 0.004
#> GSM1179020 1 0.0237 0.7947 0.996 0.000 0.004
#> GSM1179022 1 0.0237 0.7947 0.996 0.000 0.004
#> GSM1179028 2 0.0000 0.8853 0.000 1.000 0.000
#> GSM1179032 1 0.0237 0.7947 0.996 0.000 0.004
#> GSM1179041 2 0.0000 0.8853 0.000 1.000 0.000
#> GSM1179042 2 0.0000 0.8853 0.000 1.000 0.000
#> GSM1178976 2 0.0000 0.8853 0.000 1.000 0.000
#> GSM1178981 1 0.6309 0.3068 0.504 0.000 0.496
#> GSM1178982 3 0.5420 0.4505 0.240 0.008 0.752
#> GSM1178983 3 0.4960 0.6956 0.128 0.040 0.832
#> GSM1178985 3 0.8474 0.2599 0.252 0.144 0.604
#> GSM1178992 1 0.5760 0.6281 0.672 0.000 0.328
#> GSM1179005 1 0.3038 0.7725 0.896 0.000 0.104
#> GSM1179007 1 0.3116 0.7701 0.892 0.000 0.108
#> GSM1179012 1 0.3941 0.7448 0.844 0.000 0.156
#> GSM1179016 1 0.8172 0.4759 0.644 0.176 0.180
#> GSM1179030 2 0.0424 0.8811 0.000 0.992 0.008
#> GSM1179038 1 0.1529 0.7939 0.960 0.000 0.040
#> GSM1178987 1 0.6126 0.5538 0.600 0.000 0.400
#> GSM1179003 2 0.0000 0.8853 0.000 1.000 0.000
#> GSM1179004 1 0.6168 0.5376 0.588 0.000 0.412
#> GSM1179039 2 0.0000 0.8853 0.000 1.000 0.000
#> GSM1178975 3 0.6045 0.5166 0.380 0.000 0.620
#> GSM1178980 2 0.6302 -0.1021 0.000 0.520 0.480
#> GSM1178995 1 0.1411 0.7932 0.964 0.000 0.036
#> GSM1178996 1 0.9187 0.2476 0.532 0.272 0.196
#> GSM1179001 1 0.0000 0.7952 1.000 0.000 0.000
#> GSM1179002 1 0.0237 0.7955 0.996 0.000 0.004
#> GSM1179006 2 0.7798 0.4310 0.080 0.624 0.296
#> GSM1179008 1 0.0000 0.7952 1.000 0.000 0.000
#> GSM1179015 1 0.1163 0.7950 0.972 0.000 0.028
#> GSM1179017 2 0.1753 0.8531 0.000 0.952 0.048
#> GSM1179026 1 0.7841 0.5227 0.576 0.064 0.360
#> GSM1179033 2 0.6937 0.3634 0.020 0.576 0.404
#> GSM1179035 1 0.6045 0.5765 0.620 0.000 0.380
#> GSM1179036 1 0.5480 0.6767 0.732 0.004 0.264
#> GSM1178986 1 0.7948 0.2326 0.520 0.060 0.420
#> GSM1178989 2 0.2878 0.8132 0.000 0.904 0.096
#> GSM1178993 3 0.5835 0.4641 0.000 0.340 0.660
#> GSM1178999 2 0.0000 0.8853 0.000 1.000 0.000
#> GSM1179021 2 0.0000 0.8853 0.000 1.000 0.000
#> GSM1179025 2 0.0000 0.8853 0.000 1.000 0.000
#> GSM1179027 3 0.5968 0.4213 0.000 0.364 0.636
#> GSM1179011 3 0.8043 0.6187 0.128 0.228 0.644
#> GSM1179023 1 0.0237 0.7947 0.996 0.000 0.004
#> GSM1179029 1 0.0424 0.7953 0.992 0.000 0.008
#> GSM1179034 1 0.0237 0.7947 0.996 0.000 0.004
#> GSM1179040 2 0.3551 0.7523 0.000 0.868 0.132
#> GSM1178988 2 0.4702 0.6871 0.000 0.788 0.212
#> GSM1179037 1 0.6062 0.5729 0.616 0.000 0.384
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1178971 1 0.5719 0.5801 0.716 0.000 0.132 0.152
#> GSM1178979 2 0.0000 0.9052 0.000 1.000 0.000 0.000
#> GSM1179009 4 0.1151 0.7458 0.024 0.000 0.008 0.968
#> GSM1179031 2 0.0000 0.9052 0.000 1.000 0.000 0.000
#> GSM1178970 2 0.0000 0.9052 0.000 1.000 0.000 0.000
#> GSM1178972 2 0.0000 0.9052 0.000 1.000 0.000 0.000
#> GSM1178973 4 0.4994 0.1468 0.480 0.000 0.000 0.520
#> GSM1178974 2 0.0000 0.9052 0.000 1.000 0.000 0.000
#> GSM1178977 2 0.1474 0.8750 0.000 0.948 0.000 0.052
#> GSM1178978 4 0.2706 0.7188 0.020 0.000 0.080 0.900
#> GSM1178998 1 0.1474 0.8425 0.948 0.000 0.052 0.000
#> GSM1179010 1 0.5587 0.3354 0.600 0.000 0.372 0.028
#> GSM1179018 4 0.4879 0.6588 0.000 0.092 0.128 0.780
#> GSM1179024 1 0.0188 0.8510 0.996 0.000 0.004 0.000
#> GSM1178984 1 0.5519 0.5401 0.684 0.000 0.264 0.052
#> GSM1178990 1 0.0469 0.8525 0.988 0.000 0.012 0.000
#> GSM1178991 4 0.4664 0.5957 0.248 0.004 0.012 0.736
#> GSM1178994 1 0.5999 0.1882 0.552 0.000 0.404 0.044
#> GSM1178997 2 0.8852 0.0229 0.332 0.436 0.108 0.124
#> GSM1179000 1 0.1767 0.8304 0.944 0.000 0.044 0.012
#> GSM1179013 1 0.0000 0.8520 1.000 0.000 0.000 0.000
#> GSM1179014 1 0.3583 0.7013 0.816 0.000 0.180 0.004
#> GSM1179019 1 0.1452 0.8372 0.956 0.000 0.036 0.008
#> GSM1179020 1 0.0657 0.8490 0.984 0.000 0.012 0.004
#> GSM1179022 1 0.0000 0.8520 1.000 0.000 0.000 0.000
#> GSM1179028 2 0.0000 0.9052 0.000 1.000 0.000 0.000
#> GSM1179032 1 0.0000 0.8520 1.000 0.000 0.000 0.000
#> GSM1179041 2 0.0000 0.9052 0.000 1.000 0.000 0.000
#> GSM1179042 2 0.0000 0.9052 0.000 1.000 0.000 0.000
#> GSM1178976 2 0.0188 0.9035 0.000 0.996 0.000 0.004
#> GSM1178981 3 0.6878 0.4529 0.316 0.000 0.556 0.128
#> GSM1178982 4 0.7381 0.1075 0.180 0.000 0.328 0.492
#> GSM1178983 4 0.4464 0.6847 0.060 0.004 0.124 0.812
#> GSM1178985 3 0.6434 0.6027 0.128 0.028 0.700 0.144
#> GSM1178992 3 0.4647 0.5793 0.288 0.000 0.704 0.008
#> GSM1179005 1 0.4319 0.6627 0.760 0.000 0.228 0.012
#> GSM1179007 1 0.3052 0.7837 0.860 0.000 0.136 0.004
#> GSM1179012 1 0.4290 0.6821 0.772 0.000 0.212 0.016
#> GSM1179016 3 0.6085 0.4300 0.356 0.040 0.596 0.008
#> GSM1179030 2 0.1209 0.8885 0.000 0.964 0.032 0.004
#> GSM1179038 1 0.2973 0.7866 0.856 0.000 0.144 0.000
#> GSM1178987 3 0.3958 0.6654 0.112 0.000 0.836 0.052
#> GSM1179003 2 0.0000 0.9052 0.000 1.000 0.000 0.000
#> GSM1179004 3 0.4227 0.6628 0.120 0.000 0.820 0.060
#> GSM1179039 2 0.0000 0.9052 0.000 1.000 0.000 0.000
#> GSM1178975 4 0.3052 0.7112 0.136 0.000 0.004 0.860
#> GSM1178980 4 0.4304 0.5457 0.000 0.284 0.000 0.716
#> GSM1178995 1 0.2704 0.7978 0.876 0.000 0.124 0.000
#> GSM1178996 3 0.6896 0.5399 0.196 0.116 0.656 0.032
#> GSM1179001 1 0.1151 0.8507 0.968 0.000 0.024 0.008
#> GSM1179002 1 0.1890 0.8459 0.936 0.000 0.056 0.008
#> GSM1179006 3 0.5457 0.4495 0.016 0.292 0.676 0.016
#> GSM1179008 1 0.0927 0.8513 0.976 0.000 0.016 0.008
#> GSM1179015 1 0.3052 0.7980 0.860 0.000 0.136 0.004
#> GSM1179017 2 0.2868 0.8029 0.000 0.864 0.136 0.000
#> GSM1179026 3 0.1767 0.6442 0.044 0.000 0.944 0.012
#> GSM1179033 3 0.6290 0.4656 0.016 0.256 0.660 0.068
#> GSM1179035 3 0.3653 0.6698 0.128 0.000 0.844 0.028
#> GSM1179036 3 0.6038 0.2482 0.424 0.000 0.532 0.044
#> GSM1178986 3 0.9205 0.2609 0.328 0.080 0.356 0.236
#> GSM1178989 2 0.3257 0.7777 0.000 0.844 0.152 0.004
#> GSM1178993 4 0.1302 0.7430 0.000 0.044 0.000 0.956
#> GSM1178999 2 0.1151 0.8928 0.000 0.968 0.008 0.024
#> GSM1179021 2 0.0921 0.8920 0.000 0.972 0.000 0.028
#> GSM1179025 2 0.0000 0.9052 0.000 1.000 0.000 0.000
#> GSM1179027 4 0.1637 0.7384 0.000 0.060 0.000 0.940
#> GSM1179011 4 0.1820 0.7490 0.036 0.020 0.000 0.944
#> GSM1179023 1 0.0000 0.8520 1.000 0.000 0.000 0.000
#> GSM1179029 1 0.1356 0.8490 0.960 0.000 0.032 0.008
#> GSM1179034 1 0.0000 0.8520 1.000 0.000 0.000 0.000
#> GSM1179040 2 0.4454 0.5153 0.000 0.692 0.000 0.308
#> GSM1178988 2 0.5329 0.2816 0.000 0.568 0.420 0.012
#> GSM1179037 3 0.1970 0.6567 0.060 0.000 0.932 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1178971 1 0.7446 0.3037 0.520 0.000 0.228 0.116 0.136
#> GSM1178979 2 0.0000 0.8747 0.000 1.000 0.000 0.000 0.000
#> GSM1179009 4 0.1768 0.6858 0.000 0.000 0.004 0.924 0.072
#> GSM1179031 2 0.0000 0.8747 0.000 1.000 0.000 0.000 0.000
#> GSM1178970 2 0.0000 0.8747 0.000 1.000 0.000 0.000 0.000
#> GSM1178972 2 0.0000 0.8747 0.000 1.000 0.000 0.000 0.000
#> GSM1178973 4 0.5180 0.0330 0.476 0.000 0.020 0.492 0.012
#> GSM1178974 2 0.0000 0.8747 0.000 1.000 0.000 0.000 0.000
#> GSM1178977 2 0.1864 0.8322 0.000 0.924 0.004 0.068 0.004
#> GSM1178978 4 0.5185 0.4072 0.004 0.000 0.040 0.580 0.376
#> GSM1178998 1 0.3883 0.7211 0.780 0.000 0.036 0.000 0.184
#> GSM1179010 5 0.5276 0.0862 0.436 0.000 0.048 0.000 0.516
#> GSM1179018 4 0.6455 0.5275 0.000 0.084 0.124 0.640 0.152
#> GSM1179024 1 0.0404 0.8156 0.988 0.000 0.012 0.000 0.000
#> GSM1178984 1 0.5224 0.1788 0.532 0.000 0.036 0.004 0.428
#> GSM1178990 1 0.1357 0.8135 0.948 0.000 0.004 0.000 0.048
#> GSM1178991 4 0.6054 0.4758 0.224 0.000 0.080 0.644 0.052
#> GSM1178994 5 0.4996 0.1814 0.420 0.000 0.032 0.000 0.548
#> GSM1178997 2 0.9094 -0.2983 0.256 0.312 0.252 0.140 0.040
#> GSM1179000 1 0.2420 0.7835 0.896 0.000 0.088 0.008 0.008
#> GSM1179013 1 0.0000 0.8155 1.000 0.000 0.000 0.000 0.000
#> GSM1179014 1 0.4638 0.4445 0.648 0.000 0.324 0.000 0.028
#> GSM1179019 1 0.1768 0.8048 0.924 0.000 0.072 0.000 0.004
#> GSM1179020 1 0.0703 0.8153 0.976 0.000 0.024 0.000 0.000
#> GSM1179022 1 0.0162 0.8158 0.996 0.000 0.004 0.000 0.000
#> GSM1179028 2 0.0000 0.8747 0.000 1.000 0.000 0.000 0.000
#> GSM1179032 1 0.0162 0.8158 0.996 0.000 0.004 0.000 0.000
#> GSM1179041 2 0.0000 0.8747 0.000 1.000 0.000 0.000 0.000
#> GSM1179042 2 0.0000 0.8747 0.000 1.000 0.000 0.000 0.000
#> GSM1178976 2 0.0162 0.8732 0.000 0.996 0.004 0.000 0.000
#> GSM1178981 5 0.3981 0.5130 0.120 0.000 0.032 0.032 0.816
#> GSM1178982 5 0.6987 0.3350 0.120 0.000 0.092 0.216 0.572
#> GSM1178983 4 0.6911 0.4135 0.064 0.008 0.088 0.556 0.284
#> GSM1178985 5 0.4914 0.4287 0.036 0.004 0.144 0.056 0.760
#> GSM1178992 3 0.6642 0.0613 0.232 0.000 0.428 0.000 0.340
#> GSM1179005 1 0.5120 0.6215 0.700 0.000 0.104 0.004 0.192
#> GSM1179007 1 0.3868 0.7423 0.800 0.000 0.060 0.000 0.140
#> GSM1179012 1 0.4527 0.5814 0.692 0.000 0.036 0.000 0.272
#> GSM1179016 3 0.5361 0.4140 0.188 0.016 0.696 0.000 0.100
#> GSM1179030 2 0.3427 0.7751 0.000 0.848 0.104 0.016 0.032
#> GSM1179038 1 0.4949 0.6716 0.728 0.000 0.164 0.008 0.100
#> GSM1178987 5 0.3018 0.5119 0.036 0.000 0.084 0.008 0.872
#> GSM1179003 2 0.0404 0.8701 0.000 0.988 0.012 0.000 0.000
#> GSM1179004 5 0.2632 0.5128 0.032 0.000 0.072 0.004 0.892
#> GSM1179039 2 0.0000 0.8747 0.000 1.000 0.000 0.000 0.000
#> GSM1178975 4 0.4036 0.6238 0.132 0.000 0.052 0.804 0.012
#> GSM1178980 4 0.3353 0.5479 0.000 0.196 0.008 0.796 0.000
#> GSM1178995 1 0.3946 0.7538 0.800 0.000 0.080 0.000 0.120
#> GSM1178996 3 0.5383 0.4316 0.072 0.044 0.728 0.004 0.152
#> GSM1179001 1 0.3476 0.7835 0.836 0.000 0.088 0.000 0.076
#> GSM1179002 1 0.4307 0.7478 0.772 0.000 0.100 0.000 0.128
#> GSM1179006 3 0.5891 0.4187 0.000 0.216 0.616 0.004 0.164
#> GSM1179008 1 0.2376 0.8073 0.904 0.000 0.044 0.000 0.052
#> GSM1179015 1 0.3354 0.7804 0.844 0.000 0.068 0.000 0.088
#> GSM1179017 2 0.4354 0.3900 0.000 0.624 0.368 0.000 0.008
#> GSM1179026 3 0.4536 0.2951 0.016 0.004 0.656 0.000 0.324
#> GSM1179033 3 0.7392 0.2903 0.000 0.192 0.436 0.048 0.324
#> GSM1179035 5 0.4788 0.3756 0.064 0.000 0.240 0.000 0.696
#> GSM1179036 3 0.7407 0.2270 0.264 0.000 0.480 0.060 0.196
#> GSM1178986 3 0.8449 0.1898 0.240 0.012 0.412 0.176 0.160
#> GSM1178989 2 0.3906 0.7003 0.000 0.800 0.132 0.000 0.068
#> GSM1178993 4 0.0162 0.6944 0.000 0.000 0.000 0.996 0.004
#> GSM1178999 2 0.2514 0.8229 0.000 0.896 0.044 0.060 0.000
#> GSM1179021 2 0.1908 0.8202 0.000 0.908 0.000 0.092 0.000
#> GSM1179025 2 0.0000 0.8747 0.000 1.000 0.000 0.000 0.000
#> GSM1179027 4 0.0324 0.6945 0.000 0.004 0.000 0.992 0.004
#> GSM1179011 4 0.0162 0.6939 0.000 0.000 0.004 0.996 0.000
#> GSM1179023 1 0.0290 0.8159 0.992 0.000 0.008 0.000 0.000
#> GSM1179029 1 0.2754 0.7947 0.880 0.000 0.080 0.000 0.040
#> GSM1179034 1 0.0000 0.8155 1.000 0.000 0.000 0.000 0.000
#> GSM1179040 2 0.4182 0.3544 0.000 0.600 0.000 0.400 0.000
#> GSM1178988 3 0.6481 0.1947 0.000 0.408 0.408 0.000 0.184
#> GSM1179037 5 0.4341 0.1256 0.008 0.000 0.364 0.000 0.628
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1178971 1 0.7322 0.0631 0.420 0.000 0.104 0.060 0.352 0.064
#> GSM1178979 2 0.0000 0.8527 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179009 4 0.3252 0.6311 0.020 0.000 0.012 0.856 0.040 0.072
#> GSM1179031 2 0.0000 0.8527 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178970 2 0.0508 0.8479 0.000 0.984 0.004 0.000 0.012 0.000
#> GSM1178972 2 0.0146 0.8514 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM1178973 1 0.5764 0.1926 0.504 0.000 0.004 0.360 0.124 0.008
#> GSM1178974 2 0.0000 0.8527 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178977 2 0.2776 0.7533 0.000 0.860 0.004 0.104 0.032 0.000
#> GSM1178978 4 0.6805 0.1992 0.032 0.008 0.012 0.428 0.152 0.368
#> GSM1178998 1 0.4239 0.5998 0.736 0.000 0.012 0.000 0.056 0.196
#> GSM1179010 6 0.5191 -0.0837 0.448 0.000 0.032 0.000 0.032 0.488
#> GSM1179018 4 0.6382 0.4929 0.000 0.052 0.068 0.628 0.096 0.156
#> GSM1179024 1 0.1232 0.6775 0.956 0.000 0.016 0.000 0.024 0.004
#> GSM1178984 1 0.5358 0.1601 0.504 0.000 0.012 0.000 0.076 0.408
#> GSM1178990 1 0.2318 0.6868 0.904 0.000 0.020 0.000 0.048 0.028
#> GSM1178991 4 0.7278 0.1030 0.304 0.000 0.048 0.448 0.148 0.052
#> GSM1178994 6 0.5149 0.1513 0.388 0.000 0.020 0.000 0.048 0.544
#> GSM1178997 5 0.8725 0.0000 0.204 0.244 0.152 0.052 0.324 0.024
#> GSM1179000 1 0.4947 0.4997 0.716 0.000 0.096 0.016 0.156 0.016
#> GSM1179013 1 0.0622 0.6806 0.980 0.000 0.008 0.000 0.012 0.000
#> GSM1179014 1 0.6578 -0.1023 0.444 0.000 0.340 0.012 0.180 0.024
#> GSM1179019 1 0.3434 0.6100 0.820 0.000 0.032 0.004 0.132 0.012
#> GSM1179020 1 0.1682 0.6776 0.928 0.000 0.020 0.000 0.052 0.000
#> GSM1179022 1 0.0146 0.6810 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM1179028 2 0.0000 0.8527 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179032 1 0.0000 0.6814 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179041 2 0.0000 0.8527 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179042 2 0.0000 0.8527 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178976 2 0.1003 0.8374 0.000 0.964 0.016 0.000 0.020 0.000
#> GSM1178981 6 0.4143 0.4953 0.124 0.000 0.004 0.020 0.072 0.780
#> GSM1178982 6 0.7760 0.2610 0.132 0.004 0.048 0.180 0.160 0.476
#> GSM1178983 4 0.7799 0.2409 0.076 0.004 0.040 0.396 0.216 0.268
#> GSM1178985 6 0.5537 0.3638 0.020 0.008 0.084 0.032 0.168 0.688
#> GSM1178992 3 0.7187 0.1033 0.204 0.000 0.428 0.000 0.120 0.248
#> GSM1179005 1 0.5995 0.4404 0.592 0.000 0.056 0.000 0.136 0.216
#> GSM1179007 1 0.4453 0.6145 0.744 0.000 0.024 0.000 0.080 0.152
#> GSM1179012 1 0.5225 0.4237 0.612 0.000 0.040 0.000 0.048 0.300
#> GSM1179016 3 0.4451 0.2799 0.092 0.000 0.748 0.000 0.136 0.024
#> GSM1179030 2 0.5065 0.5934 0.000 0.732 0.124 0.024 0.080 0.040
#> GSM1179038 1 0.6472 0.4750 0.572 0.000 0.172 0.008 0.172 0.076
#> GSM1178987 6 0.3406 0.4683 0.012 0.000 0.072 0.004 0.076 0.836
#> GSM1179003 2 0.0717 0.8440 0.000 0.976 0.016 0.000 0.008 0.000
#> GSM1179004 6 0.2419 0.4860 0.016 0.000 0.060 0.000 0.028 0.896
#> GSM1179039 2 0.0000 0.8527 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178975 4 0.4891 0.4726 0.108 0.000 0.012 0.696 0.180 0.004
#> GSM1178980 4 0.3430 0.4413 0.000 0.208 0.004 0.772 0.016 0.000
#> GSM1178995 1 0.5446 0.5622 0.652 0.000 0.020 0.008 0.192 0.128
#> GSM1178996 3 0.5734 0.3048 0.024 0.020 0.596 0.004 0.296 0.060
#> GSM1179001 1 0.5409 0.5351 0.624 0.000 0.040 0.000 0.260 0.076
#> GSM1179002 1 0.6031 0.4804 0.564 0.000 0.044 0.000 0.256 0.136
#> GSM1179006 3 0.6905 0.3191 0.008 0.112 0.560 0.012 0.144 0.164
#> GSM1179008 1 0.4498 0.6276 0.736 0.000 0.012 0.008 0.176 0.068
#> GSM1179015 1 0.5235 0.5993 0.692 0.000 0.120 0.000 0.056 0.132
#> GSM1179017 2 0.4697 0.1268 0.000 0.548 0.404 0.000 0.048 0.000
#> GSM1179026 3 0.4327 0.3818 0.008 0.004 0.732 0.004 0.044 0.208
#> GSM1179033 3 0.8272 0.2274 0.012 0.116 0.336 0.036 0.252 0.248
#> GSM1179035 6 0.5309 0.3295 0.044 0.000 0.268 0.000 0.060 0.628
#> GSM1179036 3 0.7669 0.2279 0.128 0.000 0.428 0.060 0.292 0.092
#> GSM1178986 3 0.8201 0.0217 0.172 0.024 0.440 0.068 0.216 0.080
#> GSM1178989 2 0.4992 0.5142 0.000 0.696 0.184 0.000 0.080 0.040
#> GSM1178993 4 0.0520 0.6499 0.000 0.008 0.000 0.984 0.008 0.000
#> GSM1178999 2 0.3413 0.7336 0.000 0.828 0.052 0.104 0.016 0.000
#> GSM1179021 2 0.2558 0.7224 0.000 0.840 0.000 0.156 0.004 0.000
#> GSM1179025 2 0.0000 0.8527 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179027 4 0.0622 0.6491 0.000 0.012 0.000 0.980 0.008 0.000
#> GSM1179011 4 0.0363 0.6480 0.000 0.000 0.000 0.988 0.012 0.000
#> GSM1179023 1 0.0260 0.6813 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM1179029 1 0.4914 0.6156 0.716 0.000 0.112 0.000 0.132 0.040
#> GSM1179034 1 0.0146 0.6821 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM1179040 2 0.4161 0.1813 0.000 0.540 0.000 0.448 0.012 0.000
#> GSM1178988 3 0.7072 -0.0264 0.000 0.352 0.380 0.000 0.104 0.164
#> GSM1179037 6 0.5743 0.0505 0.024 0.000 0.372 0.004 0.084 0.516
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) protocol(p) k
#> CV:skmeans 72 0.0509 0.458 2
#> CV:skmeans 59 0.1319 0.560 3
#> CV:skmeans 61 0.0887 0.266 4
#> CV:skmeans 48 0.1068 0.164 5
#> CV:skmeans 37 0.1603 0.148 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 31632 rows and 73 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.757 0.833 0.935 0.3241 0.703 0.703
#> 3 3 0.555 0.788 0.890 0.6767 0.635 0.524
#> 4 4 0.549 0.371 0.661 0.1780 0.769 0.520
#> 5 5 0.632 0.753 0.851 0.1641 0.747 0.337
#> 6 6 0.644 0.609 0.798 0.0496 0.949 0.802
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM1178971 1 0.0000 0.93097 1.000 0.000
#> GSM1178979 2 0.6887 0.74173 0.184 0.816
#> GSM1179009 1 0.0376 0.92836 0.996 0.004
#> GSM1179031 2 0.0000 0.88091 0.000 1.000
#> GSM1178970 2 0.8813 0.57948 0.300 0.700
#> GSM1178972 2 0.0000 0.88091 0.000 1.000
#> GSM1178973 1 0.0000 0.93097 1.000 0.000
#> GSM1178974 2 0.0000 0.88091 0.000 1.000
#> GSM1178977 1 0.9686 0.32600 0.604 0.396
#> GSM1178978 1 0.0376 0.92837 0.996 0.004
#> GSM1178998 1 0.0000 0.93097 1.000 0.000
#> GSM1179010 1 0.0000 0.93097 1.000 0.000
#> GSM1179018 1 0.7674 0.68141 0.776 0.224
#> GSM1179024 1 0.0000 0.93097 1.000 0.000
#> GSM1178984 1 0.0000 0.93097 1.000 0.000
#> GSM1178990 1 0.0000 0.93097 1.000 0.000
#> GSM1178991 1 0.0376 0.92829 0.996 0.004
#> GSM1178994 1 0.0000 0.93097 1.000 0.000
#> GSM1178997 1 0.0000 0.93097 1.000 0.000
#> GSM1179000 1 0.0000 0.93097 1.000 0.000
#> GSM1179013 1 0.0000 0.93097 1.000 0.000
#> GSM1179014 1 0.0000 0.93097 1.000 0.000
#> GSM1179019 1 0.0000 0.93097 1.000 0.000
#> GSM1179020 1 0.0000 0.93097 1.000 0.000
#> GSM1179022 1 0.0000 0.93097 1.000 0.000
#> GSM1179028 2 0.0000 0.88091 0.000 1.000
#> GSM1179032 1 0.0000 0.93097 1.000 0.000
#> GSM1179041 2 0.0000 0.88091 0.000 1.000
#> GSM1179042 2 0.0000 0.88091 0.000 1.000
#> GSM1178976 2 0.9998 0.00802 0.492 0.508
#> GSM1178981 1 0.0000 0.93097 1.000 0.000
#> GSM1178982 1 0.0000 0.93097 1.000 0.000
#> GSM1178983 1 0.0000 0.93097 1.000 0.000
#> GSM1178985 1 0.0000 0.93097 1.000 0.000
#> GSM1178992 1 0.0000 0.93097 1.000 0.000
#> GSM1179005 1 0.0000 0.93097 1.000 0.000
#> GSM1179007 1 0.0000 0.93097 1.000 0.000
#> GSM1179012 1 0.0000 0.93097 1.000 0.000
#> GSM1179016 1 0.3733 0.86984 0.928 0.072
#> GSM1179030 1 0.8499 0.59605 0.724 0.276
#> GSM1179038 1 0.0000 0.93097 1.000 0.000
#> GSM1178987 1 0.0000 0.93097 1.000 0.000
#> GSM1179003 2 0.8499 0.62191 0.276 0.724
#> GSM1179004 1 0.0000 0.93097 1.000 0.000
#> GSM1179039 2 0.0000 0.88091 0.000 1.000
#> GSM1178975 1 0.0000 0.93097 1.000 0.000
#> GSM1178980 1 0.9580 0.36913 0.620 0.380
#> GSM1178995 1 0.0000 0.93097 1.000 0.000
#> GSM1178996 1 0.0000 0.93097 1.000 0.000
#> GSM1179001 1 0.0000 0.93097 1.000 0.000
#> GSM1179002 1 0.0000 0.93097 1.000 0.000
#> GSM1179006 1 0.0376 0.92836 0.996 0.004
#> GSM1179008 1 0.0000 0.93097 1.000 0.000
#> GSM1179015 1 0.0000 0.93097 1.000 0.000
#> GSM1179017 1 0.9815 0.25456 0.580 0.420
#> GSM1179026 1 0.0000 0.93097 1.000 0.000
#> GSM1179033 1 0.0000 0.93097 1.000 0.000
#> GSM1179035 1 0.0000 0.93097 1.000 0.000
#> GSM1179036 1 0.0000 0.93097 1.000 0.000
#> GSM1178986 1 0.0000 0.93097 1.000 0.000
#> GSM1178989 1 0.9552 0.37822 0.624 0.376
#> GSM1178993 1 0.4298 0.85467 0.912 0.088
#> GSM1178999 1 0.9795 0.26718 0.584 0.416
#> GSM1179021 2 0.0000 0.88091 0.000 1.000
#> GSM1179025 2 0.0000 0.88091 0.000 1.000
#> GSM1179027 1 0.4562 0.84649 0.904 0.096
#> GSM1179011 1 0.1184 0.91914 0.984 0.016
#> GSM1179023 1 0.0000 0.93097 1.000 0.000
#> GSM1179029 1 0.0000 0.93097 1.000 0.000
#> GSM1179034 1 0.0000 0.93097 1.000 0.000
#> GSM1179040 1 0.9881 0.20235 0.564 0.436
#> GSM1178988 1 0.8555 0.58791 0.720 0.280
#> GSM1179037 1 0.0000 0.93097 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1178971 3 0.4235 0.814 0.176 0.000 0.824
#> GSM1178979 3 0.5216 0.614 0.000 0.260 0.740
#> GSM1179009 3 0.5810 0.655 0.336 0.000 0.664
#> GSM1179031 2 0.0000 0.999 0.000 1.000 0.000
#> GSM1178970 3 0.0000 0.836 0.000 0.000 1.000
#> GSM1178972 2 0.0237 0.996 0.000 0.996 0.004
#> GSM1178973 1 0.0000 0.863 1.000 0.000 0.000
#> GSM1178974 2 0.0000 0.999 0.000 1.000 0.000
#> GSM1178977 3 0.0000 0.836 0.000 0.000 1.000
#> GSM1178978 3 0.4121 0.799 0.168 0.000 0.832
#> GSM1178998 1 0.0000 0.863 1.000 0.000 0.000
#> GSM1179010 1 0.6274 -0.163 0.544 0.000 0.456
#> GSM1179018 3 0.0000 0.836 0.000 0.000 1.000
#> GSM1179024 1 0.0000 0.863 1.000 0.000 0.000
#> GSM1178984 3 0.5835 0.650 0.340 0.000 0.660
#> GSM1178990 1 0.0000 0.863 1.000 0.000 0.000
#> GSM1178991 1 0.5968 0.390 0.636 0.000 0.364
#> GSM1178994 3 0.5835 0.650 0.340 0.000 0.660
#> GSM1178997 3 0.1964 0.846 0.056 0.000 0.944
#> GSM1179000 1 0.6111 0.173 0.604 0.000 0.396
#> GSM1179013 1 0.0000 0.863 1.000 0.000 0.000
#> GSM1179014 3 0.6235 0.357 0.436 0.000 0.564
#> GSM1179019 1 0.4974 0.604 0.764 0.000 0.236
#> GSM1179020 1 0.0000 0.863 1.000 0.000 0.000
#> GSM1179022 1 0.0000 0.863 1.000 0.000 0.000
#> GSM1179028 2 0.0000 0.999 0.000 1.000 0.000
#> GSM1179032 1 0.0000 0.863 1.000 0.000 0.000
#> GSM1179041 2 0.0000 0.999 0.000 1.000 0.000
#> GSM1179042 2 0.0000 0.999 0.000 1.000 0.000
#> GSM1178976 3 0.0000 0.836 0.000 0.000 1.000
#> GSM1178981 3 0.5810 0.655 0.336 0.000 0.664
#> GSM1178982 3 0.3619 0.833 0.136 0.000 0.864
#> GSM1178983 3 0.0592 0.840 0.012 0.000 0.988
#> GSM1178985 3 0.2165 0.845 0.064 0.000 0.936
#> GSM1178992 3 0.4654 0.790 0.208 0.000 0.792
#> GSM1179005 3 0.5465 0.714 0.288 0.000 0.712
#> GSM1179007 3 0.5835 0.650 0.340 0.000 0.660
#> GSM1179012 1 0.0000 0.863 1.000 0.000 0.000
#> GSM1179016 3 0.0424 0.839 0.008 0.000 0.992
#> GSM1179030 3 0.0424 0.839 0.008 0.000 0.992
#> GSM1179038 3 0.4750 0.784 0.216 0.000 0.784
#> GSM1178987 3 0.5529 0.702 0.296 0.000 0.704
#> GSM1179003 3 0.1529 0.831 0.000 0.040 0.960
#> GSM1179004 3 0.3551 0.833 0.132 0.000 0.868
#> GSM1179039 2 0.0000 0.999 0.000 1.000 0.000
#> GSM1178975 3 0.4062 0.820 0.164 0.000 0.836
#> GSM1178980 3 0.0000 0.836 0.000 0.000 1.000
#> GSM1178995 3 0.5810 0.655 0.336 0.000 0.664
#> GSM1178996 3 0.1411 0.845 0.036 0.000 0.964
#> GSM1179001 1 0.3551 0.758 0.868 0.000 0.132
#> GSM1179002 3 0.5810 0.655 0.336 0.000 0.664
#> GSM1179006 3 0.1529 0.845 0.040 0.000 0.960
#> GSM1179008 3 0.6295 0.349 0.472 0.000 0.528
#> GSM1179015 1 0.0000 0.863 1.000 0.000 0.000
#> GSM1179017 3 0.0424 0.835 0.000 0.008 0.992
#> GSM1179026 3 0.2066 0.846 0.060 0.000 0.940
#> GSM1179033 3 0.2878 0.841 0.096 0.000 0.904
#> GSM1179035 3 0.3412 0.836 0.124 0.000 0.876
#> GSM1179036 3 0.3038 0.839 0.104 0.000 0.896
#> GSM1178986 3 0.0424 0.839 0.008 0.000 0.992
#> GSM1178989 3 0.0237 0.838 0.004 0.000 0.996
#> GSM1178993 3 0.0747 0.842 0.016 0.000 0.984
#> GSM1178999 3 0.0000 0.836 0.000 0.000 1.000
#> GSM1179021 2 0.0424 0.993 0.000 0.992 0.008
#> GSM1179025 2 0.0000 0.999 0.000 1.000 0.000
#> GSM1179027 3 0.2878 0.840 0.096 0.000 0.904
#> GSM1179011 3 0.4399 0.793 0.188 0.000 0.812
#> GSM1179023 1 0.0000 0.863 1.000 0.000 0.000
#> GSM1179029 1 0.0000 0.863 1.000 0.000 0.000
#> GSM1179034 1 0.0000 0.863 1.000 0.000 0.000
#> GSM1179040 3 0.0237 0.836 0.000 0.004 0.996
#> GSM1178988 3 0.0424 0.839 0.008 0.000 0.992
#> GSM1179037 3 0.3941 0.824 0.156 0.000 0.844
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1178971 3 0.7472 0.49735 0.176 0.000 0.428 0.396
#> GSM1178979 4 0.3123 0.01506 0.000 0.156 0.000 0.844
#> GSM1179009 3 0.4669 -0.05892 0.104 0.000 0.796 0.100
#> GSM1179031 2 0.0000 0.94848 0.000 1.000 0.000 0.000
#> GSM1178970 4 0.4933 0.00943 0.000 0.000 0.432 0.568
#> GSM1178972 2 0.0000 0.94848 0.000 1.000 0.000 0.000
#> GSM1178973 1 0.1118 0.81812 0.964 0.000 0.036 0.000
#> GSM1178974 2 0.0000 0.94848 0.000 1.000 0.000 0.000
#> GSM1178977 4 0.4817 -0.01325 0.000 0.000 0.388 0.612
#> GSM1178978 3 0.5486 0.10289 0.080 0.000 0.720 0.200
#> GSM1178998 1 0.0000 0.82523 1.000 0.000 0.000 0.000
#> GSM1179010 1 0.7165 -0.26296 0.488 0.000 0.372 0.140
#> GSM1179018 4 0.4998 0.02098 0.000 0.000 0.488 0.512
#> GSM1179024 1 0.0469 0.81851 0.988 0.000 0.012 0.000
#> GSM1178984 3 0.7830 0.51974 0.272 0.000 0.404 0.324
#> GSM1178990 1 0.1118 0.81812 0.964 0.000 0.036 0.000
#> GSM1178991 3 0.5138 -0.39234 0.392 0.000 0.600 0.008
#> GSM1178994 3 0.7830 0.51976 0.272 0.000 0.404 0.324
#> GSM1178997 4 0.5780 -0.10252 0.028 0.000 0.476 0.496
#> GSM1179000 1 0.7241 0.01169 0.540 0.000 0.196 0.264
#> GSM1179013 1 0.0000 0.82523 1.000 0.000 0.000 0.000
#> GSM1179014 4 0.7844 -0.34716 0.368 0.000 0.264 0.368
#> GSM1179019 1 0.5646 0.48877 0.708 0.000 0.088 0.204
#> GSM1179020 1 0.1118 0.81812 0.964 0.000 0.036 0.000
#> GSM1179022 1 0.0000 0.82523 1.000 0.000 0.000 0.000
#> GSM1179028 2 0.0000 0.94848 0.000 1.000 0.000 0.000
#> GSM1179032 1 0.0000 0.82523 1.000 0.000 0.000 0.000
#> GSM1179041 2 0.0000 0.94848 0.000 1.000 0.000 0.000
#> GSM1179042 2 0.0000 0.94848 0.000 1.000 0.000 0.000
#> GSM1178976 4 0.4996 0.02842 0.000 0.000 0.484 0.516
#> GSM1178981 3 0.7786 0.52268 0.256 0.000 0.416 0.328
#> GSM1178982 3 0.7113 0.42455 0.128 0.000 0.456 0.416
#> GSM1178983 4 0.4998 0.02706 0.000 0.000 0.488 0.512
#> GSM1178985 3 0.6557 0.25979 0.076 0.000 0.476 0.448
#> GSM1178992 3 0.7646 0.51556 0.208 0.000 0.408 0.384
#> GSM1179005 3 0.7706 0.52767 0.228 0.000 0.424 0.348
#> GSM1179007 3 0.7824 0.52293 0.268 0.000 0.404 0.328
#> GSM1179012 1 0.0188 0.82374 0.996 0.000 0.004 0.000
#> GSM1179016 4 0.4998 0.02706 0.000 0.000 0.488 0.512
#> GSM1179030 4 0.4998 0.02706 0.000 0.000 0.488 0.512
#> GSM1179038 3 0.7663 0.51749 0.212 0.000 0.408 0.380
#> GSM1178987 3 0.7728 0.52162 0.232 0.000 0.416 0.352
#> GSM1179003 4 0.5894 -0.02640 0.000 0.036 0.428 0.536
#> GSM1179004 3 0.7210 0.45027 0.140 0.000 0.456 0.404
#> GSM1179039 2 0.0000 0.94848 0.000 1.000 0.000 0.000
#> GSM1178975 3 0.7297 0.47605 0.152 0.000 0.456 0.392
#> GSM1178980 4 0.4992 -0.19283 0.000 0.000 0.476 0.524
#> GSM1178995 3 0.7824 0.52293 0.268 0.000 0.404 0.328
#> GSM1178996 4 0.6009 -0.13654 0.040 0.000 0.468 0.492
#> GSM1179001 1 0.4055 0.69782 0.832 0.000 0.060 0.108
#> GSM1179002 3 0.7824 0.52293 0.268 0.000 0.404 0.328
#> GSM1179006 3 0.6081 0.11567 0.044 0.000 0.484 0.472
#> GSM1179008 1 0.7806 -0.47670 0.408 0.000 0.332 0.260
#> GSM1179015 1 0.0592 0.82443 0.984 0.000 0.016 0.000
#> GSM1179017 4 0.5288 0.01964 0.000 0.008 0.472 0.520
#> GSM1179026 3 0.6504 0.24138 0.072 0.000 0.476 0.452
#> GSM1179033 3 0.7040 0.39722 0.120 0.000 0.460 0.420
#> GSM1179035 3 0.7107 0.42541 0.128 0.000 0.464 0.408
#> GSM1179036 3 0.7107 0.41775 0.128 0.000 0.464 0.408
#> GSM1178986 4 0.4998 0.02706 0.000 0.000 0.488 0.512
#> GSM1178989 4 0.4998 0.02706 0.000 0.000 0.488 0.512
#> GSM1178993 4 0.4992 -0.19283 0.000 0.000 0.476 0.524
#> GSM1178999 4 0.0336 0.11396 0.000 0.000 0.008 0.992
#> GSM1179021 2 0.5697 0.55393 0.000 0.488 0.024 0.488
#> GSM1179025 2 0.0000 0.94848 0.000 1.000 0.000 0.000
#> GSM1179027 4 0.4992 -0.19283 0.000 0.000 0.476 0.524
#> GSM1179011 3 0.5000 -0.33918 0.000 0.000 0.504 0.496
#> GSM1179023 1 0.0000 0.82523 1.000 0.000 0.000 0.000
#> GSM1179029 1 0.0592 0.82316 0.984 0.000 0.016 0.000
#> GSM1179034 1 0.0000 0.82523 1.000 0.000 0.000 0.000
#> GSM1179040 4 0.4830 -0.12270 0.000 0.000 0.392 0.608
#> GSM1178988 4 0.4998 0.02706 0.000 0.000 0.488 0.512
#> GSM1179037 3 0.7396 0.47919 0.164 0.000 0.432 0.404
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1178971 3 0.3895 0.6390 0.320 0.000 0.680 0.000 0.000
#> GSM1178979 4 0.6775 0.5969 0.008 0.096 0.248 0.588 0.060
#> GSM1179009 1 0.5268 0.4490 0.588 0.000 0.048 0.360 0.004
#> GSM1179031 2 0.0000 0.9917 0.000 1.000 0.000 0.000 0.000
#> GSM1178970 3 0.2989 0.7979 0.016 0.000 0.880 0.036 0.068
#> GSM1178972 2 0.1341 0.9398 0.000 0.944 0.000 0.000 0.056
#> GSM1178973 1 0.1965 0.6948 0.904 0.000 0.000 0.000 0.096
#> GSM1178974 2 0.0000 0.9917 0.000 1.000 0.000 0.000 0.000
#> GSM1178977 3 0.3745 0.7394 0.008 0.000 0.828 0.096 0.068
#> GSM1178978 1 0.6664 0.3698 0.468 0.000 0.356 0.164 0.012
#> GSM1178998 5 0.2230 0.9461 0.116 0.000 0.000 0.000 0.884
#> GSM1179010 1 0.1444 0.7258 0.948 0.000 0.012 0.000 0.040
#> GSM1179018 3 0.1412 0.8639 0.036 0.000 0.952 0.004 0.008
#> GSM1179024 5 0.2248 0.9400 0.088 0.000 0.012 0.000 0.900
#> GSM1178984 1 0.0963 0.7441 0.964 0.000 0.036 0.000 0.000
#> GSM1178990 1 0.1908 0.6966 0.908 0.000 0.000 0.000 0.092
#> GSM1178991 1 0.6093 0.4048 0.564 0.000 0.080 0.332 0.024
#> GSM1178994 1 0.0963 0.7441 0.964 0.000 0.036 0.000 0.000
#> GSM1178997 3 0.2179 0.8177 0.112 0.000 0.888 0.000 0.000
#> GSM1179000 1 0.3019 0.7387 0.864 0.000 0.088 0.000 0.048
#> GSM1179013 5 0.2074 0.9496 0.104 0.000 0.000 0.000 0.896
#> GSM1179014 1 0.3455 0.6836 0.784 0.000 0.208 0.000 0.008
#> GSM1179019 1 0.1981 0.7307 0.924 0.000 0.028 0.000 0.048
#> GSM1179020 1 0.4287 -0.0913 0.540 0.000 0.000 0.000 0.460
#> GSM1179022 5 0.2020 0.9501 0.100 0.000 0.000 0.000 0.900
#> GSM1179028 2 0.0000 0.9917 0.000 1.000 0.000 0.000 0.000
#> GSM1179032 5 0.2020 0.9501 0.100 0.000 0.000 0.000 0.900
#> GSM1179041 2 0.0000 0.9917 0.000 1.000 0.000 0.000 0.000
#> GSM1179042 2 0.0000 0.9917 0.000 1.000 0.000 0.000 0.000
#> GSM1178976 3 0.1329 0.8640 0.032 0.000 0.956 0.004 0.008
#> GSM1178981 1 0.4067 0.5036 0.692 0.000 0.300 0.000 0.008
#> GSM1178982 3 0.3318 0.8231 0.192 0.000 0.800 0.000 0.008
#> GSM1178983 3 0.0798 0.8562 0.016 0.000 0.976 0.000 0.008
#> GSM1178985 3 0.2674 0.8494 0.140 0.000 0.856 0.000 0.004
#> GSM1178992 3 0.3730 0.7043 0.288 0.000 0.712 0.000 0.000
#> GSM1179005 1 0.3305 0.6648 0.776 0.000 0.224 0.000 0.000
#> GSM1179007 1 0.1671 0.7470 0.924 0.000 0.076 0.000 0.000
#> GSM1179012 5 0.2439 0.9225 0.120 0.000 0.004 0.000 0.876
#> GSM1179016 3 0.0451 0.8497 0.008 0.000 0.988 0.000 0.004
#> GSM1179030 3 0.0404 0.8477 0.012 0.000 0.988 0.000 0.000
#> GSM1179038 1 0.4256 0.1419 0.564 0.000 0.436 0.000 0.000
#> GSM1178987 1 0.4464 0.3506 0.584 0.000 0.408 0.000 0.008
#> GSM1179003 3 0.3949 0.7973 0.016 0.020 0.840 0.064 0.060
#> GSM1179004 3 0.3582 0.7994 0.224 0.000 0.768 0.000 0.008
#> GSM1179039 2 0.0000 0.9917 0.000 1.000 0.000 0.000 0.000
#> GSM1178975 1 0.4299 0.3575 0.608 0.000 0.388 0.000 0.004
#> GSM1178980 4 0.0000 0.7927 0.000 0.000 0.000 1.000 0.000
#> GSM1178995 1 0.1732 0.7465 0.920 0.000 0.080 0.000 0.000
#> GSM1178996 3 0.2377 0.8563 0.128 0.000 0.872 0.000 0.000
#> GSM1179001 1 0.1697 0.7200 0.932 0.000 0.008 0.000 0.060
#> GSM1179002 1 0.1671 0.7472 0.924 0.000 0.076 0.000 0.000
#> GSM1179006 3 0.2411 0.8578 0.108 0.000 0.884 0.000 0.008
#> GSM1179008 1 0.2450 0.7434 0.900 0.000 0.052 0.000 0.048
#> GSM1179015 1 0.4264 0.3011 0.620 0.000 0.004 0.000 0.376
#> GSM1179017 3 0.2150 0.8227 0.008 0.004 0.916 0.004 0.068
#> GSM1179026 3 0.2389 0.8589 0.116 0.000 0.880 0.000 0.004
#> GSM1179033 3 0.2929 0.8266 0.180 0.000 0.820 0.000 0.000
#> GSM1179035 3 0.3039 0.8187 0.192 0.000 0.808 0.000 0.000
#> GSM1179036 3 0.3123 0.8215 0.184 0.000 0.812 0.000 0.004
#> GSM1178986 3 0.0404 0.8573 0.012 0.000 0.988 0.000 0.000
#> GSM1178989 3 0.0609 0.8616 0.020 0.000 0.980 0.000 0.000
#> GSM1178993 4 0.0000 0.7927 0.000 0.000 0.000 1.000 0.000
#> GSM1178999 4 0.5548 0.5167 0.008 0.000 0.356 0.576 0.060
#> GSM1179021 4 0.4135 0.4490 0.000 0.340 0.000 0.656 0.004
#> GSM1179025 2 0.0000 0.9917 0.000 1.000 0.000 0.000 0.000
#> GSM1179027 4 0.0000 0.7927 0.000 0.000 0.000 1.000 0.000
#> GSM1179011 4 0.0000 0.7927 0.000 0.000 0.000 1.000 0.000
#> GSM1179023 5 0.2516 0.9223 0.140 0.000 0.000 0.000 0.860
#> GSM1179029 5 0.3942 0.7108 0.260 0.000 0.012 0.000 0.728
#> GSM1179034 5 0.2020 0.9501 0.100 0.000 0.000 0.000 0.900
#> GSM1179040 4 0.2647 0.7630 0.008 0.000 0.076 0.892 0.024
#> GSM1178988 3 0.1041 0.8637 0.032 0.000 0.964 0.000 0.004
#> GSM1179037 3 0.3424 0.7709 0.240 0.000 0.760 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1178971 3 0.3050 0.6341 0.000 0.000 0.764 0.000 0.000 0.236
#> GSM1178979 5 0.6073 0.3911 0.000 0.040 0.104 0.396 0.460 0.000
#> GSM1179009 6 0.4936 0.0828 0.000 0.000 0.052 0.464 0.004 0.480
#> GSM1179031 2 0.0000 0.9708 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178970 5 0.4875 0.0817 0.000 0.000 0.476 0.024 0.480 0.020
#> GSM1178972 2 0.2762 0.7722 0.000 0.804 0.000 0.000 0.196 0.000
#> GSM1178973 6 0.2092 0.6925 0.124 0.000 0.000 0.000 0.000 0.876
#> GSM1178974 2 0.0000 0.9708 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178977 3 0.4948 -0.3498 0.000 0.000 0.472 0.064 0.464 0.000
#> GSM1178978 6 0.7453 -0.1884 0.000 0.000 0.236 0.132 0.300 0.332
#> GSM1178998 1 0.1124 0.8981 0.956 0.000 0.000 0.000 0.008 0.036
#> GSM1179010 6 0.2859 0.6141 0.016 0.000 0.000 0.000 0.156 0.828
#> GSM1179018 3 0.1003 0.7218 0.000 0.000 0.964 0.000 0.020 0.016
#> GSM1179024 1 0.0363 0.9087 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM1178984 6 0.1387 0.7201 0.000 0.000 0.068 0.000 0.000 0.932
#> GSM1178990 6 0.2048 0.6943 0.120 0.000 0.000 0.000 0.000 0.880
#> GSM1178991 4 0.6634 -0.1177 0.004 0.000 0.072 0.408 0.112 0.404
#> GSM1178994 6 0.1779 0.7196 0.000 0.000 0.064 0.000 0.016 0.920
#> GSM1178997 3 0.4570 0.4138 0.000 0.000 0.668 0.000 0.252 0.080
#> GSM1179000 6 0.3410 0.7129 0.076 0.000 0.100 0.000 0.004 0.820
#> GSM1179013 1 0.0458 0.9079 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM1179014 6 0.5154 0.4453 0.008 0.000 0.108 0.000 0.260 0.624
#> GSM1179019 6 0.2436 0.7151 0.088 0.000 0.032 0.000 0.000 0.880
#> GSM1179020 6 0.3851 0.1361 0.460 0.000 0.000 0.000 0.000 0.540
#> GSM1179022 1 0.0363 0.9087 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM1179028 2 0.0000 0.9708 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179032 1 0.0363 0.9087 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM1179041 2 0.0000 0.9708 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179042 2 0.0000 0.9708 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178976 3 0.0692 0.7227 0.000 0.000 0.976 0.004 0.020 0.000
#> GSM1178981 6 0.4224 0.4569 0.000 0.000 0.340 0.000 0.028 0.632
#> GSM1178982 3 0.2868 0.7054 0.000 0.000 0.840 0.000 0.028 0.132
#> GSM1178983 3 0.3320 0.5180 0.000 0.000 0.772 0.000 0.212 0.016
#> GSM1178985 3 0.1462 0.7427 0.000 0.000 0.936 0.000 0.008 0.056
#> GSM1178992 3 0.3230 0.6515 0.000 0.000 0.776 0.000 0.012 0.212
#> GSM1179005 6 0.3575 0.5915 0.000 0.000 0.284 0.000 0.008 0.708
#> GSM1179007 6 0.2048 0.7198 0.000 0.000 0.120 0.000 0.000 0.880
#> GSM1179012 1 0.4023 0.7590 0.756 0.000 0.000 0.000 0.144 0.100
#> GSM1179016 3 0.3221 0.4431 0.000 0.000 0.736 0.000 0.264 0.000
#> GSM1179030 3 0.3541 0.4256 0.000 0.000 0.728 0.000 0.260 0.012
#> GSM1179038 3 0.3868 -0.0278 0.000 0.000 0.504 0.000 0.000 0.496
#> GSM1178987 6 0.5815 0.1822 0.000 0.000 0.264 0.000 0.240 0.496
#> GSM1179003 3 0.4708 0.3187 0.000 0.016 0.672 0.056 0.256 0.000
#> GSM1179004 3 0.2815 0.7089 0.000 0.000 0.848 0.000 0.032 0.120
#> GSM1179039 2 0.0000 0.9708 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178975 6 0.3986 0.1929 0.000 0.000 0.464 0.000 0.004 0.532
#> GSM1178980 4 0.0000 0.7282 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1178995 6 0.2092 0.7188 0.000 0.000 0.124 0.000 0.000 0.876
#> GSM1178996 3 0.1745 0.7411 0.000 0.000 0.920 0.000 0.012 0.068
#> GSM1179001 6 0.2020 0.7060 0.096 0.000 0.008 0.000 0.000 0.896
#> GSM1179002 6 0.2146 0.7213 0.000 0.000 0.116 0.000 0.004 0.880
#> GSM1179006 3 0.0972 0.7365 0.000 0.000 0.964 0.000 0.008 0.028
#> GSM1179008 6 0.2794 0.7253 0.060 0.000 0.080 0.000 0.000 0.860
#> GSM1179015 6 0.5777 0.0507 0.332 0.000 0.008 0.000 0.152 0.508
#> GSM1179017 5 0.3078 0.5004 0.012 0.000 0.192 0.000 0.796 0.000
#> GSM1179026 3 0.1141 0.7429 0.000 0.000 0.948 0.000 0.000 0.052
#> GSM1179033 3 0.1863 0.7341 0.000 0.000 0.896 0.000 0.000 0.104
#> GSM1179035 3 0.2191 0.7303 0.000 0.000 0.876 0.000 0.004 0.120
#> GSM1179036 3 0.1863 0.7339 0.000 0.000 0.896 0.000 0.000 0.104
#> GSM1178986 3 0.2948 0.5660 0.000 0.000 0.804 0.000 0.188 0.008
#> GSM1178989 3 0.1814 0.6727 0.000 0.000 0.900 0.000 0.100 0.000
#> GSM1178993 4 0.0000 0.7282 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1178999 5 0.5859 0.4802 0.000 0.000 0.168 0.384 0.444 0.004
#> GSM1179021 4 0.4938 0.2957 0.000 0.340 0.000 0.580 0.080 0.000
#> GSM1179025 2 0.0000 0.9708 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179027 4 0.0000 0.7282 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1179011 4 0.0000 0.7282 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1179023 1 0.1814 0.8439 0.900 0.000 0.000 0.000 0.000 0.100
#> GSM1179029 1 0.5254 0.5794 0.628 0.000 0.024 0.000 0.084 0.264
#> GSM1179034 1 0.0363 0.9087 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM1179040 4 0.2679 0.5815 0.000 0.000 0.096 0.864 0.040 0.000
#> GSM1178988 3 0.0000 0.7252 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1179037 3 0.2562 0.6972 0.000 0.000 0.828 0.000 0.000 0.172
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) protocol(p) k
#> CV:pam 66 0.1941 0.126710 2
#> CV:pam 68 0.6431 0.001341 3
#> CV:pam 33 0.2518 0.050448 4
#> CV:pam 64 0.0162 0.000564 5
#> CV:pam 54 0.0457 0.008610 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 31632 rows and 73 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 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 0.556 0.865 0.912 0.3506 0.686 0.686
#> 3 3 0.305 0.635 0.754 0.3873 0.767 0.696
#> 4 4 0.581 0.727 0.873 0.3321 0.658 0.467
#> 5 5 0.486 0.611 0.802 0.0645 0.837 0.591
#> 6 6 0.507 0.474 0.718 0.0979 0.904 0.701
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
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
#> GSM1178971 1 0.1414 0.895 0.980 0.020
#> GSM1178979 2 0.2236 0.949 0.036 0.964
#> GSM1179009 1 0.7602 0.820 0.780 0.220
#> GSM1179031 2 0.2236 0.949 0.036 0.964
#> GSM1178970 2 0.2236 0.949 0.036 0.964
#> GSM1178972 2 0.2236 0.949 0.036 0.964
#> GSM1178973 1 0.7602 0.820 0.780 0.220
#> GSM1178974 2 0.2236 0.949 0.036 0.964
#> GSM1178977 1 0.7453 0.822 0.788 0.212
#> GSM1178978 1 0.6973 0.838 0.812 0.188
#> GSM1178998 1 0.0376 0.897 0.996 0.004
#> GSM1179010 1 0.0000 0.897 1.000 0.000
#> GSM1179018 1 0.5946 0.853 0.856 0.144
#> GSM1179024 1 0.0376 0.895 0.996 0.004
#> GSM1178984 1 0.3431 0.886 0.936 0.064
#> GSM1178990 1 0.0376 0.895 0.996 0.004
#> GSM1178991 1 0.7299 0.830 0.796 0.204
#> GSM1178994 1 0.0000 0.897 1.000 0.000
#> GSM1178997 1 0.0000 0.897 1.000 0.000
#> GSM1179000 1 0.0376 0.895 0.996 0.004
#> GSM1179013 1 0.1843 0.894 0.972 0.028
#> GSM1179014 1 0.7528 0.822 0.784 0.216
#> GSM1179019 1 0.0376 0.895 0.996 0.004
#> GSM1179020 1 0.0376 0.895 0.996 0.004
#> GSM1179022 1 0.0376 0.895 0.996 0.004
#> GSM1179028 2 0.2236 0.949 0.036 0.964
#> GSM1179032 1 0.0376 0.895 0.996 0.004
#> GSM1179041 2 0.2236 0.949 0.036 0.964
#> GSM1179042 2 0.2236 0.949 0.036 0.964
#> GSM1178976 2 0.9427 0.379 0.360 0.640
#> GSM1178981 1 0.0000 0.897 1.000 0.000
#> GSM1178982 1 0.0376 0.897 0.996 0.004
#> GSM1178983 1 0.3274 0.887 0.940 0.060
#> GSM1178985 1 0.0000 0.897 1.000 0.000
#> GSM1178992 1 0.7528 0.822 0.784 0.216
#> GSM1179005 1 0.0000 0.897 1.000 0.000
#> GSM1179007 1 0.0376 0.895 0.996 0.004
#> GSM1179012 1 0.0000 0.897 1.000 0.000
#> GSM1179016 1 0.7528 0.822 0.784 0.216
#> GSM1179030 1 0.6973 0.829 0.812 0.188
#> GSM1179038 1 0.0376 0.895 0.996 0.004
#> GSM1178987 1 0.0000 0.897 1.000 0.000
#> GSM1179003 2 0.6048 0.834 0.148 0.852
#> GSM1179004 1 0.0000 0.897 1.000 0.000
#> GSM1179039 2 0.2236 0.949 0.036 0.964
#> GSM1178975 1 0.7602 0.820 0.780 0.220
#> GSM1178980 1 0.8016 0.796 0.756 0.244
#> GSM1178995 1 0.0000 0.897 1.000 0.000
#> GSM1178996 1 0.6531 0.844 0.832 0.168
#> GSM1179001 1 0.0376 0.895 0.996 0.004
#> GSM1179002 1 0.0000 0.897 1.000 0.000
#> GSM1179006 1 0.7528 0.822 0.784 0.216
#> GSM1179008 1 0.1633 0.894 0.976 0.024
#> GSM1179015 1 0.7528 0.822 0.784 0.216
#> GSM1179017 1 0.9661 0.539 0.608 0.392
#> GSM1179026 1 0.7453 0.823 0.788 0.212
#> GSM1179033 1 0.1184 0.896 0.984 0.016
#> GSM1179035 1 0.0000 0.897 1.000 0.000
#> GSM1179036 1 0.0376 0.897 0.996 0.004
#> GSM1178986 1 0.2778 0.889 0.952 0.048
#> GSM1178989 1 0.7602 0.819 0.780 0.220
#> GSM1178993 1 0.7602 0.820 0.780 0.220
#> GSM1178999 1 0.9460 0.556 0.636 0.364
#> GSM1179021 2 0.0376 0.923 0.004 0.996
#> GSM1179025 2 0.2236 0.949 0.036 0.964
#> GSM1179027 1 0.7602 0.820 0.780 0.220
#> GSM1179011 1 0.7602 0.820 0.780 0.220
#> GSM1179023 1 0.0376 0.895 0.996 0.004
#> GSM1179029 1 0.0376 0.895 0.996 0.004
#> GSM1179034 1 0.0376 0.895 0.996 0.004
#> GSM1179040 2 0.3733 0.890 0.072 0.928
#> GSM1178988 1 0.6801 0.835 0.820 0.180
#> GSM1179037 1 0.0672 0.897 0.992 0.008
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1178971 3 0.4196 0.7047 0.112 0.024 0.864
#> GSM1178979 2 0.4968 0.8732 0.012 0.800 0.188
#> GSM1179009 3 0.5988 0.6450 0.056 0.168 0.776
#> GSM1179031 2 0.3116 0.9496 0.000 0.892 0.108
#> GSM1178970 3 0.3918 0.6852 0.012 0.120 0.868
#> GSM1178972 2 0.3816 0.9315 0.000 0.852 0.148
#> GSM1178973 3 0.9311 0.2407 0.364 0.168 0.468
#> GSM1178974 2 0.3752 0.9337 0.000 0.856 0.144
#> GSM1178977 3 0.2492 0.7270 0.016 0.048 0.936
#> GSM1178978 3 0.1015 0.7417 0.008 0.012 0.980
#> GSM1178998 3 0.6483 0.3499 0.392 0.008 0.600
#> GSM1179010 3 0.5902 0.5260 0.316 0.004 0.680
#> GSM1179018 3 0.1015 0.7417 0.008 0.012 0.980
#> GSM1179024 1 0.4062 0.7983 0.836 0.000 0.164
#> GSM1178984 3 0.5884 0.5605 0.272 0.012 0.716
#> GSM1178990 3 0.6664 0.1671 0.464 0.008 0.528
#> GSM1178991 3 0.5298 0.6872 0.164 0.032 0.804
#> GSM1178994 3 0.5678 0.5257 0.316 0.000 0.684
#> GSM1178997 3 0.1877 0.7426 0.032 0.012 0.956
#> GSM1179000 3 0.6305 0.1341 0.484 0.000 0.516
#> GSM1179013 1 0.4555 0.7685 0.800 0.000 0.200
#> GSM1179014 3 0.6777 0.4311 0.364 0.020 0.616
#> GSM1179019 1 0.6309 -0.2105 0.504 0.000 0.496
#> GSM1179020 3 0.6309 0.0804 0.496 0.000 0.504
#> GSM1179022 1 0.2261 0.7864 0.932 0.000 0.068
#> GSM1179028 2 0.3116 0.9496 0.000 0.892 0.108
#> GSM1179032 1 0.2261 0.7864 0.932 0.000 0.068
#> GSM1179041 2 0.3116 0.9496 0.000 0.892 0.108
#> GSM1179042 2 0.3116 0.9496 0.000 0.892 0.108
#> GSM1178976 3 0.2384 0.7241 0.008 0.056 0.936
#> GSM1178981 3 0.1643 0.7407 0.044 0.000 0.956
#> GSM1178982 3 0.1170 0.7405 0.016 0.008 0.976
#> GSM1178983 3 0.2550 0.7380 0.040 0.024 0.936
#> GSM1178985 3 0.0592 0.7407 0.012 0.000 0.988
#> GSM1178992 3 0.5356 0.6641 0.196 0.020 0.784
#> GSM1179005 3 0.6180 0.4852 0.332 0.008 0.660
#> GSM1179007 3 0.6598 0.2774 0.428 0.008 0.564
#> GSM1179012 3 0.6126 0.3659 0.400 0.000 0.600
#> GSM1179016 3 0.5298 0.6947 0.164 0.032 0.804
#> GSM1179030 3 0.1620 0.7369 0.012 0.024 0.964
#> GSM1179038 3 0.6427 0.4615 0.348 0.012 0.640
#> GSM1178987 3 0.1411 0.7399 0.036 0.000 0.964
#> GSM1179003 3 0.5020 0.6298 0.012 0.192 0.796
#> GSM1179004 3 0.1411 0.7399 0.036 0.000 0.964
#> GSM1179039 2 0.3116 0.9496 0.000 0.892 0.108
#> GSM1178975 3 0.4859 0.7116 0.044 0.116 0.840
#> GSM1178980 3 0.5688 0.6448 0.044 0.168 0.788
#> GSM1178995 3 0.6434 0.4015 0.380 0.008 0.612
#> GSM1178996 3 0.0661 0.7423 0.004 0.008 0.988
#> GSM1179001 3 0.6669 0.1591 0.468 0.008 0.524
#> GSM1179002 3 0.6252 0.4590 0.344 0.008 0.648
#> GSM1179006 3 0.1170 0.7410 0.008 0.016 0.976
#> GSM1179008 3 0.6813 0.1629 0.468 0.012 0.520
#> GSM1179015 3 0.6910 0.3768 0.396 0.020 0.584
#> GSM1179017 3 0.3356 0.7197 0.036 0.056 0.908
#> GSM1179026 3 0.2031 0.7390 0.032 0.016 0.952
#> GSM1179033 3 0.1015 0.7428 0.008 0.012 0.980
#> GSM1179035 3 0.1411 0.7399 0.036 0.000 0.964
#> GSM1179036 3 0.2651 0.7284 0.060 0.012 0.928
#> GSM1178986 3 0.1877 0.7393 0.032 0.012 0.956
#> GSM1178989 3 0.2689 0.7295 0.032 0.036 0.932
#> GSM1178993 3 0.5688 0.6448 0.044 0.168 0.788
#> GSM1178999 3 0.2939 0.7171 0.012 0.072 0.916
#> GSM1179021 2 0.0983 0.8165 0.004 0.980 0.016
#> GSM1179025 2 0.3752 0.9355 0.000 0.856 0.144
#> GSM1179027 3 0.5688 0.6448 0.044 0.168 0.788
#> GSM1179011 3 0.5791 0.6432 0.048 0.168 0.784
#> GSM1179023 1 0.3686 0.8086 0.860 0.000 0.140
#> GSM1179029 3 0.6641 0.2082 0.448 0.008 0.544
#> GSM1179034 1 0.2261 0.7864 0.932 0.000 0.068
#> GSM1179040 3 0.6490 0.5744 0.036 0.256 0.708
#> GSM1178988 3 0.1905 0.7401 0.028 0.016 0.956
#> GSM1179037 3 0.1411 0.7399 0.036 0.000 0.964
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1178971 3 0.3933 0.6909 0.196 0.004 0.796 0.004
#> GSM1178979 2 0.3161 0.8015 0.000 0.864 0.124 0.012
#> GSM1179009 4 0.0895 0.8411 0.000 0.004 0.020 0.976
#> GSM1179031 2 0.0188 0.8709 0.000 0.996 0.000 0.004
#> GSM1178970 3 0.2255 0.8115 0.000 0.068 0.920 0.012
#> GSM1178972 2 0.3377 0.7861 0.000 0.848 0.140 0.012
#> GSM1178973 4 0.6269 0.2584 0.364 0.004 0.056 0.576
#> GSM1178974 2 0.1890 0.8555 0.000 0.936 0.056 0.008
#> GSM1178977 3 0.1356 0.8356 0.000 0.032 0.960 0.008
#> GSM1178978 3 0.0000 0.8539 0.000 0.000 1.000 0.000
#> GSM1178998 1 0.4872 0.6008 0.640 0.004 0.356 0.000
#> GSM1179010 3 0.4331 0.4907 0.288 0.000 0.712 0.000
#> GSM1179018 3 0.0188 0.8531 0.000 0.000 0.996 0.004
#> GSM1179024 1 0.1792 0.7854 0.932 0.000 0.068 0.000
#> GSM1178984 3 0.4356 0.4840 0.292 0.000 0.708 0.000
#> GSM1178990 1 0.3490 0.7827 0.836 0.004 0.156 0.004
#> GSM1178991 1 0.5463 0.4924 0.580 0.004 0.404 0.012
#> GSM1178994 3 0.4356 0.4817 0.292 0.000 0.708 0.000
#> GSM1178997 3 0.4608 0.5094 0.304 0.004 0.692 0.000
#> GSM1179000 1 0.1867 0.7875 0.928 0.000 0.072 0.000
#> GSM1179013 1 0.1867 0.7877 0.928 0.000 0.072 0.000
#> GSM1179014 1 0.4372 0.6767 0.728 0.004 0.268 0.000
#> GSM1179019 1 0.1867 0.7875 0.928 0.000 0.072 0.000
#> GSM1179020 1 0.1867 0.7875 0.928 0.000 0.072 0.000
#> GSM1179022 1 0.0000 0.7193 1.000 0.000 0.000 0.000
#> GSM1179028 2 0.0188 0.8709 0.000 0.996 0.000 0.004
#> GSM1179032 1 0.0000 0.7193 1.000 0.000 0.000 0.000
#> GSM1179041 2 0.0188 0.8709 0.000 0.996 0.000 0.004
#> GSM1179042 2 0.0188 0.8709 0.000 0.996 0.000 0.004
#> GSM1178976 3 0.1488 0.8303 0.000 0.032 0.956 0.012
#> GSM1178981 3 0.0000 0.8539 0.000 0.000 1.000 0.000
#> GSM1178982 3 0.0376 0.8534 0.004 0.000 0.992 0.004
#> GSM1178983 3 0.1576 0.8354 0.048 0.000 0.948 0.004
#> GSM1178985 3 0.0000 0.8539 0.000 0.000 1.000 0.000
#> GSM1178992 3 0.0188 0.8536 0.004 0.000 0.996 0.000
#> GSM1179005 3 0.4957 0.4439 0.336 0.004 0.656 0.004
#> GSM1179007 1 0.5313 0.2396 0.536 0.004 0.456 0.004
#> GSM1179012 1 0.4941 0.4507 0.564 0.000 0.436 0.000
#> GSM1179016 3 0.3306 0.7423 0.156 0.004 0.840 0.000
#> GSM1179030 3 0.0712 0.8528 0.008 0.004 0.984 0.004
#> GSM1179038 3 0.5139 0.3271 0.380 0.004 0.612 0.004
#> GSM1178987 3 0.0000 0.8539 0.000 0.000 1.000 0.000
#> GSM1179003 3 0.3895 0.7230 0.000 0.184 0.804 0.012
#> GSM1179004 3 0.0000 0.8539 0.000 0.000 1.000 0.000
#> GSM1179039 2 0.0188 0.8709 0.000 0.996 0.000 0.004
#> GSM1178975 4 0.6079 0.6061 0.160 0.004 0.140 0.696
#> GSM1178980 4 0.1452 0.8265 0.000 0.036 0.008 0.956
#> GSM1178995 3 0.5317 0.0511 0.460 0.004 0.532 0.004
#> GSM1178996 3 0.1082 0.8485 0.020 0.004 0.972 0.004
#> GSM1179001 1 0.4268 0.7357 0.760 0.004 0.232 0.004
#> GSM1179002 3 0.5125 0.3081 0.376 0.004 0.616 0.004
#> GSM1179006 3 0.0376 0.8533 0.004 0.004 0.992 0.000
#> GSM1179008 1 0.3236 0.7883 0.856 0.004 0.136 0.004
#> GSM1179015 1 0.4950 0.5646 0.620 0.004 0.376 0.000
#> GSM1179017 3 0.2731 0.8041 0.004 0.092 0.896 0.008
#> GSM1179026 3 0.0000 0.8539 0.000 0.000 1.000 0.000
#> GSM1179033 3 0.0188 0.8531 0.000 0.000 0.996 0.004
#> GSM1179035 3 0.0000 0.8539 0.000 0.000 1.000 0.000
#> GSM1179036 3 0.2156 0.8254 0.060 0.004 0.928 0.008
#> GSM1178986 3 0.2796 0.7980 0.096 0.008 0.892 0.004
#> GSM1178989 3 0.0804 0.8460 0.000 0.012 0.980 0.008
#> GSM1178993 4 0.0657 0.8441 0.000 0.004 0.012 0.984
#> GSM1178999 3 0.2402 0.8129 0.000 0.076 0.912 0.012
#> GSM1179021 2 0.4925 0.2801 0.000 0.572 0.000 0.428
#> GSM1179025 2 0.2610 0.8367 0.000 0.900 0.088 0.012
#> GSM1179027 4 0.0657 0.8441 0.000 0.004 0.012 0.984
#> GSM1179011 4 0.0657 0.8441 0.000 0.004 0.012 0.984
#> GSM1179023 1 0.1474 0.7713 0.948 0.000 0.052 0.000
#> GSM1179029 1 0.3340 0.7868 0.848 0.004 0.144 0.004
#> GSM1179034 1 0.0000 0.7193 1.000 0.000 0.000 0.000
#> GSM1179040 4 0.1489 0.8166 0.000 0.044 0.004 0.952
#> GSM1178988 3 0.0188 0.8531 0.000 0.000 0.996 0.004
#> GSM1179037 3 0.0000 0.8539 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
#> GSM1178971 3 0.4345 0.651 0.212 0.012 0.748 0.000 0.028
#> GSM1178979 5 0.5731 -0.189 0.000 0.436 0.084 0.000 0.480
#> GSM1179009 4 0.0609 0.808 0.000 0.000 0.020 0.980 0.000
#> GSM1179031 2 0.0000 0.896 0.000 1.000 0.000 0.000 0.000
#> GSM1178970 5 0.5296 0.461 0.000 0.048 0.472 0.000 0.480
#> GSM1178972 2 0.5449 0.483 0.000 0.636 0.108 0.000 0.256
#> GSM1178973 4 0.5232 0.498 0.228 0.000 0.104 0.668 0.000
#> GSM1178974 2 0.2595 0.841 0.000 0.888 0.032 0.000 0.080
#> GSM1178977 3 0.4738 -0.478 0.000 0.016 0.520 0.000 0.464
#> GSM1178978 3 0.1012 0.749 0.020 0.000 0.968 0.000 0.012
#> GSM1178998 3 0.4404 0.580 0.292 0.000 0.684 0.000 0.024
#> GSM1179010 3 0.3794 0.651 0.152 0.000 0.800 0.000 0.048
#> GSM1179018 3 0.1018 0.746 0.016 0.000 0.968 0.000 0.016
#> GSM1179024 1 0.2074 0.788 0.896 0.000 0.104 0.000 0.000
#> GSM1178984 3 0.3152 0.721 0.136 0.000 0.840 0.000 0.024
#> GSM1178990 1 0.5068 0.357 0.592 0.000 0.364 0.000 0.044
#> GSM1178991 1 0.5315 0.385 0.536 0.012 0.428 0.008 0.016
#> GSM1178994 3 0.2761 0.710 0.104 0.000 0.872 0.000 0.024
#> GSM1178997 3 0.5322 -0.112 0.456 0.028 0.504 0.000 0.012
#> GSM1179000 1 0.3424 0.716 0.760 0.000 0.240 0.000 0.000
#> GSM1179013 1 0.2573 0.786 0.880 0.000 0.104 0.000 0.016
#> GSM1179014 5 0.7376 -0.311 0.324 0.028 0.272 0.000 0.376
#> GSM1179019 1 0.3395 0.719 0.764 0.000 0.236 0.000 0.000
#> GSM1179020 1 0.2230 0.790 0.884 0.000 0.116 0.000 0.000
#> GSM1179022 1 0.1043 0.684 0.960 0.000 0.000 0.000 0.040
#> GSM1179028 2 0.0162 0.896 0.000 0.996 0.000 0.000 0.004
#> GSM1179032 1 0.1043 0.684 0.960 0.000 0.000 0.000 0.040
#> GSM1179041 2 0.0000 0.896 0.000 1.000 0.000 0.000 0.000
#> GSM1179042 2 0.0162 0.896 0.000 0.996 0.000 0.000 0.004
#> GSM1178976 3 0.4829 -0.500 0.000 0.020 0.500 0.000 0.480
#> GSM1178981 3 0.1012 0.751 0.020 0.000 0.968 0.000 0.012
#> GSM1178982 3 0.1750 0.750 0.028 0.000 0.936 0.000 0.036
#> GSM1178983 3 0.2903 0.736 0.080 0.000 0.872 0.000 0.048
#> GSM1178985 3 0.0671 0.749 0.016 0.000 0.980 0.000 0.004
#> GSM1178992 3 0.3516 0.654 0.020 0.008 0.820 0.000 0.152
#> GSM1179005 3 0.3904 0.703 0.156 0.000 0.792 0.000 0.052
#> GSM1179007 3 0.5067 0.571 0.288 0.000 0.648 0.000 0.064
#> GSM1179012 3 0.3953 0.631 0.168 0.000 0.784 0.000 0.048
#> GSM1179016 3 0.5606 0.124 0.028 0.028 0.528 0.000 0.416
#> GSM1179030 3 0.2984 0.692 0.020 0.028 0.880 0.000 0.072
#> GSM1179038 3 0.3821 0.709 0.148 0.000 0.800 0.000 0.052
#> GSM1178987 3 0.0963 0.737 0.000 0.000 0.964 0.000 0.036
#> GSM1179003 5 0.6184 0.548 0.000 0.140 0.380 0.000 0.480
#> GSM1179004 3 0.1043 0.737 0.000 0.000 0.960 0.000 0.040
#> GSM1179039 2 0.0000 0.896 0.000 1.000 0.000 0.000 0.000
#> GSM1178975 4 0.5845 0.407 0.108 0.016 0.244 0.632 0.000
#> GSM1178980 4 0.2079 0.792 0.000 0.020 0.000 0.916 0.064
#> GSM1178995 3 0.4238 0.683 0.192 0.000 0.756 0.000 0.052
#> GSM1178996 3 0.1954 0.750 0.028 0.008 0.932 0.000 0.032
#> GSM1179001 3 0.4758 0.586 0.276 0.000 0.676 0.000 0.048
#> GSM1179002 3 0.3507 0.727 0.120 0.000 0.828 0.000 0.052
#> GSM1179006 3 0.2124 0.744 0.020 0.012 0.924 0.000 0.044
#> GSM1179008 1 0.3752 0.764 0.804 0.000 0.148 0.000 0.048
#> GSM1179015 3 0.6531 0.311 0.240 0.012 0.544 0.000 0.204
#> GSM1179017 5 0.3234 0.249 0.000 0.064 0.084 0.000 0.852
#> GSM1179026 3 0.1671 0.713 0.000 0.000 0.924 0.000 0.076
#> GSM1179033 3 0.1211 0.750 0.024 0.000 0.960 0.000 0.016
#> GSM1179035 3 0.0880 0.737 0.000 0.000 0.968 0.000 0.032
#> GSM1179036 3 0.3043 0.735 0.080 0.000 0.864 0.000 0.056
#> GSM1178986 3 0.3367 0.735 0.088 0.016 0.856 0.000 0.040
#> GSM1178989 5 0.4841 0.502 0.000 0.024 0.416 0.000 0.560
#> GSM1178993 4 0.0000 0.812 0.000 0.000 0.000 1.000 0.000
#> GSM1178999 5 0.5736 0.492 0.000 0.084 0.448 0.000 0.468
#> GSM1179021 4 0.4558 0.481 0.000 0.324 0.000 0.652 0.024
#> GSM1179025 2 0.3181 0.803 0.000 0.856 0.072 0.000 0.072
#> GSM1179027 4 0.0000 0.812 0.000 0.000 0.000 1.000 0.000
#> GSM1179011 4 0.0000 0.812 0.000 0.000 0.000 1.000 0.000
#> GSM1179023 1 0.2020 0.788 0.900 0.000 0.100 0.000 0.000
#> GSM1179029 1 0.4644 0.684 0.720 0.004 0.224 0.000 0.052
#> GSM1179034 1 0.1043 0.684 0.960 0.000 0.000 0.000 0.040
#> GSM1179040 4 0.2079 0.792 0.000 0.020 0.000 0.916 0.064
#> GSM1178988 3 0.1121 0.722 0.000 0.000 0.956 0.000 0.044
#> GSM1179037 3 0.0703 0.735 0.000 0.000 0.976 0.000 0.024
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1178971 3 0.4671 0.4067 0.228 0.000 0.696 0.000 0.032 0.044
#> GSM1178979 5 0.3485 0.7085 0.000 0.112 0.028 0.000 0.824 0.036
#> GSM1179009 4 0.1082 0.7488 0.004 0.000 0.040 0.956 0.000 0.000
#> GSM1179031 2 0.0000 0.7877 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178970 5 0.3998 0.7535 0.000 0.012 0.116 0.000 0.780 0.092
#> GSM1178972 5 0.4847 0.3023 0.000 0.344 0.016 0.000 0.600 0.040
#> GSM1178973 4 0.4631 0.3670 0.320 0.000 0.060 0.620 0.000 0.000
#> GSM1178974 2 0.4325 0.1055 0.000 0.504 0.008 0.000 0.480 0.008
#> GSM1178977 5 0.4185 0.7376 0.000 0.000 0.168 0.012 0.752 0.068
#> GSM1178978 3 0.4126 0.5086 0.016 0.000 0.764 0.004 0.048 0.168
#> GSM1178998 6 0.6666 0.5329 0.272 0.000 0.308 0.000 0.032 0.388
#> GSM1179010 6 0.5586 0.7856 0.196 0.000 0.172 0.000 0.020 0.612
#> GSM1179018 3 0.3885 0.4938 0.004 0.000 0.756 0.000 0.048 0.192
#> GSM1179024 1 0.1204 0.5761 0.944 0.000 0.056 0.000 0.000 0.000
#> GSM1178984 3 0.5873 0.3175 0.172 0.000 0.600 0.000 0.040 0.188
#> GSM1178990 1 0.4010 0.2867 0.584 0.000 0.408 0.000 0.000 0.008
#> GSM1178991 1 0.6264 -0.0229 0.444 0.000 0.428 0.032 0.060 0.036
#> GSM1178994 3 0.6058 0.2176 0.192 0.000 0.548 0.000 0.028 0.232
#> GSM1178997 3 0.5951 0.1055 0.428 0.000 0.444 0.000 0.088 0.040
#> GSM1179000 1 0.3133 0.4882 0.780 0.000 0.212 0.000 0.000 0.008
#> GSM1179013 1 0.1643 0.5755 0.924 0.000 0.068 0.000 0.000 0.008
#> GSM1179014 1 0.7030 0.1292 0.428 0.000 0.244 0.000 0.244 0.084
#> GSM1179019 1 0.2915 0.5170 0.808 0.000 0.184 0.000 0.000 0.008
#> GSM1179020 1 0.1588 0.5764 0.924 0.000 0.072 0.000 0.000 0.004
#> GSM1179022 1 0.2871 0.4677 0.804 0.000 0.004 0.000 0.000 0.192
#> GSM1179028 2 0.0692 0.7824 0.000 0.976 0.000 0.004 0.020 0.000
#> GSM1179032 1 0.2871 0.4677 0.804 0.000 0.004 0.000 0.000 0.192
#> GSM1179041 2 0.0000 0.7877 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179042 2 0.0865 0.7720 0.000 0.964 0.000 0.000 0.036 0.000
#> GSM1178976 5 0.3172 0.7525 0.000 0.000 0.048 0.000 0.824 0.128
#> GSM1178981 3 0.3918 0.4869 0.008 0.000 0.748 0.000 0.036 0.208
#> GSM1178982 3 0.2009 0.5499 0.004 0.000 0.916 0.000 0.040 0.040
#> GSM1178983 3 0.1251 0.5437 0.008 0.000 0.956 0.000 0.024 0.012
#> GSM1178985 3 0.3354 0.5148 0.000 0.000 0.796 0.000 0.036 0.168
#> GSM1178992 3 0.7026 0.2024 0.168 0.000 0.484 0.000 0.184 0.164
#> GSM1179005 3 0.3550 0.4280 0.156 0.000 0.800 0.000 0.020 0.024
#> GSM1179007 3 0.4604 0.0892 0.300 0.000 0.636 0.000 0.000 0.064
#> GSM1179012 6 0.5727 0.7887 0.200 0.000 0.168 0.000 0.028 0.604
#> GSM1179016 3 0.7414 0.0511 0.196 0.000 0.384 0.000 0.264 0.156
#> GSM1179030 3 0.4097 0.5242 0.020 0.000 0.764 0.000 0.164 0.052
#> GSM1179038 3 0.3411 0.4247 0.160 0.000 0.804 0.000 0.012 0.024
#> GSM1178987 3 0.4497 0.3162 0.012 0.000 0.600 0.000 0.020 0.368
#> GSM1179003 5 0.2868 0.7668 0.000 0.032 0.112 0.000 0.852 0.004
#> GSM1179004 3 0.4687 0.3174 0.024 0.000 0.604 0.000 0.020 0.352
#> GSM1179039 2 0.0000 0.7877 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178975 4 0.5770 0.2149 0.188 0.000 0.196 0.596 0.012 0.008
#> GSM1178980 4 0.1501 0.7422 0.000 0.000 0.000 0.924 0.076 0.000
#> GSM1178995 3 0.3071 0.4067 0.180 0.000 0.804 0.000 0.000 0.016
#> GSM1178996 3 0.4291 0.5240 0.016 0.000 0.752 0.000 0.152 0.080
#> GSM1179001 3 0.4026 0.1398 0.348 0.000 0.636 0.000 0.000 0.016
#> GSM1179002 3 0.3761 0.3746 0.196 0.000 0.764 0.000 0.008 0.032
#> GSM1179006 3 0.3715 0.5179 0.000 0.000 0.764 0.000 0.188 0.048
#> GSM1179008 1 0.3911 0.3707 0.624 0.000 0.368 0.000 0.000 0.008
#> GSM1179015 1 0.7260 -0.3011 0.396 0.000 0.128 0.000 0.184 0.292
#> GSM1179017 5 0.4206 0.6009 0.028 0.000 0.056 0.000 0.764 0.152
#> GSM1179026 3 0.5619 0.3832 0.032 0.000 0.620 0.000 0.136 0.212
#> GSM1179033 3 0.2744 0.5557 0.000 0.000 0.864 0.000 0.072 0.064
#> GSM1179035 3 0.4456 0.3299 0.008 0.000 0.608 0.000 0.024 0.360
#> GSM1179036 3 0.2239 0.5139 0.008 0.000 0.900 0.000 0.020 0.072
#> GSM1178986 3 0.3210 0.5307 0.012 0.000 0.844 0.000 0.072 0.072
#> GSM1178989 5 0.4079 0.7021 0.000 0.000 0.112 0.000 0.752 0.136
#> GSM1178993 4 0.0000 0.7580 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1178999 5 0.2963 0.7641 0.004 0.000 0.152 0.000 0.828 0.016
#> GSM1179021 4 0.5789 0.2738 0.000 0.216 0.000 0.496 0.288 0.000
#> GSM1179025 2 0.4979 0.0247 0.000 0.500 0.016 0.000 0.448 0.036
#> GSM1179027 4 0.0000 0.7580 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1179011 4 0.0000 0.7580 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1179023 1 0.1141 0.5753 0.948 0.000 0.052 0.000 0.000 0.000
#> GSM1179029 1 0.4904 0.3305 0.588 0.000 0.352 0.000 0.048 0.012
#> GSM1179034 1 0.2871 0.4677 0.804 0.000 0.004 0.000 0.000 0.192
#> GSM1179040 4 0.2378 0.6984 0.000 0.000 0.000 0.848 0.152 0.000
#> GSM1178988 3 0.5010 0.4154 0.004 0.000 0.636 0.000 0.108 0.252
#> GSM1179037 3 0.4489 0.3552 0.008 0.000 0.632 0.000 0.032 0.328
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) protocol(p) k
#> CV:mclust 72 0.222 6.91e-02 2
#> CV:mclust 56 0.436 4.75e-04 3
#> CV:mclust 61 0.122 1.00e-03 4
#> CV:mclust 57 0.129 2.16e-07 5
#> CV:mclust 37 0.145 1.15e-04 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 31632 rows and 73 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.972 0.987 0.3870 0.610 0.610
#> 3 3 0.761 0.816 0.919 0.4837 0.780 0.649
#> 4 4 0.505 0.547 0.756 0.1936 0.860 0.703
#> 5 5 0.617 0.656 0.832 0.0766 0.799 0.515
#> 6 6 0.574 0.537 0.754 0.0833 0.894 0.612
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
#> GSM1178971 1 0.000 0.993 1.000 0.000
#> GSM1178979 2 0.000 0.966 0.000 1.000
#> GSM1179009 1 0.000 0.993 1.000 0.000
#> GSM1179031 2 0.000 0.966 0.000 1.000
#> GSM1178970 2 0.000 0.966 0.000 1.000
#> GSM1178972 2 0.000 0.966 0.000 1.000
#> GSM1178973 1 0.000 0.993 1.000 0.000
#> GSM1178974 2 0.000 0.966 0.000 1.000
#> GSM1178977 2 0.000 0.966 0.000 1.000
#> GSM1178978 1 0.000 0.993 1.000 0.000
#> GSM1178998 1 0.000 0.993 1.000 0.000
#> GSM1179010 1 0.000 0.993 1.000 0.000
#> GSM1179018 1 0.000 0.993 1.000 0.000
#> GSM1179024 1 0.000 0.993 1.000 0.000
#> GSM1178984 1 0.000 0.993 1.000 0.000
#> GSM1178990 1 0.000 0.993 1.000 0.000
#> GSM1178991 1 0.000 0.993 1.000 0.000
#> GSM1178994 1 0.000 0.993 1.000 0.000
#> GSM1178997 1 0.000 0.993 1.000 0.000
#> GSM1179000 1 0.000 0.993 1.000 0.000
#> GSM1179013 1 0.000 0.993 1.000 0.000
#> GSM1179014 1 0.000 0.993 1.000 0.000
#> GSM1179019 1 0.000 0.993 1.000 0.000
#> GSM1179020 1 0.000 0.993 1.000 0.000
#> GSM1179022 1 0.000 0.993 1.000 0.000
#> GSM1179028 2 0.000 0.966 0.000 1.000
#> GSM1179032 1 0.000 0.993 1.000 0.000
#> GSM1179041 2 0.000 0.966 0.000 1.000
#> GSM1179042 2 0.000 0.966 0.000 1.000
#> GSM1178976 2 0.634 0.820 0.160 0.840
#> GSM1178981 1 0.000 0.993 1.000 0.000
#> GSM1178982 1 0.000 0.993 1.000 0.000
#> GSM1178983 1 0.000 0.993 1.000 0.000
#> GSM1178985 1 0.000 0.993 1.000 0.000
#> GSM1178992 1 0.000 0.993 1.000 0.000
#> GSM1179005 1 0.000 0.993 1.000 0.000
#> GSM1179007 1 0.000 0.993 1.000 0.000
#> GSM1179012 1 0.000 0.993 1.000 0.000
#> GSM1179016 1 0.000 0.993 1.000 0.000
#> GSM1179030 1 0.000 0.993 1.000 0.000
#> GSM1179038 1 0.000 0.993 1.000 0.000
#> GSM1178987 1 0.000 0.993 1.000 0.000
#> GSM1179003 2 0.000 0.966 0.000 1.000
#> GSM1179004 1 0.000 0.993 1.000 0.000
#> GSM1179039 2 0.000 0.966 0.000 1.000
#> GSM1178975 1 0.000 0.993 1.000 0.000
#> GSM1178980 2 0.000 0.966 0.000 1.000
#> GSM1178995 1 0.000 0.993 1.000 0.000
#> GSM1178996 1 0.000 0.993 1.000 0.000
#> GSM1179001 1 0.000 0.993 1.000 0.000
#> GSM1179002 1 0.000 0.993 1.000 0.000
#> GSM1179006 1 0.000 0.993 1.000 0.000
#> GSM1179008 1 0.000 0.993 1.000 0.000
#> GSM1179015 1 0.000 0.993 1.000 0.000
#> GSM1179017 1 0.295 0.940 0.948 0.052
#> GSM1179026 1 0.000 0.993 1.000 0.000
#> GSM1179033 1 0.000 0.993 1.000 0.000
#> GSM1179035 1 0.000 0.993 1.000 0.000
#> GSM1179036 1 0.000 0.993 1.000 0.000
#> GSM1178986 1 0.000 0.993 1.000 0.000
#> GSM1178989 1 0.821 0.637 0.744 0.256
#> GSM1178993 2 0.808 0.691 0.248 0.752
#> GSM1178999 2 0.706 0.780 0.192 0.808
#> GSM1179021 2 0.000 0.966 0.000 1.000
#> GSM1179025 2 0.000 0.966 0.000 1.000
#> GSM1179027 2 0.000 0.966 0.000 1.000
#> GSM1179011 1 0.204 0.962 0.968 0.032
#> GSM1179023 1 0.000 0.993 1.000 0.000
#> GSM1179029 1 0.000 0.993 1.000 0.000
#> GSM1179034 1 0.000 0.993 1.000 0.000
#> GSM1179040 2 0.000 0.966 0.000 1.000
#> GSM1178988 1 0.000 0.993 1.000 0.000
#> GSM1179037 1 0.000 0.993 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1178971 1 0.0000 0.9345 1.000 0.000 0.000
#> GSM1178979 2 0.1643 0.9275 0.000 0.956 0.044
#> GSM1179009 1 0.1585 0.9151 0.964 0.028 0.008
#> GSM1179031 2 0.0424 0.9435 0.000 0.992 0.008
#> GSM1178970 3 0.6302 -0.0633 0.000 0.480 0.520
#> GSM1178972 3 0.6305 -0.1145 0.000 0.484 0.516
#> GSM1178973 1 0.0424 0.9307 0.992 0.008 0.000
#> GSM1178974 2 0.3412 0.8495 0.000 0.876 0.124
#> GSM1178977 2 0.0237 0.9436 0.000 0.996 0.004
#> GSM1178978 1 0.0892 0.9278 0.980 0.000 0.020
#> GSM1178998 1 0.0424 0.9346 0.992 0.000 0.008
#> GSM1179010 1 0.6244 0.1656 0.560 0.000 0.440
#> GSM1179018 3 0.6267 0.1961 0.452 0.000 0.548
#> GSM1179024 1 0.0000 0.9345 1.000 0.000 0.000
#> GSM1178984 1 0.1860 0.9207 0.948 0.000 0.052
#> GSM1178990 1 0.0424 0.9346 0.992 0.000 0.008
#> GSM1178991 1 0.0592 0.9296 0.988 0.000 0.012
#> GSM1178994 1 0.1964 0.9183 0.944 0.000 0.056
#> GSM1178997 1 0.0000 0.9345 1.000 0.000 0.000
#> GSM1179000 1 0.0000 0.9345 1.000 0.000 0.000
#> GSM1179013 1 0.0000 0.9345 1.000 0.000 0.000
#> GSM1179014 1 0.0892 0.9335 0.980 0.000 0.020
#> GSM1179019 1 0.0000 0.9345 1.000 0.000 0.000
#> GSM1179020 1 0.0000 0.9345 1.000 0.000 0.000
#> GSM1179022 1 0.0000 0.9345 1.000 0.000 0.000
#> GSM1179028 2 0.0424 0.9435 0.000 0.992 0.008
#> GSM1179032 1 0.0000 0.9345 1.000 0.000 0.000
#> GSM1179041 2 0.0237 0.9436 0.000 0.996 0.004
#> GSM1179042 2 0.0237 0.9436 0.000 0.996 0.004
#> GSM1178976 3 0.0829 0.7426 0.012 0.004 0.984
#> GSM1178981 1 0.2537 0.9007 0.920 0.000 0.080
#> GSM1178982 1 0.0592 0.9346 0.988 0.000 0.012
#> GSM1178983 1 0.0000 0.9345 1.000 0.000 0.000
#> GSM1178985 1 0.5216 0.6627 0.740 0.000 0.260
#> GSM1178992 3 0.4605 0.7047 0.204 0.000 0.796
#> GSM1179005 1 0.1289 0.9296 0.968 0.000 0.032
#> GSM1179007 1 0.1529 0.9265 0.960 0.000 0.040
#> GSM1179012 1 0.3551 0.8488 0.868 0.000 0.132
#> GSM1179016 3 0.6252 0.2229 0.444 0.000 0.556
#> GSM1179030 1 0.1989 0.9224 0.948 0.004 0.048
#> GSM1179038 1 0.1411 0.9284 0.964 0.000 0.036
#> GSM1178987 3 0.3116 0.7478 0.108 0.000 0.892
#> GSM1179003 3 0.1753 0.7034 0.000 0.048 0.952
#> GSM1179004 3 0.2448 0.7522 0.076 0.000 0.924
#> GSM1179039 2 0.0424 0.9435 0.000 0.992 0.008
#> GSM1178975 1 0.1031 0.9200 0.976 0.024 0.000
#> GSM1178980 2 0.0829 0.9407 0.004 0.984 0.012
#> GSM1178995 1 0.0000 0.9345 1.000 0.000 0.000
#> GSM1178996 1 0.3619 0.8443 0.864 0.000 0.136
#> GSM1179001 1 0.0237 0.9347 0.996 0.000 0.004
#> GSM1179002 1 0.1411 0.9282 0.964 0.000 0.036
#> GSM1179006 1 0.5058 0.6840 0.756 0.000 0.244
#> GSM1179008 1 0.0000 0.9345 1.000 0.000 0.000
#> GSM1179015 1 0.3267 0.8664 0.884 0.000 0.116
#> GSM1179017 3 0.0424 0.7316 0.000 0.008 0.992
#> GSM1179026 3 0.1031 0.7477 0.024 0.000 0.976
#> GSM1179033 1 0.2796 0.8900 0.908 0.000 0.092
#> GSM1179035 3 0.4121 0.7247 0.168 0.000 0.832
#> GSM1179036 1 0.1964 0.9182 0.944 0.000 0.056
#> GSM1178986 1 0.1643 0.9247 0.956 0.000 0.044
#> GSM1178989 3 0.0592 0.7421 0.012 0.000 0.988
#> GSM1178993 2 0.2749 0.8773 0.064 0.924 0.012
#> GSM1178999 2 0.6498 0.3566 0.008 0.596 0.396
#> GSM1179021 2 0.0424 0.9425 0.000 0.992 0.008
#> GSM1179025 2 0.1643 0.9269 0.000 0.956 0.044
#> GSM1179027 2 0.0424 0.9425 0.000 0.992 0.008
#> GSM1179011 1 0.6129 0.4524 0.668 0.324 0.008
#> GSM1179023 1 0.0000 0.9345 1.000 0.000 0.000
#> GSM1179029 1 0.1031 0.9322 0.976 0.000 0.024
#> GSM1179034 1 0.0000 0.9345 1.000 0.000 0.000
#> GSM1179040 2 0.0592 0.9419 0.000 0.988 0.012
#> GSM1178988 3 0.0747 0.7453 0.016 0.000 0.984
#> GSM1179037 3 0.4702 0.6951 0.212 0.000 0.788
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1178971 1 0.2149 0.71053 0.912 0.000 0.000 0.088
#> GSM1178979 2 0.5309 0.58864 0.000 0.700 0.044 0.256
#> GSM1179009 4 0.6625 0.10485 0.424 0.016 0.048 0.512
#> GSM1179031 2 0.0000 0.74567 0.000 1.000 0.000 0.000
#> GSM1178970 3 0.4163 0.64073 0.000 0.188 0.792 0.020
#> GSM1178972 2 0.5860 0.22216 0.000 0.580 0.380 0.040
#> GSM1178973 1 0.4746 0.35658 0.632 0.000 0.000 0.368
#> GSM1178974 2 0.2965 0.68369 0.000 0.892 0.036 0.072
#> GSM1178977 2 0.2976 0.71362 0.000 0.872 0.008 0.120
#> GSM1178978 1 0.6817 0.00859 0.492 0.000 0.100 0.408
#> GSM1178998 1 0.2714 0.69603 0.884 0.000 0.004 0.112
#> GSM1179010 3 0.4867 0.49999 0.232 0.000 0.736 0.032
#> GSM1179018 4 0.7044 0.08379 0.120 0.000 0.428 0.452
#> GSM1179024 1 0.2868 0.70631 0.864 0.000 0.000 0.136
#> GSM1178984 1 0.5351 0.59631 0.744 0.000 0.104 0.152
#> GSM1178990 1 0.1557 0.72965 0.944 0.000 0.000 0.056
#> GSM1178991 1 0.4535 0.46583 0.704 0.000 0.004 0.292
#> GSM1178994 1 0.5293 0.60341 0.748 0.000 0.100 0.152
#> GSM1178997 1 0.3768 0.67844 0.808 0.008 0.000 0.184
#> GSM1179000 1 0.3172 0.69705 0.840 0.000 0.000 0.160
#> GSM1179013 1 0.3172 0.69643 0.840 0.000 0.000 0.160
#> GSM1179014 1 0.4855 0.47610 0.600 0.000 0.000 0.400
#> GSM1179019 1 0.2760 0.71400 0.872 0.000 0.000 0.128
#> GSM1179020 1 0.2149 0.72394 0.912 0.000 0.000 0.088
#> GSM1179022 1 0.2081 0.72596 0.916 0.000 0.000 0.084
#> GSM1179028 2 0.0188 0.74540 0.000 0.996 0.000 0.004
#> GSM1179032 1 0.1211 0.73198 0.960 0.000 0.000 0.040
#> GSM1179041 2 0.0000 0.74567 0.000 1.000 0.000 0.000
#> GSM1179042 2 0.0336 0.74338 0.000 0.992 0.000 0.008
#> GSM1178976 3 0.1182 0.78503 0.000 0.016 0.968 0.016
#> GSM1178981 1 0.7203 0.28338 0.536 0.000 0.288 0.176
#> GSM1178982 1 0.5993 0.39683 0.628 0.000 0.064 0.308
#> GSM1178983 1 0.5339 0.35035 0.624 0.000 0.020 0.356
#> GSM1178985 3 0.6716 0.19438 0.320 0.000 0.568 0.112
#> GSM1178992 1 0.7814 0.13171 0.416 0.000 0.304 0.280
#> GSM1179005 1 0.2101 0.72055 0.928 0.000 0.012 0.060
#> GSM1179007 1 0.3435 0.69131 0.864 0.000 0.036 0.100
#> GSM1179012 1 0.3051 0.71214 0.884 0.000 0.088 0.028
#> GSM1179016 1 0.6145 0.31960 0.492 0.000 0.048 0.460
#> GSM1179030 1 0.3656 0.72568 0.868 0.012 0.040 0.080
#> GSM1179038 1 0.1022 0.73512 0.968 0.000 0.000 0.032
#> GSM1178987 3 0.0804 0.78950 0.012 0.000 0.980 0.008
#> GSM1179003 3 0.6664 0.41313 0.000 0.216 0.620 0.164
#> GSM1179004 3 0.0937 0.78911 0.012 0.000 0.976 0.012
#> GSM1179039 2 0.0188 0.74540 0.000 0.996 0.000 0.004
#> GSM1178975 1 0.4781 0.41949 0.660 0.004 0.000 0.336
#> GSM1178980 2 0.5662 0.31287 0.016 0.524 0.004 0.456
#> GSM1178995 1 0.2345 0.70304 0.900 0.000 0.000 0.100
#> GSM1178996 1 0.4267 0.68013 0.788 0.000 0.024 0.188
#> GSM1179001 1 0.1389 0.73607 0.952 0.000 0.000 0.048
#> GSM1179002 1 0.1637 0.72776 0.940 0.000 0.000 0.060
#> GSM1179006 1 0.6659 0.22911 0.512 0.000 0.400 0.088
#> GSM1179008 1 0.1211 0.73228 0.960 0.000 0.000 0.040
#> GSM1179015 1 0.4539 0.61739 0.720 0.000 0.008 0.272
#> GSM1179017 4 0.6826 -0.34503 0.084 0.004 0.456 0.456
#> GSM1179026 3 0.1970 0.75637 0.008 0.000 0.932 0.060
#> GSM1179033 1 0.7335 0.15129 0.488 0.000 0.344 0.168
#> GSM1179035 3 0.2670 0.75145 0.072 0.000 0.904 0.024
#> GSM1179036 1 0.2654 0.72637 0.888 0.000 0.004 0.108
#> GSM1178986 1 0.3688 0.66799 0.792 0.000 0.000 0.208
#> GSM1178989 3 0.0592 0.78211 0.000 0.000 0.984 0.016
#> GSM1178993 4 0.7126 -0.03321 0.088 0.376 0.016 0.520
#> GSM1178999 4 0.7714 -0.25308 0.004 0.372 0.192 0.432
#> GSM1179021 2 0.4477 0.56795 0.000 0.688 0.000 0.312
#> GSM1179025 2 0.0376 0.74534 0.000 0.992 0.004 0.004
#> GSM1179027 2 0.5383 0.34430 0.000 0.536 0.012 0.452
#> GSM1179011 4 0.7300 0.34828 0.304 0.180 0.000 0.516
#> GSM1179023 1 0.1302 0.73367 0.956 0.000 0.000 0.044
#> GSM1179029 1 0.4730 0.52580 0.636 0.000 0.000 0.364
#> GSM1179034 1 0.1118 0.73075 0.964 0.000 0.000 0.036
#> GSM1179040 2 0.5172 0.43922 0.000 0.588 0.008 0.404
#> GSM1178988 3 0.0524 0.78494 0.004 0.000 0.988 0.008
#> GSM1179037 3 0.2255 0.76106 0.068 0.000 0.920 0.012
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1178971 1 0.0994 0.8183 0.972 0.004 0.004 0.016 0.004
#> GSM1178979 4 0.3010 0.6879 0.000 0.172 0.000 0.824 0.004
#> GSM1179009 4 0.3962 0.6819 0.152 0.012 0.036 0.800 0.000
#> GSM1179031 2 0.1197 0.8891 0.000 0.952 0.000 0.048 0.000
#> GSM1178970 3 0.3907 0.5692 0.000 0.204 0.772 0.008 0.016
#> GSM1178972 2 0.3933 0.6990 0.000 0.776 0.196 0.008 0.020
#> GSM1178973 4 0.4437 0.1345 0.464 0.000 0.000 0.532 0.004
#> GSM1178974 2 0.2069 0.8435 0.000 0.924 0.012 0.012 0.052
#> GSM1178977 2 0.4707 0.3288 0.000 0.588 0.000 0.392 0.020
#> GSM1178978 1 0.5762 0.3272 0.588 0.000 0.308 0.100 0.004
#> GSM1178998 1 0.1377 0.8154 0.956 0.000 0.020 0.020 0.004
#> GSM1179010 3 0.2890 0.6546 0.160 0.000 0.836 0.004 0.000
#> GSM1179018 4 0.3387 0.6765 0.004 0.000 0.196 0.796 0.004
#> GSM1179024 1 0.2280 0.7764 0.880 0.000 0.000 0.000 0.120
#> GSM1178984 1 0.3851 0.6345 0.768 0.000 0.212 0.016 0.004
#> GSM1178990 1 0.0794 0.8225 0.972 0.000 0.000 0.000 0.028
#> GSM1178991 4 0.3142 0.7314 0.108 0.000 0.004 0.856 0.032
#> GSM1178994 1 0.4044 0.5861 0.732 0.000 0.252 0.012 0.004
#> GSM1178997 1 0.3003 0.7767 0.864 0.044 0.000 0.000 0.092
#> GSM1179000 1 0.2280 0.7809 0.880 0.000 0.000 0.000 0.120
#> GSM1179013 1 0.2074 0.7894 0.896 0.000 0.000 0.000 0.104
#> GSM1179014 5 0.4219 0.3722 0.416 0.000 0.000 0.000 0.584
#> GSM1179019 1 0.1121 0.8212 0.956 0.000 0.000 0.000 0.044
#> GSM1179020 1 0.1197 0.8166 0.952 0.000 0.000 0.000 0.048
#> GSM1179022 1 0.1410 0.8131 0.940 0.000 0.000 0.000 0.060
#> GSM1179028 2 0.1205 0.8888 0.000 0.956 0.000 0.040 0.004
#> GSM1179032 1 0.0703 0.8221 0.976 0.000 0.000 0.000 0.024
#> GSM1179041 2 0.1282 0.8895 0.000 0.952 0.000 0.044 0.004
#> GSM1179042 2 0.1106 0.8713 0.000 0.964 0.000 0.024 0.012
#> GSM1178976 3 0.0727 0.7097 0.012 0.004 0.980 0.004 0.000
#> GSM1178981 3 0.4774 0.2607 0.444 0.000 0.540 0.012 0.004
#> GSM1178982 1 0.5036 0.5761 0.704 0.000 0.200 0.092 0.004
#> GSM1178983 1 0.4280 0.4519 0.676 0.000 0.008 0.312 0.004
#> GSM1178985 3 0.4010 0.5755 0.240 0.004 0.744 0.008 0.004
#> GSM1178992 5 0.6743 0.1710 0.264 0.000 0.340 0.000 0.396
#> GSM1179005 1 0.0693 0.8214 0.980 0.000 0.012 0.000 0.008
#> GSM1179007 1 0.1644 0.8061 0.940 0.000 0.048 0.008 0.004
#> GSM1179012 1 0.3086 0.6927 0.816 0.000 0.180 0.004 0.000
#> GSM1179016 5 0.1809 0.5303 0.060 0.000 0.012 0.000 0.928
#> GSM1179030 1 0.4547 0.6385 0.744 0.008 0.052 0.000 0.196
#> GSM1179038 1 0.2293 0.8019 0.900 0.000 0.000 0.016 0.084
#> GSM1178987 3 0.0451 0.7085 0.008 0.000 0.988 0.004 0.000
#> GSM1179003 5 0.6107 0.2537 0.000 0.016 0.144 0.228 0.612
#> GSM1179004 3 0.0671 0.7114 0.016 0.000 0.980 0.004 0.000
#> GSM1179039 2 0.1282 0.8895 0.000 0.952 0.000 0.044 0.004
#> GSM1178975 4 0.4959 0.4202 0.308 0.020 0.000 0.652 0.020
#> GSM1178980 4 0.0613 0.7931 0.004 0.008 0.000 0.984 0.004
#> GSM1178995 1 0.0854 0.8186 0.976 0.000 0.008 0.012 0.004
#> GSM1178996 1 0.3658 0.7734 0.840 0.008 0.032 0.012 0.108
#> GSM1179001 1 0.3191 0.7786 0.872 0.040 0.000 0.024 0.064
#> GSM1179002 1 0.2429 0.8077 0.916 0.028 0.004 0.020 0.032
#> GSM1179006 3 0.6452 0.0874 0.428 0.004 0.448 0.012 0.108
#> GSM1179008 1 0.2684 0.7986 0.900 0.024 0.000 0.032 0.044
#> GSM1179015 1 0.3790 0.5390 0.724 0.000 0.004 0.000 0.272
#> GSM1179017 5 0.2331 0.4669 0.000 0.008 0.068 0.016 0.908
#> GSM1179026 3 0.4264 0.2568 0.000 0.004 0.620 0.000 0.376
#> GSM1179033 3 0.5365 0.2968 0.424 0.004 0.532 0.036 0.004
#> GSM1179035 3 0.1412 0.7131 0.036 0.004 0.952 0.008 0.000
#> GSM1179036 1 0.5542 0.5499 0.696 0.024 0.004 0.088 0.188
#> GSM1178986 5 0.4803 0.1043 0.492 0.000 0.004 0.012 0.492
#> GSM1178989 3 0.0290 0.6999 0.000 0.000 0.992 0.000 0.008
#> GSM1178993 4 0.0771 0.7930 0.004 0.020 0.000 0.976 0.000
#> GSM1178999 4 0.3733 0.7037 0.000 0.004 0.032 0.804 0.160
#> GSM1179021 4 0.2074 0.7524 0.000 0.104 0.000 0.896 0.000
#> GSM1179025 2 0.1697 0.8849 0.000 0.932 0.008 0.060 0.000
#> GSM1179027 4 0.0510 0.7925 0.000 0.016 0.000 0.984 0.000
#> GSM1179011 4 0.1568 0.7925 0.036 0.020 0.000 0.944 0.000
#> GSM1179023 1 0.0703 0.8214 0.976 0.000 0.000 0.000 0.024
#> GSM1179029 5 0.5327 0.5332 0.288 0.020 0.004 0.036 0.652
#> GSM1179034 1 0.1041 0.8219 0.964 0.000 0.000 0.004 0.032
#> GSM1179040 4 0.1478 0.7778 0.000 0.064 0.000 0.936 0.000
#> GSM1178988 3 0.1341 0.6716 0.000 0.000 0.944 0.000 0.056
#> GSM1179037 3 0.1605 0.7104 0.040 0.004 0.944 0.012 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1178971 1 0.3943 0.38459 0.724 0.000 0.016 0.008 0.248 0.004
#> GSM1178979 4 0.2512 0.74788 0.000 0.116 0.008 0.868 0.008 0.000
#> GSM1179009 4 0.4222 0.66074 0.140 0.008 0.048 0.776 0.028 0.000
#> GSM1179031 2 0.0146 0.82830 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM1178970 3 0.4183 0.55453 0.000 0.116 0.752 0.004 0.128 0.000
#> GSM1178972 2 0.5122 0.56794 0.000 0.576 0.104 0.000 0.320 0.000
#> GSM1178973 4 0.5212 0.00596 0.440 0.000 0.008 0.484 0.068 0.000
#> GSM1178974 2 0.3695 0.69714 0.000 0.712 0.000 0.000 0.272 0.016
#> GSM1178977 2 0.6945 0.18450 0.000 0.392 0.068 0.328 0.212 0.000
#> GSM1178978 3 0.6680 0.23003 0.368 0.004 0.460 0.088 0.068 0.012
#> GSM1178998 1 0.3366 0.59386 0.824 0.000 0.036 0.008 0.128 0.004
#> GSM1179010 3 0.2401 0.66920 0.060 0.000 0.892 0.000 0.044 0.004
#> GSM1179018 4 0.3577 0.69654 0.000 0.000 0.168 0.792 0.020 0.020
#> GSM1179024 1 0.3780 0.49676 0.728 0.000 0.000 0.004 0.020 0.248
#> GSM1178984 1 0.5098 0.35094 0.632 0.000 0.240 0.004 0.124 0.000
#> GSM1178990 1 0.3404 0.67082 0.824 0.000 0.016 0.008 0.020 0.132
#> GSM1178991 4 0.5196 0.54797 0.060 0.000 0.012 0.692 0.044 0.192
#> GSM1178994 3 0.4854 0.25956 0.432 0.000 0.528 0.008 0.020 0.012
#> GSM1178997 1 0.2830 0.65872 0.864 0.068 0.000 0.000 0.004 0.064
#> GSM1179000 1 0.2994 0.58598 0.788 0.004 0.000 0.000 0.000 0.208
#> GSM1179013 1 0.3541 0.49307 0.728 0.000 0.000 0.000 0.012 0.260
#> GSM1179014 6 0.3126 0.56427 0.248 0.000 0.000 0.000 0.000 0.752
#> GSM1179019 1 0.1584 0.69068 0.928 0.008 0.000 0.000 0.000 0.064
#> GSM1179020 1 0.1549 0.68540 0.936 0.000 0.000 0.000 0.020 0.044
#> GSM1179022 1 0.2420 0.66845 0.864 0.000 0.000 0.004 0.004 0.128
#> GSM1179028 2 0.0603 0.82581 0.000 0.980 0.000 0.004 0.016 0.000
#> GSM1179032 1 0.1049 0.69090 0.960 0.000 0.000 0.000 0.008 0.032
#> GSM1179041 2 0.0000 0.82781 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179042 2 0.2257 0.79784 0.000 0.876 0.000 0.008 0.116 0.000
#> GSM1178976 3 0.1588 0.66612 0.000 0.004 0.924 0.000 0.072 0.000
#> GSM1178981 3 0.3680 0.58836 0.216 0.000 0.756 0.000 0.020 0.008
#> GSM1178982 3 0.5841 0.17280 0.428 0.000 0.476 0.036 0.032 0.028
#> GSM1178983 1 0.6485 0.26622 0.556 0.000 0.084 0.272 0.036 0.052
#> GSM1178985 3 0.3588 0.63745 0.148 0.000 0.800 0.004 0.044 0.004
#> GSM1178992 6 0.5821 0.21923 0.132 0.000 0.340 0.000 0.016 0.512
#> GSM1179005 1 0.2828 0.65245 0.876 0.000 0.068 0.004 0.036 0.016
#> GSM1179007 1 0.3654 0.59130 0.812 0.000 0.072 0.004 0.104 0.008
#> GSM1179012 1 0.6074 0.13973 0.500 0.000 0.368 0.004 0.064 0.064
#> GSM1179016 6 0.2033 0.48666 0.056 0.000 0.004 0.004 0.020 0.916
#> GSM1179030 6 0.7176 0.27387 0.372 0.028 0.168 0.004 0.040 0.388
#> GSM1179038 1 0.4658 0.59376 0.744 0.000 0.020 0.012 0.084 0.140
#> GSM1178987 3 0.0717 0.66647 0.000 0.000 0.976 0.000 0.016 0.008
#> GSM1179003 5 0.6039 0.07649 0.000 0.016 0.028 0.112 0.576 0.268
#> GSM1179004 3 0.0520 0.66466 0.000 0.000 0.984 0.000 0.008 0.008
#> GSM1179039 2 0.0458 0.82729 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM1178975 4 0.5413 0.45026 0.188 0.008 0.000 0.628 0.172 0.004
#> GSM1178980 4 0.0862 0.80484 0.000 0.008 0.000 0.972 0.016 0.004
#> GSM1178995 1 0.3024 0.60357 0.844 0.000 0.028 0.004 0.120 0.004
#> GSM1178996 5 0.5758 0.37710 0.372 0.004 0.052 0.004 0.528 0.040
#> GSM1179001 5 0.4568 0.58801 0.300 0.000 0.000 0.020 0.652 0.028
#> GSM1179002 5 0.4660 0.43890 0.428 0.000 0.004 0.008 0.540 0.020
#> GSM1179006 3 0.7759 0.12912 0.244 0.000 0.356 0.012 0.148 0.240
#> GSM1179008 1 0.4938 -0.39953 0.488 0.000 0.000 0.020 0.464 0.028
#> GSM1179015 6 0.4883 0.36754 0.400 0.000 0.008 0.004 0.036 0.552
#> GSM1179017 6 0.4058 0.12621 0.000 0.000 0.016 0.004 0.320 0.660
#> GSM1179026 3 0.6009 0.14766 0.000 0.000 0.432 0.000 0.300 0.268
#> GSM1179033 3 0.6042 0.23625 0.388 0.000 0.440 0.008 0.160 0.004
#> GSM1179035 3 0.2357 0.66841 0.012 0.000 0.888 0.004 0.092 0.004
#> GSM1179036 5 0.4403 0.58759 0.280 0.000 0.000 0.024 0.676 0.020
#> GSM1178986 6 0.4967 0.57241 0.240 0.000 0.040 0.020 0.020 0.680
#> GSM1178989 3 0.2065 0.65607 0.000 0.000 0.912 0.004 0.032 0.052
#> GSM1178993 4 0.0458 0.80729 0.000 0.016 0.000 0.984 0.000 0.000
#> GSM1178999 4 0.3113 0.74284 0.000 0.004 0.004 0.828 0.020 0.144
#> GSM1179021 4 0.1219 0.80083 0.000 0.048 0.000 0.948 0.004 0.000
#> GSM1179025 2 0.1138 0.82394 0.000 0.960 0.012 0.024 0.004 0.000
#> GSM1179027 4 0.0891 0.80700 0.000 0.024 0.000 0.968 0.008 0.000
#> GSM1179011 4 0.0870 0.80672 0.012 0.012 0.000 0.972 0.004 0.000
#> GSM1179023 1 0.1265 0.69018 0.948 0.000 0.000 0.000 0.008 0.044
#> GSM1179029 6 0.6034 0.42809 0.224 0.000 0.004 0.020 0.196 0.556
#> GSM1179034 1 0.1485 0.68533 0.944 0.000 0.000 0.004 0.028 0.024
#> GSM1179040 4 0.0935 0.80712 0.000 0.032 0.000 0.964 0.004 0.000
#> GSM1178988 3 0.1556 0.64189 0.000 0.000 0.920 0.000 0.000 0.080
#> GSM1179037 3 0.2763 0.66719 0.016 0.000 0.876 0.008 0.084 0.016
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) protocol(p) k
#> CV:NMF 73 0.0820 0.0828 2
#> CV:NMF 66 0.0157 0.0338 3
#> CV:NMF 48 0.0895 0.1147 4
#> CV:NMF 59 0.0552 0.0321 5
#> CV:NMF 48 0.0243 0.0106 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 31632 rows and 73 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 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 0.640 0.810 0.908 0.3321 0.703 0.703
#> 3 3 0.289 0.259 0.638 0.6212 0.909 0.870
#> 4 4 0.353 0.550 0.745 0.1916 0.628 0.447
#> 5 5 0.481 0.598 0.755 0.1126 0.883 0.691
#> 6 6 0.529 0.626 0.793 0.0454 0.989 0.961
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
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
#> GSM1178971 1 0.1843 0.904 0.972 0.028
#> GSM1178979 2 0.9087 0.540 0.324 0.676
#> GSM1179009 1 0.5059 0.852 0.888 0.112
#> GSM1179031 2 0.0000 0.852 0.000 1.000
#> GSM1178970 1 0.9833 0.302 0.576 0.424
#> GSM1178972 2 0.0000 0.852 0.000 1.000
#> GSM1178973 1 0.0000 0.903 1.000 0.000
#> GSM1178974 2 0.0000 0.852 0.000 1.000
#> GSM1178977 1 0.9491 0.465 0.632 0.368
#> GSM1178978 1 0.5408 0.850 0.876 0.124
#> GSM1178998 1 0.0000 0.903 1.000 0.000
#> GSM1179010 1 0.0000 0.903 1.000 0.000
#> GSM1179018 1 0.4022 0.882 0.920 0.080
#> GSM1179024 1 0.0000 0.903 1.000 0.000
#> GSM1178984 1 0.2043 0.904 0.968 0.032
#> GSM1178990 1 0.0938 0.904 0.988 0.012
#> GSM1178991 1 0.0938 0.905 0.988 0.012
#> GSM1178994 1 0.2236 0.903 0.964 0.036
#> GSM1178997 1 0.0938 0.904 0.988 0.012
#> GSM1179000 1 0.0938 0.904 0.988 0.012
#> GSM1179013 1 0.0000 0.903 1.000 0.000
#> GSM1179014 1 0.2948 0.892 0.948 0.052
#> GSM1179019 1 0.0938 0.904 0.988 0.012
#> GSM1179020 1 0.0376 0.903 0.996 0.004
#> GSM1179022 1 0.0000 0.903 1.000 0.000
#> GSM1179028 2 0.0000 0.852 0.000 1.000
#> GSM1179032 1 0.0000 0.903 1.000 0.000
#> GSM1179041 2 0.0000 0.852 0.000 1.000
#> GSM1179042 2 0.0000 0.852 0.000 1.000
#> GSM1178976 1 0.8909 0.610 0.692 0.308
#> GSM1178981 1 0.2603 0.902 0.956 0.044
#> GSM1178982 1 0.3584 0.893 0.932 0.068
#> GSM1178983 1 0.4022 0.887 0.920 0.080
#> GSM1178985 1 0.4562 0.877 0.904 0.096
#> GSM1178992 1 0.1843 0.905 0.972 0.028
#> GSM1179005 1 0.1184 0.905 0.984 0.016
#> GSM1179007 1 0.1184 0.905 0.984 0.016
#> GSM1179012 1 0.0000 0.903 1.000 0.000
#> GSM1179016 1 0.9000 0.576 0.684 0.316
#> GSM1179030 1 0.4431 0.880 0.908 0.092
#> GSM1179038 1 0.1414 0.905 0.980 0.020
#> GSM1178987 1 0.2603 0.902 0.956 0.044
#> GSM1179003 2 0.9491 0.438 0.368 0.632
#> GSM1179004 1 0.1843 0.905 0.972 0.028
#> GSM1179039 2 0.0000 0.852 0.000 1.000
#> GSM1178975 1 0.0000 0.903 1.000 0.000
#> GSM1178980 2 0.9323 0.495 0.348 0.652
#> GSM1178995 1 0.1184 0.905 0.984 0.016
#> GSM1178996 1 0.4022 0.887 0.920 0.080
#> GSM1179001 1 0.0000 0.903 1.000 0.000
#> GSM1179002 1 0.0000 0.903 1.000 0.000
#> GSM1179006 1 0.5408 0.852 0.876 0.124
#> GSM1179008 1 0.0000 0.903 1.000 0.000
#> GSM1179015 1 0.0000 0.903 1.000 0.000
#> GSM1179017 1 0.9963 0.147 0.536 0.464
#> GSM1179026 1 0.2778 0.900 0.952 0.048
#> GSM1179033 1 0.2948 0.899 0.948 0.052
#> GSM1179035 1 0.2778 0.900 0.952 0.048
#> GSM1179036 1 0.3584 0.893 0.932 0.068
#> GSM1178986 1 0.3879 0.890 0.924 0.076
#> GSM1178989 1 0.8861 0.617 0.696 0.304
#> GSM1178993 1 0.8763 0.615 0.704 0.296
#> GSM1178999 2 0.7602 0.712 0.220 0.780
#> GSM1179021 2 0.7453 0.720 0.212 0.788
#> GSM1179025 2 0.0000 0.852 0.000 1.000
#> GSM1179027 1 0.9866 0.272 0.568 0.432
#> GSM1179011 1 0.2236 0.899 0.964 0.036
#> GSM1179023 1 0.0000 0.903 1.000 0.000
#> GSM1179029 1 0.0000 0.903 1.000 0.000
#> GSM1179034 1 0.0000 0.903 1.000 0.000
#> GSM1179040 1 0.9909 0.230 0.556 0.444
#> GSM1178988 1 0.7299 0.758 0.796 0.204
#> GSM1179037 1 0.2778 0.900 0.952 0.048
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1178971 1 0.5882 1.13e-01 0.652 0.000 0.348
#> GSM1178979 2 0.9573 3.83e-01 0.328 0.460 0.212
#> GSM1179009 1 0.5016 3.78e-01 0.760 0.000 0.240
#> GSM1179031 2 0.0000 8.17e-01 0.000 1.000 0.000
#> GSM1178970 1 0.9086 1.33e-01 0.552 0.220 0.228
#> GSM1178972 2 0.1163 8.10e-01 0.000 0.972 0.028
#> GSM1178973 3 0.6180 3.27e-01 0.416 0.000 0.584
#> GSM1178974 2 0.0237 8.16e-01 0.000 0.996 0.004
#> GSM1178977 1 0.8568 2.03e-01 0.604 0.168 0.228
#> GSM1178978 1 0.5291 3.60e-01 0.732 0.000 0.268
#> GSM1178998 1 0.6111 -1.80e-02 0.604 0.000 0.396
#> GSM1179010 1 0.6045 1.80e-02 0.620 0.000 0.380
#> GSM1179018 1 0.4233 4.33e-01 0.836 0.004 0.160
#> GSM1179024 1 0.6308 -2.08e-01 0.508 0.000 0.492
#> GSM1178984 1 0.4291 3.97e-01 0.820 0.000 0.180
#> GSM1178990 1 0.4974 3.13e-01 0.764 0.000 0.236
#> GSM1178991 1 0.6309 -2.97e-01 0.504 0.000 0.496
#> GSM1178994 1 0.4062 4.11e-01 0.836 0.000 0.164
#> GSM1178997 1 0.6308 -2.24e-01 0.508 0.000 0.492
#> GSM1179000 3 0.6309 3.11e-02 0.500 0.000 0.500
#> GSM1179013 1 0.6308 -2.08e-01 0.508 0.000 0.492
#> GSM1179014 1 0.6204 6.69e-05 0.576 0.000 0.424
#> GSM1179019 1 0.6309 -2.27e-01 0.504 0.000 0.496
#> GSM1179020 1 0.6308 -2.17e-01 0.508 0.000 0.492
#> GSM1179022 1 0.6308 -2.08e-01 0.508 0.000 0.492
#> GSM1179028 2 0.0000 8.17e-01 0.000 1.000 0.000
#> GSM1179032 1 0.6308 -2.08e-01 0.508 0.000 0.492
#> GSM1179041 2 0.0000 8.17e-01 0.000 1.000 0.000
#> GSM1179042 2 0.0000 8.17e-01 0.000 1.000 0.000
#> GSM1178976 1 0.7297 2.88e-01 0.708 0.120 0.172
#> GSM1178981 1 0.2301 4.75e-01 0.936 0.004 0.060
#> GSM1178982 1 0.3845 4.61e-01 0.872 0.012 0.116
#> GSM1178983 1 0.4059 4.52e-01 0.860 0.012 0.128
#> GSM1178985 1 0.3091 4.56e-01 0.912 0.016 0.072
#> GSM1178992 1 0.2400 4.74e-01 0.932 0.004 0.064
#> GSM1179005 1 0.2356 4.65e-01 0.928 0.000 0.072
#> GSM1179007 1 0.2356 4.65e-01 0.928 0.000 0.072
#> GSM1179012 1 0.6079 1.68e-02 0.612 0.000 0.388
#> GSM1179016 1 0.7368 2.11e-01 0.604 0.044 0.352
#> GSM1179030 1 0.4349 4.51e-01 0.852 0.020 0.128
#> GSM1179038 1 0.2959 4.56e-01 0.900 0.000 0.100
#> GSM1178987 1 0.2301 4.75e-01 0.936 0.004 0.060
#> GSM1179003 2 0.9892 3.49e-01 0.340 0.392 0.268
#> GSM1179004 1 0.1989 4.75e-01 0.948 0.004 0.048
#> GSM1179039 2 0.0000 8.17e-01 0.000 1.000 0.000
#> GSM1178975 3 0.6180 3.27e-01 0.416 0.000 0.584
#> GSM1178980 3 0.9811 -5.53e-01 0.240 0.380 0.380
#> GSM1178995 1 0.2537 4.63e-01 0.920 0.000 0.080
#> GSM1178996 1 0.5008 3.91e-01 0.804 0.016 0.180
#> GSM1179001 1 0.6305 -1.93e-01 0.516 0.000 0.484
#> GSM1179002 1 0.6305 -1.93e-01 0.516 0.000 0.484
#> GSM1179006 1 0.3752 4.39e-01 0.884 0.020 0.096
#> GSM1179008 1 0.6305 -1.93e-01 0.516 0.000 0.484
#> GSM1179015 1 0.6126 2.52e-03 0.600 0.000 0.400
#> GSM1179017 1 0.9306 -1.70e-02 0.480 0.172 0.348
#> GSM1179026 1 0.1765 4.74e-01 0.956 0.004 0.040
#> GSM1179033 1 0.1482 4.76e-01 0.968 0.012 0.020
#> GSM1179035 1 0.1411 4.73e-01 0.964 0.000 0.036
#> GSM1179036 1 0.3207 4.64e-01 0.904 0.012 0.084
#> GSM1178986 1 0.2703 4.70e-01 0.928 0.016 0.056
#> GSM1178989 1 0.7165 2.92e-01 0.716 0.112 0.172
#> GSM1178993 1 0.7741 1.47e-01 0.568 0.056 0.376
#> GSM1178999 2 0.9046 5.68e-01 0.152 0.516 0.332
#> GSM1179021 2 0.8938 5.77e-01 0.144 0.528 0.328
#> GSM1179025 2 0.0237 8.16e-01 0.000 0.996 0.004
#> GSM1179027 1 0.9311 -1.12e-01 0.452 0.164 0.384
#> GSM1179011 3 0.6654 1.78e-01 0.456 0.008 0.536
#> GSM1179023 1 0.6308 -2.08e-01 0.508 0.000 0.492
#> GSM1179029 1 0.6204 -5.68e-02 0.576 0.000 0.424
#> GSM1179034 1 0.6308 -2.08e-01 0.508 0.000 0.492
#> GSM1179040 1 0.9417 -1.39e-01 0.440 0.176 0.384
#> GSM1178988 1 0.5393 3.68e-01 0.808 0.044 0.148
#> GSM1179037 1 0.1411 4.73e-01 0.964 0.000 0.036
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1178971 1 0.4804 0.44329 0.708 0.000 0.276 0.016
#> GSM1178979 3 0.6862 -0.35934 0.000 0.408 0.488 0.104
#> GSM1179009 3 0.7180 0.40878 0.264 0.000 0.548 0.188
#> GSM1179031 2 0.0000 0.83976 0.000 1.000 0.000 0.000
#> GSM1178970 3 0.6167 0.02896 0.000 0.208 0.668 0.124
#> GSM1178972 2 0.1151 0.81599 0.000 0.968 0.024 0.008
#> GSM1178973 1 0.3606 0.74015 0.840 0.000 0.020 0.140
#> GSM1178974 2 0.0188 0.83735 0.000 0.996 0.004 0.000
#> GSM1178977 3 0.6924 0.12262 0.040 0.152 0.668 0.140
#> GSM1178978 3 0.6855 0.41424 0.276 0.000 0.580 0.144
#> GSM1178998 1 0.5062 0.64609 0.752 0.000 0.184 0.064
#> GSM1179010 1 0.5810 0.51401 0.672 0.000 0.256 0.072
#> GSM1179018 3 0.6594 0.56219 0.240 0.000 0.620 0.140
#> GSM1179024 1 0.0000 0.82372 1.000 0.000 0.000 0.000
#> GSM1178984 3 0.5827 0.40728 0.436 0.000 0.532 0.032
#> GSM1178990 1 0.5099 0.03713 0.612 0.000 0.380 0.008
#> GSM1178991 1 0.3443 0.74849 0.848 0.000 0.016 0.136
#> GSM1178994 3 0.5865 0.46090 0.412 0.000 0.552 0.036
#> GSM1178997 1 0.1820 0.80955 0.944 0.000 0.036 0.020
#> GSM1179000 1 0.1388 0.81364 0.960 0.000 0.028 0.012
#> GSM1179013 1 0.0000 0.82372 1.000 0.000 0.000 0.000
#> GSM1179014 1 0.5486 0.60428 0.720 0.000 0.080 0.200
#> GSM1179019 1 0.0921 0.81665 0.972 0.000 0.028 0.000
#> GSM1179020 1 0.0336 0.82211 0.992 0.000 0.008 0.000
#> GSM1179022 1 0.0000 0.82372 1.000 0.000 0.000 0.000
#> GSM1179028 2 0.0000 0.83976 0.000 1.000 0.000 0.000
#> GSM1179032 1 0.0000 0.82372 1.000 0.000 0.000 0.000
#> GSM1179041 2 0.0000 0.83976 0.000 1.000 0.000 0.000
#> GSM1179042 2 0.0000 0.83976 0.000 1.000 0.000 0.000
#> GSM1178976 3 0.4059 0.38047 0.020 0.096 0.848 0.036
#> GSM1178981 3 0.4770 0.65943 0.288 0.000 0.700 0.012
#> GSM1178982 3 0.5364 0.62977 0.320 0.000 0.652 0.028
#> GSM1178983 3 0.5473 0.61751 0.324 0.000 0.644 0.032
#> GSM1178985 3 0.4574 0.66137 0.220 0.000 0.756 0.024
#> GSM1178992 3 0.4844 0.65402 0.300 0.000 0.688 0.012
#> GSM1179005 3 0.4857 0.63307 0.324 0.000 0.668 0.008
#> GSM1179007 3 0.4978 0.63274 0.324 0.000 0.664 0.012
#> GSM1179012 1 0.5910 0.53777 0.676 0.000 0.236 0.088
#> GSM1179016 4 0.7214 0.42760 0.104 0.020 0.312 0.564
#> GSM1179030 3 0.5858 0.63686 0.292 0.008 0.656 0.044
#> GSM1179038 3 0.5189 0.58736 0.372 0.000 0.616 0.012
#> GSM1178987 3 0.4770 0.65943 0.288 0.000 0.700 0.012
#> GSM1179003 3 0.7216 -0.36343 0.000 0.336 0.508 0.156
#> GSM1179004 3 0.4844 0.65440 0.300 0.000 0.688 0.012
#> GSM1179039 2 0.0000 0.83976 0.000 1.000 0.000 0.000
#> GSM1178975 1 0.3606 0.74015 0.840 0.000 0.020 0.140
#> GSM1178980 4 0.8049 -0.15595 0.004 0.336 0.292 0.368
#> GSM1178995 3 0.4917 0.62572 0.336 0.000 0.656 0.008
#> GSM1178996 3 0.6058 0.41453 0.424 0.004 0.536 0.036
#> GSM1179001 1 0.0376 0.82361 0.992 0.000 0.004 0.004
#> GSM1179002 1 0.0376 0.82361 0.992 0.000 0.004 0.004
#> GSM1179006 3 0.4547 0.62980 0.184 0.008 0.784 0.024
#> GSM1179008 1 0.0376 0.82361 0.992 0.000 0.004 0.004
#> GSM1179015 1 0.5727 0.59213 0.704 0.000 0.200 0.096
#> GSM1179017 4 0.6945 0.44188 0.004 0.136 0.276 0.584
#> GSM1179026 3 0.4690 0.67016 0.260 0.000 0.724 0.016
#> GSM1179033 3 0.4718 0.66661 0.280 0.000 0.708 0.012
#> GSM1179035 3 0.4546 0.67085 0.256 0.000 0.732 0.012
#> GSM1179036 3 0.5233 0.62018 0.332 0.000 0.648 0.020
#> GSM1178986 3 0.5358 0.67508 0.252 0.000 0.700 0.048
#> GSM1178989 3 0.4020 0.38354 0.020 0.088 0.852 0.040
#> GSM1178993 3 0.6287 -0.00914 0.020 0.036 0.600 0.344
#> GSM1178999 2 0.7653 0.04201 0.000 0.460 0.240 0.300
#> GSM1179021 2 0.7557 0.08672 0.000 0.484 0.232 0.284
#> GSM1179025 2 0.0188 0.83735 0.000 0.996 0.004 0.000
#> GSM1179027 3 0.6961 -0.25163 0.000 0.120 0.512 0.368
#> GSM1179011 1 0.5910 0.56160 0.672 0.000 0.084 0.244
#> GSM1179023 1 0.0000 0.82372 1.000 0.000 0.000 0.000
#> GSM1179029 1 0.5091 0.64374 0.752 0.000 0.180 0.068
#> GSM1179034 1 0.0000 0.82372 1.000 0.000 0.000 0.000
#> GSM1179040 3 0.7063 -0.26345 0.000 0.132 0.508 0.360
#> GSM1178988 3 0.4417 0.53197 0.108 0.020 0.828 0.044
#> GSM1179037 3 0.4546 0.67085 0.256 0.000 0.732 0.012
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1178971 1 0.4768 0.19693 0.592 0.000 0.384 0.024 0.000
#> GSM1178979 4 0.7779 0.52665 0.004 0.312 0.312 0.328 0.044
#> GSM1179009 3 0.6989 0.24830 0.116 0.000 0.524 0.296 0.064
#> GSM1179031 2 0.0000 0.98871 0.000 1.000 0.000 0.000 0.000
#> GSM1178970 3 0.7606 -0.21384 0.004 0.184 0.448 0.304 0.060
#> GSM1178972 2 0.1588 0.93724 0.000 0.948 0.008 0.028 0.016
#> GSM1178973 1 0.3663 0.70658 0.820 0.000 0.004 0.132 0.044
#> GSM1178974 2 0.0290 0.98537 0.000 0.992 0.000 0.000 0.008
#> GSM1178977 3 0.7971 -0.16248 0.040 0.128 0.456 0.316 0.060
#> GSM1178978 3 0.7603 0.11082 0.260 0.000 0.428 0.256 0.056
#> GSM1178998 1 0.6680 -0.00318 0.500 0.000 0.240 0.008 0.252
#> GSM1179010 5 0.6803 0.47044 0.156 0.000 0.372 0.020 0.452
#> GSM1179018 3 0.5648 0.51726 0.064 0.000 0.676 0.216 0.044
#> GSM1179024 1 0.0510 0.79779 0.984 0.000 0.016 0.000 0.000
#> GSM1178984 3 0.5976 0.44988 0.208 0.000 0.632 0.016 0.144
#> GSM1178990 3 0.5365 0.19025 0.416 0.000 0.528 0.000 0.056
#> GSM1178991 1 0.3849 0.71324 0.820 0.000 0.012 0.116 0.052
#> GSM1178994 3 0.5722 0.50109 0.184 0.000 0.664 0.016 0.136
#> GSM1178997 1 0.1743 0.78354 0.940 0.000 0.028 0.028 0.004
#> GSM1179000 1 0.1211 0.78929 0.960 0.000 0.016 0.024 0.000
#> GSM1179013 1 0.0510 0.79779 0.984 0.000 0.016 0.000 0.000
#> GSM1179014 1 0.5429 0.55416 0.712 0.000 0.032 0.104 0.152
#> GSM1179019 1 0.0912 0.79229 0.972 0.000 0.016 0.012 0.000
#> GSM1179020 1 0.0451 0.79661 0.988 0.000 0.008 0.004 0.000
#> GSM1179022 1 0.0510 0.79779 0.984 0.000 0.016 0.000 0.000
#> GSM1179028 2 0.0000 0.98871 0.000 1.000 0.000 0.000 0.000
#> GSM1179032 1 0.0510 0.79779 0.984 0.000 0.016 0.000 0.000
#> GSM1179041 2 0.0000 0.98871 0.000 1.000 0.000 0.000 0.000
#> GSM1179042 2 0.0000 0.98871 0.000 1.000 0.000 0.000 0.000
#> GSM1178976 3 0.5303 0.46105 0.000 0.084 0.732 0.136 0.048
#> GSM1178981 3 0.3239 0.70503 0.068 0.000 0.868 0.020 0.044
#> GSM1178982 3 0.4473 0.66475 0.160 0.000 0.772 0.044 0.024
#> GSM1178983 3 0.4660 0.64142 0.180 0.000 0.752 0.044 0.024
#> GSM1178985 3 0.3299 0.70312 0.060 0.000 0.868 0.036 0.036
#> GSM1178992 3 0.2234 0.69418 0.044 0.000 0.916 0.004 0.036
#> GSM1179005 3 0.2726 0.68228 0.052 0.000 0.884 0.000 0.064
#> GSM1179007 3 0.2790 0.68160 0.052 0.000 0.880 0.000 0.068
#> GSM1179012 5 0.6613 0.49814 0.172 0.000 0.352 0.008 0.468
#> GSM1179016 5 0.7683 0.25216 0.072 0.000 0.236 0.248 0.444
#> GSM1179030 3 0.4930 0.65002 0.160 0.004 0.748 0.068 0.020
#> GSM1179038 3 0.3803 0.66063 0.140 0.000 0.804 0.000 0.056
#> GSM1178987 3 0.3239 0.70493 0.068 0.000 0.868 0.020 0.044
#> GSM1179003 4 0.7540 0.55002 0.000 0.240 0.332 0.384 0.044
#> GSM1179004 3 0.2515 0.69926 0.044 0.000 0.904 0.008 0.044
#> GSM1179039 2 0.0000 0.98871 0.000 1.000 0.000 0.000 0.000
#> GSM1178975 1 0.3663 0.70658 0.820 0.000 0.004 0.132 0.044
#> GSM1178980 4 0.5268 0.54882 0.000 0.216 0.076 0.692 0.016
#> GSM1178995 3 0.2927 0.68194 0.068 0.000 0.872 0.000 0.060
#> GSM1178996 3 0.5275 0.46528 0.276 0.004 0.664 0.032 0.024
#> GSM1179001 1 0.2959 0.72463 0.864 0.000 0.100 0.000 0.036
#> GSM1179002 1 0.2959 0.72463 0.864 0.000 0.100 0.000 0.036
#> GSM1179006 3 0.3117 0.67819 0.024 0.008 0.880 0.068 0.020
#> GSM1179008 1 0.2959 0.72463 0.864 0.000 0.100 0.000 0.036
#> GSM1179015 5 0.6736 0.49488 0.196 0.000 0.344 0.008 0.452
#> GSM1179017 5 0.7605 0.10319 0.000 0.096 0.164 0.260 0.480
#> GSM1179026 3 0.1954 0.69904 0.032 0.000 0.932 0.008 0.028
#> GSM1179033 3 0.1809 0.70562 0.060 0.000 0.928 0.000 0.012
#> GSM1179035 3 0.2122 0.69898 0.032 0.000 0.924 0.008 0.036
#> GSM1179036 3 0.3489 0.66533 0.148 0.000 0.824 0.012 0.016
#> GSM1178986 3 0.3771 0.70623 0.088 0.000 0.836 0.052 0.024
#> GSM1178989 3 0.5325 0.46666 0.000 0.076 0.732 0.136 0.056
#> GSM1178993 4 0.5262 0.37517 0.012 0.000 0.376 0.580 0.032
#> GSM1178999 4 0.6162 0.43091 0.000 0.364 0.072 0.536 0.028
#> GSM1179021 4 0.5818 0.42746 0.000 0.364 0.064 0.556 0.016
#> GSM1179025 2 0.0290 0.98537 0.000 0.992 0.000 0.000 0.008
#> GSM1179027 4 0.4130 0.58988 0.000 0.012 0.292 0.696 0.000
#> GSM1179011 1 0.5271 0.53077 0.652 0.000 0.016 0.284 0.048
#> GSM1179023 1 0.0510 0.79779 0.984 0.000 0.016 0.000 0.000
#> GSM1179029 1 0.6798 -0.22443 0.436 0.000 0.252 0.004 0.308
#> GSM1179034 1 0.0510 0.79779 0.984 0.000 0.016 0.000 0.000
#> GSM1179040 4 0.4404 0.59748 0.000 0.024 0.292 0.684 0.000
#> GSM1178988 3 0.4107 0.60079 0.008 0.012 0.812 0.120 0.048
#> GSM1179037 3 0.2122 0.69898 0.032 0.000 0.924 0.008 0.036
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1178971 1 0.4636 0.1401 0.568 0.000 0.396 0.000 0.012 0.024
#> GSM1178979 4 0.8279 0.3270 0.000 0.224 0.292 0.300 0.060 0.124
#> GSM1179009 3 0.7032 0.1955 0.056 0.000 0.516 0.212 0.036 0.180
#> GSM1179031 2 0.0000 0.9792 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178970 3 0.7967 -0.0186 0.000 0.132 0.436 0.224 0.076 0.132
#> GSM1178972 2 0.2386 0.8836 0.000 0.896 0.000 0.064 0.028 0.012
#> GSM1178973 1 0.4347 0.6824 0.784 0.000 0.012 0.064 0.040 0.100
#> GSM1178974 2 0.0508 0.9725 0.000 0.984 0.000 0.000 0.012 0.004
#> GSM1178977 3 0.8291 0.0172 0.032 0.076 0.440 0.232 0.084 0.136
#> GSM1178978 3 0.7851 0.1655 0.236 0.000 0.436 0.136 0.056 0.136
#> GSM1178998 1 0.5503 -0.3411 0.456 0.000 0.128 0.000 0.000 0.416
#> GSM1179010 6 0.3803 0.6383 0.056 0.000 0.184 0.000 0.000 0.760
#> GSM1179018 3 0.5668 0.4942 0.036 0.000 0.660 0.196 0.028 0.080
#> GSM1179024 1 0.0405 0.7923 0.988 0.000 0.004 0.000 0.000 0.008
#> GSM1178984 3 0.5354 0.4022 0.160 0.000 0.580 0.000 0.000 0.260
#> GSM1178990 3 0.5223 0.1939 0.396 0.000 0.508 0.000 0.000 0.096
#> GSM1178991 1 0.4410 0.6739 0.784 0.000 0.012 0.068 0.056 0.080
#> GSM1178994 3 0.5042 0.4992 0.136 0.000 0.648 0.000 0.004 0.212
#> GSM1178997 1 0.1959 0.7749 0.924 0.000 0.032 0.000 0.020 0.024
#> GSM1179000 1 0.1536 0.7825 0.944 0.000 0.020 0.000 0.012 0.024
#> GSM1179013 1 0.0405 0.7923 0.988 0.000 0.004 0.000 0.000 0.008
#> GSM1179014 1 0.3717 0.5276 0.708 0.000 0.016 0.000 0.276 0.000
#> GSM1179019 1 0.1237 0.7855 0.956 0.000 0.020 0.000 0.004 0.020
#> GSM1179020 1 0.0551 0.7913 0.984 0.000 0.008 0.000 0.004 0.004
#> GSM1179022 1 0.0405 0.7923 0.988 0.000 0.004 0.000 0.000 0.008
#> GSM1179028 2 0.0000 0.9792 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179032 1 0.0405 0.7923 0.988 0.000 0.004 0.000 0.000 0.008
#> GSM1179041 2 0.0000 0.9792 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179042 2 0.0000 0.9792 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178976 3 0.5379 0.5368 0.000 0.048 0.716 0.036 0.088 0.112
#> GSM1178981 3 0.2507 0.7335 0.032 0.000 0.888 0.004 0.004 0.072
#> GSM1178982 3 0.3755 0.7011 0.120 0.000 0.808 0.004 0.020 0.048
#> GSM1178983 3 0.3974 0.6830 0.140 0.000 0.788 0.004 0.024 0.044
#> GSM1178985 3 0.2775 0.7276 0.032 0.000 0.880 0.000 0.048 0.040
#> GSM1178992 3 0.2239 0.7287 0.020 0.000 0.900 0.000 0.008 0.072
#> GSM1179005 3 0.2605 0.7125 0.028 0.000 0.864 0.000 0.000 0.108
#> GSM1179007 3 0.2651 0.7113 0.028 0.000 0.860 0.000 0.000 0.112
#> GSM1179012 6 0.5051 0.7307 0.124 0.000 0.176 0.000 0.020 0.680
#> GSM1179016 5 0.3835 0.7094 0.056 0.000 0.188 0.000 0.756 0.000
#> GSM1179030 3 0.4436 0.6849 0.120 0.000 0.776 0.020 0.036 0.048
#> GSM1179038 3 0.3655 0.6952 0.112 0.000 0.792 0.000 0.000 0.096
#> GSM1178987 3 0.2507 0.7332 0.032 0.000 0.888 0.004 0.004 0.072
#> GSM1179003 4 0.7831 0.3965 0.000 0.156 0.280 0.412 0.072 0.080
#> GSM1179004 3 0.1973 0.7298 0.012 0.000 0.916 0.004 0.004 0.064
#> GSM1179039 2 0.0000 0.9792 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178975 1 0.4347 0.6824 0.784 0.000 0.012 0.064 0.040 0.100
#> GSM1178980 4 0.0146 0.4017 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM1178995 3 0.2842 0.7120 0.044 0.000 0.852 0.000 0.000 0.104
#> GSM1178996 3 0.4777 0.5328 0.244 0.000 0.684 0.004 0.036 0.032
#> GSM1179001 1 0.2697 0.6990 0.864 0.000 0.092 0.000 0.000 0.044
#> GSM1179002 1 0.2697 0.6990 0.864 0.000 0.092 0.000 0.000 0.044
#> GSM1179006 3 0.2883 0.7022 0.012 0.000 0.880 0.024 0.028 0.056
#> GSM1179008 1 0.2839 0.6982 0.860 0.000 0.092 0.000 0.004 0.044
#> GSM1179015 6 0.5705 0.7237 0.156 0.000 0.172 0.000 0.044 0.628
#> GSM1179017 5 0.1957 0.7332 0.000 0.008 0.072 0.008 0.912 0.000
#> GSM1179026 3 0.1448 0.7306 0.012 0.000 0.948 0.000 0.016 0.024
#> GSM1179033 3 0.1657 0.7367 0.040 0.000 0.936 0.000 0.012 0.012
#> GSM1179035 3 0.1448 0.7308 0.012 0.000 0.948 0.000 0.016 0.024
#> GSM1179036 3 0.3238 0.7083 0.120 0.000 0.832 0.000 0.012 0.036
#> GSM1178986 3 0.2897 0.7318 0.048 0.000 0.872 0.000 0.052 0.028
#> GSM1178989 3 0.5300 0.5409 0.000 0.040 0.720 0.036 0.092 0.112
#> GSM1178993 4 0.5820 0.3997 0.008 0.000 0.352 0.536 0.036 0.068
#> GSM1178999 4 0.3129 0.3876 0.000 0.152 0.004 0.820 0.024 0.000
#> GSM1179021 4 0.2482 0.3917 0.000 0.148 0.000 0.848 0.000 0.004
#> GSM1179025 2 0.0508 0.9725 0.000 0.984 0.000 0.000 0.012 0.004
#> GSM1179027 4 0.4657 0.5349 0.000 0.004 0.248 0.684 0.012 0.052
#> GSM1179011 1 0.5835 0.4766 0.620 0.000 0.012 0.228 0.040 0.100
#> GSM1179023 1 0.0405 0.7923 0.988 0.000 0.004 0.000 0.000 0.008
#> GSM1179029 6 0.5983 0.3997 0.416 0.000 0.092 0.000 0.040 0.452
#> GSM1179034 1 0.0405 0.7923 0.988 0.000 0.004 0.000 0.000 0.008
#> GSM1179040 4 0.4944 0.5392 0.000 0.016 0.248 0.672 0.012 0.052
#> GSM1178988 3 0.3984 0.6351 0.000 0.000 0.800 0.044 0.076 0.080
#> GSM1179037 3 0.1448 0.7308 0.012 0.000 0.948 0.000 0.016 0.024
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) protocol(p) k
#> MAD:hclust 66 0.1968 5.30e-02 2
#> MAD:hclust 10 NA NA 3
#> MAD:hclust 52 0.4079 1.20e-03 4
#> MAD:hclust 53 0.2724 7.63e-05 5
#> MAD:hclust 55 0.0799 1.45e-03 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 31632 rows and 73 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 0.984 0.993 0.3928 0.610 0.610
#> 3 3 0.494 0.757 0.859 0.5951 0.675 0.496
#> 4 4 0.667 0.705 0.845 0.1472 0.876 0.679
#> 5 5 0.651 0.526 0.733 0.0786 0.930 0.778
#> 6 6 0.663 0.492 0.707 0.0494 0.868 0.557
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
#> GSM1178971 1 0.000 0.994 1.000 0.000
#> GSM1178979 2 0.000 0.990 0.000 1.000
#> GSM1179009 1 0.000 0.994 1.000 0.000
#> GSM1179031 2 0.000 0.990 0.000 1.000
#> GSM1178970 2 0.000 0.990 0.000 1.000
#> GSM1178972 2 0.000 0.990 0.000 1.000
#> GSM1178973 1 0.000 0.994 1.000 0.000
#> GSM1178974 2 0.000 0.990 0.000 1.000
#> GSM1178977 2 0.000 0.990 0.000 1.000
#> GSM1178978 1 0.000 0.994 1.000 0.000
#> GSM1178998 1 0.000 0.994 1.000 0.000
#> GSM1179010 1 0.000 0.994 1.000 0.000
#> GSM1179018 1 0.000 0.994 1.000 0.000
#> GSM1179024 1 0.000 0.994 1.000 0.000
#> GSM1178984 1 0.000 0.994 1.000 0.000
#> GSM1178990 1 0.000 0.994 1.000 0.000
#> GSM1178991 1 0.000 0.994 1.000 0.000
#> GSM1178994 1 0.000 0.994 1.000 0.000
#> GSM1178997 1 0.000 0.994 1.000 0.000
#> GSM1179000 1 0.000 0.994 1.000 0.000
#> GSM1179013 1 0.000 0.994 1.000 0.000
#> GSM1179014 1 0.000 0.994 1.000 0.000
#> GSM1179019 1 0.000 0.994 1.000 0.000
#> GSM1179020 1 0.000 0.994 1.000 0.000
#> GSM1179022 1 0.000 0.994 1.000 0.000
#> GSM1179028 2 0.000 0.990 0.000 1.000
#> GSM1179032 1 0.000 0.994 1.000 0.000
#> GSM1179041 2 0.000 0.990 0.000 1.000
#> GSM1179042 2 0.000 0.990 0.000 1.000
#> GSM1178976 2 0.000 0.990 0.000 1.000
#> GSM1178981 1 0.000 0.994 1.000 0.000
#> GSM1178982 1 0.000 0.994 1.000 0.000
#> GSM1178983 1 0.000 0.994 1.000 0.000
#> GSM1178985 1 0.000 0.994 1.000 0.000
#> GSM1178992 1 0.000 0.994 1.000 0.000
#> GSM1179005 1 0.000 0.994 1.000 0.000
#> GSM1179007 1 0.000 0.994 1.000 0.000
#> GSM1179012 1 0.000 0.994 1.000 0.000
#> GSM1179016 1 0.000 0.994 1.000 0.000
#> GSM1179030 1 0.722 0.751 0.800 0.200
#> GSM1179038 1 0.000 0.994 1.000 0.000
#> GSM1178987 1 0.000 0.994 1.000 0.000
#> GSM1179003 2 0.000 0.990 0.000 1.000
#> GSM1179004 1 0.000 0.994 1.000 0.000
#> GSM1179039 2 0.000 0.990 0.000 1.000
#> GSM1178975 1 0.000 0.994 1.000 0.000
#> GSM1178980 2 0.000 0.990 0.000 1.000
#> GSM1178995 1 0.000 0.994 1.000 0.000
#> GSM1178996 1 0.000 0.994 1.000 0.000
#> GSM1179001 1 0.000 0.994 1.000 0.000
#> GSM1179002 1 0.000 0.994 1.000 0.000
#> GSM1179006 1 0.000 0.994 1.000 0.000
#> GSM1179008 1 0.000 0.994 1.000 0.000
#> GSM1179015 1 0.000 0.994 1.000 0.000
#> GSM1179017 2 0.671 0.783 0.176 0.824
#> GSM1179026 1 0.000 0.994 1.000 0.000
#> GSM1179033 1 0.000 0.994 1.000 0.000
#> GSM1179035 1 0.000 0.994 1.000 0.000
#> GSM1179036 1 0.000 0.994 1.000 0.000
#> GSM1178986 1 0.000 0.994 1.000 0.000
#> GSM1178989 2 0.000 0.990 0.000 1.000
#> GSM1178993 1 0.000 0.994 1.000 0.000
#> GSM1178999 2 0.000 0.990 0.000 1.000
#> GSM1179021 2 0.000 0.990 0.000 1.000
#> GSM1179025 2 0.000 0.990 0.000 1.000
#> GSM1179027 1 0.574 0.841 0.864 0.136
#> GSM1179011 1 0.000 0.994 1.000 0.000
#> GSM1179023 1 0.000 0.994 1.000 0.000
#> GSM1179029 1 0.000 0.994 1.000 0.000
#> GSM1179034 1 0.000 0.994 1.000 0.000
#> GSM1179040 2 0.000 0.990 0.000 1.000
#> GSM1178988 1 0.000 0.994 1.000 0.000
#> GSM1179037 1 0.000 0.994 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1178971 1 0.4796 0.6325 0.780 0.000 0.220
#> GSM1178979 2 0.2537 0.8414 0.000 0.920 0.080
#> GSM1179009 3 0.0592 0.7753 0.012 0.000 0.988
#> GSM1179031 2 0.0000 0.8525 0.000 1.000 0.000
#> GSM1178970 2 0.3879 0.8079 0.000 0.848 0.152
#> GSM1178972 2 0.0000 0.8525 0.000 1.000 0.000
#> GSM1178973 1 0.2959 0.8118 0.900 0.000 0.100
#> GSM1178974 2 0.0000 0.8525 0.000 1.000 0.000
#> GSM1178977 2 0.6577 0.5953 0.008 0.572 0.420
#> GSM1178978 3 0.5016 0.5330 0.240 0.000 0.760
#> GSM1178998 1 0.2165 0.8621 0.936 0.000 0.064
#> GSM1179010 3 0.5948 0.6247 0.360 0.000 0.640
#> GSM1179018 3 0.0000 0.7652 0.000 0.000 1.000
#> GSM1179024 1 0.0592 0.9060 0.988 0.000 0.012
#> GSM1178984 3 0.5760 0.6715 0.328 0.000 0.672
#> GSM1178990 1 0.1031 0.8987 0.976 0.000 0.024
#> GSM1178991 1 0.5138 0.6822 0.748 0.000 0.252
#> GSM1178994 3 0.5785 0.6660 0.332 0.000 0.668
#> GSM1178997 1 0.2261 0.8660 0.932 0.000 0.068
#> GSM1179000 1 0.0592 0.9060 0.988 0.000 0.012
#> GSM1179013 1 0.0592 0.9060 0.988 0.000 0.012
#> GSM1179014 1 0.0592 0.9060 0.988 0.000 0.012
#> GSM1179019 1 0.0592 0.9060 0.988 0.000 0.012
#> GSM1179020 1 0.0592 0.9060 0.988 0.000 0.012
#> GSM1179022 1 0.0592 0.9060 0.988 0.000 0.012
#> GSM1179028 2 0.0000 0.8525 0.000 1.000 0.000
#> GSM1179032 1 0.0592 0.9060 0.988 0.000 0.012
#> GSM1179041 2 0.0000 0.8525 0.000 1.000 0.000
#> GSM1179042 2 0.0000 0.8525 0.000 1.000 0.000
#> GSM1178976 3 0.5859 0.3068 0.000 0.344 0.656
#> GSM1178981 3 0.3412 0.8320 0.124 0.000 0.876
#> GSM1178982 3 0.1643 0.7985 0.044 0.000 0.956
#> GSM1178983 3 0.1411 0.7930 0.036 0.000 0.964
#> GSM1178985 3 0.3340 0.8331 0.120 0.000 0.880
#> GSM1178992 3 0.5016 0.7573 0.240 0.000 0.760
#> GSM1179005 3 0.5706 0.6802 0.320 0.000 0.680
#> GSM1179007 3 0.5968 0.6174 0.364 0.000 0.636
#> GSM1179012 3 0.6305 0.3301 0.484 0.000 0.516
#> GSM1179016 3 0.5363 0.7250 0.276 0.000 0.724
#> GSM1179030 3 0.1647 0.7591 0.004 0.036 0.960
#> GSM1179038 3 0.5733 0.6751 0.324 0.000 0.676
#> GSM1178987 3 0.3340 0.8331 0.120 0.000 0.880
#> GSM1179003 2 0.5291 0.7175 0.000 0.732 0.268
#> GSM1179004 3 0.3340 0.8331 0.120 0.000 0.880
#> GSM1179039 2 0.0000 0.8525 0.000 1.000 0.000
#> GSM1178975 1 0.3551 0.7976 0.868 0.000 0.132
#> GSM1178980 2 0.6771 0.5685 0.012 0.548 0.440
#> GSM1178995 3 0.6008 0.6047 0.372 0.000 0.628
#> GSM1178996 3 0.3482 0.8303 0.128 0.000 0.872
#> GSM1179001 1 0.0592 0.9060 0.988 0.000 0.012
#> GSM1179002 1 0.1031 0.8987 0.976 0.000 0.024
#> GSM1179006 3 0.3340 0.8331 0.120 0.000 0.880
#> GSM1179008 1 0.0592 0.9060 0.988 0.000 0.012
#> GSM1179015 1 0.6154 0.0169 0.592 0.000 0.408
#> GSM1179017 3 0.7526 0.0261 0.040 0.424 0.536
#> GSM1179026 3 0.3340 0.8331 0.120 0.000 0.880
#> GSM1179033 3 0.3267 0.8325 0.116 0.000 0.884
#> GSM1179035 3 0.3340 0.8331 0.120 0.000 0.880
#> GSM1179036 3 0.3340 0.8331 0.120 0.000 0.880
#> GSM1178986 3 0.2448 0.8177 0.076 0.000 0.924
#> GSM1178989 3 0.3539 0.7561 0.012 0.100 0.888
#> GSM1178993 3 0.0592 0.7536 0.012 0.000 0.988
#> GSM1178999 2 0.6584 0.6389 0.012 0.608 0.380
#> GSM1179021 2 0.3459 0.8371 0.012 0.892 0.096
#> GSM1179025 2 0.0000 0.8525 0.000 1.000 0.000
#> GSM1179027 3 0.0592 0.7536 0.012 0.000 0.988
#> GSM1179011 1 0.6180 0.3882 0.584 0.000 0.416
#> GSM1179023 1 0.0592 0.9060 0.988 0.000 0.012
#> GSM1179029 1 0.0592 0.9060 0.988 0.000 0.012
#> GSM1179034 1 0.0592 0.9060 0.988 0.000 0.012
#> GSM1179040 2 0.6647 0.6298 0.012 0.592 0.396
#> GSM1178988 3 0.3116 0.8302 0.108 0.000 0.892
#> GSM1179037 3 0.3340 0.8331 0.120 0.000 0.880
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1178971 1 0.5517 0.2044 0.568 0.000 0.412 0.020
#> GSM1178979 4 0.5168 0.1108 0.000 0.496 0.004 0.500
#> GSM1179009 3 0.3942 0.6806 0.000 0.000 0.764 0.236
#> GSM1179031 2 0.0000 0.9206 0.000 1.000 0.000 0.000
#> GSM1178970 2 0.5602 -0.2249 0.000 0.508 0.020 0.472
#> GSM1178972 2 0.0188 0.9171 0.000 0.996 0.004 0.000
#> GSM1178973 1 0.3870 0.7195 0.788 0.000 0.004 0.208
#> GSM1178974 2 0.0000 0.9206 0.000 1.000 0.000 0.000
#> GSM1178977 4 0.3674 0.6962 0.000 0.116 0.036 0.848
#> GSM1178978 4 0.5371 0.6187 0.080 0.000 0.188 0.732
#> GSM1178998 1 0.3903 0.7931 0.844 0.000 0.076 0.080
#> GSM1179010 3 0.4581 0.7581 0.120 0.000 0.800 0.080
#> GSM1179018 4 0.4679 0.3762 0.000 0.000 0.352 0.648
#> GSM1179024 1 0.0921 0.8911 0.972 0.000 0.000 0.028
#> GSM1178984 3 0.3885 0.7870 0.092 0.000 0.844 0.064
#> GSM1178990 1 0.1824 0.8822 0.936 0.000 0.004 0.060
#> GSM1178991 4 0.5288 -0.0609 0.472 0.000 0.008 0.520
#> GSM1178994 3 0.3687 0.7951 0.080 0.000 0.856 0.064
#> GSM1178997 1 0.1929 0.8772 0.940 0.000 0.024 0.036
#> GSM1179000 1 0.1209 0.8886 0.964 0.000 0.004 0.032
#> GSM1179013 1 0.1489 0.8881 0.952 0.000 0.004 0.044
#> GSM1179014 1 0.1978 0.8852 0.928 0.000 0.004 0.068
#> GSM1179019 1 0.1209 0.8886 0.964 0.000 0.004 0.032
#> GSM1179020 1 0.0469 0.8952 0.988 0.000 0.000 0.012
#> GSM1179022 1 0.0895 0.8952 0.976 0.000 0.004 0.020
#> GSM1179028 2 0.0000 0.9206 0.000 1.000 0.000 0.000
#> GSM1179032 1 0.0895 0.8952 0.976 0.000 0.004 0.020
#> GSM1179041 2 0.0000 0.9206 0.000 1.000 0.000 0.000
#> GSM1179042 2 0.0000 0.9206 0.000 1.000 0.000 0.000
#> GSM1178976 3 0.3156 0.7908 0.000 0.048 0.884 0.068
#> GSM1178981 3 0.1767 0.8286 0.012 0.000 0.944 0.044
#> GSM1178982 3 0.3142 0.7850 0.008 0.000 0.860 0.132
#> GSM1178983 3 0.5273 0.1544 0.008 0.000 0.536 0.456
#> GSM1178985 3 0.1004 0.8327 0.004 0.000 0.972 0.024
#> GSM1178992 3 0.1938 0.8249 0.012 0.000 0.936 0.052
#> GSM1179005 3 0.1798 0.8291 0.040 0.000 0.944 0.016
#> GSM1179007 3 0.3842 0.7715 0.128 0.000 0.836 0.036
#> GSM1179012 3 0.6806 0.3741 0.344 0.000 0.544 0.112
#> GSM1179016 3 0.2965 0.8122 0.036 0.000 0.892 0.072
#> GSM1179030 3 0.5161 -0.0595 0.004 0.000 0.520 0.476
#> GSM1179038 3 0.2060 0.8271 0.052 0.000 0.932 0.016
#> GSM1178987 3 0.1489 0.8287 0.004 0.000 0.952 0.044
#> GSM1179003 4 0.7286 0.3574 0.000 0.364 0.156 0.480
#> GSM1179004 3 0.1576 0.8288 0.004 0.000 0.948 0.048
#> GSM1179039 2 0.0000 0.9206 0.000 1.000 0.000 0.000
#> GSM1178975 1 0.5151 0.1727 0.532 0.000 0.004 0.464
#> GSM1178980 4 0.3464 0.6985 0.000 0.108 0.032 0.860
#> GSM1178995 3 0.3501 0.7791 0.132 0.000 0.848 0.020
#> GSM1178996 3 0.1545 0.8293 0.008 0.000 0.952 0.040
#> GSM1179001 1 0.0707 0.8967 0.980 0.000 0.000 0.020
#> GSM1179002 1 0.1174 0.8947 0.968 0.000 0.012 0.020
#> GSM1179006 3 0.1452 0.8291 0.008 0.000 0.956 0.036
#> GSM1179008 1 0.0707 0.8963 0.980 0.000 0.000 0.020
#> GSM1179015 3 0.6609 0.0938 0.448 0.000 0.472 0.080
#> GSM1179017 3 0.6851 0.0159 0.000 0.104 0.496 0.400
#> GSM1179026 3 0.0779 0.8325 0.004 0.000 0.980 0.016
#> GSM1179033 3 0.1452 0.8291 0.008 0.000 0.956 0.036
#> GSM1179035 3 0.0779 0.8328 0.004 0.000 0.980 0.016
#> GSM1179036 3 0.1256 0.8309 0.008 0.000 0.964 0.028
#> GSM1178986 3 0.2266 0.8097 0.004 0.000 0.912 0.084
#> GSM1178989 3 0.1902 0.8161 0.004 0.000 0.932 0.064
#> GSM1178993 4 0.2589 0.6933 0.000 0.000 0.116 0.884
#> GSM1178999 4 0.4465 0.6822 0.000 0.144 0.056 0.800
#> GSM1179021 4 0.4730 0.4140 0.000 0.364 0.000 0.636
#> GSM1179025 2 0.0000 0.9206 0.000 1.000 0.000 0.000
#> GSM1179027 4 0.2589 0.6933 0.000 0.000 0.116 0.884
#> GSM1179011 4 0.2675 0.6543 0.100 0.000 0.008 0.892
#> GSM1179023 1 0.0895 0.8952 0.976 0.000 0.004 0.020
#> GSM1179029 1 0.2053 0.8760 0.924 0.000 0.004 0.072
#> GSM1179034 1 0.0895 0.8952 0.976 0.000 0.004 0.020
#> GSM1179040 4 0.3616 0.6987 0.000 0.112 0.036 0.852
#> GSM1178988 3 0.1743 0.8203 0.004 0.000 0.940 0.056
#> GSM1179037 3 0.0657 0.8321 0.004 0.000 0.984 0.012
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1178971 1 0.5959 0.2944 0.600 0.000 0.244 0.004 0.152
#> GSM1178979 4 0.7433 0.2925 0.000 0.308 0.052 0.444 0.196
#> GSM1179009 3 0.6581 0.1020 0.000 0.000 0.452 0.224 0.324
#> GSM1179031 2 0.0000 0.9084 0.000 1.000 0.000 0.000 0.000
#> GSM1178970 2 0.8300 -0.1787 0.000 0.360 0.148 0.280 0.212
#> GSM1178972 2 0.0955 0.8889 0.000 0.968 0.000 0.004 0.028
#> GSM1178973 1 0.4558 0.6346 0.728 0.000 0.000 0.208 0.064
#> GSM1178974 2 0.0290 0.9063 0.000 0.992 0.000 0.000 0.008
#> GSM1178977 4 0.5005 0.6562 0.000 0.028 0.044 0.716 0.212
#> GSM1178978 4 0.7585 0.1840 0.084 0.000 0.144 0.408 0.364
#> GSM1178998 5 0.5272 0.3240 0.416 0.000 0.040 0.004 0.540
#> GSM1179010 5 0.4882 -0.0686 0.024 0.000 0.444 0.000 0.532
#> GSM1179018 3 0.5624 0.2329 0.000 0.000 0.532 0.388 0.080
#> GSM1179024 1 0.0609 0.8172 0.980 0.000 0.000 0.000 0.020
#> GSM1178984 3 0.4688 0.1281 0.008 0.000 0.532 0.004 0.456
#> GSM1178990 1 0.3663 0.6655 0.776 0.000 0.016 0.000 0.208
#> GSM1178991 4 0.5895 -0.0825 0.444 0.000 0.000 0.456 0.100
#> GSM1178994 3 0.4684 0.1410 0.008 0.000 0.536 0.004 0.452
#> GSM1178997 1 0.2612 0.7842 0.868 0.000 0.008 0.000 0.124
#> GSM1179000 1 0.1478 0.8104 0.936 0.000 0.000 0.000 0.064
#> GSM1179013 1 0.1410 0.8136 0.940 0.000 0.000 0.000 0.060
#> GSM1179014 1 0.3492 0.7214 0.796 0.000 0.000 0.016 0.188
#> GSM1179019 1 0.1410 0.8111 0.940 0.000 0.000 0.000 0.060
#> GSM1179020 1 0.0000 0.8183 1.000 0.000 0.000 0.000 0.000
#> GSM1179022 1 0.1341 0.8145 0.944 0.000 0.000 0.000 0.056
#> GSM1179028 2 0.0000 0.9084 0.000 1.000 0.000 0.000 0.000
#> GSM1179032 1 0.1341 0.8145 0.944 0.000 0.000 0.000 0.056
#> GSM1179041 2 0.0000 0.9084 0.000 1.000 0.000 0.000 0.000
#> GSM1179042 2 0.0000 0.9084 0.000 1.000 0.000 0.000 0.000
#> GSM1178976 3 0.3474 0.4691 0.000 0.008 0.796 0.004 0.192
#> GSM1178981 3 0.4276 0.3386 0.000 0.000 0.616 0.004 0.380
#> GSM1178982 3 0.4380 0.4344 0.000 0.000 0.676 0.020 0.304
#> GSM1178983 3 0.6018 0.3306 0.000 0.000 0.568 0.160 0.272
#> GSM1178985 3 0.3884 0.4410 0.000 0.000 0.708 0.004 0.288
#> GSM1178992 3 0.4003 0.3958 0.000 0.000 0.704 0.008 0.288
#> GSM1179005 3 0.4225 0.3340 0.004 0.000 0.632 0.000 0.364
#> GSM1179007 3 0.4637 0.1080 0.012 0.000 0.536 0.000 0.452
#> GSM1179012 5 0.5644 0.5173 0.144 0.000 0.228 0.000 0.628
#> GSM1179016 3 0.4804 0.3333 0.044 0.000 0.720 0.016 0.220
#> GSM1179030 3 0.5250 0.3762 0.000 0.000 0.668 0.108 0.224
#> GSM1179038 3 0.3741 0.4354 0.004 0.000 0.732 0.000 0.264
#> GSM1178987 3 0.4166 0.3813 0.000 0.000 0.648 0.004 0.348
#> GSM1179003 3 0.8216 -0.2634 0.000 0.144 0.388 0.264 0.204
#> GSM1179004 3 0.4196 0.3758 0.000 0.000 0.640 0.004 0.356
#> GSM1179039 2 0.0000 0.9084 0.000 1.000 0.000 0.000 0.000
#> GSM1178975 1 0.5847 0.1213 0.480 0.000 0.000 0.424 0.096
#> GSM1178980 4 0.0703 0.7203 0.000 0.024 0.000 0.976 0.000
#> GSM1178995 3 0.4640 0.2273 0.016 0.000 0.584 0.000 0.400
#> GSM1178996 3 0.1704 0.5300 0.000 0.000 0.928 0.004 0.068
#> GSM1179001 1 0.2536 0.7878 0.868 0.000 0.000 0.004 0.128
#> GSM1179002 1 0.3239 0.7539 0.828 0.000 0.012 0.004 0.156
#> GSM1179006 3 0.0162 0.5482 0.000 0.000 0.996 0.000 0.004
#> GSM1179008 1 0.2286 0.7987 0.888 0.000 0.000 0.004 0.108
#> GSM1179015 5 0.6002 0.5681 0.264 0.000 0.132 0.008 0.596
#> GSM1179017 3 0.6595 0.1175 0.000 0.036 0.492 0.096 0.376
#> GSM1179026 3 0.0609 0.5480 0.000 0.000 0.980 0.000 0.020
#> GSM1179033 3 0.0162 0.5494 0.000 0.000 0.996 0.000 0.004
#> GSM1179035 3 0.3983 0.3870 0.000 0.000 0.660 0.000 0.340
#> GSM1179036 3 0.0609 0.5487 0.000 0.000 0.980 0.000 0.020
#> GSM1178986 3 0.1408 0.5408 0.000 0.000 0.948 0.008 0.044
#> GSM1178989 3 0.3123 0.4736 0.000 0.000 0.812 0.004 0.184
#> GSM1178993 4 0.0798 0.7240 0.000 0.000 0.016 0.976 0.008
#> GSM1178999 4 0.5672 0.6347 0.000 0.060 0.112 0.708 0.120
#> GSM1179021 4 0.4465 0.5822 0.000 0.204 0.000 0.736 0.060
#> GSM1179025 2 0.0290 0.9063 0.000 0.992 0.000 0.000 0.008
#> GSM1179027 4 0.0798 0.7240 0.000 0.000 0.016 0.976 0.008
#> GSM1179011 4 0.2054 0.7013 0.028 0.000 0.000 0.920 0.052
#> GSM1179023 1 0.1270 0.8155 0.948 0.000 0.000 0.000 0.052
#> GSM1179029 1 0.4063 0.6287 0.708 0.000 0.000 0.012 0.280
#> GSM1179034 1 0.1341 0.8145 0.944 0.000 0.000 0.000 0.056
#> GSM1179040 4 0.2104 0.7167 0.000 0.024 0.000 0.916 0.060
#> GSM1178988 3 0.2471 0.5039 0.000 0.000 0.864 0.000 0.136
#> GSM1179037 3 0.2329 0.5224 0.000 0.000 0.876 0.000 0.124
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1178971 1 0.7287 -0.04994 0.332 0.000 0.244 0.000 0.100 0.324
#> GSM1178979 4 0.7077 0.40347 0.000 0.096 0.000 0.384 0.340 0.180
#> GSM1179009 3 0.3874 0.50351 0.000 0.000 0.760 0.172 0.000 0.068
#> GSM1179031 2 0.0000 0.95928 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178970 5 0.7949 -0.27757 0.000 0.152 0.048 0.188 0.424 0.188
#> GSM1178972 2 0.3367 0.81556 0.000 0.816 0.000 0.000 0.080 0.104
#> GSM1178973 1 0.5995 -0.40299 0.428 0.000 0.000 0.248 0.000 0.324
#> GSM1178974 2 0.1297 0.94255 0.000 0.948 0.000 0.000 0.012 0.040
#> GSM1178977 4 0.6308 0.40030 0.000 0.000 0.016 0.412 0.356 0.216
#> GSM1178978 6 0.7199 0.20134 0.004 0.000 0.240 0.220 0.100 0.436
#> GSM1178998 3 0.6182 0.10739 0.304 0.000 0.440 0.000 0.008 0.248
#> GSM1179010 3 0.3834 0.52933 0.028 0.000 0.748 0.000 0.008 0.216
#> GSM1179018 3 0.6777 -0.21915 0.000 0.000 0.396 0.208 0.344 0.052
#> GSM1179024 1 0.1007 0.71298 0.956 0.000 0.000 0.000 0.000 0.044
#> GSM1178984 3 0.1714 0.58864 0.000 0.000 0.908 0.000 0.000 0.092
#> GSM1178990 1 0.3808 0.58474 0.784 0.000 0.080 0.000 0.004 0.132
#> GSM1178991 6 0.6650 0.51017 0.284 0.000 0.000 0.336 0.028 0.352
#> GSM1178994 3 0.1610 0.58924 0.000 0.000 0.916 0.000 0.000 0.084
#> GSM1178997 1 0.4219 0.37635 0.592 0.000 0.000 0.000 0.020 0.388
#> GSM1179000 1 0.2964 0.63180 0.792 0.000 0.000 0.000 0.004 0.204
#> GSM1179013 1 0.0146 0.71770 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM1179014 1 0.4414 0.58529 0.704 0.000 0.000 0.000 0.092 0.204
#> GSM1179019 1 0.2738 0.65763 0.820 0.000 0.000 0.000 0.004 0.176
#> GSM1179020 1 0.1267 0.71356 0.940 0.000 0.000 0.000 0.000 0.060
#> GSM1179022 1 0.0000 0.71894 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179028 2 0.0146 0.95792 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM1179032 1 0.0000 0.71894 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179041 2 0.0000 0.95928 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179042 2 0.0000 0.95928 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178976 5 0.4573 0.50658 0.000 0.000 0.208 0.000 0.688 0.104
#> GSM1178981 3 0.1865 0.58423 0.000 0.000 0.920 0.000 0.040 0.040
#> GSM1178982 3 0.3944 0.44853 0.000 0.000 0.768 0.008 0.164 0.060
#> GSM1178983 3 0.6467 0.15760 0.000 0.000 0.500 0.056 0.160 0.284
#> GSM1178985 3 0.2730 0.50563 0.000 0.000 0.836 0.000 0.152 0.012
#> GSM1178992 3 0.5391 -0.04740 0.000 0.000 0.492 0.000 0.392 0.116
#> GSM1179005 3 0.2937 0.53969 0.000 0.000 0.848 0.000 0.096 0.056
#> GSM1179007 3 0.2950 0.57524 0.000 0.000 0.828 0.000 0.024 0.148
#> GSM1179012 3 0.5944 0.36230 0.140 0.000 0.568 0.000 0.036 0.256
#> GSM1179016 5 0.5479 0.41547 0.012 0.000 0.180 0.000 0.612 0.196
#> GSM1179030 5 0.5248 0.45590 0.000 0.000 0.188 0.040 0.672 0.100
#> GSM1179038 3 0.4284 0.30830 0.000 0.000 0.688 0.000 0.256 0.056
#> GSM1178987 3 0.2542 0.56764 0.000 0.000 0.876 0.000 0.080 0.044
#> GSM1179003 5 0.5021 0.18584 0.000 0.016 0.020 0.172 0.708 0.084
#> GSM1179004 3 0.2237 0.57517 0.000 0.000 0.896 0.000 0.068 0.036
#> GSM1179039 2 0.0000 0.95928 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178975 6 0.6113 0.43102 0.296 0.000 0.000 0.344 0.000 0.360
#> GSM1178980 4 0.0260 0.62184 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM1178995 3 0.3265 0.55089 0.008 0.000 0.836 0.000 0.088 0.068
#> GSM1178996 5 0.5373 0.45632 0.000 0.000 0.312 0.000 0.552 0.136
#> GSM1179001 1 0.4002 0.60337 0.692 0.000 0.016 0.000 0.008 0.284
#> GSM1179002 1 0.4452 0.57652 0.664 0.000 0.040 0.000 0.008 0.288
#> GSM1179006 5 0.4300 0.41328 0.000 0.000 0.432 0.000 0.548 0.020
#> GSM1179008 1 0.3799 0.61074 0.704 0.000 0.008 0.000 0.008 0.280
#> GSM1179015 3 0.7025 0.07303 0.296 0.000 0.332 0.000 0.060 0.312
#> GSM1179017 5 0.3447 0.30353 0.000 0.004 0.000 0.044 0.804 0.148
#> GSM1179026 5 0.4513 0.38677 0.000 0.000 0.440 0.000 0.528 0.032
#> GSM1179033 5 0.4328 0.37268 0.000 0.000 0.460 0.000 0.520 0.020
#> GSM1179035 3 0.3062 0.50036 0.000 0.000 0.816 0.000 0.160 0.024
#> GSM1179036 5 0.4325 0.37352 0.000 0.000 0.456 0.000 0.524 0.020
#> GSM1178986 5 0.5082 0.39746 0.000 0.000 0.408 0.000 0.512 0.080
#> GSM1178989 5 0.3652 0.54126 0.000 0.000 0.188 0.000 0.768 0.044
#> GSM1178993 4 0.0713 0.59942 0.000 0.000 0.000 0.972 0.000 0.028
#> GSM1178999 4 0.4928 0.55094 0.000 0.004 0.000 0.624 0.288 0.084
#> GSM1179021 4 0.4283 0.60661 0.000 0.104 0.000 0.776 0.072 0.048
#> GSM1179025 2 0.1367 0.94061 0.000 0.944 0.000 0.000 0.012 0.044
#> GSM1179027 4 0.0458 0.60933 0.000 0.000 0.000 0.984 0.000 0.016
#> GSM1179011 4 0.2883 0.31512 0.000 0.000 0.000 0.788 0.000 0.212
#> GSM1179023 1 0.0000 0.71894 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179029 1 0.5124 0.50024 0.668 0.000 0.036 0.000 0.076 0.220
#> GSM1179034 1 0.0000 0.71894 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179040 4 0.2448 0.63965 0.000 0.000 0.000 0.884 0.064 0.052
#> GSM1178988 5 0.3126 0.54034 0.000 0.000 0.248 0.000 0.752 0.000
#> GSM1179037 3 0.4333 -0.00223 0.000 0.000 0.596 0.000 0.376 0.028
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) protocol(p) k
#> MAD:kmeans 73 0.20011 0.280850 2
#> MAD:kmeans 68 0.36611 0.000924 3
#> MAD:kmeans 60 0.04566 0.000987 4
#> MAD:kmeans 43 0.00835 0.004632 5
#> MAD:kmeans 45 0.03738 0.013151 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 31632 rows and 73 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.859 0.894 0.957 0.4893 0.521 0.521
#> 3 3 0.870 0.909 0.959 0.3789 0.719 0.501
#> 4 4 0.763 0.777 0.893 0.1076 0.874 0.641
#> 5 5 0.728 0.641 0.820 0.0612 0.899 0.634
#> 6 6 0.693 0.482 0.755 0.0367 0.975 0.880
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM1178971 1 0.0000 0.9425 1.000 0.000
#> GSM1178979 2 0.0000 0.9715 0.000 1.000
#> GSM1179009 1 0.1633 0.9244 0.976 0.024
#> GSM1179031 2 0.0000 0.9715 0.000 1.000
#> GSM1178970 2 0.0000 0.9715 0.000 1.000
#> GSM1178972 2 0.0000 0.9715 0.000 1.000
#> GSM1178973 1 0.0000 0.9425 1.000 0.000
#> GSM1178974 2 0.0000 0.9715 0.000 1.000
#> GSM1178977 2 0.0000 0.9715 0.000 1.000
#> GSM1178978 2 0.8813 0.5427 0.300 0.700
#> GSM1178998 1 0.0000 0.9425 1.000 0.000
#> GSM1179010 1 0.0000 0.9425 1.000 0.000
#> GSM1179018 2 0.0672 0.9647 0.008 0.992
#> GSM1179024 1 0.0000 0.9425 1.000 0.000
#> GSM1178984 1 0.0000 0.9425 1.000 0.000
#> GSM1178990 1 0.0000 0.9425 1.000 0.000
#> GSM1178991 1 0.7299 0.7292 0.796 0.204
#> GSM1178994 1 0.0000 0.9425 1.000 0.000
#> GSM1178997 2 0.9491 0.3816 0.368 0.632
#> GSM1179000 1 0.0000 0.9425 1.000 0.000
#> GSM1179013 1 0.0000 0.9425 1.000 0.000
#> GSM1179014 1 0.0000 0.9425 1.000 0.000
#> GSM1179019 1 0.0000 0.9425 1.000 0.000
#> GSM1179020 1 0.0000 0.9425 1.000 0.000
#> GSM1179022 1 0.0000 0.9425 1.000 0.000
#> GSM1179028 2 0.0000 0.9715 0.000 1.000
#> GSM1179032 1 0.0000 0.9425 1.000 0.000
#> GSM1179041 2 0.0000 0.9715 0.000 1.000
#> GSM1179042 2 0.0000 0.9715 0.000 1.000
#> GSM1178976 2 0.0000 0.9715 0.000 1.000
#> GSM1178981 1 0.0000 0.9425 1.000 0.000
#> GSM1178982 1 0.7745 0.6992 0.772 0.228
#> GSM1178983 1 0.8608 0.6144 0.716 0.284
#> GSM1178985 1 0.9460 0.4521 0.636 0.364
#> GSM1178992 1 0.0000 0.9425 1.000 0.000
#> GSM1179005 1 0.0000 0.9425 1.000 0.000
#> GSM1179007 1 0.0000 0.9425 1.000 0.000
#> GSM1179012 1 0.0000 0.9425 1.000 0.000
#> GSM1179016 1 0.0376 0.9398 0.996 0.004
#> GSM1179030 2 0.0000 0.9715 0.000 1.000
#> GSM1179038 1 0.0000 0.9425 1.000 0.000
#> GSM1178987 1 0.0000 0.9425 1.000 0.000
#> GSM1179003 2 0.0000 0.9715 0.000 1.000
#> GSM1179004 1 0.0000 0.9425 1.000 0.000
#> GSM1179039 2 0.0000 0.9715 0.000 1.000
#> GSM1178975 1 0.9552 0.4106 0.624 0.376
#> GSM1178980 2 0.0000 0.9715 0.000 1.000
#> GSM1178995 1 0.0000 0.9425 1.000 0.000
#> GSM1178996 1 0.1633 0.9246 0.976 0.024
#> GSM1179001 1 0.0000 0.9425 1.000 0.000
#> GSM1179002 1 0.0000 0.9425 1.000 0.000
#> GSM1179006 1 1.0000 0.0384 0.500 0.500
#> GSM1179008 1 0.0000 0.9425 1.000 0.000
#> GSM1179015 1 0.0000 0.9425 1.000 0.000
#> GSM1179017 2 0.0000 0.9715 0.000 1.000
#> GSM1179026 1 0.0376 0.9398 0.996 0.004
#> GSM1179033 2 0.2236 0.9377 0.036 0.964
#> GSM1179035 1 0.0000 0.9425 1.000 0.000
#> GSM1179036 1 0.0000 0.9425 1.000 0.000
#> GSM1178986 1 0.9686 0.3680 0.604 0.396
#> GSM1178989 2 0.0000 0.9715 0.000 1.000
#> GSM1178993 2 0.0000 0.9715 0.000 1.000
#> GSM1178999 2 0.0000 0.9715 0.000 1.000
#> GSM1179021 2 0.0000 0.9715 0.000 1.000
#> GSM1179025 2 0.0000 0.9715 0.000 1.000
#> GSM1179027 2 0.0000 0.9715 0.000 1.000
#> GSM1179011 2 0.0000 0.9715 0.000 1.000
#> GSM1179023 1 0.0000 0.9425 1.000 0.000
#> GSM1179029 1 0.0000 0.9425 1.000 0.000
#> GSM1179034 1 0.0000 0.9425 1.000 0.000
#> GSM1179040 2 0.0000 0.9715 0.000 1.000
#> GSM1178988 2 0.0000 0.9715 0.000 1.000
#> GSM1179037 1 0.0000 0.9425 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1178971 1 0.0000 0.954 1.000 0.000 0.000
#> GSM1178979 2 0.0000 0.976 0.000 1.000 0.000
#> GSM1179009 3 0.0237 0.941 0.004 0.000 0.996
#> GSM1179031 2 0.0000 0.976 0.000 1.000 0.000
#> GSM1178970 2 0.0000 0.976 0.000 1.000 0.000
#> GSM1178972 2 0.0000 0.976 0.000 1.000 0.000
#> GSM1178973 1 0.0000 0.954 1.000 0.000 0.000
#> GSM1178974 2 0.0000 0.976 0.000 1.000 0.000
#> GSM1178977 2 0.0000 0.976 0.000 1.000 0.000
#> GSM1178978 1 0.5229 0.830 0.828 0.104 0.068
#> GSM1178998 1 0.4605 0.762 0.796 0.000 0.204
#> GSM1179010 3 0.0237 0.941 0.004 0.000 0.996
#> GSM1179018 3 0.5905 0.459 0.000 0.352 0.648
#> GSM1179024 1 0.0000 0.954 1.000 0.000 0.000
#> GSM1178984 3 0.0237 0.941 0.004 0.000 0.996
#> GSM1178990 1 0.1964 0.913 0.944 0.000 0.056
#> GSM1178991 1 0.0747 0.944 0.984 0.016 0.000
#> GSM1178994 3 0.0237 0.941 0.004 0.000 0.996
#> GSM1178997 1 0.0000 0.954 1.000 0.000 0.000
#> GSM1179000 1 0.0000 0.954 1.000 0.000 0.000
#> GSM1179013 1 0.0000 0.954 1.000 0.000 0.000
#> GSM1179014 1 0.0000 0.954 1.000 0.000 0.000
#> GSM1179019 1 0.0000 0.954 1.000 0.000 0.000
#> GSM1179020 1 0.0000 0.954 1.000 0.000 0.000
#> GSM1179022 1 0.0000 0.954 1.000 0.000 0.000
#> GSM1179028 2 0.0000 0.976 0.000 1.000 0.000
#> GSM1179032 1 0.0000 0.954 1.000 0.000 0.000
#> GSM1179041 2 0.0000 0.976 0.000 1.000 0.000
#> GSM1179042 2 0.0000 0.976 0.000 1.000 0.000
#> GSM1178976 2 0.0000 0.976 0.000 1.000 0.000
#> GSM1178981 3 0.0237 0.941 0.004 0.000 0.996
#> GSM1178982 3 0.1129 0.931 0.020 0.004 0.976
#> GSM1178983 1 0.4994 0.807 0.816 0.024 0.160
#> GSM1178985 3 0.0000 0.940 0.000 0.000 1.000
#> GSM1178992 3 0.0000 0.940 0.000 0.000 1.000
#> GSM1179005 3 0.1031 0.933 0.024 0.000 0.976
#> GSM1179007 3 0.0424 0.940 0.008 0.000 0.992
#> GSM1179012 3 0.0237 0.941 0.004 0.000 0.996
#> GSM1179016 3 0.6280 0.180 0.460 0.000 0.540
#> GSM1179030 2 0.0000 0.976 0.000 1.000 0.000
#> GSM1179038 3 0.3482 0.842 0.128 0.000 0.872
#> GSM1178987 3 0.0000 0.940 0.000 0.000 1.000
#> GSM1179003 2 0.0000 0.976 0.000 1.000 0.000
#> GSM1179004 3 0.0000 0.940 0.000 0.000 1.000
#> GSM1179039 2 0.0000 0.976 0.000 1.000 0.000
#> GSM1178975 1 0.0000 0.954 1.000 0.000 0.000
#> GSM1178980 2 0.0000 0.976 0.000 1.000 0.000
#> GSM1178995 3 0.2448 0.896 0.076 0.000 0.924
#> GSM1178996 1 0.6852 0.518 0.664 0.036 0.300
#> GSM1179001 1 0.0000 0.954 1.000 0.000 0.000
#> GSM1179002 1 0.0000 0.954 1.000 0.000 0.000
#> GSM1179006 3 0.1860 0.909 0.000 0.052 0.948
#> GSM1179008 1 0.0000 0.954 1.000 0.000 0.000
#> GSM1179015 3 0.1163 0.930 0.028 0.000 0.972
#> GSM1179017 2 0.0000 0.976 0.000 1.000 0.000
#> GSM1179026 3 0.0000 0.940 0.000 0.000 1.000
#> GSM1179033 3 0.1163 0.927 0.000 0.028 0.972
#> GSM1179035 3 0.0000 0.940 0.000 0.000 1.000
#> GSM1179036 3 0.0592 0.938 0.012 0.000 0.988
#> GSM1178986 3 0.5884 0.770 0.064 0.148 0.788
#> GSM1178989 2 0.3116 0.863 0.000 0.892 0.108
#> GSM1178993 2 0.0000 0.976 0.000 1.000 0.000
#> GSM1178999 2 0.0000 0.976 0.000 1.000 0.000
#> GSM1179021 2 0.0000 0.976 0.000 1.000 0.000
#> GSM1179025 2 0.0000 0.976 0.000 1.000 0.000
#> GSM1179027 2 0.0000 0.976 0.000 1.000 0.000
#> GSM1179011 1 0.3482 0.846 0.872 0.128 0.000
#> GSM1179023 1 0.0000 0.954 1.000 0.000 0.000
#> GSM1179029 1 0.0000 0.954 1.000 0.000 0.000
#> GSM1179034 1 0.0000 0.954 1.000 0.000 0.000
#> GSM1179040 2 0.0000 0.976 0.000 1.000 0.000
#> GSM1178988 2 0.6062 0.344 0.000 0.616 0.384
#> GSM1179037 3 0.0000 0.940 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1178971 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM1178979 2 0.0000 0.924 0.000 1.000 0.000 0.000
#> GSM1179009 4 0.4382 0.472 0.000 0.000 0.296 0.704
#> GSM1179031 2 0.0000 0.924 0.000 1.000 0.000 0.000
#> GSM1178970 2 0.0000 0.924 0.000 1.000 0.000 0.000
#> GSM1178972 2 0.0000 0.924 0.000 1.000 0.000 0.000
#> GSM1178973 1 0.4830 0.227 0.608 0.000 0.000 0.392
#> GSM1178974 2 0.0000 0.924 0.000 1.000 0.000 0.000
#> GSM1178977 2 0.0592 0.916 0.000 0.984 0.000 0.016
#> GSM1178978 4 0.3675 0.751 0.104 0.016 0.020 0.860
#> GSM1178998 1 0.5111 0.622 0.740 0.000 0.204 0.056
#> GSM1179010 3 0.2660 0.857 0.036 0.000 0.908 0.056
#> GSM1179018 4 0.1388 0.768 0.000 0.012 0.028 0.960
#> GSM1179024 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM1178984 3 0.2840 0.854 0.044 0.000 0.900 0.056
#> GSM1178990 1 0.2048 0.855 0.928 0.000 0.064 0.008
#> GSM1178991 4 0.5024 0.439 0.360 0.008 0.000 0.632
#> GSM1178994 3 0.2565 0.858 0.032 0.000 0.912 0.056
#> GSM1178997 1 0.1284 0.883 0.964 0.024 0.000 0.012
#> GSM1179000 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM1179013 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM1179014 1 0.0188 0.909 0.996 0.000 0.000 0.004
#> GSM1179019 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM1179020 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM1179022 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM1179028 2 0.0000 0.924 0.000 1.000 0.000 0.000
#> GSM1179032 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM1179041 2 0.0000 0.924 0.000 1.000 0.000 0.000
#> GSM1179042 2 0.0000 0.924 0.000 1.000 0.000 0.000
#> GSM1178976 2 0.0657 0.916 0.000 0.984 0.012 0.004
#> GSM1178981 3 0.2300 0.857 0.016 0.000 0.920 0.064
#> GSM1178982 4 0.4406 0.502 0.000 0.000 0.300 0.700
#> GSM1178983 4 0.3088 0.756 0.052 0.000 0.060 0.888
#> GSM1178985 3 0.1474 0.859 0.000 0.000 0.948 0.052
#> GSM1178992 3 0.1209 0.853 0.004 0.000 0.964 0.032
#> GSM1179005 3 0.2222 0.858 0.060 0.000 0.924 0.016
#> GSM1179007 3 0.2413 0.856 0.064 0.000 0.916 0.020
#> GSM1179012 3 0.3840 0.822 0.104 0.000 0.844 0.052
#> GSM1179016 1 0.5775 0.482 0.644 0.012 0.316 0.028
#> GSM1179030 2 0.1389 0.891 0.000 0.952 0.000 0.048
#> GSM1179038 3 0.5611 0.326 0.412 0.000 0.564 0.024
#> GSM1178987 3 0.1474 0.858 0.000 0.000 0.948 0.052
#> GSM1179003 2 0.0000 0.924 0.000 1.000 0.000 0.000
#> GSM1179004 3 0.1389 0.859 0.000 0.000 0.952 0.048
#> GSM1179039 2 0.0000 0.924 0.000 1.000 0.000 0.000
#> GSM1178975 4 0.4981 0.173 0.464 0.000 0.000 0.536
#> GSM1178980 4 0.2281 0.747 0.000 0.096 0.000 0.904
#> GSM1178995 3 0.3937 0.753 0.188 0.000 0.800 0.012
#> GSM1178996 1 0.7170 0.510 0.620 0.104 0.240 0.036
#> GSM1179001 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM1179002 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM1179006 3 0.3082 0.792 0.000 0.084 0.884 0.032
#> GSM1179008 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM1179015 3 0.4868 0.587 0.304 0.000 0.684 0.012
#> GSM1179017 2 0.1520 0.895 0.000 0.956 0.020 0.024
#> GSM1179026 3 0.1022 0.852 0.000 0.000 0.968 0.032
#> GSM1179033 3 0.2032 0.838 0.000 0.036 0.936 0.028
#> GSM1179035 3 0.0921 0.861 0.000 0.000 0.972 0.028
#> GSM1179036 3 0.2124 0.847 0.028 0.000 0.932 0.040
#> GSM1178986 3 0.7663 0.126 0.072 0.052 0.480 0.396
#> GSM1178989 2 0.2775 0.842 0.000 0.896 0.084 0.020
#> GSM1178993 4 0.1557 0.768 0.000 0.056 0.000 0.944
#> GSM1178999 2 0.4761 0.388 0.000 0.628 0.000 0.372
#> GSM1179021 2 0.4605 0.474 0.000 0.664 0.000 0.336
#> GSM1179025 2 0.0000 0.924 0.000 1.000 0.000 0.000
#> GSM1179027 4 0.1792 0.764 0.000 0.068 0.000 0.932
#> GSM1179011 4 0.2521 0.770 0.064 0.024 0.000 0.912
#> GSM1179023 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM1179029 1 0.0672 0.902 0.984 0.000 0.008 0.008
#> GSM1179034 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM1179040 4 0.4866 0.241 0.000 0.404 0.000 0.596
#> GSM1178988 2 0.4799 0.655 0.000 0.744 0.224 0.032
#> GSM1179037 3 0.0707 0.855 0.000 0.000 0.980 0.020
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1178971 1 0.2574 0.8714 0.876 0.000 0.112 0.000 0.012
#> GSM1178979 2 0.0000 0.8971 0.000 1.000 0.000 0.000 0.000
#> GSM1179009 5 0.4902 0.1862 0.000 0.000 0.028 0.408 0.564
#> GSM1179031 2 0.0000 0.8971 0.000 1.000 0.000 0.000 0.000
#> GSM1178970 2 0.0324 0.8947 0.000 0.992 0.004 0.000 0.004
#> GSM1178972 2 0.0162 0.8956 0.000 0.996 0.004 0.000 0.000
#> GSM1178973 1 0.5190 0.1007 0.540 0.000 0.028 0.424 0.008
#> GSM1178974 2 0.0000 0.8971 0.000 1.000 0.000 0.000 0.000
#> GSM1178977 2 0.2012 0.8514 0.000 0.920 0.020 0.060 0.000
#> GSM1178978 4 0.6984 0.4028 0.076 0.020 0.052 0.540 0.312
#> GSM1178998 5 0.5405 0.0857 0.460 0.000 0.056 0.000 0.484
#> GSM1179010 5 0.2233 0.6072 0.016 0.000 0.080 0.000 0.904
#> GSM1179018 4 0.3634 0.6755 0.000 0.004 0.076 0.832 0.088
#> GSM1179024 1 0.0451 0.9192 0.988 0.000 0.004 0.000 0.008
#> GSM1178984 5 0.1865 0.6159 0.024 0.000 0.032 0.008 0.936
#> GSM1178990 1 0.3239 0.8175 0.852 0.000 0.080 0.000 0.068
#> GSM1178991 4 0.4907 0.5545 0.264 0.000 0.052 0.680 0.004
#> GSM1178994 5 0.1564 0.6155 0.024 0.000 0.024 0.004 0.948
#> GSM1178997 1 0.2425 0.8880 0.916 0.012 0.040 0.024 0.008
#> GSM1179000 1 0.0898 0.9161 0.972 0.000 0.020 0.000 0.008
#> GSM1179013 1 0.0404 0.9215 0.988 0.000 0.012 0.000 0.000
#> GSM1179014 1 0.1484 0.9050 0.944 0.000 0.048 0.000 0.008
#> GSM1179019 1 0.0693 0.9188 0.980 0.000 0.012 0.000 0.008
#> GSM1179020 1 0.0000 0.9214 1.000 0.000 0.000 0.000 0.000
#> GSM1179022 1 0.0404 0.9211 0.988 0.000 0.012 0.000 0.000
#> GSM1179028 2 0.0000 0.8971 0.000 1.000 0.000 0.000 0.000
#> GSM1179032 1 0.0404 0.9211 0.988 0.000 0.012 0.000 0.000
#> GSM1179041 2 0.0000 0.8971 0.000 1.000 0.000 0.000 0.000
#> GSM1179042 2 0.0000 0.8971 0.000 1.000 0.000 0.000 0.000
#> GSM1178976 2 0.1195 0.8777 0.000 0.960 0.028 0.000 0.012
#> GSM1178981 5 0.1179 0.6073 0.004 0.000 0.016 0.016 0.964
#> GSM1178982 5 0.4908 0.2375 0.000 0.000 0.044 0.320 0.636
#> GSM1178983 4 0.5543 0.5717 0.032 0.000 0.064 0.672 0.232
#> GSM1178985 5 0.2660 0.5668 0.000 0.000 0.128 0.008 0.864
#> GSM1178992 3 0.3932 0.4634 0.000 0.000 0.672 0.000 0.328
#> GSM1179005 5 0.5629 0.2651 0.100 0.000 0.312 0.000 0.588
#> GSM1179007 5 0.5040 0.4142 0.084 0.000 0.236 0.000 0.680
#> GSM1179012 5 0.3301 0.5917 0.080 0.000 0.072 0.000 0.848
#> GSM1179016 3 0.4610 0.4688 0.248 0.004 0.712 0.004 0.032
#> GSM1179030 2 0.2689 0.8458 0.000 0.900 0.040 0.036 0.024
#> GSM1179038 3 0.6967 0.1772 0.340 0.000 0.420 0.012 0.228
#> GSM1178987 5 0.1792 0.5925 0.000 0.000 0.084 0.000 0.916
#> GSM1179003 2 0.0162 0.8958 0.000 0.996 0.004 0.000 0.000
#> GSM1179004 5 0.2329 0.5797 0.000 0.000 0.124 0.000 0.876
#> GSM1179039 2 0.0000 0.8971 0.000 1.000 0.000 0.000 0.000
#> GSM1178975 4 0.5030 0.4334 0.336 0.000 0.032 0.624 0.008
#> GSM1178980 4 0.0955 0.7341 0.000 0.028 0.004 0.968 0.000
#> GSM1178995 5 0.6613 0.1264 0.332 0.000 0.228 0.000 0.440
#> GSM1178996 3 0.4248 0.5060 0.160 0.024 0.784 0.000 0.032
#> GSM1179001 1 0.1894 0.8987 0.920 0.000 0.072 0.000 0.008
#> GSM1179002 1 0.2233 0.8934 0.904 0.000 0.080 0.000 0.016
#> GSM1179006 3 0.3656 0.5839 0.000 0.020 0.784 0.000 0.196
#> GSM1179008 1 0.1764 0.9043 0.928 0.000 0.064 0.000 0.008
#> GSM1179015 5 0.6660 0.0456 0.384 0.000 0.228 0.000 0.388
#> GSM1179017 2 0.4059 0.5840 0.000 0.700 0.292 0.004 0.004
#> GSM1179026 3 0.3305 0.5713 0.000 0.000 0.776 0.000 0.224
#> GSM1179033 3 0.4325 0.5044 0.000 0.012 0.684 0.004 0.300
#> GSM1179035 5 0.3913 0.3306 0.000 0.000 0.324 0.000 0.676
#> GSM1179036 3 0.3093 0.5866 0.008 0.000 0.824 0.000 0.168
#> GSM1178986 3 0.8019 0.3028 0.040 0.040 0.460 0.236 0.224
#> GSM1178989 2 0.4252 0.5685 0.000 0.700 0.280 0.000 0.020
#> GSM1178993 4 0.0162 0.7391 0.000 0.000 0.000 0.996 0.004
#> GSM1178999 2 0.4403 0.3817 0.000 0.608 0.008 0.384 0.000
#> GSM1179021 2 0.4171 0.3624 0.000 0.604 0.000 0.396 0.000
#> GSM1179025 2 0.0000 0.8971 0.000 1.000 0.000 0.000 0.000
#> GSM1179027 4 0.0162 0.7394 0.000 0.004 0.000 0.996 0.000
#> GSM1179011 4 0.0693 0.7390 0.008 0.000 0.012 0.980 0.000
#> GSM1179023 1 0.0162 0.9214 0.996 0.000 0.004 0.000 0.000
#> GSM1179029 1 0.2628 0.8638 0.884 0.000 0.088 0.000 0.028
#> GSM1179034 1 0.0404 0.9211 0.988 0.000 0.012 0.000 0.000
#> GSM1179040 4 0.4074 0.2835 0.000 0.364 0.000 0.636 0.000
#> GSM1178988 3 0.5598 0.2343 0.000 0.376 0.544 0.000 0.080
#> GSM1179037 3 0.4262 0.2611 0.000 0.000 0.560 0.000 0.440
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1178971 1 0.5357 0.5218 0.576 0.000 0.096 0.000 0.316 0.012
#> GSM1178979 2 0.0000 0.8496 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179009 6 0.5616 0.0194 0.000 0.000 0.036 0.444 0.060 0.460
#> GSM1179031 2 0.0000 0.8496 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178970 2 0.0458 0.8458 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM1178972 2 0.0146 0.8491 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM1178973 1 0.5259 0.1738 0.536 0.000 0.000 0.356 0.108 0.000
#> GSM1178974 2 0.0146 0.8491 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM1178977 2 0.2433 0.7873 0.000 0.884 0.000 0.072 0.044 0.000
#> GSM1178978 6 0.7043 -0.1006 0.032 0.016 0.004 0.332 0.216 0.400
#> GSM1178998 6 0.6197 0.1745 0.368 0.000 0.024 0.000 0.160 0.448
#> GSM1179010 6 0.3765 0.5240 0.016 0.000 0.084 0.000 0.096 0.804
#> GSM1179018 4 0.5239 0.3085 0.000 0.004 0.080 0.708 0.096 0.112
#> GSM1179024 1 0.0865 0.8007 0.964 0.000 0.000 0.000 0.036 0.000
#> GSM1178984 6 0.3091 0.5365 0.012 0.000 0.044 0.004 0.084 0.856
#> GSM1178990 1 0.4925 0.5985 0.724 0.000 0.064 0.000 0.124 0.088
#> GSM1178991 4 0.5660 0.2190 0.300 0.000 0.000 0.516 0.184 0.000
#> GSM1178994 6 0.2386 0.5310 0.024 0.000 0.024 0.000 0.052 0.900
#> GSM1178997 1 0.3799 0.7183 0.780 0.012 0.008 0.024 0.176 0.000
#> GSM1179000 1 0.2053 0.7759 0.888 0.000 0.004 0.000 0.108 0.000
#> GSM1179013 1 0.0146 0.8044 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM1179014 1 0.2623 0.7657 0.852 0.000 0.016 0.000 0.132 0.000
#> GSM1179019 1 0.1524 0.7932 0.932 0.000 0.008 0.000 0.060 0.000
#> GSM1179020 1 0.0260 0.8043 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM1179022 1 0.0000 0.8046 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179028 2 0.0000 0.8496 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179032 1 0.0146 0.8046 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM1179041 2 0.0000 0.8496 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179042 2 0.0000 0.8496 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178976 2 0.2711 0.7709 0.000 0.872 0.084 0.000 0.036 0.008
#> GSM1178981 6 0.1889 0.5112 0.000 0.000 0.020 0.004 0.056 0.920
#> GSM1178982 6 0.5579 0.2482 0.004 0.000 0.012 0.204 0.168 0.612
#> GSM1178983 4 0.6976 0.0259 0.040 0.000 0.024 0.440 0.176 0.320
#> GSM1178985 6 0.4214 0.4224 0.000 0.000 0.184 0.004 0.076 0.736
#> GSM1178992 3 0.5113 0.1784 0.000 0.000 0.628 0.000 0.168 0.204
#> GSM1179005 6 0.6930 0.1485 0.076 0.000 0.300 0.004 0.172 0.448
#> GSM1179007 6 0.6653 0.2745 0.084 0.000 0.256 0.000 0.156 0.504
#> GSM1179012 6 0.5063 0.4791 0.084 0.000 0.092 0.000 0.108 0.716
#> GSM1179016 3 0.5734 -0.0863 0.148 0.000 0.544 0.000 0.296 0.012
#> GSM1179030 2 0.4661 0.6787 0.000 0.756 0.012 0.052 0.128 0.052
#> GSM1179038 3 0.7762 -0.0452 0.264 0.000 0.288 0.004 0.268 0.176
#> GSM1178987 6 0.2794 0.5008 0.000 0.000 0.060 0.000 0.080 0.860
#> GSM1179003 2 0.1168 0.8313 0.000 0.956 0.028 0.000 0.016 0.000
#> GSM1179004 6 0.2858 0.5010 0.000 0.000 0.124 0.000 0.032 0.844
#> GSM1179039 2 0.0000 0.8496 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178975 4 0.5487 0.2544 0.320 0.000 0.000 0.532 0.148 0.000
#> GSM1178980 4 0.0717 0.5816 0.000 0.016 0.000 0.976 0.008 0.000
#> GSM1178995 6 0.7575 0.0354 0.256 0.000 0.248 0.000 0.164 0.332
#> GSM1178996 3 0.5069 0.0821 0.064 0.008 0.600 0.000 0.324 0.004
#> GSM1179001 1 0.3341 0.7184 0.776 0.000 0.004 0.000 0.208 0.012
#> GSM1179002 1 0.4330 0.6629 0.708 0.000 0.012 0.000 0.236 0.044
#> GSM1179006 3 0.2263 0.3567 0.000 0.000 0.896 0.000 0.048 0.056
#> GSM1179008 1 0.2631 0.7529 0.840 0.000 0.008 0.000 0.152 0.000
#> GSM1179015 1 0.7569 -0.2293 0.328 0.000 0.192 0.000 0.188 0.292
#> GSM1179017 2 0.5319 0.2920 0.000 0.568 0.296 0.000 0.136 0.000
#> GSM1179026 3 0.2527 0.3446 0.000 0.000 0.876 0.000 0.040 0.084
#> GSM1179033 3 0.5352 0.2936 0.000 0.012 0.680 0.024 0.136 0.148
#> GSM1179035 6 0.4940 0.1596 0.000 0.000 0.400 0.000 0.068 0.532
#> GSM1179036 3 0.3746 0.3595 0.000 0.000 0.780 0.000 0.140 0.080
#> GSM1178986 5 0.8163 0.0000 0.008 0.028 0.308 0.172 0.324 0.160
#> GSM1178989 2 0.5518 0.3143 0.000 0.564 0.332 0.000 0.072 0.032
#> GSM1178993 4 0.0000 0.5842 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1178999 2 0.4649 0.2945 0.000 0.560 0.004 0.400 0.036 0.000
#> GSM1179021 2 0.3843 0.2313 0.000 0.548 0.000 0.452 0.000 0.000
#> GSM1179025 2 0.0146 0.8491 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM1179027 4 0.0000 0.5842 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1179011 4 0.1267 0.5727 0.000 0.000 0.000 0.940 0.060 0.000
#> GSM1179023 1 0.0000 0.8046 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179029 1 0.4718 0.6018 0.708 0.000 0.060 0.000 0.200 0.032
#> GSM1179034 1 0.0000 0.8046 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179040 4 0.3592 0.2311 0.000 0.344 0.000 0.656 0.000 0.000
#> GSM1178988 3 0.6475 -0.0567 0.000 0.300 0.496 0.000 0.140 0.064
#> GSM1179037 3 0.4408 0.2403 0.000 0.000 0.636 0.000 0.044 0.320
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) protocol(p) k
#> MAD:skmeans 68 0.0115 0.44976 2
#> MAD:skmeans 70 0.1371 0.00391 3
#> MAD:skmeans 63 0.1298 0.00668 4
#> MAD:skmeans 53 0.0105 0.00649 5
#> MAD:skmeans 41 0.0410 0.06231 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 31632 rows and 73 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 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 0.599 0.899 0.923 0.4352 0.543 0.543
#> 3 3 0.908 0.901 0.956 0.3416 0.866 0.754
#> 4 4 0.760 0.854 0.894 0.1676 0.908 0.777
#> 5 5 0.802 0.863 0.915 0.1296 0.881 0.650
#> 6 6 0.760 0.770 0.871 0.0417 0.968 0.865
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM1178971 2 0.5842 0.930 0.140 0.860
#> GSM1178979 2 0.0000 0.902 0.000 1.000
#> GSM1179009 2 0.5629 0.932 0.132 0.868
#> GSM1179031 2 0.0000 0.902 0.000 1.000
#> GSM1178970 2 0.1843 0.916 0.028 0.972
#> GSM1178972 2 0.0000 0.902 0.000 1.000
#> GSM1178973 1 0.0000 0.934 1.000 0.000
#> GSM1178974 2 0.0000 0.902 0.000 1.000
#> GSM1178977 2 0.2603 0.922 0.044 0.956
#> GSM1178978 1 0.9580 0.456 0.620 0.380
#> GSM1178998 1 0.0000 0.934 1.000 0.000
#> GSM1179010 2 0.7139 0.875 0.196 0.804
#> GSM1179018 2 0.4431 0.932 0.092 0.908
#> GSM1179024 1 0.0000 0.934 1.000 0.000
#> GSM1178984 1 0.9286 0.434 0.656 0.344
#> GSM1178990 1 0.0000 0.934 1.000 0.000
#> GSM1178991 1 0.0000 0.934 1.000 0.000
#> GSM1178994 2 0.5842 0.930 0.140 0.860
#> GSM1178997 1 0.1843 0.912 0.972 0.028
#> GSM1179000 1 0.0000 0.934 1.000 0.000
#> GSM1179013 1 0.0000 0.934 1.000 0.000
#> GSM1179014 1 0.0000 0.934 1.000 0.000
#> GSM1179019 1 0.0000 0.934 1.000 0.000
#> GSM1179020 1 0.0000 0.934 1.000 0.000
#> GSM1179022 1 0.0000 0.934 1.000 0.000
#> GSM1179028 2 0.0000 0.902 0.000 1.000
#> GSM1179032 1 0.0000 0.934 1.000 0.000
#> GSM1179041 2 0.0000 0.902 0.000 1.000
#> GSM1179042 2 0.0000 0.902 0.000 1.000
#> GSM1178976 2 0.1843 0.916 0.028 0.972
#> GSM1178981 2 0.5737 0.932 0.136 0.864
#> GSM1178982 2 0.5737 0.932 0.136 0.864
#> GSM1178983 2 0.7528 0.844 0.216 0.784
#> GSM1178985 2 0.5737 0.932 0.136 0.864
#> GSM1178992 2 0.5737 0.932 0.136 0.864
#> GSM1179005 2 0.5737 0.932 0.136 0.864
#> GSM1179007 2 0.5842 0.930 0.140 0.860
#> GSM1179012 1 0.0000 0.934 1.000 0.000
#> GSM1179016 2 0.5737 0.932 0.136 0.864
#> GSM1179030 2 0.3274 0.926 0.060 0.940
#> GSM1179038 2 0.5737 0.932 0.136 0.864
#> GSM1178987 2 0.5737 0.932 0.136 0.864
#> GSM1179003 2 0.0000 0.902 0.000 1.000
#> GSM1179004 2 0.5737 0.932 0.136 0.864
#> GSM1179039 2 0.0000 0.902 0.000 1.000
#> GSM1178975 1 0.8955 0.512 0.688 0.312
#> GSM1178980 2 0.2423 0.921 0.040 0.960
#> GSM1178995 2 0.5842 0.930 0.140 0.860
#> GSM1178996 2 0.5737 0.932 0.136 0.864
#> GSM1179001 1 0.0000 0.934 1.000 0.000
#> GSM1179002 1 0.0938 0.925 0.988 0.012
#> GSM1179006 2 0.5737 0.932 0.136 0.864
#> GSM1179008 1 0.0000 0.934 1.000 0.000
#> GSM1179015 1 0.0000 0.934 1.000 0.000
#> GSM1179017 2 0.0672 0.907 0.008 0.992
#> GSM1179026 2 0.5737 0.932 0.136 0.864
#> GSM1179033 2 0.5737 0.932 0.136 0.864
#> GSM1179035 2 0.5737 0.932 0.136 0.864
#> GSM1179036 2 0.5737 0.932 0.136 0.864
#> GSM1178986 2 0.5737 0.932 0.136 0.864
#> GSM1178989 2 0.3274 0.926 0.060 0.940
#> GSM1178993 2 0.4690 0.933 0.100 0.900
#> GSM1178999 2 0.2423 0.921 0.040 0.960
#> GSM1179021 2 0.0000 0.902 0.000 1.000
#> GSM1179025 2 0.0000 0.902 0.000 1.000
#> GSM1179027 2 0.4431 0.932 0.092 0.908
#> GSM1179011 1 0.9209 0.489 0.664 0.336
#> GSM1179023 1 0.0000 0.934 1.000 0.000
#> GSM1179029 1 0.0000 0.934 1.000 0.000
#> GSM1179034 1 0.0000 0.934 1.000 0.000
#> GSM1179040 2 0.2423 0.921 0.040 0.960
#> GSM1178988 2 0.4939 0.933 0.108 0.892
#> GSM1179037 2 0.5737 0.932 0.136 0.864
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1178971 3 0.1289 0.961 0.032 0.000 0.968
#> GSM1178979 3 0.5905 0.443 0.000 0.352 0.648
#> GSM1179009 3 0.0747 0.969 0.016 0.000 0.984
#> GSM1179031 2 0.0000 0.968 0.000 1.000 0.000
#> GSM1178970 3 0.0000 0.968 0.000 0.000 1.000
#> GSM1178972 2 0.0000 0.968 0.000 1.000 0.000
#> GSM1178973 1 0.0000 0.898 1.000 0.000 0.000
#> GSM1178974 2 0.0000 0.968 0.000 1.000 0.000
#> GSM1178977 3 0.0000 0.968 0.000 0.000 1.000
#> GSM1178978 1 0.6154 0.421 0.592 0.000 0.408
#> GSM1178998 1 0.0592 0.893 0.988 0.000 0.012
#> GSM1179010 3 0.2878 0.896 0.096 0.000 0.904
#> GSM1179018 3 0.0000 0.968 0.000 0.000 1.000
#> GSM1179024 1 0.0000 0.898 1.000 0.000 0.000
#> GSM1178984 1 0.6192 0.363 0.580 0.000 0.420
#> GSM1178990 1 0.0000 0.898 1.000 0.000 0.000
#> GSM1178991 1 0.1860 0.867 0.948 0.000 0.052
#> GSM1178994 3 0.1031 0.966 0.024 0.000 0.976
#> GSM1178997 1 0.2537 0.843 0.920 0.000 0.080
#> GSM1179000 1 0.0000 0.898 1.000 0.000 0.000
#> GSM1179013 1 0.0000 0.898 1.000 0.000 0.000
#> GSM1179014 1 0.0424 0.892 0.992 0.000 0.008
#> GSM1179019 1 0.0000 0.898 1.000 0.000 0.000
#> GSM1179020 1 0.0000 0.898 1.000 0.000 0.000
#> GSM1179022 1 0.0000 0.898 1.000 0.000 0.000
#> GSM1179028 2 0.0000 0.968 0.000 1.000 0.000
#> GSM1179032 1 0.0000 0.898 1.000 0.000 0.000
#> GSM1179041 2 0.0000 0.968 0.000 1.000 0.000
#> GSM1179042 2 0.0000 0.968 0.000 1.000 0.000
#> GSM1178976 3 0.0000 0.968 0.000 0.000 1.000
#> GSM1178981 3 0.0592 0.969 0.012 0.000 0.988
#> GSM1178982 3 0.0237 0.969 0.004 0.000 0.996
#> GSM1178983 3 0.3038 0.868 0.104 0.000 0.896
#> GSM1178985 3 0.0592 0.969 0.012 0.000 0.988
#> GSM1178992 3 0.0892 0.968 0.020 0.000 0.980
#> GSM1179005 3 0.0892 0.968 0.020 0.000 0.980
#> GSM1179007 3 0.1860 0.945 0.052 0.000 0.948
#> GSM1179012 1 0.1411 0.876 0.964 0.000 0.036
#> GSM1179016 3 0.0237 0.969 0.004 0.000 0.996
#> GSM1179030 3 0.0237 0.969 0.004 0.000 0.996
#> GSM1179038 3 0.0892 0.968 0.020 0.000 0.980
#> GSM1178987 3 0.0237 0.969 0.004 0.000 0.996
#> GSM1179003 3 0.3619 0.838 0.000 0.136 0.864
#> GSM1179004 3 0.0592 0.969 0.012 0.000 0.988
#> GSM1179039 2 0.0000 0.968 0.000 1.000 0.000
#> GSM1178975 1 0.5905 0.502 0.648 0.000 0.352
#> GSM1178980 3 0.0000 0.968 0.000 0.000 1.000
#> GSM1178995 3 0.1964 0.941 0.056 0.000 0.944
#> GSM1178996 3 0.0892 0.968 0.020 0.000 0.980
#> GSM1179001 1 0.0000 0.898 1.000 0.000 0.000
#> GSM1179002 1 0.1031 0.885 0.976 0.000 0.024
#> GSM1179006 3 0.0747 0.969 0.016 0.000 0.984
#> GSM1179008 1 0.0000 0.898 1.000 0.000 0.000
#> GSM1179015 1 0.0000 0.898 1.000 0.000 0.000
#> GSM1179017 3 0.1860 0.932 0.000 0.052 0.948
#> GSM1179026 3 0.0747 0.969 0.016 0.000 0.984
#> GSM1179033 3 0.0892 0.968 0.020 0.000 0.980
#> GSM1179035 3 0.0892 0.968 0.020 0.000 0.980
#> GSM1179036 3 0.0892 0.968 0.020 0.000 0.980
#> GSM1178986 3 0.0237 0.969 0.004 0.000 0.996
#> GSM1178989 3 0.0237 0.969 0.004 0.000 0.996
#> GSM1178993 3 0.0000 0.968 0.000 0.000 1.000
#> GSM1178999 3 0.0000 0.968 0.000 0.000 1.000
#> GSM1179021 2 0.4605 0.737 0.000 0.796 0.204
#> GSM1179025 2 0.0000 0.968 0.000 1.000 0.000
#> GSM1179027 3 0.0424 0.969 0.008 0.000 0.992
#> GSM1179011 1 0.6180 0.411 0.584 0.000 0.416
#> GSM1179023 1 0.0000 0.898 1.000 0.000 0.000
#> GSM1179029 1 0.0237 0.896 0.996 0.000 0.004
#> GSM1179034 1 0.0000 0.898 1.000 0.000 0.000
#> GSM1179040 3 0.0000 0.968 0.000 0.000 1.000
#> GSM1178988 3 0.0237 0.969 0.004 0.000 0.996
#> GSM1179037 3 0.0747 0.969 0.016 0.000 0.984
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1178971 3 0.0817 0.902 0.024 0.000 0.976 0.000
#> GSM1178979 4 0.5690 0.739 0.000 0.168 0.116 0.716
#> GSM1179009 3 0.4483 0.723 0.004 0.000 0.712 0.284
#> GSM1179031 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1178970 3 0.1792 0.871 0.000 0.000 0.932 0.068
#> GSM1178972 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1178973 1 0.0188 0.887 0.996 0.000 0.000 0.004
#> GSM1178974 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1178977 3 0.2081 0.855 0.000 0.000 0.916 0.084
#> GSM1178978 1 0.7315 0.418 0.516 0.000 0.184 0.300
#> GSM1178998 1 0.3808 0.778 0.812 0.000 0.012 0.176
#> GSM1179010 3 0.4035 0.818 0.020 0.000 0.804 0.176
#> GSM1179018 3 0.0817 0.903 0.000 0.000 0.976 0.024
#> GSM1179024 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM1178984 1 0.7421 0.300 0.484 0.000 0.332 0.184
#> GSM1178990 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM1178991 1 0.4015 0.783 0.832 0.000 0.052 0.116
#> GSM1178994 3 0.3768 0.821 0.008 0.000 0.808 0.184
#> GSM1178997 1 0.2329 0.844 0.916 0.000 0.072 0.012
#> GSM1179000 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM1179013 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM1179014 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM1179019 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM1179020 1 0.0336 0.887 0.992 0.000 0.000 0.008
#> GSM1179022 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM1179028 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1179032 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM1179041 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1179042 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1178976 3 0.0000 0.906 0.000 0.000 1.000 0.000
#> GSM1178981 3 0.3626 0.822 0.004 0.000 0.812 0.184
#> GSM1178982 3 0.3257 0.845 0.004 0.000 0.844 0.152
#> GSM1178983 3 0.5576 0.718 0.096 0.000 0.720 0.184
#> GSM1178985 3 0.2999 0.855 0.004 0.000 0.864 0.132
#> GSM1178992 3 0.0524 0.908 0.008 0.000 0.988 0.004
#> GSM1179005 3 0.0336 0.907 0.008 0.000 0.992 0.000
#> GSM1179007 3 0.4552 0.808 0.044 0.000 0.784 0.172
#> GSM1179012 1 0.4595 0.753 0.780 0.000 0.044 0.176
#> GSM1179016 3 0.0469 0.904 0.000 0.000 0.988 0.012
#> GSM1179030 3 0.0707 0.902 0.000 0.000 0.980 0.020
#> GSM1179038 3 0.0336 0.907 0.008 0.000 0.992 0.000
#> GSM1178987 3 0.3569 0.818 0.000 0.000 0.804 0.196
#> GSM1179003 3 0.3525 0.824 0.000 0.100 0.860 0.040
#> GSM1179004 3 0.3539 0.824 0.004 0.000 0.820 0.176
#> GSM1179039 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1178975 1 0.5408 0.334 0.576 0.000 0.408 0.016
#> GSM1178980 4 0.3356 0.871 0.000 0.000 0.176 0.824
#> GSM1178995 3 0.2844 0.878 0.048 0.000 0.900 0.052
#> GSM1178996 3 0.0336 0.907 0.008 0.000 0.992 0.000
#> GSM1179001 1 0.0817 0.883 0.976 0.000 0.000 0.024
#> GSM1179002 1 0.1970 0.855 0.932 0.000 0.060 0.008
#> GSM1179006 3 0.0188 0.907 0.004 0.000 0.996 0.000
#> GSM1179008 1 0.1792 0.864 0.932 0.000 0.000 0.068
#> GSM1179015 1 0.1022 0.881 0.968 0.000 0.000 0.032
#> GSM1179017 3 0.1938 0.878 0.000 0.052 0.936 0.012
#> GSM1179026 3 0.0188 0.907 0.004 0.000 0.996 0.000
#> GSM1179033 3 0.0336 0.907 0.008 0.000 0.992 0.000
#> GSM1179035 3 0.0524 0.908 0.008 0.000 0.988 0.004
#> GSM1179036 3 0.0336 0.907 0.008 0.000 0.992 0.000
#> GSM1178986 3 0.0592 0.903 0.000 0.000 0.984 0.016
#> GSM1178989 3 0.0469 0.904 0.000 0.000 0.988 0.012
#> GSM1178993 4 0.1792 0.789 0.000 0.000 0.068 0.932
#> GSM1178999 4 0.4040 0.822 0.000 0.000 0.248 0.752
#> GSM1179021 4 0.3751 0.660 0.000 0.196 0.004 0.800
#> GSM1179025 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1179027 4 0.3569 0.869 0.000 0.000 0.196 0.804
#> GSM1179011 4 0.3494 0.871 0.004 0.000 0.172 0.824
#> GSM1179023 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM1179029 1 0.1576 0.874 0.948 0.000 0.004 0.048
#> GSM1179034 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> GSM1179040 4 0.3801 0.859 0.000 0.000 0.220 0.780
#> GSM1178988 3 0.0000 0.906 0.000 0.000 1.000 0.000
#> GSM1179037 3 0.0188 0.907 0.004 0.000 0.996 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1178971 3 0.0162 0.887 0.004 0.000 0.996 0.000 0.000
#> GSM1178979 4 0.2069 0.921 0.000 0.000 0.012 0.912 0.076
#> GSM1179009 5 0.3590 0.848 0.000 0.000 0.092 0.080 0.828
#> GSM1179031 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM1178970 3 0.5844 0.604 0.000 0.000 0.608 0.208 0.184
#> GSM1178972 2 0.0162 0.997 0.000 0.996 0.000 0.000 0.004
#> GSM1178973 1 0.1809 0.890 0.928 0.000 0.060 0.000 0.012
#> GSM1178974 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM1178977 3 0.5502 0.652 0.000 0.000 0.652 0.192 0.156
#> GSM1178978 5 0.1285 0.847 0.036 0.000 0.004 0.004 0.956
#> GSM1178998 5 0.3231 0.750 0.196 0.000 0.004 0.000 0.800
#> GSM1179010 5 0.3039 0.822 0.000 0.000 0.192 0.000 0.808
#> GSM1179018 3 0.3081 0.819 0.000 0.000 0.832 0.012 0.156
#> GSM1179024 1 0.0000 0.905 1.000 0.000 0.000 0.000 0.000
#> GSM1178984 5 0.2595 0.862 0.032 0.000 0.080 0.000 0.888
#> GSM1178990 1 0.1410 0.891 0.940 0.000 0.060 0.000 0.000
#> GSM1178991 1 0.3565 0.797 0.816 0.000 0.000 0.040 0.144
#> GSM1178994 5 0.2179 0.873 0.000 0.000 0.112 0.000 0.888
#> GSM1178997 1 0.3291 0.841 0.848 0.000 0.064 0.000 0.088
#> GSM1179000 1 0.0290 0.905 0.992 0.000 0.008 0.000 0.000
#> GSM1179013 1 0.0000 0.905 1.000 0.000 0.000 0.000 0.000
#> GSM1179014 1 0.0579 0.905 0.984 0.000 0.008 0.000 0.008
#> GSM1179019 1 0.0510 0.904 0.984 0.000 0.016 0.000 0.000
#> GSM1179020 1 0.0290 0.905 0.992 0.000 0.000 0.000 0.008
#> GSM1179022 1 0.0000 0.905 1.000 0.000 0.000 0.000 0.000
#> GSM1179028 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM1179032 1 0.0000 0.905 1.000 0.000 0.000 0.000 0.000
#> GSM1179041 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM1179042 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM1178976 3 0.1410 0.886 0.000 0.000 0.940 0.000 0.060
#> GSM1178981 5 0.1908 0.875 0.000 0.000 0.092 0.000 0.908
#> GSM1178982 5 0.2690 0.820 0.000 0.000 0.156 0.000 0.844
#> GSM1178983 5 0.1851 0.853 0.000 0.000 0.088 0.000 0.912
#> GSM1178985 3 0.4045 0.440 0.000 0.000 0.644 0.000 0.356
#> GSM1178992 3 0.0162 0.888 0.000 0.000 0.996 0.000 0.004
#> GSM1179005 3 0.0000 0.888 0.000 0.000 1.000 0.000 0.000
#> GSM1179007 3 0.3857 0.465 0.000 0.000 0.688 0.000 0.312
#> GSM1179012 5 0.3723 0.772 0.152 0.000 0.044 0.000 0.804
#> GSM1179016 3 0.1671 0.881 0.000 0.000 0.924 0.000 0.076
#> GSM1179030 3 0.2891 0.813 0.000 0.000 0.824 0.000 0.176
#> GSM1179038 3 0.0000 0.888 0.000 0.000 1.000 0.000 0.000
#> GSM1178987 5 0.1410 0.861 0.000 0.000 0.060 0.000 0.940
#> GSM1179003 3 0.4462 0.780 0.000 0.056 0.788 0.124 0.032
#> GSM1179004 5 0.3074 0.821 0.000 0.000 0.196 0.000 0.804
#> GSM1179039 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM1178975 1 0.5733 0.216 0.476 0.000 0.440 0.000 0.084
#> GSM1178980 4 0.0404 0.968 0.000 0.000 0.000 0.988 0.012
#> GSM1178995 3 0.1478 0.854 0.000 0.000 0.936 0.000 0.064
#> GSM1178996 3 0.0000 0.888 0.000 0.000 1.000 0.000 0.000
#> GSM1179001 1 0.2843 0.864 0.876 0.000 0.048 0.000 0.076
#> GSM1179002 1 0.3493 0.832 0.832 0.000 0.108 0.000 0.060
#> GSM1179006 3 0.0609 0.891 0.000 0.000 0.980 0.000 0.020
#> GSM1179008 1 0.3336 0.839 0.844 0.000 0.060 0.000 0.096
#> GSM1179015 1 0.2409 0.878 0.900 0.000 0.032 0.000 0.068
#> GSM1179017 3 0.2209 0.875 0.000 0.032 0.912 0.000 0.056
#> GSM1179026 3 0.0880 0.890 0.000 0.000 0.968 0.000 0.032
#> GSM1179033 3 0.0000 0.888 0.000 0.000 1.000 0.000 0.000
#> GSM1179035 3 0.0703 0.891 0.000 0.000 0.976 0.000 0.024
#> GSM1179036 3 0.0000 0.888 0.000 0.000 1.000 0.000 0.000
#> GSM1178986 3 0.1671 0.882 0.000 0.000 0.924 0.000 0.076
#> GSM1178989 3 0.1544 0.884 0.000 0.000 0.932 0.000 0.068
#> GSM1178993 4 0.0000 0.970 0.000 0.000 0.000 1.000 0.000
#> GSM1178999 4 0.1892 0.923 0.000 0.000 0.004 0.916 0.080
#> GSM1179021 4 0.0162 0.970 0.000 0.000 0.000 0.996 0.004
#> GSM1179025 2 0.0162 0.997 0.000 0.996 0.000 0.000 0.004
#> GSM1179027 4 0.0000 0.970 0.000 0.000 0.000 1.000 0.000
#> GSM1179011 4 0.0404 0.968 0.000 0.000 0.000 0.988 0.012
#> GSM1179023 1 0.0000 0.905 1.000 0.000 0.000 0.000 0.000
#> GSM1179029 1 0.4162 0.741 0.768 0.000 0.056 0.000 0.176
#> GSM1179034 1 0.0000 0.905 1.000 0.000 0.000 0.000 0.000
#> GSM1179040 4 0.0162 0.969 0.000 0.000 0.004 0.996 0.000
#> GSM1178988 3 0.1410 0.886 0.000 0.000 0.940 0.000 0.060
#> GSM1179037 3 0.0880 0.890 0.000 0.000 0.968 0.000 0.032
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1178971 3 0.1116 0.84922 0.004 0.000 0.960 0.008 0.000 0.028
#> GSM1178979 5 0.3042 0.75929 0.000 0.000 0.004 0.128 0.836 0.032
#> GSM1179009 6 0.4305 0.75290 0.000 0.000 0.076 0.052 0.096 0.776
#> GSM1179031 2 0.0000 0.98079 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178970 3 0.6966 0.41325 0.000 0.000 0.488 0.152 0.212 0.148
#> GSM1178972 2 0.2001 0.91101 0.000 0.912 0.000 0.040 0.048 0.000
#> GSM1178973 4 0.4419 0.50272 0.304 0.000 0.012 0.656 0.000 0.028
#> GSM1178974 2 0.0000 0.98079 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178977 3 0.6891 0.43097 0.000 0.000 0.500 0.152 0.208 0.140
#> GSM1178978 6 0.2755 0.78046 0.012 0.000 0.004 0.140 0.000 0.844
#> GSM1178998 6 0.3412 0.76008 0.064 0.000 0.000 0.128 0.000 0.808
#> GSM1179010 6 0.2664 0.77959 0.000 0.000 0.016 0.136 0.000 0.848
#> GSM1179018 3 0.2963 0.76983 0.000 0.000 0.828 0.016 0.004 0.152
#> GSM1179024 1 0.0000 0.88396 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1178984 6 0.1251 0.81974 0.024 0.000 0.012 0.008 0.000 0.956
#> GSM1178990 1 0.1218 0.85651 0.956 0.000 0.012 0.004 0.000 0.028
#> GSM1178991 4 0.4457 0.54706 0.068 0.000 0.004 0.768 0.048 0.112
#> GSM1178994 6 0.0820 0.82666 0.000 0.000 0.016 0.012 0.000 0.972
#> GSM1178997 4 0.4976 0.22462 0.412 0.000 0.012 0.532 0.000 0.044
#> GSM1179000 1 0.0146 0.88306 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM1179013 1 0.0000 0.88396 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179014 1 0.0146 0.88255 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM1179019 1 0.0146 0.88306 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM1179020 1 0.0260 0.88116 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM1179022 1 0.0000 0.88396 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179028 2 0.0000 0.98079 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179032 1 0.0000 0.88396 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179041 2 0.0000 0.98079 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179042 2 0.0000 0.98079 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178976 3 0.0363 0.85742 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM1178981 6 0.1075 0.82669 0.000 0.000 0.048 0.000 0.000 0.952
#> GSM1178982 6 0.2593 0.77207 0.000 0.000 0.148 0.008 0.000 0.844
#> GSM1178983 6 0.3190 0.76827 0.000 0.000 0.044 0.136 0.000 0.820
#> GSM1178985 3 0.3620 0.42304 0.000 0.000 0.648 0.000 0.000 0.352
#> GSM1178992 3 0.0291 0.85729 0.000 0.000 0.992 0.004 0.000 0.004
#> GSM1179005 3 0.0858 0.85095 0.000 0.000 0.968 0.004 0.000 0.028
#> GSM1179007 3 0.3769 0.47813 0.000 0.000 0.640 0.004 0.000 0.356
#> GSM1179012 6 0.3125 0.77187 0.032 0.000 0.004 0.136 0.000 0.828
#> GSM1179016 3 0.2513 0.80905 0.000 0.000 0.852 0.140 0.000 0.008
#> GSM1179030 3 0.4429 0.69497 0.000 0.000 0.716 0.140 0.000 0.144
#> GSM1179038 3 0.0858 0.85095 0.000 0.000 0.968 0.004 0.000 0.028
#> GSM1178987 6 0.2858 0.78638 0.000 0.000 0.032 0.124 0.000 0.844
#> GSM1179003 3 0.3987 0.71578 0.000 0.056 0.760 0.008 0.176 0.000
#> GSM1179004 6 0.2912 0.71049 0.000 0.000 0.216 0.000 0.000 0.784
#> GSM1179039 2 0.0000 0.98079 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178975 4 0.5617 0.54106 0.092 0.000 0.164 0.656 0.000 0.088
#> GSM1178980 4 0.3868 -0.00654 0.000 0.000 0.000 0.508 0.492 0.000
#> GSM1178995 3 0.1958 0.82182 0.000 0.000 0.896 0.004 0.000 0.100
#> GSM1178996 3 0.0291 0.85653 0.000 0.000 0.992 0.004 0.000 0.004
#> GSM1179001 1 0.3089 0.72485 0.800 0.000 0.004 0.008 0.000 0.188
#> GSM1179002 1 0.4586 0.60966 0.712 0.000 0.104 0.008 0.000 0.176
#> GSM1179006 3 0.0260 0.85748 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM1179008 1 0.4806 0.60005 0.708 0.000 0.020 0.160 0.000 0.112
#> GSM1179015 1 0.4087 0.67874 0.760 0.000 0.004 0.136 0.000 0.100
#> GSM1179017 3 0.3854 0.77152 0.000 0.016 0.788 0.140 0.056 0.000
#> GSM1179026 3 0.0363 0.85742 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM1179033 3 0.0146 0.85658 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM1179035 3 0.0603 0.85852 0.000 0.000 0.980 0.004 0.000 0.016
#> GSM1179036 3 0.0146 0.85658 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM1178986 3 0.2358 0.82452 0.000 0.000 0.876 0.108 0.000 0.016
#> GSM1178989 3 0.2165 0.82670 0.000 0.000 0.884 0.108 0.000 0.008
#> GSM1178993 5 0.1285 0.84916 0.000 0.000 0.000 0.052 0.944 0.004
#> GSM1178999 5 0.2726 0.77858 0.000 0.000 0.000 0.112 0.856 0.032
#> GSM1179021 5 0.0000 0.85366 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1179025 2 0.1010 0.95414 0.000 0.960 0.000 0.004 0.036 0.000
#> GSM1179027 5 0.1285 0.85055 0.000 0.000 0.004 0.052 0.944 0.000
#> GSM1179011 4 0.3390 0.40815 0.000 0.000 0.000 0.704 0.296 0.000
#> GSM1179023 1 0.0000 0.88396 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179029 1 0.4570 0.54528 0.664 0.000 0.012 0.044 0.000 0.280
#> GSM1179034 1 0.0000 0.88396 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179040 5 0.1644 0.83980 0.000 0.000 0.040 0.028 0.932 0.000
#> GSM1178988 3 0.0363 0.85742 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM1179037 3 0.0363 0.85742 0.000 0.000 0.988 0.000 0.000 0.012
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) protocol(p) k
#> MAD:pam 70 0.49724 5.24e-03 2
#> MAD:pam 69 0.59151 4.86e-04 3
#> MAD:pam 70 0.00839 1.91e-05 4
#> MAD:pam 70 0.00663 1.96e-05 5
#> MAD:pam 66 0.01164 8.04e-06 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "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 31632 rows and 73 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.835 0.903 0.949 0.2909 0.703 0.703
#> 3 3 0.665 0.859 0.919 0.9081 0.653 0.538
#> 4 4 0.731 0.775 0.913 0.1947 0.782 0.576
#> 5 5 0.653 0.760 0.861 0.0870 0.815 0.557
#> 6 6 0.674 0.569 0.810 0.0661 0.918 0.738
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM1178971 1 0.0000 0.964 1.000 0.000
#> GSM1178979 2 0.6887 0.821 0.184 0.816
#> GSM1179009 1 0.3733 0.912 0.928 0.072
#> GSM1179031 2 0.3431 0.887 0.064 0.936
#> GSM1178970 2 0.7883 0.769 0.236 0.764
#> GSM1178972 2 0.3431 0.887 0.064 0.936
#> GSM1178973 1 0.3733 0.912 0.928 0.072
#> GSM1178974 2 0.3431 0.887 0.064 0.936
#> GSM1178977 1 0.6247 0.800 0.844 0.156
#> GSM1178978 1 0.3733 0.912 0.928 0.072
#> GSM1178998 1 0.0000 0.964 1.000 0.000
#> GSM1179010 1 0.0000 0.964 1.000 0.000
#> GSM1179018 1 0.3584 0.915 0.932 0.068
#> GSM1179024 1 0.0000 0.964 1.000 0.000
#> GSM1178984 1 0.0000 0.964 1.000 0.000
#> GSM1178990 1 0.0000 0.964 1.000 0.000
#> GSM1178991 1 0.3733 0.912 0.928 0.072
#> GSM1178994 1 0.0000 0.964 1.000 0.000
#> GSM1178997 1 0.0000 0.964 1.000 0.000
#> GSM1179000 1 0.0000 0.964 1.000 0.000
#> GSM1179013 1 0.0000 0.964 1.000 0.000
#> GSM1179014 1 0.0000 0.964 1.000 0.000
#> GSM1179019 1 0.0000 0.964 1.000 0.000
#> GSM1179020 1 0.0000 0.964 1.000 0.000
#> GSM1179022 1 0.0000 0.964 1.000 0.000
#> GSM1179028 2 0.3431 0.887 0.064 0.936
#> GSM1179032 1 0.0000 0.964 1.000 0.000
#> GSM1179041 2 0.3431 0.887 0.064 0.936
#> GSM1179042 2 0.3431 0.887 0.064 0.936
#> GSM1178976 1 0.9129 0.403 0.672 0.328
#> GSM1178981 1 0.0000 0.964 1.000 0.000
#> GSM1178982 1 0.0000 0.964 1.000 0.000
#> GSM1178983 1 0.0000 0.964 1.000 0.000
#> GSM1178985 1 0.0000 0.964 1.000 0.000
#> GSM1178992 1 0.0376 0.962 0.996 0.004
#> GSM1179005 1 0.0000 0.964 1.000 0.000
#> GSM1179007 1 0.0000 0.964 1.000 0.000
#> GSM1179012 1 0.0000 0.964 1.000 0.000
#> GSM1179016 1 0.0672 0.959 0.992 0.008
#> GSM1179030 1 0.0672 0.959 0.992 0.008
#> GSM1179038 1 0.0000 0.964 1.000 0.000
#> GSM1178987 1 0.0000 0.964 1.000 0.000
#> GSM1179003 2 0.9881 0.404 0.436 0.564
#> GSM1179004 1 0.0000 0.964 1.000 0.000
#> GSM1179039 2 0.3431 0.887 0.064 0.936
#> GSM1178975 1 0.3733 0.912 0.928 0.072
#> GSM1178980 1 0.6973 0.781 0.812 0.188
#> GSM1178995 1 0.0000 0.964 1.000 0.000
#> GSM1178996 1 0.0000 0.964 1.000 0.000
#> GSM1179001 1 0.0000 0.964 1.000 0.000
#> GSM1179002 1 0.0000 0.964 1.000 0.000
#> GSM1179006 1 0.0000 0.964 1.000 0.000
#> GSM1179008 1 0.0000 0.964 1.000 0.000
#> GSM1179015 1 0.0000 0.964 1.000 0.000
#> GSM1179017 1 0.5842 0.806 0.860 0.140
#> GSM1179026 1 0.0000 0.964 1.000 0.000
#> GSM1179033 1 0.0000 0.964 1.000 0.000
#> GSM1179035 1 0.0000 0.964 1.000 0.000
#> GSM1179036 1 0.0000 0.964 1.000 0.000
#> GSM1178986 1 0.0376 0.962 0.996 0.004
#> GSM1178989 1 0.0672 0.959 0.992 0.008
#> GSM1178993 1 0.3733 0.912 0.928 0.072
#> GSM1178999 1 0.9044 0.426 0.680 0.320
#> GSM1179021 2 0.5294 0.827 0.120 0.880
#> GSM1179025 2 0.3431 0.887 0.064 0.936
#> GSM1179027 1 0.3733 0.912 0.928 0.072
#> GSM1179011 1 0.3733 0.912 0.928 0.072
#> GSM1179023 1 0.0000 0.964 1.000 0.000
#> GSM1179029 1 0.0000 0.964 1.000 0.000
#> GSM1179034 1 0.0000 0.964 1.000 0.000
#> GSM1179040 2 0.9933 0.239 0.452 0.548
#> GSM1178988 1 0.0376 0.962 0.996 0.004
#> GSM1179037 1 0.0000 0.964 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1178971 3 0.1482 0.910 0.020 0.012 0.968
#> GSM1178979 2 0.4002 0.756 0.000 0.840 0.160
#> GSM1179009 3 0.4110 0.845 0.004 0.152 0.844
#> GSM1179031 2 0.0237 0.962 0.004 0.996 0.000
#> GSM1178970 3 0.5497 0.682 0.000 0.292 0.708
#> GSM1178972 2 0.0000 0.963 0.000 1.000 0.000
#> GSM1178973 1 0.6231 0.741 0.772 0.148 0.080
#> GSM1178974 2 0.0000 0.963 0.000 1.000 0.000
#> GSM1178977 3 0.3879 0.847 0.000 0.152 0.848
#> GSM1178978 3 0.3879 0.847 0.000 0.152 0.848
#> GSM1178998 1 0.5016 0.773 0.760 0.000 0.240
#> GSM1179010 3 0.0237 0.913 0.004 0.000 0.996
#> GSM1179018 3 0.3482 0.862 0.000 0.128 0.872
#> GSM1179024 1 0.0747 0.853 0.984 0.000 0.016
#> GSM1178984 3 0.0237 0.913 0.004 0.000 0.996
#> GSM1178990 1 0.4931 0.781 0.768 0.000 0.232
#> GSM1178991 1 0.8847 0.442 0.552 0.148 0.300
#> GSM1178994 3 0.0237 0.913 0.004 0.000 0.996
#> GSM1178997 3 0.6542 0.718 0.204 0.060 0.736
#> GSM1179000 1 0.2625 0.871 0.916 0.000 0.084
#> GSM1179013 1 0.0424 0.848 0.992 0.000 0.008
#> GSM1179014 1 0.2772 0.869 0.916 0.004 0.080
#> GSM1179019 1 0.2625 0.871 0.916 0.000 0.084
#> GSM1179020 1 0.2066 0.871 0.940 0.000 0.060
#> GSM1179022 1 0.0424 0.848 0.992 0.000 0.008
#> GSM1179028 2 0.0237 0.962 0.004 0.996 0.000
#> GSM1179032 1 0.0237 0.845 0.996 0.000 0.004
#> GSM1179041 2 0.0237 0.962 0.004 0.996 0.000
#> GSM1179042 2 0.0000 0.963 0.000 1.000 0.000
#> GSM1178976 3 0.1753 0.904 0.000 0.048 0.952
#> GSM1178981 3 0.0000 0.914 0.000 0.000 1.000
#> GSM1178982 3 0.0000 0.914 0.000 0.000 1.000
#> GSM1178983 3 0.0000 0.914 0.000 0.000 1.000
#> GSM1178985 3 0.0000 0.914 0.000 0.000 1.000
#> GSM1178992 3 0.0000 0.914 0.000 0.000 1.000
#> GSM1179005 3 0.0237 0.913 0.004 0.000 0.996
#> GSM1179007 3 0.0424 0.911 0.008 0.000 0.992
#> GSM1179012 3 0.4121 0.736 0.168 0.000 0.832
#> GSM1179016 3 0.3083 0.895 0.024 0.060 0.916
#> GSM1179030 3 0.2066 0.899 0.000 0.060 0.940
#> GSM1179038 3 0.0237 0.913 0.004 0.000 0.996
#> GSM1178987 3 0.0000 0.914 0.000 0.000 1.000
#> GSM1179003 3 0.6045 0.515 0.000 0.380 0.620
#> GSM1179004 3 0.0000 0.914 0.000 0.000 1.000
#> GSM1179039 2 0.0237 0.962 0.004 0.996 0.000
#> GSM1178975 3 0.8930 0.331 0.316 0.148 0.536
#> GSM1178980 3 0.4110 0.845 0.004 0.152 0.844
#> GSM1178995 3 0.0237 0.913 0.004 0.000 0.996
#> GSM1178996 3 0.0237 0.914 0.000 0.004 0.996
#> GSM1179001 1 0.2537 0.872 0.920 0.000 0.080
#> GSM1179002 3 0.1529 0.893 0.040 0.000 0.960
#> GSM1179006 3 0.0000 0.914 0.000 0.000 1.000
#> GSM1179008 1 0.2066 0.871 0.940 0.000 0.060
#> GSM1179015 1 0.5138 0.759 0.748 0.000 0.252
#> GSM1179017 3 0.2448 0.893 0.000 0.076 0.924
#> GSM1179026 3 0.0000 0.914 0.000 0.000 1.000
#> GSM1179033 3 0.0000 0.914 0.000 0.000 1.000
#> GSM1179035 3 0.0000 0.914 0.000 0.000 1.000
#> GSM1179036 3 0.0000 0.914 0.000 0.000 1.000
#> GSM1178986 3 0.1643 0.906 0.000 0.044 0.956
#> GSM1178989 3 0.0592 0.913 0.000 0.012 0.988
#> GSM1178993 3 0.4110 0.845 0.004 0.152 0.844
#> GSM1178999 3 0.4452 0.811 0.000 0.192 0.808
#> GSM1179021 2 0.1989 0.911 0.004 0.948 0.048
#> GSM1179025 2 0.0000 0.963 0.000 1.000 0.000
#> GSM1179027 3 0.4110 0.845 0.004 0.152 0.844
#> GSM1179011 3 0.4228 0.845 0.008 0.148 0.844
#> GSM1179023 1 0.0424 0.848 0.992 0.000 0.008
#> GSM1179029 1 0.4399 0.814 0.812 0.000 0.188
#> GSM1179034 1 0.0237 0.845 0.996 0.000 0.004
#> GSM1179040 3 0.4629 0.812 0.004 0.188 0.808
#> GSM1178988 3 0.0000 0.914 0.000 0.000 1.000
#> GSM1179037 3 0.0000 0.914 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1178971 3 0.1716 0.8406 0.064 0.000 0.936 0.000
#> GSM1178979 2 0.5337 0.1795 0.000 0.564 0.424 0.012
#> GSM1179009 4 0.3528 0.6788 0.000 0.000 0.192 0.808
#> GSM1179031 2 0.0000 0.9054 0.000 1.000 0.000 0.000
#> GSM1178970 3 0.2928 0.7882 0.000 0.108 0.880 0.012
#> GSM1178972 2 0.0524 0.9035 0.000 0.988 0.008 0.004
#> GSM1178973 4 0.3790 0.7627 0.164 0.000 0.016 0.820
#> GSM1178974 2 0.0524 0.9035 0.000 0.988 0.008 0.004
#> GSM1178977 3 0.4356 0.5861 0.000 0.000 0.708 0.292
#> GSM1178978 3 0.3726 0.6800 0.000 0.000 0.788 0.212
#> GSM1178998 3 0.3024 0.7610 0.148 0.000 0.852 0.000
#> GSM1179010 3 0.0000 0.8793 0.000 0.000 1.000 0.000
#> GSM1179018 3 0.0817 0.8650 0.000 0.000 0.976 0.024
#> GSM1179024 1 0.0000 0.8853 1.000 0.000 0.000 0.000
#> GSM1178984 3 0.0000 0.8793 0.000 0.000 1.000 0.000
#> GSM1178990 1 0.3688 0.6851 0.792 0.000 0.208 0.000
#> GSM1178991 3 0.7593 0.1318 0.236 0.000 0.476 0.288
#> GSM1178994 3 0.0000 0.8793 0.000 0.000 1.000 0.000
#> GSM1178997 1 0.0188 0.8863 0.996 0.000 0.004 0.000
#> GSM1179000 1 0.0188 0.8863 0.996 0.000 0.004 0.000
#> GSM1179013 1 0.0000 0.8853 1.000 0.000 0.000 0.000
#> GSM1179014 1 0.0188 0.8863 0.996 0.000 0.004 0.000
#> GSM1179019 1 0.0188 0.8863 0.996 0.000 0.004 0.000
#> GSM1179020 1 0.0188 0.8863 0.996 0.000 0.004 0.000
#> GSM1179022 1 0.0000 0.8853 1.000 0.000 0.000 0.000
#> GSM1179028 2 0.0000 0.9054 0.000 1.000 0.000 0.000
#> GSM1179032 1 0.0000 0.8853 1.000 0.000 0.000 0.000
#> GSM1179041 2 0.0000 0.9054 0.000 1.000 0.000 0.000
#> GSM1179042 2 0.0188 0.9048 0.000 0.996 0.000 0.004
#> GSM1178976 3 0.0188 0.8765 0.000 0.000 0.996 0.004
#> GSM1178981 3 0.0000 0.8793 0.000 0.000 1.000 0.000
#> GSM1178982 3 0.0000 0.8793 0.000 0.000 1.000 0.000
#> GSM1178983 3 0.0000 0.8793 0.000 0.000 1.000 0.000
#> GSM1178985 3 0.0000 0.8793 0.000 0.000 1.000 0.000
#> GSM1178992 3 0.4382 0.5190 0.296 0.000 0.704 0.000
#> GSM1179005 3 0.0000 0.8793 0.000 0.000 1.000 0.000
#> GSM1179007 3 0.0000 0.8793 0.000 0.000 1.000 0.000
#> GSM1179012 3 0.0000 0.8793 0.000 0.000 1.000 0.000
#> GSM1179016 1 0.4776 0.4037 0.624 0.000 0.376 0.000
#> GSM1179030 3 0.0000 0.8793 0.000 0.000 1.000 0.000
#> GSM1179038 3 0.0000 0.8793 0.000 0.000 1.000 0.000
#> GSM1178987 3 0.0000 0.8793 0.000 0.000 1.000 0.000
#> GSM1179003 3 0.5137 0.1196 0.000 0.452 0.544 0.004
#> GSM1179004 3 0.0000 0.8793 0.000 0.000 1.000 0.000
#> GSM1179039 2 0.0000 0.9054 0.000 1.000 0.000 0.000
#> GSM1178975 3 0.7792 -0.0608 0.256 0.000 0.412 0.332
#> GSM1178980 4 0.0188 0.9235 0.000 0.000 0.004 0.996
#> GSM1178995 3 0.0000 0.8793 0.000 0.000 1.000 0.000
#> GSM1178996 3 0.4543 0.4589 0.324 0.000 0.676 0.000
#> GSM1179001 1 0.1940 0.8166 0.924 0.000 0.076 0.000
#> GSM1179002 3 0.4730 0.3908 0.364 0.000 0.636 0.000
#> GSM1179006 3 0.0000 0.8793 0.000 0.000 1.000 0.000
#> GSM1179008 1 0.0188 0.8863 0.996 0.000 0.004 0.000
#> GSM1179015 3 0.4972 0.0825 0.456 0.000 0.544 0.000
#> GSM1179017 1 0.7890 0.0483 0.396 0.372 0.228 0.004
#> GSM1179026 3 0.0000 0.8793 0.000 0.000 1.000 0.000
#> GSM1179033 3 0.0000 0.8793 0.000 0.000 1.000 0.000
#> GSM1179035 3 0.0000 0.8793 0.000 0.000 1.000 0.000
#> GSM1179036 3 0.0000 0.8793 0.000 0.000 1.000 0.000
#> GSM1178986 3 0.0000 0.8793 0.000 0.000 1.000 0.000
#> GSM1178989 3 0.0000 0.8793 0.000 0.000 1.000 0.000
#> GSM1178993 4 0.0188 0.9235 0.000 0.000 0.004 0.996
#> GSM1178999 3 0.4590 0.6861 0.000 0.036 0.772 0.192
#> GSM1179021 4 0.0000 0.9201 0.000 0.000 0.000 1.000
#> GSM1179025 2 0.0524 0.9035 0.000 0.988 0.008 0.004
#> GSM1179027 4 0.0188 0.9235 0.000 0.000 0.004 0.996
#> GSM1179011 4 0.0188 0.9235 0.000 0.000 0.004 0.996
#> GSM1179023 1 0.0000 0.8853 1.000 0.000 0.000 0.000
#> GSM1179029 1 0.2704 0.7820 0.876 0.000 0.124 0.000
#> GSM1179034 1 0.0000 0.8853 1.000 0.000 0.000 0.000
#> GSM1179040 4 0.0000 0.9201 0.000 0.000 0.000 1.000
#> GSM1178988 3 0.0000 0.8793 0.000 0.000 1.000 0.000
#> GSM1179037 3 0.0000 0.8793 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
#> GSM1178971 3 0.3236 0.730 0.152 0.000 0.828 0.000 0.020
#> GSM1178979 5 0.5500 0.612 0.000 0.212 0.140 0.000 0.648
#> GSM1179009 3 0.5550 0.345 0.000 0.000 0.528 0.400 0.072
#> GSM1179031 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000
#> GSM1178970 5 0.4339 0.788 0.000 0.020 0.296 0.000 0.684
#> GSM1178972 2 0.2654 0.892 0.000 0.884 0.032 0.000 0.084
#> GSM1178973 1 0.6276 0.244 0.508 0.000 0.056 0.392 0.044
#> GSM1178974 2 0.2209 0.911 0.000 0.912 0.032 0.000 0.056
#> GSM1178977 5 0.6598 0.511 0.000 0.000 0.260 0.276 0.464
#> GSM1178978 3 0.4333 0.605 0.000 0.000 0.740 0.212 0.048
#> GSM1178998 3 0.2471 0.801 0.000 0.000 0.864 0.000 0.136
#> GSM1179010 3 0.2424 0.802 0.000 0.000 0.868 0.000 0.132
#> GSM1179018 3 0.2260 0.803 0.000 0.000 0.908 0.028 0.064
#> GSM1179024 1 0.0000 0.895 1.000 0.000 0.000 0.000 0.000
#> GSM1178984 3 0.2424 0.803 0.000 0.000 0.868 0.000 0.132
#> GSM1178990 3 0.5161 0.342 0.432 0.000 0.532 0.004 0.032
#> GSM1178991 1 0.6413 0.477 0.612 0.000 0.128 0.216 0.044
#> GSM1178994 3 0.2471 0.801 0.000 0.000 0.864 0.000 0.136
#> GSM1178997 1 0.0486 0.893 0.988 0.004 0.004 0.000 0.004
#> GSM1179000 1 0.0162 0.895 0.996 0.000 0.004 0.000 0.000
#> GSM1179013 1 0.0000 0.895 1.000 0.000 0.000 0.000 0.000
#> GSM1179014 1 0.2284 0.834 0.896 0.004 0.004 0.000 0.096
#> GSM1179019 1 0.0162 0.895 0.996 0.000 0.004 0.000 0.000
#> GSM1179020 1 0.0162 0.895 0.996 0.000 0.004 0.000 0.000
#> GSM1179022 1 0.0000 0.895 1.000 0.000 0.000 0.000 0.000
#> GSM1179028 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000
#> GSM1179032 1 0.0000 0.895 1.000 0.000 0.000 0.000 0.000
#> GSM1179041 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000
#> GSM1179042 2 0.1485 0.926 0.000 0.948 0.020 0.000 0.032
#> GSM1178976 5 0.4015 0.767 0.000 0.000 0.348 0.000 0.652
#> GSM1178981 3 0.1043 0.823 0.000 0.000 0.960 0.000 0.040
#> GSM1178982 3 0.0880 0.821 0.000 0.000 0.968 0.000 0.032
#> GSM1178983 3 0.1341 0.811 0.000 0.000 0.944 0.000 0.056
#> GSM1178985 3 0.0794 0.813 0.000 0.000 0.972 0.000 0.028
#> GSM1178992 3 0.4276 0.669 0.168 0.000 0.764 0.000 0.068
#> GSM1179005 3 0.1732 0.823 0.000 0.000 0.920 0.000 0.080
#> GSM1179007 3 0.2471 0.801 0.000 0.000 0.864 0.000 0.136
#> GSM1179012 3 0.2424 0.802 0.000 0.000 0.868 0.000 0.132
#> GSM1179016 3 0.4962 0.609 0.108 0.004 0.720 0.000 0.168
#> GSM1179030 3 0.2690 0.675 0.000 0.000 0.844 0.000 0.156
#> GSM1179038 3 0.1792 0.821 0.000 0.000 0.916 0.000 0.084
#> GSM1178987 3 0.0290 0.821 0.000 0.000 0.992 0.000 0.008
#> GSM1179003 5 0.5475 0.759 0.000 0.124 0.232 0.000 0.644
#> GSM1179004 3 0.2020 0.815 0.000 0.000 0.900 0.000 0.100
#> GSM1179039 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000
#> GSM1178975 1 0.6948 0.298 0.516 0.000 0.144 0.296 0.044
#> GSM1178980 4 0.0162 0.862 0.000 0.000 0.004 0.996 0.000
#> GSM1178995 3 0.2694 0.805 0.004 0.000 0.864 0.004 0.128
#> GSM1178996 3 0.3771 0.685 0.164 0.000 0.796 0.000 0.040
#> GSM1179001 1 0.1267 0.880 0.960 0.000 0.012 0.004 0.024
#> GSM1179002 3 0.5163 0.444 0.368 0.000 0.588 0.004 0.040
#> GSM1179006 3 0.0880 0.812 0.000 0.000 0.968 0.000 0.032
#> GSM1179008 1 0.0162 0.895 0.996 0.000 0.004 0.000 0.000
#> GSM1179015 3 0.5335 0.608 0.200 0.000 0.668 0.000 0.132
#> GSM1179017 5 0.5079 0.645 0.092 0.024 0.148 0.000 0.736
#> GSM1179026 3 0.0963 0.812 0.000 0.000 0.964 0.000 0.036
#> GSM1179033 3 0.0794 0.813 0.000 0.000 0.972 0.000 0.028
#> GSM1179035 3 0.1671 0.820 0.000 0.000 0.924 0.000 0.076
#> GSM1179036 3 0.0880 0.816 0.000 0.000 0.968 0.000 0.032
#> GSM1178986 3 0.0510 0.816 0.000 0.000 0.984 0.000 0.016
#> GSM1178989 5 0.3949 0.775 0.000 0.000 0.332 0.000 0.668
#> GSM1178993 4 0.0162 0.862 0.000 0.000 0.004 0.996 0.000
#> GSM1178999 4 0.7143 -0.462 0.000 0.012 0.324 0.348 0.316
#> GSM1179021 4 0.1018 0.844 0.000 0.016 0.000 0.968 0.016
#> GSM1179025 2 0.3409 0.836 0.000 0.824 0.032 0.000 0.144
#> GSM1179027 4 0.0162 0.862 0.000 0.000 0.004 0.996 0.000
#> GSM1179011 4 0.0162 0.862 0.000 0.000 0.004 0.996 0.000
#> GSM1179023 1 0.0000 0.895 1.000 0.000 0.000 0.000 0.000
#> GSM1179029 1 0.2227 0.840 0.916 0.000 0.048 0.004 0.032
#> GSM1179034 1 0.0000 0.895 1.000 0.000 0.000 0.000 0.000
#> GSM1179040 4 0.0404 0.856 0.000 0.000 0.000 0.988 0.012
#> GSM1178988 3 0.0880 0.812 0.000 0.000 0.968 0.000 0.032
#> GSM1179037 3 0.0794 0.813 0.000 0.000 0.972 0.000 0.028
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1178971 3 0.5223 0.0826 0.356 0.000 0.540 0.000 0.000 0.104
#> GSM1178979 5 0.4702 0.6016 0.000 0.016 0.024 0.000 0.572 0.388
#> GSM1179009 4 0.4015 0.2196 0.000 0.000 0.372 0.616 0.000 0.012
#> GSM1179031 2 0.0000 0.8281 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178970 5 0.4950 0.6093 0.000 0.020 0.036 0.000 0.568 0.376
#> GSM1178972 2 0.3543 0.7137 0.000 0.764 0.004 0.000 0.212 0.020
#> GSM1178973 1 0.7452 -0.1055 0.348 0.000 0.220 0.292 0.000 0.140
#> GSM1178974 2 0.2362 0.7940 0.000 0.860 0.004 0.000 0.136 0.000
#> GSM1178977 5 0.7307 0.4720 0.000 0.000 0.116 0.208 0.352 0.324
#> GSM1178978 3 0.4282 0.6012 0.000 0.000 0.720 0.192 0.000 0.088
#> GSM1178998 3 0.3756 0.2223 0.000 0.000 0.600 0.000 0.000 0.400
#> GSM1179010 3 0.3620 0.3351 0.000 0.000 0.648 0.000 0.000 0.352
#> GSM1179018 3 0.2609 0.7363 0.000 0.000 0.868 0.036 0.000 0.096
#> GSM1179024 1 0.0260 0.6971 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM1178984 3 0.1204 0.7573 0.000 0.000 0.944 0.000 0.000 0.056
#> GSM1178990 1 0.3368 0.5044 0.820 0.000 0.060 0.000 0.004 0.116
#> GSM1178991 1 0.7110 -0.0793 0.424 0.000 0.276 0.196 0.000 0.104
#> GSM1178994 3 0.1204 0.7573 0.000 0.000 0.944 0.000 0.000 0.056
#> GSM1178997 1 0.0458 0.6946 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM1179000 1 0.0363 0.6961 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM1179013 1 0.1610 0.6298 0.916 0.000 0.000 0.000 0.084 0.000
#> GSM1179014 1 0.3727 0.1882 0.612 0.000 0.000 0.000 0.388 0.000
#> GSM1179019 1 0.0363 0.6961 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM1179020 1 0.0000 0.6985 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179022 1 0.0000 0.6985 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179028 2 0.0000 0.8281 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179032 1 0.0000 0.6985 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179041 2 0.0000 0.8281 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179042 2 0.2191 0.7999 0.000 0.876 0.004 0.000 0.120 0.000
#> GSM1178976 5 0.5364 0.6107 0.000 0.000 0.140 0.000 0.560 0.300
#> GSM1178981 3 0.0790 0.7718 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM1178982 3 0.1531 0.7664 0.000 0.000 0.928 0.000 0.004 0.068
#> GSM1178983 3 0.2979 0.7396 0.000 0.000 0.840 0.000 0.044 0.116
#> GSM1178985 3 0.0405 0.7738 0.000 0.000 0.988 0.000 0.008 0.004
#> GSM1178992 3 0.5376 -0.0680 0.368 0.000 0.536 0.000 0.084 0.012
#> GSM1179005 3 0.2100 0.7583 0.000 0.000 0.884 0.000 0.004 0.112
#> GSM1179007 3 0.1814 0.7280 0.000 0.000 0.900 0.000 0.000 0.100
#> GSM1179012 3 0.4084 0.1929 0.012 0.000 0.588 0.000 0.000 0.400
#> GSM1179016 5 0.4891 -0.0819 0.028 0.000 0.412 0.000 0.540 0.020
#> GSM1179030 3 0.3845 0.6478 0.000 0.000 0.772 0.000 0.140 0.088
#> GSM1179038 3 0.2288 0.7529 0.004 0.000 0.876 0.000 0.004 0.116
#> GSM1178987 3 0.0632 0.7698 0.000 0.000 0.976 0.000 0.000 0.024
#> GSM1179003 5 0.5554 0.6017 0.000 0.044 0.064 0.000 0.576 0.316
#> GSM1179004 3 0.0547 0.7688 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM1179039 2 0.0000 0.8281 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178975 1 0.7441 -0.1185 0.352 0.000 0.292 0.216 0.000 0.140
#> GSM1178980 4 0.0000 0.8663 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1178995 3 0.2146 0.7517 0.000 0.000 0.880 0.000 0.004 0.116
#> GSM1178996 3 0.6198 -0.1489 0.396 0.000 0.444 0.000 0.120 0.040
#> GSM1179001 1 0.1714 0.6349 0.908 0.000 0.000 0.000 0.000 0.092
#> GSM1179002 1 0.5445 -0.1732 0.548 0.000 0.324 0.000 0.004 0.124
#> GSM1179006 3 0.2712 0.7387 0.000 0.000 0.864 0.000 0.088 0.048
#> GSM1179008 1 0.0000 0.6985 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179015 6 0.7156 0.0000 0.328 0.000 0.152 0.000 0.128 0.392
#> GSM1179017 5 0.1176 0.3475 0.024 0.000 0.020 0.000 0.956 0.000
#> GSM1179026 3 0.2258 0.7572 0.000 0.000 0.896 0.000 0.044 0.060
#> GSM1179033 3 0.1418 0.7721 0.000 0.000 0.944 0.000 0.032 0.024
#> GSM1179035 3 0.0806 0.7719 0.000 0.000 0.972 0.000 0.008 0.020
#> GSM1179036 3 0.2218 0.7657 0.000 0.000 0.884 0.000 0.012 0.104
#> GSM1178986 3 0.2571 0.7552 0.000 0.000 0.876 0.000 0.064 0.060
#> GSM1178989 5 0.5482 0.5979 0.000 0.000 0.160 0.000 0.548 0.292
#> GSM1178993 4 0.0000 0.8663 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1178999 5 0.7381 0.2556 0.000 0.004 0.332 0.192 0.356 0.116
#> GSM1179021 4 0.0865 0.8519 0.000 0.000 0.000 0.964 0.036 0.000
#> GSM1179025 2 0.6141 0.0629 0.000 0.428 0.004 0.000 0.284 0.284
#> GSM1179027 4 0.0000 0.8663 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1179011 4 0.1141 0.8425 0.000 0.000 0.000 0.948 0.000 0.052
#> GSM1179023 1 0.0000 0.6985 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179029 1 0.2257 0.6065 0.876 0.000 0.000 0.000 0.008 0.116
#> GSM1179034 1 0.0000 0.6985 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179040 4 0.0865 0.8519 0.000 0.000 0.000 0.964 0.036 0.000
#> GSM1178988 3 0.4895 0.3757 0.000 0.000 0.632 0.000 0.104 0.264
#> GSM1179037 3 0.1225 0.7724 0.000 0.000 0.952 0.000 0.012 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) protocol(p) k
#> MAD:mclust 69 0.12448 1.43e-01 2
#> MAD:mclust 71 0.56073 3.56e-04 3
#> MAD:mclust 64 0.07538 5.16e-06 4
#> MAD:mclust 66 0.00725 3.58e-07 5
#> MAD:mclust 54 0.00439 2.15e-05 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 31632 rows and 73 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.967 0.984 0.4154 0.597 0.597
#> 3 3 0.824 0.851 0.938 0.4364 0.770 0.627
#> 4 4 0.605 0.748 0.854 0.1573 0.859 0.671
#> 5 5 0.611 0.661 0.820 0.0855 0.937 0.804
#> 6 6 0.572 0.479 0.708 0.0678 0.947 0.806
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
#> GSM1178971 1 0.0000 0.979 1.000 0.000
#> GSM1178979 2 0.0000 0.997 0.000 1.000
#> GSM1179009 1 0.7376 0.757 0.792 0.208
#> GSM1179031 2 0.0000 0.997 0.000 1.000
#> GSM1178970 2 0.0000 0.997 0.000 1.000
#> GSM1178972 2 0.0000 0.997 0.000 1.000
#> GSM1178973 1 0.0000 0.979 1.000 0.000
#> GSM1178974 2 0.0000 0.997 0.000 1.000
#> GSM1178977 2 0.0000 0.997 0.000 1.000
#> GSM1178978 1 0.0000 0.979 1.000 0.000
#> GSM1178998 1 0.0000 0.979 1.000 0.000
#> GSM1179010 1 0.0000 0.979 1.000 0.000
#> GSM1179018 1 0.8499 0.645 0.724 0.276
#> GSM1179024 1 0.0000 0.979 1.000 0.000
#> GSM1178984 1 0.0000 0.979 1.000 0.000
#> GSM1178990 1 0.0000 0.979 1.000 0.000
#> GSM1178991 1 0.0000 0.979 1.000 0.000
#> GSM1178994 1 0.0000 0.979 1.000 0.000
#> GSM1178997 1 0.0000 0.979 1.000 0.000
#> GSM1179000 1 0.0000 0.979 1.000 0.000
#> GSM1179013 1 0.0000 0.979 1.000 0.000
#> GSM1179014 1 0.0000 0.979 1.000 0.000
#> GSM1179019 1 0.0000 0.979 1.000 0.000
#> GSM1179020 1 0.0000 0.979 1.000 0.000
#> GSM1179022 1 0.0000 0.979 1.000 0.000
#> GSM1179028 2 0.0000 0.997 0.000 1.000
#> GSM1179032 1 0.0000 0.979 1.000 0.000
#> GSM1179041 2 0.0000 0.997 0.000 1.000
#> GSM1179042 2 0.0000 0.997 0.000 1.000
#> GSM1178976 2 0.0000 0.997 0.000 1.000
#> GSM1178981 1 0.0000 0.979 1.000 0.000
#> GSM1178982 1 0.0000 0.979 1.000 0.000
#> GSM1178983 1 0.0000 0.979 1.000 0.000
#> GSM1178985 1 0.0938 0.970 0.988 0.012
#> GSM1178992 1 0.0000 0.979 1.000 0.000
#> GSM1179005 1 0.0000 0.979 1.000 0.000
#> GSM1179007 1 0.0000 0.979 1.000 0.000
#> GSM1179012 1 0.0000 0.979 1.000 0.000
#> GSM1179016 1 0.0000 0.979 1.000 0.000
#> GSM1179030 1 0.6438 0.816 0.836 0.164
#> GSM1179038 1 0.0000 0.979 1.000 0.000
#> GSM1178987 1 0.0000 0.979 1.000 0.000
#> GSM1179003 2 0.0000 0.997 0.000 1.000
#> GSM1179004 1 0.3114 0.933 0.944 0.056
#> GSM1179039 2 0.0000 0.997 0.000 1.000
#> GSM1178975 1 0.0000 0.979 1.000 0.000
#> GSM1178980 2 0.0000 0.997 0.000 1.000
#> GSM1178995 1 0.0000 0.979 1.000 0.000
#> GSM1178996 1 0.0000 0.979 1.000 0.000
#> GSM1179001 1 0.0000 0.979 1.000 0.000
#> GSM1179002 1 0.0000 0.979 1.000 0.000
#> GSM1179006 1 0.0000 0.979 1.000 0.000
#> GSM1179008 1 0.0000 0.979 1.000 0.000
#> GSM1179015 1 0.0000 0.979 1.000 0.000
#> GSM1179017 1 0.8555 0.636 0.720 0.280
#> GSM1179026 1 0.0000 0.979 1.000 0.000
#> GSM1179033 1 0.1633 0.961 0.976 0.024
#> GSM1179035 1 0.0000 0.979 1.000 0.000
#> GSM1179036 1 0.0000 0.979 1.000 0.000
#> GSM1178986 1 0.0000 0.979 1.000 0.000
#> GSM1178989 2 0.0938 0.986 0.012 0.988
#> GSM1178993 2 0.2603 0.952 0.044 0.956
#> GSM1178999 2 0.0000 0.997 0.000 1.000
#> GSM1179021 2 0.0000 0.997 0.000 1.000
#> GSM1179025 2 0.0000 0.997 0.000 1.000
#> GSM1179027 2 0.0000 0.997 0.000 1.000
#> GSM1179011 1 0.2778 0.941 0.952 0.048
#> GSM1179023 1 0.0000 0.979 1.000 0.000
#> GSM1179029 1 0.0000 0.979 1.000 0.000
#> GSM1179034 1 0.0000 0.979 1.000 0.000
#> GSM1179040 2 0.0000 0.997 0.000 1.000
#> GSM1178988 1 0.2236 0.952 0.964 0.036
#> GSM1179037 1 0.0000 0.979 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1178971 1 0.0000 0.9528 1.000 0.000 0.000
#> GSM1178979 2 0.0000 0.9172 0.000 1.000 0.000
#> GSM1179009 1 0.4796 0.7295 0.780 0.000 0.220
#> GSM1179031 2 0.0000 0.9172 0.000 1.000 0.000
#> GSM1178970 2 0.6260 0.2556 0.000 0.552 0.448
#> GSM1178972 2 0.1031 0.9017 0.000 0.976 0.024
#> GSM1178973 1 0.0000 0.9528 1.000 0.000 0.000
#> GSM1178974 3 0.6307 -0.1399 0.000 0.488 0.512
#> GSM1178977 2 0.0000 0.9172 0.000 1.000 0.000
#> GSM1178978 1 0.0237 0.9525 0.996 0.000 0.004
#> GSM1178998 1 0.0237 0.9527 0.996 0.000 0.004
#> GSM1179010 3 0.5058 0.6852 0.244 0.000 0.756
#> GSM1179018 1 0.5882 0.4897 0.652 0.000 0.348
#> GSM1179024 1 0.0000 0.9528 1.000 0.000 0.000
#> GSM1178984 1 0.2066 0.9253 0.940 0.000 0.060
#> GSM1178990 1 0.0237 0.9527 0.996 0.000 0.004
#> GSM1178991 1 0.0424 0.9490 0.992 0.008 0.000
#> GSM1178994 1 0.1163 0.9447 0.972 0.000 0.028
#> GSM1178997 1 0.0000 0.9528 1.000 0.000 0.000
#> GSM1179000 1 0.0000 0.9528 1.000 0.000 0.000
#> GSM1179013 1 0.0000 0.9528 1.000 0.000 0.000
#> GSM1179014 1 0.0000 0.9528 1.000 0.000 0.000
#> GSM1179019 1 0.0000 0.9528 1.000 0.000 0.000
#> GSM1179020 1 0.0000 0.9528 1.000 0.000 0.000
#> GSM1179022 1 0.0000 0.9528 1.000 0.000 0.000
#> GSM1179028 2 0.0000 0.9172 0.000 1.000 0.000
#> GSM1179032 1 0.0000 0.9528 1.000 0.000 0.000
#> GSM1179041 2 0.0000 0.9172 0.000 1.000 0.000
#> GSM1179042 2 0.0000 0.9172 0.000 1.000 0.000
#> GSM1178976 3 0.0000 0.8456 0.000 0.000 1.000
#> GSM1178981 1 0.3038 0.8852 0.896 0.000 0.104
#> GSM1178982 1 0.0892 0.9479 0.980 0.000 0.020
#> GSM1178983 1 0.0000 0.9528 1.000 0.000 0.000
#> GSM1178985 3 0.0892 0.8396 0.020 0.000 0.980
#> GSM1178992 3 0.5397 0.6338 0.280 0.000 0.720
#> GSM1179005 1 0.1529 0.9378 0.960 0.000 0.040
#> GSM1179007 1 0.2066 0.9253 0.940 0.000 0.060
#> GSM1179012 1 0.2356 0.9159 0.928 0.000 0.072
#> GSM1179016 1 0.2261 0.9194 0.932 0.000 0.068
#> GSM1179030 1 0.2806 0.9127 0.928 0.032 0.040
#> GSM1179038 1 0.0424 0.9519 0.992 0.000 0.008
#> GSM1178987 3 0.3879 0.7595 0.152 0.000 0.848
#> GSM1179003 2 0.6235 0.2613 0.000 0.564 0.436
#> GSM1179004 3 0.0000 0.8456 0.000 0.000 1.000
#> GSM1179039 2 0.0000 0.9172 0.000 1.000 0.000
#> GSM1178975 1 0.0424 0.9488 0.992 0.008 0.000
#> GSM1178980 2 0.0000 0.9172 0.000 1.000 0.000
#> GSM1178995 1 0.0424 0.9519 0.992 0.000 0.008
#> GSM1178996 1 0.1031 0.9463 0.976 0.000 0.024
#> GSM1179001 1 0.0000 0.9528 1.000 0.000 0.000
#> GSM1179002 1 0.0237 0.9527 0.996 0.000 0.004
#> GSM1179006 1 0.6291 0.0809 0.532 0.000 0.468
#> GSM1179008 1 0.0000 0.9528 1.000 0.000 0.000
#> GSM1179015 1 0.2165 0.9222 0.936 0.000 0.064
#> GSM1179017 3 0.0237 0.8456 0.004 0.000 0.996
#> GSM1179026 3 0.0000 0.8456 0.000 0.000 1.000
#> GSM1179033 3 0.5465 0.6180 0.288 0.000 0.712
#> GSM1179035 3 0.0000 0.8456 0.000 0.000 1.000
#> GSM1179036 1 0.2066 0.9253 0.940 0.000 0.060
#> GSM1178986 1 0.0892 0.9480 0.980 0.000 0.020
#> GSM1178989 3 0.0000 0.8456 0.000 0.000 1.000
#> GSM1178993 2 0.0237 0.9140 0.004 0.996 0.000
#> GSM1178999 2 0.0000 0.9172 0.000 1.000 0.000
#> GSM1179021 2 0.0000 0.9172 0.000 1.000 0.000
#> GSM1179025 2 0.4235 0.7565 0.000 0.824 0.176
#> GSM1179027 2 0.0000 0.9172 0.000 1.000 0.000
#> GSM1179011 2 0.4399 0.6829 0.188 0.812 0.000
#> GSM1179023 1 0.0000 0.9528 1.000 0.000 0.000
#> GSM1179029 1 0.0237 0.9527 0.996 0.000 0.004
#> GSM1179034 1 0.0000 0.9528 1.000 0.000 0.000
#> GSM1179040 2 0.0000 0.9172 0.000 1.000 0.000
#> GSM1178988 3 0.0237 0.8456 0.004 0.000 0.996
#> GSM1179037 3 0.0000 0.8456 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1178971 1 0.1792 0.8859 0.932 0.000 0.000 0.068
#> GSM1178979 2 0.4898 0.1188 0.000 0.584 0.000 0.416
#> GSM1179009 4 0.5851 0.5550 0.236 0.000 0.084 0.680
#> GSM1179031 2 0.0188 0.8239 0.000 0.996 0.000 0.004
#> GSM1178970 2 0.5736 0.5308 0.000 0.628 0.328 0.044
#> GSM1178972 2 0.2670 0.8026 0.000 0.908 0.052 0.040
#> GSM1178973 4 0.4992 0.0961 0.476 0.000 0.000 0.524
#> GSM1178974 2 0.3751 0.7102 0.000 0.800 0.196 0.004
#> GSM1178977 2 0.4008 0.5823 0.000 0.756 0.000 0.244
#> GSM1178978 1 0.3801 0.7579 0.780 0.000 0.000 0.220
#> GSM1178998 1 0.2466 0.8733 0.900 0.000 0.004 0.096
#> GSM1179010 3 0.5327 0.6204 0.220 0.000 0.720 0.060
#> GSM1179018 4 0.3497 0.6330 0.024 0.000 0.124 0.852
#> GSM1179024 1 0.0817 0.8912 0.976 0.000 0.000 0.024
#> GSM1178984 1 0.3308 0.8643 0.872 0.000 0.036 0.092
#> GSM1178990 1 0.0592 0.8891 0.984 0.000 0.000 0.016
#> GSM1178991 4 0.3610 0.6166 0.200 0.000 0.000 0.800
#> GSM1178994 1 0.2342 0.8778 0.912 0.000 0.008 0.080
#> GSM1178997 1 0.2984 0.8565 0.888 0.028 0.000 0.084
#> GSM1179000 1 0.1716 0.8771 0.936 0.000 0.000 0.064
#> GSM1179013 1 0.1302 0.8836 0.956 0.000 0.000 0.044
#> GSM1179014 1 0.2530 0.8540 0.888 0.000 0.000 0.112
#> GSM1179019 1 0.1661 0.8837 0.944 0.004 0.000 0.052
#> GSM1179020 1 0.0707 0.8886 0.980 0.000 0.000 0.020
#> GSM1179022 1 0.0921 0.8872 0.972 0.000 0.000 0.028
#> GSM1179028 2 0.0000 0.8249 0.000 1.000 0.000 0.000
#> GSM1179032 1 0.1022 0.8899 0.968 0.000 0.000 0.032
#> GSM1179041 2 0.0188 0.8240 0.000 0.996 0.000 0.004
#> GSM1179042 2 0.0000 0.8249 0.000 1.000 0.000 0.000
#> GSM1178976 3 0.0000 0.8262 0.000 0.000 1.000 0.000
#> GSM1178981 1 0.5272 0.7382 0.744 0.000 0.172 0.084
#> GSM1178982 1 0.4567 0.6590 0.716 0.000 0.008 0.276
#> GSM1178983 1 0.4655 0.5806 0.684 0.000 0.004 0.312
#> GSM1178985 3 0.2402 0.8125 0.076 0.000 0.912 0.012
#> GSM1178992 3 0.6145 0.1111 0.460 0.000 0.492 0.048
#> GSM1179005 1 0.1584 0.8918 0.952 0.000 0.012 0.036
#> GSM1179007 1 0.2908 0.8776 0.896 0.000 0.040 0.064
#> GSM1179012 1 0.2214 0.8900 0.928 0.000 0.028 0.044
#> GSM1179016 1 0.3764 0.8066 0.816 0.000 0.012 0.172
#> GSM1179030 1 0.6429 0.6653 0.708 0.156 0.092 0.044
#> GSM1179038 1 0.2255 0.8832 0.920 0.000 0.012 0.068
#> GSM1178987 3 0.2796 0.8031 0.092 0.000 0.892 0.016
#> GSM1179003 4 0.5964 0.4860 0.000 0.108 0.208 0.684
#> GSM1179004 3 0.0336 0.8260 0.000 0.000 0.992 0.008
#> GSM1179039 2 0.0000 0.8249 0.000 1.000 0.000 0.000
#> GSM1178975 4 0.4999 0.5050 0.328 0.012 0.000 0.660
#> GSM1178980 4 0.3400 0.6635 0.000 0.180 0.000 0.820
#> GSM1178995 1 0.1978 0.8859 0.928 0.000 0.004 0.068
#> GSM1178996 1 0.3289 0.8361 0.852 0.004 0.004 0.140
#> GSM1179001 1 0.1716 0.8872 0.936 0.000 0.000 0.064
#> GSM1179002 1 0.1792 0.8859 0.932 0.000 0.000 0.068
#> GSM1179006 3 0.4940 0.7439 0.096 0.000 0.776 0.128
#> GSM1179008 1 0.1389 0.8905 0.952 0.000 0.000 0.048
#> GSM1179015 1 0.1890 0.8805 0.936 0.000 0.008 0.056
#> GSM1179017 3 0.6465 0.5149 0.076 0.004 0.588 0.332
#> GSM1179026 3 0.1109 0.8228 0.004 0.000 0.968 0.028
#> GSM1179033 3 0.2909 0.8022 0.092 0.000 0.888 0.020
#> GSM1179035 3 0.0657 0.8282 0.004 0.000 0.984 0.012
#> GSM1179036 1 0.3810 0.8474 0.848 0.000 0.092 0.060
#> GSM1178986 1 0.4019 0.7675 0.792 0.000 0.012 0.196
#> GSM1178989 3 0.0188 0.8250 0.000 0.000 0.996 0.004
#> GSM1178993 4 0.3973 0.6685 0.004 0.200 0.004 0.792
#> GSM1178999 4 0.3539 0.6562 0.004 0.176 0.000 0.820
#> GSM1179021 4 0.4661 0.5080 0.000 0.348 0.000 0.652
#> GSM1179025 2 0.2654 0.7832 0.000 0.888 0.108 0.004
#> GSM1179027 4 0.4088 0.6487 0.000 0.232 0.004 0.764
#> GSM1179011 4 0.4472 0.6563 0.020 0.220 0.000 0.760
#> GSM1179023 1 0.0817 0.8890 0.976 0.000 0.000 0.024
#> GSM1179029 1 0.3688 0.7694 0.792 0.000 0.000 0.208
#> GSM1179034 1 0.1022 0.8899 0.968 0.000 0.000 0.032
#> GSM1179040 4 0.4456 0.6053 0.000 0.280 0.004 0.716
#> GSM1178988 3 0.0188 0.8250 0.000 0.000 0.996 0.004
#> GSM1179037 3 0.0188 0.8268 0.000 0.000 0.996 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1178971 1 0.2462 0.7806 0.912 0.004 0.020 0.016 0.048
#> GSM1178979 4 0.3461 0.6273 0.000 0.224 0.000 0.772 0.004
#> GSM1179009 4 0.5783 0.5912 0.124 0.000 0.136 0.692 0.048
#> GSM1179031 2 0.0794 0.8557 0.000 0.972 0.000 0.028 0.000
#> GSM1178970 2 0.5980 0.4740 0.000 0.584 0.324 0.044 0.048
#> GSM1178972 2 0.3574 0.8110 0.000 0.852 0.068 0.032 0.048
#> GSM1178973 4 0.4723 0.1213 0.448 0.000 0.000 0.536 0.016
#> GSM1178974 2 0.2676 0.8245 0.000 0.884 0.080 0.000 0.036
#> GSM1178977 2 0.5999 0.3644 0.004 0.552 0.044 0.368 0.032
#> GSM1178978 1 0.5422 0.6337 0.744 0.020 0.056 0.132 0.048
#> GSM1178998 1 0.2774 0.7685 0.892 0.000 0.048 0.012 0.048
#> GSM1179010 3 0.4597 0.4673 0.260 0.000 0.696 0.000 0.044
#> GSM1179018 4 0.1978 0.8085 0.000 0.004 0.044 0.928 0.024
#> GSM1179024 1 0.1544 0.7748 0.932 0.000 0.000 0.000 0.068
#> GSM1178984 1 0.4190 0.7022 0.792 0.000 0.140 0.012 0.056
#> GSM1178990 1 0.1608 0.7744 0.928 0.000 0.000 0.000 0.072
#> GSM1178991 4 0.3432 0.7527 0.064 0.004 0.004 0.852 0.076
#> GSM1178994 1 0.2917 0.7642 0.884 0.004 0.076 0.012 0.024
#> GSM1178997 1 0.3838 0.6769 0.804 0.148 0.000 0.004 0.044
#> GSM1179000 1 0.2338 0.7518 0.884 0.004 0.000 0.000 0.112
#> GSM1179013 1 0.2230 0.7470 0.884 0.000 0.000 0.000 0.116
#> GSM1179014 1 0.4415 0.2664 0.604 0.008 0.000 0.000 0.388
#> GSM1179019 1 0.1124 0.7861 0.960 0.004 0.000 0.000 0.036
#> GSM1179020 1 0.1704 0.7745 0.928 0.000 0.000 0.004 0.068
#> GSM1179022 1 0.1121 0.7838 0.956 0.000 0.000 0.000 0.044
#> GSM1179028 2 0.0703 0.8566 0.000 0.976 0.000 0.024 0.000
#> GSM1179032 1 0.0162 0.7857 0.996 0.000 0.000 0.000 0.004
#> GSM1179041 2 0.0898 0.8559 0.000 0.972 0.000 0.020 0.008
#> GSM1179042 2 0.1012 0.8559 0.000 0.968 0.000 0.020 0.012
#> GSM1178976 3 0.0693 0.7688 0.000 0.008 0.980 0.000 0.012
#> GSM1178981 1 0.5705 0.3788 0.600 0.020 0.332 0.008 0.040
#> GSM1178982 1 0.5510 0.6167 0.716 0.004 0.092 0.152 0.036
#> GSM1178983 1 0.4766 0.6137 0.740 0.004 0.028 0.200 0.028
#> GSM1178985 3 0.3292 0.6874 0.120 0.004 0.844 0.000 0.032
#> GSM1178992 5 0.6801 0.2678 0.244 0.004 0.324 0.000 0.428
#> GSM1179005 1 0.1725 0.7880 0.936 0.000 0.044 0.000 0.020
#> GSM1179007 1 0.3186 0.7612 0.864 0.000 0.080 0.008 0.048
#> GSM1179012 1 0.2893 0.7728 0.884 0.004 0.076 0.008 0.028
#> GSM1179016 5 0.3177 0.6268 0.208 0.000 0.000 0.000 0.792
#> GSM1179030 1 0.7956 0.3076 0.540 0.124 0.084 0.056 0.196
#> GSM1179038 1 0.5302 0.2565 0.564 0.000 0.012 0.032 0.392
#> GSM1178987 3 0.4080 0.6923 0.104 0.016 0.820 0.008 0.052
#> GSM1179003 5 0.4846 0.3575 0.000 0.004 0.056 0.244 0.696
#> GSM1179004 3 0.1695 0.7558 0.000 0.008 0.940 0.008 0.044
#> GSM1179039 2 0.0865 0.8565 0.000 0.972 0.000 0.024 0.004
#> GSM1178975 4 0.3596 0.6063 0.212 0.000 0.000 0.776 0.012
#> GSM1178980 4 0.1012 0.8286 0.000 0.012 0.000 0.968 0.020
#> GSM1178995 1 0.2067 0.7820 0.924 0.000 0.028 0.004 0.044
#> GSM1178996 5 0.4438 0.4048 0.384 0.004 0.000 0.004 0.608
#> GSM1179001 1 0.2541 0.7814 0.900 0.000 0.012 0.020 0.068
#> GSM1179002 1 0.2228 0.7824 0.920 0.000 0.020 0.016 0.044
#> GSM1179006 3 0.5643 0.1760 0.024 0.000 0.480 0.032 0.464
#> GSM1179008 1 0.1845 0.7884 0.928 0.000 0.000 0.016 0.056
#> GSM1179015 1 0.3607 0.6132 0.752 0.000 0.004 0.000 0.244
#> GSM1179017 5 0.2585 0.4712 0.000 0.004 0.064 0.036 0.896
#> GSM1179026 3 0.4549 0.2889 0.000 0.000 0.528 0.008 0.464
#> GSM1179033 3 0.3748 0.7106 0.080 0.000 0.824 0.004 0.092
#> GSM1179035 3 0.1502 0.7668 0.000 0.000 0.940 0.004 0.056
#> GSM1179036 1 0.5905 0.4654 0.612 0.000 0.112 0.012 0.264
#> GSM1178986 1 0.6236 0.0622 0.512 0.000 0.008 0.120 0.360
#> GSM1178989 3 0.2395 0.7597 0.000 0.016 0.904 0.008 0.072
#> GSM1178993 4 0.0798 0.8309 0.000 0.016 0.000 0.976 0.008
#> GSM1178999 4 0.1697 0.8131 0.000 0.008 0.000 0.932 0.060
#> GSM1179021 4 0.1168 0.8275 0.000 0.032 0.000 0.960 0.008
#> GSM1179025 2 0.2789 0.8316 0.000 0.880 0.092 0.020 0.008
#> GSM1179027 4 0.1356 0.8311 0.000 0.028 0.004 0.956 0.012
#> GSM1179011 4 0.1393 0.8298 0.012 0.024 0.000 0.956 0.008
#> GSM1179023 1 0.0703 0.7855 0.976 0.000 0.000 0.000 0.024
#> GSM1179029 5 0.4508 0.5382 0.332 0.000 0.000 0.020 0.648
#> GSM1179034 1 0.0771 0.7861 0.976 0.000 0.000 0.004 0.020
#> GSM1179040 4 0.1116 0.8299 0.000 0.028 0.004 0.964 0.004
#> GSM1178988 3 0.2818 0.7385 0.000 0.004 0.860 0.008 0.128
#> GSM1179037 3 0.1410 0.7643 0.000 0.000 0.940 0.000 0.060
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1178971 1 0.4914 0.5194 0.664 0.000 0.040 0.008 0.024 0.264
#> GSM1178979 4 0.4343 0.5868 0.000 0.156 0.000 0.724 0.000 0.120
#> GSM1179009 4 0.6977 0.3346 0.132 0.000 0.148 0.536 0.016 0.168
#> GSM1179031 2 0.0622 0.9081 0.000 0.980 0.000 0.008 0.000 0.012
#> GSM1178970 6 0.6128 0.1449 0.000 0.348 0.144 0.020 0.004 0.484
#> GSM1178972 2 0.4740 0.4870 0.000 0.636 0.020 0.012 0.016 0.316
#> GSM1178973 4 0.4957 0.1725 0.424 0.000 0.000 0.520 0.008 0.048
#> GSM1178974 2 0.2186 0.8824 0.000 0.908 0.024 0.000 0.012 0.056
#> GSM1178977 6 0.6161 0.0867 0.004 0.340 0.000 0.216 0.004 0.436
#> GSM1178978 6 0.5304 0.3919 0.296 0.008 0.012 0.076 0.000 0.608
#> GSM1178998 1 0.4326 0.4312 0.608 0.000 0.016 0.000 0.008 0.368
#> GSM1179010 6 0.6165 0.0768 0.324 0.000 0.232 0.000 0.008 0.436
#> GSM1179018 4 0.4028 0.6217 0.000 0.000 0.012 0.752 0.044 0.192
#> GSM1179024 1 0.3707 0.5155 0.784 0.000 0.000 0.000 0.080 0.136
#> GSM1178984 1 0.5186 0.3781 0.572 0.000 0.072 0.000 0.012 0.344
#> GSM1178990 1 0.2984 0.5649 0.848 0.000 0.004 0.000 0.044 0.104
#> GSM1178991 4 0.5978 0.4183 0.124 0.000 0.000 0.616 0.084 0.176
#> GSM1178994 1 0.4316 0.3411 0.648 0.000 0.040 0.000 0.000 0.312
#> GSM1178997 1 0.4105 0.4773 0.720 0.240 0.000 0.000 0.020 0.020
#> GSM1179000 1 0.3138 0.5574 0.840 0.004 0.000 0.000 0.060 0.096
#> GSM1179013 1 0.4148 0.4769 0.744 0.000 0.000 0.000 0.108 0.148
#> GSM1179014 1 0.5573 0.0381 0.524 0.000 0.000 0.000 0.312 0.164
#> GSM1179019 1 0.1493 0.6165 0.936 0.004 0.000 0.000 0.004 0.056
#> GSM1179020 1 0.1845 0.6267 0.920 0.000 0.000 0.000 0.028 0.052
#> GSM1179022 1 0.1500 0.6092 0.936 0.000 0.000 0.000 0.012 0.052
#> GSM1179028 2 0.0551 0.9097 0.000 0.984 0.000 0.004 0.004 0.008
#> GSM1179032 1 0.1152 0.6226 0.952 0.000 0.000 0.000 0.004 0.044
#> GSM1179041 2 0.0363 0.9073 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM1179042 2 0.0458 0.9071 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM1178976 3 0.1155 0.6313 0.000 0.004 0.956 0.000 0.004 0.036
#> GSM1178981 6 0.6131 0.3023 0.284 0.000 0.280 0.004 0.000 0.432
#> GSM1178982 1 0.6728 -0.1857 0.384 0.000 0.048 0.204 0.000 0.364
#> GSM1178983 1 0.5788 0.3406 0.560 0.000 0.008 0.256 0.004 0.172
#> GSM1178985 3 0.4095 0.5089 0.100 0.000 0.748 0.000 0.000 0.152
#> GSM1178992 5 0.7528 0.2909 0.248 0.000 0.300 0.000 0.308 0.144
#> GSM1179005 1 0.3006 0.6106 0.844 0.000 0.092 0.000 0.000 0.064
#> GSM1179007 1 0.4844 0.5575 0.712 0.000 0.124 0.004 0.016 0.144
#> GSM1179012 1 0.4840 0.3628 0.580 0.000 0.056 0.000 0.004 0.360
#> GSM1179016 5 0.5537 0.4754 0.236 0.000 0.004 0.000 0.576 0.184
#> GSM1179030 6 0.6057 0.1917 0.248 0.052 0.020 0.004 0.068 0.608
#> GSM1179038 1 0.6277 0.2625 0.520 0.000 0.020 0.016 0.300 0.144
#> GSM1178987 6 0.4892 0.0434 0.048 0.000 0.384 0.000 0.008 0.560
#> GSM1179003 5 0.5490 0.2399 0.000 0.008 0.044 0.228 0.648 0.072
#> GSM1179004 3 0.3979 0.0988 0.000 0.000 0.540 0.000 0.004 0.456
#> GSM1179039 2 0.0291 0.9102 0.000 0.992 0.000 0.004 0.000 0.004
#> GSM1178975 4 0.3674 0.6067 0.200 0.004 0.000 0.768 0.004 0.024
#> GSM1178980 4 0.0603 0.7721 0.000 0.004 0.000 0.980 0.016 0.000
#> GSM1178995 1 0.4147 0.5818 0.764 0.000 0.044 0.004 0.020 0.168
#> GSM1178996 5 0.5616 0.3556 0.224 0.004 0.024 0.000 0.620 0.128
#> GSM1179001 1 0.6008 0.4675 0.568 0.000 0.040 0.008 0.100 0.284
#> GSM1179002 1 0.6222 0.4393 0.524 0.000 0.036 0.008 0.120 0.312
#> GSM1179006 3 0.5931 0.4158 0.076 0.000 0.632 0.028 0.216 0.048
#> GSM1179008 1 0.4661 0.5612 0.700 0.000 0.008 0.004 0.076 0.212
#> GSM1179015 1 0.5609 0.2281 0.580 0.000 0.008 0.000 0.216 0.196
#> GSM1179017 5 0.1705 0.3985 0.012 0.000 0.016 0.008 0.940 0.024
#> GSM1179026 3 0.4723 0.1762 0.000 0.000 0.484 0.004 0.476 0.036
#> GSM1179033 3 0.4981 0.4969 0.128 0.000 0.716 0.020 0.012 0.124
#> GSM1179035 3 0.3349 0.5799 0.008 0.000 0.804 0.000 0.024 0.164
#> GSM1179036 1 0.7519 0.1727 0.436 0.000 0.252 0.020 0.128 0.164
#> GSM1178986 1 0.6984 -0.2524 0.408 0.000 0.008 0.056 0.332 0.196
#> GSM1178989 3 0.2886 0.5859 0.004 0.000 0.836 0.000 0.016 0.144
#> GSM1178993 4 0.0146 0.7750 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM1178999 4 0.2165 0.7281 0.000 0.000 0.000 0.884 0.108 0.008
#> GSM1179021 4 0.0935 0.7712 0.000 0.032 0.000 0.964 0.000 0.004
#> GSM1179025 2 0.2316 0.8755 0.000 0.900 0.028 0.004 0.004 0.064
#> GSM1179027 4 0.0520 0.7751 0.000 0.008 0.000 0.984 0.000 0.008
#> GSM1179011 4 0.0508 0.7758 0.004 0.012 0.000 0.984 0.000 0.000
#> GSM1179023 1 0.1010 0.6218 0.960 0.000 0.000 0.000 0.004 0.036
#> GSM1179029 5 0.5867 0.3901 0.300 0.000 0.000 0.008 0.512 0.180
#> GSM1179034 1 0.0935 0.6256 0.964 0.000 0.000 0.000 0.004 0.032
#> GSM1179040 4 0.0458 0.7748 0.000 0.016 0.000 0.984 0.000 0.000
#> GSM1178988 3 0.5514 0.3458 0.016 0.000 0.572 0.000 0.108 0.304
#> GSM1179037 3 0.1226 0.6368 0.004 0.000 0.952 0.000 0.004 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) protocol(p) k
#> MAD:NMF 73 0.037252 0.0325 2
#> MAD:NMF 68 0.013547 0.0122 3
#> MAD:NMF 69 0.000541 0.0374 4
#> MAD:NMF 57 0.045666 0.0831 5
#> MAD:NMF 36 0.216026 0.0532 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 31632 rows and 73 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.789 0.838 0.927 0.3891 0.562 0.562
#> 3 3 0.575 0.789 0.879 0.4432 0.885 0.800
#> 4 4 0.551 0.693 0.793 0.1992 0.797 0.588
#> 5 5 0.588 0.664 0.803 0.0317 0.995 0.984
#> 6 6 0.648 0.719 0.817 0.0603 0.945 0.828
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM1178971 1 0.0000 0.971 1.000 0.000
#> GSM1178979 2 0.2778 0.780 0.048 0.952
#> GSM1179009 1 0.0376 0.970 0.996 0.004
#> GSM1179031 2 0.0000 0.789 0.000 1.000
#> GSM1178970 2 0.9970 0.425 0.468 0.532
#> GSM1178972 2 0.0000 0.789 0.000 1.000
#> GSM1178973 1 0.1414 0.953 0.980 0.020
#> GSM1178974 2 0.0000 0.789 0.000 1.000
#> GSM1178977 2 0.9970 0.425 0.468 0.532
#> GSM1178978 1 0.0000 0.971 1.000 0.000
#> GSM1178998 1 0.0000 0.971 1.000 0.000
#> GSM1179010 1 0.0000 0.971 1.000 0.000
#> GSM1179018 1 0.0376 0.970 0.996 0.004
#> GSM1179024 1 0.0000 0.971 1.000 0.000
#> GSM1178984 1 0.0000 0.971 1.000 0.000
#> GSM1178990 1 0.0000 0.971 1.000 0.000
#> GSM1178991 1 0.0000 0.971 1.000 0.000
#> GSM1178994 1 0.0000 0.971 1.000 0.000
#> GSM1178997 1 0.1843 0.943 0.972 0.028
#> GSM1179000 1 0.0000 0.971 1.000 0.000
#> GSM1179013 1 0.0000 0.971 1.000 0.000
#> GSM1179014 1 0.0000 0.971 1.000 0.000
#> GSM1179019 1 0.0000 0.971 1.000 0.000
#> GSM1179020 1 0.0000 0.971 1.000 0.000
#> GSM1179022 1 0.0000 0.971 1.000 0.000
#> GSM1179028 2 0.0000 0.789 0.000 1.000
#> GSM1179032 1 0.0000 0.971 1.000 0.000
#> GSM1179041 2 0.0000 0.789 0.000 1.000
#> GSM1179042 2 0.0000 0.789 0.000 1.000
#> GSM1178976 2 0.9970 0.425 0.468 0.532
#> GSM1178981 1 0.0376 0.970 0.996 0.004
#> GSM1178982 1 0.0376 0.970 0.996 0.004
#> GSM1178983 1 0.1184 0.957 0.984 0.016
#> GSM1178985 1 0.0376 0.970 0.996 0.004
#> GSM1178992 1 0.0000 0.971 1.000 0.000
#> GSM1179005 1 0.0000 0.971 1.000 0.000
#> GSM1179007 1 0.0000 0.971 1.000 0.000
#> GSM1179012 1 0.0000 0.971 1.000 0.000
#> GSM1179016 1 0.0000 0.971 1.000 0.000
#> GSM1179030 2 0.9977 0.415 0.472 0.528
#> GSM1179038 1 0.0376 0.970 0.996 0.004
#> GSM1178987 1 0.0376 0.970 0.996 0.004
#> GSM1179003 2 0.2778 0.780 0.048 0.952
#> GSM1179004 1 0.0376 0.970 0.996 0.004
#> GSM1179039 2 0.0000 0.789 0.000 1.000
#> GSM1178975 1 0.9983 -0.294 0.524 0.476
#> GSM1178980 2 0.7376 0.708 0.208 0.792
#> GSM1178995 1 0.0000 0.971 1.000 0.000
#> GSM1178996 1 0.0376 0.970 0.996 0.004
#> GSM1179001 1 0.0000 0.971 1.000 0.000
#> GSM1179002 1 0.0000 0.971 1.000 0.000
#> GSM1179006 1 0.0376 0.970 0.996 0.004
#> GSM1179008 1 0.0000 0.971 1.000 0.000
#> GSM1179015 1 0.0000 0.971 1.000 0.000
#> GSM1179017 1 0.9988 -0.307 0.520 0.480
#> GSM1179026 1 0.0376 0.970 0.996 0.004
#> GSM1179033 1 0.0376 0.970 0.996 0.004
#> GSM1179035 1 0.0376 0.970 0.996 0.004
#> GSM1179036 1 0.0376 0.970 0.996 0.004
#> GSM1178986 1 0.0000 0.971 1.000 0.000
#> GSM1178989 2 0.9970 0.425 0.468 0.532
#> GSM1178993 2 0.9522 0.578 0.372 0.628
#> GSM1178999 2 0.0000 0.789 0.000 1.000
#> GSM1179021 2 0.0000 0.789 0.000 1.000
#> GSM1179025 2 0.0000 0.789 0.000 1.000
#> GSM1179027 2 0.9522 0.578 0.372 0.628
#> GSM1179011 2 0.9522 0.578 0.372 0.628
#> GSM1179023 1 0.0000 0.971 1.000 0.000
#> GSM1179029 1 0.0000 0.971 1.000 0.000
#> GSM1179034 1 0.0000 0.971 1.000 0.000
#> GSM1179040 2 0.0000 0.789 0.000 1.000
#> GSM1178988 2 0.9977 0.415 0.472 0.528
#> GSM1179037 1 0.0376 0.970 0.996 0.004
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1178971 1 0.1529 0.858 0.960 0.000 0.040
#> GSM1178979 2 0.6192 0.298 0.000 0.580 0.420
#> GSM1179009 1 0.4346 0.825 0.816 0.000 0.184
#> GSM1179031 2 0.0000 0.919 0.000 1.000 0.000
#> GSM1178970 3 0.1860 0.852 0.000 0.052 0.948
#> GSM1178972 2 0.0000 0.919 0.000 1.000 0.000
#> GSM1178973 3 0.6286 -0.342 0.464 0.000 0.536
#> GSM1178974 2 0.0000 0.919 0.000 1.000 0.000
#> GSM1178977 3 0.1860 0.852 0.000 0.052 0.948
#> GSM1178978 1 0.3116 0.850 0.892 0.000 0.108
#> GSM1178998 1 0.0237 0.853 0.996 0.000 0.004
#> GSM1179010 1 0.0237 0.853 0.996 0.000 0.004
#> GSM1179018 1 0.4750 0.809 0.784 0.000 0.216
#> GSM1179024 1 0.0237 0.853 0.996 0.000 0.004
#> GSM1178984 1 0.1289 0.858 0.968 0.000 0.032
#> GSM1178990 1 0.1289 0.858 0.968 0.000 0.032
#> GSM1178991 1 0.6008 0.639 0.628 0.000 0.372
#> GSM1178994 1 0.3752 0.839 0.856 0.000 0.144
#> GSM1178997 1 0.6252 0.525 0.556 0.000 0.444
#> GSM1179000 1 0.6140 0.601 0.596 0.000 0.404
#> GSM1179013 1 0.0237 0.853 0.996 0.000 0.004
#> GSM1179014 1 0.0000 0.854 1.000 0.000 0.000
#> GSM1179019 1 0.1529 0.858 0.960 0.000 0.040
#> GSM1179020 1 0.0237 0.853 0.996 0.000 0.004
#> GSM1179022 1 0.0237 0.853 0.996 0.000 0.004
#> GSM1179028 2 0.0000 0.919 0.000 1.000 0.000
#> GSM1179032 1 0.0237 0.853 0.996 0.000 0.004
#> GSM1179041 2 0.0000 0.919 0.000 1.000 0.000
#> GSM1179042 2 0.0000 0.919 0.000 1.000 0.000
#> GSM1178976 3 0.1860 0.852 0.000 0.052 0.948
#> GSM1178981 1 0.5948 0.670 0.640 0.000 0.360
#> GSM1178982 1 0.5948 0.670 0.640 0.000 0.360
#> GSM1178983 1 0.6225 0.550 0.568 0.000 0.432
#> GSM1178985 1 0.5948 0.670 0.640 0.000 0.360
#> GSM1178992 1 0.1289 0.858 0.968 0.000 0.032
#> GSM1179005 1 0.2448 0.854 0.924 0.000 0.076
#> GSM1179007 1 0.0747 0.856 0.984 0.000 0.016
#> GSM1179012 1 0.0237 0.853 0.996 0.000 0.004
#> GSM1179016 1 0.0000 0.854 1.000 0.000 0.000
#> GSM1179030 3 0.2096 0.851 0.004 0.052 0.944
#> GSM1179038 1 0.4750 0.809 0.784 0.000 0.216
#> GSM1178987 1 0.4178 0.829 0.828 0.000 0.172
#> GSM1179003 2 0.6192 0.298 0.000 0.580 0.420
#> GSM1179004 1 0.4235 0.828 0.824 0.000 0.176
#> GSM1179039 2 0.0000 0.919 0.000 1.000 0.000
#> GSM1178975 3 0.0424 0.817 0.008 0.000 0.992
#> GSM1178980 3 0.5678 0.491 0.000 0.316 0.684
#> GSM1178995 1 0.3116 0.850 0.892 0.000 0.108
#> GSM1178996 1 0.5529 0.742 0.704 0.000 0.296
#> GSM1179001 1 0.0424 0.854 0.992 0.000 0.008
#> GSM1179002 1 0.0424 0.854 0.992 0.000 0.008
#> GSM1179006 1 0.6079 0.627 0.612 0.000 0.388
#> GSM1179008 1 0.0424 0.854 0.992 0.000 0.008
#> GSM1179015 1 0.0237 0.853 0.996 0.000 0.004
#> GSM1179017 3 0.0237 0.820 0.004 0.000 0.996
#> GSM1179026 1 0.4750 0.809 0.784 0.000 0.216
#> GSM1179033 1 0.4750 0.809 0.784 0.000 0.216
#> GSM1179035 1 0.4750 0.809 0.784 0.000 0.216
#> GSM1179036 1 0.4750 0.809 0.784 0.000 0.216
#> GSM1178986 1 0.4750 0.807 0.784 0.000 0.216
#> GSM1178989 3 0.1860 0.852 0.000 0.052 0.948
#> GSM1178993 3 0.3816 0.785 0.000 0.148 0.852
#> GSM1178999 2 0.0592 0.912 0.000 0.988 0.012
#> GSM1179021 2 0.0000 0.919 0.000 1.000 0.000
#> GSM1179025 2 0.0000 0.919 0.000 1.000 0.000
#> GSM1179027 3 0.3816 0.785 0.000 0.148 0.852
#> GSM1179011 3 0.3816 0.785 0.000 0.148 0.852
#> GSM1179023 1 0.0237 0.853 0.996 0.000 0.004
#> GSM1179029 1 0.0237 0.853 0.996 0.000 0.004
#> GSM1179034 1 0.0237 0.853 0.996 0.000 0.004
#> GSM1179040 2 0.0892 0.906 0.000 0.980 0.020
#> GSM1178988 3 0.2096 0.851 0.004 0.052 0.944
#> GSM1179037 1 0.4750 0.809 0.784 0.000 0.216
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1178971 3 0.3975 0.534 0.240 0.000 0.760 0.000
#> GSM1178979 4 0.6514 0.152 0.076 0.408 0.000 0.516
#> GSM1179009 3 0.1302 0.727 0.044 0.000 0.956 0.000
#> GSM1179031 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> GSM1178970 4 0.2408 0.836 0.000 0.000 0.104 0.896
#> GSM1178972 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> GSM1178973 3 0.5662 0.471 0.072 0.000 0.692 0.236
#> GSM1178974 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> GSM1178977 4 0.2408 0.836 0.000 0.000 0.104 0.896
#> GSM1178978 3 0.3494 0.646 0.172 0.000 0.824 0.004
#> GSM1178998 1 0.3942 0.902 0.764 0.000 0.236 0.000
#> GSM1179010 1 0.4040 0.893 0.752 0.000 0.248 0.000
#> GSM1179018 3 0.0779 0.733 0.016 0.000 0.980 0.004
#> GSM1179024 1 0.4817 0.715 0.612 0.000 0.388 0.000
#> GSM1178984 3 0.4040 0.526 0.248 0.000 0.752 0.000
#> GSM1178990 3 0.4040 0.526 0.248 0.000 0.752 0.000
#> GSM1178991 3 0.5006 0.651 0.124 0.000 0.772 0.104
#> GSM1178994 3 0.2814 0.676 0.132 0.000 0.868 0.000
#> GSM1178997 3 0.4872 0.609 0.076 0.000 0.776 0.148
#> GSM1179000 3 0.4411 0.641 0.080 0.000 0.812 0.108
#> GSM1179013 1 0.3942 0.902 0.764 0.000 0.236 0.000
#> GSM1179014 3 0.4941 -0.156 0.436 0.000 0.564 0.000
#> GSM1179019 3 0.3975 0.534 0.240 0.000 0.760 0.000
#> GSM1179020 1 0.4817 0.715 0.612 0.000 0.388 0.000
#> GSM1179022 1 0.3942 0.902 0.764 0.000 0.236 0.000
#> GSM1179028 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> GSM1179032 1 0.3942 0.902 0.764 0.000 0.236 0.000
#> GSM1179041 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> GSM1179042 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> GSM1178976 4 0.2408 0.836 0.000 0.000 0.104 0.896
#> GSM1178981 3 0.3439 0.676 0.048 0.000 0.868 0.084
#> GSM1178982 3 0.3439 0.676 0.048 0.000 0.868 0.084
#> GSM1178983 3 0.4673 0.620 0.076 0.000 0.792 0.132
#> GSM1178985 3 0.3439 0.676 0.048 0.000 0.868 0.084
#> GSM1178992 3 0.4040 0.526 0.248 0.000 0.752 0.000
#> GSM1179005 3 0.3356 0.626 0.176 0.000 0.824 0.000
#> GSM1179007 3 0.4585 0.316 0.332 0.000 0.668 0.000
#> GSM1179012 1 0.3942 0.902 0.764 0.000 0.236 0.000
#> GSM1179016 3 0.4941 -0.156 0.436 0.000 0.564 0.000
#> GSM1179030 4 0.2704 0.829 0.000 0.000 0.124 0.876
#> GSM1179038 3 0.0779 0.733 0.016 0.000 0.980 0.004
#> GSM1178987 3 0.1557 0.721 0.056 0.000 0.944 0.000
#> GSM1179003 4 0.6514 0.152 0.076 0.408 0.000 0.516
#> GSM1179004 3 0.1474 0.723 0.052 0.000 0.948 0.000
#> GSM1179039 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> GSM1178975 4 0.5599 0.694 0.072 0.000 0.228 0.700
#> GSM1178980 4 0.4824 0.659 0.076 0.144 0.000 0.780
#> GSM1178995 3 0.2973 0.661 0.144 0.000 0.856 0.000
#> GSM1178996 3 0.3156 0.706 0.068 0.000 0.884 0.048
#> GSM1179001 1 0.5000 0.360 0.500 0.000 0.500 0.000
#> GSM1179002 3 0.4790 0.134 0.380 0.000 0.620 0.000
#> GSM1179006 3 0.3935 0.658 0.060 0.000 0.840 0.100
#> GSM1179008 3 0.4790 0.134 0.380 0.000 0.620 0.000
#> GSM1179015 1 0.3942 0.902 0.764 0.000 0.236 0.000
#> GSM1179017 4 0.4336 0.752 0.128 0.000 0.060 0.812
#> GSM1179026 3 0.0779 0.733 0.016 0.000 0.980 0.004
#> GSM1179033 3 0.0779 0.733 0.016 0.000 0.980 0.004
#> GSM1179035 3 0.0779 0.733 0.016 0.000 0.980 0.004
#> GSM1179036 3 0.0779 0.733 0.016 0.000 0.980 0.004
#> GSM1178986 3 0.2699 0.723 0.068 0.000 0.904 0.028
#> GSM1178989 4 0.2408 0.836 0.000 0.000 0.104 0.896
#> GSM1178993 4 0.3464 0.815 0.056 0.000 0.076 0.868
#> GSM1178999 2 0.4344 0.833 0.076 0.816 0.000 0.108
#> GSM1179021 2 0.4163 0.844 0.076 0.828 0.000 0.096
#> GSM1179025 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> GSM1179027 4 0.3245 0.811 0.056 0.000 0.064 0.880
#> GSM1179011 4 0.3464 0.815 0.056 0.000 0.076 0.868
#> GSM1179023 1 0.3942 0.902 0.764 0.000 0.236 0.000
#> GSM1179029 1 0.4564 0.811 0.672 0.000 0.328 0.000
#> GSM1179034 1 0.3942 0.902 0.764 0.000 0.236 0.000
#> GSM1179040 2 0.4458 0.823 0.076 0.808 0.000 0.116
#> GSM1178988 4 0.2704 0.829 0.000 0.000 0.124 0.876
#> GSM1179037 3 0.0779 0.733 0.016 0.000 0.980 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1178971 3 0.399 0.544 0.252 0.000 0.732 0.000 0.016
#> GSM1178979 4 0.678 0.275 0.068 0.272 0.000 0.560 0.100
#> GSM1179009 3 0.120 0.738 0.048 0.000 0.952 0.000 0.000
#> GSM1179031 2 0.000 0.885 0.000 1.000 0.000 0.000 0.000
#> GSM1178970 4 0.185 0.766 0.000 0.000 0.088 0.912 0.000
#> GSM1178972 2 0.000 0.885 0.000 1.000 0.000 0.000 0.000
#> GSM1178973 3 0.520 0.495 0.000 0.000 0.688 0.148 0.164
#> GSM1178974 2 0.000 0.885 0.000 1.000 0.000 0.000 0.000
#> GSM1178977 4 0.185 0.766 0.000 0.000 0.088 0.912 0.000
#> GSM1178978 3 0.353 0.663 0.164 0.000 0.808 0.000 0.028
#> GSM1178998 1 0.297 0.906 0.816 0.000 0.184 0.000 0.000
#> GSM1179010 1 0.314 0.891 0.796 0.000 0.204 0.000 0.000
#> GSM1179018 3 0.051 0.744 0.016 0.000 0.984 0.000 0.000
#> GSM1179024 1 0.412 0.731 0.660 0.000 0.336 0.000 0.004
#> GSM1178984 3 0.399 0.549 0.252 0.000 0.732 0.000 0.016
#> GSM1178990 3 0.399 0.549 0.252 0.000 0.732 0.000 0.016
#> GSM1178991 3 0.399 0.661 0.028 0.000 0.756 0.000 0.216
#> GSM1178994 3 0.283 0.695 0.124 0.000 0.860 0.000 0.016
#> GSM1178997 3 0.392 0.618 0.000 0.000 0.780 0.040 0.180
#> GSM1179000 3 0.297 0.651 0.000 0.000 0.816 0.000 0.184
#> GSM1179013 1 0.297 0.906 0.816 0.000 0.184 0.000 0.000
#> GSM1179014 3 0.474 -0.216 0.476 0.000 0.508 0.000 0.016
#> GSM1179019 3 0.399 0.544 0.252 0.000 0.732 0.000 0.016
#> GSM1179020 1 0.412 0.731 0.660 0.000 0.336 0.000 0.004
#> GSM1179022 1 0.297 0.906 0.816 0.000 0.184 0.000 0.000
#> GSM1179028 2 0.000 0.885 0.000 1.000 0.000 0.000 0.000
#> GSM1179032 1 0.297 0.906 0.816 0.000 0.184 0.000 0.000
#> GSM1179041 2 0.000 0.885 0.000 1.000 0.000 0.000 0.000
#> GSM1179042 2 0.000 0.885 0.000 1.000 0.000 0.000 0.000
#> GSM1178976 4 0.185 0.766 0.000 0.000 0.088 0.912 0.000
#> GSM1178981 3 0.258 0.692 0.004 0.000 0.864 0.000 0.132
#> GSM1178982 3 0.258 0.692 0.004 0.000 0.864 0.000 0.132
#> GSM1178983 3 0.360 0.631 0.000 0.000 0.796 0.024 0.180
#> GSM1178985 3 0.258 0.692 0.004 0.000 0.864 0.000 0.132
#> GSM1178992 3 0.399 0.549 0.252 0.000 0.732 0.000 0.016
#> GSM1179005 3 0.316 0.640 0.188 0.000 0.808 0.000 0.004
#> GSM1179007 3 0.447 0.340 0.344 0.000 0.640 0.000 0.016
#> GSM1179012 1 0.297 0.906 0.816 0.000 0.184 0.000 0.000
#> GSM1179016 3 0.474 -0.216 0.476 0.000 0.508 0.000 0.016
#> GSM1179030 4 0.213 0.756 0.000 0.000 0.108 0.892 0.000
#> GSM1179038 3 0.051 0.744 0.016 0.000 0.984 0.000 0.000
#> GSM1178987 3 0.141 0.734 0.060 0.000 0.940 0.000 0.000
#> GSM1179003 4 0.678 0.275 0.068 0.272 0.000 0.560 0.100
#> GSM1179004 3 0.134 0.735 0.056 0.000 0.944 0.000 0.000
#> GSM1179039 2 0.000 0.885 0.000 1.000 0.000 0.000 0.000
#> GSM1178975 4 0.579 0.401 0.000 0.000 0.224 0.612 0.164
#> GSM1178980 4 0.394 0.587 0.068 0.020 0.000 0.824 0.088
#> GSM1178995 3 0.276 0.678 0.148 0.000 0.848 0.000 0.004
#> GSM1178996 3 0.254 0.720 0.024 0.000 0.888 0.000 0.088
#> GSM1179001 1 0.427 0.414 0.552 0.000 0.448 0.000 0.000
#> GSM1179002 3 0.446 0.129 0.408 0.000 0.584 0.000 0.008
#> GSM1179006 3 0.269 0.675 0.000 0.000 0.844 0.000 0.156
#> GSM1179008 3 0.446 0.129 0.408 0.000 0.584 0.000 0.008
#> GSM1179015 1 0.297 0.906 0.816 0.000 0.184 0.000 0.000
#> GSM1179017 5 0.516 0.000 0.116 0.000 0.004 0.180 0.700
#> GSM1179026 3 0.051 0.744 0.016 0.000 0.984 0.000 0.000
#> GSM1179033 3 0.051 0.744 0.016 0.000 0.984 0.000 0.000
#> GSM1179035 3 0.051 0.744 0.016 0.000 0.984 0.000 0.000
#> GSM1179036 3 0.051 0.744 0.016 0.000 0.984 0.000 0.000
#> GSM1178986 3 0.251 0.735 0.044 0.000 0.896 0.000 0.060
#> GSM1178989 4 0.185 0.766 0.000 0.000 0.088 0.912 0.000
#> GSM1178993 4 0.332 0.754 0.056 0.000 0.072 0.860 0.012
#> GSM1178999 2 0.611 0.647 0.068 0.668 0.000 0.152 0.112
#> GSM1179021 2 0.595 0.662 0.068 0.684 0.000 0.140 0.108
#> GSM1179025 2 0.000 0.885 0.000 1.000 0.000 0.000 0.000
#> GSM1179027 4 0.312 0.750 0.056 0.000 0.060 0.872 0.012
#> GSM1179011 4 0.332 0.754 0.056 0.000 0.072 0.860 0.012
#> GSM1179023 1 0.297 0.906 0.816 0.000 0.184 0.000 0.000
#> GSM1179029 1 0.366 0.823 0.724 0.000 0.276 0.000 0.000
#> GSM1179034 1 0.297 0.906 0.816 0.000 0.184 0.000 0.000
#> GSM1179040 2 0.619 0.636 0.068 0.660 0.000 0.160 0.112
#> GSM1178988 4 0.213 0.756 0.000 0.000 0.108 0.892 0.000
#> GSM1179037 3 0.051 0.744 0.016 0.000 0.984 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1178971 3 0.4755 0.605 0.236 0.000 0.680 0.000 0.068 0.016
#> GSM1178979 5 0.4671 0.381 0.000 0.044 0.000 0.424 0.532 0.000
#> GSM1179009 3 0.2164 0.787 0.056 0.000 0.908 0.028 0.000 0.008
#> GSM1179031 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178970 4 0.0363 0.866 0.000 0.000 0.012 0.988 0.000 0.000
#> GSM1178972 2 0.0547 0.976 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM1178973 3 0.5046 0.501 0.000 0.000 0.632 0.224 0.000 0.144
#> GSM1178974 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178977 4 0.0363 0.866 0.000 0.000 0.012 0.988 0.000 0.000
#> GSM1178978 3 0.4403 0.702 0.152 0.000 0.748 0.000 0.076 0.024
#> GSM1178998 1 0.0458 0.815 0.984 0.000 0.016 0.000 0.000 0.000
#> GSM1179010 1 0.3264 0.685 0.796 0.000 0.184 0.000 0.012 0.008
#> GSM1179018 3 0.1864 0.789 0.040 0.000 0.924 0.032 0.000 0.004
#> GSM1179024 1 0.3130 0.764 0.828 0.000 0.124 0.000 0.048 0.000
#> GSM1178984 3 0.4525 0.614 0.228 0.000 0.696 0.000 0.068 0.008
#> GSM1178990 3 0.4549 0.611 0.232 0.000 0.692 0.000 0.068 0.008
#> GSM1178991 3 0.3874 0.703 0.000 0.000 0.760 0.000 0.068 0.172
#> GSM1178994 3 0.3196 0.739 0.108 0.000 0.828 0.000 0.064 0.000
#> GSM1178997 3 0.4002 0.674 0.000 0.000 0.768 0.072 0.008 0.152
#> GSM1179000 3 0.3488 0.703 0.000 0.000 0.804 0.032 0.012 0.152
#> GSM1179013 1 0.0458 0.815 0.984 0.000 0.016 0.000 0.000 0.000
#> GSM1179014 1 0.4535 0.486 0.644 0.000 0.296 0.000 0.060 0.000
#> GSM1179019 3 0.4755 0.605 0.236 0.000 0.680 0.000 0.068 0.016
#> GSM1179020 1 0.3130 0.764 0.828 0.000 0.124 0.000 0.048 0.000
#> GSM1179022 1 0.0458 0.815 0.984 0.000 0.016 0.000 0.000 0.000
#> GSM1179028 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179032 1 0.0458 0.815 0.984 0.000 0.016 0.000 0.000 0.000
#> GSM1179041 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179042 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178976 4 0.0363 0.866 0.000 0.000 0.012 0.988 0.000 0.000
#> GSM1178981 3 0.2651 0.739 0.000 0.000 0.860 0.028 0.000 0.112
#> GSM1178982 3 0.2651 0.739 0.000 0.000 0.860 0.028 0.000 0.112
#> GSM1178983 3 0.3837 0.684 0.000 0.000 0.780 0.060 0.008 0.152
#> GSM1178985 3 0.2651 0.739 0.000 0.000 0.860 0.028 0.000 0.112
#> GSM1178992 3 0.4549 0.611 0.232 0.000 0.692 0.000 0.068 0.008
#> GSM1179005 3 0.3765 0.699 0.164 0.000 0.780 0.000 0.048 0.008
#> GSM1179007 3 0.4984 0.438 0.324 0.000 0.600 0.000 0.068 0.008
#> GSM1179012 1 0.0458 0.815 0.984 0.000 0.016 0.000 0.000 0.000
#> GSM1179016 1 0.4535 0.486 0.644 0.000 0.296 0.000 0.060 0.000
#> GSM1179030 4 0.0790 0.856 0.000 0.000 0.032 0.968 0.000 0.000
#> GSM1179038 3 0.1864 0.789 0.040 0.000 0.924 0.032 0.000 0.004
#> GSM1178987 3 0.1364 0.785 0.048 0.000 0.944 0.000 0.004 0.004
#> GSM1179003 5 0.4671 0.381 0.000 0.044 0.000 0.424 0.532 0.000
#> GSM1179004 3 0.1219 0.785 0.048 0.000 0.948 0.000 0.000 0.004
#> GSM1179039 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178975 4 0.4666 0.503 0.000 0.000 0.168 0.688 0.000 0.144
#> GSM1178980 4 0.3428 0.415 0.000 0.000 0.000 0.696 0.304 0.000
#> GSM1178995 3 0.3474 0.737 0.140 0.000 0.816 0.008 0.024 0.012
#> GSM1178996 3 0.2872 0.771 0.028 0.000 0.868 0.024 0.000 0.080
#> GSM1179001 1 0.4801 0.396 0.596 0.000 0.348 0.000 0.048 0.008
#> GSM1179002 3 0.5083 0.228 0.404 0.000 0.528 0.000 0.060 0.008
#> GSM1179006 3 0.3164 0.721 0.004 0.000 0.824 0.032 0.000 0.140
#> GSM1179008 3 0.5083 0.228 0.404 0.000 0.528 0.000 0.060 0.008
#> GSM1179015 1 0.0458 0.815 0.984 0.000 0.016 0.000 0.000 0.000
#> GSM1179017 6 0.3190 0.000 0.016 0.000 0.000 0.068 0.068 0.848
#> GSM1179026 3 0.1864 0.789 0.040 0.000 0.924 0.032 0.000 0.004
#> GSM1179033 3 0.1864 0.789 0.040 0.000 0.924 0.032 0.000 0.004
#> GSM1179035 3 0.1864 0.789 0.040 0.000 0.924 0.032 0.000 0.004
#> GSM1179036 3 0.1864 0.789 0.040 0.000 0.924 0.032 0.000 0.004
#> GSM1178986 3 0.3546 0.773 0.048 0.000 0.832 0.000 0.068 0.052
#> GSM1178989 4 0.0363 0.866 0.000 0.000 0.012 0.988 0.000 0.000
#> GSM1178993 4 0.1967 0.825 0.000 0.000 0.012 0.904 0.084 0.000
#> GSM1178999 5 0.2623 0.626 0.000 0.132 0.000 0.016 0.852 0.000
#> GSM1179021 5 0.2692 0.614 0.000 0.148 0.000 0.012 0.840 0.000
#> GSM1179025 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179027 4 0.1610 0.818 0.000 0.000 0.000 0.916 0.084 0.000
#> GSM1179011 4 0.1967 0.825 0.000 0.000 0.012 0.904 0.084 0.000
#> GSM1179023 1 0.0458 0.815 0.984 0.000 0.016 0.000 0.000 0.000
#> GSM1179029 1 0.2318 0.794 0.892 0.000 0.064 0.000 0.044 0.000
#> GSM1179034 1 0.0458 0.815 0.984 0.000 0.016 0.000 0.000 0.000
#> GSM1179040 5 0.2790 0.630 0.000 0.132 0.000 0.024 0.844 0.000
#> GSM1178988 4 0.0790 0.856 0.000 0.000 0.032 0.968 0.000 0.000
#> GSM1179037 3 0.1864 0.789 0.040 0.000 0.924 0.032 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) protocol(p) k
#> ATC:hclust 65 0.0203 0.01259 2
#> ATC:hclust 69 0.0719 0.08863 3
#> ATC:hclust 64 0.1645 0.00871 4
#> ATC:hclust 62 0.1120 0.01345 5
#> ATC:hclust 63 0.0219 0.00913 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 31632 rows and 73 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.985 0.994 0.4418 0.562 0.562
#> 3 3 1.000 0.991 0.996 0.4348 0.622 0.421
#> 4 4 0.857 0.917 0.961 0.1313 0.790 0.508
#> 5 5 0.726 0.667 0.804 0.0704 0.839 0.500
#> 6 6 0.700 0.749 0.799 0.0465 0.931 0.701
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
#> GSM1178971 1 0.0000 0.992 1.000 0.000
#> GSM1178979 2 0.0000 0.999 0.000 1.000
#> GSM1179009 1 0.0000 0.992 1.000 0.000
#> GSM1179031 2 0.0000 0.999 0.000 1.000
#> GSM1178970 2 0.0000 0.999 0.000 1.000
#> GSM1178972 2 0.0000 0.999 0.000 1.000
#> GSM1178973 1 0.0000 0.992 1.000 0.000
#> GSM1178974 2 0.0000 0.999 0.000 1.000
#> GSM1178977 2 0.0000 0.999 0.000 1.000
#> GSM1178978 1 0.0000 0.992 1.000 0.000
#> GSM1178998 1 0.0000 0.992 1.000 0.000
#> GSM1179010 1 0.0000 0.992 1.000 0.000
#> GSM1179018 1 0.0000 0.992 1.000 0.000
#> GSM1179024 1 0.0000 0.992 1.000 0.000
#> GSM1178984 1 0.0000 0.992 1.000 0.000
#> GSM1178990 1 0.0000 0.992 1.000 0.000
#> GSM1178991 1 0.0000 0.992 1.000 0.000
#> GSM1178994 1 0.0000 0.992 1.000 0.000
#> GSM1178997 1 0.0000 0.992 1.000 0.000
#> GSM1179000 1 0.0000 0.992 1.000 0.000
#> GSM1179013 1 0.0000 0.992 1.000 0.000
#> GSM1179014 1 0.0000 0.992 1.000 0.000
#> GSM1179019 1 0.0000 0.992 1.000 0.000
#> GSM1179020 1 0.0000 0.992 1.000 0.000
#> GSM1179022 1 0.0000 0.992 1.000 0.000
#> GSM1179028 2 0.0000 0.999 0.000 1.000
#> GSM1179032 1 0.0000 0.992 1.000 0.000
#> GSM1179041 2 0.0000 0.999 0.000 1.000
#> GSM1179042 2 0.0000 0.999 0.000 1.000
#> GSM1178976 2 0.0000 0.999 0.000 1.000
#> GSM1178981 1 0.0000 0.992 1.000 0.000
#> GSM1178982 1 0.0000 0.992 1.000 0.000
#> GSM1178983 1 0.0000 0.992 1.000 0.000
#> GSM1178985 1 0.0000 0.992 1.000 0.000
#> GSM1178992 1 0.0000 0.992 1.000 0.000
#> GSM1179005 1 0.0000 0.992 1.000 0.000
#> GSM1179007 1 0.0000 0.992 1.000 0.000
#> GSM1179012 1 0.0000 0.992 1.000 0.000
#> GSM1179016 1 0.0000 0.992 1.000 0.000
#> GSM1179030 2 0.0376 0.996 0.004 0.996
#> GSM1179038 1 0.0000 0.992 1.000 0.000
#> GSM1178987 1 0.0000 0.992 1.000 0.000
#> GSM1179003 2 0.0000 0.999 0.000 1.000
#> GSM1179004 1 0.0000 0.992 1.000 0.000
#> GSM1179039 2 0.0000 0.999 0.000 1.000
#> GSM1178975 1 0.9635 0.364 0.612 0.388
#> GSM1178980 2 0.0000 0.999 0.000 1.000
#> GSM1178995 1 0.0000 0.992 1.000 0.000
#> GSM1178996 1 0.0000 0.992 1.000 0.000
#> GSM1179001 1 0.0000 0.992 1.000 0.000
#> GSM1179002 1 0.0000 0.992 1.000 0.000
#> GSM1179006 1 0.0000 0.992 1.000 0.000
#> GSM1179008 1 0.0000 0.992 1.000 0.000
#> GSM1179015 1 0.0000 0.992 1.000 0.000
#> GSM1179017 2 0.0938 0.988 0.012 0.988
#> GSM1179026 1 0.0000 0.992 1.000 0.000
#> GSM1179033 1 0.0000 0.992 1.000 0.000
#> GSM1179035 1 0.0000 0.992 1.000 0.000
#> GSM1179036 1 0.0000 0.992 1.000 0.000
#> GSM1178986 1 0.0000 0.992 1.000 0.000
#> GSM1178989 2 0.0000 0.999 0.000 1.000
#> GSM1178993 2 0.0376 0.996 0.004 0.996
#> GSM1178999 2 0.0000 0.999 0.000 1.000
#> GSM1179021 2 0.0000 0.999 0.000 1.000
#> GSM1179025 2 0.0000 0.999 0.000 1.000
#> GSM1179027 2 0.0000 0.999 0.000 1.000
#> GSM1179011 2 0.0376 0.996 0.004 0.996
#> GSM1179023 1 0.0000 0.992 1.000 0.000
#> GSM1179029 1 0.0000 0.992 1.000 0.000
#> GSM1179034 1 0.0000 0.992 1.000 0.000
#> GSM1179040 2 0.0000 0.999 0.000 1.000
#> GSM1178988 1 0.0000 0.992 1.000 0.000
#> GSM1179037 1 0.0000 0.992 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1178971 1 0.000 1.000 1.000 0.000 0.000
#> GSM1178979 2 0.000 0.997 0.000 1.000 0.000
#> GSM1179009 3 0.000 0.991 0.000 0.000 1.000
#> GSM1179031 2 0.000 0.997 0.000 1.000 0.000
#> GSM1178970 3 0.000 0.991 0.000 0.000 1.000
#> GSM1178972 2 0.000 0.997 0.000 1.000 0.000
#> GSM1178973 3 0.000 0.991 0.000 0.000 1.000
#> GSM1178974 2 0.000 0.997 0.000 1.000 0.000
#> GSM1178977 3 0.000 0.991 0.000 0.000 1.000
#> GSM1178978 1 0.000 1.000 1.000 0.000 0.000
#> GSM1178998 1 0.000 1.000 1.000 0.000 0.000
#> GSM1179010 1 0.000 1.000 1.000 0.000 0.000
#> GSM1179018 3 0.000 0.991 0.000 0.000 1.000
#> GSM1179024 1 0.000 1.000 1.000 0.000 0.000
#> GSM1178984 1 0.000 1.000 1.000 0.000 0.000
#> GSM1178990 1 0.000 1.000 1.000 0.000 0.000
#> GSM1178991 3 0.327 0.862 0.116 0.000 0.884
#> GSM1178994 1 0.000 1.000 1.000 0.000 0.000
#> GSM1178997 3 0.000 0.991 0.000 0.000 1.000
#> GSM1179000 3 0.000 0.991 0.000 0.000 1.000
#> GSM1179013 1 0.000 1.000 1.000 0.000 0.000
#> GSM1179014 1 0.000 1.000 1.000 0.000 0.000
#> GSM1179019 1 0.000 1.000 1.000 0.000 0.000
#> GSM1179020 1 0.000 1.000 1.000 0.000 0.000
#> GSM1179022 1 0.000 1.000 1.000 0.000 0.000
#> GSM1179028 2 0.000 0.997 0.000 1.000 0.000
#> GSM1179032 1 0.000 1.000 1.000 0.000 0.000
#> GSM1179041 2 0.000 0.997 0.000 1.000 0.000
#> GSM1179042 2 0.000 0.997 0.000 1.000 0.000
#> GSM1178976 3 0.000 0.991 0.000 0.000 1.000
#> GSM1178981 3 0.000 0.991 0.000 0.000 1.000
#> GSM1178982 3 0.000 0.991 0.000 0.000 1.000
#> GSM1178983 3 0.000 0.991 0.000 0.000 1.000
#> GSM1178985 3 0.000 0.991 0.000 0.000 1.000
#> GSM1178992 1 0.000 1.000 1.000 0.000 0.000
#> GSM1179005 1 0.000 1.000 1.000 0.000 0.000
#> GSM1179007 1 0.000 1.000 1.000 0.000 0.000
#> GSM1179012 1 0.000 1.000 1.000 0.000 0.000
#> GSM1179016 1 0.000 1.000 1.000 0.000 0.000
#> GSM1179030 3 0.000 0.991 0.000 0.000 1.000
#> GSM1179038 3 0.000 0.991 0.000 0.000 1.000
#> GSM1178987 3 0.000 0.991 0.000 0.000 1.000
#> GSM1179003 2 0.141 0.961 0.000 0.964 0.036
#> GSM1179004 3 0.000 0.991 0.000 0.000 1.000
#> GSM1179039 2 0.000 0.997 0.000 1.000 0.000
#> GSM1178975 3 0.000 0.991 0.000 0.000 1.000
#> GSM1178980 3 0.000 0.991 0.000 0.000 1.000
#> GSM1178995 3 0.000 0.991 0.000 0.000 1.000
#> GSM1178996 3 0.000 0.991 0.000 0.000 1.000
#> GSM1179001 1 0.000 1.000 1.000 0.000 0.000
#> GSM1179002 1 0.000 1.000 1.000 0.000 0.000
#> GSM1179006 3 0.000 0.991 0.000 0.000 1.000
#> GSM1179008 1 0.000 1.000 1.000 0.000 0.000
#> GSM1179015 1 0.000 1.000 1.000 0.000 0.000
#> GSM1179017 3 0.000 0.991 0.000 0.000 1.000
#> GSM1179026 3 0.000 0.991 0.000 0.000 1.000
#> GSM1179033 3 0.000 0.991 0.000 0.000 1.000
#> GSM1179035 3 0.000 0.991 0.000 0.000 1.000
#> GSM1179036 3 0.000 0.991 0.000 0.000 1.000
#> GSM1178986 3 0.355 0.842 0.132 0.000 0.868
#> GSM1178989 3 0.000 0.991 0.000 0.000 1.000
#> GSM1178993 3 0.000 0.991 0.000 0.000 1.000
#> GSM1178999 2 0.000 0.997 0.000 1.000 0.000
#> GSM1179021 2 0.000 0.997 0.000 1.000 0.000
#> GSM1179025 2 0.000 0.997 0.000 1.000 0.000
#> GSM1179027 3 0.000 0.991 0.000 0.000 1.000
#> GSM1179011 3 0.000 0.991 0.000 0.000 1.000
#> GSM1179023 1 0.000 1.000 1.000 0.000 0.000
#> GSM1179029 1 0.000 1.000 1.000 0.000 0.000
#> GSM1179034 1 0.000 1.000 1.000 0.000 0.000
#> GSM1179040 2 0.000 0.997 0.000 1.000 0.000
#> GSM1178988 3 0.000 0.991 0.000 0.000 1.000
#> GSM1179037 3 0.000 0.991 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1178971 3 0.3123 0.814 0.156 0.000 0.844 0.000
#> GSM1178979 4 0.0336 0.950 0.000 0.008 0.000 0.992
#> GSM1179009 3 0.0000 0.956 0.000 0.000 1.000 0.000
#> GSM1179031 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM1178970 4 0.1637 0.948 0.000 0.000 0.060 0.940
#> GSM1178972 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM1178973 3 0.0000 0.956 0.000 0.000 1.000 0.000
#> GSM1178974 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM1178977 4 0.1637 0.948 0.000 0.000 0.060 0.940
#> GSM1178978 3 0.3123 0.814 0.156 0.000 0.844 0.000
#> GSM1178998 1 0.0000 0.923 1.000 0.000 0.000 0.000
#> GSM1179010 1 0.0188 0.921 0.996 0.000 0.000 0.004
#> GSM1179018 3 0.0000 0.956 0.000 0.000 1.000 0.000
#> GSM1179024 1 0.0188 0.921 0.996 0.000 0.000 0.004
#> GSM1178984 3 0.3123 0.814 0.156 0.000 0.844 0.000
#> GSM1178990 1 0.3219 0.795 0.836 0.000 0.164 0.000
#> GSM1178991 3 0.0188 0.954 0.000 0.000 0.996 0.004
#> GSM1178994 3 0.3873 0.709 0.228 0.000 0.772 0.000
#> GSM1178997 3 0.0000 0.956 0.000 0.000 1.000 0.000
#> GSM1179000 3 0.0188 0.954 0.000 0.000 0.996 0.004
#> GSM1179013 1 0.0000 0.923 1.000 0.000 0.000 0.000
#> GSM1179014 1 0.4155 0.707 0.756 0.000 0.240 0.004
#> GSM1179019 1 0.3486 0.771 0.812 0.000 0.188 0.000
#> GSM1179020 1 0.0000 0.923 1.000 0.000 0.000 0.000
#> GSM1179022 1 0.0000 0.923 1.000 0.000 0.000 0.000
#> GSM1179028 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM1179032 1 0.0000 0.923 1.000 0.000 0.000 0.000
#> GSM1179041 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM1179042 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM1178976 4 0.1792 0.943 0.000 0.000 0.068 0.932
#> GSM1178981 3 0.0000 0.956 0.000 0.000 1.000 0.000
#> GSM1178982 3 0.0000 0.956 0.000 0.000 1.000 0.000
#> GSM1178983 3 0.0000 0.956 0.000 0.000 1.000 0.000
#> GSM1178985 3 0.0000 0.956 0.000 0.000 1.000 0.000
#> GSM1178992 1 0.5088 0.301 0.572 0.000 0.424 0.004
#> GSM1179005 3 0.2408 0.868 0.104 0.000 0.896 0.000
#> GSM1179007 1 0.0000 0.923 1.000 0.000 0.000 0.000
#> GSM1179012 1 0.0000 0.923 1.000 0.000 0.000 0.000
#> GSM1179016 1 0.3448 0.790 0.828 0.000 0.168 0.004
#> GSM1179030 4 0.1637 0.948 0.000 0.000 0.060 0.940
#> GSM1179038 3 0.0000 0.956 0.000 0.000 1.000 0.000
#> GSM1178987 3 0.0000 0.956 0.000 0.000 1.000 0.000
#> GSM1179003 4 0.0336 0.950 0.000 0.008 0.000 0.992
#> GSM1179004 3 0.0000 0.956 0.000 0.000 1.000 0.000
#> GSM1179039 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM1178975 4 0.1389 0.952 0.000 0.000 0.048 0.952
#> GSM1178980 4 0.0336 0.954 0.000 0.000 0.008 0.992
#> GSM1178995 3 0.0000 0.956 0.000 0.000 1.000 0.000
#> GSM1178996 3 0.0000 0.956 0.000 0.000 1.000 0.000
#> GSM1179001 1 0.0000 0.923 1.000 0.000 0.000 0.000
#> GSM1179002 1 0.0000 0.923 1.000 0.000 0.000 0.000
#> GSM1179006 3 0.0000 0.956 0.000 0.000 1.000 0.000
#> GSM1179008 1 0.0000 0.923 1.000 0.000 0.000 0.000
#> GSM1179015 1 0.0000 0.923 1.000 0.000 0.000 0.000
#> GSM1179017 4 0.2469 0.905 0.000 0.000 0.108 0.892
#> GSM1179026 3 0.0000 0.956 0.000 0.000 1.000 0.000
#> GSM1179033 3 0.0000 0.956 0.000 0.000 1.000 0.000
#> GSM1179035 3 0.0000 0.956 0.000 0.000 1.000 0.000
#> GSM1179036 3 0.0000 0.956 0.000 0.000 1.000 0.000
#> GSM1178986 3 0.0188 0.954 0.000 0.000 0.996 0.004
#> GSM1178989 4 0.2647 0.891 0.000 0.000 0.120 0.880
#> GSM1178993 4 0.0469 0.955 0.000 0.000 0.012 0.988
#> GSM1178999 4 0.0336 0.950 0.000 0.008 0.000 0.992
#> GSM1179021 2 0.1389 0.957 0.000 0.952 0.000 0.048
#> GSM1179025 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM1179027 4 0.0336 0.954 0.000 0.000 0.008 0.992
#> GSM1179011 4 0.0469 0.955 0.000 0.000 0.012 0.988
#> GSM1179023 1 0.0000 0.923 1.000 0.000 0.000 0.000
#> GSM1179029 1 0.0188 0.921 0.996 0.000 0.000 0.004
#> GSM1179034 1 0.0000 0.923 1.000 0.000 0.000 0.000
#> GSM1179040 4 0.0336 0.950 0.000 0.008 0.000 0.992
#> GSM1178988 3 0.3610 0.709 0.000 0.000 0.800 0.200
#> GSM1179037 3 0.0000 0.956 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
#> GSM1178971 1 0.2654 0.599 0.888 0.000 0.048 0.000 0.064
#> GSM1178979 4 0.3613 0.780 0.016 0.012 0.160 0.812 0.000
#> GSM1179009 3 0.4235 0.768 0.424 0.000 0.576 0.000 0.000
#> GSM1179031 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000
#> GSM1178970 4 0.4262 0.696 0.000 0.000 0.440 0.560 0.000
#> GSM1178972 2 0.2555 0.910 0.016 0.904 0.028 0.052 0.000
#> GSM1178973 3 0.4703 0.812 0.340 0.000 0.632 0.028 0.000
#> GSM1178974 2 0.0162 0.965 0.000 0.996 0.004 0.000 0.000
#> GSM1178977 4 0.4227 0.715 0.000 0.000 0.420 0.580 0.000
#> GSM1178978 1 0.2654 0.599 0.888 0.000 0.048 0.000 0.064
#> GSM1178998 5 0.0000 0.900 0.000 0.000 0.000 0.000 1.000
#> GSM1179010 5 0.4941 0.327 0.328 0.000 0.044 0.000 0.628
#> GSM1179018 3 0.4088 0.814 0.368 0.000 0.632 0.000 0.000
#> GSM1179024 5 0.4300 -0.172 0.476 0.000 0.000 0.000 0.524
#> GSM1178984 1 0.2654 0.599 0.888 0.000 0.048 0.000 0.064
#> GSM1178990 1 0.4126 0.463 0.620 0.000 0.000 0.000 0.380
#> GSM1178991 1 0.1341 0.534 0.944 0.000 0.056 0.000 0.000
#> GSM1178994 1 0.2830 0.611 0.876 0.000 0.044 0.000 0.080
#> GSM1178997 3 0.3480 0.777 0.248 0.000 0.752 0.000 0.000
#> GSM1179000 1 0.2891 0.337 0.824 0.000 0.176 0.000 0.000
#> GSM1179013 5 0.0000 0.900 0.000 0.000 0.000 0.000 1.000
#> GSM1179014 1 0.3837 0.506 0.692 0.000 0.000 0.000 0.308
#> GSM1179019 1 0.4126 0.463 0.620 0.000 0.000 0.000 0.380
#> GSM1179020 1 0.4262 0.341 0.560 0.000 0.000 0.000 0.440
#> GSM1179022 5 0.0000 0.900 0.000 0.000 0.000 0.000 1.000
#> GSM1179028 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000
#> GSM1179032 5 0.0000 0.900 0.000 0.000 0.000 0.000 1.000
#> GSM1179041 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000
#> GSM1179042 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000
#> GSM1178976 4 0.4305 0.628 0.000 0.000 0.488 0.512 0.000
#> GSM1178981 3 0.4235 0.768 0.424 0.000 0.576 0.000 0.000
#> GSM1178982 3 0.3876 0.824 0.316 0.000 0.684 0.000 0.000
#> GSM1178983 3 0.3816 0.821 0.304 0.000 0.696 0.000 0.000
#> GSM1178985 3 0.3932 0.825 0.328 0.000 0.672 0.000 0.000
#> GSM1178992 1 0.3671 0.577 0.756 0.000 0.008 0.000 0.236
#> GSM1179005 1 0.2592 0.583 0.892 0.000 0.056 0.000 0.052
#> GSM1179007 1 0.4302 0.238 0.520 0.000 0.000 0.000 0.480
#> GSM1179012 5 0.0000 0.900 0.000 0.000 0.000 0.000 1.000
#> GSM1179016 1 0.3932 0.480 0.672 0.000 0.000 0.000 0.328
#> GSM1179030 4 0.4273 0.696 0.000 0.000 0.448 0.552 0.000
#> GSM1179038 3 0.4088 0.814 0.368 0.000 0.632 0.000 0.000
#> GSM1178987 3 0.4235 0.768 0.424 0.000 0.576 0.000 0.000
#> GSM1179003 4 0.3492 0.781 0.016 0.000 0.188 0.796 0.000
#> GSM1179004 3 0.4235 0.768 0.424 0.000 0.576 0.000 0.000
#> GSM1179039 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000
#> GSM1178975 4 0.3093 0.784 0.008 0.000 0.168 0.824 0.000
#> GSM1178980 4 0.0162 0.794 0.000 0.000 0.004 0.996 0.000
#> GSM1178995 1 0.4307 -0.656 0.500 0.000 0.500 0.000 0.000
#> GSM1178996 3 0.4171 0.794 0.396 0.000 0.604 0.000 0.000
#> GSM1179001 5 0.0162 0.897 0.004 0.000 0.000 0.000 0.996
#> GSM1179002 1 0.4273 0.327 0.552 0.000 0.000 0.000 0.448
#> GSM1179006 3 0.3999 0.821 0.344 0.000 0.656 0.000 0.000
#> GSM1179008 1 0.4283 0.313 0.544 0.000 0.000 0.000 0.456
#> GSM1179015 5 0.0000 0.900 0.000 0.000 0.000 0.000 1.000
#> GSM1179017 3 0.5507 -0.665 0.064 0.000 0.480 0.456 0.000
#> GSM1179026 3 0.4182 0.793 0.400 0.000 0.600 0.000 0.000
#> GSM1179033 3 0.3837 0.822 0.308 0.000 0.692 0.000 0.000
#> GSM1179035 3 0.3876 0.824 0.316 0.000 0.684 0.000 0.000
#> GSM1179036 3 0.3816 0.820 0.304 0.000 0.696 0.000 0.000
#> GSM1178986 1 0.1608 0.522 0.928 0.000 0.072 0.000 0.000
#> GSM1178989 3 0.4287 -0.586 0.000 0.000 0.540 0.460 0.000
#> GSM1178993 4 0.1830 0.807 0.008 0.000 0.068 0.924 0.000
#> GSM1178999 4 0.1701 0.779 0.016 0.012 0.028 0.944 0.000
#> GSM1179021 2 0.3926 0.797 0.016 0.792 0.020 0.172 0.000
#> GSM1179025 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000
#> GSM1179027 4 0.1557 0.805 0.008 0.000 0.052 0.940 0.000
#> GSM1179011 4 0.1830 0.807 0.008 0.000 0.068 0.924 0.000
#> GSM1179023 5 0.0000 0.900 0.000 0.000 0.000 0.000 1.000
#> GSM1179029 5 0.0290 0.893 0.008 0.000 0.000 0.000 0.992
#> GSM1179034 5 0.0000 0.900 0.000 0.000 0.000 0.000 1.000
#> GSM1179040 4 0.1117 0.783 0.016 0.000 0.020 0.964 0.000
#> GSM1178988 3 0.2362 0.563 0.076 0.000 0.900 0.024 0.000
#> GSM1179037 3 0.3857 0.823 0.312 0.000 0.688 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1178971 6 0.3942 0.7155 0.024 0.000 0.204 0.000 0.020 0.752
#> GSM1178979 5 0.5217 -0.0187 0.000 0.008 0.000 0.452 0.472 0.068
#> GSM1179009 3 0.2841 0.7877 0.000 0.000 0.824 0.000 0.012 0.164
#> GSM1179031 2 0.0000 0.9221 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178970 5 0.5721 0.7230 0.000 0.000 0.176 0.344 0.480 0.000
#> GSM1178972 2 0.4486 0.7042 0.000 0.704 0.000 0.004 0.208 0.084
#> GSM1178973 3 0.2428 0.8575 0.000 0.000 0.896 0.060 0.024 0.020
#> GSM1178974 2 0.0891 0.9087 0.000 0.968 0.000 0.000 0.008 0.024
#> GSM1178977 5 0.5706 0.7204 0.000 0.000 0.172 0.348 0.480 0.000
#> GSM1178978 6 0.4338 0.7178 0.024 0.000 0.200 0.000 0.044 0.732
#> GSM1178998 1 0.0000 0.9712 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179010 6 0.5020 0.2203 0.436 0.000 0.004 0.000 0.060 0.500
#> GSM1179018 3 0.0405 0.8920 0.000 0.000 0.988 0.000 0.004 0.008
#> GSM1179024 6 0.5320 0.5349 0.352 0.000 0.000 0.000 0.116 0.532
#> GSM1178984 6 0.3888 0.7114 0.024 0.000 0.208 0.000 0.016 0.752
#> GSM1178990 6 0.4848 0.7057 0.196 0.000 0.032 0.000 0.072 0.700
#> GSM1178991 6 0.5520 0.6329 0.000 0.000 0.200 0.000 0.240 0.560
#> GSM1178994 6 0.3748 0.7162 0.028 0.000 0.204 0.000 0.008 0.760
#> GSM1178997 3 0.3032 0.7774 0.000 0.000 0.852 0.040 0.096 0.012
#> GSM1179000 6 0.5608 0.4171 0.000 0.000 0.380 0.000 0.148 0.472
#> GSM1179013 1 0.0146 0.9704 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM1179014 6 0.5841 0.6698 0.128 0.000 0.048 0.000 0.220 0.604
#> GSM1179019 6 0.5087 0.7147 0.184 0.000 0.040 0.000 0.088 0.688
#> GSM1179020 6 0.4727 0.6665 0.240 0.000 0.000 0.000 0.100 0.660
#> GSM1179022 1 0.0000 0.9712 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179028 2 0.0000 0.9221 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179032 1 0.0000 0.9712 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179041 2 0.0000 0.9221 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179042 2 0.0000 0.9221 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178976 5 0.5763 0.7218 0.000 0.000 0.188 0.332 0.480 0.000
#> GSM1178981 3 0.2573 0.8442 0.000 0.000 0.864 0.000 0.024 0.112
#> GSM1178982 3 0.1088 0.8870 0.000 0.000 0.960 0.000 0.024 0.016
#> GSM1178983 3 0.1861 0.8708 0.000 0.000 0.928 0.016 0.036 0.020
#> GSM1178985 3 0.1092 0.8897 0.000 0.000 0.960 0.000 0.020 0.020
#> GSM1178992 6 0.4895 0.7398 0.072 0.000 0.120 0.000 0.080 0.728
#> GSM1179005 6 0.3357 0.6940 0.004 0.000 0.224 0.000 0.008 0.764
#> GSM1179007 6 0.3797 0.6206 0.292 0.000 0.000 0.000 0.016 0.692
#> GSM1179012 1 0.0146 0.9704 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM1179016 6 0.5740 0.6646 0.140 0.000 0.036 0.000 0.216 0.608
#> GSM1179030 5 0.5900 0.7204 0.000 0.000 0.184 0.348 0.464 0.004
#> GSM1179038 3 0.0806 0.8896 0.000 0.000 0.972 0.000 0.008 0.020
#> GSM1178987 3 0.2212 0.8432 0.000 0.000 0.880 0.000 0.008 0.112
#> GSM1179003 5 0.5116 0.0265 0.000 0.000 0.004 0.444 0.484 0.068
#> GSM1179004 3 0.2212 0.8433 0.000 0.000 0.880 0.000 0.008 0.112
#> GSM1179039 2 0.0000 0.9221 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178975 4 0.2612 0.5984 0.000 0.000 0.108 0.868 0.016 0.008
#> GSM1178980 4 0.1686 0.7783 0.000 0.000 0.000 0.924 0.064 0.012
#> GSM1178995 3 0.3043 0.7304 0.000 0.000 0.792 0.000 0.008 0.200
#> GSM1178996 3 0.0937 0.8864 0.000 0.000 0.960 0.000 0.000 0.040
#> GSM1179001 1 0.2623 0.8007 0.852 0.000 0.000 0.000 0.016 0.132
#> GSM1179002 6 0.3875 0.6305 0.280 0.000 0.004 0.000 0.016 0.700
#> GSM1179006 3 0.0363 0.8916 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM1179008 6 0.3778 0.6242 0.288 0.000 0.000 0.000 0.016 0.696
#> GSM1179015 1 0.0146 0.9704 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM1179017 5 0.6185 0.5532 0.000 0.000 0.116 0.248 0.564 0.072
#> GSM1179026 3 0.1196 0.8856 0.000 0.000 0.952 0.000 0.008 0.040
#> GSM1179033 3 0.0837 0.8850 0.000 0.000 0.972 0.004 0.020 0.004
#> GSM1179035 3 0.0436 0.8899 0.000 0.000 0.988 0.004 0.004 0.004
#> GSM1179036 3 0.0653 0.8869 0.000 0.000 0.980 0.004 0.012 0.004
#> GSM1178986 6 0.5591 0.6261 0.000 0.000 0.228 0.000 0.224 0.548
#> GSM1178989 5 0.6014 0.6731 0.000 0.000 0.236 0.292 0.468 0.004
#> GSM1178993 4 0.0363 0.7922 0.000 0.000 0.012 0.988 0.000 0.000
#> GSM1178999 4 0.4331 0.6453 0.000 0.008 0.000 0.728 0.192 0.072
#> GSM1179021 2 0.5733 0.5797 0.000 0.644 0.000 0.140 0.144 0.072
#> GSM1179025 2 0.0000 0.9221 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179027 4 0.0146 0.7940 0.000 0.000 0.004 0.996 0.000 0.000
#> GSM1179011 4 0.0363 0.7922 0.000 0.000 0.012 0.988 0.000 0.000
#> GSM1179023 1 0.0000 0.9712 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179029 1 0.1594 0.9125 0.932 0.000 0.000 0.000 0.052 0.016
#> GSM1179034 1 0.0000 0.9712 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179040 4 0.4024 0.6619 0.000 0.000 0.000 0.744 0.184 0.072
#> GSM1178988 3 0.5306 -0.0797 0.000 0.000 0.532 0.096 0.368 0.004
#> GSM1179037 3 0.0551 0.8886 0.000 0.000 0.984 0.004 0.008 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) protocol(p) k
#> ATC:kmeans 72 0.0539 0.10956 2
#> ATC:kmeans 73 0.1665 0.01375 3
#> ATC:kmeans 72 0.3090 0.01144 4
#> ATC:kmeans 60 0.2491 0.00186 5
#> ATC:kmeans 68 0.0120 0.00798 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 31632 rows and 73 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 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 0.989 0.995 0.4875 0.514 0.514
#> 3 3 0.872 0.918 0.959 0.2990 0.824 0.664
#> 4 4 0.897 0.868 0.938 0.0599 0.955 0.878
#> 5 5 0.876 0.852 0.925 0.0682 0.938 0.822
#> 6 6 0.774 0.743 0.873 0.0390 0.993 0.977
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
#> GSM1178971 1 0.0000 0.993 1.000 0.000
#> GSM1178979 2 0.0000 0.999 0.000 1.000
#> GSM1179009 1 0.0000 0.993 1.000 0.000
#> GSM1179031 2 0.0000 0.999 0.000 1.000
#> GSM1178970 2 0.0000 0.999 0.000 1.000
#> GSM1178972 2 0.0000 0.999 0.000 1.000
#> GSM1178973 1 0.0000 0.993 1.000 0.000
#> GSM1178974 2 0.0000 0.999 0.000 1.000
#> GSM1178977 2 0.0000 0.999 0.000 1.000
#> GSM1178978 1 0.0000 0.993 1.000 0.000
#> GSM1178998 1 0.0000 0.993 1.000 0.000
#> GSM1179010 1 0.0000 0.993 1.000 0.000
#> GSM1179018 1 0.0000 0.993 1.000 0.000
#> GSM1179024 1 0.0000 0.993 1.000 0.000
#> GSM1178984 1 0.0000 0.993 1.000 0.000
#> GSM1178990 1 0.0000 0.993 1.000 0.000
#> GSM1178991 1 0.0000 0.993 1.000 0.000
#> GSM1178994 1 0.0000 0.993 1.000 0.000
#> GSM1178997 2 0.0000 0.999 0.000 1.000
#> GSM1179000 1 0.0000 0.993 1.000 0.000
#> GSM1179013 1 0.0000 0.993 1.000 0.000
#> GSM1179014 1 0.0000 0.993 1.000 0.000
#> GSM1179019 1 0.0000 0.993 1.000 0.000
#> GSM1179020 1 0.0000 0.993 1.000 0.000
#> GSM1179022 1 0.0000 0.993 1.000 0.000
#> GSM1179028 2 0.0000 0.999 0.000 1.000
#> GSM1179032 1 0.0000 0.993 1.000 0.000
#> GSM1179041 2 0.0000 0.999 0.000 1.000
#> GSM1179042 2 0.0000 0.999 0.000 1.000
#> GSM1178976 2 0.0000 0.999 0.000 1.000
#> GSM1178981 1 0.0000 0.993 1.000 0.000
#> GSM1178982 1 0.8861 0.562 0.696 0.304
#> GSM1178983 2 0.1843 0.971 0.028 0.972
#> GSM1178985 1 0.0000 0.993 1.000 0.000
#> GSM1178992 1 0.0000 0.993 1.000 0.000
#> GSM1179005 1 0.0000 0.993 1.000 0.000
#> GSM1179007 1 0.0000 0.993 1.000 0.000
#> GSM1179012 1 0.0000 0.993 1.000 0.000
#> GSM1179016 1 0.0000 0.993 1.000 0.000
#> GSM1179030 2 0.0000 0.999 0.000 1.000
#> GSM1179038 1 0.0000 0.993 1.000 0.000
#> GSM1178987 1 0.0000 0.993 1.000 0.000
#> GSM1179003 2 0.0000 0.999 0.000 1.000
#> GSM1179004 1 0.0000 0.993 1.000 0.000
#> GSM1179039 2 0.0000 0.999 0.000 1.000
#> GSM1178975 2 0.0000 0.999 0.000 1.000
#> GSM1178980 2 0.0000 0.999 0.000 1.000
#> GSM1178995 1 0.0000 0.993 1.000 0.000
#> GSM1178996 1 0.0000 0.993 1.000 0.000
#> GSM1179001 1 0.0000 0.993 1.000 0.000
#> GSM1179002 1 0.0000 0.993 1.000 0.000
#> GSM1179006 1 0.0000 0.993 1.000 0.000
#> GSM1179008 1 0.0000 0.993 1.000 0.000
#> GSM1179015 1 0.0000 0.993 1.000 0.000
#> GSM1179017 2 0.0000 0.999 0.000 1.000
#> GSM1179026 1 0.0000 0.993 1.000 0.000
#> GSM1179033 2 0.0376 0.995 0.004 0.996
#> GSM1179035 1 0.0000 0.993 1.000 0.000
#> GSM1179036 2 0.0672 0.992 0.008 0.992
#> GSM1178986 1 0.0000 0.993 1.000 0.000
#> GSM1178989 2 0.0000 0.999 0.000 1.000
#> GSM1178993 2 0.0000 0.999 0.000 1.000
#> GSM1178999 2 0.0000 0.999 0.000 1.000
#> GSM1179021 2 0.0000 0.999 0.000 1.000
#> GSM1179025 2 0.0000 0.999 0.000 1.000
#> GSM1179027 2 0.0000 0.999 0.000 1.000
#> GSM1179011 2 0.0000 0.999 0.000 1.000
#> GSM1179023 1 0.0000 0.993 1.000 0.000
#> GSM1179029 1 0.0000 0.993 1.000 0.000
#> GSM1179034 1 0.0000 0.993 1.000 0.000
#> GSM1179040 2 0.0000 0.999 0.000 1.000
#> GSM1178988 2 0.0000 0.999 0.000 1.000
#> GSM1179037 1 0.0376 0.989 0.996 0.004
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1178971 1 0.0000 0.9777 1.000 0.000 0.000
#> GSM1178979 2 0.0000 0.9821 0.000 1.000 0.000
#> GSM1179009 3 0.4504 0.8197 0.196 0.000 0.804
#> GSM1179031 2 0.0000 0.9821 0.000 1.000 0.000
#> GSM1178970 2 0.0000 0.9821 0.000 1.000 0.000
#> GSM1178972 2 0.0000 0.9821 0.000 1.000 0.000
#> GSM1178973 3 0.3412 0.8546 0.124 0.000 0.876
#> GSM1178974 2 0.0000 0.9821 0.000 1.000 0.000
#> GSM1178977 2 0.0000 0.9821 0.000 1.000 0.000
#> GSM1178978 1 0.0000 0.9777 1.000 0.000 0.000
#> GSM1178998 1 0.0000 0.9777 1.000 0.000 0.000
#> GSM1179010 1 0.0000 0.9777 1.000 0.000 0.000
#> GSM1179018 3 0.1753 0.8520 0.048 0.000 0.952
#> GSM1179024 1 0.0000 0.9777 1.000 0.000 0.000
#> GSM1178984 1 0.0000 0.9777 1.000 0.000 0.000
#> GSM1178990 1 0.0000 0.9777 1.000 0.000 0.000
#> GSM1178991 1 0.0000 0.9777 1.000 0.000 0.000
#> GSM1178994 1 0.0000 0.9777 1.000 0.000 0.000
#> GSM1178997 2 0.0000 0.9821 0.000 1.000 0.000
#> GSM1179000 1 0.0000 0.9777 1.000 0.000 0.000
#> GSM1179013 1 0.0000 0.9777 1.000 0.000 0.000
#> GSM1179014 1 0.0000 0.9777 1.000 0.000 0.000
#> GSM1179019 1 0.0000 0.9777 1.000 0.000 0.000
#> GSM1179020 1 0.0000 0.9777 1.000 0.000 0.000
#> GSM1179022 1 0.0000 0.9777 1.000 0.000 0.000
#> GSM1179028 2 0.0000 0.9821 0.000 1.000 0.000
#> GSM1179032 1 0.0000 0.9777 1.000 0.000 0.000
#> GSM1179041 2 0.0000 0.9821 0.000 1.000 0.000
#> GSM1179042 2 0.0000 0.9821 0.000 1.000 0.000
#> GSM1178976 2 0.0000 0.9821 0.000 1.000 0.000
#> GSM1178981 3 0.5968 0.5986 0.364 0.000 0.636
#> GSM1178982 3 0.3349 0.8568 0.108 0.004 0.888
#> GSM1178983 2 0.6460 0.2156 0.004 0.556 0.440
#> GSM1178985 3 0.4178 0.8355 0.172 0.000 0.828
#> GSM1178992 1 0.0000 0.9777 1.000 0.000 0.000
#> GSM1179005 1 0.0000 0.9777 1.000 0.000 0.000
#> GSM1179007 1 0.0000 0.9777 1.000 0.000 0.000
#> GSM1179012 1 0.0000 0.9777 1.000 0.000 0.000
#> GSM1179016 1 0.0000 0.9777 1.000 0.000 0.000
#> GSM1179030 2 0.0000 0.9821 0.000 1.000 0.000
#> GSM1179038 3 0.3879 0.8248 0.152 0.000 0.848
#> GSM1178987 1 0.6126 0.0945 0.600 0.000 0.400
#> GSM1179003 2 0.0000 0.9821 0.000 1.000 0.000
#> GSM1179004 3 0.6180 0.4848 0.416 0.000 0.584
#> GSM1179039 2 0.0000 0.9821 0.000 1.000 0.000
#> GSM1178975 2 0.0000 0.9821 0.000 1.000 0.000
#> GSM1178980 2 0.0000 0.9821 0.000 1.000 0.000
#> GSM1178995 1 0.1411 0.9384 0.964 0.000 0.036
#> GSM1178996 1 0.3619 0.8123 0.864 0.000 0.136
#> GSM1179001 1 0.0000 0.9777 1.000 0.000 0.000
#> GSM1179002 1 0.0000 0.9777 1.000 0.000 0.000
#> GSM1179006 3 0.4452 0.8233 0.192 0.000 0.808
#> GSM1179008 1 0.0000 0.9777 1.000 0.000 0.000
#> GSM1179015 1 0.0000 0.9777 1.000 0.000 0.000
#> GSM1179017 2 0.0237 0.9787 0.000 0.996 0.004
#> GSM1179026 3 0.4121 0.8117 0.168 0.000 0.832
#> GSM1179033 3 0.1753 0.8163 0.000 0.048 0.952
#> GSM1179035 3 0.0000 0.8367 0.000 0.000 1.000
#> GSM1179036 3 0.0000 0.8367 0.000 0.000 1.000
#> GSM1178986 1 0.0000 0.9777 1.000 0.000 0.000
#> GSM1178989 2 0.0000 0.9821 0.000 1.000 0.000
#> GSM1178993 2 0.0000 0.9821 0.000 1.000 0.000
#> GSM1178999 2 0.0000 0.9821 0.000 1.000 0.000
#> GSM1179021 2 0.0000 0.9821 0.000 1.000 0.000
#> GSM1179025 2 0.0000 0.9821 0.000 1.000 0.000
#> GSM1179027 2 0.0000 0.9821 0.000 1.000 0.000
#> GSM1179011 2 0.0000 0.9821 0.000 1.000 0.000
#> GSM1179023 1 0.0000 0.9777 1.000 0.000 0.000
#> GSM1179029 1 0.0000 0.9777 1.000 0.000 0.000
#> GSM1179034 1 0.0000 0.9777 1.000 0.000 0.000
#> GSM1179040 2 0.0000 0.9821 0.000 1.000 0.000
#> GSM1178988 2 0.0424 0.9752 0.000 0.992 0.008
#> GSM1179037 3 0.0000 0.8367 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1178971 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM1178979 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM1179009 4 0.6347 0.599 0.276 0.000 0.100 0.624
#> GSM1179031 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM1178970 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM1178972 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM1178973 4 0.0000 0.650 0.000 0.000 0.000 1.000
#> GSM1178974 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM1178977 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM1178978 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM1178998 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM1179010 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM1179018 3 0.4114 0.789 0.060 0.000 0.828 0.112
#> GSM1179024 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM1178984 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM1178990 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM1178991 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM1178994 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM1178997 2 0.0817 0.918 0.000 0.976 0.000 0.024
#> GSM1179000 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM1179013 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM1179014 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM1179019 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM1179020 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM1179022 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM1179028 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM1179032 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM1179041 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM1179042 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM1178976 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM1178981 4 0.5716 0.621 0.272 0.000 0.060 0.668
#> GSM1178982 4 0.1389 0.652 0.000 0.000 0.048 0.952
#> GSM1178983 4 0.0000 0.650 0.000 0.000 0.000 1.000
#> GSM1178985 4 0.6063 0.646 0.196 0.000 0.124 0.680
#> GSM1178992 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM1179005 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM1179007 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM1179012 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM1179016 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM1179030 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM1179038 3 0.1824 0.877 0.060 0.000 0.936 0.004
#> GSM1178987 1 0.4706 0.603 0.732 0.000 0.248 0.020
#> GSM1179003 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM1179004 1 0.5738 0.180 0.540 0.000 0.432 0.028
#> GSM1179039 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM1178975 2 0.4585 0.647 0.000 0.668 0.000 0.332
#> GSM1178980 2 0.4277 0.704 0.000 0.720 0.000 0.280
#> GSM1178995 1 0.1557 0.902 0.944 0.000 0.056 0.000
#> GSM1178996 1 0.4761 0.402 0.628 0.000 0.372 0.000
#> GSM1179001 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM1179002 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM1179006 4 0.5951 0.483 0.064 0.000 0.300 0.636
#> GSM1179008 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM1179015 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM1179017 2 0.1637 0.888 0.000 0.940 0.060 0.000
#> GSM1179026 3 0.0000 0.948 0.000 0.000 1.000 0.000
#> GSM1179033 3 0.0000 0.948 0.000 0.000 1.000 0.000
#> GSM1179035 3 0.0000 0.948 0.000 0.000 1.000 0.000
#> GSM1179036 3 0.0188 0.946 0.000 0.000 0.996 0.004
#> GSM1178986 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM1178989 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM1178993 2 0.4543 0.656 0.000 0.676 0.000 0.324
#> GSM1178999 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM1179021 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM1179025 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM1179027 2 0.4477 0.670 0.000 0.688 0.000 0.312
#> GSM1179011 2 0.4585 0.647 0.000 0.668 0.000 0.332
#> GSM1179023 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM1179029 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM1179034 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM1179040 2 0.0336 0.927 0.000 0.992 0.000 0.008
#> GSM1178988 2 0.1389 0.898 0.000 0.952 0.048 0.000
#> GSM1179037 3 0.0000 0.948 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
#> GSM1178971 1 0.0898 0.929 0.972 0.000 0.000 0.008 0.020
#> GSM1178979 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM1179009 5 0.3018 0.706 0.080 0.000 0.020 0.024 0.876
#> GSM1179031 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM1178970 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM1178972 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM1178973 4 0.3949 0.488 0.000 0.000 0.000 0.668 0.332
#> GSM1178974 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM1178977 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM1178978 1 0.1557 0.916 0.940 0.000 0.000 0.008 0.052
#> GSM1178998 1 0.0798 0.930 0.976 0.000 0.000 0.008 0.016
#> GSM1179010 1 0.1764 0.907 0.928 0.000 0.000 0.008 0.064
#> GSM1179018 3 0.6540 0.363 0.076 0.000 0.568 0.064 0.292
#> GSM1179024 1 0.0451 0.931 0.988 0.000 0.004 0.000 0.008
#> GSM1178984 1 0.2707 0.843 0.860 0.000 0.000 0.008 0.132
#> GSM1178990 1 0.0162 0.933 0.996 0.000 0.000 0.000 0.004
#> GSM1178991 1 0.2196 0.890 0.916 0.000 0.004 0.056 0.024
#> GSM1178994 1 0.2660 0.846 0.864 0.000 0.000 0.008 0.128
#> GSM1178997 2 0.2536 0.851 0.000 0.868 0.000 0.128 0.004
#> GSM1179000 1 0.1278 0.920 0.960 0.000 0.004 0.020 0.016
#> GSM1179013 1 0.0000 0.934 1.000 0.000 0.000 0.000 0.000
#> GSM1179014 1 0.1653 0.910 0.944 0.000 0.004 0.028 0.024
#> GSM1179019 1 0.0000 0.934 1.000 0.000 0.000 0.000 0.000
#> GSM1179020 1 0.0000 0.934 1.000 0.000 0.000 0.000 0.000
#> GSM1179022 1 0.0000 0.934 1.000 0.000 0.000 0.000 0.000
#> GSM1179028 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM1179032 1 0.0000 0.934 1.000 0.000 0.000 0.000 0.000
#> GSM1179041 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM1179042 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM1178976 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM1178981 5 0.0794 0.736 0.028 0.000 0.000 0.000 0.972
#> GSM1178982 5 0.1831 0.658 0.000 0.000 0.004 0.076 0.920
#> GSM1178983 4 0.4306 0.192 0.000 0.000 0.000 0.508 0.492
#> GSM1178985 5 0.0794 0.736 0.028 0.000 0.000 0.000 0.972
#> GSM1178992 1 0.0566 0.932 0.984 0.000 0.004 0.000 0.012
#> GSM1179005 1 0.1484 0.917 0.944 0.000 0.000 0.008 0.048
#> GSM1179007 1 0.0992 0.928 0.968 0.000 0.000 0.008 0.024
#> GSM1179012 1 0.0162 0.933 0.996 0.000 0.000 0.000 0.004
#> GSM1179016 1 0.1471 0.915 0.952 0.000 0.004 0.024 0.020
#> GSM1179030 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM1179038 3 0.2703 0.810 0.060 0.000 0.896 0.024 0.020
#> GSM1178987 1 0.6730 0.124 0.520 0.000 0.124 0.036 0.320
#> GSM1179003 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM1179004 5 0.7409 0.135 0.344 0.000 0.252 0.032 0.372
#> GSM1179039 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM1178975 4 0.1965 0.799 0.000 0.096 0.000 0.904 0.000
#> GSM1178980 4 0.3274 0.702 0.000 0.220 0.000 0.780 0.000
#> GSM1178995 1 0.3157 0.863 0.872 0.000 0.052 0.016 0.060
#> GSM1178996 1 0.5637 0.419 0.604 0.000 0.324 0.028 0.044
#> GSM1179001 1 0.0898 0.929 0.972 0.000 0.000 0.008 0.020
#> GSM1179002 1 0.0992 0.928 0.968 0.000 0.000 0.008 0.024
#> GSM1179006 5 0.3968 0.656 0.040 0.000 0.120 0.024 0.816
#> GSM1179008 1 0.0898 0.929 0.972 0.000 0.000 0.008 0.020
#> GSM1179015 1 0.0000 0.934 1.000 0.000 0.000 0.000 0.000
#> GSM1179017 2 0.2228 0.908 0.000 0.916 0.056 0.020 0.008
#> GSM1179026 3 0.0324 0.894 0.000 0.000 0.992 0.004 0.004
#> GSM1179033 3 0.0898 0.888 0.000 0.000 0.972 0.008 0.020
#> GSM1179035 3 0.0404 0.894 0.000 0.000 0.988 0.000 0.012
#> GSM1179036 3 0.0451 0.895 0.000 0.000 0.988 0.008 0.004
#> GSM1178986 1 0.1990 0.902 0.928 0.000 0.004 0.028 0.040
#> GSM1178989 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM1178993 4 0.2020 0.801 0.000 0.100 0.000 0.900 0.000
#> GSM1178999 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM1179021 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM1179025 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM1179027 4 0.2516 0.783 0.000 0.140 0.000 0.860 0.000
#> GSM1179011 4 0.2020 0.801 0.000 0.100 0.000 0.900 0.000
#> GSM1179023 1 0.0000 0.934 1.000 0.000 0.000 0.000 0.000
#> GSM1179029 1 0.0727 0.928 0.980 0.000 0.004 0.004 0.012
#> GSM1179034 1 0.0000 0.934 1.000 0.000 0.000 0.000 0.000
#> GSM1179040 2 0.1410 0.927 0.000 0.940 0.000 0.060 0.000
#> GSM1178988 2 0.1569 0.936 0.000 0.944 0.044 0.008 0.004
#> GSM1179037 3 0.0324 0.895 0.000 0.000 0.992 0.004 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1178971 1 0.2020 0.8567 0.896 0.000 0.008 0.000 0.096 0.000
#> GSM1178979 2 0.0000 0.9551 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179009 3 0.6094 0.1578 0.184 0.000 0.576 0.000 0.192 0.048
#> GSM1179031 2 0.0000 0.9551 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178970 2 0.0405 0.9511 0.000 0.988 0.000 0.004 0.008 0.000
#> GSM1178972 2 0.0000 0.9551 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178973 4 0.4652 0.4370 0.000 0.000 0.288 0.640 0.072 0.000
#> GSM1178974 2 0.0000 0.9551 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178977 2 0.0000 0.9551 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178978 1 0.2711 0.8497 0.872 0.000 0.056 0.004 0.068 0.000
#> GSM1178998 1 0.1866 0.8585 0.908 0.000 0.008 0.000 0.084 0.000
#> GSM1179010 1 0.2651 0.8420 0.860 0.000 0.028 0.000 0.112 0.000
#> GSM1179018 5 0.7438 0.0000 0.060 0.000 0.148 0.048 0.384 0.360
#> GSM1179024 1 0.0790 0.8609 0.968 0.000 0.000 0.000 0.032 0.000
#> GSM1178984 1 0.4003 0.7620 0.760 0.000 0.116 0.000 0.124 0.000
#> GSM1178990 1 0.0713 0.8716 0.972 0.000 0.000 0.000 0.028 0.000
#> GSM1178991 1 0.3724 0.6360 0.716 0.000 0.000 0.012 0.268 0.004
#> GSM1178994 1 0.3469 0.8003 0.808 0.000 0.104 0.000 0.088 0.000
#> GSM1178997 2 0.3942 0.7595 0.000 0.784 0.012 0.084 0.120 0.000
#> GSM1179000 1 0.2278 0.8069 0.868 0.000 0.000 0.004 0.128 0.000
#> GSM1179013 1 0.0000 0.8701 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179014 1 0.2558 0.7815 0.840 0.000 0.000 0.004 0.156 0.000
#> GSM1179019 1 0.0146 0.8695 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM1179020 1 0.0260 0.8690 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM1179022 1 0.0000 0.8701 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179028 2 0.0000 0.9551 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179032 1 0.0000 0.8701 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179041 2 0.0000 0.9551 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179042 2 0.0000 0.9551 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178976 2 0.0405 0.9511 0.000 0.988 0.000 0.004 0.008 0.000
#> GSM1178981 3 0.1155 0.4741 0.004 0.000 0.956 0.000 0.036 0.004
#> GSM1178982 3 0.2322 0.4615 0.000 0.000 0.896 0.036 0.064 0.004
#> GSM1178983 3 0.4841 -0.0902 0.000 0.000 0.508 0.436 0.056 0.000
#> GSM1178985 3 0.0458 0.4803 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM1178992 1 0.0937 0.8715 0.960 0.000 0.000 0.000 0.040 0.000
#> GSM1179005 1 0.2651 0.8421 0.860 0.000 0.028 0.000 0.112 0.000
#> GSM1179007 1 0.2266 0.8495 0.880 0.000 0.012 0.000 0.108 0.000
#> GSM1179012 1 0.0547 0.8709 0.980 0.000 0.000 0.000 0.020 0.000
#> GSM1179016 1 0.2219 0.8007 0.864 0.000 0.000 0.000 0.136 0.000
#> GSM1179030 2 0.1418 0.9295 0.000 0.944 0.000 0.032 0.024 0.000
#> GSM1179038 6 0.4778 0.1988 0.060 0.000 0.012 0.000 0.276 0.652
#> GSM1178987 1 0.7380 -0.1963 0.376 0.000 0.240 0.000 0.256 0.128
#> GSM1179003 2 0.0000 0.9551 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179004 3 0.7674 -0.1961 0.216 0.000 0.308 0.000 0.260 0.216
#> GSM1179039 2 0.0000 0.9551 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178975 4 0.0858 0.8605 0.000 0.028 0.000 0.968 0.004 0.000
#> GSM1178980 4 0.2378 0.7247 0.000 0.152 0.000 0.848 0.000 0.000
#> GSM1178995 1 0.4644 0.7325 0.732 0.000 0.048 0.000 0.164 0.056
#> GSM1178996 1 0.6588 0.2581 0.496 0.000 0.044 0.004 0.244 0.212
#> GSM1179001 1 0.2118 0.8525 0.888 0.000 0.008 0.000 0.104 0.000
#> GSM1179002 1 0.2212 0.8501 0.880 0.000 0.008 0.000 0.112 0.000
#> GSM1179006 3 0.5857 0.2576 0.052 0.000 0.608 0.004 0.236 0.100
#> GSM1179008 1 0.2070 0.8538 0.892 0.000 0.008 0.000 0.100 0.000
#> GSM1179015 1 0.0000 0.8701 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179017 2 0.4324 0.7134 0.000 0.736 0.000 0.032 0.196 0.036
#> GSM1179026 6 0.1910 0.7086 0.000 0.000 0.000 0.000 0.108 0.892
#> GSM1179033 6 0.2822 0.6620 0.000 0.004 0.016 0.004 0.124 0.852
#> GSM1179035 6 0.1814 0.7166 0.000 0.000 0.000 0.000 0.100 0.900
#> GSM1179036 6 0.1838 0.7268 0.000 0.000 0.000 0.016 0.068 0.916
#> GSM1178986 1 0.3577 0.7171 0.772 0.000 0.016 0.012 0.200 0.000
#> GSM1178989 2 0.1124 0.9356 0.000 0.956 0.000 0.008 0.036 0.000
#> GSM1178993 4 0.0713 0.8616 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM1178999 2 0.0632 0.9448 0.000 0.976 0.000 0.024 0.000 0.000
#> GSM1179021 2 0.0363 0.9504 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM1179025 2 0.0000 0.9551 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179027 4 0.1204 0.8480 0.000 0.056 0.000 0.944 0.000 0.000
#> GSM1179011 4 0.0713 0.8616 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM1179023 1 0.0000 0.8701 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179029 1 0.0865 0.8593 0.964 0.000 0.000 0.000 0.036 0.000
#> GSM1179034 1 0.0000 0.8701 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179040 2 0.1957 0.8677 0.000 0.888 0.000 0.112 0.000 0.000
#> GSM1178988 2 0.3601 0.8163 0.000 0.816 0.000 0.016 0.100 0.068
#> GSM1179037 6 0.0547 0.7508 0.000 0.000 0.000 0.000 0.020 0.980
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) protocol(p) k
#> ATC:skmeans 73 0.12514 0.5398 2
#> ATC:skmeans 70 0.12743 0.0232 3
#> ATC:skmeans 70 0.05309 0.0639 4
#> ATC:skmeans 67 0.03753 0.2160 5
#> ATC:skmeans 61 0.00625 0.2839 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 31632 rows and 73 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.998 0.999 0.2985 0.703 0.703
#> 3 3 0.912 0.975 0.989 1.0349 0.663 0.530
#> 4 4 0.710 0.882 0.923 0.1197 0.916 0.790
#> 5 5 0.970 0.933 0.973 0.1283 0.821 0.512
#> 6 6 0.945 0.891 0.954 0.0298 0.974 0.889
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
#> GSM1178971 1 0.0000 0.999 1.000 0.000
#> GSM1178979 2 0.0000 1.000 0.000 1.000
#> GSM1179009 1 0.0000 0.999 1.000 0.000
#> GSM1179031 2 0.0000 1.000 0.000 1.000
#> GSM1178970 1 0.0672 0.993 0.992 0.008
#> GSM1178972 2 0.0000 1.000 0.000 1.000
#> GSM1178973 1 0.0000 0.999 1.000 0.000
#> GSM1178974 2 0.0000 1.000 0.000 1.000
#> GSM1178977 1 0.0672 0.993 0.992 0.008
#> GSM1178978 1 0.0000 0.999 1.000 0.000
#> GSM1178998 1 0.0000 0.999 1.000 0.000
#> GSM1179010 1 0.0000 0.999 1.000 0.000
#> GSM1179018 1 0.0000 0.999 1.000 0.000
#> GSM1179024 1 0.0000 0.999 1.000 0.000
#> GSM1178984 1 0.0000 0.999 1.000 0.000
#> GSM1178990 1 0.0000 0.999 1.000 0.000
#> GSM1178991 1 0.0000 0.999 1.000 0.000
#> GSM1178994 1 0.0000 0.999 1.000 0.000
#> GSM1178997 1 0.0000 0.999 1.000 0.000
#> GSM1179000 1 0.0000 0.999 1.000 0.000
#> GSM1179013 1 0.0000 0.999 1.000 0.000
#> GSM1179014 1 0.0000 0.999 1.000 0.000
#> GSM1179019 1 0.0000 0.999 1.000 0.000
#> GSM1179020 1 0.0000 0.999 1.000 0.000
#> GSM1179022 1 0.0000 0.999 1.000 0.000
#> GSM1179028 2 0.0000 1.000 0.000 1.000
#> GSM1179032 1 0.0000 0.999 1.000 0.000
#> GSM1179041 2 0.0000 1.000 0.000 1.000
#> GSM1179042 2 0.0000 1.000 0.000 1.000
#> GSM1178976 1 0.0672 0.993 0.992 0.008
#> GSM1178981 1 0.0000 0.999 1.000 0.000
#> GSM1178982 1 0.0000 0.999 1.000 0.000
#> GSM1178983 1 0.0000 0.999 1.000 0.000
#> GSM1178985 1 0.0000 0.999 1.000 0.000
#> GSM1178992 1 0.0000 0.999 1.000 0.000
#> GSM1179005 1 0.0000 0.999 1.000 0.000
#> GSM1179007 1 0.0000 0.999 1.000 0.000
#> GSM1179012 1 0.0000 0.999 1.000 0.000
#> GSM1179016 1 0.0000 0.999 1.000 0.000
#> GSM1179030 1 0.0672 0.993 0.992 0.008
#> GSM1179038 1 0.0000 0.999 1.000 0.000
#> GSM1178987 1 0.0000 0.999 1.000 0.000
#> GSM1179003 2 0.0000 1.000 0.000 1.000
#> GSM1179004 1 0.0000 0.999 1.000 0.000
#> GSM1179039 2 0.0000 1.000 0.000 1.000
#> GSM1178975 1 0.0000 0.999 1.000 0.000
#> GSM1178980 1 0.0672 0.993 0.992 0.008
#> GSM1178995 1 0.0000 0.999 1.000 0.000
#> GSM1178996 1 0.0000 0.999 1.000 0.000
#> GSM1179001 1 0.0000 0.999 1.000 0.000
#> GSM1179002 1 0.0000 0.999 1.000 0.000
#> GSM1179006 1 0.0000 0.999 1.000 0.000
#> GSM1179008 1 0.0000 0.999 1.000 0.000
#> GSM1179015 1 0.0000 0.999 1.000 0.000
#> GSM1179017 1 0.0672 0.993 0.992 0.008
#> GSM1179026 1 0.0000 0.999 1.000 0.000
#> GSM1179033 1 0.0000 0.999 1.000 0.000
#> GSM1179035 1 0.0000 0.999 1.000 0.000
#> GSM1179036 1 0.0000 0.999 1.000 0.000
#> GSM1178986 1 0.0000 0.999 1.000 0.000
#> GSM1178989 1 0.0672 0.993 0.992 0.008
#> GSM1178993 1 0.0672 0.993 0.992 0.008
#> GSM1178999 2 0.0000 1.000 0.000 1.000
#> GSM1179021 2 0.0000 1.000 0.000 1.000
#> GSM1179025 2 0.0000 1.000 0.000 1.000
#> GSM1179027 1 0.0672 0.993 0.992 0.008
#> GSM1179011 1 0.0672 0.993 0.992 0.008
#> GSM1179023 1 0.0000 0.999 1.000 0.000
#> GSM1179029 1 0.0000 0.999 1.000 0.000
#> GSM1179034 1 0.0000 0.999 1.000 0.000
#> GSM1179040 2 0.0000 1.000 0.000 1.000
#> GSM1178988 1 0.0000 0.999 1.000 0.000
#> GSM1179037 1 0.0000 0.999 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1178971 3 0.4002 0.821 0.160 0 0.840
#> GSM1178979 2 0.0000 1.000 0.000 1 0.000
#> GSM1179009 3 0.0000 0.981 0.000 0 1.000
#> GSM1179031 2 0.0000 1.000 0.000 1 0.000
#> GSM1178970 3 0.0000 0.981 0.000 0 1.000
#> GSM1178972 2 0.0000 1.000 0.000 1 0.000
#> GSM1178973 3 0.0000 0.981 0.000 0 1.000
#> GSM1178974 2 0.0000 1.000 0.000 1 0.000
#> GSM1178977 3 0.0000 0.981 0.000 0 1.000
#> GSM1178978 1 0.0000 0.989 1.000 0 0.000
#> GSM1178998 1 0.0000 0.989 1.000 0 0.000
#> GSM1179010 1 0.4121 0.756 0.832 0 0.168
#> GSM1179018 3 0.0000 0.981 0.000 0 1.000
#> GSM1179024 1 0.0000 0.989 1.000 0 0.000
#> GSM1178984 3 0.4002 0.821 0.160 0 0.840
#> GSM1178990 1 0.0000 0.989 1.000 0 0.000
#> GSM1178991 3 0.0000 0.981 0.000 0 1.000
#> GSM1178994 1 0.0000 0.989 1.000 0 0.000
#> GSM1178997 3 0.0000 0.981 0.000 0 1.000
#> GSM1179000 3 0.0000 0.981 0.000 0 1.000
#> GSM1179013 1 0.0000 0.989 1.000 0 0.000
#> GSM1179014 1 0.0237 0.984 0.996 0 0.004
#> GSM1179019 1 0.0000 0.989 1.000 0 0.000
#> GSM1179020 1 0.0000 0.989 1.000 0 0.000
#> GSM1179022 1 0.0000 0.989 1.000 0 0.000
#> GSM1179028 2 0.0000 1.000 0.000 1 0.000
#> GSM1179032 1 0.0000 0.989 1.000 0 0.000
#> GSM1179041 2 0.0000 1.000 0.000 1 0.000
#> GSM1179042 2 0.0000 1.000 0.000 1 0.000
#> GSM1178976 3 0.0000 0.981 0.000 0 1.000
#> GSM1178981 3 0.0000 0.981 0.000 0 1.000
#> GSM1178982 3 0.0000 0.981 0.000 0 1.000
#> GSM1178983 3 0.0000 0.981 0.000 0 1.000
#> GSM1178985 3 0.0000 0.981 0.000 0 1.000
#> GSM1178992 3 0.4002 0.821 0.160 0 0.840
#> GSM1179005 3 0.4002 0.821 0.160 0 0.840
#> GSM1179007 1 0.0000 0.989 1.000 0 0.000
#> GSM1179012 1 0.0000 0.989 1.000 0 0.000
#> GSM1179016 1 0.0000 0.989 1.000 0 0.000
#> GSM1179030 3 0.0000 0.981 0.000 0 1.000
#> GSM1179038 3 0.0000 0.981 0.000 0 1.000
#> GSM1178987 3 0.0000 0.981 0.000 0 1.000
#> GSM1179003 3 0.0000 0.981 0.000 0 1.000
#> GSM1179004 3 0.0000 0.981 0.000 0 1.000
#> GSM1179039 2 0.0000 1.000 0.000 1 0.000
#> GSM1178975 3 0.0000 0.981 0.000 0 1.000
#> GSM1178980 3 0.0000 0.981 0.000 0 1.000
#> GSM1178995 3 0.0000 0.981 0.000 0 1.000
#> GSM1178996 3 0.0000 0.981 0.000 0 1.000
#> GSM1179001 1 0.0000 0.989 1.000 0 0.000
#> GSM1179002 1 0.0000 0.989 1.000 0 0.000
#> GSM1179006 3 0.0000 0.981 0.000 0 1.000
#> GSM1179008 1 0.0000 0.989 1.000 0 0.000
#> GSM1179015 1 0.0000 0.989 1.000 0 0.000
#> GSM1179017 3 0.0000 0.981 0.000 0 1.000
#> GSM1179026 3 0.0000 0.981 0.000 0 1.000
#> GSM1179033 3 0.0000 0.981 0.000 0 1.000
#> GSM1179035 3 0.0000 0.981 0.000 0 1.000
#> GSM1179036 3 0.0000 0.981 0.000 0 1.000
#> GSM1178986 3 0.0000 0.981 0.000 0 1.000
#> GSM1178989 3 0.0000 0.981 0.000 0 1.000
#> GSM1178993 3 0.0000 0.981 0.000 0 1.000
#> GSM1178999 2 0.0000 1.000 0.000 1 0.000
#> GSM1179021 2 0.0000 1.000 0.000 1 0.000
#> GSM1179025 2 0.0000 1.000 0.000 1 0.000
#> GSM1179027 3 0.0000 0.981 0.000 0 1.000
#> GSM1179011 3 0.0000 0.981 0.000 0 1.000
#> GSM1179023 1 0.0000 0.989 1.000 0 0.000
#> GSM1179029 1 0.0000 0.989 1.000 0 0.000
#> GSM1179034 1 0.0000 0.989 1.000 0 0.000
#> GSM1179040 2 0.0000 1.000 0.000 1 0.000
#> GSM1178988 3 0.0000 0.981 0.000 0 1.000
#> GSM1179037 3 0.0000 0.981 0.000 0 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1178971 3 0.5948 0.678 0.160 0.000 0.696 0.144
#> GSM1178979 4 0.2973 0.779 0.000 0.144 0.000 0.856
#> GSM1179009 3 0.2868 0.853 0.000 0.000 0.864 0.136
#> GSM1179031 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM1178970 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1178972 2 0.0707 0.980 0.000 0.980 0.000 0.020
#> GSM1178973 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1178974 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM1178977 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1178978 1 0.2973 0.907 0.856 0.000 0.000 0.144
#> GSM1178998 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM1179010 1 0.3591 0.723 0.824 0.000 0.168 0.008
#> GSM1179018 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1179024 1 0.1118 0.912 0.964 0.000 0.000 0.036
#> GSM1178984 3 0.5948 0.678 0.160 0.000 0.696 0.144
#> GSM1178990 1 0.2973 0.907 0.856 0.000 0.000 0.144
#> GSM1178991 3 0.2973 0.848 0.000 0.000 0.856 0.144
#> GSM1178994 1 0.2973 0.907 0.856 0.000 0.000 0.144
#> GSM1178997 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1179000 3 0.2973 0.848 0.000 0.000 0.856 0.144
#> GSM1179013 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM1179014 1 0.3157 0.904 0.852 0.000 0.004 0.144
#> GSM1179019 1 0.2973 0.907 0.856 0.000 0.000 0.144
#> GSM1179020 1 0.2973 0.907 0.856 0.000 0.000 0.144
#> GSM1179022 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM1179028 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM1179032 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM1179041 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM1179042 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM1178976 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1178981 3 0.2973 0.848 0.000 0.000 0.856 0.144
#> GSM1178982 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1178983 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1178985 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1178992 3 0.5948 0.678 0.160 0.000 0.696 0.144
#> GSM1179005 3 0.5948 0.678 0.160 0.000 0.696 0.144
#> GSM1179007 1 0.2973 0.907 0.856 0.000 0.000 0.144
#> GSM1179012 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM1179016 1 0.2973 0.907 0.856 0.000 0.000 0.144
#> GSM1179030 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1179038 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1178987 3 0.2973 0.848 0.000 0.000 0.856 0.144
#> GSM1179003 4 0.2973 0.820 0.000 0.000 0.144 0.856
#> GSM1179004 3 0.2868 0.853 0.000 0.000 0.864 0.136
#> GSM1179039 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM1178975 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1178980 4 0.2973 0.820 0.000 0.000 0.144 0.856
#> GSM1178995 3 0.2216 0.876 0.000 0.000 0.908 0.092
#> GSM1178996 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1179001 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM1179002 1 0.2973 0.907 0.856 0.000 0.000 0.144
#> GSM1179006 3 0.0469 0.911 0.000 0.000 0.988 0.012
#> GSM1179008 1 0.2973 0.907 0.856 0.000 0.000 0.144
#> GSM1179015 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM1179017 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1179026 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1179033 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1179035 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1179036 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1178986 3 0.2973 0.848 0.000 0.000 0.856 0.144
#> GSM1178989 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1178993 4 0.4103 0.731 0.000 0.000 0.256 0.744
#> GSM1178999 4 0.2973 0.779 0.000 0.144 0.000 0.856
#> GSM1179021 4 0.3024 0.777 0.000 0.148 0.000 0.852
#> GSM1179025 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM1179027 4 0.3123 0.815 0.000 0.000 0.156 0.844
#> GSM1179011 4 0.4543 0.647 0.000 0.000 0.324 0.676
#> GSM1179023 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM1179029 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM1179034 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM1179040 4 0.2973 0.779 0.000 0.144 0.000 0.856
#> GSM1178988 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> GSM1179037 3 0.0000 0.915 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
#> GSM1178971 1 0.0000 0.961 1.000 0.000 0.000 0.000 0.000
#> GSM1178979 4 0.0000 0.894 0.000 0.000 0.000 1.000 0.000
#> GSM1179009 3 0.3857 0.549 0.312 0.000 0.688 0.000 0.000
#> GSM1179031 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM1178970 3 0.0000 0.967 0.000 0.000 1.000 0.000 0.000
#> GSM1178972 2 0.1043 0.962 0.000 0.960 0.000 0.040 0.000
#> GSM1178973 3 0.0000 0.967 0.000 0.000 1.000 0.000 0.000
#> GSM1178974 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM1178977 3 0.0000 0.967 0.000 0.000 1.000 0.000 0.000
#> GSM1178978 1 0.0000 0.961 1.000 0.000 0.000 0.000 0.000
#> GSM1178998 5 0.0000 0.995 0.000 0.000 0.000 0.000 1.000
#> GSM1179010 1 0.3730 0.586 0.712 0.000 0.000 0.000 0.288
#> GSM1179018 3 0.0000 0.967 0.000 0.000 1.000 0.000 0.000
#> GSM1179024 5 0.0963 0.952 0.036 0.000 0.000 0.000 0.964
#> GSM1178984 1 0.0000 0.961 1.000 0.000 0.000 0.000 0.000
#> GSM1178990 1 0.0000 0.961 1.000 0.000 0.000 0.000 0.000
#> GSM1178991 1 0.0404 0.953 0.988 0.000 0.012 0.000 0.000
#> GSM1178994 1 0.0000 0.961 1.000 0.000 0.000 0.000 0.000
#> GSM1178997 3 0.0000 0.967 0.000 0.000 1.000 0.000 0.000
#> GSM1179000 1 0.0703 0.943 0.976 0.000 0.024 0.000 0.000
#> GSM1179013 5 0.0000 0.995 0.000 0.000 0.000 0.000 1.000
#> GSM1179014 1 0.0000 0.961 1.000 0.000 0.000 0.000 0.000
#> GSM1179019 1 0.0510 0.952 0.984 0.000 0.000 0.000 0.016
#> GSM1179020 1 0.0609 0.949 0.980 0.000 0.000 0.000 0.020
#> GSM1179022 5 0.0000 0.995 0.000 0.000 0.000 0.000 1.000
#> GSM1179028 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM1179032 5 0.0000 0.995 0.000 0.000 0.000 0.000 1.000
#> GSM1179041 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM1179042 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM1178976 3 0.0000 0.967 0.000 0.000 1.000 0.000 0.000
#> GSM1178981 1 0.0000 0.961 1.000 0.000 0.000 0.000 0.000
#> GSM1178982 3 0.0000 0.967 0.000 0.000 1.000 0.000 0.000
#> GSM1178983 3 0.0000 0.967 0.000 0.000 1.000 0.000 0.000
#> GSM1178985 3 0.0000 0.967 0.000 0.000 1.000 0.000 0.000
#> GSM1178992 1 0.0000 0.961 1.000 0.000 0.000 0.000 0.000
#> GSM1179005 1 0.0000 0.961 1.000 0.000 0.000 0.000 0.000
#> GSM1179007 1 0.0000 0.961 1.000 0.000 0.000 0.000 0.000
#> GSM1179012 5 0.0000 0.995 0.000 0.000 0.000 0.000 1.000
#> GSM1179016 1 0.0000 0.961 1.000 0.000 0.000 0.000 0.000
#> GSM1179030 3 0.0000 0.967 0.000 0.000 1.000 0.000 0.000
#> GSM1179038 3 0.0000 0.967 0.000 0.000 1.000 0.000 0.000
#> GSM1178987 1 0.0794 0.939 0.972 0.000 0.028 0.000 0.000
#> GSM1179003 4 0.0000 0.894 0.000 0.000 0.000 1.000 0.000
#> GSM1179004 1 0.3661 0.600 0.724 0.000 0.276 0.000 0.000
#> GSM1179039 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM1178975 3 0.0000 0.967 0.000 0.000 1.000 0.000 0.000
#> GSM1178980 4 0.0000 0.894 0.000 0.000 0.000 1.000 0.000
#> GSM1178995 3 0.3586 0.622 0.264 0.000 0.736 0.000 0.000
#> GSM1178996 3 0.0000 0.967 0.000 0.000 1.000 0.000 0.000
#> GSM1179001 5 0.0000 0.995 0.000 0.000 0.000 0.000 1.000
#> GSM1179002 1 0.0000 0.961 1.000 0.000 0.000 0.000 0.000
#> GSM1179006 3 0.0609 0.946 0.020 0.000 0.980 0.000 0.000
#> GSM1179008 1 0.0000 0.961 1.000 0.000 0.000 0.000 0.000
#> GSM1179015 5 0.0000 0.995 0.000 0.000 0.000 0.000 1.000
#> GSM1179017 3 0.0000 0.967 0.000 0.000 1.000 0.000 0.000
#> GSM1179026 3 0.0000 0.967 0.000 0.000 1.000 0.000 0.000
#> GSM1179033 3 0.0000 0.967 0.000 0.000 1.000 0.000 0.000
#> GSM1179035 3 0.0000 0.967 0.000 0.000 1.000 0.000 0.000
#> GSM1179036 3 0.0000 0.967 0.000 0.000 1.000 0.000 0.000
#> GSM1178986 1 0.0000 0.961 1.000 0.000 0.000 0.000 0.000
#> GSM1178989 3 0.0000 0.967 0.000 0.000 1.000 0.000 0.000
#> GSM1178993 4 0.3534 0.672 0.000 0.000 0.256 0.744 0.000
#> GSM1178999 4 0.0000 0.894 0.000 0.000 0.000 1.000 0.000
#> GSM1179021 4 0.0290 0.890 0.000 0.008 0.000 0.992 0.000
#> GSM1179025 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM1179027 4 0.0703 0.881 0.000 0.000 0.024 0.976 0.000
#> GSM1179011 4 0.3913 0.583 0.000 0.000 0.324 0.676 0.000
#> GSM1179023 5 0.0000 0.995 0.000 0.000 0.000 0.000 1.000
#> GSM1179029 5 0.0000 0.995 0.000 0.000 0.000 0.000 1.000
#> GSM1179034 5 0.0000 0.995 0.000 0.000 0.000 0.000 1.000
#> GSM1179040 4 0.0000 0.894 0.000 0.000 0.000 1.000 0.000
#> GSM1178988 3 0.0000 0.967 0.000 0.000 1.000 0.000 0.000
#> GSM1179037 3 0.0000 0.967 0.000 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1178971 6 0.0547 0.9356 0.000 0.000 0.000 0.020 0.000 0.980
#> GSM1178979 5 0.0000 0.9142 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1179009 3 0.3464 0.5425 0.000 0.000 0.688 0.000 0.000 0.312
#> GSM1179031 2 0.0000 0.9259 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178970 3 0.3076 0.6684 0.000 0.000 0.760 0.000 0.240 0.000
#> GSM1178972 5 0.3151 0.6192 0.000 0.252 0.000 0.000 0.748 0.000
#> GSM1178973 3 0.2912 0.7068 0.000 0.000 0.784 0.216 0.000 0.000
#> GSM1178974 2 0.0000 0.9259 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178977 3 0.0000 0.9433 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1178978 6 0.0632 0.9348 0.000 0.000 0.000 0.024 0.000 0.976
#> GSM1178998 1 0.0000 0.9895 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179010 6 0.3351 0.5761 0.288 0.000 0.000 0.000 0.000 0.712
#> GSM1179018 3 0.0000 0.9433 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1179024 1 0.1492 0.9253 0.940 0.000 0.000 0.024 0.000 0.036
#> GSM1178984 6 0.0000 0.9370 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1178990 6 0.0000 0.9370 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1178991 6 0.3076 0.7097 0.000 0.000 0.000 0.240 0.000 0.760
#> GSM1178994 6 0.0000 0.9370 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1178997 3 0.0000 0.9433 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1179000 6 0.1257 0.9217 0.000 0.000 0.028 0.020 0.000 0.952
#> GSM1179013 1 0.0000 0.9895 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179014 6 0.0632 0.9348 0.000 0.000 0.000 0.024 0.000 0.976
#> GSM1179019 6 0.1088 0.9290 0.016 0.000 0.000 0.024 0.000 0.960
#> GSM1179020 6 0.1176 0.9267 0.020 0.000 0.000 0.024 0.000 0.956
#> GSM1179022 1 0.0000 0.9895 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179028 2 0.0000 0.9259 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179032 1 0.0000 0.9895 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179041 2 0.0000 0.9259 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179042 2 0.0000 0.9259 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178976 3 0.0000 0.9433 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1178981 6 0.0632 0.9276 0.000 0.000 0.024 0.000 0.000 0.976
#> GSM1178982 3 0.0000 0.9433 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1178983 3 0.0000 0.9433 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1178985 3 0.0000 0.9433 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1178992 6 0.0000 0.9370 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1179005 6 0.0000 0.9370 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1179007 6 0.0000 0.9370 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1179012 1 0.0000 0.9895 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179016 6 0.0632 0.9348 0.000 0.000 0.000 0.024 0.000 0.976
#> GSM1179030 3 0.0000 0.9433 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1179038 3 0.0000 0.9433 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1178987 6 0.1141 0.9032 0.000 0.000 0.052 0.000 0.000 0.948
#> GSM1179003 5 0.0000 0.9142 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1179004 6 0.3390 0.5598 0.000 0.000 0.296 0.000 0.000 0.704
#> GSM1179039 2 0.0000 0.9259 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178975 4 0.0632 0.8962 0.000 0.000 0.024 0.976 0.000 0.000
#> GSM1178980 4 0.0632 0.9241 0.000 0.000 0.000 0.976 0.024 0.000
#> GSM1178995 3 0.3221 0.6161 0.000 0.000 0.736 0.000 0.000 0.264
#> GSM1178996 3 0.0000 0.9433 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1179001 1 0.0632 0.9698 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM1179002 6 0.0000 0.9370 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1179006 3 0.0547 0.9258 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM1179008 6 0.0000 0.9370 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1179015 1 0.0000 0.9895 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179017 3 0.0146 0.9406 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM1179026 3 0.0000 0.9433 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1179033 3 0.0000 0.9433 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1179035 3 0.0000 0.9433 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1179036 3 0.0000 0.9433 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1178986 6 0.0692 0.9353 0.000 0.000 0.004 0.020 0.000 0.976
#> GSM1178989 3 0.0000 0.9433 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1178993 4 0.0632 0.9241 0.000 0.000 0.000 0.976 0.024 0.000
#> GSM1178999 5 0.0000 0.9142 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1179021 2 0.3862 0.0751 0.000 0.524 0.000 0.000 0.476 0.000
#> GSM1179025 2 0.0000 0.9259 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179027 4 0.3076 0.6851 0.000 0.000 0.000 0.760 0.240 0.000
#> GSM1179011 4 0.0632 0.9241 0.000 0.000 0.000 0.976 0.024 0.000
#> GSM1179023 1 0.0000 0.9895 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179029 1 0.0146 0.9870 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM1179034 1 0.0000 0.9895 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1179040 5 0.0363 0.9063 0.000 0.000 0.000 0.012 0.988 0.000
#> GSM1178988 3 0.0000 0.9433 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1179037 3 0.0000 0.9433 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) protocol(p) k
#> ATC:pam 73 0.3086 1.41e-02 2
#> ATC:pam 73 0.2633 5.02e-03 3
#> ATC:pam 73 0.0186 1.89e-04 4
#> ATC:pam 73 0.0115 7.46e-06 5
#> ATC:pam 72 0.1209 2.05e-04 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "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 31632 rows and 73 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.941 0.954 0.977 0.4747 0.521 0.521
#> 3 3 1.000 0.972 0.980 -0.0892 0.747 0.624
#> 4 4 0.694 0.849 0.898 0.2224 0.924 0.868
#> 5 5 0.553 0.443 0.703 0.3003 0.759 0.519
#> 6 6 0.535 0.574 0.724 0.0719 0.785 0.410
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
#> GSM1178971 1 0.0000 0.987 1.000 0.000
#> GSM1178979 2 0.0000 0.959 0.000 1.000
#> GSM1179009 2 0.8386 0.671 0.268 0.732
#> GSM1179031 2 0.0000 0.959 0.000 1.000
#> GSM1178970 2 0.0000 0.959 0.000 1.000
#> GSM1178972 2 0.0000 0.959 0.000 1.000
#> GSM1178973 2 0.0000 0.959 0.000 1.000
#> GSM1178974 2 0.0000 0.959 0.000 1.000
#> GSM1178977 1 0.7815 0.710 0.768 0.232
#> GSM1178978 1 0.0000 0.987 1.000 0.000
#> GSM1178998 1 0.0000 0.987 1.000 0.000
#> GSM1179010 1 0.0000 0.987 1.000 0.000
#> GSM1179018 1 0.1414 0.972 0.980 0.020
#> GSM1179024 1 0.3274 0.936 0.940 0.060
#> GSM1178984 1 0.0000 0.987 1.000 0.000
#> GSM1178990 1 0.0000 0.987 1.000 0.000
#> GSM1178991 2 0.5737 0.852 0.136 0.864
#> GSM1178994 1 0.0000 0.987 1.000 0.000
#> GSM1178997 1 0.1414 0.972 0.980 0.020
#> GSM1179000 1 0.0376 0.984 0.996 0.004
#> GSM1179013 1 0.0000 0.987 1.000 0.000
#> GSM1179014 1 0.3584 0.928 0.932 0.068
#> GSM1179019 1 0.0000 0.987 1.000 0.000
#> GSM1179020 1 0.0000 0.987 1.000 0.000
#> GSM1179022 1 0.0000 0.987 1.000 0.000
#> GSM1179028 2 0.0000 0.959 0.000 1.000
#> GSM1179032 1 0.0000 0.987 1.000 0.000
#> GSM1179041 2 0.0000 0.959 0.000 1.000
#> GSM1179042 2 0.0000 0.959 0.000 1.000
#> GSM1178976 2 0.0000 0.959 0.000 1.000
#> GSM1178981 1 0.0000 0.987 1.000 0.000
#> GSM1178982 1 0.0000 0.987 1.000 0.000
#> GSM1178983 2 0.4298 0.896 0.088 0.912
#> GSM1178985 1 0.0000 0.987 1.000 0.000
#> GSM1178992 1 0.0000 0.987 1.000 0.000
#> GSM1179005 1 0.0000 0.987 1.000 0.000
#> GSM1179007 1 0.0000 0.987 1.000 0.000
#> GSM1179012 1 0.0000 0.987 1.000 0.000
#> GSM1179016 2 0.9000 0.581 0.316 0.684
#> GSM1179030 2 0.5519 0.862 0.128 0.872
#> GSM1179038 1 0.3274 0.936 0.940 0.060
#> GSM1178987 1 0.0000 0.987 1.000 0.000
#> GSM1179003 2 0.0000 0.959 0.000 1.000
#> GSM1179004 1 0.0000 0.987 1.000 0.000
#> GSM1179039 2 0.0000 0.959 0.000 1.000
#> GSM1178975 2 0.0000 0.959 0.000 1.000
#> GSM1178980 2 0.0000 0.959 0.000 1.000
#> GSM1178995 1 0.0000 0.987 1.000 0.000
#> GSM1178996 1 0.0000 0.987 1.000 0.000
#> GSM1179001 1 0.0000 0.987 1.000 0.000
#> GSM1179002 1 0.0000 0.987 1.000 0.000
#> GSM1179006 1 0.0000 0.987 1.000 0.000
#> GSM1179008 1 0.0000 0.987 1.000 0.000
#> GSM1179015 1 0.0376 0.984 0.996 0.004
#> GSM1179017 2 0.5842 0.848 0.140 0.860
#> GSM1179026 1 0.0000 0.987 1.000 0.000
#> GSM1179033 1 0.0000 0.987 1.000 0.000
#> GSM1179035 1 0.0000 0.987 1.000 0.000
#> GSM1179036 1 0.0000 0.987 1.000 0.000
#> GSM1178986 1 0.2236 0.959 0.964 0.036
#> GSM1178989 2 0.0000 0.959 0.000 1.000
#> GSM1178993 2 0.0000 0.959 0.000 1.000
#> GSM1178999 2 0.0000 0.959 0.000 1.000
#> GSM1179021 2 0.0000 0.959 0.000 1.000
#> GSM1179025 2 0.0000 0.959 0.000 1.000
#> GSM1179027 2 0.0000 0.959 0.000 1.000
#> GSM1179011 2 0.0000 0.959 0.000 1.000
#> GSM1179023 1 0.0000 0.987 1.000 0.000
#> GSM1179029 1 0.3431 0.932 0.936 0.064
#> GSM1179034 1 0.0376 0.984 0.996 0.004
#> GSM1179040 2 0.0000 0.959 0.000 1.000
#> GSM1178988 1 0.0000 0.987 1.000 0.000
#> GSM1179037 1 0.0000 0.987 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1178971 1 0.0000 0.987 1.000 0.000 0.000
#> GSM1178979 1 0.4035 0.885 0.880 0.080 0.040
#> GSM1179009 1 0.0983 0.983 0.980 0.004 0.016
#> GSM1179031 2 0.0000 0.959 0.000 1.000 0.000
#> GSM1178970 2 0.5173 0.683 0.148 0.816 0.036
#> GSM1178972 2 0.1529 0.927 0.000 0.960 0.040
#> GSM1178973 3 0.1289 0.980 0.000 0.032 0.968
#> GSM1178974 2 0.0000 0.959 0.000 1.000 0.000
#> GSM1178977 1 0.2383 0.947 0.940 0.016 0.044
#> GSM1178978 1 0.0000 0.987 1.000 0.000 0.000
#> GSM1178998 1 0.0237 0.986 0.996 0.000 0.004
#> GSM1179010 1 0.0000 0.987 1.000 0.000 0.000
#> GSM1179018 1 0.0983 0.984 0.980 0.004 0.016
#> GSM1179024 1 0.1031 0.982 0.976 0.000 0.024
#> GSM1178984 1 0.0000 0.987 1.000 0.000 0.000
#> GSM1178990 1 0.0747 0.985 0.984 0.000 0.016
#> GSM1178991 1 0.1643 0.969 0.956 0.000 0.044
#> GSM1178994 1 0.0000 0.987 1.000 0.000 0.000
#> GSM1178997 1 0.0747 0.985 0.984 0.000 0.016
#> GSM1179000 1 0.0747 0.985 0.984 0.000 0.016
#> GSM1179013 1 0.0237 0.986 0.996 0.000 0.004
#> GSM1179014 1 0.1031 0.982 0.976 0.000 0.024
#> GSM1179019 1 0.0237 0.986 0.996 0.000 0.004
#> GSM1179020 1 0.0747 0.985 0.984 0.000 0.016
#> GSM1179022 1 0.0237 0.986 0.996 0.000 0.004
#> GSM1179028 2 0.0000 0.959 0.000 1.000 0.000
#> GSM1179032 1 0.0592 0.986 0.988 0.000 0.012
#> GSM1179041 2 0.0000 0.959 0.000 1.000 0.000
#> GSM1179042 2 0.0000 0.959 0.000 1.000 0.000
#> GSM1178976 2 0.0661 0.951 0.004 0.988 0.008
#> GSM1178981 1 0.0000 0.987 1.000 0.000 0.000
#> GSM1178982 1 0.0592 0.985 0.988 0.000 0.012
#> GSM1178983 1 0.2550 0.944 0.936 0.024 0.040
#> GSM1178985 1 0.0000 0.987 1.000 0.000 0.000
#> GSM1178992 1 0.0000 0.987 1.000 0.000 0.000
#> GSM1179005 1 0.0000 0.987 1.000 0.000 0.000
#> GSM1179007 1 0.0000 0.987 1.000 0.000 0.000
#> GSM1179012 1 0.0237 0.986 0.996 0.000 0.004
#> GSM1179016 1 0.1031 0.982 0.976 0.000 0.024
#> GSM1179030 1 0.1182 0.980 0.976 0.012 0.012
#> GSM1179038 1 0.0983 0.984 0.980 0.004 0.016
#> GSM1178987 1 0.0000 0.987 1.000 0.000 0.000
#> GSM1179003 1 0.2681 0.940 0.932 0.028 0.040
#> GSM1179004 1 0.0000 0.987 1.000 0.000 0.000
#> GSM1179039 2 0.0000 0.959 0.000 1.000 0.000
#> GSM1178975 3 0.1031 0.977 0.000 0.024 0.976
#> GSM1178980 3 0.1031 0.977 0.000 0.024 0.976
#> GSM1178995 1 0.0000 0.987 1.000 0.000 0.000
#> GSM1178996 1 0.0000 0.987 1.000 0.000 0.000
#> GSM1179001 1 0.0237 0.986 0.996 0.000 0.004
#> GSM1179002 1 0.0000 0.987 1.000 0.000 0.000
#> GSM1179006 1 0.0000 0.987 1.000 0.000 0.000
#> GSM1179008 1 0.0237 0.986 0.996 0.000 0.004
#> GSM1179015 1 0.0424 0.986 0.992 0.000 0.008
#> GSM1179017 1 0.1031 0.982 0.976 0.000 0.024
#> GSM1179026 1 0.0000 0.987 1.000 0.000 0.000
#> GSM1179033 1 0.0000 0.987 1.000 0.000 0.000
#> GSM1179035 1 0.0592 0.985 0.988 0.000 0.012
#> GSM1179036 1 0.0592 0.985 0.988 0.000 0.012
#> GSM1178986 1 0.0747 0.985 0.984 0.000 0.016
#> GSM1178989 1 0.3267 0.921 0.912 0.044 0.044
#> GSM1178993 3 0.1289 0.980 0.000 0.032 0.968
#> GSM1178999 3 0.1289 0.976 0.000 0.032 0.968
#> GSM1179021 3 0.2625 0.953 0.000 0.084 0.916
#> GSM1179025 2 0.0000 0.959 0.000 1.000 0.000
#> GSM1179027 3 0.2165 0.966 0.000 0.064 0.936
#> GSM1179011 3 0.1289 0.980 0.000 0.032 0.968
#> GSM1179023 1 0.0237 0.986 0.996 0.000 0.004
#> GSM1179029 1 0.1031 0.982 0.976 0.000 0.024
#> GSM1179034 1 0.1031 0.982 0.976 0.000 0.024
#> GSM1179040 3 0.2165 0.966 0.000 0.064 0.936
#> GSM1178988 1 0.0424 0.986 0.992 0.000 0.008
#> GSM1179037 1 0.0424 0.986 0.992 0.000 0.008
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1178971 3 0.0000 0.9069 0.000 0.000 1.000 0.000
#> GSM1178979 3 0.2868 0.7908 0.136 0.000 0.864 0.000
#> GSM1179009 3 0.2345 0.8189 0.100 0.000 0.900 0.000
#> GSM1179031 2 0.0000 0.9300 0.000 1.000 0.000 0.000
#> GSM1178970 2 0.5204 0.5994 0.088 0.752 0.160 0.000
#> GSM1178972 2 0.2149 0.8972 0.088 0.912 0.000 0.000
#> GSM1178973 4 0.0000 0.9787 0.000 0.000 0.000 1.000
#> GSM1178974 2 0.2149 0.8972 0.088 0.912 0.000 0.000
#> GSM1178977 3 0.0000 0.9069 0.000 0.000 1.000 0.000
#> GSM1178978 3 0.0336 0.9061 0.008 0.000 0.992 0.000
#> GSM1178998 3 0.0921 0.9016 0.028 0.000 0.972 0.000
#> GSM1179010 3 0.0188 0.9066 0.004 0.000 0.996 0.000
#> GSM1179018 3 0.1022 0.8944 0.032 0.000 0.968 0.000
#> GSM1179024 3 0.3688 0.7618 0.208 0.000 0.792 0.000
#> GSM1178984 3 0.0000 0.9069 0.000 0.000 1.000 0.000
#> GSM1178990 3 0.2921 0.8243 0.140 0.000 0.860 0.000
#> GSM1178991 1 0.5478 0.1958 0.540 0.000 0.444 0.016
#> GSM1178994 3 0.0000 0.9069 0.000 0.000 1.000 0.000
#> GSM1178997 3 0.1211 0.8897 0.040 0.000 0.960 0.000
#> GSM1179000 3 0.1022 0.9011 0.032 0.000 0.968 0.000
#> GSM1179013 3 0.3074 0.8144 0.152 0.000 0.848 0.000
#> GSM1179014 1 0.3837 0.6388 0.776 0.000 0.224 0.000
#> GSM1179019 3 0.0469 0.9053 0.012 0.000 0.988 0.000
#> GSM1179020 3 0.3400 0.7943 0.180 0.000 0.820 0.000
#> GSM1179022 3 0.3074 0.8144 0.152 0.000 0.848 0.000
#> GSM1179028 2 0.0000 0.9300 0.000 1.000 0.000 0.000
#> GSM1179032 3 0.3074 0.8144 0.152 0.000 0.848 0.000
#> GSM1179041 2 0.0000 0.9300 0.000 1.000 0.000 0.000
#> GSM1179042 2 0.0000 0.9300 0.000 1.000 0.000 0.000
#> GSM1178976 2 0.2149 0.8972 0.088 0.912 0.000 0.000
#> GSM1178981 3 0.0000 0.9069 0.000 0.000 1.000 0.000
#> GSM1178982 3 0.0188 0.9061 0.004 0.000 0.996 0.000
#> GSM1178983 3 0.1389 0.8852 0.048 0.000 0.952 0.000
#> GSM1178985 3 0.0000 0.9069 0.000 0.000 1.000 0.000
#> GSM1178992 3 0.2921 0.8243 0.140 0.000 0.860 0.000
#> GSM1179005 3 0.0000 0.9069 0.000 0.000 1.000 0.000
#> GSM1179007 3 0.0000 0.9069 0.000 0.000 1.000 0.000
#> GSM1179012 3 0.3074 0.8144 0.152 0.000 0.848 0.000
#> GSM1179016 1 0.2530 0.5956 0.888 0.000 0.112 0.000
#> GSM1179030 3 0.1389 0.8853 0.048 0.000 0.952 0.000
#> GSM1179038 3 0.3024 0.8302 0.148 0.000 0.852 0.000
#> GSM1178987 3 0.0000 0.9069 0.000 0.000 1.000 0.000
#> GSM1179003 3 0.2868 0.7908 0.136 0.000 0.864 0.000
#> GSM1179004 3 0.0000 0.9069 0.000 0.000 1.000 0.000
#> GSM1179039 2 0.0000 0.9300 0.000 1.000 0.000 0.000
#> GSM1178975 4 0.0000 0.9787 0.000 0.000 0.000 1.000
#> GSM1178980 4 0.0000 0.9787 0.000 0.000 0.000 1.000
#> GSM1178995 3 0.0000 0.9069 0.000 0.000 1.000 0.000
#> GSM1178996 3 0.0000 0.9069 0.000 0.000 1.000 0.000
#> GSM1179001 3 0.2589 0.8463 0.116 0.000 0.884 0.000
#> GSM1179002 3 0.0336 0.9061 0.008 0.000 0.992 0.000
#> GSM1179006 3 0.0000 0.9069 0.000 0.000 1.000 0.000
#> GSM1179008 3 0.0469 0.9056 0.012 0.000 0.988 0.000
#> GSM1179015 3 0.3074 0.8144 0.152 0.000 0.848 0.000
#> GSM1179017 1 0.0469 0.4735 0.988 0.000 0.012 0.000
#> GSM1179026 3 0.0188 0.9069 0.004 0.000 0.996 0.000
#> GSM1179033 3 0.0000 0.9069 0.000 0.000 1.000 0.000
#> GSM1179035 3 0.0000 0.9069 0.000 0.000 1.000 0.000
#> GSM1179036 3 0.0707 0.9001 0.020 0.000 0.980 0.000
#> GSM1178986 3 0.3486 0.7872 0.188 0.000 0.812 0.000
#> GSM1178989 3 0.3149 0.7917 0.088 0.032 0.880 0.000
#> GSM1178993 4 0.0000 0.9787 0.000 0.000 0.000 1.000
#> GSM1178999 4 0.2149 0.9020 0.088 0.000 0.000 0.912
#> GSM1179021 4 0.1637 0.9322 0.060 0.000 0.000 0.940
#> GSM1179025 2 0.0000 0.9300 0.000 1.000 0.000 0.000
#> GSM1179027 4 0.0000 0.9787 0.000 0.000 0.000 1.000
#> GSM1179011 4 0.0000 0.9787 0.000 0.000 0.000 1.000
#> GSM1179023 3 0.3074 0.8144 0.152 0.000 0.848 0.000
#> GSM1179029 3 0.4977 -0.0331 0.460 0.000 0.540 0.000
#> GSM1179034 3 0.3400 0.7943 0.180 0.000 0.820 0.000
#> GSM1179040 4 0.0000 0.9787 0.000 0.000 0.000 1.000
#> GSM1178988 3 0.0000 0.9069 0.000 0.000 1.000 0.000
#> GSM1179037 3 0.0000 0.9069 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
#> GSM1178971 3 0.4138 0.51031 0.384 0.000 0.616 0.000 0.000
#> GSM1178979 3 0.3877 0.16943 0.024 0.000 0.764 0.000 0.212
#> GSM1179009 3 0.6589 0.36655 0.364 0.000 0.424 0.000 0.212
#> GSM1179031 2 0.0000 0.87055 0.000 1.000 0.000 0.000 0.000
#> GSM1178970 2 0.5537 0.63286 0.036 0.684 0.068 0.000 0.212
#> GSM1178972 2 0.3109 0.78254 0.000 0.800 0.000 0.000 0.200
#> GSM1178973 4 0.0000 0.93500 0.000 0.000 0.000 1.000 0.000
#> GSM1178974 2 0.3210 0.77228 0.000 0.788 0.000 0.000 0.212
#> GSM1178977 1 0.4440 -0.07780 0.528 0.000 0.468 0.000 0.004
#> GSM1178978 3 0.4227 0.46615 0.420 0.000 0.580 0.000 0.000
#> GSM1178998 1 0.4046 0.19873 0.696 0.000 0.296 0.000 0.008
#> GSM1179010 3 0.4210 0.47999 0.412 0.000 0.588 0.000 0.000
#> GSM1179018 3 0.3999 0.22069 0.344 0.000 0.656 0.000 0.000
#> GSM1179024 1 0.3276 0.40901 0.836 0.000 0.132 0.000 0.032
#> GSM1178984 3 0.4101 0.51633 0.372 0.000 0.628 0.000 0.000
#> GSM1178990 1 0.1197 0.50288 0.952 0.000 0.048 0.000 0.000
#> GSM1178991 5 0.6599 0.52107 0.272 0.000 0.264 0.000 0.464
#> GSM1178994 3 0.4341 0.47481 0.404 0.000 0.592 0.000 0.004
#> GSM1178997 3 0.4273 0.11411 0.448 0.000 0.552 0.000 0.000
#> GSM1179000 1 0.4219 0.01974 0.584 0.000 0.416 0.000 0.000
#> GSM1179013 1 0.0451 0.50884 0.988 0.000 0.004 0.000 0.008
#> GSM1179014 5 0.3115 0.65910 0.112 0.000 0.036 0.000 0.852
#> GSM1179019 1 0.4306 -0.34498 0.508 0.000 0.492 0.000 0.000
#> GSM1179020 1 0.1410 0.49181 0.940 0.000 0.060 0.000 0.000
#> GSM1179022 1 0.1484 0.48292 0.944 0.000 0.048 0.000 0.008
#> GSM1179028 2 0.0000 0.87055 0.000 1.000 0.000 0.000 0.000
#> GSM1179032 1 0.0404 0.50876 0.988 0.000 0.012 0.000 0.000
#> GSM1179041 2 0.0000 0.87055 0.000 1.000 0.000 0.000 0.000
#> GSM1179042 2 0.0000 0.87055 0.000 1.000 0.000 0.000 0.000
#> GSM1178976 2 0.3596 0.76413 0.000 0.776 0.012 0.000 0.212
#> GSM1178981 3 0.4497 0.51840 0.352 0.000 0.632 0.000 0.016
#> GSM1178982 1 0.4306 -0.10267 0.508 0.000 0.492 0.000 0.000
#> GSM1178983 3 0.3561 0.24768 0.260 0.000 0.740 0.000 0.000
#> GSM1178985 3 0.4511 0.51706 0.356 0.000 0.628 0.000 0.016
#> GSM1178992 1 0.0703 0.50797 0.976 0.000 0.024 0.000 0.000
#> GSM1179005 3 0.4114 0.51521 0.376 0.000 0.624 0.000 0.000
#> GSM1179007 3 0.4201 0.48560 0.408 0.000 0.592 0.000 0.000
#> GSM1179012 1 0.0579 0.50613 0.984 0.000 0.008 0.000 0.008
#> GSM1179016 5 0.1893 0.64107 0.048 0.000 0.024 0.000 0.928
#> GSM1179030 3 0.3480 0.24360 0.248 0.000 0.752 0.000 0.000
#> GSM1179038 1 0.4219 0.00552 0.584 0.000 0.416 0.000 0.000
#> GSM1178987 1 0.4682 -0.05250 0.564 0.000 0.420 0.000 0.016
#> GSM1179003 3 0.3929 0.17425 0.028 0.000 0.764 0.000 0.208
#> GSM1179004 1 0.4738 -0.17979 0.520 0.000 0.464 0.000 0.016
#> GSM1179039 2 0.0000 0.87055 0.000 1.000 0.000 0.000 0.000
#> GSM1178975 4 0.0000 0.93500 0.000 0.000 0.000 1.000 0.000
#> GSM1178980 4 0.0000 0.93500 0.000 0.000 0.000 1.000 0.000
#> GSM1178995 3 0.4497 0.51840 0.352 0.000 0.632 0.000 0.016
#> GSM1178996 1 0.4235 -0.05010 0.576 0.000 0.424 0.000 0.000
#> GSM1179001 1 0.2077 0.44958 0.908 0.000 0.084 0.000 0.008
#> GSM1179002 3 0.4249 0.44194 0.432 0.000 0.568 0.000 0.000
#> GSM1179006 1 0.4375 -0.03081 0.576 0.000 0.420 0.000 0.004
#> GSM1179008 1 0.2648 0.41516 0.848 0.000 0.152 0.000 0.000
#> GSM1179015 1 0.0771 0.50439 0.976 0.000 0.004 0.000 0.020
#> GSM1179017 5 0.0807 0.61042 0.012 0.000 0.012 0.000 0.976
#> GSM1179026 1 0.4451 0.16257 0.644 0.000 0.340 0.000 0.016
#> GSM1179033 1 0.4689 -0.05579 0.560 0.000 0.424 0.000 0.016
#> GSM1179035 1 0.4256 -0.03692 0.564 0.000 0.436 0.000 0.000
#> GSM1179036 3 0.4210 0.15948 0.412 0.000 0.588 0.000 0.000
#> GSM1178986 1 0.2563 0.44487 0.872 0.000 0.120 0.000 0.008
#> GSM1178989 3 0.8205 0.30864 0.168 0.208 0.412 0.000 0.212
#> GSM1178993 4 0.0000 0.93500 0.000 0.000 0.000 1.000 0.000
#> GSM1178999 4 0.3757 0.70246 0.000 0.000 0.020 0.772 0.208
#> GSM1179021 4 0.3209 0.75412 0.000 0.000 0.008 0.812 0.180
#> GSM1179025 2 0.0000 0.87055 0.000 1.000 0.000 0.000 0.000
#> GSM1179027 4 0.0000 0.93500 0.000 0.000 0.000 1.000 0.000
#> GSM1179011 4 0.0000 0.93500 0.000 0.000 0.000 1.000 0.000
#> GSM1179023 1 0.1764 0.47026 0.928 0.000 0.064 0.000 0.008
#> GSM1179029 5 0.5509 0.23624 0.468 0.000 0.064 0.000 0.468
#> GSM1179034 1 0.1197 0.49763 0.952 0.000 0.048 0.000 0.000
#> GSM1179040 4 0.0162 0.93276 0.000 0.000 0.000 0.996 0.004
#> GSM1178988 1 0.4300 -0.06566 0.524 0.000 0.476 0.000 0.000
#> GSM1179037 1 0.4538 -0.05056 0.540 0.000 0.452 0.000 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1178971 3 0.0363 0.6862 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM1178979 6 0.7792 0.5099 0.300 0.000 0.196 0.008 0.188 0.308
#> GSM1179009 3 0.6580 0.2229 0.072 0.000 0.552 0.008 0.180 0.188
#> GSM1179031 2 0.0000 0.8258 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178970 2 0.6281 0.5097 0.004 0.596 0.168 0.008 0.172 0.052
#> GSM1178972 2 0.3495 0.6962 0.000 0.792 0.000 0.008 0.172 0.028
#> GSM1178973 4 0.0000 0.9289 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1178974 2 0.5770 0.5088 0.004 0.564 0.000 0.008 0.172 0.252
#> GSM1178977 3 0.4642 0.5381 0.040 0.000 0.648 0.008 0.004 0.300
#> GSM1178978 3 0.1334 0.6818 0.032 0.000 0.948 0.000 0.000 0.020
#> GSM1178998 3 0.3833 -0.0955 0.444 0.000 0.556 0.000 0.000 0.000
#> GSM1179010 3 0.1003 0.6860 0.020 0.000 0.964 0.000 0.000 0.016
#> GSM1179018 6 0.6095 0.6393 0.292 0.000 0.324 0.000 0.000 0.384
#> GSM1179024 1 0.4426 0.5580 0.748 0.000 0.156 0.000 0.064 0.032
#> GSM1178984 3 0.0858 0.6834 0.004 0.000 0.968 0.000 0.000 0.028
#> GSM1178990 1 0.4436 0.5763 0.636 0.000 0.324 0.000 0.004 0.036
#> GSM1178991 1 0.5289 -0.4363 0.472 0.000 0.004 0.004 0.448 0.072
#> GSM1178994 3 0.0725 0.6889 0.012 0.000 0.976 0.000 0.000 0.012
#> GSM1178997 3 0.4482 0.3709 0.036 0.000 0.580 0.000 0.000 0.384
#> GSM1179000 3 0.5024 0.5731 0.116 0.000 0.640 0.000 0.004 0.240
#> GSM1179013 1 0.3784 0.6185 0.680 0.000 0.308 0.000 0.012 0.000
#> GSM1179014 5 0.1218 0.9233 0.028 0.000 0.012 0.000 0.956 0.004
#> GSM1179019 3 0.2494 0.6027 0.120 0.000 0.864 0.000 0.000 0.016
#> GSM1179020 1 0.3595 0.5787 0.780 0.000 0.180 0.000 0.004 0.036
#> GSM1179022 1 0.3592 0.5959 0.656 0.000 0.344 0.000 0.000 0.000
#> GSM1179028 2 0.0000 0.8258 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179032 1 0.3619 0.6126 0.680 0.000 0.316 0.000 0.004 0.000
#> GSM1179041 2 0.0000 0.8258 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1179042 2 0.0000 0.8258 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178976 2 0.5793 0.5925 0.004 0.652 0.116 0.008 0.172 0.048
#> GSM1178981 3 0.1411 0.6798 0.004 0.000 0.936 0.000 0.000 0.060
#> GSM1178982 3 0.4317 0.6031 0.060 0.000 0.688 0.000 0.000 0.252
#> GSM1178983 6 0.6732 0.7822 0.308 0.000 0.236 0.000 0.044 0.412
#> GSM1178985 3 0.1285 0.6832 0.004 0.000 0.944 0.000 0.000 0.052
#> GSM1178992 1 0.5051 0.4281 0.512 0.000 0.432 0.000 0.024 0.032
#> GSM1179005 3 0.0405 0.6877 0.004 0.000 0.988 0.000 0.000 0.008
#> GSM1179007 3 0.0717 0.6885 0.016 0.000 0.976 0.000 0.000 0.008
#> GSM1179012 1 0.3578 0.5985 0.660 0.000 0.340 0.000 0.000 0.000
#> GSM1179016 5 0.1219 0.9211 0.048 0.000 0.004 0.000 0.948 0.000
#> GSM1179030 6 0.6169 0.7722 0.304 0.000 0.244 0.008 0.000 0.444
#> GSM1179038 1 0.4488 -0.3840 0.548 0.000 0.032 0.000 0.000 0.420
#> GSM1178987 3 0.3261 0.6654 0.016 0.000 0.780 0.000 0.000 0.204
#> GSM1179003 1 0.7808 -0.7167 0.304 0.000 0.208 0.008 0.184 0.296
#> GSM1179004 3 0.3078 0.6734 0.012 0.000 0.796 0.000 0.000 0.192
#> GSM1179039 2 0.0000 0.8258 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1178975 4 0.0000 0.9289 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1178980 4 0.0146 0.9282 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM1178995 3 0.1010 0.6856 0.004 0.000 0.960 0.000 0.000 0.036
#> GSM1178996 3 0.3315 0.6648 0.020 0.000 0.780 0.000 0.000 0.200
#> GSM1179001 1 0.3747 0.5320 0.604 0.000 0.396 0.000 0.000 0.000
#> GSM1179002 3 0.1866 0.6461 0.084 0.000 0.908 0.000 0.000 0.008
#> GSM1179006 3 0.3642 0.6485 0.036 0.000 0.760 0.000 0.000 0.204
#> GSM1179008 3 0.4500 0.0429 0.392 0.000 0.572 0.000 0.000 0.036
#> GSM1179015 1 0.3871 0.6190 0.676 0.000 0.308 0.000 0.016 0.000
#> GSM1179017 5 0.2009 0.8882 0.004 0.000 0.000 0.008 0.904 0.084
#> GSM1179026 3 0.4518 0.6213 0.104 0.000 0.696 0.000 0.000 0.200
#> GSM1179033 3 0.3483 0.6605 0.024 0.000 0.764 0.000 0.000 0.212
#> GSM1179035 3 0.4422 0.5857 0.088 0.000 0.700 0.000 0.000 0.212
#> GSM1179036 3 0.5937 -0.3975 0.220 0.000 0.428 0.000 0.000 0.352
#> GSM1178986 1 0.6226 0.4040 0.532 0.000 0.236 0.000 0.036 0.196
#> GSM1178989 3 0.7099 -0.1623 0.008 0.308 0.444 0.008 0.172 0.060
#> GSM1178993 4 0.0146 0.9280 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM1178999 4 0.3394 0.7164 0.012 0.000 0.000 0.788 0.188 0.012
#> GSM1179021 4 0.3296 0.7202 0.008 0.000 0.000 0.792 0.188 0.012
#> GSM1179025 2 0.0146 0.8241 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM1179027 4 0.0146 0.9280 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM1179011 4 0.0146 0.9280 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM1179023 1 0.3695 0.5601 0.624 0.000 0.376 0.000 0.000 0.000
#> GSM1179029 1 0.5573 0.0577 0.460 0.000 0.120 0.000 0.416 0.004
#> GSM1179034 1 0.3098 0.5216 0.836 0.000 0.120 0.000 0.040 0.004
#> GSM1179040 4 0.0363 0.9251 0.000 0.000 0.000 0.988 0.000 0.012
#> GSM1178988 3 0.4351 0.5551 0.044 0.000 0.676 0.004 0.000 0.276
#> GSM1179037 3 0.3572 0.6521 0.032 0.000 0.764 0.000 0.000 0.204
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) protocol(p) k
#> ATC:mclust 73 0.20234 0.1570 2
#> ATC:mclust 73 0.00304 0.1628 3
#> ATC:mclust 70 0.00569 0.2415 4
#> ATC:mclust 35 0.00941 0.5346 5
#> ATC:mclust 61 0.01540 0.0629 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 31632 rows and 73 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.957 0.983 0.4566 0.543 0.543
#> 3 3 0.732 0.823 0.912 0.2633 0.851 0.735
#> 4 4 0.645 0.693 0.846 0.1285 0.915 0.805
#> 5 5 0.644 0.645 0.816 0.1485 0.846 0.596
#> 6 6 0.604 0.555 0.761 0.0457 0.953 0.819
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
#> GSM1178971 1 0.0000 0.985 1.000 0.000
#> GSM1178979 2 0.0000 0.974 0.000 1.000
#> GSM1179009 1 0.0000 0.985 1.000 0.000
#> GSM1179031 2 0.0000 0.974 0.000 1.000
#> GSM1178970 2 0.0000 0.974 0.000 1.000
#> GSM1178972 2 0.0000 0.974 0.000 1.000
#> GSM1178973 1 0.0000 0.985 1.000 0.000
#> GSM1178974 2 0.0000 0.974 0.000 1.000
#> GSM1178977 2 0.0000 0.974 0.000 1.000
#> GSM1178978 1 0.0000 0.985 1.000 0.000
#> GSM1178998 1 0.0000 0.985 1.000 0.000
#> GSM1179010 1 0.0000 0.985 1.000 0.000
#> GSM1179018 1 0.0000 0.985 1.000 0.000
#> GSM1179024 1 0.0000 0.985 1.000 0.000
#> GSM1178984 1 0.0000 0.985 1.000 0.000
#> GSM1178990 1 0.0000 0.985 1.000 0.000
#> GSM1178991 1 0.0000 0.985 1.000 0.000
#> GSM1178994 1 0.0000 0.985 1.000 0.000
#> GSM1178997 1 0.9896 0.183 0.560 0.440
#> GSM1179000 1 0.0000 0.985 1.000 0.000
#> GSM1179013 1 0.0000 0.985 1.000 0.000
#> GSM1179014 1 0.0000 0.985 1.000 0.000
#> GSM1179019 1 0.0000 0.985 1.000 0.000
#> GSM1179020 1 0.0000 0.985 1.000 0.000
#> GSM1179022 1 0.0000 0.985 1.000 0.000
#> GSM1179028 2 0.0000 0.974 0.000 1.000
#> GSM1179032 1 0.0000 0.985 1.000 0.000
#> GSM1179041 2 0.0000 0.974 0.000 1.000
#> GSM1179042 2 0.0000 0.974 0.000 1.000
#> GSM1178976 2 0.0000 0.974 0.000 1.000
#> GSM1178981 1 0.0000 0.985 1.000 0.000
#> GSM1178982 1 0.1184 0.971 0.984 0.016
#> GSM1178983 1 0.6148 0.812 0.848 0.152
#> GSM1178985 1 0.0000 0.985 1.000 0.000
#> GSM1178992 1 0.0000 0.985 1.000 0.000
#> GSM1179005 1 0.0000 0.985 1.000 0.000
#> GSM1179007 1 0.0000 0.985 1.000 0.000
#> GSM1179012 1 0.0000 0.985 1.000 0.000
#> GSM1179016 1 0.0000 0.985 1.000 0.000
#> GSM1179030 2 0.0376 0.972 0.004 0.996
#> GSM1179038 1 0.0000 0.985 1.000 0.000
#> GSM1178987 1 0.0000 0.985 1.000 0.000
#> GSM1179003 2 0.0000 0.974 0.000 1.000
#> GSM1179004 1 0.0000 0.985 1.000 0.000
#> GSM1179039 2 0.0000 0.974 0.000 1.000
#> GSM1178975 2 0.7883 0.694 0.236 0.764
#> GSM1178980 2 0.0000 0.974 0.000 1.000
#> GSM1178995 1 0.0000 0.985 1.000 0.000
#> GSM1178996 1 0.0000 0.985 1.000 0.000
#> GSM1179001 1 0.0000 0.985 1.000 0.000
#> GSM1179002 1 0.0000 0.985 1.000 0.000
#> GSM1179006 1 0.0000 0.985 1.000 0.000
#> GSM1179008 1 0.0000 0.985 1.000 0.000
#> GSM1179015 1 0.0000 0.985 1.000 0.000
#> GSM1179017 2 0.1843 0.952 0.028 0.972
#> GSM1179026 1 0.0000 0.985 1.000 0.000
#> GSM1179033 1 0.2043 0.956 0.968 0.032
#> GSM1179035 1 0.0000 0.985 1.000 0.000
#> GSM1179036 1 0.1184 0.971 0.984 0.016
#> GSM1178986 1 0.0000 0.985 1.000 0.000
#> GSM1178989 2 0.0000 0.974 0.000 1.000
#> GSM1178993 2 0.0672 0.969 0.008 0.992
#> GSM1178999 2 0.0000 0.974 0.000 1.000
#> GSM1179021 2 0.0000 0.974 0.000 1.000
#> GSM1179025 2 0.0000 0.974 0.000 1.000
#> GSM1179027 2 0.0000 0.974 0.000 1.000
#> GSM1179011 2 0.0938 0.966 0.012 0.988
#> GSM1179023 1 0.0000 0.985 1.000 0.000
#> GSM1179029 1 0.0000 0.985 1.000 0.000
#> GSM1179034 1 0.0000 0.985 1.000 0.000
#> GSM1179040 2 0.0000 0.974 0.000 1.000
#> GSM1178988 2 0.9000 0.545 0.316 0.684
#> GSM1179037 1 0.0000 0.985 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1178971 1 0.1031 0.928 0.976 0.000 0.024
#> GSM1178979 2 0.1163 0.868 0.000 0.972 0.028
#> GSM1179009 3 0.5905 0.525 0.352 0.000 0.648
#> GSM1179031 2 0.0424 0.876 0.000 0.992 0.008
#> GSM1178970 2 0.0747 0.874 0.000 0.984 0.016
#> GSM1178972 2 0.0592 0.872 0.000 0.988 0.012
#> GSM1178973 3 0.4452 0.722 0.192 0.000 0.808
#> GSM1178974 2 0.1289 0.863 0.000 0.968 0.032
#> GSM1178977 2 0.0592 0.876 0.000 0.988 0.012
#> GSM1178978 1 0.1031 0.928 0.976 0.000 0.024
#> GSM1178998 1 0.0237 0.931 0.996 0.000 0.004
#> GSM1179010 1 0.1031 0.928 0.976 0.000 0.024
#> GSM1179018 3 0.5016 0.692 0.240 0.000 0.760
#> GSM1179024 1 0.0747 0.930 0.984 0.000 0.016
#> GSM1178984 1 0.0892 0.931 0.980 0.000 0.020
#> GSM1178990 1 0.1031 0.927 0.976 0.000 0.024
#> GSM1178991 1 0.5905 0.490 0.648 0.000 0.352
#> GSM1178994 1 0.0592 0.930 0.988 0.000 0.012
#> GSM1178997 2 0.6291 0.106 0.468 0.532 0.000
#> GSM1179000 1 0.0424 0.931 0.992 0.000 0.008
#> GSM1179013 1 0.0747 0.931 0.984 0.000 0.016
#> GSM1179014 1 0.3755 0.843 0.872 0.008 0.120
#> GSM1179019 1 0.0747 0.929 0.984 0.000 0.016
#> GSM1179020 1 0.1031 0.927 0.976 0.000 0.024
#> GSM1179022 1 0.0237 0.931 0.996 0.000 0.004
#> GSM1179028 2 0.0237 0.876 0.000 0.996 0.004
#> GSM1179032 1 0.0747 0.930 0.984 0.000 0.016
#> GSM1179041 2 0.0237 0.876 0.000 0.996 0.004
#> GSM1179042 2 0.0424 0.876 0.000 0.992 0.008
#> GSM1178976 2 0.0892 0.869 0.000 0.980 0.020
#> GSM1178981 1 0.0747 0.931 0.984 0.000 0.016
#> GSM1178982 1 0.4708 0.798 0.844 0.036 0.120
#> GSM1178983 3 0.7533 0.535 0.348 0.052 0.600
#> GSM1178985 1 0.1337 0.925 0.972 0.016 0.012
#> GSM1178992 1 0.0892 0.929 0.980 0.000 0.020
#> GSM1179005 1 0.0892 0.929 0.980 0.000 0.020
#> GSM1179007 1 0.0000 0.931 1.000 0.000 0.000
#> GSM1179012 1 0.0592 0.932 0.988 0.000 0.012
#> GSM1179016 1 0.3896 0.835 0.864 0.008 0.128
#> GSM1179030 2 0.4750 0.698 0.000 0.784 0.216
#> GSM1179038 1 0.5678 0.567 0.684 0.000 0.316
#> GSM1178987 1 0.0592 0.930 0.988 0.000 0.012
#> GSM1179003 2 0.2356 0.841 0.000 0.928 0.072
#> GSM1179004 1 0.2165 0.903 0.936 0.000 0.064
#> GSM1179039 2 0.0424 0.876 0.000 0.992 0.008
#> GSM1178975 3 0.2339 0.780 0.012 0.048 0.940
#> GSM1178980 3 0.2878 0.767 0.000 0.096 0.904
#> GSM1178995 1 0.0237 0.931 0.996 0.000 0.004
#> GSM1178996 1 0.1163 0.926 0.972 0.000 0.028
#> GSM1179001 1 0.0592 0.930 0.988 0.000 0.012
#> GSM1179002 1 0.0747 0.930 0.984 0.000 0.016
#> GSM1179006 1 0.0983 0.928 0.980 0.016 0.004
#> GSM1179008 1 0.0237 0.931 0.996 0.000 0.004
#> GSM1179015 1 0.0747 0.929 0.984 0.000 0.016
#> GSM1179017 2 0.5431 0.619 0.000 0.716 0.284
#> GSM1179026 1 0.4235 0.787 0.824 0.000 0.176
#> GSM1179033 1 0.2200 0.900 0.940 0.056 0.004
#> GSM1179035 1 0.5968 0.389 0.636 0.000 0.364
#> GSM1179036 1 0.6742 0.492 0.656 0.028 0.316
#> GSM1178986 1 0.0747 0.930 0.984 0.000 0.016
#> GSM1178989 2 0.0892 0.869 0.000 0.980 0.020
#> GSM1178993 3 0.2550 0.781 0.012 0.056 0.932
#> GSM1178999 3 0.4842 0.631 0.000 0.224 0.776
#> GSM1179021 2 0.5058 0.634 0.000 0.756 0.244
#> GSM1179025 2 0.0424 0.876 0.000 0.992 0.008
#> GSM1179027 3 0.2537 0.776 0.000 0.080 0.920
#> GSM1179011 3 0.2590 0.779 0.004 0.072 0.924
#> GSM1179023 1 0.0237 0.931 0.996 0.000 0.004
#> GSM1179029 1 0.1031 0.931 0.976 0.000 0.024
#> GSM1179034 1 0.1163 0.926 0.972 0.000 0.028
#> GSM1179040 3 0.3941 0.725 0.000 0.156 0.844
#> GSM1178988 2 0.6703 0.512 0.236 0.712 0.052
#> GSM1179037 1 0.3500 0.858 0.880 0.004 0.116
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1178971 1 0.1389 0.87107 0.952 0.000 0.048 0.000
#> GSM1178979 2 0.1474 0.78116 0.000 0.948 0.052 0.000
#> GSM1179009 4 0.5979 0.53824 0.164 0.004 0.128 0.704
#> GSM1179031 2 0.0707 0.78298 0.000 0.980 0.020 0.000
#> GSM1178970 2 0.3123 0.72060 0.000 0.844 0.156 0.000
#> GSM1178972 2 0.1022 0.78179 0.000 0.968 0.032 0.000
#> GSM1178973 4 0.1256 0.76002 0.028 0.000 0.008 0.964
#> GSM1178974 2 0.2345 0.76140 0.000 0.900 0.100 0.000
#> GSM1178977 2 0.1576 0.77517 0.000 0.948 0.048 0.004
#> GSM1178978 1 0.1940 0.86250 0.924 0.000 0.076 0.000
#> GSM1178998 1 0.1109 0.87368 0.968 0.000 0.028 0.004
#> GSM1179010 1 0.3157 0.82306 0.852 0.000 0.144 0.004
#> GSM1179018 4 0.2489 0.73523 0.068 0.000 0.020 0.912
#> GSM1179024 1 0.1637 0.86250 0.940 0.000 0.060 0.000
#> GSM1178984 1 0.3498 0.80372 0.832 0.000 0.160 0.008
#> GSM1178990 1 0.1576 0.86961 0.948 0.000 0.048 0.004
#> GSM1178991 3 0.6928 0.52788 0.268 0.000 0.576 0.156
#> GSM1178994 1 0.1576 0.87001 0.948 0.000 0.048 0.004
#> GSM1178997 2 0.5285 0.00222 0.468 0.524 0.008 0.000
#> GSM1179000 1 0.1389 0.86840 0.952 0.000 0.048 0.000
#> GSM1179013 1 0.1211 0.87096 0.960 0.000 0.040 0.000
#> GSM1179014 1 0.4343 0.59676 0.732 0.000 0.264 0.004
#> GSM1179019 1 0.1118 0.87220 0.964 0.000 0.036 0.000
#> GSM1179020 1 0.1302 0.86958 0.956 0.000 0.044 0.000
#> GSM1179022 1 0.1022 0.87306 0.968 0.000 0.032 0.000
#> GSM1179028 2 0.0469 0.78356 0.000 0.988 0.012 0.000
#> GSM1179032 1 0.1118 0.87220 0.964 0.000 0.036 0.000
#> GSM1179041 2 0.0336 0.78413 0.000 0.992 0.008 0.000
#> GSM1179042 2 0.0817 0.78188 0.000 0.976 0.024 0.000
#> GSM1178976 2 0.4661 0.59498 0.004 0.708 0.284 0.004
#> GSM1178981 1 0.3725 0.78629 0.812 0.000 0.180 0.008
#> GSM1178982 1 0.4626 0.78986 0.816 0.016 0.108 0.060
#> GSM1178983 4 0.5964 0.42351 0.256 0.044 0.020 0.680
#> GSM1178985 1 0.5057 0.71034 0.748 0.044 0.204 0.004
#> GSM1178992 1 0.2704 0.81857 0.876 0.000 0.124 0.000
#> GSM1179005 1 0.1716 0.86687 0.936 0.000 0.064 0.000
#> GSM1179007 1 0.1716 0.86653 0.936 0.000 0.064 0.000
#> GSM1179012 1 0.0707 0.87488 0.980 0.000 0.020 0.000
#> GSM1179016 1 0.5050 0.19303 0.588 0.000 0.408 0.004
#> GSM1179030 3 0.6885 0.22609 0.004 0.360 0.536 0.100
#> GSM1179038 3 0.7170 0.51789 0.268 0.000 0.548 0.184
#> GSM1178987 1 0.1576 0.87104 0.948 0.000 0.048 0.004
#> GSM1179003 2 0.5688 0.01754 0.000 0.512 0.464 0.024
#> GSM1179004 1 0.3818 0.81513 0.844 0.000 0.108 0.048
#> GSM1179039 2 0.0921 0.78085 0.000 0.972 0.028 0.000
#> GSM1178975 4 0.1209 0.75349 0.000 0.004 0.032 0.964
#> GSM1178980 4 0.2730 0.70614 0.000 0.016 0.088 0.896
#> GSM1178995 1 0.2918 0.83716 0.876 0.000 0.116 0.008
#> GSM1178996 1 0.1191 0.87649 0.968 0.004 0.024 0.004
#> GSM1179001 1 0.0188 0.87581 0.996 0.000 0.004 0.000
#> GSM1179002 1 0.1474 0.87132 0.948 0.000 0.052 0.000
#> GSM1179006 1 0.1489 0.87672 0.952 0.004 0.044 0.000
#> GSM1179008 1 0.0469 0.87577 0.988 0.000 0.012 0.000
#> GSM1179015 1 0.1211 0.87096 0.960 0.000 0.040 0.000
#> GSM1179017 3 0.5915 0.41749 0.024 0.236 0.696 0.044
#> GSM1179026 3 0.6586 0.30723 0.420 0.000 0.500 0.080
#> GSM1179033 1 0.4359 0.78323 0.804 0.016 0.164 0.016
#> GSM1179035 4 0.6915 0.09704 0.416 0.000 0.108 0.476
#> GSM1179036 1 0.6818 0.06185 0.512 0.028 0.044 0.416
#> GSM1178986 1 0.1557 0.86472 0.944 0.000 0.056 0.000
#> GSM1178989 2 0.2714 0.75095 0.004 0.884 0.112 0.000
#> GSM1178993 4 0.0657 0.75945 0.000 0.004 0.012 0.984
#> GSM1178999 3 0.7083 0.08759 0.000 0.124 0.444 0.432
#> GSM1179021 2 0.5661 0.52343 0.000 0.700 0.080 0.220
#> GSM1179025 2 0.1118 0.78016 0.000 0.964 0.036 0.000
#> GSM1179027 4 0.0672 0.76079 0.000 0.008 0.008 0.984
#> GSM1179011 4 0.0524 0.76168 0.000 0.008 0.004 0.988
#> GSM1179023 1 0.1118 0.87220 0.964 0.000 0.036 0.000
#> GSM1179029 1 0.2647 0.81543 0.880 0.000 0.120 0.000
#> GSM1179034 1 0.1211 0.87096 0.960 0.000 0.040 0.000
#> GSM1179040 4 0.2522 0.72326 0.000 0.076 0.016 0.908
#> GSM1178988 2 0.7857 -0.11588 0.352 0.440 0.200 0.008
#> GSM1179037 1 0.5783 0.62118 0.708 0.000 0.172 0.120
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1178971 1 0.0566 0.8166 0.984 0.000 0.012 0.004 0.000
#> GSM1178979 2 0.1124 0.8985 0.000 0.960 0.000 0.004 0.036
#> GSM1179009 4 0.4288 0.1867 0.000 0.000 0.384 0.612 0.004
#> GSM1179031 2 0.0162 0.9081 0.000 0.996 0.000 0.000 0.004
#> GSM1178970 2 0.2921 0.8106 0.000 0.856 0.124 0.000 0.020
#> GSM1178972 2 0.1444 0.8947 0.000 0.948 0.012 0.000 0.040
#> GSM1178973 4 0.1872 0.7296 0.020 0.000 0.052 0.928 0.000
#> GSM1178974 2 0.1872 0.8808 0.000 0.928 0.020 0.000 0.052
#> GSM1178977 2 0.0566 0.9060 0.000 0.984 0.000 0.004 0.012
#> GSM1178978 1 0.1074 0.8143 0.968 0.004 0.016 0.012 0.000
#> GSM1178998 1 0.1697 0.8039 0.932 0.000 0.060 0.008 0.000
#> GSM1179010 3 0.3942 0.5545 0.260 0.000 0.728 0.012 0.000
#> GSM1179018 4 0.3675 0.6095 0.000 0.000 0.188 0.788 0.024
#> GSM1179024 1 0.0613 0.8110 0.984 0.000 0.008 0.004 0.004
#> GSM1178984 1 0.5547 0.3129 0.564 0.000 0.356 0.080 0.000
#> GSM1178990 1 0.2221 0.7987 0.912 0.000 0.052 0.000 0.036
#> GSM1178991 5 0.5900 0.5558 0.252 0.000 0.008 0.128 0.612
#> GSM1178994 1 0.2189 0.7949 0.904 0.000 0.084 0.012 0.000
#> GSM1178997 2 0.4299 0.3097 0.388 0.608 0.004 0.000 0.000
#> GSM1179000 1 0.0579 0.8127 0.984 0.000 0.008 0.008 0.000
#> GSM1179013 1 0.0000 0.8157 1.000 0.000 0.000 0.000 0.000
#> GSM1179014 1 0.4422 0.4204 0.664 0.000 0.012 0.004 0.320
#> GSM1179019 1 0.0324 0.8144 0.992 0.000 0.004 0.004 0.000
#> GSM1179020 1 0.0671 0.8129 0.980 0.000 0.004 0.016 0.000
#> GSM1179022 1 0.0566 0.8167 0.984 0.000 0.012 0.004 0.000
#> GSM1179028 2 0.0404 0.9062 0.000 0.988 0.000 0.000 0.012
#> GSM1179032 1 0.0324 0.8163 0.992 0.000 0.004 0.004 0.000
#> GSM1179041 2 0.0000 0.9080 0.000 1.000 0.000 0.000 0.000
#> GSM1179042 2 0.0703 0.9054 0.000 0.976 0.000 0.000 0.024
#> GSM1178976 3 0.3056 0.5620 0.000 0.112 0.860 0.020 0.008
#> GSM1178981 1 0.5884 0.0469 0.480 0.000 0.420 0.100 0.000
#> GSM1178982 1 0.7511 -0.0258 0.444 0.052 0.248 0.256 0.000
#> GSM1178983 4 0.6341 0.3311 0.292 0.116 0.012 0.572 0.008
#> GSM1178985 3 0.5584 0.4375 0.312 0.000 0.592 0.096 0.000
#> GSM1178992 1 0.5304 0.4752 0.628 0.000 0.080 0.000 0.292
#> GSM1179005 1 0.4046 0.5687 0.696 0.000 0.296 0.008 0.000
#> GSM1179007 1 0.3424 0.6544 0.760 0.000 0.240 0.000 0.000
#> GSM1179012 1 0.0794 0.8155 0.972 0.000 0.028 0.000 0.000
#> GSM1179016 5 0.5203 0.5004 0.264 0.000 0.072 0.004 0.660
#> GSM1179030 5 0.3986 0.7196 0.000 0.048 0.044 0.080 0.828
#> GSM1179038 5 0.4138 0.6896 0.016 0.000 0.040 0.152 0.792
#> GSM1178987 3 0.5429 0.6002 0.228 0.000 0.660 0.108 0.004
#> GSM1179003 5 0.2861 0.7214 0.000 0.064 0.024 0.024 0.888
#> GSM1179004 3 0.5928 0.4725 0.124 0.000 0.548 0.328 0.000
#> GSM1179039 2 0.0404 0.9070 0.000 0.988 0.000 0.000 0.012
#> GSM1178975 4 0.3280 0.6514 0.024 0.004 0.004 0.848 0.120
#> GSM1178980 4 0.3997 0.5865 0.000 0.032 0.004 0.776 0.188
#> GSM1178995 1 0.5246 0.2954 0.564 0.000 0.384 0.052 0.000
#> GSM1178996 1 0.4851 0.3138 0.560 0.000 0.420 0.008 0.012
#> GSM1179001 1 0.1638 0.8034 0.932 0.000 0.064 0.004 0.000
#> GSM1179002 1 0.4025 0.5761 0.700 0.000 0.292 0.008 0.000
#> GSM1179006 3 0.3810 0.6231 0.168 0.000 0.792 0.000 0.040
#> GSM1179008 1 0.2358 0.7788 0.888 0.000 0.104 0.008 0.000
#> GSM1179015 1 0.0510 0.8170 0.984 0.000 0.016 0.000 0.000
#> GSM1179017 5 0.1772 0.7274 0.004 0.024 0.012 0.016 0.944
#> GSM1179026 3 0.5850 0.0732 0.036 0.000 0.468 0.032 0.464
#> GSM1179033 3 0.4643 0.6177 0.068 0.004 0.736 0.192 0.000
#> GSM1179035 3 0.4442 0.4945 0.016 0.000 0.676 0.304 0.004
#> GSM1179036 3 0.5488 0.3056 0.008 0.000 0.540 0.404 0.048
#> GSM1178986 1 0.0613 0.8128 0.984 0.000 0.008 0.004 0.004
#> GSM1178989 3 0.2928 0.5677 0.000 0.064 0.872 0.000 0.064
#> GSM1178993 4 0.1153 0.7323 0.004 0.024 0.000 0.964 0.008
#> GSM1178999 5 0.6003 0.3931 0.000 0.124 0.008 0.280 0.588
#> GSM1179021 2 0.2976 0.7830 0.000 0.852 0.004 0.132 0.012
#> GSM1179025 2 0.0000 0.9080 0.000 1.000 0.000 0.000 0.000
#> GSM1179027 4 0.1914 0.7309 0.000 0.016 0.060 0.924 0.000
#> GSM1179011 4 0.1834 0.7290 0.008 0.032 0.004 0.940 0.016
#> GSM1179023 1 0.0451 0.8159 0.988 0.000 0.004 0.008 0.000
#> GSM1179029 1 0.0798 0.8113 0.976 0.000 0.008 0.000 0.016
#> GSM1179034 1 0.0566 0.8146 0.984 0.000 0.004 0.012 0.000
#> GSM1179040 4 0.4616 0.5153 0.000 0.288 0.028 0.680 0.004
#> GSM1178988 3 0.5277 0.2518 0.040 0.008 0.584 0.000 0.368
#> GSM1179037 3 0.4548 0.6186 0.020 0.000 0.780 0.092 0.108
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1178971 1 0.1382 0.8184 0.948 0.000 0.008 0.000 0.008 0.036
#> GSM1178979 2 0.3828 0.7367 0.000 0.780 0.000 0.048 0.012 0.160
#> GSM1179009 4 0.5204 0.0175 0.008 0.000 0.428 0.496 0.000 0.068
#> GSM1179031 2 0.0713 0.8471 0.000 0.972 0.000 0.000 0.000 0.028
#> GSM1178970 6 0.5131 -0.1208 0.000 0.404 0.064 0.008 0.000 0.524
#> GSM1178972 2 0.2344 0.8249 0.000 0.892 0.004 0.000 0.028 0.076
#> GSM1178973 4 0.2113 0.6515 0.008 0.000 0.032 0.912 0.000 0.048
#> GSM1178974 2 0.3503 0.7442 0.000 0.788 0.012 0.000 0.020 0.180
#> GSM1178977 2 0.4067 0.7346 0.008 0.788 0.004 0.068 0.008 0.124
#> GSM1178978 1 0.6030 0.1159 0.520 0.000 0.004 0.236 0.008 0.232
#> GSM1178998 1 0.1716 0.8159 0.932 0.000 0.028 0.000 0.004 0.036
#> GSM1179010 3 0.5119 0.2855 0.264 0.000 0.608 0.000 0.000 0.128
#> GSM1179018 4 0.4647 0.5645 0.000 0.000 0.124 0.744 0.048 0.084
#> GSM1179024 1 0.1148 0.8150 0.960 0.000 0.004 0.000 0.016 0.020
#> GSM1178984 1 0.6494 0.0917 0.472 0.000 0.340 0.080 0.000 0.108
#> GSM1178990 1 0.1155 0.8188 0.956 0.000 0.036 0.000 0.004 0.004
#> GSM1178991 5 0.7031 0.3317 0.264 0.000 0.008 0.116 0.480 0.132
#> GSM1178994 1 0.5005 0.5387 0.692 0.000 0.052 0.060 0.000 0.196
#> GSM1178997 2 0.4285 0.1482 0.432 0.552 0.000 0.000 0.008 0.008
#> GSM1179000 1 0.0912 0.8177 0.972 0.000 0.004 0.004 0.008 0.012
#> GSM1179013 1 0.0508 0.8186 0.984 0.000 0.000 0.000 0.004 0.012
#> GSM1179014 1 0.4834 0.3750 0.596 0.000 0.004 0.000 0.340 0.060
#> GSM1179019 1 0.0622 0.8192 0.980 0.000 0.000 0.000 0.008 0.012
#> GSM1179020 1 0.0260 0.8194 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM1179022 1 0.0363 0.8197 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM1179028 2 0.0922 0.8480 0.000 0.968 0.000 0.004 0.004 0.024
#> GSM1179032 1 0.0458 0.8191 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM1179041 2 0.0458 0.8481 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM1179042 2 0.0767 0.8474 0.000 0.976 0.004 0.000 0.008 0.012
#> GSM1178976 3 0.3582 0.4544 0.000 0.036 0.768 0.000 0.000 0.196
#> GSM1178981 6 0.7513 0.3661 0.180 0.000 0.192 0.268 0.000 0.360
#> GSM1178982 4 0.7586 -0.3956 0.156 0.024 0.112 0.368 0.000 0.340
#> GSM1178983 4 0.5899 0.3185 0.100 0.036 0.004 0.648 0.024 0.188
#> GSM1178985 6 0.7439 0.3873 0.140 0.008 0.232 0.192 0.000 0.428
#> GSM1178992 1 0.3170 0.7649 0.840 0.000 0.032 0.000 0.112 0.016
#> GSM1179005 1 0.3481 0.7054 0.776 0.000 0.192 0.000 0.000 0.032
#> GSM1179007 1 0.3296 0.7181 0.796 0.000 0.180 0.004 0.000 0.020
#> GSM1179012 1 0.1578 0.8094 0.936 0.000 0.012 0.000 0.004 0.048
#> GSM1179016 5 0.5570 0.2207 0.280 0.000 0.004 0.000 0.556 0.160
#> GSM1179030 5 0.5856 0.4537 0.004 0.064 0.004 0.092 0.636 0.200
#> GSM1179038 5 0.5757 0.4732 0.016 0.000 0.100 0.148 0.668 0.068
#> GSM1178987 3 0.7168 -0.0511 0.164 0.000 0.424 0.060 0.024 0.328
#> GSM1179003 5 0.3130 0.5569 0.000 0.124 0.008 0.020 0.840 0.008
#> GSM1179004 3 0.6823 0.3099 0.156 0.000 0.532 0.168 0.004 0.140
#> GSM1179039 2 0.0603 0.8476 0.000 0.980 0.004 0.000 0.000 0.016
#> GSM1178975 4 0.3516 0.5896 0.008 0.000 0.004 0.824 0.076 0.088
#> GSM1178980 4 0.4368 0.4974 0.000 0.012 0.004 0.740 0.180 0.064
#> GSM1178995 1 0.4995 0.4585 0.612 0.000 0.320 0.032 0.000 0.036
#> GSM1178996 1 0.4305 0.6220 0.692 0.004 0.256 0.000 0.000 0.048
#> GSM1179001 1 0.1988 0.8092 0.920 0.000 0.048 0.004 0.004 0.024
#> GSM1179002 1 0.4336 0.6464 0.712 0.000 0.228 0.004 0.004 0.052
#> GSM1179006 6 0.7600 0.1969 0.156 0.008 0.240 0.020 0.120 0.456
#> GSM1179008 1 0.3030 0.7904 0.868 0.000 0.052 0.008 0.016 0.056
#> GSM1179015 1 0.1542 0.8078 0.936 0.000 0.008 0.000 0.004 0.052
#> GSM1179017 5 0.1148 0.5682 0.000 0.020 0.004 0.000 0.960 0.016
#> GSM1179026 3 0.5364 0.3138 0.020 0.000 0.612 0.032 0.304 0.032
#> GSM1179033 3 0.4147 0.5040 0.136 0.004 0.780 0.048 0.000 0.032
#> GSM1179035 3 0.4358 0.4913 0.000 0.000 0.732 0.176 0.008 0.084
#> GSM1179036 3 0.5772 0.4160 0.004 0.000 0.624 0.224 0.060 0.088
#> GSM1178986 1 0.6155 0.3944 0.600 0.000 0.004 0.068 0.180 0.148
#> GSM1178989 3 0.3859 0.4366 0.000 0.024 0.756 0.000 0.016 0.204
#> GSM1178993 4 0.0551 0.6582 0.004 0.000 0.004 0.984 0.008 0.000
#> GSM1178999 5 0.7493 0.3158 0.000 0.232 0.052 0.168 0.472 0.076
#> GSM1179021 2 0.3332 0.7721 0.000 0.840 0.008 0.092 0.008 0.052
#> GSM1179025 2 0.0837 0.8466 0.000 0.972 0.004 0.004 0.000 0.020
#> GSM1179027 4 0.3212 0.6333 0.000 0.008 0.104 0.844 0.008 0.036
#> GSM1179011 4 0.1340 0.6527 0.004 0.000 0.000 0.948 0.008 0.040
#> GSM1179023 1 0.0622 0.8192 0.980 0.000 0.000 0.000 0.008 0.012
#> GSM1179029 1 0.1321 0.8163 0.952 0.000 0.004 0.000 0.024 0.020
#> GSM1179034 1 0.0508 0.8189 0.984 0.000 0.004 0.000 0.000 0.012
#> GSM1179040 4 0.5797 0.3278 0.000 0.332 0.060 0.552 0.004 0.052
#> GSM1178988 5 0.6367 0.2411 0.000 0.024 0.248 0.000 0.468 0.260
#> GSM1179037 3 0.3374 0.5412 0.008 0.000 0.848 0.052 0.068 0.024
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) protocol(p) k
#> ATC:NMF 72 0.0301 0.226 2
#> ATC:NMF 69 0.0537 0.853 3
#> ATC:NMF 62 0.0390 0.839 4
#> ATC:NMF 56 0.0571 0.438 5
#> ATC:NMF 44 0.0398 0.507 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