Date: 2019-12-25 20:17:12 CET, cola version: 1.3.2
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All available functions which can be applied to this res_list object:
res_list
#> A 'ConsensusPartitionList' object with 24 methods.
#> On a matrix with 21168 rows and 85 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] 21168 85
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:skmeans | 3 | 1.000 | 0.983 | 0.993 | ** | 2 |
| CV:skmeans | 3 | 1.000 | 0.969 | 0.987 | ** | 2 |
| MAD:kmeans | 3 | 1.000 | 0.962 | 0.984 | ** | |
| MAD:skmeans | 3 | 1.000 | 0.979 | 0.990 | ** | 2 |
| ATC:NMF | 3 | 1.000 | 0.979 | 0.990 | ** | 2 |
| CV:kmeans | 3 | 0.984 | 0.954 | 0.978 | ** | |
| SD:kmeans | 3 | 0.984 | 0.937 | 0.974 | ** | |
| ATC:pam | 4 | 0.976 | 0.947 | 0.978 | ** | 2 |
| ATC:kmeans | 3 | 0.969 | 0.937 | 0.975 | ** | 2 |
| CV:NMF | 3 | 0.967 | 0.951 | 0.979 | ** | 2 |
| MAD:NMF | 3 | 0.967 | 0.957 | 0.981 | ** | 2 |
| MAD:mclust | 5 | 0.966 | 0.898 | 0.959 | ** | 3 |
| SD:NMF | 3 | 0.952 | 0.940 | 0.976 | ** | 2 |
| ATC:skmeans | 4 | 0.903 | 0.882 | 0.939 | * | 2,3 |
| MAD:pam | 4 | 0.888 | 0.880 | 0.944 | ||
| SD:pam | 6 | 0.867 | 0.815 | 0.918 | ||
| SD:mclust | 3 | 0.825 | 0.929 | 0.965 | ||
| ATC:mclust | 3 | 0.824 | 0.882 | 0.918 | ||
| CV:mclust | 3 | 0.785 | 0.760 | 0.905 | ||
| ATC:hclust | 4 | 0.688 | 0.727 | 0.830 | ||
| CV:pam | 3 | 0.634 | 0.822 | 0.910 | ||
| MAD:hclust | 5 | 0.611 | 0.684 | 0.802 | ||
| CV:hclust | 3 | 0.605 | 0.768 | 0.888 | ||
| SD:hclust | 5 | 0.589 | 0.662 | 0.806 |
**: 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 0.971 0.988 0.501 0.500 0.500
#> CV:NMF 2 1.000 0.975 0.989 0.502 0.497 0.497
#> MAD:NMF 2 1.000 0.962 0.984 0.503 0.496 0.496
#> ATC:NMF 2 1.000 0.962 0.984 0.495 0.506 0.506
#> SD:skmeans 2 1.000 0.968 0.988 0.505 0.496 0.496
#> CV:skmeans 2 1.000 0.973 0.989 0.505 0.496 0.496
#> MAD:skmeans 2 1.000 0.974 0.989 0.505 0.496 0.496
#> ATC:skmeans 2 1.000 0.989 0.995 0.500 0.500 0.500
#> SD:mclust 2 0.289 0.682 0.805 0.444 0.525 0.525
#> CV:mclust 2 0.290 0.807 0.841 0.437 0.545 0.545
#> MAD:mclust 2 0.335 0.707 0.843 0.472 0.506 0.506
#> ATC:mclust 2 0.263 0.791 0.801 0.402 0.545 0.545
#> SD:kmeans 2 0.691 0.898 0.947 0.485 0.514 0.514
#> CV:kmeans 2 0.651 0.888 0.937 0.485 0.514 0.514
#> MAD:kmeans 2 0.683 0.836 0.926 0.486 0.503 0.503
#> ATC:kmeans 2 1.000 0.973 0.989 0.482 0.514 0.514
#> SD:pam 2 0.671 0.783 0.912 0.492 0.500 0.500
#> CV:pam 2 0.563 0.892 0.936 0.447 0.570 0.570
#> MAD:pam 2 0.547 0.756 0.900 0.483 0.500 0.500
#> ATC:pam 2 1.000 0.984 0.994 0.506 0.494 0.494
#> SD:hclust 2 0.559 0.742 0.897 0.364 0.649 0.649
#> CV:hclust 2 0.666 0.849 0.930 0.304 0.722 0.722
#> MAD:hclust 2 0.361 0.800 0.878 0.421 0.519 0.519
#> ATC:hclust 2 0.608 0.839 0.919 0.442 0.525 0.525
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.952 0.940 0.976 0.344 0.725 0.501
#> CV:NMF 3 0.967 0.951 0.979 0.342 0.711 0.481
#> MAD:NMF 3 0.967 0.957 0.981 0.338 0.729 0.505
#> ATC:NMF 3 1.000 0.979 0.990 0.361 0.759 0.552
#> SD:skmeans 3 1.000 0.983 0.993 0.332 0.757 0.545
#> CV:skmeans 3 1.000 0.969 0.987 0.332 0.736 0.514
#> MAD:skmeans 3 1.000 0.979 0.990 0.327 0.757 0.545
#> ATC:skmeans 3 0.999 0.974 0.988 0.334 0.783 0.587
#> SD:mclust 3 0.825 0.929 0.965 0.509 0.728 0.516
#> CV:mclust 3 0.785 0.760 0.905 0.507 0.752 0.557
#> MAD:mclust 3 1.000 0.958 0.976 0.417 0.746 0.533
#> ATC:mclust 3 0.824 0.882 0.918 0.643 0.750 0.554
#> SD:kmeans 3 0.984 0.937 0.974 0.385 0.718 0.499
#> CV:kmeans 3 0.984 0.954 0.978 0.383 0.718 0.499
#> MAD:kmeans 3 1.000 0.962 0.984 0.385 0.729 0.507
#> ATC:kmeans 3 0.969 0.937 0.975 0.395 0.741 0.530
#> SD:pam 3 0.655 0.767 0.872 0.336 0.709 0.480
#> CV:pam 3 0.634 0.822 0.910 0.471 0.762 0.583
#> MAD:pam 3 0.660 0.799 0.889 0.363 0.722 0.497
#> ATC:pam 3 0.840 0.905 0.936 0.313 0.720 0.491
#> SD:hclust 3 0.462 0.621 0.832 0.734 0.709 0.551
#> CV:hclust 3 0.605 0.768 0.888 0.973 0.684 0.562
#> MAD:hclust 3 0.503 0.669 0.840 0.540 0.764 0.563
#> ATC:hclust 3 0.546 0.687 0.841 0.463 0.742 0.535
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.852 0.833 0.922 0.1049 0.887 0.673
#> CV:NMF 4 0.766 0.716 0.855 0.1017 0.886 0.674
#> MAD:NMF 4 0.884 0.898 0.947 0.1069 0.884 0.666
#> ATC:NMF 4 0.819 0.804 0.899 0.1020 0.887 0.674
#> SD:skmeans 4 0.804 0.765 0.894 0.0992 0.909 0.735
#> CV:skmeans 4 0.805 0.782 0.895 0.0999 0.908 0.732
#> MAD:skmeans 4 0.839 0.823 0.914 0.0915 0.944 0.832
#> ATC:skmeans 4 0.903 0.882 0.939 0.0767 0.929 0.791
#> SD:mclust 4 0.832 0.796 0.900 0.0940 0.911 0.743
#> CV:mclust 4 0.675 0.753 0.845 0.0952 0.859 0.622
#> MAD:mclust 4 0.709 0.688 0.848 0.0776 0.946 0.835
#> ATC:mclust 4 0.681 0.780 0.851 0.1163 0.882 0.662
#> SD:kmeans 4 0.744 0.770 0.851 0.1042 0.860 0.613
#> CV:kmeans 4 0.720 0.700 0.820 0.1074 0.876 0.646
#> MAD:kmeans 4 0.774 0.639 0.832 0.1079 0.955 0.865
#> ATC:kmeans 4 0.799 0.786 0.893 0.1114 0.855 0.596
#> SD:pam 4 0.692 0.808 0.835 0.1405 0.820 0.522
#> CV:pam 4 0.604 0.695 0.832 0.1037 0.922 0.778
#> MAD:pam 4 0.888 0.880 0.944 0.1443 0.826 0.539
#> ATC:pam 4 0.976 0.947 0.978 0.1295 0.850 0.587
#> SD:hclust 4 0.496 0.635 0.750 0.1311 0.818 0.547
#> CV:hclust 4 0.581 0.693 0.809 0.1801 0.829 0.595
#> MAD:hclust 4 0.513 0.471 0.680 0.1034 0.775 0.484
#> ATC:hclust 4 0.688 0.727 0.830 0.1416 0.851 0.588
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.750 0.655 0.815 0.0552 0.943 0.789
#> CV:NMF 5 0.740 0.641 0.828 0.0621 0.915 0.702
#> MAD:NMF 5 0.755 0.688 0.833 0.0470 0.965 0.869
#> ATC:NMF 5 0.752 0.695 0.843 0.0441 0.956 0.835
#> SD:skmeans 5 0.761 0.628 0.834 0.0613 0.924 0.727
#> CV:skmeans 5 0.741 0.620 0.816 0.0617 0.928 0.743
#> MAD:skmeans 5 0.764 0.638 0.827 0.0623 0.925 0.747
#> ATC:skmeans 5 0.821 0.798 0.898 0.0478 0.975 0.909
#> SD:mclust 5 0.873 0.821 0.922 0.0834 0.893 0.637
#> CV:mclust 5 0.823 0.754 0.893 0.0974 0.853 0.541
#> MAD:mclust 5 0.966 0.898 0.959 0.0925 0.891 0.636
#> ATC:mclust 5 0.659 0.615 0.780 0.0430 0.843 0.527
#> SD:kmeans 5 0.746 0.701 0.837 0.0635 0.940 0.772
#> CV:kmeans 5 0.736 0.660 0.831 0.0625 0.897 0.640
#> MAD:kmeans 5 0.731 0.643 0.815 0.0636 0.870 0.590
#> ATC:kmeans 5 0.757 0.676 0.837 0.0586 0.931 0.741
#> SD:pam 5 0.768 0.654 0.810 0.0588 0.969 0.875
#> CV:pam 5 0.681 0.556 0.750 0.0816 0.835 0.498
#> MAD:pam 5 0.824 0.724 0.864 0.0536 0.944 0.782
#> ATC:pam 5 0.866 0.810 0.917 0.0486 0.964 0.857
#> SD:hclust 5 0.589 0.662 0.806 0.0821 0.922 0.719
#> CV:hclust 5 0.630 0.647 0.806 0.0860 0.953 0.823
#> MAD:hclust 5 0.611 0.684 0.802 0.0872 0.846 0.550
#> ATC:hclust 5 0.672 0.633 0.811 0.0597 0.976 0.904
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.729 0.582 0.790 0.0400 0.904 0.632
#> CV:NMF 6 0.701 0.513 0.724 0.0408 0.893 0.574
#> MAD:NMF 6 0.733 0.598 0.785 0.0446 0.896 0.608
#> ATC:NMF 6 0.745 0.666 0.807 0.0360 0.939 0.761
#> SD:skmeans 6 0.740 0.561 0.774 0.0351 0.959 0.822
#> CV:skmeans 6 0.718 0.556 0.767 0.0365 0.937 0.739
#> MAD:skmeans 6 0.731 0.587 0.761 0.0353 0.949 0.791
#> ATC:skmeans 6 0.790 0.582 0.828 0.0413 0.958 0.843
#> SD:mclust 6 0.825 0.675 0.862 0.0220 0.963 0.835
#> CV:mclust 6 0.802 0.755 0.864 0.0295 0.959 0.818
#> MAD:mclust 6 0.879 0.751 0.880 0.0356 0.978 0.899
#> ATC:mclust 6 0.721 0.612 0.784 0.0438 0.961 0.848
#> SD:kmeans 6 0.758 0.591 0.784 0.0421 0.968 0.853
#> CV:kmeans 6 0.773 0.634 0.803 0.0416 0.952 0.794
#> MAD:kmeans 6 0.751 0.645 0.790 0.0420 0.909 0.607
#> ATC:kmeans 6 0.739 0.644 0.774 0.0406 0.937 0.735
#> SD:pam 6 0.867 0.815 0.918 0.0433 0.923 0.673
#> CV:pam 6 0.830 0.777 0.895 0.0538 0.902 0.588
#> MAD:pam 6 0.888 0.842 0.913 0.0414 0.920 0.657
#> ATC:pam 6 0.844 0.763 0.872 0.0369 0.968 0.856
#> SD:hclust 6 0.654 0.548 0.770 0.0433 0.977 0.896
#> CV:hclust 6 0.684 0.621 0.777 0.0392 0.992 0.964
#> MAD:hclust 6 0.683 0.589 0.788 0.0425 0.963 0.838
#> ATC:hclust 6 0.728 0.635 0.785 0.0425 0.945 0.760
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) cell.type(p) k
#> SD:NMF 84 8.94e-05 4.59e-04 2
#> CV:NMF 84 8.94e-05 4.59e-04 2
#> MAD:NMF 83 6.56e-05 3.42e-04 2
#> ATC:NMF 84 4.25e-06 2.72e-05 2
#> SD:skmeans 83 3.58e-05 1.92e-04 2
#> CV:skmeans 84 4.99e-05 2.64e-04 2
#> MAD:skmeans 84 2.71e-05 1.47e-04 2
#> ATC:skmeans 85 1.64e-06 1.09e-05 2
#> SD:mclust 80 2.30e-01 4.33e-01 2
#> CV:mclust 85 1.92e-01 3.83e-01 2
#> MAD:mclust 76 2.92e-05 1.66e-04 2
#> ATC:mclust 84 2.10e-01 4.08e-01 2
#> SD:kmeans 84 2.54e-05 1.50e-04 2
#> CV:kmeans 84 1.43e-05 8.68e-05 2
#> MAD:kmeans 80 3.14e-05 1.80e-04 2
#> ATC:kmeans 84 2.54e-05 1.50e-04 2
#> SD:pam 71 2.91e-03 1.38e-02 2
#> CV:pam 84 2.30e-02 4.40e-02 2
#> MAD:pam 70 5.55e-04 2.98e-03 2
#> ATC:pam 84 7.45e-05 5.12e-04 2
#> SD:hclust 73 1.31e-02 3.99e-02 2
#> CV:hclust 78 3.49e-02 1.10e-01 2
#> MAD:hclust 81 6.16e-05 3.41e-04 2
#> ATC:hclust 82 7.90e-05 4.32e-04 2
test_to_known_factors(res_list, k = 3)
#> n disease.state(p) cell.type(p) k
#> SD:NMF 83 5.12e-04 0.01152 3
#> CV:NMF 83 8.28e-04 0.01680 3
#> MAD:NMF 84 2.31e-04 0.00609 3
#> ATC:NMF 85 1.76e-04 0.00487 3
#> SD:skmeans 84 1.12e-04 0.00336 3
#> CV:skmeans 84 1.32e-04 0.00385 3
#> MAD:skmeans 85 8.48e-05 0.00267 3
#> ATC:skmeans 85 2.80e-05 0.00105 3
#> SD:mclust 83 1.97e-03 0.03264 3
#> CV:mclust 70 1.56e-04 0.00353 3
#> MAD:mclust 85 2.97e-04 0.00744 3
#> ATC:mclust 83 3.19e-04 0.00790 3
#> SD:kmeans 82 6.74e-04 0.01431 3
#> CV:kmeans 83 1.97e-03 0.03264 3
#> MAD:kmeans 84 3.89e-04 0.00926 3
#> ATC:kmeans 81 2.02e-04 0.00547 3
#> SD:pam 81 6.50e-05 0.00168 3
#> CV:pam 81 1.67e-03 0.02369 3
#> MAD:pam 81 3.72e-05 0.00135 3
#> ATC:pam 85 1.78e-04 0.00492 3
#> SD:hclust 61 5.60e-03 0.09983 3
#> CV:hclust 74 2.19e-02 0.24306 3
#> MAD:hclust 70 1.32e-04 0.00469 3
#> ATC:hclust 72 4.87e-04 0.01334 3
test_to_known_factors(res_list, k = 4)
#> n disease.state(p) cell.type(p) k
#> SD:NMF 78 1.16e-05 5.77e-04 4
#> CV:NMF 67 2.80e-04 1.09e-02 4
#> MAD:NMF 83 2.94e-05 9.99e-04 4
#> ATC:NMF 77 3.63e-05 1.57e-03 4
#> SD:skmeans 74 6.44e-05 4.22e-03 4
#> CV:skmeans 75 4.71e-05 3.29e-03 4
#> MAD:skmeans 77 8.20e-05 2.61e-03 4
#> ATC:skmeans 80 4.19e-05 2.37e-03 4
#> SD:mclust 82 2.28e-04 1.27e-02 4
#> CV:mclust 79 6.06e-04 2.56e-02 4
#> MAD:mclust 73 6.20e-04 2.15e-02 4
#> ATC:mclust 79 7.25e-05 5.52e-03 4
#> SD:kmeans 74 1.82e-04 1.41e-02 4
#> CV:kmeans 69 1.24e-03 4.48e-02 4
#> MAD:kmeans 68 2.71e-03 7.71e-02 4
#> ATC:kmeans 75 5.12e-05 4.14e-03 4
#> SD:pam 82 1.66e-06 1.92e-04 4
#> CV:pam 79 1.46e-03 4.43e-02 4
#> MAD:pam 82 4.73e-07 8.75e-05 4
#> ATC:pam 84 5.18e-06 6.31e-04 4
#> SD:hclust 66 4.34e-06 9.52e-04 4
#> CV:hclust 70 5.52e-04 2.97e-02 4
#> MAD:hclust 37 1.74e-02 9.57e-02 4
#> ATC:hclust 73 6.08e-06 1.04e-03 4
test_to_known_factors(res_list, k = 5)
#> n disease.state(p) cell.type(p) k
#> SD:NMF 67 7.51e-04 1.65e-02 5
#> CV:NMF 62 3.07e-05 5.86e-04 5
#> MAD:NMF 71 1.56e-04 3.62e-03 5
#> ATC:NMF 67 5.28e-05 1.68e-03 5
#> SD:skmeans 62 1.10e-04 1.58e-02 5
#> CV:skmeans 59 5.15e-04 2.48e-02 5
#> MAD:skmeans 64 3.35e-04 3.38e-02 5
#> ATC:skmeans 76 5.82e-05 2.77e-03 5
#> SD:mclust 80 4.54e-05 7.92e-03 5
#> CV:mclust 72 3.67e-05 8.25e-03 5
#> MAD:mclust 81 2.71e-04 1.04e-02 5
#> ATC:mclust 64 2.38e-05 3.39e-03 5
#> SD:kmeans 68 4.73e-05 1.04e-02 5
#> CV:kmeans 67 7.83e-05 1.40e-02 5
#> MAD:kmeans 62 1.49e-06 4.00e-04 5
#> ATC:kmeans 70 1.04e-04 1.84e-02 5
#> SD:pam 64 1.93e-04 1.47e-02 5
#> CV:pam 58 3.15e-04 2.75e-02 5
#> MAD:pam 74 1.17e-06 8.56e-05 5
#> ATC:pam 78 1.46e-07 9.16e-05 5
#> SD:hclust 70 5.12e-05 3.79e-03 5
#> CV:hclust 64 1.75e-05 4.91e-03 5
#> MAD:hclust 71 3.44e-06 1.50e-03 5
#> ATC:hclust 66 1.86e-06 9.24e-04 5
test_to_known_factors(res_list, k = 6)
#> n disease.state(p) cell.type(p) k
#> SD:NMF 57 1.57e-04 5.00e-03 6
#> CV:NMF 48 9.25e-03 2.10e-01 6
#> MAD:NMF 55 2.97e-03 2.42e-02 6
#> ATC:NMF 69 1.53e-03 3.53e-02 6
#> SD:skmeans 52 5.85e-04 1.26e-02 6
#> CV:skmeans 53 3.08e-04 1.66e-02 6
#> MAD:skmeans 53 2.09e-04 5.39e-03 6
#> ATC:skmeans 60 2.43e-04 9.05e-03 6
#> SD:mclust 67 2.89e-05 4.20e-03 6
#> CV:mclust 76 3.71e-05 1.61e-02 6
#> MAD:mclust 72 1.44e-04 9.40e-03 6
#> ATC:mclust 68 7.73e-05 2.82e-02 6
#> SD:kmeans 56 2.47e-04 2.24e-02 6
#> CV:kmeans 65 9.59e-06 5.03e-03 6
#> MAD:kmeans 59 3.81e-05 5.00e-03 6
#> ATC:kmeans 63 6.22e-05 1.45e-02 6
#> SD:pam 77 4.88e-06 2.71e-03 6
#> CV:pam 75 1.08e-05 4.34e-03 6
#> MAD:pam 79 6.14e-06 1.81e-03 6
#> ATC:pam 76 2.94e-08 7.66e-05 6
#> SD:hclust 53 2.88e-06 1.65e-03 6
#> CV:hclust 64 2.21e-05 5.49e-03 6
#> MAD:hclust 65 8.30e-08 2.83e-05 6
#> ATC:hclust 67 6.41e-06 4.15e-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 21168 rows and 85 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 0.559 0.742 0.897 0.3636 0.649 0.649
#> 3 3 0.462 0.621 0.832 0.7340 0.709 0.551
#> 4 4 0.496 0.635 0.750 0.1311 0.818 0.547
#> 5 5 0.589 0.662 0.806 0.0821 0.922 0.719
#> 6 6 0.654 0.548 0.770 0.0433 0.977 0.896
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
#> GSM99496 1 0.0000 0.888 1.000 0.000
#> GSM99502 1 0.0000 0.888 1.000 0.000
#> GSM99504 1 0.0000 0.888 1.000 0.000
#> GSM99506 1 0.0000 0.888 1.000 0.000
#> GSM99566 1 0.0000 0.888 1.000 0.000
#> GSM99574 1 0.0000 0.888 1.000 0.000
#> GSM99592 1 0.0000 0.888 1.000 0.000
#> GSM99594 1 0.0000 0.888 1.000 0.000
#> GSM99468 1 0.0000 0.888 1.000 0.000
#> GSM99498 1 0.0000 0.888 1.000 0.000
#> GSM99500 1 0.0000 0.888 1.000 0.000
#> GSM99508 1 0.0000 0.888 1.000 0.000
#> GSM99568 1 0.0000 0.888 1.000 0.000
#> GSM99596 1 0.0000 0.888 1.000 0.000
#> GSM99600 2 0.9087 0.566 0.324 0.676
#> GSM99458 1 0.0000 0.888 1.000 0.000
#> GSM99460 1 0.0000 0.888 1.000 0.000
#> GSM99510 1 0.0376 0.886 0.996 0.004
#> GSM99512 1 0.0376 0.886 0.996 0.004
#> GSM99514 1 0.0000 0.888 1.000 0.000
#> GSM99516 1 0.0000 0.888 1.000 0.000
#> GSM99518 1 0.0000 0.888 1.000 0.000
#> GSM99520 1 0.0672 0.884 0.992 0.008
#> GSM99522 1 0.0000 0.888 1.000 0.000
#> GSM99570 1 0.0000 0.888 1.000 0.000
#> GSM99598 1 0.0000 0.888 1.000 0.000
#> GSM99432 1 0.9833 0.186 0.576 0.424
#> GSM99434 1 0.0000 0.888 1.000 0.000
#> GSM99436 2 0.9977 0.177 0.472 0.528
#> GSM99438 2 0.0938 0.804 0.012 0.988
#> GSM99440 1 0.0000 0.888 1.000 0.000
#> GSM99442 2 0.9323 0.524 0.348 0.652
#> GSM99444 2 0.0672 0.803 0.008 0.992
#> GSM99446 2 0.9170 0.554 0.332 0.668
#> GSM99448 1 0.6048 0.765 0.852 0.148
#> GSM99450 1 0.0000 0.888 1.000 0.000
#> GSM99452 1 0.0000 0.888 1.000 0.000
#> GSM99454 1 0.0000 0.888 1.000 0.000
#> GSM99456 1 0.0000 0.888 1.000 0.000
#> GSM99462 2 0.0000 0.800 0.000 1.000
#> GSM99464 1 0.0000 0.888 1.000 0.000
#> GSM99466 1 0.8763 0.541 0.704 0.296
#> GSM99470 1 0.3584 0.842 0.932 0.068
#> GSM99472 1 0.3584 0.842 0.932 0.068
#> GSM99474 1 0.5059 0.802 0.888 0.112
#> GSM99476 1 0.4161 0.830 0.916 0.084
#> GSM99478 1 0.9286 0.435 0.656 0.344
#> GSM99480 1 0.0000 0.888 1.000 0.000
#> GSM99482 1 0.0000 0.888 1.000 0.000
#> GSM99484 1 0.9393 0.411 0.644 0.356
#> GSM99486 1 1.0000 -0.106 0.504 0.496
#> GSM99488 2 0.0000 0.800 0.000 1.000
#> GSM99490 2 0.2423 0.797 0.040 0.960
#> GSM99492 1 0.0000 0.888 1.000 0.000
#> GSM99494 2 0.0000 0.800 0.000 1.000
#> GSM99524 1 0.0000 0.888 1.000 0.000
#> GSM99526 1 0.0672 0.884 0.992 0.008
#> GSM99528 1 0.8443 0.587 0.728 0.272
#> GSM99530 1 0.0000 0.888 1.000 0.000
#> GSM99532 1 0.0000 0.888 1.000 0.000
#> GSM99534 2 0.9988 0.151 0.480 0.520
#> GSM99536 1 0.0000 0.888 1.000 0.000
#> GSM99538 1 0.9686 0.287 0.604 0.396
#> GSM99540 1 0.0000 0.888 1.000 0.000
#> GSM99542 2 0.2236 0.796 0.036 0.964
#> GSM99544 1 0.9686 0.287 0.604 0.396
#> GSM99546 1 0.8016 0.630 0.756 0.244
#> GSM99548 2 0.0000 0.800 0.000 1.000
#> GSM99550 1 0.1184 0.879 0.984 0.016
#> GSM99552 1 0.8861 0.525 0.696 0.304
#> GSM99554 2 0.9850 0.329 0.428 0.572
#> GSM99556 2 0.0376 0.802 0.004 0.996
#> GSM99558 1 0.7745 0.661 0.772 0.228
#> GSM99560 1 0.9170 0.461 0.668 0.332
#> GSM99562 1 0.0000 0.888 1.000 0.000
#> GSM99564 1 1.0000 -0.106 0.504 0.496
#> GSM99572 2 0.0938 0.804 0.012 0.988
#> GSM99576 1 0.3879 0.840 0.924 0.076
#> GSM99578 2 0.5842 0.748 0.140 0.860
#> GSM99580 1 0.5178 0.798 0.884 0.116
#> GSM99582 1 0.4298 0.827 0.912 0.088
#> GSM99584 1 0.9686 0.283 0.604 0.396
#> GSM99586 1 0.0000 0.888 1.000 0.000
#> GSM99588 2 0.9087 0.564 0.324 0.676
#> GSM99590 2 0.0938 0.804 0.012 0.988
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM99496 3 0.0237 0.7198 0.004 0.000 0.996
#> GSM99502 1 0.0000 0.8793 1.000 0.000 0.000
#> GSM99504 1 0.3192 0.8355 0.888 0.000 0.112
#> GSM99506 3 0.0237 0.7198 0.004 0.000 0.996
#> GSM99566 3 0.0237 0.7198 0.004 0.000 0.996
#> GSM99574 1 0.0000 0.8793 1.000 0.000 0.000
#> GSM99592 3 0.0237 0.7198 0.004 0.000 0.996
#> GSM99594 3 0.0237 0.7198 0.004 0.000 0.996
#> GSM99468 1 0.3192 0.8355 0.888 0.000 0.112
#> GSM99498 1 0.3192 0.8355 0.888 0.000 0.112
#> GSM99500 1 0.3192 0.8355 0.888 0.000 0.112
#> GSM99508 3 0.0892 0.7193 0.020 0.000 0.980
#> GSM99568 3 0.4796 0.6101 0.220 0.000 0.780
#> GSM99596 3 0.4178 0.6457 0.172 0.000 0.828
#> GSM99600 2 0.5760 0.4993 0.000 0.672 0.328
#> GSM99458 3 0.6305 -0.0687 0.484 0.000 0.516
#> GSM99460 3 0.5988 0.2697 0.368 0.000 0.632
#> GSM99510 3 0.0475 0.7200 0.004 0.004 0.992
#> GSM99512 3 0.0475 0.7198 0.004 0.004 0.992
#> GSM99514 3 0.0237 0.7198 0.004 0.000 0.996
#> GSM99516 1 0.0000 0.8793 1.000 0.000 0.000
#> GSM99518 1 0.1860 0.8646 0.948 0.000 0.052
#> GSM99520 3 0.1267 0.7202 0.024 0.004 0.972
#> GSM99522 3 0.1964 0.7121 0.056 0.000 0.944
#> GSM99570 1 0.0000 0.8793 1.000 0.000 0.000
#> GSM99598 1 0.0000 0.8793 1.000 0.000 0.000
#> GSM99432 3 0.6192 0.2120 0.000 0.420 0.580
#> GSM99434 3 0.2625 0.7021 0.084 0.000 0.916
#> GSM99436 2 0.6299 0.0914 0.000 0.524 0.476
#> GSM99438 2 0.0592 0.7816 0.000 0.988 0.012
#> GSM99440 1 0.0000 0.8793 1.000 0.000 0.000
#> GSM99442 2 0.5905 0.4495 0.000 0.648 0.352
#> GSM99444 2 0.0424 0.7809 0.000 0.992 0.008
#> GSM99446 2 0.5810 0.4849 0.000 0.664 0.336
#> GSM99448 3 0.3752 0.6607 0.000 0.144 0.856
#> GSM99450 3 0.2711 0.7013 0.088 0.000 0.912
#> GSM99452 1 0.0000 0.8793 1.000 0.000 0.000
#> GSM99454 1 0.0000 0.8793 1.000 0.000 0.000
#> GSM99456 1 0.1031 0.8736 0.976 0.000 0.024
#> GSM99462 2 0.0000 0.7782 0.000 1.000 0.000
#> GSM99464 3 0.5760 0.3764 0.328 0.000 0.672
#> GSM99466 3 0.6326 0.5116 0.020 0.292 0.688
#> GSM99470 1 0.7318 0.5717 0.668 0.068 0.264
#> GSM99472 1 0.7318 0.5717 0.668 0.068 0.264
#> GSM99474 3 0.5304 0.6923 0.068 0.108 0.824
#> GSM99476 3 0.2860 0.7010 0.004 0.084 0.912
#> GSM99478 3 0.6651 0.4294 0.020 0.340 0.640
#> GSM99480 1 0.0000 0.8793 1.000 0.000 0.000
#> GSM99482 1 0.0000 0.8793 1.000 0.000 0.000
#> GSM99484 3 0.7462 0.4007 0.048 0.352 0.600
#> GSM99486 3 0.6308 -0.0395 0.000 0.492 0.508
#> GSM99488 2 0.0000 0.7782 0.000 1.000 0.000
#> GSM99490 2 0.1529 0.7727 0.000 0.960 0.040
#> GSM99492 1 0.0000 0.8793 1.000 0.000 0.000
#> GSM99494 2 0.0000 0.7782 0.000 1.000 0.000
#> GSM99524 1 0.0000 0.8793 1.000 0.000 0.000
#> GSM99526 3 0.3375 0.6980 0.100 0.008 0.892
#> GSM99528 3 0.8790 0.4438 0.160 0.268 0.572
#> GSM99530 3 0.6225 0.0602 0.432 0.000 0.568
#> GSM99532 1 0.6291 0.2115 0.532 0.000 0.468
#> GSM99534 2 0.8772 0.1904 0.120 0.516 0.364
#> GSM99536 1 0.0424 0.8782 0.992 0.000 0.008
#> GSM99538 3 0.6095 0.3021 0.000 0.392 0.608
#> GSM99540 1 0.6280 0.2330 0.540 0.000 0.460
#> GSM99542 2 0.1647 0.7588 0.036 0.960 0.004
#> GSM99544 3 0.6095 0.3021 0.000 0.392 0.608
#> GSM99546 3 0.7381 0.5737 0.080 0.244 0.676
#> GSM99548 2 0.0000 0.7782 0.000 1.000 0.000
#> GSM99550 1 0.4723 0.7728 0.824 0.016 0.160
#> GSM99552 3 0.5785 0.4943 0.004 0.300 0.696
#> GSM99554 2 0.6225 0.2523 0.000 0.568 0.432
#> GSM99556 2 0.0237 0.7796 0.000 0.996 0.004
#> GSM99558 3 0.5070 0.5952 0.004 0.224 0.772
#> GSM99560 3 0.6448 0.4495 0.016 0.328 0.656
#> GSM99562 3 0.0237 0.7198 0.004 0.000 0.996
#> GSM99564 3 0.6308 -0.0395 0.000 0.492 0.508
#> GSM99572 2 0.0592 0.7816 0.000 0.988 0.012
#> GSM99576 1 0.8097 0.3211 0.540 0.072 0.388
#> GSM99578 2 0.3686 0.7139 0.000 0.860 0.140
#> GSM99580 3 0.3607 0.6837 0.008 0.112 0.880
#> GSM99582 3 0.5346 0.6950 0.088 0.088 0.824
#> GSM99584 3 0.8180 0.2874 0.076 0.392 0.532
#> GSM99586 1 0.1031 0.8736 0.976 0.000 0.024
#> GSM99588 2 0.5956 0.5114 0.004 0.672 0.324
#> GSM99590 2 0.0592 0.7816 0.000 0.988 0.012
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM99496 3 0.0188 0.6808 0.000 0.000 0.996 0.004
#> GSM99502 1 0.0000 0.8854 1.000 0.000 0.000 0.000
#> GSM99504 1 0.3325 0.8279 0.864 0.000 0.112 0.024
#> GSM99506 3 0.0188 0.6808 0.000 0.000 0.996 0.004
#> GSM99566 3 0.0188 0.6808 0.000 0.000 0.996 0.004
#> GSM99574 1 0.0000 0.8854 1.000 0.000 0.000 0.000
#> GSM99592 3 0.1211 0.6725 0.000 0.000 0.960 0.040
#> GSM99594 3 0.0188 0.6808 0.000 0.000 0.996 0.004
#> GSM99468 1 0.3325 0.8279 0.864 0.000 0.112 0.024
#> GSM99498 1 0.3325 0.8279 0.864 0.000 0.112 0.024
#> GSM99500 1 0.3325 0.8279 0.864 0.000 0.112 0.024
#> GSM99508 3 0.0524 0.6819 0.008 0.000 0.988 0.004
#> GSM99568 3 0.4511 0.5842 0.176 0.000 0.784 0.040
#> GSM99596 3 0.3863 0.5978 0.144 0.000 0.828 0.028
#> GSM99600 4 0.7042 0.4742 0.000 0.352 0.132 0.516
#> GSM99458 3 0.7838 0.2212 0.316 0.000 0.404 0.280
#> GSM99460 3 0.6835 0.4709 0.156 0.000 0.592 0.252
#> GSM99510 3 0.1557 0.6645 0.000 0.000 0.944 0.056
#> GSM99512 3 0.0895 0.6760 0.000 0.004 0.976 0.020
#> GSM99514 3 0.0336 0.6810 0.000 0.000 0.992 0.008
#> GSM99516 1 0.0000 0.8854 1.000 0.000 0.000 0.000
#> GSM99518 1 0.2385 0.8634 0.920 0.000 0.052 0.028
#> GSM99520 3 0.2376 0.6596 0.016 0.000 0.916 0.068
#> GSM99522 3 0.1584 0.6781 0.036 0.000 0.952 0.012
#> GSM99570 1 0.0000 0.8854 1.000 0.000 0.000 0.000
#> GSM99598 1 0.0000 0.8854 1.000 0.000 0.000 0.000
#> GSM99432 4 0.6854 0.6795 0.000 0.120 0.332 0.548
#> GSM99434 3 0.3842 0.6458 0.036 0.000 0.836 0.128
#> GSM99436 4 0.7042 0.6948 0.000 0.188 0.240 0.572
#> GSM99438 2 0.3074 0.8628 0.000 0.848 0.000 0.152
#> GSM99440 1 0.0000 0.8854 1.000 0.000 0.000 0.000
#> GSM99442 4 0.7164 0.5400 0.000 0.320 0.156 0.524
#> GSM99444 2 0.2868 0.8708 0.000 0.864 0.000 0.136
#> GSM99446 4 0.7058 0.4920 0.000 0.344 0.136 0.520
#> GSM99448 3 0.5062 0.2586 0.000 0.024 0.692 0.284
#> GSM99450 3 0.3706 0.6513 0.040 0.000 0.848 0.112
#> GSM99452 1 0.0000 0.8854 1.000 0.000 0.000 0.000
#> GSM99454 1 0.0000 0.8854 1.000 0.000 0.000 0.000
#> GSM99456 1 0.4746 0.7165 0.688 0.000 0.008 0.304
#> GSM99462 2 0.2011 0.8888 0.000 0.920 0.000 0.080
#> GSM99464 3 0.6538 0.4987 0.140 0.000 0.628 0.232
#> GSM99466 4 0.5993 0.5244 0.008 0.028 0.408 0.556
#> GSM99470 1 0.6994 0.5446 0.604 0.012 0.128 0.256
#> GSM99472 1 0.6994 0.5446 0.604 0.012 0.128 0.256
#> GSM99474 3 0.5378 0.4297 0.036 0.004 0.696 0.264
#> GSM99476 3 0.4372 0.3843 0.000 0.004 0.728 0.268
#> GSM99478 4 0.6401 0.6082 0.008 0.056 0.364 0.572
#> GSM99480 1 0.0000 0.8854 1.000 0.000 0.000 0.000
#> GSM99482 1 0.0707 0.8812 0.980 0.000 0.000 0.020
#> GSM99484 4 0.6394 0.6167 0.012 0.060 0.316 0.612
#> GSM99486 4 0.6868 0.6990 0.000 0.152 0.264 0.584
#> GSM99488 2 0.0336 0.8678 0.000 0.992 0.000 0.008
#> GSM99490 2 0.2706 0.8719 0.000 0.900 0.020 0.080
#> GSM99492 1 0.2589 0.8473 0.884 0.000 0.000 0.116
#> GSM99494 2 0.0336 0.8678 0.000 0.992 0.000 0.008
#> GSM99524 1 0.0000 0.8854 1.000 0.000 0.000 0.000
#> GSM99526 3 0.4418 0.6213 0.032 0.000 0.784 0.184
#> GSM99528 4 0.7142 0.3270 0.052 0.044 0.360 0.544
#> GSM99530 3 0.6991 0.4154 0.136 0.000 0.540 0.324
#> GSM99532 3 0.7717 0.2155 0.304 0.000 0.444 0.252
#> GSM99534 4 0.7778 0.5130 0.064 0.208 0.132 0.596
#> GSM99536 1 0.1256 0.8803 0.964 0.000 0.008 0.028
#> GSM99538 4 0.6589 0.6549 0.000 0.092 0.352 0.556
#> GSM99540 3 0.7731 0.1865 0.316 0.000 0.436 0.248
#> GSM99542 2 0.2654 0.8235 0.004 0.888 0.000 0.108
#> GSM99544 4 0.6589 0.6549 0.000 0.092 0.352 0.556
#> GSM99546 4 0.6528 0.3559 0.032 0.024 0.432 0.512
#> GSM99548 2 0.1389 0.8855 0.000 0.952 0.000 0.048
#> GSM99550 1 0.7006 0.5109 0.528 0.000 0.132 0.340
#> GSM99552 3 0.6366 -0.4103 0.000 0.064 0.512 0.424
#> GSM99554 4 0.7117 0.6535 0.000 0.228 0.208 0.564
#> GSM99556 2 0.1302 0.8859 0.000 0.956 0.000 0.044
#> GSM99558 3 0.6000 -0.0871 0.000 0.052 0.592 0.356
#> GSM99560 4 0.6612 0.5819 0.004 0.072 0.400 0.524
#> GSM99562 3 0.0188 0.6808 0.000 0.000 0.996 0.004
#> GSM99564 4 0.6868 0.6990 0.000 0.152 0.264 0.584
#> GSM99572 2 0.3172 0.8554 0.000 0.840 0.000 0.160
#> GSM99576 4 0.8283 -0.2476 0.320 0.012 0.308 0.360
#> GSM99578 2 0.4986 0.6517 0.000 0.740 0.044 0.216
#> GSM99580 3 0.4368 0.3917 0.004 0.004 0.748 0.244
#> GSM99582 3 0.5873 0.4016 0.056 0.004 0.660 0.280
#> GSM99584 4 0.7346 0.6407 0.032 0.096 0.304 0.568
#> GSM99586 1 0.4746 0.7165 0.688 0.000 0.008 0.304
#> GSM99588 4 0.7398 0.3536 0.000 0.412 0.164 0.424
#> GSM99590 2 0.2973 0.8662 0.000 0.856 0.000 0.144
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM99496 3 0.0451 0.746 0.000 0.000 0.988 0.004 0.008
#> GSM99502 1 0.0000 0.847 1.000 0.000 0.000 0.000 0.000
#> GSM99504 1 0.3055 0.766 0.864 0.000 0.072 0.000 0.064
#> GSM99506 3 0.0451 0.746 0.000 0.000 0.988 0.004 0.008
#> GSM99566 3 0.0771 0.742 0.000 0.000 0.976 0.004 0.020
#> GSM99574 1 0.0000 0.847 1.000 0.000 0.000 0.000 0.000
#> GSM99592 3 0.2144 0.747 0.000 0.000 0.912 0.068 0.020
#> GSM99594 3 0.0771 0.742 0.000 0.000 0.976 0.004 0.020
#> GSM99468 1 0.3055 0.766 0.864 0.000 0.072 0.000 0.064
#> GSM99498 1 0.3055 0.766 0.864 0.000 0.072 0.000 0.064
#> GSM99500 1 0.3055 0.766 0.864 0.000 0.072 0.000 0.064
#> GSM99508 3 0.0671 0.745 0.004 0.000 0.980 0.000 0.016
#> GSM99568 3 0.4922 0.481 0.156 0.000 0.732 0.008 0.104
#> GSM99596 3 0.4192 0.534 0.144 0.000 0.784 0.004 0.068
#> GSM99600 4 0.3766 0.552 0.000 0.268 0.004 0.728 0.000
#> GSM99458 5 0.7707 0.610 0.212 0.000 0.184 0.116 0.488
#> GSM99460 5 0.5271 0.571 0.052 0.000 0.272 0.016 0.660
#> GSM99510 3 0.3339 0.727 0.000 0.000 0.840 0.112 0.048
#> GSM99512 3 0.1845 0.745 0.000 0.000 0.928 0.056 0.016
#> GSM99514 3 0.0671 0.747 0.000 0.000 0.980 0.004 0.016
#> GSM99516 1 0.0000 0.847 1.000 0.000 0.000 0.000 0.000
#> GSM99518 1 0.1894 0.811 0.920 0.000 0.008 0.000 0.072
#> GSM99520 3 0.2331 0.743 0.008 0.000 0.908 0.068 0.016
#> GSM99522 3 0.1981 0.723 0.016 0.000 0.920 0.000 0.064
#> GSM99570 1 0.0000 0.847 1.000 0.000 0.000 0.000 0.000
#> GSM99598 1 0.0000 0.847 1.000 0.000 0.000 0.000 0.000
#> GSM99432 4 0.3735 0.751 0.000 0.040 0.116 0.828 0.016
#> GSM99434 3 0.5224 0.623 0.012 0.000 0.712 0.128 0.148
#> GSM99436 4 0.2628 0.726 0.000 0.088 0.028 0.884 0.000
#> GSM99438 2 0.3143 0.821 0.000 0.796 0.000 0.204 0.000
#> GSM99440 1 0.0000 0.847 1.000 0.000 0.000 0.000 0.000
#> GSM99442 4 0.3461 0.610 0.000 0.224 0.004 0.772 0.000
#> GSM99444 2 0.2813 0.845 0.000 0.832 0.000 0.168 0.000
#> GSM99446 4 0.3689 0.571 0.000 0.256 0.004 0.740 0.000
#> GSM99448 3 0.4726 0.338 0.000 0.000 0.580 0.400 0.020
#> GSM99450 3 0.5183 0.621 0.016 0.000 0.720 0.112 0.152
#> GSM99452 1 0.0000 0.847 1.000 0.000 0.000 0.000 0.000
#> GSM99454 1 0.0000 0.847 1.000 0.000 0.000 0.000 0.000
#> GSM99456 1 0.4397 0.107 0.564 0.000 0.004 0.000 0.432
#> GSM99462 2 0.2233 0.870 0.000 0.892 0.000 0.104 0.004
#> GSM99464 5 0.5235 0.509 0.036 0.000 0.300 0.020 0.644
#> GSM99466 4 0.4599 0.681 0.004 0.000 0.156 0.752 0.088
#> GSM99470 1 0.6812 0.311 0.600 0.012 0.052 0.220 0.116
#> GSM99472 1 0.6812 0.311 0.600 0.012 0.052 0.220 0.116
#> GSM99474 3 0.5537 0.561 0.012 0.000 0.648 0.256 0.084
#> GSM99476 3 0.5790 0.205 0.000 0.000 0.500 0.408 0.092
#> GSM99478 4 0.4173 0.711 0.004 0.000 0.148 0.784 0.064
#> GSM99480 1 0.0000 0.847 1.000 0.000 0.000 0.000 0.000
#> GSM99482 1 0.0740 0.839 0.980 0.004 0.000 0.008 0.008
#> GSM99484 4 0.4895 0.718 0.008 0.028 0.088 0.772 0.104
#> GSM99486 4 0.2139 0.737 0.000 0.052 0.032 0.916 0.000
#> GSM99488 2 0.1012 0.854 0.000 0.968 0.000 0.020 0.012
#> GSM99490 2 0.2389 0.855 0.000 0.880 0.000 0.116 0.004
#> GSM99492 1 0.2471 0.744 0.864 0.000 0.000 0.000 0.136
#> GSM99494 2 0.1012 0.854 0.000 0.968 0.000 0.020 0.012
#> GSM99524 1 0.0000 0.847 1.000 0.000 0.000 0.000 0.000
#> GSM99526 3 0.6591 0.166 0.012 0.000 0.460 0.148 0.380
#> GSM99528 4 0.6512 0.450 0.012 0.020 0.092 0.544 0.332
#> GSM99530 5 0.2664 0.622 0.020 0.000 0.092 0.004 0.884
#> GSM99532 5 0.5847 0.693 0.204 0.000 0.188 0.000 0.608
#> GSM99534 4 0.6319 0.531 0.060 0.192 0.008 0.652 0.088
#> GSM99536 1 0.0963 0.834 0.964 0.000 0.000 0.000 0.036
#> GSM99538 4 0.2929 0.740 0.000 0.012 0.128 0.856 0.004
#> GSM99540 5 0.5867 0.691 0.216 0.000 0.180 0.000 0.604
#> GSM99542 2 0.2592 0.793 0.000 0.892 0.000 0.052 0.056
#> GSM99544 4 0.2929 0.740 0.000 0.012 0.128 0.856 0.004
#> GSM99546 4 0.5963 0.499 0.012 0.000 0.232 0.620 0.136
#> GSM99548 2 0.1697 0.868 0.000 0.932 0.000 0.060 0.008
#> GSM99550 5 0.4867 0.283 0.404 0.004 0.008 0.008 0.576
#> GSM99552 4 0.4456 0.493 0.000 0.000 0.320 0.660 0.020
#> GSM99554 4 0.2771 0.693 0.000 0.128 0.012 0.860 0.000
#> GSM99556 2 0.1502 0.869 0.000 0.940 0.000 0.056 0.004
#> GSM99558 4 0.4781 0.136 0.000 0.000 0.428 0.552 0.020
#> GSM99560 4 0.4609 0.722 0.004 0.016 0.072 0.776 0.132
#> GSM99562 3 0.0566 0.745 0.000 0.000 0.984 0.004 0.012
#> GSM99564 4 0.2139 0.737 0.000 0.052 0.032 0.916 0.000
#> GSM99572 2 0.3210 0.812 0.000 0.788 0.000 0.212 0.000
#> GSM99576 5 0.6815 0.576 0.240 0.016 0.044 0.108 0.592
#> GSM99578 2 0.4065 0.645 0.000 0.720 0.000 0.264 0.016
#> GSM99580 3 0.4422 0.540 0.004 0.000 0.680 0.300 0.016
#> GSM99582 3 0.6742 0.264 0.028 0.000 0.488 0.352 0.132
#> GSM99584 4 0.5090 0.711 0.012 0.024 0.128 0.756 0.080
#> GSM99586 1 0.4397 0.107 0.564 0.000 0.004 0.000 0.432
#> GSM99588 4 0.4356 0.422 0.000 0.340 0.012 0.648 0.000
#> GSM99590 2 0.2891 0.840 0.000 0.824 0.000 0.176 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM99496 3 0.0000 0.71710 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99502 1 0.0000 0.83483 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99504 1 0.3208 0.75576 0.844 0.000 0.068 0.000 0.076 0.012
#> GSM99506 3 0.0000 0.71710 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99566 3 0.0909 0.71382 0.000 0.000 0.968 0.000 0.020 0.012
#> GSM99574 1 0.0000 0.83483 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99592 3 0.2940 0.68113 0.000 0.000 0.848 0.036 0.004 0.112
#> GSM99594 3 0.0909 0.71382 0.000 0.000 0.968 0.000 0.020 0.012
#> GSM99468 1 0.3208 0.75576 0.844 0.000 0.068 0.000 0.076 0.012
#> GSM99498 1 0.3208 0.75576 0.844 0.000 0.068 0.000 0.076 0.012
#> GSM99500 1 0.3208 0.75576 0.844 0.000 0.068 0.000 0.076 0.012
#> GSM99508 3 0.0458 0.71778 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM99568 3 0.4917 0.51713 0.128 0.000 0.716 0.000 0.116 0.040
#> GSM99596 3 0.3870 0.55606 0.128 0.000 0.788 0.000 0.072 0.012
#> GSM99600 4 0.3302 0.48299 0.000 0.232 0.000 0.760 0.004 0.004
#> GSM99458 5 0.7164 0.41785 0.172 0.000 0.056 0.024 0.420 0.328
#> GSM99460 5 0.5714 0.37264 0.020 0.000 0.100 0.004 0.552 0.324
#> GSM99510 3 0.4763 0.50056 0.000 0.000 0.620 0.052 0.008 0.320
#> GSM99512 3 0.3419 0.65153 0.000 0.000 0.792 0.028 0.004 0.176
#> GSM99514 3 0.0363 0.71869 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM99516 1 0.0000 0.83483 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99518 1 0.2062 0.79579 0.900 0.000 0.008 0.000 0.088 0.004
#> GSM99520 3 0.2782 0.69436 0.000 0.000 0.876 0.032 0.024 0.068
#> GSM99522 3 0.2672 0.69290 0.000 0.000 0.868 0.000 0.052 0.080
#> GSM99570 1 0.0000 0.83483 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99598 1 0.0000 0.83483 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99432 4 0.3106 0.53563 0.000 0.016 0.024 0.840 0.000 0.120
#> GSM99434 3 0.5811 0.13105 0.000 0.000 0.448 0.044 0.068 0.440
#> GSM99436 4 0.1285 0.56905 0.000 0.052 0.004 0.944 0.000 0.000
#> GSM99438 2 0.2854 0.81614 0.000 0.792 0.000 0.208 0.000 0.000
#> GSM99440 1 0.0000 0.83483 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99442 4 0.2838 0.51842 0.000 0.188 0.000 0.808 0.000 0.004
#> GSM99444 2 0.2738 0.83817 0.000 0.820 0.000 0.176 0.000 0.004
#> GSM99446 4 0.3650 0.50218 0.000 0.216 0.000 0.756 0.004 0.024
#> GSM99448 3 0.5716 0.20256 0.000 0.000 0.500 0.312 0.000 0.188
#> GSM99450 3 0.5775 0.17812 0.000 0.000 0.472 0.036 0.076 0.416
#> GSM99452 1 0.0000 0.83483 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99454 1 0.0000 0.83483 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99456 1 0.4338 -0.07178 0.492 0.000 0.000 0.000 0.488 0.020
#> GSM99462 2 0.2218 0.86158 0.000 0.884 0.000 0.104 0.000 0.012
#> GSM99464 5 0.5504 0.29938 0.004 0.000 0.108 0.004 0.536 0.348
#> GSM99466 4 0.5204 0.33518 0.000 0.000 0.072 0.632 0.028 0.268
#> GSM99470 1 0.5823 0.29577 0.564 0.000 0.016 0.072 0.028 0.320
#> GSM99472 1 0.5823 0.29577 0.564 0.000 0.016 0.072 0.028 0.320
#> GSM99474 3 0.6351 0.38062 0.000 0.000 0.568 0.172 0.084 0.176
#> GSM99476 4 0.6623 -0.18142 0.000 0.000 0.384 0.384 0.044 0.188
#> GSM99478 4 0.4917 0.39960 0.000 0.000 0.072 0.656 0.016 0.256
#> GSM99480 1 0.0363 0.83185 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM99482 1 0.0790 0.82220 0.968 0.000 0.000 0.000 0.000 0.032
#> GSM99484 4 0.4969 0.35525 0.000 0.020 0.020 0.628 0.020 0.312
#> GSM99486 4 0.0603 0.56921 0.000 0.016 0.004 0.980 0.000 0.000
#> GSM99488 2 0.0363 0.84421 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM99490 2 0.2592 0.83900 0.000 0.864 0.000 0.116 0.004 0.016
#> GSM99492 1 0.2859 0.71069 0.828 0.000 0.000 0.000 0.156 0.016
#> GSM99494 2 0.0363 0.84421 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM99524 1 0.0000 0.83483 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99526 6 0.6322 -0.00897 0.000 0.000 0.136 0.068 0.252 0.544
#> GSM99528 4 0.6782 -0.05878 0.000 0.012 0.024 0.420 0.272 0.272
#> GSM99530 5 0.1794 0.45199 0.000 0.000 0.036 0.000 0.924 0.040
#> GSM99532 5 0.5820 0.59838 0.168 0.000 0.100 0.000 0.636 0.096
#> GSM99534 4 0.6705 0.17502 0.036 0.156 0.000 0.452 0.016 0.340
#> GSM99536 1 0.1141 0.82051 0.948 0.000 0.000 0.000 0.052 0.000
#> GSM99538 4 0.3649 0.49539 0.000 0.000 0.040 0.764 0.000 0.196
#> GSM99540 5 0.5822 0.59974 0.180 0.000 0.092 0.000 0.632 0.096
#> GSM99542 2 0.2504 0.77845 0.000 0.856 0.000 0.004 0.004 0.136
#> GSM99544 4 0.3649 0.49539 0.000 0.000 0.040 0.764 0.000 0.196
#> GSM99546 6 0.5850 -0.14142 0.000 0.000 0.044 0.428 0.072 0.456
#> GSM99548 2 0.1296 0.86021 0.000 0.948 0.000 0.044 0.004 0.004
#> GSM99550 5 0.4884 0.40241 0.332 0.004 0.000 0.008 0.608 0.048
#> GSM99552 4 0.5304 0.25562 0.000 0.000 0.276 0.580 0.000 0.144
#> GSM99554 4 0.1858 0.55992 0.000 0.092 0.000 0.904 0.000 0.004
#> GSM99556 2 0.1657 0.86060 0.000 0.928 0.000 0.056 0.000 0.016
#> GSM99558 4 0.5680 0.04941 0.000 0.000 0.360 0.476 0.000 0.164
#> GSM99560 4 0.4666 0.45009 0.000 0.008 0.008 0.720 0.092 0.172
#> GSM99562 3 0.1204 0.71114 0.000 0.000 0.944 0.000 0.000 0.056
#> GSM99564 4 0.0603 0.56921 0.000 0.016 0.004 0.980 0.000 0.000
#> GSM99572 2 0.3052 0.80942 0.000 0.780 0.000 0.216 0.004 0.000
#> GSM99576 5 0.6270 0.49480 0.200 0.000 0.008 0.052 0.580 0.160
#> GSM99578 2 0.4415 0.59963 0.000 0.696 0.000 0.236 0.004 0.064
#> GSM99580 3 0.5395 0.41820 0.000 0.000 0.612 0.216 0.008 0.164
#> GSM99582 3 0.7273 -0.15862 0.004 0.000 0.404 0.296 0.108 0.188
#> GSM99584 4 0.4533 0.40822 0.000 0.004 0.032 0.736 0.048 0.180
#> GSM99586 1 0.4338 -0.07178 0.492 0.000 0.000 0.000 0.488 0.020
#> GSM99588 4 0.4975 0.41490 0.000 0.312 0.000 0.596 0.000 0.092
#> GSM99590 2 0.2664 0.83442 0.000 0.816 0.000 0.184 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) cell.type(p) k
#> SD:hclust 73 1.31e-02 0.039908 2
#> SD:hclust 61 5.60e-03 0.099827 3
#> SD:hclust 66 4.34e-06 0.000952 4
#> SD:hclust 70 5.12e-05 0.003785 5
#> SD:hclust 53 2.88e-06 0.001654 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 21168 rows and 85 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.691 0.898 0.947 0.4852 0.514 0.514
#> 3 3 0.984 0.937 0.974 0.3849 0.718 0.499
#> 4 4 0.744 0.770 0.851 0.1042 0.860 0.613
#> 5 5 0.746 0.701 0.837 0.0635 0.940 0.772
#> 6 6 0.758 0.591 0.784 0.0421 0.968 0.853
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
#> GSM99496 1 0.6531 0.844 0.832 0.168
#> GSM99502 1 0.0000 0.917 1.000 0.000
#> GSM99504 1 0.0000 0.917 1.000 0.000
#> GSM99506 1 0.6531 0.844 0.832 0.168
#> GSM99566 1 0.6531 0.844 0.832 0.168
#> GSM99574 1 0.0000 0.917 1.000 0.000
#> GSM99592 1 0.6531 0.844 0.832 0.168
#> GSM99594 1 0.6531 0.844 0.832 0.168
#> GSM99468 1 0.0000 0.917 1.000 0.000
#> GSM99498 1 0.0000 0.917 1.000 0.000
#> GSM99500 1 0.0000 0.917 1.000 0.000
#> GSM99508 1 0.5408 0.870 0.876 0.124
#> GSM99568 1 0.6531 0.844 0.832 0.168
#> GSM99596 1 0.0376 0.916 0.996 0.004
#> GSM99600 2 0.0000 0.981 0.000 1.000
#> GSM99458 1 0.0000 0.917 1.000 0.000
#> GSM99460 1 0.0000 0.917 1.000 0.000
#> GSM99510 1 0.9580 0.528 0.620 0.380
#> GSM99512 1 0.9580 0.528 0.620 0.380
#> GSM99514 1 0.6531 0.844 0.832 0.168
#> GSM99516 1 0.0000 0.917 1.000 0.000
#> GSM99518 1 0.0000 0.917 1.000 0.000
#> GSM99520 1 0.6438 0.847 0.836 0.164
#> GSM99522 1 0.0000 0.917 1.000 0.000
#> GSM99570 1 0.0000 0.917 1.000 0.000
#> GSM99598 1 0.0000 0.917 1.000 0.000
#> GSM99432 2 0.0000 0.981 0.000 1.000
#> GSM99434 1 0.8016 0.758 0.756 0.244
#> GSM99436 2 0.0000 0.981 0.000 1.000
#> GSM99438 2 0.0000 0.981 0.000 1.000
#> GSM99440 1 0.0000 0.917 1.000 0.000
#> GSM99442 2 0.0000 0.981 0.000 1.000
#> GSM99444 2 0.0000 0.981 0.000 1.000
#> GSM99446 2 0.0000 0.981 0.000 1.000
#> GSM99448 2 0.0000 0.981 0.000 1.000
#> GSM99450 1 0.4690 0.881 0.900 0.100
#> GSM99452 1 0.0000 0.917 1.000 0.000
#> GSM99454 1 0.0000 0.917 1.000 0.000
#> GSM99456 1 0.0000 0.917 1.000 0.000
#> GSM99462 2 0.0000 0.981 0.000 1.000
#> GSM99464 1 0.0000 0.917 1.000 0.000
#> GSM99466 2 0.0000 0.981 0.000 1.000
#> GSM99470 1 0.3879 0.892 0.924 0.076
#> GSM99472 1 0.0000 0.917 1.000 0.000
#> GSM99474 1 0.6531 0.844 0.832 0.168
#> GSM99476 2 0.0000 0.981 0.000 1.000
#> GSM99478 2 0.0000 0.981 0.000 1.000
#> GSM99480 1 0.0000 0.917 1.000 0.000
#> GSM99482 1 0.0000 0.917 1.000 0.000
#> GSM99484 2 0.0000 0.981 0.000 1.000
#> GSM99486 2 0.0000 0.981 0.000 1.000
#> GSM99488 2 0.0000 0.981 0.000 1.000
#> GSM99490 2 0.0000 0.981 0.000 1.000
#> GSM99492 1 0.0000 0.917 1.000 0.000
#> GSM99494 2 0.0000 0.981 0.000 1.000
#> GSM99524 1 0.0000 0.917 1.000 0.000
#> GSM99526 1 0.9358 0.586 0.648 0.352
#> GSM99528 2 0.3114 0.917 0.056 0.944
#> GSM99530 1 0.0938 0.914 0.988 0.012
#> GSM99532 1 0.0000 0.917 1.000 0.000
#> GSM99534 2 0.0000 0.981 0.000 1.000
#> GSM99536 1 0.0000 0.917 1.000 0.000
#> GSM99538 2 0.0000 0.981 0.000 1.000
#> GSM99540 1 0.0000 0.917 1.000 0.000
#> GSM99542 2 0.0000 0.981 0.000 1.000
#> GSM99544 2 0.0000 0.981 0.000 1.000
#> GSM99546 2 0.9998 -0.194 0.492 0.508
#> GSM99548 2 0.0000 0.981 0.000 1.000
#> GSM99550 1 0.0000 0.917 1.000 0.000
#> GSM99552 1 0.9286 0.603 0.656 0.344
#> GSM99554 2 0.0000 0.981 0.000 1.000
#> GSM99556 2 0.0000 0.981 0.000 1.000
#> GSM99558 2 0.0000 0.981 0.000 1.000
#> GSM99560 2 0.0000 0.981 0.000 1.000
#> GSM99562 1 0.6531 0.844 0.832 0.168
#> GSM99564 2 0.0000 0.981 0.000 1.000
#> GSM99572 2 0.0000 0.981 0.000 1.000
#> GSM99576 1 0.0000 0.917 1.000 0.000
#> GSM99578 2 0.0000 0.981 0.000 1.000
#> GSM99580 1 0.6623 0.840 0.828 0.172
#> GSM99582 1 0.4815 0.880 0.896 0.104
#> GSM99584 2 0.0000 0.981 0.000 1.000
#> GSM99586 1 0.0000 0.917 1.000 0.000
#> GSM99588 2 0.0000 0.981 0.000 1.000
#> GSM99590 2 0.0000 0.981 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM99496 3 0.0237 0.953 0.000 0.004 0.996
#> GSM99502 1 0.0237 0.998 0.996 0.000 0.004
#> GSM99504 1 0.0237 0.998 0.996 0.000 0.004
#> GSM99506 3 0.0237 0.953 0.000 0.004 0.996
#> GSM99566 3 0.0237 0.953 0.000 0.004 0.996
#> GSM99574 1 0.0237 0.998 0.996 0.000 0.004
#> GSM99592 3 0.0237 0.953 0.000 0.004 0.996
#> GSM99594 3 0.0237 0.953 0.000 0.004 0.996
#> GSM99468 1 0.0237 0.998 0.996 0.000 0.004
#> GSM99498 1 0.0237 0.998 0.996 0.000 0.004
#> GSM99500 1 0.0237 0.998 0.996 0.000 0.004
#> GSM99508 3 0.0237 0.953 0.000 0.004 0.996
#> GSM99568 3 0.0237 0.953 0.000 0.004 0.996
#> GSM99596 3 0.0237 0.950 0.004 0.000 0.996
#> GSM99600 2 0.0000 0.970 0.000 1.000 0.000
#> GSM99458 1 0.0237 0.998 0.996 0.000 0.004
#> GSM99460 1 0.0424 0.997 0.992 0.000 0.008
#> GSM99510 3 0.0237 0.953 0.000 0.004 0.996
#> GSM99512 3 0.0237 0.953 0.000 0.004 0.996
#> GSM99514 3 0.0237 0.953 0.000 0.004 0.996
#> GSM99516 1 0.0237 0.998 0.996 0.000 0.004
#> GSM99518 1 0.0237 0.998 0.996 0.000 0.004
#> GSM99520 3 0.0237 0.953 0.000 0.004 0.996
#> GSM99522 3 0.0237 0.950 0.004 0.000 0.996
#> GSM99570 1 0.0237 0.998 0.996 0.000 0.004
#> GSM99598 1 0.0237 0.998 0.996 0.000 0.004
#> GSM99432 2 0.0000 0.970 0.000 1.000 0.000
#> GSM99434 3 0.0237 0.953 0.000 0.004 0.996
#> GSM99436 2 0.0000 0.970 0.000 1.000 0.000
#> GSM99438 2 0.0000 0.970 0.000 1.000 0.000
#> GSM99440 1 0.0237 0.998 0.996 0.000 0.004
#> GSM99442 2 0.0000 0.970 0.000 1.000 0.000
#> GSM99444 2 0.0000 0.970 0.000 1.000 0.000
#> GSM99446 2 0.0000 0.970 0.000 1.000 0.000
#> GSM99448 3 0.0424 0.950 0.000 0.008 0.992
#> GSM99450 3 0.0237 0.953 0.000 0.004 0.996
#> GSM99452 1 0.0000 0.996 1.000 0.000 0.000
#> GSM99454 1 0.0237 0.998 0.996 0.000 0.004
#> GSM99456 1 0.0424 0.997 0.992 0.000 0.008
#> GSM99462 2 0.0000 0.970 0.000 1.000 0.000
#> GSM99464 3 0.0000 0.950 0.000 0.000 1.000
#> GSM99466 3 0.6386 0.295 0.004 0.412 0.584
#> GSM99470 1 0.0000 0.996 1.000 0.000 0.000
#> GSM99472 1 0.0000 0.996 1.000 0.000 0.000
#> GSM99474 3 0.0237 0.953 0.000 0.004 0.996
#> GSM99476 3 0.0475 0.951 0.004 0.004 0.992
#> GSM99478 2 0.5722 0.575 0.004 0.704 0.292
#> GSM99480 1 0.0424 0.997 0.992 0.000 0.008
#> GSM99482 1 0.0000 0.996 1.000 0.000 0.000
#> GSM99484 2 0.0237 0.968 0.004 0.996 0.000
#> GSM99486 2 0.0000 0.970 0.000 1.000 0.000
#> GSM99488 2 0.0000 0.970 0.000 1.000 0.000
#> GSM99490 2 0.0000 0.970 0.000 1.000 0.000
#> GSM99492 1 0.0424 0.997 0.992 0.000 0.008
#> GSM99494 2 0.0000 0.970 0.000 1.000 0.000
#> GSM99524 1 0.0000 0.996 1.000 0.000 0.000
#> GSM99526 3 0.0237 0.953 0.000 0.004 0.996
#> GSM99528 3 0.6359 0.317 0.004 0.404 0.592
#> GSM99530 3 0.0000 0.950 0.000 0.000 1.000
#> GSM99532 3 0.0000 0.950 0.000 0.000 1.000
#> GSM99534 2 0.0237 0.968 0.004 0.996 0.000
#> GSM99536 1 0.0424 0.997 0.992 0.000 0.008
#> GSM99538 3 0.6295 0.109 0.000 0.472 0.528
#> GSM99540 1 0.0424 0.997 0.992 0.000 0.008
#> GSM99542 2 0.0000 0.970 0.000 1.000 0.000
#> GSM99544 2 0.4504 0.748 0.000 0.804 0.196
#> GSM99546 3 0.0475 0.951 0.004 0.004 0.992
#> GSM99548 2 0.0000 0.970 0.000 1.000 0.000
#> GSM99550 1 0.0237 0.996 0.996 0.000 0.004
#> GSM99552 3 0.0475 0.951 0.004 0.004 0.992
#> GSM99554 2 0.0000 0.970 0.000 1.000 0.000
#> GSM99556 2 0.0000 0.970 0.000 1.000 0.000
#> GSM99558 3 0.0424 0.950 0.000 0.008 0.992
#> GSM99560 2 0.0000 0.970 0.000 1.000 0.000
#> GSM99562 3 0.0237 0.953 0.000 0.004 0.996
#> GSM99564 2 0.0000 0.970 0.000 1.000 0.000
#> GSM99572 2 0.0000 0.970 0.000 1.000 0.000
#> GSM99576 1 0.0237 0.996 0.996 0.000 0.004
#> GSM99578 2 0.0000 0.970 0.000 1.000 0.000
#> GSM99580 3 0.0237 0.953 0.000 0.004 0.996
#> GSM99582 3 0.0475 0.951 0.004 0.004 0.992
#> GSM99584 2 0.4702 0.724 0.000 0.788 0.212
#> GSM99586 1 0.0424 0.997 0.992 0.000 0.008
#> GSM99588 2 0.0000 0.970 0.000 1.000 0.000
#> GSM99590 2 0.0000 0.970 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM99496 3 0.0000 0.9113 0.000 0.000 1.000 0.000
#> GSM99502 1 0.0000 0.9324 1.000 0.000 0.000 0.000
#> GSM99504 1 0.0000 0.9324 1.000 0.000 0.000 0.000
#> GSM99506 3 0.0000 0.9113 0.000 0.000 1.000 0.000
#> GSM99566 3 0.0000 0.9113 0.000 0.000 1.000 0.000
#> GSM99574 1 0.0000 0.9324 1.000 0.000 0.000 0.000
#> GSM99592 3 0.0000 0.9113 0.000 0.000 1.000 0.000
#> GSM99594 3 0.0000 0.9113 0.000 0.000 1.000 0.000
#> GSM99468 1 0.0000 0.9324 1.000 0.000 0.000 0.000
#> GSM99498 1 0.0000 0.9324 1.000 0.000 0.000 0.000
#> GSM99500 1 0.0000 0.9324 1.000 0.000 0.000 0.000
#> GSM99508 3 0.0000 0.9113 0.000 0.000 1.000 0.000
#> GSM99568 3 0.0000 0.9113 0.000 0.000 1.000 0.000
#> GSM99596 3 0.0000 0.9113 0.000 0.000 1.000 0.000
#> GSM99600 4 0.4500 0.2034 0.000 0.316 0.000 0.684
#> GSM99458 1 0.3105 0.8770 0.868 0.120 0.000 0.012
#> GSM99460 1 0.4387 0.8067 0.752 0.236 0.000 0.012
#> GSM99510 3 0.3764 0.8025 0.000 0.012 0.816 0.172
#> GSM99512 3 0.0804 0.9049 0.000 0.008 0.980 0.012
#> GSM99514 3 0.0000 0.9113 0.000 0.000 1.000 0.000
#> GSM99516 1 0.0000 0.9324 1.000 0.000 0.000 0.000
#> GSM99518 1 0.0000 0.9324 1.000 0.000 0.000 0.000
#> GSM99520 3 0.0000 0.9113 0.000 0.000 1.000 0.000
#> GSM99522 3 0.0000 0.9113 0.000 0.000 1.000 0.000
#> GSM99570 1 0.0336 0.9306 0.992 0.008 0.000 0.000
#> GSM99598 1 0.0000 0.9324 1.000 0.000 0.000 0.000
#> GSM99432 4 0.0469 0.6320 0.000 0.012 0.000 0.988
#> GSM99434 3 0.3937 0.7882 0.000 0.012 0.800 0.188
#> GSM99436 4 0.3649 0.4917 0.000 0.204 0.000 0.796
#> GSM99438 2 0.4382 0.9838 0.000 0.704 0.000 0.296
#> GSM99440 1 0.0000 0.9324 1.000 0.000 0.000 0.000
#> GSM99442 2 0.4661 0.9132 0.000 0.652 0.000 0.348
#> GSM99444 2 0.4382 0.9838 0.000 0.704 0.000 0.296
#> GSM99446 4 0.3688 0.4856 0.000 0.208 0.000 0.792
#> GSM99448 3 0.2466 0.8637 0.000 0.004 0.900 0.096
#> GSM99450 3 0.3681 0.8013 0.000 0.008 0.816 0.176
#> GSM99452 1 0.0336 0.9306 0.992 0.008 0.000 0.000
#> GSM99454 1 0.0000 0.9324 1.000 0.000 0.000 0.000
#> GSM99456 1 0.4018 0.8329 0.772 0.224 0.000 0.004
#> GSM99462 2 0.4382 0.9838 0.000 0.704 0.000 0.296
#> GSM99464 3 0.7049 0.5595 0.000 0.236 0.572 0.192
#> GSM99466 4 0.1978 0.6317 0.000 0.004 0.068 0.928
#> GSM99470 1 0.5254 0.5072 0.672 0.028 0.000 0.300
#> GSM99472 1 0.1388 0.9213 0.960 0.028 0.000 0.012
#> GSM99474 3 0.0336 0.9086 0.000 0.000 0.992 0.008
#> GSM99476 4 0.4647 0.4130 0.000 0.008 0.288 0.704
#> GSM99478 4 0.0921 0.6405 0.000 0.000 0.028 0.972
#> GSM99480 1 0.2345 0.8996 0.900 0.100 0.000 0.000
#> GSM99482 1 0.0336 0.9306 0.992 0.008 0.000 0.000
#> GSM99484 4 0.2530 0.5858 0.000 0.112 0.000 0.888
#> GSM99486 4 0.3266 0.5404 0.000 0.168 0.000 0.832
#> GSM99488 2 0.4382 0.9838 0.000 0.704 0.000 0.296
#> GSM99490 2 0.4661 0.9132 0.000 0.652 0.000 0.348
#> GSM99492 1 0.2345 0.8996 0.900 0.100 0.000 0.000
#> GSM99494 2 0.4382 0.9838 0.000 0.704 0.000 0.296
#> GSM99524 1 0.0336 0.9306 0.992 0.008 0.000 0.000
#> GSM99526 4 0.7180 0.2763 0.000 0.188 0.264 0.548
#> GSM99528 4 0.4776 0.5684 0.000 0.164 0.060 0.776
#> GSM99530 3 0.4609 0.7315 0.000 0.224 0.752 0.024
#> GSM99532 3 0.3161 0.8295 0.000 0.124 0.864 0.012
#> GSM99534 4 0.3649 0.5244 0.000 0.204 0.000 0.796
#> GSM99536 1 0.1474 0.9172 0.948 0.052 0.000 0.000
#> GSM99538 4 0.3245 0.6218 0.000 0.056 0.064 0.880
#> GSM99540 1 0.3726 0.8330 0.788 0.212 0.000 0.000
#> GSM99542 2 0.4382 0.9838 0.000 0.704 0.000 0.296
#> GSM99544 4 0.1059 0.6384 0.000 0.012 0.016 0.972
#> GSM99546 4 0.5783 0.5304 0.000 0.188 0.108 0.704
#> GSM99548 2 0.4382 0.9838 0.000 0.704 0.000 0.296
#> GSM99550 4 0.7825 0.0277 0.304 0.284 0.000 0.412
#> GSM99552 3 0.2647 0.8088 0.000 0.000 0.880 0.120
#> GSM99554 4 0.3801 0.4646 0.000 0.220 0.000 0.780
#> GSM99556 2 0.4382 0.9838 0.000 0.704 0.000 0.296
#> GSM99558 4 0.4967 0.1211 0.000 0.000 0.452 0.548
#> GSM99560 4 0.2589 0.6270 0.000 0.116 0.000 0.884
#> GSM99562 3 0.0000 0.9113 0.000 0.000 1.000 0.000
#> GSM99564 4 0.3266 0.5404 0.000 0.168 0.000 0.832
#> GSM99572 2 0.4382 0.9838 0.000 0.704 0.000 0.296
#> GSM99576 1 0.4453 0.8049 0.744 0.244 0.000 0.012
#> GSM99578 4 0.3975 0.4221 0.000 0.240 0.000 0.760
#> GSM99580 3 0.0000 0.9113 0.000 0.000 1.000 0.000
#> GSM99582 3 0.4830 0.4082 0.000 0.000 0.608 0.392
#> GSM99584 4 0.1059 0.6395 0.000 0.016 0.012 0.972
#> GSM99586 1 0.3764 0.8396 0.784 0.216 0.000 0.000
#> GSM99588 4 0.4866 -0.2098 0.000 0.404 0.000 0.596
#> GSM99590 2 0.4382 0.9838 0.000 0.704 0.000 0.296
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM99496 3 0.0000 0.8647 0.000 0.000 1.000 0.000 0.000
#> GSM99502 1 0.0000 0.8675 1.000 0.000 0.000 0.000 0.000
#> GSM99504 1 0.0162 0.8649 0.996 0.000 0.004 0.000 0.000
#> GSM99506 3 0.0324 0.8628 0.000 0.000 0.992 0.004 0.004
#> GSM99566 3 0.0324 0.8628 0.000 0.000 0.992 0.004 0.004
#> GSM99574 1 0.0000 0.8675 1.000 0.000 0.000 0.000 0.000
#> GSM99592 3 0.0162 0.8639 0.000 0.000 0.996 0.004 0.000
#> GSM99594 3 0.0324 0.8628 0.000 0.000 0.992 0.004 0.004
#> GSM99468 1 0.0000 0.8675 1.000 0.000 0.000 0.000 0.000
#> GSM99498 1 0.0000 0.8675 1.000 0.000 0.000 0.000 0.000
#> GSM99500 1 0.0000 0.8675 1.000 0.000 0.000 0.000 0.000
#> GSM99508 3 0.0000 0.8647 0.000 0.000 1.000 0.000 0.000
#> GSM99568 3 0.0000 0.8647 0.000 0.000 1.000 0.000 0.000
#> GSM99596 3 0.0000 0.8647 0.000 0.000 1.000 0.000 0.000
#> GSM99600 4 0.3730 0.6471 0.000 0.288 0.000 0.712 0.000
#> GSM99458 1 0.4470 -0.0480 0.596 0.004 0.000 0.004 0.396
#> GSM99460 5 0.4898 0.4803 0.376 0.000 0.000 0.032 0.592
#> GSM99510 3 0.5799 0.5417 0.000 0.000 0.612 0.168 0.220
#> GSM99512 3 0.3182 0.7766 0.000 0.000 0.844 0.032 0.124
#> GSM99514 3 0.0000 0.8647 0.000 0.000 1.000 0.000 0.000
#> GSM99516 1 0.0000 0.8675 1.000 0.000 0.000 0.000 0.000
#> GSM99518 1 0.0162 0.8657 0.996 0.000 0.000 0.000 0.004
#> GSM99520 3 0.0000 0.8647 0.000 0.000 1.000 0.000 0.000
#> GSM99522 3 0.0000 0.8647 0.000 0.000 1.000 0.000 0.000
#> GSM99570 1 0.0740 0.8600 0.980 0.008 0.000 0.004 0.008
#> GSM99598 1 0.0000 0.8675 1.000 0.000 0.000 0.000 0.000
#> GSM99432 4 0.3146 0.7672 0.000 0.052 0.000 0.856 0.092
#> GSM99434 3 0.6176 0.4480 0.000 0.000 0.540 0.172 0.288
#> GSM99436 4 0.3242 0.7221 0.000 0.216 0.000 0.784 0.000
#> GSM99438 2 0.0703 0.9133 0.000 0.976 0.000 0.024 0.000
#> GSM99440 1 0.0000 0.8675 1.000 0.000 0.000 0.000 0.000
#> GSM99442 2 0.4045 0.3812 0.000 0.644 0.000 0.356 0.000
#> GSM99444 2 0.0992 0.9127 0.000 0.968 0.000 0.024 0.008
#> GSM99446 4 0.3336 0.7135 0.000 0.228 0.000 0.772 0.000
#> GSM99448 3 0.5329 0.6034 0.000 0.000 0.672 0.184 0.144
#> GSM99450 3 0.5903 0.4472 0.000 0.000 0.548 0.120 0.332
#> GSM99452 1 0.0854 0.8579 0.976 0.008 0.000 0.004 0.012
#> GSM99454 1 0.0000 0.8675 1.000 0.000 0.000 0.000 0.000
#> GSM99456 5 0.4321 0.4070 0.396 0.000 0.000 0.004 0.600
#> GSM99462 2 0.0992 0.9127 0.000 0.968 0.000 0.024 0.008
#> GSM99464 5 0.4559 0.4147 0.000 0.000 0.152 0.100 0.748
#> GSM99466 4 0.3474 0.7663 0.000 0.044 0.004 0.836 0.116
#> GSM99470 1 0.7112 -0.1045 0.412 0.024 0.000 0.364 0.200
#> GSM99472 1 0.4181 0.6155 0.780 0.016 0.000 0.032 0.172
#> GSM99474 3 0.0162 0.8636 0.000 0.000 0.996 0.000 0.004
#> GSM99476 4 0.4395 0.6482 0.000 0.000 0.064 0.748 0.188
#> GSM99478 4 0.3734 0.7639 0.000 0.060 0.000 0.812 0.128
#> GSM99480 1 0.3550 0.5886 0.760 0.000 0.000 0.004 0.236
#> GSM99482 1 0.1372 0.8429 0.956 0.016 0.000 0.004 0.024
#> GSM99484 4 0.3962 0.7599 0.000 0.112 0.000 0.800 0.088
#> GSM99486 4 0.2732 0.7562 0.000 0.160 0.000 0.840 0.000
#> GSM99488 2 0.0912 0.9120 0.000 0.972 0.000 0.016 0.012
#> GSM99490 2 0.4290 0.4741 0.000 0.680 0.000 0.304 0.016
#> GSM99492 1 0.3579 0.5811 0.756 0.000 0.000 0.004 0.240
#> GSM99494 2 0.0912 0.9120 0.000 0.972 0.000 0.016 0.012
#> GSM99524 1 0.0451 0.8631 0.988 0.008 0.000 0.000 0.004
#> GSM99526 5 0.4822 0.1271 0.000 0.000 0.032 0.352 0.616
#> GSM99528 4 0.4464 0.5998 0.000 0.028 0.000 0.684 0.288
#> GSM99530 5 0.5206 0.0292 0.000 0.000 0.428 0.044 0.528
#> GSM99532 3 0.4479 0.5680 0.000 0.000 0.700 0.036 0.264
#> GSM99534 4 0.5210 0.6994 0.000 0.200 0.000 0.680 0.120
#> GSM99536 1 0.1965 0.7707 0.904 0.000 0.000 0.000 0.096
#> GSM99538 4 0.2660 0.7345 0.000 0.008 0.000 0.864 0.128
#> GSM99540 5 0.4979 0.3188 0.480 0.000 0.000 0.028 0.492
#> GSM99542 2 0.1701 0.8751 0.000 0.936 0.000 0.016 0.048
#> GSM99544 4 0.3267 0.7565 0.000 0.044 0.000 0.844 0.112
#> GSM99546 4 0.4415 0.3466 0.000 0.000 0.004 0.552 0.444
#> GSM99548 2 0.0671 0.9129 0.000 0.980 0.000 0.016 0.004
#> GSM99550 5 0.3339 0.5634 0.112 0.000 0.000 0.048 0.840
#> GSM99552 3 0.1741 0.8220 0.000 0.000 0.936 0.024 0.040
#> GSM99554 4 0.3521 0.7096 0.000 0.232 0.000 0.764 0.004
#> GSM99556 2 0.0671 0.9129 0.000 0.980 0.000 0.016 0.004
#> GSM99558 4 0.3875 0.6813 0.000 0.000 0.160 0.792 0.048
#> GSM99560 4 0.2889 0.7659 0.000 0.084 0.000 0.872 0.044
#> GSM99562 3 0.0324 0.8628 0.000 0.000 0.992 0.004 0.004
#> GSM99564 4 0.2930 0.7546 0.000 0.164 0.000 0.832 0.004
#> GSM99572 2 0.0703 0.9133 0.000 0.976 0.000 0.024 0.000
#> GSM99576 5 0.5388 0.4764 0.360 0.004 0.000 0.056 0.580
#> GSM99578 4 0.5037 0.6836 0.000 0.228 0.000 0.684 0.088
#> GSM99580 3 0.0000 0.8647 0.000 0.000 1.000 0.000 0.000
#> GSM99582 3 0.6132 0.3855 0.000 0.000 0.564 0.224 0.212
#> GSM99584 4 0.3731 0.7337 0.000 0.040 0.000 0.800 0.160
#> GSM99586 5 0.4425 0.2728 0.452 0.000 0.000 0.004 0.544
#> GSM99588 4 0.4734 0.4919 0.000 0.372 0.000 0.604 0.024
#> GSM99590 2 0.0703 0.9133 0.000 0.976 0.000 0.024 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM99496 3 0.0000 0.8099 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99502 1 0.0291 0.8532 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM99504 1 0.0665 0.8506 0.980 0.000 0.008 0.000 0.004 0.008
#> GSM99506 3 0.0363 0.8084 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM99566 3 0.0748 0.8066 0.000 0.000 0.976 0.004 0.004 0.016
#> GSM99574 1 0.0291 0.8532 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM99592 3 0.0508 0.8091 0.000 0.000 0.984 0.000 0.004 0.012
#> GSM99594 3 0.0508 0.8076 0.000 0.000 0.984 0.004 0.000 0.012
#> GSM99468 1 0.0622 0.8519 0.980 0.000 0.000 0.000 0.008 0.012
#> GSM99498 1 0.0508 0.8521 0.984 0.000 0.000 0.000 0.004 0.012
#> GSM99500 1 0.0508 0.8521 0.984 0.000 0.000 0.000 0.004 0.012
#> GSM99508 3 0.0000 0.8099 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99568 3 0.0146 0.8098 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM99596 3 0.0000 0.8099 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99600 4 0.2902 0.6181 0.000 0.196 0.000 0.800 0.000 0.004
#> GSM99458 1 0.5259 -0.1908 0.468 0.000 0.000 0.000 0.436 0.096
#> GSM99460 5 0.4600 0.5359 0.136 0.000 0.000 0.004 0.708 0.152
#> GSM99510 3 0.7013 -0.0681 0.000 0.000 0.392 0.120 0.132 0.356
#> GSM99512 3 0.5177 0.5198 0.000 0.000 0.656 0.028 0.088 0.228
#> GSM99514 3 0.0000 0.8099 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99516 1 0.0363 0.8529 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM99518 1 0.0622 0.8516 0.980 0.000 0.000 0.000 0.008 0.012
#> GSM99520 3 0.0146 0.8093 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM99522 3 0.1148 0.8000 0.000 0.000 0.960 0.004 0.016 0.020
#> GSM99570 1 0.1267 0.8363 0.940 0.000 0.000 0.000 0.000 0.060
#> GSM99598 1 0.0363 0.8525 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM99432 4 0.3318 0.5431 0.000 0.024 0.000 0.824 0.020 0.132
#> GSM99434 6 0.7231 -0.0341 0.000 0.000 0.328 0.112 0.192 0.368
#> GSM99436 4 0.2320 0.6411 0.000 0.132 0.000 0.864 0.000 0.004
#> GSM99438 2 0.0146 0.9296 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM99440 1 0.0458 0.8527 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM99442 4 0.3997 0.1444 0.000 0.488 0.000 0.508 0.000 0.004
#> GSM99444 2 0.0520 0.9296 0.000 0.984 0.000 0.000 0.008 0.008
#> GSM99446 4 0.2595 0.6358 0.000 0.160 0.000 0.836 0.000 0.004
#> GSM99448 3 0.6409 0.1792 0.000 0.000 0.512 0.216 0.044 0.228
#> GSM99450 3 0.6903 -0.1336 0.000 0.000 0.376 0.060 0.220 0.344
#> GSM99452 1 0.1501 0.8288 0.924 0.000 0.000 0.000 0.000 0.076
#> GSM99454 1 0.0363 0.8525 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM99456 5 0.4949 0.5621 0.208 0.000 0.000 0.000 0.648 0.144
#> GSM99462 2 0.0993 0.9259 0.000 0.964 0.000 0.000 0.012 0.024
#> GSM99464 5 0.4260 0.3726 0.000 0.000 0.024 0.028 0.720 0.228
#> GSM99466 4 0.4316 0.3735 0.000 0.004 0.008 0.628 0.012 0.348
#> GSM99470 6 0.6861 0.0812 0.284 0.000 0.000 0.200 0.072 0.444
#> GSM99472 1 0.5135 0.4335 0.608 0.000 0.000 0.016 0.072 0.304
#> GSM99474 3 0.0622 0.8063 0.000 0.000 0.980 0.000 0.008 0.012
#> GSM99476 4 0.4857 0.3192 0.000 0.000 0.016 0.656 0.064 0.264
#> GSM99478 4 0.4388 0.3467 0.000 0.004 0.008 0.604 0.012 0.372
#> GSM99480 1 0.5138 0.3505 0.604 0.000 0.000 0.000 0.268 0.128
#> GSM99482 1 0.2750 0.7646 0.844 0.000 0.000 0.000 0.020 0.136
#> GSM99484 4 0.4527 0.4369 0.000 0.040 0.000 0.624 0.004 0.332
#> GSM99486 4 0.2003 0.6420 0.000 0.116 0.000 0.884 0.000 0.000
#> GSM99488 2 0.0993 0.9259 0.000 0.964 0.000 0.000 0.012 0.024
#> GSM99490 2 0.4300 0.3333 0.000 0.640 0.000 0.324 0.000 0.036
#> GSM99492 1 0.5347 0.2476 0.560 0.000 0.000 0.000 0.304 0.136
#> GSM99494 2 0.0993 0.9259 0.000 0.964 0.000 0.000 0.012 0.024
#> GSM99524 1 0.1327 0.8343 0.936 0.000 0.000 0.000 0.000 0.064
#> GSM99526 5 0.5585 -0.0594 0.000 0.000 0.000 0.148 0.488 0.364
#> GSM99528 6 0.6115 -0.1198 0.000 0.004 0.004 0.376 0.196 0.420
#> GSM99530 5 0.3907 0.3760 0.000 0.000 0.268 0.000 0.704 0.028
#> GSM99532 3 0.4500 0.2861 0.000 0.000 0.572 0.000 0.392 0.036
#> GSM99534 4 0.5640 0.3106 0.000 0.100 0.000 0.500 0.016 0.384
#> GSM99536 1 0.2572 0.7325 0.852 0.000 0.000 0.000 0.136 0.012
#> GSM99538 4 0.3728 0.4689 0.000 0.000 0.004 0.772 0.044 0.180
#> GSM99540 5 0.3883 0.4728 0.332 0.000 0.000 0.000 0.656 0.012
#> GSM99542 2 0.2784 0.8471 0.000 0.868 0.000 0.020 0.020 0.092
#> GSM99544 4 0.3690 0.4882 0.000 0.012 0.004 0.784 0.024 0.176
#> GSM99546 6 0.5839 0.1962 0.000 0.000 0.000 0.276 0.236 0.488
#> GSM99548 2 0.0146 0.9296 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM99550 5 0.3781 0.5325 0.036 0.000 0.000 0.004 0.756 0.204
#> GSM99552 3 0.3201 0.6098 0.000 0.000 0.780 0.012 0.000 0.208
#> GSM99554 4 0.2669 0.6370 0.000 0.156 0.000 0.836 0.000 0.008
#> GSM99556 2 0.0508 0.9306 0.000 0.984 0.000 0.000 0.004 0.012
#> GSM99558 4 0.4541 0.4612 0.000 0.000 0.096 0.704 0.004 0.196
#> GSM99560 4 0.3666 0.6052 0.000 0.084 0.000 0.820 0.064 0.032
#> GSM99562 3 0.1552 0.7929 0.000 0.000 0.940 0.004 0.020 0.036
#> GSM99564 4 0.2048 0.6420 0.000 0.120 0.000 0.880 0.000 0.000
#> GSM99572 2 0.0405 0.9253 0.000 0.988 0.000 0.008 0.000 0.004
#> GSM99576 5 0.5059 0.5491 0.172 0.000 0.000 0.020 0.680 0.128
#> GSM99578 4 0.5419 0.4368 0.000 0.132 0.000 0.568 0.004 0.296
#> GSM99580 3 0.0458 0.8086 0.000 0.000 0.984 0.000 0.000 0.016
#> GSM99582 3 0.6411 0.0977 0.000 0.000 0.492 0.112 0.072 0.324
#> GSM99584 4 0.4063 0.4303 0.000 0.004 0.000 0.736 0.052 0.208
#> GSM99586 5 0.5113 0.5305 0.236 0.000 0.000 0.000 0.620 0.144
#> GSM99588 4 0.5172 0.5086 0.000 0.284 0.000 0.592 0.000 0.124
#> GSM99590 2 0.0000 0.9304 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) cell.type(p) k
#> SD:kmeans 84 2.54e-05 0.00015 2
#> SD:kmeans 82 6.74e-04 0.01431 3
#> SD:kmeans 74 1.82e-04 0.01413 4
#> SD:kmeans 68 4.73e-05 0.01039 5
#> SD:kmeans 56 2.47e-04 0.02244 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 21168 rows and 85 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.968 0.988 0.5045 0.496 0.496
#> 3 3 1.000 0.983 0.993 0.3322 0.757 0.545
#> 4 4 0.804 0.765 0.894 0.0992 0.909 0.735
#> 5 5 0.761 0.628 0.834 0.0613 0.924 0.727
#> 6 6 0.740 0.561 0.774 0.0351 0.959 0.822
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
#> GSM99496 1 0.0000 0.988 1.000 0.000
#> GSM99502 1 0.0000 0.988 1.000 0.000
#> GSM99504 1 0.0000 0.988 1.000 0.000
#> GSM99506 1 0.0000 0.988 1.000 0.000
#> GSM99566 1 0.0000 0.988 1.000 0.000
#> GSM99574 1 0.0000 0.988 1.000 0.000
#> GSM99592 1 0.5408 0.850 0.876 0.124
#> GSM99594 1 0.0000 0.988 1.000 0.000
#> GSM99468 1 0.0000 0.988 1.000 0.000
#> GSM99498 1 0.0000 0.988 1.000 0.000
#> GSM99500 1 0.0000 0.988 1.000 0.000
#> GSM99508 1 0.0000 0.988 1.000 0.000
#> GSM99568 1 0.0000 0.988 1.000 0.000
#> GSM99596 1 0.0000 0.988 1.000 0.000
#> GSM99600 2 0.0000 0.986 0.000 1.000
#> GSM99458 1 0.0000 0.988 1.000 0.000
#> GSM99460 1 0.0000 0.988 1.000 0.000
#> GSM99510 2 0.0000 0.986 0.000 1.000
#> GSM99512 2 0.0000 0.986 0.000 1.000
#> GSM99514 1 0.0000 0.988 1.000 0.000
#> GSM99516 1 0.0000 0.988 1.000 0.000
#> GSM99518 1 0.0000 0.988 1.000 0.000
#> GSM99520 1 0.0000 0.988 1.000 0.000
#> GSM99522 1 0.0000 0.988 1.000 0.000
#> GSM99570 1 0.0000 0.988 1.000 0.000
#> GSM99598 1 0.0000 0.988 1.000 0.000
#> GSM99432 2 0.0000 0.986 0.000 1.000
#> GSM99434 2 0.5178 0.860 0.116 0.884
#> GSM99436 2 0.0000 0.986 0.000 1.000
#> GSM99438 2 0.0000 0.986 0.000 1.000
#> GSM99440 1 0.0000 0.988 1.000 0.000
#> GSM99442 2 0.0000 0.986 0.000 1.000
#> GSM99444 2 0.0000 0.986 0.000 1.000
#> GSM99446 2 0.0000 0.986 0.000 1.000
#> GSM99448 2 0.0000 0.986 0.000 1.000
#> GSM99450 1 0.0000 0.988 1.000 0.000
#> GSM99452 1 0.0000 0.988 1.000 0.000
#> GSM99454 1 0.0000 0.988 1.000 0.000
#> GSM99456 1 0.0000 0.988 1.000 0.000
#> GSM99462 2 0.0000 0.986 0.000 1.000
#> GSM99464 1 0.0000 0.988 1.000 0.000
#> GSM99466 2 0.0000 0.986 0.000 1.000
#> GSM99470 1 0.9710 0.321 0.600 0.400
#> GSM99472 1 0.0000 0.988 1.000 0.000
#> GSM99474 1 0.0000 0.988 1.000 0.000
#> GSM99476 2 0.0000 0.986 0.000 1.000
#> GSM99478 2 0.0000 0.986 0.000 1.000
#> GSM99480 1 0.0000 0.988 1.000 0.000
#> GSM99482 1 0.0000 0.988 1.000 0.000
#> GSM99484 2 0.0000 0.986 0.000 1.000
#> GSM99486 2 0.0000 0.986 0.000 1.000
#> GSM99488 2 0.0000 0.986 0.000 1.000
#> GSM99490 2 0.0000 0.986 0.000 1.000
#> GSM99492 1 0.0000 0.988 1.000 0.000
#> GSM99494 2 0.0000 0.986 0.000 1.000
#> GSM99524 1 0.0000 0.988 1.000 0.000
#> GSM99526 2 0.0376 0.983 0.004 0.996
#> GSM99528 2 0.0000 0.986 0.000 1.000
#> GSM99530 1 0.0000 0.988 1.000 0.000
#> GSM99532 1 0.0000 0.988 1.000 0.000
#> GSM99534 2 0.0000 0.986 0.000 1.000
#> GSM99536 1 0.0000 0.988 1.000 0.000
#> GSM99538 2 0.0000 0.986 0.000 1.000
#> GSM99540 1 0.0000 0.988 1.000 0.000
#> GSM99542 2 0.0000 0.986 0.000 1.000
#> GSM99544 2 0.0000 0.986 0.000 1.000
#> GSM99546 2 0.0000 0.986 0.000 1.000
#> GSM99548 2 0.0000 0.986 0.000 1.000
#> GSM99550 1 0.0000 0.988 1.000 0.000
#> GSM99552 2 0.0000 0.986 0.000 1.000
#> GSM99554 2 0.0000 0.986 0.000 1.000
#> GSM99556 2 0.0000 0.986 0.000 1.000
#> GSM99558 2 0.0000 0.986 0.000 1.000
#> GSM99560 2 0.0000 0.986 0.000 1.000
#> GSM99562 1 0.0000 0.988 1.000 0.000
#> GSM99564 2 0.0000 0.986 0.000 1.000
#> GSM99572 2 0.0000 0.986 0.000 1.000
#> GSM99576 1 0.0000 0.988 1.000 0.000
#> GSM99578 2 0.0000 0.986 0.000 1.000
#> GSM99580 2 0.9732 0.311 0.404 0.596
#> GSM99582 1 0.0000 0.988 1.000 0.000
#> GSM99584 2 0.0000 0.986 0.000 1.000
#> GSM99586 1 0.0000 0.988 1.000 0.000
#> GSM99588 2 0.0000 0.986 0.000 1.000
#> GSM99590 2 0.0000 0.986 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM99496 3 0.0000 0.998 0.000 0.000 1.000
#> GSM99502 1 0.0000 0.996 1.000 0.000 0.000
#> GSM99504 1 0.0000 0.996 1.000 0.000 0.000
#> GSM99506 3 0.0000 0.998 0.000 0.000 1.000
#> GSM99566 3 0.0000 0.998 0.000 0.000 1.000
#> GSM99574 1 0.0000 0.996 1.000 0.000 0.000
#> GSM99592 3 0.0000 0.998 0.000 0.000 1.000
#> GSM99594 3 0.0000 0.998 0.000 0.000 1.000
#> GSM99468 1 0.0000 0.996 1.000 0.000 0.000
#> GSM99498 1 0.0000 0.996 1.000 0.000 0.000
#> GSM99500 1 0.0000 0.996 1.000 0.000 0.000
#> GSM99508 3 0.0000 0.998 0.000 0.000 1.000
#> GSM99568 3 0.0000 0.998 0.000 0.000 1.000
#> GSM99596 3 0.0000 0.998 0.000 0.000 1.000
#> GSM99600 2 0.0000 0.987 0.000 1.000 0.000
#> GSM99458 1 0.0000 0.996 1.000 0.000 0.000
#> GSM99460 1 0.0000 0.996 1.000 0.000 0.000
#> GSM99510 3 0.0000 0.998 0.000 0.000 1.000
#> GSM99512 3 0.0000 0.998 0.000 0.000 1.000
#> GSM99514 3 0.0000 0.998 0.000 0.000 1.000
#> GSM99516 1 0.0000 0.996 1.000 0.000 0.000
#> GSM99518 1 0.0000 0.996 1.000 0.000 0.000
#> GSM99520 3 0.0000 0.998 0.000 0.000 1.000
#> GSM99522 3 0.0000 0.998 0.000 0.000 1.000
#> GSM99570 1 0.0000 0.996 1.000 0.000 0.000
#> GSM99598 1 0.0000 0.996 1.000 0.000 0.000
#> GSM99432 2 0.0000 0.987 0.000 1.000 0.000
#> GSM99434 3 0.0000 0.998 0.000 0.000 1.000
#> GSM99436 2 0.0000 0.987 0.000 1.000 0.000
#> GSM99438 2 0.0000 0.987 0.000 1.000 0.000
#> GSM99440 1 0.0000 0.996 1.000 0.000 0.000
#> GSM99442 2 0.0000 0.987 0.000 1.000 0.000
#> GSM99444 2 0.0000 0.987 0.000 1.000 0.000
#> GSM99446 2 0.0000 0.987 0.000 1.000 0.000
#> GSM99448 3 0.0000 0.998 0.000 0.000 1.000
#> GSM99450 3 0.0000 0.998 0.000 0.000 1.000
#> GSM99452 1 0.0000 0.996 1.000 0.000 0.000
#> GSM99454 1 0.0000 0.996 1.000 0.000 0.000
#> GSM99456 1 0.0000 0.996 1.000 0.000 0.000
#> GSM99462 2 0.0000 0.987 0.000 1.000 0.000
#> GSM99464 3 0.0000 0.998 0.000 0.000 1.000
#> GSM99466 2 0.0000 0.987 0.000 1.000 0.000
#> GSM99470 1 0.0000 0.996 1.000 0.000 0.000
#> GSM99472 1 0.0000 0.996 1.000 0.000 0.000
#> GSM99474 3 0.0000 0.998 0.000 0.000 1.000
#> GSM99476 3 0.0000 0.998 0.000 0.000 1.000
#> GSM99478 2 0.0000 0.987 0.000 1.000 0.000
#> GSM99480 1 0.0000 0.996 1.000 0.000 0.000
#> GSM99482 1 0.0000 0.996 1.000 0.000 0.000
#> GSM99484 2 0.0000 0.987 0.000 1.000 0.000
#> GSM99486 2 0.0000 0.987 0.000 1.000 0.000
#> GSM99488 2 0.0000 0.987 0.000 1.000 0.000
#> GSM99490 2 0.0000 0.987 0.000 1.000 0.000
#> GSM99492 1 0.0000 0.996 1.000 0.000 0.000
#> GSM99494 2 0.0000 0.987 0.000 1.000 0.000
#> GSM99524 1 0.0000 0.996 1.000 0.000 0.000
#> GSM99526 3 0.1860 0.944 0.000 0.052 0.948
#> GSM99528 2 0.0000 0.987 0.000 1.000 0.000
#> GSM99530 3 0.0000 0.998 0.000 0.000 1.000
#> GSM99532 3 0.0000 0.998 0.000 0.000 1.000
#> GSM99534 2 0.0000 0.987 0.000 1.000 0.000
#> GSM99536 1 0.0000 0.996 1.000 0.000 0.000
#> GSM99538 2 0.0000 0.987 0.000 1.000 0.000
#> GSM99540 1 0.0000 0.996 1.000 0.000 0.000
#> GSM99542 2 0.0000 0.987 0.000 1.000 0.000
#> GSM99544 2 0.0000 0.987 0.000 1.000 0.000
#> GSM99546 2 0.0237 0.983 0.000 0.996 0.004
#> GSM99548 2 0.0000 0.987 0.000 1.000 0.000
#> GSM99550 1 0.0000 0.996 1.000 0.000 0.000
#> GSM99552 3 0.0000 0.998 0.000 0.000 1.000
#> GSM99554 2 0.0000 0.987 0.000 1.000 0.000
#> GSM99556 2 0.0000 0.987 0.000 1.000 0.000
#> GSM99558 2 0.6095 0.356 0.000 0.608 0.392
#> GSM99560 2 0.0000 0.987 0.000 1.000 0.000
#> GSM99562 3 0.0000 0.998 0.000 0.000 1.000
#> GSM99564 2 0.0000 0.987 0.000 1.000 0.000
#> GSM99572 2 0.0000 0.987 0.000 1.000 0.000
#> GSM99576 1 0.0000 0.996 1.000 0.000 0.000
#> GSM99578 2 0.0000 0.987 0.000 1.000 0.000
#> GSM99580 3 0.0000 0.998 0.000 0.000 1.000
#> GSM99582 1 0.3267 0.869 0.884 0.000 0.116
#> GSM99584 2 0.0000 0.987 0.000 1.000 0.000
#> GSM99586 1 0.0000 0.996 1.000 0.000 0.000
#> GSM99588 2 0.0000 0.987 0.000 1.000 0.000
#> GSM99590 2 0.0000 0.987 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM99496 3 0.0000 0.8909 0.000 0.000 1.000 0.000
#> GSM99502 1 0.0000 0.9356 1.000 0.000 0.000 0.000
#> GSM99504 1 0.0469 0.9299 0.988 0.000 0.012 0.000
#> GSM99506 3 0.0000 0.8909 0.000 0.000 1.000 0.000
#> GSM99566 3 0.0000 0.8909 0.000 0.000 1.000 0.000
#> GSM99574 1 0.0000 0.9356 1.000 0.000 0.000 0.000
#> GSM99592 3 0.0921 0.8742 0.000 0.000 0.972 0.028
#> GSM99594 3 0.0000 0.8909 0.000 0.000 1.000 0.000
#> GSM99468 1 0.0000 0.9356 1.000 0.000 0.000 0.000
#> GSM99498 1 0.0000 0.9356 1.000 0.000 0.000 0.000
#> GSM99500 1 0.0000 0.9356 1.000 0.000 0.000 0.000
#> GSM99508 3 0.0000 0.8909 0.000 0.000 1.000 0.000
#> GSM99568 3 0.0000 0.8909 0.000 0.000 1.000 0.000
#> GSM99596 3 0.0000 0.8909 0.000 0.000 1.000 0.000
#> GSM99600 2 0.2281 0.8399 0.000 0.904 0.000 0.096
#> GSM99458 1 0.1940 0.9043 0.924 0.000 0.000 0.076
#> GSM99460 1 0.4040 0.7811 0.752 0.000 0.000 0.248
#> GSM99510 4 0.4817 0.3438 0.000 0.000 0.388 0.612
#> GSM99512 3 0.3486 0.6860 0.000 0.000 0.812 0.188
#> GSM99514 3 0.0000 0.8909 0.000 0.000 1.000 0.000
#> GSM99516 1 0.0000 0.9356 1.000 0.000 0.000 0.000
#> GSM99518 1 0.0707 0.9316 0.980 0.000 0.000 0.020
#> GSM99520 3 0.0000 0.8909 0.000 0.000 1.000 0.000
#> GSM99522 3 0.0188 0.8894 0.000 0.000 0.996 0.004
#> GSM99570 1 0.0000 0.9356 1.000 0.000 0.000 0.000
#> GSM99598 1 0.0000 0.9356 1.000 0.000 0.000 0.000
#> GSM99432 4 0.4996 -0.1014 0.000 0.484 0.000 0.516
#> GSM99434 4 0.4817 0.3325 0.000 0.000 0.388 0.612
#> GSM99436 2 0.3837 0.7217 0.000 0.776 0.000 0.224
#> GSM99438 2 0.0000 0.8895 0.000 1.000 0.000 0.000
#> GSM99440 1 0.0000 0.9356 1.000 0.000 0.000 0.000
#> GSM99442 2 0.0592 0.8831 0.000 0.984 0.000 0.016
#> GSM99444 2 0.0000 0.8895 0.000 1.000 0.000 0.000
#> GSM99446 2 0.3688 0.7418 0.000 0.792 0.000 0.208
#> GSM99448 4 0.4933 0.2611 0.000 0.000 0.432 0.568
#> GSM99450 3 0.4972 0.0391 0.000 0.000 0.544 0.456
#> GSM99452 1 0.0000 0.9356 1.000 0.000 0.000 0.000
#> GSM99454 1 0.0000 0.9356 1.000 0.000 0.000 0.000
#> GSM99456 1 0.3569 0.8287 0.804 0.000 0.000 0.196
#> GSM99462 2 0.0000 0.8895 0.000 1.000 0.000 0.000
#> GSM99464 4 0.5312 0.3222 0.040 0.000 0.268 0.692
#> GSM99466 2 0.4994 0.1378 0.000 0.520 0.000 0.480
#> GSM99470 1 0.0469 0.9296 0.988 0.012 0.000 0.000
#> GSM99472 1 0.0000 0.9356 1.000 0.000 0.000 0.000
#> GSM99474 3 0.0336 0.8872 0.000 0.000 0.992 0.008
#> GSM99476 4 0.3688 0.5582 0.000 0.000 0.208 0.792
#> GSM99478 2 0.3486 0.7205 0.000 0.812 0.000 0.188
#> GSM99480 1 0.0707 0.9311 0.980 0.000 0.000 0.020
#> GSM99482 1 0.0000 0.9356 1.000 0.000 0.000 0.000
#> GSM99484 2 0.0000 0.8895 0.000 1.000 0.000 0.000
#> GSM99486 2 0.4356 0.6174 0.000 0.708 0.000 0.292
#> GSM99488 2 0.0000 0.8895 0.000 1.000 0.000 0.000
#> GSM99490 2 0.0000 0.8895 0.000 1.000 0.000 0.000
#> GSM99492 1 0.1389 0.9202 0.952 0.000 0.000 0.048
#> GSM99494 2 0.0000 0.8895 0.000 1.000 0.000 0.000
#> GSM99524 1 0.0000 0.9356 1.000 0.000 0.000 0.000
#> GSM99526 4 0.0188 0.5992 0.000 0.000 0.004 0.996
#> GSM99528 2 0.3710 0.7043 0.000 0.804 0.004 0.192
#> GSM99530 3 0.4328 0.6143 0.008 0.000 0.748 0.244
#> GSM99532 3 0.2408 0.8045 0.000 0.000 0.896 0.104
#> GSM99534 2 0.0000 0.8895 0.000 1.000 0.000 0.000
#> GSM99536 1 0.0921 0.9284 0.972 0.000 0.000 0.028
#> GSM99538 4 0.4730 0.3137 0.000 0.364 0.000 0.636
#> GSM99540 1 0.2589 0.8848 0.884 0.000 0.000 0.116
#> GSM99542 2 0.0000 0.8895 0.000 1.000 0.000 0.000
#> GSM99544 4 0.4605 0.3742 0.000 0.336 0.000 0.664
#> GSM99546 4 0.1118 0.6181 0.000 0.036 0.000 0.964
#> GSM99548 2 0.0000 0.8895 0.000 1.000 0.000 0.000
#> GSM99550 1 0.4164 0.7650 0.736 0.000 0.000 0.264
#> GSM99552 3 0.0707 0.8764 0.000 0.000 0.980 0.020
#> GSM99554 2 0.2704 0.8214 0.000 0.876 0.000 0.124
#> GSM99556 2 0.0000 0.8895 0.000 1.000 0.000 0.000
#> GSM99558 3 0.7666 -0.3437 0.000 0.212 0.396 0.392
#> GSM99560 2 0.3311 0.7872 0.000 0.828 0.000 0.172
#> GSM99562 3 0.0188 0.8894 0.000 0.000 0.996 0.004
#> GSM99564 2 0.4382 0.6102 0.000 0.704 0.000 0.296
#> GSM99572 2 0.0000 0.8895 0.000 1.000 0.000 0.000
#> GSM99576 1 0.3400 0.8412 0.820 0.000 0.000 0.180
#> GSM99578 2 0.0000 0.8895 0.000 1.000 0.000 0.000
#> GSM99580 3 0.0000 0.8909 0.000 0.000 1.000 0.000
#> GSM99582 1 0.5712 0.3311 0.584 0.000 0.384 0.032
#> GSM99584 4 0.3975 0.5151 0.000 0.240 0.000 0.760
#> GSM99586 1 0.3569 0.8287 0.804 0.000 0.000 0.196
#> GSM99588 2 0.0000 0.8895 0.000 1.000 0.000 0.000
#> GSM99590 2 0.0000 0.8895 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM99496 3 0.0000 0.8986 0.000 0.000 1.000 0.000 0.000
#> GSM99502 1 0.0000 0.8473 1.000 0.000 0.000 0.000 0.000
#> GSM99504 1 0.0955 0.8262 0.968 0.000 0.028 0.000 0.004
#> GSM99506 3 0.0000 0.8986 0.000 0.000 1.000 0.000 0.000
#> GSM99566 3 0.0000 0.8986 0.000 0.000 1.000 0.000 0.000
#> GSM99574 1 0.0000 0.8473 1.000 0.000 0.000 0.000 0.000
#> GSM99592 3 0.1661 0.8762 0.000 0.000 0.940 0.024 0.036
#> GSM99594 3 0.0324 0.8985 0.000 0.000 0.992 0.004 0.004
#> GSM99468 1 0.0404 0.8455 0.988 0.000 0.000 0.000 0.012
#> GSM99498 1 0.0404 0.8455 0.988 0.000 0.000 0.000 0.012
#> GSM99500 1 0.0290 0.8465 0.992 0.000 0.000 0.000 0.008
#> GSM99508 3 0.0404 0.8987 0.000 0.000 0.988 0.000 0.012
#> GSM99568 3 0.0404 0.8981 0.000 0.000 0.988 0.000 0.012
#> GSM99596 3 0.0000 0.8986 0.000 0.000 1.000 0.000 0.000
#> GSM99600 2 0.3366 0.6314 0.000 0.768 0.000 0.232 0.000
#> GSM99458 1 0.3852 0.5582 0.760 0.000 0.000 0.020 0.220
#> GSM99460 5 0.4613 0.4484 0.360 0.000 0.000 0.020 0.620
#> GSM99510 4 0.6593 0.0524 0.000 0.000 0.368 0.420 0.212
#> GSM99512 3 0.4879 0.6506 0.000 0.000 0.720 0.156 0.124
#> GSM99514 3 0.0000 0.8986 0.000 0.000 1.000 0.000 0.000
#> GSM99516 1 0.0162 0.8467 0.996 0.000 0.000 0.000 0.004
#> GSM99518 1 0.1851 0.7912 0.912 0.000 0.000 0.000 0.088
#> GSM99520 3 0.0404 0.8988 0.000 0.000 0.988 0.000 0.012
#> GSM99522 3 0.0771 0.8966 0.000 0.000 0.976 0.004 0.020
#> GSM99570 1 0.0162 0.8467 0.996 0.000 0.000 0.000 0.004
#> GSM99598 1 0.0000 0.8473 1.000 0.000 0.000 0.000 0.000
#> GSM99432 4 0.4067 0.4231 0.000 0.300 0.000 0.692 0.008
#> GSM99434 4 0.6624 0.2204 0.000 0.000 0.264 0.456 0.280
#> GSM99436 2 0.4262 0.2066 0.000 0.560 0.000 0.440 0.000
#> GSM99438 2 0.0000 0.8367 0.000 1.000 0.000 0.000 0.000
#> GSM99440 1 0.0162 0.8474 0.996 0.000 0.000 0.000 0.004
#> GSM99442 2 0.1851 0.7824 0.000 0.912 0.000 0.088 0.000
#> GSM99444 2 0.0000 0.8367 0.000 1.000 0.000 0.000 0.000
#> GSM99446 2 0.4150 0.3451 0.000 0.612 0.000 0.388 0.000
#> GSM99448 4 0.5328 0.2566 0.000 0.000 0.352 0.584 0.064
#> GSM99450 3 0.6606 0.1625 0.000 0.000 0.444 0.228 0.328
#> GSM99452 1 0.0609 0.8459 0.980 0.000 0.000 0.000 0.020
#> GSM99454 1 0.0000 0.8473 1.000 0.000 0.000 0.000 0.000
#> GSM99456 5 0.4242 0.3049 0.428 0.000 0.000 0.000 0.572
#> GSM99462 2 0.0000 0.8367 0.000 1.000 0.000 0.000 0.000
#> GSM99464 5 0.3342 0.3613 0.008 0.000 0.020 0.136 0.836
#> GSM99466 4 0.4522 0.5131 0.000 0.176 0.000 0.744 0.080
#> GSM99470 1 0.2355 0.7833 0.916 0.024 0.000 0.024 0.036
#> GSM99472 1 0.0510 0.8438 0.984 0.000 0.000 0.000 0.016
#> GSM99474 3 0.2079 0.8634 0.000 0.000 0.916 0.020 0.064
#> GSM99476 4 0.2124 0.5298 0.000 0.000 0.028 0.916 0.056
#> GSM99478 2 0.5524 0.1631 0.000 0.516 0.000 0.416 0.068
#> GSM99480 1 0.2773 0.7110 0.836 0.000 0.000 0.000 0.164
#> GSM99482 1 0.0510 0.8438 0.984 0.000 0.000 0.000 0.016
#> GSM99484 2 0.3058 0.7383 0.000 0.860 0.000 0.096 0.044
#> GSM99486 4 0.4307 -0.0954 0.000 0.496 0.000 0.504 0.000
#> GSM99488 2 0.0000 0.8367 0.000 1.000 0.000 0.000 0.000
#> GSM99490 2 0.0000 0.8367 0.000 1.000 0.000 0.000 0.000
#> GSM99492 1 0.3480 0.5779 0.752 0.000 0.000 0.000 0.248
#> GSM99494 2 0.0000 0.8367 0.000 1.000 0.000 0.000 0.000
#> GSM99524 1 0.0290 0.8456 0.992 0.000 0.000 0.000 0.008
#> GSM99526 5 0.4262 -0.1094 0.000 0.000 0.000 0.440 0.560
#> GSM99528 2 0.6539 0.2531 0.000 0.544 0.012 0.216 0.228
#> GSM99530 5 0.4194 0.3221 0.012 0.000 0.276 0.004 0.708
#> GSM99532 3 0.4613 0.4683 0.000 0.000 0.620 0.020 0.360
#> GSM99534 2 0.0807 0.8283 0.000 0.976 0.000 0.012 0.012
#> GSM99536 1 0.2732 0.7135 0.840 0.000 0.000 0.000 0.160
#> GSM99538 4 0.4203 0.5735 0.000 0.188 0.000 0.760 0.052
#> GSM99540 1 0.4299 0.1747 0.608 0.000 0.000 0.004 0.388
#> GSM99542 2 0.0324 0.8334 0.000 0.992 0.000 0.004 0.004
#> GSM99544 4 0.3152 0.5994 0.000 0.136 0.000 0.840 0.024
#> GSM99546 4 0.4201 0.2117 0.000 0.000 0.000 0.592 0.408
#> GSM99548 2 0.0000 0.8367 0.000 1.000 0.000 0.000 0.000
#> GSM99550 5 0.3957 0.5211 0.280 0.000 0.000 0.008 0.712
#> GSM99552 3 0.3891 0.7350 0.000 0.004 0.808 0.128 0.060
#> GSM99554 2 0.3999 0.4485 0.000 0.656 0.000 0.344 0.000
#> GSM99556 2 0.0000 0.8367 0.000 1.000 0.000 0.000 0.000
#> GSM99558 4 0.6169 0.5210 0.000 0.120 0.184 0.648 0.048
#> GSM99560 2 0.4468 0.5774 0.000 0.716 0.000 0.240 0.044
#> GSM99562 3 0.1041 0.8928 0.000 0.000 0.964 0.004 0.032
#> GSM99564 4 0.4300 -0.0255 0.000 0.476 0.000 0.524 0.000
#> GSM99572 2 0.0000 0.8367 0.000 1.000 0.000 0.000 0.000
#> GSM99576 5 0.4307 0.0635 0.496 0.000 0.000 0.000 0.504
#> GSM99578 2 0.0671 0.8281 0.000 0.980 0.000 0.004 0.016
#> GSM99580 3 0.1106 0.8897 0.000 0.000 0.964 0.024 0.012
#> GSM99582 1 0.7130 -0.0568 0.440 0.000 0.384 0.116 0.060
#> GSM99584 4 0.3354 0.5789 0.000 0.088 0.000 0.844 0.068
#> GSM99586 1 0.4307 -0.2161 0.504 0.000 0.000 0.000 0.496
#> GSM99588 2 0.0162 0.8350 0.000 0.996 0.000 0.004 0.000
#> GSM99590 2 0.0000 0.8367 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM99496 3 0.0260 0.8207 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM99502 1 0.0291 0.8121 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM99504 1 0.1194 0.8019 0.956 0.000 0.032 0.000 0.004 0.008
#> GSM99506 3 0.0458 0.8211 0.000 0.000 0.984 0.000 0.000 0.016
#> GSM99566 3 0.1082 0.8205 0.000 0.000 0.956 0.000 0.004 0.040
#> GSM99574 1 0.0291 0.8121 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM99592 3 0.2103 0.8043 0.000 0.000 0.912 0.020 0.012 0.056
#> GSM99594 3 0.1010 0.8212 0.000 0.000 0.960 0.000 0.004 0.036
#> GSM99468 1 0.1398 0.8001 0.940 0.000 0.000 0.000 0.052 0.008
#> GSM99498 1 0.0891 0.8098 0.968 0.000 0.000 0.000 0.024 0.008
#> GSM99500 1 0.0717 0.8110 0.976 0.000 0.000 0.000 0.016 0.008
#> GSM99508 3 0.0146 0.8205 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM99568 3 0.0692 0.8220 0.000 0.000 0.976 0.000 0.004 0.020
#> GSM99596 3 0.0790 0.8202 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM99600 2 0.3584 0.5026 0.000 0.688 0.000 0.308 0.000 0.004
#> GSM99458 1 0.4703 0.3952 0.652 0.000 0.000 0.008 0.280 0.060
#> GSM99460 5 0.5059 0.5173 0.284 0.000 0.000 0.008 0.620 0.088
#> GSM99510 3 0.7490 -0.1545 0.000 0.000 0.304 0.300 0.132 0.264
#> GSM99512 3 0.5920 0.4988 0.000 0.000 0.604 0.108 0.068 0.220
#> GSM99514 3 0.0405 0.8210 0.000 0.000 0.988 0.000 0.004 0.008
#> GSM99516 1 0.0260 0.8121 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM99518 1 0.1812 0.7791 0.912 0.000 0.000 0.000 0.080 0.008
#> GSM99520 3 0.0653 0.8214 0.000 0.000 0.980 0.004 0.004 0.012
#> GSM99522 3 0.1464 0.8129 0.016 0.000 0.944 0.000 0.004 0.036
#> GSM99570 1 0.1049 0.8055 0.960 0.000 0.000 0.000 0.008 0.032
#> GSM99598 1 0.0000 0.8122 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99432 4 0.4248 0.4475 0.000 0.236 0.000 0.708 0.004 0.052
#> GSM99434 6 0.7473 -0.1058 0.000 0.000 0.172 0.316 0.176 0.336
#> GSM99436 4 0.3804 0.1700 0.000 0.424 0.000 0.576 0.000 0.000
#> GSM99438 2 0.0632 0.8219 0.000 0.976 0.000 0.024 0.000 0.000
#> GSM99440 1 0.0632 0.8119 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM99442 2 0.2762 0.6891 0.000 0.804 0.000 0.196 0.000 0.000
#> GSM99444 2 0.0713 0.8210 0.000 0.972 0.000 0.028 0.000 0.000
#> GSM99446 2 0.3986 0.0930 0.000 0.532 0.000 0.464 0.000 0.004
#> GSM99448 4 0.6283 -0.0165 0.000 0.000 0.336 0.476 0.036 0.152
#> GSM99450 3 0.7560 -0.0689 0.000 0.000 0.336 0.180 0.200 0.284
#> GSM99452 1 0.1649 0.8008 0.932 0.000 0.000 0.000 0.032 0.036
#> GSM99454 1 0.0405 0.8134 0.988 0.000 0.000 0.000 0.008 0.004
#> GSM99456 5 0.3499 0.4761 0.320 0.000 0.000 0.000 0.680 0.000
#> GSM99462 2 0.0632 0.8216 0.000 0.976 0.000 0.024 0.000 0.000
#> GSM99464 5 0.4488 0.3014 0.004 0.000 0.020 0.048 0.724 0.204
#> GSM99466 4 0.4989 0.1711 0.000 0.060 0.000 0.528 0.004 0.408
#> GSM99470 1 0.4601 0.5940 0.716 0.016 0.000 0.008 0.052 0.208
#> GSM99472 1 0.3213 0.7160 0.820 0.000 0.000 0.000 0.048 0.132
#> GSM99474 3 0.3325 0.7692 0.000 0.000 0.836 0.020 0.044 0.100
#> GSM99476 4 0.4703 0.2555 0.000 0.000 0.008 0.652 0.060 0.280
#> GSM99478 6 0.6064 0.2051 0.000 0.352 0.000 0.220 0.004 0.424
#> GSM99480 1 0.3101 0.5966 0.756 0.000 0.000 0.000 0.244 0.000
#> GSM99482 1 0.2889 0.7411 0.848 0.000 0.000 0.000 0.044 0.108
#> GSM99484 2 0.4251 0.5168 0.000 0.716 0.000 0.076 0.000 0.208
#> GSM99486 4 0.3927 0.3645 0.000 0.344 0.000 0.644 0.000 0.012
#> GSM99488 2 0.0000 0.8209 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99490 2 0.0146 0.8208 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM99492 1 0.3592 0.3957 0.656 0.000 0.000 0.000 0.344 0.000
#> GSM99494 2 0.0000 0.8209 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99524 1 0.1594 0.7912 0.932 0.000 0.000 0.000 0.016 0.052
#> GSM99526 5 0.6031 -0.0972 0.000 0.000 0.000 0.344 0.404 0.252
#> GSM99528 6 0.6459 0.2889 0.000 0.392 0.000 0.092 0.084 0.432
#> GSM99530 5 0.5561 0.2725 0.012 0.000 0.232 0.008 0.616 0.132
#> GSM99532 3 0.5653 0.4853 0.008 0.000 0.596 0.008 0.236 0.152
#> GSM99534 2 0.2682 0.7342 0.000 0.876 0.000 0.020 0.020 0.084
#> GSM99536 1 0.2871 0.6644 0.804 0.000 0.000 0.000 0.192 0.004
#> GSM99538 4 0.5184 0.3679 0.000 0.188 0.000 0.652 0.012 0.148
#> GSM99540 1 0.4845 0.1727 0.580 0.000 0.000 0.008 0.364 0.048
#> GSM99542 2 0.1194 0.7908 0.000 0.956 0.000 0.004 0.008 0.032
#> GSM99544 4 0.3123 0.4621 0.000 0.112 0.000 0.832 0.000 0.056
#> GSM99546 4 0.6062 -0.0877 0.000 0.004 0.000 0.444 0.320 0.232
#> GSM99548 2 0.0000 0.8209 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99550 5 0.3094 0.5474 0.140 0.000 0.000 0.000 0.824 0.036
#> GSM99552 3 0.5036 0.4422 0.000 0.000 0.604 0.076 0.008 0.312
#> GSM99554 2 0.3937 0.2464 0.000 0.572 0.000 0.424 0.000 0.004
#> GSM99556 2 0.0000 0.8209 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99558 4 0.6347 0.2516 0.000 0.048 0.144 0.552 0.008 0.248
#> GSM99560 2 0.6005 0.1593 0.000 0.524 0.000 0.336 0.080 0.060
#> GSM99562 3 0.1625 0.8099 0.000 0.000 0.928 0.000 0.012 0.060
#> GSM99564 4 0.3847 0.3573 0.000 0.348 0.000 0.644 0.000 0.008
#> GSM99572 2 0.0790 0.8198 0.000 0.968 0.000 0.032 0.000 0.000
#> GSM99576 5 0.4947 0.2912 0.384 0.000 0.000 0.004 0.552 0.060
#> GSM99578 2 0.1049 0.8014 0.000 0.960 0.000 0.008 0.000 0.032
#> GSM99580 3 0.2326 0.7862 0.000 0.000 0.888 0.012 0.008 0.092
#> GSM99582 1 0.7758 -0.1755 0.324 0.000 0.248 0.048 0.060 0.320
#> GSM99584 4 0.3020 0.4032 0.000 0.040 0.000 0.864 0.032 0.064
#> GSM99586 5 0.3765 0.3159 0.404 0.000 0.000 0.000 0.596 0.000
#> GSM99588 2 0.0993 0.8132 0.000 0.964 0.000 0.024 0.000 0.012
#> GSM99590 2 0.0363 0.8225 0.000 0.988 0.000 0.012 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) cell.type(p) k
#> SD:skmeans 83 3.58e-05 0.000192 2
#> SD:skmeans 84 1.12e-04 0.003364 3
#> SD:skmeans 74 6.44e-05 0.004225 4
#> SD:skmeans 62 1.10e-04 0.015755 5
#> SD:skmeans 52 5.85e-04 0.012583 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 21168 rows and 85 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.671 0.783 0.912 0.4917 0.500 0.500
#> 3 3 0.655 0.767 0.872 0.3358 0.709 0.480
#> 4 4 0.692 0.808 0.835 0.1405 0.820 0.522
#> 5 5 0.768 0.654 0.810 0.0588 0.969 0.875
#> 6 6 0.867 0.815 0.918 0.0433 0.923 0.673
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
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
#> GSM99496 2 0.9866 0.338 0.432 0.568
#> GSM99502 1 0.0000 0.914 1.000 0.000
#> GSM99504 1 0.0000 0.914 1.000 0.000
#> GSM99506 2 0.9850 0.348 0.428 0.572
#> GSM99566 2 0.9833 0.358 0.424 0.576
#> GSM99574 1 0.0000 0.914 1.000 0.000
#> GSM99592 2 0.8763 0.580 0.296 0.704
#> GSM99594 2 0.9580 0.445 0.380 0.620
#> GSM99468 1 0.0000 0.914 1.000 0.000
#> GSM99498 1 0.0000 0.914 1.000 0.000
#> GSM99500 1 0.0000 0.914 1.000 0.000
#> GSM99508 1 0.7883 0.653 0.764 0.236
#> GSM99568 1 0.3879 0.866 0.924 0.076
#> GSM99596 1 0.3114 0.881 0.944 0.056
#> GSM99600 2 0.0000 0.877 0.000 1.000
#> GSM99458 1 0.0000 0.914 1.000 0.000
#> GSM99460 1 0.0000 0.914 1.000 0.000
#> GSM99510 2 0.0000 0.877 0.000 1.000
#> GSM99512 2 0.0376 0.875 0.004 0.996
#> GSM99514 2 0.9866 0.338 0.432 0.568
#> GSM99516 1 0.0000 0.914 1.000 0.000
#> GSM99518 1 0.0000 0.914 1.000 0.000
#> GSM99520 2 0.9815 0.366 0.420 0.580
#> GSM99522 1 0.0000 0.914 1.000 0.000
#> GSM99570 1 0.0000 0.914 1.000 0.000
#> GSM99598 1 0.0000 0.914 1.000 0.000
#> GSM99432 2 0.0000 0.877 0.000 1.000
#> GSM99434 2 0.0938 0.870 0.012 0.988
#> GSM99436 2 0.0000 0.877 0.000 1.000
#> GSM99438 2 0.0000 0.877 0.000 1.000
#> GSM99440 1 0.0000 0.914 1.000 0.000
#> GSM99442 2 0.0000 0.877 0.000 1.000
#> GSM99444 2 0.0000 0.877 0.000 1.000
#> GSM99446 2 0.0000 0.877 0.000 1.000
#> GSM99448 2 0.0000 0.877 0.000 1.000
#> GSM99450 1 1.0000 -0.118 0.504 0.496
#> GSM99452 1 0.0000 0.914 1.000 0.000
#> GSM99454 1 0.0000 0.914 1.000 0.000
#> GSM99456 1 0.0000 0.914 1.000 0.000
#> GSM99462 2 0.0000 0.877 0.000 1.000
#> GSM99464 1 0.2948 0.884 0.948 0.052
#> GSM99466 2 0.0000 0.877 0.000 1.000
#> GSM99470 1 0.4298 0.857 0.912 0.088
#> GSM99472 1 0.0000 0.914 1.000 0.000
#> GSM99474 2 0.9754 0.391 0.408 0.592
#> GSM99476 2 0.0000 0.877 0.000 1.000
#> GSM99478 2 0.0000 0.877 0.000 1.000
#> GSM99480 1 0.0000 0.914 1.000 0.000
#> GSM99482 1 0.0000 0.914 1.000 0.000
#> GSM99484 2 0.0000 0.877 0.000 1.000
#> GSM99486 2 0.0000 0.877 0.000 1.000
#> GSM99488 2 0.0000 0.877 0.000 1.000
#> GSM99490 2 0.0000 0.877 0.000 1.000
#> GSM99492 1 0.0000 0.914 1.000 0.000
#> GSM99494 2 0.0000 0.877 0.000 1.000
#> GSM99524 1 0.0000 0.914 1.000 0.000
#> GSM99526 2 0.0376 0.874 0.004 0.996
#> GSM99528 2 0.9393 0.487 0.356 0.644
#> GSM99530 1 0.7139 0.721 0.804 0.196
#> GSM99532 1 0.9661 0.258 0.608 0.392
#> GSM99534 1 0.9996 0.108 0.512 0.488
#> GSM99536 1 0.0000 0.914 1.000 0.000
#> GSM99538 2 0.0000 0.877 0.000 1.000
#> GSM99540 1 0.0000 0.914 1.000 0.000
#> GSM99542 1 0.9129 0.510 0.672 0.328
#> GSM99544 2 0.0000 0.877 0.000 1.000
#> GSM99546 2 0.1184 0.867 0.016 0.984
#> GSM99548 2 0.0000 0.877 0.000 1.000
#> GSM99550 1 0.4690 0.848 0.900 0.100
#> GSM99552 2 0.9522 0.460 0.372 0.628
#> GSM99554 2 0.0000 0.877 0.000 1.000
#> GSM99556 2 0.0000 0.877 0.000 1.000
#> GSM99558 2 0.0000 0.877 0.000 1.000
#> GSM99560 2 0.0000 0.877 0.000 1.000
#> GSM99562 2 0.9850 0.348 0.428 0.572
#> GSM99564 2 0.0000 0.877 0.000 1.000
#> GSM99572 2 0.0000 0.877 0.000 1.000
#> GSM99576 1 0.2423 0.893 0.960 0.040
#> GSM99578 2 0.0000 0.877 0.000 1.000
#> GSM99580 2 0.9580 0.445 0.380 0.620
#> GSM99582 1 0.6623 0.764 0.828 0.172
#> GSM99584 2 0.0000 0.877 0.000 1.000
#> GSM99586 1 0.0000 0.914 1.000 0.000
#> GSM99588 2 0.0000 0.877 0.000 1.000
#> GSM99590 2 0.0000 0.877 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM99496 3 0.0747 0.815 0.016 0.000 0.984
#> GSM99502 1 0.0000 0.964 1.000 0.000 0.000
#> GSM99504 1 0.0000 0.964 1.000 0.000 0.000
#> GSM99506 3 0.0747 0.815 0.016 0.000 0.984
#> GSM99566 3 0.0747 0.815 0.016 0.000 0.984
#> GSM99574 1 0.0000 0.964 1.000 0.000 0.000
#> GSM99592 3 0.0000 0.810 0.000 0.000 1.000
#> GSM99594 3 0.0000 0.810 0.000 0.000 1.000
#> GSM99468 1 0.0000 0.964 1.000 0.000 0.000
#> GSM99498 1 0.0237 0.961 0.996 0.000 0.004
#> GSM99500 1 0.0000 0.964 1.000 0.000 0.000
#> GSM99508 3 0.4887 0.695 0.228 0.000 0.772
#> GSM99568 3 0.5621 0.582 0.308 0.000 0.692
#> GSM99596 3 0.5678 0.570 0.316 0.000 0.684
#> GSM99600 2 0.0000 0.746 0.000 1.000 0.000
#> GSM99458 1 0.0000 0.964 1.000 0.000 0.000
#> GSM99460 1 0.2625 0.883 0.916 0.000 0.084
#> GSM99510 3 0.0424 0.805 0.000 0.008 0.992
#> GSM99512 3 0.0000 0.810 0.000 0.000 1.000
#> GSM99514 3 0.0747 0.815 0.016 0.000 0.984
#> GSM99516 1 0.0000 0.964 1.000 0.000 0.000
#> GSM99518 1 0.0000 0.964 1.000 0.000 0.000
#> GSM99520 3 0.0592 0.814 0.012 0.000 0.988
#> GSM99522 3 0.6026 0.446 0.376 0.000 0.624
#> GSM99570 1 0.0000 0.964 1.000 0.000 0.000
#> GSM99598 1 0.0000 0.964 1.000 0.000 0.000
#> GSM99432 2 0.5785 0.690 0.000 0.668 0.332
#> GSM99434 3 0.0000 0.810 0.000 0.000 1.000
#> GSM99436 2 0.0000 0.746 0.000 1.000 0.000
#> GSM99438 2 0.0000 0.746 0.000 1.000 0.000
#> GSM99440 1 0.0000 0.964 1.000 0.000 0.000
#> GSM99442 2 0.0237 0.746 0.000 0.996 0.004
#> GSM99444 2 0.0000 0.746 0.000 1.000 0.000
#> GSM99446 2 0.5650 0.695 0.000 0.688 0.312
#> GSM99448 3 0.0892 0.793 0.000 0.020 0.980
#> GSM99450 3 0.2448 0.796 0.076 0.000 0.924
#> GSM99452 1 0.0000 0.964 1.000 0.000 0.000
#> GSM99454 1 0.0000 0.964 1.000 0.000 0.000
#> GSM99456 1 0.0000 0.964 1.000 0.000 0.000
#> GSM99462 2 0.0000 0.746 0.000 1.000 0.000
#> GSM99464 3 0.5785 0.548 0.332 0.000 0.668
#> GSM99466 2 0.6299 0.535 0.000 0.524 0.476
#> GSM99470 1 0.3263 0.879 0.912 0.040 0.048
#> GSM99472 1 0.0000 0.964 1.000 0.000 0.000
#> GSM99474 3 0.4654 0.683 0.208 0.000 0.792
#> GSM99476 2 0.6280 0.567 0.000 0.540 0.460
#> GSM99478 2 0.6244 0.599 0.000 0.560 0.440
#> GSM99480 1 0.0000 0.964 1.000 0.000 0.000
#> GSM99482 1 0.0000 0.964 1.000 0.000 0.000
#> GSM99484 2 0.6225 0.610 0.000 0.568 0.432
#> GSM99486 2 0.5988 0.673 0.000 0.632 0.368
#> GSM99488 2 0.0000 0.746 0.000 1.000 0.000
#> GSM99490 2 0.0237 0.746 0.000 0.996 0.004
#> GSM99492 1 0.0000 0.964 1.000 0.000 0.000
#> GSM99494 2 0.0000 0.746 0.000 1.000 0.000
#> GSM99524 1 0.0000 0.964 1.000 0.000 0.000
#> GSM99526 2 0.6500 0.556 0.004 0.532 0.464
#> GSM99528 3 0.8688 0.243 0.196 0.208 0.596
#> GSM99530 3 0.5138 0.671 0.252 0.000 0.748
#> GSM99532 3 0.2959 0.787 0.100 0.000 0.900
#> GSM99534 2 0.5414 0.609 0.212 0.772 0.016
#> GSM99536 1 0.0000 0.964 1.000 0.000 0.000
#> GSM99538 2 0.6244 0.599 0.000 0.560 0.440
#> GSM99540 1 0.3752 0.808 0.856 0.000 0.144
#> GSM99542 2 0.4002 0.605 0.160 0.840 0.000
#> GSM99544 2 0.6026 0.668 0.000 0.624 0.376
#> GSM99546 2 0.7223 0.587 0.028 0.548 0.424
#> GSM99548 2 0.0000 0.746 0.000 1.000 0.000
#> GSM99550 1 0.7935 0.484 0.648 0.236 0.116
#> GSM99552 3 0.0000 0.810 0.000 0.000 1.000
#> GSM99554 2 0.0424 0.746 0.000 0.992 0.008
#> GSM99556 2 0.0000 0.746 0.000 1.000 0.000
#> GSM99558 3 0.2959 0.691 0.000 0.100 0.900
#> GSM99560 2 0.5988 0.674 0.000 0.632 0.368
#> GSM99562 3 0.0747 0.815 0.016 0.000 0.984
#> GSM99564 2 0.5785 0.689 0.000 0.668 0.332
#> GSM99572 2 0.0000 0.746 0.000 1.000 0.000
#> GSM99576 1 0.3619 0.820 0.864 0.000 0.136
#> GSM99578 2 0.6008 0.671 0.000 0.628 0.372
#> GSM99580 3 0.0000 0.810 0.000 0.000 1.000
#> GSM99582 3 0.6252 0.304 0.444 0.000 0.556
#> GSM99584 2 0.6235 0.604 0.000 0.564 0.436
#> GSM99586 1 0.0000 0.964 1.000 0.000 0.000
#> GSM99588 2 0.6008 0.671 0.000 0.628 0.372
#> GSM99590 2 0.0000 0.746 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM99496 3 0.2921 0.8629 0.000 0.000 0.860 0.140
#> GSM99502 1 0.0000 0.9366 1.000 0.000 0.000 0.000
#> GSM99504 1 0.1004 0.9361 0.972 0.000 0.024 0.004
#> GSM99506 3 0.2921 0.8629 0.000 0.000 0.860 0.140
#> GSM99566 3 0.3074 0.8602 0.000 0.000 0.848 0.152
#> GSM99574 1 0.0000 0.9366 1.000 0.000 0.000 0.000
#> GSM99592 3 0.3172 0.8564 0.000 0.000 0.840 0.160
#> GSM99594 3 0.3172 0.8564 0.000 0.000 0.840 0.160
#> GSM99468 1 0.3249 0.9088 0.852 0.000 0.140 0.008
#> GSM99498 1 0.3249 0.9088 0.852 0.000 0.140 0.008
#> GSM99500 1 0.2799 0.9190 0.884 0.000 0.108 0.008
#> GSM99508 3 0.0469 0.8120 0.000 0.000 0.988 0.012
#> GSM99568 3 0.0000 0.8042 0.000 0.000 1.000 0.000
#> GSM99596 3 0.0000 0.8042 0.000 0.000 1.000 0.000
#> GSM99600 2 0.0188 0.9001 0.000 0.996 0.000 0.004
#> GSM99458 1 0.3249 0.9088 0.852 0.000 0.140 0.008
#> GSM99460 1 0.4996 0.8216 0.752 0.000 0.192 0.056
#> GSM99510 3 0.4877 0.4470 0.000 0.000 0.592 0.408
#> GSM99512 3 0.2921 0.8629 0.000 0.000 0.860 0.140
#> GSM99514 3 0.3123 0.8583 0.000 0.000 0.844 0.156
#> GSM99516 1 0.0000 0.9366 1.000 0.000 0.000 0.000
#> GSM99518 1 0.1489 0.9345 0.952 0.000 0.044 0.004
#> GSM99520 3 0.3266 0.8513 0.000 0.000 0.832 0.168
#> GSM99522 3 0.0000 0.8042 0.000 0.000 1.000 0.000
#> GSM99570 1 0.0000 0.9366 1.000 0.000 0.000 0.000
#> GSM99598 1 0.0000 0.9366 1.000 0.000 0.000 0.000
#> GSM99432 4 0.4072 0.7054 0.000 0.252 0.000 0.748
#> GSM99434 4 0.3528 0.6587 0.000 0.000 0.192 0.808
#> GSM99436 2 0.0188 0.9001 0.000 0.996 0.000 0.004
#> GSM99438 2 0.0000 0.9003 0.000 1.000 0.000 0.000
#> GSM99440 1 0.0000 0.9366 1.000 0.000 0.000 0.000
#> GSM99442 2 0.0336 0.8988 0.000 0.992 0.000 0.008
#> GSM99444 2 0.1302 0.8961 0.000 0.956 0.000 0.044
#> GSM99446 2 0.3356 0.7172 0.000 0.824 0.000 0.176
#> GSM99448 3 0.4761 0.5627 0.000 0.000 0.628 0.372
#> GSM99450 3 0.2868 0.8631 0.000 0.000 0.864 0.136
#> GSM99452 1 0.0000 0.9366 1.000 0.000 0.000 0.000
#> GSM99454 1 0.0000 0.9366 1.000 0.000 0.000 0.000
#> GSM99456 1 0.3249 0.9088 0.852 0.000 0.140 0.008
#> GSM99462 2 0.0000 0.9003 0.000 1.000 0.000 0.000
#> GSM99464 3 0.0000 0.8042 0.000 0.000 1.000 0.000
#> GSM99466 4 0.0336 0.8171 0.000 0.008 0.000 0.992
#> GSM99470 4 0.6215 0.5364 0.192 0.000 0.140 0.668
#> GSM99472 1 0.3249 0.9088 0.852 0.000 0.140 0.008
#> GSM99474 4 0.4872 0.2748 0.004 0.000 0.356 0.640
#> GSM99476 4 0.1557 0.8095 0.000 0.056 0.000 0.944
#> GSM99478 4 0.0336 0.8171 0.000 0.008 0.000 0.992
#> GSM99480 1 0.0000 0.9366 1.000 0.000 0.000 0.000
#> GSM99482 1 0.0000 0.9366 1.000 0.000 0.000 0.000
#> GSM99484 4 0.0336 0.8171 0.000 0.008 0.000 0.992
#> GSM99486 4 0.4543 0.6143 0.000 0.324 0.000 0.676
#> GSM99488 2 0.1867 0.8825 0.000 0.928 0.000 0.072
#> GSM99490 2 0.4222 0.6689 0.000 0.728 0.000 0.272
#> GSM99492 1 0.1474 0.9337 0.948 0.000 0.052 0.000
#> GSM99494 2 0.1389 0.8947 0.000 0.952 0.000 0.048
#> GSM99524 1 0.0000 0.9366 1.000 0.000 0.000 0.000
#> GSM99526 4 0.4642 0.7094 0.000 0.240 0.020 0.740
#> GSM99528 4 0.0336 0.8130 0.000 0.000 0.008 0.992
#> GSM99530 3 0.0592 0.8145 0.000 0.000 0.984 0.016
#> GSM99532 3 0.2868 0.8629 0.000 0.000 0.864 0.136
#> GSM99534 4 0.5998 0.6161 0.000 0.240 0.092 0.668
#> GSM99536 1 0.3249 0.9088 0.852 0.000 0.140 0.008
#> GSM99538 4 0.0469 0.8174 0.000 0.012 0.000 0.988
#> GSM99540 3 0.5220 -0.0748 0.424 0.000 0.568 0.008
#> GSM99542 2 0.4155 0.7148 0.000 0.756 0.004 0.240
#> GSM99544 4 0.4134 0.6968 0.000 0.260 0.000 0.740
#> GSM99546 4 0.2413 0.8093 0.000 0.064 0.020 0.916
#> GSM99548 2 0.1389 0.8947 0.000 0.952 0.000 0.048
#> GSM99550 4 0.3402 0.7111 0.004 0.000 0.164 0.832
#> GSM99552 4 0.1557 0.7900 0.000 0.000 0.056 0.944
#> GSM99554 2 0.0188 0.9001 0.000 0.996 0.000 0.004
#> GSM99556 2 0.3726 0.7488 0.000 0.788 0.000 0.212
#> GSM99558 4 0.0524 0.8143 0.000 0.004 0.008 0.988
#> GSM99560 4 0.4509 0.6663 0.000 0.288 0.004 0.708
#> GSM99562 3 0.2921 0.8629 0.000 0.000 0.860 0.140
#> GSM99564 2 0.3400 0.7119 0.000 0.820 0.000 0.180
#> GSM99572 2 0.0000 0.9003 0.000 1.000 0.000 0.000
#> GSM99576 4 0.5944 0.5973 0.140 0.000 0.164 0.696
#> GSM99578 4 0.0336 0.8171 0.000 0.008 0.000 0.992
#> GSM99580 3 0.3266 0.8513 0.000 0.000 0.832 0.168
#> GSM99582 4 0.4252 0.6514 0.004 0.000 0.252 0.744
#> GSM99584 4 0.3975 0.7121 0.000 0.240 0.000 0.760
#> GSM99586 1 0.3249 0.9088 0.852 0.000 0.140 0.008
#> GSM99588 4 0.0469 0.8166 0.000 0.012 0.000 0.988
#> GSM99590 2 0.1022 0.8988 0.000 0.968 0.000 0.032
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM99496 3 0.0000 0.890 0.000 0.000 1.000 0.000 0.000
#> GSM99502 1 0.0000 0.835 1.000 0.000 0.000 0.000 0.000
#> GSM99504 1 0.1608 0.809 0.928 0.000 0.000 0.000 0.072
#> GSM99506 3 0.0000 0.890 0.000 0.000 1.000 0.000 0.000
#> GSM99566 3 0.0000 0.890 0.000 0.000 1.000 0.000 0.000
#> GSM99574 1 0.0000 0.835 1.000 0.000 0.000 0.000 0.000
#> GSM99592 3 0.0000 0.890 0.000 0.000 1.000 0.000 0.000
#> GSM99594 3 0.0162 0.888 0.000 0.000 0.996 0.004 0.000
#> GSM99468 1 0.3274 0.677 0.780 0.000 0.000 0.000 0.220
#> GSM99498 1 0.3274 0.677 0.780 0.000 0.000 0.000 0.220
#> GSM99500 1 0.2377 0.772 0.872 0.000 0.000 0.000 0.128
#> GSM99508 3 0.0794 0.879 0.000 0.000 0.972 0.000 0.028
#> GSM99568 3 0.0880 0.877 0.000 0.000 0.968 0.000 0.032
#> GSM99596 3 0.0880 0.877 0.000 0.000 0.968 0.000 0.032
#> GSM99600 2 0.1908 0.578 0.000 0.908 0.000 0.092 0.000
#> GSM99458 1 0.4235 0.163 0.576 0.000 0.000 0.000 0.424
#> GSM99460 5 0.4387 0.531 0.336 0.000 0.004 0.008 0.652
#> GSM99510 3 0.3636 0.573 0.000 0.000 0.728 0.272 0.000
#> GSM99512 3 0.0000 0.890 0.000 0.000 1.000 0.000 0.000
#> GSM99514 3 0.0000 0.890 0.000 0.000 1.000 0.000 0.000
#> GSM99516 1 0.0000 0.835 1.000 0.000 0.000 0.000 0.000
#> GSM99518 1 0.2329 0.774 0.876 0.000 0.000 0.000 0.124
#> GSM99520 3 0.1197 0.860 0.000 0.000 0.952 0.048 0.000
#> GSM99522 3 0.0880 0.877 0.000 0.000 0.968 0.000 0.032
#> GSM99570 1 0.0000 0.835 1.000 0.000 0.000 0.000 0.000
#> GSM99598 1 0.0000 0.835 1.000 0.000 0.000 0.000 0.000
#> GSM99432 4 0.4278 0.463 0.000 0.452 0.000 0.548 0.000
#> GSM99434 4 0.3837 0.490 0.000 0.000 0.308 0.692 0.000
#> GSM99436 2 0.1908 0.578 0.000 0.908 0.000 0.092 0.000
#> GSM99438 2 0.4015 0.763 0.000 0.652 0.000 0.000 0.348
#> GSM99440 1 0.0000 0.835 1.000 0.000 0.000 0.000 0.000
#> GSM99442 2 0.3800 0.649 0.000 0.812 0.000 0.080 0.108
#> GSM99444 2 0.5016 0.760 0.000 0.608 0.000 0.044 0.348
#> GSM99446 2 0.3074 0.424 0.000 0.804 0.000 0.196 0.000
#> GSM99448 3 0.3774 0.530 0.000 0.000 0.704 0.296 0.000
#> GSM99450 3 0.0703 0.882 0.000 0.000 0.976 0.000 0.024
#> GSM99452 1 0.0000 0.835 1.000 0.000 0.000 0.000 0.000
#> GSM99454 1 0.0000 0.835 1.000 0.000 0.000 0.000 0.000
#> GSM99456 5 0.4015 0.516 0.348 0.000 0.000 0.000 0.652
#> GSM99462 2 0.4015 0.763 0.000 0.652 0.000 0.000 0.348
#> GSM99464 3 0.4242 0.376 0.000 0.000 0.572 0.000 0.428
#> GSM99466 4 0.0880 0.689 0.000 0.000 0.032 0.968 0.000
#> GSM99470 4 0.5394 0.201 0.132 0.000 0.000 0.660 0.208
#> GSM99472 1 0.3561 0.614 0.740 0.000 0.000 0.000 0.260
#> GSM99474 4 0.6096 0.271 0.000 0.000 0.316 0.536 0.148
#> GSM99476 4 0.1992 0.689 0.000 0.044 0.032 0.924 0.000
#> GSM99478 4 0.0880 0.689 0.000 0.000 0.032 0.968 0.000
#> GSM99480 1 0.1410 0.790 0.940 0.000 0.000 0.000 0.060
#> GSM99482 1 0.0162 0.833 0.996 0.000 0.000 0.000 0.004
#> GSM99484 4 0.0880 0.689 0.000 0.000 0.032 0.968 0.000
#> GSM99486 4 0.4307 0.385 0.000 0.500 0.000 0.500 0.000
#> GSM99488 2 0.5080 0.758 0.000 0.604 0.000 0.048 0.348
#> GSM99490 2 0.5678 0.478 0.000 0.600 0.000 0.284 0.116
#> GSM99492 1 0.4306 -0.252 0.508 0.000 0.000 0.000 0.492
#> GSM99494 2 0.5016 0.760 0.000 0.608 0.000 0.044 0.348
#> GSM99524 1 0.0000 0.835 1.000 0.000 0.000 0.000 0.000
#> GSM99526 4 0.5638 0.472 0.000 0.404 0.020 0.536 0.040
#> GSM99528 4 0.2278 0.644 0.000 0.000 0.032 0.908 0.060
#> GSM99530 3 0.1121 0.871 0.000 0.000 0.956 0.000 0.044
#> GSM99532 3 0.0000 0.890 0.000 0.000 1.000 0.000 0.000
#> GSM99534 4 0.5059 0.423 0.000 0.416 0.000 0.548 0.036
#> GSM99536 1 0.3274 0.677 0.780 0.000 0.000 0.000 0.220
#> GSM99538 4 0.1579 0.694 0.000 0.024 0.032 0.944 0.000
#> GSM99540 3 0.6794 -0.300 0.300 0.000 0.380 0.000 0.320
#> GSM99542 2 0.5822 0.713 0.000 0.548 0.000 0.108 0.344
#> GSM99544 4 0.4971 0.477 0.000 0.460 0.028 0.512 0.000
#> GSM99546 4 0.1557 0.681 0.000 0.052 0.000 0.940 0.008
#> GSM99548 2 0.5016 0.760 0.000 0.608 0.000 0.044 0.348
#> GSM99550 5 0.4015 0.407 0.000 0.000 0.000 0.348 0.652
#> GSM99552 4 0.2329 0.641 0.000 0.000 0.124 0.876 0.000
#> GSM99554 2 0.1908 0.578 0.000 0.908 0.000 0.092 0.000
#> GSM99556 2 0.5664 0.725 0.000 0.560 0.000 0.092 0.348
#> GSM99558 4 0.1410 0.679 0.000 0.000 0.060 0.940 0.000
#> GSM99560 4 0.4448 0.420 0.000 0.480 0.000 0.516 0.004
#> GSM99562 3 0.0000 0.890 0.000 0.000 1.000 0.000 0.000
#> GSM99564 2 0.3074 0.424 0.000 0.804 0.000 0.196 0.000
#> GSM99572 2 0.4015 0.763 0.000 0.652 0.000 0.000 0.348
#> GSM99576 5 0.5393 0.284 0.056 0.000 0.000 0.440 0.504
#> GSM99578 4 0.1211 0.691 0.000 0.024 0.016 0.960 0.000
#> GSM99580 3 0.2074 0.807 0.000 0.000 0.896 0.104 0.000
#> GSM99582 4 0.5030 0.428 0.000 0.000 0.104 0.696 0.200
#> GSM99584 4 0.4268 0.471 0.000 0.444 0.000 0.556 0.000
#> GSM99586 5 0.4060 0.495 0.360 0.000 0.000 0.000 0.640
#> GSM99588 4 0.1992 0.668 0.000 0.044 0.032 0.924 0.000
#> GSM99590 2 0.4733 0.763 0.000 0.624 0.000 0.028 0.348
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM99496 3 0.0000 0.91236 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99502 1 0.0000 0.90051 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99504 1 0.1387 0.88465 0.932 0.000 0.000 0.000 0.068 0.000
#> GSM99506 3 0.0000 0.91236 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99566 3 0.0000 0.91236 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99574 1 0.0000 0.90051 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99592 3 0.0000 0.91236 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99594 3 0.0260 0.90766 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM99468 1 0.2562 0.82541 0.828 0.000 0.000 0.000 0.172 0.000
#> GSM99498 1 0.2562 0.82541 0.828 0.000 0.000 0.000 0.172 0.000
#> GSM99500 1 0.1556 0.88040 0.920 0.000 0.000 0.000 0.080 0.000
#> GSM99508 3 0.0000 0.91236 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99568 3 0.0000 0.91236 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99596 3 0.0000 0.91236 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99600 4 0.0260 0.88502 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM99458 1 0.3971 0.36277 0.548 0.000 0.000 0.004 0.448 0.000
#> GSM99460 5 0.0000 0.80513 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM99510 3 0.3309 0.59816 0.000 0.000 0.720 0.000 0.000 0.280
#> GSM99512 3 0.0000 0.91236 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99514 3 0.0000 0.91236 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99516 1 0.0000 0.90051 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99518 1 0.2178 0.85109 0.868 0.000 0.000 0.000 0.132 0.000
#> GSM99520 3 0.1501 0.85512 0.000 0.000 0.924 0.000 0.000 0.076
#> GSM99522 3 0.0000 0.91236 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99570 1 0.0000 0.90051 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99598 1 0.0000 0.90051 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99432 4 0.0458 0.88330 0.000 0.000 0.000 0.984 0.000 0.016
#> GSM99434 6 0.2941 0.64292 0.000 0.000 0.220 0.000 0.000 0.780
#> GSM99436 4 0.0146 0.88529 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM99438 2 0.0000 0.99745 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99440 1 0.0000 0.90051 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99442 4 0.3647 0.47345 0.000 0.360 0.000 0.640 0.000 0.000
#> GSM99444 2 0.0000 0.99745 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99446 4 0.0458 0.88246 0.000 0.016 0.000 0.984 0.000 0.000
#> GSM99448 3 0.3563 0.49129 0.000 0.000 0.664 0.000 0.000 0.336
#> GSM99450 3 0.0937 0.88112 0.000 0.000 0.960 0.000 0.040 0.000
#> GSM99452 1 0.0000 0.90051 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99454 1 0.0000 0.90051 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99456 5 0.0000 0.80513 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM99462 2 0.0000 0.99745 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99464 5 0.3592 0.39392 0.000 0.000 0.344 0.000 0.656 0.000
#> GSM99466 6 0.0000 0.86982 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM99470 6 0.4629 0.55222 0.064 0.000 0.000 0.016 0.224 0.696
#> GSM99472 1 0.3265 0.73885 0.748 0.000 0.000 0.004 0.248 0.000
#> GSM99474 6 0.4986 0.42471 0.000 0.000 0.304 0.000 0.096 0.600
#> GSM99476 6 0.0146 0.86846 0.000 0.000 0.000 0.004 0.000 0.996
#> GSM99478 6 0.0000 0.86982 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM99480 1 0.2219 0.79228 0.864 0.000 0.000 0.000 0.136 0.000
#> GSM99482 1 0.0291 0.89824 0.992 0.000 0.000 0.004 0.004 0.000
#> GSM99484 6 0.0000 0.86982 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM99486 4 0.0146 0.88505 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM99488 2 0.0000 0.99745 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99490 4 0.5784 0.22893 0.000 0.356 0.000 0.460 0.000 0.184
#> GSM99492 5 0.2454 0.68455 0.160 0.000 0.000 0.000 0.840 0.000
#> GSM99494 2 0.0000 0.99745 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99524 1 0.0000 0.90051 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99526 4 0.3020 0.79010 0.000 0.000 0.000 0.844 0.076 0.080
#> GSM99528 6 0.0000 0.86982 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM99530 3 0.0000 0.91236 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99532 3 0.0000 0.91236 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99534 4 0.2668 0.74635 0.000 0.000 0.000 0.828 0.004 0.168
#> GSM99536 1 0.2562 0.82541 0.828 0.000 0.000 0.000 0.172 0.000
#> GSM99538 6 0.1075 0.84532 0.000 0.000 0.000 0.048 0.000 0.952
#> GSM99540 3 0.5919 -0.03204 0.228 0.000 0.452 0.000 0.320 0.000
#> GSM99542 2 0.0508 0.98184 0.000 0.984 0.000 0.000 0.004 0.012
#> GSM99544 4 0.1714 0.82597 0.000 0.000 0.000 0.908 0.000 0.092
#> GSM99546 6 0.3027 0.73615 0.000 0.000 0.000 0.148 0.028 0.824
#> GSM99548 2 0.0000 0.99745 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99550 5 0.0000 0.80513 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM99552 6 0.0000 0.86982 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM99554 4 0.0146 0.88529 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM99556 2 0.0000 0.99745 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99558 6 0.0000 0.86982 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM99560 4 0.0146 0.88505 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM99562 3 0.0000 0.91236 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99564 4 0.0146 0.88529 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM99572 2 0.0000 0.99745 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99576 5 0.3979 -0.00107 0.000 0.000 0.000 0.004 0.540 0.456
#> GSM99578 6 0.1863 0.80889 0.000 0.000 0.000 0.104 0.000 0.896
#> GSM99580 3 0.2260 0.79434 0.000 0.000 0.860 0.000 0.000 0.140
#> GSM99582 6 0.3909 0.68881 0.000 0.000 0.076 0.004 0.148 0.772
#> GSM99584 4 0.0547 0.88174 0.000 0.000 0.000 0.980 0.000 0.020
#> GSM99586 5 0.0547 0.79913 0.020 0.000 0.000 0.000 0.980 0.000
#> GSM99588 6 0.0000 0.86982 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM99590 2 0.0146 0.99372 0.000 0.996 0.000 0.004 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) cell.type(p) k
#> SD:pam 71 2.91e-03 0.013771 2
#> SD:pam 81 6.50e-05 0.001684 3
#> SD:pam 82 1.66e-06 0.000192 4
#> SD:pam 64 1.93e-04 0.014743 5
#> SD:pam 77 4.88e-06 0.002708 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 21168 rows and 85 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.289 0.682 0.805 0.4435 0.525 0.525
#> 3 3 0.825 0.929 0.965 0.5088 0.728 0.516
#> 4 4 0.832 0.796 0.900 0.0940 0.911 0.743
#> 5 5 0.873 0.821 0.922 0.0834 0.893 0.637
#> 6 6 0.825 0.675 0.862 0.0220 0.963 0.835
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
#> GSM99496 2 0.7453 0.555 0.212 0.788
#> GSM99502 1 0.0000 0.886 1.000 0.000
#> GSM99504 1 0.1184 0.874 0.984 0.016
#> GSM99506 2 0.7453 0.555 0.212 0.788
#> GSM99566 2 0.7453 0.555 0.212 0.788
#> GSM99574 1 0.0000 0.886 1.000 0.000
#> GSM99592 2 0.7453 0.555 0.212 0.788
#> GSM99594 2 0.7453 0.555 0.212 0.788
#> GSM99468 1 0.0000 0.886 1.000 0.000
#> GSM99498 1 0.0000 0.886 1.000 0.000
#> GSM99500 1 0.0000 0.886 1.000 0.000
#> GSM99508 2 0.7453 0.555 0.212 0.788
#> GSM99568 2 0.7528 0.556 0.216 0.784
#> GSM99596 2 0.7453 0.555 0.212 0.788
#> GSM99600 2 0.8861 0.705 0.304 0.696
#> GSM99458 1 0.2236 0.872 0.964 0.036
#> GSM99460 1 0.2236 0.872 0.964 0.036
#> GSM99510 2 0.3879 0.627 0.076 0.924
#> GSM99512 2 0.6531 0.580 0.168 0.832
#> GSM99514 2 0.7453 0.555 0.212 0.788
#> GSM99516 1 0.0000 0.886 1.000 0.000
#> GSM99518 1 0.0000 0.886 1.000 0.000
#> GSM99520 2 0.7453 0.555 0.212 0.788
#> GSM99522 2 0.7602 0.546 0.220 0.780
#> GSM99570 1 0.1633 0.871 0.976 0.024
#> GSM99598 1 0.0000 0.886 1.000 0.000
#> GSM99432 2 0.8661 0.704 0.288 0.712
#> GSM99434 2 0.4815 0.622 0.104 0.896
#> GSM99436 2 0.8861 0.705 0.304 0.696
#> GSM99438 2 0.8861 0.705 0.304 0.696
#> GSM99440 1 0.0000 0.886 1.000 0.000
#> GSM99442 2 0.8861 0.705 0.304 0.696
#> GSM99444 2 0.8861 0.705 0.304 0.696
#> GSM99446 2 0.8861 0.705 0.304 0.696
#> GSM99448 2 0.4939 0.605 0.108 0.892
#> GSM99450 2 0.6712 0.594 0.176 0.824
#> GSM99452 1 0.1843 0.867 0.972 0.028
#> GSM99454 1 0.0000 0.886 1.000 0.000
#> GSM99456 1 0.2236 0.872 0.964 0.036
#> GSM99462 2 0.8861 0.705 0.304 0.696
#> GSM99464 1 0.7745 0.615 0.772 0.228
#> GSM99466 2 0.8661 0.704 0.288 0.712
#> GSM99470 1 0.9044 0.232 0.680 0.320
#> GSM99472 1 0.3879 0.824 0.924 0.076
#> GSM99474 2 0.7745 0.557 0.228 0.772
#> GSM99476 2 0.4298 0.634 0.088 0.912
#> GSM99478 2 0.8763 0.705 0.296 0.704
#> GSM99480 1 0.0000 0.886 1.000 0.000
#> GSM99482 1 0.1843 0.867 0.972 0.028
#> GSM99484 2 0.8861 0.705 0.304 0.696
#> GSM99486 2 0.8861 0.705 0.304 0.696
#> GSM99488 2 0.8861 0.705 0.304 0.696
#> GSM99490 2 0.8861 0.705 0.304 0.696
#> GSM99492 1 0.0000 0.886 1.000 0.000
#> GSM99494 2 0.8861 0.705 0.304 0.696
#> GSM99524 1 0.0376 0.885 0.996 0.004
#> GSM99526 1 0.9087 0.376 0.676 0.324
#> GSM99528 2 0.8861 0.705 0.304 0.696
#> GSM99530 1 0.5842 0.734 0.860 0.140
#> GSM99532 1 0.9977 -0.377 0.528 0.472
#> GSM99534 2 0.9686 0.554 0.396 0.604
#> GSM99536 1 0.0000 0.886 1.000 0.000
#> GSM99538 2 0.8661 0.704 0.288 0.712
#> GSM99540 1 0.0938 0.878 0.988 0.012
#> GSM99542 2 0.9661 0.561 0.392 0.608
#> GSM99544 2 0.6531 0.678 0.168 0.832
#> GSM99546 2 0.9129 0.673 0.328 0.672
#> GSM99548 2 0.8861 0.705 0.304 0.696
#> GSM99550 1 0.5629 0.755 0.868 0.132
#> GSM99552 2 0.9988 0.485 0.480 0.520
#> GSM99554 2 0.8861 0.705 0.304 0.696
#> GSM99556 2 0.8861 0.705 0.304 0.696
#> GSM99558 2 0.3879 0.613 0.076 0.924
#> GSM99560 2 0.8861 0.705 0.304 0.696
#> GSM99562 2 0.7453 0.555 0.212 0.788
#> GSM99564 2 0.8661 0.704 0.288 0.712
#> GSM99572 2 0.8861 0.705 0.304 0.696
#> GSM99576 1 0.0938 0.880 0.988 0.012
#> GSM99578 2 0.8861 0.705 0.304 0.696
#> GSM99580 2 0.7453 0.555 0.212 0.788
#> GSM99582 1 0.9933 -0.365 0.548 0.452
#> GSM99584 2 0.8713 0.702 0.292 0.708
#> GSM99586 1 0.0672 0.881 0.992 0.008
#> GSM99588 2 0.8861 0.705 0.304 0.696
#> GSM99590 2 0.8861 0.705 0.304 0.696
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM99496 3 0.0000 0.9408 0.000 0.000 1.000
#> GSM99502 1 0.0000 0.9822 1.000 0.000 0.000
#> GSM99504 1 0.0000 0.9822 1.000 0.000 0.000
#> GSM99506 3 0.0000 0.9408 0.000 0.000 1.000
#> GSM99566 3 0.0000 0.9408 0.000 0.000 1.000
#> GSM99574 1 0.0000 0.9822 1.000 0.000 0.000
#> GSM99592 3 0.0000 0.9408 0.000 0.000 1.000
#> GSM99594 3 0.0000 0.9408 0.000 0.000 1.000
#> GSM99468 1 0.0000 0.9822 1.000 0.000 0.000
#> GSM99498 1 0.0000 0.9822 1.000 0.000 0.000
#> GSM99500 1 0.0000 0.9822 1.000 0.000 0.000
#> GSM99508 3 0.0000 0.9408 0.000 0.000 1.000
#> GSM99568 3 0.0000 0.9408 0.000 0.000 1.000
#> GSM99596 3 0.0000 0.9408 0.000 0.000 1.000
#> GSM99600 2 0.0000 0.9710 0.000 1.000 0.000
#> GSM99458 1 0.0237 0.9799 0.996 0.000 0.004
#> GSM99460 1 0.0237 0.9799 0.996 0.000 0.004
#> GSM99510 3 0.0000 0.9408 0.000 0.000 1.000
#> GSM99512 3 0.0000 0.9408 0.000 0.000 1.000
#> GSM99514 3 0.0000 0.9408 0.000 0.000 1.000
#> GSM99516 1 0.0000 0.9822 1.000 0.000 0.000
#> GSM99518 1 0.0000 0.9822 1.000 0.000 0.000
#> GSM99520 3 0.0000 0.9408 0.000 0.000 1.000
#> GSM99522 3 0.0000 0.9408 0.000 0.000 1.000
#> GSM99570 1 0.0000 0.9822 1.000 0.000 0.000
#> GSM99598 1 0.0000 0.9822 1.000 0.000 0.000
#> GSM99432 2 0.0237 0.9692 0.000 0.996 0.004
#> GSM99434 3 0.0000 0.9408 0.000 0.000 1.000
#> GSM99436 2 0.0000 0.9710 0.000 1.000 0.000
#> GSM99438 2 0.0000 0.9710 0.000 1.000 0.000
#> GSM99440 1 0.0000 0.9822 1.000 0.000 0.000
#> GSM99442 2 0.0000 0.9710 0.000 1.000 0.000
#> GSM99444 2 0.0000 0.9710 0.000 1.000 0.000
#> GSM99446 2 0.0000 0.9710 0.000 1.000 0.000
#> GSM99448 3 0.3038 0.8899 0.000 0.104 0.896
#> GSM99450 3 0.0000 0.9408 0.000 0.000 1.000
#> GSM99452 1 0.0000 0.9822 1.000 0.000 0.000
#> GSM99454 1 0.0000 0.9822 1.000 0.000 0.000
#> GSM99456 1 0.0237 0.9799 0.996 0.000 0.004
#> GSM99462 2 0.0000 0.9710 0.000 1.000 0.000
#> GSM99464 3 0.3038 0.8827 0.104 0.000 0.896
#> GSM99466 3 0.3267 0.8799 0.000 0.116 0.884
#> GSM99470 1 0.3349 0.8876 0.888 0.108 0.004
#> GSM99472 1 0.3349 0.8876 0.888 0.108 0.004
#> GSM99474 3 0.0000 0.9408 0.000 0.000 1.000
#> GSM99476 3 0.1031 0.9326 0.000 0.024 0.976
#> GSM99478 2 0.2878 0.8740 0.000 0.904 0.096
#> GSM99480 1 0.0000 0.9822 1.000 0.000 0.000
#> GSM99482 1 0.0000 0.9822 1.000 0.000 0.000
#> GSM99484 2 0.0237 0.9692 0.000 0.996 0.004
#> GSM99486 2 0.0237 0.9692 0.000 0.996 0.004
#> GSM99488 2 0.0000 0.9710 0.000 1.000 0.000
#> GSM99490 2 0.0000 0.9710 0.000 1.000 0.000
#> GSM99492 1 0.0000 0.9822 1.000 0.000 0.000
#> GSM99494 2 0.0000 0.9710 0.000 1.000 0.000
#> GSM99524 1 0.0000 0.9822 1.000 0.000 0.000
#> GSM99526 3 0.3590 0.8961 0.076 0.028 0.896
#> GSM99528 3 0.6095 0.4150 0.000 0.392 0.608
#> GSM99530 3 0.3038 0.8827 0.104 0.000 0.896
#> GSM99532 3 0.0892 0.9332 0.020 0.000 0.980
#> GSM99534 2 0.0237 0.9692 0.000 0.996 0.004
#> GSM99536 1 0.0000 0.9822 1.000 0.000 0.000
#> GSM99538 3 0.3116 0.8867 0.000 0.108 0.892
#> GSM99540 1 0.0237 0.9799 0.996 0.000 0.004
#> GSM99542 2 0.0237 0.9692 0.000 0.996 0.004
#> GSM99544 2 0.6274 0.0626 0.000 0.544 0.456
#> GSM99546 3 0.3038 0.8899 0.000 0.104 0.896
#> GSM99548 2 0.0000 0.9710 0.000 1.000 0.000
#> GSM99550 1 0.4095 0.8915 0.880 0.064 0.056
#> GSM99552 3 0.3038 0.8899 0.000 0.104 0.896
#> GSM99554 2 0.0000 0.9710 0.000 1.000 0.000
#> GSM99556 2 0.0000 0.9710 0.000 1.000 0.000
#> GSM99558 3 0.3038 0.8899 0.000 0.104 0.896
#> GSM99560 2 0.2711 0.8845 0.000 0.912 0.088
#> GSM99562 3 0.0000 0.9408 0.000 0.000 1.000
#> GSM99564 2 0.0237 0.9692 0.000 0.996 0.004
#> GSM99572 2 0.0000 0.9710 0.000 1.000 0.000
#> GSM99576 1 0.3349 0.8876 0.888 0.108 0.004
#> GSM99578 2 0.0000 0.9710 0.000 1.000 0.000
#> GSM99580 3 0.0000 0.9408 0.000 0.000 1.000
#> GSM99582 3 0.3038 0.8827 0.104 0.000 0.896
#> GSM99584 3 0.5706 0.5813 0.000 0.320 0.680
#> GSM99586 1 0.0000 0.9822 1.000 0.000 0.000
#> GSM99588 2 0.0000 0.9710 0.000 1.000 0.000
#> GSM99590 2 0.0000 0.9710 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM99496 3 0.0000 0.842 0.000 0.000 1.000 0.000
#> GSM99502 1 0.0000 0.955 1.000 0.000 0.000 0.000
#> GSM99504 1 0.0000 0.955 1.000 0.000 0.000 0.000
#> GSM99506 3 0.0000 0.842 0.000 0.000 1.000 0.000
#> GSM99566 3 0.0000 0.842 0.000 0.000 1.000 0.000
#> GSM99574 1 0.0000 0.955 1.000 0.000 0.000 0.000
#> GSM99592 3 0.1389 0.847 0.000 0.000 0.952 0.048
#> GSM99594 3 0.0000 0.842 0.000 0.000 1.000 0.000
#> GSM99468 1 0.0000 0.955 1.000 0.000 0.000 0.000
#> GSM99498 1 0.0000 0.955 1.000 0.000 0.000 0.000
#> GSM99500 1 0.0000 0.955 1.000 0.000 0.000 0.000
#> GSM99508 3 0.0000 0.842 0.000 0.000 1.000 0.000
#> GSM99568 3 0.1474 0.847 0.000 0.000 0.948 0.052
#> GSM99596 3 0.0000 0.842 0.000 0.000 1.000 0.000
#> GSM99600 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM99458 1 0.1557 0.898 0.944 0.000 0.000 0.056
#> GSM99460 4 0.4431 0.585 0.304 0.000 0.000 0.696
#> GSM99510 3 0.4522 0.684 0.000 0.000 0.680 0.320
#> GSM99512 3 0.1867 0.843 0.000 0.000 0.928 0.072
#> GSM99514 3 0.0000 0.842 0.000 0.000 1.000 0.000
#> GSM99516 1 0.0000 0.955 1.000 0.000 0.000 0.000
#> GSM99518 1 0.0000 0.955 1.000 0.000 0.000 0.000
#> GSM99520 3 0.0000 0.842 0.000 0.000 1.000 0.000
#> GSM99522 3 0.0336 0.843 0.000 0.000 0.992 0.008
#> GSM99570 1 0.0000 0.955 1.000 0.000 0.000 0.000
#> GSM99598 1 0.0000 0.955 1.000 0.000 0.000 0.000
#> GSM99432 2 0.4543 0.647 0.000 0.676 0.000 0.324
#> GSM99434 3 0.4543 0.680 0.000 0.000 0.676 0.324
#> GSM99436 2 0.0336 0.900 0.000 0.992 0.000 0.008
#> GSM99438 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM99440 1 0.0000 0.955 1.000 0.000 0.000 0.000
#> GSM99442 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM99444 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM99446 2 0.0336 0.900 0.000 0.992 0.000 0.008
#> GSM99448 3 0.3837 0.768 0.000 0.000 0.776 0.224
#> GSM99450 3 0.4072 0.746 0.000 0.000 0.748 0.252
#> GSM99452 1 0.0000 0.955 1.000 0.000 0.000 0.000
#> GSM99454 1 0.0000 0.955 1.000 0.000 0.000 0.000
#> GSM99456 4 0.4500 0.571 0.316 0.000 0.000 0.684
#> GSM99462 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM99464 4 0.0000 0.649 0.000 0.000 0.000 1.000
#> GSM99466 3 0.6779 0.521 0.000 0.116 0.560 0.324
#> GSM99470 1 0.0336 0.946 0.992 0.000 0.000 0.008
#> GSM99472 1 0.0336 0.946 0.992 0.000 0.000 0.008
#> GSM99474 3 0.1557 0.846 0.000 0.000 0.944 0.056
#> GSM99476 3 0.4543 0.680 0.000 0.000 0.676 0.324
#> GSM99478 2 0.4543 0.647 0.000 0.676 0.000 0.324
#> GSM99480 1 0.0188 0.952 0.996 0.000 0.000 0.004
#> GSM99482 1 0.0000 0.955 1.000 0.000 0.000 0.000
#> GSM99484 2 0.1022 0.888 0.000 0.968 0.000 0.032
#> GSM99486 2 0.2530 0.839 0.000 0.888 0.000 0.112
#> GSM99488 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM99490 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM99492 1 0.3649 0.677 0.796 0.000 0.000 0.204
#> GSM99494 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM99524 1 0.0000 0.955 1.000 0.000 0.000 0.000
#> GSM99526 4 0.4843 -0.223 0.000 0.000 0.396 0.604
#> GSM99528 2 0.5289 0.601 0.000 0.636 0.020 0.344
#> GSM99530 4 0.0817 0.647 0.000 0.000 0.024 0.976
#> GSM99532 3 0.1637 0.846 0.000 0.000 0.940 0.060
#> GSM99534 2 0.0336 0.900 0.000 0.992 0.000 0.008
#> GSM99536 1 0.0000 0.955 1.000 0.000 0.000 0.000
#> GSM99538 3 0.7861 0.218 0.000 0.284 0.392 0.324
#> GSM99540 1 0.4994 -0.144 0.520 0.000 0.000 0.480
#> GSM99542 2 0.0336 0.900 0.000 0.992 0.000 0.008
#> GSM99544 2 0.5936 0.574 0.000 0.620 0.056 0.324
#> GSM99546 3 0.4817 0.603 0.000 0.000 0.612 0.388
#> GSM99548 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM99550 4 0.0000 0.649 0.000 0.000 0.000 1.000
#> GSM99552 3 0.1557 0.846 0.000 0.000 0.944 0.056
#> GSM99554 2 0.0188 0.900 0.000 0.996 0.000 0.004
#> GSM99556 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM99558 3 0.3873 0.766 0.000 0.000 0.772 0.228
#> GSM99560 2 0.4543 0.647 0.000 0.676 0.000 0.324
#> GSM99562 3 0.0000 0.842 0.000 0.000 1.000 0.000
#> GSM99564 2 0.2868 0.821 0.000 0.864 0.000 0.136
#> GSM99572 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM99576 4 0.4543 0.562 0.324 0.000 0.000 0.676
#> GSM99578 2 0.0336 0.900 0.000 0.992 0.000 0.008
#> GSM99580 3 0.0592 0.845 0.000 0.000 0.984 0.016
#> GSM99582 3 0.3266 0.801 0.000 0.000 0.832 0.168
#> GSM99584 2 0.6316 0.534 0.000 0.596 0.080 0.324
#> GSM99586 4 0.4624 0.533 0.340 0.000 0.000 0.660
#> GSM99588 2 0.0336 0.900 0.000 0.992 0.000 0.008
#> GSM99590 2 0.0000 0.900 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM99496 3 0.0000 0.9221 0.000 0.000 1.000 0.000 0.000
#> GSM99502 1 0.0000 0.9548 1.000 0.000 0.000 0.000 0.000
#> GSM99504 1 0.0000 0.9548 1.000 0.000 0.000 0.000 0.000
#> GSM99506 3 0.0000 0.9221 0.000 0.000 1.000 0.000 0.000
#> GSM99566 3 0.0000 0.9221 0.000 0.000 1.000 0.000 0.000
#> GSM99574 1 0.0000 0.9548 1.000 0.000 0.000 0.000 0.000
#> GSM99592 3 0.0000 0.9221 0.000 0.000 1.000 0.000 0.000
#> GSM99594 3 0.0000 0.9221 0.000 0.000 1.000 0.000 0.000
#> GSM99468 1 0.0000 0.9548 1.000 0.000 0.000 0.000 0.000
#> GSM99498 1 0.0000 0.9548 1.000 0.000 0.000 0.000 0.000
#> GSM99500 1 0.0000 0.9548 1.000 0.000 0.000 0.000 0.000
#> GSM99508 3 0.0000 0.9221 0.000 0.000 1.000 0.000 0.000
#> GSM99568 3 0.0000 0.9221 0.000 0.000 1.000 0.000 0.000
#> GSM99596 3 0.0000 0.9221 0.000 0.000 1.000 0.000 0.000
#> GSM99600 2 0.3707 0.6544 0.000 0.716 0.000 0.284 0.000
#> GSM99458 1 0.4192 0.3400 0.596 0.000 0.000 0.000 0.404
#> GSM99460 5 0.0162 0.8473 0.004 0.000 0.000 0.000 0.996
#> GSM99510 3 0.3837 0.6053 0.000 0.000 0.692 0.308 0.000
#> GSM99512 3 0.1544 0.8800 0.000 0.000 0.932 0.068 0.000
#> GSM99514 3 0.0000 0.9221 0.000 0.000 1.000 0.000 0.000
#> GSM99516 1 0.0000 0.9548 1.000 0.000 0.000 0.000 0.000
#> GSM99518 1 0.0000 0.9548 1.000 0.000 0.000 0.000 0.000
#> GSM99520 3 0.0000 0.9221 0.000 0.000 1.000 0.000 0.000
#> GSM99522 3 0.0000 0.9221 0.000 0.000 1.000 0.000 0.000
#> GSM99570 1 0.0000 0.9548 1.000 0.000 0.000 0.000 0.000
#> GSM99598 1 0.0000 0.9548 1.000 0.000 0.000 0.000 0.000
#> GSM99432 4 0.0290 0.8641 0.000 0.008 0.000 0.992 0.000
#> GSM99434 3 0.3561 0.6798 0.000 0.000 0.740 0.260 0.000
#> GSM99436 4 0.4088 0.3231 0.000 0.368 0.000 0.632 0.000
#> GSM99438 2 0.0000 0.8889 0.000 1.000 0.000 0.000 0.000
#> GSM99440 1 0.0000 0.9548 1.000 0.000 0.000 0.000 0.000
#> GSM99442 2 0.0000 0.8889 0.000 1.000 0.000 0.000 0.000
#> GSM99444 2 0.0000 0.8889 0.000 1.000 0.000 0.000 0.000
#> GSM99446 4 0.3561 0.5797 0.000 0.260 0.000 0.740 0.000
#> GSM99448 3 0.4297 0.2111 0.000 0.000 0.528 0.472 0.000
#> GSM99450 3 0.2773 0.7923 0.000 0.000 0.836 0.000 0.164
#> GSM99452 1 0.0000 0.9548 1.000 0.000 0.000 0.000 0.000
#> GSM99454 1 0.0000 0.9548 1.000 0.000 0.000 0.000 0.000
#> GSM99456 5 0.0162 0.8464 0.000 0.000 0.000 0.004 0.996
#> GSM99462 2 0.0000 0.8889 0.000 1.000 0.000 0.000 0.000
#> GSM99464 5 0.0162 0.8467 0.000 0.000 0.000 0.004 0.996
#> GSM99466 4 0.0290 0.8605 0.000 0.000 0.008 0.992 0.000
#> GSM99470 1 0.1768 0.8965 0.924 0.000 0.000 0.004 0.072
#> GSM99472 1 0.1671 0.8953 0.924 0.000 0.000 0.000 0.076
#> GSM99474 3 0.0000 0.9221 0.000 0.000 1.000 0.000 0.000
#> GSM99476 4 0.4242 0.0523 0.000 0.000 0.428 0.572 0.000
#> GSM99478 4 0.0290 0.8641 0.000 0.008 0.000 0.992 0.000
#> GSM99480 1 0.1282 0.9190 0.952 0.000 0.000 0.004 0.044
#> GSM99482 1 0.0000 0.9548 1.000 0.000 0.000 0.000 0.000
#> GSM99484 4 0.3730 0.5294 0.000 0.288 0.000 0.712 0.000
#> GSM99486 4 0.0880 0.8527 0.000 0.032 0.000 0.968 0.000
#> GSM99488 2 0.0000 0.8889 0.000 1.000 0.000 0.000 0.000
#> GSM99490 2 0.0880 0.8749 0.000 0.968 0.000 0.032 0.000
#> GSM99492 1 0.3461 0.6820 0.772 0.000 0.000 0.004 0.224
#> GSM99494 2 0.0000 0.8889 0.000 1.000 0.000 0.000 0.000
#> GSM99524 1 0.0000 0.9548 1.000 0.000 0.000 0.000 0.000
#> GSM99526 5 0.6396 0.0530 0.000 0.000 0.168 0.412 0.420
#> GSM99528 4 0.0162 0.8608 0.000 0.000 0.000 0.996 0.004
#> GSM99530 5 0.2423 0.8071 0.000 0.000 0.080 0.024 0.896
#> GSM99532 3 0.0955 0.9062 0.000 0.000 0.968 0.004 0.028
#> GSM99534 2 0.3928 0.6348 0.000 0.700 0.000 0.296 0.004
#> GSM99536 1 0.0290 0.9496 0.992 0.000 0.000 0.000 0.008
#> GSM99538 4 0.0290 0.8605 0.000 0.000 0.008 0.992 0.000
#> GSM99540 5 0.3305 0.6970 0.224 0.000 0.000 0.000 0.776
#> GSM99542 2 0.0000 0.8889 0.000 1.000 0.000 0.000 0.000
#> GSM99544 4 0.0290 0.8641 0.000 0.008 0.000 0.992 0.000
#> GSM99546 4 0.2462 0.7781 0.000 0.000 0.008 0.880 0.112
#> GSM99548 2 0.0000 0.8889 0.000 1.000 0.000 0.000 0.000
#> GSM99550 5 0.0162 0.8467 0.000 0.000 0.000 0.004 0.996
#> GSM99552 3 0.1908 0.8388 0.000 0.000 0.908 0.092 0.000
#> GSM99554 2 0.3949 0.5770 0.000 0.668 0.000 0.332 0.000
#> GSM99556 2 0.0000 0.8889 0.000 1.000 0.000 0.000 0.000
#> GSM99558 4 0.0880 0.8469 0.000 0.000 0.032 0.968 0.000
#> GSM99560 4 0.0162 0.8608 0.000 0.000 0.000 0.996 0.004
#> GSM99562 3 0.0000 0.9221 0.000 0.000 1.000 0.000 0.000
#> GSM99564 4 0.0290 0.8641 0.000 0.008 0.000 0.992 0.000
#> GSM99572 2 0.0000 0.8889 0.000 1.000 0.000 0.000 0.000
#> GSM99576 5 0.2179 0.8201 0.100 0.000 0.000 0.004 0.896
#> GSM99578 2 0.3242 0.7321 0.000 0.784 0.000 0.216 0.000
#> GSM99580 3 0.0000 0.9221 0.000 0.000 1.000 0.000 0.000
#> GSM99582 3 0.1410 0.8865 0.000 0.000 0.940 0.000 0.060
#> GSM99584 4 0.0290 0.8641 0.000 0.008 0.000 0.992 0.000
#> GSM99586 5 0.2970 0.7634 0.168 0.000 0.000 0.004 0.828
#> GSM99588 2 0.3966 0.5689 0.000 0.664 0.000 0.336 0.000
#> GSM99590 2 0.0000 0.8889 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM99496 3 0.0865 0.875 0.000 0.000 0.964 0.000 0.000 0.036
#> GSM99502 1 0.0000 0.869 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99504 1 0.0000 0.869 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99506 3 0.0713 0.878 0.000 0.000 0.972 0.000 0.000 0.028
#> GSM99566 3 0.0547 0.879 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM99574 1 0.0000 0.869 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99592 3 0.0146 0.878 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM99594 3 0.0363 0.879 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM99468 1 0.0000 0.869 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99498 1 0.0000 0.869 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99500 1 0.0000 0.869 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99508 3 0.0547 0.879 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM99568 3 0.0146 0.878 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM99596 3 0.0547 0.879 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM99600 2 0.4184 -0.105 0.000 0.504 0.000 0.484 0.000 0.012
#> GSM99458 1 0.3789 0.316 0.584 0.000 0.000 0.000 0.416 0.000
#> GSM99460 5 0.1082 0.334 0.004 0.000 0.000 0.000 0.956 0.040
#> GSM99510 3 0.3982 0.669 0.000 0.000 0.740 0.200 0.000 0.060
#> GSM99512 3 0.1682 0.849 0.000 0.000 0.928 0.052 0.000 0.020
#> GSM99514 3 0.0865 0.875 0.000 0.000 0.964 0.000 0.000 0.036
#> GSM99516 1 0.0000 0.869 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99518 1 0.1501 0.823 0.924 0.000 0.000 0.000 0.076 0.000
#> GSM99520 3 0.0146 0.879 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM99522 3 0.0865 0.877 0.000 0.000 0.964 0.000 0.000 0.036
#> GSM99570 1 0.0937 0.857 0.960 0.000 0.000 0.000 0.000 0.040
#> GSM99598 1 0.0000 0.869 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99432 4 0.0000 0.832 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM99434 3 0.4907 0.543 0.000 0.000 0.644 0.096 0.004 0.256
#> GSM99436 4 0.3261 0.682 0.000 0.204 0.000 0.780 0.000 0.016
#> GSM99438 2 0.0000 0.891 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99440 1 0.0000 0.869 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99442 2 0.0260 0.887 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM99444 2 0.0000 0.891 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99446 4 0.2572 0.754 0.000 0.136 0.000 0.852 0.000 0.012
#> GSM99448 3 0.4079 0.561 0.000 0.000 0.680 0.288 0.000 0.032
#> GSM99450 3 0.4354 0.632 0.000 0.000 0.720 0.004 0.080 0.196
#> GSM99452 1 0.0790 0.860 0.968 0.000 0.000 0.000 0.000 0.032
#> GSM99454 1 0.0000 0.869 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99456 5 0.3198 0.383 0.000 0.000 0.000 0.000 0.740 0.260
#> GSM99462 2 0.0000 0.891 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99464 5 0.3862 -0.621 0.000 0.000 0.000 0.000 0.524 0.476
#> GSM99466 4 0.0146 0.831 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM99470 1 0.4392 0.640 0.720 0.000 0.000 0.000 0.136 0.144
#> GSM99472 1 0.4343 0.641 0.724 0.000 0.000 0.000 0.156 0.120
#> GSM99474 3 0.0458 0.877 0.000 0.000 0.984 0.000 0.000 0.016
#> GSM99476 3 0.5864 0.161 0.000 0.000 0.468 0.352 0.004 0.176
#> GSM99478 4 0.0146 0.831 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM99480 1 0.5539 0.312 0.552 0.000 0.000 0.000 0.188 0.260
#> GSM99482 1 0.1501 0.837 0.924 0.000 0.000 0.000 0.000 0.076
#> GSM99484 4 0.1829 0.804 0.000 0.056 0.000 0.920 0.000 0.024
#> GSM99486 4 0.0508 0.830 0.000 0.004 0.000 0.984 0.000 0.012
#> GSM99488 2 0.0000 0.891 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99490 2 0.2214 0.804 0.000 0.888 0.000 0.096 0.000 0.016
#> GSM99492 1 0.5847 0.154 0.488 0.000 0.000 0.000 0.252 0.260
#> GSM99494 2 0.0000 0.891 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99524 1 0.0790 0.860 0.968 0.000 0.000 0.000 0.000 0.032
#> GSM99526 6 0.5886 0.000 0.000 0.000 0.068 0.052 0.396 0.484
#> GSM99528 4 0.0717 0.824 0.000 0.000 0.000 0.976 0.008 0.016
#> GSM99530 5 0.4602 -0.666 0.000 0.000 0.028 0.004 0.492 0.476
#> GSM99532 3 0.2623 0.792 0.000 0.000 0.852 0.000 0.016 0.132
#> GSM99534 4 0.6440 0.137 0.000 0.364 0.000 0.456 0.068 0.112
#> GSM99536 1 0.3283 0.711 0.804 0.000 0.000 0.000 0.160 0.036
#> GSM99538 4 0.0547 0.826 0.000 0.000 0.000 0.980 0.000 0.020
#> GSM99540 5 0.3797 0.125 0.420 0.000 0.000 0.000 0.580 0.000
#> GSM99542 2 0.1863 0.813 0.000 0.896 0.000 0.000 0.000 0.104
#> GSM99544 4 0.0146 0.831 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM99546 4 0.3715 0.622 0.000 0.000 0.000 0.764 0.048 0.188
#> GSM99548 2 0.0260 0.888 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM99550 5 0.2631 0.119 0.000 0.000 0.000 0.000 0.820 0.180
#> GSM99552 3 0.2070 0.798 0.000 0.000 0.892 0.100 0.000 0.008
#> GSM99554 4 0.4258 0.116 0.000 0.468 0.000 0.516 0.000 0.016
#> GSM99556 2 0.0000 0.891 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99558 4 0.0891 0.816 0.000 0.000 0.024 0.968 0.000 0.008
#> GSM99560 4 0.0713 0.829 0.000 0.000 0.000 0.972 0.000 0.028
#> GSM99562 3 0.0713 0.877 0.000 0.000 0.972 0.000 0.000 0.028
#> GSM99564 4 0.0260 0.831 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM99572 2 0.0146 0.890 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM99576 5 0.2448 0.391 0.052 0.000 0.000 0.000 0.884 0.064
#> GSM99578 2 0.4144 0.314 0.000 0.620 0.000 0.360 0.000 0.020
#> GSM99580 3 0.0146 0.878 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM99582 3 0.1719 0.848 0.000 0.000 0.924 0.000 0.016 0.060
#> GSM99584 4 0.0291 0.831 0.000 0.000 0.000 0.992 0.004 0.004
#> GSM99586 5 0.4516 0.383 0.072 0.000 0.000 0.000 0.668 0.260
#> GSM99588 4 0.4250 0.161 0.000 0.456 0.000 0.528 0.000 0.016
#> GSM99590 2 0.0000 0.891 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) cell.type(p) k
#> SD:mclust 80 2.30e-01 0.43286 2
#> SD:mclust 83 1.97e-03 0.03264 3
#> SD:mclust 82 2.28e-04 0.01267 4
#> SD:mclust 80 4.54e-05 0.00792 5
#> SD:mclust 67 2.89e-05 0.00420 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 21168 rows and 85 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.971 0.988 0.5012 0.500 0.500
#> 3 3 0.952 0.940 0.976 0.3437 0.725 0.501
#> 4 4 0.852 0.833 0.922 0.1049 0.887 0.673
#> 5 5 0.750 0.655 0.815 0.0552 0.943 0.789
#> 6 6 0.729 0.582 0.790 0.0400 0.904 0.632
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
#> GSM99496 1 0.0000 0.984 1.000 0.000
#> GSM99502 1 0.0000 0.984 1.000 0.000
#> GSM99504 1 0.0000 0.984 1.000 0.000
#> GSM99506 1 0.0000 0.984 1.000 0.000
#> GSM99566 1 0.0000 0.984 1.000 0.000
#> GSM99574 1 0.0000 0.984 1.000 0.000
#> GSM99592 1 0.2236 0.951 0.964 0.036
#> GSM99594 1 0.0000 0.984 1.000 0.000
#> GSM99468 1 0.0000 0.984 1.000 0.000
#> GSM99498 1 0.0000 0.984 1.000 0.000
#> GSM99500 1 0.0000 0.984 1.000 0.000
#> GSM99508 1 0.0000 0.984 1.000 0.000
#> GSM99568 1 0.0000 0.984 1.000 0.000
#> GSM99596 1 0.0000 0.984 1.000 0.000
#> GSM99600 2 0.0000 0.991 0.000 1.000
#> GSM99458 1 0.0000 0.984 1.000 0.000
#> GSM99460 1 0.0000 0.984 1.000 0.000
#> GSM99510 2 0.4562 0.898 0.096 0.904
#> GSM99512 2 0.0938 0.982 0.012 0.988
#> GSM99514 1 0.0000 0.984 1.000 0.000
#> GSM99516 1 0.0000 0.984 1.000 0.000
#> GSM99518 1 0.0000 0.984 1.000 0.000
#> GSM99520 1 0.0000 0.984 1.000 0.000
#> GSM99522 1 0.0000 0.984 1.000 0.000
#> GSM99570 1 0.0000 0.984 1.000 0.000
#> GSM99598 1 0.0000 0.984 1.000 0.000
#> GSM99432 2 0.0000 0.991 0.000 1.000
#> GSM99434 1 0.9866 0.237 0.568 0.432
#> GSM99436 2 0.0000 0.991 0.000 1.000
#> GSM99438 2 0.0000 0.991 0.000 1.000
#> GSM99440 1 0.0000 0.984 1.000 0.000
#> GSM99442 2 0.0000 0.991 0.000 1.000
#> GSM99444 2 0.0000 0.991 0.000 1.000
#> GSM99446 2 0.0000 0.991 0.000 1.000
#> GSM99448 2 0.0000 0.991 0.000 1.000
#> GSM99450 1 0.0000 0.984 1.000 0.000
#> GSM99452 1 0.0000 0.984 1.000 0.000
#> GSM99454 1 0.0000 0.984 1.000 0.000
#> GSM99456 1 0.0000 0.984 1.000 0.000
#> GSM99462 2 0.0000 0.991 0.000 1.000
#> GSM99464 1 0.0000 0.984 1.000 0.000
#> GSM99466 2 0.0000 0.991 0.000 1.000
#> GSM99470 1 0.2948 0.935 0.948 0.052
#> GSM99472 1 0.0000 0.984 1.000 0.000
#> GSM99474 1 0.0000 0.984 1.000 0.000
#> GSM99476 2 0.0000 0.991 0.000 1.000
#> GSM99478 2 0.0000 0.991 0.000 1.000
#> GSM99480 1 0.0000 0.984 1.000 0.000
#> GSM99482 1 0.0000 0.984 1.000 0.000
#> GSM99484 2 0.0000 0.991 0.000 1.000
#> GSM99486 2 0.0000 0.991 0.000 1.000
#> GSM99488 2 0.0000 0.991 0.000 1.000
#> GSM99490 2 0.0000 0.991 0.000 1.000
#> GSM99492 1 0.0000 0.984 1.000 0.000
#> GSM99494 2 0.0000 0.991 0.000 1.000
#> GSM99524 1 0.0000 0.984 1.000 0.000
#> GSM99526 2 0.4690 0.894 0.100 0.900
#> GSM99528 2 0.0672 0.985 0.008 0.992
#> GSM99530 1 0.0000 0.984 1.000 0.000
#> GSM99532 1 0.0000 0.984 1.000 0.000
#> GSM99534 2 0.0000 0.991 0.000 1.000
#> GSM99536 1 0.0000 0.984 1.000 0.000
#> GSM99538 2 0.0000 0.991 0.000 1.000
#> GSM99540 1 0.0000 0.984 1.000 0.000
#> GSM99542 2 0.0000 0.991 0.000 1.000
#> GSM99544 2 0.0000 0.991 0.000 1.000
#> GSM99546 2 0.1633 0.972 0.024 0.976
#> GSM99548 2 0.0000 0.991 0.000 1.000
#> GSM99550 1 0.0000 0.984 1.000 0.000
#> GSM99552 2 0.3879 0.921 0.076 0.924
#> GSM99554 2 0.0000 0.991 0.000 1.000
#> GSM99556 2 0.0000 0.991 0.000 1.000
#> GSM99558 2 0.0000 0.991 0.000 1.000
#> GSM99560 2 0.0000 0.991 0.000 1.000
#> GSM99562 1 0.0000 0.984 1.000 0.000
#> GSM99564 2 0.0000 0.991 0.000 1.000
#> GSM99572 2 0.0000 0.991 0.000 1.000
#> GSM99576 1 0.0000 0.984 1.000 0.000
#> GSM99578 2 0.0000 0.991 0.000 1.000
#> GSM99580 1 0.7299 0.742 0.796 0.204
#> GSM99582 1 0.0000 0.984 1.000 0.000
#> GSM99584 2 0.0000 0.991 0.000 1.000
#> GSM99586 1 0.0000 0.984 1.000 0.000
#> GSM99588 2 0.0000 0.991 0.000 1.000
#> GSM99590 2 0.0000 0.991 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM99496 3 0.0000 0.9742 0.000 0.000 1.000
#> GSM99502 1 0.0000 0.9853 1.000 0.000 0.000
#> GSM99504 1 0.5291 0.6335 0.732 0.000 0.268
#> GSM99506 3 0.0000 0.9742 0.000 0.000 1.000
#> GSM99566 3 0.0000 0.9742 0.000 0.000 1.000
#> GSM99574 1 0.0000 0.9853 1.000 0.000 0.000
#> GSM99592 3 0.0000 0.9742 0.000 0.000 1.000
#> GSM99594 3 0.0000 0.9742 0.000 0.000 1.000
#> GSM99468 1 0.0000 0.9853 1.000 0.000 0.000
#> GSM99498 1 0.0000 0.9853 1.000 0.000 0.000
#> GSM99500 1 0.0000 0.9853 1.000 0.000 0.000
#> GSM99508 3 0.0000 0.9742 0.000 0.000 1.000
#> GSM99568 3 0.0000 0.9742 0.000 0.000 1.000
#> GSM99596 3 0.0000 0.9742 0.000 0.000 1.000
#> GSM99600 2 0.0000 0.9640 0.000 1.000 0.000
#> GSM99458 1 0.0000 0.9853 1.000 0.000 0.000
#> GSM99460 1 0.0000 0.9853 1.000 0.000 0.000
#> GSM99510 3 0.0000 0.9742 0.000 0.000 1.000
#> GSM99512 3 0.0000 0.9742 0.000 0.000 1.000
#> GSM99514 3 0.0000 0.9742 0.000 0.000 1.000
#> GSM99516 1 0.0000 0.9853 1.000 0.000 0.000
#> GSM99518 1 0.0000 0.9853 1.000 0.000 0.000
#> GSM99520 3 0.0000 0.9742 0.000 0.000 1.000
#> GSM99522 3 0.0000 0.9742 0.000 0.000 1.000
#> GSM99570 1 0.0000 0.9853 1.000 0.000 0.000
#> GSM99598 1 0.0000 0.9853 1.000 0.000 0.000
#> GSM99432 2 0.0000 0.9640 0.000 1.000 0.000
#> GSM99434 3 0.0000 0.9742 0.000 0.000 1.000
#> GSM99436 2 0.0000 0.9640 0.000 1.000 0.000
#> GSM99438 2 0.0000 0.9640 0.000 1.000 0.000
#> GSM99440 1 0.0000 0.9853 1.000 0.000 0.000
#> GSM99442 2 0.0000 0.9640 0.000 1.000 0.000
#> GSM99444 2 0.0000 0.9640 0.000 1.000 0.000
#> GSM99446 2 0.0000 0.9640 0.000 1.000 0.000
#> GSM99448 3 0.0000 0.9742 0.000 0.000 1.000
#> GSM99450 3 0.0000 0.9742 0.000 0.000 1.000
#> GSM99452 1 0.0000 0.9853 1.000 0.000 0.000
#> GSM99454 1 0.0000 0.9853 1.000 0.000 0.000
#> GSM99456 1 0.0000 0.9853 1.000 0.000 0.000
#> GSM99462 2 0.0000 0.9640 0.000 1.000 0.000
#> GSM99464 3 0.0237 0.9712 0.004 0.000 0.996
#> GSM99466 2 0.6309 0.0181 0.000 0.504 0.496
#> GSM99470 1 0.2959 0.8817 0.900 0.100 0.000
#> GSM99472 1 0.0000 0.9853 1.000 0.000 0.000
#> GSM99474 3 0.0000 0.9742 0.000 0.000 1.000
#> GSM99476 3 0.0000 0.9742 0.000 0.000 1.000
#> GSM99478 2 0.0892 0.9477 0.000 0.980 0.020
#> GSM99480 1 0.0000 0.9853 1.000 0.000 0.000
#> GSM99482 1 0.0000 0.9853 1.000 0.000 0.000
#> GSM99484 2 0.0000 0.9640 0.000 1.000 0.000
#> GSM99486 2 0.0000 0.9640 0.000 1.000 0.000
#> GSM99488 2 0.0000 0.9640 0.000 1.000 0.000
#> GSM99490 2 0.0000 0.9640 0.000 1.000 0.000
#> GSM99492 1 0.0000 0.9853 1.000 0.000 0.000
#> GSM99494 2 0.0000 0.9640 0.000 1.000 0.000
#> GSM99524 1 0.0000 0.9853 1.000 0.000 0.000
#> GSM99526 3 0.0424 0.9677 0.000 0.008 0.992
#> GSM99528 2 0.0237 0.9609 0.000 0.996 0.004
#> GSM99530 3 0.0237 0.9712 0.004 0.000 0.996
#> GSM99532 3 0.0000 0.9742 0.000 0.000 1.000
#> GSM99534 2 0.0000 0.9640 0.000 1.000 0.000
#> GSM99536 1 0.0000 0.9853 1.000 0.000 0.000
#> GSM99538 3 0.3941 0.7975 0.000 0.156 0.844
#> GSM99540 1 0.0000 0.9853 1.000 0.000 0.000
#> GSM99542 2 0.0000 0.9640 0.000 1.000 0.000
#> GSM99544 3 0.6168 0.2659 0.000 0.412 0.588
#> GSM99546 2 0.4796 0.7151 0.000 0.780 0.220
#> GSM99548 2 0.0000 0.9640 0.000 1.000 0.000
#> GSM99550 1 0.0424 0.9783 0.992 0.008 0.000
#> GSM99552 3 0.0000 0.9742 0.000 0.000 1.000
#> GSM99554 2 0.0000 0.9640 0.000 1.000 0.000
#> GSM99556 2 0.0000 0.9640 0.000 1.000 0.000
#> GSM99558 3 0.0000 0.9742 0.000 0.000 1.000
#> GSM99560 2 0.0000 0.9640 0.000 1.000 0.000
#> GSM99562 3 0.0000 0.9742 0.000 0.000 1.000
#> GSM99564 2 0.0000 0.9640 0.000 1.000 0.000
#> GSM99572 2 0.0000 0.9640 0.000 1.000 0.000
#> GSM99576 1 0.0000 0.9853 1.000 0.000 0.000
#> GSM99578 2 0.0000 0.9640 0.000 1.000 0.000
#> GSM99580 3 0.0000 0.9742 0.000 0.000 1.000
#> GSM99582 3 0.2959 0.8728 0.100 0.000 0.900
#> GSM99584 2 0.4931 0.6933 0.000 0.768 0.232
#> GSM99586 1 0.0000 0.9853 1.000 0.000 0.000
#> GSM99588 2 0.0000 0.9640 0.000 1.000 0.000
#> GSM99590 2 0.0000 0.9640 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM99496 3 0.0469 0.908 0.000 0.000 0.988 0.012
#> GSM99502 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM99504 3 0.3486 0.709 0.188 0.000 0.812 0.000
#> GSM99506 3 0.0921 0.910 0.000 0.000 0.972 0.028
#> GSM99566 3 0.0336 0.902 0.000 0.000 0.992 0.008
#> GSM99574 1 0.0336 0.949 0.992 0.000 0.008 0.000
#> GSM99592 3 0.2868 0.855 0.000 0.000 0.864 0.136
#> GSM99594 3 0.1302 0.909 0.000 0.000 0.956 0.044
#> GSM99468 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM99498 1 0.2469 0.845 0.892 0.000 0.108 0.000
#> GSM99500 1 0.0921 0.933 0.972 0.000 0.028 0.000
#> GSM99508 3 0.1474 0.907 0.000 0.000 0.948 0.052
#> GSM99568 3 0.2216 0.889 0.000 0.000 0.908 0.092
#> GSM99596 3 0.1302 0.910 0.000 0.000 0.956 0.044
#> GSM99600 2 0.0817 0.944 0.000 0.976 0.000 0.024
#> GSM99458 1 0.0592 0.947 0.984 0.000 0.000 0.016
#> GSM99460 4 0.4948 0.139 0.440 0.000 0.000 0.560
#> GSM99510 4 0.4998 -0.102 0.000 0.000 0.488 0.512
#> GSM99512 3 0.3873 0.736 0.000 0.000 0.772 0.228
#> GSM99514 3 0.0469 0.900 0.000 0.000 0.988 0.012
#> GSM99516 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM99518 1 0.0188 0.952 0.996 0.000 0.000 0.004
#> GSM99520 3 0.1118 0.910 0.000 0.000 0.964 0.036
#> GSM99522 3 0.0657 0.901 0.004 0.000 0.984 0.012
#> GSM99570 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM99598 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM99432 4 0.4331 0.535 0.000 0.288 0.000 0.712
#> GSM99434 4 0.2814 0.701 0.000 0.000 0.132 0.868
#> GSM99436 2 0.1716 0.920 0.000 0.936 0.000 0.064
#> GSM99438 2 0.0000 0.951 0.000 1.000 0.000 0.000
#> GSM99440 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM99442 2 0.0469 0.948 0.000 0.988 0.000 0.012
#> GSM99444 2 0.0000 0.951 0.000 1.000 0.000 0.000
#> GSM99446 2 0.2081 0.904 0.000 0.916 0.000 0.084
#> GSM99448 3 0.1792 0.892 0.000 0.000 0.932 0.068
#> GSM99450 4 0.4624 0.381 0.000 0.000 0.340 0.660
#> GSM99452 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM99454 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM99456 1 0.3123 0.807 0.844 0.000 0.000 0.156
#> GSM99462 2 0.0000 0.951 0.000 1.000 0.000 0.000
#> GSM99464 4 0.0895 0.758 0.004 0.000 0.020 0.976
#> GSM99466 2 0.4300 0.791 0.000 0.820 0.092 0.088
#> GSM99470 1 0.4907 0.270 0.580 0.420 0.000 0.000
#> GSM99472 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM99474 3 0.2345 0.884 0.000 0.000 0.900 0.100
#> GSM99476 4 0.1637 0.750 0.000 0.000 0.060 0.940
#> GSM99478 2 0.0000 0.951 0.000 1.000 0.000 0.000
#> GSM99480 1 0.0188 0.952 0.996 0.000 0.000 0.004
#> GSM99482 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM99484 2 0.0000 0.951 0.000 1.000 0.000 0.000
#> GSM99486 2 0.2174 0.917 0.000 0.928 0.020 0.052
#> GSM99488 2 0.0000 0.951 0.000 1.000 0.000 0.000
#> GSM99490 2 0.0336 0.949 0.000 0.992 0.000 0.008
#> GSM99492 1 0.0469 0.949 0.988 0.000 0.000 0.012
#> GSM99494 2 0.0000 0.951 0.000 1.000 0.000 0.000
#> GSM99524 1 0.0188 0.951 0.996 0.000 0.004 0.000
#> GSM99526 4 0.0592 0.757 0.000 0.000 0.016 0.984
#> GSM99528 2 0.2593 0.867 0.000 0.892 0.004 0.104
#> GSM99530 4 0.2197 0.738 0.004 0.000 0.080 0.916
#> GSM99532 3 0.4994 0.147 0.000 0.000 0.520 0.480
#> GSM99534 2 0.0592 0.946 0.000 0.984 0.000 0.016
#> GSM99536 1 0.0188 0.952 0.996 0.000 0.000 0.004
#> GSM99538 4 0.1389 0.754 0.000 0.000 0.048 0.952
#> GSM99540 1 0.1792 0.910 0.932 0.000 0.000 0.068
#> GSM99542 2 0.0000 0.951 0.000 1.000 0.000 0.000
#> GSM99544 4 0.5582 0.421 0.000 0.348 0.032 0.620
#> GSM99546 4 0.1637 0.750 0.000 0.060 0.000 0.940
#> GSM99548 2 0.0592 0.946 0.000 0.984 0.000 0.016
#> GSM99550 4 0.3718 0.677 0.168 0.012 0.000 0.820
#> GSM99552 3 0.0967 0.895 0.004 0.004 0.976 0.016
#> GSM99554 2 0.0592 0.946 0.000 0.984 0.000 0.016
#> GSM99556 2 0.0000 0.951 0.000 1.000 0.000 0.000
#> GSM99558 3 0.0336 0.902 0.000 0.000 0.992 0.008
#> GSM99560 2 0.5000 0.046 0.000 0.504 0.000 0.496
#> GSM99562 3 0.1637 0.905 0.000 0.000 0.940 0.060
#> GSM99564 2 0.2469 0.881 0.000 0.892 0.000 0.108
#> GSM99572 2 0.0336 0.949 0.000 0.992 0.000 0.008
#> GSM99576 1 0.1022 0.937 0.968 0.000 0.000 0.032
#> GSM99578 2 0.0000 0.951 0.000 1.000 0.000 0.000
#> GSM99580 3 0.1022 0.910 0.000 0.000 0.968 0.032
#> GSM99582 3 0.2730 0.824 0.088 0.000 0.896 0.016
#> GSM99584 4 0.3791 0.657 0.000 0.200 0.004 0.796
#> GSM99586 1 0.1716 0.912 0.936 0.000 0.000 0.064
#> GSM99588 2 0.0000 0.951 0.000 1.000 0.000 0.000
#> GSM99590 2 0.0000 0.951 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM99496 3 0.0880 0.7943 0.000 0.000 0.968 0.000 0.032
#> GSM99502 1 0.0162 0.9284 0.996 0.000 0.000 0.000 0.004
#> GSM99504 3 0.6202 0.4463 0.220 0.000 0.552 0.000 0.228
#> GSM99506 3 0.0703 0.7936 0.000 0.000 0.976 0.000 0.024
#> GSM99566 3 0.1908 0.7890 0.000 0.000 0.908 0.000 0.092
#> GSM99574 1 0.0162 0.9284 0.996 0.000 0.000 0.000 0.004
#> GSM99592 3 0.3532 0.7706 0.000 0.000 0.824 0.048 0.128
#> GSM99594 3 0.1872 0.7822 0.000 0.000 0.928 0.020 0.052
#> GSM99468 1 0.0451 0.9272 0.988 0.000 0.000 0.004 0.008
#> GSM99498 1 0.4109 0.5805 0.700 0.000 0.288 0.000 0.012
#> GSM99500 1 0.0865 0.9176 0.972 0.000 0.024 0.000 0.004
#> GSM99508 3 0.1331 0.7958 0.000 0.000 0.952 0.008 0.040
#> GSM99568 3 0.1300 0.7908 0.000 0.000 0.956 0.028 0.016
#> GSM99596 3 0.1704 0.7794 0.000 0.000 0.928 0.004 0.068
#> GSM99600 2 0.4276 0.5450 0.000 0.716 0.000 0.028 0.256
#> GSM99458 1 0.0404 0.9266 0.988 0.000 0.000 0.012 0.000
#> GSM99460 4 0.4262 0.0706 0.440 0.000 0.000 0.560 0.000
#> GSM99510 4 0.5748 0.3576 0.000 0.000 0.252 0.608 0.140
#> GSM99512 3 0.4016 0.7497 0.000 0.000 0.796 0.112 0.092
#> GSM99514 3 0.3424 0.7198 0.000 0.000 0.760 0.000 0.240
#> GSM99516 1 0.0162 0.9284 0.996 0.000 0.000 0.000 0.004
#> GSM99518 1 0.0290 0.9275 0.992 0.000 0.000 0.008 0.000
#> GSM99520 3 0.1331 0.7973 0.000 0.000 0.952 0.008 0.040
#> GSM99522 3 0.4559 0.4543 0.000 0.000 0.512 0.008 0.480
#> GSM99570 1 0.0162 0.9284 0.996 0.000 0.000 0.000 0.004
#> GSM99598 1 0.0290 0.9276 0.992 0.000 0.000 0.000 0.008
#> GSM99432 4 0.3513 0.5583 0.000 0.020 0.000 0.800 0.180
#> GSM99434 4 0.2376 0.6044 0.000 0.000 0.044 0.904 0.052
#> GSM99436 2 0.6599 -0.2916 0.000 0.436 0.000 0.220 0.344
#> GSM99438 2 0.0510 0.8033 0.000 0.984 0.000 0.000 0.016
#> GSM99440 1 0.0162 0.9281 0.996 0.000 0.000 0.000 0.004
#> GSM99442 2 0.4130 0.5171 0.000 0.696 0.000 0.012 0.292
#> GSM99444 2 0.0794 0.8008 0.000 0.972 0.000 0.000 0.028
#> GSM99446 2 0.6642 -0.2732 0.000 0.444 0.000 0.248 0.308
#> GSM99448 3 0.5142 0.5742 0.000 0.000 0.600 0.052 0.348
#> GSM99450 4 0.4482 0.5472 0.000 0.000 0.088 0.752 0.160
#> GSM99452 1 0.0290 0.9284 0.992 0.000 0.000 0.000 0.008
#> GSM99454 1 0.0162 0.9284 0.996 0.000 0.000 0.000 0.004
#> GSM99456 1 0.3724 0.7645 0.788 0.000 0.000 0.184 0.028
#> GSM99462 2 0.0880 0.7993 0.000 0.968 0.000 0.000 0.032
#> GSM99464 4 0.1862 0.5910 0.004 0.000 0.048 0.932 0.016
#> GSM99466 5 0.7173 0.3151 0.000 0.340 0.028 0.204 0.428
#> GSM99470 1 0.3421 0.7840 0.840 0.080 0.000 0.000 0.080
#> GSM99472 1 0.0290 0.9277 0.992 0.000 0.000 0.000 0.008
#> GSM99474 3 0.1701 0.7847 0.000 0.000 0.936 0.048 0.016
#> GSM99476 4 0.3461 0.5365 0.000 0.000 0.004 0.772 0.224
#> GSM99478 2 0.3100 0.7015 0.000 0.876 0.028 0.028 0.068
#> GSM99480 1 0.0451 0.9268 0.988 0.000 0.000 0.008 0.004
#> GSM99482 1 0.0162 0.9284 0.996 0.000 0.000 0.000 0.004
#> GSM99484 2 0.3366 0.6288 0.000 0.768 0.000 0.000 0.232
#> GSM99486 5 0.5543 0.4406 0.000 0.224 0.000 0.136 0.640
#> GSM99488 2 0.0290 0.8006 0.000 0.992 0.000 0.000 0.008
#> GSM99490 2 0.0404 0.7990 0.000 0.988 0.000 0.000 0.012
#> GSM99492 1 0.1310 0.9118 0.956 0.000 0.000 0.024 0.020
#> GSM99494 2 0.0290 0.8006 0.000 0.992 0.000 0.000 0.008
#> GSM99524 1 0.0510 0.9242 0.984 0.000 0.000 0.000 0.016
#> GSM99526 4 0.0703 0.6039 0.000 0.000 0.000 0.976 0.024
#> GSM99528 3 0.7316 0.1367 0.000 0.368 0.440 0.084 0.108
#> GSM99530 3 0.6157 0.2824 0.004 0.004 0.524 0.360 0.108
#> GSM99532 3 0.5066 0.5620 0.000 0.000 0.676 0.240 0.084
#> GSM99534 2 0.3675 0.6333 0.004 0.772 0.000 0.008 0.216
#> GSM99536 1 0.0566 0.9256 0.984 0.000 0.000 0.012 0.004
#> GSM99538 4 0.4964 0.4461 0.000 0.020 0.220 0.712 0.048
#> GSM99540 1 0.4928 0.7278 0.748 0.000 0.064 0.156 0.032
#> GSM99542 2 0.0290 0.8006 0.000 0.992 0.000 0.000 0.008
#> GSM99544 4 0.4824 0.3081 0.000 0.028 0.000 0.596 0.376
#> GSM99546 4 0.3039 0.5631 0.000 0.000 0.000 0.808 0.192
#> GSM99548 2 0.0703 0.7922 0.000 0.976 0.000 0.000 0.024
#> GSM99550 4 0.4415 0.4996 0.132 0.008 0.016 0.792 0.052
#> GSM99552 3 0.3039 0.7663 0.000 0.012 0.836 0.000 0.152
#> GSM99554 2 0.4794 0.3647 0.000 0.624 0.000 0.032 0.344
#> GSM99556 2 0.0162 0.8012 0.000 0.996 0.000 0.000 0.004
#> GSM99558 3 0.2377 0.7786 0.000 0.000 0.872 0.000 0.128
#> GSM99560 4 0.6636 -0.2985 0.000 0.312 0.000 0.444 0.244
#> GSM99562 3 0.3961 0.7023 0.000 0.000 0.736 0.016 0.248
#> GSM99564 5 0.6583 0.3845 0.000 0.256 0.000 0.276 0.468
#> GSM99572 2 0.1041 0.7996 0.000 0.964 0.000 0.004 0.032
#> GSM99576 1 0.7100 0.5985 0.640 0.104 0.116 0.076 0.064
#> GSM99578 2 0.0290 0.8039 0.000 0.992 0.000 0.000 0.008
#> GSM99580 3 0.1041 0.7961 0.000 0.000 0.964 0.004 0.032
#> GSM99582 5 0.6088 -0.2283 0.156 0.000 0.296 0.000 0.548
#> GSM99584 4 0.4387 0.3699 0.000 0.012 0.000 0.640 0.348
#> GSM99586 1 0.3090 0.8364 0.856 0.000 0.000 0.104 0.040
#> GSM99588 2 0.0404 0.8015 0.000 0.988 0.000 0.000 0.012
#> GSM99590 2 0.0510 0.8034 0.000 0.984 0.000 0.000 0.016
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM99496 3 0.2402 0.5174 0.000 0.000 0.856 0.000 0.140 0.004
#> GSM99502 1 0.0547 0.9121 0.980 0.000 0.000 0.000 0.020 0.000
#> GSM99504 3 0.5304 -0.0364 0.200 0.000 0.600 0.000 0.200 0.000
#> GSM99506 3 0.0891 0.5113 0.000 0.000 0.968 0.000 0.024 0.008
#> GSM99566 3 0.3440 0.2026 0.000 0.000 0.776 0.000 0.196 0.028
#> GSM99574 1 0.0937 0.9102 0.960 0.000 0.000 0.000 0.040 0.000
#> GSM99592 3 0.4341 0.1268 0.000 0.000 0.736 0.004 0.136 0.124
#> GSM99594 3 0.3207 0.4917 0.000 0.000 0.828 0.004 0.124 0.044
#> GSM99468 1 0.0858 0.9076 0.968 0.000 0.000 0.000 0.028 0.004
#> GSM99498 1 0.4858 0.3703 0.588 0.000 0.348 0.000 0.060 0.004
#> GSM99500 1 0.3078 0.8352 0.852 0.000 0.080 0.004 0.060 0.004
#> GSM99508 3 0.1826 0.4628 0.000 0.000 0.924 0.004 0.052 0.020
#> GSM99568 3 0.1719 0.5181 0.000 0.000 0.924 0.000 0.060 0.016
#> GSM99596 3 0.4305 0.4214 0.000 0.000 0.656 0.020 0.312 0.012
#> GSM99600 4 0.3144 0.6951 0.000 0.172 0.000 0.808 0.016 0.004
#> GSM99458 1 0.0508 0.9126 0.984 0.000 0.000 0.000 0.012 0.004
#> GSM99460 6 0.3925 0.3456 0.332 0.000 0.000 0.004 0.008 0.656
#> GSM99510 6 0.5719 -0.1120 0.000 0.000 0.300 0.004 0.172 0.524
#> GSM99512 6 0.6138 -0.4581 0.000 0.004 0.396 0.004 0.200 0.396
#> GSM99514 3 0.3053 0.4047 0.000 0.000 0.812 0.012 0.172 0.004
#> GSM99516 1 0.0858 0.9099 0.968 0.000 0.000 0.000 0.028 0.004
#> GSM99518 1 0.0291 0.9132 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM99520 3 0.2742 0.5191 0.000 0.000 0.852 0.008 0.128 0.012
#> GSM99522 5 0.5525 0.0000 0.004 0.000 0.404 0.012 0.500 0.080
#> GSM99570 1 0.0865 0.9099 0.964 0.000 0.000 0.000 0.036 0.000
#> GSM99598 1 0.0547 0.9116 0.980 0.000 0.000 0.000 0.020 0.000
#> GSM99432 4 0.3995 0.2778 0.000 0.004 0.000 0.516 0.000 0.480
#> GSM99434 6 0.2560 0.5416 0.000 0.000 0.088 0.016 0.016 0.880
#> GSM99436 4 0.2136 0.7253 0.000 0.048 0.000 0.904 0.000 0.048
#> GSM99438 2 0.1219 0.9114 0.000 0.948 0.000 0.048 0.004 0.000
#> GSM99440 1 0.0260 0.9124 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM99442 4 0.2994 0.6598 0.000 0.208 0.000 0.788 0.004 0.000
#> GSM99444 2 0.0935 0.9192 0.000 0.964 0.000 0.032 0.004 0.000
#> GSM99446 4 0.3611 0.7158 0.000 0.108 0.000 0.796 0.000 0.096
#> GSM99448 3 0.6366 -0.6512 0.000 0.000 0.444 0.020 0.300 0.236
#> GSM99450 6 0.4283 0.5150 0.000 0.000 0.104 0.072 0.048 0.776
#> GSM99452 1 0.0146 0.9123 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM99454 1 0.0260 0.9129 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM99456 1 0.4033 0.7749 0.776 0.000 0.000 0.012 0.088 0.124
#> GSM99462 2 0.0858 0.9194 0.000 0.968 0.000 0.028 0.004 0.000
#> GSM99464 6 0.1851 0.5774 0.000 0.000 0.012 0.024 0.036 0.928
#> GSM99466 4 0.3645 0.6728 0.000 0.000 0.056 0.804 0.128 0.012
#> GSM99470 1 0.3499 0.7571 0.796 0.008 0.000 0.164 0.032 0.000
#> GSM99472 1 0.1398 0.8909 0.940 0.000 0.000 0.052 0.008 0.000
#> GSM99474 3 0.3627 0.3178 0.000 0.000 0.792 0.000 0.080 0.128
#> GSM99476 4 0.3488 0.6534 0.000 0.000 0.004 0.764 0.016 0.216
#> GSM99478 4 0.7426 0.2341 0.000 0.052 0.220 0.368 0.328 0.032
#> GSM99480 1 0.0632 0.9103 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM99482 1 0.0547 0.9116 0.980 0.000 0.000 0.000 0.020 0.000
#> GSM99484 4 0.3943 0.6811 0.004 0.172 0.012 0.772 0.040 0.000
#> GSM99486 4 0.1592 0.7170 0.000 0.008 0.000 0.940 0.032 0.020
#> GSM99488 2 0.0000 0.9166 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99490 2 0.3368 0.6889 0.000 0.756 0.000 0.232 0.012 0.000
#> GSM99492 1 0.1686 0.8895 0.924 0.000 0.000 0.000 0.064 0.012
#> GSM99494 2 0.0146 0.9160 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM99524 1 0.0777 0.9116 0.972 0.000 0.000 0.004 0.024 0.000
#> GSM99526 6 0.1349 0.5709 0.000 0.000 0.004 0.056 0.000 0.940
#> GSM99528 3 0.7278 0.2028 0.016 0.124 0.412 0.028 0.372 0.048
#> GSM99530 6 0.6485 0.0143 0.012 0.000 0.348 0.004 0.264 0.372
#> GSM99532 6 0.5040 0.1110 0.000 0.000 0.408 0.000 0.076 0.516
#> GSM99534 2 0.3969 0.6791 0.044 0.740 0.000 0.212 0.004 0.000
#> GSM99536 1 0.0717 0.9109 0.976 0.000 0.000 0.000 0.016 0.008
#> GSM99538 6 0.3456 0.5647 0.000 0.008 0.064 0.028 0.056 0.844
#> GSM99540 1 0.4091 0.7586 0.772 0.000 0.020 0.000 0.064 0.144
#> GSM99542 2 0.0000 0.9166 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99544 4 0.4779 0.1962 0.000 0.000 0.004 0.488 0.040 0.468
#> GSM99546 6 0.2730 0.5146 0.000 0.000 0.000 0.152 0.012 0.836
#> GSM99548 2 0.2358 0.8521 0.000 0.876 0.000 0.108 0.016 0.000
#> GSM99550 6 0.6732 0.2357 0.140 0.000 0.000 0.224 0.120 0.516
#> GSM99552 3 0.4110 0.4454 0.000 0.000 0.692 0.040 0.268 0.000
#> GSM99554 4 0.2772 0.7232 0.000 0.092 0.000 0.864 0.040 0.004
#> GSM99556 2 0.0603 0.9207 0.000 0.980 0.000 0.016 0.004 0.000
#> GSM99558 3 0.4819 0.4028 0.000 0.000 0.656 0.116 0.228 0.000
#> GSM99560 4 0.4207 0.6828 0.000 0.024 0.000 0.764 0.064 0.148
#> GSM99562 3 0.5586 -0.7615 0.000 0.000 0.472 0.000 0.384 0.144
#> GSM99564 4 0.1082 0.7165 0.000 0.004 0.000 0.956 0.000 0.040
#> GSM99572 2 0.2212 0.8642 0.000 0.880 0.000 0.112 0.008 0.000
#> GSM99576 1 0.5144 0.7403 0.736 0.052 0.036 0.004 0.128 0.044
#> GSM99578 4 0.5637 0.4893 0.000 0.292 0.040 0.592 0.072 0.004
#> GSM99580 3 0.2846 0.3789 0.000 0.000 0.856 0.000 0.084 0.060
#> GSM99582 4 0.6001 0.3873 0.024 0.000 0.244 0.564 0.164 0.004
#> GSM99584 4 0.3984 0.4943 0.000 0.000 0.000 0.648 0.016 0.336
#> GSM99586 1 0.3220 0.8353 0.840 0.000 0.004 0.004 0.096 0.056
#> GSM99588 2 0.0405 0.9189 0.000 0.988 0.000 0.008 0.004 0.000
#> GSM99590 2 0.0363 0.9204 0.000 0.988 0.000 0.012 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) cell.type(p) k
#> SD:NMF 84 8.94e-05 0.000459 2
#> SD:NMF 83 5.12e-04 0.011515 3
#> SD:NMF 78 1.16e-05 0.000577 4
#> SD:NMF 67 7.51e-04 0.016450 5
#> SD:NMF 57 1.57e-04 0.005002 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 21168 rows and 85 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 0.666 0.849 0.930 0.3044 0.722 0.722
#> 3 3 0.605 0.768 0.888 0.9728 0.684 0.562
#> 4 4 0.581 0.693 0.809 0.1801 0.829 0.595
#> 5 5 0.630 0.647 0.806 0.0860 0.953 0.823
#> 6 6 0.684 0.621 0.777 0.0392 0.992 0.964
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
#> GSM99496 1 0.0000 0.9300 1.000 0.000
#> GSM99502 1 0.0000 0.9300 1.000 0.000
#> GSM99504 1 0.0000 0.9300 1.000 0.000
#> GSM99506 1 0.0000 0.9300 1.000 0.000
#> GSM99566 1 0.0000 0.9300 1.000 0.000
#> GSM99574 1 0.0000 0.9300 1.000 0.000
#> GSM99592 1 0.0000 0.9300 1.000 0.000
#> GSM99594 1 0.0000 0.9300 1.000 0.000
#> GSM99468 1 0.0000 0.9300 1.000 0.000
#> GSM99498 1 0.0000 0.9300 1.000 0.000
#> GSM99500 1 0.0000 0.9300 1.000 0.000
#> GSM99508 1 0.0000 0.9300 1.000 0.000
#> GSM99568 1 0.0000 0.9300 1.000 0.000
#> GSM99596 1 0.0000 0.9300 1.000 0.000
#> GSM99600 1 0.9988 0.0534 0.520 0.480
#> GSM99458 1 0.0000 0.9300 1.000 0.000
#> GSM99460 1 0.0000 0.9300 1.000 0.000
#> GSM99510 1 0.0000 0.9300 1.000 0.000
#> GSM99512 1 0.0000 0.9300 1.000 0.000
#> GSM99514 1 0.0000 0.9300 1.000 0.000
#> GSM99516 1 0.0000 0.9300 1.000 0.000
#> GSM99518 1 0.0000 0.9300 1.000 0.000
#> GSM99520 1 0.0000 0.9300 1.000 0.000
#> GSM99522 1 0.0000 0.9300 1.000 0.000
#> GSM99570 1 0.0000 0.9300 1.000 0.000
#> GSM99598 1 0.0000 0.9300 1.000 0.000
#> GSM99432 1 0.7219 0.7700 0.800 0.200
#> GSM99434 1 0.0376 0.9285 0.996 0.004
#> GSM99436 1 0.8144 0.6926 0.748 0.252
#> GSM99438 2 0.2603 0.8649 0.044 0.956
#> GSM99440 1 0.0000 0.9300 1.000 0.000
#> GSM99442 2 0.9635 0.3877 0.388 0.612
#> GSM99444 2 0.2948 0.8634 0.052 0.948
#> GSM99446 1 0.9358 0.4881 0.648 0.352
#> GSM99448 1 0.4298 0.8848 0.912 0.088
#> GSM99450 1 0.0000 0.9300 1.000 0.000
#> GSM99452 1 0.0000 0.9300 1.000 0.000
#> GSM99454 1 0.0000 0.9300 1.000 0.000
#> GSM99456 1 0.0000 0.9300 1.000 0.000
#> GSM99462 2 0.0000 0.8614 0.000 1.000
#> GSM99464 1 0.0000 0.9300 1.000 0.000
#> GSM99466 1 0.4690 0.8745 0.900 0.100
#> GSM99470 1 0.4161 0.8876 0.916 0.084
#> GSM99472 1 0.4161 0.8876 0.916 0.084
#> GSM99474 1 0.0000 0.9300 1.000 0.000
#> GSM99476 1 0.4431 0.8804 0.908 0.092
#> GSM99478 1 0.5408 0.8551 0.876 0.124
#> GSM99480 1 0.0000 0.9300 1.000 0.000
#> GSM99482 1 0.0000 0.9300 1.000 0.000
#> GSM99484 1 0.5946 0.8379 0.856 0.144
#> GSM99486 1 0.7950 0.7111 0.760 0.240
#> GSM99488 2 0.0000 0.8614 0.000 1.000
#> GSM99490 2 0.5408 0.8097 0.124 0.876
#> GSM99492 1 0.0000 0.9300 1.000 0.000
#> GSM99494 2 0.0000 0.8614 0.000 1.000
#> GSM99524 1 0.0000 0.9300 1.000 0.000
#> GSM99526 1 0.0376 0.9285 0.996 0.004
#> GSM99528 1 0.3733 0.8974 0.928 0.072
#> GSM99530 1 0.0000 0.9300 1.000 0.000
#> GSM99532 1 0.0000 0.9300 1.000 0.000
#> GSM99534 1 0.9491 0.4422 0.632 0.368
#> GSM99536 1 0.0000 0.9300 1.000 0.000
#> GSM99538 1 0.5842 0.8397 0.860 0.140
#> GSM99540 1 0.0000 0.9300 1.000 0.000
#> GSM99542 2 0.1414 0.8639 0.020 0.980
#> GSM99544 1 0.6247 0.8225 0.844 0.156
#> GSM99546 1 0.6148 0.8272 0.848 0.152
#> GSM99548 2 0.0000 0.8614 0.000 1.000
#> GSM99550 1 0.0938 0.9256 0.988 0.012
#> GSM99552 1 0.3114 0.9057 0.944 0.056
#> GSM99554 1 0.9491 0.4433 0.632 0.368
#> GSM99556 2 0.0000 0.8614 0.000 1.000
#> GSM99558 1 0.3733 0.8957 0.928 0.072
#> GSM99560 1 0.5519 0.8529 0.872 0.128
#> GSM99562 1 0.0000 0.9300 1.000 0.000
#> GSM99564 1 0.7950 0.7111 0.760 0.240
#> GSM99572 2 0.2948 0.8634 0.052 0.948
#> GSM99576 1 0.1843 0.9187 0.972 0.028
#> GSM99578 2 0.9922 0.2052 0.448 0.552
#> GSM99580 1 0.3274 0.9023 0.940 0.060
#> GSM99582 1 0.4161 0.8866 0.916 0.084
#> GSM99584 1 0.6531 0.8089 0.832 0.168
#> GSM99586 1 0.0000 0.9300 1.000 0.000
#> GSM99588 2 0.9775 0.3208 0.412 0.588
#> GSM99590 2 0.3114 0.8615 0.056 0.944
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM99496 3 0.0592 0.84592 0.012 0.000 0.988
#> GSM99502 1 0.0000 0.91390 1.000 0.000 0.000
#> GSM99504 1 0.1529 0.89514 0.960 0.000 0.040
#> GSM99506 3 0.0592 0.84592 0.012 0.000 0.988
#> GSM99566 3 0.0747 0.84615 0.016 0.000 0.984
#> GSM99574 1 0.0000 0.91390 1.000 0.000 0.000
#> GSM99592 3 0.0592 0.84592 0.012 0.000 0.988
#> GSM99594 3 0.0747 0.84615 0.016 0.000 0.984
#> GSM99468 1 0.1411 0.89802 0.964 0.000 0.036
#> GSM99498 1 0.1411 0.89802 0.964 0.000 0.036
#> GSM99500 1 0.1411 0.89802 0.964 0.000 0.036
#> GSM99508 3 0.0747 0.84600 0.016 0.000 0.984
#> GSM99568 3 0.1643 0.84054 0.044 0.000 0.956
#> GSM99596 3 0.1643 0.84175 0.044 0.000 0.956
#> GSM99600 3 0.6291 0.15627 0.000 0.468 0.532
#> GSM99458 3 0.5859 0.49065 0.344 0.000 0.656
#> GSM99460 1 0.6302 0.00632 0.520 0.000 0.480
#> GSM99510 3 0.0592 0.84592 0.012 0.000 0.988
#> GSM99512 3 0.0592 0.84592 0.012 0.000 0.988
#> GSM99514 3 0.0592 0.84592 0.012 0.000 0.988
#> GSM99516 1 0.0000 0.91390 1.000 0.000 0.000
#> GSM99518 1 0.1031 0.90484 0.976 0.000 0.024
#> GSM99520 3 0.1289 0.84412 0.032 0.000 0.968
#> GSM99522 3 0.1529 0.84291 0.040 0.000 0.960
#> GSM99570 1 0.0000 0.91390 1.000 0.000 0.000
#> GSM99598 1 0.0000 0.91390 1.000 0.000 0.000
#> GSM99432 3 0.4399 0.76674 0.000 0.188 0.812
#> GSM99434 3 0.0424 0.84569 0.008 0.000 0.992
#> GSM99436 3 0.5016 0.70517 0.000 0.240 0.760
#> GSM99438 2 0.1964 0.84923 0.000 0.944 0.056
#> GSM99440 1 0.0000 0.91390 1.000 0.000 0.000
#> GSM99442 2 0.6126 0.31655 0.000 0.600 0.400
#> GSM99444 2 0.2165 0.84746 0.000 0.936 0.064
#> GSM99446 3 0.5835 0.53807 0.000 0.340 0.660
#> GSM99448 3 0.2772 0.83816 0.004 0.080 0.916
#> GSM99450 3 0.1753 0.84042 0.048 0.000 0.952
#> GSM99452 1 0.0000 0.91390 1.000 0.000 0.000
#> GSM99454 1 0.0237 0.91322 0.996 0.000 0.004
#> GSM99456 1 0.0237 0.91272 0.996 0.000 0.004
#> GSM99462 2 0.0237 0.84122 0.000 0.996 0.004
#> GSM99464 3 0.3340 0.79539 0.120 0.000 0.880
#> GSM99466 3 0.3213 0.83157 0.008 0.092 0.900
#> GSM99470 1 0.8162 0.30232 0.568 0.084 0.348
#> GSM99472 1 0.8162 0.30232 0.568 0.084 0.348
#> GSM99474 3 0.2625 0.82152 0.084 0.000 0.916
#> GSM99476 3 0.3043 0.83438 0.008 0.084 0.908
#> GSM99478 3 0.3500 0.82181 0.004 0.116 0.880
#> GSM99480 1 0.0000 0.91390 1.000 0.000 0.000
#> GSM99482 1 0.0000 0.91390 1.000 0.000 0.000
#> GSM99484 3 0.4345 0.81046 0.016 0.136 0.848
#> GSM99486 3 0.4887 0.71852 0.000 0.228 0.772
#> GSM99488 2 0.0000 0.83950 0.000 1.000 0.000
#> GSM99490 2 0.3619 0.78909 0.000 0.864 0.136
#> GSM99492 1 0.0000 0.91390 1.000 0.000 0.000
#> GSM99494 2 0.0000 0.83950 0.000 1.000 0.000
#> GSM99524 1 0.0237 0.91322 0.996 0.000 0.004
#> GSM99526 3 0.1031 0.84712 0.024 0.000 0.976
#> GSM99528 3 0.3993 0.83425 0.052 0.064 0.884
#> GSM99530 3 0.4452 0.72077 0.192 0.000 0.808
#> GSM99532 3 0.4702 0.71111 0.212 0.000 0.788
#> GSM99534 3 0.8705 0.29608 0.116 0.360 0.524
#> GSM99536 1 0.0000 0.91390 1.000 0.000 0.000
#> GSM99538 3 0.3482 0.81201 0.000 0.128 0.872
#> GSM99540 3 0.5254 0.64658 0.264 0.000 0.736
#> GSM99542 2 0.0892 0.83172 0.020 0.980 0.000
#> GSM99544 3 0.3752 0.80051 0.000 0.144 0.856
#> GSM99546 3 0.5634 0.78493 0.056 0.144 0.800
#> GSM99548 2 0.0424 0.84161 0.000 0.992 0.008
#> GSM99550 1 0.1989 0.88228 0.948 0.004 0.048
#> GSM99552 3 0.2280 0.84665 0.008 0.052 0.940
#> GSM99554 3 0.5926 0.49588 0.000 0.356 0.644
#> GSM99556 2 0.0237 0.84122 0.000 0.996 0.004
#> GSM99558 3 0.2400 0.84239 0.004 0.064 0.932
#> GSM99560 3 0.3918 0.82254 0.012 0.120 0.868
#> GSM99562 3 0.0592 0.84592 0.012 0.000 0.988
#> GSM99564 3 0.4887 0.71852 0.000 0.228 0.772
#> GSM99572 2 0.2165 0.84733 0.000 0.936 0.064
#> GSM99576 3 0.6859 0.45556 0.356 0.024 0.620
#> GSM99578 2 0.6647 0.11314 0.008 0.540 0.452
#> GSM99580 3 0.2096 0.84393 0.004 0.052 0.944
#> GSM99582 3 0.4838 0.81987 0.076 0.076 0.848
#> GSM99584 3 0.4172 0.79221 0.004 0.156 0.840
#> GSM99586 1 0.0237 0.91264 0.996 0.000 0.004
#> GSM99588 2 0.6204 0.23875 0.000 0.576 0.424
#> GSM99590 2 0.2261 0.84538 0.000 0.932 0.068
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM99496 3 0.0000 0.7748 0.000 0.000 1.000 0.000
#> GSM99502 1 0.0000 0.9050 1.000 0.000 0.000 0.000
#> GSM99504 1 0.1545 0.8911 0.952 0.000 0.040 0.008
#> GSM99506 3 0.0000 0.7748 0.000 0.000 1.000 0.000
#> GSM99566 3 0.0336 0.7747 0.000 0.000 0.992 0.008
#> GSM99574 1 0.0000 0.9050 1.000 0.000 0.000 0.000
#> GSM99592 3 0.1557 0.7597 0.000 0.000 0.944 0.056
#> GSM99594 3 0.0336 0.7747 0.000 0.000 0.992 0.008
#> GSM99468 1 0.1452 0.8937 0.956 0.000 0.036 0.008
#> GSM99498 1 0.1452 0.8937 0.956 0.000 0.036 0.008
#> GSM99500 1 0.1452 0.8937 0.956 0.000 0.036 0.008
#> GSM99508 3 0.0188 0.7760 0.004 0.000 0.996 0.000
#> GSM99568 3 0.1356 0.7726 0.032 0.000 0.960 0.008
#> GSM99596 3 0.1209 0.7729 0.032 0.000 0.964 0.004
#> GSM99600 4 0.6805 0.5047 0.000 0.260 0.148 0.592
#> GSM99458 3 0.7296 0.2675 0.320 0.000 0.508 0.172
#> GSM99460 1 0.6817 -0.0171 0.492 0.000 0.408 0.100
#> GSM99510 3 0.2408 0.7303 0.000 0.000 0.896 0.104
#> GSM99512 3 0.0336 0.7752 0.000 0.000 0.992 0.008
#> GSM99514 3 0.0188 0.7756 0.004 0.000 0.996 0.000
#> GSM99516 1 0.0000 0.9050 1.000 0.000 0.000 0.000
#> GSM99518 1 0.1151 0.8989 0.968 0.000 0.024 0.008
#> GSM99520 3 0.1406 0.7765 0.016 0.000 0.960 0.024
#> GSM99522 3 0.2111 0.7662 0.024 0.000 0.932 0.044
#> GSM99570 1 0.0000 0.9050 1.000 0.000 0.000 0.000
#> GSM99598 1 0.0000 0.9050 1.000 0.000 0.000 0.000
#> GSM99432 4 0.5367 0.6944 0.000 0.032 0.304 0.664
#> GSM99434 3 0.3494 0.6768 0.004 0.000 0.824 0.172
#> GSM99436 4 0.4671 0.7054 0.000 0.028 0.220 0.752
#> GSM99438 2 0.3172 0.8760 0.000 0.840 0.000 0.160
#> GSM99440 1 0.0000 0.9050 1.000 0.000 0.000 0.000
#> GSM99442 4 0.6882 0.1641 0.000 0.392 0.108 0.500
#> GSM99444 2 0.3710 0.8590 0.000 0.804 0.004 0.192
#> GSM99446 4 0.6373 0.6841 0.000 0.148 0.200 0.652
#> GSM99448 3 0.4655 0.2879 0.000 0.004 0.684 0.312
#> GSM99450 3 0.3749 0.7190 0.032 0.000 0.840 0.128
#> GSM99452 1 0.0000 0.9050 1.000 0.000 0.000 0.000
#> GSM99454 1 0.0188 0.9049 0.996 0.000 0.004 0.000
#> GSM99456 1 0.2593 0.8592 0.892 0.000 0.004 0.104
#> GSM99462 2 0.1792 0.8941 0.000 0.932 0.000 0.068
#> GSM99464 3 0.5250 0.6627 0.068 0.000 0.736 0.196
#> GSM99466 4 0.5183 0.5894 0.008 0.000 0.408 0.584
#> GSM99470 1 0.7513 0.2898 0.548 0.012 0.180 0.260
#> GSM99472 1 0.7513 0.2898 0.548 0.012 0.180 0.260
#> GSM99474 3 0.3198 0.7496 0.040 0.000 0.880 0.080
#> GSM99476 4 0.5257 0.5244 0.008 0.000 0.444 0.548
#> GSM99478 4 0.5039 0.6015 0.004 0.000 0.404 0.592
#> GSM99480 1 0.0000 0.9050 1.000 0.000 0.000 0.000
#> GSM99482 1 0.0707 0.8999 0.980 0.000 0.000 0.020
#> GSM99484 4 0.5633 0.6544 0.016 0.012 0.348 0.624
#> GSM99486 4 0.4284 0.7046 0.000 0.012 0.224 0.764
#> GSM99488 2 0.0000 0.8808 0.000 1.000 0.000 0.000
#> GSM99490 2 0.4744 0.7747 0.000 0.736 0.024 0.240
#> GSM99492 1 0.1022 0.8973 0.968 0.000 0.000 0.032
#> GSM99494 2 0.0000 0.8808 0.000 1.000 0.000 0.000
#> GSM99524 1 0.0188 0.9049 0.996 0.000 0.004 0.000
#> GSM99526 3 0.4391 0.6063 0.008 0.000 0.740 0.252
#> GSM99528 3 0.5633 0.3122 0.016 0.008 0.596 0.380
#> GSM99530 3 0.4881 0.6062 0.048 0.000 0.756 0.196
#> GSM99532 3 0.5664 0.6141 0.124 0.000 0.720 0.156
#> GSM99534 4 0.7228 0.5575 0.092 0.140 0.104 0.664
#> GSM99536 1 0.0336 0.9045 0.992 0.000 0.000 0.008
#> GSM99538 4 0.5099 0.6384 0.000 0.008 0.380 0.612
#> GSM99540 3 0.6282 0.5537 0.176 0.000 0.664 0.160
#> GSM99542 2 0.0817 0.8751 0.000 0.976 0.000 0.024
#> GSM99544 4 0.4973 0.6676 0.000 0.008 0.348 0.644
#> GSM99546 4 0.6163 0.4927 0.052 0.000 0.416 0.532
#> GSM99548 2 0.1389 0.8933 0.000 0.952 0.000 0.048
#> GSM99550 1 0.3862 0.8122 0.824 0.000 0.024 0.152
#> GSM99552 3 0.4535 0.3530 0.004 0.000 0.704 0.292
#> GSM99554 4 0.6096 0.6628 0.000 0.136 0.184 0.680
#> GSM99556 2 0.0707 0.8889 0.000 0.980 0.000 0.020
#> GSM99558 3 0.4313 0.4690 0.000 0.004 0.736 0.260
#> GSM99560 4 0.5263 0.3309 0.000 0.008 0.448 0.544
#> GSM99562 3 0.0188 0.7747 0.000 0.000 0.996 0.004
#> GSM99564 4 0.4284 0.7046 0.000 0.012 0.224 0.764
#> GSM99572 2 0.3668 0.8599 0.000 0.808 0.004 0.188
#> GSM99576 3 0.7285 0.3327 0.300 0.000 0.520 0.180
#> GSM99578 4 0.7479 0.2664 0.008 0.384 0.140 0.468
#> GSM99580 3 0.3494 0.6233 0.000 0.004 0.824 0.172
#> GSM99582 4 0.6438 0.4437 0.068 0.000 0.436 0.496
#> GSM99584 4 0.5232 0.6730 0.004 0.012 0.340 0.644
#> GSM99586 1 0.2888 0.8465 0.872 0.000 0.004 0.124
#> GSM99588 4 0.7253 0.1648 0.000 0.428 0.144 0.428
#> GSM99590 2 0.3626 0.8617 0.000 0.812 0.004 0.184
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM99496 3 0.0162 0.741 0.000 0.000 0.996 0.000 0.004
#> GSM99502 1 0.0000 0.877 1.000 0.000 0.000 0.000 0.000
#> GSM99504 1 0.1485 0.861 0.948 0.000 0.020 0.000 0.032
#> GSM99506 3 0.0162 0.742 0.000 0.000 0.996 0.000 0.004
#> GSM99566 3 0.1410 0.724 0.000 0.000 0.940 0.000 0.060
#> GSM99574 1 0.0000 0.877 1.000 0.000 0.000 0.000 0.000
#> GSM99592 3 0.3242 0.694 0.000 0.000 0.852 0.072 0.076
#> GSM99594 3 0.1410 0.724 0.000 0.000 0.940 0.000 0.060
#> GSM99468 1 0.1469 0.862 0.948 0.000 0.016 0.000 0.036
#> GSM99498 1 0.1386 0.863 0.952 0.000 0.016 0.000 0.032
#> GSM99500 1 0.1386 0.863 0.952 0.000 0.016 0.000 0.032
#> GSM99508 3 0.0404 0.741 0.000 0.000 0.988 0.000 0.012
#> GSM99568 3 0.1568 0.726 0.020 0.000 0.944 0.000 0.036
#> GSM99596 3 0.1493 0.725 0.024 0.000 0.948 0.000 0.028
#> GSM99600 4 0.4603 0.548 0.000 0.248 0.028 0.712 0.012
#> GSM99458 5 0.8282 0.408 0.256 0.000 0.168 0.192 0.384
#> GSM99460 1 0.7385 -0.207 0.444 0.000 0.136 0.072 0.348
#> GSM99510 3 0.4757 0.564 0.000 0.000 0.732 0.148 0.120
#> GSM99512 3 0.1522 0.738 0.000 0.000 0.944 0.012 0.044
#> GSM99514 3 0.0290 0.742 0.000 0.000 0.992 0.000 0.008
#> GSM99516 1 0.0000 0.877 1.000 0.000 0.000 0.000 0.000
#> GSM99518 1 0.1082 0.869 0.964 0.000 0.008 0.000 0.028
#> GSM99520 3 0.2196 0.729 0.004 0.000 0.916 0.024 0.056
#> GSM99522 3 0.3226 0.695 0.016 0.000 0.868 0.060 0.056
#> GSM99570 1 0.0162 0.876 0.996 0.000 0.000 0.000 0.004
#> GSM99598 1 0.0000 0.877 1.000 0.000 0.000 0.000 0.000
#> GSM99432 4 0.3666 0.702 0.000 0.020 0.092 0.840 0.048
#> GSM99434 3 0.6337 0.205 0.000 0.000 0.524 0.216 0.260
#> GSM99436 4 0.1731 0.701 0.000 0.012 0.040 0.940 0.008
#> GSM99438 2 0.3010 0.854 0.000 0.824 0.000 0.172 0.004
#> GSM99440 1 0.0000 0.877 1.000 0.000 0.000 0.000 0.000
#> GSM99442 4 0.4759 0.223 0.000 0.380 0.008 0.600 0.012
#> GSM99444 2 0.3353 0.838 0.000 0.796 0.000 0.196 0.008
#> GSM99446 4 0.4036 0.676 0.000 0.132 0.052 0.804 0.012
#> GSM99448 3 0.5568 0.267 0.000 0.000 0.540 0.384 0.076
#> GSM99450 3 0.6366 0.320 0.016 0.000 0.576 0.164 0.244
#> GSM99452 1 0.0162 0.876 0.996 0.000 0.000 0.000 0.004
#> GSM99454 1 0.0162 0.877 0.996 0.000 0.000 0.000 0.004
#> GSM99456 1 0.2966 0.754 0.816 0.000 0.000 0.000 0.184
#> GSM99462 2 0.1704 0.879 0.000 0.928 0.000 0.068 0.004
#> GSM99464 5 0.6178 0.471 0.020 0.000 0.244 0.132 0.604
#> GSM99466 4 0.4541 0.626 0.000 0.000 0.172 0.744 0.084
#> GSM99470 1 0.7027 0.119 0.512 0.004 0.064 0.324 0.096
#> GSM99472 1 0.7027 0.119 0.512 0.004 0.064 0.324 0.096
#> GSM99474 3 0.4617 0.554 0.016 0.000 0.744 0.044 0.196
#> GSM99476 4 0.5091 0.579 0.000 0.000 0.196 0.692 0.112
#> GSM99478 4 0.4573 0.641 0.000 0.000 0.164 0.744 0.092
#> GSM99480 1 0.0162 0.876 0.996 0.000 0.000 0.000 0.004
#> GSM99482 1 0.1124 0.860 0.960 0.000 0.000 0.004 0.036
#> GSM99484 4 0.4153 0.669 0.004 0.004 0.116 0.800 0.076
#> GSM99486 4 0.1569 0.701 0.000 0.004 0.044 0.944 0.008
#> GSM99488 2 0.0290 0.861 0.000 0.992 0.000 0.000 0.008
#> GSM99490 2 0.3942 0.757 0.000 0.728 0.000 0.260 0.012
#> GSM99492 1 0.1043 0.865 0.960 0.000 0.000 0.000 0.040
#> GSM99494 2 0.0290 0.861 0.000 0.992 0.000 0.000 0.008
#> GSM99524 1 0.0162 0.877 0.996 0.000 0.000 0.000 0.004
#> GSM99526 5 0.6731 0.255 0.000 0.000 0.304 0.280 0.416
#> GSM99528 5 0.6378 0.135 0.008 0.004 0.112 0.404 0.472
#> GSM99530 5 0.3870 0.442 0.004 0.000 0.260 0.004 0.732
#> GSM99532 5 0.6450 0.495 0.084 0.000 0.320 0.044 0.552
#> GSM99534 4 0.4915 0.592 0.032 0.132 0.000 0.756 0.080
#> GSM99536 1 0.0404 0.876 0.988 0.000 0.000 0.000 0.012
#> GSM99538 4 0.4203 0.672 0.000 0.000 0.128 0.780 0.092
#> GSM99540 5 0.6795 0.542 0.136 0.000 0.260 0.048 0.556
#> GSM99542 2 0.0955 0.854 0.000 0.968 0.000 0.004 0.028
#> GSM99544 4 0.3601 0.685 0.000 0.000 0.128 0.820 0.052
#> GSM99546 4 0.5505 0.489 0.004 0.000 0.128 0.660 0.208
#> GSM99548 2 0.1357 0.878 0.000 0.948 0.000 0.048 0.004
#> GSM99550 1 0.3942 0.681 0.748 0.000 0.000 0.020 0.232
#> GSM99552 3 0.4874 0.326 0.000 0.000 0.600 0.368 0.032
#> GSM99554 4 0.3653 0.664 0.000 0.124 0.036 0.828 0.012
#> GSM99556 2 0.0771 0.872 0.000 0.976 0.000 0.020 0.004
#> GSM99558 3 0.5006 0.424 0.000 0.000 0.624 0.328 0.048
#> GSM99560 4 0.5024 0.371 0.000 0.004 0.044 0.640 0.312
#> GSM99562 3 0.0955 0.738 0.000 0.000 0.968 0.004 0.028
#> GSM99564 4 0.1569 0.701 0.000 0.004 0.044 0.944 0.008
#> GSM99572 2 0.3462 0.836 0.000 0.792 0.000 0.196 0.012
#> GSM99576 5 0.7519 0.496 0.268 0.000 0.128 0.112 0.492
#> GSM99578 4 0.5368 0.291 0.000 0.376 0.020 0.576 0.028
#> GSM99580 3 0.4400 0.570 0.000 0.000 0.736 0.212 0.052
#> GSM99582 4 0.6366 0.465 0.036 0.000 0.224 0.608 0.132
#> GSM99584 4 0.3825 0.680 0.000 0.000 0.136 0.804 0.060
#> GSM99586 1 0.3143 0.736 0.796 0.000 0.000 0.000 0.204
#> GSM99588 4 0.5726 0.199 0.000 0.420 0.056 0.512 0.012
#> GSM99590 2 0.3231 0.840 0.000 0.800 0.000 0.196 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM99496 3 0.0632 0.7229 0.000 0.000 0.976 0.024 NA 0.000
#> GSM99502 1 0.0000 0.8507 1.000 0.000 0.000 0.000 NA 0.000
#> GSM99504 1 0.1636 0.8366 0.936 0.000 0.024 0.000 NA 0.036
#> GSM99506 3 0.0891 0.7230 0.000 0.000 0.968 0.024 NA 0.000
#> GSM99566 3 0.2163 0.6770 0.000 0.000 0.892 0.000 NA 0.016
#> GSM99574 1 0.0000 0.8507 1.000 0.000 0.000 0.000 NA 0.000
#> GSM99592 3 0.4688 0.6426 0.000 0.000 0.748 0.076 NA 0.080
#> GSM99594 3 0.2112 0.6778 0.000 0.000 0.896 0.000 NA 0.016
#> GSM99468 1 0.1693 0.8368 0.932 0.000 0.020 0.000 NA 0.044
#> GSM99498 1 0.1552 0.8385 0.940 0.000 0.020 0.000 NA 0.036
#> GSM99500 1 0.1552 0.8385 0.940 0.000 0.020 0.000 NA 0.036
#> GSM99508 3 0.0891 0.7230 0.000 0.000 0.968 0.024 NA 0.008
#> GSM99568 3 0.2145 0.7134 0.016 0.000 0.920 0.020 NA 0.032
#> GSM99596 3 0.1892 0.7128 0.020 0.000 0.932 0.020 NA 0.020
#> GSM99600 4 0.3665 0.5456 0.000 0.252 0.000 0.728 NA 0.000
#> GSM99458 6 0.7691 0.4206 0.240 0.000 0.044 0.128 NA 0.448
#> GSM99460 1 0.6834 -0.1791 0.416 0.000 0.032 0.044 NA 0.396
#> GSM99510 3 0.6487 0.4095 0.000 0.000 0.564 0.128 NA 0.152
#> GSM99512 3 0.3167 0.6768 0.000 0.000 0.836 0.012 NA 0.032
#> GSM99514 3 0.0777 0.7233 0.000 0.000 0.972 0.024 NA 0.000
#> GSM99516 1 0.0000 0.8507 1.000 0.000 0.000 0.000 NA 0.000
#> GSM99518 1 0.1226 0.8443 0.952 0.000 0.004 0.000 NA 0.040
#> GSM99520 3 0.2782 0.7048 0.000 0.000 0.876 0.032 NA 0.068
#> GSM99522 3 0.4559 0.6467 0.016 0.000 0.776 0.064 NA 0.080
#> GSM99570 1 0.0363 0.8497 0.988 0.000 0.000 0.000 NA 0.000
#> GSM99598 1 0.0000 0.8507 1.000 0.000 0.000 0.000 NA 0.000
#> GSM99432 4 0.2990 0.6991 0.000 0.020 0.008 0.872 NA 0.048
#> GSM99434 6 0.7504 0.1514 0.000 0.000 0.276 0.168 NA 0.356
#> GSM99436 4 0.1003 0.7001 0.000 0.016 0.000 0.964 NA 0.000
#> GSM99438 2 0.2859 0.8449 0.000 0.828 0.000 0.156 NA 0.000
#> GSM99440 1 0.0146 0.8502 0.996 0.000 0.000 0.000 NA 0.000
#> GSM99442 4 0.4409 0.2350 0.000 0.380 0.000 0.588 NA 0.000
#> GSM99444 2 0.3136 0.8254 0.000 0.796 0.000 0.188 NA 0.000
#> GSM99446 4 0.3074 0.6787 0.000 0.132 0.004 0.836 NA 0.004
#> GSM99448 3 0.6391 0.1283 0.000 0.000 0.420 0.412 NA 0.076
#> GSM99450 3 0.7631 -0.0394 0.016 0.000 0.380 0.132 NA 0.296
#> GSM99452 1 0.0458 0.8492 0.984 0.000 0.000 0.000 NA 0.000
#> GSM99454 1 0.0405 0.8509 0.988 0.000 0.000 0.000 NA 0.008
#> GSM99456 1 0.4650 0.6289 0.688 0.000 0.000 0.000 NA 0.132
#> GSM99462 2 0.1584 0.8704 0.000 0.928 0.000 0.064 NA 0.000
#> GSM99464 6 0.4928 0.5503 0.008 0.000 0.060 0.064 NA 0.732
#> GSM99466 4 0.4828 0.6217 0.000 0.000 0.072 0.736 NA 0.096
#> GSM99470 1 0.6834 0.1237 0.484 0.000 0.024 0.288 NA 0.040
#> GSM99472 1 0.6834 0.1237 0.484 0.000 0.024 0.288 NA 0.040
#> GSM99474 3 0.5135 0.5131 0.008 0.000 0.664 0.048 NA 0.244
#> GSM99476 4 0.5260 0.5879 0.000 0.000 0.080 0.696 NA 0.128
#> GSM99478 4 0.4557 0.6442 0.000 0.000 0.060 0.756 NA 0.108
#> GSM99480 1 0.1049 0.8443 0.960 0.000 0.000 0.000 NA 0.008
#> GSM99482 1 0.1327 0.8283 0.936 0.000 0.000 0.000 NA 0.000
#> GSM99484 4 0.4327 0.6564 0.000 0.004 0.028 0.772 NA 0.084
#> GSM99486 4 0.0972 0.6982 0.000 0.008 0.000 0.964 NA 0.000
#> GSM99488 2 0.0632 0.8492 0.000 0.976 0.000 0.000 NA 0.000
#> GSM99490 2 0.4050 0.7424 0.000 0.716 0.000 0.236 NA 0.000
#> GSM99492 1 0.2309 0.8091 0.888 0.000 0.000 0.000 NA 0.028
#> GSM99494 2 0.0632 0.8492 0.000 0.976 0.000 0.000 NA 0.000
#> GSM99524 1 0.0405 0.8509 0.988 0.000 0.000 0.000 NA 0.008
#> GSM99526 6 0.6514 0.4129 0.000 0.000 0.068 0.180 NA 0.524
#> GSM99528 6 0.6352 0.1464 0.000 0.000 0.044 0.328 NA 0.480
#> GSM99530 6 0.5371 0.4238 0.000 0.000 0.176 0.000 NA 0.584
#> GSM99532 6 0.4933 0.4948 0.068 0.000 0.224 0.012 NA 0.684
#> GSM99534 4 0.5494 0.5195 0.008 0.104 0.000 0.588 NA 0.008
#> GSM99536 1 0.0909 0.8485 0.968 0.000 0.000 0.000 NA 0.012
#> GSM99538 4 0.3859 0.6653 0.000 0.000 0.028 0.804 NA 0.088
#> GSM99540 6 0.4976 0.5379 0.112 0.000 0.160 0.012 NA 0.704
#> GSM99542 2 0.1387 0.8363 0.000 0.932 0.000 0.000 NA 0.000
#> GSM99544 4 0.3284 0.6786 0.000 0.000 0.024 0.844 NA 0.052
#> GSM99546 4 0.6161 0.3687 0.000 0.004 0.012 0.504 NA 0.220
#> GSM99548 2 0.1562 0.8665 0.000 0.940 0.000 0.024 NA 0.004
#> GSM99550 1 0.5277 0.5381 0.620 0.000 0.000 0.004 NA 0.172
#> GSM99552 3 0.5101 0.3181 0.000 0.000 0.544 0.392 NA 0.020
#> GSM99554 4 0.2826 0.6638 0.000 0.128 0.000 0.844 NA 0.000
#> GSM99556 2 0.0603 0.8642 0.000 0.980 0.000 0.016 NA 0.000
#> GSM99558 3 0.5774 0.3733 0.000 0.000 0.528 0.356 NA 0.052
#> GSM99560 4 0.5377 0.3435 0.000 0.004 0.012 0.596 NA 0.296
#> GSM99562 3 0.2122 0.6921 0.000 0.000 0.900 0.000 NA 0.024
#> GSM99564 4 0.0972 0.6982 0.000 0.008 0.000 0.964 NA 0.000
#> GSM99572 2 0.3312 0.8256 0.000 0.792 0.000 0.180 NA 0.000
#> GSM99576 6 0.7282 0.4745 0.228 0.000 0.068 0.084 NA 0.516
#> GSM99578 4 0.5328 0.3102 0.000 0.364 0.008 0.556 NA 0.012
#> GSM99580 3 0.5291 0.5265 0.000 0.000 0.652 0.232 NA 0.056
#> GSM99582 4 0.6109 0.4771 0.016 0.000 0.152 0.624 NA 0.152
#> GSM99584 4 0.3375 0.6777 0.000 0.000 0.008 0.828 NA 0.088
#> GSM99586 1 0.4843 0.6018 0.664 0.000 0.000 0.000 NA 0.144
#> GSM99588 4 0.4936 0.2209 0.000 0.408 0.016 0.540 NA 0.000
#> GSM99590 2 0.3104 0.8275 0.000 0.800 0.000 0.184 NA 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) cell.type(p) k
#> CV:hclust 78 3.49e-02 0.10965 2
#> CV:hclust 74 2.19e-02 0.24306 3
#> CV:hclust 70 5.52e-04 0.02966 4
#> CV:hclust 64 1.75e-05 0.00491 5
#> CV:hclust 64 2.21e-05 0.00549 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 21168 rows and 85 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.651 0.888 0.937 0.4847 0.514 0.514
#> 3 3 0.984 0.954 0.978 0.3830 0.718 0.499
#> 4 4 0.720 0.700 0.820 0.1074 0.876 0.646
#> 5 5 0.736 0.660 0.831 0.0625 0.897 0.640
#> 6 6 0.773 0.634 0.803 0.0416 0.952 0.794
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
#> GSM99496 1 0.7602 0.795 0.780 0.220
#> GSM99502 1 0.0000 0.894 1.000 0.000
#> GSM99504 1 0.0000 0.894 1.000 0.000
#> GSM99506 1 0.7602 0.795 0.780 0.220
#> GSM99566 1 0.7602 0.795 0.780 0.220
#> GSM99574 1 0.0000 0.894 1.000 0.000
#> GSM99592 1 0.7883 0.778 0.764 0.236
#> GSM99594 1 0.7602 0.795 0.780 0.220
#> GSM99468 1 0.0000 0.894 1.000 0.000
#> GSM99498 1 0.0000 0.894 1.000 0.000
#> GSM99500 1 0.0000 0.894 1.000 0.000
#> GSM99508 1 0.6048 0.840 0.852 0.148
#> GSM99568 1 0.7453 0.801 0.788 0.212
#> GSM99596 1 0.1184 0.891 0.984 0.016
#> GSM99600 2 0.0000 0.986 0.000 1.000
#> GSM99458 1 0.0000 0.894 1.000 0.000
#> GSM99460 1 0.0000 0.894 1.000 0.000
#> GSM99510 1 0.9460 0.589 0.636 0.364
#> GSM99512 1 0.9460 0.589 0.636 0.364
#> GSM99514 1 0.7602 0.795 0.780 0.220
#> GSM99516 1 0.0000 0.894 1.000 0.000
#> GSM99518 1 0.0000 0.894 1.000 0.000
#> GSM99520 1 0.7602 0.795 0.780 0.220
#> GSM99522 1 0.0000 0.894 1.000 0.000
#> GSM99570 1 0.0000 0.894 1.000 0.000
#> GSM99598 1 0.0000 0.894 1.000 0.000
#> GSM99432 2 0.0000 0.986 0.000 1.000
#> GSM99434 1 0.8909 0.683 0.692 0.308
#> GSM99436 2 0.0000 0.986 0.000 1.000
#> GSM99438 2 0.0000 0.986 0.000 1.000
#> GSM99440 1 0.0000 0.894 1.000 0.000
#> GSM99442 2 0.0000 0.986 0.000 1.000
#> GSM99444 2 0.0000 0.986 0.000 1.000
#> GSM99446 2 0.0000 0.986 0.000 1.000
#> GSM99448 2 0.0000 0.986 0.000 1.000
#> GSM99450 1 0.6438 0.831 0.836 0.164
#> GSM99452 1 0.0000 0.894 1.000 0.000
#> GSM99454 1 0.0000 0.894 1.000 0.000
#> GSM99456 1 0.0000 0.894 1.000 0.000
#> GSM99462 2 0.0000 0.986 0.000 1.000
#> GSM99464 1 0.0376 0.894 0.996 0.004
#> GSM99466 2 0.0000 0.986 0.000 1.000
#> GSM99470 1 0.5294 0.853 0.880 0.120
#> GSM99472 1 0.0000 0.894 1.000 0.000
#> GSM99474 1 0.7602 0.795 0.780 0.220
#> GSM99476 2 0.0000 0.986 0.000 1.000
#> GSM99478 2 0.0000 0.986 0.000 1.000
#> GSM99480 1 0.0000 0.894 1.000 0.000
#> GSM99482 1 0.0000 0.894 1.000 0.000
#> GSM99484 2 0.0000 0.986 0.000 1.000
#> GSM99486 2 0.0000 0.986 0.000 1.000
#> GSM99488 2 0.0000 0.986 0.000 1.000
#> GSM99490 2 0.0000 0.986 0.000 1.000
#> GSM99492 1 0.0000 0.894 1.000 0.000
#> GSM99494 2 0.0000 0.986 0.000 1.000
#> GSM99524 1 0.0000 0.894 1.000 0.000
#> GSM99526 1 0.9460 0.589 0.636 0.364
#> GSM99528 2 0.5519 0.821 0.128 0.872
#> GSM99530 1 0.2948 0.878 0.948 0.052
#> GSM99532 1 0.0376 0.894 0.996 0.004
#> GSM99534 2 0.0000 0.986 0.000 1.000
#> GSM99536 1 0.0000 0.894 1.000 0.000
#> GSM99538 2 0.0000 0.986 0.000 1.000
#> GSM99540 1 0.0000 0.894 1.000 0.000
#> GSM99542 2 0.0000 0.986 0.000 1.000
#> GSM99544 2 0.0000 0.986 0.000 1.000
#> GSM99546 2 0.8443 0.537 0.272 0.728
#> GSM99548 2 0.0000 0.986 0.000 1.000
#> GSM99550 1 0.0000 0.894 1.000 0.000
#> GSM99552 1 0.9988 0.297 0.520 0.480
#> GSM99554 2 0.0000 0.986 0.000 1.000
#> GSM99556 2 0.0000 0.986 0.000 1.000
#> GSM99558 2 0.0000 0.986 0.000 1.000
#> GSM99560 2 0.0000 0.986 0.000 1.000
#> GSM99562 1 0.7602 0.795 0.780 0.220
#> GSM99564 2 0.0000 0.986 0.000 1.000
#> GSM99572 2 0.0000 0.986 0.000 1.000
#> GSM99576 1 0.0000 0.894 1.000 0.000
#> GSM99578 2 0.0000 0.986 0.000 1.000
#> GSM99580 1 0.7602 0.795 0.780 0.220
#> GSM99582 1 0.6343 0.833 0.840 0.160
#> GSM99584 2 0.0000 0.986 0.000 1.000
#> GSM99586 1 0.0000 0.894 1.000 0.000
#> GSM99588 2 0.0000 0.986 0.000 1.000
#> GSM99590 2 0.0000 0.986 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM99496 3 0.0424 0.984 0.000 0.008 0.992
#> GSM99502 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99504 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99506 3 0.0424 0.984 0.000 0.008 0.992
#> GSM99566 3 0.0424 0.984 0.000 0.008 0.992
#> GSM99574 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99592 3 0.0424 0.984 0.000 0.008 0.992
#> GSM99594 3 0.0424 0.984 0.000 0.008 0.992
#> GSM99468 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99498 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99500 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99508 3 0.0475 0.981 0.004 0.004 0.992
#> GSM99568 3 0.0424 0.984 0.000 0.008 0.992
#> GSM99596 3 0.0424 0.978 0.008 0.000 0.992
#> GSM99600 2 0.0000 0.954 0.000 1.000 0.000
#> GSM99458 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99460 1 0.0237 0.997 0.996 0.000 0.004
#> GSM99510 3 0.0424 0.984 0.000 0.008 0.992
#> GSM99512 3 0.0424 0.984 0.000 0.008 0.992
#> GSM99514 3 0.0424 0.984 0.000 0.008 0.992
#> GSM99516 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99518 1 0.0237 0.997 0.996 0.000 0.004
#> GSM99520 3 0.0424 0.984 0.000 0.008 0.992
#> GSM99522 3 0.0424 0.978 0.008 0.000 0.992
#> GSM99570 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99598 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99432 2 0.0000 0.954 0.000 1.000 0.000
#> GSM99434 3 0.0424 0.984 0.000 0.008 0.992
#> GSM99436 2 0.0000 0.954 0.000 1.000 0.000
#> GSM99438 2 0.0000 0.954 0.000 1.000 0.000
#> GSM99440 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99442 2 0.0000 0.954 0.000 1.000 0.000
#> GSM99444 2 0.0000 0.954 0.000 1.000 0.000
#> GSM99446 2 0.0000 0.954 0.000 1.000 0.000
#> GSM99448 3 0.0424 0.984 0.000 0.008 0.992
#> GSM99450 3 0.0424 0.984 0.000 0.008 0.992
#> GSM99452 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99454 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99456 1 0.0424 0.996 0.992 0.000 0.008
#> GSM99462 2 0.0000 0.954 0.000 1.000 0.000
#> GSM99464 3 0.0000 0.979 0.000 0.000 1.000
#> GSM99466 3 0.3482 0.863 0.000 0.128 0.872
#> GSM99470 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99472 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99474 3 0.0424 0.984 0.000 0.008 0.992
#> GSM99476 3 0.0424 0.984 0.000 0.008 0.992
#> GSM99478 2 0.5650 0.551 0.000 0.688 0.312
#> GSM99480 1 0.0424 0.996 0.992 0.000 0.008
#> GSM99482 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99484 2 0.0000 0.954 0.000 1.000 0.000
#> GSM99486 2 0.0000 0.954 0.000 1.000 0.000
#> GSM99488 2 0.0000 0.954 0.000 1.000 0.000
#> GSM99490 2 0.0000 0.954 0.000 1.000 0.000
#> GSM99492 1 0.0424 0.996 0.992 0.000 0.008
#> GSM99494 2 0.0000 0.954 0.000 1.000 0.000
#> GSM99524 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99526 3 0.0424 0.984 0.000 0.008 0.992
#> GSM99528 3 0.3412 0.868 0.000 0.124 0.876
#> GSM99530 3 0.0000 0.979 0.000 0.000 1.000
#> GSM99532 3 0.0237 0.979 0.004 0.000 0.996
#> GSM99534 2 0.0000 0.954 0.000 1.000 0.000
#> GSM99536 1 0.0237 0.997 0.996 0.000 0.004
#> GSM99538 3 0.3551 0.858 0.000 0.132 0.868
#> GSM99540 1 0.0237 0.997 0.996 0.000 0.004
#> GSM99542 2 0.0000 0.954 0.000 1.000 0.000
#> GSM99544 2 0.6260 0.204 0.000 0.552 0.448
#> GSM99546 3 0.1529 0.957 0.000 0.040 0.960
#> GSM99548 2 0.0000 0.954 0.000 1.000 0.000
#> GSM99550 1 0.0424 0.996 0.992 0.000 0.008
#> GSM99552 3 0.0424 0.984 0.000 0.008 0.992
#> GSM99554 2 0.0000 0.954 0.000 1.000 0.000
#> GSM99556 2 0.0000 0.954 0.000 1.000 0.000
#> GSM99558 3 0.0424 0.984 0.000 0.008 0.992
#> GSM99560 2 0.1163 0.930 0.000 0.972 0.028
#> GSM99562 3 0.0424 0.984 0.000 0.008 0.992
#> GSM99564 2 0.0000 0.954 0.000 1.000 0.000
#> GSM99572 2 0.0000 0.954 0.000 1.000 0.000
#> GSM99576 1 0.0424 0.996 0.992 0.000 0.008
#> GSM99578 2 0.0000 0.954 0.000 1.000 0.000
#> GSM99580 3 0.0424 0.984 0.000 0.008 0.992
#> GSM99582 3 0.0424 0.984 0.000 0.008 0.992
#> GSM99584 2 0.5948 0.449 0.000 0.640 0.360
#> GSM99586 1 0.0424 0.996 0.992 0.000 0.008
#> GSM99588 2 0.0000 0.954 0.000 1.000 0.000
#> GSM99590 2 0.0000 0.954 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM99496 3 0.0188 0.88702 0.000 0.000 0.996 0.004
#> GSM99502 1 0.0000 0.91748 1.000 0.000 0.000 0.000
#> GSM99504 1 0.0188 0.91605 0.996 0.000 0.004 0.000
#> GSM99506 3 0.0188 0.88702 0.000 0.000 0.996 0.004
#> GSM99566 3 0.0188 0.88702 0.000 0.000 0.996 0.004
#> GSM99574 1 0.0000 0.91748 1.000 0.000 0.000 0.000
#> GSM99592 3 0.0188 0.88702 0.000 0.000 0.996 0.004
#> GSM99594 3 0.0188 0.88702 0.000 0.000 0.996 0.004
#> GSM99468 1 0.0188 0.91730 0.996 0.000 0.000 0.004
#> GSM99498 1 0.0188 0.91730 0.996 0.000 0.000 0.004
#> GSM99500 1 0.0000 0.91748 1.000 0.000 0.000 0.000
#> GSM99508 3 0.0000 0.88594 0.000 0.000 1.000 0.000
#> GSM99568 3 0.0000 0.88594 0.000 0.000 1.000 0.000
#> GSM99596 3 0.0188 0.88702 0.000 0.000 0.996 0.004
#> GSM99600 2 0.4605 0.53468 0.000 0.664 0.000 0.336
#> GSM99458 1 0.2647 0.87096 0.880 0.000 0.000 0.120
#> GSM99460 1 0.4800 0.70245 0.656 0.000 0.004 0.340
#> GSM99510 3 0.3873 0.67277 0.000 0.000 0.772 0.228
#> GSM99512 3 0.0336 0.88399 0.000 0.000 0.992 0.008
#> GSM99514 3 0.0188 0.88702 0.000 0.000 0.996 0.004
#> GSM99516 1 0.0000 0.91748 1.000 0.000 0.000 0.000
#> GSM99518 1 0.1389 0.90765 0.952 0.000 0.000 0.048
#> GSM99520 3 0.0188 0.88702 0.000 0.000 0.996 0.004
#> GSM99522 3 0.0188 0.88490 0.000 0.000 0.996 0.004
#> GSM99570 1 0.0000 0.91748 1.000 0.000 0.000 0.000
#> GSM99598 1 0.0000 0.91748 1.000 0.000 0.000 0.000
#> GSM99432 4 0.4746 0.37094 0.000 0.368 0.000 0.632
#> GSM99434 3 0.4304 0.58331 0.000 0.000 0.716 0.284
#> GSM99436 2 0.4933 0.28965 0.000 0.568 0.000 0.432
#> GSM99438 2 0.0000 0.79310 0.000 1.000 0.000 0.000
#> GSM99440 1 0.0188 0.91730 0.996 0.000 0.000 0.004
#> GSM99442 2 0.1867 0.76855 0.000 0.928 0.000 0.072
#> GSM99444 2 0.0000 0.79310 0.000 1.000 0.000 0.000
#> GSM99446 2 0.4761 0.46571 0.000 0.628 0.000 0.372
#> GSM99448 3 0.3486 0.72345 0.000 0.000 0.812 0.188
#> GSM99450 3 0.4564 0.53505 0.000 0.000 0.672 0.328
#> GSM99452 1 0.0188 0.91730 0.996 0.000 0.000 0.004
#> GSM99454 1 0.0000 0.91748 1.000 0.000 0.000 0.000
#> GSM99456 1 0.4277 0.78658 0.720 0.000 0.000 0.280
#> GSM99462 2 0.0000 0.79310 0.000 1.000 0.000 0.000
#> GSM99464 4 0.4933 -0.18185 0.000 0.000 0.432 0.568
#> GSM99466 4 0.6327 0.58433 0.000 0.124 0.228 0.648
#> GSM99470 1 0.4830 0.39506 0.608 0.000 0.000 0.392
#> GSM99472 1 0.2216 0.88220 0.908 0.000 0.000 0.092
#> GSM99474 3 0.0188 0.88497 0.000 0.000 0.996 0.004
#> GSM99476 4 0.4679 0.42287 0.000 0.000 0.352 0.648
#> GSM99478 4 0.6089 0.51295 0.000 0.280 0.080 0.640
#> GSM99480 1 0.2469 0.88355 0.892 0.000 0.000 0.108
#> GSM99482 1 0.0000 0.91748 1.000 0.000 0.000 0.000
#> GSM99484 4 0.4855 0.30120 0.000 0.400 0.000 0.600
#> GSM99486 4 0.4877 0.28120 0.000 0.408 0.000 0.592
#> GSM99488 2 0.0000 0.79310 0.000 1.000 0.000 0.000
#> GSM99490 2 0.1867 0.76860 0.000 0.928 0.000 0.072
#> GSM99492 1 0.2530 0.88196 0.888 0.000 0.000 0.112
#> GSM99494 2 0.0000 0.79310 0.000 1.000 0.000 0.000
#> GSM99524 1 0.0000 0.91748 1.000 0.000 0.000 0.000
#> GSM99526 4 0.4222 0.36244 0.000 0.000 0.272 0.728
#> GSM99528 4 0.4188 0.59812 0.000 0.040 0.148 0.812
#> GSM99530 3 0.3942 0.65915 0.000 0.000 0.764 0.236
#> GSM99532 3 0.2149 0.82186 0.000 0.000 0.912 0.088
#> GSM99534 2 0.4761 0.48000 0.000 0.628 0.000 0.372
#> GSM99536 1 0.1637 0.90199 0.940 0.000 0.000 0.060
#> GSM99538 4 0.5633 0.60204 0.000 0.100 0.184 0.716
#> GSM99540 1 0.4040 0.79087 0.752 0.000 0.000 0.248
#> GSM99542 2 0.0000 0.79310 0.000 1.000 0.000 0.000
#> GSM99544 4 0.5883 0.49119 0.000 0.300 0.060 0.640
#> GSM99546 4 0.2799 0.57710 0.000 0.008 0.108 0.884
#> GSM99548 2 0.0000 0.79310 0.000 1.000 0.000 0.000
#> GSM99550 4 0.4936 -0.20557 0.372 0.000 0.004 0.624
#> GSM99552 3 0.3074 0.72155 0.000 0.000 0.848 0.152
#> GSM99554 2 0.4697 0.49968 0.000 0.644 0.000 0.356
#> GSM99556 2 0.0000 0.79310 0.000 1.000 0.000 0.000
#> GSM99558 4 0.4977 0.20634 0.000 0.000 0.460 0.540
#> GSM99560 4 0.3837 0.50998 0.000 0.224 0.000 0.776
#> GSM99562 3 0.0188 0.88490 0.000 0.000 0.996 0.004
#> GSM99564 4 0.4877 0.28120 0.000 0.408 0.000 0.592
#> GSM99572 2 0.0000 0.79310 0.000 1.000 0.000 0.000
#> GSM99576 1 0.4454 0.74496 0.692 0.000 0.000 0.308
#> GSM99578 2 0.4585 0.54039 0.000 0.668 0.000 0.332
#> GSM99580 3 0.0188 0.88702 0.000 0.000 0.996 0.004
#> GSM99582 3 0.4985 -0.00104 0.000 0.000 0.532 0.468
#> GSM99584 4 0.4964 0.51305 0.000 0.256 0.028 0.716
#> GSM99586 1 0.3726 0.82837 0.788 0.000 0.000 0.212
#> GSM99588 2 0.4304 0.59787 0.000 0.716 0.000 0.284
#> GSM99590 2 0.0000 0.79310 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM99496 3 0.0162 0.8371 0.000 0.000 0.996 0.000 0.004
#> GSM99502 1 0.0000 0.8519 1.000 0.000 0.000 0.000 0.000
#> GSM99504 1 0.1043 0.8162 0.960 0.000 0.040 0.000 0.000
#> GSM99506 3 0.0162 0.8371 0.000 0.000 0.996 0.000 0.004
#> GSM99566 3 0.0510 0.8331 0.000 0.000 0.984 0.000 0.016
#> GSM99574 1 0.0000 0.8519 1.000 0.000 0.000 0.000 0.000
#> GSM99592 3 0.0000 0.8377 0.000 0.000 1.000 0.000 0.000
#> GSM99594 3 0.0510 0.8331 0.000 0.000 0.984 0.000 0.016
#> GSM99468 1 0.0000 0.8519 1.000 0.000 0.000 0.000 0.000
#> GSM99498 1 0.0000 0.8519 1.000 0.000 0.000 0.000 0.000
#> GSM99500 1 0.0000 0.8519 1.000 0.000 0.000 0.000 0.000
#> GSM99508 3 0.0000 0.8377 0.000 0.000 1.000 0.000 0.000
#> GSM99568 3 0.0000 0.8377 0.000 0.000 1.000 0.000 0.000
#> GSM99596 3 0.0000 0.8377 0.000 0.000 1.000 0.000 0.000
#> GSM99600 4 0.3274 0.6548 0.000 0.220 0.000 0.780 0.000
#> GSM99458 1 0.4591 0.3868 0.648 0.008 0.000 0.012 0.332
#> GSM99460 5 0.4397 0.4318 0.276 0.000 0.000 0.028 0.696
#> GSM99510 3 0.5808 0.4899 0.000 0.000 0.608 0.160 0.232
#> GSM99512 3 0.2522 0.7833 0.000 0.000 0.880 0.012 0.108
#> GSM99514 3 0.0000 0.8377 0.000 0.000 1.000 0.000 0.000
#> GSM99516 1 0.0000 0.8519 1.000 0.000 0.000 0.000 0.000
#> GSM99518 1 0.1965 0.7919 0.904 0.000 0.000 0.000 0.096
#> GSM99520 3 0.0000 0.8377 0.000 0.000 1.000 0.000 0.000
#> GSM99522 3 0.0000 0.8377 0.000 0.000 1.000 0.000 0.000
#> GSM99570 1 0.0162 0.8511 0.996 0.004 0.000 0.000 0.000
#> GSM99598 1 0.0000 0.8519 1.000 0.000 0.000 0.000 0.000
#> GSM99432 4 0.2325 0.7141 0.000 0.028 0.000 0.904 0.068
#> GSM99434 3 0.6287 0.3440 0.000 0.000 0.512 0.176 0.312
#> GSM99436 4 0.2605 0.7137 0.000 0.148 0.000 0.852 0.000
#> GSM99438 2 0.1410 0.9562 0.000 0.940 0.000 0.060 0.000
#> GSM99440 1 0.0000 0.8519 1.000 0.000 0.000 0.000 0.000
#> GSM99442 4 0.4302 0.0197 0.000 0.480 0.000 0.520 0.000
#> GSM99444 2 0.1410 0.9562 0.000 0.940 0.000 0.060 0.000
#> GSM99446 4 0.2966 0.6898 0.000 0.184 0.000 0.816 0.000
#> GSM99448 3 0.5472 0.5423 0.000 0.000 0.652 0.208 0.140
#> GSM99450 3 0.6235 0.3106 0.000 0.000 0.500 0.156 0.344
#> GSM99452 1 0.0290 0.8502 0.992 0.008 0.000 0.000 0.000
#> GSM99454 1 0.0162 0.8512 0.996 0.004 0.000 0.000 0.000
#> GSM99456 5 0.5299 -0.0560 0.436 0.040 0.000 0.004 0.520
#> GSM99462 2 0.1571 0.9559 0.000 0.936 0.000 0.060 0.004
#> GSM99464 5 0.4219 0.4762 0.000 0.000 0.116 0.104 0.780
#> GSM99466 4 0.3708 0.6842 0.000 0.004 0.044 0.816 0.136
#> GSM99470 4 0.7071 -0.0675 0.360 0.020 0.000 0.412 0.208
#> GSM99472 1 0.4208 0.6135 0.760 0.020 0.000 0.016 0.204
#> GSM99474 3 0.1205 0.8188 0.000 0.000 0.956 0.004 0.040
#> GSM99476 4 0.4373 0.5863 0.000 0.000 0.080 0.760 0.160
#> GSM99478 4 0.3357 0.7038 0.000 0.016 0.012 0.836 0.136
#> GSM99480 1 0.4370 0.5949 0.724 0.040 0.000 0.000 0.236
#> GSM99482 1 0.1059 0.8387 0.968 0.020 0.000 0.004 0.008
#> GSM99484 4 0.2708 0.7282 0.000 0.044 0.000 0.884 0.072
#> GSM99486 4 0.1410 0.7343 0.000 0.060 0.000 0.940 0.000
#> GSM99488 2 0.1914 0.9516 0.000 0.924 0.000 0.060 0.016
#> GSM99490 2 0.4118 0.4994 0.000 0.660 0.000 0.336 0.004
#> GSM99492 1 0.4503 0.5677 0.704 0.040 0.000 0.000 0.256
#> GSM99494 2 0.1914 0.9516 0.000 0.924 0.000 0.060 0.016
#> GSM99524 1 0.0451 0.8486 0.988 0.008 0.000 0.000 0.004
#> GSM99526 5 0.5409 0.2532 0.000 0.000 0.080 0.316 0.604
#> GSM99528 4 0.4478 0.4357 0.000 0.004 0.008 0.628 0.360
#> GSM99530 3 0.4713 0.2725 0.000 0.000 0.544 0.016 0.440
#> GSM99532 3 0.3530 0.6737 0.000 0.000 0.784 0.012 0.204
#> GSM99534 4 0.5581 0.5726 0.000 0.224 0.000 0.636 0.140
#> GSM99536 1 0.3123 0.7140 0.828 0.012 0.000 0.000 0.160
#> GSM99538 4 0.4114 0.5218 0.000 0.000 0.016 0.712 0.272
#> GSM99540 1 0.4452 -0.0547 0.500 0.000 0.000 0.004 0.496
#> GSM99542 2 0.1774 0.9370 0.000 0.932 0.000 0.052 0.016
#> GSM99544 4 0.3293 0.6521 0.000 0.008 0.008 0.824 0.160
#> GSM99546 5 0.4449 -0.1612 0.000 0.000 0.004 0.484 0.512
#> GSM99548 2 0.1410 0.9562 0.000 0.940 0.000 0.060 0.000
#> GSM99550 5 0.4232 0.5041 0.152 0.040 0.000 0.020 0.788
#> GSM99552 3 0.2735 0.7544 0.000 0.000 0.880 0.084 0.036
#> GSM99554 4 0.3074 0.6776 0.000 0.196 0.000 0.804 0.000
#> GSM99556 2 0.1571 0.9559 0.000 0.936 0.000 0.060 0.004
#> GSM99558 4 0.4088 0.6141 0.000 0.000 0.168 0.776 0.056
#> GSM99560 4 0.3399 0.6543 0.000 0.020 0.000 0.812 0.168
#> GSM99562 3 0.0162 0.8371 0.000 0.000 0.996 0.000 0.004
#> GSM99564 4 0.1410 0.7343 0.000 0.060 0.000 0.940 0.000
#> GSM99572 2 0.1608 0.9480 0.000 0.928 0.000 0.072 0.000
#> GSM99576 5 0.4682 0.1230 0.420 0.000 0.000 0.016 0.564
#> GSM99578 4 0.4269 0.6731 0.000 0.188 0.000 0.756 0.056
#> GSM99580 3 0.0000 0.8377 0.000 0.000 1.000 0.000 0.000
#> GSM99582 3 0.6315 0.0052 0.000 0.000 0.448 0.396 0.156
#> GSM99584 4 0.3010 0.6459 0.000 0.004 0.000 0.824 0.172
#> GSM99586 1 0.5137 0.2215 0.536 0.040 0.000 0.000 0.424
#> GSM99588 4 0.3957 0.5706 0.000 0.280 0.000 0.712 0.008
#> GSM99590 2 0.1410 0.9562 0.000 0.940 0.000 0.060 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM99496 3 0.0146 0.82340 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM99502 1 0.0000 0.79818 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99504 1 0.1155 0.77315 0.956 0.000 0.036 0.000 0.004 0.004
#> GSM99506 3 0.0717 0.82060 0.000 0.000 0.976 0.000 0.008 0.016
#> GSM99566 3 0.1297 0.80820 0.000 0.000 0.948 0.000 0.012 0.040
#> GSM99574 1 0.0146 0.79766 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM99592 3 0.0777 0.82143 0.000 0.000 0.972 0.000 0.004 0.024
#> GSM99594 3 0.1297 0.80820 0.000 0.000 0.948 0.000 0.012 0.040
#> GSM99468 1 0.0405 0.79625 0.988 0.000 0.000 0.000 0.004 0.008
#> GSM99498 1 0.0405 0.79625 0.988 0.000 0.000 0.000 0.004 0.008
#> GSM99500 1 0.0405 0.79625 0.988 0.000 0.000 0.000 0.004 0.008
#> GSM99508 3 0.0146 0.82340 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM99568 3 0.0291 0.82277 0.000 0.000 0.992 0.000 0.004 0.004
#> GSM99596 3 0.0146 0.82340 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM99600 4 0.2165 0.72919 0.000 0.108 0.000 0.884 0.008 0.000
#> GSM99458 1 0.6037 -0.05704 0.508 0.004 0.000 0.008 0.284 0.196
#> GSM99460 6 0.5423 -0.18938 0.088 0.004 0.000 0.004 0.408 0.496
#> GSM99510 6 0.4302 0.42302 0.000 0.000 0.368 0.020 0.004 0.608
#> GSM99512 3 0.3969 0.41402 0.000 0.000 0.652 0.000 0.016 0.332
#> GSM99514 3 0.0146 0.82269 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM99516 1 0.0146 0.79805 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM99518 1 0.2724 0.68388 0.864 0.000 0.000 0.000 0.084 0.052
#> GSM99520 3 0.0603 0.82105 0.000 0.000 0.980 0.000 0.004 0.016
#> GSM99522 3 0.0725 0.82098 0.000 0.000 0.976 0.000 0.012 0.012
#> GSM99570 1 0.0777 0.78994 0.972 0.000 0.000 0.004 0.024 0.000
#> GSM99598 1 0.0146 0.79805 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM99432 4 0.2994 0.70252 0.000 0.008 0.000 0.820 0.008 0.164
#> GSM99434 6 0.4135 0.53234 0.000 0.000 0.300 0.032 0.000 0.668
#> GSM99436 4 0.1606 0.74131 0.000 0.056 0.000 0.932 0.004 0.008
#> GSM99438 2 0.0291 0.93052 0.000 0.992 0.000 0.004 0.004 0.000
#> GSM99440 1 0.0000 0.79818 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99442 4 0.3774 0.47675 0.000 0.328 0.000 0.664 0.008 0.000
#> GSM99444 2 0.0291 0.93075 0.000 0.992 0.000 0.004 0.004 0.000
#> GSM99446 4 0.2009 0.73647 0.000 0.084 0.000 0.904 0.008 0.004
#> GSM99448 3 0.5887 -0.10481 0.000 0.000 0.484 0.192 0.004 0.320
#> GSM99450 6 0.4605 0.53914 0.000 0.000 0.308 0.024 0.024 0.644
#> GSM99452 1 0.0692 0.79295 0.976 0.000 0.000 0.004 0.020 0.000
#> GSM99454 1 0.0000 0.79818 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99456 5 0.3230 0.70615 0.212 0.000 0.000 0.000 0.776 0.012
#> GSM99462 2 0.0653 0.92942 0.000 0.980 0.000 0.004 0.004 0.012
#> GSM99464 6 0.4400 0.27980 0.000 0.000 0.032 0.004 0.332 0.632
#> GSM99466 4 0.4844 0.67445 0.000 0.004 0.004 0.672 0.092 0.228
#> GSM99470 1 0.7513 -0.13459 0.368 0.004 0.000 0.244 0.256 0.128
#> GSM99472 1 0.4914 0.41302 0.672 0.004 0.000 0.020 0.244 0.060
#> GSM99474 3 0.1672 0.79478 0.000 0.000 0.932 0.004 0.016 0.048
#> GSM99476 4 0.4158 0.61293 0.000 0.000 0.012 0.688 0.020 0.280
#> GSM99478 4 0.4837 0.67558 0.000 0.008 0.000 0.668 0.092 0.232
#> GSM99480 1 0.3823 -0.00909 0.564 0.000 0.000 0.000 0.436 0.000
#> GSM99482 1 0.2089 0.74829 0.908 0.004 0.000 0.004 0.072 0.012
#> GSM99484 4 0.4088 0.70889 0.000 0.020 0.000 0.780 0.096 0.104
#> GSM99486 4 0.1168 0.74295 0.000 0.028 0.000 0.956 0.000 0.016
#> GSM99488 2 0.1053 0.92524 0.000 0.964 0.000 0.004 0.012 0.020
#> GSM99490 2 0.4936 0.27202 0.000 0.576 0.000 0.364 0.048 0.012
#> GSM99492 1 0.3868 -0.20380 0.504 0.000 0.000 0.000 0.496 0.000
#> GSM99494 2 0.1053 0.92524 0.000 0.964 0.000 0.004 0.012 0.020
#> GSM99524 1 0.0777 0.78994 0.972 0.000 0.000 0.004 0.024 0.000
#> GSM99526 6 0.4044 0.47787 0.000 0.000 0.008 0.084 0.140 0.768
#> GSM99528 4 0.6017 0.34136 0.000 0.000 0.004 0.424 0.204 0.368
#> GSM99530 3 0.6365 -0.08299 0.000 0.000 0.380 0.012 0.340 0.268
#> GSM99532 3 0.4886 0.46555 0.000 0.000 0.664 0.012 0.084 0.240
#> GSM99534 4 0.6628 0.49170 0.000 0.144 0.000 0.540 0.192 0.124
#> GSM99536 1 0.3522 0.54995 0.784 0.000 0.000 0.000 0.172 0.044
#> GSM99538 4 0.4076 0.48909 0.000 0.000 0.000 0.592 0.012 0.396
#> GSM99540 5 0.6147 0.56697 0.340 0.000 0.000 0.012 0.448 0.200
#> GSM99542 2 0.1710 0.90988 0.000 0.936 0.000 0.016 0.020 0.028
#> GSM99544 4 0.3703 0.58529 0.000 0.004 0.000 0.688 0.004 0.304
#> GSM99546 6 0.4828 0.38773 0.000 0.004 0.000 0.220 0.108 0.668
#> GSM99548 2 0.0665 0.92715 0.000 0.980 0.000 0.004 0.008 0.008
#> GSM99550 5 0.2619 0.55368 0.048 0.000 0.000 0.012 0.884 0.056
#> GSM99552 3 0.3836 0.65990 0.000 0.000 0.808 0.036 0.064 0.092
#> GSM99554 4 0.2001 0.73572 0.000 0.092 0.000 0.900 0.004 0.004
#> GSM99556 2 0.0551 0.93036 0.000 0.984 0.000 0.004 0.004 0.008
#> GSM99558 4 0.4513 0.68508 0.000 0.000 0.056 0.732 0.032 0.180
#> GSM99560 4 0.3815 0.64145 0.000 0.000 0.000 0.776 0.092 0.132
#> GSM99562 3 0.0972 0.81727 0.000 0.000 0.964 0.000 0.008 0.028
#> GSM99564 4 0.1257 0.74235 0.000 0.028 0.000 0.952 0.000 0.020
#> GSM99572 2 0.1483 0.90350 0.000 0.944 0.000 0.036 0.012 0.008
#> GSM99576 5 0.5836 0.61075 0.216 0.000 0.000 0.020 0.572 0.192
#> GSM99578 4 0.4693 0.70023 0.000 0.076 0.000 0.748 0.088 0.088
#> GSM99580 3 0.0363 0.82184 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM99582 3 0.6796 0.19755 0.000 0.000 0.516 0.200 0.140 0.144
#> GSM99584 4 0.3953 0.53966 0.000 0.000 0.000 0.656 0.016 0.328
#> GSM99586 5 0.3126 0.69417 0.248 0.000 0.000 0.000 0.752 0.000
#> GSM99588 4 0.4225 0.70320 0.000 0.140 0.000 0.768 0.032 0.060
#> GSM99590 2 0.0291 0.93075 0.000 0.992 0.000 0.004 0.004 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) cell.type(p) k
#> CV:kmeans 84 1.43e-05 8.68e-05 2
#> CV:kmeans 83 1.97e-03 3.26e-02 3
#> CV:kmeans 69 1.24e-03 4.48e-02 4
#> CV:kmeans 67 7.83e-05 1.40e-02 5
#> CV:kmeans 65 9.59e-06 5.03e-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["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 21168 rows and 85 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.973 0.989 0.5047 0.496 0.496
#> 3 3 1.000 0.969 0.987 0.3322 0.736 0.514
#> 4 4 0.805 0.782 0.895 0.0999 0.908 0.732
#> 5 5 0.741 0.620 0.816 0.0617 0.928 0.743
#> 6 6 0.718 0.556 0.767 0.0365 0.937 0.739
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
#> GSM99496 1 0.0000 0.989 1.000 0.000
#> GSM99502 1 0.0000 0.989 1.000 0.000
#> GSM99504 1 0.0000 0.989 1.000 0.000
#> GSM99506 1 0.0000 0.989 1.000 0.000
#> GSM99566 1 0.0000 0.989 1.000 0.000
#> GSM99574 1 0.0000 0.989 1.000 0.000
#> GSM99592 1 0.6712 0.782 0.824 0.176
#> GSM99594 1 0.0000 0.989 1.000 0.000
#> GSM99468 1 0.0000 0.989 1.000 0.000
#> GSM99498 1 0.0000 0.989 1.000 0.000
#> GSM99500 1 0.0000 0.989 1.000 0.000
#> GSM99508 1 0.0000 0.989 1.000 0.000
#> GSM99568 1 0.0000 0.989 1.000 0.000
#> GSM99596 1 0.0000 0.989 1.000 0.000
#> GSM99600 2 0.0000 0.989 0.000 1.000
#> GSM99458 1 0.0000 0.989 1.000 0.000
#> GSM99460 1 0.0000 0.989 1.000 0.000
#> GSM99510 2 0.0000 0.989 0.000 1.000
#> GSM99512 2 0.0376 0.985 0.004 0.996
#> GSM99514 1 0.0000 0.989 1.000 0.000
#> GSM99516 1 0.0000 0.989 1.000 0.000
#> GSM99518 1 0.0000 0.989 1.000 0.000
#> GSM99520 1 0.0000 0.989 1.000 0.000
#> GSM99522 1 0.0000 0.989 1.000 0.000
#> GSM99570 1 0.0000 0.989 1.000 0.000
#> GSM99598 1 0.0000 0.989 1.000 0.000
#> GSM99432 2 0.0000 0.989 0.000 1.000
#> GSM99434 2 0.2043 0.958 0.032 0.968
#> GSM99436 2 0.0000 0.989 0.000 1.000
#> GSM99438 2 0.0000 0.989 0.000 1.000
#> GSM99440 1 0.0000 0.989 1.000 0.000
#> GSM99442 2 0.0000 0.989 0.000 1.000
#> GSM99444 2 0.0000 0.989 0.000 1.000
#> GSM99446 2 0.0000 0.989 0.000 1.000
#> GSM99448 2 0.0000 0.989 0.000 1.000
#> GSM99450 1 0.0000 0.989 1.000 0.000
#> GSM99452 1 0.0000 0.989 1.000 0.000
#> GSM99454 1 0.0000 0.989 1.000 0.000
#> GSM99456 1 0.0000 0.989 1.000 0.000
#> GSM99462 2 0.0000 0.989 0.000 1.000
#> GSM99464 1 0.0000 0.989 1.000 0.000
#> GSM99466 2 0.0000 0.989 0.000 1.000
#> GSM99470 2 0.9661 0.346 0.392 0.608
#> GSM99472 1 0.0000 0.989 1.000 0.000
#> GSM99474 1 0.0000 0.989 1.000 0.000
#> GSM99476 2 0.0000 0.989 0.000 1.000
#> GSM99478 2 0.0000 0.989 0.000 1.000
#> GSM99480 1 0.0000 0.989 1.000 0.000
#> GSM99482 1 0.0000 0.989 1.000 0.000
#> GSM99484 2 0.0000 0.989 0.000 1.000
#> GSM99486 2 0.0000 0.989 0.000 1.000
#> GSM99488 2 0.0000 0.989 0.000 1.000
#> GSM99490 2 0.0000 0.989 0.000 1.000
#> GSM99492 1 0.0000 0.989 1.000 0.000
#> GSM99494 2 0.0000 0.989 0.000 1.000
#> GSM99524 1 0.0000 0.989 1.000 0.000
#> GSM99526 2 0.0000 0.989 0.000 1.000
#> GSM99528 2 0.0000 0.989 0.000 1.000
#> GSM99530 1 0.0000 0.989 1.000 0.000
#> GSM99532 1 0.0000 0.989 1.000 0.000
#> GSM99534 2 0.0000 0.989 0.000 1.000
#> GSM99536 1 0.0000 0.989 1.000 0.000
#> GSM99538 2 0.0000 0.989 0.000 1.000
#> GSM99540 1 0.0000 0.989 1.000 0.000
#> GSM99542 2 0.0000 0.989 0.000 1.000
#> GSM99544 2 0.0000 0.989 0.000 1.000
#> GSM99546 2 0.0000 0.989 0.000 1.000
#> GSM99548 2 0.0000 0.989 0.000 1.000
#> GSM99550 1 0.0000 0.989 1.000 0.000
#> GSM99552 2 0.0000 0.989 0.000 1.000
#> GSM99554 2 0.0000 0.989 0.000 1.000
#> GSM99556 2 0.0000 0.989 0.000 1.000
#> GSM99558 2 0.0000 0.989 0.000 1.000
#> GSM99560 2 0.0000 0.989 0.000 1.000
#> GSM99562 1 0.0000 0.989 1.000 0.000
#> GSM99564 2 0.0000 0.989 0.000 1.000
#> GSM99572 2 0.0000 0.989 0.000 1.000
#> GSM99576 1 0.0000 0.989 1.000 0.000
#> GSM99578 2 0.0000 0.989 0.000 1.000
#> GSM99580 1 0.9000 0.533 0.684 0.316
#> GSM99582 1 0.0000 0.989 1.000 0.000
#> GSM99584 2 0.0000 0.989 0.000 1.000
#> GSM99586 1 0.0000 0.989 1.000 0.000
#> GSM99588 2 0.0000 0.989 0.000 1.000
#> GSM99590 2 0.0000 0.989 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM99496 3 0.0000 0.973 0.000 0.000 1.000
#> GSM99502 1 0.0000 0.986 1.000 0.000 0.000
#> GSM99504 1 0.0000 0.986 1.000 0.000 0.000
#> GSM99506 3 0.0000 0.973 0.000 0.000 1.000
#> GSM99566 3 0.0000 0.973 0.000 0.000 1.000
#> GSM99574 1 0.0000 0.986 1.000 0.000 0.000
#> GSM99592 3 0.0000 0.973 0.000 0.000 1.000
#> GSM99594 3 0.0000 0.973 0.000 0.000 1.000
#> GSM99468 1 0.0000 0.986 1.000 0.000 0.000
#> GSM99498 1 0.0000 0.986 1.000 0.000 0.000
#> GSM99500 1 0.0000 0.986 1.000 0.000 0.000
#> GSM99508 3 0.0000 0.973 0.000 0.000 1.000
#> GSM99568 3 0.0000 0.973 0.000 0.000 1.000
#> GSM99596 3 0.0000 0.973 0.000 0.000 1.000
#> GSM99600 2 0.0000 0.998 0.000 1.000 0.000
#> GSM99458 1 0.0000 0.986 1.000 0.000 0.000
#> GSM99460 1 0.0000 0.986 1.000 0.000 0.000
#> GSM99510 3 0.0000 0.973 0.000 0.000 1.000
#> GSM99512 3 0.0000 0.973 0.000 0.000 1.000
#> GSM99514 3 0.0000 0.973 0.000 0.000 1.000
#> GSM99516 1 0.0000 0.986 1.000 0.000 0.000
#> GSM99518 1 0.0000 0.986 1.000 0.000 0.000
#> GSM99520 3 0.0000 0.973 0.000 0.000 1.000
#> GSM99522 3 0.0424 0.967 0.008 0.000 0.992
#> GSM99570 1 0.0000 0.986 1.000 0.000 0.000
#> GSM99598 1 0.0000 0.986 1.000 0.000 0.000
#> GSM99432 2 0.0000 0.998 0.000 1.000 0.000
#> GSM99434 3 0.0000 0.973 0.000 0.000 1.000
#> GSM99436 2 0.0000 0.998 0.000 1.000 0.000
#> GSM99438 2 0.0000 0.998 0.000 1.000 0.000
#> GSM99440 1 0.0000 0.986 1.000 0.000 0.000
#> GSM99442 2 0.0000 0.998 0.000 1.000 0.000
#> GSM99444 2 0.0000 0.998 0.000 1.000 0.000
#> GSM99446 2 0.0000 0.998 0.000 1.000 0.000
#> GSM99448 3 0.0000 0.973 0.000 0.000 1.000
#> GSM99450 3 0.0000 0.973 0.000 0.000 1.000
#> GSM99452 1 0.0000 0.986 1.000 0.000 0.000
#> GSM99454 1 0.0000 0.986 1.000 0.000 0.000
#> GSM99456 1 0.0000 0.986 1.000 0.000 0.000
#> GSM99462 2 0.0000 0.998 0.000 1.000 0.000
#> GSM99464 3 0.0424 0.967 0.008 0.000 0.992
#> GSM99466 2 0.0000 0.998 0.000 1.000 0.000
#> GSM99470 1 0.0237 0.982 0.996 0.004 0.000
#> GSM99472 1 0.0000 0.986 1.000 0.000 0.000
#> GSM99474 3 0.0000 0.973 0.000 0.000 1.000
#> GSM99476 3 0.1643 0.936 0.000 0.044 0.956
#> GSM99478 2 0.0000 0.998 0.000 1.000 0.000
#> GSM99480 1 0.0000 0.986 1.000 0.000 0.000
#> GSM99482 1 0.0000 0.986 1.000 0.000 0.000
#> GSM99484 2 0.0000 0.998 0.000 1.000 0.000
#> GSM99486 2 0.0000 0.998 0.000 1.000 0.000
#> GSM99488 2 0.0000 0.998 0.000 1.000 0.000
#> GSM99490 2 0.0000 0.998 0.000 1.000 0.000
#> GSM99492 1 0.0000 0.986 1.000 0.000 0.000
#> GSM99494 2 0.0000 0.998 0.000 1.000 0.000
#> GSM99524 1 0.0000 0.986 1.000 0.000 0.000
#> GSM99526 3 0.5529 0.590 0.000 0.296 0.704
#> GSM99528 2 0.0237 0.994 0.000 0.996 0.004
#> GSM99530 3 0.0000 0.973 0.000 0.000 1.000
#> GSM99532 3 0.0000 0.973 0.000 0.000 1.000
#> GSM99534 2 0.0000 0.998 0.000 1.000 0.000
#> GSM99536 1 0.0000 0.986 1.000 0.000 0.000
#> GSM99538 2 0.1964 0.939 0.000 0.944 0.056
#> GSM99540 1 0.0000 0.986 1.000 0.000 0.000
#> GSM99542 2 0.0000 0.998 0.000 1.000 0.000
#> GSM99544 2 0.0000 0.998 0.000 1.000 0.000
#> GSM99546 2 0.0000 0.998 0.000 1.000 0.000
#> GSM99548 2 0.0000 0.998 0.000 1.000 0.000
#> GSM99550 1 0.0000 0.986 1.000 0.000 0.000
#> GSM99552 3 0.0000 0.973 0.000 0.000 1.000
#> GSM99554 2 0.0000 0.998 0.000 1.000 0.000
#> GSM99556 2 0.0000 0.998 0.000 1.000 0.000
#> GSM99558 3 0.5397 0.619 0.000 0.280 0.720
#> GSM99560 2 0.0000 0.998 0.000 1.000 0.000
#> GSM99562 3 0.0000 0.973 0.000 0.000 1.000
#> GSM99564 2 0.0000 0.998 0.000 1.000 0.000
#> GSM99572 2 0.0000 0.998 0.000 1.000 0.000
#> GSM99576 1 0.0000 0.986 1.000 0.000 0.000
#> GSM99578 2 0.0000 0.998 0.000 1.000 0.000
#> GSM99580 3 0.0000 0.973 0.000 0.000 1.000
#> GSM99582 1 0.6008 0.403 0.628 0.000 0.372
#> GSM99584 2 0.0000 0.998 0.000 1.000 0.000
#> GSM99586 1 0.0000 0.986 1.000 0.000 0.000
#> GSM99588 2 0.0000 0.998 0.000 1.000 0.000
#> GSM99590 2 0.0000 0.998 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM99496 3 0.0000 0.86968 0.000 0.000 1.000 0.000
#> GSM99502 1 0.0188 0.94834 0.996 0.000 0.000 0.004
#> GSM99504 1 0.1209 0.93042 0.964 0.000 0.032 0.004
#> GSM99506 3 0.0000 0.86968 0.000 0.000 1.000 0.000
#> GSM99566 3 0.0000 0.86968 0.000 0.000 1.000 0.000
#> GSM99574 1 0.0188 0.94834 0.996 0.000 0.000 0.004
#> GSM99592 3 0.0817 0.85691 0.000 0.000 0.976 0.024
#> GSM99594 3 0.0000 0.86968 0.000 0.000 1.000 0.000
#> GSM99468 1 0.0000 0.94866 1.000 0.000 0.000 0.000
#> GSM99498 1 0.0000 0.94866 1.000 0.000 0.000 0.000
#> GSM99500 1 0.0000 0.94866 1.000 0.000 0.000 0.000
#> GSM99508 3 0.0000 0.86968 0.000 0.000 1.000 0.000
#> GSM99568 3 0.0000 0.86968 0.000 0.000 1.000 0.000
#> GSM99596 3 0.0000 0.86968 0.000 0.000 1.000 0.000
#> GSM99600 2 0.1389 0.88219 0.000 0.952 0.000 0.048
#> GSM99458 1 0.2281 0.90618 0.904 0.000 0.000 0.096
#> GSM99460 1 0.4277 0.74039 0.720 0.000 0.000 0.280
#> GSM99510 4 0.4898 0.32326 0.000 0.000 0.416 0.584
#> GSM99512 3 0.3219 0.71836 0.000 0.000 0.836 0.164
#> GSM99514 3 0.0000 0.86968 0.000 0.000 1.000 0.000
#> GSM99516 1 0.0188 0.94834 0.996 0.000 0.000 0.004
#> GSM99518 1 0.1211 0.93956 0.960 0.000 0.000 0.040
#> GSM99520 3 0.0188 0.86824 0.000 0.000 0.996 0.004
#> GSM99522 3 0.0376 0.86693 0.004 0.000 0.992 0.004
#> GSM99570 1 0.0188 0.94834 0.996 0.000 0.000 0.004
#> GSM99598 1 0.0188 0.94834 0.996 0.000 0.000 0.004
#> GSM99432 2 0.4817 0.39133 0.000 0.612 0.000 0.388
#> GSM99434 4 0.4643 0.43588 0.000 0.000 0.344 0.656
#> GSM99436 2 0.3486 0.77146 0.000 0.812 0.000 0.188
#> GSM99438 2 0.0000 0.90002 0.000 1.000 0.000 0.000
#> GSM99440 1 0.0000 0.94866 1.000 0.000 0.000 0.000
#> GSM99442 2 0.0707 0.89456 0.000 0.980 0.000 0.020
#> GSM99444 2 0.0000 0.90002 0.000 1.000 0.000 0.000
#> GSM99446 2 0.3356 0.78449 0.000 0.824 0.000 0.176
#> GSM99448 3 0.4977 -0.00807 0.000 0.000 0.540 0.460
#> GSM99450 4 0.4955 0.23511 0.000 0.000 0.444 0.556
#> GSM99452 1 0.0000 0.94866 1.000 0.000 0.000 0.000
#> GSM99454 1 0.0000 0.94866 1.000 0.000 0.000 0.000
#> GSM99456 1 0.2868 0.88839 0.864 0.000 0.000 0.136
#> GSM99462 2 0.0000 0.90002 0.000 1.000 0.000 0.000
#> GSM99464 4 0.4378 0.52435 0.040 0.000 0.164 0.796
#> GSM99466 4 0.5000 -0.13172 0.000 0.496 0.000 0.504
#> GSM99470 1 0.2489 0.88783 0.912 0.068 0.000 0.020
#> GSM99472 1 0.0188 0.94834 0.996 0.000 0.000 0.004
#> GSM99474 3 0.1022 0.85533 0.000 0.000 0.968 0.032
#> GSM99476 4 0.4175 0.58674 0.000 0.016 0.200 0.784
#> GSM99478 2 0.3649 0.74246 0.000 0.796 0.000 0.204
#> GSM99480 1 0.0817 0.94399 0.976 0.000 0.000 0.024
#> GSM99482 1 0.0188 0.94834 0.996 0.000 0.000 0.004
#> GSM99484 2 0.1118 0.88994 0.000 0.964 0.000 0.036
#> GSM99486 2 0.4040 0.69063 0.000 0.752 0.000 0.248
#> GSM99488 2 0.0000 0.90002 0.000 1.000 0.000 0.000
#> GSM99490 2 0.0000 0.90002 0.000 1.000 0.000 0.000
#> GSM99492 1 0.1302 0.93808 0.956 0.000 0.000 0.044
#> GSM99494 2 0.0000 0.90002 0.000 1.000 0.000 0.000
#> GSM99524 1 0.0188 0.94834 0.996 0.000 0.000 0.004
#> GSM99526 4 0.1863 0.62155 0.004 0.012 0.040 0.944
#> GSM99528 2 0.4675 0.61781 0.000 0.736 0.020 0.244
#> GSM99530 3 0.4808 0.60032 0.028 0.000 0.736 0.236
#> GSM99532 3 0.2704 0.77848 0.000 0.000 0.876 0.124
#> GSM99534 2 0.0817 0.89055 0.000 0.976 0.000 0.024
#> GSM99536 1 0.1302 0.93776 0.956 0.000 0.000 0.044
#> GSM99538 4 0.4792 0.47798 0.000 0.312 0.008 0.680
#> GSM99540 1 0.2408 0.90887 0.896 0.000 0.000 0.104
#> GSM99542 2 0.0000 0.90002 0.000 1.000 0.000 0.000
#> GSM99544 4 0.4624 0.42336 0.000 0.340 0.000 0.660
#> GSM99546 4 0.2334 0.65190 0.000 0.088 0.004 0.908
#> GSM99548 2 0.0000 0.90002 0.000 1.000 0.000 0.000
#> GSM99550 1 0.4103 0.77595 0.744 0.000 0.000 0.256
#> GSM99552 3 0.2101 0.82159 0.000 0.012 0.928 0.060
#> GSM99554 2 0.2216 0.85590 0.000 0.908 0.000 0.092
#> GSM99556 2 0.0000 0.90002 0.000 1.000 0.000 0.000
#> GSM99558 3 0.6770 0.19803 0.000 0.128 0.580 0.292
#> GSM99560 2 0.3528 0.77088 0.000 0.808 0.000 0.192
#> GSM99562 3 0.0000 0.86968 0.000 0.000 1.000 0.000
#> GSM99564 2 0.4250 0.64490 0.000 0.724 0.000 0.276
#> GSM99572 2 0.0000 0.90002 0.000 1.000 0.000 0.000
#> GSM99576 1 0.3266 0.86183 0.832 0.000 0.000 0.168
#> GSM99578 2 0.0000 0.90002 0.000 1.000 0.000 0.000
#> GSM99580 3 0.0188 0.86820 0.000 0.000 0.996 0.004
#> GSM99582 3 0.6805 0.19204 0.400 0.000 0.500 0.100
#> GSM99584 4 0.4134 0.54592 0.000 0.260 0.000 0.740
#> GSM99586 1 0.2868 0.88794 0.864 0.000 0.000 0.136
#> GSM99588 2 0.0188 0.89844 0.000 0.996 0.000 0.004
#> GSM99590 2 0.0000 0.90002 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM99496 3 0.0162 0.87249 0.000 0.000 0.996 0.000 0.004
#> GSM99502 1 0.0000 0.86146 1.000 0.000 0.000 0.000 0.000
#> GSM99504 1 0.1484 0.83132 0.944 0.000 0.048 0.000 0.008
#> GSM99506 3 0.0000 0.87198 0.000 0.000 1.000 0.000 0.000
#> GSM99566 3 0.0324 0.87194 0.000 0.000 0.992 0.004 0.004
#> GSM99574 1 0.0000 0.86146 1.000 0.000 0.000 0.000 0.000
#> GSM99592 3 0.2291 0.83834 0.000 0.000 0.908 0.056 0.036
#> GSM99594 3 0.0898 0.86912 0.000 0.000 0.972 0.008 0.020
#> GSM99468 1 0.0794 0.86191 0.972 0.000 0.000 0.000 0.028
#> GSM99498 1 0.0703 0.86161 0.976 0.000 0.000 0.000 0.024
#> GSM99500 1 0.0510 0.86207 0.984 0.000 0.000 0.000 0.016
#> GSM99508 3 0.0000 0.87198 0.000 0.000 1.000 0.000 0.000
#> GSM99568 3 0.0290 0.87228 0.000 0.000 0.992 0.000 0.008
#> GSM99596 3 0.0566 0.87121 0.000 0.000 0.984 0.004 0.012
#> GSM99600 2 0.3305 0.66959 0.000 0.776 0.000 0.224 0.000
#> GSM99458 1 0.3970 0.65780 0.744 0.000 0.000 0.020 0.236
#> GSM99460 5 0.5016 0.18260 0.348 0.000 0.000 0.044 0.608
#> GSM99510 4 0.6586 -0.03057 0.000 0.000 0.384 0.408 0.208
#> GSM99512 3 0.4772 0.62205 0.000 0.000 0.728 0.108 0.164
#> GSM99514 3 0.0162 0.87258 0.000 0.000 0.996 0.000 0.004
#> GSM99516 1 0.0000 0.86146 1.000 0.000 0.000 0.000 0.000
#> GSM99518 1 0.1732 0.84068 0.920 0.000 0.000 0.000 0.080
#> GSM99520 3 0.1211 0.86702 0.000 0.000 0.960 0.024 0.016
#> GSM99522 3 0.2067 0.83562 0.044 0.000 0.924 0.004 0.028
#> GSM99570 1 0.0290 0.86011 0.992 0.000 0.000 0.000 0.008
#> GSM99598 1 0.0000 0.86146 1.000 0.000 0.000 0.000 0.000
#> GSM99432 4 0.4451 0.30545 0.000 0.340 0.000 0.644 0.016
#> GSM99434 4 0.6432 -0.05088 0.000 0.000 0.196 0.484 0.320
#> GSM99436 2 0.4235 0.30356 0.000 0.576 0.000 0.424 0.000
#> GSM99438 2 0.0510 0.81944 0.000 0.984 0.000 0.016 0.000
#> GSM99440 1 0.0703 0.86187 0.976 0.000 0.000 0.000 0.024
#> GSM99442 2 0.2488 0.76077 0.000 0.872 0.000 0.124 0.004
#> GSM99444 2 0.0404 0.81951 0.000 0.988 0.000 0.012 0.000
#> GSM99446 2 0.4088 0.42427 0.000 0.632 0.000 0.368 0.000
#> GSM99448 4 0.5576 0.18908 0.000 0.000 0.388 0.536 0.076
#> GSM99450 5 0.6824 0.00216 0.000 0.000 0.328 0.328 0.344
#> GSM99452 1 0.0963 0.86022 0.964 0.000 0.000 0.000 0.036
#> GSM99454 1 0.0404 0.86300 0.988 0.000 0.000 0.000 0.012
#> GSM99456 1 0.4390 0.43306 0.568 0.000 0.000 0.004 0.428
#> GSM99462 2 0.0510 0.81944 0.000 0.984 0.000 0.016 0.000
#> GSM99464 5 0.3864 0.37851 0.008 0.000 0.020 0.188 0.784
#> GSM99466 4 0.3882 0.49925 0.000 0.168 0.000 0.788 0.044
#> GSM99470 1 0.3623 0.76367 0.848 0.052 0.000 0.028 0.072
#> GSM99472 1 0.1331 0.85021 0.952 0.000 0.000 0.008 0.040
#> GSM99474 3 0.3317 0.78249 0.000 0.000 0.840 0.044 0.116
#> GSM99476 4 0.1918 0.43879 0.000 0.000 0.036 0.928 0.036
#> GSM99478 2 0.5148 0.20631 0.000 0.528 0.000 0.432 0.040
#> GSM99480 1 0.2891 0.78120 0.824 0.000 0.000 0.000 0.176
#> GSM99482 1 0.0955 0.85674 0.968 0.000 0.000 0.004 0.028
#> GSM99484 2 0.4141 0.64096 0.000 0.728 0.000 0.248 0.024
#> GSM99486 4 0.4557 -0.09861 0.000 0.476 0.000 0.516 0.008
#> GSM99488 2 0.0290 0.81768 0.000 0.992 0.000 0.000 0.008
#> GSM99490 2 0.0609 0.81353 0.000 0.980 0.000 0.000 0.020
#> GSM99492 1 0.3561 0.69912 0.740 0.000 0.000 0.000 0.260
#> GSM99494 2 0.0162 0.81836 0.000 0.996 0.000 0.000 0.004
#> GSM99524 1 0.0404 0.85914 0.988 0.000 0.000 0.000 0.012
#> GSM99526 5 0.4590 0.10963 0.000 0.000 0.012 0.420 0.568
#> GSM99528 2 0.6635 0.15436 0.000 0.484 0.004 0.228 0.284
#> GSM99530 5 0.5057 0.13239 0.016 0.000 0.384 0.016 0.584
#> GSM99532 3 0.4462 0.52929 0.004 0.000 0.672 0.016 0.308
#> GSM99534 2 0.1403 0.81017 0.000 0.952 0.000 0.024 0.024
#> GSM99536 1 0.2605 0.80128 0.852 0.000 0.000 0.000 0.148
#> GSM99538 4 0.5032 0.50116 0.000 0.168 0.000 0.704 0.128
#> GSM99540 1 0.4321 0.47780 0.600 0.000 0.000 0.004 0.396
#> GSM99542 2 0.0404 0.81662 0.000 0.988 0.000 0.000 0.012
#> GSM99544 4 0.4114 0.52920 0.000 0.164 0.000 0.776 0.060
#> GSM99546 4 0.5188 0.03797 0.000 0.044 0.000 0.540 0.416
#> GSM99548 2 0.0404 0.81672 0.000 0.988 0.000 0.000 0.012
#> GSM99550 5 0.4449 0.23946 0.288 0.004 0.000 0.020 0.688
#> GSM99552 3 0.3920 0.71672 0.000 0.004 0.796 0.156 0.044
#> GSM99554 2 0.4193 0.54739 0.000 0.684 0.000 0.304 0.012
#> GSM99556 2 0.0000 0.81895 0.000 1.000 0.000 0.000 0.000
#> GSM99558 4 0.6461 0.36611 0.000 0.108 0.288 0.568 0.036
#> GSM99560 2 0.5787 0.43945 0.000 0.608 0.000 0.240 0.152
#> GSM99562 3 0.0880 0.86686 0.000 0.000 0.968 0.000 0.032
#> GSM99564 4 0.4434 -0.03152 0.000 0.460 0.000 0.536 0.004
#> GSM99572 2 0.0510 0.81948 0.000 0.984 0.000 0.016 0.000
#> GSM99576 1 0.4450 0.28936 0.508 0.000 0.000 0.004 0.488
#> GSM99578 2 0.1818 0.80154 0.000 0.932 0.000 0.044 0.024
#> GSM99580 3 0.0798 0.87010 0.000 0.000 0.976 0.016 0.008
#> GSM99582 3 0.8009 -0.14294 0.348 0.000 0.360 0.180 0.112
#> GSM99584 4 0.3916 0.47767 0.000 0.092 0.000 0.804 0.104
#> GSM99586 1 0.4101 0.54500 0.628 0.000 0.000 0.000 0.372
#> GSM99588 2 0.1168 0.81490 0.000 0.960 0.000 0.032 0.008
#> GSM99590 2 0.0290 0.81974 0.000 0.992 0.000 0.008 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM99496 3 0.0405 0.8392 0.000 0.000 0.988 0.008 0.000 0.004
#> GSM99502 1 0.0291 0.7616 0.992 0.000 0.000 0.004 0.004 0.000
#> GSM99504 1 0.1542 0.7365 0.936 0.000 0.052 0.000 0.008 0.004
#> GSM99506 3 0.1180 0.8406 0.000 0.000 0.960 0.016 0.012 0.012
#> GSM99566 3 0.1409 0.8400 0.000 0.000 0.948 0.012 0.008 0.032
#> GSM99574 1 0.0363 0.7620 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM99592 3 0.4137 0.7293 0.000 0.000 0.780 0.068 0.032 0.120
#> GSM99594 3 0.2115 0.8347 0.000 0.000 0.916 0.020 0.032 0.032
#> GSM99468 1 0.1471 0.7510 0.932 0.000 0.000 0.000 0.064 0.004
#> GSM99498 1 0.1082 0.7588 0.956 0.000 0.000 0.000 0.040 0.004
#> GSM99500 1 0.1010 0.7597 0.960 0.000 0.000 0.000 0.036 0.004
#> GSM99508 3 0.0653 0.8390 0.000 0.000 0.980 0.004 0.004 0.012
#> GSM99568 3 0.1364 0.8389 0.000 0.000 0.952 0.012 0.020 0.016
#> GSM99596 3 0.0862 0.8401 0.000 0.000 0.972 0.004 0.008 0.016
#> GSM99600 2 0.3337 0.5596 0.000 0.736 0.000 0.260 0.000 0.004
#> GSM99458 1 0.5653 0.1521 0.584 0.000 0.000 0.012 0.212 0.192
#> GSM99460 5 0.6261 0.3443 0.232 0.000 0.000 0.012 0.424 0.332
#> GSM99510 6 0.5442 0.4204 0.000 0.000 0.312 0.128 0.004 0.556
#> GSM99512 3 0.5247 0.3499 0.000 0.000 0.560 0.044 0.032 0.364
#> GSM99514 3 0.0000 0.8390 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99516 1 0.0291 0.7612 0.992 0.000 0.000 0.004 0.004 0.000
#> GSM99518 1 0.2963 0.6647 0.828 0.000 0.000 0.004 0.152 0.016
#> GSM99520 3 0.2696 0.8190 0.000 0.000 0.884 0.032 0.032 0.052
#> GSM99522 3 0.3689 0.7365 0.068 0.000 0.808 0.008 0.004 0.112
#> GSM99570 1 0.1155 0.7545 0.956 0.000 0.000 0.004 0.036 0.004
#> GSM99598 1 0.0146 0.7606 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM99432 4 0.5401 0.4563 0.000 0.332 0.000 0.568 0.020 0.080
#> GSM99434 6 0.5178 0.5972 0.000 0.000 0.124 0.164 0.032 0.680
#> GSM99436 4 0.4179 0.0676 0.000 0.472 0.000 0.516 0.000 0.012
#> GSM99438 2 0.0632 0.7877 0.000 0.976 0.000 0.024 0.000 0.000
#> GSM99440 1 0.1267 0.7546 0.940 0.000 0.000 0.000 0.060 0.000
#> GSM99442 2 0.2814 0.6799 0.000 0.820 0.000 0.172 0.000 0.008
#> GSM99444 2 0.0865 0.7851 0.000 0.964 0.000 0.036 0.000 0.000
#> GSM99446 2 0.4051 0.1120 0.000 0.560 0.000 0.432 0.000 0.008
#> GSM99448 4 0.6678 -0.1817 0.000 0.008 0.336 0.388 0.020 0.248
#> GSM99450 6 0.5267 0.6016 0.004 0.000 0.224 0.060 0.048 0.664
#> GSM99452 1 0.2734 0.7151 0.840 0.000 0.000 0.008 0.148 0.004
#> GSM99454 1 0.0865 0.7637 0.964 0.000 0.000 0.000 0.036 0.000
#> GSM99456 5 0.4938 0.4696 0.356 0.000 0.000 0.000 0.568 0.076
#> GSM99462 2 0.0713 0.7871 0.000 0.972 0.000 0.028 0.000 0.000
#> GSM99464 6 0.4121 0.3046 0.004 0.000 0.004 0.004 0.384 0.604
#> GSM99466 4 0.4976 0.4789 0.000 0.100 0.000 0.724 0.092 0.084
#> GSM99470 1 0.6125 0.3947 0.636 0.048 0.000 0.076 0.188 0.052
#> GSM99472 1 0.3343 0.6694 0.812 0.000 0.000 0.040 0.144 0.004
#> GSM99474 3 0.4747 0.6888 0.000 0.000 0.732 0.040 0.100 0.128
#> GSM99476 4 0.5229 0.2794 0.000 0.012 0.032 0.644 0.044 0.268
#> GSM99478 4 0.6307 0.1924 0.000 0.392 0.000 0.448 0.088 0.072
#> GSM99480 1 0.3240 0.5645 0.752 0.000 0.000 0.000 0.244 0.004
#> GSM99482 1 0.2804 0.7087 0.852 0.000 0.000 0.024 0.120 0.004
#> GSM99484 2 0.5158 0.3184 0.000 0.584 0.000 0.340 0.052 0.024
#> GSM99486 4 0.4170 0.4290 0.000 0.328 0.000 0.648 0.004 0.020
#> GSM99488 2 0.0146 0.7860 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM99490 2 0.1078 0.7826 0.000 0.964 0.000 0.016 0.008 0.012
#> GSM99492 1 0.3965 0.1963 0.604 0.000 0.000 0.000 0.388 0.008
#> GSM99494 2 0.0146 0.7860 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM99524 1 0.1578 0.7428 0.936 0.000 0.000 0.012 0.048 0.004
#> GSM99526 6 0.4218 0.5905 0.000 0.000 0.000 0.108 0.156 0.736
#> GSM99528 2 0.7412 -0.1132 0.000 0.364 0.004 0.216 0.304 0.112
#> GSM99530 5 0.6251 -0.0638 0.004 0.000 0.236 0.032 0.540 0.188
#> GSM99532 3 0.6701 0.1844 0.020 0.000 0.476 0.024 0.204 0.276
#> GSM99534 2 0.3419 0.6922 0.000 0.840 0.000 0.056 0.040 0.064
#> GSM99536 1 0.3271 0.5683 0.760 0.000 0.000 0.000 0.232 0.008
#> GSM99538 4 0.6653 0.4048 0.000 0.184 0.016 0.516 0.040 0.244
#> GSM99540 1 0.5263 0.0283 0.556 0.000 0.000 0.012 0.356 0.076
#> GSM99542 2 0.1088 0.7722 0.000 0.960 0.000 0.016 0.024 0.000
#> GSM99544 4 0.5265 0.4911 0.000 0.148 0.000 0.640 0.012 0.200
#> GSM99546 6 0.5188 0.5462 0.000 0.032 0.000 0.156 0.132 0.680
#> GSM99548 2 0.0405 0.7859 0.000 0.988 0.000 0.008 0.004 0.000
#> GSM99550 5 0.4505 0.4430 0.120 0.000 0.000 0.012 0.732 0.136
#> GSM99552 3 0.5691 0.5452 0.000 0.008 0.652 0.192 0.076 0.072
#> GSM99554 2 0.4101 0.2265 0.000 0.580 0.000 0.408 0.000 0.012
#> GSM99556 2 0.0291 0.7869 0.000 0.992 0.000 0.004 0.000 0.004
#> GSM99558 4 0.6344 0.3116 0.000 0.064 0.232 0.596 0.044 0.064
#> GSM99560 2 0.6566 0.0108 0.000 0.472 0.000 0.328 0.120 0.080
#> GSM99562 3 0.2013 0.8245 0.000 0.000 0.908 0.008 0.008 0.076
#> GSM99564 4 0.3816 0.4803 0.000 0.296 0.000 0.688 0.000 0.016
#> GSM99572 2 0.0790 0.7882 0.000 0.968 0.000 0.032 0.000 0.000
#> GSM99576 5 0.4770 0.4737 0.328 0.000 0.000 0.012 0.616 0.044
#> GSM99578 2 0.2108 0.7651 0.000 0.912 0.000 0.056 0.016 0.016
#> GSM99580 3 0.2383 0.8226 0.000 0.000 0.900 0.028 0.020 0.052
#> GSM99582 1 0.8651 -0.2671 0.280 0.000 0.260 0.212 0.144 0.104
#> GSM99584 4 0.5124 0.3263 0.000 0.072 0.000 0.592 0.012 0.324
#> GSM99586 5 0.4246 0.2498 0.452 0.000 0.000 0.000 0.532 0.016
#> GSM99588 2 0.1728 0.7679 0.000 0.924 0.000 0.064 0.004 0.008
#> GSM99590 2 0.0713 0.7871 0.000 0.972 0.000 0.028 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) cell.type(p) k
#> CV:skmeans 84 4.99e-05 0.000264 2
#> CV:skmeans 84 1.32e-04 0.003853 3
#> CV:skmeans 75 4.71e-05 0.003285 4
#> CV:skmeans 59 5.15e-04 0.024792 5
#> CV:skmeans 53 3.08e-04 0.016645 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 21168 rows and 85 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 0.563 0.892 0.936 0.4474 0.570 0.570
#> 3 3 0.634 0.822 0.910 0.4707 0.762 0.583
#> 4 4 0.604 0.695 0.832 0.1037 0.922 0.778
#> 5 5 0.681 0.556 0.750 0.0816 0.835 0.498
#> 6 6 0.830 0.777 0.895 0.0538 0.902 0.588
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
#> GSM99496 2 0.6531 0.848 0.168 0.832
#> GSM99502 1 0.0000 0.981 1.000 0.000
#> GSM99504 1 0.0000 0.981 1.000 0.000
#> GSM99506 2 0.6438 0.850 0.164 0.836
#> GSM99566 2 0.6343 0.853 0.160 0.840
#> GSM99574 1 0.0000 0.981 1.000 0.000
#> GSM99592 2 0.5629 0.867 0.132 0.868
#> GSM99594 2 0.6438 0.850 0.164 0.836
#> GSM99468 1 0.0000 0.981 1.000 0.000
#> GSM99498 1 0.0000 0.981 1.000 0.000
#> GSM99500 1 0.0000 0.981 1.000 0.000
#> GSM99508 2 0.6623 0.845 0.172 0.828
#> GSM99568 2 0.6973 0.834 0.188 0.812
#> GSM99596 2 0.8713 0.718 0.292 0.708
#> GSM99600 2 0.0000 0.909 0.000 1.000
#> GSM99458 1 0.0000 0.981 1.000 0.000
#> GSM99460 1 0.0000 0.981 1.000 0.000
#> GSM99510 2 0.0000 0.909 0.000 1.000
#> GSM99512 2 0.1184 0.906 0.016 0.984
#> GSM99514 2 0.6531 0.848 0.168 0.832
#> GSM99516 1 0.0000 0.981 1.000 0.000
#> GSM99518 1 0.0000 0.981 1.000 0.000
#> GSM99520 2 0.6438 0.850 0.164 0.836
#> GSM99522 1 0.5629 0.817 0.868 0.132
#> GSM99570 1 0.0000 0.981 1.000 0.000
#> GSM99598 1 0.0000 0.981 1.000 0.000
#> GSM99432 2 0.0000 0.909 0.000 1.000
#> GSM99434 2 0.0000 0.909 0.000 1.000
#> GSM99436 2 0.0000 0.909 0.000 1.000
#> GSM99438 2 0.0000 0.909 0.000 1.000
#> GSM99440 1 0.0000 0.981 1.000 0.000
#> GSM99442 2 0.0000 0.909 0.000 1.000
#> GSM99444 2 0.0000 0.909 0.000 1.000
#> GSM99446 2 0.0000 0.909 0.000 1.000
#> GSM99448 2 0.0000 0.909 0.000 1.000
#> GSM99450 2 0.7602 0.804 0.220 0.780
#> GSM99452 1 0.0000 0.981 1.000 0.000
#> GSM99454 1 0.0000 0.981 1.000 0.000
#> GSM99456 1 0.0000 0.981 1.000 0.000
#> GSM99462 2 0.0000 0.909 0.000 1.000
#> GSM99464 2 0.8713 0.718 0.292 0.708
#> GSM99466 2 0.0000 0.909 0.000 1.000
#> GSM99470 1 0.8443 0.590 0.728 0.272
#> GSM99472 1 0.0938 0.969 0.988 0.012
#> GSM99474 2 0.7815 0.792 0.232 0.768
#> GSM99476 2 0.0000 0.909 0.000 1.000
#> GSM99478 2 0.0000 0.909 0.000 1.000
#> GSM99480 1 0.0000 0.981 1.000 0.000
#> GSM99482 1 0.0000 0.981 1.000 0.000
#> GSM99484 2 0.0000 0.909 0.000 1.000
#> GSM99486 2 0.0000 0.909 0.000 1.000
#> GSM99488 2 0.0000 0.909 0.000 1.000
#> GSM99490 2 0.0000 0.909 0.000 1.000
#> GSM99492 1 0.0000 0.981 1.000 0.000
#> GSM99494 2 0.0000 0.909 0.000 1.000
#> GSM99524 1 0.0000 0.981 1.000 0.000
#> GSM99526 2 0.0938 0.905 0.012 0.988
#> GSM99528 2 0.5294 0.872 0.120 0.880
#> GSM99530 2 0.6801 0.839 0.180 0.820
#> GSM99532 2 0.8555 0.735 0.280 0.720
#> GSM99534 2 0.5178 0.846 0.116 0.884
#> GSM99536 1 0.0000 0.981 1.000 0.000
#> GSM99538 2 0.0000 0.909 0.000 1.000
#> GSM99540 1 0.0000 0.981 1.000 0.000
#> GSM99542 2 0.6531 0.827 0.168 0.832
#> GSM99544 2 0.0000 0.909 0.000 1.000
#> GSM99546 2 0.5519 0.868 0.128 0.872
#> GSM99548 2 0.0000 0.909 0.000 1.000
#> GSM99550 2 0.8861 0.698 0.304 0.696
#> GSM99552 2 0.5737 0.865 0.136 0.864
#> GSM99554 2 0.0000 0.909 0.000 1.000
#> GSM99556 2 0.0000 0.909 0.000 1.000
#> GSM99558 2 0.0000 0.909 0.000 1.000
#> GSM99560 2 0.0000 0.909 0.000 1.000
#> GSM99562 2 0.6438 0.850 0.164 0.836
#> GSM99564 2 0.0000 0.909 0.000 1.000
#> GSM99572 2 0.0000 0.909 0.000 1.000
#> GSM99576 2 0.9963 0.345 0.464 0.536
#> GSM99578 2 0.0000 0.909 0.000 1.000
#> GSM99580 2 0.6438 0.850 0.164 0.836
#> GSM99582 2 0.8608 0.729 0.284 0.716
#> GSM99584 2 0.0000 0.909 0.000 1.000
#> GSM99586 1 0.0000 0.981 1.000 0.000
#> GSM99588 2 0.0000 0.909 0.000 1.000
#> GSM99590 2 0.0000 0.909 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM99496 3 0.0000 0.8546 0.000 0.000 1.000
#> GSM99502 1 0.0000 0.9588 1.000 0.000 0.000
#> GSM99504 1 0.0000 0.9588 1.000 0.000 0.000
#> GSM99506 3 0.0000 0.8546 0.000 0.000 1.000
#> GSM99566 3 0.0000 0.8546 0.000 0.000 1.000
#> GSM99574 1 0.0000 0.9588 1.000 0.000 0.000
#> GSM99592 3 0.0000 0.8546 0.000 0.000 1.000
#> GSM99594 3 0.0000 0.8546 0.000 0.000 1.000
#> GSM99468 1 0.0000 0.9588 1.000 0.000 0.000
#> GSM99498 1 0.0000 0.9588 1.000 0.000 0.000
#> GSM99500 1 0.0000 0.9588 1.000 0.000 0.000
#> GSM99508 3 0.0424 0.8529 0.008 0.000 0.992
#> GSM99568 3 0.1289 0.8444 0.032 0.000 0.968
#> GSM99596 3 0.3340 0.7933 0.120 0.000 0.880
#> GSM99600 2 0.1163 0.8789 0.000 0.972 0.028
#> GSM99458 1 0.0000 0.9588 1.000 0.000 0.000
#> GSM99460 1 0.2537 0.8904 0.920 0.000 0.080
#> GSM99510 3 0.0424 0.8522 0.000 0.008 0.992
#> GSM99512 3 0.0000 0.8546 0.000 0.000 1.000
#> GSM99514 3 0.0000 0.8546 0.000 0.000 1.000
#> GSM99516 1 0.0000 0.9588 1.000 0.000 0.000
#> GSM99518 1 0.0000 0.9588 1.000 0.000 0.000
#> GSM99520 3 0.0000 0.8546 0.000 0.000 1.000
#> GSM99522 1 0.6095 0.3904 0.608 0.000 0.392
#> GSM99570 1 0.0000 0.9588 1.000 0.000 0.000
#> GSM99598 1 0.0000 0.9588 1.000 0.000 0.000
#> GSM99432 2 0.4654 0.8008 0.000 0.792 0.208
#> GSM99434 3 0.0000 0.8546 0.000 0.000 1.000
#> GSM99436 2 0.0000 0.8800 0.000 1.000 0.000
#> GSM99438 2 0.0000 0.8800 0.000 1.000 0.000
#> GSM99440 1 0.0000 0.9588 1.000 0.000 0.000
#> GSM99442 2 0.3482 0.8458 0.000 0.872 0.128
#> GSM99444 2 0.1964 0.8602 0.000 0.944 0.056
#> GSM99446 2 0.4452 0.8122 0.000 0.808 0.192
#> GSM99448 3 0.0000 0.8546 0.000 0.000 1.000
#> GSM99450 3 0.3267 0.8028 0.116 0.000 0.884
#> GSM99452 1 0.0000 0.9588 1.000 0.000 0.000
#> GSM99454 1 0.0000 0.9588 1.000 0.000 0.000
#> GSM99456 1 0.0000 0.9588 1.000 0.000 0.000
#> GSM99462 2 0.0000 0.8800 0.000 1.000 0.000
#> GSM99464 3 0.4235 0.7586 0.176 0.000 0.824
#> GSM99466 3 0.5098 0.6455 0.000 0.248 0.752
#> GSM99470 1 0.7807 0.5725 0.672 0.144 0.184
#> GSM99472 1 0.1860 0.9112 0.948 0.052 0.000
#> GSM99474 3 0.4346 0.7554 0.184 0.000 0.816
#> GSM99476 3 0.5560 0.5565 0.000 0.300 0.700
#> GSM99478 3 0.5098 0.6456 0.000 0.248 0.752
#> GSM99480 1 0.0000 0.9588 1.000 0.000 0.000
#> GSM99482 1 0.0000 0.9588 1.000 0.000 0.000
#> GSM99484 3 0.5327 0.6084 0.000 0.272 0.728
#> GSM99486 2 0.4796 0.7895 0.000 0.780 0.220
#> GSM99488 2 0.0000 0.8800 0.000 1.000 0.000
#> GSM99490 2 0.0000 0.8800 0.000 1.000 0.000
#> GSM99492 1 0.0000 0.9588 1.000 0.000 0.000
#> GSM99494 2 0.0000 0.8800 0.000 1.000 0.000
#> GSM99524 1 0.0000 0.9588 1.000 0.000 0.000
#> GSM99526 2 0.5708 0.7886 0.028 0.768 0.204
#> GSM99528 3 0.5780 0.7492 0.080 0.120 0.800
#> GSM99530 3 0.0892 0.8491 0.020 0.000 0.980
#> GSM99532 3 0.3340 0.7936 0.120 0.000 0.880
#> GSM99534 2 0.2959 0.8288 0.100 0.900 0.000
#> GSM99536 1 0.0000 0.9588 1.000 0.000 0.000
#> GSM99538 3 0.5216 0.6278 0.000 0.260 0.740
#> GSM99540 1 0.3879 0.8113 0.848 0.000 0.152
#> GSM99542 2 0.1529 0.8575 0.040 0.960 0.000
#> GSM99544 3 0.6302 -0.0108 0.000 0.480 0.520
#> GSM99546 2 0.7393 0.7107 0.140 0.704 0.156
#> GSM99548 2 0.0000 0.8800 0.000 1.000 0.000
#> GSM99550 3 0.9328 0.4405 0.232 0.248 0.520
#> GSM99552 3 0.0000 0.8546 0.000 0.000 1.000
#> GSM99554 2 0.2537 0.8665 0.000 0.920 0.080
#> GSM99556 2 0.0000 0.8800 0.000 1.000 0.000
#> GSM99558 3 0.0892 0.8468 0.000 0.020 0.980
#> GSM99560 2 0.4702 0.7974 0.000 0.788 0.212
#> GSM99562 3 0.0000 0.8546 0.000 0.000 1.000
#> GSM99564 2 0.4750 0.7936 0.000 0.784 0.216
#> GSM99572 2 0.0000 0.8800 0.000 1.000 0.000
#> GSM99576 3 0.5948 0.4730 0.360 0.000 0.640
#> GSM99578 2 0.5785 0.5968 0.000 0.668 0.332
#> GSM99580 3 0.0000 0.8546 0.000 0.000 1.000
#> GSM99582 3 0.4605 0.7330 0.204 0.000 0.796
#> GSM99584 2 0.4842 0.7852 0.000 0.776 0.224
#> GSM99586 1 0.0000 0.9588 1.000 0.000 0.000
#> GSM99588 3 0.5058 0.6516 0.000 0.244 0.756
#> GSM99590 2 0.0000 0.8800 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM99496 3 0.0000 0.79805 0.000 0.000 1.000 0.000
#> GSM99502 1 0.0000 0.81227 1.000 0.000 0.000 0.000
#> GSM99504 1 0.0779 0.80835 0.980 0.000 0.004 0.016
#> GSM99506 3 0.0000 0.79805 0.000 0.000 1.000 0.000
#> GSM99566 3 0.0000 0.79805 0.000 0.000 1.000 0.000
#> GSM99574 1 0.0000 0.81227 1.000 0.000 0.000 0.000
#> GSM99592 3 0.1389 0.80520 0.000 0.000 0.952 0.048
#> GSM99594 3 0.0336 0.80007 0.000 0.000 0.992 0.008
#> GSM99468 1 0.2760 0.75805 0.872 0.000 0.000 0.128
#> GSM99498 1 0.2760 0.75805 0.872 0.000 0.000 0.128
#> GSM99500 1 0.1557 0.80023 0.944 0.000 0.000 0.056
#> GSM99508 3 0.1356 0.78139 0.008 0.000 0.960 0.032
#> GSM99568 3 0.1118 0.78376 0.000 0.000 0.964 0.036
#> GSM99596 3 0.3392 0.67519 0.020 0.000 0.856 0.124
#> GSM99600 2 0.1297 0.81330 0.000 0.964 0.016 0.020
#> GSM99458 1 0.4605 0.46295 0.664 0.000 0.000 0.336
#> GSM99460 4 0.4617 0.72272 0.204 0.000 0.032 0.764
#> GSM99510 3 0.2053 0.80452 0.000 0.004 0.924 0.072
#> GSM99512 3 0.0000 0.79805 0.000 0.000 1.000 0.000
#> GSM99514 3 0.0336 0.80026 0.000 0.000 0.992 0.008
#> GSM99516 1 0.0000 0.81227 1.000 0.000 0.000 0.000
#> GSM99518 1 0.2868 0.75915 0.864 0.000 0.000 0.136
#> GSM99520 3 0.1940 0.80341 0.000 0.000 0.924 0.076
#> GSM99522 3 0.7449 -0.25922 0.356 0.000 0.464 0.180
#> GSM99570 1 0.0000 0.81227 1.000 0.000 0.000 0.000
#> GSM99598 1 0.0000 0.81227 1.000 0.000 0.000 0.000
#> GSM99432 2 0.5396 0.74136 0.000 0.740 0.156 0.104
#> GSM99434 3 0.4103 0.75504 0.000 0.000 0.744 0.256
#> GSM99436 2 0.0592 0.81018 0.000 0.984 0.000 0.016
#> GSM99438 2 0.0707 0.80639 0.000 0.980 0.000 0.020
#> GSM99440 1 0.0000 0.81227 1.000 0.000 0.000 0.000
#> GSM99442 2 0.3674 0.79268 0.000 0.852 0.104 0.044
#> GSM99444 2 0.2385 0.79318 0.000 0.920 0.052 0.028
#> GSM99446 2 0.4614 0.76832 0.000 0.792 0.144 0.064
#> GSM99448 3 0.2921 0.79497 0.000 0.000 0.860 0.140
#> GSM99450 3 0.3653 0.70565 0.028 0.000 0.844 0.128
#> GSM99452 1 0.2408 0.77014 0.896 0.000 0.000 0.104
#> GSM99454 1 0.0188 0.81205 0.996 0.000 0.000 0.004
#> GSM99456 4 0.4193 0.66440 0.268 0.000 0.000 0.732
#> GSM99462 2 0.0707 0.80639 0.000 0.980 0.000 0.020
#> GSM99464 4 0.5383 0.60470 0.036 0.000 0.292 0.672
#> GSM99466 3 0.6521 0.66658 0.000 0.124 0.620 0.256
#> GSM99470 1 0.8678 -0.23060 0.400 0.092 0.116 0.392
#> GSM99472 1 0.4678 0.58162 0.744 0.024 0.000 0.232
#> GSM99474 3 0.5395 0.73248 0.084 0.000 0.732 0.184
#> GSM99476 3 0.6975 0.58968 0.000 0.200 0.584 0.216
#> GSM99478 3 0.6538 0.66937 0.000 0.140 0.628 0.232
#> GSM99480 1 0.2149 0.75442 0.912 0.000 0.000 0.088
#> GSM99482 1 0.2149 0.77470 0.912 0.000 0.000 0.088
#> GSM99484 3 0.6672 0.64516 0.000 0.168 0.620 0.212
#> GSM99486 2 0.5325 0.74120 0.000 0.744 0.160 0.096
#> GSM99488 2 0.1022 0.80505 0.000 0.968 0.000 0.032
#> GSM99490 2 0.0469 0.81133 0.000 0.988 0.000 0.012
#> GSM99492 1 0.4972 -0.11908 0.544 0.000 0.000 0.456
#> GSM99494 2 0.0707 0.80639 0.000 0.980 0.000 0.020
#> GSM99524 1 0.0000 0.81227 1.000 0.000 0.000 0.000
#> GSM99526 2 0.6022 0.67370 0.004 0.668 0.076 0.252
#> GSM99528 3 0.5454 0.69324 0.028 0.004 0.664 0.304
#> GSM99530 3 0.1389 0.78528 0.000 0.000 0.952 0.048
#> GSM99532 3 0.2635 0.73146 0.020 0.000 0.904 0.076
#> GSM99534 2 0.4720 0.65577 0.016 0.720 0.000 0.264
#> GSM99536 1 0.2868 0.75370 0.864 0.000 0.000 0.136
#> GSM99538 3 0.6683 0.61824 0.000 0.204 0.620 0.176
#> GSM99540 1 0.7232 0.13581 0.516 0.000 0.164 0.320
#> GSM99542 2 0.3610 0.68562 0.000 0.800 0.000 0.200
#> GSM99544 2 0.7251 -0.00348 0.000 0.440 0.416 0.144
#> GSM99546 2 0.7068 0.51612 0.032 0.556 0.064 0.348
#> GSM99548 2 0.0817 0.80574 0.000 0.976 0.000 0.024
#> GSM99550 4 0.3363 0.71185 0.072 0.024 0.020 0.884
#> GSM99552 3 0.3801 0.76786 0.000 0.000 0.780 0.220
#> GSM99554 2 0.2675 0.81047 0.000 0.908 0.048 0.044
#> GSM99556 2 0.2149 0.78374 0.000 0.912 0.000 0.088
#> GSM99558 3 0.3852 0.77806 0.000 0.008 0.800 0.192
#> GSM99560 2 0.5321 0.75622 0.000 0.748 0.112 0.140
#> GSM99562 3 0.0000 0.79805 0.000 0.000 1.000 0.000
#> GSM99564 2 0.5141 0.74832 0.000 0.756 0.160 0.084
#> GSM99572 2 0.0707 0.80639 0.000 0.980 0.000 0.020
#> GSM99576 4 0.5066 0.67626 0.112 0.000 0.120 0.768
#> GSM99578 2 0.6500 0.56911 0.000 0.620 0.260 0.120
#> GSM99580 3 0.2408 0.80088 0.000 0.000 0.896 0.104
#> GSM99582 3 0.6293 0.59911 0.096 0.000 0.628 0.276
#> GSM99584 2 0.5574 0.74574 0.000 0.728 0.124 0.148
#> GSM99586 4 0.4454 0.60426 0.308 0.000 0.000 0.692
#> GSM99588 3 0.6403 0.68039 0.000 0.128 0.640 0.232
#> GSM99590 2 0.0336 0.80880 0.000 0.992 0.000 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM99496 3 0.0000 0.833 0.000 0.000 1.000 0.000 0.000
#> GSM99502 1 0.0000 0.876 1.000 0.000 0.000 0.000 0.000
#> GSM99504 1 0.0404 0.874 0.988 0.000 0.000 0.000 0.012
#> GSM99506 3 0.0000 0.833 0.000 0.000 1.000 0.000 0.000
#> GSM99566 3 0.0000 0.833 0.000 0.000 1.000 0.000 0.000
#> GSM99574 1 0.0000 0.876 1.000 0.000 0.000 0.000 0.000
#> GSM99592 3 0.3932 0.358 0.000 0.000 0.672 0.328 0.000
#> GSM99594 3 0.1478 0.794 0.000 0.000 0.936 0.064 0.000
#> GSM99468 1 0.1965 0.839 0.904 0.000 0.000 0.000 0.096
#> GSM99498 1 0.1965 0.839 0.904 0.000 0.000 0.000 0.096
#> GSM99500 1 0.1197 0.865 0.952 0.000 0.000 0.000 0.048
#> GSM99508 3 0.0703 0.826 0.000 0.000 0.976 0.000 0.024
#> GSM99568 3 0.0703 0.826 0.000 0.000 0.976 0.000 0.024
#> GSM99596 3 0.1792 0.776 0.000 0.000 0.916 0.000 0.084
#> GSM99600 2 0.4508 0.667 0.000 0.648 0.000 0.332 0.020
#> GSM99458 1 0.4273 0.254 0.552 0.000 0.000 0.000 0.448
#> GSM99460 5 0.0955 0.660 0.028 0.000 0.004 0.000 0.968
#> GSM99510 3 0.3636 0.487 0.000 0.000 0.728 0.272 0.000
#> GSM99512 3 0.0162 0.832 0.000 0.000 0.996 0.004 0.000
#> GSM99514 3 0.0703 0.824 0.000 0.000 0.976 0.024 0.000
#> GSM99516 1 0.0000 0.876 1.000 0.000 0.000 0.000 0.000
#> GSM99518 1 0.3143 0.726 0.796 0.000 0.000 0.000 0.204
#> GSM99520 3 0.4171 0.172 0.000 0.000 0.604 0.396 0.000
#> GSM99522 3 0.3644 0.643 0.096 0.000 0.824 0.000 0.080
#> GSM99570 1 0.0000 0.876 1.000 0.000 0.000 0.000 0.000
#> GSM99598 1 0.0000 0.876 1.000 0.000 0.000 0.000 0.000
#> GSM99432 4 0.4781 -0.378 0.000 0.428 0.000 0.552 0.020
#> GSM99434 4 0.5086 0.469 0.000 0.000 0.304 0.636 0.060
#> GSM99436 2 0.4473 0.672 0.000 0.656 0.000 0.324 0.020
#> GSM99438 2 0.0000 0.756 0.000 1.000 0.000 0.000 0.000
#> GSM99440 1 0.0000 0.876 1.000 0.000 0.000 0.000 0.000
#> GSM99442 2 0.5334 0.595 0.000 0.588 0.028 0.364 0.020
#> GSM99444 2 0.0609 0.747 0.000 0.980 0.000 0.020 0.000
#> GSM99446 2 0.4830 0.444 0.000 0.492 0.000 0.488 0.020
#> GSM99448 4 0.4088 0.408 0.000 0.000 0.368 0.632 0.000
#> GSM99450 3 0.3160 0.666 0.000 0.000 0.808 0.004 0.188
#> GSM99452 1 0.2648 0.776 0.848 0.000 0.000 0.000 0.152
#> GSM99454 1 0.0290 0.875 0.992 0.000 0.000 0.000 0.008
#> GSM99456 5 0.1043 0.657 0.040 0.000 0.000 0.000 0.960
#> GSM99462 2 0.0000 0.756 0.000 1.000 0.000 0.000 0.000
#> GSM99464 3 0.4397 0.163 0.004 0.000 0.564 0.000 0.432
#> GSM99466 4 0.4042 0.553 0.000 0.000 0.212 0.756 0.032
#> GSM99470 5 0.8216 0.222 0.328 0.088 0.056 0.092 0.436
#> GSM99472 1 0.4444 0.389 0.624 0.000 0.000 0.012 0.364
#> GSM99474 4 0.4892 0.480 0.008 0.000 0.304 0.656 0.032
#> GSM99476 4 0.5152 0.546 0.000 0.064 0.200 0.712 0.024
#> GSM99478 4 0.3789 0.551 0.000 0.000 0.224 0.760 0.016
#> GSM99480 1 0.2127 0.798 0.892 0.000 0.000 0.000 0.108
#> GSM99482 1 0.2329 0.799 0.876 0.000 0.000 0.000 0.124
#> GSM99484 4 0.4065 0.556 0.000 0.020 0.212 0.760 0.008
#> GSM99486 4 0.4767 -0.361 0.000 0.420 0.000 0.560 0.020
#> GSM99488 2 0.0290 0.754 0.000 0.992 0.000 0.008 0.000
#> GSM99490 2 0.4437 0.683 0.000 0.664 0.000 0.316 0.020
#> GSM99492 5 0.4242 0.111 0.428 0.000 0.000 0.000 0.572
#> GSM99494 2 0.0000 0.756 0.000 1.000 0.000 0.000 0.000
#> GSM99524 1 0.0000 0.876 1.000 0.000 0.000 0.000 0.000
#> GSM99526 2 0.6728 0.402 0.000 0.416 0.000 0.276 0.308
#> GSM99528 4 0.4898 0.515 0.000 0.000 0.248 0.684 0.068
#> GSM99530 3 0.1965 0.810 0.000 0.000 0.924 0.052 0.024
#> GSM99532 3 0.0162 0.833 0.000 0.000 0.996 0.004 0.000
#> GSM99534 2 0.6773 0.336 0.000 0.380 0.000 0.276 0.344
#> GSM99536 1 0.2074 0.835 0.896 0.000 0.000 0.000 0.104
#> GSM99538 4 0.3487 0.556 0.000 0.008 0.212 0.780 0.000
#> GSM99540 5 0.6324 0.151 0.156 0.000 0.412 0.000 0.432
#> GSM99542 2 0.1670 0.707 0.000 0.936 0.000 0.012 0.052
#> GSM99544 4 0.4823 0.402 0.000 0.156 0.096 0.740 0.008
#> GSM99546 5 0.6719 -0.384 0.000 0.372 0.000 0.248 0.380
#> GSM99548 2 0.0290 0.754 0.000 0.992 0.000 0.008 0.000
#> GSM99550 5 0.0693 0.659 0.008 0.000 0.000 0.012 0.980
#> GSM99552 4 0.4348 0.476 0.000 0.000 0.316 0.668 0.016
#> GSM99554 2 0.4626 0.636 0.000 0.616 0.000 0.364 0.020
#> GSM99556 2 0.0404 0.752 0.000 0.988 0.000 0.012 0.000
#> GSM99558 4 0.4165 0.473 0.000 0.000 0.320 0.672 0.008
#> GSM99560 4 0.5721 -0.436 0.000 0.424 0.000 0.492 0.084
#> GSM99562 3 0.0000 0.833 0.000 0.000 1.000 0.000 0.000
#> GSM99564 4 0.4798 -0.398 0.000 0.440 0.000 0.540 0.020
#> GSM99572 2 0.0000 0.756 0.000 1.000 0.000 0.000 0.000
#> GSM99576 5 0.3349 0.625 0.016 0.000 0.052 0.072 0.860
#> GSM99578 4 0.5858 -0.123 0.000 0.348 0.064 0.568 0.020
#> GSM99580 4 0.4287 0.213 0.000 0.000 0.460 0.540 0.000
#> GSM99582 4 0.6686 0.148 0.012 0.000 0.400 0.428 0.160
#> GSM99584 4 0.6158 -0.455 0.000 0.416 0.000 0.452 0.132
#> GSM99586 5 0.2377 0.600 0.128 0.000 0.000 0.000 0.872
#> GSM99588 4 0.4153 0.545 0.000 0.008 0.236 0.740 0.016
#> GSM99590 2 0.2690 0.741 0.000 0.844 0.000 0.156 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM99496 3 0.0363 0.8771 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM99502 1 0.0000 0.8659 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99504 1 0.0870 0.8619 0.972 0.000 0.012 0.000 0.004 0.012
#> GSM99506 3 0.0458 0.8774 0.000 0.000 0.984 0.000 0.000 0.016
#> GSM99566 3 0.0547 0.8768 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM99574 1 0.0000 0.8659 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99592 6 0.3847 0.2161 0.000 0.000 0.456 0.000 0.000 0.544
#> GSM99594 3 0.2378 0.7714 0.000 0.000 0.848 0.000 0.000 0.152
#> GSM99468 1 0.1585 0.8571 0.940 0.000 0.012 0.000 0.036 0.012
#> GSM99498 1 0.1585 0.8571 0.940 0.000 0.012 0.000 0.036 0.012
#> GSM99500 1 0.1511 0.8583 0.944 0.000 0.012 0.000 0.032 0.012
#> GSM99508 3 0.0146 0.8755 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM99568 3 0.0146 0.8745 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM99596 3 0.0000 0.8736 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99600 4 0.0363 0.9000 0.000 0.012 0.000 0.988 0.000 0.000
#> GSM99458 1 0.3945 0.4427 0.612 0.000 0.000 0.008 0.380 0.000
#> GSM99460 5 0.0260 0.8527 0.000 0.000 0.000 0.008 0.992 0.000
#> GSM99510 3 0.3727 0.3752 0.000 0.000 0.612 0.000 0.000 0.388
#> GSM99512 3 0.0790 0.8750 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM99514 3 0.1387 0.8553 0.000 0.000 0.932 0.000 0.000 0.068
#> GSM99516 1 0.0000 0.8659 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99518 1 0.3231 0.7442 0.800 0.000 0.008 0.000 0.180 0.012
#> GSM99520 6 0.3706 0.4528 0.000 0.000 0.380 0.000 0.000 0.620
#> GSM99522 3 0.0405 0.8722 0.000 0.000 0.988 0.000 0.004 0.008
#> GSM99570 1 0.0000 0.8659 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99598 1 0.0000 0.8659 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99432 4 0.0937 0.8925 0.000 0.000 0.000 0.960 0.000 0.040
#> GSM99434 6 0.1010 0.8342 0.000 0.000 0.036 0.000 0.004 0.960
#> GSM99436 4 0.0363 0.9003 0.000 0.012 0.000 0.988 0.000 0.000
#> GSM99438 2 0.0937 0.9043 0.000 0.960 0.000 0.040 0.000 0.000
#> GSM99440 1 0.0000 0.8659 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99442 4 0.2190 0.8594 0.000 0.040 0.000 0.900 0.000 0.060
#> GSM99444 2 0.0363 0.9124 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM99446 4 0.0291 0.9006 0.000 0.004 0.000 0.992 0.000 0.004
#> GSM99448 6 0.1387 0.8263 0.000 0.000 0.068 0.000 0.000 0.932
#> GSM99450 3 0.3594 0.7140 0.000 0.000 0.780 0.008 0.184 0.028
#> GSM99452 1 0.2734 0.7802 0.840 0.000 0.004 0.000 0.148 0.008
#> GSM99454 1 0.0260 0.8655 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM99456 5 0.0260 0.8527 0.000 0.000 0.000 0.008 0.992 0.000
#> GSM99462 2 0.0146 0.9130 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM99464 3 0.3421 0.6332 0.000 0.000 0.736 0.008 0.256 0.000
#> GSM99466 6 0.0458 0.8361 0.000 0.000 0.000 0.016 0.000 0.984
#> GSM99470 1 0.7297 -0.1306 0.348 0.000 0.000 0.132 0.344 0.176
#> GSM99472 1 0.4161 0.4827 0.632 0.000 0.000 0.016 0.348 0.004
#> GSM99474 6 0.1003 0.8341 0.000 0.000 0.016 0.000 0.020 0.964
#> GSM99476 6 0.2416 0.7533 0.000 0.000 0.000 0.156 0.000 0.844
#> GSM99478 6 0.0405 0.8387 0.000 0.000 0.004 0.008 0.000 0.988
#> GSM99480 1 0.2048 0.7748 0.880 0.000 0.000 0.000 0.120 0.000
#> GSM99482 1 0.1910 0.8092 0.892 0.000 0.000 0.000 0.108 0.000
#> GSM99484 6 0.2340 0.7737 0.000 0.000 0.000 0.148 0.000 0.852
#> GSM99486 4 0.0260 0.9006 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM99488 2 0.0000 0.9113 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99490 4 0.1908 0.8496 0.000 0.096 0.000 0.900 0.000 0.004
#> GSM99492 5 0.3804 0.4449 0.336 0.000 0.000 0.000 0.656 0.008
#> GSM99494 2 0.0000 0.9113 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99524 1 0.0000 0.8659 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99526 4 0.2762 0.7534 0.000 0.000 0.000 0.804 0.196 0.000
#> GSM99528 6 0.0260 0.8389 0.000 0.000 0.008 0.000 0.000 0.992
#> GSM99530 3 0.2340 0.7708 0.000 0.000 0.852 0.000 0.000 0.148
#> GSM99532 3 0.0865 0.8742 0.000 0.000 0.964 0.000 0.000 0.036
#> GSM99534 4 0.3023 0.7050 0.000 0.000 0.000 0.768 0.232 0.000
#> GSM99536 1 0.1657 0.8563 0.936 0.000 0.012 0.000 0.040 0.012
#> GSM99538 6 0.1141 0.8282 0.000 0.000 0.000 0.052 0.000 0.948
#> GSM99540 3 0.4512 0.3955 0.024 0.000 0.616 0.000 0.348 0.012
#> GSM99542 2 0.0146 0.9097 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM99544 6 0.3706 0.3850 0.000 0.000 0.000 0.380 0.000 0.620
#> GSM99546 4 0.3915 0.6086 0.000 0.000 0.004 0.692 0.288 0.016
#> GSM99548 2 0.0937 0.9043 0.000 0.960 0.000 0.040 0.000 0.000
#> GSM99550 5 0.0291 0.8529 0.000 0.000 0.000 0.004 0.992 0.004
#> GSM99552 6 0.0363 0.8397 0.000 0.000 0.012 0.000 0.000 0.988
#> GSM99554 4 0.0790 0.8950 0.000 0.032 0.000 0.968 0.000 0.000
#> GSM99556 2 0.0260 0.9136 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM99558 6 0.0547 0.8404 0.000 0.000 0.020 0.000 0.000 0.980
#> GSM99560 4 0.0260 0.9006 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM99562 3 0.0458 0.8773 0.000 0.000 0.984 0.000 0.000 0.016
#> GSM99564 4 0.0260 0.9006 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM99572 2 0.0937 0.9043 0.000 0.960 0.000 0.040 0.000 0.000
#> GSM99576 5 0.2709 0.7579 0.000 0.000 0.020 0.000 0.848 0.132
#> GSM99578 4 0.2597 0.7570 0.000 0.000 0.000 0.824 0.000 0.176
#> GSM99580 6 0.2762 0.7384 0.000 0.000 0.196 0.000 0.000 0.804
#> GSM99582 6 0.4858 0.5908 0.000 0.000 0.180 0.000 0.156 0.664
#> GSM99584 4 0.1196 0.8884 0.000 0.000 0.000 0.952 0.040 0.008
#> GSM99586 5 0.1700 0.8208 0.080 0.000 0.000 0.000 0.916 0.004
#> GSM99588 6 0.0405 0.8395 0.000 0.000 0.008 0.004 0.000 0.988
#> GSM99590 2 0.3867 -0.0122 0.000 0.512 0.000 0.488 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) cell.type(p) k
#> CV:pam 84 2.30e-02 0.04396 2
#> CV:pam 81 1.67e-03 0.02369 3
#> CV:pam 79 1.46e-03 0.04433 4
#> CV:pam 58 3.15e-04 0.02751 5
#> CV:pam 75 1.08e-05 0.00434 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 21168 rows and 85 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.290 0.807 0.841 0.4366 0.545 0.545
#> 3 3 0.785 0.760 0.905 0.5069 0.752 0.557
#> 4 4 0.675 0.753 0.845 0.0952 0.859 0.622
#> 5 5 0.823 0.754 0.893 0.0974 0.853 0.541
#> 6 6 0.802 0.755 0.864 0.0295 0.959 0.818
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
#> GSM99496 2 0.5519 0.697 0.128 0.872
#> GSM99502 1 0.0000 0.950 1.000 0.000
#> GSM99504 1 0.0376 0.947 0.996 0.004
#> GSM99506 2 0.5519 0.697 0.128 0.872
#> GSM99566 2 0.5519 0.697 0.128 0.872
#> GSM99574 1 0.0000 0.950 1.000 0.000
#> GSM99592 2 0.5519 0.697 0.128 0.872
#> GSM99594 2 0.5519 0.697 0.128 0.872
#> GSM99468 1 0.0000 0.950 1.000 0.000
#> GSM99498 1 0.0000 0.950 1.000 0.000
#> GSM99500 1 0.0000 0.950 1.000 0.000
#> GSM99508 2 0.5519 0.697 0.128 0.872
#> GSM99568 2 0.5519 0.697 0.128 0.872
#> GSM99596 2 0.6887 0.721 0.184 0.816
#> GSM99600 2 0.8207 0.809 0.256 0.744
#> GSM99458 1 0.2948 0.922 0.948 0.052
#> GSM99460 1 0.2948 0.922 0.948 0.052
#> GSM99510 2 0.2423 0.721 0.040 0.960
#> GSM99512 2 0.4690 0.717 0.100 0.900
#> GSM99514 2 0.6801 0.719 0.180 0.820
#> GSM99516 1 0.0000 0.950 1.000 0.000
#> GSM99518 1 0.0000 0.950 1.000 0.000
#> GSM99520 2 0.5519 0.697 0.128 0.872
#> GSM99522 2 0.9209 0.699 0.336 0.664
#> GSM99570 1 0.0376 0.947 0.996 0.004
#> GSM99598 1 0.0000 0.950 1.000 0.000
#> GSM99432 2 0.8016 0.809 0.244 0.756
#> GSM99434 2 0.1843 0.721 0.028 0.972
#> GSM99436 2 0.8207 0.809 0.256 0.744
#> GSM99438 2 0.8207 0.809 0.256 0.744
#> GSM99440 1 0.0000 0.950 1.000 0.000
#> GSM99442 2 0.8207 0.809 0.256 0.744
#> GSM99444 2 0.8207 0.809 0.256 0.744
#> GSM99446 2 0.8207 0.809 0.256 0.744
#> GSM99448 2 0.4431 0.720 0.092 0.908
#> GSM99450 2 0.5408 0.691 0.124 0.876
#> GSM99452 1 0.1184 0.938 0.984 0.016
#> GSM99454 1 0.0000 0.950 1.000 0.000
#> GSM99456 1 0.2948 0.922 0.948 0.052
#> GSM99462 2 0.8207 0.809 0.256 0.744
#> GSM99464 1 0.8499 0.549 0.724 0.276
#> GSM99466 2 0.8016 0.809 0.244 0.756
#> GSM99470 1 0.6048 0.783 0.852 0.148
#> GSM99472 1 0.2778 0.925 0.952 0.048
#> GSM99474 2 0.5946 0.705 0.144 0.856
#> GSM99476 2 0.1414 0.720 0.020 0.980
#> GSM99478 2 0.8081 0.810 0.248 0.752
#> GSM99480 1 0.0000 0.950 1.000 0.000
#> GSM99482 1 0.1184 0.938 0.984 0.016
#> GSM99484 2 0.8207 0.809 0.256 0.744
#> GSM99486 2 0.8081 0.810 0.248 0.752
#> GSM99488 2 0.8207 0.809 0.256 0.744
#> GSM99490 2 0.8207 0.809 0.256 0.744
#> GSM99492 1 0.0000 0.950 1.000 0.000
#> GSM99494 2 0.8207 0.809 0.256 0.744
#> GSM99524 1 0.0000 0.950 1.000 0.000
#> GSM99526 2 0.9522 0.685 0.372 0.628
#> GSM99528 2 0.8081 0.810 0.248 0.752
#> GSM99530 1 0.7883 0.582 0.764 0.236
#> GSM99532 2 0.9833 0.639 0.424 0.576
#> GSM99534 2 0.9608 0.638 0.384 0.616
#> GSM99536 1 0.0000 0.950 1.000 0.000
#> GSM99538 2 0.8144 0.808 0.252 0.748
#> GSM99540 1 0.2603 0.923 0.956 0.044
#> GSM99542 2 0.9580 0.645 0.380 0.620
#> GSM99544 2 0.7674 0.808 0.224 0.776
#> GSM99546 2 0.9248 0.731 0.340 0.660
#> GSM99548 2 0.8207 0.809 0.256 0.744
#> GSM99550 1 0.4690 0.875 0.900 0.100
#> GSM99552 2 0.9460 0.734 0.364 0.636
#> GSM99554 2 0.8207 0.809 0.256 0.744
#> GSM99556 2 0.8207 0.809 0.256 0.744
#> GSM99558 2 0.5408 0.755 0.124 0.876
#> GSM99560 2 0.8081 0.810 0.248 0.752
#> GSM99562 2 0.5519 0.697 0.128 0.872
#> GSM99564 2 0.8016 0.809 0.244 0.756
#> GSM99572 2 0.8207 0.809 0.256 0.744
#> GSM99576 1 0.2778 0.925 0.952 0.048
#> GSM99578 2 0.8207 0.809 0.256 0.744
#> GSM99580 2 0.5519 0.697 0.128 0.872
#> GSM99582 2 0.9775 0.680 0.412 0.588
#> GSM99584 2 0.8555 0.793 0.280 0.720
#> GSM99586 1 0.0000 0.950 1.000 0.000
#> GSM99588 2 0.8207 0.809 0.256 0.744
#> GSM99590 2 0.8207 0.809 0.256 0.744
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM99496 3 0.0000 0.8185 0.000 0.000 1.000
#> GSM99502 1 0.0000 0.9803 1.000 0.000 0.000
#> GSM99504 1 0.0000 0.9803 1.000 0.000 0.000
#> GSM99506 3 0.0000 0.8185 0.000 0.000 1.000
#> GSM99566 3 0.0000 0.8185 0.000 0.000 1.000
#> GSM99574 1 0.0000 0.9803 1.000 0.000 0.000
#> GSM99592 3 0.0237 0.8186 0.000 0.004 0.996
#> GSM99594 3 0.0237 0.8186 0.000 0.004 0.996
#> GSM99468 1 0.0000 0.9803 1.000 0.000 0.000
#> GSM99498 1 0.0000 0.9803 1.000 0.000 0.000
#> GSM99500 1 0.0000 0.9803 1.000 0.000 0.000
#> GSM99508 3 0.0000 0.8185 0.000 0.000 1.000
#> GSM99568 3 0.0237 0.8186 0.000 0.004 0.996
#> GSM99596 3 0.0592 0.8153 0.012 0.000 0.988
#> GSM99600 2 0.0000 0.8467 0.000 1.000 0.000
#> GSM99458 1 0.1643 0.9525 0.956 0.000 0.044
#> GSM99460 1 0.2356 0.9239 0.928 0.000 0.072
#> GSM99510 3 0.0000 0.8185 0.000 0.000 1.000
#> GSM99512 3 0.0237 0.8186 0.000 0.004 0.996
#> GSM99514 3 0.0237 0.8186 0.000 0.004 0.996
#> GSM99516 1 0.0000 0.9803 1.000 0.000 0.000
#> GSM99518 1 0.0000 0.9803 1.000 0.000 0.000
#> GSM99520 3 0.0000 0.8185 0.000 0.000 1.000
#> GSM99522 3 0.6079 0.4355 0.388 0.000 0.612
#> GSM99570 1 0.0000 0.9803 1.000 0.000 0.000
#> GSM99598 1 0.0000 0.9803 1.000 0.000 0.000
#> GSM99432 2 0.2448 0.8091 0.000 0.924 0.076
#> GSM99434 3 0.0747 0.8126 0.000 0.016 0.984
#> GSM99436 2 0.0592 0.8458 0.000 0.988 0.012
#> GSM99438 2 0.0000 0.8467 0.000 1.000 0.000
#> GSM99440 1 0.0000 0.9803 1.000 0.000 0.000
#> GSM99442 2 0.0000 0.8467 0.000 1.000 0.000
#> GSM99444 2 0.0000 0.8467 0.000 1.000 0.000
#> GSM99446 2 0.0592 0.8458 0.000 0.988 0.012
#> GSM99448 3 0.6168 0.2186 0.000 0.412 0.588
#> GSM99450 3 0.0892 0.8100 0.000 0.020 0.980
#> GSM99452 1 0.0000 0.9803 1.000 0.000 0.000
#> GSM99454 1 0.0000 0.9803 1.000 0.000 0.000
#> GSM99456 1 0.1411 0.9593 0.964 0.000 0.036
#> GSM99462 2 0.0000 0.8467 0.000 1.000 0.000
#> GSM99464 3 0.7102 0.3628 0.420 0.024 0.556
#> GSM99466 2 0.6307 0.0822 0.000 0.512 0.488
#> GSM99470 1 0.1289 0.9622 0.968 0.000 0.032
#> GSM99472 1 0.1289 0.9622 0.968 0.000 0.032
#> GSM99474 3 0.0237 0.8186 0.000 0.004 0.996
#> GSM99476 3 0.3412 0.7195 0.000 0.124 0.876
#> GSM99478 2 0.5397 0.5626 0.000 0.720 0.280
#> GSM99480 1 0.0000 0.9803 1.000 0.000 0.000
#> GSM99482 1 0.0237 0.9786 0.996 0.000 0.004
#> GSM99484 2 0.1411 0.8342 0.000 0.964 0.036
#> GSM99486 2 0.3340 0.7702 0.000 0.880 0.120
#> GSM99488 2 0.0000 0.8467 0.000 1.000 0.000
#> GSM99490 2 0.0000 0.8467 0.000 1.000 0.000
#> GSM99492 1 0.0000 0.9803 1.000 0.000 0.000
#> GSM99494 2 0.0000 0.8467 0.000 1.000 0.000
#> GSM99524 1 0.0000 0.9803 1.000 0.000 0.000
#> GSM99526 3 0.8513 0.3644 0.116 0.316 0.568
#> GSM99528 2 0.6307 0.0822 0.000 0.512 0.488
#> GSM99530 3 0.6192 0.3742 0.420 0.000 0.580
#> GSM99532 3 0.1643 0.7988 0.044 0.000 0.956
#> GSM99534 2 0.1289 0.8362 0.000 0.968 0.032
#> GSM99536 1 0.0000 0.9803 1.000 0.000 0.000
#> GSM99538 2 0.6308 0.0673 0.000 0.508 0.492
#> GSM99540 1 0.1289 0.9622 0.968 0.000 0.032
#> GSM99542 2 0.0592 0.8458 0.000 0.988 0.012
#> GSM99544 2 0.6305 0.0957 0.000 0.516 0.484
#> GSM99546 3 0.6252 0.1207 0.000 0.444 0.556
#> GSM99548 2 0.0000 0.8467 0.000 1.000 0.000
#> GSM99550 1 0.3983 0.8209 0.852 0.004 0.144
#> GSM99552 3 0.6168 0.2186 0.000 0.412 0.588
#> GSM99554 2 0.0000 0.8467 0.000 1.000 0.000
#> GSM99556 2 0.0000 0.8467 0.000 1.000 0.000
#> GSM99558 3 0.6192 0.1950 0.000 0.420 0.580
#> GSM99560 2 0.6302 0.1080 0.000 0.520 0.480
#> GSM99562 3 0.0000 0.8185 0.000 0.000 1.000
#> GSM99564 2 0.2537 0.8061 0.000 0.920 0.080
#> GSM99572 2 0.0000 0.8467 0.000 1.000 0.000
#> GSM99576 1 0.1289 0.9622 0.968 0.000 0.032
#> GSM99578 2 0.0592 0.8458 0.000 0.988 0.012
#> GSM99580 3 0.0000 0.8185 0.000 0.000 1.000
#> GSM99582 3 0.6192 0.3742 0.420 0.000 0.580
#> GSM99584 2 0.6305 0.0873 0.000 0.516 0.484
#> GSM99586 1 0.0237 0.9786 0.996 0.000 0.004
#> GSM99588 2 0.0592 0.8458 0.000 0.988 0.012
#> GSM99590 2 0.0000 0.8467 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM99496 3 0.4761 0.702 0.372 0.000 0.628 0.000
#> GSM99502 1 0.4761 0.934 0.628 0.000 0.000 0.372
#> GSM99504 1 0.4761 0.934 0.628 0.000 0.000 0.372
#> GSM99506 3 0.4761 0.702 0.372 0.000 0.628 0.000
#> GSM99566 3 0.4761 0.702 0.372 0.000 0.628 0.000
#> GSM99574 1 0.4761 0.934 0.628 0.000 0.000 0.372
#> GSM99592 3 0.2921 0.805 0.140 0.000 0.860 0.000
#> GSM99594 3 0.4761 0.702 0.372 0.000 0.628 0.000
#> GSM99468 1 0.4761 0.934 0.628 0.000 0.000 0.372
#> GSM99498 1 0.4761 0.934 0.628 0.000 0.000 0.372
#> GSM99500 1 0.4761 0.934 0.628 0.000 0.000 0.372
#> GSM99508 3 0.4761 0.702 0.372 0.000 0.628 0.000
#> GSM99568 3 0.2921 0.805 0.140 0.000 0.860 0.000
#> GSM99596 3 0.4761 0.702 0.372 0.000 0.628 0.000
#> GSM99600 2 0.0707 0.878 0.000 0.980 0.020 0.000
#> GSM99458 1 0.6651 0.639 0.616 0.000 0.148 0.236
#> GSM99460 4 0.5256 0.657 0.064 0.000 0.204 0.732
#> GSM99510 3 0.0592 0.790 0.016 0.000 0.984 0.000
#> GSM99512 3 0.2011 0.806 0.080 0.000 0.920 0.000
#> GSM99514 3 0.4761 0.702 0.372 0.000 0.628 0.000
#> GSM99516 1 0.4761 0.934 0.628 0.000 0.000 0.372
#> GSM99518 1 0.4877 0.891 0.592 0.000 0.000 0.408
#> GSM99520 3 0.3801 0.781 0.220 0.000 0.780 0.000
#> GSM99522 3 0.4175 0.781 0.200 0.000 0.784 0.016
#> GSM99570 1 0.4761 0.934 0.628 0.000 0.000 0.372
#> GSM99598 1 0.4761 0.934 0.628 0.000 0.000 0.372
#> GSM99432 2 0.4936 0.577 0.000 0.624 0.372 0.004
#> GSM99434 3 0.0779 0.788 0.016 0.000 0.980 0.004
#> GSM99436 2 0.1389 0.869 0.000 0.952 0.048 0.000
#> GSM99438 2 0.0000 0.880 0.000 1.000 0.000 0.000
#> GSM99440 1 0.4761 0.934 0.628 0.000 0.000 0.372
#> GSM99442 2 0.0000 0.880 0.000 1.000 0.000 0.000
#> GSM99444 2 0.0000 0.880 0.000 1.000 0.000 0.000
#> GSM99446 2 0.2760 0.816 0.000 0.872 0.128 0.000
#> GSM99448 3 0.1716 0.804 0.064 0.000 0.936 0.000
#> GSM99450 3 0.0779 0.788 0.016 0.000 0.980 0.004
#> GSM99452 1 0.4776 0.930 0.624 0.000 0.000 0.376
#> GSM99454 1 0.4761 0.934 0.628 0.000 0.000 0.372
#> GSM99456 4 0.3351 0.688 0.008 0.000 0.148 0.844
#> GSM99462 2 0.0000 0.880 0.000 1.000 0.000 0.000
#> GSM99464 3 0.3907 0.536 0.000 0.000 0.768 0.232
#> GSM99466 3 0.0188 0.782 0.000 0.000 0.996 0.004
#> GSM99470 1 0.6613 0.602 0.628 0.000 0.172 0.200
#> GSM99472 1 0.6565 0.655 0.628 0.000 0.148 0.224
#> GSM99474 3 0.2868 0.805 0.136 0.000 0.864 0.000
#> GSM99476 3 0.0188 0.782 0.000 0.000 0.996 0.004
#> GSM99478 2 0.4978 0.561 0.000 0.612 0.384 0.004
#> GSM99480 4 0.4500 -0.262 0.316 0.000 0.000 0.684
#> GSM99482 1 0.4761 0.934 0.628 0.000 0.000 0.372
#> GSM99484 2 0.4277 0.676 0.000 0.720 0.280 0.000
#> GSM99486 2 0.4730 0.591 0.000 0.636 0.364 0.000
#> GSM99488 2 0.0000 0.880 0.000 1.000 0.000 0.000
#> GSM99490 2 0.0000 0.880 0.000 1.000 0.000 0.000
#> GSM99492 4 0.2408 0.423 0.104 0.000 0.000 0.896
#> GSM99494 2 0.0000 0.880 0.000 1.000 0.000 0.000
#> GSM99524 1 0.4761 0.934 0.628 0.000 0.000 0.372
#> GSM99526 3 0.1557 0.754 0.000 0.000 0.944 0.056
#> GSM99528 3 0.4274 0.619 0.000 0.044 0.808 0.148
#> GSM99530 4 0.5577 0.495 0.036 0.000 0.328 0.636
#> GSM99532 3 0.2814 0.806 0.132 0.000 0.868 0.000
#> GSM99534 2 0.3356 0.763 0.000 0.824 0.176 0.000
#> GSM99536 4 0.3444 0.242 0.184 0.000 0.000 0.816
#> GSM99538 3 0.0188 0.782 0.000 0.000 0.996 0.004
#> GSM99540 4 0.3547 0.685 0.016 0.000 0.144 0.840
#> GSM99542 2 0.0707 0.878 0.000 0.980 0.020 0.000
#> GSM99544 3 0.1824 0.740 0.000 0.060 0.936 0.004
#> GSM99546 3 0.0817 0.773 0.000 0.000 0.976 0.024
#> GSM99548 2 0.0000 0.880 0.000 1.000 0.000 0.000
#> GSM99550 4 0.4697 0.504 0.000 0.000 0.356 0.644
#> GSM99552 3 0.2647 0.806 0.120 0.000 0.880 0.000
#> GSM99554 2 0.0707 0.878 0.000 0.980 0.020 0.000
#> GSM99556 2 0.0000 0.880 0.000 1.000 0.000 0.000
#> GSM99558 3 0.1637 0.803 0.060 0.000 0.940 0.000
#> GSM99560 3 0.4819 0.225 0.000 0.344 0.652 0.004
#> GSM99562 3 0.4761 0.702 0.372 0.000 0.628 0.000
#> GSM99564 2 0.4746 0.587 0.000 0.632 0.368 0.000
#> GSM99572 2 0.0000 0.880 0.000 1.000 0.000 0.000
#> GSM99576 4 0.3257 0.688 0.004 0.000 0.152 0.844
#> GSM99578 2 0.0707 0.878 0.000 0.980 0.020 0.000
#> GSM99580 3 0.4250 0.756 0.276 0.000 0.724 0.000
#> GSM99582 3 0.3048 0.803 0.108 0.000 0.876 0.016
#> GSM99584 3 0.4283 0.468 0.000 0.256 0.740 0.004
#> GSM99586 4 0.0188 0.544 0.004 0.000 0.000 0.996
#> GSM99588 2 0.1792 0.857 0.000 0.932 0.068 0.000
#> GSM99590 2 0.0000 0.880 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM99496 3 0.0162 0.872 0.000 0.000 0.996 0.000 0.004
#> GSM99502 1 0.0000 0.905 1.000 0.000 0.000 0.000 0.000
#> GSM99504 1 0.0000 0.905 1.000 0.000 0.000 0.000 0.000
#> GSM99506 3 0.0162 0.872 0.000 0.000 0.996 0.000 0.004
#> GSM99566 3 0.0162 0.872 0.000 0.000 0.996 0.000 0.004
#> GSM99574 1 0.0000 0.905 1.000 0.000 0.000 0.000 0.000
#> GSM99592 3 0.0000 0.871 0.000 0.000 1.000 0.000 0.000
#> GSM99594 3 0.0162 0.872 0.000 0.000 0.996 0.000 0.004
#> GSM99468 1 0.0000 0.905 1.000 0.000 0.000 0.000 0.000
#> GSM99498 1 0.0000 0.905 1.000 0.000 0.000 0.000 0.000
#> GSM99500 1 0.0000 0.905 1.000 0.000 0.000 0.000 0.000
#> GSM99508 3 0.0162 0.872 0.000 0.000 0.996 0.000 0.004
#> GSM99568 3 0.0000 0.871 0.000 0.000 1.000 0.000 0.000
#> GSM99596 3 0.0162 0.872 0.000 0.000 0.996 0.000 0.004
#> GSM99600 4 0.4150 0.488 0.000 0.388 0.000 0.612 0.000
#> GSM99458 1 0.4088 0.359 0.632 0.000 0.000 0.000 0.368
#> GSM99460 5 0.1043 0.721 0.040 0.000 0.000 0.000 0.960
#> GSM99510 3 0.3707 0.659 0.000 0.000 0.716 0.284 0.000
#> GSM99512 3 0.2020 0.812 0.000 0.000 0.900 0.100 0.000
#> GSM99514 3 0.0162 0.872 0.000 0.000 0.996 0.000 0.004
#> GSM99516 1 0.0000 0.905 1.000 0.000 0.000 0.000 0.000
#> GSM99518 1 0.1792 0.827 0.916 0.000 0.000 0.000 0.084
#> GSM99520 3 0.0000 0.871 0.000 0.000 1.000 0.000 0.000
#> GSM99522 3 0.0000 0.871 0.000 0.000 1.000 0.000 0.000
#> GSM99570 1 0.0000 0.905 1.000 0.000 0.000 0.000 0.000
#> GSM99598 1 0.0000 0.905 1.000 0.000 0.000 0.000 0.000
#> GSM99432 4 0.0404 0.831 0.000 0.012 0.000 0.988 0.000
#> GSM99434 3 0.3814 0.664 0.000 0.000 0.720 0.276 0.004
#> GSM99436 4 0.3336 0.692 0.000 0.228 0.000 0.772 0.000
#> GSM99438 2 0.0000 0.949 0.000 1.000 0.000 0.000 0.000
#> GSM99440 1 0.0162 0.903 0.996 0.000 0.000 0.000 0.004
#> GSM99442 2 0.4171 0.098 0.000 0.604 0.000 0.396 0.000
#> GSM99444 2 0.0000 0.949 0.000 1.000 0.000 0.000 0.000
#> GSM99446 4 0.2020 0.794 0.000 0.100 0.000 0.900 0.000
#> GSM99448 3 0.3895 0.622 0.000 0.000 0.680 0.320 0.000
#> GSM99450 3 0.3336 0.684 0.000 0.000 0.772 0.000 0.228
#> GSM99452 1 0.0290 0.901 0.992 0.000 0.000 0.000 0.008
#> GSM99454 1 0.0000 0.905 1.000 0.000 0.000 0.000 0.000
#> GSM99456 5 0.0324 0.724 0.004 0.000 0.000 0.004 0.992
#> GSM99462 2 0.0000 0.949 0.000 1.000 0.000 0.000 0.000
#> GSM99464 5 0.4193 0.340 0.000 0.000 0.304 0.012 0.684
#> GSM99466 4 0.0404 0.827 0.000 0.000 0.012 0.988 0.000
#> GSM99470 1 0.1043 0.874 0.960 0.000 0.000 0.000 0.040
#> GSM99472 1 0.1121 0.870 0.956 0.000 0.000 0.000 0.044
#> GSM99474 3 0.0000 0.871 0.000 0.000 1.000 0.000 0.000
#> GSM99476 3 0.4182 0.510 0.000 0.000 0.600 0.400 0.000
#> GSM99478 4 0.0451 0.830 0.000 0.008 0.004 0.988 0.000
#> GSM99480 1 0.4264 0.227 0.620 0.000 0.000 0.004 0.376
#> GSM99482 1 0.0000 0.905 1.000 0.000 0.000 0.000 0.000
#> GSM99484 4 0.0794 0.828 0.000 0.028 0.000 0.972 0.000
#> GSM99486 4 0.0404 0.831 0.000 0.012 0.000 0.988 0.000
#> GSM99488 2 0.0000 0.949 0.000 1.000 0.000 0.000 0.000
#> GSM99490 2 0.1121 0.904 0.000 0.956 0.000 0.044 0.000
#> GSM99492 5 0.4430 0.227 0.456 0.000 0.000 0.004 0.540
#> GSM99494 2 0.0000 0.949 0.000 1.000 0.000 0.000 0.000
#> GSM99524 1 0.0000 0.905 1.000 0.000 0.000 0.000 0.000
#> GSM99526 3 0.5535 0.420 0.000 0.000 0.568 0.080 0.352
#> GSM99528 4 0.2011 0.762 0.000 0.000 0.004 0.908 0.088
#> GSM99530 5 0.4040 0.560 0.000 0.000 0.276 0.012 0.712
#> GSM99532 3 0.0404 0.867 0.000 0.000 0.988 0.000 0.012
#> GSM99534 4 0.4242 0.412 0.000 0.428 0.000 0.572 0.000
#> GSM99536 1 0.4307 -0.201 0.504 0.000 0.000 0.000 0.496
#> GSM99538 4 0.0404 0.826 0.000 0.000 0.012 0.988 0.000
#> GSM99540 5 0.3452 0.654 0.244 0.000 0.000 0.000 0.756
#> GSM99542 2 0.0000 0.949 0.000 1.000 0.000 0.000 0.000
#> GSM99544 4 0.0404 0.827 0.000 0.000 0.012 0.988 0.000
#> GSM99546 4 0.3662 0.646 0.000 0.000 0.004 0.744 0.252
#> GSM99548 2 0.0000 0.949 0.000 1.000 0.000 0.000 0.000
#> GSM99550 5 0.0404 0.722 0.000 0.000 0.000 0.012 0.988
#> GSM99552 3 0.4227 0.191 0.000 0.000 0.580 0.420 0.000
#> GSM99554 4 0.4210 0.446 0.000 0.412 0.000 0.588 0.000
#> GSM99556 2 0.0000 0.949 0.000 1.000 0.000 0.000 0.000
#> GSM99558 4 0.0703 0.823 0.000 0.000 0.024 0.976 0.000
#> GSM99560 4 0.0324 0.827 0.000 0.000 0.004 0.992 0.004
#> GSM99562 3 0.0162 0.872 0.000 0.000 0.996 0.000 0.004
#> GSM99564 4 0.0404 0.831 0.000 0.012 0.000 0.988 0.000
#> GSM99572 2 0.0000 0.949 0.000 1.000 0.000 0.000 0.000
#> GSM99576 5 0.3461 0.671 0.224 0.000 0.000 0.004 0.772
#> GSM99578 4 0.4235 0.421 0.000 0.424 0.000 0.576 0.000
#> GSM99580 3 0.0000 0.871 0.000 0.000 1.000 0.000 0.000
#> GSM99582 3 0.0162 0.870 0.000 0.000 0.996 0.000 0.004
#> GSM99584 4 0.0740 0.830 0.000 0.008 0.004 0.980 0.008
#> GSM99586 5 0.3715 0.637 0.260 0.000 0.000 0.004 0.736
#> GSM99588 4 0.4192 0.462 0.000 0.404 0.000 0.596 0.000
#> GSM99590 2 0.0000 0.949 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM99496 3 0.1863 0.863 0.000 0.000 0.896 0.000 0.000 0.104
#> GSM99502 1 0.0000 0.917 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99504 1 0.0000 0.917 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99506 3 0.1814 0.864 0.000 0.000 0.900 0.000 0.000 0.100
#> GSM99566 3 0.1814 0.864 0.000 0.000 0.900 0.000 0.000 0.100
#> GSM99574 1 0.0000 0.917 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99592 3 0.0146 0.865 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM99594 3 0.1814 0.864 0.000 0.000 0.900 0.000 0.000 0.100
#> GSM99468 1 0.0146 0.916 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM99498 1 0.0146 0.916 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM99500 1 0.0000 0.917 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99508 3 0.1714 0.865 0.000 0.000 0.908 0.000 0.000 0.092
#> GSM99568 3 0.0260 0.865 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM99596 3 0.1714 0.865 0.000 0.000 0.908 0.000 0.000 0.092
#> GSM99600 4 0.2996 0.718 0.000 0.228 0.000 0.772 0.000 0.000
#> GSM99458 1 0.5111 0.343 0.624 0.000 0.000 0.000 0.152 0.224
#> GSM99460 5 0.5029 0.441 0.080 0.000 0.000 0.000 0.544 0.376
#> GSM99510 3 0.4604 0.700 0.000 0.000 0.716 0.184 0.084 0.016
#> GSM99512 3 0.1462 0.846 0.000 0.000 0.936 0.056 0.000 0.008
#> GSM99514 3 0.1863 0.863 0.000 0.000 0.896 0.000 0.000 0.104
#> GSM99516 1 0.0000 0.917 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99518 1 0.2454 0.700 0.840 0.000 0.000 0.000 0.000 0.160
#> GSM99520 3 0.0260 0.865 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM99522 3 0.0363 0.865 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM99570 1 0.0363 0.913 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM99598 1 0.0000 0.917 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99432 4 0.0146 0.786 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM99434 3 0.5052 0.641 0.000 0.000 0.656 0.108 0.224 0.012
#> GSM99436 4 0.1444 0.784 0.000 0.072 0.000 0.928 0.000 0.000
#> GSM99438 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99440 1 0.1267 0.862 0.940 0.000 0.000 0.000 0.000 0.060
#> GSM99442 4 0.3857 0.348 0.000 0.468 0.000 0.532 0.000 0.000
#> GSM99444 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99446 4 0.0790 0.791 0.000 0.032 0.000 0.968 0.000 0.000
#> GSM99448 3 0.3071 0.746 0.000 0.000 0.804 0.180 0.000 0.016
#> GSM99450 3 0.3584 0.646 0.000 0.000 0.688 0.000 0.308 0.004
#> GSM99452 1 0.0458 0.907 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM99454 1 0.0000 0.917 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99456 6 0.2378 0.279 0.000 0.000 0.000 0.000 0.152 0.848
#> GSM99462 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99464 5 0.0972 0.597 0.000 0.000 0.028 0.000 0.964 0.008
#> GSM99466 4 0.0603 0.783 0.000 0.000 0.000 0.980 0.004 0.016
#> GSM99470 1 0.2911 0.745 0.832 0.000 0.000 0.000 0.024 0.144
#> GSM99472 1 0.2872 0.749 0.836 0.000 0.000 0.000 0.024 0.140
#> GSM99474 3 0.0260 0.865 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM99476 3 0.5456 0.562 0.000 0.000 0.608 0.248 0.128 0.016
#> GSM99478 4 0.0000 0.787 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM99480 6 0.3706 0.720 0.380 0.000 0.000 0.000 0.000 0.620
#> GSM99482 1 0.0458 0.911 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM99484 4 0.1075 0.790 0.000 0.048 0.000 0.952 0.000 0.000
#> GSM99486 4 0.0000 0.787 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM99488 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99490 2 0.1007 0.945 0.000 0.956 0.000 0.044 0.000 0.000
#> GSM99492 6 0.3620 0.731 0.352 0.000 0.000 0.000 0.000 0.648
#> GSM99494 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99524 1 0.0363 0.913 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM99526 5 0.2121 0.568 0.000 0.000 0.096 0.012 0.892 0.000
#> GSM99528 5 0.4158 0.307 0.000 0.000 0.004 0.416 0.572 0.008
#> GSM99530 5 0.3620 0.551 0.000 0.000 0.184 0.000 0.772 0.044
#> GSM99532 3 0.1462 0.845 0.000 0.000 0.936 0.000 0.056 0.008
#> GSM99534 4 0.4348 0.590 0.000 0.320 0.000 0.640 0.000 0.040
#> GSM99536 6 0.3727 0.709 0.388 0.000 0.000 0.000 0.000 0.612
#> GSM99538 4 0.1951 0.741 0.000 0.000 0.000 0.908 0.076 0.016
#> GSM99540 5 0.5907 0.113 0.216 0.000 0.000 0.000 0.444 0.340
#> GSM99542 2 0.0547 0.975 0.000 0.980 0.000 0.000 0.000 0.020
#> GSM99544 4 0.0603 0.783 0.000 0.000 0.000 0.980 0.004 0.016
#> GSM99546 4 0.3795 0.520 0.000 0.000 0.000 0.632 0.364 0.004
#> GSM99548 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99550 5 0.3175 0.579 0.000 0.000 0.000 0.000 0.744 0.256
#> GSM99552 3 0.4322 0.300 0.000 0.000 0.600 0.372 0.000 0.028
#> GSM99554 4 0.3390 0.654 0.000 0.296 0.000 0.704 0.000 0.000
#> GSM99556 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99558 4 0.2398 0.735 0.000 0.000 0.104 0.876 0.000 0.020
#> GSM99560 4 0.3996 -0.200 0.000 0.000 0.000 0.512 0.484 0.004
#> GSM99562 3 0.1814 0.864 0.000 0.000 0.900 0.000 0.000 0.100
#> GSM99564 4 0.0146 0.787 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM99572 2 0.0146 0.989 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM99576 5 0.5336 0.438 0.124 0.000 0.000 0.000 0.544 0.332
#> GSM99578 4 0.3547 0.607 0.000 0.332 0.000 0.668 0.000 0.000
#> GSM99580 3 0.0363 0.867 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM99582 3 0.0405 0.865 0.000 0.000 0.988 0.004 0.000 0.008
#> GSM99584 4 0.2311 0.753 0.000 0.000 0.000 0.880 0.104 0.016
#> GSM99586 6 0.2744 0.563 0.144 0.000 0.000 0.000 0.016 0.840
#> GSM99588 4 0.3330 0.667 0.000 0.284 0.000 0.716 0.000 0.000
#> GSM99590 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) cell.type(p) k
#> CV:mclust 85 1.92e-01 0.38259 2
#> CV:mclust 70 1.56e-04 0.00353 3
#> CV:mclust 79 6.06e-04 0.02557 4
#> CV:mclust 72 3.67e-05 0.00825 5
#> CV:mclust 76 3.71e-05 0.01613 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 21168 rows and 85 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.975 0.989 0.5019 0.497 0.497
#> 3 3 0.967 0.951 0.979 0.3418 0.711 0.481
#> 4 4 0.766 0.716 0.855 0.1017 0.886 0.674
#> 5 5 0.740 0.641 0.828 0.0621 0.915 0.702
#> 6 6 0.701 0.513 0.724 0.0408 0.893 0.574
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
#> GSM99496 1 0.0000 0.992 1.000 0.000
#> GSM99502 1 0.0000 0.992 1.000 0.000
#> GSM99504 1 0.0000 0.992 1.000 0.000
#> GSM99506 1 0.0000 0.992 1.000 0.000
#> GSM99566 1 0.0000 0.992 1.000 0.000
#> GSM99574 1 0.0000 0.992 1.000 0.000
#> GSM99592 1 0.5408 0.859 0.876 0.124
#> GSM99594 1 0.0000 0.992 1.000 0.000
#> GSM99468 1 0.0000 0.992 1.000 0.000
#> GSM99498 1 0.0000 0.992 1.000 0.000
#> GSM99500 1 0.0000 0.992 1.000 0.000
#> GSM99508 1 0.0000 0.992 1.000 0.000
#> GSM99568 1 0.0000 0.992 1.000 0.000
#> GSM99596 1 0.0000 0.992 1.000 0.000
#> GSM99600 2 0.0000 0.984 0.000 1.000
#> GSM99458 1 0.0000 0.992 1.000 0.000
#> GSM99460 1 0.0000 0.992 1.000 0.000
#> GSM99510 2 0.4022 0.911 0.080 0.920
#> GSM99512 2 0.2236 0.955 0.036 0.964
#> GSM99514 1 0.0000 0.992 1.000 0.000
#> GSM99516 1 0.0000 0.992 1.000 0.000
#> GSM99518 1 0.0000 0.992 1.000 0.000
#> GSM99520 1 0.0000 0.992 1.000 0.000
#> GSM99522 1 0.0000 0.992 1.000 0.000
#> GSM99570 1 0.0000 0.992 1.000 0.000
#> GSM99598 1 0.0000 0.992 1.000 0.000
#> GSM99432 2 0.0000 0.984 0.000 1.000
#> GSM99434 2 0.9460 0.431 0.364 0.636
#> GSM99436 2 0.0000 0.984 0.000 1.000
#> GSM99438 2 0.0000 0.984 0.000 1.000
#> GSM99440 1 0.0000 0.992 1.000 0.000
#> GSM99442 2 0.0000 0.984 0.000 1.000
#> GSM99444 2 0.0000 0.984 0.000 1.000
#> GSM99446 2 0.0000 0.984 0.000 1.000
#> GSM99448 2 0.0000 0.984 0.000 1.000
#> GSM99450 1 0.0000 0.992 1.000 0.000
#> GSM99452 1 0.0000 0.992 1.000 0.000
#> GSM99454 1 0.0000 0.992 1.000 0.000
#> GSM99456 1 0.0000 0.992 1.000 0.000
#> GSM99462 2 0.0000 0.984 0.000 1.000
#> GSM99464 1 0.0000 0.992 1.000 0.000
#> GSM99466 2 0.0000 0.984 0.000 1.000
#> GSM99470 1 0.4562 0.894 0.904 0.096
#> GSM99472 1 0.0000 0.992 1.000 0.000
#> GSM99474 1 0.0000 0.992 1.000 0.000
#> GSM99476 2 0.0000 0.984 0.000 1.000
#> GSM99478 2 0.0000 0.984 0.000 1.000
#> GSM99480 1 0.0000 0.992 1.000 0.000
#> GSM99482 1 0.0000 0.992 1.000 0.000
#> GSM99484 2 0.0000 0.984 0.000 1.000
#> GSM99486 2 0.0000 0.984 0.000 1.000
#> GSM99488 2 0.0000 0.984 0.000 1.000
#> GSM99490 2 0.0000 0.984 0.000 1.000
#> GSM99492 1 0.0000 0.992 1.000 0.000
#> GSM99494 2 0.0000 0.984 0.000 1.000
#> GSM99524 1 0.0000 0.992 1.000 0.000
#> GSM99526 2 0.3584 0.925 0.068 0.932
#> GSM99528 2 0.0376 0.981 0.004 0.996
#> GSM99530 1 0.0000 0.992 1.000 0.000
#> GSM99532 1 0.0000 0.992 1.000 0.000
#> GSM99534 2 0.0000 0.984 0.000 1.000
#> GSM99536 1 0.0000 0.992 1.000 0.000
#> GSM99538 2 0.0000 0.984 0.000 1.000
#> GSM99540 1 0.0000 0.992 1.000 0.000
#> GSM99542 2 0.0000 0.984 0.000 1.000
#> GSM99544 2 0.0000 0.984 0.000 1.000
#> GSM99546 2 0.0376 0.981 0.004 0.996
#> GSM99548 2 0.0000 0.984 0.000 1.000
#> GSM99550 1 0.0000 0.992 1.000 0.000
#> GSM99552 2 0.3114 0.936 0.056 0.944
#> GSM99554 2 0.0000 0.984 0.000 1.000
#> GSM99556 2 0.0000 0.984 0.000 1.000
#> GSM99558 2 0.0000 0.984 0.000 1.000
#> GSM99560 2 0.0000 0.984 0.000 1.000
#> GSM99562 1 0.0000 0.992 1.000 0.000
#> GSM99564 2 0.0000 0.984 0.000 1.000
#> GSM99572 2 0.0000 0.984 0.000 1.000
#> GSM99576 1 0.0000 0.992 1.000 0.000
#> GSM99578 2 0.0000 0.984 0.000 1.000
#> GSM99580 1 0.5737 0.844 0.864 0.136
#> GSM99582 1 0.0000 0.992 1.000 0.000
#> GSM99584 2 0.0000 0.984 0.000 1.000
#> GSM99586 1 0.0000 0.992 1.000 0.000
#> GSM99588 2 0.0000 0.984 0.000 1.000
#> GSM99590 2 0.0000 0.984 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM99496 3 0.0000 0.971 0.000 0.000 1.000
#> GSM99502 1 0.0000 0.984 1.000 0.000 0.000
#> GSM99504 1 0.5178 0.653 0.744 0.000 0.256
#> GSM99506 3 0.0000 0.971 0.000 0.000 1.000
#> GSM99566 3 0.0000 0.971 0.000 0.000 1.000
#> GSM99574 1 0.0000 0.984 1.000 0.000 0.000
#> GSM99592 3 0.0000 0.971 0.000 0.000 1.000
#> GSM99594 3 0.0000 0.971 0.000 0.000 1.000
#> GSM99468 1 0.0000 0.984 1.000 0.000 0.000
#> GSM99498 1 0.0000 0.984 1.000 0.000 0.000
#> GSM99500 1 0.0000 0.984 1.000 0.000 0.000
#> GSM99508 3 0.0000 0.971 0.000 0.000 1.000
#> GSM99568 3 0.0000 0.971 0.000 0.000 1.000
#> GSM99596 3 0.0000 0.971 0.000 0.000 1.000
#> GSM99600 2 0.0000 0.980 0.000 1.000 0.000
#> GSM99458 1 0.0000 0.984 1.000 0.000 0.000
#> GSM99460 1 0.0000 0.984 1.000 0.000 0.000
#> GSM99510 3 0.0000 0.971 0.000 0.000 1.000
#> GSM99512 3 0.0000 0.971 0.000 0.000 1.000
#> GSM99514 3 0.0000 0.971 0.000 0.000 1.000
#> GSM99516 1 0.0000 0.984 1.000 0.000 0.000
#> GSM99518 1 0.0000 0.984 1.000 0.000 0.000
#> GSM99520 3 0.0000 0.971 0.000 0.000 1.000
#> GSM99522 3 0.0000 0.971 0.000 0.000 1.000
#> GSM99570 1 0.0000 0.984 1.000 0.000 0.000
#> GSM99598 1 0.0000 0.984 1.000 0.000 0.000
#> GSM99432 2 0.0000 0.980 0.000 1.000 0.000
#> GSM99434 3 0.0000 0.971 0.000 0.000 1.000
#> GSM99436 2 0.0000 0.980 0.000 1.000 0.000
#> GSM99438 2 0.0000 0.980 0.000 1.000 0.000
#> GSM99440 1 0.0000 0.984 1.000 0.000 0.000
#> GSM99442 2 0.0000 0.980 0.000 1.000 0.000
#> GSM99444 2 0.0000 0.980 0.000 1.000 0.000
#> GSM99446 2 0.0000 0.980 0.000 1.000 0.000
#> GSM99448 3 0.0000 0.971 0.000 0.000 1.000
#> GSM99450 3 0.0000 0.971 0.000 0.000 1.000
#> GSM99452 1 0.0000 0.984 1.000 0.000 0.000
#> GSM99454 1 0.0000 0.984 1.000 0.000 0.000
#> GSM99456 1 0.0000 0.984 1.000 0.000 0.000
#> GSM99462 2 0.0000 0.980 0.000 1.000 0.000
#> GSM99464 3 0.0000 0.971 0.000 0.000 1.000
#> GSM99466 3 0.5948 0.439 0.000 0.360 0.640
#> GSM99470 1 0.3482 0.847 0.872 0.128 0.000
#> GSM99472 1 0.0000 0.984 1.000 0.000 0.000
#> GSM99474 3 0.0000 0.971 0.000 0.000 1.000
#> GSM99476 3 0.0000 0.971 0.000 0.000 1.000
#> GSM99478 2 0.0424 0.974 0.000 0.992 0.008
#> GSM99480 1 0.0000 0.984 1.000 0.000 0.000
#> GSM99482 1 0.0000 0.984 1.000 0.000 0.000
#> GSM99484 2 0.0000 0.980 0.000 1.000 0.000
#> GSM99486 2 0.1163 0.956 0.000 0.972 0.028
#> GSM99488 2 0.0000 0.980 0.000 1.000 0.000
#> GSM99490 2 0.0000 0.980 0.000 1.000 0.000
#> GSM99492 1 0.0000 0.984 1.000 0.000 0.000
#> GSM99494 2 0.0000 0.980 0.000 1.000 0.000
#> GSM99524 1 0.0000 0.984 1.000 0.000 0.000
#> GSM99526 3 0.0592 0.961 0.000 0.012 0.988
#> GSM99528 2 0.0237 0.977 0.000 0.996 0.004
#> GSM99530 3 0.0000 0.971 0.000 0.000 1.000
#> GSM99532 3 0.0000 0.971 0.000 0.000 1.000
#> GSM99534 2 0.0000 0.980 0.000 1.000 0.000
#> GSM99536 1 0.0000 0.984 1.000 0.000 0.000
#> GSM99538 3 0.1643 0.932 0.000 0.044 0.956
#> GSM99540 1 0.0424 0.978 0.992 0.000 0.008
#> GSM99542 2 0.0000 0.980 0.000 1.000 0.000
#> GSM99544 3 0.5397 0.614 0.000 0.280 0.720
#> GSM99546 2 0.2959 0.879 0.000 0.900 0.100
#> GSM99548 2 0.0000 0.980 0.000 1.000 0.000
#> GSM99550 1 0.0237 0.981 0.996 0.004 0.000
#> GSM99552 3 0.0000 0.971 0.000 0.000 1.000
#> GSM99554 2 0.0000 0.980 0.000 1.000 0.000
#> GSM99556 2 0.0000 0.980 0.000 1.000 0.000
#> GSM99558 3 0.0000 0.971 0.000 0.000 1.000
#> GSM99560 2 0.0000 0.980 0.000 1.000 0.000
#> GSM99562 3 0.0000 0.971 0.000 0.000 1.000
#> GSM99564 2 0.0424 0.974 0.000 0.992 0.008
#> GSM99572 2 0.0000 0.980 0.000 1.000 0.000
#> GSM99576 1 0.0000 0.984 1.000 0.000 0.000
#> GSM99578 2 0.0000 0.980 0.000 1.000 0.000
#> GSM99580 3 0.0000 0.971 0.000 0.000 1.000
#> GSM99582 3 0.3482 0.837 0.128 0.000 0.872
#> GSM99584 2 0.6045 0.370 0.000 0.620 0.380
#> GSM99586 1 0.0000 0.984 1.000 0.000 0.000
#> GSM99588 2 0.0000 0.980 0.000 1.000 0.000
#> GSM99590 2 0.0000 0.980 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM99496 3 0.1118 0.7761 0.000 0.000 0.964 0.036
#> GSM99502 1 0.0000 0.9332 1.000 0.000 0.000 0.000
#> GSM99504 3 0.5420 0.4440 0.272 0.000 0.684 0.044
#> GSM99506 3 0.2011 0.7737 0.000 0.000 0.920 0.080
#> GSM99566 3 0.1389 0.7766 0.000 0.000 0.952 0.048
#> GSM99574 1 0.0000 0.9332 1.000 0.000 0.000 0.000
#> GSM99592 3 0.3801 0.6766 0.000 0.000 0.780 0.220
#> GSM99594 3 0.3400 0.7227 0.000 0.000 0.820 0.180
#> GSM99468 1 0.0336 0.9317 0.992 0.000 0.000 0.008
#> GSM99498 1 0.2124 0.8747 0.924 0.000 0.068 0.008
#> GSM99500 1 0.1004 0.9174 0.972 0.000 0.024 0.004
#> GSM99508 3 0.2216 0.7697 0.000 0.000 0.908 0.092
#> GSM99568 3 0.3311 0.7291 0.000 0.000 0.828 0.172
#> GSM99596 3 0.2814 0.7537 0.000 0.000 0.868 0.132
#> GSM99600 2 0.1022 0.8883 0.000 0.968 0.000 0.032
#> GSM99458 1 0.0469 0.9289 0.988 0.000 0.000 0.012
#> GSM99460 4 0.5290 -0.0710 0.476 0.000 0.008 0.516
#> GSM99510 3 0.4790 0.3976 0.000 0.000 0.620 0.380
#> GSM99512 3 0.4605 0.5011 0.000 0.000 0.664 0.336
#> GSM99514 3 0.2760 0.7155 0.000 0.000 0.872 0.128
#> GSM99516 1 0.0000 0.9332 1.000 0.000 0.000 0.000
#> GSM99518 1 0.0336 0.9318 0.992 0.000 0.000 0.008
#> GSM99520 3 0.1940 0.7738 0.000 0.000 0.924 0.076
#> GSM99522 3 0.3074 0.7033 0.000 0.000 0.848 0.152
#> GSM99570 1 0.0000 0.9332 1.000 0.000 0.000 0.000
#> GSM99598 1 0.0000 0.9332 1.000 0.000 0.000 0.000
#> GSM99432 2 0.4916 0.2977 0.000 0.576 0.000 0.424
#> GSM99434 4 0.4564 0.4498 0.000 0.000 0.328 0.672
#> GSM99436 2 0.1716 0.8721 0.000 0.936 0.000 0.064
#> GSM99438 2 0.0336 0.8924 0.000 0.992 0.000 0.008
#> GSM99440 1 0.0188 0.9326 0.996 0.000 0.000 0.004
#> GSM99442 2 0.1022 0.8870 0.000 0.968 0.000 0.032
#> GSM99444 2 0.0188 0.8921 0.000 0.996 0.000 0.004
#> GSM99446 2 0.2081 0.8617 0.000 0.916 0.000 0.084
#> GSM99448 3 0.2868 0.7226 0.000 0.000 0.864 0.136
#> GSM99450 4 0.4855 0.2607 0.000 0.000 0.400 0.600
#> GSM99452 1 0.0000 0.9332 1.000 0.000 0.000 0.000
#> GSM99454 1 0.0000 0.9332 1.000 0.000 0.000 0.000
#> GSM99456 1 0.2345 0.8684 0.900 0.000 0.000 0.100
#> GSM99462 2 0.0469 0.8913 0.000 0.988 0.000 0.012
#> GSM99464 4 0.3649 0.5569 0.000 0.000 0.204 0.796
#> GSM99466 2 0.6571 0.4543 0.000 0.612 0.124 0.264
#> GSM99470 1 0.5894 0.2684 0.568 0.392 0.000 0.040
#> GSM99472 1 0.0000 0.9332 1.000 0.000 0.000 0.000
#> GSM99474 3 0.3975 0.6605 0.000 0.000 0.760 0.240
#> GSM99476 4 0.4477 0.4684 0.000 0.000 0.312 0.688
#> GSM99478 2 0.0469 0.8916 0.000 0.988 0.000 0.012
#> GSM99480 1 0.0188 0.9326 0.996 0.000 0.000 0.004
#> GSM99482 1 0.0000 0.9332 1.000 0.000 0.000 0.000
#> GSM99484 2 0.1474 0.8798 0.000 0.948 0.000 0.052
#> GSM99486 2 0.5288 0.6696 0.000 0.720 0.056 0.224
#> GSM99488 2 0.0336 0.8924 0.000 0.992 0.000 0.008
#> GSM99490 2 0.0707 0.8900 0.000 0.980 0.000 0.020
#> GSM99492 1 0.0921 0.9220 0.972 0.000 0.000 0.028
#> GSM99494 2 0.0336 0.8924 0.000 0.992 0.000 0.008
#> GSM99524 1 0.0000 0.9332 1.000 0.000 0.000 0.000
#> GSM99526 4 0.3569 0.5643 0.000 0.000 0.196 0.804
#> GSM99528 2 0.6813 0.0568 0.000 0.516 0.104 0.380
#> GSM99530 4 0.4855 0.2136 0.000 0.000 0.400 0.600
#> GSM99532 3 0.4967 0.1884 0.000 0.000 0.548 0.452
#> GSM99534 2 0.0817 0.8887 0.000 0.976 0.000 0.024
#> GSM99536 1 0.0469 0.9303 0.988 0.000 0.000 0.012
#> GSM99538 4 0.4122 0.5413 0.000 0.004 0.236 0.760
#> GSM99540 1 0.6661 0.3416 0.604 0.000 0.132 0.264
#> GSM99542 2 0.0336 0.8924 0.000 0.992 0.000 0.008
#> GSM99544 4 0.6797 0.2605 0.000 0.356 0.108 0.536
#> GSM99546 4 0.5193 0.3488 0.000 0.324 0.020 0.656
#> GSM99548 2 0.1118 0.8824 0.000 0.964 0.000 0.036
#> GSM99550 4 0.6826 0.4844 0.208 0.048 0.080 0.664
#> GSM99552 3 0.3448 0.6822 0.000 0.004 0.828 0.168
#> GSM99554 2 0.1557 0.8777 0.000 0.944 0.000 0.056
#> GSM99556 2 0.0336 0.8924 0.000 0.992 0.000 0.008
#> GSM99558 3 0.2760 0.7157 0.000 0.000 0.872 0.128
#> GSM99560 2 0.4866 0.3608 0.000 0.596 0.000 0.404
#> GSM99562 3 0.1867 0.7722 0.000 0.000 0.928 0.072
#> GSM99564 2 0.3401 0.8014 0.000 0.840 0.008 0.152
#> GSM99572 2 0.0817 0.8907 0.000 0.976 0.000 0.024
#> GSM99576 1 0.4331 0.7880 0.820 0.028 0.016 0.136
#> GSM99578 2 0.0336 0.8924 0.000 0.992 0.000 0.008
#> GSM99580 3 0.1211 0.7757 0.000 0.000 0.960 0.040
#> GSM99582 3 0.4549 0.6412 0.036 0.000 0.776 0.188
#> GSM99584 4 0.5837 0.0605 0.000 0.400 0.036 0.564
#> GSM99586 1 0.2081 0.8809 0.916 0.000 0.000 0.084
#> GSM99588 2 0.0336 0.8920 0.000 0.992 0.000 0.008
#> GSM99590 2 0.0336 0.8924 0.000 0.992 0.000 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM99496 3 0.0880 0.7056 0.000 0.000 0.968 0.000 0.032
#> GSM99502 1 0.0290 0.8860 0.992 0.000 0.000 0.000 0.008
#> GSM99504 3 0.5925 0.1096 0.188 0.000 0.596 0.000 0.216
#> GSM99506 3 0.0703 0.7081 0.000 0.000 0.976 0.000 0.024
#> GSM99566 3 0.0963 0.7070 0.000 0.000 0.964 0.000 0.036
#> GSM99574 1 0.0451 0.8853 0.988 0.000 0.004 0.000 0.008
#> GSM99592 3 0.2848 0.6776 0.000 0.000 0.868 0.028 0.104
#> GSM99594 3 0.1732 0.6921 0.000 0.000 0.920 0.000 0.080
#> GSM99468 1 0.0404 0.8854 0.988 0.000 0.000 0.000 0.012
#> GSM99498 1 0.4942 0.1899 0.540 0.000 0.432 0.000 0.028
#> GSM99500 1 0.2411 0.7932 0.884 0.000 0.108 0.000 0.008
#> GSM99508 3 0.0703 0.7052 0.000 0.000 0.976 0.000 0.024
#> GSM99568 3 0.1270 0.7038 0.000 0.000 0.948 0.000 0.052
#> GSM99596 3 0.1544 0.6984 0.000 0.000 0.932 0.000 0.068
#> GSM99600 2 0.2359 0.8517 0.000 0.904 0.000 0.060 0.036
#> GSM99458 1 0.0579 0.8836 0.984 0.000 0.000 0.008 0.008
#> GSM99460 4 0.5447 0.4508 0.248 0.000 0.000 0.640 0.112
#> GSM99510 4 0.5575 0.3720 0.000 0.000 0.188 0.644 0.168
#> GSM99512 3 0.4535 0.5770 0.000 0.000 0.752 0.108 0.140
#> GSM99514 3 0.3508 0.4712 0.000 0.000 0.748 0.000 0.252
#> GSM99516 1 0.0290 0.8860 0.992 0.000 0.000 0.000 0.008
#> GSM99518 1 0.0404 0.8852 0.988 0.000 0.000 0.000 0.012
#> GSM99520 3 0.0880 0.6999 0.000 0.000 0.968 0.000 0.032
#> GSM99522 3 0.4658 -0.2819 0.000 0.000 0.504 0.012 0.484
#> GSM99570 1 0.0290 0.8860 0.992 0.000 0.000 0.000 0.008
#> GSM99598 1 0.0162 0.8864 0.996 0.000 0.000 0.000 0.004
#> GSM99432 4 0.2388 0.6221 0.000 0.072 0.000 0.900 0.028
#> GSM99434 4 0.3182 0.6281 0.000 0.000 0.032 0.844 0.124
#> GSM99436 2 0.6205 0.3089 0.000 0.512 0.000 0.332 0.156
#> GSM99438 2 0.0162 0.8862 0.000 0.996 0.000 0.004 0.000
#> GSM99440 1 0.0290 0.8857 0.992 0.000 0.000 0.000 0.008
#> GSM99442 2 0.3731 0.7923 0.000 0.816 0.000 0.072 0.112
#> GSM99444 2 0.0290 0.8861 0.000 0.992 0.000 0.000 0.008
#> GSM99446 2 0.6092 0.2632 0.000 0.504 0.000 0.364 0.132
#> GSM99448 5 0.5425 0.2202 0.000 0.000 0.420 0.060 0.520
#> GSM99450 4 0.3146 0.6088 0.000 0.000 0.028 0.844 0.128
#> GSM99452 1 0.0162 0.8861 0.996 0.000 0.000 0.000 0.004
#> GSM99454 1 0.0000 0.8864 1.000 0.000 0.000 0.000 0.000
#> GSM99456 1 0.3517 0.7736 0.832 0.000 0.000 0.068 0.100
#> GSM99462 2 0.0898 0.8814 0.000 0.972 0.000 0.008 0.020
#> GSM99464 4 0.3847 0.6031 0.000 0.000 0.036 0.784 0.180
#> GSM99466 4 0.6800 0.2353 0.000 0.272 0.012 0.488 0.228
#> GSM99470 1 0.3574 0.7500 0.836 0.072 0.000 0.004 0.088
#> GSM99472 1 0.0290 0.8860 0.992 0.000 0.000 0.000 0.008
#> GSM99474 3 0.2439 0.6679 0.000 0.000 0.876 0.004 0.120
#> GSM99476 4 0.1430 0.6363 0.000 0.000 0.004 0.944 0.052
#> GSM99478 2 0.0771 0.8813 0.000 0.976 0.004 0.020 0.000
#> GSM99480 1 0.0290 0.8857 0.992 0.000 0.000 0.000 0.008
#> GSM99482 1 0.0162 0.8864 0.996 0.000 0.000 0.000 0.004
#> GSM99484 2 0.4054 0.7706 0.000 0.788 0.000 0.072 0.140
#> GSM99486 5 0.5954 -0.1356 0.000 0.152 0.000 0.272 0.576
#> GSM99488 2 0.0510 0.8818 0.000 0.984 0.000 0.000 0.016
#> GSM99490 2 0.0451 0.8850 0.000 0.988 0.000 0.004 0.008
#> GSM99492 1 0.1043 0.8726 0.960 0.000 0.000 0.000 0.040
#> GSM99494 2 0.0404 0.8833 0.000 0.988 0.000 0.000 0.012
#> GSM99524 1 0.0290 0.8862 0.992 0.000 0.000 0.000 0.008
#> GSM99526 4 0.2629 0.6325 0.000 0.000 0.004 0.860 0.136
#> GSM99528 3 0.7051 0.2397 0.008 0.244 0.512 0.020 0.216
#> GSM99530 3 0.6083 0.3412 0.000 0.000 0.564 0.176 0.260
#> GSM99532 3 0.5526 0.4382 0.000 0.000 0.648 0.152 0.200
#> GSM99534 2 0.3849 0.7853 0.000 0.808 0.000 0.112 0.080
#> GSM99536 1 0.0794 0.8784 0.972 0.000 0.000 0.000 0.028
#> GSM99538 4 0.5597 0.4853 0.000 0.000 0.160 0.640 0.200
#> GSM99540 1 0.7718 0.1588 0.428 0.000 0.280 0.072 0.220
#> GSM99542 2 0.0609 0.8797 0.000 0.980 0.000 0.000 0.020
#> GSM99544 4 0.3880 0.5585 0.000 0.028 0.004 0.784 0.184
#> GSM99546 4 0.1357 0.6361 0.000 0.004 0.000 0.948 0.048
#> GSM99548 2 0.1251 0.8687 0.000 0.956 0.000 0.008 0.036
#> GSM99550 4 0.6108 0.4995 0.140 0.000 0.020 0.620 0.220
#> GSM99552 3 0.3659 0.4973 0.000 0.012 0.768 0.000 0.220
#> GSM99554 2 0.4569 0.7296 0.000 0.748 0.000 0.104 0.148
#> GSM99556 2 0.0510 0.8818 0.000 0.984 0.000 0.000 0.016
#> GSM99558 3 0.3790 0.4209 0.000 0.004 0.724 0.000 0.272
#> GSM99560 4 0.7412 0.1799 0.000 0.356 0.032 0.360 0.252
#> GSM99562 3 0.3724 0.5266 0.000 0.000 0.776 0.020 0.204
#> GSM99564 4 0.6616 0.0895 0.000 0.216 0.000 0.404 0.380
#> GSM99572 2 0.0693 0.8848 0.000 0.980 0.000 0.012 0.008
#> GSM99576 1 0.8190 0.0464 0.376 0.092 0.312 0.008 0.212
#> GSM99578 2 0.0510 0.8864 0.000 0.984 0.000 0.000 0.016
#> GSM99580 3 0.1197 0.6935 0.000 0.000 0.952 0.000 0.048
#> GSM99582 5 0.6083 0.2130 0.108 0.000 0.400 0.004 0.488
#> GSM99584 4 0.3805 0.5569 0.000 0.032 0.000 0.784 0.184
#> GSM99586 1 0.2771 0.7998 0.860 0.000 0.000 0.012 0.128
#> GSM99588 2 0.0162 0.8854 0.000 0.996 0.000 0.000 0.004
#> GSM99590 2 0.0162 0.8856 0.000 0.996 0.000 0.000 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM99496 5 0.4264 -0.070465 0.000 0.000 0.484 0.016 0.500 0.000
#> GSM99502 1 0.0146 0.907954 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM99504 3 0.4454 0.267010 0.144 0.000 0.736 0.012 0.108 0.000
#> GSM99506 5 0.4594 -0.170932 0.000 0.000 0.480 0.000 0.484 0.036
#> GSM99566 3 0.5286 0.197572 0.000 0.000 0.528 0.012 0.388 0.072
#> GSM99574 1 0.1413 0.894554 0.948 0.000 0.036 0.008 0.004 0.004
#> GSM99592 3 0.5728 0.194703 0.000 0.000 0.488 0.004 0.356 0.152
#> GSM99594 5 0.5481 -0.089865 0.000 0.000 0.360 0.016 0.536 0.088
#> GSM99468 1 0.1251 0.903047 0.956 0.000 0.008 0.012 0.024 0.000
#> GSM99498 1 0.6055 -0.000716 0.472 0.000 0.184 0.012 0.332 0.000
#> GSM99500 1 0.4541 0.681627 0.732 0.000 0.088 0.020 0.160 0.000
#> GSM99508 3 0.4246 0.088420 0.000 0.000 0.576 0.008 0.408 0.008
#> GSM99568 5 0.4876 -0.011572 0.000 0.000 0.444 0.048 0.504 0.004
#> GSM99596 5 0.4567 0.062730 0.000 0.000 0.332 0.052 0.616 0.000
#> GSM99600 4 0.4046 0.456523 0.000 0.368 0.000 0.620 0.004 0.008
#> GSM99458 1 0.0858 0.903122 0.968 0.000 0.000 0.000 0.004 0.028
#> GSM99460 6 0.3571 0.527241 0.216 0.000 0.004 0.000 0.020 0.760
#> GSM99510 6 0.5819 0.146872 0.000 0.000 0.340 0.076 0.048 0.536
#> GSM99512 3 0.7097 0.114198 0.000 0.020 0.364 0.032 0.260 0.324
#> GSM99514 3 0.3316 0.348208 0.000 0.000 0.804 0.028 0.164 0.004
#> GSM99516 1 0.0767 0.907032 0.976 0.000 0.012 0.000 0.008 0.004
#> GSM99518 1 0.1485 0.896171 0.944 0.000 0.004 0.000 0.024 0.028
#> GSM99520 5 0.4763 -0.075037 0.000 0.000 0.476 0.032 0.484 0.008
#> GSM99522 3 0.3910 0.358053 0.000 0.000 0.792 0.100 0.016 0.092
#> GSM99570 1 0.0912 0.905326 0.972 0.000 0.012 0.008 0.004 0.004
#> GSM99598 1 0.0000 0.908189 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99432 6 0.4329 0.233495 0.000 0.012 0.000 0.404 0.008 0.576
#> GSM99434 6 0.1710 0.680892 0.000 0.000 0.028 0.020 0.016 0.936
#> GSM99436 4 0.4638 0.581534 0.000 0.144 0.000 0.704 0.004 0.148
#> GSM99438 2 0.1007 0.875775 0.000 0.956 0.000 0.044 0.000 0.000
#> GSM99440 1 0.0806 0.907677 0.972 0.000 0.000 0.008 0.020 0.000
#> GSM99442 2 0.3986 -0.107111 0.000 0.532 0.000 0.464 0.004 0.000
#> GSM99444 2 0.1010 0.881440 0.000 0.960 0.000 0.036 0.004 0.000
#> GSM99446 4 0.5354 0.557470 0.000 0.212 0.000 0.608 0.004 0.176
#> GSM99448 3 0.5395 0.318770 0.000 0.000 0.644 0.124 0.028 0.204
#> GSM99450 6 0.3605 0.656734 0.000 0.000 0.084 0.108 0.004 0.804
#> GSM99452 1 0.0363 0.909084 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM99454 1 0.0146 0.908660 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM99456 1 0.4747 0.715870 0.736 0.000 0.000 0.052 0.084 0.128
#> GSM99462 2 0.1010 0.881067 0.000 0.960 0.000 0.036 0.004 0.000
#> GSM99464 6 0.2737 0.671116 0.000 0.000 0.004 0.044 0.084 0.868
#> GSM99466 4 0.4811 0.530175 0.000 0.016 0.100 0.752 0.088 0.044
#> GSM99470 1 0.3492 0.769321 0.816 0.028 0.016 0.136 0.004 0.000
#> GSM99472 1 0.1285 0.887968 0.944 0.000 0.000 0.052 0.004 0.000
#> GSM99474 5 0.5625 -0.067529 0.000 0.000 0.356 0.008 0.512 0.124
#> GSM99476 4 0.4927 0.296380 0.000 0.000 0.036 0.616 0.028 0.320
#> GSM99478 4 0.6954 0.454613 0.000 0.144 0.080 0.476 0.288 0.012
#> GSM99480 1 0.0820 0.906327 0.972 0.000 0.000 0.012 0.016 0.000
#> GSM99482 1 0.0363 0.908371 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM99484 4 0.4419 0.526447 0.000 0.304 0.040 0.652 0.004 0.000
#> GSM99486 4 0.5033 0.501909 0.000 0.040 0.084 0.736 0.024 0.116
#> GSM99488 2 0.0146 0.876583 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM99490 2 0.3641 0.616331 0.000 0.748 0.000 0.224 0.028 0.000
#> GSM99492 1 0.1707 0.888400 0.928 0.000 0.000 0.012 0.056 0.004
#> GSM99494 2 0.0551 0.871598 0.000 0.984 0.004 0.004 0.008 0.000
#> GSM99524 1 0.0363 0.908371 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM99526 6 0.1498 0.685010 0.000 0.000 0.000 0.028 0.032 0.940
#> GSM99528 5 0.5496 0.158450 0.004 0.112 0.060 0.104 0.704 0.016
#> GSM99530 5 0.4517 0.192309 0.000 0.000 0.056 0.024 0.720 0.200
#> GSM99532 5 0.5631 0.076253 0.000 0.000 0.128 0.008 0.520 0.344
#> GSM99534 2 0.3437 0.765785 0.028 0.840 0.008 0.100 0.004 0.020
#> GSM99536 1 0.0862 0.906718 0.972 0.000 0.000 0.008 0.016 0.004
#> GSM99538 6 0.4078 0.630152 0.000 0.000 0.004 0.068 0.180 0.748
#> GSM99540 5 0.5991 0.047465 0.384 0.000 0.004 0.008 0.452 0.152
#> GSM99542 2 0.0291 0.874511 0.000 0.992 0.000 0.004 0.004 0.000
#> GSM99544 6 0.4453 0.507261 0.000 0.000 0.032 0.296 0.012 0.660
#> GSM99546 6 0.2170 0.670547 0.000 0.000 0.012 0.100 0.000 0.888
#> GSM99548 2 0.2357 0.801695 0.000 0.872 0.000 0.116 0.012 0.000
#> GSM99550 6 0.6795 0.352349 0.076 0.004 0.000 0.268 0.164 0.488
#> GSM99552 3 0.4578 0.187972 0.000 0.000 0.624 0.056 0.320 0.000
#> GSM99554 4 0.4454 0.469947 0.000 0.348 0.032 0.616 0.004 0.000
#> GSM99556 2 0.0363 0.882584 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM99558 3 0.6036 0.101064 0.000 0.008 0.484 0.220 0.288 0.000
#> GSM99560 4 0.6390 0.398601 0.000 0.088 0.000 0.564 0.164 0.184
#> GSM99562 3 0.5850 0.307581 0.000 0.000 0.612 0.048 0.180 0.160
#> GSM99564 4 0.3964 0.520952 0.000 0.048 0.012 0.764 0.000 0.176
#> GSM99572 2 0.1411 0.864510 0.000 0.936 0.000 0.060 0.004 0.000
#> GSM99576 5 0.5950 0.159156 0.328 0.060 0.000 0.016 0.552 0.044
#> GSM99578 4 0.4975 0.266585 0.000 0.428 0.000 0.504 0.068 0.000
#> GSM99580 3 0.4848 0.196597 0.000 0.000 0.608 0.024 0.336 0.032
#> GSM99582 4 0.6038 0.033766 0.004 0.000 0.376 0.412 0.208 0.000
#> GSM99584 6 0.4195 0.232238 0.000 0.000 0.004 0.440 0.008 0.548
#> GSM99586 1 0.3802 0.791127 0.804 0.000 0.000 0.032 0.116 0.048
#> GSM99588 2 0.0458 0.883052 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM99590 2 0.0508 0.882534 0.000 0.984 0.000 0.012 0.004 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) cell.type(p) k
#> CV:NMF 84 8.94e-05 0.000459 2
#> CV:NMF 83 8.28e-04 0.016801 3
#> CV:NMF 67 2.80e-04 0.010857 4
#> CV:NMF 62 3.07e-05 0.000586 5
#> CV:NMF 48 9.25e-03 0.209661 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 21168 rows and 85 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 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 0.361 0.800 0.878 0.4205 0.519 0.519
#> 3 3 0.503 0.669 0.840 0.5398 0.764 0.563
#> 4 4 0.513 0.471 0.680 0.1034 0.775 0.484
#> 5 5 0.611 0.684 0.802 0.0872 0.846 0.550
#> 6 6 0.683 0.589 0.788 0.0425 0.963 0.838
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
#> GSM99496 1 0.4939 0.8791 0.892 0.108
#> GSM99502 1 0.0000 0.9151 1.000 0.000
#> GSM99504 1 0.0000 0.9151 1.000 0.000
#> GSM99506 1 0.4939 0.8791 0.892 0.108
#> GSM99566 1 0.4939 0.8791 0.892 0.108
#> GSM99574 1 0.0000 0.9151 1.000 0.000
#> GSM99592 1 0.4939 0.8791 0.892 0.108
#> GSM99594 1 0.4939 0.8791 0.892 0.108
#> GSM99468 1 0.0000 0.9151 1.000 0.000
#> GSM99498 1 0.0000 0.9151 1.000 0.000
#> GSM99500 1 0.0000 0.9151 1.000 0.000
#> GSM99508 1 0.4939 0.8791 0.892 0.108
#> GSM99568 1 0.4690 0.8838 0.900 0.100
#> GSM99596 1 0.4939 0.8791 0.892 0.108
#> GSM99600 2 0.6343 0.7817 0.160 0.840
#> GSM99458 1 0.0672 0.9155 0.992 0.008
#> GSM99460 1 0.0672 0.9155 0.992 0.008
#> GSM99510 1 0.5178 0.8722 0.884 0.116
#> GSM99512 1 0.5408 0.8636 0.876 0.124
#> GSM99514 1 0.4939 0.8791 0.892 0.108
#> GSM99516 1 0.0000 0.9151 1.000 0.000
#> GSM99518 1 0.0000 0.9151 1.000 0.000
#> GSM99520 1 0.5408 0.8626 0.876 0.124
#> GSM99522 1 0.4815 0.8815 0.896 0.104
#> GSM99570 1 0.0000 0.9151 1.000 0.000
#> GSM99598 1 0.0000 0.9151 1.000 0.000
#> GSM99432 2 0.8081 0.7604 0.248 0.752
#> GSM99434 1 0.4161 0.8931 0.916 0.084
#> GSM99436 2 0.7376 0.7800 0.208 0.792
#> GSM99438 2 0.0000 0.7523 0.000 1.000
#> GSM99440 1 0.0000 0.9151 1.000 0.000
#> GSM99442 2 0.6438 0.7821 0.164 0.836
#> GSM99444 2 0.0000 0.7523 0.000 1.000
#> GSM99446 2 0.7453 0.7793 0.212 0.788
#> GSM99448 1 0.9815 0.0615 0.580 0.420
#> GSM99450 1 0.3733 0.8982 0.928 0.072
#> GSM99452 1 0.0000 0.9151 1.000 0.000
#> GSM99454 1 0.0000 0.9151 1.000 0.000
#> GSM99456 1 0.0000 0.9151 1.000 0.000
#> GSM99462 2 0.0000 0.7523 0.000 1.000
#> GSM99464 1 0.0672 0.9155 0.992 0.008
#> GSM99466 2 0.9909 0.5060 0.444 0.556
#> GSM99470 1 0.2423 0.9041 0.960 0.040
#> GSM99472 1 0.2423 0.9041 0.960 0.040
#> GSM99474 1 0.4815 0.8804 0.896 0.104
#> GSM99476 1 0.8207 0.6347 0.744 0.256
#> GSM99478 2 0.9815 0.5611 0.420 0.580
#> GSM99480 1 0.0000 0.9151 1.000 0.000
#> GSM99482 1 0.0376 0.9148 0.996 0.004
#> GSM99484 2 0.9866 0.5405 0.432 0.568
#> GSM99486 2 0.7376 0.7797 0.208 0.792
#> GSM99488 2 0.0000 0.7523 0.000 1.000
#> GSM99490 2 0.0000 0.7523 0.000 1.000
#> GSM99492 1 0.0000 0.9151 1.000 0.000
#> GSM99494 2 0.0000 0.7523 0.000 1.000
#> GSM99524 1 0.0000 0.9151 1.000 0.000
#> GSM99526 1 0.3733 0.8985 0.928 0.072
#> GSM99528 2 0.9988 0.4225 0.480 0.520
#> GSM99530 1 0.0672 0.9155 0.992 0.008
#> GSM99532 1 0.0672 0.9155 0.992 0.008
#> GSM99534 2 0.9393 0.6729 0.356 0.644
#> GSM99536 1 0.0000 0.9151 1.000 0.000
#> GSM99538 2 0.8955 0.7092 0.312 0.688
#> GSM99540 1 0.0672 0.9155 0.992 0.008
#> GSM99542 2 0.8955 0.6556 0.312 0.688
#> GSM99544 2 0.8909 0.7129 0.308 0.692
#> GSM99546 2 0.9815 0.5696 0.420 0.580
#> GSM99548 2 0.0000 0.7523 0.000 1.000
#> GSM99550 1 0.1184 0.9106 0.984 0.016
#> GSM99552 2 0.9909 0.4674 0.444 0.556
#> GSM99554 2 0.7219 0.7810 0.200 0.800
#> GSM99556 2 0.0000 0.7523 0.000 1.000
#> GSM99558 2 0.9998 0.3073 0.492 0.508
#> GSM99560 2 0.9248 0.6797 0.340 0.660
#> GSM99562 1 0.4939 0.8791 0.892 0.108
#> GSM99564 2 0.7376 0.7797 0.208 0.792
#> GSM99572 2 0.0000 0.7523 0.000 1.000
#> GSM99576 1 0.4161 0.8661 0.916 0.084
#> GSM99578 2 0.2603 0.7543 0.044 0.956
#> GSM99580 1 0.8608 0.5575 0.716 0.284
#> GSM99582 1 0.7299 0.7160 0.796 0.204
#> GSM99584 2 0.8555 0.7434 0.280 0.720
#> GSM99586 1 0.0000 0.9151 1.000 0.000
#> GSM99588 2 0.7528 0.7776 0.216 0.784
#> GSM99590 2 0.0000 0.7523 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM99496 3 0.0424 0.7684 0.008 0.000 0.992
#> GSM99502 1 0.0000 0.9118 1.000 0.000 0.000
#> GSM99504 1 0.3340 0.8547 0.880 0.000 0.120
#> GSM99506 3 0.0424 0.7684 0.008 0.000 0.992
#> GSM99566 3 0.0237 0.7670 0.004 0.000 0.996
#> GSM99574 1 0.0000 0.9118 1.000 0.000 0.000
#> GSM99592 3 0.0424 0.7684 0.008 0.000 0.992
#> GSM99594 3 0.0237 0.7670 0.004 0.000 0.996
#> GSM99468 1 0.3340 0.8547 0.880 0.000 0.120
#> GSM99498 1 0.3340 0.8547 0.880 0.000 0.120
#> GSM99500 1 0.3340 0.8547 0.880 0.000 0.120
#> GSM99508 3 0.0424 0.7684 0.008 0.000 0.992
#> GSM99568 3 0.3340 0.7266 0.120 0.000 0.880
#> GSM99596 3 0.3192 0.7294 0.112 0.000 0.888
#> GSM99600 2 0.4842 0.7278 0.000 0.776 0.224
#> GSM99458 3 0.6126 0.2481 0.400 0.000 0.600
#> GSM99460 3 0.6111 0.2597 0.396 0.000 0.604
#> GSM99510 3 0.0848 0.7667 0.008 0.008 0.984
#> GSM99512 3 0.0983 0.7610 0.004 0.016 0.980
#> GSM99514 3 0.0424 0.7684 0.008 0.000 0.992
#> GSM99516 1 0.0000 0.9118 1.000 0.000 0.000
#> GSM99518 1 0.1529 0.9020 0.960 0.000 0.040
#> GSM99520 3 0.1482 0.7610 0.012 0.020 0.968
#> GSM99522 3 0.0592 0.7682 0.012 0.000 0.988
#> GSM99570 1 0.0000 0.9118 1.000 0.000 0.000
#> GSM99598 1 0.0000 0.9118 1.000 0.000 0.000
#> GSM99432 2 0.5785 0.6709 0.000 0.668 0.332
#> GSM99434 3 0.2165 0.7554 0.064 0.000 0.936
#> GSM99436 2 0.5560 0.6960 0.000 0.700 0.300
#> GSM99438 2 0.0000 0.7243 0.000 1.000 0.000
#> GSM99440 1 0.0000 0.9118 1.000 0.000 0.000
#> GSM99442 2 0.4062 0.7335 0.000 0.836 0.164
#> GSM99444 2 0.0000 0.7243 0.000 1.000 0.000
#> GSM99446 2 0.5327 0.7122 0.000 0.728 0.272
#> GSM99448 3 0.5621 0.2712 0.000 0.308 0.692
#> GSM99450 3 0.2537 0.7496 0.080 0.000 0.920
#> GSM99452 1 0.0000 0.9118 1.000 0.000 0.000
#> GSM99454 1 0.0000 0.9118 1.000 0.000 0.000
#> GSM99456 1 0.1529 0.9022 0.960 0.000 0.040
#> GSM99462 2 0.0000 0.7243 0.000 1.000 0.000
#> GSM99464 3 0.6111 0.2597 0.396 0.000 0.604
#> GSM99466 2 0.8140 0.3749 0.068 0.476 0.456
#> GSM99470 1 0.2050 0.8867 0.952 0.028 0.020
#> GSM99472 1 0.2050 0.8867 0.952 0.028 0.020
#> GSM99474 3 0.3966 0.7377 0.100 0.024 0.876
#> GSM99476 3 0.3983 0.6266 0.004 0.144 0.852
#> GSM99478 2 0.8050 0.4364 0.064 0.500 0.436
#> GSM99480 1 0.0000 0.9118 1.000 0.000 0.000
#> GSM99482 1 0.0237 0.9105 0.996 0.004 0.000
#> GSM99484 2 0.8316 0.4246 0.080 0.496 0.424
#> GSM99486 2 0.5650 0.6878 0.000 0.688 0.312
#> GSM99488 2 0.0000 0.7243 0.000 1.000 0.000
#> GSM99490 2 0.0237 0.7246 0.000 0.996 0.004
#> GSM99492 1 0.0000 0.9118 1.000 0.000 0.000
#> GSM99494 2 0.0000 0.7243 0.000 1.000 0.000
#> GSM99524 1 0.0000 0.9118 1.000 0.000 0.000
#> GSM99526 3 0.3918 0.7100 0.140 0.004 0.856
#> GSM99528 3 0.8524 -0.3654 0.092 0.452 0.456
#> GSM99530 3 0.6309 -0.1018 0.500 0.000 0.500
#> GSM99532 1 0.6140 0.3703 0.596 0.000 0.404
#> GSM99534 2 0.8525 0.5894 0.200 0.612 0.188
#> GSM99536 1 0.0237 0.9113 0.996 0.000 0.004
#> GSM99538 2 0.6192 0.5603 0.000 0.580 0.420
#> GSM99540 1 0.6140 0.3703 0.596 0.000 0.404
#> GSM99542 2 0.5873 0.4481 0.312 0.684 0.004
#> GSM99544 2 0.6180 0.5661 0.000 0.584 0.416
#> GSM99546 2 0.8627 0.4704 0.104 0.504 0.392
#> GSM99548 2 0.0000 0.7243 0.000 1.000 0.000
#> GSM99550 1 0.4692 0.7861 0.820 0.012 0.168
#> GSM99552 3 0.6483 -0.2636 0.004 0.452 0.544
#> GSM99554 2 0.5016 0.7231 0.000 0.760 0.240
#> GSM99556 2 0.0000 0.7243 0.000 1.000 0.000
#> GSM99558 3 0.6140 -0.0816 0.000 0.404 0.596
#> GSM99560 2 0.6745 0.5277 0.012 0.560 0.428
#> GSM99562 3 0.0237 0.7670 0.004 0.000 0.996
#> GSM99564 2 0.5650 0.6878 0.000 0.688 0.312
#> GSM99572 2 0.0000 0.7243 0.000 1.000 0.000
#> GSM99576 1 0.7145 0.6206 0.692 0.072 0.236
#> GSM99578 2 0.2564 0.7211 0.028 0.936 0.036
#> GSM99580 3 0.4700 0.5729 0.008 0.180 0.812
#> GSM99582 3 0.6511 0.6191 0.104 0.136 0.760
#> GSM99584 2 0.6510 0.6325 0.012 0.624 0.364
#> GSM99586 1 0.1529 0.9022 0.960 0.000 0.040
#> GSM99588 2 0.5138 0.7198 0.000 0.748 0.252
#> GSM99590 2 0.0237 0.7251 0.000 0.996 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM99496 3 0.4713 0.33228 0.000 0.000 0.640 0.360
#> GSM99502 1 0.0000 0.83523 1.000 0.000 0.000 0.000
#> GSM99504 1 0.4323 0.69456 0.788 0.000 0.028 0.184
#> GSM99506 3 0.4713 0.33228 0.000 0.000 0.640 0.360
#> GSM99566 3 0.4730 0.33230 0.000 0.000 0.636 0.364
#> GSM99574 1 0.0000 0.83523 1.000 0.000 0.000 0.000
#> GSM99592 3 0.4522 0.34809 0.000 0.000 0.680 0.320
#> GSM99594 3 0.4730 0.33230 0.000 0.000 0.636 0.364
#> GSM99468 1 0.4323 0.69456 0.788 0.000 0.028 0.184
#> GSM99498 1 0.4323 0.69456 0.788 0.000 0.028 0.184
#> GSM99500 1 0.4323 0.69456 0.788 0.000 0.028 0.184
#> GSM99508 3 0.4713 0.33228 0.000 0.000 0.640 0.360
#> GSM99568 3 0.5731 0.16253 0.028 0.000 0.544 0.428
#> GSM99596 3 0.5716 0.17354 0.028 0.000 0.552 0.420
#> GSM99600 2 0.5607 0.20546 0.000 0.492 0.488 0.020
#> GSM99458 4 0.6587 0.62073 0.112 0.000 0.292 0.596
#> GSM99460 4 0.6538 0.61604 0.108 0.000 0.292 0.600
#> GSM99510 3 0.4585 0.34309 0.000 0.000 0.668 0.332
#> GSM99512 3 0.4585 0.34861 0.000 0.000 0.668 0.332
#> GSM99514 3 0.4713 0.33228 0.000 0.000 0.640 0.360
#> GSM99516 1 0.0000 0.83523 1.000 0.000 0.000 0.000
#> GSM99518 1 0.2654 0.78512 0.888 0.000 0.004 0.108
#> GSM99520 3 0.4564 0.34971 0.000 0.000 0.672 0.328
#> GSM99522 3 0.4920 0.32448 0.004 0.000 0.628 0.368
#> GSM99570 1 0.0000 0.83523 1.000 0.000 0.000 0.000
#> GSM99598 1 0.0000 0.83523 1.000 0.000 0.000 0.000
#> GSM99432 3 0.5482 0.05979 0.000 0.368 0.608 0.024
#> GSM99434 3 0.5143 0.25393 0.012 0.000 0.628 0.360
#> GSM99436 3 0.5660 -0.02318 0.000 0.396 0.576 0.028
#> GSM99438 2 0.1637 0.82262 0.000 0.940 0.060 0.000
#> GSM99440 1 0.0000 0.83523 1.000 0.000 0.000 0.000
#> GSM99442 2 0.5517 0.33547 0.000 0.568 0.412 0.020
#> GSM99444 2 0.1302 0.82763 0.000 0.956 0.044 0.000
#> GSM99446 3 0.5570 -0.13145 0.000 0.440 0.540 0.020
#> GSM99448 3 0.5434 0.43410 0.000 0.132 0.740 0.128
#> GSM99450 3 0.5339 0.21800 0.016 0.000 0.600 0.384
#> GSM99452 1 0.0469 0.83110 0.988 0.000 0.000 0.012
#> GSM99454 1 0.0000 0.83523 1.000 0.000 0.000 0.000
#> GSM99456 1 0.5151 0.29352 0.532 0.000 0.004 0.464
#> GSM99462 2 0.0592 0.82986 0.000 0.984 0.016 0.000
#> GSM99464 4 0.6538 0.61604 0.108 0.000 0.292 0.600
#> GSM99466 3 0.6325 0.34394 0.016 0.212 0.680 0.092
#> GSM99470 1 0.5945 0.52699 0.648 0.012 0.040 0.300
#> GSM99472 1 0.5945 0.52699 0.648 0.012 0.040 0.300
#> GSM99474 3 0.5536 0.21980 0.024 0.000 0.592 0.384
#> GSM99476 3 0.4793 0.39044 0.000 0.040 0.756 0.204
#> GSM99478 3 0.6164 0.31826 0.012 0.228 0.680 0.080
#> GSM99480 1 0.0000 0.83523 1.000 0.000 0.000 0.000
#> GSM99482 1 0.4482 0.63903 0.728 0.000 0.008 0.264
#> GSM99484 3 0.6595 0.30688 0.016 0.232 0.652 0.100
#> GSM99486 3 0.5548 0.00647 0.000 0.388 0.588 0.024
#> GSM99488 2 0.0188 0.82581 0.000 0.996 0.000 0.004
#> GSM99490 2 0.0524 0.82802 0.000 0.988 0.008 0.004
#> GSM99492 1 0.1389 0.82279 0.952 0.000 0.000 0.048
#> GSM99494 2 0.0188 0.82581 0.000 0.996 0.000 0.004
#> GSM99524 1 0.0000 0.83523 1.000 0.000 0.000 0.000
#> GSM99526 3 0.5488 0.02777 0.016 0.000 0.532 0.452
#> GSM99528 3 0.6954 0.34193 0.028 0.220 0.640 0.112
#> GSM99530 4 0.4920 0.65847 0.068 0.000 0.164 0.768
#> GSM99532 4 0.6732 0.68603 0.220 0.000 0.168 0.612
#> GSM99534 3 0.8652 -0.13322 0.076 0.344 0.440 0.140
#> GSM99536 1 0.0376 0.83318 0.992 0.000 0.004 0.004
#> GSM99538 3 0.5367 0.22328 0.000 0.304 0.664 0.032
#> GSM99540 4 0.6732 0.68603 0.220 0.000 0.168 0.612
#> GSM99542 2 0.5527 0.49101 0.016 0.664 0.016 0.304
#> GSM99544 3 0.5389 0.21572 0.000 0.308 0.660 0.032
#> GSM99546 3 0.7252 0.25907 0.016 0.240 0.592 0.152
#> GSM99548 2 0.0524 0.82856 0.000 0.988 0.008 0.004
#> GSM99550 4 0.6699 0.16793 0.388 0.004 0.080 0.528
#> GSM99552 3 0.6954 0.35961 0.000 0.280 0.568 0.152
#> GSM99554 3 0.5695 -0.20567 0.000 0.476 0.500 0.024
#> GSM99556 2 0.0000 0.82699 0.000 1.000 0.000 0.000
#> GSM99558 3 0.6134 0.42492 0.000 0.216 0.668 0.116
#> GSM99560 3 0.5790 0.25084 0.004 0.304 0.648 0.044
#> GSM99562 3 0.4730 0.33230 0.000 0.000 0.636 0.364
#> GSM99564 3 0.5548 0.00647 0.000 0.388 0.588 0.024
#> GSM99572 2 0.1474 0.82596 0.000 0.948 0.052 0.000
#> GSM99576 4 0.7223 0.43967 0.252 0.020 0.132 0.596
#> GSM99578 2 0.3036 0.78721 0.008 0.892 0.080 0.020
#> GSM99580 3 0.5361 0.40160 0.000 0.060 0.716 0.224
#> GSM99582 3 0.6401 0.27956 0.044 0.032 0.644 0.280
#> GSM99584 3 0.5596 0.13696 0.000 0.332 0.632 0.036
#> GSM99586 1 0.5151 0.29352 0.532 0.000 0.004 0.464
#> GSM99588 2 0.5250 0.25729 0.000 0.552 0.440 0.008
#> GSM99590 2 0.1576 0.82642 0.000 0.948 0.048 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM99496 3 0.0798 0.77362 0.000 0.000 0.976 0.016 0.008
#> GSM99502 1 0.0000 0.85637 1.000 0.000 0.000 0.000 0.000
#> GSM99504 1 0.4159 0.68155 0.776 0.000 0.068 0.000 0.156
#> GSM99506 3 0.1018 0.77357 0.000 0.000 0.968 0.016 0.016
#> GSM99566 3 0.1597 0.76687 0.000 0.000 0.940 0.012 0.048
#> GSM99574 1 0.0000 0.85637 1.000 0.000 0.000 0.000 0.000
#> GSM99592 3 0.3517 0.74417 0.000 0.000 0.832 0.100 0.068
#> GSM99594 3 0.1597 0.76687 0.000 0.000 0.940 0.012 0.048
#> GSM99468 1 0.4159 0.68155 0.776 0.000 0.068 0.000 0.156
#> GSM99498 1 0.4159 0.68155 0.776 0.000 0.068 0.000 0.156
#> GSM99500 1 0.4159 0.68155 0.776 0.000 0.068 0.000 0.156
#> GSM99508 3 0.0798 0.77362 0.000 0.000 0.976 0.016 0.008
#> GSM99568 3 0.3601 0.67901 0.024 0.000 0.832 0.020 0.124
#> GSM99596 3 0.3409 0.68073 0.024 0.000 0.844 0.016 0.116
#> GSM99600 4 0.2929 0.67677 0.000 0.180 0.000 0.820 0.000
#> GSM99458 5 0.5337 0.42652 0.040 0.000 0.328 0.016 0.616
#> GSM99460 5 0.5189 0.42082 0.036 0.000 0.332 0.012 0.620
#> GSM99510 3 0.3741 0.74435 0.000 0.000 0.816 0.108 0.076
#> GSM99512 3 0.3003 0.75665 0.000 0.000 0.864 0.092 0.044
#> GSM99514 3 0.0798 0.77362 0.000 0.000 0.976 0.016 0.008
#> GSM99516 1 0.0000 0.85637 1.000 0.000 0.000 0.000 0.000
#> GSM99518 1 0.2389 0.78344 0.880 0.000 0.004 0.000 0.116
#> GSM99520 3 0.2291 0.76859 0.000 0.000 0.908 0.056 0.036
#> GSM99522 3 0.1597 0.77094 0.000 0.000 0.940 0.012 0.048
#> GSM99570 1 0.0000 0.85637 1.000 0.000 0.000 0.000 0.000
#> GSM99598 1 0.0000 0.85637 1.000 0.000 0.000 0.000 0.000
#> GSM99432 4 0.2074 0.77809 0.000 0.036 0.044 0.920 0.000
#> GSM99434 3 0.5345 0.61013 0.000 0.000 0.668 0.136 0.196
#> GSM99436 4 0.2046 0.76396 0.000 0.068 0.016 0.916 0.000
#> GSM99438 2 0.3395 0.85044 0.000 0.764 0.000 0.236 0.000
#> GSM99440 1 0.0000 0.85637 1.000 0.000 0.000 0.000 0.000
#> GSM99442 4 0.3766 0.55113 0.000 0.268 0.004 0.728 0.000
#> GSM99444 2 0.3177 0.87484 0.000 0.792 0.000 0.208 0.000
#> GSM99446 4 0.2964 0.73831 0.000 0.120 0.024 0.856 0.000
#> GSM99448 4 0.5045 0.00462 0.000 0.004 0.464 0.508 0.024
#> GSM99450 3 0.5327 0.58605 0.000 0.000 0.664 0.120 0.216
#> GSM99452 1 0.0579 0.84897 0.984 0.008 0.000 0.000 0.008
#> GSM99454 1 0.0000 0.85637 1.000 0.000 0.000 0.000 0.000
#> GSM99456 5 0.4572 0.16967 0.452 0.004 0.004 0.000 0.540
#> GSM99462 2 0.2773 0.89319 0.000 0.836 0.000 0.164 0.000
#> GSM99464 5 0.5189 0.42082 0.036 0.000 0.332 0.012 0.620
#> GSM99466 4 0.4794 0.71988 0.000 0.020 0.120 0.760 0.100
#> GSM99470 1 0.6798 0.45116 0.616 0.108 0.012 0.068 0.196
#> GSM99472 1 0.6798 0.45116 0.616 0.108 0.012 0.068 0.196
#> GSM99474 3 0.5189 0.62502 0.012 0.000 0.700 0.084 0.204
#> GSM99476 3 0.6124 0.16929 0.000 0.000 0.460 0.412 0.128
#> GSM99478 4 0.4447 0.74193 0.000 0.020 0.100 0.788 0.092
#> GSM99480 1 0.0000 0.85637 1.000 0.000 0.000 0.000 0.000
#> GSM99482 1 0.5646 0.58217 0.700 0.096 0.012 0.020 0.172
#> GSM99484 4 0.4983 0.72997 0.000 0.036 0.104 0.756 0.104
#> GSM99486 4 0.1800 0.76971 0.000 0.048 0.020 0.932 0.000
#> GSM99488 2 0.2179 0.89334 0.000 0.888 0.000 0.112 0.000
#> GSM99490 2 0.2439 0.89535 0.000 0.876 0.000 0.120 0.004
#> GSM99492 1 0.1478 0.82896 0.936 0.000 0.000 0.000 0.064
#> GSM99494 2 0.2179 0.89334 0.000 0.888 0.000 0.112 0.000
#> GSM99524 1 0.0000 0.85637 1.000 0.000 0.000 0.000 0.000
#> GSM99526 3 0.6142 0.22763 0.000 0.000 0.472 0.132 0.396
#> GSM99528 4 0.5442 0.70223 0.004 0.024 0.116 0.716 0.140
#> GSM99530 5 0.3280 0.54432 0.000 0.004 0.160 0.012 0.824
#> GSM99532 5 0.5751 0.63687 0.160 0.000 0.172 0.012 0.656
#> GSM99534 4 0.5594 0.63319 0.052 0.160 0.004 0.712 0.072
#> GSM99536 1 0.0290 0.85370 0.992 0.000 0.000 0.000 0.008
#> GSM99538 4 0.2692 0.77957 0.000 0.008 0.092 0.884 0.016
#> GSM99540 5 0.5751 0.63687 0.160 0.000 0.172 0.012 0.656
#> GSM99542 2 0.4517 0.56712 0.000 0.756 0.012 0.052 0.180
#> GSM99544 4 0.2589 0.77857 0.000 0.008 0.092 0.888 0.012
#> GSM99546 4 0.4812 0.71431 0.004 0.016 0.112 0.764 0.104
#> GSM99548 2 0.2329 0.89599 0.000 0.876 0.000 0.124 0.000
#> GSM99550 5 0.5260 0.47753 0.304 0.004 0.024 0.024 0.644
#> GSM99552 4 0.4047 0.56151 0.000 0.004 0.320 0.676 0.000
#> GSM99554 4 0.2886 0.71050 0.000 0.148 0.008 0.844 0.000
#> GSM99556 2 0.2280 0.89562 0.000 0.880 0.000 0.120 0.000
#> GSM99558 4 0.4709 0.48648 0.000 0.004 0.324 0.648 0.024
#> GSM99560 4 0.3613 0.77831 0.000 0.016 0.072 0.844 0.068
#> GSM99562 3 0.1444 0.76594 0.000 0.000 0.948 0.012 0.040
#> GSM99564 4 0.1800 0.76971 0.000 0.048 0.020 0.932 0.000
#> GSM99572 2 0.3242 0.86983 0.000 0.784 0.000 0.216 0.000
#> GSM99576 5 0.7777 0.48361 0.188 0.072 0.060 0.120 0.560
#> GSM99578 2 0.4019 0.82417 0.000 0.768 0.004 0.200 0.028
#> GSM99580 3 0.4326 0.58086 0.000 0.000 0.708 0.264 0.028
#> GSM99582 3 0.7058 0.23677 0.024 0.000 0.444 0.336 0.196
#> GSM99584 4 0.2277 0.78434 0.000 0.016 0.052 0.916 0.016
#> GSM99586 5 0.4572 0.16967 0.452 0.004 0.004 0.000 0.540
#> GSM99588 4 0.4276 0.57380 0.000 0.256 0.028 0.716 0.000
#> GSM99590 2 0.3274 0.86830 0.000 0.780 0.000 0.220 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM99496 3 0.0405 0.73662 0.000 0.000 0.988 0.000 0.004 0.008
#> GSM99502 1 0.0000 0.77402 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99504 1 0.4329 0.61639 0.776 0.000 0.060 0.000 0.080 0.084
#> GSM99506 3 0.0458 0.73601 0.000 0.000 0.984 0.000 0.000 0.016
#> GSM99566 3 0.1464 0.72700 0.000 0.004 0.944 0.000 0.016 0.036
#> GSM99574 1 0.0000 0.77402 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99592 3 0.4949 0.63200 0.000 0.000 0.704 0.084 0.172 0.040
#> GSM99594 3 0.1464 0.72700 0.000 0.004 0.944 0.000 0.016 0.036
#> GSM99468 1 0.4329 0.61639 0.776 0.000 0.060 0.000 0.080 0.084
#> GSM99498 1 0.4329 0.61639 0.776 0.000 0.060 0.000 0.080 0.084
#> GSM99500 1 0.4329 0.61639 0.776 0.000 0.060 0.000 0.080 0.084
#> GSM99508 3 0.0405 0.73662 0.000 0.000 0.988 0.000 0.004 0.008
#> GSM99568 3 0.3552 0.65725 0.024 0.000 0.832 0.004 0.064 0.076
#> GSM99596 3 0.3292 0.65987 0.024 0.000 0.844 0.000 0.056 0.076
#> GSM99600 4 0.3709 0.66193 0.000 0.204 0.000 0.756 0.000 0.040
#> GSM99458 5 0.2604 0.49634 0.020 0.000 0.100 0.000 0.872 0.008
#> GSM99460 5 0.2405 0.49938 0.016 0.000 0.100 0.000 0.880 0.004
#> GSM99510 3 0.6058 0.57337 0.000 0.000 0.600 0.068 0.168 0.164
#> GSM99512 3 0.4565 0.66766 0.000 0.004 0.744 0.072 0.028 0.152
#> GSM99514 3 0.0405 0.73662 0.000 0.000 0.988 0.000 0.004 0.008
#> GSM99516 1 0.0000 0.77402 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99518 1 0.2512 0.70699 0.880 0.000 0.000 0.000 0.060 0.060
#> GSM99520 3 0.3840 0.69192 0.000 0.000 0.796 0.052 0.128 0.024
#> GSM99522 3 0.2866 0.72493 0.000 0.004 0.860 0.000 0.084 0.052
#> GSM99570 1 0.0000 0.77402 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99598 1 0.0000 0.77402 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99432 4 0.2006 0.74625 0.000 0.036 0.008 0.924 0.008 0.024
#> GSM99434 3 0.6940 0.26350 0.000 0.000 0.420 0.100 0.332 0.148
#> GSM99436 4 0.1838 0.74395 0.000 0.068 0.000 0.916 0.000 0.016
#> GSM99438 2 0.2750 0.85075 0.000 0.844 0.000 0.136 0.000 0.020
#> GSM99440 1 0.0000 0.77402 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99442 4 0.3936 0.57342 0.000 0.288 0.000 0.688 0.000 0.024
#> GSM99444 2 0.2450 0.86671 0.000 0.868 0.000 0.116 0.000 0.016
#> GSM99446 4 0.2734 0.73585 0.000 0.116 0.004 0.860 0.004 0.016
#> GSM99448 4 0.6056 0.12987 0.000 0.004 0.344 0.520 0.080 0.052
#> GSM99450 3 0.6515 0.26205 0.000 0.000 0.440 0.084 0.376 0.100
#> GSM99452 1 0.0458 0.76553 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM99454 1 0.0000 0.77402 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99456 1 0.5765 -0.30300 0.420 0.000 0.000 0.000 0.408 0.172
#> GSM99462 2 0.1471 0.88615 0.000 0.932 0.000 0.064 0.000 0.004
#> GSM99464 5 0.2405 0.49938 0.016 0.000 0.100 0.000 0.880 0.004
#> GSM99466 4 0.5247 0.66434 0.000 0.004 0.064 0.704 0.116 0.112
#> GSM99470 1 0.4527 0.15157 0.564 0.004 0.000 0.020 0.004 0.408
#> GSM99472 1 0.4527 0.15157 0.564 0.004 0.000 0.020 0.004 0.408
#> GSM99474 3 0.5969 0.47272 0.012 0.000 0.572 0.068 0.296 0.052
#> GSM99476 4 0.7138 0.04403 0.000 0.000 0.292 0.396 0.220 0.092
#> GSM99478 4 0.4893 0.68367 0.000 0.004 0.048 0.732 0.104 0.112
#> GSM99480 1 0.0000 0.77402 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99482 1 0.3607 0.35757 0.652 0.000 0.000 0.000 0.000 0.348
#> GSM99484 4 0.5379 0.66760 0.000 0.012 0.056 0.700 0.112 0.120
#> GSM99486 4 0.1865 0.74192 0.000 0.040 0.000 0.920 0.000 0.040
#> GSM99488 2 0.0260 0.87772 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM99490 2 0.0891 0.88343 0.000 0.968 0.000 0.024 0.000 0.008
#> GSM99492 1 0.2001 0.73272 0.912 0.000 0.000 0.000 0.048 0.040
#> GSM99494 2 0.0260 0.87772 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM99524 1 0.0000 0.77402 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99526 5 0.5878 0.27482 0.000 0.000 0.176 0.096 0.628 0.100
#> GSM99528 4 0.5732 0.63615 0.000 0.008 0.056 0.656 0.140 0.140
#> GSM99530 5 0.4673 0.19384 0.000 0.000 0.080 0.000 0.648 0.272
#> GSM99532 5 0.6047 0.14168 0.148 0.000 0.088 0.000 0.612 0.152
#> GSM99534 4 0.5258 0.59146 0.008 0.100 0.000 0.648 0.012 0.232
#> GSM99536 1 0.0260 0.77117 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM99538 4 0.2222 0.73601 0.000 0.004 0.012 0.912 0.040 0.032
#> GSM99540 5 0.6047 0.14168 0.148 0.000 0.088 0.000 0.612 0.152
#> GSM99542 2 0.3578 0.52123 0.000 0.660 0.000 0.000 0.000 0.340
#> GSM99544 4 0.2171 0.73546 0.000 0.004 0.016 0.916 0.032 0.032
#> GSM99546 4 0.5521 0.63851 0.004 0.004 0.060 0.684 0.112 0.136
#> GSM99548 2 0.0692 0.88199 0.000 0.976 0.000 0.020 0.000 0.004
#> GSM99550 5 0.5993 -0.28801 0.272 0.000 0.000 0.020 0.532 0.176
#> GSM99552 4 0.4264 0.56615 0.000 0.004 0.284 0.680 0.004 0.028
#> GSM99554 4 0.3172 0.71489 0.000 0.148 0.000 0.816 0.000 0.036
#> GSM99556 2 0.0935 0.88558 0.000 0.964 0.000 0.032 0.000 0.004
#> GSM99558 4 0.5478 0.53238 0.000 0.004 0.224 0.648 0.072 0.052
#> GSM99560 4 0.3935 0.73097 0.000 0.016 0.020 0.812 0.080 0.072
#> GSM99562 3 0.2182 0.72068 0.000 0.004 0.900 0.000 0.020 0.076
#> GSM99564 4 0.1865 0.74192 0.000 0.040 0.000 0.920 0.000 0.040
#> GSM99572 2 0.2536 0.86606 0.000 0.864 0.000 0.116 0.000 0.020
#> GSM99576 6 0.7370 0.00000 0.176 0.004 0.028 0.060 0.300 0.432
#> GSM99578 2 0.3237 0.81173 0.000 0.840 0.004 0.112 0.016 0.028
#> GSM99580 3 0.5665 0.50495 0.000 0.000 0.596 0.264 0.104 0.036
#> GSM99582 3 0.7395 0.00504 0.020 0.000 0.332 0.316 0.276 0.056
#> GSM99584 4 0.2452 0.74542 0.000 0.012 0.016 0.904 0.028 0.040
#> GSM99586 1 0.5765 -0.30300 0.420 0.000 0.000 0.000 0.408 0.172
#> GSM99588 4 0.3850 0.61592 0.000 0.260 0.004 0.716 0.000 0.020
#> GSM99590 2 0.2623 0.85961 0.000 0.852 0.000 0.132 0.000 0.016
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) cell.type(p) k
#> MAD:hclust 81 6.16e-05 3.41e-04 2
#> MAD:hclust 70 1.32e-04 4.69e-03 3
#> MAD:hclust 37 1.74e-02 9.57e-02 4
#> MAD:hclust 71 3.44e-06 1.50e-03 5
#> MAD:hclust 65 8.30e-08 2.83e-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", "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 21168 rows and 85 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.683 0.836 0.926 0.4862 0.503 0.503
#> 3 3 1.000 0.962 0.984 0.3849 0.729 0.507
#> 4 4 0.774 0.639 0.832 0.1079 0.955 0.865
#> 5 5 0.731 0.643 0.815 0.0636 0.870 0.590
#> 6 6 0.751 0.645 0.790 0.0420 0.909 0.607
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
#> GSM99496 1 0.8555 0.6989 0.720 0.280
#> GSM99502 1 0.0000 0.8895 1.000 0.000
#> GSM99504 1 0.0000 0.8895 1.000 0.000
#> GSM99506 1 0.8555 0.6989 0.720 0.280
#> GSM99566 1 0.8763 0.6762 0.704 0.296
#> GSM99574 1 0.0000 0.8895 1.000 0.000
#> GSM99592 1 0.8813 0.6701 0.700 0.300
#> GSM99594 1 0.8608 0.6934 0.716 0.284
#> GSM99468 1 0.0000 0.8895 1.000 0.000
#> GSM99498 1 0.0000 0.8895 1.000 0.000
#> GSM99500 1 0.0000 0.8895 1.000 0.000
#> GSM99508 1 0.6887 0.7874 0.816 0.184
#> GSM99568 1 0.8555 0.6989 0.720 0.280
#> GSM99596 1 0.3431 0.8617 0.936 0.064
#> GSM99600 2 0.0000 0.9438 0.000 1.000
#> GSM99458 1 0.0000 0.8895 1.000 0.000
#> GSM99460 1 0.0000 0.8895 1.000 0.000
#> GSM99510 2 0.9896 0.0552 0.440 0.560
#> GSM99512 2 0.9850 0.1038 0.428 0.572
#> GSM99514 1 0.8555 0.6989 0.720 0.280
#> GSM99516 1 0.0000 0.8895 1.000 0.000
#> GSM99518 1 0.0000 0.8895 1.000 0.000
#> GSM99520 1 0.8555 0.6989 0.720 0.280
#> GSM99522 1 0.0000 0.8895 1.000 0.000
#> GSM99570 1 0.0000 0.8895 1.000 0.000
#> GSM99598 1 0.0000 0.8895 1.000 0.000
#> GSM99432 2 0.0000 0.9438 0.000 1.000
#> GSM99434 1 0.9129 0.6219 0.672 0.328
#> GSM99436 2 0.0000 0.9438 0.000 1.000
#> GSM99438 2 0.0000 0.9438 0.000 1.000
#> GSM99440 1 0.0000 0.8895 1.000 0.000
#> GSM99442 2 0.0000 0.9438 0.000 1.000
#> GSM99444 2 0.0000 0.9438 0.000 1.000
#> GSM99446 2 0.0000 0.9438 0.000 1.000
#> GSM99448 2 0.0000 0.9438 0.000 1.000
#> GSM99450 1 0.5842 0.8185 0.860 0.140
#> GSM99452 1 0.0000 0.8895 1.000 0.000
#> GSM99454 1 0.0000 0.8895 1.000 0.000
#> GSM99456 1 0.0000 0.8895 1.000 0.000
#> GSM99462 2 0.0000 0.9438 0.000 1.000
#> GSM99464 1 0.0000 0.8895 1.000 0.000
#> GSM99466 2 0.0000 0.9438 0.000 1.000
#> GSM99470 1 0.0376 0.8880 0.996 0.004
#> GSM99472 1 0.0000 0.8895 1.000 0.000
#> GSM99474 1 0.8443 0.7074 0.728 0.272
#> GSM99476 2 0.0000 0.9438 0.000 1.000
#> GSM99478 2 0.0000 0.9438 0.000 1.000
#> GSM99480 1 0.0000 0.8895 1.000 0.000
#> GSM99482 1 0.0000 0.8895 1.000 0.000
#> GSM99484 2 0.0000 0.9438 0.000 1.000
#> GSM99486 2 0.0000 0.9438 0.000 1.000
#> GSM99488 2 0.0000 0.9438 0.000 1.000
#> GSM99490 2 0.0000 0.9438 0.000 1.000
#> GSM99492 1 0.0000 0.8895 1.000 0.000
#> GSM99494 2 0.0000 0.9438 0.000 1.000
#> GSM99524 1 0.0000 0.8895 1.000 0.000
#> GSM99526 1 0.9988 0.2274 0.520 0.480
#> GSM99528 2 0.3584 0.8721 0.068 0.932
#> GSM99530 1 0.4161 0.8519 0.916 0.084
#> GSM99532 1 0.0000 0.8895 1.000 0.000
#> GSM99534 2 0.0000 0.9438 0.000 1.000
#> GSM99536 1 0.0000 0.8895 1.000 0.000
#> GSM99538 2 0.0000 0.9438 0.000 1.000
#> GSM99540 1 0.0000 0.8895 1.000 0.000
#> GSM99542 2 0.0000 0.9438 0.000 1.000
#> GSM99544 2 0.0000 0.9438 0.000 1.000
#> GSM99546 2 0.9000 0.4459 0.316 0.684
#> GSM99548 2 0.0000 0.9438 0.000 1.000
#> GSM99550 1 0.0000 0.8895 1.000 0.000
#> GSM99552 2 0.9850 0.1038 0.428 0.572
#> GSM99554 2 0.0000 0.9438 0.000 1.000
#> GSM99556 2 0.0000 0.9438 0.000 1.000
#> GSM99558 2 0.0000 0.9438 0.000 1.000
#> GSM99560 2 0.0000 0.9438 0.000 1.000
#> GSM99562 1 0.8555 0.6989 0.720 0.280
#> GSM99564 2 0.0000 0.9438 0.000 1.000
#> GSM99572 2 0.0000 0.9438 0.000 1.000
#> GSM99576 1 0.0000 0.8895 1.000 0.000
#> GSM99578 2 0.0000 0.9438 0.000 1.000
#> GSM99580 1 0.8955 0.6506 0.688 0.312
#> GSM99582 1 0.6712 0.7935 0.824 0.176
#> GSM99584 2 0.0000 0.9438 0.000 1.000
#> GSM99586 1 0.0000 0.8895 1.000 0.000
#> GSM99588 2 0.0000 0.9438 0.000 1.000
#> GSM99590 2 0.0000 0.9438 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM99496 3 0.0237 0.9799 0.000 0.004 0.996
#> GSM99502 1 0.0000 0.9987 1.000 0.000 0.000
#> GSM99504 1 0.0000 0.9987 1.000 0.000 0.000
#> GSM99506 3 0.0237 0.9799 0.000 0.004 0.996
#> GSM99566 3 0.0237 0.9799 0.000 0.004 0.996
#> GSM99574 1 0.0000 0.9987 1.000 0.000 0.000
#> GSM99592 3 0.0237 0.9799 0.000 0.004 0.996
#> GSM99594 3 0.0237 0.9799 0.000 0.004 0.996
#> GSM99468 1 0.0000 0.9987 1.000 0.000 0.000
#> GSM99498 1 0.0000 0.9987 1.000 0.000 0.000
#> GSM99500 1 0.0000 0.9987 1.000 0.000 0.000
#> GSM99508 3 0.0237 0.9799 0.000 0.004 0.996
#> GSM99568 3 0.0237 0.9799 0.000 0.004 0.996
#> GSM99596 3 0.0237 0.9767 0.004 0.000 0.996
#> GSM99600 2 0.0000 0.9729 0.000 1.000 0.000
#> GSM99458 1 0.0000 0.9987 1.000 0.000 0.000
#> GSM99460 1 0.0237 0.9975 0.996 0.000 0.004
#> GSM99510 3 0.0237 0.9799 0.000 0.004 0.996
#> GSM99512 3 0.0237 0.9799 0.000 0.004 0.996
#> GSM99514 3 0.0237 0.9799 0.000 0.004 0.996
#> GSM99516 1 0.0000 0.9987 1.000 0.000 0.000
#> GSM99518 1 0.0000 0.9987 1.000 0.000 0.000
#> GSM99520 3 0.0237 0.9799 0.000 0.004 0.996
#> GSM99522 3 0.0237 0.9767 0.004 0.000 0.996
#> GSM99570 1 0.0000 0.9987 1.000 0.000 0.000
#> GSM99598 1 0.0000 0.9987 1.000 0.000 0.000
#> GSM99432 2 0.0000 0.9729 0.000 1.000 0.000
#> GSM99434 3 0.0237 0.9799 0.000 0.004 0.996
#> GSM99436 2 0.0000 0.9729 0.000 1.000 0.000
#> GSM99438 2 0.0000 0.9729 0.000 1.000 0.000
#> GSM99440 1 0.0000 0.9987 1.000 0.000 0.000
#> GSM99442 2 0.0000 0.9729 0.000 1.000 0.000
#> GSM99444 2 0.0000 0.9729 0.000 1.000 0.000
#> GSM99446 2 0.0000 0.9729 0.000 1.000 0.000
#> GSM99448 3 0.0237 0.9799 0.000 0.004 0.996
#> GSM99450 3 0.0237 0.9799 0.000 0.004 0.996
#> GSM99452 1 0.0000 0.9987 1.000 0.000 0.000
#> GSM99454 1 0.0000 0.9987 1.000 0.000 0.000
#> GSM99456 1 0.0237 0.9975 0.996 0.000 0.004
#> GSM99462 2 0.0000 0.9729 0.000 1.000 0.000
#> GSM99464 3 0.0000 0.9770 0.000 0.000 1.000
#> GSM99466 2 0.5465 0.6065 0.000 0.712 0.288
#> GSM99470 1 0.0000 0.9987 1.000 0.000 0.000
#> GSM99472 1 0.0000 0.9987 1.000 0.000 0.000
#> GSM99474 3 0.0237 0.9799 0.000 0.004 0.996
#> GSM99476 3 0.0237 0.9799 0.000 0.004 0.996
#> GSM99478 2 0.4750 0.7298 0.000 0.784 0.216
#> GSM99480 1 0.0237 0.9975 0.996 0.000 0.004
#> GSM99482 1 0.0000 0.9987 1.000 0.000 0.000
#> GSM99484 2 0.0000 0.9729 0.000 1.000 0.000
#> GSM99486 2 0.0000 0.9729 0.000 1.000 0.000
#> GSM99488 2 0.0000 0.9729 0.000 1.000 0.000
#> GSM99490 2 0.0000 0.9729 0.000 1.000 0.000
#> GSM99492 1 0.0237 0.9975 0.996 0.000 0.004
#> GSM99494 2 0.0000 0.9729 0.000 1.000 0.000
#> GSM99524 1 0.0000 0.9987 1.000 0.000 0.000
#> GSM99526 3 0.0237 0.9799 0.000 0.004 0.996
#> GSM99528 3 0.6291 0.0667 0.000 0.468 0.532
#> GSM99530 3 0.0000 0.9770 0.000 0.000 1.000
#> GSM99532 3 0.0000 0.9770 0.000 0.000 1.000
#> GSM99534 2 0.0000 0.9729 0.000 1.000 0.000
#> GSM99536 1 0.0237 0.9975 0.996 0.000 0.004
#> GSM99538 2 0.4796 0.7241 0.000 0.780 0.220
#> GSM99540 1 0.0237 0.9975 0.996 0.000 0.004
#> GSM99542 2 0.0000 0.9729 0.000 1.000 0.000
#> GSM99544 2 0.0000 0.9729 0.000 1.000 0.000
#> GSM99546 3 0.1411 0.9499 0.000 0.036 0.964
#> GSM99548 2 0.0000 0.9729 0.000 1.000 0.000
#> GSM99550 1 0.0592 0.9907 0.988 0.000 0.012
#> GSM99552 3 0.0237 0.9799 0.000 0.004 0.996
#> GSM99554 2 0.0000 0.9729 0.000 1.000 0.000
#> GSM99556 2 0.0000 0.9729 0.000 1.000 0.000
#> GSM99558 3 0.0892 0.9659 0.000 0.020 0.980
#> GSM99560 2 0.0000 0.9729 0.000 1.000 0.000
#> GSM99562 3 0.0237 0.9799 0.000 0.004 0.996
#> GSM99564 2 0.0000 0.9729 0.000 1.000 0.000
#> GSM99572 2 0.0000 0.9729 0.000 1.000 0.000
#> GSM99576 1 0.0237 0.9975 0.996 0.000 0.004
#> GSM99578 2 0.0000 0.9729 0.000 1.000 0.000
#> GSM99580 3 0.0237 0.9799 0.000 0.004 0.996
#> GSM99582 3 0.0237 0.9799 0.000 0.004 0.996
#> GSM99584 2 0.0000 0.9729 0.000 1.000 0.000
#> GSM99586 1 0.0237 0.9975 0.996 0.000 0.004
#> GSM99588 2 0.0000 0.9729 0.000 1.000 0.000
#> GSM99590 2 0.0000 0.9729 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM99496 3 0.0000 0.8625 0.000 0.000 1.000 0.000
#> GSM99502 1 0.0000 0.9163 1.000 0.000 0.000 0.000
#> GSM99504 1 0.0000 0.9163 1.000 0.000 0.000 0.000
#> GSM99506 3 0.0000 0.8625 0.000 0.000 1.000 0.000
#> GSM99566 3 0.0000 0.8625 0.000 0.000 1.000 0.000
#> GSM99574 1 0.0000 0.9163 1.000 0.000 0.000 0.000
#> GSM99592 3 0.0000 0.8625 0.000 0.000 1.000 0.000
#> GSM99594 3 0.0000 0.8625 0.000 0.000 1.000 0.000
#> GSM99468 1 0.0000 0.9163 1.000 0.000 0.000 0.000
#> GSM99498 1 0.0000 0.9163 1.000 0.000 0.000 0.000
#> GSM99500 1 0.0000 0.9163 1.000 0.000 0.000 0.000
#> GSM99508 3 0.0000 0.8625 0.000 0.000 1.000 0.000
#> GSM99568 3 0.0000 0.8625 0.000 0.000 1.000 0.000
#> GSM99596 3 0.0000 0.8625 0.000 0.000 1.000 0.000
#> GSM99600 2 0.4790 0.6500 0.000 0.620 0.000 0.380
#> GSM99458 1 0.3764 0.7988 0.784 0.000 0.000 0.216
#> GSM99460 1 0.4193 0.7596 0.732 0.000 0.000 0.268
#> GSM99510 3 0.4137 0.7040 0.000 0.012 0.780 0.208
#> GSM99512 3 0.0817 0.8525 0.000 0.000 0.976 0.024
#> GSM99514 3 0.0000 0.8625 0.000 0.000 1.000 0.000
#> GSM99516 1 0.0000 0.9163 1.000 0.000 0.000 0.000
#> GSM99518 1 0.0000 0.9163 1.000 0.000 0.000 0.000
#> GSM99520 3 0.0000 0.8625 0.000 0.000 1.000 0.000
#> GSM99522 3 0.0000 0.8625 0.000 0.000 1.000 0.000
#> GSM99570 1 0.0188 0.9160 0.996 0.000 0.000 0.004
#> GSM99598 1 0.0000 0.9163 1.000 0.000 0.000 0.000
#> GSM99432 2 0.3801 -0.0501 0.000 0.780 0.000 0.220
#> GSM99434 3 0.4635 0.6328 0.000 0.012 0.720 0.268
#> GSM99436 2 0.0000 0.4159 0.000 1.000 0.000 0.000
#> GSM99438 2 0.4866 0.6514 0.000 0.596 0.000 0.404
#> GSM99440 1 0.0469 0.9146 0.988 0.000 0.000 0.012
#> GSM99442 2 0.4855 0.6515 0.000 0.600 0.000 0.400
#> GSM99444 2 0.4866 0.6514 0.000 0.596 0.000 0.404
#> GSM99446 2 0.0592 0.4314 0.000 0.984 0.000 0.016
#> GSM99448 3 0.4614 0.6969 0.000 0.064 0.792 0.144
#> GSM99450 3 0.3907 0.6983 0.000 0.000 0.768 0.232
#> GSM99452 1 0.0469 0.9146 0.988 0.000 0.000 0.012
#> GSM99454 1 0.0188 0.9160 0.996 0.000 0.000 0.004
#> GSM99456 1 0.4164 0.7825 0.736 0.000 0.000 0.264
#> GSM99462 2 0.4866 0.6514 0.000 0.596 0.000 0.404
#> GSM99464 3 0.4992 0.3165 0.000 0.000 0.524 0.476
#> GSM99466 2 0.5522 -0.3593 0.000 0.668 0.044 0.288
#> GSM99470 1 0.6469 0.5142 0.644 0.192 0.000 0.164
#> GSM99472 1 0.3266 0.8340 0.832 0.000 0.000 0.168
#> GSM99474 3 0.0469 0.8577 0.000 0.000 0.988 0.012
#> GSM99476 2 0.7834 -0.6145 0.000 0.404 0.320 0.276
#> GSM99478 2 0.5247 -0.3112 0.000 0.684 0.032 0.284
#> GSM99480 1 0.2011 0.8885 0.920 0.000 0.000 0.080
#> GSM99482 1 0.0336 0.9154 0.992 0.000 0.000 0.008
#> GSM99484 2 0.3219 0.1420 0.000 0.836 0.000 0.164
#> GSM99486 2 0.1557 0.3412 0.000 0.944 0.000 0.056
#> GSM99488 2 0.4866 0.6514 0.000 0.596 0.000 0.404
#> GSM99490 2 0.4817 0.6512 0.000 0.612 0.000 0.388
#> GSM99492 1 0.2011 0.8885 0.920 0.000 0.000 0.080
#> GSM99494 2 0.4866 0.6514 0.000 0.596 0.000 0.404
#> GSM99524 1 0.0188 0.9160 0.996 0.000 0.000 0.004
#> GSM99526 4 0.6702 0.8884 0.000 0.396 0.092 0.512
#> GSM99528 4 0.6337 0.8330 0.000 0.468 0.060 0.472
#> GSM99530 3 0.4193 0.6369 0.000 0.000 0.732 0.268
#> GSM99532 3 0.3688 0.7033 0.000 0.000 0.792 0.208
#> GSM99534 2 0.2647 0.3509 0.000 0.880 0.000 0.120
#> GSM99536 1 0.0921 0.9090 0.972 0.000 0.000 0.028
#> GSM99538 2 0.5648 -0.3210 0.000 0.684 0.064 0.252
#> GSM99540 1 0.3649 0.8121 0.796 0.000 0.000 0.204
#> GSM99542 2 0.4972 0.6292 0.000 0.544 0.000 0.456
#> GSM99544 2 0.3688 -0.0141 0.000 0.792 0.000 0.208
#> GSM99546 4 0.6562 0.8948 0.000 0.404 0.080 0.516
#> GSM99548 2 0.4866 0.6514 0.000 0.596 0.000 0.404
#> GSM99550 4 0.5869 0.8106 0.044 0.360 0.000 0.596
#> GSM99552 3 0.0188 0.8604 0.000 0.004 0.996 0.000
#> GSM99554 2 0.4585 0.6364 0.000 0.668 0.000 0.332
#> GSM99556 2 0.4866 0.6514 0.000 0.596 0.000 0.404
#> GSM99558 3 0.7276 -0.3217 0.000 0.404 0.448 0.148
#> GSM99560 2 0.3649 0.0282 0.000 0.796 0.000 0.204
#> GSM99562 3 0.0000 0.8625 0.000 0.000 1.000 0.000
#> GSM99564 2 0.0921 0.3814 0.000 0.972 0.000 0.028
#> GSM99572 2 0.4866 0.6514 0.000 0.596 0.000 0.404
#> GSM99576 1 0.4304 0.7487 0.716 0.000 0.000 0.284
#> GSM99578 2 0.4643 0.5967 0.000 0.656 0.000 0.344
#> GSM99580 3 0.0000 0.8625 0.000 0.000 1.000 0.000
#> GSM99582 3 0.7173 0.1205 0.000 0.228 0.556 0.216
#> GSM99584 2 0.4431 -0.2774 0.000 0.696 0.000 0.304
#> GSM99586 1 0.4072 0.7925 0.748 0.000 0.000 0.252
#> GSM99588 2 0.4817 0.6512 0.000 0.612 0.000 0.388
#> GSM99590 2 0.4866 0.6514 0.000 0.596 0.000 0.404
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM99496 3 0.0162 0.8363 0.000 0.000 0.996 0.000 0.004
#> GSM99502 1 0.0404 0.8870 0.988 0.000 0.000 0.012 0.000
#> GSM99504 1 0.0404 0.8866 0.988 0.000 0.000 0.012 0.000
#> GSM99506 3 0.0162 0.8363 0.000 0.000 0.996 0.000 0.004
#> GSM99566 3 0.0162 0.8363 0.000 0.000 0.996 0.000 0.004
#> GSM99574 1 0.0404 0.8870 0.988 0.000 0.000 0.012 0.000
#> GSM99592 3 0.0290 0.8349 0.000 0.000 0.992 0.000 0.008
#> GSM99594 3 0.0324 0.8356 0.000 0.000 0.992 0.004 0.004
#> GSM99468 1 0.0510 0.8866 0.984 0.000 0.000 0.016 0.000
#> GSM99498 1 0.0404 0.8866 0.988 0.000 0.000 0.012 0.000
#> GSM99500 1 0.0404 0.8866 0.988 0.000 0.000 0.012 0.000
#> GSM99508 3 0.0162 0.8363 0.000 0.000 0.996 0.000 0.004
#> GSM99568 3 0.0162 0.8357 0.000 0.000 0.996 0.000 0.004
#> GSM99596 3 0.0324 0.8356 0.000 0.000 0.992 0.004 0.004
#> GSM99600 2 0.4419 0.4035 0.000 0.668 0.000 0.312 0.020
#> GSM99458 5 0.4321 0.3257 0.396 0.000 0.000 0.004 0.600
#> GSM99460 5 0.4218 0.4219 0.332 0.000 0.000 0.008 0.660
#> GSM99510 3 0.5775 0.5107 0.000 0.000 0.608 0.244 0.148
#> GSM99512 3 0.3110 0.7623 0.000 0.000 0.860 0.080 0.060
#> GSM99514 3 0.0162 0.8363 0.000 0.000 0.996 0.000 0.004
#> GSM99516 1 0.0162 0.8870 0.996 0.000 0.000 0.000 0.004
#> GSM99518 1 0.0912 0.8821 0.972 0.000 0.000 0.016 0.012
#> GSM99520 3 0.0000 0.8360 0.000 0.000 1.000 0.000 0.000
#> GSM99522 3 0.0798 0.8299 0.000 0.000 0.976 0.008 0.016
#> GSM99570 1 0.0912 0.8821 0.972 0.000 0.000 0.012 0.016
#> GSM99598 1 0.0324 0.8871 0.992 0.000 0.000 0.004 0.004
#> GSM99432 4 0.2612 0.7089 0.000 0.124 0.000 0.868 0.008
#> GSM99434 3 0.6433 0.3478 0.000 0.000 0.504 0.268 0.228
#> GSM99436 4 0.4524 0.5772 0.000 0.336 0.000 0.644 0.020
#> GSM99438 2 0.0000 0.8713 0.000 1.000 0.000 0.000 0.000
#> GSM99440 1 0.0451 0.8865 0.988 0.000 0.000 0.008 0.004
#> GSM99442 2 0.2144 0.8194 0.000 0.912 0.000 0.068 0.020
#> GSM99444 2 0.0162 0.8704 0.000 0.996 0.000 0.000 0.004
#> GSM99446 4 0.4540 0.5707 0.000 0.340 0.000 0.640 0.020
#> GSM99448 3 0.4976 0.2403 0.000 0.000 0.504 0.468 0.028
#> GSM99450 3 0.6120 0.4097 0.000 0.000 0.556 0.176 0.268
#> GSM99452 1 0.1012 0.8806 0.968 0.000 0.000 0.012 0.020
#> GSM99454 1 0.0162 0.8872 0.996 0.000 0.000 0.000 0.004
#> GSM99456 5 0.5009 0.1437 0.428 0.000 0.000 0.032 0.540
#> GSM99462 2 0.0162 0.8704 0.000 0.996 0.000 0.000 0.004
#> GSM99464 5 0.5268 0.4457 0.004 0.000 0.168 0.136 0.692
#> GSM99466 4 0.4730 0.6506 0.000 0.068 0.008 0.736 0.188
#> GSM99470 5 0.6779 0.2048 0.332 0.000 0.000 0.284 0.384
#> GSM99472 1 0.5218 0.2942 0.604 0.000 0.000 0.060 0.336
#> GSM99474 3 0.0992 0.8241 0.000 0.000 0.968 0.008 0.024
#> GSM99476 4 0.3758 0.5714 0.000 0.000 0.088 0.816 0.096
#> GSM99478 4 0.4730 0.6506 0.000 0.068 0.008 0.736 0.188
#> GSM99480 1 0.2450 0.8204 0.896 0.000 0.000 0.028 0.076
#> GSM99482 1 0.1557 0.8582 0.940 0.000 0.000 0.008 0.052
#> GSM99484 4 0.5472 0.6615 0.000 0.140 0.000 0.652 0.208
#> GSM99486 4 0.4526 0.6198 0.000 0.300 0.000 0.672 0.028
#> GSM99488 2 0.0162 0.8704 0.000 0.996 0.000 0.000 0.004
#> GSM99490 2 0.2761 0.7856 0.000 0.872 0.000 0.104 0.024
#> GSM99492 1 0.2535 0.8169 0.892 0.000 0.000 0.032 0.076
#> GSM99494 2 0.0162 0.8704 0.000 0.996 0.000 0.000 0.004
#> GSM99524 1 0.0798 0.8816 0.976 0.000 0.000 0.008 0.016
#> GSM99526 5 0.4276 0.3102 0.000 0.000 0.004 0.380 0.616
#> GSM99528 4 0.5021 0.3096 0.000 0.020 0.008 0.556 0.416
#> GSM99530 5 0.4827 -0.1128 0.000 0.000 0.476 0.020 0.504
#> GSM99532 3 0.4717 0.2983 0.000 0.000 0.584 0.020 0.396
#> GSM99534 4 0.6805 0.2979 0.000 0.316 0.000 0.372 0.312
#> GSM99536 1 0.1216 0.8767 0.960 0.000 0.000 0.020 0.020
#> GSM99538 4 0.3418 0.6803 0.000 0.068 0.028 0.860 0.044
#> GSM99540 1 0.4738 -0.1003 0.520 0.000 0.000 0.016 0.464
#> GSM99542 2 0.3090 0.7459 0.000 0.860 0.000 0.052 0.088
#> GSM99544 4 0.2771 0.7073 0.000 0.128 0.000 0.860 0.012
#> GSM99546 5 0.4452 -0.0181 0.000 0.000 0.004 0.496 0.500
#> GSM99548 2 0.0000 0.8713 0.000 1.000 0.000 0.000 0.000
#> GSM99550 5 0.2411 0.4756 0.008 0.000 0.000 0.108 0.884
#> GSM99552 3 0.2482 0.7663 0.000 0.000 0.892 0.024 0.084
#> GSM99554 4 0.4811 0.3258 0.000 0.452 0.000 0.528 0.020
#> GSM99556 2 0.0000 0.8713 0.000 1.000 0.000 0.000 0.000
#> GSM99558 4 0.4028 0.5688 0.000 0.000 0.192 0.768 0.040
#> GSM99560 4 0.4810 0.6799 0.000 0.204 0.000 0.712 0.084
#> GSM99562 3 0.0566 0.8327 0.000 0.000 0.984 0.004 0.012
#> GSM99564 4 0.4456 0.5984 0.000 0.320 0.000 0.660 0.020
#> GSM99572 2 0.0000 0.8713 0.000 1.000 0.000 0.000 0.000
#> GSM99576 5 0.4584 0.4045 0.312 0.000 0.000 0.028 0.660
#> GSM99578 2 0.6433 -0.0783 0.000 0.464 0.000 0.352 0.184
#> GSM99580 3 0.0000 0.8360 0.000 0.000 1.000 0.000 0.000
#> GSM99582 3 0.6623 0.1097 0.000 0.000 0.444 0.236 0.320
#> GSM99584 4 0.2989 0.6685 0.000 0.060 0.000 0.868 0.072
#> GSM99586 1 0.5047 -0.0568 0.496 0.000 0.000 0.032 0.472
#> GSM99588 2 0.3687 0.6690 0.000 0.792 0.000 0.180 0.028
#> GSM99590 2 0.0000 0.8713 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM99496 3 0.0260 0.8906 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM99502 1 0.0622 0.9491 0.980 0.000 0.000 0.000 0.012 0.008
#> GSM99504 1 0.0909 0.9475 0.968 0.000 0.000 0.000 0.012 0.020
#> GSM99506 3 0.0260 0.8907 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM99566 3 0.0260 0.8907 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM99574 1 0.0622 0.9491 0.980 0.000 0.000 0.000 0.012 0.008
#> GSM99592 3 0.0405 0.8891 0.000 0.000 0.988 0.004 0.008 0.000
#> GSM99594 3 0.0405 0.8905 0.000 0.000 0.988 0.000 0.004 0.008
#> GSM99468 1 0.0820 0.9484 0.972 0.000 0.000 0.000 0.012 0.016
#> GSM99498 1 0.0909 0.9475 0.968 0.000 0.000 0.000 0.012 0.020
#> GSM99500 1 0.0909 0.9475 0.968 0.000 0.000 0.000 0.012 0.020
#> GSM99508 3 0.0146 0.8910 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM99568 3 0.0508 0.8897 0.000 0.000 0.984 0.000 0.004 0.012
#> GSM99596 3 0.0363 0.8898 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM99600 4 0.3838 0.1937 0.000 0.448 0.000 0.552 0.000 0.000
#> GSM99458 5 0.4416 0.4886 0.212 0.000 0.000 0.004 0.708 0.076
#> GSM99460 5 0.3220 0.5236 0.108 0.000 0.000 0.004 0.832 0.056
#> GSM99510 3 0.7476 0.0220 0.000 0.000 0.388 0.204 0.192 0.216
#> GSM99512 3 0.5683 0.5303 0.000 0.000 0.640 0.064 0.112 0.184
#> GSM99514 3 0.0146 0.8907 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM99516 1 0.0146 0.9489 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM99518 1 0.0806 0.9480 0.972 0.000 0.000 0.000 0.020 0.008
#> GSM99520 3 0.0146 0.8904 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM99522 3 0.1788 0.8630 0.000 0.000 0.928 0.004 0.028 0.040
#> GSM99570 1 0.0520 0.9461 0.984 0.000 0.000 0.000 0.008 0.008
#> GSM99598 1 0.0146 0.9489 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM99432 4 0.2867 0.6052 0.000 0.040 0.000 0.868 0.016 0.076
#> GSM99434 5 0.7557 0.2367 0.000 0.000 0.240 0.200 0.360 0.200
#> GSM99436 4 0.2883 0.5949 0.000 0.212 0.000 0.788 0.000 0.000
#> GSM99438 2 0.0000 0.8878 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99440 1 0.0260 0.9480 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM99442 2 0.3050 0.6591 0.000 0.764 0.000 0.236 0.000 0.000
#> GSM99444 2 0.0260 0.8869 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM99446 4 0.2969 0.5880 0.000 0.224 0.000 0.776 0.000 0.000
#> GSM99448 4 0.6434 0.2324 0.000 0.000 0.256 0.508 0.048 0.188
#> GSM99450 5 0.6846 0.1976 0.000 0.000 0.328 0.116 0.440 0.116
#> GSM99452 1 0.1088 0.9362 0.960 0.000 0.000 0.000 0.016 0.024
#> GSM99454 1 0.0146 0.9487 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM99456 5 0.5586 0.4081 0.284 0.000 0.000 0.004 0.552 0.160
#> GSM99462 2 0.0820 0.8807 0.000 0.972 0.000 0.000 0.012 0.016
#> GSM99464 5 0.2325 0.5081 0.000 0.000 0.044 0.048 0.900 0.008
#> GSM99466 4 0.4604 0.0124 0.000 0.008 0.000 0.536 0.024 0.432
#> GSM99470 6 0.6041 0.4460 0.180 0.000 0.000 0.128 0.084 0.608
#> GSM99472 6 0.5052 0.1798 0.388 0.000 0.000 0.000 0.080 0.532
#> GSM99474 3 0.2680 0.7737 0.000 0.000 0.856 0.016 0.124 0.004
#> GSM99476 4 0.4395 0.4997 0.000 0.000 0.016 0.740 0.080 0.164
#> GSM99478 4 0.4624 -0.0465 0.000 0.008 0.000 0.516 0.024 0.452
#> GSM99480 1 0.2697 0.8481 0.864 0.000 0.000 0.000 0.044 0.092
#> GSM99482 1 0.2932 0.7923 0.820 0.000 0.000 0.000 0.016 0.164
#> GSM99484 6 0.4536 0.0592 0.000 0.024 0.000 0.476 0.004 0.496
#> GSM99486 4 0.3156 0.5998 0.000 0.180 0.000 0.800 0.000 0.020
#> GSM99488 2 0.0909 0.8806 0.000 0.968 0.000 0.000 0.012 0.020
#> GSM99490 2 0.3445 0.7268 0.000 0.796 0.000 0.156 0.000 0.048
#> GSM99492 1 0.3159 0.8172 0.836 0.000 0.000 0.004 0.052 0.108
#> GSM99494 2 0.0909 0.8806 0.000 0.968 0.000 0.000 0.012 0.020
#> GSM99524 1 0.1265 0.9255 0.948 0.000 0.000 0.000 0.008 0.044
#> GSM99526 5 0.4849 0.3940 0.000 0.000 0.000 0.188 0.664 0.148
#> GSM99528 6 0.5576 0.4130 0.000 0.000 0.004 0.244 0.184 0.568
#> GSM99530 5 0.4207 0.4481 0.000 0.000 0.244 0.024 0.712 0.020
#> GSM99532 5 0.4591 0.2862 0.000 0.000 0.372 0.020 0.592 0.016
#> GSM99534 6 0.5827 0.4465 0.000 0.148 0.000 0.220 0.036 0.596
#> GSM99536 1 0.1421 0.9338 0.944 0.000 0.000 0.000 0.028 0.028
#> GSM99538 4 0.3057 0.5769 0.000 0.008 0.004 0.844 0.024 0.120
#> GSM99540 5 0.4183 0.4521 0.296 0.000 0.000 0.000 0.668 0.036
#> GSM99542 2 0.3744 0.5958 0.000 0.724 0.000 0.004 0.016 0.256
#> GSM99544 4 0.3059 0.6037 0.000 0.040 0.000 0.856 0.020 0.084
#> GSM99546 5 0.5911 0.2085 0.000 0.000 0.000 0.252 0.468 0.280
#> GSM99548 2 0.0146 0.8876 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM99550 5 0.3940 0.4268 0.008 0.000 0.000 0.016 0.704 0.272
#> GSM99552 3 0.3398 0.5826 0.000 0.000 0.740 0.008 0.000 0.252
#> GSM99554 4 0.3371 0.5239 0.000 0.292 0.000 0.708 0.000 0.000
#> GSM99556 2 0.0146 0.8876 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM99558 4 0.4418 0.4778 0.000 0.000 0.076 0.728 0.012 0.184
#> GSM99560 4 0.3955 0.5391 0.000 0.092 0.000 0.784 0.012 0.112
#> GSM99562 3 0.1757 0.8611 0.000 0.000 0.928 0.008 0.012 0.052
#> GSM99564 4 0.2823 0.5986 0.000 0.204 0.000 0.796 0.000 0.000
#> GSM99572 2 0.0000 0.8878 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99576 5 0.5399 0.3500 0.116 0.000 0.000 0.008 0.576 0.300
#> GSM99578 6 0.5926 0.2777 0.000 0.260 0.000 0.276 0.000 0.464
#> GSM99580 3 0.0665 0.8877 0.000 0.000 0.980 0.004 0.008 0.008
#> GSM99582 6 0.6731 0.1440 0.000 0.000 0.364 0.064 0.164 0.408
#> GSM99584 4 0.3703 0.5514 0.000 0.008 0.000 0.796 0.064 0.132
#> GSM99586 5 0.5833 0.2500 0.380 0.000 0.000 0.004 0.452 0.164
#> GSM99588 2 0.4843 0.5148 0.000 0.652 0.000 0.232 0.000 0.116
#> GSM99590 2 0.0000 0.8878 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) cell.type(p) k
#> MAD:kmeans 80 3.14e-05 0.00018 2
#> MAD:kmeans 84 3.89e-04 0.00926 3
#> MAD:kmeans 68 2.71e-03 0.07714 4
#> MAD:kmeans 62 1.49e-06 0.00040 5
#> MAD:kmeans 59 3.81e-05 0.00500 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 21168 rows and 85 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.974 0.989 0.5053 0.496 0.496
#> 3 3 1.000 0.979 0.990 0.3274 0.757 0.545
#> 4 4 0.839 0.823 0.914 0.0915 0.944 0.832
#> 5 5 0.764 0.638 0.827 0.0623 0.925 0.747
#> 6 6 0.731 0.587 0.761 0.0353 0.949 0.791
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
#> GSM99496 1 0.0000 0.982 1.000 0.000
#> GSM99502 1 0.0000 0.982 1.000 0.000
#> GSM99504 1 0.0000 0.982 1.000 0.000
#> GSM99506 1 0.0000 0.982 1.000 0.000
#> GSM99566 1 0.6712 0.787 0.824 0.176
#> GSM99574 1 0.0000 0.982 1.000 0.000
#> GSM99592 1 0.7745 0.710 0.772 0.228
#> GSM99594 1 0.0672 0.975 0.992 0.008
#> GSM99468 1 0.0000 0.982 1.000 0.000
#> GSM99498 1 0.0000 0.982 1.000 0.000
#> GSM99500 1 0.0000 0.982 1.000 0.000
#> GSM99508 1 0.0000 0.982 1.000 0.000
#> GSM99568 1 0.0000 0.982 1.000 0.000
#> GSM99596 1 0.0000 0.982 1.000 0.000
#> GSM99600 2 0.0000 0.996 0.000 1.000
#> GSM99458 1 0.0000 0.982 1.000 0.000
#> GSM99460 1 0.0000 0.982 1.000 0.000
#> GSM99510 2 0.0000 0.996 0.000 1.000
#> GSM99512 2 0.0000 0.996 0.000 1.000
#> GSM99514 1 0.0000 0.982 1.000 0.000
#> GSM99516 1 0.0000 0.982 1.000 0.000
#> GSM99518 1 0.0000 0.982 1.000 0.000
#> GSM99520 1 0.0000 0.982 1.000 0.000
#> GSM99522 1 0.0000 0.982 1.000 0.000
#> GSM99570 1 0.0000 0.982 1.000 0.000
#> GSM99598 1 0.0000 0.982 1.000 0.000
#> GSM99432 2 0.0000 0.996 0.000 1.000
#> GSM99434 2 0.3584 0.926 0.068 0.932
#> GSM99436 2 0.0000 0.996 0.000 1.000
#> GSM99438 2 0.0000 0.996 0.000 1.000
#> GSM99440 1 0.0000 0.982 1.000 0.000
#> GSM99442 2 0.0000 0.996 0.000 1.000
#> GSM99444 2 0.0000 0.996 0.000 1.000
#> GSM99446 2 0.0000 0.996 0.000 1.000
#> GSM99448 2 0.0000 0.996 0.000 1.000
#> GSM99450 1 0.0000 0.982 1.000 0.000
#> GSM99452 1 0.0000 0.982 1.000 0.000
#> GSM99454 1 0.0000 0.982 1.000 0.000
#> GSM99456 1 0.0000 0.982 1.000 0.000
#> GSM99462 2 0.0000 0.996 0.000 1.000
#> GSM99464 1 0.0000 0.982 1.000 0.000
#> GSM99466 2 0.0000 0.996 0.000 1.000
#> GSM99470 1 0.9608 0.381 0.616 0.384
#> GSM99472 1 0.0000 0.982 1.000 0.000
#> GSM99474 1 0.0000 0.982 1.000 0.000
#> GSM99476 2 0.0000 0.996 0.000 1.000
#> GSM99478 2 0.0000 0.996 0.000 1.000
#> GSM99480 1 0.0000 0.982 1.000 0.000
#> GSM99482 1 0.0000 0.982 1.000 0.000
#> GSM99484 2 0.0000 0.996 0.000 1.000
#> GSM99486 2 0.0000 0.996 0.000 1.000
#> GSM99488 2 0.0000 0.996 0.000 1.000
#> GSM99490 2 0.0000 0.996 0.000 1.000
#> GSM99492 1 0.0000 0.982 1.000 0.000
#> GSM99494 2 0.0000 0.996 0.000 1.000
#> GSM99524 1 0.0000 0.982 1.000 0.000
#> GSM99526 2 0.0000 0.996 0.000 1.000
#> GSM99528 2 0.0000 0.996 0.000 1.000
#> GSM99530 1 0.0000 0.982 1.000 0.000
#> GSM99532 1 0.0000 0.982 1.000 0.000
#> GSM99534 2 0.0000 0.996 0.000 1.000
#> GSM99536 1 0.0000 0.982 1.000 0.000
#> GSM99538 2 0.0000 0.996 0.000 1.000
#> GSM99540 1 0.0000 0.982 1.000 0.000
#> GSM99542 2 0.0000 0.996 0.000 1.000
#> GSM99544 2 0.0000 0.996 0.000 1.000
#> GSM99546 2 0.0000 0.996 0.000 1.000
#> GSM99548 2 0.0000 0.996 0.000 1.000
#> GSM99550 1 0.0000 0.982 1.000 0.000
#> GSM99552 2 0.0000 0.996 0.000 1.000
#> GSM99554 2 0.0000 0.996 0.000 1.000
#> GSM99556 2 0.0000 0.996 0.000 1.000
#> GSM99558 2 0.0000 0.996 0.000 1.000
#> GSM99560 2 0.0000 0.996 0.000 1.000
#> GSM99562 1 0.0000 0.982 1.000 0.000
#> GSM99564 2 0.0000 0.996 0.000 1.000
#> GSM99572 2 0.0000 0.996 0.000 1.000
#> GSM99576 1 0.0000 0.982 1.000 0.000
#> GSM99578 2 0.0000 0.996 0.000 1.000
#> GSM99580 2 0.3584 0.926 0.068 0.932
#> GSM99582 1 0.0000 0.982 1.000 0.000
#> GSM99584 2 0.0000 0.996 0.000 1.000
#> GSM99586 1 0.0000 0.982 1.000 0.000
#> GSM99588 2 0.0000 0.996 0.000 1.000
#> GSM99590 2 0.0000 0.996 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM99496 3 0.0000 0.975 0.000 0.000 1.000
#> GSM99502 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99504 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99506 3 0.0000 0.975 0.000 0.000 1.000
#> GSM99566 3 0.0000 0.975 0.000 0.000 1.000
#> GSM99574 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99592 3 0.0000 0.975 0.000 0.000 1.000
#> GSM99594 3 0.0000 0.975 0.000 0.000 1.000
#> GSM99468 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99498 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99500 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99508 3 0.0000 0.975 0.000 0.000 1.000
#> GSM99568 3 0.0000 0.975 0.000 0.000 1.000
#> GSM99596 3 0.0000 0.975 0.000 0.000 1.000
#> GSM99600 2 0.0000 0.994 0.000 1.000 0.000
#> GSM99458 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99460 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99510 3 0.0000 0.975 0.000 0.000 1.000
#> GSM99512 3 0.0000 0.975 0.000 0.000 1.000
#> GSM99514 3 0.0000 0.975 0.000 0.000 1.000
#> GSM99516 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99518 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99520 3 0.0000 0.975 0.000 0.000 1.000
#> GSM99522 3 0.0000 0.975 0.000 0.000 1.000
#> GSM99570 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99598 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99432 2 0.0000 0.994 0.000 1.000 0.000
#> GSM99434 3 0.0000 0.975 0.000 0.000 1.000
#> GSM99436 2 0.0000 0.994 0.000 1.000 0.000
#> GSM99438 2 0.0000 0.994 0.000 1.000 0.000
#> GSM99440 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99442 2 0.0000 0.994 0.000 1.000 0.000
#> GSM99444 2 0.0000 0.994 0.000 1.000 0.000
#> GSM99446 2 0.0000 0.994 0.000 1.000 0.000
#> GSM99448 3 0.0000 0.975 0.000 0.000 1.000
#> GSM99450 3 0.0000 0.975 0.000 0.000 1.000
#> GSM99452 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99454 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99456 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99462 2 0.0000 0.994 0.000 1.000 0.000
#> GSM99464 3 0.4796 0.719 0.220 0.000 0.780
#> GSM99466 2 0.0000 0.994 0.000 1.000 0.000
#> GSM99470 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99472 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99474 3 0.0000 0.975 0.000 0.000 1.000
#> GSM99476 3 0.2959 0.882 0.000 0.100 0.900
#> GSM99478 2 0.0000 0.994 0.000 1.000 0.000
#> GSM99480 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99482 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99484 2 0.0000 0.994 0.000 1.000 0.000
#> GSM99486 2 0.0000 0.994 0.000 1.000 0.000
#> GSM99488 2 0.0000 0.994 0.000 1.000 0.000
#> GSM99490 2 0.0000 0.994 0.000 1.000 0.000
#> GSM99492 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99494 2 0.0000 0.994 0.000 1.000 0.000
#> GSM99524 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99526 3 0.5480 0.650 0.004 0.264 0.732
#> GSM99528 2 0.0000 0.994 0.000 1.000 0.000
#> GSM99530 3 0.0000 0.975 0.000 0.000 1.000
#> GSM99532 3 0.0000 0.975 0.000 0.000 1.000
#> GSM99534 2 0.0000 0.994 0.000 1.000 0.000
#> GSM99536 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99538 2 0.0237 0.990 0.000 0.996 0.004
#> GSM99540 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99542 2 0.0000 0.994 0.000 1.000 0.000
#> GSM99544 2 0.0000 0.994 0.000 1.000 0.000
#> GSM99546 2 0.0237 0.990 0.000 0.996 0.004
#> GSM99548 2 0.0000 0.994 0.000 1.000 0.000
#> GSM99550 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99552 3 0.0237 0.972 0.000 0.004 0.996
#> GSM99554 2 0.0000 0.994 0.000 1.000 0.000
#> GSM99556 2 0.0000 0.994 0.000 1.000 0.000
#> GSM99558 2 0.4291 0.779 0.000 0.820 0.180
#> GSM99560 2 0.0000 0.994 0.000 1.000 0.000
#> GSM99562 3 0.0000 0.975 0.000 0.000 1.000
#> GSM99564 2 0.0000 0.994 0.000 1.000 0.000
#> GSM99572 2 0.0000 0.994 0.000 1.000 0.000
#> GSM99576 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99578 2 0.0000 0.994 0.000 1.000 0.000
#> GSM99580 3 0.0000 0.975 0.000 0.000 1.000
#> GSM99582 1 0.1643 0.953 0.956 0.000 0.044
#> GSM99584 2 0.0000 0.994 0.000 1.000 0.000
#> GSM99586 1 0.0000 0.998 1.000 0.000 0.000
#> GSM99588 2 0.0000 0.994 0.000 1.000 0.000
#> GSM99590 2 0.0000 0.994 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM99496 3 0.0000 0.9286 0.000 0.000 1.000 0.000
#> GSM99502 1 0.0000 0.9382 1.000 0.000 0.000 0.000
#> GSM99504 1 0.0469 0.9305 0.988 0.000 0.012 0.000
#> GSM99506 3 0.0000 0.9286 0.000 0.000 1.000 0.000
#> GSM99566 3 0.0000 0.9286 0.000 0.000 1.000 0.000
#> GSM99574 1 0.0000 0.9382 1.000 0.000 0.000 0.000
#> GSM99592 3 0.1211 0.9010 0.000 0.000 0.960 0.040
#> GSM99594 3 0.0000 0.9286 0.000 0.000 1.000 0.000
#> GSM99468 1 0.0000 0.9382 1.000 0.000 0.000 0.000
#> GSM99498 1 0.0000 0.9382 1.000 0.000 0.000 0.000
#> GSM99500 1 0.0000 0.9382 1.000 0.000 0.000 0.000
#> GSM99508 3 0.0000 0.9286 0.000 0.000 1.000 0.000
#> GSM99568 3 0.0000 0.9286 0.000 0.000 1.000 0.000
#> GSM99596 3 0.0000 0.9286 0.000 0.000 1.000 0.000
#> GSM99600 2 0.0592 0.9023 0.000 0.984 0.000 0.016
#> GSM99458 1 0.2530 0.8673 0.888 0.000 0.000 0.112
#> GSM99460 1 0.4193 0.6950 0.732 0.000 0.000 0.268
#> GSM99510 4 0.4477 0.6185 0.000 0.000 0.312 0.688
#> GSM99512 3 0.4304 0.4672 0.000 0.000 0.716 0.284
#> GSM99514 3 0.0000 0.9286 0.000 0.000 1.000 0.000
#> GSM99516 1 0.0000 0.9382 1.000 0.000 0.000 0.000
#> GSM99518 1 0.0000 0.9382 1.000 0.000 0.000 0.000
#> GSM99520 3 0.0000 0.9286 0.000 0.000 1.000 0.000
#> GSM99522 3 0.1004 0.9033 0.024 0.000 0.972 0.004
#> GSM99570 1 0.0000 0.9382 1.000 0.000 0.000 0.000
#> GSM99598 1 0.0000 0.9382 1.000 0.000 0.000 0.000
#> GSM99432 2 0.4331 0.6717 0.000 0.712 0.000 0.288
#> GSM99434 4 0.3688 0.6996 0.000 0.000 0.208 0.792
#> GSM99436 2 0.2408 0.8619 0.000 0.896 0.000 0.104
#> GSM99438 2 0.0000 0.9066 0.000 1.000 0.000 0.000
#> GSM99440 1 0.0000 0.9382 1.000 0.000 0.000 0.000
#> GSM99442 2 0.0000 0.9066 0.000 1.000 0.000 0.000
#> GSM99444 2 0.0000 0.9066 0.000 1.000 0.000 0.000
#> GSM99446 2 0.2081 0.8734 0.000 0.916 0.000 0.084
#> GSM99448 4 0.5147 0.3141 0.000 0.004 0.460 0.536
#> GSM99450 4 0.4679 0.5182 0.000 0.000 0.352 0.648
#> GSM99452 1 0.0000 0.9382 1.000 0.000 0.000 0.000
#> GSM99454 1 0.0000 0.9382 1.000 0.000 0.000 0.000
#> GSM99456 1 0.2469 0.8737 0.892 0.000 0.000 0.108
#> GSM99462 2 0.0000 0.9066 0.000 1.000 0.000 0.000
#> GSM99464 4 0.4487 0.6323 0.100 0.000 0.092 0.808
#> GSM99466 2 0.4008 0.7393 0.000 0.756 0.000 0.244
#> GSM99470 1 0.0188 0.9361 0.996 0.000 0.000 0.004
#> GSM99472 1 0.0000 0.9382 1.000 0.000 0.000 0.000
#> GSM99474 3 0.0817 0.9153 0.000 0.000 0.976 0.024
#> GSM99476 4 0.3856 0.7182 0.000 0.032 0.136 0.832
#> GSM99478 2 0.2868 0.8341 0.000 0.864 0.000 0.136
#> GSM99480 1 0.0000 0.9382 1.000 0.000 0.000 0.000
#> GSM99482 1 0.0000 0.9382 1.000 0.000 0.000 0.000
#> GSM99484 2 0.0469 0.9012 0.000 0.988 0.000 0.012
#> GSM99486 2 0.2760 0.8453 0.000 0.872 0.000 0.128
#> GSM99488 2 0.0000 0.9066 0.000 1.000 0.000 0.000
#> GSM99490 2 0.0000 0.9066 0.000 1.000 0.000 0.000
#> GSM99492 1 0.0000 0.9382 1.000 0.000 0.000 0.000
#> GSM99494 2 0.0000 0.9066 0.000 1.000 0.000 0.000
#> GSM99524 1 0.0000 0.9382 1.000 0.000 0.000 0.000
#> GSM99526 4 0.0469 0.7111 0.000 0.000 0.012 0.988
#> GSM99528 2 0.2647 0.8392 0.000 0.880 0.000 0.120
#> GSM99530 3 0.4500 0.5183 0.000 0.000 0.684 0.316
#> GSM99532 3 0.4040 0.6389 0.000 0.000 0.752 0.248
#> GSM99534 2 0.0000 0.9066 0.000 1.000 0.000 0.000
#> GSM99536 1 0.0000 0.9382 1.000 0.000 0.000 0.000
#> GSM99538 2 0.5161 0.4488 0.000 0.592 0.008 0.400
#> GSM99540 1 0.1716 0.9053 0.936 0.000 0.000 0.064
#> GSM99542 2 0.0000 0.9066 0.000 1.000 0.000 0.000
#> GSM99544 2 0.4916 0.4048 0.000 0.576 0.000 0.424
#> GSM99546 4 0.0817 0.7103 0.000 0.024 0.000 0.976
#> GSM99548 2 0.0000 0.9066 0.000 1.000 0.000 0.000
#> GSM99550 1 0.4888 0.4447 0.588 0.000 0.000 0.412
#> GSM99552 3 0.0804 0.9124 0.000 0.008 0.980 0.012
#> GSM99554 2 0.0336 0.9046 0.000 0.992 0.000 0.008
#> GSM99556 2 0.0000 0.9066 0.000 1.000 0.000 0.000
#> GSM99558 2 0.7315 0.3056 0.000 0.532 0.252 0.216
#> GSM99560 2 0.1867 0.8821 0.000 0.928 0.000 0.072
#> GSM99562 3 0.0188 0.9265 0.000 0.000 0.996 0.004
#> GSM99564 2 0.2704 0.8482 0.000 0.876 0.000 0.124
#> GSM99572 2 0.0000 0.9066 0.000 1.000 0.000 0.000
#> GSM99576 1 0.2081 0.8929 0.916 0.000 0.000 0.084
#> GSM99578 2 0.0000 0.9066 0.000 1.000 0.000 0.000
#> GSM99580 3 0.0000 0.9286 0.000 0.000 1.000 0.000
#> GSM99582 1 0.6137 0.0879 0.504 0.000 0.448 0.048
#> GSM99584 4 0.4585 0.2938 0.000 0.332 0.000 0.668
#> GSM99586 1 0.2149 0.8887 0.912 0.000 0.000 0.088
#> GSM99588 2 0.0000 0.9066 0.000 1.000 0.000 0.000
#> GSM99590 2 0.0000 0.9066 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM99496 3 0.0000 0.86038 0.000 0.000 1.000 0.000 0.000
#> GSM99502 1 0.0290 0.88829 0.992 0.000 0.000 0.000 0.008
#> GSM99504 1 0.0912 0.88613 0.972 0.000 0.012 0.000 0.016
#> GSM99506 3 0.0000 0.86038 0.000 0.000 1.000 0.000 0.000
#> GSM99566 3 0.0162 0.86014 0.000 0.000 0.996 0.004 0.000
#> GSM99574 1 0.0404 0.88862 0.988 0.000 0.000 0.000 0.012
#> GSM99592 3 0.2378 0.82415 0.000 0.000 0.904 0.048 0.048
#> GSM99594 3 0.0912 0.85814 0.000 0.000 0.972 0.012 0.016
#> GSM99468 1 0.0609 0.88874 0.980 0.000 0.000 0.000 0.020
#> GSM99498 1 0.0404 0.88862 0.988 0.000 0.000 0.000 0.012
#> GSM99500 1 0.0510 0.88874 0.984 0.000 0.000 0.000 0.016
#> GSM99508 3 0.0162 0.86063 0.000 0.000 0.996 0.000 0.004
#> GSM99568 3 0.0404 0.86057 0.000 0.000 0.988 0.000 0.012
#> GSM99596 3 0.0000 0.86038 0.000 0.000 1.000 0.000 0.000
#> GSM99600 2 0.2516 0.69408 0.000 0.860 0.000 0.140 0.000
#> GSM99458 1 0.3551 0.72436 0.772 0.000 0.000 0.008 0.220
#> GSM99460 5 0.4708 -0.06650 0.436 0.000 0.000 0.016 0.548
#> GSM99510 3 0.6818 -0.26025 0.000 0.000 0.352 0.336 0.312
#> GSM99512 3 0.5263 0.53837 0.000 0.000 0.680 0.144 0.176
#> GSM99514 3 0.0162 0.86037 0.000 0.000 0.996 0.004 0.000
#> GSM99516 1 0.0404 0.88791 0.988 0.000 0.000 0.000 0.012
#> GSM99518 1 0.0963 0.88582 0.964 0.000 0.000 0.000 0.036
#> GSM99520 3 0.0771 0.85955 0.000 0.000 0.976 0.004 0.020
#> GSM99522 3 0.2308 0.82273 0.036 0.000 0.912 0.004 0.048
#> GSM99570 1 0.0404 0.88788 0.988 0.000 0.000 0.000 0.012
#> GSM99598 1 0.0290 0.88829 0.992 0.000 0.000 0.000 0.008
#> GSM99432 4 0.4627 0.29288 0.000 0.444 0.000 0.544 0.012
#> GSM99434 5 0.6536 0.31310 0.000 0.000 0.220 0.312 0.468
#> GSM99436 2 0.4101 0.25627 0.000 0.628 0.000 0.372 0.000
#> GSM99438 2 0.0290 0.78494 0.000 0.992 0.000 0.008 0.000
#> GSM99440 1 0.0510 0.88846 0.984 0.000 0.000 0.000 0.016
#> GSM99442 2 0.1270 0.76711 0.000 0.948 0.000 0.052 0.000
#> GSM99444 2 0.0290 0.78494 0.000 0.992 0.000 0.008 0.000
#> GSM99446 2 0.3999 0.33290 0.000 0.656 0.000 0.344 0.000
#> GSM99448 4 0.5960 0.06207 0.000 0.004 0.328 0.556 0.112
#> GSM99450 5 0.6107 0.17251 0.000 0.000 0.372 0.132 0.496
#> GSM99452 1 0.0671 0.88676 0.980 0.000 0.000 0.004 0.016
#> GSM99454 1 0.0000 0.88855 1.000 0.000 0.000 0.000 0.000
#> GSM99456 1 0.4135 0.57934 0.656 0.000 0.000 0.004 0.340
#> GSM99462 2 0.0162 0.78513 0.000 0.996 0.000 0.004 0.000
#> GSM99464 5 0.3164 0.50180 0.020 0.000 0.028 0.084 0.868
#> GSM99466 4 0.4428 0.49164 0.000 0.268 0.000 0.700 0.032
#> GSM99470 1 0.4153 0.75966 0.808 0.024 0.000 0.112 0.056
#> GSM99472 1 0.2153 0.85795 0.916 0.000 0.000 0.044 0.040
#> GSM99474 3 0.2850 0.79803 0.000 0.000 0.872 0.036 0.092
#> GSM99476 4 0.3876 0.31339 0.000 0.012 0.024 0.796 0.168
#> GSM99478 2 0.4747 0.01623 0.000 0.500 0.000 0.484 0.016
#> GSM99480 1 0.1341 0.87822 0.944 0.000 0.000 0.000 0.056
#> GSM99482 1 0.1918 0.86567 0.928 0.000 0.000 0.036 0.036
#> GSM99484 2 0.3530 0.60960 0.000 0.784 0.000 0.204 0.012
#> GSM99486 2 0.4283 -0.04948 0.000 0.544 0.000 0.456 0.000
#> GSM99488 2 0.0324 0.78418 0.000 0.992 0.000 0.004 0.004
#> GSM99490 2 0.0566 0.78420 0.000 0.984 0.000 0.012 0.004
#> GSM99492 1 0.2011 0.86008 0.908 0.000 0.000 0.004 0.088
#> GSM99494 2 0.0162 0.78444 0.000 0.996 0.000 0.000 0.004
#> GSM99524 1 0.0693 0.88546 0.980 0.000 0.000 0.008 0.012
#> GSM99526 5 0.3928 0.39849 0.000 0.004 0.000 0.296 0.700
#> GSM99528 2 0.5959 0.25996 0.000 0.576 0.004 0.296 0.124
#> GSM99530 5 0.4776 0.19520 0.004 0.000 0.364 0.020 0.612
#> GSM99532 3 0.5218 0.16607 0.004 0.000 0.536 0.036 0.424
#> GSM99534 2 0.1965 0.74462 0.000 0.924 0.000 0.052 0.024
#> GSM99536 1 0.1608 0.87310 0.928 0.000 0.000 0.000 0.072
#> GSM99538 4 0.5234 0.55377 0.000 0.332 0.004 0.612 0.052
#> GSM99540 1 0.3715 0.69705 0.736 0.000 0.000 0.004 0.260
#> GSM99542 2 0.2171 0.73467 0.000 0.912 0.000 0.064 0.024
#> GSM99544 4 0.4963 0.52293 0.000 0.352 0.000 0.608 0.040
#> GSM99546 5 0.4390 0.24389 0.000 0.004 0.000 0.428 0.568
#> GSM99548 2 0.0451 0.78298 0.000 0.988 0.000 0.008 0.004
#> GSM99550 5 0.4169 0.39928 0.240 0.000 0.000 0.028 0.732
#> GSM99552 3 0.3280 0.71612 0.000 0.000 0.812 0.176 0.012
#> GSM99554 2 0.3039 0.63532 0.000 0.808 0.000 0.192 0.000
#> GSM99556 2 0.0451 0.78298 0.000 0.988 0.000 0.008 0.004
#> GSM99558 4 0.6138 0.48763 0.000 0.188 0.208 0.596 0.008
#> GSM99560 2 0.4104 0.56561 0.000 0.748 0.000 0.220 0.032
#> GSM99562 3 0.1522 0.84792 0.000 0.000 0.944 0.012 0.044
#> GSM99564 2 0.4291 -0.08425 0.000 0.536 0.000 0.464 0.000
#> GSM99572 2 0.0566 0.78451 0.000 0.984 0.000 0.012 0.004
#> GSM99576 1 0.4573 0.67656 0.700 0.000 0.000 0.044 0.256
#> GSM99578 2 0.1571 0.75434 0.000 0.936 0.000 0.060 0.004
#> GSM99580 3 0.1638 0.83918 0.000 0.000 0.932 0.064 0.004
#> GSM99582 1 0.7943 -0.00553 0.428 0.000 0.284 0.152 0.136
#> GSM99584 4 0.5810 0.56683 0.000 0.244 0.000 0.604 0.152
#> GSM99586 1 0.3783 0.71264 0.740 0.000 0.000 0.008 0.252
#> GSM99588 2 0.0609 0.78332 0.000 0.980 0.000 0.020 0.000
#> GSM99590 2 0.0290 0.78494 0.000 0.992 0.000 0.008 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM99496 3 0.0146 0.8532 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM99502 1 0.0603 0.8519 0.980 0.000 0.000 0.000 0.016 0.004
#> GSM99504 1 0.1426 0.8402 0.948 0.000 0.028 0.000 0.008 0.016
#> GSM99506 3 0.0653 0.8544 0.000 0.000 0.980 0.004 0.004 0.012
#> GSM99566 3 0.0405 0.8547 0.000 0.000 0.988 0.008 0.000 0.004
#> GSM99574 1 0.0508 0.8520 0.984 0.000 0.000 0.000 0.012 0.004
#> GSM99592 3 0.3320 0.8079 0.000 0.000 0.844 0.060 0.028 0.068
#> GSM99594 3 0.1332 0.8534 0.000 0.000 0.952 0.008 0.012 0.028
#> GSM99468 1 0.1245 0.8512 0.952 0.000 0.000 0.000 0.032 0.016
#> GSM99498 1 0.0820 0.8516 0.972 0.000 0.000 0.000 0.016 0.012
#> GSM99500 1 0.0725 0.8516 0.976 0.000 0.000 0.000 0.012 0.012
#> GSM99508 3 0.0508 0.8548 0.000 0.000 0.984 0.004 0.000 0.012
#> GSM99568 3 0.1802 0.8479 0.000 0.000 0.932 0.020 0.024 0.024
#> GSM99596 3 0.0547 0.8541 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM99600 2 0.2838 0.6778 0.000 0.808 0.000 0.188 0.000 0.004
#> GSM99458 1 0.5018 0.4736 0.604 0.000 0.000 0.028 0.328 0.040
#> GSM99460 5 0.4624 0.1604 0.340 0.000 0.000 0.032 0.616 0.012
#> GSM99510 4 0.7472 -0.2357 0.000 0.000 0.256 0.372 0.212 0.160
#> GSM99512 3 0.6270 0.4529 0.000 0.000 0.580 0.196 0.096 0.128
#> GSM99514 3 0.0000 0.8529 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99516 1 0.0000 0.8515 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99518 1 0.1918 0.8352 0.904 0.000 0.000 0.000 0.088 0.008
#> GSM99520 3 0.1657 0.8459 0.000 0.000 0.936 0.012 0.012 0.040
#> GSM99522 3 0.4370 0.7587 0.044 0.000 0.796 0.036 0.068 0.056
#> GSM99570 1 0.0363 0.8515 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM99598 1 0.0000 0.8515 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99432 4 0.4597 0.3156 0.000 0.376 0.000 0.584 0.004 0.036
#> GSM99434 4 0.7177 -0.3158 0.000 0.000 0.144 0.408 0.304 0.144
#> GSM99436 2 0.4242 0.0501 0.000 0.536 0.000 0.448 0.000 0.016
#> GSM99438 2 0.0363 0.8130 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM99440 1 0.0717 0.8530 0.976 0.000 0.000 0.000 0.016 0.008
#> GSM99442 2 0.1958 0.7690 0.000 0.896 0.000 0.100 0.000 0.004
#> GSM99444 2 0.0458 0.8128 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM99446 2 0.3807 0.3283 0.000 0.628 0.000 0.368 0.000 0.004
#> GSM99448 4 0.5752 0.1097 0.000 0.008 0.304 0.576 0.032 0.080
#> GSM99450 5 0.7299 0.2765 0.000 0.000 0.264 0.208 0.400 0.128
#> GSM99452 1 0.1572 0.8461 0.936 0.000 0.000 0.000 0.028 0.036
#> GSM99454 1 0.0458 0.8532 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM99456 1 0.4873 0.3365 0.508 0.000 0.000 0.004 0.440 0.048
#> GSM99462 2 0.0363 0.8128 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM99464 5 0.2844 0.4910 0.004 0.000 0.004 0.092 0.864 0.036
#> GSM99466 6 0.5806 0.1296 0.000 0.156 0.000 0.408 0.004 0.432
#> GSM99470 1 0.4954 0.4634 0.580 0.012 0.000 0.004 0.040 0.364
#> GSM99472 1 0.3455 0.7379 0.784 0.000 0.000 0.000 0.036 0.180
#> GSM99474 3 0.4207 0.7439 0.000 0.000 0.780 0.040 0.104 0.076
#> GSM99476 4 0.4327 0.1709 0.000 0.016 0.000 0.728 0.052 0.204
#> GSM99478 6 0.5922 0.3603 0.000 0.340 0.000 0.220 0.000 0.440
#> GSM99480 1 0.1838 0.8384 0.916 0.000 0.000 0.000 0.068 0.016
#> GSM99482 1 0.2704 0.7855 0.844 0.000 0.000 0.000 0.016 0.140
#> GSM99484 2 0.4687 0.2970 0.000 0.632 0.000 0.072 0.000 0.296
#> GSM99486 4 0.4169 0.1139 0.000 0.456 0.000 0.532 0.000 0.012
#> GSM99488 2 0.0146 0.8110 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM99490 2 0.0547 0.8088 0.000 0.980 0.000 0.000 0.000 0.020
#> GSM99492 1 0.3317 0.7755 0.808 0.000 0.000 0.004 0.156 0.032
#> GSM99494 2 0.0146 0.8110 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM99524 1 0.1152 0.8419 0.952 0.000 0.000 0.000 0.004 0.044
#> GSM99526 5 0.5357 0.3890 0.000 0.000 0.000 0.340 0.536 0.124
#> GSM99528 6 0.5933 0.3966 0.000 0.328 0.004 0.088 0.040 0.540
#> GSM99530 5 0.5803 0.2460 0.000 0.000 0.292 0.040 0.568 0.100
#> GSM99532 3 0.6607 0.1230 0.016 0.000 0.456 0.056 0.372 0.100
#> GSM99534 2 0.3582 0.6108 0.000 0.776 0.000 0.024 0.008 0.192
#> GSM99536 1 0.1913 0.8375 0.908 0.000 0.000 0.000 0.080 0.012
#> GSM99538 4 0.4892 0.3145 0.000 0.280 0.000 0.632 0.004 0.084
#> GSM99540 1 0.4370 0.6275 0.672 0.000 0.000 0.008 0.284 0.036
#> GSM99542 2 0.2278 0.7062 0.000 0.868 0.000 0.000 0.004 0.128
#> GSM99544 4 0.3608 0.3865 0.000 0.272 0.000 0.716 0.000 0.012
#> GSM99546 5 0.5783 0.2810 0.000 0.004 0.000 0.408 0.436 0.152
#> GSM99548 2 0.0260 0.8110 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM99550 5 0.4895 0.3784 0.140 0.000 0.000 0.032 0.712 0.116
#> GSM99552 3 0.4617 0.4961 0.000 0.000 0.644 0.056 0.004 0.296
#> GSM99554 2 0.3468 0.5601 0.000 0.728 0.000 0.264 0.000 0.008
#> GSM99556 2 0.0458 0.8058 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM99558 4 0.6856 -0.0292 0.000 0.156 0.104 0.508 0.004 0.228
#> GSM99560 2 0.4879 0.3690 0.000 0.620 0.000 0.312 0.012 0.056
#> GSM99562 3 0.2670 0.8266 0.000 0.000 0.884 0.044 0.020 0.052
#> GSM99564 4 0.4246 0.1276 0.000 0.452 0.000 0.532 0.000 0.016
#> GSM99572 2 0.0806 0.8110 0.000 0.972 0.000 0.020 0.000 0.008
#> GSM99576 1 0.5410 0.5494 0.588 0.000 0.000 0.008 0.276 0.128
#> GSM99578 2 0.2178 0.7153 0.000 0.868 0.000 0.000 0.000 0.132
#> GSM99580 3 0.2066 0.8360 0.000 0.000 0.908 0.040 0.000 0.052
#> GSM99582 6 0.8152 -0.0740 0.256 0.000 0.216 0.068 0.100 0.360
#> GSM99584 4 0.4585 0.3505 0.000 0.164 0.000 0.736 0.048 0.052
#> GSM99586 1 0.4628 0.5506 0.608 0.000 0.000 0.004 0.344 0.044
#> GSM99588 2 0.1575 0.7959 0.000 0.936 0.000 0.032 0.000 0.032
#> GSM99590 2 0.0458 0.8129 0.000 0.984 0.000 0.016 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) cell.type(p) k
#> MAD:skmeans 84 2.71e-05 0.000147 2
#> MAD:skmeans 85 8.48e-05 0.002667 3
#> MAD:skmeans 77 8.20e-05 0.002607 4
#> MAD:skmeans 64 3.35e-04 0.033821 5
#> MAD:skmeans 53 2.09e-04 0.005393 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 21168 rows and 85 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 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 0.547 0.756 0.900 0.4834 0.500 0.500
#> 3 3 0.660 0.799 0.889 0.3627 0.722 0.497
#> 4 4 0.888 0.880 0.944 0.1443 0.826 0.539
#> 5 5 0.824 0.724 0.864 0.0536 0.944 0.782
#> 6 6 0.888 0.842 0.913 0.0414 0.920 0.657
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
#> GSM99496 1 0.9686 0.433 0.604 0.396
#> GSM99502 1 0.0000 0.859 1.000 0.000
#> GSM99504 1 0.0000 0.859 1.000 0.000
#> GSM99506 1 0.9754 0.405 0.592 0.408
#> GSM99566 1 0.9850 0.352 0.572 0.428
#> GSM99574 1 0.0000 0.859 1.000 0.000
#> GSM99592 2 0.7674 0.656 0.224 0.776
#> GSM99594 2 0.9522 0.346 0.372 0.628
#> GSM99468 1 0.0000 0.859 1.000 0.000
#> GSM99498 1 0.0000 0.859 1.000 0.000
#> GSM99500 1 0.0000 0.859 1.000 0.000
#> GSM99508 1 0.7815 0.690 0.768 0.232
#> GSM99568 1 0.9635 0.438 0.612 0.388
#> GSM99596 1 0.7950 0.678 0.760 0.240
#> GSM99600 2 0.0000 0.894 0.000 1.000
#> GSM99458 1 0.0000 0.859 1.000 0.000
#> GSM99460 1 0.0000 0.859 1.000 0.000
#> GSM99510 2 0.0000 0.894 0.000 1.000
#> GSM99512 2 0.1633 0.879 0.024 0.976
#> GSM99514 1 0.9686 0.433 0.604 0.396
#> GSM99516 1 0.0000 0.859 1.000 0.000
#> GSM99518 1 0.0000 0.859 1.000 0.000
#> GSM99520 2 0.9491 0.362 0.368 0.632
#> GSM99522 1 0.0938 0.853 0.988 0.012
#> GSM99570 1 0.0000 0.859 1.000 0.000
#> GSM99598 1 0.0000 0.859 1.000 0.000
#> GSM99432 2 0.0000 0.894 0.000 1.000
#> GSM99434 2 0.0938 0.887 0.012 0.988
#> GSM99436 2 0.0000 0.894 0.000 1.000
#> GSM99438 2 0.0000 0.894 0.000 1.000
#> GSM99440 1 0.0000 0.859 1.000 0.000
#> GSM99442 2 0.0000 0.894 0.000 1.000
#> GSM99444 2 0.0000 0.894 0.000 1.000
#> GSM99446 2 0.0000 0.894 0.000 1.000
#> GSM99448 2 0.0000 0.894 0.000 1.000
#> GSM99450 2 0.9881 0.181 0.436 0.564
#> GSM99452 1 0.0000 0.859 1.000 0.000
#> GSM99454 1 0.0000 0.859 1.000 0.000
#> GSM99456 1 0.0000 0.859 1.000 0.000
#> GSM99462 2 0.0000 0.894 0.000 1.000
#> GSM99464 1 0.6531 0.752 0.832 0.168
#> GSM99466 2 0.0000 0.894 0.000 1.000
#> GSM99470 2 0.9983 0.108 0.476 0.524
#> GSM99472 1 0.4939 0.780 0.892 0.108
#> GSM99474 1 0.9993 0.115 0.516 0.484
#> GSM99476 2 0.0000 0.894 0.000 1.000
#> GSM99478 2 0.0000 0.894 0.000 1.000
#> GSM99480 1 0.0000 0.859 1.000 0.000
#> GSM99482 1 0.0000 0.859 1.000 0.000
#> GSM99484 2 0.0000 0.894 0.000 1.000
#> GSM99486 2 0.0000 0.894 0.000 1.000
#> GSM99488 2 0.0000 0.894 0.000 1.000
#> GSM99490 2 0.0000 0.894 0.000 1.000
#> GSM99492 1 0.0000 0.859 1.000 0.000
#> GSM99494 2 0.0000 0.894 0.000 1.000
#> GSM99524 1 0.0000 0.859 1.000 0.000
#> GSM99526 2 0.2236 0.869 0.036 0.964
#> GSM99528 2 0.6438 0.739 0.164 0.836
#> GSM99530 1 0.9732 0.406 0.596 0.404
#> GSM99532 1 0.7745 0.696 0.772 0.228
#> GSM99534 2 0.5519 0.777 0.128 0.872
#> GSM99536 1 0.0000 0.859 1.000 0.000
#> GSM99538 2 0.0000 0.894 0.000 1.000
#> GSM99540 1 0.0000 0.859 1.000 0.000
#> GSM99542 2 0.8555 0.588 0.280 0.720
#> GSM99544 2 0.0000 0.894 0.000 1.000
#> GSM99546 2 0.1843 0.875 0.028 0.972
#> GSM99548 2 0.0000 0.894 0.000 1.000
#> GSM99550 2 0.9933 0.153 0.452 0.548
#> GSM99552 2 0.7950 0.632 0.240 0.760
#> GSM99554 2 0.0000 0.894 0.000 1.000
#> GSM99556 2 0.0000 0.894 0.000 1.000
#> GSM99558 2 0.0000 0.894 0.000 1.000
#> GSM99560 2 0.0000 0.894 0.000 1.000
#> GSM99562 1 0.9661 0.441 0.608 0.392
#> GSM99564 2 0.0000 0.894 0.000 1.000
#> GSM99572 2 0.0000 0.894 0.000 1.000
#> GSM99576 1 0.6887 0.738 0.816 0.184
#> GSM99578 2 0.0000 0.894 0.000 1.000
#> GSM99580 2 0.9170 0.447 0.332 0.668
#> GSM99582 2 0.9970 0.070 0.468 0.532
#> GSM99584 2 0.0000 0.894 0.000 1.000
#> GSM99586 1 0.0000 0.859 1.000 0.000
#> GSM99588 2 0.0000 0.894 0.000 1.000
#> GSM99590 2 0.0000 0.894 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM99496 3 0.2165 0.8803 0.064 0.000 0.936
#> GSM99502 1 0.0000 0.9436 1.000 0.000 0.000
#> GSM99504 1 0.0000 0.9436 1.000 0.000 0.000
#> GSM99506 3 0.2066 0.8816 0.060 0.000 0.940
#> GSM99566 3 0.1860 0.8824 0.052 0.000 0.948
#> GSM99574 1 0.0000 0.9436 1.000 0.000 0.000
#> GSM99592 3 0.0000 0.8709 0.000 0.000 1.000
#> GSM99594 3 0.0237 0.8730 0.004 0.000 0.996
#> GSM99468 1 0.0000 0.9436 1.000 0.000 0.000
#> GSM99498 1 0.0000 0.9436 1.000 0.000 0.000
#> GSM99500 1 0.0000 0.9436 1.000 0.000 0.000
#> GSM99508 3 0.3686 0.8367 0.140 0.000 0.860
#> GSM99568 3 0.2261 0.8778 0.068 0.000 0.932
#> GSM99596 3 0.4121 0.8058 0.168 0.000 0.832
#> GSM99600 2 0.0000 0.8080 0.000 1.000 0.000
#> GSM99458 1 0.0000 0.9436 1.000 0.000 0.000
#> GSM99460 1 0.4750 0.6875 0.784 0.000 0.216
#> GSM99510 3 0.1163 0.8571 0.000 0.028 0.972
#> GSM99512 3 0.0000 0.8709 0.000 0.000 1.000
#> GSM99514 3 0.2165 0.8803 0.064 0.000 0.936
#> GSM99516 1 0.0000 0.9436 1.000 0.000 0.000
#> GSM99518 1 0.0000 0.9436 1.000 0.000 0.000
#> GSM99520 3 0.1031 0.8797 0.024 0.000 0.976
#> GSM99522 3 0.5650 0.5503 0.312 0.000 0.688
#> GSM99570 1 0.0000 0.9436 1.000 0.000 0.000
#> GSM99598 1 0.0000 0.9436 1.000 0.000 0.000
#> GSM99432 2 0.3482 0.7963 0.000 0.872 0.128
#> GSM99434 3 0.0592 0.8664 0.000 0.012 0.988
#> GSM99436 2 0.0000 0.8080 0.000 1.000 0.000
#> GSM99438 2 0.0000 0.8080 0.000 1.000 0.000
#> GSM99440 1 0.0000 0.9436 1.000 0.000 0.000
#> GSM99442 2 0.0000 0.8080 0.000 1.000 0.000
#> GSM99444 2 0.0000 0.8080 0.000 1.000 0.000
#> GSM99446 2 0.3551 0.7915 0.000 0.868 0.132
#> GSM99448 3 0.3192 0.7546 0.000 0.112 0.888
#> GSM99450 3 0.1860 0.8781 0.052 0.000 0.948
#> GSM99452 1 0.0000 0.9436 1.000 0.000 0.000
#> GSM99454 1 0.0000 0.9436 1.000 0.000 0.000
#> GSM99456 1 0.0000 0.9436 1.000 0.000 0.000
#> GSM99462 2 0.0000 0.8080 0.000 1.000 0.000
#> GSM99464 3 0.4346 0.7857 0.184 0.000 0.816
#> GSM99466 2 0.6235 0.5443 0.000 0.564 0.436
#> GSM99470 1 0.7926 0.4789 0.656 0.216 0.128
#> GSM99472 1 0.1015 0.9261 0.980 0.008 0.012
#> GSM99474 3 0.3293 0.8645 0.088 0.012 0.900
#> GSM99476 2 0.6126 0.6136 0.000 0.600 0.400
#> GSM99478 2 0.6079 0.6292 0.000 0.612 0.388
#> GSM99480 1 0.0000 0.9436 1.000 0.000 0.000
#> GSM99482 1 0.0000 0.9436 1.000 0.000 0.000
#> GSM99484 2 0.5905 0.6761 0.000 0.648 0.352
#> GSM99486 2 0.5529 0.7276 0.000 0.704 0.296
#> GSM99488 2 0.0000 0.8080 0.000 1.000 0.000
#> GSM99490 2 0.1529 0.8068 0.000 0.960 0.040
#> GSM99492 1 0.0000 0.9436 1.000 0.000 0.000
#> GSM99494 2 0.0000 0.8080 0.000 1.000 0.000
#> GSM99524 1 0.0000 0.9436 1.000 0.000 0.000
#> GSM99526 2 0.6950 0.5695 0.020 0.572 0.408
#> GSM99528 3 0.7190 0.0579 0.036 0.356 0.608
#> GSM99530 3 0.1643 0.8842 0.044 0.000 0.956
#> GSM99532 3 0.3482 0.8477 0.128 0.000 0.872
#> GSM99534 2 0.4087 0.7894 0.052 0.880 0.068
#> GSM99536 1 0.0000 0.9436 1.000 0.000 0.000
#> GSM99538 2 0.6140 0.6045 0.000 0.596 0.404
#> GSM99540 1 0.5678 0.5043 0.684 0.000 0.316
#> GSM99542 2 0.1525 0.7930 0.032 0.964 0.004
#> GSM99544 2 0.5650 0.7152 0.000 0.688 0.312
#> GSM99546 2 0.7013 0.6384 0.028 0.608 0.364
#> GSM99548 2 0.0000 0.8080 0.000 1.000 0.000
#> GSM99550 2 0.9520 0.3125 0.196 0.452 0.352
#> GSM99552 3 0.0592 0.8664 0.000 0.012 0.988
#> GSM99554 2 0.0000 0.8080 0.000 1.000 0.000
#> GSM99556 2 0.0000 0.8080 0.000 1.000 0.000
#> GSM99558 3 0.4796 0.5542 0.000 0.220 0.780
#> GSM99560 2 0.5291 0.7426 0.000 0.732 0.268
#> GSM99562 3 0.2066 0.8815 0.060 0.000 0.940
#> GSM99564 2 0.3038 0.7979 0.000 0.896 0.104
#> GSM99572 2 0.0000 0.8080 0.000 1.000 0.000
#> GSM99576 1 0.6773 0.4094 0.636 0.024 0.340
#> GSM99578 2 0.5529 0.7276 0.000 0.704 0.296
#> GSM99580 3 0.0000 0.8709 0.000 0.000 1.000
#> GSM99582 3 0.4345 0.8295 0.136 0.016 0.848
#> GSM99584 2 0.5905 0.6760 0.000 0.648 0.352
#> GSM99586 1 0.0000 0.9436 1.000 0.000 0.000
#> GSM99588 2 0.5529 0.7276 0.000 0.704 0.296
#> GSM99590 2 0.0000 0.8080 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM99496 3 0.0000 0.984 0.000 0.000 1.000 0.000
#> GSM99502 1 0.0000 0.972 1.000 0.000 0.000 0.000
#> GSM99504 1 0.0000 0.972 1.000 0.000 0.000 0.000
#> GSM99506 3 0.0000 0.984 0.000 0.000 1.000 0.000
#> GSM99566 3 0.0000 0.984 0.000 0.000 1.000 0.000
#> GSM99574 1 0.0000 0.972 1.000 0.000 0.000 0.000
#> GSM99592 3 0.0000 0.984 0.000 0.000 1.000 0.000
#> GSM99594 3 0.0000 0.984 0.000 0.000 1.000 0.000
#> GSM99468 1 0.0000 0.972 1.000 0.000 0.000 0.000
#> GSM99498 1 0.0000 0.972 1.000 0.000 0.000 0.000
#> GSM99500 1 0.0000 0.972 1.000 0.000 0.000 0.000
#> GSM99508 3 0.0000 0.984 0.000 0.000 1.000 0.000
#> GSM99568 3 0.0000 0.984 0.000 0.000 1.000 0.000
#> GSM99596 3 0.0000 0.984 0.000 0.000 1.000 0.000
#> GSM99600 2 0.0000 0.954 0.000 1.000 0.000 0.000
#> GSM99458 1 0.0000 0.972 1.000 0.000 0.000 0.000
#> GSM99460 1 0.1975 0.918 0.936 0.000 0.016 0.048
#> GSM99510 3 0.4072 0.628 0.000 0.000 0.748 0.252
#> GSM99512 3 0.0000 0.984 0.000 0.000 1.000 0.000
#> GSM99514 3 0.0000 0.984 0.000 0.000 1.000 0.000
#> GSM99516 1 0.0000 0.972 1.000 0.000 0.000 0.000
#> GSM99518 1 0.0000 0.972 1.000 0.000 0.000 0.000
#> GSM99520 3 0.0000 0.984 0.000 0.000 1.000 0.000
#> GSM99522 3 0.0000 0.984 0.000 0.000 1.000 0.000
#> GSM99570 1 0.0000 0.972 1.000 0.000 0.000 0.000
#> GSM99598 1 0.0000 0.972 1.000 0.000 0.000 0.000
#> GSM99432 4 0.4072 0.715 0.000 0.252 0.000 0.748
#> GSM99434 4 0.2921 0.777 0.000 0.000 0.140 0.860
#> GSM99436 2 0.0000 0.954 0.000 1.000 0.000 0.000
#> GSM99438 2 0.0000 0.954 0.000 1.000 0.000 0.000
#> GSM99440 1 0.0000 0.972 1.000 0.000 0.000 0.000
#> GSM99442 2 0.0000 0.954 0.000 1.000 0.000 0.000
#> GSM99444 2 0.0188 0.953 0.000 0.996 0.000 0.004
#> GSM99446 2 0.0469 0.945 0.000 0.988 0.000 0.012
#> GSM99448 4 0.4916 0.295 0.000 0.000 0.424 0.576
#> GSM99450 3 0.0000 0.984 0.000 0.000 1.000 0.000
#> GSM99452 1 0.0000 0.972 1.000 0.000 0.000 0.000
#> GSM99454 1 0.0000 0.972 1.000 0.000 0.000 0.000
#> GSM99456 1 0.0000 0.972 1.000 0.000 0.000 0.000
#> GSM99462 2 0.0000 0.954 0.000 1.000 0.000 0.000
#> GSM99464 3 0.0336 0.976 0.008 0.000 0.992 0.000
#> GSM99466 4 0.0000 0.855 0.000 0.000 0.000 1.000
#> GSM99470 4 0.2469 0.781 0.108 0.000 0.000 0.892
#> GSM99472 1 0.2149 0.887 0.912 0.000 0.000 0.088
#> GSM99474 4 0.5402 0.145 0.012 0.000 0.472 0.516
#> GSM99476 4 0.0188 0.855 0.000 0.004 0.000 0.996
#> GSM99478 4 0.0000 0.855 0.000 0.000 0.000 1.000
#> GSM99480 1 0.0000 0.972 1.000 0.000 0.000 0.000
#> GSM99482 1 0.0000 0.972 1.000 0.000 0.000 0.000
#> GSM99484 4 0.0000 0.855 0.000 0.000 0.000 1.000
#> GSM99486 4 0.4304 0.682 0.000 0.284 0.000 0.716
#> GSM99488 2 0.2216 0.876 0.000 0.908 0.000 0.092
#> GSM99490 4 0.4406 0.567 0.000 0.300 0.000 0.700
#> GSM99492 1 0.0000 0.972 1.000 0.000 0.000 0.000
#> GSM99494 2 0.0188 0.953 0.000 0.996 0.000 0.004
#> GSM99524 1 0.0000 0.972 1.000 0.000 0.000 0.000
#> GSM99526 4 0.4252 0.714 0.000 0.252 0.004 0.744
#> GSM99528 4 0.0000 0.855 0.000 0.000 0.000 1.000
#> GSM99530 3 0.0000 0.984 0.000 0.000 1.000 0.000
#> GSM99532 3 0.0000 0.984 0.000 0.000 1.000 0.000
#> GSM99534 4 0.3356 0.771 0.000 0.176 0.000 0.824
#> GSM99536 1 0.0000 0.972 1.000 0.000 0.000 0.000
#> GSM99538 4 0.0188 0.854 0.000 0.004 0.000 0.996
#> GSM99540 1 0.4961 0.191 0.552 0.000 0.448 0.000
#> GSM99542 2 0.4304 0.628 0.000 0.716 0.000 0.284
#> GSM99544 4 0.4164 0.704 0.000 0.264 0.000 0.736
#> GSM99546 4 0.0188 0.855 0.000 0.004 0.000 0.996
#> GSM99548 2 0.0188 0.953 0.000 0.996 0.000 0.004
#> GSM99550 4 0.0188 0.854 0.004 0.000 0.000 0.996
#> GSM99552 4 0.0188 0.854 0.000 0.000 0.004 0.996
#> GSM99554 2 0.0000 0.954 0.000 1.000 0.000 0.000
#> GSM99556 2 0.3649 0.744 0.000 0.796 0.000 0.204
#> GSM99558 4 0.0000 0.855 0.000 0.000 0.000 1.000
#> GSM99560 4 0.4543 0.626 0.000 0.324 0.000 0.676
#> GSM99562 3 0.0000 0.984 0.000 0.000 1.000 0.000
#> GSM99564 2 0.0000 0.954 0.000 1.000 0.000 0.000
#> GSM99572 2 0.0000 0.954 0.000 1.000 0.000 0.000
#> GSM99576 4 0.0707 0.846 0.020 0.000 0.000 0.980
#> GSM99578 4 0.0000 0.855 0.000 0.000 0.000 1.000
#> GSM99580 3 0.0000 0.984 0.000 0.000 1.000 0.000
#> GSM99582 4 0.0524 0.853 0.004 0.000 0.008 0.988
#> GSM99584 4 0.4072 0.715 0.000 0.252 0.000 0.748
#> GSM99586 1 0.0000 0.972 1.000 0.000 0.000 0.000
#> GSM99588 4 0.0188 0.854 0.000 0.004 0.000 0.996
#> GSM99590 2 0.0000 0.954 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM99496 3 0.0000 0.93936 0.000 0.000 1.000 0.000 0.000
#> GSM99502 1 0.0000 0.89940 1.000 0.000 0.000 0.000 0.000
#> GSM99504 1 0.0162 0.89879 0.996 0.000 0.000 0.000 0.004
#> GSM99506 3 0.0000 0.93936 0.000 0.000 1.000 0.000 0.000
#> GSM99566 3 0.0000 0.93936 0.000 0.000 1.000 0.000 0.000
#> GSM99574 1 0.0000 0.89940 1.000 0.000 0.000 0.000 0.000
#> GSM99592 3 0.0000 0.93936 0.000 0.000 1.000 0.000 0.000
#> GSM99594 3 0.0000 0.93936 0.000 0.000 1.000 0.000 0.000
#> GSM99468 1 0.0510 0.89431 0.984 0.000 0.000 0.000 0.016
#> GSM99498 1 0.0510 0.89431 0.984 0.000 0.000 0.000 0.016
#> GSM99500 1 0.0404 0.89632 0.988 0.000 0.000 0.000 0.012
#> GSM99508 3 0.0000 0.93936 0.000 0.000 1.000 0.000 0.000
#> GSM99568 3 0.0000 0.93936 0.000 0.000 1.000 0.000 0.000
#> GSM99596 3 0.0000 0.93936 0.000 0.000 1.000 0.000 0.000
#> GSM99600 2 0.3707 0.76631 0.000 0.716 0.000 0.284 0.000
#> GSM99458 5 0.3857 0.54785 0.312 0.000 0.000 0.000 0.688
#> GSM99460 5 0.3707 0.57309 0.284 0.000 0.000 0.000 0.716
#> GSM99510 3 0.3728 0.61765 0.000 0.000 0.748 0.244 0.008
#> GSM99512 3 0.0000 0.93936 0.000 0.000 1.000 0.000 0.000
#> GSM99514 3 0.0000 0.93936 0.000 0.000 1.000 0.000 0.000
#> GSM99516 1 0.0000 0.89940 1.000 0.000 0.000 0.000 0.000
#> GSM99518 1 0.0794 0.88531 0.972 0.000 0.000 0.000 0.028
#> GSM99520 3 0.0000 0.93936 0.000 0.000 1.000 0.000 0.000
#> GSM99522 3 0.0162 0.93709 0.000 0.000 0.996 0.000 0.004
#> GSM99570 1 0.0000 0.89940 1.000 0.000 0.000 0.000 0.000
#> GSM99598 1 0.0000 0.89940 1.000 0.000 0.000 0.000 0.000
#> GSM99432 4 0.2179 0.56250 0.000 0.112 0.000 0.888 0.000
#> GSM99434 4 0.5422 0.66317 0.000 0.000 0.132 0.656 0.212
#> GSM99436 2 0.3774 0.75971 0.000 0.704 0.000 0.296 0.000
#> GSM99438 2 0.0000 0.86246 0.000 1.000 0.000 0.000 0.000
#> GSM99440 1 0.0000 0.89940 1.000 0.000 0.000 0.000 0.000
#> GSM99442 2 0.2329 0.83209 0.000 0.876 0.000 0.124 0.000
#> GSM99444 2 0.0000 0.86246 0.000 1.000 0.000 0.000 0.000
#> GSM99446 2 0.3837 0.75120 0.000 0.692 0.000 0.308 0.000
#> GSM99448 4 0.6188 0.25684 0.000 0.000 0.416 0.448 0.136
#> GSM99450 3 0.0963 0.90991 0.000 0.000 0.964 0.000 0.036
#> GSM99452 1 0.0162 0.89884 0.996 0.000 0.000 0.000 0.004
#> GSM99454 1 0.0000 0.89940 1.000 0.000 0.000 0.000 0.000
#> GSM99456 5 0.3774 0.56398 0.296 0.000 0.000 0.000 0.704
#> GSM99462 2 0.0000 0.86246 0.000 1.000 0.000 0.000 0.000
#> GSM99464 5 0.4088 0.21890 0.000 0.000 0.368 0.000 0.632
#> GSM99466 4 0.3774 0.75294 0.000 0.000 0.000 0.704 0.296
#> GSM99470 4 0.5295 0.62343 0.052 0.000 0.000 0.540 0.408
#> GSM99472 1 0.4465 0.41726 0.672 0.000 0.000 0.024 0.304
#> GSM99474 3 0.6289 -0.17019 0.000 0.000 0.452 0.396 0.152
#> GSM99476 4 0.4046 0.75204 0.000 0.008 0.000 0.696 0.296
#> GSM99478 4 0.3774 0.75294 0.000 0.000 0.000 0.704 0.296
#> GSM99480 1 0.0162 0.89827 0.996 0.000 0.000 0.000 0.004
#> GSM99482 1 0.1341 0.84945 0.944 0.000 0.000 0.000 0.056
#> GSM99484 4 0.3774 0.75294 0.000 0.000 0.000 0.704 0.296
#> GSM99486 4 0.2561 0.53627 0.000 0.144 0.000 0.856 0.000
#> GSM99488 2 0.0794 0.84753 0.000 0.972 0.000 0.028 0.000
#> GSM99490 4 0.6549 0.50426 0.000 0.280 0.000 0.476 0.244
#> GSM99492 1 0.4242 -0.00524 0.572 0.000 0.000 0.000 0.428
#> GSM99494 2 0.0290 0.85986 0.000 0.992 0.000 0.008 0.000
#> GSM99524 1 0.0000 0.89940 1.000 0.000 0.000 0.000 0.000
#> GSM99526 4 0.5785 0.09866 0.000 0.112 0.000 0.568 0.320
#> GSM99528 4 0.3774 0.75294 0.000 0.000 0.000 0.704 0.296
#> GSM99530 3 0.0404 0.93182 0.000 0.000 0.988 0.000 0.012
#> GSM99532 3 0.0703 0.92271 0.000 0.000 0.976 0.000 0.024
#> GSM99534 4 0.4522 0.53988 0.000 0.068 0.000 0.736 0.196
#> GSM99536 1 0.0703 0.88887 0.976 0.000 0.000 0.000 0.024
#> GSM99538 4 0.3928 0.75298 0.000 0.004 0.000 0.700 0.296
#> GSM99540 1 0.6669 -0.23247 0.400 0.000 0.232 0.000 0.368
#> GSM99542 2 0.3759 0.69901 0.000 0.808 0.000 0.136 0.056
#> GSM99544 4 0.2280 0.55754 0.000 0.120 0.000 0.880 0.000
#> GSM99546 4 0.4341 0.71376 0.000 0.008 0.000 0.628 0.364
#> GSM99548 2 0.0290 0.85986 0.000 0.992 0.000 0.008 0.000
#> GSM99550 5 0.1908 0.28947 0.000 0.000 0.000 0.092 0.908
#> GSM99552 4 0.4046 0.75042 0.000 0.000 0.008 0.696 0.296
#> GSM99554 2 0.3774 0.75971 0.000 0.704 0.000 0.296 0.000
#> GSM99556 2 0.1792 0.79692 0.000 0.916 0.000 0.084 0.000
#> GSM99558 4 0.3774 0.75294 0.000 0.000 0.000 0.704 0.296
#> GSM99560 4 0.3209 0.47662 0.000 0.180 0.000 0.812 0.008
#> GSM99562 3 0.0000 0.93936 0.000 0.000 1.000 0.000 0.000
#> GSM99564 2 0.3816 0.75460 0.000 0.696 0.000 0.304 0.000
#> GSM99572 2 0.0000 0.86246 0.000 1.000 0.000 0.000 0.000
#> GSM99576 5 0.3766 -0.16779 0.004 0.000 0.000 0.268 0.728
#> GSM99578 4 0.3774 0.75294 0.000 0.000 0.000 0.704 0.296
#> GSM99580 3 0.0290 0.93327 0.000 0.000 0.992 0.008 0.000
#> GSM99582 4 0.3895 0.74328 0.000 0.000 0.000 0.680 0.320
#> GSM99584 4 0.2179 0.56250 0.000 0.112 0.000 0.888 0.000
#> GSM99586 5 0.4171 0.39794 0.396 0.000 0.000 0.000 0.604
#> GSM99588 4 0.3928 0.75255 0.000 0.004 0.000 0.700 0.296
#> GSM99590 2 0.0000 0.86246 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM99496 3 0.0000 0.9755 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99502 1 0.0000 0.9299 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99504 1 0.0146 0.9295 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM99506 3 0.0000 0.9755 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99566 3 0.0000 0.9755 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99574 1 0.0000 0.9299 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99592 3 0.0000 0.9755 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99594 3 0.0000 0.9755 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99468 1 0.0547 0.9242 0.980 0.000 0.000 0.000 0.020 0.000
#> GSM99498 1 0.0547 0.9242 0.980 0.000 0.000 0.000 0.020 0.000
#> GSM99500 1 0.0458 0.9263 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM99508 3 0.0000 0.9755 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99568 3 0.0000 0.9755 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99596 3 0.0000 0.9755 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99600 4 0.3050 0.7557 0.000 0.236 0.000 0.764 0.000 0.000
#> GSM99458 5 0.1088 0.9038 0.024 0.000 0.000 0.016 0.960 0.000
#> GSM99460 5 0.0000 0.9117 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM99510 3 0.3420 0.6515 0.000 0.000 0.748 0.012 0.000 0.240
#> GSM99512 3 0.0000 0.9755 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99514 3 0.0000 0.9755 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99516 1 0.0000 0.9299 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99518 1 0.0547 0.9241 0.980 0.000 0.000 0.000 0.020 0.000
#> GSM99520 3 0.0000 0.9755 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99522 3 0.0146 0.9730 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM99570 1 0.0000 0.9299 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99598 1 0.0000 0.9299 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99432 4 0.2597 0.8152 0.000 0.000 0.000 0.824 0.000 0.176
#> GSM99434 6 0.2473 0.7439 0.000 0.000 0.136 0.008 0.000 0.856
#> GSM99436 4 0.2631 0.8060 0.000 0.180 0.000 0.820 0.000 0.000
#> GSM99438 2 0.0000 0.9542 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99440 1 0.0000 0.9299 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99442 2 0.2730 0.7032 0.000 0.808 0.000 0.192 0.000 0.000
#> GSM99444 2 0.0000 0.9542 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99446 4 0.2527 0.8123 0.000 0.168 0.000 0.832 0.000 0.000
#> GSM99448 6 0.4010 0.3578 0.000 0.000 0.408 0.008 0.000 0.584
#> GSM99450 3 0.1341 0.9409 0.000 0.000 0.948 0.024 0.028 0.000
#> GSM99452 1 0.0146 0.9295 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM99454 1 0.0000 0.9299 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99456 5 0.0000 0.9117 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM99462 2 0.0000 0.9542 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99464 5 0.1564 0.8849 0.000 0.000 0.040 0.024 0.936 0.000
#> GSM99466 6 0.0000 0.8490 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM99470 6 0.3627 0.7212 0.008 0.000 0.000 0.136 0.056 0.800
#> GSM99472 1 0.5377 0.6219 0.684 0.000 0.000 0.136 0.100 0.080
#> GSM99474 6 0.5115 0.1934 0.000 0.000 0.436 0.024 0.036 0.504
#> GSM99476 6 0.0000 0.8490 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM99478 6 0.0000 0.8490 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM99480 1 0.0547 0.9198 0.980 0.000 0.000 0.000 0.020 0.000
#> GSM99482 1 0.3254 0.7716 0.816 0.000 0.000 0.136 0.048 0.000
#> GSM99484 6 0.0000 0.8490 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM99486 4 0.2831 0.8327 0.000 0.024 0.000 0.840 0.000 0.136
#> GSM99488 2 0.0000 0.9542 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99490 6 0.5253 0.3566 0.000 0.168 0.000 0.228 0.000 0.604
#> GSM99492 5 0.2912 0.7458 0.216 0.000 0.000 0.000 0.784 0.000
#> GSM99494 2 0.0000 0.9542 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99524 1 0.0000 0.9299 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99526 4 0.2703 0.7205 0.000 0.000 0.000 0.824 0.172 0.004
#> GSM99528 6 0.0000 0.8490 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM99530 3 0.1088 0.9507 0.000 0.000 0.960 0.024 0.016 0.000
#> GSM99532 3 0.1088 0.9507 0.000 0.000 0.960 0.024 0.016 0.000
#> GSM99534 4 0.4312 0.4269 0.000 0.000 0.000 0.676 0.052 0.272
#> GSM99536 1 0.0713 0.9196 0.972 0.000 0.000 0.000 0.028 0.000
#> GSM99538 6 0.0363 0.8451 0.000 0.000 0.000 0.012 0.000 0.988
#> GSM99540 1 0.6636 -0.0408 0.396 0.000 0.252 0.032 0.320 0.000
#> GSM99542 2 0.3871 0.7386 0.000 0.792 0.000 0.136 0.044 0.028
#> GSM99544 4 0.2631 0.8264 0.000 0.008 0.000 0.840 0.000 0.152
#> GSM99546 6 0.1434 0.8268 0.000 0.000 0.000 0.012 0.048 0.940
#> GSM99548 2 0.0000 0.9542 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99550 5 0.1501 0.8729 0.000 0.000 0.000 0.000 0.924 0.076
#> GSM99552 6 0.0000 0.8490 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM99554 4 0.2793 0.7931 0.000 0.200 0.000 0.800 0.000 0.000
#> GSM99556 2 0.0000 0.9542 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99558 6 0.0000 0.8490 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM99560 4 0.3025 0.8296 0.000 0.024 0.000 0.820 0.000 0.156
#> GSM99562 3 0.0000 0.9755 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99564 4 0.2454 0.8148 0.000 0.160 0.000 0.840 0.000 0.000
#> GSM99572 2 0.0000 0.9542 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99576 6 0.4903 0.3081 0.000 0.000 0.000 0.068 0.380 0.552
#> GSM99578 6 0.1663 0.8099 0.000 0.000 0.000 0.088 0.000 0.912
#> GSM99580 3 0.0000 0.9755 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99582 6 0.0260 0.8474 0.000 0.000 0.000 0.008 0.000 0.992
#> GSM99584 4 0.2454 0.8206 0.000 0.000 0.000 0.840 0.000 0.160
#> GSM99586 5 0.1141 0.9021 0.052 0.000 0.000 0.000 0.948 0.000
#> GSM99588 6 0.0146 0.8479 0.000 0.004 0.000 0.000 0.000 0.996
#> GSM99590 2 0.0000 0.9542 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) cell.type(p) k
#> MAD:pam 70 5.55e-04 2.98e-03 2
#> MAD:pam 81 3.72e-05 1.35e-03 3
#> MAD:pam 82 4.73e-07 8.75e-05 4
#> MAD:pam 74 1.17e-06 8.56e-05 5
#> MAD:pam 79 6.14e-06 1.81e-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", "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 21168 rows and 85 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 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 0.335 0.707 0.843 0.4719 0.506 0.506
#> 3 3 1.000 0.958 0.976 0.4170 0.746 0.533
#> 4 4 0.709 0.688 0.848 0.0776 0.946 0.835
#> 5 5 0.966 0.898 0.959 0.0925 0.891 0.636
#> 6 6 0.879 0.751 0.880 0.0356 0.978 0.899
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
#> attr(,"optional")
#> [1] 3
There is also optional best \(k\) = 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM99496 1 0.7950 0.6843 0.760 0.240
#> GSM99502 1 0.5842 0.7737 0.860 0.140
#> GSM99504 1 0.3584 0.7643 0.932 0.068
#> GSM99506 1 0.7950 0.6843 0.760 0.240
#> GSM99566 1 0.7950 0.6843 0.760 0.240
#> GSM99574 1 0.5842 0.7737 0.860 0.140
#> GSM99592 1 0.7950 0.6843 0.760 0.240
#> GSM99594 1 0.7950 0.6843 0.760 0.240
#> GSM99468 1 0.5842 0.7737 0.860 0.140
#> GSM99498 1 0.5842 0.7737 0.860 0.140
#> GSM99500 1 0.5842 0.7737 0.860 0.140
#> GSM99508 1 0.7950 0.6843 0.760 0.240
#> GSM99568 1 0.7950 0.6843 0.760 0.240
#> GSM99596 1 0.8016 0.6845 0.756 0.244
#> GSM99600 2 0.0000 0.8734 0.000 1.000
#> GSM99458 1 0.3733 0.7654 0.928 0.072
#> GSM99460 1 0.3584 0.7643 0.932 0.068
#> GSM99510 2 0.9909 0.1463 0.444 0.556
#> GSM99512 1 0.9427 0.5085 0.640 0.360
#> GSM99514 1 0.7950 0.6843 0.760 0.240
#> GSM99516 1 0.5842 0.7737 0.860 0.140
#> GSM99518 1 0.5842 0.7737 0.860 0.140
#> GSM99520 1 0.7950 0.6843 0.760 0.240
#> GSM99522 1 0.7883 0.6869 0.764 0.236
#> GSM99570 1 0.6048 0.7695 0.852 0.148
#> GSM99598 1 0.5842 0.7737 0.860 0.140
#> GSM99432 2 0.2778 0.8367 0.048 0.952
#> GSM99434 2 0.9909 0.1463 0.444 0.556
#> GSM99436 2 0.0000 0.8734 0.000 1.000
#> GSM99438 2 0.0000 0.8734 0.000 1.000
#> GSM99440 1 0.5842 0.7737 0.860 0.140
#> GSM99442 2 0.0000 0.8734 0.000 1.000
#> GSM99444 2 0.0000 0.8734 0.000 1.000
#> GSM99446 2 0.0000 0.8734 0.000 1.000
#> GSM99448 2 0.9988 0.0128 0.480 0.520
#> GSM99450 1 0.8443 0.6510 0.728 0.272
#> GSM99452 1 0.6438 0.7589 0.836 0.164
#> GSM99454 1 0.5842 0.7737 0.860 0.140
#> GSM99456 1 0.3584 0.7643 0.932 0.068
#> GSM99462 2 0.0000 0.8734 0.000 1.000
#> GSM99464 1 0.9993 0.0729 0.516 0.484
#> GSM99466 2 0.1414 0.8596 0.020 0.980
#> GSM99470 1 0.6887 0.7527 0.816 0.184
#> GSM99472 1 0.6438 0.7589 0.836 0.164
#> GSM99474 1 0.8016 0.6842 0.756 0.244
#> GSM99476 2 0.9881 0.1531 0.436 0.564
#> GSM99478 2 0.0000 0.8734 0.000 1.000
#> GSM99480 1 0.5842 0.7737 0.860 0.140
#> GSM99482 1 0.6438 0.7589 0.836 0.164
#> GSM99484 2 0.0000 0.8734 0.000 1.000
#> GSM99486 2 0.0376 0.8710 0.004 0.996
#> GSM99488 2 0.0000 0.8734 0.000 1.000
#> GSM99490 2 0.0000 0.8734 0.000 1.000
#> GSM99492 1 0.5842 0.7737 0.860 0.140
#> GSM99494 2 0.0000 0.8734 0.000 1.000
#> GSM99524 1 0.6048 0.7696 0.852 0.148
#> GSM99526 1 0.9996 0.0623 0.512 0.488
#> GSM99528 2 0.0672 0.8675 0.008 0.992
#> GSM99530 1 0.8499 0.6911 0.724 0.276
#> GSM99532 1 0.7883 0.7028 0.764 0.236
#> GSM99534 2 0.7056 0.6234 0.192 0.808
#> GSM99536 1 0.5842 0.7737 0.860 0.140
#> GSM99538 2 0.3879 0.8107 0.076 0.924
#> GSM99540 1 0.4431 0.7696 0.908 0.092
#> GSM99542 2 0.7056 0.6234 0.192 0.808
#> GSM99544 2 0.3733 0.8143 0.072 0.928
#> GSM99546 2 0.9954 0.0231 0.460 0.540
#> GSM99548 2 0.0000 0.8734 0.000 1.000
#> GSM99550 1 0.9491 0.3240 0.632 0.368
#> GSM99552 1 0.8763 0.6772 0.704 0.296
#> GSM99554 2 0.0000 0.8734 0.000 1.000
#> GSM99556 2 0.0000 0.8734 0.000 1.000
#> GSM99558 2 0.9686 0.2309 0.396 0.604
#> GSM99560 2 0.0000 0.8734 0.000 1.000
#> GSM99562 1 0.7950 0.6843 0.760 0.240
#> GSM99564 2 0.0000 0.8734 0.000 1.000
#> GSM99572 2 0.0000 0.8734 0.000 1.000
#> GSM99576 1 0.6438 0.7589 0.836 0.164
#> GSM99578 2 0.0000 0.8734 0.000 1.000
#> GSM99580 1 0.7950 0.6843 0.760 0.240
#> GSM99582 1 0.9129 0.6674 0.672 0.328
#> GSM99584 2 0.3733 0.8143 0.072 0.928
#> GSM99586 1 0.5737 0.7739 0.864 0.136
#> GSM99588 2 0.0000 0.8734 0.000 1.000
#> GSM99590 2 0.0000 0.8734 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM99496 3 0.0000 1.000 0.000 0.000 1.000
#> GSM99502 1 0.0000 0.983 1.000 0.000 0.000
#> GSM99504 1 0.0000 0.983 1.000 0.000 0.000
#> GSM99506 3 0.0000 1.000 0.000 0.000 1.000
#> GSM99566 3 0.0000 1.000 0.000 0.000 1.000
#> GSM99574 1 0.0000 0.983 1.000 0.000 0.000
#> GSM99592 3 0.0000 1.000 0.000 0.000 1.000
#> GSM99594 3 0.0000 1.000 0.000 0.000 1.000
#> GSM99468 1 0.0000 0.983 1.000 0.000 0.000
#> GSM99498 1 0.0000 0.983 1.000 0.000 0.000
#> GSM99500 1 0.0000 0.983 1.000 0.000 0.000
#> GSM99508 3 0.0000 1.000 0.000 0.000 1.000
#> GSM99568 3 0.0000 1.000 0.000 0.000 1.000
#> GSM99596 3 0.0000 1.000 0.000 0.000 1.000
#> GSM99600 2 0.0000 0.942 0.000 1.000 0.000
#> GSM99458 1 0.1643 0.958 0.956 0.000 0.044
#> GSM99460 1 0.2066 0.945 0.940 0.000 0.060
#> GSM99510 3 0.0000 1.000 0.000 0.000 1.000
#> GSM99512 3 0.0000 1.000 0.000 0.000 1.000
#> GSM99514 3 0.0000 1.000 0.000 0.000 1.000
#> GSM99516 1 0.0000 0.983 1.000 0.000 0.000
#> GSM99518 1 0.0000 0.983 1.000 0.000 0.000
#> GSM99520 3 0.0000 1.000 0.000 0.000 1.000
#> GSM99522 3 0.0000 1.000 0.000 0.000 1.000
#> GSM99570 1 0.0000 0.983 1.000 0.000 0.000
#> GSM99598 1 0.0000 0.983 1.000 0.000 0.000
#> GSM99432 2 0.2066 0.934 0.000 0.940 0.060
#> GSM99434 3 0.0000 1.000 0.000 0.000 1.000
#> GSM99436 2 0.0747 0.943 0.000 0.984 0.016
#> GSM99438 2 0.0000 0.942 0.000 1.000 0.000
#> GSM99440 1 0.0000 0.983 1.000 0.000 0.000
#> GSM99442 2 0.0000 0.942 0.000 1.000 0.000
#> GSM99444 2 0.0000 0.942 0.000 1.000 0.000
#> GSM99446 2 0.0747 0.943 0.000 0.984 0.016
#> GSM99448 3 0.0000 1.000 0.000 0.000 1.000
#> GSM99450 3 0.0000 1.000 0.000 0.000 1.000
#> GSM99452 1 0.0000 0.983 1.000 0.000 0.000
#> GSM99454 1 0.0000 0.983 1.000 0.000 0.000
#> GSM99456 1 0.1289 0.966 0.968 0.000 0.032
#> GSM99462 2 0.0000 0.942 0.000 1.000 0.000
#> GSM99464 3 0.0000 1.000 0.000 0.000 1.000
#> GSM99466 2 0.5785 0.590 0.000 0.668 0.332
#> GSM99470 1 0.2066 0.945 0.940 0.000 0.060
#> GSM99472 1 0.1753 0.955 0.952 0.000 0.048
#> GSM99474 3 0.0000 1.000 0.000 0.000 1.000
#> GSM99476 3 0.0000 1.000 0.000 0.000 1.000
#> GSM99478 2 0.3192 0.892 0.000 0.888 0.112
#> GSM99480 1 0.0000 0.983 1.000 0.000 0.000
#> GSM99482 1 0.0000 0.983 1.000 0.000 0.000
#> GSM99484 2 0.2066 0.934 0.000 0.940 0.060
#> GSM99486 2 0.2066 0.934 0.000 0.940 0.060
#> GSM99488 2 0.0000 0.942 0.000 1.000 0.000
#> GSM99490 2 0.0000 0.942 0.000 1.000 0.000
#> GSM99492 1 0.0000 0.983 1.000 0.000 0.000
#> GSM99494 2 0.0000 0.942 0.000 1.000 0.000
#> GSM99524 1 0.0000 0.983 1.000 0.000 0.000
#> GSM99526 3 0.0000 1.000 0.000 0.000 1.000
#> GSM99528 2 0.5882 0.558 0.000 0.652 0.348
#> GSM99530 3 0.0000 1.000 0.000 0.000 1.000
#> GSM99532 3 0.0000 1.000 0.000 0.000 1.000
#> GSM99534 2 0.2066 0.934 0.000 0.940 0.060
#> GSM99536 1 0.0000 0.983 1.000 0.000 0.000
#> GSM99538 2 0.5216 0.712 0.000 0.740 0.260
#> GSM99540 1 0.0892 0.973 0.980 0.000 0.020
#> GSM99542 2 0.2066 0.934 0.000 0.940 0.060
#> GSM99544 2 0.2066 0.934 0.000 0.940 0.060
#> GSM99546 3 0.0592 0.987 0.000 0.012 0.988
#> GSM99548 2 0.0000 0.942 0.000 1.000 0.000
#> GSM99550 1 0.2066 0.945 0.940 0.000 0.060
#> GSM99552 3 0.0000 1.000 0.000 0.000 1.000
#> GSM99554 2 0.0000 0.942 0.000 1.000 0.000
#> GSM99556 2 0.0000 0.942 0.000 1.000 0.000
#> GSM99558 3 0.0000 1.000 0.000 0.000 1.000
#> GSM99560 2 0.2066 0.934 0.000 0.940 0.060
#> GSM99562 3 0.0000 1.000 0.000 0.000 1.000
#> GSM99564 2 0.1411 0.941 0.000 0.964 0.036
#> GSM99572 2 0.0000 0.942 0.000 1.000 0.000
#> GSM99576 1 0.2066 0.945 0.940 0.000 0.060
#> GSM99578 2 0.1529 0.940 0.000 0.960 0.040
#> GSM99580 3 0.0000 1.000 0.000 0.000 1.000
#> GSM99582 3 0.0000 1.000 0.000 0.000 1.000
#> GSM99584 2 0.2066 0.934 0.000 0.940 0.060
#> GSM99586 1 0.0000 0.983 1.000 0.000 0.000
#> GSM99588 2 0.1289 0.942 0.000 0.968 0.032
#> GSM99590 2 0.0000 0.942 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM99496 3 0.0000 0.727 0.000 0.000 1.000 0.000
#> GSM99502 1 0.0000 0.950 1.000 0.000 0.000 0.000
#> GSM99504 1 0.0000 0.950 1.000 0.000 0.000 0.000
#> GSM99506 3 0.0000 0.727 0.000 0.000 1.000 0.000
#> GSM99566 3 0.0000 0.727 0.000 0.000 1.000 0.000
#> GSM99574 1 0.0000 0.950 1.000 0.000 0.000 0.000
#> GSM99592 3 0.3024 0.714 0.000 0.148 0.852 0.000
#> GSM99594 3 0.0000 0.727 0.000 0.000 1.000 0.000
#> GSM99468 1 0.0000 0.950 1.000 0.000 0.000 0.000
#> GSM99498 1 0.0000 0.950 1.000 0.000 0.000 0.000
#> GSM99500 1 0.0000 0.950 1.000 0.000 0.000 0.000
#> GSM99508 3 0.0000 0.727 0.000 0.000 1.000 0.000
#> GSM99568 3 0.3024 0.714 0.000 0.148 0.852 0.000
#> GSM99596 3 0.0000 0.727 0.000 0.000 1.000 0.000
#> GSM99600 2 0.4500 0.693 0.000 0.684 0.000 0.316
#> GSM99458 1 0.2494 0.887 0.916 0.036 0.000 0.048
#> GSM99460 4 0.7743 0.533 0.256 0.308 0.000 0.436
#> GSM99510 3 0.7858 -0.271 0.000 0.316 0.396 0.288
#> GSM99512 3 0.5517 0.536 0.000 0.316 0.648 0.036
#> GSM99514 3 0.0000 0.727 0.000 0.000 1.000 0.000
#> GSM99516 1 0.0000 0.950 1.000 0.000 0.000 0.000
#> GSM99518 1 0.0000 0.950 1.000 0.000 0.000 0.000
#> GSM99520 3 0.2011 0.726 0.000 0.080 0.920 0.000
#> GSM99522 3 0.3123 0.710 0.000 0.156 0.844 0.000
#> GSM99570 1 0.0000 0.950 1.000 0.000 0.000 0.000
#> GSM99598 1 0.0000 0.950 1.000 0.000 0.000 0.000
#> GSM99432 2 0.3074 0.467 0.000 0.848 0.000 0.152
#> GSM99434 4 0.7901 0.417 0.000 0.316 0.312 0.372
#> GSM99436 2 0.1637 0.667 0.000 0.940 0.000 0.060
#> GSM99438 2 0.4500 0.693 0.000 0.684 0.000 0.316
#> GSM99440 1 0.0000 0.950 1.000 0.000 0.000 0.000
#> GSM99442 2 0.4500 0.693 0.000 0.684 0.000 0.316
#> GSM99444 2 0.4500 0.693 0.000 0.684 0.000 0.316
#> GSM99446 2 0.1302 0.664 0.000 0.956 0.000 0.044
#> GSM99448 3 0.5250 0.554 0.000 0.316 0.660 0.024
#> GSM99450 3 0.7313 0.171 0.000 0.316 0.508 0.176
#> GSM99452 1 0.0000 0.950 1.000 0.000 0.000 0.000
#> GSM99454 1 0.0000 0.950 1.000 0.000 0.000 0.000
#> GSM99456 1 0.5106 0.660 0.720 0.040 0.000 0.240
#> GSM99462 2 0.4500 0.693 0.000 0.684 0.000 0.316
#> GSM99464 4 0.4500 0.806 0.000 0.316 0.000 0.684
#> GSM99466 2 0.3907 0.315 0.000 0.768 0.000 0.232
#> GSM99470 1 0.4500 0.391 0.684 0.316 0.000 0.000
#> GSM99472 1 0.2345 0.842 0.900 0.100 0.000 0.000
#> GSM99474 3 0.4844 0.591 0.000 0.300 0.688 0.012
#> GSM99476 4 0.7889 0.435 0.000 0.316 0.304 0.380
#> GSM99478 2 0.2408 0.534 0.000 0.896 0.000 0.104
#> GSM99480 1 0.0000 0.950 1.000 0.000 0.000 0.000
#> GSM99482 1 0.0188 0.947 0.996 0.004 0.000 0.000
#> GSM99484 2 0.0000 0.640 0.000 1.000 0.000 0.000
#> GSM99486 2 0.0188 0.643 0.000 0.996 0.000 0.004
#> GSM99488 2 0.4500 0.693 0.000 0.684 0.000 0.316
#> GSM99490 2 0.4250 0.692 0.000 0.724 0.000 0.276
#> GSM99492 1 0.0000 0.950 1.000 0.000 0.000 0.000
#> GSM99494 2 0.4500 0.693 0.000 0.684 0.000 0.316
#> GSM99524 1 0.0000 0.950 1.000 0.000 0.000 0.000
#> GSM99526 4 0.4500 0.806 0.000 0.316 0.000 0.684
#> GSM99528 2 0.3569 0.392 0.000 0.804 0.000 0.196
#> GSM99530 4 0.5966 0.777 0.000 0.316 0.060 0.624
#> GSM99532 3 0.5047 0.564 0.000 0.316 0.668 0.016
#> GSM99534 2 0.0000 0.640 0.000 1.000 0.000 0.000
#> GSM99536 1 0.0000 0.950 1.000 0.000 0.000 0.000
#> GSM99538 2 0.4356 0.148 0.000 0.708 0.000 0.292
#> GSM99540 1 0.0336 0.944 0.992 0.008 0.000 0.000
#> GSM99542 2 0.0000 0.640 0.000 1.000 0.000 0.000
#> GSM99544 2 0.3726 0.360 0.000 0.788 0.000 0.212
#> GSM99546 4 0.4500 0.806 0.000 0.316 0.000 0.684
#> GSM99548 2 0.4500 0.693 0.000 0.684 0.000 0.316
#> GSM99550 4 0.4500 0.806 0.000 0.316 0.000 0.684
#> GSM99552 3 0.4500 0.583 0.000 0.316 0.684 0.000
#> GSM99554 2 0.4500 0.693 0.000 0.684 0.000 0.316
#> GSM99556 2 0.4500 0.693 0.000 0.684 0.000 0.316
#> GSM99558 3 0.4500 0.583 0.000 0.316 0.684 0.000
#> GSM99560 2 0.4250 0.199 0.000 0.724 0.000 0.276
#> GSM99562 3 0.0000 0.727 0.000 0.000 1.000 0.000
#> GSM99564 2 0.0592 0.651 0.000 0.984 0.000 0.016
#> GSM99572 2 0.4500 0.693 0.000 0.684 0.000 0.316
#> GSM99576 1 0.3569 0.683 0.804 0.196 0.000 0.000
#> GSM99578 2 0.0000 0.640 0.000 1.000 0.000 0.000
#> GSM99580 3 0.0188 0.727 0.000 0.004 0.996 0.000
#> GSM99582 3 0.5432 0.540 0.000 0.316 0.652 0.032
#> GSM99584 2 0.4431 0.106 0.000 0.696 0.000 0.304
#> GSM99586 1 0.0000 0.950 1.000 0.000 0.000 0.000
#> GSM99588 2 0.1118 0.661 0.000 0.964 0.000 0.036
#> GSM99590 2 0.4500 0.693 0.000 0.684 0.000 0.316
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM99496 3 0.0290 0.9289 0.000 0.000 0.992 0.000 0.008
#> GSM99502 1 0.0000 0.9935 1.000 0.000 0.000 0.000 0.000
#> GSM99504 1 0.0000 0.9935 1.000 0.000 0.000 0.000 0.000
#> GSM99506 3 0.0290 0.9289 0.000 0.000 0.992 0.000 0.008
#> GSM99566 3 0.0290 0.9289 0.000 0.000 0.992 0.000 0.008
#> GSM99574 1 0.0000 0.9935 1.000 0.000 0.000 0.000 0.000
#> GSM99592 3 0.0000 0.9306 0.000 0.000 1.000 0.000 0.000
#> GSM99594 3 0.0000 0.9306 0.000 0.000 1.000 0.000 0.000
#> GSM99468 1 0.0000 0.9935 1.000 0.000 0.000 0.000 0.000
#> GSM99498 1 0.0000 0.9935 1.000 0.000 0.000 0.000 0.000
#> GSM99500 1 0.0000 0.9935 1.000 0.000 0.000 0.000 0.000
#> GSM99508 3 0.0000 0.9306 0.000 0.000 1.000 0.000 0.000
#> GSM99568 3 0.0000 0.9306 0.000 0.000 1.000 0.000 0.000
#> GSM99596 3 0.0000 0.9306 0.000 0.000 1.000 0.000 0.000
#> GSM99600 2 0.0000 0.9633 0.000 1.000 0.000 0.000 0.000
#> GSM99458 5 0.3274 0.6811 0.220 0.000 0.000 0.000 0.780
#> GSM99460 5 0.0290 0.8521 0.008 0.000 0.000 0.000 0.992
#> GSM99510 3 0.4235 0.3406 0.000 0.000 0.576 0.424 0.000
#> GSM99512 3 0.1908 0.8566 0.000 0.000 0.908 0.092 0.000
#> GSM99514 3 0.0290 0.9289 0.000 0.000 0.992 0.000 0.008
#> GSM99516 1 0.0000 0.9935 1.000 0.000 0.000 0.000 0.000
#> GSM99518 1 0.0000 0.9935 1.000 0.000 0.000 0.000 0.000
#> GSM99520 3 0.0000 0.9306 0.000 0.000 1.000 0.000 0.000
#> GSM99522 3 0.0000 0.9306 0.000 0.000 1.000 0.000 0.000
#> GSM99570 1 0.0000 0.9935 1.000 0.000 0.000 0.000 0.000
#> GSM99598 1 0.0000 0.9935 1.000 0.000 0.000 0.000 0.000
#> GSM99432 4 0.0000 0.9326 0.000 0.000 0.000 1.000 0.000
#> GSM99434 3 0.4309 0.5679 0.000 0.000 0.676 0.308 0.016
#> GSM99436 2 0.4297 0.0534 0.000 0.528 0.000 0.472 0.000
#> GSM99438 2 0.0000 0.9633 0.000 1.000 0.000 0.000 0.000
#> GSM99440 1 0.0000 0.9935 1.000 0.000 0.000 0.000 0.000
#> GSM99442 2 0.0000 0.9633 0.000 1.000 0.000 0.000 0.000
#> GSM99444 2 0.0000 0.9633 0.000 1.000 0.000 0.000 0.000
#> GSM99446 4 0.3837 0.5360 0.000 0.308 0.000 0.692 0.000
#> GSM99448 4 0.0609 0.9163 0.000 0.000 0.020 0.980 0.000
#> GSM99450 3 0.3160 0.7497 0.000 0.000 0.808 0.004 0.188
#> GSM99452 1 0.0000 0.9935 1.000 0.000 0.000 0.000 0.000
#> GSM99454 1 0.0000 0.9935 1.000 0.000 0.000 0.000 0.000
#> GSM99456 5 0.1341 0.8315 0.056 0.000 0.000 0.000 0.944
#> GSM99462 2 0.0000 0.9633 0.000 1.000 0.000 0.000 0.000
#> GSM99464 5 0.0290 0.8525 0.000 0.000 0.000 0.008 0.992
#> GSM99466 4 0.0000 0.9326 0.000 0.000 0.000 1.000 0.000
#> GSM99470 1 0.0290 0.9840 0.992 0.000 0.000 0.008 0.000
#> GSM99472 1 0.0000 0.9935 1.000 0.000 0.000 0.000 0.000
#> GSM99474 3 0.0000 0.9306 0.000 0.000 1.000 0.000 0.000
#> GSM99476 4 0.0000 0.9326 0.000 0.000 0.000 1.000 0.000
#> GSM99478 4 0.0000 0.9326 0.000 0.000 0.000 1.000 0.000
#> GSM99480 1 0.0000 0.9935 1.000 0.000 0.000 0.000 0.000
#> GSM99482 1 0.0000 0.9935 1.000 0.000 0.000 0.000 0.000
#> GSM99484 2 0.1197 0.9216 0.000 0.952 0.000 0.048 0.000
#> GSM99486 4 0.0794 0.9122 0.000 0.028 0.000 0.972 0.000
#> GSM99488 2 0.0000 0.9633 0.000 1.000 0.000 0.000 0.000
#> GSM99490 2 0.0290 0.9604 0.000 0.992 0.000 0.008 0.000
#> GSM99492 1 0.0000 0.9935 1.000 0.000 0.000 0.000 0.000
#> GSM99494 2 0.0000 0.9633 0.000 1.000 0.000 0.000 0.000
#> GSM99524 1 0.0000 0.9935 1.000 0.000 0.000 0.000 0.000
#> GSM99526 5 0.0510 0.8488 0.000 0.000 0.000 0.016 0.984
#> GSM99528 4 0.0000 0.9326 0.000 0.000 0.000 1.000 0.000
#> GSM99530 5 0.4249 0.1963 0.000 0.000 0.432 0.000 0.568
#> GSM99532 3 0.2074 0.8469 0.000 0.000 0.896 0.000 0.104
#> GSM99534 2 0.0290 0.9604 0.000 0.992 0.000 0.008 0.000
#> GSM99536 1 0.0000 0.9935 1.000 0.000 0.000 0.000 0.000
#> GSM99538 4 0.0000 0.9326 0.000 0.000 0.000 1.000 0.000
#> GSM99540 1 0.1608 0.9205 0.928 0.000 0.000 0.000 0.072
#> GSM99542 2 0.0290 0.9604 0.000 0.992 0.000 0.008 0.000
#> GSM99544 4 0.0000 0.9326 0.000 0.000 0.000 1.000 0.000
#> GSM99546 4 0.4192 0.3371 0.000 0.000 0.000 0.596 0.404
#> GSM99548 2 0.0000 0.9633 0.000 1.000 0.000 0.000 0.000
#> GSM99550 5 0.0290 0.8525 0.000 0.000 0.000 0.008 0.992
#> GSM99552 3 0.0290 0.9264 0.000 0.000 0.992 0.008 0.000
#> GSM99554 2 0.0162 0.9620 0.000 0.996 0.000 0.004 0.000
#> GSM99556 2 0.0000 0.9633 0.000 1.000 0.000 0.000 0.000
#> GSM99558 4 0.0162 0.9300 0.000 0.000 0.004 0.996 0.000
#> GSM99560 4 0.0000 0.9326 0.000 0.000 0.000 1.000 0.000
#> GSM99562 3 0.0000 0.9306 0.000 0.000 1.000 0.000 0.000
#> GSM99564 4 0.1121 0.8972 0.000 0.044 0.000 0.956 0.000
#> GSM99572 2 0.0000 0.9633 0.000 1.000 0.000 0.000 0.000
#> GSM99576 1 0.1197 0.9485 0.952 0.000 0.000 0.000 0.048
#> GSM99578 2 0.0290 0.9604 0.000 0.992 0.000 0.008 0.000
#> GSM99580 3 0.0000 0.9306 0.000 0.000 1.000 0.000 0.000
#> GSM99582 3 0.0798 0.9190 0.000 0.000 0.976 0.008 0.016
#> GSM99584 4 0.0000 0.9326 0.000 0.000 0.000 1.000 0.000
#> GSM99586 1 0.0162 0.9903 0.996 0.000 0.000 0.000 0.004
#> GSM99588 2 0.0290 0.9604 0.000 0.992 0.000 0.008 0.000
#> GSM99590 2 0.0000 0.9633 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM99496 3 0.0713 0.8400 0.000 0.000 0.972 0.000 0.000 0.028
#> GSM99502 1 0.0000 0.8916 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99504 1 0.0000 0.8916 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99506 3 0.0713 0.8400 0.000 0.000 0.972 0.000 0.000 0.028
#> GSM99566 3 0.0632 0.8417 0.000 0.000 0.976 0.000 0.000 0.024
#> GSM99574 1 0.0000 0.8916 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99592 3 0.1556 0.8165 0.000 0.000 0.920 0.000 0.000 0.080
#> GSM99594 3 0.0632 0.8417 0.000 0.000 0.976 0.000 0.000 0.024
#> GSM99468 1 0.0000 0.8916 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99498 1 0.0000 0.8916 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99500 1 0.0000 0.8916 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99508 3 0.0000 0.8421 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99568 3 0.1556 0.8161 0.000 0.000 0.920 0.000 0.000 0.080
#> GSM99596 3 0.0632 0.8417 0.000 0.000 0.976 0.000 0.000 0.024
#> GSM99600 2 0.0146 0.9173 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM99458 5 0.1204 0.6529 0.056 0.000 0.000 0.000 0.944 0.000
#> GSM99460 5 0.0000 0.6928 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM99510 3 0.6107 -0.4962 0.000 0.000 0.372 0.332 0.000 0.296
#> GSM99512 3 0.3602 0.6552 0.000 0.000 0.796 0.088 0.000 0.116
#> GSM99514 3 0.0713 0.8400 0.000 0.000 0.972 0.000 0.000 0.028
#> GSM99516 1 0.0000 0.8916 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99518 1 0.0000 0.8916 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99520 3 0.0865 0.8355 0.000 0.000 0.964 0.000 0.000 0.036
#> GSM99522 3 0.1444 0.8219 0.000 0.000 0.928 0.000 0.000 0.072
#> GSM99570 1 0.0000 0.8916 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99598 1 0.0000 0.8916 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99432 4 0.0000 0.8944 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM99434 6 0.5763 0.5218 0.000 0.000 0.292 0.208 0.000 0.500
#> GSM99436 4 0.3515 0.5158 0.000 0.324 0.000 0.676 0.000 0.000
#> GSM99438 2 0.0000 0.9191 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99440 1 0.0000 0.8916 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99442 2 0.0000 0.9191 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99444 2 0.0000 0.9191 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99446 4 0.2562 0.7315 0.000 0.172 0.000 0.828 0.000 0.000
#> GSM99448 4 0.1930 0.8420 0.000 0.000 0.048 0.916 0.000 0.036
#> GSM99450 3 0.5346 -0.0748 0.000 0.000 0.548 0.000 0.128 0.324
#> GSM99452 1 0.0000 0.8916 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99454 1 0.0000 0.8916 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99456 5 0.0972 0.6822 0.008 0.000 0.000 0.000 0.964 0.028
#> GSM99462 2 0.0000 0.9191 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99464 5 0.3672 0.4630 0.000 0.000 0.000 0.000 0.632 0.368
#> GSM99466 4 0.0000 0.8944 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM99470 1 0.5481 0.2731 0.440 0.000 0.000 0.000 0.124 0.436
#> GSM99472 1 0.5480 0.2801 0.444 0.000 0.000 0.000 0.124 0.432
#> GSM99474 3 0.2003 0.7897 0.000 0.000 0.884 0.000 0.000 0.116
#> GSM99476 4 0.3290 0.6049 0.000 0.000 0.004 0.744 0.000 0.252
#> GSM99478 4 0.0000 0.8944 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM99480 1 0.0713 0.8755 0.972 0.000 0.000 0.000 0.000 0.028
#> GSM99482 1 0.2053 0.8180 0.888 0.000 0.000 0.000 0.004 0.108
#> GSM99484 2 0.4490 0.3621 0.000 0.604 0.000 0.360 0.004 0.032
#> GSM99486 4 0.0260 0.8924 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM99488 2 0.0000 0.9191 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99490 2 0.0146 0.9173 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM99492 1 0.0713 0.8755 0.972 0.000 0.000 0.000 0.000 0.028
#> GSM99494 2 0.0000 0.9191 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99524 1 0.0000 0.8916 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99526 5 0.3819 0.4541 0.000 0.000 0.000 0.004 0.624 0.372
#> GSM99528 4 0.3121 0.7180 0.000 0.008 0.000 0.796 0.004 0.192
#> GSM99530 6 0.5894 0.3453 0.000 0.000 0.244 0.000 0.284 0.472
#> GSM99532 3 0.3588 0.6615 0.000 0.000 0.788 0.000 0.060 0.152
#> GSM99534 2 0.4886 0.3955 0.000 0.520 0.000 0.012 0.036 0.432
#> GSM99536 1 0.0000 0.8916 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99538 4 0.0000 0.8944 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM99540 1 0.2378 0.7713 0.848 0.000 0.000 0.000 0.152 0.000
#> GSM99542 2 0.3944 0.4635 0.000 0.568 0.000 0.000 0.004 0.428
#> GSM99544 4 0.0000 0.8944 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM99546 5 0.6079 0.0759 0.000 0.000 0.000 0.280 0.392 0.328
#> GSM99548 2 0.0000 0.9191 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99550 5 0.0000 0.6928 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM99552 3 0.0632 0.8417 0.000 0.000 0.976 0.000 0.000 0.024
#> GSM99554 2 0.0260 0.9142 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM99556 2 0.0000 0.9191 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99558 4 0.1010 0.8734 0.000 0.000 0.036 0.960 0.000 0.004
#> GSM99560 4 0.0146 0.8928 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM99562 3 0.0146 0.8419 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM99564 4 0.1075 0.8652 0.000 0.048 0.000 0.952 0.000 0.000
#> GSM99572 2 0.0000 0.9191 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99576 1 0.5607 0.2823 0.448 0.000 0.000 0.000 0.144 0.408
#> GSM99578 2 0.0000 0.9191 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99580 3 0.0363 0.8424 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM99582 3 0.2402 0.7772 0.000 0.000 0.868 0.000 0.012 0.120
#> GSM99584 4 0.0000 0.8944 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM99586 1 0.4343 0.3999 0.592 0.000 0.000 0.000 0.380 0.028
#> GSM99588 2 0.0146 0.9173 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM99590 2 0.0000 0.9191 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) cell.type(p) k
#> MAD:mclust 76 2.92e-05 0.000166 2
#> MAD:mclust 85 2.97e-04 0.007444 3
#> MAD:mclust 73 6.20e-04 0.021537 4
#> MAD:mclust 81 2.71e-04 0.010396 5
#> MAD:mclust 72 1.44e-04 0.009396 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 21168 rows and 85 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.962 0.984 0.5032 0.496 0.496
#> 3 3 0.967 0.957 0.981 0.3384 0.729 0.505
#> 4 4 0.884 0.898 0.947 0.1069 0.884 0.666
#> 5 5 0.755 0.688 0.833 0.0470 0.965 0.869
#> 6 6 0.733 0.598 0.785 0.0446 0.896 0.608
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
#> GSM99496 1 0.0000 0.991 1.000 0.000
#> GSM99502 1 0.0000 0.991 1.000 0.000
#> GSM99504 1 0.0000 0.991 1.000 0.000
#> GSM99506 1 0.0000 0.991 1.000 0.000
#> GSM99566 1 0.3733 0.918 0.928 0.072
#> GSM99574 1 0.0000 0.991 1.000 0.000
#> GSM99592 1 0.8267 0.639 0.740 0.260
#> GSM99594 1 0.0000 0.991 1.000 0.000
#> GSM99468 1 0.0000 0.991 1.000 0.000
#> GSM99498 1 0.0000 0.991 1.000 0.000
#> GSM99500 1 0.0000 0.991 1.000 0.000
#> GSM99508 1 0.0000 0.991 1.000 0.000
#> GSM99568 1 0.0000 0.991 1.000 0.000
#> GSM99596 1 0.0000 0.991 1.000 0.000
#> GSM99600 2 0.0000 0.975 0.000 1.000
#> GSM99458 1 0.0000 0.991 1.000 0.000
#> GSM99460 1 0.0000 0.991 1.000 0.000
#> GSM99510 2 0.3431 0.918 0.064 0.936
#> GSM99512 2 0.0672 0.969 0.008 0.992
#> GSM99514 1 0.0000 0.991 1.000 0.000
#> GSM99516 1 0.0000 0.991 1.000 0.000
#> GSM99518 1 0.0000 0.991 1.000 0.000
#> GSM99520 1 0.0000 0.991 1.000 0.000
#> GSM99522 1 0.0000 0.991 1.000 0.000
#> GSM99570 1 0.0000 0.991 1.000 0.000
#> GSM99598 1 0.0000 0.991 1.000 0.000
#> GSM99432 2 0.0000 0.975 0.000 1.000
#> GSM99434 2 0.9635 0.376 0.388 0.612
#> GSM99436 2 0.0000 0.975 0.000 1.000
#> GSM99438 2 0.0000 0.975 0.000 1.000
#> GSM99440 1 0.0000 0.991 1.000 0.000
#> GSM99442 2 0.0000 0.975 0.000 1.000
#> GSM99444 2 0.0000 0.975 0.000 1.000
#> GSM99446 2 0.0000 0.975 0.000 1.000
#> GSM99448 2 0.0000 0.975 0.000 1.000
#> GSM99450 1 0.0000 0.991 1.000 0.000
#> GSM99452 1 0.0000 0.991 1.000 0.000
#> GSM99454 1 0.0000 0.991 1.000 0.000
#> GSM99456 1 0.0000 0.991 1.000 0.000
#> GSM99462 2 0.0000 0.975 0.000 1.000
#> GSM99464 1 0.0000 0.991 1.000 0.000
#> GSM99466 2 0.0000 0.975 0.000 1.000
#> GSM99470 1 0.3114 0.935 0.944 0.056
#> GSM99472 1 0.0000 0.991 1.000 0.000
#> GSM99474 1 0.0000 0.991 1.000 0.000
#> GSM99476 2 0.0000 0.975 0.000 1.000
#> GSM99478 2 0.0000 0.975 0.000 1.000
#> GSM99480 1 0.0000 0.991 1.000 0.000
#> GSM99482 1 0.0000 0.991 1.000 0.000
#> GSM99484 2 0.0000 0.975 0.000 1.000
#> GSM99486 2 0.0000 0.975 0.000 1.000
#> GSM99488 2 0.0000 0.975 0.000 1.000
#> GSM99490 2 0.0000 0.975 0.000 1.000
#> GSM99492 1 0.0000 0.991 1.000 0.000
#> GSM99494 2 0.0000 0.975 0.000 1.000
#> GSM99524 1 0.0000 0.991 1.000 0.000
#> GSM99526 2 0.3274 0.922 0.060 0.940
#> GSM99528 2 0.0000 0.975 0.000 1.000
#> GSM99530 1 0.0000 0.991 1.000 0.000
#> GSM99532 1 0.0000 0.991 1.000 0.000
#> GSM99534 2 0.0000 0.975 0.000 1.000
#> GSM99536 1 0.0000 0.991 1.000 0.000
#> GSM99538 2 0.0000 0.975 0.000 1.000
#> GSM99540 1 0.0000 0.991 1.000 0.000
#> GSM99542 2 0.0000 0.975 0.000 1.000
#> GSM99544 2 0.0000 0.975 0.000 1.000
#> GSM99546 2 0.0376 0.972 0.004 0.996
#> GSM99548 2 0.0000 0.975 0.000 1.000
#> GSM99550 1 0.0000 0.991 1.000 0.000
#> GSM99552 2 0.1633 0.956 0.024 0.976
#> GSM99554 2 0.0000 0.975 0.000 1.000
#> GSM99556 2 0.0000 0.975 0.000 1.000
#> GSM99558 2 0.0000 0.975 0.000 1.000
#> GSM99560 2 0.0000 0.975 0.000 1.000
#> GSM99562 1 0.0000 0.991 1.000 0.000
#> GSM99564 2 0.0000 0.975 0.000 1.000
#> GSM99572 2 0.0000 0.975 0.000 1.000
#> GSM99576 1 0.0000 0.991 1.000 0.000
#> GSM99578 2 0.0000 0.975 0.000 1.000
#> GSM99580 2 0.9754 0.329 0.408 0.592
#> GSM99582 1 0.0000 0.991 1.000 0.000
#> GSM99584 2 0.0000 0.975 0.000 1.000
#> GSM99586 1 0.0000 0.991 1.000 0.000
#> GSM99588 2 0.0000 0.975 0.000 1.000
#> GSM99590 2 0.0000 0.975 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM99496 3 0.0000 0.972 0.000 0.000 1.000
#> GSM99502 1 0.0000 0.988 1.000 0.000 0.000
#> GSM99504 1 0.3340 0.863 0.880 0.000 0.120
#> GSM99506 3 0.0000 0.972 0.000 0.000 1.000
#> GSM99566 3 0.0000 0.972 0.000 0.000 1.000
#> GSM99574 1 0.0000 0.988 1.000 0.000 0.000
#> GSM99592 3 0.0000 0.972 0.000 0.000 1.000
#> GSM99594 3 0.0000 0.972 0.000 0.000 1.000
#> GSM99468 1 0.0000 0.988 1.000 0.000 0.000
#> GSM99498 1 0.0000 0.988 1.000 0.000 0.000
#> GSM99500 1 0.0000 0.988 1.000 0.000 0.000
#> GSM99508 3 0.0000 0.972 0.000 0.000 1.000
#> GSM99568 3 0.0000 0.972 0.000 0.000 1.000
#> GSM99596 3 0.0000 0.972 0.000 0.000 1.000
#> GSM99600 2 0.0000 0.979 0.000 1.000 0.000
#> GSM99458 1 0.0000 0.988 1.000 0.000 0.000
#> GSM99460 1 0.0000 0.988 1.000 0.000 0.000
#> GSM99510 3 0.0000 0.972 0.000 0.000 1.000
#> GSM99512 3 0.0000 0.972 0.000 0.000 1.000
#> GSM99514 3 0.0000 0.972 0.000 0.000 1.000
#> GSM99516 1 0.0000 0.988 1.000 0.000 0.000
#> GSM99518 1 0.0000 0.988 1.000 0.000 0.000
#> GSM99520 3 0.0000 0.972 0.000 0.000 1.000
#> GSM99522 3 0.0000 0.972 0.000 0.000 1.000
#> GSM99570 1 0.0000 0.988 1.000 0.000 0.000
#> GSM99598 1 0.0000 0.988 1.000 0.000 0.000
#> GSM99432 2 0.0237 0.977 0.000 0.996 0.004
#> GSM99434 3 0.0000 0.972 0.000 0.000 1.000
#> GSM99436 2 0.0000 0.979 0.000 1.000 0.000
#> GSM99438 2 0.0000 0.979 0.000 1.000 0.000
#> GSM99440 1 0.0000 0.988 1.000 0.000 0.000
#> GSM99442 2 0.0000 0.979 0.000 1.000 0.000
#> GSM99444 2 0.0000 0.979 0.000 1.000 0.000
#> GSM99446 2 0.0000 0.979 0.000 1.000 0.000
#> GSM99448 3 0.0000 0.972 0.000 0.000 1.000
#> GSM99450 3 0.0000 0.972 0.000 0.000 1.000
#> GSM99452 1 0.0000 0.988 1.000 0.000 0.000
#> GSM99454 1 0.0000 0.988 1.000 0.000 0.000
#> GSM99456 1 0.0000 0.988 1.000 0.000 0.000
#> GSM99462 2 0.0000 0.979 0.000 1.000 0.000
#> GSM99464 3 0.0000 0.972 0.000 0.000 1.000
#> GSM99466 2 0.3619 0.842 0.000 0.864 0.136
#> GSM99470 1 0.3340 0.865 0.880 0.120 0.000
#> GSM99472 1 0.0000 0.988 1.000 0.000 0.000
#> GSM99474 3 0.0000 0.972 0.000 0.000 1.000
#> GSM99476 3 0.0000 0.972 0.000 0.000 1.000
#> GSM99478 2 0.0237 0.977 0.000 0.996 0.004
#> GSM99480 1 0.0000 0.988 1.000 0.000 0.000
#> GSM99482 1 0.0000 0.988 1.000 0.000 0.000
#> GSM99484 2 0.0000 0.979 0.000 1.000 0.000
#> GSM99486 2 0.0237 0.977 0.000 0.996 0.004
#> GSM99488 2 0.0000 0.979 0.000 1.000 0.000
#> GSM99490 2 0.0000 0.979 0.000 1.000 0.000
#> GSM99492 1 0.0000 0.988 1.000 0.000 0.000
#> GSM99494 2 0.0000 0.979 0.000 1.000 0.000
#> GSM99524 1 0.0000 0.988 1.000 0.000 0.000
#> GSM99526 3 0.4002 0.800 0.000 0.160 0.840
#> GSM99528 2 0.0000 0.979 0.000 1.000 0.000
#> GSM99530 3 0.0000 0.972 0.000 0.000 1.000
#> GSM99532 3 0.0000 0.972 0.000 0.000 1.000
#> GSM99534 2 0.0000 0.979 0.000 1.000 0.000
#> GSM99536 1 0.0000 0.988 1.000 0.000 0.000
#> GSM99538 3 0.5810 0.479 0.000 0.336 0.664
#> GSM99540 1 0.0592 0.978 0.988 0.000 0.012
#> GSM99542 2 0.0000 0.979 0.000 1.000 0.000
#> GSM99544 2 0.5706 0.527 0.000 0.680 0.320
#> GSM99546 2 0.2796 0.893 0.000 0.908 0.092
#> GSM99548 2 0.0000 0.979 0.000 1.000 0.000
#> GSM99550 1 0.1860 0.942 0.948 0.052 0.000
#> GSM99552 3 0.0237 0.969 0.000 0.004 0.996
#> GSM99554 2 0.0000 0.979 0.000 1.000 0.000
#> GSM99556 2 0.0000 0.979 0.000 1.000 0.000
#> GSM99558 3 0.0237 0.969 0.000 0.004 0.996
#> GSM99560 2 0.0000 0.979 0.000 1.000 0.000
#> GSM99562 3 0.0000 0.972 0.000 0.000 1.000
#> GSM99564 2 0.0000 0.979 0.000 1.000 0.000
#> GSM99572 2 0.0000 0.979 0.000 1.000 0.000
#> GSM99576 1 0.0000 0.988 1.000 0.000 0.000
#> GSM99578 2 0.0000 0.979 0.000 1.000 0.000
#> GSM99580 3 0.0000 0.972 0.000 0.000 1.000
#> GSM99582 3 0.4702 0.722 0.212 0.000 0.788
#> GSM99584 2 0.0892 0.964 0.000 0.980 0.020
#> GSM99586 1 0.0000 0.988 1.000 0.000 0.000
#> GSM99588 2 0.0000 0.979 0.000 1.000 0.000
#> GSM99590 2 0.0000 0.979 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM99496 3 0.0000 0.941 0.000 0.000 1.000 0.000
#> GSM99502 1 0.0000 0.961 1.000 0.000 0.000 0.000
#> GSM99504 3 0.2149 0.875 0.088 0.000 0.912 0.000
#> GSM99506 3 0.0188 0.942 0.000 0.000 0.996 0.004
#> GSM99566 3 0.0000 0.941 0.000 0.000 1.000 0.000
#> GSM99574 1 0.0000 0.961 1.000 0.000 0.000 0.000
#> GSM99592 3 0.2408 0.899 0.000 0.000 0.896 0.104
#> GSM99594 3 0.0336 0.942 0.000 0.000 0.992 0.008
#> GSM99468 1 0.0000 0.961 1.000 0.000 0.000 0.000
#> GSM99498 1 0.3444 0.750 0.816 0.000 0.184 0.000
#> GSM99500 1 0.0592 0.949 0.984 0.000 0.016 0.000
#> GSM99508 3 0.1022 0.940 0.000 0.000 0.968 0.032
#> GSM99568 3 0.1022 0.940 0.000 0.000 0.968 0.032
#> GSM99596 3 0.0469 0.940 0.000 0.000 0.988 0.012
#> GSM99600 2 0.0469 0.966 0.000 0.988 0.000 0.012
#> GSM99458 1 0.0817 0.945 0.976 0.000 0.000 0.024
#> GSM99460 4 0.4790 0.401 0.380 0.000 0.000 0.620
#> GSM99510 4 0.4164 0.613 0.000 0.000 0.264 0.736
#> GSM99512 3 0.3569 0.793 0.000 0.000 0.804 0.196
#> GSM99514 3 0.0188 0.942 0.000 0.000 0.996 0.004
#> GSM99516 1 0.0000 0.961 1.000 0.000 0.000 0.000
#> GSM99518 1 0.0000 0.961 1.000 0.000 0.000 0.000
#> GSM99520 3 0.0817 0.941 0.000 0.000 0.976 0.024
#> GSM99522 3 0.1209 0.937 0.004 0.000 0.964 0.032
#> GSM99570 1 0.0000 0.961 1.000 0.000 0.000 0.000
#> GSM99598 1 0.0000 0.961 1.000 0.000 0.000 0.000
#> GSM99432 4 0.3172 0.771 0.000 0.160 0.000 0.840
#> GSM99434 4 0.1792 0.833 0.000 0.000 0.068 0.932
#> GSM99436 2 0.2589 0.888 0.000 0.884 0.000 0.116
#> GSM99438 2 0.0188 0.967 0.000 0.996 0.000 0.004
#> GSM99440 1 0.0000 0.961 1.000 0.000 0.000 0.000
#> GSM99442 2 0.0469 0.966 0.000 0.988 0.000 0.012
#> GSM99444 2 0.0188 0.967 0.000 0.996 0.000 0.004
#> GSM99446 2 0.2408 0.900 0.000 0.896 0.000 0.104
#> GSM99448 3 0.2081 0.911 0.000 0.000 0.916 0.084
#> GSM99450 4 0.3311 0.748 0.000 0.000 0.172 0.828
#> GSM99452 1 0.0000 0.961 1.000 0.000 0.000 0.000
#> GSM99454 1 0.0000 0.961 1.000 0.000 0.000 0.000
#> GSM99456 1 0.1557 0.916 0.944 0.000 0.000 0.056
#> GSM99462 2 0.0188 0.967 0.000 0.996 0.000 0.004
#> GSM99464 4 0.0336 0.853 0.000 0.000 0.008 0.992
#> GSM99466 2 0.1938 0.937 0.000 0.936 0.012 0.052
#> GSM99470 1 0.4933 0.232 0.568 0.432 0.000 0.000
#> GSM99472 1 0.0000 0.961 1.000 0.000 0.000 0.000
#> GSM99474 3 0.1211 0.936 0.000 0.000 0.960 0.040
#> GSM99476 4 0.0592 0.852 0.000 0.000 0.016 0.984
#> GSM99478 2 0.0376 0.964 0.000 0.992 0.004 0.004
#> GSM99480 1 0.0000 0.961 1.000 0.000 0.000 0.000
#> GSM99482 1 0.0000 0.961 1.000 0.000 0.000 0.000
#> GSM99484 2 0.0188 0.967 0.000 0.996 0.000 0.004
#> GSM99486 2 0.1022 0.956 0.000 0.968 0.000 0.032
#> GSM99488 2 0.0000 0.967 0.000 1.000 0.000 0.000
#> GSM99490 2 0.0188 0.967 0.000 0.996 0.000 0.004
#> GSM99492 1 0.0000 0.961 1.000 0.000 0.000 0.000
#> GSM99494 2 0.0000 0.967 0.000 1.000 0.000 0.000
#> GSM99524 1 0.0000 0.961 1.000 0.000 0.000 0.000
#> GSM99526 4 0.0336 0.853 0.000 0.000 0.008 0.992
#> GSM99528 2 0.1406 0.944 0.000 0.960 0.016 0.024
#> GSM99530 4 0.3444 0.747 0.000 0.000 0.184 0.816
#> GSM99532 3 0.4431 0.617 0.000 0.000 0.696 0.304
#> GSM99534 2 0.0469 0.966 0.000 0.988 0.000 0.012
#> GSM99536 1 0.0000 0.961 1.000 0.000 0.000 0.000
#> GSM99538 4 0.1109 0.855 0.000 0.028 0.004 0.968
#> GSM99540 1 0.0592 0.952 0.984 0.000 0.000 0.016
#> GSM99542 2 0.0000 0.967 0.000 1.000 0.000 0.000
#> GSM99544 4 0.2973 0.789 0.000 0.144 0.000 0.856
#> GSM99546 4 0.1302 0.850 0.000 0.044 0.000 0.956
#> GSM99548 2 0.0188 0.967 0.000 0.996 0.000 0.004
#> GSM99550 4 0.3836 0.753 0.168 0.016 0.000 0.816
#> GSM99552 3 0.0188 0.940 0.000 0.004 0.996 0.000
#> GSM99554 2 0.0469 0.966 0.000 0.988 0.000 0.012
#> GSM99556 2 0.0000 0.967 0.000 1.000 0.000 0.000
#> GSM99558 3 0.0188 0.940 0.000 0.004 0.996 0.000
#> GSM99560 2 0.4356 0.617 0.000 0.708 0.000 0.292
#> GSM99562 3 0.2011 0.916 0.000 0.000 0.920 0.080
#> GSM99564 2 0.2647 0.883 0.000 0.880 0.000 0.120
#> GSM99572 2 0.0188 0.967 0.000 0.996 0.000 0.004
#> GSM99576 1 0.0524 0.954 0.988 0.004 0.000 0.008
#> GSM99578 2 0.0000 0.967 0.000 1.000 0.000 0.000
#> GSM99580 3 0.0188 0.942 0.000 0.000 0.996 0.004
#> GSM99582 3 0.2924 0.852 0.100 0.000 0.884 0.016
#> GSM99584 4 0.1792 0.840 0.000 0.068 0.000 0.932
#> GSM99586 1 0.0592 0.952 0.984 0.000 0.000 0.016
#> GSM99588 2 0.0000 0.967 0.000 1.000 0.000 0.000
#> GSM99590 2 0.0188 0.967 0.000 0.996 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM99496 3 0.0880 0.7554 0.000 0.000 0.968 0.000 0.032
#> GSM99502 1 0.0290 0.9322 0.992 0.000 0.000 0.000 0.008
#> GSM99504 3 0.5642 0.3457 0.240 0.000 0.624 0.000 0.136
#> GSM99506 3 0.0290 0.7570 0.000 0.000 0.992 0.000 0.008
#> GSM99566 3 0.1851 0.7460 0.000 0.000 0.912 0.000 0.088
#> GSM99574 1 0.0880 0.9236 0.968 0.000 0.000 0.000 0.032
#> GSM99592 3 0.3459 0.7234 0.000 0.000 0.832 0.052 0.116
#> GSM99594 3 0.2411 0.7280 0.000 0.000 0.884 0.008 0.108
#> GSM99468 1 0.0162 0.9323 0.996 0.000 0.000 0.000 0.004
#> GSM99498 1 0.3961 0.6542 0.760 0.000 0.212 0.000 0.028
#> GSM99500 1 0.0162 0.9323 0.996 0.000 0.000 0.000 0.004
#> GSM99508 3 0.1792 0.7439 0.000 0.000 0.916 0.000 0.084
#> GSM99568 3 0.1282 0.7521 0.000 0.000 0.952 0.004 0.044
#> GSM99596 3 0.2516 0.7132 0.000 0.000 0.860 0.000 0.140
#> GSM99600 2 0.2719 0.7480 0.000 0.852 0.000 0.004 0.144
#> GSM99458 1 0.0693 0.9305 0.980 0.000 0.000 0.012 0.008
#> GSM99460 4 0.4537 0.2638 0.396 0.000 0.000 0.592 0.012
#> GSM99510 4 0.5375 0.5277 0.000 0.000 0.176 0.668 0.156
#> GSM99512 3 0.5190 0.6271 0.000 0.000 0.688 0.140 0.172
#> GSM99514 3 0.2732 0.7100 0.000 0.000 0.840 0.000 0.160
#> GSM99516 1 0.0510 0.9307 0.984 0.000 0.000 0.000 0.016
#> GSM99518 1 0.0162 0.9325 0.996 0.000 0.000 0.004 0.000
#> GSM99520 3 0.0451 0.7575 0.000 0.000 0.988 0.004 0.008
#> GSM99522 3 0.4510 0.4199 0.008 0.000 0.560 0.000 0.432
#> GSM99570 1 0.0609 0.9294 0.980 0.000 0.000 0.000 0.020
#> GSM99598 1 0.0404 0.9318 0.988 0.000 0.000 0.000 0.012
#> GSM99432 4 0.4501 0.6183 0.000 0.128 0.000 0.756 0.116
#> GSM99434 4 0.1012 0.7308 0.000 0.000 0.020 0.968 0.012
#> GSM99436 2 0.5678 0.4324 0.000 0.612 0.000 0.128 0.260
#> GSM99438 2 0.0290 0.8025 0.000 0.992 0.000 0.000 0.008
#> GSM99440 1 0.0000 0.9328 1.000 0.000 0.000 0.000 0.000
#> GSM99442 2 0.3424 0.6657 0.000 0.760 0.000 0.000 0.240
#> GSM99444 2 0.1410 0.7904 0.000 0.940 0.000 0.000 0.060
#> GSM99446 2 0.5120 0.5615 0.000 0.684 0.000 0.104 0.212
#> GSM99448 3 0.5142 0.4924 0.000 0.000 0.600 0.052 0.348
#> GSM99450 4 0.3590 0.6961 0.000 0.000 0.080 0.828 0.092
#> GSM99452 1 0.0000 0.9328 1.000 0.000 0.000 0.000 0.000
#> GSM99454 1 0.0000 0.9328 1.000 0.000 0.000 0.000 0.000
#> GSM99456 1 0.3346 0.8269 0.844 0.000 0.000 0.092 0.064
#> GSM99462 2 0.0703 0.8006 0.000 0.976 0.000 0.000 0.024
#> GSM99464 4 0.1557 0.7183 0.000 0.000 0.008 0.940 0.052
#> GSM99466 2 0.6220 0.3984 0.000 0.572 0.032 0.084 0.312
#> GSM99470 1 0.4078 0.6803 0.784 0.148 0.000 0.000 0.068
#> GSM99472 1 0.0510 0.9310 0.984 0.000 0.000 0.000 0.016
#> GSM99474 3 0.2491 0.7374 0.000 0.000 0.896 0.036 0.068
#> GSM99476 4 0.2989 0.7145 0.000 0.008 0.008 0.852 0.132
#> GSM99478 2 0.3126 0.6962 0.000 0.868 0.048 0.008 0.076
#> GSM99480 1 0.0000 0.9328 1.000 0.000 0.000 0.000 0.000
#> GSM99482 1 0.0290 0.9322 0.992 0.000 0.000 0.000 0.008
#> GSM99484 2 0.2648 0.7451 0.000 0.848 0.000 0.000 0.152
#> GSM99486 5 0.5778 -0.4511 0.000 0.448 0.000 0.088 0.464
#> GSM99488 2 0.0794 0.7952 0.000 0.972 0.000 0.000 0.028
#> GSM99490 2 0.0609 0.7989 0.000 0.980 0.000 0.000 0.020
#> GSM99492 1 0.1251 0.9133 0.956 0.000 0.000 0.008 0.036
#> GSM99494 2 0.0703 0.7998 0.000 0.976 0.000 0.000 0.024
#> GSM99524 1 0.0404 0.9318 0.988 0.000 0.000 0.000 0.012
#> GSM99526 4 0.0794 0.7329 0.000 0.000 0.000 0.972 0.028
#> GSM99528 3 0.7464 0.0436 0.008 0.344 0.392 0.024 0.232
#> GSM99530 3 0.6619 0.2678 0.004 0.000 0.480 0.304 0.212
#> GSM99532 3 0.5939 0.4405 0.000 0.000 0.576 0.276 0.148
#> GSM99534 2 0.2997 0.7417 0.012 0.840 0.000 0.000 0.148
#> GSM99536 1 0.0566 0.9284 0.984 0.000 0.000 0.004 0.012
#> GSM99538 4 0.4796 0.5988 0.000 0.020 0.156 0.752 0.072
#> GSM99540 1 0.4528 0.7635 0.784 0.000 0.024 0.108 0.084
#> GSM99542 2 0.0963 0.7908 0.000 0.964 0.000 0.000 0.036
#> GSM99544 4 0.5657 0.4885 0.000 0.128 0.000 0.616 0.256
#> GSM99546 4 0.2505 0.7225 0.000 0.020 0.000 0.888 0.092
#> GSM99548 2 0.1357 0.7843 0.000 0.948 0.000 0.004 0.048
#> GSM99550 4 0.4166 0.6307 0.116 0.004 0.000 0.792 0.088
#> GSM99552 3 0.2179 0.7368 0.000 0.000 0.888 0.000 0.112
#> GSM99554 2 0.3480 0.6574 0.000 0.752 0.000 0.000 0.248
#> GSM99556 2 0.0703 0.7974 0.000 0.976 0.000 0.000 0.024
#> GSM99558 3 0.1469 0.7526 0.000 0.016 0.948 0.000 0.036
#> GSM99560 2 0.6231 0.2627 0.000 0.532 0.000 0.288 0.180
#> GSM99562 3 0.3730 0.6125 0.000 0.000 0.712 0.000 0.288
#> GSM99564 2 0.6282 0.1372 0.000 0.496 0.000 0.164 0.340
#> GSM99572 2 0.0162 0.8024 0.000 0.996 0.000 0.000 0.004
#> GSM99576 1 0.5650 0.6786 0.712 0.056 0.028 0.028 0.176
#> GSM99578 2 0.0703 0.8005 0.000 0.976 0.000 0.000 0.024
#> GSM99580 3 0.1197 0.7541 0.000 0.000 0.952 0.000 0.048
#> GSM99582 5 0.6579 -0.3266 0.208 0.000 0.372 0.000 0.420
#> GSM99584 4 0.5074 0.5503 0.000 0.072 0.000 0.660 0.268
#> GSM99586 1 0.2645 0.8658 0.888 0.000 0.000 0.044 0.068
#> GSM99588 2 0.0703 0.7995 0.000 0.976 0.000 0.000 0.024
#> GSM99590 2 0.0404 0.8023 0.000 0.988 0.000 0.000 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM99496 3 0.4230 0.14053 0.000 0.000 0.584 0.008 0.008 0.400
#> GSM99502 1 0.0260 0.92419 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM99504 3 0.5025 0.28525 0.232 0.000 0.672 0.016 0.008 0.072
#> GSM99506 3 0.2969 0.48626 0.000 0.000 0.776 0.000 0.000 0.224
#> GSM99566 3 0.1003 0.59120 0.000 0.000 0.964 0.004 0.004 0.028
#> GSM99574 1 0.0622 0.92332 0.980 0.000 0.008 0.000 0.000 0.012
#> GSM99592 3 0.2998 0.58978 0.000 0.000 0.856 0.008 0.064 0.072
#> GSM99594 3 0.4199 0.29194 0.000 0.000 0.620 0.004 0.016 0.360
#> GSM99468 1 0.0405 0.92378 0.988 0.000 0.000 0.004 0.000 0.008
#> GSM99498 1 0.4302 0.63967 0.728 0.000 0.156 0.000 0.000 0.116
#> GSM99500 1 0.2201 0.87720 0.896 0.000 0.028 0.000 0.000 0.076
#> GSM99508 3 0.2431 0.56021 0.000 0.000 0.860 0.000 0.008 0.132
#> GSM99568 3 0.3409 0.40120 0.000 0.000 0.700 0.000 0.000 0.300
#> GSM99596 6 0.3330 0.47156 0.000 0.000 0.284 0.000 0.000 0.716
#> GSM99600 4 0.4171 0.37337 0.000 0.380 0.000 0.604 0.012 0.004
#> GSM99458 1 0.0964 0.92131 0.968 0.000 0.000 0.004 0.012 0.016
#> GSM99460 5 0.4086 0.00541 0.464 0.000 0.000 0.000 0.528 0.008
#> GSM99510 3 0.5317 0.21000 0.000 0.000 0.524 0.032 0.400 0.044
#> GSM99512 3 0.5224 0.44824 0.000 0.020 0.668 0.012 0.220 0.080
#> GSM99514 3 0.4201 0.49105 0.000 0.000 0.760 0.056 0.024 0.160
#> GSM99516 1 0.0363 0.92449 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM99518 1 0.0508 0.92499 0.984 0.000 0.000 0.000 0.004 0.012
#> GSM99520 3 0.4249 0.09225 0.000 0.000 0.568 0.012 0.004 0.416
#> GSM99522 3 0.5157 0.48547 0.000 0.000 0.700 0.080 0.072 0.148
#> GSM99570 1 0.0653 0.92418 0.980 0.000 0.004 0.004 0.000 0.012
#> GSM99598 1 0.0405 0.92435 0.988 0.000 0.000 0.004 0.000 0.008
#> GSM99432 5 0.4306 -0.17869 0.000 0.012 0.000 0.464 0.520 0.004
#> GSM99434 5 0.3051 0.62317 0.000 0.000 0.112 0.036 0.844 0.008
#> GSM99436 4 0.4013 0.64297 0.000 0.104 0.000 0.768 0.124 0.004
#> GSM99438 2 0.1387 0.85934 0.000 0.932 0.000 0.068 0.000 0.000
#> GSM99440 1 0.0146 0.92414 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM99442 4 0.3841 0.38535 0.000 0.380 0.000 0.616 0.000 0.004
#> GSM99444 2 0.2260 0.80428 0.000 0.860 0.000 0.140 0.000 0.000
#> GSM99446 4 0.5079 0.51869 0.000 0.304 0.000 0.600 0.092 0.004
#> GSM99448 3 0.4966 0.49855 0.000 0.000 0.712 0.048 0.148 0.092
#> GSM99450 5 0.3868 0.59291 0.000 0.000 0.100 0.096 0.792 0.012
#> GSM99452 1 0.0146 0.92414 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM99454 1 0.0405 0.92494 0.988 0.000 0.000 0.004 0.000 0.008
#> GSM99456 1 0.3548 0.80558 0.816 0.000 0.000 0.016 0.116 0.052
#> GSM99462 2 0.1204 0.85886 0.000 0.944 0.000 0.056 0.000 0.000
#> GSM99464 5 0.2164 0.64383 0.000 0.000 0.028 0.016 0.912 0.044
#> GSM99466 4 0.4352 0.50449 0.000 0.016 0.012 0.704 0.016 0.252
#> GSM99470 1 0.3859 0.73368 0.772 0.016 0.000 0.176 0.000 0.036
#> GSM99472 1 0.1461 0.90411 0.940 0.000 0.000 0.044 0.000 0.016
#> GSM99474 3 0.4447 0.48080 0.000 0.000 0.704 0.000 0.100 0.196
#> GSM99476 4 0.4224 0.21076 0.000 0.000 0.000 0.552 0.432 0.016
#> GSM99478 6 0.5861 0.22233 0.000 0.076 0.040 0.268 0.016 0.600
#> GSM99480 1 0.0146 0.92377 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM99482 1 0.0692 0.92266 0.976 0.000 0.000 0.004 0.000 0.020
#> GSM99484 4 0.4361 0.49798 0.000 0.308 0.000 0.648 0.000 0.044
#> GSM99486 4 0.2553 0.62888 0.000 0.056 0.000 0.888 0.044 0.012
#> GSM99488 2 0.0000 0.85040 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99490 2 0.3606 0.63610 0.000 0.728 0.000 0.256 0.000 0.016
#> GSM99492 1 0.1483 0.90518 0.944 0.000 0.000 0.008 0.012 0.036
#> GSM99494 2 0.0146 0.84967 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM99524 1 0.1049 0.91807 0.960 0.000 0.000 0.008 0.000 0.032
#> GSM99526 5 0.1888 0.63465 0.000 0.000 0.004 0.068 0.916 0.012
#> GSM99528 6 0.5145 0.49947 0.004 0.060 0.120 0.024 0.056 0.736
#> GSM99530 6 0.6109 0.12414 0.000 0.000 0.204 0.008 0.364 0.424
#> GSM99532 5 0.5951 -0.01925 0.000 0.000 0.332 0.004 0.464 0.200
#> GSM99534 2 0.4256 0.67390 0.044 0.744 0.000 0.192 0.004 0.016
#> GSM99536 1 0.0405 0.92331 0.988 0.000 0.000 0.004 0.008 0.000
#> GSM99538 5 0.4587 0.55015 0.000 0.008 0.096 0.024 0.752 0.120
#> GSM99540 1 0.4540 0.72181 0.744 0.000 0.032 0.000 0.140 0.084
#> GSM99542 2 0.0146 0.84780 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM99544 4 0.5462 0.10626 0.000 0.028 0.016 0.476 0.452 0.028
#> GSM99546 5 0.2488 0.59663 0.000 0.004 0.000 0.124 0.864 0.008
#> GSM99548 2 0.2432 0.81779 0.000 0.876 0.000 0.100 0.000 0.024
#> GSM99550 5 0.5611 0.47692 0.068 0.004 0.000 0.160 0.664 0.104
#> GSM99552 6 0.4514 0.37348 0.000 0.004 0.336 0.024 0.008 0.628
#> GSM99554 4 0.3512 0.54190 0.000 0.272 0.000 0.720 0.000 0.008
#> GSM99556 2 0.0865 0.86199 0.000 0.964 0.000 0.036 0.000 0.000
#> GSM99558 6 0.5600 0.22695 0.000 0.004 0.412 0.096 0.008 0.480
#> GSM99560 4 0.5899 0.51687 0.000 0.108 0.000 0.584 0.256 0.052
#> GSM99562 3 0.4203 0.53305 0.000 0.000 0.772 0.024 0.088 0.116
#> GSM99564 4 0.3402 0.63784 0.000 0.072 0.000 0.820 0.104 0.004
#> GSM99572 2 0.1863 0.84229 0.000 0.896 0.000 0.104 0.000 0.000
#> GSM99576 1 0.4856 0.74801 0.748 0.032 0.012 0.012 0.056 0.140
#> GSM99578 2 0.5058 0.01929 0.000 0.500 0.000 0.424 0.000 0.076
#> GSM99580 3 0.1333 0.59285 0.000 0.000 0.944 0.000 0.008 0.048
#> GSM99582 4 0.6069 0.20692 0.036 0.000 0.132 0.592 0.012 0.228
#> GSM99584 4 0.4317 0.31824 0.000 0.004 0.000 0.572 0.408 0.016
#> GSM99586 1 0.3017 0.84837 0.860 0.000 0.000 0.016 0.060 0.064
#> GSM99588 2 0.0458 0.85774 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM99590 2 0.1141 0.86280 0.000 0.948 0.000 0.052 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) cell.type(p) k
#> MAD:NMF 83 6.56e-05 0.000342 2
#> MAD:NMF 84 2.31e-04 0.006091 3
#> MAD:NMF 83 2.94e-05 0.000999 4
#> MAD:NMF 71 1.56e-04 0.003625 5
#> MAD:NMF 55 2.97e-03 0.024170 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 21168 rows and 85 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 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 0.608 0.839 0.919 0.4421 0.525 0.525
#> 3 3 0.546 0.687 0.841 0.4631 0.742 0.535
#> 4 4 0.688 0.727 0.830 0.1416 0.851 0.588
#> 5 5 0.672 0.633 0.811 0.0597 0.976 0.904
#> 6 6 0.728 0.635 0.785 0.0425 0.945 0.760
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
#> GSM99496 1 0.000 0.9445 1.000 0.000
#> GSM99502 1 0.000 0.9445 1.000 0.000
#> GSM99504 1 0.000 0.9445 1.000 0.000
#> GSM99506 1 0.000 0.9445 1.000 0.000
#> GSM99566 1 0.000 0.9445 1.000 0.000
#> GSM99574 1 0.000 0.9445 1.000 0.000
#> GSM99592 1 0.662 0.7674 0.828 0.172
#> GSM99594 1 0.000 0.9445 1.000 0.000
#> GSM99468 1 0.000 0.9445 1.000 0.000
#> GSM99498 1 0.000 0.9445 1.000 0.000
#> GSM99500 1 0.000 0.9445 1.000 0.000
#> GSM99508 1 0.000 0.9445 1.000 0.000
#> GSM99568 1 0.000 0.9445 1.000 0.000
#> GSM99596 1 0.000 0.9445 1.000 0.000
#> GSM99600 2 0.204 0.8303 0.032 0.968
#> GSM99458 1 0.000 0.9445 1.000 0.000
#> GSM99460 1 0.000 0.9445 1.000 0.000
#> GSM99510 1 0.224 0.9201 0.964 0.036
#> GSM99512 1 0.184 0.9257 0.972 0.028
#> GSM99514 1 0.000 0.9445 1.000 0.000
#> GSM99516 1 0.000 0.9445 1.000 0.000
#> GSM99518 1 0.000 0.9445 1.000 0.000
#> GSM99520 1 0.000 0.9445 1.000 0.000
#> GSM99522 1 0.000 0.9445 1.000 0.000
#> GSM99570 1 0.000 0.9445 1.000 0.000
#> GSM99598 1 0.000 0.9445 1.000 0.000
#> GSM99432 2 0.932 0.6216 0.348 0.652
#> GSM99434 1 0.680 0.7553 0.820 0.180
#> GSM99436 2 0.808 0.7490 0.248 0.752
#> GSM99438 2 0.000 0.8340 0.000 1.000
#> GSM99440 1 0.000 0.9445 1.000 0.000
#> GSM99442 2 0.000 0.8340 0.000 1.000
#> GSM99444 2 0.000 0.8340 0.000 1.000
#> GSM99446 2 0.204 0.8303 0.032 0.968
#> GSM99448 2 0.871 0.7058 0.292 0.708
#> GSM99450 1 0.615 0.7936 0.848 0.152
#> GSM99452 1 0.000 0.9445 1.000 0.000
#> GSM99454 1 0.000 0.9445 1.000 0.000
#> GSM99456 1 0.000 0.9445 1.000 0.000
#> GSM99462 2 0.000 0.8340 0.000 1.000
#> GSM99464 1 0.000 0.9445 1.000 0.000
#> GSM99466 2 0.981 0.4697 0.420 0.580
#> GSM99470 1 0.443 0.8710 0.908 0.092
#> GSM99472 1 0.443 0.8710 0.908 0.092
#> GSM99474 1 0.000 0.9445 1.000 0.000
#> GSM99476 1 0.722 0.7247 0.800 0.200
#> GSM99478 2 0.808 0.7375 0.248 0.752
#> GSM99480 1 0.000 0.9445 1.000 0.000
#> GSM99482 1 0.000 0.9445 1.000 0.000
#> GSM99484 2 0.671 0.7856 0.176 0.824
#> GSM99486 2 0.808 0.7490 0.248 0.752
#> GSM99488 2 0.000 0.8340 0.000 1.000
#> GSM99490 2 0.000 0.8340 0.000 1.000
#> GSM99492 1 0.000 0.9445 1.000 0.000
#> GSM99494 2 0.000 0.8340 0.000 1.000
#> GSM99524 1 0.000 0.9445 1.000 0.000
#> GSM99526 1 0.781 0.6655 0.768 0.232
#> GSM99528 2 0.876 0.6784 0.296 0.704
#> GSM99530 1 0.000 0.9445 1.000 0.000
#> GSM99532 1 0.000 0.9445 1.000 0.000
#> GSM99534 2 0.000 0.8340 0.000 1.000
#> GSM99536 1 0.000 0.9445 1.000 0.000
#> GSM99538 2 0.871 0.7058 0.292 0.708
#> GSM99540 1 0.000 0.9445 1.000 0.000
#> GSM99542 2 0.000 0.8340 0.000 1.000
#> GSM99544 2 0.861 0.7144 0.284 0.716
#> GSM99546 1 0.850 0.5699 0.724 0.276
#> GSM99548 2 0.000 0.8340 0.000 1.000
#> GSM99550 1 0.278 0.9106 0.952 0.048
#> GSM99552 1 0.994 -0.0754 0.544 0.456
#> GSM99554 2 0.808 0.7490 0.248 0.752
#> GSM99556 2 0.000 0.8340 0.000 1.000
#> GSM99558 2 0.991 0.4020 0.444 0.556
#> GSM99560 2 0.929 0.6299 0.344 0.656
#> GSM99562 1 0.000 0.9445 1.000 0.000
#> GSM99564 2 0.808 0.7490 0.248 0.752
#> GSM99572 2 0.000 0.8340 0.000 1.000
#> GSM99576 1 0.430 0.8747 0.912 0.088
#> GSM99578 2 0.000 0.8340 0.000 1.000
#> GSM99580 1 0.430 0.8723 0.912 0.088
#> GSM99582 1 0.706 0.7376 0.808 0.192
#> GSM99584 2 0.949 0.5850 0.368 0.632
#> GSM99586 1 0.000 0.9445 1.000 0.000
#> GSM99588 2 0.000 0.8340 0.000 1.000
#> GSM99590 2 0.000 0.8340 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM99496 3 0.4605 0.7647 0.204 0.000 0.796
#> GSM99502 1 0.0000 0.9212 1.000 0.000 0.000
#> GSM99504 1 0.0000 0.9212 1.000 0.000 0.000
#> GSM99506 3 0.4605 0.7647 0.204 0.000 0.796
#> GSM99566 3 0.4555 0.7658 0.200 0.000 0.800
#> GSM99574 1 0.0000 0.9212 1.000 0.000 0.000
#> GSM99592 3 0.1163 0.7112 0.028 0.000 0.972
#> GSM99594 3 0.4555 0.7658 0.200 0.000 0.800
#> GSM99468 1 0.0000 0.9212 1.000 0.000 0.000
#> GSM99498 1 0.0000 0.9212 1.000 0.000 0.000
#> GSM99500 1 0.0000 0.9212 1.000 0.000 0.000
#> GSM99508 3 0.4605 0.7647 0.204 0.000 0.796
#> GSM99568 3 0.4605 0.7647 0.204 0.000 0.796
#> GSM99596 3 0.4605 0.7647 0.204 0.000 0.796
#> GSM99600 2 0.1289 0.7916 0.000 0.968 0.032
#> GSM99458 3 0.6305 0.2766 0.484 0.000 0.516
#> GSM99460 3 0.6305 0.2766 0.484 0.000 0.516
#> GSM99510 3 0.4062 0.7657 0.164 0.000 0.836
#> GSM99512 3 0.4178 0.7653 0.172 0.000 0.828
#> GSM99514 3 0.4605 0.7647 0.204 0.000 0.796
#> GSM99516 1 0.0000 0.9212 1.000 0.000 0.000
#> GSM99518 1 0.2878 0.8286 0.904 0.000 0.096
#> GSM99520 3 0.4555 0.7658 0.200 0.000 0.800
#> GSM99522 3 0.4605 0.7647 0.204 0.000 0.796
#> GSM99570 1 0.0000 0.9212 1.000 0.000 0.000
#> GSM99598 1 0.0000 0.9212 1.000 0.000 0.000
#> GSM99432 2 0.6309 0.3556 0.000 0.504 0.496
#> GSM99434 3 0.0892 0.7041 0.020 0.000 0.980
#> GSM99436 2 0.6095 0.5624 0.000 0.608 0.392
#> GSM99438 2 0.0237 0.7997 0.000 0.996 0.004
#> GSM99440 1 0.0000 0.9212 1.000 0.000 0.000
#> GSM99442 2 0.0237 0.7997 0.000 0.996 0.004
#> GSM99444 2 0.0237 0.7997 0.000 0.996 0.004
#> GSM99446 2 0.1411 0.7909 0.000 0.964 0.036
#> GSM99448 2 0.6295 0.4515 0.000 0.528 0.472
#> GSM99450 3 0.1860 0.7242 0.052 0.000 0.948
#> GSM99452 1 0.0000 0.9212 1.000 0.000 0.000
#> GSM99454 1 0.0000 0.9212 1.000 0.000 0.000
#> GSM99456 1 0.0000 0.9212 1.000 0.000 0.000
#> GSM99462 2 0.0237 0.7997 0.000 0.996 0.004
#> GSM99464 3 0.6286 0.3300 0.464 0.000 0.536
#> GSM99466 3 0.6062 -0.1165 0.000 0.384 0.616
#> GSM99470 1 0.6295 0.6584 0.728 0.036 0.236
#> GSM99472 1 0.6295 0.6584 0.728 0.036 0.236
#> GSM99474 3 0.4555 0.7658 0.200 0.000 0.800
#> GSM99476 3 0.1781 0.6936 0.020 0.020 0.960
#> GSM99478 2 0.6244 0.5024 0.000 0.560 0.440
#> GSM99480 1 0.0000 0.9212 1.000 0.000 0.000
#> GSM99482 1 0.0000 0.9212 1.000 0.000 0.000
#> GSM99484 2 0.5926 0.6111 0.000 0.644 0.356
#> GSM99486 2 0.6095 0.5624 0.000 0.608 0.392
#> GSM99488 2 0.0237 0.7997 0.000 0.996 0.004
#> GSM99490 2 0.0000 0.8000 0.000 1.000 0.000
#> GSM99492 1 0.0000 0.9212 1.000 0.000 0.000
#> GSM99494 2 0.0237 0.7997 0.000 0.996 0.004
#> GSM99524 1 0.0000 0.9212 1.000 0.000 0.000
#> GSM99526 3 0.3649 0.6708 0.036 0.068 0.896
#> GSM99528 2 0.6308 0.3927 0.000 0.508 0.492
#> GSM99530 1 0.6215 0.1236 0.572 0.000 0.428
#> GSM99532 3 0.4654 0.7613 0.208 0.000 0.792
#> GSM99534 2 0.1411 0.7921 0.000 0.964 0.036
#> GSM99536 1 0.0000 0.9212 1.000 0.000 0.000
#> GSM99538 2 0.6295 0.4515 0.000 0.528 0.472
#> GSM99540 1 0.3267 0.8023 0.884 0.000 0.116
#> GSM99542 2 0.1031 0.7932 0.000 0.976 0.024
#> GSM99544 2 0.6215 0.5037 0.000 0.572 0.428
#> GSM99546 3 0.4371 0.6213 0.032 0.108 0.860
#> GSM99548 2 0.0000 0.8000 0.000 1.000 0.000
#> GSM99550 1 0.5318 0.7091 0.780 0.016 0.204
#> GSM99552 3 0.5480 0.2804 0.004 0.264 0.732
#> GSM99554 2 0.6095 0.5624 0.000 0.608 0.392
#> GSM99556 2 0.0000 0.8000 0.000 1.000 0.000
#> GSM99558 3 0.6247 -0.0538 0.004 0.376 0.620
#> GSM99560 3 0.6291 -0.3550 0.000 0.468 0.532
#> GSM99562 3 0.4605 0.7647 0.204 0.000 0.796
#> GSM99564 2 0.6095 0.5624 0.000 0.608 0.392
#> GSM99572 2 0.0237 0.7997 0.000 0.996 0.004
#> GSM99576 1 0.6183 0.6632 0.732 0.032 0.236
#> GSM99578 2 0.0000 0.8000 0.000 1.000 0.000
#> GSM99580 3 0.3500 0.7598 0.116 0.004 0.880
#> GSM99582 3 0.2050 0.7002 0.028 0.020 0.952
#> GSM99584 3 0.6305 -0.3485 0.000 0.484 0.516
#> GSM99586 1 0.0000 0.9212 1.000 0.000 0.000
#> GSM99588 2 0.0237 0.7999 0.000 0.996 0.004
#> GSM99590 2 0.0237 0.7997 0.000 0.996 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM99496 3 0.0592 0.7887 0.016 0.000 0.984 0.000
#> GSM99502 1 0.0000 0.9199 1.000 0.000 0.000 0.000
#> GSM99504 1 0.0000 0.9199 1.000 0.000 0.000 0.000
#> GSM99506 3 0.0592 0.7887 0.016 0.000 0.984 0.000
#> GSM99566 3 0.0469 0.7884 0.012 0.000 0.988 0.000
#> GSM99574 1 0.0000 0.9199 1.000 0.000 0.000 0.000
#> GSM99592 3 0.4967 0.1992 0.000 0.000 0.548 0.452
#> GSM99594 3 0.1174 0.7892 0.012 0.000 0.968 0.020
#> GSM99468 1 0.0000 0.9199 1.000 0.000 0.000 0.000
#> GSM99498 1 0.0000 0.9199 1.000 0.000 0.000 0.000
#> GSM99500 1 0.0000 0.9199 1.000 0.000 0.000 0.000
#> GSM99508 3 0.1297 0.7903 0.016 0.000 0.964 0.020
#> GSM99568 3 0.1297 0.7903 0.016 0.000 0.964 0.020
#> GSM99596 3 0.1297 0.7903 0.016 0.000 0.964 0.020
#> GSM99600 2 0.2011 0.9180 0.000 0.920 0.000 0.080
#> GSM99458 3 0.5536 0.3443 0.384 0.000 0.592 0.024
#> GSM99460 3 0.5536 0.3443 0.384 0.000 0.592 0.024
#> GSM99510 3 0.2408 0.7444 0.000 0.000 0.896 0.104
#> GSM99512 3 0.1716 0.7715 0.000 0.000 0.936 0.064
#> GSM99514 3 0.0592 0.7887 0.016 0.000 0.984 0.000
#> GSM99516 1 0.0000 0.9199 1.000 0.000 0.000 0.000
#> GSM99518 1 0.2530 0.8472 0.896 0.000 0.100 0.004
#> GSM99520 3 0.1854 0.7813 0.012 0.000 0.940 0.048
#> GSM99522 3 0.0592 0.7887 0.016 0.000 0.984 0.000
#> GSM99570 1 0.2363 0.8960 0.920 0.000 0.024 0.056
#> GSM99598 1 0.0000 0.9199 1.000 0.000 0.000 0.000
#> GSM99432 4 0.5833 0.6950 0.000 0.212 0.096 0.692
#> GSM99434 3 0.5000 0.0779 0.000 0.000 0.504 0.496
#> GSM99436 4 0.4477 0.6248 0.000 0.312 0.000 0.688
#> GSM99438 2 0.0000 0.9396 0.000 1.000 0.000 0.000
#> GSM99440 1 0.0000 0.9199 1.000 0.000 0.000 0.000
#> GSM99442 2 0.0000 0.9396 0.000 1.000 0.000 0.000
#> GSM99444 2 0.0000 0.9396 0.000 1.000 0.000 0.000
#> GSM99446 2 0.3074 0.8413 0.000 0.848 0.000 0.152
#> GSM99448 4 0.4399 0.6892 0.000 0.224 0.016 0.760
#> GSM99450 3 0.5353 0.2044 0.012 0.000 0.556 0.432
#> GSM99452 1 0.2363 0.8960 0.920 0.000 0.024 0.056
#> GSM99454 1 0.0000 0.9199 1.000 0.000 0.000 0.000
#> GSM99456 1 0.1938 0.8982 0.936 0.000 0.012 0.052
#> GSM99462 2 0.0000 0.9396 0.000 1.000 0.000 0.000
#> GSM99464 3 0.5452 0.4020 0.360 0.000 0.616 0.024
#> GSM99466 4 0.4163 0.6985 0.000 0.096 0.076 0.828
#> GSM99470 1 0.6368 0.6517 0.648 0.004 0.104 0.244
#> GSM99472 1 0.6368 0.6517 0.648 0.004 0.104 0.244
#> GSM99474 3 0.1854 0.7813 0.012 0.000 0.940 0.048
#> GSM99476 4 0.4916 0.0815 0.000 0.000 0.424 0.576
#> GSM99478 4 0.5085 0.6394 0.000 0.260 0.032 0.708
#> GSM99480 1 0.0000 0.9199 1.000 0.000 0.000 0.000
#> GSM99482 1 0.2363 0.8960 0.920 0.000 0.024 0.056
#> GSM99484 4 0.5055 0.5266 0.000 0.368 0.008 0.624
#> GSM99486 4 0.4477 0.6248 0.000 0.312 0.000 0.688
#> GSM99488 2 0.0000 0.9396 0.000 1.000 0.000 0.000
#> GSM99490 2 0.2081 0.9202 0.000 0.916 0.000 0.084
#> GSM99492 1 0.0000 0.9199 1.000 0.000 0.000 0.000
#> GSM99494 2 0.0000 0.9396 0.000 1.000 0.000 0.000
#> GSM99524 1 0.2363 0.8960 0.920 0.000 0.024 0.056
#> GSM99526 4 0.4981 -0.0242 0.000 0.000 0.464 0.536
#> GSM99528 4 0.4994 0.6512 0.000 0.208 0.048 0.744
#> GSM99530 3 0.6262 0.2334 0.400 0.000 0.540 0.060
#> GSM99532 3 0.2089 0.7815 0.020 0.000 0.932 0.048
#> GSM99534 2 0.3377 0.8635 0.000 0.848 0.012 0.140
#> GSM99536 1 0.0000 0.9199 1.000 0.000 0.000 0.000
#> GSM99538 4 0.4399 0.6892 0.000 0.224 0.016 0.760
#> GSM99540 1 0.2831 0.8248 0.876 0.000 0.120 0.004
#> GSM99542 2 0.2741 0.9081 0.000 0.892 0.012 0.096
#> GSM99544 4 0.4776 0.6634 0.000 0.272 0.016 0.712
#> GSM99546 4 0.5070 0.1314 0.000 0.004 0.416 0.580
#> GSM99548 2 0.1302 0.9366 0.000 0.956 0.000 0.044
#> GSM99550 1 0.6031 0.6745 0.676 0.000 0.108 0.216
#> GSM99552 4 0.4584 0.4433 0.000 0.004 0.300 0.696
#> GSM99554 4 0.4477 0.6248 0.000 0.312 0.000 0.688
#> GSM99556 2 0.1302 0.9367 0.000 0.956 0.000 0.044
#> GSM99558 4 0.6501 0.5673 0.000 0.116 0.268 0.616
#> GSM99560 4 0.3625 0.6972 0.000 0.160 0.012 0.828
#> GSM99562 3 0.0592 0.7887 0.016 0.000 0.984 0.000
#> GSM99564 4 0.4477 0.6248 0.000 0.312 0.000 0.688
#> GSM99572 2 0.0000 0.9396 0.000 1.000 0.000 0.000
#> GSM99576 1 0.6192 0.6556 0.652 0.000 0.104 0.244
#> GSM99578 2 0.2081 0.9202 0.000 0.916 0.000 0.084
#> GSM99580 3 0.4770 0.5103 0.012 0.000 0.700 0.288
#> GSM99582 4 0.5105 0.0537 0.004 0.000 0.432 0.564
#> GSM99584 4 0.5820 0.6968 0.000 0.192 0.108 0.700
#> GSM99586 1 0.1938 0.8982 0.936 0.000 0.012 0.052
#> GSM99588 2 0.2011 0.9218 0.000 0.920 0.000 0.080
#> GSM99590 2 0.0000 0.9396 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM99496 3 0.0703 0.7865 0.000 0.000 0.976 0.000 0.024
#> GSM99502 1 0.0000 0.7781 1.000 0.000 0.000 0.000 0.000
#> GSM99504 1 0.0000 0.7781 1.000 0.000 0.000 0.000 0.000
#> GSM99506 3 0.0703 0.7865 0.000 0.000 0.976 0.000 0.024
#> GSM99566 3 0.0865 0.7872 0.000 0.000 0.972 0.004 0.024
#> GSM99574 1 0.0000 0.7781 1.000 0.000 0.000 0.000 0.000
#> GSM99592 3 0.5794 0.1734 0.000 0.000 0.520 0.384 0.096
#> GSM99594 3 0.0324 0.7883 0.000 0.000 0.992 0.004 0.004
#> GSM99468 1 0.0404 0.7703 0.988 0.000 0.000 0.000 0.012
#> GSM99498 1 0.0000 0.7781 1.000 0.000 0.000 0.000 0.000
#> GSM99500 1 0.0000 0.7781 1.000 0.000 0.000 0.000 0.000
#> GSM99508 3 0.0000 0.7888 0.000 0.000 1.000 0.000 0.000
#> GSM99568 3 0.0162 0.7886 0.000 0.000 0.996 0.000 0.004
#> GSM99596 3 0.0162 0.7885 0.000 0.000 0.996 0.000 0.004
#> GSM99600 2 0.2280 0.8801 0.000 0.880 0.000 0.120 0.000
#> GSM99458 3 0.6294 0.2614 0.160 0.000 0.532 0.004 0.304
#> GSM99460 3 0.6294 0.2614 0.160 0.000 0.532 0.004 0.304
#> GSM99510 3 0.3110 0.7272 0.000 0.000 0.860 0.080 0.060
#> GSM99512 3 0.2193 0.7628 0.000 0.000 0.912 0.028 0.060
#> GSM99514 3 0.0703 0.7865 0.000 0.000 0.976 0.000 0.024
#> GSM99516 1 0.0000 0.7781 1.000 0.000 0.000 0.000 0.000
#> GSM99518 1 0.3291 0.6139 0.848 0.000 0.088 0.000 0.064
#> GSM99520 3 0.1195 0.7814 0.000 0.000 0.960 0.028 0.012
#> GSM99522 3 0.1197 0.7820 0.000 0.000 0.952 0.000 0.048
#> GSM99570 1 0.4161 0.0930 0.608 0.000 0.000 0.000 0.392
#> GSM99598 1 0.0000 0.7781 1.000 0.000 0.000 0.000 0.000
#> GSM99432 4 0.4974 0.6967 0.000 0.116 0.092 0.756 0.036
#> GSM99434 3 0.5931 0.0161 0.000 0.000 0.460 0.436 0.104
#> GSM99436 4 0.3695 0.6569 0.000 0.164 0.000 0.800 0.036
#> GSM99438 2 0.0000 0.9048 0.000 1.000 0.000 0.000 0.000
#> GSM99440 1 0.0000 0.7781 1.000 0.000 0.000 0.000 0.000
#> GSM99442 2 0.0000 0.9048 0.000 1.000 0.000 0.000 0.000
#> GSM99444 2 0.0000 0.9048 0.000 1.000 0.000 0.000 0.000
#> GSM99446 2 0.3274 0.7925 0.000 0.780 0.000 0.220 0.000
#> GSM99448 4 0.2754 0.6991 0.000 0.080 0.000 0.880 0.040
#> GSM99450 3 0.5484 0.1690 0.000 0.000 0.540 0.392 0.068
#> GSM99452 1 0.4161 0.0930 0.608 0.000 0.000 0.000 0.392
#> GSM99454 1 0.0510 0.7674 0.984 0.000 0.000 0.000 0.016
#> GSM99456 1 0.4306 0.0239 0.508 0.000 0.000 0.000 0.492
#> GSM99462 2 0.0000 0.9048 0.000 1.000 0.000 0.000 0.000
#> GSM99464 3 0.6187 0.3188 0.156 0.000 0.556 0.004 0.284
#> GSM99466 4 0.3040 0.6727 0.000 0.012 0.068 0.876 0.044
#> GSM99470 5 0.5939 0.7937 0.320 0.000 0.032 0.060 0.588
#> GSM99472 5 0.5939 0.7937 0.320 0.000 0.032 0.060 0.588
#> GSM99474 3 0.1195 0.7814 0.000 0.000 0.960 0.028 0.012
#> GSM99476 4 0.5808 0.1210 0.000 0.000 0.392 0.512 0.096
#> GSM99478 4 0.3948 0.6555 0.000 0.128 0.008 0.808 0.056
#> GSM99480 1 0.0000 0.7781 1.000 0.000 0.000 0.000 0.000
#> GSM99482 1 0.4201 0.0365 0.592 0.000 0.000 0.000 0.408
#> GSM99484 4 0.4453 0.5787 0.000 0.228 0.000 0.724 0.048
#> GSM99486 4 0.3695 0.6569 0.000 0.164 0.000 0.800 0.036
#> GSM99488 2 0.0000 0.9048 0.000 1.000 0.000 0.000 0.000
#> GSM99490 2 0.3123 0.8584 0.000 0.828 0.000 0.160 0.012
#> GSM99492 1 0.0000 0.7781 1.000 0.000 0.000 0.000 0.000
#> GSM99494 2 0.0000 0.9048 0.000 1.000 0.000 0.000 0.000
#> GSM99524 1 0.4182 0.0657 0.600 0.000 0.000 0.000 0.400
#> GSM99526 4 0.5959 0.0252 0.000 0.000 0.420 0.472 0.108
#> GSM99528 4 0.4568 0.6401 0.000 0.116 0.024 0.780 0.080
#> GSM99530 3 0.6215 0.2730 0.152 0.000 0.500 0.000 0.348
#> GSM99532 3 0.1569 0.7802 0.008 0.000 0.948 0.032 0.012
#> GSM99534 2 0.4161 0.7991 0.000 0.752 0.000 0.208 0.040
#> GSM99536 1 0.0000 0.7781 1.000 0.000 0.000 0.000 0.000
#> GSM99538 4 0.2754 0.6991 0.000 0.080 0.000 0.880 0.040
#> GSM99540 1 0.3727 0.5782 0.824 0.000 0.104 0.004 0.068
#> GSM99542 2 0.3565 0.8589 0.000 0.816 0.000 0.144 0.040
#> GSM99544 4 0.3262 0.6828 0.000 0.124 0.000 0.840 0.036
#> GSM99546 4 0.5861 0.1706 0.000 0.000 0.376 0.520 0.104
#> GSM99548 2 0.1732 0.8981 0.000 0.920 0.000 0.080 0.000
#> GSM99550 5 0.5047 0.4457 0.216 0.000 0.036 0.036 0.712
#> GSM99552 4 0.5218 0.4514 0.000 0.000 0.296 0.632 0.072
#> GSM99554 4 0.3695 0.6569 0.000 0.164 0.000 0.800 0.036
#> GSM99556 2 0.1732 0.8982 0.000 0.920 0.000 0.080 0.000
#> GSM99558 4 0.6065 0.5530 0.000 0.068 0.276 0.612 0.044
#> GSM99560 4 0.3457 0.6823 0.000 0.048 0.016 0.852 0.084
#> GSM99562 3 0.1197 0.7820 0.000 0.000 0.952 0.000 0.048
#> GSM99564 4 0.3695 0.6569 0.000 0.164 0.000 0.800 0.036
#> GSM99572 2 0.0000 0.9048 0.000 1.000 0.000 0.000 0.000
#> GSM99576 5 0.5896 0.7888 0.324 0.000 0.032 0.056 0.588
#> GSM99578 2 0.3123 0.8584 0.000 0.828 0.000 0.160 0.012
#> GSM99580 3 0.4678 0.5180 0.000 0.000 0.712 0.224 0.064
#> GSM99582 4 0.5934 0.1084 0.000 0.000 0.396 0.496 0.108
#> GSM99584 4 0.5007 0.6905 0.000 0.100 0.104 0.756 0.040
#> GSM99586 1 0.4306 0.0239 0.508 0.000 0.000 0.000 0.492
#> GSM99588 2 0.2953 0.8671 0.000 0.844 0.000 0.144 0.012
#> GSM99590 2 0.0000 0.9048 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM99496 3 0.0146 0.7322 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM99502 1 0.0000 0.8186 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99504 1 0.0000 0.8186 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99506 3 0.0146 0.7322 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM99566 3 0.0632 0.7330 0.000 0.000 0.976 0.000 0.000 0.024
#> GSM99574 1 0.0000 0.8186 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99592 6 0.5052 0.6925 0.000 0.000 0.308 0.088 0.004 0.600
#> GSM99594 3 0.1387 0.7246 0.000 0.000 0.932 0.000 0.000 0.068
#> GSM99468 1 0.0458 0.8072 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM99498 1 0.0000 0.8186 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99500 1 0.0000 0.8186 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99508 3 0.1411 0.7296 0.000 0.000 0.936 0.000 0.004 0.060
#> GSM99568 3 0.1701 0.7297 0.000 0.000 0.920 0.000 0.008 0.072
#> GSM99596 3 0.1075 0.7294 0.000 0.000 0.952 0.000 0.000 0.048
#> GSM99600 2 0.3319 0.8181 0.000 0.800 0.000 0.164 0.000 0.036
#> GSM99458 3 0.6815 0.2196 0.064 0.000 0.452 0.000 0.252 0.232
#> GSM99460 3 0.6815 0.2196 0.064 0.000 0.452 0.000 0.252 0.232
#> GSM99510 3 0.4582 0.4953 0.000 0.000 0.672 0.024 0.032 0.272
#> GSM99512 3 0.3957 0.6076 0.000 0.000 0.752 0.012 0.036 0.200
#> GSM99514 3 0.0146 0.7322 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM99516 1 0.0000 0.8186 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99518 1 0.3410 0.6212 0.836 0.000 0.076 0.000 0.064 0.024
#> GSM99520 3 0.1918 0.7105 0.000 0.000 0.904 0.008 0.000 0.088
#> GSM99522 3 0.2309 0.6991 0.000 0.000 0.888 0.000 0.028 0.084
#> GSM99570 1 0.3810 0.1181 0.572 0.000 0.000 0.000 0.428 0.000
#> GSM99598 1 0.0000 0.8186 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99432 4 0.4264 0.5470 0.000 0.028 0.004 0.680 0.004 0.284
#> GSM99434 6 0.4825 0.7477 0.000 0.000 0.216 0.100 0.008 0.676
#> GSM99436 4 0.1141 0.7208 0.000 0.052 0.000 0.948 0.000 0.000
#> GSM99438 2 0.0547 0.8554 0.000 0.980 0.000 0.020 0.000 0.000
#> GSM99440 1 0.0000 0.8186 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99442 2 0.0000 0.8552 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99444 2 0.0000 0.8552 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99446 2 0.4165 0.6932 0.000 0.672 0.000 0.292 0.000 0.036
#> GSM99448 4 0.0937 0.7138 0.000 0.000 0.000 0.960 0.000 0.040
#> GSM99450 6 0.5042 0.6539 0.000 0.000 0.332 0.092 0.000 0.576
#> GSM99452 1 0.3810 0.1181 0.572 0.000 0.000 0.000 0.428 0.000
#> GSM99454 1 0.0632 0.8005 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM99456 5 0.5617 0.3528 0.388 0.000 0.000 0.000 0.464 0.148
#> GSM99462 2 0.0000 0.8552 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99464 3 0.6729 0.2575 0.060 0.000 0.468 0.000 0.232 0.240
#> GSM99466 4 0.4196 0.4604 0.000 0.000 0.028 0.640 0.000 0.332
#> GSM99470 5 0.6020 0.5336 0.288 0.000 0.016 0.012 0.548 0.136
#> GSM99472 5 0.6020 0.5336 0.288 0.000 0.016 0.012 0.548 0.136
#> GSM99474 3 0.1918 0.7105 0.000 0.000 0.904 0.008 0.000 0.088
#> GSM99476 6 0.5532 0.7214 0.000 0.000 0.212 0.204 0.004 0.580
#> GSM99478 4 0.5447 0.5461 0.000 0.048 0.008 0.596 0.036 0.312
#> GSM99480 1 0.0000 0.8186 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99482 1 0.3833 0.0688 0.556 0.000 0.000 0.000 0.444 0.000
#> GSM99484 4 0.5598 0.5509 0.000 0.116 0.000 0.612 0.032 0.240
#> GSM99486 4 0.1141 0.7208 0.000 0.052 0.000 0.948 0.000 0.000
#> GSM99488 2 0.0000 0.8552 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99490 2 0.4738 0.7731 0.000 0.712 0.000 0.188 0.032 0.068
#> GSM99492 1 0.0000 0.8186 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99494 2 0.0000 0.8552 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99524 1 0.3823 0.0905 0.564 0.000 0.000 0.000 0.436 0.000
#> GSM99526 6 0.5839 0.6888 0.000 0.000 0.208 0.200 0.020 0.572
#> GSM99528 4 0.5598 0.4763 0.000 0.048 0.008 0.544 0.036 0.364
#> GSM99530 3 0.6282 0.1610 0.080 0.000 0.436 0.000 0.408 0.076
#> GSM99532 3 0.2256 0.7109 0.004 0.000 0.892 0.008 0.004 0.092
#> GSM99534 2 0.5583 0.6986 0.000 0.624 0.000 0.236 0.048 0.092
#> GSM99536 1 0.0000 0.8186 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99538 4 0.0937 0.7138 0.000 0.000 0.000 0.960 0.000 0.040
#> GSM99540 1 0.3748 0.5808 0.812 0.000 0.092 0.000 0.068 0.028
#> GSM99542 2 0.5068 0.7718 0.000 0.700 0.000 0.160 0.048 0.092
#> GSM99544 4 0.1418 0.7203 0.000 0.032 0.000 0.944 0.000 0.024
#> GSM99546 6 0.5895 0.6418 0.000 0.000 0.176 0.248 0.020 0.556
#> GSM99548 2 0.1958 0.8466 0.000 0.896 0.000 0.100 0.000 0.004
#> GSM99550 5 0.5207 0.4200 0.092 0.000 0.020 0.000 0.636 0.252
#> GSM99552 6 0.6042 0.0628 0.000 0.000 0.208 0.388 0.004 0.400
#> GSM99554 4 0.1141 0.7208 0.000 0.052 0.000 0.948 0.000 0.000
#> GSM99556 2 0.2889 0.8415 0.000 0.848 0.000 0.108 0.000 0.044
#> GSM99558 4 0.5743 0.1160 0.000 0.000 0.204 0.504 0.000 0.292
#> GSM99560 4 0.3614 0.6113 0.000 0.000 0.000 0.752 0.028 0.220
#> GSM99562 3 0.2309 0.6991 0.000 0.000 0.888 0.000 0.028 0.084
#> GSM99564 4 0.1141 0.7208 0.000 0.052 0.000 0.948 0.000 0.000
#> GSM99572 2 0.0547 0.8554 0.000 0.980 0.000 0.020 0.000 0.000
#> GSM99576 5 0.5945 0.5291 0.292 0.000 0.016 0.008 0.548 0.136
#> GSM99578 2 0.4738 0.7731 0.000 0.712 0.000 0.188 0.032 0.068
#> GSM99580 3 0.4567 0.1068 0.000 0.000 0.616 0.052 0.000 0.332
#> GSM99582 6 0.6110 0.7257 0.000 0.000 0.220 0.200 0.032 0.548
#> GSM99584 4 0.4467 0.4816 0.000 0.028 0.004 0.632 0.004 0.332
#> GSM99586 5 0.5617 0.3528 0.388 0.000 0.000 0.000 0.464 0.148
#> GSM99588 2 0.4624 0.7830 0.000 0.724 0.000 0.180 0.032 0.064
#> GSM99590 2 0.0547 0.8554 0.000 0.980 0.000 0.020 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) cell.type(p) k
#> ATC:hclust 82 7.90e-05 0.000432 2
#> ATC:hclust 72 4.87e-04 0.013337 3
#> ATC:hclust 73 6.08e-06 0.001043 4
#> ATC:hclust 66 1.86e-06 0.000924 5
#> ATC:hclust 67 6.41e-06 0.004149 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 21168 rows and 85 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 0.973 0.989 0.4819 0.514 0.514
#> 3 3 0.969 0.937 0.975 0.3949 0.741 0.530
#> 4 4 0.799 0.786 0.893 0.1114 0.855 0.596
#> 5 5 0.757 0.676 0.837 0.0586 0.931 0.741
#> 6 6 0.739 0.644 0.774 0.0406 0.937 0.735
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
#> GSM99496 1 0.000 0.999 1.000 0.000
#> GSM99502 1 0.000 0.999 1.000 0.000
#> GSM99504 1 0.000 0.999 1.000 0.000
#> GSM99506 1 0.000 0.999 1.000 0.000
#> GSM99566 1 0.000 0.999 1.000 0.000
#> GSM99574 1 0.000 0.999 1.000 0.000
#> GSM99592 1 0.000 0.999 1.000 0.000
#> GSM99594 1 0.000 0.999 1.000 0.000
#> GSM99468 1 0.000 0.999 1.000 0.000
#> GSM99498 1 0.000 0.999 1.000 0.000
#> GSM99500 1 0.000 0.999 1.000 0.000
#> GSM99508 1 0.000 0.999 1.000 0.000
#> GSM99568 1 0.000 0.999 1.000 0.000
#> GSM99596 1 0.000 0.999 1.000 0.000
#> GSM99600 2 0.000 0.973 0.000 1.000
#> GSM99458 1 0.000 0.999 1.000 0.000
#> GSM99460 1 0.000 0.999 1.000 0.000
#> GSM99510 1 0.000 0.999 1.000 0.000
#> GSM99512 1 0.000 0.999 1.000 0.000
#> GSM99514 1 0.000 0.999 1.000 0.000
#> GSM99516 1 0.000 0.999 1.000 0.000
#> GSM99518 1 0.000 0.999 1.000 0.000
#> GSM99520 1 0.000 0.999 1.000 0.000
#> GSM99522 1 0.000 0.999 1.000 0.000
#> GSM99570 1 0.000 0.999 1.000 0.000
#> GSM99598 1 0.000 0.999 1.000 0.000
#> GSM99432 2 0.000 0.973 0.000 1.000
#> GSM99434 1 0.000 0.999 1.000 0.000
#> GSM99436 2 0.000 0.973 0.000 1.000
#> GSM99438 2 0.000 0.973 0.000 1.000
#> GSM99440 1 0.000 0.999 1.000 0.000
#> GSM99442 2 0.000 0.973 0.000 1.000
#> GSM99444 2 0.000 0.973 0.000 1.000
#> GSM99446 2 0.000 0.973 0.000 1.000
#> GSM99448 2 0.000 0.973 0.000 1.000
#> GSM99450 1 0.000 0.999 1.000 0.000
#> GSM99452 1 0.000 0.999 1.000 0.000
#> GSM99454 1 0.000 0.999 1.000 0.000
#> GSM99456 1 0.000 0.999 1.000 0.000
#> GSM99462 2 0.000 0.973 0.000 1.000
#> GSM99464 1 0.000 0.999 1.000 0.000
#> GSM99466 2 0.000 0.973 0.000 1.000
#> GSM99470 1 0.000 0.999 1.000 0.000
#> GSM99472 1 0.000 0.999 1.000 0.000
#> GSM99474 1 0.000 0.999 1.000 0.000
#> GSM99476 2 0.821 0.663 0.256 0.744
#> GSM99478 2 0.000 0.973 0.000 1.000
#> GSM99480 1 0.000 0.999 1.000 0.000
#> GSM99482 1 0.000 0.999 1.000 0.000
#> GSM99484 2 0.000 0.973 0.000 1.000
#> GSM99486 2 0.000 0.973 0.000 1.000
#> GSM99488 2 0.000 0.973 0.000 1.000
#> GSM99490 2 0.000 0.973 0.000 1.000
#> GSM99492 1 0.000 0.999 1.000 0.000
#> GSM99494 2 0.000 0.973 0.000 1.000
#> GSM99524 1 0.000 0.999 1.000 0.000
#> GSM99526 1 0.000 0.999 1.000 0.000
#> GSM99528 2 0.991 0.223 0.444 0.556
#> GSM99530 1 0.000 0.999 1.000 0.000
#> GSM99532 1 0.000 0.999 1.000 0.000
#> GSM99534 2 0.000 0.973 0.000 1.000
#> GSM99536 1 0.000 0.999 1.000 0.000
#> GSM99538 2 0.000 0.973 0.000 1.000
#> GSM99540 1 0.000 0.999 1.000 0.000
#> GSM99542 2 0.000 0.973 0.000 1.000
#> GSM99544 2 0.000 0.973 0.000 1.000
#> GSM99546 2 0.689 0.773 0.184 0.816
#> GSM99548 2 0.000 0.973 0.000 1.000
#> GSM99550 1 0.000 0.999 1.000 0.000
#> GSM99552 1 0.343 0.929 0.936 0.064
#> GSM99554 2 0.000 0.973 0.000 1.000
#> GSM99556 2 0.000 0.973 0.000 1.000
#> GSM99558 2 0.000 0.973 0.000 1.000
#> GSM99560 2 0.000 0.973 0.000 1.000
#> GSM99562 1 0.000 0.999 1.000 0.000
#> GSM99564 2 0.000 0.973 0.000 1.000
#> GSM99572 2 0.000 0.973 0.000 1.000
#> GSM99576 1 0.000 0.999 1.000 0.000
#> GSM99578 2 0.000 0.973 0.000 1.000
#> GSM99580 1 0.000 0.999 1.000 0.000
#> GSM99582 1 0.000 0.999 1.000 0.000
#> GSM99584 2 0.000 0.973 0.000 1.000
#> GSM99586 1 0.000 0.999 1.000 0.000
#> GSM99588 2 0.000 0.973 0.000 1.000
#> GSM99590 2 0.000 0.973 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM99496 3 0.0000 0.945 0.000 0.000 1.000
#> GSM99502 1 0.0000 0.975 1.000 0.000 0.000
#> GSM99504 1 0.0000 0.975 1.000 0.000 0.000
#> GSM99506 3 0.0000 0.945 0.000 0.000 1.000
#> GSM99566 3 0.0000 0.945 0.000 0.000 1.000
#> GSM99574 1 0.0000 0.975 1.000 0.000 0.000
#> GSM99592 3 0.0000 0.945 0.000 0.000 1.000
#> GSM99594 3 0.0000 0.945 0.000 0.000 1.000
#> GSM99468 1 0.0000 0.975 1.000 0.000 0.000
#> GSM99498 1 0.0000 0.975 1.000 0.000 0.000
#> GSM99500 1 0.0000 0.975 1.000 0.000 0.000
#> GSM99508 3 0.0000 0.945 0.000 0.000 1.000
#> GSM99568 3 0.0000 0.945 0.000 0.000 1.000
#> GSM99596 3 0.0000 0.945 0.000 0.000 1.000
#> GSM99600 2 0.0000 1.000 0.000 1.000 0.000
#> GSM99458 1 0.0000 0.975 1.000 0.000 0.000
#> GSM99460 1 0.0000 0.975 1.000 0.000 0.000
#> GSM99510 3 0.0000 0.945 0.000 0.000 1.000
#> GSM99512 3 0.0000 0.945 0.000 0.000 1.000
#> GSM99514 3 0.0000 0.945 0.000 0.000 1.000
#> GSM99516 1 0.0000 0.975 1.000 0.000 0.000
#> GSM99518 1 0.0000 0.975 1.000 0.000 0.000
#> GSM99520 3 0.0000 0.945 0.000 0.000 1.000
#> GSM99522 3 0.0000 0.945 0.000 0.000 1.000
#> GSM99570 1 0.0000 0.975 1.000 0.000 0.000
#> GSM99598 1 0.0000 0.975 1.000 0.000 0.000
#> GSM99432 2 0.0000 1.000 0.000 1.000 0.000
#> GSM99434 3 0.0000 0.945 0.000 0.000 1.000
#> GSM99436 2 0.0000 1.000 0.000 1.000 0.000
#> GSM99438 2 0.0000 1.000 0.000 1.000 0.000
#> GSM99440 1 0.0000 0.975 1.000 0.000 0.000
#> GSM99442 2 0.0000 1.000 0.000 1.000 0.000
#> GSM99444 2 0.0000 1.000 0.000 1.000 0.000
#> GSM99446 2 0.0000 1.000 0.000 1.000 0.000
#> GSM99448 3 0.5859 0.470 0.000 0.344 0.656
#> GSM99450 3 0.0000 0.945 0.000 0.000 1.000
#> GSM99452 1 0.0000 0.975 1.000 0.000 0.000
#> GSM99454 1 0.0000 0.975 1.000 0.000 0.000
#> GSM99456 1 0.0000 0.975 1.000 0.000 0.000
#> GSM99462 2 0.0000 1.000 0.000 1.000 0.000
#> GSM99464 3 0.0000 0.945 0.000 0.000 1.000
#> GSM99466 2 0.0424 0.991 0.000 0.992 0.008
#> GSM99470 3 0.6975 0.382 0.356 0.028 0.616
#> GSM99472 1 0.5397 0.611 0.720 0.000 0.280
#> GSM99474 3 0.0000 0.945 0.000 0.000 1.000
#> GSM99476 3 0.0000 0.945 0.000 0.000 1.000
#> GSM99478 2 0.0000 1.000 0.000 1.000 0.000
#> GSM99480 1 0.0000 0.975 1.000 0.000 0.000
#> GSM99482 1 0.0000 0.975 1.000 0.000 0.000
#> GSM99484 2 0.0000 1.000 0.000 1.000 0.000
#> GSM99486 2 0.0000 1.000 0.000 1.000 0.000
#> GSM99488 2 0.0000 1.000 0.000 1.000 0.000
#> GSM99490 2 0.0000 1.000 0.000 1.000 0.000
#> GSM99492 1 0.0000 0.975 1.000 0.000 0.000
#> GSM99494 2 0.0000 1.000 0.000 1.000 0.000
#> GSM99524 1 0.0000 0.975 1.000 0.000 0.000
#> GSM99526 3 0.0000 0.945 0.000 0.000 1.000
#> GSM99528 3 0.0000 0.945 0.000 0.000 1.000
#> GSM99530 3 0.0000 0.945 0.000 0.000 1.000
#> GSM99532 3 0.0000 0.945 0.000 0.000 1.000
#> GSM99534 2 0.0000 1.000 0.000 1.000 0.000
#> GSM99536 1 0.0000 0.975 1.000 0.000 0.000
#> GSM99538 2 0.0000 1.000 0.000 1.000 0.000
#> GSM99540 1 0.0000 0.975 1.000 0.000 0.000
#> GSM99542 2 0.0000 1.000 0.000 1.000 0.000
#> GSM99544 2 0.0000 1.000 0.000 1.000 0.000
#> GSM99546 3 0.0000 0.945 0.000 0.000 1.000
#> GSM99548 2 0.0000 1.000 0.000 1.000 0.000
#> GSM99550 3 0.5948 0.408 0.360 0.000 0.640
#> GSM99552 3 0.0000 0.945 0.000 0.000 1.000
#> GSM99554 2 0.0000 1.000 0.000 1.000 0.000
#> GSM99556 2 0.0000 1.000 0.000 1.000 0.000
#> GSM99558 3 0.6235 0.235 0.000 0.436 0.564
#> GSM99560 2 0.0000 1.000 0.000 1.000 0.000
#> GSM99562 3 0.0000 0.945 0.000 0.000 1.000
#> GSM99564 2 0.0000 1.000 0.000 1.000 0.000
#> GSM99572 2 0.0000 1.000 0.000 1.000 0.000
#> GSM99576 1 0.5397 0.611 0.720 0.000 0.280
#> GSM99578 2 0.0000 1.000 0.000 1.000 0.000
#> GSM99580 3 0.0000 0.945 0.000 0.000 1.000
#> GSM99582 3 0.0000 0.945 0.000 0.000 1.000
#> GSM99584 2 0.0000 1.000 0.000 1.000 0.000
#> GSM99586 1 0.0000 0.975 1.000 0.000 0.000
#> GSM99588 2 0.0000 1.000 0.000 1.000 0.000
#> GSM99590 2 0.0000 1.000 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM99496 3 0.0000 0.97724 0.000 0.000 1.000 0.000
#> GSM99502 1 0.0188 0.95238 0.996 0.000 0.000 0.004
#> GSM99504 1 0.0000 0.95262 1.000 0.000 0.000 0.000
#> GSM99506 3 0.0000 0.97724 0.000 0.000 1.000 0.000
#> GSM99566 3 0.0000 0.97724 0.000 0.000 1.000 0.000
#> GSM99574 1 0.0188 0.95238 0.996 0.000 0.000 0.004
#> GSM99592 3 0.0817 0.96813 0.000 0.000 0.976 0.024
#> GSM99594 3 0.0000 0.97724 0.000 0.000 1.000 0.000
#> GSM99468 1 0.0336 0.95161 0.992 0.000 0.000 0.008
#> GSM99498 1 0.0000 0.95262 1.000 0.000 0.000 0.000
#> GSM99500 1 0.0000 0.95262 1.000 0.000 0.000 0.000
#> GSM99508 3 0.0000 0.97724 0.000 0.000 1.000 0.000
#> GSM99568 3 0.0000 0.97724 0.000 0.000 1.000 0.000
#> GSM99596 3 0.0000 0.97724 0.000 0.000 1.000 0.000
#> GSM99600 2 0.2921 0.75521 0.000 0.860 0.000 0.140
#> GSM99458 1 0.1940 0.91437 0.924 0.000 0.000 0.076
#> GSM99460 1 0.1940 0.91437 0.924 0.000 0.000 0.076
#> GSM99510 3 0.1022 0.96451 0.000 0.000 0.968 0.032
#> GSM99512 3 0.1022 0.96451 0.000 0.000 0.968 0.032
#> GSM99514 3 0.0000 0.97724 0.000 0.000 1.000 0.000
#> GSM99516 1 0.0000 0.95262 1.000 0.000 0.000 0.000
#> GSM99518 1 0.0000 0.95262 1.000 0.000 0.000 0.000
#> GSM99520 3 0.0000 0.97724 0.000 0.000 1.000 0.000
#> GSM99522 3 0.0336 0.97499 0.000 0.000 0.992 0.008
#> GSM99570 1 0.0336 0.95223 0.992 0.000 0.000 0.008
#> GSM99598 1 0.0188 0.95238 0.996 0.000 0.000 0.004
#> GSM99432 4 0.3172 0.68427 0.000 0.160 0.000 0.840
#> GSM99434 3 0.3400 0.77610 0.000 0.000 0.820 0.180
#> GSM99436 2 0.4898 0.36537 0.000 0.584 0.000 0.416
#> GSM99438 2 0.0000 0.82781 0.000 1.000 0.000 0.000
#> GSM99440 1 0.0336 0.95223 0.992 0.000 0.000 0.008
#> GSM99442 2 0.0000 0.82781 0.000 1.000 0.000 0.000
#> GSM99444 2 0.0000 0.82781 0.000 1.000 0.000 0.000
#> GSM99446 2 0.4843 0.42588 0.000 0.604 0.000 0.396
#> GSM99448 4 0.3307 0.70041 0.000 0.028 0.104 0.868
#> GSM99450 3 0.0921 0.96592 0.000 0.000 0.972 0.028
#> GSM99452 1 0.0469 0.95122 0.988 0.000 0.000 0.012
#> GSM99454 1 0.0000 0.95262 1.000 0.000 0.000 0.000
#> GSM99456 1 0.1792 0.93228 0.932 0.000 0.000 0.068
#> GSM99462 2 0.0000 0.82781 0.000 1.000 0.000 0.000
#> GSM99464 3 0.2216 0.91820 0.000 0.000 0.908 0.092
#> GSM99466 4 0.2760 0.69471 0.000 0.128 0.000 0.872
#> GSM99470 4 0.2814 0.67772 0.052 0.008 0.032 0.908
#> GSM99472 1 0.5678 0.25078 0.524 0.000 0.024 0.452
#> GSM99474 3 0.0000 0.97724 0.000 0.000 1.000 0.000
#> GSM99476 4 0.4761 0.38884 0.000 0.000 0.372 0.628
#> GSM99478 4 0.3172 0.68427 0.000 0.160 0.000 0.840
#> GSM99480 1 0.1302 0.93778 0.956 0.000 0.000 0.044
#> GSM99482 1 0.0921 0.94619 0.972 0.000 0.000 0.028
#> GSM99484 4 0.3172 0.68427 0.000 0.160 0.000 0.840
#> GSM99486 4 0.4843 0.22424 0.000 0.396 0.000 0.604
#> GSM99488 2 0.0000 0.82781 0.000 1.000 0.000 0.000
#> GSM99490 2 0.4477 0.60527 0.000 0.688 0.000 0.312
#> GSM99492 1 0.1302 0.93778 0.956 0.000 0.000 0.044
#> GSM99494 2 0.0000 0.82781 0.000 1.000 0.000 0.000
#> GSM99524 1 0.0592 0.95033 0.984 0.000 0.000 0.016
#> GSM99526 4 0.4888 0.25582 0.000 0.000 0.412 0.588
#> GSM99528 4 0.2530 0.69434 0.000 0.004 0.100 0.896
#> GSM99530 3 0.1211 0.95051 0.000 0.000 0.960 0.040
#> GSM99532 3 0.0469 0.97115 0.000 0.000 0.988 0.012
#> GSM99534 4 0.4304 0.52065 0.000 0.284 0.000 0.716
#> GSM99536 1 0.0188 0.95238 0.996 0.000 0.000 0.004
#> GSM99538 4 0.3172 0.68427 0.000 0.160 0.000 0.840
#> GSM99540 1 0.0592 0.94889 0.984 0.000 0.000 0.016
#> GSM99542 2 0.1716 0.80118 0.000 0.936 0.000 0.064
#> GSM99544 4 0.4981 -0.00304 0.000 0.464 0.000 0.536
#> GSM99546 4 0.2216 0.69339 0.000 0.000 0.092 0.908
#> GSM99548 2 0.0000 0.82781 0.000 1.000 0.000 0.000
#> GSM99550 4 0.6655 0.44691 0.192 0.000 0.184 0.624
#> GSM99552 4 0.4072 0.63716 0.000 0.000 0.252 0.748
#> GSM99554 2 0.4431 0.60658 0.000 0.696 0.000 0.304
#> GSM99556 2 0.0000 0.82781 0.000 1.000 0.000 0.000
#> GSM99558 4 0.3899 0.70306 0.000 0.052 0.108 0.840
#> GSM99560 4 0.2704 0.69535 0.000 0.124 0.000 0.876
#> GSM99562 3 0.0336 0.97499 0.000 0.000 0.992 0.008
#> GSM99564 4 0.5000 -0.14255 0.000 0.500 0.000 0.500
#> GSM99572 2 0.0000 0.82781 0.000 1.000 0.000 0.000
#> GSM99576 1 0.5105 0.63463 0.696 0.000 0.028 0.276
#> GSM99578 2 0.4661 0.54630 0.000 0.652 0.000 0.348
#> GSM99580 3 0.0000 0.97724 0.000 0.000 1.000 0.000
#> GSM99582 4 0.4730 0.43241 0.000 0.000 0.364 0.636
#> GSM99584 4 0.3172 0.68427 0.000 0.160 0.000 0.840
#> GSM99586 1 0.1716 0.93378 0.936 0.000 0.000 0.064
#> GSM99588 2 0.4477 0.60527 0.000 0.688 0.000 0.312
#> GSM99590 2 0.0000 0.82781 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM99496 3 0.0162 0.9111 0.000 0.000 0.996 0.000 0.004
#> GSM99502 1 0.0451 0.8863 0.988 0.000 0.000 0.008 0.004
#> GSM99504 1 0.0290 0.8872 0.992 0.000 0.000 0.000 0.008
#> GSM99506 3 0.0162 0.9111 0.000 0.000 0.996 0.000 0.004
#> GSM99566 3 0.0162 0.9111 0.000 0.000 0.996 0.000 0.004
#> GSM99574 1 0.0451 0.8863 0.988 0.000 0.000 0.008 0.004
#> GSM99592 3 0.2677 0.8516 0.000 0.000 0.872 0.016 0.112
#> GSM99594 3 0.0162 0.9111 0.000 0.000 0.996 0.000 0.004
#> GSM99468 1 0.1197 0.8803 0.952 0.000 0.000 0.000 0.048
#> GSM99498 1 0.0290 0.8872 0.992 0.000 0.000 0.000 0.008
#> GSM99500 1 0.0290 0.8872 0.992 0.000 0.000 0.000 0.008
#> GSM99508 3 0.0000 0.9109 0.000 0.000 1.000 0.000 0.000
#> GSM99568 3 0.0000 0.9109 0.000 0.000 1.000 0.000 0.000
#> GSM99596 3 0.0162 0.9111 0.000 0.000 0.996 0.000 0.004
#> GSM99600 2 0.4147 0.4292 0.000 0.676 0.000 0.316 0.008
#> GSM99458 1 0.4225 0.5719 0.632 0.000 0.000 0.004 0.364
#> GSM99460 1 0.4066 0.6368 0.672 0.000 0.000 0.004 0.324
#> GSM99510 3 0.4489 0.7489 0.000 0.000 0.740 0.068 0.192
#> GSM99512 3 0.4252 0.7721 0.000 0.000 0.764 0.064 0.172
#> GSM99514 3 0.0162 0.9111 0.000 0.000 0.996 0.000 0.004
#> GSM99516 1 0.0000 0.8869 1.000 0.000 0.000 0.000 0.000
#> GSM99518 1 0.0290 0.8872 0.992 0.000 0.000 0.000 0.008
#> GSM99520 3 0.0162 0.9111 0.000 0.000 0.996 0.000 0.004
#> GSM99522 3 0.0000 0.9109 0.000 0.000 1.000 0.000 0.000
#> GSM99570 1 0.2012 0.8767 0.920 0.000 0.000 0.020 0.060
#> GSM99598 1 0.0451 0.8863 0.988 0.000 0.000 0.008 0.004
#> GSM99432 4 0.1628 0.6274 0.000 0.056 0.000 0.936 0.008
#> GSM99434 3 0.5185 0.6591 0.000 0.000 0.672 0.100 0.228
#> GSM99436 4 0.4235 0.4492 0.000 0.336 0.000 0.656 0.008
#> GSM99438 2 0.0000 0.8476 0.000 1.000 0.000 0.000 0.000
#> GSM99440 1 0.1549 0.8782 0.944 0.000 0.000 0.016 0.040
#> GSM99442 2 0.0162 0.8464 0.000 0.996 0.000 0.004 0.000
#> GSM99444 2 0.0000 0.8476 0.000 1.000 0.000 0.000 0.000
#> GSM99446 4 0.4046 0.4901 0.000 0.296 0.000 0.696 0.008
#> GSM99448 4 0.2782 0.5418 0.000 0.000 0.048 0.880 0.072
#> GSM99450 3 0.3152 0.8315 0.000 0.000 0.840 0.024 0.136
#> GSM99452 1 0.2953 0.8373 0.844 0.000 0.000 0.012 0.144
#> GSM99454 1 0.0000 0.8869 1.000 0.000 0.000 0.000 0.000
#> GSM99456 1 0.4250 0.7603 0.720 0.000 0.000 0.028 0.252
#> GSM99462 2 0.0000 0.8476 0.000 1.000 0.000 0.000 0.000
#> GSM99464 3 0.4442 0.6846 0.000 0.000 0.688 0.028 0.284
#> GSM99466 4 0.3958 0.5488 0.000 0.040 0.000 0.776 0.184
#> GSM99470 5 0.4403 0.3791 0.008 0.000 0.004 0.340 0.648
#> GSM99472 5 0.4001 0.5537 0.208 0.000 0.004 0.024 0.764
#> GSM99474 3 0.1410 0.8863 0.000 0.000 0.940 0.000 0.060
#> GSM99476 4 0.6538 -0.0421 0.000 0.000 0.272 0.480 0.248
#> GSM99478 4 0.4096 0.5590 0.000 0.052 0.000 0.772 0.176
#> GSM99480 1 0.2850 0.8466 0.872 0.000 0.000 0.036 0.092
#> GSM99482 1 0.4371 0.5904 0.644 0.000 0.000 0.012 0.344
#> GSM99484 4 0.4190 0.5684 0.000 0.060 0.000 0.768 0.172
#> GSM99486 4 0.2561 0.6302 0.000 0.144 0.000 0.856 0.000
#> GSM99488 2 0.0162 0.8468 0.000 0.996 0.000 0.000 0.004
#> GSM99490 2 0.5238 -0.0244 0.000 0.484 0.000 0.472 0.044
#> GSM99492 1 0.2850 0.8466 0.872 0.000 0.000 0.036 0.092
#> GSM99494 2 0.0162 0.8468 0.000 0.996 0.000 0.000 0.004
#> GSM99524 1 0.3333 0.7673 0.788 0.000 0.000 0.004 0.208
#> GSM99526 4 0.6685 -0.1576 0.000 0.000 0.244 0.416 0.340
#> GSM99528 5 0.4748 0.0577 0.000 0.000 0.016 0.492 0.492
#> GSM99530 3 0.2719 0.8040 0.000 0.000 0.852 0.004 0.144
#> GSM99532 3 0.0955 0.8995 0.000 0.000 0.968 0.004 0.028
#> GSM99534 4 0.6053 0.4507 0.000 0.196 0.000 0.576 0.228
#> GSM99536 1 0.0451 0.8863 0.988 0.000 0.000 0.008 0.004
#> GSM99538 4 0.1872 0.6269 0.000 0.052 0.000 0.928 0.020
#> GSM99540 1 0.2389 0.8402 0.880 0.000 0.000 0.004 0.116
#> GSM99542 2 0.3732 0.6612 0.000 0.792 0.000 0.176 0.032
#> GSM99544 4 0.2813 0.6231 0.000 0.168 0.000 0.832 0.000
#> GSM99546 4 0.4846 0.0440 0.000 0.000 0.028 0.588 0.384
#> GSM99548 2 0.0404 0.8450 0.000 0.988 0.000 0.000 0.012
#> GSM99550 5 0.2152 0.5807 0.032 0.000 0.004 0.044 0.920
#> GSM99552 4 0.6536 -0.2578 0.000 0.000 0.196 0.408 0.396
#> GSM99554 4 0.4517 0.2020 0.000 0.436 0.000 0.556 0.008
#> GSM99556 2 0.0404 0.8450 0.000 0.988 0.000 0.000 0.012
#> GSM99558 4 0.2696 0.5978 0.000 0.012 0.040 0.896 0.052
#> GSM99560 4 0.3565 0.5799 0.000 0.040 0.000 0.816 0.144
#> GSM99562 3 0.0000 0.9109 0.000 0.000 1.000 0.000 0.000
#> GSM99564 4 0.3752 0.5299 0.000 0.292 0.000 0.708 0.000
#> GSM99572 2 0.0000 0.8476 0.000 1.000 0.000 0.000 0.000
#> GSM99576 5 0.3643 0.5197 0.212 0.000 0.004 0.008 0.776
#> GSM99578 4 0.6144 0.2793 0.000 0.344 0.000 0.512 0.144
#> GSM99580 3 0.1697 0.8821 0.000 0.000 0.932 0.008 0.060
#> GSM99582 5 0.6131 0.3369 0.000 0.000 0.208 0.228 0.564
#> GSM99584 4 0.1341 0.6287 0.000 0.056 0.000 0.944 0.000
#> GSM99586 1 0.3897 0.7987 0.768 0.000 0.000 0.028 0.204
#> GSM99588 2 0.5115 -0.0271 0.000 0.484 0.000 0.480 0.036
#> GSM99590 2 0.0000 0.8476 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM99496 3 0.0000 0.837 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99502 1 0.0858 0.811 0.968 0.000 0.000 0.000 0.004 0.028
#> GSM99504 1 0.1367 0.809 0.944 0.000 0.000 0.000 0.012 0.044
#> GSM99506 3 0.0000 0.837 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99566 3 0.0000 0.837 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99574 1 0.0858 0.811 0.968 0.000 0.000 0.000 0.004 0.028
#> GSM99592 3 0.3728 0.217 0.000 0.000 0.652 0.000 0.004 0.344
#> GSM99594 3 0.0000 0.837 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99468 1 0.2724 0.793 0.864 0.000 0.000 0.000 0.084 0.052
#> GSM99498 1 0.1367 0.809 0.944 0.000 0.000 0.000 0.012 0.044
#> GSM99500 1 0.1367 0.809 0.944 0.000 0.000 0.000 0.012 0.044
#> GSM99508 3 0.0000 0.837 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99568 3 0.0146 0.836 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM99596 3 0.0000 0.837 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99600 4 0.4461 0.311 0.000 0.404 0.000 0.564 0.000 0.032
#> GSM99458 1 0.5896 0.335 0.444 0.000 0.000 0.000 0.344 0.212
#> GSM99460 1 0.5854 0.383 0.468 0.000 0.000 0.000 0.320 0.212
#> GSM99510 6 0.4408 0.225 0.000 0.000 0.468 0.008 0.012 0.512
#> GSM99512 3 0.4413 -0.308 0.000 0.000 0.496 0.008 0.012 0.484
#> GSM99514 3 0.0000 0.837 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99516 1 0.0603 0.812 0.980 0.000 0.000 0.000 0.004 0.016
#> GSM99518 1 0.1434 0.808 0.940 0.000 0.000 0.000 0.012 0.048
#> GSM99520 3 0.0291 0.834 0.000 0.000 0.992 0.000 0.004 0.004
#> GSM99522 3 0.0692 0.827 0.000 0.000 0.976 0.000 0.004 0.020
#> GSM99570 1 0.2679 0.794 0.864 0.000 0.000 0.000 0.096 0.040
#> GSM99598 1 0.1082 0.809 0.956 0.000 0.000 0.000 0.004 0.040
#> GSM99432 4 0.0547 0.685 0.000 0.000 0.000 0.980 0.000 0.020
#> GSM99434 6 0.4601 0.390 0.000 0.000 0.408 0.032 0.004 0.556
#> GSM99436 4 0.2572 0.655 0.000 0.136 0.000 0.852 0.000 0.012
#> GSM99438 2 0.0458 0.960 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM99440 1 0.1845 0.803 0.920 0.000 0.000 0.000 0.028 0.052
#> GSM99442 2 0.0547 0.958 0.000 0.980 0.000 0.020 0.000 0.000
#> GSM99444 2 0.0458 0.960 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM99446 4 0.2066 0.687 0.000 0.072 0.000 0.904 0.000 0.024
#> GSM99448 4 0.4090 0.122 0.000 0.000 0.008 0.604 0.004 0.384
#> GSM99450 3 0.3747 0.047 0.000 0.000 0.604 0.000 0.000 0.396
#> GSM99452 1 0.3529 0.741 0.764 0.000 0.000 0.000 0.208 0.028
#> GSM99454 1 0.0777 0.813 0.972 0.000 0.000 0.000 0.004 0.024
#> GSM99456 1 0.5736 0.631 0.580 0.016 0.000 0.000 0.212 0.192
#> GSM99462 2 0.0458 0.960 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM99464 6 0.5358 0.191 0.000 0.000 0.392 0.000 0.112 0.496
#> GSM99466 4 0.4682 0.487 0.000 0.000 0.000 0.640 0.284 0.076
#> GSM99470 5 0.3602 0.535 0.000 0.000 0.000 0.160 0.784 0.056
#> GSM99472 5 0.2537 0.562 0.096 0.000 0.000 0.000 0.872 0.032
#> GSM99474 3 0.1643 0.781 0.000 0.000 0.924 0.000 0.008 0.068
#> GSM99476 6 0.5743 0.496 0.000 0.000 0.148 0.276 0.016 0.560
#> GSM99478 4 0.4905 0.486 0.000 0.000 0.000 0.620 0.284 0.096
#> GSM99480 1 0.4092 0.733 0.772 0.016 0.000 0.000 0.076 0.136
#> GSM99482 1 0.4399 0.405 0.516 0.000 0.000 0.000 0.460 0.024
#> GSM99484 4 0.4892 0.514 0.000 0.000 0.000 0.628 0.272 0.100
#> GSM99486 4 0.0858 0.693 0.000 0.028 0.000 0.968 0.000 0.004
#> GSM99488 2 0.0603 0.959 0.000 0.980 0.000 0.016 0.000 0.004
#> GSM99490 4 0.6455 0.509 0.000 0.228 0.000 0.548 0.120 0.104
#> GSM99492 1 0.4130 0.730 0.768 0.016 0.000 0.000 0.076 0.140
#> GSM99494 2 0.0603 0.959 0.000 0.980 0.000 0.016 0.000 0.004
#> GSM99524 1 0.4109 0.608 0.648 0.000 0.000 0.000 0.328 0.024
#> GSM99526 6 0.5832 0.450 0.000 0.000 0.084 0.208 0.088 0.620
#> GSM99528 5 0.5807 0.327 0.000 0.000 0.004 0.284 0.516 0.196
#> GSM99530 3 0.4148 0.543 0.000 0.000 0.744 0.000 0.108 0.148
#> GSM99532 3 0.2762 0.713 0.000 0.000 0.860 0.000 0.048 0.092
#> GSM99534 4 0.6050 0.464 0.000 0.056 0.000 0.544 0.300 0.100
#> GSM99536 1 0.1320 0.809 0.948 0.000 0.000 0.000 0.016 0.036
#> GSM99538 4 0.0458 0.688 0.000 0.000 0.000 0.984 0.000 0.016
#> GSM99540 1 0.4392 0.696 0.720 0.000 0.000 0.000 0.136 0.144
#> GSM99542 2 0.5133 0.594 0.000 0.688 0.000 0.180 0.048 0.084
#> GSM99544 4 0.0806 0.690 0.000 0.020 0.000 0.972 0.000 0.008
#> GSM99546 6 0.5074 0.256 0.000 0.000 0.000 0.296 0.108 0.596
#> GSM99548 2 0.1245 0.945 0.000 0.952 0.000 0.016 0.000 0.032
#> GSM99550 5 0.3452 0.479 0.000 0.004 0.000 0.004 0.736 0.256
#> GSM99552 5 0.7174 0.367 0.000 0.000 0.168 0.176 0.456 0.200
#> GSM99554 4 0.3134 0.639 0.000 0.168 0.000 0.808 0.000 0.024
#> GSM99556 2 0.1245 0.945 0.000 0.952 0.000 0.016 0.000 0.032
#> GSM99558 4 0.4118 0.598 0.000 0.000 0.004 0.748 0.172 0.076
#> GSM99560 4 0.3432 0.623 0.000 0.000 0.000 0.800 0.148 0.052
#> GSM99562 3 0.0508 0.831 0.000 0.000 0.984 0.000 0.004 0.012
#> GSM99564 4 0.2191 0.659 0.000 0.120 0.000 0.876 0.000 0.004
#> GSM99572 2 0.0458 0.960 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM99576 5 0.3655 0.501 0.112 0.000 0.000 0.000 0.792 0.096
#> GSM99578 4 0.6630 0.471 0.000 0.124 0.000 0.516 0.252 0.108
#> GSM99580 3 0.2473 0.690 0.000 0.000 0.856 0.000 0.008 0.136
#> GSM99582 5 0.6906 0.301 0.000 0.000 0.120 0.132 0.460 0.288
#> GSM99584 4 0.0363 0.686 0.000 0.000 0.000 0.988 0.000 0.012
#> GSM99586 1 0.5591 0.648 0.604 0.016 0.000 0.000 0.192 0.188
#> GSM99588 4 0.6386 0.534 0.000 0.196 0.000 0.568 0.128 0.108
#> GSM99590 2 0.0458 0.960 0.000 0.984 0.000 0.016 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) cell.type(p) k
#> ATC:kmeans 84 2.54e-05 0.00015 2
#> ATC:kmeans 81 2.02e-04 0.00547 3
#> ATC:kmeans 75 5.12e-05 0.00414 4
#> ATC:kmeans 70 1.04e-04 0.01845 5
#> ATC:kmeans 63 6.22e-05 0.01451 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 21168 rows and 85 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.989 0.995 0.5003 0.500 0.500
#> 3 3 0.999 0.974 0.988 0.3336 0.783 0.587
#> 4 4 0.903 0.882 0.939 0.0767 0.929 0.791
#> 5 5 0.821 0.798 0.898 0.0478 0.975 0.909
#> 6 6 0.790 0.582 0.828 0.0413 0.958 0.843
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM99496 1 0.000 0.997 1.000 0.000
#> GSM99502 1 0.000 0.997 1.000 0.000
#> GSM99504 1 0.000 0.997 1.000 0.000
#> GSM99506 1 0.000 0.997 1.000 0.000
#> GSM99566 1 0.000 0.997 1.000 0.000
#> GSM99574 1 0.000 0.997 1.000 0.000
#> GSM99592 1 0.000 0.997 1.000 0.000
#> GSM99594 1 0.000 0.997 1.000 0.000
#> GSM99468 1 0.000 0.997 1.000 0.000
#> GSM99498 1 0.000 0.997 1.000 0.000
#> GSM99500 1 0.000 0.997 1.000 0.000
#> GSM99508 1 0.000 0.997 1.000 0.000
#> GSM99568 1 0.000 0.997 1.000 0.000
#> GSM99596 1 0.000 0.997 1.000 0.000
#> GSM99600 2 0.000 0.993 0.000 1.000
#> GSM99458 1 0.000 0.997 1.000 0.000
#> GSM99460 1 0.000 0.997 1.000 0.000
#> GSM99510 1 0.000 0.997 1.000 0.000
#> GSM99512 1 0.563 0.846 0.868 0.132
#> GSM99514 1 0.000 0.997 1.000 0.000
#> GSM99516 1 0.000 0.997 1.000 0.000
#> GSM99518 1 0.000 0.997 1.000 0.000
#> GSM99520 1 0.000 0.997 1.000 0.000
#> GSM99522 1 0.000 0.997 1.000 0.000
#> GSM99570 1 0.000 0.997 1.000 0.000
#> GSM99598 1 0.000 0.997 1.000 0.000
#> GSM99432 2 0.000 0.993 0.000 1.000
#> GSM99434 2 0.844 0.624 0.272 0.728
#> GSM99436 2 0.000 0.993 0.000 1.000
#> GSM99438 2 0.000 0.993 0.000 1.000
#> GSM99440 1 0.000 0.997 1.000 0.000
#> GSM99442 2 0.000 0.993 0.000 1.000
#> GSM99444 2 0.000 0.993 0.000 1.000
#> GSM99446 2 0.000 0.993 0.000 1.000
#> GSM99448 2 0.000 0.993 0.000 1.000
#> GSM99450 1 0.000 0.997 1.000 0.000
#> GSM99452 1 0.000 0.997 1.000 0.000
#> GSM99454 1 0.000 0.997 1.000 0.000
#> GSM99456 1 0.000 0.997 1.000 0.000
#> GSM99462 2 0.000 0.993 0.000 1.000
#> GSM99464 1 0.000 0.997 1.000 0.000
#> GSM99466 2 0.000 0.993 0.000 1.000
#> GSM99470 2 0.000 0.993 0.000 1.000
#> GSM99472 1 0.000 0.997 1.000 0.000
#> GSM99474 1 0.000 0.997 1.000 0.000
#> GSM99476 2 0.000 0.993 0.000 1.000
#> GSM99478 2 0.000 0.993 0.000 1.000
#> GSM99480 1 0.000 0.997 1.000 0.000
#> GSM99482 1 0.000 0.997 1.000 0.000
#> GSM99484 2 0.000 0.993 0.000 1.000
#> GSM99486 2 0.000 0.993 0.000 1.000
#> GSM99488 2 0.000 0.993 0.000 1.000
#> GSM99490 2 0.000 0.993 0.000 1.000
#> GSM99492 1 0.000 0.997 1.000 0.000
#> GSM99494 2 0.000 0.993 0.000 1.000
#> GSM99524 1 0.000 0.997 1.000 0.000
#> GSM99526 2 0.000 0.993 0.000 1.000
#> GSM99528 2 0.000 0.993 0.000 1.000
#> GSM99530 1 0.000 0.997 1.000 0.000
#> GSM99532 1 0.000 0.997 1.000 0.000
#> GSM99534 2 0.000 0.993 0.000 1.000
#> GSM99536 1 0.000 0.997 1.000 0.000
#> GSM99538 2 0.000 0.993 0.000 1.000
#> GSM99540 1 0.000 0.997 1.000 0.000
#> GSM99542 2 0.000 0.993 0.000 1.000
#> GSM99544 2 0.000 0.993 0.000 1.000
#> GSM99546 2 0.000 0.993 0.000 1.000
#> GSM99548 2 0.000 0.993 0.000 1.000
#> GSM99550 1 0.000 0.997 1.000 0.000
#> GSM99552 2 0.000 0.993 0.000 1.000
#> GSM99554 2 0.000 0.993 0.000 1.000
#> GSM99556 2 0.000 0.993 0.000 1.000
#> GSM99558 2 0.000 0.993 0.000 1.000
#> GSM99560 2 0.000 0.993 0.000 1.000
#> GSM99562 1 0.000 0.997 1.000 0.000
#> GSM99564 2 0.000 0.993 0.000 1.000
#> GSM99572 2 0.000 0.993 0.000 1.000
#> GSM99576 1 0.000 0.997 1.000 0.000
#> GSM99578 2 0.000 0.993 0.000 1.000
#> GSM99580 1 0.000 0.997 1.000 0.000
#> GSM99582 1 0.000 0.997 1.000 0.000
#> GSM99584 2 0.000 0.993 0.000 1.000
#> GSM99586 1 0.000 0.997 1.000 0.000
#> GSM99588 2 0.000 0.993 0.000 1.000
#> GSM99590 2 0.000 0.993 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM99496 3 0.0000 0.980 0.000 0.000 1.000
#> GSM99502 1 0.0000 0.993 1.000 0.000 0.000
#> GSM99504 1 0.0000 0.993 1.000 0.000 0.000
#> GSM99506 3 0.0000 0.980 0.000 0.000 1.000
#> GSM99566 3 0.0000 0.980 0.000 0.000 1.000
#> GSM99574 1 0.0000 0.993 1.000 0.000 0.000
#> GSM99592 3 0.0000 0.980 0.000 0.000 1.000
#> GSM99594 3 0.0000 0.980 0.000 0.000 1.000
#> GSM99468 1 0.0000 0.993 1.000 0.000 0.000
#> GSM99498 1 0.0000 0.993 1.000 0.000 0.000
#> GSM99500 1 0.0000 0.993 1.000 0.000 0.000
#> GSM99508 3 0.0000 0.980 0.000 0.000 1.000
#> GSM99568 3 0.0000 0.980 0.000 0.000 1.000
#> GSM99596 3 0.0000 0.980 0.000 0.000 1.000
#> GSM99600 2 0.0000 0.986 0.000 1.000 0.000
#> GSM99458 1 0.0000 0.993 1.000 0.000 0.000
#> GSM99460 1 0.0000 0.993 1.000 0.000 0.000
#> GSM99510 3 0.0000 0.980 0.000 0.000 1.000
#> GSM99512 3 0.0000 0.980 0.000 0.000 1.000
#> GSM99514 3 0.0000 0.980 0.000 0.000 1.000
#> GSM99516 1 0.0000 0.993 1.000 0.000 0.000
#> GSM99518 1 0.0000 0.993 1.000 0.000 0.000
#> GSM99520 3 0.0000 0.980 0.000 0.000 1.000
#> GSM99522 3 0.0000 0.980 0.000 0.000 1.000
#> GSM99570 1 0.0000 0.993 1.000 0.000 0.000
#> GSM99598 1 0.0000 0.993 1.000 0.000 0.000
#> GSM99432 2 0.0000 0.986 0.000 1.000 0.000
#> GSM99434 3 0.0000 0.980 0.000 0.000 1.000
#> GSM99436 2 0.0000 0.986 0.000 1.000 0.000
#> GSM99438 2 0.0000 0.986 0.000 1.000 0.000
#> GSM99440 1 0.0000 0.993 1.000 0.000 0.000
#> GSM99442 2 0.0000 0.986 0.000 1.000 0.000
#> GSM99444 2 0.0000 0.986 0.000 1.000 0.000
#> GSM99446 2 0.0000 0.986 0.000 1.000 0.000
#> GSM99448 2 0.4504 0.755 0.000 0.804 0.196
#> GSM99450 3 0.0000 0.980 0.000 0.000 1.000
#> GSM99452 1 0.0000 0.993 1.000 0.000 0.000
#> GSM99454 1 0.0000 0.993 1.000 0.000 0.000
#> GSM99456 1 0.0000 0.993 1.000 0.000 0.000
#> GSM99462 2 0.0000 0.986 0.000 1.000 0.000
#> GSM99464 3 0.0592 0.972 0.012 0.000 0.988
#> GSM99466 2 0.0000 0.986 0.000 1.000 0.000
#> GSM99470 1 0.3879 0.817 0.848 0.152 0.000
#> GSM99472 1 0.0000 0.993 1.000 0.000 0.000
#> GSM99474 3 0.0000 0.980 0.000 0.000 1.000
#> GSM99476 3 0.2448 0.915 0.000 0.076 0.924
#> GSM99478 2 0.0000 0.986 0.000 1.000 0.000
#> GSM99480 1 0.0000 0.993 1.000 0.000 0.000
#> GSM99482 1 0.0000 0.993 1.000 0.000 0.000
#> GSM99484 2 0.0000 0.986 0.000 1.000 0.000
#> GSM99486 2 0.0000 0.986 0.000 1.000 0.000
#> GSM99488 2 0.0000 0.986 0.000 1.000 0.000
#> GSM99490 2 0.0000 0.986 0.000 1.000 0.000
#> GSM99492 1 0.0000 0.993 1.000 0.000 0.000
#> GSM99494 2 0.0000 0.986 0.000 1.000 0.000
#> GSM99524 1 0.0000 0.993 1.000 0.000 0.000
#> GSM99526 3 0.3752 0.835 0.000 0.144 0.856
#> GSM99528 2 0.0000 0.986 0.000 1.000 0.000
#> GSM99530 3 0.2066 0.934 0.060 0.000 0.940
#> GSM99532 3 0.2878 0.898 0.096 0.000 0.904
#> GSM99534 2 0.0000 0.986 0.000 1.000 0.000
#> GSM99536 1 0.0000 0.993 1.000 0.000 0.000
#> GSM99538 2 0.0000 0.986 0.000 1.000 0.000
#> GSM99540 1 0.0000 0.993 1.000 0.000 0.000
#> GSM99542 2 0.0000 0.986 0.000 1.000 0.000
#> GSM99544 2 0.0000 0.986 0.000 1.000 0.000
#> GSM99546 2 0.0000 0.986 0.000 1.000 0.000
#> GSM99548 2 0.0000 0.986 0.000 1.000 0.000
#> GSM99550 1 0.0000 0.993 1.000 0.000 0.000
#> GSM99552 2 0.5058 0.680 0.000 0.756 0.244
#> GSM99554 2 0.0000 0.986 0.000 1.000 0.000
#> GSM99556 2 0.0000 0.986 0.000 1.000 0.000
#> GSM99558 2 0.0000 0.986 0.000 1.000 0.000
#> GSM99560 2 0.0000 0.986 0.000 1.000 0.000
#> GSM99562 3 0.0000 0.980 0.000 0.000 1.000
#> GSM99564 2 0.0000 0.986 0.000 1.000 0.000
#> GSM99572 2 0.0000 0.986 0.000 1.000 0.000
#> GSM99576 1 0.0000 0.993 1.000 0.000 0.000
#> GSM99578 2 0.0000 0.986 0.000 1.000 0.000
#> GSM99580 3 0.0000 0.980 0.000 0.000 1.000
#> GSM99582 3 0.2165 0.929 0.064 0.000 0.936
#> GSM99584 2 0.0000 0.986 0.000 1.000 0.000
#> GSM99586 1 0.0000 0.993 1.000 0.000 0.000
#> GSM99588 2 0.0000 0.986 0.000 1.000 0.000
#> GSM99590 2 0.0000 0.986 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM99496 3 0.0000 0.923 0.000 0.000 1.000 0.000
#> GSM99502 1 0.0000 0.978 1.000 0.000 0.000 0.000
#> GSM99504 1 0.0000 0.978 1.000 0.000 0.000 0.000
#> GSM99506 3 0.0000 0.923 0.000 0.000 1.000 0.000
#> GSM99566 3 0.0000 0.923 0.000 0.000 1.000 0.000
#> GSM99574 1 0.0000 0.978 1.000 0.000 0.000 0.000
#> GSM99592 4 0.4866 0.514 0.000 0.000 0.404 0.596
#> GSM99594 3 0.0000 0.923 0.000 0.000 1.000 0.000
#> GSM99468 1 0.0000 0.978 1.000 0.000 0.000 0.000
#> GSM99498 1 0.0000 0.978 1.000 0.000 0.000 0.000
#> GSM99500 1 0.0000 0.978 1.000 0.000 0.000 0.000
#> GSM99508 3 0.0000 0.923 0.000 0.000 1.000 0.000
#> GSM99568 3 0.0000 0.923 0.000 0.000 1.000 0.000
#> GSM99596 3 0.0000 0.923 0.000 0.000 1.000 0.000
#> GSM99600 2 0.0188 0.956 0.000 0.996 0.000 0.004
#> GSM99458 1 0.0000 0.978 1.000 0.000 0.000 0.000
#> GSM99460 1 0.0000 0.978 1.000 0.000 0.000 0.000
#> GSM99510 4 0.3873 0.708 0.000 0.000 0.228 0.772
#> GSM99512 4 0.4994 0.317 0.000 0.000 0.480 0.520
#> GSM99514 3 0.0000 0.923 0.000 0.000 1.000 0.000
#> GSM99516 1 0.0000 0.978 1.000 0.000 0.000 0.000
#> GSM99518 1 0.0000 0.978 1.000 0.000 0.000 0.000
#> GSM99520 3 0.0000 0.923 0.000 0.000 1.000 0.000
#> GSM99522 3 0.0188 0.919 0.004 0.000 0.996 0.000
#> GSM99570 1 0.0000 0.978 1.000 0.000 0.000 0.000
#> GSM99598 1 0.0000 0.978 1.000 0.000 0.000 0.000
#> GSM99432 2 0.2921 0.886 0.000 0.860 0.000 0.140
#> GSM99434 4 0.3311 0.724 0.000 0.000 0.172 0.828
#> GSM99436 2 0.2589 0.904 0.000 0.884 0.000 0.116
#> GSM99438 2 0.0000 0.957 0.000 1.000 0.000 0.000
#> GSM99440 1 0.0000 0.978 1.000 0.000 0.000 0.000
#> GSM99442 2 0.0188 0.956 0.000 0.996 0.000 0.004
#> GSM99444 2 0.0000 0.957 0.000 1.000 0.000 0.000
#> GSM99446 2 0.0188 0.956 0.000 0.996 0.000 0.004
#> GSM99448 4 0.5039 0.157 0.000 0.404 0.004 0.592
#> GSM99450 4 0.4406 0.662 0.000 0.000 0.300 0.700
#> GSM99452 1 0.0000 0.978 1.000 0.000 0.000 0.000
#> GSM99454 1 0.0000 0.978 1.000 0.000 0.000 0.000
#> GSM99456 1 0.0000 0.978 1.000 0.000 0.000 0.000
#> GSM99462 2 0.0000 0.957 0.000 1.000 0.000 0.000
#> GSM99464 4 0.5113 0.680 0.036 0.000 0.252 0.712
#> GSM99466 2 0.2868 0.896 0.000 0.864 0.000 0.136
#> GSM99470 1 0.6179 0.423 0.608 0.320 0.000 0.072
#> GSM99472 1 0.1118 0.954 0.964 0.000 0.000 0.036
#> GSM99474 3 0.0000 0.923 0.000 0.000 1.000 0.000
#> GSM99476 4 0.2142 0.717 0.000 0.016 0.056 0.928
#> GSM99478 2 0.0921 0.940 0.000 0.972 0.000 0.028
#> GSM99480 1 0.0000 0.978 1.000 0.000 0.000 0.000
#> GSM99482 1 0.1118 0.954 0.964 0.000 0.000 0.036
#> GSM99484 2 0.0000 0.957 0.000 1.000 0.000 0.000
#> GSM99486 2 0.2760 0.895 0.000 0.872 0.000 0.128
#> GSM99488 2 0.0000 0.957 0.000 1.000 0.000 0.000
#> GSM99490 2 0.0000 0.957 0.000 1.000 0.000 0.000
#> GSM99492 1 0.0000 0.978 1.000 0.000 0.000 0.000
#> GSM99494 2 0.0000 0.957 0.000 1.000 0.000 0.000
#> GSM99524 1 0.0000 0.978 1.000 0.000 0.000 0.000
#> GSM99526 4 0.2224 0.714 0.000 0.032 0.040 0.928
#> GSM99528 2 0.1118 0.935 0.000 0.964 0.000 0.036
#> GSM99530 3 0.1118 0.880 0.036 0.000 0.964 0.000
#> GSM99532 3 0.1792 0.837 0.068 0.000 0.932 0.000
#> GSM99534 2 0.0000 0.957 0.000 1.000 0.000 0.000
#> GSM99536 1 0.0000 0.978 1.000 0.000 0.000 0.000
#> GSM99538 2 0.2469 0.910 0.000 0.892 0.000 0.108
#> GSM99540 1 0.0000 0.978 1.000 0.000 0.000 0.000
#> GSM99542 2 0.0000 0.957 0.000 1.000 0.000 0.000
#> GSM99544 2 0.2814 0.892 0.000 0.868 0.000 0.132
#> GSM99546 4 0.2281 0.676 0.000 0.096 0.000 0.904
#> GSM99548 2 0.0000 0.957 0.000 1.000 0.000 0.000
#> GSM99550 1 0.0707 0.965 0.980 0.000 0.000 0.020
#> GSM99552 3 0.5256 0.417 0.000 0.272 0.692 0.036
#> GSM99554 2 0.0188 0.956 0.000 0.996 0.000 0.004
#> GSM99556 2 0.0000 0.957 0.000 1.000 0.000 0.000
#> GSM99558 2 0.2081 0.923 0.000 0.916 0.000 0.084
#> GSM99560 2 0.2081 0.923 0.000 0.916 0.000 0.084
#> GSM99562 3 0.0000 0.923 0.000 0.000 1.000 0.000
#> GSM99564 2 0.2760 0.895 0.000 0.872 0.000 0.128
#> GSM99572 2 0.0000 0.957 0.000 1.000 0.000 0.000
#> GSM99576 1 0.1118 0.954 0.964 0.000 0.000 0.036
#> GSM99578 2 0.0000 0.957 0.000 1.000 0.000 0.000
#> GSM99580 3 0.0000 0.923 0.000 0.000 1.000 0.000
#> GSM99582 3 0.5808 0.102 0.032 0.000 0.544 0.424
#> GSM99584 2 0.2921 0.886 0.000 0.860 0.000 0.140
#> GSM99586 1 0.0000 0.978 1.000 0.000 0.000 0.000
#> GSM99588 2 0.0000 0.957 0.000 1.000 0.000 0.000
#> GSM99590 2 0.0000 0.957 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM99496 3 0.0000 0.94822 0.000 0.000 1.000 0.000 0.000
#> GSM99502 1 0.0000 0.93706 1.000 0.000 0.000 0.000 0.000
#> GSM99504 1 0.0000 0.93706 1.000 0.000 0.000 0.000 0.000
#> GSM99506 3 0.0000 0.94822 0.000 0.000 1.000 0.000 0.000
#> GSM99566 3 0.0000 0.94822 0.000 0.000 1.000 0.000 0.000
#> GSM99574 1 0.0000 0.93706 1.000 0.000 0.000 0.000 0.000
#> GSM99592 4 0.4420 0.29837 0.000 0.000 0.448 0.548 0.004
#> GSM99594 3 0.0000 0.94822 0.000 0.000 1.000 0.000 0.000
#> GSM99468 1 0.0000 0.93706 1.000 0.000 0.000 0.000 0.000
#> GSM99498 1 0.0000 0.93706 1.000 0.000 0.000 0.000 0.000
#> GSM99500 1 0.0000 0.93706 1.000 0.000 0.000 0.000 0.000
#> GSM99508 3 0.0000 0.94822 0.000 0.000 1.000 0.000 0.000
#> GSM99568 3 0.0290 0.94356 0.000 0.000 0.992 0.008 0.000
#> GSM99596 3 0.0000 0.94822 0.000 0.000 1.000 0.000 0.000
#> GSM99600 2 0.1341 0.88192 0.000 0.944 0.000 0.000 0.056
#> GSM99458 1 0.0162 0.93639 0.996 0.000 0.000 0.000 0.004
#> GSM99460 1 0.0510 0.93323 0.984 0.000 0.000 0.000 0.016
#> GSM99510 4 0.2230 0.67078 0.000 0.000 0.116 0.884 0.000
#> GSM99512 4 0.4341 0.37182 0.000 0.000 0.404 0.592 0.004
#> GSM99514 3 0.0000 0.94822 0.000 0.000 1.000 0.000 0.000
#> GSM99516 1 0.0162 0.93592 0.996 0.000 0.000 0.000 0.004
#> GSM99518 1 0.0000 0.93706 1.000 0.000 0.000 0.000 0.000
#> GSM99520 3 0.0000 0.94822 0.000 0.000 1.000 0.000 0.000
#> GSM99522 3 0.0451 0.94123 0.004 0.000 0.988 0.008 0.000
#> GSM99570 1 0.1478 0.90588 0.936 0.000 0.000 0.000 0.064
#> GSM99598 1 0.0000 0.93706 1.000 0.000 0.000 0.000 0.000
#> GSM99432 2 0.3849 0.81130 0.000 0.808 0.000 0.080 0.112
#> GSM99434 4 0.1043 0.67946 0.000 0.000 0.040 0.960 0.000
#> GSM99436 2 0.3339 0.83526 0.000 0.840 0.000 0.048 0.112
#> GSM99438 2 0.0000 0.88880 0.000 1.000 0.000 0.000 0.000
#> GSM99440 1 0.0000 0.93706 1.000 0.000 0.000 0.000 0.000
#> GSM99442 2 0.1121 0.88447 0.000 0.956 0.000 0.000 0.044
#> GSM99444 2 0.0000 0.88880 0.000 1.000 0.000 0.000 0.000
#> GSM99446 2 0.1544 0.87922 0.000 0.932 0.000 0.000 0.068
#> GSM99448 4 0.5717 -0.00573 0.000 0.368 0.000 0.540 0.092
#> GSM99450 4 0.3109 0.61977 0.000 0.000 0.200 0.800 0.000
#> GSM99452 1 0.2074 0.87969 0.896 0.000 0.000 0.000 0.104
#> GSM99454 1 0.0000 0.93706 1.000 0.000 0.000 0.000 0.000
#> GSM99456 1 0.1197 0.91763 0.952 0.000 0.000 0.000 0.048
#> GSM99462 2 0.0000 0.88880 0.000 1.000 0.000 0.000 0.000
#> GSM99464 4 0.4293 0.61898 0.076 0.000 0.092 0.804 0.028
#> GSM99466 2 0.5010 0.40701 0.000 0.572 0.000 0.036 0.392
#> GSM99470 5 0.3578 0.36856 0.048 0.132 0.000 0.000 0.820
#> GSM99472 1 0.4150 0.55382 0.612 0.000 0.000 0.000 0.388
#> GSM99474 3 0.0000 0.94822 0.000 0.000 1.000 0.000 0.000
#> GSM99476 4 0.0794 0.66219 0.000 0.000 0.000 0.972 0.028
#> GSM99478 2 0.3774 0.48807 0.000 0.704 0.000 0.000 0.296
#> GSM99480 1 0.0404 0.93444 0.988 0.000 0.000 0.000 0.012
#> GSM99482 1 0.3949 0.63872 0.668 0.000 0.000 0.000 0.332
#> GSM99484 2 0.2424 0.78048 0.000 0.868 0.000 0.000 0.132
#> GSM99486 2 0.3409 0.83281 0.000 0.836 0.000 0.052 0.112
#> GSM99488 2 0.0404 0.88650 0.000 0.988 0.000 0.000 0.012
#> GSM99490 2 0.0404 0.88650 0.000 0.988 0.000 0.000 0.012
#> GSM99492 1 0.1121 0.91947 0.956 0.000 0.000 0.000 0.044
#> GSM99494 2 0.0404 0.88650 0.000 0.988 0.000 0.000 0.012
#> GSM99524 1 0.2230 0.87075 0.884 0.000 0.000 0.000 0.116
#> GSM99526 4 0.0000 0.66849 0.000 0.000 0.000 1.000 0.000
#> GSM99528 5 0.4287 0.15061 0.000 0.460 0.000 0.000 0.540
#> GSM99530 3 0.4272 0.59517 0.196 0.000 0.752 0.000 0.052
#> GSM99532 3 0.3209 0.67959 0.180 0.000 0.812 0.008 0.000
#> GSM99534 2 0.0404 0.88650 0.000 0.988 0.000 0.000 0.012
#> GSM99536 1 0.0290 0.93547 0.992 0.000 0.000 0.000 0.008
#> GSM99538 2 0.3237 0.84215 0.000 0.848 0.000 0.048 0.104
#> GSM99540 1 0.0290 0.93547 0.992 0.000 0.000 0.000 0.008
#> GSM99542 2 0.0510 0.88494 0.000 0.984 0.000 0.000 0.016
#> GSM99544 2 0.3543 0.82746 0.000 0.828 0.000 0.060 0.112
#> GSM99546 4 0.2149 0.62368 0.000 0.036 0.000 0.916 0.048
#> GSM99548 2 0.0404 0.88650 0.000 0.988 0.000 0.000 0.012
#> GSM99550 1 0.2329 0.87224 0.876 0.000 0.000 0.000 0.124
#> GSM99552 5 0.6235 0.39830 0.000 0.156 0.344 0.000 0.500
#> GSM99554 2 0.1851 0.87247 0.000 0.912 0.000 0.000 0.088
#> GSM99556 2 0.0404 0.88650 0.000 0.988 0.000 0.000 0.012
#> GSM99558 2 0.4136 0.77579 0.000 0.764 0.000 0.048 0.188
#> GSM99560 2 0.2006 0.87544 0.000 0.916 0.000 0.012 0.072
#> GSM99562 3 0.0290 0.94356 0.000 0.000 0.992 0.008 0.000
#> GSM99564 2 0.3409 0.83281 0.000 0.836 0.000 0.052 0.112
#> GSM99572 2 0.0000 0.88880 0.000 1.000 0.000 0.000 0.000
#> GSM99576 1 0.4015 0.64163 0.652 0.000 0.000 0.000 0.348
#> GSM99578 2 0.0609 0.88337 0.000 0.980 0.000 0.000 0.020
#> GSM99580 3 0.0290 0.94228 0.000 0.000 0.992 0.000 0.008
#> GSM99582 5 0.7408 -0.00180 0.028 0.000 0.316 0.296 0.360
#> GSM99584 2 0.3849 0.81130 0.000 0.808 0.000 0.080 0.112
#> GSM99586 1 0.1197 0.91763 0.952 0.000 0.000 0.000 0.048
#> GSM99588 2 0.0609 0.88353 0.000 0.980 0.000 0.000 0.020
#> GSM99590 2 0.0000 0.88880 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM99496 3 0.0000 0.8484 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99502 1 0.0000 0.8837 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99504 1 0.0000 0.8837 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99506 3 0.0000 0.8484 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99566 3 0.0146 0.8479 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM99574 1 0.0000 0.8837 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99592 3 0.4300 0.2599 0.000 0.000 0.608 0.028 0.000 0.364
#> GSM99594 3 0.0146 0.8479 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM99468 1 0.0146 0.8835 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM99498 1 0.0000 0.8837 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99500 1 0.0000 0.8837 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99508 3 0.0363 0.8467 0.000 0.000 0.988 0.012 0.000 0.000
#> GSM99568 3 0.0717 0.8435 0.000 0.000 0.976 0.016 0.000 0.008
#> GSM99596 3 0.0260 0.8474 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM99600 2 0.1444 0.6782 0.000 0.928 0.000 0.072 0.000 0.000
#> GSM99458 1 0.1152 0.8646 0.952 0.000 0.000 0.044 0.004 0.000
#> GSM99460 1 0.2094 0.8396 0.908 0.000 0.000 0.068 0.016 0.008
#> GSM99510 6 0.3295 0.6702 0.000 0.000 0.128 0.056 0.000 0.816
#> GSM99512 6 0.5179 0.3873 0.000 0.000 0.348 0.088 0.004 0.560
#> GSM99514 3 0.0000 0.8484 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99516 1 0.0000 0.8837 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99518 1 0.0146 0.8835 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM99520 3 0.0000 0.8484 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM99522 3 0.1148 0.8362 0.004 0.000 0.960 0.016 0.000 0.020
#> GSM99570 1 0.2135 0.7782 0.872 0.000 0.000 0.000 0.128 0.000
#> GSM99598 1 0.0000 0.8837 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99432 2 0.4859 0.0634 0.000 0.612 0.000 0.304 0.000 0.084
#> GSM99434 6 0.1327 0.6856 0.000 0.000 0.064 0.000 0.000 0.936
#> GSM99436 2 0.4552 0.1630 0.000 0.640 0.000 0.300 0.000 0.060
#> GSM99438 2 0.0000 0.7201 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99440 1 0.0547 0.8771 0.980 0.000 0.000 0.000 0.020 0.000
#> GSM99442 2 0.1075 0.6960 0.000 0.952 0.000 0.048 0.000 0.000
#> GSM99444 2 0.0000 0.7201 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99446 2 0.1910 0.6445 0.000 0.892 0.000 0.108 0.000 0.000
#> GSM99448 6 0.6101 -0.2445 0.000 0.204 0.000 0.356 0.008 0.432
#> GSM99450 6 0.4131 0.5449 0.000 0.000 0.272 0.040 0.000 0.688
#> GSM99452 1 0.3151 0.5835 0.748 0.000 0.000 0.000 0.252 0.000
#> GSM99454 1 0.0146 0.8830 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM99456 1 0.3946 0.6889 0.756 0.000 0.000 0.168 0.076 0.000
#> GSM99462 2 0.0000 0.7201 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99464 6 0.6227 0.4845 0.084 0.000 0.084 0.212 0.016 0.604
#> GSM99466 4 0.6374 0.0000 0.000 0.384 0.000 0.408 0.180 0.028
#> GSM99470 5 0.2036 0.3026 0.028 0.048 0.000 0.008 0.916 0.000
#> GSM99472 5 0.3737 0.3081 0.392 0.000 0.000 0.000 0.608 0.000
#> GSM99474 3 0.0692 0.8409 0.000 0.000 0.976 0.020 0.004 0.000
#> GSM99476 6 0.2558 0.6424 0.000 0.000 0.000 0.156 0.004 0.840
#> GSM99478 2 0.4691 -0.0200 0.000 0.680 0.000 0.124 0.196 0.000
#> GSM99480 1 0.1649 0.8608 0.932 0.000 0.000 0.032 0.036 0.000
#> GSM99482 5 0.3828 0.2115 0.440 0.000 0.000 0.000 0.560 0.000
#> GSM99484 2 0.1745 0.6490 0.000 0.924 0.000 0.020 0.056 0.000
#> GSM99486 2 0.4655 0.1381 0.000 0.632 0.000 0.300 0.000 0.068
#> GSM99488 2 0.0405 0.7183 0.000 0.988 0.000 0.004 0.008 0.000
#> GSM99490 2 0.0405 0.7183 0.000 0.988 0.000 0.004 0.008 0.000
#> GSM99492 1 0.3270 0.7593 0.820 0.000 0.000 0.120 0.060 0.000
#> GSM99494 2 0.0405 0.7183 0.000 0.988 0.000 0.004 0.008 0.000
#> GSM99524 1 0.3390 0.4830 0.704 0.000 0.000 0.000 0.296 0.000
#> GSM99526 6 0.0777 0.6764 0.000 0.000 0.004 0.024 0.000 0.972
#> GSM99528 5 0.5991 -0.2191 0.000 0.256 0.000 0.308 0.436 0.000
#> GSM99530 3 0.6460 0.3378 0.168 0.000 0.540 0.236 0.048 0.008
#> GSM99532 3 0.4186 0.5978 0.180 0.000 0.744 0.068 0.000 0.008
#> GSM99534 2 0.0909 0.7033 0.000 0.968 0.000 0.012 0.020 0.000
#> GSM99536 1 0.0725 0.8780 0.976 0.000 0.000 0.012 0.012 0.000
#> GSM99538 2 0.4349 0.2714 0.000 0.684 0.000 0.264 0.004 0.048
#> GSM99540 1 0.0909 0.8757 0.968 0.000 0.000 0.020 0.012 0.000
#> GSM99542 2 0.0622 0.7138 0.000 0.980 0.000 0.008 0.012 0.000
#> GSM99544 2 0.4655 0.1385 0.000 0.632 0.000 0.300 0.000 0.068
#> GSM99546 6 0.3098 0.6341 0.000 0.040 0.000 0.120 0.004 0.836
#> GSM99548 2 0.0405 0.7183 0.000 0.988 0.000 0.004 0.008 0.000
#> GSM99550 1 0.5582 0.3811 0.576 0.000 0.000 0.252 0.164 0.008
#> GSM99552 5 0.6549 0.0478 0.000 0.028 0.232 0.348 0.392 0.000
#> GSM99554 2 0.2664 0.5473 0.000 0.816 0.000 0.184 0.000 0.000
#> GSM99556 2 0.0405 0.7183 0.000 0.988 0.000 0.004 0.008 0.000
#> GSM99558 2 0.5516 -0.5756 0.000 0.488 0.000 0.424 0.048 0.040
#> GSM99560 2 0.3691 0.4720 0.000 0.768 0.000 0.192 0.004 0.036
#> GSM99562 3 0.1003 0.8375 0.000 0.000 0.964 0.016 0.000 0.020
#> GSM99564 2 0.4655 0.1381 0.000 0.632 0.000 0.300 0.000 0.068
#> GSM99572 2 0.0000 0.7201 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99576 5 0.5558 0.0450 0.416 0.000 0.000 0.136 0.448 0.000
#> GSM99578 2 0.0622 0.7136 0.000 0.980 0.000 0.012 0.008 0.000
#> GSM99580 3 0.2632 0.7315 0.000 0.000 0.832 0.164 0.004 0.000
#> GSM99582 3 0.8416 -0.2447 0.048 0.000 0.276 0.216 0.236 0.224
#> GSM99584 2 0.4859 0.0633 0.000 0.612 0.000 0.304 0.000 0.084
#> GSM99586 1 0.3893 0.7005 0.764 0.000 0.000 0.156 0.080 0.000
#> GSM99588 2 0.0820 0.7081 0.000 0.972 0.000 0.016 0.012 0.000
#> GSM99590 2 0.0000 0.7201 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) cell.type(p) k
#> ATC:skmeans 85 1.64e-06 1.09e-05 2
#> ATC:skmeans 85 2.80e-05 1.05e-03 3
#> ATC:skmeans 80 4.19e-05 2.37e-03 4
#> ATC:skmeans 76 5.82e-05 2.77e-03 5
#> ATC:skmeans 60 2.43e-04 9.05e-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["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 21168 rows and 85 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.984 0.994 0.5061 0.494 0.494
#> 3 3 0.840 0.905 0.936 0.3128 0.720 0.491
#> 4 4 0.976 0.947 0.978 0.1295 0.850 0.587
#> 5 5 0.866 0.810 0.917 0.0486 0.964 0.857
#> 6 6 0.844 0.763 0.872 0.0369 0.968 0.856
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM99496 1 0.0000 0.988 1.000 0.000
#> GSM99502 1 0.0000 0.988 1.000 0.000
#> GSM99504 1 0.0000 0.988 1.000 0.000
#> GSM99506 1 0.0000 0.988 1.000 0.000
#> GSM99566 1 0.0000 0.988 1.000 0.000
#> GSM99574 1 0.0000 0.988 1.000 0.000
#> GSM99592 2 0.0000 1.000 0.000 1.000
#> GSM99594 1 0.9922 0.192 0.552 0.448
#> GSM99468 1 0.0000 0.988 1.000 0.000
#> GSM99498 1 0.0000 0.988 1.000 0.000
#> GSM99500 1 0.0000 0.988 1.000 0.000
#> GSM99508 1 0.0000 0.988 1.000 0.000
#> GSM99568 1 0.0000 0.988 1.000 0.000
#> GSM99596 1 0.0000 0.988 1.000 0.000
#> GSM99600 2 0.0000 1.000 0.000 1.000
#> GSM99458 1 0.0000 0.988 1.000 0.000
#> GSM99460 1 0.0000 0.988 1.000 0.000
#> GSM99510 2 0.0000 1.000 0.000 1.000
#> GSM99512 2 0.0376 0.996 0.004 0.996
#> GSM99514 1 0.0000 0.988 1.000 0.000
#> GSM99516 1 0.0000 0.988 1.000 0.000
#> GSM99518 1 0.0000 0.988 1.000 0.000
#> GSM99520 1 0.0000 0.988 1.000 0.000
#> GSM99522 1 0.0000 0.988 1.000 0.000
#> GSM99570 1 0.0000 0.988 1.000 0.000
#> GSM99598 1 0.0000 0.988 1.000 0.000
#> GSM99432 2 0.0000 1.000 0.000 1.000
#> GSM99434 2 0.0000 1.000 0.000 1.000
#> GSM99436 2 0.0000 1.000 0.000 1.000
#> GSM99438 2 0.0000 1.000 0.000 1.000
#> GSM99440 1 0.0000 0.988 1.000 0.000
#> GSM99442 2 0.0000 1.000 0.000 1.000
#> GSM99444 2 0.0000 1.000 0.000 1.000
#> GSM99446 2 0.0000 1.000 0.000 1.000
#> GSM99448 2 0.0000 1.000 0.000 1.000
#> GSM99450 1 0.0000 0.988 1.000 0.000
#> GSM99452 1 0.0000 0.988 1.000 0.000
#> GSM99454 1 0.0000 0.988 1.000 0.000
#> GSM99456 1 0.0000 0.988 1.000 0.000
#> GSM99462 2 0.0000 1.000 0.000 1.000
#> GSM99464 1 0.0000 0.988 1.000 0.000
#> GSM99466 2 0.0000 1.000 0.000 1.000
#> GSM99470 2 0.0000 1.000 0.000 1.000
#> GSM99472 1 0.1184 0.974 0.984 0.016
#> GSM99474 1 0.1414 0.970 0.980 0.020
#> GSM99476 2 0.0000 1.000 0.000 1.000
#> GSM99478 2 0.0000 1.000 0.000 1.000
#> GSM99480 1 0.0000 0.988 1.000 0.000
#> GSM99482 1 0.0000 0.988 1.000 0.000
#> GSM99484 2 0.0000 1.000 0.000 1.000
#> GSM99486 2 0.0000 1.000 0.000 1.000
#> GSM99488 2 0.0000 1.000 0.000 1.000
#> GSM99490 2 0.0000 1.000 0.000 1.000
#> GSM99492 1 0.0000 0.988 1.000 0.000
#> GSM99494 2 0.0000 1.000 0.000 1.000
#> GSM99524 1 0.0000 0.988 1.000 0.000
#> GSM99526 2 0.0000 1.000 0.000 1.000
#> GSM99528 2 0.0000 1.000 0.000 1.000
#> GSM99530 1 0.0000 0.988 1.000 0.000
#> GSM99532 1 0.0000 0.988 1.000 0.000
#> GSM99534 2 0.0000 1.000 0.000 1.000
#> GSM99536 1 0.0000 0.988 1.000 0.000
#> GSM99538 2 0.0000 1.000 0.000 1.000
#> GSM99540 1 0.0000 0.988 1.000 0.000
#> GSM99542 2 0.0000 1.000 0.000 1.000
#> GSM99544 2 0.0000 1.000 0.000 1.000
#> GSM99546 2 0.0000 1.000 0.000 1.000
#> GSM99548 2 0.0000 1.000 0.000 1.000
#> GSM99550 1 0.0672 0.981 0.992 0.008
#> GSM99552 2 0.0000 1.000 0.000 1.000
#> GSM99554 2 0.0000 1.000 0.000 1.000
#> GSM99556 2 0.0000 1.000 0.000 1.000
#> GSM99558 2 0.0000 1.000 0.000 1.000
#> GSM99560 2 0.0000 1.000 0.000 1.000
#> GSM99562 1 0.0000 0.988 1.000 0.000
#> GSM99564 2 0.0000 1.000 0.000 1.000
#> GSM99572 2 0.0000 1.000 0.000 1.000
#> GSM99576 1 0.0000 0.988 1.000 0.000
#> GSM99578 2 0.0000 1.000 0.000 1.000
#> GSM99580 2 0.0000 1.000 0.000 1.000
#> GSM99582 2 0.0000 1.000 0.000 1.000
#> GSM99584 2 0.0000 1.000 0.000 1.000
#> GSM99586 1 0.0000 0.988 1.000 0.000
#> GSM99588 2 0.0000 1.000 0.000 1.000
#> GSM99590 2 0.0000 1.000 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM99496 3 0.2165 0.905 0.064 0.000 0.936
#> GSM99502 1 0.0000 0.987 1.000 0.000 0.000
#> GSM99504 1 0.0000 0.987 1.000 0.000 0.000
#> GSM99506 3 0.2165 0.905 0.064 0.000 0.936
#> GSM99566 3 0.2165 0.905 0.064 0.000 0.936
#> GSM99574 1 0.0000 0.987 1.000 0.000 0.000
#> GSM99592 3 0.0000 0.887 0.000 0.000 1.000
#> GSM99594 3 0.2165 0.905 0.064 0.000 0.936
#> GSM99468 1 0.0000 0.987 1.000 0.000 0.000
#> GSM99498 1 0.0000 0.987 1.000 0.000 0.000
#> GSM99500 1 0.0000 0.987 1.000 0.000 0.000
#> GSM99508 3 0.2165 0.905 0.064 0.000 0.936
#> GSM99568 3 0.2165 0.905 0.064 0.000 0.936
#> GSM99596 3 0.2165 0.905 0.064 0.000 0.936
#> GSM99600 2 0.0000 0.935 0.000 1.000 0.000
#> GSM99458 1 0.0000 0.987 1.000 0.000 0.000
#> GSM99460 1 0.0000 0.987 1.000 0.000 0.000
#> GSM99510 3 0.0000 0.887 0.000 0.000 1.000
#> GSM99512 3 0.0000 0.887 0.000 0.000 1.000
#> GSM99514 3 0.2165 0.905 0.064 0.000 0.936
#> GSM99516 1 0.0000 0.987 1.000 0.000 0.000
#> GSM99518 1 0.0000 0.987 1.000 0.000 0.000
#> GSM99520 3 0.2165 0.905 0.064 0.000 0.936
#> GSM99522 3 0.3267 0.862 0.116 0.000 0.884
#> GSM99570 1 0.0000 0.987 1.000 0.000 0.000
#> GSM99598 1 0.0000 0.987 1.000 0.000 0.000
#> GSM99432 2 0.2448 0.922 0.000 0.924 0.076
#> GSM99434 3 0.0000 0.887 0.000 0.000 1.000
#> GSM99436 2 0.0000 0.935 0.000 1.000 0.000
#> GSM99438 2 0.0000 0.935 0.000 1.000 0.000
#> GSM99440 1 0.0000 0.987 1.000 0.000 0.000
#> GSM99442 2 0.0000 0.935 0.000 1.000 0.000
#> GSM99444 2 0.0000 0.935 0.000 1.000 0.000
#> GSM99446 2 0.2165 0.929 0.000 0.936 0.064
#> GSM99448 2 0.5810 0.581 0.000 0.664 0.336
#> GSM99450 3 0.2165 0.905 0.064 0.000 0.936
#> GSM99452 1 0.0000 0.987 1.000 0.000 0.000
#> GSM99454 1 0.0000 0.987 1.000 0.000 0.000
#> GSM99456 1 0.0000 0.987 1.000 0.000 0.000
#> GSM99462 2 0.0000 0.935 0.000 1.000 0.000
#> GSM99464 3 0.2165 0.905 0.064 0.000 0.936
#> GSM99466 2 0.4605 0.806 0.000 0.796 0.204
#> GSM99470 3 0.8309 0.585 0.180 0.188 0.632
#> GSM99472 1 0.2165 0.919 0.936 0.000 0.064
#> GSM99474 3 0.2165 0.905 0.064 0.000 0.936
#> GSM99476 3 0.4399 0.748 0.000 0.188 0.812
#> GSM99478 2 0.3879 0.862 0.000 0.848 0.152
#> GSM99480 1 0.0000 0.987 1.000 0.000 0.000
#> GSM99482 1 0.0000 0.987 1.000 0.000 0.000
#> GSM99484 2 0.2165 0.929 0.000 0.936 0.064
#> GSM99486 2 0.2165 0.929 0.000 0.936 0.064
#> GSM99488 2 0.0000 0.935 0.000 1.000 0.000
#> GSM99490 2 0.2165 0.929 0.000 0.936 0.064
#> GSM99492 1 0.0000 0.987 1.000 0.000 0.000
#> GSM99494 2 0.0000 0.935 0.000 1.000 0.000
#> GSM99524 1 0.0000 0.987 1.000 0.000 0.000
#> GSM99526 3 0.3619 0.800 0.000 0.136 0.864
#> GSM99528 3 0.4452 0.743 0.000 0.192 0.808
#> GSM99530 3 0.2165 0.905 0.064 0.000 0.936
#> GSM99532 3 0.2165 0.905 0.064 0.000 0.936
#> GSM99534 2 0.2165 0.929 0.000 0.936 0.064
#> GSM99536 1 0.0000 0.987 1.000 0.000 0.000
#> GSM99538 2 0.4504 0.816 0.000 0.804 0.196
#> GSM99540 1 0.0000 0.987 1.000 0.000 0.000
#> GSM99542 2 0.0000 0.935 0.000 1.000 0.000
#> GSM99544 2 0.0892 0.935 0.000 0.980 0.020
#> GSM99546 3 0.4654 0.720 0.000 0.208 0.792
#> GSM99548 2 0.0000 0.935 0.000 1.000 0.000
#> GSM99550 3 0.6935 0.770 0.088 0.188 0.724
#> GSM99552 3 0.4399 0.748 0.000 0.188 0.812
#> GSM99554 2 0.0000 0.935 0.000 1.000 0.000
#> GSM99556 2 0.0000 0.935 0.000 1.000 0.000
#> GSM99558 2 0.5560 0.654 0.000 0.700 0.300
#> GSM99560 2 0.4346 0.831 0.000 0.816 0.184
#> GSM99562 3 0.2165 0.905 0.064 0.000 0.936
#> GSM99564 2 0.0592 0.935 0.000 0.988 0.012
#> GSM99572 2 0.0000 0.935 0.000 1.000 0.000
#> GSM99576 1 0.4654 0.704 0.792 0.000 0.208
#> GSM99578 2 0.2165 0.929 0.000 0.936 0.064
#> GSM99580 3 0.0000 0.887 0.000 0.000 1.000
#> GSM99582 3 0.4399 0.748 0.000 0.188 0.812
#> GSM99584 2 0.2165 0.929 0.000 0.936 0.064
#> GSM99586 1 0.0000 0.987 1.000 0.000 0.000
#> GSM99588 2 0.2165 0.929 0.000 0.936 0.064
#> GSM99590 2 0.0000 0.935 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM99496 3 0.0000 0.978 0.000 0.000 1.000 0.000
#> GSM99502 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM99504 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM99506 3 0.0000 0.978 0.000 0.000 1.000 0.000
#> GSM99566 3 0.0000 0.978 0.000 0.000 1.000 0.000
#> GSM99574 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM99592 3 0.0000 0.978 0.000 0.000 1.000 0.000
#> GSM99594 3 0.0000 0.978 0.000 0.000 1.000 0.000
#> GSM99468 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM99498 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM99500 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM99508 3 0.0000 0.978 0.000 0.000 1.000 0.000
#> GSM99568 3 0.0000 0.978 0.000 0.000 1.000 0.000
#> GSM99596 3 0.0000 0.978 0.000 0.000 1.000 0.000
#> GSM99600 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> GSM99458 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM99460 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM99510 3 0.0000 0.978 0.000 0.000 1.000 0.000
#> GSM99512 3 0.0707 0.960 0.000 0.000 0.980 0.020
#> GSM99514 3 0.0000 0.978 0.000 0.000 1.000 0.000
#> GSM99516 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM99518 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM99520 3 0.0000 0.978 0.000 0.000 1.000 0.000
#> GSM99522 3 0.0000 0.978 0.000 0.000 1.000 0.000
#> GSM99570 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM99598 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM99432 4 0.0000 0.948 0.000 0.000 0.000 1.000
#> GSM99434 3 0.4356 0.571 0.000 0.000 0.708 0.292
#> GSM99436 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> GSM99438 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> GSM99440 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM99442 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> GSM99444 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> GSM99446 4 0.0000 0.948 0.000 0.000 0.000 1.000
#> GSM99448 4 0.0000 0.948 0.000 0.000 0.000 1.000
#> GSM99450 3 0.0000 0.978 0.000 0.000 1.000 0.000
#> GSM99452 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM99454 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM99456 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM99462 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> GSM99464 3 0.0000 0.978 0.000 0.000 1.000 0.000
#> GSM99466 4 0.0000 0.948 0.000 0.000 0.000 1.000
#> GSM99470 4 0.0000 0.948 0.000 0.000 0.000 1.000
#> GSM99472 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM99474 3 0.0000 0.978 0.000 0.000 1.000 0.000
#> GSM99476 4 0.0000 0.948 0.000 0.000 0.000 1.000
#> GSM99478 4 0.0000 0.948 0.000 0.000 0.000 1.000
#> GSM99480 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM99482 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM99484 4 0.0000 0.948 0.000 0.000 0.000 1.000
#> GSM99486 4 0.0000 0.948 0.000 0.000 0.000 1.000
#> GSM99488 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> GSM99490 4 0.0000 0.948 0.000 0.000 0.000 1.000
#> GSM99492 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM99494 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> GSM99524 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM99526 4 0.4431 0.571 0.000 0.000 0.304 0.696
#> GSM99528 4 0.0000 0.948 0.000 0.000 0.000 1.000
#> GSM99530 3 0.0000 0.978 0.000 0.000 1.000 0.000
#> GSM99532 3 0.0000 0.978 0.000 0.000 1.000 0.000
#> GSM99534 4 0.0000 0.948 0.000 0.000 0.000 1.000
#> GSM99536 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM99538 4 0.0000 0.948 0.000 0.000 0.000 1.000
#> GSM99540 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM99542 2 0.4103 0.655 0.000 0.744 0.000 0.256
#> GSM99544 4 0.4898 0.248 0.000 0.416 0.000 0.584
#> GSM99546 4 0.0000 0.948 0.000 0.000 0.000 1.000
#> GSM99548 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> GSM99550 4 0.3982 0.712 0.004 0.000 0.220 0.776
#> GSM99552 4 0.0000 0.948 0.000 0.000 0.000 1.000
#> GSM99554 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> GSM99556 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> GSM99558 4 0.0000 0.948 0.000 0.000 0.000 1.000
#> GSM99560 4 0.0000 0.948 0.000 0.000 0.000 1.000
#> GSM99562 3 0.0000 0.978 0.000 0.000 1.000 0.000
#> GSM99564 2 0.2345 0.877 0.000 0.900 0.000 0.100
#> GSM99572 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> GSM99576 1 0.0921 0.968 0.972 0.000 0.028 0.000
#> GSM99578 4 0.0000 0.948 0.000 0.000 0.000 1.000
#> GSM99580 3 0.2011 0.900 0.000 0.000 0.920 0.080
#> GSM99582 4 0.2868 0.822 0.000 0.000 0.136 0.864
#> GSM99584 4 0.0000 0.948 0.000 0.000 0.000 1.000
#> GSM99586 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM99588 4 0.0000 0.948 0.000 0.000 0.000 1.000
#> GSM99590 2 0.0000 0.974 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM99496 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000
#> GSM99502 1 0.0000 0.733 1.000 0.000 0.000 0.000 0.000
#> GSM99504 1 0.2929 0.769 0.820 0.000 0.000 0.000 0.180
#> GSM99506 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000
#> GSM99566 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000
#> GSM99574 1 0.0000 0.733 1.000 0.000 0.000 0.000 0.000
#> GSM99592 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000
#> GSM99594 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000
#> GSM99468 1 0.2929 0.769 0.820 0.000 0.000 0.000 0.180
#> GSM99498 1 0.2929 0.769 0.820 0.000 0.000 0.000 0.180
#> GSM99500 1 0.2929 0.769 0.820 0.000 0.000 0.000 0.180
#> GSM99508 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000
#> GSM99568 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000
#> GSM99596 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000
#> GSM99600 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000
#> GSM99458 1 0.2966 0.766 0.816 0.000 0.000 0.000 0.184
#> GSM99460 1 0.2929 0.769 0.820 0.000 0.000 0.000 0.180
#> GSM99510 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000
#> GSM99512 3 0.1270 0.909 0.000 0.000 0.948 0.052 0.000
#> GSM99514 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000
#> GSM99516 1 0.0000 0.733 1.000 0.000 0.000 0.000 0.000
#> GSM99518 1 0.2929 0.769 0.820 0.000 0.000 0.000 0.180
#> GSM99520 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000
#> GSM99522 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000
#> GSM99570 1 0.0000 0.733 1.000 0.000 0.000 0.000 0.000
#> GSM99598 1 0.0000 0.733 1.000 0.000 0.000 0.000 0.000
#> GSM99432 4 0.0162 0.941 0.000 0.000 0.000 0.996 0.004
#> GSM99434 3 0.4045 0.447 0.000 0.000 0.644 0.356 0.000
#> GSM99436 2 0.0162 0.963 0.000 0.996 0.000 0.000 0.004
#> GSM99438 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000
#> GSM99440 1 0.4192 -0.266 0.596 0.000 0.000 0.000 0.404
#> GSM99442 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000
#> GSM99444 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000
#> GSM99446 4 0.0162 0.941 0.000 0.000 0.000 0.996 0.004
#> GSM99448 4 0.0000 0.942 0.000 0.000 0.000 1.000 0.000
#> GSM99450 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000
#> GSM99452 1 0.1732 0.759 0.920 0.000 0.000 0.000 0.080
#> GSM99454 1 0.0000 0.733 1.000 0.000 0.000 0.000 0.000
#> GSM99456 5 0.3177 0.614 0.208 0.000 0.000 0.000 0.792
#> GSM99462 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000
#> GSM99464 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000
#> GSM99466 4 0.0000 0.942 0.000 0.000 0.000 1.000 0.000
#> GSM99470 4 0.3143 0.759 0.000 0.000 0.000 0.796 0.204
#> GSM99472 1 0.4138 0.494 0.616 0.000 0.000 0.000 0.384
#> GSM99474 3 0.1671 0.887 0.000 0.000 0.924 0.000 0.076
#> GSM99476 4 0.0000 0.942 0.000 0.000 0.000 1.000 0.000
#> GSM99478 4 0.0000 0.942 0.000 0.000 0.000 1.000 0.000
#> GSM99480 5 0.4150 0.581 0.388 0.000 0.000 0.000 0.612
#> GSM99482 1 0.3949 0.514 0.668 0.000 0.000 0.000 0.332
#> GSM99484 4 0.0000 0.942 0.000 0.000 0.000 1.000 0.000
#> GSM99486 4 0.0162 0.941 0.000 0.000 0.000 0.996 0.004
#> GSM99488 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000
#> GSM99490 4 0.0000 0.942 0.000 0.000 0.000 1.000 0.000
#> GSM99492 5 0.4150 0.581 0.388 0.000 0.000 0.000 0.612
#> GSM99494 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000
#> GSM99524 1 0.2230 0.764 0.884 0.000 0.000 0.000 0.116
#> GSM99526 4 0.3242 0.682 0.000 0.000 0.216 0.784 0.000
#> GSM99528 4 0.0000 0.942 0.000 0.000 0.000 1.000 0.000
#> GSM99530 3 0.2280 0.834 0.000 0.000 0.880 0.000 0.120
#> GSM99532 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000
#> GSM99534 4 0.0963 0.920 0.000 0.000 0.000 0.964 0.036
#> GSM99536 1 0.4287 -0.290 0.540 0.000 0.000 0.000 0.460
#> GSM99538 4 0.0000 0.942 0.000 0.000 0.000 1.000 0.000
#> GSM99540 1 0.2929 0.769 0.820 0.000 0.000 0.000 0.180
#> GSM99542 2 0.3534 0.629 0.000 0.744 0.000 0.256 0.000
#> GSM99544 4 0.4359 0.260 0.000 0.412 0.000 0.584 0.004
#> GSM99546 4 0.0794 0.926 0.000 0.000 0.000 0.972 0.028
#> GSM99548 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000
#> GSM99550 5 0.3543 0.478 0.000 0.000 0.060 0.112 0.828
#> GSM99552 4 0.0000 0.942 0.000 0.000 0.000 1.000 0.000
#> GSM99554 2 0.0162 0.963 0.000 0.996 0.000 0.000 0.004
#> GSM99556 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000
#> GSM99558 4 0.0000 0.942 0.000 0.000 0.000 1.000 0.000
#> GSM99560 4 0.0162 0.941 0.000 0.000 0.000 0.996 0.004
#> GSM99562 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000
#> GSM99564 2 0.2179 0.848 0.000 0.896 0.000 0.100 0.004
#> GSM99572 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000
#> GSM99576 5 0.4341 -0.120 0.404 0.000 0.004 0.000 0.592
#> GSM99578 4 0.0000 0.942 0.000 0.000 0.000 1.000 0.000
#> GSM99580 3 0.2074 0.848 0.000 0.000 0.896 0.104 0.000
#> GSM99582 4 0.3143 0.759 0.000 0.000 0.000 0.796 0.204
#> GSM99584 4 0.0162 0.941 0.000 0.000 0.000 0.996 0.004
#> GSM99586 5 0.3177 0.614 0.208 0.000 0.000 0.000 0.792
#> GSM99588 4 0.0000 0.942 0.000 0.000 0.000 1.000 0.000
#> GSM99590 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM99496 3 0.0146 0.945 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM99502 1 0.2260 0.801 0.860 0.000 0.000 0.000 0.000 0.140
#> GSM99504 1 0.0000 0.823 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99506 3 0.0146 0.945 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM99566 3 0.0146 0.945 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM99574 1 0.2260 0.801 0.860 0.000 0.000 0.000 0.000 0.140
#> GSM99592 3 0.0146 0.945 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM99594 3 0.1257 0.933 0.000 0.000 0.952 0.000 0.020 0.028
#> GSM99468 1 0.0000 0.823 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99498 1 0.0000 0.823 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99500 1 0.0713 0.823 0.972 0.000 0.000 0.000 0.000 0.028
#> GSM99508 3 0.0146 0.945 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM99568 3 0.0146 0.945 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM99596 3 0.0146 0.945 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM99600 2 0.2178 0.818 0.000 0.868 0.000 0.000 0.132 0.000
#> GSM99458 1 0.3482 0.322 0.684 0.000 0.000 0.000 0.316 0.000
#> GSM99460 1 0.0000 0.823 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99510 3 0.1421 0.929 0.000 0.000 0.944 0.000 0.028 0.028
#> GSM99512 3 0.2201 0.912 0.000 0.000 0.912 0.032 0.028 0.028
#> GSM99514 3 0.0146 0.945 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM99516 1 0.2219 0.803 0.864 0.000 0.000 0.000 0.000 0.136
#> GSM99518 1 0.0146 0.824 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM99520 3 0.1421 0.930 0.000 0.000 0.944 0.000 0.028 0.028
#> GSM99522 3 0.0146 0.945 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM99570 1 0.2219 0.804 0.864 0.000 0.000 0.000 0.000 0.136
#> GSM99598 1 0.2527 0.777 0.832 0.000 0.000 0.000 0.000 0.168
#> GSM99432 4 0.3547 0.675 0.000 0.000 0.000 0.696 0.300 0.004
#> GSM99434 3 0.4794 0.438 0.000 0.000 0.608 0.340 0.024 0.028
#> GSM99436 2 0.3636 0.679 0.000 0.676 0.000 0.000 0.320 0.004
#> GSM99438 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99440 6 0.2996 0.633 0.228 0.000 0.000 0.000 0.000 0.772
#> GSM99442 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99444 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99446 4 0.3619 0.662 0.000 0.000 0.000 0.680 0.316 0.004
#> GSM99448 4 0.0000 0.842 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM99450 3 0.0146 0.945 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM99452 1 0.4563 0.344 0.628 0.000 0.000 0.000 0.316 0.056
#> GSM99454 1 0.2219 0.803 0.864 0.000 0.000 0.000 0.000 0.136
#> GSM99456 6 0.2527 0.678 0.168 0.000 0.000 0.000 0.000 0.832
#> GSM99462 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99464 3 0.0146 0.945 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM99466 4 0.0000 0.842 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM99470 5 0.3620 0.391 0.000 0.000 0.000 0.352 0.648 0.000
#> GSM99472 5 0.3620 0.607 0.352 0.000 0.000 0.000 0.648 0.000
#> GSM99474 3 0.2274 0.912 0.036 0.000 0.908 0.000 0.028 0.028
#> GSM99476 4 0.0000 0.842 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM99478 4 0.0000 0.842 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM99480 6 0.0790 0.722 0.032 0.000 0.000 0.000 0.000 0.968
#> GSM99482 5 0.4219 0.600 0.320 0.000 0.000 0.000 0.648 0.032
#> GSM99484 4 0.0000 0.842 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM99486 4 0.3636 0.658 0.000 0.000 0.000 0.676 0.320 0.004
#> GSM99488 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99490 4 0.0000 0.842 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM99492 6 0.0790 0.722 0.032 0.000 0.000 0.000 0.000 0.968
#> GSM99494 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99524 1 0.4497 0.315 0.624 0.000 0.000 0.000 0.328 0.048
#> GSM99526 4 0.4713 0.591 0.000 0.000 0.168 0.720 0.084 0.028
#> GSM99528 4 0.0000 0.842 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM99530 3 0.2247 0.895 0.060 0.000 0.904 0.000 0.012 0.024
#> GSM99532 3 0.2466 0.901 0.052 0.000 0.896 0.000 0.024 0.028
#> GSM99534 4 0.0547 0.829 0.000 0.000 0.000 0.980 0.020 0.000
#> GSM99536 6 0.3847 0.293 0.456 0.000 0.000 0.000 0.000 0.544
#> GSM99538 4 0.0000 0.842 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM99540 1 0.0000 0.823 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99542 2 0.3175 0.599 0.000 0.744 0.000 0.256 0.000 0.000
#> GSM99544 4 0.6169 0.186 0.000 0.268 0.000 0.408 0.320 0.004
#> GSM99546 4 0.0717 0.828 0.000 0.000 0.000 0.976 0.016 0.008
#> GSM99548 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99550 5 0.6136 0.254 0.112 0.000 0.008 0.028 0.496 0.356
#> GSM99552 4 0.0000 0.842 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM99554 2 0.3636 0.679 0.000 0.676 0.000 0.000 0.320 0.004
#> GSM99556 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99558 4 0.0000 0.842 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM99560 4 0.3371 0.683 0.000 0.000 0.000 0.708 0.292 0.000
#> GSM99562 3 0.0146 0.945 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM99564 2 0.4713 0.619 0.000 0.620 0.000 0.056 0.320 0.004
#> GSM99572 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99576 5 0.4616 0.645 0.280 0.000 0.000 0.000 0.648 0.072
#> GSM99578 4 0.0000 0.842 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM99580 3 0.3249 0.835 0.000 0.000 0.840 0.104 0.028 0.028
#> GSM99582 4 0.4938 -0.119 0.000 0.000 0.020 0.488 0.464 0.028
#> GSM99584 4 0.3351 0.686 0.000 0.000 0.000 0.712 0.288 0.000
#> GSM99586 6 0.2527 0.678 0.168 0.000 0.000 0.000 0.000 0.832
#> GSM99588 4 0.0000 0.842 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM99590 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) cell.type(p) k
#> ATC:pam 84 7.45e-05 5.12e-04 2
#> ATC:pam 85 1.78e-04 4.92e-03 3
#> ATC:pam 84 5.18e-06 6.31e-04 4
#> ATC:pam 78 1.46e-07 9.16e-05 5
#> ATC:pam 76 2.94e-08 7.66e-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["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 21168 rows and 85 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 0.263 0.791 0.801 0.4017 0.545 0.545
#> 3 3 0.824 0.882 0.918 0.6432 0.750 0.554
#> 4 4 0.681 0.780 0.851 0.1163 0.882 0.662
#> 5 5 0.659 0.615 0.780 0.0430 0.843 0.527
#> 6 6 0.721 0.612 0.784 0.0438 0.961 0.848
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
#> GSM99496 2 0.4022 0.689 0.080 0.920
#> GSM99502 1 0.5842 0.964 0.860 0.140
#> GSM99504 1 0.5842 0.964 0.860 0.140
#> GSM99506 2 0.4022 0.689 0.080 0.920
#> GSM99566 2 0.4022 0.689 0.080 0.920
#> GSM99574 1 0.5842 0.964 0.860 0.140
#> GSM99592 2 0.1414 0.708 0.020 0.980
#> GSM99594 2 0.4022 0.689 0.080 0.920
#> GSM99468 1 0.5842 0.964 0.860 0.140
#> GSM99498 1 0.5842 0.964 0.860 0.140
#> GSM99500 1 0.5842 0.964 0.860 0.140
#> GSM99508 2 0.4022 0.689 0.080 0.920
#> GSM99568 2 0.4022 0.689 0.080 0.920
#> GSM99596 2 0.4431 0.694 0.092 0.908
#> GSM99600 2 0.9087 0.745 0.324 0.676
#> GSM99458 1 0.5842 0.964 0.860 0.140
#> GSM99460 1 0.5946 0.959 0.856 0.144
#> GSM99510 2 0.0672 0.710 0.008 0.992
#> GSM99512 2 0.3584 0.694 0.068 0.932
#> GSM99514 2 0.4022 0.689 0.080 0.920
#> GSM99516 1 0.5842 0.964 0.860 0.140
#> GSM99518 1 0.5842 0.964 0.860 0.140
#> GSM99520 2 0.4022 0.689 0.080 0.920
#> GSM99522 2 0.4022 0.689 0.080 0.920
#> GSM99570 1 0.5842 0.964 0.860 0.140
#> GSM99598 1 0.5842 0.964 0.860 0.140
#> GSM99432 2 0.7950 0.770 0.240 0.760
#> GSM99434 2 0.0672 0.710 0.008 0.992
#> GSM99436 2 0.7950 0.770 0.240 0.760
#> GSM99438 2 0.9580 0.715 0.380 0.620
#> GSM99440 1 0.5842 0.964 0.860 0.140
#> GSM99442 2 0.9580 0.715 0.380 0.620
#> GSM99444 2 0.9580 0.715 0.380 0.620
#> GSM99446 2 0.7950 0.770 0.240 0.760
#> GSM99448 2 0.0000 0.709 0.000 1.000
#> GSM99450 2 0.1184 0.709 0.016 0.984
#> GSM99452 1 0.5842 0.964 0.860 0.140
#> GSM99454 1 0.5842 0.964 0.860 0.140
#> GSM99456 1 0.5842 0.964 0.860 0.140
#> GSM99462 2 0.9580 0.715 0.380 0.620
#> GSM99464 2 0.9522 0.574 0.372 0.628
#> GSM99466 2 0.7950 0.770 0.240 0.760
#> GSM99470 1 0.8661 0.725 0.712 0.288
#> GSM99472 1 0.5842 0.964 0.860 0.140
#> GSM99474 2 0.4022 0.689 0.080 0.920
#> GSM99476 2 0.8016 0.768 0.244 0.756
#> GSM99478 2 0.7950 0.770 0.240 0.760
#> GSM99480 1 0.5842 0.964 0.860 0.140
#> GSM99482 1 0.5842 0.964 0.860 0.140
#> GSM99484 2 0.7950 0.770 0.240 0.760
#> GSM99486 2 0.7950 0.770 0.240 0.760
#> GSM99488 2 0.9580 0.715 0.380 0.620
#> GSM99490 2 0.8661 0.760 0.288 0.712
#> GSM99492 1 0.5842 0.964 0.860 0.140
#> GSM99494 2 0.9580 0.715 0.380 0.620
#> GSM99524 1 0.5842 0.964 0.860 0.140
#> GSM99526 2 0.8081 0.766 0.248 0.752
#> GSM99528 2 0.8608 0.743 0.284 0.716
#> GSM99530 2 0.9866 0.488 0.432 0.568
#> GSM99532 2 0.9000 0.710 0.316 0.684
#> GSM99534 1 0.9460 0.567 0.636 0.364
#> GSM99536 1 0.5842 0.964 0.860 0.140
#> GSM99538 2 0.7950 0.770 0.240 0.760
#> GSM99540 1 0.5842 0.964 0.860 0.140
#> GSM99542 1 0.9460 0.567 0.636 0.364
#> GSM99544 2 0.7950 0.770 0.240 0.760
#> GSM99546 2 0.7950 0.770 0.240 0.760
#> GSM99548 2 0.9608 0.712 0.384 0.616
#> GSM99550 1 0.7139 0.886 0.804 0.196
#> GSM99552 2 0.9000 0.712 0.316 0.684
#> GSM99554 2 0.8443 0.765 0.272 0.728
#> GSM99556 2 0.9580 0.715 0.380 0.620
#> GSM99558 2 0.8555 0.746 0.280 0.720
#> GSM99560 2 0.7950 0.770 0.240 0.760
#> GSM99562 2 0.4022 0.689 0.080 0.920
#> GSM99564 2 0.7950 0.770 0.240 0.760
#> GSM99572 2 0.9580 0.715 0.380 0.620
#> GSM99576 1 0.5842 0.964 0.860 0.140
#> GSM99578 2 0.7950 0.770 0.240 0.760
#> GSM99580 2 0.3879 0.691 0.076 0.924
#> GSM99582 2 0.8608 0.743 0.284 0.716
#> GSM99584 2 0.7950 0.770 0.240 0.760
#> GSM99586 1 0.5842 0.964 0.860 0.140
#> GSM99588 2 0.7950 0.770 0.240 0.760
#> GSM99590 2 0.9580 0.715 0.380 0.620
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM99496 3 0.2152 0.889 0.036 0.016 0.948
#> GSM99502 1 0.0000 0.974 1.000 0.000 0.000
#> GSM99504 1 0.0000 0.974 1.000 0.000 0.000
#> GSM99506 3 0.2152 0.889 0.036 0.016 0.948
#> GSM99566 3 0.2152 0.889 0.036 0.016 0.948
#> GSM99574 1 0.0000 0.974 1.000 0.000 0.000
#> GSM99592 3 0.3183 0.849 0.016 0.076 0.908
#> GSM99594 3 0.2152 0.889 0.036 0.016 0.948
#> GSM99468 1 0.0000 0.974 1.000 0.000 0.000
#> GSM99498 1 0.0000 0.974 1.000 0.000 0.000
#> GSM99500 1 0.0000 0.974 1.000 0.000 0.000
#> GSM99508 3 0.2269 0.889 0.040 0.016 0.944
#> GSM99568 3 0.2269 0.889 0.040 0.016 0.944
#> GSM99596 3 0.2152 0.889 0.036 0.016 0.948
#> GSM99600 2 0.0475 0.921 0.004 0.992 0.004
#> GSM99458 1 0.0424 0.970 0.992 0.000 0.008
#> GSM99460 1 0.1643 0.941 0.956 0.000 0.044
#> GSM99510 3 0.5158 0.728 0.004 0.232 0.764
#> GSM99512 3 0.2297 0.889 0.036 0.020 0.944
#> GSM99514 3 0.2152 0.889 0.036 0.016 0.948
#> GSM99516 1 0.0000 0.974 1.000 0.000 0.000
#> GSM99518 1 0.0000 0.974 1.000 0.000 0.000
#> GSM99520 3 0.2152 0.889 0.036 0.016 0.948
#> GSM99522 3 0.1529 0.884 0.040 0.000 0.960
#> GSM99570 1 0.0000 0.974 1.000 0.000 0.000
#> GSM99598 1 0.0000 0.974 1.000 0.000 0.000
#> GSM99432 2 0.2945 0.917 0.004 0.908 0.088
#> GSM99434 3 0.5158 0.728 0.004 0.232 0.764
#> GSM99436 2 0.2945 0.917 0.004 0.908 0.088
#> GSM99438 2 0.0000 0.919 0.000 1.000 0.000
#> GSM99440 1 0.0000 0.974 1.000 0.000 0.000
#> GSM99442 2 0.0000 0.919 0.000 1.000 0.000
#> GSM99444 2 0.0000 0.919 0.000 1.000 0.000
#> GSM99446 2 0.2550 0.919 0.024 0.936 0.040
#> GSM99448 3 0.3356 0.878 0.036 0.056 0.908
#> GSM99450 3 0.5115 0.729 0.004 0.228 0.768
#> GSM99452 1 0.0000 0.974 1.000 0.000 0.000
#> GSM99454 1 0.0000 0.974 1.000 0.000 0.000
#> GSM99456 1 0.0237 0.971 0.996 0.000 0.004
#> GSM99462 2 0.0000 0.919 0.000 1.000 0.000
#> GSM99464 3 0.5292 0.728 0.008 0.228 0.764
#> GSM99466 2 0.2926 0.913 0.036 0.924 0.040
#> GSM99470 1 0.8087 0.225 0.560 0.364 0.076
#> GSM99472 1 0.0424 0.970 0.992 0.000 0.008
#> GSM99474 3 0.2269 0.889 0.040 0.016 0.944
#> GSM99476 3 0.5158 0.728 0.004 0.232 0.764
#> GSM99478 2 0.2926 0.913 0.036 0.924 0.040
#> GSM99480 1 0.0000 0.974 1.000 0.000 0.000
#> GSM99482 1 0.0237 0.971 0.996 0.000 0.004
#> GSM99484 2 0.3832 0.889 0.036 0.888 0.076
#> GSM99486 2 0.2945 0.917 0.004 0.908 0.088
#> GSM99488 2 0.0000 0.919 0.000 1.000 0.000
#> GSM99490 2 0.2414 0.921 0.020 0.940 0.040
#> GSM99492 1 0.0000 0.974 1.000 0.000 0.000
#> GSM99494 2 0.0000 0.919 0.000 1.000 0.000
#> GSM99524 1 0.0000 0.974 1.000 0.000 0.000
#> GSM99526 3 0.5115 0.729 0.004 0.228 0.768
#> GSM99528 3 0.7128 0.427 0.036 0.344 0.620
#> GSM99530 3 0.2599 0.884 0.052 0.016 0.932
#> GSM99532 3 0.2269 0.889 0.040 0.016 0.944
#> GSM99534 2 0.6142 0.740 0.212 0.748 0.040
#> GSM99536 1 0.0000 0.974 1.000 0.000 0.000
#> GSM99538 2 0.2926 0.913 0.036 0.924 0.040
#> GSM99540 1 0.0000 0.974 1.000 0.000 0.000
#> GSM99542 2 0.6835 0.615 0.284 0.676 0.040
#> GSM99544 2 0.2772 0.919 0.004 0.916 0.080
#> GSM99546 3 0.5656 0.650 0.004 0.284 0.712
#> GSM99548 2 0.1289 0.923 0.000 0.968 0.032
#> GSM99550 1 0.3879 0.817 0.848 0.000 0.152
#> GSM99552 3 0.2689 0.885 0.036 0.032 0.932
#> GSM99554 2 0.2749 0.922 0.012 0.924 0.064
#> GSM99556 2 0.0000 0.919 0.000 1.000 0.000
#> GSM99558 3 0.4092 0.848 0.036 0.088 0.876
#> GSM99560 2 0.3030 0.916 0.004 0.904 0.092
#> GSM99562 3 0.1950 0.887 0.040 0.008 0.952
#> GSM99564 2 0.2945 0.917 0.004 0.908 0.088
#> GSM99572 2 0.0000 0.919 0.000 1.000 0.000
#> GSM99576 1 0.0424 0.970 0.992 0.000 0.008
#> GSM99578 2 0.4413 0.862 0.036 0.860 0.104
#> GSM99580 3 0.2297 0.889 0.036 0.020 0.944
#> GSM99582 3 0.6211 0.743 0.036 0.228 0.736
#> GSM99584 2 0.2945 0.917 0.004 0.908 0.088
#> GSM99586 1 0.0000 0.974 1.000 0.000 0.000
#> GSM99588 2 0.6597 0.624 0.036 0.696 0.268
#> GSM99590 2 0.0000 0.919 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM99496 3 0.0000 0.925 0.000 0.000 1.000 0.000
#> GSM99502 1 0.0000 0.929 1.000 0.000 0.000 0.000
#> GSM99504 1 0.2408 0.849 0.896 0.000 0.104 0.000
#> GSM99506 3 0.0000 0.925 0.000 0.000 1.000 0.000
#> GSM99566 3 0.0000 0.925 0.000 0.000 1.000 0.000
#> GSM99574 1 0.0000 0.929 1.000 0.000 0.000 0.000
#> GSM99592 3 0.4134 0.510 0.000 0.000 0.740 0.260
#> GSM99594 3 0.0000 0.925 0.000 0.000 1.000 0.000
#> GSM99468 1 0.0000 0.929 1.000 0.000 0.000 0.000
#> GSM99498 1 0.0000 0.929 1.000 0.000 0.000 0.000
#> GSM99500 1 0.0000 0.929 1.000 0.000 0.000 0.000
#> GSM99508 3 0.0000 0.925 0.000 0.000 1.000 0.000
#> GSM99568 3 0.0000 0.925 0.000 0.000 1.000 0.000
#> GSM99596 3 0.0000 0.925 0.000 0.000 1.000 0.000
#> GSM99600 2 0.0336 0.828 0.000 0.992 0.000 0.008
#> GSM99458 1 0.1389 0.900 0.952 0.000 0.048 0.000
#> GSM99460 1 0.6894 0.379 0.536 0.000 0.120 0.344
#> GSM99510 4 0.4855 0.487 0.000 0.000 0.400 0.600
#> GSM99512 3 0.0336 0.920 0.000 0.000 0.992 0.008
#> GSM99514 3 0.0000 0.925 0.000 0.000 1.000 0.000
#> GSM99516 1 0.0000 0.929 1.000 0.000 0.000 0.000
#> GSM99518 1 0.0000 0.929 1.000 0.000 0.000 0.000
#> GSM99520 3 0.0000 0.925 0.000 0.000 1.000 0.000
#> GSM99522 3 0.0336 0.920 0.000 0.000 0.992 0.008
#> GSM99570 1 0.0000 0.929 1.000 0.000 0.000 0.000
#> GSM99598 1 0.0000 0.929 1.000 0.000 0.000 0.000
#> GSM99432 4 0.4193 0.610 0.000 0.268 0.000 0.732
#> GSM99434 4 0.4843 0.493 0.000 0.000 0.396 0.604
#> GSM99436 4 0.4888 0.390 0.000 0.412 0.000 0.588
#> GSM99438 2 0.0000 0.829 0.000 1.000 0.000 0.000
#> GSM99440 1 0.0000 0.929 1.000 0.000 0.000 0.000
#> GSM99442 2 0.0000 0.829 0.000 1.000 0.000 0.000
#> GSM99444 2 0.0000 0.829 0.000 1.000 0.000 0.000
#> GSM99446 2 0.2011 0.806 0.000 0.920 0.000 0.080
#> GSM99448 3 0.4008 0.641 0.000 0.000 0.756 0.244
#> GSM99450 4 0.4866 0.479 0.000 0.000 0.404 0.596
#> GSM99452 1 0.0000 0.929 1.000 0.000 0.000 0.000
#> GSM99454 1 0.0000 0.929 1.000 0.000 0.000 0.000
#> GSM99456 1 0.4072 0.782 0.748 0.000 0.000 0.252
#> GSM99462 2 0.0000 0.829 0.000 1.000 0.000 0.000
#> GSM99464 4 0.4669 0.577 0.100 0.000 0.104 0.796
#> GSM99466 2 0.6397 0.635 0.000 0.652 0.164 0.184
#> GSM99470 1 0.4466 0.699 0.784 0.180 0.000 0.036
#> GSM99472 1 0.0000 0.929 1.000 0.000 0.000 0.000
#> GSM99474 3 0.0000 0.925 0.000 0.000 1.000 0.000
#> GSM99476 4 0.3764 0.642 0.000 0.000 0.216 0.784
#> GSM99478 2 0.6295 0.645 0.000 0.660 0.196 0.144
#> GSM99480 1 0.3266 0.845 0.832 0.000 0.000 0.168
#> GSM99482 1 0.0000 0.929 1.000 0.000 0.000 0.000
#> GSM99484 2 0.6251 0.649 0.000 0.664 0.196 0.140
#> GSM99486 4 0.4605 0.501 0.000 0.336 0.000 0.664
#> GSM99488 2 0.0000 0.829 0.000 1.000 0.000 0.000
#> GSM99490 2 0.2408 0.789 0.000 0.896 0.000 0.104
#> GSM99492 1 0.3311 0.843 0.828 0.000 0.000 0.172
#> GSM99494 2 0.0000 0.829 0.000 1.000 0.000 0.000
#> GSM99524 1 0.0000 0.929 1.000 0.000 0.000 0.000
#> GSM99526 4 0.3649 0.645 0.000 0.000 0.204 0.796
#> GSM99528 2 0.6690 0.572 0.000 0.608 0.248 0.144
#> GSM99530 3 0.6221 0.515 0.100 0.000 0.644 0.256
#> GSM99532 3 0.0469 0.916 0.000 0.000 0.988 0.012
#> GSM99534 2 0.4839 0.656 0.200 0.756 0.000 0.044
#> GSM99536 1 0.0000 0.929 1.000 0.000 0.000 0.000
#> GSM99538 2 0.6585 0.612 0.000 0.632 0.180 0.188
#> GSM99540 1 0.1022 0.911 0.968 0.000 0.032 0.000
#> GSM99542 2 0.4175 0.663 0.200 0.784 0.000 0.016
#> GSM99544 4 0.4331 0.587 0.000 0.288 0.000 0.712
#> GSM99546 4 0.3751 0.656 0.000 0.004 0.196 0.800
#> GSM99548 2 0.0469 0.827 0.000 0.988 0.000 0.012
#> GSM99550 1 0.4661 0.675 0.652 0.000 0.000 0.348
#> GSM99552 3 0.2345 0.830 0.000 0.000 0.900 0.100
#> GSM99554 2 0.3649 0.683 0.000 0.796 0.000 0.204
#> GSM99556 2 0.0000 0.829 0.000 1.000 0.000 0.000
#> GSM99558 3 0.2973 0.784 0.000 0.000 0.856 0.144
#> GSM99560 4 0.4222 0.607 0.000 0.272 0.000 0.728
#> GSM99562 3 0.0000 0.925 0.000 0.000 1.000 0.000
#> GSM99564 4 0.4250 0.602 0.000 0.276 0.000 0.724
#> GSM99572 2 0.0000 0.829 0.000 1.000 0.000 0.000
#> GSM99576 1 0.0592 0.923 0.984 0.000 0.000 0.016
#> GSM99578 2 0.4800 0.719 0.000 0.760 0.196 0.044
#> GSM99580 3 0.0000 0.925 0.000 0.000 1.000 0.000
#> GSM99582 4 0.4790 0.478 0.000 0.000 0.380 0.620
#> GSM99584 4 0.4193 0.610 0.000 0.268 0.000 0.732
#> GSM99586 1 0.3356 0.840 0.824 0.000 0.000 0.176
#> GSM99588 2 0.4716 0.721 0.000 0.764 0.196 0.040
#> GSM99590 2 0.0000 0.829 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM99496 3 0.3274 0.6346 0.000 0.000 0.780 0.000 0.220
#> GSM99502 1 0.0290 0.8134 0.992 0.000 0.000 0.000 0.008
#> GSM99504 1 0.1668 0.7930 0.940 0.000 0.028 0.000 0.032
#> GSM99506 3 0.3274 0.6346 0.000 0.000 0.780 0.000 0.220
#> GSM99566 3 0.3274 0.6346 0.000 0.000 0.780 0.000 0.220
#> GSM99574 1 0.0290 0.8134 0.992 0.000 0.000 0.000 0.008
#> GSM99592 3 0.4555 0.6234 0.000 0.000 0.732 0.200 0.068
#> GSM99594 3 0.1965 0.7020 0.000 0.000 0.904 0.000 0.096
#> GSM99468 1 0.1168 0.8077 0.960 0.008 0.000 0.000 0.032
#> GSM99498 1 0.1168 0.8077 0.960 0.008 0.000 0.000 0.032
#> GSM99500 1 0.1329 0.8067 0.956 0.008 0.004 0.000 0.032
#> GSM99508 3 0.1430 0.7163 0.000 0.000 0.944 0.004 0.052
#> GSM99568 3 0.1281 0.7216 0.000 0.000 0.956 0.012 0.032
#> GSM99596 3 0.1270 0.7128 0.000 0.000 0.948 0.000 0.052
#> GSM99600 4 0.4291 0.2079 0.000 0.464 0.000 0.536 0.000
#> GSM99458 1 0.5608 0.3340 0.712 0.008 0.128 0.028 0.124
#> GSM99460 1 0.7513 -0.3106 0.532 0.016 0.140 0.072 0.240
#> GSM99510 3 0.5903 0.4886 0.000 0.000 0.548 0.332 0.120
#> GSM99512 3 0.1981 0.7123 0.000 0.000 0.924 0.028 0.048
#> GSM99514 3 0.3274 0.6346 0.000 0.000 0.780 0.000 0.220
#> GSM99516 1 0.0290 0.8134 0.992 0.000 0.000 0.000 0.008
#> GSM99518 1 0.1168 0.8077 0.960 0.008 0.000 0.000 0.032
#> GSM99520 3 0.1121 0.7135 0.000 0.000 0.956 0.000 0.044
#> GSM99522 3 0.2522 0.7055 0.000 0.000 0.896 0.052 0.052
#> GSM99570 1 0.0693 0.8107 0.980 0.012 0.000 0.000 0.008
#> GSM99598 1 0.0290 0.8134 0.992 0.000 0.000 0.000 0.008
#> GSM99432 4 0.0992 0.6772 0.000 0.008 0.000 0.968 0.024
#> GSM99434 3 0.5873 0.4766 0.000 0.000 0.540 0.348 0.112
#> GSM99436 4 0.1579 0.6888 0.000 0.032 0.000 0.944 0.024
#> GSM99438 2 0.1043 0.8860 0.000 0.960 0.000 0.040 0.000
#> GSM99440 1 0.0290 0.8134 0.992 0.000 0.000 0.000 0.008
#> GSM99442 2 0.1671 0.8845 0.000 0.924 0.000 0.076 0.000
#> GSM99444 2 0.1043 0.8860 0.000 0.960 0.000 0.040 0.000
#> GSM99446 4 0.3967 0.5697 0.000 0.264 0.000 0.724 0.012
#> GSM99448 4 0.5154 0.3670 0.000 0.000 0.372 0.580 0.048
#> GSM99450 3 0.5903 0.4913 0.000 0.000 0.548 0.332 0.120
#> GSM99452 1 0.0404 0.8129 0.988 0.012 0.000 0.000 0.000
#> GSM99454 1 0.0290 0.8143 0.992 0.000 0.000 0.000 0.008
#> GSM99456 1 0.4288 0.2447 0.612 0.000 0.000 0.004 0.384
#> GSM99462 2 0.1043 0.8860 0.000 0.960 0.000 0.040 0.000
#> GSM99464 3 0.7029 0.3293 0.000 0.020 0.436 0.340 0.204
#> GSM99466 4 0.4519 0.6968 0.000 0.060 0.084 0.796 0.060
#> GSM99470 4 0.8982 -0.3793 0.272 0.036 0.124 0.308 0.260
#> GSM99472 1 0.6445 0.0451 0.624 0.012 0.128 0.028 0.208
#> GSM99474 3 0.0798 0.7212 0.000 0.000 0.976 0.016 0.008
#> GSM99476 3 0.6201 0.4315 0.000 0.008 0.500 0.380 0.112
#> GSM99478 4 0.6259 0.6548 0.000 0.116 0.108 0.664 0.112
#> GSM99480 1 0.3480 0.5471 0.752 0.000 0.000 0.000 0.248
#> GSM99482 1 0.1012 0.8093 0.968 0.012 0.000 0.000 0.020
#> GSM99484 4 0.6809 0.6220 0.000 0.128 0.108 0.608 0.156
#> GSM99486 4 0.1661 0.6897 0.000 0.036 0.000 0.940 0.024
#> GSM99488 2 0.1197 0.8846 0.000 0.952 0.000 0.048 0.000
#> GSM99490 4 0.4691 0.5646 0.000 0.276 0.000 0.680 0.044
#> GSM99492 1 0.3480 0.5471 0.752 0.000 0.000 0.000 0.248
#> GSM99494 2 0.1043 0.8860 0.000 0.960 0.000 0.040 0.000
#> GSM99524 1 0.1281 0.8075 0.956 0.012 0.000 0.000 0.032
#> GSM99526 3 0.6267 0.4264 0.000 0.008 0.496 0.376 0.120
#> GSM99528 4 0.7756 0.3699 0.000 0.072 0.304 0.408 0.216
#> GSM99530 3 0.3314 0.6527 0.000 0.020 0.852 0.020 0.108
#> GSM99532 3 0.2632 0.6946 0.000 0.000 0.888 0.040 0.072
#> GSM99534 4 0.7068 0.4732 0.140 0.164 0.000 0.580 0.116
#> GSM99536 1 0.0609 0.8106 0.980 0.000 0.000 0.000 0.020
#> GSM99538 4 0.4702 0.6931 0.000 0.052 0.108 0.780 0.060
#> GSM99540 1 0.1251 0.8059 0.956 0.008 0.000 0.000 0.036
#> GSM99542 2 0.7659 0.3516 0.140 0.488 0.000 0.244 0.128
#> GSM99544 4 0.1661 0.6894 0.000 0.036 0.000 0.940 0.024
#> GSM99546 4 0.4866 0.3906 0.000 0.004 0.148 0.732 0.116
#> GSM99548 2 0.3789 0.7265 0.000 0.768 0.000 0.212 0.020
#> GSM99550 5 0.7573 0.0000 0.244 0.016 0.128 0.084 0.528
#> GSM99552 3 0.4719 0.3826 0.000 0.000 0.696 0.248 0.056
#> GSM99554 4 0.3812 0.6173 0.000 0.204 0.000 0.772 0.024
#> GSM99556 2 0.2471 0.8481 0.000 0.864 0.000 0.136 0.000
#> GSM99558 4 0.5405 0.4516 0.000 0.000 0.380 0.556 0.064
#> GSM99560 4 0.0798 0.6637 0.000 0.008 0.000 0.976 0.016
#> GSM99562 3 0.1399 0.7206 0.000 0.000 0.952 0.020 0.028
#> GSM99564 4 0.1403 0.6862 0.000 0.024 0.000 0.952 0.024
#> GSM99572 2 0.2732 0.8207 0.000 0.840 0.000 0.160 0.000
#> GSM99576 1 0.5676 0.1179 0.632 0.000 0.124 0.004 0.240
#> GSM99578 4 0.7117 0.5883 0.000 0.172 0.108 0.572 0.148
#> GSM99580 3 0.0451 0.7198 0.000 0.000 0.988 0.004 0.008
#> GSM99582 3 0.5427 0.5576 0.000 0.000 0.636 0.260 0.104
#> GSM99584 4 0.1106 0.6800 0.000 0.012 0.000 0.964 0.024
#> GSM99586 1 0.3586 0.5211 0.736 0.000 0.000 0.000 0.264
#> GSM99588 4 0.7089 0.5991 0.000 0.152 0.108 0.576 0.164
#> GSM99590 2 0.1671 0.8845 0.000 0.924 0.000 0.076 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM99496 3 0.3136 0.626749 0.000 0.000 0.796 0.000 0.188 0.016
#> GSM99502 1 0.0000 0.805918 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99504 1 0.1196 0.796206 0.952 0.000 0.008 0.000 0.000 0.040
#> GSM99506 3 0.3136 0.626749 0.000 0.000 0.796 0.000 0.188 0.016
#> GSM99566 3 0.3136 0.626749 0.000 0.000 0.796 0.000 0.188 0.016
#> GSM99574 1 0.0000 0.805918 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99592 3 0.5097 0.228502 0.000 0.004 0.664 0.080 0.232 0.020
#> GSM99594 3 0.1367 0.707474 0.000 0.000 0.944 0.000 0.044 0.012
#> GSM99468 1 0.0865 0.800045 0.964 0.000 0.000 0.000 0.000 0.036
#> GSM99498 1 0.0937 0.799211 0.960 0.000 0.000 0.000 0.000 0.040
#> GSM99500 1 0.0937 0.799211 0.960 0.000 0.000 0.000 0.000 0.040
#> GSM99508 3 0.0405 0.718534 0.000 0.000 0.988 0.000 0.004 0.008
#> GSM99568 3 0.0405 0.718283 0.000 0.000 0.988 0.008 0.000 0.004
#> GSM99596 3 0.0806 0.717024 0.000 0.000 0.972 0.000 0.020 0.008
#> GSM99600 4 0.4301 0.512286 0.000 0.392 0.000 0.584 0.000 0.024
#> GSM99458 1 0.4958 0.406420 0.704 0.000 0.044 0.008 0.048 0.196
#> GSM99460 1 0.7389 -0.176446 0.464 0.000 0.096 0.024 0.212 0.204
#> GSM99510 3 0.6328 -0.335329 0.000 0.016 0.488 0.116 0.352 0.028
#> GSM99512 3 0.1693 0.706974 0.000 0.000 0.936 0.012 0.020 0.032
#> GSM99514 3 0.3136 0.626749 0.000 0.000 0.796 0.000 0.188 0.016
#> GSM99516 1 0.0000 0.805918 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99518 1 0.0790 0.800768 0.968 0.000 0.000 0.000 0.000 0.032
#> GSM99520 3 0.0146 0.718402 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM99522 3 0.1777 0.703771 0.000 0.000 0.932 0.024 0.032 0.012
#> GSM99570 1 0.2697 0.677265 0.812 0.000 0.000 0.000 0.000 0.188
#> GSM99598 1 0.0146 0.805594 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM99432 4 0.2520 0.702035 0.000 0.152 0.000 0.844 0.004 0.000
#> GSM99434 3 0.6240 -0.418134 0.000 0.016 0.464 0.116 0.384 0.020
#> GSM99436 4 0.2520 0.702035 0.000 0.152 0.000 0.844 0.004 0.000
#> GSM99438 2 0.0000 0.935681 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99440 1 0.0363 0.805027 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM99442 2 0.0363 0.934461 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM99444 2 0.0000 0.935681 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99446 4 0.2912 0.675164 0.000 0.216 0.000 0.784 0.000 0.000
#> GSM99448 4 0.5512 0.585199 0.000 0.008 0.176 0.660 0.032 0.124
#> GSM99450 3 0.5535 -0.163477 0.000 0.000 0.548 0.124 0.320 0.008
#> GSM99452 1 0.2823 0.667630 0.796 0.000 0.000 0.000 0.000 0.204
#> GSM99454 1 0.0000 0.805918 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99456 1 0.5358 0.425908 0.596 0.000 0.000 0.008 0.272 0.124
#> GSM99462 2 0.0000 0.935681 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99464 5 0.5741 0.513280 0.000 0.000 0.296 0.112 0.564 0.028
#> GSM99466 4 0.4526 0.676719 0.000 0.024 0.072 0.752 0.008 0.144
#> GSM99470 6 0.3429 0.752883 0.128 0.000 0.028 0.012 0.008 0.824
#> GSM99472 6 0.4062 0.864199 0.236 0.000 0.028 0.000 0.012 0.724
#> GSM99474 3 0.1003 0.716241 0.000 0.000 0.964 0.020 0.000 0.016
#> GSM99476 5 0.6524 0.415824 0.000 0.028 0.404 0.116 0.428 0.024
#> GSM99478 4 0.4532 0.660315 0.000 0.028 0.036 0.716 0.004 0.216
#> GSM99480 1 0.3835 0.648782 0.756 0.000 0.000 0.000 0.188 0.056
#> GSM99482 1 0.3765 0.187294 0.596 0.000 0.000 0.000 0.000 0.404
#> GSM99484 4 0.5386 0.636666 0.000 0.048 0.028 0.664 0.032 0.228
#> GSM99486 4 0.2520 0.702035 0.000 0.152 0.000 0.844 0.004 0.000
#> GSM99488 2 0.0000 0.935681 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99490 4 0.5798 0.582231 0.000 0.312 0.008 0.532 0.004 0.144
#> GSM99492 1 0.3865 0.644872 0.752 0.000 0.000 0.000 0.192 0.056
#> GSM99494 2 0.0000 0.935681 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM99524 1 0.3175 0.623539 0.744 0.000 0.000 0.000 0.000 0.256
#> GSM99526 5 0.6304 0.470406 0.000 0.000 0.376 0.116 0.456 0.052
#> GSM99528 4 0.6311 0.437520 0.000 0.000 0.252 0.448 0.016 0.284
#> GSM99530 3 0.3438 0.529455 0.000 0.000 0.788 0.020 0.184 0.008
#> GSM99532 3 0.1714 0.706154 0.000 0.000 0.936 0.024 0.024 0.016
#> GSM99534 4 0.6446 0.450187 0.036 0.140 0.000 0.472 0.008 0.344
#> GSM99536 1 0.0000 0.805918 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99538 4 0.4158 0.688435 0.000 0.024 0.056 0.776 0.004 0.140
#> GSM99540 1 0.0865 0.800073 0.964 0.000 0.000 0.000 0.000 0.036
#> GSM99542 2 0.5394 0.315770 0.036 0.552 0.000 0.040 0.004 0.368
#> GSM99544 4 0.2416 0.700967 0.000 0.156 0.000 0.844 0.000 0.000
#> GSM99546 4 0.5956 0.163777 0.000 0.000 0.048 0.480 0.392 0.080
#> GSM99548 2 0.2394 0.864097 0.000 0.900 0.008 0.052 0.004 0.036
#> GSM99550 5 0.6496 -0.460868 0.080 0.000 0.048 0.024 0.444 0.404
#> GSM99552 3 0.4912 0.344207 0.000 0.000 0.680 0.148 0.008 0.164
#> GSM99554 4 0.3240 0.658962 0.000 0.244 0.000 0.752 0.000 0.004
#> GSM99556 2 0.0603 0.931185 0.000 0.980 0.000 0.016 0.000 0.004
#> GSM99558 4 0.5245 0.593179 0.000 0.000 0.192 0.636 0.008 0.164
#> GSM99560 4 0.4978 0.588173 0.000 0.008 0.020 0.700 0.184 0.088
#> GSM99562 3 0.1194 0.711230 0.000 0.000 0.956 0.004 0.032 0.008
#> GSM99564 4 0.2520 0.702035 0.000 0.152 0.000 0.844 0.004 0.000
#> GSM99572 2 0.0806 0.926178 0.000 0.972 0.000 0.020 0.000 0.008
#> GSM99576 6 0.4290 0.833079 0.260 0.000 0.028 0.000 0.016 0.696
#> GSM99578 4 0.5976 0.612052 0.000 0.096 0.028 0.616 0.032 0.228
#> GSM99580 3 0.1265 0.709299 0.000 0.000 0.948 0.000 0.008 0.044
#> GSM99582 3 0.5881 0.000291 0.000 0.000 0.572 0.140 0.256 0.032
#> GSM99584 4 0.2631 0.701756 0.000 0.152 0.000 0.840 0.008 0.000
#> GSM99586 1 0.3896 0.640530 0.748 0.000 0.000 0.000 0.196 0.056
#> GSM99588 4 0.6070 0.624352 0.000 0.084 0.048 0.616 0.028 0.224
#> GSM99590 2 0.0363 0.934461 0.000 0.988 0.000 0.012 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) cell.type(p) k
#> ATC:mclust 84 2.10e-01 0.40818 2
#> ATC:mclust 83 3.19e-04 0.00790 3
#> ATC:mclust 79 7.25e-05 0.00552 4
#> ATC:mclust 64 2.38e-05 0.00339 5
#> ATC:mclust 68 7.73e-05 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["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 21168 rows and 85 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.962 0.984 0.4946 0.506 0.506
#> 3 3 1.000 0.979 0.990 0.3611 0.759 0.552
#> 4 4 0.819 0.804 0.899 0.1020 0.887 0.674
#> 5 5 0.752 0.695 0.843 0.0441 0.956 0.835
#> 6 6 0.745 0.666 0.807 0.0360 0.939 0.761
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
#> GSM99496 1 0.0000 0.983 1.000 0.000
#> GSM99502 1 0.0000 0.983 1.000 0.000
#> GSM99504 1 0.0000 0.983 1.000 0.000
#> GSM99506 1 0.0000 0.983 1.000 0.000
#> GSM99566 1 0.0000 0.983 1.000 0.000
#> GSM99574 1 0.0000 0.983 1.000 0.000
#> GSM99592 1 0.0376 0.980 0.996 0.004
#> GSM99594 1 0.0000 0.983 1.000 0.000
#> GSM99468 1 0.0000 0.983 1.000 0.000
#> GSM99498 1 0.0000 0.983 1.000 0.000
#> GSM99500 1 0.0000 0.983 1.000 0.000
#> GSM99508 1 0.0000 0.983 1.000 0.000
#> GSM99568 1 0.0000 0.983 1.000 0.000
#> GSM99596 1 0.0000 0.983 1.000 0.000
#> GSM99600 2 0.0000 0.983 0.000 1.000
#> GSM99458 1 0.0000 0.983 1.000 0.000
#> GSM99460 1 0.0000 0.983 1.000 0.000
#> GSM99510 1 0.0938 0.973 0.988 0.012
#> GSM99512 1 0.5519 0.847 0.872 0.128
#> GSM99514 1 0.0000 0.983 1.000 0.000
#> GSM99516 1 0.0000 0.983 1.000 0.000
#> GSM99518 1 0.0000 0.983 1.000 0.000
#> GSM99520 1 0.0000 0.983 1.000 0.000
#> GSM99522 1 0.0000 0.983 1.000 0.000
#> GSM99570 1 0.0000 0.983 1.000 0.000
#> GSM99598 1 0.0000 0.983 1.000 0.000
#> GSM99432 2 0.0000 0.983 0.000 1.000
#> GSM99434 1 0.7602 0.716 0.780 0.220
#> GSM99436 2 0.0000 0.983 0.000 1.000
#> GSM99438 2 0.0000 0.983 0.000 1.000
#> GSM99440 1 0.0000 0.983 1.000 0.000
#> GSM99442 2 0.0000 0.983 0.000 1.000
#> GSM99444 2 0.0000 0.983 0.000 1.000
#> GSM99446 2 0.0000 0.983 0.000 1.000
#> GSM99448 2 0.0000 0.983 0.000 1.000
#> GSM99450 1 0.0000 0.983 1.000 0.000
#> GSM99452 1 0.0000 0.983 1.000 0.000
#> GSM99454 1 0.0000 0.983 1.000 0.000
#> GSM99456 1 0.0000 0.983 1.000 0.000
#> GSM99462 2 0.0000 0.983 0.000 1.000
#> GSM99464 1 0.0000 0.983 1.000 0.000
#> GSM99466 2 0.0000 0.983 0.000 1.000
#> GSM99470 1 0.9732 0.318 0.596 0.404
#> GSM99472 1 0.0000 0.983 1.000 0.000
#> GSM99474 1 0.0000 0.983 1.000 0.000
#> GSM99476 2 0.0000 0.983 0.000 1.000
#> GSM99478 2 0.0000 0.983 0.000 1.000
#> GSM99480 1 0.0000 0.983 1.000 0.000
#> GSM99482 1 0.0000 0.983 1.000 0.000
#> GSM99484 2 0.0000 0.983 0.000 1.000
#> GSM99486 2 0.0000 0.983 0.000 1.000
#> GSM99488 2 0.0000 0.983 0.000 1.000
#> GSM99490 2 0.0000 0.983 0.000 1.000
#> GSM99492 1 0.0000 0.983 1.000 0.000
#> GSM99494 2 0.0000 0.983 0.000 1.000
#> GSM99524 1 0.0000 0.983 1.000 0.000
#> GSM99526 2 0.9044 0.525 0.320 0.680
#> GSM99528 2 0.0938 0.973 0.012 0.988
#> GSM99530 1 0.0000 0.983 1.000 0.000
#> GSM99532 1 0.0000 0.983 1.000 0.000
#> GSM99534 2 0.0000 0.983 0.000 1.000
#> GSM99536 1 0.0000 0.983 1.000 0.000
#> GSM99538 2 0.0000 0.983 0.000 1.000
#> GSM99540 1 0.0000 0.983 1.000 0.000
#> GSM99542 2 0.0000 0.983 0.000 1.000
#> GSM99544 2 0.0000 0.983 0.000 1.000
#> GSM99546 2 0.3431 0.922 0.064 0.936
#> GSM99548 2 0.0000 0.983 0.000 1.000
#> GSM99550 1 0.0000 0.983 1.000 0.000
#> GSM99552 2 0.6623 0.790 0.172 0.828
#> GSM99554 2 0.0000 0.983 0.000 1.000
#> GSM99556 2 0.0000 0.983 0.000 1.000
#> GSM99558 2 0.0000 0.983 0.000 1.000
#> GSM99560 2 0.0000 0.983 0.000 1.000
#> GSM99562 1 0.0000 0.983 1.000 0.000
#> GSM99564 2 0.0000 0.983 0.000 1.000
#> GSM99572 2 0.0000 0.983 0.000 1.000
#> GSM99576 1 0.0000 0.983 1.000 0.000
#> GSM99578 2 0.0000 0.983 0.000 1.000
#> GSM99580 1 0.1843 0.958 0.972 0.028
#> GSM99582 1 0.0000 0.983 1.000 0.000
#> GSM99584 2 0.0000 0.983 0.000 1.000
#> GSM99586 1 0.0000 0.983 1.000 0.000
#> GSM99588 2 0.0000 0.983 0.000 1.000
#> GSM99590 2 0.0000 0.983 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM99496 3 0.0000 0.984 0.000 0.000 1.000
#> GSM99502 1 0.0000 0.994 1.000 0.000 0.000
#> GSM99504 1 0.0747 0.979 0.984 0.000 0.016
#> GSM99506 3 0.0000 0.984 0.000 0.000 1.000
#> GSM99566 3 0.0000 0.984 0.000 0.000 1.000
#> GSM99574 1 0.0000 0.994 1.000 0.000 0.000
#> GSM99592 3 0.0000 0.984 0.000 0.000 1.000
#> GSM99594 3 0.0000 0.984 0.000 0.000 1.000
#> GSM99468 1 0.0000 0.994 1.000 0.000 0.000
#> GSM99498 1 0.0000 0.994 1.000 0.000 0.000
#> GSM99500 1 0.0000 0.994 1.000 0.000 0.000
#> GSM99508 3 0.0000 0.984 0.000 0.000 1.000
#> GSM99568 3 0.0000 0.984 0.000 0.000 1.000
#> GSM99596 3 0.0000 0.984 0.000 0.000 1.000
#> GSM99600 2 0.0000 0.991 0.000 1.000 0.000
#> GSM99458 1 0.0000 0.994 1.000 0.000 0.000
#> GSM99460 1 0.0000 0.994 1.000 0.000 0.000
#> GSM99510 3 0.0000 0.984 0.000 0.000 1.000
#> GSM99512 3 0.0000 0.984 0.000 0.000 1.000
#> GSM99514 3 0.0000 0.984 0.000 0.000 1.000
#> GSM99516 1 0.0000 0.994 1.000 0.000 0.000
#> GSM99518 1 0.0000 0.994 1.000 0.000 0.000
#> GSM99520 3 0.0000 0.984 0.000 0.000 1.000
#> GSM99522 3 0.0000 0.984 0.000 0.000 1.000
#> GSM99570 1 0.0000 0.994 1.000 0.000 0.000
#> GSM99598 1 0.0000 0.994 1.000 0.000 0.000
#> GSM99432 2 0.1289 0.963 0.000 0.968 0.032
#> GSM99434 3 0.0000 0.984 0.000 0.000 1.000
#> GSM99436 2 0.0000 0.991 0.000 1.000 0.000
#> GSM99438 2 0.0000 0.991 0.000 1.000 0.000
#> GSM99440 1 0.0000 0.994 1.000 0.000 0.000
#> GSM99442 2 0.0000 0.991 0.000 1.000 0.000
#> GSM99444 2 0.0000 0.991 0.000 1.000 0.000
#> GSM99446 2 0.0000 0.991 0.000 1.000 0.000
#> GSM99448 3 0.0000 0.984 0.000 0.000 1.000
#> GSM99450 3 0.0000 0.984 0.000 0.000 1.000
#> GSM99452 1 0.0000 0.994 1.000 0.000 0.000
#> GSM99454 1 0.0000 0.994 1.000 0.000 0.000
#> GSM99456 1 0.0000 0.994 1.000 0.000 0.000
#> GSM99462 2 0.0000 0.991 0.000 1.000 0.000
#> GSM99464 3 0.0747 0.973 0.016 0.000 0.984
#> GSM99466 2 0.0237 0.987 0.000 0.996 0.004
#> GSM99470 1 0.3551 0.848 0.868 0.132 0.000
#> GSM99472 1 0.0000 0.994 1.000 0.000 0.000
#> GSM99474 3 0.0000 0.984 0.000 0.000 1.000
#> GSM99476 3 0.0000 0.984 0.000 0.000 1.000
#> GSM99478 2 0.0000 0.991 0.000 1.000 0.000
#> GSM99480 1 0.0000 0.994 1.000 0.000 0.000
#> GSM99482 1 0.0000 0.994 1.000 0.000 0.000
#> GSM99484 2 0.0000 0.991 0.000 1.000 0.000
#> GSM99486 2 0.0000 0.991 0.000 1.000 0.000
#> GSM99488 2 0.0000 0.991 0.000 1.000 0.000
#> GSM99490 2 0.0000 0.991 0.000 1.000 0.000
#> GSM99492 1 0.0000 0.994 1.000 0.000 0.000
#> GSM99494 2 0.0000 0.991 0.000 1.000 0.000
#> GSM99524 1 0.0000 0.994 1.000 0.000 0.000
#> GSM99526 3 0.1643 0.946 0.000 0.044 0.956
#> GSM99528 2 0.0000 0.991 0.000 1.000 0.000
#> GSM99530 3 0.3116 0.884 0.108 0.000 0.892
#> GSM99532 3 0.1753 0.946 0.048 0.000 0.952
#> GSM99534 2 0.0000 0.991 0.000 1.000 0.000
#> GSM99536 1 0.0000 0.994 1.000 0.000 0.000
#> GSM99538 2 0.1163 0.966 0.000 0.972 0.028
#> GSM99540 1 0.0000 0.994 1.000 0.000 0.000
#> GSM99542 2 0.0000 0.991 0.000 1.000 0.000
#> GSM99544 2 0.0000 0.991 0.000 1.000 0.000
#> GSM99546 2 0.5109 0.723 0.008 0.780 0.212
#> GSM99548 2 0.0000 0.991 0.000 1.000 0.000
#> GSM99550 1 0.0000 0.994 1.000 0.000 0.000
#> GSM99552 3 0.0000 0.984 0.000 0.000 1.000
#> GSM99554 2 0.0000 0.991 0.000 1.000 0.000
#> GSM99556 2 0.0000 0.991 0.000 1.000 0.000
#> GSM99558 3 0.0237 0.981 0.000 0.004 0.996
#> GSM99560 2 0.0000 0.991 0.000 1.000 0.000
#> GSM99562 3 0.0000 0.984 0.000 0.000 1.000
#> GSM99564 2 0.0000 0.991 0.000 1.000 0.000
#> GSM99572 2 0.0000 0.991 0.000 1.000 0.000
#> GSM99576 1 0.0000 0.994 1.000 0.000 0.000
#> GSM99578 2 0.0000 0.991 0.000 1.000 0.000
#> GSM99580 3 0.0000 0.984 0.000 0.000 1.000
#> GSM99582 3 0.4555 0.763 0.200 0.000 0.800
#> GSM99584 2 0.0000 0.991 0.000 1.000 0.000
#> GSM99586 1 0.0000 0.994 1.000 0.000 0.000
#> GSM99588 2 0.0000 0.991 0.000 1.000 0.000
#> GSM99590 2 0.0000 0.991 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM99496 3 0.0188 0.8626 0.000 0.000 0.996 0.004
#> GSM99502 1 0.0000 0.9599 1.000 0.000 0.000 0.000
#> GSM99504 3 0.4996 0.0545 0.484 0.000 0.516 0.000
#> GSM99506 3 0.0336 0.8658 0.000 0.000 0.992 0.008
#> GSM99566 3 0.1022 0.8675 0.000 0.000 0.968 0.032
#> GSM99574 1 0.0000 0.9599 1.000 0.000 0.000 0.000
#> GSM99592 3 0.4431 0.6207 0.000 0.000 0.696 0.304
#> GSM99594 3 0.0592 0.8658 0.000 0.000 0.984 0.016
#> GSM99468 1 0.0000 0.9599 1.000 0.000 0.000 0.000
#> GSM99498 1 0.1389 0.9217 0.952 0.000 0.048 0.000
#> GSM99500 1 0.0469 0.9526 0.988 0.000 0.012 0.000
#> GSM99508 3 0.2281 0.8505 0.000 0.000 0.904 0.096
#> GSM99568 3 0.2081 0.8545 0.000 0.000 0.916 0.084
#> GSM99596 3 0.1211 0.8485 0.000 0.000 0.960 0.040
#> GSM99600 2 0.0817 0.9227 0.000 0.976 0.000 0.024
#> GSM99458 1 0.0188 0.9584 0.996 0.000 0.000 0.004
#> GSM99460 1 0.3123 0.8132 0.844 0.000 0.000 0.156
#> GSM99510 4 0.4989 -0.1025 0.000 0.000 0.472 0.528
#> GSM99512 3 0.2814 0.8293 0.000 0.000 0.868 0.132
#> GSM99514 3 0.0921 0.8676 0.000 0.000 0.972 0.028
#> GSM99516 1 0.0000 0.9599 1.000 0.000 0.000 0.000
#> GSM99518 1 0.0000 0.9599 1.000 0.000 0.000 0.000
#> GSM99520 3 0.1118 0.8667 0.000 0.000 0.964 0.036
#> GSM99522 3 0.3448 0.7989 0.004 0.000 0.828 0.168
#> GSM99570 1 0.0000 0.9599 1.000 0.000 0.000 0.000
#> GSM99598 1 0.0000 0.9599 1.000 0.000 0.000 0.000
#> GSM99432 4 0.3266 0.7051 0.000 0.168 0.000 0.832
#> GSM99434 4 0.3569 0.5898 0.000 0.000 0.196 0.804
#> GSM99436 4 0.4933 0.3813 0.000 0.432 0.000 0.568
#> GSM99438 2 0.0188 0.9281 0.000 0.996 0.000 0.004
#> GSM99440 1 0.0000 0.9599 1.000 0.000 0.000 0.000
#> GSM99442 2 0.0921 0.9206 0.000 0.972 0.000 0.028
#> GSM99444 2 0.0336 0.9276 0.000 0.992 0.000 0.008
#> GSM99446 2 0.1389 0.9065 0.000 0.952 0.000 0.048
#> GSM99448 3 0.5097 0.3137 0.000 0.004 0.568 0.428
#> GSM99450 4 0.3975 0.5348 0.000 0.000 0.240 0.760
#> GSM99452 1 0.0000 0.9599 1.000 0.000 0.000 0.000
#> GSM99454 1 0.0000 0.9599 1.000 0.000 0.000 0.000
#> GSM99456 1 0.1209 0.9428 0.964 0.000 0.004 0.032
#> GSM99462 2 0.0000 0.9279 0.000 1.000 0.000 0.000
#> GSM99464 4 0.3245 0.6536 0.028 0.000 0.100 0.872
#> GSM99466 2 0.0921 0.9206 0.000 0.972 0.000 0.028
#> GSM99470 1 0.4898 0.2749 0.584 0.416 0.000 0.000
#> GSM99472 1 0.0000 0.9599 1.000 0.000 0.000 0.000
#> GSM99474 3 0.1211 0.8677 0.000 0.000 0.960 0.040
#> GSM99476 4 0.2589 0.6547 0.000 0.000 0.116 0.884
#> GSM99478 2 0.0188 0.9280 0.000 0.996 0.000 0.004
#> GSM99480 1 0.0000 0.9599 1.000 0.000 0.000 0.000
#> GSM99482 1 0.0000 0.9599 1.000 0.000 0.000 0.000
#> GSM99484 2 0.0817 0.9215 0.000 0.976 0.000 0.024
#> GSM99486 4 0.4977 0.3102 0.000 0.460 0.000 0.540
#> GSM99488 2 0.1022 0.9177 0.000 0.968 0.000 0.032
#> GSM99490 2 0.0188 0.9281 0.000 0.996 0.000 0.004
#> GSM99492 1 0.0921 0.9473 0.972 0.000 0.000 0.028
#> GSM99494 2 0.0188 0.9278 0.000 0.996 0.000 0.004
#> GSM99524 1 0.0000 0.9599 1.000 0.000 0.000 0.000
#> GSM99526 4 0.2759 0.6948 0.000 0.052 0.044 0.904
#> GSM99528 2 0.5798 0.5791 0.000 0.696 0.208 0.096
#> GSM99530 3 0.3863 0.7537 0.028 0.000 0.828 0.144
#> GSM99532 3 0.2976 0.8382 0.008 0.000 0.872 0.120
#> GSM99534 2 0.0817 0.9227 0.000 0.976 0.000 0.024
#> GSM99536 1 0.0000 0.9599 1.000 0.000 0.000 0.000
#> GSM99538 2 0.3652 0.8166 0.000 0.856 0.052 0.092
#> GSM99540 1 0.0188 0.9584 0.996 0.000 0.000 0.004
#> GSM99542 2 0.1118 0.9155 0.000 0.964 0.000 0.036
#> GSM99544 2 0.4624 0.3405 0.000 0.660 0.000 0.340
#> GSM99546 4 0.3142 0.7182 0.000 0.132 0.008 0.860
#> GSM99548 2 0.0921 0.9208 0.000 0.972 0.000 0.028
#> GSM99550 1 0.3806 0.8167 0.824 0.000 0.020 0.156
#> GSM99552 3 0.0921 0.8537 0.000 0.000 0.972 0.028
#> GSM99554 2 0.3172 0.7626 0.000 0.840 0.000 0.160
#> GSM99556 2 0.0336 0.9273 0.000 0.992 0.000 0.008
#> GSM99558 3 0.1182 0.8540 0.000 0.016 0.968 0.016
#> GSM99560 4 0.4564 0.5571 0.000 0.328 0.000 0.672
#> GSM99562 3 0.3074 0.8157 0.000 0.000 0.848 0.152
#> GSM99564 4 0.4697 0.5290 0.000 0.356 0.000 0.644
#> GSM99572 2 0.0188 0.9281 0.000 0.996 0.000 0.004
#> GSM99576 1 0.1022 0.9452 0.968 0.000 0.000 0.032
#> GSM99578 2 0.1824 0.8970 0.000 0.936 0.004 0.060
#> GSM99580 3 0.0921 0.8557 0.000 0.000 0.972 0.028
#> GSM99582 4 0.6812 0.4250 0.076 0.024 0.288 0.612
#> GSM99584 4 0.3942 0.6595 0.000 0.236 0.000 0.764
#> GSM99586 1 0.1022 0.9452 0.968 0.000 0.000 0.032
#> GSM99588 2 0.1661 0.9027 0.000 0.944 0.004 0.052
#> GSM99590 2 0.0817 0.9227 0.000 0.976 0.000 0.024
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM99496 3 0.3010 0.6226 0.000 0.000 0.824 0.004 0.172
#> GSM99502 1 0.0000 0.9276 1.000 0.000 0.000 0.000 0.000
#> GSM99504 1 0.5299 0.1156 0.520 0.000 0.436 0.004 0.040
#> GSM99506 3 0.1410 0.7071 0.000 0.000 0.940 0.000 0.060
#> GSM99566 3 0.1704 0.7053 0.000 0.000 0.928 0.004 0.068
#> GSM99574 1 0.0290 0.9277 0.992 0.000 0.000 0.000 0.008
#> GSM99592 3 0.4522 0.5949 0.000 0.000 0.744 0.176 0.080
#> GSM99594 3 0.1571 0.7129 0.000 0.000 0.936 0.004 0.060
#> GSM99468 1 0.0404 0.9267 0.988 0.000 0.000 0.000 0.012
#> GSM99498 1 0.1270 0.8932 0.948 0.000 0.052 0.000 0.000
#> GSM99500 1 0.0162 0.9271 0.996 0.000 0.004 0.000 0.000
#> GSM99508 3 0.2209 0.7056 0.000 0.000 0.912 0.032 0.056
#> GSM99568 3 0.2331 0.7100 0.000 0.000 0.900 0.020 0.080
#> GSM99596 3 0.4101 0.3843 0.000 0.000 0.664 0.004 0.332
#> GSM99600 2 0.1082 0.8670 0.000 0.964 0.000 0.028 0.008
#> GSM99458 1 0.0324 0.9275 0.992 0.000 0.000 0.004 0.004
#> GSM99460 1 0.2707 0.8259 0.860 0.000 0.000 0.132 0.008
#> GSM99510 3 0.6436 0.1034 0.000 0.000 0.428 0.396 0.176
#> GSM99512 3 0.4444 0.6109 0.000 0.000 0.756 0.088 0.156
#> GSM99514 3 0.1831 0.7018 0.000 0.000 0.920 0.004 0.076
#> GSM99516 1 0.0000 0.9276 1.000 0.000 0.000 0.000 0.000
#> GSM99518 1 0.0162 0.9276 0.996 0.000 0.000 0.000 0.004
#> GSM99520 3 0.2017 0.7041 0.000 0.000 0.912 0.008 0.080
#> GSM99522 3 0.3710 0.6533 0.000 0.000 0.808 0.048 0.144
#> GSM99570 1 0.0162 0.9270 0.996 0.000 0.000 0.000 0.004
#> GSM99598 1 0.0000 0.9276 1.000 0.000 0.000 0.000 0.000
#> GSM99432 4 0.2295 0.6277 0.000 0.088 0.004 0.900 0.008
#> GSM99434 4 0.5282 0.3631 0.000 0.000 0.268 0.644 0.088
#> GSM99436 4 0.4585 0.4582 0.000 0.352 0.000 0.628 0.020
#> GSM99438 2 0.0566 0.8705 0.000 0.984 0.000 0.004 0.012
#> GSM99440 1 0.0162 0.9276 0.996 0.000 0.000 0.000 0.004
#> GSM99442 2 0.2069 0.8353 0.000 0.912 0.000 0.076 0.012
#> GSM99444 2 0.0290 0.8703 0.000 0.992 0.000 0.008 0.000
#> GSM99446 2 0.1877 0.8532 0.000 0.924 0.000 0.064 0.012
#> GSM99448 3 0.7007 0.1661 0.000 0.044 0.468 0.356 0.132
#> GSM99450 4 0.5353 0.3627 0.000 0.000 0.272 0.636 0.092
#> GSM99452 1 0.0000 0.9276 1.000 0.000 0.000 0.000 0.000
#> GSM99454 1 0.0000 0.9276 1.000 0.000 0.000 0.000 0.000
#> GSM99456 1 0.3953 0.7752 0.792 0.000 0.000 0.060 0.148
#> GSM99462 2 0.0324 0.8702 0.000 0.992 0.000 0.004 0.004
#> GSM99464 4 0.4031 0.4966 0.004 0.000 0.048 0.788 0.160
#> GSM99466 2 0.5418 0.5749 0.000 0.684 0.016 0.208 0.092
#> GSM99470 1 0.4325 0.5743 0.724 0.240 0.000 0.000 0.036
#> GSM99472 1 0.0771 0.9199 0.976 0.000 0.000 0.004 0.020
#> GSM99474 3 0.1331 0.7164 0.000 0.000 0.952 0.008 0.040
#> GSM99476 4 0.1901 0.5976 0.000 0.004 0.024 0.932 0.040
#> GSM99478 2 0.1914 0.8605 0.000 0.928 0.008 0.008 0.056
#> GSM99480 1 0.0510 0.9255 0.984 0.000 0.000 0.000 0.016
#> GSM99482 1 0.0510 0.9231 0.984 0.000 0.000 0.000 0.016
#> GSM99484 2 0.0898 0.8694 0.000 0.972 0.000 0.008 0.020
#> GSM99486 4 0.5435 0.2435 0.000 0.428 0.000 0.512 0.060
#> GSM99488 2 0.1638 0.8487 0.000 0.932 0.000 0.004 0.064
#> GSM99490 2 0.2305 0.8391 0.000 0.896 0.000 0.012 0.092
#> GSM99492 1 0.1956 0.8862 0.916 0.000 0.000 0.008 0.076
#> GSM99494 2 0.0290 0.8696 0.000 0.992 0.000 0.000 0.008
#> GSM99524 1 0.0794 0.9181 0.972 0.000 0.000 0.000 0.028
#> GSM99526 4 0.1774 0.5895 0.000 0.000 0.016 0.932 0.052
#> GSM99528 5 0.5841 0.4928 0.000 0.256 0.148 0.000 0.596
#> GSM99530 5 0.5197 0.2900 0.000 0.000 0.316 0.064 0.620
#> GSM99532 3 0.5161 0.5849 0.016 0.000 0.716 0.092 0.176
#> GSM99534 2 0.1522 0.8575 0.000 0.944 0.000 0.044 0.012
#> GSM99536 1 0.0290 0.9273 0.992 0.000 0.000 0.000 0.008
#> GSM99538 2 0.6306 0.2482 0.000 0.568 0.052 0.064 0.316
#> GSM99540 1 0.0693 0.9240 0.980 0.000 0.000 0.008 0.012
#> GSM99542 2 0.1638 0.8487 0.000 0.932 0.000 0.004 0.064
#> GSM99544 2 0.4288 0.4425 0.000 0.664 0.000 0.324 0.012
#> GSM99546 4 0.3289 0.6267 0.016 0.088 0.000 0.860 0.036
#> GSM99548 2 0.3550 0.6864 0.000 0.760 0.000 0.004 0.236
#> GSM99550 4 0.7346 -0.0413 0.312 0.008 0.012 0.376 0.292
#> GSM99552 3 0.4009 0.4443 0.000 0.000 0.684 0.004 0.312
#> GSM99554 2 0.4157 0.5664 0.000 0.716 0.000 0.264 0.020
#> GSM99556 2 0.0955 0.8685 0.000 0.968 0.000 0.004 0.028
#> GSM99558 3 0.5137 0.4101 0.000 0.108 0.684 0.000 0.208
#> GSM99560 4 0.5631 0.4812 0.000 0.200 0.000 0.636 0.164
#> GSM99562 3 0.3543 0.6683 0.000 0.000 0.828 0.060 0.112
#> GSM99564 4 0.4040 0.5757 0.000 0.260 0.000 0.724 0.016
#> GSM99572 2 0.0671 0.8705 0.000 0.980 0.000 0.004 0.016
#> GSM99576 1 0.2411 0.8640 0.884 0.000 0.000 0.008 0.108
#> GSM99578 2 0.2561 0.7961 0.000 0.856 0.000 0.000 0.144
#> GSM99580 3 0.3353 0.6288 0.000 0.000 0.796 0.008 0.196
#> GSM99582 4 0.7415 0.4697 0.072 0.044 0.144 0.596 0.144
#> GSM99584 4 0.4157 0.5761 0.000 0.264 0.000 0.716 0.020
#> GSM99586 1 0.3284 0.8140 0.828 0.000 0.000 0.024 0.148
#> GSM99588 2 0.2068 0.8286 0.000 0.904 0.000 0.004 0.092
#> GSM99590 2 0.0609 0.8682 0.000 0.980 0.000 0.020 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM99496 6 0.3534 0.584262 0.000 0.000 0.276 0.000 0.008 0.716
#> GSM99502 1 0.0146 0.920039 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM99504 1 0.5617 0.314639 0.584 0.000 0.148 0.004 0.008 0.256
#> GSM99506 3 0.3668 0.482546 0.000 0.000 0.668 0.004 0.000 0.328
#> GSM99566 3 0.3997 0.511794 0.000 0.000 0.688 0.004 0.020 0.288
#> GSM99574 1 0.0260 0.920447 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM99592 3 0.3952 0.652643 0.000 0.000 0.788 0.108 0.016 0.088
#> GSM99594 3 0.3109 0.625447 0.000 0.000 0.772 0.004 0.000 0.224
#> GSM99468 1 0.0363 0.919334 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM99498 1 0.1624 0.885945 0.936 0.000 0.020 0.004 0.000 0.040
#> GSM99500 1 0.0717 0.917494 0.976 0.000 0.000 0.000 0.008 0.016
#> GSM99508 3 0.2823 0.647928 0.000 0.000 0.796 0.000 0.000 0.204
#> GSM99568 3 0.2632 0.668276 0.000 0.000 0.832 0.000 0.004 0.164
#> GSM99596 6 0.3370 0.656730 0.000 0.000 0.148 0.000 0.048 0.804
#> GSM99600 2 0.3398 0.730629 0.000 0.768 0.000 0.216 0.012 0.004
#> GSM99458 1 0.0146 0.920590 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM99460 1 0.2784 0.834579 0.880 0.000 0.064 0.020 0.032 0.004
#> GSM99510 3 0.2505 0.645709 0.000 0.000 0.888 0.040 0.064 0.008
#> GSM99512 3 0.1426 0.674952 0.000 0.000 0.948 0.008 0.016 0.028
#> GSM99514 6 0.4513 0.294079 0.000 0.000 0.396 0.004 0.028 0.572
#> GSM99516 1 0.0458 0.917986 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM99518 1 0.0000 0.920232 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99520 3 0.4067 0.148919 0.000 0.000 0.548 0.000 0.008 0.444
#> GSM99522 3 0.1623 0.684075 0.004 0.000 0.940 0.004 0.020 0.032
#> GSM99570 1 0.0458 0.917986 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM99598 1 0.0000 0.920232 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99432 4 0.3620 0.602889 0.000 0.036 0.020 0.804 0.140 0.000
#> GSM99434 3 0.5515 0.248789 0.000 0.000 0.596 0.204 0.192 0.008
#> GSM99436 4 0.2985 0.668975 0.000 0.116 0.000 0.844 0.036 0.004
#> GSM99438 2 0.0935 0.824133 0.000 0.964 0.000 0.032 0.004 0.000
#> GSM99440 1 0.0260 0.919754 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM99442 2 0.4506 0.497042 0.000 0.616 0.000 0.344 0.036 0.004
#> GSM99444 2 0.2094 0.815725 0.000 0.900 0.000 0.080 0.020 0.000
#> GSM99446 2 0.3284 0.747865 0.000 0.784 0.000 0.196 0.020 0.000
#> GSM99448 3 0.3484 0.638825 0.000 0.020 0.844 0.040 0.076 0.020
#> GSM99450 3 0.5275 0.099889 0.000 0.000 0.532 0.372 0.092 0.004
#> GSM99452 1 0.0000 0.920232 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99454 1 0.0000 0.920232 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM99456 1 0.3240 0.695785 0.752 0.000 0.000 0.004 0.244 0.000
#> GSM99462 2 0.0622 0.822879 0.000 0.980 0.000 0.008 0.012 0.000
#> GSM99464 5 0.6090 0.089822 0.004 0.000 0.224 0.368 0.404 0.000
#> GSM99466 4 0.6123 0.484088 0.000 0.080 0.000 0.568 0.096 0.256
#> GSM99470 1 0.4450 0.734207 0.788 0.056 0.000 0.024 0.068 0.064
#> GSM99472 1 0.0891 0.912162 0.968 0.000 0.000 0.000 0.024 0.008
#> GSM99474 3 0.2920 0.672328 0.000 0.000 0.820 0.004 0.008 0.168
#> GSM99476 4 0.3381 0.531583 0.000 0.000 0.040 0.808 0.148 0.004
#> GSM99478 2 0.6757 0.327667 0.000 0.460 0.000 0.148 0.084 0.308
#> GSM99480 1 0.0363 0.919334 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM99482 1 0.0632 0.915179 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM99484 2 0.4262 0.743422 0.000 0.760 0.000 0.148 0.068 0.024
#> GSM99486 4 0.3883 0.657139 0.000 0.088 0.000 0.800 0.088 0.024
#> GSM99488 2 0.1075 0.812462 0.000 0.952 0.000 0.000 0.048 0.000
#> GSM99490 2 0.3063 0.796059 0.000 0.840 0.000 0.068 0.092 0.000
#> GSM99492 1 0.1863 0.861768 0.896 0.000 0.000 0.000 0.104 0.000
#> GSM99494 2 0.0547 0.820215 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM99524 1 0.1794 0.885500 0.924 0.000 0.000 0.000 0.036 0.040
#> GSM99526 4 0.5926 -0.050087 0.000 0.000 0.232 0.496 0.268 0.004
#> GSM99528 6 0.5700 0.054690 0.000 0.132 0.012 0.000 0.324 0.532
#> GSM99530 5 0.6226 0.000692 0.020 0.000 0.108 0.024 0.516 0.332
#> GSM99532 3 0.4126 0.630945 0.012 0.000 0.788 0.020 0.124 0.056
#> GSM99534 2 0.3571 0.787547 0.016 0.812 0.000 0.124 0.048 0.000
#> GSM99536 1 0.0363 0.919334 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM99538 2 0.5778 0.382625 0.000 0.544 0.060 0.020 0.352 0.024
#> GSM99540 1 0.0993 0.912953 0.964 0.000 0.012 0.000 0.024 0.000
#> GSM99542 2 0.1267 0.809293 0.000 0.940 0.000 0.000 0.060 0.000
#> GSM99544 2 0.5251 0.609276 0.000 0.656 0.048 0.248 0.036 0.012
#> GSM99546 4 0.4968 0.500957 0.008 0.020 0.108 0.728 0.128 0.008
#> GSM99548 2 0.3782 0.688054 0.000 0.740 0.000 0.036 0.224 0.000
#> GSM99550 5 0.6035 0.327410 0.184 0.012 0.000 0.216 0.572 0.016
#> GSM99552 6 0.2579 0.618766 0.000 0.000 0.088 0.004 0.032 0.876
#> GSM99554 4 0.4867 0.524862 0.000 0.256 0.000 0.660 0.068 0.016
#> GSM99556 2 0.0725 0.823502 0.000 0.976 0.000 0.012 0.012 0.000
#> GSM99558 6 0.4490 0.639709 0.000 0.108 0.172 0.000 0.004 0.716
#> GSM99560 4 0.4554 0.592514 0.000 0.104 0.000 0.716 0.172 0.008
#> GSM99562 3 0.0806 0.689902 0.000 0.000 0.972 0.000 0.008 0.020
#> GSM99564 4 0.2402 0.676911 0.000 0.084 0.000 0.888 0.020 0.008
#> GSM99572 2 0.1913 0.816886 0.000 0.908 0.000 0.080 0.012 0.000
#> GSM99576 1 0.2146 0.849650 0.880 0.004 0.000 0.000 0.116 0.000
#> GSM99578 2 0.1707 0.813468 0.000 0.928 0.000 0.004 0.056 0.012
#> GSM99580 3 0.3514 0.613652 0.000 0.000 0.752 0.000 0.020 0.228
#> GSM99582 4 0.5756 0.457329 0.024 0.012 0.000 0.608 0.108 0.248
#> GSM99584 4 0.3322 0.666176 0.000 0.088 0.020 0.848 0.032 0.012
#> GSM99586 1 0.3215 0.700760 0.756 0.000 0.000 0.004 0.240 0.000
#> GSM99588 2 0.1700 0.801821 0.000 0.916 0.000 0.000 0.080 0.004
#> GSM99590 2 0.1700 0.816079 0.000 0.916 0.000 0.080 0.004 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) cell.type(p) k
#> ATC:NMF 84 4.25e-06 2.72e-05 2
#> ATC:NMF 85 1.76e-04 4.87e-03 3
#> ATC:NMF 77 3.63e-05 1.57e-03 4
#> ATC:NMF 67 5.28e-05 1.68e-03 5
#> ATC:NMF 69 1.53e-03 3.53e-02 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