Date: 2019-12-25 20:17:11 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 14502 rows and 83 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] 14502 83
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 | ||
|---|---|---|---|---|---|
| SD:pam | 2 | 1.000 | 0.989 | 0.995 | ** |
| MAD:pam | 2 | 1.000 | 0.920 | 0.950 | ** |
| ATC:kmeans | 2 | 1.000 | 0.966 | 0.987 | ** |
| ATC:pam | 2 | 0.949 | 0.935 | 0.974 | * |
| ATC:skmeans | 2 | 0.878 | 0.899 | 0.959 | |
| CV:kmeans | 2 | 0.745 | 0.882 | 0.935 | |
| CV:skmeans | 2 | 0.741 | 0.853 | 0.942 | |
| ATC:NMF | 2 | 0.684 | 0.856 | 0.935 | |
| MAD:NMF | 2 | 0.633 | 0.800 | 0.917 | |
| SD:NMF | 5 | 0.633 | 0.613 | 0.799 | |
| CV:pam | 5 | 0.615 | 0.657 | 0.803 | |
| SD:skmeans | 2 | 0.613 | 0.814 | 0.927 | |
| CV:mclust | 4 | 0.595 | 0.720 | 0.844 | |
| MAD:skmeans | 2 | 0.586 | 0.781 | 0.914 | |
| SD:kmeans | 2 | 0.565 | 0.787 | 0.903 | |
| MAD:kmeans | 2 | 0.546 | 0.589 | 0.829 | |
| CV:NMF | 2 | 0.510 | 0.825 | 0.902 | |
| ATC:mclust | 4 | 0.505 | 0.760 | 0.820 | |
| SD:mclust | 5 | 0.504 | 0.519 | 0.729 | |
| ATC:hclust | 2 | 0.461 | 0.788 | 0.896 | |
| CV:hclust | 3 | 0.396 | 0.686 | 0.820 | |
| MAD:mclust | 3 | 0.379 | 0.715 | 0.770 | |
| SD:hclust | 2 | 0.276 | 0.735 | 0.852 | |
| MAD:hclust | 2 | 0.250 | 0.768 | 0.854 |
**: 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 0.657 0.826 0.927 0.409 0.574 0.574
#> CV:NMF 2 0.510 0.825 0.902 0.467 0.533 0.533
#> MAD:NMF 2 0.633 0.800 0.917 0.455 0.540 0.540
#> ATC:NMF 2 0.684 0.856 0.935 0.492 0.500 0.500
#> SD:skmeans 2 0.613 0.814 0.927 0.498 0.496 0.496
#> CV:skmeans 2 0.741 0.853 0.942 0.501 0.500 0.500
#> MAD:skmeans 2 0.586 0.781 0.914 0.504 0.494 0.494
#> ATC:skmeans 2 0.878 0.899 0.959 0.499 0.500 0.500
#> SD:mclust 2 0.300 0.529 0.795 0.413 0.520 0.520
#> CV:mclust 2 0.372 0.833 0.895 0.351 0.685 0.685
#> MAD:mclust 2 0.449 0.831 0.898 0.369 0.700 0.700
#> ATC:mclust 2 0.225 0.469 0.781 0.311 0.750 0.750
#> SD:kmeans 2 0.565 0.787 0.903 0.452 0.533 0.533
#> CV:kmeans 2 0.745 0.882 0.935 0.469 0.533 0.533
#> MAD:kmeans 2 0.546 0.589 0.829 0.473 0.617 0.617
#> ATC:kmeans 2 1.000 0.966 0.987 0.455 0.540 0.540
#> SD:pam 2 1.000 0.989 0.995 0.240 0.767 0.767
#> CV:pam 2 0.438 0.784 0.878 0.345 0.670 0.670
#> MAD:pam 2 1.000 0.920 0.950 0.313 0.700 0.700
#> ATC:pam 2 0.949 0.935 0.974 0.405 0.606 0.606
#> SD:hclust 2 0.276 0.735 0.852 0.387 0.630 0.630
#> CV:hclust 2 0.472 0.793 0.907 0.301 0.785 0.785
#> MAD:hclust 2 0.250 0.768 0.854 0.423 0.584 0.584
#> ATC:hclust 2 0.461 0.788 0.896 0.414 0.584 0.584
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.319 0.450 0.715 0.500 0.654 0.460
#> CV:NMF 3 0.486 0.656 0.814 0.371 0.745 0.557
#> MAD:NMF 3 0.435 0.718 0.808 0.425 0.677 0.461
#> ATC:NMF 3 0.612 0.782 0.889 0.352 0.694 0.462
#> SD:skmeans 3 0.603 0.795 0.863 0.334 0.702 0.476
#> CV:skmeans 3 0.562 0.779 0.853 0.330 0.719 0.492
#> MAD:skmeans 3 0.499 0.539 0.781 0.326 0.772 0.569
#> ATC:skmeans 3 0.695 0.785 0.890 0.294 0.778 0.591
#> SD:mclust 3 0.356 0.401 0.699 0.556 0.686 0.470
#> CV:mclust 3 0.223 0.659 0.730 0.598 0.727 0.614
#> MAD:mclust 3 0.379 0.715 0.770 0.664 0.431 0.300
#> ATC:mclust 3 0.177 0.444 0.675 0.660 0.494 0.369
#> SD:kmeans 3 0.438 0.773 0.842 0.343 0.703 0.512
#> CV:kmeans 3 0.367 0.449 0.659 0.314 0.808 0.661
#> MAD:kmeans 3 0.311 0.527 0.693 0.336 0.673 0.498
#> ATC:kmeans 3 0.487 0.542 0.717 0.390 0.724 0.520
#> SD:pam 3 0.496 0.744 0.865 0.891 0.802 0.745
#> CV:pam 3 0.246 0.470 0.747 0.689 0.718 0.591
#> MAD:pam 3 0.241 0.429 0.727 0.732 0.761 0.670
#> ATC:pam 3 0.598 0.727 0.851 0.477 0.797 0.670
#> SD:hclust 3 0.281 0.585 0.740 0.309 0.950 0.921
#> CV:hclust 3 0.396 0.686 0.820 0.537 0.815 0.764
#> MAD:hclust 3 0.260 0.684 0.771 0.236 0.960 0.932
#> ATC:hclust 3 0.321 0.417 0.718 0.396 0.918 0.865
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.451 0.603 0.760 0.1602 0.653 0.297
#> CV:NMF 4 0.459 0.648 0.779 0.1609 0.771 0.457
#> MAD:NMF 4 0.500 0.642 0.809 0.1282 0.797 0.486
#> ATC:NMF 4 0.720 0.747 0.872 0.1275 0.797 0.481
#> SD:skmeans 4 0.577 0.459 0.709 0.1164 0.760 0.435
#> CV:skmeans 4 0.609 0.706 0.833 0.1243 0.893 0.688
#> MAD:skmeans 4 0.594 0.727 0.813 0.1258 0.849 0.589
#> ATC:skmeans 4 0.864 0.839 0.930 0.1386 0.828 0.570
#> SD:mclust 4 0.482 0.536 0.724 0.0594 0.804 0.554
#> CV:mclust 4 0.595 0.720 0.844 0.2947 0.758 0.493
#> MAD:mclust 4 0.451 0.638 0.771 0.1391 0.892 0.707
#> ATC:mclust 4 0.505 0.760 0.820 0.3174 0.753 0.427
#> SD:kmeans 4 0.561 0.744 0.805 0.1396 0.914 0.787
#> CV:kmeans 4 0.439 0.575 0.724 0.1594 0.777 0.496
#> MAD:kmeans 4 0.420 0.453 0.664 0.1386 0.852 0.626
#> ATC:kmeans 4 0.692 0.777 0.871 0.1676 0.756 0.418
#> SD:pam 4 0.502 0.715 0.826 0.3205 0.862 0.767
#> CV:pam 4 0.374 0.567 0.731 0.1690 0.804 0.591
#> MAD:pam 4 0.546 0.526 0.739 0.2161 0.828 0.678
#> ATC:pam 4 0.893 0.884 0.931 0.1685 0.784 0.538
#> SD:hclust 4 0.325 0.637 0.789 0.2168 0.749 0.594
#> CV:hclust 4 0.279 0.594 0.752 0.2230 0.931 0.884
#> MAD:hclust 4 0.299 0.648 0.730 0.2353 0.781 0.616
#> ATC:hclust 4 0.493 0.573 0.720 0.2350 0.619 0.362
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.633 0.613 0.799 0.0700 0.854 0.550
#> CV:NMF 5 0.636 0.675 0.793 0.0693 0.885 0.597
#> MAD:NMF 5 0.629 0.629 0.825 0.0665 0.827 0.453
#> ATC:NMF 5 0.584 0.587 0.756 0.0560 0.896 0.633
#> SD:skmeans 5 0.641 0.585 0.750 0.0715 0.896 0.639
#> CV:skmeans 5 0.655 0.647 0.773 0.0671 0.927 0.730
#> MAD:skmeans 5 0.646 0.547 0.694 0.0615 0.892 0.609
#> ATC:skmeans 5 0.778 0.683 0.853 0.0721 0.908 0.679
#> SD:mclust 5 0.504 0.519 0.729 0.0694 0.890 0.696
#> CV:mclust 5 0.618 0.674 0.798 0.0695 0.862 0.541
#> MAD:mclust 5 0.501 0.578 0.742 0.0832 0.874 0.595
#> ATC:mclust 5 0.561 0.691 0.798 0.0944 0.860 0.540
#> SD:kmeans 5 0.570 0.561 0.736 0.0828 0.940 0.826
#> CV:kmeans 5 0.551 0.524 0.685 0.0774 0.946 0.797
#> MAD:kmeans 5 0.509 0.459 0.616 0.0732 0.833 0.487
#> ATC:kmeans 5 0.677 0.643 0.795 0.0730 0.859 0.528
#> SD:pam 5 0.559 0.761 0.836 0.0908 0.935 0.860
#> CV:pam 5 0.615 0.657 0.803 0.1206 0.791 0.458
#> MAD:pam 5 0.594 0.352 0.660 0.1251 0.793 0.517
#> ATC:pam 5 0.823 0.834 0.904 0.1234 0.904 0.679
#> SD:hclust 5 0.461 0.611 0.762 0.1112 0.941 0.855
#> CV:hclust 5 0.324 0.435 0.675 0.1851 0.748 0.564
#> MAD:hclust 5 0.449 0.615 0.734 0.0833 0.957 0.888
#> ATC:hclust 5 0.635 0.592 0.754 0.0848 0.944 0.800
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.578 0.486 0.688 0.0543 0.894 0.611
#> CV:NMF 6 0.602 0.478 0.700 0.0386 0.974 0.878
#> MAD:NMF 6 0.576 0.474 0.690 0.0514 0.916 0.635
#> ATC:NMF 6 0.612 0.495 0.697 0.0391 0.931 0.707
#> SD:skmeans 6 0.704 0.705 0.803 0.0441 0.924 0.661
#> CV:skmeans 6 0.667 0.535 0.741 0.0403 0.931 0.708
#> MAD:skmeans 6 0.705 0.639 0.794 0.0423 0.902 0.578
#> ATC:skmeans 6 0.773 0.629 0.816 0.0429 0.938 0.729
#> SD:mclust 6 0.486 0.331 0.637 0.0651 0.922 0.742
#> CV:mclust 6 0.676 0.616 0.752 0.0499 0.951 0.774
#> MAD:mclust 6 0.585 0.659 0.772 0.0469 0.957 0.814
#> ATC:mclust 6 0.781 0.786 0.861 0.1094 0.890 0.541
#> SD:kmeans 6 0.619 0.458 0.688 0.0534 0.963 0.878
#> CV:kmeans 6 0.577 0.611 0.720 0.0484 0.904 0.630
#> MAD:kmeans 6 0.631 0.576 0.695 0.0509 0.894 0.564
#> ATC:kmeans 6 0.722 0.673 0.783 0.0406 0.945 0.742
#> SD:pam 6 0.601 0.659 0.816 0.1046 0.847 0.634
#> CV:pam 6 0.672 0.564 0.773 0.0593 0.864 0.503
#> MAD:pam 6 0.702 0.529 0.791 0.0962 0.755 0.282
#> ATC:pam 6 0.766 0.736 0.850 0.0339 0.964 0.831
#> SD:hclust 6 0.575 0.598 0.783 0.0468 0.953 0.871
#> CV:hclust 6 0.411 0.429 0.703 0.0982 0.863 0.649
#> MAD:hclust 6 0.614 0.598 0.737 0.1061 0.855 0.593
#> ATC:hclust 6 0.669 0.640 0.740 0.0461 0.875 0.525
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 cell.line(p) agent(p) time(p) k
#> SD:NMF 75 1.43e-07 0.5848 2.94e-01 2
#> CV:NMF 79 5.42e-07 0.4410 4.91e-03 2
#> MAD:NMF 75 8.35e-07 0.5693 2.12e-01 2
#> ATC:NMF 78 5.09e-02 0.0193 1.01e-03 2
#> SD:skmeans 73 9.95e-05 0.9519 2.16e-01 2
#> CV:skmeans 76 1.87e-08 0.1268 2.28e-02 2
#> MAD:skmeans 73 3.58e-07 0.7595 2.14e-01 2
#> ATC:skmeans 79 8.50e-01 0.0961 6.51e-06 2
#> SD:mclust 68 1.22e-03 0.7435 3.61e-03 2
#> CV:mclust 79 2.38e-02 0.5530 1.23e-04 2
#> MAD:mclust 80 1.96e-02 0.6273 1.32e-01 2
#> ATC:mclust 59 3.57e-03 0.4602 2.17e-03 2
#> SD:kmeans 75 9.77e-06 0.8819 6.70e-01 2
#> CV:kmeans 79 3.23e-09 0.3117 2.67e-02 2
#> MAD:kmeans 62 1.62e-04 0.7144 1.35e-01 2
#> ATC:kmeans 81 2.30e-01 0.1749 1.71e-05 2
#> SD:pam 83 4.87e-05 0.1842 6.54e-02 2
#> CV:pam 78 5.04e-03 0.0732 3.28e-04 2
#> MAD:pam 81 5.50e-06 0.2261 3.71e-01 2
#> ATC:pam 81 8.09e-02 0.3273 9.83e-05 2
#> SD:hclust 74 1.78e-04 0.8439 6.00e-01 2
#> CV:hclust 73 3.52e-02 0.3951 4.87e-05 2
#> MAD:hclust 78 3.29e-03 0.5201 4.81e-01 2
#> ATC:hclust 75 4.01e-01 0.1773 1.28e-04 2
test_to_known_factors(res_list, k = 3)
#> n cell.line(p) agent(p) time(p) k
#> SD:NMF 42 2.18e-03 0.3622 5.47e-05 3
#> CV:NMF 74 1.38e-06 0.0537 1.40e-03 3
#> MAD:NMF 74 1.64e-06 0.5705 7.03e-05 3
#> ATC:NMF 78 1.54e-05 0.3815 6.81e-05 3
#> SD:skmeans 80 8.71e-09 0.6281 7.02e-03 3
#> CV:skmeans 79 1.02e-12 0.7205 1.48e-05 3
#> MAD:skmeans 59 5.49e-12 0.1047 8.30e-01 3
#> ATC:skmeans 76 8.39e-12 0.4412 1.72e-02 3
#> SD:mclust 30 1.76e-02 0.5699 4.54e-05 3
#> CV:mclust 77 1.17e-10 0.7113 3.66e-04 3
#> MAD:mclust 77 1.10e-12 0.2077 1.57e-01 3
#> ATC:mclust 44 1.62e-01 0.7149 1.81e-03 3
#> SD:kmeans 77 1.61e-06 0.8077 3.80e-05 3
#> CV:kmeans 47 4.94e-09 0.3493 2.44e-01 3
#> MAD:kmeans 49 1.34e-07 0.0836 1.40e-01 3
#> ATC:kmeans 62 1.60e-02 0.4697 6.34e-04 3
#> SD:pam 78 6.32e-06 0.2401 3.26e-03 3
#> CV:pam 52 6.93e-06 0.2531 9.80e-04 3
#> MAD:pam 39 2.04e-01 0.6123 5.89e-01 3
#> ATC:pam 77 4.48e-08 0.4366 1.55e-03 3
#> SD:hclust 66 3.35e-04 0.6164 6.12e-04 3
#> CV:hclust 69 1.34e-06 0.1669 6.89e-06 3
#> MAD:hclust 76 2.14e-03 0.4906 1.14e-03 3
#> ATC:hclust 45 2.35e-03 0.4795 1.18e-03 3
test_to_known_factors(res_list, k = 4)
#> n cell.line(p) agent(p) time(p) k
#> SD:NMF 65 2.45e-06 0.1399 8.40e-05 4
#> CV:NMF 72 1.02e-11 0.6430 2.74e-06 4
#> MAD:NMF 69 6.52e-06 0.1498 3.06e-06 4
#> ATC:NMF 73 3.72e-08 0.0777 6.42e-07 4
#> SD:skmeans 40 4.26e-04 0.8155 3.19e-01 4
#> CV:skmeans 72 2.95e-12 0.7097 1.46e-07 4
#> MAD:skmeans 75 1.19e-16 0.8352 1.88e-01 4
#> ATC:skmeans 77 6.75e-10 0.3696 2.35e-04 4
#> SD:mclust 55 1.08e-05 0.5444 5.51e-04 4
#> CV:mclust 74 2.95e-13 0.7887 1.34e-05 4
#> MAD:mclust 72 5.63e-14 0.3209 2.90e-02 4
#> ATC:mclust 77 1.70e-09 0.7146 6.18e-05 4
#> SD:kmeans 78 1.87e-06 0.6641 9.13e-08 4
#> CV:kmeans 59 6.11e-10 0.5325 4.36e-06 4
#> MAD:kmeans 38 2.73e-02 0.5487 2.47e-02 4
#> ATC:kmeans 72 3.53e-09 0.6980 6.52e-04 4
#> SD:pam 77 3.58e-07 0.8269 1.05e-04 4
#> CV:pam 60 2.52e-09 0.4305 6.67e-06 4
#> MAD:pam 60 7.67e-07 0.8202 9.33e-04 4
#> ATC:pam 80 7.79e-10 0.3672 6.09e-02 4
#> SD:hclust 70 1.43e-03 0.2751 2.41e-07 4
#> CV:hclust 62 7.35e-06 0.0080 4.30e-05 4
#> MAD:hclust 69 7.35e-03 0.5993 3.88e-07 4
#> ATC:hclust 55 1.29e-08 0.4662 7.79e-05 4
test_to_known_factors(res_list, k = 5)
#> n cell.line(p) agent(p) time(p) k
#> SD:NMF 63 2.27e-08 0.1533 3.50e-06 5
#> CV:NMF 72 1.83e-11 0.1116 5.84e-07 5
#> MAD:NMF 66 4.65e-10 0.1580 3.40e-05 5
#> ATC:NMF 60 1.07e-05 0.1530 5.19e-08 5
#> SD:skmeans 56 4.61e-09 0.9215 1.29e-07 5
#> CV:skmeans 70 1.28e-14 0.5543 1.48e-09 5
#> MAD:skmeans 63 1.02e-12 0.8570 1.93e-05 5
#> ATC:skmeans 65 3.59e-09 0.3210 8.99e-06 5
#> SD:mclust 49 2.00e-06 0.6435 2.25e-04 5
#> CV:mclust 71 5.36e-11 0.2944 2.43e-04 5
#> MAD:mclust 60 4.77e-15 0.8322 1.10e-03 5
#> ATC:mclust 75 1.63e-08 0.4024 1.62e-07 5
#> SD:kmeans 59 4.35e-05 0.7279 9.71e-09 5
#> CV:kmeans 53 4.44e-08 0.5910 5.09e-06 5
#> MAD:kmeans 44 6.49e-07 0.4453 6.49e-04 5
#> ATC:kmeans 60 1.60e-08 0.9426 8.77e-03 5
#> SD:pam 79 3.86e-10 0.8739 8.06e-06 5
#> CV:pam 66 4.32e-12 0.1193 1.99e-06 5
#> MAD:pam 31 9.20e-03 0.4070 1.69e-02 5
#> ATC:pam 77 2.10e-11 0.1625 2.79e-02 5
#> SD:hclust 69 1.44e-03 0.2792 8.69e-09 5
#> CV:hclust 41 1.38e-04 0.0464 1.75e-06 5
#> MAD:hclust 64 1.98e-03 0.4807 9.91e-08 5
#> ATC:hclust 62 2.67e-09 0.4267 2.42e-04 5
test_to_known_factors(res_list, k = 6)
#> n cell.line(p) agent(p) time(p) k
#> SD:NMF 50 8.95e-07 0.0685 2.04e-05 6
#> CV:NMF 52 1.16e-10 0.3268 2.60e-05 6
#> MAD:NMF 45 1.64e-09 0.2767 9.10e-06 6
#> ATC:NMF 44 5.60e-05 0.2050 9.87e-09 6
#> SD:skmeans 75 2.98e-13 0.8558 1.32e-09 6
#> CV:skmeans 53 1.11e-11 0.0832 1.28e-06 6
#> MAD:skmeans 65 4.81e-12 0.7387 1.77e-08 6
#> ATC:skmeans 61 3.14e-07 0.2247 7.28e-05 6
#> SD:mclust 20 5.42e-02 0.2536 1.92e-02 6
#> CV:mclust 66 2.25e-13 0.5032 8.69e-06 6
#> MAD:mclust 70 2.00e-14 0.4624 6.12e-04 6
#> ATC:mclust 77 2.09e-09 0.7413 2.89e-04 6
#> SD:kmeans 41 3.19e-04 0.1910 3.53e-05 6
#> CV:kmeans 59 2.09e-12 0.3761 7.81e-06 6
#> MAD:kmeans 57 7.45e-09 0.9585 5.64e-08 6
#> ATC:kmeans 72 5.17e-10 0.7534 1.44e-03 6
#> SD:pam 68 3.60e-09 0.2001 1.73e-04 6
#> CV:pam 59 4.65e-15 0.2316 1.66e-05 6
#> MAD:pam 54 7.45e-16 0.7127 1.62e-03 6
#> ATC:pam 72 8.26e-10 0.1396 1.99e-02 6
#> SD:hclust 60 2.53e-02 0.2963 1.56e-09 6
#> CV:hclust 36 2.37e-05 0.3045 6.63e-06 6
#> MAD:hclust 62 1.18e-03 0.2215 1.73e-06 6
#> ATC:hclust 70 6.65e-10 0.8467 2.51e-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 14502 rows and 83 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.276 0.735 0.852 0.3869 0.630 0.630
#> 3 3 0.281 0.585 0.740 0.3088 0.950 0.921
#> 4 4 0.325 0.637 0.789 0.2168 0.749 0.594
#> 5 5 0.461 0.611 0.762 0.1112 0.941 0.855
#> 6 6 0.575 0.598 0.783 0.0468 0.953 0.871
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM11708 2 0.4161 0.81196 0.084 0.916
#> GSM11735 2 0.4161 0.81196 0.084 0.916
#> GSM11733 2 0.9686 0.55809 0.396 0.604
#> GSM11863 2 0.9686 0.55809 0.396 0.604
#> GSM11710 2 0.4431 0.81823 0.092 0.908
#> GSM11712 1 0.2423 0.83174 0.960 0.040
#> GSM11732 1 0.9286 0.31312 0.656 0.344
#> GSM11844 1 0.9286 0.31312 0.656 0.344
#> GSM11842 1 0.9000 0.44588 0.684 0.316
#> GSM11860 1 0.9000 0.44588 0.684 0.316
#> GSM11686 2 0.6531 0.83504 0.168 0.832
#> GSM11688 2 0.6048 0.83392 0.148 0.852
#> GSM11846 1 0.9044 0.45223 0.680 0.320
#> GSM11680 1 0.5059 0.79956 0.888 0.112
#> GSM11698 1 0.5178 0.79683 0.884 0.116
#> GSM11840 2 0.9686 0.55809 0.396 0.604
#> GSM11847 2 0.9686 0.55809 0.396 0.604
#> GSM11685 2 0.6048 0.83392 0.148 0.852
#> GSM11699 1 0.5178 0.79683 0.884 0.116
#> GSM27950 2 0.9358 0.63226 0.352 0.648
#> GSM27946 1 0.4815 0.80445 0.896 0.104
#> GSM11709 1 0.6438 0.74291 0.836 0.164
#> GSM11720 1 0.0376 0.83411 0.996 0.004
#> GSM11726 1 0.4161 0.81433 0.916 0.084
#> GSM11837 1 0.4161 0.81433 0.916 0.084
#> GSM11725 1 0.3879 0.81877 0.924 0.076
#> GSM11864 1 0.3879 0.81877 0.924 0.076
#> GSM11687 1 0.0672 0.83486 0.992 0.008
#> GSM11693 1 0.0672 0.83486 0.992 0.008
#> GSM11727 1 0.4161 0.81433 0.916 0.084
#> GSM11838 1 0.4161 0.81433 0.916 0.084
#> GSM11681 2 0.6531 0.83504 0.168 0.832
#> GSM11689 1 0.0672 0.83486 0.992 0.008
#> GSM11704 1 0.0672 0.83486 0.992 0.008
#> GSM11703 1 0.3879 0.81796 0.924 0.076
#> GSM11705 1 0.7602 0.64766 0.780 0.220
#> GSM11722 1 0.4690 0.81157 0.900 0.100
#> GSM11730 1 0.4161 0.81433 0.916 0.084
#> GSM11713 2 0.7299 0.81341 0.204 0.796
#> GSM11728 2 0.7745 0.79239 0.228 0.772
#> GSM27947 1 0.4815 0.80445 0.896 0.104
#> GSM27951 1 0.9909 0.00942 0.556 0.444
#> GSM11707 2 0.4431 0.81823 0.092 0.908
#> GSM11716 1 0.4298 0.81977 0.912 0.088
#> GSM11850 1 0.4431 0.82109 0.908 0.092
#> GSM11851 1 0.4431 0.82109 0.908 0.092
#> GSM11721 1 0.2603 0.82942 0.956 0.044
#> GSM11852 1 0.2603 0.82942 0.956 0.044
#> GSM11694 1 0.4815 0.80445 0.896 0.104
#> GSM11695 1 0.4815 0.80445 0.896 0.104
#> GSM11734 1 0.4161 0.81433 0.916 0.084
#> GSM11861 1 0.2423 0.82946 0.960 0.040
#> GSM11843 1 0.4022 0.82058 0.920 0.080
#> GSM11862 1 0.2423 0.82946 0.960 0.040
#> GSM11697 1 0.5178 0.79683 0.884 0.116
#> GSM11714 2 0.4431 0.81823 0.092 0.908
#> GSM11723 1 0.4298 0.81977 0.912 0.088
#> GSM11845 1 0.4298 0.81977 0.912 0.088
#> GSM11683 2 1.0000 0.24699 0.500 0.500
#> GSM11691 1 0.9427 0.30693 0.640 0.360
#> GSM27949 1 0.9993 -0.22521 0.516 0.484
#> GSM27945 1 0.4815 0.80445 0.896 0.104
#> GSM11706 2 0.4939 0.82440 0.108 0.892
#> GSM11853 1 0.5178 0.79683 0.884 0.116
#> GSM11729 1 0.4161 0.81433 0.916 0.084
#> GSM11746 1 0.4161 0.81433 0.916 0.084
#> GSM11711 1 0.5519 0.78099 0.872 0.128
#> GSM11854 1 0.5178 0.79683 0.884 0.116
#> GSM11731 1 0.4161 0.81433 0.916 0.084
#> GSM11839 1 0.4161 0.81433 0.916 0.084
#> GSM11836 1 0.6438 0.80754 0.836 0.164
#> GSM11849 1 0.6148 0.76328 0.848 0.152
#> GSM11682 2 0.6531 0.83504 0.168 0.832
#> GSM11690 1 0.6048 0.76726 0.852 0.148
#> GSM11692 1 0.2423 0.83174 0.960 0.040
#> GSM11841 1 0.2423 0.83174 0.960 0.040
#> GSM11901 1 0.2423 0.83174 0.960 0.040
#> GSM11715 1 0.6801 0.76493 0.820 0.180
#> GSM11724 1 0.6801 0.76493 0.820 0.180
#> GSM11684 1 0.6048 0.76726 0.852 0.148
#> GSM11696 1 0.6048 0.76726 0.852 0.148
#> GSM27952 2 0.6531 0.83504 0.168 0.832
#> GSM27948 1 0.6048 0.76726 0.852 0.148
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM11708 2 0.6763 0.4334 0.012 0.552 0.436
#> GSM11735 2 0.6763 0.4334 0.012 0.552 0.436
#> GSM11733 2 0.9773 0.5614 0.340 0.420 0.240
#> GSM11863 2 0.9773 0.5614 0.340 0.420 0.240
#> GSM11710 3 0.5696 0.5031 0.064 0.136 0.800
#> GSM11712 1 0.2443 0.7655 0.940 0.032 0.028
#> GSM11732 1 0.8350 0.1203 0.600 0.280 0.120
#> GSM11844 1 0.8408 0.1178 0.596 0.280 0.124
#> GSM11842 1 0.7772 0.4243 0.676 0.152 0.172
#> GSM11860 1 0.7772 0.4243 0.676 0.152 0.172
#> GSM11686 3 0.2165 0.6512 0.064 0.000 0.936
#> GSM11688 3 0.3045 0.6415 0.064 0.020 0.916
#> GSM11846 1 0.6647 0.3216 0.592 0.012 0.396
#> GSM11680 1 0.3998 0.7319 0.884 0.056 0.060
#> GSM11698 1 0.4095 0.7295 0.880 0.056 0.064
#> GSM11840 2 0.9773 0.5614 0.340 0.420 0.240
#> GSM11847 2 0.9773 0.5614 0.340 0.420 0.240
#> GSM11685 3 0.3045 0.6415 0.064 0.020 0.916
#> GSM11699 1 0.3998 0.7312 0.884 0.056 0.060
#> GSM27950 3 0.9633 -0.3374 0.236 0.300 0.464
#> GSM27946 1 0.3583 0.7378 0.900 0.056 0.044
#> GSM11709 1 0.4808 0.6753 0.804 0.008 0.188
#> GSM11720 1 0.0747 0.7660 0.984 0.016 0.000
#> GSM11726 1 0.5785 0.6247 0.668 0.332 0.000
#> GSM11837 1 0.5785 0.6247 0.668 0.332 0.000
#> GSM11725 1 0.3267 0.7480 0.884 0.116 0.000
#> GSM11864 1 0.3267 0.7480 0.884 0.116 0.000
#> GSM11687 1 0.0848 0.7662 0.984 0.008 0.008
#> GSM11693 1 0.0848 0.7662 0.984 0.008 0.008
#> GSM11727 1 0.5785 0.6247 0.668 0.332 0.000
#> GSM11838 1 0.5785 0.6247 0.668 0.332 0.000
#> GSM11681 3 0.2165 0.6512 0.064 0.000 0.936
#> GSM11689 1 0.0848 0.7662 0.984 0.008 0.008
#> GSM11704 1 0.0848 0.7662 0.984 0.008 0.008
#> GSM11703 1 0.3134 0.7512 0.916 0.052 0.032
#> GSM11705 1 0.7222 0.5389 0.684 0.072 0.244
#> GSM11722 1 0.6264 0.6797 0.724 0.244 0.032
#> GSM11730 1 0.5785 0.6247 0.668 0.332 0.000
#> GSM11713 3 0.5764 0.5902 0.076 0.124 0.800
#> GSM11728 3 0.6176 0.5822 0.100 0.120 0.780
#> GSM27947 1 0.3583 0.7378 0.900 0.056 0.044
#> GSM27951 3 0.7491 0.0581 0.472 0.036 0.492
#> GSM11707 2 0.6819 0.3961 0.012 0.512 0.476
#> GSM11716 1 0.2959 0.7508 0.900 0.100 0.000
#> GSM11850 1 0.2711 0.7518 0.912 0.088 0.000
#> GSM11851 1 0.2711 0.7518 0.912 0.088 0.000
#> GSM11721 1 0.1585 0.7617 0.964 0.008 0.028
#> GSM11852 1 0.1585 0.7617 0.964 0.008 0.028
#> GSM11694 1 0.3583 0.7378 0.900 0.056 0.044
#> GSM11695 1 0.3583 0.7378 0.900 0.056 0.044
#> GSM11734 1 0.5216 0.6724 0.740 0.260 0.000
#> GSM11861 1 0.1411 0.7602 0.964 0.000 0.036
#> GSM11843 1 0.5024 0.6974 0.776 0.220 0.004
#> GSM11862 1 0.1411 0.7602 0.964 0.000 0.036
#> GSM11697 1 0.3797 0.7335 0.892 0.056 0.052
#> GSM11714 2 0.6822 0.3897 0.012 0.508 0.480
#> GSM11723 1 0.2959 0.7508 0.900 0.100 0.000
#> GSM11845 1 0.2959 0.7508 0.900 0.100 0.000
#> GSM11683 3 0.7715 0.1115 0.428 0.048 0.524
#> GSM11691 1 0.7334 0.3743 0.624 0.048 0.328
#> GSM27949 1 0.9776 -0.3411 0.440 0.276 0.284
#> GSM27945 1 0.3583 0.7378 0.900 0.056 0.044
#> GSM11706 3 0.7293 -0.4499 0.028 0.476 0.496
#> GSM11853 1 0.3998 0.7312 0.884 0.056 0.060
#> GSM11729 1 0.5397 0.6603 0.720 0.280 0.000
#> GSM11746 1 0.5397 0.6603 0.720 0.280 0.000
#> GSM11711 1 0.4768 0.7189 0.848 0.052 0.100
#> GSM11854 1 0.3998 0.7312 0.884 0.056 0.060
#> GSM11731 1 0.5216 0.6724 0.740 0.260 0.000
#> GSM11839 1 0.5216 0.6724 0.740 0.260 0.000
#> GSM11836 1 0.7680 0.6685 0.680 0.188 0.132
#> GSM11849 1 0.7651 0.5692 0.680 0.124 0.196
#> GSM11682 3 0.2165 0.6512 0.064 0.000 0.936
#> GSM11690 1 0.7124 0.5872 0.708 0.088 0.204
#> GSM11692 1 0.2443 0.7655 0.940 0.032 0.028
#> GSM11841 1 0.2443 0.7655 0.940 0.032 0.028
#> GSM11901 1 0.2443 0.7655 0.940 0.032 0.028
#> GSM11715 1 0.9131 0.4558 0.520 0.312 0.168
#> GSM11724 1 0.9131 0.4558 0.520 0.312 0.168
#> GSM11684 1 0.7124 0.5872 0.708 0.088 0.204
#> GSM11696 1 0.7124 0.5872 0.708 0.088 0.204
#> GSM27952 3 0.2165 0.6512 0.064 0.000 0.936
#> GSM27948 1 0.7124 0.5872 0.708 0.088 0.204
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM11708 4 0.0000 0.5667 0.000 0.000 0.000 1.000
#> GSM11735 4 0.0000 0.5667 0.000 0.000 0.000 1.000
#> GSM11733 4 0.4855 0.5747 0.004 0.000 0.352 0.644
#> GSM11863 4 0.4855 0.5747 0.004 0.000 0.352 0.644
#> GSM11710 1 0.6292 0.6620 0.592 0.000 0.076 0.332
#> GSM11712 3 0.2216 0.7145 0.000 0.092 0.908 0.000
#> GSM11732 3 0.4978 0.1982 0.004 0.000 0.612 0.384
#> GSM11844 3 0.5112 0.1991 0.008 0.000 0.608 0.384
#> GSM11842 3 0.4584 0.4412 0.000 0.004 0.696 0.300
#> GSM11860 3 0.4584 0.4412 0.000 0.004 0.696 0.300
#> GSM11686 1 0.4740 0.9113 0.788 0.000 0.080 0.132
#> GSM11688 1 0.5077 0.8997 0.760 0.000 0.080 0.160
#> GSM11846 3 0.6315 0.4506 0.300 0.004 0.620 0.076
#> GSM11680 3 0.2521 0.7558 0.024 0.000 0.912 0.064
#> GSM11698 3 0.2623 0.7543 0.028 0.000 0.908 0.064
#> GSM11840 4 0.4855 0.5747 0.004 0.000 0.352 0.644
#> GSM11847 4 0.4855 0.5747 0.004 0.000 0.352 0.644
#> GSM11685 1 0.5077 0.8997 0.760 0.000 0.080 0.160
#> GSM11699 3 0.2521 0.7554 0.024 0.000 0.912 0.064
#> GSM27950 4 0.7700 0.2810 0.304 0.000 0.248 0.448
#> GSM27946 3 0.2234 0.7587 0.008 0.004 0.924 0.064
#> GSM11709 3 0.4188 0.6937 0.144 0.008 0.820 0.028
#> GSM11720 3 0.1488 0.7469 0.012 0.032 0.956 0.000
#> GSM11726 2 0.2589 0.7484 0.000 0.884 0.116 0.000
#> GSM11837 2 0.2589 0.7484 0.000 0.884 0.116 0.000
#> GSM11725 3 0.5035 0.5667 0.052 0.204 0.744 0.000
#> GSM11864 3 0.5035 0.5667 0.052 0.204 0.744 0.000
#> GSM11687 3 0.1520 0.7500 0.020 0.024 0.956 0.000
#> GSM11693 3 0.1520 0.7500 0.020 0.024 0.956 0.000
#> GSM11727 2 0.2589 0.7484 0.000 0.884 0.116 0.000
#> GSM11838 2 0.2589 0.7484 0.000 0.884 0.116 0.000
#> GSM11681 1 0.4740 0.9113 0.788 0.000 0.080 0.132
#> GSM11689 3 0.1520 0.7500 0.020 0.024 0.956 0.000
#> GSM11704 3 0.1520 0.7500 0.020 0.024 0.956 0.000
#> GSM11703 3 0.3001 0.7566 0.024 0.024 0.904 0.048
#> GSM11705 3 0.6337 0.5844 0.240 0.028 0.672 0.060
#> GSM11722 2 0.5517 0.7152 0.036 0.648 0.316 0.000
#> GSM11730 2 0.2589 0.7484 0.000 0.884 0.116 0.000
#> GSM11713 1 0.2266 0.8198 0.912 0.004 0.084 0.000
#> GSM11728 1 0.2654 0.8028 0.888 0.004 0.108 0.000
#> GSM27947 3 0.2234 0.7587 0.008 0.004 0.924 0.064
#> GSM27951 3 0.5938 0.0258 0.476 0.000 0.488 0.036
#> GSM11707 4 0.1637 0.5460 0.060 0.000 0.000 0.940
#> GSM11716 3 0.5096 0.6171 0.084 0.156 0.760 0.000
#> GSM11850 3 0.4955 0.6242 0.084 0.144 0.772 0.000
#> GSM11851 3 0.4955 0.6242 0.084 0.144 0.772 0.000
#> GSM11721 3 0.0376 0.7548 0.004 0.004 0.992 0.000
#> GSM11852 3 0.0376 0.7548 0.004 0.004 0.992 0.000
#> GSM11694 3 0.2048 0.7577 0.008 0.000 0.928 0.064
#> GSM11695 3 0.2048 0.7577 0.008 0.000 0.928 0.064
#> GSM11734 2 0.5694 0.6367 0.080 0.696 0.224 0.000
#> GSM11861 3 0.0336 0.7558 0.008 0.000 0.992 0.000
#> GSM11843 2 0.6206 0.4232 0.056 0.540 0.404 0.000
#> GSM11862 3 0.0336 0.7558 0.008 0.000 0.992 0.000
#> GSM11697 3 0.2300 0.7560 0.016 0.000 0.920 0.064
#> GSM11714 4 0.1716 0.5424 0.064 0.000 0.000 0.936
#> GSM11723 3 0.5141 0.6139 0.084 0.160 0.756 0.000
#> GSM11845 3 0.5096 0.6171 0.084 0.156 0.760 0.000
#> GSM11683 3 0.7115 -0.0733 0.420 0.000 0.452 0.128
#> GSM11691 3 0.6327 0.4661 0.228 0.000 0.648 0.124
#> GSM27949 3 0.7243 -0.1718 0.144 0.000 0.452 0.404
#> GSM27945 3 0.2048 0.7577 0.008 0.000 0.928 0.064
#> GSM11706 4 0.3144 0.5311 0.072 0.000 0.044 0.884
#> GSM11853 3 0.2521 0.7551 0.024 0.000 0.912 0.064
#> GSM11729 2 0.4103 0.7743 0.000 0.744 0.256 0.000
#> GSM11746 2 0.4103 0.7743 0.000 0.744 0.256 0.000
#> GSM11711 3 0.4401 0.7372 0.080 0.024 0.836 0.060
#> GSM11854 3 0.2521 0.7551 0.024 0.000 0.912 0.064
#> GSM11731 2 0.4123 0.7526 0.008 0.772 0.220 0.000
#> GSM11839 2 0.4123 0.7526 0.008 0.772 0.220 0.000
#> GSM11836 2 0.7119 0.3258 0.128 0.444 0.428 0.000
#> GSM11849 3 0.6465 0.4189 0.228 0.136 0.636 0.000
#> GSM11682 1 0.4740 0.9113 0.788 0.000 0.080 0.132
#> GSM11690 3 0.5041 0.5756 0.232 0.040 0.728 0.000
#> GSM11692 3 0.2216 0.7145 0.000 0.092 0.908 0.000
#> GSM11841 3 0.2216 0.7145 0.000 0.092 0.908 0.000
#> GSM11901 3 0.2216 0.7145 0.000 0.092 0.908 0.000
#> GSM11715 2 0.7220 0.6294 0.212 0.548 0.240 0.000
#> GSM11724 2 0.7220 0.6294 0.212 0.548 0.240 0.000
#> GSM11684 3 0.5041 0.5756 0.232 0.040 0.728 0.000
#> GSM11696 3 0.5041 0.5756 0.232 0.040 0.728 0.000
#> GSM27952 1 0.4740 0.9113 0.788 0.000 0.080 0.132
#> GSM27948 3 0.5041 0.5756 0.232 0.040 0.728 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM11708 3 0.0000 0.875 0.000 0.000 1.000 0.000 0.000
#> GSM11735 3 0.0000 0.875 0.000 0.000 1.000 0.000 0.000
#> GSM11733 5 0.6963 0.835 0.044 0.000 0.404 0.120 0.432
#> GSM11863 5 0.6963 0.835 0.044 0.000 0.404 0.120 0.432
#> GSM11710 1 0.3957 0.410 0.712 0.000 0.280 0.008 0.000
#> GSM11712 4 0.2130 0.736 0.000 0.080 0.000 0.908 0.012
#> GSM11732 4 0.6972 -0.449 0.012 0.000 0.224 0.404 0.360
#> GSM11844 4 0.7046 -0.438 0.016 0.000 0.224 0.412 0.348
#> GSM11842 4 0.6055 0.389 0.040 0.000 0.204 0.648 0.108
#> GSM11860 4 0.6055 0.389 0.040 0.000 0.204 0.648 0.108
#> GSM11686 1 0.2069 0.670 0.912 0.000 0.076 0.012 0.000
#> GSM11688 1 0.2470 0.655 0.884 0.000 0.104 0.012 0.000
#> GSM11846 4 0.5034 0.398 0.348 0.000 0.020 0.616 0.016
#> GSM11680 4 0.3046 0.741 0.028 0.000 0.020 0.876 0.076
#> GSM11698 4 0.3129 0.739 0.032 0.000 0.020 0.872 0.076
#> GSM11840 5 0.6963 0.835 0.044 0.000 0.404 0.120 0.432
#> GSM11847 5 0.6963 0.835 0.044 0.000 0.404 0.120 0.432
#> GSM11685 1 0.2470 0.655 0.884 0.000 0.104 0.012 0.000
#> GSM11699 4 0.3046 0.740 0.028 0.000 0.020 0.876 0.076
#> GSM27950 1 0.7851 -0.445 0.348 0.000 0.252 0.068 0.332
#> GSM27946 4 0.2700 0.745 0.012 0.004 0.020 0.896 0.068
#> GSM11709 4 0.3544 0.685 0.164 0.000 0.008 0.812 0.016
#> GSM11720 4 0.1399 0.755 0.000 0.028 0.000 0.952 0.020
#> GSM11726 2 0.0404 0.710 0.000 0.988 0.000 0.012 0.000
#> GSM11837 2 0.0404 0.710 0.000 0.988 0.000 0.012 0.000
#> GSM11725 4 0.4818 0.594 0.000 0.180 0.000 0.720 0.100
#> GSM11864 4 0.4818 0.594 0.000 0.180 0.000 0.720 0.100
#> GSM11687 4 0.1503 0.756 0.008 0.020 0.000 0.952 0.020
#> GSM11693 4 0.1503 0.756 0.008 0.020 0.000 0.952 0.020
#> GSM11727 2 0.0404 0.710 0.000 0.988 0.000 0.012 0.000
#> GSM11838 2 0.0404 0.710 0.000 0.988 0.000 0.012 0.000
#> GSM11681 1 0.2069 0.670 0.912 0.000 0.076 0.012 0.000
#> GSM11689 4 0.1503 0.756 0.008 0.020 0.000 0.952 0.020
#> GSM11704 4 0.1503 0.756 0.008 0.020 0.000 0.952 0.020
#> GSM11703 4 0.3291 0.748 0.024 0.020 0.012 0.872 0.072
#> GSM11705 4 0.6144 0.574 0.200 0.020 0.012 0.648 0.120
#> GSM11722 2 0.4438 0.697 0.012 0.748 0.000 0.204 0.036
#> GSM11730 2 0.0404 0.710 0.000 0.988 0.000 0.012 0.000
#> GSM11713 1 0.2971 0.540 0.836 0.008 0.000 0.000 0.156
#> GSM11728 1 0.3606 0.533 0.816 0.008 0.000 0.024 0.152
#> GSM27947 4 0.2700 0.745 0.012 0.004 0.020 0.896 0.068
#> GSM27951 1 0.4450 -0.116 0.508 0.000 0.000 0.488 0.004
#> GSM11707 3 0.1544 0.897 0.068 0.000 0.932 0.000 0.000
#> GSM11716 4 0.4101 0.528 0.000 0.004 0.000 0.664 0.332
#> GSM11850 4 0.4047 0.535 0.000 0.004 0.000 0.676 0.320
#> GSM11851 4 0.4047 0.535 0.000 0.004 0.000 0.676 0.320
#> GSM11721 4 0.0451 0.755 0.000 0.004 0.000 0.988 0.008
#> GSM11852 4 0.0451 0.755 0.000 0.004 0.000 0.988 0.008
#> GSM11694 4 0.2666 0.743 0.012 0.000 0.020 0.892 0.076
#> GSM11695 4 0.2666 0.743 0.012 0.000 0.020 0.892 0.076
#> GSM11734 2 0.6117 0.554 0.000 0.540 0.000 0.156 0.304
#> GSM11861 4 0.1168 0.756 0.008 0.000 0.000 0.960 0.032
#> GSM11843 2 0.6439 0.375 0.000 0.448 0.000 0.372 0.180
#> GSM11862 4 0.0451 0.756 0.008 0.000 0.000 0.988 0.004
#> GSM11697 4 0.2866 0.742 0.020 0.000 0.020 0.884 0.076
#> GSM11714 3 0.1544 0.896 0.068 0.000 0.932 0.000 0.000
#> GSM11723 4 0.4218 0.524 0.000 0.008 0.000 0.660 0.332
#> GSM11845 4 0.4101 0.528 0.000 0.004 0.000 0.664 0.332
#> GSM11683 1 0.6615 0.095 0.476 0.000 0.060 0.400 0.064
#> GSM11691 4 0.6328 0.369 0.280 0.000 0.060 0.592 0.068
#> GSM27949 5 0.8433 0.470 0.176 0.000 0.220 0.264 0.340
#> GSM27945 4 0.2666 0.743 0.012 0.000 0.020 0.892 0.076
#> GSM11706 3 0.3003 0.816 0.092 0.000 0.864 0.044 0.000
#> GSM11853 4 0.3046 0.740 0.028 0.000 0.020 0.876 0.076
#> GSM11729 2 0.4410 0.729 0.000 0.764 0.000 0.124 0.112
#> GSM11746 2 0.4410 0.729 0.000 0.764 0.000 0.124 0.112
#> GSM11711 4 0.4447 0.719 0.092 0.020 0.012 0.804 0.072
#> GSM11854 4 0.3046 0.740 0.028 0.000 0.020 0.876 0.076
#> GSM11731 2 0.4807 0.705 0.000 0.728 0.000 0.140 0.132
#> GSM11839 2 0.4807 0.705 0.000 0.728 0.000 0.140 0.132
#> GSM11836 2 0.7204 0.304 0.068 0.452 0.000 0.364 0.116
#> GSM11849 4 0.6447 0.432 0.072 0.072 0.000 0.596 0.260
#> GSM11682 1 0.2069 0.670 0.912 0.000 0.076 0.012 0.000
#> GSM11690 4 0.5274 0.614 0.080 0.036 0.000 0.724 0.160
#> GSM11692 4 0.2130 0.736 0.000 0.080 0.000 0.908 0.012
#> GSM11841 4 0.2130 0.736 0.000 0.080 0.000 0.908 0.012
#> GSM11901 4 0.2130 0.736 0.000 0.080 0.000 0.908 0.012
#> GSM11715 2 0.6725 0.601 0.060 0.572 0.000 0.112 0.256
#> GSM11724 2 0.6725 0.601 0.060 0.572 0.000 0.112 0.256
#> GSM11684 4 0.5274 0.614 0.080 0.036 0.000 0.724 0.160
#> GSM11696 4 0.5274 0.614 0.080 0.036 0.000 0.724 0.160
#> GSM27952 1 0.2069 0.670 0.912 0.000 0.076 0.012 0.000
#> GSM27948 4 0.5274 0.614 0.080 0.036 0.000 0.724 0.160
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM11708 6 0.127 0.9107 0.000 0.000 0.000 0.000 0.060 0.940
#> GSM11735 6 0.127 0.9107 0.000 0.000 0.000 0.000 0.060 0.940
#> GSM11733 5 0.101 0.6256 0.000 0.000 0.004 0.000 0.960 0.036
#> GSM11863 5 0.101 0.6256 0.000 0.000 0.004 0.000 0.960 0.036
#> GSM11710 1 0.387 0.4653 0.704 0.000 0.008 0.000 0.012 0.276
#> GSM11712 3 0.171 0.7193 0.000 0.000 0.908 0.092 0.000 0.000
#> GSM11732 5 0.446 0.4186 0.000 0.000 0.352 0.016 0.616 0.016
#> GSM11844 5 0.426 0.4151 0.004 0.000 0.364 0.004 0.616 0.012
#> GSM11842 3 0.485 0.2798 0.000 0.012 0.548 0.000 0.404 0.036
#> GSM11860 3 0.485 0.2798 0.000 0.012 0.548 0.000 0.404 0.036
#> GSM11686 1 0.216 0.7073 0.904 0.000 0.012 0.000 0.012 0.072
#> GSM11688 1 0.252 0.6950 0.876 0.000 0.012 0.000 0.012 0.100
#> GSM11846 3 0.497 0.4051 0.332 0.028 0.604 0.000 0.036 0.000
#> GSM11680 3 0.263 0.7462 0.020 0.004 0.864 0.000 0.112 0.000
#> GSM11698 3 0.272 0.7443 0.024 0.004 0.860 0.000 0.112 0.000
#> GSM11840 5 0.101 0.6256 0.000 0.000 0.004 0.000 0.960 0.036
#> GSM11847 5 0.101 0.6256 0.000 0.000 0.004 0.000 0.960 0.036
#> GSM11685 1 0.252 0.6950 0.876 0.000 0.012 0.000 0.012 0.100
#> GSM11699 3 0.254 0.7484 0.020 0.004 0.872 0.000 0.104 0.000
#> GSM27950 5 0.511 0.3510 0.336 0.000 0.040 0.000 0.592 0.032
#> GSM27946 3 0.216 0.7520 0.008 0.000 0.892 0.004 0.096 0.000
#> GSM11709 3 0.368 0.6855 0.156 0.028 0.796 0.000 0.016 0.004
#> GSM11720 3 0.172 0.7455 0.000 0.036 0.932 0.028 0.004 0.000
#> GSM11726 2 0.462 0.6436 0.000 0.644 0.000 0.304 0.012 0.040
#> GSM11837 2 0.462 0.6436 0.000 0.644 0.000 0.304 0.012 0.040
#> GSM11725 3 0.467 0.5189 0.000 0.088 0.692 0.212 0.008 0.000
#> GSM11864 3 0.467 0.5189 0.000 0.088 0.692 0.212 0.008 0.000
#> GSM11687 3 0.174 0.7487 0.008 0.032 0.936 0.020 0.004 0.000
#> GSM11693 3 0.174 0.7487 0.008 0.032 0.936 0.020 0.004 0.000
#> GSM11727 2 0.462 0.6436 0.000 0.644 0.000 0.304 0.012 0.040
#> GSM11838 2 0.462 0.6436 0.000 0.644 0.000 0.304 0.012 0.040
#> GSM11681 1 0.216 0.7073 0.904 0.000 0.012 0.000 0.012 0.072
#> GSM11689 3 0.174 0.7487 0.008 0.032 0.936 0.020 0.004 0.000
#> GSM11704 3 0.174 0.7487 0.008 0.032 0.936 0.020 0.004 0.000
#> GSM11703 3 0.298 0.7517 0.020 0.028 0.864 0.004 0.084 0.000
#> GSM11705 3 0.581 0.5971 0.172 0.100 0.644 0.004 0.080 0.000
#> GSM11722 2 0.555 0.3190 0.004 0.588 0.160 0.244 0.004 0.000
#> GSM11730 2 0.462 0.6436 0.000 0.644 0.000 0.304 0.012 0.040
#> GSM11713 1 0.301 0.5352 0.800 0.192 0.000 0.004 0.004 0.000
#> GSM11728 1 0.358 0.5257 0.780 0.188 0.024 0.004 0.004 0.000
#> GSM27947 3 0.216 0.7520 0.008 0.000 0.892 0.004 0.096 0.000
#> GSM27951 1 0.400 -0.1192 0.508 0.000 0.488 0.004 0.000 0.000
#> GSM11707 6 0.153 0.9218 0.068 0.000 0.000 0.000 0.004 0.928
#> GSM11716 3 0.518 0.3968 0.000 0.004 0.608 0.312 0.056 0.020
#> GSM11850 3 0.513 0.4102 0.000 0.004 0.620 0.300 0.056 0.020
#> GSM11851 3 0.513 0.4102 0.000 0.004 0.620 0.300 0.056 0.020
#> GSM11721 3 0.052 0.7508 0.000 0.008 0.984 0.008 0.000 0.000
#> GSM11852 3 0.052 0.7508 0.000 0.008 0.984 0.008 0.000 0.000
#> GSM11694 3 0.231 0.7490 0.008 0.004 0.880 0.000 0.108 0.000
#> GSM11695 3 0.231 0.7490 0.008 0.004 0.880 0.000 0.108 0.000
#> GSM11734 4 0.191 0.5443 0.000 0.004 0.096 0.900 0.000 0.000
#> GSM11861 3 0.180 0.7515 0.008 0.000 0.936 0.016 0.020 0.020
#> GSM11843 4 0.470 0.4140 0.000 0.044 0.368 0.584 0.004 0.000
#> GSM11862 3 0.052 0.7517 0.008 0.000 0.984 0.008 0.000 0.000
#> GSM11697 3 0.241 0.7495 0.016 0.004 0.880 0.000 0.100 0.000
#> GSM11714 6 0.139 0.9207 0.068 0.000 0.000 0.000 0.000 0.932
#> GSM11723 3 0.507 0.3903 0.000 0.004 0.608 0.320 0.052 0.016
#> GSM11845 3 0.518 0.3968 0.000 0.004 0.608 0.312 0.056 0.020
#> GSM11683 1 0.604 0.1141 0.464 0.000 0.400 0.000 0.088 0.048
#> GSM11691 3 0.593 0.3786 0.268 0.000 0.588 0.008 0.088 0.048
#> GSM27949 5 0.534 0.5034 0.164 0.004 0.224 0.000 0.608 0.000
#> GSM27945 3 0.231 0.7490 0.008 0.004 0.880 0.000 0.108 0.000
#> GSM11706 6 0.284 0.8613 0.092 0.000 0.044 0.000 0.004 0.860
#> GSM11853 3 0.257 0.7477 0.024 0.004 0.872 0.000 0.100 0.000
#> GSM11729 2 0.417 0.5687 0.000 0.708 0.056 0.236 0.000 0.000
#> GSM11746 2 0.417 0.5687 0.000 0.708 0.056 0.236 0.000 0.000
#> GSM11711 3 0.410 0.7244 0.088 0.028 0.792 0.004 0.088 0.000
#> GSM11854 3 0.257 0.7477 0.024 0.004 0.872 0.000 0.100 0.000
#> GSM11731 4 0.462 0.4961 0.000 0.236 0.092 0.672 0.000 0.000
#> GSM11839 4 0.462 0.4961 0.000 0.236 0.092 0.672 0.000 0.000
#> GSM11836 2 0.652 -0.0163 0.048 0.464 0.316 0.172 0.000 0.000
#> GSM11849 3 0.460 0.3558 0.032 0.408 0.556 0.004 0.000 0.000
#> GSM11682 1 0.216 0.7073 0.904 0.000 0.012 0.000 0.012 0.072
#> GSM11690 3 0.451 0.5627 0.036 0.236 0.704 0.020 0.004 0.000
#> GSM11692 3 0.171 0.7193 0.000 0.000 0.908 0.092 0.000 0.000
#> GSM11841 3 0.171 0.7193 0.000 0.000 0.908 0.092 0.000 0.000
#> GSM11901 3 0.171 0.7193 0.000 0.000 0.908 0.092 0.000 0.000
#> GSM11715 2 0.181 0.4725 0.020 0.920 0.060 0.000 0.000 0.000
#> GSM11724 2 0.181 0.4725 0.020 0.920 0.060 0.000 0.000 0.000
#> GSM11684 3 0.451 0.5627 0.036 0.236 0.704 0.020 0.004 0.000
#> GSM11696 3 0.451 0.5627 0.036 0.236 0.704 0.020 0.004 0.000
#> GSM27952 1 0.216 0.7073 0.904 0.000 0.012 0.000 0.012 0.072
#> GSM27948 3 0.451 0.5627 0.036 0.236 0.704 0.020 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 cell.line(p) agent(p) time(p) k
#> SD:hclust 74 0.000178 0.844 6.00e-01 2
#> SD:hclust 66 0.000335 0.616 6.12e-04 3
#> SD:hclust 70 0.001431 0.275 2.41e-07 4
#> SD:hclust 69 0.001444 0.279 8.69e-09 5
#> SD:hclust 60 0.025299 0.296 1.56e-09 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 14502 rows and 83 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.565 0.787 0.903 0.4518 0.533 0.533
#> 3 3 0.438 0.773 0.842 0.3430 0.703 0.512
#> 4 4 0.561 0.744 0.805 0.1396 0.914 0.787
#> 5 5 0.570 0.561 0.736 0.0828 0.940 0.826
#> 6 6 0.619 0.458 0.688 0.0534 0.963 0.878
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM11708 2 0.000 0.87155 0.000 1.000
#> GSM11735 2 0.000 0.87155 0.000 1.000
#> GSM11733 2 0.000 0.87155 0.000 1.000
#> GSM11863 2 0.204 0.85876 0.032 0.968
#> GSM11710 2 0.000 0.87155 0.000 1.000
#> GSM11712 1 0.141 0.89848 0.980 0.020
#> GSM11732 1 1.000 0.00580 0.500 0.500
#> GSM11844 2 1.000 -0.02038 0.492 0.508
#> GSM11842 2 0.204 0.85876 0.032 0.968
#> GSM11860 2 0.204 0.85876 0.032 0.968
#> GSM11686 2 0.494 0.80262 0.108 0.892
#> GSM11688 2 0.000 0.87155 0.000 1.000
#> GSM11846 2 0.000 0.87155 0.000 1.000
#> GSM11680 1 0.995 0.17519 0.540 0.460
#> GSM11698 2 1.000 -0.00372 0.488 0.512
#> GSM11840 2 0.000 0.87155 0.000 1.000
#> GSM11847 2 0.000 0.87155 0.000 1.000
#> GSM11685 2 0.000 0.87155 0.000 1.000
#> GSM11699 1 0.634 0.80032 0.840 0.160
#> GSM27950 2 0.000 0.87155 0.000 1.000
#> GSM27946 1 0.615 0.80752 0.848 0.152
#> GSM11709 2 0.958 0.40451 0.380 0.620
#> GSM11720 1 0.141 0.89848 0.980 0.020
#> GSM11726 1 0.000 0.89521 1.000 0.000
#> GSM11837 1 0.000 0.89521 1.000 0.000
#> GSM11725 1 0.000 0.89521 1.000 0.000
#> GSM11864 1 0.141 0.89848 0.980 0.020
#> GSM11687 1 0.141 0.89848 0.980 0.020
#> GSM11693 1 0.141 0.89848 0.980 0.020
#> GSM11727 1 0.000 0.89521 1.000 0.000
#> GSM11838 1 0.000 0.89521 1.000 0.000
#> GSM11681 2 0.000 0.87155 0.000 1.000
#> GSM11689 1 0.141 0.89848 0.980 0.020
#> GSM11704 1 0.141 0.89848 0.980 0.020
#> GSM11703 1 0.141 0.89848 0.980 0.020
#> GSM11705 2 0.969 0.36314 0.396 0.604
#> GSM11722 1 0.000 0.89521 1.000 0.000
#> GSM11730 1 0.000 0.89521 1.000 0.000
#> GSM11713 2 0.373 0.83427 0.072 0.928
#> GSM11728 2 0.932 0.47772 0.348 0.652
#> GSM27947 1 0.141 0.89848 0.980 0.020
#> GSM27951 2 0.966 0.37391 0.392 0.608
#> GSM11707 2 0.000 0.87155 0.000 1.000
#> GSM11716 1 0.141 0.89848 0.980 0.020
#> GSM11850 1 0.861 0.64387 0.716 0.284
#> GSM11851 1 0.881 0.61626 0.700 0.300
#> GSM11721 1 0.118 0.89799 0.984 0.016
#> GSM11852 1 0.866 0.63648 0.712 0.288
#> GSM11694 1 0.855 0.65033 0.720 0.280
#> GSM11695 1 0.876 0.62398 0.704 0.296
#> GSM11734 1 0.000 0.89521 1.000 0.000
#> GSM11861 1 0.634 0.79984 0.840 0.160
#> GSM11843 1 0.141 0.89848 0.980 0.020
#> GSM11862 1 0.615 0.80752 0.848 0.152
#> GSM11697 1 0.855 0.65033 0.720 0.280
#> GSM11714 2 0.000 0.87155 0.000 1.000
#> GSM11723 1 0.000 0.89521 1.000 0.000
#> GSM11845 1 0.141 0.89848 0.980 0.020
#> GSM11683 2 0.000 0.87155 0.000 1.000
#> GSM11691 1 0.615 0.80752 0.848 0.152
#> GSM27949 2 0.706 0.71877 0.192 0.808
#> GSM27945 1 0.615 0.80752 0.848 0.152
#> GSM11706 2 0.000 0.87155 0.000 1.000
#> GSM11853 1 0.861 0.64323 0.716 0.284
#> GSM11729 1 0.000 0.89521 1.000 0.000
#> GSM11746 1 0.000 0.89521 1.000 0.000
#> GSM11711 2 0.706 0.71891 0.192 0.808
#> GSM11854 1 0.871 0.62995 0.708 0.292
#> GSM11731 1 0.000 0.89521 1.000 0.000
#> GSM11839 1 0.000 0.89521 1.000 0.000
#> GSM11836 1 0.204 0.87591 0.968 0.032
#> GSM11849 1 0.000 0.89521 1.000 0.000
#> GSM11682 2 0.000 0.87155 0.000 1.000
#> GSM11690 1 0.141 0.89848 0.980 0.020
#> GSM11692 1 0.141 0.89848 0.980 0.020
#> GSM11841 1 0.141 0.89848 0.980 0.020
#> GSM11901 1 0.141 0.89848 0.980 0.020
#> GSM11715 1 0.000 0.89521 1.000 0.000
#> GSM11724 1 0.000 0.89521 1.000 0.000
#> GSM11684 1 0.000 0.89521 1.000 0.000
#> GSM11696 1 0.000 0.89521 1.000 0.000
#> GSM27952 2 0.000 0.87155 0.000 1.000
#> GSM27948 1 0.141 0.89848 0.980 0.020
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM11708 3 0.348 0.815 0.000 0.128 0.872
#> GSM11735 3 0.397 0.813 0.008 0.132 0.860
#> GSM11733 3 0.514 0.810 0.044 0.132 0.824
#> GSM11863 3 0.666 0.778 0.116 0.132 0.752
#> GSM11710 3 0.140 0.851 0.028 0.004 0.968
#> GSM11712 1 0.334 0.800 0.880 0.120 0.000
#> GSM11732 1 0.399 0.783 0.864 0.012 0.124
#> GSM11844 1 0.350 0.784 0.880 0.004 0.116
#> GSM11842 3 0.666 0.778 0.116 0.132 0.752
#> GSM11860 3 0.673 0.776 0.120 0.132 0.748
#> GSM11686 3 0.460 0.732 0.204 0.000 0.796
#> GSM11688 3 0.196 0.851 0.056 0.000 0.944
#> GSM11846 3 0.388 0.811 0.152 0.000 0.848
#> GSM11680 1 0.319 0.794 0.896 0.004 0.100
#> GSM11698 1 0.392 0.763 0.856 0.004 0.140
#> GSM11840 3 0.514 0.810 0.044 0.132 0.824
#> GSM11847 3 0.514 0.810 0.044 0.132 0.824
#> GSM11685 3 0.207 0.850 0.060 0.000 0.940
#> GSM11699 1 0.134 0.832 0.972 0.016 0.012
#> GSM27950 3 0.186 0.851 0.052 0.000 0.948
#> GSM27946 1 0.148 0.833 0.968 0.020 0.012
#> GSM11709 1 0.765 0.526 0.644 0.080 0.276
#> GSM11720 1 0.455 0.754 0.800 0.200 0.000
#> GSM11726 2 0.412 0.918 0.168 0.832 0.000
#> GSM11837 2 0.406 0.920 0.164 0.836 0.000
#> GSM11725 1 0.573 0.546 0.676 0.324 0.000
#> GSM11864 1 0.475 0.736 0.784 0.216 0.000
#> GSM11687 1 0.355 0.797 0.868 0.132 0.000
#> GSM11693 1 0.412 0.778 0.832 0.168 0.000
#> GSM11727 2 0.375 0.920 0.144 0.856 0.000
#> GSM11838 2 0.369 0.921 0.140 0.860 0.000
#> GSM11681 3 0.254 0.845 0.080 0.000 0.920
#> GSM11689 1 0.418 0.775 0.828 0.172 0.000
#> GSM11704 1 0.418 0.775 0.828 0.172 0.000
#> GSM11703 1 0.400 0.785 0.840 0.160 0.000
#> GSM11705 1 0.774 0.486 0.632 0.080 0.288
#> GSM11722 2 0.394 0.922 0.156 0.844 0.000
#> GSM11730 2 0.369 0.920 0.140 0.860 0.000
#> GSM11713 3 0.849 0.321 0.096 0.384 0.520
#> GSM11728 3 0.967 0.133 0.216 0.360 0.424
#> GSM27947 1 0.228 0.829 0.940 0.052 0.008
#> GSM27951 1 0.802 0.448 0.604 0.088 0.308
#> GSM11707 3 0.127 0.851 0.024 0.004 0.972
#> GSM11716 1 0.295 0.820 0.908 0.088 0.004
#> GSM11850 1 0.203 0.829 0.952 0.016 0.032
#> GSM11851 1 0.176 0.826 0.956 0.004 0.040
#> GSM11721 1 0.319 0.813 0.896 0.100 0.004
#> GSM11852 1 0.164 0.831 0.964 0.016 0.020
#> GSM11694 1 0.200 0.828 0.952 0.012 0.036
#> GSM11695 1 0.200 0.828 0.952 0.012 0.036
#> GSM11734 2 0.588 0.673 0.348 0.652 0.000
#> GSM11861 1 0.148 0.831 0.968 0.020 0.012
#> GSM11843 1 0.394 0.776 0.844 0.156 0.000
#> GSM11862 1 0.127 0.831 0.972 0.024 0.004
#> GSM11697 1 0.175 0.830 0.960 0.012 0.028
#> GSM11714 3 0.127 0.851 0.024 0.004 0.972
#> GSM11723 1 0.445 0.727 0.808 0.192 0.000
#> GSM11845 1 0.341 0.798 0.876 0.124 0.000
#> GSM11683 3 0.424 0.770 0.176 0.000 0.824
#> GSM11691 1 0.134 0.832 0.972 0.012 0.016
#> GSM27949 1 0.575 0.556 0.700 0.004 0.296
#> GSM27945 1 0.148 0.831 0.968 0.012 0.020
#> GSM11706 3 0.127 0.851 0.024 0.004 0.972
#> GSM11853 1 0.127 0.831 0.972 0.004 0.024
#> GSM11729 2 0.424 0.921 0.176 0.824 0.000
#> GSM11746 2 0.424 0.921 0.176 0.824 0.000
#> GSM11711 1 0.595 0.428 0.640 0.000 0.360
#> GSM11854 1 0.127 0.830 0.972 0.004 0.024
#> GSM11731 2 0.450 0.908 0.196 0.804 0.000
#> GSM11839 2 0.450 0.906 0.196 0.804 0.000
#> GSM11836 2 0.506 0.889 0.148 0.820 0.032
#> GSM11849 2 0.557 0.861 0.184 0.784 0.032
#> GSM11682 3 0.277 0.843 0.080 0.004 0.916
#> GSM11690 1 0.400 0.804 0.868 0.116 0.016
#> GSM11692 1 0.341 0.803 0.876 0.124 0.000
#> GSM11841 1 0.355 0.798 0.868 0.132 0.000
#> GSM11901 1 0.355 0.798 0.868 0.132 0.000
#> GSM11715 2 0.388 0.921 0.152 0.848 0.000
#> GSM11724 2 0.388 0.921 0.152 0.848 0.000
#> GSM11684 2 0.678 0.547 0.396 0.588 0.016
#> GSM11696 1 0.631 -0.224 0.512 0.488 0.000
#> GSM27952 3 0.207 0.850 0.060 0.000 0.940
#> GSM27948 1 0.304 0.809 0.896 0.104 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM11708 4 0.2546 0.8167 0.092 0.008 0.000 0.900
#> GSM11735 4 0.1970 0.8618 0.060 0.008 0.000 0.932
#> GSM11733 4 0.1004 0.9274 0.004 0.000 0.024 0.972
#> GSM11863 4 0.1661 0.9114 0.000 0.004 0.052 0.944
#> GSM11710 1 0.5592 0.7470 0.608 0.008 0.016 0.368
#> GSM11712 3 0.4521 0.7931 0.056 0.092 0.828 0.024
#> GSM11732 3 0.3658 0.8078 0.068 0.004 0.864 0.064
#> GSM11844 3 0.2739 0.8171 0.036 0.000 0.904 0.060
#> GSM11842 4 0.1847 0.9079 0.004 0.004 0.052 0.940
#> GSM11860 4 0.2164 0.8875 0.004 0.004 0.068 0.924
#> GSM11686 1 0.6188 0.7609 0.636 0.004 0.072 0.288
#> GSM11688 1 0.5717 0.7637 0.608 0.004 0.028 0.360
#> GSM11846 1 0.6733 0.6858 0.564 0.000 0.112 0.324
#> GSM11680 3 0.2924 0.8186 0.036 0.004 0.900 0.060
#> GSM11698 3 0.3016 0.8174 0.040 0.004 0.896 0.060
#> GSM11840 4 0.1004 0.9274 0.004 0.000 0.024 0.972
#> GSM11847 4 0.1004 0.9274 0.004 0.000 0.024 0.972
#> GSM11685 1 0.5717 0.7637 0.608 0.004 0.028 0.360
#> GSM11699 3 0.1509 0.8245 0.012 0.008 0.960 0.020
#> GSM27950 1 0.5717 0.7637 0.608 0.004 0.028 0.360
#> GSM27946 3 0.1745 0.8253 0.020 0.008 0.952 0.020
#> GSM11709 3 0.6902 0.0337 0.428 0.048 0.496 0.028
#> GSM11720 3 0.4957 0.7482 0.060 0.164 0.772 0.004
#> GSM11726 2 0.3928 0.7918 0.088 0.848 0.060 0.004
#> GSM11837 2 0.3077 0.8031 0.068 0.892 0.036 0.004
#> GSM11725 3 0.6329 0.4912 0.064 0.344 0.588 0.004
#> GSM11864 3 0.5467 0.7148 0.056 0.224 0.716 0.004
#> GSM11687 3 0.4296 0.7735 0.060 0.112 0.824 0.004
#> GSM11693 3 0.4371 0.7741 0.064 0.112 0.820 0.004
#> GSM11727 2 0.3625 0.8037 0.120 0.852 0.024 0.004
#> GSM11838 2 0.3264 0.8069 0.096 0.876 0.024 0.004
#> GSM11681 1 0.5873 0.7607 0.660 0.004 0.056 0.280
#> GSM11689 3 0.4651 0.7713 0.080 0.112 0.804 0.004
#> GSM11704 3 0.4707 0.7703 0.080 0.116 0.800 0.004
#> GSM11703 3 0.3862 0.7904 0.060 0.084 0.852 0.004
#> GSM11705 1 0.6167 0.3373 0.568 0.016 0.388 0.028
#> GSM11722 2 0.4452 0.8147 0.156 0.796 0.048 0.000
#> GSM11730 2 0.4186 0.7992 0.164 0.808 0.024 0.004
#> GSM11713 1 0.5292 0.5337 0.776 0.140 0.028 0.056
#> GSM11728 1 0.5579 0.5373 0.768 0.100 0.100 0.032
#> GSM27947 3 0.1631 0.8277 0.020 0.016 0.956 0.008
#> GSM27951 1 0.5527 0.5045 0.700 0.020 0.256 0.024
#> GSM11707 1 0.5592 0.7470 0.608 0.008 0.016 0.368
#> GSM11716 3 0.5357 0.7813 0.108 0.068 0.784 0.040
#> GSM11850 3 0.4260 0.7939 0.116 0.008 0.828 0.048
#> GSM11851 3 0.4277 0.7957 0.116 0.004 0.824 0.056
#> GSM11721 3 0.4890 0.7822 0.084 0.084 0.808 0.024
#> GSM11852 3 0.2484 0.8219 0.040 0.012 0.924 0.024
#> GSM11694 3 0.2500 0.8192 0.044 0.000 0.916 0.040
#> GSM11695 3 0.2500 0.8192 0.044 0.000 0.916 0.040
#> GSM11734 2 0.6558 0.5907 0.132 0.664 0.192 0.012
#> GSM11861 3 0.4213 0.8030 0.136 0.012 0.824 0.028
#> GSM11843 3 0.5858 0.7385 0.088 0.180 0.720 0.012
#> GSM11862 3 0.3657 0.8133 0.096 0.016 0.864 0.024
#> GSM11697 3 0.2500 0.8192 0.044 0.000 0.916 0.040
#> GSM11714 1 0.5592 0.7470 0.608 0.008 0.016 0.368
#> GSM11723 3 0.6997 0.6518 0.156 0.200 0.628 0.016
#> GSM11845 3 0.6269 0.7430 0.156 0.112 0.708 0.024
#> GSM11683 1 0.6644 0.7230 0.624 0.004 0.124 0.248
#> GSM11691 3 0.0895 0.8284 0.020 0.004 0.976 0.000
#> GSM27949 3 0.4867 0.7313 0.144 0.004 0.784 0.068
#> GSM27945 3 0.2089 0.8234 0.048 0.000 0.932 0.020
#> GSM11706 1 0.5592 0.7470 0.608 0.008 0.016 0.368
#> GSM11853 3 0.1174 0.8255 0.020 0.000 0.968 0.012
#> GSM11729 2 0.1953 0.8145 0.012 0.940 0.044 0.004
#> GSM11746 2 0.1953 0.8145 0.012 0.940 0.044 0.004
#> GSM11711 3 0.6233 0.0980 0.388 0.000 0.552 0.060
#> GSM11854 3 0.1745 0.8249 0.020 0.008 0.952 0.020
#> GSM11731 2 0.2996 0.7988 0.064 0.892 0.044 0.000
#> GSM11839 2 0.3876 0.7890 0.068 0.856 0.068 0.008
#> GSM11836 2 0.5449 0.7803 0.132 0.768 0.076 0.024
#> GSM11849 2 0.6132 0.7436 0.168 0.712 0.100 0.020
#> GSM11682 1 0.5751 0.7579 0.664 0.004 0.048 0.284
#> GSM11690 3 0.6552 0.6565 0.164 0.120 0.688 0.028
#> GSM11692 3 0.4939 0.7740 0.060 0.108 0.804 0.028
#> GSM11841 3 0.4996 0.7734 0.060 0.112 0.800 0.028
#> GSM11901 3 0.4996 0.7734 0.060 0.112 0.800 0.028
#> GSM11715 2 0.3491 0.8136 0.104 0.864 0.028 0.004
#> GSM11724 2 0.3491 0.8136 0.104 0.864 0.028 0.004
#> GSM11684 2 0.7952 0.5018 0.192 0.496 0.292 0.020
#> GSM11696 2 0.8076 0.2426 0.180 0.412 0.388 0.020
#> GSM27952 1 0.5701 0.7646 0.612 0.004 0.028 0.356
#> GSM27948 3 0.5541 0.7450 0.108 0.096 0.768 0.028
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM11708 5 0.4886 0.7001 0.032 0.000 0.000 0.372 0.596
#> GSM11735 5 0.4723 0.8337 0.032 0.000 0.008 0.272 0.688
#> GSM11733 5 0.4096 0.9156 0.000 0.000 0.040 0.200 0.760
#> GSM11863 5 0.4453 0.9076 0.008 0.000 0.064 0.164 0.764
#> GSM11710 4 0.1444 0.8069 0.040 0.000 0.000 0.948 0.012
#> GSM11712 3 0.5152 0.4594 0.272 0.016 0.672 0.004 0.036
#> GSM11732 3 0.3481 0.6231 0.100 0.000 0.840 0.004 0.056
#> GSM11844 3 0.2747 0.6484 0.060 0.000 0.888 0.004 0.048
#> GSM11842 5 0.4453 0.9076 0.008 0.000 0.064 0.164 0.764
#> GSM11860 5 0.4436 0.8997 0.008 0.000 0.068 0.156 0.768
#> GSM11686 4 0.2395 0.8070 0.036 0.000 0.040 0.912 0.012
#> GSM11688 4 0.0000 0.8204 0.000 0.000 0.000 1.000 0.000
#> GSM11846 4 0.3599 0.6743 0.016 0.000 0.140 0.824 0.020
#> GSM11680 3 0.2278 0.6537 0.032 0.000 0.916 0.008 0.044
#> GSM11698 3 0.2515 0.6523 0.044 0.000 0.904 0.008 0.044
#> GSM11840 5 0.4096 0.9180 0.000 0.000 0.040 0.200 0.760
#> GSM11847 5 0.4096 0.9180 0.000 0.000 0.040 0.200 0.760
#> GSM11685 4 0.0000 0.8204 0.000 0.000 0.000 1.000 0.000
#> GSM11699 3 0.2756 0.6405 0.092 0.000 0.880 0.004 0.024
#> GSM27950 4 0.0981 0.8170 0.012 0.000 0.008 0.972 0.008
#> GSM27946 3 0.2784 0.6341 0.108 0.000 0.872 0.004 0.016
#> GSM11709 3 0.7817 0.3289 0.092 0.068 0.544 0.224 0.072
#> GSM11720 3 0.6019 0.5344 0.116 0.112 0.684 0.000 0.088
#> GSM11726 2 0.1278 0.6910 0.020 0.960 0.016 0.000 0.004
#> GSM11837 2 0.0566 0.7045 0.012 0.984 0.004 0.000 0.000
#> GSM11725 3 0.7698 0.0937 0.208 0.276 0.440 0.000 0.076
#> GSM11864 3 0.6914 0.4015 0.188 0.160 0.580 0.000 0.072
#> GSM11687 3 0.5681 0.5518 0.112 0.088 0.724 0.008 0.068
#> GSM11693 3 0.5816 0.5511 0.124 0.088 0.712 0.008 0.068
#> GSM11727 2 0.0771 0.7048 0.020 0.976 0.000 0.000 0.004
#> GSM11838 2 0.0162 0.7086 0.004 0.996 0.000 0.000 0.000
#> GSM11681 4 0.2930 0.7992 0.032 0.000 0.032 0.888 0.048
#> GSM11689 3 0.5982 0.5390 0.140 0.088 0.696 0.008 0.068
#> GSM11704 3 0.5982 0.5390 0.140 0.088 0.696 0.008 0.068
#> GSM11703 3 0.5449 0.5689 0.116 0.068 0.740 0.008 0.068
#> GSM11705 3 0.8150 0.1832 0.136 0.048 0.468 0.280 0.068
#> GSM11722 2 0.5386 0.5683 0.256 0.668 0.036 0.000 0.040
#> GSM11730 2 0.2873 0.6442 0.120 0.860 0.000 0.000 0.020
#> GSM11713 4 0.6847 0.5525 0.220 0.136 0.004 0.584 0.056
#> GSM11728 4 0.7688 0.5074 0.228 0.108 0.056 0.548 0.060
#> GSM27947 3 0.2589 0.6435 0.076 0.004 0.896 0.004 0.020
#> GSM27951 4 0.7312 0.4985 0.148 0.020 0.168 0.584 0.080
#> GSM11707 4 0.1522 0.8069 0.044 0.000 0.000 0.944 0.012
#> GSM11716 3 0.5038 0.5154 0.220 0.008 0.700 0.000 0.072
#> GSM11850 3 0.4742 0.5282 0.220 0.000 0.716 0.004 0.060
#> GSM11851 3 0.4679 0.5378 0.220 0.000 0.720 0.004 0.056
#> GSM11721 3 0.5582 0.3313 0.356 0.004 0.576 0.004 0.060
#> GSM11852 3 0.4070 0.5956 0.164 0.000 0.784 0.004 0.048
#> GSM11694 3 0.2609 0.6485 0.048 0.000 0.896 0.004 0.052
#> GSM11695 3 0.2609 0.6485 0.048 0.000 0.896 0.004 0.052
#> GSM11734 1 0.6350 -0.1557 0.536 0.352 0.044 0.000 0.068
#> GSM11861 3 0.5376 0.4425 0.356 0.000 0.584 0.004 0.056
#> GSM11843 3 0.6806 0.3337 0.296 0.084 0.544 0.000 0.076
#> GSM11862 3 0.4842 0.5200 0.264 0.000 0.684 0.004 0.048
#> GSM11697 3 0.2390 0.6510 0.044 0.000 0.908 0.004 0.044
#> GSM11714 4 0.1626 0.8076 0.044 0.000 0.000 0.940 0.016
#> GSM11723 1 0.7179 -0.1873 0.416 0.104 0.408 0.000 0.072
#> GSM11845 3 0.6016 0.3237 0.392 0.020 0.520 0.000 0.068
#> GSM11683 4 0.2407 0.7806 0.004 0.000 0.088 0.896 0.012
#> GSM11691 3 0.2227 0.6607 0.048 0.000 0.916 0.004 0.032
#> GSM27949 3 0.3683 0.6305 0.048 0.000 0.848 0.056 0.048
#> GSM27945 3 0.2378 0.6505 0.048 0.000 0.904 0.000 0.048
#> GSM11706 4 0.1522 0.8069 0.044 0.000 0.000 0.944 0.012
#> GSM11853 3 0.1996 0.6549 0.036 0.000 0.928 0.004 0.032
#> GSM11729 2 0.4151 0.6861 0.156 0.788 0.012 0.000 0.044
#> GSM11746 2 0.4151 0.6861 0.156 0.788 0.012 0.000 0.044
#> GSM11711 3 0.4809 0.4995 0.024 0.000 0.724 0.216 0.036
#> GSM11854 3 0.2569 0.6457 0.068 0.000 0.896 0.004 0.032
#> GSM11731 2 0.5629 0.4061 0.388 0.544 0.008 0.000 0.060
#> GSM11839 2 0.5921 0.3044 0.420 0.504 0.024 0.000 0.052
#> GSM11836 1 0.6080 -0.3192 0.476 0.440 0.032 0.000 0.052
#> GSM11849 1 0.7205 -0.2751 0.432 0.420 0.052 0.024 0.072
#> GSM11682 4 0.2095 0.8061 0.060 0.000 0.008 0.920 0.012
#> GSM11690 1 0.6401 0.2619 0.532 0.020 0.372 0.040 0.036
#> GSM11692 3 0.5261 0.4002 0.308 0.016 0.640 0.004 0.032
#> GSM11841 3 0.5485 0.3658 0.320 0.024 0.620 0.004 0.032
#> GSM11901 3 0.5485 0.3658 0.320 0.024 0.620 0.004 0.032
#> GSM11715 2 0.5481 0.5580 0.324 0.608 0.012 0.000 0.056
#> GSM11724 2 0.5481 0.5580 0.324 0.608 0.012 0.000 0.056
#> GSM11684 1 0.7093 0.4454 0.568 0.076 0.268 0.032 0.056
#> GSM11696 1 0.6881 0.4433 0.560 0.068 0.296 0.020 0.056
#> GSM27952 4 0.0162 0.8201 0.004 0.000 0.000 0.996 0.000
#> GSM27948 3 0.5798 0.0264 0.436 0.012 0.504 0.012 0.036
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM11708 5 0.6208 0.50732 0.160 0.000 0.000 0.052 0.556 0.232
#> GSM11735 5 0.4844 0.74215 0.156 0.000 0.000 0.048 0.720 0.076
#> GSM11733 5 0.1398 0.90182 0.000 0.000 0.008 0.000 0.940 0.052
#> GSM11863 5 0.1511 0.89913 0.004 0.000 0.012 0.000 0.940 0.044
#> GSM11710 6 0.4393 0.69254 0.164 0.000 0.000 0.052 0.036 0.748
#> GSM11712 3 0.6341 0.26892 0.128 0.016 0.512 0.316 0.028 0.000
#> GSM11732 3 0.2904 0.43979 0.108 0.004 0.860 0.004 0.012 0.012
#> GSM11844 3 0.2178 0.49742 0.056 0.000 0.912 0.008 0.012 0.012
#> GSM11842 5 0.1624 0.89875 0.008 0.000 0.012 0.000 0.936 0.044
#> GSM11860 5 0.1624 0.89875 0.008 0.000 0.012 0.000 0.936 0.044
#> GSM11686 6 0.1483 0.77994 0.008 0.000 0.012 0.036 0.000 0.944
#> GSM11688 6 0.0508 0.78111 0.000 0.000 0.004 0.000 0.012 0.984
#> GSM11846 6 0.4202 0.62655 0.040 0.000 0.160 0.008 0.024 0.768
#> GSM11680 3 0.2127 0.52062 0.032 0.000 0.920 0.016 0.008 0.024
#> GSM11698 3 0.2618 0.51212 0.036 0.000 0.896 0.036 0.012 0.020
#> GSM11840 5 0.1398 0.90182 0.000 0.000 0.008 0.000 0.940 0.052
#> GSM11847 5 0.1398 0.90182 0.000 0.000 0.008 0.000 0.940 0.052
#> GSM11685 6 0.0508 0.78111 0.000 0.000 0.004 0.000 0.012 0.984
#> GSM11699 3 0.3551 0.52877 0.024 0.000 0.808 0.148 0.012 0.008
#> GSM27950 6 0.1109 0.77770 0.004 0.000 0.004 0.012 0.016 0.964
#> GSM27946 3 0.3875 0.52864 0.052 0.000 0.796 0.132 0.012 0.008
#> GSM11709 3 0.7132 0.34678 0.236 0.076 0.528 0.080 0.000 0.080
#> GSM11720 3 0.6194 0.40433 0.264 0.100 0.564 0.068 0.000 0.004
#> GSM11726 2 0.1363 0.64042 0.028 0.952 0.012 0.004 0.004 0.000
#> GSM11837 2 0.0405 0.64929 0.008 0.988 0.004 0.000 0.000 0.000
#> GSM11725 3 0.7191 0.05679 0.316 0.224 0.388 0.060 0.012 0.000
#> GSM11864 3 0.6905 0.25223 0.308 0.148 0.460 0.076 0.008 0.000
#> GSM11687 3 0.6055 0.43866 0.232 0.076 0.596 0.092 0.000 0.004
#> GSM11693 3 0.6260 0.43146 0.240 0.080 0.572 0.104 0.000 0.004
#> GSM11727 2 0.1693 0.64105 0.020 0.932 0.000 0.044 0.004 0.000
#> GSM11838 2 0.0937 0.64736 0.000 0.960 0.000 0.040 0.000 0.000
#> GSM11681 6 0.1832 0.77483 0.032 0.000 0.008 0.032 0.000 0.928
#> GSM11689 3 0.6334 0.42783 0.240 0.080 0.564 0.112 0.000 0.004
#> GSM11704 3 0.6353 0.42485 0.244 0.080 0.560 0.112 0.000 0.004
#> GSM11703 3 0.6167 0.44070 0.232 0.072 0.584 0.108 0.000 0.004
#> GSM11705 3 0.7797 0.26737 0.220 0.044 0.456 0.144 0.004 0.132
#> GSM11722 2 0.6271 0.28799 0.132 0.488 0.020 0.348 0.008 0.004
#> GSM11730 2 0.3485 0.50475 0.020 0.772 0.000 0.204 0.004 0.000
#> GSM11713 6 0.6257 0.30118 0.064 0.068 0.000 0.400 0.008 0.460
#> GSM11728 6 0.6787 0.23189 0.064 0.068 0.024 0.412 0.008 0.424
#> GSM27947 3 0.3697 0.53387 0.068 0.004 0.812 0.104 0.012 0.000
#> GSM27951 6 0.6569 0.45193 0.180 0.008 0.064 0.180 0.004 0.564
#> GSM11707 6 0.4518 0.68758 0.172 0.000 0.000 0.056 0.036 0.736
#> GSM11716 3 0.4696 -0.03163 0.332 0.024 0.620 0.000 0.024 0.000
#> GSM11850 3 0.4682 0.04083 0.312 0.004 0.644 0.012 0.020 0.008
#> GSM11851 3 0.4698 0.03515 0.316 0.004 0.640 0.012 0.020 0.008
#> GSM11721 3 0.6868 0.11661 0.156 0.004 0.432 0.356 0.032 0.020
#> GSM11852 3 0.5294 0.43768 0.072 0.000 0.676 0.208 0.024 0.020
#> GSM11694 3 0.1820 0.49760 0.056 0.000 0.924 0.000 0.012 0.008
#> GSM11695 3 0.1820 0.49760 0.056 0.000 0.924 0.000 0.012 0.008
#> GSM11734 1 0.6745 -0.00969 0.480 0.268 0.024 0.204 0.024 0.000
#> GSM11861 3 0.6699 -0.20829 0.376 0.000 0.420 0.156 0.028 0.020
#> GSM11843 3 0.7536 -0.05267 0.280 0.080 0.416 0.192 0.032 0.000
#> GSM11862 3 0.6316 0.28352 0.160 0.000 0.564 0.228 0.028 0.020
#> GSM11697 3 0.1555 0.51007 0.040 0.000 0.940 0.000 0.012 0.008
#> GSM11714 6 0.4481 0.68836 0.176 0.000 0.000 0.056 0.032 0.736
#> GSM11723 1 0.6692 0.55295 0.464 0.068 0.360 0.088 0.020 0.000
#> GSM11845 1 0.6411 0.44748 0.436 0.052 0.416 0.080 0.016 0.000
#> GSM11683 6 0.1514 0.77495 0.012 0.000 0.036 0.004 0.004 0.944
#> GSM11691 3 0.1672 0.52391 0.028 0.000 0.940 0.016 0.004 0.012
#> GSM27949 3 0.2635 0.48589 0.048 0.000 0.888 0.004 0.012 0.048
#> GSM27945 3 0.1787 0.50665 0.068 0.000 0.920 0.000 0.008 0.004
#> GSM11706 6 0.4518 0.68758 0.172 0.000 0.000 0.056 0.036 0.736
#> GSM11853 3 0.3508 0.53704 0.048 0.000 0.832 0.096 0.016 0.008
#> GSM11729 2 0.4520 0.57348 0.132 0.728 0.004 0.132 0.004 0.000
#> GSM11746 2 0.4520 0.57348 0.132 0.728 0.004 0.132 0.004 0.000
#> GSM11711 3 0.4439 0.48868 0.052 0.000 0.776 0.040 0.016 0.116
#> GSM11854 3 0.3682 0.53267 0.044 0.000 0.820 0.108 0.016 0.012
#> GSM11731 2 0.6721 0.24525 0.200 0.440 0.020 0.320 0.020 0.000
#> GSM11839 2 0.6897 0.09145 0.200 0.376 0.028 0.376 0.020 0.000
#> GSM11836 4 0.5105 0.27048 0.080 0.224 0.004 0.672 0.016 0.004
#> GSM11849 4 0.5266 0.33199 0.052 0.212 0.024 0.684 0.004 0.024
#> GSM11682 6 0.1615 0.77338 0.004 0.000 0.004 0.064 0.000 0.928
#> GSM11690 4 0.4814 0.44139 0.032 0.000 0.164 0.732 0.016 0.056
#> GSM11692 3 0.6126 0.22438 0.112 0.012 0.476 0.380 0.020 0.000
#> GSM11841 3 0.6292 0.20427 0.124 0.016 0.464 0.376 0.020 0.000
#> GSM11901 3 0.6292 0.20427 0.124 0.016 0.464 0.376 0.020 0.000
#> GSM11715 4 0.5261 -0.19266 0.096 0.444 0.000 0.460 0.000 0.000
#> GSM11724 4 0.5261 -0.19266 0.096 0.444 0.000 0.460 0.000 0.000
#> GSM11684 4 0.3656 0.52927 0.004 0.024 0.112 0.824 0.008 0.028
#> GSM11696 4 0.3696 0.52732 0.008 0.024 0.120 0.820 0.008 0.020
#> GSM27952 6 0.0653 0.78232 0.000 0.000 0.004 0.012 0.004 0.980
#> GSM27948 4 0.5614 0.08413 0.056 0.004 0.344 0.564 0.016 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 cell.line(p) agent(p) time(p) k
#> SD:kmeans 75 9.77e-06 0.882 6.70e-01 2
#> SD:kmeans 77 1.61e-06 0.808 3.80e-05 3
#> SD:kmeans 78 1.87e-06 0.664 9.13e-08 4
#> SD:kmeans 59 4.35e-05 0.728 9.71e-09 5
#> SD:kmeans 41 3.19e-04 0.191 3.53e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "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 14502 rows and 83 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.613 0.814 0.927 0.4980 0.496 0.496
#> 3 3 0.603 0.795 0.863 0.3342 0.702 0.476
#> 4 4 0.577 0.459 0.709 0.1164 0.760 0.435
#> 5 5 0.641 0.585 0.750 0.0715 0.896 0.639
#> 6 6 0.704 0.705 0.803 0.0441 0.924 0.661
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM11708 1 0.0000 0.884 1.000 0.000
#> GSM11735 1 0.0000 0.884 1.000 0.000
#> GSM11733 1 0.0000 0.884 1.000 0.000
#> GSM11863 1 0.0000 0.884 1.000 0.000
#> GSM11710 1 0.0000 0.884 1.000 0.000
#> GSM11712 2 0.0000 0.939 0.000 1.000
#> GSM11732 1 0.0376 0.882 0.996 0.004
#> GSM11844 1 0.0000 0.884 1.000 0.000
#> GSM11842 1 0.0000 0.884 1.000 0.000
#> GSM11860 1 0.0000 0.884 1.000 0.000
#> GSM11686 1 0.0000 0.884 1.000 0.000
#> GSM11688 1 0.0000 0.884 1.000 0.000
#> GSM11846 1 0.0000 0.884 1.000 0.000
#> GSM11680 1 0.7883 0.658 0.764 0.236
#> GSM11698 1 0.0000 0.884 1.000 0.000
#> GSM11840 1 0.0000 0.884 1.000 0.000
#> GSM11847 1 0.0000 0.884 1.000 0.000
#> GSM11685 1 0.0000 0.884 1.000 0.000
#> GSM11699 2 0.7528 0.695 0.216 0.784
#> GSM27950 1 0.0000 0.884 1.000 0.000
#> GSM27946 2 0.4939 0.839 0.108 0.892
#> GSM11709 1 0.4939 0.808 0.892 0.108
#> GSM11720 2 0.0000 0.939 0.000 1.000
#> GSM11726 2 0.0000 0.939 0.000 1.000
#> GSM11837 2 0.0000 0.939 0.000 1.000
#> GSM11725 2 0.0000 0.939 0.000 1.000
#> GSM11864 2 0.0000 0.939 0.000 1.000
#> GSM11687 2 0.0000 0.939 0.000 1.000
#> GSM11693 2 0.0000 0.939 0.000 1.000
#> GSM11727 2 0.0000 0.939 0.000 1.000
#> GSM11838 2 0.0000 0.939 0.000 1.000
#> GSM11681 1 0.0000 0.884 1.000 0.000
#> GSM11689 2 0.0000 0.939 0.000 1.000
#> GSM11704 2 0.0000 0.939 0.000 1.000
#> GSM11703 2 0.0000 0.939 0.000 1.000
#> GSM11705 1 0.4939 0.808 0.892 0.108
#> GSM11722 2 0.0000 0.939 0.000 1.000
#> GSM11730 2 0.0000 0.939 0.000 1.000
#> GSM11713 1 0.4939 0.808 0.892 0.108
#> GSM11728 1 0.4939 0.808 0.892 0.108
#> GSM27947 2 0.0000 0.939 0.000 1.000
#> GSM27951 1 0.4939 0.808 0.892 0.108
#> GSM11707 1 0.0000 0.884 1.000 0.000
#> GSM11716 2 0.0000 0.939 0.000 1.000
#> GSM11850 1 0.9850 0.314 0.572 0.428
#> GSM11851 1 0.9850 0.314 0.572 0.428
#> GSM11721 2 0.0000 0.939 0.000 1.000
#> GSM11852 1 0.9866 0.304 0.568 0.432
#> GSM11694 1 0.9983 0.167 0.524 0.476
#> GSM11695 1 0.9850 0.314 0.572 0.428
#> GSM11734 2 0.0000 0.939 0.000 1.000
#> GSM11861 2 0.7299 0.716 0.204 0.796
#> GSM11843 2 0.0000 0.939 0.000 1.000
#> GSM11862 2 0.5059 0.835 0.112 0.888
#> GSM11697 2 1.0000 -0.107 0.496 0.504
#> GSM11714 1 0.0000 0.884 1.000 0.000
#> GSM11723 2 0.0000 0.939 0.000 1.000
#> GSM11845 2 0.0000 0.939 0.000 1.000
#> GSM11683 1 0.0000 0.884 1.000 0.000
#> GSM11691 2 0.5178 0.831 0.116 0.884
#> GSM27949 1 0.0000 0.884 1.000 0.000
#> GSM27945 2 0.5059 0.835 0.112 0.888
#> GSM11706 1 0.0000 0.884 1.000 0.000
#> GSM11853 1 0.9866 0.304 0.568 0.432
#> GSM11729 2 0.0000 0.939 0.000 1.000
#> GSM11746 2 0.0000 0.939 0.000 1.000
#> GSM11711 1 0.0000 0.884 1.000 0.000
#> GSM11854 1 0.9850 0.314 0.572 0.428
#> GSM11731 2 0.0000 0.939 0.000 1.000
#> GSM11839 2 0.0000 0.939 0.000 1.000
#> GSM11836 2 0.9850 0.184 0.428 0.572
#> GSM11849 2 0.9850 0.184 0.428 0.572
#> GSM11682 1 0.0000 0.884 1.000 0.000
#> GSM11690 2 0.0000 0.939 0.000 1.000
#> GSM11692 2 0.0000 0.939 0.000 1.000
#> GSM11841 2 0.0000 0.939 0.000 1.000
#> GSM11901 2 0.0000 0.939 0.000 1.000
#> GSM11715 2 0.0000 0.939 0.000 1.000
#> GSM11724 2 0.0000 0.939 0.000 1.000
#> GSM11684 2 0.0000 0.939 0.000 1.000
#> GSM11696 2 0.0000 0.939 0.000 1.000
#> GSM27952 1 0.0000 0.884 1.000 0.000
#> GSM27948 2 0.0000 0.939 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM11708 3 0.0000 0.944 0.000 0.000 1.000
#> GSM11735 3 0.0237 0.944 0.004 0.000 0.996
#> GSM11733 3 0.0237 0.944 0.004 0.000 0.996
#> GSM11863 3 0.0237 0.944 0.004 0.000 0.996
#> GSM11710 3 0.0592 0.942 0.012 0.000 0.988
#> GSM11712 1 0.3879 0.750 0.848 0.152 0.000
#> GSM11732 3 0.3340 0.845 0.120 0.000 0.880
#> GSM11844 3 0.2066 0.907 0.060 0.000 0.940
#> GSM11842 3 0.0424 0.943 0.008 0.000 0.992
#> GSM11860 3 0.0237 0.944 0.004 0.000 0.996
#> GSM11686 3 0.0747 0.940 0.016 0.000 0.984
#> GSM11688 3 0.0747 0.940 0.016 0.000 0.984
#> GSM11846 3 0.0237 0.944 0.004 0.000 0.996
#> GSM11680 1 0.6079 0.451 0.612 0.000 0.388
#> GSM11698 3 0.2261 0.901 0.068 0.000 0.932
#> GSM11840 3 0.0237 0.944 0.004 0.000 0.996
#> GSM11847 3 0.0237 0.944 0.004 0.000 0.996
#> GSM11685 3 0.0747 0.940 0.016 0.000 0.984
#> GSM11699 1 0.2599 0.779 0.932 0.052 0.016
#> GSM27950 3 0.0000 0.944 0.000 0.000 1.000
#> GSM27946 1 0.1031 0.784 0.976 0.024 0.000
#> GSM11709 3 0.8343 0.472 0.132 0.256 0.612
#> GSM11720 1 0.5621 0.655 0.692 0.308 0.000
#> GSM11726 2 0.1860 0.841 0.052 0.948 0.000
#> GSM11837 2 0.1289 0.857 0.032 0.968 0.000
#> GSM11725 1 0.5859 0.621 0.656 0.344 0.000
#> GSM11864 1 0.5216 0.701 0.740 0.260 0.000
#> GSM11687 1 0.5815 0.655 0.692 0.304 0.004
#> GSM11693 1 0.5621 0.655 0.692 0.308 0.000
#> GSM11727 2 0.0892 0.864 0.020 0.980 0.000
#> GSM11838 2 0.0892 0.864 0.020 0.980 0.000
#> GSM11681 3 0.1491 0.931 0.016 0.016 0.968
#> GSM11689 1 0.5621 0.655 0.692 0.308 0.000
#> GSM11704 1 0.5621 0.655 0.692 0.308 0.000
#> GSM11703 1 0.5621 0.655 0.692 0.308 0.000
#> GSM11705 3 0.7053 0.596 0.064 0.244 0.692
#> GSM11722 2 0.0892 0.864 0.020 0.980 0.000
#> GSM11730 2 0.0892 0.864 0.020 0.980 0.000
#> GSM11713 2 0.5643 0.653 0.020 0.760 0.220
#> GSM11728 2 0.5680 0.666 0.024 0.764 0.212
#> GSM27947 1 0.2448 0.784 0.924 0.076 0.000
#> GSM27951 3 0.6927 0.610 0.060 0.240 0.700
#> GSM11707 3 0.0000 0.944 0.000 0.000 1.000
#> GSM11716 1 0.3112 0.778 0.900 0.096 0.004
#> GSM11850 1 0.3412 0.769 0.876 0.000 0.124
#> GSM11851 1 0.3752 0.760 0.856 0.000 0.144
#> GSM11721 1 0.5988 0.411 0.632 0.368 0.000
#> GSM11852 1 0.3502 0.772 0.896 0.020 0.084
#> GSM11694 1 0.3482 0.767 0.872 0.000 0.128
#> GSM11695 1 0.3551 0.765 0.868 0.000 0.132
#> GSM11734 1 0.5785 0.538 0.668 0.332 0.000
#> GSM11861 1 0.2096 0.779 0.944 0.052 0.004
#> GSM11843 1 0.2711 0.779 0.912 0.088 0.000
#> GSM11862 1 0.2261 0.775 0.932 0.068 0.000
#> GSM11697 1 0.3482 0.767 0.872 0.000 0.128
#> GSM11714 3 0.0000 0.944 0.000 0.000 1.000
#> GSM11723 1 0.3482 0.764 0.872 0.128 0.000
#> GSM11845 1 0.2066 0.785 0.940 0.060 0.000
#> GSM11683 3 0.0747 0.940 0.016 0.000 0.984
#> GSM11691 1 0.0848 0.789 0.984 0.008 0.008
#> GSM27949 3 0.1643 0.920 0.044 0.000 0.956
#> GSM27945 1 0.2774 0.784 0.920 0.008 0.072
#> GSM11706 3 0.0000 0.944 0.000 0.000 1.000
#> GSM11853 1 0.3349 0.775 0.888 0.004 0.108
#> GSM11729 2 0.1753 0.864 0.048 0.952 0.000
#> GSM11746 2 0.1643 0.863 0.044 0.956 0.000
#> GSM11711 3 0.0000 0.944 0.000 0.000 1.000
#> GSM11854 1 0.4047 0.754 0.848 0.004 0.148
#> GSM11731 2 0.4654 0.728 0.208 0.792 0.000
#> GSM11839 2 0.4842 0.711 0.224 0.776 0.000
#> GSM11836 2 0.3375 0.848 0.100 0.892 0.008
#> GSM11849 2 0.2625 0.858 0.084 0.916 0.000
#> GSM11682 3 0.1620 0.927 0.024 0.012 0.964
#> GSM11690 2 0.5327 0.655 0.272 0.728 0.000
#> GSM11692 1 0.5254 0.638 0.736 0.264 0.000
#> GSM11841 1 0.5291 0.638 0.732 0.268 0.000
#> GSM11901 1 0.5254 0.638 0.736 0.264 0.000
#> GSM11715 2 0.1964 0.863 0.056 0.944 0.000
#> GSM11724 2 0.1964 0.863 0.056 0.944 0.000
#> GSM11684 2 0.3340 0.841 0.120 0.880 0.000
#> GSM11696 2 0.3412 0.838 0.124 0.876 0.000
#> GSM27952 3 0.0747 0.940 0.016 0.000 0.984
#> GSM27948 1 0.5560 0.561 0.700 0.300 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM11708 1 0.4621 0.69440 0.708 0.000 0.008 0.284
#> GSM11735 1 0.6295 0.64701 0.616 0.000 0.088 0.296
#> GSM11733 1 0.6336 0.64297 0.608 0.000 0.088 0.304
#> GSM11863 1 0.6336 0.64297 0.608 0.000 0.088 0.304
#> GSM11710 1 0.0469 0.78711 0.988 0.000 0.000 0.012
#> GSM11712 4 0.5414 0.55318 0.000 0.020 0.376 0.604
#> GSM11732 3 0.7189 0.34381 0.084 0.036 0.592 0.288
#> GSM11844 3 0.7933 0.25631 0.184 0.036 0.548 0.232
#> GSM11842 1 0.6336 0.64297 0.608 0.000 0.088 0.304
#> GSM11860 1 0.6336 0.64297 0.608 0.000 0.088 0.304
#> GSM11686 1 0.1716 0.77413 0.936 0.000 0.000 0.064
#> GSM11688 1 0.0921 0.78439 0.972 0.000 0.000 0.028
#> GSM11846 1 0.0817 0.78810 0.976 0.000 0.000 0.024
#> GSM11680 3 0.2722 0.60670 0.064 0.000 0.904 0.032
#> GSM11698 3 0.6759 0.17810 0.344 0.000 0.548 0.108
#> GSM11840 1 0.6336 0.64297 0.608 0.000 0.088 0.304
#> GSM11847 1 0.6336 0.64297 0.608 0.000 0.088 0.304
#> GSM11685 1 0.1022 0.78367 0.968 0.000 0.000 0.032
#> GSM11699 3 0.4477 0.35745 0.000 0.000 0.688 0.312
#> GSM27950 1 0.0336 0.78648 0.992 0.000 0.008 0.000
#> GSM27946 3 0.4522 0.34787 0.000 0.000 0.680 0.320
#> GSM11709 1 0.7112 0.28132 0.504 0.408 0.044 0.044
#> GSM11720 2 0.6482 0.23368 0.000 0.504 0.424 0.072
#> GSM11726 2 0.0188 0.49006 0.000 0.996 0.004 0.000
#> GSM11837 2 0.1635 0.49762 0.000 0.948 0.008 0.044
#> GSM11725 2 0.6265 0.32162 0.000 0.588 0.340 0.072
#> GSM11864 2 0.6642 0.22002 0.000 0.492 0.424 0.084
#> GSM11687 2 0.6919 0.24396 0.012 0.508 0.404 0.076
#> GSM11693 2 0.6514 0.25053 0.000 0.516 0.408 0.076
#> GSM11727 2 0.1118 0.49774 0.000 0.964 0.000 0.036
#> GSM11838 2 0.1302 0.49714 0.000 0.956 0.000 0.044
#> GSM11681 1 0.1985 0.77739 0.940 0.016 0.004 0.040
#> GSM11689 2 0.6514 0.25053 0.000 0.516 0.408 0.076
#> GSM11704 2 0.6514 0.25053 0.000 0.516 0.408 0.076
#> GSM11703 2 0.6514 0.25053 0.000 0.516 0.408 0.076
#> GSM11705 1 0.6475 0.38286 0.572 0.368 0.028 0.032
#> GSM11722 2 0.1118 0.49774 0.000 0.964 0.000 0.036
#> GSM11730 2 0.1716 0.49022 0.000 0.936 0.000 0.064
#> GSM11713 1 0.6165 0.53586 0.652 0.264 0.004 0.080
#> GSM11728 1 0.6111 0.55095 0.660 0.256 0.004 0.080
#> GSM27947 3 0.5998 0.38728 0.000 0.116 0.684 0.200
#> GSM27951 1 0.7036 0.39994 0.564 0.332 0.020 0.084
#> GSM11707 1 0.1211 0.78488 0.960 0.000 0.000 0.040
#> GSM11716 3 0.0672 0.62745 0.000 0.008 0.984 0.008
#> GSM11850 3 0.1821 0.62013 0.012 0.032 0.948 0.008
#> GSM11851 3 0.1059 0.63115 0.012 0.000 0.972 0.016
#> GSM11721 4 0.6703 0.60434 0.000 0.156 0.232 0.612
#> GSM11852 3 0.5400 -0.04610 0.008 0.004 0.560 0.428
#> GSM11694 3 0.0657 0.63187 0.012 0.000 0.984 0.004
#> GSM11695 3 0.0657 0.63187 0.012 0.000 0.984 0.004
#> GSM11734 2 0.7541 -0.15786 0.000 0.424 0.188 0.388
#> GSM11861 3 0.4761 0.14936 0.000 0.000 0.628 0.372
#> GSM11843 3 0.7421 -0.26784 0.000 0.176 0.468 0.356
#> GSM11862 4 0.5000 0.20956 0.000 0.000 0.500 0.500
#> GSM11697 3 0.0469 0.63144 0.012 0.000 0.988 0.000
#> GSM11714 1 0.0000 0.78658 1.000 0.000 0.000 0.000
#> GSM11723 3 0.6548 0.24370 0.000 0.188 0.636 0.176
#> GSM11845 3 0.5332 0.39046 0.000 0.080 0.736 0.184
#> GSM11683 1 0.1118 0.78333 0.964 0.000 0.000 0.036
#> GSM11691 3 0.2675 0.58821 0.000 0.008 0.892 0.100
#> GSM27949 3 0.4989 -0.00235 0.472 0.000 0.528 0.000
#> GSM27945 3 0.0336 0.62938 0.000 0.000 0.992 0.008
#> GSM11706 1 0.1118 0.78535 0.964 0.000 0.000 0.036
#> GSM11853 3 0.4492 0.53409 0.016 0.016 0.792 0.176
#> GSM11729 2 0.3529 0.44138 0.000 0.836 0.012 0.152
#> GSM11746 2 0.3324 0.45343 0.000 0.852 0.012 0.136
#> GSM11711 1 0.1209 0.78616 0.964 0.004 0.000 0.032
#> GSM11854 3 0.5166 0.48777 0.044 0.004 0.736 0.216
#> GSM11731 2 0.4898 0.10836 0.000 0.584 0.000 0.416
#> GSM11839 2 0.5147 -0.01200 0.000 0.536 0.004 0.460
#> GSM11836 2 0.4985 0.00786 0.000 0.532 0.000 0.468
#> GSM11849 2 0.5503 0.01364 0.016 0.516 0.000 0.468
#> GSM11682 1 0.1867 0.77080 0.928 0.000 0.000 0.072
#> GSM11690 4 0.5360 0.32469 0.016 0.316 0.008 0.660
#> GSM11692 4 0.5558 0.57736 0.000 0.028 0.364 0.608
#> GSM11841 4 0.5558 0.57736 0.000 0.028 0.364 0.608
#> GSM11901 4 0.5630 0.58151 0.000 0.032 0.360 0.608
#> GSM11715 2 0.4713 0.22651 0.000 0.640 0.000 0.360
#> GSM11724 2 0.4730 0.21980 0.000 0.636 0.000 0.364
#> GSM11684 4 0.4978 0.22757 0.000 0.384 0.004 0.612
#> GSM11696 4 0.5237 0.29908 0.000 0.356 0.016 0.628
#> GSM27952 1 0.1118 0.78281 0.964 0.000 0.000 0.036
#> GSM27948 4 0.5970 0.62062 0.000 0.088 0.244 0.668
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM11708 5 0.4291 0.504 0.464 0.000 0.000 0.000 0.536
#> GSM11735 5 0.3519 0.938 0.216 0.000 0.008 0.000 0.776
#> GSM11733 5 0.3421 0.949 0.204 0.000 0.008 0.000 0.788
#> GSM11863 5 0.3421 0.949 0.204 0.000 0.008 0.000 0.788
#> GSM11710 1 0.0609 0.845 0.980 0.000 0.000 0.000 0.020
#> GSM11712 4 0.2692 0.733 0.000 0.016 0.092 0.884 0.008
#> GSM11732 3 0.4774 0.499 0.012 0.028 0.684 0.000 0.276
#> GSM11844 3 0.5971 0.453 0.064 0.028 0.628 0.008 0.272
#> GSM11842 5 0.3421 0.949 0.204 0.000 0.008 0.000 0.788
#> GSM11860 5 0.3421 0.949 0.204 0.000 0.008 0.000 0.788
#> GSM11686 1 0.0324 0.850 0.992 0.000 0.000 0.004 0.004
#> GSM11688 1 0.0162 0.851 0.996 0.000 0.000 0.000 0.004
#> GSM11846 1 0.3039 0.619 0.808 0.000 0.000 0.000 0.192
#> GSM11680 3 0.5785 0.497 0.080 0.000 0.660 0.224 0.036
#> GSM11698 3 0.6642 0.429 0.292 0.000 0.560 0.080 0.068
#> GSM11840 5 0.3421 0.949 0.204 0.000 0.008 0.000 0.788
#> GSM11847 5 0.3421 0.949 0.204 0.000 0.008 0.000 0.788
#> GSM11685 1 0.0162 0.851 0.996 0.000 0.000 0.000 0.004
#> GSM11699 4 0.3819 0.617 0.016 0.000 0.228 0.756 0.000
#> GSM27950 1 0.0693 0.849 0.980 0.000 0.012 0.000 0.008
#> GSM27946 4 0.3586 0.610 0.000 0.000 0.264 0.736 0.000
#> GSM11709 1 0.7564 0.414 0.520 0.196 0.044 0.024 0.216
#> GSM11720 3 0.8254 -0.219 0.000 0.324 0.344 0.164 0.168
#> GSM11726 2 0.1200 0.623 0.000 0.964 0.008 0.012 0.016
#> GSM11837 2 0.0451 0.627 0.000 0.988 0.008 0.004 0.000
#> GSM11725 2 0.7583 0.340 0.000 0.500 0.228 0.164 0.108
#> GSM11864 2 0.8132 0.184 0.000 0.368 0.244 0.280 0.108
#> GSM11687 2 0.8793 0.183 0.012 0.312 0.256 0.244 0.176
#> GSM11693 2 0.8483 0.175 0.000 0.312 0.236 0.276 0.176
#> GSM11727 2 0.0671 0.626 0.000 0.980 0.000 0.004 0.016
#> GSM11838 2 0.0162 0.627 0.000 0.996 0.000 0.004 0.000
#> GSM11681 1 0.1798 0.823 0.928 0.004 0.000 0.004 0.064
#> GSM11689 2 0.8473 0.174 0.000 0.312 0.228 0.284 0.176
#> GSM11704 2 0.8473 0.174 0.000 0.312 0.228 0.284 0.176
#> GSM11703 2 0.8487 0.172 0.000 0.308 0.228 0.284 0.180
#> GSM11705 1 0.5743 0.610 0.688 0.100 0.008 0.024 0.180
#> GSM11722 2 0.1106 0.626 0.000 0.964 0.000 0.012 0.024
#> GSM11730 2 0.1668 0.620 0.000 0.940 0.000 0.032 0.028
#> GSM11713 1 0.4659 0.724 0.784 0.080 0.000 0.044 0.092
#> GSM11728 1 0.4785 0.717 0.776 0.084 0.000 0.048 0.092
#> GSM27947 4 0.6968 0.130 0.000 0.040 0.408 0.424 0.128
#> GSM27951 1 0.4899 0.670 0.736 0.048 0.004 0.020 0.192
#> GSM11707 1 0.1410 0.818 0.940 0.000 0.000 0.000 0.060
#> GSM11716 3 0.0898 0.673 0.000 0.000 0.972 0.020 0.008
#> GSM11850 3 0.1686 0.671 0.000 0.028 0.944 0.008 0.020
#> GSM11851 3 0.1485 0.669 0.000 0.000 0.948 0.032 0.020
#> GSM11721 4 0.3059 0.726 0.000 0.028 0.108 0.860 0.004
#> GSM11852 4 0.4724 0.610 0.040 0.000 0.248 0.704 0.008
#> GSM11694 3 0.1153 0.678 0.004 0.000 0.964 0.008 0.024
#> GSM11695 3 0.1153 0.678 0.004 0.000 0.964 0.008 0.024
#> GSM11734 2 0.6132 0.346 0.000 0.576 0.140 0.276 0.008
#> GSM11861 4 0.4562 0.197 0.000 0.000 0.492 0.500 0.008
#> GSM11843 4 0.7263 0.147 0.000 0.244 0.352 0.380 0.024
#> GSM11862 4 0.3783 0.637 0.000 0.000 0.252 0.740 0.008
#> GSM11697 3 0.1267 0.678 0.004 0.000 0.960 0.012 0.024
#> GSM11714 1 0.0162 0.851 0.996 0.000 0.000 0.000 0.004
#> GSM11723 3 0.5564 0.445 0.000 0.200 0.664 0.128 0.008
#> GSM11845 3 0.4893 0.426 0.000 0.064 0.712 0.216 0.008
#> GSM11683 1 0.0290 0.850 0.992 0.000 0.008 0.000 0.000
#> GSM11691 3 0.2068 0.635 0.000 0.000 0.904 0.092 0.004
#> GSM27949 3 0.5000 0.300 0.388 0.000 0.576 0.000 0.036
#> GSM27945 3 0.1357 0.657 0.000 0.000 0.948 0.048 0.004
#> GSM11706 1 0.1270 0.825 0.948 0.000 0.000 0.000 0.052
#> GSM11853 3 0.5151 0.100 0.000 0.004 0.592 0.364 0.040
#> GSM11729 2 0.1082 0.625 0.000 0.964 0.008 0.028 0.000
#> GSM11746 2 0.1082 0.625 0.000 0.964 0.008 0.028 0.000
#> GSM11711 1 0.1341 0.827 0.944 0.000 0.000 0.000 0.056
#> GSM11854 3 0.5689 -0.156 0.040 0.000 0.492 0.448 0.020
#> GSM11731 2 0.3662 0.488 0.000 0.744 0.000 0.252 0.004
#> GSM11839 2 0.4009 0.412 0.000 0.684 0.000 0.312 0.004
#> GSM11836 2 0.5556 0.447 0.004 0.656 0.000 0.204 0.136
#> GSM11849 2 0.6024 0.394 0.084 0.616 0.000 0.268 0.032
#> GSM11682 1 0.1117 0.839 0.964 0.000 0.000 0.016 0.020
#> GSM11690 4 0.2882 0.666 0.028 0.060 0.000 0.888 0.024
#> GSM11692 4 0.2189 0.737 0.000 0.012 0.084 0.904 0.000
#> GSM11841 4 0.2293 0.737 0.000 0.016 0.084 0.900 0.000
#> GSM11901 4 0.2130 0.737 0.000 0.012 0.080 0.908 0.000
#> GSM11715 2 0.3724 0.545 0.000 0.788 0.000 0.184 0.028
#> GSM11724 2 0.3724 0.545 0.000 0.788 0.000 0.184 0.028
#> GSM11684 4 0.4699 0.418 0.016 0.236 0.000 0.716 0.032
#> GSM11696 4 0.2813 0.653 0.004 0.084 0.000 0.880 0.032
#> GSM27952 1 0.0000 0.851 1.000 0.000 0.000 0.000 0.000
#> GSM27948 4 0.1644 0.722 0.004 0.012 0.028 0.948 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM11708 5 0.4428 0.233 0.008 0.004 0.008 0.000 0.540 0.440
#> GSM11735 5 0.1901 0.906 0.004 0.000 0.008 0.000 0.912 0.076
#> GSM11733 5 0.1267 0.926 0.000 0.000 0.000 0.000 0.940 0.060
#> GSM11863 5 0.1267 0.926 0.000 0.000 0.000 0.000 0.940 0.060
#> GSM11710 6 0.1586 0.859 0.012 0.004 0.004 0.000 0.040 0.940
#> GSM11712 4 0.4425 0.694 0.156 0.092 0.008 0.740 0.004 0.000
#> GSM11732 3 0.3116 0.718 0.016 0.012 0.836 0.004 0.132 0.000
#> GSM11844 3 0.4263 0.699 0.008 0.012 0.788 0.012 0.104 0.076
#> GSM11842 5 0.1267 0.926 0.000 0.000 0.000 0.000 0.940 0.060
#> GSM11860 5 0.1204 0.922 0.000 0.000 0.000 0.000 0.944 0.056
#> GSM11686 6 0.0692 0.866 0.000 0.000 0.004 0.020 0.000 0.976
#> GSM11688 6 0.0146 0.868 0.000 0.000 0.004 0.000 0.000 0.996
#> GSM11846 6 0.4015 0.584 0.000 0.000 0.008 0.028 0.244 0.720
#> GSM11680 3 0.5646 0.568 0.072 0.000 0.652 0.200 0.008 0.068
#> GSM11698 3 0.6108 0.570 0.036 0.000 0.624 0.124 0.032 0.184
#> GSM11840 5 0.1267 0.926 0.000 0.000 0.000 0.000 0.940 0.060
#> GSM11847 5 0.1267 0.926 0.000 0.000 0.000 0.000 0.940 0.060
#> GSM11685 6 0.0146 0.868 0.000 0.000 0.004 0.000 0.000 0.996
#> GSM11699 4 0.5063 0.601 0.104 0.008 0.204 0.676 0.004 0.004
#> GSM27950 6 0.1138 0.864 0.004 0.000 0.012 0.000 0.024 0.960
#> GSM27946 4 0.5218 0.607 0.188 0.000 0.160 0.644 0.004 0.004
#> GSM11709 1 0.4596 0.212 0.616 0.008 0.000 0.000 0.036 0.340
#> GSM11720 1 0.2618 0.763 0.888 0.036 0.060 0.012 0.004 0.000
#> GSM11726 2 0.2772 0.787 0.180 0.816 0.000 0.000 0.004 0.000
#> GSM11837 2 0.2146 0.824 0.116 0.880 0.000 0.000 0.004 0.000
#> GSM11725 1 0.4736 0.657 0.728 0.152 0.092 0.024 0.004 0.000
#> GSM11864 1 0.3201 0.752 0.852 0.092 0.024 0.024 0.008 0.000
#> GSM11687 1 0.1223 0.786 0.960 0.008 0.012 0.016 0.004 0.000
#> GSM11693 1 0.1268 0.790 0.952 0.008 0.004 0.036 0.000 0.000
#> GSM11727 2 0.2340 0.816 0.148 0.852 0.000 0.000 0.000 0.000
#> GSM11838 2 0.1957 0.828 0.112 0.888 0.000 0.000 0.000 0.000
#> GSM11681 6 0.1152 0.854 0.044 0.000 0.000 0.000 0.004 0.952
#> GSM11689 1 0.1268 0.790 0.952 0.008 0.004 0.036 0.000 0.000
#> GSM11704 1 0.1268 0.790 0.952 0.008 0.004 0.036 0.000 0.000
#> GSM11703 1 0.1413 0.789 0.948 0.008 0.004 0.036 0.004 0.000
#> GSM11705 6 0.4356 0.178 0.480 0.008 0.004 0.000 0.004 0.504
#> GSM11722 2 0.3263 0.816 0.152 0.816 0.016 0.016 0.000 0.000
#> GSM11730 2 0.2950 0.811 0.148 0.828 0.000 0.024 0.000 0.000
#> GSM11713 6 0.4300 0.756 0.088 0.076 0.004 0.040 0.004 0.788
#> GSM11728 6 0.4376 0.754 0.088 0.072 0.004 0.048 0.004 0.784
#> GSM27947 1 0.4637 0.515 0.700 0.008 0.072 0.216 0.004 0.000
#> GSM27951 6 0.4470 0.507 0.336 0.004 0.004 0.020 0.004 0.632
#> GSM11707 6 0.2202 0.839 0.012 0.004 0.008 0.000 0.072 0.904
#> GSM11716 3 0.2965 0.758 0.108 0.008 0.856 0.012 0.016 0.000
#> GSM11850 3 0.1785 0.727 0.008 0.000 0.928 0.048 0.016 0.000
#> GSM11851 3 0.3009 0.701 0.024 0.000 0.860 0.092 0.020 0.004
#> GSM11721 4 0.4413 0.664 0.060 0.040 0.084 0.792 0.020 0.004
#> GSM11852 4 0.5420 0.605 0.088 0.000 0.136 0.704 0.032 0.040
#> GSM11694 3 0.2346 0.764 0.124 0.000 0.868 0.000 0.008 0.000
#> GSM11695 3 0.2346 0.764 0.124 0.000 0.868 0.000 0.008 0.000
#> GSM11734 2 0.7080 0.424 0.148 0.540 0.156 0.128 0.028 0.000
#> GSM11861 4 0.5904 0.198 0.028 0.008 0.420 0.484 0.044 0.016
#> GSM11843 1 0.7828 0.109 0.392 0.204 0.148 0.232 0.024 0.000
#> GSM11862 4 0.5968 0.566 0.096 0.008 0.180 0.652 0.040 0.024
#> GSM11697 3 0.2615 0.759 0.136 0.000 0.852 0.004 0.008 0.000
#> GSM11714 6 0.1312 0.864 0.012 0.004 0.008 0.000 0.020 0.956
#> GSM11723 3 0.6462 0.515 0.096 0.208 0.592 0.076 0.028 0.000
#> GSM11845 3 0.6464 0.563 0.164 0.088 0.608 0.112 0.028 0.000
#> GSM11683 6 0.0363 0.868 0.000 0.000 0.012 0.000 0.000 0.988
#> GSM11691 3 0.5088 0.627 0.168 0.000 0.688 0.120 0.020 0.004
#> GSM27949 3 0.4389 0.522 0.008 0.000 0.660 0.004 0.024 0.304
#> GSM27945 3 0.3099 0.736 0.176 0.000 0.808 0.008 0.008 0.000
#> GSM11706 6 0.2202 0.839 0.012 0.004 0.008 0.000 0.072 0.904
#> GSM11853 4 0.6640 0.253 0.192 0.000 0.344 0.428 0.024 0.012
#> GSM11729 2 0.1949 0.833 0.088 0.904 0.000 0.004 0.004 0.000
#> GSM11746 2 0.1949 0.833 0.088 0.904 0.000 0.004 0.004 0.000
#> GSM11711 6 0.2451 0.852 0.028 0.004 0.016 0.004 0.044 0.904
#> GSM11854 4 0.6730 0.406 0.136 0.000 0.292 0.504 0.032 0.036
#> GSM11731 2 0.3839 0.710 0.020 0.784 0.016 0.168 0.012 0.000
#> GSM11839 2 0.4095 0.673 0.020 0.752 0.016 0.200 0.012 0.000
#> GSM11836 2 0.2412 0.788 0.000 0.880 0.000 0.092 0.028 0.000
#> GSM11849 2 0.3580 0.742 0.008 0.824 0.004 0.112 0.008 0.044
#> GSM11682 6 0.0520 0.866 0.000 0.000 0.000 0.008 0.008 0.984
#> GSM11690 4 0.4139 0.685 0.064 0.116 0.000 0.788 0.008 0.024
#> GSM11692 4 0.4364 0.704 0.144 0.096 0.008 0.748 0.004 0.000
#> GSM11841 4 0.4364 0.704 0.144 0.096 0.008 0.748 0.004 0.000
#> GSM11901 4 0.4364 0.704 0.144 0.096 0.008 0.748 0.004 0.000
#> GSM11715 2 0.1493 0.812 0.000 0.936 0.004 0.056 0.004 0.000
#> GSM11724 2 0.1349 0.813 0.000 0.940 0.000 0.056 0.004 0.000
#> GSM11684 4 0.4403 0.633 0.028 0.204 0.004 0.736 0.008 0.020
#> GSM11696 4 0.4171 0.681 0.064 0.140 0.004 0.776 0.008 0.008
#> GSM27952 6 0.0000 0.868 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM27948 4 0.3827 0.696 0.084 0.096 0.000 0.804 0.008 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.line(p) agent(p) time(p) k
#> SD:skmeans 73 9.95e-05 0.952 2.16e-01 2
#> SD:skmeans 80 8.71e-09 0.628 7.02e-03 3
#> SD:skmeans 40 4.26e-04 0.815 3.19e-01 4
#> SD:skmeans 56 4.61e-09 0.921 1.29e-07 5
#> SD:skmeans 75 2.98e-13 0.856 1.32e-09 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 14502 rows and 83 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.989 0.995 0.2404 0.767 0.767
#> 3 3 0.496 0.744 0.865 0.8911 0.802 0.745
#> 4 4 0.502 0.715 0.826 0.3205 0.862 0.767
#> 5 5 0.559 0.761 0.836 0.0908 0.935 0.860
#> 6 6 0.601 0.659 0.816 0.1046 0.847 0.634
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM11708 2 0.0000 1.000 0.000 1.000
#> GSM11735 2 0.0000 1.000 0.000 1.000
#> GSM11733 2 0.0000 1.000 0.000 1.000
#> GSM11863 2 0.0000 1.000 0.000 1.000
#> GSM11710 2 0.0000 1.000 0.000 1.000
#> GSM11712 1 0.0000 0.994 1.000 0.000
#> GSM11732 1 0.0000 0.994 1.000 0.000
#> GSM11844 1 0.0000 0.994 1.000 0.000
#> GSM11842 2 0.0000 1.000 0.000 1.000
#> GSM11860 2 0.0000 1.000 0.000 1.000
#> GSM11686 1 0.0000 0.994 1.000 0.000
#> GSM11688 1 0.4161 0.908 0.916 0.084
#> GSM11846 1 0.2236 0.960 0.964 0.036
#> GSM11680 1 0.0000 0.994 1.000 0.000
#> GSM11698 1 0.0000 0.994 1.000 0.000
#> GSM11840 2 0.0000 1.000 0.000 1.000
#> GSM11847 2 0.0000 1.000 0.000 1.000
#> GSM11685 1 0.0672 0.987 0.992 0.008
#> GSM11699 1 0.0000 0.994 1.000 0.000
#> GSM27950 1 0.0000 0.994 1.000 0.000
#> GSM27946 1 0.0000 0.994 1.000 0.000
#> GSM11709 1 0.0000 0.994 1.000 0.000
#> GSM11720 1 0.0000 0.994 1.000 0.000
#> GSM11726 1 0.0000 0.994 1.000 0.000
#> GSM11837 1 0.0000 0.994 1.000 0.000
#> GSM11725 1 0.0000 0.994 1.000 0.000
#> GSM11864 1 0.0000 0.994 1.000 0.000
#> GSM11687 1 0.0000 0.994 1.000 0.000
#> GSM11693 1 0.0000 0.994 1.000 0.000
#> GSM11727 1 0.0000 0.994 1.000 0.000
#> GSM11838 1 0.0000 0.994 1.000 0.000
#> GSM11681 1 0.0000 0.994 1.000 0.000
#> GSM11689 1 0.0000 0.994 1.000 0.000
#> GSM11704 1 0.0000 0.994 1.000 0.000
#> GSM11703 1 0.0000 0.994 1.000 0.000
#> GSM11705 1 0.0000 0.994 1.000 0.000
#> GSM11722 1 0.0000 0.994 1.000 0.000
#> GSM11730 1 0.0000 0.994 1.000 0.000
#> GSM11713 1 0.0000 0.994 1.000 0.000
#> GSM11728 1 0.0000 0.994 1.000 0.000
#> GSM27947 1 0.0000 0.994 1.000 0.000
#> GSM27951 1 0.0000 0.994 1.000 0.000
#> GSM11707 2 0.0000 1.000 0.000 1.000
#> GSM11716 1 0.0000 0.994 1.000 0.000
#> GSM11850 1 0.0000 0.994 1.000 0.000
#> GSM11851 1 0.0000 0.994 1.000 0.000
#> GSM11721 1 0.0000 0.994 1.000 0.000
#> GSM11852 1 0.0000 0.994 1.000 0.000
#> GSM11694 1 0.0000 0.994 1.000 0.000
#> GSM11695 1 0.0000 0.994 1.000 0.000
#> GSM11734 1 0.0000 0.994 1.000 0.000
#> GSM11861 1 0.0000 0.994 1.000 0.000
#> GSM11843 1 0.0000 0.994 1.000 0.000
#> GSM11862 1 0.0000 0.994 1.000 0.000
#> GSM11697 1 0.0000 0.994 1.000 0.000
#> GSM11714 2 0.0000 1.000 0.000 1.000
#> GSM11723 1 0.0000 0.994 1.000 0.000
#> GSM11845 1 0.0000 0.994 1.000 0.000
#> GSM11683 1 0.0000 0.994 1.000 0.000
#> GSM11691 1 0.0000 0.994 1.000 0.000
#> GSM27949 1 0.0000 0.994 1.000 0.000
#> GSM27945 1 0.0000 0.994 1.000 0.000
#> GSM11706 1 0.8443 0.630 0.728 0.272
#> GSM11853 1 0.0000 0.994 1.000 0.000
#> GSM11729 1 0.0000 0.994 1.000 0.000
#> GSM11746 1 0.0000 0.994 1.000 0.000
#> GSM11711 1 0.0000 0.994 1.000 0.000
#> GSM11854 1 0.0000 0.994 1.000 0.000
#> GSM11731 1 0.0000 0.994 1.000 0.000
#> GSM11839 1 0.0000 0.994 1.000 0.000
#> GSM11836 1 0.0000 0.994 1.000 0.000
#> GSM11849 1 0.0000 0.994 1.000 0.000
#> GSM11682 1 0.0000 0.994 1.000 0.000
#> GSM11690 1 0.0000 0.994 1.000 0.000
#> GSM11692 1 0.0000 0.994 1.000 0.000
#> GSM11841 1 0.0000 0.994 1.000 0.000
#> GSM11901 1 0.0000 0.994 1.000 0.000
#> GSM11715 1 0.0000 0.994 1.000 0.000
#> GSM11724 1 0.0000 0.994 1.000 0.000
#> GSM11684 1 0.0000 0.994 1.000 0.000
#> GSM11696 1 0.0000 0.994 1.000 0.000
#> GSM27952 1 0.0000 0.994 1.000 0.000
#> GSM27948 1 0.0000 0.994 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM11708 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11735 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11733 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11863 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11710 3 0.6045 0.138 0.000 0.380 0.620
#> GSM11712 1 0.5016 0.706 0.760 0.000 0.240
#> GSM11732 1 0.0000 0.849 1.000 0.000 0.000
#> GSM11844 1 0.0000 0.849 1.000 0.000 0.000
#> GSM11842 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11860 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11686 3 0.6244 0.640 0.440 0.000 0.560
#> GSM11688 3 0.6062 0.691 0.384 0.000 0.616
#> GSM11846 3 0.6476 0.624 0.448 0.004 0.548
#> GSM11680 1 0.0000 0.849 1.000 0.000 0.000
#> GSM11698 1 0.0424 0.845 0.992 0.000 0.008
#> GSM11840 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11847 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11685 3 0.3941 0.566 0.156 0.000 0.844
#> GSM11699 1 0.5058 0.702 0.756 0.000 0.244
#> GSM27950 3 0.6095 0.690 0.392 0.000 0.608
#> GSM27946 1 0.0000 0.849 1.000 0.000 0.000
#> GSM11709 1 0.1031 0.837 0.976 0.000 0.024
#> GSM11720 1 0.0424 0.845 0.992 0.000 0.008
#> GSM11726 1 0.1031 0.837 0.976 0.000 0.024
#> GSM11837 1 0.0000 0.849 1.000 0.000 0.000
#> GSM11725 1 0.0000 0.849 1.000 0.000 0.000
#> GSM11864 1 0.0000 0.849 1.000 0.000 0.000
#> GSM11687 1 0.0424 0.845 0.992 0.000 0.008
#> GSM11693 1 0.0424 0.845 0.992 0.000 0.008
#> GSM11727 1 0.1031 0.837 0.976 0.000 0.024
#> GSM11838 1 0.3619 0.739 0.864 0.000 0.136
#> GSM11681 3 0.6062 0.690 0.384 0.000 0.616
#> GSM11689 1 0.0424 0.845 0.992 0.000 0.008
#> GSM11704 1 0.0000 0.849 1.000 0.000 0.000
#> GSM11703 1 0.1031 0.837 0.976 0.000 0.024
#> GSM11705 1 0.1031 0.837 0.976 0.000 0.024
#> GSM11722 1 0.2959 0.783 0.900 0.000 0.100
#> GSM11730 1 0.1643 0.836 0.956 0.000 0.044
#> GSM11713 3 0.6168 0.469 0.412 0.000 0.588
#> GSM11728 1 0.1031 0.837 0.976 0.000 0.024
#> GSM27947 1 0.0000 0.849 1.000 0.000 0.000
#> GSM27951 1 0.1031 0.837 0.976 0.000 0.024
#> GSM11707 3 0.6062 0.130 0.000 0.384 0.616
#> GSM11716 1 0.0000 0.849 1.000 0.000 0.000
#> GSM11850 1 0.0000 0.849 1.000 0.000 0.000
#> GSM11851 1 0.0000 0.849 1.000 0.000 0.000
#> GSM11721 1 0.5058 0.702 0.756 0.000 0.244
#> GSM11852 1 0.0000 0.849 1.000 0.000 0.000
#> GSM11694 1 0.0000 0.849 1.000 0.000 0.000
#> GSM11695 1 0.0000 0.849 1.000 0.000 0.000
#> GSM11734 1 0.0000 0.849 1.000 0.000 0.000
#> GSM11861 1 0.0000 0.849 1.000 0.000 0.000
#> GSM11843 1 0.0000 0.849 1.000 0.000 0.000
#> GSM11862 1 0.0000 0.849 1.000 0.000 0.000
#> GSM11697 1 0.0000 0.849 1.000 0.000 0.000
#> GSM11714 3 0.6045 0.138 0.000 0.380 0.620
#> GSM11723 1 0.5058 0.702 0.756 0.000 0.244
#> GSM11845 1 0.5058 0.702 0.756 0.000 0.244
#> GSM11683 3 0.3879 0.569 0.152 0.000 0.848
#> GSM11691 1 0.2537 0.811 0.920 0.000 0.080
#> GSM27949 1 0.0237 0.847 0.996 0.000 0.004
#> GSM27945 1 0.0000 0.849 1.000 0.000 0.000
#> GSM11706 1 0.7740 -0.497 0.508 0.048 0.444
#> GSM11853 1 0.0000 0.849 1.000 0.000 0.000
#> GSM11729 1 0.5591 0.640 0.696 0.000 0.304
#> GSM11746 1 0.3619 0.739 0.864 0.000 0.136
#> GSM11711 1 0.1031 0.837 0.976 0.000 0.024
#> GSM11854 1 0.0000 0.849 1.000 0.000 0.000
#> GSM11731 1 0.5948 0.587 0.640 0.000 0.360
#> GSM11839 1 0.5016 0.706 0.760 0.000 0.240
#> GSM11836 1 0.5098 0.700 0.752 0.000 0.248
#> GSM11849 1 0.6079 0.556 0.612 0.000 0.388
#> GSM11682 3 0.3816 0.567 0.148 0.000 0.852
#> GSM11690 1 0.5058 0.702 0.756 0.000 0.244
#> GSM11692 1 0.5058 0.702 0.756 0.000 0.244
#> GSM11841 1 0.5058 0.702 0.756 0.000 0.244
#> GSM11901 1 0.5058 0.702 0.756 0.000 0.244
#> GSM11715 1 0.6062 0.560 0.616 0.000 0.384
#> GSM11724 1 0.6062 0.560 0.616 0.000 0.384
#> GSM11684 1 0.6095 0.553 0.608 0.000 0.392
#> GSM11696 1 0.6045 0.562 0.620 0.000 0.380
#> GSM27952 3 0.6045 0.690 0.380 0.000 0.620
#> GSM27948 1 0.5058 0.702 0.756 0.000 0.244
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM11708 4 0.0000 1.0000 0.000 0.000 0.000 1.000
#> GSM11735 4 0.0000 1.0000 0.000 0.000 0.000 1.000
#> GSM11733 4 0.0000 1.0000 0.000 0.000 0.000 1.000
#> GSM11863 4 0.0000 1.0000 0.000 0.000 0.000 1.000
#> GSM11710 1 0.4678 0.5262 0.744 0.024 0.000 0.232
#> GSM11712 3 0.0000 0.7794 0.000 0.000 1.000 0.000
#> GSM11732 3 0.4103 0.7420 0.256 0.000 0.744 0.000
#> GSM11844 3 0.4103 0.7420 0.256 0.000 0.744 0.000
#> GSM11842 4 0.0000 1.0000 0.000 0.000 0.000 1.000
#> GSM11860 4 0.0000 1.0000 0.000 0.000 0.000 1.000
#> GSM11686 1 0.3606 0.6758 0.840 0.020 0.140 0.000
#> GSM11688 1 0.3432 0.7106 0.884 0.020 0.060 0.036
#> GSM11846 1 0.6755 0.5908 0.660 0.180 0.140 0.020
#> GSM11680 3 0.3907 0.7526 0.232 0.000 0.768 0.000
#> GSM11698 3 0.4103 0.7420 0.256 0.000 0.744 0.000
#> GSM11840 4 0.0000 1.0000 0.000 0.000 0.000 1.000
#> GSM11847 4 0.0000 1.0000 0.000 0.000 0.000 1.000
#> GSM11685 1 0.4585 0.4904 0.668 0.000 0.332 0.000
#> GSM11699 3 0.0817 0.7829 0.024 0.000 0.976 0.000
#> GSM27950 1 0.1940 0.6864 0.924 0.000 0.076 0.000
#> GSM27946 3 0.0000 0.7794 0.000 0.000 1.000 0.000
#> GSM11709 3 0.5873 0.6884 0.076 0.256 0.668 0.000
#> GSM11720 3 0.4422 0.7369 0.008 0.256 0.736 0.000
#> GSM11726 3 0.5744 0.6954 0.068 0.256 0.676 0.000
#> GSM11837 3 0.0000 0.7794 0.000 0.000 1.000 0.000
#> GSM11725 3 0.3907 0.7498 0.000 0.232 0.768 0.000
#> GSM11864 3 0.3907 0.7498 0.000 0.232 0.768 0.000
#> GSM11687 3 0.4103 0.7409 0.000 0.256 0.744 0.000
#> GSM11693 3 0.4103 0.7409 0.000 0.256 0.744 0.000
#> GSM11727 3 0.6209 0.4190 0.052 0.456 0.492 0.000
#> GSM11838 2 0.0817 0.6065 0.000 0.976 0.024 0.000
#> GSM11681 1 0.5537 0.5173 0.688 0.256 0.056 0.000
#> GSM11689 3 0.4103 0.7409 0.000 0.256 0.744 0.000
#> GSM11704 3 0.3907 0.7498 0.000 0.232 0.768 0.000
#> GSM11703 3 0.6050 0.6971 0.100 0.232 0.668 0.000
#> GSM11705 3 0.5873 0.6884 0.076 0.256 0.668 0.000
#> GSM11722 3 0.6141 0.6516 0.076 0.300 0.624 0.000
#> GSM11730 3 0.6409 0.5343 0.076 0.364 0.560 0.000
#> GSM11713 2 0.6135 -0.0948 0.376 0.568 0.056 0.000
#> GSM11728 3 0.2742 0.7457 0.076 0.024 0.900 0.000
#> GSM27947 3 0.2011 0.7859 0.000 0.080 0.920 0.000
#> GSM27951 3 0.5873 0.6884 0.076 0.256 0.668 0.000
#> GSM11707 1 0.1284 0.6998 0.964 0.024 0.000 0.012
#> GSM11716 3 0.4103 0.7420 0.256 0.000 0.744 0.000
#> GSM11850 3 0.4103 0.7420 0.256 0.000 0.744 0.000
#> GSM11851 3 0.4103 0.7420 0.256 0.000 0.744 0.000
#> GSM11721 3 0.0000 0.7794 0.000 0.000 1.000 0.000
#> GSM11852 3 0.0000 0.7794 0.000 0.000 1.000 0.000
#> GSM11694 3 0.4103 0.7420 0.256 0.000 0.744 0.000
#> GSM11695 3 0.4103 0.7420 0.256 0.000 0.744 0.000
#> GSM11734 3 0.0336 0.7811 0.000 0.008 0.992 0.000
#> GSM11861 3 0.3873 0.7514 0.228 0.000 0.772 0.000
#> GSM11843 3 0.3907 0.7499 0.232 0.000 0.768 0.000
#> GSM11862 3 0.2281 0.7835 0.096 0.000 0.904 0.000
#> GSM11697 3 0.4103 0.7420 0.256 0.000 0.744 0.000
#> GSM11714 1 0.0817 0.6997 0.976 0.024 0.000 0.000
#> GSM11723 3 0.0000 0.7794 0.000 0.000 1.000 0.000
#> GSM11845 3 0.0000 0.7794 0.000 0.000 1.000 0.000
#> GSM11683 1 0.1716 0.6968 0.936 0.000 0.064 0.000
#> GSM11691 3 0.4103 0.7420 0.256 0.000 0.744 0.000
#> GSM27949 3 0.4103 0.7420 0.256 0.000 0.744 0.000
#> GSM27945 3 0.4103 0.7420 0.256 0.000 0.744 0.000
#> GSM11706 1 0.6859 0.5407 0.652 0.024 0.196 0.128
#> GSM11853 3 0.0000 0.7794 0.000 0.000 1.000 0.000
#> GSM11729 2 0.4103 0.7742 0.000 0.744 0.256 0.000
#> GSM11746 2 0.0817 0.6065 0.000 0.976 0.024 0.000
#> GSM11711 3 0.3205 0.7527 0.104 0.024 0.872 0.000
#> GSM11854 3 0.0000 0.7794 0.000 0.000 1.000 0.000
#> GSM11731 3 0.4804 -0.0226 0.000 0.384 0.616 0.000
#> GSM11839 3 0.0000 0.7794 0.000 0.000 1.000 0.000
#> GSM11836 3 0.4222 0.3722 0.000 0.272 0.728 0.000
#> GSM11849 2 0.4103 0.7742 0.000 0.744 0.256 0.000
#> GSM11682 1 0.4406 0.5072 0.700 0.000 0.300 0.000
#> GSM11690 3 0.0000 0.7794 0.000 0.000 1.000 0.000
#> GSM11692 3 0.0000 0.7794 0.000 0.000 1.000 0.000
#> GSM11841 3 0.0000 0.7794 0.000 0.000 1.000 0.000
#> GSM11901 3 0.0000 0.7794 0.000 0.000 1.000 0.000
#> GSM11715 2 0.4103 0.7742 0.000 0.744 0.256 0.000
#> GSM11724 2 0.4103 0.7742 0.000 0.744 0.256 0.000
#> GSM11684 2 0.4103 0.7742 0.000 0.744 0.256 0.000
#> GSM11696 3 0.4193 0.3920 0.000 0.268 0.732 0.000
#> GSM27952 1 0.4678 0.5313 0.744 0.024 0.232 0.000
#> GSM27948 3 0.0000 0.7794 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM11708 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM11735 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM11733 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM11863 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM11710 4 0.2520 0.7264 0.000 0.056 0.000 0.896 0.048
#> GSM11712 3 0.0000 0.7921 0.000 0.000 1.000 0.000 0.000
#> GSM11732 3 0.4302 0.7914 0.208 0.000 0.744 0.048 0.000
#> GSM11844 3 0.4302 0.7914 0.208 0.000 0.744 0.048 0.000
#> GSM11842 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM11860 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM11686 4 0.2450 0.7481 0.048 0.000 0.052 0.900 0.000
#> GSM11688 4 0.1522 0.7483 0.044 0.000 0.000 0.944 0.012
#> GSM11846 4 0.3498 0.7070 0.012 0.008 0.116 0.844 0.020
#> GSM11680 3 0.3988 0.7992 0.196 0.000 0.768 0.036 0.000
#> GSM11698 3 0.4455 0.7754 0.068 0.000 0.744 0.188 0.000
#> GSM11840 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM11847 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM11685 4 0.3336 0.5677 0.000 0.000 0.228 0.772 0.000
#> GSM11699 3 0.0162 0.7932 0.000 0.000 0.996 0.004 0.000
#> GSM27950 4 0.3333 0.6299 0.208 0.000 0.004 0.788 0.000
#> GSM27946 3 0.0000 0.7921 0.000 0.000 1.000 0.000 0.000
#> GSM11709 3 0.5625 0.7333 0.048 0.196 0.688 0.068 0.000
#> GSM11720 3 0.5094 0.7730 0.048 0.156 0.740 0.056 0.000
#> GSM11726 2 0.0955 0.8273 0.000 0.968 0.004 0.028 0.000
#> GSM11837 2 0.3305 0.5548 0.000 0.776 0.224 0.000 0.000
#> GSM11725 3 0.4109 0.7847 0.048 0.168 0.780 0.004 0.000
#> GSM11864 3 0.3953 0.7854 0.048 0.168 0.784 0.000 0.000
#> GSM11687 3 0.4935 0.7744 0.048 0.168 0.744 0.040 0.000
#> GSM11693 3 0.4935 0.7744 0.048 0.168 0.744 0.040 0.000
#> GSM11727 2 0.0404 0.8202 0.000 0.988 0.012 0.000 0.000
#> GSM11838 2 0.1341 0.7882 0.056 0.944 0.000 0.000 0.000
#> GSM11681 4 0.5800 0.5408 0.048 0.220 0.068 0.664 0.000
#> GSM11689 3 0.4935 0.7744 0.048 0.168 0.744 0.040 0.000
#> GSM11704 3 0.3953 0.7854 0.048 0.168 0.784 0.000 0.000
#> GSM11703 3 0.5614 0.7350 0.044 0.196 0.688 0.072 0.000
#> GSM11705 3 0.5536 0.7146 0.048 0.056 0.688 0.208 0.000
#> GSM11722 3 0.6414 0.6796 0.104 0.200 0.628 0.068 0.000
#> GSM11730 2 0.1845 0.8178 0.000 0.928 0.016 0.056 0.000
#> GSM11713 2 0.3563 0.6587 0.012 0.780 0.000 0.208 0.000
#> GSM11728 3 0.4434 0.7271 0.000 0.056 0.736 0.208 0.000
#> GSM27947 3 0.1809 0.8028 0.012 0.060 0.928 0.000 0.000
#> GSM27951 3 0.5387 0.7345 0.048 0.224 0.688 0.040 0.000
#> GSM11707 4 0.1502 0.7495 0.000 0.056 0.000 0.940 0.004
#> GSM11716 3 0.4302 0.7914 0.208 0.000 0.744 0.048 0.000
#> GSM11850 3 0.4302 0.7914 0.208 0.000 0.744 0.048 0.000
#> GSM11851 3 0.4302 0.7914 0.208 0.000 0.744 0.048 0.000
#> GSM11721 3 0.0000 0.7921 0.000 0.000 1.000 0.000 0.000
#> GSM11852 3 0.2516 0.7873 0.000 0.000 0.860 0.140 0.000
#> GSM11694 3 0.4302 0.7914 0.208 0.000 0.744 0.048 0.000
#> GSM11695 3 0.4302 0.7914 0.208 0.000 0.744 0.048 0.000
#> GSM11734 3 0.0290 0.7942 0.000 0.008 0.992 0.000 0.000
#> GSM11861 3 0.4201 0.7940 0.204 0.000 0.752 0.044 0.000
#> GSM11843 3 0.4233 0.7925 0.208 0.000 0.748 0.044 0.000
#> GSM11862 3 0.2124 0.8106 0.096 0.000 0.900 0.004 0.000
#> GSM11697 3 0.4302 0.7914 0.208 0.000 0.744 0.048 0.000
#> GSM11714 4 0.1341 0.7496 0.000 0.056 0.000 0.944 0.000
#> GSM11723 3 0.0000 0.7921 0.000 0.000 1.000 0.000 0.000
#> GSM11845 3 0.0000 0.7921 0.000 0.000 1.000 0.000 0.000
#> GSM11683 4 0.6046 0.5867 0.208 0.052 0.088 0.652 0.000
#> GSM11691 3 0.4302 0.7914 0.208 0.000 0.744 0.048 0.000
#> GSM27949 3 0.4302 0.7914 0.208 0.000 0.744 0.048 0.000
#> GSM27945 3 0.4302 0.7914 0.208 0.000 0.744 0.048 0.000
#> GSM11706 4 0.6009 0.4996 0.000 0.056 0.216 0.652 0.076
#> GSM11853 3 0.2516 0.7873 0.000 0.000 0.860 0.140 0.000
#> GSM11729 1 0.4337 0.8184 0.744 0.052 0.204 0.000 0.000
#> GSM11746 1 0.3732 0.5546 0.792 0.176 0.032 0.000 0.000
#> GSM11711 3 0.4496 0.7265 0.000 0.056 0.728 0.216 0.000
#> GSM11854 3 0.2516 0.7873 0.000 0.000 0.860 0.140 0.000
#> GSM11731 3 0.4138 -0.0513 0.384 0.000 0.616 0.000 0.000
#> GSM11839 3 0.0000 0.7921 0.000 0.000 1.000 0.000 0.000
#> GSM11836 3 0.3636 0.3595 0.272 0.000 0.728 0.000 0.000
#> GSM11849 1 0.4630 0.6992 0.744 0.000 0.116 0.140 0.000
#> GSM11682 4 0.2230 0.7050 0.000 0.000 0.116 0.884 0.000
#> GSM11690 3 0.0162 0.7911 0.000 0.000 0.996 0.004 0.000
#> GSM11692 3 0.0000 0.7921 0.000 0.000 1.000 0.000 0.000
#> GSM11841 3 0.0000 0.7921 0.000 0.000 1.000 0.000 0.000
#> GSM11901 3 0.0000 0.7921 0.000 0.000 1.000 0.000 0.000
#> GSM11715 1 0.3534 0.8495 0.744 0.000 0.256 0.000 0.000
#> GSM11724 1 0.3534 0.8495 0.744 0.000 0.256 0.000 0.000
#> GSM11684 1 0.3534 0.8495 0.744 0.000 0.256 0.000 0.000
#> GSM11696 3 0.3612 0.3880 0.268 0.000 0.732 0.000 0.000
#> GSM27952 4 0.1197 0.7428 0.000 0.000 0.048 0.952 0.000
#> GSM27948 3 0.0000 0.7921 0.000 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM11708 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11735 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11733 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11863 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11710 6 0.3756 0.142 0.352 0.000 0.000 0.000 0.004 0.644
#> GSM11712 3 0.3266 0.732 0.000 0.000 0.728 0.272 0.000 0.000
#> GSM11732 3 0.0603 0.769 0.016 0.000 0.980 0.000 0.000 0.004
#> GSM11844 3 0.0820 0.770 0.016 0.000 0.972 0.000 0.000 0.012
#> GSM11842 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11860 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11686 6 0.1219 0.670 0.004 0.000 0.048 0.000 0.000 0.948
#> GSM11688 6 0.0146 0.698 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM11846 6 0.4026 0.474 0.160 0.000 0.088 0.000 0.000 0.752
#> GSM11680 3 0.0951 0.777 0.008 0.000 0.968 0.020 0.000 0.004
#> GSM11698 3 0.3073 0.701 0.008 0.000 0.788 0.000 0.000 0.204
#> GSM11840 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11847 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11685 6 0.2703 0.561 0.000 0.000 0.004 0.172 0.000 0.824
#> GSM11699 3 0.3468 0.735 0.008 0.000 0.728 0.264 0.000 0.000
#> GSM27950 6 0.3349 0.532 0.008 0.000 0.244 0.000 0.000 0.748
#> GSM27946 3 0.3151 0.742 0.000 0.000 0.748 0.252 0.000 0.000
#> GSM11709 1 0.2527 0.582 0.832 0.000 0.168 0.000 0.000 0.000
#> GSM11720 3 0.3221 0.705 0.264 0.000 0.736 0.000 0.000 0.000
#> GSM11726 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11837 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11725 3 0.3151 0.714 0.252 0.000 0.748 0.000 0.000 0.000
#> GSM11864 3 0.3151 0.714 0.252 0.000 0.748 0.000 0.000 0.000
#> GSM11687 3 0.3175 0.712 0.256 0.000 0.744 0.000 0.000 0.000
#> GSM11693 3 0.3175 0.712 0.256 0.000 0.744 0.000 0.000 0.000
#> GSM11727 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11838 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11681 1 0.3986 -0.100 0.532 0.000 0.004 0.000 0.000 0.464
#> GSM11689 3 0.3175 0.712 0.256 0.000 0.744 0.000 0.000 0.000
#> GSM11704 3 0.3151 0.714 0.252 0.000 0.748 0.000 0.000 0.000
#> GSM11703 1 0.2793 0.576 0.800 0.000 0.200 0.000 0.000 0.000
#> GSM11705 1 0.5088 0.591 0.632 0.000 0.168 0.000 0.000 0.200
#> GSM11722 1 0.3426 0.490 0.720 0.000 0.276 0.004 0.000 0.000
#> GSM11730 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11713 1 0.5421 0.394 0.580 0.216 0.000 0.000 0.000 0.204
#> GSM11728 1 0.6090 0.566 0.580 0.000 0.168 0.052 0.000 0.200
#> GSM27947 3 0.4030 0.756 0.080 0.000 0.748 0.172 0.000 0.000
#> GSM27951 1 0.2730 0.577 0.808 0.000 0.192 0.000 0.000 0.000
#> GSM11707 1 0.4453 0.252 0.524 0.000 0.020 0.000 0.004 0.452
#> GSM11716 3 0.0692 0.767 0.020 0.000 0.976 0.000 0.000 0.004
#> GSM11850 3 0.0692 0.767 0.020 0.000 0.976 0.000 0.000 0.004
#> GSM11851 3 0.0692 0.767 0.020 0.000 0.976 0.000 0.000 0.004
#> GSM11721 3 0.4783 0.632 0.088 0.000 0.636 0.276 0.000 0.000
#> GSM11852 3 0.3867 0.700 0.000 0.000 0.748 0.052 0.000 0.200
#> GSM11694 3 0.0603 0.769 0.016 0.000 0.980 0.000 0.000 0.004
#> GSM11695 3 0.0603 0.769 0.016 0.000 0.980 0.000 0.000 0.004
#> GSM11734 3 0.5076 0.610 0.132 0.000 0.620 0.248 0.000 0.000
#> GSM11861 3 0.0508 0.777 0.004 0.000 0.984 0.012 0.000 0.000
#> GSM11843 3 0.0508 0.776 0.000 0.000 0.984 0.012 0.000 0.004
#> GSM11862 3 0.2378 0.775 0.000 0.000 0.848 0.152 0.000 0.000
#> GSM11697 3 0.0603 0.769 0.016 0.000 0.980 0.000 0.000 0.004
#> GSM11714 1 0.4675 0.364 0.580 0.000 0.052 0.000 0.000 0.368
#> GSM11723 3 0.3586 0.735 0.012 0.000 0.720 0.268 0.000 0.000
#> GSM11845 3 0.3426 0.728 0.004 0.000 0.720 0.276 0.000 0.000
#> GSM11683 6 0.6003 0.287 0.268 0.000 0.252 0.004 0.000 0.476
#> GSM11691 3 0.0603 0.769 0.016 0.000 0.980 0.000 0.000 0.004
#> GSM27949 3 0.0603 0.769 0.016 0.000 0.980 0.000 0.000 0.004
#> GSM27945 3 0.0405 0.771 0.008 0.000 0.988 0.000 0.000 0.004
#> GSM11706 1 0.5294 0.417 0.580 0.000 0.044 0.000 0.040 0.336
#> GSM11853 3 0.3867 0.700 0.000 0.000 0.748 0.052 0.000 0.200
#> GSM11729 4 0.3364 0.306 0.024 0.196 0.000 0.780 0.000 0.000
#> GSM11746 4 0.3288 0.317 0.276 0.000 0.000 0.724 0.000 0.000
#> GSM11711 1 0.6001 0.571 0.580 0.000 0.180 0.040 0.000 0.200
#> GSM11854 3 0.3867 0.700 0.000 0.000 0.748 0.052 0.000 0.200
#> GSM11731 4 0.5081 0.363 0.128 0.000 0.256 0.616 0.000 0.000
#> GSM11839 3 0.5138 0.573 0.124 0.000 0.600 0.276 0.000 0.000
#> GSM11836 4 0.4165 -0.202 0.012 0.000 0.452 0.536 0.000 0.000
#> GSM11849 4 0.3394 0.312 0.024 0.000 0.000 0.776 0.000 0.200
#> GSM11682 6 0.0146 0.698 0.000 0.000 0.004 0.000 0.000 0.996
#> GSM11690 3 0.3534 0.727 0.000 0.000 0.716 0.276 0.000 0.008
#> GSM11692 3 0.3288 0.729 0.000 0.000 0.724 0.276 0.000 0.000
#> GSM11841 3 0.3288 0.729 0.000 0.000 0.724 0.276 0.000 0.000
#> GSM11901 3 0.3288 0.729 0.000 0.000 0.724 0.276 0.000 0.000
#> GSM11715 4 0.0632 0.545 0.024 0.000 0.000 0.976 0.000 0.000
#> GSM11724 4 0.0632 0.545 0.024 0.000 0.000 0.976 0.000 0.000
#> GSM11684 4 0.0146 0.543 0.000 0.000 0.004 0.996 0.000 0.000
#> GSM11696 4 0.3862 -0.282 0.000 0.000 0.476 0.524 0.000 0.000
#> GSM27952 6 0.0146 0.698 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM27948 3 0.3288 0.729 0.000 0.000 0.724 0.276 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 cell.line(p) agent(p) time(p) k
#> SD:pam 83 4.87e-05 0.184 6.54e-02 2
#> SD:pam 78 6.32e-06 0.240 3.26e-03 3
#> SD:pam 77 3.58e-07 0.827 1.05e-04 4
#> SD:pam 79 3.86e-10 0.874 8.06e-06 5
#> SD:pam 68 3.60e-09 0.200 1.73e-04 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 14502 rows and 83 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 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 0.300 0.529 0.795 0.4127 0.520 0.520
#> 3 3 0.356 0.401 0.699 0.5555 0.686 0.470
#> 4 4 0.482 0.536 0.724 0.0594 0.804 0.554
#> 5 5 0.504 0.519 0.729 0.0694 0.890 0.696
#> 6 6 0.486 0.331 0.637 0.0651 0.922 0.742
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
#> GSM11708 2 0.4161 0.5925 0.084 0.916
#> GSM11735 2 0.4161 0.5925 0.084 0.916
#> GSM11733 2 0.2236 0.5915 0.036 0.964
#> GSM11863 2 0.9248 0.6067 0.340 0.660
#> GSM11710 2 0.8267 0.6027 0.260 0.740
#> GSM11712 1 0.3274 0.7476 0.940 0.060
#> GSM11732 1 0.9833 -0.2422 0.576 0.424
#> GSM11844 1 0.9850 -0.2383 0.572 0.428
#> GSM11842 2 0.9248 0.6067 0.340 0.660
#> GSM11860 2 0.9248 0.6067 0.340 0.660
#> GSM11686 2 0.7815 0.5763 0.232 0.768
#> GSM11688 2 0.7376 0.5990 0.208 0.792
#> GSM11846 1 0.9881 -0.2699 0.564 0.436
#> GSM11680 1 0.2778 0.7527 0.952 0.048
#> GSM11698 1 0.2948 0.7502 0.948 0.052
#> GSM11840 2 0.8327 0.6423 0.264 0.736
#> GSM11847 2 0.8327 0.6423 0.264 0.736
#> GSM11685 2 0.7299 0.5990 0.204 0.796
#> GSM11699 1 0.3114 0.7501 0.944 0.056
#> GSM27950 2 0.8327 0.5993 0.264 0.736
#> GSM27946 1 0.3114 0.7501 0.944 0.056
#> GSM11709 1 0.9795 -0.1824 0.584 0.416
#> GSM11720 1 0.1184 0.7472 0.984 0.016
#> GSM11726 2 0.9909 0.5268 0.444 0.556
#> GSM11837 2 0.9608 0.6054 0.384 0.616
#> GSM11725 1 0.1414 0.7454 0.980 0.020
#> GSM11864 1 0.0938 0.7490 0.988 0.012
#> GSM11687 1 0.1184 0.7472 0.984 0.016
#> GSM11693 1 0.1184 0.7472 0.984 0.016
#> GSM11727 2 0.9608 0.6054 0.384 0.616
#> GSM11838 2 0.9608 0.6054 0.384 0.616
#> GSM11681 2 0.8207 0.6000 0.256 0.744
#> GSM11689 1 0.1184 0.7472 0.984 0.016
#> GSM11704 1 0.1184 0.7472 0.984 0.016
#> GSM11703 1 0.1184 0.7472 0.984 0.016
#> GSM11705 1 0.9833 -0.2071 0.576 0.424
#> GSM11722 1 0.9881 -0.2447 0.564 0.436
#> GSM11730 2 0.9608 0.6054 0.384 0.616
#> GSM11713 2 0.9896 0.5303 0.440 0.560
#> GSM11728 1 0.9896 -0.2569 0.560 0.440
#> GSM27947 1 0.0938 0.7547 0.988 0.012
#> GSM27951 1 0.9732 -0.1455 0.596 0.404
#> GSM11707 2 0.8267 0.6027 0.260 0.740
#> GSM11716 1 0.0000 0.7516 1.000 0.000
#> GSM11850 1 0.0000 0.7516 1.000 0.000
#> GSM11851 1 0.2043 0.7553 0.968 0.032
#> GSM11721 1 0.3274 0.7476 0.940 0.060
#> GSM11852 1 0.3114 0.7501 0.944 0.056
#> GSM11694 1 0.0672 0.7505 0.992 0.008
#> GSM11695 1 0.0672 0.7505 0.992 0.008
#> GSM11734 1 0.4815 0.7261 0.896 0.104
#> GSM11861 1 0.3114 0.7501 0.944 0.056
#> GSM11843 1 0.3114 0.7501 0.944 0.056
#> GSM11862 1 0.3114 0.7501 0.944 0.056
#> GSM11697 1 0.0672 0.7505 0.992 0.008
#> GSM11714 2 0.8267 0.6027 0.260 0.740
#> GSM11723 1 0.2603 0.7548 0.956 0.044
#> GSM11845 1 0.3114 0.7501 0.944 0.056
#> GSM11683 1 0.9795 0.0950 0.584 0.416
#> GSM11691 1 0.0000 0.7516 1.000 0.000
#> GSM27949 1 0.5178 0.6460 0.884 0.116
#> GSM27945 1 0.0672 0.7505 0.992 0.008
#> GSM11706 2 0.8267 0.6027 0.260 0.740
#> GSM11853 1 0.0672 0.7505 0.992 0.008
#> GSM11729 2 0.9608 0.6054 0.384 0.616
#> GSM11746 2 0.9608 0.6054 0.384 0.616
#> GSM11711 1 0.9732 -0.1812 0.596 0.404
#> GSM11854 1 0.2423 0.7545 0.960 0.040
#> GSM11731 2 0.9993 0.3120 0.484 0.516
#> GSM11839 1 0.9933 -0.1506 0.548 0.452
#> GSM11836 2 0.9170 0.6077 0.332 0.668
#> GSM11849 2 0.9286 0.5997 0.344 0.656
#> GSM11682 2 0.7219 0.6015 0.200 0.800
#> GSM11690 1 0.9795 -0.0402 0.584 0.416
#> GSM11692 1 0.3274 0.7476 0.940 0.060
#> GSM11841 1 0.3274 0.7476 0.940 0.060
#> GSM11901 1 0.3274 0.7476 0.940 0.060
#> GSM11715 2 0.9087 0.6080 0.324 0.676
#> GSM11724 2 0.9129 0.6081 0.328 0.672
#> GSM11684 1 0.9993 -0.2690 0.516 0.484
#> GSM11696 1 0.9977 -0.2333 0.528 0.472
#> GSM27952 2 0.7299 0.6018 0.204 0.796
#> GSM27948 1 0.3274 0.7476 0.940 0.060
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM11708 2 0.6168 0.3187 0.000 0.588 0.412
#> GSM11735 2 0.6168 0.3187 0.000 0.588 0.412
#> GSM11733 2 0.7251 0.5550 0.348 0.612 0.040
#> GSM11863 2 0.6398 0.5524 0.372 0.620 0.008
#> GSM11710 3 0.1647 0.5677 0.004 0.036 0.960
#> GSM11712 1 0.0892 0.5559 0.980 0.000 0.020
#> GSM11732 3 0.1399 0.5817 0.004 0.028 0.968
#> GSM11844 3 0.1399 0.5795 0.004 0.028 0.968
#> GSM11842 2 0.6398 0.5524 0.372 0.620 0.008
#> GSM11860 2 0.8392 0.4608 0.148 0.616 0.236
#> GSM11686 3 0.5905 0.3814 0.352 0.000 0.648
#> GSM11688 3 0.1315 0.5828 0.020 0.008 0.972
#> GSM11846 3 0.0829 0.5818 0.004 0.012 0.984
#> GSM11680 1 0.6427 0.4987 0.640 0.012 0.348
#> GSM11698 3 0.6470 0.0394 0.356 0.012 0.632
#> GSM11840 2 0.6529 0.5530 0.368 0.620 0.012
#> GSM11847 2 0.6398 0.5524 0.372 0.620 0.008
#> GSM11685 3 0.6079 0.2593 0.388 0.000 0.612
#> GSM11699 1 0.1860 0.5715 0.948 0.000 0.052
#> GSM27950 3 0.1031 0.5820 0.024 0.000 0.976
#> GSM27946 1 0.2356 0.5729 0.928 0.000 0.072
#> GSM11709 3 0.6704 0.3711 0.016 0.376 0.608
#> GSM11720 1 0.6566 0.4273 0.612 0.376 0.012
#> GSM11726 2 0.4723 0.4293 0.016 0.824 0.160
#> GSM11837 2 0.4059 0.4601 0.012 0.860 0.128
#> GSM11725 2 0.9952 -0.2839 0.292 0.376 0.332
#> GSM11864 1 0.8295 0.4486 0.548 0.088 0.364
#> GSM11687 1 0.6704 0.4253 0.608 0.376 0.016
#> GSM11693 1 0.6566 0.4273 0.612 0.376 0.012
#> GSM11727 2 0.4209 0.4586 0.016 0.856 0.128
#> GSM11838 2 0.4059 0.4601 0.012 0.860 0.128
#> GSM11681 3 0.6369 0.4252 0.016 0.316 0.668
#> GSM11689 1 0.6704 0.4253 0.608 0.376 0.016
#> GSM11704 1 0.6899 0.4323 0.612 0.364 0.024
#> GSM11703 1 0.6686 0.4293 0.612 0.372 0.016
#> GSM11705 3 0.6952 0.3718 0.024 0.376 0.600
#> GSM11722 3 0.9642 0.2688 0.208 0.376 0.416
#> GSM11730 2 0.4475 0.4458 0.016 0.840 0.144
#> GSM11713 2 0.5580 0.2961 0.008 0.736 0.256
#> GSM11728 3 0.4209 0.5078 0.020 0.120 0.860
#> GSM27947 1 0.6667 0.4934 0.616 0.016 0.368
#> GSM27951 3 0.9138 0.3390 0.148 0.376 0.476
#> GSM11707 3 0.5988 0.3739 0.000 0.368 0.632
#> GSM11716 1 0.7637 0.5005 0.616 0.064 0.320
#> GSM11850 1 0.8258 0.4967 0.604 0.112 0.284
#> GSM11851 1 0.7032 0.4860 0.604 0.028 0.368
#> GSM11721 1 0.1964 0.5327 0.944 0.000 0.056
#> GSM11852 1 0.1289 0.5673 0.968 0.000 0.032
#> GSM11694 1 0.7209 0.4911 0.604 0.036 0.360
#> GSM11695 1 0.7209 0.4911 0.604 0.036 0.360
#> GSM11734 1 0.4842 0.3547 0.776 0.000 0.224
#> GSM11861 1 0.1411 0.5668 0.964 0.000 0.036
#> GSM11843 1 0.6129 0.5184 0.668 0.008 0.324
#> GSM11862 1 0.0237 0.5563 0.996 0.000 0.004
#> GSM11697 1 0.7209 0.4911 0.604 0.036 0.360
#> GSM11714 3 0.5497 0.4408 0.000 0.292 0.708
#> GSM11723 3 0.6822 -0.3472 0.480 0.012 0.508
#> GSM11845 1 0.2625 0.5727 0.916 0.000 0.084
#> GSM11683 3 0.5706 0.1449 0.320 0.000 0.680
#> GSM11691 1 0.6667 0.4934 0.616 0.016 0.368
#> GSM27949 3 0.6934 0.0516 0.348 0.028 0.624
#> GSM27945 1 0.7209 0.4911 0.604 0.036 0.360
#> GSM11706 3 0.0661 0.5810 0.004 0.008 0.988
#> GSM11853 1 0.7209 0.4911 0.604 0.036 0.360
#> GSM11729 2 0.7075 0.2768 0.020 0.496 0.484
#> GSM11746 2 0.6941 0.2915 0.016 0.520 0.464
#> GSM11711 3 0.1170 0.5833 0.008 0.016 0.976
#> GSM11854 1 0.6832 0.4851 0.604 0.020 0.376
#> GSM11731 1 0.8432 -0.0397 0.576 0.112 0.312
#> GSM11839 1 0.6180 -0.0757 0.584 0.000 0.416
#> GSM11836 2 0.8895 0.5245 0.392 0.484 0.124
#> GSM11849 1 0.9651 -0.5318 0.396 0.396 0.208
#> GSM11682 3 0.7610 0.1885 0.388 0.048 0.564
#> GSM11690 1 0.5733 0.1429 0.676 0.000 0.324
#> GSM11692 1 0.1529 0.5415 0.960 0.000 0.040
#> GSM11841 1 0.3619 0.4630 0.864 0.000 0.136
#> GSM11901 1 0.3551 0.4675 0.868 0.000 0.132
#> GSM11715 2 0.8895 0.5245 0.392 0.484 0.124
#> GSM11724 2 0.8895 0.5245 0.392 0.484 0.124
#> GSM11684 3 0.8440 0.0976 0.420 0.088 0.492
#> GSM11696 1 0.5733 0.1488 0.676 0.000 0.324
#> GSM27952 3 0.2537 0.5596 0.080 0.000 0.920
#> GSM27948 1 0.2165 0.5271 0.936 0.000 0.064
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM11708 4 0.6411 0.5340 0.308 0.000 0.092 0.600
#> GSM11735 4 0.4868 0.5760 0.304 0.000 0.012 0.684
#> GSM11733 4 0.1635 0.7853 0.008 0.000 0.044 0.948
#> GSM11863 4 0.1118 0.7904 0.000 0.000 0.036 0.964
#> GSM11710 1 0.3142 0.5493 0.860 0.008 0.132 0.000
#> GSM11712 3 0.6582 0.6136 0.088 0.008 0.612 0.292
#> GSM11732 1 0.5223 0.4661 0.584 0.004 0.408 0.004
#> GSM11844 1 0.5060 0.4656 0.584 0.004 0.412 0.000
#> GSM11842 4 0.1118 0.7904 0.000 0.000 0.036 0.964
#> GSM11860 4 0.4422 0.5836 0.008 0.000 0.256 0.736
#> GSM11686 1 0.7412 0.4074 0.504 0.000 0.296 0.200
#> GSM11688 1 0.2999 0.5500 0.864 0.004 0.132 0.000
#> GSM11846 1 0.5055 0.4845 0.624 0.008 0.368 0.000
#> GSM11680 3 0.1576 0.7088 0.004 0.000 0.948 0.048
#> GSM11698 3 0.1211 0.6802 0.040 0.000 0.960 0.000
#> GSM11840 4 0.1118 0.7904 0.000 0.000 0.036 0.964
#> GSM11847 4 0.1118 0.7904 0.000 0.000 0.036 0.964
#> GSM11685 1 0.5366 0.4440 0.684 0.000 0.040 0.276
#> GSM11699 3 0.5623 0.6383 0.048 0.000 0.660 0.292
#> GSM27950 1 0.2814 0.5499 0.868 0.000 0.132 0.000
#> GSM27946 3 0.5195 0.6490 0.032 0.000 0.692 0.276
#> GSM11709 1 0.5582 0.3417 0.576 0.400 0.024 0.000
#> GSM11720 3 0.4843 0.5011 0.000 0.396 0.604 0.000
#> GSM11726 2 0.3196 0.4947 0.136 0.856 0.008 0.000
#> GSM11837 2 0.0188 0.5908 0.000 0.996 0.004 0.000
#> GSM11725 3 0.7446 0.2148 0.172 0.396 0.432 0.000
#> GSM11864 3 0.2238 0.6964 0.004 0.072 0.920 0.004
#> GSM11687 3 0.4843 0.5011 0.000 0.396 0.604 0.000
#> GSM11693 3 0.4843 0.5011 0.000 0.396 0.604 0.000
#> GSM11727 2 0.0895 0.5918 0.020 0.976 0.004 0.000
#> GSM11838 2 0.0188 0.5908 0.000 0.996 0.004 0.000
#> GSM11681 1 0.4194 0.4606 0.764 0.228 0.008 0.000
#> GSM11689 3 0.4843 0.5011 0.000 0.396 0.604 0.000
#> GSM11704 3 0.4843 0.5011 0.000 0.396 0.604 0.000
#> GSM11703 3 0.4843 0.5011 0.000 0.396 0.604 0.000
#> GSM11705 1 0.5398 0.3384 0.580 0.404 0.016 0.000
#> GSM11722 1 0.7398 0.2531 0.424 0.412 0.164 0.000
#> GSM11730 2 0.4188 0.3156 0.244 0.752 0.004 0.000
#> GSM11713 1 0.4994 0.2373 0.520 0.480 0.000 0.000
#> GSM11728 1 0.3498 0.4896 0.832 0.160 0.008 0.000
#> GSM27947 3 0.0524 0.7066 0.004 0.008 0.988 0.000
#> GSM27951 1 0.7629 0.2356 0.404 0.392 0.204 0.000
#> GSM11707 1 0.3279 0.5450 0.872 0.032 0.096 0.000
#> GSM11716 3 0.0657 0.7079 0.004 0.012 0.984 0.000
#> GSM11850 3 0.0469 0.7072 0.000 0.012 0.988 0.000
#> GSM11851 3 0.0188 0.7049 0.004 0.000 0.996 0.000
#> GSM11721 3 0.6578 0.6036 0.096 0.004 0.604 0.296
#> GSM11852 3 0.5851 0.6324 0.068 0.000 0.660 0.272
#> GSM11694 3 0.0188 0.7049 0.004 0.000 0.996 0.000
#> GSM11695 3 0.0188 0.7049 0.004 0.000 0.996 0.000
#> GSM11734 3 0.7421 0.5281 0.164 0.008 0.536 0.292
#> GSM11861 3 0.5972 0.6292 0.068 0.000 0.640 0.292
#> GSM11843 3 0.1722 0.7105 0.000 0.008 0.944 0.048
#> GSM11862 3 0.6295 0.6134 0.088 0.000 0.616 0.296
#> GSM11697 3 0.0188 0.7049 0.004 0.000 0.996 0.000
#> GSM11714 1 0.2741 0.5424 0.892 0.012 0.096 0.000
#> GSM11723 3 0.1356 0.7082 0.000 0.008 0.960 0.032
#> GSM11845 3 0.5185 0.6687 0.032 0.008 0.728 0.232
#> GSM11683 3 0.4222 0.5294 0.272 0.000 0.728 0.000
#> GSM11691 3 0.0524 0.7066 0.004 0.008 0.988 0.000
#> GSM27949 3 0.1940 0.6466 0.076 0.000 0.924 0.000
#> GSM27945 3 0.0000 0.7053 0.000 0.000 1.000 0.000
#> GSM11706 1 0.3196 0.5504 0.856 0.008 0.136 0.000
#> GSM11853 3 0.0188 0.7049 0.004 0.000 0.996 0.000
#> GSM11729 2 0.5047 0.3651 0.004 0.636 0.356 0.004
#> GSM11746 2 0.4786 0.4256 0.004 0.688 0.304 0.004
#> GSM11711 1 0.4877 0.4695 0.592 0.000 0.408 0.000
#> GSM11854 3 0.0188 0.7049 0.004 0.000 0.996 0.000
#> GSM11731 1 0.7861 0.3715 0.536 0.040 0.132 0.292
#> GSM11839 1 0.7759 0.3735 0.536 0.028 0.148 0.288
#> GSM11836 2 0.6536 0.3469 0.096 0.612 0.004 0.288
#> GSM11849 1 0.7088 0.3199 0.564 0.144 0.004 0.288
#> GSM11682 1 0.4770 0.4274 0.700 0.012 0.000 0.288
#> GSM11690 1 0.8266 -0.0547 0.364 0.012 0.336 0.288
#> GSM11692 3 0.6524 0.6070 0.092 0.004 0.608 0.296
#> GSM11841 3 0.6962 0.5958 0.108 0.012 0.588 0.292
#> GSM11901 3 0.6751 0.5941 0.108 0.004 0.588 0.300
#> GSM11715 2 0.6536 0.3469 0.096 0.612 0.004 0.288
#> GSM11724 2 0.6536 0.3469 0.096 0.612 0.004 0.288
#> GSM11684 1 0.7293 0.3973 0.576 0.024 0.112 0.288
#> GSM11696 1 0.8246 0.0197 0.384 0.012 0.316 0.288
#> GSM27952 1 0.3375 0.5527 0.864 0.008 0.116 0.012
#> GSM27948 3 0.6578 0.6036 0.096 0.004 0.604 0.296
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM11708 5 0.4854 0.5895 0.000 0.000 0.308 0.044 0.648
#> GSM11735 5 0.3958 0.7155 0.000 0.000 0.184 0.040 0.776
#> GSM11733 5 0.3736 0.8686 0.072 0.000 0.004 0.100 0.824
#> GSM11863 5 0.3639 0.8697 0.076 0.000 0.000 0.100 0.824
#> GSM11710 3 0.2787 0.7082 0.000 0.004 0.856 0.136 0.004
#> GSM11712 4 0.4938 0.2249 0.448 0.008 0.004 0.532 0.008
#> GSM11732 3 0.4851 0.6074 0.004 0.004 0.608 0.368 0.016
#> GSM11844 3 0.4414 0.6114 0.004 0.004 0.616 0.376 0.000
#> GSM11842 5 0.3644 0.8653 0.080 0.000 0.000 0.096 0.824
#> GSM11860 5 0.5007 0.7024 0.032 0.000 0.024 0.256 0.688
#> GSM11686 4 0.4541 0.4486 0.032 0.000 0.288 0.680 0.000
#> GSM11688 3 0.3246 0.6994 0.008 0.000 0.808 0.184 0.000
#> GSM11846 3 0.4505 0.6162 0.004 0.008 0.620 0.368 0.000
#> GSM11680 4 0.1739 0.6172 0.024 0.004 0.032 0.940 0.000
#> GSM11698 4 0.1862 0.6056 0.016 0.004 0.048 0.932 0.000
#> GSM11840 5 0.3639 0.8697 0.076 0.000 0.000 0.100 0.824
#> GSM11847 5 0.3639 0.8697 0.076 0.000 0.000 0.100 0.824
#> GSM11685 3 0.5975 0.5726 0.132 0.000 0.684 0.112 0.072
#> GSM11699 4 0.4111 0.4972 0.280 0.004 0.008 0.708 0.000
#> GSM27950 3 0.4012 0.6814 0.012 0.000 0.760 0.216 0.012
#> GSM27946 4 0.3737 0.5465 0.224 0.004 0.008 0.764 0.000
#> GSM11709 3 0.5099 0.4465 0.004 0.384 0.584 0.020 0.008
#> GSM11720 4 0.6177 0.4082 0.084 0.376 0.000 0.520 0.020
#> GSM11726 2 0.1377 0.6739 0.020 0.956 0.020 0.004 0.000
#> GSM11837 2 0.1857 0.6813 0.000 0.928 0.008 0.004 0.060
#> GSM11725 4 0.7326 0.3935 0.084 0.332 0.024 0.500 0.060
#> GSM11864 4 0.6843 0.5086 0.084 0.120 0.036 0.652 0.108
#> GSM11687 4 0.5158 0.4358 0.036 0.392 0.004 0.568 0.000
#> GSM11693 4 0.5542 0.4217 0.072 0.396 0.000 0.532 0.000
#> GSM11727 2 0.1179 0.6751 0.016 0.964 0.016 0.004 0.000
#> GSM11838 2 0.1205 0.6817 0.000 0.956 0.000 0.004 0.040
#> GSM11681 3 0.6508 0.5253 0.016 0.240 0.592 0.140 0.012
#> GSM11689 4 0.5330 0.4280 0.056 0.396 0.000 0.548 0.000
#> GSM11704 4 0.5290 0.4337 0.044 0.392 0.000 0.560 0.004
#> GSM11703 4 0.5213 0.4356 0.048 0.396 0.000 0.556 0.000
#> GSM11705 3 0.5440 0.4463 0.008 0.372 0.580 0.028 0.012
#> GSM11722 1 0.5895 -0.1077 0.556 0.376 0.032 0.016 0.020
#> GSM11730 2 0.1739 0.6673 0.032 0.940 0.024 0.004 0.000
#> GSM11713 2 0.3456 0.6325 0.036 0.844 0.108 0.000 0.012
#> GSM11728 3 0.6375 0.5508 0.080 0.248 0.620 0.040 0.012
#> GSM27947 4 0.1569 0.6262 0.032 0.008 0.012 0.948 0.000
#> GSM27951 4 0.6556 0.3898 0.020 0.332 0.096 0.540 0.012
#> GSM11707 3 0.2609 0.6614 0.000 0.004 0.896 0.048 0.052
#> GSM11716 4 0.3827 0.6087 0.016 0.060 0.008 0.840 0.076
#> GSM11850 4 0.1996 0.6222 0.000 0.032 0.004 0.928 0.036
#> GSM11851 4 0.2610 0.6060 0.076 0.000 0.028 0.892 0.004
#> GSM11721 1 0.4451 -0.2832 0.504 0.000 0.004 0.492 0.000
#> GSM11852 4 0.4645 0.3989 0.376 0.008 0.008 0.608 0.000
#> GSM11694 4 0.0693 0.6208 0.000 0.000 0.008 0.980 0.012
#> GSM11695 4 0.0451 0.6190 0.004 0.000 0.008 0.988 0.000
#> GSM11734 1 0.6414 0.0451 0.508 0.008 0.040 0.392 0.052
#> GSM11861 4 0.4562 0.2869 0.444 0.004 0.004 0.548 0.000
#> GSM11843 4 0.6046 0.4923 0.196 0.008 0.044 0.668 0.084
#> GSM11862 4 0.4302 0.2187 0.480 0.000 0.000 0.520 0.000
#> GSM11697 4 0.0451 0.6214 0.004 0.000 0.008 0.988 0.000
#> GSM11714 3 0.2623 0.6655 0.004 0.004 0.900 0.048 0.044
#> GSM11723 4 0.5514 0.5427 0.160 0.016 0.024 0.720 0.080
#> GSM11845 4 0.5179 0.4874 0.244 0.008 0.004 0.684 0.060
#> GSM11683 4 0.3756 0.5068 0.008 0.000 0.248 0.744 0.000
#> GSM11691 4 0.2629 0.6075 0.104 0.004 0.012 0.880 0.000
#> GSM27949 4 0.1408 0.6089 0.008 0.000 0.044 0.948 0.000
#> GSM27945 4 0.0693 0.6231 0.012 0.000 0.000 0.980 0.008
#> GSM11706 3 0.3264 0.7056 0.000 0.004 0.840 0.132 0.024
#> GSM11853 4 0.0771 0.6193 0.004 0.000 0.020 0.976 0.000
#> GSM11729 2 0.6128 0.5629 0.008 0.672 0.044 0.160 0.116
#> GSM11746 2 0.5512 0.5919 0.000 0.712 0.040 0.136 0.112
#> GSM11711 3 0.4264 0.6145 0.004 0.000 0.620 0.376 0.000
#> GSM11854 4 0.1471 0.6161 0.020 0.004 0.024 0.952 0.000
#> GSM11731 1 0.2800 0.4400 0.900 0.020 0.032 0.008 0.040
#> GSM11839 1 0.1616 0.4564 0.948 0.008 0.032 0.008 0.004
#> GSM11836 2 0.4676 0.4129 0.392 0.592 0.004 0.000 0.012
#> GSM11849 2 0.5014 0.3716 0.432 0.536 0.032 0.000 0.000
#> GSM11682 3 0.4365 0.4587 0.308 0.004 0.676 0.012 0.000
#> GSM11690 1 0.5289 0.1412 0.556 0.008 0.036 0.400 0.000
#> GSM11692 4 0.4278 0.2454 0.452 0.000 0.000 0.548 0.000
#> GSM11841 4 0.4305 0.1810 0.488 0.000 0.000 0.512 0.000
#> GSM11901 4 0.4307 0.1703 0.496 0.000 0.000 0.504 0.000
#> GSM11715 2 0.5299 0.4739 0.336 0.612 0.036 0.000 0.016
#> GSM11724 2 0.5242 0.4708 0.340 0.612 0.032 0.000 0.016
#> GSM11684 1 0.2623 0.4048 0.884 0.016 0.096 0.004 0.000
#> GSM11696 1 0.4160 0.5103 0.772 0.008 0.036 0.184 0.000
#> GSM27952 3 0.2629 0.7085 0.004 0.000 0.860 0.136 0.000
#> GSM27948 4 0.4420 0.2414 0.448 0.000 0.004 0.548 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM11708 5 0.3935 0.57704 0.008 0.000 0.000 0.012 0.692 0.288
#> GSM11735 5 0.2994 0.67497 0.008 0.000 0.000 0.008 0.820 0.164
#> GSM11733 5 0.1958 0.85545 0.000 0.000 0.100 0.000 0.896 0.004
#> GSM11863 5 0.1863 0.85804 0.000 0.000 0.104 0.000 0.896 0.000
#> GSM11710 6 0.4813 0.54121 0.200 0.000 0.092 0.000 0.016 0.692
#> GSM11712 3 0.5991 0.06318 0.004 0.256 0.480 0.260 0.000 0.000
#> GSM11732 6 0.5077 0.39900 0.008 0.000 0.400 0.060 0.000 0.532
#> GSM11844 6 0.4427 0.39976 0.004 0.000 0.428 0.020 0.000 0.548
#> GSM11842 5 0.1863 0.85804 0.000 0.000 0.104 0.000 0.896 0.000
#> GSM11860 5 0.4921 0.60969 0.000 0.044 0.288 0.000 0.640 0.028
#> GSM11686 6 0.4703 0.12569 0.000 0.000 0.380 0.052 0.000 0.568
#> GSM11688 6 0.4671 0.54607 0.148 0.000 0.112 0.012 0.004 0.724
#> GSM11846 6 0.5688 0.46718 0.140 0.000 0.384 0.004 0.000 0.472
#> GSM11680 3 0.1168 0.50506 0.000 0.000 0.956 0.016 0.000 0.028
#> GSM11698 3 0.3385 0.37726 0.004 0.000 0.796 0.028 0.000 0.172
#> GSM11840 5 0.1863 0.85804 0.000 0.000 0.104 0.000 0.896 0.000
#> GSM11847 5 0.1863 0.85804 0.000 0.000 0.104 0.000 0.896 0.000
#> GSM11685 6 0.3984 0.45400 0.012 0.008 0.056 0.012 0.104 0.808
#> GSM11699 3 0.4544 0.40797 0.008 0.092 0.712 0.188 0.000 0.000
#> GSM27950 6 0.4256 0.51460 0.016 0.000 0.156 0.004 0.064 0.760
#> GSM27946 3 0.3656 0.45694 0.008 0.076 0.804 0.112 0.000 0.000
#> GSM11709 6 0.5183 -0.05273 0.396 0.004 0.040 0.020 0.000 0.540
#> GSM11720 3 0.5786 0.22050 0.364 0.008 0.484 0.144 0.000 0.000
#> GSM11726 2 0.4400 0.35815 0.428 0.552 0.004 0.004 0.000 0.012
#> GSM11837 2 0.4751 0.44033 0.316 0.620 0.004 0.060 0.000 0.000
#> GSM11725 4 0.7829 -0.05965 0.304 0.016 0.216 0.320 0.000 0.144
#> GSM11864 3 0.6404 0.15257 0.064 0.116 0.472 0.348 0.000 0.000
#> GSM11687 3 0.5283 0.25252 0.400 0.004 0.508 0.088 0.000 0.000
#> GSM11693 3 0.5558 0.24023 0.396 0.008 0.488 0.108 0.000 0.000
#> GSM11727 2 0.4093 0.34985 0.440 0.552 0.004 0.000 0.000 0.004
#> GSM11838 2 0.4441 0.42522 0.344 0.620 0.004 0.032 0.000 0.000
#> GSM11681 6 0.6350 -0.00289 0.220 0.000 0.072 0.124 0.008 0.576
#> GSM11689 3 0.5596 0.23443 0.400 0.008 0.480 0.112 0.000 0.000
#> GSM11704 3 0.5524 0.24190 0.396 0.008 0.492 0.104 0.000 0.000
#> GSM11703 3 0.5296 0.24800 0.396 0.008 0.516 0.080 0.000 0.000
#> GSM11705 6 0.4955 -0.01242 0.380 0.004 0.020 0.020 0.004 0.572
#> GSM11722 1 0.6280 0.25726 0.504 0.020 0.008 0.296 0.000 0.172
#> GSM11730 1 0.4716 -0.28386 0.552 0.404 0.004 0.000 0.000 0.040
#> GSM11713 1 0.6073 0.13823 0.564 0.212 0.000 0.020 0.008 0.196
#> GSM11728 1 0.5296 0.17507 0.536 0.036 0.000 0.024 0.008 0.396
#> GSM27947 3 0.1049 0.50371 0.008 0.000 0.960 0.032 0.000 0.000
#> GSM27951 1 0.7721 -0.02397 0.292 0.000 0.284 0.136 0.008 0.280
#> GSM11707 6 0.4845 0.47028 0.204 0.000 0.004 0.012 0.088 0.692
#> GSM11716 3 0.5130 0.40426 0.080 0.008 0.672 0.220 0.000 0.020
#> GSM11850 3 0.3023 0.47848 0.044 0.000 0.836 0.120 0.000 0.000
#> GSM11851 3 0.3487 0.42058 0.000 0.000 0.756 0.224 0.000 0.020
#> GSM11721 3 0.6493 -0.01781 0.000 0.264 0.424 0.288 0.000 0.024
#> GSM11852 3 0.4976 0.34480 0.012 0.088 0.652 0.248 0.000 0.000
#> GSM11694 3 0.1908 0.48385 0.004 0.000 0.900 0.096 0.000 0.000
#> GSM11695 3 0.1700 0.49063 0.004 0.000 0.916 0.080 0.000 0.000
#> GSM11734 4 0.7202 0.31260 0.000 0.220 0.252 0.416 0.000 0.112
#> GSM11861 4 0.5808 -0.18163 0.004 0.156 0.420 0.420 0.000 0.000
#> GSM11843 3 0.5602 0.21639 0.000 0.188 0.536 0.276 0.000 0.000
#> GSM11862 3 0.6100 0.09423 0.012 0.260 0.492 0.236 0.000 0.000
#> GSM11697 3 0.0777 0.50407 0.004 0.000 0.972 0.024 0.000 0.000
#> GSM11714 6 0.4771 0.47186 0.200 0.000 0.004 0.012 0.084 0.700
#> GSM11723 3 0.5443 0.10504 0.000 0.124 0.492 0.384 0.000 0.000
#> GSM11845 3 0.5558 0.13990 0.000 0.144 0.492 0.364 0.000 0.000
#> GSM11683 3 0.4477 0.15286 0.004 0.000 0.552 0.016 0.004 0.424
#> GSM11691 3 0.3011 0.45761 0.004 0.000 0.800 0.192 0.000 0.004
#> GSM27949 3 0.3269 0.35515 0.000 0.000 0.792 0.024 0.000 0.184
#> GSM27945 3 0.1958 0.48310 0.004 0.000 0.896 0.100 0.000 0.000
#> GSM11706 6 0.6085 0.53268 0.204 0.000 0.096 0.012 0.072 0.616
#> GSM11853 3 0.0363 0.50593 0.000 0.000 0.988 0.012 0.000 0.000
#> GSM11729 2 0.4478 0.48727 0.036 0.748 0.068 0.148 0.000 0.000
#> GSM11746 2 0.4881 0.48699 0.060 0.720 0.068 0.152 0.000 0.000
#> GSM11711 6 0.4049 0.42736 0.004 0.000 0.412 0.004 0.000 0.580
#> GSM11854 3 0.0976 0.50564 0.008 0.000 0.968 0.016 0.000 0.008
#> GSM11731 4 0.7183 0.20642 0.112 0.284 0.004 0.432 0.000 0.168
#> GSM11839 4 0.7121 0.29222 0.104 0.268 0.004 0.448 0.000 0.176
#> GSM11836 2 0.3296 0.37581 0.004 0.824 0.000 0.132 0.036 0.004
#> GSM11849 2 0.6375 0.03976 0.296 0.512 0.000 0.128 0.000 0.064
#> GSM11682 6 0.6110 0.29196 0.260 0.044 0.004 0.112 0.004 0.576
#> GSM11690 4 0.8325 0.42733 0.044 0.260 0.220 0.292 0.000 0.184
#> GSM11692 3 0.6018 0.04712 0.004 0.264 0.472 0.260 0.000 0.000
#> GSM11841 3 0.6182 -0.10911 0.004 0.264 0.392 0.340 0.000 0.000
#> GSM11901 3 0.6154 -0.07180 0.004 0.264 0.416 0.316 0.000 0.000
#> GSM11715 2 0.0858 0.50253 0.028 0.968 0.000 0.004 0.000 0.000
#> GSM11724 2 0.0858 0.50253 0.028 0.968 0.000 0.004 0.000 0.000
#> GSM11684 1 0.7682 -0.34045 0.280 0.260 0.000 0.268 0.000 0.192
#> GSM11696 4 0.8385 0.43878 0.084 0.264 0.132 0.340 0.000 0.180
#> GSM27952 6 0.4451 0.54557 0.148 0.000 0.092 0.012 0.004 0.744
#> GSM27948 3 0.6707 0.00437 0.008 0.264 0.440 0.260 0.000 0.028
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.line(p) agent(p) time(p) k
#> SD:mclust 68 1.22e-03 0.744 3.61e-03 2
#> SD:mclust 30 1.76e-02 0.570 4.54e-05 3
#> SD:mclust 55 1.08e-05 0.544 5.51e-04 4
#> SD:mclust 49 2.00e-06 0.643 2.25e-04 5
#> SD:mclust 20 5.42e-02 0.254 1.92e-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.
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 14502 rows and 83 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 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 0.657 0.826 0.927 0.4089 0.574 0.574
#> 3 3 0.319 0.450 0.715 0.4995 0.654 0.460
#> 4 4 0.451 0.603 0.760 0.1602 0.653 0.297
#> 5 5 0.633 0.613 0.799 0.0700 0.854 0.550
#> 6 6 0.578 0.486 0.688 0.0543 0.894 0.611
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
#> GSM11708 2 0.0000 0.8421 0.000 1.000
#> GSM11735 2 0.0000 0.8421 0.000 1.000
#> GSM11733 2 0.0000 0.8421 0.000 1.000
#> GSM11863 2 0.0000 0.8421 0.000 1.000
#> GSM11710 2 0.0000 0.8421 0.000 1.000
#> GSM11712 1 0.0000 0.9440 1.000 0.000
#> GSM11732 2 0.0000 0.8421 0.000 1.000
#> GSM11844 1 0.9661 0.2319 0.608 0.392
#> GSM11842 2 0.2043 0.8310 0.032 0.968
#> GSM11860 2 0.8386 0.6164 0.268 0.732
#> GSM11686 2 0.9896 0.3514 0.440 0.560
#> GSM11688 2 0.6048 0.7866 0.148 0.852
#> GSM11846 2 0.0938 0.8400 0.012 0.988
#> GSM11680 2 0.9944 0.3061 0.456 0.544
#> GSM11698 1 0.9833 0.1182 0.576 0.424
#> GSM11840 2 0.0000 0.8421 0.000 1.000
#> GSM11847 2 0.0000 0.8421 0.000 1.000
#> GSM11685 2 0.6973 0.7624 0.188 0.812
#> GSM11699 1 0.1414 0.9292 0.980 0.020
#> GSM27950 2 0.0000 0.8421 0.000 1.000
#> GSM27946 1 0.0000 0.9440 1.000 0.000
#> GSM11709 1 0.3733 0.8757 0.928 0.072
#> GSM11720 1 0.0000 0.9440 1.000 0.000
#> GSM11726 1 0.0000 0.9440 1.000 0.000
#> GSM11837 1 0.0000 0.9440 1.000 0.000
#> GSM11725 1 0.0000 0.9440 1.000 0.000
#> GSM11864 1 0.0000 0.9440 1.000 0.000
#> GSM11687 1 0.0000 0.9440 1.000 0.000
#> GSM11693 1 0.0000 0.9440 1.000 0.000
#> GSM11727 1 0.0000 0.9440 1.000 0.000
#> GSM11838 1 0.0000 0.9440 1.000 0.000
#> GSM11681 1 0.9815 0.1324 0.580 0.420
#> GSM11689 1 0.0000 0.9440 1.000 0.000
#> GSM11704 1 0.0000 0.9440 1.000 0.000
#> GSM11703 1 0.0000 0.9440 1.000 0.000
#> GSM11705 1 0.0000 0.9440 1.000 0.000
#> GSM11722 1 0.0000 0.9440 1.000 0.000
#> GSM11730 1 0.0000 0.9440 1.000 0.000
#> GSM11713 1 0.1633 0.9257 0.976 0.024
#> GSM11728 1 0.4690 0.8464 0.900 0.100
#> GSM27947 1 0.0000 0.9440 1.000 0.000
#> GSM27951 1 0.0000 0.9440 1.000 0.000
#> GSM11707 2 0.0000 0.8421 0.000 1.000
#> GSM11716 1 0.0376 0.9412 0.996 0.004
#> GSM11850 1 0.2423 0.9118 0.960 0.040
#> GSM11851 2 0.9970 0.2689 0.468 0.532
#> GSM11721 1 0.0000 0.9440 1.000 0.000
#> GSM11852 1 0.5178 0.8271 0.884 0.116
#> GSM11694 1 0.7674 0.6662 0.776 0.224
#> GSM11695 2 0.9427 0.5397 0.360 0.640
#> GSM11734 1 0.0000 0.9440 1.000 0.000
#> GSM11861 1 0.0000 0.9440 1.000 0.000
#> GSM11843 1 0.0000 0.9440 1.000 0.000
#> GSM11862 1 0.0000 0.9440 1.000 0.000
#> GSM11697 1 0.5294 0.8234 0.880 0.120
#> GSM11714 2 0.0000 0.8421 0.000 1.000
#> GSM11723 1 0.0000 0.9440 1.000 0.000
#> GSM11845 1 0.0000 0.9440 1.000 0.000
#> GSM11683 2 0.9661 0.4679 0.392 0.608
#> GSM11691 1 0.0000 0.9440 1.000 0.000
#> GSM27949 2 0.6973 0.7624 0.188 0.812
#> GSM27945 1 0.1414 0.9291 0.980 0.020
#> GSM11706 2 0.0000 0.8421 0.000 1.000
#> GSM11853 1 0.0938 0.9357 0.988 0.012
#> GSM11729 1 0.0000 0.9440 1.000 0.000
#> GSM11746 1 0.0000 0.9440 1.000 0.000
#> GSM11711 2 0.7376 0.7458 0.208 0.792
#> GSM11854 1 0.7299 0.6957 0.796 0.204
#> GSM11731 1 0.0000 0.9440 1.000 0.000
#> GSM11839 1 0.0000 0.9440 1.000 0.000
#> GSM11836 1 0.0000 0.9440 1.000 0.000
#> GSM11849 1 0.0000 0.9440 1.000 0.000
#> GSM11682 1 0.9896 0.0507 0.560 0.440
#> GSM11690 1 0.0000 0.9440 1.000 0.000
#> GSM11692 1 0.0000 0.9440 1.000 0.000
#> GSM11841 1 0.0000 0.9440 1.000 0.000
#> GSM11901 1 0.0000 0.9440 1.000 0.000
#> GSM11715 1 0.0000 0.9440 1.000 0.000
#> GSM11724 1 0.0000 0.9440 1.000 0.000
#> GSM11684 1 0.0000 0.9440 1.000 0.000
#> GSM11696 1 0.0000 0.9440 1.000 0.000
#> GSM27952 2 0.7883 0.7164 0.236 0.764
#> GSM27948 1 0.0000 0.9440 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM11708 3 0.0000 0.7709 0.000 0.000 1.000
#> GSM11735 3 0.0000 0.7709 0.000 0.000 1.000
#> GSM11733 3 0.0592 0.7704 0.000 0.012 0.988
#> GSM11863 3 0.6252 0.4461 0.000 0.444 0.556
#> GSM11710 3 0.3038 0.7325 0.104 0.000 0.896
#> GSM11712 2 0.6274 0.1533 0.456 0.544 0.000
#> GSM11732 3 0.3482 0.7228 0.000 0.128 0.872
#> GSM11844 3 0.8538 0.1271 0.380 0.100 0.520
#> GSM11842 3 0.6286 0.4188 0.000 0.464 0.536
#> GSM11860 3 0.6295 0.4058 0.000 0.472 0.528
#> GSM11686 1 0.4291 0.4752 0.820 0.000 0.180
#> GSM11688 1 0.6295 -0.2118 0.528 0.000 0.472
#> GSM11846 3 0.2063 0.7637 0.044 0.008 0.948
#> GSM11680 1 0.6513 -0.0168 0.520 0.004 0.476
#> GSM11698 1 0.8056 0.2939 0.532 0.068 0.400
#> GSM11840 3 0.2625 0.7587 0.000 0.084 0.916
#> GSM11847 3 0.2261 0.7631 0.000 0.068 0.932
#> GSM11685 1 0.6215 -0.1083 0.572 0.000 0.428
#> GSM11699 1 0.2448 0.5850 0.924 0.076 0.000
#> GSM27950 3 0.4974 0.6520 0.236 0.000 0.764
#> GSM27946 1 0.5948 0.3012 0.640 0.360 0.000
#> GSM11709 1 0.9531 0.1319 0.476 0.216 0.308
#> GSM11720 2 0.5785 0.4126 0.332 0.668 0.000
#> GSM11726 2 0.5529 0.4878 0.296 0.704 0.000
#> GSM11837 2 0.0000 0.6049 0.000 1.000 0.000
#> GSM11725 2 0.2066 0.6252 0.060 0.940 0.000
#> GSM11864 2 0.4555 0.5676 0.200 0.800 0.000
#> GSM11687 1 0.5926 0.3051 0.644 0.356 0.000
#> GSM11693 1 0.5988 0.2875 0.632 0.368 0.000
#> GSM11727 2 0.6286 0.1155 0.464 0.536 0.000
#> GSM11838 2 0.5016 0.5433 0.240 0.760 0.000
#> GSM11681 1 0.0237 0.5805 0.996 0.000 0.004
#> GSM11689 1 0.5988 0.2876 0.632 0.368 0.000
#> GSM11704 1 0.5988 0.2876 0.632 0.368 0.000
#> GSM11703 1 0.5988 0.2876 0.632 0.368 0.000
#> GSM11705 1 0.2625 0.5839 0.916 0.084 0.000
#> GSM11722 2 0.6302 0.0640 0.480 0.520 0.000
#> GSM11730 1 0.5905 0.2878 0.648 0.352 0.000
#> GSM11713 1 0.3941 0.4504 0.844 0.156 0.000
#> GSM11728 1 0.3752 0.4643 0.856 0.144 0.000
#> GSM27947 1 0.6008 0.2793 0.628 0.372 0.000
#> GSM27951 1 0.0000 0.5816 1.000 0.000 0.000
#> GSM11707 3 0.0000 0.7709 0.000 0.000 1.000
#> GSM11716 2 0.5269 0.5612 0.200 0.784 0.016
#> GSM11850 2 0.9827 0.0334 0.376 0.380 0.244
#> GSM11851 3 0.6796 0.3341 0.368 0.020 0.612
#> GSM11721 1 0.3192 0.5715 0.888 0.112 0.000
#> GSM11852 1 0.0592 0.5855 0.988 0.012 0.000
#> GSM11694 1 0.7883 0.1737 0.516 0.056 0.428
#> GSM11695 3 0.5835 0.4140 0.340 0.000 0.660
#> GSM11734 2 0.2625 0.6245 0.084 0.916 0.000
#> GSM11861 1 0.3551 0.5623 0.868 0.132 0.000
#> GSM11843 2 0.5138 0.5308 0.252 0.748 0.000
#> GSM11862 1 0.1529 0.5890 0.960 0.040 0.000
#> GSM11697 1 0.8278 0.4023 0.620 0.132 0.248
#> GSM11714 3 0.4121 0.6897 0.168 0.000 0.832
#> GSM11723 2 0.1860 0.6241 0.052 0.948 0.000
#> GSM11845 2 0.4654 0.5639 0.208 0.792 0.000
#> GSM11683 1 0.3816 0.5007 0.852 0.000 0.148
#> GSM11691 1 0.1643 0.5890 0.956 0.044 0.000
#> GSM27949 3 0.4887 0.6140 0.228 0.000 0.772
#> GSM27945 2 0.8463 0.0993 0.444 0.468 0.088
#> GSM11706 3 0.0000 0.7709 0.000 0.000 1.000
#> GSM11853 1 0.8220 0.3824 0.636 0.212 0.152
#> GSM11729 2 0.0000 0.6049 0.000 1.000 0.000
#> GSM11746 2 0.0000 0.6049 0.000 1.000 0.000
#> GSM11711 3 0.4796 0.6193 0.220 0.000 0.780
#> GSM11854 1 0.6854 0.4858 0.716 0.068 0.216
#> GSM11731 2 0.2448 0.6261 0.076 0.924 0.000
#> GSM11839 2 0.6286 0.1074 0.464 0.536 0.000
#> GSM11836 2 0.6008 0.3578 0.372 0.628 0.000
#> GSM11849 1 0.4974 0.4266 0.764 0.236 0.000
#> GSM11682 1 0.0747 0.5778 0.984 0.000 0.016
#> GSM11690 1 0.0424 0.5841 0.992 0.008 0.000
#> GSM11692 1 0.5968 0.2945 0.636 0.364 0.000
#> GSM11841 1 0.6274 0.0451 0.544 0.456 0.000
#> GSM11901 1 0.6095 0.2355 0.608 0.392 0.000
#> GSM11715 2 0.4974 0.5476 0.236 0.764 0.000
#> GSM11724 2 0.4931 0.5511 0.232 0.768 0.000
#> GSM11684 1 0.4842 0.4461 0.776 0.224 0.000
#> GSM11696 1 0.4291 0.5321 0.820 0.180 0.000
#> GSM27952 1 0.5431 0.2926 0.716 0.000 0.284
#> GSM27948 1 0.2625 0.5826 0.916 0.084 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM11708 4 0.0000 0.7935 0.000 0.000 0.000 1.000
#> GSM11735 4 0.0188 0.7932 0.000 0.004 0.000 0.996
#> GSM11733 4 0.1792 0.7757 0.000 0.068 0.000 0.932
#> GSM11863 2 0.4571 0.4262 0.008 0.736 0.004 0.252
#> GSM11710 4 0.3528 0.7604 0.192 0.000 0.000 0.808
#> GSM11712 3 0.3219 0.7300 0.000 0.164 0.836 0.000
#> GSM11732 4 0.1256 0.7862 0.000 0.008 0.028 0.964
#> GSM11844 3 0.5773 0.3284 0.016 0.008 0.536 0.440
#> GSM11842 2 0.3852 0.5047 0.008 0.800 0.000 0.192
#> GSM11860 2 0.3992 0.5082 0.004 0.800 0.008 0.188
#> GSM11686 1 0.5926 0.5089 0.632 0.000 0.308 0.060
#> GSM11688 4 0.6143 0.3578 0.456 0.000 0.048 0.496
#> GSM11846 4 0.3382 0.7533 0.004 0.040 0.080 0.876
#> GSM11680 3 0.5623 0.5847 0.044 0.004 0.676 0.276
#> GSM11698 3 0.4175 0.6979 0.012 0.000 0.776 0.212
#> GSM11840 4 0.5141 0.5924 0.032 0.268 0.000 0.700
#> GSM11847 4 0.5537 0.5976 0.056 0.256 0.000 0.688
#> GSM11685 4 0.6449 0.3055 0.452 0.000 0.068 0.480
#> GSM11699 3 0.4356 0.4703 0.292 0.000 0.708 0.000
#> GSM27950 4 0.3157 0.7747 0.144 0.000 0.004 0.852
#> GSM27946 3 0.1854 0.7671 0.048 0.012 0.940 0.000
#> GSM11709 3 0.6742 0.3948 0.088 0.012 0.600 0.300
#> GSM11720 3 0.2342 0.7640 0.008 0.080 0.912 0.000
#> GSM11726 3 0.7521 -0.0192 0.264 0.212 0.520 0.004
#> GSM11837 2 0.6881 0.4913 0.132 0.592 0.272 0.004
#> GSM11725 3 0.5172 0.5589 0.036 0.260 0.704 0.000
#> GSM11864 3 0.3710 0.6991 0.004 0.192 0.804 0.000
#> GSM11687 3 0.2928 0.7213 0.108 0.012 0.880 0.000
#> GSM11693 3 0.0804 0.7738 0.012 0.008 0.980 0.000
#> GSM11727 1 0.5842 0.5685 0.704 0.168 0.128 0.000
#> GSM11838 2 0.6031 0.5351 0.216 0.676 0.108 0.000
#> GSM11681 1 0.3271 0.7003 0.856 0.000 0.132 0.012
#> GSM11689 3 0.0895 0.7716 0.020 0.004 0.976 0.000
#> GSM11704 3 0.0779 0.7722 0.016 0.004 0.980 0.000
#> GSM11703 3 0.1584 0.7650 0.036 0.012 0.952 0.000
#> GSM11705 1 0.5364 0.4456 0.592 0.016 0.392 0.000
#> GSM11722 1 0.6546 0.4970 0.636 0.172 0.192 0.000
#> GSM11730 1 0.5484 0.5906 0.732 0.164 0.104 0.000
#> GSM11713 1 0.4300 0.6470 0.820 0.088 0.092 0.000
#> GSM11728 1 0.3894 0.6554 0.844 0.068 0.088 0.000
#> GSM27947 3 0.1022 0.7752 0.000 0.032 0.968 0.000
#> GSM27951 1 0.3972 0.6930 0.788 0.008 0.204 0.000
#> GSM11707 4 0.1118 0.7988 0.036 0.000 0.000 0.964
#> GSM11716 3 0.3694 0.7474 0.000 0.124 0.844 0.032
#> GSM11850 3 0.3568 0.7613 0.004 0.024 0.856 0.116
#> GSM11851 3 0.3157 0.7571 0.004 0.000 0.852 0.144
#> GSM11721 1 0.6163 0.3350 0.532 0.052 0.416 0.000
#> GSM11852 3 0.4343 0.5428 0.264 0.000 0.732 0.004
#> GSM11694 3 0.2704 0.7644 0.000 0.000 0.876 0.124
#> GSM11695 3 0.2973 0.7574 0.000 0.000 0.856 0.144
#> GSM11734 2 0.5368 0.3728 0.024 0.636 0.340 0.000
#> GSM11861 3 0.3893 0.6400 0.196 0.008 0.796 0.000
#> GSM11843 3 0.3311 0.7248 0.000 0.172 0.828 0.000
#> GSM11862 3 0.5295 -0.1940 0.488 0.008 0.504 0.000
#> GSM11697 3 0.2530 0.7686 0.000 0.000 0.888 0.112
#> GSM11714 4 0.3105 0.7759 0.140 0.000 0.004 0.856
#> GSM11723 3 0.4609 0.6503 0.024 0.224 0.752 0.000
#> GSM11845 3 0.3024 0.7380 0.000 0.148 0.852 0.000
#> GSM11683 1 0.5452 0.6436 0.736 0.000 0.156 0.108
#> GSM11691 3 0.1940 0.7652 0.076 0.000 0.924 0.000
#> GSM27949 3 0.5384 0.5670 0.028 0.000 0.648 0.324
#> GSM27945 3 0.2131 0.7782 0.000 0.036 0.932 0.032
#> GSM11706 4 0.1118 0.7988 0.036 0.000 0.000 0.964
#> GSM11853 3 0.1593 0.7807 0.004 0.016 0.956 0.024
#> GSM11729 2 0.3601 0.6476 0.056 0.860 0.084 0.000
#> GSM11746 2 0.4964 0.6111 0.068 0.764 0.168 0.000
#> GSM11711 4 0.4974 0.5994 0.040 0.000 0.224 0.736
#> GSM11854 3 0.2408 0.7695 0.044 0.000 0.920 0.036
#> GSM11731 2 0.2797 0.6466 0.068 0.900 0.032 0.000
#> GSM11839 2 0.5496 0.4536 0.312 0.652 0.036 0.000
#> GSM11836 2 0.4594 0.5274 0.280 0.712 0.008 0.000
#> GSM11849 1 0.3498 0.5942 0.832 0.160 0.008 0.000
#> GSM11682 1 0.2586 0.6870 0.900 0.004 0.092 0.004
#> GSM11690 1 0.4019 0.6695 0.792 0.012 0.196 0.000
#> GSM11692 3 0.6548 0.4811 0.188 0.176 0.636 0.000
#> GSM11841 2 0.5602 -0.0392 0.020 0.508 0.472 0.000
#> GSM11901 2 0.6451 -0.0224 0.068 0.476 0.456 0.000
#> GSM11715 2 0.4426 0.6073 0.204 0.772 0.024 0.000
#> GSM11724 2 0.4245 0.6115 0.196 0.784 0.020 0.000
#> GSM11684 1 0.5110 0.6675 0.764 0.132 0.104 0.000
#> GSM11696 1 0.5673 0.6334 0.660 0.052 0.288 0.000
#> GSM27952 1 0.3037 0.6453 0.888 0.000 0.036 0.076
#> GSM27948 1 0.5691 0.3304 0.564 0.028 0.408 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM11708 3 0.1270 0.7404 0.000 0.000 0.948 0.000 0.052
#> GSM11735 3 0.1608 0.7373 0.000 0.000 0.928 0.000 0.072
#> GSM11733 3 0.3861 0.6071 0.000 0.000 0.712 0.004 0.284
#> GSM11863 5 0.1768 0.5204 0.000 0.000 0.072 0.004 0.924
#> GSM11710 3 0.3656 0.6727 0.000 0.000 0.784 0.196 0.020
#> GSM11712 1 0.2850 0.7878 0.872 0.000 0.000 0.092 0.036
#> GSM11732 3 0.3221 0.6921 0.064 0.048 0.872 0.008 0.008
#> GSM11844 3 0.5635 -0.0073 0.468 0.044 0.476 0.004 0.008
#> GSM11842 5 0.0865 0.5564 0.000 0.000 0.024 0.004 0.972
#> GSM11860 5 0.0566 0.5632 0.000 0.000 0.012 0.004 0.984
#> GSM11686 4 0.1809 0.6851 0.060 0.000 0.012 0.928 0.000
#> GSM11688 4 0.1478 0.6291 0.000 0.000 0.064 0.936 0.000
#> GSM11846 3 0.6894 0.5439 0.064 0.000 0.560 0.128 0.248
#> GSM11680 1 0.3837 0.3907 0.692 0.000 0.000 0.308 0.000
#> GSM11698 1 0.1251 0.8348 0.956 0.000 0.008 0.036 0.000
#> GSM11840 3 0.4450 0.3147 0.000 0.000 0.508 0.004 0.488
#> GSM11847 5 0.4907 -0.3910 0.000 0.000 0.484 0.024 0.492
#> GSM11685 4 0.1408 0.6488 0.008 0.000 0.044 0.948 0.000
#> GSM11699 4 0.4302 0.3194 0.480 0.000 0.000 0.520 0.000
#> GSM27950 3 0.2798 0.7082 0.008 0.000 0.852 0.140 0.000
#> GSM27946 1 0.4015 0.2715 0.652 0.000 0.000 0.348 0.000
#> GSM11709 1 0.7261 -0.0231 0.404 0.260 0.316 0.016 0.004
#> GSM11720 1 0.1248 0.8413 0.964 0.016 0.004 0.008 0.008
#> GSM11726 2 0.1074 0.7101 0.016 0.968 0.000 0.004 0.012
#> GSM11837 2 0.2843 0.5346 0.008 0.848 0.000 0.000 0.144
#> GSM11725 1 0.5310 0.4931 0.672 0.236 0.000 0.008 0.084
#> GSM11864 1 0.1331 0.8395 0.952 0.000 0.000 0.008 0.040
#> GSM11687 1 0.3126 0.7953 0.868 0.048 0.008 0.076 0.000
#> GSM11693 1 0.1117 0.8390 0.964 0.020 0.000 0.016 0.000
#> GSM11727 2 0.0000 0.7253 0.000 1.000 0.000 0.000 0.000
#> GSM11838 2 0.0963 0.6980 0.000 0.964 0.000 0.000 0.036
#> GSM11681 4 0.3474 0.5611 0.008 0.148 0.020 0.824 0.000
#> GSM11689 1 0.2193 0.8187 0.912 0.028 0.000 0.060 0.000
#> GSM11704 1 0.2079 0.8199 0.916 0.020 0.000 0.064 0.000
#> GSM11703 1 0.3031 0.7798 0.852 0.128 0.000 0.016 0.004
#> GSM11705 2 0.3943 0.6810 0.016 0.784 0.016 0.184 0.000
#> GSM11722 2 0.0000 0.7253 0.000 1.000 0.000 0.000 0.000
#> GSM11730 2 0.0000 0.7253 0.000 1.000 0.000 0.000 0.000
#> GSM11713 2 0.3391 0.6870 0.000 0.800 0.012 0.188 0.000
#> GSM11728 2 0.3480 0.6552 0.000 0.752 0.000 0.248 0.000
#> GSM27947 1 0.0703 0.8372 0.976 0.000 0.000 0.024 0.000
#> GSM27951 2 0.5271 0.3397 0.048 0.520 0.000 0.432 0.000
#> GSM11707 3 0.0451 0.7383 0.004 0.000 0.988 0.000 0.008
#> GSM11716 1 0.1686 0.8364 0.944 0.000 0.028 0.008 0.020
#> GSM11850 1 0.3001 0.7567 0.844 0.000 0.144 0.008 0.004
#> GSM11851 1 0.1168 0.8394 0.960 0.000 0.032 0.008 0.000
#> GSM11721 4 0.3461 0.6937 0.224 0.000 0.000 0.772 0.004
#> GSM11852 4 0.4306 0.2972 0.492 0.000 0.000 0.508 0.000
#> GSM11694 1 0.0794 0.8405 0.972 0.000 0.028 0.000 0.000
#> GSM11695 1 0.1571 0.8276 0.936 0.000 0.060 0.004 0.000
#> GSM11734 5 0.6299 0.1960 0.380 0.112 0.000 0.012 0.496
#> GSM11861 1 0.4166 0.2588 0.648 0.000 0.004 0.348 0.000
#> GSM11843 1 0.1626 0.8369 0.940 0.000 0.000 0.016 0.044
#> GSM11862 4 0.4126 0.5389 0.380 0.000 0.000 0.620 0.000
#> GSM11697 1 0.0609 0.8421 0.980 0.000 0.020 0.000 0.000
#> GSM11714 3 0.1310 0.7374 0.000 0.020 0.956 0.024 0.000
#> GSM11723 1 0.3206 0.7913 0.864 0.024 0.004 0.012 0.096
#> GSM11845 1 0.1082 0.8401 0.964 0.000 0.000 0.008 0.028
#> GSM11683 4 0.3054 0.6573 0.032 0.028 0.060 0.880 0.000
#> GSM11691 1 0.1211 0.8409 0.960 0.000 0.016 0.024 0.000
#> GSM27949 1 0.3266 0.7157 0.796 0.000 0.200 0.004 0.000
#> GSM27945 1 0.0324 0.8404 0.992 0.000 0.004 0.004 0.000
#> GSM11706 3 0.0880 0.7413 0.000 0.000 0.968 0.000 0.032
#> GSM11853 1 0.0566 0.8398 0.984 0.000 0.004 0.012 0.000
#> GSM11729 5 0.4455 0.5261 0.008 0.404 0.000 0.000 0.588
#> GSM11746 5 0.4517 0.4899 0.008 0.436 0.000 0.000 0.556
#> GSM11711 3 0.4437 0.4719 0.316 0.000 0.664 0.020 0.000
#> GSM11854 1 0.3160 0.6566 0.808 0.000 0.004 0.188 0.000
#> GSM11731 5 0.4067 0.5887 0.000 0.300 0.000 0.008 0.692
#> GSM11839 5 0.6234 0.4657 0.000 0.296 0.000 0.176 0.528
#> GSM11836 5 0.4295 0.6026 0.000 0.216 0.000 0.044 0.740
#> GSM11849 2 0.3966 0.3960 0.000 0.664 0.000 0.336 0.000
#> GSM11682 4 0.0807 0.6474 0.000 0.012 0.012 0.976 0.000
#> GSM11690 4 0.0671 0.6658 0.016 0.000 0.000 0.980 0.004
#> GSM11692 4 0.4942 0.4098 0.432 0.000 0.000 0.540 0.028
#> GSM11841 4 0.6622 0.3840 0.364 0.000 0.000 0.416 0.220
#> GSM11901 4 0.6275 0.5276 0.308 0.000 0.000 0.516 0.176
#> GSM11715 5 0.4437 0.4613 0.000 0.464 0.000 0.004 0.532
#> GSM11724 5 0.4415 0.4891 0.000 0.444 0.000 0.004 0.552
#> GSM11684 4 0.4048 0.6423 0.064 0.108 0.000 0.812 0.016
#> GSM11696 4 0.5333 0.6810 0.228 0.052 0.000 0.688 0.032
#> GSM27952 4 0.1282 0.6391 0.000 0.004 0.044 0.952 0.000
#> GSM27948 4 0.3527 0.7014 0.192 0.000 0.000 0.792 0.016
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM11708 6 0.0914 0.6830 0.000 0.000 0.000 0.016 0.016 0.968
#> GSM11735 6 0.0993 0.6814 0.000 0.000 0.000 0.012 0.024 0.964
#> GSM11733 6 0.5327 0.2879 0.000 0.072 0.000 0.028 0.296 0.604
#> GSM11863 5 0.4943 0.5280 0.000 0.328 0.000 0.004 0.596 0.072
#> GSM11710 6 0.4351 0.5930 0.052 0.000 0.000 0.176 0.028 0.744
#> GSM11712 3 0.4257 0.6416 0.012 0.028 0.756 0.024 0.180 0.000
#> GSM11732 6 0.4857 0.5483 0.012 0.196 0.048 0.000 0.032 0.712
#> GSM11844 6 0.7027 0.2658 0.012 0.288 0.188 0.008 0.044 0.460
#> GSM11842 5 0.4591 0.5068 0.004 0.360 0.000 0.008 0.604 0.024
#> GSM11860 5 0.4012 0.5067 0.000 0.344 0.000 0.000 0.640 0.016
#> GSM11686 4 0.2272 0.7044 0.004 0.000 0.056 0.900 0.040 0.000
#> GSM11688 4 0.2240 0.6845 0.008 0.000 0.000 0.904 0.056 0.032
#> GSM11846 5 0.5556 0.0966 0.008 0.008 0.012 0.312 0.588 0.072
#> GSM11680 3 0.4552 0.5798 0.012 0.000 0.708 0.232 0.024 0.024
#> GSM11698 3 0.2993 0.6976 0.012 0.000 0.876 0.044 0.036 0.032
#> GSM11840 5 0.6214 0.3746 0.004 0.184 0.000 0.020 0.508 0.284
#> GSM11847 5 0.6455 0.3665 0.004 0.164 0.000 0.044 0.508 0.280
#> GSM11685 4 0.1036 0.6975 0.004 0.000 0.000 0.964 0.008 0.024
#> GSM11699 3 0.5467 0.4252 0.020 0.000 0.608 0.256 0.116 0.000
#> GSM27950 6 0.4805 0.4829 0.012 0.000 0.012 0.300 0.032 0.644
#> GSM27946 3 0.4012 0.5826 0.008 0.000 0.712 0.256 0.024 0.000
#> GSM11709 1 0.7750 0.0790 0.412 0.024 0.288 0.012 0.172 0.092
#> GSM11720 3 0.4736 0.6373 0.072 0.040 0.736 0.004 0.148 0.000
#> GSM11726 2 0.4761 0.0642 0.468 0.492 0.008 0.000 0.032 0.000
#> GSM11837 2 0.3721 0.4623 0.308 0.684 0.004 0.000 0.004 0.000
#> GSM11725 3 0.6362 0.2102 0.048 0.368 0.452 0.000 0.132 0.000
#> GSM11864 3 0.4613 0.6289 0.036 0.048 0.716 0.000 0.200 0.000
#> GSM11687 3 0.7378 0.3193 0.252 0.024 0.468 0.084 0.168 0.004
#> GSM11693 3 0.5506 0.6105 0.096 0.024 0.680 0.032 0.168 0.000
#> GSM11727 1 0.3975 -0.1107 0.544 0.452 0.000 0.000 0.004 0.000
#> GSM11838 2 0.3907 0.3045 0.408 0.588 0.000 0.000 0.004 0.000
#> GSM11681 4 0.5385 0.4342 0.240 0.000 0.020 0.624 0.116 0.000
#> GSM11689 3 0.7245 0.4222 0.192 0.024 0.504 0.116 0.164 0.000
#> GSM11704 3 0.7089 0.4822 0.144 0.024 0.532 0.128 0.172 0.000
#> GSM11703 3 0.5384 0.5615 0.232 0.016 0.640 0.008 0.104 0.000
#> GSM11705 1 0.3322 0.5107 0.856 0.012 0.032 0.044 0.056 0.000
#> GSM11722 1 0.3619 0.2876 0.680 0.316 0.000 0.000 0.004 0.000
#> GSM11730 1 0.3446 0.3002 0.692 0.308 0.000 0.000 0.000 0.000
#> GSM11713 1 0.2675 0.5125 0.876 0.076 0.000 0.040 0.008 0.000
#> GSM11728 1 0.2725 0.5118 0.880 0.040 0.000 0.060 0.020 0.000
#> GSM27947 3 0.3188 0.6911 0.024 0.004 0.848 0.024 0.100 0.000
#> GSM27951 1 0.6701 -0.0442 0.424 0.004 0.052 0.360 0.160 0.000
#> GSM11707 6 0.0146 0.6834 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM11716 3 0.2853 0.6905 0.008 0.032 0.888 0.008 0.040 0.024
#> GSM11850 3 0.5362 0.6084 0.024 0.052 0.728 0.016 0.056 0.124
#> GSM11851 3 0.3415 0.6813 0.016 0.016 0.860 0.020 0.056 0.032
#> GSM11721 4 0.5877 0.4175 0.032 0.008 0.264 0.588 0.108 0.000
#> GSM11852 3 0.5408 0.2785 0.012 0.000 0.536 0.364 0.088 0.000
#> GSM11694 3 0.2808 0.6870 0.024 0.000 0.876 0.000 0.040 0.060
#> GSM11695 3 0.3689 0.6692 0.024 0.004 0.824 0.004 0.044 0.100
#> GSM11734 2 0.5610 0.2853 0.016 0.556 0.328 0.004 0.096 0.000
#> GSM11861 3 0.5394 0.4910 0.016 0.008 0.644 0.220 0.112 0.000
#> GSM11843 3 0.2803 0.6912 0.004 0.016 0.868 0.016 0.096 0.000
#> GSM11862 3 0.6041 0.0283 0.024 0.004 0.440 0.420 0.112 0.000
#> GSM11697 3 0.1719 0.6998 0.016 0.000 0.924 0.000 0.000 0.060
#> GSM11714 6 0.2963 0.6360 0.152 0.000 0.000 0.016 0.004 0.828
#> GSM11723 3 0.5717 0.1586 0.016 0.384 0.508 0.008 0.084 0.000
#> GSM11845 3 0.3298 0.6763 0.012 0.048 0.852 0.016 0.072 0.000
#> GSM11683 4 0.4625 0.6812 0.036 0.000 0.060 0.772 0.100 0.032
#> GSM11691 3 0.2897 0.6962 0.028 0.000 0.872 0.052 0.048 0.000
#> GSM27949 3 0.5241 0.5026 0.024 0.000 0.628 0.012 0.048 0.288
#> GSM27945 3 0.1760 0.7004 0.020 0.000 0.928 0.004 0.048 0.000
#> GSM11706 6 0.0520 0.6829 0.008 0.000 0.000 0.000 0.008 0.984
#> GSM11853 3 0.2257 0.6991 0.008 0.004 0.900 0.012 0.076 0.000
#> GSM11729 2 0.1003 0.6622 0.028 0.964 0.000 0.004 0.004 0.000
#> GSM11746 2 0.1642 0.6561 0.032 0.936 0.004 0.000 0.028 0.000
#> GSM11711 6 0.7042 0.0361 0.100 0.000 0.336 0.008 0.128 0.428
#> GSM11854 3 0.3036 0.6896 0.004 0.000 0.848 0.108 0.036 0.004
#> GSM11731 2 0.1409 0.6612 0.008 0.948 0.012 0.000 0.032 0.000
#> GSM11839 2 0.3172 0.6378 0.020 0.864 0.040 0.016 0.060 0.000
#> GSM11836 2 0.2926 0.5636 0.004 0.844 0.000 0.028 0.124 0.000
#> GSM11849 2 0.6029 0.2834 0.356 0.496 0.000 0.112 0.036 0.000
#> GSM11682 4 0.1624 0.7036 0.040 0.004 0.000 0.936 0.020 0.000
#> GSM11690 4 0.3018 0.6969 0.036 0.004 0.028 0.868 0.064 0.000
#> GSM11692 3 0.6169 0.2879 0.016 0.008 0.516 0.292 0.168 0.000
#> GSM11841 5 0.6494 0.1449 0.004 0.076 0.348 0.096 0.476 0.000
#> GSM11901 5 0.6665 0.0354 0.008 0.040 0.356 0.164 0.432 0.000
#> GSM11715 2 0.3202 0.6461 0.144 0.816 0.000 0.000 0.040 0.000
#> GSM11724 2 0.3123 0.6508 0.136 0.824 0.000 0.000 0.040 0.000
#> GSM11684 4 0.7770 0.3417 0.232 0.056 0.072 0.412 0.228 0.000
#> GSM11696 4 0.8216 0.1968 0.140 0.048 0.220 0.324 0.268 0.000
#> GSM27952 4 0.2466 0.6829 0.028 0.000 0.000 0.896 0.052 0.024
#> GSM27948 4 0.5127 0.5868 0.036 0.004 0.168 0.696 0.096 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 cell.line(p) agent(p) time(p) k
#> SD:NMF 75 1.43e-07 0.5848 2.94e-01 2
#> SD:NMF 42 2.18e-03 0.3622 5.47e-05 3
#> SD:NMF 65 2.45e-06 0.1399 8.40e-05 4
#> SD:NMF 63 2.27e-08 0.1533 3.50e-06 5
#> SD:NMF 50 8.95e-07 0.0685 2.04e-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["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 14502 rows and 83 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 0.472 0.793 0.907 0.3008 0.785 0.785
#> 3 3 0.396 0.686 0.820 0.5372 0.815 0.764
#> 4 4 0.279 0.594 0.752 0.2230 0.931 0.884
#> 5 5 0.324 0.435 0.675 0.1851 0.748 0.564
#> 6 6 0.411 0.429 0.703 0.0982 0.863 0.649
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
#> GSM11708 1 0.0000 0.8900 1.000 0.000
#> GSM11735 1 0.0000 0.8900 1.000 0.000
#> GSM11733 1 0.0000 0.8900 1.000 0.000
#> GSM11863 1 0.0000 0.8900 1.000 0.000
#> GSM11710 1 0.0000 0.8900 1.000 0.000
#> GSM11712 1 0.0000 0.8900 1.000 0.000
#> GSM11732 1 0.1414 0.8832 0.980 0.020
#> GSM11844 1 0.1414 0.8832 0.980 0.020
#> GSM11842 1 0.9580 0.3690 0.620 0.380
#> GSM11860 1 0.9580 0.3690 0.620 0.380
#> GSM11686 1 0.0000 0.8900 1.000 0.000
#> GSM11688 1 0.0000 0.8900 1.000 0.000
#> GSM11846 1 0.0376 0.8893 0.996 0.004
#> GSM11680 1 0.0000 0.8900 1.000 0.000
#> GSM11698 1 0.0000 0.8900 1.000 0.000
#> GSM11840 1 0.0000 0.8900 1.000 0.000
#> GSM11847 1 0.0000 0.8900 1.000 0.000
#> GSM11685 1 0.0000 0.8900 1.000 0.000
#> GSM11699 1 0.0000 0.8900 1.000 0.000
#> GSM27950 1 0.0000 0.8900 1.000 0.000
#> GSM27946 1 0.0376 0.8893 0.996 0.004
#> GSM11709 1 0.9358 0.4634 0.648 0.352
#> GSM11720 1 0.5408 0.8160 0.876 0.124
#> GSM11726 2 0.1843 0.8859 0.028 0.972
#> GSM11837 2 0.1843 0.8859 0.028 0.972
#> GSM11725 1 0.9996 -0.0132 0.512 0.488
#> GSM11864 1 0.9983 0.0417 0.524 0.476
#> GSM11687 1 0.5294 0.8177 0.880 0.120
#> GSM11693 1 0.5294 0.8177 0.880 0.120
#> GSM11727 2 0.0000 0.8700 0.000 1.000
#> GSM11838 2 0.0000 0.8700 0.000 1.000
#> GSM11681 1 0.9248 0.4773 0.660 0.340
#> GSM11689 1 0.9358 0.4634 0.648 0.352
#> GSM11704 1 0.9358 0.4634 0.648 0.352
#> GSM11703 1 0.5294 0.8177 0.880 0.120
#> GSM11705 1 0.5294 0.8177 0.880 0.120
#> GSM11722 1 0.8386 0.6173 0.732 0.268
#> GSM11730 1 0.8713 0.5778 0.708 0.292
#> GSM11713 1 0.8713 0.5778 0.708 0.292
#> GSM11728 1 0.5842 0.7923 0.860 0.140
#> GSM27947 1 0.0376 0.8893 0.996 0.004
#> GSM27951 1 0.9323 0.4679 0.652 0.348
#> GSM11707 1 0.1633 0.8803 0.976 0.024
#> GSM11716 1 0.1184 0.8847 0.984 0.016
#> GSM11850 1 0.0000 0.8900 1.000 0.000
#> GSM11851 1 0.0000 0.8900 1.000 0.000
#> GSM11721 1 0.0376 0.8891 0.996 0.004
#> GSM11852 1 0.0376 0.8891 0.996 0.004
#> GSM11694 1 0.0376 0.8891 0.996 0.004
#> GSM11695 1 0.0376 0.8891 0.996 0.004
#> GSM11734 2 0.7219 0.8202 0.200 0.800
#> GSM11861 1 0.0672 0.8881 0.992 0.008
#> GSM11843 1 0.9775 0.2878 0.588 0.412
#> GSM11862 1 0.0938 0.8871 0.988 0.012
#> GSM11697 1 0.0000 0.8900 1.000 0.000
#> GSM11714 1 0.3114 0.8635 0.944 0.056
#> GSM11723 1 0.5519 0.8054 0.872 0.128
#> GSM11845 1 0.5519 0.8054 0.872 0.128
#> GSM11683 1 0.2423 0.8741 0.960 0.040
#> GSM11691 1 0.2423 0.8741 0.960 0.040
#> GSM27949 1 0.0000 0.8900 1.000 0.000
#> GSM27945 1 0.0376 0.8893 0.996 0.004
#> GSM11706 1 0.0000 0.8900 1.000 0.000
#> GSM11853 1 0.0000 0.8900 1.000 0.000
#> GSM11729 2 0.5059 0.8977 0.112 0.888
#> GSM11746 2 0.5629 0.8931 0.132 0.868
#> GSM11711 1 0.0000 0.8900 1.000 0.000
#> GSM11854 1 0.0000 0.8900 1.000 0.000
#> GSM11731 2 0.7056 0.8293 0.192 0.808
#> GSM11839 1 0.8144 0.6372 0.748 0.252
#> GSM11836 1 0.7883 0.6597 0.764 0.236
#> GSM11849 1 0.7745 0.6746 0.772 0.228
#> GSM11682 1 0.0000 0.8900 1.000 0.000
#> GSM11690 1 0.0000 0.8900 1.000 0.000
#> GSM11692 1 0.0000 0.8900 1.000 0.000
#> GSM11841 1 0.0000 0.8900 1.000 0.000
#> GSM11901 1 0.0000 0.8900 1.000 0.000
#> GSM11715 2 0.6048 0.8835 0.148 0.852
#> GSM11724 2 0.6048 0.8835 0.148 0.852
#> GSM11684 1 0.1633 0.8808 0.976 0.024
#> GSM11696 1 0.1633 0.8808 0.976 0.024
#> GSM27952 1 0.0000 0.8900 1.000 0.000
#> GSM27948 1 0.0000 0.8900 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM11708 3 0.1163 0.7857 0.028 0.000 0.972
#> GSM11735 3 0.1163 0.7857 0.028 0.000 0.972
#> GSM11733 3 0.1411 0.7863 0.036 0.000 0.964
#> GSM11863 3 0.1411 0.7863 0.036 0.000 0.964
#> GSM11710 3 0.0592 0.7887 0.012 0.000 0.988
#> GSM11712 3 0.1411 0.7900 0.036 0.000 0.964
#> GSM11732 3 0.5072 0.6791 0.196 0.012 0.792
#> GSM11844 3 0.5072 0.6791 0.196 0.012 0.792
#> GSM11842 1 0.7922 0.7846 0.532 0.060 0.408
#> GSM11860 1 0.7922 0.7846 0.532 0.060 0.408
#> GSM11686 3 0.0424 0.7888 0.008 0.000 0.992
#> GSM11688 3 0.0424 0.7888 0.008 0.000 0.992
#> GSM11846 3 0.0592 0.7886 0.012 0.000 0.988
#> GSM11680 3 0.1163 0.7865 0.028 0.000 0.972
#> GSM11698 3 0.1860 0.7848 0.052 0.000 0.948
#> GSM11840 3 0.1411 0.7863 0.036 0.000 0.964
#> GSM11847 3 0.1411 0.7863 0.036 0.000 0.964
#> GSM11685 3 0.0424 0.7888 0.008 0.000 0.992
#> GSM11699 3 0.1529 0.7868 0.040 0.000 0.960
#> GSM27950 3 0.1163 0.7865 0.028 0.000 0.972
#> GSM27946 3 0.0747 0.7893 0.016 0.000 0.984
#> GSM11709 1 0.6717 0.8462 0.628 0.020 0.352
#> GSM11720 3 0.6702 0.3047 0.328 0.024 0.648
#> GSM11726 2 0.1525 0.8660 0.032 0.964 0.004
#> GSM11837 2 0.1525 0.8660 0.032 0.964 0.004
#> GSM11725 1 0.8982 0.7478 0.548 0.168 0.284
#> GSM11864 1 0.8491 0.7802 0.588 0.128 0.284
#> GSM11687 3 0.6416 0.3373 0.304 0.020 0.676
#> GSM11693 3 0.6416 0.3373 0.304 0.020 0.676
#> GSM11727 2 0.0237 0.8609 0.004 0.996 0.000
#> GSM11838 2 0.0237 0.8609 0.004 0.996 0.000
#> GSM11681 1 0.6398 0.8366 0.620 0.008 0.372
#> GSM11689 1 0.6603 0.8505 0.648 0.020 0.332
#> GSM11704 1 0.6603 0.8505 0.648 0.020 0.332
#> GSM11703 3 0.6553 0.3185 0.324 0.020 0.656
#> GSM11705 3 0.6553 0.3185 0.324 0.020 0.656
#> GSM11722 3 0.9721 -0.0163 0.284 0.264 0.452
#> GSM11730 3 0.9714 -0.0208 0.256 0.292 0.452
#> GSM11713 3 0.9718 -0.0198 0.260 0.288 0.452
#> GSM11728 3 0.8546 0.2563 0.276 0.136 0.588
#> GSM27947 3 0.0747 0.7893 0.016 0.000 0.984
#> GSM27951 1 0.6521 0.8517 0.644 0.016 0.340
#> GSM11707 3 0.3415 0.7677 0.080 0.020 0.900
#> GSM11716 3 0.5220 0.6677 0.208 0.012 0.780
#> GSM11850 3 0.4504 0.6894 0.196 0.000 0.804
#> GSM11851 3 0.4452 0.6921 0.192 0.000 0.808
#> GSM11721 3 0.4974 0.6370 0.236 0.000 0.764
#> GSM11852 3 0.4974 0.6370 0.236 0.000 0.764
#> GSM11694 3 0.1525 0.7882 0.032 0.004 0.964
#> GSM11695 3 0.1525 0.7882 0.032 0.004 0.964
#> GSM11734 2 0.5864 0.8010 0.288 0.704 0.008
#> GSM11861 3 0.5497 0.5799 0.292 0.000 0.708
#> GSM11843 1 0.6728 0.6129 0.736 0.080 0.184
#> GSM11862 3 0.5560 0.5725 0.300 0.000 0.700
#> GSM11697 3 0.1529 0.7884 0.040 0.000 0.960
#> GSM11714 3 0.5343 0.7043 0.132 0.052 0.816
#> GSM11723 3 0.7673 0.4558 0.236 0.100 0.664
#> GSM11845 3 0.7673 0.4558 0.236 0.100 0.664
#> GSM11683 3 0.5180 0.7090 0.156 0.032 0.812
#> GSM11691 3 0.5180 0.7090 0.156 0.032 0.812
#> GSM27949 3 0.1163 0.7865 0.028 0.000 0.972
#> GSM27945 3 0.0747 0.7893 0.016 0.000 0.984
#> GSM11706 3 0.0747 0.7911 0.016 0.000 0.984
#> GSM11853 3 0.0892 0.7904 0.020 0.000 0.980
#> GSM11729 2 0.4749 0.8747 0.172 0.816 0.012
#> GSM11746 2 0.5122 0.8661 0.200 0.788 0.012
#> GSM11711 3 0.0892 0.7904 0.020 0.000 0.980
#> GSM11854 3 0.0892 0.7904 0.020 0.000 0.980
#> GSM11731 2 0.5327 0.8135 0.272 0.728 0.000
#> GSM11839 3 0.9303 0.1188 0.316 0.184 0.500
#> GSM11836 3 0.7535 0.4582 0.132 0.176 0.692
#> GSM11849 3 0.8753 0.3334 0.224 0.188 0.588
#> GSM11682 3 0.0592 0.7888 0.012 0.000 0.988
#> GSM11690 3 0.0424 0.7888 0.008 0.000 0.992
#> GSM11692 3 0.1411 0.7900 0.036 0.000 0.964
#> GSM11841 3 0.1411 0.7900 0.036 0.000 0.964
#> GSM11901 3 0.1411 0.7900 0.036 0.000 0.964
#> GSM11715 2 0.5247 0.8666 0.224 0.768 0.008
#> GSM11724 2 0.5247 0.8666 0.224 0.768 0.008
#> GSM11684 3 0.5092 0.6515 0.176 0.020 0.804
#> GSM11696 3 0.5092 0.6515 0.176 0.020 0.804
#> GSM27952 3 0.0424 0.7888 0.008 0.000 0.992
#> GSM27948 3 0.0424 0.7888 0.008 0.000 0.992
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM11708 3 0.3634 0.6920 0.048 0.000 0.856 0.096
#> GSM11735 3 0.3634 0.6920 0.048 0.000 0.856 0.096
#> GSM11733 3 0.4370 0.6777 0.044 0.000 0.800 0.156
#> GSM11863 3 0.4370 0.6777 0.044 0.000 0.800 0.156
#> GSM11710 3 0.1733 0.6898 0.028 0.000 0.948 0.024
#> GSM11712 3 0.3556 0.7000 0.020 0.012 0.864 0.104
#> GSM11732 3 0.7815 0.4545 0.216 0.028 0.552 0.204
#> GSM11844 3 0.7815 0.4545 0.216 0.028 0.552 0.204
#> GSM11842 1 0.6820 0.7178 0.616 0.060 0.288 0.036
#> GSM11860 1 0.6820 0.7178 0.616 0.060 0.288 0.036
#> GSM11686 3 0.0927 0.6998 0.008 0.000 0.976 0.016
#> GSM11688 3 0.0927 0.6998 0.008 0.000 0.976 0.016
#> GSM11846 3 0.0469 0.7008 0.012 0.000 0.988 0.000
#> GSM11680 3 0.3037 0.7001 0.036 0.000 0.888 0.076
#> GSM11698 3 0.2781 0.7011 0.040 0.012 0.912 0.036
#> GSM11840 3 0.4370 0.6777 0.044 0.000 0.800 0.156
#> GSM11847 3 0.4370 0.6777 0.044 0.000 0.800 0.156
#> GSM11685 3 0.1174 0.6997 0.012 0.000 0.968 0.020
#> GSM11699 3 0.2224 0.7016 0.040 0.000 0.928 0.032
#> GSM27950 3 0.3037 0.7001 0.036 0.000 0.888 0.076
#> GSM27946 3 0.1297 0.7074 0.020 0.000 0.964 0.016
#> GSM11709 1 0.4538 0.7598 0.760 0.000 0.216 0.024
#> GSM11720 3 0.5483 0.1111 0.448 0.000 0.536 0.016
#> GSM11726 2 0.3342 0.8240 0.032 0.868 0.000 0.100
#> GSM11837 2 0.3342 0.8240 0.032 0.868 0.000 0.100
#> GSM11725 1 0.7360 0.6898 0.596 0.196 0.188 0.020
#> GSM11864 1 0.7187 0.7167 0.628 0.156 0.188 0.028
#> GSM11687 3 0.5345 0.1462 0.428 0.000 0.560 0.012
#> GSM11693 3 0.5345 0.1462 0.428 0.000 0.560 0.012
#> GSM11727 2 0.2345 0.8156 0.000 0.900 0.000 0.100
#> GSM11838 2 0.2345 0.8156 0.000 0.900 0.000 0.100
#> GSM11681 1 0.4452 0.7557 0.732 0.000 0.260 0.008
#> GSM11689 1 0.4098 0.7691 0.784 0.000 0.204 0.012
#> GSM11704 1 0.4098 0.7691 0.784 0.000 0.204 0.012
#> GSM11703 3 0.5372 0.1261 0.444 0.000 0.544 0.012
#> GSM11705 3 0.5372 0.1261 0.444 0.000 0.544 0.012
#> GSM11722 4 0.8366 0.8352 0.172 0.056 0.264 0.508
#> GSM11730 4 0.9374 0.7821 0.128 0.196 0.264 0.412
#> GSM11713 4 0.8162 0.8328 0.148 0.056 0.264 0.532
#> GSM11728 4 0.8288 0.6451 0.176 0.032 0.380 0.412
#> GSM27947 3 0.1297 0.7074 0.020 0.000 0.964 0.016
#> GSM27951 1 0.4049 0.7729 0.780 0.000 0.212 0.008
#> GSM11707 3 0.6327 0.5071 0.124 0.000 0.648 0.228
#> GSM11716 3 0.7805 0.4466 0.228 0.024 0.544 0.204
#> GSM11850 3 0.7244 0.4992 0.224 0.020 0.604 0.152
#> GSM11851 3 0.7215 0.5032 0.220 0.020 0.608 0.152
#> GSM11721 3 0.5743 0.5205 0.176 0.016 0.732 0.076
#> GSM11852 3 0.5743 0.5205 0.176 0.016 0.732 0.076
#> GSM11694 3 0.3198 0.7004 0.040 0.000 0.880 0.080
#> GSM11695 3 0.3198 0.7004 0.040 0.000 0.880 0.080
#> GSM11734 2 0.7461 0.5692 0.188 0.544 0.008 0.260
#> GSM11861 3 0.7004 0.3986 0.308 0.028 0.588 0.076
#> GSM11843 1 0.6065 0.5483 0.748 0.092 0.080 0.080
#> GSM11862 3 0.6807 0.3818 0.328 0.016 0.580 0.076
#> GSM11697 3 0.3301 0.7006 0.048 0.000 0.876 0.076
#> GSM11714 3 0.6874 0.3209 0.136 0.000 0.568 0.296
#> GSM11723 3 0.9146 0.2006 0.252 0.124 0.452 0.172
#> GSM11845 3 0.9146 0.2006 0.252 0.124 0.452 0.172
#> GSM11683 3 0.7085 0.3331 0.156 0.000 0.544 0.300
#> GSM11691 3 0.7085 0.3331 0.156 0.000 0.544 0.300
#> GSM27949 3 0.3037 0.7001 0.036 0.000 0.888 0.076
#> GSM27945 3 0.1297 0.7074 0.020 0.000 0.964 0.016
#> GSM11706 3 0.1543 0.6973 0.032 0.004 0.956 0.008
#> GSM11853 3 0.1271 0.7001 0.012 0.012 0.968 0.008
#> GSM11729 2 0.2796 0.8340 0.096 0.892 0.004 0.008
#> GSM11746 2 0.3043 0.8287 0.112 0.876 0.004 0.008
#> GSM11711 3 0.1271 0.7001 0.012 0.012 0.968 0.008
#> GSM11854 3 0.1271 0.7001 0.012 0.012 0.968 0.008
#> GSM11731 2 0.4638 0.7531 0.152 0.788 0.000 0.060
#> GSM11839 3 0.8763 -0.0711 0.192 0.256 0.476 0.076
#> GSM11836 3 0.6746 0.3980 0.076 0.236 0.652 0.036
#> GSM11849 3 0.7963 0.1373 0.120 0.256 0.560 0.064
#> GSM11682 3 0.1297 0.6991 0.016 0.000 0.964 0.020
#> GSM11690 3 0.1174 0.6997 0.012 0.000 0.968 0.020
#> GSM11692 3 0.3556 0.7000 0.020 0.012 0.864 0.104
#> GSM11841 3 0.3556 0.7000 0.020 0.012 0.864 0.104
#> GSM11901 3 0.3556 0.7000 0.020 0.012 0.864 0.104
#> GSM11715 2 0.3941 0.8254 0.104 0.844 0.004 0.048
#> GSM11724 2 0.3941 0.8254 0.104 0.844 0.004 0.048
#> GSM11684 3 0.6730 0.0820 0.156 0.004 0.628 0.212
#> GSM11696 3 0.6730 0.0820 0.156 0.004 0.628 0.212
#> GSM27952 3 0.1174 0.6997 0.012 0.000 0.968 0.020
#> GSM27948 3 0.1174 0.6997 0.012 0.000 0.968 0.020
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM11708 4 0.6004 0.4474 0.332 0.000 0.040 0.576 0.052
#> GSM11735 4 0.6004 0.4474 0.332 0.000 0.040 0.576 0.052
#> GSM11733 4 0.4752 0.4201 0.412 0.000 0.020 0.568 0.000
#> GSM11863 4 0.4752 0.4201 0.412 0.000 0.020 0.568 0.000
#> GSM11710 4 0.2908 0.6294 0.108 0.000 0.008 0.868 0.016
#> GSM11712 4 0.3647 0.5822 0.228 0.004 0.004 0.764 0.000
#> GSM11732 1 0.6339 0.1940 0.572 0.048 0.060 0.316 0.004
#> GSM11844 1 0.6339 0.1940 0.572 0.048 0.060 0.316 0.004
#> GSM11842 1 0.8306 0.3204 0.484 0.064 0.064 0.172 0.216
#> GSM11860 1 0.8306 0.3204 0.484 0.064 0.064 0.172 0.216
#> GSM11686 4 0.0000 0.6777 0.000 0.000 0.000 1.000 0.000
#> GSM11688 4 0.0000 0.6777 0.000 0.000 0.000 1.000 0.000
#> GSM11846 4 0.0955 0.6755 0.028 0.000 0.000 0.968 0.004
#> GSM11680 4 0.5107 0.5535 0.228 0.000 0.024 0.700 0.048
#> GSM11698 4 0.2398 0.6546 0.064 0.020 0.004 0.908 0.004
#> GSM11840 4 0.4752 0.4201 0.412 0.000 0.020 0.568 0.000
#> GSM11847 4 0.4752 0.4201 0.412 0.000 0.020 0.568 0.000
#> GSM11685 4 0.0324 0.6771 0.000 0.000 0.004 0.992 0.004
#> GSM11699 4 0.2354 0.6601 0.076 0.000 0.012 0.904 0.008
#> GSM27950 4 0.5107 0.5535 0.228 0.000 0.024 0.700 0.048
#> GSM27946 4 0.2295 0.6660 0.088 0.000 0.008 0.900 0.004
#> GSM11709 1 0.6400 0.2051 0.516 0.004 0.056 0.044 0.380
#> GSM11720 1 0.7215 0.2164 0.460 0.004 0.060 0.364 0.112
#> GSM11726 2 0.2408 0.7885 0.000 0.892 0.016 0.000 0.092
#> GSM11837 2 0.2408 0.7885 0.000 0.892 0.016 0.000 0.092
#> GSM11725 1 0.9065 0.1835 0.400 0.208 0.072 0.120 0.200
#> GSM11864 1 0.8953 0.2097 0.420 0.168 0.072 0.120 0.220
#> GSM11687 1 0.7058 0.2334 0.440 0.004 0.048 0.400 0.108
#> GSM11693 1 0.7058 0.2334 0.440 0.004 0.048 0.400 0.108
#> GSM11727 2 0.3075 0.7797 0.000 0.860 0.048 0.000 0.092
#> GSM11838 2 0.3075 0.7797 0.000 0.860 0.048 0.000 0.092
#> GSM11681 1 0.7773 0.2743 0.392 0.008 0.060 0.180 0.360
#> GSM11689 1 0.7021 0.2329 0.484 0.008 0.072 0.068 0.368
#> GSM11704 1 0.7021 0.2329 0.484 0.008 0.072 0.068 0.368
#> GSM11703 1 0.7133 0.2231 0.464 0.004 0.056 0.368 0.108
#> GSM11705 1 0.7133 0.2231 0.464 0.004 0.056 0.368 0.108
#> GSM11722 5 0.5141 0.8459 0.024 0.024 0.020 0.216 0.716
#> GSM11730 5 0.6383 0.7695 0.020 0.176 0.000 0.216 0.588
#> GSM11713 5 0.4483 0.8414 0.020 0.024 0.000 0.216 0.740
#> GSM11728 5 0.5976 0.7469 0.136 0.008 0.000 0.252 0.604
#> GSM27947 4 0.2295 0.6660 0.088 0.000 0.008 0.900 0.004
#> GSM27951 1 0.7067 0.2371 0.480 0.008 0.068 0.076 0.368
#> GSM11707 1 0.7310 -0.0468 0.440 0.000 0.040 0.320 0.200
#> GSM11716 1 0.6418 0.2082 0.572 0.048 0.068 0.308 0.004
#> GSM11850 1 0.6499 0.1339 0.512 0.044 0.064 0.376 0.004
#> GSM11851 1 0.6454 0.1274 0.512 0.044 0.060 0.380 0.004
#> GSM11721 4 0.5120 0.4945 0.080 0.004 0.196 0.712 0.008
#> GSM11852 4 0.5120 0.4945 0.080 0.004 0.196 0.712 0.008
#> GSM11694 4 0.5265 0.5397 0.252 0.000 0.024 0.676 0.048
#> GSM11695 4 0.5265 0.5397 0.252 0.000 0.024 0.676 0.048
#> GSM11734 3 0.3558 0.0000 0.020 0.156 0.816 0.008 0.000
#> GSM11861 4 0.7040 0.1400 0.248 0.016 0.180 0.536 0.020
#> GSM11843 1 0.8418 0.0481 0.412 0.084 0.260 0.028 0.216
#> GSM11862 4 0.6971 0.1304 0.232 0.008 0.212 0.528 0.020
#> GSM11697 4 0.5423 0.5387 0.252 0.000 0.032 0.668 0.048
#> GSM11714 1 0.7505 -0.1293 0.400 0.000 0.040 0.272 0.288
#> GSM11723 1 0.7377 0.3115 0.528 0.104 0.112 0.252 0.004
#> GSM11845 1 0.7377 0.3115 0.528 0.104 0.112 0.252 0.004
#> GSM11683 1 0.7305 0.0523 0.472 0.000 0.044 0.268 0.216
#> GSM11691 1 0.7305 0.0523 0.472 0.000 0.044 0.268 0.216
#> GSM27949 4 0.5107 0.5535 0.228 0.000 0.024 0.700 0.048
#> GSM27945 4 0.2295 0.6660 0.088 0.000 0.008 0.900 0.004
#> GSM11706 4 0.2753 0.6259 0.104 0.012 0.000 0.876 0.008
#> GSM11853 4 0.1365 0.6760 0.040 0.004 0.000 0.952 0.004
#> GSM11729 2 0.1996 0.7814 0.036 0.928 0.032 0.004 0.000
#> GSM11746 2 0.2411 0.7741 0.052 0.912 0.024 0.004 0.008
#> GSM11711 4 0.1365 0.6760 0.040 0.004 0.000 0.952 0.004
#> GSM11854 4 0.1365 0.6760 0.040 0.004 0.000 0.952 0.004
#> GSM11731 2 0.3689 0.5299 0.004 0.740 0.256 0.000 0.000
#> GSM11839 4 0.7776 0.0691 0.064 0.208 0.240 0.476 0.012
#> GSM11836 4 0.7040 0.2752 0.148 0.204 0.048 0.584 0.016
#> GSM11849 4 0.7385 0.2013 0.100 0.252 0.028 0.552 0.068
#> GSM11682 4 0.0613 0.6775 0.004 0.000 0.004 0.984 0.008
#> GSM11690 4 0.0324 0.6771 0.000 0.000 0.004 0.992 0.004
#> GSM11692 4 0.3647 0.5822 0.228 0.004 0.004 0.764 0.000
#> GSM11841 4 0.3647 0.5822 0.228 0.004 0.004 0.764 0.000
#> GSM11901 4 0.3647 0.5822 0.228 0.004 0.004 0.764 0.000
#> GSM11715 2 0.3819 0.7540 0.064 0.844 0.036 0.004 0.052
#> GSM11724 2 0.3819 0.7540 0.064 0.844 0.036 0.004 0.052
#> GSM11684 4 0.6571 -0.3076 0.144 0.004 0.008 0.488 0.356
#> GSM11696 4 0.6571 -0.3076 0.144 0.004 0.008 0.488 0.356
#> GSM27952 4 0.0324 0.6771 0.000 0.000 0.004 0.992 0.004
#> GSM27948 4 0.0324 0.6771 0.000 0.000 0.004 0.992 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM11708 3 0.6368 0.2684 0.008 0.000 0.412 0.312 0.004 0.264
#> GSM11735 3 0.6368 0.2684 0.008 0.000 0.412 0.312 0.004 0.264
#> GSM11733 3 0.4144 0.3509 0.008 0.000 0.580 0.408 0.000 0.004
#> GSM11863 3 0.4144 0.3509 0.008 0.000 0.580 0.408 0.000 0.004
#> GSM11710 4 0.2945 0.5378 0.020 0.000 0.156 0.824 0.000 0.000
#> GSM11712 4 0.3314 0.4248 0.004 0.000 0.256 0.740 0.000 0.000
#> GSM11732 3 0.4119 0.5429 0.068 0.004 0.756 0.168 0.000 0.004
#> GSM11844 3 0.4119 0.5429 0.068 0.004 0.756 0.168 0.000 0.004
#> GSM11842 1 0.5758 0.3970 0.596 0.040 0.268 0.092 0.000 0.004
#> GSM11860 1 0.5758 0.3970 0.596 0.040 0.268 0.092 0.000 0.004
#> GSM11686 4 0.0146 0.6276 0.000 0.000 0.004 0.996 0.000 0.000
#> GSM11688 4 0.0146 0.6276 0.000 0.000 0.004 0.996 0.000 0.000
#> GSM11846 4 0.1152 0.6207 0.004 0.000 0.044 0.952 0.000 0.000
#> GSM11680 4 0.5656 0.0726 0.000 0.000 0.256 0.532 0.000 0.212
#> GSM11698 4 0.2051 0.6007 0.004 0.004 0.096 0.896 0.000 0.000
#> GSM11840 3 0.4144 0.3509 0.008 0.000 0.580 0.408 0.000 0.004
#> GSM11847 3 0.4144 0.3509 0.008 0.000 0.580 0.408 0.000 0.004
#> GSM11685 4 0.0146 0.6283 0.000 0.000 0.004 0.996 0.000 0.000
#> GSM11699 4 0.2507 0.6067 0.040 0.000 0.072 0.884 0.000 0.004
#> GSM27950 4 0.5656 0.0726 0.000 0.000 0.256 0.532 0.000 0.212
#> GSM27946 4 0.2520 0.5645 0.004 0.000 0.152 0.844 0.000 0.000
#> GSM11709 1 0.2408 0.4853 0.900 0.000 0.056 0.012 0.004 0.028
#> GSM11720 1 0.4908 0.4324 0.596 0.000 0.068 0.332 0.000 0.004
#> GSM11726 2 0.2060 0.8143 0.000 0.900 0.016 0.000 0.000 0.084
#> GSM11837 2 0.2060 0.8143 0.000 0.900 0.016 0.000 0.000 0.084
#> GSM11725 1 0.5702 0.4250 0.648 0.160 0.080 0.112 0.000 0.000
#> GSM11864 1 0.5446 0.4490 0.680 0.120 0.088 0.112 0.000 0.000
#> GSM11687 1 0.4818 0.4358 0.572 0.000 0.064 0.364 0.000 0.000
#> GSM11693 1 0.4818 0.4358 0.572 0.000 0.064 0.364 0.000 0.000
#> GSM11727 2 0.2290 0.8081 0.000 0.892 0.004 0.000 0.020 0.084
#> GSM11838 2 0.2290 0.8081 0.000 0.892 0.004 0.000 0.020 0.084
#> GSM11681 1 0.3048 0.5241 0.824 0.000 0.004 0.152 0.000 0.020
#> GSM11689 1 0.1408 0.5271 0.944 0.000 0.000 0.036 0.000 0.020
#> GSM11704 1 0.1408 0.5271 0.944 0.000 0.000 0.036 0.000 0.020
#> GSM11703 1 0.4822 0.4354 0.596 0.000 0.072 0.332 0.000 0.000
#> GSM11705 1 0.4822 0.4354 0.596 0.000 0.072 0.332 0.000 0.000
#> GSM11722 6 0.4505 0.4979 0.160 0.016 0.000 0.092 0.000 0.732
#> GSM11730 6 0.6246 0.4398 0.136 0.188 0.000 0.092 0.000 0.584
#> GSM11713 6 0.4289 0.4928 0.136 0.016 0.000 0.092 0.000 0.756
#> GSM11728 6 0.5237 0.4989 0.268 0.004 0.000 0.124 0.000 0.604
#> GSM27947 4 0.2520 0.5645 0.004 0.000 0.152 0.844 0.000 0.000
#> GSM27951 1 0.1549 0.5308 0.936 0.000 0.000 0.044 0.000 0.020
#> GSM11707 6 0.7220 0.1174 0.152 0.000 0.352 0.092 0.012 0.392
#> GSM11716 3 0.4051 0.5358 0.076 0.004 0.756 0.164 0.000 0.000
#> GSM11850 3 0.4865 0.5213 0.076 0.004 0.672 0.240 0.004 0.004
#> GSM11851 3 0.4751 0.5218 0.076 0.004 0.672 0.244 0.000 0.004
#> GSM11721 4 0.4693 0.4585 0.004 0.004 0.100 0.700 0.192 0.000
#> GSM11852 4 0.4693 0.4585 0.004 0.004 0.100 0.700 0.192 0.000
#> GSM11694 4 0.6202 0.0475 0.024 0.000 0.256 0.508 0.000 0.212
#> GSM11695 4 0.6202 0.0475 0.024 0.000 0.256 0.508 0.000 0.212
#> GSM11734 5 0.1644 0.0000 0.000 0.012 0.052 0.004 0.932 0.000
#> GSM11861 4 0.6883 0.1896 0.136 0.000 0.224 0.496 0.144 0.000
#> GSM11843 1 0.6144 0.2629 0.592 0.060 0.140 0.000 0.204 0.004
#> GSM11862 4 0.7065 0.2035 0.140 0.004 0.172 0.492 0.192 0.000
#> GSM11697 4 0.6346 0.0382 0.032 0.000 0.260 0.496 0.000 0.212
#> GSM11714 6 0.6913 0.2299 0.172 0.000 0.260 0.076 0.008 0.484
#> GSM11723 3 0.6079 0.4453 0.104 0.032 0.660 0.136 0.064 0.004
#> GSM11845 3 0.6079 0.4453 0.104 0.032 0.660 0.136 0.064 0.004
#> GSM11683 3 0.7234 -0.1030 0.196 0.000 0.428 0.092 0.008 0.276
#> GSM11691 3 0.7300 -0.1011 0.192 0.000 0.428 0.092 0.012 0.276
#> GSM27949 4 0.5656 0.0726 0.000 0.000 0.256 0.532 0.000 0.212
#> GSM27945 4 0.2520 0.5645 0.004 0.000 0.152 0.844 0.000 0.000
#> GSM11706 4 0.2839 0.5800 0.092 0.000 0.044 0.860 0.000 0.004
#> GSM11853 4 0.1349 0.6242 0.000 0.000 0.056 0.940 0.000 0.004
#> GSM11729 2 0.2585 0.8089 0.048 0.880 0.068 0.000 0.004 0.000
#> GSM11746 2 0.2714 0.8054 0.060 0.872 0.064 0.000 0.004 0.000
#> GSM11711 4 0.1349 0.6242 0.000 0.000 0.056 0.940 0.000 0.004
#> GSM11854 4 0.1349 0.6242 0.000 0.000 0.056 0.940 0.000 0.004
#> GSM11731 2 0.3622 0.5994 0.004 0.744 0.016 0.000 0.236 0.000
#> GSM11839 4 0.7204 0.1495 0.008 0.220 0.096 0.452 0.224 0.000
#> GSM11836 4 0.6909 0.2915 0.100 0.204 0.112 0.552 0.032 0.000
#> GSM11849 4 0.7238 0.2616 0.052 0.220 0.144 0.520 0.004 0.060
#> GSM11682 4 0.0405 0.6287 0.004 0.000 0.008 0.988 0.000 0.000
#> GSM11690 4 0.0146 0.6283 0.000 0.000 0.004 0.996 0.000 0.000
#> GSM11692 4 0.3314 0.4248 0.004 0.000 0.256 0.740 0.000 0.000
#> GSM11841 4 0.3314 0.4248 0.004 0.000 0.256 0.740 0.000 0.000
#> GSM11901 4 0.3314 0.4248 0.004 0.000 0.256 0.740 0.000 0.000
#> GSM11715 2 0.4156 0.7770 0.072 0.796 0.068 0.000 0.004 0.060
#> GSM11724 2 0.4156 0.7770 0.072 0.796 0.068 0.000 0.004 0.060
#> GSM11684 4 0.6437 -0.3423 0.264 0.000 0.016 0.364 0.000 0.356
#> GSM11696 4 0.6437 -0.3423 0.264 0.000 0.016 0.364 0.000 0.356
#> GSM27952 4 0.0146 0.6283 0.000 0.000 0.004 0.996 0.000 0.000
#> GSM27948 4 0.0146 0.6283 0.000 0.000 0.004 0.996 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 cell.line(p) agent(p) time(p) k
#> CV:hclust 73 3.52e-02 0.3951 4.87e-05 2
#> CV:hclust 69 1.34e-06 0.1669 6.89e-06 3
#> CV:hclust 62 7.35e-06 0.0080 4.30e-05 4
#> CV:hclust 41 1.38e-04 0.0464 1.75e-06 5
#> CV:hclust 36 2.37e-05 0.3045 6.63e-06 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 14502 rows and 83 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.745 0.882 0.935 0.4690 0.533 0.533
#> 3 3 0.367 0.449 0.659 0.3136 0.808 0.661
#> 4 4 0.439 0.575 0.724 0.1594 0.777 0.496
#> 5 5 0.551 0.524 0.685 0.0774 0.946 0.797
#> 6 6 0.577 0.611 0.720 0.0484 0.904 0.630
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM11708 1 0.0938 0.922 0.988 0.012
#> GSM11735 1 0.0938 0.922 0.988 0.012
#> GSM11733 1 0.0938 0.922 0.988 0.012
#> GSM11863 1 0.1843 0.916 0.972 0.028
#> GSM11710 1 0.0000 0.928 1.000 0.000
#> GSM11712 1 0.0000 0.928 1.000 0.000
#> GSM11732 1 0.1414 0.919 0.980 0.020
#> GSM11844 1 0.0938 0.923 0.988 0.012
#> GSM11842 1 0.1843 0.916 0.972 0.028
#> GSM11860 1 0.1633 0.918 0.976 0.024
#> GSM11686 1 0.0000 0.928 1.000 0.000
#> GSM11688 1 0.0000 0.928 1.000 0.000
#> GSM11846 1 0.0000 0.928 1.000 0.000
#> GSM11680 1 0.0000 0.928 1.000 0.000
#> GSM11698 1 0.0000 0.928 1.000 0.000
#> GSM11840 1 0.0938 0.922 0.988 0.012
#> GSM11847 1 0.0938 0.922 0.988 0.012
#> GSM11685 1 0.0000 0.928 1.000 0.000
#> GSM11699 1 0.0000 0.928 1.000 0.000
#> GSM27950 1 0.0000 0.928 1.000 0.000
#> GSM27946 1 0.0000 0.928 1.000 0.000
#> GSM11709 2 0.3733 0.941 0.072 0.928
#> GSM11720 2 0.3114 0.946 0.056 0.944
#> GSM11726 2 0.0938 0.945 0.012 0.988
#> GSM11837 2 0.0938 0.945 0.012 0.988
#> GSM11725 2 0.2948 0.947 0.052 0.948
#> GSM11864 2 0.7219 0.798 0.200 0.800
#> GSM11687 2 0.3733 0.941 0.072 0.928
#> GSM11693 2 0.3733 0.941 0.072 0.928
#> GSM11727 2 0.0938 0.945 0.012 0.988
#> GSM11838 2 0.0938 0.945 0.012 0.988
#> GSM11681 2 0.7815 0.769 0.232 0.768
#> GSM11689 2 0.3733 0.941 0.072 0.928
#> GSM11704 2 0.3114 0.946 0.056 0.944
#> GSM11703 2 0.4161 0.933 0.084 0.916
#> GSM11705 2 0.4161 0.933 0.084 0.916
#> GSM11722 2 0.0938 0.945 0.012 0.988
#> GSM11730 2 0.0938 0.945 0.012 0.988
#> GSM11713 2 0.1843 0.943 0.028 0.972
#> GSM11728 1 0.9775 0.367 0.588 0.412
#> GSM27947 1 0.0000 0.928 1.000 0.000
#> GSM27951 2 0.3733 0.941 0.072 0.928
#> GSM11707 1 0.1414 0.919 0.980 0.020
#> GSM11716 1 0.8763 0.547 0.704 0.296
#> GSM11850 1 0.7453 0.751 0.788 0.212
#> GSM11851 1 0.0000 0.928 1.000 0.000
#> GSM11721 1 0.6048 0.811 0.852 0.148
#> GSM11852 1 0.0000 0.928 1.000 0.000
#> GSM11694 1 0.0938 0.923 0.988 0.012
#> GSM11695 1 0.0376 0.927 0.996 0.004
#> GSM11734 2 0.2778 0.947 0.048 0.952
#> GSM11861 1 0.7219 0.757 0.800 0.200
#> GSM11843 2 0.2948 0.947 0.052 0.948
#> GSM11862 1 0.7376 0.748 0.792 0.208
#> GSM11697 1 0.0376 0.927 0.996 0.004
#> GSM11714 1 0.6623 0.789 0.828 0.172
#> GSM11723 2 0.3274 0.944 0.060 0.940
#> GSM11845 2 0.7299 0.795 0.204 0.796
#> GSM11683 1 0.9460 0.472 0.636 0.364
#> GSM11691 1 0.9460 0.472 0.636 0.364
#> GSM27949 1 0.0000 0.928 1.000 0.000
#> GSM27945 1 0.0000 0.928 1.000 0.000
#> GSM11706 1 0.0000 0.928 1.000 0.000
#> GSM11853 1 0.0000 0.928 1.000 0.000
#> GSM11729 2 0.0938 0.945 0.012 0.988
#> GSM11746 2 0.0938 0.945 0.012 0.988
#> GSM11711 1 0.0000 0.928 1.000 0.000
#> GSM11854 1 0.0000 0.928 1.000 0.000
#> GSM11731 2 0.0938 0.945 0.012 0.988
#> GSM11839 2 0.0938 0.945 0.012 0.988
#> GSM11836 2 0.6887 0.801 0.184 0.816
#> GSM11849 1 0.9815 0.369 0.580 0.420
#> GSM11682 1 0.0000 0.928 1.000 0.000
#> GSM11690 1 0.0000 0.928 1.000 0.000
#> GSM11692 1 0.0000 0.928 1.000 0.000
#> GSM11841 1 0.1184 0.921 0.984 0.016
#> GSM11901 1 0.1184 0.921 0.984 0.016
#> GSM11715 2 0.0938 0.945 0.012 0.988
#> GSM11724 2 0.0938 0.945 0.012 0.988
#> GSM11684 1 0.7219 0.759 0.800 0.200
#> GSM11696 1 0.7219 0.759 0.800 0.200
#> GSM27952 1 0.0000 0.928 1.000 0.000
#> GSM27948 1 0.0000 0.928 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM11708 3 0.7589 0.6183 0.052 0.360 0.588
#> GSM11735 3 0.7607 0.6152 0.052 0.364 0.584
#> GSM11733 3 0.6867 0.6491 0.028 0.336 0.636
#> GSM11863 3 0.7032 0.6257 0.028 0.368 0.604
#> GSM11710 3 0.1015 0.7573 0.008 0.012 0.980
#> GSM11712 3 0.2280 0.7502 0.008 0.052 0.940
#> GSM11732 2 0.8271 -0.3483 0.080 0.520 0.400
#> GSM11844 3 0.7676 0.6113 0.056 0.360 0.584
#> GSM11842 3 0.7083 0.6134 0.028 0.380 0.592
#> GSM11860 3 0.7777 0.6019 0.060 0.364 0.576
#> GSM11686 3 0.0000 0.7570 0.000 0.000 1.000
#> GSM11688 3 0.1031 0.7588 0.000 0.024 0.976
#> GSM11846 3 0.3310 0.7551 0.028 0.064 0.908
#> GSM11680 3 0.6491 0.6947 0.052 0.216 0.732
#> GSM11698 3 0.6124 0.6999 0.036 0.220 0.744
#> GSM11840 3 0.6867 0.6491 0.028 0.336 0.636
#> GSM11847 3 0.6867 0.6491 0.028 0.336 0.636
#> GSM11685 3 0.1711 0.7591 0.008 0.032 0.960
#> GSM11699 3 0.3192 0.6960 0.112 0.000 0.888
#> GSM27950 3 0.6535 0.6939 0.052 0.220 0.728
#> GSM27946 3 0.0592 0.7555 0.000 0.012 0.988
#> GSM11709 1 0.2860 0.5434 0.912 0.004 0.084
#> GSM11720 1 0.2682 0.5373 0.920 0.004 0.076
#> GSM11726 1 0.4555 0.2769 0.800 0.200 0.000
#> GSM11837 2 0.6244 0.4004 0.440 0.560 0.000
#> GSM11725 1 0.7056 -0.2884 0.572 0.404 0.024
#> GSM11864 1 0.7997 -0.2189 0.568 0.360 0.072
#> GSM11687 1 0.3030 0.5462 0.904 0.004 0.092
#> GSM11693 1 0.3193 0.5462 0.896 0.004 0.100
#> GSM11727 1 0.6305 -0.3327 0.516 0.484 0.000
#> GSM11838 2 0.6244 0.4004 0.440 0.560 0.000
#> GSM11681 1 0.4121 0.5106 0.832 0.000 0.168
#> GSM11689 1 0.2945 0.5434 0.908 0.004 0.088
#> GSM11704 1 0.2945 0.5434 0.908 0.004 0.088
#> GSM11703 1 0.4261 0.5260 0.848 0.012 0.140
#> GSM11705 1 0.3918 0.5373 0.868 0.012 0.120
#> GSM11722 1 0.6062 -0.1012 0.616 0.384 0.000
#> GSM11730 1 0.5178 0.2118 0.744 0.256 0.000
#> GSM11713 1 0.5366 0.3181 0.776 0.208 0.016
#> GSM11728 1 0.7479 0.4001 0.660 0.076 0.264
#> GSM27947 3 0.1337 0.7581 0.016 0.012 0.972
#> GSM27951 1 0.2959 0.5465 0.900 0.000 0.100
#> GSM11707 3 0.9916 0.3495 0.316 0.288 0.396
#> GSM11716 2 0.8820 -0.3650 0.116 0.476 0.408
#> GSM11850 2 0.9857 -0.3471 0.252 0.380 0.368
#> GSM11851 3 0.6148 0.7044 0.028 0.244 0.728
#> GSM11721 3 0.5746 0.6422 0.180 0.040 0.780
#> GSM11852 3 0.4280 0.6958 0.124 0.020 0.856
#> GSM11694 3 0.9679 0.3825 0.320 0.232 0.448
#> GSM11695 3 0.9574 0.4401 0.292 0.232 0.476
#> GSM11734 1 0.7188 -0.3672 0.492 0.484 0.024
#> GSM11861 3 0.7146 0.4868 0.264 0.060 0.676
#> GSM11843 1 0.6937 -0.2400 0.576 0.404 0.020
#> GSM11862 3 0.6956 0.4431 0.300 0.040 0.660
#> GSM11697 3 0.9574 0.4401 0.292 0.232 0.476
#> GSM11714 1 0.9811 -0.2797 0.384 0.240 0.376
#> GSM11723 2 0.7438 0.2858 0.428 0.536 0.036
#> GSM11845 2 0.8326 0.1986 0.432 0.488 0.080
#> GSM11683 1 0.8496 0.0408 0.492 0.092 0.416
#> GSM11691 1 0.8556 0.0390 0.488 0.096 0.416
#> GSM27949 3 0.6124 0.7002 0.036 0.220 0.744
#> GSM27945 3 0.5932 0.7175 0.056 0.164 0.780
#> GSM11706 3 0.2229 0.7584 0.012 0.044 0.944
#> GSM11853 3 0.1170 0.7580 0.016 0.008 0.976
#> GSM11729 2 0.6280 0.4283 0.460 0.540 0.000
#> GSM11746 2 0.6295 0.4176 0.472 0.528 0.000
#> GSM11711 3 0.0747 0.7571 0.016 0.000 0.984
#> GSM11854 3 0.0848 0.7563 0.008 0.008 0.984
#> GSM11731 2 0.6235 0.4347 0.436 0.564 0.000
#> GSM11839 2 0.6823 0.3524 0.484 0.504 0.012
#> GSM11836 2 0.8991 0.2736 0.392 0.476 0.132
#> GSM11849 3 0.8849 0.2096 0.292 0.152 0.556
#> GSM11682 3 0.1337 0.7506 0.016 0.012 0.972
#> GSM11690 3 0.1751 0.7473 0.012 0.028 0.960
#> GSM11692 3 0.2229 0.7473 0.012 0.044 0.944
#> GSM11841 3 0.3690 0.7229 0.016 0.100 0.884
#> GSM11901 3 0.3690 0.7229 0.016 0.100 0.884
#> GSM11715 2 0.6244 0.4303 0.440 0.560 0.000
#> GSM11724 2 0.6244 0.4303 0.440 0.560 0.000
#> GSM11684 3 0.7768 0.2552 0.344 0.064 0.592
#> GSM11696 3 0.7768 0.2552 0.344 0.064 0.592
#> GSM27952 3 0.1015 0.7538 0.008 0.012 0.980
#> GSM27948 3 0.1751 0.7473 0.012 0.028 0.960
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM11708 3 0.6945 0.5817 0.032 0.084 0.624 0.260
#> GSM11735 3 0.6627 0.5914 0.032 0.072 0.656 0.240
#> GSM11733 3 0.7101 0.5164 0.032 0.068 0.560 0.340
#> GSM11863 3 0.7090 0.5318 0.032 0.076 0.584 0.308
#> GSM11710 4 0.2894 0.7282 0.020 0.024 0.048 0.908
#> GSM11712 4 0.2552 0.7231 0.012 0.020 0.048 0.920
#> GSM11732 3 0.6701 0.5494 0.024 0.160 0.672 0.144
#> GSM11844 3 0.6642 0.5838 0.024 0.116 0.672 0.188
#> GSM11842 3 0.7360 0.5325 0.032 0.100 0.572 0.296
#> GSM11860 3 0.7537 0.5369 0.040 0.100 0.560 0.300
#> GSM11686 4 0.2275 0.7387 0.004 0.020 0.048 0.928
#> GSM11688 4 0.3442 0.6984 0.012 0.028 0.084 0.876
#> GSM11846 4 0.4596 0.6297 0.028 0.024 0.140 0.808
#> GSM11680 3 0.6380 0.4066 0.052 0.004 0.480 0.464
#> GSM11698 4 0.5607 -0.4098 0.020 0.000 0.488 0.492
#> GSM11840 3 0.7101 0.5164 0.032 0.068 0.560 0.340
#> GSM11847 3 0.7101 0.5164 0.032 0.068 0.560 0.340
#> GSM11685 4 0.3057 0.7139 0.012 0.024 0.068 0.896
#> GSM11699 4 0.2739 0.7263 0.060 0.000 0.036 0.904
#> GSM27950 3 0.6735 0.4257 0.048 0.020 0.496 0.436
#> GSM27946 4 0.1082 0.7551 0.020 0.004 0.004 0.972
#> GSM11709 1 0.2360 0.7508 0.924 0.020 0.004 0.052
#> GSM11720 1 0.2486 0.7478 0.920 0.028 0.004 0.048
#> GSM11726 1 0.6370 0.3888 0.644 0.252 0.100 0.004
#> GSM11837 2 0.5784 0.6725 0.200 0.700 0.100 0.000
#> GSM11725 2 0.5675 0.7349 0.272 0.676 0.048 0.004
#> GSM11864 2 0.7569 0.6275 0.316 0.552 0.076 0.056
#> GSM11687 1 0.2467 0.7493 0.920 0.024 0.004 0.052
#> GSM11693 1 0.2408 0.7525 0.920 0.016 0.004 0.060
#> GSM11727 2 0.6450 0.5562 0.276 0.616 0.108 0.000
#> GSM11838 2 0.5875 0.6679 0.204 0.692 0.104 0.000
#> GSM11681 1 0.2983 0.7153 0.880 0.008 0.004 0.108
#> GSM11689 1 0.2408 0.7525 0.920 0.016 0.004 0.060
#> GSM11704 1 0.2408 0.7525 0.920 0.016 0.004 0.060
#> GSM11703 1 0.2716 0.7441 0.908 0.012 0.012 0.068
#> GSM11705 1 0.2587 0.7492 0.916 0.020 0.008 0.056
#> GSM11722 1 0.6957 -0.0851 0.472 0.416 0.112 0.000
#> GSM11730 1 0.6641 0.3332 0.600 0.276 0.124 0.000
#> GSM11713 1 0.6483 0.4756 0.664 0.192 0.136 0.008
#> GSM11728 1 0.5633 0.6534 0.772 0.056 0.072 0.100
#> GSM27947 4 0.1362 0.7556 0.020 0.004 0.012 0.964
#> GSM27951 1 0.2408 0.7525 0.920 0.016 0.004 0.060
#> GSM11707 3 0.8003 0.4457 0.312 0.048 0.516 0.124
#> GSM11716 3 0.7157 0.5810 0.040 0.136 0.644 0.180
#> GSM11850 3 0.7875 0.4603 0.108 0.184 0.604 0.104
#> GSM11851 3 0.5919 0.3536 0.016 0.012 0.492 0.480
#> GSM11721 4 0.5391 0.6095 0.160 0.036 0.040 0.764
#> GSM11852 4 0.4331 0.6585 0.136 0.016 0.028 0.820
#> GSM11694 3 0.7781 0.4190 0.316 0.012 0.488 0.184
#> GSM11695 3 0.7711 0.4290 0.312 0.008 0.488 0.192
#> GSM11734 2 0.5176 0.7623 0.192 0.748 0.056 0.004
#> GSM11861 4 0.7348 0.3954 0.256 0.048 0.092 0.604
#> GSM11843 2 0.6350 0.6500 0.296 0.612 0.092 0.000
#> GSM11862 4 0.7272 0.3871 0.280 0.052 0.072 0.596
#> GSM11697 3 0.7725 0.4342 0.308 0.008 0.488 0.196
#> GSM11714 3 0.7827 0.2960 0.372 0.036 0.480 0.112
#> GSM11723 2 0.6753 0.5854 0.092 0.620 0.272 0.016
#> GSM11845 2 0.8101 0.4561 0.104 0.536 0.284 0.076
#> GSM11683 1 0.8289 0.0761 0.468 0.028 0.268 0.236
#> GSM11691 1 0.8545 0.0515 0.448 0.040 0.276 0.236
#> GSM27949 3 0.6670 0.4173 0.044 0.020 0.496 0.440
#> GSM27945 4 0.6249 -0.2404 0.048 0.004 0.408 0.540
#> GSM11706 4 0.3204 0.7097 0.016 0.028 0.064 0.892
#> GSM11853 4 0.1059 0.7561 0.016 0.000 0.012 0.972
#> GSM11729 2 0.3636 0.7757 0.172 0.820 0.008 0.000
#> GSM11746 2 0.3494 0.7748 0.172 0.824 0.004 0.000
#> GSM11711 4 0.2196 0.7510 0.016 0.016 0.032 0.936
#> GSM11854 4 0.1059 0.7561 0.016 0.000 0.012 0.972
#> GSM11731 2 0.3913 0.7785 0.148 0.824 0.028 0.000
#> GSM11839 2 0.5257 0.7562 0.172 0.764 0.032 0.032
#> GSM11836 2 0.5974 0.7108 0.096 0.744 0.040 0.120
#> GSM11849 4 0.7244 0.3251 0.256 0.180 0.004 0.560
#> GSM11682 4 0.1993 0.7546 0.016 0.016 0.024 0.944
#> GSM11690 4 0.1082 0.7559 0.020 0.004 0.004 0.972
#> GSM11692 4 0.1697 0.7474 0.016 0.004 0.028 0.952
#> GSM11841 4 0.3722 0.6914 0.016 0.044 0.072 0.868
#> GSM11901 4 0.3722 0.6914 0.016 0.044 0.072 0.868
#> GSM11715 2 0.3672 0.7717 0.164 0.824 0.012 0.000
#> GSM11724 2 0.3900 0.7694 0.164 0.816 0.020 0.000
#> GSM11684 4 0.6703 0.4394 0.292 0.036 0.052 0.620
#> GSM11696 4 0.6703 0.4394 0.292 0.036 0.052 0.620
#> GSM27952 4 0.2089 0.7476 0.012 0.020 0.028 0.940
#> GSM27948 4 0.0895 0.7556 0.020 0.004 0.000 0.976
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM11708 5 0.4069 0.4565 0.000 0.004 0.088 0.108 0.800
#> GSM11735 5 0.3237 0.4737 0.000 0.000 0.048 0.104 0.848
#> GSM11733 5 0.3109 0.5288 0.000 0.000 0.000 0.200 0.800
#> GSM11863 5 0.3562 0.5212 0.000 0.000 0.016 0.196 0.788
#> GSM11710 4 0.3322 0.7534 0.000 0.012 0.064 0.860 0.064
#> GSM11712 4 0.1800 0.7537 0.000 0.000 0.020 0.932 0.048
#> GSM11732 5 0.6586 -0.0518 0.012 0.060 0.372 0.040 0.516
#> GSM11844 5 0.6549 -0.0267 0.012 0.032 0.368 0.068 0.520
#> GSM11842 5 0.4210 0.5075 0.000 0.016 0.028 0.184 0.772
#> GSM11860 5 0.4702 0.4992 0.008 0.016 0.032 0.200 0.744
#> GSM11686 4 0.3517 0.7456 0.012 0.012 0.056 0.860 0.060
#> GSM11688 4 0.4117 0.7246 0.012 0.012 0.060 0.820 0.096
#> GSM11846 4 0.4764 0.6766 0.024 0.012 0.064 0.780 0.120
#> GSM11680 5 0.7691 -0.0574 0.048 0.000 0.316 0.304 0.332
#> GSM11698 4 0.7225 -0.4440 0.016 0.000 0.320 0.336 0.328
#> GSM11840 5 0.3109 0.5288 0.000 0.000 0.000 0.200 0.800
#> GSM11847 5 0.3109 0.5288 0.000 0.000 0.000 0.200 0.800
#> GSM11685 4 0.3348 0.7484 0.004 0.012 0.056 0.864 0.064
#> GSM11699 4 0.2609 0.7535 0.052 0.000 0.048 0.896 0.004
#> GSM27950 5 0.7769 0.0307 0.040 0.008 0.300 0.272 0.380
#> GSM27946 4 0.1153 0.7662 0.008 0.000 0.024 0.964 0.004
#> GSM11709 1 0.1507 0.8153 0.952 0.012 0.012 0.024 0.000
#> GSM11720 1 0.1806 0.8131 0.940 0.016 0.016 0.028 0.000
#> GSM11726 1 0.6777 0.4307 0.540 0.220 0.220 0.008 0.012
#> GSM11837 2 0.4492 0.6545 0.052 0.740 0.204 0.000 0.004
#> GSM11725 2 0.4755 0.6920 0.172 0.744 0.072 0.000 0.012
#> GSM11864 2 0.6274 0.5856 0.264 0.608 0.088 0.004 0.036
#> GSM11687 1 0.1106 0.8160 0.964 0.012 0.000 0.024 0.000
#> GSM11693 1 0.0992 0.8161 0.968 0.008 0.000 0.024 0.000
#> GSM11727 2 0.5289 0.5918 0.108 0.680 0.208 0.000 0.004
#> GSM11838 2 0.4459 0.6561 0.052 0.744 0.200 0.000 0.004
#> GSM11681 1 0.1124 0.8049 0.960 0.004 0.000 0.036 0.000
#> GSM11689 1 0.0992 0.8161 0.968 0.008 0.000 0.024 0.000
#> GSM11704 1 0.0992 0.8161 0.968 0.008 0.000 0.024 0.000
#> GSM11703 1 0.1954 0.8059 0.932 0.008 0.032 0.028 0.000
#> GSM11705 1 0.1690 0.8095 0.944 0.008 0.024 0.024 0.000
#> GSM11722 2 0.6814 -0.0467 0.356 0.404 0.236 0.000 0.004
#> GSM11730 1 0.6908 0.3434 0.444 0.220 0.324 0.000 0.012
#> GSM11713 1 0.6772 0.4057 0.480 0.176 0.328 0.000 0.016
#> GSM11728 1 0.5964 0.5822 0.632 0.040 0.276 0.036 0.016
#> GSM27947 4 0.1690 0.7637 0.008 0.000 0.024 0.944 0.024
#> GSM27951 1 0.0992 0.8161 0.968 0.008 0.000 0.024 0.000
#> GSM11707 5 0.7435 -0.3616 0.292 0.008 0.248 0.024 0.428
#> GSM11716 5 0.7454 -0.1939 0.056 0.036 0.412 0.072 0.424
#> GSM11850 3 0.7511 0.1869 0.068 0.092 0.444 0.020 0.376
#> GSM11851 3 0.7163 -0.0746 0.016 0.000 0.388 0.272 0.324
#> GSM11721 4 0.5399 0.6453 0.096 0.020 0.088 0.752 0.044
#> GSM11852 4 0.4897 0.6593 0.096 0.008 0.084 0.776 0.036
#> GSM11694 3 0.8046 0.4899 0.276 0.000 0.348 0.088 0.288
#> GSM11695 3 0.8046 0.4899 0.276 0.000 0.348 0.088 0.288
#> GSM11734 2 0.4841 0.6945 0.056 0.752 0.160 0.000 0.032
#> GSM11861 4 0.6765 0.4524 0.092 0.020 0.236 0.604 0.048
#> GSM11843 2 0.6297 0.6172 0.148 0.644 0.164 0.004 0.040
#> GSM11862 4 0.7002 0.4644 0.148 0.032 0.172 0.608 0.040
#> GSM11697 3 0.8041 0.4742 0.252 0.000 0.364 0.092 0.292
#> GSM11714 3 0.7737 0.3845 0.292 0.012 0.336 0.028 0.332
#> GSM11723 2 0.6674 0.1292 0.036 0.452 0.412 0.000 0.100
#> GSM11845 3 0.7627 -0.1319 0.052 0.384 0.416 0.020 0.128
#> GSM11683 3 0.7948 0.4311 0.376 0.012 0.384 0.136 0.092
#> GSM11691 3 0.8132 0.4294 0.328 0.016 0.412 0.136 0.108
#> GSM27949 5 0.7876 0.0184 0.048 0.008 0.300 0.272 0.372
#> GSM27945 4 0.7766 -0.3700 0.068 0.000 0.320 0.388 0.224
#> GSM11706 4 0.4087 0.7277 0.008 0.012 0.072 0.820 0.088
#> GSM11853 4 0.2228 0.7640 0.000 0.012 0.040 0.920 0.028
#> GSM11729 2 0.1877 0.7474 0.052 0.932 0.008 0.004 0.004
#> GSM11746 2 0.1752 0.7472 0.052 0.936 0.004 0.004 0.004
#> GSM11711 4 0.2774 0.7579 0.000 0.012 0.048 0.892 0.048
#> GSM11854 4 0.2305 0.7641 0.000 0.012 0.044 0.916 0.028
#> GSM11731 2 0.3251 0.7350 0.040 0.864 0.080 0.000 0.016
#> GSM11839 2 0.5510 0.6875 0.072 0.740 0.124 0.044 0.020
#> GSM11836 2 0.5412 0.6714 0.048 0.740 0.088 0.116 0.008
#> GSM11849 4 0.6277 0.5429 0.068 0.200 0.064 0.656 0.012
#> GSM11682 4 0.2452 0.7652 0.012 0.000 0.052 0.908 0.028
#> GSM11690 4 0.1369 0.7620 0.008 0.000 0.028 0.956 0.008
#> GSM11692 4 0.2379 0.7513 0.012 0.000 0.048 0.912 0.028
#> GSM11841 4 0.3472 0.7288 0.012 0.008 0.064 0.860 0.056
#> GSM11901 4 0.3472 0.7288 0.012 0.008 0.064 0.860 0.056
#> GSM11715 2 0.2609 0.7423 0.048 0.896 0.052 0.004 0.000
#> GSM11724 2 0.2769 0.7418 0.048 0.892 0.052 0.004 0.004
#> GSM11684 4 0.6470 0.4924 0.172 0.016 0.192 0.608 0.012
#> GSM11696 4 0.6470 0.4924 0.172 0.016 0.192 0.608 0.012
#> GSM27952 4 0.2985 0.7576 0.008 0.012 0.044 0.888 0.048
#> GSM27948 4 0.1082 0.7617 0.000 0.000 0.028 0.964 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM11708 5 0.5490 0.6562 0.000 0.008 0.244 0.052 0.640 0.056
#> GSM11735 5 0.4616 0.7444 0.000 0.008 0.196 0.048 0.724 0.024
#> GSM11733 5 0.3375 0.8762 0.000 0.000 0.096 0.088 0.816 0.000
#> GSM11863 5 0.3198 0.8608 0.000 0.000 0.060 0.084 0.844 0.012
#> GSM11710 4 0.4045 0.7142 0.004 0.004 0.080 0.808 0.044 0.060
#> GSM11712 4 0.2325 0.7336 0.000 0.008 0.004 0.900 0.068 0.020
#> GSM11732 3 0.5254 0.3694 0.000 0.096 0.656 0.008 0.224 0.016
#> GSM11844 3 0.5410 0.3751 0.000 0.080 0.656 0.024 0.224 0.016
#> GSM11842 5 0.3889 0.8423 0.000 0.016 0.056 0.088 0.816 0.024
#> GSM11860 5 0.4391 0.8261 0.004 0.016 0.068 0.104 0.784 0.024
#> GSM11686 4 0.4326 0.6925 0.004 0.004 0.140 0.772 0.032 0.048
#> GSM11688 4 0.4511 0.6805 0.000 0.004 0.140 0.756 0.052 0.048
#> GSM11846 4 0.4589 0.6767 0.012 0.000 0.140 0.756 0.052 0.040
#> GSM11680 3 0.4471 0.5249 0.016 0.000 0.684 0.268 0.028 0.004
#> GSM11698 3 0.4248 0.5026 0.004 0.000 0.672 0.296 0.024 0.004
#> GSM11840 5 0.3375 0.8762 0.000 0.000 0.096 0.088 0.816 0.000
#> GSM11847 5 0.3375 0.8762 0.000 0.000 0.096 0.088 0.816 0.000
#> GSM11685 4 0.3492 0.7188 0.000 0.004 0.084 0.836 0.028 0.048
#> GSM11699 4 0.2948 0.7330 0.028 0.000 0.072 0.872 0.012 0.016
#> GSM27950 3 0.5654 0.4776 0.012 0.004 0.640 0.236 0.068 0.040
#> GSM27946 4 0.2876 0.7307 0.004 0.008 0.104 0.860 0.024 0.000
#> GSM11709 1 0.0551 0.9160 0.984 0.000 0.000 0.004 0.004 0.008
#> GSM11720 1 0.0603 0.9135 0.980 0.000 0.000 0.004 0.000 0.016
#> GSM11726 6 0.4768 0.4249 0.416 0.052 0.000 0.000 0.000 0.532
#> GSM11837 6 0.4780 0.2452 0.040 0.472 0.000 0.000 0.004 0.484
#> GSM11725 2 0.4374 0.6359 0.160 0.752 0.064 0.000 0.004 0.020
#> GSM11864 2 0.6940 0.4681 0.252 0.548 0.088 0.012 0.052 0.048
#> GSM11687 1 0.0291 0.9185 0.992 0.004 0.000 0.004 0.000 0.000
#> GSM11693 1 0.0551 0.9168 0.984 0.004 0.008 0.004 0.000 0.000
#> GSM11727 6 0.5004 0.3457 0.060 0.420 0.000 0.000 0.004 0.516
#> GSM11838 6 0.4780 0.2452 0.040 0.472 0.000 0.000 0.004 0.484
#> GSM11681 1 0.0909 0.8984 0.968 0.000 0.020 0.012 0.000 0.000
#> GSM11689 1 0.0436 0.9195 0.988 0.004 0.004 0.004 0.000 0.000
#> GSM11704 1 0.0436 0.9195 0.988 0.004 0.004 0.004 0.000 0.000
#> GSM11703 1 0.1511 0.8913 0.940 0.000 0.012 0.004 0.000 0.044
#> GSM11705 1 0.1484 0.8886 0.944 0.000 0.008 0.004 0.004 0.040
#> GSM11722 6 0.5689 0.5883 0.252 0.180 0.000 0.000 0.008 0.560
#> GSM11730 6 0.4254 0.5613 0.272 0.048 0.000 0.000 0.000 0.680
#> GSM11713 6 0.4693 0.4866 0.312 0.028 0.000 0.000 0.024 0.636
#> GSM11728 1 0.5270 0.1006 0.516 0.004 0.020 0.008 0.028 0.424
#> GSM27947 4 0.3192 0.7262 0.012 0.008 0.100 0.848 0.032 0.000
#> GSM27951 1 0.0436 0.9195 0.988 0.004 0.004 0.004 0.000 0.000
#> GSM11707 3 0.7498 0.3630 0.240 0.008 0.476 0.024 0.144 0.108
#> GSM11716 3 0.5516 0.4881 0.028 0.100 0.716 0.028 0.108 0.020
#> GSM11850 3 0.5585 0.4923 0.028 0.128 0.712 0.032 0.076 0.024
#> GSM11851 3 0.5610 0.4454 0.000 0.028 0.624 0.256 0.076 0.016
#> GSM11721 4 0.5986 0.6135 0.092 0.080 0.044 0.700 0.032 0.052
#> GSM11852 4 0.6164 0.6163 0.092 0.076 0.064 0.688 0.032 0.048
#> GSM11694 3 0.5016 0.5668 0.268 0.004 0.636 0.088 0.004 0.000
#> GSM11695 3 0.5016 0.5668 0.268 0.004 0.636 0.088 0.004 0.000
#> GSM11734 2 0.4614 0.6148 0.012 0.744 0.164 0.000 0.044 0.036
#> GSM11861 4 0.7706 0.3708 0.044 0.088 0.240 0.504 0.048 0.076
#> GSM11843 2 0.6437 0.5328 0.120 0.644 0.076 0.004 0.084 0.072
#> GSM11862 4 0.8192 0.3981 0.128 0.116 0.120 0.500 0.040 0.096
#> GSM11697 3 0.5019 0.5716 0.248 0.000 0.652 0.088 0.004 0.008
#> GSM11714 3 0.7035 0.4539 0.260 0.004 0.524 0.040 0.076 0.096
#> GSM11723 3 0.6048 -0.0433 0.000 0.408 0.464 0.004 0.080 0.044
#> GSM11845 3 0.6750 0.0618 0.008 0.348 0.476 0.016 0.100 0.052
#> GSM11683 3 0.7395 0.3867 0.332 0.028 0.448 0.096 0.020 0.076
#> GSM11691 3 0.7931 0.4398 0.252 0.084 0.468 0.096 0.024 0.076
#> GSM27949 3 0.5600 0.4863 0.020 0.004 0.648 0.236 0.056 0.036
#> GSM27945 3 0.4838 0.5183 0.048 0.000 0.640 0.296 0.012 0.004
#> GSM11706 4 0.4509 0.6825 0.000 0.004 0.116 0.764 0.056 0.060
#> GSM11853 4 0.2684 0.7380 0.004 0.000 0.052 0.888 0.032 0.024
#> GSM11729 2 0.3603 0.6429 0.032 0.820 0.008 0.004 0.012 0.124
#> GSM11746 2 0.3558 0.6265 0.052 0.808 0.004 0.004 0.000 0.132
#> GSM11711 4 0.3303 0.7262 0.004 0.004 0.080 0.852 0.024 0.036
#> GSM11854 4 0.2684 0.7378 0.004 0.000 0.052 0.888 0.032 0.024
#> GSM11731 2 0.2859 0.6764 0.024 0.884 0.032 0.000 0.016 0.044
#> GSM11839 2 0.5490 0.5974 0.040 0.740 0.056 0.044 0.044 0.076
#> GSM11836 2 0.5186 0.6005 0.004 0.740 0.056 0.108 0.040 0.052
#> GSM11849 4 0.7291 0.5209 0.064 0.128 0.040 0.548 0.024 0.196
#> GSM11682 4 0.4155 0.7197 0.004 0.012 0.080 0.796 0.016 0.092
#> GSM11690 4 0.3545 0.7171 0.004 0.012 0.032 0.840 0.024 0.088
#> GSM11692 4 0.4199 0.6964 0.000 0.012 0.036 0.788 0.044 0.120
#> GSM11841 4 0.5777 0.6147 0.000 0.028 0.044 0.668 0.112 0.148
#> GSM11901 4 0.5777 0.6147 0.000 0.028 0.044 0.668 0.112 0.148
#> GSM11715 2 0.3845 0.6018 0.024 0.772 0.000 0.004 0.016 0.184
#> GSM11724 2 0.3877 0.6009 0.024 0.768 0.000 0.004 0.016 0.188
#> GSM11684 4 0.7206 0.4024 0.088 0.016 0.044 0.472 0.052 0.328
#> GSM11696 4 0.7206 0.4024 0.088 0.016 0.044 0.472 0.052 0.328
#> GSM27952 4 0.3689 0.7172 0.004 0.004 0.100 0.824 0.024 0.044
#> GSM27948 4 0.3494 0.7197 0.004 0.012 0.032 0.844 0.024 0.084
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 cell.line(p) agent(p) time(p) k
#> CV:kmeans 79 3.23e-09 0.312 2.67e-02 2
#> CV:kmeans 47 4.94e-09 0.349 2.44e-01 3
#> CV:kmeans 59 6.11e-10 0.532 4.36e-06 4
#> CV:kmeans 53 4.44e-08 0.591 5.09e-06 5
#> CV:kmeans 59 2.09e-12 0.376 7.81e-06 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 14502 rows and 83 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.741 0.853 0.942 0.5009 0.500 0.500
#> 3 3 0.562 0.779 0.853 0.3299 0.719 0.492
#> 4 4 0.609 0.706 0.833 0.1243 0.893 0.688
#> 5 5 0.655 0.647 0.773 0.0671 0.927 0.730
#> 6 6 0.667 0.535 0.741 0.0403 0.931 0.708
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM11708 1 0.0000 0.9348 1.000 0.000
#> GSM11735 1 0.0000 0.9348 1.000 0.000
#> GSM11733 1 0.0000 0.9348 1.000 0.000
#> GSM11863 1 0.0000 0.9348 1.000 0.000
#> GSM11710 1 0.0000 0.9348 1.000 0.000
#> GSM11712 1 0.0000 0.9348 1.000 0.000
#> GSM11732 1 0.4939 0.8353 0.892 0.108
#> GSM11844 1 0.0000 0.9348 1.000 0.000
#> GSM11842 1 0.0000 0.9348 1.000 0.000
#> GSM11860 1 0.3733 0.8724 0.928 0.072
#> GSM11686 1 0.0000 0.9348 1.000 0.000
#> GSM11688 1 0.0000 0.9348 1.000 0.000
#> GSM11846 1 0.0000 0.9348 1.000 0.000
#> GSM11680 1 0.0000 0.9348 1.000 0.000
#> GSM11698 1 0.0000 0.9348 1.000 0.000
#> GSM11840 1 0.0000 0.9348 1.000 0.000
#> GSM11847 1 0.0000 0.9348 1.000 0.000
#> GSM11685 1 0.0000 0.9348 1.000 0.000
#> GSM11699 1 0.0000 0.9348 1.000 0.000
#> GSM27950 1 0.0000 0.9348 1.000 0.000
#> GSM27946 1 0.0000 0.9348 1.000 0.000
#> GSM11709 2 0.0000 0.9321 0.000 1.000
#> GSM11720 2 0.0000 0.9321 0.000 1.000
#> GSM11726 2 0.0000 0.9321 0.000 1.000
#> GSM11837 2 0.0000 0.9321 0.000 1.000
#> GSM11725 2 0.0000 0.9321 0.000 1.000
#> GSM11864 2 0.7219 0.7310 0.200 0.800
#> GSM11687 2 0.0000 0.9321 0.000 1.000
#> GSM11693 2 0.0000 0.9321 0.000 1.000
#> GSM11727 2 0.0000 0.9321 0.000 1.000
#> GSM11838 2 0.0000 0.9321 0.000 1.000
#> GSM11681 2 0.6712 0.7626 0.176 0.824
#> GSM11689 2 0.0000 0.9321 0.000 1.000
#> GSM11704 2 0.0000 0.9321 0.000 1.000
#> GSM11703 2 0.0000 0.9321 0.000 1.000
#> GSM11705 2 0.0000 0.9321 0.000 1.000
#> GSM11722 2 0.0000 0.9321 0.000 1.000
#> GSM11730 2 0.0000 0.9321 0.000 1.000
#> GSM11713 2 0.0000 0.9321 0.000 1.000
#> GSM11728 2 0.0000 0.9321 0.000 1.000
#> GSM27947 1 0.0000 0.9348 1.000 0.000
#> GSM27951 2 0.0000 0.9321 0.000 1.000
#> GSM11707 1 0.6973 0.7405 0.812 0.188
#> GSM11716 1 0.9775 0.2732 0.588 0.412
#> GSM11850 2 0.9635 0.3286 0.388 0.612
#> GSM11851 1 0.0000 0.9348 1.000 0.000
#> GSM11721 1 0.7219 0.7186 0.800 0.200
#> GSM11852 1 0.0000 0.9348 1.000 0.000
#> GSM11694 1 0.8608 0.5815 0.716 0.284
#> GSM11695 1 0.1184 0.9231 0.984 0.016
#> GSM11734 2 0.0000 0.9321 0.000 1.000
#> GSM11861 1 0.9983 0.0892 0.524 0.476
#> GSM11843 2 0.0000 0.9321 0.000 1.000
#> GSM11862 1 0.9983 0.0892 0.524 0.476
#> GSM11697 1 0.1184 0.9231 0.984 0.016
#> GSM11714 1 0.9775 0.3049 0.588 0.412
#> GSM11723 2 0.0000 0.9321 0.000 1.000
#> GSM11845 2 0.7219 0.7310 0.200 0.800
#> GSM11683 2 0.7453 0.7125 0.212 0.788
#> GSM11691 2 0.6801 0.7578 0.180 0.820
#> GSM27949 1 0.0000 0.9348 1.000 0.000
#> GSM27945 1 0.0000 0.9348 1.000 0.000
#> GSM11706 1 0.0000 0.9348 1.000 0.000
#> GSM11853 1 0.0000 0.9348 1.000 0.000
#> GSM11729 2 0.0000 0.9321 0.000 1.000
#> GSM11746 2 0.0000 0.9321 0.000 1.000
#> GSM11711 1 0.0000 0.9348 1.000 0.000
#> GSM11854 1 0.0000 0.9348 1.000 0.000
#> GSM11731 2 0.0000 0.9321 0.000 1.000
#> GSM11839 2 0.0000 0.9321 0.000 1.000
#> GSM11836 2 0.0672 0.9266 0.008 0.992
#> GSM11849 2 0.2423 0.9037 0.040 0.960
#> GSM11682 1 0.0000 0.9348 1.000 0.000
#> GSM11690 1 0.0000 0.9348 1.000 0.000
#> GSM11692 1 0.0000 0.9348 1.000 0.000
#> GSM11841 1 0.0000 0.9348 1.000 0.000
#> GSM11901 1 0.0000 0.9348 1.000 0.000
#> GSM11715 2 0.0000 0.9321 0.000 1.000
#> GSM11724 2 0.0000 0.9321 0.000 1.000
#> GSM11684 2 0.9661 0.3560 0.392 0.608
#> GSM11696 2 0.9661 0.3560 0.392 0.608
#> GSM27952 1 0.0000 0.9348 1.000 0.000
#> GSM27948 1 0.0000 0.9348 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM11708 3 0.4555 0.774 0.200 0.000 0.800
#> GSM11735 3 0.4555 0.774 0.200 0.000 0.800
#> GSM11733 3 0.5905 0.635 0.352 0.000 0.648
#> GSM11863 3 0.5902 0.652 0.316 0.004 0.680
#> GSM11710 1 0.0424 0.889 0.992 0.000 0.008
#> GSM11712 1 0.0592 0.885 0.988 0.000 0.012
#> GSM11732 3 0.4902 0.759 0.064 0.092 0.844
#> GSM11844 3 0.4921 0.765 0.084 0.072 0.844
#> GSM11842 3 0.6445 0.658 0.308 0.020 0.672
#> GSM11860 3 0.7495 0.689 0.248 0.084 0.668
#> GSM11686 1 0.0892 0.885 0.980 0.000 0.020
#> GSM11688 1 0.2796 0.822 0.908 0.000 0.092
#> GSM11846 1 0.4887 0.606 0.772 0.000 0.228
#> GSM11680 3 0.4504 0.775 0.196 0.000 0.804
#> GSM11698 3 0.4555 0.774 0.200 0.000 0.800
#> GSM11840 3 0.5926 0.629 0.356 0.000 0.644
#> GSM11847 3 0.5926 0.629 0.356 0.000 0.644
#> GSM11685 1 0.0592 0.888 0.988 0.000 0.012
#> GSM11699 1 0.2200 0.863 0.940 0.004 0.056
#> GSM27950 3 0.4504 0.775 0.196 0.000 0.804
#> GSM27946 1 0.0000 0.889 1.000 0.000 0.000
#> GSM11709 2 0.3879 0.875 0.000 0.848 0.152
#> GSM11720 2 0.3816 0.877 0.000 0.852 0.148
#> GSM11726 2 0.1411 0.890 0.000 0.964 0.036
#> GSM11837 2 0.1411 0.884 0.000 0.964 0.036
#> GSM11725 2 0.1753 0.880 0.000 0.952 0.048
#> GSM11864 2 0.6054 0.719 0.052 0.768 0.180
#> GSM11687 2 0.3941 0.875 0.000 0.844 0.156
#> GSM11693 2 0.3941 0.875 0.000 0.844 0.156
#> GSM11727 2 0.0000 0.889 0.000 1.000 0.000
#> GSM11838 2 0.1411 0.884 0.000 0.964 0.036
#> GSM11681 2 0.7016 0.785 0.116 0.728 0.156
#> GSM11689 2 0.3941 0.875 0.000 0.844 0.156
#> GSM11704 2 0.3941 0.875 0.000 0.844 0.156
#> GSM11703 2 0.3879 0.875 0.000 0.848 0.152
#> GSM11705 2 0.3879 0.875 0.000 0.848 0.152
#> GSM11722 2 0.0424 0.890 0.000 0.992 0.008
#> GSM11730 2 0.2448 0.887 0.000 0.924 0.076
#> GSM11713 2 0.3340 0.881 0.000 0.880 0.120
#> GSM11728 2 0.5237 0.854 0.056 0.824 0.120
#> GSM27947 1 0.0747 0.886 0.984 0.000 0.016
#> GSM27951 2 0.3941 0.875 0.000 0.844 0.156
#> GSM11707 3 0.2050 0.743 0.028 0.020 0.952
#> GSM11716 3 0.4921 0.765 0.084 0.072 0.844
#> GSM11850 3 0.4750 0.684 0.000 0.216 0.784
#> GSM11851 3 0.4796 0.764 0.220 0.000 0.780
#> GSM11721 1 0.5413 0.748 0.800 0.164 0.036
#> GSM11852 1 0.3482 0.816 0.872 0.000 0.128
#> GSM11694 3 0.1585 0.745 0.028 0.008 0.964
#> GSM11695 3 0.1525 0.746 0.032 0.004 0.964
#> GSM11734 2 0.2165 0.870 0.000 0.936 0.064
#> GSM11861 1 0.6705 0.710 0.740 0.084 0.176
#> GSM11843 2 0.3267 0.884 0.000 0.884 0.116
#> GSM11862 1 0.6856 0.682 0.740 0.128 0.132
#> GSM11697 3 0.1774 0.743 0.024 0.016 0.960
#> GSM11714 3 0.4609 0.660 0.028 0.128 0.844
#> GSM11723 3 0.6299 0.187 0.000 0.476 0.524
#> GSM11845 3 0.7850 0.514 0.076 0.316 0.608
#> GSM11683 3 0.6398 0.174 0.008 0.372 0.620
#> GSM11691 3 0.6228 0.168 0.004 0.372 0.624
#> GSM27949 3 0.4504 0.775 0.196 0.000 0.804
#> GSM27945 3 0.4605 0.773 0.204 0.000 0.796
#> GSM11706 1 0.1163 0.879 0.972 0.000 0.028
#> GSM11853 1 0.0747 0.887 0.984 0.000 0.016
#> GSM11729 2 0.1411 0.884 0.000 0.964 0.036
#> GSM11746 2 0.1411 0.884 0.000 0.964 0.036
#> GSM11711 1 0.0747 0.887 0.984 0.000 0.016
#> GSM11854 1 0.0424 0.889 0.992 0.000 0.008
#> GSM11731 2 0.1529 0.883 0.000 0.960 0.040
#> GSM11839 2 0.2116 0.880 0.012 0.948 0.040
#> GSM11836 2 0.6506 0.622 0.236 0.720 0.044
#> GSM11849 1 0.6825 0.138 0.500 0.488 0.012
#> GSM11682 1 0.0000 0.889 1.000 0.000 0.000
#> GSM11690 1 0.0000 0.889 1.000 0.000 0.000
#> GSM11692 1 0.0000 0.889 1.000 0.000 0.000
#> GSM11841 1 0.1647 0.868 0.960 0.004 0.036
#> GSM11901 1 0.1647 0.868 0.960 0.004 0.036
#> GSM11715 2 0.1411 0.884 0.000 0.964 0.036
#> GSM11724 2 0.1411 0.884 0.000 0.964 0.036
#> GSM11684 1 0.5737 0.750 0.804 0.104 0.092
#> GSM11696 1 0.5737 0.750 0.804 0.104 0.092
#> GSM27952 1 0.0000 0.889 1.000 0.000 0.000
#> GSM27948 1 0.0000 0.889 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM11708 3 0.1724 0.7733 0.000 0.020 0.948 0.032
#> GSM11735 3 0.1733 0.7737 0.000 0.024 0.948 0.028
#> GSM11733 3 0.5420 0.5601 0.000 0.044 0.684 0.272
#> GSM11863 3 0.6690 0.5709 0.000 0.188 0.620 0.192
#> GSM11710 4 0.1576 0.8422 0.000 0.004 0.048 0.948
#> GSM11712 4 0.1284 0.8453 0.000 0.024 0.012 0.964
#> GSM11732 3 0.2149 0.7615 0.000 0.088 0.912 0.000
#> GSM11844 3 0.2281 0.7636 0.000 0.096 0.904 0.000
#> GSM11842 3 0.6798 0.3290 0.000 0.396 0.504 0.100
#> GSM11860 3 0.7484 0.2968 0.060 0.392 0.496 0.052
#> GSM11686 4 0.2654 0.8126 0.000 0.004 0.108 0.888
#> GSM11688 4 0.3982 0.6973 0.000 0.004 0.220 0.776
#> GSM11846 4 0.6848 0.1291 0.056 0.020 0.420 0.504
#> GSM11680 3 0.1296 0.7768 0.004 0.004 0.964 0.028
#> GSM11698 3 0.1284 0.7767 0.000 0.012 0.964 0.024
#> GSM11840 3 0.5592 0.5120 0.000 0.044 0.656 0.300
#> GSM11847 3 0.5569 0.5194 0.000 0.044 0.660 0.296
#> GSM11685 4 0.0921 0.8451 0.000 0.000 0.028 0.972
#> GSM11699 4 0.1732 0.8457 0.008 0.004 0.040 0.948
#> GSM27950 3 0.1004 0.7764 0.004 0.000 0.972 0.024
#> GSM27946 4 0.1305 0.8445 0.000 0.004 0.036 0.960
#> GSM11709 1 0.0592 0.8360 0.984 0.016 0.000 0.000
#> GSM11720 1 0.0921 0.8294 0.972 0.028 0.000 0.000
#> GSM11726 1 0.4632 0.4347 0.688 0.308 0.004 0.000
#> GSM11837 2 0.3402 0.8343 0.164 0.832 0.004 0.000
#> GSM11725 2 0.3852 0.8126 0.180 0.808 0.012 0.000
#> GSM11864 2 0.6110 0.6685 0.176 0.680 0.144 0.000
#> GSM11687 1 0.0188 0.8381 0.996 0.004 0.000 0.000
#> GSM11693 1 0.0188 0.8381 0.996 0.004 0.000 0.000
#> GSM11727 2 0.4741 0.6088 0.328 0.668 0.004 0.000
#> GSM11838 2 0.3448 0.8315 0.168 0.828 0.004 0.000
#> GSM11681 1 0.1807 0.7927 0.940 0.008 0.000 0.052
#> GSM11689 1 0.0188 0.8381 0.996 0.004 0.000 0.000
#> GSM11704 1 0.0188 0.8381 0.996 0.004 0.000 0.000
#> GSM11703 1 0.0336 0.8373 0.992 0.008 0.000 0.000
#> GSM11705 1 0.0469 0.8371 0.988 0.012 0.000 0.000
#> GSM11722 2 0.5163 0.2080 0.480 0.516 0.004 0.000
#> GSM11730 1 0.4761 0.3876 0.664 0.332 0.004 0.000
#> GSM11713 1 0.2773 0.7626 0.880 0.116 0.004 0.000
#> GSM11728 1 0.3043 0.7757 0.876 0.112 0.004 0.008
#> GSM27947 4 0.2197 0.8252 0.004 0.000 0.080 0.916
#> GSM27951 1 0.0188 0.8381 0.996 0.004 0.000 0.000
#> GSM11707 3 0.2992 0.7448 0.084 0.016 0.892 0.008
#> GSM11716 3 0.2149 0.7617 0.000 0.088 0.912 0.000
#> GSM11850 3 0.4746 0.4547 0.000 0.368 0.632 0.000
#> GSM11851 3 0.5463 0.5937 0.000 0.052 0.692 0.256
#> GSM11721 4 0.4772 0.7573 0.044 0.152 0.012 0.792
#> GSM11852 4 0.4358 0.7775 0.016 0.036 0.124 0.824
#> GSM11694 3 0.5136 0.6284 0.188 0.056 0.752 0.004
#> GSM11695 3 0.5200 0.6289 0.188 0.052 0.752 0.008
#> GSM11734 2 0.2179 0.8326 0.064 0.924 0.012 0.000
#> GSM11861 4 0.6467 0.6677 0.168 0.144 0.012 0.676
#> GSM11843 2 0.4018 0.7423 0.224 0.772 0.004 0.000
#> GSM11862 4 0.6133 0.6435 0.220 0.100 0.004 0.676
#> GSM11697 3 0.3842 0.7042 0.128 0.036 0.836 0.000
#> GSM11714 3 0.5173 0.4165 0.320 0.020 0.660 0.000
#> GSM11723 2 0.1970 0.7903 0.008 0.932 0.060 0.000
#> GSM11845 2 0.4119 0.6452 0.012 0.796 0.188 0.004
#> GSM11683 1 0.6176 0.1892 0.524 0.052 0.424 0.000
#> GSM11691 1 0.6384 0.2105 0.532 0.068 0.400 0.000
#> GSM27949 3 0.1004 0.7764 0.004 0.000 0.972 0.024
#> GSM27945 3 0.3279 0.7612 0.008 0.024 0.880 0.088
#> GSM11706 4 0.2928 0.8055 0.000 0.012 0.108 0.880
#> GSM11853 4 0.1209 0.8442 0.000 0.004 0.032 0.964
#> GSM11729 2 0.2814 0.8491 0.132 0.868 0.000 0.000
#> GSM11746 2 0.2973 0.8456 0.144 0.856 0.000 0.000
#> GSM11711 4 0.1109 0.8443 0.000 0.004 0.028 0.968
#> GSM11854 4 0.1109 0.8451 0.000 0.004 0.028 0.968
#> GSM11731 2 0.2401 0.8458 0.092 0.904 0.004 0.000
#> GSM11839 2 0.2156 0.8349 0.060 0.928 0.004 0.008
#> GSM11836 2 0.2300 0.8282 0.048 0.924 0.000 0.028
#> GSM11849 4 0.7372 0.0776 0.140 0.400 0.004 0.456
#> GSM11682 4 0.0817 0.8411 0.000 0.024 0.000 0.976
#> GSM11690 4 0.0817 0.8411 0.000 0.024 0.000 0.976
#> GSM11692 4 0.1191 0.8416 0.004 0.024 0.004 0.968
#> GSM11841 4 0.4051 0.7217 0.004 0.208 0.004 0.784
#> GSM11901 4 0.3933 0.7347 0.004 0.196 0.004 0.796
#> GSM11715 2 0.2814 0.8491 0.132 0.868 0.000 0.000
#> GSM11724 2 0.2944 0.8488 0.128 0.868 0.004 0.000
#> GSM11684 4 0.5242 0.6789 0.184 0.064 0.004 0.748
#> GSM11696 4 0.5242 0.6789 0.184 0.064 0.004 0.748
#> GSM27952 4 0.0657 0.8457 0.000 0.004 0.012 0.984
#> GSM27948 4 0.0817 0.8411 0.000 0.024 0.000 0.976
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM11708 5 0.3966 0.3604 0.000 0.000 0.336 0.000 0.664
#> GSM11735 5 0.4074 0.2717 0.000 0.000 0.364 0.000 0.636
#> GSM11733 5 0.2344 0.7266 0.000 0.000 0.064 0.032 0.904
#> GSM11863 5 0.2476 0.7225 0.000 0.012 0.064 0.020 0.904
#> GSM11710 4 0.4327 0.6174 0.000 0.000 0.008 0.632 0.360
#> GSM11712 4 0.3920 0.6810 0.000 0.004 0.004 0.724 0.268
#> GSM11732 3 0.4828 0.5365 0.000 0.056 0.712 0.008 0.224
#> GSM11844 3 0.5002 0.4094 0.000 0.036 0.644 0.008 0.312
#> GSM11842 5 0.3698 0.6676 0.000 0.104 0.052 0.012 0.832
#> GSM11860 5 0.4362 0.6277 0.020 0.136 0.048 0.004 0.792
#> GSM11686 4 0.4907 0.6501 0.000 0.000 0.056 0.664 0.280
#> GSM11688 4 0.5230 0.4076 0.000 0.000 0.044 0.504 0.452
#> GSM11846 5 0.5705 0.1887 0.024 0.000 0.064 0.288 0.624
#> GSM11680 3 0.3877 0.6427 0.000 0.000 0.764 0.024 0.212
#> GSM11698 3 0.3844 0.6576 0.000 0.000 0.792 0.044 0.164
#> GSM11840 5 0.2344 0.7266 0.000 0.000 0.064 0.032 0.904
#> GSM11847 5 0.2344 0.7266 0.000 0.000 0.064 0.032 0.904
#> GSM11685 4 0.4141 0.6979 0.000 0.000 0.028 0.736 0.236
#> GSM11699 4 0.4411 0.7097 0.004 0.000 0.096 0.772 0.128
#> GSM27950 3 0.3999 0.6223 0.000 0.000 0.740 0.020 0.240
#> GSM27946 4 0.3488 0.7163 0.000 0.000 0.024 0.808 0.168
#> GSM11709 1 0.0992 0.8937 0.968 0.024 0.008 0.000 0.000
#> GSM11720 1 0.1205 0.8876 0.956 0.040 0.004 0.000 0.000
#> GSM11726 1 0.4801 0.3459 0.584 0.396 0.012 0.000 0.008
#> GSM11837 2 0.1498 0.8261 0.024 0.952 0.008 0.000 0.016
#> GSM11725 2 0.4166 0.7620 0.148 0.788 0.056 0.000 0.008
#> GSM11864 2 0.6032 0.6499 0.204 0.652 0.100 0.000 0.044
#> GSM11687 1 0.0162 0.8937 0.996 0.000 0.004 0.000 0.000
#> GSM11693 1 0.0162 0.8937 0.996 0.000 0.004 0.000 0.000
#> GSM11727 2 0.2533 0.7796 0.096 0.888 0.008 0.000 0.008
#> GSM11838 2 0.1153 0.8248 0.024 0.964 0.004 0.000 0.008
#> GSM11681 1 0.1059 0.8800 0.968 0.000 0.008 0.020 0.004
#> GSM11689 1 0.0162 0.8937 0.996 0.000 0.004 0.000 0.000
#> GSM11704 1 0.0162 0.8937 0.996 0.000 0.004 0.000 0.000
#> GSM11703 1 0.1728 0.8854 0.940 0.036 0.020 0.000 0.004
#> GSM11705 1 0.1568 0.8866 0.944 0.036 0.020 0.000 0.000
#> GSM11722 2 0.4082 0.5820 0.240 0.740 0.008 0.000 0.012
#> GSM11730 2 0.5236 0.0107 0.432 0.532 0.016 0.000 0.020
#> GSM11713 1 0.5185 0.6955 0.716 0.212 0.028 0.016 0.028
#> GSM11728 1 0.5762 0.7045 0.704 0.180 0.028 0.056 0.032
#> GSM27947 4 0.4965 0.6914 0.040 0.000 0.028 0.716 0.216
#> GSM27951 1 0.0162 0.8937 0.996 0.000 0.004 0.000 0.000
#> GSM11707 3 0.4744 0.0650 0.016 0.000 0.508 0.000 0.476
#> GSM11716 3 0.4042 0.6210 0.000 0.044 0.792 0.008 0.156
#> GSM11850 3 0.3888 0.5935 0.000 0.120 0.804 0.000 0.076
#> GSM11851 5 0.5980 0.2435 0.000 0.004 0.412 0.096 0.488
#> GSM11721 4 0.7226 0.6122 0.060 0.080 0.056 0.600 0.204
#> GSM11852 4 0.6296 0.5954 0.052 0.004 0.056 0.584 0.304
#> GSM11694 3 0.3180 0.6849 0.136 0.004 0.844 0.004 0.012
#> GSM11695 3 0.3087 0.6875 0.128 0.004 0.852 0.004 0.012
#> GSM11734 2 0.3521 0.7678 0.008 0.808 0.172 0.000 0.012
#> GSM11861 4 0.6947 0.4337 0.056 0.028 0.244 0.592 0.080
#> GSM11843 2 0.5129 0.6922 0.180 0.724 0.068 0.000 0.028
#> GSM11862 4 0.7331 0.4204 0.200 0.036 0.100 0.588 0.076
#> GSM11697 3 0.2569 0.6970 0.068 0.000 0.896 0.004 0.032
#> GSM11714 3 0.4910 0.6190 0.208 0.036 0.724 0.000 0.032
#> GSM11723 2 0.4665 0.6593 0.000 0.692 0.260 0.000 0.048
#> GSM11845 2 0.5599 0.5062 0.000 0.580 0.328 0.000 0.092
#> GSM11683 3 0.5632 0.5519 0.260 0.040 0.660 0.012 0.028
#> GSM11691 3 0.5561 0.5505 0.260 0.036 0.664 0.012 0.028
#> GSM27949 3 0.4223 0.6122 0.000 0.000 0.724 0.028 0.248
#> GSM27945 3 0.4126 0.6390 0.004 0.000 0.796 0.096 0.104
#> GSM11706 4 0.4743 0.4210 0.000 0.000 0.016 0.512 0.472
#> GSM11853 4 0.4003 0.6817 0.000 0.000 0.008 0.704 0.288
#> GSM11729 2 0.0798 0.8273 0.016 0.976 0.000 0.000 0.008
#> GSM11746 2 0.0898 0.8277 0.020 0.972 0.000 0.000 0.008
#> GSM11711 4 0.4016 0.6847 0.000 0.000 0.012 0.716 0.272
#> GSM11854 4 0.3980 0.6847 0.000 0.000 0.008 0.708 0.284
#> GSM11731 2 0.2152 0.8191 0.032 0.924 0.032 0.000 0.012
#> GSM11839 2 0.2807 0.8141 0.028 0.900 0.040 0.024 0.008
#> GSM11836 2 0.1616 0.8223 0.008 0.948 0.008 0.032 0.004
#> GSM11849 4 0.5431 0.0541 0.032 0.444 0.004 0.512 0.008
#> GSM11682 4 0.0889 0.6994 0.004 0.004 0.004 0.976 0.012
#> GSM11690 4 0.0613 0.6995 0.000 0.004 0.004 0.984 0.008
#> GSM11692 4 0.2488 0.6810 0.000 0.004 0.000 0.872 0.124
#> GSM11841 4 0.3694 0.6286 0.000 0.032 0.000 0.796 0.172
#> GSM11901 4 0.3612 0.6306 0.000 0.028 0.000 0.800 0.172
#> GSM11715 2 0.0510 0.8264 0.016 0.984 0.000 0.000 0.000
#> GSM11724 2 0.0693 0.8253 0.012 0.980 0.000 0.000 0.008
#> GSM11684 4 0.4345 0.6296 0.040 0.076 0.016 0.820 0.048
#> GSM11696 4 0.4419 0.6270 0.044 0.076 0.016 0.816 0.048
#> GSM27952 4 0.3690 0.7019 0.000 0.000 0.012 0.764 0.224
#> GSM27948 4 0.1285 0.7071 0.000 0.004 0.004 0.956 0.036
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM11708 5 0.4405 0.58194 0.000 0.000 0.240 0.000 0.688 0.072
#> GSM11735 5 0.3487 0.62703 0.000 0.000 0.224 0.000 0.756 0.020
#> GSM11733 5 0.1151 0.81499 0.000 0.000 0.012 0.000 0.956 0.032
#> GSM11863 5 0.0964 0.80876 0.000 0.004 0.012 0.000 0.968 0.016
#> GSM11710 6 0.2748 0.56863 0.000 0.000 0.000 0.024 0.128 0.848
#> GSM11712 6 0.4203 0.48901 0.000 0.000 0.000 0.124 0.136 0.740
#> GSM11732 3 0.5912 0.39465 0.000 0.056 0.580 0.100 0.264 0.000
#> GSM11844 3 0.6241 0.26610 0.000 0.052 0.504 0.100 0.340 0.004
#> GSM11842 5 0.1003 0.79628 0.000 0.028 0.004 0.000 0.964 0.004
#> GSM11860 5 0.2055 0.78709 0.012 0.036 0.004 0.004 0.924 0.020
#> GSM11686 6 0.3716 0.55894 0.000 0.000 0.044 0.044 0.096 0.816
#> GSM11688 6 0.4748 0.44443 0.000 0.000 0.040 0.036 0.240 0.684
#> GSM11846 6 0.6021 0.28752 0.036 0.000 0.048 0.036 0.328 0.552
#> GSM11680 3 0.3694 0.58254 0.000 0.000 0.788 0.008 0.156 0.048
#> GSM11698 3 0.4225 0.59295 0.000 0.000 0.764 0.016 0.116 0.104
#> GSM11840 5 0.1151 0.81499 0.000 0.000 0.012 0.000 0.956 0.032
#> GSM11847 5 0.1151 0.81499 0.000 0.000 0.012 0.000 0.956 0.032
#> GSM11685 6 0.2688 0.59216 0.000 0.000 0.024 0.044 0.048 0.884
#> GSM11699 6 0.5149 0.37084 0.000 0.000 0.120 0.184 0.024 0.672
#> GSM27950 3 0.4267 0.52331 0.000 0.000 0.728 0.012 0.208 0.052
#> GSM27946 6 0.4116 0.54867 0.000 0.000 0.036 0.140 0.048 0.776
#> GSM11709 1 0.1852 0.84268 0.928 0.024 0.004 0.040 0.004 0.000
#> GSM11720 1 0.2321 0.83245 0.900 0.052 0.008 0.040 0.000 0.000
#> GSM11726 2 0.5417 -0.00763 0.436 0.488 0.016 0.052 0.008 0.000
#> GSM11837 2 0.1578 0.71162 0.012 0.944 0.012 0.028 0.004 0.000
#> GSM11725 2 0.4372 0.63001 0.184 0.744 0.036 0.032 0.004 0.000
#> GSM11864 2 0.6061 0.48151 0.284 0.580 0.068 0.036 0.032 0.000
#> GSM11687 1 0.0000 0.85436 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11693 1 0.0000 0.85436 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11727 2 0.3327 0.67973 0.060 0.844 0.016 0.076 0.004 0.000
#> GSM11838 2 0.1801 0.70965 0.012 0.932 0.012 0.040 0.004 0.000
#> GSM11681 1 0.0520 0.84431 0.984 0.000 0.008 0.000 0.000 0.008
#> GSM11689 1 0.0000 0.85436 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11704 1 0.0000 0.85436 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11703 1 0.2637 0.82015 0.872 0.024 0.008 0.096 0.000 0.000
#> GSM11705 1 0.2666 0.82126 0.872 0.028 0.008 0.092 0.000 0.000
#> GSM11722 2 0.4794 0.58061 0.152 0.716 0.016 0.112 0.004 0.000
#> GSM11730 2 0.6300 0.25576 0.276 0.512 0.016 0.184 0.012 0.000
#> GSM11713 1 0.6750 0.24526 0.408 0.268 0.020 0.292 0.012 0.000
#> GSM11728 1 0.6928 0.31027 0.420 0.188 0.024 0.344 0.012 0.012
#> GSM27947 6 0.5394 0.52515 0.048 0.000 0.040 0.132 0.068 0.712
#> GSM27951 1 0.0000 0.85436 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11707 5 0.6015 0.16858 0.004 0.000 0.392 0.056 0.484 0.064
#> GSM11716 3 0.5419 0.50698 0.000 0.080 0.680 0.104 0.136 0.000
#> GSM11850 3 0.5657 0.49805 0.000 0.104 0.660 0.124 0.112 0.000
#> GSM11851 3 0.7222 0.20568 0.000 0.004 0.444 0.112 0.224 0.216
#> GSM11721 6 0.5945 0.17808 0.016 0.024 0.012 0.308 0.064 0.576
#> GSM11852 6 0.5512 0.26302 0.016 0.000 0.020 0.276 0.072 0.616
#> GSM11694 3 0.3194 0.63551 0.104 0.000 0.840 0.044 0.012 0.000
#> GSM11695 3 0.3058 0.63683 0.104 0.000 0.848 0.036 0.012 0.000
#> GSM11734 2 0.4435 0.62746 0.008 0.748 0.140 0.096 0.008 0.000
#> GSM11861 4 0.6658 0.40854 0.008 0.008 0.176 0.516 0.036 0.256
#> GSM11843 2 0.5418 0.58632 0.068 0.668 0.024 0.212 0.028 0.000
#> GSM11862 4 0.6376 0.43704 0.056 0.012 0.036 0.588 0.048 0.260
#> GSM11697 3 0.2706 0.64119 0.028 0.000 0.880 0.068 0.024 0.000
#> GSM11714 3 0.6735 0.51186 0.096 0.024 0.600 0.192 0.060 0.028
#> GSM11723 2 0.6265 0.29732 0.000 0.492 0.316 0.156 0.036 0.000
#> GSM11845 2 0.6758 0.10216 0.000 0.392 0.380 0.160 0.068 0.000
#> GSM11683 3 0.5931 0.45765 0.104 0.028 0.576 0.280 0.012 0.000
#> GSM11691 3 0.5612 0.46714 0.096 0.012 0.584 0.296 0.012 0.000
#> GSM27949 3 0.4485 0.52160 0.000 0.000 0.716 0.012 0.200 0.072
#> GSM27945 3 0.3746 0.61077 0.004 0.000 0.812 0.020 0.056 0.108
#> GSM11706 6 0.3673 0.47449 0.000 0.000 0.016 0.004 0.244 0.736
#> GSM11853 6 0.1838 0.59327 0.000 0.000 0.000 0.016 0.068 0.916
#> GSM11729 2 0.0748 0.71249 0.004 0.976 0.000 0.016 0.004 0.000
#> GSM11746 2 0.0717 0.71424 0.016 0.976 0.000 0.008 0.000 0.000
#> GSM11711 6 0.1745 0.59116 0.000 0.000 0.000 0.012 0.068 0.920
#> GSM11854 6 0.1926 0.59255 0.000 0.000 0.000 0.020 0.068 0.912
#> GSM11731 2 0.2757 0.68227 0.008 0.848 0.004 0.136 0.004 0.000
#> GSM11839 2 0.3530 0.65827 0.008 0.776 0.012 0.200 0.000 0.004
#> GSM11836 2 0.2473 0.69622 0.000 0.876 0.012 0.104 0.000 0.008
#> GSM11849 2 0.6015 -0.15431 0.012 0.444 0.000 0.380 0.000 0.164
#> GSM11682 6 0.3955 0.27330 0.004 0.000 0.008 0.340 0.000 0.648
#> GSM11690 6 0.4022 0.24694 0.004 0.000 0.000 0.360 0.008 0.628
#> GSM11692 6 0.5067 0.21435 0.000 0.004 0.000 0.312 0.088 0.596
#> GSM11841 6 0.5882 0.06121 0.000 0.012 0.000 0.328 0.156 0.504
#> GSM11901 6 0.5838 0.06484 0.000 0.012 0.000 0.332 0.148 0.508
#> GSM11715 2 0.1555 0.70974 0.004 0.932 0.000 0.060 0.004 0.000
#> GSM11724 2 0.1588 0.70613 0.004 0.924 0.000 0.072 0.000 0.000
#> GSM11684 4 0.4946 0.50539 0.008 0.048 0.004 0.624 0.004 0.312
#> GSM11696 4 0.4946 0.50539 0.008 0.048 0.004 0.624 0.004 0.312
#> GSM27952 6 0.2683 0.58611 0.000 0.000 0.012 0.056 0.052 0.880
#> GSM27948 6 0.3670 0.35537 0.000 0.000 0.000 0.284 0.012 0.704
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 cell.line(p) agent(p) time(p) k
#> CV:skmeans 76 1.87e-08 0.1268 2.28e-02 2
#> CV:skmeans 79 1.02e-12 0.7205 1.48e-05 3
#> CV:skmeans 72 2.95e-12 0.7097 1.46e-07 4
#> CV:skmeans 70 1.28e-14 0.5543 1.48e-09 5
#> CV:skmeans 53 1.11e-11 0.0832 1.28e-06 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 14502 rows and 83 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 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 0.438 0.784 0.878 0.3445 0.670 0.670
#> 3 3 0.246 0.470 0.747 0.6893 0.718 0.591
#> 4 4 0.374 0.567 0.731 0.1690 0.804 0.591
#> 5 5 0.615 0.657 0.803 0.1206 0.791 0.458
#> 6 6 0.672 0.564 0.773 0.0593 0.864 0.503
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
#> GSM11708 1 0.0000 0.8533 1.000 0.000
#> GSM11735 1 0.0000 0.8533 1.000 0.000
#> GSM11733 1 0.0000 0.8533 1.000 0.000
#> GSM11863 1 0.2423 0.8562 0.960 0.040
#> GSM11710 1 0.1414 0.8551 0.980 0.020
#> GSM11712 1 0.2423 0.8562 0.960 0.040
#> GSM11732 1 0.2603 0.8563 0.956 0.044
#> GSM11844 1 0.2043 0.8565 0.968 0.032
#> GSM11842 1 0.2603 0.8563 0.956 0.044
#> GSM11860 1 0.2603 0.8563 0.956 0.044
#> GSM11686 1 0.0000 0.8533 1.000 0.000
#> GSM11688 1 0.0000 0.8533 1.000 0.000
#> GSM11846 1 0.0000 0.8533 1.000 0.000
#> GSM11680 1 0.2423 0.8562 0.960 0.040
#> GSM11698 1 0.0000 0.8533 1.000 0.000
#> GSM11840 1 0.1184 0.8556 0.984 0.016
#> GSM11847 1 0.2423 0.8562 0.960 0.040
#> GSM11685 1 0.0000 0.8533 1.000 0.000
#> GSM11699 1 0.5842 0.8230 0.860 0.140
#> GSM27950 1 0.1633 0.8558 0.976 0.024
#> GSM27946 1 0.2423 0.8562 0.960 0.040
#> GSM11709 1 0.7376 0.7837 0.792 0.208
#> GSM11720 1 0.8386 0.7105 0.732 0.268
#> GSM11726 1 0.7745 0.7854 0.772 0.228
#> GSM11837 2 0.9087 0.4911 0.324 0.676
#> GSM11725 2 0.9522 0.3685 0.372 0.628
#> GSM11864 1 0.7883 0.7917 0.764 0.236
#> GSM11687 1 0.8081 0.7816 0.752 0.248
#> GSM11693 1 0.7883 0.7917 0.764 0.236
#> GSM11727 2 0.7950 0.6425 0.240 0.760
#> GSM11838 2 0.0000 0.7993 0.000 1.000
#> GSM11681 1 0.7883 0.7917 0.764 0.236
#> GSM11689 1 0.7883 0.7917 0.764 0.236
#> GSM11704 1 0.7883 0.7917 0.764 0.236
#> GSM11703 1 0.7453 0.7844 0.788 0.212
#> GSM11705 1 0.7376 0.7837 0.792 0.208
#> GSM11722 2 0.0000 0.7993 0.000 1.000
#> GSM11730 2 0.7745 0.6586 0.228 0.772
#> GSM11713 2 0.2423 0.7849 0.040 0.960
#> GSM11728 1 0.7745 0.7852 0.772 0.228
#> GSM27947 1 0.2603 0.8563 0.956 0.044
#> GSM27951 1 0.8081 0.7816 0.752 0.248
#> GSM11707 1 0.7376 0.7837 0.792 0.208
#> GSM11716 1 0.2948 0.8575 0.948 0.052
#> GSM11850 1 0.6623 0.8081 0.828 0.172
#> GSM11851 1 0.0000 0.8533 1.000 0.000
#> GSM11721 1 0.7139 0.7918 0.804 0.196
#> GSM11852 1 0.4815 0.8371 0.896 0.104
#> GSM11694 1 0.7883 0.7917 0.764 0.236
#> GSM11695 1 0.7883 0.7917 0.764 0.236
#> GSM11734 2 0.9998 0.0356 0.492 0.508
#> GSM11861 1 0.6973 0.7991 0.812 0.188
#> GSM11843 1 0.8081 0.7816 0.752 0.248
#> GSM11862 1 0.7745 0.7939 0.772 0.228
#> GSM11697 1 0.8016 0.7853 0.756 0.244
#> GSM11714 1 0.7376 0.7837 0.792 0.208
#> GSM11723 2 0.6887 0.6769 0.184 0.816
#> GSM11845 1 0.2778 0.8567 0.952 0.048
#> GSM11683 1 0.8016 0.7830 0.756 0.244
#> GSM11691 1 0.8081 0.7816 0.752 0.248
#> GSM27949 1 0.0000 0.8533 1.000 0.000
#> GSM27945 1 0.2423 0.8562 0.960 0.040
#> GSM11706 1 0.0000 0.8533 1.000 0.000
#> GSM11853 1 0.0000 0.8533 1.000 0.000
#> GSM11729 2 0.0376 0.7992 0.004 0.996
#> GSM11746 2 0.4815 0.7817 0.104 0.896
#> GSM11711 1 0.0000 0.8533 1.000 0.000
#> GSM11854 1 0.0000 0.8533 1.000 0.000
#> GSM11731 2 0.0672 0.7994 0.008 0.992
#> GSM11839 1 0.8713 0.7229 0.708 0.292
#> GSM11836 1 0.9129 0.3305 0.672 0.328
#> GSM11849 2 0.9896 0.2970 0.440 0.560
#> GSM11682 1 0.0000 0.8533 1.000 0.000
#> GSM11690 1 0.2423 0.8562 0.960 0.040
#> GSM11692 1 0.2423 0.8562 0.960 0.040
#> GSM11841 1 0.2423 0.8562 0.960 0.040
#> GSM11901 1 0.2423 0.8562 0.960 0.040
#> GSM11715 2 0.0000 0.7993 0.000 1.000
#> GSM11724 2 0.0000 0.7993 0.000 1.000
#> GSM11684 2 0.5946 0.7690 0.144 0.856
#> GSM11696 2 0.4690 0.7805 0.100 0.900
#> GSM27952 1 0.0000 0.8533 1.000 0.000
#> GSM27948 1 0.2423 0.8562 0.960 0.040
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM11708 1 0.5678 0.2813 0.684 0.000 0.316
#> GSM11735 1 0.4452 0.4645 0.808 0.000 0.192
#> GSM11733 3 0.5926 0.4956 0.356 0.000 0.644
#> GSM11863 3 0.3752 0.5788 0.144 0.000 0.856
#> GSM11710 3 0.5894 0.5633 0.220 0.028 0.752
#> GSM11712 3 0.0000 0.6266 0.000 0.000 1.000
#> GSM11732 3 0.6483 -0.3705 0.452 0.004 0.544
#> GSM11844 3 0.3619 0.5597 0.136 0.000 0.864
#> GSM11842 3 0.3752 0.5788 0.144 0.000 0.856
#> GSM11860 3 0.3816 0.5797 0.148 0.000 0.852
#> GSM11686 3 0.4750 0.5694 0.216 0.000 0.784
#> GSM11688 3 0.4750 0.5694 0.216 0.000 0.784
#> GSM11846 3 0.4750 0.5694 0.216 0.000 0.784
#> GSM11680 3 0.4931 0.3237 0.212 0.004 0.784
#> GSM11698 1 0.5810 0.4550 0.664 0.000 0.336
#> GSM11840 3 0.4291 0.5825 0.180 0.000 0.820
#> GSM11847 3 0.3752 0.5788 0.144 0.000 0.856
#> GSM11685 3 0.4750 0.5694 0.216 0.000 0.784
#> GSM11699 1 0.5378 0.5540 0.756 0.008 0.236
#> GSM27950 1 0.5650 0.4837 0.688 0.000 0.312
#> GSM27946 3 0.0000 0.6266 0.000 0.000 1.000
#> GSM11709 3 0.8355 0.3619 0.408 0.084 0.508
#> GSM11720 1 0.9512 0.1751 0.492 0.260 0.248
#> GSM11726 3 0.8868 0.3826 0.228 0.196 0.576
#> GSM11837 2 0.5291 0.5442 0.000 0.732 0.268
#> GSM11725 2 0.9305 0.3156 0.188 0.504 0.308
#> GSM11864 3 0.6858 0.4668 0.188 0.084 0.728
#> GSM11687 3 0.6906 0.4623 0.192 0.084 0.724
#> GSM11693 3 0.6808 0.4713 0.184 0.084 0.732
#> GSM11727 2 0.5115 0.5874 0.004 0.768 0.228
#> GSM11838 2 0.0000 0.6946 0.000 1.000 0.000
#> GSM11681 3 0.6808 0.4713 0.184 0.084 0.732
#> GSM11689 3 0.6808 0.4713 0.184 0.084 0.732
#> GSM11704 3 0.6808 0.4713 0.184 0.084 0.732
#> GSM11703 1 0.6252 0.5583 0.772 0.084 0.144
#> GSM11705 1 0.8363 -0.1982 0.504 0.084 0.412
#> GSM11722 2 0.0237 0.6952 0.004 0.996 0.000
#> GSM11730 2 0.8972 0.3213 0.236 0.564 0.200
#> GSM11713 2 0.0237 0.6952 0.004 0.996 0.000
#> GSM11728 3 0.6431 0.5258 0.156 0.084 0.760
#> GSM27947 3 0.0424 0.6249 0.000 0.008 0.992
#> GSM27951 3 0.6906 0.4623 0.192 0.084 0.724
#> GSM11707 1 0.4921 0.5580 0.844 0.084 0.072
#> GSM11716 3 0.7049 -0.3905 0.452 0.020 0.528
#> GSM11850 1 0.6239 0.5878 0.768 0.072 0.160
#> GSM11851 3 0.5016 0.5512 0.240 0.000 0.760
#> GSM11721 3 0.7940 0.4468 0.332 0.076 0.592
#> GSM11852 3 0.7400 0.5174 0.264 0.072 0.664
#> GSM11694 1 0.8064 0.5359 0.588 0.084 0.328
#> GSM11695 1 0.8179 0.5382 0.564 0.084 0.352
#> GSM11734 3 0.9955 -0.2851 0.304 0.316 0.380
#> GSM11861 3 0.7842 0.4604 0.328 0.072 0.600
#> GSM11843 1 0.7788 0.4986 0.632 0.084 0.284
#> GSM11862 3 0.6313 0.5188 0.148 0.084 0.768
#> GSM11697 1 0.8162 0.5402 0.568 0.084 0.348
#> GSM11714 1 0.4830 0.5548 0.848 0.084 0.068
#> GSM11723 2 0.4233 0.6042 0.004 0.836 0.160
#> GSM11845 3 0.6925 -0.3817 0.452 0.016 0.532
#> GSM11683 1 0.7697 0.5192 0.644 0.084 0.272
#> GSM11691 1 0.7758 0.5042 0.636 0.084 0.280
#> GSM27949 1 0.5810 0.4538 0.664 0.000 0.336
#> GSM27945 3 0.0829 0.6212 0.012 0.004 0.984
#> GSM11706 3 0.4750 0.5694 0.216 0.000 0.784
#> GSM11853 3 0.4750 0.5694 0.216 0.000 0.784
#> GSM11729 2 0.3607 0.7009 0.112 0.880 0.008
#> GSM11746 2 0.7756 0.5127 0.128 0.672 0.200
#> GSM11711 3 0.4750 0.5694 0.216 0.000 0.784
#> GSM11854 3 0.4750 0.5694 0.216 0.000 0.784
#> GSM11731 2 0.2165 0.7069 0.064 0.936 0.000
#> GSM11839 3 0.7160 0.4571 0.148 0.132 0.720
#> GSM11836 3 0.4887 0.4586 0.000 0.228 0.772
#> GSM11849 2 0.9888 0.0407 0.328 0.400 0.272
#> GSM11682 3 0.4750 0.5694 0.216 0.000 0.784
#> GSM11690 3 0.0000 0.6266 0.000 0.000 1.000
#> GSM11692 3 0.0000 0.6266 0.000 0.000 1.000
#> GSM11841 3 0.0000 0.6266 0.000 0.000 1.000
#> GSM11901 3 0.0000 0.6266 0.000 0.000 1.000
#> GSM11715 2 0.3192 0.6997 0.112 0.888 0.000
#> GSM11724 2 0.3425 0.7008 0.112 0.884 0.004
#> GSM11684 2 0.7731 0.5254 0.228 0.664 0.108
#> GSM11696 1 0.7913 -0.0600 0.492 0.452 0.056
#> GSM27952 3 0.4750 0.5694 0.216 0.000 0.784
#> GSM27948 3 0.0000 0.6266 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM11708 4 0.4322 0.8542 0.152 0.000 0.044 0.804
#> GSM11735 4 0.3486 0.7055 0.000 0.000 0.188 0.812
#> GSM11733 4 0.3486 0.8839 0.188 0.000 0.000 0.812
#> GSM11863 4 0.4336 0.7936 0.060 0.128 0.000 0.812
#> GSM11710 1 0.2469 0.6630 0.892 0.000 0.108 0.000
#> GSM11712 1 0.4336 0.6534 0.812 0.128 0.060 0.000
#> GSM11732 3 0.5522 0.5731 0.288 0.000 0.668 0.044
#> GSM11844 1 0.3895 0.6010 0.832 0.000 0.132 0.036
#> GSM11842 4 0.4336 0.7936 0.060 0.128 0.000 0.812
#> GSM11860 4 0.3486 0.8839 0.188 0.000 0.000 0.812
#> GSM11686 1 0.0000 0.6780 1.000 0.000 0.000 0.000
#> GSM11688 1 0.0000 0.6780 1.000 0.000 0.000 0.000
#> GSM11846 1 0.0188 0.6775 0.996 0.000 0.004 0.000
#> GSM11680 1 0.4888 0.1619 0.588 0.000 0.412 0.000
#> GSM11698 3 0.5000 0.4226 0.496 0.000 0.504 0.000
#> GSM11840 4 0.3486 0.8839 0.188 0.000 0.000 0.812
#> GSM11847 4 0.3486 0.8839 0.188 0.000 0.000 0.812
#> GSM11685 1 0.1792 0.6743 0.932 0.068 0.000 0.000
#> GSM11699 3 0.4972 0.4657 0.456 0.000 0.544 0.000
#> GSM27950 3 0.4746 0.5492 0.368 0.000 0.632 0.000
#> GSM27946 1 0.1637 0.6777 0.940 0.000 0.060 0.000
#> GSM11709 1 0.7374 0.4163 0.504 0.000 0.308 0.188
#> GSM11720 3 0.9565 -0.0196 0.280 0.160 0.380 0.180
#> GSM11726 1 0.7663 0.4681 0.584 0.168 0.212 0.036
#> GSM11837 2 0.5244 0.6710 0.084 0.796 0.056 0.064
#> GSM11725 3 0.9232 -0.3402 0.100 0.356 0.356 0.188
#> GSM11864 1 0.7509 0.4223 0.452 0.000 0.360 0.188
#> GSM11687 1 0.7521 0.4139 0.444 0.000 0.368 0.188
#> GSM11693 1 0.7509 0.4223 0.452 0.000 0.360 0.188
#> GSM11727 2 0.5962 0.6725 0.040 0.740 0.076 0.144
#> GSM11838 2 0.2760 0.7049 0.000 0.872 0.000 0.128
#> GSM11681 1 0.7502 0.4250 0.456 0.000 0.356 0.188
#> GSM11689 1 0.7509 0.4223 0.452 0.000 0.360 0.188
#> GSM11704 1 0.7509 0.4223 0.452 0.000 0.360 0.188
#> GSM11703 3 0.4206 0.4761 0.048 0.000 0.816 0.136
#> GSM11705 1 0.6111 0.3762 0.556 0.000 0.392 0.052
#> GSM11722 2 0.3335 0.7111 0.000 0.856 0.016 0.128
#> GSM11730 2 0.7963 0.2698 0.016 0.440 0.364 0.180
#> GSM11713 2 0.3217 0.7069 0.000 0.860 0.012 0.128
#> GSM11728 1 0.4134 0.6126 0.740 0.000 0.260 0.000
#> GSM27947 1 0.1792 0.6785 0.932 0.000 0.068 0.000
#> GSM27951 1 0.7521 0.4139 0.444 0.000 0.368 0.188
#> GSM11707 3 0.3764 0.5529 0.216 0.000 0.784 0.000
#> GSM11716 3 0.3942 0.6116 0.236 0.000 0.764 0.000
#> GSM11850 3 0.3400 0.6286 0.180 0.000 0.820 0.000
#> GSM11851 1 0.2596 0.6476 0.908 0.000 0.068 0.024
#> GSM11721 1 0.6075 0.5862 0.680 0.128 0.192 0.000
#> GSM11852 1 0.3400 0.6226 0.820 0.000 0.180 0.000
#> GSM11694 3 0.1940 0.6302 0.076 0.000 0.924 0.000
#> GSM11695 3 0.2408 0.6365 0.104 0.000 0.896 0.000
#> GSM11734 3 0.9913 -0.1464 0.252 0.272 0.288 0.188
#> GSM11861 1 0.3311 0.6395 0.828 0.000 0.172 0.000
#> GSM11843 3 0.2032 0.5613 0.036 0.000 0.936 0.028
#> GSM11862 1 0.4193 0.6082 0.732 0.000 0.268 0.000
#> GSM11697 3 0.2408 0.6368 0.104 0.000 0.896 0.000
#> GSM11714 3 0.2011 0.5980 0.080 0.000 0.920 0.000
#> GSM11723 2 0.5784 0.6070 0.100 0.700 0.200 0.000
#> GSM11845 3 0.5592 0.5779 0.264 0.056 0.680 0.000
#> GSM11683 3 0.1118 0.6079 0.036 0.000 0.964 0.000
#> GSM11691 3 0.0707 0.5962 0.020 0.000 0.980 0.000
#> GSM27949 3 0.4746 0.5492 0.368 0.000 0.632 0.000
#> GSM27945 1 0.3688 0.6002 0.792 0.000 0.208 0.000
#> GSM11706 1 0.0000 0.6780 1.000 0.000 0.000 0.000
#> GSM11853 1 0.0000 0.6780 1.000 0.000 0.000 0.000
#> GSM11729 2 0.3498 0.7071 0.008 0.832 0.160 0.000
#> GSM11746 2 0.8752 0.4808 0.204 0.516 0.160 0.120
#> GSM11711 1 0.0188 0.6780 0.996 0.000 0.004 0.000
#> GSM11854 1 0.0000 0.6780 1.000 0.000 0.000 0.000
#> GSM11731 2 0.2216 0.7219 0.000 0.908 0.092 0.000
#> GSM11839 1 0.7566 0.4873 0.508 0.172 0.312 0.008
#> GSM11836 1 0.5865 0.4426 0.612 0.340 0.048 0.000
#> GSM11849 1 0.7310 0.0158 0.480 0.360 0.160 0.000
#> GSM11682 1 0.0000 0.6780 1.000 0.000 0.000 0.000
#> GSM11690 1 0.4336 0.6534 0.812 0.128 0.060 0.000
#> GSM11692 1 0.4336 0.6534 0.812 0.128 0.060 0.000
#> GSM11841 1 0.4518 0.6521 0.808 0.128 0.060 0.004
#> GSM11901 1 0.4336 0.6534 0.812 0.128 0.060 0.000
#> GSM11715 2 0.3266 0.7063 0.000 0.832 0.168 0.000
#> GSM11724 2 0.3402 0.7073 0.004 0.832 0.164 0.000
#> GSM11684 2 0.6089 0.5006 0.080 0.640 0.280 0.000
#> GSM11696 3 0.5290 0.1277 0.012 0.404 0.584 0.000
#> GSM27952 1 0.0000 0.6780 1.000 0.000 0.000 0.000
#> GSM27948 1 0.4336 0.6534 0.812 0.128 0.060 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM11708 5 0.2020 0.8536 0.000 0.000 0.000 0.100 0.900
#> GSM11735 5 0.1965 0.7746 0.000 0.000 0.096 0.000 0.904
#> GSM11733 5 0.1965 0.8566 0.000 0.000 0.000 0.096 0.904
#> GSM11863 5 0.0000 0.7947 0.000 0.000 0.000 0.000 1.000
#> GSM11710 4 0.2127 0.7445 0.108 0.000 0.000 0.892 0.000
#> GSM11712 4 0.3340 0.7309 0.000 0.044 0.008 0.852 0.096
#> GSM11732 3 0.3548 0.7046 0.012 0.000 0.796 0.188 0.004
#> GSM11844 4 0.6147 0.3322 0.004 0.000 0.188 0.580 0.228
#> GSM11842 5 0.0000 0.7947 0.000 0.000 0.000 0.000 1.000
#> GSM11860 5 0.1965 0.8566 0.000 0.000 0.000 0.096 0.904
#> GSM11686 4 0.0000 0.7889 0.000 0.000 0.000 1.000 0.000
#> GSM11688 4 0.0000 0.7889 0.000 0.000 0.000 1.000 0.000
#> GSM11846 4 0.0510 0.7871 0.016 0.000 0.000 0.984 0.000
#> GSM11680 3 0.3949 0.6090 0.004 0.000 0.696 0.300 0.000
#> GSM11698 4 0.4066 0.3763 0.004 0.000 0.324 0.672 0.000
#> GSM11840 5 0.1965 0.8566 0.000 0.000 0.000 0.096 0.904
#> GSM11847 5 0.1965 0.8566 0.000 0.000 0.000 0.096 0.904
#> GSM11685 4 0.1943 0.7671 0.000 0.020 0.000 0.924 0.056
#> GSM11699 4 0.5156 0.3190 0.060 0.000 0.320 0.620 0.000
#> GSM27950 3 0.3177 0.6974 0.000 0.000 0.792 0.208 0.000
#> GSM27946 4 0.0290 0.7877 0.000 0.000 0.008 0.992 0.000
#> GSM11709 1 0.0771 0.7924 0.976 0.020 0.000 0.004 0.000
#> GSM11720 1 0.5312 0.3680 0.628 0.056 0.008 0.308 0.000
#> GSM11726 4 0.7295 0.2490 0.244 0.056 0.200 0.500 0.000
#> GSM11837 2 0.4829 0.7267 0.068 0.724 0.200 0.008 0.000
#> GSM11725 1 0.0566 0.8002 0.984 0.012 0.000 0.004 0.000
#> GSM11864 1 0.1168 0.8227 0.960 0.000 0.008 0.032 0.000
#> GSM11687 1 0.1168 0.8227 0.960 0.000 0.008 0.032 0.000
#> GSM11693 1 0.1168 0.8227 0.960 0.000 0.008 0.032 0.000
#> GSM11727 2 0.5958 0.5926 0.204 0.592 0.204 0.000 0.000
#> GSM11838 2 0.5490 0.6721 0.148 0.652 0.200 0.000 0.000
#> GSM11681 1 0.1251 0.8201 0.956 0.000 0.008 0.036 0.000
#> GSM11689 1 0.1168 0.8227 0.960 0.000 0.008 0.032 0.000
#> GSM11704 1 0.1168 0.8227 0.960 0.000 0.008 0.032 0.000
#> GSM11703 1 0.6763 -0.1089 0.396 0.000 0.324 0.280 0.000
#> GSM11705 4 0.4666 0.2721 0.412 0.000 0.016 0.572 0.000
#> GSM11722 2 0.1121 0.7792 0.044 0.956 0.000 0.000 0.000
#> GSM11730 1 0.5354 0.4305 0.664 0.128 0.208 0.000 0.000
#> GSM11713 2 0.4237 0.7381 0.048 0.752 0.200 0.000 0.000
#> GSM11728 4 0.4455 0.6139 0.216 0.012 0.032 0.740 0.000
#> GSM27947 4 0.0693 0.7874 0.012 0.000 0.008 0.980 0.000
#> GSM27951 1 0.1168 0.8227 0.960 0.000 0.008 0.032 0.000
#> GSM11707 3 0.6554 0.1650 0.200 0.000 0.408 0.392 0.000
#> GSM11716 3 0.3906 0.7249 0.068 0.000 0.800 0.132 0.000
#> GSM11850 3 0.3462 0.7244 0.196 0.000 0.792 0.012 0.000
#> GSM11851 4 0.2411 0.7343 0.008 0.000 0.108 0.884 0.000
#> GSM11721 4 0.5956 0.5879 0.200 0.044 0.000 0.660 0.096
#> GSM11852 4 0.3003 0.6661 0.188 0.000 0.000 0.812 0.000
#> GSM11694 3 0.3109 0.7240 0.200 0.000 0.800 0.000 0.000
#> GSM11695 3 0.3109 0.7240 0.200 0.000 0.800 0.000 0.000
#> GSM11734 1 0.5120 0.5524 0.716 0.064 0.024 0.196 0.000
#> GSM11861 4 0.3039 0.6755 0.192 0.000 0.000 0.808 0.000
#> GSM11843 3 0.4341 0.4348 0.404 0.000 0.592 0.004 0.000
#> GSM11862 4 0.3700 0.6091 0.240 0.000 0.008 0.752 0.000
#> GSM11697 3 0.3109 0.7240 0.200 0.000 0.800 0.000 0.000
#> GSM11714 3 0.3388 0.7221 0.200 0.000 0.792 0.008 0.000
#> GSM11723 2 0.2463 0.7525 0.004 0.888 0.100 0.008 0.000
#> GSM11845 3 0.5353 0.6961 0.036 0.028 0.736 0.164 0.036
#> GSM11683 3 0.3109 0.7240 0.200 0.000 0.800 0.000 0.000
#> GSM11691 3 0.3109 0.7240 0.200 0.000 0.800 0.000 0.000
#> GSM27949 3 0.3210 0.6961 0.000 0.000 0.788 0.212 0.000
#> GSM27945 3 0.4201 0.4163 0.000 0.000 0.592 0.408 0.000
#> GSM11706 4 0.0000 0.7889 0.000 0.000 0.000 1.000 0.000
#> GSM11853 4 0.0000 0.7889 0.000 0.000 0.000 1.000 0.000
#> GSM11729 2 0.0000 0.7835 0.000 1.000 0.000 0.000 0.000
#> GSM11746 2 0.2408 0.7656 0.092 0.892 0.000 0.016 0.000
#> GSM11711 4 0.0162 0.7885 0.004 0.000 0.000 0.996 0.000
#> GSM11854 4 0.0000 0.7889 0.000 0.000 0.000 1.000 0.000
#> GSM11731 2 0.4283 0.7653 0.068 0.812 0.064 0.000 0.056
#> GSM11839 3 0.9364 0.1404 0.296 0.196 0.304 0.108 0.096
#> GSM11836 2 0.5766 0.3645 0.000 0.560 0.004 0.348 0.088
#> GSM11849 4 0.4201 0.3403 0.000 0.408 0.000 0.592 0.000
#> GSM11682 4 0.0000 0.7889 0.000 0.000 0.000 1.000 0.000
#> GSM11690 4 0.3340 0.7309 0.000 0.044 0.008 0.852 0.096
#> GSM11692 4 0.3340 0.7309 0.000 0.044 0.008 0.852 0.096
#> GSM11841 5 0.5476 0.0233 0.000 0.044 0.008 0.440 0.508
#> GSM11901 4 0.5706 0.4317 0.000 0.260 0.012 0.632 0.096
#> GSM11715 2 0.1341 0.7744 0.000 0.944 0.000 0.000 0.056
#> GSM11724 2 0.1341 0.7744 0.000 0.944 0.000 0.000 0.056
#> GSM11684 2 0.2812 0.7432 0.004 0.876 0.000 0.024 0.096
#> GSM11696 2 0.5933 0.3718 0.012 0.584 0.308 0.000 0.096
#> GSM27952 4 0.0000 0.7889 0.000 0.000 0.000 1.000 0.000
#> GSM27948 4 0.3340 0.7309 0.000 0.044 0.008 0.852 0.096
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM11708 5 0.0713 0.9580 0.000 0.000 0.000 0.000 0.972 0.028
#> GSM11735 5 0.0000 0.9941 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11733 5 0.0000 0.9941 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11863 5 0.0000 0.9941 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11710 6 0.5790 0.5544 0.020 0.000 0.140 0.284 0.000 0.556
#> GSM11712 4 0.0000 0.6840 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM11732 3 0.1333 0.7311 0.008 0.000 0.944 0.048 0.000 0.000
#> GSM11844 3 0.7509 -0.1017 0.000 0.000 0.308 0.136 0.288 0.268
#> GSM11842 5 0.0000 0.9941 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11860 5 0.0000 0.9941 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11686 6 0.4057 0.5889 0.008 0.000 0.000 0.436 0.000 0.556
#> GSM11688 6 0.4057 0.5889 0.008 0.000 0.000 0.436 0.000 0.556
#> GSM11846 6 0.4289 0.5876 0.020 0.000 0.000 0.424 0.000 0.556
#> GSM11680 3 0.2664 0.6456 0.000 0.000 0.816 0.184 0.000 0.000
#> GSM11698 6 0.4952 0.2315 0.000 0.000 0.408 0.068 0.000 0.524
#> GSM11840 5 0.0000 0.9941 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11847 5 0.0000 0.9941 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11685 4 0.2883 0.2710 0.000 0.000 0.000 0.788 0.000 0.212
#> GSM11699 6 0.5159 0.2144 0.016 0.000 0.408 0.052 0.000 0.524
#> GSM27950 3 0.2491 0.6690 0.000 0.000 0.836 0.164 0.000 0.000
#> GSM27946 6 0.3843 0.5783 0.000 0.000 0.000 0.452 0.000 0.548
#> GSM11709 1 0.1644 0.8285 0.920 0.076 0.004 0.000 0.000 0.000
#> GSM11720 1 0.6946 0.3336 0.528 0.220 0.036 0.056 0.000 0.160
#> GSM11726 2 0.4249 0.2579 0.032 0.640 0.000 0.000 0.000 0.328
#> GSM11837 2 0.0000 0.7180 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11725 1 0.0000 0.8928 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11864 1 0.0000 0.8928 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11687 1 0.0000 0.8928 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11693 1 0.0000 0.8928 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11727 2 0.0000 0.7180 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11838 2 0.0000 0.7180 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11681 1 0.0000 0.8928 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11689 1 0.0000 0.8928 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11704 1 0.0000 0.8928 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11703 3 0.6327 0.0875 0.260 0.000 0.408 0.012 0.000 0.320
#> GSM11705 6 0.5836 0.3583 0.352 0.000 0.044 0.080 0.000 0.524
#> GSM11722 2 0.3833 0.5883 0.000 0.556 0.000 0.000 0.000 0.444
#> GSM11730 2 0.1444 0.6603 0.072 0.928 0.000 0.000 0.000 0.000
#> GSM11713 2 0.0632 0.7182 0.000 0.976 0.000 0.000 0.000 0.024
#> GSM11728 6 0.7258 0.4631 0.196 0.056 0.052 0.196 0.000 0.500
#> GSM27947 6 0.4057 0.5889 0.008 0.000 0.000 0.436 0.000 0.556
#> GSM27951 1 0.0000 0.8928 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11707 3 0.4829 0.1015 0.056 0.000 0.520 0.000 0.000 0.424
#> GSM11716 3 0.1418 0.7364 0.024 0.000 0.944 0.032 0.000 0.000
#> GSM11850 3 0.1204 0.7356 0.056 0.000 0.944 0.000 0.000 0.000
#> GSM11851 6 0.5908 0.4780 0.000 0.000 0.248 0.284 0.000 0.468
#> GSM11721 4 0.5861 0.3592 0.100 0.000 0.100 0.632 0.000 0.168
#> GSM11852 6 0.5726 0.5412 0.008 0.000 0.192 0.244 0.000 0.556
#> GSM11694 3 0.1556 0.7331 0.080 0.000 0.920 0.000 0.000 0.000
#> GSM11695 3 0.2597 0.6723 0.176 0.000 0.824 0.000 0.000 0.000
#> GSM11734 1 0.5453 0.3377 0.592 0.220 0.004 0.184 0.000 0.000
#> GSM11861 6 0.5614 0.5294 0.176 0.000 0.004 0.264 0.000 0.556
#> GSM11843 3 0.3634 0.3341 0.356 0.000 0.644 0.000 0.000 0.000
#> GSM11862 6 0.6319 0.5021 0.160 0.000 0.064 0.224 0.000 0.552
#> GSM11697 3 0.1204 0.7356 0.056 0.000 0.944 0.000 0.000 0.000
#> GSM11714 3 0.0146 0.7300 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM11723 2 0.6117 0.3195 0.000 0.356 0.344 0.000 0.000 0.300
#> GSM11845 3 0.2446 0.6965 0.012 0.000 0.864 0.124 0.000 0.000
#> GSM11683 3 0.0000 0.7285 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11691 3 0.2260 0.6657 0.140 0.000 0.860 0.000 0.000 0.000
#> GSM27949 3 0.2762 0.6355 0.000 0.000 0.804 0.196 0.000 0.000
#> GSM27945 3 0.3695 0.3282 0.000 0.000 0.624 0.376 0.000 0.000
#> GSM11706 6 0.3833 0.5861 0.000 0.000 0.000 0.444 0.000 0.556
#> GSM11853 6 0.3833 0.5861 0.000 0.000 0.000 0.444 0.000 0.556
#> GSM11729 2 0.3833 0.5883 0.000 0.556 0.000 0.000 0.000 0.444
#> GSM11746 6 0.5548 -0.4913 0.184 0.268 0.000 0.000 0.000 0.548
#> GSM11711 6 0.5035 0.5787 0.000 0.000 0.084 0.360 0.000 0.556
#> GSM11854 6 0.3961 0.5875 0.000 0.000 0.004 0.440 0.000 0.556
#> GSM11731 2 0.7323 0.4495 0.056 0.492 0.056 0.184 0.000 0.212
#> GSM11839 4 0.7291 0.0701 0.228 0.016 0.336 0.360 0.000 0.060
#> GSM11836 4 0.4544 0.5336 0.004 0.076 0.000 0.688 0.000 0.232
#> GSM11849 6 0.0790 0.3006 0.000 0.000 0.000 0.032 0.000 0.968
#> GSM11682 6 0.3833 0.5861 0.000 0.000 0.000 0.444 0.000 0.556
#> GSM11690 4 0.0000 0.6840 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM11692 4 0.0000 0.6840 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM11841 4 0.0790 0.6742 0.000 0.000 0.000 0.968 0.032 0.000
#> GSM11901 4 0.0000 0.6840 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM11715 6 0.5833 -0.5710 0.000 0.364 0.000 0.192 0.000 0.444
#> GSM11724 6 0.5847 -0.5686 0.000 0.360 0.000 0.196 0.000 0.444
#> GSM11684 4 0.4388 0.1783 0.004 0.004 0.012 0.560 0.000 0.420
#> GSM11696 4 0.4961 0.1889 0.004 0.000 0.368 0.564 0.000 0.064
#> GSM27952 6 0.3833 0.5861 0.000 0.000 0.000 0.444 0.000 0.556
#> GSM27948 4 0.0000 0.6840 0.000 0.000 0.000 1.000 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 cell.line(p) agent(p) time(p) k
#> CV:pam 78 5.04e-03 0.0732 3.28e-04 2
#> CV:pam 52 6.93e-06 0.2531 9.80e-04 3
#> CV:pam 60 2.52e-09 0.4305 6.67e-06 4
#> CV:pam 66 4.32e-12 0.1193 1.99e-06 5
#> CV:pam 59 4.65e-15 0.2316 1.66e-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["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 14502 rows and 83 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.372 0.833 0.895 0.3515 0.685 0.685
#> 3 3 0.223 0.659 0.730 0.5981 0.727 0.614
#> 4 4 0.595 0.720 0.844 0.2947 0.758 0.493
#> 5 5 0.618 0.674 0.798 0.0695 0.862 0.541
#> 6 6 0.676 0.616 0.752 0.0499 0.951 0.774
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
#> GSM11708 1 0.5737 0.825 0.864 0.136
#> GSM11735 1 0.5737 0.825 0.864 0.136
#> GSM11733 1 0.6048 0.815 0.852 0.148
#> GSM11863 1 0.5737 0.825 0.864 0.136
#> GSM11710 1 0.4939 0.841 0.892 0.108
#> GSM11712 1 0.0376 0.887 0.996 0.004
#> GSM11732 1 0.7219 0.765 0.800 0.200
#> GSM11844 1 0.7219 0.765 0.800 0.200
#> GSM11842 1 0.5737 0.825 0.864 0.136
#> GSM11860 1 0.5737 0.825 0.864 0.136
#> GSM11686 1 0.5059 0.842 0.888 0.112
#> GSM11688 1 0.4939 0.841 0.892 0.108
#> GSM11846 1 0.3274 0.867 0.940 0.060
#> GSM11680 1 0.2948 0.871 0.948 0.052
#> GSM11698 1 0.3584 0.863 0.932 0.068
#> GSM11840 1 0.5737 0.825 0.864 0.136
#> GSM11847 1 0.5737 0.825 0.864 0.136
#> GSM11685 1 0.4939 0.841 0.892 0.108
#> GSM11699 1 0.4161 0.858 0.916 0.084
#> GSM27950 1 0.0672 0.886 0.992 0.008
#> GSM27946 1 0.3584 0.863 0.932 0.068
#> GSM11709 1 0.5842 0.826 0.860 0.140
#> GSM11720 1 0.7674 0.714 0.776 0.224
#> GSM11726 1 0.8713 0.624 0.708 0.292
#> GSM11837 2 0.4815 0.929 0.104 0.896
#> GSM11725 2 0.4815 0.929 0.104 0.896
#> GSM11864 2 0.6148 0.897 0.152 0.848
#> GSM11687 1 0.0938 0.887 0.988 0.012
#> GSM11693 1 0.0672 0.887 0.992 0.008
#> GSM11727 2 0.4815 0.929 0.104 0.896
#> GSM11838 2 0.4815 0.929 0.104 0.896
#> GSM11681 1 0.0938 0.887 0.988 0.012
#> GSM11689 1 0.6712 0.723 0.824 0.176
#> GSM11704 2 0.9996 0.343 0.488 0.512
#> GSM11703 1 0.0672 0.887 0.992 0.008
#> GSM11705 1 0.0672 0.887 0.992 0.008
#> GSM11722 2 0.4815 0.929 0.104 0.896
#> GSM11730 2 0.8016 0.783 0.244 0.756
#> GSM11713 1 0.9323 0.345 0.652 0.348
#> GSM11728 1 0.1184 0.886 0.984 0.016
#> GSM27947 1 0.4431 0.848 0.908 0.092
#> GSM27951 1 0.0672 0.887 0.992 0.008
#> GSM11707 1 0.5842 0.824 0.860 0.140
#> GSM11716 1 0.5946 0.819 0.856 0.144
#> GSM11850 1 0.7219 0.765 0.800 0.200
#> GSM11851 1 0.6048 0.844 0.852 0.148
#> GSM11721 1 0.5946 0.823 0.856 0.144
#> GSM11852 1 0.4939 0.841 0.892 0.108
#> GSM11694 1 0.0376 0.887 0.996 0.004
#> GSM11695 1 0.0376 0.887 0.996 0.004
#> GSM11734 2 0.4815 0.929 0.104 0.896
#> GSM11861 1 0.2603 0.878 0.956 0.044
#> GSM11843 2 0.7674 0.818 0.224 0.776
#> GSM11862 1 0.0938 0.887 0.988 0.012
#> GSM11697 1 0.0376 0.887 0.996 0.004
#> GSM11714 1 0.0672 0.887 0.992 0.008
#> GSM11723 2 0.8499 0.729 0.276 0.724
#> GSM11845 1 0.9491 0.417 0.632 0.368
#> GSM11683 1 0.1633 0.884 0.976 0.024
#> GSM11691 1 0.1414 0.885 0.980 0.020
#> GSM27949 1 0.1414 0.883 0.980 0.020
#> GSM27945 1 0.2423 0.876 0.960 0.040
#> GSM11706 1 0.3431 0.865 0.936 0.064
#> GSM11853 1 0.4815 0.839 0.896 0.104
#> GSM11729 2 0.4815 0.929 0.104 0.896
#> GSM11746 2 0.4815 0.929 0.104 0.896
#> GSM11711 1 0.4815 0.839 0.896 0.104
#> GSM11854 1 0.4815 0.839 0.896 0.104
#> GSM11731 2 0.4815 0.929 0.104 0.896
#> GSM11839 1 0.9732 0.334 0.596 0.404
#> GSM11836 1 0.7299 0.762 0.796 0.204
#> GSM11849 1 0.3114 0.872 0.944 0.056
#> GSM11682 1 0.0376 0.887 0.996 0.004
#> GSM11690 1 0.0000 0.887 1.000 0.000
#> GSM11692 1 0.0000 0.887 1.000 0.000
#> GSM11841 1 0.0376 0.887 0.996 0.004
#> GSM11901 1 0.0376 0.887 0.996 0.004
#> GSM11715 2 0.4815 0.929 0.104 0.896
#> GSM11724 2 0.4815 0.929 0.104 0.896
#> GSM11684 1 0.0376 0.887 0.996 0.004
#> GSM11696 1 0.0376 0.887 0.996 0.004
#> GSM27952 1 0.4690 0.847 0.900 0.100
#> GSM27948 1 0.0000 0.887 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM11708 3 0.5058 0.7306 0.032 0.148 0.820
#> GSM11735 3 0.5058 0.7306 0.032 0.148 0.820
#> GSM11733 3 0.5285 0.7263 0.040 0.148 0.812
#> GSM11863 3 0.5058 0.7306 0.032 0.148 0.820
#> GSM11710 3 0.5690 0.6750 0.288 0.004 0.708
#> GSM11712 3 0.7766 0.7456 0.176 0.148 0.676
#> GSM11732 3 0.6297 0.6024 0.008 0.352 0.640
#> GSM11844 3 0.5506 0.6977 0.016 0.220 0.764
#> GSM11842 3 0.5180 0.7299 0.032 0.156 0.812
#> GSM11860 3 0.5235 0.7356 0.036 0.152 0.812
#> GSM11686 3 0.5656 0.6866 0.264 0.008 0.728
#> GSM11688 3 0.2682 0.7211 0.076 0.004 0.920
#> GSM11846 3 0.1905 0.7360 0.016 0.028 0.956
#> GSM11680 3 0.2434 0.7430 0.024 0.036 0.940
#> GSM11698 3 0.1905 0.7352 0.016 0.028 0.956
#> GSM11840 3 0.5058 0.7306 0.032 0.148 0.820
#> GSM11847 3 0.5058 0.7306 0.032 0.148 0.820
#> GSM11685 3 0.5588 0.6824 0.276 0.004 0.720
#> GSM11699 3 0.6333 0.6507 0.332 0.012 0.656
#> GSM27950 3 0.3590 0.7540 0.028 0.076 0.896
#> GSM27946 3 0.5574 0.7351 0.184 0.032 0.784
#> GSM11709 1 0.8476 0.5894 0.560 0.332 0.108
#> GSM11720 1 0.7671 0.5404 0.544 0.408 0.048
#> GSM11726 2 0.9281 0.0395 0.204 0.520 0.276
#> GSM11837 2 0.0848 0.7740 0.008 0.984 0.008
#> GSM11725 2 0.0237 0.7746 0.000 0.996 0.004
#> GSM11864 2 0.4136 0.6677 0.020 0.864 0.116
#> GSM11687 1 0.6402 0.7336 0.744 0.200 0.056
#> GSM11693 1 0.6527 0.7348 0.744 0.188 0.068
#> GSM11727 2 0.1315 0.7676 0.020 0.972 0.008
#> GSM11838 2 0.0848 0.7740 0.008 0.984 0.008
#> GSM11681 1 0.6431 0.6926 0.760 0.084 0.156
#> GSM11689 1 0.6319 0.7279 0.732 0.228 0.040
#> GSM11704 1 0.6744 0.6948 0.668 0.300 0.032
#> GSM11703 1 0.5181 0.6917 0.832 0.084 0.084
#> GSM11705 1 0.6001 0.6907 0.784 0.072 0.144
#> GSM11722 2 0.5618 0.3687 0.260 0.732 0.008
#> GSM11730 1 0.6633 0.4917 0.548 0.444 0.008
#> GSM11713 1 0.6598 0.5257 0.564 0.428 0.008
#> GSM11728 1 0.7091 0.2097 0.676 0.056 0.268
#> GSM27947 3 0.4723 0.7350 0.160 0.016 0.824
#> GSM27951 1 0.6292 0.7266 0.740 0.216 0.044
#> GSM11707 3 0.8030 0.6847 0.144 0.204 0.652
#> GSM11716 3 0.5008 0.7212 0.016 0.180 0.804
#> GSM11850 3 0.6228 0.5801 0.004 0.372 0.624
#> GSM11851 3 0.2774 0.7342 0.008 0.072 0.920
#> GSM11721 3 0.9335 0.6639 0.324 0.184 0.492
#> GSM11852 3 0.6255 0.6553 0.320 0.012 0.668
#> GSM11694 3 0.7661 0.7062 0.144 0.172 0.684
#> GSM11695 3 0.7603 0.7086 0.140 0.172 0.688
#> GSM11734 2 0.0237 0.7746 0.000 0.996 0.004
#> GSM11861 3 0.9480 0.6382 0.296 0.216 0.488
#> GSM11843 2 0.4033 0.5908 0.136 0.856 0.008
#> GSM11862 3 0.9367 0.6252 0.344 0.180 0.476
#> GSM11697 3 0.7595 0.7101 0.136 0.176 0.688
#> GSM11714 3 0.8542 0.6494 0.172 0.220 0.608
#> GSM11723 2 0.0661 0.7743 0.004 0.988 0.008
#> GSM11845 2 0.4413 0.6569 0.024 0.852 0.124
#> GSM11683 3 0.7710 0.5268 0.368 0.056 0.576
#> GSM11691 3 0.7726 0.5179 0.372 0.056 0.572
#> GSM27949 3 0.3031 0.7471 0.012 0.076 0.912
#> GSM27945 3 0.4489 0.7468 0.108 0.036 0.856
#> GSM11706 3 0.2031 0.7374 0.016 0.032 0.952
#> GSM11853 3 0.3983 0.7233 0.144 0.004 0.852
#> GSM11729 2 0.0237 0.7746 0.000 0.996 0.004
#> GSM11746 2 0.0424 0.7751 0.000 0.992 0.008
#> GSM11711 3 0.5201 0.6933 0.236 0.004 0.760
#> GSM11854 3 0.5285 0.6972 0.244 0.004 0.752
#> GSM11731 2 0.0237 0.7746 0.000 0.996 0.004
#> GSM11839 2 0.6521 0.1636 0.016 0.644 0.340
#> GSM11836 2 0.8141 -0.4165 0.068 0.472 0.460
#> GSM11849 3 0.9756 0.5852 0.316 0.248 0.436
#> GSM11682 3 0.8157 0.7067 0.308 0.096 0.596
#> GSM11690 3 0.8526 0.7101 0.308 0.120 0.572
#> GSM11692 3 0.7635 0.7333 0.212 0.112 0.676
#> GSM11841 3 0.8355 0.7138 0.184 0.188 0.628
#> GSM11901 3 0.8355 0.7138 0.184 0.188 0.628
#> GSM11715 2 0.0829 0.7704 0.012 0.984 0.004
#> GSM11724 2 0.1015 0.7705 0.012 0.980 0.008
#> GSM11684 3 0.9254 0.6375 0.332 0.172 0.496
#> GSM11696 3 0.9239 0.6422 0.328 0.172 0.500
#> GSM27952 3 0.5156 0.7004 0.216 0.008 0.776
#> GSM27948 3 0.7501 0.7329 0.212 0.104 0.684
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM11708 3 0.0524 0.7913 0.000 0.008 0.988 0.004
#> GSM11735 3 0.0524 0.7913 0.000 0.008 0.988 0.004
#> GSM11733 3 0.0469 0.7904 0.000 0.012 0.988 0.000
#> GSM11863 3 0.0469 0.7904 0.000 0.012 0.988 0.000
#> GSM11710 4 0.4844 0.4497 0.012 0.000 0.300 0.688
#> GSM11712 4 0.1867 0.7653 0.000 0.000 0.072 0.928
#> GSM11732 3 0.4249 0.7445 0.008 0.176 0.800 0.016
#> GSM11844 3 0.4388 0.7921 0.004 0.048 0.812 0.136
#> GSM11842 3 0.0657 0.7921 0.000 0.012 0.984 0.004
#> GSM11860 3 0.0657 0.7921 0.000 0.012 0.984 0.004
#> GSM11686 4 0.3945 0.5954 0.004 0.000 0.216 0.780
#> GSM11688 4 0.4898 0.2058 0.000 0.000 0.416 0.584
#> GSM11846 3 0.3975 0.7408 0.000 0.000 0.760 0.240
#> GSM11680 3 0.4134 0.7455 0.000 0.000 0.740 0.260
#> GSM11698 3 0.4193 0.7224 0.000 0.000 0.732 0.268
#> GSM11840 3 0.0336 0.7908 0.000 0.008 0.992 0.000
#> GSM11847 3 0.0524 0.7913 0.000 0.008 0.988 0.004
#> GSM11685 4 0.1792 0.7579 0.000 0.000 0.068 0.932
#> GSM11699 4 0.1406 0.7735 0.024 0.000 0.016 0.960
#> GSM27950 3 0.4302 0.7674 0.004 0.004 0.756 0.236
#> GSM27946 4 0.3837 0.6199 0.000 0.000 0.224 0.776
#> GSM11709 1 0.4271 0.7763 0.816 0.140 0.004 0.040
#> GSM11720 1 0.2515 0.8166 0.912 0.072 0.004 0.012
#> GSM11726 1 0.3972 0.7214 0.816 0.164 0.016 0.004
#> GSM11837 2 0.1661 0.9053 0.052 0.944 0.000 0.004
#> GSM11725 2 0.0188 0.9192 0.004 0.996 0.000 0.000
#> GSM11864 2 0.3052 0.7937 0.004 0.860 0.000 0.136
#> GSM11687 1 0.1389 0.8556 0.952 0.000 0.000 0.048
#> GSM11693 1 0.1576 0.8567 0.948 0.000 0.004 0.048
#> GSM11727 2 0.1978 0.8998 0.068 0.928 0.000 0.004
#> GSM11838 2 0.1743 0.9053 0.056 0.940 0.000 0.004
#> GSM11681 1 0.2238 0.8462 0.920 0.004 0.004 0.072
#> GSM11689 1 0.1576 0.8567 0.948 0.000 0.004 0.048
#> GSM11704 1 0.1762 0.8560 0.944 0.004 0.004 0.048
#> GSM11703 1 0.1576 0.8567 0.948 0.000 0.004 0.048
#> GSM11705 1 0.1576 0.8567 0.948 0.000 0.004 0.048
#> GSM11722 2 0.4509 0.5966 0.288 0.708 0.000 0.004
#> GSM11730 1 0.3355 0.7232 0.836 0.160 0.000 0.004
#> GSM11713 1 0.4425 0.7590 0.800 0.160 0.004 0.036
#> GSM11728 1 0.3583 0.7591 0.816 0.000 0.004 0.180
#> GSM27947 4 0.4877 0.1445 0.000 0.000 0.408 0.592
#> GSM27951 1 0.1576 0.8567 0.948 0.000 0.004 0.048
#> GSM11707 3 0.6792 0.6593 0.140 0.140 0.680 0.040
#> GSM11716 3 0.3708 0.7912 0.000 0.020 0.832 0.148
#> GSM11850 3 0.3688 0.7260 0.000 0.208 0.792 0.000
#> GSM11851 3 0.3895 0.7785 0.000 0.012 0.804 0.184
#> GSM11721 4 0.4171 0.6950 0.084 0.088 0.000 0.828
#> GSM11852 4 0.1707 0.7743 0.020 0.004 0.024 0.952
#> GSM11694 3 0.5914 0.6662 0.228 0.008 0.692 0.072
#> GSM11695 3 0.5954 0.7405 0.112 0.008 0.712 0.168
#> GSM11734 2 0.0188 0.9192 0.004 0.996 0.000 0.000
#> GSM11861 4 0.3612 0.7230 0.100 0.044 0.000 0.856
#> GSM11843 2 0.3479 0.7897 0.148 0.840 0.000 0.012
#> GSM11862 4 0.3450 0.6755 0.156 0.008 0.000 0.836
#> GSM11697 3 0.5982 0.7435 0.108 0.008 0.708 0.176
#> GSM11714 3 0.7391 0.5517 0.224 0.132 0.608 0.036
#> GSM11723 2 0.0188 0.9192 0.004 0.996 0.000 0.000
#> GSM11845 2 0.3052 0.7937 0.004 0.860 0.000 0.136
#> GSM11683 1 0.6597 0.1680 0.540 0.000 0.372 0.088
#> GSM11691 1 0.5990 0.3281 0.608 0.000 0.336 0.056
#> GSM27949 3 0.3626 0.7805 0.000 0.004 0.812 0.184
#> GSM27945 3 0.4605 0.6451 0.000 0.000 0.664 0.336
#> GSM11706 3 0.4193 0.7276 0.000 0.000 0.732 0.268
#> GSM11853 3 0.4996 0.2088 0.000 0.000 0.516 0.484
#> GSM11729 2 0.0188 0.9197 0.004 0.996 0.000 0.000
#> GSM11746 2 0.0188 0.9197 0.004 0.996 0.000 0.000
#> GSM11711 4 0.4978 0.2005 0.004 0.000 0.384 0.612
#> GSM11854 4 0.4837 0.3321 0.004 0.000 0.348 0.648
#> GSM11731 2 0.0657 0.9177 0.012 0.984 0.000 0.004
#> GSM11839 2 0.2988 0.8415 0.012 0.876 0.000 0.112
#> GSM11836 4 0.4999 -0.0544 0.000 0.492 0.000 0.508
#> GSM11849 4 0.4841 0.6562 0.080 0.140 0.000 0.780
#> GSM11682 4 0.0779 0.7761 0.000 0.004 0.016 0.980
#> GSM11690 4 0.0376 0.7744 0.004 0.000 0.004 0.992
#> GSM11692 4 0.1302 0.7723 0.000 0.000 0.044 0.956
#> GSM11841 4 0.1211 0.7731 0.000 0.000 0.040 0.960
#> GSM11901 4 0.1211 0.7731 0.000 0.000 0.040 0.960
#> GSM11715 2 0.0188 0.9197 0.004 0.996 0.000 0.000
#> GSM11724 2 0.0188 0.9197 0.004 0.996 0.000 0.000
#> GSM11684 4 0.3508 0.6955 0.136 0.012 0.004 0.848
#> GSM11696 4 0.3914 0.6949 0.120 0.036 0.004 0.840
#> GSM27952 4 0.1389 0.7730 0.000 0.000 0.048 0.952
#> GSM27948 4 0.1302 0.7723 0.000 0.000 0.044 0.956
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM11708 3 0.4287 0.3096 0.000 0.000 0.540 0.000 0.460
#> GSM11735 3 0.4305 0.2369 0.000 0.000 0.512 0.000 0.488
#> GSM11733 5 0.0771 0.8242 0.000 0.004 0.020 0.000 0.976
#> GSM11863 5 0.0162 0.8235 0.000 0.000 0.004 0.000 0.996
#> GSM11710 3 0.1608 0.6708 0.000 0.000 0.928 0.072 0.000
#> GSM11712 4 0.3882 0.7794 0.000 0.000 0.224 0.756 0.020
#> GSM11732 5 0.4027 0.7648 0.000 0.144 0.044 0.012 0.800
#> GSM11844 5 0.3909 0.7234 0.000 0.048 0.148 0.004 0.800
#> GSM11842 5 0.0000 0.8233 0.000 0.000 0.000 0.000 1.000
#> GSM11860 5 0.0510 0.8241 0.000 0.000 0.016 0.000 0.984
#> GSM11686 3 0.2127 0.6533 0.000 0.000 0.892 0.108 0.000
#> GSM11688 3 0.0880 0.6897 0.000 0.000 0.968 0.032 0.000
#> GSM11846 3 0.2852 0.6750 0.000 0.000 0.828 0.000 0.172
#> GSM11680 3 0.2929 0.6686 0.000 0.000 0.820 0.000 0.180
#> GSM11698 3 0.2719 0.6875 0.000 0.000 0.852 0.004 0.144
#> GSM11840 5 0.1965 0.7772 0.000 0.000 0.096 0.000 0.904
#> GSM11847 5 0.3966 0.2927 0.000 0.000 0.336 0.000 0.664
#> GSM11685 3 0.2424 0.6286 0.000 0.000 0.868 0.132 0.000
#> GSM11699 4 0.5006 0.6896 0.048 0.000 0.328 0.624 0.000
#> GSM27950 3 0.3210 0.6460 0.000 0.000 0.788 0.000 0.212
#> GSM27946 3 0.4504 -0.0359 0.000 0.000 0.564 0.428 0.008
#> GSM11709 1 0.3265 0.7918 0.868 0.068 0.000 0.036 0.028
#> GSM11720 1 0.1251 0.8383 0.956 0.036 0.000 0.000 0.008
#> GSM11726 1 0.4811 0.6899 0.748 0.096 0.000 0.144 0.012
#> GSM11837 2 0.3365 0.7964 0.004 0.808 0.000 0.180 0.008
#> GSM11725 2 0.0794 0.8464 0.000 0.972 0.000 0.028 0.000
#> GSM11864 2 0.3088 0.7295 0.000 0.828 0.164 0.004 0.004
#> GSM11687 1 0.0000 0.8515 1.000 0.000 0.000 0.000 0.000
#> GSM11693 1 0.0000 0.8515 1.000 0.000 0.000 0.000 0.000
#> GSM11727 2 0.4022 0.7770 0.024 0.772 0.000 0.196 0.008
#> GSM11838 2 0.3509 0.7882 0.004 0.792 0.000 0.196 0.008
#> GSM11681 1 0.0671 0.8480 0.980 0.016 0.000 0.004 0.000
#> GSM11689 1 0.0000 0.8515 1.000 0.000 0.000 0.000 0.000
#> GSM11704 1 0.0290 0.8496 0.992 0.000 0.000 0.000 0.008
#> GSM11703 1 0.0162 0.8513 0.996 0.004 0.000 0.000 0.000
#> GSM11705 1 0.0000 0.8515 1.000 0.000 0.000 0.000 0.000
#> GSM11722 2 0.6555 0.3255 0.316 0.500 0.000 0.176 0.008
#> GSM11730 1 0.5430 0.6181 0.680 0.124 0.000 0.188 0.008
#> GSM11713 1 0.5398 0.6221 0.684 0.124 0.000 0.184 0.008
#> GSM11728 1 0.1041 0.8324 0.964 0.004 0.000 0.032 0.000
#> GSM27947 3 0.3362 0.6922 0.000 0.000 0.844 0.076 0.080
#> GSM27951 1 0.0000 0.8515 1.000 0.000 0.000 0.000 0.000
#> GSM11707 3 0.7703 0.4476 0.188 0.060 0.528 0.028 0.196
#> GSM11716 5 0.3538 0.7029 0.000 0.016 0.176 0.004 0.804
#> GSM11850 5 0.3807 0.7337 0.004 0.176 0.000 0.028 0.792
#> GSM11851 3 0.3707 0.6355 0.000 0.008 0.768 0.004 0.220
#> GSM11721 4 0.5058 0.7708 0.172 0.028 0.068 0.732 0.000
#> GSM11852 3 0.5360 -0.1945 0.060 0.000 0.556 0.384 0.000
#> GSM11694 3 0.6392 0.4587 0.272 0.004 0.532 0.000 0.192
#> GSM11695 3 0.6078 0.5209 0.212 0.004 0.592 0.000 0.192
#> GSM11734 2 0.0794 0.8464 0.000 0.972 0.000 0.028 0.000
#> GSM11861 4 0.5391 0.7626 0.192 0.020 0.072 0.708 0.008
#> GSM11843 2 0.3039 0.7133 0.192 0.808 0.000 0.000 0.000
#> GSM11862 4 0.5044 0.7396 0.224 0.004 0.060 0.704 0.008
#> GSM11697 3 0.6046 0.5241 0.216 0.004 0.596 0.000 0.184
#> GSM11714 3 0.7655 0.4251 0.268 0.048 0.516 0.040 0.128
#> GSM11723 2 0.1243 0.8464 0.004 0.960 0.000 0.028 0.008
#> GSM11845 2 0.3477 0.7277 0.004 0.816 0.164 0.004 0.012
#> GSM11683 1 0.4649 0.1229 0.580 0.000 0.404 0.000 0.016
#> GSM11691 1 0.4015 0.3177 0.652 0.000 0.348 0.000 0.000
#> GSM27949 3 0.3305 0.6344 0.000 0.000 0.776 0.000 0.224
#> GSM27945 3 0.3326 0.6884 0.000 0.000 0.824 0.024 0.152
#> GSM11706 3 0.2471 0.6863 0.000 0.000 0.864 0.000 0.136
#> GSM11853 3 0.2248 0.6787 0.000 0.000 0.900 0.088 0.012
#> GSM11729 2 0.0324 0.8526 0.000 0.992 0.000 0.004 0.004
#> GSM11746 2 0.0162 0.8518 0.000 0.996 0.000 0.004 0.000
#> GSM11711 3 0.1732 0.6751 0.000 0.000 0.920 0.080 0.000
#> GSM11854 3 0.2179 0.6490 0.000 0.000 0.888 0.112 0.000
#> GSM11731 2 0.0566 0.8523 0.000 0.984 0.000 0.012 0.004
#> GSM11839 2 0.3963 0.5737 0.008 0.732 0.000 0.256 0.004
#> GSM11836 4 0.4675 0.1378 0.004 0.444 0.000 0.544 0.008
#> GSM11849 4 0.5487 0.7384 0.184 0.052 0.044 0.712 0.008
#> GSM11682 4 0.4111 0.7541 0.008 0.000 0.280 0.708 0.004
#> GSM11690 4 0.3491 0.7884 0.004 0.000 0.228 0.768 0.000
#> GSM11692 4 0.3336 0.7869 0.000 0.000 0.228 0.772 0.000
#> GSM11841 4 0.3305 0.7880 0.000 0.000 0.224 0.776 0.000
#> GSM11901 4 0.3305 0.7880 0.000 0.000 0.224 0.776 0.000
#> GSM11715 2 0.0162 0.8525 0.000 0.996 0.000 0.004 0.000
#> GSM11724 2 0.0324 0.8523 0.004 0.992 0.000 0.000 0.004
#> GSM11684 4 0.5117 0.7620 0.196 0.012 0.064 0.720 0.008
#> GSM11696 4 0.5117 0.7620 0.196 0.012 0.064 0.720 0.008
#> GSM27952 3 0.2813 0.5776 0.000 0.000 0.832 0.168 0.000
#> GSM27948 4 0.3366 0.7861 0.000 0.000 0.232 0.768 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM11708 6 0.4844 0.42849 0.000 0.000 0.080 0.000 0.312 0.608
#> GSM11735 6 0.4760 0.39540 0.000 0.000 0.068 0.000 0.328 0.604
#> GSM11733 5 0.1082 0.83295 0.000 0.000 0.004 0.000 0.956 0.040
#> GSM11863 5 0.0547 0.83856 0.000 0.000 0.000 0.000 0.980 0.020
#> GSM11710 3 0.1390 0.58125 0.032 0.004 0.948 0.016 0.000 0.000
#> GSM11712 4 0.2665 0.75252 0.000 0.000 0.060 0.884 0.032 0.024
#> GSM11732 5 0.3864 0.78699 0.000 0.096 0.008 0.004 0.796 0.096
#> GSM11844 5 0.4094 0.79116 0.000 0.068 0.036 0.008 0.800 0.088
#> GSM11842 5 0.0000 0.83631 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11860 5 0.0972 0.83670 0.000 0.000 0.008 0.000 0.964 0.028
#> GSM11686 3 0.2454 0.58801 0.000 0.000 0.840 0.160 0.000 0.000
#> GSM11688 3 0.1109 0.57471 0.004 0.004 0.964 0.012 0.000 0.016
#> GSM11846 3 0.5181 0.01064 0.004 0.000 0.544 0.008 0.060 0.384
#> GSM11680 3 0.5272 0.09401 0.008 0.000 0.576 0.008 0.068 0.340
#> GSM11698 3 0.3954 0.48452 0.008 0.000 0.788 0.012 0.052 0.140
#> GSM11840 5 0.1480 0.82506 0.000 0.000 0.020 0.000 0.940 0.040
#> GSM11847 5 0.3551 0.57110 0.000 0.000 0.192 0.000 0.772 0.036
#> GSM11685 3 0.2527 0.58494 0.000 0.000 0.832 0.168 0.000 0.000
#> GSM11699 3 0.4750 0.41511 0.128 0.004 0.688 0.180 0.000 0.000
#> GSM27950 3 0.5366 -0.18756 0.004 0.000 0.476 0.004 0.080 0.436
#> GSM27946 3 0.3725 0.50234 0.000 0.000 0.676 0.316 0.000 0.008
#> GSM11709 1 0.3839 0.73776 0.816 0.060 0.004 0.004 0.024 0.092
#> GSM11720 1 0.1816 0.80604 0.936 0.028 0.004 0.016 0.004 0.012
#> GSM11726 1 0.4804 0.65024 0.712 0.124 0.000 0.008 0.008 0.148
#> GSM11837 2 0.3288 0.75885 0.008 0.800 0.000 0.016 0.000 0.176
#> GSM11725 2 0.1958 0.80332 0.000 0.896 0.000 0.004 0.000 0.100
#> GSM11864 2 0.3215 0.79291 0.008 0.852 0.048 0.012 0.000 0.080
#> GSM11687 1 0.0146 0.82018 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM11693 1 0.0436 0.82030 0.988 0.004 0.004 0.004 0.000 0.000
#> GSM11727 2 0.4158 0.72238 0.036 0.740 0.000 0.020 0.000 0.204
#> GSM11838 2 0.3623 0.73872 0.008 0.764 0.000 0.020 0.000 0.208
#> GSM11681 1 0.1149 0.81277 0.960 0.024 0.008 0.008 0.000 0.000
#> GSM11689 1 0.0146 0.82018 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM11704 1 0.0767 0.81973 0.976 0.008 0.004 0.000 0.000 0.012
#> GSM11703 1 0.0508 0.81895 0.984 0.004 0.012 0.000 0.000 0.000
#> GSM11705 1 0.0146 0.82018 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM11722 2 0.6491 0.08117 0.368 0.428 0.004 0.032 0.000 0.168
#> GSM11730 1 0.5590 0.56331 0.624 0.148 0.004 0.020 0.000 0.204
#> GSM11713 1 0.5718 0.56879 0.624 0.148 0.008 0.024 0.000 0.196
#> GSM11728 1 0.1942 0.79049 0.928 0.004 0.020 0.020 0.000 0.028
#> GSM27947 3 0.3050 0.55699 0.004 0.000 0.856 0.028 0.016 0.096
#> GSM27951 1 0.0551 0.81971 0.984 0.008 0.004 0.004 0.000 0.000
#> GSM11707 6 0.7626 0.63642 0.168 0.056 0.212 0.004 0.080 0.480
#> GSM11716 5 0.4159 0.77832 0.004 0.036 0.096 0.008 0.800 0.056
#> GSM11850 5 0.4122 0.78501 0.004 0.080 0.000 0.016 0.780 0.120
#> GSM11851 3 0.6831 0.00151 0.004 0.036 0.464 0.008 0.260 0.228
#> GSM11721 4 0.4015 0.74332 0.160 0.016 0.016 0.780 0.000 0.028
#> GSM11852 3 0.3098 0.50170 0.120 0.004 0.836 0.040 0.000 0.000
#> GSM11694 6 0.7660 0.63408 0.244 0.008 0.232 0.008 0.112 0.396
#> GSM11695 6 0.7350 0.61292 0.240 0.004 0.260 0.004 0.088 0.404
#> GSM11734 2 0.1858 0.80724 0.000 0.904 0.000 0.004 0.000 0.092
#> GSM11861 4 0.4883 0.74845 0.160 0.040 0.060 0.728 0.000 0.012
#> GSM11843 2 0.3109 0.71442 0.168 0.812 0.004 0.016 0.000 0.000
#> GSM11862 4 0.4289 0.72089 0.216 0.016 0.044 0.724 0.000 0.000
#> GSM11697 6 0.7384 0.55897 0.224 0.004 0.304 0.004 0.088 0.376
#> GSM11714 6 0.7559 0.61546 0.212 0.052 0.216 0.004 0.056 0.460
#> GSM11723 2 0.2101 0.80166 0.000 0.892 0.000 0.004 0.004 0.100
#> GSM11845 2 0.3320 0.78966 0.008 0.848 0.052 0.008 0.004 0.080
#> GSM11683 1 0.5052 0.01974 0.600 0.000 0.308 0.004 0.000 0.088
#> GSM11691 1 0.3734 0.34889 0.716 0.000 0.264 0.000 0.000 0.020
#> GSM27949 3 0.5764 -0.20153 0.008 0.004 0.464 0.008 0.088 0.428
#> GSM27945 3 0.5590 0.22001 0.004 0.000 0.580 0.052 0.048 0.316
#> GSM11706 3 0.5067 0.21456 0.008 0.000 0.624 0.008 0.064 0.296
#> GSM11853 3 0.4061 0.58561 0.000 0.000 0.748 0.164 0.000 0.088
#> GSM11729 2 0.0260 0.82858 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM11746 2 0.0363 0.82789 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM11711 3 0.3381 0.59831 0.004 0.000 0.808 0.148 0.000 0.040
#> GSM11854 3 0.2581 0.60143 0.000 0.000 0.856 0.128 0.000 0.016
#> GSM11731 2 0.1442 0.82070 0.004 0.944 0.000 0.012 0.000 0.040
#> GSM11839 2 0.4245 0.37300 0.004 0.644 0.000 0.328 0.000 0.024
#> GSM11836 4 0.5357 0.27272 0.000 0.340 0.000 0.536 0.000 0.124
#> GSM11849 4 0.4839 0.74283 0.168 0.048 0.044 0.728 0.000 0.012
#> GSM11682 4 0.4746 0.20599 0.000 0.004 0.424 0.532 0.000 0.040
#> GSM11690 4 0.2510 0.76171 0.008 0.000 0.080 0.884 0.000 0.028
#> GSM11692 4 0.1765 0.76820 0.000 0.000 0.052 0.924 0.000 0.024
#> GSM11841 4 0.1765 0.76820 0.000 0.000 0.052 0.924 0.000 0.024
#> GSM11901 4 0.1765 0.76820 0.000 0.000 0.052 0.924 0.000 0.024
#> GSM11715 2 0.0291 0.82818 0.004 0.992 0.000 0.004 0.000 0.000
#> GSM11724 2 0.0508 0.82851 0.004 0.984 0.000 0.012 0.000 0.000
#> GSM11684 4 0.4930 0.74367 0.176 0.016 0.044 0.720 0.000 0.044
#> GSM11696 4 0.4866 0.74541 0.176 0.016 0.044 0.724 0.000 0.040
#> GSM27952 3 0.2805 0.57405 0.000 0.000 0.812 0.184 0.000 0.004
#> GSM27948 4 0.2019 0.76278 0.000 0.000 0.088 0.900 0.000 0.012
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.line(p) agent(p) time(p) k
#> CV:mclust 79 2.38e-02 0.553 1.23e-04 2
#> CV:mclust 77 1.17e-10 0.711 3.66e-04 3
#> CV:mclust 74 2.95e-13 0.789 1.34e-05 4
#> CV:mclust 71 5.36e-11 0.294 2.43e-04 5
#> CV:mclust 66 2.25e-13 0.503 8.69e-06 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 14502 rows and 83 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.510 0.825 0.902 0.4671 0.533 0.533
#> 3 3 0.486 0.656 0.814 0.3706 0.745 0.557
#> 4 4 0.459 0.648 0.779 0.1609 0.771 0.457
#> 5 5 0.636 0.675 0.793 0.0693 0.885 0.597
#> 6 6 0.602 0.478 0.700 0.0386 0.974 0.878
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM11708 1 0.0000 0.8597 1.000 0.000
#> GSM11735 1 0.0000 0.8597 1.000 0.000
#> GSM11733 1 0.0000 0.8597 1.000 0.000
#> GSM11863 1 0.0000 0.8597 1.000 0.000
#> GSM11710 1 0.0376 0.8597 0.996 0.004
#> GSM11712 1 0.7745 0.8055 0.772 0.228
#> GSM11732 1 0.8016 0.7872 0.756 0.244
#> GSM11844 1 0.6973 0.8297 0.812 0.188
#> GSM11842 1 0.1843 0.8521 0.972 0.028
#> GSM11860 1 0.0000 0.8597 1.000 0.000
#> GSM11686 1 0.0376 0.8597 0.996 0.004
#> GSM11688 1 0.0000 0.8597 1.000 0.000
#> GSM11846 1 0.0000 0.8597 1.000 0.000
#> GSM11680 1 0.0000 0.8597 1.000 0.000
#> GSM11698 1 0.0000 0.8597 1.000 0.000
#> GSM11840 1 0.0000 0.8597 1.000 0.000
#> GSM11847 1 0.0000 0.8597 1.000 0.000
#> GSM11685 1 0.2043 0.8638 0.968 0.032
#> GSM11699 1 0.7219 0.8240 0.800 0.200
#> GSM27950 1 0.0000 0.8597 1.000 0.000
#> GSM27946 1 0.2603 0.8645 0.956 0.044
#> GSM11709 2 0.5842 0.7966 0.140 0.860
#> GSM11720 2 0.0000 0.9437 0.000 1.000
#> GSM11726 2 0.0376 0.9431 0.004 0.996
#> GSM11837 2 0.0376 0.9431 0.004 0.996
#> GSM11725 2 0.0376 0.9431 0.004 0.996
#> GSM11864 2 0.0000 0.9437 0.000 1.000
#> GSM11687 2 0.0000 0.9437 0.000 1.000
#> GSM11693 2 0.3879 0.8645 0.076 0.924
#> GSM11727 2 0.0000 0.9437 0.000 1.000
#> GSM11838 2 0.0376 0.9431 0.004 0.996
#> GSM11681 1 0.8386 0.7593 0.732 0.268
#> GSM11689 2 0.0000 0.9437 0.000 1.000
#> GSM11704 2 0.0000 0.9437 0.000 1.000
#> GSM11703 2 0.6973 0.6975 0.188 0.812
#> GSM11705 1 0.9732 0.5305 0.596 0.404
#> GSM11722 2 0.0000 0.9437 0.000 1.000
#> GSM11730 2 0.0000 0.9437 0.000 1.000
#> GSM11713 2 0.0000 0.9437 0.000 1.000
#> GSM11728 1 0.9795 0.5072 0.584 0.416
#> GSM27947 1 0.0938 0.8615 0.988 0.012
#> GSM27951 2 0.0000 0.9437 0.000 1.000
#> GSM11707 1 0.0000 0.8597 1.000 0.000
#> GSM11716 1 0.9491 0.3724 0.632 0.368
#> GSM11850 2 0.9944 -0.1217 0.456 0.544
#> GSM11851 1 0.0000 0.8597 1.000 0.000
#> GSM11721 1 0.7219 0.8240 0.800 0.200
#> GSM11852 1 0.3584 0.8648 0.932 0.068
#> GSM11694 1 0.5059 0.8593 0.888 0.112
#> GSM11695 1 0.6623 0.8387 0.828 0.172
#> GSM11734 2 0.0376 0.9431 0.004 0.996
#> GSM11861 1 0.7453 0.8158 0.788 0.212
#> GSM11843 2 0.0000 0.9437 0.000 1.000
#> GSM11862 1 0.8081 0.7848 0.752 0.248
#> GSM11697 1 0.5178 0.8583 0.884 0.116
#> GSM11714 1 0.3584 0.8645 0.932 0.068
#> GSM11723 2 0.0376 0.9431 0.004 0.996
#> GSM11845 2 0.0376 0.9431 0.004 0.996
#> GSM11683 1 0.9686 0.5535 0.604 0.396
#> GSM11691 1 0.9732 0.5351 0.596 0.404
#> GSM27949 1 0.0000 0.8597 1.000 0.000
#> GSM27945 1 0.5059 0.8594 0.888 0.112
#> GSM11706 1 0.0000 0.8597 1.000 0.000
#> GSM11853 1 0.6343 0.8442 0.840 0.160
#> GSM11729 2 0.0376 0.9431 0.004 0.996
#> GSM11746 2 0.0376 0.9431 0.004 0.996
#> GSM11711 1 0.5629 0.8541 0.868 0.132
#> GSM11854 1 0.3733 0.8646 0.928 0.072
#> GSM11731 2 0.0376 0.9431 0.004 0.996
#> GSM11839 2 0.0000 0.9437 0.000 1.000
#> GSM11836 2 0.0938 0.9379 0.012 0.988
#> GSM11849 2 0.9754 0.0627 0.408 0.592
#> GSM11682 1 0.5842 0.8520 0.860 0.140
#> GSM11690 1 0.7219 0.8240 0.800 0.200
#> GSM11692 1 0.7219 0.8240 0.800 0.200
#> GSM11841 1 0.9850 0.4735 0.572 0.428
#> GSM11901 1 0.8713 0.7347 0.708 0.292
#> GSM11715 2 0.0000 0.9437 0.000 1.000
#> GSM11724 2 0.0000 0.9437 0.000 1.000
#> GSM11684 1 0.7219 0.8240 0.800 0.200
#> GSM11696 1 0.7299 0.8217 0.796 0.204
#> GSM27952 1 0.0672 0.8607 0.992 0.008
#> GSM27948 1 0.7219 0.8240 0.800 0.200
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM11708 3 0.0892 0.725 0.020 0.000 0.980
#> GSM11735 3 0.0475 0.722 0.004 0.004 0.992
#> GSM11733 3 0.1411 0.710 0.000 0.036 0.964
#> GSM11863 3 0.2261 0.693 0.000 0.068 0.932
#> GSM11710 3 0.4887 0.728 0.228 0.000 0.772
#> GSM11712 3 0.9217 0.542 0.260 0.208 0.532
#> GSM11732 2 0.5621 0.510 0.000 0.692 0.308
#> GSM11844 3 0.5956 0.470 0.004 0.324 0.672
#> GSM11842 3 0.4796 0.512 0.000 0.220 0.780
#> GSM11860 3 0.2096 0.703 0.004 0.052 0.944
#> GSM11686 3 0.5859 0.686 0.344 0.000 0.656
#> GSM11688 3 0.1964 0.735 0.056 0.000 0.944
#> GSM11846 3 0.1753 0.728 0.048 0.000 0.952
#> GSM11680 3 0.2537 0.735 0.080 0.000 0.920
#> GSM11698 3 0.1031 0.730 0.024 0.000 0.976
#> GSM11840 3 0.0592 0.720 0.000 0.012 0.988
#> GSM11847 3 0.0237 0.722 0.000 0.004 0.996
#> GSM11685 3 0.5706 0.699 0.320 0.000 0.680
#> GSM11699 3 0.5948 0.669 0.360 0.000 0.640
#> GSM27950 3 0.1289 0.728 0.032 0.000 0.968
#> GSM27946 3 0.5882 0.679 0.348 0.000 0.652
#> GSM11709 1 0.7501 0.518 0.684 0.104 0.212
#> GSM11720 1 0.4605 0.657 0.796 0.204 0.000
#> GSM11726 2 0.6308 0.093 0.492 0.508 0.000
#> GSM11837 2 0.1031 0.819 0.024 0.976 0.000
#> GSM11725 2 0.1411 0.817 0.036 0.964 0.000
#> GSM11864 2 0.0892 0.818 0.020 0.980 0.000
#> GSM11687 1 0.2400 0.814 0.932 0.064 0.004
#> GSM11693 1 0.1129 0.834 0.976 0.020 0.004
#> GSM11727 2 0.5465 0.544 0.288 0.712 0.000
#> GSM11838 2 0.2165 0.804 0.064 0.936 0.000
#> GSM11681 1 0.0424 0.828 0.992 0.000 0.008
#> GSM11689 1 0.2165 0.816 0.936 0.064 0.000
#> GSM11704 1 0.3116 0.779 0.892 0.108 0.000
#> GSM11703 1 0.0424 0.833 0.992 0.008 0.000
#> GSM11705 1 0.0661 0.834 0.988 0.008 0.004
#> GSM11722 2 0.6302 0.127 0.480 0.520 0.000
#> GSM11730 1 0.6079 0.214 0.612 0.388 0.000
#> GSM11713 1 0.4062 0.719 0.836 0.164 0.000
#> GSM11728 1 0.0424 0.833 0.992 0.008 0.000
#> GSM27947 3 0.6126 0.623 0.400 0.000 0.600
#> GSM27951 1 0.0892 0.834 0.980 0.020 0.000
#> GSM11707 3 0.2066 0.722 0.060 0.000 0.940
#> GSM11716 3 0.6308 -0.149 0.000 0.492 0.508
#> GSM11850 2 0.6282 0.327 0.004 0.612 0.384
#> GSM11851 3 0.1267 0.724 0.004 0.024 0.972
#> GSM11721 3 0.6546 0.711 0.240 0.044 0.716
#> GSM11852 3 0.5591 0.708 0.304 0.000 0.696
#> GSM11694 3 0.5754 0.686 0.296 0.004 0.700
#> GSM11695 3 0.6180 0.599 0.416 0.000 0.584
#> GSM11734 2 0.1964 0.809 0.056 0.944 0.000
#> GSM11861 1 0.4475 0.781 0.864 0.064 0.072
#> GSM11843 2 0.3879 0.689 0.152 0.848 0.000
#> GSM11862 1 0.4654 0.531 0.792 0.000 0.208
#> GSM11697 3 0.6140 0.598 0.404 0.000 0.596
#> GSM11714 3 0.6079 0.525 0.388 0.000 0.612
#> GSM11723 2 0.0237 0.816 0.000 0.996 0.004
#> GSM11845 2 0.1491 0.814 0.016 0.968 0.016
#> GSM11683 1 0.5708 0.562 0.768 0.028 0.204
#> GSM11691 1 0.1129 0.835 0.976 0.020 0.004
#> GSM27949 3 0.1289 0.728 0.032 0.000 0.968
#> GSM27945 3 0.6026 0.657 0.376 0.000 0.624
#> GSM11706 3 0.2959 0.739 0.100 0.000 0.900
#> GSM11853 3 0.5678 0.700 0.316 0.000 0.684
#> GSM11729 2 0.0237 0.816 0.000 0.996 0.004
#> GSM11746 2 0.1411 0.817 0.036 0.964 0.000
#> GSM11711 3 0.5948 0.678 0.360 0.000 0.640
#> GSM11854 3 0.5706 0.699 0.320 0.000 0.680
#> GSM11731 2 0.0237 0.816 0.000 0.996 0.004
#> GSM11839 2 0.1289 0.818 0.032 0.968 0.000
#> GSM11836 2 0.1129 0.811 0.004 0.976 0.020
#> GSM11849 1 0.3933 0.785 0.880 0.092 0.028
#> GSM11682 1 0.6204 -0.246 0.576 0.000 0.424
#> GSM11690 3 0.6168 0.607 0.412 0.000 0.588
#> GSM11692 3 0.6333 0.686 0.332 0.012 0.656
#> GSM11841 2 0.9887 -0.154 0.288 0.408 0.304
#> GSM11901 3 0.9956 0.336 0.308 0.312 0.380
#> GSM11715 2 0.0747 0.817 0.016 0.984 0.000
#> GSM11724 2 0.1964 0.811 0.056 0.944 0.000
#> GSM11684 1 0.1163 0.812 0.972 0.000 0.028
#> GSM11696 1 0.1399 0.817 0.968 0.004 0.028
#> GSM27952 3 0.6079 0.646 0.388 0.000 0.612
#> GSM27948 3 0.6189 0.665 0.364 0.004 0.632
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM11708 3 0.0000 0.7764 0.000 0.000 1.000 0.000
#> GSM11735 3 0.0188 0.7768 0.000 0.000 0.996 0.004
#> GSM11733 3 0.2310 0.7694 0.004 0.008 0.920 0.068
#> GSM11863 3 0.4265 0.7467 0.016 0.068 0.840 0.076
#> GSM11710 4 0.5678 0.2857 0.024 0.000 0.452 0.524
#> GSM11712 4 0.7051 0.5809 0.032 0.268 0.088 0.612
#> GSM11732 2 0.5244 -0.0116 0.008 0.556 0.436 0.000
#> GSM11844 3 0.5622 0.5310 0.024 0.328 0.640 0.008
#> GSM11842 3 0.6401 0.3806 0.016 0.360 0.580 0.044
#> GSM11860 3 0.3380 0.7428 0.088 0.028 0.876 0.008
#> GSM11686 4 0.5972 0.7303 0.132 0.000 0.176 0.692
#> GSM11688 3 0.5085 0.1443 0.008 0.000 0.616 0.376
#> GSM11846 3 0.3821 0.7192 0.120 0.000 0.840 0.040
#> GSM11680 3 0.2021 0.7735 0.012 0.000 0.932 0.056
#> GSM11698 3 0.2342 0.7675 0.008 0.000 0.912 0.080
#> GSM11840 3 0.2384 0.7680 0.004 0.008 0.916 0.072
#> GSM11847 3 0.2197 0.7654 0.000 0.004 0.916 0.080
#> GSM11685 4 0.4122 0.7040 0.004 0.000 0.236 0.760
#> GSM11699 4 0.3497 0.7582 0.024 0.000 0.124 0.852
#> GSM27950 3 0.0707 0.7774 0.000 0.000 0.980 0.020
#> GSM27946 4 0.5110 0.7379 0.132 0.000 0.104 0.764
#> GSM11709 1 0.4604 0.6084 0.756 0.012 0.224 0.008
#> GSM11720 1 0.5712 0.6978 0.756 0.072 0.036 0.136
#> GSM11726 1 0.6786 0.4886 0.640 0.256 0.044 0.060
#> GSM11837 2 0.3088 0.7923 0.128 0.864 0.000 0.008
#> GSM11725 2 0.4008 0.6762 0.244 0.756 0.000 0.000
#> GSM11864 2 0.4059 0.7483 0.200 0.788 0.000 0.012
#> GSM11687 1 0.2055 0.7428 0.936 0.008 0.008 0.048
#> GSM11693 1 0.2048 0.7442 0.928 0.000 0.008 0.064
#> GSM11727 1 0.6878 0.1231 0.472 0.424 0.000 0.104
#> GSM11838 2 0.5292 0.6420 0.208 0.728 0.000 0.064
#> GSM11681 1 0.3626 0.6882 0.812 0.000 0.004 0.184
#> GSM11689 1 0.2382 0.7446 0.912 0.004 0.004 0.080
#> GSM11704 1 0.2376 0.7438 0.916 0.016 0.000 0.068
#> GSM11703 1 0.4222 0.6275 0.728 0.000 0.000 0.272
#> GSM11705 1 0.3992 0.7199 0.800 0.004 0.008 0.188
#> GSM11722 1 0.6729 0.4731 0.588 0.284 0.000 0.128
#> GSM11730 1 0.5951 0.6344 0.696 0.152 0.000 0.152
#> GSM11713 1 0.5508 0.6945 0.692 0.056 0.000 0.252
#> GSM11728 1 0.5088 0.5176 0.572 0.000 0.004 0.424
#> GSM27947 4 0.6461 0.6448 0.240 0.000 0.128 0.632
#> GSM27951 1 0.2401 0.7398 0.904 0.000 0.004 0.092
#> GSM11707 3 0.1356 0.7746 0.032 0.000 0.960 0.008
#> GSM11716 3 0.5628 0.6123 0.080 0.216 0.704 0.000
#> GSM11850 3 0.5987 0.2206 0.040 0.440 0.520 0.000
#> GSM11851 3 0.5447 0.7148 0.048 0.052 0.776 0.124
#> GSM11721 4 0.6312 0.7319 0.080 0.052 0.148 0.720
#> GSM11852 4 0.5532 0.7175 0.068 0.000 0.228 0.704
#> GSM11694 3 0.4423 0.6894 0.176 0.000 0.788 0.036
#> GSM11695 3 0.5123 0.6317 0.232 0.000 0.724 0.044
#> GSM11734 2 0.3743 0.7899 0.160 0.824 0.000 0.016
#> GSM11861 4 0.6119 0.5407 0.272 0.052 0.016 0.660
#> GSM11843 2 0.4328 0.7068 0.244 0.748 0.000 0.008
#> GSM11862 4 0.5021 0.5736 0.240 0.000 0.036 0.724
#> GSM11697 3 0.4458 0.7144 0.116 0.000 0.808 0.076
#> GSM11714 3 0.5185 0.6710 0.176 0.000 0.748 0.076
#> GSM11723 2 0.1109 0.8062 0.028 0.968 0.000 0.004
#> GSM11845 2 0.3547 0.7548 0.144 0.840 0.000 0.016
#> GSM11683 1 0.6510 0.4313 0.524 0.004 0.064 0.408
#> GSM11691 1 0.4648 0.6962 0.748 0.004 0.016 0.232
#> GSM27949 3 0.0469 0.7769 0.012 0.000 0.988 0.000
#> GSM27945 3 0.7880 -0.1563 0.284 0.000 0.372 0.344
#> GSM11706 3 0.2281 0.7573 0.000 0.000 0.904 0.096
#> GSM11853 4 0.6483 0.4606 0.096 0.000 0.312 0.592
#> GSM11729 2 0.0592 0.8054 0.016 0.984 0.000 0.000
#> GSM11746 2 0.2888 0.7927 0.124 0.872 0.000 0.004
#> GSM11711 4 0.6309 0.5174 0.076 0.000 0.336 0.588
#> GSM11854 4 0.4814 0.5996 0.008 0.000 0.316 0.676
#> GSM11731 2 0.0336 0.8044 0.008 0.992 0.000 0.000
#> GSM11839 2 0.3320 0.8094 0.068 0.876 0.000 0.056
#> GSM11836 2 0.3278 0.7378 0.020 0.864 0.000 0.116
#> GSM11849 4 0.4470 0.5605 0.172 0.032 0.004 0.792
#> GSM11682 4 0.4535 0.7219 0.112 0.000 0.084 0.804
#> GSM11690 4 0.3935 0.7503 0.060 0.000 0.100 0.840
#> GSM11692 4 0.3317 0.7545 0.008 0.012 0.112 0.868
#> GSM11841 4 0.5512 0.5909 0.020 0.268 0.020 0.692
#> GSM11901 4 0.4932 0.6855 0.024 0.160 0.032 0.784
#> GSM11715 2 0.2335 0.8073 0.060 0.920 0.000 0.020
#> GSM11724 2 0.5383 0.7054 0.100 0.740 0.000 0.160
#> GSM11684 4 0.2859 0.6367 0.112 0.000 0.008 0.880
#> GSM11696 4 0.2345 0.6406 0.100 0.000 0.000 0.900
#> GSM27952 4 0.4776 0.7582 0.060 0.000 0.164 0.776
#> GSM27948 4 0.3013 0.7533 0.032 0.000 0.080 0.888
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM11708 3 0.0290 0.8266 0.000 0.000 0.992 0.008 0.000
#> GSM11735 3 0.0290 0.8266 0.000 0.000 0.992 0.008 0.000
#> GSM11733 3 0.1978 0.8200 0.004 0.024 0.928 0.044 0.000
#> GSM11863 3 0.3936 0.7371 0.004 0.144 0.800 0.052 0.000
#> GSM11710 4 0.3544 0.7784 0.028 0.000 0.120 0.836 0.016
#> GSM11712 4 0.3435 0.7696 0.012 0.148 0.004 0.828 0.008
#> GSM11732 3 0.4456 0.6145 0.000 0.320 0.660 0.000 0.020
#> GSM11844 3 0.4143 0.7097 0.004 0.260 0.724 0.004 0.008
#> GSM11842 2 0.5041 0.2189 0.004 0.564 0.404 0.028 0.000
#> GSM11860 3 0.6183 -0.0643 0.404 0.088 0.492 0.016 0.000
#> GSM11686 4 0.4035 0.7557 0.220 0.000 0.008 0.756 0.016
#> GSM11688 4 0.4990 0.5657 0.048 0.000 0.324 0.628 0.000
#> GSM11846 1 0.4286 0.6262 0.716 0.004 0.260 0.020 0.000
#> GSM11680 3 0.1869 0.8330 0.036 0.000 0.936 0.016 0.012
#> GSM11698 3 0.3896 0.8205 0.044 0.032 0.848 0.056 0.020
#> GSM11840 3 0.2125 0.8163 0.004 0.024 0.920 0.052 0.000
#> GSM11847 3 0.2166 0.8122 0.004 0.012 0.912 0.072 0.000
#> GSM11685 4 0.0740 0.8294 0.004 0.000 0.008 0.980 0.008
#> GSM11699 4 0.1630 0.8331 0.036 0.000 0.004 0.944 0.016
#> GSM27950 3 0.1106 0.8316 0.024 0.000 0.964 0.012 0.000
#> GSM27946 4 0.4237 0.6999 0.240 0.008 0.004 0.736 0.012
#> GSM11709 1 0.4779 0.7073 0.748 0.008 0.124 0.000 0.120
#> GSM11720 1 0.4489 0.7351 0.780 0.028 0.008 0.028 0.156
#> GSM11726 5 0.3457 0.7132 0.048 0.084 0.016 0.000 0.852
#> GSM11837 2 0.4101 0.4532 0.000 0.628 0.000 0.000 0.372
#> GSM11725 2 0.5706 0.2629 0.380 0.540 0.004 0.000 0.076
#> GSM11864 1 0.6271 0.1473 0.480 0.384 0.004 0.000 0.132
#> GSM11687 1 0.2722 0.7625 0.868 0.008 0.000 0.004 0.120
#> GSM11693 1 0.2326 0.7730 0.908 0.012 0.004 0.004 0.072
#> GSM11727 5 0.2574 0.6940 0.012 0.112 0.000 0.000 0.876
#> GSM11838 5 0.3838 0.4952 0.004 0.280 0.000 0.000 0.716
#> GSM11681 1 0.2964 0.7325 0.856 0.000 0.000 0.024 0.120
#> GSM11689 1 0.1205 0.7764 0.956 0.000 0.000 0.004 0.040
#> GSM11704 1 0.1365 0.7760 0.952 0.004 0.000 0.004 0.040
#> GSM11703 1 0.4521 0.7161 0.748 0.000 0.000 0.088 0.164
#> GSM11705 5 0.4995 0.2341 0.384 0.000 0.004 0.028 0.584
#> GSM11722 5 0.2514 0.7319 0.044 0.060 0.000 0.000 0.896
#> GSM11730 5 0.1800 0.7396 0.048 0.020 0.000 0.000 0.932
#> GSM11713 5 0.2439 0.7316 0.120 0.000 0.000 0.004 0.876
#> GSM11728 5 0.3904 0.6987 0.156 0.000 0.000 0.052 0.792
#> GSM27947 1 0.3521 0.7136 0.824 0.000 0.024 0.144 0.008
#> GSM27951 1 0.2172 0.7739 0.908 0.000 0.000 0.016 0.076
#> GSM11707 3 0.0486 0.8272 0.004 0.000 0.988 0.004 0.004
#> GSM11716 3 0.5275 0.7399 0.096 0.156 0.724 0.004 0.020
#> GSM11850 3 0.5188 0.5931 0.036 0.320 0.632 0.004 0.008
#> GSM11851 3 0.5422 0.7779 0.060 0.104 0.752 0.064 0.020
#> GSM11721 4 0.3646 0.8046 0.036 0.032 0.000 0.844 0.088
#> GSM11852 4 0.4474 0.7977 0.056 0.012 0.052 0.812 0.068
#> GSM11694 3 0.4232 0.7750 0.152 0.040 0.788 0.000 0.020
#> GSM11695 3 0.4892 0.7327 0.208 0.044 0.724 0.000 0.024
#> GSM11734 2 0.3527 0.6648 0.024 0.804 0.000 0.000 0.172
#> GSM11861 4 0.6037 0.6436 0.240 0.092 0.000 0.632 0.036
#> GSM11843 2 0.4541 0.6171 0.140 0.760 0.004 0.000 0.096
#> GSM11862 4 0.5363 0.7261 0.156 0.040 0.000 0.720 0.084
#> GSM11697 3 0.4426 0.8015 0.080 0.040 0.816 0.020 0.044
#> GSM11714 3 0.4026 0.7925 0.080 0.012 0.820 0.004 0.084
#> GSM11723 2 0.2529 0.6945 0.032 0.904 0.004 0.004 0.056
#> GSM11845 2 0.3523 0.6613 0.076 0.844 0.008 0.000 0.072
#> GSM11683 5 0.5433 0.6554 0.120 0.020 0.080 0.036 0.744
#> GSM11691 5 0.4915 0.6752 0.144 0.028 0.036 0.024 0.768
#> GSM27949 3 0.0794 0.8296 0.028 0.000 0.972 0.000 0.000
#> GSM27945 1 0.3225 0.7422 0.880 0.052 0.012 0.032 0.024
#> GSM11706 3 0.2286 0.8063 0.004 0.000 0.888 0.108 0.000
#> GSM11853 1 0.4944 0.1246 0.508 0.004 0.012 0.472 0.004
#> GSM11729 2 0.2284 0.6936 0.000 0.896 0.004 0.004 0.096
#> GSM11746 2 0.4111 0.6727 0.084 0.796 0.004 0.000 0.116
#> GSM11711 4 0.5049 -0.0612 0.472 0.000 0.024 0.500 0.004
#> GSM11854 4 0.2196 0.8249 0.056 0.000 0.024 0.916 0.004
#> GSM11731 2 0.1908 0.6963 0.000 0.908 0.000 0.000 0.092
#> GSM11839 2 0.4712 0.6055 0.020 0.716 0.000 0.028 0.236
#> GSM11836 2 0.5730 0.3208 0.000 0.548 0.000 0.356 0.096
#> GSM11849 4 0.4672 0.7137 0.032 0.024 0.000 0.736 0.208
#> GSM11682 4 0.3340 0.8123 0.124 0.000 0.004 0.840 0.032
#> GSM11690 4 0.2074 0.8312 0.060 0.000 0.004 0.920 0.016
#> GSM11692 4 0.0324 0.8278 0.000 0.004 0.000 0.992 0.004
#> GSM11841 4 0.2411 0.8018 0.000 0.108 0.000 0.884 0.008
#> GSM11901 4 0.0798 0.8279 0.000 0.016 0.000 0.976 0.008
#> GSM11715 2 0.3274 0.6573 0.000 0.780 0.000 0.000 0.220
#> GSM11724 5 0.5049 0.0490 0.004 0.408 0.000 0.028 0.560
#> GSM11684 4 0.2966 0.7957 0.016 0.000 0.000 0.848 0.136
#> GSM11696 4 0.2727 0.8073 0.016 0.000 0.000 0.868 0.116
#> GSM27952 4 0.2452 0.8268 0.084 0.000 0.004 0.896 0.016
#> GSM27948 4 0.0703 0.8297 0.024 0.000 0.000 0.976 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM11708 3 0.0551 0.64354 0.004 0.000 0.984 0.004 0.000 0.008
#> GSM11735 3 0.0665 0.64286 0.000 0.004 0.980 0.008 0.000 0.008
#> GSM11733 3 0.3467 0.58281 0.004 0.092 0.836 0.032 0.000 0.036
#> GSM11863 3 0.6672 0.08326 0.004 0.324 0.476 0.092 0.000 0.104
#> GSM11710 4 0.5259 0.60817 0.128 0.004 0.112 0.708 0.008 0.040
#> GSM11712 4 0.5409 0.59874 0.036 0.152 0.008 0.688 0.004 0.112
#> GSM11732 3 0.3975 0.54969 0.000 0.244 0.716 0.000 0.000 0.040
#> GSM11844 3 0.3744 0.59076 0.000 0.200 0.756 0.000 0.000 0.044
#> GSM11842 2 0.6722 0.16035 0.004 0.460 0.332 0.076 0.000 0.128
#> GSM11860 3 0.7695 -0.03186 0.308 0.180 0.392 0.032 0.004 0.084
#> GSM11686 4 0.4876 0.62378 0.220 0.000 0.024 0.696 0.012 0.048
#> GSM11688 4 0.5420 0.44622 0.120 0.000 0.296 0.576 0.000 0.008
#> GSM11846 1 0.4305 0.54976 0.724 0.000 0.216 0.048 0.004 0.008
#> GSM11680 3 0.4150 0.60488 0.012 0.000 0.740 0.048 0.000 0.200
#> GSM11698 3 0.4656 0.56639 0.008 0.000 0.668 0.064 0.000 0.260
#> GSM11840 3 0.5293 0.46451 0.004 0.120 0.692 0.136 0.000 0.048
#> GSM11847 3 0.4229 0.53790 0.004 0.056 0.776 0.132 0.000 0.032
#> GSM11685 4 0.1377 0.69937 0.004 0.000 0.024 0.952 0.004 0.016
#> GSM11699 4 0.4052 0.55483 0.012 0.000 0.004 0.692 0.008 0.284
#> GSM27950 3 0.2063 0.65399 0.020 0.000 0.912 0.008 0.000 0.060
#> GSM27946 4 0.4037 0.62748 0.200 0.000 0.000 0.736 0.000 0.064
#> GSM11709 1 0.3963 0.66543 0.748 0.000 0.016 0.000 0.208 0.028
#> GSM11720 1 0.3894 0.68646 0.776 0.008 0.000 0.000 0.152 0.064
#> GSM11726 5 0.3364 0.65682 0.024 0.104 0.020 0.000 0.840 0.012
#> GSM11837 2 0.4720 0.20529 0.000 0.560 0.000 0.000 0.388 0.052
#> GSM11725 2 0.5058 0.12790 0.400 0.540 0.000 0.000 0.020 0.040
#> GSM11864 1 0.6912 0.14791 0.416 0.336 0.000 0.000 0.088 0.160
#> GSM11687 1 0.3473 0.68201 0.780 0.000 0.000 0.004 0.192 0.024
#> GSM11693 1 0.3663 0.66350 0.784 0.000 0.000 0.000 0.068 0.148
#> GSM11727 5 0.2234 0.65586 0.000 0.124 0.000 0.000 0.872 0.004
#> GSM11838 5 0.4712 0.14409 0.000 0.384 0.000 0.000 0.564 0.052
#> GSM11681 1 0.3223 0.65535 0.836 0.000 0.000 0.008 0.104 0.052
#> GSM11689 1 0.2145 0.69058 0.900 0.000 0.000 0.000 0.028 0.072
#> GSM11704 1 0.2795 0.68646 0.856 0.000 0.000 0.000 0.044 0.100
#> GSM11703 1 0.6758 0.15444 0.356 0.000 0.000 0.036 0.316 0.292
#> GSM11705 5 0.4089 0.15658 0.352 0.000 0.000 0.004 0.632 0.012
#> GSM11722 5 0.1493 0.68781 0.004 0.056 0.000 0.000 0.936 0.004
#> GSM11730 5 0.0984 0.68891 0.012 0.012 0.000 0.000 0.968 0.008
#> GSM11713 5 0.2563 0.66090 0.040 0.000 0.000 0.008 0.884 0.068
#> GSM11728 5 0.5213 0.51185 0.160 0.000 0.000 0.036 0.680 0.124
#> GSM27947 1 0.4452 0.59625 0.764 0.000 0.036 0.120 0.004 0.076
#> GSM27951 1 0.2261 0.70866 0.884 0.000 0.000 0.004 0.104 0.008
#> GSM11707 3 0.0820 0.64173 0.012 0.000 0.972 0.000 0.016 0.000
#> GSM11716 3 0.5154 0.53508 0.008 0.080 0.632 0.008 0.000 0.272
#> GSM11850 3 0.5484 0.42524 0.000 0.148 0.568 0.004 0.000 0.280
#> GSM11851 3 0.4809 0.56152 0.000 0.024 0.668 0.052 0.000 0.256
#> GSM11721 4 0.4726 0.66927 0.036 0.028 0.008 0.776 0.072 0.080
#> GSM11852 4 0.4365 0.64186 0.044 0.000 0.020 0.788 0.052 0.096
#> GSM11694 3 0.4893 0.54747 0.040 0.008 0.668 0.004 0.016 0.264
#> GSM11695 3 0.5081 0.50480 0.036 0.004 0.624 0.024 0.004 0.308
#> GSM11734 2 0.5453 0.08083 0.000 0.464 0.000 0.004 0.104 0.428
#> GSM11861 6 0.5199 0.17703 0.032 0.040 0.000 0.368 0.000 0.560
#> GSM11843 2 0.5653 0.03199 0.048 0.520 0.004 0.000 0.044 0.384
#> GSM11862 4 0.5846 0.23840 0.064 0.004 0.000 0.548 0.052 0.332
#> GSM11697 3 0.4788 0.52911 0.020 0.000 0.640 0.020 0.012 0.308
#> GSM11714 3 0.4952 0.55175 0.036 0.000 0.708 0.000 0.148 0.108
#> GSM11723 6 0.5323 -0.00852 0.000 0.460 0.044 0.008 0.016 0.472
#> GSM11845 6 0.4294 0.26900 0.004 0.304 0.008 0.008 0.008 0.668
#> GSM11683 6 0.7352 0.27336 0.036 0.000 0.216 0.048 0.280 0.420
#> GSM11691 6 0.6043 0.44137 0.032 0.000 0.096 0.056 0.172 0.644
#> GSM27949 3 0.1531 0.65369 0.004 0.000 0.928 0.000 0.000 0.068
#> GSM27945 6 0.5839 0.08505 0.384 0.012 0.020 0.080 0.000 0.504
#> GSM11706 3 0.5740 0.29467 0.160 0.000 0.580 0.244 0.004 0.012
#> GSM11853 1 0.4242 0.09889 0.536 0.000 0.000 0.448 0.000 0.016
#> GSM11729 2 0.1649 0.53085 0.000 0.932 0.000 0.000 0.036 0.032
#> GSM11746 2 0.4635 0.46963 0.148 0.712 0.000 0.000 0.132 0.008
#> GSM11711 4 0.4572 0.05855 0.460 0.000 0.016 0.512 0.000 0.012
#> GSM11854 4 0.2113 0.69833 0.044 0.000 0.028 0.916 0.004 0.008
#> GSM11731 2 0.1261 0.52463 0.000 0.952 0.000 0.000 0.024 0.024
#> GSM11839 2 0.6080 0.39635 0.012 0.584 0.000 0.032 0.236 0.136
#> GSM11836 2 0.5647 0.34147 0.000 0.596 0.004 0.288 0.056 0.056
#> GSM11849 4 0.4291 0.57253 0.020 0.020 0.000 0.708 0.248 0.004
#> GSM11682 4 0.3920 0.66889 0.136 0.000 0.000 0.788 0.024 0.052
#> GSM11690 4 0.2471 0.69629 0.056 0.000 0.000 0.888 0.004 0.052
#> GSM11692 4 0.3016 0.67199 0.000 0.016 0.000 0.836 0.012 0.136
#> GSM11841 4 0.4979 0.56642 0.000 0.164 0.000 0.672 0.008 0.156
#> GSM11901 4 0.4436 0.62173 0.000 0.080 0.000 0.728 0.012 0.180
#> GSM11715 2 0.4380 0.39561 0.000 0.700 0.000 0.000 0.220 0.080
#> GSM11724 5 0.6255 0.33394 0.000 0.292 0.000 0.040 0.512 0.156
#> GSM11684 4 0.5804 0.41333 0.012 0.000 0.000 0.552 0.252 0.184
#> GSM11696 4 0.5292 0.47764 0.000 0.000 0.000 0.600 0.180 0.220
#> GSM27952 4 0.2948 0.69171 0.144 0.000 0.008 0.836 0.004 0.008
#> GSM27948 4 0.0914 0.69899 0.016 0.000 0.000 0.968 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 cell.line(p) agent(p) time(p) k
#> CV:NMF 79 5.42e-07 0.4410 4.91e-03 2
#> CV:NMF 74 1.38e-06 0.0537 1.40e-03 3
#> CV:NMF 72 1.02e-11 0.6430 2.74e-06 4
#> CV:NMF 72 1.83e-11 0.1116 5.84e-07 5
#> CV:NMF 52 1.16e-10 0.3268 2.60e-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", "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 14502 rows and 83 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.250 0.768 0.854 0.4234 0.584 0.584
#> 3 3 0.260 0.684 0.771 0.2362 0.960 0.932
#> 4 4 0.299 0.648 0.730 0.2353 0.781 0.616
#> 5 5 0.449 0.615 0.734 0.0833 0.957 0.888
#> 6 6 0.614 0.598 0.737 0.1061 0.855 0.593
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM11708 2 0.000 0.847 0.000 1.000
#> GSM11735 2 0.000 0.847 0.000 1.000
#> GSM11733 2 0.730 0.732 0.204 0.796
#> GSM11863 2 0.730 0.732 0.204 0.796
#> GSM11710 2 0.141 0.853 0.020 0.980
#> GSM11712 1 0.625 0.833 0.844 0.156
#> GSM11732 2 0.943 0.476 0.360 0.640
#> GSM11844 2 0.961 0.412 0.384 0.616
#> GSM11842 1 0.913 0.645 0.672 0.328
#> GSM11860 1 0.913 0.645 0.672 0.328
#> GSM11686 2 0.311 0.835 0.056 0.944
#> GSM11688 2 0.141 0.853 0.020 0.980
#> GSM11846 1 0.929 0.632 0.656 0.344
#> GSM11680 1 0.855 0.754 0.720 0.280
#> GSM11698 1 0.861 0.749 0.716 0.284
#> GSM11840 2 0.730 0.732 0.204 0.796
#> GSM11847 2 0.730 0.732 0.204 0.796
#> GSM11685 2 0.141 0.853 0.020 0.980
#> GSM11699 1 0.781 0.797 0.768 0.232
#> GSM27950 2 0.416 0.824 0.084 0.916
#> GSM27946 1 0.775 0.791 0.772 0.228
#> GSM11709 1 0.861 0.697 0.716 0.284
#> GSM11720 1 0.000 0.820 1.000 0.000
#> GSM11726 1 0.000 0.820 1.000 0.000
#> GSM11837 1 0.000 0.820 1.000 0.000
#> GSM11725 1 0.000 0.820 1.000 0.000
#> GSM11864 1 0.000 0.820 1.000 0.000
#> GSM11687 1 0.775 0.756 0.772 0.228
#> GSM11693 1 0.775 0.756 0.772 0.228
#> GSM11727 1 0.000 0.820 1.000 0.000
#> GSM11838 1 0.000 0.820 1.000 0.000
#> GSM11681 2 0.141 0.853 0.020 0.980
#> GSM11689 1 0.775 0.756 0.772 0.228
#> GSM11704 1 0.775 0.756 0.772 0.228
#> GSM11703 1 0.714 0.812 0.804 0.196
#> GSM11705 1 0.745 0.802 0.788 0.212
#> GSM11722 1 0.000 0.820 1.000 0.000
#> GSM11730 1 0.000 0.820 1.000 0.000
#> GSM11713 2 0.141 0.853 0.020 0.980
#> GSM11728 2 0.141 0.853 0.020 0.980
#> GSM27947 1 0.775 0.791 0.772 0.228
#> GSM27951 1 0.991 0.407 0.556 0.444
#> GSM11707 2 0.000 0.847 0.000 1.000
#> GSM11716 1 0.343 0.826 0.936 0.064
#> GSM11850 1 0.949 0.525 0.632 0.368
#> GSM11851 1 0.949 0.525 0.632 0.368
#> GSM11721 1 0.634 0.832 0.840 0.160
#> GSM11852 1 0.634 0.832 0.840 0.160
#> GSM11694 1 0.821 0.756 0.744 0.256
#> GSM11695 1 0.821 0.756 0.744 0.256
#> GSM11734 1 0.000 0.820 1.000 0.000
#> GSM11861 1 0.644 0.832 0.836 0.164
#> GSM11843 1 0.000 0.820 1.000 0.000
#> GSM11862 1 0.634 0.832 0.840 0.160
#> GSM11697 1 0.833 0.758 0.736 0.264
#> GSM11714 2 0.000 0.847 0.000 1.000
#> GSM11723 1 0.327 0.825 0.940 0.060
#> GSM11845 1 0.327 0.825 0.940 0.060
#> GSM11683 2 0.952 0.229 0.372 0.628
#> GSM11691 2 0.961 0.184 0.384 0.616
#> GSM27949 2 0.653 0.772 0.168 0.832
#> GSM27945 1 0.821 0.756 0.744 0.256
#> GSM11706 2 0.000 0.847 0.000 1.000
#> GSM11853 1 0.775 0.795 0.772 0.228
#> GSM11729 1 0.000 0.820 1.000 0.000
#> GSM11746 1 0.000 0.820 1.000 0.000
#> GSM11711 1 0.839 0.760 0.732 0.268
#> GSM11854 1 0.775 0.795 0.772 0.228
#> GSM11731 1 0.000 0.820 1.000 0.000
#> GSM11839 1 0.000 0.820 1.000 0.000
#> GSM11836 1 0.653 0.833 0.832 0.168
#> GSM11849 1 0.653 0.833 0.832 0.168
#> GSM11682 2 0.141 0.853 0.020 0.980
#> GSM11690 1 0.625 0.834 0.844 0.156
#> GSM11692 1 0.625 0.833 0.844 0.156
#> GSM11841 1 0.625 0.833 0.844 0.156
#> GSM11901 1 0.625 0.833 0.844 0.156
#> GSM11715 1 0.204 0.822 0.968 0.032
#> GSM11724 1 0.204 0.822 0.968 0.032
#> GSM11684 1 0.625 0.834 0.844 0.156
#> GSM11696 1 0.625 0.834 0.844 0.156
#> GSM27952 2 0.141 0.853 0.020 0.980
#> GSM27948 1 0.625 0.834 0.844 0.156
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM11708 3 0.327 0.517 0.000 0.116 0.884
#> GSM11735 3 0.327 0.517 0.000 0.116 0.884
#> GSM11733 3 0.433 0.648 0.100 0.036 0.864
#> GSM11863 3 0.433 0.648 0.100 0.036 0.864
#> GSM11710 2 0.784 0.845 0.072 0.600 0.328
#> GSM11712 1 0.321 0.775 0.904 0.084 0.012
#> GSM11732 3 0.554 0.552 0.252 0.008 0.740
#> GSM11844 3 0.626 0.519 0.284 0.020 0.696
#> GSM11842 1 0.754 0.552 0.632 0.064 0.304
#> GSM11860 1 0.754 0.552 0.632 0.064 0.304
#> GSM11686 2 0.821 0.838 0.104 0.600 0.296
#> GSM11688 2 0.759 0.889 0.072 0.640 0.288
#> GSM11846 1 0.759 0.544 0.624 0.064 0.312
#> GSM11680 1 0.710 0.672 0.692 0.068 0.240
#> GSM11698 1 0.714 0.677 0.700 0.080 0.220
#> GSM11840 3 0.433 0.648 0.100 0.036 0.864
#> GSM11847 3 0.433 0.648 0.100 0.036 0.864
#> GSM11685 2 0.764 0.883 0.072 0.632 0.296
#> GSM11699 1 0.641 0.723 0.756 0.072 0.172
#> GSM27950 3 0.641 0.487 0.080 0.160 0.760
#> GSM27946 1 0.648 0.682 0.716 0.040 0.244
#> GSM11709 1 0.642 0.684 0.752 0.180 0.068
#> GSM11720 1 0.482 0.763 0.848 0.088 0.064
#> GSM11726 1 0.414 0.752 0.860 0.124 0.016
#> GSM11837 1 0.414 0.752 0.860 0.124 0.016
#> GSM11725 1 0.482 0.763 0.848 0.088 0.064
#> GSM11864 1 0.482 0.763 0.848 0.088 0.064
#> GSM11687 1 0.504 0.726 0.808 0.172 0.020
#> GSM11693 1 0.504 0.726 0.808 0.172 0.020
#> GSM11727 1 0.334 0.754 0.880 0.120 0.000
#> GSM11838 1 0.334 0.754 0.880 0.120 0.000
#> GSM11681 2 0.756 0.891 0.072 0.644 0.284
#> GSM11689 1 0.504 0.726 0.808 0.172 0.020
#> GSM11704 1 0.504 0.726 0.808 0.172 0.020
#> GSM11703 1 0.585 0.731 0.780 0.048 0.172
#> GSM11705 1 0.611 0.719 0.760 0.048 0.192
#> GSM11722 1 0.327 0.755 0.884 0.116 0.000
#> GSM11730 1 0.334 0.754 0.880 0.120 0.000
#> GSM11713 2 0.447 0.723 0.076 0.864 0.060
#> GSM11728 2 0.447 0.723 0.076 0.864 0.060
#> GSM27947 1 0.648 0.682 0.716 0.040 0.244
#> GSM27951 1 0.740 0.493 0.612 0.340 0.048
#> GSM11707 3 0.327 0.517 0.000 0.116 0.884
#> GSM11716 1 0.628 0.729 0.760 0.064 0.176
#> GSM11850 1 0.681 0.236 0.520 0.012 0.468
#> GSM11851 1 0.681 0.236 0.520 0.012 0.468
#> GSM11721 1 0.329 0.773 0.900 0.088 0.012
#> GSM11852 1 0.329 0.773 0.900 0.088 0.012
#> GSM11694 1 0.714 0.606 0.644 0.044 0.312
#> GSM11695 1 0.714 0.606 0.644 0.044 0.312
#> GSM11734 1 0.355 0.749 0.868 0.132 0.000
#> GSM11861 1 0.397 0.773 0.880 0.088 0.032
#> GSM11843 1 0.375 0.756 0.872 0.120 0.008
#> GSM11862 1 0.372 0.774 0.888 0.088 0.024
#> GSM11697 1 0.700 0.635 0.672 0.048 0.280
#> GSM11714 3 0.362 0.486 0.000 0.136 0.864
#> GSM11723 1 0.623 0.731 0.764 0.064 0.172
#> GSM11845 1 0.623 0.731 0.764 0.064 0.172
#> GSM11683 3 0.963 0.203 0.340 0.216 0.444
#> GSM11691 3 0.955 0.166 0.352 0.200 0.448
#> GSM27949 3 0.603 0.605 0.116 0.096 0.788
#> GSM27945 1 0.714 0.606 0.644 0.044 0.312
#> GSM11706 3 0.327 0.517 0.000 0.116 0.884
#> GSM11853 1 0.630 0.716 0.756 0.060 0.184
#> GSM11729 1 0.421 0.751 0.856 0.128 0.016
#> GSM11746 1 0.421 0.751 0.856 0.128 0.016
#> GSM11711 1 0.685 0.682 0.712 0.064 0.224
#> GSM11854 1 0.630 0.716 0.756 0.060 0.184
#> GSM11731 1 0.355 0.749 0.868 0.132 0.000
#> GSM11839 1 0.355 0.749 0.868 0.132 0.000
#> GSM11836 1 0.354 0.773 0.888 0.100 0.012
#> GSM11849 1 0.354 0.773 0.888 0.100 0.012
#> GSM11682 2 0.756 0.891 0.072 0.644 0.284
#> GSM11690 1 0.329 0.774 0.900 0.088 0.012
#> GSM11692 1 0.321 0.775 0.904 0.084 0.012
#> GSM11841 1 0.321 0.775 0.904 0.084 0.012
#> GSM11901 1 0.321 0.775 0.904 0.084 0.012
#> GSM11715 1 0.362 0.753 0.864 0.136 0.000
#> GSM11724 1 0.362 0.753 0.864 0.136 0.000
#> GSM11684 1 0.329 0.774 0.900 0.088 0.012
#> GSM11696 1 0.329 0.774 0.900 0.088 0.012
#> GSM27952 2 0.756 0.891 0.072 0.644 0.284
#> GSM27948 1 0.329 0.774 0.900 0.088 0.012
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM11708 3 0.162 0.614 0.028 0.020 0.952 0.000
#> GSM11735 3 0.162 0.614 0.028 0.020 0.952 0.000
#> GSM11733 3 0.557 0.700 0.008 0.044 0.700 0.248
#> GSM11863 3 0.557 0.700 0.008 0.044 0.700 0.248
#> GSM11710 1 0.657 0.830 0.604 0.000 0.280 0.116
#> GSM11712 4 0.334 0.650 0.016 0.128 0.000 0.856
#> GSM11732 3 0.701 0.580 0.008 0.124 0.580 0.288
#> GSM11844 3 0.720 0.517 0.016 0.100 0.536 0.348
#> GSM11842 4 0.599 0.560 0.012 0.084 0.200 0.704
#> GSM11860 4 0.599 0.560 0.012 0.084 0.200 0.704
#> GSM11686 1 0.675 0.828 0.604 0.000 0.244 0.152
#> GSM11688 1 0.632 0.872 0.644 0.000 0.240 0.116
#> GSM11846 4 0.536 0.572 0.012 0.048 0.200 0.740
#> GSM11680 4 0.412 0.660 0.004 0.048 0.116 0.832
#> GSM11698 4 0.349 0.675 0.012 0.020 0.100 0.868
#> GSM11840 3 0.557 0.700 0.008 0.044 0.700 0.248
#> GSM11847 3 0.557 0.700 0.008 0.044 0.700 0.248
#> GSM11685 1 0.637 0.868 0.636 0.000 0.248 0.116
#> GSM11699 4 0.283 0.689 0.004 0.032 0.060 0.904
#> GSM27950 3 0.625 0.533 0.120 0.016 0.700 0.164
#> GSM27946 4 0.464 0.668 0.004 0.076 0.116 0.804
#> GSM11709 4 0.701 0.616 0.184 0.108 0.048 0.660
#> GSM11720 4 0.581 0.353 0.012 0.460 0.012 0.516
#> GSM11726 2 0.435 0.888 0.000 0.756 0.012 0.232
#> GSM11837 2 0.435 0.888 0.000 0.756 0.012 0.232
#> GSM11725 4 0.581 0.353 0.012 0.460 0.012 0.516
#> GSM11864 4 0.581 0.353 0.012 0.460 0.012 0.516
#> GSM11687 4 0.572 0.609 0.176 0.112 0.000 0.712
#> GSM11693 4 0.572 0.609 0.176 0.112 0.000 0.712
#> GSM11727 2 0.417 0.894 0.012 0.776 0.000 0.212
#> GSM11838 2 0.417 0.894 0.012 0.776 0.000 0.212
#> GSM11681 1 0.626 0.875 0.652 0.000 0.232 0.116
#> GSM11689 4 0.572 0.609 0.176 0.112 0.000 0.712
#> GSM11704 4 0.572 0.609 0.176 0.112 0.000 0.712
#> GSM11703 4 0.385 0.687 0.012 0.060 0.068 0.860
#> GSM11705 4 0.440 0.686 0.016 0.068 0.084 0.832
#> GSM11722 2 0.410 0.896 0.012 0.784 0.000 0.204
#> GSM11730 2 0.417 0.894 0.012 0.776 0.000 0.212
#> GSM11713 1 0.172 0.675 0.944 0.008 0.000 0.048
#> GSM11728 1 0.172 0.675 0.944 0.008 0.000 0.048
#> GSM27947 4 0.464 0.668 0.004 0.076 0.116 0.804
#> GSM27951 4 0.585 0.420 0.356 0.044 0.000 0.600
#> GSM11707 3 0.162 0.614 0.028 0.020 0.952 0.000
#> GSM11716 4 0.635 0.430 0.016 0.396 0.036 0.552
#> GSM11850 4 0.747 0.282 0.016 0.136 0.312 0.536
#> GSM11851 4 0.747 0.282 0.016 0.136 0.312 0.536
#> GSM11721 4 0.328 0.650 0.016 0.124 0.000 0.860
#> GSM11852 4 0.328 0.650 0.016 0.124 0.000 0.860
#> GSM11694 4 0.694 0.497 0.008 0.212 0.164 0.616
#> GSM11695 4 0.694 0.497 0.008 0.212 0.164 0.616
#> GSM11734 2 0.215 0.825 0.000 0.912 0.000 0.088
#> GSM11861 4 0.339 0.665 0.016 0.132 0.000 0.852
#> GSM11843 2 0.344 0.726 0.000 0.816 0.000 0.184
#> GSM11862 4 0.328 0.659 0.016 0.124 0.000 0.860
#> GSM11697 4 0.494 0.626 0.004 0.072 0.144 0.780
#> GSM11714 3 0.217 0.586 0.052 0.020 0.928 0.000
#> GSM11723 4 0.626 0.428 0.012 0.400 0.036 0.552
#> GSM11845 4 0.626 0.428 0.012 0.400 0.036 0.552
#> GSM11683 4 0.781 0.106 0.164 0.016 0.344 0.476
#> GSM11691 4 0.788 0.117 0.148 0.024 0.348 0.480
#> GSM27949 3 0.649 0.653 0.080 0.052 0.704 0.164
#> GSM27945 4 0.694 0.497 0.008 0.212 0.164 0.616
#> GSM11706 3 0.162 0.614 0.028 0.020 0.952 0.000
#> GSM11853 4 0.333 0.688 0.008 0.044 0.064 0.884
#> GSM11729 2 0.425 0.889 0.000 0.768 0.012 0.220
#> GSM11746 2 0.425 0.889 0.000 0.768 0.012 0.220
#> GSM11711 4 0.415 0.677 0.012 0.048 0.100 0.840
#> GSM11854 4 0.333 0.688 0.008 0.044 0.064 0.884
#> GSM11731 2 0.222 0.830 0.000 0.908 0.000 0.092
#> GSM11839 2 0.222 0.830 0.000 0.908 0.000 0.092
#> GSM11836 4 0.448 0.624 0.052 0.152 0.000 0.796
#> GSM11849 4 0.448 0.624 0.052 0.152 0.000 0.796
#> GSM11682 1 0.626 0.875 0.652 0.000 0.232 0.116
#> GSM11690 4 0.376 0.640 0.024 0.144 0.000 0.832
#> GSM11692 4 0.334 0.650 0.016 0.128 0.000 0.856
#> GSM11841 4 0.334 0.650 0.016 0.128 0.000 0.856
#> GSM11901 4 0.334 0.650 0.016 0.128 0.000 0.856
#> GSM11715 2 0.506 0.873 0.044 0.732 0.000 0.224
#> GSM11724 2 0.506 0.873 0.044 0.732 0.000 0.224
#> GSM11684 4 0.376 0.640 0.024 0.144 0.000 0.832
#> GSM11696 4 0.376 0.640 0.024 0.144 0.000 0.832
#> GSM27952 1 0.626 0.875 0.652 0.000 0.232 0.116
#> GSM27948 4 0.376 0.640 0.024 0.144 0.000 0.832
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM11708 3 0.463 0.9862 0.188 0.000 0.732 0.000 0.080
#> GSM11735 3 0.463 0.9862 0.188 0.000 0.732 0.000 0.080
#> GSM11733 5 0.351 0.6499 0.036 0.000 0.040 0.068 0.856
#> GSM11863 5 0.351 0.6499 0.036 0.000 0.040 0.068 0.856
#> GSM11710 1 0.327 0.8314 0.852 0.000 0.044 0.100 0.004
#> GSM11712 4 0.127 0.6592 0.000 0.052 0.000 0.948 0.000
#> GSM11732 5 0.345 0.6366 0.000 0.016 0.012 0.144 0.828
#> GSM11844 5 0.418 0.5999 0.008 0.008 0.016 0.204 0.764
#> GSM11842 4 0.544 0.4289 0.000 0.036 0.032 0.640 0.292
#> GSM11860 4 0.544 0.4289 0.000 0.036 0.032 0.640 0.292
#> GSM11686 1 0.302 0.8144 0.848 0.000 0.004 0.136 0.012
#> GSM11688 1 0.230 0.8639 0.892 0.000 0.008 0.100 0.000
#> GSM11846 4 0.458 0.4509 0.000 0.000 0.032 0.672 0.296
#> GSM11680 4 0.448 0.5720 0.008 0.016 0.008 0.724 0.244
#> GSM11698 4 0.400 0.5951 0.012 0.004 0.008 0.768 0.208
#> GSM11840 5 0.351 0.6499 0.036 0.000 0.040 0.068 0.856
#> GSM11847 5 0.351 0.6499 0.036 0.000 0.040 0.068 0.856
#> GSM11685 1 0.257 0.8613 0.884 0.000 0.012 0.100 0.004
#> GSM11699 4 0.321 0.6289 0.004 0.008 0.000 0.824 0.164
#> GSM27950 5 0.761 0.1928 0.152 0.000 0.236 0.116 0.496
#> GSM27946 4 0.424 0.5733 0.004 0.016 0.000 0.712 0.268
#> GSM11709 4 0.623 0.5603 0.128 0.024 0.028 0.672 0.148
#> GSM11720 4 0.727 0.2981 0.000 0.368 0.048 0.424 0.160
#> GSM11726 2 0.298 0.8786 0.000 0.860 0.000 0.108 0.032
#> GSM11837 2 0.298 0.8786 0.000 0.860 0.000 0.108 0.032
#> GSM11725 4 0.728 0.2935 0.000 0.372 0.048 0.420 0.160
#> GSM11864 4 0.728 0.2935 0.000 0.372 0.048 0.420 0.160
#> GSM11687 4 0.547 0.5917 0.120 0.028 0.024 0.740 0.088
#> GSM11693 4 0.547 0.5917 0.120 0.028 0.024 0.740 0.088
#> GSM11727 2 0.230 0.8770 0.008 0.892 0.000 0.100 0.000
#> GSM11838 2 0.230 0.8770 0.008 0.892 0.000 0.100 0.000
#> GSM11681 1 0.202 0.8665 0.900 0.000 0.000 0.100 0.000
#> GSM11689 4 0.547 0.5917 0.120 0.028 0.024 0.740 0.088
#> GSM11704 4 0.547 0.5917 0.120 0.028 0.024 0.740 0.088
#> GSM11703 4 0.400 0.6150 0.004 0.016 0.000 0.748 0.232
#> GSM11705 4 0.438 0.5996 0.008 0.020 0.000 0.716 0.256
#> GSM11722 2 0.317 0.8664 0.008 0.836 0.008 0.148 0.000
#> GSM11730 2 0.230 0.8770 0.008 0.892 0.000 0.100 0.000
#> GSM11713 1 0.477 0.6040 0.728 0.008 0.216 0.008 0.040
#> GSM11728 1 0.477 0.6040 0.728 0.008 0.216 0.008 0.040
#> GSM27947 4 0.424 0.5733 0.004 0.016 0.000 0.712 0.268
#> GSM27951 4 0.574 0.4397 0.256 0.008 0.072 0.648 0.016
#> GSM11707 3 0.463 0.9862 0.188 0.000 0.732 0.000 0.080
#> GSM11716 4 0.762 0.2487 0.000 0.260 0.052 0.408 0.280
#> GSM11850 5 0.492 -0.0238 0.000 0.024 0.004 0.384 0.588
#> GSM11851 5 0.492 -0.0238 0.000 0.024 0.004 0.384 0.588
#> GSM11721 4 0.120 0.6585 0.000 0.048 0.000 0.952 0.000
#> GSM11852 4 0.120 0.6585 0.000 0.048 0.000 0.952 0.000
#> GSM11694 4 0.680 0.2995 0.004 0.104 0.036 0.488 0.368
#> GSM11695 4 0.680 0.2995 0.004 0.104 0.036 0.488 0.368
#> GSM11734 2 0.284 0.8205 0.000 0.892 0.048 0.036 0.024
#> GSM11861 4 0.213 0.6622 0.000 0.052 0.004 0.920 0.024
#> GSM11843 2 0.455 0.7212 0.000 0.776 0.048 0.144 0.032
#> GSM11862 4 0.167 0.6612 0.000 0.052 0.000 0.936 0.012
#> GSM11697 4 0.449 0.5101 0.004 0.004 0.008 0.660 0.324
#> GSM11714 3 0.449 0.9429 0.224 0.000 0.724 0.000 0.052
#> GSM11723 4 0.762 0.2518 0.000 0.264 0.052 0.408 0.276
#> GSM11845 4 0.762 0.2518 0.000 0.264 0.052 0.408 0.276
#> GSM11683 4 0.698 -0.0600 0.172 0.000 0.024 0.420 0.384
#> GSM11691 4 0.697 -0.0559 0.156 0.000 0.028 0.420 0.396
#> GSM27949 5 0.648 0.4122 0.068 0.000 0.224 0.096 0.612
#> GSM27945 4 0.680 0.2995 0.004 0.104 0.036 0.488 0.368
#> GSM11706 3 0.463 0.9862 0.188 0.000 0.732 0.000 0.080
#> GSM11853 4 0.358 0.6157 0.008 0.004 0.000 0.784 0.204
#> GSM11729 2 0.298 0.8776 0.000 0.864 0.000 0.096 0.040
#> GSM11746 2 0.298 0.8776 0.000 0.864 0.000 0.096 0.040
#> GSM11711 4 0.414 0.5896 0.012 0.004 0.004 0.736 0.244
#> GSM11854 4 0.358 0.6157 0.008 0.004 0.000 0.784 0.204
#> GSM11731 2 0.299 0.8284 0.000 0.884 0.048 0.044 0.024
#> GSM11839 2 0.299 0.8284 0.000 0.884 0.048 0.044 0.024
#> GSM11836 4 0.304 0.6374 0.040 0.100 0.000 0.860 0.000
#> GSM11849 4 0.298 0.6382 0.040 0.096 0.000 0.864 0.000
#> GSM11682 1 0.202 0.8665 0.900 0.000 0.000 0.100 0.000
#> GSM11690 4 0.207 0.6532 0.012 0.076 0.000 0.912 0.000
#> GSM11692 4 0.127 0.6592 0.000 0.052 0.000 0.948 0.000
#> GSM11841 4 0.127 0.6592 0.000 0.052 0.000 0.948 0.000
#> GSM11901 4 0.127 0.6592 0.000 0.052 0.000 0.948 0.000
#> GSM11715 2 0.419 0.7968 0.040 0.748 0.000 0.212 0.000
#> GSM11724 2 0.419 0.7968 0.040 0.748 0.000 0.212 0.000
#> GSM11684 4 0.207 0.6532 0.012 0.076 0.000 0.912 0.000
#> GSM11696 4 0.207 0.6532 0.012 0.076 0.000 0.912 0.000
#> GSM27952 1 0.202 0.8665 0.900 0.000 0.000 0.100 0.000
#> GSM27948 4 0.207 0.6532 0.012 0.076 0.000 0.912 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM11708 5 0.3385 0.98428 0.000 0.000 0.032 0.000 0.788 0.180
#> GSM11735 5 0.3385 0.98428 0.000 0.000 0.032 0.000 0.788 0.180
#> GSM11733 3 0.2013 0.68730 0.008 0.000 0.908 0.000 0.008 0.076
#> GSM11863 3 0.2013 0.68730 0.008 0.000 0.908 0.000 0.008 0.076
#> GSM11710 6 0.1780 0.80990 0.000 0.000 0.000 0.028 0.048 0.924
#> GSM11712 4 0.0713 0.69592 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM11732 3 0.3314 0.48181 0.256 0.000 0.740 0.004 0.000 0.000
#> GSM11844 3 0.4497 0.46533 0.232 0.000 0.696 0.064 0.000 0.008
#> GSM11842 4 0.5613 0.41627 0.064 0.036 0.300 0.592 0.008 0.000
#> GSM11860 4 0.5613 0.41627 0.064 0.036 0.300 0.592 0.008 0.000
#> GSM11686 6 0.1779 0.79630 0.000 0.000 0.016 0.064 0.000 0.920
#> GSM11688 6 0.0972 0.84288 0.000 0.000 0.000 0.028 0.008 0.964
#> GSM11846 4 0.4755 0.45947 0.056 0.000 0.304 0.632 0.008 0.000
#> GSM11680 4 0.5103 0.59953 0.120 0.000 0.200 0.664 0.000 0.016
#> GSM11698 4 0.4604 0.63271 0.084 0.000 0.184 0.716 0.000 0.016
#> GSM11840 3 0.2013 0.68730 0.008 0.000 0.908 0.000 0.008 0.076
#> GSM11847 3 0.2013 0.68730 0.008 0.000 0.908 0.000 0.008 0.076
#> GSM11685 6 0.1218 0.84004 0.000 0.000 0.004 0.028 0.012 0.956
#> GSM11699 4 0.3812 0.66293 0.072 0.000 0.132 0.788 0.000 0.008
#> GSM27950 3 0.6458 0.36047 0.008 0.000 0.540 0.044 0.212 0.196
#> GSM27946 4 0.5118 0.57595 0.132 0.004 0.208 0.652 0.000 0.004
#> GSM11709 1 0.6901 0.41475 0.472 0.032 0.048 0.364 0.024 0.060
#> GSM11720 1 0.3343 0.52175 0.824 0.128 0.016 0.032 0.000 0.000
#> GSM11726 2 0.1882 0.79732 0.060 0.920 0.008 0.012 0.000 0.000
#> GSM11837 2 0.1882 0.79732 0.060 0.920 0.008 0.012 0.000 0.000
#> GSM11725 1 0.3233 0.51799 0.828 0.132 0.016 0.024 0.000 0.000
#> GSM11864 1 0.3233 0.51799 0.828 0.132 0.016 0.024 0.000 0.000
#> GSM11687 1 0.5924 0.36970 0.456 0.032 0.000 0.440 0.020 0.052
#> GSM11693 1 0.5924 0.36970 0.456 0.032 0.000 0.440 0.020 0.052
#> GSM11727 2 0.0458 0.79441 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM11838 2 0.0458 0.79441 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM11681 6 0.0713 0.84574 0.000 0.000 0.000 0.028 0.000 0.972
#> GSM11689 1 0.5924 0.36970 0.456 0.032 0.000 0.440 0.020 0.052
#> GSM11704 1 0.5924 0.36970 0.456 0.032 0.000 0.440 0.020 0.052
#> GSM11703 4 0.6081 0.06956 0.364 0.016 0.144 0.472 0.000 0.004
#> GSM11705 4 0.6290 0.00559 0.376 0.016 0.160 0.440 0.000 0.008
#> GSM11722 2 0.2623 0.75430 0.016 0.852 0.000 0.132 0.000 0.000
#> GSM11730 2 0.0458 0.79441 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM11713 6 0.6888 0.52853 0.112 0.020 0.084 0.012 0.208 0.564
#> GSM11728 6 0.6888 0.52853 0.112 0.020 0.084 0.012 0.208 0.564
#> GSM27947 4 0.5118 0.57595 0.132 0.004 0.208 0.652 0.000 0.004
#> GSM27951 4 0.6337 0.40511 0.056 0.020 0.052 0.656 0.068 0.148
#> GSM11707 5 0.3385 0.98428 0.000 0.000 0.032 0.000 0.788 0.180
#> GSM11716 1 0.3015 0.51550 0.844 0.024 0.120 0.012 0.000 0.000
#> GSM11850 1 0.4045 0.13979 0.564 0.000 0.428 0.008 0.000 0.000
#> GSM11851 1 0.4045 0.13979 0.564 0.000 0.428 0.008 0.000 0.000
#> GSM11721 4 0.0632 0.69563 0.000 0.024 0.000 0.976 0.000 0.000
#> GSM11852 4 0.0632 0.69563 0.000 0.024 0.000 0.976 0.000 0.000
#> GSM11694 4 0.6190 0.20073 0.340 0.000 0.268 0.388 0.000 0.004
#> GSM11695 4 0.6190 0.20073 0.340 0.000 0.268 0.388 0.000 0.004
#> GSM11734 2 0.4274 0.67534 0.336 0.636 0.000 0.024 0.004 0.000
#> GSM11861 4 0.1693 0.69417 0.032 0.020 0.012 0.936 0.000 0.000
#> GSM11843 2 0.5407 0.54341 0.348 0.536 0.000 0.112 0.004 0.000
#> GSM11862 4 0.1490 0.69598 0.016 0.024 0.008 0.948 0.004 0.000
#> GSM11697 4 0.5461 0.50581 0.164 0.000 0.248 0.584 0.000 0.004
#> GSM11714 5 0.3052 0.94137 0.000 0.000 0.004 0.000 0.780 0.216
#> GSM11723 1 0.3048 0.51844 0.844 0.028 0.116 0.012 0.000 0.000
#> GSM11845 1 0.3048 0.51844 0.844 0.028 0.116 0.012 0.000 0.000
#> GSM11683 3 0.6616 0.16005 0.020 0.000 0.396 0.376 0.012 0.196
#> GSM11691 3 0.6732 0.15636 0.032 0.000 0.400 0.376 0.012 0.180
#> GSM27949 3 0.6273 0.50963 0.084 0.000 0.616 0.036 0.200 0.064
#> GSM27945 4 0.6190 0.20073 0.340 0.000 0.268 0.388 0.000 0.004
#> GSM11706 5 0.3455 0.98030 0.000 0.000 0.036 0.000 0.784 0.180
#> GSM11853 4 0.4430 0.63912 0.108 0.000 0.152 0.732 0.000 0.008
#> GSM11729 2 0.2425 0.79809 0.100 0.880 0.008 0.012 0.000 0.000
#> GSM11746 2 0.2425 0.79809 0.100 0.880 0.008 0.012 0.000 0.000
#> GSM11711 4 0.5080 0.61227 0.124 0.000 0.184 0.676 0.004 0.012
#> GSM11854 4 0.4430 0.63912 0.108 0.000 0.152 0.732 0.000 0.008
#> GSM11731 2 0.4385 0.67946 0.328 0.636 0.000 0.032 0.004 0.000
#> GSM11839 2 0.4385 0.67946 0.328 0.636 0.000 0.032 0.004 0.000
#> GSM11836 4 0.2728 0.66839 0.012 0.084 0.004 0.876 0.000 0.024
#> GSM11849 4 0.2675 0.67003 0.012 0.080 0.004 0.880 0.000 0.024
#> GSM11682 6 0.0713 0.84574 0.000 0.000 0.000 0.028 0.000 0.972
#> GSM11690 4 0.1578 0.69013 0.012 0.048 0.000 0.936 0.000 0.004
#> GSM11692 4 0.0713 0.69592 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM11841 4 0.0713 0.69592 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM11901 4 0.0713 0.69592 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM11715 2 0.3967 0.65879 0.012 0.748 0.004 0.212 0.000 0.024
#> GSM11724 2 0.3967 0.65879 0.012 0.748 0.004 0.212 0.000 0.024
#> GSM11684 4 0.1578 0.69013 0.012 0.048 0.000 0.936 0.000 0.004
#> GSM11696 4 0.1578 0.69013 0.012 0.048 0.000 0.936 0.000 0.004
#> GSM27952 6 0.0713 0.84574 0.000 0.000 0.000 0.028 0.000 0.972
#> GSM27948 4 0.1578 0.69013 0.012 0.048 0.000 0.936 0.000 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.line(p) agent(p) time(p) k
#> MAD:hclust 78 0.00329 0.520 4.81e-01 2
#> MAD:hclust 76 0.00214 0.491 1.14e-03 3
#> MAD:hclust 69 0.00735 0.599 3.88e-07 4
#> MAD:hclust 64 0.00198 0.481 9.91e-08 5
#> MAD:hclust 62 0.00118 0.222 1.73e-06 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "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 14502 rows and 83 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.546 0.589 0.829 0.4730 0.617 0.617
#> 3 3 0.311 0.527 0.693 0.3364 0.673 0.498
#> 4 4 0.420 0.453 0.664 0.1386 0.852 0.626
#> 5 5 0.509 0.459 0.616 0.0732 0.833 0.487
#> 6 6 0.631 0.576 0.695 0.0509 0.894 0.564
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM11708 2 0.997 0.9828 0.468 0.532
#> GSM11735 2 0.997 0.9828 0.468 0.532
#> GSM11733 2 0.997 0.9828 0.468 0.532
#> GSM11863 1 0.992 -0.8366 0.552 0.448
#> GSM11710 2 0.995 0.9811 0.460 0.540
#> GSM11712 1 0.995 0.7559 0.540 0.460
#> GSM11732 1 0.900 -0.5926 0.684 0.316
#> GSM11844 1 0.850 -0.4897 0.724 0.276
#> GSM11842 1 1.000 -0.6892 0.512 0.488
#> GSM11860 1 1.000 -0.6892 0.512 0.488
#> GSM11686 2 0.995 0.9811 0.460 0.540
#> GSM11688 2 0.995 0.9811 0.460 0.540
#> GSM11846 2 0.996 0.9822 0.464 0.536
#> GSM11680 1 0.814 -0.4203 0.748 0.252
#> GSM11698 1 0.855 -0.4959 0.720 0.280
#> GSM11840 2 0.997 0.9828 0.468 0.532
#> GSM11847 2 0.997 0.9828 0.468 0.532
#> GSM11685 2 0.995 0.9811 0.460 0.540
#> GSM11699 1 0.358 0.4449 0.932 0.068
#> GSM27950 2 0.997 0.9828 0.468 0.532
#> GSM27946 1 0.714 0.5905 0.804 0.196
#> GSM11709 1 0.969 -0.0471 0.604 0.396
#> GSM11720 1 0.995 0.7559 0.540 0.460
#> GSM11726 1 0.995 0.7559 0.540 0.460
#> GSM11837 1 0.995 0.7559 0.540 0.460
#> GSM11725 1 0.995 0.7559 0.540 0.460
#> GSM11864 1 0.995 0.7559 0.540 0.460
#> GSM11687 1 0.995 0.7559 0.540 0.460
#> GSM11693 1 0.995 0.7559 0.540 0.460
#> GSM11727 1 0.997 0.7532 0.532 0.468
#> GSM11838 1 0.997 0.7532 0.532 0.468
#> GSM11681 2 0.995 0.9811 0.460 0.540
#> GSM11689 1 0.995 0.7559 0.540 0.460
#> GSM11704 1 0.995 0.7559 0.540 0.460
#> GSM11703 1 0.995 0.7559 0.540 0.460
#> GSM11705 1 0.971 -0.2156 0.600 0.400
#> GSM11722 1 0.997 0.7532 0.532 0.468
#> GSM11730 1 0.997 0.7532 0.532 0.468
#> GSM11713 2 0.971 0.7037 0.400 0.600
#> GSM11728 1 0.929 -0.0282 0.656 0.344
#> GSM27947 1 0.995 0.7559 0.540 0.460
#> GSM27951 1 0.827 0.3944 0.740 0.260
#> GSM11707 2 0.997 0.9828 0.468 0.532
#> GSM11716 1 0.995 0.7559 0.540 0.460
#> GSM11850 1 0.373 0.1635 0.928 0.072
#> GSM11851 1 0.469 0.0794 0.900 0.100
#> GSM11721 1 0.981 0.7410 0.580 0.420
#> GSM11852 1 0.204 0.2670 0.968 0.032
#> GSM11694 1 0.224 0.2584 0.964 0.036
#> GSM11695 1 0.469 0.0794 0.900 0.100
#> GSM11734 1 0.995 0.7559 0.540 0.460
#> GSM11861 1 0.689 0.5782 0.816 0.184
#> GSM11843 1 0.995 0.7559 0.540 0.460
#> GSM11862 1 0.775 0.6167 0.772 0.228
#> GSM11697 1 0.184 0.2759 0.972 0.028
#> GSM11714 2 0.995 0.9811 0.460 0.540
#> GSM11723 1 0.995 0.7559 0.540 0.460
#> GSM11845 1 0.995 0.7559 0.540 0.460
#> GSM11683 2 0.997 0.9828 0.468 0.532
#> GSM11691 1 0.242 0.4012 0.960 0.040
#> GSM27949 2 0.997 0.9828 0.468 0.532
#> GSM27945 1 0.506 0.5013 0.888 0.112
#> GSM11706 2 0.997 0.9828 0.468 0.532
#> GSM11853 1 0.204 0.2670 0.968 0.032
#> GSM11729 1 0.995 0.7559 0.540 0.460
#> GSM11746 1 0.995 0.7559 0.540 0.460
#> GSM11711 2 0.997 0.9828 0.468 0.532
#> GSM11854 1 0.224 0.2580 0.964 0.036
#> GSM11731 1 0.995 0.7559 0.540 0.460
#> GSM11839 1 0.995 0.7559 0.540 0.460
#> GSM11836 1 0.998 0.7481 0.528 0.472
#> GSM11849 1 0.998 0.7481 0.528 0.472
#> GSM11682 2 0.995 0.9811 0.460 0.540
#> GSM11690 1 0.983 0.7391 0.576 0.424
#> GSM11692 1 0.995 0.7559 0.540 0.460
#> GSM11841 1 0.995 0.7559 0.540 0.460
#> GSM11901 1 0.995 0.7559 0.540 0.460
#> GSM11715 1 0.997 0.7532 0.532 0.468
#> GSM11724 1 0.997 0.7532 0.532 0.468
#> GSM11684 1 0.995 0.7527 0.540 0.460
#> GSM11696 1 0.997 0.7532 0.532 0.468
#> GSM27952 2 0.995 0.9811 0.460 0.540
#> GSM27948 1 0.995 0.7527 0.540 0.460
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM11708 3 0.228 0.8102 0.008 0.052 0.940
#> GSM11735 3 0.238 0.8088 0.008 0.056 0.936
#> GSM11733 3 0.517 0.7783 0.116 0.056 0.828
#> GSM11863 3 0.749 0.6193 0.248 0.084 0.668
#> GSM11710 3 0.230 0.8308 0.060 0.004 0.936
#> GSM11712 1 0.522 0.4167 0.740 0.260 0.000
#> GSM11732 1 0.719 0.3376 0.608 0.036 0.356
#> GSM11844 1 0.695 0.3421 0.620 0.028 0.352
#> GSM11842 3 0.778 0.5902 0.264 0.092 0.644
#> GSM11860 3 0.775 0.4940 0.340 0.064 0.596
#> GSM11686 3 0.397 0.8125 0.088 0.032 0.880
#> GSM11688 3 0.275 0.8282 0.064 0.012 0.924
#> GSM11846 3 0.506 0.7303 0.244 0.000 0.756
#> GSM11680 1 0.587 0.4455 0.684 0.004 0.312
#> GSM11698 1 0.610 0.3663 0.648 0.004 0.348
#> GSM11840 3 0.547 0.7703 0.128 0.060 0.812
#> GSM11847 3 0.547 0.7703 0.128 0.060 0.812
#> GSM11685 3 0.294 0.8260 0.072 0.012 0.916
#> GSM11699 1 0.321 0.5974 0.912 0.028 0.060
#> GSM27950 3 0.164 0.8326 0.044 0.000 0.956
#> GSM27946 1 0.231 0.5951 0.944 0.024 0.032
#> GSM11709 1 0.832 0.4325 0.604 0.276 0.120
#> GSM11720 1 0.620 0.3626 0.576 0.424 0.000
#> GSM11726 1 0.629 0.2776 0.536 0.464 0.000
#> GSM11837 2 0.604 0.1560 0.380 0.620 0.000
#> GSM11725 1 0.630 0.2393 0.520 0.480 0.000
#> GSM11864 1 0.620 0.3169 0.576 0.424 0.000
#> GSM11687 1 0.586 0.4487 0.656 0.344 0.000
#> GSM11693 1 0.595 0.4335 0.640 0.360 0.000
#> GSM11727 2 0.271 0.6348 0.088 0.912 0.000
#> GSM11838 2 0.271 0.6323 0.088 0.912 0.000
#> GSM11681 3 0.563 0.7609 0.144 0.056 0.800
#> GSM11689 1 0.597 0.4284 0.636 0.364 0.000
#> GSM11704 1 0.597 0.4284 0.636 0.364 0.000
#> GSM11703 1 0.588 0.4440 0.652 0.348 0.000
#> GSM11705 1 0.888 0.3441 0.572 0.244 0.184
#> GSM11722 2 0.271 0.6326 0.088 0.912 0.000
#> GSM11730 2 0.271 0.6348 0.088 0.912 0.000
#> GSM11713 2 0.921 0.2720 0.184 0.520 0.296
#> GSM11728 2 0.923 0.3116 0.204 0.528 0.268
#> GSM27947 1 0.383 0.5865 0.868 0.124 0.008
#> GSM27951 2 0.925 0.2066 0.392 0.452 0.156
#> GSM11707 3 0.164 0.8326 0.044 0.000 0.956
#> GSM11716 1 0.562 0.5302 0.744 0.244 0.012
#> GSM11850 1 0.481 0.6082 0.804 0.008 0.188
#> GSM11851 1 0.483 0.6009 0.792 0.004 0.204
#> GSM11721 1 0.585 0.2927 0.720 0.268 0.012
#> GSM11852 1 0.323 0.5986 0.908 0.020 0.072
#> GSM11694 1 0.470 0.6099 0.812 0.008 0.180
#> GSM11695 1 0.463 0.6069 0.808 0.004 0.188
#> GSM11734 2 0.627 0.0953 0.456 0.544 0.000
#> GSM11861 1 0.249 0.5789 0.936 0.048 0.016
#> GSM11843 1 0.613 0.3073 0.600 0.400 0.000
#> GSM11862 1 0.327 0.5563 0.904 0.080 0.016
#> GSM11697 1 0.470 0.6099 0.812 0.008 0.180
#> GSM11714 3 0.165 0.8322 0.036 0.004 0.960
#> GSM11723 1 0.601 0.3481 0.628 0.372 0.000
#> GSM11845 1 0.581 0.4066 0.664 0.336 0.000
#> GSM11683 3 0.413 0.8031 0.132 0.012 0.856
#> GSM11691 1 0.313 0.6110 0.904 0.008 0.088
#> GSM27949 1 0.631 -0.0522 0.508 0.000 0.492
#> GSM27945 1 0.441 0.6197 0.844 0.016 0.140
#> GSM11706 3 0.164 0.8326 0.044 0.000 0.956
#> GSM11853 1 0.364 0.6151 0.872 0.004 0.124
#> GSM11729 2 0.595 0.2723 0.360 0.640 0.000
#> GSM11746 2 0.595 0.2723 0.360 0.640 0.000
#> GSM11711 3 0.651 0.2739 0.472 0.004 0.524
#> GSM11854 1 0.385 0.6065 0.860 0.004 0.136
#> GSM11731 2 0.497 0.5895 0.236 0.764 0.000
#> GSM11839 2 0.553 0.5818 0.296 0.704 0.000
#> GSM11836 2 0.556 0.6032 0.300 0.700 0.000
#> GSM11849 2 0.651 0.5868 0.300 0.676 0.024
#> GSM11682 3 0.644 0.7035 0.168 0.076 0.756
#> GSM11690 2 0.668 0.5079 0.404 0.584 0.012
#> GSM11692 1 0.556 0.2409 0.700 0.300 0.000
#> GSM11841 1 0.590 0.2020 0.648 0.352 0.000
#> GSM11901 1 0.583 0.2040 0.660 0.340 0.000
#> GSM11715 2 0.334 0.6426 0.120 0.880 0.000
#> GSM11724 2 0.334 0.6426 0.120 0.880 0.000
#> GSM11684 2 0.620 0.5794 0.336 0.656 0.008
#> GSM11696 2 0.581 0.5851 0.336 0.664 0.000
#> GSM27952 3 0.359 0.8158 0.088 0.020 0.892
#> GSM27948 2 0.651 0.4055 0.476 0.520 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM11708 1 0.388 0.66992 0.824 0.004 0.016 0.156
#> GSM11735 1 0.510 0.64273 0.732 0.004 0.036 0.228
#> GSM11733 1 0.703 0.57771 0.568 0.004 0.136 0.292
#> GSM11863 1 0.756 0.47290 0.456 0.004 0.168 0.372
#> GSM11710 1 0.141 0.70327 0.960 0.000 0.020 0.020
#> GSM11712 3 0.748 -0.12405 0.000 0.176 0.416 0.408
#> GSM11732 3 0.389 0.61686 0.132 0.004 0.836 0.028
#> GSM11844 3 0.346 0.62764 0.124 0.004 0.856 0.016
#> GSM11842 1 0.757 0.46510 0.448 0.004 0.168 0.380
#> GSM11860 1 0.789 0.43716 0.412 0.004 0.232 0.352
#> GSM11686 1 0.487 0.62205 0.776 0.012 0.036 0.176
#> GSM11688 1 0.281 0.69129 0.904 0.004 0.028 0.064
#> GSM11846 1 0.559 0.50923 0.652 0.004 0.312 0.032
#> GSM11680 3 0.284 0.64928 0.076 0.000 0.896 0.028
#> GSM11698 3 0.312 0.64255 0.092 0.000 0.880 0.028
#> GSM11840 1 0.713 0.57153 0.556 0.004 0.144 0.296
#> GSM11847 1 0.713 0.57153 0.556 0.004 0.144 0.296
#> GSM11685 1 0.317 0.68293 0.884 0.004 0.028 0.084
#> GSM11699 3 0.437 0.56682 0.008 0.004 0.760 0.228
#> GSM27950 1 0.158 0.70542 0.948 0.000 0.048 0.004
#> GSM27946 3 0.493 0.53559 0.004 0.016 0.712 0.268
#> GSM11709 3 0.802 0.34665 0.080 0.276 0.548 0.096
#> GSM11720 3 0.624 0.24814 0.000 0.392 0.548 0.060
#> GSM11726 2 0.590 0.27168 0.000 0.616 0.332 0.052
#> GSM11837 2 0.464 0.48794 0.000 0.776 0.180 0.044
#> GSM11725 2 0.675 0.16841 0.000 0.540 0.356 0.104
#> GSM11864 2 0.694 0.09905 0.000 0.508 0.376 0.116
#> GSM11687 3 0.667 0.37476 0.004 0.304 0.592 0.100
#> GSM11693 3 0.701 0.34651 0.004 0.316 0.556 0.124
#> GSM11727 2 0.333 0.44978 0.000 0.864 0.024 0.112
#> GSM11838 2 0.181 0.49140 0.000 0.940 0.008 0.052
#> GSM11681 1 0.641 0.51617 0.672 0.028 0.068 0.232
#> GSM11689 3 0.728 0.30439 0.004 0.324 0.524 0.148
#> GSM11704 3 0.729 0.29780 0.004 0.328 0.520 0.148
#> GSM11703 3 0.667 0.37695 0.004 0.304 0.592 0.100
#> GSM11705 3 0.877 0.28573 0.140 0.252 0.496 0.112
#> GSM11722 2 0.295 0.47813 0.000 0.888 0.024 0.088
#> GSM11730 2 0.366 0.42548 0.000 0.840 0.024 0.136
#> GSM11713 1 0.875 -0.13524 0.336 0.304 0.036 0.324
#> GSM11728 4 0.875 0.08025 0.308 0.320 0.036 0.336
#> GSM27947 3 0.439 0.61664 0.000 0.052 0.804 0.144
#> GSM27951 4 0.988 0.04605 0.232 0.292 0.184 0.292
#> GSM11707 1 0.112 0.70613 0.964 0.000 0.036 0.000
#> GSM11716 3 0.298 0.63302 0.000 0.120 0.872 0.008
#> GSM11850 3 0.145 0.66530 0.036 0.000 0.956 0.008
#> GSM11851 3 0.209 0.66150 0.048 0.000 0.932 0.020
#> GSM11721 4 0.702 0.32360 0.000 0.132 0.344 0.524
#> GSM11852 3 0.520 0.47880 0.016 0.004 0.668 0.312
#> GSM11694 3 0.121 0.66589 0.040 0.000 0.960 0.000
#> GSM11695 3 0.121 0.66589 0.040 0.000 0.960 0.000
#> GSM11734 2 0.710 0.24642 0.000 0.540 0.156 0.304
#> GSM11861 3 0.492 0.44055 0.000 0.008 0.656 0.336
#> GSM11843 3 0.776 -0.07538 0.000 0.372 0.392 0.236
#> GSM11862 3 0.555 0.32521 0.000 0.024 0.588 0.388
#> GSM11697 3 0.121 0.66589 0.040 0.000 0.960 0.000
#> GSM11714 1 0.121 0.70623 0.960 0.000 0.040 0.000
#> GSM11723 3 0.699 0.24305 0.000 0.304 0.552 0.144
#> GSM11845 3 0.684 0.32512 0.000 0.260 0.588 0.152
#> GSM11683 1 0.539 0.60592 0.752 0.004 0.140 0.104
#> GSM11691 3 0.241 0.66078 0.016 0.004 0.920 0.060
#> GSM27949 3 0.376 0.59724 0.172 0.000 0.816 0.012
#> GSM27945 3 0.106 0.66659 0.016 0.012 0.972 0.000
#> GSM11706 1 0.112 0.70613 0.964 0.000 0.036 0.000
#> GSM11853 3 0.303 0.65693 0.020 0.004 0.888 0.088
#> GSM11729 2 0.512 0.51530 0.000 0.764 0.128 0.108
#> GSM11746 2 0.500 0.51757 0.000 0.772 0.128 0.100
#> GSM11711 3 0.551 0.49311 0.252 0.000 0.692 0.056
#> GSM11854 3 0.334 0.64358 0.012 0.004 0.860 0.124
#> GSM11731 2 0.593 0.20528 0.000 0.596 0.048 0.356
#> GSM11839 2 0.618 0.00695 0.000 0.520 0.052 0.428
#> GSM11836 4 0.587 0.33001 0.000 0.416 0.036 0.548
#> GSM11849 4 0.650 0.35400 0.016 0.396 0.044 0.544
#> GSM11682 1 0.557 0.51001 0.692 0.028 0.016 0.264
#> GSM11690 4 0.669 0.46500 0.012 0.280 0.092 0.616
#> GSM11692 4 0.743 0.32146 0.000 0.184 0.336 0.480
#> GSM11841 4 0.754 0.30781 0.000 0.204 0.328 0.468
#> GSM11901 4 0.754 0.30781 0.000 0.204 0.328 0.468
#> GSM11715 2 0.445 0.32433 0.000 0.732 0.008 0.260
#> GSM11724 2 0.445 0.32433 0.000 0.732 0.008 0.260
#> GSM11684 4 0.643 0.42702 0.012 0.340 0.056 0.592
#> GSM11696 4 0.649 0.43486 0.008 0.336 0.068 0.588
#> GSM27952 1 0.389 0.64622 0.828 0.004 0.020 0.148
#> GSM27948 4 0.625 0.45215 0.000 0.224 0.120 0.656
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM11708 4 0.4539 0.56601 0.044 0.000 0.008 0.736 0.212
#> GSM11735 4 0.5630 0.26378 0.044 0.000 0.016 0.528 0.412
#> GSM11733 5 0.5671 0.10482 0.000 0.000 0.096 0.336 0.568
#> GSM11863 5 0.5403 0.25670 0.000 0.000 0.108 0.248 0.644
#> GSM11710 4 0.2447 0.76540 0.032 0.000 0.032 0.912 0.024
#> GSM11712 5 0.8478 0.20953 0.260 0.184 0.228 0.000 0.328
#> GSM11732 3 0.1739 0.71766 0.004 0.000 0.940 0.024 0.032
#> GSM11844 3 0.1310 0.72576 0.000 0.000 0.956 0.020 0.024
#> GSM11842 5 0.5798 0.25893 0.004 0.008 0.108 0.244 0.636
#> GSM11860 5 0.6120 0.25243 0.012 0.008 0.120 0.240 0.620
#> GSM11686 4 0.4286 0.73925 0.016 0.016 0.072 0.816 0.080
#> GSM11688 4 0.2037 0.77207 0.004 0.000 0.064 0.920 0.012
#> GSM11846 4 0.5656 0.40088 0.020 0.004 0.332 0.600 0.044
#> GSM11680 3 0.1012 0.73223 0.000 0.000 0.968 0.020 0.012
#> GSM11698 3 0.0912 0.73191 0.000 0.000 0.972 0.016 0.012
#> GSM11840 5 0.5683 0.17330 0.000 0.000 0.108 0.304 0.588
#> GSM11847 5 0.5683 0.17330 0.000 0.000 0.108 0.304 0.588
#> GSM11685 4 0.2037 0.77207 0.004 0.000 0.064 0.920 0.012
#> GSM11699 3 0.5566 0.57489 0.108 0.012 0.700 0.012 0.168
#> GSM27950 4 0.2925 0.76950 0.036 0.000 0.064 0.884 0.016
#> GSM27946 3 0.6283 0.51566 0.164 0.012 0.624 0.012 0.188
#> GSM11709 1 0.4846 0.64408 0.612 0.000 0.360 0.024 0.004
#> GSM11720 1 0.5152 0.66163 0.632 0.052 0.312 0.000 0.004
#> GSM11726 1 0.6281 0.15599 0.460 0.388 0.152 0.000 0.000
#> GSM11837 2 0.6022 0.13684 0.396 0.516 0.068 0.000 0.020
#> GSM11725 1 0.6131 0.50896 0.616 0.172 0.196 0.000 0.016
#> GSM11864 1 0.6092 0.50696 0.628 0.160 0.192 0.000 0.020
#> GSM11687 1 0.4341 0.65140 0.628 0.000 0.364 0.000 0.008
#> GSM11693 1 0.4127 0.68240 0.680 0.000 0.312 0.000 0.008
#> GSM11727 2 0.3730 0.40520 0.288 0.712 0.000 0.000 0.000
#> GSM11838 2 0.3700 0.42742 0.240 0.752 0.000 0.000 0.008
#> GSM11681 4 0.6120 0.63570 0.156 0.024 0.056 0.692 0.072
#> GSM11689 1 0.4206 0.68155 0.708 0.000 0.272 0.000 0.020
#> GSM11704 1 0.4206 0.68155 0.708 0.000 0.272 0.000 0.020
#> GSM11703 1 0.4268 0.66852 0.648 0.000 0.344 0.000 0.008
#> GSM11705 1 0.6223 0.60260 0.564 0.016 0.328 0.084 0.008
#> GSM11722 2 0.4268 0.40317 0.344 0.648 0.000 0.000 0.008
#> GSM11730 2 0.3814 0.41259 0.276 0.720 0.000 0.000 0.004
#> GSM11713 4 0.7894 0.00692 0.160 0.372 0.004 0.372 0.092
#> GSM11728 2 0.8115 -0.05288 0.172 0.380 0.008 0.340 0.100
#> GSM27947 3 0.4973 0.51717 0.236 0.004 0.692 0.000 0.068
#> GSM27951 1 0.8485 0.17599 0.460 0.136 0.088 0.252 0.064
#> GSM11707 4 0.2772 0.76070 0.044 0.000 0.032 0.896 0.028
#> GSM11716 3 0.4211 0.58622 0.148 0.028 0.792 0.000 0.032
#> GSM11850 3 0.2149 0.71454 0.036 0.000 0.924 0.012 0.028
#> GSM11851 3 0.2152 0.71807 0.032 0.000 0.924 0.012 0.032
#> GSM11721 5 0.8691 0.21576 0.208 0.204 0.240 0.008 0.340
#> GSM11852 3 0.6590 0.46863 0.156 0.020 0.596 0.012 0.216
#> GSM11694 3 0.0912 0.72707 0.016 0.000 0.972 0.012 0.000
#> GSM11695 3 0.0912 0.72707 0.016 0.000 0.972 0.012 0.000
#> GSM11734 2 0.7201 0.29096 0.308 0.460 0.036 0.000 0.196
#> GSM11861 3 0.7237 0.38344 0.172 0.044 0.524 0.008 0.252
#> GSM11843 1 0.8398 0.01985 0.344 0.256 0.240 0.000 0.160
#> GSM11862 3 0.7777 0.20880 0.192 0.068 0.456 0.008 0.276
#> GSM11697 3 0.0912 0.72707 0.016 0.000 0.972 0.012 0.000
#> GSM11714 4 0.3081 0.76626 0.044 0.000 0.048 0.880 0.028
#> GSM11723 3 0.7812 0.15933 0.208 0.188 0.476 0.000 0.128
#> GSM11845 3 0.7488 0.25725 0.216 0.140 0.520 0.000 0.124
#> GSM11683 4 0.3674 0.71931 0.008 0.004 0.152 0.816 0.020
#> GSM11691 3 0.2196 0.71383 0.056 0.000 0.916 0.004 0.024
#> GSM27949 3 0.1430 0.71055 0.000 0.000 0.944 0.052 0.004
#> GSM27945 3 0.1430 0.71949 0.052 0.000 0.944 0.004 0.000
#> GSM11706 4 0.2772 0.76070 0.044 0.000 0.032 0.896 0.028
#> GSM11853 3 0.3108 0.69073 0.068 0.004 0.872 0.004 0.052
#> GSM11729 2 0.6440 0.18888 0.388 0.500 0.060 0.000 0.052
#> GSM11746 2 0.6440 0.18888 0.388 0.500 0.060 0.000 0.052
#> GSM11711 3 0.4564 0.60952 0.052 0.000 0.780 0.132 0.036
#> GSM11854 3 0.3349 0.68841 0.060 0.004 0.864 0.012 0.060
#> GSM11731 2 0.6607 0.34055 0.228 0.544 0.016 0.000 0.212
#> GSM11839 2 0.6928 0.23087 0.220 0.468 0.016 0.000 0.296
#> GSM11836 2 0.6553 0.20707 0.100 0.520 0.020 0.008 0.352
#> GSM11849 2 0.5996 0.33142 0.056 0.640 0.020 0.024 0.260
#> GSM11682 4 0.5141 0.67782 0.024 0.052 0.036 0.764 0.124
#> GSM11690 5 0.7903 -0.14795 0.136 0.388 0.044 0.040 0.392
#> GSM11692 5 0.8474 0.21161 0.240 0.224 0.196 0.000 0.340
#> GSM11841 5 0.8460 0.20993 0.240 0.224 0.192 0.000 0.344
#> GSM11901 5 0.8460 0.20993 0.240 0.224 0.192 0.000 0.344
#> GSM11715 2 0.3181 0.52182 0.072 0.856 0.000 0.000 0.072
#> GSM11724 2 0.3181 0.52182 0.072 0.856 0.000 0.000 0.072
#> GSM11684 2 0.7328 0.19453 0.120 0.508 0.040 0.024 0.308
#> GSM11696 2 0.7441 0.16243 0.140 0.484 0.040 0.020 0.316
#> GSM27952 4 0.2979 0.75896 0.004 0.004 0.056 0.880 0.056
#> GSM27948 5 0.8222 -0.00506 0.184 0.320 0.080 0.020 0.396
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM11708 6 0.571 0.4965 0.060 0.056 0.016 0.000 0.232 0.636
#> GSM11735 5 0.581 0.4109 0.056 0.056 0.012 0.000 0.596 0.280
#> GSM11733 5 0.307 0.8844 0.000 0.000 0.056 0.024 0.860 0.060
#> GSM11863 5 0.354 0.9086 0.000 0.000 0.072 0.052 0.832 0.044
#> GSM11710 6 0.416 0.7166 0.056 0.048 0.024 0.000 0.064 0.808
#> GSM11712 4 0.481 0.5926 0.068 0.028 0.120 0.752 0.032 0.000
#> GSM11732 3 0.186 0.7580 0.008 0.004 0.924 0.000 0.056 0.008
#> GSM11844 3 0.206 0.7609 0.008 0.004 0.920 0.008 0.052 0.008
#> GSM11842 5 0.379 0.9053 0.004 0.000 0.076 0.056 0.820 0.044
#> GSM11860 5 0.379 0.9053 0.004 0.000 0.076 0.056 0.820 0.044
#> GSM11686 6 0.274 0.7175 0.028 0.004 0.040 0.028 0.008 0.892
#> GSM11688 6 0.149 0.7351 0.000 0.000 0.036 0.000 0.024 0.940
#> GSM11846 6 0.612 0.3029 0.032 0.012 0.336 0.028 0.044 0.548
#> GSM11680 3 0.169 0.7670 0.000 0.000 0.936 0.032 0.020 0.012
#> GSM11698 3 0.184 0.7660 0.004 0.000 0.932 0.032 0.020 0.012
#> GSM11840 5 0.355 0.9100 0.000 0.000 0.064 0.048 0.832 0.056
#> GSM11847 5 0.355 0.9100 0.000 0.000 0.064 0.048 0.832 0.056
#> GSM11685 6 0.149 0.7351 0.000 0.000 0.036 0.000 0.024 0.940
#> GSM11699 3 0.474 0.4383 0.036 0.000 0.632 0.316 0.012 0.004
#> GSM27950 6 0.375 0.7249 0.032 0.048 0.048 0.000 0.036 0.836
#> GSM27946 3 0.502 0.3292 0.048 0.000 0.572 0.364 0.016 0.000
#> GSM11709 1 0.409 0.7411 0.680 0.004 0.296 0.004 0.000 0.016
#> GSM11720 1 0.502 0.6875 0.648 0.084 0.256 0.008 0.004 0.000
#> GSM11726 2 0.504 0.4430 0.348 0.580 0.064 0.004 0.004 0.000
#> GSM11837 2 0.462 0.5961 0.220 0.712 0.024 0.032 0.012 0.000
#> GSM11725 1 0.717 0.3428 0.532 0.212 0.124 0.092 0.036 0.004
#> GSM11864 1 0.735 0.3410 0.524 0.188 0.120 0.124 0.040 0.004
#> GSM11687 1 0.380 0.7579 0.692 0.000 0.292 0.016 0.000 0.000
#> GSM11693 1 0.429 0.7642 0.688 0.004 0.264 0.044 0.000 0.000
#> GSM11727 2 0.431 0.6303 0.220 0.712 0.000 0.064 0.000 0.004
#> GSM11838 2 0.333 0.6683 0.132 0.820 0.000 0.040 0.008 0.000
#> GSM11681 6 0.395 0.6149 0.200 0.004 0.016 0.016 0.004 0.760
#> GSM11689 1 0.454 0.7515 0.688 0.004 0.232 0.076 0.000 0.000
#> GSM11704 1 0.454 0.7515 0.688 0.004 0.232 0.076 0.000 0.000
#> GSM11703 1 0.403 0.7612 0.680 0.000 0.292 0.028 0.000 0.000
#> GSM11705 1 0.486 0.7153 0.660 0.008 0.272 0.016 0.000 0.044
#> GSM11722 2 0.537 0.5793 0.268 0.608 0.000 0.112 0.008 0.004
#> GSM11730 2 0.495 0.6120 0.220 0.676 0.000 0.088 0.012 0.004
#> GSM11713 6 0.789 0.0186 0.236 0.268 0.004 0.108 0.024 0.360
#> GSM11728 6 0.802 -0.0228 0.240 0.268 0.004 0.128 0.024 0.336
#> GSM27947 3 0.507 0.5162 0.164 0.000 0.668 0.156 0.012 0.000
#> GSM27951 1 0.647 0.2700 0.580 0.036 0.068 0.052 0.008 0.256
#> GSM11707 6 0.461 0.7061 0.060 0.056 0.036 0.000 0.068 0.780
#> GSM11716 3 0.472 0.6085 0.120 0.040 0.768 0.020 0.040 0.012
#> GSM11850 3 0.250 0.7408 0.048 0.012 0.904 0.012 0.016 0.008
#> GSM11851 3 0.289 0.7418 0.044 0.020 0.888 0.020 0.016 0.012
#> GSM11721 4 0.473 0.5980 0.060 0.028 0.116 0.760 0.036 0.000
#> GSM11852 4 0.620 0.0643 0.056 0.020 0.408 0.472 0.040 0.004
#> GSM11694 3 0.115 0.7611 0.020 0.000 0.960 0.000 0.016 0.004
#> GSM11695 3 0.115 0.7611 0.020 0.000 0.960 0.000 0.016 0.004
#> GSM11734 4 0.768 0.1150 0.148 0.300 0.028 0.428 0.080 0.016
#> GSM11861 4 0.727 0.1563 0.092 0.048 0.364 0.432 0.052 0.012
#> GSM11843 4 0.870 0.1655 0.192 0.228 0.128 0.352 0.084 0.016
#> GSM11862 4 0.689 0.3868 0.080 0.048 0.260 0.548 0.052 0.012
#> GSM11697 3 0.115 0.7629 0.016 0.000 0.960 0.000 0.020 0.004
#> GSM11714 6 0.458 0.7126 0.060 0.056 0.044 0.000 0.056 0.784
#> GSM11723 3 0.845 0.0763 0.168 0.144 0.400 0.208 0.064 0.016
#> GSM11845 3 0.848 0.0404 0.168 0.128 0.384 0.236 0.068 0.016
#> GSM11683 6 0.201 0.7272 0.000 0.000 0.080 0.000 0.016 0.904
#> GSM11691 3 0.218 0.7512 0.056 0.004 0.912 0.020 0.004 0.004
#> GSM27949 3 0.184 0.7565 0.004 0.004 0.932 0.004 0.020 0.036
#> GSM27945 3 0.131 0.7586 0.032 0.000 0.952 0.008 0.008 0.000
#> GSM11706 6 0.455 0.7076 0.056 0.056 0.036 0.000 0.068 0.784
#> GSM11853 3 0.378 0.7048 0.064 0.012 0.824 0.072 0.028 0.000
#> GSM11729 2 0.621 0.5531 0.276 0.576 0.020 0.080 0.044 0.004
#> GSM11746 2 0.621 0.5531 0.276 0.576 0.020 0.080 0.044 0.004
#> GSM11711 3 0.422 0.6927 0.056 0.008 0.812 0.040 0.024 0.060
#> GSM11854 3 0.402 0.6987 0.056 0.012 0.812 0.088 0.028 0.004
#> GSM11731 4 0.626 0.1476 0.084 0.312 0.000 0.532 0.064 0.008
#> GSM11839 4 0.437 0.4846 0.040 0.152 0.000 0.760 0.044 0.004
#> GSM11836 4 0.511 0.4460 0.072 0.124 0.000 0.732 0.040 0.032
#> GSM11849 4 0.660 0.2399 0.092 0.224 0.004 0.584 0.044 0.052
#> GSM11682 6 0.376 0.6582 0.056 0.004 0.012 0.080 0.020 0.828
#> GSM11690 4 0.474 0.5088 0.064 0.048 0.016 0.784 0.032 0.056
#> GSM11692 4 0.349 0.6115 0.044 0.012 0.092 0.836 0.016 0.000
#> GSM11841 4 0.344 0.6114 0.044 0.012 0.088 0.840 0.016 0.000
#> GSM11901 4 0.344 0.6114 0.044 0.012 0.088 0.840 0.016 0.000
#> GSM11715 2 0.618 0.4085 0.072 0.560 0.000 0.296 0.052 0.020
#> GSM11724 2 0.618 0.4085 0.072 0.560 0.000 0.296 0.052 0.020
#> GSM11684 4 0.583 0.3976 0.076 0.128 0.004 0.688 0.044 0.060
#> GSM11696 4 0.529 0.4399 0.060 0.112 0.004 0.732 0.044 0.048
#> GSM27952 6 0.107 0.7314 0.004 0.004 0.024 0.000 0.004 0.964
#> GSM27948 4 0.356 0.5705 0.032 0.016 0.036 0.856 0.024 0.036
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.line(p) agent(p) time(p) k
#> MAD:kmeans 62 1.62e-04 0.7144 1.35e-01 2
#> MAD:kmeans 49 1.34e-07 0.0836 1.40e-01 3
#> MAD:kmeans 38 2.73e-02 0.5487 2.47e-02 4
#> MAD:kmeans 44 6.49e-07 0.4453 6.49e-04 5
#> MAD:kmeans 57 7.45e-09 0.9585 5.64e-08 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 14502 rows and 83 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.586 0.781 0.914 0.5038 0.494 0.494
#> 3 3 0.499 0.539 0.781 0.3264 0.772 0.569
#> 4 4 0.594 0.727 0.813 0.1258 0.849 0.589
#> 5 5 0.646 0.547 0.694 0.0615 0.892 0.609
#> 6 6 0.705 0.639 0.794 0.0423 0.902 0.578
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM11708 1 0.0000 0.8759 1.000 0.000
#> GSM11735 1 0.0000 0.8759 1.000 0.000
#> GSM11733 1 0.0000 0.8759 1.000 0.000
#> GSM11863 1 0.0000 0.8759 1.000 0.000
#> GSM11710 1 0.0000 0.8759 1.000 0.000
#> GSM11712 2 0.0000 0.9115 0.000 1.000
#> GSM11732 1 0.0000 0.8759 1.000 0.000
#> GSM11844 1 0.0000 0.8759 1.000 0.000
#> GSM11842 1 0.0000 0.8759 1.000 0.000
#> GSM11860 1 0.0000 0.8759 1.000 0.000
#> GSM11686 1 0.0000 0.8759 1.000 0.000
#> GSM11688 1 0.0000 0.8759 1.000 0.000
#> GSM11846 1 0.0000 0.8759 1.000 0.000
#> GSM11680 1 0.6973 0.7608 0.812 0.188
#> GSM11698 1 0.0000 0.8759 1.000 0.000
#> GSM11840 1 0.0000 0.8759 1.000 0.000
#> GSM11847 1 0.0000 0.8759 1.000 0.000
#> GSM11685 1 0.0000 0.8759 1.000 0.000
#> GSM11699 2 0.9988 -0.0483 0.480 0.520
#> GSM27950 1 0.0000 0.8759 1.000 0.000
#> GSM27946 2 0.9775 0.1915 0.412 0.588
#> GSM11709 1 0.9775 0.2470 0.588 0.412
#> GSM11720 2 0.0000 0.9115 0.000 1.000
#> GSM11726 2 0.5737 0.7872 0.136 0.864
#> GSM11837 2 0.0000 0.9115 0.000 1.000
#> GSM11725 2 0.0000 0.9115 0.000 1.000
#> GSM11864 2 0.0000 0.9115 0.000 1.000
#> GSM11687 2 0.0000 0.9115 0.000 1.000
#> GSM11693 2 0.0000 0.9115 0.000 1.000
#> GSM11727 2 0.5408 0.7994 0.124 0.876
#> GSM11838 2 0.0000 0.9115 0.000 1.000
#> GSM11681 1 0.0000 0.8759 1.000 0.000
#> GSM11689 2 0.0000 0.9115 0.000 1.000
#> GSM11704 2 0.0000 0.9115 0.000 1.000
#> GSM11703 2 0.0000 0.9115 0.000 1.000
#> GSM11705 1 0.9775 0.2470 0.588 0.412
#> GSM11722 2 0.0000 0.9115 0.000 1.000
#> GSM11730 2 0.5408 0.7994 0.124 0.876
#> GSM11713 1 0.9881 0.1796 0.564 0.436
#> GSM11728 1 0.9896 0.1679 0.560 0.440
#> GSM27947 2 0.0000 0.9115 0.000 1.000
#> GSM27951 2 0.9896 0.2134 0.440 0.560
#> GSM11707 1 0.0000 0.8759 1.000 0.000
#> GSM11716 2 0.1184 0.8989 0.016 0.984
#> GSM11850 1 0.7139 0.7546 0.804 0.196
#> GSM11851 1 0.7139 0.7546 0.804 0.196
#> GSM11721 2 0.0672 0.9056 0.008 0.992
#> GSM11852 1 0.7219 0.7505 0.800 0.200
#> GSM11694 1 0.7139 0.7546 0.804 0.196
#> GSM11695 1 0.7139 0.7546 0.804 0.196
#> GSM11734 2 0.0000 0.9115 0.000 1.000
#> GSM11861 2 0.9944 0.0446 0.456 0.544
#> GSM11843 2 0.0000 0.9115 0.000 1.000
#> GSM11862 2 0.9686 0.2387 0.396 0.604
#> GSM11697 1 0.7219 0.7507 0.800 0.200
#> GSM11714 1 0.0000 0.8759 1.000 0.000
#> GSM11723 2 0.0000 0.9115 0.000 1.000
#> GSM11845 2 0.0000 0.9115 0.000 1.000
#> GSM11683 1 0.0000 0.8759 1.000 0.000
#> GSM11691 1 0.8016 0.6942 0.756 0.244
#> GSM27949 1 0.0000 0.8759 1.000 0.000
#> GSM27945 1 0.9988 0.1496 0.520 0.480
#> GSM11706 1 0.0000 0.8759 1.000 0.000
#> GSM11853 1 0.7139 0.7546 0.804 0.196
#> GSM11729 2 0.0000 0.9115 0.000 1.000
#> GSM11746 2 0.0000 0.9115 0.000 1.000
#> GSM11711 1 0.0000 0.8759 1.000 0.000
#> GSM11854 1 0.7139 0.7546 0.804 0.196
#> GSM11731 2 0.0000 0.9115 0.000 1.000
#> GSM11839 2 0.0000 0.9115 0.000 1.000
#> GSM11836 2 0.7139 0.7104 0.196 0.804
#> GSM11849 2 0.7139 0.7104 0.196 0.804
#> GSM11682 1 0.0000 0.8759 1.000 0.000
#> GSM11690 2 0.0376 0.9086 0.004 0.996
#> GSM11692 2 0.0000 0.9115 0.000 1.000
#> GSM11841 2 0.0000 0.9115 0.000 1.000
#> GSM11901 2 0.0000 0.9115 0.000 1.000
#> GSM11715 2 0.0000 0.9115 0.000 1.000
#> GSM11724 2 0.0000 0.9115 0.000 1.000
#> GSM11684 2 0.0000 0.9115 0.000 1.000
#> GSM11696 2 0.0000 0.9115 0.000 1.000
#> GSM27952 1 0.0000 0.8759 1.000 0.000
#> GSM27948 2 0.0000 0.9115 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM11708 3 0.0000 0.7951 0.000 0.000 1.000
#> GSM11735 3 0.0000 0.7951 0.000 0.000 1.000
#> GSM11733 3 0.0000 0.7951 0.000 0.000 1.000
#> GSM11863 3 0.4062 0.6664 0.000 0.164 0.836
#> GSM11710 3 0.0424 0.7937 0.000 0.008 0.992
#> GSM11712 2 0.3816 0.5299 0.148 0.852 0.000
#> GSM11732 3 0.3695 0.7345 0.108 0.012 0.880
#> GSM11844 3 0.1015 0.7912 0.008 0.012 0.980
#> GSM11842 3 0.5363 0.5008 0.000 0.276 0.724
#> GSM11860 3 0.4915 0.6777 0.036 0.132 0.832
#> GSM11686 3 0.1411 0.7836 0.000 0.036 0.964
#> GSM11688 3 0.0424 0.7937 0.000 0.008 0.992
#> GSM11846 3 0.0000 0.7951 0.000 0.000 1.000
#> GSM11680 3 0.6319 0.6011 0.040 0.228 0.732
#> GSM11698 3 0.1337 0.7893 0.012 0.016 0.972
#> GSM11840 3 0.0000 0.7951 0.000 0.000 1.000
#> GSM11847 3 0.0000 0.7951 0.000 0.000 1.000
#> GSM11685 3 0.1289 0.7856 0.000 0.032 0.968
#> GSM11699 2 0.4799 0.4973 0.032 0.836 0.132
#> GSM27950 3 0.0000 0.7951 0.000 0.000 1.000
#> GSM27946 2 0.4589 0.4684 0.172 0.820 0.008
#> GSM11709 1 0.4974 0.5109 0.764 0.000 0.236
#> GSM11720 1 0.4555 0.6119 0.800 0.200 0.000
#> GSM11726 1 0.1182 0.5898 0.976 0.012 0.012
#> GSM11837 1 0.1643 0.5799 0.956 0.044 0.000
#> GSM11725 1 0.4654 0.6139 0.792 0.208 0.000
#> GSM11864 1 0.4887 0.5965 0.772 0.228 0.000
#> GSM11687 1 0.4452 0.6166 0.808 0.192 0.000
#> GSM11693 1 0.4452 0.6166 0.808 0.192 0.000
#> GSM11727 1 0.5678 0.2632 0.684 0.316 0.000
#> GSM11838 1 0.5678 0.2632 0.684 0.316 0.000
#> GSM11681 3 0.5470 0.6224 0.168 0.036 0.796
#> GSM11689 1 0.4555 0.6174 0.800 0.200 0.000
#> GSM11704 1 0.4555 0.6174 0.800 0.200 0.000
#> GSM11703 1 0.4452 0.6166 0.808 0.192 0.000
#> GSM11705 1 0.6126 0.2724 0.600 0.000 0.400
#> GSM11722 1 0.5678 0.2632 0.684 0.316 0.000
#> GSM11730 1 0.5678 0.2632 0.684 0.316 0.000
#> GSM11713 1 0.8756 0.1084 0.540 0.332 0.128
#> GSM11728 1 0.8821 0.0729 0.524 0.348 0.128
#> GSM27947 1 0.5291 0.5501 0.732 0.268 0.000
#> GSM27951 1 0.7474 0.3815 0.696 0.128 0.176
#> GSM11707 3 0.0000 0.7951 0.000 0.000 1.000
#> GSM11716 1 0.5285 0.5715 0.752 0.244 0.004
#> GSM11850 3 0.9713 0.2288 0.316 0.240 0.444
#> GSM11851 3 0.9484 0.3167 0.264 0.240 0.496
#> GSM11721 2 0.4504 0.6243 0.196 0.804 0.000
#> GSM11852 2 0.6143 0.3689 0.024 0.720 0.256
#> GSM11694 3 0.9700 0.2377 0.312 0.240 0.448
#> GSM11695 3 0.9700 0.2377 0.312 0.240 0.448
#> GSM11734 2 0.4346 0.4806 0.184 0.816 0.000
#> GSM11861 2 0.1753 0.5979 0.048 0.952 0.000
#> GSM11843 2 0.6267 -0.0206 0.452 0.548 0.000
#> GSM11862 2 0.0237 0.6213 0.004 0.996 0.000
#> GSM11697 3 0.9700 0.2377 0.312 0.240 0.448
#> GSM11714 3 0.0000 0.7951 0.000 0.000 1.000
#> GSM11723 2 0.6274 -0.0339 0.456 0.544 0.000
#> GSM11845 2 0.6260 -0.0124 0.448 0.552 0.000
#> GSM11683 3 0.1289 0.7856 0.000 0.032 0.968
#> GSM11691 2 0.9991 -0.1214 0.332 0.352 0.316
#> GSM27949 3 0.1337 0.7889 0.016 0.012 0.972
#> GSM27945 3 0.9829 0.1277 0.352 0.248 0.400
#> GSM11706 3 0.0000 0.7951 0.000 0.000 1.000
#> GSM11853 3 0.9767 0.2105 0.320 0.248 0.432
#> GSM11729 1 0.3551 0.5069 0.868 0.132 0.000
#> GSM11746 1 0.2165 0.5649 0.936 0.064 0.000
#> GSM11711 3 0.0000 0.7951 0.000 0.000 1.000
#> GSM11854 3 0.9355 0.3523 0.232 0.252 0.516
#> GSM11731 2 0.5327 0.5919 0.272 0.728 0.000
#> GSM11839 2 0.4750 0.6210 0.216 0.784 0.000
#> GSM11836 2 0.5335 0.6046 0.232 0.760 0.008
#> GSM11849 2 0.5216 0.5875 0.260 0.740 0.000
#> GSM11682 3 0.4047 0.6928 0.004 0.148 0.848
#> GSM11690 2 0.4702 0.6190 0.212 0.788 0.000
#> GSM11692 2 0.0892 0.6229 0.020 0.980 0.000
#> GSM11841 2 0.1163 0.6211 0.028 0.972 0.000
#> GSM11901 2 0.0892 0.6229 0.020 0.980 0.000
#> GSM11715 2 0.5926 0.5056 0.356 0.644 0.000
#> GSM11724 2 0.5859 0.5210 0.344 0.656 0.000
#> GSM11684 2 0.5016 0.6033 0.240 0.760 0.000
#> GSM11696 2 0.5016 0.6033 0.240 0.760 0.000
#> GSM27952 3 0.1411 0.7836 0.000 0.036 0.964
#> GSM27948 2 0.4654 0.6213 0.208 0.792 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM11708 1 0.1209 0.848 0.964 0.004 0.032 0.000
#> GSM11735 1 0.3852 0.753 0.808 0.012 0.180 0.000
#> GSM11733 1 0.5972 0.715 0.716 0.088 0.180 0.016
#> GSM11863 1 0.6770 0.692 0.676 0.088 0.188 0.048
#> GSM11710 1 0.0000 0.852 1.000 0.000 0.000 0.000
#> GSM11712 4 0.3674 0.760 0.000 0.036 0.116 0.848
#> GSM11732 3 0.3828 0.768 0.068 0.084 0.848 0.000
#> GSM11844 3 0.4194 0.669 0.228 0.008 0.764 0.000
#> GSM11842 1 0.6989 0.679 0.660 0.088 0.196 0.056
#> GSM11860 1 0.6722 0.687 0.668 0.100 0.200 0.032
#> GSM11686 1 0.0592 0.847 0.984 0.000 0.000 0.016
#> GSM11688 1 0.0000 0.852 1.000 0.000 0.000 0.000
#> GSM11846 1 0.0524 0.853 0.988 0.004 0.008 0.000
#> GSM11680 3 0.3505 0.800 0.088 0.000 0.864 0.048
#> GSM11698 3 0.4788 0.671 0.232 0.008 0.744 0.016
#> GSM11840 1 0.6038 0.716 0.716 0.088 0.176 0.020
#> GSM11847 1 0.6038 0.716 0.716 0.088 0.176 0.020
#> GSM11685 1 0.0000 0.852 1.000 0.000 0.000 0.000
#> GSM11699 4 0.6504 0.356 0.044 0.016 0.396 0.544
#> GSM27950 1 0.0921 0.851 0.972 0.000 0.028 0.000
#> GSM27946 4 0.6351 0.391 0.020 0.032 0.388 0.560
#> GSM11709 2 0.4406 0.728 0.192 0.780 0.028 0.000
#> GSM11720 2 0.3444 0.796 0.000 0.816 0.184 0.000
#> GSM11726 2 0.1811 0.798 0.020 0.948 0.028 0.004
#> GSM11837 2 0.2623 0.796 0.000 0.908 0.064 0.028
#> GSM11725 2 0.4136 0.792 0.000 0.788 0.196 0.016
#> GSM11864 2 0.4175 0.788 0.000 0.784 0.200 0.016
#> GSM11687 2 0.3355 0.808 0.000 0.836 0.160 0.004
#> GSM11693 2 0.3577 0.808 0.000 0.832 0.156 0.012
#> GSM11727 2 0.3266 0.747 0.000 0.832 0.000 0.168
#> GSM11838 2 0.3991 0.740 0.000 0.808 0.020 0.172
#> GSM11681 1 0.2266 0.804 0.912 0.084 0.000 0.004
#> GSM11689 2 0.3547 0.810 0.000 0.840 0.144 0.016
#> GSM11704 2 0.3547 0.810 0.000 0.840 0.144 0.016
#> GSM11703 2 0.3529 0.809 0.000 0.836 0.152 0.012
#> GSM11705 2 0.4040 0.657 0.248 0.752 0.000 0.000
#> GSM11722 2 0.3266 0.747 0.000 0.832 0.000 0.168
#> GSM11730 2 0.3266 0.747 0.000 0.832 0.000 0.168
#> GSM11713 1 0.7082 0.300 0.540 0.308 0.000 0.152
#> GSM11728 1 0.7102 0.331 0.548 0.288 0.000 0.164
#> GSM27947 2 0.6845 0.122 0.000 0.452 0.448 0.100
#> GSM27951 2 0.5560 0.673 0.156 0.728 0.000 0.116
#> GSM11707 1 0.0779 0.852 0.980 0.004 0.016 0.000
#> GSM11716 3 0.0707 0.817 0.000 0.020 0.980 0.000
#> GSM11850 3 0.1042 0.833 0.020 0.008 0.972 0.000
#> GSM11851 3 0.1004 0.832 0.024 0.004 0.972 0.000
#> GSM11721 4 0.1526 0.789 0.016 0.012 0.012 0.960
#> GSM11852 4 0.6815 0.562 0.168 0.004 0.208 0.620
#> GSM11694 3 0.1042 0.833 0.020 0.008 0.972 0.000
#> GSM11695 3 0.1042 0.833 0.020 0.008 0.972 0.000
#> GSM11734 4 0.6324 0.640 0.000 0.168 0.172 0.660
#> GSM11861 4 0.5291 0.569 0.024 0.000 0.324 0.652
#> GSM11843 4 0.7519 0.399 0.000 0.256 0.248 0.496
#> GSM11862 4 0.4018 0.738 0.016 0.004 0.168 0.812
#> GSM11697 3 0.1042 0.833 0.020 0.008 0.972 0.000
#> GSM11714 1 0.0592 0.853 0.984 0.000 0.016 0.000
#> GSM11723 3 0.6049 0.479 0.000 0.120 0.680 0.200
#> GSM11845 3 0.6278 0.421 0.000 0.120 0.652 0.228
#> GSM11683 1 0.0336 0.851 0.992 0.000 0.008 0.000
#> GSM11691 3 0.4256 0.761 0.132 0.012 0.824 0.032
#> GSM27949 3 0.4283 0.647 0.256 0.004 0.740 0.000
#> GSM27945 3 0.1411 0.829 0.020 0.020 0.960 0.000
#> GSM11706 1 0.0779 0.852 0.980 0.004 0.016 0.000
#> GSM11853 3 0.4260 0.781 0.080 0.016 0.840 0.064
#> GSM11729 2 0.3687 0.771 0.000 0.856 0.064 0.080
#> GSM11746 2 0.3323 0.785 0.000 0.876 0.064 0.060
#> GSM11711 1 0.0524 0.853 0.988 0.004 0.008 0.000
#> GSM11854 3 0.5686 0.693 0.156 0.004 0.728 0.112
#> GSM11731 4 0.2813 0.769 0.000 0.080 0.024 0.896
#> GSM11839 4 0.1284 0.790 0.000 0.024 0.012 0.964
#> GSM11836 4 0.2271 0.762 0.000 0.076 0.008 0.916
#> GSM11849 4 0.3616 0.729 0.036 0.112 0.000 0.852
#> GSM11682 1 0.2142 0.816 0.928 0.016 0.000 0.056
#> GSM11690 4 0.1174 0.784 0.012 0.020 0.000 0.968
#> GSM11692 4 0.3342 0.771 0.000 0.032 0.100 0.868
#> GSM11841 4 0.3342 0.771 0.000 0.032 0.100 0.868
#> GSM11901 4 0.3279 0.773 0.000 0.032 0.096 0.872
#> GSM11715 4 0.4767 0.571 0.000 0.256 0.020 0.724
#> GSM11724 4 0.4642 0.597 0.000 0.240 0.020 0.740
#> GSM11684 4 0.1584 0.780 0.012 0.036 0.000 0.952
#> GSM11696 4 0.0927 0.785 0.008 0.016 0.000 0.976
#> GSM27952 1 0.0188 0.851 0.996 0.000 0.000 0.004
#> GSM27948 4 0.0657 0.787 0.012 0.000 0.004 0.984
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM11708 5 0.4641 -0.4023 0.456 0.000 0.012 0.000 0.532
#> GSM11735 5 0.3064 0.6412 0.108 0.000 0.036 0.000 0.856
#> GSM11733 5 0.1455 0.7526 0.008 0.000 0.032 0.008 0.952
#> GSM11863 5 0.2277 0.7365 0.000 0.028 0.024 0.028 0.920
#> GSM11710 1 0.4283 0.5248 0.544 0.000 0.000 0.000 0.456
#> GSM11712 4 0.2122 0.7584 0.008 0.040 0.008 0.928 0.016
#> GSM11732 3 0.2439 0.7526 0.004 0.000 0.876 0.000 0.120
#> GSM11844 3 0.3911 0.6961 0.060 0.000 0.796 0.000 0.144
#> GSM11842 5 0.2444 0.7308 0.000 0.036 0.024 0.028 0.912
#> GSM11860 5 0.2745 0.7220 0.016 0.040 0.024 0.016 0.904
#> GSM11686 1 0.4903 0.5667 0.576 0.000 0.008 0.016 0.400
#> GSM11688 1 0.4735 0.5651 0.572 0.000 0.008 0.008 0.412
#> GSM11846 5 0.4182 -0.2207 0.400 0.000 0.000 0.000 0.600
#> GSM11680 3 0.3406 0.7525 0.040 0.000 0.856 0.084 0.020
#> GSM11698 3 0.3845 0.7168 0.100 0.000 0.824 0.012 0.064
#> GSM11840 5 0.1455 0.7526 0.008 0.000 0.032 0.008 0.952
#> GSM11847 5 0.1455 0.7526 0.008 0.000 0.032 0.008 0.952
#> GSM11685 1 0.4828 0.5666 0.572 0.000 0.008 0.012 0.408
#> GSM11699 4 0.4819 0.5362 0.024 0.012 0.252 0.704 0.008
#> GSM27950 1 0.5175 0.5352 0.548 0.000 0.044 0.000 0.408
#> GSM27946 4 0.4463 0.5893 0.016 0.012 0.212 0.748 0.012
#> GSM11709 1 0.4976 -0.4263 0.540 0.436 0.012 0.000 0.012
#> GSM11720 2 0.6390 0.6262 0.264 0.572 0.144 0.020 0.000
#> GSM11726 2 0.3888 0.6677 0.112 0.816 0.008 0.000 0.064
#> GSM11837 2 0.2426 0.6436 0.004 0.908 0.008 0.016 0.064
#> GSM11725 2 0.5813 0.6473 0.160 0.684 0.112 0.044 0.000
#> GSM11864 2 0.6211 0.6409 0.168 0.660 0.116 0.052 0.004
#> GSM11687 2 0.6640 0.6122 0.352 0.500 0.120 0.028 0.000
#> GSM11693 2 0.6839 0.6182 0.340 0.500 0.116 0.044 0.000
#> GSM11727 2 0.3454 0.6208 0.156 0.816 0.000 0.028 0.000
#> GSM11838 2 0.2616 0.6006 0.076 0.888 0.000 0.036 0.000
#> GSM11681 1 0.3659 0.4706 0.768 0.000 0.000 0.012 0.220
#> GSM11689 2 0.6898 0.6215 0.340 0.500 0.104 0.056 0.000
#> GSM11704 2 0.6898 0.6215 0.340 0.500 0.104 0.056 0.000
#> GSM11703 2 0.6839 0.6182 0.340 0.500 0.116 0.044 0.000
#> GSM11705 1 0.4193 -0.1065 0.684 0.304 0.000 0.000 0.012
#> GSM11722 2 0.3194 0.6302 0.148 0.832 0.000 0.020 0.000
#> GSM11730 2 0.3527 0.6176 0.172 0.804 0.000 0.024 0.000
#> GSM11713 1 0.4957 0.3528 0.752 0.136 0.000 0.032 0.080
#> GSM11728 1 0.5456 0.3126 0.708 0.172 0.000 0.040 0.080
#> GSM27947 3 0.8872 -0.1947 0.204 0.240 0.280 0.264 0.012
#> GSM27951 1 0.3318 0.1103 0.800 0.192 0.000 0.008 0.000
#> GSM11707 1 0.4641 0.5005 0.532 0.000 0.012 0.000 0.456
#> GSM11716 3 0.0771 0.7953 0.000 0.020 0.976 0.000 0.004
#> GSM11850 3 0.0451 0.7994 0.000 0.000 0.988 0.004 0.008
#> GSM11851 3 0.1106 0.7991 0.000 0.000 0.964 0.012 0.024
#> GSM11721 4 0.1256 0.7615 0.012 0.008 0.004 0.964 0.012
#> GSM11852 4 0.4551 0.6680 0.112 0.000 0.048 0.788 0.052
#> GSM11694 3 0.0000 0.7995 0.000 0.000 1.000 0.000 0.000
#> GSM11695 3 0.0000 0.7995 0.000 0.000 1.000 0.000 0.000
#> GSM11734 4 0.6560 0.0969 0.012 0.428 0.108 0.444 0.008
#> GSM11861 4 0.4970 0.5851 0.028 0.004 0.216 0.720 0.032
#> GSM11843 2 0.6899 0.1746 0.016 0.496 0.160 0.320 0.008
#> GSM11862 4 0.2604 0.7478 0.024 0.004 0.036 0.908 0.028
#> GSM11697 3 0.0000 0.7995 0.000 0.000 1.000 0.000 0.000
#> GSM11714 1 0.4767 0.5461 0.560 0.000 0.020 0.000 0.420
#> GSM11723 3 0.6396 0.3459 0.004 0.272 0.560 0.156 0.008
#> GSM11845 3 0.6703 0.3122 0.008 0.264 0.532 0.188 0.008
#> GSM11683 1 0.4920 0.5671 0.572 0.000 0.012 0.012 0.404
#> GSM11691 3 0.1806 0.7887 0.016 0.000 0.940 0.028 0.016
#> GSM27949 3 0.3555 0.7032 0.124 0.000 0.824 0.000 0.052
#> GSM27945 3 0.0671 0.7948 0.004 0.016 0.980 0.000 0.000
#> GSM11706 1 0.4443 0.4872 0.524 0.000 0.004 0.000 0.472
#> GSM11853 3 0.5951 0.6496 0.068 0.012 0.700 0.148 0.072
#> GSM11729 2 0.2869 0.6302 0.004 0.888 0.008 0.036 0.064
#> GSM11746 2 0.2616 0.6380 0.004 0.900 0.008 0.024 0.064
#> GSM11711 1 0.4787 0.5183 0.528 0.000 0.012 0.004 0.456
#> GSM11854 3 0.6824 0.4444 0.060 0.004 0.564 0.272 0.100
#> GSM11731 4 0.4686 0.3963 0.012 0.396 0.000 0.588 0.004
#> GSM11839 4 0.3934 0.6340 0.012 0.236 0.000 0.748 0.004
#> GSM11836 4 0.6903 0.3557 0.084 0.368 0.000 0.480 0.068
#> GSM11849 4 0.6246 0.4304 0.132 0.324 0.000 0.536 0.008
#> GSM11682 1 0.5220 0.5378 0.596 0.004 0.004 0.036 0.360
#> GSM11690 4 0.2592 0.7447 0.056 0.052 0.000 0.892 0.000
#> GSM11692 4 0.1243 0.7615 0.000 0.028 0.008 0.960 0.004
#> GSM11841 4 0.1455 0.7605 0.000 0.032 0.008 0.952 0.008
#> GSM11901 4 0.1243 0.7615 0.000 0.028 0.008 0.960 0.004
#> GSM11715 2 0.5473 0.1214 0.080 0.620 0.000 0.296 0.004
#> GSM11724 2 0.5526 0.0854 0.080 0.608 0.000 0.308 0.004
#> GSM11684 4 0.3967 0.6930 0.092 0.108 0.000 0.800 0.000
#> GSM11696 4 0.3180 0.7309 0.076 0.068 0.000 0.856 0.000
#> GSM27952 1 0.4806 0.5656 0.572 0.000 0.004 0.016 0.408
#> GSM27948 4 0.1106 0.7606 0.012 0.024 0.000 0.964 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM11708 6 0.3010 0.7565 0.000 0.004 0.028 0.000 0.132 0.836
#> GSM11735 5 0.4555 0.5591 0.000 0.004 0.040 0.000 0.616 0.340
#> GSM11733 5 0.2312 0.9324 0.000 0.000 0.012 0.000 0.876 0.112
#> GSM11863 5 0.2070 0.9361 0.000 0.000 0.008 0.000 0.892 0.100
#> GSM11710 6 0.1082 0.8421 0.000 0.000 0.004 0.000 0.040 0.956
#> GSM11712 4 0.2338 0.7475 0.012 0.068 0.004 0.900 0.016 0.000
#> GSM11732 3 0.2001 0.7568 0.000 0.004 0.900 0.000 0.092 0.004
#> GSM11844 3 0.2940 0.7321 0.000 0.004 0.848 0.000 0.112 0.036
#> GSM11842 5 0.2020 0.9337 0.000 0.000 0.008 0.000 0.896 0.096
#> GSM11860 5 0.1970 0.9309 0.000 0.000 0.008 0.000 0.900 0.092
#> GSM11686 6 0.0665 0.8407 0.008 0.008 0.004 0.000 0.000 0.980
#> GSM11688 6 0.0363 0.8452 0.000 0.000 0.000 0.000 0.012 0.988
#> GSM11846 6 0.3724 0.5393 0.000 0.012 0.004 0.000 0.268 0.716
#> GSM11680 3 0.3219 0.7500 0.000 0.008 0.848 0.048 0.008 0.088
#> GSM11698 3 0.3331 0.7178 0.000 0.008 0.828 0.008 0.028 0.128
#> GSM11840 5 0.2165 0.9367 0.000 0.000 0.008 0.000 0.884 0.108
#> GSM11847 5 0.2165 0.9367 0.000 0.000 0.008 0.000 0.884 0.108
#> GSM11685 6 0.0363 0.8452 0.000 0.000 0.000 0.000 0.012 0.988
#> GSM11699 4 0.4274 0.6946 0.008 0.024 0.160 0.768 0.004 0.036
#> GSM27950 6 0.1769 0.8327 0.000 0.004 0.060 0.000 0.012 0.924
#> GSM27946 4 0.3725 0.7207 0.012 0.020 0.104 0.828 0.016 0.020
#> GSM11709 1 0.2538 0.6640 0.860 0.000 0.016 0.000 0.000 0.124
#> GSM11720 1 0.2445 0.7001 0.896 0.060 0.032 0.004 0.008 0.000
#> GSM11726 1 0.5256 -0.1920 0.476 0.452 0.004 0.008 0.060 0.000
#> GSM11837 2 0.5221 0.4697 0.268 0.640 0.008 0.024 0.060 0.000
#> GSM11725 1 0.4755 0.5186 0.716 0.204 0.032 0.020 0.028 0.000
#> GSM11864 1 0.5039 0.5044 0.700 0.204 0.036 0.024 0.036 0.000
#> GSM11687 1 0.0363 0.7402 0.988 0.000 0.012 0.000 0.000 0.000
#> GSM11693 1 0.0508 0.7408 0.984 0.000 0.012 0.004 0.000 0.000
#> GSM11727 2 0.3429 0.5344 0.252 0.740 0.000 0.004 0.004 0.000
#> GSM11838 2 0.3018 0.5915 0.168 0.816 0.000 0.004 0.012 0.000
#> GSM11681 6 0.2615 0.7509 0.136 0.008 0.000 0.000 0.004 0.852
#> GSM11689 1 0.0508 0.7408 0.984 0.000 0.012 0.004 0.000 0.000
#> GSM11704 1 0.0508 0.7408 0.984 0.000 0.012 0.004 0.000 0.000
#> GSM11703 1 0.0363 0.7402 0.988 0.000 0.012 0.000 0.000 0.000
#> GSM11705 1 0.3463 0.5693 0.748 0.004 0.008 0.000 0.000 0.240
#> GSM11722 2 0.3421 0.5457 0.256 0.736 0.000 0.000 0.008 0.000
#> GSM11730 2 0.3667 0.5356 0.240 0.740 0.000 0.008 0.012 0.000
#> GSM11713 6 0.6521 0.3428 0.172 0.276 0.000 0.016 0.028 0.508
#> GSM11728 6 0.6609 0.3288 0.172 0.280 0.000 0.020 0.028 0.500
#> GSM27947 1 0.5533 0.4658 0.632 0.032 0.100 0.232 0.004 0.000
#> GSM27951 1 0.5374 0.3777 0.584 0.136 0.000 0.000 0.004 0.276
#> GSM11707 6 0.2052 0.8291 0.000 0.004 0.028 0.000 0.056 0.912
#> GSM11716 3 0.2450 0.7703 0.040 0.048 0.896 0.000 0.016 0.000
#> GSM11850 3 0.1086 0.7876 0.012 0.012 0.964 0.000 0.012 0.000
#> GSM11851 3 0.2716 0.7759 0.012 0.024 0.896 0.020 0.040 0.008
#> GSM11721 4 0.2080 0.7553 0.004 0.016 0.012 0.924 0.036 0.008
#> GSM11852 4 0.4816 0.6899 0.004 0.040 0.056 0.772 0.056 0.072
#> GSM11694 3 0.0982 0.7888 0.020 0.004 0.968 0.000 0.004 0.004
#> GSM11695 3 0.0982 0.7888 0.020 0.004 0.968 0.000 0.004 0.004
#> GSM11734 2 0.7001 0.3811 0.136 0.512 0.048 0.256 0.048 0.000
#> GSM11861 4 0.6114 0.5760 0.012 0.048 0.180 0.652 0.072 0.036
#> GSM11843 2 0.7972 0.3054 0.184 0.404 0.120 0.240 0.052 0.000
#> GSM11862 4 0.4562 0.7013 0.004 0.048 0.060 0.788 0.068 0.032
#> GSM11697 3 0.1210 0.7886 0.020 0.008 0.960 0.000 0.004 0.008
#> GSM11714 6 0.1599 0.8425 0.000 0.008 0.028 0.000 0.024 0.940
#> GSM11723 3 0.7150 0.1160 0.068 0.344 0.444 0.096 0.048 0.000
#> GSM11845 3 0.7821 0.0272 0.100 0.312 0.384 0.152 0.052 0.000
#> GSM11683 6 0.1642 0.8376 0.000 0.004 0.032 0.000 0.028 0.936
#> GSM11691 3 0.3786 0.7533 0.024 0.028 0.840 0.064 0.028 0.016
#> GSM27949 3 0.2905 0.7149 0.000 0.008 0.836 0.000 0.012 0.144
#> GSM27945 3 0.1780 0.7856 0.044 0.008 0.932 0.008 0.008 0.000
#> GSM11706 6 0.1890 0.8297 0.000 0.000 0.024 0.000 0.060 0.916
#> GSM11853 3 0.7606 0.3996 0.120 0.036 0.500 0.240 0.072 0.032
#> GSM11729 2 0.5264 0.4826 0.256 0.644 0.008 0.024 0.068 0.000
#> GSM11746 2 0.5264 0.4826 0.256 0.644 0.008 0.024 0.068 0.000
#> GSM11711 6 0.1989 0.8355 0.000 0.000 0.028 0.004 0.052 0.916
#> GSM11854 3 0.7404 0.1760 0.024 0.032 0.432 0.356 0.068 0.088
#> GSM11731 2 0.5084 0.2581 0.016 0.556 0.004 0.384 0.040 0.000
#> GSM11839 4 0.4896 0.0787 0.016 0.424 0.000 0.528 0.032 0.000
#> GSM11836 2 0.5266 0.3283 0.008 0.632 0.000 0.268 0.076 0.016
#> GSM11849 2 0.5303 0.2871 0.016 0.632 0.000 0.280 0.028 0.044
#> GSM11682 6 0.1804 0.8172 0.008 0.020 0.000 0.016 0.020 0.936
#> GSM11690 4 0.4455 0.6539 0.012 0.196 0.000 0.736 0.028 0.028
#> GSM11692 4 0.2086 0.7595 0.012 0.064 0.004 0.912 0.008 0.000
#> GSM11841 4 0.2144 0.7586 0.012 0.068 0.004 0.908 0.008 0.000
#> GSM11901 4 0.1985 0.7596 0.008 0.064 0.004 0.916 0.008 0.000
#> GSM11715 2 0.2573 0.6028 0.012 0.872 0.000 0.104 0.012 0.000
#> GSM11724 2 0.2573 0.6028 0.012 0.872 0.000 0.104 0.012 0.000
#> GSM11684 4 0.4842 0.5156 0.008 0.308 0.000 0.636 0.028 0.020
#> GSM11696 4 0.4447 0.5923 0.008 0.260 0.000 0.692 0.028 0.012
#> GSM27952 6 0.0405 0.8419 0.004 0.008 0.000 0.000 0.000 0.988
#> GSM27948 4 0.3057 0.7392 0.012 0.100 0.000 0.856 0.012 0.020
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.line(p) agent(p) time(p) k
#> MAD:skmeans 73 3.58e-07 0.759 2.14e-01 2
#> MAD:skmeans 59 5.49e-12 0.105 8.30e-01 3
#> MAD:skmeans 75 1.19e-16 0.835 1.88e-01 4
#> MAD:skmeans 63 1.02e-12 0.857 1.93e-05 5
#> MAD:skmeans 65 4.81e-12 0.739 1.77e-08 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 14502 rows and 83 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.920 0.950 0.3129 0.700 0.700
#> 3 3 0.241 0.429 0.727 0.7322 0.761 0.670
#> 4 4 0.546 0.526 0.739 0.2161 0.828 0.678
#> 5 5 0.594 0.352 0.660 0.1251 0.793 0.517
#> 6 6 0.702 0.529 0.791 0.0962 0.755 0.282
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM11708 2 0.0000 0.929 0.000 1.000
#> GSM11735 2 0.0000 0.929 0.000 1.000
#> GSM11733 2 0.0000 0.929 0.000 1.000
#> GSM11863 2 0.3879 0.894 0.076 0.924
#> GSM11710 2 0.0000 0.929 0.000 1.000
#> GSM11712 1 0.0000 0.950 1.000 0.000
#> GSM11732 1 0.3584 0.950 0.932 0.068
#> GSM11844 1 0.3879 0.948 0.924 0.076
#> GSM11842 2 0.3879 0.894 0.076 0.924
#> GSM11860 2 0.0672 0.927 0.008 0.992
#> GSM11686 1 0.3879 0.948 0.924 0.076
#> GSM11688 2 0.4690 0.854 0.100 0.900
#> GSM11846 2 0.9988 -0.051 0.480 0.520
#> GSM11680 1 0.0000 0.950 1.000 0.000
#> GSM11698 1 0.3879 0.948 0.924 0.076
#> GSM11840 2 0.0000 0.929 0.000 1.000
#> GSM11847 2 0.2043 0.919 0.032 0.968
#> GSM11685 2 0.3431 0.901 0.064 0.936
#> GSM11699 1 0.2043 0.951 0.968 0.032
#> GSM27950 1 0.4022 0.946 0.920 0.080
#> GSM27946 1 0.0000 0.950 1.000 0.000
#> GSM11709 1 0.3879 0.948 0.924 0.076
#> GSM11720 1 0.3584 0.950 0.932 0.068
#> GSM11726 1 0.3733 0.949 0.928 0.072
#> GSM11837 1 0.0000 0.950 1.000 0.000
#> GSM11725 1 0.0000 0.950 1.000 0.000
#> GSM11864 1 0.0000 0.950 1.000 0.000
#> GSM11687 1 0.3584 0.950 0.932 0.068
#> GSM11693 1 0.3584 0.950 0.932 0.068
#> GSM11727 1 0.0000 0.950 1.000 0.000
#> GSM11838 1 0.0000 0.950 1.000 0.000
#> GSM11681 1 0.3879 0.948 0.924 0.076
#> GSM11689 1 0.3584 0.950 0.932 0.068
#> GSM11704 1 0.0000 0.950 1.000 0.000
#> GSM11703 1 0.3584 0.950 0.932 0.068
#> GSM11705 1 0.3879 0.948 0.924 0.076
#> GSM11722 1 0.0000 0.950 1.000 0.000
#> GSM11730 1 0.0000 0.950 1.000 0.000
#> GSM11713 1 0.3879 0.948 0.924 0.076
#> GSM11728 1 0.3879 0.948 0.924 0.076
#> GSM27947 1 0.0000 0.950 1.000 0.000
#> GSM27951 1 0.3733 0.949 0.928 0.072
#> GSM11707 2 0.0000 0.929 0.000 1.000
#> GSM11716 1 0.3114 0.951 0.944 0.056
#> GSM11850 1 0.3879 0.948 0.924 0.076
#> GSM11851 1 0.3879 0.948 0.924 0.076
#> GSM11721 1 0.0000 0.950 1.000 0.000
#> GSM11852 1 0.3879 0.948 0.924 0.076
#> GSM11694 1 0.3584 0.950 0.932 0.068
#> GSM11695 1 0.3584 0.950 0.932 0.068
#> GSM11734 1 0.0000 0.950 1.000 0.000
#> GSM11861 1 0.3584 0.950 0.932 0.068
#> GSM11843 1 0.0000 0.950 1.000 0.000
#> GSM11862 1 0.0000 0.950 1.000 0.000
#> GSM11697 1 0.3584 0.950 0.932 0.068
#> GSM11714 2 0.0000 0.929 0.000 1.000
#> GSM11723 1 0.0000 0.950 1.000 0.000
#> GSM11845 1 0.0000 0.950 1.000 0.000
#> GSM11683 1 0.3879 0.948 0.924 0.076
#> GSM11691 1 0.0000 0.950 1.000 0.000
#> GSM27949 1 0.3879 0.948 0.924 0.076
#> GSM27945 1 0.3584 0.950 0.932 0.068
#> GSM11706 2 0.4022 0.875 0.080 0.920
#> GSM11853 1 0.3879 0.948 0.924 0.076
#> GSM11729 1 0.0000 0.950 1.000 0.000
#> GSM11746 1 0.3584 0.950 0.932 0.068
#> GSM11711 1 0.3879 0.948 0.924 0.076
#> GSM11854 1 0.3879 0.948 0.924 0.076
#> GSM11731 1 0.0000 0.950 1.000 0.000
#> GSM11839 1 0.0000 0.950 1.000 0.000
#> GSM11836 1 0.0376 0.948 0.996 0.004
#> GSM11849 1 0.3879 0.948 0.924 0.076
#> GSM11682 1 0.7883 0.754 0.764 0.236
#> GSM11690 1 0.0000 0.950 1.000 0.000
#> GSM11692 1 0.0000 0.950 1.000 0.000
#> GSM11841 1 0.0000 0.950 1.000 0.000
#> GSM11901 1 0.0000 0.950 1.000 0.000
#> GSM11715 1 0.0000 0.950 1.000 0.000
#> GSM11724 1 0.0000 0.950 1.000 0.000
#> GSM11684 1 0.0000 0.950 1.000 0.000
#> GSM11696 1 0.0000 0.950 1.000 0.000
#> GSM27952 1 0.9954 0.211 0.540 0.460
#> GSM27948 1 0.0000 0.950 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM11708 3 0.6026 0.4537 0.000 0.376 0.624
#> GSM11735 3 0.6026 0.4537 0.000 0.376 0.624
#> GSM11733 3 0.6026 0.4537 0.000 0.376 0.624
#> GSM11863 2 0.6286 -0.2993 0.000 0.536 0.464
#> GSM11710 3 0.0000 0.5263 0.000 0.000 1.000
#> GSM11712 1 0.6095 0.2470 0.608 0.392 0.000
#> GSM11732 1 0.4062 0.6476 0.836 0.000 0.164
#> GSM11844 1 0.4293 0.6472 0.832 0.004 0.164
#> GSM11842 2 0.6286 -0.2993 0.000 0.536 0.464
#> GSM11860 3 0.6026 0.4537 0.000 0.376 0.624
#> GSM11686 1 0.6081 0.4388 0.652 0.004 0.344
#> GSM11688 3 0.3377 0.5065 0.092 0.012 0.896
#> GSM11846 3 0.6566 0.1914 0.376 0.012 0.612
#> GSM11680 1 0.4062 0.6084 0.836 0.164 0.000
#> GSM11698 1 0.4293 0.6472 0.832 0.004 0.164
#> GSM11840 3 0.6026 0.4537 0.000 0.376 0.624
#> GSM11847 3 0.6260 0.3510 0.000 0.448 0.552
#> GSM11685 3 0.6154 0.1143 0.000 0.408 0.592
#> GSM11699 1 0.7291 0.2747 0.604 0.356 0.040
#> GSM27950 3 0.6305 -0.1257 0.484 0.000 0.516
#> GSM27946 1 0.4062 0.6084 0.836 0.164 0.000
#> GSM11709 1 0.4605 0.5243 0.796 0.000 0.204
#> GSM11720 1 0.4121 0.5552 0.832 0.000 0.168
#> GSM11726 1 0.5397 0.5247 0.720 0.000 0.280
#> GSM11837 1 0.4062 0.6084 0.836 0.164 0.000
#> GSM11725 1 0.0000 0.6455 1.000 0.000 0.000
#> GSM11864 1 0.0000 0.6455 1.000 0.000 0.000
#> GSM11687 1 0.4452 0.5339 0.808 0.000 0.192
#> GSM11693 1 0.0000 0.6455 1.000 0.000 0.000
#> GSM11727 1 0.5778 0.4944 0.768 0.032 0.200
#> GSM11838 1 0.4887 0.3418 0.772 0.228 0.000
#> GSM11681 1 0.6026 0.1811 0.624 0.000 0.376
#> GSM11689 1 0.0000 0.6455 1.000 0.000 0.000
#> GSM11704 1 0.0000 0.6455 1.000 0.000 0.000
#> GSM11703 1 0.4555 0.5258 0.800 0.000 0.200
#> GSM11705 1 0.5968 0.4773 0.636 0.000 0.364
#> GSM11722 1 0.8802 0.1795 0.584 0.216 0.200
#> GSM11730 1 0.8838 0.1839 0.580 0.220 0.200
#> GSM11713 3 0.9213 0.2414 0.228 0.236 0.536
#> GSM11728 1 0.6189 0.4787 0.632 0.004 0.364
#> GSM27947 1 0.0000 0.6455 1.000 0.000 0.000
#> GSM27951 1 0.4605 0.5243 0.796 0.000 0.204
#> GSM11707 3 0.0000 0.5263 0.000 0.000 1.000
#> GSM11716 1 0.0000 0.6455 1.000 0.000 0.000
#> GSM11850 1 0.4062 0.6476 0.836 0.000 0.164
#> GSM11851 1 0.4293 0.6472 0.832 0.004 0.164
#> GSM11721 1 0.6111 0.2378 0.604 0.396 0.000
#> GSM11852 1 0.4293 0.6472 0.832 0.004 0.164
#> GSM11694 1 0.0237 0.6466 0.996 0.000 0.004
#> GSM11695 1 0.4002 0.6487 0.840 0.000 0.160
#> GSM11734 1 0.4062 0.6084 0.836 0.164 0.000
#> GSM11861 1 0.4353 0.6485 0.836 0.008 0.156
#> GSM11843 1 0.3752 0.6181 0.856 0.144 0.000
#> GSM11862 1 0.4062 0.6084 0.836 0.164 0.000
#> GSM11697 1 0.4233 0.6480 0.836 0.004 0.160
#> GSM11714 3 0.0000 0.5263 0.000 0.000 1.000
#> GSM11723 1 0.6079 0.2557 0.612 0.388 0.000
#> GSM11845 1 0.6111 0.2378 0.604 0.396 0.000
#> GSM11683 3 0.9213 0.1326 0.228 0.236 0.536
#> GSM11691 1 0.4121 0.6053 0.832 0.168 0.000
#> GSM27949 1 0.4062 0.6476 0.836 0.000 0.164
#> GSM27945 1 0.0000 0.6455 1.000 0.000 0.000
#> GSM11706 3 0.4914 0.5173 0.068 0.088 0.844
#> GSM11853 1 0.4293 0.6472 0.832 0.004 0.164
#> GSM11729 1 0.6204 0.1194 0.576 0.424 0.000
#> GSM11746 1 0.4887 0.3418 0.772 0.228 0.000
#> GSM11711 1 0.6189 0.4787 0.632 0.004 0.364
#> GSM11854 1 0.4293 0.6472 0.832 0.004 0.164
#> GSM11731 2 0.6026 0.4430 0.376 0.624 0.000
#> GSM11839 1 0.6111 0.2378 0.604 0.396 0.000
#> GSM11836 2 0.6111 0.3997 0.396 0.604 0.000
#> GSM11849 2 0.9417 0.1730 0.180 0.456 0.364
#> GSM11682 3 0.9243 0.1265 0.232 0.236 0.532
#> GSM11690 1 0.6111 0.2378 0.604 0.396 0.000
#> GSM11692 1 0.6111 0.2378 0.604 0.396 0.000
#> GSM11841 1 0.6111 0.2378 0.604 0.396 0.000
#> GSM11901 1 0.6111 0.2378 0.604 0.396 0.000
#> GSM11715 2 0.8399 0.4587 0.188 0.624 0.188
#> GSM11724 2 0.8221 0.4806 0.248 0.624 0.128
#> GSM11684 2 0.6839 0.4625 0.352 0.624 0.024
#> GSM11696 2 0.6026 0.4430 0.376 0.624 0.000
#> GSM27952 3 0.6215 0.0365 0.428 0.000 0.572
#> GSM27948 1 0.6111 0.2378 0.604 0.396 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM11708 4 0.4933 0.823 0.432 0.000 0.000 0.568
#> GSM11735 4 0.4933 0.823 0.432 0.000 0.000 0.568
#> GSM11733 4 0.4933 0.823 0.432 0.000 0.000 0.568
#> GSM11863 4 0.4933 0.823 0.432 0.000 0.000 0.568
#> GSM11710 1 0.1042 0.322 0.972 0.008 0.020 0.000
#> GSM11712 3 0.4933 0.605 0.000 0.000 0.568 0.432
#> GSM11732 3 0.0000 0.578 0.000 0.000 1.000 0.000
#> GSM11844 3 0.0188 0.576 0.004 0.000 0.996 0.000
#> GSM11842 4 0.4933 0.823 0.432 0.000 0.000 0.568
#> GSM11860 4 0.4933 0.823 0.432 0.000 0.000 0.568
#> GSM11686 1 0.6144 0.552 0.508 0.008 0.452 0.032
#> GSM11688 1 0.2675 0.287 0.908 0.000 0.044 0.048
#> GSM11846 1 0.5351 0.450 0.756 0.172 0.056 0.016
#> GSM11680 3 0.0707 0.585 0.000 0.000 0.980 0.020
#> GSM11698 3 0.0188 0.576 0.004 0.000 0.996 0.000
#> GSM11840 4 0.4933 0.823 0.432 0.000 0.000 0.568
#> GSM11847 4 0.4933 0.823 0.432 0.000 0.000 0.568
#> GSM11685 1 0.4989 0.174 0.528 0.000 0.000 0.472
#> GSM11699 3 0.4837 0.612 0.004 0.000 0.648 0.348
#> GSM27950 1 0.4998 0.543 0.512 0.000 0.488 0.000
#> GSM27946 3 0.4933 0.605 0.000 0.000 0.568 0.432
#> GSM11709 3 0.6928 0.456 0.068 0.416 0.500 0.016
#> GSM11720 3 0.6869 0.458 0.064 0.416 0.504 0.016
#> GSM11726 3 0.6903 0.463 0.068 0.400 0.516 0.016
#> GSM11837 3 0.4933 0.605 0.000 0.000 0.568 0.432
#> GSM11725 3 0.5602 0.522 0.000 0.408 0.568 0.024
#> GSM11864 3 0.5602 0.522 0.000 0.408 0.568 0.024
#> GSM11687 3 0.6869 0.458 0.064 0.416 0.504 0.016
#> GSM11693 3 0.5427 0.519 0.000 0.416 0.568 0.016
#> GSM11727 2 0.5321 0.324 0.064 0.764 0.156 0.016
#> GSM11838 2 0.0336 0.453 0.000 0.992 0.000 0.008
#> GSM11681 1 0.6746 0.180 0.512 0.416 0.056 0.016
#> GSM11689 3 0.5427 0.519 0.000 0.416 0.568 0.016
#> GSM11704 3 0.5602 0.522 0.000 0.408 0.568 0.024
#> GSM11703 3 0.6347 0.458 0.064 0.412 0.524 0.000
#> GSM11705 3 0.6895 0.464 0.068 0.396 0.520 0.016
#> GSM11722 2 0.5397 0.270 0.064 0.716 0.220 0.000
#> GSM11730 2 0.2809 0.430 0.064 0.904 0.004 0.028
#> GSM11713 2 0.4642 0.213 0.240 0.740 0.020 0.000
#> GSM11728 3 0.6691 0.558 0.068 0.008 0.520 0.404
#> GSM27947 3 0.5602 0.522 0.000 0.408 0.568 0.024
#> GSM27951 3 0.6928 0.456 0.068 0.416 0.500 0.016
#> GSM11707 1 0.5161 0.568 0.592 0.008 0.400 0.000
#> GSM11716 3 0.0707 0.582 0.000 0.020 0.980 0.000
#> GSM11850 3 0.0188 0.576 0.004 0.000 0.996 0.000
#> GSM11851 3 0.0188 0.576 0.004 0.000 0.996 0.000
#> GSM11721 3 0.4933 0.605 0.000 0.000 0.568 0.432
#> GSM11852 3 0.5060 0.606 0.004 0.000 0.584 0.412
#> GSM11694 3 0.0707 0.582 0.000 0.020 0.980 0.000
#> GSM11695 3 0.0000 0.578 0.000 0.000 1.000 0.000
#> GSM11734 3 0.4933 0.605 0.000 0.000 0.568 0.432
#> GSM11861 3 0.2589 0.624 0.000 0.000 0.884 0.116
#> GSM11843 3 0.2412 0.613 0.000 0.008 0.908 0.084
#> GSM11862 3 0.4933 0.605 0.000 0.000 0.568 0.432
#> GSM11697 3 0.0000 0.578 0.000 0.000 1.000 0.000
#> GSM11714 1 0.5220 0.566 0.568 0.008 0.424 0.000
#> GSM11723 3 0.4888 0.605 0.000 0.000 0.588 0.412
#> GSM11845 3 0.4933 0.605 0.000 0.000 0.568 0.432
#> GSM11683 1 0.4981 0.558 0.536 0.000 0.464 0.000
#> GSM11691 3 0.0707 0.585 0.000 0.000 0.980 0.020
#> GSM27949 3 0.0188 0.576 0.004 0.000 0.996 0.000
#> GSM27945 3 0.1297 0.591 0.000 0.020 0.964 0.016
#> GSM11706 1 0.5641 -0.435 0.636 0.008 0.024 0.332
#> GSM11853 3 0.5060 0.606 0.004 0.000 0.584 0.412
#> GSM11729 2 0.4898 0.589 0.000 0.584 0.000 0.416
#> GSM11746 2 0.0336 0.453 0.000 0.992 0.000 0.008
#> GSM11711 3 0.6005 0.601 0.068 0.032 0.724 0.176
#> GSM11854 3 0.5050 0.608 0.004 0.000 0.588 0.408
#> GSM11731 4 0.7545 -0.549 0.000 0.396 0.188 0.416
#> GSM11839 3 0.4933 0.605 0.000 0.000 0.568 0.432
#> GSM11836 2 0.5444 0.578 0.000 0.560 0.016 0.424
#> GSM11849 2 0.5476 0.577 0.000 0.584 0.020 0.396
#> GSM11682 1 0.6222 0.177 0.532 0.000 0.056 0.412
#> GSM11690 3 0.4933 0.605 0.000 0.000 0.568 0.432
#> GSM11692 3 0.4933 0.605 0.000 0.000 0.568 0.432
#> GSM11841 3 0.4933 0.605 0.000 0.000 0.568 0.432
#> GSM11901 3 0.4933 0.605 0.000 0.000 0.568 0.432
#> GSM11715 2 0.4898 0.589 0.000 0.584 0.000 0.416
#> GSM11724 2 0.4898 0.589 0.000 0.584 0.000 0.416
#> GSM11684 2 0.4898 0.589 0.000 0.584 0.000 0.416
#> GSM11696 2 0.7184 0.464 0.000 0.448 0.136 0.416
#> GSM27952 1 0.3105 0.396 0.888 0.008 0.020 0.084
#> GSM27948 3 0.4933 0.605 0.000 0.000 0.568 0.432
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM11708 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM11735 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM11733 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM11863 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM11710 4 0.6288 0.6103 0.360 0.004 0.084 0.532 0.020
#> GSM11712 1 0.4171 0.5870 0.604 0.000 0.000 0.396 0.000
#> GSM11732 3 0.4307 -0.3498 0.500 0.000 0.500 0.000 0.000
#> GSM11844 3 0.4307 -0.3498 0.500 0.000 0.500 0.000 0.000
#> GSM11842 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM11860 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM11686 4 0.4321 0.6458 0.396 0.000 0.004 0.600 0.000
#> GSM11688 4 0.5056 0.6452 0.360 0.000 0.000 0.596 0.044
#> GSM11846 4 0.6981 0.4500 0.372 0.004 0.212 0.404 0.008
#> GSM11680 1 0.4307 0.2966 0.500 0.000 0.500 0.000 0.000
#> GSM11698 1 0.2516 0.3077 0.860 0.000 0.140 0.000 0.000
#> GSM11840 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM11847 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM11685 4 0.1732 0.2726 0.080 0.000 0.000 0.920 0.000
#> GSM11699 1 0.5896 0.5542 0.564 0.000 0.128 0.308 0.000
#> GSM27950 4 0.5010 0.2927 0.036 0.000 0.392 0.572 0.000
#> GSM27946 1 0.4171 0.5870 0.604 0.000 0.000 0.396 0.000
#> GSM11709 3 0.6100 0.2519 0.108 0.416 0.472 0.004 0.000
#> GSM11720 2 0.6637 -0.3050 0.188 0.416 0.392 0.004 0.000
#> GSM11726 3 0.6547 0.2780 0.216 0.276 0.504 0.004 0.000
#> GSM11837 1 0.5531 0.5474 0.560 0.020 0.036 0.384 0.000
#> GSM11725 1 0.4934 0.3348 0.544 0.432 0.020 0.004 0.000
#> GSM11864 1 0.4924 0.3672 0.552 0.420 0.000 0.028 0.000
#> GSM11687 3 0.6205 0.2471 0.120 0.416 0.460 0.004 0.000
#> GSM11693 1 0.5206 0.3216 0.544 0.416 0.036 0.004 0.000
#> GSM11727 3 0.5683 0.2332 0.068 0.428 0.500 0.004 0.000
#> GSM11838 2 0.1041 0.3211 0.000 0.964 0.032 0.004 0.000
#> GSM11681 3 0.6724 0.2169 0.016 0.416 0.416 0.152 0.000
#> GSM11689 1 0.5206 0.3216 0.544 0.416 0.036 0.004 0.000
#> GSM11704 1 0.5052 0.3320 0.552 0.412 0.036 0.000 0.000
#> GSM11703 3 0.5130 0.2569 0.032 0.412 0.552 0.004 0.000
#> GSM11705 3 0.5550 0.1248 0.468 0.056 0.472 0.004 0.000
#> GSM11722 2 0.4803 -0.2887 0.012 0.500 0.484 0.004 0.000
#> GSM11730 3 0.5081 0.1740 0.008 0.472 0.500 0.020 0.000
#> GSM11713 3 0.6584 0.0480 0.360 0.112 0.500 0.028 0.000
#> GSM11728 1 0.4594 -0.4278 0.508 0.004 0.484 0.004 0.000
#> GSM27947 1 0.5052 0.3711 0.552 0.412 0.000 0.036 0.000
#> GSM27951 3 0.6136 0.2500 0.112 0.416 0.468 0.004 0.000
#> GSM11707 3 0.5657 -0.0152 0.360 0.004 0.560 0.076 0.000
#> GSM11716 1 0.4307 0.2966 0.500 0.000 0.500 0.000 0.000
#> GSM11850 1 0.4307 0.2966 0.500 0.000 0.500 0.000 0.000
#> GSM11851 3 0.4307 -0.3498 0.500 0.000 0.500 0.000 0.000
#> GSM11721 1 0.4171 0.5870 0.604 0.000 0.000 0.396 0.000
#> GSM11852 1 0.0963 0.4147 0.964 0.000 0.000 0.036 0.000
#> GSM11694 3 0.4307 -0.3498 0.500 0.000 0.500 0.000 0.000
#> GSM11695 1 0.4307 0.2966 0.500 0.000 0.500 0.000 0.000
#> GSM11734 1 0.4171 0.5870 0.604 0.000 0.000 0.396 0.000
#> GSM11861 1 0.1892 0.4377 0.916 0.000 0.080 0.004 0.000
#> GSM11843 1 0.4251 0.4150 0.624 0.004 0.372 0.000 0.000
#> GSM11862 1 0.4171 0.5870 0.604 0.000 0.000 0.396 0.000
#> GSM11697 3 0.4307 -0.3498 0.500 0.000 0.500 0.000 0.000
#> GSM11714 3 0.6128 -0.1093 0.380 0.004 0.500 0.116 0.000
#> GSM11723 1 0.5729 0.5628 0.516 0.000 0.088 0.396 0.000
#> GSM11845 1 0.4171 0.5870 0.604 0.000 0.000 0.396 0.000
#> GSM11683 3 0.2300 0.1117 0.040 0.000 0.908 0.052 0.000
#> GSM11691 1 0.4307 0.2966 0.500 0.000 0.500 0.000 0.000
#> GSM27949 3 0.4307 -0.3498 0.500 0.000 0.500 0.000 0.000
#> GSM27945 1 0.4235 0.3722 0.576 0.000 0.424 0.000 0.000
#> GSM11706 3 0.6821 -0.0246 0.360 0.004 0.468 0.016 0.152
#> GSM11853 1 0.0963 0.4147 0.964 0.000 0.000 0.036 0.000
#> GSM11729 2 0.5193 0.5074 0.052 0.584 0.000 0.364 0.000
#> GSM11746 2 0.0162 0.3321 0.000 0.996 0.000 0.004 0.000
#> GSM11711 3 0.4562 0.0944 0.444 0.004 0.548 0.004 0.000
#> GSM11854 1 0.1661 0.4042 0.940 0.000 0.024 0.036 0.000
#> GSM11731 4 0.6697 -0.4471 0.240 0.376 0.000 0.384 0.000
#> GSM11839 1 0.4171 0.5870 0.604 0.000 0.000 0.396 0.000
#> GSM11836 2 0.5591 0.4882 0.076 0.528 0.000 0.396 0.000
#> GSM11849 2 0.4682 -0.0300 0.420 0.564 0.000 0.016 0.000
#> GSM11682 4 0.4088 0.6447 0.368 0.000 0.000 0.632 0.000
#> GSM11690 1 0.4219 0.5758 0.584 0.000 0.000 0.416 0.000
#> GSM11692 1 0.4171 0.5870 0.604 0.000 0.000 0.396 0.000
#> GSM11841 1 0.4171 0.5870 0.604 0.000 0.000 0.396 0.000
#> GSM11901 1 0.4171 0.5870 0.604 0.000 0.000 0.396 0.000
#> GSM11715 2 0.5193 0.5074 0.052 0.584 0.000 0.364 0.000
#> GSM11724 2 0.5193 0.5074 0.052 0.584 0.000 0.364 0.000
#> GSM11684 2 0.5386 0.4943 0.060 0.544 0.000 0.396 0.000
#> GSM11696 2 0.6536 0.3169 0.196 0.408 0.000 0.396 0.000
#> GSM27952 4 0.5070 0.6416 0.360 0.004 0.036 0.600 0.000
#> GSM27948 1 0.4171 0.5870 0.604 0.000 0.000 0.396 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM11708 5 0.0000 0.9105 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11735 5 0.0000 0.9105 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11733 5 0.0000 0.9105 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11863 5 0.0000 0.9105 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11710 6 0.3742 0.6661 0.004 0.348 0.000 0.000 0.000 0.648
#> GSM11712 4 0.0000 0.7945 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM11732 3 0.0260 0.7754 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM11844 3 0.0547 0.7708 0.000 0.000 0.980 0.020 0.000 0.000
#> GSM11842 5 0.0000 0.9105 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11860 5 0.0000 0.9105 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11686 6 0.4026 0.6648 0.000 0.348 0.016 0.000 0.000 0.636
#> GSM11688 6 0.4026 0.6653 0.000 0.348 0.000 0.000 0.016 0.636
#> GSM11846 6 0.4384 0.6359 0.036 0.348 0.000 0.000 0.000 0.616
#> GSM11680 3 0.1075 0.7558 0.000 0.000 0.952 0.048 0.000 0.000
#> GSM11698 3 0.4580 0.3564 0.000 0.348 0.608 0.040 0.000 0.004
#> GSM11840 5 0.0000 0.9105 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11847 5 0.0000 0.9105 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11685 6 0.4687 0.2922 0.000 0.072 0.000 0.296 0.000 0.632
#> GSM11699 3 0.5065 0.3488 0.000 0.092 0.568 0.340 0.000 0.000
#> GSM27950 6 0.3747 0.1973 0.000 0.000 0.396 0.000 0.000 0.604
#> GSM27946 4 0.0000 0.7945 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM11709 1 0.1657 0.7186 0.928 0.000 0.000 0.056 0.000 0.016
#> GSM11720 1 0.3457 0.6688 0.800 0.000 0.164 0.020 0.000 0.016
#> GSM11726 1 0.6244 0.0819 0.456 0.148 0.032 0.000 0.000 0.364
#> GSM11837 6 0.8043 -0.2541 0.064 0.148 0.116 0.324 0.000 0.348
#> GSM11725 1 0.3345 0.7127 0.788 0.000 0.028 0.184 0.000 0.000
#> GSM11864 1 0.3542 0.7134 0.788 0.000 0.052 0.160 0.000 0.000
#> GSM11687 1 0.1267 0.7245 0.940 0.000 0.000 0.060 0.000 0.000
#> GSM11693 1 0.3703 0.6986 0.788 0.000 0.104 0.108 0.000 0.000
#> GSM11727 1 0.5811 0.1183 0.492 0.152 0.008 0.000 0.000 0.348
#> GSM11838 2 0.4909 0.3123 0.056 0.588 0.008 0.000 0.000 0.348
#> GSM11681 1 0.2823 0.5906 0.796 0.000 0.000 0.000 0.000 0.204
#> GSM11689 1 0.2883 0.7034 0.788 0.000 0.000 0.212 0.000 0.000
#> GSM11704 1 0.2883 0.7034 0.788 0.000 0.000 0.212 0.000 0.000
#> GSM11703 1 0.2581 0.6704 0.856 0.000 0.128 0.000 0.000 0.016
#> GSM11705 1 0.5323 0.2318 0.576 0.348 0.012 0.044 0.000 0.020
#> GSM11722 1 0.1942 0.6898 0.928 0.028 0.004 0.020 0.000 0.020
#> GSM11730 2 0.6140 0.2502 0.212 0.416 0.008 0.000 0.000 0.364
#> GSM11713 2 0.3980 0.0209 0.216 0.732 0.000 0.000 0.000 0.052
#> GSM11728 4 0.7376 -0.1177 0.176 0.356 0.080 0.368 0.000 0.020
#> GSM27947 1 0.2996 0.6929 0.772 0.000 0.000 0.228 0.000 0.000
#> GSM27951 1 0.1204 0.7225 0.944 0.000 0.000 0.056 0.000 0.000
#> GSM11707 2 0.7560 -0.3521 0.152 0.348 0.192 0.000 0.004 0.304
#> GSM11716 3 0.0260 0.7754 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM11850 3 0.0260 0.7754 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM11851 3 0.0260 0.7754 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM11721 4 0.0000 0.7945 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM11852 4 0.3742 0.3426 0.000 0.348 0.000 0.648 0.000 0.004
#> GSM11694 3 0.0260 0.7754 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM11695 3 0.0260 0.7754 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM11734 4 0.0547 0.7832 0.020 0.000 0.000 0.980 0.000 0.000
#> GSM11861 3 0.6083 0.0677 0.000 0.272 0.364 0.364 0.000 0.000
#> GSM11843 3 0.5714 0.1487 0.168 0.000 0.464 0.368 0.000 0.000
#> GSM11862 4 0.1196 0.7681 0.008 0.000 0.040 0.952 0.000 0.000
#> GSM11697 3 0.0260 0.7754 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM11714 2 0.7383 -0.3503 0.120 0.348 0.236 0.000 0.000 0.296
#> GSM11723 4 0.3868 -0.0526 0.000 0.000 0.492 0.508 0.000 0.000
#> GSM11845 4 0.1765 0.7189 0.000 0.000 0.096 0.904 0.000 0.000
#> GSM11683 3 0.3439 0.6088 0.120 0.000 0.808 0.000 0.000 0.072
#> GSM11691 3 0.0260 0.7754 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM27949 3 0.0260 0.7754 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM27945 3 0.1007 0.7549 0.000 0.000 0.956 0.044 0.000 0.000
#> GSM11706 5 0.7087 -0.1813 0.156 0.348 0.000 0.000 0.384 0.112
#> GSM11853 4 0.3742 0.3426 0.000 0.348 0.000 0.648 0.000 0.004
#> GSM11729 2 0.5574 0.3555 0.000 0.504 0.000 0.152 0.000 0.344
#> GSM11746 2 0.4097 -0.2145 0.488 0.504 0.000 0.000 0.000 0.008
#> GSM11711 3 0.6467 0.1143 0.156 0.348 0.460 0.016 0.000 0.020
#> GSM11854 3 0.6149 0.1131 0.000 0.348 0.400 0.248 0.000 0.004
#> GSM11731 4 0.1075 0.7637 0.000 0.048 0.000 0.952 0.000 0.000
#> GSM11839 4 0.0000 0.7945 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM11836 4 0.3706 0.3059 0.000 0.380 0.000 0.620 0.000 0.000
#> GSM11849 2 0.2340 0.1642 0.000 0.852 0.000 0.148 0.000 0.000
#> GSM11682 6 0.4026 0.6635 0.000 0.348 0.000 0.016 0.000 0.636
#> GSM11690 4 0.0000 0.7945 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM11692 4 0.0000 0.7945 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM11841 4 0.0000 0.7945 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM11901 4 0.0000 0.7945 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM11715 2 0.3868 -0.1159 0.000 0.504 0.000 0.496 0.000 0.000
#> GSM11724 2 0.3868 -0.1159 0.000 0.504 0.000 0.496 0.000 0.000
#> GSM11684 4 0.3499 0.4219 0.000 0.320 0.000 0.680 0.000 0.000
#> GSM11696 4 0.1267 0.7522 0.000 0.060 0.000 0.940 0.000 0.000
#> GSM27952 6 0.3607 0.6676 0.000 0.348 0.000 0.000 0.000 0.652
#> GSM27948 4 0.0000 0.7945 0.000 0.000 0.000 1.000 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 cell.line(p) agent(p) time(p) k
#> MAD:pam 81 5.50e-06 0.226 0.371088 2
#> MAD:pam 39 2.04e-01 0.612 0.588873 3
#> MAD:pam 60 7.67e-07 0.820 0.000933 4
#> MAD:pam 31 9.20e-03 0.407 0.016859 5
#> MAD:pam 54 7.45e-16 0.713 0.001618 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 14502 rows and 83 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.449 0.831 0.898 0.3693 0.700 0.700
#> 3 3 0.379 0.715 0.770 0.6643 0.431 0.300
#> 4 4 0.451 0.638 0.771 0.1391 0.892 0.707
#> 5 5 0.501 0.578 0.742 0.0832 0.874 0.595
#> 6 6 0.585 0.659 0.772 0.0469 0.957 0.814
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
#> GSM11708 2 0.0672 0.949 0.008 0.992
#> GSM11735 2 0.0672 0.949 0.008 0.992
#> GSM11733 2 0.1414 0.949 0.020 0.980
#> GSM11863 1 0.8207 0.763 0.744 0.256
#> GSM11710 2 0.1414 0.958 0.020 0.980
#> GSM11712 1 0.0000 0.874 1.000 0.000
#> GSM11732 1 0.7139 0.783 0.804 0.196
#> GSM11844 1 0.6887 0.790 0.816 0.184
#> GSM11842 1 0.7528 0.786 0.784 0.216
#> GSM11860 1 0.7453 0.787 0.788 0.212
#> GSM11686 2 0.6623 0.793 0.172 0.828
#> GSM11688 2 0.1414 0.958 0.020 0.980
#> GSM11846 1 0.9775 0.540 0.588 0.412
#> GSM11680 1 0.7453 0.728 0.788 0.212
#> GSM11698 1 0.7745 0.725 0.772 0.228
#> GSM11840 1 0.9970 0.423 0.532 0.468
#> GSM11847 1 0.9909 0.483 0.556 0.444
#> GSM11685 2 0.1414 0.958 0.020 0.980
#> GSM11699 1 0.3114 0.858 0.944 0.056
#> GSM27950 2 0.2603 0.941 0.044 0.956
#> GSM27946 1 0.0376 0.874 0.996 0.004
#> GSM11709 1 0.5408 0.839 0.876 0.124
#> GSM11720 1 0.0000 0.874 1.000 0.000
#> GSM11726 1 0.7219 0.794 0.800 0.200
#> GSM11837 1 0.7219 0.794 0.800 0.200
#> GSM11725 1 0.0000 0.874 1.000 0.000
#> GSM11864 1 0.0000 0.874 1.000 0.000
#> GSM11687 1 0.0376 0.873 0.996 0.004
#> GSM11693 1 0.0376 0.873 0.996 0.004
#> GSM11727 1 0.7219 0.794 0.800 0.200
#> GSM11838 1 0.7219 0.794 0.800 0.200
#> GSM11681 2 0.2778 0.938 0.048 0.952
#> GSM11689 1 0.0376 0.873 0.996 0.004
#> GSM11704 1 0.0376 0.873 0.996 0.004
#> GSM11703 1 0.0376 0.873 0.996 0.004
#> GSM11705 1 0.5946 0.836 0.856 0.144
#> GSM11722 1 0.0000 0.874 1.000 0.000
#> GSM11730 1 0.7219 0.794 0.800 0.200
#> GSM11713 1 0.8909 0.708 0.692 0.308
#> GSM11728 1 0.9000 0.698 0.684 0.316
#> GSM27947 1 0.0000 0.874 1.000 0.000
#> GSM27951 1 0.2948 0.868 0.948 0.052
#> GSM11707 2 0.1414 0.958 0.020 0.980
#> GSM11716 1 0.0000 0.874 1.000 0.000
#> GSM11850 1 0.1414 0.871 0.980 0.020
#> GSM11851 1 0.6343 0.786 0.840 0.160
#> GSM11721 1 0.0000 0.874 1.000 0.000
#> GSM11852 1 0.5842 0.804 0.860 0.140
#> GSM11694 1 0.2948 0.861 0.948 0.052
#> GSM11695 1 0.6148 0.796 0.848 0.152
#> GSM11734 1 0.0000 0.874 1.000 0.000
#> GSM11861 1 0.0376 0.874 0.996 0.004
#> GSM11843 1 0.0000 0.874 1.000 0.000
#> GSM11862 1 0.0000 0.874 1.000 0.000
#> GSM11697 1 0.4298 0.843 0.912 0.088
#> GSM11714 2 0.1414 0.958 0.020 0.980
#> GSM11723 1 0.0000 0.874 1.000 0.000
#> GSM11845 1 0.0000 0.874 1.000 0.000
#> GSM11683 2 0.8327 0.670 0.264 0.736
#> GSM11691 1 0.1414 0.871 0.980 0.020
#> GSM27949 1 0.9608 0.447 0.616 0.384
#> GSM27945 1 0.0376 0.873 0.996 0.004
#> GSM11706 2 0.1414 0.958 0.020 0.980
#> GSM11853 1 0.1633 0.870 0.976 0.024
#> GSM11729 1 0.7219 0.794 0.800 0.200
#> GSM11746 1 0.7219 0.794 0.800 0.200
#> GSM11711 1 0.8713 0.695 0.708 0.292
#> GSM11854 1 0.5737 0.807 0.864 0.136
#> GSM11731 1 0.0000 0.874 1.000 0.000
#> GSM11839 1 0.0000 0.874 1.000 0.000
#> GSM11836 1 0.7299 0.791 0.796 0.204
#> GSM11849 1 0.7139 0.796 0.804 0.196
#> GSM11682 2 0.1633 0.956 0.024 0.976
#> GSM11690 1 0.2603 0.870 0.956 0.044
#> GSM11692 1 0.0000 0.874 1.000 0.000
#> GSM11841 1 0.0000 0.874 1.000 0.000
#> GSM11901 1 0.0000 0.874 1.000 0.000
#> GSM11715 1 0.7219 0.794 0.800 0.200
#> GSM11724 1 0.7219 0.794 0.800 0.200
#> GSM11684 1 0.6973 0.801 0.812 0.188
#> GSM11696 1 0.0000 0.874 1.000 0.000
#> GSM27952 2 0.1414 0.958 0.020 0.980
#> GSM27948 1 0.0000 0.874 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM11708 3 0.5363 0.611 0.000 0.276 0.724
#> GSM11735 3 0.5363 0.611 0.000 0.276 0.724
#> GSM11733 2 0.3043 0.608 0.008 0.908 0.084
#> GSM11863 2 0.3183 0.656 0.076 0.908 0.016
#> GSM11710 3 0.0829 0.716 0.004 0.012 0.984
#> GSM11712 2 0.7558 0.767 0.284 0.644 0.072
#> GSM11732 3 0.3193 0.759 0.100 0.004 0.896
#> GSM11844 3 0.3213 0.760 0.092 0.008 0.900
#> GSM11842 2 0.3183 0.656 0.076 0.908 0.016
#> GSM11860 3 0.8100 0.451 0.068 0.420 0.512
#> GSM11686 3 0.6159 0.731 0.196 0.048 0.756
#> GSM11688 3 0.0475 0.715 0.004 0.004 0.992
#> GSM11846 3 0.3183 0.753 0.076 0.016 0.908
#> GSM11680 3 0.5797 0.764 0.280 0.008 0.712
#> GSM11698 3 0.5588 0.768 0.276 0.004 0.720
#> GSM11840 2 0.3234 0.654 0.072 0.908 0.020
#> GSM11847 2 0.3183 0.656 0.076 0.908 0.016
#> GSM11685 2 0.6470 0.641 0.012 0.632 0.356
#> GSM11699 2 0.9391 0.617 0.284 0.504 0.212
#> GSM27950 3 0.1015 0.721 0.008 0.012 0.980
#> GSM27946 2 0.9741 0.474 0.284 0.448 0.268
#> GSM11709 1 0.4504 0.779 0.804 0.000 0.196
#> GSM11720 1 0.0237 0.789 0.996 0.000 0.004
#> GSM11726 1 0.5659 0.773 0.796 0.052 0.152
#> GSM11837 3 0.6857 0.596 0.252 0.052 0.696
#> GSM11725 1 0.0237 0.789 0.996 0.000 0.004
#> GSM11864 3 0.5988 0.708 0.368 0.000 0.632
#> GSM11687 1 0.0237 0.789 0.996 0.000 0.004
#> GSM11693 1 0.0237 0.789 0.996 0.000 0.004
#> GSM11727 1 0.6808 0.757 0.732 0.084 0.184
#> GSM11838 1 0.6808 0.757 0.732 0.084 0.184
#> GSM11681 1 0.5517 0.735 0.728 0.004 0.268
#> GSM11689 1 0.0237 0.789 0.996 0.000 0.004
#> GSM11704 1 0.0237 0.789 0.996 0.000 0.004
#> GSM11703 1 0.0237 0.789 0.996 0.000 0.004
#> GSM11705 1 0.4504 0.779 0.804 0.000 0.196
#> GSM11722 1 0.2200 0.780 0.940 0.056 0.004
#> GSM11730 1 0.6808 0.757 0.732 0.084 0.184
#> GSM11713 1 0.6804 0.749 0.724 0.072 0.204
#> GSM11728 3 0.6804 0.485 0.204 0.072 0.724
#> GSM27947 3 0.5656 0.764 0.284 0.004 0.712
#> GSM27951 1 0.2486 0.780 0.932 0.060 0.008
#> GSM11707 3 0.5643 0.439 0.220 0.020 0.760
#> GSM11716 3 0.5465 0.765 0.288 0.000 0.712
#> GSM11850 3 0.5591 0.761 0.304 0.000 0.696
#> GSM11851 3 0.5763 0.767 0.276 0.008 0.716
#> GSM11721 2 0.7384 0.772 0.272 0.660 0.068
#> GSM11852 2 0.8435 0.739 0.284 0.592 0.124
#> GSM11694 3 0.5763 0.767 0.276 0.008 0.716
#> GSM11695 3 0.5623 0.768 0.280 0.004 0.716
#> GSM11734 2 0.7528 0.768 0.280 0.648 0.072
#> GSM11861 2 0.8938 0.690 0.284 0.552 0.164
#> GSM11843 3 0.6262 0.754 0.284 0.020 0.696
#> GSM11862 2 0.7558 0.767 0.284 0.644 0.072
#> GSM11697 3 0.5763 0.767 0.276 0.008 0.716
#> GSM11714 3 0.3910 0.636 0.104 0.020 0.876
#> GSM11723 3 0.7220 0.711 0.284 0.056 0.660
#> GSM11845 2 0.8491 0.733 0.284 0.588 0.128
#> GSM11683 3 0.4473 0.767 0.164 0.008 0.828
#> GSM11691 3 0.5497 0.765 0.292 0.000 0.708
#> GSM27949 3 0.3983 0.775 0.144 0.004 0.852
#> GSM27945 3 0.5763 0.767 0.276 0.008 0.716
#> GSM11706 3 0.0747 0.719 0.000 0.016 0.984
#> GSM11853 3 0.5763 0.767 0.276 0.008 0.716
#> GSM11729 3 0.4790 0.753 0.096 0.056 0.848
#> GSM11746 3 0.4920 0.751 0.108 0.052 0.840
#> GSM11711 3 0.2711 0.756 0.088 0.000 0.912
#> GSM11854 3 0.5763 0.767 0.276 0.008 0.716
#> GSM11731 2 0.7145 0.774 0.236 0.692 0.072
#> GSM11839 2 0.7022 0.772 0.232 0.700 0.068
#> GSM11836 2 0.5881 0.652 0.016 0.728 0.256
#> GSM11849 2 0.6912 0.470 0.016 0.540 0.444
#> GSM11682 2 0.6275 0.639 0.008 0.644 0.348
#> GSM11690 2 0.6939 0.768 0.216 0.712 0.072
#> GSM11692 2 0.7528 0.768 0.280 0.648 0.072
#> GSM11841 2 0.5953 0.753 0.280 0.708 0.012
#> GSM11901 2 0.6096 0.755 0.280 0.704 0.016
#> GSM11715 2 0.7072 0.371 0.020 0.504 0.476
#> GSM11724 2 0.6294 0.649 0.020 0.692 0.288
#> GSM11684 2 0.6887 0.705 0.076 0.720 0.204
#> GSM11696 2 0.6897 0.768 0.220 0.712 0.068
#> GSM27952 3 0.0661 0.715 0.004 0.008 0.988
#> GSM27948 2 0.6897 0.768 0.220 0.712 0.068
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM11708 2 0.6996 0.6184 0.004 0.600 0.200 0.196
#> GSM11735 2 0.5384 0.5347 0.000 0.728 0.076 0.196
#> GSM11733 4 0.4576 0.5648 0.020 0.232 0.000 0.748
#> GSM11863 4 0.4722 0.5680 0.020 0.228 0.004 0.748
#> GSM11710 2 0.7599 0.7923 0.196 0.520 0.276 0.008
#> GSM11712 4 0.3907 0.7878 0.000 0.000 0.232 0.768
#> GSM11732 3 0.3933 0.4491 0.196 0.004 0.796 0.004
#> GSM11844 3 0.3544 0.5864 0.128 0.012 0.852 0.008
#> GSM11842 4 0.4722 0.5680 0.020 0.228 0.004 0.748
#> GSM11860 3 0.7150 0.1872 0.012 0.100 0.520 0.368
#> GSM11686 2 0.8054 0.2764 0.016 0.428 0.360 0.196
#> GSM11688 2 0.8070 0.7839 0.196 0.528 0.240 0.036
#> GSM11846 3 0.7834 -0.5085 0.196 0.352 0.444 0.008
#> GSM11680 3 0.4499 0.5706 0.000 0.072 0.804 0.124
#> GSM11698 3 0.3052 0.6467 0.004 0.104 0.880 0.012
#> GSM11840 4 0.4722 0.5680 0.020 0.228 0.004 0.748
#> GSM11847 4 0.4722 0.5680 0.020 0.228 0.004 0.748
#> GSM11685 4 0.6425 0.5965 0.200 0.092 0.024 0.684
#> GSM11699 4 0.4713 0.6559 0.000 0.000 0.360 0.640
#> GSM27950 2 0.7626 0.7913 0.200 0.516 0.276 0.008
#> GSM27946 4 0.4661 0.6783 0.000 0.000 0.348 0.652
#> GSM11709 1 0.1109 0.7209 0.968 0.004 0.028 0.000
#> GSM11720 1 0.3873 0.8039 0.772 0.000 0.228 0.000
#> GSM11726 1 0.4627 0.7426 0.772 0.196 0.028 0.004
#> GSM11837 3 0.7189 0.3940 0.136 0.256 0.592 0.016
#> GSM11725 1 0.3873 0.8039 0.772 0.000 0.228 0.000
#> GSM11864 3 0.3334 0.6794 0.048 0.060 0.884 0.008
#> GSM11687 1 0.4018 0.8050 0.772 0.000 0.224 0.004
#> GSM11693 1 0.4018 0.8050 0.772 0.000 0.224 0.004
#> GSM11727 1 0.4686 0.7401 0.780 0.184 0.016 0.020
#> GSM11838 1 0.4606 0.7316 0.772 0.200 0.008 0.020
#> GSM11681 1 0.0927 0.7120 0.976 0.008 0.016 0.000
#> GSM11689 1 0.4018 0.8050 0.772 0.000 0.224 0.004
#> GSM11704 1 0.4018 0.8050 0.772 0.000 0.224 0.004
#> GSM11703 1 0.4018 0.8050 0.772 0.000 0.224 0.004
#> GSM11705 1 0.1109 0.7209 0.968 0.004 0.028 0.000
#> GSM11722 1 0.3982 0.8048 0.776 0.000 0.220 0.004
#> GSM11730 1 0.4686 0.7401 0.780 0.184 0.016 0.020
#> GSM11713 1 0.0927 0.7137 0.976 0.008 0.016 0.000
#> GSM11728 1 0.6293 0.0144 0.628 0.276 0.096 0.000
#> GSM27947 3 0.0188 0.7323 0.000 0.000 0.996 0.004
#> GSM27951 1 0.3801 0.8056 0.780 0.000 0.220 0.000
#> GSM11707 2 0.7487 0.7907 0.196 0.520 0.280 0.004
#> GSM11716 3 0.1637 0.7130 0.000 0.060 0.940 0.000
#> GSM11850 3 0.0000 0.7325 0.000 0.000 1.000 0.000
#> GSM11851 3 0.0376 0.7313 0.000 0.004 0.992 0.004
#> GSM11721 4 0.3649 0.7979 0.000 0.000 0.204 0.796
#> GSM11852 4 0.4543 0.7061 0.000 0.000 0.324 0.676
#> GSM11694 3 0.0000 0.7325 0.000 0.000 1.000 0.000
#> GSM11695 3 0.0336 0.7313 0.000 0.008 0.992 0.000
#> GSM11734 4 0.4040 0.7786 0.000 0.000 0.248 0.752
#> GSM11861 4 0.4661 0.6739 0.000 0.000 0.348 0.652
#> GSM11843 3 0.2335 0.7049 0.000 0.060 0.920 0.020
#> GSM11862 4 0.4008 0.7781 0.000 0.000 0.244 0.756
#> GSM11697 3 0.0188 0.7324 0.000 0.004 0.996 0.000
#> GSM11714 2 0.7469 0.7921 0.196 0.524 0.276 0.004
#> GSM11723 3 0.2131 0.7075 0.000 0.036 0.932 0.032
#> GSM11845 3 0.4916 -0.1413 0.000 0.000 0.576 0.424
#> GSM11683 3 0.5464 -0.3320 0.008 0.492 0.496 0.004
#> GSM11691 3 0.0779 0.7275 0.000 0.016 0.980 0.004
#> GSM27949 3 0.3768 0.5364 0.008 0.184 0.808 0.000
#> GSM27945 3 0.0000 0.7325 0.000 0.000 1.000 0.000
#> GSM11706 2 0.7487 0.7907 0.196 0.520 0.280 0.004
#> GSM11853 3 0.0188 0.7324 0.000 0.004 0.996 0.000
#> GSM11729 3 0.5404 0.4934 0.012 0.256 0.704 0.028
#> GSM11746 3 0.5883 0.4796 0.040 0.256 0.684 0.020
#> GSM11711 3 0.7369 -0.2231 0.196 0.256 0.544 0.004
#> GSM11854 3 0.0927 0.7256 0.000 0.016 0.976 0.008
#> GSM11731 4 0.3893 0.7994 0.008 0.000 0.196 0.796
#> GSM11839 4 0.3791 0.7989 0.004 0.000 0.200 0.796
#> GSM11836 4 0.3950 0.6857 0.008 0.184 0.004 0.804
#> GSM11849 4 0.5405 0.6552 0.156 0.052 0.028 0.764
#> GSM11682 4 0.5075 0.6240 0.200 0.040 0.008 0.752
#> GSM11690 4 0.3973 0.7988 0.004 0.004 0.200 0.792
#> GSM11692 4 0.3726 0.7953 0.000 0.000 0.212 0.788
#> GSM11841 4 0.3649 0.7982 0.000 0.000 0.204 0.796
#> GSM11901 4 0.3610 0.7982 0.000 0.000 0.200 0.800
#> GSM11715 4 0.6900 0.5590 0.016 0.184 0.160 0.640
#> GSM11724 4 0.4547 0.6794 0.008 0.184 0.024 0.784
#> GSM11684 4 0.4235 0.7980 0.016 0.004 0.188 0.792
#> GSM11696 4 0.3933 0.7984 0.004 0.004 0.196 0.796
#> GSM27952 2 0.8574 0.7404 0.200 0.524 0.188 0.088
#> GSM27948 4 0.3791 0.7989 0.004 0.000 0.200 0.796
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM11708 4 0.5528 0.64351 0.000 0.000 0.140 0.644 0.216
#> GSM11735 4 0.4497 0.39759 0.000 0.000 0.008 0.568 0.424
#> GSM11733 5 0.5498 0.57184 0.000 0.096 0.292 0.000 0.612
#> GSM11863 5 0.5498 0.57184 0.000 0.096 0.292 0.000 0.612
#> GSM11710 4 0.2929 0.80351 0.000 0.000 0.180 0.820 0.000
#> GSM11712 2 0.3246 0.73268 0.008 0.808 0.184 0.000 0.000
#> GSM11732 3 0.3525 0.55982 0.004 0.016 0.840 0.120 0.020
#> GSM11844 3 0.3366 0.59537 0.004 0.040 0.860 0.084 0.012
#> GSM11842 5 0.5498 0.57184 0.000 0.096 0.292 0.000 0.612
#> GSM11860 3 0.5956 0.04509 0.000 0.140 0.564 0.000 0.296
#> GSM11686 4 0.6829 0.60592 0.016 0.180 0.224 0.564 0.016
#> GSM11688 4 0.3289 0.80233 0.000 0.008 0.172 0.816 0.004
#> GSM11846 3 0.3913 0.32634 0.000 0.000 0.676 0.324 0.000
#> GSM11680 3 0.2407 0.63729 0.000 0.088 0.896 0.004 0.012
#> GSM11698 3 0.2130 0.65231 0.004 0.060 0.920 0.004 0.012
#> GSM11840 5 0.5498 0.57184 0.000 0.096 0.292 0.000 0.612
#> GSM11847 5 0.5498 0.57184 0.000 0.096 0.292 0.000 0.612
#> GSM11685 4 0.5726 0.51422 0.004 0.188 0.000 0.640 0.168
#> GSM11699 3 0.4165 0.40525 0.000 0.320 0.672 0.000 0.008
#> GSM27950 4 0.3575 0.79528 0.004 0.016 0.180 0.800 0.000
#> GSM27946 3 0.4218 0.38744 0.000 0.332 0.660 0.000 0.008
#> GSM11709 1 0.4377 0.71659 0.776 0.016 0.036 0.168 0.004
#> GSM11720 1 0.4848 0.72040 0.724 0.016 0.208 0.000 0.052
#> GSM11726 1 0.2657 0.71743 0.900 0.000 0.024 0.024 0.052
#> GSM11837 5 0.8057 0.26417 0.216 0.000 0.240 0.124 0.420
#> GSM11725 1 0.7343 0.43853 0.452 0.044 0.204 0.000 0.300
#> GSM11864 3 0.7990 -0.05643 0.060 0.032 0.420 0.140 0.348
#> GSM11687 1 0.4150 0.74392 0.772 0.044 0.180 0.000 0.004
#> GSM11693 1 0.3519 0.73941 0.776 0.008 0.216 0.000 0.000
#> GSM11727 1 0.1248 0.71105 0.964 0.016 0.008 0.008 0.004
#> GSM11838 1 0.4928 0.44365 0.664 0.028 0.004 0.008 0.296
#> GSM11681 1 0.4894 0.62316 0.692 0.024 0.008 0.264 0.012
#> GSM11689 1 0.3519 0.73941 0.776 0.008 0.216 0.000 0.000
#> GSM11704 1 0.3596 0.73992 0.776 0.012 0.212 0.000 0.000
#> GSM11703 1 0.3876 0.74237 0.776 0.032 0.192 0.000 0.000
#> GSM11705 1 0.4377 0.71659 0.776 0.016 0.036 0.168 0.004
#> GSM11722 1 0.7241 0.55928 0.532 0.172 0.048 0.008 0.240
#> GSM11730 1 0.1220 0.70839 0.964 0.020 0.004 0.008 0.004
#> GSM11713 1 0.3269 0.71220 0.836 0.004 0.004 0.144 0.012
#> GSM11728 1 0.6757 0.50137 0.536 0.028 0.104 0.320 0.012
#> GSM27947 3 0.1026 0.66934 0.000 0.024 0.968 0.004 0.004
#> GSM27951 1 0.4674 0.73908 0.776 0.116 0.088 0.008 0.012
#> GSM11707 4 0.2929 0.80351 0.000 0.000 0.180 0.820 0.000
#> GSM11716 3 0.3896 0.49406 0.012 0.008 0.780 0.004 0.196
#> GSM11850 3 0.0451 0.66829 0.008 0.004 0.988 0.000 0.000
#> GSM11851 3 0.1243 0.66381 0.000 0.008 0.960 0.004 0.028
#> GSM11721 2 0.2516 0.76186 0.000 0.860 0.140 0.000 0.000
#> GSM11852 3 0.4252 0.36324 0.000 0.340 0.652 0.000 0.008
#> GSM11694 3 0.0000 0.66953 0.000 0.000 1.000 0.000 0.000
#> GSM11695 3 0.0162 0.67005 0.000 0.004 0.996 0.000 0.000
#> GSM11734 2 0.8070 0.37479 0.008 0.432 0.168 0.108 0.284
#> GSM11861 3 0.4415 0.27890 0.000 0.388 0.604 0.000 0.008
#> GSM11843 3 0.8078 -0.00685 0.020 0.092 0.440 0.144 0.304
#> GSM11862 2 0.3274 0.70708 0.000 0.780 0.220 0.000 0.000
#> GSM11697 3 0.0000 0.66953 0.000 0.000 1.000 0.000 0.000
#> GSM11714 4 0.2929 0.80351 0.000 0.000 0.180 0.820 0.000
#> GSM11723 3 0.6298 0.24383 0.016 0.076 0.588 0.020 0.300
#> GSM11845 3 0.7105 0.08829 0.020 0.252 0.444 0.000 0.284
#> GSM11683 3 0.5719 0.22657 0.012 0.072 0.588 0.328 0.000
#> GSM11691 3 0.0775 0.66957 0.004 0.004 0.980 0.004 0.008
#> GSM27949 3 0.2460 0.63893 0.004 0.072 0.900 0.024 0.000
#> GSM27945 3 0.0000 0.66953 0.000 0.000 1.000 0.000 0.000
#> GSM11706 4 0.2929 0.80351 0.000 0.000 0.180 0.820 0.000
#> GSM11853 3 0.0510 0.66980 0.000 0.016 0.984 0.000 0.000
#> GSM11729 5 0.8965 0.25683 0.144 0.060 0.248 0.148 0.400
#> GSM11746 5 0.8106 0.26493 0.164 0.000 0.252 0.164 0.420
#> GSM11711 3 0.3819 0.47175 0.004 0.016 0.772 0.208 0.000
#> GSM11854 3 0.0968 0.66960 0.000 0.012 0.972 0.004 0.012
#> GSM11731 2 0.4783 0.57245 0.012 0.700 0.020 0.008 0.260
#> GSM11839 2 0.0865 0.74940 0.000 0.972 0.024 0.004 0.000
#> GSM11836 2 0.3231 0.67983 0.196 0.800 0.000 0.004 0.000
#> GSM11849 2 0.5471 0.62252 0.128 0.692 0.000 0.164 0.016
#> GSM11682 4 0.5441 0.25324 0.032 0.376 0.000 0.572 0.020
#> GSM11690 2 0.1518 0.75634 0.004 0.944 0.048 0.004 0.000
#> GSM11692 2 0.2848 0.75378 0.004 0.840 0.156 0.000 0.000
#> GSM11841 2 0.2770 0.76855 0.008 0.864 0.124 0.000 0.004
#> GSM11901 2 0.2597 0.77010 0.000 0.872 0.120 0.004 0.004
#> GSM11715 2 0.8308 0.35239 0.196 0.428 0.008 0.148 0.220
#> GSM11724 2 0.8148 0.37586 0.196 0.444 0.004 0.148 0.208
#> GSM11684 2 0.0775 0.73206 0.004 0.980 0.004 0.008 0.004
#> GSM11696 2 0.1991 0.76906 0.000 0.916 0.076 0.004 0.004
#> GSM27952 4 0.3980 0.79476 0.012 0.012 0.168 0.796 0.012
#> GSM27948 2 0.2233 0.77066 0.000 0.892 0.104 0.004 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM11708 6 0.4109 0.5641 0.000 0.012 0.040 0.000 0.212 0.736
#> GSM11735 5 0.4150 0.2199 0.000 0.012 0.000 0.004 0.612 0.372
#> GSM11733 5 0.1858 0.8737 0.000 0.000 0.092 0.004 0.904 0.000
#> GSM11863 5 0.1918 0.8716 0.000 0.000 0.088 0.008 0.904 0.000
#> GSM11710 6 0.2442 0.7471 0.000 0.000 0.144 0.004 0.000 0.852
#> GSM11712 4 0.2595 0.7951 0.004 0.000 0.160 0.836 0.000 0.000
#> GSM11732 3 0.4868 0.7113 0.028 0.068 0.768 0.012 0.036 0.088
#> GSM11844 3 0.2978 0.7432 0.028 0.012 0.872 0.020 0.000 0.068
#> GSM11842 5 0.3175 0.7964 0.000 0.000 0.080 0.088 0.832 0.000
#> GSM11860 3 0.5705 0.3696 0.000 0.004 0.548 0.156 0.288 0.004
#> GSM11686 6 0.6284 0.6408 0.008 0.056 0.176 0.144 0.008 0.608
#> GSM11688 6 0.3014 0.7435 0.000 0.056 0.068 0.016 0.000 0.860
#> GSM11846 3 0.3243 0.6139 0.004 0.008 0.780 0.000 0.000 0.208
#> GSM11680 3 0.2360 0.7521 0.000 0.012 0.900 0.044 0.000 0.044
#> GSM11698 3 0.2063 0.7550 0.000 0.008 0.912 0.060 0.000 0.020
#> GSM11840 5 0.1858 0.8737 0.000 0.000 0.092 0.004 0.904 0.000
#> GSM11847 5 0.1858 0.8737 0.000 0.000 0.092 0.004 0.904 0.000
#> GSM11685 6 0.6005 0.1666 0.024 0.056 0.000 0.032 0.392 0.496
#> GSM11699 3 0.4424 0.4351 0.000 0.024 0.628 0.340 0.004 0.004
#> GSM27950 6 0.3430 0.7397 0.024 0.008 0.076 0.004 0.040 0.848
#> GSM27946 3 0.4266 0.5093 0.000 0.024 0.668 0.300 0.004 0.004
#> GSM11709 1 0.3324 0.7646 0.824 0.004 0.040 0.004 0.000 0.128
#> GSM11720 1 0.4267 0.7641 0.772 0.028 0.148 0.040 0.012 0.000
#> GSM11726 1 0.3359 0.7361 0.836 0.024 0.004 0.000 0.108 0.028
#> GSM11837 2 0.5678 0.5315 0.112 0.660 0.072 0.000 0.152 0.004
#> GSM11725 1 0.6327 0.5362 0.560 0.236 0.152 0.040 0.012 0.000
#> GSM11864 2 0.5410 0.5701 0.068 0.660 0.228 0.028 0.012 0.004
#> GSM11687 1 0.3493 0.7693 0.796 0.000 0.148 0.056 0.000 0.000
#> GSM11693 1 0.3279 0.7680 0.796 0.000 0.176 0.028 0.000 0.000
#> GSM11727 1 0.1523 0.7353 0.940 0.044 0.000 0.008 0.008 0.000
#> GSM11838 1 0.3589 0.5609 0.752 0.228 0.000 0.008 0.012 0.000
#> GSM11681 1 0.5207 0.7013 0.708 0.016 0.004 0.060 0.040 0.172
#> GSM11689 1 0.3318 0.7693 0.796 0.000 0.172 0.032 0.000 0.000
#> GSM11704 1 0.3318 0.7693 0.796 0.000 0.172 0.032 0.000 0.000
#> GSM11703 1 0.3417 0.7673 0.796 0.000 0.160 0.044 0.000 0.000
#> GSM11705 1 0.3343 0.7553 0.816 0.004 0.024 0.000 0.008 0.148
#> GSM11722 1 0.5033 0.7420 0.720 0.080 0.020 0.160 0.012 0.008
#> GSM11730 1 0.1410 0.7361 0.944 0.044 0.000 0.008 0.004 0.000
#> GSM11713 1 0.3648 0.7284 0.820 0.008 0.000 0.020 0.040 0.112
#> GSM11728 1 0.7265 0.5469 0.584 0.124 0.084 0.040 0.040 0.128
#> GSM27947 3 0.1296 0.7557 0.004 0.004 0.948 0.044 0.000 0.000
#> GSM27951 1 0.4278 0.7626 0.768 0.004 0.016 0.164 0.024 0.024
#> GSM11707 6 0.2917 0.7493 0.000 0.004 0.104 0.000 0.040 0.852
#> GSM11716 3 0.5489 0.5914 0.052 0.228 0.664 0.024 0.012 0.020
#> GSM11850 3 0.3121 0.7227 0.044 0.116 0.836 0.004 0.000 0.000
#> GSM11851 3 0.3930 0.7258 0.008 0.120 0.808 0.016 0.012 0.036
#> GSM11721 4 0.2442 0.8078 0.000 0.000 0.144 0.852 0.000 0.004
#> GSM11852 3 0.4499 0.3634 0.000 0.024 0.604 0.364 0.004 0.004
#> GSM11694 3 0.2222 0.7475 0.012 0.084 0.896 0.008 0.000 0.000
#> GSM11695 3 0.2282 0.7562 0.012 0.068 0.900 0.020 0.000 0.000
#> GSM11734 2 0.5549 0.3647 0.000 0.532 0.164 0.304 0.000 0.000
#> GSM11861 3 0.4629 0.2437 0.000 0.028 0.576 0.388 0.004 0.004
#> GSM11843 2 0.4728 0.5831 0.004 0.660 0.256 0.080 0.000 0.000
#> GSM11862 4 0.2913 0.7731 0.000 0.004 0.180 0.812 0.000 0.004
#> GSM11697 3 0.1737 0.7579 0.008 0.040 0.932 0.020 0.000 0.000
#> GSM11714 6 0.2451 0.7410 0.000 0.004 0.068 0.000 0.040 0.888
#> GSM11723 3 0.5190 0.2576 0.004 0.324 0.576 0.096 0.000 0.000
#> GSM11845 3 0.6187 -0.0497 0.004 0.268 0.392 0.336 0.000 0.000
#> GSM11683 3 0.4712 0.5852 0.020 0.012 0.708 0.044 0.000 0.216
#> GSM11691 3 0.1167 0.7602 0.020 0.012 0.960 0.008 0.000 0.000
#> GSM27949 3 0.2024 0.7607 0.020 0.012 0.924 0.036 0.000 0.008
#> GSM27945 3 0.2315 0.7501 0.008 0.084 0.892 0.016 0.000 0.000
#> GSM11706 6 0.3682 0.7083 0.000 0.004 0.200 0.000 0.032 0.764
#> GSM11853 3 0.1296 0.7574 0.004 0.012 0.952 0.032 0.000 0.000
#> GSM11729 2 0.5724 0.5876 0.036 0.684 0.080 0.060 0.140 0.000
#> GSM11746 2 0.5011 0.5550 0.040 0.720 0.080 0.004 0.152 0.004
#> GSM11711 3 0.3306 0.6657 0.032 0.004 0.820 0.004 0.000 0.140
#> GSM11854 3 0.1082 0.7556 0.000 0.004 0.956 0.040 0.000 0.000
#> GSM11731 4 0.2587 0.7218 0.004 0.120 0.004 0.864 0.000 0.008
#> GSM11839 4 0.1230 0.7953 0.000 0.028 0.008 0.956 0.000 0.008
#> GSM11836 4 0.3385 0.6926 0.172 0.028 0.000 0.796 0.004 0.000
#> GSM11849 4 0.6292 0.4701 0.124 0.148 0.024 0.624 0.000 0.080
#> GSM11682 6 0.6869 0.3932 0.064 0.060 0.020 0.296 0.032 0.528
#> GSM11690 4 0.0665 0.7946 0.000 0.004 0.008 0.980 0.000 0.008
#> GSM11692 4 0.2442 0.8074 0.000 0.000 0.144 0.852 0.000 0.004
#> GSM11841 4 0.2538 0.8126 0.000 0.016 0.124 0.860 0.000 0.000
#> GSM11901 4 0.2389 0.8132 0.000 0.008 0.128 0.864 0.000 0.000
#> GSM11715 2 0.6295 0.3529 0.172 0.472 0.008 0.332 0.000 0.016
#> GSM11724 2 0.6383 0.3312 0.172 0.460 0.008 0.340 0.000 0.020
#> GSM11684 4 0.3126 0.7615 0.060 0.016 0.012 0.864 0.000 0.048
#> GSM11696 4 0.2046 0.8018 0.000 0.008 0.032 0.916 0.000 0.044
#> GSM27952 6 0.5895 0.7069 0.056 0.060 0.144 0.024 0.028 0.688
#> GSM27948 4 0.1524 0.8190 0.000 0.000 0.060 0.932 0.000 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.line(p) agent(p) time(p) k
#> MAD:mclust 80 1.96e-02 0.627 0.132299 2
#> MAD:mclust 77 1.10e-12 0.208 0.156890 3
#> MAD:mclust 72 5.63e-14 0.321 0.028965 4
#> MAD:mclust 60 4.77e-15 0.832 0.001103 5
#> MAD:mclust 70 2.00e-14 0.462 0.000612 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 14502 rows and 83 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.633 0.800 0.917 0.4554 0.540 0.540
#> 3 3 0.435 0.718 0.808 0.4251 0.677 0.461
#> 4 4 0.500 0.642 0.809 0.1282 0.797 0.486
#> 5 5 0.629 0.629 0.825 0.0665 0.827 0.453
#> 6 6 0.576 0.474 0.690 0.0514 0.916 0.635
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM11708 2 0.0000 0.8635 0.000 1.000
#> GSM11735 2 0.0000 0.8635 0.000 1.000
#> GSM11733 2 0.0000 0.8635 0.000 1.000
#> GSM11863 2 0.0000 0.8635 0.000 1.000
#> GSM11710 2 0.0000 0.8635 0.000 1.000
#> GSM11712 1 0.0000 0.9204 1.000 0.000
#> GSM11732 2 0.0000 0.8635 0.000 1.000
#> GSM11844 2 0.9129 0.5609 0.328 0.672
#> GSM11842 2 0.9944 0.1254 0.456 0.544
#> GSM11860 1 0.8555 0.5823 0.720 0.280
#> GSM11686 2 0.9358 0.5260 0.352 0.648
#> GSM11688 2 0.0000 0.8635 0.000 1.000
#> GSM11846 2 0.4298 0.8180 0.088 0.912
#> GSM11680 2 0.8909 0.5962 0.308 0.692
#> GSM11698 2 0.9608 0.4664 0.384 0.616
#> GSM11840 2 0.0000 0.8635 0.000 1.000
#> GSM11847 2 0.0000 0.8635 0.000 1.000
#> GSM11685 2 0.0000 0.8635 0.000 1.000
#> GSM11699 1 0.7745 0.6571 0.772 0.228
#> GSM27950 2 0.0000 0.8635 0.000 1.000
#> GSM27946 1 0.0672 0.9151 0.992 0.008
#> GSM11709 1 0.6438 0.7648 0.836 0.164
#> GSM11720 1 0.0000 0.9204 1.000 0.000
#> GSM11726 1 0.6887 0.7381 0.816 0.184
#> GSM11837 1 0.6623 0.7546 0.828 0.172
#> GSM11725 1 0.0000 0.9204 1.000 0.000
#> GSM11864 1 0.0000 0.9204 1.000 0.000
#> GSM11687 1 0.0000 0.9204 1.000 0.000
#> GSM11693 1 0.0000 0.9204 1.000 0.000
#> GSM11727 1 0.0000 0.9204 1.000 0.000
#> GSM11838 1 0.0000 0.9204 1.000 0.000
#> GSM11681 2 0.9775 0.3999 0.412 0.588
#> GSM11689 1 0.0000 0.9204 1.000 0.000
#> GSM11704 1 0.0000 0.9204 1.000 0.000
#> GSM11703 1 0.0000 0.9204 1.000 0.000
#> GSM11705 1 0.0000 0.9204 1.000 0.000
#> GSM11722 1 0.0000 0.9204 1.000 0.000
#> GSM11730 1 0.0000 0.9204 1.000 0.000
#> GSM11713 1 0.3274 0.8747 0.940 0.060
#> GSM11728 1 0.8081 0.6213 0.752 0.248
#> GSM27947 1 0.0000 0.9204 1.000 0.000
#> GSM27951 1 0.0000 0.9204 1.000 0.000
#> GSM11707 2 0.0000 0.8635 0.000 1.000
#> GSM11716 1 0.6712 0.7496 0.824 0.176
#> GSM11850 1 0.9850 0.2306 0.572 0.428
#> GSM11851 2 0.1184 0.8592 0.016 0.984
#> GSM11721 1 0.0000 0.9204 1.000 0.000
#> GSM11852 1 0.9580 0.2945 0.620 0.380
#> GSM11694 2 0.9993 0.0412 0.484 0.516
#> GSM11695 2 0.2948 0.8423 0.052 0.948
#> GSM11734 1 0.0000 0.9204 1.000 0.000
#> GSM11861 1 0.0000 0.9204 1.000 0.000
#> GSM11843 1 0.0000 0.9204 1.000 0.000
#> GSM11862 1 0.0000 0.9204 1.000 0.000
#> GSM11697 1 0.8861 0.5063 0.696 0.304
#> GSM11714 2 0.0000 0.8635 0.000 1.000
#> GSM11723 1 0.0000 0.9204 1.000 0.000
#> GSM11845 1 0.0000 0.9204 1.000 0.000
#> GSM11683 2 0.2043 0.8530 0.032 0.968
#> GSM11691 1 0.4161 0.8522 0.916 0.084
#> GSM27949 2 0.0000 0.8635 0.000 1.000
#> GSM27945 1 0.5294 0.8163 0.880 0.120
#> GSM11706 2 0.0000 0.8635 0.000 1.000
#> GSM11853 1 0.3431 0.8786 0.936 0.064
#> GSM11729 1 0.0000 0.9204 1.000 0.000
#> GSM11746 1 0.0000 0.9204 1.000 0.000
#> GSM11711 2 0.1414 0.8578 0.020 0.980
#> GSM11854 1 0.9754 0.2017 0.592 0.408
#> GSM11731 1 0.0000 0.9204 1.000 0.000
#> GSM11839 1 0.0000 0.9204 1.000 0.000
#> GSM11836 1 0.0000 0.9204 1.000 0.000
#> GSM11849 1 0.0000 0.9204 1.000 0.000
#> GSM11682 2 0.9686 0.4370 0.396 0.604
#> GSM11690 1 0.6343 0.7623 0.840 0.160
#> GSM11692 1 0.0000 0.9204 1.000 0.000
#> GSM11841 1 0.0000 0.9204 1.000 0.000
#> GSM11901 1 0.0000 0.9204 1.000 0.000
#> GSM11715 1 0.0000 0.9204 1.000 0.000
#> GSM11724 1 0.0000 0.9204 1.000 0.000
#> GSM11684 1 0.0000 0.9204 1.000 0.000
#> GSM11696 1 0.0000 0.9204 1.000 0.000
#> GSM27952 2 0.3879 0.8264 0.076 0.924
#> GSM27948 1 0.0000 0.9204 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM11708 3 0.0000 0.8127 0.000 0.000 1.000
#> GSM11735 3 0.0000 0.8127 0.000 0.000 1.000
#> GSM11733 3 0.0983 0.8124 0.016 0.004 0.980
#> GSM11863 3 0.6559 0.7185 0.040 0.252 0.708
#> GSM11710 3 0.0424 0.8109 0.008 0.000 0.992
#> GSM11712 2 0.3340 0.8016 0.120 0.880 0.000
#> GSM11732 3 0.3192 0.7949 0.000 0.112 0.888
#> GSM11844 3 0.7011 0.7051 0.092 0.188 0.720
#> GSM11842 3 0.6835 0.6909 0.040 0.284 0.676
#> GSM11860 3 0.7424 0.5633 0.040 0.388 0.572
#> GSM11686 1 0.4677 0.7614 0.840 0.028 0.132
#> GSM11688 1 0.6111 0.3882 0.604 0.000 0.396
#> GSM11846 3 0.2356 0.8129 0.000 0.072 0.928
#> GSM11680 3 0.6511 0.6882 0.136 0.104 0.760
#> GSM11698 3 0.7453 0.6338 0.152 0.148 0.700
#> GSM11840 3 0.4369 0.7944 0.040 0.096 0.864
#> GSM11847 3 0.4206 0.7929 0.040 0.088 0.872
#> GSM11685 1 0.6008 0.4380 0.628 0.000 0.372
#> GSM11699 1 0.4121 0.7121 0.832 0.168 0.000
#> GSM27950 3 0.0000 0.8127 0.000 0.000 1.000
#> GSM27946 2 0.5859 0.6788 0.344 0.656 0.000
#> GSM11709 2 0.6590 0.7447 0.112 0.756 0.132
#> GSM11720 2 0.2878 0.7904 0.096 0.904 0.000
#> GSM11726 2 0.4979 0.6819 0.020 0.812 0.168
#> GSM11837 2 0.1636 0.7655 0.020 0.964 0.016
#> GSM11725 2 0.0892 0.7850 0.020 0.980 0.000
#> GSM11864 2 0.0237 0.7780 0.004 0.996 0.000
#> GSM11687 2 0.5465 0.7496 0.288 0.712 0.000
#> GSM11693 2 0.5138 0.7649 0.252 0.748 0.000
#> GSM11727 2 0.6225 0.5859 0.432 0.568 0.000
#> GSM11838 2 0.4555 0.7875 0.200 0.800 0.000
#> GSM11681 1 0.1647 0.8229 0.960 0.036 0.004
#> GSM11689 2 0.5431 0.7462 0.284 0.716 0.000
#> GSM11704 2 0.5397 0.7502 0.280 0.720 0.000
#> GSM11703 2 0.5363 0.7507 0.276 0.724 0.000
#> GSM11705 2 0.6280 0.4877 0.460 0.540 0.000
#> GSM11722 2 0.5859 0.7075 0.344 0.656 0.000
#> GSM11730 1 0.5948 0.0945 0.640 0.360 0.000
#> GSM11713 1 0.1163 0.8243 0.972 0.028 0.000
#> GSM11728 1 0.1163 0.8243 0.972 0.028 0.000
#> GSM27947 2 0.5058 0.7687 0.244 0.756 0.000
#> GSM27951 1 0.1643 0.8203 0.956 0.044 0.000
#> GSM11707 3 0.0000 0.8127 0.000 0.000 1.000
#> GSM11716 2 0.1015 0.7784 0.008 0.980 0.012
#> GSM11850 3 0.7223 0.4481 0.028 0.424 0.548
#> GSM11851 3 0.2945 0.8006 0.004 0.088 0.908
#> GSM11721 1 0.1643 0.8192 0.956 0.044 0.000
#> GSM11852 1 0.4539 0.7425 0.836 0.148 0.016
#> GSM11694 3 0.7820 0.5582 0.072 0.324 0.604
#> GSM11695 3 0.2703 0.8066 0.016 0.056 0.928
#> GSM11734 2 0.2448 0.7992 0.076 0.924 0.000
#> GSM11861 1 0.5327 0.5177 0.728 0.272 0.000
#> GSM11843 2 0.0424 0.7799 0.008 0.992 0.000
#> GSM11862 1 0.2261 0.8096 0.932 0.068 0.000
#> GSM11697 3 0.9319 0.2202 0.176 0.340 0.484
#> GSM11714 3 0.0237 0.8118 0.004 0.000 0.996
#> GSM11723 2 0.1031 0.7862 0.024 0.976 0.000
#> GSM11845 2 0.0424 0.7799 0.008 0.992 0.000
#> GSM11683 1 0.5268 0.6832 0.776 0.012 0.212
#> GSM11691 1 0.6062 0.4933 0.708 0.276 0.016
#> GSM27949 3 0.0892 0.8135 0.000 0.020 0.980
#> GSM27945 2 0.3550 0.7865 0.080 0.896 0.024
#> GSM11706 3 0.0000 0.8127 0.000 0.000 1.000
#> GSM11853 2 0.7984 0.6808 0.216 0.652 0.132
#> GSM11729 2 0.1643 0.7653 0.044 0.956 0.000
#> GSM11746 2 0.1529 0.7670 0.040 0.960 0.000
#> GSM11711 3 0.0661 0.8139 0.008 0.004 0.988
#> GSM11854 3 0.9452 0.2935 0.232 0.268 0.500
#> GSM11731 2 0.3752 0.7863 0.144 0.856 0.000
#> GSM11839 2 0.5948 0.7067 0.360 0.640 0.000
#> GSM11836 1 0.3412 0.7340 0.876 0.124 0.000
#> GSM11849 1 0.0000 0.8233 1.000 0.000 0.000
#> GSM11682 1 0.1031 0.8201 0.976 0.000 0.024
#> GSM11690 1 0.0000 0.8233 1.000 0.000 0.000
#> GSM11692 2 0.6299 0.4553 0.476 0.524 0.000
#> GSM11841 2 0.4346 0.7929 0.184 0.816 0.000
#> GSM11901 2 0.5560 0.7496 0.300 0.700 0.000
#> GSM11715 2 0.4842 0.7766 0.224 0.776 0.000
#> GSM11724 2 0.5138 0.7609 0.252 0.748 0.000
#> GSM11684 1 0.0000 0.8233 1.000 0.000 0.000
#> GSM11696 1 0.0592 0.8251 0.988 0.012 0.000
#> GSM27952 1 0.4702 0.6846 0.788 0.000 0.212
#> GSM27948 1 0.0592 0.8256 0.988 0.012 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM11708 3 0.0000 0.77335 0.000 0.000 1.000 0.000
#> GSM11735 3 0.0336 0.77196 0.000 0.008 0.992 0.000
#> GSM11733 3 0.2644 0.73601 0.000 0.032 0.908 0.060
#> GSM11863 2 0.3687 0.66803 0.000 0.856 0.080 0.064
#> GSM11710 3 0.2589 0.70932 0.000 0.000 0.884 0.116
#> GSM11712 2 0.4872 0.36632 0.356 0.640 0.000 0.004
#> GSM11732 3 0.1042 0.77166 0.020 0.008 0.972 0.000
#> GSM11844 3 0.5167 0.45694 0.340 0.016 0.644 0.000
#> GSM11842 2 0.2623 0.70411 0.000 0.908 0.028 0.064
#> GSM11860 2 0.1042 0.72533 0.000 0.972 0.020 0.008
#> GSM11686 4 0.3681 0.69707 0.176 0.000 0.008 0.816
#> GSM11688 4 0.4998 0.00939 0.000 0.000 0.488 0.512
#> GSM11846 3 0.1398 0.76340 0.004 0.040 0.956 0.000
#> GSM11680 3 0.5940 0.52432 0.304 0.004 0.640 0.052
#> GSM11698 3 0.5310 0.29922 0.412 0.012 0.576 0.000
#> GSM11840 3 0.6412 0.39838 0.000 0.320 0.592 0.088
#> GSM11847 3 0.6746 0.38078 0.000 0.316 0.568 0.116
#> GSM11685 4 0.4697 0.42086 0.000 0.000 0.356 0.644
#> GSM11699 4 0.4539 0.66415 0.272 0.008 0.000 0.720
#> GSM27950 3 0.0188 0.77309 0.000 0.000 0.996 0.004
#> GSM27946 1 0.5174 0.62503 0.740 0.048 0.004 0.208
#> GSM11709 1 0.3486 0.68987 0.812 0.000 0.188 0.000
#> GSM11720 1 0.2081 0.78576 0.916 0.084 0.000 0.000
#> GSM11726 1 0.6401 0.64183 0.724 0.068 0.104 0.104
#> GSM11837 1 0.4991 0.44077 0.608 0.388 0.000 0.004
#> GSM11725 1 0.3400 0.74619 0.820 0.180 0.000 0.000
#> GSM11864 1 0.3649 0.73156 0.796 0.204 0.000 0.000
#> GSM11687 1 0.0817 0.77448 0.976 0.000 0.000 0.024
#> GSM11693 1 0.0817 0.78707 0.976 0.024 0.000 0.000
#> GSM11727 4 0.4477 0.63151 0.312 0.000 0.000 0.688
#> GSM11838 2 0.5448 0.58955 0.244 0.700 0.000 0.056
#> GSM11681 4 0.3494 0.74463 0.172 0.000 0.004 0.824
#> GSM11689 1 0.0188 0.78207 0.996 0.000 0.000 0.004
#> GSM11704 1 0.0188 0.78223 0.996 0.000 0.000 0.004
#> GSM11703 1 0.0000 0.78249 1.000 0.000 0.000 0.000
#> GSM11705 1 0.3893 0.60135 0.796 0.000 0.008 0.196
#> GSM11722 1 0.5297 0.45884 0.676 0.032 0.000 0.292
#> GSM11730 4 0.3649 0.72930 0.204 0.000 0.000 0.796
#> GSM11713 4 0.3311 0.74264 0.172 0.000 0.000 0.828
#> GSM11728 4 0.3219 0.74537 0.164 0.000 0.000 0.836
#> GSM27947 1 0.2216 0.78346 0.908 0.092 0.000 0.000
#> GSM27951 4 0.4103 0.69440 0.256 0.000 0.000 0.744
#> GSM11707 3 0.0000 0.77335 0.000 0.000 1.000 0.000
#> GSM11716 1 0.4282 0.77008 0.816 0.124 0.060 0.000
#> GSM11850 1 0.3486 0.73868 0.812 0.000 0.188 0.000
#> GSM11851 3 0.5167 0.03778 0.488 0.004 0.508 0.000
#> GSM11721 4 0.5228 0.65499 0.124 0.120 0.000 0.756
#> GSM11852 4 0.4632 0.61473 0.308 0.000 0.004 0.688
#> GSM11694 1 0.3710 0.73365 0.804 0.004 0.192 0.000
#> GSM11695 1 0.4406 0.58499 0.700 0.000 0.300 0.000
#> GSM11734 2 0.3710 0.66191 0.192 0.804 0.000 0.004
#> GSM11861 4 0.5268 0.48235 0.396 0.012 0.000 0.592
#> GSM11843 1 0.3942 0.70359 0.764 0.236 0.000 0.000
#> GSM11862 4 0.4088 0.68943 0.232 0.004 0.000 0.764
#> GSM11697 1 0.3668 0.73369 0.808 0.004 0.188 0.000
#> GSM11714 3 0.0188 0.77309 0.000 0.000 0.996 0.004
#> GSM11723 1 0.4304 0.64255 0.716 0.284 0.000 0.000
#> GSM11845 1 0.4277 0.64969 0.720 0.280 0.000 0.000
#> GSM11683 4 0.5407 0.71765 0.108 0.000 0.152 0.740
#> GSM11691 1 0.0992 0.78453 0.976 0.008 0.004 0.012
#> GSM27949 3 0.4697 0.41908 0.356 0.000 0.644 0.000
#> GSM27945 1 0.4171 0.77697 0.828 0.084 0.088 0.000
#> GSM11706 3 0.0000 0.77335 0.000 0.000 1.000 0.000
#> GSM11853 1 0.3550 0.78461 0.860 0.044 0.096 0.000
#> GSM11729 2 0.3688 0.59952 0.208 0.792 0.000 0.000
#> GSM11746 2 0.4992 -0.14764 0.476 0.524 0.000 0.000
#> GSM11711 3 0.2149 0.74389 0.088 0.000 0.912 0.000
#> GSM11854 1 0.5112 0.54267 0.716 0.004 0.252 0.028
#> GSM11731 2 0.0804 0.73372 0.008 0.980 0.000 0.012
#> GSM11839 2 0.4673 0.54553 0.008 0.700 0.000 0.292
#> GSM11836 2 0.4250 0.56676 0.000 0.724 0.000 0.276
#> GSM11849 4 0.1356 0.75698 0.032 0.008 0.000 0.960
#> GSM11682 4 0.0000 0.75201 0.000 0.000 0.000 1.000
#> GSM11690 4 0.0592 0.74854 0.000 0.016 0.000 0.984
#> GSM11692 2 0.7566 0.25218 0.212 0.468 0.000 0.320
#> GSM11841 2 0.4008 0.69430 0.148 0.820 0.000 0.032
#> GSM11901 2 0.5309 0.67049 0.164 0.744 0.000 0.092
#> GSM11715 2 0.1677 0.73886 0.012 0.948 0.000 0.040
#> GSM11724 2 0.1635 0.73826 0.008 0.948 0.000 0.044
#> GSM11684 4 0.1042 0.75111 0.008 0.020 0.000 0.972
#> GSM11696 4 0.3015 0.76262 0.092 0.024 0.000 0.884
#> GSM27952 4 0.0524 0.75308 0.004 0.000 0.008 0.988
#> GSM27948 4 0.3731 0.71905 0.120 0.036 0.000 0.844
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM11708 3 0.0290 0.8256 0.000 0.000 0.992 0.008 0.000
#> GSM11735 3 0.0290 0.8256 0.000 0.000 0.992 0.008 0.000
#> GSM11733 3 0.3562 0.6257 0.000 0.000 0.788 0.016 0.196
#> GSM11863 5 0.0880 0.7506 0.000 0.000 0.032 0.000 0.968
#> GSM11710 3 0.3661 0.6157 0.000 0.000 0.724 0.276 0.000
#> GSM11712 1 0.4410 0.6536 0.764 0.000 0.000 0.112 0.124
#> GSM11732 3 0.1116 0.8146 0.028 0.004 0.964 0.004 0.000
#> GSM11844 3 0.4610 0.2348 0.388 0.000 0.596 0.016 0.000
#> GSM11842 5 0.0290 0.7530 0.000 0.000 0.008 0.000 0.992
#> GSM11860 5 0.0162 0.7526 0.000 0.000 0.004 0.000 0.996
#> GSM11686 4 0.1270 0.7892 0.052 0.000 0.000 0.948 0.000
#> GSM11688 4 0.0794 0.7649 0.000 0.000 0.028 0.972 0.000
#> GSM11846 3 0.3188 0.7552 0.028 0.000 0.860 0.012 0.100
#> GSM11680 1 0.4323 0.3081 0.656 0.000 0.012 0.332 0.000
#> GSM11698 1 0.2193 0.7761 0.912 0.000 0.060 0.028 0.000
#> GSM11840 5 0.4278 0.1537 0.000 0.000 0.452 0.000 0.548
#> GSM11847 5 0.4774 0.2004 0.000 0.000 0.424 0.020 0.556
#> GSM11685 4 0.0703 0.7671 0.000 0.000 0.024 0.976 0.000
#> GSM11699 4 0.4278 0.3938 0.452 0.000 0.000 0.548 0.000
#> GSM27950 3 0.1544 0.8029 0.000 0.000 0.932 0.068 0.000
#> GSM27946 1 0.4249 -0.0773 0.568 0.000 0.000 0.432 0.000
#> GSM11709 2 0.5847 0.4320 0.264 0.592 0.144 0.000 0.000
#> GSM11720 1 0.3218 0.7492 0.848 0.124 0.016 0.000 0.012
#> GSM11726 2 0.1173 0.7746 0.020 0.964 0.012 0.000 0.004
#> GSM11837 2 0.5008 0.1246 0.024 0.544 0.004 0.000 0.428
#> GSM11725 1 0.4258 0.7029 0.768 0.072 0.000 0.000 0.160
#> GSM11864 1 0.2522 0.7736 0.880 0.012 0.000 0.000 0.108
#> GSM11687 2 0.4504 0.1741 0.428 0.564 0.008 0.000 0.000
#> GSM11693 1 0.1965 0.7754 0.904 0.096 0.000 0.000 0.000
#> GSM11727 2 0.0451 0.7850 0.000 0.988 0.000 0.008 0.004
#> GSM11838 2 0.1892 0.7397 0.004 0.916 0.000 0.000 0.080
#> GSM11681 2 0.3895 0.4974 0.000 0.680 0.000 0.320 0.000
#> GSM11689 1 0.3741 0.6166 0.732 0.264 0.000 0.004 0.000
#> GSM11704 1 0.3612 0.6724 0.764 0.228 0.000 0.008 0.000
#> GSM11703 1 0.4074 0.4593 0.636 0.364 0.000 0.000 0.000
#> GSM11705 2 0.0324 0.7826 0.004 0.992 0.004 0.000 0.000
#> GSM11722 2 0.0451 0.7850 0.000 0.988 0.000 0.008 0.004
#> GSM11730 2 0.0451 0.7850 0.000 0.988 0.000 0.008 0.004
#> GSM11713 2 0.0703 0.7824 0.000 0.976 0.000 0.024 0.000
#> GSM11728 2 0.1121 0.7764 0.000 0.956 0.000 0.044 0.000
#> GSM27947 1 0.0290 0.7820 0.992 0.000 0.000 0.008 0.000
#> GSM27951 2 0.2127 0.7446 0.000 0.892 0.000 0.108 0.000
#> GSM11707 3 0.0000 0.8252 0.000 0.000 1.000 0.000 0.000
#> GSM11716 1 0.3018 0.7657 0.860 0.012 0.116 0.000 0.012
#> GSM11850 1 0.3934 0.5895 0.716 0.008 0.276 0.000 0.000
#> GSM11851 1 0.2971 0.7477 0.836 0.000 0.156 0.008 0.000
#> GSM11721 4 0.2777 0.7887 0.120 0.000 0.000 0.864 0.016
#> GSM11852 4 0.4201 0.4704 0.408 0.000 0.000 0.592 0.000
#> GSM11694 1 0.2233 0.7762 0.892 0.004 0.104 0.000 0.000
#> GSM11695 1 0.3675 0.6749 0.772 0.008 0.216 0.004 0.000
#> GSM11734 5 0.4383 0.1368 0.424 0.004 0.000 0.000 0.572
#> GSM11861 1 0.4291 -0.2035 0.536 0.000 0.000 0.464 0.000
#> GSM11843 1 0.2352 0.7807 0.896 0.008 0.000 0.004 0.092
#> GSM11862 4 0.3861 0.6754 0.284 0.004 0.000 0.712 0.000
#> GSM11697 1 0.1892 0.7856 0.916 0.000 0.080 0.004 0.000
#> GSM11714 3 0.0451 0.8253 0.000 0.004 0.988 0.008 0.000
#> GSM11723 1 0.3128 0.7387 0.824 0.004 0.000 0.004 0.168
#> GSM11845 1 0.1764 0.7842 0.928 0.000 0.000 0.008 0.064
#> GSM11683 4 0.3544 0.7291 0.016 0.028 0.120 0.836 0.000
#> GSM11691 1 0.1197 0.7688 0.952 0.000 0.000 0.048 0.000
#> GSM27949 3 0.4449 -0.0876 0.484 0.000 0.512 0.004 0.000
#> GSM27945 1 0.0162 0.7829 0.996 0.000 0.000 0.004 0.000
#> GSM11706 3 0.0000 0.8252 0.000 0.000 1.000 0.000 0.000
#> GSM11853 1 0.0693 0.7842 0.980 0.000 0.012 0.008 0.000
#> GSM11729 5 0.1830 0.7340 0.008 0.068 0.000 0.000 0.924
#> GSM11746 5 0.3141 0.7018 0.040 0.096 0.004 0.000 0.860
#> GSM11711 3 0.0693 0.8222 0.008 0.012 0.980 0.000 0.000
#> GSM11854 1 0.3455 0.5989 0.784 0.000 0.008 0.208 0.000
#> GSM11731 5 0.0324 0.7525 0.000 0.004 0.000 0.004 0.992
#> GSM11839 5 0.3662 0.5572 0.004 0.000 0.000 0.252 0.744
#> GSM11836 5 0.1410 0.7406 0.000 0.000 0.000 0.060 0.940
#> GSM11849 2 0.4617 0.1472 0.000 0.552 0.000 0.436 0.012
#> GSM11682 4 0.0963 0.7633 0.000 0.036 0.000 0.964 0.000
#> GSM11690 4 0.1153 0.7716 0.008 0.024 0.000 0.964 0.004
#> GSM11692 4 0.4608 0.5943 0.336 0.000 0.000 0.640 0.024
#> GSM11841 5 0.6569 -0.0162 0.232 0.000 0.000 0.304 0.464
#> GSM11901 4 0.6202 0.5419 0.228 0.000 0.000 0.552 0.220
#> GSM11715 5 0.2773 0.6671 0.000 0.164 0.000 0.000 0.836
#> GSM11724 5 0.2329 0.7034 0.000 0.124 0.000 0.000 0.876
#> GSM11684 4 0.3299 0.6925 0.004 0.152 0.000 0.828 0.016
#> GSM11696 4 0.4564 0.7480 0.196 0.036 0.000 0.748 0.020
#> GSM27952 4 0.0955 0.7651 0.000 0.028 0.004 0.968 0.000
#> GSM27948 4 0.2672 0.7904 0.116 0.004 0.000 0.872 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM11708 6 0.0000 0.7473 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM11735 6 0.0000 0.7473 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM11733 6 0.4423 0.4233 0.016 0.000 0.000 0.020 0.320 0.644
#> GSM11863 5 0.0972 0.6478 0.008 0.000 0.000 0.000 0.964 0.028
#> GSM11710 6 0.5237 0.4987 0.140 0.000 0.000 0.240 0.004 0.616
#> GSM11712 3 0.6257 0.3797 0.052 0.000 0.544 0.124 0.276 0.004
#> GSM11732 6 0.2432 0.7044 0.024 0.000 0.100 0.000 0.000 0.876
#> GSM11844 6 0.4567 0.2892 0.004 0.024 0.352 0.008 0.000 0.612
#> GSM11842 5 0.0653 0.6496 0.004 0.000 0.000 0.004 0.980 0.012
#> GSM11860 5 0.0935 0.6457 0.032 0.000 0.000 0.000 0.964 0.004
#> GSM11686 4 0.2800 0.6951 0.100 0.000 0.036 0.860 0.000 0.004
#> GSM11688 4 0.2831 0.6609 0.136 0.000 0.000 0.840 0.000 0.024
#> GSM11846 1 0.7097 0.1876 0.440 0.000 0.004 0.112 0.296 0.148
#> GSM11680 3 0.5267 0.4760 0.028 0.000 0.644 0.236 0.000 0.092
#> GSM11698 3 0.4165 0.6091 0.020 0.000 0.772 0.088 0.000 0.120
#> GSM11840 5 0.2963 0.5883 0.016 0.000 0.000 0.004 0.828 0.152
#> GSM11847 5 0.3782 0.5700 0.016 0.000 0.000 0.044 0.788 0.152
#> GSM11685 4 0.1713 0.6885 0.044 0.000 0.000 0.928 0.000 0.028
#> GSM11699 3 0.5172 -0.0209 0.060 0.012 0.524 0.404 0.000 0.000
#> GSM27950 6 0.2215 0.7321 0.012 0.000 0.012 0.076 0.000 0.900
#> GSM27946 3 0.5400 0.0175 0.116 0.000 0.484 0.400 0.000 0.000
#> GSM11709 1 0.5979 0.5356 0.656 0.104 0.132 0.000 0.020 0.088
#> GSM11720 1 0.5507 0.4178 0.532 0.044 0.376 0.000 0.048 0.000
#> GSM11726 2 0.4323 0.4154 0.324 0.648 0.012 0.000 0.012 0.004
#> GSM11837 2 0.6380 -0.2162 0.136 0.428 0.036 0.000 0.396 0.004
#> GSM11725 1 0.6288 0.3806 0.472 0.048 0.356 0.000 0.124 0.000
#> GSM11864 3 0.5727 -0.2843 0.396 0.004 0.456 0.000 0.144 0.000
#> GSM11687 1 0.4468 0.5965 0.712 0.076 0.204 0.008 0.000 0.000
#> GSM11693 1 0.4307 0.4549 0.604 0.008 0.376 0.004 0.008 0.000
#> GSM11727 2 0.1765 0.7168 0.096 0.904 0.000 0.000 0.000 0.000
#> GSM11838 2 0.2954 0.6196 0.048 0.852 0.004 0.000 0.096 0.000
#> GSM11681 1 0.4934 0.2085 0.628 0.108 0.000 0.264 0.000 0.000
#> GSM11689 1 0.4456 0.5675 0.676 0.028 0.276 0.020 0.000 0.000
#> GSM11704 1 0.4433 0.5421 0.656 0.016 0.304 0.024 0.000 0.000
#> GSM11703 1 0.5223 0.4348 0.508 0.096 0.396 0.000 0.000 0.000
#> GSM11705 1 0.4089 -0.2214 0.524 0.468 0.008 0.000 0.000 0.000
#> GSM11722 2 0.1910 0.7185 0.108 0.892 0.000 0.000 0.000 0.000
#> GSM11730 2 0.1714 0.7211 0.092 0.908 0.000 0.000 0.000 0.000
#> GSM11713 2 0.3374 0.6408 0.208 0.772 0.000 0.020 0.000 0.000
#> GSM11728 2 0.3290 0.6448 0.208 0.776 0.000 0.016 0.000 0.000
#> GSM27947 3 0.4335 0.2012 0.324 0.000 0.644 0.024 0.008 0.000
#> GSM27951 1 0.4012 0.3307 0.752 0.164 0.000 0.084 0.000 0.000
#> GSM11707 6 0.0363 0.7468 0.012 0.000 0.000 0.000 0.000 0.988
#> GSM11716 3 0.2519 0.6000 0.044 0.004 0.884 0.000 0.000 0.068
#> GSM11850 3 0.4214 0.4805 0.044 0.000 0.680 0.000 0.000 0.276
#> GSM11851 3 0.3141 0.5808 0.012 0.000 0.788 0.000 0.000 0.200
#> GSM11721 4 0.3718 0.6830 0.052 0.000 0.080 0.824 0.040 0.004
#> GSM11852 4 0.4809 0.5009 0.080 0.000 0.272 0.644 0.000 0.004
#> GSM11694 3 0.3948 0.5460 0.064 0.000 0.748 0.000 0.000 0.188
#> GSM11695 3 0.4652 0.4277 0.064 0.000 0.624 0.000 0.000 0.312
#> GSM11734 3 0.5677 0.2603 0.012 0.136 0.596 0.008 0.248 0.000
#> GSM11861 3 0.3848 0.4816 0.040 0.000 0.752 0.204 0.004 0.000
#> GSM11843 3 0.2630 0.5870 0.032 0.004 0.872 0.000 0.092 0.000
#> GSM11862 4 0.5487 0.2547 0.052 0.012 0.416 0.504 0.016 0.000
#> GSM11697 3 0.3239 0.5909 0.024 0.000 0.808 0.004 0.000 0.164
#> GSM11714 6 0.1555 0.7356 0.004 0.060 0.000 0.004 0.000 0.932
#> GSM11723 3 0.3493 0.5421 0.016 0.144 0.812 0.004 0.024 0.000
#> GSM11845 3 0.1312 0.6071 0.012 0.004 0.956 0.008 0.020 0.000
#> GSM11683 4 0.7053 0.2803 0.104 0.064 0.044 0.480 0.000 0.308
#> GSM11691 3 0.3298 0.6109 0.060 0.000 0.844 0.072 0.000 0.024
#> GSM27949 6 0.4799 0.2364 0.068 0.000 0.340 0.000 0.000 0.592
#> GSM27945 3 0.2196 0.5689 0.108 0.000 0.884 0.004 0.000 0.004
#> GSM11706 6 0.2362 0.6852 0.136 0.000 0.000 0.000 0.004 0.860
#> GSM11853 3 0.4808 0.0641 0.384 0.000 0.568 0.036 0.012 0.000
#> GSM11729 5 0.5479 0.5353 0.104 0.240 0.024 0.004 0.628 0.000
#> GSM11746 5 0.6111 0.4353 0.196 0.240 0.020 0.004 0.540 0.000
#> GSM11711 6 0.4389 0.1641 0.448 0.000 0.024 0.000 0.000 0.528
#> GSM11854 3 0.5081 0.4305 0.128 0.000 0.616 0.256 0.000 0.000
#> GSM11731 5 0.4605 0.5972 0.016 0.216 0.056 0.004 0.708 0.000
#> GSM11839 5 0.7201 0.4668 0.016 0.196 0.144 0.144 0.500 0.000
#> GSM11836 5 0.3777 0.6320 0.004 0.124 0.000 0.084 0.788 0.000
#> GSM11849 2 0.4750 0.4150 0.064 0.672 0.004 0.252 0.008 0.000
#> GSM11682 4 0.2165 0.6788 0.108 0.008 0.000 0.884 0.000 0.000
#> GSM11690 4 0.1925 0.7029 0.060 0.004 0.008 0.920 0.008 0.000
#> GSM11692 4 0.6036 0.5045 0.088 0.016 0.252 0.596 0.048 0.000
#> GSM11841 5 0.7026 -0.0571 0.044 0.008 0.300 0.224 0.420 0.004
#> GSM11901 4 0.7428 0.3047 0.064 0.016 0.272 0.396 0.248 0.004
#> GSM11715 5 0.5622 0.4221 0.048 0.388 0.024 0.016 0.524 0.000
#> GSM11724 5 0.5613 0.4421 0.044 0.376 0.028 0.016 0.536 0.000
#> GSM11684 4 0.6080 0.3802 0.048 0.328 0.036 0.548 0.040 0.000
#> GSM11696 4 0.7584 0.4643 0.084 0.224 0.196 0.452 0.044 0.000
#> GSM27952 4 0.2544 0.6627 0.140 0.004 0.000 0.852 0.000 0.004
#> GSM27948 4 0.3667 0.6889 0.088 0.004 0.056 0.824 0.028 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 cell.line(p) agent(p) time(p) k
#> MAD:NMF 75 8.35e-07 0.569 2.12e-01 2
#> MAD:NMF 74 1.64e-06 0.571 7.03e-05 3
#> MAD:NMF 69 6.52e-06 0.150 3.06e-06 4
#> MAD:NMF 66 4.65e-10 0.158 3.40e-05 5
#> MAD:NMF 45 1.64e-09 0.277 9.10e-06 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 14502 rows and 83 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.461 0.788 0.896 0.4139 0.584 0.584
#> 3 3 0.321 0.417 0.718 0.3963 0.918 0.865
#> 4 4 0.493 0.573 0.720 0.2350 0.619 0.362
#> 5 5 0.635 0.592 0.754 0.0848 0.944 0.800
#> 6 6 0.669 0.640 0.740 0.0461 0.875 0.525
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM11708 1 0.0938 0.8831 0.988 0.012
#> GSM11735 1 0.0938 0.8831 0.988 0.012
#> GSM11733 1 0.8555 0.6022 0.720 0.280
#> GSM11863 2 0.8813 0.6630 0.300 0.700
#> GSM11710 1 0.0938 0.8831 0.988 0.012
#> GSM11712 2 0.8813 0.6630 0.300 0.700
#> GSM11732 1 0.9580 0.3858 0.620 0.380
#> GSM11844 1 0.9580 0.3858 0.620 0.380
#> GSM11842 2 0.6531 0.8229 0.168 0.832
#> GSM11860 2 0.7299 0.7907 0.204 0.796
#> GSM11686 1 0.0938 0.8831 0.988 0.012
#> GSM11688 1 0.0938 0.8831 0.988 0.012
#> GSM11846 1 0.1843 0.8867 0.972 0.028
#> GSM11680 1 0.0000 0.8862 1.000 0.000
#> GSM11698 1 0.1633 0.8866 0.976 0.024
#> GSM11840 1 0.8608 0.5951 0.716 0.284
#> GSM11847 1 0.8608 0.5951 0.716 0.284
#> GSM11685 1 0.0938 0.8831 0.988 0.012
#> GSM11699 1 0.1843 0.8861 0.972 0.028
#> GSM27950 1 0.0938 0.8831 0.988 0.012
#> GSM27946 1 0.2043 0.8854 0.968 0.032
#> GSM11709 1 0.1414 0.8876 0.980 0.020
#> GSM11720 1 0.5946 0.7879 0.856 0.144
#> GSM11726 1 0.5946 0.7879 0.856 0.144
#> GSM11837 2 0.3733 0.8533 0.072 0.928
#> GSM11725 2 0.0938 0.8482 0.012 0.988
#> GSM11864 2 0.0938 0.8482 0.012 0.988
#> GSM11687 1 0.1414 0.8876 0.980 0.020
#> GSM11693 1 0.1414 0.8876 0.980 0.020
#> GSM11727 2 0.5946 0.8375 0.144 0.856
#> GSM11838 2 0.0938 0.8482 0.012 0.988
#> GSM11681 1 0.1184 0.8876 0.984 0.016
#> GSM11689 1 0.1414 0.8876 0.980 0.020
#> GSM11704 1 0.1414 0.8876 0.980 0.020
#> GSM11703 1 0.1633 0.8869 0.976 0.024
#> GSM11705 1 0.1633 0.8869 0.976 0.024
#> GSM11722 1 0.9944 0.0763 0.544 0.456
#> GSM11730 1 0.9944 0.0763 0.544 0.456
#> GSM11713 1 0.1184 0.8876 0.984 0.016
#> GSM11728 1 0.1184 0.8876 0.984 0.016
#> GSM27947 1 0.2043 0.8854 0.968 0.032
#> GSM27951 1 0.1414 0.8876 0.980 0.020
#> GSM11707 1 0.0938 0.8831 0.988 0.012
#> GSM11716 2 0.8016 0.7404 0.244 0.756
#> GSM11850 1 0.5059 0.8355 0.888 0.112
#> GSM11851 1 0.2236 0.8842 0.964 0.036
#> GSM11721 1 0.9393 0.4410 0.644 0.356
#> GSM11852 1 0.2043 0.8856 0.968 0.032
#> GSM11694 1 0.0376 0.8869 0.996 0.004
#> GSM11695 1 0.0376 0.8869 0.996 0.004
#> GSM11734 2 0.0938 0.8482 0.012 0.988
#> GSM11861 1 0.9393 0.4410 0.644 0.356
#> GSM11843 2 0.2423 0.8522 0.040 0.960
#> GSM11862 1 0.9393 0.4410 0.644 0.356
#> GSM11697 1 0.0000 0.8862 1.000 0.000
#> GSM11714 1 0.0938 0.8831 0.988 0.012
#> GSM11723 2 0.5178 0.8486 0.116 0.884
#> GSM11845 2 0.5178 0.8486 0.116 0.884
#> GSM11683 1 0.2043 0.8852 0.968 0.032
#> GSM11691 1 0.1633 0.8870 0.976 0.024
#> GSM27949 1 0.0938 0.8831 0.988 0.012
#> GSM27945 1 0.2043 0.8854 0.968 0.032
#> GSM11706 1 0.0938 0.8831 0.988 0.012
#> GSM11853 1 0.2043 0.8856 0.968 0.032
#> GSM11729 2 0.0938 0.8482 0.012 0.988
#> GSM11746 2 0.0938 0.8482 0.012 0.988
#> GSM11711 1 0.2043 0.8856 0.968 0.032
#> GSM11854 1 0.2043 0.8856 0.968 0.032
#> GSM11731 2 0.0938 0.8482 0.012 0.988
#> GSM11839 2 0.5519 0.8458 0.128 0.872
#> GSM11836 2 0.6048 0.8363 0.148 0.852
#> GSM11849 1 0.6048 0.7880 0.852 0.148
#> GSM11682 1 0.0938 0.8831 0.988 0.012
#> GSM11690 1 0.6148 0.7889 0.848 0.152
#> GSM11692 2 0.9977 0.1649 0.472 0.528
#> GSM11841 2 0.8813 0.6630 0.300 0.700
#> GSM11901 2 0.8813 0.6630 0.300 0.700
#> GSM11715 2 0.0938 0.8482 0.012 0.988
#> GSM11724 2 0.0938 0.8482 0.012 0.988
#> GSM11684 1 0.5519 0.8082 0.872 0.128
#> GSM11696 1 0.5519 0.8082 0.872 0.128
#> GSM27952 1 0.0938 0.8831 0.988 0.012
#> GSM27948 1 0.6887 0.7490 0.816 0.184
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM11708 1 0.5706 0.511765 0.680 0.000 0.320
#> GSM11735 1 0.5706 0.511765 0.680 0.000 0.320
#> GSM11733 1 0.5678 0.233355 0.684 0.000 0.316
#> GSM11863 3 0.9894 0.610660 0.264 0.356 0.380
#> GSM11710 1 0.5706 0.521823 0.680 0.000 0.320
#> GSM11712 3 0.9894 0.610660 0.264 0.356 0.380
#> GSM11732 1 0.7676 -0.050157 0.584 0.056 0.360
#> GSM11844 1 0.7676 -0.050157 0.584 0.056 0.360
#> GSM11842 2 0.9130 -0.146850 0.152 0.492 0.356
#> GSM11860 2 0.9442 -0.269044 0.184 0.456 0.360
#> GSM11686 1 0.5733 0.512204 0.676 0.000 0.324
#> GSM11688 1 0.5733 0.512204 0.676 0.000 0.324
#> GSM11846 1 0.2711 0.611546 0.912 0.000 0.088
#> GSM11680 1 0.2165 0.617420 0.936 0.000 0.064
#> GSM11698 1 0.1163 0.618979 0.972 0.000 0.028
#> GSM11840 1 0.5902 0.224732 0.680 0.004 0.316
#> GSM11847 1 0.5902 0.224732 0.680 0.004 0.316
#> GSM11685 1 0.5733 0.512204 0.676 0.000 0.324
#> GSM11699 1 0.0892 0.617772 0.980 0.000 0.020
#> GSM27950 1 0.5706 0.511765 0.680 0.000 0.320
#> GSM27946 1 0.1031 0.616872 0.976 0.000 0.024
#> GSM11709 1 0.5968 0.425046 0.636 0.000 0.364
#> GSM11720 1 0.8610 0.264017 0.548 0.116 0.336
#> GSM11726 1 0.8610 0.264017 0.548 0.116 0.336
#> GSM11837 2 0.5117 0.520135 0.060 0.832 0.108
#> GSM11725 2 0.0000 0.625647 0.000 1.000 0.000
#> GSM11864 2 0.0000 0.625647 0.000 1.000 0.000
#> GSM11687 1 0.5968 0.425046 0.636 0.000 0.364
#> GSM11693 1 0.5968 0.425046 0.636 0.000 0.364
#> GSM11727 2 0.6936 0.356917 0.108 0.732 0.160
#> GSM11838 2 0.0000 0.625647 0.000 1.000 0.000
#> GSM11681 1 0.6045 0.429074 0.620 0.000 0.380
#> GSM11689 1 0.5968 0.425046 0.636 0.000 0.364
#> GSM11704 1 0.5968 0.425046 0.636 0.000 0.364
#> GSM11703 1 0.6148 0.426734 0.640 0.004 0.356
#> GSM11705 1 0.6148 0.426734 0.640 0.004 0.356
#> GSM11722 3 0.9951 0.375098 0.296 0.324 0.380
#> GSM11730 3 0.9951 0.375098 0.296 0.324 0.380
#> GSM11713 1 0.5835 0.452004 0.660 0.000 0.340
#> GSM11728 1 0.5835 0.452004 0.660 0.000 0.340
#> GSM27947 1 0.1031 0.616872 0.976 0.000 0.024
#> GSM27951 1 0.5968 0.425046 0.636 0.000 0.364
#> GSM11707 1 0.5706 0.511765 0.680 0.000 0.320
#> GSM11716 2 0.9714 -0.503339 0.224 0.420 0.356
#> GSM11850 1 0.3875 0.570094 0.888 0.044 0.068
#> GSM11851 1 0.1411 0.615007 0.964 0.000 0.036
#> GSM11721 1 0.7339 -0.026827 0.572 0.036 0.392
#> GSM11852 1 0.1529 0.617467 0.960 0.000 0.040
#> GSM11694 1 0.0747 0.621325 0.984 0.000 0.016
#> GSM11695 1 0.0747 0.621325 0.984 0.000 0.016
#> GSM11734 2 0.0000 0.625647 0.000 1.000 0.000
#> GSM11861 1 0.7339 -0.026827 0.572 0.036 0.392
#> GSM11843 2 0.6608 0.317584 0.016 0.628 0.356
#> GSM11862 1 0.7339 -0.026827 0.572 0.036 0.392
#> GSM11697 1 0.1031 0.621375 0.976 0.000 0.024
#> GSM11714 1 0.5706 0.511765 0.680 0.000 0.320
#> GSM11723 2 0.8457 0.080121 0.100 0.544 0.356
#> GSM11845 2 0.8457 0.080121 0.100 0.544 0.356
#> GSM11683 1 0.4931 0.563649 0.768 0.000 0.232
#> GSM11691 1 0.0892 0.619658 0.980 0.000 0.020
#> GSM27949 1 0.5291 0.538368 0.732 0.000 0.268
#> GSM27945 1 0.1031 0.616872 0.976 0.000 0.024
#> GSM11706 1 0.5706 0.511765 0.680 0.000 0.320
#> GSM11853 1 0.1529 0.617467 0.960 0.000 0.040
#> GSM11729 2 0.0000 0.625647 0.000 1.000 0.000
#> GSM11746 2 0.0000 0.625647 0.000 1.000 0.000
#> GSM11711 1 0.1529 0.617467 0.960 0.000 0.040
#> GSM11854 1 0.1529 0.617467 0.960 0.000 0.040
#> GSM11731 2 0.0000 0.625647 0.000 1.000 0.000
#> GSM11839 2 0.8346 0.093674 0.092 0.548 0.360
#> GSM11836 2 0.8649 0.000203 0.112 0.528 0.360
#> GSM11849 1 0.4974 0.456582 0.764 0.000 0.236
#> GSM11682 1 0.5859 0.514436 0.656 0.000 0.344
#> GSM11690 1 0.5327 0.453525 0.728 0.000 0.272
#> GSM11692 1 0.9520 -0.518219 0.416 0.188 0.396
#> GSM11841 3 0.9894 0.610660 0.264 0.356 0.380
#> GSM11901 3 0.9894 0.610660 0.264 0.356 0.380
#> GSM11715 2 0.0000 0.625647 0.000 1.000 0.000
#> GSM11724 2 0.0000 0.625647 0.000 1.000 0.000
#> GSM11684 1 0.4750 0.484854 0.784 0.000 0.216
#> GSM11696 1 0.4750 0.484854 0.784 0.000 0.216
#> GSM27952 1 0.5706 0.514785 0.680 0.000 0.320
#> GSM27948 1 0.6025 0.403145 0.740 0.028 0.232
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM11708 3 0.0000 0.6847 0.000 0.000 1.000 0.000
#> GSM11735 3 0.0000 0.6847 0.000 0.000 1.000 0.000
#> GSM11733 4 0.4671 0.3675 0.028 0.000 0.220 0.752
#> GSM11863 4 0.4277 0.3134 0.000 0.280 0.000 0.720
#> GSM11710 3 0.2944 0.6451 0.004 0.000 0.868 0.128
#> GSM11712 4 0.4277 0.3134 0.000 0.280 0.000 0.720
#> GSM11732 4 0.3577 0.4869 0.000 0.012 0.156 0.832
#> GSM11844 4 0.3577 0.4869 0.000 0.012 0.156 0.832
#> GSM11842 4 0.5337 0.0715 0.012 0.424 0.000 0.564
#> GSM11860 4 0.6306 0.1425 0.064 0.392 0.000 0.544
#> GSM11686 3 0.2281 0.6472 0.000 0.000 0.904 0.096
#> GSM11688 3 0.2281 0.6472 0.000 0.000 0.904 0.096
#> GSM11846 3 0.7325 0.5760 0.208 0.000 0.528 0.264
#> GSM11680 3 0.5633 0.7153 0.100 0.000 0.716 0.184
#> GSM11698 3 0.6377 0.6988 0.112 0.000 0.632 0.256
#> GSM11840 4 0.5397 0.3322 0.064 0.000 0.220 0.716
#> GSM11847 4 0.5397 0.3322 0.064 0.000 0.220 0.716
#> GSM11685 3 0.2281 0.6472 0.000 0.000 0.904 0.096
#> GSM11699 3 0.6477 0.6920 0.116 0.000 0.620 0.264
#> GSM27950 3 0.0188 0.6855 0.000 0.000 0.996 0.004
#> GSM27946 3 0.6422 0.6872 0.104 0.000 0.616 0.280
#> GSM11709 1 0.0000 0.8679 1.000 0.000 0.000 0.000
#> GSM11720 1 0.4426 0.7289 0.812 0.092 0.000 0.096
#> GSM11726 1 0.4426 0.7289 0.812 0.092 0.000 0.096
#> GSM11837 2 0.3649 0.6657 0.000 0.796 0.000 0.204
#> GSM11725 2 0.0000 0.8462 0.000 1.000 0.000 0.000
#> GSM11864 2 0.0000 0.8462 0.000 1.000 0.000 0.000
#> GSM11687 1 0.0000 0.8679 1.000 0.000 0.000 0.000
#> GSM11693 1 0.0000 0.8679 1.000 0.000 0.000 0.000
#> GSM11727 2 0.5657 0.5291 0.068 0.688 0.000 0.244
#> GSM11838 2 0.0000 0.8462 0.000 1.000 0.000 0.000
#> GSM11681 1 0.1356 0.8504 0.960 0.000 0.032 0.008
#> GSM11689 1 0.0000 0.8679 1.000 0.000 0.000 0.000
#> GSM11704 1 0.0000 0.8679 1.000 0.000 0.000 0.000
#> GSM11703 1 0.0376 0.8665 0.992 0.000 0.004 0.004
#> GSM11705 1 0.0376 0.8665 0.992 0.000 0.004 0.004
#> GSM11722 1 0.7622 0.1954 0.472 0.280 0.000 0.248
#> GSM11730 1 0.7622 0.1954 0.472 0.280 0.000 0.248
#> GSM11713 1 0.1624 0.8405 0.952 0.000 0.028 0.020
#> GSM11728 1 0.1624 0.8405 0.952 0.000 0.028 0.020
#> GSM27947 3 0.6422 0.6872 0.104 0.000 0.616 0.280
#> GSM27951 1 0.0000 0.8679 1.000 0.000 0.000 0.000
#> GSM11707 3 0.0000 0.6847 0.000 0.000 1.000 0.000
#> GSM11716 4 0.5428 0.1480 0.004 0.360 0.016 0.620
#> GSM11850 3 0.6502 0.5144 0.048 0.012 0.528 0.412
#> GSM11851 3 0.6240 0.6624 0.076 0.000 0.604 0.320
#> GSM11721 4 0.4957 0.4379 0.112 0.000 0.112 0.776
#> GSM11852 3 0.6477 0.6768 0.100 0.000 0.600 0.300
#> GSM11694 3 0.6198 0.7093 0.116 0.000 0.660 0.224
#> GSM11695 3 0.6198 0.7093 0.116 0.000 0.660 0.224
#> GSM11734 2 0.0000 0.8462 0.000 1.000 0.000 0.000
#> GSM11861 4 0.5012 0.4369 0.116 0.000 0.112 0.772
#> GSM11843 2 0.4898 0.2528 0.000 0.584 0.000 0.416
#> GSM11862 4 0.5012 0.4369 0.116 0.000 0.112 0.772
#> GSM11697 3 0.6083 0.7111 0.112 0.000 0.672 0.216
#> GSM11714 3 0.0000 0.6847 0.000 0.000 1.000 0.000
#> GSM11723 4 0.4996 -0.1049 0.000 0.484 0.000 0.516
#> GSM11845 4 0.4996 -0.1049 0.000 0.484 0.000 0.516
#> GSM11683 3 0.3734 0.6871 0.108 0.000 0.848 0.044
#> GSM11691 3 0.6373 0.7011 0.116 0.000 0.636 0.248
#> GSM27949 3 0.1940 0.7022 0.000 0.000 0.924 0.076
#> GSM27945 3 0.6422 0.6872 0.104 0.000 0.616 0.280
#> GSM11706 3 0.2216 0.6491 0.000 0.000 0.908 0.092
#> GSM11853 3 0.6477 0.6768 0.100 0.000 0.600 0.300
#> GSM11729 2 0.0000 0.8462 0.000 1.000 0.000 0.000
#> GSM11746 2 0.0000 0.8462 0.000 1.000 0.000 0.000
#> GSM11711 3 0.6477 0.6768 0.100 0.000 0.600 0.300
#> GSM11854 3 0.6477 0.6768 0.100 0.000 0.600 0.300
#> GSM11731 2 0.0000 0.8462 0.000 1.000 0.000 0.000
#> GSM11839 2 0.5697 0.0287 0.024 0.488 0.000 0.488
#> GSM11836 4 0.5688 -0.0615 0.024 0.464 0.000 0.512
#> GSM11849 4 0.7106 0.2403 0.324 0.000 0.148 0.528
#> GSM11682 3 0.3166 0.6306 0.016 0.000 0.868 0.116
#> GSM11690 4 0.7443 0.2263 0.312 0.000 0.196 0.492
#> GSM11692 4 0.4734 0.4930 0.072 0.128 0.004 0.796
#> GSM11841 4 0.4277 0.3134 0.000 0.280 0.000 0.720
#> GSM11901 4 0.4277 0.3134 0.000 0.280 0.000 0.720
#> GSM11715 2 0.0000 0.8462 0.000 1.000 0.000 0.000
#> GSM11724 2 0.0000 0.8462 0.000 1.000 0.000 0.000
#> GSM11684 4 0.7207 0.2090 0.376 0.000 0.144 0.480
#> GSM11696 4 0.7207 0.2090 0.376 0.000 0.144 0.480
#> GSM27952 3 0.2466 0.6474 0.004 0.000 0.900 0.096
#> GSM27948 4 0.6729 0.2965 0.312 0.000 0.116 0.572
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM11708 3 0.0162 0.571 0.000 0.000 0.996 0.000 0.004
#> GSM11735 3 0.0162 0.571 0.000 0.000 0.996 0.000 0.004
#> GSM11733 5 0.6392 -0.131 0.000 0.000 0.176 0.356 0.468
#> GSM11863 5 0.2069 0.621 0.000 0.012 0.000 0.076 0.912
#> GSM11710 3 0.3607 0.423 0.000 0.000 0.752 0.244 0.004
#> GSM11712 5 0.3242 0.632 0.000 0.012 0.000 0.172 0.816
#> GSM11732 5 0.5365 0.177 0.000 0.000 0.116 0.228 0.656
#> GSM11844 5 0.5365 0.177 0.000 0.000 0.116 0.228 0.656
#> GSM11842 5 0.5917 0.613 0.000 0.180 0.000 0.224 0.596
#> GSM11860 5 0.6735 0.569 0.020 0.176 0.000 0.288 0.516
#> GSM11686 3 0.3333 0.440 0.000 0.000 0.788 0.208 0.004
#> GSM11688 3 0.3333 0.440 0.000 0.000 0.788 0.208 0.004
#> GSM11846 3 0.6991 0.447 0.148 0.000 0.492 0.320 0.040
#> GSM11680 3 0.4577 0.602 0.024 0.000 0.676 0.296 0.004
#> GSM11698 3 0.5161 0.586 0.024 0.000 0.568 0.396 0.012
#> GSM11840 4 0.6439 0.122 0.000 0.000 0.176 0.416 0.408
#> GSM11847 4 0.6439 0.122 0.000 0.000 0.176 0.416 0.408
#> GSM11685 3 0.3333 0.440 0.000 0.000 0.788 0.208 0.004
#> GSM11699 3 0.5270 0.578 0.024 0.000 0.556 0.404 0.016
#> GSM27950 3 0.0510 0.576 0.000 0.000 0.984 0.016 0.000
#> GSM27946 3 0.5121 0.574 0.012 0.000 0.552 0.416 0.020
#> GSM11709 1 0.0162 0.865 0.996 0.000 0.000 0.004 0.000
#> GSM11720 1 0.3556 0.741 0.808 0.020 0.000 0.004 0.168
#> GSM11726 1 0.3556 0.741 0.808 0.020 0.000 0.004 0.168
#> GSM11837 2 0.4030 0.407 0.000 0.648 0.000 0.000 0.352
#> GSM11725 2 0.0000 0.904 0.000 1.000 0.000 0.000 0.000
#> GSM11864 2 0.0000 0.904 0.000 1.000 0.000 0.000 0.000
#> GSM11687 1 0.0162 0.865 0.996 0.000 0.000 0.004 0.000
#> GSM11693 1 0.0162 0.865 0.996 0.000 0.000 0.004 0.000
#> GSM11727 2 0.6795 0.151 0.048 0.524 0.000 0.112 0.316
#> GSM11838 2 0.0000 0.904 0.000 1.000 0.000 0.000 0.000
#> GSM11681 1 0.1564 0.844 0.948 0.000 0.024 0.024 0.004
#> GSM11689 1 0.0162 0.865 0.996 0.000 0.000 0.004 0.000
#> GSM11704 1 0.0162 0.865 0.996 0.000 0.000 0.004 0.000
#> GSM11703 1 0.0566 0.862 0.984 0.000 0.000 0.012 0.004
#> GSM11705 1 0.0566 0.862 0.984 0.000 0.000 0.012 0.004
#> GSM11722 1 0.7572 0.206 0.452 0.116 0.000 0.112 0.320
#> GSM11730 1 0.7572 0.206 0.452 0.116 0.000 0.112 0.320
#> GSM11713 1 0.1628 0.835 0.936 0.000 0.008 0.056 0.000
#> GSM11728 1 0.1628 0.835 0.936 0.000 0.008 0.056 0.000
#> GSM27947 3 0.5121 0.574 0.012 0.000 0.552 0.416 0.020
#> GSM27951 1 0.0162 0.862 0.996 0.000 0.000 0.000 0.004
#> GSM11707 3 0.0162 0.571 0.000 0.000 0.996 0.000 0.004
#> GSM11716 5 0.3222 0.596 0.004 0.104 0.012 0.020 0.860
#> GSM11850 3 0.6684 0.404 0.008 0.000 0.488 0.296 0.208
#> GSM11851 3 0.5718 0.551 0.008 0.000 0.544 0.380 0.068
#> GSM11721 4 0.2179 0.581 0.000 0.000 0.000 0.888 0.112
#> GSM11852 3 0.4855 0.562 0.004 0.000 0.544 0.436 0.016
#> GSM11694 3 0.4934 0.594 0.024 0.000 0.616 0.352 0.008
#> GSM11695 3 0.4934 0.594 0.024 0.000 0.616 0.352 0.008
#> GSM11734 2 0.0000 0.904 0.000 1.000 0.000 0.000 0.000
#> GSM11861 4 0.2020 0.591 0.000 0.000 0.000 0.900 0.100
#> GSM11843 5 0.6374 0.398 0.000 0.360 0.000 0.172 0.468
#> GSM11862 4 0.2020 0.591 0.000 0.000 0.000 0.900 0.100
#> GSM11697 3 0.4790 0.597 0.024 0.000 0.628 0.344 0.004
#> GSM11714 3 0.0162 0.571 0.000 0.000 0.996 0.000 0.004
#> GSM11723 5 0.3727 0.533 0.000 0.216 0.000 0.016 0.768
#> GSM11845 5 0.3727 0.533 0.000 0.216 0.000 0.016 0.768
#> GSM11683 3 0.3865 0.554 0.100 0.000 0.808 0.092 0.000
#> GSM11691 3 0.5152 0.588 0.024 0.000 0.572 0.392 0.012
#> GSM27949 3 0.2020 0.593 0.000 0.000 0.900 0.100 0.000
#> GSM27945 3 0.5121 0.574 0.012 0.000 0.552 0.416 0.020
#> GSM11706 3 0.3160 0.463 0.000 0.000 0.808 0.188 0.004
#> GSM11853 3 0.4855 0.562 0.004 0.000 0.544 0.436 0.016
#> GSM11729 2 0.0000 0.904 0.000 1.000 0.000 0.000 0.000
#> GSM11746 2 0.0000 0.904 0.000 1.000 0.000 0.000 0.000
#> GSM11711 3 0.4855 0.562 0.004 0.000 0.544 0.436 0.016
#> GSM11854 3 0.4855 0.562 0.004 0.000 0.544 0.436 0.016
#> GSM11731 2 0.0000 0.904 0.000 1.000 0.000 0.000 0.000
#> GSM11839 5 0.6523 0.489 0.000 0.232 0.000 0.288 0.480
#> GSM11836 5 0.6402 0.514 0.000 0.208 0.000 0.288 0.504
#> GSM11849 4 0.3843 0.684 0.184 0.000 0.012 0.788 0.016
#> GSM11682 3 0.3963 0.395 0.008 0.000 0.732 0.256 0.004
#> GSM11690 4 0.4709 0.659 0.176 0.000 0.060 0.748 0.016
#> GSM11692 5 0.4420 0.250 0.000 0.004 0.000 0.448 0.548
#> GSM11841 5 0.3242 0.632 0.000 0.012 0.000 0.172 0.816
#> GSM11901 5 0.3242 0.632 0.000 0.012 0.000 0.172 0.816
#> GSM11715 2 0.0000 0.904 0.000 1.000 0.000 0.000 0.000
#> GSM11724 2 0.0000 0.904 0.000 1.000 0.000 0.000 0.000
#> GSM11684 4 0.4153 0.656 0.236 0.000 0.008 0.740 0.016
#> GSM11696 4 0.4153 0.656 0.236 0.000 0.008 0.740 0.016
#> GSM27952 3 0.3489 0.439 0.004 0.000 0.784 0.208 0.004
#> GSM27948 4 0.4059 0.682 0.172 0.000 0.000 0.776 0.052
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM11708 6 0.3419 0.74208 0.000 0.000 0.084 0.104 0.000 0.812
#> GSM11735 6 0.3419 0.74208 0.000 0.000 0.084 0.104 0.000 0.812
#> GSM11733 3 0.4989 0.21532 0.000 0.000 0.640 0.092 0.260 0.008
#> GSM11863 5 0.2135 0.69573 0.000 0.000 0.128 0.000 0.872 0.000
#> GSM11710 6 0.1984 0.75468 0.000 0.000 0.056 0.032 0.000 0.912
#> GSM11712 5 0.0713 0.72580 0.000 0.000 0.028 0.000 0.972 0.000
#> GSM11732 3 0.5005 -0.00464 0.000 0.000 0.612 0.088 0.296 0.004
#> GSM11844 3 0.5005 -0.00464 0.000 0.000 0.612 0.088 0.296 0.004
#> GSM11842 5 0.3973 0.70122 0.000 0.048 0.028 0.140 0.784 0.000
#> GSM11860 5 0.5475 0.63229 0.020 0.048 0.092 0.148 0.692 0.000
#> GSM11686 6 0.1176 0.77813 0.000 0.000 0.020 0.024 0.000 0.956
#> GSM11688 6 0.1176 0.77813 0.000 0.000 0.020 0.024 0.000 0.956
#> GSM11846 3 0.5881 0.54368 0.140 0.000 0.572 0.032 0.000 0.256
#> GSM11680 3 0.4399 0.41969 0.000 0.000 0.516 0.024 0.000 0.460
#> GSM11698 3 0.4098 0.65687 0.000 0.000 0.676 0.032 0.000 0.292
#> GSM11840 3 0.4467 0.27604 0.000 0.000 0.696 0.060 0.236 0.008
#> GSM11847 3 0.4467 0.27604 0.000 0.000 0.696 0.060 0.236 0.008
#> GSM11685 6 0.1176 0.77813 0.000 0.000 0.020 0.024 0.000 0.956
#> GSM11699 3 0.4040 0.66355 0.000 0.000 0.688 0.032 0.000 0.280
#> GSM27950 6 0.2994 0.62050 0.000 0.000 0.208 0.004 0.000 0.788
#> GSM27946 3 0.3799 0.66990 0.000 0.000 0.704 0.020 0.000 0.276
#> GSM11709 1 0.0000 0.89492 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11720 1 0.3098 0.74723 0.812 0.000 0.000 0.024 0.164 0.000
#> GSM11726 1 0.3098 0.74723 0.812 0.000 0.000 0.024 0.164 0.000
#> GSM11837 2 0.5544 0.35135 0.000 0.608 0.092 0.036 0.264 0.000
#> GSM11725 2 0.0000 0.89093 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11864 2 0.1088 0.86164 0.000 0.960 0.000 0.016 0.024 0.000
#> GSM11687 1 0.0000 0.89492 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11693 1 0.0000 0.89492 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11727 2 0.6523 -0.03161 0.048 0.448 0.000 0.164 0.340 0.000
#> GSM11838 2 0.0146 0.88924 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM11681 1 0.2467 0.84722 0.884 0.000 0.012 0.088 0.000 0.016
#> GSM11689 1 0.0000 0.89492 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11704 1 0.0000 0.89492 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11703 1 0.0405 0.89195 0.988 0.000 0.008 0.000 0.004 0.000
#> GSM11705 1 0.0405 0.89195 0.988 0.000 0.008 0.000 0.004 0.000
#> GSM11722 4 0.6780 -0.11289 0.264 0.040 0.000 0.356 0.340 0.000
#> GSM11730 4 0.6780 -0.11289 0.264 0.040 0.000 0.356 0.340 0.000
#> GSM11713 1 0.3802 0.64189 0.676 0.000 0.012 0.312 0.000 0.000
#> GSM11728 1 0.3802 0.64189 0.676 0.000 0.012 0.312 0.000 0.000
#> GSM27947 3 0.3799 0.66990 0.000 0.000 0.704 0.020 0.000 0.276
#> GSM27951 1 0.0935 0.88447 0.964 0.000 0.004 0.032 0.000 0.000
#> GSM11707 6 0.3419 0.74208 0.000 0.000 0.084 0.104 0.000 0.812
#> GSM11716 5 0.5306 0.59651 0.004 0.024 0.276 0.072 0.624 0.000
#> GSM11850 3 0.6228 0.54686 0.000 0.000 0.552 0.064 0.128 0.256
#> GSM11851 3 0.4570 0.65055 0.000 0.000 0.672 0.048 0.012 0.268
#> GSM11721 4 0.7462 0.56682 0.000 0.000 0.204 0.384 0.240 0.172
#> GSM11852 3 0.4214 0.65739 0.000 0.000 0.680 0.044 0.000 0.276
#> GSM11694 3 0.4292 0.56697 0.000 0.000 0.588 0.024 0.000 0.388
#> GSM11695 3 0.4292 0.56697 0.000 0.000 0.588 0.024 0.000 0.388
#> GSM11734 2 0.0146 0.88848 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM11861 4 0.7416 0.57689 0.000 0.000 0.204 0.400 0.224 0.172
#> GSM11843 5 0.4503 0.59407 0.000 0.240 0.000 0.080 0.680 0.000
#> GSM11862 4 0.7416 0.57689 0.000 0.000 0.204 0.400 0.224 0.172
#> GSM11697 3 0.4319 0.54589 0.000 0.000 0.576 0.024 0.000 0.400
#> GSM11714 6 0.3419 0.74208 0.000 0.000 0.084 0.104 0.000 0.812
#> GSM11723 5 0.5786 0.66515 0.000 0.064 0.188 0.120 0.628 0.000
#> GSM11845 5 0.5786 0.66515 0.000 0.064 0.188 0.120 0.628 0.000
#> GSM11683 6 0.5763 0.31011 0.048 0.000 0.320 0.076 0.000 0.556
#> GSM11691 3 0.4011 0.64840 0.000 0.000 0.672 0.024 0.000 0.304
#> GSM27949 6 0.3499 0.36539 0.000 0.000 0.320 0.000 0.000 0.680
#> GSM27945 3 0.3717 0.66943 0.000 0.000 0.708 0.016 0.000 0.276
#> GSM11706 6 0.1719 0.77843 0.000 0.000 0.060 0.016 0.000 0.924
#> GSM11853 3 0.4214 0.65739 0.000 0.000 0.680 0.044 0.000 0.276
#> GSM11729 2 0.0000 0.89093 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11746 2 0.0000 0.89093 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11711 3 0.4214 0.65739 0.000 0.000 0.680 0.044 0.000 0.276
#> GSM11854 3 0.4214 0.65739 0.000 0.000 0.680 0.044 0.000 0.276
#> GSM11731 2 0.0000 0.89093 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11839 5 0.4770 0.61412 0.000 0.100 0.004 0.224 0.672 0.000
#> GSM11836 5 0.4560 0.62376 0.000 0.088 0.004 0.212 0.696 0.000
#> GSM11849 4 0.6009 0.68204 0.004 0.000 0.244 0.556 0.020 0.176
#> GSM11682 6 0.2199 0.73757 0.000 0.000 0.020 0.088 0.000 0.892
#> GSM11690 4 0.6070 0.67061 0.000 0.000 0.228 0.528 0.020 0.224
#> GSM11692 5 0.4662 0.36136 0.000 0.000 0.172 0.140 0.688 0.000
#> GSM11841 5 0.0713 0.72580 0.000 0.000 0.028 0.000 0.972 0.000
#> GSM11901 5 0.0713 0.72580 0.000 0.000 0.028 0.000 0.972 0.000
#> GSM11715 2 0.0000 0.89093 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11724 2 0.0000 0.89093 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11684 4 0.5302 0.67225 0.004 0.000 0.208 0.616 0.000 0.172
#> GSM11696 4 0.5302 0.67225 0.004 0.000 0.208 0.616 0.000 0.172
#> GSM27952 6 0.1257 0.77726 0.000 0.000 0.020 0.028 0.000 0.952
#> GSM27948 4 0.6290 0.67924 0.000 0.000 0.244 0.536 0.048 0.172
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.line(p) agent(p) time(p) k
#> ATC:hclust 75 4.01e-01 0.177 1.28e-04 2
#> ATC:hclust 45 2.35e-03 0.480 1.18e-03 3
#> ATC:hclust 55 1.29e-08 0.466 7.79e-05 4
#> ATC:hclust 62 2.67e-09 0.427 2.42e-04 5
#> ATC:hclust 70 6.65e-10 0.847 2.51e-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", "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 14502 rows and 83 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.966 0.987 0.4552 0.540 0.540
#> 3 3 0.487 0.542 0.717 0.3897 0.724 0.520
#> 4 4 0.692 0.777 0.871 0.1676 0.756 0.418
#> 5 5 0.677 0.643 0.795 0.0730 0.859 0.528
#> 6 6 0.722 0.673 0.783 0.0406 0.945 0.742
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM11708 1 0.000 0.996 1.000 0.000
#> GSM11735 1 0.000 0.996 1.000 0.000
#> GSM11733 1 0.000 0.996 1.000 0.000
#> GSM11863 2 0.000 0.968 0.000 1.000
#> GSM11710 1 0.000 0.996 1.000 0.000
#> GSM11712 2 0.000 0.968 0.000 1.000
#> GSM11732 2 0.997 0.136 0.468 0.532
#> GSM11844 1 0.000 0.996 1.000 0.000
#> GSM11842 2 0.000 0.968 0.000 1.000
#> GSM11860 2 0.000 0.968 0.000 1.000
#> GSM11686 1 0.000 0.996 1.000 0.000
#> GSM11688 1 0.000 0.996 1.000 0.000
#> GSM11846 1 0.000 0.996 1.000 0.000
#> GSM11680 1 0.000 0.996 1.000 0.000
#> GSM11698 1 0.000 0.996 1.000 0.000
#> GSM11840 1 0.000 0.996 1.000 0.000
#> GSM11847 1 0.000 0.996 1.000 0.000
#> GSM11685 1 0.000 0.996 1.000 0.000
#> GSM11699 1 0.000 0.996 1.000 0.000
#> GSM27950 1 0.000 0.996 1.000 0.000
#> GSM27946 1 0.000 0.996 1.000 0.000
#> GSM11709 1 0.000 0.996 1.000 0.000
#> GSM11720 2 0.000 0.968 0.000 1.000
#> GSM11726 2 0.000 0.968 0.000 1.000
#> GSM11837 2 0.000 0.968 0.000 1.000
#> GSM11725 2 0.000 0.968 0.000 1.000
#> GSM11864 2 0.000 0.968 0.000 1.000
#> GSM11687 1 0.000 0.996 1.000 0.000
#> GSM11693 1 0.000 0.996 1.000 0.000
#> GSM11727 2 0.000 0.968 0.000 1.000
#> GSM11838 2 0.000 0.968 0.000 1.000
#> GSM11681 1 0.000 0.996 1.000 0.000
#> GSM11689 1 0.000 0.996 1.000 0.000
#> GSM11704 2 0.985 0.271 0.428 0.572
#> GSM11703 1 0.000 0.996 1.000 0.000
#> GSM11705 1 0.000 0.996 1.000 0.000
#> GSM11722 2 0.000 0.968 0.000 1.000
#> GSM11730 2 0.000 0.968 0.000 1.000
#> GSM11713 1 0.000 0.996 1.000 0.000
#> GSM11728 1 0.000 0.996 1.000 0.000
#> GSM27947 1 0.000 0.996 1.000 0.000
#> GSM27951 1 0.000 0.996 1.000 0.000
#> GSM11707 1 0.000 0.996 1.000 0.000
#> GSM11716 2 0.000 0.968 0.000 1.000
#> GSM11850 1 0.000 0.996 1.000 0.000
#> GSM11851 1 0.000 0.996 1.000 0.000
#> GSM11721 1 0.443 0.897 0.908 0.092
#> GSM11852 1 0.000 0.996 1.000 0.000
#> GSM11694 1 0.000 0.996 1.000 0.000
#> GSM11695 1 0.000 0.996 1.000 0.000
#> GSM11734 2 0.000 0.968 0.000 1.000
#> GSM11861 1 0.000 0.996 1.000 0.000
#> GSM11843 2 0.000 0.968 0.000 1.000
#> GSM11862 1 0.000 0.996 1.000 0.000
#> GSM11697 1 0.000 0.996 1.000 0.000
#> GSM11714 1 0.000 0.996 1.000 0.000
#> GSM11723 2 0.000 0.968 0.000 1.000
#> GSM11845 2 0.000 0.968 0.000 1.000
#> GSM11683 1 0.000 0.996 1.000 0.000
#> GSM11691 1 0.000 0.996 1.000 0.000
#> GSM27949 1 0.000 0.996 1.000 0.000
#> GSM27945 1 0.000 0.996 1.000 0.000
#> GSM11706 1 0.000 0.996 1.000 0.000
#> GSM11853 1 0.000 0.996 1.000 0.000
#> GSM11729 2 0.000 0.968 0.000 1.000
#> GSM11746 2 0.000 0.968 0.000 1.000
#> GSM11711 1 0.000 0.996 1.000 0.000
#> GSM11854 1 0.000 0.996 1.000 0.000
#> GSM11731 2 0.000 0.968 0.000 1.000
#> GSM11839 2 0.000 0.968 0.000 1.000
#> GSM11836 2 0.000 0.968 0.000 1.000
#> GSM11849 1 0.000 0.996 1.000 0.000
#> GSM11682 1 0.000 0.996 1.000 0.000
#> GSM11690 1 0.000 0.996 1.000 0.000
#> GSM11692 1 0.443 0.897 0.908 0.092
#> GSM11841 2 0.000 0.968 0.000 1.000
#> GSM11901 2 0.000 0.968 0.000 1.000
#> GSM11715 2 0.000 0.968 0.000 1.000
#> GSM11724 2 0.000 0.968 0.000 1.000
#> GSM11684 1 0.000 0.996 1.000 0.000
#> GSM11696 1 0.000 0.996 1.000 0.000
#> GSM27952 1 0.000 0.996 1.000 0.000
#> GSM27948 1 0.000 0.996 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM11708 3 0.4974 0.6562 0.236 0.000 0.764
#> GSM11735 3 0.4974 0.6562 0.236 0.000 0.764
#> GSM11733 1 0.3349 0.6221 0.888 0.004 0.108
#> GSM11863 2 0.5926 0.6008 0.356 0.644 0.000
#> GSM11710 3 0.5363 0.6269 0.276 0.000 0.724
#> GSM11712 2 0.5926 0.6008 0.356 0.644 0.000
#> GSM11732 1 0.6056 0.5768 0.744 0.032 0.224
#> GSM11844 1 0.5406 0.5858 0.764 0.012 0.224
#> GSM11842 2 0.5926 0.6008 0.356 0.644 0.000
#> GSM11860 1 0.6745 -0.0861 0.560 0.428 0.012
#> GSM11686 3 0.5216 0.6468 0.260 0.000 0.740
#> GSM11688 3 0.5216 0.6468 0.260 0.000 0.740
#> GSM11846 1 0.6008 0.3337 0.628 0.000 0.372
#> GSM11680 3 0.4974 0.6562 0.236 0.000 0.764
#> GSM11698 3 0.4974 0.6562 0.236 0.000 0.764
#> GSM11840 1 0.2866 0.6416 0.916 0.008 0.076
#> GSM11847 1 0.2866 0.6416 0.916 0.008 0.076
#> GSM11685 3 0.5216 0.6468 0.260 0.000 0.740
#> GSM11699 1 0.3267 0.6445 0.884 0.000 0.116
#> GSM27950 3 0.4974 0.6562 0.236 0.000 0.764
#> GSM27946 1 0.1529 0.6668 0.960 0.000 0.040
#> GSM11709 3 0.6931 -0.1283 0.456 0.016 0.528
#> GSM11720 2 0.4733 0.7456 0.004 0.800 0.196
#> GSM11726 1 0.9813 0.1842 0.424 0.316 0.260
#> GSM11837 2 0.1289 0.8455 0.000 0.968 0.032
#> GSM11725 2 0.1289 0.8455 0.000 0.968 0.032
#> GSM11864 2 0.1289 0.8455 0.000 0.968 0.032
#> GSM11687 3 0.6654 -0.1243 0.456 0.008 0.536
#> GSM11693 3 0.6931 -0.1283 0.456 0.016 0.528
#> GSM11727 2 0.4110 0.7786 0.004 0.844 0.152
#> GSM11838 2 0.1289 0.8455 0.000 0.968 0.032
#> GSM11681 3 0.5291 0.2857 0.268 0.000 0.732
#> GSM11689 3 0.6936 -0.1289 0.460 0.016 0.524
#> GSM11704 1 0.9520 0.1956 0.460 0.200 0.340
#> GSM11703 3 0.6676 -0.1548 0.476 0.008 0.516
#> GSM11705 3 0.6664 -0.1284 0.464 0.008 0.528
#> GSM11722 2 0.3879 0.7793 0.000 0.848 0.152
#> GSM11730 2 0.9757 -0.0481 0.384 0.388 0.228
#> GSM11713 1 0.6307 0.1308 0.512 0.000 0.488
#> GSM11728 1 0.6260 0.2018 0.552 0.000 0.448
#> GSM27947 1 0.4504 0.5867 0.804 0.000 0.196
#> GSM27951 3 0.6659 -0.1245 0.460 0.008 0.532
#> GSM11707 3 0.4974 0.6562 0.236 0.000 0.764
#> GSM11716 2 0.1989 0.8404 0.004 0.948 0.048
#> GSM11850 1 0.5591 0.4877 0.696 0.000 0.304
#> GSM11851 1 0.2711 0.6427 0.912 0.000 0.088
#> GSM11721 1 0.1643 0.6363 0.956 0.044 0.000
#> GSM11852 1 0.1643 0.6661 0.956 0.000 0.044
#> GSM11694 1 0.6140 0.2702 0.596 0.000 0.404
#> GSM11695 1 0.6225 0.1887 0.568 0.000 0.432
#> GSM11734 2 0.0424 0.8509 0.008 0.992 0.000
#> GSM11861 1 0.1163 0.6475 0.972 0.028 0.000
#> GSM11843 2 0.0424 0.8509 0.008 0.992 0.000
#> GSM11862 1 0.1289 0.6448 0.968 0.032 0.000
#> GSM11697 1 0.6225 0.1887 0.568 0.000 0.432
#> GSM11714 3 0.4974 0.6562 0.236 0.000 0.764
#> GSM11723 2 0.0424 0.8509 0.008 0.992 0.000
#> GSM11845 2 0.0424 0.8509 0.008 0.992 0.000
#> GSM11683 3 0.5178 0.6490 0.256 0.000 0.744
#> GSM11691 1 0.5785 0.3318 0.668 0.000 0.332
#> GSM27949 3 0.4887 0.6498 0.228 0.000 0.772
#> GSM27945 1 0.4750 0.5838 0.784 0.000 0.216
#> GSM11706 3 0.4974 0.6562 0.236 0.000 0.764
#> GSM11853 1 0.4974 0.5769 0.764 0.000 0.236
#> GSM11729 2 0.0000 0.8502 0.000 1.000 0.000
#> GSM11746 2 0.1289 0.8455 0.000 0.968 0.032
#> GSM11711 1 0.6008 0.3081 0.628 0.000 0.372
#> GSM11854 1 0.3482 0.6445 0.872 0.000 0.128
#> GSM11731 2 0.0424 0.8509 0.008 0.992 0.000
#> GSM11839 2 0.0592 0.8498 0.012 0.988 0.000
#> GSM11836 2 0.5926 0.6008 0.356 0.644 0.000
#> GSM11849 1 0.1289 0.6666 0.968 0.000 0.032
#> GSM11682 3 0.5733 0.5913 0.324 0.000 0.676
#> GSM11690 1 0.1411 0.6664 0.964 0.000 0.036
#> GSM11692 1 0.1643 0.6363 0.956 0.044 0.000
#> GSM11841 2 0.5926 0.6008 0.356 0.644 0.000
#> GSM11901 2 0.5948 0.5955 0.360 0.640 0.000
#> GSM11715 2 0.0424 0.8509 0.008 0.992 0.000
#> GSM11724 2 0.0424 0.8509 0.008 0.992 0.000
#> GSM11684 1 0.2066 0.6599 0.940 0.000 0.060
#> GSM11696 1 0.1964 0.6596 0.944 0.000 0.056
#> GSM27952 3 0.5216 0.6468 0.260 0.000 0.740
#> GSM27948 1 0.1031 0.6497 0.976 0.024 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM11708 3 0.0817 0.838 0.024 0.000 0.976 0.000
#> GSM11735 3 0.0707 0.837 0.020 0.000 0.980 0.000
#> GSM11733 4 0.2480 0.789 0.008 0.000 0.088 0.904
#> GSM11863 4 0.3625 0.731 0.012 0.160 0.000 0.828
#> GSM11710 3 0.2222 0.826 0.016 0.000 0.924 0.060
#> GSM11712 4 0.3895 0.707 0.012 0.184 0.000 0.804
#> GSM11732 4 0.7064 0.487 0.208 0.000 0.220 0.572
#> GSM11844 4 0.6640 0.554 0.168 0.000 0.208 0.624
#> GSM11842 4 0.4012 0.707 0.016 0.184 0.000 0.800
#> GSM11860 4 0.6193 0.634 0.180 0.148 0.000 0.672
#> GSM11686 3 0.1722 0.830 0.008 0.000 0.944 0.048
#> GSM11688 3 0.1722 0.830 0.008 0.000 0.944 0.048
#> GSM11846 1 0.6102 0.512 0.672 0.000 0.212 0.116
#> GSM11680 3 0.0895 0.838 0.020 0.000 0.976 0.004
#> GSM11698 3 0.1297 0.832 0.016 0.000 0.964 0.020
#> GSM11840 4 0.1545 0.801 0.008 0.000 0.040 0.952
#> GSM11847 4 0.1452 0.801 0.008 0.000 0.036 0.956
#> GSM11685 3 0.1807 0.829 0.008 0.000 0.940 0.052
#> GSM11699 4 0.2965 0.791 0.072 0.000 0.036 0.892
#> GSM27950 3 0.0592 0.838 0.016 0.000 0.984 0.000
#> GSM27946 4 0.2125 0.797 0.076 0.000 0.004 0.920
#> GSM11709 1 0.1109 0.925 0.968 0.000 0.004 0.028
#> GSM11720 1 0.4857 0.440 0.668 0.324 0.000 0.008
#> GSM11726 1 0.1339 0.911 0.964 0.008 0.004 0.024
#> GSM11837 2 0.0469 0.955 0.012 0.988 0.000 0.000
#> GSM11725 2 0.0336 0.955 0.008 0.992 0.000 0.000
#> GSM11864 2 0.0336 0.955 0.008 0.992 0.000 0.000
#> GSM11687 1 0.1109 0.925 0.968 0.000 0.004 0.028
#> GSM11693 1 0.1109 0.925 0.968 0.000 0.004 0.028
#> GSM11727 2 0.3545 0.815 0.164 0.828 0.000 0.008
#> GSM11838 2 0.0336 0.955 0.008 0.992 0.000 0.000
#> GSM11681 1 0.1637 0.884 0.940 0.000 0.060 0.000
#> GSM11689 1 0.1109 0.925 0.968 0.000 0.004 0.028
#> GSM11704 1 0.1004 0.924 0.972 0.000 0.004 0.024
#> GSM11703 1 0.1109 0.925 0.968 0.000 0.004 0.028
#> GSM11705 1 0.1109 0.925 0.968 0.000 0.004 0.028
#> GSM11722 2 0.3306 0.825 0.156 0.840 0.000 0.004
#> GSM11730 1 0.2124 0.890 0.932 0.040 0.000 0.028
#> GSM11713 1 0.2124 0.906 0.932 0.000 0.040 0.028
#> GSM11728 1 0.2751 0.895 0.904 0.000 0.040 0.056
#> GSM27947 4 0.5771 0.250 0.460 0.000 0.028 0.512
#> GSM27951 1 0.1004 0.924 0.972 0.000 0.004 0.024
#> GSM11707 3 0.0817 0.838 0.024 0.000 0.976 0.000
#> GSM11716 2 0.5032 0.648 0.220 0.744 0.016 0.020
#> GSM11850 4 0.7588 0.343 0.312 0.000 0.220 0.468
#> GSM11851 4 0.3806 0.731 0.020 0.000 0.156 0.824
#> GSM11721 4 0.0712 0.801 0.008 0.004 0.004 0.984
#> GSM11852 4 0.2402 0.796 0.076 0.000 0.012 0.912
#> GSM11694 3 0.7203 0.356 0.312 0.000 0.524 0.164
#> GSM11695 3 0.6993 0.408 0.296 0.000 0.556 0.148
#> GSM11734 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM11861 4 0.1191 0.803 0.024 0.004 0.004 0.968
#> GSM11843 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM11862 4 0.0844 0.802 0.012 0.004 0.004 0.980
#> GSM11697 3 0.6993 0.408 0.296 0.000 0.556 0.148
#> GSM11714 3 0.0707 0.838 0.020 0.000 0.980 0.000
#> GSM11723 2 0.0672 0.950 0.008 0.984 0.000 0.008
#> GSM11845 2 0.0672 0.950 0.008 0.984 0.000 0.008
#> GSM11683 3 0.1938 0.829 0.012 0.000 0.936 0.052
#> GSM11691 3 0.7218 0.374 0.316 0.000 0.520 0.164
#> GSM27949 3 0.1182 0.834 0.016 0.000 0.968 0.016
#> GSM27945 4 0.7253 0.404 0.308 0.000 0.172 0.520
#> GSM11706 3 0.0817 0.838 0.024 0.000 0.976 0.000
#> GSM11853 4 0.7099 0.462 0.280 0.000 0.168 0.552
#> GSM11729 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM11746 2 0.0336 0.955 0.008 0.992 0.000 0.000
#> GSM11711 3 0.7644 0.301 0.260 0.000 0.468 0.272
#> GSM11854 4 0.5011 0.706 0.076 0.000 0.160 0.764
#> GSM11731 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM11839 2 0.0927 0.946 0.008 0.976 0.000 0.016
#> GSM11836 4 0.3937 0.703 0.012 0.188 0.000 0.800
#> GSM11849 4 0.2708 0.795 0.076 0.004 0.016 0.904
#> GSM11682 3 0.2048 0.823 0.008 0.000 0.928 0.064
#> GSM11690 4 0.2708 0.795 0.076 0.004 0.016 0.904
#> GSM11692 4 0.0712 0.801 0.008 0.004 0.004 0.984
#> GSM11841 4 0.3852 0.710 0.012 0.180 0.000 0.808
#> GSM11901 4 0.3377 0.745 0.012 0.140 0.000 0.848
#> GSM11715 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM11724 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM11684 4 0.2658 0.794 0.080 0.004 0.012 0.904
#> GSM11696 4 0.2658 0.794 0.080 0.004 0.012 0.904
#> GSM27952 3 0.1970 0.826 0.008 0.000 0.932 0.060
#> GSM27948 4 0.0967 0.802 0.016 0.004 0.004 0.976
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM11708 4 0.2304 8.54e-01 0.000 0.000 0.100 0.892 0.008
#> GSM11735 4 0.2358 8.52e-01 0.000 0.000 0.104 0.888 0.008
#> GSM11733 5 0.4152 4.42e-01 0.000 0.000 0.296 0.012 0.692
#> GSM11863 5 0.0955 7.55e-01 0.000 0.028 0.004 0.000 0.968
#> GSM11710 4 0.2069 8.46e-01 0.000 0.000 0.076 0.912 0.012
#> GSM11712 5 0.0794 7.55e-01 0.000 0.028 0.000 0.000 0.972
#> GSM11732 3 0.5973 2.72e-01 0.020 0.004 0.516 0.052 0.408
#> GSM11844 3 0.5759 3.12e-01 0.020 0.004 0.568 0.044 0.364
#> GSM11842 5 0.0955 7.55e-01 0.000 0.028 0.004 0.000 0.968
#> GSM11860 5 0.4500 4.98e-01 0.040 0.020 0.180 0.000 0.760
#> GSM11686 4 0.1341 8.58e-01 0.000 0.000 0.056 0.944 0.000
#> GSM11688 4 0.1341 8.58e-01 0.000 0.000 0.056 0.944 0.000
#> GSM11846 3 0.5617 2.81e-01 0.424 0.000 0.516 0.048 0.012
#> GSM11680 4 0.4256 2.91e-01 0.000 0.000 0.436 0.564 0.000
#> GSM11698 3 0.4242 5.15e-02 0.000 0.000 0.572 0.428 0.000
#> GSM11840 5 0.2068 7.58e-01 0.000 0.000 0.092 0.004 0.904
#> GSM11847 5 0.2068 7.58e-01 0.000 0.000 0.092 0.004 0.904
#> GSM11685 4 0.1341 8.58e-01 0.000 0.000 0.056 0.944 0.000
#> GSM11699 3 0.6094 3.84e-02 0.024 0.000 0.516 0.068 0.392
#> GSM27950 4 0.2020 8.54e-01 0.000 0.000 0.100 0.900 0.000
#> GSM27946 5 0.5087 3.74e-01 0.028 0.000 0.376 0.008 0.588
#> GSM11709 1 0.0854 8.95e-01 0.976 0.000 0.012 0.004 0.008
#> GSM11720 1 0.5738 6.25e-01 0.696 0.160 0.080 0.000 0.064
#> GSM11726 1 0.3494 8.05e-01 0.848 0.012 0.084 0.000 0.056
#> GSM11837 2 0.2630 8.84e-01 0.016 0.892 0.080 0.000 0.012
#> GSM11725 2 0.0451 9.14e-01 0.004 0.988 0.008 0.000 0.000
#> GSM11864 2 0.0162 9.15e-01 0.000 0.996 0.004 0.000 0.000
#> GSM11687 1 0.0854 8.95e-01 0.976 0.000 0.012 0.004 0.008
#> GSM11693 1 0.0854 8.95e-01 0.976 0.000 0.012 0.004 0.008
#> GSM11727 2 0.6169 6.56e-01 0.200 0.648 0.088 0.000 0.064
#> GSM11838 2 0.0451 9.14e-01 0.004 0.988 0.008 0.000 0.000
#> GSM11681 1 0.1568 8.77e-01 0.944 0.000 0.036 0.020 0.000
#> GSM11689 1 0.0854 8.95e-01 0.976 0.000 0.012 0.004 0.008
#> GSM11704 1 0.0854 8.94e-01 0.976 0.004 0.012 0.000 0.008
#> GSM11703 1 0.0960 8.94e-01 0.972 0.000 0.016 0.004 0.008
#> GSM11705 1 0.0960 8.94e-01 0.972 0.000 0.016 0.004 0.008
#> GSM11722 2 0.5006 7.99e-01 0.104 0.760 0.084 0.000 0.052
#> GSM11730 1 0.4011 7.99e-01 0.808 0.012 0.124 0.000 0.056
#> GSM11713 1 0.3196 7.71e-01 0.804 0.000 0.192 0.004 0.000
#> GSM11728 1 0.4588 4.94e-01 0.604 0.000 0.380 0.016 0.000
#> GSM27947 3 0.6143 4.90e-01 0.272 0.000 0.584 0.012 0.132
#> GSM27951 1 0.0771 8.90e-01 0.976 0.000 0.020 0.004 0.000
#> GSM11707 4 0.2304 8.54e-01 0.000 0.000 0.100 0.892 0.008
#> GSM11716 3 0.8041 -6.64e-02 0.120 0.332 0.372 0.000 0.176
#> GSM11850 3 0.5937 5.38e-01 0.132 0.004 0.688 0.048 0.128
#> GSM11851 3 0.5126 3.51e-01 0.008 0.000 0.596 0.032 0.364
#> GSM11721 5 0.2561 7.53e-01 0.000 0.000 0.144 0.000 0.856
#> GSM11852 5 0.5804 2.32e-01 0.024 0.000 0.420 0.044 0.512
#> GSM11694 3 0.5885 5.11e-01 0.120 0.000 0.644 0.216 0.020
#> GSM11695 3 0.5771 4.99e-01 0.108 0.000 0.644 0.232 0.016
#> GSM11734 2 0.0290 9.15e-01 0.000 0.992 0.000 0.000 0.008
#> GSM11861 5 0.3461 6.89e-01 0.004 0.000 0.224 0.000 0.772
#> GSM11843 2 0.0510 9.15e-01 0.000 0.984 0.000 0.000 0.016
#> GSM11862 5 0.3074 7.21e-01 0.000 0.000 0.196 0.000 0.804
#> GSM11697 3 0.5771 4.99e-01 0.108 0.000 0.644 0.232 0.016
#> GSM11714 4 0.2304 8.54e-01 0.000 0.000 0.100 0.892 0.008
#> GSM11723 2 0.4237 8.38e-01 0.012 0.796 0.080 0.000 0.112
#> GSM11845 2 0.4498 8.23e-01 0.012 0.772 0.076 0.000 0.140
#> GSM11683 4 0.1792 8.47e-01 0.000 0.000 0.084 0.916 0.000
#> GSM11691 3 0.5557 5.19e-01 0.120 0.000 0.680 0.184 0.016
#> GSM27949 3 0.4291 6.58e-05 0.000 0.000 0.536 0.464 0.000
#> GSM27945 3 0.6424 5.17e-01 0.148 0.000 0.612 0.040 0.200
#> GSM11706 4 0.2411 8.53e-01 0.000 0.000 0.108 0.884 0.008
#> GSM11853 3 0.6390 4.97e-01 0.120 0.000 0.604 0.040 0.236
#> GSM11729 2 0.0162 9.15e-01 0.000 0.996 0.000 0.000 0.004
#> GSM11746 2 0.0451 9.14e-01 0.004 0.988 0.008 0.000 0.000
#> GSM11711 3 0.5793 5.49e-01 0.072 0.000 0.688 0.172 0.068
#> GSM11854 3 0.5319 4.08e-01 0.024 0.000 0.640 0.036 0.300
#> GSM11731 2 0.0290 9.15e-01 0.000 0.992 0.000 0.000 0.008
#> GSM11839 2 0.4339 8.16e-01 0.012 0.772 0.048 0.000 0.168
#> GSM11836 5 0.1668 7.33e-01 0.000 0.028 0.032 0.000 0.940
#> GSM11849 3 0.5845 -2.14e-01 0.032 0.000 0.484 0.036 0.448
#> GSM11682 4 0.3628 7.04e-01 0.012 0.000 0.216 0.772 0.000
#> GSM11690 3 0.6186 -1.69e-01 0.036 0.000 0.488 0.056 0.420
#> GSM11692 5 0.2471 7.55e-01 0.000 0.000 0.136 0.000 0.864
#> GSM11841 5 0.0794 7.55e-01 0.000 0.028 0.000 0.000 0.972
#> GSM11901 5 0.0703 7.57e-01 0.000 0.024 0.000 0.000 0.976
#> GSM11715 2 0.0290 9.15e-01 0.000 0.992 0.000 0.000 0.008
#> GSM11724 2 0.0671 9.15e-01 0.000 0.980 0.004 0.000 0.016
#> GSM11684 3 0.6173 -1.62e-01 0.036 0.000 0.500 0.056 0.408
#> GSM11696 3 0.6173 -1.62e-01 0.036 0.000 0.500 0.056 0.408
#> GSM27952 4 0.1792 8.42e-01 0.000 0.000 0.084 0.916 0.000
#> GSM27948 5 0.3835 6.50e-01 0.000 0.000 0.260 0.008 0.732
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM11708 6 0.1908 0.810 0.000 0.000 0.096 0.000 0.004 0.900
#> GSM11735 6 0.1908 0.810 0.000 0.000 0.096 0.000 0.004 0.900
#> GSM11733 5 0.5081 0.252 0.000 0.000 0.376 0.064 0.552 0.008
#> GSM11863 5 0.1630 0.715 0.000 0.016 0.020 0.024 0.940 0.000
#> GSM11710 6 0.3718 0.795 0.000 0.000 0.052 0.164 0.004 0.780
#> GSM11712 5 0.0603 0.721 0.000 0.016 0.004 0.000 0.980 0.000
#> GSM11732 3 0.5748 0.510 0.012 0.000 0.616 0.116 0.232 0.024
#> GSM11844 3 0.5075 0.585 0.008 0.000 0.688 0.080 0.200 0.024
#> GSM11842 5 0.1173 0.719 0.000 0.016 0.016 0.008 0.960 0.000
#> GSM11860 5 0.4725 0.586 0.036 0.012 0.132 0.072 0.748 0.000
#> GSM11686 6 0.3419 0.806 0.000 0.000 0.028 0.176 0.004 0.792
#> GSM11688 6 0.3419 0.806 0.000 0.000 0.028 0.176 0.004 0.792
#> GSM11846 3 0.3711 0.589 0.260 0.000 0.720 0.020 0.000 0.000
#> GSM11680 3 0.3731 0.595 0.000 0.000 0.736 0.020 0.004 0.240
#> GSM11698 3 0.3650 0.618 0.000 0.000 0.756 0.024 0.004 0.216
#> GSM11840 5 0.3513 0.671 0.000 0.000 0.144 0.060 0.796 0.000
#> GSM11847 5 0.3513 0.671 0.000 0.000 0.144 0.060 0.796 0.000
#> GSM11685 6 0.3419 0.806 0.000 0.000 0.028 0.176 0.004 0.792
#> GSM11699 3 0.5426 0.278 0.000 0.000 0.656 0.160 0.148 0.036
#> GSM27950 6 0.2356 0.811 0.000 0.000 0.096 0.016 0.004 0.884
#> GSM27946 3 0.5505 0.134 0.008 0.000 0.604 0.120 0.260 0.008
#> GSM11709 1 0.0000 0.869 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11720 1 0.5612 0.633 0.668 0.072 0.032 0.192 0.036 0.000
#> GSM11726 1 0.4638 0.696 0.732 0.020 0.032 0.188 0.028 0.000
#> GSM11837 2 0.3866 0.785 0.000 0.764 0.036 0.188 0.012 0.000
#> GSM11725 2 0.1010 0.847 0.000 0.960 0.004 0.036 0.000 0.000
#> GSM11864 2 0.0935 0.848 0.000 0.964 0.004 0.032 0.000 0.000
#> GSM11687 1 0.0146 0.868 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM11693 1 0.0146 0.868 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM11727 2 0.6846 0.545 0.188 0.520 0.036 0.220 0.036 0.000
#> GSM11838 2 0.0622 0.847 0.000 0.980 0.008 0.012 0.000 0.000
#> GSM11681 1 0.1434 0.845 0.940 0.000 0.000 0.048 0.000 0.012
#> GSM11689 1 0.0146 0.869 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM11704 1 0.0146 0.869 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM11703 1 0.0291 0.868 0.992 0.000 0.004 0.004 0.000 0.000
#> GSM11705 1 0.0603 0.866 0.980 0.000 0.004 0.016 0.000 0.000
#> GSM11722 2 0.5841 0.705 0.076 0.636 0.036 0.220 0.032 0.000
#> GSM11730 1 0.4851 0.609 0.608 0.000 0.028 0.336 0.028 0.000
#> GSM11713 1 0.4473 0.378 0.576 0.000 0.008 0.396 0.000 0.020
#> GSM11728 4 0.5978 0.347 0.292 0.000 0.152 0.532 0.000 0.024
#> GSM27947 3 0.3646 0.659 0.132 0.000 0.800 0.008 0.060 0.000
#> GSM27951 1 0.0790 0.859 0.968 0.000 0.000 0.032 0.000 0.000
#> GSM11707 6 0.1908 0.810 0.000 0.000 0.096 0.000 0.004 0.900
#> GSM11716 3 0.7907 0.250 0.056 0.160 0.436 0.212 0.136 0.000
#> GSM11850 3 0.4477 0.674 0.064 0.000 0.784 0.076 0.056 0.020
#> GSM11851 3 0.3513 0.634 0.000 0.000 0.796 0.060 0.144 0.000
#> GSM11721 5 0.4218 0.593 0.000 0.000 0.112 0.136 0.748 0.004
#> GSM11852 3 0.6589 -0.416 0.000 0.000 0.444 0.264 0.256 0.036
#> GSM11694 3 0.3301 0.685 0.068 0.000 0.828 0.004 0.000 0.100
#> GSM11695 3 0.3301 0.685 0.068 0.000 0.828 0.004 0.000 0.100
#> GSM11734 2 0.0547 0.845 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM11861 5 0.5495 0.376 0.000 0.000 0.156 0.228 0.604 0.012
#> GSM11843 2 0.2301 0.828 0.000 0.884 0.000 0.020 0.096 0.000
#> GSM11862 5 0.5401 0.404 0.000 0.000 0.144 0.228 0.616 0.012
#> GSM11697 3 0.3510 0.683 0.068 0.000 0.820 0.012 0.000 0.100
#> GSM11714 6 0.1908 0.810 0.000 0.000 0.096 0.000 0.004 0.900
#> GSM11723 2 0.5681 0.726 0.000 0.616 0.032 0.196 0.156 0.000
#> GSM11845 2 0.5904 0.699 0.000 0.584 0.032 0.188 0.196 0.000
#> GSM11683 6 0.4668 0.725 0.000 0.000 0.116 0.204 0.000 0.680
#> GSM11691 3 0.3405 0.683 0.068 0.000 0.832 0.016 0.000 0.084
#> GSM27949 3 0.3426 0.623 0.000 0.000 0.764 0.012 0.004 0.220
#> GSM27945 3 0.3266 0.680 0.084 0.000 0.832 0.004 0.080 0.000
#> GSM11706 6 0.2243 0.809 0.000 0.000 0.112 0.004 0.004 0.880
#> GSM11853 3 0.3610 0.668 0.052 0.000 0.824 0.036 0.088 0.000
#> GSM11729 2 0.0000 0.845 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11746 2 0.1010 0.847 0.000 0.960 0.004 0.036 0.000 0.000
#> GSM11711 3 0.2878 0.666 0.020 0.000 0.884 0.032 0.024 0.040
#> GSM11854 3 0.3076 0.633 0.000 0.000 0.840 0.044 0.112 0.004
#> GSM11731 2 0.0547 0.845 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM11839 2 0.5518 0.640 0.000 0.596 0.024 0.104 0.276 0.000
#> GSM11836 5 0.1887 0.699 0.000 0.016 0.012 0.048 0.924 0.000
#> GSM11849 4 0.6506 0.713 0.000 0.000 0.260 0.456 0.252 0.032
#> GSM11682 6 0.4739 0.437 0.000 0.000 0.048 0.436 0.000 0.516
#> GSM11690 4 0.6641 0.744 0.000 0.000 0.256 0.464 0.232 0.048
#> GSM11692 5 0.3740 0.628 0.000 0.000 0.096 0.120 0.784 0.000
#> GSM11841 5 0.0914 0.718 0.000 0.016 0.000 0.016 0.968 0.000
#> GSM11901 5 0.0717 0.718 0.000 0.008 0.000 0.016 0.976 0.000
#> GSM11715 2 0.0993 0.846 0.000 0.964 0.000 0.012 0.024 0.000
#> GSM11724 2 0.1552 0.845 0.000 0.940 0.004 0.020 0.036 0.000
#> GSM11684 4 0.6141 0.783 0.000 0.000 0.236 0.552 0.172 0.040
#> GSM11696 4 0.6141 0.783 0.000 0.000 0.236 0.552 0.172 0.040
#> GSM27952 6 0.3512 0.790 0.000 0.000 0.032 0.196 0.000 0.772
#> GSM27948 5 0.5496 0.270 0.000 0.000 0.184 0.228 0.584 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.line(p) agent(p) time(p) k
#> ATC:kmeans 81 2.30e-01 0.175 1.71e-05 2
#> ATC:kmeans 62 1.60e-02 0.470 6.34e-04 3
#> ATC:kmeans 72 3.53e-09 0.698 6.52e-04 4
#> ATC:kmeans 60 1.60e-08 0.943 8.77e-03 5
#> ATC:kmeans 72 5.17e-10 0.753 1.44e-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", "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 14502 rows and 83 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.878 0.899 0.959 0.4986 0.500 0.500
#> 3 3 0.695 0.785 0.890 0.2941 0.778 0.591
#> 4 4 0.864 0.839 0.930 0.1386 0.828 0.570
#> 5 5 0.778 0.683 0.853 0.0721 0.908 0.679
#> 6 6 0.773 0.629 0.816 0.0429 0.938 0.729
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM11708 1 0.000 0.967 1.000 0.000
#> GSM11735 1 0.000 0.967 1.000 0.000
#> GSM11733 1 0.981 0.191 0.580 0.420
#> GSM11863 2 0.000 0.940 0.000 1.000
#> GSM11710 1 0.000 0.967 1.000 0.000
#> GSM11712 2 0.000 0.940 0.000 1.000
#> GSM11732 2 0.000 0.940 0.000 1.000
#> GSM11844 2 0.827 0.660 0.260 0.740
#> GSM11842 2 0.000 0.940 0.000 1.000
#> GSM11860 2 0.000 0.940 0.000 1.000
#> GSM11686 1 0.000 0.967 1.000 0.000
#> GSM11688 1 0.000 0.967 1.000 0.000
#> GSM11846 1 0.000 0.967 1.000 0.000
#> GSM11680 1 0.000 0.967 1.000 0.000
#> GSM11698 1 0.000 0.967 1.000 0.000
#> GSM11840 2 0.814 0.671 0.252 0.748
#> GSM11847 2 0.991 0.263 0.444 0.556
#> GSM11685 1 0.000 0.967 1.000 0.000
#> GSM11699 1 0.000 0.967 1.000 0.000
#> GSM27950 1 0.000 0.967 1.000 0.000
#> GSM27946 1 0.000 0.967 1.000 0.000
#> GSM11709 1 0.833 0.635 0.736 0.264
#> GSM11720 2 0.000 0.940 0.000 1.000
#> GSM11726 2 0.000 0.940 0.000 1.000
#> GSM11837 2 0.000 0.940 0.000 1.000
#> GSM11725 2 0.000 0.940 0.000 1.000
#> GSM11864 2 0.000 0.940 0.000 1.000
#> GSM11687 1 0.388 0.893 0.924 0.076
#> GSM11693 1 0.802 0.669 0.756 0.244
#> GSM11727 2 0.000 0.940 0.000 1.000
#> GSM11838 2 0.000 0.940 0.000 1.000
#> GSM11681 1 0.000 0.967 1.000 0.000
#> GSM11689 1 0.861 0.599 0.716 0.284
#> GSM11704 2 0.981 0.246 0.420 0.580
#> GSM11703 1 0.000 0.967 1.000 0.000
#> GSM11705 1 0.000 0.967 1.000 0.000
#> GSM11722 2 0.000 0.940 0.000 1.000
#> GSM11730 2 0.000 0.940 0.000 1.000
#> GSM11713 1 0.000 0.967 1.000 0.000
#> GSM11728 1 0.000 0.967 1.000 0.000
#> GSM27947 1 0.000 0.967 1.000 0.000
#> GSM27951 1 0.000 0.967 1.000 0.000
#> GSM11707 1 0.000 0.967 1.000 0.000
#> GSM11716 2 0.000 0.940 0.000 1.000
#> GSM11850 1 0.388 0.897 0.924 0.076
#> GSM11851 1 0.000 0.967 1.000 0.000
#> GSM11721 2 0.000 0.940 0.000 1.000
#> GSM11852 1 0.000 0.967 1.000 0.000
#> GSM11694 1 0.000 0.967 1.000 0.000
#> GSM11695 1 0.000 0.967 1.000 0.000
#> GSM11734 2 0.000 0.940 0.000 1.000
#> GSM11861 2 0.814 0.673 0.252 0.748
#> GSM11843 2 0.000 0.940 0.000 1.000
#> GSM11862 2 0.000 0.940 0.000 1.000
#> GSM11697 1 0.000 0.967 1.000 0.000
#> GSM11714 1 0.000 0.967 1.000 0.000
#> GSM11723 2 0.000 0.940 0.000 1.000
#> GSM11845 2 0.000 0.940 0.000 1.000
#> GSM11683 1 0.000 0.967 1.000 0.000
#> GSM11691 1 0.000 0.967 1.000 0.000
#> GSM27949 1 0.000 0.967 1.000 0.000
#> GSM27945 1 0.000 0.967 1.000 0.000
#> GSM11706 1 0.000 0.967 1.000 0.000
#> GSM11853 1 0.000 0.967 1.000 0.000
#> GSM11729 2 0.000 0.940 0.000 1.000
#> GSM11746 2 0.000 0.940 0.000 1.000
#> GSM11711 1 0.000 0.967 1.000 0.000
#> GSM11854 1 0.000 0.967 1.000 0.000
#> GSM11731 2 0.000 0.940 0.000 1.000
#> GSM11839 2 0.000 0.940 0.000 1.000
#> GSM11836 2 0.000 0.940 0.000 1.000
#> GSM11849 1 0.000 0.967 1.000 0.000
#> GSM11682 1 0.000 0.967 1.000 0.000
#> GSM11690 1 0.000 0.967 1.000 0.000
#> GSM11692 2 0.000 0.940 0.000 1.000
#> GSM11841 2 0.000 0.940 0.000 1.000
#> GSM11901 2 0.000 0.940 0.000 1.000
#> GSM11715 2 0.000 0.940 0.000 1.000
#> GSM11724 2 0.000 0.940 0.000 1.000
#> GSM11684 1 0.000 0.967 1.000 0.000
#> GSM11696 1 0.000 0.967 1.000 0.000
#> GSM27952 1 0.000 0.967 1.000 0.000
#> GSM27948 2 0.966 0.407 0.392 0.608
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM11708 3 0.0000 0.9026 0.000 0.000 1.000
#> GSM11735 3 0.0000 0.9026 0.000 0.000 1.000
#> GSM11733 3 0.3802 0.8502 0.080 0.032 0.888
#> GSM11863 2 0.2448 0.8315 0.076 0.924 0.000
#> GSM11710 3 0.0424 0.9005 0.008 0.000 0.992
#> GSM11712 2 0.2448 0.8315 0.076 0.924 0.000
#> GSM11732 2 0.6008 0.3902 0.000 0.628 0.372
#> GSM11844 3 0.5621 0.5583 0.000 0.308 0.692
#> GSM11842 2 0.2448 0.8315 0.076 0.924 0.000
#> GSM11860 2 0.1031 0.8551 0.024 0.976 0.000
#> GSM11686 3 0.0000 0.9026 0.000 0.000 1.000
#> GSM11688 3 0.0000 0.9026 0.000 0.000 1.000
#> GSM11846 3 0.6062 0.3026 0.384 0.000 0.616
#> GSM11680 3 0.0000 0.9026 0.000 0.000 1.000
#> GSM11698 3 0.0000 0.9026 0.000 0.000 1.000
#> GSM11840 3 0.7653 0.5659 0.080 0.276 0.644
#> GSM11847 3 0.5339 0.8001 0.080 0.096 0.824
#> GSM11685 3 0.0237 0.9016 0.004 0.000 0.996
#> GSM11699 3 0.3141 0.8643 0.068 0.020 0.912
#> GSM27950 3 0.0000 0.9026 0.000 0.000 1.000
#> GSM27946 3 0.3550 0.8542 0.080 0.024 0.896
#> GSM11709 1 0.2902 0.8839 0.920 0.016 0.064
#> GSM11720 1 0.5859 0.5062 0.656 0.344 0.000
#> GSM11726 1 0.5650 0.5725 0.688 0.312 0.000
#> GSM11837 2 0.2796 0.8196 0.092 0.908 0.000
#> GSM11725 2 0.2878 0.8166 0.096 0.904 0.000
#> GSM11864 2 0.2796 0.8196 0.092 0.908 0.000
#> GSM11687 1 0.2902 0.8839 0.920 0.016 0.064
#> GSM11693 1 0.2902 0.8839 0.920 0.016 0.064
#> GSM11727 2 0.6192 0.2067 0.420 0.580 0.000
#> GSM11838 2 0.2796 0.8196 0.092 0.908 0.000
#> GSM11681 1 0.3267 0.8655 0.884 0.000 0.116
#> GSM11689 1 0.2982 0.8796 0.920 0.024 0.056
#> GSM11704 1 0.2682 0.8368 0.920 0.076 0.004
#> GSM11703 1 0.2774 0.8840 0.920 0.008 0.072
#> GSM11705 1 0.2878 0.8772 0.904 0.000 0.096
#> GSM11722 2 0.6308 -0.0632 0.492 0.508 0.000
#> GSM11730 1 0.5497 0.6064 0.708 0.292 0.000
#> GSM11713 1 0.2959 0.8757 0.900 0.000 0.100
#> GSM11728 1 0.3619 0.8504 0.864 0.000 0.136
#> GSM27947 1 0.4887 0.7478 0.772 0.000 0.228
#> GSM27951 1 0.2537 0.8827 0.920 0.000 0.080
#> GSM11707 3 0.0000 0.9026 0.000 0.000 1.000
#> GSM11716 2 0.2878 0.8166 0.096 0.904 0.000
#> GSM11850 3 0.3780 0.8393 0.044 0.064 0.892
#> GSM11851 3 0.2165 0.8762 0.064 0.000 0.936
#> GSM11721 2 0.2537 0.8294 0.080 0.920 0.000
#> GSM11852 3 0.3276 0.8620 0.068 0.024 0.908
#> GSM11694 3 0.0000 0.9026 0.000 0.000 1.000
#> GSM11695 3 0.0000 0.9026 0.000 0.000 1.000
#> GSM11734 2 0.1031 0.8551 0.024 0.976 0.000
#> GSM11861 2 0.6807 0.6215 0.092 0.736 0.172
#> GSM11843 2 0.1031 0.8551 0.024 0.976 0.000
#> GSM11862 2 0.2537 0.8294 0.080 0.920 0.000
#> GSM11697 3 0.0000 0.9026 0.000 0.000 1.000
#> GSM11714 3 0.0000 0.9026 0.000 0.000 1.000
#> GSM11723 2 0.1031 0.8551 0.024 0.976 0.000
#> GSM11845 2 0.1031 0.8551 0.024 0.976 0.000
#> GSM11683 3 0.0000 0.9026 0.000 0.000 1.000
#> GSM11691 3 0.0000 0.9026 0.000 0.000 1.000
#> GSM27949 3 0.0000 0.9026 0.000 0.000 1.000
#> GSM27945 3 0.0424 0.8982 0.008 0.000 0.992
#> GSM11706 3 0.0000 0.9026 0.000 0.000 1.000
#> GSM11853 3 0.0000 0.9026 0.000 0.000 1.000
#> GSM11729 2 0.1031 0.8551 0.024 0.976 0.000
#> GSM11746 2 0.2796 0.8196 0.092 0.908 0.000
#> GSM11711 3 0.0000 0.9026 0.000 0.000 1.000
#> GSM11854 3 0.2165 0.8762 0.064 0.000 0.936
#> GSM11731 2 0.1031 0.8551 0.024 0.976 0.000
#> GSM11839 2 0.0237 0.8527 0.004 0.996 0.000
#> GSM11836 2 0.0592 0.8494 0.012 0.988 0.000
#> GSM11849 3 0.7974 0.5254 0.312 0.084 0.604
#> GSM11682 3 0.1289 0.8872 0.032 0.000 0.968
#> GSM11690 3 0.5650 0.7928 0.108 0.084 0.808
#> GSM11692 2 0.2537 0.8294 0.080 0.920 0.000
#> GSM11841 2 0.2448 0.8315 0.076 0.924 0.000
#> GSM11901 2 0.2537 0.8294 0.080 0.920 0.000
#> GSM11715 2 0.1031 0.8551 0.024 0.976 0.000
#> GSM11724 2 0.1031 0.8551 0.024 0.976 0.000
#> GSM11684 3 0.8257 0.3993 0.372 0.084 0.544
#> GSM11696 3 0.8257 0.3993 0.372 0.084 0.544
#> GSM27952 3 0.0237 0.9016 0.004 0.000 0.996
#> GSM27948 2 0.8744 -0.0973 0.108 0.448 0.444
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM11708 3 0.0000 0.9385 0.000 0.000 1.000 0.000
#> GSM11735 3 0.0000 0.9385 0.000 0.000 1.000 0.000
#> GSM11733 3 0.4543 0.5142 0.000 0.000 0.676 0.324
#> GSM11863 4 0.4605 0.5731 0.000 0.336 0.000 0.664
#> GSM11710 3 0.0817 0.9252 0.000 0.000 0.976 0.024
#> GSM11712 4 0.4643 0.5599 0.000 0.344 0.000 0.656
#> GSM11732 2 0.5040 0.4161 0.000 0.628 0.364 0.008
#> GSM11844 3 0.3803 0.7819 0.000 0.132 0.836 0.032
#> GSM11842 4 0.4661 0.5526 0.000 0.348 0.000 0.652
#> GSM11860 2 0.0000 0.9396 0.000 1.000 0.000 0.000
#> GSM11686 3 0.0188 0.9374 0.000 0.000 0.996 0.004
#> GSM11688 3 0.0188 0.9374 0.000 0.000 0.996 0.004
#> GSM11846 3 0.4907 0.2970 0.420 0.000 0.580 0.000
#> GSM11680 3 0.0000 0.9385 0.000 0.000 1.000 0.000
#> GSM11698 3 0.0000 0.9385 0.000 0.000 1.000 0.000
#> GSM11840 4 0.2081 0.8069 0.000 0.000 0.084 0.916
#> GSM11847 4 0.1637 0.8183 0.000 0.000 0.060 0.940
#> GSM11685 3 0.0707 0.9280 0.000 0.000 0.980 0.020
#> GSM11699 3 0.4855 0.3074 0.000 0.000 0.600 0.400
#> GSM27950 3 0.0000 0.9385 0.000 0.000 1.000 0.000
#> GSM27946 4 0.2281 0.8114 0.000 0.000 0.096 0.904
#> GSM11709 1 0.0000 0.9358 1.000 0.000 0.000 0.000
#> GSM11720 2 0.4103 0.6372 0.256 0.744 0.000 0.000
#> GSM11726 2 0.4661 0.4560 0.348 0.652 0.000 0.000
#> GSM11837 2 0.0000 0.9396 0.000 1.000 0.000 0.000
#> GSM11725 2 0.0000 0.9396 0.000 1.000 0.000 0.000
#> GSM11864 2 0.0000 0.9396 0.000 1.000 0.000 0.000
#> GSM11687 1 0.0000 0.9358 1.000 0.000 0.000 0.000
#> GSM11693 1 0.0000 0.9358 1.000 0.000 0.000 0.000
#> GSM11727 2 0.0817 0.9225 0.024 0.976 0.000 0.000
#> GSM11838 2 0.0000 0.9396 0.000 1.000 0.000 0.000
#> GSM11681 1 0.0000 0.9358 1.000 0.000 0.000 0.000
#> GSM11689 1 0.0000 0.9358 1.000 0.000 0.000 0.000
#> GSM11704 1 0.0000 0.9358 1.000 0.000 0.000 0.000
#> GSM11703 1 0.0000 0.9358 1.000 0.000 0.000 0.000
#> GSM11705 1 0.0000 0.9358 1.000 0.000 0.000 0.000
#> GSM11722 2 0.1792 0.8830 0.068 0.932 0.000 0.000
#> GSM11730 1 0.4999 -0.0634 0.508 0.492 0.000 0.000
#> GSM11713 1 0.0188 0.9333 0.996 0.000 0.000 0.004
#> GSM11728 1 0.1389 0.8986 0.952 0.000 0.000 0.048
#> GSM27947 1 0.3474 0.8143 0.868 0.000 0.064 0.068
#> GSM27951 1 0.0000 0.9358 1.000 0.000 0.000 0.000
#> GSM11707 3 0.0000 0.9385 0.000 0.000 1.000 0.000
#> GSM11716 2 0.0000 0.9396 0.000 1.000 0.000 0.000
#> GSM11850 3 0.0921 0.9158 0.000 0.028 0.972 0.000
#> GSM11851 3 0.0188 0.9367 0.000 0.000 0.996 0.004
#> GSM11721 4 0.0000 0.8257 0.000 0.000 0.000 1.000
#> GSM11852 4 0.4661 0.4257 0.000 0.000 0.348 0.652
#> GSM11694 3 0.0000 0.9385 0.000 0.000 1.000 0.000
#> GSM11695 3 0.0000 0.9385 0.000 0.000 1.000 0.000
#> GSM11734 2 0.0000 0.9396 0.000 1.000 0.000 0.000
#> GSM11861 4 0.0000 0.8257 0.000 0.000 0.000 1.000
#> GSM11843 2 0.0000 0.9396 0.000 1.000 0.000 0.000
#> GSM11862 4 0.0000 0.8257 0.000 0.000 0.000 1.000
#> GSM11697 3 0.0000 0.9385 0.000 0.000 1.000 0.000
#> GSM11714 3 0.0000 0.9385 0.000 0.000 1.000 0.000
#> GSM11723 2 0.0000 0.9396 0.000 1.000 0.000 0.000
#> GSM11845 2 0.0000 0.9396 0.000 1.000 0.000 0.000
#> GSM11683 3 0.0188 0.9374 0.000 0.000 0.996 0.004
#> GSM11691 3 0.0188 0.9374 0.000 0.000 0.996 0.004
#> GSM27949 3 0.0000 0.9385 0.000 0.000 1.000 0.000
#> GSM27945 3 0.0376 0.9355 0.004 0.000 0.992 0.004
#> GSM11706 3 0.0000 0.9385 0.000 0.000 1.000 0.000
#> GSM11853 3 0.0000 0.9385 0.000 0.000 1.000 0.000
#> GSM11729 2 0.0000 0.9396 0.000 1.000 0.000 0.000
#> GSM11746 2 0.0000 0.9396 0.000 1.000 0.000 0.000
#> GSM11711 3 0.0000 0.9385 0.000 0.000 1.000 0.000
#> GSM11854 3 0.0188 0.9372 0.000 0.000 0.996 0.004
#> GSM11731 2 0.0000 0.9396 0.000 1.000 0.000 0.000
#> GSM11839 2 0.0000 0.9396 0.000 1.000 0.000 0.000
#> GSM11836 2 0.0592 0.9254 0.000 0.984 0.000 0.016
#> GSM11849 4 0.2149 0.8168 0.000 0.000 0.088 0.912
#> GSM11682 3 0.3688 0.7215 0.000 0.000 0.792 0.208
#> GSM11690 4 0.2149 0.8168 0.000 0.000 0.088 0.912
#> GSM11692 4 0.0000 0.8257 0.000 0.000 0.000 1.000
#> GSM11841 4 0.4193 0.6634 0.000 0.268 0.000 0.732
#> GSM11901 4 0.3266 0.7579 0.000 0.168 0.000 0.832
#> GSM11715 2 0.0000 0.9396 0.000 1.000 0.000 0.000
#> GSM11724 2 0.0000 0.9396 0.000 1.000 0.000 0.000
#> GSM11684 4 0.2149 0.8168 0.000 0.000 0.088 0.912
#> GSM11696 4 0.2149 0.8168 0.000 0.000 0.088 0.912
#> GSM27952 3 0.0921 0.9224 0.000 0.000 0.972 0.028
#> GSM27948 4 0.0000 0.8257 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM11708 3 0.0510 0.79020 0.000 0.000 0.984 0.016 0.000
#> GSM11735 3 0.0404 0.78841 0.000 0.000 0.988 0.000 0.012
#> GSM11733 5 0.2362 0.57389 0.000 0.000 0.076 0.024 0.900
#> GSM11863 5 0.2903 0.66899 0.000 0.080 0.000 0.048 0.872
#> GSM11710 3 0.4211 0.47699 0.000 0.000 0.636 0.360 0.004
#> GSM11712 5 0.4847 0.63053 0.000 0.216 0.000 0.080 0.704
#> GSM11732 5 0.6145 -0.06808 0.000 0.076 0.416 0.020 0.488
#> GSM11844 3 0.4829 0.16140 0.000 0.000 0.500 0.020 0.480
#> GSM11842 5 0.4558 0.63407 0.000 0.216 0.000 0.060 0.724
#> GSM11860 2 0.1121 0.91292 0.000 0.956 0.000 0.000 0.044
#> GSM11686 3 0.4196 0.48386 0.000 0.000 0.640 0.356 0.004
#> GSM11688 3 0.4196 0.48386 0.000 0.000 0.640 0.356 0.004
#> GSM11846 1 0.4875 0.24917 0.576 0.000 0.400 0.020 0.004
#> GSM11680 3 0.0566 0.78983 0.000 0.000 0.984 0.012 0.004
#> GSM11698 3 0.0566 0.79024 0.000 0.000 0.984 0.012 0.004
#> GSM11840 5 0.0703 0.63782 0.000 0.000 0.000 0.024 0.976
#> GSM11847 5 0.0794 0.63888 0.000 0.000 0.000 0.028 0.972
#> GSM11685 3 0.4225 0.46964 0.000 0.000 0.632 0.364 0.004
#> GSM11699 4 0.4610 0.01810 0.000 0.000 0.432 0.556 0.012
#> GSM27950 3 0.0404 0.79029 0.000 0.000 0.988 0.012 0.000
#> GSM27946 4 0.2719 0.67631 0.000 0.000 0.068 0.884 0.048
#> GSM11709 1 0.0000 0.91289 1.000 0.000 0.000 0.000 0.000
#> GSM11720 2 0.3707 0.63771 0.284 0.716 0.000 0.000 0.000
#> GSM11726 2 0.4101 0.46766 0.372 0.628 0.000 0.000 0.000
#> GSM11837 2 0.0000 0.94425 0.000 1.000 0.000 0.000 0.000
#> GSM11725 2 0.0000 0.94425 0.000 1.000 0.000 0.000 0.000
#> GSM11864 2 0.0000 0.94425 0.000 1.000 0.000 0.000 0.000
#> GSM11687 1 0.0000 0.91289 1.000 0.000 0.000 0.000 0.000
#> GSM11693 1 0.0000 0.91289 1.000 0.000 0.000 0.000 0.000
#> GSM11727 2 0.0451 0.93810 0.008 0.988 0.000 0.000 0.004
#> GSM11838 2 0.0000 0.94425 0.000 1.000 0.000 0.000 0.000
#> GSM11681 1 0.0000 0.91289 1.000 0.000 0.000 0.000 0.000
#> GSM11689 1 0.0000 0.91289 1.000 0.000 0.000 0.000 0.000
#> GSM11704 1 0.0000 0.91289 1.000 0.000 0.000 0.000 0.000
#> GSM11703 1 0.0000 0.91289 1.000 0.000 0.000 0.000 0.000
#> GSM11705 1 0.0000 0.91289 1.000 0.000 0.000 0.000 0.000
#> GSM11722 2 0.0566 0.93553 0.012 0.984 0.000 0.000 0.004
#> GSM11730 2 0.3456 0.74162 0.204 0.788 0.000 0.004 0.004
#> GSM11713 1 0.3398 0.67235 0.780 0.000 0.000 0.216 0.004
#> GSM11728 4 0.4783 0.00448 0.452 0.000 0.012 0.532 0.004
#> GSM27947 1 0.3446 0.78024 0.844 0.000 0.044 0.104 0.008
#> GSM27951 1 0.0000 0.91289 1.000 0.000 0.000 0.000 0.000
#> GSM11707 3 0.0510 0.79020 0.000 0.000 0.984 0.016 0.000
#> GSM11716 2 0.1557 0.90087 0.000 0.940 0.008 0.000 0.052
#> GSM11850 3 0.4318 0.55065 0.000 0.000 0.688 0.020 0.292
#> GSM11851 3 0.5077 0.41451 0.000 0.000 0.568 0.040 0.392
#> GSM11721 5 0.4297 0.20333 0.000 0.000 0.000 0.472 0.528
#> GSM11852 4 0.2189 0.66537 0.000 0.000 0.084 0.904 0.012
#> GSM11694 3 0.1012 0.78329 0.000 0.000 0.968 0.012 0.020
#> GSM11695 3 0.1012 0.78329 0.000 0.000 0.968 0.012 0.020
#> GSM11734 2 0.0000 0.94425 0.000 1.000 0.000 0.000 0.000
#> GSM11861 4 0.4242 -0.06803 0.000 0.000 0.000 0.572 0.428
#> GSM11843 2 0.0000 0.94425 0.000 1.000 0.000 0.000 0.000
#> GSM11862 4 0.4300 -0.20014 0.000 0.000 0.000 0.524 0.476
#> GSM11697 3 0.0671 0.78703 0.000 0.000 0.980 0.004 0.016
#> GSM11714 3 0.0510 0.79020 0.000 0.000 0.984 0.016 0.000
#> GSM11723 2 0.0000 0.94425 0.000 1.000 0.000 0.000 0.000
#> GSM11845 2 0.0000 0.94425 0.000 1.000 0.000 0.000 0.000
#> GSM11683 3 0.4084 0.52260 0.000 0.000 0.668 0.328 0.004
#> GSM11691 3 0.2011 0.75559 0.000 0.000 0.908 0.088 0.004
#> GSM27949 3 0.0162 0.78972 0.000 0.000 0.996 0.000 0.004
#> GSM27945 3 0.2269 0.76427 0.020 0.000 0.920 0.032 0.028
#> GSM11706 3 0.1041 0.78552 0.000 0.000 0.964 0.032 0.004
#> GSM11853 3 0.4522 0.60368 0.000 0.000 0.708 0.044 0.248
#> GSM11729 2 0.0000 0.94425 0.000 1.000 0.000 0.000 0.000
#> GSM11746 2 0.0000 0.94425 0.000 1.000 0.000 0.000 0.000
#> GSM11711 3 0.1952 0.76270 0.000 0.000 0.912 0.084 0.004
#> GSM11854 3 0.5216 0.60311 0.000 0.000 0.660 0.092 0.248
#> GSM11731 2 0.0000 0.94425 0.000 1.000 0.000 0.000 0.000
#> GSM11839 2 0.0000 0.94425 0.000 1.000 0.000 0.000 0.000
#> GSM11836 2 0.0880 0.91972 0.000 0.968 0.000 0.000 0.032
#> GSM11849 4 0.1893 0.68667 0.000 0.000 0.048 0.928 0.024
#> GSM11682 4 0.3730 0.43439 0.000 0.000 0.288 0.712 0.000
#> GSM11690 4 0.1893 0.68667 0.000 0.000 0.048 0.928 0.024
#> GSM11692 5 0.4150 0.38211 0.000 0.000 0.000 0.388 0.612
#> GSM11841 5 0.5127 0.63387 0.000 0.184 0.000 0.124 0.692
#> GSM11901 5 0.5122 0.61161 0.000 0.112 0.000 0.200 0.688
#> GSM11715 2 0.0000 0.94425 0.000 1.000 0.000 0.000 0.000
#> GSM11724 2 0.0000 0.94425 0.000 1.000 0.000 0.000 0.000
#> GSM11684 4 0.1893 0.68667 0.000 0.000 0.048 0.928 0.024
#> GSM11696 4 0.1893 0.68667 0.000 0.000 0.048 0.928 0.024
#> GSM27952 3 0.4341 0.38647 0.000 0.000 0.592 0.404 0.004
#> GSM27948 4 0.3336 0.41377 0.000 0.000 0.000 0.772 0.228
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM11708 6 0.2048 0.6888 0.000 0.000 0.120 0.000 0.000 0.880
#> GSM11735 6 0.3081 0.5968 0.000 0.000 0.220 0.000 0.004 0.776
#> GSM11733 5 0.4249 0.4083 0.000 0.000 0.328 0.000 0.640 0.032
#> GSM11863 5 0.1341 0.7058 0.000 0.024 0.028 0.000 0.948 0.000
#> GSM11710 6 0.1995 0.6762 0.000 0.000 0.036 0.052 0.000 0.912
#> GSM11712 5 0.2776 0.6990 0.000 0.088 0.000 0.052 0.860 0.000
#> GSM11732 3 0.4259 0.4295 0.000 0.012 0.744 0.004 0.188 0.052
#> GSM11844 3 0.4288 0.4070 0.000 0.000 0.716 0.004 0.216 0.064
#> GSM11842 5 0.2068 0.7025 0.000 0.080 0.008 0.008 0.904 0.000
#> GSM11860 2 0.2199 0.8513 0.000 0.892 0.020 0.000 0.088 0.000
#> GSM11686 6 0.1501 0.6888 0.000 0.000 0.000 0.076 0.000 0.924
#> GSM11688 6 0.1501 0.6888 0.000 0.000 0.000 0.076 0.000 0.924
#> GSM11846 1 0.5472 0.0697 0.464 0.000 0.124 0.000 0.000 0.412
#> GSM11680 6 0.4076 0.3418 0.000 0.000 0.364 0.016 0.000 0.620
#> GSM11698 6 0.3337 0.5625 0.000 0.000 0.260 0.004 0.000 0.736
#> GSM11840 5 0.2912 0.6038 0.000 0.000 0.216 0.000 0.784 0.000
#> GSM11847 5 0.2793 0.6176 0.000 0.000 0.200 0.000 0.800 0.000
#> GSM11685 6 0.1700 0.6875 0.000 0.000 0.004 0.080 0.000 0.916
#> GSM11699 6 0.4911 0.3357 0.000 0.000 0.060 0.332 0.008 0.600
#> GSM27950 6 0.2340 0.6741 0.000 0.000 0.148 0.000 0.000 0.852
#> GSM27946 4 0.5056 0.6086 0.000 0.000 0.092 0.716 0.080 0.112
#> GSM11709 1 0.0000 0.8728 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11720 2 0.3725 0.5620 0.316 0.676 0.008 0.000 0.000 0.000
#> GSM11726 2 0.4372 0.2752 0.432 0.544 0.024 0.000 0.000 0.000
#> GSM11837 2 0.0146 0.9140 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM11725 2 0.0146 0.9140 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM11864 2 0.0146 0.9140 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM11687 1 0.0000 0.8728 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11693 1 0.0000 0.8728 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11727 2 0.0291 0.9125 0.004 0.992 0.000 0.000 0.004 0.000
#> GSM11838 2 0.0000 0.9140 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11681 1 0.0547 0.8597 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM11689 1 0.0000 0.8728 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11704 1 0.0000 0.8728 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11703 1 0.0000 0.8728 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11705 1 0.0000 0.8728 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11722 2 0.0291 0.9125 0.004 0.992 0.000 0.000 0.004 0.000
#> GSM11730 2 0.4311 0.6367 0.228 0.708 0.000 0.060 0.004 0.000
#> GSM11713 1 0.4386 0.3467 0.600 0.000 0.000 0.372 0.004 0.024
#> GSM11728 4 0.4617 0.3923 0.284 0.000 0.000 0.652 0.004 0.060
#> GSM27947 1 0.5116 0.5814 0.684 0.000 0.188 0.088 0.000 0.040
#> GSM27951 1 0.0000 0.8728 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11707 6 0.2048 0.6888 0.000 0.000 0.120 0.000 0.000 0.880
#> GSM11716 2 0.3746 0.6394 0.000 0.712 0.272 0.004 0.012 0.000
#> GSM11850 3 0.2714 0.5139 0.000 0.000 0.872 0.004 0.060 0.064
#> GSM11851 3 0.5446 0.3709 0.000 0.000 0.568 0.000 0.176 0.256
#> GSM11721 5 0.3714 0.4594 0.000 0.000 0.004 0.340 0.656 0.000
#> GSM11852 4 0.4449 0.6042 0.000 0.000 0.036 0.684 0.016 0.264
#> GSM11694 3 0.4254 0.2113 0.000 0.000 0.576 0.020 0.000 0.404
#> GSM11695 3 0.4261 0.2030 0.000 0.000 0.572 0.020 0.000 0.408
#> GSM11734 2 0.0363 0.9145 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM11861 4 0.4676 -0.0250 0.000 0.000 0.044 0.528 0.428 0.000
#> GSM11843 2 0.0363 0.9145 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM11862 5 0.4592 0.0908 0.000 0.000 0.036 0.468 0.496 0.000
#> GSM11697 3 0.4328 0.0428 0.000 0.000 0.520 0.020 0.000 0.460
#> GSM11714 6 0.2048 0.6888 0.000 0.000 0.120 0.000 0.000 0.880
#> GSM11723 2 0.0458 0.9140 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM11845 2 0.0458 0.9140 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM11683 6 0.2237 0.6967 0.000 0.000 0.036 0.068 0.000 0.896
#> GSM11691 6 0.4411 0.2821 0.004 0.000 0.356 0.028 0.000 0.612
#> GSM27949 6 0.3833 0.3810 0.000 0.000 0.344 0.008 0.000 0.648
#> GSM27945 3 0.5255 0.3131 0.028 0.000 0.596 0.048 0.004 0.324
#> GSM11706 6 0.1387 0.6916 0.000 0.000 0.068 0.000 0.000 0.932
#> GSM11853 3 0.4838 0.2246 0.000 0.000 0.544 0.000 0.060 0.396
#> GSM11729 2 0.0146 0.9145 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM11746 2 0.0146 0.9140 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM11711 6 0.1913 0.6830 0.000 0.000 0.080 0.012 0.000 0.908
#> GSM11854 6 0.4878 -0.1146 0.000 0.000 0.424 0.000 0.060 0.516
#> GSM11731 2 0.0458 0.9140 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM11839 2 0.0935 0.9040 0.000 0.964 0.000 0.004 0.032 0.000
#> GSM11836 2 0.2176 0.8492 0.000 0.896 0.000 0.024 0.080 0.000
#> GSM11849 4 0.0972 0.7153 0.000 0.000 0.000 0.964 0.008 0.028
#> GSM11682 4 0.3765 0.3501 0.000 0.000 0.000 0.596 0.000 0.404
#> GSM11690 4 0.1594 0.7123 0.000 0.000 0.000 0.932 0.016 0.052
#> GSM11692 5 0.2912 0.6378 0.000 0.000 0.000 0.216 0.784 0.000
#> GSM11841 5 0.3295 0.6942 0.000 0.056 0.000 0.128 0.816 0.000
#> GSM11901 5 0.3139 0.6871 0.000 0.032 0.000 0.152 0.816 0.000
#> GSM11715 2 0.0458 0.9140 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM11724 2 0.0458 0.9140 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM11684 4 0.0547 0.7134 0.000 0.000 0.000 0.980 0.000 0.020
#> GSM11696 4 0.0603 0.7118 0.000 0.000 0.000 0.980 0.004 0.016
#> GSM27952 6 0.1958 0.6677 0.000 0.000 0.004 0.100 0.000 0.896
#> GSM27948 4 0.3411 0.5028 0.000 0.000 0.004 0.756 0.232 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.line(p) agent(p) time(p) k
#> ATC:skmeans 79 8.50e-01 0.0961 6.51e-06 2
#> ATC:skmeans 76 8.39e-12 0.4412 1.72e-02 3
#> ATC:skmeans 77 6.75e-10 0.3696 2.35e-04 4
#> ATC:skmeans 65 3.59e-09 0.3210 8.99e-06 5
#> ATC:skmeans 61 3.14e-07 0.2247 7.28e-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", "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 14502 rows and 83 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.949 0.935 0.974 0.4047 0.606 0.606
#> 3 3 0.598 0.727 0.851 0.4771 0.797 0.670
#> 4 4 0.893 0.884 0.931 0.1685 0.784 0.538
#> 5 5 0.823 0.834 0.904 0.1234 0.904 0.679
#> 6 6 0.766 0.736 0.850 0.0339 0.964 0.831
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM11708 1 0.000 0.972 1.000 0.000
#> GSM11735 1 0.000 0.972 1.000 0.000
#> GSM11733 1 0.000 0.972 1.000 0.000
#> GSM11863 1 0.973 0.317 0.596 0.404
#> GSM11710 1 0.000 0.972 1.000 0.000
#> GSM11712 2 0.913 0.507 0.328 0.672
#> GSM11732 1 0.000 0.972 1.000 0.000
#> GSM11844 1 0.000 0.972 1.000 0.000
#> GSM11842 2 0.827 0.643 0.260 0.740
#> GSM11860 1 0.689 0.761 0.816 0.184
#> GSM11686 1 0.000 0.972 1.000 0.000
#> GSM11688 1 0.000 0.972 1.000 0.000
#> GSM11846 1 0.000 0.972 1.000 0.000
#> GSM11680 1 0.000 0.972 1.000 0.000
#> GSM11698 1 0.000 0.972 1.000 0.000
#> GSM11840 1 0.000 0.972 1.000 0.000
#> GSM11847 1 0.000 0.972 1.000 0.000
#> GSM11685 1 0.000 0.972 1.000 0.000
#> GSM11699 1 0.000 0.972 1.000 0.000
#> GSM27950 1 0.000 0.972 1.000 0.000
#> GSM27946 1 0.000 0.972 1.000 0.000
#> GSM11709 1 0.000 0.972 1.000 0.000
#> GSM11720 1 0.973 0.317 0.596 0.404
#> GSM11726 1 0.000 0.972 1.000 0.000
#> GSM11837 2 0.000 0.971 0.000 1.000
#> GSM11725 2 0.000 0.971 0.000 1.000
#> GSM11864 2 0.000 0.971 0.000 1.000
#> GSM11687 1 0.000 0.972 1.000 0.000
#> GSM11693 1 0.000 0.972 1.000 0.000
#> GSM11727 2 0.000 0.971 0.000 1.000
#> GSM11838 2 0.000 0.971 0.000 1.000
#> GSM11681 1 0.000 0.972 1.000 0.000
#> GSM11689 1 0.000 0.972 1.000 0.000
#> GSM11704 1 0.000 0.972 1.000 0.000
#> GSM11703 1 0.000 0.972 1.000 0.000
#> GSM11705 1 0.000 0.972 1.000 0.000
#> GSM11722 2 0.000 0.971 0.000 1.000
#> GSM11730 2 0.000 0.971 0.000 1.000
#> GSM11713 1 0.000 0.972 1.000 0.000
#> GSM11728 1 0.000 0.972 1.000 0.000
#> GSM27947 1 0.000 0.972 1.000 0.000
#> GSM27951 1 0.000 0.972 1.000 0.000
#> GSM11707 1 0.000 0.972 1.000 0.000
#> GSM11716 1 0.913 0.506 0.672 0.328
#> GSM11850 1 0.000 0.972 1.000 0.000
#> GSM11851 1 0.000 0.972 1.000 0.000
#> GSM11721 1 0.000 0.972 1.000 0.000
#> GSM11852 1 0.000 0.972 1.000 0.000
#> GSM11694 1 0.000 0.972 1.000 0.000
#> GSM11695 1 0.000 0.972 1.000 0.000
#> GSM11734 2 0.000 0.971 0.000 1.000
#> GSM11861 1 0.000 0.972 1.000 0.000
#> GSM11843 2 0.000 0.971 0.000 1.000
#> GSM11862 1 0.000 0.972 1.000 0.000
#> GSM11697 1 0.000 0.972 1.000 0.000
#> GSM11714 1 0.000 0.972 1.000 0.000
#> GSM11723 2 0.000 0.971 0.000 1.000
#> GSM11845 2 0.000 0.971 0.000 1.000
#> GSM11683 1 0.000 0.972 1.000 0.000
#> GSM11691 1 0.000 0.972 1.000 0.000
#> GSM27949 1 0.000 0.972 1.000 0.000
#> GSM27945 1 0.000 0.972 1.000 0.000
#> GSM11706 1 0.000 0.972 1.000 0.000
#> GSM11853 1 0.000 0.972 1.000 0.000
#> GSM11729 2 0.000 0.971 0.000 1.000
#> GSM11746 2 0.000 0.971 0.000 1.000
#> GSM11711 1 0.000 0.972 1.000 0.000
#> GSM11854 1 0.000 0.972 1.000 0.000
#> GSM11731 2 0.000 0.971 0.000 1.000
#> GSM11839 2 0.000 0.971 0.000 1.000
#> GSM11836 2 0.000 0.971 0.000 1.000
#> GSM11849 1 0.000 0.972 1.000 0.000
#> GSM11682 1 0.000 0.972 1.000 0.000
#> GSM11690 1 0.000 0.972 1.000 0.000
#> GSM11692 1 0.000 0.972 1.000 0.000
#> GSM11841 2 0.000 0.971 0.000 1.000
#> GSM11901 2 0.000 0.971 0.000 1.000
#> GSM11715 2 0.000 0.971 0.000 1.000
#> GSM11724 2 0.000 0.971 0.000 1.000
#> GSM11684 1 0.260 0.931 0.956 0.044
#> GSM11696 1 0.722 0.737 0.800 0.200
#> GSM27952 1 0.000 0.972 1.000 0.000
#> GSM27948 1 0.000 0.972 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM11708 3 0.2711 0.818 0.088 0.000 0.912
#> GSM11735 3 0.2711 0.818 0.088 0.000 0.912
#> GSM11733 3 0.0000 0.837 0.000 0.000 1.000
#> GSM11863 2 0.8458 -0.171 0.088 0.476 0.436
#> GSM11710 3 0.2711 0.818 0.088 0.000 0.912
#> GSM11712 2 0.4063 0.672 0.020 0.868 0.112
#> GSM11732 3 0.2878 0.806 0.096 0.000 0.904
#> GSM11844 3 0.0892 0.835 0.020 0.000 0.980
#> GSM11842 2 0.1753 0.770 0.000 0.952 0.048
#> GSM11860 3 0.6168 0.236 0.412 0.000 0.588
#> GSM11686 3 0.2711 0.818 0.088 0.000 0.912
#> GSM11688 3 0.2711 0.818 0.088 0.000 0.912
#> GSM11846 3 0.0000 0.837 0.000 0.000 1.000
#> GSM11680 3 0.3267 0.829 0.116 0.000 0.884
#> GSM11698 3 0.2448 0.823 0.076 0.000 0.924
#> GSM11840 3 0.4369 0.786 0.096 0.040 0.864
#> GSM11847 3 0.7677 0.588 0.096 0.244 0.660
#> GSM11685 3 0.2711 0.818 0.088 0.000 0.912
#> GSM11699 3 0.0000 0.837 0.000 0.000 1.000
#> GSM27950 3 0.2711 0.818 0.088 0.000 0.912
#> GSM27946 3 0.5663 0.744 0.096 0.096 0.808
#> GSM11709 1 0.2711 0.799 0.912 0.000 0.088
#> GSM11720 1 0.3590 0.768 0.896 0.028 0.076
#> GSM11726 1 0.2711 0.799 0.912 0.000 0.088
#> GSM11837 2 0.5058 0.738 0.244 0.756 0.000
#> GSM11725 2 0.5058 0.738 0.244 0.756 0.000
#> GSM11864 2 0.5058 0.738 0.244 0.756 0.000
#> GSM11687 1 0.2711 0.799 0.912 0.000 0.088
#> GSM11693 1 0.2711 0.799 0.912 0.000 0.088
#> GSM11727 2 0.8169 0.377 0.388 0.536 0.076
#> GSM11838 2 0.5058 0.738 0.244 0.756 0.000
#> GSM11681 1 0.6215 0.536 0.572 0.000 0.428
#> GSM11689 1 0.2711 0.799 0.912 0.000 0.088
#> GSM11704 1 0.2711 0.799 0.912 0.000 0.088
#> GSM11703 1 0.5785 0.618 0.668 0.000 0.332
#> GSM11705 3 0.6252 -0.255 0.444 0.000 0.556
#> GSM11722 2 0.5058 0.738 0.244 0.756 0.000
#> GSM11730 1 0.8213 0.264 0.568 0.344 0.088
#> GSM11713 3 0.0000 0.837 0.000 0.000 1.000
#> GSM11728 3 0.2165 0.822 0.064 0.000 0.936
#> GSM27947 1 0.6235 0.402 0.564 0.000 0.436
#> GSM27951 1 0.6192 0.546 0.580 0.000 0.420
#> GSM11707 3 0.2711 0.818 0.088 0.000 0.912
#> GSM11716 1 0.2945 0.797 0.908 0.004 0.088
#> GSM11850 3 0.2878 0.806 0.096 0.000 0.904
#> GSM11851 3 0.0000 0.837 0.000 0.000 1.000
#> GSM11721 3 0.7677 0.588 0.096 0.244 0.660
#> GSM11852 3 0.0000 0.837 0.000 0.000 1.000
#> GSM11694 3 0.2878 0.806 0.096 0.000 0.904
#> GSM11695 3 0.2878 0.806 0.096 0.000 0.904
#> GSM11734 2 0.1643 0.807 0.044 0.956 0.000
#> GSM11861 3 0.2280 0.827 0.052 0.008 0.940
#> GSM11843 2 0.4291 0.767 0.180 0.820 0.000
#> GSM11862 3 0.7677 0.588 0.096 0.244 0.660
#> GSM11697 3 0.1163 0.834 0.028 0.000 0.972
#> GSM11714 3 0.2711 0.818 0.088 0.000 0.912
#> GSM11723 2 0.0000 0.813 0.000 1.000 0.000
#> GSM11845 2 0.0000 0.813 0.000 1.000 0.000
#> GSM11683 3 0.2537 0.822 0.080 0.000 0.920
#> GSM11691 3 0.2878 0.806 0.096 0.000 0.904
#> GSM27949 3 0.2448 0.823 0.076 0.000 0.924
#> GSM27945 3 0.2878 0.806 0.096 0.000 0.904
#> GSM11706 3 0.1289 0.834 0.032 0.000 0.968
#> GSM11853 3 0.0000 0.837 0.000 0.000 1.000
#> GSM11729 2 0.5058 0.738 0.244 0.756 0.000
#> GSM11746 2 0.5058 0.738 0.244 0.756 0.000
#> GSM11711 3 0.0000 0.837 0.000 0.000 1.000
#> GSM11854 3 0.0000 0.837 0.000 0.000 1.000
#> GSM11731 2 0.0000 0.813 0.000 1.000 0.000
#> GSM11839 2 0.0000 0.813 0.000 1.000 0.000
#> GSM11836 2 0.0237 0.811 0.000 0.996 0.004
#> GSM11849 3 0.2448 0.817 0.076 0.000 0.924
#> GSM11682 3 0.2711 0.818 0.088 0.000 0.912
#> GSM11690 3 0.7677 0.588 0.096 0.244 0.660
#> GSM11692 3 0.7677 0.588 0.096 0.244 0.660
#> GSM11841 2 0.0000 0.813 0.000 1.000 0.000
#> GSM11901 2 0.0000 0.813 0.000 1.000 0.000
#> GSM11715 2 0.0000 0.813 0.000 1.000 0.000
#> GSM11724 2 0.0000 0.813 0.000 1.000 0.000
#> GSM11684 3 0.6026 0.634 0.024 0.244 0.732
#> GSM11696 3 0.7713 0.583 0.096 0.248 0.656
#> GSM27952 3 0.2711 0.818 0.088 0.000 0.912
#> GSM27948 3 0.7677 0.588 0.096 0.244 0.660
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM11708 3 0.0804 0.926 0.008 0.000 0.980 0.012
#> GSM11735 3 0.0188 0.929 0.000 0.000 0.996 0.004
#> GSM11733 3 0.2334 0.928 0.004 0.000 0.908 0.088
#> GSM11863 4 0.0657 0.886 0.012 0.004 0.000 0.984
#> GSM11710 3 0.1151 0.933 0.024 0.000 0.968 0.008
#> GSM11712 4 0.1557 0.878 0.000 0.056 0.000 0.944
#> GSM11732 3 0.4679 0.811 0.044 0.000 0.772 0.184
#> GSM11844 3 0.2751 0.934 0.040 0.000 0.904 0.056
#> GSM11842 4 0.1940 0.872 0.000 0.076 0.000 0.924
#> GSM11860 3 0.6595 0.555 0.120 0.000 0.604 0.276
#> GSM11686 3 0.0672 0.927 0.008 0.000 0.984 0.008
#> GSM11688 3 0.0804 0.926 0.008 0.000 0.980 0.012
#> GSM11846 3 0.2489 0.932 0.068 0.000 0.912 0.020
#> GSM11680 3 0.1174 0.935 0.020 0.000 0.968 0.012
#> GSM11698 3 0.0376 0.932 0.004 0.000 0.992 0.004
#> GSM11840 4 0.4453 0.616 0.012 0.000 0.244 0.744
#> GSM11847 4 0.0469 0.886 0.012 0.000 0.000 0.988
#> GSM11685 3 0.0804 0.926 0.008 0.000 0.980 0.012
#> GSM11699 3 0.2565 0.936 0.032 0.000 0.912 0.056
#> GSM27950 3 0.0804 0.926 0.008 0.000 0.980 0.012
#> GSM27946 4 0.4417 0.694 0.044 0.000 0.160 0.796
#> GSM11709 1 0.0336 0.900 0.992 0.000 0.000 0.008
#> GSM11720 1 0.1109 0.899 0.968 0.004 0.000 0.028
#> GSM11726 1 0.1637 0.886 0.940 0.000 0.000 0.060
#> GSM11837 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM11725 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM11864 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM11687 1 0.0336 0.900 0.992 0.000 0.000 0.008
#> GSM11693 1 0.0592 0.902 0.984 0.000 0.000 0.016
#> GSM11727 1 0.1677 0.893 0.948 0.012 0.000 0.040
#> GSM11838 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM11681 1 0.0707 0.888 0.980 0.000 0.020 0.000
#> GSM11689 1 0.0592 0.902 0.984 0.000 0.000 0.016
#> GSM11704 1 0.0336 0.900 0.992 0.000 0.000 0.008
#> GSM11703 1 0.0707 0.902 0.980 0.000 0.000 0.020
#> GSM11705 1 0.4661 0.447 0.652 0.000 0.348 0.000
#> GSM11722 1 0.2011 0.839 0.920 0.080 0.000 0.000
#> GSM11730 1 0.1474 0.891 0.948 0.000 0.000 0.052
#> GSM11713 3 0.2266 0.925 0.084 0.000 0.912 0.004
#> GSM11728 3 0.2699 0.934 0.068 0.000 0.904 0.028
#> GSM27947 1 0.6733 0.367 0.564 0.000 0.324 0.112
#> GSM27951 1 0.0592 0.891 0.984 0.000 0.016 0.000
#> GSM11707 3 0.0188 0.929 0.000 0.000 0.996 0.004
#> GSM11716 1 0.1792 0.880 0.932 0.000 0.000 0.068
#> GSM11850 3 0.2996 0.930 0.044 0.000 0.892 0.064
#> GSM11851 3 0.2565 0.936 0.032 0.000 0.912 0.056
#> GSM11721 4 0.0469 0.886 0.012 0.000 0.000 0.988
#> GSM11852 3 0.2565 0.936 0.032 0.000 0.912 0.056
#> GSM11694 3 0.2996 0.930 0.044 0.000 0.892 0.064
#> GSM11695 3 0.2996 0.930 0.044 0.000 0.892 0.064
#> GSM11734 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM11861 4 0.5250 0.091 0.008 0.000 0.440 0.552
#> GSM11843 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM11862 4 0.0469 0.886 0.012 0.000 0.000 0.988
#> GSM11697 3 0.2644 0.936 0.032 0.000 0.908 0.060
#> GSM11714 3 0.0804 0.926 0.008 0.000 0.980 0.012
#> GSM11723 4 0.1940 0.872 0.000 0.076 0.000 0.924
#> GSM11845 4 0.1940 0.872 0.000 0.076 0.000 0.924
#> GSM11683 3 0.0524 0.933 0.008 0.000 0.988 0.004
#> GSM11691 3 0.2996 0.930 0.044 0.000 0.892 0.064
#> GSM27949 3 0.0657 0.935 0.004 0.000 0.984 0.012
#> GSM27945 3 0.2996 0.930 0.044 0.000 0.892 0.064
#> GSM11706 3 0.2089 0.936 0.048 0.000 0.932 0.020
#> GSM11853 3 0.2565 0.936 0.032 0.000 0.912 0.056
#> GSM11729 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM11746 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM11711 3 0.2546 0.934 0.060 0.000 0.912 0.028
#> GSM11854 3 0.2565 0.936 0.032 0.000 0.912 0.056
#> GSM11731 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM11839 4 0.1940 0.872 0.000 0.076 0.000 0.924
#> GSM11836 4 0.1940 0.872 0.000 0.076 0.000 0.924
#> GSM11849 3 0.2830 0.933 0.040 0.000 0.900 0.060
#> GSM11682 3 0.0672 0.927 0.008 0.000 0.984 0.008
#> GSM11690 4 0.0469 0.886 0.012 0.000 0.000 0.988
#> GSM11692 4 0.0469 0.886 0.012 0.000 0.000 0.988
#> GSM11841 4 0.1940 0.872 0.000 0.076 0.000 0.924
#> GSM11901 4 0.1940 0.872 0.000 0.076 0.000 0.924
#> GSM11715 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM11724 4 0.3610 0.744 0.000 0.200 0.000 0.800
#> GSM11684 4 0.0592 0.882 0.000 0.000 0.016 0.984
#> GSM11696 4 0.0469 0.886 0.012 0.000 0.000 0.988
#> GSM27952 3 0.0672 0.927 0.008 0.000 0.984 0.008
#> GSM27948 4 0.0469 0.886 0.012 0.000 0.000 0.988
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM11708 4 0.3816 0.6896 0.000 0.000 0.304 0.696 0.000
#> GSM11735 3 0.1965 0.7352 0.000 0.000 0.904 0.096 0.000
#> GSM11733 4 0.0162 0.8669 0.000 0.000 0.000 0.996 0.004
#> GSM11863 5 0.0000 0.9331 0.000 0.000 0.000 0.000 1.000
#> GSM11710 4 0.0162 0.8684 0.004 0.000 0.000 0.996 0.000
#> GSM11712 5 0.0000 0.9331 0.000 0.000 0.000 0.000 1.000
#> GSM11732 3 0.5072 0.6806 0.000 0.000 0.696 0.116 0.188
#> GSM11844 4 0.0000 0.8681 0.000 0.000 0.000 1.000 0.000
#> GSM11842 5 0.0000 0.9331 0.000 0.000 0.000 0.000 1.000
#> GSM11860 4 0.5635 0.4886 0.128 0.000 0.000 0.620 0.252
#> GSM11686 4 0.3586 0.7233 0.000 0.000 0.264 0.736 0.000
#> GSM11688 4 0.3816 0.6896 0.000 0.000 0.304 0.696 0.000
#> GSM11846 4 0.0162 0.8684 0.004 0.000 0.000 0.996 0.000
#> GSM11680 3 0.2471 0.7561 0.000 0.000 0.864 0.136 0.000
#> GSM11698 4 0.1121 0.8481 0.000 0.000 0.044 0.956 0.000
#> GSM11840 5 0.3586 0.6337 0.000 0.000 0.000 0.264 0.736
#> GSM11847 5 0.0162 0.9318 0.000 0.000 0.000 0.004 0.996
#> GSM11685 4 0.3816 0.6896 0.000 0.000 0.304 0.696 0.000
#> GSM11699 4 0.0703 0.8490 0.000 0.000 0.024 0.976 0.000
#> GSM27950 3 0.0000 0.6494 0.000 0.000 1.000 0.000 0.000
#> GSM27946 5 0.3109 0.7337 0.000 0.000 0.000 0.200 0.800
#> GSM11709 1 0.0000 0.9303 1.000 0.000 0.000 0.000 0.000
#> GSM11720 1 0.0162 0.9310 0.996 0.000 0.000 0.004 0.000
#> GSM11726 1 0.0290 0.9281 0.992 0.000 0.000 0.008 0.000
#> GSM11837 2 0.0000 0.9995 0.000 1.000 0.000 0.000 0.000
#> GSM11725 2 0.0000 0.9995 0.000 1.000 0.000 0.000 0.000
#> GSM11864 2 0.0000 0.9995 0.000 1.000 0.000 0.000 0.000
#> GSM11687 1 0.0000 0.9303 1.000 0.000 0.000 0.000 0.000
#> GSM11693 1 0.0162 0.9310 0.996 0.000 0.000 0.004 0.000
#> GSM11727 1 0.0162 0.9310 0.996 0.000 0.000 0.004 0.000
#> GSM11838 2 0.0000 0.9995 0.000 1.000 0.000 0.000 0.000
#> GSM11681 1 0.0000 0.9303 1.000 0.000 0.000 0.000 0.000
#> GSM11689 1 0.0162 0.9310 0.996 0.000 0.000 0.004 0.000
#> GSM11704 1 0.0000 0.9303 1.000 0.000 0.000 0.000 0.000
#> GSM11703 1 0.0609 0.9161 0.980 0.000 0.020 0.000 0.000
#> GSM11705 1 0.3932 0.4866 0.672 0.000 0.000 0.328 0.000
#> GSM11722 1 0.0162 0.9310 0.996 0.000 0.000 0.004 0.000
#> GSM11730 1 0.0162 0.9310 0.996 0.000 0.000 0.004 0.000
#> GSM11713 4 0.0609 0.8615 0.020 0.000 0.000 0.980 0.000
#> GSM11728 4 0.0162 0.8684 0.004 0.000 0.000 0.996 0.000
#> GSM27947 1 0.5707 0.3602 0.568 0.000 0.004 0.344 0.084
#> GSM27951 1 0.0000 0.9303 1.000 0.000 0.000 0.000 0.000
#> GSM11707 4 0.3366 0.7378 0.000 0.000 0.232 0.768 0.000
#> GSM11716 3 0.4791 0.4046 0.336 0.000 0.636 0.020 0.008
#> GSM11850 3 0.3816 0.8139 0.000 0.000 0.696 0.304 0.000
#> GSM11851 4 0.0000 0.8681 0.000 0.000 0.000 1.000 0.000
#> GSM11721 5 0.0000 0.9331 0.000 0.000 0.000 0.000 1.000
#> GSM11852 4 0.0000 0.8681 0.000 0.000 0.000 1.000 0.000
#> GSM11694 3 0.3816 0.8139 0.000 0.000 0.696 0.304 0.000
#> GSM11695 3 0.3816 0.8139 0.000 0.000 0.696 0.304 0.000
#> GSM11734 2 0.0000 0.9995 0.000 1.000 0.000 0.000 0.000
#> GSM11861 5 0.4273 0.1611 0.000 0.000 0.000 0.448 0.552
#> GSM11843 2 0.0162 0.9957 0.000 0.996 0.000 0.000 0.004
#> GSM11862 5 0.0000 0.9331 0.000 0.000 0.000 0.000 1.000
#> GSM11697 3 0.3816 0.8139 0.000 0.000 0.696 0.304 0.000
#> GSM11714 3 0.4114 -0.0366 0.000 0.000 0.624 0.376 0.000
#> GSM11723 5 0.0000 0.9331 0.000 0.000 0.000 0.000 1.000
#> GSM11845 5 0.0000 0.9331 0.000 0.000 0.000 0.000 1.000
#> GSM11683 3 0.3913 0.7851 0.000 0.000 0.676 0.324 0.000
#> GSM11691 3 0.3816 0.8139 0.000 0.000 0.696 0.304 0.000
#> GSM27949 3 0.3774 0.8126 0.000 0.000 0.704 0.296 0.000
#> GSM27945 3 0.3932 0.7950 0.000 0.000 0.672 0.328 0.000
#> GSM11706 4 0.0162 0.8684 0.004 0.000 0.000 0.996 0.000
#> GSM11853 4 0.0000 0.8681 0.000 0.000 0.000 1.000 0.000
#> GSM11729 2 0.0000 0.9995 0.000 1.000 0.000 0.000 0.000
#> GSM11746 2 0.0000 0.9995 0.000 1.000 0.000 0.000 0.000
#> GSM11711 4 0.0162 0.8684 0.004 0.000 0.000 0.996 0.000
#> GSM11854 4 0.0000 0.8681 0.000 0.000 0.000 1.000 0.000
#> GSM11731 2 0.0000 0.9995 0.000 1.000 0.000 0.000 0.000
#> GSM11839 5 0.0000 0.9331 0.000 0.000 0.000 0.000 1.000
#> GSM11836 5 0.0000 0.9331 0.000 0.000 0.000 0.000 1.000
#> GSM11849 4 0.0000 0.8681 0.000 0.000 0.000 1.000 0.000
#> GSM11682 4 0.3003 0.7793 0.000 0.000 0.188 0.812 0.000
#> GSM11690 5 0.0162 0.9318 0.000 0.000 0.000 0.004 0.996
#> GSM11692 5 0.0162 0.9318 0.000 0.000 0.000 0.004 0.996
#> GSM11841 5 0.0000 0.9331 0.000 0.000 0.000 0.000 1.000
#> GSM11901 5 0.0000 0.9331 0.000 0.000 0.000 0.000 1.000
#> GSM11715 2 0.0000 0.9995 0.000 1.000 0.000 0.000 0.000
#> GSM11724 5 0.3109 0.7153 0.000 0.200 0.000 0.000 0.800
#> GSM11684 5 0.0290 0.9293 0.000 0.000 0.000 0.008 0.992
#> GSM11696 5 0.0162 0.9318 0.000 0.000 0.000 0.004 0.996
#> GSM27952 4 0.2773 0.7931 0.000 0.000 0.164 0.836 0.000
#> GSM27948 5 0.0162 0.9318 0.000 0.000 0.000 0.004 0.996
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM11708 6 0.5410 0.5676 0.000 0.000 0.280 0.000 0.156 0.564
#> GSM11735 3 0.2724 0.6721 0.000 0.000 0.864 0.000 0.052 0.084
#> GSM11733 6 0.0520 0.8262 0.000 0.000 0.000 0.008 0.008 0.984
#> GSM11863 4 0.0260 0.9002 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM11710 6 0.0405 0.8294 0.004 0.000 0.000 0.000 0.008 0.988
#> GSM11712 4 0.0000 0.9031 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM11732 3 0.4777 0.5573 0.000 0.000 0.712 0.168 0.096 0.024
#> GSM11844 6 0.0405 0.8267 0.000 0.000 0.004 0.000 0.008 0.988
#> GSM11842 4 0.0260 0.9002 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM11860 6 0.5368 0.4655 0.116 0.000 0.000 0.252 0.016 0.616
#> GSM11686 6 0.4827 0.6502 0.000 0.000 0.236 0.000 0.112 0.652
#> GSM11688 6 0.5029 0.6174 0.000 0.000 0.276 0.000 0.112 0.612
#> GSM11846 6 0.0458 0.8284 0.016 0.000 0.000 0.000 0.000 0.984
#> GSM11680 3 0.2178 0.7290 0.000 0.000 0.868 0.000 0.000 0.132
#> GSM11698 6 0.1204 0.8024 0.000 0.000 0.056 0.000 0.000 0.944
#> GSM11840 4 0.3398 0.5983 0.000 0.000 0.000 0.740 0.008 0.252
#> GSM11847 4 0.0260 0.9002 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM11685 6 0.5029 0.6174 0.000 0.000 0.276 0.000 0.112 0.612
#> GSM11699 6 0.1007 0.8018 0.000 0.000 0.044 0.000 0.000 0.956
#> GSM27950 3 0.2482 0.5061 0.000 0.000 0.848 0.000 0.148 0.004
#> GSM27946 4 0.2793 0.6898 0.000 0.000 0.000 0.800 0.000 0.200
#> GSM11709 1 0.0458 0.8462 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM11720 1 0.2146 0.7635 0.880 0.000 0.000 0.000 0.116 0.004
#> GSM11726 1 0.2257 0.7620 0.876 0.000 0.000 0.000 0.116 0.008
#> GSM11837 2 0.2048 0.8174 0.000 0.880 0.000 0.000 0.120 0.000
#> GSM11725 2 0.0000 0.9272 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11864 2 0.0000 0.9272 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11687 1 0.0000 0.8494 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11693 1 0.0146 0.8499 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM11727 5 0.3652 0.4461 0.324 0.000 0.000 0.000 0.672 0.004
#> GSM11838 5 0.3851 0.0886 0.000 0.460 0.000 0.000 0.540 0.000
#> GSM11681 1 0.0000 0.8494 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11689 1 0.0146 0.8499 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM11704 1 0.0405 0.8476 0.988 0.000 0.000 0.000 0.008 0.004
#> GSM11703 1 0.1074 0.8296 0.960 0.000 0.028 0.000 0.000 0.012
#> GSM11705 1 0.3563 0.4140 0.664 0.000 0.000 0.000 0.000 0.336
#> GSM11722 5 0.2491 0.5768 0.164 0.000 0.000 0.000 0.836 0.000
#> GSM11730 5 0.3714 0.4198 0.340 0.000 0.000 0.000 0.656 0.004
#> GSM11713 5 0.4504 0.2419 0.032 0.000 0.000 0.000 0.536 0.432
#> GSM11728 6 0.0603 0.8283 0.016 0.000 0.004 0.000 0.000 0.980
#> GSM27947 1 0.5493 0.2983 0.544 0.000 0.016 0.092 0.000 0.348
#> GSM27951 1 0.0000 0.8494 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11707 6 0.4142 0.6640 0.000 0.000 0.232 0.000 0.056 0.712
#> GSM11716 3 0.5458 0.4680 0.184 0.000 0.644 0.004 0.148 0.020
#> GSM11850 3 0.4545 0.7285 0.000 0.000 0.696 0.000 0.112 0.192
#> GSM11851 6 0.0146 0.8284 0.000 0.000 0.004 0.000 0.000 0.996
#> GSM11721 4 0.0000 0.9031 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM11852 6 0.0146 0.8295 0.000 0.000 0.000 0.004 0.000 0.996
#> GSM11694 3 0.3309 0.7809 0.000 0.000 0.720 0.000 0.000 0.280
#> GSM11695 3 0.3309 0.7809 0.000 0.000 0.720 0.000 0.000 0.280
#> GSM11734 2 0.0000 0.9272 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11861 4 0.3838 0.1413 0.000 0.000 0.000 0.552 0.000 0.448
#> GSM11843 2 0.2631 0.7945 0.000 0.820 0.000 0.000 0.180 0.000
#> GSM11862 4 0.0000 0.9031 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM11697 3 0.3309 0.7809 0.000 0.000 0.720 0.000 0.000 0.280
#> GSM11714 3 0.5229 0.1750 0.000 0.000 0.604 0.000 0.156 0.240
#> GSM11723 5 0.2562 0.5663 0.000 0.000 0.000 0.172 0.828 0.000
#> GSM11845 4 0.2631 0.7315 0.000 0.000 0.000 0.820 0.180 0.000
#> GSM11683 3 0.3592 0.7256 0.000 0.000 0.656 0.000 0.000 0.344
#> GSM11691 3 0.3309 0.7809 0.000 0.000 0.720 0.000 0.000 0.280
#> GSM27949 3 0.3266 0.7802 0.000 0.000 0.728 0.000 0.000 0.272
#> GSM27945 3 0.3499 0.7582 0.000 0.000 0.680 0.000 0.000 0.320
#> GSM11706 6 0.0260 0.8297 0.008 0.000 0.000 0.000 0.000 0.992
#> GSM11853 6 0.0146 0.8294 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM11729 2 0.0000 0.9272 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11746 2 0.0000 0.9272 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11711 6 0.0260 0.8297 0.008 0.000 0.000 0.000 0.000 0.992
#> GSM11854 6 0.0146 0.8295 0.000 0.000 0.000 0.004 0.000 0.996
#> GSM11731 2 0.0000 0.9272 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11839 4 0.2631 0.7315 0.000 0.000 0.000 0.820 0.180 0.000
#> GSM11836 4 0.0146 0.9012 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM11849 6 0.0146 0.8295 0.000 0.000 0.000 0.004 0.000 0.996
#> GSM11682 6 0.4319 0.7022 0.000 0.000 0.168 0.000 0.108 0.724
#> GSM11690 4 0.0000 0.9031 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM11692 4 0.0000 0.9031 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM11841 4 0.0000 0.9031 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM11901 4 0.0000 0.9031 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM11715 2 0.2793 0.7780 0.000 0.800 0.000 0.000 0.200 0.000
#> GSM11724 5 0.3629 0.4886 0.000 0.016 0.000 0.260 0.724 0.000
#> GSM11684 4 0.0146 0.9008 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM11696 4 0.0000 0.9031 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM27952 6 0.4104 0.7160 0.000 0.000 0.148 0.000 0.104 0.748
#> GSM27948 4 0.0000 0.9031 0.000 0.000 0.000 1.000 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 cell.line(p) agent(p) time(p) k
#> ATC:pam 81 8.09e-02 0.327 9.83e-05 2
#> ATC:pam 77 4.48e-08 0.437 1.55e-03 3
#> ATC:pam 80 7.79e-10 0.367 6.09e-02 4
#> ATC:pam 77 2.10e-11 0.163 2.79e-02 5
#> ATC:pam 72 8.26e-10 0.140 1.99e-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.
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 14502 rows and 83 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 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 0.225 0.469 0.781 0.3113 0.750 0.750
#> 3 3 0.177 0.444 0.675 0.6598 0.494 0.369
#> 4 4 0.505 0.760 0.820 0.3174 0.753 0.427
#> 5 5 0.561 0.691 0.798 0.0944 0.860 0.540
#> 6 6 0.781 0.786 0.861 0.1094 0.890 0.541
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
#> GSM11708 1 0.7815 0.52499 0.768 0.232
#> GSM11735 1 0.1414 0.67241 0.980 0.020
#> GSM11733 1 0.0376 0.66710 0.996 0.004
#> GSM11863 1 0.8813 -0.32598 0.700 0.300
#> GSM11710 1 0.0672 0.67168 0.992 0.008
#> GSM11712 1 0.9248 -0.48223 0.660 0.340
#> GSM11732 1 0.0000 0.66927 1.000 0.000
#> GSM11844 1 0.0000 0.66927 1.000 0.000
#> GSM11842 1 0.9286 -0.48706 0.656 0.344
#> GSM11860 1 0.5519 0.50659 0.872 0.128
#> GSM11686 1 0.2948 0.66097 0.948 0.052
#> GSM11688 1 0.2423 0.66622 0.960 0.040
#> GSM11846 1 0.5519 0.50659 0.872 0.128
#> GSM11680 1 0.7815 0.52499 0.768 0.232
#> GSM11698 1 0.5946 0.60111 0.856 0.144
#> GSM11840 1 0.0376 0.66710 0.996 0.004
#> GSM11847 1 0.0376 0.66710 0.996 0.004
#> GSM11685 1 0.0000 0.66927 1.000 0.000
#> GSM11699 1 0.0000 0.66927 1.000 0.000
#> GSM27950 1 0.7815 0.52499 0.768 0.232
#> GSM27946 1 0.0000 0.66927 1.000 0.000
#> GSM11709 1 0.9460 0.23763 0.636 0.364
#> GSM11720 1 0.9977 -0.90403 0.528 0.472
#> GSM11726 1 0.5629 0.49925 0.868 0.132
#> GSM11837 2 1.0000 0.99805 0.496 0.504
#> GSM11725 2 0.9998 0.99031 0.492 0.508
#> GSM11864 2 1.0000 0.99805 0.496 0.504
#> GSM11687 1 0.9460 0.23763 0.636 0.364
#> GSM11693 1 0.9460 0.23763 0.636 0.364
#> GSM11727 1 0.9970 -0.89849 0.532 0.468
#> GSM11838 2 0.9998 0.99031 0.492 0.508
#> GSM11681 1 0.8081 0.37947 0.752 0.248
#> GSM11689 1 0.9460 0.23763 0.636 0.364
#> GSM11704 1 0.9460 0.23763 0.636 0.364
#> GSM11703 1 0.5629 0.49925 0.868 0.132
#> GSM11705 1 0.8955 0.29918 0.688 0.312
#> GSM11722 1 0.9988 -0.92669 0.520 0.480
#> GSM11730 1 0.8499 -0.04676 0.724 0.276
#> GSM11713 1 0.5842 0.49281 0.860 0.140
#> GSM11728 1 0.1184 0.66008 0.984 0.016
#> GSM27947 1 0.1843 0.67149 0.972 0.028
#> GSM27951 1 0.9460 0.23763 0.636 0.364
#> GSM11707 1 0.2778 0.66214 0.952 0.048
#> GSM11716 1 0.9248 -0.48562 0.660 0.340
#> GSM11850 1 0.6247 0.59094 0.844 0.156
#> GSM11851 1 0.0000 0.66927 1.000 0.000
#> GSM11721 1 0.0672 0.66842 0.992 0.008
#> GSM11852 1 0.0000 0.66927 1.000 0.000
#> GSM11694 1 0.7453 0.54268 0.788 0.212
#> GSM11695 1 0.7815 0.52499 0.768 0.232
#> GSM11734 2 1.0000 0.99805 0.496 0.504
#> GSM11861 1 0.0672 0.67081 0.992 0.008
#> GSM11843 2 1.0000 0.99805 0.496 0.504
#> GSM11862 1 0.0672 0.67084 0.992 0.008
#> GSM11697 1 0.7815 0.52499 0.768 0.232
#> GSM11714 1 0.7815 0.52499 0.768 0.232
#> GSM11723 2 1.0000 0.99805 0.496 0.504
#> GSM11845 1 0.9988 -0.93626 0.520 0.480
#> GSM11683 1 0.1633 0.67142 0.976 0.024
#> GSM11691 1 0.0938 0.67219 0.988 0.012
#> GSM27949 1 0.7815 0.52499 0.768 0.232
#> GSM27945 1 0.6712 0.57410 0.824 0.176
#> GSM11706 1 0.7815 0.52499 0.768 0.232
#> GSM11853 1 0.5629 0.60981 0.868 0.132
#> GSM11729 2 1.0000 0.99805 0.496 0.504
#> GSM11746 2 1.0000 0.99805 0.496 0.504
#> GSM11711 1 0.3114 0.65896 0.944 0.056
#> GSM11854 1 0.0000 0.66927 1.000 0.000
#> GSM11731 2 1.0000 0.99805 0.496 0.504
#> GSM11839 1 0.9286 -0.49594 0.656 0.344
#> GSM11836 1 0.6247 0.36835 0.844 0.156
#> GSM11849 1 0.0000 0.66927 1.000 0.000
#> GSM11682 1 0.1414 0.67269 0.980 0.020
#> GSM11690 1 0.1184 0.66968 0.984 0.016
#> GSM11692 1 0.0672 0.66842 0.992 0.008
#> GSM11841 1 0.9286 -0.48706 0.656 0.344
#> GSM11901 1 0.7950 -0.00138 0.760 0.240
#> GSM11715 2 1.0000 0.99805 0.496 0.504
#> GSM11724 2 1.0000 0.99805 0.496 0.504
#> GSM11684 1 0.2043 0.66570 0.968 0.032
#> GSM11696 1 0.1843 0.66530 0.972 0.028
#> GSM27952 1 0.1414 0.67189 0.980 0.020
#> GSM27948 1 0.0672 0.67081 0.992 0.008
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM11708 3 0.0592 0.4465 0.012 0.000 0.988
#> GSM11735 3 0.5785 0.6312 0.332 0.000 0.668
#> GSM11733 1 0.4062 0.6054 0.836 0.000 0.164
#> GSM11863 1 0.3771 0.6584 0.876 0.012 0.112
#> GSM11710 1 0.2261 0.6843 0.932 0.000 0.068
#> GSM11712 1 0.1182 0.6901 0.976 0.012 0.012
#> GSM11732 3 0.6280 0.5435 0.460 0.000 0.540
#> GSM11844 3 0.6280 0.5435 0.460 0.000 0.540
#> GSM11842 1 0.1182 0.6901 0.976 0.012 0.012
#> GSM11860 1 0.9152 -0.2220 0.484 0.152 0.364
#> GSM11686 3 0.5926 0.6140 0.356 0.000 0.644
#> GSM11688 3 0.6095 0.5699 0.392 0.000 0.608
#> GSM11846 1 0.8918 -0.2560 0.492 0.128 0.380
#> GSM11680 3 0.4796 0.6377 0.220 0.000 0.780
#> GSM11698 3 0.4931 0.6419 0.232 0.000 0.768
#> GSM11840 1 0.3686 0.6323 0.860 0.000 0.140
#> GSM11847 1 0.3619 0.6363 0.864 0.000 0.136
#> GSM11685 1 0.5016 0.4984 0.760 0.000 0.240
#> GSM11699 1 0.2448 0.6810 0.924 0.000 0.076
#> GSM27950 3 0.0592 0.4465 0.012 0.000 0.988
#> GSM27946 1 0.3752 0.5895 0.856 0.000 0.144
#> GSM11709 2 0.6079 0.4890 0.388 0.612 0.000
#> GSM11720 2 0.6280 0.3947 0.460 0.540 0.000
#> GSM11726 1 0.9356 -0.1442 0.460 0.368 0.172
#> GSM11837 2 0.8824 0.0916 0.124 0.512 0.364
#> GSM11725 2 0.3412 0.4598 0.124 0.876 0.000
#> GSM11864 2 0.8812 0.0987 0.124 0.516 0.360
#> GSM11687 2 0.6079 0.4890 0.388 0.612 0.000
#> GSM11693 2 0.6079 0.4890 0.388 0.612 0.000
#> GSM11727 1 0.9653 -0.1449 0.456 0.232 0.312
#> GSM11838 2 0.3412 0.4598 0.124 0.876 0.000
#> GSM11681 2 0.6079 0.4890 0.388 0.612 0.000
#> GSM11689 2 0.6079 0.4890 0.388 0.612 0.000
#> GSM11704 2 0.6079 0.4890 0.388 0.612 0.000
#> GSM11703 2 0.6948 0.3757 0.472 0.512 0.016
#> GSM11705 2 0.6079 0.4890 0.388 0.612 0.000
#> GSM11722 2 0.6244 0.4149 0.440 0.560 0.000
#> GSM11730 2 0.6280 0.3947 0.460 0.540 0.000
#> GSM11713 2 0.6295 0.3929 0.472 0.528 0.000
#> GSM11728 1 0.5968 -0.0957 0.636 0.000 0.364
#> GSM27947 1 0.5988 -0.1088 0.632 0.000 0.368
#> GSM27951 2 0.6079 0.4890 0.388 0.612 0.000
#> GSM11707 3 0.0747 0.4477 0.016 0.000 0.984
#> GSM11716 3 0.6280 0.5435 0.460 0.000 0.540
#> GSM11850 3 0.6274 0.5508 0.456 0.000 0.544
#> GSM11851 1 0.4178 0.6002 0.828 0.000 0.172
#> GSM11721 1 0.0592 0.6906 0.988 0.000 0.012
#> GSM11852 1 0.0592 0.6977 0.988 0.000 0.012
#> GSM11694 3 0.6168 0.5980 0.412 0.000 0.588
#> GSM11695 3 0.5905 0.6348 0.352 0.000 0.648
#> GSM11734 2 0.6307 0.2385 0.488 0.512 0.000
#> GSM11861 1 0.0237 0.6943 0.996 0.004 0.000
#> GSM11843 2 0.6307 0.2385 0.488 0.512 0.000
#> GSM11862 1 0.0424 0.6925 0.992 0.000 0.008
#> GSM11697 3 0.5859 0.6371 0.344 0.000 0.656
#> GSM11714 3 0.0592 0.4465 0.012 0.000 0.988
#> GSM11723 1 0.8925 -0.2014 0.504 0.132 0.364
#> GSM11845 1 0.5010 0.6091 0.840 0.076 0.084
#> GSM11683 1 0.6062 -0.1425 0.616 0.000 0.384
#> GSM11691 1 0.6192 -0.2597 0.580 0.000 0.420
#> GSM27949 3 0.5760 0.6408 0.328 0.000 0.672
#> GSM27945 3 0.6274 0.5508 0.456 0.000 0.544
#> GSM11706 3 0.4796 0.6371 0.220 0.000 0.780
#> GSM11853 3 0.6274 0.5508 0.456 0.000 0.544
#> GSM11729 2 0.8824 0.0916 0.124 0.512 0.364
#> GSM11746 2 0.8824 0.0916 0.124 0.512 0.364
#> GSM11711 3 0.6295 0.5176 0.472 0.000 0.528
#> GSM11854 1 0.6225 -0.2312 0.568 0.000 0.432
#> GSM11731 2 0.6307 0.2385 0.488 0.512 0.000
#> GSM11839 1 0.1129 0.6882 0.976 0.020 0.004
#> GSM11836 1 0.1182 0.6901 0.976 0.012 0.012
#> GSM11849 1 0.0000 0.6939 1.000 0.000 0.000
#> GSM11682 1 0.0592 0.6977 0.988 0.000 0.012
#> GSM11690 1 0.0829 0.6975 0.984 0.004 0.012
#> GSM11692 1 0.0592 0.6906 0.988 0.000 0.012
#> GSM11841 1 0.1182 0.6901 0.976 0.012 0.012
#> GSM11901 1 0.1182 0.6901 0.976 0.012 0.012
#> GSM11715 2 0.6307 0.2385 0.488 0.512 0.000
#> GSM11724 2 0.6307 0.2385 0.488 0.512 0.000
#> GSM11684 1 0.2116 0.6694 0.948 0.040 0.012
#> GSM11696 1 0.2116 0.6694 0.948 0.040 0.012
#> GSM27952 1 0.4235 0.5729 0.824 0.000 0.176
#> GSM27948 1 0.0237 0.6943 0.996 0.004 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM11708 3 0.3172 0.663 0.000 0.000 0.840 0.160
#> GSM11735 3 0.0336 0.813 0.000 0.000 0.992 0.008
#> GSM11733 4 0.4193 0.823 0.000 0.000 0.268 0.732
#> GSM11863 4 0.3172 0.932 0.000 0.000 0.160 0.840
#> GSM11710 3 0.4761 0.407 0.000 0.004 0.664 0.332
#> GSM11712 4 0.3172 0.932 0.000 0.000 0.160 0.840
#> GSM11732 3 0.3074 0.786 0.000 0.000 0.848 0.152
#> GSM11844 3 0.2760 0.798 0.000 0.000 0.872 0.128
#> GSM11842 4 0.3172 0.932 0.000 0.000 0.160 0.840
#> GSM11860 2 0.6930 0.180 0.000 0.524 0.356 0.120
#> GSM11686 3 0.1398 0.817 0.000 0.004 0.956 0.040
#> GSM11688 3 0.3157 0.740 0.000 0.004 0.852 0.144
#> GSM11846 3 0.5403 0.738 0.116 0.016 0.768 0.100
#> GSM11680 3 0.0000 0.810 0.000 0.000 1.000 0.000
#> GSM11698 3 0.0592 0.816 0.000 0.000 0.984 0.016
#> GSM11840 4 0.3528 0.916 0.000 0.000 0.192 0.808
#> GSM11847 4 0.3569 0.913 0.000 0.000 0.196 0.804
#> GSM11685 4 0.5105 0.540 0.000 0.004 0.432 0.564
#> GSM11699 4 0.3764 0.904 0.000 0.000 0.216 0.784
#> GSM27950 3 0.3172 0.663 0.000 0.000 0.840 0.160
#> GSM27946 3 0.4761 0.416 0.000 0.000 0.628 0.372
#> GSM11709 1 0.0000 0.785 1.000 0.000 0.000 0.000
#> GSM11720 1 0.6914 0.668 0.652 0.204 0.112 0.032
#> GSM11726 1 0.6710 0.712 0.684 0.112 0.164 0.040
#> GSM11837 2 0.1492 0.787 0.036 0.956 0.004 0.004
#> GSM11725 2 0.3257 0.708 0.152 0.844 0.000 0.004
#> GSM11864 2 0.2382 0.769 0.080 0.912 0.004 0.004
#> GSM11687 1 0.0000 0.785 1.000 0.000 0.000 0.000
#> GSM11693 1 0.0000 0.785 1.000 0.000 0.000 0.000
#> GSM11727 2 0.4450 0.687 0.040 0.832 0.096 0.032
#> GSM11838 2 0.2197 0.769 0.080 0.916 0.000 0.004
#> GSM11681 1 0.4144 0.762 0.816 0.004 0.152 0.028
#> GSM11689 1 0.0000 0.785 1.000 0.000 0.000 0.000
#> GSM11704 1 0.0000 0.785 1.000 0.000 0.000 0.000
#> GSM11703 1 0.6138 0.730 0.716 0.076 0.176 0.032
#> GSM11705 1 0.4549 0.783 0.820 0.056 0.108 0.016
#> GSM11722 2 0.5168 -0.119 0.492 0.504 0.000 0.004
#> GSM11730 1 0.7536 0.626 0.592 0.216 0.160 0.032
#> GSM11713 1 0.5859 0.750 0.740 0.072 0.156 0.032
#> GSM11728 3 0.5169 0.616 0.000 0.032 0.696 0.272
#> GSM27947 3 0.2973 0.794 0.000 0.000 0.856 0.144
#> GSM27951 1 0.0000 0.785 1.000 0.000 0.000 0.000
#> GSM11707 3 0.3172 0.663 0.000 0.000 0.840 0.160
#> GSM11716 2 0.7002 0.308 0.032 0.544 0.368 0.056
#> GSM11850 3 0.2345 0.813 0.000 0.000 0.900 0.100
#> GSM11851 4 0.4855 0.596 0.000 0.000 0.400 0.600
#> GSM11721 4 0.3172 0.932 0.000 0.000 0.160 0.840
#> GSM11852 4 0.4188 0.861 0.000 0.004 0.244 0.752
#> GSM11694 3 0.2345 0.813 0.000 0.000 0.900 0.100
#> GSM11695 3 0.0921 0.818 0.000 0.000 0.972 0.028
#> GSM11734 2 0.1716 0.812 0.000 0.936 0.000 0.064
#> GSM11861 4 0.3583 0.927 0.000 0.004 0.180 0.816
#> GSM11843 2 0.1716 0.812 0.000 0.936 0.000 0.064
#> GSM11862 4 0.3172 0.932 0.000 0.000 0.160 0.840
#> GSM11697 3 0.0921 0.818 0.000 0.000 0.972 0.028
#> GSM11714 3 0.3172 0.663 0.000 0.000 0.840 0.160
#> GSM11723 2 0.2473 0.800 0.000 0.908 0.012 0.080
#> GSM11845 2 0.3441 0.760 0.000 0.856 0.024 0.120
#> GSM11683 3 0.3569 0.710 0.000 0.000 0.804 0.196
#> GSM11691 3 0.2281 0.816 0.000 0.000 0.904 0.096
#> GSM27949 3 0.0000 0.810 0.000 0.000 1.000 0.000
#> GSM27945 3 0.2345 0.813 0.000 0.000 0.900 0.100
#> GSM11706 3 0.0188 0.812 0.000 0.000 0.996 0.004
#> GSM11853 3 0.2345 0.813 0.000 0.000 0.900 0.100
#> GSM11729 2 0.1576 0.811 0.000 0.948 0.004 0.048
#> GSM11746 2 0.1585 0.786 0.040 0.952 0.004 0.004
#> GSM11711 3 0.2345 0.813 0.000 0.000 0.900 0.100
#> GSM11854 3 0.3528 0.741 0.000 0.000 0.808 0.192
#> GSM11731 2 0.1716 0.812 0.000 0.936 0.000 0.064
#> GSM11839 4 0.5141 0.847 0.000 0.084 0.160 0.756
#> GSM11836 4 0.3172 0.932 0.000 0.000 0.160 0.840
#> GSM11849 4 0.3945 0.898 0.000 0.004 0.216 0.780
#> GSM11682 3 0.4889 0.350 0.000 0.004 0.636 0.360
#> GSM11690 4 0.3583 0.927 0.000 0.004 0.180 0.816
#> GSM11692 4 0.3172 0.932 0.000 0.000 0.160 0.840
#> GSM11841 4 0.3172 0.932 0.000 0.000 0.160 0.840
#> GSM11901 4 0.3172 0.932 0.000 0.000 0.160 0.840
#> GSM11715 2 0.1637 0.812 0.000 0.940 0.000 0.060
#> GSM11724 2 0.1716 0.812 0.000 0.936 0.000 0.064
#> GSM11684 4 0.3768 0.925 0.000 0.008 0.184 0.808
#> GSM11696 4 0.3768 0.925 0.000 0.008 0.184 0.808
#> GSM27952 3 0.4401 0.577 0.000 0.004 0.724 0.272
#> GSM27948 4 0.3355 0.931 0.000 0.004 0.160 0.836
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM11708 3 0.5887 0.6360 0.000 0.000 0.592 0.156 0.252
#> GSM11735 3 0.4779 0.6146 0.000 0.000 0.588 0.388 0.024
#> GSM11733 5 0.6009 0.6603 0.000 0.000 0.180 0.240 0.580
#> GSM11863 5 0.3662 0.8952 0.000 0.000 0.004 0.252 0.744
#> GSM11710 4 0.1043 0.6853 0.000 0.000 0.040 0.960 0.000
#> GSM11712 5 0.3508 0.8962 0.000 0.000 0.000 0.252 0.748
#> GSM11732 3 0.3671 0.7046 0.000 0.000 0.756 0.236 0.008
#> GSM11844 3 0.3452 0.7045 0.000 0.000 0.756 0.244 0.000
#> GSM11842 5 0.3508 0.8962 0.000 0.000 0.000 0.252 0.748
#> GSM11860 2 0.7057 0.0551 0.000 0.460 0.264 0.256 0.020
#> GSM11686 4 0.3966 0.1604 0.000 0.000 0.336 0.664 0.000
#> GSM11688 4 0.3707 0.3287 0.000 0.000 0.284 0.716 0.000
#> GSM11846 3 0.3170 0.7327 0.008 0.004 0.828 0.160 0.000
#> GSM11680 3 0.2690 0.6745 0.000 0.000 0.844 0.156 0.000
#> GSM11698 3 0.2690 0.6745 0.000 0.000 0.844 0.156 0.000
#> GSM11840 5 0.4602 0.8495 0.000 0.000 0.052 0.240 0.708
#> GSM11847 5 0.4086 0.8739 0.000 0.000 0.024 0.240 0.736
#> GSM11685 4 0.0955 0.6881 0.000 0.000 0.028 0.968 0.004
#> GSM11699 4 0.3368 0.7051 0.000 0.000 0.024 0.820 0.156
#> GSM27950 3 0.5887 0.6360 0.000 0.000 0.592 0.156 0.252
#> GSM27946 4 0.5163 0.5883 0.000 0.000 0.152 0.692 0.156
#> GSM11709 1 0.0000 0.7769 1.000 0.000 0.000 0.000 0.000
#> GSM11720 2 0.6138 0.1869 0.324 0.548 0.000 0.120 0.008
#> GSM11726 1 0.7446 0.3597 0.440 0.292 0.028 0.232 0.008
#> GSM11837 2 0.0290 0.8441 0.000 0.992 0.000 0.000 0.008
#> GSM11725 2 0.0000 0.8451 0.000 1.000 0.000 0.000 0.000
#> GSM11864 2 0.0000 0.8451 0.000 1.000 0.000 0.000 0.000
#> GSM11687 1 0.0000 0.7769 1.000 0.000 0.000 0.000 0.000
#> GSM11693 1 0.0000 0.7769 1.000 0.000 0.000 0.000 0.000
#> GSM11727 2 0.3373 0.6436 0.008 0.816 0.000 0.168 0.008
#> GSM11838 2 0.0000 0.8451 0.000 1.000 0.000 0.000 0.000
#> GSM11681 1 0.3521 0.6334 0.764 0.000 0.004 0.232 0.000
#> GSM11689 1 0.0000 0.7769 1.000 0.000 0.000 0.000 0.000
#> GSM11704 1 0.0000 0.7769 1.000 0.000 0.000 0.000 0.000
#> GSM11703 1 0.3706 0.6284 0.756 0.004 0.004 0.236 0.000
#> GSM11705 1 0.1991 0.7608 0.916 0.004 0.004 0.076 0.000
#> GSM11722 2 0.3783 0.5649 0.252 0.740 0.000 0.000 0.008
#> GSM11730 1 0.6804 0.4371 0.500 0.256 0.004 0.232 0.008
#> GSM11713 1 0.3676 0.6329 0.760 0.004 0.004 0.232 0.000
#> GSM11728 4 0.3425 0.6500 0.112 0.000 0.004 0.840 0.044
#> GSM27947 3 0.3424 0.7077 0.000 0.000 0.760 0.240 0.000
#> GSM27951 1 0.0000 0.7769 1.000 0.000 0.000 0.000 0.000
#> GSM11707 3 0.5887 0.6360 0.000 0.000 0.592 0.156 0.252
#> GSM11716 3 0.5527 0.6092 0.000 0.104 0.656 0.232 0.008
#> GSM11850 3 0.3424 0.7077 0.000 0.000 0.760 0.240 0.000
#> GSM11851 3 0.4276 0.6755 0.000 0.000 0.724 0.244 0.032
#> GSM11721 5 0.3561 0.8924 0.000 0.000 0.000 0.260 0.740
#> GSM11852 4 0.3368 0.7051 0.000 0.000 0.024 0.820 0.156
#> GSM11694 3 0.2179 0.7343 0.000 0.000 0.888 0.112 0.000
#> GSM11695 3 0.0290 0.6959 0.000 0.000 0.992 0.008 0.000
#> GSM11734 2 0.1831 0.8379 0.000 0.920 0.000 0.004 0.076
#> GSM11861 4 0.2848 0.6996 0.000 0.000 0.004 0.840 0.156
#> GSM11843 2 0.1831 0.8379 0.000 0.920 0.000 0.004 0.076
#> GSM11862 5 0.4306 0.3810 0.000 0.000 0.000 0.492 0.508
#> GSM11697 3 0.0404 0.6966 0.000 0.000 0.988 0.012 0.000
#> GSM11714 3 0.5887 0.6360 0.000 0.000 0.592 0.156 0.252
#> GSM11723 2 0.2362 0.8323 0.000 0.900 0.000 0.024 0.076
#> GSM11845 2 0.3003 0.8083 0.000 0.864 0.000 0.044 0.092
#> GSM11683 4 0.4219 -0.1848 0.000 0.000 0.416 0.584 0.000
#> GSM11691 3 0.3452 0.7079 0.000 0.000 0.756 0.244 0.000
#> GSM27949 3 0.2690 0.6745 0.000 0.000 0.844 0.156 0.000
#> GSM27945 3 0.3424 0.7077 0.000 0.000 0.760 0.240 0.000
#> GSM11706 3 0.2690 0.6745 0.000 0.000 0.844 0.156 0.000
#> GSM11853 3 0.3242 0.7207 0.000 0.000 0.784 0.216 0.000
#> GSM11729 2 0.0162 0.8453 0.000 0.996 0.000 0.004 0.000
#> GSM11746 2 0.0000 0.8451 0.000 1.000 0.000 0.000 0.000
#> GSM11711 3 0.2424 0.7373 0.000 0.000 0.868 0.132 0.000
#> GSM11854 3 0.3452 0.7045 0.000 0.000 0.756 0.244 0.000
#> GSM11731 2 0.1831 0.8379 0.000 0.920 0.000 0.004 0.076
#> GSM11839 5 0.5875 0.6957 0.000 0.152 0.000 0.256 0.592
#> GSM11836 5 0.3809 0.8899 0.000 0.008 0.000 0.256 0.736
#> GSM11849 4 0.2848 0.6996 0.000 0.000 0.004 0.840 0.156
#> GSM11682 4 0.0510 0.6892 0.000 0.000 0.016 0.984 0.000
#> GSM11690 4 0.2848 0.6996 0.000 0.000 0.004 0.840 0.156
#> GSM11692 5 0.3586 0.8913 0.000 0.000 0.000 0.264 0.736
#> GSM11841 5 0.3508 0.8962 0.000 0.000 0.000 0.252 0.748
#> GSM11901 5 0.3508 0.8962 0.000 0.000 0.000 0.252 0.748
#> GSM11715 2 0.0566 0.8467 0.000 0.984 0.000 0.004 0.012
#> GSM11724 2 0.1952 0.8370 0.000 0.912 0.000 0.004 0.084
#> GSM11684 4 0.2690 0.6962 0.000 0.000 0.000 0.844 0.156
#> GSM11696 4 0.2690 0.6962 0.000 0.000 0.000 0.844 0.156
#> GSM27952 4 0.0880 0.6885 0.000 0.000 0.032 0.968 0.000
#> GSM27948 4 0.3123 0.6676 0.000 0.000 0.004 0.812 0.184
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM11708 6 0.3221 0.8799 0.000 0.000 0.264 0.000 0.000 0.736
#> GSM11735 6 0.3221 0.8799 0.000 0.000 0.264 0.000 0.000 0.736
#> GSM11733 3 0.3464 0.5147 0.000 0.000 0.688 0.000 0.312 0.000
#> GSM11863 5 0.0000 0.8735 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11710 6 0.3531 0.4999 0.000 0.000 0.000 0.328 0.000 0.672
#> GSM11712 5 0.0000 0.8735 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11732 3 0.1812 0.8077 0.000 0.000 0.912 0.000 0.008 0.080
#> GSM11844 3 0.0000 0.8455 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11842 5 0.0000 0.8735 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11860 3 0.4663 0.5951 0.000 0.132 0.700 0.000 0.164 0.004
#> GSM11686 6 0.4191 0.8647 0.000 0.000 0.240 0.056 0.000 0.704
#> GSM11688 6 0.4620 0.8061 0.000 0.000 0.176 0.132 0.000 0.692
#> GSM11846 3 0.0622 0.8386 0.012 0.000 0.980 0.000 0.000 0.008
#> GSM11680 6 0.3351 0.8673 0.000 0.000 0.288 0.000 0.000 0.712
#> GSM11698 6 0.3330 0.8706 0.000 0.000 0.284 0.000 0.000 0.716
#> GSM11840 3 0.3860 0.1171 0.000 0.000 0.528 0.000 0.472 0.000
#> GSM11847 5 0.3823 0.0961 0.000 0.000 0.436 0.000 0.564 0.000
#> GSM11685 6 0.3601 0.5227 0.000 0.000 0.000 0.312 0.004 0.684
#> GSM11699 4 0.2178 0.8039 0.000 0.000 0.132 0.868 0.000 0.000
#> GSM27950 6 0.3221 0.8799 0.000 0.000 0.264 0.000 0.000 0.736
#> GSM27946 3 0.2854 0.6763 0.000 0.000 0.792 0.208 0.000 0.000
#> GSM11709 1 0.0000 0.8833 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11720 1 0.6510 0.3590 0.520 0.232 0.000 0.000 0.064 0.184
#> GSM11726 1 0.6518 0.5987 0.608 0.080 0.064 0.000 0.064 0.184
#> GSM11837 2 0.3490 0.8435 0.000 0.784 0.000 0.000 0.040 0.176
#> GSM11725 2 0.2664 0.8482 0.000 0.816 0.000 0.000 0.000 0.184
#> GSM11864 2 0.2664 0.8482 0.000 0.816 0.000 0.000 0.000 0.184
#> GSM11687 1 0.0000 0.8833 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11693 1 0.0000 0.8833 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11727 2 0.5831 0.7071 0.128 0.624 0.000 0.000 0.064 0.184
#> GSM11838 2 0.2664 0.8482 0.000 0.816 0.000 0.000 0.000 0.184
#> GSM11681 1 0.0000 0.8833 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11689 1 0.0000 0.8833 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11704 1 0.0000 0.8833 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11703 1 0.2664 0.7787 0.816 0.000 0.000 0.000 0.000 0.184
#> GSM11705 1 0.0146 0.8824 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM11722 2 0.5603 0.7377 0.104 0.648 0.000 0.000 0.064 0.184
#> GSM11730 1 0.5643 0.6099 0.644 0.108 0.000 0.000 0.064 0.184
#> GSM11713 1 0.0291 0.8812 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM11728 4 0.2664 0.6860 0.000 0.000 0.184 0.816 0.000 0.000
#> GSM27947 3 0.0000 0.8455 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM27951 1 0.0000 0.8833 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11707 6 0.3221 0.8799 0.000 0.000 0.264 0.000 0.000 0.736
#> GSM11716 3 0.4392 0.5919 0.000 0.000 0.680 0.000 0.064 0.256
#> GSM11850 3 0.0000 0.8455 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11851 3 0.3172 0.7268 0.000 0.000 0.824 0.048 0.128 0.000
#> GSM11721 5 0.1462 0.8439 0.000 0.000 0.008 0.056 0.936 0.000
#> GSM11852 4 0.0260 0.9119 0.000 0.000 0.008 0.992 0.000 0.000
#> GSM11694 3 0.0000 0.8455 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11695 3 0.0000 0.8455 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11734 2 0.0000 0.8635 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11861 4 0.0260 0.9119 0.000 0.000 0.008 0.992 0.000 0.000
#> GSM11843 2 0.0937 0.8615 0.000 0.960 0.000 0.000 0.040 0.000
#> GSM11862 5 0.2980 0.6983 0.000 0.000 0.008 0.192 0.800 0.000
#> GSM11697 3 0.0000 0.8455 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11714 6 0.3221 0.8799 0.000 0.000 0.264 0.000 0.000 0.736
#> GSM11723 2 0.1387 0.8523 0.000 0.932 0.000 0.000 0.068 0.000
#> GSM11845 2 0.2378 0.7824 0.000 0.848 0.000 0.000 0.152 0.000
#> GSM11683 6 0.5202 0.7415 0.000 0.000 0.196 0.188 0.000 0.616
#> GSM11691 3 0.0000 0.8455 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM27949 3 0.3428 0.2569 0.000 0.000 0.696 0.000 0.000 0.304
#> GSM27945 3 0.0000 0.8455 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11706 6 0.3330 0.8706 0.000 0.000 0.284 0.000 0.000 0.716
#> GSM11853 3 0.0000 0.8455 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11729 2 0.0000 0.8635 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11746 2 0.2664 0.8482 0.000 0.816 0.000 0.000 0.000 0.184
#> GSM11711 3 0.0000 0.8455 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11854 3 0.0790 0.8303 0.000 0.000 0.968 0.032 0.000 0.000
#> GSM11731 2 0.0000 0.8635 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11839 5 0.2416 0.7725 0.000 0.156 0.000 0.000 0.844 0.000
#> GSM11836 5 0.2632 0.7630 0.000 0.164 0.000 0.004 0.832 0.000
#> GSM11849 4 0.0260 0.9119 0.000 0.000 0.008 0.992 0.000 0.000
#> GSM11682 4 0.1204 0.8688 0.000 0.000 0.000 0.944 0.000 0.056
#> GSM11690 4 0.0260 0.9119 0.000 0.000 0.008 0.992 0.000 0.000
#> GSM11692 5 0.1462 0.8439 0.000 0.000 0.008 0.056 0.936 0.000
#> GSM11841 5 0.0000 0.8735 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11901 5 0.0000 0.8735 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11715 2 0.0000 0.8635 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11724 2 0.1204 0.8577 0.000 0.944 0.000 0.000 0.056 0.000
#> GSM11684 4 0.0260 0.9119 0.000 0.000 0.008 0.992 0.000 0.000
#> GSM11696 4 0.0260 0.9119 0.000 0.000 0.008 0.992 0.000 0.000
#> GSM27952 4 0.3725 0.4648 0.000 0.000 0.008 0.676 0.000 0.316
#> GSM27948 4 0.0622 0.9050 0.000 0.000 0.008 0.980 0.012 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 cell.line(p) agent(p) time(p) k
#> ATC:mclust 59 3.57e-03 0.460 2.17e-03 2
#> ATC:mclust 44 1.62e-01 0.715 1.81e-03 3
#> ATC:mclust 77 1.70e-09 0.715 6.18e-05 4
#> ATC:mclust 75 1.63e-08 0.402 1.62e-07 5
#> ATC:mclust 77 2.09e-09 0.741 2.89e-04 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "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 14502 rows and 83 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.684 0.856 0.935 0.4922 0.500 0.500
#> 3 3 0.612 0.782 0.889 0.3518 0.694 0.462
#> 4 4 0.720 0.747 0.872 0.1275 0.797 0.481
#> 5 5 0.584 0.587 0.756 0.0560 0.896 0.633
#> 6 6 0.612 0.495 0.697 0.0391 0.931 0.707
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM11708 1 0.0000 0.905 1.000 0.000
#> GSM11735 1 0.0000 0.905 1.000 0.000
#> GSM11733 1 0.0000 0.905 1.000 0.000
#> GSM11863 2 0.0000 0.953 0.000 1.000
#> GSM11710 1 0.0000 0.905 1.000 0.000
#> GSM11712 2 0.0000 0.953 0.000 1.000
#> GSM11732 2 0.8267 0.609 0.260 0.740
#> GSM11844 1 0.9993 0.178 0.516 0.484
#> GSM11842 2 0.0000 0.953 0.000 1.000
#> GSM11860 2 0.0000 0.953 0.000 1.000
#> GSM11686 1 0.0000 0.905 1.000 0.000
#> GSM11688 1 0.0000 0.905 1.000 0.000
#> GSM11846 1 0.7139 0.781 0.804 0.196
#> GSM11680 1 0.0000 0.905 1.000 0.000
#> GSM11698 1 0.0000 0.905 1.000 0.000
#> GSM11840 1 0.7528 0.759 0.784 0.216
#> GSM11847 1 0.4298 0.863 0.912 0.088
#> GSM11685 1 0.0000 0.905 1.000 0.000
#> GSM11699 1 0.0000 0.905 1.000 0.000
#> GSM27950 1 0.0000 0.905 1.000 0.000
#> GSM27946 1 0.5946 0.826 0.856 0.144
#> GSM11709 2 0.6438 0.774 0.164 0.836
#> GSM11720 2 0.0000 0.953 0.000 1.000
#> GSM11726 2 0.0000 0.953 0.000 1.000
#> GSM11837 2 0.0000 0.953 0.000 1.000
#> GSM11725 2 0.0000 0.953 0.000 1.000
#> GSM11864 2 0.0000 0.953 0.000 1.000
#> GSM11687 2 0.9881 0.104 0.436 0.564
#> GSM11693 2 0.6247 0.785 0.156 0.844
#> GSM11727 2 0.0000 0.953 0.000 1.000
#> GSM11838 2 0.0000 0.953 0.000 1.000
#> GSM11681 1 0.0000 0.905 1.000 0.000
#> GSM11689 2 0.0376 0.951 0.004 0.996
#> GSM11704 2 0.0000 0.953 0.000 1.000
#> GSM11703 1 0.9983 0.210 0.524 0.476
#> GSM11705 1 0.7602 0.755 0.780 0.220
#> GSM11722 2 0.0000 0.953 0.000 1.000
#> GSM11730 2 0.0000 0.953 0.000 1.000
#> GSM11713 1 0.7299 0.773 0.796 0.204
#> GSM11728 1 0.3879 0.870 0.924 0.076
#> GSM27947 1 0.8016 0.724 0.756 0.244
#> GSM27951 1 0.9209 0.576 0.664 0.336
#> GSM11707 1 0.0000 0.905 1.000 0.000
#> GSM11716 2 0.0000 0.953 0.000 1.000
#> GSM11850 1 0.9552 0.492 0.624 0.376
#> GSM11851 1 0.0000 0.905 1.000 0.000
#> GSM11721 2 0.1184 0.941 0.016 0.984
#> GSM11852 1 0.0000 0.905 1.000 0.000
#> GSM11694 1 0.0000 0.905 1.000 0.000
#> GSM11695 1 0.0000 0.905 1.000 0.000
#> GSM11734 2 0.0000 0.953 0.000 1.000
#> GSM11861 2 0.9209 0.431 0.336 0.664
#> GSM11843 2 0.0000 0.953 0.000 1.000
#> GSM11862 2 0.2948 0.908 0.052 0.948
#> GSM11697 1 0.0000 0.905 1.000 0.000
#> GSM11714 1 0.0000 0.905 1.000 0.000
#> GSM11723 2 0.0000 0.953 0.000 1.000
#> GSM11845 2 0.0000 0.953 0.000 1.000
#> GSM11683 1 0.0000 0.905 1.000 0.000
#> GSM11691 1 0.0000 0.905 1.000 0.000
#> GSM27949 1 0.0000 0.905 1.000 0.000
#> GSM27945 1 0.6247 0.817 0.844 0.156
#> GSM11706 1 0.0000 0.905 1.000 0.000
#> GSM11853 1 0.5842 0.829 0.860 0.140
#> GSM11729 2 0.0000 0.953 0.000 1.000
#> GSM11746 2 0.0000 0.953 0.000 1.000
#> GSM11711 1 0.0000 0.905 1.000 0.000
#> GSM11854 1 0.0000 0.905 1.000 0.000
#> GSM11731 2 0.0000 0.953 0.000 1.000
#> GSM11839 2 0.0000 0.953 0.000 1.000
#> GSM11836 2 0.0000 0.953 0.000 1.000
#> GSM11849 1 0.6973 0.790 0.812 0.188
#> GSM11682 1 0.0000 0.905 1.000 0.000
#> GSM11690 1 0.0000 0.905 1.000 0.000
#> GSM11692 2 0.1184 0.941 0.016 0.984
#> GSM11841 2 0.0000 0.953 0.000 1.000
#> GSM11901 2 0.0000 0.953 0.000 1.000
#> GSM11715 2 0.0000 0.953 0.000 1.000
#> GSM11724 2 0.0000 0.953 0.000 1.000
#> GSM11684 1 0.0000 0.905 1.000 0.000
#> GSM11696 1 0.2603 0.886 0.956 0.044
#> GSM27952 1 0.0000 0.905 1.000 0.000
#> GSM27948 1 0.9491 0.509 0.632 0.368
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM11708 3 0.5835 0.465 0.340 0.000 0.660
#> GSM11735 3 0.3412 0.768 0.124 0.000 0.876
#> GSM11733 3 0.0747 0.831 0.000 0.016 0.984
#> GSM11863 2 0.5327 0.571 0.000 0.728 0.272
#> GSM11710 3 0.0000 0.832 0.000 0.000 1.000
#> GSM11712 2 0.1753 0.887 0.000 0.952 0.048
#> GSM11732 2 0.2749 0.878 0.012 0.924 0.064
#> GSM11844 3 0.6305 0.204 0.000 0.484 0.516
#> GSM11842 2 0.2165 0.875 0.000 0.936 0.064
#> GSM11860 2 0.0424 0.914 0.008 0.992 0.000
#> GSM11686 3 0.1163 0.824 0.028 0.000 0.972
#> GSM11688 3 0.0592 0.829 0.012 0.000 0.988
#> GSM11846 1 0.1878 0.891 0.952 0.044 0.004
#> GSM11680 1 0.5254 0.611 0.736 0.000 0.264
#> GSM11698 3 0.2796 0.792 0.092 0.000 0.908
#> GSM11840 3 0.4555 0.720 0.000 0.200 0.800
#> GSM11847 3 0.3116 0.794 0.000 0.108 0.892
#> GSM11685 3 0.0237 0.831 0.004 0.000 0.996
#> GSM11699 3 0.0000 0.832 0.000 0.000 1.000
#> GSM27950 3 0.6140 0.311 0.404 0.000 0.596
#> GSM27946 3 0.3454 0.797 0.008 0.104 0.888
#> GSM11709 1 0.1031 0.893 0.976 0.024 0.000
#> GSM11720 1 0.5810 0.506 0.664 0.336 0.000
#> GSM11726 1 0.4702 0.736 0.788 0.212 0.000
#> GSM11837 2 0.1163 0.907 0.028 0.972 0.000
#> GSM11725 2 0.2356 0.878 0.072 0.928 0.000
#> GSM11864 2 0.0892 0.911 0.020 0.980 0.000
#> GSM11687 1 0.0747 0.892 0.984 0.016 0.000
#> GSM11693 1 0.1031 0.893 0.976 0.024 0.000
#> GSM11727 2 0.2959 0.855 0.100 0.900 0.000
#> GSM11838 2 0.0892 0.911 0.020 0.980 0.000
#> GSM11681 1 0.0000 0.888 1.000 0.000 0.000
#> GSM11689 1 0.1411 0.891 0.964 0.036 0.000
#> GSM11704 1 0.1860 0.886 0.948 0.052 0.000
#> GSM11703 1 0.1753 0.888 0.952 0.048 0.000
#> GSM11705 1 0.0237 0.889 0.996 0.004 0.000
#> GSM11722 2 0.4346 0.762 0.184 0.816 0.000
#> GSM11730 2 0.5678 0.542 0.316 0.684 0.000
#> GSM11713 1 0.1753 0.889 0.952 0.048 0.000
#> GSM11728 1 0.6128 0.802 0.780 0.084 0.136
#> GSM27947 1 0.3272 0.855 0.892 0.104 0.004
#> GSM27951 1 0.0424 0.890 0.992 0.008 0.000
#> GSM11707 1 0.5216 0.639 0.740 0.000 0.260
#> GSM11716 2 0.5678 0.540 0.316 0.684 0.000
#> GSM11850 1 0.4555 0.752 0.800 0.200 0.000
#> GSM11851 3 0.0000 0.832 0.000 0.000 1.000
#> GSM11721 3 0.5882 0.518 0.000 0.348 0.652
#> GSM11852 3 0.0000 0.832 0.000 0.000 1.000
#> GSM11694 1 0.1529 0.877 0.960 0.000 0.040
#> GSM11695 1 0.2959 0.837 0.900 0.000 0.100
#> GSM11734 2 0.0000 0.915 0.000 1.000 0.000
#> GSM11861 3 0.5882 0.522 0.000 0.348 0.652
#> GSM11843 2 0.0000 0.915 0.000 1.000 0.000
#> GSM11862 3 0.6008 0.475 0.000 0.372 0.628
#> GSM11697 1 0.1964 0.868 0.944 0.000 0.056
#> GSM11714 3 0.5363 0.581 0.276 0.000 0.724
#> GSM11723 2 0.0000 0.915 0.000 1.000 0.000
#> GSM11845 2 0.0000 0.915 0.000 1.000 0.000
#> GSM11683 3 0.0424 0.831 0.008 0.000 0.992
#> GSM11691 1 0.1031 0.882 0.976 0.000 0.024
#> GSM27949 1 0.3686 0.801 0.860 0.000 0.140
#> GSM27945 1 0.4636 0.858 0.852 0.104 0.044
#> GSM11706 3 0.4974 0.640 0.236 0.000 0.764
#> GSM11853 3 0.8512 0.521 0.212 0.176 0.612
#> GSM11729 2 0.0000 0.915 0.000 1.000 0.000
#> GSM11746 2 0.1289 0.905 0.032 0.968 0.000
#> GSM11711 3 0.1753 0.816 0.048 0.000 0.952
#> GSM11854 3 0.0000 0.832 0.000 0.000 1.000
#> GSM11731 2 0.0000 0.915 0.000 1.000 0.000
#> GSM11839 2 0.0237 0.913 0.000 0.996 0.004
#> GSM11836 2 0.0237 0.913 0.000 0.996 0.004
#> GSM11849 3 0.4062 0.759 0.000 0.164 0.836
#> GSM11682 3 0.0000 0.832 0.000 0.000 1.000
#> GSM11690 3 0.0237 0.832 0.000 0.004 0.996
#> GSM11692 3 0.6274 0.269 0.000 0.456 0.544
#> GSM11841 2 0.2796 0.848 0.000 0.908 0.092
#> GSM11901 2 0.4931 0.651 0.000 0.768 0.232
#> GSM11715 2 0.0000 0.915 0.000 1.000 0.000
#> GSM11724 2 0.0000 0.915 0.000 1.000 0.000
#> GSM11684 3 0.0592 0.831 0.000 0.012 0.988
#> GSM11696 3 0.1753 0.823 0.000 0.048 0.952
#> GSM27952 3 0.0000 0.832 0.000 0.000 1.000
#> GSM27948 3 0.5058 0.671 0.000 0.244 0.756
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM11708 3 0.1118 0.8360 0.000 0.000 0.964 0.036
#> GSM11735 3 0.0592 0.8358 0.000 0.000 0.984 0.016
#> GSM11733 3 0.4567 0.6782 0.000 0.008 0.716 0.276
#> GSM11863 2 0.2002 0.8622 0.000 0.936 0.044 0.020
#> GSM11710 3 0.4866 0.4653 0.000 0.000 0.596 0.404
#> GSM11712 2 0.0921 0.8876 0.000 0.972 0.000 0.028
#> GSM11732 3 0.1716 0.8236 0.000 0.064 0.936 0.000
#> GSM11844 3 0.2944 0.7841 0.000 0.128 0.868 0.004
#> GSM11842 2 0.0895 0.8915 0.000 0.976 0.004 0.020
#> GSM11860 2 0.0000 0.8999 0.000 1.000 0.000 0.000
#> GSM11686 4 0.3443 0.6923 0.016 0.000 0.136 0.848
#> GSM11688 4 0.5112 0.1219 0.008 0.000 0.384 0.608
#> GSM11846 3 0.5614 0.4018 0.336 0.036 0.628 0.000
#> GSM11680 3 0.5699 0.4292 0.380 0.000 0.588 0.032
#> GSM11698 3 0.2888 0.8113 0.004 0.000 0.872 0.124
#> GSM11840 3 0.7486 0.3839 0.000 0.272 0.500 0.228
#> GSM11847 4 0.7442 0.0802 0.000 0.184 0.340 0.476
#> GSM11685 4 0.1305 0.7866 0.004 0.000 0.036 0.960
#> GSM11699 4 0.0592 0.7965 0.000 0.000 0.016 0.984
#> GSM27950 3 0.2542 0.8287 0.012 0.000 0.904 0.084
#> GSM27946 4 0.2530 0.7853 0.112 0.000 0.000 0.888
#> GSM11709 1 0.3208 0.7833 0.848 0.004 0.148 0.000
#> GSM11720 2 0.5695 0.0645 0.476 0.500 0.024 0.000
#> GSM11726 1 0.7400 0.1404 0.468 0.360 0.172 0.000
#> GSM11837 2 0.0188 0.8993 0.004 0.996 0.000 0.000
#> GSM11725 2 0.0921 0.8886 0.028 0.972 0.000 0.000
#> GSM11864 2 0.0188 0.8993 0.004 0.996 0.000 0.000
#> GSM11687 1 0.0779 0.8992 0.980 0.004 0.016 0.000
#> GSM11693 1 0.0657 0.9005 0.984 0.004 0.012 0.000
#> GSM11727 2 0.4164 0.6259 0.264 0.736 0.000 0.000
#> GSM11838 2 0.0592 0.8954 0.016 0.984 0.000 0.000
#> GSM11681 1 0.0817 0.8952 0.976 0.000 0.000 0.024
#> GSM11689 1 0.0376 0.9022 0.992 0.004 0.004 0.000
#> GSM11704 1 0.0336 0.9023 0.992 0.008 0.000 0.000
#> GSM11703 1 0.0657 0.9014 0.984 0.004 0.000 0.012
#> GSM11705 1 0.0779 0.8991 0.980 0.004 0.016 0.000
#> GSM11722 2 0.5000 0.0628 0.496 0.504 0.000 0.000
#> GSM11730 1 0.2399 0.8699 0.920 0.048 0.000 0.032
#> GSM11713 1 0.2281 0.8342 0.904 0.000 0.000 0.096
#> GSM11728 1 0.4008 0.6131 0.756 0.000 0.000 0.244
#> GSM27947 1 0.0657 0.9019 0.984 0.000 0.004 0.012
#> GSM27951 1 0.0000 0.9025 1.000 0.000 0.000 0.000
#> GSM11707 3 0.0921 0.8319 0.028 0.000 0.972 0.000
#> GSM11716 2 0.5366 0.5551 0.040 0.684 0.276 0.000
#> GSM11850 3 0.1629 0.8321 0.024 0.024 0.952 0.000
#> GSM11851 3 0.4158 0.7366 0.000 0.008 0.768 0.224
#> GSM11721 4 0.2149 0.7928 0.000 0.088 0.000 0.912
#> GSM11852 4 0.0188 0.7991 0.000 0.000 0.004 0.996
#> GSM11694 3 0.1118 0.8307 0.036 0.000 0.964 0.000
#> GSM11695 3 0.1022 0.8315 0.032 0.000 0.968 0.000
#> GSM11734 2 0.0000 0.8999 0.000 1.000 0.000 0.000
#> GSM11861 4 0.1867 0.7973 0.000 0.072 0.000 0.928
#> GSM11843 2 0.0188 0.8989 0.000 0.996 0.000 0.004
#> GSM11862 4 0.2760 0.7718 0.000 0.128 0.000 0.872
#> GSM11697 3 0.2011 0.8151 0.080 0.000 0.920 0.000
#> GSM11714 3 0.1970 0.8339 0.008 0.000 0.932 0.060
#> GSM11723 2 0.0000 0.8999 0.000 1.000 0.000 0.000
#> GSM11845 2 0.0000 0.8999 0.000 1.000 0.000 0.000
#> GSM11683 4 0.3099 0.7897 0.104 0.000 0.020 0.876
#> GSM11691 1 0.1256 0.8925 0.964 0.000 0.008 0.028
#> GSM27949 3 0.1022 0.8313 0.032 0.000 0.968 0.000
#> GSM27945 3 0.4800 0.6941 0.196 0.044 0.760 0.000
#> GSM11706 3 0.1118 0.8357 0.000 0.000 0.964 0.036
#> GSM11853 3 0.2156 0.8253 0.004 0.060 0.928 0.008
#> GSM11729 2 0.0000 0.8999 0.000 1.000 0.000 0.000
#> GSM11746 2 0.0336 0.8983 0.008 0.992 0.000 0.000
#> GSM11711 3 0.3444 0.7732 0.000 0.000 0.816 0.184
#> GSM11854 3 0.4382 0.6551 0.000 0.000 0.704 0.296
#> GSM11731 2 0.0188 0.8989 0.000 0.996 0.000 0.004
#> GSM11839 2 0.0469 0.8961 0.000 0.988 0.000 0.012
#> GSM11836 2 0.1940 0.8482 0.000 0.924 0.000 0.076
#> GSM11849 4 0.3975 0.6793 0.240 0.000 0.000 0.760
#> GSM11682 4 0.3726 0.7133 0.212 0.000 0.000 0.788
#> GSM11690 4 0.2814 0.7735 0.132 0.000 0.000 0.868
#> GSM11692 4 0.2704 0.7756 0.000 0.124 0.000 0.876
#> GSM11841 2 0.4250 0.5577 0.000 0.724 0.000 0.276
#> GSM11901 4 0.4925 0.2768 0.000 0.428 0.000 0.572
#> GSM11715 2 0.0376 0.8996 0.004 0.992 0.000 0.004
#> GSM11724 2 0.0376 0.8996 0.004 0.992 0.000 0.004
#> GSM11684 4 0.4164 0.6452 0.264 0.000 0.000 0.736
#> GSM11696 4 0.3975 0.6788 0.240 0.000 0.000 0.760
#> GSM27952 4 0.0804 0.7995 0.012 0.000 0.008 0.980
#> GSM27948 4 0.1677 0.8040 0.040 0.012 0.000 0.948
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM11708 3 0.1281 0.8710 0.000 0.000 0.956 0.032 0.012
#> GSM11735 3 0.0727 0.8714 0.004 0.000 0.980 0.012 0.004
#> GSM11733 3 0.4302 0.7920 0.016 0.016 0.800 0.136 0.032
#> GSM11863 2 0.4399 0.7294 0.028 0.800 0.016 0.128 0.028
#> GSM11710 4 0.4318 0.5194 0.008 0.000 0.296 0.688 0.008
#> GSM11712 2 0.6343 0.4939 0.124 0.596 0.016 0.256 0.008
#> GSM11732 3 0.2894 0.8027 0.008 0.124 0.860 0.000 0.008
#> GSM11844 3 0.2536 0.8033 0.004 0.128 0.868 0.000 0.000
#> GSM11842 2 0.5605 0.5935 0.084 0.672 0.012 0.224 0.008
#> GSM11860 2 0.6131 0.3318 0.384 0.528 0.012 0.064 0.012
#> GSM11686 4 0.5629 0.5624 0.076 0.000 0.148 0.708 0.068
#> GSM11688 4 0.4982 0.5146 0.032 0.000 0.228 0.708 0.032
#> GSM11846 1 0.5132 0.5185 0.764 0.072 0.108 0.044 0.012
#> GSM11680 3 0.5686 0.6928 0.120 0.000 0.688 0.032 0.160
#> GSM11698 3 0.3495 0.8275 0.024 0.000 0.844 0.024 0.108
#> GSM11840 4 0.7537 0.3077 0.024 0.256 0.256 0.448 0.016
#> GSM11847 4 0.6224 0.5546 0.016 0.116 0.164 0.668 0.036
#> GSM11685 4 0.2434 0.6444 0.008 0.000 0.036 0.908 0.048
#> GSM11699 4 0.5078 0.5906 0.052 0.000 0.028 0.716 0.204
#> GSM27950 3 0.3107 0.8581 0.012 0.000 0.868 0.088 0.032
#> GSM27946 4 0.4337 0.6022 0.204 0.000 0.000 0.744 0.052
#> GSM11709 1 0.4986 0.5437 0.716 0.004 0.104 0.000 0.176
#> GSM11720 1 0.4692 0.4009 0.688 0.276 0.012 0.000 0.024
#> GSM11726 1 0.7214 0.2508 0.468 0.348 0.100 0.000 0.084
#> GSM11837 2 0.0162 0.7979 0.000 0.996 0.000 0.000 0.004
#> GSM11725 2 0.2563 0.7522 0.120 0.872 0.000 0.000 0.008
#> GSM11864 2 0.3885 0.6251 0.268 0.724 0.000 0.000 0.008
#> GSM11687 1 0.3132 0.5563 0.820 0.000 0.008 0.000 0.172
#> GSM11693 1 0.2741 0.5633 0.860 0.004 0.004 0.000 0.132
#> GSM11727 2 0.3988 0.6509 0.036 0.768 0.000 0.000 0.196
#> GSM11838 2 0.1205 0.7932 0.004 0.956 0.000 0.000 0.040
#> GSM11681 1 0.5304 0.2043 0.560 0.000 0.000 0.056 0.384
#> GSM11689 1 0.3491 0.5208 0.768 0.000 0.000 0.004 0.228
#> GSM11704 1 0.3906 0.4788 0.704 0.004 0.000 0.000 0.292
#> GSM11703 1 0.3774 0.4310 0.704 0.000 0.000 0.000 0.296
#> GSM11705 1 0.5308 0.3485 0.532 0.000 0.052 0.000 0.416
#> GSM11722 2 0.5341 0.2992 0.060 0.564 0.000 0.000 0.376
#> GSM11730 5 0.5458 0.5035 0.140 0.140 0.000 0.020 0.700
#> GSM11713 5 0.3555 0.5671 0.124 0.000 0.000 0.052 0.824
#> GSM11728 5 0.2983 0.5969 0.076 0.000 0.000 0.056 0.868
#> GSM27947 1 0.2935 0.5338 0.860 0.000 0.004 0.016 0.120
#> GSM27951 1 0.4003 0.4672 0.704 0.000 0.000 0.008 0.288
#> GSM11707 3 0.1251 0.8636 0.008 0.000 0.956 0.000 0.036
#> GSM11716 2 0.5427 0.2863 0.044 0.544 0.404 0.000 0.008
#> GSM11850 3 0.1701 0.8661 0.012 0.016 0.944 0.000 0.028
#> GSM11851 3 0.6868 0.3426 0.196 0.008 0.516 0.268 0.012
#> GSM11721 4 0.2897 0.6540 0.000 0.072 0.020 0.884 0.024
#> GSM11852 4 0.3110 0.6572 0.044 0.000 0.020 0.876 0.060
#> GSM11694 3 0.1106 0.8692 0.024 0.000 0.964 0.000 0.012
#> GSM11695 3 0.1012 0.8685 0.020 0.000 0.968 0.000 0.012
#> GSM11734 2 0.0162 0.7983 0.000 0.996 0.000 0.004 0.000
#> GSM11861 4 0.4124 0.6268 0.140 0.052 0.000 0.796 0.012
#> GSM11843 2 0.3734 0.7021 0.184 0.792 0.000 0.016 0.008
#> GSM11862 4 0.4084 0.6437 0.092 0.056 0.008 0.824 0.020
#> GSM11697 3 0.4203 0.7622 0.092 0.000 0.780 0.000 0.128
#> GSM11714 3 0.1893 0.8681 0.000 0.000 0.928 0.048 0.024
#> GSM11723 2 0.1430 0.7936 0.004 0.944 0.000 0.000 0.052
#> GSM11845 2 0.1399 0.7985 0.020 0.952 0.000 0.000 0.028
#> GSM11683 4 0.5971 0.5055 0.068 0.000 0.088 0.676 0.168
#> GSM11691 5 0.4962 -0.0733 0.432 0.000 0.016 0.008 0.544
#> GSM27949 3 0.0579 0.8694 0.008 0.000 0.984 0.000 0.008
#> GSM27945 1 0.6107 0.4779 0.700 0.064 0.148 0.048 0.040
#> GSM11706 3 0.2407 0.8528 0.004 0.000 0.896 0.088 0.012
#> GSM11853 1 0.7217 0.1891 0.480 0.056 0.360 0.088 0.016
#> GSM11729 2 0.0000 0.7979 0.000 1.000 0.000 0.000 0.000
#> GSM11746 2 0.1608 0.7810 0.072 0.928 0.000 0.000 0.000
#> GSM11711 1 0.7027 -0.0137 0.384 0.000 0.364 0.240 0.012
#> GSM11854 4 0.6859 0.3656 0.216 0.008 0.240 0.524 0.012
#> GSM11731 2 0.0324 0.7985 0.004 0.992 0.000 0.004 0.000
#> GSM11839 2 0.0740 0.7992 0.004 0.980 0.000 0.008 0.008
#> GSM11836 2 0.1116 0.7988 0.004 0.964 0.000 0.028 0.004
#> GSM11849 4 0.5112 0.0150 0.036 0.000 0.000 0.496 0.468
#> GSM11682 4 0.5092 0.4904 0.092 0.000 0.008 0.708 0.192
#> GSM11690 4 0.4170 0.5503 0.048 0.000 0.000 0.760 0.192
#> GSM11692 4 0.4573 0.5641 0.004 0.044 0.004 0.736 0.212
#> GSM11841 2 0.5521 0.5352 0.004 0.656 0.000 0.216 0.124
#> GSM11901 4 0.6505 0.3262 0.008 0.300 0.000 0.516 0.176
#> GSM11715 2 0.2011 0.7749 0.004 0.908 0.000 0.000 0.088
#> GSM11724 2 0.3491 0.6609 0.004 0.768 0.000 0.000 0.228
#> GSM11684 5 0.4251 0.3688 0.012 0.000 0.000 0.316 0.672
#> GSM11696 5 0.4808 0.2722 0.032 0.000 0.000 0.348 0.620
#> GSM27952 4 0.2786 0.6315 0.020 0.000 0.012 0.884 0.084
#> GSM27948 4 0.2946 0.6412 0.044 0.000 0.000 0.868 0.088
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM11708 3 0.0806 0.85219 0.000 0.000 0.972 0.000 0.008 0.020
#> GSM11735 3 0.0777 0.85239 0.000 0.000 0.972 0.000 0.004 0.024
#> GSM11733 3 0.4227 0.72618 0.000 0.000 0.764 0.028 0.060 0.148
#> GSM11863 2 0.5974 0.52361 0.000 0.628 0.012 0.088 0.200 0.072
#> GSM11710 6 0.4763 0.49199 0.000 0.000 0.172 0.004 0.136 0.688
#> GSM11712 2 0.7119 0.00597 0.000 0.360 0.004 0.060 0.280 0.296
#> GSM11732 3 0.2431 0.78501 0.000 0.132 0.860 0.000 0.008 0.000
#> GSM11844 3 0.2655 0.78061 0.000 0.140 0.848 0.000 0.008 0.004
#> GSM11842 2 0.6851 0.17997 0.000 0.432 0.000 0.060 0.256 0.252
#> GSM11860 5 0.4585 0.36187 0.028 0.204 0.000 0.012 0.724 0.032
#> GSM11686 6 0.5762 0.51137 0.164 0.000 0.156 0.036 0.008 0.636
#> GSM11688 6 0.3593 0.56719 0.064 0.000 0.132 0.004 0.000 0.800
#> GSM11846 5 0.4799 0.22617 0.248 0.004 0.032 0.000 0.680 0.036
#> GSM11680 3 0.6708 0.57352 0.096 0.000 0.612 0.076 0.104 0.112
#> GSM11698 3 0.4154 0.78212 0.012 0.000 0.800 0.064 0.084 0.040
#> GSM11840 6 0.7727 0.30726 0.000 0.172 0.108 0.072 0.168 0.480
#> GSM11847 6 0.7607 0.40132 0.000 0.096 0.120 0.120 0.152 0.512
#> GSM11685 6 0.2713 0.59523 0.016 0.000 0.076 0.024 0.004 0.880
#> GSM11699 4 0.6340 0.04462 0.004 0.000 0.012 0.452 0.240 0.292
#> GSM27950 3 0.2292 0.83059 0.004 0.000 0.884 0.004 0.004 0.104
#> GSM27946 6 0.6433 0.39835 0.140 0.000 0.000 0.080 0.240 0.540
#> GSM11709 1 0.5561 0.46925 0.544 0.000 0.060 0.040 0.356 0.000
#> GSM11720 5 0.5120 0.18220 0.236 0.080 0.020 0.004 0.660 0.000
#> GSM11726 2 0.7940 -0.20622 0.276 0.348 0.080 0.052 0.244 0.000
#> GSM11837 2 0.0405 0.72580 0.000 0.988 0.000 0.004 0.008 0.000
#> GSM11725 2 0.2128 0.70465 0.032 0.908 0.000 0.004 0.056 0.000
#> GSM11864 2 0.4253 0.41901 0.008 0.608 0.000 0.012 0.372 0.000
#> GSM11687 1 0.4411 0.55120 0.628 0.000 0.012 0.020 0.340 0.000
#> GSM11693 1 0.4736 0.44150 0.532 0.000 0.008 0.024 0.432 0.004
#> GSM11727 2 0.3718 0.61086 0.052 0.780 0.000 0.164 0.004 0.000
#> GSM11838 2 0.0806 0.72243 0.008 0.972 0.000 0.020 0.000 0.000
#> GSM11681 1 0.3396 0.44376 0.828 0.000 0.000 0.060 0.012 0.100
#> GSM11689 1 0.3692 0.60914 0.736 0.000 0.000 0.012 0.244 0.008
#> GSM11704 1 0.3671 0.62109 0.784 0.000 0.000 0.040 0.168 0.008
#> GSM11703 5 0.6439 -0.28761 0.268 0.000 0.000 0.340 0.376 0.016
#> GSM11705 1 0.6540 0.42862 0.444 0.000 0.032 0.276 0.248 0.000
#> GSM11722 2 0.5624 0.27379 0.124 0.544 0.000 0.320 0.012 0.000
#> GSM11730 4 0.4419 0.44262 0.220 0.072 0.000 0.704 0.004 0.000
#> GSM11713 4 0.4113 0.40209 0.308 0.000 0.000 0.668 0.008 0.016
#> GSM11728 4 0.3898 0.49080 0.216 0.008 0.000 0.748 0.004 0.024
#> GSM27947 5 0.5782 -0.04597 0.308 0.000 0.000 0.112 0.552 0.028
#> GSM27951 1 0.3266 0.59934 0.824 0.000 0.000 0.036 0.132 0.008
#> GSM11707 3 0.1148 0.85235 0.016 0.000 0.960 0.000 0.020 0.004
#> GSM11716 2 0.5809 0.08810 0.012 0.464 0.428 0.016 0.080 0.000
#> GSM11850 3 0.1666 0.84826 0.008 0.020 0.936 0.000 0.036 0.000
#> GSM11851 5 0.5999 0.25330 0.000 0.000 0.320 0.004 0.460 0.216
#> GSM11721 6 0.3324 0.58394 0.000 0.024 0.000 0.048 0.088 0.840
#> GSM11852 6 0.3756 0.57527 0.004 0.000 0.000 0.076 0.132 0.788
#> GSM11694 3 0.2404 0.83176 0.008 0.000 0.880 0.004 0.104 0.004
#> GSM11695 3 0.2349 0.83202 0.020 0.000 0.892 0.000 0.080 0.008
#> GSM11734 2 0.0146 0.72559 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM11861 6 0.4935 0.47392 0.012 0.020 0.000 0.032 0.292 0.644
#> GSM11843 2 0.3984 0.49168 0.000 0.648 0.000 0.016 0.336 0.000
#> GSM11862 6 0.5110 0.47886 0.004 0.032 0.000 0.048 0.272 0.644
#> GSM11697 3 0.5271 0.67872 0.044 0.000 0.708 0.096 0.136 0.016
#> GSM11714 3 0.1477 0.84659 0.000 0.000 0.940 0.004 0.008 0.048
#> GSM11723 2 0.0603 0.72546 0.000 0.980 0.000 0.016 0.004 0.000
#> GSM11845 2 0.4486 0.60372 0.004 0.720 0.000 0.152 0.124 0.000
#> GSM11683 6 0.6591 0.41298 0.188 0.000 0.168 0.080 0.008 0.556
#> GSM11691 1 0.7635 0.09155 0.372 0.000 0.052 0.344 0.164 0.068
#> GSM27949 3 0.1225 0.85113 0.012 0.000 0.952 0.000 0.036 0.000
#> GSM27945 5 0.5295 0.27097 0.160 0.004 0.028 0.084 0.704 0.020
#> GSM11706 3 0.3656 0.77032 0.012 0.000 0.808 0.000 0.072 0.108
#> GSM11853 5 0.4519 0.43566 0.052 0.012 0.120 0.000 0.768 0.048
#> GSM11729 2 0.0405 0.72556 0.000 0.988 0.000 0.004 0.008 0.000
#> GSM11746 2 0.0837 0.72543 0.004 0.972 0.000 0.004 0.020 0.000
#> GSM11711 5 0.6048 0.40998 0.016 0.000 0.248 0.004 0.540 0.192
#> GSM11854 5 0.5547 0.17230 0.000 0.000 0.148 0.000 0.508 0.344
#> GSM11731 2 0.0291 0.72512 0.000 0.992 0.000 0.004 0.004 0.000
#> GSM11839 2 0.0622 0.72610 0.000 0.980 0.000 0.008 0.012 0.000
#> GSM11836 2 0.1036 0.71995 0.004 0.964 0.000 0.008 0.000 0.024
#> GSM11849 6 0.5499 0.12082 0.072 0.000 0.000 0.380 0.024 0.524
#> GSM11682 6 0.4963 0.46482 0.264 0.000 0.004 0.076 0.008 0.648
#> GSM11690 6 0.4763 0.43994 0.072 0.000 0.000 0.216 0.020 0.692
#> GSM11692 6 0.5720 0.01873 0.000 0.020 0.000 0.440 0.096 0.444
#> GSM11841 2 0.6861 0.23853 0.000 0.488 0.000 0.244 0.112 0.156
#> GSM11901 4 0.7278 0.05422 0.000 0.244 0.004 0.384 0.088 0.280
#> GSM11715 2 0.1349 0.71294 0.000 0.940 0.000 0.056 0.004 0.000
#> GSM11724 2 0.3405 0.54574 0.000 0.724 0.000 0.272 0.004 0.000
#> GSM11684 4 0.3470 0.55059 0.028 0.000 0.000 0.820 0.028 0.124
#> GSM11696 4 0.3603 0.53084 0.016 0.000 0.000 0.804 0.040 0.140
#> GSM27952 6 0.3509 0.57945 0.128 0.000 0.024 0.032 0.000 0.816
#> GSM27948 6 0.3891 0.53770 0.004 0.000 0.000 0.164 0.064 0.768
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 cell.line(p) agent(p) time(p) k
#> ATC:NMF 78 5.09e-02 0.0193 1.01e-03 2
#> ATC:NMF 78 1.54e-05 0.3815 6.81e-05 3
#> ATC:NMF 73 3.72e-08 0.0777 6.42e-07 4
#> ATC:NMF 60 1.07e-05 0.1530 5.19e-08 5
#> ATC:NMF 44 5.60e-05 0.2050 9.87e-09 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