Date: 2019-12-25 22:01:42 CET, cola version: 1.3.2
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All available functions which can be applied to this res_list object:
res_list
#> A 'ConsensusPartitionList' object with 24 methods.
#> On a matrix with 51941 rows and 70 columns.
#> Top rows are extracted by 'SD, CV, MAD, ATC' methods.
#> Subgroups are detected by 'hclust, kmeans, skmeans, pam, mclust, NMF' method.
#> Number of partitions are tried for k = 2, 3, 4, 5, 6.
#> Performed in total 30000 partitions by row resampling.
#>
#> Following methods can be applied to this 'ConsensusPartitionList' object:
#> [1] "cola_report" "collect_classes" "collect_plots" "collect_stats"
#> [5] "colnames" "functional_enrichment" "get_anno_col" "get_anno"
#> [9] "get_classes" "get_matrix" "get_membership" "get_stats"
#> [13] "is_best_k" "is_stable_k" "ncol" "nrow"
#> [17] "rownames" "show" "suggest_best_k" "test_to_known_factors"
#> [21] "top_rows_heatmap" "top_rows_overlap"
#>
#> You can get result for a single method by, e.g. object["SD", "hclust"] or object["SD:hclust"]
#> or a subset of methods by object[c("SD", "CV")], c("hclust", "kmeans")]
The call of run_all_consensus_partition_methods() was:
#> run_all_consensus_partition_methods(data = mat, mc.cores = 4, anno = anno)
Dimension of the input matrix:
mat = get_matrix(res_list)
dim(mat)
#> [1] 51941 70
The density distribution for each sample is visualized as in one column in the following heatmap. The clustering is based on the distance which is the Kolmogorov-Smirnov statistic between two distributions.
library(ComplexHeatmap)
densityHeatmap(mat, top_annotation = HeatmapAnnotation(df = get_anno(res_list),
col = get_anno_col(res_list)), ylab = "value", cluster_columns = TRUE, show_column_names = FALSE,
mc.cores = 4)
Folowing table shows the best k (number of partitions) for each combination
of top-value methods and partition methods. Clicking on the method name in
the table goes to the section for a single combination of methods.
The cola vignette explains the definition of the metrics used for determining the best number of partitions.
suggest_best_k(res_list)
| The best k | 1-PAC | Mean silhouette | Concordance | Optional k | ||
|---|---|---|---|---|---|---|
| SD:kmeans | 2 | 1.000 | 0.975 | 0.991 | ** | |
| SD:skmeans | 2 | 1.000 | 0.978 | 0.991 | ** | |
| SD:NMF | 2 | 1.000 | 0.960 | 0.985 | ** | |
| CV:skmeans | 2 | 1.000 | 0.966 | 0.986 | ** | |
| ATC:skmeans | 4 | 1.000 | 0.988 | 0.994 | ** | 2,3 |
| MAD:skmeans | 3 | 0.977 | 0.939 | 0.974 | ** | 2 |
| ATC:NMF | 4 | 0.961 | 0.939 | 0.972 | ** | 2,3 |
| CV:NMF | 2 | 0.940 | 0.929 | 0.973 | * | |
| ATC:kmeans | 3 | 0.929 | 0.885 | 0.933 | * | |
| SD:pam | 5 | 0.919 | 0.852 | 0.925 | * | 2 |
| ATC:pam | 6 | 0.900 | 0.791 | 0.920 | * | 5 |
| ATC:mclust | 4 | 0.886 | 0.930 | 0.951 | ||
| MAD:NMF | 2 | 0.879 | 0.904 | 0.961 | ||
| CV:kmeans | 2 | 0.828 | 0.890 | 0.932 | ||
| MAD:kmeans | 2 | 0.771 | 0.942 | 0.951 | ||
| CV:pam | 5 | 0.770 | 0.773 | 0.895 | ||
| MAD:pam | 2 | 0.766 | 0.916 | 0.961 | ||
| MAD:mclust | 4 | 0.751 | 0.883 | 0.916 | ||
| SD:hclust | 2 | 0.736 | 0.871 | 0.942 | ||
| ATC:hclust | 2 | 0.649 | 0.867 | 0.923 | ||
| CV:mclust | 2 | 0.452 | 0.775 | 0.881 | ||
| SD:mclust | 2 | 0.446 | 0.870 | 0.912 | ||
| MAD:hclust | 3 | 0.415 | 0.691 | 0.820 | ||
| CV:hclust | 2 | 0.289 | 0.696 | 0.826 |
**: 1-PAC > 0.95, *: 1-PAC > 0.9
Cumulative distribution function curves of consensus matrix for all methods.
collect_plots(res_list, fun = plot_ecdf)
Consensus heatmaps for all methods. (What is a consensus heatmap?)
collect_plots(res_list, k = 2, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = consensus_heatmap, mc.cores = 4)
Membership heatmaps for all methods. (What is a membership heatmap?)
collect_plots(res_list, k = 2, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = membership_heatmap, mc.cores = 4)
Signature heatmaps for all methods. (What is a signature heatmap?)
Note in following heatmaps, rows are scaled.
collect_plots(res_list, k = 2, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 3, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 4, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 5, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 6, fun = get_signatures, mc.cores = 4)
The statistics used for measuring the stability of consensus partitioning. (How are they defined?)
get_stats(res_list, k = 2)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 2 1.000 0.960 0.985 0.499 0.499 0.499
#> CV:NMF 2 0.940 0.929 0.973 0.494 0.508 0.508
#> MAD:NMF 2 0.879 0.904 0.961 0.500 0.499 0.499
#> ATC:NMF 2 1.000 0.972 0.989 0.494 0.503 0.503
#> SD:skmeans 2 1.000 0.978 0.991 0.500 0.503 0.503
#> CV:skmeans 2 1.000 0.966 0.986 0.500 0.499 0.499
#> MAD:skmeans 2 0.971 0.968 0.986 0.499 0.499 0.499
#> ATC:skmeans 2 1.000 0.984 0.992 0.504 0.496 0.496
#> SD:mclust 2 0.446 0.870 0.912 0.464 0.499 0.499
#> CV:mclust 2 0.452 0.775 0.881 0.470 0.513 0.513
#> MAD:mclust 2 0.412 0.725 0.843 0.397 0.612 0.612
#> ATC:mclust 2 0.681 0.871 0.913 0.498 0.494 0.494
#> SD:kmeans 2 1.000 0.975 0.991 0.495 0.503 0.503
#> CV:kmeans 2 0.828 0.890 0.932 0.444 0.543 0.543
#> MAD:kmeans 2 0.771 0.942 0.951 0.490 0.513 0.513
#> ATC:kmeans 2 0.503 0.884 0.919 0.490 0.503 0.503
#> SD:pam 2 0.940 0.938 0.974 0.479 0.526 0.526
#> CV:pam 2 0.826 0.907 0.958 0.364 0.612 0.612
#> MAD:pam 2 0.766 0.916 0.961 0.505 0.494 0.494
#> ATC:pam 2 0.462 0.854 0.862 0.457 0.503 0.503
#> SD:hclust 2 0.736 0.871 0.942 0.486 0.508 0.508
#> CV:hclust 2 0.289 0.696 0.826 0.403 0.552 0.552
#> MAD:hclust 2 0.125 0.665 0.778 0.452 0.526 0.526
#> ATC:hclust 2 0.649 0.867 0.923 0.463 0.543 0.543
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.579 0.726 0.817 0.316 0.769 0.565
#> CV:NMF 3 0.465 0.484 0.710 0.322 0.832 0.680
#> MAD:NMF 3 0.537 0.685 0.851 0.341 0.721 0.494
#> ATC:NMF 3 1.000 0.943 0.978 0.360 0.740 0.522
#> SD:skmeans 3 0.837 0.862 0.914 0.322 0.814 0.636
#> CV:skmeans 3 0.615 0.735 0.868 0.328 0.756 0.547
#> MAD:skmeans 3 0.977 0.939 0.974 0.343 0.764 0.556
#> ATC:skmeans 3 1.000 0.994 0.997 0.325 0.786 0.589
#> SD:mclust 3 0.481 0.693 0.813 0.332 0.746 0.552
#> CV:mclust 3 0.359 0.466 0.662 0.298 0.742 0.534
#> MAD:mclust 3 0.538 0.661 0.845 0.430 0.622 0.450
#> ATC:mclust 3 0.661 0.778 0.884 0.303 0.678 0.441
#> SD:kmeans 3 0.569 0.618 0.710 0.282 0.822 0.652
#> CV:kmeans 3 0.462 0.456 0.754 0.351 0.801 0.674
#> MAD:kmeans 3 0.854 0.913 0.933 0.361 0.800 0.616
#> ATC:kmeans 3 0.929 0.885 0.933 0.338 0.771 0.574
#> SD:pam 3 0.650 0.833 0.897 0.372 0.783 0.595
#> CV:pam 3 0.503 0.692 0.832 0.518 0.789 0.665
#> MAD:pam 3 0.677 0.764 0.839 0.295 0.824 0.655
#> ATC:pam 3 0.855 0.825 0.932 0.429 0.728 0.510
#> SD:hclust 3 0.502 0.619 0.801 0.264 0.955 0.912
#> CV:hclust 3 0.302 0.575 0.728 0.391 0.675 0.482
#> MAD:hclust 3 0.415 0.691 0.820 0.407 0.810 0.639
#> ATC:hclust 3 0.617 0.781 0.873 0.335 0.851 0.725
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.642 0.558 0.784 0.140 0.824 0.531
#> CV:NMF 4 0.518 0.410 0.630 0.130 0.722 0.386
#> MAD:NMF 4 0.767 0.842 0.908 0.127 0.856 0.597
#> ATC:NMF 4 0.961 0.939 0.972 0.128 0.833 0.545
#> SD:skmeans 4 0.743 0.796 0.873 0.126 0.914 0.747
#> CV:skmeans 4 0.659 0.666 0.809 0.123 0.825 0.542
#> MAD:skmeans 4 0.850 0.837 0.921 0.122 0.847 0.579
#> ATC:skmeans 4 1.000 0.988 0.994 0.124 0.906 0.721
#> SD:mclust 4 0.642 0.719 0.851 0.164 0.844 0.618
#> CV:mclust 4 0.415 0.599 0.772 0.146 0.815 0.535
#> MAD:mclust 4 0.751 0.883 0.916 0.218 0.812 0.573
#> ATC:mclust 4 0.886 0.930 0.951 0.154 0.784 0.457
#> SD:kmeans 4 0.576 0.622 0.771 0.146 0.798 0.491
#> CV:kmeans 4 0.433 0.393 0.628 0.132 0.725 0.478
#> MAD:kmeans 4 0.728 0.720 0.842 0.119 0.868 0.628
#> ATC:kmeans 4 0.841 0.735 0.887 0.128 0.859 0.621
#> SD:pam 4 0.867 0.855 0.940 0.139 0.839 0.562
#> CV:pam 4 0.662 0.732 0.838 0.221 0.800 0.566
#> MAD:pam 4 0.630 0.752 0.864 0.136 0.847 0.595
#> ATC:pam 4 0.726 0.773 0.880 0.144 0.828 0.542
#> SD:hclust 4 0.498 0.523 0.664 0.146 0.792 0.566
#> CV:hclust 4 0.473 0.576 0.683 0.173 0.882 0.705
#> MAD:hclust 4 0.516 0.474 0.720 0.135 0.902 0.733
#> ATC:hclust 4 0.733 0.832 0.872 0.177 0.876 0.686
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.699 0.671 0.769 0.0681 0.884 0.588
#> CV:NMF 5 0.620 0.597 0.743 0.0778 0.857 0.524
#> MAD:NMF 5 0.763 0.732 0.862 0.0589 0.867 0.543
#> ATC:NMF 5 0.793 0.797 0.876 0.0521 0.913 0.673
#> SD:skmeans 5 0.732 0.780 0.807 0.0658 0.940 0.774
#> CV:skmeans 5 0.696 0.698 0.821 0.0687 0.940 0.769
#> MAD:skmeans 5 0.748 0.690 0.814 0.0570 0.943 0.777
#> ATC:skmeans 5 0.889 0.869 0.917 0.0621 0.945 0.783
#> SD:mclust 5 0.658 0.560 0.780 0.0860 0.878 0.600
#> CV:mclust 5 0.601 0.624 0.702 0.0910 0.921 0.726
#> MAD:mclust 5 0.697 0.662 0.787 0.1245 0.789 0.422
#> ATC:mclust 5 0.819 0.875 0.904 0.0551 0.944 0.778
#> SD:kmeans 5 0.666 0.721 0.811 0.0802 0.925 0.723
#> CV:kmeans 5 0.593 0.716 0.801 0.1058 0.864 0.598
#> MAD:kmeans 5 0.712 0.570 0.765 0.0649 0.952 0.813
#> ATC:kmeans 5 0.798 0.718 0.834 0.0755 0.892 0.626
#> SD:pam 5 0.919 0.852 0.925 0.0545 0.937 0.754
#> CV:pam 5 0.770 0.773 0.895 0.0844 0.924 0.751
#> MAD:pam 5 0.817 0.773 0.889 0.0661 0.909 0.673
#> ATC:pam 5 0.905 0.851 0.936 0.0809 0.886 0.582
#> SD:hclust 5 0.539 0.579 0.713 0.0913 0.936 0.784
#> CV:hclust 5 0.548 0.505 0.698 0.1036 0.740 0.389
#> MAD:hclust 5 0.570 0.425 0.676 0.0739 0.854 0.567
#> ATC:hclust 5 0.759 0.781 0.849 0.0582 0.952 0.824
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.767 0.623 0.786 0.0420 0.910 0.616
#> CV:NMF 6 0.781 0.691 0.801 0.0506 0.928 0.673
#> MAD:NMF 6 0.721 0.627 0.786 0.0418 0.947 0.751
#> ATC:NMF 6 0.762 0.569 0.786 0.0421 0.947 0.765
#> SD:skmeans 6 0.750 0.678 0.798 0.0460 0.965 0.835
#> CV:skmeans 6 0.741 0.628 0.791 0.0465 0.916 0.624
#> MAD:skmeans 6 0.742 0.617 0.783 0.0390 0.954 0.790
#> ATC:skmeans 6 0.874 0.762 0.885 0.0387 0.949 0.753
#> SD:mclust 6 0.735 0.669 0.825 0.0591 0.899 0.579
#> CV:mclust 6 0.710 0.658 0.799 0.0575 0.953 0.796
#> MAD:mclust 6 0.719 0.637 0.767 0.0547 0.948 0.761
#> ATC:mclust 6 0.864 0.890 0.918 0.0531 0.900 0.574
#> SD:kmeans 6 0.778 0.611 0.761 0.0483 0.912 0.632
#> CV:kmeans 6 0.788 0.757 0.818 0.0582 0.946 0.784
#> MAD:kmeans 6 0.708 0.501 0.705 0.0442 0.900 0.592
#> ATC:kmeans 6 0.847 0.767 0.847 0.0434 0.915 0.619
#> SD:pam 6 0.857 0.725 0.879 0.0489 0.943 0.735
#> CV:pam 6 0.715 0.696 0.850 0.0541 0.973 0.889
#> MAD:pam 6 0.889 0.803 0.906 0.0445 0.933 0.705
#> ATC:pam 6 0.900 0.791 0.920 0.0420 0.937 0.695
#> SD:hclust 6 0.634 0.476 0.698 0.0512 0.959 0.837
#> CV:hclust 6 0.662 0.685 0.784 0.0648 0.884 0.618
#> MAD:hclust 6 0.642 0.386 0.664 0.0446 0.860 0.507
#> ATC:hclust 6 0.778 0.685 0.835 0.0393 0.968 0.865
Following heatmap plots the partition for each combination of methods and the lightness correspond to the silhouette scores for samples in each method. On top the consensus subgroup is inferred from all methods by taking the mean silhouette scores as weight.
collect_stats(res_list, k = 2)
collect_stats(res_list, k = 3)
collect_stats(res_list, k = 4)
collect_stats(res_list, k = 5)
collect_stats(res_list, k = 6)
Collect partitions from all methods:
collect_classes(res_list, k = 2)
collect_classes(res_list, k = 3)
collect_classes(res_list, k = 4)
collect_classes(res_list, k = 5)
collect_classes(res_list, k = 6)
Overlap of top rows from different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "euler")
top_rows_overlap(res_list, top_n = 2000, method = "euler")
top_rows_overlap(res_list, top_n = 3000, method = "euler")
top_rows_overlap(res_list, top_n = 4000, method = "euler")
top_rows_overlap(res_list, top_n = 5000, method = "euler")
Also visualize the correspondance of rankings between different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "correspondance")
top_rows_overlap(res_list, top_n = 2000, method = "correspondance")
top_rows_overlap(res_list, top_n = 3000, method = "correspondance")
top_rows_overlap(res_list, top_n = 4000, method = "correspondance")
top_rows_overlap(res_list, top_n = 5000, method = "correspondance")
Heatmaps of the top rows:
top_rows_heatmap(res_list, top_n = 1000)
top_rows_heatmap(res_list, top_n = 2000)
top_rows_heatmap(res_list, top_n = 3000)
top_rows_heatmap(res_list, top_n = 4000)
top_rows_heatmap(res_list, top_n = 5000)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res_list, k = 2)
#> n disease.state(p) k
#> SD:NMF 69 0.11244 2
#> CV:NMF 68 0.06188 2
#> MAD:NMF 66 0.29384 2
#> ATC:NMF 68 0.75291 2
#> SD:skmeans 69 0.11244 2
#> CV:skmeans 69 0.11244 2
#> MAD:skmeans 69 0.11853 2
#> ATC:skmeans 70 0.30169 2
#> SD:mclust 65 0.12095 2
#> CV:mclust 62 0.13830 2
#> MAD:mclust 66 0.63911 2
#> ATC:mclust 69 0.22992 2
#> SD:kmeans 69 0.08026 2
#> CV:kmeans 68 0.14917 2
#> MAD:kmeans 70 0.14223 2
#> ATC:kmeans 68 0.75291 2
#> SD:pam 69 0.14812 2
#> CV:pam 66 0.00703 2
#> MAD:pam 69 0.23235 2
#> ATC:pam 69 0.19978 2
#> SD:hclust 66 0.05422 2
#> CV:hclust 61 0.15003 2
#> MAD:hclust 59 0.04933 2
#> ATC:hclust 66 0.91840 2
test_to_known_factors(res_list, k = 3)
#> n disease.state(p) k
#> SD:NMF 59 0.0864 3
#> CV:NMF 45 0.1935 3
#> MAD:NMF 59 0.3370 3
#> ATC:NMF 67 0.4343 3
#> SD:skmeans 68 0.1332 3
#> CV:skmeans 60 0.0554 3
#> MAD:skmeans 68 0.3437 3
#> ATC:skmeans 70 0.4530 3
#> SD:mclust 61 0.0945 3
#> CV:mclust 40 0.0435 3
#> MAD:mclust 60 0.2615 3
#> ATC:mclust 63 0.1034 3
#> SD:kmeans 57 0.0353 3
#> CV:kmeans 44 0.0987 3
#> MAD:kmeans 68 0.3437 3
#> ATC:kmeans 66 0.0803 3
#> SD:pam 66 0.1497 3
#> CV:pam 60 0.0424 3
#> MAD:pam 68 0.2869 3
#> ATC:pam 61 0.1215 3
#> SD:hclust 60 0.0942 3
#> CV:hclust 46 0.1528 3
#> MAD:hclust 60 0.0243 3
#> ATC:hclust 65 0.0171 3
test_to_known_factors(res_list, k = 4)
#> n disease.state(p) k
#> SD:NMF 47 0.53315 4
#> CV:NMF 27 0.25883 4
#> MAD:NMF 66 0.84857 4
#> ATC:NMF 68 0.47402 4
#> SD:skmeans 67 0.07535 4
#> CV:skmeans 60 0.00842 4
#> MAD:skmeans 67 0.52621 4
#> ATC:skmeans 70 0.48733 4
#> SD:mclust 61 0.17046 4
#> CV:mclust 57 0.06704 4
#> MAD:mclust 69 0.09468 4
#> ATC:mclust 69 0.14151 4
#> SD:kmeans 57 0.09027 4
#> CV:kmeans 33 0.58829 4
#> MAD:kmeans 56 0.04331 4
#> ATC:kmeans 58 0.06341 4
#> SD:pam 63 0.20035 4
#> CV:pam 61 0.03282 4
#> MAD:pam 62 0.38166 4
#> ATC:pam 59 0.28422 4
#> SD:hclust 50 0.08701 4
#> CV:hclust 46 0.14654 4
#> MAD:hclust 42 0.01574 4
#> ATC:hclust 69 0.08867 4
test_to_known_factors(res_list, k = 5)
#> n disease.state(p) k
#> SD:NMF 59 0.2447 5
#> CV:NMF 45 0.0401 5
#> MAD:NMF 61 0.3269 5
#> ATC:NMF 66 0.1802 5
#> SD:skmeans 65 0.0998 5
#> CV:skmeans 59 0.0225 5
#> MAD:skmeans 57 0.2684 5
#> ATC:skmeans 67 0.5694 5
#> SD:mclust 46 0.2096 5
#> CV:mclust 58 0.3163 5
#> MAD:mclust 59 0.0103 5
#> ATC:mclust 69 0.0949 5
#> SD:kmeans 62 0.0192 5
#> CV:kmeans 61 0.0379 5
#> MAD:kmeans 47 0.0581 5
#> ATC:kmeans 61 0.0141 5
#> SD:pam 64 0.0972 5
#> CV:pam 62 0.0203 5
#> MAD:pam 61 0.1792 5
#> ATC:pam 65 0.1502 5
#> SD:hclust 53 0.1027 5
#> CV:hclust 39 0.0424 5
#> MAD:hclust 35 0.1432 5
#> ATC:hclust 66 0.1642 5
test_to_known_factors(res_list, k = 6)
#> n disease.state(p) k
#> SD:NMF 45 0.6343 6
#> CV:NMF 54 0.0236 6
#> MAD:NMF 53 0.0371 6
#> ATC:NMF 45 0.0861 6
#> SD:skmeans 53 0.0529 6
#> CV:skmeans 50 0.0599 6
#> MAD:skmeans 55 0.4640 6
#> ATC:skmeans 57 0.0818 6
#> SD:mclust 57 0.2847 6
#> CV:mclust 58 0.0862 6
#> MAD:mclust 52 0.0204 6
#> ATC:mclust 69 0.0350 6
#> SD:kmeans 43 0.0327 6
#> CV:kmeans 64 0.0666 6
#> MAD:kmeans 34 0.1445 6
#> ATC:kmeans 61 0.0580 6
#> SD:pam 56 0.0769 6
#> CV:pam 59 0.0526 6
#> MAD:pam 62 0.1845 6
#> ATC:pam 59 0.0639 6
#> SD:hclust 45 0.1044 6
#> CV:hclust 56 0.0517 6
#> MAD:hclust 32 0.0302 6
#> ATC:hclust 58 0.0867 6
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "hclust"]
# you can also extract it by
# res = res_list["SD:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 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 0.736 0.871 0.942 0.4860 0.508 0.508
#> 3 3 0.502 0.619 0.801 0.2640 0.955 0.912
#> 4 4 0.498 0.523 0.664 0.1460 0.792 0.566
#> 5 5 0.539 0.579 0.713 0.0913 0.936 0.784
#> 6 6 0.634 0.476 0.698 0.0512 0.959 0.837
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
#> GSM1299517 2 0.0000 0.9467 0.000 1.000
#> GSM1299518 2 0.1843 0.9363 0.028 0.972
#> GSM1299519 2 0.0000 0.9467 0.000 1.000
#> GSM1299520 1 0.0938 0.9211 0.988 0.012
#> GSM1299521 1 0.0000 0.9209 1.000 0.000
#> GSM1299522 2 0.0000 0.9467 0.000 1.000
#> GSM1299523 1 0.4022 0.8890 0.920 0.080
#> GSM1299524 2 0.7139 0.7433 0.196 0.804
#> GSM1299525 2 0.5294 0.8544 0.120 0.880
#> GSM1299526 2 0.0000 0.9467 0.000 1.000
#> GSM1299527 2 0.0376 0.9466 0.004 0.996
#> GSM1299528 2 0.0672 0.9455 0.008 0.992
#> GSM1299529 2 0.5946 0.8266 0.144 0.856
#> GSM1299530 1 0.0938 0.9211 0.988 0.012
#> GSM1299531 2 0.0376 0.9465 0.004 0.996
#> GSM1299575 1 0.1414 0.9193 0.980 0.020
#> GSM1299532 2 0.0000 0.9467 0.000 1.000
#> GSM1299533 2 0.9993 -0.0208 0.484 0.516
#> GSM1299534 2 0.0000 0.9467 0.000 1.000
#> GSM1299535 2 0.2603 0.9267 0.044 0.956
#> GSM1299536 1 0.6531 0.8014 0.832 0.168
#> GSM1299537 2 0.0376 0.9465 0.004 0.996
#> GSM1299538 1 0.6973 0.7836 0.812 0.188
#> GSM1299539 2 0.9933 0.1274 0.452 0.548
#> GSM1299540 2 0.4690 0.8795 0.100 0.900
#> GSM1299541 2 0.0376 0.9463 0.004 0.996
#> GSM1299542 2 0.0000 0.9467 0.000 1.000
#> GSM1299543 2 0.0000 0.9467 0.000 1.000
#> GSM1299544 2 0.0376 0.9464 0.004 0.996
#> GSM1299545 1 0.4161 0.8852 0.916 0.084
#> GSM1299546 2 0.0000 0.9467 0.000 1.000
#> GSM1299547 1 0.1184 0.9199 0.984 0.016
#> GSM1299548 2 0.0672 0.9454 0.008 0.992
#> GSM1299549 1 0.0000 0.9209 1.000 0.000
#> GSM1299550 1 0.9661 0.4043 0.608 0.392
#> GSM1299551 2 0.0000 0.9467 0.000 1.000
#> GSM1299552 1 0.0000 0.9209 1.000 0.000
#> GSM1299553 1 0.9866 0.2715 0.568 0.432
#> GSM1299554 2 0.0672 0.9454 0.008 0.992
#> GSM1299555 2 0.4022 0.8979 0.080 0.920
#> GSM1299556 2 0.1633 0.9386 0.024 0.976
#> GSM1299557 2 0.5519 0.8453 0.128 0.872
#> GSM1299558 2 0.0000 0.9467 0.000 1.000
#> GSM1299559 2 0.1633 0.9386 0.024 0.976
#> GSM1299560 2 0.0000 0.9467 0.000 1.000
#> GSM1299576 1 0.0000 0.9209 1.000 0.000
#> GSM1299577 1 0.0376 0.9212 0.996 0.004
#> GSM1299561 2 0.1843 0.9363 0.028 0.972
#> GSM1299562 2 0.1414 0.9411 0.020 0.980
#> GSM1299563 1 0.3114 0.9036 0.944 0.056
#> GSM1299564 1 0.6623 0.8033 0.828 0.172
#> GSM1299565 2 0.0000 0.9467 0.000 1.000
#> GSM1299566 2 0.2236 0.9300 0.036 0.964
#> GSM1299567 1 0.4022 0.8891 0.920 0.080
#> GSM1299568 2 0.0000 0.9467 0.000 1.000
#> GSM1299569 2 0.0376 0.9464 0.004 0.996
#> GSM1299570 1 0.0938 0.9211 0.988 0.012
#> GSM1299571 2 0.0000 0.9467 0.000 1.000
#> GSM1299572 1 0.9129 0.5482 0.672 0.328
#> GSM1299573 2 0.0000 0.9467 0.000 1.000
#> GSM1299574 2 0.0376 0.9464 0.004 0.996
#> GSM1299578 1 0.1414 0.9193 0.980 0.020
#> GSM1299579 1 0.0000 0.9209 1.000 0.000
#> GSM1299580 1 0.1414 0.9193 0.980 0.020
#> GSM1299581 1 0.0000 0.9209 1.000 0.000
#> GSM1299582 1 0.0000 0.9209 1.000 0.000
#> GSM1299583 1 0.0000 0.9209 1.000 0.000
#> GSM1299584 1 0.0000 0.9209 1.000 0.000
#> GSM1299585 1 0.0000 0.9209 1.000 0.000
#> GSM1299586 1 0.0000 0.9209 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1299517 3 0.3038 0.7310 0.000 0.104 0.896
#> GSM1299518 3 0.3607 0.7438 0.008 0.112 0.880
#> GSM1299519 3 0.4605 0.7115 0.000 0.204 0.796
#> GSM1299520 1 0.2866 0.7816 0.916 0.076 0.008
#> GSM1299521 1 0.4931 0.6557 0.768 0.232 0.000
#> GSM1299522 3 0.4504 0.7148 0.000 0.196 0.804
#> GSM1299523 1 0.5173 0.7183 0.816 0.148 0.036
#> GSM1299524 3 0.7106 0.4703 0.076 0.224 0.700
#> GSM1299525 3 0.7337 0.1021 0.032 0.428 0.540
#> GSM1299526 3 0.4504 0.7148 0.000 0.196 0.804
#> GSM1299527 3 0.4409 0.6829 0.004 0.172 0.824
#> GSM1299528 3 0.5291 0.6106 0.000 0.268 0.732
#> GSM1299529 2 0.7491 -0.1845 0.036 0.492 0.472
#> GSM1299530 1 0.2866 0.7816 0.916 0.076 0.008
#> GSM1299531 3 0.4452 0.7275 0.000 0.192 0.808
#> GSM1299575 1 0.2496 0.7856 0.928 0.068 0.004
#> GSM1299532 3 0.1964 0.7457 0.000 0.056 0.944
#> GSM1299533 3 0.9730 -0.3183 0.228 0.352 0.420
#> GSM1299534 3 0.3879 0.6918 0.000 0.152 0.848
#> GSM1299535 3 0.4782 0.7203 0.016 0.164 0.820
#> GSM1299536 1 0.8475 0.3139 0.568 0.320 0.112
#> GSM1299537 3 0.2796 0.7352 0.000 0.092 0.908
#> GSM1299538 1 0.7213 0.5613 0.700 0.212 0.088
#> GSM1299539 2 0.9657 0.3299 0.300 0.460 0.240
#> GSM1299540 3 0.6283 0.6351 0.064 0.176 0.760
#> GSM1299541 3 0.2878 0.7507 0.000 0.096 0.904
#> GSM1299542 3 0.1964 0.7418 0.000 0.056 0.944
#> GSM1299543 3 0.4702 0.7227 0.000 0.212 0.788
#> GSM1299544 3 0.5216 0.6199 0.000 0.260 0.740
#> GSM1299545 1 0.4636 0.7470 0.848 0.116 0.036
#> GSM1299546 3 0.4605 0.7115 0.000 0.204 0.796
#> GSM1299547 1 0.5884 0.6031 0.716 0.272 0.012
#> GSM1299548 3 0.2860 0.7387 0.004 0.084 0.912
#> GSM1299549 1 0.4887 0.6592 0.772 0.228 0.000
#> GSM1299550 2 0.9842 0.0458 0.368 0.384 0.248
#> GSM1299551 3 0.4605 0.7115 0.000 0.204 0.796
#> GSM1299552 1 0.4887 0.6592 0.772 0.228 0.000
#> GSM1299553 1 0.9357 -0.2352 0.440 0.392 0.168
#> GSM1299554 3 0.3619 0.7213 0.000 0.136 0.864
#> GSM1299555 3 0.5847 0.6668 0.048 0.172 0.780
#> GSM1299556 3 0.3769 0.7312 0.016 0.104 0.880
#> GSM1299557 3 0.7489 -0.0832 0.036 0.468 0.496
#> GSM1299558 3 0.4399 0.7248 0.000 0.188 0.812
#> GSM1299559 3 0.3769 0.7312 0.016 0.104 0.880
#> GSM1299560 3 0.1964 0.7457 0.000 0.056 0.944
#> GSM1299576 1 0.0747 0.7918 0.984 0.016 0.000
#> GSM1299577 1 0.1129 0.7918 0.976 0.020 0.004
#> GSM1299561 3 0.2774 0.7469 0.008 0.072 0.920
#> GSM1299562 3 0.3851 0.7482 0.004 0.136 0.860
#> GSM1299563 1 0.4137 0.7619 0.872 0.096 0.032
#> GSM1299564 1 0.6902 0.6053 0.732 0.168 0.100
#> GSM1299565 3 0.4504 0.7148 0.000 0.196 0.804
#> GSM1299566 3 0.5785 0.5626 0.004 0.300 0.696
#> GSM1299567 1 0.4862 0.7285 0.820 0.160 0.020
#> GSM1299568 3 0.3879 0.6919 0.000 0.152 0.848
#> GSM1299569 3 0.4654 0.6569 0.000 0.208 0.792
#> GSM1299570 1 0.2866 0.7816 0.916 0.076 0.008
#> GSM1299571 3 0.4504 0.7148 0.000 0.196 0.804
#> GSM1299572 1 0.9812 -0.2162 0.412 0.340 0.248
#> GSM1299573 3 0.2711 0.7370 0.000 0.088 0.912
#> GSM1299574 3 0.4702 0.7079 0.000 0.212 0.788
#> GSM1299578 1 0.2496 0.7856 0.928 0.068 0.004
#> GSM1299579 1 0.1753 0.7771 0.952 0.048 0.000
#> GSM1299580 1 0.2496 0.7856 0.928 0.068 0.004
#> GSM1299581 1 0.0000 0.7904 1.000 0.000 0.000
#> GSM1299582 1 0.0000 0.7904 1.000 0.000 0.000
#> GSM1299583 1 0.1753 0.7771 0.952 0.048 0.000
#> GSM1299584 1 0.0000 0.7904 1.000 0.000 0.000
#> GSM1299585 1 0.4931 0.6557 0.768 0.232 0.000
#> GSM1299586 1 0.0747 0.7918 0.984 0.016 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1299517 3 0.194 0.6109 0.000 0.032 0.940 0.028
#> GSM1299518 3 0.601 0.4251 0.016 0.204 0.704 0.076
#> GSM1299519 2 0.494 0.5281 0.000 0.564 0.436 0.000
#> GSM1299520 1 0.244 0.7689 0.916 0.024 0.000 0.060
#> GSM1299521 4 0.493 0.5538 0.432 0.000 0.000 0.568
#> GSM1299522 2 0.512 0.5202 0.000 0.556 0.440 0.004
#> GSM1299523 1 0.442 0.7119 0.836 0.056 0.028 0.080
#> GSM1299524 3 0.670 0.3294 0.004 0.124 0.616 0.256
#> GSM1299525 2 0.783 0.2269 0.020 0.524 0.264 0.192
#> GSM1299526 2 0.513 0.5118 0.000 0.548 0.448 0.004
#> GSM1299527 3 0.333 0.5696 0.000 0.088 0.872 0.040
#> GSM1299528 3 0.702 0.4147 0.004 0.248 0.588 0.160
#> GSM1299529 2 0.783 0.2182 0.028 0.548 0.192 0.232
#> GSM1299530 1 0.244 0.7689 0.916 0.024 0.000 0.060
#> GSM1299531 3 0.630 0.3003 0.000 0.348 0.580 0.072
#> GSM1299575 1 0.205 0.7774 0.928 0.008 0.000 0.064
#> GSM1299532 3 0.202 0.6000 0.000 0.056 0.932 0.012
#> GSM1299533 4 0.707 0.1874 0.012 0.096 0.356 0.536
#> GSM1299534 3 0.566 0.5226 0.000 0.212 0.704 0.084
#> GSM1299535 3 0.710 0.2736 0.020 0.288 0.588 0.104
#> GSM1299536 4 0.700 0.6009 0.264 0.012 0.124 0.600
#> GSM1299537 3 0.180 0.6109 0.000 0.040 0.944 0.016
#> GSM1299538 1 0.626 0.5775 0.716 0.104 0.032 0.148
#> GSM1299539 2 0.938 -0.0786 0.284 0.344 0.092 0.280
#> GSM1299540 3 0.820 0.1038 0.068 0.328 0.496 0.108
#> GSM1299541 3 0.390 0.5035 0.000 0.164 0.816 0.020
#> GSM1299542 3 0.139 0.6086 0.000 0.028 0.960 0.012
#> GSM1299543 3 0.636 0.1004 0.000 0.420 0.516 0.064
#> GSM1299544 3 0.676 0.4305 0.000 0.252 0.600 0.148
#> GSM1299545 1 0.371 0.7341 0.864 0.076 0.008 0.052
#> GSM1299546 2 0.494 0.5281 0.000 0.564 0.436 0.000
#> GSM1299547 4 0.541 0.5823 0.380 0.008 0.008 0.604
#> GSM1299548 3 0.232 0.6210 0.004 0.032 0.928 0.036
#> GSM1299549 4 0.511 0.5457 0.436 0.004 0.000 0.560
#> GSM1299550 4 0.790 0.4931 0.132 0.044 0.284 0.540
#> GSM1299551 2 0.494 0.5281 0.000 0.564 0.436 0.000
#> GSM1299552 4 0.511 0.5457 0.436 0.004 0.000 0.560
#> GSM1299553 1 0.873 0.1279 0.440 0.308 0.060 0.192
#> GSM1299554 3 0.303 0.6069 0.004 0.052 0.896 0.048
#> GSM1299555 3 0.793 0.1415 0.052 0.320 0.520 0.108
#> GSM1299556 3 0.320 0.5979 0.012 0.076 0.888 0.024
#> GSM1299557 2 0.791 0.2082 0.024 0.528 0.228 0.220
#> GSM1299558 3 0.626 0.3248 0.000 0.324 0.600 0.076
#> GSM1299559 3 0.320 0.5979 0.012 0.076 0.888 0.024
#> GSM1299560 3 0.202 0.6000 0.000 0.056 0.932 0.012
#> GSM1299576 1 0.277 0.7426 0.880 0.004 0.000 0.116
#> GSM1299577 1 0.278 0.7614 0.896 0.020 0.000 0.084
#> GSM1299561 3 0.485 0.5465 0.016 0.104 0.804 0.076
#> GSM1299562 3 0.596 0.1551 0.008 0.344 0.612 0.036
#> GSM1299563 1 0.346 0.7524 0.880 0.028 0.020 0.072
#> GSM1299564 1 0.591 0.6118 0.756 0.064 0.080 0.100
#> GSM1299565 2 0.512 0.5202 0.000 0.556 0.440 0.004
#> GSM1299566 3 0.749 0.3754 0.012 0.268 0.548 0.172
#> GSM1299567 1 0.415 0.7148 0.836 0.080 0.004 0.080
#> GSM1299568 3 0.587 0.5134 0.000 0.216 0.688 0.096
#> GSM1299569 3 0.610 0.4900 0.000 0.200 0.676 0.124
#> GSM1299570 1 0.244 0.7689 0.916 0.024 0.000 0.060
#> GSM1299571 2 0.513 0.5188 0.000 0.552 0.444 0.004
#> GSM1299572 4 0.795 0.5640 0.152 0.048 0.244 0.556
#> GSM1299573 3 0.162 0.6189 0.000 0.028 0.952 0.020
#> GSM1299574 2 0.492 0.5245 0.000 0.572 0.428 0.000
#> GSM1299578 1 0.205 0.7774 0.928 0.008 0.000 0.064
#> GSM1299579 1 0.371 0.6597 0.804 0.004 0.000 0.192
#> GSM1299580 1 0.205 0.7774 0.928 0.008 0.000 0.064
#> GSM1299581 1 0.300 0.7345 0.864 0.004 0.000 0.132
#> GSM1299582 1 0.300 0.7345 0.864 0.004 0.000 0.132
#> GSM1299583 1 0.371 0.6597 0.804 0.004 0.000 0.192
#> GSM1299584 1 0.300 0.7345 0.864 0.004 0.000 0.132
#> GSM1299585 4 0.493 0.5538 0.432 0.000 0.000 0.568
#> GSM1299586 1 0.265 0.7483 0.888 0.004 0.000 0.108
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1299517 3 0.282 0.6627 0.000 0.076 0.884 0.032 0.008
#> GSM1299518 3 0.705 0.4069 0.016 0.236 0.572 0.128 0.048
#> GSM1299519 2 0.157 0.7751 0.000 0.936 0.060 0.004 0.000
#> GSM1299520 1 0.313 0.7367 0.864 0.004 0.000 0.080 0.052
#> GSM1299521 5 0.300 0.6775 0.188 0.000 0.000 0.000 0.812
#> GSM1299522 2 0.183 0.7810 0.000 0.920 0.076 0.004 0.000
#> GSM1299523 1 0.383 0.6521 0.820 0.008 0.020 0.136 0.016
#> GSM1299524 3 0.708 0.3902 0.004 0.092 0.556 0.096 0.252
#> GSM1299525 4 0.662 0.4333 0.032 0.368 0.092 0.504 0.004
#> GSM1299526 2 0.173 0.7804 0.000 0.920 0.080 0.000 0.000
#> GSM1299527 3 0.418 0.6340 0.000 0.100 0.792 0.104 0.004
#> GSM1299528 3 0.589 0.4180 0.000 0.044 0.564 0.356 0.036
#> GSM1299529 4 0.605 0.5760 0.040 0.292 0.056 0.608 0.004
#> GSM1299530 1 0.313 0.7367 0.864 0.004 0.000 0.080 0.052
#> GSM1299531 2 0.706 -0.0717 0.000 0.388 0.372 0.224 0.016
#> GSM1299575 1 0.233 0.7544 0.876 0.000 0.000 0.000 0.124
#> GSM1299532 3 0.316 0.6441 0.000 0.128 0.848 0.012 0.012
#> GSM1299533 5 0.687 0.3236 0.000 0.088 0.288 0.080 0.544
#> GSM1299534 3 0.547 0.5688 0.000 0.072 0.676 0.228 0.024
#> GSM1299535 3 0.800 0.2269 0.016 0.288 0.444 0.176 0.076
#> GSM1299536 5 0.478 0.6648 0.084 0.004 0.116 0.024 0.772
#> GSM1299537 3 0.273 0.6604 0.000 0.088 0.884 0.020 0.008
#> GSM1299538 1 0.523 0.4908 0.688 0.008 0.024 0.248 0.032
#> GSM1299539 4 0.573 0.5113 0.268 0.012 0.048 0.648 0.024
#> GSM1299540 3 0.886 0.0890 0.060 0.320 0.344 0.192 0.084
#> GSM1299541 3 0.517 0.5140 0.000 0.248 0.676 0.068 0.008
#> GSM1299542 3 0.286 0.6548 0.000 0.104 0.872 0.012 0.012
#> GSM1299543 2 0.649 0.3272 0.000 0.544 0.264 0.180 0.012
#> GSM1299544 3 0.581 0.4381 0.000 0.044 0.588 0.332 0.036
#> GSM1299545 1 0.430 0.6992 0.804 0.020 0.004 0.108 0.064
#> GSM1299546 2 0.157 0.7751 0.000 0.936 0.060 0.004 0.000
#> GSM1299547 5 0.337 0.6937 0.144 0.004 0.004 0.016 0.832
#> GSM1299548 3 0.271 0.6690 0.004 0.044 0.900 0.040 0.012
#> GSM1299549 5 0.339 0.6747 0.188 0.000 0.000 0.012 0.800
#> GSM1299550 5 0.703 0.4609 0.064 0.008 0.272 0.104 0.552
#> GSM1299551 2 0.157 0.7751 0.000 0.936 0.060 0.004 0.000
#> GSM1299552 5 0.339 0.6747 0.188 0.000 0.000 0.012 0.800
#> GSM1299553 4 0.571 0.2206 0.416 0.008 0.024 0.528 0.024
#> GSM1299554 3 0.331 0.6566 0.004 0.040 0.864 0.080 0.012
#> GSM1299555 3 0.862 0.1198 0.044 0.320 0.372 0.180 0.084
#> GSM1299556 3 0.423 0.6434 0.008 0.108 0.812 0.052 0.020
#> GSM1299557 4 0.646 0.5467 0.036 0.304 0.088 0.568 0.004
#> GSM1299558 3 0.687 0.0326 0.000 0.376 0.416 0.196 0.012
#> GSM1299559 3 0.423 0.6434 0.008 0.108 0.812 0.052 0.020
#> GSM1299560 3 0.316 0.6441 0.000 0.128 0.848 0.012 0.012
#> GSM1299576 1 0.380 0.7158 0.756 0.008 0.000 0.004 0.232
#> GSM1299577 1 0.368 0.7444 0.804 0.008 0.000 0.020 0.168
#> GSM1299561 3 0.553 0.5975 0.016 0.072 0.736 0.128 0.048
#> GSM1299562 2 0.657 0.1856 0.004 0.508 0.368 0.088 0.032
#> GSM1299563 1 0.447 0.7160 0.800 0.008 0.024 0.100 0.068
#> GSM1299564 1 0.565 0.5849 0.720 0.008 0.088 0.132 0.052
#> GSM1299565 2 0.189 0.7799 0.000 0.916 0.080 0.004 0.000
#> GSM1299566 3 0.616 0.3686 0.008 0.036 0.528 0.388 0.040
#> GSM1299567 1 0.363 0.6473 0.820 0.012 0.000 0.144 0.024
#> GSM1299568 3 0.549 0.5583 0.000 0.064 0.664 0.248 0.024
#> GSM1299569 3 0.518 0.5247 0.000 0.028 0.668 0.272 0.032
#> GSM1299570 1 0.313 0.7367 0.864 0.004 0.000 0.080 0.052
#> GSM1299571 2 0.173 0.7808 0.000 0.920 0.080 0.000 0.000
#> GSM1299572 5 0.561 0.5727 0.028 0.012 0.208 0.060 0.692
#> GSM1299573 3 0.239 0.6659 0.000 0.048 0.908 0.040 0.004
#> GSM1299574 2 0.174 0.7663 0.000 0.932 0.056 0.012 0.000
#> GSM1299578 1 0.233 0.7544 0.876 0.000 0.000 0.000 0.124
#> GSM1299579 1 0.445 0.5857 0.636 0.008 0.000 0.004 0.352
#> GSM1299580 1 0.233 0.7544 0.876 0.000 0.000 0.000 0.124
#> GSM1299581 1 0.396 0.7068 0.732 0.008 0.000 0.004 0.256
#> GSM1299582 1 0.396 0.7068 0.732 0.008 0.000 0.004 0.256
#> GSM1299583 1 0.443 0.5918 0.640 0.008 0.000 0.004 0.348
#> GSM1299584 1 0.396 0.7068 0.732 0.008 0.000 0.004 0.256
#> GSM1299585 5 0.300 0.6775 0.188 0.000 0.000 0.000 0.812
#> GSM1299586 1 0.371 0.7235 0.768 0.008 0.000 0.004 0.220
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1299517 3 0.2467 0.56212 0.000 0.048 0.896 0.020 0.000 0.036
#> GSM1299518 3 0.6996 -0.04136 0.004 0.184 0.484 0.068 0.008 0.252
#> GSM1299519 2 0.0291 0.71611 0.000 0.992 0.000 0.004 0.000 0.004
#> GSM1299520 1 0.5136 0.60410 0.704 0.000 0.000 0.120 0.060 0.116
#> GSM1299521 5 0.1765 0.70569 0.096 0.000 0.000 0.000 0.904 0.000
#> GSM1299522 2 0.0622 0.72066 0.000 0.980 0.008 0.000 0.000 0.012
#> GSM1299523 1 0.5258 0.50218 0.672 0.000 0.012 0.176 0.012 0.128
#> GSM1299524 3 0.7338 0.03570 0.000 0.048 0.472 0.068 0.144 0.268
#> GSM1299525 4 0.5293 0.49994 0.016 0.356 0.040 0.572 0.000 0.016
#> GSM1299526 2 0.0622 0.71979 0.000 0.980 0.012 0.000 0.000 0.008
#> GSM1299527 3 0.4211 0.50403 0.000 0.076 0.772 0.124 0.000 0.028
#> GSM1299528 3 0.5365 0.05439 0.000 0.016 0.492 0.056 0.004 0.432
#> GSM1299529 4 0.4434 0.62158 0.016 0.252 0.020 0.700 0.000 0.012
#> GSM1299530 1 0.5136 0.60410 0.704 0.000 0.000 0.120 0.060 0.116
#> GSM1299531 2 0.6755 -0.00422 0.000 0.360 0.312 0.036 0.000 0.292
#> GSM1299575 1 0.2178 0.67391 0.868 0.000 0.000 0.000 0.132 0.000
#> GSM1299532 3 0.3098 0.53960 0.000 0.120 0.836 0.000 0.004 0.040
#> GSM1299533 5 0.7800 0.32869 0.000 0.088 0.200 0.060 0.436 0.216
#> GSM1299534 3 0.5157 0.33887 0.000 0.068 0.624 0.024 0.000 0.284
#> GSM1299535 3 0.7826 -0.49906 0.004 0.248 0.336 0.100 0.020 0.292
#> GSM1299536 5 0.4493 0.65596 0.020 0.000 0.104 0.024 0.772 0.080
#> GSM1299537 3 0.2918 0.56013 0.000 0.056 0.872 0.016 0.004 0.052
#> GSM1299538 1 0.6324 0.34282 0.532 0.000 0.016 0.260 0.020 0.172
#> GSM1299539 4 0.4654 0.49036 0.188 0.000 0.020 0.720 0.004 0.068
#> GSM1299540 6 0.8349 0.41026 0.032 0.272 0.252 0.100 0.024 0.320
#> GSM1299541 3 0.5277 0.34673 0.000 0.200 0.656 0.016 0.004 0.124
#> GSM1299542 3 0.2452 0.55497 0.000 0.084 0.884 0.000 0.004 0.028
#> GSM1299543 2 0.5930 0.31498 0.000 0.564 0.192 0.024 0.000 0.220
#> GSM1299544 3 0.5207 0.09351 0.000 0.016 0.508 0.044 0.004 0.428
#> GSM1299545 1 0.4654 0.58517 0.748 0.000 0.000 0.096 0.056 0.100
#> GSM1299546 2 0.0291 0.71611 0.000 0.992 0.000 0.004 0.000 0.004
#> GSM1299547 5 0.2614 0.71752 0.056 0.000 0.004 0.004 0.884 0.052
#> GSM1299548 3 0.2375 0.54463 0.000 0.004 0.896 0.028 0.004 0.068
#> GSM1299549 5 0.2121 0.70359 0.096 0.000 0.000 0.012 0.892 0.000
#> GSM1299550 5 0.7066 0.45904 0.024 0.000 0.232 0.076 0.504 0.164
#> GSM1299551 2 0.0291 0.71611 0.000 0.992 0.000 0.004 0.000 0.004
#> GSM1299552 5 0.2121 0.70359 0.096 0.000 0.000 0.012 0.892 0.000
#> GSM1299553 4 0.4437 0.25179 0.392 0.000 0.004 0.584 0.012 0.008
#> GSM1299554 3 0.3089 0.52858 0.000 0.028 0.848 0.020 0.000 0.104
#> GSM1299555 6 0.8056 0.40310 0.016 0.272 0.272 0.088 0.024 0.328
#> GSM1299556 3 0.4307 0.50461 0.008 0.076 0.792 0.028 0.008 0.088
#> GSM1299557 4 0.4957 0.59805 0.016 0.280 0.048 0.648 0.000 0.008
#> GSM1299558 2 0.6584 -0.01970 0.000 0.376 0.352 0.028 0.000 0.244
#> GSM1299559 3 0.4307 0.50461 0.008 0.076 0.792 0.028 0.008 0.088
#> GSM1299560 3 0.3098 0.53960 0.000 0.120 0.836 0.000 0.004 0.040
#> GSM1299576 1 0.3488 0.63564 0.744 0.000 0.000 0.004 0.244 0.008
#> GSM1299577 1 0.3699 0.66481 0.780 0.000 0.000 0.032 0.176 0.012
#> GSM1299561 3 0.5059 0.26524 0.004 0.016 0.676 0.064 0.008 0.232
#> GSM1299562 2 0.6388 0.11306 0.000 0.520 0.280 0.036 0.008 0.156
#> GSM1299563 1 0.6045 0.56983 0.636 0.000 0.012 0.132 0.076 0.144
#> GSM1299564 1 0.6866 0.42294 0.556 0.000 0.068 0.156 0.036 0.184
#> GSM1299565 2 0.0717 0.72007 0.000 0.976 0.008 0.000 0.000 0.016
#> GSM1299566 6 0.5775 -0.32989 0.004 0.008 0.440 0.100 0.004 0.444
#> GSM1299567 1 0.4811 0.51902 0.700 0.000 0.000 0.176 0.016 0.108
#> GSM1299568 3 0.5155 0.31170 0.000 0.060 0.608 0.024 0.000 0.308
#> GSM1299569 3 0.5065 0.25071 0.000 0.028 0.596 0.032 0.004 0.340
#> GSM1299570 1 0.5136 0.60410 0.704 0.000 0.000 0.120 0.060 0.116
#> GSM1299571 2 0.0622 0.72025 0.000 0.980 0.008 0.000 0.000 0.012
#> GSM1299572 5 0.5973 0.59421 0.004 0.004 0.152 0.048 0.624 0.168
#> GSM1299573 3 0.2202 0.55560 0.000 0.028 0.908 0.012 0.000 0.052
#> GSM1299574 2 0.0508 0.70991 0.000 0.984 0.000 0.012 0.000 0.004
#> GSM1299578 1 0.2178 0.67391 0.868 0.000 0.000 0.000 0.132 0.000
#> GSM1299579 1 0.4090 0.49836 0.604 0.000 0.000 0.004 0.384 0.008
#> GSM1299580 1 0.2178 0.67391 0.868 0.000 0.000 0.000 0.132 0.000
#> GSM1299581 1 0.3672 0.62631 0.712 0.000 0.000 0.004 0.276 0.008
#> GSM1299582 1 0.3672 0.62631 0.712 0.000 0.000 0.004 0.276 0.008
#> GSM1299583 1 0.4058 0.51798 0.616 0.000 0.000 0.004 0.372 0.008
#> GSM1299584 1 0.3672 0.62631 0.712 0.000 0.000 0.004 0.276 0.008
#> GSM1299585 5 0.1765 0.70569 0.096 0.000 0.000 0.000 0.904 0.000
#> GSM1299586 1 0.3384 0.64545 0.760 0.000 0.000 0.004 0.228 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 disease.state(p) k
#> SD:hclust 66 0.0542 2
#> SD:hclust 60 0.0942 3
#> SD:hclust 50 0.0870 4
#> SD:hclust 53 0.1027 5
#> SD:hclust 45 0.1044 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "kmeans"]
# you can also extract it by
# res = res_list["SD:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.975 0.991 0.4947 0.503 0.503
#> 3 3 0.569 0.618 0.710 0.2817 0.822 0.652
#> 4 4 0.576 0.622 0.771 0.1463 0.798 0.491
#> 5 5 0.666 0.721 0.811 0.0802 0.925 0.723
#> 6 6 0.778 0.611 0.761 0.0483 0.912 0.632
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
#> GSM1299517 2 0.000 0.9985 0.000 1.000
#> GSM1299518 2 0.000 0.9985 0.000 1.000
#> GSM1299519 2 0.000 0.9985 0.000 1.000
#> GSM1299520 1 0.000 0.9795 1.000 0.000
#> GSM1299521 1 0.000 0.9795 1.000 0.000
#> GSM1299522 2 0.000 0.9985 0.000 1.000
#> GSM1299523 1 0.118 0.9677 0.984 0.016
#> GSM1299524 2 0.000 0.9985 0.000 1.000
#> GSM1299525 2 0.000 0.9985 0.000 1.000
#> GSM1299526 2 0.000 0.9985 0.000 1.000
#> GSM1299527 2 0.000 0.9985 0.000 1.000
#> GSM1299528 2 0.000 0.9985 0.000 1.000
#> GSM1299529 2 0.000 0.9985 0.000 1.000
#> GSM1299530 1 0.000 0.9795 1.000 0.000
#> GSM1299531 2 0.000 0.9985 0.000 1.000
#> GSM1299575 1 0.000 0.9795 1.000 0.000
#> GSM1299532 2 0.000 0.9985 0.000 1.000
#> GSM1299533 2 0.242 0.9577 0.040 0.960
#> GSM1299534 2 0.000 0.9985 0.000 1.000
#> GSM1299535 2 0.000 0.9985 0.000 1.000
#> GSM1299536 1 0.000 0.9795 1.000 0.000
#> GSM1299537 2 0.000 0.9985 0.000 1.000
#> GSM1299538 1 0.204 0.9540 0.968 0.032
#> GSM1299539 1 0.204 0.9540 0.968 0.032
#> GSM1299540 2 0.118 0.9832 0.016 0.984
#> GSM1299541 2 0.000 0.9985 0.000 1.000
#> GSM1299542 2 0.000 0.9985 0.000 1.000
#> GSM1299543 2 0.000 0.9985 0.000 1.000
#> GSM1299544 2 0.000 0.9985 0.000 1.000
#> GSM1299545 1 0.000 0.9795 1.000 0.000
#> GSM1299546 2 0.000 0.9985 0.000 1.000
#> GSM1299547 1 0.000 0.9795 1.000 0.000
#> GSM1299548 2 0.000 0.9985 0.000 1.000
#> GSM1299549 1 0.000 0.9795 1.000 0.000
#> GSM1299550 1 1.000 0.0381 0.508 0.492
#> GSM1299551 2 0.000 0.9985 0.000 1.000
#> GSM1299552 1 0.000 0.9795 1.000 0.000
#> GSM1299553 1 0.000 0.9795 1.000 0.000
#> GSM1299554 2 0.000 0.9985 0.000 1.000
#> GSM1299555 2 0.000 0.9985 0.000 1.000
#> GSM1299556 2 0.000 0.9985 0.000 1.000
#> GSM1299557 2 0.000 0.9985 0.000 1.000
#> GSM1299558 2 0.000 0.9985 0.000 1.000
#> GSM1299559 2 0.000 0.9985 0.000 1.000
#> GSM1299560 2 0.000 0.9985 0.000 1.000
#> GSM1299576 1 0.000 0.9795 1.000 0.000
#> GSM1299577 1 0.000 0.9795 1.000 0.000
#> GSM1299561 2 0.000 0.9985 0.000 1.000
#> GSM1299562 2 0.000 0.9985 0.000 1.000
#> GSM1299563 1 0.000 0.9795 1.000 0.000
#> GSM1299564 1 0.141 0.9647 0.980 0.020
#> GSM1299565 2 0.000 0.9985 0.000 1.000
#> GSM1299566 2 0.000 0.9985 0.000 1.000
#> GSM1299567 1 0.000 0.9795 1.000 0.000
#> GSM1299568 2 0.000 0.9985 0.000 1.000
#> GSM1299569 2 0.000 0.9985 0.000 1.000
#> GSM1299570 1 0.000 0.9795 1.000 0.000
#> GSM1299571 2 0.000 0.9985 0.000 1.000
#> GSM1299572 1 0.000 0.9795 1.000 0.000
#> GSM1299573 2 0.000 0.9985 0.000 1.000
#> GSM1299574 2 0.000 0.9985 0.000 1.000
#> GSM1299578 1 0.000 0.9795 1.000 0.000
#> GSM1299579 1 0.000 0.9795 1.000 0.000
#> GSM1299580 1 0.000 0.9795 1.000 0.000
#> GSM1299581 1 0.000 0.9795 1.000 0.000
#> GSM1299582 1 0.000 0.9795 1.000 0.000
#> GSM1299583 1 0.000 0.9795 1.000 0.000
#> GSM1299584 1 0.000 0.9795 1.000 0.000
#> GSM1299585 1 0.000 0.9795 1.000 0.000
#> GSM1299586 1 0.000 0.9795 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1299517 3 0.6225 0.77767 0.000 0.432 0.568
#> GSM1299518 2 0.5529 0.13597 0.000 0.704 0.296
#> GSM1299519 2 0.0000 0.64061 0.000 1.000 0.000
#> GSM1299520 1 0.5058 0.84729 0.756 0.000 0.244
#> GSM1299521 1 0.4605 0.81396 0.796 0.000 0.204
#> GSM1299522 2 0.0000 0.64061 0.000 1.000 0.000
#> GSM1299523 1 0.5397 0.82719 0.720 0.000 0.280
#> GSM1299524 3 0.6204 0.78296 0.000 0.424 0.576
#> GSM1299525 2 0.3340 0.57005 0.000 0.880 0.120
#> GSM1299526 2 0.0000 0.64061 0.000 1.000 0.000
#> GSM1299527 3 0.6225 0.77767 0.000 0.432 0.568
#> GSM1299528 2 0.6026 0.00993 0.000 0.624 0.376
#> GSM1299529 2 0.2711 0.57195 0.000 0.912 0.088
#> GSM1299530 1 0.4605 0.86076 0.796 0.000 0.204
#> GSM1299531 2 0.3340 0.56206 0.000 0.880 0.120
#> GSM1299575 1 0.1529 0.87468 0.960 0.000 0.040
#> GSM1299532 3 0.6235 0.77474 0.000 0.436 0.564
#> GSM1299533 2 0.7583 0.18465 0.040 0.492 0.468
#> GSM1299534 2 0.6192 -0.30180 0.000 0.580 0.420
#> GSM1299535 2 0.6225 -0.32751 0.000 0.568 0.432
#> GSM1299536 1 0.5560 0.81993 0.700 0.000 0.300
#> GSM1299537 3 0.6180 0.78440 0.000 0.416 0.584
#> GSM1299538 1 0.6096 0.81967 0.704 0.016 0.280
#> GSM1299539 1 0.6475 0.81299 0.692 0.028 0.280
#> GSM1299540 3 0.8570 0.09914 0.096 0.428 0.476
#> GSM1299541 3 0.6192 0.78553 0.000 0.420 0.580
#> GSM1299542 3 0.6235 0.77474 0.000 0.436 0.564
#> GSM1299543 2 0.0000 0.64061 0.000 1.000 0.000
#> GSM1299544 2 0.6168 -0.25496 0.000 0.588 0.412
#> GSM1299545 1 0.3412 0.87376 0.876 0.000 0.124
#> GSM1299546 2 0.0000 0.64061 0.000 1.000 0.000
#> GSM1299547 1 0.5178 0.81948 0.744 0.000 0.256
#> GSM1299548 3 0.6168 0.78446 0.000 0.412 0.588
#> GSM1299549 1 0.5591 0.81842 0.696 0.000 0.304
#> GSM1299550 3 0.5911 0.14500 0.156 0.060 0.784
#> GSM1299551 2 0.0000 0.64061 0.000 1.000 0.000
#> GSM1299552 1 0.5138 0.81946 0.748 0.000 0.252
#> GSM1299553 1 0.4235 0.86341 0.824 0.000 0.176
#> GSM1299554 3 0.6111 0.76499 0.000 0.396 0.604
#> GSM1299555 2 0.6235 -0.25372 0.000 0.564 0.436
#> GSM1299556 3 0.6062 0.74715 0.000 0.384 0.616
#> GSM1299557 3 0.6260 0.50706 0.000 0.448 0.552
#> GSM1299558 2 0.2959 0.58193 0.000 0.900 0.100
#> GSM1299559 3 0.5560 0.60491 0.000 0.300 0.700
#> GSM1299560 3 0.6244 0.76811 0.000 0.440 0.560
#> GSM1299576 1 0.0592 0.87318 0.988 0.000 0.012
#> GSM1299577 1 0.2625 0.87777 0.916 0.000 0.084
#> GSM1299561 3 0.6180 0.78607 0.000 0.416 0.584
#> GSM1299562 2 0.4842 0.38814 0.000 0.776 0.224
#> GSM1299563 1 0.4974 0.85029 0.764 0.000 0.236
#> GSM1299564 1 0.5678 0.80027 0.684 0.000 0.316
#> GSM1299565 2 0.0000 0.64061 0.000 1.000 0.000
#> GSM1299566 2 0.6140 0.07707 0.000 0.596 0.404
#> GSM1299567 1 0.6062 0.71946 0.616 0.000 0.384
#> GSM1299568 2 0.5948 -0.04466 0.000 0.640 0.360
#> GSM1299569 2 0.6215 -0.31897 0.000 0.572 0.428
#> GSM1299570 1 0.5058 0.84729 0.756 0.000 0.244
#> GSM1299571 2 0.0000 0.64061 0.000 1.000 0.000
#> GSM1299572 1 0.5291 0.82029 0.732 0.000 0.268
#> GSM1299573 3 0.6225 0.77767 0.000 0.432 0.568
#> GSM1299574 2 0.0424 0.63558 0.000 0.992 0.008
#> GSM1299578 1 0.1163 0.87460 0.972 0.000 0.028
#> GSM1299579 1 0.1163 0.87113 0.972 0.000 0.028
#> GSM1299580 1 0.1529 0.87468 0.960 0.000 0.040
#> GSM1299581 1 0.0592 0.87318 0.988 0.000 0.012
#> GSM1299582 1 0.0000 0.87393 1.000 0.000 0.000
#> GSM1299583 1 0.1753 0.86714 0.952 0.000 0.048
#> GSM1299584 1 0.0592 0.87318 0.988 0.000 0.012
#> GSM1299585 1 0.4605 0.81396 0.796 0.000 0.204
#> GSM1299586 1 0.0592 0.87318 0.988 0.000 0.012
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1299517 3 0.316 0.7900 0.004 0.144 0.852 0.000
#> GSM1299518 2 0.528 0.0752 0.004 0.560 0.432 0.004
#> GSM1299519 2 0.130 0.8256 0.000 0.956 0.044 0.000
#> GSM1299520 4 0.253 0.7644 0.112 0.000 0.000 0.888
#> GSM1299521 1 0.524 0.5539 0.768 0.008 0.136 0.088
#> GSM1299522 2 0.158 0.8260 0.000 0.948 0.048 0.004
#> GSM1299523 4 0.271 0.7640 0.112 0.004 0.000 0.884
#> GSM1299524 3 0.469 0.7813 0.024 0.140 0.804 0.032
#> GSM1299525 2 0.278 0.7600 0.000 0.896 0.020 0.084
#> GSM1299526 2 0.158 0.8260 0.000 0.948 0.048 0.004
#> GSM1299527 3 0.316 0.7900 0.004 0.144 0.852 0.000
#> GSM1299528 3 0.678 0.5503 0.004 0.328 0.568 0.100
#> GSM1299529 2 0.140 0.7768 0.000 0.956 0.004 0.040
#> GSM1299530 4 0.271 0.7617 0.112 0.000 0.004 0.884
#> GSM1299531 2 0.552 0.5555 0.008 0.712 0.232 0.048
#> GSM1299575 1 0.482 0.4531 0.652 0.004 0.000 0.344
#> GSM1299532 3 0.297 0.7904 0.000 0.144 0.856 0.000
#> GSM1299533 2 0.926 0.1144 0.332 0.344 0.240 0.084
#> GSM1299534 3 0.617 0.6361 0.000 0.284 0.632 0.084
#> GSM1299535 3 0.624 0.6466 0.024 0.260 0.664 0.052
#> GSM1299536 1 0.712 0.3542 0.592 0.012 0.140 0.256
#> GSM1299537 3 0.368 0.7872 0.004 0.140 0.840 0.016
#> GSM1299538 4 0.180 0.7189 0.032 0.016 0.004 0.948
#> GSM1299539 4 0.232 0.7114 0.032 0.036 0.004 0.928
#> GSM1299540 4 0.837 -0.1273 0.020 0.252 0.352 0.376
#> GSM1299541 3 0.343 0.7896 0.004 0.140 0.848 0.008
#> GSM1299542 3 0.297 0.7904 0.000 0.144 0.856 0.000
#> GSM1299543 2 0.158 0.8253 0.000 0.948 0.048 0.004
#> GSM1299544 3 0.650 0.6186 0.004 0.292 0.612 0.092
#> GSM1299545 4 0.431 0.5964 0.260 0.004 0.000 0.736
#> GSM1299546 2 0.139 0.8261 0.000 0.952 0.048 0.000
#> GSM1299547 1 0.646 0.5010 0.668 0.008 0.140 0.184
#> GSM1299548 3 0.324 0.7898 0.004 0.136 0.856 0.004
#> GSM1299549 1 0.683 0.4710 0.652 0.020 0.140 0.188
#> GSM1299550 3 0.810 -0.0744 0.228 0.012 0.408 0.352
#> GSM1299551 2 0.130 0.8256 0.000 0.956 0.044 0.000
#> GSM1299552 1 0.646 0.5074 0.676 0.012 0.136 0.176
#> GSM1299553 4 0.507 0.6605 0.224 0.036 0.004 0.736
#> GSM1299554 3 0.472 0.7648 0.000 0.136 0.788 0.076
#> GSM1299555 3 0.733 0.2760 0.020 0.380 0.504 0.096
#> GSM1299556 3 0.507 0.7431 0.020 0.116 0.792 0.072
#> GSM1299557 3 0.619 0.6266 0.004 0.288 0.636 0.072
#> GSM1299558 2 0.546 0.5566 0.004 0.712 0.232 0.052
#> GSM1299559 3 0.543 0.6266 0.020 0.044 0.744 0.192
#> GSM1299560 3 0.297 0.7904 0.000 0.144 0.856 0.000
#> GSM1299576 1 0.384 0.6191 0.776 0.000 0.000 0.224
#> GSM1299577 4 0.492 0.1795 0.424 0.000 0.000 0.576
#> GSM1299561 3 0.297 0.7904 0.000 0.144 0.856 0.000
#> GSM1299562 2 0.568 0.5348 0.020 0.704 0.240 0.036
#> GSM1299563 4 0.253 0.7644 0.112 0.000 0.000 0.888
#> GSM1299564 4 0.244 0.7469 0.068 0.004 0.012 0.916
#> GSM1299565 2 0.158 0.8260 0.000 0.948 0.048 0.004
#> GSM1299566 3 0.804 0.4230 0.020 0.328 0.464 0.188
#> GSM1299567 4 0.392 0.6651 0.056 0.000 0.104 0.840
#> GSM1299568 3 0.648 0.5710 0.000 0.324 0.584 0.092
#> GSM1299569 3 0.646 0.6287 0.004 0.284 0.620 0.092
#> GSM1299570 4 0.253 0.7644 0.112 0.000 0.000 0.888
#> GSM1299571 2 0.139 0.8261 0.000 0.952 0.048 0.000
#> GSM1299572 1 0.642 0.4804 0.680 0.012 0.140 0.168
#> GSM1299573 3 0.292 0.7905 0.000 0.140 0.860 0.000
#> GSM1299574 2 0.149 0.8144 0.000 0.956 0.032 0.012
#> GSM1299578 1 0.482 0.4531 0.652 0.004 0.000 0.344
#> GSM1299579 1 0.387 0.6206 0.772 0.000 0.000 0.228
#> GSM1299580 1 0.482 0.4531 0.652 0.004 0.000 0.344
#> GSM1299581 1 0.384 0.6191 0.776 0.000 0.000 0.224
#> GSM1299582 1 0.413 0.5811 0.740 0.000 0.000 0.260
#> GSM1299583 1 0.353 0.6229 0.808 0.000 0.000 0.192
#> GSM1299584 1 0.384 0.6191 0.776 0.000 0.000 0.224
#> GSM1299585 1 0.524 0.5539 0.768 0.008 0.136 0.088
#> GSM1299586 1 0.384 0.6191 0.776 0.000 0.000 0.224
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1299517 3 0.0566 0.7806 0.000 0.000 0.984 0.004 0.012
#> GSM1299518 3 0.4971 -0.0737 0.000 0.472 0.504 0.004 0.020
#> GSM1299519 2 0.1270 0.8581 0.000 0.948 0.052 0.000 0.000
#> GSM1299520 4 0.2969 0.8402 0.128 0.000 0.000 0.852 0.020
#> GSM1299521 5 0.4401 0.7807 0.328 0.000 0.000 0.016 0.656
#> GSM1299522 2 0.1697 0.8586 0.000 0.932 0.060 0.000 0.008
#> GSM1299523 4 0.2824 0.8414 0.116 0.000 0.000 0.864 0.020
#> GSM1299524 3 0.3264 0.7509 0.000 0.004 0.836 0.020 0.140
#> GSM1299525 2 0.4843 0.6995 0.000 0.756 0.020 0.104 0.120
#> GSM1299526 2 0.1697 0.8586 0.000 0.932 0.060 0.000 0.008
#> GSM1299527 3 0.0865 0.7792 0.000 0.000 0.972 0.004 0.024
#> GSM1299528 3 0.7255 0.5073 0.000 0.176 0.544 0.088 0.192
#> GSM1299529 2 0.4187 0.7190 0.000 0.804 0.016 0.080 0.100
#> GSM1299530 4 0.3060 0.8394 0.128 0.000 0.000 0.848 0.024
#> GSM1299531 2 0.6674 0.4154 0.000 0.556 0.268 0.036 0.140
#> GSM1299575 1 0.2248 0.8405 0.900 0.012 0.000 0.088 0.000
#> GSM1299532 3 0.0290 0.7806 0.000 0.000 0.992 0.000 0.008
#> GSM1299533 5 0.4521 0.6702 0.040 0.116 0.040 0.008 0.796
#> GSM1299534 3 0.6040 0.6277 0.000 0.116 0.672 0.060 0.152
#> GSM1299535 3 0.4316 0.7204 0.000 0.068 0.808 0.044 0.080
#> GSM1299536 5 0.5159 0.8246 0.180 0.004 0.000 0.116 0.700
#> GSM1299537 3 0.1753 0.7656 0.000 0.000 0.936 0.032 0.032
#> GSM1299538 4 0.2618 0.7915 0.052 0.012 0.000 0.900 0.036
#> GSM1299539 4 0.4056 0.7520 0.052 0.044 0.000 0.824 0.080
#> GSM1299540 4 0.7126 0.0240 0.004 0.080 0.392 0.448 0.076
#> GSM1299541 3 0.0898 0.7781 0.000 0.000 0.972 0.008 0.020
#> GSM1299542 3 0.0798 0.7808 0.000 0.000 0.976 0.008 0.016
#> GSM1299543 2 0.1502 0.8578 0.000 0.940 0.056 0.000 0.004
#> GSM1299544 3 0.6477 0.5963 0.000 0.124 0.628 0.068 0.180
#> GSM1299545 4 0.4607 0.6746 0.276 0.012 0.000 0.692 0.020
#> GSM1299546 2 0.1410 0.8593 0.000 0.940 0.060 0.000 0.000
#> GSM1299547 5 0.5140 0.8349 0.252 0.000 0.000 0.084 0.664
#> GSM1299548 3 0.0451 0.7807 0.000 0.000 0.988 0.004 0.008
#> GSM1299549 5 0.4693 0.8318 0.196 0.000 0.000 0.080 0.724
#> GSM1299550 5 0.4055 0.6438 0.000 0.012 0.048 0.140 0.800
#> GSM1299551 2 0.1270 0.8581 0.000 0.948 0.052 0.000 0.000
#> GSM1299552 5 0.4955 0.8366 0.248 0.000 0.000 0.072 0.680
#> GSM1299553 4 0.5907 0.6815 0.196 0.052 0.000 0.668 0.084
#> GSM1299554 3 0.4082 0.7287 0.000 0.008 0.796 0.056 0.140
#> GSM1299555 3 0.6740 0.4815 0.000 0.172 0.608 0.136 0.084
#> GSM1299556 3 0.3180 0.7314 0.000 0.000 0.856 0.076 0.068
#> GSM1299557 3 0.6793 0.5116 0.000 0.164 0.608 0.104 0.124
#> GSM1299558 2 0.6602 0.4415 0.000 0.568 0.260 0.036 0.136
#> GSM1299559 3 0.4589 0.6029 0.000 0.000 0.724 0.212 0.064
#> GSM1299560 3 0.0290 0.7796 0.000 0.000 0.992 0.000 0.008
#> GSM1299576 1 0.0000 0.8800 1.000 0.000 0.000 0.000 0.000
#> GSM1299577 1 0.4522 -0.0167 0.552 0.000 0.000 0.440 0.008
#> GSM1299561 3 0.1012 0.7812 0.000 0.000 0.968 0.012 0.020
#> GSM1299562 2 0.6463 0.4276 0.000 0.556 0.280 0.020 0.144
#> GSM1299563 4 0.3099 0.8395 0.124 0.000 0.000 0.848 0.028
#> GSM1299564 4 0.2864 0.8406 0.112 0.000 0.000 0.864 0.024
#> GSM1299565 2 0.1697 0.8586 0.000 0.932 0.060 0.000 0.008
#> GSM1299566 3 0.7747 0.4603 0.000 0.176 0.484 0.124 0.216
#> GSM1299567 4 0.3980 0.7962 0.104 0.008 0.032 0.828 0.028
#> GSM1299568 3 0.6533 0.5741 0.000 0.156 0.620 0.060 0.164
#> GSM1299569 3 0.6182 0.6200 0.000 0.116 0.656 0.060 0.168
#> GSM1299570 4 0.2969 0.8402 0.128 0.000 0.000 0.852 0.020
#> GSM1299571 2 0.1410 0.8593 0.000 0.940 0.060 0.000 0.000
#> GSM1299572 5 0.5157 0.8402 0.224 0.004 0.004 0.076 0.692
#> GSM1299573 3 0.0898 0.7807 0.000 0.000 0.972 0.008 0.020
#> GSM1299574 2 0.1430 0.8572 0.000 0.944 0.052 0.000 0.004
#> GSM1299578 1 0.2248 0.8405 0.900 0.012 0.000 0.088 0.000
#> GSM1299579 1 0.1205 0.8374 0.956 0.000 0.000 0.004 0.040
#> GSM1299580 1 0.2248 0.8405 0.900 0.012 0.000 0.088 0.000
#> GSM1299581 1 0.0000 0.8800 1.000 0.000 0.000 0.000 0.000
#> GSM1299582 1 0.0290 0.8789 0.992 0.000 0.000 0.008 0.000
#> GSM1299583 1 0.0880 0.8471 0.968 0.000 0.000 0.000 0.032
#> GSM1299584 1 0.0000 0.8800 1.000 0.000 0.000 0.000 0.000
#> GSM1299585 5 0.4401 0.7807 0.328 0.000 0.000 0.016 0.656
#> GSM1299586 1 0.0000 0.8800 1.000 0.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1299517 3 0.3965 0.31350 0.000 0.000 0.616 0.004 0.004 0.376
#> GSM1299518 2 0.5995 -0.05184 0.000 0.508 0.228 0.004 0.004 0.256
#> GSM1299519 2 0.0363 0.83838 0.000 0.988 0.012 0.000 0.000 0.000
#> GSM1299520 4 0.2106 0.86520 0.064 0.000 0.000 0.904 0.032 0.000
#> GSM1299521 5 0.2482 0.89244 0.148 0.000 0.000 0.004 0.848 0.000
#> GSM1299522 2 0.0653 0.83823 0.000 0.980 0.012 0.000 0.004 0.004
#> GSM1299523 4 0.1921 0.86466 0.052 0.000 0.000 0.916 0.032 0.000
#> GSM1299524 3 0.4087 0.31441 0.000 0.000 0.744 0.004 0.064 0.188
#> GSM1299525 2 0.6379 0.50988 0.000 0.572 0.028 0.100 0.048 0.252
#> GSM1299526 2 0.0653 0.83823 0.000 0.980 0.012 0.000 0.004 0.004
#> GSM1299527 3 0.4118 0.26753 0.000 0.000 0.592 0.008 0.004 0.396
#> GSM1299528 3 0.3243 0.39410 0.000 0.064 0.860 0.024 0.016 0.036
#> GSM1299529 2 0.5625 0.55455 0.000 0.620 0.000 0.096 0.048 0.236
#> GSM1299530 4 0.2106 0.86520 0.064 0.000 0.000 0.904 0.032 0.000
#> GSM1299531 3 0.4885 0.02442 0.000 0.372 0.576 0.000 0.028 0.024
#> GSM1299575 1 0.2854 0.84169 0.860 0.004 0.000 0.048 0.000 0.088
#> GSM1299532 3 0.3907 0.25201 0.000 0.000 0.588 0.000 0.004 0.408
#> GSM1299533 5 0.2471 0.85542 0.004 0.020 0.032 0.000 0.900 0.044
#> GSM1299534 3 0.1625 0.44148 0.000 0.060 0.928 0.000 0.000 0.012
#> GSM1299535 6 0.6033 0.30392 0.000 0.032 0.424 0.012 0.076 0.456
#> GSM1299536 5 0.2711 0.90980 0.048 0.000 0.008 0.052 0.884 0.008
#> GSM1299537 6 0.3838 0.05990 0.000 0.000 0.448 0.000 0.000 0.552
#> GSM1299538 4 0.1413 0.81677 0.008 0.000 0.004 0.948 0.004 0.036
#> GSM1299539 4 0.4369 0.67403 0.012 0.008 0.004 0.724 0.028 0.224
#> GSM1299540 6 0.6553 0.47325 0.004 0.052 0.072 0.192 0.072 0.608
#> GSM1299541 3 0.3747 0.28424 0.000 0.000 0.604 0.000 0.000 0.396
#> GSM1299542 3 0.3563 0.35355 0.000 0.000 0.664 0.000 0.000 0.336
#> GSM1299543 2 0.0622 0.83656 0.000 0.980 0.012 0.000 0.000 0.008
#> GSM1299544 3 0.2734 0.42815 0.000 0.064 0.884 0.008 0.016 0.028
#> GSM1299545 4 0.5264 0.65810 0.220 0.000 0.000 0.656 0.036 0.088
#> GSM1299546 2 0.0363 0.83838 0.000 0.988 0.012 0.000 0.000 0.000
#> GSM1299547 5 0.2658 0.91596 0.100 0.000 0.000 0.036 0.864 0.000
#> GSM1299548 3 0.3923 0.31709 0.000 0.000 0.620 0.008 0.000 0.372
#> GSM1299549 5 0.2544 0.91655 0.072 0.000 0.004 0.028 0.888 0.008
#> GSM1299550 5 0.3597 0.83322 0.000 0.000 0.092 0.048 0.824 0.036
#> GSM1299551 2 0.0363 0.83838 0.000 0.988 0.012 0.000 0.000 0.000
#> GSM1299552 5 0.2476 0.91728 0.092 0.000 0.000 0.024 0.880 0.004
#> GSM1299553 4 0.6081 0.56421 0.100 0.008 0.000 0.560 0.044 0.288
#> GSM1299554 3 0.3213 0.39823 0.000 0.000 0.784 0.008 0.004 0.204
#> GSM1299555 6 0.7012 0.53528 0.000 0.100 0.164 0.084 0.080 0.572
#> GSM1299556 6 0.4347 0.47342 0.000 0.000 0.288 0.012 0.028 0.672
#> GSM1299557 6 0.7244 0.23781 0.000 0.088 0.260 0.108 0.048 0.496
#> GSM1299558 3 0.4502 -0.03086 0.000 0.404 0.568 0.000 0.016 0.012
#> GSM1299559 6 0.5365 0.54676 0.000 0.000 0.184 0.128 0.032 0.656
#> GSM1299560 3 0.3774 0.25449 0.000 0.000 0.592 0.000 0.000 0.408
#> GSM1299576 1 0.0603 0.89820 0.980 0.000 0.000 0.000 0.004 0.016
#> GSM1299577 1 0.4566 0.00707 0.540 0.000 0.000 0.428 0.028 0.004
#> GSM1299561 3 0.3607 0.34812 0.000 0.000 0.652 0.000 0.000 0.348
#> GSM1299562 2 0.6905 0.21402 0.000 0.488 0.224 0.004 0.084 0.200
#> GSM1299563 4 0.2106 0.86520 0.064 0.000 0.000 0.904 0.032 0.000
#> GSM1299564 4 0.1856 0.86374 0.048 0.000 0.000 0.920 0.032 0.000
#> GSM1299565 2 0.0653 0.83823 0.000 0.980 0.012 0.000 0.004 0.004
#> GSM1299566 3 0.5106 0.26158 0.000 0.072 0.728 0.044 0.024 0.132
#> GSM1299567 4 0.3804 0.77946 0.044 0.000 0.000 0.772 0.008 0.176
#> GSM1299568 3 0.1327 0.43962 0.000 0.064 0.936 0.000 0.000 0.000
#> GSM1299569 3 0.1769 0.43561 0.000 0.060 0.924 0.004 0.012 0.000
#> GSM1299570 4 0.2106 0.86520 0.064 0.000 0.000 0.904 0.032 0.000
#> GSM1299571 2 0.0653 0.83823 0.000 0.980 0.012 0.000 0.004 0.004
#> GSM1299572 5 0.2145 0.90539 0.044 0.000 0.004 0.016 0.916 0.020
#> GSM1299573 3 0.3983 0.34157 0.000 0.000 0.640 0.008 0.004 0.348
#> GSM1299574 2 0.0622 0.83358 0.000 0.980 0.008 0.000 0.000 0.012
#> GSM1299578 1 0.2854 0.84169 0.860 0.004 0.000 0.048 0.000 0.088
#> GSM1299579 1 0.0603 0.89276 0.980 0.000 0.000 0.000 0.016 0.004
#> GSM1299580 1 0.2854 0.84169 0.860 0.004 0.000 0.048 0.000 0.088
#> GSM1299581 1 0.0291 0.89766 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM1299582 1 0.0291 0.89796 0.992 0.000 0.000 0.004 0.004 0.000
#> GSM1299583 1 0.0603 0.89276 0.980 0.000 0.000 0.000 0.016 0.004
#> GSM1299584 1 0.0146 0.89806 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM1299585 5 0.2482 0.89244 0.148 0.000 0.000 0.004 0.848 0.000
#> GSM1299586 1 0.0508 0.89789 0.984 0.000 0.000 0.000 0.004 0.012
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:kmeans 69 0.0803 2
#> SD:kmeans 57 0.0353 3
#> SD:kmeans 57 0.0903 4
#> SD:kmeans 62 0.0192 5
#> SD:kmeans 43 0.0327 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "skmeans"]
# you can also extract it by
# res = res_list["SD:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 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 1.000 0.978 0.991 0.4995 0.503 0.503
#> 3 3 0.837 0.862 0.914 0.3215 0.814 0.636
#> 4 4 0.743 0.796 0.873 0.1258 0.914 0.747
#> 5 5 0.732 0.780 0.807 0.0658 0.940 0.774
#> 6 6 0.750 0.678 0.798 0.0460 0.965 0.835
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
#> GSM1299517 2 0.0000 0.984 0.000 1.000
#> GSM1299518 2 0.0000 0.984 0.000 1.000
#> GSM1299519 2 0.0000 0.984 0.000 1.000
#> GSM1299520 1 0.0000 1.000 1.000 0.000
#> GSM1299521 1 0.0000 1.000 1.000 0.000
#> GSM1299522 2 0.0000 0.984 0.000 1.000
#> GSM1299523 1 0.0000 1.000 1.000 0.000
#> GSM1299524 2 0.0000 0.984 0.000 1.000
#> GSM1299525 2 0.0000 0.984 0.000 1.000
#> GSM1299526 2 0.0000 0.984 0.000 1.000
#> GSM1299527 2 0.0000 0.984 0.000 1.000
#> GSM1299528 2 0.0000 0.984 0.000 1.000
#> GSM1299529 2 0.0000 0.984 0.000 1.000
#> GSM1299530 1 0.0000 1.000 1.000 0.000
#> GSM1299531 2 0.0000 0.984 0.000 1.000
#> GSM1299575 1 0.0000 1.000 1.000 0.000
#> GSM1299532 2 0.0000 0.984 0.000 1.000
#> GSM1299533 2 0.9795 0.302 0.416 0.584
#> GSM1299534 2 0.0000 0.984 0.000 1.000
#> GSM1299535 2 0.0000 0.984 0.000 1.000
#> GSM1299536 1 0.0000 1.000 1.000 0.000
#> GSM1299537 2 0.0000 0.984 0.000 1.000
#> GSM1299538 1 0.0000 1.000 1.000 0.000
#> GSM1299539 1 0.0000 1.000 1.000 0.000
#> GSM1299540 2 0.7219 0.749 0.200 0.800
#> GSM1299541 2 0.0000 0.984 0.000 1.000
#> GSM1299542 2 0.0000 0.984 0.000 1.000
#> GSM1299543 2 0.0000 0.984 0.000 1.000
#> GSM1299544 2 0.0000 0.984 0.000 1.000
#> GSM1299545 1 0.0000 1.000 1.000 0.000
#> GSM1299546 2 0.0000 0.984 0.000 1.000
#> GSM1299547 1 0.0000 1.000 1.000 0.000
#> GSM1299548 2 0.0000 0.984 0.000 1.000
#> GSM1299549 1 0.0000 1.000 1.000 0.000
#> GSM1299550 1 0.0000 1.000 1.000 0.000
#> GSM1299551 2 0.0000 0.984 0.000 1.000
#> GSM1299552 1 0.0000 1.000 1.000 0.000
#> GSM1299553 1 0.0000 1.000 1.000 0.000
#> GSM1299554 2 0.0000 0.984 0.000 1.000
#> GSM1299555 2 0.0000 0.984 0.000 1.000
#> GSM1299556 2 0.0000 0.984 0.000 1.000
#> GSM1299557 2 0.0000 0.984 0.000 1.000
#> GSM1299558 2 0.0000 0.984 0.000 1.000
#> GSM1299559 2 0.0672 0.977 0.008 0.992
#> GSM1299560 2 0.0000 0.984 0.000 1.000
#> GSM1299576 1 0.0000 1.000 1.000 0.000
#> GSM1299577 1 0.0000 1.000 1.000 0.000
#> GSM1299561 2 0.0000 0.984 0.000 1.000
#> GSM1299562 2 0.0000 0.984 0.000 1.000
#> GSM1299563 1 0.0000 1.000 1.000 0.000
#> GSM1299564 1 0.0000 1.000 1.000 0.000
#> GSM1299565 2 0.0000 0.984 0.000 1.000
#> GSM1299566 2 0.0000 0.984 0.000 1.000
#> GSM1299567 1 0.0000 1.000 1.000 0.000
#> GSM1299568 2 0.0000 0.984 0.000 1.000
#> GSM1299569 2 0.0000 0.984 0.000 1.000
#> GSM1299570 1 0.0000 1.000 1.000 0.000
#> GSM1299571 2 0.0000 0.984 0.000 1.000
#> GSM1299572 1 0.0000 1.000 1.000 0.000
#> GSM1299573 2 0.0000 0.984 0.000 1.000
#> GSM1299574 2 0.0000 0.984 0.000 1.000
#> GSM1299578 1 0.0000 1.000 1.000 0.000
#> GSM1299579 1 0.0000 1.000 1.000 0.000
#> GSM1299580 1 0.0000 1.000 1.000 0.000
#> GSM1299581 1 0.0000 1.000 1.000 0.000
#> GSM1299582 1 0.0000 1.000 1.000 0.000
#> GSM1299583 1 0.0000 1.000 1.000 0.000
#> GSM1299584 1 0.0000 1.000 1.000 0.000
#> GSM1299585 1 0.0000 1.000 1.000 0.000
#> GSM1299586 1 0.0000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1299517 3 0.2711 0.857 0.000 0.088 0.912
#> GSM1299518 2 0.5650 0.535 0.000 0.688 0.312
#> GSM1299519 2 0.0000 0.912 0.000 1.000 0.000
#> GSM1299520 1 0.0424 0.970 0.992 0.000 0.008
#> GSM1299521 1 0.2537 0.937 0.920 0.000 0.080
#> GSM1299522 2 0.0000 0.912 0.000 1.000 0.000
#> GSM1299523 1 0.0424 0.970 0.992 0.000 0.008
#> GSM1299524 3 0.0424 0.791 0.000 0.008 0.992
#> GSM1299525 2 0.0000 0.912 0.000 1.000 0.000
#> GSM1299526 2 0.0000 0.912 0.000 1.000 0.000
#> GSM1299527 3 0.2711 0.857 0.000 0.088 0.912
#> GSM1299528 3 0.6111 0.580 0.000 0.396 0.604
#> GSM1299529 2 0.0000 0.912 0.000 1.000 0.000
#> GSM1299530 1 0.0424 0.970 0.992 0.000 0.008
#> GSM1299531 2 0.1163 0.893 0.000 0.972 0.028
#> GSM1299575 1 0.0237 0.970 0.996 0.000 0.004
#> GSM1299532 3 0.2711 0.857 0.000 0.088 0.912
#> GSM1299533 2 0.4035 0.802 0.040 0.880 0.080
#> GSM1299534 3 0.5560 0.701 0.000 0.300 0.700
#> GSM1299535 2 0.2711 0.854 0.000 0.912 0.088
#> GSM1299536 1 0.2537 0.937 0.920 0.000 0.080
#> GSM1299537 3 0.2711 0.857 0.000 0.088 0.912
#> GSM1299538 1 0.1315 0.958 0.972 0.020 0.008
#> GSM1299539 1 0.2384 0.929 0.936 0.056 0.008
#> GSM1299540 2 0.7844 0.529 0.084 0.624 0.292
#> GSM1299541 3 0.2711 0.857 0.000 0.088 0.912
#> GSM1299542 3 0.2711 0.857 0.000 0.088 0.912
#> GSM1299543 2 0.0000 0.912 0.000 1.000 0.000
#> GSM1299544 3 0.6008 0.617 0.000 0.372 0.628
#> GSM1299545 1 0.0237 0.970 0.996 0.000 0.004
#> GSM1299546 2 0.0000 0.912 0.000 1.000 0.000
#> GSM1299547 1 0.2537 0.937 0.920 0.000 0.080
#> GSM1299548 3 0.2711 0.857 0.000 0.088 0.912
#> GSM1299549 1 0.2537 0.937 0.920 0.000 0.080
#> GSM1299550 3 0.6033 0.391 0.336 0.004 0.660
#> GSM1299551 2 0.0000 0.912 0.000 1.000 0.000
#> GSM1299552 1 0.2537 0.937 0.920 0.000 0.080
#> GSM1299553 1 0.0237 0.970 0.996 0.000 0.004
#> GSM1299554 3 0.2711 0.857 0.000 0.088 0.912
#> GSM1299555 2 0.5497 0.575 0.000 0.708 0.292
#> GSM1299556 3 0.2537 0.852 0.000 0.080 0.920
#> GSM1299557 2 0.3879 0.772 0.000 0.848 0.152
#> GSM1299558 2 0.0892 0.899 0.000 0.980 0.020
#> GSM1299559 3 0.2096 0.833 0.004 0.052 0.944
#> GSM1299560 3 0.2959 0.849 0.000 0.100 0.900
#> GSM1299576 1 0.0000 0.971 1.000 0.000 0.000
#> GSM1299577 1 0.0000 0.971 1.000 0.000 0.000
#> GSM1299561 3 0.2711 0.857 0.000 0.088 0.912
#> GSM1299562 2 0.0237 0.910 0.000 0.996 0.004
#> GSM1299563 1 0.0424 0.970 0.992 0.000 0.008
#> GSM1299564 1 0.0424 0.970 0.992 0.000 0.008
#> GSM1299565 2 0.0000 0.912 0.000 1.000 0.000
#> GSM1299566 3 0.6280 0.449 0.000 0.460 0.540
#> GSM1299567 1 0.4291 0.787 0.820 0.000 0.180
#> GSM1299568 3 0.6079 0.594 0.000 0.388 0.612
#> GSM1299569 3 0.5835 0.658 0.000 0.340 0.660
#> GSM1299570 1 0.0424 0.970 0.992 0.000 0.008
#> GSM1299571 2 0.0000 0.912 0.000 1.000 0.000
#> GSM1299572 1 0.2537 0.937 0.920 0.000 0.080
#> GSM1299573 3 0.2711 0.857 0.000 0.088 0.912
#> GSM1299574 2 0.0000 0.912 0.000 1.000 0.000
#> GSM1299578 1 0.0237 0.970 0.996 0.000 0.004
#> GSM1299579 1 0.0000 0.971 1.000 0.000 0.000
#> GSM1299580 1 0.0237 0.970 0.996 0.000 0.004
#> GSM1299581 1 0.0000 0.971 1.000 0.000 0.000
#> GSM1299582 1 0.0000 0.971 1.000 0.000 0.000
#> GSM1299583 1 0.0000 0.971 1.000 0.000 0.000
#> GSM1299584 1 0.0000 0.971 1.000 0.000 0.000
#> GSM1299585 1 0.2537 0.937 0.920 0.000 0.080
#> GSM1299586 1 0.0000 0.971 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1299517 3 0.0657 0.860 0.004 0.012 0.984 0.000
#> GSM1299518 2 0.4781 0.510 0.004 0.660 0.336 0.000
#> GSM1299519 2 0.0000 0.887 0.000 1.000 0.000 0.000
#> GSM1299520 4 0.0927 0.800 0.016 0.000 0.008 0.976
#> GSM1299521 1 0.1637 0.911 0.940 0.000 0.000 0.060
#> GSM1299522 2 0.0000 0.887 0.000 1.000 0.000 0.000
#> GSM1299523 4 0.1356 0.793 0.032 0.000 0.008 0.960
#> GSM1299524 3 0.3024 0.746 0.148 0.000 0.852 0.000
#> GSM1299525 2 0.0927 0.879 0.016 0.976 0.000 0.008
#> GSM1299526 2 0.0000 0.887 0.000 1.000 0.000 0.000
#> GSM1299527 3 0.0657 0.860 0.004 0.012 0.984 0.000
#> GSM1299528 3 0.6357 0.510 0.044 0.348 0.592 0.016
#> GSM1299529 2 0.0779 0.880 0.016 0.980 0.000 0.004
#> GSM1299530 4 0.1545 0.800 0.040 0.000 0.008 0.952
#> GSM1299531 2 0.1807 0.853 0.008 0.940 0.052 0.000
#> GSM1299575 4 0.3688 0.834 0.208 0.000 0.000 0.792
#> GSM1299532 3 0.0469 0.860 0.000 0.012 0.988 0.000
#> GSM1299533 1 0.3266 0.758 0.832 0.168 0.000 0.000
#> GSM1299534 3 0.4775 0.700 0.028 0.232 0.740 0.000
#> GSM1299535 2 0.3610 0.741 0.000 0.800 0.200 0.000
#> GSM1299536 1 0.2814 0.851 0.868 0.000 0.000 0.132
#> GSM1299537 3 0.0937 0.858 0.012 0.012 0.976 0.000
#> GSM1299538 4 0.1890 0.776 0.056 0.000 0.008 0.936
#> GSM1299539 4 0.2353 0.769 0.056 0.012 0.008 0.924
#> GSM1299540 2 0.8067 0.240 0.008 0.420 0.300 0.272
#> GSM1299541 3 0.0927 0.859 0.008 0.016 0.976 0.000
#> GSM1299542 3 0.0469 0.860 0.000 0.012 0.988 0.000
#> GSM1299543 2 0.0000 0.887 0.000 1.000 0.000 0.000
#> GSM1299544 3 0.5308 0.640 0.036 0.280 0.684 0.000
#> GSM1299545 4 0.3528 0.837 0.192 0.000 0.000 0.808
#> GSM1299546 2 0.0000 0.887 0.000 1.000 0.000 0.000
#> GSM1299547 1 0.1557 0.913 0.944 0.000 0.000 0.056
#> GSM1299548 3 0.0804 0.860 0.008 0.012 0.980 0.000
#> GSM1299549 1 0.1557 0.913 0.944 0.000 0.000 0.056
#> GSM1299550 1 0.4462 0.730 0.804 0.000 0.064 0.132
#> GSM1299551 2 0.0000 0.887 0.000 1.000 0.000 0.000
#> GSM1299552 1 0.1557 0.913 0.944 0.000 0.000 0.056
#> GSM1299553 4 0.3219 0.833 0.164 0.000 0.000 0.836
#> GSM1299554 3 0.1471 0.854 0.024 0.012 0.960 0.004
#> GSM1299555 2 0.5266 0.498 0.008 0.640 0.344 0.008
#> GSM1299556 3 0.0992 0.851 0.012 0.004 0.976 0.008
#> GSM1299557 2 0.5153 0.717 0.048 0.768 0.168 0.016
#> GSM1299558 2 0.1902 0.845 0.004 0.932 0.064 0.000
#> GSM1299559 3 0.2563 0.801 0.020 0.000 0.908 0.072
#> GSM1299560 3 0.1305 0.850 0.004 0.036 0.960 0.000
#> GSM1299576 4 0.4008 0.821 0.244 0.000 0.000 0.756
#> GSM1299577 4 0.3610 0.836 0.200 0.000 0.000 0.800
#> GSM1299561 3 0.0657 0.860 0.004 0.012 0.984 0.000
#> GSM1299562 2 0.0657 0.883 0.004 0.984 0.012 0.000
#> GSM1299563 4 0.2611 0.767 0.096 0.000 0.008 0.896
#> GSM1299564 4 0.1545 0.790 0.040 0.000 0.008 0.952
#> GSM1299565 2 0.0000 0.887 0.000 1.000 0.000 0.000
#> GSM1299566 3 0.7678 0.335 0.048 0.380 0.492 0.080
#> GSM1299567 4 0.1488 0.792 0.012 0.000 0.032 0.956
#> GSM1299568 3 0.5453 0.587 0.032 0.320 0.648 0.000
#> GSM1299569 3 0.5055 0.672 0.032 0.256 0.712 0.000
#> GSM1299570 4 0.0927 0.803 0.016 0.000 0.008 0.976
#> GSM1299571 2 0.0000 0.887 0.000 1.000 0.000 0.000
#> GSM1299572 1 0.1637 0.911 0.940 0.000 0.000 0.060
#> GSM1299573 3 0.0657 0.860 0.004 0.012 0.984 0.000
#> GSM1299574 2 0.0188 0.885 0.000 0.996 0.004 0.000
#> GSM1299578 4 0.3801 0.831 0.220 0.000 0.000 0.780
#> GSM1299579 4 0.4564 0.740 0.328 0.000 0.000 0.672
#> GSM1299580 4 0.3688 0.834 0.208 0.000 0.000 0.792
#> GSM1299581 4 0.4008 0.821 0.244 0.000 0.000 0.756
#> GSM1299582 4 0.4008 0.821 0.244 0.000 0.000 0.756
#> GSM1299583 4 0.4697 0.688 0.356 0.000 0.000 0.644
#> GSM1299584 4 0.4008 0.821 0.244 0.000 0.000 0.756
#> GSM1299585 1 0.1637 0.911 0.940 0.000 0.000 0.060
#> GSM1299586 4 0.4008 0.821 0.244 0.000 0.000 0.756
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1299517 3 0.0898 0.808 0.000 0.000 0.972 0.020 0.008
#> GSM1299518 2 0.3779 0.657 0.000 0.752 0.236 0.012 0.000
#> GSM1299519 2 0.0000 0.859 0.000 1.000 0.000 0.000 0.000
#> GSM1299520 4 0.4817 0.754 0.404 0.000 0.000 0.572 0.024
#> GSM1299521 5 0.1792 0.963 0.084 0.000 0.000 0.000 0.916
#> GSM1299522 2 0.0162 0.859 0.000 0.996 0.000 0.000 0.004
#> GSM1299523 4 0.4668 0.770 0.352 0.000 0.000 0.624 0.024
#> GSM1299524 3 0.5244 0.686 0.000 0.008 0.700 0.116 0.176
#> GSM1299525 2 0.2798 0.800 0.000 0.852 0.000 0.140 0.008
#> GSM1299526 2 0.0000 0.859 0.000 1.000 0.000 0.000 0.000
#> GSM1299527 3 0.1012 0.807 0.000 0.000 0.968 0.020 0.012
#> GSM1299528 3 0.7164 0.513 0.000 0.200 0.532 0.208 0.060
#> GSM1299529 2 0.2488 0.809 0.000 0.872 0.000 0.124 0.004
#> GSM1299530 4 0.5272 0.748 0.396 0.000 0.000 0.552 0.052
#> GSM1299531 2 0.4790 0.717 0.000 0.764 0.104 0.108 0.024
#> GSM1299575 1 0.0404 0.922 0.988 0.000 0.000 0.012 0.000
#> GSM1299532 3 0.1018 0.808 0.000 0.000 0.968 0.016 0.016
#> GSM1299533 5 0.1990 0.916 0.028 0.040 0.000 0.004 0.928
#> GSM1299534 3 0.5524 0.701 0.000 0.112 0.716 0.124 0.048
#> GSM1299535 2 0.6497 0.498 0.000 0.572 0.216 0.192 0.020
#> GSM1299536 5 0.1992 0.939 0.044 0.000 0.000 0.032 0.924
#> GSM1299537 3 0.2305 0.780 0.000 0.000 0.896 0.092 0.012
#> GSM1299538 4 0.3992 0.728 0.268 0.000 0.000 0.720 0.012
#> GSM1299539 4 0.3890 0.709 0.252 0.000 0.000 0.736 0.012
#> GSM1299540 4 0.8818 0.135 0.228 0.224 0.212 0.324 0.012
#> GSM1299541 3 0.1408 0.802 0.000 0.000 0.948 0.044 0.008
#> GSM1299542 3 0.0609 0.810 0.000 0.000 0.980 0.020 0.000
#> GSM1299543 2 0.0865 0.856 0.000 0.972 0.000 0.024 0.004
#> GSM1299544 3 0.6567 0.617 0.000 0.152 0.612 0.180 0.056
#> GSM1299545 1 0.1282 0.897 0.952 0.000 0.000 0.044 0.004
#> GSM1299546 2 0.0000 0.859 0.000 1.000 0.000 0.000 0.000
#> GSM1299547 5 0.1792 0.963 0.084 0.000 0.000 0.000 0.916
#> GSM1299548 3 0.0865 0.807 0.000 0.000 0.972 0.024 0.004
#> GSM1299549 5 0.2068 0.960 0.092 0.000 0.000 0.004 0.904
#> GSM1299550 5 0.1628 0.886 0.000 0.000 0.008 0.056 0.936
#> GSM1299551 2 0.0290 0.858 0.000 0.992 0.000 0.008 0.000
#> GSM1299552 5 0.1908 0.961 0.092 0.000 0.000 0.000 0.908
#> GSM1299553 1 0.2890 0.729 0.836 0.000 0.000 0.160 0.004
#> GSM1299554 3 0.2595 0.793 0.000 0.000 0.888 0.080 0.032
#> GSM1299555 2 0.6849 0.255 0.000 0.476 0.312 0.196 0.016
#> GSM1299556 3 0.3343 0.726 0.000 0.000 0.812 0.172 0.016
#> GSM1299557 2 0.6338 0.586 0.000 0.624 0.188 0.148 0.040
#> GSM1299558 2 0.5002 0.706 0.000 0.752 0.104 0.112 0.032
#> GSM1299559 3 0.4835 0.424 0.000 0.000 0.592 0.380 0.028
#> GSM1299560 3 0.2710 0.777 0.000 0.064 0.892 0.036 0.008
#> GSM1299576 1 0.0404 0.930 0.988 0.000 0.000 0.000 0.012
#> GSM1299577 1 0.1597 0.897 0.940 0.000 0.000 0.048 0.012
#> GSM1299561 3 0.0955 0.810 0.000 0.000 0.968 0.028 0.004
#> GSM1299562 2 0.2472 0.835 0.000 0.908 0.020 0.052 0.020
#> GSM1299563 4 0.6113 0.683 0.332 0.000 0.000 0.524 0.144
#> GSM1299564 4 0.5099 0.768 0.348 0.000 0.004 0.608 0.040
#> GSM1299565 2 0.0290 0.858 0.000 0.992 0.000 0.000 0.008
#> GSM1299566 3 0.7713 0.388 0.000 0.224 0.432 0.272 0.072
#> GSM1299567 4 0.4630 0.713 0.416 0.000 0.008 0.572 0.004
#> GSM1299568 3 0.6471 0.610 0.000 0.180 0.620 0.148 0.052
#> GSM1299569 3 0.6039 0.667 0.000 0.124 0.668 0.156 0.052
#> GSM1299570 4 0.4841 0.744 0.416 0.000 0.000 0.560 0.024
#> GSM1299571 2 0.0000 0.859 0.000 1.000 0.000 0.000 0.000
#> GSM1299572 5 0.1732 0.963 0.080 0.000 0.000 0.000 0.920
#> GSM1299573 3 0.1216 0.809 0.000 0.000 0.960 0.020 0.020
#> GSM1299574 2 0.0290 0.858 0.000 0.992 0.000 0.008 0.000
#> GSM1299578 1 0.0290 0.924 0.992 0.000 0.000 0.008 0.000
#> GSM1299579 1 0.2230 0.811 0.884 0.000 0.000 0.000 0.116
#> GSM1299580 1 0.0404 0.922 0.988 0.000 0.000 0.012 0.000
#> GSM1299581 1 0.0404 0.930 0.988 0.000 0.000 0.000 0.012
#> GSM1299582 1 0.0290 0.929 0.992 0.000 0.000 0.000 0.008
#> GSM1299583 1 0.1908 0.841 0.908 0.000 0.000 0.000 0.092
#> GSM1299584 1 0.0404 0.930 0.988 0.000 0.000 0.000 0.012
#> GSM1299585 5 0.1908 0.961 0.092 0.000 0.000 0.000 0.908
#> GSM1299586 1 0.0404 0.930 0.988 0.000 0.000 0.000 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1299517 3 0.4135 0.419 0.000 0.004 0.584 0.000 0.008 0.404
#> GSM1299518 2 0.4531 0.515 0.000 0.716 0.140 0.004 0.000 0.140
#> GSM1299519 2 0.0146 0.797 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM1299520 4 0.2100 0.879 0.112 0.000 0.000 0.884 0.004 0.000
#> GSM1299521 5 0.0865 0.971 0.036 0.000 0.000 0.000 0.964 0.000
#> GSM1299522 2 0.0000 0.797 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299523 4 0.1897 0.874 0.084 0.000 0.000 0.908 0.004 0.004
#> GSM1299524 3 0.4830 0.424 0.000 0.008 0.712 0.012 0.104 0.164
#> GSM1299525 2 0.5665 0.572 0.000 0.636 0.012 0.112 0.028 0.212
#> GSM1299526 2 0.0291 0.796 0.000 0.992 0.004 0.000 0.000 0.004
#> GSM1299527 3 0.4002 0.419 0.000 0.000 0.588 0.000 0.008 0.404
#> GSM1299528 3 0.4244 0.452 0.000 0.116 0.776 0.024 0.004 0.080
#> GSM1299529 2 0.5101 0.590 0.000 0.664 0.000 0.092 0.024 0.220
#> GSM1299530 4 0.3054 0.870 0.136 0.000 0.000 0.828 0.036 0.000
#> GSM1299531 2 0.4667 0.506 0.000 0.632 0.308 0.004 0.000 0.056
#> GSM1299575 1 0.0291 0.927 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM1299532 3 0.3769 0.473 0.000 0.004 0.640 0.000 0.000 0.356
#> GSM1299533 5 0.1592 0.940 0.008 0.020 0.000 0.000 0.940 0.032
#> GSM1299534 3 0.2308 0.554 0.000 0.076 0.896 0.012 0.000 0.016
#> GSM1299535 2 0.6673 0.134 0.000 0.416 0.168 0.032 0.012 0.372
#> GSM1299536 5 0.0951 0.965 0.020 0.000 0.000 0.008 0.968 0.004
#> GSM1299537 6 0.3854 -0.249 0.000 0.000 0.464 0.000 0.000 0.536
#> GSM1299538 4 0.2278 0.818 0.032 0.000 0.000 0.904 0.012 0.052
#> GSM1299539 4 0.4126 0.691 0.024 0.004 0.012 0.768 0.016 0.176
#> GSM1299540 6 0.7562 0.317 0.136 0.156 0.032 0.184 0.004 0.488
#> GSM1299541 3 0.3915 0.357 0.000 0.000 0.584 0.004 0.000 0.412
#> GSM1299542 3 0.3330 0.532 0.000 0.000 0.716 0.000 0.000 0.284
#> GSM1299543 2 0.0870 0.792 0.000 0.972 0.012 0.004 0.000 0.012
#> GSM1299544 3 0.3320 0.529 0.000 0.080 0.844 0.016 0.004 0.056
#> GSM1299545 1 0.2510 0.831 0.872 0.000 0.000 0.100 0.000 0.028
#> GSM1299546 2 0.0146 0.797 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM1299547 5 0.0865 0.971 0.036 0.000 0.000 0.000 0.964 0.000
#> GSM1299548 3 0.3699 0.484 0.000 0.000 0.660 0.004 0.000 0.336
#> GSM1299549 5 0.1838 0.950 0.040 0.000 0.000 0.012 0.928 0.020
#> GSM1299550 5 0.2384 0.908 0.004 0.000 0.032 0.044 0.904 0.016
#> GSM1299551 2 0.0260 0.796 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM1299552 5 0.1007 0.967 0.044 0.000 0.000 0.000 0.956 0.000
#> GSM1299553 1 0.5713 0.465 0.600 0.000 0.000 0.200 0.024 0.176
#> GSM1299554 3 0.2833 0.571 0.000 0.000 0.836 0.004 0.012 0.148
#> GSM1299555 6 0.5889 0.333 0.004 0.320 0.064 0.048 0.004 0.560
#> GSM1299556 6 0.3982 0.279 0.000 0.000 0.280 0.016 0.008 0.696
#> GSM1299557 2 0.7500 0.198 0.000 0.396 0.116 0.108 0.036 0.344
#> GSM1299558 2 0.4201 0.591 0.000 0.704 0.252 0.008 0.000 0.036
#> GSM1299559 6 0.5042 0.438 0.004 0.000 0.140 0.172 0.008 0.676
#> GSM1299560 3 0.5127 0.284 0.000 0.088 0.528 0.000 0.000 0.384
#> GSM1299576 1 0.0146 0.930 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM1299577 1 0.2191 0.827 0.876 0.000 0.000 0.120 0.000 0.004
#> GSM1299561 3 0.3337 0.544 0.000 0.000 0.736 0.004 0.000 0.260
#> GSM1299562 2 0.3197 0.737 0.000 0.848 0.072 0.004 0.008 0.068
#> GSM1299563 4 0.4040 0.835 0.140 0.000 0.000 0.772 0.076 0.012
#> GSM1299564 4 0.2643 0.874 0.108 0.000 0.004 0.868 0.004 0.016
#> GSM1299565 2 0.0146 0.796 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM1299566 3 0.6414 0.242 0.000 0.152 0.584 0.108 0.004 0.152
#> GSM1299567 4 0.4488 0.770 0.164 0.000 0.000 0.708 0.000 0.128
#> GSM1299568 3 0.2846 0.517 0.000 0.116 0.856 0.016 0.004 0.008
#> GSM1299569 3 0.2518 0.540 0.000 0.068 0.892 0.016 0.004 0.020
#> GSM1299570 4 0.2558 0.868 0.156 0.000 0.000 0.840 0.004 0.000
#> GSM1299571 2 0.0260 0.795 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM1299572 5 0.0935 0.970 0.032 0.000 0.000 0.000 0.964 0.004
#> GSM1299573 3 0.3265 0.555 0.000 0.000 0.748 0.004 0.000 0.248
#> GSM1299574 2 0.0363 0.796 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM1299578 1 0.0291 0.929 0.992 0.000 0.000 0.004 0.004 0.000
#> GSM1299579 1 0.1267 0.894 0.940 0.000 0.000 0.000 0.060 0.000
#> GSM1299580 1 0.0291 0.927 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM1299581 1 0.0146 0.930 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM1299582 1 0.0146 0.930 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM1299583 1 0.0937 0.909 0.960 0.000 0.000 0.000 0.040 0.000
#> GSM1299584 1 0.0146 0.930 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM1299585 5 0.0937 0.970 0.040 0.000 0.000 0.000 0.960 0.000
#> GSM1299586 1 0.0146 0.930 0.996 0.000 0.000 0.000 0.004 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:skmeans 69 0.1124 2
#> SD:skmeans 68 0.1332 3
#> SD:skmeans 67 0.0753 4
#> SD:skmeans 65 0.0998 5
#> SD:skmeans 53 0.0529 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "pam"]
# you can also extract it by
# res = res_list["SD:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 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 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 0.940 0.938 0.974 0.4790 0.526 0.526
#> 3 3 0.650 0.833 0.897 0.3717 0.783 0.595
#> 4 4 0.867 0.855 0.940 0.1388 0.839 0.562
#> 5 5 0.919 0.852 0.925 0.0545 0.937 0.754
#> 6 6 0.857 0.725 0.879 0.0489 0.943 0.735
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM1299517 2 0.0000 0.967 0.000 1.000
#> GSM1299518 2 0.0000 0.967 0.000 1.000
#> GSM1299519 2 0.0000 0.967 0.000 1.000
#> GSM1299520 1 0.0672 0.974 0.992 0.008
#> GSM1299521 1 0.0000 0.980 1.000 0.000
#> GSM1299522 2 0.0000 0.967 0.000 1.000
#> GSM1299523 1 0.9815 0.214 0.580 0.420
#> GSM1299524 2 0.0000 0.967 0.000 1.000
#> GSM1299525 2 0.0000 0.967 0.000 1.000
#> GSM1299526 2 0.0000 0.967 0.000 1.000
#> GSM1299527 2 0.0000 0.967 0.000 1.000
#> GSM1299528 2 0.0000 0.967 0.000 1.000
#> GSM1299529 2 0.0000 0.967 0.000 1.000
#> GSM1299530 1 0.0000 0.980 1.000 0.000
#> GSM1299531 2 0.0000 0.967 0.000 1.000
#> GSM1299575 1 0.0000 0.980 1.000 0.000
#> GSM1299532 2 0.0000 0.967 0.000 1.000
#> GSM1299533 1 0.1843 0.954 0.972 0.028
#> GSM1299534 2 0.0000 0.967 0.000 1.000
#> GSM1299535 2 0.0000 0.967 0.000 1.000
#> GSM1299536 1 0.0000 0.980 1.000 0.000
#> GSM1299537 2 0.0000 0.967 0.000 1.000
#> GSM1299538 2 0.7745 0.714 0.228 0.772
#> GSM1299539 2 0.8267 0.663 0.260 0.740
#> GSM1299540 2 0.0000 0.967 0.000 1.000
#> GSM1299541 2 0.0000 0.967 0.000 1.000
#> GSM1299542 2 0.0000 0.967 0.000 1.000
#> GSM1299543 2 0.0000 0.967 0.000 1.000
#> GSM1299544 2 0.0000 0.967 0.000 1.000
#> GSM1299545 1 0.0000 0.980 1.000 0.000
#> GSM1299546 2 0.0000 0.967 0.000 1.000
#> GSM1299547 1 0.0000 0.980 1.000 0.000
#> GSM1299548 2 0.0000 0.967 0.000 1.000
#> GSM1299549 1 0.0000 0.980 1.000 0.000
#> GSM1299550 2 0.8861 0.586 0.304 0.696
#> GSM1299551 2 0.0000 0.967 0.000 1.000
#> GSM1299552 1 0.0000 0.980 1.000 0.000
#> GSM1299553 1 0.0376 0.977 0.996 0.004
#> GSM1299554 2 0.0000 0.967 0.000 1.000
#> GSM1299555 2 0.0000 0.967 0.000 1.000
#> GSM1299556 2 0.0376 0.964 0.004 0.996
#> GSM1299557 2 0.0000 0.967 0.000 1.000
#> GSM1299558 2 0.0000 0.967 0.000 1.000
#> GSM1299559 2 0.2043 0.941 0.032 0.968
#> GSM1299560 2 0.0000 0.967 0.000 1.000
#> GSM1299576 1 0.0000 0.980 1.000 0.000
#> GSM1299577 1 0.0000 0.980 1.000 0.000
#> GSM1299561 2 0.0000 0.967 0.000 1.000
#> GSM1299562 2 0.0000 0.967 0.000 1.000
#> GSM1299563 1 0.0000 0.980 1.000 0.000
#> GSM1299564 2 0.6801 0.784 0.180 0.820
#> GSM1299565 2 0.0000 0.967 0.000 1.000
#> GSM1299566 2 0.0938 0.958 0.012 0.988
#> GSM1299567 2 0.9170 0.510 0.332 0.668
#> GSM1299568 2 0.0000 0.967 0.000 1.000
#> GSM1299569 2 0.0000 0.967 0.000 1.000
#> GSM1299570 1 0.0000 0.980 1.000 0.000
#> GSM1299571 2 0.0000 0.967 0.000 1.000
#> GSM1299572 1 0.0000 0.980 1.000 0.000
#> GSM1299573 2 0.0000 0.967 0.000 1.000
#> GSM1299574 2 0.0000 0.967 0.000 1.000
#> GSM1299578 1 0.0000 0.980 1.000 0.000
#> GSM1299579 1 0.0000 0.980 1.000 0.000
#> GSM1299580 1 0.0000 0.980 1.000 0.000
#> GSM1299581 1 0.0000 0.980 1.000 0.000
#> GSM1299582 1 0.0000 0.980 1.000 0.000
#> GSM1299583 1 0.0000 0.980 1.000 0.000
#> GSM1299584 1 0.0000 0.980 1.000 0.000
#> GSM1299585 1 0.0000 0.980 1.000 0.000
#> GSM1299586 1 0.0000 0.980 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1299517 3 0.3340 0.911 0.000 0.120 0.880
#> GSM1299518 2 0.1860 0.830 0.000 0.948 0.052
#> GSM1299519 2 0.0000 0.855 0.000 1.000 0.000
#> GSM1299520 1 0.3752 0.865 0.856 0.000 0.144
#> GSM1299521 1 0.0000 0.944 1.000 0.000 0.000
#> GSM1299522 2 0.0000 0.855 0.000 1.000 0.000
#> GSM1299523 1 0.6008 0.555 0.628 0.000 0.372
#> GSM1299524 3 0.3340 0.911 0.000 0.120 0.880
#> GSM1299525 2 0.1163 0.849 0.000 0.972 0.028
#> GSM1299526 2 0.0000 0.855 0.000 1.000 0.000
#> GSM1299527 3 0.3340 0.911 0.000 0.120 0.880
#> GSM1299528 3 0.3686 0.899 0.000 0.140 0.860
#> GSM1299529 2 0.1163 0.847 0.000 0.972 0.028
#> GSM1299530 1 0.3340 0.884 0.880 0.000 0.120
#> GSM1299531 2 0.5058 0.631 0.000 0.756 0.244
#> GSM1299575 1 0.0000 0.944 1.000 0.000 0.000
#> GSM1299532 3 0.3412 0.909 0.000 0.124 0.876
#> GSM1299533 1 0.4755 0.734 0.808 0.184 0.008
#> GSM1299534 3 0.3816 0.894 0.000 0.148 0.852
#> GSM1299535 3 0.5882 0.581 0.000 0.348 0.652
#> GSM1299536 1 0.0000 0.944 1.000 0.000 0.000
#> GSM1299537 3 0.3340 0.911 0.000 0.120 0.880
#> GSM1299538 2 0.9924 0.280 0.288 0.392 0.320
#> GSM1299539 2 0.8120 0.600 0.136 0.640 0.224
#> GSM1299540 3 0.2537 0.851 0.000 0.080 0.920
#> GSM1299541 3 0.3340 0.911 0.000 0.120 0.880
#> GSM1299542 3 0.3340 0.911 0.000 0.120 0.880
#> GSM1299543 2 0.0592 0.853 0.000 0.988 0.012
#> GSM1299544 3 0.3340 0.911 0.000 0.120 0.880
#> GSM1299545 1 0.0237 0.942 0.996 0.000 0.004
#> GSM1299546 2 0.0000 0.855 0.000 1.000 0.000
#> GSM1299547 1 0.0000 0.944 1.000 0.000 0.000
#> GSM1299548 3 0.3340 0.911 0.000 0.120 0.880
#> GSM1299549 1 0.0000 0.944 1.000 0.000 0.000
#> GSM1299550 1 0.7176 0.614 0.684 0.068 0.248
#> GSM1299551 2 0.0000 0.855 0.000 1.000 0.000
#> GSM1299552 1 0.0000 0.944 1.000 0.000 0.000
#> GSM1299553 1 0.2537 0.907 0.920 0.000 0.080
#> GSM1299554 3 0.3340 0.911 0.000 0.120 0.880
#> GSM1299555 2 0.6154 0.237 0.000 0.592 0.408
#> GSM1299556 3 0.1163 0.835 0.000 0.028 0.972
#> GSM1299557 3 0.6286 0.308 0.000 0.464 0.536
#> GSM1299558 2 0.3412 0.784 0.000 0.876 0.124
#> GSM1299559 3 0.0000 0.811 0.000 0.000 1.000
#> GSM1299560 3 0.4121 0.874 0.000 0.168 0.832
#> GSM1299576 1 0.0000 0.944 1.000 0.000 0.000
#> GSM1299577 1 0.1163 0.932 0.972 0.000 0.028
#> GSM1299561 3 0.3340 0.911 0.000 0.120 0.880
#> GSM1299562 2 0.3752 0.763 0.000 0.856 0.144
#> GSM1299563 1 0.3340 0.884 0.880 0.000 0.120
#> GSM1299564 3 0.4702 0.550 0.212 0.000 0.788
#> GSM1299565 2 0.0000 0.855 0.000 1.000 0.000
#> GSM1299566 2 0.5810 0.456 0.000 0.664 0.336
#> GSM1299567 3 0.2066 0.759 0.060 0.000 0.940
#> GSM1299568 3 0.4002 0.883 0.000 0.160 0.840
#> GSM1299569 3 0.3482 0.907 0.000 0.128 0.872
#> GSM1299570 1 0.3340 0.884 0.880 0.000 0.120
#> GSM1299571 2 0.0000 0.855 0.000 1.000 0.000
#> GSM1299572 1 0.0000 0.944 1.000 0.000 0.000
#> GSM1299573 3 0.3340 0.911 0.000 0.120 0.880
#> GSM1299574 2 0.0000 0.855 0.000 1.000 0.000
#> GSM1299578 1 0.0000 0.944 1.000 0.000 0.000
#> GSM1299579 1 0.0000 0.944 1.000 0.000 0.000
#> GSM1299580 1 0.0000 0.944 1.000 0.000 0.000
#> GSM1299581 1 0.0000 0.944 1.000 0.000 0.000
#> GSM1299582 1 0.0000 0.944 1.000 0.000 0.000
#> GSM1299583 1 0.0000 0.944 1.000 0.000 0.000
#> GSM1299584 1 0.0000 0.944 1.000 0.000 0.000
#> GSM1299585 1 0.0000 0.944 1.000 0.000 0.000
#> GSM1299586 1 0.0000 0.944 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1299517 3 0.0000 0.949 0.000 0.000 1.000 0.000
#> GSM1299518 2 0.0592 0.882 0.000 0.984 0.016 0.000
#> GSM1299519 2 0.0000 0.891 0.000 1.000 0.000 0.000
#> GSM1299520 4 0.0000 0.857 0.000 0.000 0.000 1.000
#> GSM1299521 1 0.0000 0.983 1.000 0.000 0.000 0.000
#> GSM1299522 2 0.0000 0.891 0.000 1.000 0.000 0.000
#> GSM1299523 4 0.0188 0.855 0.000 0.000 0.004 0.996
#> GSM1299524 3 0.0000 0.949 0.000 0.000 1.000 0.000
#> GSM1299525 2 0.1792 0.841 0.000 0.932 0.000 0.068
#> GSM1299526 2 0.0000 0.891 0.000 1.000 0.000 0.000
#> GSM1299527 3 0.0000 0.949 0.000 0.000 1.000 0.000
#> GSM1299528 3 0.0000 0.949 0.000 0.000 1.000 0.000
#> GSM1299529 2 0.0000 0.891 0.000 1.000 0.000 0.000
#> GSM1299530 4 0.0188 0.855 0.004 0.000 0.000 0.996
#> GSM1299531 2 0.4877 0.371 0.000 0.592 0.408 0.000
#> GSM1299575 1 0.0188 0.984 0.996 0.000 0.000 0.004
#> GSM1299532 3 0.0188 0.947 0.000 0.004 0.996 0.000
#> GSM1299533 1 0.3649 0.728 0.796 0.204 0.000 0.000
#> GSM1299534 3 0.0000 0.949 0.000 0.000 1.000 0.000
#> GSM1299535 3 0.4643 0.374 0.000 0.344 0.656 0.000
#> GSM1299536 1 0.0000 0.983 1.000 0.000 0.000 0.000
#> GSM1299537 3 0.0000 0.949 0.000 0.000 1.000 0.000
#> GSM1299538 4 0.0000 0.857 0.000 0.000 0.000 1.000
#> GSM1299539 4 0.0000 0.857 0.000 0.000 0.000 1.000
#> GSM1299540 3 0.3208 0.777 0.000 0.004 0.848 0.148
#> GSM1299541 3 0.0000 0.949 0.000 0.000 1.000 0.000
#> GSM1299542 3 0.0000 0.949 0.000 0.000 1.000 0.000
#> GSM1299543 2 0.0000 0.891 0.000 1.000 0.000 0.000
#> GSM1299544 3 0.0000 0.949 0.000 0.000 1.000 0.000
#> GSM1299545 1 0.0592 0.973 0.984 0.000 0.000 0.016
#> GSM1299546 2 0.0000 0.891 0.000 1.000 0.000 0.000
#> GSM1299547 1 0.0000 0.983 1.000 0.000 0.000 0.000
#> GSM1299548 3 0.0000 0.949 0.000 0.000 1.000 0.000
#> GSM1299549 1 0.0000 0.983 1.000 0.000 0.000 0.000
#> GSM1299550 4 0.3266 0.794 0.108 0.000 0.024 0.868
#> GSM1299551 2 0.0000 0.891 0.000 1.000 0.000 0.000
#> GSM1299552 1 0.0000 0.983 1.000 0.000 0.000 0.000
#> GSM1299553 4 0.4072 0.640 0.252 0.000 0.000 0.748
#> GSM1299554 3 0.0000 0.949 0.000 0.000 1.000 0.000
#> GSM1299555 3 0.4713 0.368 0.000 0.360 0.640 0.000
#> GSM1299556 3 0.0376 0.944 0.000 0.004 0.992 0.004
#> GSM1299557 2 0.4679 0.452 0.000 0.648 0.352 0.000
#> GSM1299558 2 0.3649 0.729 0.000 0.796 0.204 0.000
#> GSM1299559 4 0.4830 0.331 0.000 0.000 0.392 0.608
#> GSM1299560 3 0.0336 0.944 0.000 0.008 0.992 0.000
#> GSM1299576 1 0.0188 0.984 0.996 0.000 0.000 0.004
#> GSM1299577 4 0.4830 0.364 0.392 0.000 0.000 0.608
#> GSM1299561 3 0.0000 0.949 0.000 0.000 1.000 0.000
#> GSM1299562 2 0.4454 0.576 0.000 0.692 0.308 0.000
#> GSM1299563 4 0.0000 0.857 0.000 0.000 0.000 1.000
#> GSM1299564 4 0.0469 0.852 0.000 0.000 0.012 0.988
#> GSM1299565 2 0.0000 0.891 0.000 1.000 0.000 0.000
#> GSM1299566 4 0.7432 0.247 0.000 0.180 0.348 0.472
#> GSM1299567 4 0.0000 0.857 0.000 0.000 0.000 1.000
#> GSM1299568 3 0.0000 0.949 0.000 0.000 1.000 0.000
#> GSM1299569 3 0.0000 0.949 0.000 0.000 1.000 0.000
#> GSM1299570 4 0.0000 0.857 0.000 0.000 0.000 1.000
#> GSM1299571 2 0.0000 0.891 0.000 1.000 0.000 0.000
#> GSM1299572 1 0.0000 0.983 1.000 0.000 0.000 0.000
#> GSM1299573 3 0.0000 0.949 0.000 0.000 1.000 0.000
#> GSM1299574 2 0.0000 0.891 0.000 1.000 0.000 0.000
#> GSM1299578 1 0.0188 0.984 0.996 0.000 0.000 0.004
#> GSM1299579 1 0.0188 0.984 0.996 0.000 0.000 0.004
#> GSM1299580 1 0.0188 0.984 0.996 0.000 0.000 0.004
#> GSM1299581 1 0.0188 0.984 0.996 0.000 0.000 0.004
#> GSM1299582 1 0.0188 0.984 0.996 0.000 0.000 0.004
#> GSM1299583 1 0.0188 0.984 0.996 0.000 0.000 0.004
#> GSM1299584 1 0.0188 0.984 0.996 0.000 0.000 0.004
#> GSM1299585 1 0.0000 0.983 1.000 0.000 0.000 0.000
#> GSM1299586 1 0.0188 0.984 0.996 0.000 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1299517 3 0.0880 0.914 0.000 0.000 0.968 0.000 0.032
#> GSM1299518 2 0.1300 0.859 0.000 0.956 0.028 0.000 0.016
#> GSM1299519 2 0.0000 0.883 0.000 1.000 0.000 0.000 0.000
#> GSM1299520 4 0.0000 0.876 0.000 0.000 0.000 1.000 0.000
#> GSM1299521 5 0.1908 0.956 0.092 0.000 0.000 0.000 0.908
#> GSM1299522 2 0.0000 0.883 0.000 1.000 0.000 0.000 0.000
#> GSM1299523 4 0.0000 0.876 0.000 0.000 0.000 1.000 0.000
#> GSM1299524 3 0.1410 0.910 0.000 0.000 0.940 0.000 0.060
#> GSM1299525 2 0.1768 0.831 0.000 0.924 0.000 0.072 0.004
#> GSM1299526 2 0.0000 0.883 0.000 1.000 0.000 0.000 0.000
#> GSM1299527 3 0.0880 0.914 0.000 0.000 0.968 0.000 0.032
#> GSM1299528 3 0.1410 0.910 0.000 0.000 0.940 0.000 0.060
#> GSM1299529 2 0.0000 0.883 0.000 1.000 0.000 0.000 0.000
#> GSM1299530 4 0.0000 0.876 0.000 0.000 0.000 1.000 0.000
#> GSM1299531 2 0.5036 0.292 0.000 0.560 0.404 0.000 0.036
#> GSM1299575 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM1299532 3 0.0566 0.917 0.000 0.004 0.984 0.000 0.012
#> GSM1299533 5 0.2069 0.941 0.076 0.012 0.000 0.000 0.912
#> GSM1299534 3 0.1341 0.911 0.000 0.000 0.944 0.000 0.056
#> GSM1299535 3 0.4524 0.386 0.000 0.336 0.644 0.000 0.020
#> GSM1299536 5 0.1908 0.956 0.092 0.000 0.000 0.000 0.908
#> GSM1299537 3 0.0880 0.914 0.000 0.000 0.968 0.000 0.032
#> GSM1299538 4 0.0000 0.876 0.000 0.000 0.000 1.000 0.000
#> GSM1299539 4 0.0000 0.876 0.000 0.000 0.000 1.000 0.000
#> GSM1299540 3 0.3609 0.753 0.000 0.004 0.816 0.148 0.032
#> GSM1299541 3 0.0880 0.914 0.000 0.000 0.968 0.000 0.032
#> GSM1299542 3 0.0404 0.917 0.000 0.000 0.988 0.000 0.012
#> GSM1299543 2 0.0162 0.881 0.000 0.996 0.000 0.000 0.004
#> GSM1299544 3 0.1410 0.910 0.000 0.000 0.940 0.000 0.060
#> GSM1299545 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM1299546 2 0.0000 0.883 0.000 1.000 0.000 0.000 0.000
#> GSM1299547 5 0.1908 0.956 0.092 0.000 0.000 0.000 0.908
#> GSM1299548 3 0.0880 0.914 0.000 0.000 0.968 0.000 0.032
#> GSM1299549 5 0.1908 0.956 0.092 0.000 0.000 0.000 0.908
#> GSM1299550 5 0.3885 0.541 0.000 0.000 0.008 0.268 0.724
#> GSM1299551 2 0.0000 0.883 0.000 1.000 0.000 0.000 0.000
#> GSM1299552 5 0.1908 0.956 0.092 0.000 0.000 0.000 0.908
#> GSM1299553 1 0.1544 0.918 0.932 0.000 0.000 0.068 0.000
#> GSM1299554 3 0.0880 0.916 0.000 0.000 0.968 0.000 0.032
#> GSM1299555 3 0.4679 0.453 0.000 0.316 0.652 0.000 0.032
#> GSM1299556 3 0.0880 0.914 0.000 0.000 0.968 0.000 0.032
#> GSM1299557 2 0.4401 0.481 0.000 0.656 0.328 0.000 0.016
#> GSM1299558 2 0.3656 0.711 0.000 0.784 0.196 0.000 0.020
#> GSM1299559 4 0.4982 0.254 0.000 0.000 0.412 0.556 0.032
#> GSM1299560 3 0.1041 0.913 0.000 0.004 0.964 0.000 0.032
#> GSM1299576 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM1299577 1 0.1792 0.900 0.916 0.000 0.000 0.084 0.000
#> GSM1299561 3 0.0880 0.916 0.000 0.000 0.968 0.000 0.032
#> GSM1299562 2 0.4748 0.527 0.000 0.660 0.300 0.000 0.040
#> GSM1299563 4 0.0000 0.876 0.000 0.000 0.000 1.000 0.000
#> GSM1299564 4 0.0290 0.870 0.000 0.000 0.008 0.992 0.000
#> GSM1299565 2 0.0000 0.883 0.000 1.000 0.000 0.000 0.000
#> GSM1299566 4 0.7374 0.112 0.000 0.152 0.364 0.424 0.060
#> GSM1299567 4 0.0000 0.876 0.000 0.000 0.000 1.000 0.000
#> GSM1299568 3 0.1410 0.910 0.000 0.000 0.940 0.000 0.060
#> GSM1299569 3 0.1410 0.910 0.000 0.000 0.940 0.000 0.060
#> GSM1299570 4 0.0000 0.876 0.000 0.000 0.000 1.000 0.000
#> GSM1299571 2 0.0000 0.883 0.000 1.000 0.000 0.000 0.000
#> GSM1299572 5 0.1908 0.956 0.092 0.000 0.000 0.000 0.908
#> GSM1299573 3 0.1043 0.915 0.000 0.000 0.960 0.000 0.040
#> GSM1299574 2 0.0000 0.883 0.000 1.000 0.000 0.000 0.000
#> GSM1299578 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM1299579 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM1299580 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM1299581 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM1299582 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM1299583 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM1299584 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM1299585 5 0.1908 0.956 0.092 0.000 0.000 0.000 0.908
#> GSM1299586 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1299517 3 0.3672 0.4767 0.000 0.000 0.632 0.000 0.000 0.368
#> GSM1299518 2 0.1327 0.8309 0.000 0.936 0.064 0.000 0.000 0.000
#> GSM1299519 2 0.0000 0.8623 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299520 4 0.0000 0.9893 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1299521 5 0.0000 0.9447 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1299522 2 0.0000 0.8623 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299523 4 0.0000 0.9893 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1299524 3 0.2491 0.6468 0.000 0.000 0.836 0.000 0.000 0.164
#> GSM1299525 2 0.2415 0.8224 0.000 0.888 0.012 0.016 0.000 0.084
#> GSM1299526 2 0.0000 0.8623 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299527 6 0.3782 -0.0827 0.000 0.000 0.412 0.000 0.000 0.588
#> GSM1299528 3 0.0146 0.5786 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM1299529 2 0.1219 0.8451 0.000 0.948 0.004 0.000 0.000 0.048
#> GSM1299530 4 0.0000 0.9893 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1299531 2 0.4264 0.2315 0.000 0.500 0.484 0.000 0.000 0.016
#> GSM1299575 1 0.0260 0.9947 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM1299532 3 0.3765 0.4107 0.000 0.000 0.596 0.000 0.000 0.404
#> GSM1299533 5 0.0000 0.9447 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1299534 3 0.2491 0.6468 0.000 0.000 0.836 0.000 0.000 0.164
#> GSM1299535 6 0.5875 0.0734 0.000 0.264 0.256 0.000 0.000 0.480
#> GSM1299536 5 0.0000 0.9447 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1299537 6 0.3847 -0.1618 0.000 0.000 0.456 0.000 0.000 0.544
#> GSM1299538 4 0.0000 0.9893 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1299539 4 0.0632 0.9740 0.000 0.000 0.024 0.976 0.000 0.000
#> GSM1299540 6 0.2001 0.5364 0.000 0.000 0.040 0.048 0.000 0.912
#> GSM1299541 3 0.3838 0.3059 0.000 0.000 0.552 0.000 0.000 0.448
#> GSM1299542 3 0.3244 0.5992 0.000 0.000 0.732 0.000 0.000 0.268
#> GSM1299543 2 0.2030 0.8272 0.000 0.908 0.028 0.000 0.000 0.064
#> GSM1299544 3 0.0458 0.5676 0.000 0.000 0.984 0.000 0.000 0.016
#> GSM1299545 1 0.0000 0.9972 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299546 2 0.0000 0.8623 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299547 5 0.0000 0.9447 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1299548 6 0.3862 -0.2136 0.000 0.000 0.476 0.000 0.000 0.524
#> GSM1299549 5 0.0713 0.9260 0.000 0.000 0.000 0.000 0.972 0.028
#> GSM1299550 5 0.6660 0.4344 0.000 0.000 0.164 0.204 0.528 0.104
#> GSM1299551 2 0.0000 0.8623 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299552 5 0.0000 0.9447 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1299553 1 0.0146 0.9961 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM1299554 3 0.3851 0.2719 0.000 0.000 0.540 0.000 0.000 0.460
#> GSM1299555 6 0.1408 0.5343 0.000 0.036 0.020 0.000 0.000 0.944
#> GSM1299556 6 0.1387 0.5306 0.000 0.000 0.068 0.000 0.000 0.932
#> GSM1299557 2 0.5219 0.4770 0.000 0.612 0.212 0.000 0.000 0.176
#> GSM1299558 2 0.4462 0.5904 0.000 0.660 0.280 0.000 0.000 0.060
#> GSM1299559 6 0.1644 0.5253 0.000 0.000 0.004 0.076 0.000 0.920
#> GSM1299560 3 0.3843 0.3043 0.000 0.000 0.548 0.000 0.000 0.452
#> GSM1299576 1 0.0000 0.9972 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299577 1 0.0363 0.9884 0.988 0.000 0.000 0.012 0.000 0.000
#> GSM1299561 3 0.2883 0.6364 0.000 0.000 0.788 0.000 0.000 0.212
#> GSM1299562 2 0.4131 0.4472 0.000 0.600 0.384 0.000 0.000 0.016
#> GSM1299563 4 0.0000 0.9893 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1299564 4 0.1480 0.9383 0.000 0.000 0.020 0.940 0.000 0.040
#> GSM1299565 2 0.0000 0.8623 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299566 3 0.6549 0.0201 0.000 0.104 0.548 0.180 0.000 0.168
#> GSM1299567 4 0.0146 0.9872 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM1299568 3 0.1075 0.6129 0.000 0.000 0.952 0.000 0.000 0.048
#> GSM1299569 3 0.0713 0.6023 0.000 0.000 0.972 0.000 0.000 0.028
#> GSM1299570 4 0.0000 0.9893 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1299571 2 0.0000 0.8623 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299572 5 0.0000 0.9447 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1299573 3 0.3175 0.6102 0.000 0.000 0.744 0.000 0.000 0.256
#> GSM1299574 2 0.0000 0.8623 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299578 1 0.0260 0.9947 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM1299579 1 0.0000 0.9972 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299580 1 0.0260 0.9947 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM1299581 1 0.0000 0.9972 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299582 1 0.0000 0.9972 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299583 1 0.0000 0.9972 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299584 1 0.0000 0.9972 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299585 5 0.0000 0.9447 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1299586 1 0.0000 0.9972 1.000 0.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:pam 69 0.1481 2
#> SD:pam 66 0.1497 3
#> SD:pam 63 0.2003 4
#> SD:pam 64 0.0972 5
#> SD:pam 56 0.0769 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "mclust"]
# you can also extract it by
# res = res_list["SD:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 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 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 0.446 0.870 0.912 0.4644 0.499 0.499
#> 3 3 0.481 0.693 0.813 0.3315 0.746 0.552
#> 4 4 0.642 0.719 0.851 0.1637 0.844 0.618
#> 5 5 0.658 0.560 0.780 0.0860 0.878 0.600
#> 6 6 0.735 0.669 0.825 0.0591 0.899 0.579
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
#> GSM1299517 2 0.4815 0.935 0.104 0.896
#> GSM1299518 2 0.5629 0.932 0.132 0.868
#> GSM1299519 2 0.1843 0.888 0.028 0.972
#> GSM1299520 1 0.0938 0.919 0.988 0.012
#> GSM1299521 1 0.0000 0.928 1.000 0.000
#> GSM1299522 2 0.1843 0.888 0.028 0.972
#> GSM1299523 1 0.2043 0.903 0.968 0.032
#> GSM1299524 1 0.9635 0.272 0.612 0.388
#> GSM1299525 2 0.5629 0.932 0.132 0.868
#> GSM1299526 2 0.2043 0.891 0.032 0.968
#> GSM1299527 2 0.5059 0.935 0.112 0.888
#> GSM1299528 2 0.5946 0.925 0.144 0.856
#> GSM1299529 2 0.1843 0.888 0.028 0.972
#> GSM1299530 1 0.0000 0.928 1.000 0.000
#> GSM1299531 2 0.5629 0.932 0.132 0.868
#> GSM1299575 1 0.0000 0.928 1.000 0.000
#> GSM1299532 2 0.5059 0.935 0.112 0.888
#> GSM1299533 1 0.9087 0.462 0.676 0.324
#> GSM1299534 2 0.4815 0.935 0.104 0.896
#> GSM1299535 2 0.5629 0.932 0.132 0.868
#> GSM1299536 1 0.0000 0.928 1.000 0.000
#> GSM1299537 2 0.5059 0.935 0.112 0.888
#> GSM1299538 1 0.9044 0.461 0.680 0.320
#> GSM1299539 2 0.9909 0.363 0.444 0.556
#> GSM1299540 2 0.8081 0.802 0.248 0.752
#> GSM1299541 2 0.5059 0.935 0.112 0.888
#> GSM1299542 2 0.5059 0.935 0.112 0.888
#> GSM1299543 2 0.1843 0.888 0.028 0.972
#> GSM1299544 2 0.4815 0.935 0.104 0.896
#> GSM1299545 1 0.0000 0.928 1.000 0.000
#> GSM1299546 2 0.1843 0.888 0.028 0.972
#> GSM1299547 1 0.0000 0.928 1.000 0.000
#> GSM1299548 2 0.5059 0.935 0.112 0.888
#> GSM1299549 1 0.0000 0.928 1.000 0.000
#> GSM1299550 1 0.6712 0.732 0.824 0.176
#> GSM1299551 2 0.1843 0.888 0.028 0.972
#> GSM1299552 1 0.0000 0.928 1.000 0.000
#> GSM1299553 1 0.4022 0.854 0.920 0.080
#> GSM1299554 2 0.5519 0.927 0.128 0.872
#> GSM1299555 2 0.5629 0.932 0.132 0.868
#> GSM1299556 2 0.5408 0.932 0.124 0.876
#> GSM1299557 2 0.5629 0.932 0.132 0.868
#> GSM1299558 2 0.5629 0.932 0.132 0.868
#> GSM1299559 2 0.5519 0.930 0.128 0.872
#> GSM1299560 2 0.5059 0.935 0.112 0.888
#> GSM1299576 1 0.0000 0.928 1.000 0.000
#> GSM1299577 1 0.0000 0.928 1.000 0.000
#> GSM1299561 2 0.5059 0.935 0.112 0.888
#> GSM1299562 2 0.5629 0.932 0.132 0.868
#> GSM1299563 1 0.0000 0.928 1.000 0.000
#> GSM1299564 1 0.9996 -0.185 0.512 0.488
#> GSM1299565 2 0.1843 0.888 0.028 0.972
#> GSM1299566 2 0.7299 0.864 0.204 0.796
#> GSM1299567 1 0.0000 0.928 1.000 0.000
#> GSM1299568 2 0.5629 0.932 0.132 0.868
#> GSM1299569 2 0.4815 0.935 0.104 0.896
#> GSM1299570 1 0.0000 0.928 1.000 0.000
#> GSM1299571 2 0.1843 0.888 0.028 0.972
#> GSM1299572 1 0.0000 0.928 1.000 0.000
#> GSM1299573 2 0.5059 0.935 0.112 0.888
#> GSM1299574 2 0.1843 0.888 0.028 0.972
#> GSM1299578 1 0.0000 0.928 1.000 0.000
#> GSM1299579 1 0.0000 0.928 1.000 0.000
#> GSM1299580 1 0.0000 0.928 1.000 0.000
#> GSM1299581 1 0.0000 0.928 1.000 0.000
#> GSM1299582 1 0.0000 0.928 1.000 0.000
#> GSM1299583 1 0.0000 0.928 1.000 0.000
#> GSM1299584 1 0.0000 0.928 1.000 0.000
#> GSM1299585 1 0.0000 0.928 1.000 0.000
#> GSM1299586 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
#> GSM1299517 3 0.0000 0.7374 0.000 0.000 1.000
#> GSM1299518 3 0.6800 0.5196 0.032 0.308 0.660
#> GSM1299519 2 0.3896 0.8961 0.008 0.864 0.128
#> GSM1299520 1 0.5408 0.7778 0.812 0.052 0.136
#> GSM1299521 1 0.4094 0.8425 0.872 0.100 0.028
#> GSM1299522 2 0.3482 0.8998 0.000 0.872 0.128
#> GSM1299523 1 0.6904 0.5862 0.684 0.048 0.268
#> GSM1299524 3 0.8625 0.4130 0.136 0.288 0.576
#> GSM1299525 3 0.6556 0.5611 0.032 0.276 0.692
#> GSM1299526 2 0.5363 0.6866 0.000 0.724 0.276
#> GSM1299527 3 0.0000 0.7374 0.000 0.000 1.000
#> GSM1299528 3 0.3551 0.6928 0.000 0.132 0.868
#> GSM1299529 2 0.6793 0.6645 0.036 0.672 0.292
#> GSM1299530 1 0.1585 0.8682 0.964 0.008 0.028
#> GSM1299531 3 0.7453 0.2855 0.036 0.436 0.528
#> GSM1299575 1 0.2448 0.8381 0.924 0.000 0.076
#> GSM1299532 3 0.0000 0.7374 0.000 0.000 1.000
#> GSM1299533 3 0.9760 0.2398 0.236 0.344 0.420
#> GSM1299534 3 0.1129 0.7380 0.004 0.020 0.976
#> GSM1299535 3 0.6099 0.6214 0.032 0.228 0.740
#> GSM1299536 1 0.8286 0.5947 0.624 0.140 0.236
#> GSM1299537 3 0.0000 0.7374 0.000 0.000 1.000
#> GSM1299538 3 0.8755 0.2434 0.400 0.112 0.488
#> GSM1299539 1 0.9527 -0.0708 0.436 0.192 0.372
#> GSM1299540 3 0.8172 0.5307 0.176 0.180 0.644
#> GSM1299541 3 0.0000 0.7374 0.000 0.000 1.000
#> GSM1299542 3 0.0000 0.7374 0.000 0.000 1.000
#> GSM1299543 2 0.4551 0.8791 0.024 0.844 0.132
#> GSM1299544 3 0.1753 0.7270 0.000 0.048 0.952
#> GSM1299545 1 0.3213 0.8380 0.912 0.028 0.060
#> GSM1299546 2 0.3482 0.8998 0.000 0.872 0.128
#> GSM1299547 1 0.4172 0.8423 0.868 0.104 0.028
#> GSM1299548 3 0.0892 0.7395 0.020 0.000 0.980
#> GSM1299549 1 0.3921 0.8513 0.884 0.080 0.036
#> GSM1299550 3 0.9547 -0.0171 0.392 0.192 0.416
#> GSM1299551 2 0.3482 0.8998 0.000 0.872 0.128
#> GSM1299552 1 0.3765 0.8491 0.888 0.084 0.028
#> GSM1299553 1 0.6463 0.7014 0.756 0.080 0.164
#> GSM1299554 3 0.0747 0.7388 0.000 0.016 0.984
#> GSM1299555 3 0.5521 0.6550 0.032 0.180 0.788
#> GSM1299556 3 0.4861 0.6671 0.012 0.180 0.808
#> GSM1299557 3 0.6183 0.6131 0.032 0.236 0.732
#> GSM1299558 3 0.7263 0.3200 0.032 0.400 0.568
#> GSM1299559 3 0.5581 0.6640 0.036 0.176 0.788
#> GSM1299560 3 0.1482 0.7398 0.020 0.012 0.968
#> GSM1299576 1 0.0000 0.8618 1.000 0.000 0.000
#> GSM1299577 1 0.2793 0.8591 0.928 0.044 0.028
#> GSM1299561 3 0.0237 0.7361 0.000 0.004 0.996
#> GSM1299562 3 0.7295 0.3996 0.036 0.380 0.584
#> GSM1299563 1 0.1585 0.8682 0.964 0.008 0.028
#> GSM1299564 3 0.8419 0.2206 0.408 0.088 0.504
#> GSM1299565 2 0.3482 0.8998 0.000 0.872 0.128
#> GSM1299566 3 0.5318 0.6511 0.016 0.204 0.780
#> GSM1299567 1 0.6129 0.5414 0.668 0.008 0.324
#> GSM1299568 3 0.3499 0.7222 0.028 0.072 0.900
#> GSM1299569 3 0.1031 0.7354 0.000 0.024 0.976
#> GSM1299570 1 0.1585 0.8682 0.964 0.008 0.028
#> GSM1299571 2 0.3482 0.8998 0.000 0.872 0.128
#> GSM1299572 1 0.8527 0.6095 0.612 0.196 0.192
#> GSM1299573 3 0.0000 0.7374 0.000 0.000 1.000
#> GSM1299574 2 0.6019 0.7001 0.012 0.700 0.288
#> GSM1299578 1 0.0000 0.8618 1.000 0.000 0.000
#> GSM1299579 1 0.2050 0.8678 0.952 0.020 0.028
#> GSM1299580 1 0.1289 0.8595 0.968 0.000 0.032
#> GSM1299581 1 0.0000 0.8618 1.000 0.000 0.000
#> GSM1299582 1 0.0000 0.8618 1.000 0.000 0.000
#> GSM1299583 1 0.2056 0.8673 0.952 0.024 0.024
#> GSM1299584 1 0.0000 0.8618 1.000 0.000 0.000
#> GSM1299585 1 0.4094 0.8425 0.872 0.100 0.028
#> GSM1299586 1 0.0000 0.8618 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1299517 3 0.0000 0.796 0.000 0.000 1.000 0.000
#> GSM1299518 3 0.5271 0.683 0.076 0.144 0.768 0.012
#> GSM1299519 2 0.0000 0.838 0.000 1.000 0.000 0.000
#> GSM1299520 1 0.1209 0.855 0.964 0.000 0.004 0.032
#> GSM1299521 4 0.3764 0.781 0.216 0.000 0.000 0.784
#> GSM1299522 2 0.0000 0.838 0.000 1.000 0.000 0.000
#> GSM1299523 1 0.2271 0.812 0.928 0.008 0.052 0.012
#> GSM1299524 3 0.4477 0.573 0.000 0.000 0.688 0.312
#> GSM1299525 2 0.7388 0.398 0.096 0.584 0.280 0.040
#> GSM1299526 2 0.0895 0.827 0.000 0.976 0.020 0.004
#> GSM1299527 3 0.0000 0.796 0.000 0.000 1.000 0.000
#> GSM1299528 3 0.4831 0.734 0.000 0.040 0.752 0.208
#> GSM1299529 2 0.2530 0.768 0.100 0.896 0.004 0.000
#> GSM1299530 1 0.1022 0.855 0.968 0.000 0.000 0.032
#> GSM1299531 2 0.7590 0.121 0.004 0.472 0.344 0.180
#> GSM1299575 1 0.0000 0.863 1.000 0.000 0.000 0.000
#> GSM1299532 3 0.0000 0.796 0.000 0.000 1.000 0.000
#> GSM1299533 4 0.1661 0.686 0.000 0.004 0.052 0.944
#> GSM1299534 3 0.3311 0.766 0.000 0.000 0.828 0.172
#> GSM1299535 3 0.7768 0.640 0.088 0.160 0.616 0.136
#> GSM1299536 4 0.0336 0.716 0.000 0.000 0.008 0.992
#> GSM1299537 3 0.0000 0.796 0.000 0.000 1.000 0.000
#> GSM1299538 1 0.8319 0.302 0.536 0.064 0.188 0.212
#> GSM1299539 1 0.7712 0.307 0.524 0.112 0.036 0.328
#> GSM1299540 3 0.6695 0.155 0.416 0.076 0.504 0.004
#> GSM1299541 3 0.0000 0.796 0.000 0.000 1.000 0.000
#> GSM1299542 3 0.0000 0.796 0.000 0.000 1.000 0.000
#> GSM1299543 2 0.2048 0.799 0.064 0.928 0.008 0.000
#> GSM1299544 3 0.3688 0.750 0.000 0.000 0.792 0.208
#> GSM1299545 1 0.0000 0.863 1.000 0.000 0.000 0.000
#> GSM1299546 2 0.0000 0.838 0.000 1.000 0.000 0.000
#> GSM1299547 4 0.3649 0.786 0.204 0.000 0.000 0.796
#> GSM1299548 3 0.0188 0.796 0.000 0.000 0.996 0.004
#> GSM1299549 4 0.6015 0.668 0.268 0.000 0.080 0.652
#> GSM1299550 4 0.3764 0.420 0.000 0.000 0.216 0.784
#> GSM1299551 2 0.0000 0.838 0.000 1.000 0.000 0.000
#> GSM1299552 4 0.3801 0.778 0.220 0.000 0.000 0.780
#> GSM1299553 1 0.0921 0.857 0.972 0.000 0.000 0.028
#> GSM1299554 3 0.3688 0.750 0.000 0.000 0.792 0.208
#> GSM1299555 3 0.5473 0.658 0.100 0.152 0.744 0.004
#> GSM1299556 3 0.2125 0.778 0.000 0.076 0.920 0.004
#> GSM1299557 3 0.8610 0.583 0.120 0.144 0.532 0.204
#> GSM1299558 2 0.6730 0.362 0.072 0.588 0.324 0.016
#> GSM1299559 3 0.2125 0.778 0.000 0.076 0.920 0.004
#> GSM1299560 3 0.2830 0.775 0.032 0.060 0.904 0.004
#> GSM1299576 1 0.0000 0.863 1.000 0.000 0.000 0.000
#> GSM1299577 1 0.1022 0.855 0.968 0.000 0.000 0.032
#> GSM1299561 3 0.0000 0.796 0.000 0.000 1.000 0.000
#> GSM1299562 3 0.7834 0.643 0.064 0.124 0.584 0.228
#> GSM1299563 1 0.3852 0.692 0.800 0.000 0.008 0.192
#> GSM1299564 3 0.9024 0.389 0.308 0.076 0.408 0.208
#> GSM1299565 2 0.0000 0.838 0.000 1.000 0.000 0.000
#> GSM1299566 3 0.6386 0.674 0.000 0.124 0.640 0.236
#> GSM1299567 1 0.4252 0.589 0.744 0.000 0.252 0.004
#> GSM1299568 3 0.5100 0.741 0.004 0.052 0.752 0.192
#> GSM1299569 3 0.3688 0.750 0.000 0.000 0.792 0.208
#> GSM1299570 1 0.1109 0.857 0.968 0.000 0.004 0.028
#> GSM1299571 2 0.0000 0.838 0.000 1.000 0.000 0.000
#> GSM1299572 4 0.3142 0.789 0.132 0.000 0.008 0.860
#> GSM1299573 3 0.0000 0.796 0.000 0.000 1.000 0.000
#> GSM1299574 2 0.0000 0.838 0.000 1.000 0.000 0.000
#> GSM1299578 1 0.0000 0.863 1.000 0.000 0.000 0.000
#> GSM1299579 1 0.4522 0.466 0.680 0.000 0.000 0.320
#> GSM1299580 1 0.0000 0.863 1.000 0.000 0.000 0.000
#> GSM1299581 1 0.0000 0.863 1.000 0.000 0.000 0.000
#> GSM1299582 1 0.0000 0.863 1.000 0.000 0.000 0.000
#> GSM1299583 1 0.4040 0.579 0.752 0.000 0.000 0.248
#> GSM1299584 1 0.0000 0.863 1.000 0.000 0.000 0.000
#> GSM1299585 4 0.3764 0.781 0.216 0.000 0.000 0.784
#> GSM1299586 1 0.0000 0.863 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1299517 3 0.0000 0.7347 0.000 0.000 1.000 0.000 0.000
#> GSM1299518 3 0.4565 0.2542 0.000 0.012 0.580 0.408 0.000
#> GSM1299519 2 0.0000 0.9409 0.000 1.000 0.000 0.000 0.000
#> GSM1299520 1 0.6261 0.6337 0.536 0.000 0.000 0.264 0.200
#> GSM1299521 5 0.1478 0.7643 0.064 0.000 0.000 0.000 0.936
#> GSM1299522 2 0.0000 0.9409 0.000 1.000 0.000 0.000 0.000
#> GSM1299523 1 0.6895 0.6016 0.488 0.000 0.020 0.292 0.200
#> GSM1299524 3 0.6551 0.1116 0.000 0.000 0.468 0.228 0.304
#> GSM1299525 4 0.6824 0.4104 0.068 0.232 0.124 0.576 0.000
#> GSM1299526 2 0.0000 0.9409 0.000 1.000 0.000 0.000 0.000
#> GSM1299527 3 0.0000 0.7347 0.000 0.000 1.000 0.000 0.000
#> GSM1299528 3 0.4287 0.0913 0.000 0.000 0.540 0.460 0.000
#> GSM1299529 2 0.3995 0.6850 0.180 0.776 0.000 0.044 0.000
#> GSM1299530 1 0.4883 0.6760 0.708 0.000 0.000 0.092 0.200
#> GSM1299531 4 0.4999 0.4496 0.000 0.108 0.148 0.732 0.012
#> GSM1299575 1 0.3561 0.7150 0.740 0.000 0.000 0.260 0.000
#> GSM1299532 3 0.0000 0.7347 0.000 0.000 1.000 0.000 0.000
#> GSM1299533 5 0.4182 0.3069 0.000 0.000 0.000 0.400 0.600
#> GSM1299534 3 0.4015 0.3606 0.000 0.000 0.652 0.348 0.000
#> GSM1299535 4 0.3715 0.3880 0.004 0.000 0.260 0.736 0.000
#> GSM1299536 5 0.0162 0.7759 0.000 0.000 0.000 0.004 0.996
#> GSM1299537 3 0.0000 0.7347 0.000 0.000 1.000 0.000 0.000
#> GSM1299538 4 0.5947 -0.2892 0.312 0.000 0.000 0.556 0.132
#> GSM1299539 4 0.5917 -0.2697 0.304 0.000 0.000 0.564 0.132
#> GSM1299540 4 0.6811 -0.2852 0.304 0.000 0.336 0.360 0.000
#> GSM1299541 3 0.0162 0.7340 0.000 0.000 0.996 0.004 0.000
#> GSM1299542 3 0.0000 0.7347 0.000 0.000 1.000 0.000 0.000
#> GSM1299543 2 0.3421 0.7588 0.000 0.788 0.008 0.204 0.000
#> GSM1299544 3 0.4192 0.2421 0.000 0.000 0.596 0.404 0.000
#> GSM1299545 1 0.2516 0.7267 0.860 0.000 0.000 0.140 0.000
#> GSM1299546 2 0.0000 0.9409 0.000 1.000 0.000 0.000 0.000
#> GSM1299547 5 0.0162 0.7759 0.000 0.000 0.000 0.004 0.996
#> GSM1299548 3 0.0880 0.7243 0.000 0.000 0.968 0.032 0.000
#> GSM1299549 5 0.2234 0.7591 0.036 0.000 0.004 0.044 0.916
#> GSM1299550 5 0.4994 0.4471 0.000 0.000 0.096 0.208 0.696
#> GSM1299551 2 0.0000 0.9409 0.000 1.000 0.000 0.000 0.000
#> GSM1299552 5 0.1571 0.7679 0.060 0.000 0.000 0.004 0.936
#> GSM1299553 1 0.5357 0.6912 0.640 0.000 0.000 0.264 0.096
#> GSM1299554 3 0.3895 0.4233 0.000 0.000 0.680 0.320 0.000
#> GSM1299555 3 0.5640 0.2422 0.104 0.000 0.592 0.304 0.000
#> GSM1299556 3 0.1121 0.7188 0.000 0.000 0.956 0.044 0.000
#> GSM1299557 4 0.5908 0.3836 0.156 0.000 0.256 0.588 0.000
#> GSM1299558 4 0.4764 0.4451 0.000 0.128 0.140 0.732 0.000
#> GSM1299559 3 0.1121 0.7188 0.000 0.000 0.956 0.044 0.000
#> GSM1299560 3 0.2813 0.6089 0.000 0.000 0.832 0.168 0.000
#> GSM1299576 1 0.0000 0.7085 1.000 0.000 0.000 0.000 0.000
#> GSM1299577 1 0.5810 0.6790 0.604 0.000 0.000 0.244 0.152
#> GSM1299561 3 0.0162 0.7342 0.000 0.000 0.996 0.004 0.000
#> GSM1299562 4 0.3534 0.3883 0.000 0.000 0.256 0.744 0.000
#> GSM1299563 5 0.6875 -0.4448 0.344 0.000 0.004 0.260 0.392
#> GSM1299564 1 0.8497 0.3796 0.300 0.000 0.196 0.296 0.208
#> GSM1299565 2 0.0000 0.9409 0.000 1.000 0.000 0.000 0.000
#> GSM1299566 4 0.4300 -0.0638 0.000 0.000 0.476 0.524 0.000
#> GSM1299567 1 0.7485 0.5184 0.464 0.000 0.208 0.268 0.060
#> GSM1299568 4 0.4030 0.2541 0.000 0.000 0.352 0.648 0.000
#> GSM1299569 3 0.3999 0.3584 0.000 0.000 0.656 0.344 0.000
#> GSM1299570 1 0.6185 0.6442 0.548 0.000 0.000 0.264 0.188
#> GSM1299571 2 0.0000 0.9409 0.000 1.000 0.000 0.000 0.000
#> GSM1299572 5 0.0162 0.7759 0.000 0.000 0.000 0.004 0.996
#> GSM1299573 3 0.0000 0.7347 0.000 0.000 1.000 0.000 0.000
#> GSM1299574 2 0.0963 0.9145 0.000 0.964 0.000 0.036 0.000
#> GSM1299578 1 0.0000 0.7085 1.000 0.000 0.000 0.000 0.000
#> GSM1299579 1 0.4161 0.2790 0.608 0.000 0.000 0.000 0.392
#> GSM1299580 1 0.3561 0.7150 0.740 0.000 0.000 0.260 0.000
#> GSM1299581 1 0.0000 0.7085 1.000 0.000 0.000 0.000 0.000
#> GSM1299582 1 0.0000 0.7085 1.000 0.000 0.000 0.000 0.000
#> GSM1299583 1 0.2732 0.5367 0.840 0.000 0.000 0.000 0.160
#> GSM1299584 1 0.0000 0.7085 1.000 0.000 0.000 0.000 0.000
#> GSM1299585 5 0.1965 0.7414 0.096 0.000 0.000 0.000 0.904
#> GSM1299586 1 0.0000 0.7085 1.000 0.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1299517 3 0.0260 0.7622 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM1299518 6 0.3769 0.3296 0.000 0.000 0.356 0.000 0.004 0.640
#> GSM1299519 2 0.0146 0.8763 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM1299520 4 0.2968 0.7467 0.052 0.000 0.000 0.852 0.092 0.004
#> GSM1299521 5 0.1418 0.8399 0.032 0.000 0.000 0.024 0.944 0.000
#> GSM1299522 2 0.0000 0.8783 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299523 4 0.2214 0.7391 0.012 0.000 0.000 0.892 0.092 0.004
#> GSM1299524 3 0.5571 0.2019 0.000 0.000 0.496 0.000 0.148 0.356
#> GSM1299525 6 0.2635 0.7615 0.004 0.068 0.000 0.036 0.008 0.884
#> GSM1299526 2 0.0000 0.8783 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299527 3 0.0000 0.7637 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299528 6 0.4184 0.1189 0.000 0.000 0.408 0.000 0.016 0.576
#> GSM1299529 2 0.4467 0.5296 0.000 0.632 0.000 0.048 0.000 0.320
#> GSM1299530 4 0.4729 0.6555 0.248 0.000 0.000 0.656 0.096 0.000
#> GSM1299531 6 0.0146 0.7966 0.000 0.000 0.004 0.000 0.000 0.996
#> GSM1299575 4 0.3756 0.5096 0.400 0.000 0.000 0.600 0.000 0.000
#> GSM1299532 3 0.0146 0.7632 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM1299533 5 0.3852 0.3364 0.000 0.000 0.000 0.004 0.612 0.384
#> GSM1299534 3 0.3912 0.4753 0.000 0.000 0.648 0.000 0.012 0.340
#> GSM1299535 6 0.0964 0.7955 0.004 0.000 0.000 0.012 0.016 0.968
#> GSM1299536 5 0.1814 0.8689 0.000 0.000 0.000 0.100 0.900 0.000
#> GSM1299537 3 0.0000 0.7637 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299538 4 0.4148 0.6970 0.000 0.000 0.000 0.744 0.108 0.148
#> GSM1299539 4 0.4928 0.6021 0.000 0.004 0.000 0.640 0.096 0.260
#> GSM1299540 4 0.4141 0.5067 0.000 0.000 0.080 0.756 0.008 0.156
#> GSM1299541 3 0.0146 0.7636 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM1299542 3 0.0000 0.7637 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299543 2 0.3371 0.6398 0.000 0.708 0.000 0.000 0.000 0.292
#> GSM1299544 3 0.4209 0.3483 0.000 0.000 0.596 0.000 0.020 0.384
#> GSM1299545 4 0.4310 0.4212 0.440 0.000 0.000 0.540 0.020 0.000
#> GSM1299546 2 0.0000 0.8783 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299547 5 0.1910 0.8691 0.000 0.000 0.000 0.108 0.892 0.000
#> GSM1299548 3 0.1075 0.7432 0.000 0.000 0.952 0.000 0.000 0.048
#> GSM1299549 5 0.2163 0.8630 0.000 0.000 0.000 0.092 0.892 0.016
#> GSM1299550 5 0.3795 0.7851 0.000 0.000 0.004 0.096 0.788 0.112
#> GSM1299551 2 0.0000 0.8783 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299552 5 0.2277 0.8628 0.032 0.000 0.000 0.076 0.892 0.000
#> GSM1299553 4 0.4711 0.6425 0.280 0.000 0.000 0.640 0.080 0.000
#> GSM1299554 3 0.3245 0.6236 0.000 0.000 0.764 0.000 0.008 0.228
#> GSM1299555 6 0.5617 0.4487 0.004 0.000 0.148 0.256 0.008 0.584
#> GSM1299556 3 0.5721 0.3262 0.000 0.000 0.520 0.236 0.000 0.244
#> GSM1299557 6 0.1672 0.7832 0.004 0.000 0.000 0.048 0.016 0.932
#> GSM1299558 6 0.0146 0.7966 0.000 0.000 0.004 0.000 0.000 0.996
#> GSM1299559 3 0.5919 0.2479 0.000 0.000 0.464 0.288 0.000 0.248
#> GSM1299560 3 0.3512 0.5164 0.000 0.000 0.720 0.000 0.008 0.272
#> GSM1299576 1 0.0146 0.8169 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM1299577 4 0.3502 0.7411 0.108 0.000 0.000 0.812 0.076 0.004
#> GSM1299561 3 0.0260 0.7623 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM1299562 6 0.0405 0.7961 0.000 0.000 0.000 0.004 0.008 0.988
#> GSM1299563 4 0.3508 0.5897 0.000 0.000 0.000 0.704 0.292 0.004
#> GSM1299564 4 0.2658 0.7332 0.000 0.000 0.008 0.864 0.112 0.016
#> GSM1299565 2 0.0000 0.8783 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299566 6 0.2665 0.7284 0.000 0.000 0.104 0.016 0.012 0.868
#> GSM1299567 4 0.1700 0.6485 0.000 0.000 0.080 0.916 0.000 0.004
#> GSM1299568 6 0.2070 0.7409 0.000 0.000 0.092 0.000 0.012 0.896
#> GSM1299569 3 0.4052 0.4064 0.000 0.000 0.628 0.000 0.016 0.356
#> GSM1299570 4 0.2968 0.7472 0.052 0.000 0.000 0.852 0.092 0.004
#> GSM1299571 2 0.0000 0.8783 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299572 5 0.1910 0.8691 0.000 0.000 0.000 0.108 0.892 0.000
#> GSM1299573 3 0.0000 0.7637 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299574 2 0.3309 0.6383 0.000 0.720 0.000 0.000 0.000 0.280
#> GSM1299578 1 0.2219 0.6757 0.864 0.000 0.000 0.136 0.000 0.000
#> GSM1299579 1 0.5115 0.0633 0.464 0.000 0.000 0.080 0.456 0.000
#> GSM1299580 4 0.3756 0.5096 0.400 0.000 0.000 0.600 0.000 0.000
#> GSM1299581 1 0.0146 0.8169 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM1299582 1 0.0146 0.8169 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM1299583 1 0.4076 0.3996 0.592 0.000 0.000 0.012 0.396 0.000
#> GSM1299584 1 0.0790 0.7997 0.968 0.000 0.000 0.032 0.000 0.000
#> GSM1299585 5 0.1682 0.8201 0.052 0.000 0.000 0.020 0.928 0.000
#> GSM1299586 1 0.0146 0.8169 0.996 0.000 0.000 0.004 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:mclust 65 0.1209 2
#> SD:mclust 61 0.0945 3
#> SD:mclust 61 0.1705 4
#> SD:mclust 46 0.2096 5
#> SD:mclust 57 0.2847 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "NMF"]
# you can also extract it by
# res = res_list["SD:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.960 0.985 0.4985 0.499 0.499
#> 3 3 0.579 0.726 0.817 0.3156 0.769 0.565
#> 4 4 0.642 0.558 0.784 0.1398 0.824 0.531
#> 5 5 0.699 0.671 0.769 0.0681 0.884 0.588
#> 6 6 0.767 0.623 0.786 0.0420 0.910 0.616
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
#> GSM1299517 2 0.0000 0.9939 0.000 1.000
#> GSM1299518 2 0.0000 0.9939 0.000 1.000
#> GSM1299519 2 0.0000 0.9939 0.000 1.000
#> GSM1299520 1 0.0000 0.9721 1.000 0.000
#> GSM1299521 1 0.0000 0.9721 1.000 0.000
#> GSM1299522 2 0.0000 0.9939 0.000 1.000
#> GSM1299523 1 0.0000 0.9721 1.000 0.000
#> GSM1299524 2 0.0000 0.9939 0.000 1.000
#> GSM1299525 2 0.0000 0.9939 0.000 1.000
#> GSM1299526 2 0.0000 0.9939 0.000 1.000
#> GSM1299527 2 0.0000 0.9939 0.000 1.000
#> GSM1299528 2 0.0000 0.9939 0.000 1.000
#> GSM1299529 2 0.0000 0.9939 0.000 1.000
#> GSM1299530 1 0.0000 0.9721 1.000 0.000
#> GSM1299531 2 0.0000 0.9939 0.000 1.000
#> GSM1299575 1 0.0000 0.9721 1.000 0.000
#> GSM1299532 2 0.0000 0.9939 0.000 1.000
#> GSM1299533 1 0.9996 0.0541 0.512 0.488
#> GSM1299534 2 0.0000 0.9939 0.000 1.000
#> GSM1299535 2 0.0000 0.9939 0.000 1.000
#> GSM1299536 1 0.0000 0.9721 1.000 0.000
#> GSM1299537 2 0.0000 0.9939 0.000 1.000
#> GSM1299538 1 0.0938 0.9618 0.988 0.012
#> GSM1299539 1 0.0376 0.9688 0.996 0.004
#> GSM1299540 2 0.7602 0.7062 0.220 0.780
#> GSM1299541 2 0.0000 0.9939 0.000 1.000
#> GSM1299542 2 0.0000 0.9939 0.000 1.000
#> GSM1299543 2 0.0000 0.9939 0.000 1.000
#> GSM1299544 2 0.0000 0.9939 0.000 1.000
#> GSM1299545 1 0.0000 0.9721 1.000 0.000
#> GSM1299546 2 0.0000 0.9939 0.000 1.000
#> GSM1299547 1 0.0000 0.9721 1.000 0.000
#> GSM1299548 2 0.0000 0.9939 0.000 1.000
#> GSM1299549 1 0.0000 0.9721 1.000 0.000
#> GSM1299550 1 0.9044 0.5330 0.680 0.320
#> GSM1299551 2 0.0000 0.9939 0.000 1.000
#> GSM1299552 1 0.0000 0.9721 1.000 0.000
#> GSM1299553 1 0.0000 0.9721 1.000 0.000
#> GSM1299554 2 0.0000 0.9939 0.000 1.000
#> GSM1299555 2 0.0000 0.9939 0.000 1.000
#> GSM1299556 2 0.0000 0.9939 0.000 1.000
#> GSM1299557 2 0.0000 0.9939 0.000 1.000
#> GSM1299558 2 0.0000 0.9939 0.000 1.000
#> GSM1299559 2 0.0376 0.9900 0.004 0.996
#> GSM1299560 2 0.0000 0.9939 0.000 1.000
#> GSM1299576 1 0.0000 0.9721 1.000 0.000
#> GSM1299577 1 0.0000 0.9721 1.000 0.000
#> GSM1299561 2 0.0000 0.9939 0.000 1.000
#> GSM1299562 2 0.0000 0.9939 0.000 1.000
#> GSM1299563 1 0.0000 0.9721 1.000 0.000
#> GSM1299564 1 0.0000 0.9721 1.000 0.000
#> GSM1299565 2 0.0000 0.9939 0.000 1.000
#> GSM1299566 2 0.0000 0.9939 0.000 1.000
#> GSM1299567 1 0.0000 0.9721 1.000 0.000
#> GSM1299568 2 0.0000 0.9939 0.000 1.000
#> GSM1299569 2 0.0000 0.9939 0.000 1.000
#> GSM1299570 1 0.0000 0.9721 1.000 0.000
#> GSM1299571 2 0.0000 0.9939 0.000 1.000
#> GSM1299572 1 0.0000 0.9721 1.000 0.000
#> GSM1299573 2 0.0000 0.9939 0.000 1.000
#> GSM1299574 2 0.0000 0.9939 0.000 1.000
#> GSM1299578 1 0.0000 0.9721 1.000 0.000
#> GSM1299579 1 0.0000 0.9721 1.000 0.000
#> GSM1299580 1 0.0000 0.9721 1.000 0.000
#> GSM1299581 1 0.0000 0.9721 1.000 0.000
#> GSM1299582 1 0.0000 0.9721 1.000 0.000
#> GSM1299583 1 0.0000 0.9721 1.000 0.000
#> GSM1299584 1 0.0000 0.9721 1.000 0.000
#> GSM1299585 1 0.0000 0.9721 1.000 0.000
#> GSM1299586 1 0.0000 0.9721 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1299517 3 0.5098 0.8456 0.000 0.248 0.752
#> GSM1299518 2 0.6111 0.0653 0.000 0.604 0.396
#> GSM1299519 2 0.1964 0.7658 0.000 0.944 0.056
#> GSM1299520 1 0.3267 0.8834 0.884 0.000 0.116
#> GSM1299521 1 0.4291 0.8625 0.820 0.000 0.180
#> GSM1299522 2 0.2066 0.7651 0.000 0.940 0.060
#> GSM1299523 1 0.3816 0.8717 0.852 0.000 0.148
#> GSM1299524 3 0.3412 0.7356 0.000 0.124 0.876
#> GSM1299525 2 0.1964 0.7265 0.000 0.944 0.056
#> GSM1299526 2 0.2066 0.7651 0.000 0.940 0.060
#> GSM1299527 3 0.5058 0.8488 0.000 0.244 0.756
#> GSM1299528 2 0.4931 0.5291 0.000 0.768 0.232
#> GSM1299529 2 0.1753 0.7319 0.000 0.952 0.048
#> GSM1299530 1 0.4062 0.8743 0.836 0.000 0.164
#> GSM1299531 2 0.1964 0.7641 0.000 0.944 0.056
#> GSM1299575 1 0.0000 0.8993 1.000 0.000 0.000
#> GSM1299532 3 0.5058 0.8488 0.000 0.244 0.756
#> GSM1299533 2 0.9736 0.1307 0.324 0.436 0.240
#> GSM1299534 3 0.5138 0.8422 0.000 0.252 0.748
#> GSM1299535 2 0.2165 0.7652 0.000 0.936 0.064
#> GSM1299536 1 0.4555 0.8558 0.800 0.000 0.200
#> GSM1299537 3 0.5016 0.8496 0.000 0.240 0.760
#> GSM1299538 1 0.8239 0.2397 0.532 0.388 0.080
#> GSM1299539 2 0.7644 0.4208 0.296 0.632 0.072
#> GSM1299540 2 0.9947 0.1770 0.328 0.380 0.292
#> GSM1299541 3 0.5016 0.8496 0.000 0.240 0.760
#> GSM1299542 3 0.5058 0.8488 0.000 0.244 0.756
#> GSM1299543 2 0.0424 0.7493 0.000 0.992 0.008
#> GSM1299544 2 0.6026 0.1061 0.000 0.624 0.376
#> GSM1299545 1 0.0592 0.8964 0.988 0.000 0.012
#> GSM1299546 2 0.1964 0.7658 0.000 0.944 0.056
#> GSM1299547 1 0.4399 0.8609 0.812 0.000 0.188
#> GSM1299548 3 0.4887 0.8428 0.000 0.228 0.772
#> GSM1299549 1 0.4452 0.8601 0.808 0.000 0.192
#> GSM1299550 3 0.6827 0.3947 0.192 0.080 0.728
#> GSM1299551 2 0.1163 0.7628 0.000 0.972 0.028
#> GSM1299552 1 0.4452 0.8610 0.808 0.000 0.192
#> GSM1299553 1 0.2743 0.8753 0.928 0.020 0.052
#> GSM1299554 3 0.5178 0.7734 0.000 0.256 0.744
#> GSM1299555 2 0.5497 0.4115 0.000 0.708 0.292
#> GSM1299556 3 0.5244 0.8487 0.004 0.240 0.756
#> GSM1299557 2 0.3941 0.6869 0.000 0.844 0.156
#> GSM1299558 2 0.0237 0.7548 0.000 0.996 0.004
#> GSM1299559 3 0.4504 0.8163 0.000 0.196 0.804
#> GSM1299560 3 0.5327 0.8186 0.000 0.272 0.728
#> GSM1299576 1 0.0000 0.8993 1.000 0.000 0.000
#> GSM1299577 1 0.0237 0.8992 0.996 0.000 0.004
#> GSM1299561 3 0.5016 0.8496 0.000 0.240 0.760
#> GSM1299562 2 0.4750 0.6405 0.000 0.784 0.216
#> GSM1299563 1 0.4654 0.8635 0.792 0.000 0.208
#> GSM1299564 3 0.6513 -0.0948 0.400 0.008 0.592
#> GSM1299565 2 0.2066 0.7651 0.000 0.940 0.060
#> GSM1299566 2 0.5465 0.5051 0.000 0.712 0.288
#> GSM1299567 1 0.6095 0.4047 0.608 0.000 0.392
#> GSM1299568 2 0.4702 0.5939 0.000 0.788 0.212
#> GSM1299569 3 0.6295 0.4379 0.000 0.472 0.528
#> GSM1299570 1 0.2448 0.8846 0.924 0.000 0.076
#> GSM1299571 2 0.2066 0.7651 0.000 0.940 0.060
#> GSM1299572 1 0.4399 0.8609 0.812 0.000 0.188
#> GSM1299573 3 0.5058 0.8488 0.000 0.244 0.756
#> GSM1299574 2 0.2066 0.7651 0.000 0.940 0.060
#> GSM1299578 1 0.0000 0.8993 1.000 0.000 0.000
#> GSM1299579 1 0.1411 0.8961 0.964 0.000 0.036
#> GSM1299580 1 0.0000 0.8993 1.000 0.000 0.000
#> GSM1299581 1 0.0000 0.8993 1.000 0.000 0.000
#> GSM1299582 1 0.0000 0.8993 1.000 0.000 0.000
#> GSM1299583 1 0.1529 0.8954 0.960 0.000 0.040
#> GSM1299584 1 0.0000 0.8993 1.000 0.000 0.000
#> GSM1299585 1 0.4178 0.8643 0.828 0.000 0.172
#> GSM1299586 1 0.0000 0.8993 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1299517 3 0.0376 0.8535 0.000 0.004 0.992 0.004
#> GSM1299518 2 0.5070 0.3351 0.000 0.580 0.416 0.004
#> GSM1299519 2 0.1211 0.8526 0.000 0.960 0.040 0.000
#> GSM1299520 4 0.5110 0.5347 0.296 0.016 0.004 0.684
#> GSM1299521 1 0.0000 0.6038 1.000 0.000 0.000 0.000
#> GSM1299522 2 0.1211 0.8526 0.000 0.960 0.040 0.000
#> GSM1299523 4 0.5217 0.5495 0.244 0.024 0.012 0.720
#> GSM1299524 3 0.2452 0.8033 0.084 0.004 0.908 0.004
#> GSM1299525 2 0.5183 0.4519 0.000 0.584 0.008 0.408
#> GSM1299526 2 0.1211 0.8526 0.000 0.960 0.040 0.000
#> GSM1299527 3 0.0779 0.8514 0.000 0.016 0.980 0.004
#> GSM1299528 3 0.7476 -0.0621 0.000 0.408 0.416 0.176
#> GSM1299529 2 0.3123 0.7453 0.000 0.844 0.000 0.156
#> GSM1299530 4 0.5343 0.5132 0.340 0.016 0.004 0.640
#> GSM1299531 2 0.1489 0.8503 0.000 0.952 0.044 0.004
#> GSM1299575 4 0.5407 -0.2495 0.484 0.012 0.000 0.504
#> GSM1299532 3 0.0188 0.8533 0.000 0.004 0.996 0.000
#> GSM1299533 1 0.4188 0.3125 0.752 0.244 0.000 0.004
#> GSM1299534 3 0.0927 0.8505 0.000 0.008 0.976 0.016
#> GSM1299535 2 0.2500 0.8351 0.000 0.916 0.044 0.040
#> GSM1299536 1 0.1022 0.5781 0.968 0.000 0.000 0.032
#> GSM1299537 3 0.0000 0.8537 0.000 0.000 1.000 0.000
#> GSM1299538 4 0.4695 0.5014 0.076 0.120 0.004 0.800
#> GSM1299539 4 0.5069 0.4909 0.096 0.124 0.004 0.776
#> GSM1299540 4 0.6484 0.3795 0.016 0.232 0.092 0.660
#> GSM1299541 3 0.0000 0.8537 0.000 0.000 1.000 0.000
#> GSM1299542 3 0.0376 0.8533 0.000 0.004 0.992 0.004
#> GSM1299543 2 0.1118 0.8515 0.000 0.964 0.036 0.000
#> GSM1299544 3 0.6764 0.4228 0.000 0.260 0.596 0.144
#> GSM1299545 4 0.5360 -0.1132 0.436 0.012 0.000 0.552
#> GSM1299546 2 0.1211 0.8526 0.000 0.960 0.040 0.000
#> GSM1299547 1 0.0000 0.6038 1.000 0.000 0.000 0.000
#> GSM1299548 3 0.0000 0.8537 0.000 0.000 1.000 0.000
#> GSM1299549 1 0.1492 0.5749 0.956 0.004 0.004 0.036
#> GSM1299550 3 0.7613 0.3959 0.268 0.004 0.504 0.224
#> GSM1299551 2 0.1118 0.8515 0.000 0.964 0.036 0.000
#> GSM1299552 1 0.0592 0.5943 0.984 0.000 0.000 0.016
#> GSM1299553 4 0.2654 0.5034 0.108 0.004 0.000 0.888
#> GSM1299554 3 0.0927 0.8502 0.000 0.008 0.976 0.016
#> GSM1299555 2 0.5608 0.5972 0.000 0.684 0.256 0.060
#> GSM1299556 3 0.0895 0.8467 0.000 0.004 0.976 0.020
#> GSM1299557 2 0.7143 0.3643 0.000 0.484 0.136 0.380
#> GSM1299558 2 0.1576 0.8467 0.000 0.948 0.048 0.004
#> GSM1299559 3 0.3166 0.7570 0.000 0.016 0.868 0.116
#> GSM1299560 3 0.0817 0.8448 0.000 0.024 0.976 0.000
#> GSM1299576 1 0.5407 0.2111 0.504 0.012 0.000 0.484
#> GSM1299577 4 0.5406 -0.2422 0.480 0.012 0.000 0.508
#> GSM1299561 3 0.0188 0.8533 0.000 0.004 0.996 0.000
#> GSM1299562 2 0.3774 0.7714 0.008 0.844 0.128 0.020
#> GSM1299563 4 0.5764 0.4259 0.404 0.024 0.004 0.568
#> GSM1299564 4 0.6074 0.5197 0.164 0.024 0.092 0.720
#> GSM1299565 2 0.1211 0.8526 0.000 0.960 0.040 0.000
#> GSM1299566 3 0.8952 0.0370 0.060 0.316 0.388 0.236
#> GSM1299567 4 0.4719 0.4514 0.016 0.008 0.224 0.752
#> GSM1299568 2 0.7078 0.0401 0.000 0.456 0.420 0.124
#> GSM1299569 3 0.4982 0.6950 0.000 0.092 0.772 0.136
#> GSM1299570 4 0.4809 0.5323 0.252 0.016 0.004 0.728
#> GSM1299571 2 0.1211 0.8526 0.000 0.960 0.040 0.000
#> GSM1299572 1 0.0000 0.6038 1.000 0.000 0.000 0.000
#> GSM1299573 3 0.0524 0.8529 0.000 0.004 0.988 0.008
#> GSM1299574 2 0.1211 0.8526 0.000 0.960 0.040 0.000
#> GSM1299578 1 0.5408 0.2019 0.500 0.012 0.000 0.488
#> GSM1299579 1 0.3625 0.5470 0.828 0.012 0.000 0.160
#> GSM1299580 4 0.5406 -0.2377 0.480 0.012 0.000 0.508
#> GSM1299581 1 0.5407 0.2139 0.504 0.012 0.000 0.484
#> GSM1299582 1 0.5406 0.2221 0.508 0.012 0.000 0.480
#> GSM1299583 1 0.4175 0.5225 0.776 0.012 0.000 0.212
#> GSM1299584 1 0.5392 0.2551 0.528 0.012 0.000 0.460
#> GSM1299585 1 0.0000 0.6038 1.000 0.000 0.000 0.000
#> GSM1299586 1 0.5407 0.2139 0.504 0.012 0.000 0.484
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1299517 3 0.1661 0.8071 0.000 0.000 0.940 0.036 0.024
#> GSM1299518 2 0.4318 0.5656 0.000 0.688 0.292 0.020 0.000
#> GSM1299519 2 0.0000 0.8828 0.000 1.000 0.000 0.000 0.000
#> GSM1299520 4 0.5056 0.6086 0.360 0.000 0.000 0.596 0.044
#> GSM1299521 5 0.3424 0.8066 0.240 0.000 0.000 0.000 0.760
#> GSM1299522 2 0.0000 0.8828 0.000 1.000 0.000 0.000 0.000
#> GSM1299523 4 0.4914 0.6527 0.280 0.000 0.008 0.672 0.040
#> GSM1299524 3 0.3928 0.6964 0.000 0.008 0.788 0.028 0.176
#> GSM1299525 4 0.5386 0.4119 0.000 0.168 0.004 0.680 0.148
#> GSM1299526 2 0.0000 0.8828 0.000 1.000 0.000 0.000 0.000
#> GSM1299527 3 0.1741 0.7975 0.000 0.000 0.936 0.040 0.024
#> GSM1299528 3 0.8049 0.3986 0.000 0.148 0.412 0.284 0.156
#> GSM1299529 2 0.6407 0.1562 0.000 0.448 0.004 0.400 0.148
#> GSM1299530 4 0.5188 0.6193 0.344 0.000 0.000 0.600 0.056
#> GSM1299531 2 0.3171 0.8073 0.000 0.864 0.008 0.044 0.084
#> GSM1299575 1 0.0162 0.7849 0.996 0.000 0.000 0.000 0.004
#> GSM1299532 3 0.0162 0.8170 0.000 0.000 0.996 0.004 0.000
#> GSM1299533 5 0.5027 0.6687 0.112 0.188 0.000 0.000 0.700
#> GSM1299534 3 0.3572 0.7700 0.000 0.008 0.840 0.064 0.088
#> GSM1299535 2 0.1969 0.8623 0.012 0.936 0.008 0.012 0.032
#> GSM1299536 5 0.3427 0.8011 0.192 0.000 0.000 0.012 0.796
#> GSM1299537 3 0.0451 0.8166 0.000 0.000 0.988 0.008 0.004
#> GSM1299538 4 0.3160 0.6357 0.116 0.004 0.000 0.852 0.028
#> GSM1299539 4 0.3195 0.5620 0.040 0.004 0.000 0.856 0.100
#> GSM1299540 1 0.7241 0.0989 0.544 0.196 0.064 0.192 0.004
#> GSM1299541 3 0.0613 0.8174 0.000 0.004 0.984 0.004 0.008
#> GSM1299542 3 0.0854 0.8166 0.000 0.004 0.976 0.012 0.008
#> GSM1299543 2 0.0693 0.8759 0.000 0.980 0.000 0.008 0.012
#> GSM1299544 3 0.7168 0.5281 0.000 0.068 0.528 0.252 0.152
#> GSM1299545 1 0.1965 0.6921 0.904 0.000 0.000 0.096 0.000
#> GSM1299546 2 0.0000 0.8828 0.000 1.000 0.000 0.000 0.000
#> GSM1299547 5 0.3395 0.8087 0.236 0.000 0.000 0.000 0.764
#> GSM1299548 3 0.0324 0.8167 0.000 0.000 0.992 0.004 0.004
#> GSM1299549 5 0.4970 0.7094 0.136 0.000 0.012 0.116 0.736
#> GSM1299550 5 0.6076 0.2189 0.000 0.000 0.196 0.232 0.572
#> GSM1299551 2 0.0000 0.8828 0.000 1.000 0.000 0.000 0.000
#> GSM1299552 5 0.3409 0.7867 0.160 0.000 0.000 0.024 0.816
#> GSM1299553 1 0.6213 -0.2773 0.452 0.000 0.000 0.408 0.140
#> GSM1299554 3 0.2171 0.8020 0.000 0.000 0.912 0.024 0.064
#> GSM1299555 2 0.4159 0.7468 0.024 0.800 0.144 0.028 0.004
#> GSM1299556 3 0.0798 0.8152 0.000 0.000 0.976 0.016 0.008
#> GSM1299557 4 0.6592 0.3337 0.000 0.188 0.056 0.608 0.148
#> GSM1299558 2 0.4730 0.7153 0.000 0.752 0.008 0.112 0.128
#> GSM1299559 3 0.3456 0.6352 0.004 0.000 0.788 0.204 0.004
#> GSM1299560 3 0.1894 0.7860 0.000 0.072 0.920 0.000 0.008
#> GSM1299576 1 0.0324 0.7866 0.992 0.000 0.000 0.004 0.004
#> GSM1299577 1 0.1965 0.6990 0.904 0.000 0.000 0.096 0.000
#> GSM1299561 3 0.0451 0.8174 0.000 0.004 0.988 0.000 0.008
#> GSM1299562 2 0.2818 0.7855 0.000 0.860 0.004 0.128 0.008
#> GSM1299563 4 0.5032 0.6034 0.128 0.000 0.000 0.704 0.168
#> GSM1299564 4 0.5498 0.6469 0.292 0.000 0.028 0.636 0.044
#> GSM1299565 2 0.0000 0.8828 0.000 1.000 0.000 0.000 0.000
#> GSM1299566 3 0.8057 0.3614 0.000 0.132 0.392 0.308 0.168
#> GSM1299567 4 0.5423 0.5137 0.388 0.000 0.064 0.548 0.000
#> GSM1299568 3 0.7876 0.4695 0.000 0.160 0.464 0.232 0.144
#> GSM1299569 3 0.6018 0.6380 0.000 0.028 0.644 0.200 0.128
#> GSM1299570 4 0.5002 0.6038 0.364 0.000 0.000 0.596 0.040
#> GSM1299571 2 0.0000 0.8828 0.000 1.000 0.000 0.000 0.000
#> GSM1299572 5 0.3395 0.8087 0.236 0.000 0.000 0.000 0.764
#> GSM1299573 3 0.0162 0.8179 0.000 0.000 0.996 0.004 0.000
#> GSM1299574 2 0.0162 0.8817 0.000 0.996 0.000 0.000 0.004
#> GSM1299578 1 0.0162 0.7876 0.996 0.000 0.000 0.000 0.004
#> GSM1299579 1 0.4383 -0.1003 0.572 0.000 0.000 0.004 0.424
#> GSM1299580 1 0.0290 0.7814 0.992 0.000 0.000 0.008 0.000
#> GSM1299581 1 0.0324 0.7866 0.992 0.000 0.000 0.004 0.004
#> GSM1299582 1 0.0162 0.7876 0.996 0.000 0.000 0.000 0.004
#> GSM1299583 1 0.4101 0.1932 0.664 0.000 0.000 0.004 0.332
#> GSM1299584 1 0.0162 0.7876 0.996 0.000 0.000 0.000 0.004
#> GSM1299585 5 0.3424 0.8066 0.240 0.000 0.000 0.000 0.760
#> GSM1299586 1 0.0162 0.7876 0.996 0.000 0.000 0.000 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1299517 3 0.5331 0.3612 0.000 0.000 0.528 0.056 0.024 0.392
#> GSM1299518 2 0.4207 0.5999 0.000 0.720 0.232 0.028 0.000 0.020
#> GSM1299519 2 0.0000 0.8516 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299520 4 0.1663 0.9292 0.088 0.000 0.000 0.912 0.000 0.000
#> GSM1299521 5 0.1863 0.8062 0.104 0.000 0.000 0.000 0.896 0.000
#> GSM1299522 2 0.0000 0.8516 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299523 4 0.1556 0.9300 0.080 0.000 0.000 0.920 0.000 0.000
#> GSM1299524 3 0.5425 0.3376 0.000 0.000 0.504 0.000 0.124 0.372
#> GSM1299525 3 0.7886 -0.1029 0.000 0.048 0.388 0.252 0.092 0.220
#> GSM1299526 2 0.0000 0.8516 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299527 3 0.2772 0.3101 0.000 0.000 0.816 0.000 0.004 0.180
#> GSM1299528 6 0.1908 0.7747 0.000 0.028 0.056 0.000 0.000 0.916
#> GSM1299529 3 0.8220 -0.1156 0.000 0.204 0.392 0.104 0.092 0.208
#> GSM1299530 4 0.1866 0.9294 0.084 0.000 0.000 0.908 0.008 0.000
#> GSM1299531 2 0.3151 0.6484 0.000 0.748 0.000 0.000 0.000 0.252
#> GSM1299575 1 0.0260 0.8624 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM1299532 3 0.3833 0.4590 0.000 0.000 0.556 0.000 0.000 0.444
#> GSM1299533 5 0.2633 0.7481 0.020 0.112 0.000 0.000 0.864 0.004
#> GSM1299534 6 0.2762 0.4731 0.000 0.000 0.196 0.000 0.000 0.804
#> GSM1299535 2 0.4900 0.7103 0.000 0.744 0.104 0.084 0.056 0.012
#> GSM1299536 5 0.2070 0.8052 0.092 0.000 0.000 0.000 0.896 0.012
#> GSM1299537 3 0.4045 0.4619 0.000 0.000 0.564 0.000 0.008 0.428
#> GSM1299538 4 0.1789 0.9016 0.032 0.000 0.000 0.924 0.000 0.044
#> GSM1299539 4 0.4628 0.6167 0.000 0.000 0.112 0.684 0.000 0.204
#> GSM1299540 2 0.6768 0.1026 0.236 0.440 0.028 0.284 0.012 0.000
#> GSM1299541 3 0.3966 0.4582 0.000 0.000 0.552 0.000 0.004 0.444
#> GSM1299542 3 0.3862 0.4301 0.000 0.000 0.524 0.000 0.000 0.476
#> GSM1299543 2 0.1327 0.8230 0.000 0.936 0.000 0.000 0.000 0.064
#> GSM1299544 6 0.0508 0.8024 0.000 0.012 0.004 0.000 0.000 0.984
#> GSM1299545 1 0.3714 0.5653 0.720 0.000 0.008 0.264 0.008 0.000
#> GSM1299546 2 0.0000 0.8516 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299547 5 0.1863 0.8062 0.104 0.000 0.000 0.000 0.896 0.000
#> GSM1299548 3 0.3828 0.4609 0.000 0.000 0.560 0.000 0.000 0.440
#> GSM1299549 5 0.5797 0.4097 0.012 0.000 0.380 0.092 0.504 0.012
#> GSM1299550 5 0.4524 0.2079 0.000 0.000 0.024 0.004 0.520 0.452
#> GSM1299551 2 0.0146 0.8510 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM1299552 5 0.2537 0.7261 0.008 0.000 0.024 0.088 0.880 0.000
#> GSM1299553 3 0.7372 -0.1877 0.280 0.000 0.388 0.232 0.092 0.008
#> GSM1299554 3 0.3989 0.4220 0.000 0.000 0.528 0.000 0.004 0.468
#> GSM1299555 2 0.2985 0.7973 0.000 0.868 0.068 0.044 0.012 0.008
#> GSM1299556 3 0.4446 0.4474 0.000 0.000 0.588 0.020 0.008 0.384
#> GSM1299557 3 0.7851 -0.1043 0.000 0.056 0.420 0.204 0.092 0.228
#> GSM1299558 2 0.3869 0.1904 0.000 0.500 0.000 0.000 0.000 0.500
#> GSM1299559 3 0.4964 0.1792 0.000 0.000 0.540 0.404 0.012 0.044
#> GSM1299560 3 0.5479 0.3626 0.000 0.136 0.556 0.000 0.004 0.304
#> GSM1299576 1 0.0000 0.8636 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299577 1 0.3164 0.7011 0.804 0.000 0.008 0.180 0.004 0.004
#> GSM1299561 3 0.3847 0.4519 0.000 0.000 0.544 0.000 0.000 0.456
#> GSM1299562 2 0.2266 0.7975 0.000 0.880 0.000 0.108 0.000 0.012
#> GSM1299563 4 0.2077 0.9214 0.056 0.000 0.008 0.916 0.008 0.012
#> GSM1299564 4 0.1788 0.9300 0.076 0.000 0.004 0.916 0.000 0.004
#> GSM1299565 2 0.0146 0.8507 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM1299566 6 0.3441 0.7029 0.000 0.080 0.048 0.028 0.004 0.840
#> GSM1299567 4 0.2695 0.8713 0.144 0.000 0.004 0.844 0.008 0.000
#> GSM1299568 6 0.1265 0.8055 0.000 0.044 0.008 0.000 0.000 0.948
#> GSM1299569 6 0.1444 0.7377 0.000 0.000 0.072 0.000 0.000 0.928
#> GSM1299570 4 0.1858 0.9259 0.092 0.000 0.000 0.904 0.004 0.000
#> GSM1299571 2 0.0000 0.8516 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299572 5 0.1863 0.8062 0.104 0.000 0.000 0.000 0.896 0.000
#> GSM1299573 3 0.3843 0.4541 0.000 0.000 0.548 0.000 0.000 0.452
#> GSM1299574 2 0.0291 0.8503 0.000 0.992 0.004 0.000 0.004 0.000
#> GSM1299578 1 0.0260 0.8624 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM1299579 1 0.4392 0.0219 0.504 0.000 0.016 0.000 0.476 0.004
#> GSM1299580 1 0.0260 0.8624 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM1299581 1 0.0291 0.8620 0.992 0.000 0.004 0.000 0.000 0.004
#> GSM1299582 1 0.0000 0.8636 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299583 1 0.3738 0.4903 0.680 0.000 0.004 0.000 0.312 0.004
#> GSM1299584 1 0.0291 0.8620 0.992 0.000 0.004 0.000 0.000 0.004
#> GSM1299585 5 0.2006 0.8045 0.104 0.000 0.000 0.000 0.892 0.004
#> GSM1299586 1 0.0000 0.8636 1.000 0.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:NMF 69 0.1124 2
#> SD:NMF 59 0.0864 3
#> SD:NMF 47 0.5332 4
#> SD:NMF 59 0.2447 5
#> SD:NMF 45 0.6343 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "hclust"]
# you can also extract it by
# res = res_list["CV:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 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 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 0.289 0.696 0.826 0.4028 0.552 0.552
#> 3 3 0.302 0.575 0.728 0.3911 0.675 0.482
#> 4 4 0.473 0.576 0.683 0.1730 0.882 0.705
#> 5 5 0.548 0.505 0.698 0.1036 0.740 0.389
#> 6 6 0.662 0.685 0.784 0.0648 0.884 0.618
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
#> GSM1299517 2 0.0938 0.809 0.012 0.988
#> GSM1299518 2 0.4939 0.786 0.108 0.892
#> GSM1299519 2 0.4562 0.783 0.096 0.904
#> GSM1299520 1 0.9944 0.639 0.544 0.456
#> GSM1299521 1 0.8081 0.920 0.752 0.248
#> GSM1299522 2 0.4562 0.783 0.096 0.904
#> GSM1299523 2 0.9922 -0.393 0.448 0.552
#> GSM1299524 2 0.9833 -0.278 0.424 0.576
#> GSM1299525 2 0.8081 0.650 0.248 0.752
#> GSM1299526 2 0.4562 0.783 0.096 0.904
#> GSM1299527 2 0.0938 0.809 0.012 0.988
#> GSM1299528 2 0.0000 0.810 0.000 1.000
#> GSM1299529 2 0.8081 0.650 0.248 0.752
#> GSM1299530 1 0.9933 0.649 0.548 0.452
#> GSM1299531 2 0.0938 0.808 0.012 0.988
#> GSM1299575 1 0.8144 0.921 0.748 0.252
#> GSM1299532 2 0.0938 0.809 0.012 0.988
#> GSM1299533 1 0.8207 0.919 0.744 0.256
#> GSM1299534 2 0.0672 0.809 0.008 0.992
#> GSM1299535 2 0.1184 0.806 0.016 0.984
#> GSM1299536 1 0.9460 0.818 0.636 0.364
#> GSM1299537 2 0.0938 0.809 0.012 0.988
#> GSM1299538 2 0.7453 0.495 0.212 0.788
#> GSM1299539 2 0.8081 0.650 0.248 0.752
#> GSM1299540 2 0.8555 0.336 0.280 0.720
#> GSM1299541 2 0.4562 0.791 0.096 0.904
#> GSM1299542 2 0.0938 0.809 0.012 0.988
#> GSM1299543 2 0.3584 0.794 0.068 0.932
#> GSM1299544 2 0.0000 0.810 0.000 1.000
#> GSM1299545 2 0.9881 -0.326 0.436 0.564
#> GSM1299546 2 0.4562 0.783 0.096 0.904
#> GSM1299547 1 0.8555 0.907 0.720 0.280
#> GSM1299548 2 0.0938 0.809 0.012 0.988
#> GSM1299549 1 0.9286 0.845 0.656 0.344
#> GSM1299550 1 0.9710 0.765 0.600 0.400
#> GSM1299551 2 0.4562 0.783 0.096 0.904
#> GSM1299552 1 0.8555 0.907 0.720 0.280
#> GSM1299553 2 0.8016 0.653 0.244 0.756
#> GSM1299554 2 0.0938 0.809 0.012 0.988
#> GSM1299555 2 0.8207 0.401 0.256 0.744
#> GSM1299556 2 0.0938 0.809 0.012 0.988
#> GSM1299557 2 0.8081 0.650 0.248 0.752
#> GSM1299558 2 0.0000 0.810 0.000 1.000
#> GSM1299559 2 0.0938 0.809 0.012 0.988
#> GSM1299560 2 0.0938 0.809 0.012 0.988
#> GSM1299576 1 0.8081 0.920 0.752 0.248
#> GSM1299577 1 0.9044 0.872 0.680 0.320
#> GSM1299561 2 0.1184 0.807 0.016 0.984
#> GSM1299562 2 0.2423 0.786 0.040 0.960
#> GSM1299563 2 0.9881 -0.347 0.436 0.564
#> GSM1299564 2 0.9909 -0.381 0.444 0.556
#> GSM1299565 2 0.4562 0.783 0.096 0.904
#> GSM1299566 2 0.0000 0.810 0.000 1.000
#> GSM1299567 2 0.9909 -0.363 0.444 0.556
#> GSM1299568 2 0.0672 0.809 0.008 0.992
#> GSM1299569 2 0.0672 0.809 0.008 0.992
#> GSM1299570 1 0.9933 0.649 0.548 0.452
#> GSM1299571 2 0.4562 0.783 0.096 0.904
#> GSM1299572 1 0.8207 0.919 0.744 0.256
#> GSM1299573 2 0.0938 0.809 0.012 0.988
#> GSM1299574 2 0.4562 0.783 0.096 0.904
#> GSM1299578 1 0.8144 0.921 0.748 0.252
#> GSM1299579 1 0.8081 0.920 0.752 0.248
#> GSM1299580 1 0.8144 0.921 0.748 0.252
#> GSM1299581 1 0.8081 0.920 0.752 0.248
#> GSM1299582 1 0.8081 0.920 0.752 0.248
#> GSM1299583 1 0.8081 0.920 0.752 0.248
#> GSM1299584 1 0.8081 0.920 0.752 0.248
#> GSM1299585 1 0.8081 0.920 0.752 0.248
#> GSM1299586 1 0.8144 0.921 0.748 0.252
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1299517 3 0.9087 0.62260 0.188 0.268 0.544
#> GSM1299518 3 0.3670 0.50054 0.020 0.092 0.888
#> GSM1299519 3 0.0592 0.46779 0.000 0.012 0.988
#> GSM1299520 1 0.4702 0.68050 0.788 0.212 0.000
#> GSM1299521 1 0.0000 0.79538 1.000 0.000 0.000
#> GSM1299522 3 0.1529 0.46058 0.000 0.040 0.960
#> GSM1299523 1 0.8045 0.46759 0.624 0.272 0.104
#> GSM1299524 1 0.8009 0.38297 0.624 0.100 0.276
#> GSM1299525 2 0.0424 0.63763 0.000 0.992 0.008
#> GSM1299526 3 0.0000 0.46891 0.000 0.000 1.000
#> GSM1299527 3 0.9087 0.62260 0.188 0.268 0.544
#> GSM1299528 2 0.8307 0.38513 0.176 0.632 0.192
#> GSM1299529 2 0.0237 0.63693 0.000 0.996 0.004
#> GSM1299530 1 0.4654 0.68417 0.792 0.208 0.000
#> GSM1299531 3 0.9234 0.39620 0.160 0.364 0.476
#> GSM1299575 1 0.0237 0.79656 0.996 0.004 0.000
#> GSM1299532 3 0.9087 0.62260 0.188 0.268 0.544
#> GSM1299533 1 0.0424 0.79522 0.992 0.000 0.008
#> GSM1299534 3 0.9303 0.56080 0.184 0.316 0.500
#> GSM1299535 3 0.9045 0.61875 0.192 0.256 0.552
#> GSM1299536 1 0.3618 0.76007 0.884 0.104 0.012
#> GSM1299537 3 0.9087 0.62260 0.188 0.268 0.544
#> GSM1299538 2 0.8618 0.18703 0.388 0.508 0.104
#> GSM1299539 2 0.0237 0.63693 0.000 0.996 0.004
#> GSM1299540 1 0.9485 0.02989 0.484 0.212 0.304
#> GSM1299541 3 0.5375 0.52435 0.056 0.128 0.816
#> GSM1299542 3 0.9061 0.62309 0.188 0.264 0.548
#> GSM1299543 3 0.8339 0.00568 0.080 0.448 0.472
#> GSM1299544 2 0.8350 0.37601 0.176 0.628 0.196
#> GSM1299545 1 0.8246 0.46711 0.632 0.220 0.148
#> GSM1299546 3 0.0592 0.46779 0.000 0.012 0.988
#> GSM1299547 1 0.1482 0.79236 0.968 0.020 0.012
#> GSM1299548 3 0.9112 0.61855 0.188 0.272 0.540
#> GSM1299549 1 0.3499 0.76297 0.900 0.072 0.028
#> GSM1299550 1 0.5695 0.70493 0.804 0.120 0.076
#> GSM1299551 3 0.0592 0.46779 0.000 0.012 0.988
#> GSM1299552 1 0.1453 0.79240 0.968 0.024 0.008
#> GSM1299553 2 0.0000 0.63739 0.000 1.000 0.000
#> GSM1299554 3 0.9073 0.62100 0.184 0.272 0.544
#> GSM1299555 1 0.9676 -0.16616 0.432 0.220 0.348
#> GSM1299556 3 0.9087 0.62260 0.188 0.268 0.544
#> GSM1299557 2 0.0424 0.63763 0.000 0.992 0.008
#> GSM1299558 2 0.9089 0.14186 0.176 0.536 0.288
#> GSM1299559 3 0.9087 0.62260 0.188 0.268 0.544
#> GSM1299560 3 0.9048 0.62319 0.184 0.268 0.548
#> GSM1299576 1 0.0000 0.79538 1.000 0.000 0.000
#> GSM1299577 1 0.4357 0.74116 0.868 0.052 0.080
#> GSM1299561 3 0.8787 0.61717 0.188 0.228 0.584
#> GSM1299562 3 0.9025 0.46636 0.284 0.172 0.544
#> GSM1299563 1 0.8318 0.43108 0.612 0.260 0.128
#> GSM1299564 1 0.8173 0.45812 0.620 0.264 0.116
#> GSM1299565 3 0.1964 0.44501 0.000 0.056 0.944
#> GSM1299566 2 0.8307 0.38513 0.176 0.632 0.192
#> GSM1299567 1 0.8300 0.44817 0.620 0.244 0.136
#> GSM1299568 3 0.9303 0.56080 0.184 0.316 0.500
#> GSM1299569 3 0.9320 0.55413 0.184 0.320 0.496
#> GSM1299570 1 0.4654 0.68417 0.792 0.208 0.000
#> GSM1299571 3 0.0237 0.47108 0.000 0.004 0.996
#> GSM1299572 1 0.0424 0.79522 0.992 0.000 0.008
#> GSM1299573 3 0.9112 0.61855 0.188 0.272 0.540
#> GSM1299574 3 0.0592 0.46779 0.000 0.012 0.988
#> GSM1299578 1 0.0237 0.79656 0.996 0.004 0.000
#> GSM1299579 1 0.0000 0.79538 1.000 0.000 0.000
#> GSM1299580 1 0.0237 0.79656 0.996 0.004 0.000
#> GSM1299581 1 0.0000 0.79538 1.000 0.000 0.000
#> GSM1299582 1 0.0000 0.79538 1.000 0.000 0.000
#> GSM1299583 1 0.0000 0.79538 1.000 0.000 0.000
#> GSM1299584 1 0.0000 0.79538 1.000 0.000 0.000
#> GSM1299585 1 0.0000 0.79538 1.000 0.000 0.000
#> GSM1299586 1 0.0237 0.79656 0.996 0.004 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1299517 3 0.6474 0.5948 0.000 0.076 0.536 0.388
#> GSM1299518 3 0.2924 0.5069 0.000 0.016 0.884 0.100
#> GSM1299519 3 0.0524 0.4811 0.000 0.008 0.988 0.004
#> GSM1299520 4 0.4252 0.4741 0.252 0.004 0.000 0.744
#> GSM1299521 1 0.0000 0.7918 1.000 0.000 0.000 0.000
#> GSM1299522 3 0.1488 0.4725 0.000 0.012 0.956 0.032
#> GSM1299523 4 0.6645 0.6249 0.208 0.028 0.096 0.668
#> GSM1299524 1 0.7616 -0.1175 0.520 0.008 0.268 0.204
#> GSM1299525 2 0.1584 0.9255 0.000 0.952 0.012 0.036
#> GSM1299526 3 0.0336 0.4814 0.000 0.008 0.992 0.000
#> GSM1299527 3 0.6474 0.5948 0.000 0.076 0.536 0.388
#> GSM1299528 4 0.6750 0.2772 0.000 0.208 0.180 0.612
#> GSM1299529 2 0.1452 0.9237 0.000 0.956 0.008 0.036
#> GSM1299530 4 0.4283 0.4688 0.256 0.004 0.000 0.740
#> GSM1299531 3 0.6960 0.3630 0.000 0.112 0.468 0.420
#> GSM1299575 1 0.3444 0.7986 0.816 0.000 0.000 0.184
#> GSM1299532 3 0.6474 0.5948 0.000 0.076 0.536 0.388
#> GSM1299533 1 0.1109 0.7954 0.968 0.000 0.004 0.028
#> GSM1299534 3 0.6595 0.5392 0.000 0.080 0.492 0.428
#> GSM1299535 3 0.6286 0.5881 0.000 0.064 0.552 0.384
#> GSM1299536 1 0.3345 0.7368 0.860 0.012 0.004 0.124
#> GSM1299537 3 0.6474 0.5948 0.000 0.076 0.536 0.388
#> GSM1299538 4 0.4750 0.5071 0.008 0.092 0.096 0.804
#> GSM1299539 2 0.4608 0.6667 0.000 0.692 0.004 0.304
#> GSM1299540 4 0.5911 0.2556 0.032 0.016 0.304 0.648
#> GSM1299541 3 0.4149 0.5249 0.000 0.036 0.812 0.152
#> GSM1299542 3 0.6417 0.5950 0.000 0.072 0.540 0.388
#> GSM1299543 3 0.7441 0.1322 0.000 0.180 0.468 0.352
#> GSM1299544 4 0.6785 0.2710 0.000 0.208 0.184 0.608
#> GSM1299545 4 0.6429 0.5781 0.172 0.008 0.148 0.672
#> GSM1299546 3 0.0524 0.4811 0.000 0.008 0.988 0.004
#> GSM1299547 1 0.1398 0.7872 0.956 0.000 0.004 0.040
#> GSM1299548 3 0.6483 0.5905 0.000 0.076 0.532 0.392
#> GSM1299549 1 0.5757 0.3258 0.652 0.020 0.020 0.308
#> GSM1299550 1 0.5766 0.4965 0.716 0.012 0.068 0.204
#> GSM1299551 3 0.0524 0.4811 0.000 0.008 0.988 0.004
#> GSM1299552 1 0.2847 0.7601 0.896 0.016 0.004 0.084
#> GSM1299553 2 0.1545 0.9243 0.000 0.952 0.008 0.040
#> GSM1299554 3 0.6474 0.5941 0.000 0.076 0.536 0.388
#> GSM1299555 4 0.6025 0.1531 0.032 0.012 0.352 0.604
#> GSM1299556 3 0.6474 0.5948 0.000 0.076 0.536 0.388
#> GSM1299557 2 0.1584 0.9255 0.000 0.952 0.012 0.036
#> GSM1299558 4 0.7271 0.0565 0.000 0.192 0.276 0.532
#> GSM1299559 3 0.6474 0.5948 0.000 0.076 0.536 0.388
#> GSM1299560 3 0.6464 0.5963 0.000 0.076 0.540 0.384
#> GSM1299576 1 0.3400 0.7998 0.820 0.000 0.000 0.180
#> GSM1299577 1 0.6382 0.3980 0.580 0.000 0.080 0.340
#> GSM1299561 3 0.6097 0.5892 0.000 0.056 0.580 0.364
#> GSM1299562 3 0.6384 0.4449 0.004 0.056 0.532 0.408
#> GSM1299563 4 0.7151 0.6100 0.228 0.032 0.116 0.624
#> GSM1299564 4 0.6820 0.6227 0.216 0.028 0.104 0.652
#> GSM1299565 3 0.1888 0.4588 0.000 0.016 0.940 0.044
#> GSM1299566 4 0.6750 0.2772 0.000 0.208 0.180 0.612
#> GSM1299567 4 0.6485 0.5952 0.184 0.012 0.132 0.672
#> GSM1299568 3 0.6591 0.5416 0.000 0.080 0.496 0.424
#> GSM1299569 3 0.6595 0.5358 0.000 0.080 0.492 0.428
#> GSM1299570 4 0.4283 0.4688 0.256 0.004 0.000 0.740
#> GSM1299571 3 0.0188 0.4838 0.000 0.004 0.996 0.000
#> GSM1299572 1 0.1109 0.7954 0.968 0.000 0.004 0.028
#> GSM1299573 3 0.6483 0.5905 0.000 0.076 0.532 0.392
#> GSM1299574 3 0.0524 0.4811 0.000 0.008 0.988 0.004
#> GSM1299578 1 0.3444 0.7986 0.816 0.000 0.000 0.184
#> GSM1299579 1 0.1211 0.8037 0.960 0.000 0.000 0.040
#> GSM1299580 1 0.3444 0.7986 0.816 0.000 0.000 0.184
#> GSM1299581 1 0.3400 0.7998 0.820 0.000 0.000 0.180
#> GSM1299582 1 0.3400 0.7998 0.820 0.000 0.000 0.180
#> GSM1299583 1 0.1211 0.8037 0.960 0.000 0.000 0.040
#> GSM1299584 1 0.3400 0.7998 0.820 0.000 0.000 0.180
#> GSM1299585 1 0.0000 0.7918 1.000 0.000 0.000 0.000
#> GSM1299586 1 0.3444 0.7986 0.816 0.000 0.000 0.184
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1299517 3 0.0000 0.6187 0.000 0.000 1.000 0.000 0.000
#> GSM1299518 2 0.4562 0.7025 0.000 0.500 0.492 0.000 0.008
#> GSM1299519 2 0.3983 0.9505 0.000 0.660 0.340 0.000 0.000
#> GSM1299520 5 0.7770 0.0890 0.360 0.056 0.156 0.016 0.412
#> GSM1299521 5 0.4307 0.1683 0.500 0.000 0.000 0.000 0.500
#> GSM1299522 2 0.4440 0.9271 0.000 0.660 0.324 0.004 0.012
#> GSM1299523 3 0.8461 0.1312 0.300 0.084 0.368 0.024 0.224
#> GSM1299524 3 0.6802 -0.1153 0.172 0.016 0.456 0.000 0.356
#> GSM1299525 4 0.0794 0.9136 0.000 0.000 0.028 0.972 0.000
#> GSM1299526 2 0.3999 0.9455 0.000 0.656 0.344 0.000 0.000
#> GSM1299527 3 0.0000 0.6187 0.000 0.000 1.000 0.000 0.000
#> GSM1299528 3 0.6372 0.4643 0.000 0.292 0.576 0.040 0.092
#> GSM1299529 4 0.0609 0.9108 0.000 0.000 0.020 0.980 0.000
#> GSM1299530 5 0.7723 0.0876 0.364 0.052 0.156 0.016 0.412
#> GSM1299531 3 0.4538 0.5073 0.000 0.180 0.752 0.008 0.060
#> GSM1299575 1 0.0451 0.7508 0.988 0.000 0.008 0.000 0.004
#> GSM1299532 3 0.0000 0.6187 0.000 0.000 1.000 0.000 0.000
#> GSM1299533 5 0.4906 0.2276 0.480 0.000 0.024 0.000 0.496
#> GSM1299534 3 0.1662 0.6166 0.000 0.056 0.936 0.004 0.004
#> GSM1299535 3 0.1026 0.6064 0.004 0.024 0.968 0.000 0.004
#> GSM1299536 5 0.6181 0.2776 0.388 0.032 0.064 0.000 0.516
#> GSM1299537 3 0.0000 0.6187 0.000 0.000 1.000 0.000 0.000
#> GSM1299538 3 0.8676 0.2765 0.100 0.272 0.356 0.028 0.244
#> GSM1299539 4 0.6330 0.6480 0.000 0.236 0.028 0.600 0.136
#> GSM1299540 3 0.7265 0.3445 0.140 0.060 0.548 0.012 0.240
#> GSM1299541 3 0.4392 -0.4206 0.000 0.380 0.612 0.000 0.008
#> GSM1299542 3 0.0290 0.6178 0.000 0.008 0.992 0.000 0.000
#> GSM1299543 3 0.6199 0.2499 0.000 0.384 0.520 0.040 0.056
#> GSM1299544 3 0.6354 0.4691 0.000 0.288 0.580 0.040 0.092
#> GSM1299545 3 0.7897 0.1557 0.300 0.048 0.396 0.012 0.244
#> GSM1299546 2 0.3983 0.9505 0.000 0.660 0.340 0.000 0.000
#> GSM1299547 5 0.5178 0.2374 0.480 0.000 0.040 0.000 0.480
#> GSM1299548 3 0.0162 0.6197 0.000 0.004 0.996 0.000 0.000
#> GSM1299549 5 0.6705 0.2541 0.284 0.008 0.176 0.008 0.524
#> GSM1299550 5 0.7059 0.2709 0.264 0.032 0.208 0.000 0.496
#> GSM1299551 2 0.3983 0.9505 0.000 0.660 0.340 0.000 0.000
#> GSM1299552 5 0.5586 0.2644 0.432 0.000 0.052 0.008 0.508
#> GSM1299553 4 0.0703 0.9127 0.000 0.000 0.024 0.976 0.000
#> GSM1299554 3 0.0404 0.6187 0.000 0.012 0.988 0.000 0.000
#> GSM1299555 3 0.6447 0.4497 0.140 0.056 0.656 0.012 0.136
#> GSM1299556 3 0.0000 0.6187 0.000 0.000 1.000 0.000 0.000
#> GSM1299557 4 0.0794 0.9136 0.000 0.000 0.028 0.972 0.000
#> GSM1299558 3 0.5805 0.4891 0.000 0.272 0.632 0.040 0.056
#> GSM1299559 3 0.0000 0.6187 0.000 0.000 1.000 0.000 0.000
#> GSM1299560 3 0.0162 0.6158 0.000 0.004 0.996 0.000 0.000
#> GSM1299576 1 0.0451 0.7496 0.988 0.000 0.008 0.000 0.004
#> GSM1299577 1 0.4465 0.2569 0.732 0.000 0.212 0.000 0.056
#> GSM1299561 3 0.1571 0.5675 0.000 0.060 0.936 0.000 0.004
#> GSM1299562 3 0.5177 0.2132 0.000 0.132 0.688 0.000 0.180
#> GSM1299563 3 0.7881 0.2259 0.304 0.060 0.448 0.020 0.168
#> GSM1299564 3 0.8249 0.1723 0.296 0.076 0.400 0.020 0.208
#> GSM1299565 2 0.4365 0.9076 0.000 0.676 0.308 0.004 0.012
#> GSM1299566 3 0.6372 0.4643 0.000 0.292 0.576 0.040 0.092
#> GSM1299567 3 0.7740 0.2364 0.284 0.048 0.444 0.012 0.212
#> GSM1299568 3 0.1731 0.6155 0.000 0.060 0.932 0.004 0.004
#> GSM1299569 3 0.1798 0.6152 0.000 0.064 0.928 0.004 0.004
#> GSM1299570 5 0.7723 0.0876 0.364 0.052 0.156 0.016 0.412
#> GSM1299571 2 0.4030 0.9438 0.000 0.648 0.352 0.000 0.000
#> GSM1299572 5 0.4906 0.2276 0.480 0.000 0.024 0.000 0.496
#> GSM1299573 3 0.0162 0.6197 0.000 0.004 0.996 0.000 0.000
#> GSM1299574 2 0.3983 0.9505 0.000 0.660 0.340 0.000 0.000
#> GSM1299578 1 0.0451 0.7508 0.988 0.000 0.008 0.000 0.004
#> GSM1299579 1 0.3661 0.2762 0.724 0.000 0.000 0.000 0.276
#> GSM1299580 1 0.0451 0.7508 0.988 0.000 0.008 0.000 0.004
#> GSM1299581 1 0.0798 0.7399 0.976 0.000 0.008 0.000 0.016
#> GSM1299582 1 0.0290 0.7513 0.992 0.000 0.008 0.000 0.000
#> GSM1299583 1 0.3636 0.2859 0.728 0.000 0.000 0.000 0.272
#> GSM1299584 1 0.0290 0.7513 0.992 0.000 0.008 0.000 0.000
#> GSM1299585 1 0.4307 -0.3069 0.500 0.000 0.000 0.000 0.500
#> GSM1299586 1 0.0451 0.7508 0.988 0.000 0.008 0.000 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1299517 3 0.0000 0.779 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299518 2 0.4253 0.635 0.000 0.524 0.460 0.016 0.000 0.000
#> GSM1299519 2 0.3266 0.945 0.000 0.728 0.272 0.000 0.000 0.000
#> GSM1299520 4 0.3053 0.563 0.168 0.000 0.020 0.812 0.000 0.000
#> GSM1299521 5 0.1477 0.796 0.048 0.004 0.000 0.008 0.940 0.000
#> GSM1299522 2 0.3679 0.923 0.000 0.724 0.260 0.012 0.004 0.000
#> GSM1299523 4 0.5437 0.678 0.108 0.012 0.272 0.604 0.004 0.000
#> GSM1299524 5 0.4563 0.217 0.012 0.016 0.448 0.000 0.524 0.000
#> GSM1299525 6 0.0405 0.906 0.000 0.000 0.008 0.004 0.000 0.988
#> GSM1299526 2 0.3309 0.940 0.000 0.720 0.280 0.000 0.000 0.000
#> GSM1299527 3 0.0000 0.779 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299528 3 0.5800 0.353 0.000 0.264 0.564 0.152 0.020 0.000
#> GSM1299529 6 0.0000 0.904 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1299530 4 0.3088 0.564 0.172 0.000 0.020 0.808 0.000 0.000
#> GSM1299531 3 0.4345 0.615 0.000 0.188 0.732 0.068 0.012 0.000
#> GSM1299575 1 0.0260 0.872 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM1299532 3 0.0000 0.779 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299533 5 0.1391 0.808 0.040 0.000 0.016 0.000 0.944 0.000
#> GSM1299534 3 0.1500 0.758 0.000 0.052 0.936 0.012 0.000 0.000
#> GSM1299535 3 0.1003 0.761 0.000 0.020 0.964 0.016 0.000 0.000
#> GSM1299536 5 0.3737 0.768 0.032 0.032 0.052 0.048 0.836 0.000
#> GSM1299537 3 0.0000 0.779 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299538 4 0.5574 0.481 0.004 0.156 0.256 0.580 0.004 0.000
#> GSM1299539 6 0.5471 0.593 0.000 0.164 0.004 0.224 0.004 0.604
#> GSM1299540 4 0.5285 0.383 0.060 0.016 0.436 0.488 0.000 0.000
#> GSM1299541 3 0.4150 -0.285 0.000 0.392 0.592 0.016 0.000 0.000
#> GSM1299542 3 0.0260 0.778 0.000 0.008 0.992 0.000 0.000 0.000
#> GSM1299543 3 0.5519 0.316 0.000 0.392 0.496 0.104 0.008 0.000
#> GSM1299544 3 0.5783 0.360 0.000 0.260 0.568 0.152 0.020 0.000
#> GSM1299545 4 0.5388 0.662 0.120 0.004 0.280 0.592 0.004 0.000
#> GSM1299546 2 0.3266 0.945 0.000 0.728 0.272 0.000 0.000 0.000
#> GSM1299547 5 0.2144 0.808 0.048 0.004 0.032 0.004 0.912 0.000
#> GSM1299548 3 0.0146 0.779 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM1299549 5 0.5614 0.608 0.032 0.000 0.132 0.180 0.648 0.008
#> GSM1299550 5 0.4945 0.616 0.016 0.032 0.196 0.048 0.708 0.000
#> GSM1299551 2 0.3266 0.945 0.000 0.728 0.272 0.000 0.000 0.000
#> GSM1299552 5 0.2968 0.787 0.040 0.000 0.040 0.036 0.876 0.008
#> GSM1299553 6 0.0146 0.906 0.000 0.000 0.004 0.000 0.000 0.996
#> GSM1299554 3 0.0363 0.778 0.000 0.012 0.988 0.000 0.000 0.000
#> GSM1299555 3 0.5186 -0.215 0.060 0.016 0.556 0.368 0.000 0.000
#> GSM1299556 3 0.0000 0.779 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299557 6 0.0405 0.906 0.000 0.000 0.008 0.004 0.000 0.988
#> GSM1299558 3 0.5208 0.462 0.000 0.248 0.624 0.120 0.008 0.000
#> GSM1299559 3 0.0000 0.779 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299560 3 0.0146 0.776 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM1299576 1 0.0000 0.871 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299577 1 0.3954 0.419 0.740 0.000 0.204 0.056 0.000 0.000
#> GSM1299561 3 0.1625 0.725 0.000 0.060 0.928 0.012 0.000 0.000
#> GSM1299562 3 0.5483 0.242 0.000 0.132 0.640 0.196 0.032 0.000
#> GSM1299563 4 0.5993 0.540 0.136 0.008 0.392 0.456 0.008 0.000
#> GSM1299564 4 0.5723 0.644 0.120 0.012 0.320 0.544 0.004 0.000
#> GSM1299565 2 0.3697 0.907 0.000 0.732 0.248 0.016 0.004 0.000
#> GSM1299566 3 0.5800 0.353 0.000 0.264 0.564 0.152 0.020 0.000
#> GSM1299567 4 0.5304 0.646 0.104 0.004 0.336 0.556 0.000 0.000
#> GSM1299568 3 0.1563 0.758 0.000 0.056 0.932 0.012 0.000 0.000
#> GSM1299569 3 0.1625 0.755 0.000 0.060 0.928 0.012 0.000 0.000
#> GSM1299570 4 0.3088 0.564 0.172 0.000 0.020 0.808 0.000 0.000
#> GSM1299571 2 0.3351 0.937 0.000 0.712 0.288 0.000 0.000 0.000
#> GSM1299572 5 0.1391 0.808 0.040 0.000 0.016 0.000 0.944 0.000
#> GSM1299573 3 0.0146 0.779 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM1299574 2 0.3266 0.945 0.000 0.728 0.272 0.000 0.000 0.000
#> GSM1299578 1 0.0260 0.872 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM1299579 1 0.3789 0.466 0.668 0.004 0.000 0.004 0.324 0.000
#> GSM1299580 1 0.0260 0.872 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM1299581 1 0.0363 0.865 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM1299582 1 0.0146 0.872 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM1299583 1 0.3756 0.482 0.676 0.004 0.000 0.004 0.316 0.000
#> GSM1299584 1 0.0146 0.872 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM1299585 5 0.1477 0.796 0.048 0.004 0.000 0.008 0.940 0.000
#> GSM1299586 1 0.0260 0.872 0.992 0.000 0.000 0.008 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:hclust 61 0.1500 2
#> CV:hclust 46 0.1528 3
#> CV:hclust 46 0.1465 4
#> CV:hclust 39 0.0424 5
#> CV:hclust 56 0.0517 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "kmeans"]
# you can also extract it by
# res = res_list["CV:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 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 0.828 0.890 0.932 0.4439 0.543 0.543
#> 3 3 0.462 0.456 0.754 0.3508 0.801 0.674
#> 4 4 0.433 0.393 0.628 0.1318 0.725 0.478
#> 5 5 0.593 0.716 0.801 0.1058 0.864 0.598
#> 6 6 0.788 0.757 0.818 0.0582 0.946 0.784
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
#> GSM1299517 2 0.1633 0.950 0.024 0.976
#> GSM1299518 2 0.0000 0.943 0.000 1.000
#> GSM1299519 2 0.1633 0.928 0.024 0.976
#> GSM1299520 1 0.8861 0.570 0.696 0.304
#> GSM1299521 1 0.2948 0.935 0.948 0.052
#> GSM1299522 2 0.0000 0.943 0.000 1.000
#> GSM1299523 2 0.9686 0.388 0.396 0.604
#> GSM1299524 2 0.1633 0.950 0.024 0.976
#> GSM1299525 2 0.3114 0.910 0.056 0.944
#> GSM1299526 2 0.0000 0.943 0.000 1.000
#> GSM1299527 2 0.1414 0.949 0.020 0.980
#> GSM1299528 2 0.1633 0.950 0.024 0.976
#> GSM1299529 2 0.2948 0.907 0.052 0.948
#> GSM1299530 1 0.1184 0.904 0.984 0.016
#> GSM1299531 2 0.1633 0.950 0.024 0.976
#> GSM1299575 1 0.2948 0.935 0.948 0.052
#> GSM1299532 2 0.1633 0.950 0.024 0.976
#> GSM1299533 1 0.7056 0.793 0.808 0.192
#> GSM1299534 2 0.1633 0.950 0.024 0.976
#> GSM1299535 2 0.1633 0.950 0.024 0.976
#> GSM1299536 1 0.2948 0.935 0.948 0.052
#> GSM1299537 2 0.1633 0.950 0.024 0.976
#> GSM1299538 2 0.4022 0.907 0.080 0.920
#> GSM1299539 2 0.4939 0.884 0.108 0.892
#> GSM1299540 2 0.2236 0.942 0.036 0.964
#> GSM1299541 2 0.1633 0.950 0.024 0.976
#> GSM1299542 2 0.1633 0.950 0.024 0.976
#> GSM1299543 2 0.0000 0.943 0.000 1.000
#> GSM1299544 2 0.1633 0.950 0.024 0.976
#> GSM1299545 1 0.2948 0.925 0.948 0.052
#> GSM1299546 2 0.0000 0.943 0.000 1.000
#> GSM1299547 1 0.2948 0.935 0.948 0.052
#> GSM1299548 2 0.1633 0.950 0.024 0.976
#> GSM1299549 1 0.9087 0.520 0.676 0.324
#> GSM1299550 2 0.1633 0.950 0.024 0.976
#> GSM1299551 2 0.1633 0.928 0.024 0.976
#> GSM1299552 1 0.0938 0.906 0.988 0.012
#> GSM1299553 2 0.9358 0.501 0.352 0.648
#> GSM1299554 2 0.1633 0.950 0.024 0.976
#> GSM1299555 2 0.1633 0.950 0.024 0.976
#> GSM1299556 2 0.1633 0.950 0.024 0.976
#> GSM1299557 2 0.3114 0.910 0.056 0.944
#> GSM1299558 2 0.1633 0.950 0.024 0.976
#> GSM1299559 2 0.1633 0.950 0.024 0.976
#> GSM1299560 2 0.1633 0.950 0.024 0.976
#> GSM1299576 1 0.2948 0.935 0.948 0.052
#> GSM1299577 1 0.3114 0.932 0.944 0.056
#> GSM1299561 2 0.1633 0.950 0.024 0.976
#> GSM1299562 2 0.3274 0.926 0.060 0.940
#> GSM1299563 1 0.9775 0.372 0.588 0.412
#> GSM1299564 2 0.8909 0.545 0.308 0.692
#> GSM1299565 2 0.0000 0.943 0.000 1.000
#> GSM1299566 2 0.1633 0.950 0.024 0.976
#> GSM1299567 2 0.9000 0.534 0.316 0.684
#> GSM1299568 2 0.1414 0.949 0.020 0.980
#> GSM1299569 2 0.1633 0.950 0.024 0.976
#> GSM1299570 1 0.4939 0.855 0.892 0.108
#> GSM1299571 2 0.0000 0.943 0.000 1.000
#> GSM1299572 1 0.2948 0.935 0.948 0.052
#> GSM1299573 2 0.1633 0.950 0.024 0.976
#> GSM1299574 2 0.0000 0.943 0.000 1.000
#> GSM1299578 1 0.2948 0.935 0.948 0.052
#> GSM1299579 1 0.2948 0.935 0.948 0.052
#> GSM1299580 1 0.2948 0.935 0.948 0.052
#> GSM1299581 1 0.2948 0.935 0.948 0.052
#> GSM1299582 1 0.2948 0.935 0.948 0.052
#> GSM1299583 1 0.2948 0.935 0.948 0.052
#> GSM1299584 1 0.2948 0.935 0.948 0.052
#> GSM1299585 1 0.2948 0.935 0.948 0.052
#> GSM1299586 1 0.2948 0.935 0.948 0.052
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1299517 3 0.0829 0.59404 0.004 0.012 0.984
#> GSM1299518 3 0.4931 0.19038 0.000 0.232 0.768
#> GSM1299519 2 0.6307 0.41639 0.000 0.512 0.488
#> GSM1299520 3 0.9724 0.00583 0.236 0.328 0.436
#> GSM1299521 1 0.4861 0.82430 0.800 0.192 0.008
#> GSM1299522 3 0.6192 -0.29431 0.000 0.420 0.580
#> GSM1299523 3 0.8841 0.12789 0.136 0.328 0.536
#> GSM1299524 3 0.3573 0.52018 0.004 0.120 0.876
#> GSM1299525 2 0.6489 0.44391 0.004 0.540 0.456
#> GSM1299526 3 0.6192 -0.29431 0.000 0.420 0.580
#> GSM1299527 3 0.0829 0.59404 0.004 0.012 0.984
#> GSM1299528 3 0.3784 0.52380 0.004 0.132 0.864
#> GSM1299529 2 0.5982 0.54870 0.004 0.668 0.328
#> GSM1299530 1 0.7492 0.60165 0.608 0.340 0.052
#> GSM1299531 3 0.2711 0.53475 0.000 0.088 0.912
#> GSM1299575 1 0.1711 0.85489 0.960 0.032 0.008
#> GSM1299532 3 0.0475 0.59607 0.004 0.004 0.992
#> GSM1299533 1 0.7960 0.73662 0.648 0.232 0.120
#> GSM1299534 3 0.1765 0.58058 0.004 0.040 0.956
#> GSM1299535 3 0.0829 0.59404 0.004 0.012 0.984
#> GSM1299536 1 0.7831 0.74481 0.632 0.280 0.088
#> GSM1299537 3 0.0983 0.59691 0.004 0.016 0.980
#> GSM1299538 3 0.8068 0.18820 0.088 0.316 0.596
#> GSM1299539 2 0.6984 0.43884 0.040 0.656 0.304
#> GSM1299540 3 0.5526 0.41537 0.036 0.172 0.792
#> GSM1299541 3 0.0424 0.59637 0.000 0.008 0.992
#> GSM1299542 3 0.0237 0.59713 0.004 0.000 0.996
#> GSM1299543 3 0.6235 -0.34285 0.000 0.436 0.564
#> GSM1299544 3 0.2682 0.55012 0.004 0.076 0.920
#> GSM1299545 1 0.7660 0.58535 0.612 0.324 0.064
#> GSM1299546 3 0.6274 -0.38826 0.000 0.456 0.544
#> GSM1299547 1 0.6025 0.81501 0.740 0.232 0.028
#> GSM1299548 3 0.0829 0.59705 0.004 0.012 0.984
#> GSM1299549 3 0.8622 0.13664 0.132 0.296 0.572
#> GSM1299550 3 0.4978 0.42271 0.004 0.216 0.780
#> GSM1299551 2 0.6307 0.41639 0.000 0.512 0.488
#> GSM1299552 1 0.5692 0.80888 0.724 0.268 0.008
#> GSM1299553 2 0.8817 0.31133 0.160 0.568 0.272
#> GSM1299554 3 0.0983 0.59684 0.004 0.016 0.980
#> GSM1299555 3 0.0983 0.59691 0.004 0.016 0.980
#> GSM1299556 3 0.0983 0.59691 0.004 0.016 0.980
#> GSM1299557 3 0.6513 -0.42530 0.004 0.476 0.520
#> GSM1299558 3 0.4121 0.41368 0.000 0.168 0.832
#> GSM1299559 3 0.1647 0.58822 0.004 0.036 0.960
#> GSM1299560 3 0.0424 0.59429 0.000 0.008 0.992
#> GSM1299576 1 0.0661 0.86180 0.988 0.004 0.008
#> GSM1299577 1 0.6679 0.73106 0.748 0.152 0.100
#> GSM1299561 3 0.0661 0.59774 0.004 0.008 0.988
#> GSM1299562 3 0.3784 0.49131 0.004 0.132 0.864
#> GSM1299563 3 0.9601 0.03804 0.224 0.312 0.464
#> GSM1299564 3 0.8592 0.15185 0.116 0.332 0.552
#> GSM1299565 3 0.6192 -0.29431 0.000 0.420 0.580
#> GSM1299566 3 0.3983 0.51709 0.004 0.144 0.852
#> GSM1299567 3 0.8462 0.18128 0.124 0.288 0.588
#> GSM1299568 3 0.2625 0.53853 0.000 0.084 0.916
#> GSM1299569 3 0.1765 0.58058 0.004 0.040 0.956
#> GSM1299570 3 0.9937 -0.05076 0.288 0.328 0.384
#> GSM1299571 3 0.6192 -0.29431 0.000 0.420 0.580
#> GSM1299572 1 0.6025 0.81501 0.740 0.232 0.028
#> GSM1299573 3 0.0661 0.59774 0.004 0.008 0.988
#> GSM1299574 3 0.6291 -0.41904 0.000 0.468 0.532
#> GSM1299578 1 0.1711 0.85489 0.960 0.032 0.008
#> GSM1299579 1 0.1015 0.86157 0.980 0.012 0.008
#> GSM1299580 1 0.1711 0.85489 0.960 0.032 0.008
#> GSM1299581 1 0.0661 0.86180 0.988 0.004 0.008
#> GSM1299582 1 0.0661 0.86180 0.988 0.004 0.008
#> GSM1299583 1 0.2280 0.85095 0.940 0.052 0.008
#> GSM1299584 1 0.0424 0.86151 0.992 0.000 0.008
#> GSM1299585 1 0.4861 0.82430 0.800 0.192 0.008
#> GSM1299586 1 0.0661 0.86180 0.988 0.004 0.008
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1299517 3 0.0000 0.7836 0.000 0.000 1.000 0.000
#> GSM1299518 3 0.7250 0.0561 0.000 0.316 0.516 0.168
#> GSM1299519 2 0.7517 0.1471 0.000 0.484 0.212 0.304
#> GSM1299520 4 0.8600 0.5116 0.144 0.072 0.328 0.456
#> GSM1299521 1 0.1211 0.6785 0.960 0.040 0.000 0.000
#> GSM1299522 2 0.7693 0.2033 0.000 0.424 0.352 0.224
#> GSM1299523 4 0.8264 0.4652 0.100 0.072 0.372 0.456
#> GSM1299524 3 0.3903 0.6432 0.156 0.008 0.824 0.012
#> GSM1299525 4 0.6897 0.3239 0.000 0.180 0.228 0.592
#> GSM1299526 2 0.7693 0.2033 0.000 0.424 0.352 0.224
#> GSM1299527 3 0.0000 0.7836 0.000 0.000 1.000 0.000
#> GSM1299528 3 0.3923 0.6990 0.008 0.016 0.828 0.148
#> GSM1299529 4 0.6639 0.0388 0.000 0.284 0.120 0.596
#> GSM1299530 4 0.8943 0.3344 0.288 0.108 0.148 0.456
#> GSM1299531 3 0.2774 0.7514 0.008 0.024 0.908 0.060
#> GSM1299575 2 0.6137 -0.2599 0.448 0.504 0.000 0.048
#> GSM1299532 3 0.0000 0.7836 0.000 0.000 1.000 0.000
#> GSM1299533 1 0.3533 0.6326 0.864 0.008 0.104 0.024
#> GSM1299534 3 0.1677 0.7671 0.000 0.012 0.948 0.040
#> GSM1299535 3 0.0000 0.7836 0.000 0.000 1.000 0.000
#> GSM1299536 1 0.3928 0.6262 0.852 0.008 0.084 0.056
#> GSM1299537 3 0.0188 0.7825 0.000 0.000 0.996 0.004
#> GSM1299538 4 0.7057 0.3458 0.040 0.044 0.420 0.496
#> GSM1299539 4 0.4409 0.4682 0.008 0.068 0.100 0.824
#> GSM1299540 3 0.5214 0.3652 0.008 0.024 0.708 0.260
#> GSM1299541 3 0.0000 0.7836 0.000 0.000 1.000 0.000
#> GSM1299542 3 0.0000 0.7836 0.000 0.000 1.000 0.000
#> GSM1299543 3 0.7887 -0.1287 0.000 0.332 0.376 0.292
#> GSM1299544 3 0.3190 0.7354 0.008 0.016 0.880 0.096
#> GSM1299545 4 0.9040 0.3148 0.280 0.124 0.144 0.452
#> GSM1299546 2 0.7756 0.2047 0.000 0.428 0.320 0.252
#> GSM1299547 1 0.1520 0.7010 0.956 0.000 0.024 0.020
#> GSM1299548 3 0.0188 0.7825 0.000 0.000 0.996 0.004
#> GSM1299549 3 0.7665 -0.1817 0.240 0.004 0.496 0.260
#> GSM1299550 3 0.6345 0.3972 0.244 0.012 0.660 0.084
#> GSM1299551 2 0.7366 0.1167 0.000 0.484 0.172 0.344
#> GSM1299552 1 0.2048 0.6843 0.928 0.008 0.000 0.064
#> GSM1299553 4 0.5592 0.4865 0.016 0.092 0.140 0.752
#> GSM1299554 3 0.0336 0.7819 0.000 0.008 0.992 0.000
#> GSM1299555 3 0.0336 0.7808 0.000 0.000 0.992 0.008
#> GSM1299556 3 0.0188 0.7825 0.000 0.000 0.996 0.004
#> GSM1299557 4 0.6955 0.3453 0.000 0.144 0.296 0.560
#> GSM1299558 3 0.5041 0.6449 0.008 0.092 0.784 0.116
#> GSM1299559 3 0.1824 0.7360 0.004 0.000 0.936 0.060
#> GSM1299560 3 0.0000 0.7836 0.000 0.000 1.000 0.000
#> GSM1299576 2 0.5776 -0.2683 0.468 0.504 0.000 0.028
#> GSM1299577 1 0.9896 -0.0401 0.284 0.272 0.180 0.264
#> GSM1299561 3 0.0000 0.7836 0.000 0.000 1.000 0.000
#> GSM1299562 3 0.4988 0.4264 0.036 0.000 0.728 0.236
#> GSM1299563 4 0.8491 0.4252 0.140 0.060 0.396 0.404
#> GSM1299564 3 0.7657 -0.3252 0.076 0.048 0.476 0.400
#> GSM1299565 2 0.7706 0.2026 0.000 0.424 0.348 0.228
#> GSM1299566 3 0.4148 0.6880 0.012 0.016 0.816 0.156
#> GSM1299567 3 0.7192 -0.2736 0.032 0.064 0.508 0.396
#> GSM1299568 3 0.2796 0.7415 0.000 0.016 0.892 0.092
#> GSM1299569 3 0.2781 0.7497 0.008 0.016 0.904 0.072
#> GSM1299570 4 0.8997 0.5161 0.168 0.104 0.272 0.456
#> GSM1299571 2 0.7693 0.2033 0.000 0.424 0.352 0.224
#> GSM1299572 1 0.1610 0.7001 0.952 0.000 0.032 0.016
#> GSM1299573 3 0.0000 0.7836 0.000 0.000 1.000 0.000
#> GSM1299574 2 0.7738 0.2020 0.000 0.436 0.312 0.252
#> GSM1299578 2 0.6071 -0.2603 0.452 0.504 0.000 0.044
#> GSM1299579 1 0.5781 0.1819 0.492 0.480 0.000 0.028
#> GSM1299580 2 0.6137 -0.2599 0.448 0.504 0.000 0.048
#> GSM1299581 2 0.5858 -0.2684 0.468 0.500 0.000 0.032
#> GSM1299582 2 0.5933 -0.2647 0.464 0.500 0.000 0.036
#> GSM1299583 1 0.5281 0.2410 0.528 0.464 0.000 0.008
#> GSM1299584 2 0.5858 -0.2684 0.468 0.500 0.000 0.032
#> GSM1299585 1 0.1211 0.6785 0.960 0.040 0.000 0.000
#> GSM1299586 2 0.5856 -0.2645 0.464 0.504 0.000 0.032
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1299517 3 0.0162 0.8256 0.000 0.000 0.996 0.004 0.000
#> GSM1299518 2 0.4192 0.5564 0.000 0.596 0.404 0.000 0.000
#> GSM1299519 2 0.1341 0.7529 0.000 0.944 0.056 0.000 0.000
#> GSM1299520 4 0.5305 0.6864 0.076 0.004 0.132 0.740 0.048
#> GSM1299521 5 0.3980 0.8560 0.284 0.008 0.000 0.000 0.708
#> GSM1299522 2 0.3010 0.8323 0.000 0.824 0.172 0.000 0.004
#> GSM1299523 4 0.5065 0.6920 0.068 0.000 0.156 0.740 0.036
#> GSM1299524 3 0.2536 0.7676 0.000 0.004 0.868 0.000 0.128
#> GSM1299525 4 0.7147 0.0796 0.000 0.348 0.036 0.444 0.172
#> GSM1299526 2 0.3010 0.8323 0.000 0.824 0.172 0.000 0.004
#> GSM1299527 3 0.0162 0.8256 0.000 0.000 0.996 0.004 0.000
#> GSM1299528 3 0.5934 0.6750 0.000 0.072 0.688 0.128 0.112
#> GSM1299529 2 0.6408 0.3020 0.000 0.568 0.016 0.252 0.164
#> GSM1299530 4 0.5520 0.6653 0.100 0.004 0.096 0.732 0.068
#> GSM1299531 3 0.4928 0.7291 0.000 0.064 0.768 0.072 0.096
#> GSM1299575 1 0.0771 0.9592 0.976 0.000 0.000 0.020 0.004
#> GSM1299532 3 0.0000 0.8266 0.000 0.000 1.000 0.000 0.000
#> GSM1299533 5 0.5078 0.8615 0.144 0.000 0.072 0.040 0.744
#> GSM1299534 3 0.4329 0.7507 0.000 0.048 0.808 0.068 0.076
#> GSM1299535 3 0.0000 0.8266 0.000 0.000 1.000 0.000 0.000
#> GSM1299536 5 0.4729 0.8623 0.140 0.000 0.044 0.048 0.768
#> GSM1299537 3 0.0000 0.8266 0.000 0.000 1.000 0.000 0.000
#> GSM1299538 4 0.3798 0.6791 0.024 0.000 0.160 0.804 0.012
#> GSM1299539 4 0.5648 0.3867 0.000 0.152 0.004 0.648 0.196
#> GSM1299540 3 0.4972 -0.2848 0.020 0.004 0.500 0.476 0.000
#> GSM1299541 3 0.0000 0.8266 0.000 0.000 1.000 0.000 0.000
#> GSM1299542 3 0.0000 0.8266 0.000 0.000 1.000 0.000 0.000
#> GSM1299543 2 0.6490 0.5016 0.000 0.572 0.292 0.068 0.068
#> GSM1299544 3 0.5403 0.7099 0.000 0.064 0.732 0.096 0.108
#> GSM1299545 4 0.5475 0.6551 0.136 0.000 0.092 0.720 0.052
#> GSM1299546 2 0.2732 0.8320 0.000 0.840 0.160 0.000 0.000
#> GSM1299547 5 0.4923 0.9085 0.212 0.000 0.024 0.044 0.720
#> GSM1299548 3 0.0000 0.8266 0.000 0.000 1.000 0.000 0.000
#> GSM1299549 4 0.6771 0.4903 0.016 0.004 0.324 0.500 0.156
#> GSM1299550 3 0.6019 0.5467 0.000 0.012 0.608 0.132 0.248
#> GSM1299551 2 0.0955 0.7284 0.000 0.968 0.028 0.004 0.000
#> GSM1299552 5 0.4772 0.8894 0.208 0.004 0.000 0.068 0.720
#> GSM1299553 4 0.6814 0.4413 0.028 0.160 0.028 0.612 0.172
#> GSM1299554 3 0.0486 0.8243 0.000 0.004 0.988 0.004 0.004
#> GSM1299555 3 0.0162 0.8243 0.000 0.000 0.996 0.004 0.000
#> GSM1299556 3 0.0000 0.8266 0.000 0.000 1.000 0.000 0.000
#> GSM1299557 4 0.8079 0.1532 0.000 0.288 0.144 0.404 0.164
#> GSM1299558 3 0.6171 0.6274 0.000 0.140 0.668 0.084 0.108
#> GSM1299559 3 0.2424 0.6883 0.000 0.000 0.868 0.132 0.000
#> GSM1299560 3 0.0000 0.8266 0.000 0.000 1.000 0.000 0.000
#> GSM1299576 1 0.0000 0.9702 1.000 0.000 0.000 0.000 0.000
#> GSM1299577 4 0.6782 0.3494 0.380 0.000 0.164 0.440 0.016
#> GSM1299561 3 0.0000 0.8266 0.000 0.000 1.000 0.000 0.000
#> GSM1299562 3 0.4913 -0.2437 0.000 0.008 0.496 0.484 0.012
#> GSM1299563 4 0.5770 0.6683 0.064 0.000 0.224 0.664 0.048
#> GSM1299564 4 0.4956 0.6603 0.032 0.000 0.248 0.696 0.024
#> GSM1299565 2 0.2930 0.8316 0.000 0.832 0.164 0.000 0.004
#> GSM1299566 3 0.5975 0.6714 0.000 0.072 0.684 0.132 0.112
#> GSM1299567 4 0.5041 0.6028 0.044 0.000 0.316 0.636 0.004
#> GSM1299568 3 0.5136 0.7228 0.000 0.060 0.752 0.084 0.104
#> GSM1299569 3 0.5185 0.7212 0.000 0.060 0.748 0.084 0.108
#> GSM1299570 4 0.5337 0.6825 0.088 0.004 0.120 0.740 0.048
#> GSM1299571 2 0.3010 0.8323 0.000 0.824 0.172 0.000 0.004
#> GSM1299572 5 0.4935 0.9086 0.212 0.000 0.028 0.040 0.720
#> GSM1299573 3 0.0000 0.8266 0.000 0.000 1.000 0.000 0.000
#> GSM1299574 2 0.2690 0.8307 0.000 0.844 0.156 0.000 0.000
#> GSM1299578 1 0.0771 0.9592 0.976 0.000 0.000 0.020 0.004
#> GSM1299579 1 0.1173 0.9544 0.964 0.012 0.000 0.004 0.020
#> GSM1299580 1 0.0771 0.9592 0.976 0.000 0.000 0.020 0.004
#> GSM1299581 1 0.0613 0.9705 0.984 0.008 0.000 0.004 0.004
#> GSM1299582 1 0.0613 0.9705 0.984 0.008 0.000 0.004 0.004
#> GSM1299583 1 0.1605 0.9268 0.944 0.012 0.000 0.004 0.040
#> GSM1299584 1 0.0613 0.9705 0.984 0.008 0.000 0.004 0.004
#> GSM1299585 5 0.3980 0.8560 0.284 0.008 0.000 0.000 0.708
#> GSM1299586 1 0.0162 0.9695 0.996 0.000 0.000 0.000 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1299517 3 0.0291 0.7804 0.000 0.004 0.992 0.000 0.000 0.004
#> GSM1299518 2 0.4411 0.4678 0.000 0.628 0.340 0.012 0.020 0.000
#> GSM1299519 2 0.1965 0.7771 0.000 0.924 0.024 0.004 0.008 0.040
#> GSM1299520 4 0.2544 0.7524 0.028 0.004 0.048 0.896 0.024 0.000
#> GSM1299521 5 0.3693 0.9332 0.128 0.012 0.000 0.032 0.812 0.016
#> GSM1299522 2 0.2102 0.8251 0.000 0.908 0.068 0.012 0.012 0.000
#> GSM1299523 4 0.2323 0.7670 0.012 0.000 0.084 0.892 0.012 0.000
#> GSM1299524 3 0.2923 0.7243 0.000 0.008 0.856 0.004 0.108 0.024
#> GSM1299525 6 0.4404 0.7780 0.000 0.136 0.024 0.088 0.000 0.752
#> GSM1299526 2 0.2252 0.8243 0.000 0.900 0.072 0.016 0.012 0.000
#> GSM1299527 3 0.0291 0.7804 0.000 0.004 0.992 0.000 0.000 0.004
#> GSM1299528 3 0.6793 0.5976 0.000 0.040 0.544 0.064 0.104 0.248
#> GSM1299529 6 0.3852 0.6522 0.000 0.256 0.008 0.016 0.000 0.720
#> GSM1299530 4 0.2489 0.7443 0.028 0.004 0.040 0.900 0.028 0.000
#> GSM1299531 3 0.6506 0.6176 0.000 0.040 0.580 0.052 0.100 0.228
#> GSM1299575 1 0.1931 0.9588 0.928 0.032 0.000 0.016 0.004 0.020
#> GSM1299532 3 0.0146 0.7804 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM1299533 5 0.2693 0.9120 0.052 0.000 0.036 0.028 0.884 0.000
#> GSM1299534 3 0.6157 0.6410 0.000 0.032 0.624 0.060 0.084 0.200
#> GSM1299535 3 0.0146 0.7804 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM1299536 5 0.2466 0.9116 0.052 0.000 0.024 0.028 0.896 0.000
#> GSM1299537 3 0.0551 0.7766 0.000 0.008 0.984 0.000 0.004 0.004
#> GSM1299538 4 0.2711 0.7384 0.000 0.000 0.080 0.876 0.024 0.020
#> GSM1299539 6 0.3843 0.7456 0.000 0.008 0.004 0.232 0.016 0.740
#> GSM1299540 4 0.4408 0.4359 0.000 0.008 0.468 0.512 0.012 0.000
#> GSM1299541 3 0.0508 0.7764 0.000 0.004 0.984 0.000 0.012 0.000
#> GSM1299542 3 0.0000 0.7807 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299543 2 0.7517 0.0543 0.000 0.420 0.316 0.052 0.072 0.140
#> GSM1299544 3 0.6707 0.6069 0.000 0.040 0.556 0.060 0.104 0.240
#> GSM1299545 4 0.2950 0.7587 0.040 0.004 0.060 0.872 0.024 0.000
#> GSM1299546 2 0.1845 0.8272 0.000 0.916 0.072 0.004 0.008 0.000
#> GSM1299547 5 0.3003 0.9468 0.104 0.000 0.016 0.028 0.852 0.000
#> GSM1299548 3 0.0291 0.7792 0.000 0.004 0.992 0.000 0.000 0.004
#> GSM1299549 4 0.5944 0.4863 0.004 0.004 0.328 0.544 0.088 0.032
#> GSM1299550 3 0.6630 0.5777 0.000 0.012 0.544 0.072 0.140 0.232
#> GSM1299551 2 0.1901 0.7605 0.000 0.924 0.012 0.004 0.008 0.052
#> GSM1299552 5 0.3767 0.9351 0.100 0.012 0.000 0.040 0.820 0.028
#> GSM1299553 6 0.4040 0.7306 0.008 0.012 0.004 0.256 0.004 0.716
#> GSM1299554 3 0.0291 0.7806 0.000 0.004 0.992 0.004 0.000 0.000
#> GSM1299555 3 0.1338 0.7467 0.000 0.008 0.952 0.032 0.004 0.004
#> GSM1299556 3 0.0551 0.7766 0.000 0.008 0.984 0.000 0.004 0.004
#> GSM1299557 6 0.4752 0.7136 0.000 0.036 0.156 0.084 0.000 0.724
#> GSM1299558 3 0.6974 0.5815 0.000 0.064 0.536 0.056 0.104 0.240
#> GSM1299559 3 0.3550 0.3834 0.000 0.008 0.752 0.232 0.004 0.004
#> GSM1299560 3 0.0146 0.7804 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM1299576 1 0.1321 0.9656 0.952 0.024 0.000 0.004 0.000 0.020
#> GSM1299577 4 0.5279 0.6272 0.136 0.004 0.176 0.668 0.008 0.008
#> GSM1299561 3 0.0260 0.7794 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM1299562 4 0.5044 0.4558 0.000 0.028 0.428 0.520 0.020 0.004
#> GSM1299563 4 0.3302 0.7494 0.028 0.000 0.136 0.824 0.008 0.004
#> GSM1299564 4 0.2563 0.7687 0.008 0.000 0.108 0.872 0.004 0.008
#> GSM1299565 2 0.1787 0.8272 0.000 0.920 0.068 0.004 0.008 0.000
#> GSM1299566 3 0.6793 0.5976 0.000 0.040 0.544 0.064 0.104 0.248
#> GSM1299567 4 0.3370 0.7309 0.004 0.004 0.188 0.792 0.008 0.004
#> GSM1299568 3 0.6510 0.6186 0.000 0.036 0.580 0.060 0.096 0.228
#> GSM1299569 3 0.6688 0.6101 0.000 0.040 0.560 0.060 0.104 0.236
#> GSM1299570 4 0.2544 0.7524 0.028 0.004 0.048 0.896 0.024 0.000
#> GSM1299571 2 0.1732 0.8284 0.000 0.920 0.072 0.004 0.004 0.000
#> GSM1299572 5 0.3003 0.9468 0.104 0.000 0.016 0.028 0.852 0.000
#> GSM1299573 3 0.0000 0.7807 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299574 2 0.1845 0.8272 0.000 0.916 0.072 0.004 0.008 0.000
#> GSM1299578 1 0.1854 0.9604 0.932 0.028 0.000 0.016 0.004 0.020
#> GSM1299579 1 0.0603 0.9592 0.980 0.000 0.000 0.000 0.004 0.016
#> GSM1299580 1 0.1931 0.9588 0.928 0.032 0.000 0.016 0.004 0.020
#> GSM1299581 1 0.0146 0.9651 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM1299582 1 0.0000 0.9657 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299583 1 0.0603 0.9592 0.980 0.000 0.000 0.000 0.004 0.016
#> GSM1299584 1 0.0146 0.9651 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM1299585 5 0.3693 0.9332 0.128 0.012 0.000 0.032 0.812 0.016
#> GSM1299586 1 0.1659 0.9623 0.940 0.028 0.000 0.008 0.004 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 disease.state(p) k
#> CV:kmeans 68 0.1492 2
#> CV:kmeans 44 0.0987 3
#> CV:kmeans 33 0.5883 4
#> CV:kmeans 61 0.0379 5
#> CV:kmeans 64 0.0666 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "skmeans"]
# you can also extract it by
# res = res_list["CV:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 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 1.000 0.966 0.986 0.4998 0.499 0.499
#> 3 3 0.615 0.735 0.868 0.3285 0.756 0.547
#> 4 4 0.659 0.666 0.809 0.1228 0.825 0.542
#> 5 5 0.696 0.698 0.821 0.0687 0.940 0.769
#> 6 6 0.741 0.628 0.791 0.0465 0.916 0.624
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
#> GSM1299517 2 0.000 0.991 0.000 1.000
#> GSM1299518 2 0.000 0.991 0.000 1.000
#> GSM1299519 2 0.000 0.991 0.000 1.000
#> GSM1299520 1 0.000 0.977 1.000 0.000
#> GSM1299521 1 0.000 0.977 1.000 0.000
#> GSM1299522 2 0.000 0.991 0.000 1.000
#> GSM1299523 1 0.000 0.977 1.000 0.000
#> GSM1299524 2 0.416 0.903 0.084 0.916
#> GSM1299525 2 0.000 0.991 0.000 1.000
#> GSM1299526 2 0.000 0.991 0.000 1.000
#> GSM1299527 2 0.000 0.991 0.000 1.000
#> GSM1299528 2 0.000 0.991 0.000 1.000
#> GSM1299529 2 0.000 0.991 0.000 1.000
#> GSM1299530 1 0.000 0.977 1.000 0.000
#> GSM1299531 2 0.000 0.991 0.000 1.000
#> GSM1299575 1 0.000 0.977 1.000 0.000
#> GSM1299532 2 0.000 0.991 0.000 1.000
#> GSM1299533 1 0.000 0.977 1.000 0.000
#> GSM1299534 2 0.000 0.991 0.000 1.000
#> GSM1299535 2 0.000 0.991 0.000 1.000
#> GSM1299536 1 0.000 0.977 1.000 0.000
#> GSM1299537 2 0.000 0.991 0.000 1.000
#> GSM1299538 1 0.184 0.952 0.972 0.028
#> GSM1299539 1 0.971 0.354 0.600 0.400
#> GSM1299540 2 0.795 0.677 0.240 0.760
#> GSM1299541 2 0.000 0.991 0.000 1.000
#> GSM1299542 2 0.000 0.991 0.000 1.000
#> GSM1299543 2 0.000 0.991 0.000 1.000
#> GSM1299544 2 0.000 0.991 0.000 1.000
#> GSM1299545 1 0.000 0.977 1.000 0.000
#> GSM1299546 2 0.000 0.991 0.000 1.000
#> GSM1299547 1 0.000 0.977 1.000 0.000
#> GSM1299548 2 0.000 0.991 0.000 1.000
#> GSM1299549 1 0.000 0.977 1.000 0.000
#> GSM1299550 1 0.795 0.684 0.760 0.240
#> GSM1299551 2 0.000 0.991 0.000 1.000
#> GSM1299552 1 0.000 0.977 1.000 0.000
#> GSM1299553 1 0.000 0.977 1.000 0.000
#> GSM1299554 2 0.000 0.991 0.000 1.000
#> GSM1299555 2 0.000 0.991 0.000 1.000
#> GSM1299556 2 0.000 0.991 0.000 1.000
#> GSM1299557 2 0.000 0.991 0.000 1.000
#> GSM1299558 2 0.000 0.991 0.000 1.000
#> GSM1299559 2 0.000 0.991 0.000 1.000
#> GSM1299560 2 0.000 0.991 0.000 1.000
#> GSM1299576 1 0.000 0.977 1.000 0.000
#> GSM1299577 1 0.000 0.977 1.000 0.000
#> GSM1299561 2 0.000 0.991 0.000 1.000
#> GSM1299562 2 0.000 0.991 0.000 1.000
#> GSM1299563 1 0.000 0.977 1.000 0.000
#> GSM1299564 1 0.000 0.977 1.000 0.000
#> GSM1299565 2 0.000 0.991 0.000 1.000
#> GSM1299566 2 0.000 0.991 0.000 1.000
#> GSM1299567 1 0.000 0.977 1.000 0.000
#> GSM1299568 2 0.000 0.991 0.000 1.000
#> GSM1299569 2 0.000 0.991 0.000 1.000
#> GSM1299570 1 0.000 0.977 1.000 0.000
#> GSM1299571 2 0.000 0.991 0.000 1.000
#> GSM1299572 1 0.000 0.977 1.000 0.000
#> GSM1299573 2 0.000 0.991 0.000 1.000
#> GSM1299574 2 0.000 0.991 0.000 1.000
#> GSM1299578 1 0.000 0.977 1.000 0.000
#> GSM1299579 1 0.000 0.977 1.000 0.000
#> GSM1299580 1 0.000 0.977 1.000 0.000
#> GSM1299581 1 0.000 0.977 1.000 0.000
#> GSM1299582 1 0.000 0.977 1.000 0.000
#> GSM1299583 1 0.000 0.977 1.000 0.000
#> GSM1299584 1 0.000 0.977 1.000 0.000
#> GSM1299585 1 0.000 0.977 1.000 0.000
#> GSM1299586 1 0.000 0.977 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1299517 3 0.0000 0.7583 0.000 0.000 1.000
#> GSM1299518 2 0.5835 0.5788 0.000 0.660 0.340
#> GSM1299519 2 0.4121 0.7902 0.000 0.832 0.168
#> GSM1299520 1 0.3551 0.8848 0.868 0.132 0.000
#> GSM1299521 1 0.1163 0.9383 0.972 0.028 0.000
#> GSM1299522 2 0.4121 0.7902 0.000 0.832 0.168
#> GSM1299523 1 0.4293 0.8565 0.832 0.164 0.004
#> GSM1299524 3 0.3678 0.6750 0.080 0.028 0.892
#> GSM1299525 2 0.1163 0.7599 0.000 0.972 0.028
#> GSM1299526 2 0.4399 0.7770 0.000 0.812 0.188
#> GSM1299527 3 0.0592 0.7531 0.000 0.012 0.988
#> GSM1299528 3 0.6168 0.3563 0.000 0.412 0.588
#> GSM1299529 2 0.1289 0.7620 0.000 0.968 0.032
#> GSM1299530 1 0.3482 0.8869 0.872 0.128 0.000
#> GSM1299531 3 0.6215 0.2926 0.000 0.428 0.572
#> GSM1299575 1 0.0000 0.9454 1.000 0.000 0.000
#> GSM1299532 3 0.0000 0.7583 0.000 0.000 1.000
#> GSM1299533 1 0.2116 0.9259 0.948 0.040 0.012
#> GSM1299534 3 0.5465 0.5454 0.000 0.288 0.712
#> GSM1299535 3 0.4605 0.5875 0.000 0.204 0.796
#> GSM1299536 1 0.1163 0.9383 0.972 0.028 0.000
#> GSM1299537 3 0.0000 0.7583 0.000 0.000 1.000
#> GSM1299538 2 0.6595 0.5583 0.180 0.744 0.076
#> GSM1299539 2 0.1525 0.7394 0.032 0.964 0.004
#> GSM1299540 2 0.7657 0.0929 0.044 0.508 0.448
#> GSM1299541 3 0.0000 0.7583 0.000 0.000 1.000
#> GSM1299542 3 0.0000 0.7583 0.000 0.000 1.000
#> GSM1299543 2 0.4062 0.7856 0.000 0.836 0.164
#> GSM1299544 3 0.5859 0.4730 0.000 0.344 0.656
#> GSM1299545 1 0.3038 0.9015 0.896 0.104 0.000
#> GSM1299546 2 0.4121 0.7902 0.000 0.832 0.168
#> GSM1299547 1 0.1163 0.9383 0.972 0.028 0.000
#> GSM1299548 3 0.0000 0.7583 0.000 0.000 1.000
#> GSM1299549 1 0.4172 0.8850 0.840 0.156 0.004
#> GSM1299550 3 0.8971 0.3446 0.336 0.144 0.520
#> GSM1299551 2 0.4002 0.7879 0.000 0.840 0.160
#> GSM1299552 1 0.1163 0.9383 0.972 0.028 0.000
#> GSM1299553 2 0.6095 0.1459 0.392 0.608 0.000
#> GSM1299554 3 0.0592 0.7543 0.000 0.012 0.988
#> GSM1299555 3 0.3941 0.6220 0.000 0.156 0.844
#> GSM1299556 3 0.0000 0.7583 0.000 0.000 1.000
#> GSM1299557 2 0.2165 0.7597 0.000 0.936 0.064
#> GSM1299558 3 0.6267 0.2424 0.000 0.452 0.548
#> GSM1299559 3 0.1964 0.7187 0.000 0.056 0.944
#> GSM1299560 3 0.0000 0.7583 0.000 0.000 1.000
#> GSM1299576 1 0.0000 0.9454 1.000 0.000 0.000
#> GSM1299577 1 0.0000 0.9454 1.000 0.000 0.000
#> GSM1299561 3 0.0000 0.7583 0.000 0.000 1.000
#> GSM1299562 2 0.2860 0.7345 0.004 0.912 0.084
#> GSM1299563 1 0.3965 0.8811 0.860 0.132 0.008
#> GSM1299564 1 0.7043 0.7445 0.728 0.136 0.136
#> GSM1299565 2 0.4121 0.7902 0.000 0.832 0.168
#> GSM1299566 3 0.6192 0.3450 0.000 0.420 0.580
#> GSM1299567 3 0.8996 0.1070 0.356 0.140 0.504
#> GSM1299568 3 0.6045 0.4112 0.000 0.380 0.620
#> GSM1299569 3 0.5591 0.5291 0.000 0.304 0.696
#> GSM1299570 1 0.3551 0.8848 0.868 0.132 0.000
#> GSM1299571 2 0.4178 0.7884 0.000 0.828 0.172
#> GSM1299572 1 0.1163 0.9383 0.972 0.028 0.000
#> GSM1299573 3 0.0000 0.7583 0.000 0.000 1.000
#> GSM1299574 2 0.4121 0.7902 0.000 0.832 0.168
#> GSM1299578 1 0.0000 0.9454 1.000 0.000 0.000
#> GSM1299579 1 0.0000 0.9454 1.000 0.000 0.000
#> GSM1299580 1 0.0000 0.9454 1.000 0.000 0.000
#> GSM1299581 1 0.0000 0.9454 1.000 0.000 0.000
#> GSM1299582 1 0.0000 0.9454 1.000 0.000 0.000
#> GSM1299583 1 0.0000 0.9454 1.000 0.000 0.000
#> GSM1299584 1 0.0000 0.9454 1.000 0.000 0.000
#> GSM1299585 1 0.1163 0.9383 0.972 0.028 0.000
#> GSM1299586 1 0.0000 0.9454 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1299517 3 0.0469 0.8348 0.000 0.012 0.988 0.000
#> GSM1299518 2 0.3266 0.7309 0.000 0.832 0.168 0.000
#> GSM1299519 2 0.0921 0.8402 0.000 0.972 0.028 0.000
#> GSM1299520 1 0.2197 0.6102 0.928 0.024 0.000 0.048
#> GSM1299521 4 0.0336 0.8141 0.008 0.000 0.000 0.992
#> GSM1299522 2 0.1118 0.8394 0.000 0.964 0.036 0.000
#> GSM1299523 1 0.2115 0.6083 0.936 0.024 0.004 0.036
#> GSM1299524 4 0.5573 0.2678 0.012 0.008 0.396 0.584
#> GSM1299525 2 0.2654 0.7907 0.108 0.888 0.004 0.000
#> GSM1299526 2 0.1389 0.8356 0.000 0.952 0.048 0.000
#> GSM1299527 3 0.1576 0.8158 0.004 0.048 0.948 0.000
#> GSM1299528 3 0.6969 0.4445 0.112 0.308 0.572 0.008
#> GSM1299529 2 0.2266 0.8026 0.084 0.912 0.004 0.000
#> GSM1299530 1 0.3946 0.5995 0.812 0.020 0.000 0.168
#> GSM1299531 2 0.5721 0.0589 0.020 0.548 0.428 0.004
#> GSM1299575 1 0.5016 0.6469 0.600 0.004 0.000 0.396
#> GSM1299532 3 0.0000 0.8375 0.000 0.000 1.000 0.000
#> GSM1299533 4 0.0336 0.8110 0.000 0.008 0.000 0.992
#> GSM1299534 3 0.4989 0.6823 0.036 0.200 0.756 0.008
#> GSM1299535 3 0.4644 0.6451 0.024 0.228 0.748 0.000
#> GSM1299536 4 0.1302 0.7888 0.044 0.000 0.000 0.956
#> GSM1299537 3 0.0000 0.8375 0.000 0.000 1.000 0.000
#> GSM1299538 1 0.2940 0.5485 0.892 0.088 0.008 0.012
#> GSM1299539 2 0.4761 0.5767 0.332 0.664 0.000 0.004
#> GSM1299540 1 0.6906 0.0859 0.484 0.108 0.408 0.000
#> GSM1299541 3 0.0592 0.8341 0.000 0.016 0.984 0.000
#> GSM1299542 3 0.0000 0.8375 0.000 0.000 1.000 0.000
#> GSM1299543 2 0.1610 0.8367 0.016 0.952 0.032 0.000
#> GSM1299544 3 0.6202 0.5631 0.072 0.268 0.652 0.008
#> GSM1299545 1 0.4214 0.6506 0.780 0.016 0.000 0.204
#> GSM1299546 2 0.1022 0.8402 0.000 0.968 0.032 0.000
#> GSM1299547 4 0.0336 0.8141 0.008 0.000 0.000 0.992
#> GSM1299548 3 0.0000 0.8375 0.000 0.000 1.000 0.000
#> GSM1299549 4 0.3806 0.6693 0.156 0.020 0.000 0.824
#> GSM1299550 4 0.6650 0.4938 0.176 0.000 0.200 0.624
#> GSM1299551 2 0.0921 0.8402 0.000 0.972 0.028 0.000
#> GSM1299552 4 0.0592 0.8102 0.016 0.000 0.000 0.984
#> GSM1299553 1 0.6061 0.1984 0.552 0.400 0.000 0.048
#> GSM1299554 3 0.0927 0.8328 0.016 0.000 0.976 0.008
#> GSM1299555 3 0.4485 0.6937 0.052 0.152 0.796 0.000
#> GSM1299556 3 0.0188 0.8373 0.000 0.004 0.996 0.000
#> GSM1299557 2 0.3525 0.7807 0.100 0.860 0.040 0.000
#> GSM1299558 2 0.5943 -0.0917 0.028 0.504 0.464 0.004
#> GSM1299559 3 0.3048 0.7508 0.108 0.016 0.876 0.000
#> GSM1299560 3 0.0188 0.8373 0.000 0.004 0.996 0.000
#> GSM1299576 1 0.5039 0.6430 0.592 0.004 0.000 0.404
#> GSM1299577 1 0.4855 0.6528 0.644 0.004 0.000 0.352
#> GSM1299561 3 0.0000 0.8375 0.000 0.000 1.000 0.000
#> GSM1299562 2 0.7927 0.4522 0.160 0.576 0.056 0.208
#> GSM1299563 1 0.3658 0.5751 0.836 0.020 0.000 0.144
#> GSM1299564 1 0.3470 0.5700 0.884 0.024 0.040 0.052
#> GSM1299565 2 0.1118 0.8394 0.000 0.964 0.036 0.000
#> GSM1299566 3 0.7141 0.3882 0.120 0.328 0.544 0.008
#> GSM1299567 1 0.4323 0.5027 0.776 0.020 0.204 0.000
#> GSM1299568 3 0.5905 0.4842 0.036 0.332 0.624 0.008
#> GSM1299569 3 0.5914 0.6195 0.072 0.228 0.692 0.008
#> GSM1299570 1 0.2335 0.6191 0.920 0.020 0.000 0.060
#> GSM1299571 2 0.1118 0.8399 0.000 0.964 0.036 0.000
#> GSM1299572 4 0.0336 0.8141 0.008 0.000 0.000 0.992
#> GSM1299573 3 0.0188 0.8371 0.004 0.000 0.996 0.000
#> GSM1299574 2 0.0921 0.8402 0.000 0.972 0.028 0.000
#> GSM1299578 1 0.5028 0.6456 0.596 0.004 0.000 0.400
#> GSM1299579 1 0.5097 0.6149 0.568 0.004 0.000 0.428
#> GSM1299580 1 0.5016 0.6469 0.600 0.004 0.000 0.396
#> GSM1299581 1 0.5039 0.6430 0.592 0.004 0.000 0.404
#> GSM1299582 1 0.5028 0.6456 0.596 0.004 0.000 0.400
#> GSM1299583 1 0.5119 0.5983 0.556 0.004 0.000 0.440
#> GSM1299584 1 0.5028 0.6456 0.596 0.004 0.000 0.400
#> GSM1299585 4 0.0336 0.8141 0.008 0.000 0.000 0.992
#> GSM1299586 1 0.5039 0.6430 0.592 0.004 0.000 0.404
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1299517 3 0.1461 0.7890 0.000 0.016 0.952 0.028 0.004
#> GSM1299518 2 0.1704 0.7438 0.000 0.928 0.068 0.000 0.004
#> GSM1299519 2 0.0000 0.7744 0.000 1.000 0.000 0.000 0.000
#> GSM1299520 4 0.4106 0.6886 0.256 0.000 0.000 0.724 0.020
#> GSM1299521 5 0.2020 0.9125 0.100 0.000 0.000 0.000 0.900
#> GSM1299522 2 0.0566 0.7746 0.000 0.984 0.012 0.004 0.000
#> GSM1299523 4 0.3492 0.7131 0.188 0.000 0.000 0.796 0.016
#> GSM1299524 5 0.2445 0.8044 0.004 0.000 0.108 0.004 0.884
#> GSM1299525 2 0.4851 0.4785 0.000 0.624 0.000 0.340 0.036
#> GSM1299526 2 0.0162 0.7754 0.000 0.996 0.004 0.000 0.000
#> GSM1299527 3 0.1934 0.7802 0.000 0.020 0.932 0.040 0.008
#> GSM1299528 3 0.7181 0.5100 0.000 0.124 0.528 0.264 0.084
#> GSM1299529 2 0.4326 0.5829 0.000 0.708 0.000 0.264 0.028
#> GSM1299530 4 0.5288 0.6710 0.244 0.000 0.000 0.656 0.100
#> GSM1299531 2 0.7059 0.0952 0.000 0.492 0.332 0.112 0.064
#> GSM1299575 1 0.0000 0.9438 1.000 0.000 0.000 0.000 0.000
#> GSM1299532 3 0.0324 0.7937 0.000 0.000 0.992 0.004 0.004
#> GSM1299533 5 0.2112 0.9139 0.084 0.000 0.004 0.004 0.908
#> GSM1299534 3 0.5969 0.6393 0.000 0.144 0.676 0.128 0.052
#> GSM1299535 3 0.5933 0.4827 0.000 0.268 0.612 0.104 0.016
#> GSM1299536 5 0.1809 0.9026 0.060 0.000 0.000 0.012 0.928
#> GSM1299537 3 0.0771 0.7894 0.000 0.000 0.976 0.020 0.004
#> GSM1299538 4 0.1928 0.6769 0.072 0.000 0.004 0.920 0.004
#> GSM1299539 4 0.4605 0.2435 0.000 0.248 0.004 0.708 0.040
#> GSM1299540 4 0.7750 0.2734 0.096 0.132 0.356 0.412 0.004
#> GSM1299541 3 0.1830 0.7794 0.000 0.052 0.932 0.012 0.004
#> GSM1299542 3 0.0162 0.7936 0.000 0.000 0.996 0.000 0.004
#> GSM1299543 2 0.3980 0.7044 0.000 0.824 0.056 0.092 0.028
#> GSM1299544 3 0.6833 0.5694 0.000 0.124 0.588 0.208 0.080
#> GSM1299545 1 0.4770 0.2430 0.644 0.000 0.000 0.320 0.036
#> GSM1299546 2 0.0162 0.7754 0.000 0.996 0.004 0.000 0.000
#> GSM1299547 5 0.2068 0.9150 0.092 0.000 0.000 0.004 0.904
#> GSM1299548 3 0.0290 0.7923 0.000 0.000 0.992 0.008 0.000
#> GSM1299549 5 0.5344 0.6041 0.092 0.004 0.000 0.244 0.660
#> GSM1299550 5 0.2628 0.7937 0.000 0.000 0.028 0.088 0.884
#> GSM1299551 2 0.0912 0.7693 0.000 0.972 0.000 0.016 0.012
#> GSM1299552 5 0.2068 0.9115 0.092 0.000 0.000 0.004 0.904
#> GSM1299553 4 0.7230 0.2922 0.344 0.216 0.000 0.412 0.028
#> GSM1299554 3 0.2077 0.7813 0.000 0.000 0.920 0.040 0.040
#> GSM1299555 3 0.5240 0.5492 0.000 0.228 0.676 0.092 0.004
#> GSM1299556 3 0.1243 0.7880 0.000 0.008 0.960 0.028 0.004
#> GSM1299557 2 0.5804 0.4798 0.000 0.604 0.044 0.312 0.040
#> GSM1299558 2 0.7351 -0.1428 0.000 0.404 0.396 0.132 0.068
#> GSM1299559 3 0.3554 0.5851 0.004 0.000 0.776 0.216 0.004
#> GSM1299560 3 0.1952 0.7710 0.000 0.084 0.912 0.004 0.000
#> GSM1299576 1 0.0162 0.9430 0.996 0.000 0.000 0.000 0.004
#> GSM1299577 1 0.1121 0.8979 0.956 0.000 0.000 0.044 0.000
#> GSM1299561 3 0.0000 0.7934 0.000 0.000 1.000 0.000 0.000
#> GSM1299562 2 0.6460 0.0454 0.000 0.448 0.008 0.404 0.140
#> GSM1299563 4 0.5261 0.6930 0.200 0.000 0.012 0.696 0.092
#> GSM1299564 4 0.4575 0.7087 0.196 0.000 0.024 0.748 0.032
#> GSM1299565 2 0.0912 0.7720 0.000 0.972 0.012 0.016 0.000
#> GSM1299566 3 0.7391 0.4503 0.000 0.124 0.476 0.312 0.088
#> GSM1299567 4 0.6116 0.5864 0.268 0.000 0.156 0.572 0.004
#> GSM1299568 3 0.6862 0.5411 0.000 0.188 0.584 0.160 0.068
#> GSM1299569 3 0.6532 0.6025 0.000 0.124 0.624 0.180 0.072
#> GSM1299570 4 0.4290 0.6493 0.304 0.000 0.000 0.680 0.016
#> GSM1299571 2 0.0451 0.7752 0.000 0.988 0.008 0.004 0.000
#> GSM1299572 5 0.2068 0.9150 0.092 0.000 0.000 0.004 0.904
#> GSM1299573 3 0.0798 0.7941 0.000 0.000 0.976 0.008 0.016
#> GSM1299574 2 0.0000 0.7744 0.000 1.000 0.000 0.000 0.000
#> GSM1299578 1 0.0000 0.9438 1.000 0.000 0.000 0.000 0.000
#> GSM1299579 1 0.0898 0.9257 0.972 0.000 0.000 0.008 0.020
#> GSM1299580 1 0.0000 0.9438 1.000 0.000 0.000 0.000 0.000
#> GSM1299581 1 0.0162 0.9430 0.996 0.000 0.000 0.000 0.004
#> GSM1299582 1 0.0000 0.9438 1.000 0.000 0.000 0.000 0.000
#> GSM1299583 1 0.0703 0.9243 0.976 0.000 0.000 0.000 0.024
#> GSM1299584 1 0.0162 0.9430 0.996 0.000 0.000 0.000 0.004
#> GSM1299585 5 0.2020 0.9125 0.100 0.000 0.000 0.000 0.900
#> GSM1299586 1 0.0000 0.9438 1.000 0.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1299517 3 0.2680 0.71439 0.000 0.000 0.856 0.016 0.004 0.124
#> GSM1299518 2 0.2451 0.77506 0.000 0.892 0.076 0.012 0.004 0.016
#> GSM1299519 2 0.0547 0.84495 0.000 0.980 0.000 0.000 0.000 0.020
#> GSM1299520 4 0.2617 0.75285 0.100 0.000 0.000 0.872 0.016 0.012
#> GSM1299521 5 0.1075 0.90858 0.048 0.000 0.000 0.000 0.952 0.000
#> GSM1299522 2 0.0865 0.84241 0.000 0.964 0.000 0.000 0.000 0.036
#> GSM1299523 4 0.2375 0.74563 0.060 0.000 0.000 0.896 0.008 0.036
#> GSM1299524 5 0.3381 0.79344 0.004 0.004 0.088 0.004 0.836 0.064
#> GSM1299525 6 0.6252 0.09038 0.000 0.336 0.004 0.156 0.024 0.480
#> GSM1299526 2 0.0551 0.84806 0.000 0.984 0.004 0.004 0.000 0.008
#> GSM1299527 3 0.4069 0.58761 0.000 0.004 0.740 0.028 0.012 0.216
#> GSM1299528 6 0.5441 0.27813 0.000 0.044 0.348 0.032 0.008 0.568
#> GSM1299529 6 0.5969 -0.02425 0.000 0.408 0.000 0.120 0.024 0.448
#> GSM1299530 4 0.3536 0.74301 0.116 0.000 0.000 0.812 0.064 0.008
#> GSM1299531 2 0.5962 -0.13070 0.000 0.416 0.188 0.000 0.004 0.392
#> GSM1299575 1 0.0405 0.93151 0.988 0.000 0.000 0.004 0.000 0.008
#> GSM1299532 3 0.1053 0.74932 0.000 0.000 0.964 0.012 0.004 0.020
#> GSM1299533 5 0.1152 0.90750 0.044 0.004 0.000 0.000 0.952 0.000
#> GSM1299534 3 0.5303 0.00164 0.000 0.060 0.528 0.008 0.008 0.396
#> GSM1299535 3 0.7239 0.22262 0.000 0.208 0.460 0.084 0.016 0.232
#> GSM1299536 5 0.1082 0.90649 0.040 0.000 0.000 0.000 0.956 0.004
#> GSM1299537 3 0.1485 0.74646 0.000 0.000 0.944 0.024 0.004 0.028
#> GSM1299538 4 0.3240 0.65148 0.008 0.004 0.004 0.816 0.008 0.160
#> GSM1299539 6 0.5401 -0.00136 0.000 0.080 0.000 0.332 0.020 0.568
#> GSM1299540 4 0.7275 0.35706 0.052 0.124 0.280 0.488 0.008 0.048
#> GSM1299541 3 0.2488 0.73250 0.000 0.076 0.888 0.016 0.000 0.020
#> GSM1299542 3 0.0937 0.74231 0.000 0.000 0.960 0.000 0.000 0.040
#> GSM1299543 2 0.4056 0.56365 0.000 0.704 0.024 0.008 0.000 0.264
#> GSM1299544 6 0.5258 0.22753 0.000 0.044 0.392 0.016 0.008 0.540
#> GSM1299545 1 0.5898 0.22179 0.540 0.000 0.000 0.316 0.036 0.108
#> GSM1299546 2 0.0260 0.85052 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM1299547 5 0.1075 0.90858 0.048 0.000 0.000 0.000 0.952 0.000
#> GSM1299548 3 0.0976 0.75083 0.000 0.000 0.968 0.008 0.008 0.016
#> GSM1299549 5 0.6188 0.38272 0.048 0.004 0.000 0.256 0.560 0.132
#> GSM1299550 5 0.2655 0.82357 0.000 0.000 0.020 0.012 0.872 0.096
#> GSM1299551 2 0.1501 0.80922 0.000 0.924 0.000 0.000 0.000 0.076
#> GSM1299552 5 0.2024 0.88537 0.036 0.000 0.000 0.016 0.920 0.028
#> GSM1299553 6 0.7477 -0.00131 0.192 0.100 0.000 0.240 0.024 0.444
#> GSM1299554 3 0.3192 0.67308 0.000 0.004 0.844 0.016 0.028 0.108
#> GSM1299555 3 0.6409 0.38075 0.000 0.248 0.540 0.152 0.004 0.056
#> GSM1299556 3 0.2222 0.73913 0.000 0.012 0.912 0.040 0.004 0.032
#> GSM1299557 6 0.6893 0.12118 0.000 0.312 0.056 0.132 0.024 0.476
#> GSM1299558 6 0.6014 0.24605 0.000 0.292 0.236 0.004 0.000 0.468
#> GSM1299559 3 0.4372 0.41167 0.000 0.000 0.652 0.308 0.004 0.036
#> GSM1299560 3 0.3339 0.67396 0.000 0.144 0.816 0.012 0.000 0.028
#> GSM1299576 1 0.0000 0.93387 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299577 1 0.1908 0.84614 0.900 0.000 0.000 0.096 0.000 0.004
#> GSM1299561 3 0.1296 0.74188 0.000 0.004 0.948 0.004 0.000 0.044
#> GSM1299562 4 0.7193 0.12676 0.000 0.376 0.024 0.396 0.092 0.112
#> GSM1299563 4 0.5125 0.69330 0.076 0.000 0.012 0.728 0.100 0.084
#> GSM1299564 4 0.3943 0.71800 0.040 0.000 0.036 0.816 0.020 0.088
#> GSM1299565 2 0.1327 0.82525 0.000 0.936 0.000 0.000 0.000 0.064
#> GSM1299566 6 0.5604 0.28698 0.000 0.040 0.324 0.052 0.008 0.576
#> GSM1299567 4 0.4868 0.66147 0.124 0.000 0.136 0.712 0.000 0.028
#> GSM1299568 6 0.5466 0.17352 0.000 0.072 0.416 0.008 0.008 0.496
#> GSM1299569 6 0.5343 0.18937 0.000 0.048 0.412 0.016 0.008 0.516
#> GSM1299570 4 0.2846 0.74306 0.140 0.000 0.000 0.840 0.016 0.004
#> GSM1299571 2 0.0260 0.85060 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM1299572 5 0.1075 0.90858 0.048 0.000 0.000 0.000 0.952 0.000
#> GSM1299573 3 0.2205 0.70928 0.000 0.008 0.896 0.004 0.004 0.088
#> GSM1299574 2 0.0508 0.84806 0.000 0.984 0.004 0.000 0.000 0.012
#> GSM1299578 1 0.0260 0.93298 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM1299579 1 0.1196 0.90334 0.952 0.000 0.000 0.008 0.040 0.000
#> GSM1299580 1 0.0405 0.93151 0.988 0.000 0.000 0.004 0.000 0.008
#> GSM1299581 1 0.0000 0.93387 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299582 1 0.0000 0.93387 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299583 1 0.0865 0.91007 0.964 0.000 0.000 0.000 0.036 0.000
#> GSM1299584 1 0.0000 0.93387 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299585 5 0.1075 0.90858 0.048 0.000 0.000 0.000 0.952 0.000
#> GSM1299586 1 0.0146 0.93352 0.996 0.000 0.000 0.000 0.000 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:skmeans 69 0.11244 2
#> CV:skmeans 60 0.05535 3
#> CV:skmeans 60 0.00842 4
#> CV:skmeans 59 0.02252 5
#> CV:skmeans 50 0.05988 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "pam"]
# you can also extract it by
# res = res_list["CV:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 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 0.826 0.907 0.958 0.3636 0.612 0.612
#> 3 3 0.503 0.692 0.832 0.5185 0.789 0.665
#> 4 4 0.662 0.732 0.838 0.2205 0.800 0.566
#> 5 5 0.770 0.773 0.895 0.0844 0.924 0.751
#> 6 6 0.715 0.696 0.850 0.0541 0.973 0.889
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
#> GSM1299517 2 0.0000 0.983 0.000 1.000
#> GSM1299518 2 0.0000 0.983 0.000 1.000
#> GSM1299519 2 0.0000 0.983 0.000 1.000
#> GSM1299520 2 0.0000 0.983 0.000 1.000
#> GSM1299521 1 0.0000 0.866 1.000 0.000
#> GSM1299522 2 0.0000 0.983 0.000 1.000
#> GSM1299523 2 0.0000 0.983 0.000 1.000
#> GSM1299524 2 0.0000 0.983 0.000 1.000
#> GSM1299525 2 0.0000 0.983 0.000 1.000
#> GSM1299526 2 0.0000 0.983 0.000 1.000
#> GSM1299527 2 0.0000 0.983 0.000 1.000
#> GSM1299528 2 0.0000 0.983 0.000 1.000
#> GSM1299529 2 0.0000 0.983 0.000 1.000
#> GSM1299530 1 0.9686 0.476 0.604 0.396
#> GSM1299531 2 0.0000 0.983 0.000 1.000
#> GSM1299575 1 0.9988 0.254 0.520 0.480
#> GSM1299532 2 0.0000 0.983 0.000 1.000
#> GSM1299533 2 0.8386 0.577 0.268 0.732
#> GSM1299534 2 0.0000 0.983 0.000 1.000
#> GSM1299535 2 0.0000 0.983 0.000 1.000
#> GSM1299536 1 0.9170 0.580 0.668 0.332
#> GSM1299537 2 0.0000 0.983 0.000 1.000
#> GSM1299538 2 0.0000 0.983 0.000 1.000
#> GSM1299539 2 0.0000 0.983 0.000 1.000
#> GSM1299540 2 0.0000 0.983 0.000 1.000
#> GSM1299541 2 0.0000 0.983 0.000 1.000
#> GSM1299542 2 0.0000 0.983 0.000 1.000
#> GSM1299543 2 0.0000 0.983 0.000 1.000
#> GSM1299544 2 0.0000 0.983 0.000 1.000
#> GSM1299545 2 0.5294 0.833 0.120 0.880
#> GSM1299546 2 0.0000 0.983 0.000 1.000
#> GSM1299547 1 0.4939 0.835 0.892 0.108
#> GSM1299548 2 0.0000 0.983 0.000 1.000
#> GSM1299549 2 0.2778 0.929 0.048 0.952
#> GSM1299550 2 0.0000 0.983 0.000 1.000
#> GSM1299551 2 0.0000 0.983 0.000 1.000
#> GSM1299552 1 0.0672 0.866 0.992 0.008
#> GSM1299553 2 0.0000 0.983 0.000 1.000
#> GSM1299554 2 0.0000 0.983 0.000 1.000
#> GSM1299555 2 0.0000 0.983 0.000 1.000
#> GSM1299556 2 0.0000 0.983 0.000 1.000
#> GSM1299557 2 0.0000 0.983 0.000 1.000
#> GSM1299558 2 0.0000 0.983 0.000 1.000
#> GSM1299559 2 0.0000 0.983 0.000 1.000
#> GSM1299560 2 0.0000 0.983 0.000 1.000
#> GSM1299576 1 0.0000 0.866 1.000 0.000
#> GSM1299577 1 0.9996 0.232 0.512 0.488
#> GSM1299561 2 0.0000 0.983 0.000 1.000
#> GSM1299562 2 0.0000 0.983 0.000 1.000
#> GSM1299563 2 0.0000 0.983 0.000 1.000
#> GSM1299564 2 0.0000 0.983 0.000 1.000
#> GSM1299565 2 0.0000 0.983 0.000 1.000
#> GSM1299566 2 0.0000 0.983 0.000 1.000
#> GSM1299567 2 0.0000 0.983 0.000 1.000
#> GSM1299568 2 0.0000 0.983 0.000 1.000
#> GSM1299569 2 0.0000 0.983 0.000 1.000
#> GSM1299570 2 0.9044 0.419 0.320 0.680
#> GSM1299571 2 0.0000 0.983 0.000 1.000
#> GSM1299572 1 0.5059 0.833 0.888 0.112
#> GSM1299573 2 0.0000 0.983 0.000 1.000
#> GSM1299574 2 0.0000 0.983 0.000 1.000
#> GSM1299578 1 0.3274 0.861 0.940 0.060
#> GSM1299579 1 0.0000 0.866 1.000 0.000
#> GSM1299580 1 0.4690 0.843 0.900 0.100
#> GSM1299581 1 0.0000 0.866 1.000 0.000
#> GSM1299582 1 0.3274 0.861 0.940 0.060
#> GSM1299583 1 0.0000 0.866 1.000 0.000
#> GSM1299584 1 0.0000 0.866 1.000 0.000
#> GSM1299585 1 0.0000 0.866 1.000 0.000
#> GSM1299586 1 0.3114 0.862 0.944 0.056
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1299517 3 0.0237 0.7976 0.000 0.004 0.996
#> GSM1299518 3 0.5465 0.1803 0.000 0.288 0.712
#> GSM1299519 2 0.5905 0.9043 0.000 0.648 0.352
#> GSM1299520 3 0.4164 0.7052 0.008 0.144 0.848
#> GSM1299521 1 0.4702 0.8185 0.788 0.212 0.000
#> GSM1299522 2 0.5926 0.9061 0.000 0.644 0.356
#> GSM1299523 3 0.3686 0.7111 0.000 0.140 0.860
#> GSM1299524 3 0.0892 0.7950 0.000 0.020 0.980
#> GSM1299525 3 0.6299 -0.6378 0.000 0.476 0.524
#> GSM1299526 2 0.5988 0.8998 0.000 0.632 0.368
#> GSM1299527 3 0.0592 0.7975 0.000 0.012 0.988
#> GSM1299528 3 0.1031 0.7928 0.000 0.024 0.976
#> GSM1299529 2 0.6244 0.8162 0.000 0.560 0.440
#> GSM1299530 1 0.9177 0.0505 0.452 0.148 0.400
#> GSM1299531 3 0.4235 0.5446 0.000 0.176 0.824
#> GSM1299575 1 0.5722 0.5179 0.704 0.004 0.292
#> GSM1299532 3 0.0424 0.7982 0.000 0.008 0.992
#> GSM1299533 3 0.9489 0.0205 0.280 0.228 0.492
#> GSM1299534 3 0.1753 0.7665 0.000 0.048 0.952
#> GSM1299535 3 0.0592 0.7971 0.000 0.012 0.988
#> GSM1299536 1 0.8758 0.6322 0.588 0.220 0.192
#> GSM1299537 3 0.0000 0.7983 0.000 0.000 1.000
#> GSM1299538 3 0.3752 0.7111 0.000 0.144 0.856
#> GSM1299539 2 0.6235 0.3950 0.000 0.564 0.436
#> GSM1299540 3 0.0237 0.7983 0.000 0.004 0.996
#> GSM1299541 3 0.0237 0.7986 0.000 0.004 0.996
#> GSM1299542 3 0.0592 0.7974 0.000 0.012 0.988
#> GSM1299543 2 0.6309 0.6610 0.000 0.504 0.496
#> GSM1299544 3 0.0892 0.7938 0.000 0.020 0.980
#> GSM1299545 3 0.8587 0.3639 0.260 0.148 0.592
#> GSM1299546 2 0.5926 0.9061 0.000 0.644 0.356
#> GSM1299547 1 0.5643 0.8116 0.760 0.220 0.020
#> GSM1299548 3 0.0000 0.7983 0.000 0.000 1.000
#> GSM1299549 3 0.2301 0.7605 0.060 0.004 0.936
#> GSM1299550 3 0.3116 0.7553 0.000 0.108 0.892
#> GSM1299551 2 0.5948 0.9009 0.000 0.640 0.360
#> GSM1299552 1 0.5156 0.8168 0.776 0.216 0.008
#> GSM1299553 3 0.4953 0.6876 0.016 0.176 0.808
#> GSM1299554 3 0.0592 0.7974 0.000 0.012 0.988
#> GSM1299555 3 0.0424 0.7977 0.000 0.008 0.992
#> GSM1299556 3 0.0424 0.7985 0.000 0.008 0.992
#> GSM1299557 3 0.1411 0.7804 0.000 0.036 0.964
#> GSM1299558 3 0.6291 -0.6136 0.000 0.468 0.532
#> GSM1299559 3 0.0000 0.7983 0.000 0.000 1.000
#> GSM1299560 3 0.0237 0.7983 0.000 0.004 0.996
#> GSM1299576 1 0.0000 0.8593 1.000 0.000 0.000
#> GSM1299577 3 0.8799 0.2743 0.300 0.144 0.556
#> GSM1299561 3 0.0592 0.7974 0.000 0.012 0.988
#> GSM1299562 3 0.4654 0.4594 0.000 0.208 0.792
#> GSM1299563 3 0.4679 0.6992 0.020 0.148 0.832
#> GSM1299564 3 0.3879 0.7120 0.000 0.152 0.848
#> GSM1299565 2 0.5926 0.9061 0.000 0.644 0.356
#> GSM1299566 3 0.5785 0.4575 0.000 0.332 0.668
#> GSM1299567 3 0.3752 0.7116 0.000 0.144 0.856
#> GSM1299568 3 0.0747 0.7951 0.000 0.016 0.984
#> GSM1299569 3 0.1031 0.7928 0.000 0.024 0.976
#> GSM1299570 3 0.6843 0.5823 0.116 0.144 0.740
#> GSM1299571 2 0.5948 0.9051 0.000 0.640 0.360
#> GSM1299572 1 0.5597 0.8129 0.764 0.216 0.020
#> GSM1299573 3 0.0747 0.7961 0.000 0.016 0.984
#> GSM1299574 2 0.5948 0.9050 0.000 0.640 0.360
#> GSM1299578 1 0.0592 0.8556 0.988 0.000 0.012
#> GSM1299579 1 0.0000 0.8593 1.000 0.000 0.000
#> GSM1299580 1 0.0983 0.8522 0.980 0.004 0.016
#> GSM1299581 1 0.0000 0.8593 1.000 0.000 0.000
#> GSM1299582 1 0.0000 0.8593 1.000 0.000 0.000
#> GSM1299583 1 0.0237 0.8593 0.996 0.004 0.000
#> GSM1299584 1 0.0000 0.8593 1.000 0.000 0.000
#> GSM1299585 1 0.4702 0.8185 0.788 0.212 0.000
#> GSM1299586 1 0.0000 0.8593 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1299517 3 0.0336 0.888 0.000 0.008 0.992 0.000
#> GSM1299518 2 0.5039 0.360 0.000 0.592 0.404 0.004
#> GSM1299519 2 0.0000 0.786 0.000 1.000 0.000 0.000
#> GSM1299520 4 0.5243 0.835 0.004 0.004 0.416 0.576
#> GSM1299521 1 0.0000 0.727 1.000 0.000 0.000 0.000
#> GSM1299522 2 0.0336 0.791 0.000 0.992 0.008 0.000
#> GSM1299523 4 0.4916 0.832 0.000 0.000 0.424 0.576
#> GSM1299524 3 0.0469 0.890 0.000 0.012 0.988 0.000
#> GSM1299525 2 0.4713 0.370 0.000 0.640 0.360 0.000
#> GSM1299526 2 0.0336 0.791 0.000 0.992 0.008 0.000
#> GSM1299527 3 0.0336 0.888 0.000 0.008 0.992 0.000
#> GSM1299528 3 0.0657 0.889 0.000 0.012 0.984 0.004
#> GSM1299529 2 0.3649 0.631 0.000 0.796 0.204 0.000
#> GSM1299530 4 0.6263 0.799 0.068 0.000 0.356 0.576
#> GSM1299531 3 0.1305 0.868 0.000 0.036 0.960 0.004
#> GSM1299575 1 0.7037 0.697 0.464 0.000 0.120 0.416
#> GSM1299532 3 0.0188 0.891 0.000 0.004 0.996 0.000
#> GSM1299533 1 0.4382 0.354 0.704 0.000 0.296 0.000
#> GSM1299534 3 0.0188 0.892 0.000 0.000 0.996 0.004
#> GSM1299535 3 0.0336 0.888 0.000 0.008 0.992 0.000
#> GSM1299536 1 0.0188 0.724 0.996 0.000 0.004 0.000
#> GSM1299537 3 0.0188 0.891 0.000 0.004 0.996 0.000
#> GSM1299538 4 0.5203 0.835 0.000 0.008 0.416 0.576
#> GSM1299539 4 0.5649 0.830 0.000 0.028 0.392 0.580
#> GSM1299540 3 0.0188 0.892 0.000 0.004 0.996 0.000
#> GSM1299541 3 0.0336 0.890 0.000 0.008 0.992 0.000
#> GSM1299542 3 0.0376 0.892 0.000 0.004 0.992 0.004
#> GSM1299543 2 0.4585 0.421 0.000 0.668 0.332 0.000
#> GSM1299544 3 0.0524 0.890 0.000 0.008 0.988 0.004
#> GSM1299545 4 0.2799 0.449 0.000 0.008 0.108 0.884
#> GSM1299546 2 0.0336 0.791 0.000 0.992 0.008 0.000
#> GSM1299547 1 0.0000 0.727 1.000 0.000 0.000 0.000
#> GSM1299548 3 0.0000 0.892 0.000 0.000 1.000 0.000
#> GSM1299549 3 0.3272 0.707 0.128 0.008 0.860 0.004
#> GSM1299550 3 0.2234 0.822 0.004 0.008 0.924 0.064
#> GSM1299551 2 0.0469 0.782 0.000 0.988 0.012 0.000
#> GSM1299552 1 0.0000 0.727 1.000 0.000 0.000 0.000
#> GSM1299553 3 0.5417 0.333 0.000 0.056 0.704 0.240
#> GSM1299554 3 0.0376 0.892 0.000 0.004 0.992 0.004
#> GSM1299555 3 0.0469 0.890 0.000 0.012 0.988 0.000
#> GSM1299556 3 0.0336 0.892 0.000 0.008 0.992 0.000
#> GSM1299557 3 0.3024 0.704 0.000 0.148 0.852 0.000
#> GSM1299558 2 0.4888 0.279 0.000 0.588 0.412 0.000
#> GSM1299559 3 0.0000 0.892 0.000 0.000 1.000 0.000
#> GSM1299560 3 0.0188 0.892 0.000 0.004 0.996 0.000
#> GSM1299576 1 0.4907 0.809 0.580 0.000 0.000 0.420
#> GSM1299577 4 0.3444 0.603 0.000 0.000 0.184 0.816
#> GSM1299561 3 0.0376 0.892 0.000 0.004 0.992 0.004
#> GSM1299562 3 0.3873 0.572 0.000 0.228 0.772 0.000
#> GSM1299563 4 0.5355 0.836 0.004 0.008 0.408 0.580
#> GSM1299564 4 0.5276 0.807 0.004 0.004 0.432 0.560
#> GSM1299565 2 0.0336 0.791 0.000 0.992 0.008 0.000
#> GSM1299566 3 0.5452 -0.463 0.000 0.016 0.556 0.428
#> GSM1299567 3 0.5155 -0.602 0.000 0.004 0.528 0.468
#> GSM1299568 3 0.0188 0.892 0.000 0.000 0.996 0.004
#> GSM1299569 3 0.0657 0.889 0.000 0.012 0.984 0.004
#> GSM1299570 4 0.5193 0.837 0.000 0.008 0.412 0.580
#> GSM1299571 2 0.0336 0.791 0.000 0.992 0.008 0.000
#> GSM1299572 1 0.0000 0.727 1.000 0.000 0.000 0.000
#> GSM1299573 3 0.0657 0.889 0.000 0.012 0.984 0.004
#> GSM1299574 2 0.0469 0.790 0.000 0.988 0.012 0.000
#> GSM1299578 1 0.5300 0.804 0.580 0.000 0.012 0.408
#> GSM1299579 1 0.4907 0.809 0.580 0.000 0.000 0.420
#> GSM1299580 1 0.4907 0.809 0.580 0.000 0.000 0.420
#> GSM1299581 1 0.4907 0.809 0.580 0.000 0.000 0.420
#> GSM1299582 1 0.4907 0.809 0.580 0.000 0.000 0.420
#> GSM1299583 1 0.4855 0.808 0.600 0.000 0.000 0.400
#> GSM1299584 1 0.4907 0.809 0.580 0.000 0.000 0.420
#> GSM1299585 1 0.0000 0.727 1.000 0.000 0.000 0.000
#> GSM1299586 1 0.4907 0.809 0.580 0.000 0.000 0.420
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1299517 3 0.0671 0.891 0.000 0.004 0.980 0.016 0.000
#> GSM1299518 2 0.4455 0.314 0.000 0.588 0.404 0.008 0.000
#> GSM1299519 2 0.0000 0.787 0.000 1.000 0.000 0.000 0.000
#> GSM1299520 4 0.1544 0.687 0.000 0.000 0.068 0.932 0.000
#> GSM1299521 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> GSM1299522 2 0.0162 0.790 0.000 0.996 0.004 0.000 0.000
#> GSM1299523 4 0.1608 0.689 0.000 0.000 0.072 0.928 0.000
#> GSM1299524 3 0.1894 0.862 0.000 0.008 0.920 0.072 0.000
#> GSM1299525 2 0.5556 0.472 0.000 0.616 0.276 0.108 0.000
#> GSM1299526 2 0.0162 0.790 0.000 0.996 0.004 0.000 0.000
#> GSM1299527 3 0.0671 0.891 0.000 0.004 0.980 0.016 0.000
#> GSM1299528 3 0.0290 0.897 0.000 0.008 0.992 0.000 0.000
#> GSM1299529 2 0.3656 0.643 0.000 0.784 0.196 0.020 0.000
#> GSM1299530 4 0.1704 0.683 0.000 0.000 0.068 0.928 0.004
#> GSM1299531 3 0.0703 0.890 0.000 0.024 0.976 0.000 0.000
#> GSM1299575 1 0.1430 0.874 0.944 0.000 0.004 0.052 0.000
#> GSM1299532 3 0.0290 0.896 0.000 0.000 0.992 0.008 0.000
#> GSM1299533 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> GSM1299534 3 0.0000 0.897 0.000 0.000 1.000 0.000 0.000
#> GSM1299535 3 0.0671 0.891 0.000 0.004 0.980 0.016 0.000
#> GSM1299536 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> GSM1299537 3 0.1892 0.862 0.000 0.004 0.916 0.080 0.000
#> GSM1299538 4 0.4276 0.690 0.000 0.004 0.380 0.616 0.000
#> GSM1299539 4 0.4238 0.687 0.000 0.004 0.368 0.628 0.000
#> GSM1299540 3 0.1768 0.863 0.000 0.004 0.924 0.072 0.000
#> GSM1299541 3 0.1082 0.891 0.000 0.008 0.964 0.028 0.000
#> GSM1299542 3 0.0162 0.897 0.000 0.004 0.996 0.000 0.000
#> GSM1299543 2 0.4066 0.483 0.000 0.672 0.324 0.004 0.000
#> GSM1299544 3 0.0324 0.897 0.000 0.004 0.992 0.004 0.000
#> GSM1299545 1 0.3085 0.793 0.868 0.004 0.068 0.060 0.000
#> GSM1299546 2 0.0162 0.790 0.000 0.996 0.004 0.000 0.000
#> GSM1299547 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> GSM1299548 3 0.1270 0.878 0.000 0.000 0.948 0.052 0.000
#> GSM1299549 3 0.5395 0.520 0.000 0.004 0.676 0.132 0.188
#> GSM1299550 3 0.1731 0.853 0.000 0.004 0.932 0.060 0.004
#> GSM1299551 2 0.0290 0.784 0.000 0.992 0.008 0.000 0.000
#> GSM1299552 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> GSM1299553 1 0.4801 0.249 0.604 0.004 0.372 0.020 0.000
#> GSM1299554 3 0.0162 0.897 0.000 0.004 0.996 0.000 0.000
#> GSM1299555 3 0.1894 0.862 0.000 0.008 0.920 0.072 0.000
#> GSM1299556 3 0.1792 0.862 0.000 0.000 0.916 0.084 0.000
#> GSM1299557 3 0.3106 0.729 0.000 0.140 0.840 0.020 0.000
#> GSM1299558 2 0.4210 0.340 0.000 0.588 0.412 0.000 0.000
#> GSM1299559 3 0.1608 0.863 0.000 0.000 0.928 0.072 0.000
#> GSM1299560 3 0.0324 0.897 0.000 0.004 0.992 0.004 0.000
#> GSM1299576 1 0.0000 0.881 1.000 0.000 0.000 0.000 0.000
#> GSM1299577 1 0.6138 0.233 0.552 0.000 0.176 0.272 0.000
#> GSM1299561 3 0.0162 0.897 0.000 0.004 0.996 0.000 0.000
#> GSM1299562 3 0.5355 0.379 0.000 0.120 0.660 0.220 0.000
#> GSM1299563 4 0.4375 0.701 0.000 0.004 0.364 0.628 0.004
#> GSM1299564 4 0.4201 0.641 0.000 0.000 0.408 0.592 0.000
#> GSM1299565 2 0.0162 0.790 0.000 0.996 0.004 0.000 0.000
#> GSM1299566 3 0.4522 -0.328 0.000 0.008 0.552 0.440 0.000
#> GSM1299567 4 0.4390 0.520 0.000 0.004 0.428 0.568 0.000
#> GSM1299568 3 0.0162 0.897 0.000 0.000 0.996 0.004 0.000
#> GSM1299569 3 0.0290 0.897 0.000 0.008 0.992 0.000 0.000
#> GSM1299570 4 0.1608 0.689 0.000 0.000 0.072 0.928 0.000
#> GSM1299571 2 0.0162 0.790 0.000 0.996 0.004 0.000 0.000
#> GSM1299572 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> GSM1299573 3 0.0290 0.897 0.000 0.008 0.992 0.000 0.000
#> GSM1299574 2 0.0290 0.789 0.000 0.992 0.008 0.000 0.000
#> GSM1299578 1 0.1670 0.871 0.936 0.000 0.012 0.052 0.000
#> GSM1299579 1 0.0000 0.881 1.000 0.000 0.000 0.000 0.000
#> GSM1299580 1 0.1270 0.873 0.948 0.000 0.000 0.052 0.000
#> GSM1299581 1 0.0000 0.881 1.000 0.000 0.000 0.000 0.000
#> GSM1299582 1 0.0000 0.881 1.000 0.000 0.000 0.000 0.000
#> GSM1299583 1 0.0703 0.871 0.976 0.000 0.000 0.000 0.024
#> GSM1299584 1 0.0000 0.881 1.000 0.000 0.000 0.000 0.000
#> GSM1299585 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> GSM1299586 1 0.1270 0.873 0.948 0.000 0.000 0.052 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1299517 3 0.1007 0.8244 0.000 0.000 0.956 0.000 0.000 0.044
#> GSM1299518 2 0.3934 0.0934 0.000 0.616 0.376 0.008 0.000 0.000
#> GSM1299519 2 0.0000 0.7476 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299520 4 0.0000 0.5598 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1299521 5 0.0000 0.9983 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1299522 2 0.0146 0.7454 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM1299523 4 0.0000 0.5598 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1299524 3 0.2039 0.8105 0.000 0.000 0.904 0.076 0.000 0.020
#> GSM1299525 6 0.5915 0.7054 0.000 0.224 0.212 0.016 0.000 0.548
#> GSM1299526 2 0.0000 0.7476 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299527 3 0.1204 0.8197 0.000 0.000 0.944 0.000 0.000 0.056
#> GSM1299528 3 0.2969 0.7003 0.000 0.000 0.776 0.000 0.000 0.224
#> GSM1299529 6 0.4983 0.4939 0.000 0.356 0.080 0.000 0.000 0.564
#> GSM1299530 4 0.0000 0.5598 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1299531 3 0.3287 0.6946 0.000 0.012 0.768 0.000 0.000 0.220
#> GSM1299575 1 0.2964 0.8093 0.792 0.000 0.004 0.000 0.000 0.204
#> GSM1299532 3 0.0713 0.8299 0.000 0.000 0.972 0.000 0.000 0.028
#> GSM1299533 5 0.0000 0.9983 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1299534 3 0.1444 0.8140 0.000 0.000 0.928 0.000 0.000 0.072
#> GSM1299535 3 0.1204 0.8197 0.000 0.000 0.944 0.000 0.000 0.056
#> GSM1299536 5 0.0000 0.9983 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1299537 3 0.2509 0.7918 0.000 0.000 0.876 0.088 0.000 0.036
#> GSM1299538 4 0.4218 0.5424 0.000 0.000 0.360 0.616 0.000 0.024
#> GSM1299539 4 0.5081 0.4943 0.000 0.000 0.308 0.588 0.000 0.104
#> GSM1299540 3 0.2019 0.7982 0.000 0.000 0.900 0.088 0.000 0.012
#> GSM1299541 3 0.1148 0.8324 0.000 0.004 0.960 0.020 0.000 0.016
#> GSM1299542 3 0.0146 0.8328 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM1299543 2 0.5575 0.0278 0.000 0.528 0.304 0.000 0.000 0.168
#> GSM1299544 3 0.3076 0.6997 0.000 0.000 0.760 0.000 0.000 0.240
#> GSM1299545 1 0.2747 0.7749 0.880 0.000 0.040 0.024 0.000 0.056
#> GSM1299546 2 0.0000 0.7476 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299547 5 0.0000 0.9983 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1299548 3 0.1584 0.8161 0.000 0.000 0.928 0.064 0.000 0.008
#> GSM1299549 3 0.7112 -0.1399 0.000 0.000 0.420 0.124 0.156 0.300
#> GSM1299550 3 0.3756 0.6828 0.000 0.000 0.736 0.016 0.008 0.240
#> GSM1299551 2 0.0000 0.7476 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299552 5 0.0000 0.9983 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1299553 6 0.5486 0.5601 0.224 0.000 0.208 0.000 0.000 0.568
#> GSM1299554 3 0.0000 0.8327 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299555 3 0.1806 0.7981 0.000 0.000 0.908 0.088 0.000 0.004
#> GSM1299556 3 0.2509 0.7942 0.000 0.000 0.876 0.088 0.000 0.036
#> GSM1299557 6 0.5351 0.6832 0.000 0.144 0.288 0.000 0.000 0.568
#> GSM1299558 2 0.5883 -0.0721 0.000 0.436 0.360 0.000 0.000 0.204
#> GSM1299559 3 0.1918 0.7992 0.000 0.000 0.904 0.088 0.000 0.008
#> GSM1299560 3 0.0260 0.8328 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM1299576 1 0.0000 0.8605 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299577 1 0.5790 0.1221 0.512 0.000 0.184 0.300 0.000 0.004
#> GSM1299561 3 0.0458 0.8323 0.000 0.000 0.984 0.000 0.000 0.016
#> GSM1299562 3 0.5955 0.2599 0.000 0.112 0.576 0.260 0.000 0.052
#> GSM1299563 4 0.4278 0.5502 0.000 0.000 0.352 0.624 0.008 0.016
#> GSM1299564 4 0.4712 0.4879 0.000 0.000 0.384 0.564 0.000 0.052
#> GSM1299565 2 0.1141 0.7102 0.000 0.948 0.000 0.000 0.000 0.052
#> GSM1299566 3 0.5571 0.2165 0.000 0.000 0.552 0.220 0.000 0.228
#> GSM1299567 4 0.4335 0.2517 0.000 0.000 0.472 0.508 0.000 0.020
#> GSM1299568 3 0.1714 0.8096 0.000 0.000 0.908 0.000 0.000 0.092
#> GSM1299569 3 0.1814 0.8028 0.000 0.000 0.900 0.000 0.000 0.100
#> GSM1299570 4 0.0000 0.5598 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1299571 2 0.0000 0.7476 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299572 5 0.0000 0.9983 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1299573 3 0.0363 0.8332 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM1299574 2 0.0000 0.7476 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299578 1 0.3103 0.8049 0.784 0.000 0.008 0.000 0.000 0.208
#> GSM1299579 1 0.0000 0.8605 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299580 1 0.2854 0.8099 0.792 0.000 0.000 0.000 0.000 0.208
#> GSM1299581 1 0.0000 0.8605 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299582 1 0.0146 0.8602 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM1299583 1 0.0363 0.8561 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM1299584 1 0.0146 0.8602 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM1299585 5 0.0260 0.9895 0.008 0.000 0.000 0.000 0.992 0.000
#> GSM1299586 1 0.2823 0.8102 0.796 0.000 0.000 0.000 0.000 0.204
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:pam 66 0.00703 2
#> CV:pam 60 0.04243 3
#> CV:pam 61 0.03282 4
#> CV:pam 62 0.02030 5
#> CV:pam 59 0.05262 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "mclust"]
# you can also extract it by
# res = res_list["CV:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 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 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 0.452 0.775 0.881 0.4701 0.513 0.513
#> 3 3 0.359 0.466 0.662 0.2984 0.742 0.534
#> 4 4 0.415 0.599 0.772 0.1460 0.815 0.535
#> 5 5 0.601 0.624 0.702 0.0910 0.921 0.726
#> 6 6 0.710 0.658 0.799 0.0575 0.953 0.796
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
#> GSM1299517 2 0.1184 0.82106 0.016 0.984
#> GSM1299518 2 0.2948 0.82611 0.052 0.948
#> GSM1299519 2 0.8713 0.68794 0.292 0.708
#> GSM1299520 1 0.8443 0.50940 0.728 0.272
#> GSM1299521 1 0.0000 0.92665 1.000 0.000
#> GSM1299522 2 0.4939 0.83122 0.108 0.892
#> GSM1299523 1 0.9732 0.06981 0.596 0.404
#> GSM1299524 1 0.4298 0.85348 0.912 0.088
#> GSM1299525 2 0.9661 0.55771 0.392 0.608
#> GSM1299526 2 0.3584 0.82924 0.068 0.932
#> GSM1299527 2 0.3431 0.82057 0.064 0.936
#> GSM1299528 2 0.7219 0.77849 0.200 0.800
#> GSM1299529 2 0.9661 0.55771 0.392 0.608
#> GSM1299530 1 0.0376 0.92486 0.996 0.004
#> GSM1299531 2 0.7674 0.75576 0.224 0.776
#> GSM1299575 1 0.0376 0.92594 0.996 0.004
#> GSM1299532 2 0.0000 0.81657 0.000 1.000
#> GSM1299533 1 0.1184 0.92091 0.984 0.016
#> GSM1299534 2 0.4022 0.83198 0.080 0.920
#> GSM1299535 2 0.5178 0.82979 0.116 0.884
#> GSM1299536 1 0.1184 0.92091 0.984 0.016
#> GSM1299537 2 0.0000 0.81657 0.000 1.000
#> GSM1299538 2 0.9944 0.41381 0.456 0.544
#> GSM1299539 2 0.9833 0.49830 0.424 0.576
#> GSM1299540 2 0.9988 0.32999 0.480 0.520
#> GSM1299541 2 0.0000 0.81657 0.000 1.000
#> GSM1299542 2 0.0000 0.81657 0.000 1.000
#> GSM1299543 2 0.6438 0.80929 0.164 0.836
#> GSM1299544 2 0.6343 0.80650 0.160 0.840
#> GSM1299545 1 0.3733 0.86683 0.928 0.072
#> GSM1299546 2 0.4939 0.83122 0.108 0.892
#> GSM1299547 1 0.0000 0.92665 1.000 0.000
#> GSM1299548 2 0.0000 0.81657 0.000 1.000
#> GSM1299549 1 0.1414 0.91877 0.980 0.020
#> GSM1299550 1 0.1633 0.91741 0.976 0.024
#> GSM1299551 2 0.9286 0.62948 0.344 0.656
#> GSM1299552 1 0.0000 0.92665 1.000 0.000
#> GSM1299553 2 0.9933 0.43500 0.452 0.548
#> GSM1299554 2 0.4022 0.83198 0.080 0.920
#> GSM1299555 2 0.0000 0.81657 0.000 1.000
#> GSM1299556 2 0.0000 0.81657 0.000 1.000
#> GSM1299557 2 0.9635 0.56426 0.388 0.612
#> GSM1299558 2 0.5408 0.82551 0.124 0.876
#> GSM1299559 2 0.0376 0.81775 0.004 0.996
#> GSM1299560 2 0.0000 0.81657 0.000 1.000
#> GSM1299576 1 0.0000 0.92665 1.000 0.000
#> GSM1299577 1 0.5294 0.80542 0.880 0.120
#> GSM1299561 2 0.0000 0.81657 0.000 1.000
#> GSM1299562 2 0.9866 0.44688 0.432 0.568
#> GSM1299563 1 0.2236 0.90920 0.964 0.036
#> GSM1299564 2 0.9977 0.36951 0.472 0.528
#> GSM1299565 2 0.4939 0.83122 0.108 0.892
#> GSM1299566 2 0.7745 0.75733 0.228 0.772
#> GSM1299567 1 0.9833 -0.00789 0.576 0.424
#> GSM1299568 2 0.4022 0.83198 0.080 0.920
#> GSM1299569 2 0.5629 0.82083 0.132 0.868
#> GSM1299570 1 0.0938 0.92254 0.988 0.012
#> GSM1299571 2 0.3733 0.83221 0.072 0.928
#> GSM1299572 1 0.0000 0.92665 1.000 0.000
#> GSM1299573 2 0.0000 0.81657 0.000 1.000
#> GSM1299574 2 0.4939 0.83122 0.108 0.892
#> GSM1299578 1 0.0000 0.92665 1.000 0.000
#> GSM1299579 1 0.0000 0.92665 1.000 0.000
#> GSM1299580 1 0.0376 0.92594 0.996 0.004
#> GSM1299581 1 0.0000 0.92665 1.000 0.000
#> GSM1299582 1 0.0000 0.92665 1.000 0.000
#> GSM1299583 1 0.0000 0.92665 1.000 0.000
#> GSM1299584 1 0.0000 0.92665 1.000 0.000
#> GSM1299585 1 0.0000 0.92665 1.000 0.000
#> GSM1299586 1 0.0000 0.92665 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1299517 3 0.640 0.5218 0.004 0.416 0.580
#> GSM1299518 2 0.653 -0.0268 0.008 0.588 0.404
#> GSM1299519 2 0.390 0.4626 0.056 0.888 0.056
#> GSM1299520 1 0.616 0.7205 0.760 0.188 0.052
#> GSM1299521 1 0.967 0.6373 0.436 0.220 0.344
#> GSM1299522 2 0.478 0.4337 0.004 0.796 0.200
#> GSM1299523 1 0.733 0.5637 0.636 0.312 0.052
#> GSM1299524 3 0.949 -0.6552 0.404 0.184 0.412
#> GSM1299525 2 0.412 0.4371 0.108 0.868 0.024
#> GSM1299526 2 0.590 0.3216 0.008 0.700 0.292
#> GSM1299527 3 0.690 0.4903 0.016 0.436 0.548
#> GSM1299528 3 0.852 0.1834 0.092 0.448 0.460
#> GSM1299529 2 0.375 0.4329 0.120 0.872 0.008
#> GSM1299530 1 0.567 0.7606 0.800 0.140 0.060
#> GSM1299531 3 0.729 0.0790 0.048 0.320 0.632
#> GSM1299575 1 0.000 0.7417 1.000 0.000 0.000
#> GSM1299532 3 0.603 0.5761 0.000 0.376 0.624
#> GSM1299533 1 0.946 0.6111 0.416 0.180 0.404
#> GSM1299534 3 0.630 0.3540 0.000 0.484 0.516
#> GSM1299535 2 0.717 -0.2880 0.024 0.516 0.460
#> GSM1299536 1 0.946 0.6094 0.412 0.180 0.408
#> GSM1299537 3 0.679 0.5823 0.028 0.324 0.648
#> GSM1299538 1 0.802 0.3175 0.520 0.416 0.064
#> GSM1299539 2 0.615 0.3477 0.204 0.752 0.044
#> GSM1299540 1 0.816 0.3876 0.556 0.364 0.080
#> GSM1299541 3 0.645 0.5926 0.016 0.328 0.656
#> GSM1299542 3 0.665 0.5859 0.024 0.320 0.656
#> GSM1299543 2 0.522 0.4466 0.016 0.788 0.196
#> GSM1299544 2 0.650 -0.2800 0.004 0.532 0.464
#> GSM1299545 1 0.738 0.7342 0.704 0.164 0.132
#> GSM1299546 2 0.473 0.4379 0.004 0.800 0.196
#> GSM1299547 1 0.968 0.6323 0.420 0.216 0.364
#> GSM1299548 3 0.595 0.5882 0.000 0.360 0.640
#> GSM1299549 1 0.915 0.6782 0.544 0.220 0.236
#> GSM1299550 1 0.949 0.6099 0.416 0.184 0.400
#> GSM1299551 2 0.386 0.4593 0.072 0.888 0.040
#> GSM1299552 1 0.921 0.6726 0.536 0.220 0.244
#> GSM1299553 2 0.642 0.3085 0.288 0.688 0.024
#> GSM1299554 3 0.808 0.3948 0.068 0.412 0.520
#> GSM1299555 3 0.621 0.5810 0.004 0.368 0.628
#> GSM1299556 3 0.621 0.5810 0.004 0.368 0.628
#> GSM1299557 2 0.414 0.4341 0.116 0.864 0.020
#> GSM1299558 2 0.623 -0.1948 0.000 0.564 0.436
#> GSM1299559 3 0.615 0.5890 0.004 0.356 0.640
#> GSM1299560 3 0.590 0.5931 0.000 0.352 0.648
#> GSM1299576 1 0.000 0.7417 1.000 0.000 0.000
#> GSM1299577 1 0.617 0.7484 0.776 0.144 0.080
#> GSM1299561 3 0.586 0.5962 0.000 0.344 0.656
#> GSM1299562 3 0.852 -0.0800 0.104 0.356 0.540
#> GSM1299563 1 0.572 0.7345 0.792 0.156 0.052
#> GSM1299564 1 0.672 0.6835 0.724 0.212 0.064
#> GSM1299565 2 0.473 0.4379 0.004 0.800 0.196
#> GSM1299566 3 0.915 0.1605 0.148 0.384 0.468
#> GSM1299567 1 0.617 0.7166 0.768 0.168 0.064
#> GSM1299568 2 0.648 -0.2451 0.004 0.548 0.448
#> GSM1299569 2 0.651 -0.3060 0.004 0.524 0.472
#> GSM1299570 1 0.489 0.7527 0.836 0.124 0.040
#> GSM1299571 2 0.586 0.3327 0.008 0.704 0.288
#> GSM1299572 1 0.946 0.6128 0.420 0.180 0.400
#> GSM1299573 3 0.588 0.5956 0.000 0.348 0.652
#> GSM1299574 2 0.465 0.4531 0.008 0.816 0.176
#> GSM1299578 1 0.129 0.7503 0.968 0.032 0.000
#> GSM1299579 1 0.378 0.7565 0.892 0.044 0.064
#> GSM1299580 1 0.000 0.7417 1.000 0.000 0.000
#> GSM1299581 1 0.000 0.7417 1.000 0.000 0.000
#> GSM1299582 1 0.103 0.7418 0.976 0.000 0.024
#> GSM1299583 1 0.388 0.7599 0.888 0.068 0.044
#> GSM1299584 1 0.141 0.7414 0.964 0.000 0.036
#> GSM1299585 1 0.967 0.6373 0.436 0.220 0.344
#> GSM1299586 1 0.000 0.7417 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1299517 3 0.3528 0.670 0.000 0.192 0.808 0.000
#> GSM1299518 3 0.5311 0.165 0.004 0.392 0.596 0.008
#> GSM1299519 2 0.3617 0.680 0.000 0.860 0.064 0.076
#> GSM1299520 1 0.7975 0.597 0.604 0.120 0.136 0.140
#> GSM1299521 4 0.1356 0.822 0.032 0.008 0.000 0.960
#> GSM1299522 2 0.4431 0.529 0.000 0.696 0.304 0.000
#> GSM1299523 1 0.9215 0.473 0.452 0.188 0.228 0.132
#> GSM1299524 4 0.4989 0.600 0.008 0.036 0.200 0.756
#> GSM1299525 2 0.4330 0.648 0.032 0.836 0.032 0.100
#> GSM1299526 2 0.5427 0.348 0.004 0.544 0.444 0.008
#> GSM1299527 3 0.4353 0.649 0.000 0.232 0.756 0.012
#> GSM1299528 3 0.6279 0.602 0.036 0.188 0.704 0.072
#> GSM1299529 2 0.4072 0.651 0.032 0.848 0.024 0.096
#> GSM1299530 1 0.5942 0.621 0.716 0.072 0.020 0.192
#> GSM1299531 3 0.7714 0.497 0.072 0.220 0.600 0.108
#> GSM1299575 1 0.0188 0.665 0.996 0.000 0.000 0.004
#> GSM1299532 3 0.1792 0.752 0.000 0.068 0.932 0.000
#> GSM1299533 4 0.0804 0.826 0.012 0.008 0.000 0.980
#> GSM1299534 3 0.3351 0.718 0.000 0.148 0.844 0.008
#> GSM1299535 3 0.5173 0.502 0.000 0.320 0.660 0.020
#> GSM1299536 4 0.0524 0.823 0.004 0.008 0.000 0.988
#> GSM1299537 3 0.2521 0.742 0.020 0.060 0.916 0.004
#> GSM1299538 1 0.9439 0.288 0.368 0.296 0.224 0.112
#> GSM1299539 2 0.5725 0.568 0.044 0.748 0.048 0.160
#> GSM1299540 3 0.8902 -0.267 0.376 0.164 0.380 0.080
#> GSM1299541 3 0.0779 0.751 0.000 0.016 0.980 0.004
#> GSM1299542 3 0.2010 0.745 0.004 0.060 0.932 0.004
#> GSM1299543 2 0.5092 0.608 0.016 0.728 0.240 0.016
#> GSM1299544 3 0.5034 0.672 0.008 0.172 0.768 0.052
#> GSM1299545 1 0.6996 0.564 0.636 0.080 0.044 0.240
#> GSM1299546 2 0.4072 0.594 0.000 0.748 0.252 0.000
#> GSM1299547 4 0.0779 0.825 0.016 0.004 0.000 0.980
#> GSM1299548 3 0.0657 0.751 0.000 0.012 0.984 0.004
#> GSM1299549 1 0.9282 0.214 0.344 0.092 0.220 0.344
#> GSM1299550 4 0.6725 0.544 0.072 0.068 0.172 0.688
#> GSM1299551 2 0.3837 0.667 0.020 0.860 0.032 0.088
#> GSM1299552 4 0.6398 0.133 0.344 0.080 0.000 0.576
#> GSM1299553 2 0.6425 0.474 0.136 0.692 0.020 0.152
#> GSM1299554 3 0.3047 0.732 0.000 0.116 0.872 0.012
#> GSM1299555 3 0.1824 0.750 0.000 0.060 0.936 0.004
#> GSM1299556 3 0.1305 0.753 0.000 0.036 0.960 0.004
#> GSM1299557 2 0.4681 0.661 0.032 0.820 0.048 0.100
#> GSM1299558 3 0.5403 0.505 0.000 0.348 0.628 0.024
#> GSM1299559 3 0.1675 0.752 0.004 0.044 0.948 0.004
#> GSM1299560 3 0.0779 0.750 0.000 0.016 0.980 0.004
#> GSM1299576 1 0.0000 0.665 1.000 0.000 0.000 0.000
#> GSM1299577 1 0.5852 0.657 0.752 0.064 0.052 0.132
#> GSM1299561 3 0.0376 0.748 0.000 0.004 0.992 0.004
#> GSM1299562 3 0.8935 0.252 0.120 0.208 0.492 0.180
#> GSM1299563 1 0.8688 0.516 0.508 0.096 0.232 0.164
#> GSM1299564 1 0.9261 0.425 0.424 0.184 0.272 0.120
#> GSM1299565 2 0.4382 0.534 0.000 0.704 0.296 0.000
#> GSM1299566 3 0.6143 0.599 0.040 0.160 0.724 0.076
#> GSM1299567 1 0.8795 0.515 0.500 0.136 0.240 0.124
#> GSM1299568 3 0.4963 0.636 0.000 0.284 0.696 0.020
#> GSM1299569 3 0.4733 0.681 0.004 0.172 0.780 0.044
#> GSM1299570 1 0.6944 0.635 0.684 0.084 0.092 0.140
#> GSM1299571 2 0.5080 0.377 0.004 0.576 0.420 0.000
#> GSM1299572 4 0.0927 0.826 0.016 0.008 0.000 0.976
#> GSM1299573 3 0.0376 0.749 0.000 0.004 0.992 0.004
#> GSM1299574 2 0.4502 0.622 0.000 0.748 0.236 0.016
#> GSM1299578 1 0.1389 0.667 0.952 0.000 0.000 0.048
#> GSM1299579 1 0.4284 0.607 0.780 0.020 0.000 0.200
#> GSM1299580 1 0.0188 0.665 0.996 0.000 0.000 0.004
#> GSM1299581 1 0.0000 0.665 1.000 0.000 0.000 0.000
#> GSM1299582 1 0.0000 0.665 1.000 0.000 0.000 0.000
#> GSM1299583 1 0.5085 0.449 0.676 0.020 0.000 0.304
#> GSM1299584 1 0.1118 0.645 0.964 0.000 0.000 0.036
#> GSM1299585 4 0.1356 0.822 0.032 0.008 0.000 0.960
#> GSM1299586 1 0.0000 0.665 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1299517 3 0.5136 0.562 0.016 0.332 0.624 0.028 0.000
#> GSM1299518 3 0.5309 0.383 0.016 0.360 0.592 0.032 0.000
#> GSM1299519 2 0.5325 0.573 0.300 0.640 0.032 0.028 0.000
#> GSM1299520 4 0.2452 0.770 0.052 0.000 0.028 0.908 0.012
#> GSM1299521 5 0.1356 0.886 0.012 0.004 0.000 0.028 0.956
#> GSM1299522 2 0.3970 0.454 0.000 0.752 0.224 0.024 0.000
#> GSM1299523 4 0.2784 0.776 0.040 0.004 0.048 0.896 0.012
#> GSM1299524 5 0.3834 0.758 0.000 0.012 0.140 0.036 0.812
#> GSM1299525 2 0.6344 0.505 0.408 0.496 0.028 0.060 0.008
#> GSM1299526 2 0.5261 0.358 0.012 0.600 0.352 0.036 0.000
#> GSM1299527 3 0.5396 0.541 0.016 0.344 0.600 0.040 0.000
#> GSM1299528 3 0.6513 0.598 0.168 0.080 0.660 0.068 0.024
#> GSM1299529 2 0.6129 0.494 0.416 0.500 0.012 0.060 0.012
#> GSM1299530 4 0.4070 0.652 0.072 0.016 0.000 0.812 0.100
#> GSM1299531 3 0.5040 0.726 0.036 0.220 0.716 0.016 0.012
#> GSM1299575 1 0.4437 0.620 0.532 0.000 0.000 0.464 0.004
#> GSM1299532 3 0.2763 0.765 0.000 0.148 0.848 0.004 0.000
#> GSM1299533 5 0.1603 0.888 0.004 0.004 0.012 0.032 0.948
#> GSM1299534 3 0.3839 0.751 0.008 0.188 0.788 0.008 0.008
#> GSM1299535 3 0.5434 0.576 0.016 0.332 0.612 0.036 0.004
#> GSM1299536 5 0.1492 0.889 0.004 0.000 0.008 0.040 0.948
#> GSM1299537 3 0.0290 0.777 0.000 0.000 0.992 0.008 0.000
#> GSM1299538 4 0.5608 0.634 0.144 0.052 0.068 0.724 0.012
#> GSM1299539 1 0.7479 -0.472 0.420 0.392 0.024 0.128 0.036
#> GSM1299540 4 0.4292 0.630 0.008 0.016 0.204 0.760 0.012
#> GSM1299541 3 0.0162 0.778 0.000 0.000 0.996 0.004 0.000
#> GSM1299542 3 0.0290 0.777 0.000 0.000 0.992 0.008 0.000
#> GSM1299543 2 0.6577 0.506 0.132 0.600 0.216 0.052 0.000
#> GSM1299544 3 0.6299 0.683 0.072 0.160 0.680 0.060 0.028
#> GSM1299545 4 0.4191 0.601 0.096 0.004 0.012 0.808 0.080
#> GSM1299546 2 0.4173 0.486 0.008 0.760 0.204 0.028 0.000
#> GSM1299547 5 0.1282 0.887 0.000 0.004 0.000 0.044 0.952
#> GSM1299548 3 0.0324 0.779 0.000 0.004 0.992 0.004 0.000
#> GSM1299549 4 0.5950 0.582 0.048 0.024 0.040 0.676 0.212
#> GSM1299550 5 0.4703 0.776 0.044 0.012 0.068 0.080 0.796
#> GSM1299551 2 0.5754 0.546 0.384 0.548 0.028 0.040 0.000
#> GSM1299552 5 0.5602 0.488 0.060 0.020 0.000 0.296 0.624
#> GSM1299553 1 0.6708 -0.391 0.428 0.396 0.000 0.164 0.012
#> GSM1299554 3 0.3929 0.760 0.004 0.164 0.796 0.032 0.004
#> GSM1299555 3 0.1059 0.774 0.004 0.020 0.968 0.008 0.000
#> GSM1299556 3 0.0324 0.778 0.004 0.000 0.992 0.004 0.000
#> GSM1299557 2 0.6349 0.507 0.412 0.492 0.028 0.060 0.008
#> GSM1299558 3 0.5757 0.689 0.048 0.228 0.676 0.024 0.024
#> GSM1299559 3 0.0807 0.776 0.000 0.012 0.976 0.012 0.000
#> GSM1299560 3 0.0162 0.778 0.004 0.000 0.996 0.000 0.000
#> GSM1299576 1 0.4434 0.629 0.536 0.000 0.000 0.460 0.004
#> GSM1299577 4 0.3043 0.652 0.088 0.000 0.020 0.872 0.020
#> GSM1299561 3 0.0000 0.778 0.000 0.000 1.000 0.000 0.000
#> GSM1299562 3 0.7389 0.504 0.024 0.276 0.536 0.084 0.080
#> GSM1299563 4 0.3924 0.766 0.052 0.024 0.040 0.848 0.036
#> GSM1299564 4 0.3976 0.754 0.052 0.016 0.088 0.832 0.012
#> GSM1299565 2 0.3993 0.462 0.000 0.756 0.216 0.028 0.000
#> GSM1299566 3 0.6596 0.596 0.168 0.076 0.656 0.072 0.028
#> GSM1299567 4 0.3692 0.732 0.020 0.024 0.100 0.844 0.012
#> GSM1299568 3 0.5388 0.706 0.032 0.232 0.692 0.032 0.012
#> GSM1299569 3 0.5452 0.728 0.036 0.168 0.728 0.044 0.024
#> GSM1299570 4 0.1804 0.744 0.024 0.000 0.024 0.940 0.012
#> GSM1299571 2 0.4620 0.386 0.000 0.652 0.320 0.028 0.000
#> GSM1299572 5 0.1573 0.889 0.004 0.004 0.008 0.036 0.948
#> GSM1299573 3 0.0671 0.780 0.000 0.016 0.980 0.004 0.000
#> GSM1299574 2 0.5298 0.607 0.180 0.712 0.080 0.028 0.000
#> GSM1299578 1 0.4552 0.615 0.524 0.000 0.000 0.468 0.008
#> GSM1299579 1 0.6575 0.304 0.428 0.004 0.000 0.392 0.176
#> GSM1299580 1 0.4437 0.620 0.532 0.000 0.000 0.464 0.004
#> GSM1299581 1 0.4434 0.629 0.536 0.000 0.000 0.460 0.004
#> GSM1299582 1 0.4434 0.629 0.536 0.000 0.000 0.460 0.004
#> GSM1299583 1 0.6622 0.348 0.416 0.000 0.000 0.364 0.220
#> GSM1299584 1 0.4434 0.629 0.536 0.000 0.000 0.460 0.004
#> GSM1299585 5 0.1461 0.885 0.016 0.004 0.000 0.028 0.952
#> GSM1299586 1 0.4434 0.629 0.536 0.000 0.000 0.460 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1299517 3 0.4174 0.3880 0.000 0.352 0.628 0.004 0.000 0.016
#> GSM1299518 2 0.4389 0.1267 0.000 0.512 0.468 0.004 0.000 0.016
#> GSM1299519 6 0.4631 0.5960 0.000 0.352 0.052 0.000 0.000 0.596
#> GSM1299520 4 0.1518 0.7320 0.024 0.000 0.008 0.944 0.000 0.024
#> GSM1299521 5 0.2257 0.8094 0.008 0.020 0.000 0.016 0.912 0.044
#> GSM1299522 2 0.2740 0.6745 0.000 0.864 0.076 0.000 0.000 0.060
#> GSM1299523 4 0.1858 0.7340 0.024 0.004 0.016 0.932 0.000 0.024
#> GSM1299524 5 0.3621 0.6834 0.000 0.012 0.144 0.020 0.808 0.016
#> GSM1299525 6 0.3321 0.8112 0.000 0.180 0.016 0.008 0.000 0.796
#> GSM1299526 2 0.4476 0.6207 0.000 0.664 0.272 0.000 0.000 0.064
#> GSM1299527 3 0.4474 0.3612 0.000 0.360 0.608 0.012 0.000 0.020
#> GSM1299528 3 0.5716 0.5716 0.000 0.136 0.628 0.028 0.008 0.200
#> GSM1299529 6 0.3121 0.8112 0.000 0.180 0.012 0.004 0.000 0.804
#> GSM1299530 4 0.6637 0.3167 0.280 0.004 0.000 0.468 0.208 0.040
#> GSM1299531 3 0.4723 0.6498 0.000 0.260 0.672 0.004 0.012 0.052
#> GSM1299575 1 0.0603 0.9317 0.980 0.000 0.000 0.016 0.004 0.000
#> GSM1299532 3 0.1493 0.7634 0.000 0.056 0.936 0.004 0.000 0.004
#> GSM1299533 5 0.1554 0.8221 0.004 0.004 0.000 0.044 0.940 0.008
#> GSM1299534 3 0.3158 0.7216 0.000 0.164 0.812 0.000 0.004 0.020
#> GSM1299535 3 0.4842 0.4600 0.000 0.316 0.624 0.036 0.000 0.024
#> GSM1299536 5 0.1285 0.8205 0.000 0.000 0.000 0.052 0.944 0.004
#> GSM1299537 3 0.0000 0.7712 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299538 4 0.3608 0.6650 0.004 0.016 0.032 0.824 0.008 0.116
#> GSM1299539 6 0.2868 0.7383 0.004 0.052 0.008 0.056 0.004 0.876
#> GSM1299540 4 0.4297 0.5090 0.024 0.004 0.284 0.680 0.000 0.008
#> GSM1299541 3 0.0000 0.7712 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299542 3 0.0000 0.7712 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299543 2 0.3593 0.5759 0.000 0.800 0.064 0.004 0.000 0.132
#> GSM1299544 3 0.5107 0.5900 0.000 0.272 0.636 0.008 0.008 0.076
#> GSM1299545 4 0.5741 0.3643 0.352 0.016 0.000 0.548 0.048 0.036
#> GSM1299546 2 0.2857 0.6679 0.000 0.856 0.072 0.000 0.000 0.072
#> GSM1299547 5 0.2526 0.8177 0.004 0.020 0.000 0.052 0.896 0.028
#> GSM1299548 3 0.0146 0.7707 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM1299549 4 0.6714 -0.0812 0.044 0.032 0.008 0.440 0.404 0.072
#> GSM1299550 5 0.3304 0.7792 0.000 0.032 0.012 0.064 0.856 0.036
#> GSM1299551 6 0.4185 0.6940 0.000 0.332 0.020 0.004 0.000 0.644
#> GSM1299552 5 0.5998 0.5287 0.020 0.040 0.000 0.252 0.600 0.088
#> GSM1299553 6 0.5019 0.7004 0.076 0.072 0.000 0.104 0.012 0.736
#> GSM1299554 3 0.2095 0.7599 0.000 0.076 0.904 0.016 0.000 0.004
#> GSM1299555 3 0.1086 0.7665 0.000 0.012 0.964 0.012 0.000 0.012
#> GSM1299556 3 0.0976 0.7673 0.000 0.016 0.968 0.008 0.000 0.008
#> GSM1299557 6 0.3946 0.8060 0.004 0.160 0.036 0.020 0.000 0.780
#> GSM1299558 3 0.5105 0.5745 0.000 0.320 0.600 0.004 0.008 0.068
#> GSM1299559 3 0.1092 0.7608 0.000 0.020 0.960 0.020 0.000 0.000
#> GSM1299560 3 0.0622 0.7702 0.000 0.008 0.980 0.000 0.000 0.012
#> GSM1299576 1 0.0000 0.9335 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299577 4 0.3819 0.5073 0.316 0.000 0.000 0.672 0.012 0.000
#> GSM1299561 3 0.0000 0.7712 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299562 3 0.6414 0.4885 0.000 0.200 0.600 0.028 0.096 0.076
#> GSM1299563 4 0.1696 0.7280 0.016 0.008 0.008 0.944 0.012 0.012
#> GSM1299564 4 0.2095 0.7273 0.016 0.004 0.052 0.916 0.000 0.012
#> GSM1299565 2 0.2629 0.6666 0.000 0.872 0.068 0.000 0.000 0.060
#> GSM1299566 3 0.5671 0.5725 0.000 0.128 0.632 0.028 0.008 0.204
#> GSM1299567 4 0.4420 0.6388 0.072 0.004 0.168 0.744 0.004 0.008
#> GSM1299568 3 0.4894 0.4589 0.000 0.412 0.532 0.000 0.004 0.052
#> GSM1299569 3 0.4914 0.6282 0.000 0.244 0.668 0.008 0.008 0.072
#> GSM1299570 4 0.1779 0.7271 0.064 0.000 0.000 0.920 0.000 0.016
#> GSM1299571 2 0.4158 0.6428 0.000 0.704 0.244 0.000 0.000 0.052
#> GSM1299572 5 0.1152 0.8224 0.004 0.000 0.000 0.044 0.952 0.000
#> GSM1299573 3 0.0405 0.7709 0.000 0.004 0.988 0.008 0.000 0.000
#> GSM1299574 2 0.4921 -0.1602 0.000 0.508 0.052 0.004 0.000 0.436
#> GSM1299578 1 0.1219 0.9056 0.948 0.000 0.000 0.048 0.000 0.004
#> GSM1299579 1 0.5586 0.4890 0.616 0.000 0.000 0.152 0.208 0.024
#> GSM1299580 1 0.0603 0.9317 0.980 0.000 0.000 0.016 0.004 0.000
#> GSM1299581 1 0.0000 0.9335 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299582 1 0.0000 0.9335 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299583 5 0.5218 0.0190 0.460 0.000 0.000 0.068 0.464 0.008
#> GSM1299584 1 0.0547 0.9294 0.980 0.000 0.000 0.020 0.000 0.000
#> GSM1299585 5 0.2341 0.8086 0.008 0.024 0.000 0.016 0.908 0.044
#> GSM1299586 1 0.0146 0.9330 0.996 0.000 0.000 0.000 0.000 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:mclust 62 0.1383 2
#> CV:mclust 40 0.0435 3
#> CV:mclust 57 0.0670 4
#> CV:mclust 58 0.3163 5
#> CV:mclust 58 0.0862 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "NMF"]
# you can also extract it by
# res = res_list["CV:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 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 0.940 0.929 0.973 0.4936 0.508 0.508
#> 3 3 0.465 0.484 0.710 0.3217 0.832 0.680
#> 4 4 0.518 0.410 0.630 0.1301 0.722 0.386
#> 5 5 0.620 0.597 0.743 0.0778 0.857 0.524
#> 6 6 0.781 0.691 0.801 0.0506 0.928 0.673
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
#> GSM1299517 2 0.0000 0.9721 0.000 1.000
#> GSM1299518 2 0.0000 0.9721 0.000 1.000
#> GSM1299519 2 0.0000 0.9721 0.000 1.000
#> GSM1299520 1 0.0000 0.9702 1.000 0.000
#> GSM1299521 1 0.0000 0.9702 1.000 0.000
#> GSM1299522 2 0.0000 0.9721 0.000 1.000
#> GSM1299523 1 0.0672 0.9632 0.992 0.008
#> GSM1299524 2 0.7528 0.7221 0.216 0.784
#> GSM1299525 2 0.0000 0.9721 0.000 1.000
#> GSM1299526 2 0.0000 0.9721 0.000 1.000
#> GSM1299527 2 0.0000 0.9721 0.000 1.000
#> GSM1299528 2 0.0000 0.9721 0.000 1.000
#> GSM1299529 2 0.0000 0.9721 0.000 1.000
#> GSM1299530 1 0.0000 0.9702 1.000 0.000
#> GSM1299531 2 0.0000 0.9721 0.000 1.000
#> GSM1299575 1 0.0000 0.9702 1.000 0.000
#> GSM1299532 2 0.0000 0.9721 0.000 1.000
#> GSM1299533 1 0.0000 0.9702 1.000 0.000
#> GSM1299534 2 0.0000 0.9721 0.000 1.000
#> GSM1299535 2 0.0000 0.9721 0.000 1.000
#> GSM1299536 1 0.0000 0.9702 1.000 0.000
#> GSM1299537 2 0.0000 0.9721 0.000 1.000
#> GSM1299538 2 0.9970 0.1021 0.468 0.532
#> GSM1299539 2 0.0000 0.9721 0.000 1.000
#> GSM1299540 2 0.5629 0.8369 0.132 0.868
#> GSM1299541 2 0.0000 0.9721 0.000 1.000
#> GSM1299542 2 0.0000 0.9721 0.000 1.000
#> GSM1299543 2 0.0000 0.9721 0.000 1.000
#> GSM1299544 2 0.0000 0.9721 0.000 1.000
#> GSM1299545 1 0.0000 0.9702 1.000 0.000
#> GSM1299546 2 0.0000 0.9721 0.000 1.000
#> GSM1299547 1 0.0000 0.9702 1.000 0.000
#> GSM1299548 2 0.0000 0.9721 0.000 1.000
#> GSM1299549 1 0.0376 0.9669 0.996 0.004
#> GSM1299550 1 0.8955 0.5287 0.688 0.312
#> GSM1299551 2 0.0000 0.9721 0.000 1.000
#> GSM1299552 1 0.0000 0.9702 1.000 0.000
#> GSM1299553 1 0.9988 0.0642 0.520 0.480
#> GSM1299554 2 0.0000 0.9721 0.000 1.000
#> GSM1299555 2 0.0000 0.9721 0.000 1.000
#> GSM1299556 2 0.0000 0.9721 0.000 1.000
#> GSM1299557 2 0.0000 0.9721 0.000 1.000
#> GSM1299558 2 0.0000 0.9721 0.000 1.000
#> GSM1299559 2 0.8267 0.6490 0.260 0.740
#> GSM1299560 2 0.0000 0.9721 0.000 1.000
#> GSM1299576 1 0.0000 0.9702 1.000 0.000
#> GSM1299577 1 0.0000 0.9702 1.000 0.000
#> GSM1299561 2 0.0000 0.9721 0.000 1.000
#> GSM1299562 2 0.0000 0.9721 0.000 1.000
#> GSM1299563 1 0.0000 0.9702 1.000 0.000
#> GSM1299564 1 0.0000 0.9702 1.000 0.000
#> GSM1299565 2 0.0000 0.9721 0.000 1.000
#> GSM1299566 2 0.0000 0.9721 0.000 1.000
#> GSM1299567 1 0.0000 0.9702 1.000 0.000
#> GSM1299568 2 0.0000 0.9721 0.000 1.000
#> GSM1299569 2 0.0000 0.9721 0.000 1.000
#> GSM1299570 1 0.0000 0.9702 1.000 0.000
#> GSM1299571 2 0.0000 0.9721 0.000 1.000
#> GSM1299572 1 0.0000 0.9702 1.000 0.000
#> GSM1299573 2 0.0000 0.9721 0.000 1.000
#> GSM1299574 2 0.0000 0.9721 0.000 1.000
#> GSM1299578 1 0.0000 0.9702 1.000 0.000
#> GSM1299579 1 0.0000 0.9702 1.000 0.000
#> GSM1299580 1 0.0000 0.9702 1.000 0.000
#> GSM1299581 1 0.0000 0.9702 1.000 0.000
#> GSM1299582 1 0.0000 0.9702 1.000 0.000
#> GSM1299583 1 0.0000 0.9702 1.000 0.000
#> GSM1299584 1 0.0000 0.9702 1.000 0.000
#> GSM1299585 1 0.0000 0.9702 1.000 0.000
#> GSM1299586 1 0.0000 0.9702 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1299517 2 0.5497 0.5657 0.000 0.708 0.292
#> GSM1299518 2 0.4062 0.5766 0.000 0.836 0.164
#> GSM1299519 2 0.0000 0.6215 0.000 1.000 0.000
#> GSM1299520 3 0.6299 -0.0329 0.476 0.000 0.524
#> GSM1299521 1 0.4654 0.7696 0.792 0.000 0.208
#> GSM1299522 2 0.0000 0.6215 0.000 1.000 0.000
#> GSM1299523 3 0.5465 0.3806 0.288 0.000 0.712
#> GSM1299524 3 0.6798 -0.1906 0.016 0.400 0.584
#> GSM1299525 2 0.6140 0.1970 0.000 0.596 0.404
#> GSM1299526 2 0.0424 0.6212 0.000 0.992 0.008
#> GSM1299527 2 0.6180 0.4123 0.000 0.584 0.416
#> GSM1299528 2 0.6204 0.4158 0.000 0.576 0.424
#> GSM1299529 2 0.6095 0.2122 0.000 0.608 0.392
#> GSM1299530 1 0.5591 0.5525 0.696 0.000 0.304
#> GSM1299531 2 0.1860 0.6251 0.000 0.948 0.052
#> GSM1299575 1 0.0000 0.8249 1.000 0.000 0.000
#> GSM1299532 2 0.6079 0.5218 0.000 0.612 0.388
#> GSM1299533 1 0.5061 0.7645 0.784 0.008 0.208
#> GSM1299534 2 0.5431 0.5672 0.000 0.716 0.284
#> GSM1299535 2 0.4235 0.5093 0.000 0.824 0.176
#> GSM1299536 1 0.5327 0.7143 0.728 0.000 0.272
#> GSM1299537 2 0.6126 0.5093 0.000 0.600 0.400
#> GSM1299538 3 0.8649 0.3690 0.204 0.196 0.600
#> GSM1299539 2 0.6678 0.0916 0.008 0.512 0.480
#> GSM1299540 3 0.9266 0.0745 0.156 0.420 0.424
#> GSM1299541 2 0.6079 0.5218 0.000 0.612 0.388
#> GSM1299542 2 0.6079 0.5218 0.000 0.612 0.388
#> GSM1299543 2 0.4452 0.4851 0.000 0.808 0.192
#> GSM1299544 2 0.6235 0.4252 0.000 0.564 0.436
#> GSM1299545 1 0.3686 0.6974 0.860 0.000 0.140
#> GSM1299546 2 0.0000 0.6215 0.000 1.000 0.000
#> GSM1299547 1 0.4654 0.7696 0.792 0.000 0.208
#> GSM1299548 2 0.6095 0.5178 0.000 0.608 0.392
#> GSM1299549 3 0.6235 -0.2078 0.436 0.000 0.564
#> GSM1299550 3 0.7187 0.3008 0.232 0.076 0.692
#> GSM1299551 2 0.0000 0.6215 0.000 1.000 0.000
#> GSM1299552 1 0.5785 0.6769 0.668 0.000 0.332
#> GSM1299553 3 0.9836 0.2624 0.344 0.252 0.404
#> GSM1299554 3 0.6280 -0.4571 0.000 0.460 0.540
#> GSM1299555 2 0.4796 0.5581 0.000 0.780 0.220
#> GSM1299556 2 0.6062 0.5226 0.000 0.616 0.384
#> GSM1299557 2 0.6095 0.2122 0.000 0.608 0.392
#> GSM1299558 2 0.4235 0.5851 0.000 0.824 0.176
#> GSM1299559 3 0.8768 -0.1810 0.112 0.408 0.480
#> GSM1299560 2 0.5760 0.5447 0.000 0.672 0.328
#> GSM1299576 1 0.0000 0.8249 1.000 0.000 0.000
#> GSM1299577 1 0.0000 0.8249 1.000 0.000 0.000
#> GSM1299561 2 0.6079 0.5218 0.000 0.612 0.388
#> GSM1299562 3 0.6460 -0.1447 0.004 0.440 0.556
#> GSM1299563 3 0.6309 -0.1598 0.496 0.000 0.504
#> GSM1299564 3 0.5016 0.4226 0.240 0.000 0.760
#> GSM1299565 2 0.0000 0.6215 0.000 1.000 0.000
#> GSM1299566 2 0.6307 0.3173 0.000 0.512 0.488
#> GSM1299567 1 0.6260 0.0368 0.552 0.000 0.448
#> GSM1299568 2 0.5733 0.5261 0.000 0.676 0.324
#> GSM1299569 2 0.6260 0.4311 0.000 0.552 0.448
#> GSM1299570 1 0.5785 0.4821 0.668 0.000 0.332
#> GSM1299571 2 0.0000 0.6215 0.000 1.000 0.000
#> GSM1299572 1 0.4654 0.7696 0.792 0.000 0.208
#> GSM1299573 2 0.6079 0.5218 0.000 0.612 0.388
#> GSM1299574 2 0.0000 0.6215 0.000 1.000 0.000
#> GSM1299578 1 0.0000 0.8249 1.000 0.000 0.000
#> GSM1299579 1 0.2165 0.8170 0.936 0.000 0.064
#> GSM1299580 1 0.0000 0.8249 1.000 0.000 0.000
#> GSM1299581 1 0.0237 0.8250 0.996 0.000 0.004
#> GSM1299582 1 0.0000 0.8249 1.000 0.000 0.000
#> GSM1299583 1 0.2625 0.8053 0.916 0.000 0.084
#> GSM1299584 1 0.0237 0.8247 0.996 0.000 0.004
#> GSM1299585 1 0.4605 0.7713 0.796 0.000 0.204
#> GSM1299586 1 0.0000 0.8249 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1299517 3 0.2271 0.6017 0.008 0.076 0.916 0.000
#> GSM1299518 3 0.4961 -0.2286 0.000 0.448 0.552 0.000
#> GSM1299519 2 0.4776 0.5267 0.000 0.624 0.376 0.000
#> GSM1299520 1 0.6272 0.3506 0.720 0.124 0.036 0.120
#> GSM1299521 4 0.0000 0.7136 0.000 0.000 0.000 1.000
#> GSM1299522 2 0.4790 0.5260 0.000 0.620 0.380 0.000
#> GSM1299523 1 0.6934 0.3361 0.680 0.148 0.064 0.108
#> GSM1299524 3 0.4790 0.3323 0.000 0.000 0.620 0.380
#> GSM1299525 2 0.5022 0.3664 0.220 0.736 0.044 0.000
#> GSM1299526 2 0.4804 0.5210 0.000 0.616 0.384 0.000
#> GSM1299527 3 0.5427 0.2857 0.020 0.336 0.640 0.004
#> GSM1299528 3 0.7697 0.1132 0.176 0.348 0.468 0.008
#> GSM1299529 2 0.4356 0.4182 0.140 0.812 0.044 0.004
#> GSM1299530 1 0.7300 0.3546 0.584 0.100 0.032 0.284
#> GSM1299531 2 0.5161 0.3192 0.004 0.520 0.476 0.000
#> GSM1299575 1 0.4855 0.4413 0.600 0.000 0.000 0.400
#> GSM1299532 3 0.0000 0.6363 0.000 0.000 1.000 0.000
#> GSM1299533 4 0.0921 0.7010 0.000 0.028 0.000 0.972
#> GSM1299534 3 0.2596 0.5934 0.024 0.068 0.908 0.000
#> GSM1299535 2 0.5638 0.3368 0.028 0.584 0.388 0.000
#> GSM1299536 4 0.1854 0.6801 0.048 0.012 0.000 0.940
#> GSM1299537 3 0.0524 0.6358 0.004 0.008 0.988 0.000
#> GSM1299538 1 0.5633 0.2146 0.624 0.348 0.016 0.012
#> GSM1299539 2 0.5993 0.3214 0.276 0.664 0.044 0.016
#> GSM1299540 3 0.7153 0.0553 0.424 0.132 0.444 0.000
#> GSM1299541 3 0.1022 0.6233 0.000 0.032 0.968 0.000
#> GSM1299542 3 0.0188 0.6359 0.000 0.004 0.996 0.000
#> GSM1299543 2 0.4158 0.4735 0.008 0.768 0.224 0.000
#> GSM1299544 3 0.7384 0.1596 0.156 0.336 0.504 0.004
#> GSM1299545 1 0.4711 0.4441 0.740 0.024 0.000 0.236
#> GSM1299546 2 0.4790 0.5260 0.000 0.620 0.380 0.000
#> GSM1299547 4 0.0000 0.7136 0.000 0.000 0.000 1.000
#> GSM1299548 3 0.0336 0.6366 0.000 0.008 0.992 0.000
#> GSM1299549 4 0.8390 0.2163 0.180 0.140 0.120 0.560
#> GSM1299550 4 0.8364 0.2890 0.168 0.104 0.168 0.560
#> GSM1299551 2 0.3942 0.5246 0.000 0.764 0.236 0.000
#> GSM1299552 4 0.1284 0.6993 0.024 0.012 0.000 0.964
#> GSM1299553 2 0.6622 -0.0620 0.440 0.500 0.032 0.028
#> GSM1299554 3 0.2593 0.5850 0.004 0.104 0.892 0.000
#> GSM1299555 3 0.5673 0.2094 0.052 0.288 0.660 0.000
#> GSM1299556 3 0.0592 0.6317 0.000 0.016 0.984 0.000
#> GSM1299557 2 0.5020 0.3924 0.184 0.760 0.052 0.004
#> GSM1299558 2 0.5858 0.0358 0.032 0.500 0.468 0.000
#> GSM1299559 3 0.4704 0.4645 0.204 0.028 0.764 0.004
#> GSM1299560 3 0.2216 0.5688 0.000 0.092 0.908 0.000
#> GSM1299576 1 0.4855 0.4413 0.600 0.000 0.000 0.400
#> GSM1299577 1 0.4790 0.4432 0.620 0.000 0.000 0.380
#> GSM1299561 3 0.0188 0.6359 0.000 0.004 0.996 0.000
#> GSM1299562 2 0.9013 0.1662 0.184 0.412 0.320 0.084
#> GSM1299563 1 0.7083 0.2878 0.628 0.176 0.020 0.176
#> GSM1299564 1 0.7703 0.2754 0.616 0.184 0.084 0.116
#> GSM1299565 2 0.4790 0.5260 0.000 0.620 0.380 0.000
#> GSM1299566 3 0.7800 0.1152 0.176 0.344 0.468 0.012
#> GSM1299567 1 0.6092 0.3148 0.652 0.072 0.272 0.004
#> GSM1299568 3 0.6585 0.2275 0.104 0.312 0.584 0.000
#> GSM1299569 3 0.7370 0.2472 0.156 0.272 0.560 0.012
#> GSM1299570 1 0.6478 0.3803 0.644 0.100 0.008 0.248
#> GSM1299571 2 0.4790 0.5260 0.000 0.620 0.380 0.000
#> GSM1299572 4 0.0000 0.7136 0.000 0.000 0.000 1.000
#> GSM1299573 3 0.0000 0.6363 0.000 0.000 1.000 0.000
#> GSM1299574 2 0.4790 0.5260 0.000 0.620 0.380 0.000
#> GSM1299578 1 0.4855 0.4413 0.600 0.000 0.000 0.400
#> GSM1299579 4 0.4907 -0.1238 0.420 0.000 0.000 0.580
#> GSM1299580 1 0.4855 0.4413 0.600 0.000 0.000 0.400
#> GSM1299581 1 0.4855 0.4413 0.600 0.000 0.000 0.400
#> GSM1299582 1 0.4855 0.4413 0.600 0.000 0.000 0.400
#> GSM1299583 4 0.4817 0.0614 0.388 0.000 0.000 0.612
#> GSM1299584 1 0.4855 0.4413 0.600 0.000 0.000 0.400
#> GSM1299585 4 0.0188 0.7108 0.004 0.000 0.000 0.996
#> GSM1299586 1 0.4855 0.4413 0.600 0.000 0.000 0.400
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1299517 3 0.4295 0.6285 0.000 0.092 0.808 0.052 0.048
#> GSM1299518 2 0.3210 0.7333 0.000 0.788 0.212 0.000 0.000
#> GSM1299519 2 0.2516 0.7763 0.000 0.860 0.140 0.000 0.000
#> GSM1299520 4 0.4542 0.5304 0.264 0.000 0.016 0.704 0.016
#> GSM1299521 5 0.2966 0.8824 0.184 0.000 0.000 0.000 0.816
#> GSM1299522 2 0.2561 0.7787 0.000 0.856 0.144 0.000 0.000
#> GSM1299523 4 0.4065 0.5679 0.212 0.000 0.020 0.760 0.008
#> GSM1299524 3 0.4504 0.1703 0.008 0.000 0.564 0.000 0.428
#> GSM1299525 4 0.6784 0.2532 0.000 0.360 0.040 0.488 0.112
#> GSM1299526 2 0.2561 0.7787 0.000 0.856 0.144 0.000 0.000
#> GSM1299527 3 0.6869 0.3723 0.000 0.212 0.584 0.120 0.084
#> GSM1299528 3 0.7134 0.3929 0.000 0.068 0.460 0.364 0.108
#> GSM1299529 2 0.6571 -0.1815 0.000 0.464 0.024 0.400 0.112
#> GSM1299530 4 0.5608 0.4701 0.304 0.000 0.016 0.616 0.064
#> GSM1299531 2 0.4878 0.6669 0.000 0.720 0.208 0.012 0.060
#> GSM1299575 1 0.0162 0.9066 0.996 0.000 0.000 0.004 0.000
#> GSM1299532 3 0.0162 0.7130 0.000 0.004 0.996 0.000 0.000
#> GSM1299533 5 0.3171 0.8794 0.176 0.008 0.000 0.000 0.816
#> GSM1299534 3 0.3980 0.6591 0.000 0.036 0.828 0.076 0.060
#> GSM1299535 2 0.7765 0.0618 0.000 0.428 0.300 0.184 0.088
#> GSM1299536 5 0.2886 0.8648 0.148 0.000 0.000 0.008 0.844
#> GSM1299537 3 0.0671 0.7109 0.000 0.004 0.980 0.016 0.000
#> GSM1299538 4 0.1638 0.5994 0.064 0.000 0.004 0.932 0.000
#> GSM1299539 4 0.5852 0.3981 0.000 0.160 0.028 0.668 0.144
#> GSM1299540 4 0.7551 0.3665 0.308 0.084 0.152 0.456 0.000
#> GSM1299541 3 0.1571 0.6774 0.000 0.060 0.936 0.004 0.000
#> GSM1299542 3 0.0451 0.7122 0.000 0.008 0.988 0.000 0.004
#> GSM1299543 2 0.5029 0.6620 0.000 0.756 0.100 0.100 0.044
#> GSM1299544 3 0.6984 0.4423 0.000 0.064 0.500 0.332 0.104
#> GSM1299545 1 0.4045 0.2397 0.644 0.000 0.000 0.356 0.000
#> GSM1299546 2 0.2561 0.7787 0.000 0.856 0.144 0.000 0.000
#> GSM1299547 5 0.2966 0.8824 0.184 0.000 0.000 0.000 0.816
#> GSM1299548 3 0.0324 0.7132 0.000 0.004 0.992 0.004 0.000
#> GSM1299549 4 0.7476 0.1233 0.032 0.060 0.076 0.440 0.392
#> GSM1299550 5 0.6416 0.2243 0.000 0.016 0.160 0.260 0.564
#> GSM1299551 2 0.0693 0.6592 0.000 0.980 0.012 0.000 0.008
#> GSM1299552 5 0.3555 0.8238 0.124 0.000 0.000 0.052 0.824
#> GSM1299553 4 0.8354 0.3778 0.136 0.260 0.036 0.456 0.112
#> GSM1299554 3 0.1648 0.7068 0.000 0.040 0.940 0.020 0.000
#> GSM1299555 2 0.5182 0.4085 0.000 0.544 0.412 0.044 0.000
#> GSM1299556 3 0.0510 0.7083 0.000 0.016 0.984 0.000 0.000
#> GSM1299557 4 0.6897 0.1763 0.000 0.404 0.044 0.440 0.112
#> GSM1299558 2 0.7494 0.0680 0.000 0.420 0.368 0.120 0.092
#> GSM1299559 3 0.4047 0.3616 0.000 0.004 0.676 0.320 0.000
#> GSM1299560 3 0.3336 0.4517 0.000 0.228 0.772 0.000 0.000
#> GSM1299576 1 0.0000 0.9088 1.000 0.000 0.000 0.000 0.000
#> GSM1299577 1 0.0963 0.8741 0.964 0.000 0.000 0.036 0.000
#> GSM1299561 3 0.0451 0.7132 0.000 0.008 0.988 0.004 0.000
#> GSM1299562 4 0.5908 0.1329 0.000 0.404 0.080 0.508 0.008
#> GSM1299563 4 0.2580 0.5971 0.064 0.000 0.016 0.900 0.020
#> GSM1299564 4 0.3090 0.5909 0.052 0.000 0.056 0.876 0.016
#> GSM1299565 2 0.2561 0.7787 0.000 0.856 0.144 0.000 0.000
#> GSM1299566 3 0.7127 0.3849 0.000 0.064 0.456 0.368 0.112
#> GSM1299567 4 0.5432 0.3462 0.392 0.000 0.064 0.544 0.000
#> GSM1299568 3 0.6736 0.4949 0.000 0.064 0.568 0.264 0.104
#> GSM1299569 3 0.6661 0.4772 0.000 0.056 0.540 0.316 0.088
#> GSM1299570 4 0.4960 0.4319 0.352 0.000 0.016 0.616 0.016
#> GSM1299571 2 0.2561 0.7787 0.000 0.856 0.144 0.000 0.000
#> GSM1299572 5 0.2966 0.8824 0.184 0.000 0.000 0.000 0.816
#> GSM1299573 3 0.0162 0.7130 0.000 0.004 0.996 0.000 0.000
#> GSM1299574 2 0.2561 0.7787 0.000 0.856 0.144 0.000 0.000
#> GSM1299578 1 0.0000 0.9088 1.000 0.000 0.000 0.000 0.000
#> GSM1299579 1 0.2648 0.7337 0.848 0.000 0.000 0.000 0.152
#> GSM1299580 1 0.0162 0.9066 0.996 0.000 0.000 0.004 0.000
#> GSM1299581 1 0.0000 0.9088 1.000 0.000 0.000 0.000 0.000
#> GSM1299582 1 0.0000 0.9088 1.000 0.000 0.000 0.000 0.000
#> GSM1299583 1 0.2891 0.6869 0.824 0.000 0.000 0.000 0.176
#> GSM1299584 1 0.0000 0.9088 1.000 0.000 0.000 0.000 0.000
#> GSM1299585 5 0.2966 0.8824 0.184 0.000 0.000 0.000 0.816
#> GSM1299586 1 0.0000 0.9088 1.000 0.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1299517 3 0.3464 0.3404 0.000 0.000 0.688 0.000 0.000 0.312
#> GSM1299518 2 0.0865 0.8989 0.000 0.964 0.036 0.000 0.000 0.000
#> GSM1299519 2 0.0146 0.9203 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM1299520 4 0.2320 0.8246 0.132 0.000 0.004 0.864 0.000 0.000
#> GSM1299521 5 0.1075 0.8562 0.048 0.000 0.000 0.000 0.952 0.000
#> GSM1299522 2 0.0146 0.9203 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM1299523 4 0.2420 0.8239 0.128 0.000 0.004 0.864 0.000 0.004
#> GSM1299524 5 0.4135 0.3246 0.000 0.008 0.404 0.000 0.584 0.004
#> GSM1299525 6 0.3577 0.6855 0.000 0.088 0.012 0.084 0.000 0.816
#> GSM1299526 2 0.0146 0.9203 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM1299527 6 0.3742 0.3684 0.000 0.000 0.348 0.004 0.000 0.648
#> GSM1299528 3 0.6967 0.2615 0.000 0.008 0.396 0.216 0.048 0.332
#> GSM1299529 6 0.3385 0.6656 0.000 0.144 0.008 0.036 0.000 0.812
#> GSM1299530 4 0.2734 0.8222 0.148 0.000 0.004 0.840 0.008 0.000
#> GSM1299531 2 0.1732 0.8688 0.000 0.920 0.004 0.000 0.004 0.072
#> GSM1299575 1 0.0405 0.9641 0.988 0.000 0.004 0.000 0.000 0.008
#> GSM1299532 3 0.0777 0.6733 0.000 0.024 0.972 0.004 0.000 0.000
#> GSM1299533 5 0.1075 0.8562 0.048 0.000 0.000 0.000 0.952 0.000
#> GSM1299534 3 0.5201 0.5435 0.000 0.016 0.716 0.100 0.044 0.124
#> GSM1299535 6 0.4784 0.6072 0.000 0.140 0.136 0.016 0.000 0.708
#> GSM1299536 5 0.0713 0.8451 0.028 0.000 0.000 0.000 0.972 0.000
#> GSM1299537 3 0.0909 0.6717 0.000 0.020 0.968 0.012 0.000 0.000
#> GSM1299538 4 0.0458 0.7583 0.016 0.000 0.000 0.984 0.000 0.000
#> GSM1299539 6 0.4948 0.4214 0.000 0.000 0.020 0.316 0.048 0.616
#> GSM1299540 4 0.5218 0.7337 0.168 0.064 0.080 0.688 0.000 0.000
#> GSM1299541 3 0.2320 0.6038 0.000 0.132 0.864 0.004 0.000 0.000
#> GSM1299542 3 0.1003 0.6734 0.000 0.028 0.964 0.004 0.000 0.004
#> GSM1299543 2 0.4934 0.5640 0.000 0.704 0.032 0.028 0.028 0.208
#> GSM1299544 3 0.6863 0.3205 0.000 0.012 0.444 0.176 0.048 0.320
#> GSM1299545 4 0.3907 0.4807 0.408 0.000 0.000 0.588 0.000 0.004
#> GSM1299546 2 0.0146 0.9203 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM1299547 5 0.1075 0.8562 0.048 0.000 0.000 0.000 0.952 0.000
#> GSM1299548 3 0.0820 0.6720 0.000 0.016 0.972 0.012 0.000 0.000
#> GSM1299549 6 0.6239 0.2735 0.000 0.000 0.016 0.296 0.224 0.464
#> GSM1299550 5 0.5875 0.3983 0.000 0.000 0.068 0.144 0.624 0.164
#> GSM1299551 2 0.2300 0.7793 0.000 0.856 0.000 0.000 0.000 0.144
#> GSM1299552 5 0.2020 0.7813 0.008 0.000 0.000 0.000 0.896 0.096
#> GSM1299553 6 0.3733 0.6667 0.020 0.048 0.008 0.108 0.000 0.816
#> GSM1299554 3 0.0837 0.6657 0.000 0.004 0.972 0.004 0.000 0.020
#> GSM1299555 2 0.3065 0.7497 0.000 0.820 0.152 0.028 0.000 0.000
#> GSM1299556 3 0.1010 0.6698 0.000 0.036 0.960 0.004 0.000 0.000
#> GSM1299557 6 0.3617 0.6868 0.000 0.088 0.016 0.080 0.000 0.816
#> GSM1299558 6 0.8292 -0.1344 0.000 0.264 0.236 0.152 0.048 0.300
#> GSM1299559 3 0.3817 0.0521 0.000 0.000 0.568 0.432 0.000 0.000
#> GSM1299560 3 0.3563 0.3581 0.000 0.336 0.664 0.000 0.000 0.000
#> GSM1299576 1 0.0291 0.9641 0.992 0.000 0.004 0.000 0.000 0.004
#> GSM1299577 1 0.1364 0.9163 0.944 0.004 0.004 0.048 0.000 0.000
#> GSM1299561 3 0.0858 0.6735 0.000 0.028 0.968 0.004 0.000 0.000
#> GSM1299562 4 0.4079 0.3831 0.000 0.380 0.008 0.608 0.000 0.004
#> GSM1299563 4 0.1003 0.7628 0.020 0.000 0.016 0.964 0.000 0.000
#> GSM1299564 4 0.0909 0.7641 0.020 0.000 0.012 0.968 0.000 0.000
#> GSM1299565 2 0.0146 0.9203 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM1299566 3 0.6873 0.2544 0.000 0.004 0.400 0.216 0.048 0.332
#> GSM1299567 4 0.3053 0.8122 0.168 0.000 0.020 0.812 0.000 0.000
#> GSM1299568 3 0.6751 0.3381 0.000 0.012 0.464 0.156 0.048 0.320
#> GSM1299569 3 0.6842 0.3396 0.000 0.012 0.460 0.180 0.048 0.300
#> GSM1299570 4 0.2595 0.8191 0.160 0.000 0.004 0.836 0.000 0.000
#> GSM1299571 2 0.0146 0.9203 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM1299572 5 0.1075 0.8562 0.048 0.000 0.000 0.000 0.952 0.000
#> GSM1299573 3 0.0922 0.6737 0.000 0.024 0.968 0.004 0.000 0.004
#> GSM1299574 2 0.0146 0.9203 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM1299578 1 0.0405 0.9641 0.988 0.000 0.004 0.000 0.000 0.008
#> GSM1299579 1 0.1788 0.9021 0.916 0.004 0.004 0.000 0.076 0.000
#> GSM1299580 1 0.0405 0.9641 0.988 0.000 0.004 0.000 0.000 0.008
#> GSM1299581 1 0.0436 0.9608 0.988 0.004 0.004 0.000 0.000 0.004
#> GSM1299582 1 0.0146 0.9628 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM1299583 1 0.2292 0.8686 0.884 0.004 0.004 0.000 0.104 0.004
#> GSM1299584 1 0.0291 0.9621 0.992 0.004 0.000 0.000 0.000 0.004
#> GSM1299585 5 0.1075 0.8562 0.048 0.000 0.000 0.000 0.952 0.000
#> GSM1299586 1 0.0405 0.9641 0.988 0.000 0.004 0.000 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 disease.state(p) k
#> CV:NMF 68 0.0619 2
#> CV:NMF 45 0.1935 3
#> CV:NMF 27 0.2588 4
#> CV:NMF 45 0.0401 5
#> CV:NMF 54 0.0236 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "hclust"]
# you can also extract it by
# res = res_list["MAD:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 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 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 0.125 0.665 0.778 0.4519 0.526 0.526
#> 3 3 0.415 0.691 0.820 0.4069 0.810 0.639
#> 4 4 0.516 0.474 0.720 0.1347 0.902 0.733
#> 5 5 0.570 0.425 0.676 0.0739 0.854 0.567
#> 6 6 0.642 0.386 0.664 0.0446 0.860 0.507
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
#> GSM1299517 2 0.876 0.653 0.296 0.704
#> GSM1299518 2 0.738 0.646 0.208 0.792
#> GSM1299519 2 0.730 0.703 0.204 0.796
#> GSM1299520 1 0.224 0.845 0.964 0.036
#> GSM1299521 1 0.402 0.807 0.920 0.080
#> GSM1299522 2 0.730 0.703 0.204 0.796
#> GSM1299523 1 0.224 0.845 0.964 0.036
#> GSM1299524 2 0.821 0.699 0.256 0.744
#> GSM1299525 2 0.904 0.612 0.320 0.680
#> GSM1299526 2 0.844 0.704 0.272 0.728
#> GSM1299527 2 0.722 0.617 0.200 0.800
#> GSM1299528 2 0.981 0.452 0.420 0.580
#> GSM1299529 2 0.961 0.524 0.384 0.616
#> GSM1299530 1 0.224 0.845 0.964 0.036
#> GSM1299531 2 0.730 0.703 0.204 0.796
#> GSM1299575 1 0.141 0.843 0.980 0.020
#> GSM1299532 2 0.671 0.652 0.176 0.824
#> GSM1299533 2 0.767 0.702 0.224 0.776
#> GSM1299534 2 0.722 0.691 0.200 0.800
#> GSM1299535 2 0.730 0.716 0.204 0.796
#> GSM1299536 2 0.975 0.470 0.408 0.592
#> GSM1299537 2 0.808 0.607 0.248 0.752
#> GSM1299538 2 0.985 0.435 0.428 0.572
#> GSM1299539 2 0.987 0.426 0.432 0.568
#> GSM1299540 2 0.921 0.523 0.336 0.664
#> GSM1299541 2 0.808 0.607 0.248 0.752
#> GSM1299542 2 0.722 0.617 0.200 0.800
#> GSM1299543 2 0.706 0.697 0.192 0.808
#> GSM1299544 2 0.917 0.599 0.332 0.668
#> GSM1299545 1 0.184 0.839 0.972 0.028
#> GSM1299546 2 0.730 0.703 0.204 0.796
#> GSM1299547 1 0.662 0.718 0.828 0.172
#> GSM1299548 2 0.961 0.562 0.384 0.616
#> GSM1299549 1 0.891 0.395 0.692 0.308
#> GSM1299550 2 0.975 0.470 0.408 0.592
#> GSM1299551 2 0.730 0.703 0.204 0.796
#> GSM1299552 1 0.891 0.395 0.692 0.308
#> GSM1299553 1 0.506 0.775 0.888 0.112
#> GSM1299554 2 0.991 0.391 0.444 0.556
#> GSM1299555 2 0.921 0.523 0.336 0.664
#> GSM1299556 2 0.808 0.607 0.248 0.752
#> GSM1299557 1 0.891 0.395 0.692 0.308
#> GSM1299558 2 0.706 0.697 0.192 0.808
#> GSM1299559 2 0.808 0.607 0.248 0.752
#> GSM1299560 2 0.722 0.617 0.200 0.800
#> GSM1299576 1 0.141 0.843 0.980 0.020
#> GSM1299577 1 0.373 0.820 0.928 0.072
#> GSM1299561 2 0.738 0.646 0.208 0.792
#> GSM1299562 2 0.760 0.696 0.220 0.780
#> GSM1299563 1 0.662 0.718 0.828 0.172
#> GSM1299564 1 0.730 0.652 0.796 0.204
#> GSM1299565 2 0.844 0.704 0.272 0.728
#> GSM1299566 2 0.981 0.452 0.420 0.580
#> GSM1299567 1 0.904 0.438 0.680 0.320
#> GSM1299568 2 0.833 0.695 0.264 0.736
#> GSM1299569 2 0.921 0.601 0.336 0.664
#> GSM1299570 1 0.224 0.845 0.964 0.036
#> GSM1299571 2 0.821 0.707 0.256 0.744
#> GSM1299572 2 0.881 0.665 0.300 0.700
#> GSM1299573 2 0.671 0.673 0.176 0.824
#> GSM1299574 2 0.730 0.703 0.204 0.796
#> GSM1299578 1 0.141 0.843 0.980 0.020
#> GSM1299579 1 0.722 0.658 0.800 0.200
#> GSM1299580 1 0.141 0.843 0.980 0.020
#> GSM1299581 1 0.141 0.843 0.980 0.020
#> GSM1299582 1 0.141 0.843 0.980 0.020
#> GSM1299583 1 0.278 0.833 0.952 0.048
#> GSM1299584 1 0.141 0.843 0.980 0.020
#> GSM1299585 1 0.402 0.807 0.920 0.080
#> GSM1299586 1 0.141 0.843 0.980 0.020
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1299517 3 0.6349 0.674 0.080 0.156 0.764
#> GSM1299518 3 0.4539 0.779 0.016 0.148 0.836
#> GSM1299519 2 0.3116 0.752 0.000 0.892 0.108
#> GSM1299520 1 0.2200 0.848 0.940 0.056 0.004
#> GSM1299521 1 0.3551 0.821 0.868 0.132 0.000
#> GSM1299522 2 0.3116 0.752 0.000 0.892 0.108
#> GSM1299523 1 0.2301 0.848 0.936 0.060 0.004
#> GSM1299524 2 0.6853 0.685 0.064 0.712 0.224
#> GSM1299525 2 0.4945 0.760 0.104 0.840 0.056
#> GSM1299526 2 0.5465 0.578 0.000 0.712 0.288
#> GSM1299527 3 0.3267 0.784 0.000 0.116 0.884
#> GSM1299528 2 0.4062 0.718 0.164 0.836 0.000
#> GSM1299529 2 0.4679 0.736 0.148 0.832 0.020
#> GSM1299530 1 0.2301 0.848 0.936 0.060 0.004
#> GSM1299531 2 0.3116 0.752 0.000 0.892 0.108
#> GSM1299575 1 0.0000 0.845 1.000 0.000 0.000
#> GSM1299532 3 0.4750 0.741 0.000 0.216 0.784
#> GSM1299533 3 0.6587 0.341 0.008 0.424 0.568
#> GSM1299534 2 0.6822 -0.160 0.012 0.508 0.480
#> GSM1299535 2 0.6161 0.576 0.020 0.708 0.272
#> GSM1299536 2 0.3941 0.719 0.156 0.844 0.000
#> GSM1299537 3 0.0892 0.762 0.020 0.000 0.980
#> GSM1299538 2 0.4346 0.700 0.184 0.816 0.000
#> GSM1299539 2 0.4399 0.696 0.188 0.812 0.000
#> GSM1299540 3 0.6662 0.723 0.120 0.128 0.752
#> GSM1299541 3 0.0892 0.762 0.020 0.000 0.980
#> GSM1299542 3 0.3267 0.784 0.000 0.116 0.884
#> GSM1299543 2 0.2878 0.754 0.000 0.904 0.096
#> GSM1299544 2 0.4609 0.759 0.092 0.856 0.052
#> GSM1299545 1 0.0424 0.842 0.992 0.000 0.008
#> GSM1299546 2 0.3116 0.752 0.000 0.892 0.108
#> GSM1299547 1 0.5178 0.723 0.744 0.256 0.000
#> GSM1299548 2 0.9067 0.174 0.140 0.476 0.384
#> GSM1299549 1 0.7043 0.387 0.576 0.400 0.024
#> GSM1299550 2 0.3879 0.721 0.152 0.848 0.000
#> GSM1299551 2 0.3116 0.752 0.000 0.892 0.108
#> GSM1299552 1 0.7043 0.387 0.576 0.400 0.024
#> GSM1299553 1 0.3425 0.817 0.884 0.112 0.004
#> GSM1299554 2 0.5331 0.681 0.184 0.792 0.024
#> GSM1299555 3 0.6662 0.723 0.120 0.128 0.752
#> GSM1299556 3 0.0892 0.762 0.020 0.000 0.980
#> GSM1299557 1 0.7043 0.387 0.576 0.400 0.024
#> GSM1299558 2 0.2959 0.754 0.000 0.900 0.100
#> GSM1299559 3 0.0892 0.762 0.020 0.000 0.980
#> GSM1299560 3 0.3340 0.785 0.000 0.120 0.880
#> GSM1299576 1 0.0000 0.845 1.000 0.000 0.000
#> GSM1299577 1 0.3551 0.821 0.868 0.132 0.000
#> GSM1299561 3 0.4539 0.779 0.016 0.148 0.836
#> GSM1299562 3 0.6688 0.385 0.012 0.408 0.580
#> GSM1299563 1 0.5178 0.723 0.744 0.256 0.000
#> GSM1299564 1 0.5431 0.692 0.716 0.284 0.000
#> GSM1299565 2 0.5465 0.578 0.000 0.712 0.288
#> GSM1299566 2 0.4062 0.718 0.164 0.836 0.000
#> GSM1299567 1 0.6267 0.174 0.548 0.000 0.452
#> GSM1299568 2 0.6488 0.718 0.064 0.744 0.192
#> GSM1299569 2 0.4807 0.758 0.092 0.848 0.060
#> GSM1299570 1 0.2301 0.848 0.936 0.060 0.004
#> GSM1299571 2 0.4842 0.637 0.000 0.776 0.224
#> GSM1299572 3 0.9594 0.297 0.204 0.360 0.436
#> GSM1299573 3 0.6298 0.491 0.004 0.388 0.608
#> GSM1299574 2 0.3116 0.752 0.000 0.892 0.108
#> GSM1299578 1 0.0000 0.845 1.000 0.000 0.000
#> GSM1299579 1 0.5178 0.702 0.744 0.256 0.000
#> GSM1299580 1 0.0000 0.845 1.000 0.000 0.000
#> GSM1299581 1 0.0000 0.845 1.000 0.000 0.000
#> GSM1299582 1 0.0000 0.845 1.000 0.000 0.000
#> GSM1299583 1 0.2066 0.844 0.940 0.060 0.000
#> GSM1299584 1 0.0000 0.845 1.000 0.000 0.000
#> GSM1299585 1 0.3551 0.821 0.868 0.132 0.000
#> GSM1299586 1 0.0000 0.845 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1299517 3 0.5000 0.48818 0.000 0.128 0.772 0.100
#> GSM1299518 3 0.7008 0.66403 0.000 0.160 0.564 0.276
#> GSM1299519 2 0.0000 0.52540 0.000 1.000 0.000 0.000
#> GSM1299520 1 0.3232 0.81094 0.872 0.016 0.004 0.108
#> GSM1299521 1 0.4436 0.78018 0.800 0.052 0.000 0.148
#> GSM1299522 2 0.0469 0.52542 0.000 0.988 0.000 0.012
#> GSM1299523 1 0.3232 0.81099 0.872 0.016 0.004 0.108
#> GSM1299524 2 0.5951 0.29639 0.000 0.636 0.064 0.300
#> GSM1299525 2 0.4420 0.34793 0.012 0.748 0.000 0.240
#> GSM1299526 2 0.4605 0.39573 0.000 0.800 0.108 0.092
#> GSM1299527 3 0.6640 0.67838 0.000 0.168 0.624 0.208
#> GSM1299528 2 0.6087 0.01202 0.048 0.540 0.000 0.412
#> GSM1299529 2 0.5793 0.16238 0.048 0.628 0.000 0.324
#> GSM1299530 1 0.3232 0.81099 0.872 0.016 0.004 0.108
#> GSM1299531 2 0.0469 0.52542 0.000 0.988 0.000 0.012
#> GSM1299575 1 0.0000 0.81197 1.000 0.000 0.000 0.000
#> GSM1299532 3 0.7704 0.55623 0.000 0.232 0.432 0.336
#> GSM1299533 2 0.7438 -0.12251 0.000 0.484 0.328 0.188
#> GSM1299534 4 0.6611 -0.06807 0.000 0.456 0.080 0.464
#> GSM1299535 2 0.5325 0.36153 0.000 0.744 0.096 0.160
#> GSM1299536 4 0.5372 0.06961 0.012 0.444 0.000 0.544
#> GSM1299537 3 0.0188 0.66138 0.000 0.000 0.996 0.004
#> GSM1299538 2 0.6400 -0.00517 0.068 0.524 0.000 0.408
#> GSM1299539 2 0.6458 -0.01259 0.072 0.520 0.000 0.408
#> GSM1299540 3 0.8487 0.54966 0.096 0.152 0.536 0.216
#> GSM1299541 3 0.0188 0.66138 0.000 0.000 0.996 0.004
#> GSM1299542 3 0.7084 0.66353 0.000 0.176 0.560 0.264
#> GSM1299543 2 0.1302 0.51533 0.000 0.956 0.000 0.044
#> GSM1299544 2 0.4999 0.26849 0.000 0.660 0.012 0.328
#> GSM1299545 1 0.0672 0.80807 0.984 0.000 0.008 0.008
#> GSM1299546 2 0.0000 0.52540 0.000 1.000 0.000 0.000
#> GSM1299547 1 0.5785 0.69882 0.664 0.064 0.000 0.272
#> GSM1299548 4 0.8047 0.18031 0.012 0.212 0.368 0.408
#> GSM1299549 1 0.7877 0.26773 0.452 0.212 0.008 0.328
#> GSM1299550 4 0.5132 0.06799 0.004 0.448 0.000 0.548
#> GSM1299551 2 0.0000 0.52540 0.000 1.000 0.000 0.000
#> GSM1299552 1 0.7877 0.26773 0.452 0.212 0.008 0.328
#> GSM1299553 1 0.3328 0.77961 0.872 0.024 0.004 0.100
#> GSM1299554 4 0.5334 0.15170 0.012 0.364 0.004 0.620
#> GSM1299555 3 0.8487 0.54966 0.096 0.152 0.536 0.216
#> GSM1299556 3 0.0000 0.66301 0.000 0.000 1.000 0.000
#> GSM1299557 1 0.7877 0.26773 0.452 0.212 0.008 0.328
#> GSM1299558 2 0.2271 0.50407 0.000 0.916 0.008 0.076
#> GSM1299559 3 0.0000 0.66301 0.000 0.000 1.000 0.000
#> GSM1299560 3 0.7105 0.66192 0.000 0.176 0.556 0.268
#> GSM1299576 1 0.0000 0.81197 1.000 0.000 0.000 0.000
#> GSM1299577 1 0.4204 0.78217 0.788 0.020 0.000 0.192
#> GSM1299561 3 0.7008 0.66403 0.000 0.160 0.564 0.276
#> GSM1299562 2 0.7771 -0.22304 0.000 0.432 0.292 0.276
#> GSM1299563 1 0.5785 0.69882 0.664 0.064 0.000 0.272
#> GSM1299564 1 0.5530 0.67496 0.632 0.032 0.000 0.336
#> GSM1299565 2 0.4605 0.39573 0.000 0.800 0.108 0.092
#> GSM1299566 2 0.6087 0.01202 0.048 0.540 0.000 0.412
#> GSM1299567 1 0.5594 0.15763 0.520 0.000 0.460 0.020
#> GSM1299568 2 0.5599 0.33010 0.000 0.664 0.048 0.288
#> GSM1299569 2 0.5323 0.22909 0.000 0.628 0.020 0.352
#> GSM1299570 1 0.3232 0.81099 0.872 0.016 0.004 0.108
#> GSM1299571 2 0.3542 0.43538 0.000 0.864 0.060 0.076
#> GSM1299572 2 0.9836 -0.22472 0.196 0.340 0.244 0.220
#> GSM1299573 4 0.7782 -0.34844 0.000 0.360 0.244 0.396
#> GSM1299574 2 0.0000 0.52540 0.000 1.000 0.000 0.000
#> GSM1299578 1 0.0000 0.81197 1.000 0.000 0.000 0.000
#> GSM1299579 1 0.6339 0.62856 0.656 0.148 0.000 0.196
#> GSM1299580 1 0.0000 0.81197 1.000 0.000 0.000 0.000
#> GSM1299581 1 0.0707 0.81409 0.980 0.000 0.000 0.020
#> GSM1299582 1 0.0000 0.81197 1.000 0.000 0.000 0.000
#> GSM1299583 1 0.2443 0.81096 0.916 0.024 0.000 0.060
#> GSM1299584 1 0.0000 0.81197 1.000 0.000 0.000 0.000
#> GSM1299585 1 0.4436 0.78018 0.800 0.052 0.000 0.148
#> GSM1299586 1 0.0000 0.81197 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1299517 3 0.7257 -0.0907 0.000 0.052 0.472 0.312 0.164
#> GSM1299518 3 0.3319 0.2633 0.000 0.016 0.848 0.116 0.020
#> GSM1299519 2 0.0162 0.7049 0.000 0.996 0.004 0.000 0.000
#> GSM1299520 1 0.4322 0.7758 0.768 0.000 0.000 0.088 0.144
#> GSM1299521 1 0.4554 0.7322 0.736 0.016 0.000 0.032 0.216
#> GSM1299522 2 0.0404 0.7001 0.000 0.988 0.000 0.000 0.012
#> GSM1299523 1 0.4334 0.7765 0.768 0.000 0.000 0.092 0.140
#> GSM1299524 2 0.8024 0.1368 0.000 0.396 0.136 0.156 0.312
#> GSM1299525 2 0.4029 0.2812 0.004 0.680 0.000 0.000 0.316
#> GSM1299526 2 0.4190 0.6198 0.000 0.768 0.060 0.172 0.000
#> GSM1299527 3 0.2249 0.2495 0.000 0.008 0.896 0.096 0.000
#> GSM1299528 5 0.4935 0.4565 0.040 0.344 0.000 0.000 0.616
#> GSM1299529 2 0.5265 -0.1044 0.040 0.544 0.000 0.004 0.412
#> GSM1299530 1 0.4334 0.7765 0.768 0.000 0.000 0.092 0.140
#> GSM1299531 2 0.0566 0.7014 0.000 0.984 0.000 0.004 0.012
#> GSM1299575 1 0.0162 0.8021 0.996 0.000 0.000 0.004 0.000
#> GSM1299532 3 0.2949 0.2554 0.000 0.028 0.884 0.064 0.024
#> GSM1299533 2 0.6712 -0.1478 0.000 0.416 0.260 0.324 0.000
#> GSM1299534 3 0.7429 0.0979 0.000 0.164 0.504 0.248 0.084
#> GSM1299535 2 0.6835 0.4515 0.000 0.600 0.136 0.092 0.172
#> GSM1299536 5 0.3211 0.5262 0.004 0.164 0.000 0.008 0.824
#> GSM1299537 3 0.4307 -0.2550 0.000 0.000 0.500 0.500 0.000
#> GSM1299538 5 0.5145 0.4685 0.056 0.332 0.000 0.000 0.612
#> GSM1299539 5 0.5338 0.4711 0.060 0.328 0.000 0.004 0.608
#> GSM1299540 4 0.6272 0.4660 0.036 0.056 0.380 0.524 0.004
#> GSM1299541 4 0.4307 -0.1690 0.000 0.000 0.500 0.500 0.000
#> GSM1299542 3 0.0898 0.2914 0.000 0.008 0.972 0.020 0.000
#> GSM1299543 2 0.1197 0.6780 0.000 0.952 0.000 0.000 0.048
#> GSM1299544 5 0.5555 0.0668 0.000 0.452 0.000 0.068 0.480
#> GSM1299545 1 0.1671 0.7858 0.924 0.000 0.000 0.076 0.000
#> GSM1299546 2 0.0162 0.7049 0.000 0.996 0.004 0.000 0.000
#> GSM1299547 1 0.5126 0.6305 0.600 0.004 0.000 0.040 0.356
#> GSM1299548 5 0.6537 0.0299 0.000 0.012 0.232 0.212 0.544
#> GSM1299549 5 0.6841 -0.0142 0.428 0.084 0.004 0.048 0.436
#> GSM1299550 5 0.3203 0.5221 0.000 0.168 0.000 0.012 0.820
#> GSM1299551 2 0.0162 0.7049 0.000 0.996 0.004 0.000 0.000
#> GSM1299552 5 0.6841 -0.0142 0.428 0.084 0.004 0.048 0.436
#> GSM1299553 1 0.3069 0.7449 0.864 0.016 0.000 0.016 0.104
#> GSM1299554 5 0.3757 0.4933 0.000 0.088 0.008 0.076 0.828
#> GSM1299555 4 0.6272 0.4660 0.036 0.056 0.380 0.524 0.004
#> GSM1299556 3 0.4307 -0.2502 0.000 0.000 0.504 0.496 0.000
#> GSM1299557 5 0.6841 -0.0142 0.428 0.084 0.004 0.048 0.436
#> GSM1299558 2 0.2438 0.6593 0.000 0.900 0.000 0.040 0.060
#> GSM1299559 3 0.4307 -0.2502 0.000 0.000 0.504 0.496 0.000
#> GSM1299560 3 0.0798 0.2923 0.000 0.008 0.976 0.016 0.000
#> GSM1299576 1 0.0324 0.8026 0.992 0.000 0.000 0.004 0.004
#> GSM1299577 1 0.5284 0.7184 0.660 0.000 0.000 0.104 0.236
#> GSM1299561 3 0.3319 0.2633 0.000 0.016 0.848 0.116 0.020
#> GSM1299562 3 0.7344 -0.1429 0.000 0.312 0.364 0.300 0.024
#> GSM1299563 1 0.5126 0.6305 0.600 0.004 0.000 0.040 0.356
#> GSM1299564 1 0.5255 0.5872 0.560 0.000 0.000 0.052 0.388
#> GSM1299565 2 0.4190 0.6198 0.000 0.768 0.060 0.172 0.000
#> GSM1299566 5 0.4935 0.4565 0.040 0.344 0.000 0.000 0.616
#> GSM1299567 1 0.6108 -0.0491 0.456 0.000 0.108 0.432 0.004
#> GSM1299568 2 0.7803 0.1629 0.000 0.424 0.112 0.148 0.316
#> GSM1299569 5 0.6328 0.1750 0.000 0.376 0.012 0.116 0.496
#> GSM1299570 1 0.4334 0.7765 0.768 0.000 0.000 0.092 0.140
#> GSM1299571 2 0.3262 0.6525 0.000 0.840 0.036 0.124 0.000
#> GSM1299572 3 0.9494 -0.0956 0.172 0.172 0.356 0.196 0.104
#> GSM1299573 3 0.6246 0.1078 0.000 0.080 0.604 0.268 0.048
#> GSM1299574 2 0.0162 0.7049 0.000 0.996 0.004 0.000 0.000
#> GSM1299578 1 0.0324 0.8026 0.992 0.000 0.000 0.004 0.004
#> GSM1299579 1 0.6073 0.5330 0.612 0.088 0.000 0.032 0.268
#> GSM1299580 1 0.0162 0.8021 0.996 0.000 0.000 0.004 0.000
#> GSM1299581 1 0.0671 0.8047 0.980 0.000 0.000 0.004 0.016
#> GSM1299582 1 0.0162 0.8021 0.996 0.000 0.000 0.004 0.000
#> GSM1299583 1 0.2414 0.7947 0.900 0.008 0.000 0.012 0.080
#> GSM1299584 1 0.0162 0.8021 0.996 0.000 0.000 0.004 0.000
#> GSM1299585 1 0.4554 0.7322 0.736 0.016 0.000 0.032 0.216
#> GSM1299586 1 0.0324 0.8026 0.992 0.000 0.000 0.004 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1299517 3 0.4130 0.4004 0.000 0.044 0.760 0.004 0.016 0.176
#> GSM1299518 3 0.4400 0.3374 0.000 0.000 0.524 0.456 0.008 0.012
#> GSM1299519 2 0.0000 0.7034 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299520 1 0.5287 0.6082 0.636 0.000 0.000 0.080 0.252 0.032
#> GSM1299521 1 0.4203 0.5229 0.608 0.008 0.000 0.004 0.376 0.004
#> GSM1299522 2 0.0508 0.6996 0.000 0.984 0.000 0.000 0.012 0.004
#> GSM1299523 1 0.5287 0.6092 0.636 0.000 0.000 0.080 0.252 0.032
#> GSM1299524 6 0.5965 0.4240 0.000 0.272 0.004 0.152 0.020 0.552
#> GSM1299525 2 0.4869 0.3255 0.000 0.628 0.000 0.000 0.276 0.096
#> GSM1299526 2 0.4687 0.5807 0.000 0.760 0.076 0.088 0.008 0.068
#> GSM1299527 3 0.4084 0.3991 0.000 0.000 0.588 0.400 0.000 0.012
#> GSM1299528 5 0.6135 0.2393 0.016 0.248 0.000 0.000 0.500 0.236
#> GSM1299529 2 0.5913 0.0552 0.016 0.492 0.000 0.004 0.368 0.120
#> GSM1299530 1 0.5287 0.6092 0.636 0.000 0.000 0.080 0.252 0.032
#> GSM1299531 2 0.0725 0.7005 0.000 0.976 0.000 0.000 0.012 0.012
#> GSM1299575 1 0.0000 0.7106 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299532 4 0.4273 -0.2787 0.000 0.000 0.380 0.596 0.000 0.024
#> GSM1299533 2 0.7344 -0.1695 0.000 0.408 0.160 0.312 0.012 0.108
#> GSM1299534 4 0.4550 0.2801 0.000 0.044 0.008 0.692 0.008 0.248
#> GSM1299535 2 0.5447 0.2242 0.000 0.580 0.000 0.152 0.004 0.264
#> GSM1299536 5 0.4652 0.1082 0.000 0.072 0.000 0.000 0.640 0.288
#> GSM1299537 3 0.0458 0.5218 0.000 0.000 0.984 0.016 0.000 0.000
#> GSM1299538 5 0.6427 0.2548 0.028 0.236 0.000 0.004 0.496 0.236
#> GSM1299539 5 0.6456 0.2558 0.032 0.232 0.000 0.004 0.500 0.232
#> GSM1299540 4 0.6957 0.3290 0.012 0.044 0.312 0.484 0.020 0.128
#> GSM1299541 3 0.0458 0.5218 0.000 0.000 0.984 0.016 0.000 0.000
#> GSM1299542 3 0.4181 0.3403 0.000 0.000 0.512 0.476 0.000 0.012
#> GSM1299543 2 0.1285 0.6783 0.000 0.944 0.000 0.000 0.052 0.004
#> GSM1299544 2 0.6611 -0.2379 0.000 0.344 0.000 0.024 0.320 0.312
#> GSM1299545 1 0.1951 0.6845 0.908 0.000 0.000 0.076 0.000 0.016
#> GSM1299546 2 0.0000 0.7034 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299547 5 0.4454 -0.4267 0.476 0.004 0.000 0.008 0.504 0.008
#> GSM1299548 6 0.6101 0.0993 0.000 0.004 0.360 0.008 0.176 0.452
#> GSM1299549 1 0.6878 0.1825 0.412 0.060 0.000 0.000 0.228 0.300
#> GSM1299550 5 0.4751 0.0707 0.000 0.072 0.000 0.000 0.616 0.312
#> GSM1299551 2 0.0000 0.7034 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299552 1 0.6878 0.1825 0.412 0.060 0.000 0.000 0.228 0.300
#> GSM1299553 1 0.3331 0.6293 0.840 0.016 0.000 0.008 0.104 0.032
#> GSM1299554 6 0.4835 0.2249 0.000 0.048 0.000 0.004 0.408 0.540
#> GSM1299555 4 0.6957 0.3290 0.012 0.044 0.312 0.484 0.020 0.128
#> GSM1299556 3 0.0146 0.5281 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM1299557 1 0.6878 0.1825 0.412 0.060 0.000 0.000 0.228 0.300
#> GSM1299558 2 0.2583 0.6442 0.000 0.884 0.000 0.008 0.056 0.052
#> GSM1299559 3 0.0146 0.5281 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM1299560 3 0.4183 0.3356 0.000 0.000 0.508 0.480 0.000 0.012
#> GSM1299576 1 0.0146 0.7109 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM1299577 1 0.5662 0.4519 0.484 0.000 0.000 0.084 0.408 0.024
#> GSM1299561 3 0.4400 0.3374 0.000 0.000 0.524 0.456 0.008 0.012
#> GSM1299562 4 0.7094 0.3307 0.000 0.292 0.140 0.464 0.016 0.088
#> GSM1299563 5 0.4454 -0.4267 0.476 0.004 0.000 0.008 0.504 0.008
#> GSM1299564 5 0.4636 -0.3650 0.396 0.000 0.000 0.012 0.568 0.024
#> GSM1299565 2 0.4687 0.5807 0.000 0.760 0.076 0.088 0.008 0.068
#> GSM1299566 5 0.6135 0.2393 0.016 0.248 0.000 0.000 0.500 0.236
#> GSM1299567 3 0.6074 -0.0475 0.432 0.000 0.436 0.096 0.008 0.028
#> GSM1299568 6 0.5719 0.4138 0.000 0.300 0.000 0.124 0.020 0.556
#> GSM1299569 6 0.6551 0.1814 0.000 0.188 0.000 0.048 0.292 0.472
#> GSM1299570 1 0.5287 0.6092 0.636 0.000 0.000 0.080 0.252 0.032
#> GSM1299571 2 0.3632 0.6222 0.000 0.832 0.036 0.080 0.008 0.044
#> GSM1299572 4 0.8953 0.2882 0.152 0.156 0.096 0.408 0.120 0.068
#> GSM1299573 4 0.5129 0.2479 0.000 0.004 0.120 0.644 0.004 0.228
#> GSM1299574 2 0.0000 0.7034 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299578 1 0.0146 0.7109 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM1299579 1 0.5542 0.3335 0.496 0.060 0.000 0.004 0.416 0.024
#> GSM1299580 1 0.0000 0.7106 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299581 1 0.1007 0.7072 0.956 0.000 0.000 0.000 0.044 0.000
#> GSM1299582 1 0.0000 0.7106 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299583 1 0.2700 0.6729 0.836 0.000 0.000 0.004 0.156 0.004
#> GSM1299584 1 0.0000 0.7106 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299585 1 0.4203 0.5229 0.608 0.008 0.000 0.004 0.376 0.004
#> GSM1299586 1 0.0146 0.7109 0.996 0.000 0.000 0.000 0.004 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:hclust 59 0.0493 2
#> MAD:hclust 60 0.0243 3
#> MAD:hclust 42 0.0157 4
#> MAD:hclust 35 0.1432 5
#> MAD:hclust 32 0.0302 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "kmeans"]
# you can also extract it by
# res = res_list["MAD:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 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 0.771 0.942 0.951 0.4898 0.513 0.513
#> 3 3 0.854 0.913 0.933 0.3611 0.800 0.616
#> 4 4 0.728 0.720 0.842 0.1195 0.868 0.628
#> 5 5 0.712 0.570 0.765 0.0649 0.952 0.813
#> 6 6 0.708 0.501 0.705 0.0442 0.900 0.592
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
#> GSM1299517 2 0.2236 0.934 0.036 0.964
#> GSM1299518 2 0.2423 0.934 0.040 0.960
#> GSM1299519 2 0.3584 0.944 0.068 0.932
#> GSM1299520 1 0.0376 0.967 0.996 0.004
#> GSM1299521 1 0.0376 0.967 0.996 0.004
#> GSM1299522 2 0.3584 0.944 0.068 0.932
#> GSM1299523 1 0.3274 0.951 0.940 0.060
#> GSM1299524 2 0.0376 0.935 0.004 0.996
#> GSM1299525 2 0.3584 0.944 0.068 0.932
#> GSM1299526 2 0.0376 0.935 0.004 0.996
#> GSM1299527 2 0.2423 0.934 0.040 0.960
#> GSM1299528 2 0.7219 0.824 0.200 0.800
#> GSM1299529 2 0.3584 0.944 0.068 0.932
#> GSM1299530 1 0.0376 0.967 0.996 0.004
#> GSM1299531 2 0.3584 0.944 0.068 0.932
#> GSM1299575 1 0.3584 0.947 0.932 0.068
#> GSM1299532 2 0.0376 0.935 0.004 0.996
#> GSM1299533 2 0.3274 0.944 0.060 0.940
#> GSM1299534 2 0.3584 0.944 0.068 0.932
#> GSM1299535 2 0.3431 0.944 0.064 0.936
#> GSM1299536 1 0.0376 0.967 0.996 0.004
#> GSM1299537 2 0.2423 0.934 0.040 0.960
#> GSM1299538 1 0.2423 0.936 0.960 0.040
#> GSM1299539 1 0.2423 0.936 0.960 0.040
#> GSM1299540 2 0.2423 0.934 0.040 0.960
#> GSM1299541 2 0.2423 0.934 0.040 0.960
#> GSM1299542 2 0.2423 0.934 0.040 0.960
#> GSM1299543 2 0.3584 0.944 0.068 0.932
#> GSM1299544 2 0.3584 0.944 0.068 0.932
#> GSM1299545 1 0.3584 0.947 0.932 0.068
#> GSM1299546 2 0.3584 0.944 0.068 0.932
#> GSM1299547 1 0.0376 0.967 0.996 0.004
#> GSM1299548 2 0.2423 0.934 0.040 0.960
#> GSM1299549 1 0.0376 0.967 0.996 0.004
#> GSM1299550 2 0.7219 0.824 0.200 0.800
#> GSM1299551 2 0.3584 0.944 0.068 0.932
#> GSM1299552 1 0.0376 0.967 0.996 0.004
#> GSM1299553 1 0.0376 0.967 0.996 0.004
#> GSM1299554 2 0.3584 0.944 0.068 0.932
#> GSM1299555 2 0.2423 0.934 0.040 0.960
#> GSM1299556 2 0.2423 0.934 0.040 0.960
#> GSM1299557 2 0.2948 0.937 0.052 0.948
#> GSM1299558 2 0.3584 0.944 0.068 0.932
#> GSM1299559 2 0.2423 0.934 0.040 0.960
#> GSM1299560 2 0.2423 0.934 0.040 0.960
#> GSM1299576 1 0.1184 0.966 0.984 0.016
#> GSM1299577 1 0.3584 0.947 0.932 0.068
#> GSM1299561 2 0.2423 0.934 0.040 0.960
#> GSM1299562 2 0.3733 0.944 0.072 0.928
#> GSM1299563 1 0.0000 0.967 1.000 0.000
#> GSM1299564 1 0.0000 0.967 1.000 0.000
#> GSM1299565 2 0.3584 0.944 0.068 0.932
#> GSM1299566 2 0.7219 0.824 0.200 0.800
#> GSM1299567 1 0.3584 0.947 0.932 0.068
#> GSM1299568 2 0.3584 0.944 0.068 0.932
#> GSM1299569 2 0.3584 0.944 0.068 0.932
#> GSM1299570 1 0.3274 0.951 0.940 0.060
#> GSM1299571 2 0.3274 0.944 0.060 0.940
#> GSM1299572 2 0.2423 0.934 0.040 0.960
#> GSM1299573 2 0.2423 0.934 0.040 0.960
#> GSM1299574 2 0.3584 0.944 0.068 0.932
#> GSM1299578 1 0.0376 0.967 0.996 0.004
#> GSM1299579 1 0.0376 0.967 0.996 0.004
#> GSM1299580 1 0.3584 0.947 0.932 0.068
#> GSM1299581 1 0.1184 0.966 0.984 0.016
#> GSM1299582 1 0.3584 0.947 0.932 0.068
#> GSM1299583 1 0.0376 0.967 0.996 0.004
#> GSM1299584 1 0.3584 0.947 0.932 0.068
#> GSM1299585 1 0.0376 0.967 0.996 0.004
#> GSM1299586 1 0.3584 0.947 0.932 0.068
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1299517 3 0.1031 0.948 0.000 0.024 0.976
#> GSM1299518 3 0.1031 0.948 0.000 0.024 0.976
#> GSM1299519 2 0.2448 0.933 0.000 0.924 0.076
#> GSM1299520 1 0.2845 0.955 0.920 0.068 0.012
#> GSM1299521 1 0.2066 0.959 0.940 0.060 0.000
#> GSM1299522 2 0.2448 0.933 0.000 0.924 0.076
#> GSM1299523 1 0.2383 0.960 0.940 0.044 0.016
#> GSM1299524 3 0.1031 0.948 0.000 0.024 0.976
#> GSM1299525 2 0.0848 0.888 0.008 0.984 0.008
#> GSM1299526 3 0.5291 0.613 0.000 0.268 0.732
#> GSM1299527 3 0.1031 0.948 0.000 0.024 0.976
#> GSM1299528 2 0.1015 0.885 0.012 0.980 0.008
#> GSM1299529 2 0.0000 0.887 0.000 1.000 0.000
#> GSM1299530 1 0.1950 0.961 0.952 0.040 0.008
#> GSM1299531 2 0.2448 0.933 0.000 0.924 0.076
#> GSM1299575 1 0.0829 0.955 0.984 0.004 0.012
#> GSM1299532 3 0.1031 0.948 0.000 0.024 0.976
#> GSM1299533 2 0.2537 0.932 0.000 0.920 0.080
#> GSM1299534 2 0.6154 0.473 0.000 0.592 0.408
#> GSM1299535 2 0.2537 0.932 0.000 0.920 0.080
#> GSM1299536 1 0.3183 0.951 0.908 0.076 0.016
#> GSM1299537 3 0.0424 0.945 0.000 0.008 0.992
#> GSM1299538 1 0.5247 0.791 0.768 0.224 0.008
#> GSM1299539 1 0.2866 0.953 0.916 0.076 0.008
#> GSM1299540 3 0.0237 0.939 0.004 0.000 0.996
#> GSM1299541 3 0.0424 0.945 0.000 0.008 0.992
#> GSM1299542 3 0.1031 0.948 0.000 0.024 0.976
#> GSM1299543 2 0.2448 0.933 0.000 0.924 0.076
#> GSM1299544 2 0.2261 0.930 0.000 0.932 0.068
#> GSM1299545 1 0.1620 0.955 0.964 0.012 0.024
#> GSM1299546 2 0.2448 0.933 0.000 0.924 0.076
#> GSM1299547 1 0.2356 0.956 0.928 0.072 0.000
#> GSM1299548 3 0.0424 0.945 0.000 0.008 0.992
#> GSM1299549 1 0.2537 0.956 0.920 0.080 0.000
#> GSM1299550 2 0.4539 0.793 0.016 0.836 0.148
#> GSM1299551 2 0.2448 0.933 0.000 0.924 0.076
#> GSM1299552 1 0.2356 0.957 0.928 0.072 0.000
#> GSM1299553 1 0.2448 0.957 0.924 0.076 0.000
#> GSM1299554 2 0.5450 0.687 0.012 0.760 0.228
#> GSM1299555 3 0.0592 0.946 0.000 0.012 0.988
#> GSM1299556 3 0.0000 0.941 0.000 0.000 1.000
#> GSM1299557 3 0.1753 0.933 0.000 0.048 0.952
#> GSM1299558 2 0.2448 0.933 0.000 0.924 0.076
#> GSM1299559 3 0.0000 0.941 0.000 0.000 1.000
#> GSM1299560 3 0.1031 0.948 0.000 0.024 0.976
#> GSM1299576 1 0.0661 0.956 0.988 0.004 0.008
#> GSM1299577 1 0.1453 0.955 0.968 0.008 0.024
#> GSM1299561 3 0.1031 0.948 0.000 0.024 0.976
#> GSM1299562 2 0.4605 0.823 0.000 0.796 0.204
#> GSM1299563 1 0.2939 0.954 0.916 0.072 0.012
#> GSM1299564 1 0.3031 0.952 0.912 0.076 0.012
#> GSM1299565 2 0.2537 0.932 0.000 0.920 0.080
#> GSM1299566 2 0.1170 0.870 0.016 0.976 0.008
#> GSM1299567 3 0.6483 0.321 0.392 0.008 0.600
#> GSM1299568 2 0.2537 0.932 0.000 0.920 0.080
#> GSM1299569 2 0.2796 0.923 0.000 0.908 0.092
#> GSM1299570 1 0.2383 0.960 0.940 0.044 0.016
#> GSM1299571 2 0.2537 0.932 0.000 0.920 0.080
#> GSM1299572 3 0.0592 0.946 0.000 0.012 0.988
#> GSM1299573 3 0.1031 0.948 0.000 0.024 0.976
#> GSM1299574 2 0.2448 0.933 0.000 0.924 0.076
#> GSM1299578 1 0.0237 0.958 0.996 0.004 0.000
#> GSM1299579 1 0.1964 0.959 0.944 0.056 0.000
#> GSM1299580 1 0.0829 0.955 0.984 0.004 0.012
#> GSM1299581 1 0.0661 0.956 0.988 0.004 0.008
#> GSM1299582 1 0.0829 0.955 0.984 0.004 0.012
#> GSM1299583 1 0.0237 0.958 0.996 0.004 0.000
#> GSM1299584 1 0.0829 0.955 0.984 0.004 0.012
#> GSM1299585 1 0.0237 0.958 0.996 0.004 0.000
#> GSM1299586 1 0.0829 0.955 0.984 0.004 0.012
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1299517 3 0.2918 0.89612 0.000 0.008 0.876 0.116
#> GSM1299518 3 0.0779 0.90662 0.000 0.004 0.980 0.016
#> GSM1299519 2 0.0804 0.89612 0.000 0.980 0.008 0.012
#> GSM1299520 4 0.4991 0.56869 0.388 0.000 0.004 0.608
#> GSM1299521 1 0.3668 0.60017 0.808 0.004 0.000 0.188
#> GSM1299522 2 0.0188 0.89736 0.000 0.996 0.004 0.000
#> GSM1299523 4 0.5165 0.46098 0.484 0.000 0.004 0.512
#> GSM1299524 3 0.1661 0.89682 0.000 0.004 0.944 0.052
#> GSM1299525 2 0.1211 0.88457 0.000 0.960 0.000 0.040
#> GSM1299526 2 0.6634 0.32397 0.000 0.580 0.312 0.108
#> GSM1299527 3 0.0779 0.90814 0.000 0.004 0.980 0.016
#> GSM1299528 2 0.4250 0.69915 0.000 0.724 0.000 0.276
#> GSM1299529 2 0.1302 0.88397 0.000 0.956 0.000 0.044
#> GSM1299530 4 0.5167 0.45282 0.488 0.000 0.004 0.508
#> GSM1299531 2 0.0336 0.89747 0.000 0.992 0.008 0.000
#> GSM1299575 1 0.0188 0.78785 0.996 0.000 0.000 0.004
#> GSM1299532 3 0.1305 0.90179 0.000 0.004 0.960 0.036
#> GSM1299533 2 0.1798 0.88467 0.000 0.944 0.016 0.040
#> GSM1299534 3 0.6756 0.47912 0.000 0.200 0.612 0.188
#> GSM1299535 2 0.1798 0.88579 0.000 0.944 0.016 0.040
#> GSM1299536 4 0.3306 0.63695 0.156 0.004 0.000 0.840
#> GSM1299537 3 0.2401 0.90072 0.000 0.004 0.904 0.092
#> GSM1299538 4 0.4624 0.63145 0.164 0.052 0.000 0.784
#> GSM1299539 4 0.3982 0.64617 0.220 0.004 0.000 0.776
#> GSM1299540 3 0.3172 0.88418 0.000 0.000 0.840 0.160
#> GSM1299541 3 0.2266 0.90243 0.000 0.004 0.912 0.084
#> GSM1299542 3 0.0188 0.90836 0.000 0.004 0.996 0.000
#> GSM1299543 2 0.0188 0.89736 0.000 0.996 0.004 0.000
#> GSM1299544 2 0.4123 0.75966 0.000 0.772 0.008 0.220
#> GSM1299545 1 0.5150 0.00467 0.596 0.000 0.008 0.396
#> GSM1299546 2 0.0336 0.89747 0.000 0.992 0.008 0.000
#> GSM1299547 4 0.5163 0.31690 0.480 0.004 0.000 0.516
#> GSM1299548 3 0.1661 0.90746 0.000 0.004 0.944 0.052
#> GSM1299549 1 0.5203 0.05650 0.576 0.008 0.000 0.416
#> GSM1299550 4 0.3681 0.52246 0.004 0.124 0.024 0.848
#> GSM1299551 2 0.0336 0.89747 0.000 0.992 0.008 0.000
#> GSM1299552 1 0.4560 0.42096 0.700 0.004 0.000 0.296
#> GSM1299553 1 0.4920 0.16068 0.628 0.004 0.000 0.368
#> GSM1299554 4 0.4231 0.51500 0.000 0.080 0.096 0.824
#> GSM1299555 3 0.2647 0.89313 0.000 0.000 0.880 0.120
#> GSM1299556 3 0.2814 0.89037 0.000 0.000 0.868 0.132
#> GSM1299557 3 0.4074 0.85917 0.004 0.008 0.792 0.196
#> GSM1299558 2 0.0188 0.89736 0.000 0.996 0.004 0.000
#> GSM1299559 3 0.2868 0.88887 0.000 0.000 0.864 0.136
#> GSM1299560 3 0.0188 0.90836 0.000 0.004 0.996 0.000
#> GSM1299576 1 0.0000 0.79150 1.000 0.000 0.000 0.000
#> GSM1299577 4 0.5167 0.43219 0.488 0.000 0.004 0.508
#> GSM1299561 3 0.0188 0.90836 0.000 0.004 0.996 0.000
#> GSM1299562 2 0.3876 0.80196 0.000 0.836 0.124 0.040
#> GSM1299563 4 0.4920 0.57967 0.368 0.000 0.004 0.628
#> GSM1299564 4 0.3583 0.64551 0.180 0.004 0.000 0.816
#> GSM1299565 2 0.0672 0.89680 0.000 0.984 0.008 0.008
#> GSM1299566 2 0.4992 0.33691 0.000 0.524 0.000 0.476
#> GSM1299567 3 0.7276 0.45054 0.236 0.000 0.540 0.224
#> GSM1299568 2 0.1388 0.89196 0.000 0.960 0.012 0.028
#> GSM1299569 2 0.5235 0.72309 0.000 0.716 0.048 0.236
#> GSM1299570 4 0.5158 0.46800 0.472 0.000 0.004 0.524
#> GSM1299571 2 0.1151 0.89247 0.000 0.968 0.008 0.024
#> GSM1299572 3 0.2081 0.89815 0.000 0.000 0.916 0.084
#> GSM1299573 3 0.1305 0.90179 0.000 0.004 0.960 0.036
#> GSM1299574 2 0.0524 0.89706 0.000 0.988 0.004 0.008
#> GSM1299578 1 0.0000 0.79150 1.000 0.000 0.000 0.000
#> GSM1299579 1 0.4624 0.26922 0.660 0.000 0.000 0.340
#> GSM1299580 1 0.0188 0.78785 0.996 0.000 0.000 0.004
#> GSM1299581 1 0.0000 0.79150 1.000 0.000 0.000 0.000
#> GSM1299582 1 0.0000 0.79150 1.000 0.000 0.000 0.000
#> GSM1299583 1 0.0000 0.79150 1.000 0.000 0.000 0.000
#> GSM1299584 1 0.0000 0.79150 1.000 0.000 0.000 0.000
#> GSM1299585 1 0.0000 0.79150 1.000 0.000 0.000 0.000
#> GSM1299586 1 0.0000 0.79150 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1299517 3 0.4218 0.5442 0.000 0.000 0.660 0.008 0.332
#> GSM1299518 3 0.0404 0.7314 0.000 0.000 0.988 0.000 0.012
#> GSM1299519 2 0.0404 0.8705 0.000 0.988 0.000 0.000 0.012
#> GSM1299520 4 0.5998 0.4062 0.228 0.000 0.000 0.584 0.188
#> GSM1299521 1 0.4645 0.5576 0.724 0.000 0.000 0.204 0.072
#> GSM1299522 2 0.0162 0.8722 0.000 0.996 0.000 0.004 0.000
#> GSM1299523 4 0.6394 0.3361 0.292 0.000 0.000 0.504 0.204
#> GSM1299524 3 0.4221 0.5488 0.000 0.000 0.732 0.032 0.236
#> GSM1299525 2 0.1740 0.8469 0.000 0.932 0.000 0.056 0.012
#> GSM1299526 2 0.4291 0.6944 0.000 0.772 0.092 0.000 0.136
#> GSM1299527 3 0.1041 0.7295 0.000 0.000 0.964 0.004 0.032
#> GSM1299528 4 0.6269 -0.1820 0.000 0.408 0.000 0.444 0.148
#> GSM1299529 2 0.3493 0.7846 0.000 0.832 0.000 0.108 0.060
#> GSM1299530 4 0.6363 0.3420 0.304 0.000 0.000 0.504 0.192
#> GSM1299531 2 0.0162 0.8722 0.000 0.996 0.000 0.004 0.000
#> GSM1299575 1 0.1544 0.7400 0.932 0.000 0.000 0.000 0.068
#> GSM1299532 3 0.2358 0.6950 0.000 0.000 0.888 0.008 0.104
#> GSM1299533 2 0.2707 0.8134 0.000 0.860 0.008 0.000 0.132
#> GSM1299534 3 0.5989 0.4170 0.000 0.036 0.636 0.088 0.240
#> GSM1299535 2 0.2964 0.8079 0.000 0.840 0.004 0.004 0.152
#> GSM1299536 4 0.1764 0.5003 0.008 0.000 0.000 0.928 0.064
#> GSM1299537 3 0.3074 0.6643 0.000 0.000 0.804 0.000 0.196
#> GSM1299538 4 0.1830 0.5197 0.040 0.000 0.000 0.932 0.028
#> GSM1299539 4 0.2054 0.5213 0.052 0.000 0.000 0.920 0.028
#> GSM1299540 3 0.4449 0.3766 0.000 0.004 0.512 0.000 0.484
#> GSM1299541 3 0.2732 0.6850 0.000 0.000 0.840 0.000 0.160
#> GSM1299542 3 0.0162 0.7315 0.000 0.000 0.996 0.000 0.004
#> GSM1299543 2 0.0162 0.8722 0.000 0.996 0.000 0.004 0.000
#> GSM1299544 2 0.6326 0.3234 0.000 0.492 0.000 0.336 0.172
#> GSM1299545 5 0.7032 -0.1005 0.328 0.000 0.012 0.252 0.408
#> GSM1299546 2 0.0162 0.8722 0.000 0.996 0.000 0.004 0.000
#> GSM1299547 4 0.6084 0.1166 0.360 0.000 0.000 0.508 0.132
#> GSM1299548 3 0.2930 0.6872 0.000 0.000 0.832 0.004 0.164
#> GSM1299549 1 0.6381 0.1189 0.448 0.000 0.000 0.384 0.168
#> GSM1299550 4 0.2690 0.4513 0.000 0.000 0.000 0.844 0.156
#> GSM1299551 2 0.0162 0.8722 0.000 0.996 0.000 0.004 0.000
#> GSM1299552 1 0.6172 0.2267 0.500 0.000 0.000 0.356 0.144
#> GSM1299553 1 0.6289 0.0921 0.452 0.000 0.000 0.396 0.152
#> GSM1299554 4 0.3766 0.3831 0.000 0.000 0.004 0.728 0.268
#> GSM1299555 3 0.4101 0.5265 0.000 0.004 0.664 0.000 0.332
#> GSM1299556 3 0.4074 0.5200 0.000 0.000 0.636 0.000 0.364
#> GSM1299557 5 0.7014 -0.1255 0.032 0.016 0.292 0.124 0.536
#> GSM1299558 2 0.0162 0.8722 0.000 0.996 0.000 0.004 0.000
#> GSM1299559 3 0.4150 0.4849 0.000 0.000 0.612 0.000 0.388
#> GSM1299560 3 0.0162 0.7315 0.000 0.000 0.996 0.000 0.004
#> GSM1299576 1 0.0000 0.7594 1.000 0.000 0.000 0.000 0.000
#> GSM1299577 4 0.6608 0.2559 0.300 0.000 0.000 0.456 0.244
#> GSM1299561 3 0.0000 0.7314 0.000 0.000 1.000 0.000 0.000
#> GSM1299562 2 0.3555 0.7882 0.000 0.824 0.052 0.000 0.124
#> GSM1299563 4 0.5902 0.4093 0.208 0.000 0.000 0.600 0.192
#> GSM1299564 4 0.1725 0.5161 0.020 0.000 0.000 0.936 0.044
#> GSM1299565 2 0.0404 0.8705 0.000 0.988 0.000 0.000 0.012
#> GSM1299566 4 0.5224 0.3348 0.000 0.176 0.000 0.684 0.140
#> GSM1299567 5 0.7216 0.2725 0.132 0.000 0.256 0.084 0.528
#> GSM1299568 2 0.3847 0.7429 0.000 0.784 0.000 0.036 0.180
#> GSM1299569 2 0.7530 0.2137 0.000 0.416 0.060 0.340 0.184
#> GSM1299570 4 0.6424 0.3292 0.288 0.000 0.000 0.500 0.212
#> GSM1299571 2 0.0510 0.8697 0.000 0.984 0.000 0.000 0.016
#> GSM1299572 3 0.4109 0.5842 0.000 0.000 0.700 0.012 0.288
#> GSM1299573 3 0.2513 0.6900 0.000 0.000 0.876 0.008 0.116
#> GSM1299574 2 0.0404 0.8705 0.000 0.988 0.000 0.000 0.012
#> GSM1299578 1 0.0404 0.7582 0.988 0.000 0.000 0.000 0.012
#> GSM1299579 1 0.4425 0.2924 0.600 0.000 0.000 0.392 0.008
#> GSM1299580 1 0.1544 0.7400 0.932 0.000 0.000 0.000 0.068
#> GSM1299581 1 0.0000 0.7594 1.000 0.000 0.000 0.000 0.000
#> GSM1299582 1 0.1410 0.7438 0.940 0.000 0.000 0.000 0.060
#> GSM1299583 1 0.0000 0.7594 1.000 0.000 0.000 0.000 0.000
#> GSM1299584 1 0.1410 0.7438 0.940 0.000 0.000 0.000 0.060
#> GSM1299585 1 0.0324 0.7568 0.992 0.000 0.000 0.004 0.004
#> GSM1299586 1 0.0880 0.7537 0.968 0.000 0.000 0.000 0.032
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1299517 3 0.4026 0.36318 0.000 0.008 0.800 0.028 0.060 0.104
#> GSM1299518 3 0.4079 0.09974 0.000 0.000 0.608 0.008 0.004 0.380
#> GSM1299519 2 0.0260 0.86001 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM1299520 4 0.2436 0.62192 0.088 0.000 0.000 0.880 0.032 0.000
#> GSM1299521 1 0.5913 0.49037 0.632 0.000 0.000 0.140 0.124 0.104
#> GSM1299522 2 0.0458 0.86091 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM1299523 4 0.2135 0.63433 0.128 0.000 0.000 0.872 0.000 0.000
#> GSM1299524 6 0.5556 0.39574 0.000 0.000 0.264 0.000 0.188 0.548
#> GSM1299525 2 0.2743 0.74593 0.000 0.828 0.000 0.000 0.164 0.008
#> GSM1299526 2 0.3574 0.76735 0.000 0.824 0.104 0.008 0.012 0.052
#> GSM1299527 3 0.4187 0.18548 0.000 0.000 0.652 0.012 0.012 0.324
#> GSM1299528 5 0.5055 0.54705 0.000 0.184 0.000 0.080 0.692 0.044
#> GSM1299529 2 0.3631 0.71545 0.000 0.792 0.000 0.012 0.160 0.036
#> GSM1299530 4 0.2135 0.63433 0.128 0.000 0.000 0.872 0.000 0.000
#> GSM1299531 2 0.0458 0.86091 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM1299575 1 0.1370 0.82512 0.948 0.000 0.000 0.036 0.004 0.012
#> GSM1299532 6 0.4875 0.18816 0.000 0.000 0.460 0.008 0.040 0.492
#> GSM1299533 2 0.3706 0.73821 0.000 0.776 0.000 0.024 0.016 0.184
#> GSM1299534 6 0.5922 0.38853 0.000 0.004 0.248 0.008 0.200 0.540
#> GSM1299535 2 0.4826 0.62933 0.000 0.660 0.000 0.028 0.044 0.268
#> GSM1299536 5 0.3634 0.24297 0.000 0.000 0.000 0.356 0.644 0.000
#> GSM1299537 3 0.0291 0.45624 0.000 0.000 0.992 0.004 0.000 0.004
#> GSM1299538 4 0.4314 -0.03580 0.004 0.000 0.000 0.500 0.484 0.012
#> GSM1299539 4 0.4408 0.01185 0.008 0.000 0.000 0.512 0.468 0.012
#> GSM1299540 3 0.6081 0.10842 0.004 0.008 0.524 0.124 0.016 0.324
#> GSM1299541 3 0.0790 0.45248 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM1299542 3 0.3955 0.19817 0.000 0.000 0.648 0.008 0.004 0.340
#> GSM1299543 2 0.0865 0.85508 0.000 0.964 0.000 0.000 0.036 0.000
#> GSM1299544 5 0.4913 0.46553 0.000 0.252 0.000 0.000 0.636 0.112
#> GSM1299545 4 0.6233 0.45186 0.112 0.000 0.060 0.632 0.036 0.160
#> GSM1299546 2 0.0458 0.86091 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM1299547 4 0.7472 0.19881 0.256 0.000 0.000 0.344 0.264 0.136
#> GSM1299548 3 0.2159 0.42436 0.000 0.000 0.904 0.012 0.012 0.072
#> GSM1299549 5 0.7797 -0.17964 0.284 0.008 0.000 0.196 0.320 0.192
#> GSM1299550 5 0.3221 0.40608 0.000 0.000 0.000 0.264 0.736 0.000
#> GSM1299551 2 0.0547 0.86027 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM1299552 1 0.7378 0.04550 0.388 0.000 0.000 0.188 0.272 0.152
#> GSM1299553 4 0.7574 0.14223 0.280 0.000 0.000 0.312 0.252 0.156
#> GSM1299554 5 0.4039 0.42025 0.000 0.000 0.000 0.156 0.752 0.092
#> GSM1299555 6 0.5911 0.00272 0.000 0.008 0.356 0.120 0.012 0.504
#> GSM1299556 3 0.3240 0.39545 0.000 0.000 0.812 0.040 0.000 0.148
#> GSM1299557 6 0.8206 -0.02567 0.024 0.020 0.220 0.112 0.284 0.340
#> GSM1299558 2 0.1007 0.85193 0.000 0.956 0.000 0.000 0.044 0.000
#> GSM1299559 3 0.3637 0.37337 0.000 0.000 0.780 0.056 0.000 0.164
#> GSM1299560 3 0.3955 0.19817 0.000 0.000 0.648 0.008 0.004 0.340
#> GSM1299576 1 0.0964 0.83134 0.968 0.000 0.000 0.004 0.012 0.016
#> GSM1299577 4 0.3272 0.61601 0.124 0.000 0.000 0.824 0.004 0.048
#> GSM1299561 3 0.3940 0.20311 0.000 0.000 0.652 0.008 0.004 0.336
#> GSM1299562 2 0.4571 0.61704 0.000 0.652 0.000 0.024 0.024 0.300
#> GSM1299563 4 0.3761 0.57943 0.100 0.000 0.000 0.804 0.080 0.016
#> GSM1299564 4 0.3684 0.37419 0.004 0.000 0.000 0.692 0.300 0.004
#> GSM1299565 2 0.0405 0.85960 0.000 0.988 0.000 0.004 0.000 0.008
#> GSM1299566 5 0.5065 0.52161 0.000 0.100 0.000 0.172 0.692 0.036
#> GSM1299567 3 0.6628 0.10275 0.064 0.000 0.452 0.352 0.004 0.128
#> GSM1299568 2 0.5544 0.37618 0.000 0.568 0.000 0.004 0.260 0.168
#> GSM1299569 5 0.5707 0.46545 0.000 0.184 0.052 0.000 0.632 0.132
#> GSM1299570 4 0.2446 0.63140 0.124 0.000 0.000 0.864 0.000 0.012
#> GSM1299571 2 0.0862 0.85472 0.000 0.972 0.000 0.004 0.008 0.016
#> GSM1299572 6 0.5122 0.25244 0.000 0.004 0.240 0.072 0.024 0.660
#> GSM1299573 6 0.5065 0.30628 0.000 0.000 0.400 0.012 0.052 0.536
#> GSM1299574 2 0.0260 0.86001 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM1299578 1 0.0458 0.83351 0.984 0.000 0.000 0.016 0.000 0.000
#> GSM1299579 1 0.5877 0.24251 0.556 0.000 0.000 0.256 0.168 0.020
#> GSM1299580 1 0.1370 0.82512 0.948 0.000 0.000 0.036 0.004 0.012
#> GSM1299581 1 0.0964 0.83134 0.968 0.000 0.000 0.004 0.012 0.016
#> GSM1299582 1 0.1124 0.82808 0.956 0.000 0.000 0.036 0.000 0.008
#> GSM1299583 1 0.0964 0.83074 0.968 0.000 0.000 0.004 0.016 0.012
#> GSM1299584 1 0.1124 0.82808 0.956 0.000 0.000 0.036 0.000 0.008
#> GSM1299585 1 0.1148 0.82763 0.960 0.000 0.000 0.004 0.016 0.020
#> GSM1299586 1 0.0713 0.83169 0.972 0.000 0.000 0.028 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:kmeans 70 0.1422 2
#> MAD:kmeans 68 0.3437 3
#> MAD:kmeans 56 0.0433 4
#> MAD:kmeans 47 0.0581 5
#> MAD:kmeans 34 0.1445 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "skmeans"]
# you can also extract it by
# res = res_list["MAD:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.971 0.968 0.986 0.499 0.499 0.499
#> 3 3 0.977 0.939 0.974 0.343 0.764 0.556
#> 4 4 0.850 0.837 0.921 0.122 0.847 0.579
#> 5 5 0.748 0.690 0.814 0.057 0.943 0.777
#> 6 6 0.742 0.617 0.783 0.039 0.954 0.790
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM1299517 2 0.0000 0.992 0.000 1.000
#> GSM1299518 2 0.0000 0.992 0.000 1.000
#> GSM1299519 2 0.0000 0.992 0.000 1.000
#> GSM1299520 1 0.0000 0.976 1.000 0.000
#> GSM1299521 1 0.0000 0.976 1.000 0.000
#> GSM1299522 2 0.0000 0.992 0.000 1.000
#> GSM1299523 1 0.0000 0.976 1.000 0.000
#> GSM1299524 2 0.0000 0.992 0.000 1.000
#> GSM1299525 2 0.0000 0.992 0.000 1.000
#> GSM1299526 2 0.0000 0.992 0.000 1.000
#> GSM1299527 2 0.0000 0.992 0.000 1.000
#> GSM1299528 1 0.9686 0.373 0.604 0.396
#> GSM1299529 2 0.0000 0.992 0.000 1.000
#> GSM1299530 1 0.0000 0.976 1.000 0.000
#> GSM1299531 2 0.0000 0.992 0.000 1.000
#> GSM1299575 1 0.0000 0.976 1.000 0.000
#> GSM1299532 2 0.0000 0.992 0.000 1.000
#> GSM1299533 2 0.0000 0.992 0.000 1.000
#> GSM1299534 2 0.0000 0.992 0.000 1.000
#> GSM1299535 2 0.0000 0.992 0.000 1.000
#> GSM1299536 1 0.0000 0.976 1.000 0.000
#> GSM1299537 2 0.0000 0.992 0.000 1.000
#> GSM1299538 1 0.0000 0.976 1.000 0.000
#> GSM1299539 1 0.0000 0.976 1.000 0.000
#> GSM1299540 2 0.5059 0.875 0.112 0.888
#> GSM1299541 2 0.0000 0.992 0.000 1.000
#> GSM1299542 2 0.0000 0.992 0.000 1.000
#> GSM1299543 2 0.0000 0.992 0.000 1.000
#> GSM1299544 2 0.0000 0.992 0.000 1.000
#> GSM1299545 1 0.0000 0.976 1.000 0.000
#> GSM1299546 2 0.0000 0.992 0.000 1.000
#> GSM1299547 1 0.0000 0.976 1.000 0.000
#> GSM1299548 2 0.0000 0.992 0.000 1.000
#> GSM1299549 1 0.0000 0.976 1.000 0.000
#> GSM1299550 1 0.5519 0.850 0.872 0.128
#> GSM1299551 2 0.0000 0.992 0.000 1.000
#> GSM1299552 1 0.0000 0.976 1.000 0.000
#> GSM1299553 1 0.0000 0.976 1.000 0.000
#> GSM1299554 2 0.0672 0.986 0.008 0.992
#> GSM1299555 2 0.0000 0.992 0.000 1.000
#> GSM1299556 2 0.1414 0.975 0.020 0.980
#> GSM1299557 2 0.5519 0.855 0.128 0.872
#> GSM1299558 2 0.0000 0.992 0.000 1.000
#> GSM1299559 2 0.1184 0.979 0.016 0.984
#> GSM1299560 2 0.0000 0.992 0.000 1.000
#> GSM1299576 1 0.0000 0.976 1.000 0.000
#> GSM1299577 1 0.0000 0.976 1.000 0.000
#> GSM1299561 2 0.0000 0.992 0.000 1.000
#> GSM1299562 2 0.0000 0.992 0.000 1.000
#> GSM1299563 1 0.0000 0.976 1.000 0.000
#> GSM1299564 1 0.0000 0.976 1.000 0.000
#> GSM1299565 2 0.0000 0.992 0.000 1.000
#> GSM1299566 1 0.7056 0.770 0.808 0.192
#> GSM1299567 1 0.0000 0.976 1.000 0.000
#> GSM1299568 2 0.0000 0.992 0.000 1.000
#> GSM1299569 2 0.0000 0.992 0.000 1.000
#> GSM1299570 1 0.0000 0.976 1.000 0.000
#> GSM1299571 2 0.0000 0.992 0.000 1.000
#> GSM1299572 2 0.0000 0.992 0.000 1.000
#> GSM1299573 2 0.0000 0.992 0.000 1.000
#> GSM1299574 2 0.0000 0.992 0.000 1.000
#> GSM1299578 1 0.0000 0.976 1.000 0.000
#> GSM1299579 1 0.0000 0.976 1.000 0.000
#> GSM1299580 1 0.0000 0.976 1.000 0.000
#> GSM1299581 1 0.0000 0.976 1.000 0.000
#> GSM1299582 1 0.0000 0.976 1.000 0.000
#> GSM1299583 1 0.0000 0.976 1.000 0.000
#> GSM1299584 1 0.0000 0.976 1.000 0.000
#> GSM1299585 1 0.0000 0.976 1.000 0.000
#> GSM1299586 1 0.0000 0.976 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1299517 3 0.000 0.958 0.000 0.000 1.000
#> GSM1299518 3 0.000 0.958 0.000 0.000 1.000
#> GSM1299519 2 0.000 0.959 0.000 1.000 0.000
#> GSM1299520 1 0.000 0.993 1.000 0.000 0.000
#> GSM1299521 1 0.000 0.993 1.000 0.000 0.000
#> GSM1299522 2 0.000 0.959 0.000 1.000 0.000
#> GSM1299523 1 0.000 0.993 1.000 0.000 0.000
#> GSM1299524 3 0.000 0.958 0.000 0.000 1.000
#> GSM1299525 2 0.000 0.959 0.000 1.000 0.000
#> GSM1299526 3 0.565 0.538 0.000 0.312 0.688
#> GSM1299527 3 0.000 0.958 0.000 0.000 1.000
#> GSM1299528 2 0.000 0.959 0.000 1.000 0.000
#> GSM1299529 2 0.000 0.959 0.000 1.000 0.000
#> GSM1299530 1 0.000 0.993 1.000 0.000 0.000
#> GSM1299531 2 0.000 0.959 0.000 1.000 0.000
#> GSM1299575 1 0.000 0.993 1.000 0.000 0.000
#> GSM1299532 3 0.000 0.958 0.000 0.000 1.000
#> GSM1299533 2 0.129 0.935 0.000 0.968 0.032
#> GSM1299534 2 0.619 0.329 0.000 0.580 0.420
#> GSM1299535 2 0.000 0.959 0.000 1.000 0.000
#> GSM1299536 1 0.000 0.993 1.000 0.000 0.000
#> GSM1299537 3 0.000 0.958 0.000 0.000 1.000
#> GSM1299538 1 0.424 0.782 0.824 0.176 0.000
#> GSM1299539 1 0.000 0.993 1.000 0.000 0.000
#> GSM1299540 3 0.000 0.958 0.000 0.000 1.000
#> GSM1299541 3 0.000 0.958 0.000 0.000 1.000
#> GSM1299542 3 0.000 0.958 0.000 0.000 1.000
#> GSM1299543 2 0.000 0.959 0.000 1.000 0.000
#> GSM1299544 2 0.000 0.959 0.000 1.000 0.000
#> GSM1299545 1 0.000 0.993 1.000 0.000 0.000
#> GSM1299546 2 0.000 0.959 0.000 1.000 0.000
#> GSM1299547 1 0.000 0.993 1.000 0.000 0.000
#> GSM1299548 3 0.000 0.958 0.000 0.000 1.000
#> GSM1299549 1 0.000 0.993 1.000 0.000 0.000
#> GSM1299550 2 0.327 0.885 0.016 0.904 0.080
#> GSM1299551 2 0.000 0.959 0.000 1.000 0.000
#> GSM1299552 1 0.000 0.993 1.000 0.000 0.000
#> GSM1299553 1 0.000 0.993 1.000 0.000 0.000
#> GSM1299554 2 0.522 0.664 0.000 0.740 0.260
#> GSM1299555 3 0.000 0.958 0.000 0.000 1.000
#> GSM1299556 3 0.000 0.958 0.000 0.000 1.000
#> GSM1299557 3 0.265 0.897 0.060 0.012 0.928
#> GSM1299558 2 0.000 0.959 0.000 1.000 0.000
#> GSM1299559 3 0.000 0.958 0.000 0.000 1.000
#> GSM1299560 3 0.000 0.958 0.000 0.000 1.000
#> GSM1299576 1 0.000 0.993 1.000 0.000 0.000
#> GSM1299577 1 0.000 0.993 1.000 0.000 0.000
#> GSM1299561 3 0.000 0.958 0.000 0.000 1.000
#> GSM1299562 2 0.236 0.903 0.000 0.928 0.072
#> GSM1299563 1 0.000 0.993 1.000 0.000 0.000
#> GSM1299564 1 0.000 0.993 1.000 0.000 0.000
#> GSM1299565 2 0.000 0.959 0.000 1.000 0.000
#> GSM1299566 2 0.000 0.959 0.000 1.000 0.000
#> GSM1299567 3 0.590 0.457 0.352 0.000 0.648
#> GSM1299568 2 0.000 0.959 0.000 1.000 0.000
#> GSM1299569 2 0.000 0.959 0.000 1.000 0.000
#> GSM1299570 1 0.000 0.993 1.000 0.000 0.000
#> GSM1299571 2 0.000 0.959 0.000 1.000 0.000
#> GSM1299572 3 0.000 0.958 0.000 0.000 1.000
#> GSM1299573 3 0.000 0.958 0.000 0.000 1.000
#> GSM1299574 2 0.000 0.959 0.000 1.000 0.000
#> GSM1299578 1 0.000 0.993 1.000 0.000 0.000
#> GSM1299579 1 0.000 0.993 1.000 0.000 0.000
#> GSM1299580 1 0.000 0.993 1.000 0.000 0.000
#> GSM1299581 1 0.000 0.993 1.000 0.000 0.000
#> GSM1299582 1 0.000 0.993 1.000 0.000 0.000
#> GSM1299583 1 0.000 0.993 1.000 0.000 0.000
#> GSM1299584 1 0.000 0.993 1.000 0.000 0.000
#> GSM1299585 1 0.000 0.993 1.000 0.000 0.000
#> GSM1299586 1 0.000 0.993 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1299517 3 0.0336 0.946 0.000 0.000 0.992 0.008
#> GSM1299518 3 0.0000 0.950 0.000 0.000 1.000 0.000
#> GSM1299519 2 0.0000 0.943 0.000 1.000 0.000 0.000
#> GSM1299520 4 0.3528 0.758 0.192 0.000 0.000 0.808
#> GSM1299521 1 0.1022 0.884 0.968 0.000 0.000 0.032
#> GSM1299522 2 0.0000 0.943 0.000 1.000 0.000 0.000
#> GSM1299523 4 0.4624 0.648 0.340 0.000 0.000 0.660
#> GSM1299524 3 0.0188 0.948 0.000 0.000 0.996 0.004
#> GSM1299525 2 0.0592 0.936 0.000 0.984 0.000 0.016
#> GSM1299526 2 0.2868 0.813 0.000 0.864 0.136 0.000
#> GSM1299527 3 0.0000 0.950 0.000 0.000 1.000 0.000
#> GSM1299528 2 0.4643 0.567 0.000 0.656 0.000 0.344
#> GSM1299529 2 0.0707 0.935 0.000 0.980 0.000 0.020
#> GSM1299530 4 0.4643 0.643 0.344 0.000 0.000 0.656
#> GSM1299531 2 0.0000 0.943 0.000 1.000 0.000 0.000
#> GSM1299575 1 0.0000 0.899 1.000 0.000 0.000 0.000
#> GSM1299532 3 0.0000 0.950 0.000 0.000 1.000 0.000
#> GSM1299533 2 0.0000 0.943 0.000 1.000 0.000 0.000
#> GSM1299534 3 0.7134 0.280 0.000 0.312 0.532 0.156
#> GSM1299535 2 0.0336 0.939 0.000 0.992 0.008 0.000
#> GSM1299536 4 0.0336 0.791 0.008 0.000 0.000 0.992
#> GSM1299537 3 0.0000 0.950 0.000 0.000 1.000 0.000
#> GSM1299538 4 0.1557 0.798 0.056 0.000 0.000 0.944
#> GSM1299539 4 0.1637 0.798 0.060 0.000 0.000 0.940
#> GSM1299540 3 0.0336 0.947 0.000 0.000 0.992 0.008
#> GSM1299541 3 0.0000 0.950 0.000 0.000 1.000 0.000
#> GSM1299542 3 0.0000 0.950 0.000 0.000 1.000 0.000
#> GSM1299543 2 0.0000 0.943 0.000 1.000 0.000 0.000
#> GSM1299544 2 0.3726 0.765 0.000 0.788 0.000 0.212
#> GSM1299545 1 0.2704 0.770 0.876 0.000 0.000 0.124
#> GSM1299546 2 0.0000 0.943 0.000 1.000 0.000 0.000
#> GSM1299547 1 0.4250 0.602 0.724 0.000 0.000 0.276
#> GSM1299548 3 0.0000 0.950 0.000 0.000 1.000 0.000
#> GSM1299549 1 0.2081 0.850 0.916 0.000 0.000 0.084
#> GSM1299550 4 0.0469 0.787 0.000 0.000 0.012 0.988
#> GSM1299551 2 0.0000 0.943 0.000 1.000 0.000 0.000
#> GSM1299552 1 0.1792 0.862 0.932 0.000 0.000 0.068
#> GSM1299553 1 0.0921 0.886 0.972 0.000 0.000 0.028
#> GSM1299554 4 0.1545 0.772 0.000 0.008 0.040 0.952
#> GSM1299555 3 0.0336 0.947 0.000 0.000 0.992 0.008
#> GSM1299556 3 0.0336 0.947 0.000 0.000 0.992 0.008
#> GSM1299557 1 0.6383 0.483 0.636 0.028 0.292 0.044
#> GSM1299558 2 0.0000 0.943 0.000 1.000 0.000 0.000
#> GSM1299559 3 0.0336 0.947 0.000 0.000 0.992 0.008
#> GSM1299560 3 0.0000 0.950 0.000 0.000 1.000 0.000
#> GSM1299576 1 0.0000 0.899 1.000 0.000 0.000 0.000
#> GSM1299577 4 0.4804 0.571 0.384 0.000 0.000 0.616
#> GSM1299561 3 0.0000 0.950 0.000 0.000 1.000 0.000
#> GSM1299562 2 0.1557 0.899 0.000 0.944 0.056 0.000
#> GSM1299563 4 0.3569 0.749 0.196 0.000 0.000 0.804
#> GSM1299564 4 0.0469 0.792 0.012 0.000 0.000 0.988
#> GSM1299565 2 0.0000 0.943 0.000 1.000 0.000 0.000
#> GSM1299566 4 0.3801 0.577 0.000 0.220 0.000 0.780
#> GSM1299567 3 0.6330 0.502 0.200 0.000 0.656 0.144
#> GSM1299568 2 0.0336 0.940 0.000 0.992 0.000 0.008
#> GSM1299569 2 0.4353 0.732 0.000 0.756 0.012 0.232
#> GSM1299570 4 0.4585 0.657 0.332 0.000 0.000 0.668
#> GSM1299571 2 0.0000 0.943 0.000 1.000 0.000 0.000
#> GSM1299572 3 0.0469 0.945 0.000 0.000 0.988 0.012
#> GSM1299573 3 0.0000 0.950 0.000 0.000 1.000 0.000
#> GSM1299574 2 0.0000 0.943 0.000 1.000 0.000 0.000
#> GSM1299578 1 0.0000 0.899 1.000 0.000 0.000 0.000
#> GSM1299579 1 0.4907 0.119 0.580 0.000 0.000 0.420
#> GSM1299580 1 0.0000 0.899 1.000 0.000 0.000 0.000
#> GSM1299581 1 0.0000 0.899 1.000 0.000 0.000 0.000
#> GSM1299582 1 0.0000 0.899 1.000 0.000 0.000 0.000
#> GSM1299583 1 0.0000 0.899 1.000 0.000 0.000 0.000
#> GSM1299584 1 0.0000 0.899 1.000 0.000 0.000 0.000
#> GSM1299585 1 0.0000 0.899 1.000 0.000 0.000 0.000
#> GSM1299586 1 0.0000 0.899 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1299517 3 0.3521 0.8268 0.000 0.008 0.824 0.144 0.024
#> GSM1299518 3 0.0290 0.8622 0.000 0.000 0.992 0.008 0.000
#> GSM1299519 2 0.0162 0.9102 0.000 0.996 0.000 0.004 0.000
#> GSM1299520 5 0.5597 -0.4903 0.072 0.000 0.000 0.440 0.488
#> GSM1299521 1 0.2825 0.7976 0.860 0.000 0.000 0.124 0.016
#> GSM1299522 2 0.0000 0.9104 0.000 1.000 0.000 0.000 0.000
#> GSM1299523 4 0.6292 0.5640 0.152 0.000 0.000 0.448 0.400
#> GSM1299524 3 0.3741 0.7631 0.000 0.000 0.816 0.108 0.076
#> GSM1299525 2 0.2389 0.8299 0.000 0.880 0.000 0.004 0.116
#> GSM1299526 2 0.3477 0.7639 0.000 0.832 0.112 0.056 0.000
#> GSM1299527 3 0.0703 0.8621 0.000 0.000 0.976 0.024 0.000
#> GSM1299528 5 0.4963 0.2706 0.000 0.352 0.000 0.040 0.608
#> GSM1299529 2 0.2464 0.8459 0.000 0.888 0.000 0.016 0.096
#> GSM1299530 4 0.6366 0.5676 0.164 0.000 0.000 0.440 0.396
#> GSM1299531 2 0.0290 0.9092 0.000 0.992 0.000 0.008 0.000
#> GSM1299575 1 0.1270 0.8238 0.948 0.000 0.000 0.052 0.000
#> GSM1299532 3 0.1671 0.8405 0.000 0.000 0.924 0.076 0.000
#> GSM1299533 2 0.0865 0.9045 0.000 0.972 0.004 0.024 0.000
#> GSM1299534 3 0.6909 0.3934 0.000 0.088 0.576 0.112 0.224
#> GSM1299535 2 0.2026 0.8817 0.000 0.924 0.012 0.056 0.008
#> GSM1299536 5 0.1851 0.5006 0.000 0.000 0.000 0.088 0.912
#> GSM1299537 3 0.2074 0.8504 0.000 0.000 0.896 0.104 0.000
#> GSM1299538 5 0.2605 0.4580 0.000 0.000 0.000 0.148 0.852
#> GSM1299539 5 0.2971 0.4487 0.008 0.000 0.000 0.156 0.836
#> GSM1299540 3 0.4009 0.7276 0.004 0.000 0.684 0.312 0.000
#> GSM1299541 3 0.1851 0.8537 0.000 0.000 0.912 0.088 0.000
#> GSM1299542 3 0.0404 0.8629 0.000 0.000 0.988 0.012 0.000
#> GSM1299543 2 0.0162 0.9099 0.000 0.996 0.000 0.004 0.000
#> GSM1299544 2 0.5599 0.0576 0.000 0.484 0.000 0.072 0.444
#> GSM1299545 4 0.4973 0.3285 0.408 0.000 0.004 0.564 0.024
#> GSM1299546 2 0.0000 0.9104 0.000 1.000 0.000 0.000 0.000
#> GSM1299547 1 0.5464 0.6190 0.648 0.000 0.000 0.224 0.128
#> GSM1299548 3 0.1851 0.8571 0.000 0.000 0.912 0.088 0.000
#> GSM1299549 1 0.4238 0.7406 0.756 0.000 0.000 0.192 0.052
#> GSM1299550 5 0.0290 0.5231 0.000 0.000 0.000 0.008 0.992
#> GSM1299551 2 0.0000 0.9104 0.000 1.000 0.000 0.000 0.000
#> GSM1299552 1 0.3639 0.7629 0.792 0.000 0.000 0.184 0.024
#> GSM1299553 1 0.3563 0.7644 0.780 0.000 0.000 0.208 0.012
#> GSM1299554 5 0.4734 0.4192 0.000 0.000 0.096 0.176 0.728
#> GSM1299555 3 0.3395 0.7865 0.000 0.000 0.764 0.236 0.000
#> GSM1299556 3 0.3424 0.7915 0.000 0.000 0.760 0.240 0.000
#> GSM1299557 1 0.7468 0.3451 0.460 0.020 0.188 0.308 0.024
#> GSM1299558 2 0.0451 0.9083 0.000 0.988 0.000 0.008 0.004
#> GSM1299559 3 0.3508 0.7826 0.000 0.000 0.748 0.252 0.000
#> GSM1299560 3 0.0290 0.8623 0.000 0.000 0.992 0.008 0.000
#> GSM1299576 1 0.0000 0.8381 1.000 0.000 0.000 0.000 0.000
#> GSM1299577 4 0.6556 0.5604 0.260 0.000 0.000 0.476 0.264
#> GSM1299561 3 0.0290 0.8627 0.000 0.000 0.992 0.008 0.000
#> GSM1299562 2 0.2929 0.8314 0.000 0.876 0.076 0.044 0.004
#> GSM1299563 4 0.5929 0.3795 0.104 0.000 0.000 0.464 0.432
#> GSM1299564 5 0.3796 0.1831 0.000 0.000 0.000 0.300 0.700
#> GSM1299565 2 0.0162 0.9102 0.000 0.996 0.000 0.004 0.000
#> GSM1299566 5 0.2723 0.5143 0.000 0.124 0.000 0.012 0.864
#> GSM1299567 4 0.6476 0.1554 0.152 0.000 0.288 0.544 0.016
#> GSM1299568 2 0.4435 0.7285 0.000 0.776 0.008 0.092 0.124
#> GSM1299569 5 0.7319 0.1523 0.000 0.340 0.104 0.092 0.464
#> GSM1299570 4 0.6217 0.5428 0.140 0.000 0.000 0.444 0.416
#> GSM1299571 2 0.0162 0.9102 0.000 0.996 0.000 0.004 0.000
#> GSM1299572 3 0.3366 0.7980 0.000 0.000 0.784 0.212 0.004
#> GSM1299573 3 0.2136 0.8339 0.000 0.000 0.904 0.088 0.008
#> GSM1299574 2 0.0162 0.9102 0.000 0.996 0.000 0.004 0.000
#> GSM1299578 1 0.0290 0.8370 0.992 0.000 0.000 0.008 0.000
#> GSM1299579 1 0.4840 0.5128 0.676 0.000 0.000 0.056 0.268
#> GSM1299580 1 0.1270 0.8238 0.948 0.000 0.000 0.052 0.000
#> GSM1299581 1 0.0000 0.8381 1.000 0.000 0.000 0.000 0.000
#> GSM1299582 1 0.1197 0.8250 0.952 0.000 0.000 0.048 0.000
#> GSM1299583 1 0.0290 0.8379 0.992 0.000 0.000 0.008 0.000
#> GSM1299584 1 0.1197 0.8250 0.952 0.000 0.000 0.048 0.000
#> GSM1299585 1 0.0703 0.8359 0.976 0.000 0.000 0.024 0.000
#> GSM1299586 1 0.0963 0.8297 0.964 0.000 0.000 0.036 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1299517 3 0.4253 0.3419 0.000 0.008 0.608 0.000 0.012 0.372
#> GSM1299518 3 0.0790 0.6794 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM1299519 2 0.0146 0.8934 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM1299520 4 0.2383 0.6919 0.024 0.000 0.000 0.880 0.096 0.000
#> GSM1299521 1 0.3736 0.7457 0.804 0.000 0.000 0.056 0.020 0.120
#> GSM1299522 2 0.0363 0.8939 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM1299523 4 0.2263 0.7639 0.100 0.000 0.000 0.884 0.016 0.000
#> GSM1299524 3 0.4125 0.5289 0.000 0.000 0.748 0.000 0.128 0.124
#> GSM1299525 2 0.3457 0.6943 0.000 0.752 0.000 0.000 0.232 0.016
#> GSM1299526 2 0.3307 0.7666 0.000 0.820 0.072 0.000 0.000 0.108
#> GSM1299527 3 0.1643 0.6778 0.000 0.000 0.924 0.000 0.008 0.068
#> GSM1299528 5 0.3455 0.6253 0.000 0.132 0.000 0.036 0.816 0.016
#> GSM1299529 2 0.3976 0.7089 0.000 0.748 0.000 0.004 0.196 0.052
#> GSM1299530 4 0.2489 0.7576 0.128 0.000 0.000 0.860 0.012 0.000
#> GSM1299531 2 0.0363 0.8939 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM1299575 1 0.1478 0.8107 0.944 0.000 0.000 0.032 0.004 0.020
#> GSM1299532 3 0.2537 0.6307 0.000 0.000 0.872 0.000 0.032 0.096
#> GSM1299533 2 0.1327 0.8733 0.000 0.936 0.000 0.000 0.000 0.064
#> GSM1299534 3 0.5667 0.3374 0.000 0.020 0.588 0.000 0.248 0.144
#> GSM1299535 2 0.3716 0.8024 0.000 0.820 0.068 0.000 0.044 0.068
#> GSM1299536 5 0.4322 0.4495 0.000 0.000 0.000 0.372 0.600 0.028
#> GSM1299537 3 0.3151 0.5181 0.000 0.000 0.748 0.000 0.000 0.252
#> GSM1299538 5 0.4433 0.3745 0.008 0.000 0.000 0.416 0.560 0.016
#> GSM1299539 5 0.4329 0.4013 0.012 0.000 0.000 0.404 0.576 0.008
#> GSM1299540 6 0.5031 0.0519 0.000 0.000 0.404 0.064 0.004 0.528
#> GSM1299541 3 0.2664 0.5939 0.000 0.000 0.816 0.000 0.000 0.184
#> GSM1299542 3 0.0937 0.6804 0.000 0.000 0.960 0.000 0.000 0.040
#> GSM1299543 2 0.0865 0.8879 0.000 0.964 0.000 0.000 0.036 0.000
#> GSM1299544 5 0.4631 0.4486 0.000 0.288 0.008 0.000 0.652 0.052
#> GSM1299545 4 0.5901 0.2708 0.180 0.000 0.000 0.500 0.008 0.312
#> GSM1299546 2 0.0260 0.8938 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM1299547 1 0.6734 0.5072 0.508 0.000 0.000 0.152 0.104 0.236
#> GSM1299548 3 0.2553 0.6419 0.000 0.000 0.848 0.000 0.008 0.144
#> GSM1299549 1 0.6408 0.5015 0.512 0.000 0.000 0.088 0.100 0.300
#> GSM1299550 5 0.3481 0.6156 0.000 0.000 0.000 0.192 0.776 0.032
#> GSM1299551 2 0.0547 0.8924 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM1299552 1 0.5899 0.5954 0.600 0.000 0.000 0.088 0.076 0.236
#> GSM1299553 1 0.6378 0.5696 0.552 0.000 0.000 0.164 0.072 0.212
#> GSM1299554 5 0.5309 0.5437 0.000 0.004 0.056 0.100 0.692 0.148
#> GSM1299555 6 0.4937 -0.0740 0.000 0.004 0.468 0.052 0.000 0.476
#> GSM1299556 3 0.4076 0.0946 0.000 0.000 0.540 0.008 0.000 0.452
#> GSM1299557 6 0.8027 -0.1196 0.240 0.016 0.116 0.080 0.092 0.456
#> GSM1299558 2 0.1387 0.8754 0.000 0.932 0.000 0.000 0.068 0.000
#> GSM1299559 3 0.4473 -0.0698 0.000 0.000 0.488 0.028 0.000 0.484
#> GSM1299560 3 0.0632 0.6790 0.000 0.000 0.976 0.000 0.000 0.024
#> GSM1299576 1 0.0146 0.8213 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM1299577 4 0.3876 0.7010 0.156 0.000 0.000 0.772 0.004 0.068
#> GSM1299561 3 0.0865 0.6795 0.000 0.000 0.964 0.000 0.000 0.036
#> GSM1299562 2 0.3699 0.7905 0.000 0.812 0.092 0.000 0.020 0.076
#> GSM1299563 4 0.3434 0.6840 0.052 0.000 0.000 0.840 0.052 0.056
#> GSM1299564 4 0.3993 0.2862 0.000 0.000 0.000 0.676 0.300 0.024
#> GSM1299565 2 0.0146 0.8934 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM1299566 5 0.3207 0.6446 0.000 0.044 0.000 0.124 0.828 0.004
#> GSM1299567 6 0.6822 0.0607 0.080 0.000 0.132 0.356 0.004 0.428
#> GSM1299568 2 0.5385 0.5149 0.000 0.628 0.052 0.000 0.260 0.060
#> GSM1299569 5 0.5501 0.5420 0.000 0.152 0.108 0.000 0.668 0.072
#> GSM1299570 4 0.2169 0.7635 0.080 0.000 0.000 0.900 0.008 0.012
#> GSM1299571 2 0.0260 0.8926 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM1299572 3 0.5241 0.3076 0.000 0.000 0.616 0.056 0.036 0.292
#> GSM1299573 3 0.3190 0.6173 0.000 0.000 0.820 0.000 0.044 0.136
#> GSM1299574 2 0.0146 0.8934 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM1299578 1 0.0405 0.8205 0.988 0.000 0.000 0.008 0.000 0.004
#> GSM1299579 1 0.4779 0.6079 0.712 0.000 0.000 0.152 0.116 0.020
#> GSM1299580 1 0.1478 0.8107 0.944 0.000 0.000 0.032 0.004 0.020
#> GSM1299581 1 0.0000 0.8211 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299582 1 0.1390 0.8124 0.948 0.000 0.000 0.032 0.004 0.016
#> GSM1299583 1 0.0146 0.8211 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM1299584 1 0.1390 0.8124 0.948 0.000 0.000 0.032 0.004 0.016
#> GSM1299585 1 0.1225 0.8119 0.952 0.000 0.000 0.012 0.000 0.036
#> GSM1299586 1 0.0909 0.8181 0.968 0.000 0.000 0.020 0.000 0.012
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:skmeans 69 0.119 2
#> MAD:skmeans 68 0.344 3
#> MAD:skmeans 67 0.526 4
#> MAD:skmeans 57 0.268 5
#> MAD:skmeans 55 0.464 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "pam"]
# you can also extract it by
# res = res_list["MAD:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 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 0.766 0.916 0.961 0.5053 0.494 0.494
#> 3 3 0.677 0.764 0.839 0.2954 0.824 0.655
#> 4 4 0.630 0.752 0.864 0.1358 0.847 0.595
#> 5 5 0.817 0.773 0.889 0.0661 0.909 0.673
#> 6 6 0.889 0.803 0.906 0.0445 0.933 0.705
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
#> GSM1299517 2 0.0000 0.957 0.000 1.000
#> GSM1299518 2 0.0000 0.957 0.000 1.000
#> GSM1299519 2 0.0000 0.957 0.000 1.000
#> GSM1299520 1 0.0000 0.957 1.000 0.000
#> GSM1299521 1 0.0000 0.957 1.000 0.000
#> GSM1299522 2 0.0000 0.957 0.000 1.000
#> GSM1299523 1 0.0000 0.957 1.000 0.000
#> GSM1299524 2 0.0000 0.957 0.000 1.000
#> GSM1299525 2 0.6048 0.842 0.148 0.852
#> GSM1299526 2 0.0000 0.957 0.000 1.000
#> GSM1299527 2 0.0000 0.957 0.000 1.000
#> GSM1299528 2 0.9954 0.198 0.460 0.540
#> GSM1299529 2 0.2603 0.930 0.044 0.956
#> GSM1299530 1 0.0000 0.957 1.000 0.000
#> GSM1299531 2 0.0000 0.957 0.000 1.000
#> GSM1299575 1 0.0000 0.957 1.000 0.000
#> GSM1299532 2 0.0000 0.957 0.000 1.000
#> GSM1299533 2 0.0000 0.957 0.000 1.000
#> GSM1299534 2 0.0000 0.957 0.000 1.000
#> GSM1299535 2 0.0000 0.957 0.000 1.000
#> GSM1299536 1 0.0000 0.957 1.000 0.000
#> GSM1299537 2 0.0000 0.957 0.000 1.000
#> GSM1299538 1 0.0672 0.951 0.992 0.008
#> GSM1299539 1 0.0000 0.957 1.000 0.000
#> GSM1299540 2 0.0000 0.957 0.000 1.000
#> GSM1299541 2 0.1843 0.938 0.028 0.972
#> GSM1299542 2 0.0000 0.957 0.000 1.000
#> GSM1299543 2 0.5059 0.876 0.112 0.888
#> GSM1299544 2 0.6048 0.842 0.148 0.852
#> GSM1299545 1 0.6048 0.830 0.852 0.148
#> GSM1299546 2 0.0000 0.957 0.000 1.000
#> GSM1299547 1 0.0000 0.957 1.000 0.000
#> GSM1299548 1 0.9323 0.527 0.652 0.348
#> GSM1299549 1 0.0000 0.957 1.000 0.000
#> GSM1299550 1 0.0000 0.957 1.000 0.000
#> GSM1299551 2 0.0000 0.957 0.000 1.000
#> GSM1299552 1 0.0000 0.957 1.000 0.000
#> GSM1299553 1 0.0000 0.957 1.000 0.000
#> GSM1299554 2 0.6148 0.838 0.152 0.848
#> GSM1299555 2 0.0000 0.957 0.000 1.000
#> GSM1299556 1 0.6148 0.827 0.848 0.152
#> GSM1299557 2 0.0000 0.957 0.000 1.000
#> GSM1299558 2 0.3431 0.916 0.064 0.936
#> GSM1299559 1 0.6973 0.789 0.812 0.188
#> GSM1299560 2 0.0000 0.957 0.000 1.000
#> GSM1299576 1 0.0000 0.957 1.000 0.000
#> GSM1299577 1 0.0000 0.957 1.000 0.000
#> GSM1299561 2 0.0000 0.957 0.000 1.000
#> GSM1299562 2 0.0000 0.957 0.000 1.000
#> GSM1299563 1 0.0000 0.957 1.000 0.000
#> GSM1299564 1 0.0000 0.957 1.000 0.000
#> GSM1299565 2 0.0000 0.957 0.000 1.000
#> GSM1299566 1 0.8861 0.540 0.696 0.304
#> GSM1299567 1 0.6048 0.830 0.852 0.148
#> GSM1299568 2 0.0000 0.957 0.000 1.000
#> GSM1299569 2 0.6048 0.842 0.148 0.852
#> GSM1299570 1 0.0000 0.957 1.000 0.000
#> GSM1299571 2 0.0000 0.957 0.000 1.000
#> GSM1299572 2 0.6048 0.842 0.148 0.852
#> GSM1299573 2 0.0000 0.957 0.000 1.000
#> GSM1299574 2 0.0000 0.957 0.000 1.000
#> GSM1299578 1 0.0000 0.957 1.000 0.000
#> GSM1299579 1 0.0000 0.957 1.000 0.000
#> GSM1299580 1 0.0376 0.955 0.996 0.004
#> GSM1299581 1 0.0000 0.957 1.000 0.000
#> GSM1299582 1 0.0000 0.957 1.000 0.000
#> GSM1299583 1 0.0000 0.957 1.000 0.000
#> GSM1299584 1 0.0000 0.957 1.000 0.000
#> GSM1299585 1 0.0000 0.957 1.000 0.000
#> GSM1299586 1 0.0000 0.957 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1299517 3 0.6252 0.7300 0.000 0.444 0.556
#> GSM1299518 2 0.0000 0.7363 0.000 1.000 0.000
#> GSM1299519 2 0.0000 0.7363 0.000 1.000 0.000
#> GSM1299520 1 0.5431 0.7181 0.716 0.000 0.284
#> GSM1299521 1 0.0000 0.9115 1.000 0.000 0.000
#> GSM1299522 2 0.0000 0.7363 0.000 1.000 0.000
#> GSM1299523 1 0.0000 0.9115 1.000 0.000 0.000
#> GSM1299524 3 0.6192 0.7600 0.000 0.420 0.580
#> GSM1299525 2 0.5497 0.7157 0.000 0.708 0.292
#> GSM1299526 2 0.0000 0.7363 0.000 1.000 0.000
#> GSM1299527 3 0.5497 0.8949 0.000 0.292 0.708
#> GSM1299528 2 0.9070 0.5313 0.172 0.536 0.292
#> GSM1299529 2 0.5497 0.7157 0.000 0.708 0.292
#> GSM1299530 1 0.0000 0.9115 1.000 0.000 0.000
#> GSM1299531 2 0.5497 0.7157 0.000 0.708 0.292
#> GSM1299575 1 0.0000 0.9115 1.000 0.000 0.000
#> GSM1299532 3 0.6062 0.7234 0.000 0.384 0.616
#> GSM1299533 2 0.0424 0.7300 0.000 0.992 0.008
#> GSM1299534 2 0.5529 0.7146 0.000 0.704 0.296
#> GSM1299535 2 0.0000 0.7363 0.000 1.000 0.000
#> GSM1299536 1 0.5560 0.7063 0.700 0.000 0.300
#> GSM1299537 3 0.5497 0.8949 0.000 0.292 0.708
#> GSM1299538 1 0.5896 0.7045 0.700 0.008 0.292
#> GSM1299539 1 0.5497 0.7116 0.708 0.000 0.292
#> GSM1299540 2 0.6308 -0.6306 0.000 0.508 0.492
#> GSM1299541 3 0.5497 0.8949 0.000 0.292 0.708
#> GSM1299542 3 0.5560 0.8902 0.000 0.300 0.700
#> GSM1299543 2 0.5497 0.7157 0.000 0.708 0.292
#> GSM1299544 2 0.5497 0.7157 0.000 0.708 0.292
#> GSM1299545 1 0.0237 0.9088 0.996 0.000 0.004
#> GSM1299546 2 0.0000 0.7363 0.000 1.000 0.000
#> GSM1299547 1 0.0000 0.9115 1.000 0.000 0.000
#> GSM1299548 3 0.6161 0.8802 0.020 0.272 0.708
#> GSM1299549 1 0.0000 0.9115 1.000 0.000 0.000
#> GSM1299550 1 0.5560 0.7063 0.700 0.000 0.300
#> GSM1299551 2 0.5216 0.7220 0.000 0.740 0.260
#> GSM1299552 1 0.0000 0.9115 1.000 0.000 0.000
#> GSM1299553 1 0.0000 0.9115 1.000 0.000 0.000
#> GSM1299554 3 0.0424 0.5272 0.000 0.008 0.992
#> GSM1299555 2 0.3686 0.5270 0.000 0.860 0.140
#> GSM1299556 3 0.5497 0.8949 0.000 0.292 0.708
#> GSM1299557 2 0.0000 0.7363 0.000 1.000 0.000
#> GSM1299558 2 0.5497 0.7157 0.000 0.708 0.292
#> GSM1299559 3 0.5497 0.8949 0.000 0.292 0.708
#> GSM1299560 3 0.5497 0.8949 0.000 0.292 0.708
#> GSM1299576 1 0.0000 0.9115 1.000 0.000 0.000
#> GSM1299577 1 0.0000 0.9115 1.000 0.000 0.000
#> GSM1299561 3 0.5497 0.8949 0.000 0.292 0.708
#> GSM1299562 2 0.0000 0.7363 0.000 1.000 0.000
#> GSM1299563 1 0.0424 0.9060 0.992 0.000 0.008
#> GSM1299564 1 0.5529 0.7090 0.704 0.000 0.296
#> GSM1299565 2 0.0000 0.7363 0.000 1.000 0.000
#> GSM1299566 1 0.9889 0.0441 0.408 0.296 0.296
#> GSM1299567 3 0.9184 0.7047 0.188 0.284 0.528
#> GSM1299568 2 0.5397 0.7191 0.000 0.720 0.280
#> GSM1299569 2 0.5560 0.7129 0.000 0.700 0.300
#> GSM1299570 1 0.0000 0.9115 1.000 0.000 0.000
#> GSM1299571 2 0.0000 0.7363 0.000 1.000 0.000
#> GSM1299572 2 0.6051 0.5350 0.292 0.696 0.012
#> GSM1299573 2 0.0424 0.7300 0.000 0.992 0.008
#> GSM1299574 2 0.0000 0.7363 0.000 1.000 0.000
#> GSM1299578 1 0.0000 0.9115 1.000 0.000 0.000
#> GSM1299579 1 0.0000 0.9115 1.000 0.000 0.000
#> GSM1299580 1 0.0000 0.9115 1.000 0.000 0.000
#> GSM1299581 1 0.0000 0.9115 1.000 0.000 0.000
#> GSM1299582 1 0.0000 0.9115 1.000 0.000 0.000
#> GSM1299583 1 0.0000 0.9115 1.000 0.000 0.000
#> GSM1299584 1 0.0000 0.9115 1.000 0.000 0.000
#> GSM1299585 1 0.0000 0.9115 1.000 0.000 0.000
#> GSM1299586 1 0.0000 0.9115 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1299517 3 0.4164 0.7524 0.000 0.264 0.736 0.000
#> GSM1299518 2 0.0188 0.9107 0.000 0.996 0.004 0.000
#> GSM1299519 2 0.0188 0.9107 0.000 0.996 0.004 0.000
#> GSM1299520 4 0.1118 0.7407 0.036 0.000 0.000 0.964
#> GSM1299521 1 0.0188 0.8249 0.996 0.000 0.000 0.004
#> GSM1299522 2 0.0000 0.9111 0.000 1.000 0.000 0.000
#> GSM1299523 4 0.4599 0.5648 0.088 0.000 0.112 0.800
#> GSM1299524 3 0.5188 0.7504 0.000 0.240 0.716 0.044
#> GSM1299525 2 0.3569 0.7730 0.000 0.804 0.000 0.196
#> GSM1299526 2 0.0188 0.9107 0.000 0.996 0.004 0.000
#> GSM1299527 3 0.2530 0.8654 0.000 0.112 0.888 0.000
#> GSM1299528 4 0.4643 0.4804 0.000 0.344 0.000 0.656
#> GSM1299529 4 0.4925 0.3358 0.000 0.428 0.000 0.572
#> GSM1299530 1 0.6792 0.5376 0.548 0.000 0.112 0.340
#> GSM1299531 2 0.2530 0.8578 0.000 0.888 0.000 0.112
#> GSM1299575 1 0.2530 0.8398 0.888 0.000 0.112 0.000
#> GSM1299532 3 0.5310 0.4537 0.000 0.412 0.576 0.012
#> GSM1299533 2 0.0188 0.9107 0.000 0.996 0.004 0.000
#> GSM1299534 2 0.2944 0.8501 0.000 0.868 0.004 0.128
#> GSM1299535 2 0.0000 0.9111 0.000 1.000 0.000 0.000
#> GSM1299536 4 0.0817 0.7530 0.024 0.000 0.000 0.976
#> GSM1299537 3 0.2530 0.8654 0.000 0.112 0.888 0.000
#> GSM1299538 4 0.0000 0.7527 0.000 0.000 0.000 1.000
#> GSM1299539 4 0.0469 0.7552 0.012 0.000 0.000 0.988
#> GSM1299540 3 0.4857 0.6423 0.004 0.176 0.772 0.048
#> GSM1299541 3 0.2530 0.8654 0.000 0.112 0.888 0.000
#> GSM1299542 3 0.2530 0.8654 0.000 0.112 0.888 0.000
#> GSM1299543 2 0.2589 0.8559 0.000 0.884 0.000 0.116
#> GSM1299544 4 0.4981 0.1829 0.000 0.464 0.000 0.536
#> GSM1299545 1 0.6664 0.5799 0.580 0.000 0.112 0.308
#> GSM1299546 2 0.0000 0.9111 0.000 1.000 0.000 0.000
#> GSM1299547 1 0.0188 0.8249 0.996 0.000 0.000 0.004
#> GSM1299548 3 0.0188 0.7650 0.004 0.000 0.996 0.000
#> GSM1299549 1 0.0188 0.8249 0.996 0.000 0.000 0.004
#> GSM1299550 4 0.0188 0.7527 0.000 0.004 0.000 0.996
#> GSM1299551 2 0.2345 0.8666 0.000 0.900 0.000 0.100
#> GSM1299552 1 0.0188 0.8249 0.996 0.000 0.000 0.004
#> GSM1299553 1 0.4985 -0.0674 0.532 0.000 0.000 0.468
#> GSM1299554 4 0.3545 0.6488 0.000 0.008 0.164 0.828
#> GSM1299555 2 0.2921 0.7587 0.000 0.860 0.140 0.000
#> GSM1299556 3 0.2530 0.8654 0.000 0.112 0.888 0.000
#> GSM1299557 2 0.0657 0.9078 0.012 0.984 0.004 0.000
#> GSM1299558 2 0.3219 0.8134 0.000 0.836 0.000 0.164
#> GSM1299559 3 0.2530 0.8654 0.000 0.112 0.888 0.000
#> GSM1299560 3 0.2530 0.8654 0.000 0.112 0.888 0.000
#> GSM1299576 1 0.0188 0.8249 0.996 0.000 0.000 0.004
#> GSM1299577 1 0.6792 0.5376 0.548 0.000 0.112 0.340
#> GSM1299561 3 0.2530 0.8654 0.000 0.112 0.888 0.000
#> GSM1299562 2 0.0188 0.9107 0.000 0.996 0.004 0.000
#> GSM1299563 4 0.3975 0.5382 0.240 0.000 0.000 0.760
#> GSM1299564 4 0.1940 0.7175 0.076 0.000 0.000 0.924
#> GSM1299565 2 0.0188 0.9107 0.000 0.996 0.004 0.000
#> GSM1299566 4 0.2589 0.7269 0.000 0.116 0.000 0.884
#> GSM1299567 3 0.4800 0.3571 0.004 0.000 0.656 0.340
#> GSM1299568 2 0.2704 0.8518 0.000 0.876 0.000 0.124
#> GSM1299569 4 0.4776 0.4248 0.000 0.376 0.000 0.624
#> GSM1299570 1 0.6894 0.4786 0.512 0.000 0.112 0.376
#> GSM1299571 2 0.0188 0.9107 0.000 0.996 0.004 0.000
#> GSM1299572 2 0.5272 0.6821 0.112 0.752 0.000 0.136
#> GSM1299573 2 0.2714 0.8373 0.112 0.884 0.000 0.004
#> GSM1299574 2 0.0000 0.9111 0.000 1.000 0.000 0.000
#> GSM1299578 1 0.2530 0.8398 0.888 0.000 0.112 0.000
#> GSM1299579 1 0.0188 0.8249 0.996 0.000 0.000 0.004
#> GSM1299580 1 0.2530 0.8398 0.888 0.000 0.112 0.000
#> GSM1299581 1 0.2530 0.8398 0.888 0.000 0.112 0.000
#> GSM1299582 1 0.2530 0.8398 0.888 0.000 0.112 0.000
#> GSM1299583 1 0.2530 0.8398 0.888 0.000 0.112 0.000
#> GSM1299584 1 0.2530 0.8398 0.888 0.000 0.112 0.000
#> GSM1299585 1 0.0188 0.8249 0.996 0.000 0.000 0.004
#> GSM1299586 1 0.2530 0.8398 0.888 0.000 0.112 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1299517 3 0.2648 0.7497 0.000 0.152 0.848 0.000 0.000
#> GSM1299518 2 0.0162 0.8953 0.000 0.996 0.004 0.000 0.000
#> GSM1299519 2 0.0162 0.8953 0.000 0.996 0.004 0.000 0.000
#> GSM1299520 4 0.2329 0.7287 0.000 0.000 0.000 0.876 0.124
#> GSM1299521 1 0.1041 0.9306 0.964 0.000 0.000 0.004 0.032
#> GSM1299522 2 0.0000 0.8952 0.000 1.000 0.000 0.000 0.000
#> GSM1299523 4 0.2020 0.7406 0.000 0.000 0.000 0.900 0.100
#> GSM1299524 3 0.6516 0.4029 0.000 0.036 0.528 0.096 0.340
#> GSM1299525 2 0.4302 0.0261 0.000 0.520 0.000 0.000 0.480
#> GSM1299526 2 0.0162 0.8953 0.000 0.996 0.004 0.000 0.000
#> GSM1299527 3 0.0000 0.8598 0.000 0.000 1.000 0.000 0.000
#> GSM1299528 5 0.1851 0.8761 0.000 0.088 0.000 0.000 0.912
#> GSM1299529 2 0.2020 0.8269 0.000 0.900 0.000 0.000 0.100
#> GSM1299530 4 0.2020 0.7309 0.100 0.000 0.000 0.900 0.000
#> GSM1299531 2 0.0000 0.8952 0.000 1.000 0.000 0.000 0.000
#> GSM1299575 1 0.0703 0.9349 0.976 0.000 0.000 0.024 0.000
#> GSM1299532 3 0.7159 0.2905 0.000 0.340 0.480 0.096 0.084
#> GSM1299533 2 0.3047 0.8163 0.000 0.868 0.004 0.044 0.084
#> GSM1299534 2 0.3796 0.7985 0.000 0.820 0.004 0.076 0.100
#> GSM1299535 2 0.0000 0.8952 0.000 1.000 0.000 0.000 0.000
#> GSM1299536 5 0.1732 0.8849 0.000 0.000 0.000 0.080 0.920
#> GSM1299537 3 0.0000 0.8598 0.000 0.000 1.000 0.000 0.000
#> GSM1299538 4 0.4138 0.3738 0.000 0.000 0.000 0.616 0.384
#> GSM1299539 5 0.2338 0.8691 0.004 0.000 0.000 0.112 0.884
#> GSM1299540 3 0.5846 0.7002 0.028 0.112 0.724 0.052 0.084
#> GSM1299541 3 0.0000 0.8598 0.000 0.000 1.000 0.000 0.000
#> GSM1299542 3 0.0000 0.8598 0.000 0.000 1.000 0.000 0.000
#> GSM1299543 2 0.0510 0.8888 0.000 0.984 0.000 0.000 0.016
#> GSM1299544 5 0.2329 0.8527 0.000 0.124 0.000 0.000 0.876
#> GSM1299545 4 0.1544 0.7239 0.068 0.000 0.000 0.932 0.000
#> GSM1299546 2 0.0000 0.8952 0.000 1.000 0.000 0.000 0.000
#> GSM1299547 1 0.1124 0.9288 0.960 0.000 0.000 0.004 0.036
#> GSM1299548 3 0.0162 0.8573 0.004 0.000 0.996 0.000 0.000
#> GSM1299549 1 0.1041 0.9306 0.964 0.000 0.000 0.004 0.032
#> GSM1299550 5 0.0880 0.8659 0.000 0.000 0.000 0.032 0.968
#> GSM1299551 2 0.0000 0.8952 0.000 1.000 0.000 0.000 0.000
#> GSM1299552 1 0.1041 0.9306 0.964 0.000 0.000 0.004 0.032
#> GSM1299553 1 0.6127 0.0201 0.484 0.000 0.000 0.384 0.132
#> GSM1299554 4 0.4300 0.1631 0.000 0.000 0.000 0.524 0.476
#> GSM1299555 2 0.5823 0.6442 0.000 0.700 0.120 0.096 0.084
#> GSM1299556 3 0.0404 0.8562 0.000 0.000 0.988 0.000 0.012
#> GSM1299557 2 0.1372 0.8748 0.016 0.956 0.004 0.000 0.024
#> GSM1299558 2 0.4300 0.0360 0.000 0.524 0.000 0.000 0.476
#> GSM1299559 3 0.0000 0.8598 0.000 0.000 1.000 0.000 0.000
#> GSM1299560 3 0.0000 0.8598 0.000 0.000 1.000 0.000 0.000
#> GSM1299576 1 0.1041 0.9306 0.964 0.000 0.000 0.004 0.032
#> GSM1299577 4 0.1121 0.7468 0.044 0.000 0.000 0.956 0.000
#> GSM1299561 3 0.3702 0.7612 0.000 0.000 0.820 0.096 0.084
#> GSM1299562 2 0.0162 0.8953 0.000 0.996 0.004 0.000 0.000
#> GSM1299563 4 0.2193 0.7477 0.028 0.000 0.000 0.912 0.060
#> GSM1299564 4 0.2707 0.7384 0.024 0.000 0.000 0.876 0.100
#> GSM1299565 2 0.0162 0.8953 0.000 0.996 0.004 0.000 0.000
#> GSM1299566 5 0.2416 0.8824 0.000 0.012 0.000 0.100 0.888
#> GSM1299567 4 0.4990 0.2735 0.036 0.000 0.384 0.580 0.000
#> GSM1299568 2 0.1478 0.8560 0.000 0.936 0.000 0.000 0.064
#> GSM1299569 5 0.1792 0.8817 0.000 0.084 0.000 0.000 0.916
#> GSM1299570 4 0.2248 0.7372 0.088 0.000 0.000 0.900 0.012
#> GSM1299571 2 0.0162 0.8953 0.000 0.996 0.004 0.000 0.000
#> GSM1299572 4 0.6479 0.2314 0.024 0.332 0.000 0.528 0.116
#> GSM1299573 2 0.4835 0.7306 0.024 0.760 0.000 0.100 0.116
#> GSM1299574 2 0.0000 0.8952 0.000 1.000 0.000 0.000 0.000
#> GSM1299578 1 0.0703 0.9349 0.976 0.000 0.000 0.024 0.000
#> GSM1299579 1 0.0963 0.9298 0.964 0.000 0.000 0.000 0.036
#> GSM1299580 1 0.0703 0.9349 0.976 0.000 0.000 0.024 0.000
#> GSM1299581 1 0.0703 0.9349 0.976 0.000 0.000 0.024 0.000
#> GSM1299582 1 0.0703 0.9349 0.976 0.000 0.000 0.024 0.000
#> GSM1299583 1 0.0703 0.9349 0.976 0.000 0.000 0.024 0.000
#> GSM1299584 1 0.0703 0.9349 0.976 0.000 0.000 0.024 0.000
#> GSM1299585 1 0.1041 0.9306 0.964 0.000 0.000 0.004 0.032
#> GSM1299586 1 0.0703 0.9349 0.976 0.000 0.000 0.024 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1299517 3 0.2378 0.7430 0.000 0.152 0.848 0.000 0.000 0.000
#> GSM1299518 2 0.0146 0.9432 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM1299519 2 0.0000 0.9457 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299520 4 0.0146 0.8321 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM1299521 1 0.1327 0.9119 0.936 0.000 0.000 0.000 0.000 0.064
#> GSM1299522 2 0.0000 0.9457 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299523 4 0.0146 0.8321 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM1299524 6 0.2595 0.8118 0.000 0.000 0.084 0.000 0.044 0.872
#> GSM1299525 5 0.3782 0.4009 0.000 0.412 0.000 0.000 0.588 0.000
#> GSM1299526 2 0.0000 0.9457 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299527 3 0.0363 0.9173 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM1299528 5 0.0146 0.8292 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM1299529 2 0.1204 0.8973 0.000 0.944 0.000 0.000 0.056 0.000
#> GSM1299530 4 0.0146 0.8317 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM1299531 2 0.0000 0.9457 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299575 1 0.0363 0.9182 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM1299532 6 0.2962 0.8347 0.000 0.068 0.084 0.000 0.000 0.848
#> GSM1299533 2 0.3864 -0.1240 0.000 0.520 0.000 0.000 0.000 0.480
#> GSM1299534 6 0.4356 0.4707 0.000 0.360 0.000 0.000 0.032 0.608
#> GSM1299535 2 0.0000 0.9457 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299536 5 0.0820 0.8264 0.000 0.000 0.000 0.012 0.972 0.016
#> GSM1299537 3 0.0000 0.9148 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299538 4 0.3330 0.5964 0.000 0.000 0.000 0.716 0.284 0.000
#> GSM1299539 5 0.0632 0.8216 0.000 0.000 0.000 0.024 0.976 0.000
#> GSM1299540 3 0.4943 0.2241 0.044 0.012 0.552 0.000 0.000 0.392
#> GSM1299541 3 0.0363 0.9173 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM1299542 3 0.0363 0.9173 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM1299543 2 0.0547 0.9318 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM1299544 5 0.1204 0.8183 0.000 0.056 0.000 0.000 0.944 0.000
#> GSM1299545 4 0.4834 0.5156 0.104 0.000 0.000 0.644 0.000 0.252
#> GSM1299546 2 0.0000 0.9457 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299547 1 0.2544 0.8712 0.852 0.000 0.000 0.004 0.004 0.140
#> GSM1299548 3 0.0363 0.9164 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM1299549 1 0.2288 0.8864 0.876 0.000 0.000 0.004 0.004 0.116
#> GSM1299550 5 0.1644 0.7935 0.000 0.000 0.000 0.004 0.920 0.076
#> GSM1299551 2 0.0000 0.9457 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299552 1 0.2288 0.8864 0.876 0.000 0.000 0.004 0.004 0.116
#> GSM1299553 1 0.6371 0.0319 0.416 0.000 0.000 0.412 0.056 0.116
#> GSM1299554 4 0.5876 0.3003 0.000 0.000 0.000 0.480 0.260 0.260
#> GSM1299555 6 0.2696 0.8254 0.000 0.116 0.028 0.000 0.000 0.856
#> GSM1299556 3 0.0547 0.9049 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM1299557 2 0.2306 0.8389 0.008 0.888 0.000 0.004 0.004 0.096
#> GSM1299558 5 0.3756 0.4263 0.000 0.400 0.000 0.000 0.600 0.000
#> GSM1299559 3 0.0000 0.9148 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299560 3 0.0363 0.9173 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM1299576 1 0.1327 0.9119 0.936 0.000 0.000 0.000 0.000 0.064
#> GSM1299577 4 0.0146 0.8316 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM1299561 6 0.2178 0.7922 0.000 0.000 0.132 0.000 0.000 0.868
#> GSM1299562 2 0.0000 0.9457 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299563 4 0.0146 0.8316 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM1299564 4 0.1204 0.8102 0.000 0.000 0.000 0.944 0.056 0.000
#> GSM1299565 2 0.0000 0.9457 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299566 5 0.0260 0.8276 0.000 0.000 0.000 0.008 0.992 0.000
#> GSM1299567 4 0.5102 0.3355 0.064 0.000 0.348 0.576 0.000 0.012
#> GSM1299568 2 0.1444 0.8810 0.000 0.928 0.000 0.000 0.072 0.000
#> GSM1299569 5 0.1418 0.8229 0.000 0.032 0.000 0.000 0.944 0.024
#> GSM1299570 4 0.0146 0.8317 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM1299571 2 0.0000 0.9457 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299572 6 0.2107 0.8140 0.012 0.024 0.008 0.036 0.000 0.920
#> GSM1299573 6 0.1757 0.8319 0.012 0.052 0.000 0.000 0.008 0.928
#> GSM1299574 2 0.0000 0.9457 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299578 1 0.0363 0.9182 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM1299579 1 0.1327 0.9119 0.936 0.000 0.000 0.000 0.000 0.064
#> GSM1299580 1 0.0363 0.9182 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM1299581 1 0.0000 0.9191 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299582 1 0.0363 0.9182 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM1299583 1 0.0000 0.9191 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299584 1 0.0363 0.9182 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM1299585 1 0.1327 0.9119 0.936 0.000 0.000 0.000 0.000 0.064
#> GSM1299586 1 0.0363 0.9182 0.988 0.000 0.000 0.000 0.000 0.012
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:pam 69 0.232 2
#> MAD:pam 68 0.287 3
#> MAD:pam 62 0.382 4
#> MAD:pam 61 0.179 5
#> MAD:pam 62 0.185 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "mclust"]
# you can also extract it by
# res = res_list["MAD:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 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 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 0.412 0.725 0.843 0.3969 0.612 0.612
#> 3 3 0.538 0.661 0.845 0.4305 0.622 0.450
#> 4 4 0.751 0.883 0.916 0.2176 0.812 0.573
#> 5 5 0.697 0.662 0.787 0.1245 0.789 0.422
#> 6 6 0.719 0.637 0.767 0.0547 0.948 0.761
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
#> GSM1299517 2 0.9087 0.338 0.324 0.676
#> GSM1299518 1 0.9580 0.651 0.620 0.380
#> GSM1299519 2 0.0000 0.886 0.000 1.000
#> GSM1299520 1 0.1414 0.761 0.980 0.020
#> GSM1299521 1 0.1414 0.761 0.980 0.020
#> GSM1299522 2 0.0000 0.886 0.000 1.000
#> GSM1299523 1 0.1414 0.761 0.980 0.020
#> GSM1299524 1 0.9580 0.651 0.620 0.380
#> GSM1299525 2 0.9129 0.326 0.328 0.672
#> GSM1299526 2 0.0000 0.886 0.000 1.000
#> GSM1299527 1 0.9580 0.651 0.620 0.380
#> GSM1299528 1 0.8661 0.710 0.712 0.288
#> GSM1299529 2 0.8499 0.476 0.276 0.724
#> GSM1299530 1 0.0938 0.758 0.988 0.012
#> GSM1299531 2 0.0000 0.886 0.000 1.000
#> GSM1299575 1 0.0000 0.751 1.000 0.000
#> GSM1299532 1 0.9580 0.651 0.620 0.380
#> GSM1299533 2 0.0000 0.886 0.000 1.000
#> GSM1299534 1 0.9580 0.651 0.620 0.380
#> GSM1299535 2 0.0000 0.886 0.000 1.000
#> GSM1299536 1 0.6712 0.757 0.824 0.176
#> GSM1299537 1 0.9580 0.651 0.620 0.380
#> GSM1299538 1 0.6438 0.759 0.836 0.164
#> GSM1299539 1 0.2236 0.764 0.964 0.036
#> GSM1299540 1 0.9491 0.659 0.632 0.368
#> GSM1299541 1 0.9580 0.651 0.620 0.380
#> GSM1299542 1 0.9580 0.651 0.620 0.380
#> GSM1299543 2 0.0000 0.886 0.000 1.000
#> GSM1299544 1 0.9922 0.510 0.552 0.448
#> GSM1299545 1 0.2603 0.764 0.956 0.044
#> GSM1299546 2 0.0000 0.886 0.000 1.000
#> GSM1299547 1 0.5178 0.764 0.884 0.116
#> GSM1299548 1 0.9580 0.651 0.620 0.380
#> GSM1299549 1 0.5408 0.764 0.876 0.124
#> GSM1299550 1 0.7299 0.748 0.796 0.204
#> GSM1299551 2 0.0000 0.886 0.000 1.000
#> GSM1299552 1 0.1414 0.761 0.980 0.020
#> GSM1299553 1 0.1414 0.761 0.980 0.020
#> GSM1299554 1 0.7745 0.739 0.772 0.228
#> GSM1299555 1 0.9580 0.651 0.620 0.380
#> GSM1299556 1 0.9580 0.651 0.620 0.380
#> GSM1299557 1 0.9491 0.659 0.632 0.368
#> GSM1299558 2 0.0000 0.886 0.000 1.000
#> GSM1299559 1 0.9580 0.651 0.620 0.380
#> GSM1299560 1 0.9580 0.651 0.620 0.380
#> GSM1299576 1 0.0000 0.751 1.000 0.000
#> GSM1299577 1 0.1414 0.761 0.980 0.020
#> GSM1299561 1 0.9580 0.651 0.620 0.380
#> GSM1299562 2 0.3114 0.835 0.056 0.944
#> GSM1299563 1 0.1633 0.762 0.976 0.024
#> GSM1299564 1 0.6438 0.759 0.836 0.164
#> GSM1299565 2 0.0000 0.886 0.000 1.000
#> GSM1299566 1 0.7745 0.739 0.772 0.228
#> GSM1299567 1 0.6438 0.759 0.836 0.164
#> GSM1299568 2 0.9460 0.183 0.364 0.636
#> GSM1299569 1 0.9580 0.651 0.620 0.380
#> GSM1299570 1 0.1414 0.761 0.980 0.020
#> GSM1299571 2 0.0000 0.886 0.000 1.000
#> GSM1299572 1 0.9580 0.651 0.620 0.380
#> GSM1299573 1 0.9580 0.651 0.620 0.380
#> GSM1299574 2 0.0000 0.886 0.000 1.000
#> GSM1299578 1 0.0000 0.751 1.000 0.000
#> GSM1299579 1 0.1414 0.761 0.980 0.020
#> GSM1299580 1 0.0000 0.751 1.000 0.000
#> GSM1299581 1 0.0000 0.751 1.000 0.000
#> GSM1299582 1 0.0000 0.751 1.000 0.000
#> GSM1299583 1 0.0000 0.751 1.000 0.000
#> GSM1299584 1 0.0000 0.751 1.000 0.000
#> GSM1299585 1 0.0000 0.751 1.000 0.000
#> GSM1299586 1 0.0000 0.751 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1299517 3 0.0592 0.8359 0.000 0.012 0.988
#> GSM1299518 3 0.0237 0.8360 0.000 0.004 0.996
#> GSM1299519 2 0.0747 0.8997 0.000 0.984 0.016
#> GSM1299520 1 0.6754 0.5382 0.556 0.012 0.432
#> GSM1299521 1 0.6724 0.5479 0.568 0.012 0.420
#> GSM1299522 2 0.0747 0.8997 0.000 0.984 0.016
#> GSM1299523 1 0.6754 0.5382 0.556 0.012 0.432
#> GSM1299524 3 0.0000 0.8360 0.000 0.000 1.000
#> GSM1299525 3 0.3193 0.8003 0.004 0.100 0.896
#> GSM1299526 2 0.5760 0.5987 0.000 0.672 0.328
#> GSM1299527 3 0.0000 0.8360 0.000 0.000 1.000
#> GSM1299528 3 0.3528 0.7996 0.016 0.092 0.892
#> GSM1299529 3 0.5650 0.4591 0.000 0.312 0.688
#> GSM1299530 1 0.6735 0.5461 0.564 0.012 0.424
#> GSM1299531 2 0.0747 0.8997 0.000 0.984 0.016
#> GSM1299575 1 0.0237 0.6211 0.996 0.004 0.000
#> GSM1299532 3 0.0000 0.8360 0.000 0.000 1.000
#> GSM1299533 2 0.4796 0.7430 0.000 0.780 0.220
#> GSM1299534 3 0.0000 0.8360 0.000 0.000 1.000
#> GSM1299535 3 0.6045 0.2661 0.000 0.380 0.620
#> GSM1299536 3 0.6688 -0.0487 0.408 0.012 0.580
#> GSM1299537 3 0.0000 0.8360 0.000 0.000 1.000
#> GSM1299538 3 0.6811 -0.0266 0.404 0.016 0.580
#> GSM1299539 1 0.6745 0.5412 0.560 0.012 0.428
#> GSM1299540 3 0.0592 0.8359 0.000 0.012 0.988
#> GSM1299541 3 0.0000 0.8360 0.000 0.000 1.000
#> GSM1299542 3 0.0000 0.8360 0.000 0.000 1.000
#> GSM1299543 2 0.0747 0.8997 0.000 0.984 0.016
#> GSM1299544 3 0.2878 0.8025 0.000 0.096 0.904
#> GSM1299545 1 0.6936 0.4552 0.524 0.016 0.460
#> GSM1299546 2 0.0747 0.8997 0.000 0.984 0.016
#> GSM1299547 3 0.6763 -0.1744 0.436 0.012 0.552
#> GSM1299548 3 0.0000 0.8360 0.000 0.000 1.000
#> GSM1299549 3 0.5812 0.4694 0.264 0.012 0.724
#> GSM1299550 3 0.6578 0.5157 0.224 0.052 0.724
#> GSM1299551 2 0.0747 0.8997 0.000 0.984 0.016
#> GSM1299552 1 0.6745 0.5412 0.560 0.012 0.428
#> GSM1299553 1 0.6745 0.5412 0.560 0.012 0.428
#> GSM1299554 3 0.2492 0.8190 0.016 0.048 0.936
#> GSM1299555 3 0.0592 0.8359 0.000 0.012 0.988
#> GSM1299556 3 0.0424 0.8360 0.000 0.008 0.992
#> GSM1299557 3 0.1399 0.8322 0.004 0.028 0.968
#> GSM1299558 2 0.5650 0.5713 0.000 0.688 0.312
#> GSM1299559 3 0.0424 0.8360 0.000 0.008 0.992
#> GSM1299560 3 0.0000 0.8360 0.000 0.000 1.000
#> GSM1299576 1 0.0237 0.6211 0.996 0.004 0.000
#> GSM1299577 1 0.6754 0.5382 0.556 0.012 0.432
#> GSM1299561 3 0.0000 0.8360 0.000 0.000 1.000
#> GSM1299562 3 0.2711 0.8093 0.000 0.088 0.912
#> GSM1299563 1 0.6793 0.4896 0.536 0.012 0.452
#> GSM1299564 3 0.6701 -0.0666 0.412 0.012 0.576
#> GSM1299565 2 0.0747 0.8997 0.000 0.984 0.016
#> GSM1299566 3 0.3805 0.7950 0.024 0.092 0.884
#> GSM1299567 3 0.6783 -0.0149 0.396 0.016 0.588
#> GSM1299568 3 0.3038 0.7974 0.000 0.104 0.896
#> GSM1299569 3 0.2796 0.8048 0.000 0.092 0.908
#> GSM1299570 1 0.6754 0.5382 0.556 0.012 0.432
#> GSM1299571 2 0.2711 0.8652 0.000 0.912 0.088
#> GSM1299572 3 0.0592 0.8359 0.000 0.012 0.988
#> GSM1299573 3 0.0237 0.8360 0.000 0.004 0.996
#> GSM1299574 2 0.1411 0.8934 0.000 0.964 0.036
#> GSM1299578 1 0.0237 0.6211 0.996 0.004 0.000
#> GSM1299579 1 0.6724 0.5479 0.568 0.012 0.420
#> GSM1299580 1 0.0661 0.6235 0.988 0.004 0.008
#> GSM1299581 1 0.0237 0.6211 0.996 0.004 0.000
#> GSM1299582 1 0.0237 0.6211 0.996 0.004 0.000
#> GSM1299583 1 0.0237 0.6211 0.996 0.004 0.000
#> GSM1299584 1 0.0237 0.6211 0.996 0.004 0.000
#> GSM1299585 1 0.0592 0.6248 0.988 0.000 0.012
#> GSM1299586 1 0.0237 0.6211 0.996 0.004 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1299517 3 0.0188 0.919 0.000 0.004 0.996 0.000
#> GSM1299518 3 0.0000 0.920 0.000 0.000 1.000 0.000
#> GSM1299519 2 0.0000 0.917 0.000 1.000 0.000 0.000
#> GSM1299520 4 0.0000 0.910 0.000 0.000 0.000 1.000
#> GSM1299521 4 0.0336 0.911 0.008 0.000 0.000 0.992
#> GSM1299522 2 0.0000 0.917 0.000 1.000 0.000 0.000
#> GSM1299523 4 0.0336 0.911 0.008 0.000 0.000 0.992
#> GSM1299524 3 0.0000 0.920 0.000 0.000 1.000 0.000
#> GSM1299525 3 0.3569 0.819 0.000 0.196 0.804 0.000
#> GSM1299526 3 0.3400 0.831 0.000 0.180 0.820 0.000
#> GSM1299527 3 0.0000 0.920 0.000 0.000 1.000 0.000
#> GSM1299528 3 0.3950 0.823 0.008 0.184 0.804 0.004
#> GSM1299529 3 0.3569 0.819 0.000 0.196 0.804 0.000
#> GSM1299530 4 0.0336 0.911 0.008 0.000 0.000 0.992
#> GSM1299531 2 0.0000 0.917 0.000 1.000 0.000 0.000
#> GSM1299575 1 0.3486 1.000 0.812 0.000 0.000 0.188
#> GSM1299532 3 0.0000 0.920 0.000 0.000 1.000 0.000
#> GSM1299533 3 0.3569 0.819 0.000 0.196 0.804 0.000
#> GSM1299534 3 0.0000 0.920 0.000 0.000 1.000 0.000
#> GSM1299535 3 0.3569 0.819 0.000 0.196 0.804 0.000
#> GSM1299536 4 0.3668 0.753 0.188 0.000 0.004 0.808
#> GSM1299537 3 0.0000 0.920 0.000 0.000 1.000 0.000
#> GSM1299538 4 0.3529 0.716 0.012 0.000 0.152 0.836
#> GSM1299539 4 0.0469 0.904 0.012 0.000 0.000 0.988
#> GSM1299540 3 0.0188 0.919 0.000 0.000 0.996 0.004
#> GSM1299541 3 0.0000 0.920 0.000 0.000 1.000 0.000
#> GSM1299542 3 0.0000 0.920 0.000 0.000 1.000 0.000
#> GSM1299543 2 0.0000 0.917 0.000 1.000 0.000 0.000
#> GSM1299544 3 0.3768 0.824 0.008 0.184 0.808 0.000
#> GSM1299545 4 0.0524 0.910 0.008 0.000 0.004 0.988
#> GSM1299546 2 0.0000 0.917 0.000 1.000 0.000 0.000
#> GSM1299547 4 0.2081 0.853 0.084 0.000 0.000 0.916
#> GSM1299548 3 0.0000 0.920 0.000 0.000 1.000 0.000
#> GSM1299549 4 0.2861 0.804 0.016 0.000 0.096 0.888
#> GSM1299550 3 0.3937 0.823 0.188 0.000 0.800 0.012
#> GSM1299551 2 0.0000 0.917 0.000 1.000 0.000 0.000
#> GSM1299552 4 0.0336 0.911 0.008 0.000 0.000 0.992
#> GSM1299553 4 0.0336 0.911 0.008 0.000 0.000 0.992
#> GSM1299554 3 0.3810 0.825 0.188 0.000 0.804 0.008
#> GSM1299555 3 0.0188 0.919 0.000 0.000 0.996 0.004
#> GSM1299556 3 0.0188 0.919 0.000 0.000 0.996 0.004
#> GSM1299557 3 0.0804 0.915 0.000 0.008 0.980 0.012
#> GSM1299558 2 0.1022 0.895 0.000 0.968 0.032 0.000
#> GSM1299559 3 0.0188 0.919 0.000 0.000 0.996 0.004
#> GSM1299560 3 0.0000 0.920 0.000 0.000 1.000 0.000
#> GSM1299576 1 0.3486 1.000 0.812 0.000 0.000 0.188
#> GSM1299577 4 0.0336 0.911 0.008 0.000 0.000 0.992
#> GSM1299561 3 0.0000 0.920 0.000 0.000 1.000 0.000
#> GSM1299562 3 0.1211 0.908 0.000 0.040 0.960 0.000
#> GSM1299563 4 0.0188 0.908 0.004 0.000 0.000 0.996
#> GSM1299564 4 0.3668 0.753 0.188 0.000 0.004 0.808
#> GSM1299565 2 0.0000 0.917 0.000 1.000 0.000 0.000
#> GSM1299566 3 0.4657 0.837 0.136 0.048 0.804 0.012
#> GSM1299567 4 0.0672 0.909 0.008 0.000 0.008 0.984
#> GSM1299568 3 0.3726 0.803 0.000 0.212 0.788 0.000
#> GSM1299569 3 0.4337 0.840 0.140 0.052 0.808 0.000
#> GSM1299570 4 0.0336 0.911 0.008 0.000 0.000 0.992
#> GSM1299571 2 0.3873 0.690 0.000 0.772 0.228 0.000
#> GSM1299572 3 0.0188 0.919 0.000 0.000 0.996 0.004
#> GSM1299573 3 0.0000 0.920 0.000 0.000 1.000 0.000
#> GSM1299574 2 0.4072 0.648 0.000 0.748 0.252 0.000
#> GSM1299578 1 0.3486 1.000 0.812 0.000 0.000 0.188
#> GSM1299579 4 0.0469 0.909 0.012 0.000 0.000 0.988
#> GSM1299580 1 0.3486 1.000 0.812 0.000 0.000 0.188
#> GSM1299581 1 0.3486 1.000 0.812 0.000 0.000 0.188
#> GSM1299582 1 0.3486 1.000 0.812 0.000 0.000 0.188
#> GSM1299583 1 0.3486 1.000 0.812 0.000 0.000 0.188
#> GSM1299584 1 0.3486 1.000 0.812 0.000 0.000 0.188
#> GSM1299585 4 0.4746 0.179 0.368 0.000 0.000 0.632
#> GSM1299586 1 0.3486 1.000 0.812 0.000 0.000 0.188
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1299517 4 0.4876 0.68029 0.000 0.028 0.396 0.576 0.000
#> GSM1299518 3 0.0404 0.72679 0.000 0.000 0.988 0.012 0.000
#> GSM1299519 2 0.0912 0.85307 0.000 0.972 0.016 0.012 0.000
#> GSM1299520 5 0.2966 0.72683 0.184 0.000 0.000 0.000 0.816
#> GSM1299521 1 0.3730 0.48421 0.712 0.000 0.000 0.000 0.288
#> GSM1299522 2 0.0000 0.84907 0.000 1.000 0.000 0.000 0.000
#> GSM1299523 5 0.3160 0.72628 0.188 0.000 0.000 0.004 0.808
#> GSM1299524 3 0.0162 0.73405 0.000 0.000 0.996 0.004 0.000
#> GSM1299525 2 0.5824 0.59173 0.000 0.628 0.100 0.256 0.016
#> GSM1299526 2 0.3368 0.76236 0.000 0.820 0.156 0.024 0.000
#> GSM1299527 3 0.0000 0.73596 0.000 0.000 1.000 0.000 0.000
#> GSM1299528 5 0.7956 0.10497 0.004 0.176 0.096 0.308 0.416
#> GSM1299529 2 0.5102 0.65629 0.000 0.684 0.100 0.216 0.000
#> GSM1299530 5 0.3752 0.67396 0.292 0.000 0.000 0.000 0.708
#> GSM1299531 2 0.0000 0.84907 0.000 1.000 0.000 0.000 0.000
#> GSM1299575 1 0.0000 0.90510 1.000 0.000 0.000 0.000 0.000
#> GSM1299532 3 0.0000 0.73596 0.000 0.000 1.000 0.000 0.000
#> GSM1299533 2 0.2740 0.81867 0.000 0.876 0.096 0.028 0.000
#> GSM1299534 3 0.0162 0.73405 0.000 0.000 0.996 0.004 0.000
#> GSM1299535 2 0.5263 0.62572 0.000 0.660 0.100 0.240 0.000
#> GSM1299536 5 0.1197 0.65131 0.000 0.000 0.000 0.048 0.952
#> GSM1299537 3 0.0000 0.73596 0.000 0.000 1.000 0.000 0.000
#> GSM1299538 5 0.4473 0.63854 0.324 0.000 0.000 0.020 0.656
#> GSM1299539 5 0.3983 0.62868 0.340 0.000 0.000 0.000 0.660
#> GSM1299540 4 0.3427 0.71674 0.000 0.012 0.192 0.796 0.000
#> GSM1299541 3 0.0000 0.73596 0.000 0.000 1.000 0.000 0.000
#> GSM1299542 3 0.0000 0.73596 0.000 0.000 1.000 0.000 0.000
#> GSM1299543 2 0.0000 0.84907 0.000 1.000 0.000 0.000 0.000
#> GSM1299544 3 0.7402 0.03244 0.000 0.184 0.460 0.300 0.056
#> GSM1299545 5 0.6055 0.49466 0.380 0.000 0.016 0.080 0.524
#> GSM1299546 2 0.0000 0.84907 0.000 1.000 0.000 0.000 0.000
#> GSM1299547 5 0.1851 0.70731 0.088 0.000 0.000 0.000 0.912
#> GSM1299548 3 0.1818 0.68602 0.000 0.000 0.932 0.024 0.044
#> GSM1299549 5 0.5002 0.63407 0.312 0.000 0.000 0.052 0.636
#> GSM1299550 5 0.3904 0.51499 0.000 0.000 0.052 0.156 0.792
#> GSM1299551 2 0.0000 0.84907 0.000 1.000 0.000 0.000 0.000
#> GSM1299552 5 0.4192 0.53971 0.404 0.000 0.000 0.000 0.596
#> GSM1299553 5 0.4171 0.55936 0.396 0.000 0.000 0.000 0.604
#> GSM1299554 3 0.6207 0.15910 0.000 0.000 0.460 0.140 0.400
#> GSM1299555 4 0.3519 0.72658 0.000 0.008 0.216 0.776 0.000
#> GSM1299556 4 0.4304 0.57630 0.000 0.000 0.484 0.516 0.000
#> GSM1299557 4 0.6296 0.69897 0.032 0.052 0.268 0.620 0.028
#> GSM1299558 2 0.1469 0.85239 0.000 0.948 0.036 0.016 0.000
#> GSM1299559 4 0.4440 0.59507 0.000 0.000 0.468 0.528 0.004
#> GSM1299560 3 0.0000 0.73596 0.000 0.000 1.000 0.000 0.000
#> GSM1299576 1 0.0963 0.90314 0.964 0.000 0.000 0.036 0.000
#> GSM1299577 5 0.3196 0.72564 0.192 0.000 0.000 0.004 0.804
#> GSM1299561 3 0.0000 0.73596 0.000 0.000 1.000 0.000 0.000
#> GSM1299562 2 0.6102 0.43954 0.000 0.560 0.176 0.264 0.000
#> GSM1299563 5 0.2929 0.72702 0.180 0.000 0.000 0.000 0.820
#> GSM1299564 5 0.0880 0.65810 0.000 0.000 0.000 0.032 0.968
#> GSM1299565 2 0.0566 0.84989 0.000 0.984 0.004 0.012 0.000
#> GSM1299566 5 0.6214 0.30684 0.004 0.028 0.084 0.292 0.592
#> GSM1299567 5 0.5975 0.55016 0.052 0.000 0.076 0.220 0.652
#> GSM1299568 3 0.6544 0.00588 0.000 0.308 0.468 0.224 0.000
#> GSM1299569 3 0.5691 0.42280 0.000 0.036 0.684 0.096 0.184
#> GSM1299570 5 0.3160 0.72628 0.188 0.000 0.000 0.004 0.808
#> GSM1299571 2 0.1872 0.84758 0.000 0.928 0.052 0.020 0.000
#> GSM1299572 3 0.4957 -0.56367 0.000 0.000 0.528 0.444 0.028
#> GSM1299573 3 0.2074 0.61590 0.000 0.000 0.896 0.104 0.000
#> GSM1299574 2 0.1628 0.84825 0.000 0.936 0.056 0.008 0.000
#> GSM1299578 1 0.0963 0.90314 0.964 0.000 0.000 0.036 0.000
#> GSM1299579 1 0.3752 0.47521 0.708 0.000 0.000 0.000 0.292
#> GSM1299580 1 0.0000 0.90510 1.000 0.000 0.000 0.000 0.000
#> GSM1299581 1 0.0963 0.90314 0.964 0.000 0.000 0.036 0.000
#> GSM1299582 1 0.0000 0.90510 1.000 0.000 0.000 0.000 0.000
#> GSM1299583 1 0.0963 0.90314 0.964 0.000 0.000 0.036 0.000
#> GSM1299584 1 0.0000 0.90510 1.000 0.000 0.000 0.000 0.000
#> GSM1299585 1 0.2554 0.84574 0.892 0.000 0.000 0.036 0.072
#> GSM1299586 1 0.0000 0.90510 1.000 0.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1299517 6 0.3309 0.7022 0.000 0.000 0.280 0.000 0.000 0.720
#> GSM1299518 3 0.1814 0.7491 0.000 0.000 0.900 0.000 0.000 0.100
#> GSM1299519 2 0.0000 0.8351 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299520 4 0.4276 0.6562 0.104 0.000 0.000 0.728 0.168 0.000
#> GSM1299521 1 0.3892 0.2901 0.640 0.000 0.000 0.352 0.004 0.004
#> GSM1299522 2 0.2178 0.8253 0.000 0.868 0.000 0.000 0.132 0.000
#> GSM1299523 4 0.4595 0.6635 0.136 0.000 0.000 0.696 0.168 0.000
#> GSM1299524 3 0.0000 0.8358 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299525 2 0.6355 0.3412 0.000 0.472 0.004 0.016 0.260 0.248
#> GSM1299526 2 0.2660 0.7622 0.000 0.868 0.048 0.000 0.000 0.084
#> GSM1299527 3 0.0000 0.8358 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299528 5 0.5705 0.4096 0.000 0.052 0.000 0.300 0.576 0.072
#> GSM1299529 2 0.5986 0.4262 0.000 0.528 0.004 0.008 0.212 0.248
#> GSM1299530 4 0.3081 0.6461 0.220 0.000 0.000 0.776 0.004 0.000
#> GSM1299531 2 0.2178 0.8253 0.000 0.868 0.000 0.000 0.132 0.000
#> GSM1299575 1 0.1536 0.8818 0.940 0.000 0.000 0.004 0.016 0.040
#> GSM1299532 3 0.0000 0.8358 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299533 2 0.1649 0.8182 0.000 0.936 0.016 0.000 0.008 0.040
#> GSM1299534 3 0.1524 0.7933 0.000 0.000 0.932 0.000 0.060 0.008
#> GSM1299535 2 0.5163 0.2706 0.000 0.536 0.020 0.000 0.048 0.396
#> GSM1299536 4 0.3838 0.1337 0.000 0.000 0.000 0.552 0.448 0.000
#> GSM1299537 3 0.0000 0.8358 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299538 4 0.4460 0.5508 0.112 0.000 0.000 0.736 0.140 0.012
#> GSM1299539 4 0.4011 0.6196 0.228 0.000 0.000 0.732 0.028 0.012
#> GSM1299540 6 0.2376 0.6431 0.000 0.044 0.068 0.000 0.000 0.888
#> GSM1299541 3 0.0000 0.8358 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299542 3 0.0000 0.8358 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299543 2 0.2178 0.8253 0.000 0.868 0.000 0.000 0.132 0.000
#> GSM1299544 5 0.7006 -0.0624 0.000 0.048 0.320 0.004 0.352 0.276
#> GSM1299545 4 0.6346 0.3985 0.232 0.000 0.020 0.536 0.016 0.196
#> GSM1299546 2 0.0363 0.8358 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM1299547 4 0.2442 0.5762 0.004 0.000 0.000 0.852 0.144 0.000
#> GSM1299548 3 0.2546 0.7488 0.000 0.000 0.888 0.060 0.040 0.012
#> GSM1299549 4 0.4347 0.6073 0.152 0.000 0.000 0.744 0.092 0.012
#> GSM1299550 5 0.3795 0.1955 0.000 0.000 0.000 0.364 0.632 0.004
#> GSM1299551 2 0.2178 0.8253 0.000 0.868 0.000 0.000 0.132 0.000
#> GSM1299552 4 0.3608 0.6199 0.248 0.000 0.000 0.736 0.004 0.012
#> GSM1299553 4 0.3716 0.6195 0.248 0.000 0.000 0.732 0.008 0.012
#> GSM1299554 5 0.5862 0.4176 0.000 0.000 0.232 0.228 0.532 0.008
#> GSM1299555 6 0.1531 0.6560 0.000 0.004 0.068 0.000 0.000 0.928
#> GSM1299556 6 0.3607 0.6520 0.000 0.000 0.348 0.000 0.000 0.652
#> GSM1299557 6 0.5221 0.6554 0.004 0.020 0.120 0.076 0.052 0.728
#> GSM1299558 2 0.3494 0.7995 0.000 0.792 0.004 0.000 0.168 0.036
#> GSM1299559 6 0.3531 0.6652 0.000 0.000 0.328 0.000 0.000 0.672
#> GSM1299560 3 0.0000 0.8358 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299576 1 0.0260 0.8833 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM1299577 4 0.4442 0.6551 0.120 0.000 0.000 0.712 0.168 0.000
#> GSM1299561 3 0.0000 0.8358 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299562 6 0.6467 0.1424 0.000 0.372 0.140 0.000 0.052 0.436
#> GSM1299563 4 0.3815 0.6646 0.092 0.000 0.000 0.776 0.132 0.000
#> GSM1299564 4 0.3782 0.2128 0.000 0.000 0.000 0.588 0.412 0.000
#> GSM1299565 2 0.0000 0.8351 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299566 5 0.4571 0.4167 0.000 0.004 0.004 0.308 0.644 0.040
#> GSM1299567 4 0.7508 0.3951 0.104 0.000 0.036 0.468 0.168 0.224
#> GSM1299568 3 0.7110 -0.2200 0.000 0.316 0.324 0.004 0.056 0.300
#> GSM1299569 3 0.4979 0.3594 0.000 0.004 0.624 0.008 0.300 0.064
#> GSM1299570 4 0.4595 0.6665 0.136 0.000 0.000 0.696 0.168 0.000
#> GSM1299571 2 0.0000 0.8351 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299572 6 0.3684 0.5990 0.000 0.000 0.372 0.000 0.000 0.628
#> GSM1299573 3 0.3464 0.3553 0.000 0.000 0.688 0.000 0.000 0.312
#> GSM1299574 2 0.0146 0.8343 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM1299578 1 0.0260 0.8833 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM1299579 1 0.3850 0.3134 0.652 0.000 0.000 0.340 0.004 0.004
#> GSM1299580 1 0.1391 0.8829 0.944 0.000 0.000 0.000 0.016 0.040
#> GSM1299581 1 0.0260 0.8833 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM1299582 1 0.1391 0.8829 0.944 0.000 0.000 0.000 0.016 0.040
#> GSM1299583 1 0.0260 0.8833 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM1299584 1 0.1391 0.8829 0.944 0.000 0.000 0.000 0.016 0.040
#> GSM1299585 1 0.0935 0.8650 0.964 0.000 0.000 0.032 0.000 0.004
#> GSM1299586 1 0.1391 0.8829 0.944 0.000 0.000 0.000 0.016 0.040
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:mclust 66 0.6391 2
#> MAD:mclust 60 0.2615 3
#> MAD:mclust 69 0.0947 4
#> MAD:mclust 59 0.0103 5
#> MAD:mclust 52 0.0204 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "NMF"]
# you can also extract it by
# res = res_list["MAD:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 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 0.879 0.904 0.961 0.4997 0.499 0.499
#> 3 3 0.537 0.685 0.851 0.3412 0.721 0.494
#> 4 4 0.767 0.842 0.908 0.1270 0.856 0.597
#> 5 5 0.763 0.732 0.862 0.0589 0.867 0.543
#> 6 6 0.721 0.627 0.786 0.0418 0.947 0.751
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
#> GSM1299517 2 0.0000 0.9587 0.000 1.000
#> GSM1299518 2 0.0000 0.9587 0.000 1.000
#> GSM1299519 2 0.0000 0.9587 0.000 1.000
#> GSM1299520 1 0.0000 0.9554 1.000 0.000
#> GSM1299521 1 0.0000 0.9554 1.000 0.000
#> GSM1299522 2 0.0000 0.9587 0.000 1.000
#> GSM1299523 1 0.0000 0.9554 1.000 0.000
#> GSM1299524 2 0.0000 0.9587 0.000 1.000
#> GSM1299525 2 0.0000 0.9587 0.000 1.000
#> GSM1299526 2 0.0000 0.9587 0.000 1.000
#> GSM1299527 2 0.0000 0.9587 0.000 1.000
#> GSM1299528 2 0.0000 0.9587 0.000 1.000
#> GSM1299529 2 0.0000 0.9587 0.000 1.000
#> GSM1299530 1 0.0000 0.9554 1.000 0.000
#> GSM1299531 2 0.0000 0.9587 0.000 1.000
#> GSM1299575 1 0.0000 0.9554 1.000 0.000
#> GSM1299532 2 0.0000 0.9587 0.000 1.000
#> GSM1299533 2 0.0000 0.9587 0.000 1.000
#> GSM1299534 2 0.0000 0.9587 0.000 1.000
#> GSM1299535 2 0.0000 0.9587 0.000 1.000
#> GSM1299536 1 0.8144 0.6721 0.748 0.252
#> GSM1299537 2 0.9248 0.4660 0.340 0.660
#> GSM1299538 2 0.0938 0.9490 0.012 0.988
#> GSM1299539 2 0.9710 0.3228 0.400 0.600
#> GSM1299540 1 0.4022 0.8933 0.920 0.080
#> GSM1299541 1 0.9460 0.4368 0.636 0.364
#> GSM1299542 2 0.0000 0.9587 0.000 1.000
#> GSM1299543 2 0.0000 0.9587 0.000 1.000
#> GSM1299544 2 0.0000 0.9587 0.000 1.000
#> GSM1299545 1 0.0000 0.9554 1.000 0.000
#> GSM1299546 2 0.0000 0.9587 0.000 1.000
#> GSM1299547 1 0.0000 0.9554 1.000 0.000
#> GSM1299548 1 0.9170 0.5121 0.668 0.332
#> GSM1299549 1 0.2603 0.9233 0.956 0.044
#> GSM1299550 2 0.0000 0.9587 0.000 1.000
#> GSM1299551 2 0.0000 0.9587 0.000 1.000
#> GSM1299552 1 0.0000 0.9554 1.000 0.000
#> GSM1299553 1 0.0000 0.9554 1.000 0.000
#> GSM1299554 2 0.0000 0.9587 0.000 1.000
#> GSM1299555 2 0.0000 0.9587 0.000 1.000
#> GSM1299556 1 0.2948 0.9184 0.948 0.052
#> GSM1299557 2 0.9963 0.0958 0.464 0.536
#> GSM1299558 2 0.0000 0.9587 0.000 1.000
#> GSM1299559 1 0.5294 0.8517 0.880 0.120
#> GSM1299560 2 0.0000 0.9587 0.000 1.000
#> GSM1299576 1 0.0000 0.9554 1.000 0.000
#> GSM1299577 1 0.0000 0.9554 1.000 0.000
#> GSM1299561 2 0.3274 0.9067 0.060 0.940
#> GSM1299562 2 0.0000 0.9587 0.000 1.000
#> GSM1299563 1 0.0000 0.9554 1.000 0.000
#> GSM1299564 1 0.0938 0.9480 0.988 0.012
#> GSM1299565 2 0.0000 0.9587 0.000 1.000
#> GSM1299566 2 0.0000 0.9587 0.000 1.000
#> GSM1299567 1 0.0000 0.9554 1.000 0.000
#> GSM1299568 2 0.0000 0.9587 0.000 1.000
#> GSM1299569 2 0.0000 0.9587 0.000 1.000
#> GSM1299570 1 0.0000 0.9554 1.000 0.000
#> GSM1299571 2 0.0000 0.9587 0.000 1.000
#> GSM1299572 2 0.4298 0.8791 0.088 0.912
#> GSM1299573 2 0.4690 0.8651 0.100 0.900
#> GSM1299574 2 0.0000 0.9587 0.000 1.000
#> GSM1299578 1 0.0000 0.9554 1.000 0.000
#> GSM1299579 1 0.0000 0.9554 1.000 0.000
#> GSM1299580 1 0.0000 0.9554 1.000 0.000
#> GSM1299581 1 0.0000 0.9554 1.000 0.000
#> GSM1299582 1 0.0000 0.9554 1.000 0.000
#> GSM1299583 1 0.0000 0.9554 1.000 0.000
#> GSM1299584 1 0.0000 0.9554 1.000 0.000
#> GSM1299585 1 0.0000 0.9554 1.000 0.000
#> GSM1299586 1 0.0000 0.9554 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1299517 3 0.6140 0.4774 0.000 0.404 0.596
#> GSM1299518 3 0.5497 0.6489 0.000 0.292 0.708
#> GSM1299519 2 0.0000 0.8668 0.000 1.000 0.000
#> GSM1299520 1 0.3038 0.7685 0.896 0.000 0.104
#> GSM1299521 1 0.0000 0.8157 1.000 0.000 0.000
#> GSM1299522 2 0.0000 0.8668 0.000 1.000 0.000
#> GSM1299523 3 0.5706 0.1559 0.320 0.000 0.680
#> GSM1299524 3 0.5785 0.6002 0.000 0.332 0.668
#> GSM1299525 2 0.3715 0.7735 0.128 0.868 0.004
#> GSM1299526 2 0.5988 0.1909 0.000 0.632 0.368
#> GSM1299527 3 0.4399 0.7264 0.000 0.188 0.812
#> GSM1299528 2 0.3192 0.7902 0.112 0.888 0.000
#> GSM1299529 2 0.0000 0.8668 0.000 1.000 0.000
#> GSM1299530 1 0.0424 0.8145 0.992 0.000 0.008
#> GSM1299531 2 0.0000 0.8668 0.000 1.000 0.000
#> GSM1299575 1 0.5397 0.7097 0.720 0.000 0.280
#> GSM1299532 3 0.5678 0.6213 0.000 0.316 0.684
#> GSM1299533 2 0.3192 0.7550 0.000 0.888 0.112
#> GSM1299534 3 0.6286 0.3433 0.000 0.464 0.536
#> GSM1299535 2 0.0000 0.8668 0.000 1.000 0.000
#> GSM1299536 1 0.8822 0.2668 0.540 0.136 0.324
#> GSM1299537 3 0.0592 0.7346 0.000 0.012 0.988
#> GSM1299538 2 0.5588 0.6170 0.276 0.720 0.004
#> GSM1299539 1 0.6330 0.2022 0.600 0.396 0.004
#> GSM1299540 3 0.4062 0.5681 0.164 0.000 0.836
#> GSM1299541 3 0.0592 0.7346 0.000 0.012 0.988
#> GSM1299542 3 0.4750 0.7120 0.000 0.216 0.784
#> GSM1299543 2 0.0000 0.8668 0.000 1.000 0.000
#> GSM1299544 2 0.0000 0.8668 0.000 1.000 0.000
#> GSM1299545 1 0.5397 0.7074 0.720 0.000 0.280
#> GSM1299546 2 0.0000 0.8668 0.000 1.000 0.000
#> GSM1299547 1 0.0237 0.8146 0.996 0.000 0.004
#> GSM1299548 3 0.0424 0.7325 0.000 0.008 0.992
#> GSM1299549 1 0.0424 0.8131 0.992 0.008 0.000
#> GSM1299550 2 0.6187 0.6339 0.248 0.724 0.028
#> GSM1299551 2 0.0000 0.8668 0.000 1.000 0.000
#> GSM1299552 1 0.0000 0.8157 1.000 0.000 0.000
#> GSM1299553 1 0.0000 0.8157 1.000 0.000 0.000
#> GSM1299554 2 0.8896 0.3096 0.156 0.552 0.292
#> GSM1299555 3 0.5591 0.6236 0.000 0.304 0.696
#> GSM1299556 3 0.0237 0.7264 0.004 0.000 0.996
#> GSM1299557 3 0.6247 0.3276 0.004 0.376 0.620
#> GSM1299558 2 0.0000 0.8668 0.000 1.000 0.000
#> GSM1299559 3 0.0475 0.7295 0.004 0.004 0.992
#> GSM1299560 3 0.4842 0.7066 0.000 0.224 0.776
#> GSM1299576 1 0.3116 0.8093 0.892 0.000 0.108
#> GSM1299577 1 0.6079 0.5653 0.612 0.000 0.388
#> GSM1299561 3 0.2261 0.7524 0.000 0.068 0.932
#> GSM1299562 2 0.0000 0.8668 0.000 1.000 0.000
#> GSM1299563 1 0.2711 0.7793 0.912 0.000 0.088
#> GSM1299564 1 0.5948 0.3849 0.640 0.000 0.360
#> GSM1299565 2 0.0000 0.8668 0.000 1.000 0.000
#> GSM1299566 2 0.4409 0.7323 0.172 0.824 0.004
#> GSM1299567 3 0.0237 0.7264 0.004 0.000 0.996
#> GSM1299568 2 0.0000 0.8668 0.000 1.000 0.000
#> GSM1299569 2 0.0237 0.8641 0.000 0.996 0.004
#> GSM1299570 3 0.6062 0.0836 0.384 0.000 0.616
#> GSM1299571 2 0.2711 0.7843 0.000 0.912 0.088
#> GSM1299572 2 0.7054 -0.1889 0.020 0.524 0.456
#> GSM1299573 3 0.2796 0.7561 0.000 0.092 0.908
#> GSM1299574 2 0.0000 0.8668 0.000 1.000 0.000
#> GSM1299578 1 0.3192 0.8086 0.888 0.000 0.112
#> GSM1299579 1 0.0000 0.8157 1.000 0.000 0.000
#> GSM1299580 1 0.5465 0.7013 0.712 0.000 0.288
#> GSM1299581 1 0.3340 0.8055 0.880 0.000 0.120
#> GSM1299582 1 0.4931 0.7498 0.768 0.000 0.232
#> GSM1299583 1 0.2356 0.8151 0.928 0.000 0.072
#> GSM1299584 1 0.5058 0.7409 0.756 0.000 0.244
#> GSM1299585 1 0.0424 0.8169 0.992 0.000 0.008
#> GSM1299586 1 0.4750 0.7598 0.784 0.000 0.216
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1299517 3 0.4206 0.806 0.000 0.048 0.816 0.136
#> GSM1299518 3 0.1151 0.853 0.000 0.024 0.968 0.008
#> GSM1299519 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM1299520 4 0.3796 0.787 0.096 0.000 0.056 0.848
#> GSM1299521 1 0.0000 0.955 1.000 0.000 0.000 0.000
#> GSM1299522 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM1299523 3 0.4994 0.681 0.048 0.000 0.744 0.208
#> GSM1299524 3 0.3105 0.833 0.000 0.012 0.868 0.120
#> GSM1299525 4 0.4454 0.630 0.000 0.308 0.000 0.692
#> GSM1299526 2 0.1940 0.899 0.000 0.924 0.076 0.000
#> GSM1299527 3 0.2675 0.841 0.000 0.008 0.892 0.100
#> GSM1299528 4 0.4072 0.705 0.000 0.252 0.000 0.748
#> GSM1299529 2 0.0592 0.974 0.000 0.984 0.000 0.016
#> GSM1299530 1 0.4501 0.694 0.764 0.000 0.024 0.212
#> GSM1299531 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM1299575 1 0.1211 0.936 0.960 0.000 0.040 0.000
#> GSM1299532 3 0.2198 0.848 0.000 0.008 0.920 0.072
#> GSM1299533 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM1299534 3 0.4690 0.721 0.000 0.016 0.724 0.260
#> GSM1299535 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM1299536 4 0.0000 0.821 0.000 0.000 0.000 1.000
#> GSM1299537 3 0.0469 0.853 0.000 0.000 0.988 0.012
#> GSM1299538 4 0.3606 0.790 0.020 0.140 0.000 0.840
#> GSM1299539 4 0.2345 0.812 0.100 0.000 0.000 0.900
#> GSM1299540 3 0.3266 0.795 0.108 0.024 0.868 0.000
#> GSM1299541 3 0.0000 0.852 0.000 0.000 1.000 0.000
#> GSM1299542 3 0.0804 0.854 0.000 0.008 0.980 0.012
#> GSM1299543 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM1299544 4 0.4697 0.482 0.000 0.356 0.000 0.644
#> GSM1299545 1 0.0707 0.947 0.980 0.000 0.020 0.000
#> GSM1299546 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM1299547 4 0.2704 0.800 0.124 0.000 0.000 0.876
#> GSM1299548 3 0.3528 0.798 0.000 0.000 0.808 0.192
#> GSM1299549 1 0.2216 0.886 0.908 0.000 0.000 0.092
#> GSM1299550 4 0.0000 0.821 0.000 0.000 0.000 1.000
#> GSM1299551 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM1299552 1 0.0921 0.940 0.972 0.000 0.000 0.028
#> GSM1299553 1 0.0469 0.950 0.988 0.000 0.000 0.012
#> GSM1299554 4 0.0336 0.819 0.000 0.000 0.008 0.992
#> GSM1299555 3 0.4804 0.457 0.000 0.384 0.616 0.000
#> GSM1299556 3 0.0000 0.852 0.000 0.000 1.000 0.000
#> GSM1299557 3 0.9279 0.269 0.148 0.324 0.392 0.136
#> GSM1299558 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM1299559 3 0.0336 0.852 0.000 0.000 0.992 0.008
#> GSM1299560 3 0.0672 0.854 0.000 0.008 0.984 0.008
#> GSM1299576 1 0.0000 0.955 1.000 0.000 0.000 0.000
#> GSM1299577 1 0.4534 0.776 0.800 0.000 0.132 0.068
#> GSM1299561 3 0.0804 0.854 0.000 0.008 0.980 0.012
#> GSM1299562 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM1299563 4 0.3852 0.745 0.180 0.000 0.012 0.808
#> GSM1299564 4 0.0592 0.820 0.000 0.000 0.016 0.984
#> GSM1299565 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM1299566 4 0.1474 0.825 0.000 0.052 0.000 0.948
#> GSM1299567 3 0.0817 0.847 0.000 0.000 0.976 0.024
#> GSM1299568 2 0.1302 0.944 0.000 0.956 0.000 0.044
#> GSM1299569 4 0.3142 0.783 0.000 0.132 0.008 0.860
#> GSM1299570 3 0.5807 0.658 0.160 0.000 0.708 0.132
#> GSM1299571 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM1299572 3 0.6426 0.588 0.108 0.272 0.620 0.000
#> GSM1299573 3 0.3052 0.819 0.000 0.004 0.860 0.136
#> GSM1299574 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM1299578 1 0.0000 0.955 1.000 0.000 0.000 0.000
#> GSM1299579 4 0.4992 0.208 0.476 0.000 0.000 0.524
#> GSM1299580 1 0.1211 0.935 0.960 0.000 0.040 0.000
#> GSM1299581 1 0.0000 0.955 1.000 0.000 0.000 0.000
#> GSM1299582 1 0.0000 0.955 1.000 0.000 0.000 0.000
#> GSM1299583 1 0.0000 0.955 1.000 0.000 0.000 0.000
#> GSM1299584 1 0.0336 0.953 0.992 0.000 0.008 0.000
#> GSM1299585 1 0.0000 0.955 1.000 0.000 0.000 0.000
#> GSM1299586 1 0.0000 0.955 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1299517 3 0.4293 0.7318 0.000 0.064 0.772 0.004 0.160
#> GSM1299518 3 0.1697 0.7940 0.000 0.060 0.932 0.000 0.008
#> GSM1299519 2 0.0000 0.9284 0.000 1.000 0.000 0.000 0.000
#> GSM1299520 4 0.0324 0.8308 0.000 0.000 0.004 0.992 0.004
#> GSM1299521 1 0.2104 0.8470 0.916 0.000 0.000 0.024 0.060
#> GSM1299522 2 0.0000 0.9284 0.000 1.000 0.000 0.000 0.000
#> GSM1299523 4 0.2054 0.8074 0.028 0.000 0.052 0.920 0.000
#> GSM1299524 3 0.4464 0.6213 0.000 0.008 0.676 0.012 0.304
#> GSM1299525 2 0.4062 0.6651 0.000 0.764 0.000 0.196 0.040
#> GSM1299526 2 0.2280 0.8142 0.000 0.880 0.120 0.000 0.000
#> GSM1299527 3 0.3274 0.7131 0.000 0.000 0.780 0.000 0.220
#> GSM1299528 5 0.5659 0.4951 0.000 0.204 0.000 0.164 0.632
#> GSM1299529 2 0.1205 0.9010 0.000 0.956 0.000 0.004 0.040
#> GSM1299530 4 0.1282 0.8274 0.044 0.000 0.004 0.952 0.000
#> GSM1299531 2 0.0000 0.9284 0.000 1.000 0.000 0.000 0.000
#> GSM1299575 1 0.1768 0.8291 0.924 0.000 0.072 0.004 0.000
#> GSM1299532 3 0.3561 0.6835 0.000 0.000 0.740 0.000 0.260
#> GSM1299533 2 0.0000 0.9284 0.000 1.000 0.000 0.000 0.000
#> GSM1299534 5 0.3724 0.5695 0.000 0.000 0.184 0.028 0.788
#> GSM1299535 2 0.0865 0.9135 0.000 0.972 0.004 0.000 0.024
#> GSM1299536 4 0.3636 0.6253 0.000 0.000 0.000 0.728 0.272
#> GSM1299537 3 0.1341 0.7989 0.000 0.000 0.944 0.056 0.000
#> GSM1299538 4 0.2278 0.8245 0.032 0.008 0.000 0.916 0.044
#> GSM1299539 4 0.2782 0.8099 0.048 0.000 0.000 0.880 0.072
#> GSM1299540 3 0.3216 0.7457 0.096 0.044 0.856 0.004 0.000
#> GSM1299541 3 0.0671 0.8042 0.000 0.000 0.980 0.016 0.004
#> GSM1299542 3 0.0771 0.8050 0.000 0.004 0.976 0.000 0.020
#> GSM1299543 2 0.0000 0.9284 0.000 1.000 0.000 0.000 0.000
#> GSM1299544 5 0.2370 0.7073 0.000 0.056 0.000 0.040 0.904
#> GSM1299545 1 0.4029 0.6268 0.744 0.000 0.024 0.232 0.000
#> GSM1299546 2 0.0000 0.9284 0.000 1.000 0.000 0.000 0.000
#> GSM1299547 1 0.5242 0.3168 0.516 0.000 0.004 0.036 0.444
#> GSM1299548 3 0.4088 0.5478 0.000 0.000 0.632 0.000 0.368
#> GSM1299549 1 0.4142 0.6219 0.684 0.000 0.004 0.004 0.308
#> GSM1299550 5 0.4201 0.0946 0.000 0.000 0.000 0.408 0.592
#> GSM1299551 2 0.0000 0.9284 0.000 1.000 0.000 0.000 0.000
#> GSM1299552 1 0.2338 0.8322 0.884 0.000 0.000 0.004 0.112
#> GSM1299553 1 0.2470 0.8345 0.884 0.000 0.000 0.012 0.104
#> GSM1299554 5 0.1774 0.6935 0.000 0.000 0.016 0.052 0.932
#> GSM1299555 2 0.5010 0.2777 0.036 0.572 0.392 0.000 0.000
#> GSM1299556 3 0.0162 0.8035 0.000 0.000 0.996 0.004 0.000
#> GSM1299557 5 0.6561 0.1340 0.332 0.000 0.216 0.000 0.452
#> GSM1299558 2 0.2280 0.8188 0.000 0.880 0.000 0.000 0.120
#> GSM1299559 3 0.1942 0.7917 0.012 0.000 0.920 0.068 0.000
#> GSM1299560 3 0.1956 0.7858 0.000 0.076 0.916 0.000 0.008
#> GSM1299576 1 0.0703 0.8609 0.976 0.000 0.000 0.000 0.024
#> GSM1299577 4 0.3771 0.7003 0.164 0.000 0.040 0.796 0.000
#> GSM1299561 3 0.1197 0.8024 0.000 0.000 0.952 0.000 0.048
#> GSM1299562 2 0.0000 0.9284 0.000 1.000 0.000 0.000 0.000
#> GSM1299563 4 0.2747 0.8112 0.060 0.000 0.004 0.888 0.048
#> GSM1299564 4 0.0404 0.8304 0.000 0.000 0.000 0.988 0.012
#> GSM1299565 2 0.0000 0.9284 0.000 1.000 0.000 0.000 0.000
#> GSM1299566 4 0.5816 -0.0455 0.000 0.092 0.000 0.468 0.440
#> GSM1299567 3 0.3454 0.7365 0.064 0.000 0.836 0.100 0.000
#> GSM1299568 5 0.3381 0.6622 0.000 0.176 0.016 0.000 0.808
#> GSM1299569 5 0.2768 0.7106 0.000 0.040 0.024 0.040 0.896
#> GSM1299570 4 0.1211 0.8277 0.016 0.000 0.024 0.960 0.000
#> GSM1299571 2 0.0000 0.9284 0.000 1.000 0.000 0.000 0.000
#> GSM1299572 3 0.6909 0.4620 0.180 0.212 0.568 0.028 0.012
#> GSM1299573 3 0.4300 0.2829 0.000 0.000 0.524 0.000 0.476
#> GSM1299574 2 0.0000 0.9284 0.000 1.000 0.000 0.000 0.000
#> GSM1299578 1 0.0162 0.8625 0.996 0.000 0.000 0.004 0.000
#> GSM1299579 1 0.5473 0.1783 0.520 0.000 0.000 0.416 0.064
#> GSM1299580 1 0.1768 0.8291 0.924 0.000 0.072 0.004 0.000
#> GSM1299581 1 0.0162 0.8625 0.996 0.000 0.000 0.004 0.000
#> GSM1299582 1 0.0162 0.8625 0.996 0.000 0.000 0.004 0.000
#> GSM1299583 1 0.0510 0.8624 0.984 0.000 0.000 0.000 0.016
#> GSM1299584 1 0.0162 0.8625 0.996 0.000 0.000 0.004 0.000
#> GSM1299585 1 0.2193 0.8459 0.912 0.000 0.000 0.028 0.060
#> GSM1299586 1 0.0162 0.8625 0.996 0.000 0.000 0.004 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1299517 3 0.5201 0.3068 0.000 0.032 0.540 0.004 0.028 0.396
#> GSM1299518 3 0.3388 0.6907 0.000 0.028 0.848 0.008 0.068 0.048
#> GSM1299519 2 0.0000 0.9035 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299520 4 0.0767 0.8363 0.000 0.000 0.008 0.976 0.004 0.012
#> GSM1299521 1 0.4756 0.3515 0.564 0.000 0.000 0.056 0.000 0.380
#> GSM1299522 2 0.0291 0.9026 0.000 0.992 0.000 0.000 0.004 0.004
#> GSM1299523 4 0.1615 0.8072 0.004 0.000 0.064 0.928 0.000 0.004
#> GSM1299524 5 0.5056 -0.1008 0.000 0.000 0.424 0.004 0.508 0.064
#> GSM1299525 2 0.5254 0.6199 0.000 0.696 0.000 0.088 0.132 0.084
#> GSM1299526 2 0.2536 0.8061 0.000 0.864 0.116 0.000 0.000 0.020
#> GSM1299527 3 0.4663 0.6019 0.000 0.000 0.684 0.000 0.124 0.192
#> GSM1299528 5 0.3664 0.5748 0.000 0.072 0.000 0.052 0.824 0.052
#> GSM1299529 2 0.4303 0.5782 0.000 0.676 0.000 0.008 0.032 0.284
#> GSM1299530 4 0.0951 0.8363 0.008 0.000 0.000 0.968 0.004 0.020
#> GSM1299531 2 0.1285 0.8794 0.000 0.944 0.000 0.000 0.052 0.004
#> GSM1299575 1 0.2450 0.6678 0.892 0.000 0.068 0.004 0.004 0.032
#> GSM1299532 3 0.4239 0.6215 0.000 0.000 0.740 0.008 0.180 0.072
#> GSM1299533 2 0.0260 0.9024 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM1299534 5 0.3477 0.5631 0.000 0.000 0.132 0.004 0.808 0.056
#> GSM1299535 2 0.1858 0.8538 0.000 0.904 0.000 0.000 0.004 0.092
#> GSM1299536 4 0.5235 0.2372 0.000 0.000 0.012 0.508 0.416 0.064
#> GSM1299537 3 0.2532 0.6983 0.000 0.000 0.884 0.060 0.004 0.052
#> GSM1299538 4 0.2945 0.8068 0.004 0.012 0.000 0.868 0.052 0.064
#> GSM1299539 4 0.4334 0.7395 0.020 0.000 0.000 0.756 0.092 0.132
#> GSM1299540 3 0.6081 0.3249 0.340 0.084 0.524 0.008 0.000 0.044
#> GSM1299541 3 0.1296 0.7058 0.000 0.000 0.952 0.012 0.004 0.032
#> GSM1299542 3 0.2085 0.7055 0.000 0.008 0.912 0.000 0.056 0.024
#> GSM1299543 2 0.2255 0.8435 0.000 0.892 0.000 0.000 0.080 0.028
#> GSM1299544 5 0.0837 0.6095 0.000 0.000 0.004 0.004 0.972 0.020
#> GSM1299545 1 0.4632 0.3710 0.656 0.000 0.064 0.276 0.000 0.004
#> GSM1299546 2 0.0146 0.9031 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM1299547 6 0.5205 0.6606 0.188 0.000 0.000 0.040 0.096 0.676
#> GSM1299548 3 0.5597 0.4583 0.000 0.000 0.560 0.004 0.260 0.176
#> GSM1299549 6 0.3983 0.7104 0.108 0.000 0.004 0.004 0.104 0.780
#> GSM1299550 5 0.4414 0.2544 0.000 0.000 0.004 0.336 0.628 0.032
#> GSM1299551 2 0.0146 0.9031 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM1299552 6 0.4877 0.6648 0.268 0.000 0.000 0.016 0.064 0.652
#> GSM1299553 6 0.4917 0.6181 0.308 0.000 0.000 0.048 0.020 0.624
#> GSM1299554 5 0.5197 0.0555 0.000 0.000 0.076 0.004 0.484 0.436
#> GSM1299555 2 0.3394 0.6643 0.000 0.752 0.236 0.012 0.000 0.000
#> GSM1299556 3 0.2405 0.6889 0.016 0.000 0.892 0.008 0.004 0.080
#> GSM1299557 6 0.5685 0.4519 0.112 0.000 0.164 0.000 0.076 0.648
#> GSM1299558 5 0.3998 -0.0560 0.000 0.492 0.000 0.000 0.504 0.004
#> GSM1299559 3 0.3542 0.6482 0.000 0.000 0.788 0.160 0.000 0.052
#> GSM1299560 3 0.2068 0.6911 0.000 0.080 0.904 0.008 0.008 0.000
#> GSM1299576 1 0.2527 0.6717 0.832 0.000 0.000 0.000 0.000 0.168
#> GSM1299577 4 0.3185 0.7523 0.116 0.000 0.048 0.832 0.004 0.000
#> GSM1299561 3 0.1908 0.6958 0.000 0.000 0.900 0.000 0.096 0.004
#> GSM1299562 2 0.0692 0.8967 0.000 0.976 0.020 0.000 0.004 0.000
#> GSM1299563 4 0.4114 0.6886 0.052 0.000 0.000 0.740 0.008 0.200
#> GSM1299564 4 0.1434 0.8355 0.000 0.000 0.008 0.948 0.020 0.024
#> GSM1299565 2 0.0000 0.9035 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299566 5 0.4690 0.4710 0.000 0.032 0.000 0.204 0.708 0.056
#> GSM1299567 3 0.6092 0.3788 0.244 0.000 0.552 0.168 0.000 0.036
#> GSM1299568 5 0.3230 0.6126 0.000 0.052 0.060 0.000 0.852 0.036
#> GSM1299569 5 0.1693 0.6158 0.000 0.000 0.044 0.004 0.932 0.020
#> GSM1299570 4 0.0858 0.8272 0.004 0.000 0.028 0.968 0.000 0.000
#> GSM1299571 2 0.0000 0.9035 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299572 3 0.8415 0.2074 0.112 0.196 0.412 0.032 0.048 0.200
#> GSM1299573 3 0.5488 0.4373 0.000 0.000 0.556 0.000 0.272 0.172
#> GSM1299574 2 0.0000 0.9035 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299578 1 0.0146 0.7302 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM1299579 1 0.6075 0.1168 0.436 0.000 0.000 0.176 0.012 0.376
#> GSM1299580 1 0.2333 0.6740 0.900 0.000 0.060 0.004 0.004 0.032
#> GSM1299581 1 0.1663 0.7173 0.912 0.000 0.000 0.000 0.000 0.088
#> GSM1299582 1 0.0146 0.7290 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM1299583 1 0.2823 0.6553 0.796 0.000 0.000 0.000 0.000 0.204
#> GSM1299584 1 0.0000 0.7301 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299585 1 0.4252 0.4147 0.604 0.000 0.000 0.024 0.000 0.372
#> GSM1299586 1 0.0000 0.7301 1.000 0.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:NMF 66 0.2938 2
#> MAD:NMF 59 0.3370 3
#> MAD:NMF 66 0.8486 4
#> MAD:NMF 61 0.3269 5
#> MAD:NMF 53 0.0371 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "hclust"]
# you can also extract it by
# res = res_list["ATC:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 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 0.649 0.867 0.923 0.4631 0.543 0.543
#> 3 3 0.617 0.781 0.873 0.3353 0.851 0.725
#> 4 4 0.733 0.832 0.872 0.1772 0.876 0.686
#> 5 5 0.759 0.781 0.849 0.0582 0.952 0.824
#> 6 6 0.778 0.685 0.835 0.0393 0.968 0.865
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 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
#> GSM1299517 1 0.2043 0.908 0.968 0.032
#> GSM1299518 1 0.2603 0.909 0.956 0.044
#> GSM1299519 2 0.1184 0.960 0.016 0.984
#> GSM1299520 1 1.0000 0.226 0.504 0.496
#> GSM1299521 1 0.7674 0.736 0.776 0.224
#> GSM1299522 2 0.1184 0.960 0.016 0.984
#> GSM1299523 1 0.8813 0.658 0.700 0.300
#> GSM1299524 1 0.4562 0.887 0.904 0.096
#> GSM1299525 2 0.0672 0.961 0.008 0.992
#> GSM1299526 1 0.2423 0.909 0.960 0.040
#> GSM1299527 1 0.2603 0.909 0.956 0.044
#> GSM1299528 2 0.0000 0.961 0.000 1.000
#> GSM1299529 2 0.1184 0.959 0.016 0.984
#> GSM1299530 1 0.6048 0.851 0.852 0.148
#> GSM1299531 2 0.1184 0.960 0.016 0.984
#> GSM1299575 1 0.0000 0.898 1.000 0.000
#> GSM1299532 1 0.3274 0.906 0.940 0.060
#> GSM1299533 1 0.3431 0.904 0.936 0.064
#> GSM1299534 2 0.0938 0.959 0.012 0.988
#> GSM1299535 1 0.4562 0.887 0.904 0.096
#> GSM1299536 2 0.0000 0.961 0.000 1.000
#> GSM1299537 1 0.1633 0.907 0.976 0.024
#> GSM1299538 2 0.1843 0.948 0.028 0.972
#> GSM1299539 2 0.0000 0.961 0.000 1.000
#> GSM1299540 1 0.1633 0.907 0.976 0.024
#> GSM1299541 1 0.1633 0.907 0.976 0.024
#> GSM1299542 1 0.2603 0.909 0.956 0.044
#> GSM1299543 2 0.0000 0.961 0.000 1.000
#> GSM1299544 2 0.0000 0.961 0.000 1.000
#> GSM1299545 1 0.5294 0.872 0.880 0.120
#> GSM1299546 2 0.1184 0.960 0.016 0.984
#> GSM1299547 1 0.9896 0.377 0.560 0.440
#> GSM1299548 1 0.2423 0.909 0.960 0.040
#> GSM1299549 1 0.5178 0.875 0.884 0.116
#> GSM1299550 2 0.0000 0.961 0.000 1.000
#> GSM1299551 2 0.1184 0.960 0.016 0.984
#> GSM1299552 1 0.5178 0.875 0.884 0.116
#> GSM1299553 1 0.5946 0.857 0.856 0.144
#> GSM1299554 2 0.7745 0.691 0.228 0.772
#> GSM1299555 1 0.3431 0.904 0.936 0.064
#> GSM1299556 1 0.1633 0.907 0.976 0.024
#> GSM1299557 1 0.2603 0.909 0.956 0.044
#> GSM1299558 2 0.0000 0.961 0.000 1.000
#> GSM1299559 1 0.1633 0.907 0.976 0.024
#> GSM1299560 1 0.2603 0.909 0.956 0.044
#> GSM1299576 1 0.0000 0.898 1.000 0.000
#> GSM1299577 1 0.5842 0.858 0.860 0.140
#> GSM1299561 1 0.2603 0.909 0.956 0.044
#> GSM1299562 2 0.6712 0.780 0.176 0.824
#> GSM1299563 1 1.0000 0.226 0.504 0.496
#> GSM1299564 1 0.9983 0.286 0.524 0.476
#> GSM1299565 2 0.1184 0.960 0.016 0.984
#> GSM1299566 2 0.0000 0.961 0.000 1.000
#> GSM1299567 1 0.1633 0.907 0.976 0.024
#> GSM1299568 2 0.7056 0.749 0.192 0.808
#> GSM1299569 2 0.0000 0.961 0.000 1.000
#> GSM1299570 1 0.5946 0.854 0.856 0.144
#> GSM1299571 1 0.3431 0.904 0.936 0.064
#> GSM1299572 1 0.3274 0.906 0.940 0.060
#> GSM1299573 1 0.2603 0.909 0.956 0.044
#> GSM1299574 2 0.2423 0.943 0.040 0.960
#> GSM1299578 1 0.3879 0.880 0.924 0.076
#> GSM1299579 2 0.0000 0.961 0.000 1.000
#> GSM1299580 1 0.0000 0.898 1.000 0.000
#> GSM1299581 1 0.0000 0.898 1.000 0.000
#> GSM1299582 1 0.0000 0.898 1.000 0.000
#> GSM1299583 1 0.0000 0.898 1.000 0.000
#> GSM1299584 1 0.0000 0.898 1.000 0.000
#> GSM1299585 1 0.3879 0.880 0.924 0.076
#> GSM1299586 1 0.0000 0.898 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1299517 3 0.0592 0.793 0.012 0.000 0.988
#> GSM1299518 3 0.0000 0.796 0.000 0.000 1.000
#> GSM1299519 2 0.2066 0.927 0.000 0.940 0.060
#> GSM1299520 3 0.8688 0.400 0.112 0.372 0.516
#> GSM1299521 3 0.8843 0.262 0.436 0.116 0.448
#> GSM1299522 2 0.2066 0.927 0.000 0.940 0.060
#> GSM1299523 3 0.8835 0.521 0.268 0.164 0.568
#> GSM1299524 3 0.1860 0.777 0.000 0.052 0.948
#> GSM1299525 2 0.1289 0.931 0.000 0.968 0.032
#> GSM1299526 3 0.0237 0.795 0.004 0.000 0.996
#> GSM1299527 3 0.0000 0.796 0.000 0.000 1.000
#> GSM1299528 2 0.0000 0.928 0.000 1.000 0.000
#> GSM1299529 2 0.1753 0.929 0.000 0.952 0.048
#> GSM1299530 3 0.7114 0.501 0.388 0.028 0.584
#> GSM1299531 2 0.2066 0.927 0.000 0.940 0.060
#> GSM1299575 1 0.3412 0.934 0.876 0.000 0.124
#> GSM1299532 3 0.0747 0.795 0.000 0.016 0.984
#> GSM1299533 3 0.0892 0.794 0.000 0.020 0.980
#> GSM1299534 2 0.0892 0.931 0.000 0.980 0.020
#> GSM1299535 3 0.1860 0.777 0.000 0.052 0.948
#> GSM1299536 2 0.1860 0.906 0.052 0.948 0.000
#> GSM1299537 3 0.0892 0.790 0.020 0.000 0.980
#> GSM1299538 2 0.2564 0.907 0.036 0.936 0.028
#> GSM1299539 2 0.0000 0.928 0.000 1.000 0.000
#> GSM1299540 3 0.1031 0.790 0.024 0.000 0.976
#> GSM1299541 3 0.0892 0.790 0.020 0.000 0.980
#> GSM1299542 3 0.0000 0.796 0.000 0.000 1.000
#> GSM1299543 2 0.0000 0.928 0.000 1.000 0.000
#> GSM1299544 2 0.0000 0.928 0.000 1.000 0.000
#> GSM1299545 3 0.6879 0.528 0.360 0.024 0.616
#> GSM1299546 2 0.2066 0.927 0.000 0.940 0.060
#> GSM1299547 3 0.8614 0.501 0.128 0.304 0.568
#> GSM1299548 3 0.0237 0.795 0.004 0.000 0.996
#> GSM1299549 3 0.6859 0.530 0.356 0.024 0.620
#> GSM1299550 2 0.0000 0.928 0.000 1.000 0.000
#> GSM1299551 2 0.2066 0.927 0.000 0.940 0.060
#> GSM1299552 3 0.6859 0.530 0.356 0.024 0.620
#> GSM1299553 3 0.7271 0.532 0.352 0.040 0.608
#> GSM1299554 2 0.5327 0.664 0.000 0.728 0.272
#> GSM1299555 3 0.0892 0.794 0.000 0.020 0.980
#> GSM1299556 3 0.1031 0.790 0.024 0.000 0.976
#> GSM1299557 3 0.3192 0.737 0.112 0.000 0.888
#> GSM1299558 2 0.0000 0.928 0.000 1.000 0.000
#> GSM1299559 3 0.1031 0.790 0.024 0.000 0.976
#> GSM1299560 3 0.0000 0.796 0.000 0.000 1.000
#> GSM1299576 1 0.3267 0.932 0.884 0.000 0.116
#> GSM1299577 3 0.6985 0.508 0.384 0.024 0.592
#> GSM1299561 3 0.0000 0.796 0.000 0.000 1.000
#> GSM1299562 2 0.4796 0.759 0.000 0.780 0.220
#> GSM1299563 3 0.8688 0.400 0.112 0.372 0.516
#> GSM1299564 3 0.8645 0.447 0.116 0.344 0.540
#> GSM1299565 2 0.2066 0.927 0.000 0.940 0.060
#> GSM1299566 2 0.0000 0.928 0.000 1.000 0.000
#> GSM1299567 3 0.1031 0.790 0.024 0.000 0.976
#> GSM1299568 2 0.4974 0.725 0.000 0.764 0.236
#> GSM1299569 2 0.0000 0.928 0.000 1.000 0.000
#> GSM1299570 3 0.7001 0.505 0.388 0.024 0.588
#> GSM1299571 3 0.0892 0.794 0.000 0.020 0.980
#> GSM1299572 3 0.0983 0.795 0.004 0.016 0.980
#> GSM1299573 3 0.0000 0.796 0.000 0.000 1.000
#> GSM1299574 2 0.2625 0.910 0.000 0.916 0.084
#> GSM1299578 1 0.2959 0.829 0.900 0.000 0.100
#> GSM1299579 2 0.1860 0.906 0.052 0.948 0.000
#> GSM1299580 1 0.3412 0.934 0.876 0.000 0.124
#> GSM1299581 1 0.3267 0.932 0.884 0.000 0.116
#> GSM1299582 1 0.3412 0.934 0.876 0.000 0.124
#> GSM1299583 1 0.3412 0.917 0.876 0.000 0.124
#> GSM1299584 1 0.3412 0.934 0.876 0.000 0.124
#> GSM1299585 1 0.5497 0.479 0.708 0.000 0.292
#> GSM1299586 1 0.3412 0.934 0.876 0.000 0.124
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1299517 3 0.0469 0.943 0.000 0.000 0.988 0.012
#> GSM1299518 3 0.0469 0.947 0.000 0.000 0.988 0.012
#> GSM1299519 2 0.1929 0.867 0.000 0.940 0.036 0.024
#> GSM1299520 4 0.2859 0.652 0.000 0.112 0.008 0.880
#> GSM1299521 4 0.4456 0.614 0.280 0.000 0.004 0.716
#> GSM1299522 2 0.1929 0.867 0.000 0.940 0.036 0.024
#> GSM1299523 4 0.3375 0.737 0.116 0.008 0.012 0.864
#> GSM1299524 3 0.3239 0.893 0.000 0.052 0.880 0.068
#> GSM1299525 2 0.1174 0.869 0.000 0.968 0.012 0.020
#> GSM1299526 3 0.0188 0.947 0.000 0.000 0.996 0.004
#> GSM1299527 3 0.0336 0.947 0.000 0.000 0.992 0.008
#> GSM1299528 2 0.2814 0.849 0.000 0.868 0.000 0.132
#> GSM1299529 2 0.1610 0.868 0.000 0.952 0.016 0.032
#> GSM1299530 4 0.4606 0.731 0.264 0.000 0.012 0.724
#> GSM1299531 2 0.1929 0.867 0.000 0.940 0.036 0.024
#> GSM1299575 1 0.0188 0.905 0.996 0.000 0.004 0.000
#> GSM1299532 3 0.2300 0.922 0.000 0.016 0.920 0.064
#> GSM1299533 3 0.2489 0.917 0.000 0.020 0.912 0.068
#> GSM1299534 2 0.1398 0.868 0.000 0.956 0.004 0.040
#> GSM1299535 3 0.3239 0.893 0.000 0.052 0.880 0.068
#> GSM1299536 2 0.4454 0.693 0.000 0.692 0.000 0.308
#> GSM1299537 3 0.0921 0.937 0.000 0.000 0.972 0.028
#> GSM1299538 2 0.3764 0.775 0.000 0.784 0.000 0.216
#> GSM1299539 2 0.2814 0.849 0.000 0.868 0.000 0.132
#> GSM1299540 3 0.1256 0.934 0.008 0.000 0.964 0.028
#> GSM1299541 3 0.0921 0.937 0.000 0.000 0.972 0.028
#> GSM1299542 3 0.0336 0.947 0.000 0.000 0.992 0.008
#> GSM1299543 2 0.2216 0.862 0.000 0.908 0.000 0.092
#> GSM1299544 2 0.2216 0.862 0.000 0.908 0.000 0.092
#> GSM1299545 4 0.5772 0.723 0.260 0.000 0.068 0.672
#> GSM1299546 2 0.1929 0.867 0.000 0.940 0.036 0.024
#> GSM1299547 4 0.2040 0.692 0.004 0.048 0.012 0.936
#> GSM1299548 3 0.0592 0.947 0.000 0.000 0.984 0.016
#> GSM1299549 4 0.6248 0.697 0.260 0.000 0.100 0.640
#> GSM1299550 2 0.2589 0.855 0.000 0.884 0.000 0.116
#> GSM1299551 2 0.1929 0.867 0.000 0.940 0.036 0.024
#> GSM1299552 4 0.6248 0.697 0.260 0.000 0.100 0.640
#> GSM1299553 4 0.5774 0.738 0.236 0.004 0.068 0.692
#> GSM1299554 2 0.5384 0.668 0.000 0.728 0.196 0.076
#> GSM1299555 3 0.2489 0.917 0.000 0.020 0.912 0.068
#> GSM1299556 3 0.1256 0.934 0.008 0.000 0.964 0.028
#> GSM1299557 3 0.4046 0.790 0.124 0.000 0.828 0.048
#> GSM1299558 2 0.2216 0.862 0.000 0.908 0.000 0.092
#> GSM1299559 3 0.1256 0.934 0.008 0.000 0.964 0.028
#> GSM1299560 3 0.0336 0.947 0.000 0.000 0.992 0.008
#> GSM1299576 1 0.0524 0.904 0.988 0.000 0.004 0.008
#> GSM1299577 4 0.4826 0.734 0.264 0.000 0.020 0.716
#> GSM1299561 3 0.0469 0.947 0.000 0.000 0.988 0.012
#> GSM1299562 2 0.4804 0.736 0.000 0.780 0.148 0.072
#> GSM1299563 4 0.2859 0.652 0.000 0.112 0.008 0.880
#> GSM1299564 4 0.2412 0.672 0.000 0.084 0.008 0.908
#> GSM1299565 2 0.1929 0.867 0.000 0.940 0.036 0.024
#> GSM1299566 2 0.2814 0.849 0.000 0.868 0.000 0.132
#> GSM1299567 3 0.1256 0.934 0.008 0.000 0.964 0.028
#> GSM1299568 2 0.5011 0.715 0.000 0.764 0.160 0.076
#> GSM1299569 2 0.2589 0.855 0.000 0.884 0.000 0.116
#> GSM1299570 4 0.4720 0.733 0.264 0.000 0.016 0.720
#> GSM1299571 3 0.2489 0.917 0.000 0.020 0.912 0.068
#> GSM1299572 3 0.2561 0.917 0.004 0.016 0.912 0.068
#> GSM1299573 3 0.0592 0.946 0.000 0.000 0.984 0.016
#> GSM1299574 2 0.2500 0.855 0.000 0.916 0.044 0.040
#> GSM1299578 1 0.3569 0.704 0.804 0.000 0.000 0.196
#> GSM1299579 2 0.4454 0.693 0.000 0.692 0.000 0.308
#> GSM1299580 1 0.0188 0.905 0.996 0.000 0.004 0.000
#> GSM1299581 1 0.0524 0.904 0.988 0.000 0.004 0.008
#> GSM1299582 1 0.0188 0.905 0.996 0.000 0.004 0.000
#> GSM1299583 1 0.1637 0.863 0.940 0.000 0.000 0.060
#> GSM1299584 1 0.0188 0.905 0.996 0.000 0.004 0.000
#> GSM1299585 1 0.4817 0.190 0.612 0.000 0.000 0.388
#> GSM1299586 1 0.0188 0.905 0.996 0.000 0.004 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1299517 3 0.0290 0.942 0.000 0.008 0.992 0.000 0.000
#> GSM1299518 3 0.0880 0.946 0.000 0.032 0.968 0.000 0.000
#> GSM1299519 2 0.0290 0.782 0.000 0.992 0.008 0.000 0.000
#> GSM1299520 4 0.4210 0.563 0.000 0.036 0.000 0.740 0.224
#> GSM1299521 4 0.3911 0.701 0.060 0.000 0.000 0.796 0.144
#> GSM1299522 2 0.0290 0.782 0.000 0.992 0.008 0.000 0.000
#> GSM1299523 4 0.1270 0.739 0.000 0.000 0.000 0.948 0.052
#> GSM1299524 3 0.3184 0.893 0.000 0.100 0.852 0.048 0.000
#> GSM1299525 2 0.0794 0.769 0.000 0.972 0.000 0.000 0.028
#> GSM1299526 3 0.0880 0.947 0.000 0.032 0.968 0.000 0.000
#> GSM1299527 3 0.0794 0.946 0.000 0.028 0.972 0.000 0.000
#> GSM1299528 5 0.2561 0.878 0.000 0.144 0.000 0.000 0.856
#> GSM1299529 2 0.0798 0.776 0.000 0.976 0.000 0.008 0.016
#> GSM1299530 4 0.2127 0.775 0.108 0.000 0.000 0.892 0.000
#> GSM1299531 2 0.0290 0.782 0.000 0.992 0.008 0.000 0.000
#> GSM1299575 1 0.0000 0.933 1.000 0.000 0.000 0.000 0.000
#> GSM1299532 3 0.2580 0.922 0.000 0.064 0.892 0.044 0.000
#> GSM1299533 3 0.2719 0.918 0.000 0.068 0.884 0.048 0.000
#> GSM1299534 2 0.2017 0.737 0.000 0.912 0.000 0.008 0.080
#> GSM1299535 3 0.3184 0.893 0.000 0.100 0.852 0.048 0.000
#> GSM1299536 5 0.4827 0.819 0.000 0.116 0.000 0.160 0.724
#> GSM1299537 3 0.0290 0.937 0.000 0.000 0.992 0.000 0.008
#> GSM1299538 2 0.6085 -0.215 0.000 0.472 0.000 0.124 0.404
#> GSM1299539 5 0.2561 0.878 0.000 0.144 0.000 0.000 0.856
#> GSM1299540 3 0.0579 0.934 0.008 0.000 0.984 0.000 0.008
#> GSM1299541 3 0.0290 0.937 0.000 0.000 0.992 0.000 0.008
#> GSM1299542 3 0.0794 0.946 0.000 0.028 0.972 0.000 0.000
#> GSM1299543 2 0.3857 0.541 0.000 0.688 0.000 0.000 0.312
#> GSM1299544 2 0.3857 0.541 0.000 0.688 0.000 0.000 0.312
#> GSM1299545 4 0.3427 0.766 0.108 0.000 0.056 0.836 0.000
#> GSM1299546 2 0.0290 0.782 0.000 0.992 0.008 0.000 0.000
#> GSM1299547 4 0.3318 0.646 0.000 0.012 0.000 0.808 0.180
#> GSM1299548 3 0.0609 0.945 0.000 0.020 0.980 0.000 0.000
#> GSM1299549 4 0.3912 0.746 0.108 0.000 0.088 0.804 0.000
#> GSM1299550 2 0.4192 0.360 0.000 0.596 0.000 0.000 0.404
#> GSM1299551 2 0.0290 0.782 0.000 0.992 0.008 0.000 0.000
#> GSM1299552 4 0.3912 0.746 0.108 0.000 0.088 0.804 0.000
#> GSM1299553 4 0.3260 0.776 0.084 0.000 0.056 0.856 0.004
#> GSM1299554 2 0.4021 0.597 0.000 0.780 0.168 0.052 0.000
#> GSM1299555 3 0.2719 0.918 0.000 0.068 0.884 0.048 0.000
#> GSM1299556 3 0.0579 0.934 0.008 0.000 0.984 0.000 0.008
#> GSM1299557 3 0.4420 0.803 0.080 0.040 0.800 0.080 0.000
#> GSM1299558 2 0.3857 0.541 0.000 0.688 0.000 0.000 0.312
#> GSM1299559 3 0.0579 0.934 0.008 0.000 0.984 0.000 0.008
#> GSM1299560 3 0.0794 0.946 0.000 0.028 0.972 0.000 0.000
#> GSM1299576 1 0.0290 0.930 0.992 0.000 0.000 0.008 0.000
#> GSM1299577 4 0.2411 0.777 0.108 0.000 0.008 0.884 0.000
#> GSM1299561 3 0.0880 0.946 0.000 0.032 0.968 0.000 0.000
#> GSM1299562 2 0.3437 0.661 0.000 0.832 0.120 0.048 0.000
#> GSM1299563 4 0.4210 0.563 0.000 0.036 0.000 0.740 0.224
#> GSM1299564 4 0.3727 0.604 0.000 0.016 0.000 0.768 0.216
#> GSM1299565 2 0.0290 0.782 0.000 0.992 0.008 0.000 0.000
#> GSM1299566 5 0.2561 0.878 0.000 0.144 0.000 0.000 0.856
#> GSM1299567 3 0.0579 0.934 0.008 0.000 0.984 0.000 0.008
#> GSM1299568 2 0.3849 0.639 0.000 0.808 0.136 0.052 0.004
#> GSM1299569 2 0.4045 0.464 0.000 0.644 0.000 0.000 0.356
#> GSM1299570 4 0.2286 0.776 0.108 0.000 0.004 0.888 0.000
#> GSM1299571 3 0.2719 0.918 0.000 0.068 0.884 0.048 0.000
#> GSM1299572 3 0.2726 0.918 0.000 0.064 0.884 0.052 0.000
#> GSM1299573 3 0.1124 0.945 0.000 0.036 0.960 0.004 0.000
#> GSM1299574 2 0.1018 0.769 0.000 0.968 0.016 0.016 0.000
#> GSM1299578 1 0.5493 0.522 0.632 0.000 0.000 0.256 0.112
#> GSM1299579 5 0.4827 0.819 0.000 0.116 0.000 0.160 0.724
#> GSM1299580 1 0.0000 0.933 1.000 0.000 0.000 0.000 0.000
#> GSM1299581 1 0.0290 0.930 0.992 0.000 0.000 0.008 0.000
#> GSM1299582 1 0.0000 0.933 1.000 0.000 0.000 0.000 0.000
#> GSM1299583 1 0.3427 0.824 0.836 0.000 0.000 0.056 0.108
#> GSM1299584 1 0.0000 0.933 1.000 0.000 0.000 0.000 0.000
#> GSM1299585 4 0.5965 0.143 0.392 0.000 0.000 0.496 0.112
#> GSM1299586 1 0.0000 0.933 1.000 0.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1299517 3 0.1285 0.8712 0.000 0.004 0.944 0.000 0.000 0.052
#> GSM1299518 3 0.0458 0.8833 0.000 0.016 0.984 0.000 0.000 0.000
#> GSM1299519 2 0.0260 0.8113 0.000 0.992 0.008 0.000 0.000 0.000
#> GSM1299520 6 0.5961 0.9631 0.000 0.008 0.000 0.392 0.168 0.432
#> GSM1299521 4 0.4100 0.2702 0.000 0.004 0.000 0.600 0.008 0.388
#> GSM1299522 2 0.0260 0.8113 0.000 0.992 0.008 0.000 0.000 0.000
#> GSM1299523 4 0.4010 -0.4643 0.000 0.000 0.000 0.584 0.008 0.408
#> GSM1299524 3 0.3168 0.8376 0.000 0.076 0.852 0.048 0.000 0.024
#> GSM1299525 2 0.0790 0.7983 0.000 0.968 0.000 0.000 0.032 0.000
#> GSM1299526 3 0.0820 0.8835 0.000 0.016 0.972 0.000 0.000 0.012
#> GSM1299527 3 0.0508 0.8830 0.000 0.012 0.984 0.000 0.000 0.004
#> GSM1299528 5 0.0363 0.6446 0.000 0.012 0.000 0.000 0.988 0.000
#> GSM1299529 2 0.0951 0.8055 0.000 0.968 0.004 0.008 0.020 0.000
#> GSM1299530 4 0.0260 0.6004 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM1299531 2 0.0260 0.8113 0.000 0.992 0.008 0.000 0.000 0.000
#> GSM1299575 1 0.0000 0.9316 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299532 3 0.2554 0.8605 0.000 0.040 0.892 0.044 0.000 0.024
#> GSM1299533 3 0.2688 0.8569 0.000 0.044 0.884 0.048 0.000 0.024
#> GSM1299534 2 0.2001 0.7542 0.000 0.900 0.000 0.004 0.092 0.004
#> GSM1299535 3 0.3168 0.8376 0.000 0.076 0.852 0.048 0.000 0.024
#> GSM1299536 5 0.3384 0.4689 0.000 0.008 0.000 0.004 0.760 0.228
#> GSM1299537 3 0.2762 0.8042 0.000 0.000 0.804 0.000 0.000 0.196
#> GSM1299538 5 0.6060 0.2824 0.000 0.380 0.000 0.024 0.460 0.136
#> GSM1299539 5 0.0363 0.6446 0.000 0.012 0.000 0.000 0.988 0.000
#> GSM1299540 3 0.3314 0.7650 0.004 0.000 0.740 0.000 0.000 0.256
#> GSM1299541 3 0.2762 0.8042 0.000 0.000 0.804 0.000 0.000 0.196
#> GSM1299542 3 0.0725 0.8827 0.000 0.012 0.976 0.000 0.000 0.012
#> GSM1299543 2 0.3659 0.4559 0.000 0.636 0.000 0.000 0.364 0.000
#> GSM1299544 2 0.3659 0.4559 0.000 0.636 0.000 0.000 0.364 0.000
#> GSM1299545 4 0.1204 0.6143 0.000 0.000 0.056 0.944 0.000 0.000
#> GSM1299546 2 0.0260 0.8113 0.000 0.992 0.008 0.000 0.000 0.000
#> GSM1299547 4 0.5495 -0.7511 0.000 0.008 0.000 0.512 0.104 0.376
#> GSM1299548 3 0.1074 0.8804 0.000 0.012 0.960 0.000 0.000 0.028
#> GSM1299549 4 0.1812 0.6002 0.000 0.000 0.080 0.912 0.000 0.008
#> GSM1299550 5 0.3868 -0.2320 0.000 0.492 0.000 0.000 0.508 0.000
#> GSM1299551 2 0.0260 0.8113 0.000 0.992 0.008 0.000 0.000 0.000
#> GSM1299552 4 0.1812 0.6002 0.000 0.000 0.080 0.912 0.000 0.008
#> GSM1299553 4 0.2052 0.6010 0.000 0.000 0.056 0.912 0.004 0.028
#> GSM1299554 2 0.4210 0.6118 0.000 0.756 0.168 0.052 0.000 0.024
#> GSM1299555 3 0.2688 0.8569 0.000 0.044 0.884 0.048 0.000 0.024
#> GSM1299556 3 0.3314 0.7650 0.004 0.000 0.740 0.000 0.000 0.256
#> GSM1299557 3 0.3502 0.7635 0.000 0.024 0.800 0.160 0.000 0.016
#> GSM1299558 2 0.3659 0.4559 0.000 0.636 0.000 0.000 0.364 0.000
#> GSM1299559 3 0.3314 0.7650 0.004 0.000 0.740 0.000 0.000 0.256
#> GSM1299560 3 0.0622 0.8829 0.000 0.012 0.980 0.000 0.000 0.008
#> GSM1299576 1 0.0405 0.9287 0.988 0.000 0.000 0.004 0.000 0.008
#> GSM1299577 4 0.0520 0.6078 0.000 0.000 0.008 0.984 0.000 0.008
#> GSM1299561 3 0.0458 0.8833 0.000 0.016 0.984 0.000 0.000 0.000
#> GSM1299562 2 0.3527 0.6872 0.000 0.820 0.112 0.048 0.000 0.020
#> GSM1299563 6 0.5961 0.9631 0.000 0.008 0.000 0.392 0.168 0.432
#> GSM1299564 6 0.5809 0.9230 0.000 0.008 0.000 0.424 0.140 0.428
#> GSM1299565 2 0.0260 0.8113 0.000 0.992 0.008 0.000 0.000 0.000
#> GSM1299566 5 0.0363 0.6446 0.000 0.012 0.000 0.000 0.988 0.000
#> GSM1299567 3 0.3314 0.7650 0.004 0.000 0.740 0.000 0.000 0.256
#> GSM1299568 2 0.3935 0.6557 0.000 0.788 0.140 0.052 0.004 0.016
#> GSM1299569 2 0.3747 0.3832 0.000 0.604 0.000 0.000 0.396 0.000
#> GSM1299570 4 0.0405 0.6056 0.000 0.000 0.004 0.988 0.000 0.008
#> GSM1299571 3 0.2688 0.8569 0.000 0.044 0.884 0.048 0.000 0.024
#> GSM1299572 3 0.2685 0.8569 0.000 0.040 0.884 0.052 0.000 0.024
#> GSM1299573 3 0.0837 0.8832 0.000 0.020 0.972 0.004 0.000 0.004
#> GSM1299574 2 0.0914 0.8001 0.000 0.968 0.016 0.016 0.000 0.000
#> GSM1299578 1 0.5274 0.5910 0.596 0.004 0.000 0.088 0.008 0.304
#> GSM1299579 5 0.3384 0.4689 0.000 0.008 0.000 0.004 0.760 0.228
#> GSM1299580 1 0.0000 0.9316 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299581 1 0.0405 0.9287 0.988 0.000 0.000 0.004 0.000 0.008
#> GSM1299582 1 0.0000 0.9316 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299583 1 0.3601 0.8043 0.800 0.004 0.000 0.036 0.008 0.152
#> GSM1299584 1 0.0000 0.9316 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299585 4 0.6436 -0.0778 0.332 0.004 0.000 0.368 0.008 0.288
#> GSM1299586 1 0.0000 0.9316 1.000 0.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:hclust 66 0.9184 2
#> ATC:hclust 65 0.0171 3
#> ATC:hclust 69 0.0887 4
#> ATC:hclust 66 0.1642 5
#> ATC:hclust 58 0.0867 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "kmeans"]
# you can also extract it by
# res = res_list["ATC:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.503 0.884 0.919 0.4900 0.503 0.503
#> 3 3 0.929 0.885 0.933 0.3382 0.771 0.574
#> 4 4 0.841 0.735 0.887 0.1275 0.859 0.621
#> 5 5 0.798 0.718 0.834 0.0755 0.892 0.626
#> 6 6 0.847 0.767 0.847 0.0434 0.915 0.619
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
#> GSM1299517 1 0.2603 0.923 0.956 0.044
#> GSM1299518 1 0.2603 0.923 0.956 0.044
#> GSM1299519 2 0.5294 0.905 0.120 0.880
#> GSM1299520 2 0.0376 0.886 0.004 0.996
#> GSM1299521 2 0.9686 0.254 0.396 0.604
#> GSM1299522 2 0.5294 0.905 0.120 0.880
#> GSM1299523 2 0.9850 0.126 0.428 0.572
#> GSM1299524 1 0.2603 0.923 0.956 0.044
#> GSM1299525 2 0.5178 0.907 0.116 0.884
#> GSM1299526 1 0.2603 0.923 0.956 0.044
#> GSM1299527 1 0.2603 0.923 0.956 0.044
#> GSM1299528 2 0.0000 0.887 0.000 1.000
#> GSM1299529 2 0.5178 0.907 0.116 0.884
#> GSM1299530 1 0.5294 0.891 0.880 0.120
#> GSM1299531 2 0.5294 0.905 0.120 0.880
#> GSM1299575 1 0.5294 0.891 0.880 0.120
#> GSM1299532 1 0.2603 0.923 0.956 0.044
#> GSM1299533 1 0.2603 0.923 0.956 0.044
#> GSM1299534 2 0.5178 0.907 0.116 0.884
#> GSM1299535 1 0.2603 0.923 0.956 0.044
#> GSM1299536 2 0.0376 0.886 0.004 0.996
#> GSM1299537 1 0.2603 0.923 0.956 0.044
#> GSM1299538 2 0.0376 0.886 0.004 0.996
#> GSM1299539 2 0.0376 0.886 0.004 0.996
#> GSM1299540 1 0.0376 0.918 0.996 0.004
#> GSM1299541 1 0.2423 0.923 0.960 0.040
#> GSM1299542 1 0.2603 0.923 0.956 0.044
#> GSM1299543 2 0.5178 0.907 0.116 0.884
#> GSM1299544 2 0.4298 0.905 0.088 0.912
#> GSM1299545 1 0.0376 0.918 0.996 0.004
#> GSM1299546 2 0.5294 0.905 0.120 0.880
#> GSM1299547 2 0.0376 0.886 0.004 0.996
#> GSM1299548 1 0.2603 0.923 0.956 0.044
#> GSM1299549 1 0.4690 0.913 0.900 0.100
#> GSM1299550 2 0.0000 0.887 0.000 1.000
#> GSM1299551 2 0.5294 0.905 0.120 0.880
#> GSM1299552 1 0.5294 0.891 0.880 0.120
#> GSM1299553 1 0.6343 0.890 0.840 0.160
#> GSM1299554 2 0.6973 0.848 0.188 0.812
#> GSM1299555 1 0.2603 0.923 0.956 0.044
#> GSM1299556 1 0.0376 0.918 0.996 0.004
#> GSM1299557 1 0.2603 0.923 0.956 0.044
#> GSM1299558 2 0.5178 0.907 0.116 0.884
#> GSM1299559 1 0.0376 0.918 0.996 0.004
#> GSM1299560 1 0.2603 0.923 0.956 0.044
#> GSM1299576 1 0.5294 0.891 0.880 0.120
#> GSM1299577 1 0.5294 0.891 0.880 0.120
#> GSM1299561 1 0.2603 0.923 0.956 0.044
#> GSM1299562 2 0.5294 0.905 0.120 0.880
#> GSM1299563 2 0.0376 0.886 0.004 0.996
#> GSM1299564 2 0.0376 0.886 0.004 0.996
#> GSM1299565 2 0.5294 0.905 0.120 0.880
#> GSM1299566 2 0.0000 0.887 0.000 1.000
#> GSM1299567 1 0.0000 0.918 1.000 0.000
#> GSM1299568 2 0.5294 0.905 0.120 0.880
#> GSM1299569 2 0.4298 0.905 0.088 0.912
#> GSM1299570 1 0.5294 0.891 0.880 0.120
#> GSM1299571 1 0.2603 0.923 0.956 0.044
#> GSM1299572 1 0.2603 0.923 0.956 0.044
#> GSM1299573 1 0.2603 0.923 0.956 0.044
#> GSM1299574 2 0.5294 0.905 0.120 0.880
#> GSM1299578 1 0.5294 0.891 0.880 0.120
#> GSM1299579 2 0.0376 0.886 0.004 0.996
#> GSM1299580 1 0.5294 0.891 0.880 0.120
#> GSM1299581 1 0.5294 0.891 0.880 0.120
#> GSM1299582 1 0.5294 0.891 0.880 0.120
#> GSM1299583 1 0.5294 0.891 0.880 0.120
#> GSM1299584 1 0.5294 0.891 0.880 0.120
#> GSM1299585 1 0.5294 0.891 0.880 0.120
#> GSM1299586 1 0.5294 0.891 0.880 0.120
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1299517 3 0.0000 0.931 0.000 0.000 1.000
#> GSM1299518 3 0.0237 0.928 0.000 0.004 0.996
#> GSM1299519 2 0.0892 0.926 0.000 0.980 0.020
#> GSM1299520 2 0.2711 0.937 0.088 0.912 0.000
#> GSM1299521 1 0.0000 0.883 1.000 0.000 0.000
#> GSM1299522 2 0.0000 0.940 0.000 1.000 0.000
#> GSM1299523 1 0.5115 0.600 0.768 0.228 0.004
#> GSM1299524 3 0.0747 0.920 0.000 0.016 0.984
#> GSM1299525 2 0.0000 0.940 0.000 1.000 0.000
#> GSM1299526 3 0.0000 0.931 0.000 0.000 1.000
#> GSM1299527 3 0.0000 0.931 0.000 0.000 1.000
#> GSM1299528 2 0.2537 0.939 0.080 0.920 0.000
#> GSM1299529 2 0.0000 0.940 0.000 1.000 0.000
#> GSM1299530 1 0.0237 0.887 0.996 0.000 0.004
#> GSM1299531 2 0.0000 0.940 0.000 1.000 0.000
#> GSM1299575 1 0.2711 0.938 0.912 0.000 0.088
#> GSM1299532 3 0.2356 0.876 0.000 0.072 0.928
#> GSM1299533 3 0.0000 0.931 0.000 0.000 1.000
#> GSM1299534 2 0.0892 0.942 0.020 0.980 0.000
#> GSM1299535 3 0.2356 0.876 0.000 0.072 0.928
#> GSM1299536 2 0.2711 0.937 0.088 0.912 0.000
#> GSM1299537 3 0.0000 0.931 0.000 0.000 1.000
#> GSM1299538 2 0.2711 0.937 0.088 0.912 0.000
#> GSM1299539 2 0.2711 0.937 0.088 0.912 0.000
#> GSM1299540 3 0.0000 0.931 0.000 0.000 1.000
#> GSM1299541 3 0.0000 0.931 0.000 0.000 1.000
#> GSM1299542 3 0.0000 0.931 0.000 0.000 1.000
#> GSM1299543 2 0.0000 0.940 0.000 1.000 0.000
#> GSM1299544 2 0.1753 0.942 0.048 0.952 0.000
#> GSM1299545 3 0.0000 0.931 0.000 0.000 1.000
#> GSM1299546 2 0.0000 0.940 0.000 1.000 0.000
#> GSM1299547 2 0.2711 0.937 0.088 0.912 0.000
#> GSM1299548 3 0.0000 0.931 0.000 0.000 1.000
#> GSM1299549 3 0.4178 0.737 0.172 0.000 0.828
#> GSM1299550 2 0.2711 0.937 0.088 0.912 0.000
#> GSM1299551 2 0.0000 0.940 0.000 1.000 0.000
#> GSM1299552 1 0.3941 0.877 0.844 0.000 0.156
#> GSM1299553 3 0.9091 0.170 0.344 0.152 0.504
#> GSM1299554 3 0.5968 0.489 0.000 0.364 0.636
#> GSM1299555 3 0.0000 0.931 0.000 0.000 1.000
#> GSM1299556 3 0.0000 0.931 0.000 0.000 1.000
#> GSM1299557 3 0.0000 0.931 0.000 0.000 1.000
#> GSM1299558 2 0.0000 0.940 0.000 1.000 0.000
#> GSM1299559 3 0.0000 0.931 0.000 0.000 1.000
#> GSM1299560 3 0.0000 0.931 0.000 0.000 1.000
#> GSM1299576 1 0.2711 0.938 0.912 0.000 0.088
#> GSM1299577 1 0.2711 0.938 0.912 0.000 0.088
#> GSM1299561 3 0.0000 0.931 0.000 0.000 1.000
#> GSM1299562 3 0.6026 0.466 0.000 0.376 0.624
#> GSM1299563 2 0.2711 0.937 0.088 0.912 0.000
#> GSM1299564 2 0.2711 0.937 0.088 0.912 0.000
#> GSM1299565 2 0.0000 0.940 0.000 1.000 0.000
#> GSM1299566 2 0.2537 0.939 0.080 0.920 0.000
#> GSM1299567 3 0.0000 0.931 0.000 0.000 1.000
#> GSM1299568 2 0.0000 0.940 0.000 1.000 0.000
#> GSM1299569 2 0.1860 0.942 0.052 0.948 0.000
#> GSM1299570 1 0.5431 0.695 0.716 0.000 0.284
#> GSM1299571 3 0.2448 0.873 0.000 0.076 0.924
#> GSM1299572 3 0.0000 0.931 0.000 0.000 1.000
#> GSM1299573 3 0.0000 0.931 0.000 0.000 1.000
#> GSM1299574 2 0.6111 0.238 0.000 0.604 0.396
#> GSM1299578 1 0.0747 0.895 0.984 0.000 0.016
#> GSM1299579 2 0.2711 0.937 0.088 0.912 0.000
#> GSM1299580 1 0.2711 0.938 0.912 0.000 0.088
#> GSM1299581 1 0.2711 0.938 0.912 0.000 0.088
#> GSM1299582 1 0.2711 0.938 0.912 0.000 0.088
#> GSM1299583 1 0.2711 0.938 0.912 0.000 0.088
#> GSM1299584 1 0.2711 0.938 0.912 0.000 0.088
#> GSM1299585 1 0.2711 0.938 0.912 0.000 0.088
#> GSM1299586 1 0.2711 0.938 0.912 0.000 0.088
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1299517 3 0.0000 0.9302 0.000 0.000 1.000 0.000
#> GSM1299518 3 0.1474 0.9230 0.000 0.000 0.948 0.052
#> GSM1299519 2 0.1305 0.8247 0.000 0.960 0.004 0.036
#> GSM1299520 4 0.1557 0.7089 0.000 0.056 0.000 0.944
#> GSM1299521 4 0.5163 -0.1066 0.480 0.004 0.000 0.516
#> GSM1299522 2 0.0000 0.8508 0.000 1.000 0.000 0.000
#> GSM1299523 4 0.1059 0.6899 0.016 0.012 0.000 0.972
#> GSM1299524 3 0.2174 0.9157 0.000 0.020 0.928 0.052
#> GSM1299525 2 0.1022 0.8362 0.000 0.968 0.000 0.032
#> GSM1299526 3 0.0000 0.9302 0.000 0.000 1.000 0.000
#> GSM1299527 3 0.0000 0.9302 0.000 0.000 1.000 0.000
#> GSM1299528 4 0.4866 0.1796 0.000 0.404 0.000 0.596
#> GSM1299529 2 0.0000 0.8508 0.000 1.000 0.000 0.000
#> GSM1299530 4 0.5163 -0.1119 0.480 0.004 0.000 0.516
#> GSM1299531 2 0.0000 0.8508 0.000 1.000 0.000 0.000
#> GSM1299575 1 0.0000 0.9365 1.000 0.000 0.000 0.000
#> GSM1299532 3 0.2483 0.9093 0.000 0.032 0.916 0.052
#> GSM1299533 3 0.1807 0.9208 0.000 0.008 0.940 0.052
#> GSM1299534 2 0.4916 0.2427 0.000 0.576 0.000 0.424
#> GSM1299535 3 0.2483 0.9093 0.000 0.032 0.916 0.052
#> GSM1299536 4 0.1940 0.7066 0.000 0.076 0.000 0.924
#> GSM1299537 3 0.0000 0.9302 0.000 0.000 1.000 0.000
#> GSM1299538 4 0.2589 0.6828 0.000 0.116 0.000 0.884
#> GSM1299539 4 0.3610 0.6022 0.000 0.200 0.000 0.800
#> GSM1299540 3 0.0000 0.9302 0.000 0.000 1.000 0.000
#> GSM1299541 3 0.0000 0.9302 0.000 0.000 1.000 0.000
#> GSM1299542 3 0.0000 0.9302 0.000 0.000 1.000 0.000
#> GSM1299543 2 0.1302 0.8306 0.000 0.956 0.000 0.044
#> GSM1299544 2 0.4994 0.1124 0.000 0.520 0.000 0.480
#> GSM1299545 3 0.1557 0.9219 0.000 0.000 0.944 0.056
#> GSM1299546 2 0.0000 0.8508 0.000 1.000 0.000 0.000
#> GSM1299547 4 0.0707 0.6944 0.000 0.020 0.000 0.980
#> GSM1299548 3 0.0000 0.9302 0.000 0.000 1.000 0.000
#> GSM1299549 3 0.7847 0.2687 0.120 0.036 0.500 0.344
#> GSM1299550 4 0.3610 0.6022 0.000 0.200 0.000 0.800
#> GSM1299551 2 0.0000 0.8508 0.000 1.000 0.000 0.000
#> GSM1299552 1 0.5670 0.3088 0.572 0.004 0.020 0.404
#> GSM1299553 4 0.7290 0.3840 0.120 0.044 0.208 0.628
#> GSM1299554 3 0.7812 0.0682 0.000 0.256 0.396 0.348
#> GSM1299555 3 0.1474 0.9230 0.000 0.000 0.948 0.052
#> GSM1299556 3 0.0000 0.9302 0.000 0.000 1.000 0.000
#> GSM1299557 3 0.1389 0.9242 0.000 0.000 0.952 0.048
#> GSM1299558 2 0.1211 0.8336 0.000 0.960 0.000 0.040
#> GSM1299559 3 0.0000 0.9302 0.000 0.000 1.000 0.000
#> GSM1299560 3 0.0000 0.9302 0.000 0.000 1.000 0.000
#> GSM1299576 1 0.0188 0.9368 0.996 0.000 0.000 0.004
#> GSM1299577 1 0.3853 0.7617 0.820 0.000 0.020 0.160
#> GSM1299561 3 0.0000 0.9302 0.000 0.000 1.000 0.000
#> GSM1299562 2 0.3474 0.7292 0.000 0.868 0.064 0.068
#> GSM1299563 4 0.1716 0.7090 0.000 0.064 0.000 0.936
#> GSM1299564 4 0.1792 0.7077 0.000 0.068 0.000 0.932
#> GSM1299565 2 0.0000 0.8508 0.000 1.000 0.000 0.000
#> GSM1299566 4 0.4866 0.1796 0.000 0.404 0.000 0.596
#> GSM1299567 3 0.0188 0.9282 0.004 0.000 0.996 0.000
#> GSM1299568 2 0.0707 0.8399 0.000 0.980 0.000 0.020
#> GSM1299569 2 0.4998 0.0869 0.000 0.512 0.000 0.488
#> GSM1299570 4 0.7914 -0.0676 0.360 0.004 0.236 0.400
#> GSM1299571 3 0.2483 0.9093 0.000 0.032 0.916 0.052
#> GSM1299572 3 0.2722 0.9017 0.000 0.032 0.904 0.064
#> GSM1299573 3 0.1118 0.9265 0.000 0.000 0.964 0.036
#> GSM1299574 2 0.1661 0.8083 0.000 0.944 0.004 0.052
#> GSM1299578 1 0.0188 0.9368 0.996 0.000 0.000 0.004
#> GSM1299579 4 0.1940 0.7066 0.000 0.076 0.000 0.924
#> GSM1299580 1 0.0000 0.9365 1.000 0.000 0.000 0.000
#> GSM1299581 1 0.0188 0.9368 0.996 0.000 0.000 0.004
#> GSM1299582 1 0.0000 0.9365 1.000 0.000 0.000 0.000
#> GSM1299583 1 0.0188 0.9368 0.996 0.000 0.000 0.004
#> GSM1299584 1 0.0000 0.9365 1.000 0.000 0.000 0.000
#> GSM1299585 1 0.0188 0.9368 0.996 0.000 0.000 0.004
#> GSM1299586 1 0.0000 0.9365 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1299517 3 0.0000 0.7842 0.000 0.000 1.000 0.000 0.000
#> GSM1299518 3 0.4210 0.6024 0.000 0.000 0.588 0.412 0.000
#> GSM1299519 2 0.2230 0.8061 0.000 0.884 0.000 0.116 0.000
#> GSM1299520 5 0.3074 0.5454 0.000 0.000 0.000 0.196 0.804
#> GSM1299521 4 0.5263 0.4411 0.056 0.000 0.000 0.576 0.368
#> GSM1299522 2 0.0000 0.8756 0.000 1.000 0.000 0.000 0.000
#> GSM1299523 4 0.4227 0.3832 0.000 0.000 0.000 0.580 0.420
#> GSM1299524 3 0.4752 0.5856 0.000 0.020 0.568 0.412 0.000
#> GSM1299525 2 0.1430 0.8461 0.000 0.944 0.000 0.004 0.052
#> GSM1299526 3 0.0000 0.7842 0.000 0.000 1.000 0.000 0.000
#> GSM1299527 3 0.0000 0.7842 0.000 0.000 1.000 0.000 0.000
#> GSM1299528 5 0.2648 0.7992 0.000 0.152 0.000 0.000 0.848
#> GSM1299529 2 0.0162 0.8746 0.000 0.996 0.000 0.004 0.000
#> GSM1299530 4 0.5174 0.4827 0.056 0.000 0.000 0.604 0.340
#> GSM1299531 2 0.0000 0.8756 0.000 1.000 0.000 0.000 0.000
#> GSM1299575 1 0.0000 0.9941 1.000 0.000 0.000 0.000 0.000
#> GSM1299532 3 0.5118 0.5656 0.000 0.040 0.548 0.412 0.000
#> GSM1299533 3 0.4210 0.6024 0.000 0.000 0.588 0.412 0.000
#> GSM1299534 2 0.4009 0.4003 0.000 0.684 0.000 0.004 0.312
#> GSM1299535 3 0.5302 0.5519 0.000 0.052 0.536 0.412 0.000
#> GSM1299536 5 0.1628 0.7816 0.000 0.056 0.000 0.008 0.936
#> GSM1299537 3 0.0000 0.7842 0.000 0.000 1.000 0.000 0.000
#> GSM1299538 5 0.1894 0.7887 0.000 0.072 0.000 0.008 0.920
#> GSM1299539 5 0.2561 0.8011 0.000 0.144 0.000 0.000 0.856
#> GSM1299540 3 0.0000 0.7842 0.000 0.000 1.000 0.000 0.000
#> GSM1299541 3 0.0000 0.7842 0.000 0.000 1.000 0.000 0.000
#> GSM1299542 3 0.0000 0.7842 0.000 0.000 1.000 0.000 0.000
#> GSM1299543 2 0.1430 0.8461 0.000 0.944 0.000 0.004 0.052
#> GSM1299544 5 0.4009 0.5969 0.000 0.312 0.000 0.004 0.684
#> GSM1299545 4 0.3452 0.2831 0.000 0.000 0.244 0.756 0.000
#> GSM1299546 2 0.0000 0.8756 0.000 1.000 0.000 0.000 0.000
#> GSM1299547 4 0.4227 0.3832 0.000 0.000 0.000 0.580 0.420
#> GSM1299548 3 0.0000 0.7842 0.000 0.000 1.000 0.000 0.000
#> GSM1299549 4 0.0324 0.6523 0.004 0.000 0.004 0.992 0.000
#> GSM1299550 5 0.2561 0.8011 0.000 0.144 0.000 0.000 0.856
#> GSM1299551 2 0.0000 0.8756 0.000 1.000 0.000 0.000 0.000
#> GSM1299552 4 0.3339 0.6821 0.040 0.000 0.000 0.836 0.124
#> GSM1299553 4 0.2536 0.6876 0.004 0.000 0.000 0.868 0.128
#> GSM1299554 4 0.1430 0.6279 0.000 0.052 0.004 0.944 0.000
#> GSM1299555 3 0.4210 0.6024 0.000 0.000 0.588 0.412 0.000
#> GSM1299556 3 0.0000 0.7842 0.000 0.000 1.000 0.000 0.000
#> GSM1299557 3 0.4192 0.6068 0.000 0.000 0.596 0.404 0.000
#> GSM1299558 2 0.1430 0.8461 0.000 0.944 0.000 0.004 0.052
#> GSM1299559 3 0.0000 0.7842 0.000 0.000 1.000 0.000 0.000
#> GSM1299560 3 0.0000 0.7842 0.000 0.000 1.000 0.000 0.000
#> GSM1299576 1 0.0451 0.9937 0.988 0.000 0.000 0.004 0.008
#> GSM1299577 4 0.3535 0.6700 0.088 0.000 0.000 0.832 0.080
#> GSM1299561 3 0.0000 0.7842 0.000 0.000 1.000 0.000 0.000
#> GSM1299562 2 0.4367 0.3350 0.000 0.580 0.004 0.416 0.000
#> GSM1299563 5 0.3196 0.5526 0.000 0.004 0.000 0.192 0.804
#> GSM1299564 5 0.4171 0.0509 0.000 0.000 0.000 0.396 0.604
#> GSM1299565 2 0.0000 0.8756 0.000 1.000 0.000 0.000 0.000
#> GSM1299566 5 0.2648 0.7992 0.000 0.152 0.000 0.000 0.848
#> GSM1299567 3 0.0000 0.7842 0.000 0.000 1.000 0.000 0.000
#> GSM1299568 2 0.1792 0.8334 0.000 0.916 0.000 0.084 0.000
#> GSM1299569 5 0.3814 0.6566 0.000 0.276 0.000 0.004 0.720
#> GSM1299570 4 0.2536 0.6876 0.004 0.000 0.000 0.868 0.128
#> GSM1299571 3 0.5359 0.5473 0.000 0.056 0.532 0.412 0.000
#> GSM1299572 4 0.4473 -0.0409 0.000 0.020 0.324 0.656 0.000
#> GSM1299573 3 0.4192 0.6068 0.000 0.000 0.596 0.404 0.000
#> GSM1299574 2 0.2471 0.7878 0.000 0.864 0.000 0.136 0.000
#> GSM1299578 1 0.0566 0.9929 0.984 0.000 0.000 0.004 0.012
#> GSM1299579 5 0.1557 0.7790 0.000 0.052 0.000 0.008 0.940
#> GSM1299580 1 0.0000 0.9941 1.000 0.000 0.000 0.000 0.000
#> GSM1299581 1 0.0451 0.9937 0.988 0.000 0.000 0.004 0.008
#> GSM1299582 1 0.0000 0.9941 1.000 0.000 0.000 0.000 0.000
#> GSM1299583 1 0.0566 0.9929 0.984 0.000 0.000 0.004 0.012
#> GSM1299584 1 0.0000 0.9941 1.000 0.000 0.000 0.000 0.000
#> GSM1299585 1 0.0566 0.9929 0.984 0.000 0.000 0.004 0.012
#> GSM1299586 1 0.0000 0.9941 1.000 0.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1299517 3 0.3756 0.9657 0.000 0.000 0.644 0.004 0.000 0.352
#> GSM1299518 6 0.0000 0.7718 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1299519 2 0.0547 0.9312 0.000 0.980 0.000 0.000 0.000 0.020
#> GSM1299520 5 0.5574 0.2161 0.000 0.000 0.152 0.344 0.504 0.000
#> GSM1299521 4 0.4330 0.6625 0.076 0.000 0.144 0.756 0.024 0.000
#> GSM1299522 2 0.0000 0.9399 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299523 4 0.3176 0.6967 0.000 0.000 0.156 0.812 0.032 0.000
#> GSM1299524 6 0.0260 0.7753 0.000 0.008 0.000 0.000 0.000 0.992
#> GSM1299525 2 0.1261 0.9242 0.000 0.952 0.024 0.000 0.024 0.000
#> GSM1299526 3 0.3756 0.9657 0.000 0.000 0.644 0.004 0.000 0.352
#> GSM1299527 6 0.3857 -0.6998 0.000 0.000 0.468 0.000 0.000 0.532
#> GSM1299528 5 0.1492 0.8475 0.000 0.024 0.036 0.000 0.940 0.000
#> GSM1299529 2 0.0363 0.9387 0.000 0.988 0.012 0.000 0.000 0.000
#> GSM1299530 4 0.2358 0.7183 0.000 0.000 0.108 0.876 0.016 0.000
#> GSM1299531 2 0.0000 0.9399 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299575 1 0.1644 0.9378 0.920 0.000 0.076 0.000 0.004 0.000
#> GSM1299532 6 0.0508 0.7767 0.000 0.012 0.000 0.004 0.000 0.984
#> GSM1299533 6 0.0146 0.7704 0.000 0.000 0.000 0.004 0.000 0.996
#> GSM1299534 2 0.4767 0.4348 0.000 0.620 0.076 0.000 0.304 0.000
#> GSM1299535 6 0.0692 0.7753 0.000 0.020 0.000 0.004 0.000 0.976
#> GSM1299536 5 0.1464 0.8325 0.000 0.004 0.016 0.036 0.944 0.000
#> GSM1299537 3 0.3620 0.9663 0.000 0.000 0.648 0.000 0.000 0.352
#> GSM1299538 5 0.1620 0.8394 0.000 0.012 0.024 0.024 0.940 0.000
#> GSM1299539 5 0.1408 0.8481 0.000 0.020 0.036 0.000 0.944 0.000
#> GSM1299540 3 0.3996 0.9646 0.000 0.000 0.636 0.008 0.004 0.352
#> GSM1299541 3 0.3620 0.9663 0.000 0.000 0.648 0.000 0.000 0.352
#> GSM1299542 3 0.3620 0.9663 0.000 0.000 0.648 0.000 0.000 0.352
#> GSM1299543 2 0.2263 0.8898 0.000 0.896 0.056 0.000 0.048 0.000
#> GSM1299544 5 0.2250 0.8288 0.000 0.040 0.064 0.000 0.896 0.000
#> GSM1299545 4 0.4126 0.0321 0.000 0.000 0.004 0.512 0.004 0.480
#> GSM1299546 2 0.0146 0.9395 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM1299547 4 0.4039 0.6557 0.000 0.000 0.156 0.752 0.092 0.000
#> GSM1299548 3 0.3634 0.9648 0.000 0.000 0.644 0.000 0.000 0.356
#> GSM1299549 4 0.3890 0.2772 0.000 0.000 0.004 0.596 0.000 0.400
#> GSM1299550 5 0.1148 0.8473 0.000 0.020 0.016 0.004 0.960 0.000
#> GSM1299551 2 0.0146 0.9395 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM1299552 4 0.1082 0.7455 0.000 0.000 0.004 0.956 0.000 0.040
#> GSM1299553 4 0.2126 0.7363 0.000 0.000 0.020 0.904 0.004 0.072
#> GSM1299554 6 0.4748 0.3364 0.000 0.040 0.020 0.296 0.000 0.644
#> GSM1299555 6 0.0000 0.7718 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1299556 3 0.3996 0.9646 0.000 0.000 0.636 0.008 0.004 0.352
#> GSM1299557 6 0.1196 0.7612 0.000 0.000 0.008 0.040 0.000 0.952
#> GSM1299558 2 0.2197 0.8926 0.000 0.900 0.056 0.000 0.044 0.000
#> GSM1299559 3 0.3996 0.9646 0.000 0.000 0.636 0.008 0.004 0.352
#> GSM1299560 3 0.3857 0.8016 0.000 0.000 0.532 0.000 0.000 0.468
#> GSM1299576 1 0.0692 0.9319 0.976 0.000 0.000 0.020 0.004 0.000
#> GSM1299577 4 0.1226 0.7442 0.004 0.000 0.000 0.952 0.004 0.040
#> GSM1299561 3 0.3810 0.8739 0.000 0.000 0.572 0.000 0.000 0.428
#> GSM1299562 6 0.4194 0.3449 0.000 0.352 0.012 0.008 0.000 0.628
#> GSM1299563 5 0.5574 0.2161 0.000 0.000 0.152 0.344 0.504 0.000
#> GSM1299564 4 0.5648 0.0608 0.000 0.000 0.156 0.472 0.372 0.000
#> GSM1299565 2 0.0146 0.9398 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM1299566 5 0.1492 0.8475 0.000 0.024 0.036 0.000 0.940 0.000
#> GSM1299567 3 0.3996 0.9646 0.000 0.000 0.636 0.008 0.004 0.352
#> GSM1299568 2 0.1245 0.9296 0.000 0.952 0.032 0.000 0.000 0.016
#> GSM1299569 5 0.2145 0.8360 0.000 0.028 0.072 0.000 0.900 0.000
#> GSM1299570 4 0.0937 0.7456 0.000 0.000 0.000 0.960 0.000 0.040
#> GSM1299571 6 0.1082 0.7642 0.000 0.040 0.000 0.004 0.000 0.956
#> GSM1299572 6 0.3512 0.5151 0.000 0.008 0.004 0.248 0.000 0.740
#> GSM1299573 6 0.0363 0.7598 0.000 0.000 0.012 0.000 0.000 0.988
#> GSM1299574 2 0.0632 0.9287 0.000 0.976 0.000 0.000 0.000 0.024
#> GSM1299578 1 0.2333 0.8981 0.896 0.000 0.040 0.060 0.004 0.000
#> GSM1299579 5 0.1464 0.8325 0.000 0.004 0.016 0.036 0.944 0.000
#> GSM1299580 1 0.1644 0.9378 0.920 0.000 0.076 0.000 0.004 0.000
#> GSM1299581 1 0.0692 0.9319 0.976 0.000 0.000 0.020 0.004 0.000
#> GSM1299582 1 0.1644 0.9378 0.920 0.000 0.076 0.000 0.004 0.000
#> GSM1299583 1 0.1552 0.9207 0.940 0.000 0.036 0.020 0.004 0.000
#> GSM1299584 1 0.1644 0.9378 0.920 0.000 0.076 0.000 0.004 0.000
#> GSM1299585 1 0.2333 0.8981 0.896 0.000 0.040 0.060 0.004 0.000
#> GSM1299586 1 0.1644 0.9378 0.920 0.000 0.076 0.000 0.004 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:kmeans 68 0.7529 2
#> ATC:kmeans 66 0.0803 3
#> ATC:kmeans 58 0.0634 4
#> ATC:kmeans 61 0.0141 5
#> ATC:kmeans 61 0.0580 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "skmeans"]
# you can also extract it by
# res = res_list["ATC:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.984 0.992 0.5040 0.496 0.496
#> 3 3 1.000 0.994 0.997 0.3253 0.786 0.589
#> 4 4 1.000 0.988 0.994 0.1240 0.906 0.721
#> 5 5 0.889 0.869 0.917 0.0621 0.945 0.783
#> 6 6 0.874 0.762 0.885 0.0387 0.949 0.753
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM1299517 1 0.0000 0.992 1.000 0.000
#> GSM1299518 1 0.0000 0.992 1.000 0.000
#> GSM1299519 2 0.0376 0.992 0.004 0.996
#> GSM1299520 2 0.0000 0.992 0.000 1.000
#> GSM1299521 2 0.0000 0.992 0.000 1.000
#> GSM1299522 2 0.0376 0.992 0.004 0.996
#> GSM1299523 2 0.0000 0.992 0.000 1.000
#> GSM1299524 1 0.0000 0.992 1.000 0.000
#> GSM1299525 2 0.0000 0.992 0.000 1.000
#> GSM1299526 1 0.0000 0.992 1.000 0.000
#> GSM1299527 1 0.0000 0.992 1.000 0.000
#> GSM1299528 2 0.0000 0.992 0.000 1.000
#> GSM1299529 2 0.0376 0.992 0.004 0.996
#> GSM1299530 2 0.6247 0.814 0.156 0.844
#> GSM1299531 2 0.0376 0.992 0.004 0.996
#> GSM1299575 1 0.0376 0.991 0.996 0.004
#> GSM1299532 1 0.0000 0.992 1.000 0.000
#> GSM1299533 1 0.0000 0.992 1.000 0.000
#> GSM1299534 2 0.0376 0.992 0.004 0.996
#> GSM1299535 1 0.0000 0.992 1.000 0.000
#> GSM1299536 2 0.0000 0.992 0.000 1.000
#> GSM1299537 1 0.0000 0.992 1.000 0.000
#> GSM1299538 2 0.0000 0.992 0.000 1.000
#> GSM1299539 2 0.0000 0.992 0.000 1.000
#> GSM1299540 1 0.0000 0.992 1.000 0.000
#> GSM1299541 1 0.0000 0.992 1.000 0.000
#> GSM1299542 1 0.0000 0.992 1.000 0.000
#> GSM1299543 2 0.0376 0.992 0.004 0.996
#> GSM1299544 2 0.0000 0.992 0.000 1.000
#> GSM1299545 1 0.0000 0.992 1.000 0.000
#> GSM1299546 2 0.0376 0.992 0.004 0.996
#> GSM1299547 2 0.0000 0.992 0.000 1.000
#> GSM1299548 1 0.0000 0.992 1.000 0.000
#> GSM1299549 1 0.0376 0.991 0.996 0.004
#> GSM1299550 2 0.0000 0.992 0.000 1.000
#> GSM1299551 2 0.0376 0.992 0.004 0.996
#> GSM1299552 1 0.0376 0.991 0.996 0.004
#> GSM1299553 2 0.2236 0.959 0.036 0.964
#> GSM1299554 2 0.0376 0.992 0.004 0.996
#> GSM1299555 1 0.0000 0.992 1.000 0.000
#> GSM1299556 1 0.0000 0.992 1.000 0.000
#> GSM1299557 1 0.0000 0.992 1.000 0.000
#> GSM1299558 2 0.0376 0.992 0.004 0.996
#> GSM1299559 1 0.0000 0.992 1.000 0.000
#> GSM1299560 1 0.0000 0.992 1.000 0.000
#> GSM1299576 1 0.0376 0.991 0.996 0.004
#> GSM1299577 1 0.0376 0.991 0.996 0.004
#> GSM1299561 1 0.0000 0.992 1.000 0.000
#> GSM1299562 2 0.0376 0.992 0.004 0.996
#> GSM1299563 2 0.0000 0.992 0.000 1.000
#> GSM1299564 2 0.0000 0.992 0.000 1.000
#> GSM1299565 2 0.0376 0.992 0.004 0.996
#> GSM1299566 2 0.0000 0.992 0.000 1.000
#> GSM1299567 1 0.0000 0.992 1.000 0.000
#> GSM1299568 2 0.0376 0.992 0.004 0.996
#> GSM1299569 2 0.0000 0.992 0.000 1.000
#> GSM1299570 1 0.0376 0.991 0.996 0.004
#> GSM1299571 1 0.0000 0.992 1.000 0.000
#> GSM1299572 1 0.0000 0.992 1.000 0.000
#> GSM1299573 1 0.0000 0.992 1.000 0.000
#> GSM1299574 2 0.0376 0.992 0.004 0.996
#> GSM1299578 1 0.8144 0.663 0.748 0.252
#> GSM1299579 2 0.0000 0.992 0.000 1.000
#> GSM1299580 1 0.0376 0.991 0.996 0.004
#> GSM1299581 1 0.0376 0.991 0.996 0.004
#> GSM1299582 1 0.0376 0.991 0.996 0.004
#> GSM1299583 1 0.0376 0.991 0.996 0.004
#> GSM1299584 1 0.0376 0.991 0.996 0.004
#> GSM1299585 1 0.0376 0.991 0.996 0.004
#> GSM1299586 1 0.0376 0.991 0.996 0.004
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1299517 3 0.000 1.00 0.00 0 1.00
#> GSM1299518 3 0.000 1.00 0.00 0 1.00
#> GSM1299519 2 0.000 1.00 0.00 1 0.00
#> GSM1299520 2 0.000 1.00 0.00 1 0.00
#> GSM1299521 1 0.000 0.99 1.00 0 0.00
#> GSM1299522 2 0.000 1.00 0.00 1 0.00
#> GSM1299523 1 0.000 0.99 1.00 0 0.00
#> GSM1299524 3 0.000 1.00 0.00 0 1.00
#> GSM1299525 2 0.000 1.00 0.00 1 0.00
#> GSM1299526 3 0.000 1.00 0.00 0 1.00
#> GSM1299527 3 0.000 1.00 0.00 0 1.00
#> GSM1299528 2 0.000 1.00 0.00 1 0.00
#> GSM1299529 2 0.000 1.00 0.00 1 0.00
#> GSM1299530 1 0.000 0.99 1.00 0 0.00
#> GSM1299531 2 0.000 1.00 0.00 1 0.00
#> GSM1299575 1 0.000 0.99 1.00 0 0.00
#> GSM1299532 3 0.000 1.00 0.00 0 1.00
#> GSM1299533 3 0.000 1.00 0.00 0 1.00
#> GSM1299534 2 0.000 1.00 0.00 1 0.00
#> GSM1299535 3 0.000 1.00 0.00 0 1.00
#> GSM1299536 2 0.000 1.00 0.00 1 0.00
#> GSM1299537 3 0.000 1.00 0.00 0 1.00
#> GSM1299538 2 0.000 1.00 0.00 1 0.00
#> GSM1299539 2 0.000 1.00 0.00 1 0.00
#> GSM1299540 3 0.000 1.00 0.00 0 1.00
#> GSM1299541 3 0.000 1.00 0.00 0 1.00
#> GSM1299542 3 0.000 1.00 0.00 0 1.00
#> GSM1299543 2 0.000 1.00 0.00 1 0.00
#> GSM1299544 2 0.000 1.00 0.00 1 0.00
#> GSM1299545 1 0.429 0.78 0.82 0 0.18
#> GSM1299546 2 0.000 1.00 0.00 1 0.00
#> GSM1299547 2 0.000 1.00 0.00 1 0.00
#> GSM1299548 3 0.000 1.00 0.00 0 1.00
#> GSM1299549 1 0.000 0.99 1.00 0 0.00
#> GSM1299550 2 0.000 1.00 0.00 1 0.00
#> GSM1299551 2 0.000 1.00 0.00 1 0.00
#> GSM1299552 1 0.000 0.99 1.00 0 0.00
#> GSM1299553 1 0.000 0.99 1.00 0 0.00
#> GSM1299554 2 0.000 1.00 0.00 1 0.00
#> GSM1299555 3 0.000 1.00 0.00 0 1.00
#> GSM1299556 3 0.000 1.00 0.00 0 1.00
#> GSM1299557 3 0.000 1.00 0.00 0 1.00
#> GSM1299558 2 0.000 1.00 0.00 1 0.00
#> GSM1299559 3 0.000 1.00 0.00 0 1.00
#> GSM1299560 3 0.000 1.00 0.00 0 1.00
#> GSM1299576 1 0.000 0.99 1.00 0 0.00
#> GSM1299577 1 0.000 0.99 1.00 0 0.00
#> GSM1299561 3 0.000 1.00 0.00 0 1.00
#> GSM1299562 2 0.000 1.00 0.00 1 0.00
#> GSM1299563 2 0.000 1.00 0.00 1 0.00
#> GSM1299564 2 0.000 1.00 0.00 1 0.00
#> GSM1299565 2 0.000 1.00 0.00 1 0.00
#> GSM1299566 2 0.000 1.00 0.00 1 0.00
#> GSM1299567 3 0.000 1.00 0.00 0 1.00
#> GSM1299568 2 0.000 1.00 0.00 1 0.00
#> GSM1299569 2 0.000 1.00 0.00 1 0.00
#> GSM1299570 1 0.000 0.99 1.00 0 0.00
#> GSM1299571 3 0.000 1.00 0.00 0 1.00
#> GSM1299572 3 0.000 1.00 0.00 0 1.00
#> GSM1299573 3 0.000 1.00 0.00 0 1.00
#> GSM1299574 2 0.000 1.00 0.00 1 0.00
#> GSM1299578 1 0.000 0.99 1.00 0 0.00
#> GSM1299579 2 0.000 1.00 0.00 1 0.00
#> GSM1299580 1 0.000 0.99 1.00 0 0.00
#> GSM1299581 1 0.000 0.99 1.00 0 0.00
#> GSM1299582 1 0.000 0.99 1.00 0 0.00
#> GSM1299583 1 0.000 0.99 1.00 0 0.00
#> GSM1299584 1 0.000 0.99 1.00 0 0.00
#> GSM1299585 1 0.000 0.99 1.00 0 0.00
#> GSM1299586 1 0.000 0.99 1.00 0 0.00
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1299517 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM1299518 3 0.0188 0.997 0.000 0.004 0.996 0.000
#> GSM1299519 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM1299520 4 0.0000 0.997 0.000 0.000 0.000 1.000
#> GSM1299521 1 0.0188 0.978 0.996 0.000 0.000 0.004
#> GSM1299522 2 0.0188 0.999 0.000 0.996 0.000 0.004
#> GSM1299523 4 0.0592 0.983 0.016 0.000 0.000 0.984
#> GSM1299524 3 0.0188 0.997 0.000 0.004 0.996 0.000
#> GSM1299525 2 0.0188 0.999 0.000 0.996 0.000 0.004
#> GSM1299526 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM1299527 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM1299528 4 0.0000 0.997 0.000 0.000 0.000 1.000
#> GSM1299529 2 0.0188 0.999 0.000 0.996 0.000 0.004
#> GSM1299530 1 0.0188 0.978 0.996 0.000 0.000 0.004
#> GSM1299531 2 0.0188 0.999 0.000 0.996 0.000 0.004
#> GSM1299575 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM1299532 3 0.0188 0.997 0.000 0.004 0.996 0.000
#> GSM1299533 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM1299534 4 0.0469 0.988 0.000 0.012 0.000 0.988
#> GSM1299535 3 0.0188 0.997 0.000 0.004 0.996 0.000
#> GSM1299536 4 0.0000 0.997 0.000 0.000 0.000 1.000
#> GSM1299537 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM1299538 4 0.0000 0.997 0.000 0.000 0.000 1.000
#> GSM1299539 4 0.0000 0.997 0.000 0.000 0.000 1.000
#> GSM1299540 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM1299541 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM1299542 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM1299543 2 0.0188 0.999 0.000 0.996 0.000 0.004
#> GSM1299544 4 0.0188 0.995 0.000 0.004 0.000 0.996
#> GSM1299545 1 0.3311 0.793 0.828 0.000 0.172 0.000
#> GSM1299546 2 0.0188 0.999 0.000 0.996 0.000 0.004
#> GSM1299547 4 0.0000 0.997 0.000 0.000 0.000 1.000
#> GSM1299548 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM1299549 1 0.0188 0.977 0.996 0.004 0.000 0.000
#> GSM1299550 4 0.0000 0.997 0.000 0.000 0.000 1.000
#> GSM1299551 2 0.0188 0.999 0.000 0.996 0.000 0.004
#> GSM1299552 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM1299553 1 0.2868 0.842 0.864 0.000 0.000 0.136
#> GSM1299554 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM1299555 3 0.0188 0.997 0.000 0.004 0.996 0.000
#> GSM1299556 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM1299557 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM1299558 2 0.0188 0.999 0.000 0.996 0.000 0.004
#> GSM1299559 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM1299560 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM1299576 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM1299577 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM1299561 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM1299562 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM1299563 4 0.0000 0.997 0.000 0.000 0.000 1.000
#> GSM1299564 4 0.0000 0.997 0.000 0.000 0.000 1.000
#> GSM1299565 2 0.0188 0.999 0.000 0.996 0.000 0.004
#> GSM1299566 4 0.0000 0.997 0.000 0.000 0.000 1.000
#> GSM1299567 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM1299568 2 0.0188 0.999 0.000 0.996 0.000 0.004
#> GSM1299569 4 0.0188 0.995 0.000 0.004 0.000 0.996
#> GSM1299570 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM1299571 3 0.0817 0.978 0.000 0.024 0.976 0.000
#> GSM1299572 3 0.0188 0.997 0.000 0.004 0.996 0.000
#> GSM1299573 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM1299574 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM1299578 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM1299579 4 0.0000 0.997 0.000 0.000 0.000 1.000
#> GSM1299580 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM1299581 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM1299582 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM1299583 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM1299584 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM1299585 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM1299586 1 0.0000 0.980 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1299517 3 0.0000 0.907 0.000 0.000 1.000 0.000 0.000
#> GSM1299518 4 0.3983 0.785 0.000 0.000 0.340 0.660 0.000
#> GSM1299519 2 0.0000 0.990 0.000 1.000 0.000 0.000 0.000
#> GSM1299520 5 0.1732 0.931 0.000 0.000 0.000 0.080 0.920
#> GSM1299521 1 0.2674 0.852 0.856 0.000 0.000 0.140 0.004
#> GSM1299522 2 0.0000 0.990 0.000 1.000 0.000 0.000 0.000
#> GSM1299523 5 0.3409 0.863 0.032 0.000 0.000 0.144 0.824
#> GSM1299524 4 0.3534 0.869 0.000 0.000 0.256 0.744 0.000
#> GSM1299525 2 0.0609 0.976 0.000 0.980 0.000 0.000 0.020
#> GSM1299526 3 0.0963 0.890 0.000 0.000 0.964 0.036 0.000
#> GSM1299527 3 0.2230 0.813 0.000 0.000 0.884 0.116 0.000
#> GSM1299528 5 0.0000 0.951 0.000 0.000 0.000 0.000 1.000
#> GSM1299529 2 0.0000 0.990 0.000 1.000 0.000 0.000 0.000
#> GSM1299530 1 0.2674 0.853 0.856 0.000 0.000 0.140 0.004
#> GSM1299531 2 0.0000 0.990 0.000 1.000 0.000 0.000 0.000
#> GSM1299575 1 0.0000 0.911 1.000 0.000 0.000 0.000 0.000
#> GSM1299532 4 0.3561 0.868 0.000 0.000 0.260 0.740 0.000
#> GSM1299533 3 0.4305 -0.415 0.000 0.000 0.512 0.488 0.000
#> GSM1299534 5 0.1792 0.901 0.000 0.084 0.000 0.000 0.916
#> GSM1299535 4 0.3662 0.869 0.000 0.004 0.252 0.744 0.000
#> GSM1299536 5 0.0000 0.951 0.000 0.000 0.000 0.000 1.000
#> GSM1299537 3 0.0000 0.907 0.000 0.000 1.000 0.000 0.000
#> GSM1299538 5 0.0000 0.951 0.000 0.000 0.000 0.000 1.000
#> GSM1299539 5 0.0000 0.951 0.000 0.000 0.000 0.000 1.000
#> GSM1299540 3 0.0000 0.907 0.000 0.000 1.000 0.000 0.000
#> GSM1299541 3 0.0000 0.907 0.000 0.000 1.000 0.000 0.000
#> GSM1299542 3 0.0510 0.902 0.000 0.000 0.984 0.016 0.000
#> GSM1299543 2 0.0404 0.983 0.000 0.988 0.000 0.000 0.012
#> GSM1299544 5 0.1544 0.915 0.000 0.068 0.000 0.000 0.932
#> GSM1299545 1 0.5019 0.343 0.568 0.000 0.396 0.036 0.000
#> GSM1299546 2 0.0000 0.990 0.000 1.000 0.000 0.000 0.000
#> GSM1299547 5 0.2280 0.909 0.000 0.000 0.000 0.120 0.880
#> GSM1299548 3 0.0000 0.907 0.000 0.000 1.000 0.000 0.000
#> GSM1299549 1 0.3816 0.711 0.696 0.000 0.000 0.304 0.000
#> GSM1299550 5 0.0000 0.951 0.000 0.000 0.000 0.000 1.000
#> GSM1299551 2 0.0000 0.990 0.000 1.000 0.000 0.000 0.000
#> GSM1299552 1 0.2852 0.837 0.828 0.000 0.000 0.172 0.000
#> GSM1299553 1 0.6063 0.577 0.568 0.000 0.000 0.256 0.176
#> GSM1299554 4 0.3561 0.423 0.000 0.260 0.000 0.740 0.000
#> GSM1299555 4 0.4088 0.733 0.000 0.000 0.368 0.632 0.000
#> GSM1299556 3 0.0000 0.907 0.000 0.000 1.000 0.000 0.000
#> GSM1299557 3 0.1270 0.868 0.000 0.000 0.948 0.052 0.000
#> GSM1299558 2 0.0404 0.983 0.000 0.988 0.000 0.000 0.012
#> GSM1299559 3 0.0000 0.907 0.000 0.000 1.000 0.000 0.000
#> GSM1299560 3 0.2329 0.802 0.000 0.000 0.876 0.124 0.000
#> GSM1299576 1 0.0000 0.911 1.000 0.000 0.000 0.000 0.000
#> GSM1299577 1 0.0162 0.910 0.996 0.000 0.000 0.004 0.000
#> GSM1299561 3 0.0510 0.902 0.000 0.000 0.984 0.016 0.000
#> GSM1299562 2 0.1410 0.933 0.000 0.940 0.000 0.060 0.000
#> GSM1299563 5 0.1732 0.931 0.000 0.000 0.000 0.080 0.920
#> GSM1299564 5 0.1732 0.931 0.000 0.000 0.000 0.080 0.920
#> GSM1299565 2 0.0000 0.990 0.000 1.000 0.000 0.000 0.000
#> GSM1299566 5 0.0000 0.951 0.000 0.000 0.000 0.000 1.000
#> GSM1299567 3 0.0404 0.896 0.012 0.000 0.988 0.000 0.000
#> GSM1299568 2 0.0000 0.990 0.000 1.000 0.000 0.000 0.000
#> GSM1299569 5 0.1270 0.926 0.000 0.052 0.000 0.000 0.948
#> GSM1299570 1 0.1478 0.892 0.936 0.000 0.000 0.064 0.000
#> GSM1299571 4 0.3756 0.867 0.000 0.008 0.248 0.744 0.000
#> GSM1299572 4 0.3508 0.867 0.000 0.000 0.252 0.748 0.000
#> GSM1299573 3 0.2813 0.736 0.000 0.000 0.832 0.168 0.000
#> GSM1299574 2 0.0404 0.982 0.000 0.988 0.000 0.012 0.000
#> GSM1299578 1 0.0162 0.911 0.996 0.000 0.000 0.004 0.000
#> GSM1299579 5 0.0000 0.951 0.000 0.000 0.000 0.000 1.000
#> GSM1299580 1 0.0000 0.911 1.000 0.000 0.000 0.000 0.000
#> GSM1299581 1 0.0000 0.911 1.000 0.000 0.000 0.000 0.000
#> GSM1299582 1 0.0000 0.911 1.000 0.000 0.000 0.000 0.000
#> GSM1299583 1 0.0162 0.911 0.996 0.000 0.000 0.004 0.000
#> GSM1299584 1 0.0000 0.911 1.000 0.000 0.000 0.000 0.000
#> GSM1299585 1 0.0162 0.911 0.996 0.000 0.000 0.004 0.000
#> GSM1299586 1 0.0000 0.911 1.000 0.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1299517 3 0.0000 0.9008 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299518 6 0.3489 0.6586 0.000 0.000 0.288 0.004 0.000 0.708
#> GSM1299519 2 0.0146 0.9751 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM1299520 5 0.3706 0.4697 0.000 0.000 0.000 0.380 0.620 0.000
#> GSM1299521 4 0.4284 0.2776 0.440 0.000 0.000 0.544 0.004 0.012
#> GSM1299522 2 0.0000 0.9759 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299523 4 0.3819 0.1794 0.012 0.000 0.000 0.672 0.316 0.000
#> GSM1299524 6 0.1765 0.8202 0.000 0.000 0.096 0.000 0.000 0.904
#> GSM1299525 2 0.1327 0.9352 0.000 0.936 0.000 0.000 0.064 0.000
#> GSM1299526 3 0.1714 0.8590 0.000 0.000 0.908 0.000 0.000 0.092
#> GSM1299527 3 0.3109 0.7063 0.000 0.000 0.772 0.004 0.000 0.224
#> GSM1299528 5 0.0000 0.8708 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1299529 2 0.0146 0.9752 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM1299530 4 0.4187 0.3762 0.356 0.000 0.000 0.624 0.004 0.016
#> GSM1299531 2 0.0000 0.9759 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299575 1 0.0000 0.8992 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299532 6 0.2006 0.8199 0.000 0.000 0.104 0.004 0.000 0.892
#> GSM1299533 6 0.3838 0.3045 0.000 0.000 0.448 0.000 0.000 0.552
#> GSM1299534 5 0.1267 0.8188 0.000 0.060 0.000 0.000 0.940 0.000
#> GSM1299535 6 0.1866 0.8161 0.000 0.008 0.084 0.000 0.000 0.908
#> GSM1299536 5 0.0000 0.8708 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1299537 3 0.0000 0.9008 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299538 5 0.0000 0.8708 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1299539 5 0.0000 0.8708 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1299540 3 0.0146 0.9003 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM1299541 3 0.0000 0.9008 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299542 3 0.1349 0.8813 0.000 0.000 0.940 0.004 0.000 0.056
#> GSM1299543 2 0.1007 0.9546 0.000 0.956 0.000 0.000 0.044 0.000
#> GSM1299544 5 0.0713 0.8514 0.000 0.028 0.000 0.000 0.972 0.000
#> GSM1299545 1 0.5976 0.0877 0.476 0.000 0.368 0.136 0.000 0.020
#> GSM1299546 2 0.0146 0.9751 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM1299547 4 0.3817 -0.1458 0.000 0.000 0.000 0.568 0.432 0.000
#> GSM1299548 3 0.0000 0.9008 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299549 4 0.5675 0.2569 0.344 0.000 0.000 0.488 0.000 0.168
#> GSM1299550 5 0.0000 0.8708 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1299551 2 0.0000 0.9759 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299552 4 0.5091 0.1702 0.416 0.000 0.000 0.504 0.000 0.080
#> GSM1299553 4 0.1483 0.4835 0.008 0.000 0.000 0.944 0.012 0.036
#> GSM1299554 6 0.5527 0.3331 0.000 0.136 0.000 0.220 0.024 0.620
#> GSM1299555 6 0.3215 0.7236 0.000 0.000 0.240 0.004 0.000 0.756
#> GSM1299556 3 0.0146 0.9003 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM1299557 3 0.2129 0.8400 0.000 0.000 0.904 0.040 0.000 0.056
#> GSM1299558 2 0.0865 0.9603 0.000 0.964 0.000 0.000 0.036 0.000
#> GSM1299559 3 0.0146 0.9003 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM1299560 3 0.3240 0.6721 0.000 0.000 0.752 0.004 0.000 0.244
#> GSM1299576 1 0.0000 0.8992 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299577 1 0.0858 0.8742 0.968 0.000 0.000 0.028 0.000 0.004
#> GSM1299561 3 0.1531 0.8746 0.000 0.000 0.928 0.004 0.000 0.068
#> GSM1299562 2 0.1644 0.9108 0.000 0.920 0.000 0.004 0.000 0.076
#> GSM1299563 5 0.3659 0.4935 0.000 0.000 0.000 0.364 0.636 0.000
#> GSM1299564 5 0.3717 0.4631 0.000 0.000 0.000 0.384 0.616 0.000
#> GSM1299565 2 0.0000 0.9759 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299566 5 0.0000 0.8708 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1299567 3 0.0777 0.8795 0.024 0.000 0.972 0.004 0.000 0.000
#> GSM1299568 2 0.0951 0.9657 0.000 0.968 0.000 0.004 0.020 0.008
#> GSM1299569 5 0.0363 0.8642 0.000 0.012 0.000 0.000 0.988 0.000
#> GSM1299570 1 0.3791 0.5436 0.732 0.000 0.000 0.236 0.000 0.032
#> GSM1299571 6 0.2039 0.8087 0.000 0.020 0.076 0.000 0.000 0.904
#> GSM1299572 6 0.1663 0.8178 0.000 0.000 0.088 0.000 0.000 0.912
#> GSM1299573 3 0.3489 0.5887 0.000 0.000 0.708 0.004 0.000 0.288
#> GSM1299574 2 0.0291 0.9739 0.000 0.992 0.000 0.004 0.000 0.004
#> GSM1299578 1 0.0820 0.8834 0.972 0.000 0.000 0.016 0.000 0.012
#> GSM1299579 5 0.0632 0.8576 0.000 0.000 0.000 0.024 0.976 0.000
#> GSM1299580 1 0.0000 0.8992 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299581 1 0.0000 0.8992 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299582 1 0.0000 0.8992 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299583 1 0.0508 0.8912 0.984 0.000 0.000 0.004 0.000 0.012
#> GSM1299584 1 0.0000 0.8992 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299585 1 0.0622 0.8888 0.980 0.000 0.000 0.008 0.000 0.012
#> GSM1299586 1 0.0000 0.8992 1.000 0.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:skmeans 70 0.3017 2
#> ATC:skmeans 70 0.4530 3
#> ATC:skmeans 70 0.4873 4
#> ATC:skmeans 67 0.5694 5
#> ATC:skmeans 57 0.0818 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "pam"]
# you can also extract it by
# res = res_list["ATC:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.462 0.854 0.862 0.4568 0.503 0.503
#> 3 3 0.855 0.825 0.932 0.4292 0.728 0.510
#> 4 4 0.726 0.773 0.880 0.1436 0.828 0.542
#> 5 5 0.905 0.851 0.936 0.0809 0.886 0.582
#> 6 6 0.900 0.791 0.920 0.0420 0.937 0.695
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 5
There is also optional best \(k\) = 5 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM1299517 1 0.8555 0.864 0.720 0.280
#> GSM1299518 1 0.8555 0.864 0.720 0.280
#> GSM1299519 2 0.0672 0.949 0.008 0.992
#> GSM1299520 2 0.0000 0.957 0.000 1.000
#> GSM1299521 2 0.8016 0.685 0.244 0.756
#> GSM1299522 2 0.0000 0.957 0.000 1.000
#> GSM1299523 2 0.4690 0.853 0.100 0.900
#> GSM1299524 1 0.8555 0.864 0.720 0.280
#> GSM1299525 2 0.0000 0.957 0.000 1.000
#> GSM1299526 1 0.8555 0.864 0.720 0.280
#> GSM1299527 1 0.8555 0.864 0.720 0.280
#> GSM1299528 2 0.0000 0.957 0.000 1.000
#> GSM1299529 2 0.0000 0.957 0.000 1.000
#> GSM1299530 2 0.8955 0.625 0.312 0.688
#> GSM1299531 2 0.0000 0.957 0.000 1.000
#> GSM1299575 1 0.0000 0.745 1.000 0.000
#> GSM1299532 1 0.8555 0.864 0.720 0.280
#> GSM1299533 1 0.8555 0.864 0.720 0.280
#> GSM1299534 2 0.0000 0.957 0.000 1.000
#> GSM1299535 1 0.8555 0.864 0.720 0.280
#> GSM1299536 2 0.0000 0.957 0.000 1.000
#> GSM1299537 1 0.8555 0.864 0.720 0.280
#> GSM1299538 2 0.0000 0.957 0.000 1.000
#> GSM1299539 2 0.0000 0.957 0.000 1.000
#> GSM1299540 1 0.8555 0.864 0.720 0.280
#> GSM1299541 1 0.8555 0.864 0.720 0.280
#> GSM1299542 1 0.8555 0.864 0.720 0.280
#> GSM1299543 2 0.0000 0.957 0.000 1.000
#> GSM1299544 2 0.0000 0.957 0.000 1.000
#> GSM1299545 1 0.8555 0.864 0.720 0.280
#> GSM1299546 2 0.0000 0.957 0.000 1.000
#> GSM1299547 2 0.0000 0.957 0.000 1.000
#> GSM1299548 1 0.8555 0.864 0.720 0.280
#> GSM1299549 1 0.8555 0.864 0.720 0.280
#> GSM1299550 2 0.0000 0.957 0.000 1.000
#> GSM1299551 2 0.0000 0.957 0.000 1.000
#> GSM1299552 1 0.4562 0.790 0.904 0.096
#> GSM1299553 1 0.9954 0.565 0.540 0.460
#> GSM1299554 1 0.8555 0.864 0.720 0.280
#> GSM1299555 1 0.8555 0.864 0.720 0.280
#> GSM1299556 1 0.8081 0.853 0.752 0.248
#> GSM1299557 1 0.8555 0.864 0.720 0.280
#> GSM1299558 2 0.0000 0.957 0.000 1.000
#> GSM1299559 1 0.8016 0.851 0.756 0.244
#> GSM1299560 1 0.8555 0.864 0.720 0.280
#> GSM1299576 1 0.0000 0.745 1.000 0.000
#> GSM1299577 1 0.3114 0.772 0.944 0.056
#> GSM1299561 1 0.8555 0.864 0.720 0.280
#> GSM1299562 2 0.3274 0.885 0.060 0.940
#> GSM1299563 2 0.0000 0.957 0.000 1.000
#> GSM1299564 2 0.0000 0.957 0.000 1.000
#> GSM1299565 2 0.0000 0.957 0.000 1.000
#> GSM1299566 2 0.0000 0.957 0.000 1.000
#> GSM1299567 1 0.6623 0.827 0.828 0.172
#> GSM1299568 2 0.0000 0.957 0.000 1.000
#> GSM1299569 2 0.0000 0.957 0.000 1.000
#> GSM1299570 1 0.5059 0.798 0.888 0.112
#> GSM1299571 1 0.8555 0.864 0.720 0.280
#> GSM1299572 1 0.8555 0.864 0.720 0.280
#> GSM1299573 1 0.8555 0.864 0.720 0.280
#> GSM1299574 2 0.2948 0.896 0.052 0.948
#> GSM1299578 1 0.9491 0.119 0.632 0.368
#> GSM1299579 2 0.6973 0.753 0.188 0.812
#> GSM1299580 1 0.0000 0.745 1.000 0.000
#> GSM1299581 1 0.0000 0.745 1.000 0.000
#> GSM1299582 1 0.0000 0.745 1.000 0.000
#> GSM1299583 1 0.0000 0.745 1.000 0.000
#> GSM1299584 1 0.0000 0.745 1.000 0.000
#> GSM1299585 1 0.0000 0.745 1.000 0.000
#> GSM1299586 1 0.0000 0.745 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1299517 3 0.0000 0.930 0.000 0.000 1.000
#> GSM1299518 3 0.0000 0.930 0.000 0.000 1.000
#> GSM1299519 3 0.6274 0.118 0.000 0.456 0.544
#> GSM1299520 2 0.0000 0.926 0.000 1.000 0.000
#> GSM1299521 1 0.1753 0.862 0.952 0.048 0.000
#> GSM1299522 2 0.2625 0.863 0.000 0.916 0.084
#> GSM1299523 2 0.1289 0.901 0.032 0.968 0.000
#> GSM1299524 3 0.0000 0.930 0.000 0.000 1.000
#> GSM1299525 2 0.0000 0.926 0.000 1.000 0.000
#> GSM1299526 3 0.0000 0.930 0.000 0.000 1.000
#> GSM1299527 3 0.0000 0.930 0.000 0.000 1.000
#> GSM1299528 2 0.0000 0.926 0.000 1.000 0.000
#> GSM1299529 2 0.0237 0.925 0.000 0.996 0.004
#> GSM1299530 1 0.4605 0.705 0.796 0.204 0.000
#> GSM1299531 2 0.0747 0.917 0.000 0.984 0.016
#> GSM1299575 1 0.0000 0.888 1.000 0.000 0.000
#> GSM1299532 3 0.0000 0.930 0.000 0.000 1.000
#> GSM1299533 3 0.0000 0.930 0.000 0.000 1.000
#> GSM1299534 2 0.0237 0.925 0.000 0.996 0.004
#> GSM1299535 3 0.0000 0.930 0.000 0.000 1.000
#> GSM1299536 2 0.0000 0.926 0.000 1.000 0.000
#> GSM1299537 3 0.0000 0.930 0.000 0.000 1.000
#> GSM1299538 2 0.0000 0.926 0.000 1.000 0.000
#> GSM1299539 2 0.0000 0.926 0.000 1.000 0.000
#> GSM1299540 3 0.0000 0.930 0.000 0.000 1.000
#> GSM1299541 3 0.0000 0.930 0.000 0.000 1.000
#> GSM1299542 3 0.0000 0.930 0.000 0.000 1.000
#> GSM1299543 2 0.0000 0.926 0.000 1.000 0.000
#> GSM1299544 2 0.0000 0.926 0.000 1.000 0.000
#> GSM1299545 3 0.0892 0.910 0.020 0.000 0.980
#> GSM1299546 2 0.6295 0.090 0.000 0.528 0.472
#> GSM1299547 2 0.0000 0.926 0.000 1.000 0.000
#> GSM1299548 3 0.0000 0.930 0.000 0.000 1.000
#> GSM1299549 1 0.6260 0.326 0.552 0.000 0.448
#> GSM1299550 2 0.0000 0.926 0.000 1.000 0.000
#> GSM1299551 2 0.2165 0.879 0.000 0.936 0.064
#> GSM1299552 1 0.3752 0.795 0.856 0.000 0.144
#> GSM1299553 1 0.9431 0.406 0.496 0.212 0.292
#> GSM1299554 2 0.5835 0.465 0.000 0.660 0.340
#> GSM1299555 3 0.0000 0.930 0.000 0.000 1.000
#> GSM1299556 3 0.0000 0.930 0.000 0.000 1.000
#> GSM1299557 3 0.0000 0.930 0.000 0.000 1.000
#> GSM1299558 2 0.0000 0.926 0.000 1.000 0.000
#> GSM1299559 3 0.0000 0.930 0.000 0.000 1.000
#> GSM1299560 3 0.0000 0.930 0.000 0.000 1.000
#> GSM1299576 1 0.0000 0.888 1.000 0.000 0.000
#> GSM1299577 1 0.1860 0.863 0.948 0.000 0.052
#> GSM1299561 3 0.0000 0.930 0.000 0.000 1.000
#> GSM1299562 3 0.6260 0.145 0.000 0.448 0.552
#> GSM1299563 2 0.0000 0.926 0.000 1.000 0.000
#> GSM1299564 2 0.0000 0.926 0.000 1.000 0.000
#> GSM1299565 2 0.6260 0.165 0.000 0.552 0.448
#> GSM1299566 2 0.0000 0.926 0.000 1.000 0.000
#> GSM1299567 3 0.1753 0.880 0.048 0.000 0.952
#> GSM1299568 2 0.2165 0.879 0.000 0.936 0.064
#> GSM1299569 2 0.0000 0.926 0.000 1.000 0.000
#> GSM1299570 1 0.6140 0.427 0.596 0.000 0.404
#> GSM1299571 3 0.0000 0.930 0.000 0.000 1.000
#> GSM1299572 3 0.0000 0.930 0.000 0.000 1.000
#> GSM1299573 3 0.0000 0.930 0.000 0.000 1.000
#> GSM1299574 3 0.6260 0.145 0.000 0.448 0.552
#> GSM1299578 1 0.0000 0.888 1.000 0.000 0.000
#> GSM1299579 2 0.0000 0.926 0.000 1.000 0.000
#> GSM1299580 1 0.0000 0.888 1.000 0.000 0.000
#> GSM1299581 1 0.0000 0.888 1.000 0.000 0.000
#> GSM1299582 1 0.0000 0.888 1.000 0.000 0.000
#> GSM1299583 1 0.0000 0.888 1.000 0.000 0.000
#> GSM1299584 1 0.0000 0.888 1.000 0.000 0.000
#> GSM1299585 1 0.0000 0.888 1.000 0.000 0.000
#> GSM1299586 1 0.0000 0.888 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1299517 3 0.0000 0.880 0.000 0.000 1.000 0.000
#> GSM1299518 3 0.4907 0.422 0.000 0.420 0.580 0.000
#> GSM1299519 2 0.3074 0.741 0.000 0.848 0.000 0.152
#> GSM1299520 4 0.0000 0.996 0.000 0.000 0.000 1.000
#> GSM1299521 1 0.2773 0.831 0.900 0.028 0.000 0.072
#> GSM1299522 2 0.3486 0.733 0.000 0.812 0.000 0.188
#> GSM1299523 4 0.1022 0.953 0.000 0.032 0.000 0.968
#> GSM1299524 3 0.3801 0.757 0.000 0.220 0.780 0.000
#> GSM1299525 2 0.4431 0.628 0.000 0.696 0.000 0.304
#> GSM1299526 3 0.0000 0.880 0.000 0.000 1.000 0.000
#> GSM1299527 3 0.0000 0.880 0.000 0.000 1.000 0.000
#> GSM1299528 4 0.0000 0.996 0.000 0.000 0.000 1.000
#> GSM1299529 2 0.3764 0.717 0.000 0.784 0.000 0.216
#> GSM1299530 1 0.2845 0.829 0.896 0.028 0.000 0.076
#> GSM1299531 2 0.3764 0.717 0.000 0.784 0.000 0.216
#> GSM1299575 1 0.0000 0.872 1.000 0.000 0.000 0.000
#> GSM1299532 2 0.4624 0.277 0.000 0.660 0.340 0.000
#> GSM1299533 2 0.4661 0.256 0.000 0.652 0.348 0.000
#> GSM1299534 2 0.4967 0.388 0.000 0.548 0.000 0.452
#> GSM1299535 2 0.4134 0.439 0.000 0.740 0.260 0.000
#> GSM1299536 4 0.0000 0.996 0.000 0.000 0.000 1.000
#> GSM1299537 3 0.0000 0.880 0.000 0.000 1.000 0.000
#> GSM1299538 4 0.0000 0.996 0.000 0.000 0.000 1.000
#> GSM1299539 4 0.0000 0.996 0.000 0.000 0.000 1.000
#> GSM1299540 3 0.0000 0.880 0.000 0.000 1.000 0.000
#> GSM1299541 3 0.0000 0.880 0.000 0.000 1.000 0.000
#> GSM1299542 3 0.0000 0.880 0.000 0.000 1.000 0.000
#> GSM1299543 2 0.4406 0.633 0.000 0.700 0.000 0.300
#> GSM1299544 4 0.0000 0.996 0.000 0.000 0.000 1.000
#> GSM1299545 3 0.7433 0.352 0.276 0.216 0.508 0.000
#> GSM1299546 2 0.3356 0.738 0.000 0.824 0.000 0.176
#> GSM1299547 4 0.0188 0.991 0.000 0.004 0.000 0.996
#> GSM1299548 3 0.0000 0.880 0.000 0.000 1.000 0.000
#> GSM1299549 1 0.7536 0.339 0.484 0.296 0.220 0.000
#> GSM1299550 4 0.0000 0.996 0.000 0.000 0.000 1.000
#> GSM1299551 2 0.3356 0.738 0.000 0.824 0.000 0.176
#> GSM1299552 1 0.5200 0.704 0.744 0.184 0.072 0.000
#> GSM1299553 1 0.7934 0.362 0.496 0.268 0.220 0.016
#> GSM1299554 2 0.5327 0.469 0.000 0.720 0.220 0.060
#> GSM1299555 3 0.4564 0.616 0.000 0.328 0.672 0.000
#> GSM1299556 3 0.0000 0.880 0.000 0.000 1.000 0.000
#> GSM1299557 3 0.3610 0.773 0.000 0.200 0.800 0.000
#> GSM1299558 2 0.4040 0.690 0.000 0.752 0.000 0.248
#> GSM1299559 3 0.0000 0.880 0.000 0.000 1.000 0.000
#> GSM1299560 3 0.2589 0.826 0.000 0.116 0.884 0.000
#> GSM1299576 1 0.0000 0.872 1.000 0.000 0.000 0.000
#> GSM1299577 1 0.2892 0.821 0.896 0.036 0.068 0.000
#> GSM1299561 3 0.0000 0.880 0.000 0.000 1.000 0.000
#> GSM1299562 2 0.0188 0.715 0.000 0.996 0.000 0.004
#> GSM1299563 4 0.0000 0.996 0.000 0.000 0.000 1.000
#> GSM1299564 4 0.0000 0.996 0.000 0.000 0.000 1.000
#> GSM1299565 2 0.3764 0.717 0.000 0.784 0.000 0.216
#> GSM1299566 4 0.0000 0.996 0.000 0.000 0.000 1.000
#> GSM1299567 3 0.0000 0.880 0.000 0.000 1.000 0.000
#> GSM1299568 2 0.1022 0.731 0.000 0.968 0.000 0.032
#> GSM1299569 4 0.0000 0.996 0.000 0.000 0.000 1.000
#> GSM1299570 1 0.7065 0.452 0.572 0.212 0.216 0.000
#> GSM1299571 2 0.1118 0.697 0.000 0.964 0.036 0.000
#> GSM1299572 2 0.4543 0.311 0.000 0.676 0.324 0.000
#> GSM1299573 3 0.3726 0.763 0.000 0.212 0.788 0.000
#> GSM1299574 2 0.0469 0.721 0.000 0.988 0.000 0.012
#> GSM1299578 1 0.0000 0.872 1.000 0.000 0.000 0.000
#> GSM1299579 4 0.0000 0.996 0.000 0.000 0.000 1.000
#> GSM1299580 1 0.0000 0.872 1.000 0.000 0.000 0.000
#> GSM1299581 1 0.0000 0.872 1.000 0.000 0.000 0.000
#> GSM1299582 1 0.0000 0.872 1.000 0.000 0.000 0.000
#> GSM1299583 1 0.0000 0.872 1.000 0.000 0.000 0.000
#> GSM1299584 1 0.0000 0.872 1.000 0.000 0.000 0.000
#> GSM1299585 1 0.0188 0.871 0.996 0.004 0.000 0.000
#> GSM1299586 1 0.0000 0.872 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1299517 3 0.0000 0.9706 0.000 0.000 1.000 0.000 0.000
#> GSM1299518 4 0.0880 0.9170 0.000 0.000 0.032 0.968 0.000
#> GSM1299519 2 0.0000 0.8903 0.000 1.000 0.000 0.000 0.000
#> GSM1299520 5 0.0000 0.9614 0.000 0.000 0.000 0.000 1.000
#> GSM1299521 1 0.3409 0.7901 0.816 0.000 0.000 0.160 0.024
#> GSM1299522 2 0.0000 0.8903 0.000 1.000 0.000 0.000 0.000
#> GSM1299523 5 0.1341 0.9207 0.000 0.000 0.000 0.056 0.944
#> GSM1299524 4 0.0880 0.9170 0.000 0.000 0.032 0.968 0.000
#> GSM1299525 2 0.0000 0.8903 0.000 1.000 0.000 0.000 0.000
#> GSM1299526 3 0.0000 0.9706 0.000 0.000 1.000 0.000 0.000
#> GSM1299527 3 0.0000 0.9706 0.000 0.000 1.000 0.000 0.000
#> GSM1299528 5 0.0000 0.9614 0.000 0.000 0.000 0.000 1.000
#> GSM1299529 2 0.0000 0.8903 0.000 1.000 0.000 0.000 0.000
#> GSM1299530 1 0.4473 0.5994 0.656 0.000 0.000 0.324 0.020
#> GSM1299531 2 0.0000 0.8903 0.000 1.000 0.000 0.000 0.000
#> GSM1299575 1 0.0000 0.9003 1.000 0.000 0.000 0.000 0.000
#> GSM1299532 4 0.0880 0.9170 0.000 0.000 0.032 0.968 0.000
#> GSM1299533 4 0.0880 0.9170 0.000 0.000 0.032 0.968 0.000
#> GSM1299534 2 0.6361 0.2739 0.000 0.484 0.000 0.176 0.340
#> GSM1299535 4 0.0992 0.9071 0.000 0.024 0.008 0.968 0.000
#> GSM1299536 5 0.0000 0.9614 0.000 0.000 0.000 0.000 1.000
#> GSM1299537 3 0.0000 0.9706 0.000 0.000 1.000 0.000 0.000
#> GSM1299538 5 0.0000 0.9614 0.000 0.000 0.000 0.000 1.000
#> GSM1299539 5 0.0000 0.9614 0.000 0.000 0.000 0.000 1.000
#> GSM1299540 3 0.0000 0.9706 0.000 0.000 1.000 0.000 0.000
#> GSM1299541 3 0.0000 0.9706 0.000 0.000 1.000 0.000 0.000
#> GSM1299542 3 0.0000 0.9706 0.000 0.000 1.000 0.000 0.000
#> GSM1299543 2 0.0000 0.8903 0.000 1.000 0.000 0.000 0.000
#> GSM1299544 5 0.0000 0.9614 0.000 0.000 0.000 0.000 1.000
#> GSM1299545 4 0.0000 0.9106 0.000 0.000 0.000 1.000 0.000
#> GSM1299546 2 0.0000 0.8903 0.000 1.000 0.000 0.000 0.000
#> GSM1299547 5 0.4392 0.4055 0.000 0.008 0.000 0.380 0.612
#> GSM1299548 3 0.0000 0.9706 0.000 0.000 1.000 0.000 0.000
#> GSM1299549 4 0.0963 0.8847 0.036 0.000 0.000 0.964 0.000
#> GSM1299550 5 0.0000 0.9614 0.000 0.000 0.000 0.000 1.000
#> GSM1299551 2 0.0000 0.8903 0.000 1.000 0.000 0.000 0.000
#> GSM1299552 1 0.4030 0.5463 0.648 0.000 0.000 0.352 0.000
#> GSM1299553 4 0.0000 0.9106 0.000 0.000 0.000 1.000 0.000
#> GSM1299554 4 0.0000 0.9106 0.000 0.000 0.000 1.000 0.000
#> GSM1299555 4 0.0880 0.9170 0.000 0.000 0.032 0.968 0.000
#> GSM1299556 3 0.0000 0.9706 0.000 0.000 1.000 0.000 0.000
#> GSM1299557 4 0.3305 0.6970 0.000 0.000 0.224 0.776 0.000
#> GSM1299558 2 0.0000 0.8903 0.000 1.000 0.000 0.000 0.000
#> GSM1299559 3 0.0000 0.9706 0.000 0.000 1.000 0.000 0.000
#> GSM1299560 3 0.3796 0.5361 0.000 0.000 0.700 0.300 0.000
#> GSM1299576 1 0.0000 0.9003 1.000 0.000 0.000 0.000 0.000
#> GSM1299577 1 0.4088 0.5389 0.632 0.000 0.000 0.368 0.000
#> GSM1299561 3 0.0510 0.9572 0.000 0.000 0.984 0.016 0.000
#> GSM1299562 2 0.4101 0.3987 0.000 0.628 0.000 0.372 0.000
#> GSM1299563 5 0.0000 0.9614 0.000 0.000 0.000 0.000 1.000
#> GSM1299564 5 0.0992 0.9413 0.000 0.008 0.000 0.024 0.968
#> GSM1299565 2 0.0000 0.8903 0.000 1.000 0.000 0.000 0.000
#> GSM1299566 5 0.0000 0.9614 0.000 0.000 0.000 0.000 1.000
#> GSM1299567 3 0.0162 0.9669 0.004 0.000 0.996 0.000 0.000
#> GSM1299568 4 0.4060 0.3285 0.000 0.360 0.000 0.640 0.000
#> GSM1299569 5 0.0000 0.9614 0.000 0.000 0.000 0.000 1.000
#> GSM1299570 4 0.3039 0.6699 0.192 0.000 0.000 0.808 0.000
#> GSM1299571 2 0.4562 -0.0172 0.000 0.496 0.008 0.496 0.000
#> GSM1299572 4 0.0162 0.9121 0.000 0.000 0.004 0.996 0.000
#> GSM1299573 4 0.0880 0.9170 0.000 0.000 0.032 0.968 0.000
#> GSM1299574 2 0.0000 0.8903 0.000 1.000 0.000 0.000 0.000
#> GSM1299578 1 0.0404 0.8972 0.988 0.000 0.000 0.012 0.000
#> GSM1299579 5 0.0000 0.9614 0.000 0.000 0.000 0.000 1.000
#> GSM1299580 1 0.0000 0.9003 1.000 0.000 0.000 0.000 0.000
#> GSM1299581 1 0.0000 0.9003 1.000 0.000 0.000 0.000 0.000
#> GSM1299582 1 0.0000 0.9003 1.000 0.000 0.000 0.000 0.000
#> GSM1299583 1 0.0000 0.9003 1.000 0.000 0.000 0.000 0.000
#> GSM1299584 1 0.0000 0.9003 1.000 0.000 0.000 0.000 0.000
#> GSM1299585 1 0.0703 0.8922 0.976 0.000 0.000 0.024 0.000
#> GSM1299586 1 0.0000 0.9003 1.000 0.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1299517 3 0.0000 0.9637 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299518 6 0.0000 0.8686 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1299519 2 0.0000 0.9001 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299520 5 0.2219 0.8367 0.000 0.000 0.000 0.136 0.864 0.000
#> GSM1299521 4 0.0937 0.7851 0.040 0.000 0.000 0.960 0.000 0.000
#> GSM1299522 2 0.0000 0.9001 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299523 4 0.0000 0.8006 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1299524 6 0.0000 0.8686 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1299525 2 0.0000 0.9001 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299526 3 0.0000 0.9637 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299527 3 0.0000 0.9637 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299528 5 0.0000 0.9296 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1299529 2 0.0000 0.9001 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299530 4 0.0000 0.8006 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1299531 2 0.0000 0.9001 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299575 1 0.0000 0.9181 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299532 6 0.0000 0.8686 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1299533 6 0.0000 0.8686 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1299534 2 0.6350 0.0733 0.000 0.392 0.000 0.332 0.012 0.264
#> GSM1299535 6 0.0000 0.8686 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1299536 5 0.1387 0.8942 0.000 0.000 0.000 0.068 0.932 0.000
#> GSM1299537 3 0.0000 0.9637 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299538 5 0.0790 0.9190 0.000 0.000 0.000 0.032 0.968 0.000
#> GSM1299539 5 0.0000 0.9296 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1299540 3 0.0000 0.9637 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299541 3 0.0000 0.9637 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299542 3 0.0000 0.9637 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299543 2 0.1814 0.8195 0.000 0.900 0.000 0.000 0.100 0.000
#> GSM1299544 5 0.0000 0.9296 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1299545 6 0.3872 0.2549 0.000 0.000 0.004 0.392 0.000 0.604
#> GSM1299546 2 0.0000 0.9001 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299547 4 0.0363 0.7963 0.000 0.000 0.000 0.988 0.012 0.000
#> GSM1299548 3 0.0000 0.9637 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299549 6 0.3869 -0.0964 0.000 0.000 0.000 0.500 0.000 0.500
#> GSM1299550 5 0.0000 0.9296 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1299551 2 0.0000 0.9001 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299552 4 0.1049 0.7898 0.032 0.000 0.000 0.960 0.000 0.008
#> GSM1299553 4 0.0260 0.8005 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM1299554 6 0.0000 0.8686 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1299555 6 0.0000 0.8686 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1299556 3 0.0000 0.9637 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299557 6 0.0713 0.8469 0.000 0.000 0.028 0.000 0.000 0.972
#> GSM1299558 2 0.0000 0.9001 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299559 3 0.0000 0.9637 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299560 3 0.3659 0.4186 0.000 0.000 0.636 0.000 0.000 0.364
#> GSM1299576 1 0.0000 0.9181 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299577 4 0.5486 0.4315 0.188 0.000 0.000 0.564 0.000 0.248
#> GSM1299561 3 0.0458 0.9492 0.000 0.000 0.984 0.000 0.000 0.016
#> GSM1299562 2 0.3843 0.1711 0.000 0.548 0.000 0.000 0.000 0.452
#> GSM1299563 5 0.3810 0.3472 0.000 0.000 0.000 0.428 0.572 0.000
#> GSM1299564 4 0.3706 0.1221 0.000 0.000 0.000 0.620 0.380 0.000
#> GSM1299565 2 0.0000 0.9001 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299566 5 0.0000 0.9296 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1299567 3 0.0000 0.9637 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1299568 6 0.2092 0.7638 0.000 0.124 0.000 0.000 0.000 0.876
#> GSM1299569 5 0.0000 0.9296 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1299570 4 0.4109 0.2100 0.012 0.000 0.000 0.576 0.000 0.412
#> GSM1299571 6 0.3659 0.3794 0.000 0.364 0.000 0.000 0.000 0.636
#> GSM1299572 6 0.0000 0.8686 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1299573 6 0.0000 0.8686 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1299574 2 0.0000 0.9001 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299578 1 0.3288 0.6107 0.724 0.000 0.000 0.276 0.000 0.000
#> GSM1299579 5 0.0363 0.9266 0.000 0.000 0.000 0.012 0.988 0.000
#> GSM1299580 1 0.0000 0.9181 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299581 1 0.0000 0.9181 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299582 1 0.0000 0.9181 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299583 1 0.0000 0.9181 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299584 1 0.0000 0.9181 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299585 1 0.3695 0.4051 0.624 0.000 0.000 0.376 0.000 0.000
#> GSM1299586 1 0.0000 0.9181 1.000 0.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:pam 69 0.1998 2
#> ATC:pam 61 0.1215 3
#> ATC:pam 59 0.2842 4
#> ATC:pam 65 0.1502 5
#> ATC:pam 59 0.0639 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "mclust"]
# you can also extract it by
# res = res_list["ATC:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 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 0.681 0.871 0.913 0.4980 0.494 0.494
#> 3 3 0.661 0.778 0.884 0.3030 0.678 0.441
#> 4 4 0.886 0.930 0.951 0.1538 0.784 0.457
#> 5 5 0.819 0.875 0.904 0.0551 0.944 0.778
#> 6 6 0.864 0.890 0.918 0.0531 0.900 0.574
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
#> GSM1299517 2 0.0000 0.882 0.000 1.000
#> GSM1299518 2 0.0000 0.882 0.000 1.000
#> GSM1299519 2 0.8499 0.782 0.276 0.724
#> GSM1299520 1 0.0000 0.926 1.000 0.000
#> GSM1299521 1 0.4562 0.922 0.904 0.096
#> GSM1299522 2 0.8499 0.782 0.276 0.724
#> GSM1299523 1 0.0000 0.926 1.000 0.000
#> GSM1299524 2 0.0000 0.882 0.000 1.000
#> GSM1299525 2 0.8763 0.760 0.296 0.704
#> GSM1299526 2 0.0000 0.882 0.000 1.000
#> GSM1299527 2 0.0000 0.882 0.000 1.000
#> GSM1299528 1 0.0000 0.926 1.000 0.000
#> GSM1299529 2 0.8555 0.778 0.280 0.720
#> GSM1299530 1 0.0938 0.927 0.988 0.012
#> GSM1299531 2 0.8499 0.782 0.276 0.724
#> GSM1299575 1 0.4562 0.922 0.904 0.096
#> GSM1299532 2 0.0000 0.882 0.000 1.000
#> GSM1299533 2 0.4562 0.854 0.096 0.904
#> GSM1299534 1 0.0000 0.926 1.000 0.000
#> GSM1299535 2 0.4562 0.854 0.096 0.904
#> GSM1299536 1 0.0000 0.926 1.000 0.000
#> GSM1299537 2 0.0000 0.882 0.000 1.000
#> GSM1299538 1 0.0000 0.926 1.000 0.000
#> GSM1299539 1 0.0000 0.926 1.000 0.000
#> GSM1299540 2 0.0000 0.882 0.000 1.000
#> GSM1299541 2 0.0000 0.882 0.000 1.000
#> GSM1299542 2 0.0000 0.882 0.000 1.000
#> GSM1299543 2 0.8763 0.760 0.296 0.704
#> GSM1299544 1 0.4161 0.850 0.916 0.084
#> GSM1299545 1 0.9922 0.361 0.552 0.448
#> GSM1299546 2 0.8499 0.782 0.276 0.724
#> GSM1299547 1 0.0000 0.926 1.000 0.000
#> GSM1299548 2 0.0000 0.882 0.000 1.000
#> GSM1299549 1 0.5059 0.911 0.888 0.112
#> GSM1299550 1 0.0000 0.926 1.000 0.000
#> GSM1299551 2 0.8499 0.782 0.276 0.724
#> GSM1299552 1 0.4562 0.922 0.904 0.096
#> GSM1299553 1 0.0000 0.926 1.000 0.000
#> GSM1299554 2 0.8499 0.782 0.276 0.724
#> GSM1299555 2 0.0000 0.882 0.000 1.000
#> GSM1299556 2 0.0000 0.882 0.000 1.000
#> GSM1299557 2 0.0000 0.882 0.000 1.000
#> GSM1299558 2 0.8763 0.760 0.296 0.704
#> GSM1299559 2 0.0000 0.882 0.000 1.000
#> GSM1299560 2 0.0000 0.882 0.000 1.000
#> GSM1299576 1 0.4562 0.922 0.904 0.096
#> GSM1299577 1 0.4562 0.922 0.904 0.096
#> GSM1299561 2 0.0000 0.882 0.000 1.000
#> GSM1299562 2 0.8499 0.782 0.276 0.724
#> GSM1299563 1 0.0000 0.926 1.000 0.000
#> GSM1299564 1 0.0000 0.926 1.000 0.000
#> GSM1299565 2 0.8713 0.765 0.292 0.708
#> GSM1299566 1 0.0000 0.926 1.000 0.000
#> GSM1299567 2 0.0000 0.882 0.000 1.000
#> GSM1299568 2 0.8499 0.782 0.276 0.724
#> GSM1299569 1 0.0376 0.924 0.996 0.004
#> GSM1299570 1 0.4562 0.922 0.904 0.096
#> GSM1299571 2 0.4562 0.854 0.096 0.904
#> GSM1299572 2 0.0672 0.879 0.008 0.992
#> GSM1299573 2 0.0000 0.882 0.000 1.000
#> GSM1299574 2 0.5408 0.850 0.124 0.876
#> GSM1299578 1 0.4562 0.922 0.904 0.096
#> GSM1299579 1 0.0000 0.926 1.000 0.000
#> GSM1299580 1 0.4562 0.922 0.904 0.096
#> GSM1299581 1 0.4562 0.922 0.904 0.096
#> GSM1299582 1 0.4562 0.922 0.904 0.096
#> GSM1299583 1 0.4562 0.922 0.904 0.096
#> GSM1299584 1 0.4562 0.922 0.904 0.096
#> GSM1299585 1 0.4562 0.922 0.904 0.096
#> GSM1299586 1 0.4562 0.922 0.904 0.096
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1299517 3 0.0000 0.931 0.000 0.000 1.000
#> GSM1299518 3 0.0237 0.929 0.000 0.004 0.996
#> GSM1299519 2 0.4931 0.731 0.000 0.768 0.232
#> GSM1299520 2 0.5397 0.499 0.280 0.720 0.000
#> GSM1299521 1 0.0000 0.893 1.000 0.000 0.000
#> GSM1299522 2 0.4931 0.731 0.000 0.768 0.232
#> GSM1299523 2 0.5591 0.458 0.304 0.696 0.000
#> GSM1299524 3 0.0237 0.929 0.000 0.004 0.996
#> GSM1299525 2 0.5493 0.737 0.012 0.756 0.232
#> GSM1299526 3 0.0237 0.929 0.000 0.004 0.996
#> GSM1299527 3 0.0000 0.931 0.000 0.000 1.000
#> GSM1299528 2 0.1643 0.728 0.044 0.956 0.000
#> GSM1299529 2 0.4931 0.731 0.000 0.768 0.232
#> GSM1299530 1 0.4504 0.809 0.804 0.196 0.000
#> GSM1299531 2 0.4931 0.731 0.000 0.768 0.232
#> GSM1299575 1 0.0000 0.893 1.000 0.000 0.000
#> GSM1299532 3 0.0237 0.929 0.000 0.004 0.996
#> GSM1299533 3 0.0000 0.931 0.000 0.000 1.000
#> GSM1299534 2 0.2383 0.737 0.044 0.940 0.016
#> GSM1299535 3 0.0000 0.931 0.000 0.000 1.000
#> GSM1299536 2 0.5431 0.493 0.284 0.716 0.000
#> GSM1299537 3 0.0237 0.929 0.000 0.004 0.996
#> GSM1299538 2 0.4291 0.630 0.180 0.820 0.000
#> GSM1299539 2 0.2711 0.708 0.088 0.912 0.000
#> GSM1299540 3 0.0000 0.931 0.000 0.000 1.000
#> GSM1299541 3 0.0237 0.929 0.000 0.004 0.996
#> GSM1299542 3 0.0237 0.929 0.000 0.004 0.996
#> GSM1299543 2 0.5493 0.737 0.012 0.756 0.232
#> GSM1299544 2 0.2152 0.738 0.036 0.948 0.016
#> GSM1299545 3 0.5147 0.691 0.020 0.180 0.800
#> GSM1299546 2 0.4974 0.729 0.000 0.764 0.236
#> GSM1299547 1 0.5905 0.604 0.648 0.352 0.000
#> GSM1299548 3 0.0000 0.931 0.000 0.000 1.000
#> GSM1299549 3 0.5559 0.676 0.028 0.192 0.780
#> GSM1299550 2 0.2625 0.710 0.084 0.916 0.000
#> GSM1299551 2 0.4931 0.731 0.000 0.768 0.232
#> GSM1299552 1 0.4861 0.814 0.808 0.180 0.012
#> GSM1299553 1 0.6183 0.759 0.732 0.236 0.032
#> GSM1299554 3 0.6683 -0.239 0.008 0.492 0.500
#> GSM1299555 3 0.0000 0.931 0.000 0.000 1.000
#> GSM1299556 3 0.0237 0.929 0.000 0.004 0.996
#> GSM1299557 3 0.0000 0.931 0.000 0.000 1.000
#> GSM1299558 2 0.5493 0.737 0.012 0.756 0.232
#> GSM1299559 3 0.0237 0.929 0.000 0.004 0.996
#> GSM1299560 3 0.0000 0.931 0.000 0.000 1.000
#> GSM1299576 1 0.0000 0.893 1.000 0.000 0.000
#> GSM1299577 1 0.5852 0.795 0.776 0.180 0.044
#> GSM1299561 3 0.0000 0.931 0.000 0.000 1.000
#> GSM1299562 3 0.6683 -0.237 0.008 0.492 0.500
#> GSM1299563 2 0.5397 0.499 0.280 0.720 0.000
#> GSM1299564 2 0.5497 0.480 0.292 0.708 0.000
#> GSM1299565 2 0.6361 0.739 0.040 0.728 0.232
#> GSM1299566 2 0.1643 0.728 0.044 0.956 0.000
#> GSM1299567 3 0.0892 0.915 0.000 0.020 0.980
#> GSM1299568 2 0.6361 0.739 0.040 0.728 0.232
#> GSM1299569 2 0.1999 0.737 0.036 0.952 0.012
#> GSM1299570 1 0.6109 0.784 0.760 0.192 0.048
#> GSM1299571 3 0.0237 0.929 0.000 0.004 0.996
#> GSM1299572 3 0.0592 0.924 0.000 0.012 0.988
#> GSM1299573 3 0.0000 0.931 0.000 0.000 1.000
#> GSM1299574 3 0.1289 0.908 0.000 0.032 0.968
#> GSM1299578 1 0.0000 0.893 1.000 0.000 0.000
#> GSM1299579 1 0.5363 0.697 0.724 0.276 0.000
#> GSM1299580 1 0.0000 0.893 1.000 0.000 0.000
#> GSM1299581 1 0.0000 0.893 1.000 0.000 0.000
#> GSM1299582 1 0.0000 0.893 1.000 0.000 0.000
#> GSM1299583 1 0.0000 0.893 1.000 0.000 0.000
#> GSM1299584 1 0.0000 0.893 1.000 0.000 0.000
#> GSM1299585 1 0.0000 0.893 1.000 0.000 0.000
#> GSM1299586 1 0.0000 0.893 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1299517 3 0.0000 0.994 0.000 0.000 1.000 0.000
#> GSM1299518 3 0.0469 0.989 0.000 0.012 0.988 0.000
#> GSM1299519 2 0.1474 0.910 0.000 0.948 0.000 0.052
#> GSM1299520 4 0.0000 0.959 0.000 0.000 0.000 1.000
#> GSM1299521 1 0.0524 0.946 0.988 0.004 0.000 0.008
#> GSM1299522 2 0.1474 0.910 0.000 0.948 0.000 0.052
#> GSM1299523 4 0.1545 0.936 0.008 0.040 0.000 0.952
#> GSM1299524 3 0.0469 0.989 0.000 0.012 0.988 0.000
#> GSM1299525 2 0.1557 0.910 0.000 0.944 0.000 0.056
#> GSM1299526 3 0.0000 0.994 0.000 0.000 1.000 0.000
#> GSM1299527 3 0.0000 0.994 0.000 0.000 1.000 0.000
#> GSM1299528 4 0.1637 0.936 0.000 0.060 0.000 0.940
#> GSM1299529 2 0.1557 0.910 0.000 0.944 0.000 0.056
#> GSM1299530 4 0.3372 0.872 0.096 0.036 0.000 0.868
#> GSM1299531 2 0.1474 0.910 0.000 0.948 0.000 0.052
#> GSM1299575 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM1299532 3 0.0469 0.989 0.000 0.012 0.988 0.000
#> GSM1299533 2 0.3486 0.834 0.000 0.812 0.188 0.000
#> GSM1299534 4 0.2469 0.925 0.000 0.108 0.000 0.892
#> GSM1299535 2 0.3528 0.832 0.000 0.808 0.192 0.000
#> GSM1299536 4 0.0000 0.959 0.000 0.000 0.000 1.000
#> GSM1299537 3 0.0188 0.994 0.000 0.004 0.996 0.000
#> GSM1299538 4 0.0000 0.959 0.000 0.000 0.000 1.000
#> GSM1299539 4 0.0000 0.959 0.000 0.000 0.000 1.000
#> GSM1299540 3 0.0188 0.994 0.000 0.004 0.996 0.000
#> GSM1299541 3 0.0188 0.994 0.000 0.004 0.996 0.000
#> GSM1299542 3 0.0000 0.994 0.000 0.000 1.000 0.000
#> GSM1299543 2 0.1867 0.902 0.000 0.928 0.000 0.072
#> GSM1299544 4 0.1792 0.931 0.000 0.068 0.000 0.932
#> GSM1299545 3 0.1114 0.978 0.004 0.016 0.972 0.008
#> GSM1299546 2 0.1474 0.910 0.000 0.948 0.000 0.052
#> GSM1299547 4 0.0592 0.955 0.000 0.016 0.000 0.984
#> GSM1299548 3 0.0000 0.994 0.000 0.000 1.000 0.000
#> GSM1299549 2 0.3508 0.879 0.004 0.872 0.064 0.060
#> GSM1299550 4 0.0000 0.959 0.000 0.000 0.000 1.000
#> GSM1299551 2 0.1474 0.910 0.000 0.948 0.000 0.052
#> GSM1299552 1 0.3948 0.834 0.840 0.064 0.000 0.096
#> GSM1299553 4 0.2125 0.926 0.004 0.076 0.000 0.920
#> GSM1299554 2 0.3245 0.890 0.000 0.880 0.064 0.056
#> GSM1299555 3 0.0469 0.989 0.000 0.012 0.988 0.000
#> GSM1299556 3 0.0188 0.994 0.000 0.004 0.996 0.000
#> GSM1299557 3 0.0188 0.993 0.000 0.004 0.996 0.000
#> GSM1299558 2 0.1557 0.910 0.000 0.944 0.000 0.056
#> GSM1299559 3 0.0188 0.994 0.000 0.004 0.996 0.000
#> GSM1299560 3 0.0000 0.994 0.000 0.000 1.000 0.000
#> GSM1299576 1 0.0188 0.947 0.996 0.000 0.000 0.004
#> GSM1299577 1 0.6306 0.282 0.544 0.064 0.000 0.392
#> GSM1299561 3 0.0000 0.994 0.000 0.000 1.000 0.000
#> GSM1299562 2 0.3090 0.893 0.000 0.888 0.056 0.056
#> GSM1299563 4 0.0000 0.959 0.000 0.000 0.000 1.000
#> GSM1299564 4 0.0592 0.955 0.000 0.016 0.000 0.984
#> GSM1299565 2 0.1940 0.888 0.000 0.924 0.000 0.076
#> GSM1299566 4 0.1716 0.934 0.000 0.064 0.000 0.936
#> GSM1299567 3 0.0188 0.994 0.000 0.004 0.996 0.000
#> GSM1299568 2 0.1940 0.888 0.000 0.924 0.000 0.076
#> GSM1299569 4 0.1792 0.931 0.000 0.068 0.000 0.932
#> GSM1299570 4 0.2060 0.927 0.016 0.052 0.000 0.932
#> GSM1299571 2 0.3528 0.832 0.000 0.808 0.192 0.000
#> GSM1299572 2 0.3725 0.839 0.000 0.812 0.180 0.008
#> GSM1299573 3 0.0188 0.993 0.000 0.004 0.996 0.000
#> GSM1299574 2 0.3695 0.859 0.000 0.828 0.156 0.016
#> GSM1299578 1 0.0937 0.940 0.976 0.012 0.000 0.012
#> GSM1299579 4 0.0188 0.958 0.004 0.000 0.000 0.996
#> GSM1299580 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM1299581 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM1299582 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM1299583 1 0.0469 0.945 0.988 0.000 0.000 0.012
#> GSM1299584 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM1299585 1 0.0524 0.946 0.988 0.004 0.000 0.008
#> GSM1299586 1 0.0000 0.947 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1299517 3 0.2127 0.886 0.000 0.000 0.892 0.108 0.000
#> GSM1299518 3 0.3437 0.865 0.000 0.048 0.832 0.120 0.000
#> GSM1299519 2 0.0290 0.888 0.000 0.992 0.000 0.008 0.000
#> GSM1299520 5 0.0771 0.923 0.000 0.004 0.000 0.020 0.976
#> GSM1299521 1 0.1331 0.958 0.952 0.000 0.000 0.040 0.008
#> GSM1299522 2 0.0162 0.889 0.000 0.996 0.000 0.004 0.000
#> GSM1299523 5 0.0865 0.922 0.000 0.004 0.000 0.024 0.972
#> GSM1299524 3 0.3507 0.862 0.000 0.052 0.828 0.120 0.000
#> GSM1299525 2 0.1106 0.873 0.000 0.964 0.000 0.024 0.012
#> GSM1299526 3 0.2230 0.884 0.000 0.000 0.884 0.116 0.000
#> GSM1299527 3 0.0000 0.904 0.000 0.000 1.000 0.000 0.000
#> GSM1299528 5 0.1697 0.927 0.000 0.060 0.000 0.008 0.932
#> GSM1299529 2 0.0290 0.888 0.000 0.992 0.000 0.008 0.000
#> GSM1299530 4 0.4609 0.779 0.104 0.000 0.000 0.744 0.152
#> GSM1299531 2 0.0162 0.889 0.000 0.996 0.000 0.004 0.000
#> GSM1299575 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000
#> GSM1299532 3 0.3575 0.861 0.000 0.056 0.824 0.120 0.000
#> GSM1299533 2 0.4457 0.781 0.000 0.760 0.124 0.116 0.000
#> GSM1299534 5 0.2595 0.904 0.000 0.080 0.000 0.032 0.888
#> GSM1299535 2 0.4406 0.781 0.000 0.764 0.128 0.108 0.000
#> GSM1299536 5 0.0579 0.930 0.000 0.008 0.000 0.008 0.984
#> GSM1299537 3 0.1831 0.891 0.000 0.000 0.920 0.076 0.004
#> GSM1299538 5 0.1493 0.931 0.000 0.024 0.000 0.028 0.948
#> GSM1299539 5 0.0898 0.933 0.000 0.020 0.000 0.008 0.972
#> GSM1299540 3 0.1831 0.891 0.000 0.000 0.920 0.076 0.004
#> GSM1299541 3 0.1831 0.891 0.000 0.000 0.920 0.076 0.004
#> GSM1299542 3 0.0162 0.904 0.000 0.000 0.996 0.004 0.000
#> GSM1299543 2 0.1741 0.849 0.000 0.936 0.000 0.024 0.040
#> GSM1299544 5 0.2482 0.908 0.000 0.084 0.000 0.024 0.892
#> GSM1299545 4 0.4238 0.686 0.000 0.056 0.112 0.804 0.028
#> GSM1299546 2 0.0162 0.889 0.000 0.996 0.000 0.004 0.000
#> GSM1299547 4 0.5118 0.387 0.000 0.040 0.000 0.548 0.412
#> GSM1299548 3 0.0000 0.904 0.000 0.000 1.000 0.000 0.000
#> GSM1299549 4 0.3522 0.728 0.000 0.104 0.032 0.844 0.020
#> GSM1299550 5 0.1493 0.931 0.000 0.024 0.000 0.028 0.948
#> GSM1299551 2 0.0162 0.889 0.000 0.996 0.000 0.004 0.000
#> GSM1299552 4 0.4642 0.734 0.168 0.032 0.000 0.760 0.040
#> GSM1299553 4 0.4313 0.778 0.000 0.068 0.000 0.760 0.172
#> GSM1299554 2 0.3759 0.828 0.000 0.812 0.028 0.148 0.012
#> GSM1299555 3 0.3641 0.856 0.000 0.060 0.820 0.120 0.000
#> GSM1299556 3 0.1892 0.889 0.000 0.000 0.916 0.080 0.004
#> GSM1299557 3 0.3214 0.873 0.000 0.036 0.844 0.120 0.000
#> GSM1299558 2 0.1117 0.870 0.000 0.964 0.000 0.020 0.016
#> GSM1299559 3 0.1892 0.889 0.000 0.000 0.916 0.080 0.004
#> GSM1299560 3 0.0290 0.904 0.000 0.000 0.992 0.008 0.000
#> GSM1299576 1 0.0566 0.977 0.984 0.000 0.000 0.012 0.004
#> GSM1299577 4 0.4671 0.785 0.120 0.024 0.000 0.772 0.084
#> GSM1299561 3 0.0162 0.904 0.000 0.000 0.996 0.004 0.000
#> GSM1299562 2 0.3841 0.826 0.000 0.808 0.032 0.148 0.012
#> GSM1299563 5 0.0451 0.931 0.000 0.008 0.000 0.004 0.988
#> GSM1299564 5 0.2378 0.899 0.000 0.048 0.000 0.048 0.904
#> GSM1299565 2 0.1331 0.878 0.000 0.952 0.000 0.008 0.040
#> GSM1299566 5 0.1697 0.927 0.000 0.060 0.000 0.008 0.932
#> GSM1299567 3 0.1892 0.889 0.000 0.000 0.916 0.080 0.004
#> GSM1299568 2 0.3339 0.840 0.000 0.836 0.000 0.124 0.040
#> GSM1299569 5 0.2482 0.908 0.000 0.084 0.000 0.024 0.892
#> GSM1299570 4 0.4672 0.785 0.028 0.040 0.000 0.752 0.180
#> GSM1299571 2 0.2536 0.840 0.000 0.868 0.128 0.004 0.000
#> GSM1299572 2 0.4557 0.788 0.000 0.760 0.104 0.132 0.004
#> GSM1299573 3 0.3051 0.875 0.000 0.028 0.852 0.120 0.000
#> GSM1299574 2 0.1965 0.859 0.000 0.904 0.096 0.000 0.000
#> GSM1299578 1 0.2171 0.926 0.912 0.000 0.000 0.064 0.024
#> GSM1299579 5 0.2970 0.758 0.000 0.004 0.000 0.168 0.828
#> GSM1299580 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000
#> GSM1299581 1 0.0162 0.980 0.996 0.000 0.000 0.000 0.004
#> GSM1299582 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000
#> GSM1299583 1 0.0451 0.978 0.988 0.000 0.000 0.004 0.008
#> GSM1299584 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000
#> GSM1299585 1 0.0992 0.969 0.968 0.000 0.000 0.024 0.008
#> GSM1299586 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1299517 6 0.3240 0.7153 0.000 0.000 0.244 0.004 0.000 0.752
#> GSM1299518 6 0.1663 0.8889 0.000 0.000 0.088 0.000 0.000 0.912
#> GSM1299519 2 0.0260 0.9643 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM1299520 5 0.0713 0.9334 0.000 0.000 0.000 0.000 0.972 0.028
#> GSM1299521 1 0.4097 0.0792 0.500 0.000 0.000 0.492 0.000 0.008
#> GSM1299522 2 0.0000 0.9651 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299523 5 0.2340 0.9030 0.000 0.000 0.004 0.056 0.896 0.044
#> GSM1299524 6 0.1610 0.8897 0.000 0.000 0.084 0.000 0.000 0.916
#> GSM1299525 2 0.1003 0.9525 0.000 0.964 0.000 0.016 0.020 0.000
#> GSM1299526 6 0.2006 0.8799 0.000 0.000 0.104 0.004 0.000 0.892
#> GSM1299527 3 0.2053 0.9321 0.000 0.000 0.888 0.004 0.000 0.108
#> GSM1299528 5 0.1801 0.9287 0.000 0.056 0.000 0.004 0.924 0.016
#> GSM1299529 2 0.0291 0.9649 0.000 0.992 0.000 0.000 0.004 0.004
#> GSM1299530 4 0.1049 0.8923 0.032 0.000 0.000 0.960 0.000 0.008
#> GSM1299531 2 0.0000 0.9651 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1299575 1 0.0000 0.9282 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299532 6 0.1866 0.8900 0.000 0.008 0.084 0.000 0.000 0.908
#> GSM1299533 6 0.3366 0.8591 0.000 0.044 0.052 0.060 0.000 0.844
#> GSM1299534 5 0.2933 0.8763 0.000 0.128 0.000 0.016 0.844 0.012
#> GSM1299535 6 0.2687 0.8812 0.000 0.044 0.072 0.008 0.000 0.876
#> GSM1299536 5 0.0363 0.9352 0.000 0.000 0.000 0.000 0.988 0.012
#> GSM1299537 3 0.0632 0.9477 0.000 0.000 0.976 0.000 0.000 0.024
#> GSM1299538 5 0.1167 0.9366 0.000 0.008 0.000 0.020 0.960 0.012
#> GSM1299539 5 0.0964 0.9362 0.000 0.012 0.000 0.004 0.968 0.016
#> GSM1299540 3 0.0632 0.9474 0.000 0.000 0.976 0.000 0.000 0.024
#> GSM1299541 3 0.0547 0.9468 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM1299542 3 0.1501 0.9437 0.000 0.000 0.924 0.000 0.000 0.076
#> GSM1299543 2 0.1594 0.9215 0.000 0.932 0.000 0.016 0.052 0.000
#> GSM1299544 5 0.2405 0.9053 0.000 0.100 0.000 0.016 0.880 0.004
#> GSM1299545 4 0.4383 0.6975 0.000 0.004 0.040 0.736 0.024 0.196
#> GSM1299546 2 0.0363 0.9638 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM1299547 5 0.2631 0.8644 0.000 0.004 0.000 0.128 0.856 0.012
#> GSM1299548 3 0.2006 0.9361 0.000 0.000 0.892 0.004 0.000 0.104
#> GSM1299549 4 0.2907 0.8357 0.000 0.028 0.008 0.860 0.004 0.100
#> GSM1299550 5 0.1065 0.9368 0.000 0.008 0.000 0.020 0.964 0.008
#> GSM1299551 2 0.0146 0.9648 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM1299552 4 0.0632 0.8961 0.024 0.000 0.000 0.976 0.000 0.000
#> GSM1299553 4 0.1672 0.8859 0.000 0.004 0.000 0.932 0.048 0.016
#> GSM1299554 6 0.3479 0.8200 0.000 0.104 0.012 0.040 0.012 0.832
#> GSM1299555 6 0.1610 0.8897 0.000 0.000 0.084 0.000 0.000 0.916
#> GSM1299556 3 0.0632 0.9474 0.000 0.000 0.976 0.000 0.000 0.024
#> GSM1299557 6 0.1610 0.8897 0.000 0.000 0.084 0.000 0.000 0.916
#> GSM1299558 2 0.0820 0.9553 0.000 0.972 0.000 0.016 0.012 0.000
#> GSM1299559 3 0.0547 0.9465 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM1299560 3 0.2278 0.9156 0.000 0.000 0.868 0.004 0.000 0.128
#> GSM1299576 1 0.0458 0.9241 0.984 0.000 0.000 0.016 0.000 0.000
#> GSM1299577 4 0.0777 0.8970 0.024 0.000 0.000 0.972 0.004 0.000
#> GSM1299561 3 0.1958 0.9367 0.000 0.000 0.896 0.004 0.000 0.100
#> GSM1299562 6 0.3410 0.8221 0.000 0.104 0.012 0.036 0.012 0.836
#> GSM1299563 5 0.0363 0.9352 0.000 0.000 0.000 0.000 0.988 0.012
#> GSM1299564 5 0.1225 0.9323 0.000 0.000 0.000 0.036 0.952 0.012
#> GSM1299565 2 0.1138 0.9497 0.000 0.960 0.000 0.004 0.024 0.012
#> GSM1299566 5 0.1829 0.9259 0.000 0.064 0.000 0.004 0.920 0.012
#> GSM1299567 3 0.0508 0.9408 0.004 0.000 0.984 0.000 0.000 0.012
#> GSM1299568 6 0.3650 0.7217 0.000 0.216 0.000 0.004 0.024 0.756
#> GSM1299569 5 0.2306 0.9082 0.000 0.092 0.000 0.016 0.888 0.004
#> GSM1299570 4 0.1578 0.8861 0.000 0.004 0.000 0.936 0.048 0.012
#> GSM1299571 6 0.4737 0.6768 0.000 0.256 0.072 0.008 0.000 0.664
#> GSM1299572 6 0.3397 0.8449 0.000 0.044 0.032 0.076 0.004 0.844
#> GSM1299573 6 0.1863 0.8817 0.000 0.000 0.104 0.000 0.000 0.896
#> GSM1299574 2 0.2263 0.8522 0.000 0.896 0.056 0.000 0.000 0.048
#> GSM1299578 1 0.2697 0.8467 0.872 0.000 0.004 0.092 0.004 0.028
#> GSM1299579 5 0.1867 0.9239 0.000 0.000 0.000 0.020 0.916 0.064
#> GSM1299580 1 0.0000 0.9282 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299581 1 0.0260 0.9274 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM1299582 1 0.0000 0.9282 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299583 1 0.0260 0.9274 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM1299584 1 0.0000 0.9282 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1299585 1 0.1327 0.8969 0.936 0.000 0.000 0.064 0.000 0.000
#> GSM1299586 1 0.0000 0.9282 1.000 0.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:mclust 69 0.2299 2
#> ATC:mclust 63 0.1034 3
#> ATC:mclust 69 0.1415 4
#> ATC:mclust 69 0.0949 5
#> ATC:mclust 69 0.0350 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "NMF"]
# you can also extract it by
# res = res_list["ATC:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 70 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.972 0.989 0.4937 0.503 0.503
#> 3 3 1.000 0.943 0.978 0.3598 0.740 0.522
#> 4 4 0.961 0.939 0.972 0.1282 0.833 0.545
#> 5 5 0.793 0.797 0.876 0.0521 0.913 0.673
#> 6 6 0.762 0.569 0.786 0.0421 0.947 0.765
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM1299517 1 0.0000 1.000 1.000 0.000
#> GSM1299518 1 0.0000 1.000 1.000 0.000
#> GSM1299519 2 0.0000 0.973 0.000 1.000
#> GSM1299520 2 0.0000 0.973 0.000 1.000
#> GSM1299521 2 0.9491 0.435 0.368 0.632
#> GSM1299522 2 0.0000 0.973 0.000 1.000
#> GSM1299523 2 0.9686 0.366 0.396 0.604
#> GSM1299524 1 0.0000 1.000 1.000 0.000
#> GSM1299525 2 0.0000 0.973 0.000 1.000
#> GSM1299526 1 0.0000 1.000 1.000 0.000
#> GSM1299527 1 0.0000 1.000 1.000 0.000
#> GSM1299528 2 0.0000 0.973 0.000 1.000
#> GSM1299529 2 0.0000 0.973 0.000 1.000
#> GSM1299530 1 0.0000 1.000 1.000 0.000
#> GSM1299531 2 0.0000 0.973 0.000 1.000
#> GSM1299575 1 0.0000 1.000 1.000 0.000
#> GSM1299532 1 0.0000 1.000 1.000 0.000
#> GSM1299533 1 0.0000 1.000 1.000 0.000
#> GSM1299534 2 0.0000 0.973 0.000 1.000
#> GSM1299535 1 0.0000 1.000 1.000 0.000
#> GSM1299536 2 0.0000 0.973 0.000 1.000
#> GSM1299537 1 0.0000 1.000 1.000 0.000
#> GSM1299538 2 0.0000 0.973 0.000 1.000
#> GSM1299539 2 0.0000 0.973 0.000 1.000
#> GSM1299540 1 0.0000 1.000 1.000 0.000
#> GSM1299541 1 0.0000 1.000 1.000 0.000
#> GSM1299542 1 0.0000 1.000 1.000 0.000
#> GSM1299543 2 0.0000 0.973 0.000 1.000
#> GSM1299544 2 0.0000 0.973 0.000 1.000
#> GSM1299545 1 0.0000 1.000 1.000 0.000
#> GSM1299546 2 0.0000 0.973 0.000 1.000
#> GSM1299547 2 0.0000 0.973 0.000 1.000
#> GSM1299548 1 0.0000 1.000 1.000 0.000
#> GSM1299549 1 0.0000 1.000 1.000 0.000
#> GSM1299550 2 0.0000 0.973 0.000 1.000
#> GSM1299551 2 0.0000 0.973 0.000 1.000
#> GSM1299552 1 0.0000 1.000 1.000 0.000
#> GSM1299553 1 0.0938 0.987 0.988 0.012
#> GSM1299554 2 0.0000 0.973 0.000 1.000
#> GSM1299555 1 0.0000 1.000 1.000 0.000
#> GSM1299556 1 0.0000 1.000 1.000 0.000
#> GSM1299557 1 0.0000 1.000 1.000 0.000
#> GSM1299558 2 0.0000 0.973 0.000 1.000
#> GSM1299559 1 0.0000 1.000 1.000 0.000
#> GSM1299560 1 0.0000 1.000 1.000 0.000
#> GSM1299576 1 0.0000 1.000 1.000 0.000
#> GSM1299577 1 0.0000 1.000 1.000 0.000
#> GSM1299561 1 0.0000 1.000 1.000 0.000
#> GSM1299562 2 0.0000 0.973 0.000 1.000
#> GSM1299563 2 0.0000 0.973 0.000 1.000
#> GSM1299564 2 0.0000 0.973 0.000 1.000
#> GSM1299565 2 0.0000 0.973 0.000 1.000
#> GSM1299566 2 0.0000 0.973 0.000 1.000
#> GSM1299567 1 0.0000 1.000 1.000 0.000
#> GSM1299568 2 0.0000 0.973 0.000 1.000
#> GSM1299569 2 0.0000 0.973 0.000 1.000
#> GSM1299570 1 0.0000 1.000 1.000 0.000
#> GSM1299571 1 0.0000 1.000 1.000 0.000
#> GSM1299572 1 0.0000 1.000 1.000 0.000
#> GSM1299573 1 0.0000 1.000 1.000 0.000
#> GSM1299574 2 0.0000 0.973 0.000 1.000
#> GSM1299578 1 0.0000 1.000 1.000 0.000
#> GSM1299579 2 0.0000 0.973 0.000 1.000
#> GSM1299580 1 0.0000 1.000 1.000 0.000
#> GSM1299581 1 0.0000 1.000 1.000 0.000
#> GSM1299582 1 0.0000 1.000 1.000 0.000
#> GSM1299583 1 0.0000 1.000 1.000 0.000
#> GSM1299584 1 0.0000 1.000 1.000 0.000
#> GSM1299585 1 0.0000 1.000 1.000 0.000
#> GSM1299586 1 0.0000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1299517 3 0.0000 0.952 0.000 0.000 1.000
#> GSM1299518 3 0.0000 0.952 0.000 0.000 1.000
#> GSM1299519 3 0.6168 0.347 0.000 0.412 0.588
#> GSM1299520 2 0.0000 0.999 0.000 1.000 0.000
#> GSM1299521 1 0.0000 0.975 1.000 0.000 0.000
#> GSM1299522 2 0.0000 0.999 0.000 1.000 0.000
#> GSM1299523 1 0.0000 0.975 1.000 0.000 0.000
#> GSM1299524 3 0.0000 0.952 0.000 0.000 1.000
#> GSM1299525 2 0.0000 0.999 0.000 1.000 0.000
#> GSM1299526 3 0.0000 0.952 0.000 0.000 1.000
#> GSM1299527 3 0.0000 0.952 0.000 0.000 1.000
#> GSM1299528 2 0.0000 0.999 0.000 1.000 0.000
#> GSM1299529 2 0.0000 0.999 0.000 1.000 0.000
#> GSM1299530 1 0.0000 0.975 1.000 0.000 0.000
#> GSM1299531 2 0.0000 0.999 0.000 1.000 0.000
#> GSM1299575 1 0.0000 0.975 1.000 0.000 0.000
#> GSM1299532 3 0.0000 0.952 0.000 0.000 1.000
#> GSM1299533 3 0.0000 0.952 0.000 0.000 1.000
#> GSM1299534 2 0.0000 0.999 0.000 1.000 0.000
#> GSM1299535 3 0.0000 0.952 0.000 0.000 1.000
#> GSM1299536 2 0.0000 0.999 0.000 1.000 0.000
#> GSM1299537 3 0.0000 0.952 0.000 0.000 1.000
#> GSM1299538 2 0.0000 0.999 0.000 1.000 0.000
#> GSM1299539 2 0.0000 0.999 0.000 1.000 0.000
#> GSM1299540 3 0.0000 0.952 0.000 0.000 1.000
#> GSM1299541 3 0.0000 0.952 0.000 0.000 1.000
#> GSM1299542 3 0.0000 0.952 0.000 0.000 1.000
#> GSM1299543 2 0.0000 0.999 0.000 1.000 0.000
#> GSM1299544 2 0.0000 0.999 0.000 1.000 0.000
#> GSM1299545 1 0.0000 0.975 1.000 0.000 0.000
#> GSM1299546 2 0.0000 0.999 0.000 1.000 0.000
#> GSM1299547 2 0.0000 0.999 0.000 1.000 0.000
#> GSM1299548 3 0.0000 0.952 0.000 0.000 1.000
#> GSM1299549 1 0.0000 0.975 1.000 0.000 0.000
#> GSM1299550 2 0.0000 0.999 0.000 1.000 0.000
#> GSM1299551 2 0.0000 0.999 0.000 1.000 0.000
#> GSM1299552 1 0.0000 0.975 1.000 0.000 0.000
#> GSM1299553 1 0.0000 0.975 1.000 0.000 0.000
#> GSM1299554 2 0.0000 0.999 0.000 1.000 0.000
#> GSM1299555 3 0.0000 0.952 0.000 0.000 1.000
#> GSM1299556 3 0.0000 0.952 0.000 0.000 1.000
#> GSM1299557 3 0.0000 0.952 0.000 0.000 1.000
#> GSM1299558 2 0.0000 0.999 0.000 1.000 0.000
#> GSM1299559 3 0.0000 0.952 0.000 0.000 1.000
#> GSM1299560 3 0.0000 0.952 0.000 0.000 1.000
#> GSM1299576 1 0.0000 0.975 1.000 0.000 0.000
#> GSM1299577 1 0.0000 0.975 1.000 0.000 0.000
#> GSM1299561 3 0.0000 0.952 0.000 0.000 1.000
#> GSM1299562 3 0.5254 0.654 0.000 0.264 0.736
#> GSM1299563 2 0.0000 0.999 0.000 1.000 0.000
#> GSM1299564 2 0.0000 0.999 0.000 1.000 0.000
#> GSM1299565 2 0.0592 0.987 0.000 0.988 0.012
#> GSM1299566 2 0.0000 0.999 0.000 1.000 0.000
#> GSM1299567 1 0.6286 0.147 0.536 0.000 0.464
#> GSM1299568 2 0.0000 0.999 0.000 1.000 0.000
#> GSM1299569 2 0.0000 0.999 0.000 1.000 0.000
#> GSM1299570 1 0.0000 0.975 1.000 0.000 0.000
#> GSM1299571 3 0.0000 0.952 0.000 0.000 1.000
#> GSM1299572 3 0.0424 0.945 0.008 0.000 0.992
#> GSM1299573 3 0.0000 0.952 0.000 0.000 1.000
#> GSM1299574 3 0.5988 0.454 0.000 0.368 0.632
#> GSM1299578 1 0.0000 0.975 1.000 0.000 0.000
#> GSM1299579 2 0.0000 0.999 0.000 1.000 0.000
#> GSM1299580 1 0.0000 0.975 1.000 0.000 0.000
#> GSM1299581 1 0.0000 0.975 1.000 0.000 0.000
#> GSM1299582 1 0.0000 0.975 1.000 0.000 0.000
#> GSM1299583 1 0.0000 0.975 1.000 0.000 0.000
#> GSM1299584 1 0.0000 0.975 1.000 0.000 0.000
#> GSM1299585 1 0.0000 0.975 1.000 0.000 0.000
#> GSM1299586 1 0.0000 0.975 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1299517 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1299518 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1299519 2 0.0000 0.902 0.000 1.000 0.000 0.000
#> GSM1299520 4 0.0000 0.968 0.000 0.000 0.000 1.000
#> GSM1299521 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM1299522 2 0.0000 0.902 0.000 1.000 0.000 0.000
#> GSM1299523 4 0.1557 0.917 0.056 0.000 0.000 0.944
#> GSM1299524 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1299525 4 0.4304 0.610 0.000 0.284 0.000 0.716
#> GSM1299526 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1299527 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1299528 4 0.0000 0.968 0.000 0.000 0.000 1.000
#> GSM1299529 2 0.0921 0.889 0.000 0.972 0.000 0.028
#> GSM1299530 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM1299531 2 0.0000 0.902 0.000 1.000 0.000 0.000
#> GSM1299575 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM1299532 3 0.0188 0.996 0.000 0.004 0.996 0.000
#> GSM1299533 2 0.4961 0.260 0.000 0.552 0.448 0.000
#> GSM1299534 4 0.0000 0.968 0.000 0.000 0.000 1.000
#> GSM1299535 2 0.3024 0.804 0.000 0.852 0.148 0.000
#> GSM1299536 4 0.0000 0.968 0.000 0.000 0.000 1.000
#> GSM1299537 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1299538 4 0.0000 0.968 0.000 0.000 0.000 1.000
#> GSM1299539 4 0.0000 0.968 0.000 0.000 0.000 1.000
#> GSM1299540 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1299541 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1299542 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1299543 2 0.3123 0.764 0.000 0.844 0.000 0.156
#> GSM1299544 4 0.0000 0.968 0.000 0.000 0.000 1.000
#> GSM1299545 1 0.1302 0.948 0.956 0.000 0.044 0.000
#> GSM1299546 2 0.0000 0.902 0.000 1.000 0.000 0.000
#> GSM1299547 4 0.0000 0.968 0.000 0.000 0.000 1.000
#> GSM1299548 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1299549 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM1299550 4 0.0000 0.968 0.000 0.000 0.000 1.000
#> GSM1299551 2 0.0000 0.902 0.000 1.000 0.000 0.000
#> GSM1299552 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM1299553 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM1299554 4 0.3024 0.826 0.000 0.148 0.000 0.852
#> GSM1299555 3 0.0188 0.996 0.000 0.004 0.996 0.000
#> GSM1299556 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1299557 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1299558 2 0.1022 0.886 0.000 0.968 0.000 0.032
#> GSM1299559 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1299560 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1299576 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM1299577 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM1299561 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1299562 2 0.0000 0.902 0.000 1.000 0.000 0.000
#> GSM1299563 4 0.0000 0.968 0.000 0.000 0.000 1.000
#> GSM1299564 4 0.0000 0.968 0.000 0.000 0.000 1.000
#> GSM1299565 2 0.0000 0.902 0.000 1.000 0.000 0.000
#> GSM1299566 4 0.0000 0.968 0.000 0.000 0.000 1.000
#> GSM1299567 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1299568 2 0.0336 0.899 0.000 0.992 0.000 0.008
#> GSM1299569 4 0.0000 0.968 0.000 0.000 0.000 1.000
#> GSM1299570 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM1299571 2 0.3486 0.761 0.000 0.812 0.188 0.000
#> GSM1299572 2 0.6052 0.485 0.320 0.616 0.064 0.000
#> GSM1299573 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1299574 2 0.0000 0.902 0.000 1.000 0.000 0.000
#> GSM1299578 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM1299579 4 0.0000 0.968 0.000 0.000 0.000 1.000
#> GSM1299580 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM1299581 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM1299582 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM1299583 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM1299584 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM1299585 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM1299586 1 0.0000 0.997 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1299517 3 0.1121 0.8858 0.000 0.000 0.956 0.044 0.000
#> GSM1299518 3 0.2871 0.8612 0.000 0.040 0.872 0.088 0.000
#> GSM1299519 2 0.0162 0.7923 0.000 0.996 0.000 0.000 0.004
#> GSM1299520 4 0.3452 0.8610 0.000 0.000 0.000 0.756 0.244
#> GSM1299521 1 0.2605 0.8405 0.852 0.000 0.000 0.148 0.000
#> GSM1299522 2 0.1851 0.7806 0.000 0.912 0.000 0.000 0.088
#> GSM1299523 4 0.3300 0.8581 0.004 0.000 0.000 0.792 0.204
#> GSM1299524 3 0.2535 0.8697 0.000 0.032 0.892 0.076 0.000
#> GSM1299525 5 0.3242 0.6949 0.000 0.216 0.000 0.000 0.784
#> GSM1299526 3 0.1579 0.8814 0.000 0.032 0.944 0.024 0.000
#> GSM1299527 3 0.1892 0.8791 0.000 0.004 0.916 0.080 0.000
#> GSM1299528 5 0.0290 0.8140 0.000 0.000 0.000 0.008 0.992
#> GSM1299529 2 0.4278 -0.0045 0.000 0.548 0.000 0.000 0.452
#> GSM1299530 4 0.3366 0.6395 0.232 0.000 0.000 0.768 0.000
#> GSM1299531 2 0.2011 0.7801 0.000 0.908 0.000 0.004 0.088
#> GSM1299575 1 0.1341 0.9407 0.944 0.000 0.000 0.056 0.000
#> GSM1299532 3 0.4953 0.6547 0.000 0.216 0.696 0.088 0.000
#> GSM1299533 2 0.4503 0.5139 0.000 0.664 0.312 0.024 0.000
#> GSM1299534 5 0.1357 0.8064 0.000 0.004 0.000 0.048 0.948
#> GSM1299535 2 0.3012 0.7384 0.000 0.852 0.124 0.024 0.000
#> GSM1299536 5 0.1478 0.7838 0.000 0.000 0.000 0.064 0.936
#> GSM1299537 3 0.0963 0.8864 0.000 0.000 0.964 0.036 0.000
#> GSM1299538 5 0.2074 0.7448 0.000 0.000 0.000 0.104 0.896
#> GSM1299539 5 0.1341 0.7905 0.000 0.000 0.000 0.056 0.944
#> GSM1299540 3 0.1197 0.8851 0.000 0.000 0.952 0.048 0.000
#> GSM1299541 3 0.1270 0.8853 0.000 0.000 0.948 0.052 0.000
#> GSM1299542 3 0.1197 0.8859 0.000 0.000 0.952 0.048 0.000
#> GSM1299543 5 0.3707 0.6071 0.000 0.284 0.000 0.000 0.716
#> GSM1299544 5 0.0794 0.8144 0.000 0.028 0.000 0.000 0.972
#> GSM1299545 3 0.6362 0.2265 0.368 0.000 0.464 0.168 0.000
#> GSM1299546 2 0.1121 0.7932 0.000 0.956 0.000 0.000 0.044
#> GSM1299547 4 0.3519 0.8639 0.008 0.000 0.000 0.776 0.216
#> GSM1299548 3 0.1544 0.8790 0.000 0.000 0.932 0.068 0.000
#> GSM1299549 1 0.0609 0.9511 0.980 0.000 0.000 0.020 0.000
#> GSM1299550 5 0.1121 0.7984 0.000 0.000 0.000 0.044 0.956
#> GSM1299551 2 0.1608 0.7875 0.000 0.928 0.000 0.000 0.072
#> GSM1299552 1 0.1043 0.9432 0.960 0.000 0.000 0.040 0.000
#> GSM1299553 4 0.3622 0.7713 0.136 0.000 0.000 0.816 0.048
#> GSM1299554 5 0.3248 0.7723 0.000 0.048 0.040 0.040 0.872
#> GSM1299555 3 0.3631 0.8324 0.000 0.072 0.824 0.104 0.000
#> GSM1299556 3 0.1792 0.8724 0.000 0.000 0.916 0.084 0.000
#> GSM1299557 3 0.1608 0.8790 0.000 0.000 0.928 0.072 0.000
#> GSM1299558 5 0.4150 0.4185 0.000 0.388 0.000 0.000 0.612
#> GSM1299559 3 0.1851 0.8704 0.000 0.000 0.912 0.088 0.000
#> GSM1299560 3 0.2331 0.8732 0.000 0.020 0.900 0.080 0.000
#> GSM1299576 1 0.0162 0.9540 0.996 0.000 0.000 0.004 0.000
#> GSM1299577 1 0.2074 0.9031 0.896 0.000 0.000 0.104 0.000
#> GSM1299561 3 0.1410 0.8852 0.000 0.000 0.940 0.060 0.000
#> GSM1299562 2 0.4713 0.5694 0.000 0.676 0.044 0.280 0.000
#> GSM1299563 4 0.3586 0.8405 0.000 0.000 0.000 0.736 0.264
#> GSM1299564 4 0.3452 0.8610 0.000 0.000 0.000 0.756 0.244
#> GSM1299565 2 0.1908 0.7779 0.000 0.908 0.000 0.000 0.092
#> GSM1299566 5 0.0000 0.8158 0.000 0.000 0.000 0.000 1.000
#> GSM1299567 3 0.3055 0.8334 0.016 0.000 0.840 0.144 0.000
#> GSM1299568 5 0.4313 0.4784 0.000 0.356 0.008 0.000 0.636
#> GSM1299569 5 0.0290 0.8165 0.000 0.008 0.000 0.000 0.992
#> GSM1299570 1 0.2424 0.8926 0.868 0.000 0.000 0.132 0.000
#> GSM1299571 2 0.3012 0.7397 0.000 0.852 0.124 0.024 0.000
#> GSM1299572 2 0.6010 0.5504 0.012 0.624 0.176 0.188 0.000
#> GSM1299573 3 0.1792 0.8804 0.000 0.000 0.916 0.084 0.000
#> GSM1299574 2 0.0290 0.7931 0.000 0.992 0.000 0.000 0.008
#> GSM1299578 1 0.0000 0.9540 1.000 0.000 0.000 0.000 0.000
#> GSM1299579 5 0.2471 0.7056 0.000 0.000 0.000 0.136 0.864
#> GSM1299580 1 0.1851 0.9188 0.912 0.000 0.000 0.088 0.000
#> GSM1299581 1 0.0290 0.9536 0.992 0.000 0.000 0.008 0.000
#> GSM1299582 1 0.0404 0.9533 0.988 0.000 0.000 0.012 0.000
#> GSM1299583 1 0.0162 0.9538 0.996 0.000 0.000 0.004 0.000
#> GSM1299584 1 0.1270 0.9418 0.948 0.000 0.000 0.052 0.000
#> GSM1299585 1 0.0290 0.9537 0.992 0.000 0.000 0.008 0.000
#> GSM1299586 1 0.0794 0.9494 0.972 0.000 0.000 0.028 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1299517 3 0.2165 0.5343 0.000 0.000 0.884 0.008 0.000 0.108
#> GSM1299518 3 0.4076 0.2236 0.000 0.008 0.540 0.000 0.000 0.452
#> GSM1299519 2 0.0790 0.7145 0.000 0.968 0.000 0.000 0.000 0.032
#> GSM1299520 4 0.1196 0.9644 0.000 0.000 0.000 0.952 0.040 0.008
#> GSM1299521 1 0.3110 0.7488 0.848 0.000 0.000 0.072 0.008 0.072
#> GSM1299522 2 0.0692 0.7257 0.000 0.976 0.000 0.000 0.020 0.004
#> GSM1299523 4 0.1036 0.9639 0.004 0.000 0.000 0.964 0.024 0.008
#> GSM1299524 3 0.3923 0.2829 0.000 0.000 0.580 0.004 0.000 0.416
#> GSM1299525 2 0.3975 0.0649 0.000 0.544 0.000 0.000 0.452 0.004
#> GSM1299526 3 0.3710 0.3989 0.000 0.000 0.696 0.012 0.000 0.292
#> GSM1299527 3 0.3659 0.3760 0.000 0.000 0.636 0.000 0.000 0.364
#> GSM1299528 5 0.0260 0.8082 0.000 0.008 0.000 0.000 0.992 0.000
#> GSM1299529 2 0.3076 0.5441 0.000 0.760 0.000 0.000 0.240 0.000
#> GSM1299530 4 0.1176 0.9453 0.024 0.000 0.000 0.956 0.000 0.020
#> GSM1299531 2 0.1578 0.7131 0.000 0.936 0.000 0.012 0.048 0.004
#> GSM1299575 1 0.3819 0.7440 0.652 0.000 0.000 0.008 0.000 0.340
#> GSM1299532 3 0.5033 0.0522 0.000 0.072 0.476 0.000 0.000 0.452
#> GSM1299533 3 0.6555 -0.0865 0.016 0.208 0.432 0.012 0.000 0.332
#> GSM1299534 5 0.5360 0.6362 0.000 0.144 0.000 0.080 0.684 0.092
#> GSM1299535 2 0.5973 -0.0547 0.000 0.476 0.164 0.012 0.000 0.348
#> GSM1299536 5 0.1498 0.7940 0.000 0.000 0.000 0.028 0.940 0.032
#> GSM1299537 3 0.0547 0.5462 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM1299538 5 0.2527 0.7542 0.000 0.000 0.000 0.108 0.868 0.024
#> GSM1299539 5 0.0820 0.8042 0.000 0.000 0.000 0.016 0.972 0.012
#> GSM1299540 3 0.1663 0.5091 0.000 0.000 0.912 0.000 0.000 0.088
#> GSM1299541 3 0.0632 0.5407 0.000 0.000 0.976 0.000 0.000 0.024
#> GSM1299542 3 0.3151 0.4720 0.000 0.000 0.748 0.000 0.000 0.252
#> GSM1299543 5 0.3868 -0.0423 0.000 0.496 0.000 0.000 0.504 0.000
#> GSM1299544 5 0.1007 0.7965 0.000 0.044 0.000 0.000 0.956 0.000
#> GSM1299545 6 0.6805 -0.0372 0.116 0.000 0.376 0.104 0.000 0.404
#> GSM1299546 2 0.0146 0.7265 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM1299547 4 0.0632 0.9653 0.000 0.000 0.000 0.976 0.024 0.000
#> GSM1299548 3 0.0937 0.5306 0.000 0.000 0.960 0.000 0.000 0.040
#> GSM1299549 1 0.2526 0.7660 0.876 0.000 0.004 0.024 0.000 0.096
#> GSM1299550 5 0.0146 0.8081 0.000 0.000 0.000 0.004 0.996 0.000
#> GSM1299551 2 0.0777 0.7260 0.000 0.972 0.000 0.000 0.024 0.004
#> GSM1299552 1 0.2436 0.7724 0.880 0.000 0.000 0.032 0.000 0.088
#> GSM1299553 4 0.1563 0.9208 0.012 0.000 0.000 0.932 0.000 0.056
#> GSM1299554 5 0.6584 0.4712 0.020 0.048 0.092 0.016 0.568 0.256
#> GSM1299555 6 0.5017 -0.3375 0.000 0.044 0.460 0.012 0.000 0.484
#> GSM1299556 3 0.1714 0.4950 0.000 0.000 0.908 0.000 0.000 0.092
#> GSM1299557 3 0.2513 0.4593 0.000 0.000 0.852 0.008 0.000 0.140
#> GSM1299558 2 0.3789 0.1869 0.000 0.584 0.000 0.000 0.416 0.000
#> GSM1299559 3 0.1863 0.4825 0.000 0.000 0.896 0.000 0.000 0.104
#> GSM1299560 3 0.3765 0.3130 0.000 0.000 0.596 0.000 0.000 0.404
#> GSM1299576 1 0.2178 0.8237 0.868 0.000 0.000 0.000 0.000 0.132
#> GSM1299577 1 0.4234 0.7735 0.676 0.000 0.000 0.044 0.000 0.280
#> GSM1299561 3 0.2996 0.4791 0.000 0.000 0.772 0.000 0.000 0.228
#> GSM1299562 2 0.5530 0.1882 0.000 0.496 0.000 0.364 0.000 0.140
#> GSM1299563 4 0.1075 0.9617 0.000 0.000 0.000 0.952 0.048 0.000
#> GSM1299564 4 0.1007 0.9642 0.000 0.000 0.000 0.956 0.044 0.000
#> GSM1299565 2 0.1794 0.7239 0.000 0.924 0.000 0.000 0.040 0.036
#> GSM1299566 5 0.0260 0.8082 0.000 0.008 0.000 0.000 0.992 0.000
#> GSM1299567 3 0.4179 0.0945 0.016 0.000 0.652 0.008 0.000 0.324
#> GSM1299568 5 0.5537 0.4990 0.000 0.192 0.016 0.000 0.612 0.180
#> GSM1299569 5 0.0858 0.8034 0.000 0.028 0.000 0.000 0.968 0.004
#> GSM1299570 1 0.6095 0.5922 0.476 0.000 0.016 0.148 0.004 0.356
#> GSM1299571 2 0.5789 0.0783 0.000 0.520 0.144 0.012 0.000 0.324
#> GSM1299572 6 0.7479 0.0755 0.124 0.112 0.232 0.048 0.000 0.484
#> GSM1299573 3 0.3390 0.4341 0.000 0.000 0.704 0.000 0.000 0.296
#> GSM1299574 2 0.0790 0.7158 0.000 0.968 0.000 0.000 0.000 0.032
#> GSM1299578 1 0.1007 0.8120 0.956 0.000 0.000 0.000 0.000 0.044
#> GSM1299579 5 0.4218 0.6881 0.064 0.000 0.000 0.108 0.780 0.048
#> GSM1299580 1 0.4101 0.7274 0.632 0.000 0.008 0.008 0.000 0.352
#> GSM1299581 1 0.1908 0.8245 0.900 0.000 0.000 0.004 0.000 0.096
#> GSM1299582 1 0.2706 0.8210 0.832 0.000 0.000 0.008 0.000 0.160
#> GSM1299583 1 0.0547 0.8054 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM1299584 1 0.3690 0.7645 0.684 0.000 0.000 0.008 0.000 0.308
#> GSM1299585 1 0.0972 0.8004 0.964 0.000 0.000 0.008 0.000 0.028
#> GSM1299586 1 0.2703 0.8195 0.824 0.000 0.000 0.004 0.000 0.172
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:NMF 68 0.7529 2
#> ATC:NMF 67 0.4343 3
#> ATC:NMF 68 0.4740 4
#> ATC:NMF 66 0.1802 5
#> ATC:NMF 45 0.0861 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