Date: 2019-12-25 22:08:15 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 86 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 86
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:pam | 3 | 1.000 | 1.000 | 1.000 | ** | 2 |
| SD:NMF | 2 | 1.000 | 0.942 | 0.978 | ** | |
| ATC:kmeans | 2 | 1.000 | 1.000 | 1.000 | ** | |
| ATC:pam | 2 | 1.000 | 1.000 | 1.000 | ** | |
| ATC:NMF | 2 | 1.000 | 1.000 | 1.000 | ** | |
| CV:NMF | 3 | 0.990 | 0.963 | 0.978 | ** | 2 |
| MAD:pam | 4 | 0.987 | 0.956 | 0.983 | ** | 2,3 |
| CV:pam | 6 | 0.959 | 0.916 | 0.968 | ** | 2,3 |
| ATC:skmeans | 5 | 0.943 | 0.937 | 0.939 | * | 2,3,4 |
| SD:mclust | 3 | 0.941 | 0.930 | 0.958 | * | |
| SD:skmeans | 3 | 0.940 | 0.926 | 0.969 | * | |
| MAD:mclust | 3 | 0.940 | 0.890 | 0.952 | * | 2 |
| ATC:hclust | 5 | 0.930 | 0.842 | 0.941 | * | 2,4 |
| MAD:skmeans | 4 | 0.929 | 0.881 | 0.949 | * | 3 |
| ATC:mclust | 4 | 0.923 | 0.963 | 0.961 | * | 2 |
| MAD:NMF | 3 | 0.913 | 0.906 | 0.945 | * | 2 |
| CV:hclust | 5 | 0.865 | 0.877 | 0.920 | ||
| CV:skmeans | 3 | 0.859 | 0.930 | 0.967 | ||
| SD:kmeans | 2 | 0.829 | 0.953 | 0.971 | ||
| MAD:kmeans | 2 | 0.829 | 0.979 | 0.989 | ||
| MAD:hclust | 5 | 0.823 | 0.774 | 0.895 | ||
| SD:hclust | 3 | 0.778 | 0.843 | 0.917 | ||
| CV:kmeans | 3 | 0.714 | 0.937 | 0.934 | ||
| CV:mclust | 2 | 0.693 | 0.881 | 0.947 |
**: 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 0.942 0.978 0.465 0.540 0.540
#> CV:NMF 2 0.976 0.973 0.987 0.445 0.564 0.564
#> MAD:NMF 2 0.905 0.932 0.972 0.468 0.540 0.540
#> ATC:NMF 2 1.000 1.000 1.000 0.453 0.548 0.548
#> SD:skmeans 2 0.829 0.910 0.962 0.470 0.548 0.548
#> CV:skmeans 2 0.829 0.903 0.958 0.477 0.504 0.504
#> MAD:skmeans 2 0.827 0.953 0.977 0.464 0.548 0.548
#> ATC:skmeans 2 1.000 1.000 1.000 0.453 0.548 0.548
#> SD:mclust 2 0.829 0.944 0.974 0.465 0.548 0.548
#> CV:mclust 2 0.693 0.881 0.947 0.482 0.504 0.504
#> MAD:mclust 2 1.000 0.983 0.991 0.457 0.548 0.548
#> ATC:mclust 2 1.000 1.000 1.000 0.453 0.548 0.548
#> SD:kmeans 2 0.829 0.953 0.971 0.462 0.548 0.548
#> CV:kmeans 2 0.799 0.887 0.928 0.452 0.548 0.548
#> MAD:kmeans 2 0.829 0.979 0.989 0.458 0.548 0.548
#> ATC:kmeans 2 1.000 1.000 1.000 0.453 0.548 0.548
#> SD:pam 2 1.000 1.000 1.000 0.453 0.548 0.548
#> CV:pam 2 1.000 0.992 0.997 0.451 0.548 0.548
#> MAD:pam 2 1.000 1.000 1.000 0.453 0.548 0.548
#> ATC:pam 2 1.000 1.000 1.000 0.453 0.548 0.548
#> SD:hclust 2 0.625 0.842 0.917 0.450 0.521 0.521
#> CV:hclust 2 0.419 0.625 0.851 0.456 0.495 0.495
#> MAD:hclust 2 0.561 0.738 0.892 0.386 0.583 0.583
#> ATC:hclust 2 1.000 1.000 1.000 0.453 0.548 0.548
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.866 0.895 0.951 0.4253 0.785 0.607
#> CV:NMF 3 0.990 0.963 0.978 0.4845 0.773 0.598
#> MAD:NMF 3 0.913 0.906 0.945 0.4111 0.781 0.600
#> ATC:NMF 3 0.873 0.885 0.951 0.4727 0.778 0.595
#> SD:skmeans 3 0.940 0.926 0.969 0.4083 0.783 0.604
#> CV:skmeans 3 0.859 0.930 0.967 0.3930 0.763 0.560
#> MAD:skmeans 3 0.984 0.972 0.984 0.4361 0.781 0.600
#> ATC:skmeans 3 1.000 0.991 0.996 0.4672 0.789 0.615
#> SD:mclust 3 0.941 0.930 0.958 0.2604 0.893 0.804
#> CV:mclust 3 0.822 0.874 0.917 0.2285 0.852 0.715
#> MAD:mclust 3 0.940 0.890 0.952 0.3026 0.871 0.765
#> ATC:mclust 3 0.740 0.766 0.864 0.2684 0.969 0.944
#> SD:kmeans 3 0.833 0.896 0.934 0.3708 0.814 0.660
#> CV:kmeans 3 0.714 0.937 0.934 0.3445 0.805 0.649
#> MAD:kmeans 3 0.749 0.925 0.917 0.4001 0.781 0.600
#> ATC:kmeans 3 0.726 0.949 0.887 0.3619 0.789 0.615
#> SD:pam 3 1.000 1.000 1.000 0.2366 0.893 0.804
#> CV:pam 3 1.000 0.987 0.994 0.2387 0.893 0.804
#> MAD:pam 3 1.000 1.000 1.000 0.2366 0.893 0.804
#> ATC:pam 3 0.827 0.932 0.949 0.1210 0.985 0.973
#> SD:hclust 3 0.778 0.843 0.917 0.4670 0.810 0.635
#> CV:hclust 3 0.494 0.632 0.837 0.2395 0.877 0.763
#> MAD:hclust 3 0.754 0.689 0.851 0.6701 0.590 0.411
#> ATC:hclust 3 1.000 1.000 1.000 0.0326 0.985 0.973
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.769 0.685 0.848 0.0739 0.933 0.809
#> CV:NMF 4 0.826 0.746 0.869 0.0810 0.958 0.876
#> MAD:NMF 4 0.688 0.756 0.839 0.0896 0.868 0.638
#> ATC:NMF 4 0.758 0.752 0.844 0.0831 0.904 0.718
#> SD:skmeans 4 0.871 0.886 0.938 0.0913 0.885 0.681
#> CV:skmeans 4 0.801 0.836 0.923 0.1094 0.843 0.587
#> MAD:skmeans 4 0.929 0.881 0.949 0.0867 0.882 0.674
#> ATC:skmeans 4 1.000 0.977 0.983 0.0919 0.941 0.825
#> SD:mclust 4 0.801 0.863 0.896 0.1989 0.839 0.635
#> CV:mclust 4 0.849 0.767 0.888 0.1636 0.935 0.833
#> MAD:mclust 4 0.836 0.911 0.939 0.2047 0.835 0.616
#> ATC:mclust 4 0.923 0.963 0.961 0.1850 0.789 0.600
#> SD:kmeans 4 0.714 0.783 0.834 0.1194 0.852 0.625
#> CV:kmeans 4 0.745 0.824 0.844 0.1181 0.980 0.947
#> MAD:kmeans 4 0.762 0.787 0.843 0.1153 0.903 0.723
#> ATC:kmeans 4 0.630 0.508 0.838 0.1251 0.982 0.946
#> SD:pam 4 0.823 0.964 0.953 0.2335 0.856 0.672
#> CV:pam 4 0.832 0.935 0.950 0.1581 0.922 0.825
#> MAD:pam 4 0.987 0.956 0.983 0.2571 0.856 0.672
#> ATC:pam 4 0.700 0.785 0.890 0.2294 0.871 0.759
#> SD:hclust 4 0.776 0.837 0.903 0.0645 0.965 0.894
#> CV:hclust 4 0.781 0.746 0.883 0.2707 0.754 0.476
#> MAD:hclust 4 0.749 0.727 0.842 0.0876 0.791 0.528
#> ATC:hclust 4 0.998 0.938 0.974 0.4519 0.793 0.612
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.840 0.804 0.898 0.0607 0.905 0.706
#> CV:NMF 5 0.837 0.831 0.904 0.0525 0.937 0.796
#> MAD:NMF 5 0.809 0.772 0.865 0.0602 0.940 0.783
#> ATC:NMF 5 0.745 0.658 0.819 0.0407 0.879 0.617
#> SD:skmeans 5 0.895 0.854 0.921 0.0697 0.920 0.723
#> CV:skmeans 5 0.862 0.840 0.909 0.0468 0.957 0.842
#> MAD:skmeans 5 0.894 0.884 0.931 0.0672 0.940 0.789
#> ATC:skmeans 5 0.943 0.937 0.939 0.0465 0.962 0.862
#> SD:mclust 5 0.693 0.677 0.782 0.0831 0.874 0.598
#> CV:mclust 5 0.694 0.587 0.755 0.0751 0.952 0.859
#> MAD:mclust 5 0.631 0.695 0.779 0.0571 0.916 0.717
#> ATC:mclust 5 0.832 0.756 0.863 0.0937 0.925 0.769
#> SD:kmeans 5 0.682 0.616 0.715 0.0716 0.904 0.674
#> CV:kmeans 5 0.747 0.847 0.817 0.0984 0.866 0.628
#> MAD:kmeans 5 0.715 0.635 0.738 0.0708 0.925 0.742
#> ATC:kmeans 5 0.799 0.730 0.832 0.0811 0.917 0.750
#> SD:pam 5 0.884 0.918 0.952 0.0764 0.954 0.845
#> CV:pam 5 0.845 0.922 0.943 0.1494 0.881 0.677
#> MAD:pam 5 0.865 0.773 0.893 0.0682 0.962 0.872
#> ATC:pam 5 0.728 0.809 0.883 0.1190 0.889 0.729
#> SD:hclust 5 0.752 0.703 0.819 0.0653 0.930 0.766
#> CV:hclust 5 0.865 0.877 0.920 0.0544 0.904 0.685
#> MAD:hclust 5 0.823 0.774 0.895 0.0829 0.873 0.606
#> ATC:hclust 5 0.930 0.842 0.941 0.0686 0.937 0.814
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.781 0.724 0.859 0.0342 0.919 0.709
#> CV:NMF 6 0.826 0.801 0.890 0.0457 0.922 0.720
#> MAD:NMF 6 0.847 0.779 0.885 0.0250 0.925 0.714
#> ATC:NMF 6 0.657 0.630 0.742 0.0351 0.951 0.817
#> SD:skmeans 6 0.846 0.798 0.880 0.0614 0.928 0.690
#> CV:skmeans 6 0.813 0.706 0.819 0.0495 0.945 0.772
#> MAD:skmeans 6 0.858 0.790 0.882 0.0615 0.916 0.654
#> ATC:skmeans 6 0.849 0.856 0.894 0.0395 0.985 0.938
#> SD:mclust 6 0.796 0.615 0.831 0.0748 0.895 0.587
#> CV:mclust 6 0.723 0.654 0.824 0.0691 0.812 0.448
#> MAD:mclust 6 0.713 0.586 0.768 0.0678 0.917 0.663
#> ATC:mclust 6 0.787 0.687 0.826 0.0563 0.965 0.865
#> SD:kmeans 6 0.753 0.679 0.748 0.0569 0.930 0.692
#> CV:kmeans 6 0.754 0.807 0.839 0.0609 0.953 0.803
#> MAD:kmeans 6 0.745 0.696 0.791 0.0483 0.923 0.680
#> ATC:kmeans 6 0.743 0.626 0.670 0.0362 0.890 0.596
#> SD:pam 6 0.830 0.866 0.922 0.0456 0.982 0.930
#> CV:pam 6 0.959 0.916 0.968 0.0670 0.962 0.846
#> MAD:pam 6 0.780 0.698 0.832 0.0486 0.945 0.794
#> ATC:pam 6 0.855 0.846 0.930 0.0754 0.953 0.847
#> SD:hclust 6 0.706 0.678 0.796 0.0714 0.925 0.700
#> CV:hclust 6 0.867 0.826 0.901 0.0140 0.973 0.891
#> MAD:hclust 6 0.800 0.783 0.849 0.0483 0.925 0.705
#> ATC:hclust 6 0.853 0.780 0.881 0.0432 0.976 0.918
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 other(p) k
#> SD:NMF 83 0.774 2
#> CV:NMF 86 0.416 2
#> MAD:NMF 84 0.728 2
#> ATC:NMF 86 0.744 2
#> SD:skmeans 78 0.572 2
#> CV:skmeans 78 0.572 2
#> MAD:skmeans 85 0.756 2
#> ATC:skmeans 86 0.744 2
#> SD:mclust 86 0.744 2
#> CV:mclust 86 0.303 2
#> MAD:mclust 86 0.744 2
#> ATC:mclust 86 0.744 2
#> SD:kmeans 86 0.744 2
#> CV:kmeans 78 0.572 2
#> MAD:kmeans 86 0.744 2
#> ATC:kmeans 86 0.744 2
#> SD:pam 86 0.744 2
#> CV:pam 86 0.744 2
#> MAD:pam 86 0.744 2
#> ATC:pam 86 0.744 2
#> SD:hclust 81 0.447 2
#> CV:hclust 63 0.309 2
#> MAD:hclust 71 0.531 2
#> ATC:hclust 86 0.744 2
test_to_known_factors(res_list, k = 3)
#> n other(p) k
#> SD:NMF 82 0.645 3
#> CV:NMF 86 0.153 3
#> MAD:NMF 84 0.788 3
#> ATC:NMF 82 0.914 3
#> SD:skmeans 81 0.677 3
#> CV:skmeans 86 0.153 3
#> MAD:skmeans 86 0.863 3
#> ATC:skmeans 86 0.889 3
#> SD:mclust 85 0.356 3
#> CV:mclust 82 0.168 3
#> MAD:mclust 81 0.322 3
#> ATC:mclust 80 0.591 3
#> SD:kmeans 83 0.592 3
#> CV:kmeans 86 0.266 3
#> MAD:kmeans 86 0.863 3
#> ATC:kmeans 86 0.889 3
#> SD:pam 86 0.326 3
#> CV:pam 86 0.326 3
#> MAD:pam 86 0.326 3
#> ATC:pam 86 0.390 3
#> SD:hclust 80 0.765 3
#> CV:hclust 61 0.252 3
#> MAD:hclust 66 0.491 3
#> ATC:hclust 86 0.390 3
test_to_known_factors(res_list, k = 4)
#> n other(p) k
#> SD:NMF 67 0.387 4
#> CV:NMF 74 0.359 4
#> MAD:NMF 74 0.823 4
#> ATC:NMF 75 0.863 4
#> SD:skmeans 83 0.490 4
#> CV:skmeans 78 0.630 4
#> MAD:skmeans 77 0.435 4
#> ATC:skmeans 86 0.552 4
#> SD:mclust 79 0.711 4
#> CV:mclust 72 0.412 4
#> MAD:mclust 84 0.600 4
#> ATC:mclust 86 0.463 4
#> SD:kmeans 82 0.556 4
#> CV:kmeans 85 0.218 4
#> MAD:kmeans 78 0.590 4
#> ATC:kmeans 53 0.893 4
#> SD:pam 86 0.394 4
#> CV:pam 86 0.260 4
#> MAD:pam 85 0.453 4
#> ATC:pam 79 0.241 4
#> SD:hclust 80 0.606 4
#> CV:hclust 69 0.334 4
#> MAD:hclust 70 0.571 4
#> ATC:hclust 83 0.318 4
test_to_known_factors(res_list, k = 5)
#> n other(p) k
#> SD:NMF 79 0.703 5
#> CV:NMF 81 0.199 5
#> MAD:NMF 76 0.384 5
#> ATC:NMF 71 0.684 5
#> SD:skmeans 79 0.418 5
#> CV:skmeans 82 0.401 5
#> MAD:skmeans 81 0.585 5
#> ATC:skmeans 86 0.588 5
#> SD:mclust 77 0.555 5
#> CV:mclust 63 0.268 5
#> MAD:mclust 74 0.453 5
#> ATC:mclust 74 0.615 5
#> SD:kmeans 71 0.683 5
#> CV:kmeans 84 0.484 5
#> MAD:kmeans 65 0.594 5
#> ATC:kmeans 82 0.374 5
#> SD:pam 85 0.302 5
#> CV:pam 84 0.360 5
#> MAD:pam 78 0.614 5
#> ATC:pam 79 0.163 5
#> SD:hclust 73 0.606 5
#> CV:hclust 80 0.239 5
#> MAD:hclust 74 0.318 5
#> ATC:hclust 78 0.402 5
test_to_known_factors(res_list, k = 6)
#> n other(p) k
#> SD:NMF 70 0.321 6
#> CV:NMF 81 0.472 6
#> MAD:NMF 76 0.454 6
#> ATC:NMF 66 0.695 6
#> SD:skmeans 76 0.545 6
#> CV:skmeans 71 0.266 6
#> MAD:skmeans 76 0.705 6
#> ATC:skmeans 86 0.424 6
#> SD:mclust 50 0.687 6
#> CV:mclust 69 0.113 6
#> MAD:mclust 55 0.356 6
#> ATC:mclust 73 0.348 6
#> SD:kmeans 74 0.375 6
#> CV:kmeans 82 0.624 6
#> MAD:kmeans 74 0.695 6
#> ATC:kmeans 65 0.555 6
#> SD:pam 86 0.414 6
#> CV:pam 82 0.397 6
#> MAD:pam 66 0.545 6
#> ATC:pam 80 0.304 6
#> SD:hclust 68 0.568 6
#> CV:hclust 80 0.250 6
#> MAD:hclust 80 0.393 6
#> ATC:hclust 81 0.286 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 86 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 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 0.625 0.842 0.917 0.4496 0.521 0.521
#> 3 3 0.778 0.843 0.917 0.4670 0.810 0.635
#> 4 4 0.776 0.837 0.903 0.0645 0.965 0.894
#> 5 5 0.752 0.703 0.819 0.0653 0.930 0.766
#> 6 6 0.706 0.678 0.796 0.0714 0.925 0.700
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
#> GSM381194 2 0.3274 0.895 0.060 0.940
#> GSM381199 2 0.0000 0.946 0.000 1.000
#> GSM381205 2 0.0000 0.946 0.000 1.000
#> GSM381211 2 0.0000 0.946 0.000 1.000
#> GSM381220 2 0.0000 0.946 0.000 1.000
#> GSM381222 1 0.8499 0.751 0.724 0.276
#> GSM381224 1 0.8499 0.753 0.724 0.276
#> GSM381232 2 0.0000 0.946 0.000 1.000
#> GSM381240 1 0.0376 0.840 0.996 0.004
#> GSM381250 2 0.9393 0.369 0.356 0.644
#> GSM381252 2 0.0000 0.946 0.000 1.000
#> GSM381254 1 0.0000 0.839 1.000 0.000
#> GSM381256 2 0.0000 0.946 0.000 1.000
#> GSM381257 1 0.1184 0.842 0.984 0.016
#> GSM381259 1 0.0000 0.839 1.000 0.000
#> GSM381260 1 0.8555 0.747 0.720 0.280
#> GSM381261 2 0.0000 0.946 0.000 1.000
#> GSM381263 2 0.8555 0.565 0.280 0.720
#> GSM381265 1 0.0000 0.839 1.000 0.000
#> GSM381268 2 0.4298 0.864 0.088 0.912
#> GSM381270 2 0.0000 0.946 0.000 1.000
#> GSM381271 2 0.0000 0.946 0.000 1.000
#> GSM381275 2 0.0000 0.946 0.000 1.000
#> GSM381279 2 0.0000 0.946 0.000 1.000
#> GSM381195 1 0.0000 0.839 1.000 0.000
#> GSM381196 2 0.9427 0.357 0.360 0.640
#> GSM381198 2 0.0000 0.946 0.000 1.000
#> GSM381200 2 0.0000 0.946 0.000 1.000
#> GSM381201 2 0.0938 0.938 0.012 0.988
#> GSM381203 1 0.9460 0.539 0.636 0.364
#> GSM381204 1 0.0000 0.839 1.000 0.000
#> GSM381209 1 0.0000 0.839 1.000 0.000
#> GSM381212 1 0.0000 0.839 1.000 0.000
#> GSM381213 2 0.0000 0.946 0.000 1.000
#> GSM381214 2 0.0000 0.946 0.000 1.000
#> GSM381216 1 0.9087 0.692 0.676 0.324
#> GSM381225 2 0.4298 0.867 0.088 0.912
#> GSM381231 2 0.0000 0.946 0.000 1.000
#> GSM381235 1 0.8909 0.714 0.692 0.308
#> GSM381237 1 0.0000 0.839 1.000 0.000
#> GSM381241 2 0.0000 0.946 0.000 1.000
#> GSM381243 2 0.0000 0.946 0.000 1.000
#> GSM381245 1 0.4161 0.837 0.916 0.084
#> GSM381246 2 0.0000 0.946 0.000 1.000
#> GSM381251 2 0.0672 0.941 0.008 0.992
#> GSM381264 1 0.0000 0.839 1.000 0.000
#> GSM381206 2 0.0000 0.946 0.000 1.000
#> GSM381217 1 0.9922 0.397 0.552 0.448
#> GSM381218 2 0.0000 0.946 0.000 1.000
#> GSM381226 2 0.0000 0.946 0.000 1.000
#> GSM381227 2 0.0000 0.946 0.000 1.000
#> GSM381228 2 0.0000 0.946 0.000 1.000
#> GSM381236 2 0.0000 0.946 0.000 1.000
#> GSM381244 1 0.6801 0.811 0.820 0.180
#> GSM381272 2 0.0000 0.946 0.000 1.000
#> GSM381277 1 0.9000 0.703 0.684 0.316
#> GSM381278 2 0.0376 0.944 0.004 0.996
#> GSM381197 1 0.6973 0.807 0.812 0.188
#> GSM381202 1 0.7219 0.789 0.800 0.200
#> GSM381207 1 0.3733 0.838 0.928 0.072
#> GSM381208 2 0.0000 0.946 0.000 1.000
#> GSM381210 1 0.1184 0.842 0.984 0.016
#> GSM381215 2 0.7602 0.661 0.220 0.780
#> GSM381219 2 0.0000 0.946 0.000 1.000
#> GSM381221 2 0.0000 0.946 0.000 1.000
#> GSM381223 2 0.0000 0.946 0.000 1.000
#> GSM381229 2 0.0672 0.941 0.008 0.992
#> GSM381230 1 0.1843 0.842 0.972 0.028
#> GSM381233 1 0.8499 0.751 0.724 0.276
#> GSM381234 1 0.0000 0.839 1.000 0.000
#> GSM381238 2 0.0000 0.946 0.000 1.000
#> GSM381239 2 0.0000 0.946 0.000 1.000
#> GSM381242 1 0.8555 0.747 0.720 0.280
#> GSM381247 2 0.0000 0.946 0.000 1.000
#> GSM381248 1 0.1843 0.839 0.972 0.028
#> GSM381249 1 0.8081 0.775 0.752 0.248
#> GSM381253 2 0.9393 0.369 0.356 0.644
#> GSM381255 2 0.0000 0.946 0.000 1.000
#> GSM381258 2 0.9608 0.200 0.384 0.616
#> GSM381262 2 0.4161 0.868 0.084 0.916
#> GSM381266 2 0.0376 0.944 0.004 0.996
#> GSM381267 2 0.0000 0.946 0.000 1.000
#> GSM381269 1 0.8144 0.772 0.748 0.252
#> GSM381273 2 0.0672 0.941 0.008 0.992
#> GSM381274 2 0.0000 0.946 0.000 1.000
#> GSM381276 1 0.9000 0.703 0.684 0.316
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM381194 3 0.1964 0.856 0.056 0.000 0.944
#> GSM381199 2 0.0000 0.999 0.000 1.000 0.000
#> GSM381205 2 0.0000 0.999 0.000 1.000 0.000
#> GSM381211 2 0.0000 0.999 0.000 1.000 0.000
#> GSM381220 2 0.0000 0.999 0.000 1.000 0.000
#> GSM381222 1 0.5397 0.728 0.720 0.000 0.280
#> GSM381224 1 0.5397 0.731 0.720 0.000 0.280
#> GSM381232 3 0.0237 0.877 0.000 0.004 0.996
#> GSM381240 1 0.0237 0.826 0.996 0.000 0.004
#> GSM381250 3 0.5905 0.452 0.352 0.000 0.648
#> GSM381252 2 0.0000 0.999 0.000 1.000 0.000
#> GSM381254 1 0.0000 0.825 1.000 0.000 0.000
#> GSM381256 2 0.0000 0.999 0.000 1.000 0.000
#> GSM381257 1 0.0747 0.828 0.984 0.000 0.016
#> GSM381259 1 0.0000 0.825 1.000 0.000 0.000
#> GSM381260 1 0.5431 0.724 0.716 0.000 0.284
#> GSM381261 2 0.0000 0.999 0.000 1.000 0.000
#> GSM381263 3 0.5363 0.613 0.276 0.000 0.724
#> GSM381265 1 0.0000 0.825 1.000 0.000 0.000
#> GSM381268 3 0.2625 0.838 0.084 0.000 0.916
#> GSM381270 2 0.0000 0.999 0.000 1.000 0.000
#> GSM381271 3 0.0237 0.877 0.000 0.004 0.996
#> GSM381275 2 0.0000 0.999 0.000 1.000 0.000
#> GSM381279 2 0.0000 0.999 0.000 1.000 0.000
#> GSM381195 1 0.0237 0.826 0.996 0.000 0.004
#> GSM381196 3 0.5926 0.441 0.356 0.000 0.644
#> GSM381198 2 0.0000 0.999 0.000 1.000 0.000
#> GSM381200 2 0.0000 0.999 0.000 1.000 0.000
#> GSM381201 3 0.0424 0.876 0.008 0.000 0.992
#> GSM381203 1 0.5988 0.458 0.632 0.000 0.368
#> GSM381204 1 0.0000 0.825 1.000 0.000 0.000
#> GSM381209 1 0.0000 0.825 1.000 0.000 0.000
#> GSM381212 1 0.0000 0.825 1.000 0.000 0.000
#> GSM381213 2 0.0000 0.999 0.000 1.000 0.000
#> GSM381214 2 0.0000 0.999 0.000 1.000 0.000
#> GSM381216 1 0.5760 0.671 0.672 0.000 0.328
#> GSM381225 3 0.2625 0.839 0.084 0.000 0.916
#> GSM381231 3 0.0237 0.877 0.000 0.004 0.996
#> GSM381235 1 0.5650 0.692 0.688 0.000 0.312
#> GSM381237 1 0.0000 0.825 1.000 0.000 0.000
#> GSM381241 2 0.0000 0.999 0.000 1.000 0.000
#> GSM381243 2 0.0000 0.999 0.000 1.000 0.000
#> GSM381245 1 0.2711 0.821 0.912 0.000 0.088
#> GSM381246 2 0.0000 0.999 0.000 1.000 0.000
#> GSM381251 3 0.0237 0.877 0.004 0.000 0.996
#> GSM381264 1 0.0237 0.826 0.996 0.000 0.004
#> GSM381206 2 0.0000 0.999 0.000 1.000 0.000
#> GSM381217 1 0.6267 0.346 0.548 0.000 0.452
#> GSM381218 2 0.0000 0.999 0.000 1.000 0.000
#> GSM381226 2 0.0000 0.999 0.000 1.000 0.000
#> GSM381227 2 0.0000 0.999 0.000 1.000 0.000
#> GSM381228 3 0.0237 0.877 0.000 0.004 0.996
#> GSM381236 3 0.0237 0.877 0.000 0.004 0.996
#> GSM381244 1 0.4346 0.791 0.816 0.000 0.184
#> GSM381272 3 0.0237 0.877 0.000 0.004 0.996
#> GSM381277 1 0.5706 0.681 0.680 0.000 0.320
#> GSM381278 3 0.0000 0.877 0.000 0.000 1.000
#> GSM381197 1 0.4452 0.786 0.808 0.000 0.192
#> GSM381202 1 0.4605 0.759 0.796 0.000 0.204
#> GSM381207 1 0.2448 0.822 0.924 0.000 0.076
#> GSM381208 2 0.0424 0.991 0.000 0.992 0.008
#> GSM381210 1 0.0892 0.828 0.980 0.000 0.020
#> GSM381215 3 0.4750 0.671 0.216 0.000 0.784
#> GSM381219 2 0.0000 0.999 0.000 1.000 0.000
#> GSM381221 2 0.0000 0.999 0.000 1.000 0.000
#> GSM381223 2 0.0000 0.999 0.000 1.000 0.000
#> GSM381229 3 0.0237 0.877 0.004 0.000 0.996
#> GSM381230 1 0.1163 0.827 0.972 0.000 0.028
#> GSM381233 1 0.5397 0.728 0.720 0.000 0.280
#> GSM381234 1 0.0000 0.825 1.000 0.000 0.000
#> GSM381238 3 0.0237 0.877 0.000 0.004 0.996
#> GSM381239 3 0.0237 0.877 0.000 0.004 0.996
#> GSM381242 1 0.5431 0.724 0.716 0.000 0.284
#> GSM381247 2 0.0000 0.999 0.000 1.000 0.000
#> GSM381248 1 0.1163 0.822 0.972 0.000 0.028
#> GSM381249 1 0.5138 0.753 0.748 0.000 0.252
#> GSM381253 3 0.5905 0.452 0.352 0.000 0.648
#> GSM381255 2 0.0000 0.999 0.000 1.000 0.000
#> GSM381258 3 0.6045 0.230 0.380 0.000 0.620
#> GSM381262 3 0.2537 0.840 0.080 0.000 0.920
#> GSM381266 3 0.0000 0.877 0.000 0.000 1.000
#> GSM381267 2 0.0424 0.991 0.000 0.992 0.008
#> GSM381269 1 0.5178 0.751 0.744 0.000 0.256
#> GSM381273 3 0.0237 0.877 0.004 0.000 0.996
#> GSM381274 2 0.0000 0.999 0.000 1.000 0.000
#> GSM381276 1 0.5706 0.681 0.680 0.000 0.320
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM381194 3 0.3612 0.740 0.044 0.000 0.856 0.100
#> GSM381199 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM381205 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM381211 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM381220 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM381222 1 0.5719 0.730 0.712 0.000 0.176 0.112
#> GSM381224 1 0.5719 0.733 0.712 0.000 0.176 0.112
#> GSM381232 4 0.0000 0.999 0.000 0.000 0.000 1.000
#> GSM381240 1 0.0336 0.822 0.992 0.000 0.008 0.000
#> GSM381250 3 0.6219 0.478 0.344 0.000 0.588 0.068
#> GSM381252 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM381254 1 0.0000 0.820 1.000 0.000 0.000 0.000
#> GSM381256 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM381257 1 0.0592 0.823 0.984 0.000 0.000 0.016
#> GSM381259 1 0.0000 0.820 1.000 0.000 0.000 0.000
#> GSM381260 1 0.5816 0.728 0.708 0.000 0.144 0.148
#> GSM381261 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM381263 3 0.5953 0.605 0.268 0.000 0.656 0.076
#> GSM381265 1 0.0000 0.820 1.000 0.000 0.000 0.000
#> GSM381268 3 0.3144 0.753 0.072 0.000 0.884 0.044
#> GSM381270 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM381271 4 0.0000 0.999 0.000 0.000 0.000 1.000
#> GSM381275 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM381279 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM381195 1 0.0188 0.822 0.996 0.000 0.004 0.000
#> GSM381196 3 0.6234 0.468 0.348 0.000 0.584 0.068
#> GSM381198 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM381200 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM381201 3 0.0895 0.718 0.004 0.000 0.976 0.020
#> GSM381203 1 0.5966 0.399 0.624 0.000 0.316 0.060
#> GSM381204 1 0.0000 0.820 1.000 0.000 0.000 0.000
#> GSM381209 1 0.0000 0.820 1.000 0.000 0.000 0.000
#> GSM381212 1 0.0000 0.820 1.000 0.000 0.000 0.000
#> GSM381213 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM381214 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM381216 1 0.6229 0.682 0.664 0.000 0.204 0.132
#> GSM381225 3 0.3691 0.739 0.076 0.000 0.856 0.068
#> GSM381231 4 0.0000 0.999 0.000 0.000 0.000 1.000
#> GSM381235 1 0.6075 0.699 0.680 0.000 0.192 0.128
#> GSM381237 1 0.0000 0.820 1.000 0.000 0.000 0.000
#> GSM381241 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM381243 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM381245 1 0.2623 0.816 0.908 0.000 0.028 0.064
#> GSM381246 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM381251 3 0.0707 0.716 0.000 0.000 0.980 0.020
#> GSM381264 1 0.0188 0.822 0.996 0.000 0.004 0.000
#> GSM381206 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM381217 1 0.6750 0.351 0.540 0.000 0.356 0.104
#> GSM381218 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM381226 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM381227 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM381228 4 0.0000 0.999 0.000 0.000 0.000 1.000
#> GSM381236 4 0.0000 0.999 0.000 0.000 0.000 1.000
#> GSM381244 1 0.4525 0.787 0.804 0.000 0.116 0.080
#> GSM381272 4 0.0000 0.999 0.000 0.000 0.000 1.000
#> GSM381277 1 0.6193 0.691 0.672 0.000 0.180 0.148
#> GSM381278 3 0.2149 0.714 0.000 0.000 0.912 0.088
#> GSM381197 1 0.4635 0.779 0.796 0.000 0.124 0.080
#> GSM381202 1 0.4740 0.751 0.788 0.000 0.132 0.080
#> GSM381207 1 0.2300 0.816 0.920 0.000 0.016 0.064
#> GSM381208 2 0.0336 0.992 0.000 0.992 0.000 0.008
#> GSM381210 1 0.0817 0.823 0.976 0.000 0.024 0.000
#> GSM381215 3 0.6118 0.615 0.208 0.000 0.672 0.120
#> GSM381219 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM381221 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM381223 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM381229 3 0.0707 0.716 0.000 0.000 0.980 0.020
#> GSM381230 1 0.0921 0.820 0.972 0.000 0.028 0.000
#> GSM381233 1 0.5719 0.730 0.712 0.000 0.176 0.112
#> GSM381234 1 0.0000 0.820 1.000 0.000 0.000 0.000
#> GSM381238 4 0.0188 0.995 0.000 0.000 0.004 0.996
#> GSM381239 4 0.0000 0.999 0.000 0.000 0.000 1.000
#> GSM381242 1 0.5816 0.728 0.708 0.000 0.144 0.148
#> GSM381247 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM381248 1 0.0921 0.814 0.972 0.000 0.028 0.000
#> GSM381249 1 0.5423 0.753 0.740 0.000 0.144 0.116
#> GSM381253 3 0.6219 0.478 0.344 0.000 0.588 0.068
#> GSM381255 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM381258 3 0.7200 0.143 0.372 0.000 0.484 0.144
#> GSM381262 3 0.3320 0.753 0.068 0.000 0.876 0.056
#> GSM381266 3 0.2149 0.714 0.000 0.000 0.912 0.088
#> GSM381267 2 0.0336 0.992 0.000 0.992 0.000 0.008
#> GSM381269 1 0.5476 0.751 0.736 0.000 0.144 0.120
#> GSM381273 3 0.0707 0.716 0.000 0.000 0.980 0.020
#> GSM381274 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM381276 1 0.6193 0.691 0.672 0.000 0.180 0.148
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM381194 3 0.4238 0.7007 0.028 0.000 0.740 0.004 0.228
#> GSM381199 2 0.2127 0.9225 0.000 0.892 0.000 0.000 0.108
#> GSM381205 2 0.0000 0.9324 0.000 1.000 0.000 0.000 0.000
#> GSM381211 2 0.0000 0.9324 0.000 1.000 0.000 0.000 0.000
#> GSM381220 2 0.2127 0.9225 0.000 0.892 0.000 0.000 0.108
#> GSM381222 5 0.4713 0.7348 0.440 0.000 0.016 0.000 0.544
#> GSM381224 5 0.4448 0.6540 0.480 0.000 0.004 0.000 0.516
#> GSM381232 4 0.0000 0.9983 0.000 0.000 0.000 1.000 0.000
#> GSM381240 1 0.1732 0.6875 0.920 0.000 0.000 0.000 0.080
#> GSM381250 3 0.6525 0.3380 0.288 0.000 0.504 0.004 0.204
#> GSM381252 2 0.0000 0.9324 0.000 1.000 0.000 0.000 0.000
#> GSM381254 1 0.0404 0.7306 0.988 0.000 0.000 0.000 0.012
#> GSM381256 2 0.1410 0.9306 0.000 0.940 0.000 0.000 0.060
#> GSM381257 1 0.1043 0.7196 0.960 0.000 0.000 0.000 0.040
#> GSM381259 1 0.0162 0.7249 0.996 0.000 0.000 0.000 0.004
#> GSM381260 1 0.4800 -0.5485 0.508 0.000 0.012 0.004 0.476
#> GSM381261 2 0.3707 0.8040 0.000 0.716 0.000 0.000 0.284
#> GSM381263 3 0.6209 0.4958 0.216 0.000 0.572 0.004 0.208
#> GSM381265 1 0.0404 0.7293 0.988 0.000 0.000 0.000 0.012
#> GSM381268 3 0.3804 0.7121 0.044 0.000 0.796 0.000 0.160
#> GSM381270 2 0.2127 0.9225 0.000 0.892 0.000 0.000 0.108
#> GSM381271 4 0.0000 0.9983 0.000 0.000 0.000 1.000 0.000
#> GSM381275 2 0.3707 0.8040 0.000 0.716 0.000 0.000 0.284
#> GSM381279 2 0.2127 0.9225 0.000 0.892 0.000 0.000 0.108
#> GSM381195 1 0.0510 0.7298 0.984 0.000 0.000 0.000 0.016
#> GSM381196 3 0.6547 0.3277 0.288 0.000 0.500 0.004 0.208
#> GSM381198 2 0.0000 0.9324 0.000 1.000 0.000 0.000 0.000
#> GSM381200 2 0.1478 0.9310 0.000 0.936 0.000 0.000 0.064
#> GSM381201 3 0.0162 0.6926 0.000 0.000 0.996 0.000 0.004
#> GSM381203 1 0.5983 -0.0546 0.580 0.000 0.252 0.000 0.168
#> GSM381204 1 0.0000 0.7287 1.000 0.000 0.000 0.000 0.000
#> GSM381209 1 0.0880 0.7242 0.968 0.000 0.000 0.000 0.032
#> GSM381212 1 0.0000 0.7287 1.000 0.000 0.000 0.000 0.000
#> GSM381213 2 0.0000 0.9324 0.000 1.000 0.000 0.000 0.000
#> GSM381214 2 0.0000 0.9324 0.000 1.000 0.000 0.000 0.000
#> GSM381216 5 0.5010 0.7241 0.392 0.000 0.036 0.000 0.572
#> GSM381225 3 0.4801 0.6629 0.048 0.000 0.668 0.000 0.284
#> GSM381231 4 0.0000 0.9983 0.000 0.000 0.000 1.000 0.000
#> GSM381235 5 0.4909 0.7366 0.412 0.000 0.028 0.000 0.560
#> GSM381237 1 0.0000 0.7287 1.000 0.000 0.000 0.000 0.000
#> GSM381241 2 0.0162 0.9328 0.000 0.996 0.000 0.000 0.004
#> GSM381243 2 0.2127 0.9225 0.000 0.892 0.000 0.000 0.108
#> GSM381245 1 0.3010 0.5416 0.824 0.000 0.004 0.000 0.172
#> GSM381246 2 0.0880 0.9332 0.000 0.968 0.000 0.000 0.032
#> GSM381251 3 0.0000 0.6921 0.000 0.000 1.000 0.000 0.000
#> GSM381264 1 0.0290 0.7281 0.992 0.000 0.000 0.000 0.008
#> GSM381206 2 0.0000 0.9324 0.000 1.000 0.000 0.000 0.000
#> GSM381217 5 0.6534 0.4779 0.388 0.000 0.196 0.000 0.416
#> GSM381218 2 0.0000 0.9324 0.000 1.000 0.000 0.000 0.000
#> GSM381226 2 0.0880 0.9332 0.000 0.968 0.000 0.000 0.032
#> GSM381227 2 0.2127 0.9225 0.000 0.892 0.000 0.000 0.108
#> GSM381228 4 0.0000 0.9983 0.000 0.000 0.000 1.000 0.000
#> GSM381236 4 0.0000 0.9983 0.000 0.000 0.000 1.000 0.000
#> GSM381244 1 0.5353 -0.1610 0.604 0.000 0.060 0.004 0.332
#> GSM381272 4 0.0000 0.9983 0.000 0.000 0.000 1.000 0.000
#> GSM381277 5 0.4695 0.6126 0.464 0.000 0.008 0.004 0.524
#> GSM381278 3 0.3766 0.6641 0.000 0.000 0.728 0.004 0.268
#> GSM381197 1 0.5434 -0.1123 0.604 0.000 0.068 0.004 0.324
#> GSM381202 1 0.5460 0.0568 0.640 0.000 0.092 0.004 0.264
#> GSM381207 1 0.2690 0.5741 0.844 0.000 0.000 0.000 0.156
#> GSM381208 2 0.1557 0.9024 0.000 0.940 0.008 0.000 0.052
#> GSM381210 1 0.2127 0.6626 0.892 0.000 0.000 0.000 0.108
#> GSM381215 3 0.5499 0.4807 0.056 0.000 0.532 0.004 0.408
#> GSM381219 2 0.0000 0.9324 0.000 1.000 0.000 0.000 0.000
#> GSM381221 2 0.1851 0.9273 0.000 0.912 0.000 0.000 0.088
#> GSM381223 2 0.3707 0.8040 0.000 0.716 0.000 0.000 0.284
#> GSM381229 3 0.0162 0.6947 0.000 0.000 0.996 0.000 0.004
#> GSM381230 1 0.1851 0.6783 0.912 0.000 0.000 0.000 0.088
#> GSM381233 5 0.4713 0.7348 0.440 0.000 0.016 0.000 0.544
#> GSM381234 1 0.0404 0.7306 0.988 0.000 0.000 0.000 0.012
#> GSM381238 4 0.0404 0.9879 0.000 0.000 0.000 0.988 0.012
#> GSM381239 4 0.0000 0.9983 0.000 0.000 0.000 1.000 0.000
#> GSM381242 1 0.4800 -0.5485 0.508 0.000 0.012 0.004 0.476
#> GSM381247 2 0.2127 0.9225 0.000 0.892 0.000 0.000 0.108
#> GSM381248 1 0.1197 0.7055 0.952 0.000 0.000 0.000 0.048
#> GSM381249 5 0.4294 0.7007 0.468 0.000 0.000 0.000 0.532
#> GSM381253 3 0.6525 0.3380 0.288 0.000 0.504 0.004 0.204
#> GSM381255 2 0.0000 0.9324 0.000 1.000 0.000 0.000 0.000
#> GSM381258 5 0.5822 0.0841 0.112 0.000 0.292 0.004 0.592
#> GSM381262 3 0.3922 0.7121 0.040 0.000 0.780 0.000 0.180
#> GSM381266 3 0.3766 0.6641 0.000 0.000 0.728 0.004 0.268
#> GSM381267 2 0.1557 0.9024 0.000 0.940 0.008 0.000 0.052
#> GSM381269 5 0.4291 0.7068 0.464 0.000 0.000 0.000 0.536
#> GSM381273 3 0.0000 0.6921 0.000 0.000 1.000 0.000 0.000
#> GSM381274 2 0.3707 0.8040 0.000 0.716 0.000 0.000 0.284
#> GSM381276 5 0.4695 0.6126 0.464 0.000 0.008 0.004 0.524
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM381194 3 0.3874 0.666 0.008 0.000 0.704 0.000 0.276 0.012
#> GSM381199 2 0.3804 0.338 0.000 0.576 0.000 0.000 0.000 0.424
#> GSM381205 2 0.0000 0.733 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381211 2 0.0000 0.733 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381220 2 0.3695 0.416 0.000 0.624 0.000 0.000 0.000 0.376
#> GSM381222 5 0.2834 0.744 0.128 0.000 0.016 0.000 0.848 0.008
#> GSM381224 5 0.3772 0.741 0.160 0.000 0.000 0.000 0.772 0.068
#> GSM381232 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381240 1 0.2668 0.748 0.828 0.000 0.000 0.000 0.168 0.004
#> GSM381250 3 0.5627 0.378 0.132 0.000 0.484 0.000 0.380 0.004
#> GSM381252 2 0.0000 0.733 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381254 1 0.0458 0.853 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM381256 2 0.2730 0.616 0.000 0.808 0.000 0.000 0.000 0.192
#> GSM381257 1 0.1806 0.810 0.908 0.000 0.000 0.000 0.088 0.004
#> GSM381259 1 0.0146 0.848 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM381260 5 0.3900 0.732 0.180 0.000 0.008 0.000 0.764 0.048
#> GSM381261 6 0.2793 1.000 0.000 0.200 0.000 0.000 0.000 0.800
#> GSM381263 3 0.5389 0.485 0.116 0.000 0.552 0.000 0.328 0.004
#> GSM381265 1 0.0405 0.852 0.988 0.000 0.000 0.000 0.008 0.004
#> GSM381268 3 0.3273 0.688 0.008 0.000 0.776 0.000 0.212 0.004
#> GSM381270 2 0.3804 0.338 0.000 0.576 0.000 0.000 0.000 0.424
#> GSM381271 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381275 6 0.2793 1.000 0.000 0.200 0.000 0.000 0.000 0.800
#> GSM381279 2 0.3804 0.338 0.000 0.576 0.000 0.000 0.000 0.424
#> GSM381195 1 0.0777 0.851 0.972 0.000 0.000 0.000 0.024 0.004
#> GSM381196 3 0.5633 0.368 0.132 0.000 0.480 0.000 0.384 0.004
#> GSM381198 2 0.0000 0.733 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381200 2 0.3578 0.479 0.000 0.660 0.000 0.000 0.000 0.340
#> GSM381201 3 0.0405 0.690 0.000 0.000 0.988 0.000 0.004 0.008
#> GSM381203 1 0.6000 -0.235 0.420 0.000 0.244 0.000 0.336 0.000
#> GSM381204 1 0.0146 0.852 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM381209 1 0.1267 0.841 0.940 0.000 0.000 0.000 0.060 0.000
#> GSM381212 1 0.0146 0.852 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM381213 2 0.0000 0.733 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381214 2 0.0000 0.733 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381216 5 0.2485 0.722 0.084 0.000 0.024 0.000 0.884 0.008
#> GSM381225 3 0.5163 0.623 0.016 0.000 0.628 0.000 0.268 0.088
#> GSM381231 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381235 5 0.2833 0.734 0.104 0.000 0.024 0.000 0.860 0.012
#> GSM381237 1 0.0146 0.852 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM381241 2 0.0146 0.732 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM381243 2 0.3804 0.338 0.000 0.576 0.000 0.000 0.000 0.424
#> GSM381245 1 0.3650 0.577 0.716 0.000 0.004 0.000 0.272 0.008
#> GSM381246 2 0.2697 0.637 0.000 0.812 0.000 0.000 0.000 0.188
#> GSM381251 3 0.0260 0.690 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM381264 1 0.0291 0.850 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM381206 2 0.0000 0.733 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381217 5 0.5275 0.459 0.168 0.000 0.192 0.000 0.632 0.008
#> GSM381218 2 0.0000 0.733 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381226 2 0.2697 0.637 0.000 0.812 0.000 0.000 0.000 0.188
#> GSM381227 2 0.3804 0.338 0.000 0.576 0.000 0.000 0.000 0.424
#> GSM381228 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381236 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381244 5 0.4830 0.648 0.260 0.000 0.052 0.000 0.664 0.024
#> GSM381272 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381277 5 0.3883 0.723 0.144 0.000 0.000 0.000 0.768 0.088
#> GSM381278 3 0.4422 0.626 0.000 0.000 0.700 0.000 0.212 0.088
#> GSM381197 5 0.4830 0.631 0.260 0.000 0.052 0.000 0.664 0.024
#> GSM381202 5 0.5371 0.389 0.392 0.000 0.088 0.000 0.512 0.008
#> GSM381207 1 0.3398 0.613 0.740 0.000 0.000 0.000 0.252 0.008
#> GSM381208 2 0.1757 0.657 0.000 0.916 0.008 0.000 0.000 0.076
#> GSM381210 1 0.3023 0.701 0.784 0.000 0.004 0.000 0.212 0.000
#> GSM381215 5 0.3999 -0.424 0.004 0.000 0.496 0.000 0.500 0.000
#> GSM381219 2 0.0146 0.732 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM381221 2 0.3563 0.487 0.000 0.664 0.000 0.000 0.000 0.336
#> GSM381223 6 0.2793 1.000 0.000 0.200 0.000 0.000 0.000 0.800
#> GSM381229 3 0.0146 0.691 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM381230 1 0.2482 0.770 0.848 0.000 0.000 0.000 0.148 0.004
#> GSM381233 5 0.2834 0.744 0.128 0.000 0.016 0.000 0.848 0.008
#> GSM381234 1 0.0632 0.853 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM381238 4 0.0458 0.985 0.000 0.000 0.000 0.984 0.016 0.000
#> GSM381239 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381242 5 0.3900 0.732 0.180 0.000 0.008 0.000 0.764 0.048
#> GSM381247 2 0.3804 0.338 0.000 0.576 0.000 0.000 0.000 0.424
#> GSM381248 1 0.2294 0.816 0.892 0.000 0.000 0.000 0.072 0.036
#> GSM381249 5 0.2734 0.746 0.148 0.000 0.004 0.000 0.840 0.008
#> GSM381253 3 0.5627 0.378 0.132 0.000 0.484 0.000 0.380 0.004
#> GSM381255 2 0.0000 0.733 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381258 5 0.3620 0.270 0.008 0.000 0.248 0.000 0.736 0.008
#> GSM381262 3 0.3481 0.686 0.004 0.000 0.756 0.000 0.228 0.012
#> GSM381266 3 0.4422 0.626 0.000 0.000 0.700 0.000 0.212 0.088
#> GSM381267 2 0.1757 0.657 0.000 0.916 0.008 0.000 0.000 0.076
#> GSM381269 5 0.2695 0.746 0.144 0.000 0.004 0.000 0.844 0.008
#> GSM381273 3 0.0260 0.690 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM381274 6 0.2793 1.000 0.000 0.200 0.000 0.000 0.000 0.800
#> GSM381276 5 0.3883 0.723 0.144 0.000 0.000 0.000 0.768 0.088
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 other(p) k
#> SD:hclust 81 0.447 2
#> SD:hclust 80 0.765 3
#> SD:hclust 80 0.606 4
#> SD:hclust 73 0.606 5
#> SD:hclust 68 0.568 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 86 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.829 0.953 0.971 0.4616 0.548 0.548
#> 3 3 0.833 0.896 0.934 0.3708 0.814 0.660
#> 4 4 0.714 0.783 0.834 0.1194 0.852 0.625
#> 5 5 0.682 0.616 0.715 0.0716 0.904 0.674
#> 6 6 0.753 0.679 0.748 0.0569 0.930 0.692
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
#> GSM381194 1 0.1414 0.955 0.980 0.020
#> GSM381199 2 0.1414 0.995 0.020 0.980
#> GSM381205 2 0.1414 0.995 0.020 0.980
#> GSM381211 2 0.1414 0.995 0.020 0.980
#> GSM381220 2 0.0000 0.983 0.000 1.000
#> GSM381222 1 0.0000 0.964 1.000 0.000
#> GSM381224 1 0.0000 0.964 1.000 0.000
#> GSM381232 1 0.7745 0.760 0.772 0.228
#> GSM381240 1 0.0000 0.964 1.000 0.000
#> GSM381250 1 0.0000 0.964 1.000 0.000
#> GSM381252 2 0.1414 0.995 0.020 0.980
#> GSM381254 1 0.0000 0.964 1.000 0.000
#> GSM381256 2 0.1414 0.995 0.020 0.980
#> GSM381257 1 0.0000 0.964 1.000 0.000
#> GSM381259 1 0.0000 0.964 1.000 0.000
#> GSM381260 1 0.0000 0.964 1.000 0.000
#> GSM381261 2 0.1414 0.995 0.020 0.980
#> GSM381263 1 0.0000 0.964 1.000 0.000
#> GSM381265 1 0.0000 0.964 1.000 0.000
#> GSM381268 1 0.1414 0.955 0.980 0.020
#> GSM381270 2 0.0000 0.983 0.000 1.000
#> GSM381271 1 0.7745 0.760 0.772 0.228
#> GSM381275 2 0.1414 0.995 0.020 0.980
#> GSM381279 2 0.0000 0.983 0.000 1.000
#> GSM381195 1 0.0000 0.964 1.000 0.000
#> GSM381196 1 0.0000 0.964 1.000 0.000
#> GSM381198 2 0.1414 0.995 0.020 0.980
#> GSM381200 2 0.1414 0.995 0.020 0.980
#> GSM381201 1 0.1414 0.955 0.980 0.020
#> GSM381203 1 0.0000 0.964 1.000 0.000
#> GSM381204 1 0.0000 0.964 1.000 0.000
#> GSM381209 1 0.0000 0.964 1.000 0.000
#> GSM381212 1 0.0000 0.964 1.000 0.000
#> GSM381213 2 0.0000 0.983 0.000 1.000
#> GSM381214 2 0.1414 0.995 0.020 0.980
#> GSM381216 1 0.0000 0.964 1.000 0.000
#> GSM381225 1 0.0000 0.964 1.000 0.000
#> GSM381231 1 0.7745 0.760 0.772 0.228
#> GSM381235 1 0.0000 0.964 1.000 0.000
#> GSM381237 1 0.0000 0.964 1.000 0.000
#> GSM381241 2 0.1414 0.995 0.020 0.980
#> GSM381243 2 0.0000 0.983 0.000 1.000
#> GSM381245 1 0.0000 0.964 1.000 0.000
#> GSM381246 2 0.1414 0.995 0.020 0.980
#> GSM381251 1 0.1414 0.955 0.980 0.020
#> GSM381264 1 0.0000 0.964 1.000 0.000
#> GSM381206 2 0.1414 0.995 0.020 0.980
#> GSM381217 1 0.0000 0.964 1.000 0.000
#> GSM381218 2 0.1414 0.995 0.020 0.980
#> GSM381226 2 0.1414 0.995 0.020 0.980
#> GSM381227 2 0.1414 0.995 0.020 0.980
#> GSM381228 1 0.7745 0.760 0.772 0.228
#> GSM381236 1 0.7745 0.760 0.772 0.228
#> GSM381244 1 0.0000 0.964 1.000 0.000
#> GSM381272 1 0.7745 0.760 0.772 0.228
#> GSM381277 1 0.0000 0.964 1.000 0.000
#> GSM381278 1 0.1414 0.955 0.980 0.020
#> GSM381197 1 0.0000 0.964 1.000 0.000
#> GSM381202 1 0.0000 0.964 1.000 0.000
#> GSM381207 1 0.0000 0.964 1.000 0.000
#> GSM381208 2 0.1414 0.995 0.020 0.980
#> GSM381210 1 0.0000 0.964 1.000 0.000
#> GSM381215 1 0.1414 0.955 0.980 0.020
#> GSM381219 2 0.1414 0.995 0.020 0.980
#> GSM381221 2 0.1414 0.995 0.020 0.980
#> GSM381223 2 0.1414 0.995 0.020 0.980
#> GSM381229 1 0.1414 0.955 0.980 0.020
#> GSM381230 1 0.0000 0.964 1.000 0.000
#> GSM381233 1 0.0000 0.964 1.000 0.000
#> GSM381234 1 0.0000 0.964 1.000 0.000
#> GSM381238 1 0.7745 0.760 0.772 0.228
#> GSM381239 1 0.7745 0.760 0.772 0.228
#> GSM381242 1 0.0000 0.964 1.000 0.000
#> GSM381247 2 0.0000 0.983 0.000 1.000
#> GSM381248 1 0.0000 0.964 1.000 0.000
#> GSM381249 1 0.0000 0.964 1.000 0.000
#> GSM381253 1 0.0000 0.964 1.000 0.000
#> GSM381255 2 0.1414 0.995 0.020 0.980
#> GSM381258 1 0.1414 0.955 0.980 0.020
#> GSM381262 1 0.1414 0.955 0.980 0.020
#> GSM381266 1 0.1414 0.955 0.980 0.020
#> GSM381267 2 0.0000 0.983 0.000 1.000
#> GSM381269 1 0.0000 0.964 1.000 0.000
#> GSM381273 1 0.1414 0.955 0.980 0.020
#> GSM381274 2 0.1414 0.995 0.020 0.980
#> GSM381276 1 0.0938 0.958 0.988 0.012
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM381194 3 0.3879 0.91833 0.152 0.000 0.848
#> GSM381199 2 0.1753 0.97241 0.000 0.952 0.048
#> GSM381205 2 0.0237 0.97827 0.000 0.996 0.004
#> GSM381211 2 0.0237 0.97827 0.000 0.996 0.004
#> GSM381220 2 0.0892 0.97820 0.000 0.980 0.020
#> GSM381222 1 0.0592 0.91575 0.988 0.000 0.012
#> GSM381224 1 0.0237 0.91766 0.996 0.000 0.004
#> GSM381232 3 0.2496 0.92453 0.068 0.004 0.928
#> GSM381240 1 0.0000 0.91838 1.000 0.000 0.000
#> GSM381250 1 0.4504 0.74596 0.804 0.000 0.196
#> GSM381252 2 0.0237 0.97827 0.000 0.996 0.004
#> GSM381254 1 0.0000 0.91838 1.000 0.000 0.000
#> GSM381256 2 0.0000 0.97850 0.000 1.000 0.000
#> GSM381257 1 0.0000 0.91838 1.000 0.000 0.000
#> GSM381259 1 0.0000 0.91838 1.000 0.000 0.000
#> GSM381260 1 0.3412 0.82842 0.876 0.000 0.124
#> GSM381261 2 0.2261 0.96731 0.000 0.932 0.068
#> GSM381263 1 0.5431 0.60310 0.716 0.000 0.284
#> GSM381265 1 0.0000 0.91838 1.000 0.000 0.000
#> GSM381268 1 0.6126 0.30570 0.600 0.000 0.400
#> GSM381270 2 0.2165 0.96840 0.000 0.936 0.064
#> GSM381271 3 0.2496 0.92453 0.068 0.004 0.928
#> GSM381275 2 0.2261 0.96731 0.000 0.932 0.068
#> GSM381279 2 0.2165 0.96840 0.000 0.936 0.064
#> GSM381195 1 0.0000 0.91838 1.000 0.000 0.000
#> GSM381196 1 0.4452 0.75132 0.808 0.000 0.192
#> GSM381198 2 0.0237 0.97827 0.000 0.996 0.004
#> GSM381200 2 0.1753 0.97241 0.000 0.952 0.048
#> GSM381201 3 0.3879 0.91833 0.152 0.000 0.848
#> GSM381203 1 0.0000 0.91838 1.000 0.000 0.000
#> GSM381204 1 0.0000 0.91838 1.000 0.000 0.000
#> GSM381209 1 0.0000 0.91838 1.000 0.000 0.000
#> GSM381212 1 0.0000 0.91838 1.000 0.000 0.000
#> GSM381213 2 0.1289 0.97649 0.000 0.968 0.032
#> GSM381214 2 0.0237 0.97827 0.000 0.996 0.004
#> GSM381216 1 0.0592 0.91575 0.988 0.000 0.012
#> GSM381225 1 0.5465 0.59535 0.712 0.000 0.288
#> GSM381231 3 0.2496 0.92453 0.068 0.004 0.928
#> GSM381235 1 0.0592 0.91575 0.988 0.000 0.012
#> GSM381237 1 0.0000 0.91838 1.000 0.000 0.000
#> GSM381241 2 0.0237 0.97827 0.000 0.996 0.004
#> GSM381243 2 0.2165 0.96840 0.000 0.936 0.064
#> GSM381245 1 0.0000 0.91838 1.000 0.000 0.000
#> GSM381246 2 0.0237 0.97823 0.000 0.996 0.004
#> GSM381251 3 0.3879 0.91833 0.152 0.000 0.848
#> GSM381264 1 0.0000 0.91838 1.000 0.000 0.000
#> GSM381206 2 0.0237 0.97827 0.000 0.996 0.004
#> GSM381217 1 0.0592 0.91575 0.988 0.000 0.012
#> GSM381218 2 0.0237 0.97827 0.000 0.996 0.004
#> GSM381226 2 0.0592 0.97814 0.000 0.988 0.012
#> GSM381227 2 0.2261 0.96731 0.000 0.932 0.068
#> GSM381228 3 0.2496 0.92453 0.068 0.004 0.928
#> GSM381236 3 0.2496 0.92453 0.068 0.004 0.928
#> GSM381244 1 0.0424 0.91678 0.992 0.000 0.008
#> GSM381272 3 0.2496 0.92453 0.068 0.004 0.928
#> GSM381277 1 0.0000 0.91838 1.000 0.000 0.000
#> GSM381278 3 0.3686 0.92387 0.140 0.000 0.860
#> GSM381197 1 0.3340 0.83011 0.880 0.000 0.120
#> GSM381202 1 0.0000 0.91838 1.000 0.000 0.000
#> GSM381207 1 0.0424 0.91678 0.992 0.000 0.008
#> GSM381208 2 0.0237 0.97827 0.000 0.996 0.004
#> GSM381210 1 0.0000 0.91838 1.000 0.000 0.000
#> GSM381215 3 0.6026 0.49387 0.376 0.000 0.624
#> GSM381219 2 0.0000 0.97850 0.000 1.000 0.000
#> GSM381221 2 0.0000 0.97850 0.000 1.000 0.000
#> GSM381223 2 0.2261 0.96731 0.000 0.932 0.068
#> GSM381229 3 0.3879 0.91833 0.152 0.000 0.848
#> GSM381230 1 0.0000 0.91838 1.000 0.000 0.000
#> GSM381233 1 0.0592 0.91575 0.988 0.000 0.012
#> GSM381234 1 0.0000 0.91838 1.000 0.000 0.000
#> GSM381238 3 0.2496 0.92453 0.068 0.004 0.928
#> GSM381239 3 0.2496 0.92453 0.068 0.004 0.928
#> GSM381242 1 0.3482 0.82560 0.872 0.000 0.128
#> GSM381247 2 0.2165 0.96840 0.000 0.936 0.064
#> GSM381248 1 0.0000 0.91838 1.000 0.000 0.000
#> GSM381249 1 0.0237 0.91766 0.996 0.000 0.004
#> GSM381253 1 0.2959 0.85104 0.900 0.000 0.100
#> GSM381255 2 0.0237 0.97827 0.000 0.996 0.004
#> GSM381258 1 0.6299 0.00288 0.524 0.000 0.476
#> GSM381262 3 0.3879 0.91833 0.152 0.000 0.848
#> GSM381266 3 0.3686 0.92387 0.140 0.000 0.860
#> GSM381267 2 0.0892 0.97820 0.000 0.980 0.020
#> GSM381269 1 0.0592 0.91575 0.988 0.000 0.012
#> GSM381273 3 0.3686 0.92387 0.140 0.000 0.860
#> GSM381274 2 0.2261 0.96731 0.000 0.932 0.068
#> GSM381276 1 0.5465 0.59535 0.712 0.000 0.288
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM381194 3 0.5972 0.6685 0.064 0.000 0.632 0.304
#> GSM381199 2 0.3668 0.8743 0.000 0.808 0.188 0.004
#> GSM381205 2 0.0000 0.8917 0.000 1.000 0.000 0.000
#> GSM381211 2 0.0000 0.8917 0.000 1.000 0.000 0.000
#> GSM381220 2 0.2589 0.8901 0.000 0.884 0.116 0.000
#> GSM381222 1 0.3032 0.7667 0.868 0.000 0.124 0.008
#> GSM381224 1 0.1211 0.8508 0.960 0.000 0.040 0.000
#> GSM381232 4 0.0804 1.0000 0.012 0.000 0.008 0.980
#> GSM381240 1 0.0000 0.8774 1.000 0.000 0.000 0.000
#> GSM381250 3 0.5913 0.6998 0.352 0.000 0.600 0.048
#> GSM381252 2 0.0000 0.8917 0.000 1.000 0.000 0.000
#> GSM381254 1 0.0000 0.8774 1.000 0.000 0.000 0.000
#> GSM381256 2 0.0188 0.8921 0.000 0.996 0.004 0.000
#> GSM381257 1 0.0000 0.8774 1.000 0.000 0.000 0.000
#> GSM381259 1 0.0000 0.8774 1.000 0.000 0.000 0.000
#> GSM381260 1 0.5408 -0.4509 0.500 0.000 0.488 0.012
#> GSM381261 2 0.4914 0.8229 0.000 0.676 0.312 0.012
#> GSM381263 3 0.6375 0.7329 0.312 0.000 0.600 0.088
#> GSM381265 1 0.0000 0.8774 1.000 0.000 0.000 0.000
#> GSM381268 3 0.6216 0.7672 0.220 0.000 0.660 0.120
#> GSM381270 2 0.4356 0.8416 0.000 0.708 0.292 0.000
#> GSM381271 4 0.0804 1.0000 0.012 0.000 0.008 0.980
#> GSM381275 2 0.4820 0.8309 0.000 0.692 0.296 0.012
#> GSM381279 2 0.4356 0.8416 0.000 0.708 0.292 0.000
#> GSM381195 1 0.0000 0.8774 1.000 0.000 0.000 0.000
#> GSM381196 3 0.5855 0.6952 0.356 0.000 0.600 0.044
#> GSM381198 2 0.0000 0.8917 0.000 1.000 0.000 0.000
#> GSM381200 2 0.3494 0.8778 0.000 0.824 0.172 0.004
#> GSM381201 3 0.5972 0.6685 0.064 0.000 0.632 0.304
#> GSM381203 1 0.4830 -0.0769 0.608 0.000 0.392 0.000
#> GSM381204 1 0.0000 0.8774 1.000 0.000 0.000 0.000
#> GSM381209 1 0.0000 0.8774 1.000 0.000 0.000 0.000
#> GSM381212 1 0.0000 0.8774 1.000 0.000 0.000 0.000
#> GSM381213 2 0.2814 0.8770 0.000 0.868 0.132 0.000
#> GSM381214 2 0.0000 0.8917 0.000 1.000 0.000 0.000
#> GSM381216 3 0.5112 0.6152 0.384 0.000 0.608 0.008
#> GSM381225 3 0.6056 0.7576 0.248 0.000 0.660 0.092
#> GSM381231 4 0.0804 1.0000 0.012 0.000 0.008 0.980
#> GSM381235 3 0.4936 0.6764 0.340 0.000 0.652 0.008
#> GSM381237 1 0.0000 0.8774 1.000 0.000 0.000 0.000
#> GSM381241 2 0.0000 0.8917 0.000 1.000 0.000 0.000
#> GSM381243 2 0.4356 0.8416 0.000 0.708 0.292 0.000
#> GSM381245 1 0.0188 0.8750 0.996 0.000 0.004 0.000
#> GSM381246 2 0.0895 0.8926 0.000 0.976 0.020 0.004
#> GSM381251 3 0.5972 0.6685 0.064 0.000 0.632 0.304
#> GSM381264 1 0.0000 0.8774 1.000 0.000 0.000 0.000
#> GSM381206 2 0.0000 0.8917 0.000 1.000 0.000 0.000
#> GSM381217 3 0.5112 0.6152 0.384 0.000 0.608 0.008
#> GSM381218 2 0.0000 0.8917 0.000 1.000 0.000 0.000
#> GSM381226 2 0.2831 0.8882 0.000 0.876 0.120 0.004
#> GSM381227 2 0.4382 0.8399 0.000 0.704 0.296 0.000
#> GSM381228 4 0.0804 1.0000 0.012 0.000 0.008 0.980
#> GSM381236 4 0.0804 1.0000 0.012 0.000 0.008 0.980
#> GSM381244 3 0.5105 0.5246 0.432 0.000 0.564 0.004
#> GSM381272 4 0.0804 1.0000 0.012 0.000 0.008 0.980
#> GSM381277 1 0.0000 0.8774 1.000 0.000 0.000 0.000
#> GSM381278 3 0.5697 0.6708 0.056 0.000 0.664 0.280
#> GSM381197 1 0.5408 -0.4524 0.500 0.000 0.488 0.012
#> GSM381202 1 0.4250 0.3859 0.724 0.000 0.276 0.000
#> GSM381207 1 0.0657 0.8673 0.984 0.000 0.012 0.004
#> GSM381208 2 0.0657 0.8853 0.000 0.984 0.012 0.004
#> GSM381210 1 0.0000 0.8774 1.000 0.000 0.000 0.000
#> GSM381215 3 0.6243 0.7547 0.160 0.000 0.668 0.172
#> GSM381219 2 0.0000 0.8917 0.000 1.000 0.000 0.000
#> GSM381221 2 0.2081 0.8926 0.000 0.916 0.084 0.000
#> GSM381223 2 0.4820 0.8309 0.000 0.692 0.296 0.012
#> GSM381229 3 0.5972 0.6685 0.064 0.000 0.632 0.304
#> GSM381230 1 0.0000 0.8774 1.000 0.000 0.000 0.000
#> GSM381233 1 0.3032 0.7667 0.868 0.000 0.124 0.008
#> GSM381234 1 0.0000 0.8774 1.000 0.000 0.000 0.000
#> GSM381238 4 0.0804 1.0000 0.012 0.000 0.008 0.980
#> GSM381239 4 0.0804 1.0000 0.012 0.000 0.008 0.980
#> GSM381242 3 0.5398 0.5886 0.404 0.000 0.580 0.016
#> GSM381247 2 0.4356 0.8416 0.000 0.708 0.292 0.000
#> GSM381248 1 0.0000 0.8774 1.000 0.000 0.000 0.000
#> GSM381249 1 0.2281 0.8026 0.904 0.000 0.096 0.000
#> GSM381253 3 0.5138 0.6427 0.392 0.000 0.600 0.008
#> GSM381255 2 0.0000 0.8917 0.000 1.000 0.000 0.000
#> GSM381258 3 0.6260 0.7694 0.192 0.000 0.664 0.144
#> GSM381262 3 0.5972 0.6685 0.064 0.000 0.632 0.304
#> GSM381266 3 0.5898 0.6517 0.056 0.000 0.628 0.316
#> GSM381267 2 0.2593 0.8900 0.000 0.892 0.104 0.004
#> GSM381269 1 0.3032 0.7667 0.868 0.000 0.124 0.008
#> GSM381273 3 0.5878 0.6539 0.056 0.000 0.632 0.312
#> GSM381274 2 0.4795 0.8324 0.000 0.696 0.292 0.012
#> GSM381276 3 0.6494 0.7063 0.340 0.000 0.572 0.088
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM381194 3 0.1121 0.6906 0.044 0.000 0.956 0.000 0.000
#> GSM381199 2 0.3379 0.4694 0.000 0.828 0.016 0.008 0.148
#> GSM381205 5 0.4446 0.9640 0.000 0.476 0.000 0.004 0.520
#> GSM381211 5 0.4911 0.9551 0.000 0.476 0.012 0.008 0.504
#> GSM381220 2 0.4086 -0.0272 0.000 0.704 0.012 0.000 0.284
#> GSM381222 1 0.5117 0.6119 0.652 0.000 0.072 0.276 0.000
#> GSM381224 1 0.4422 0.6514 0.680 0.000 0.016 0.300 0.004
#> GSM381232 4 0.6664 0.7657 0.012 0.000 0.156 0.420 0.412
#> GSM381240 1 0.0404 0.8464 0.988 0.000 0.000 0.012 0.000
#> GSM381250 3 0.4645 0.7052 0.204 0.000 0.724 0.072 0.000
#> GSM381252 5 0.4446 0.9634 0.000 0.476 0.004 0.000 0.520
#> GSM381254 1 0.0162 0.8472 0.996 0.000 0.000 0.004 0.000
#> GSM381256 5 0.4704 0.9507 0.000 0.480 0.008 0.004 0.508
#> GSM381257 1 0.0162 0.8470 0.996 0.000 0.000 0.000 0.004
#> GSM381259 1 0.0000 0.8481 1.000 0.000 0.000 0.000 0.000
#> GSM381260 3 0.7219 0.3921 0.308 0.000 0.348 0.328 0.016
#> GSM381261 2 0.2830 0.6176 0.000 0.884 0.016 0.080 0.020
#> GSM381263 3 0.4514 0.7091 0.188 0.000 0.740 0.072 0.000
#> GSM381265 1 0.0000 0.8481 1.000 0.000 0.000 0.000 0.000
#> GSM381268 3 0.3019 0.7210 0.108 0.000 0.864 0.012 0.016
#> GSM381270 2 0.0162 0.6408 0.000 0.996 0.004 0.000 0.000
#> GSM381271 4 0.6664 0.7660 0.012 0.000 0.156 0.424 0.408
#> GSM381275 2 0.3009 0.6174 0.000 0.876 0.016 0.080 0.028
#> GSM381279 2 0.0162 0.6408 0.000 0.996 0.004 0.000 0.000
#> GSM381195 1 0.0000 0.8481 1.000 0.000 0.000 0.000 0.000
#> GSM381196 3 0.4645 0.7052 0.204 0.000 0.724 0.072 0.000
#> GSM381198 5 0.4446 0.9634 0.000 0.476 0.004 0.000 0.520
#> GSM381200 2 0.3870 0.4612 0.000 0.808 0.024 0.020 0.148
#> GSM381201 3 0.1830 0.6903 0.052 0.000 0.932 0.012 0.004
#> GSM381203 1 0.5534 -0.2291 0.508 0.000 0.424 0.068 0.000
#> GSM381204 1 0.0000 0.8481 1.000 0.000 0.000 0.000 0.000
#> GSM381209 1 0.0000 0.8481 1.000 0.000 0.000 0.000 0.000
#> GSM381212 1 0.0000 0.8481 1.000 0.000 0.000 0.000 0.000
#> GSM381213 2 0.4152 -0.1441 0.000 0.692 0.012 0.000 0.296
#> GSM381214 5 0.4911 0.9551 0.000 0.476 0.012 0.008 0.504
#> GSM381216 3 0.6459 0.5106 0.180 0.000 0.420 0.400 0.000
#> GSM381225 3 0.3554 0.7217 0.136 0.000 0.828 0.020 0.016
#> GSM381231 4 0.6664 0.7660 0.012 0.000 0.156 0.424 0.408
#> GSM381235 3 0.6344 0.5287 0.160 0.000 0.440 0.400 0.000
#> GSM381237 1 0.0000 0.8481 1.000 0.000 0.000 0.000 0.000
#> GSM381241 5 0.4446 0.9634 0.000 0.476 0.004 0.000 0.520
#> GSM381243 2 0.0162 0.6408 0.000 0.996 0.004 0.000 0.000
#> GSM381245 1 0.1740 0.8266 0.932 0.000 0.000 0.056 0.012
#> GSM381246 2 0.5567 -0.8480 0.000 0.484 0.020 0.032 0.464
#> GSM381251 3 0.1717 0.6901 0.052 0.000 0.936 0.008 0.004
#> GSM381264 1 0.0000 0.8481 1.000 0.000 0.000 0.000 0.000
#> GSM381206 5 0.4446 0.9640 0.000 0.476 0.000 0.004 0.520
#> GSM381217 3 0.6480 0.5070 0.184 0.000 0.416 0.400 0.000
#> GSM381218 5 0.4744 0.9604 0.000 0.476 0.016 0.000 0.508
#> GSM381226 2 0.5276 -0.2293 0.000 0.624 0.024 0.028 0.324
#> GSM381227 2 0.0486 0.6399 0.000 0.988 0.004 0.004 0.004
#> GSM381228 4 0.6656 0.7660 0.012 0.000 0.156 0.440 0.392
#> GSM381236 4 0.6659 0.7656 0.012 0.000 0.156 0.436 0.396
#> GSM381244 4 0.7182 -0.5167 0.248 0.000 0.328 0.404 0.020
#> GSM381272 4 0.6664 0.7660 0.012 0.000 0.156 0.424 0.408
#> GSM381277 1 0.3789 0.7135 0.760 0.000 0.000 0.224 0.016
#> GSM381278 3 0.2694 0.6890 0.040 0.000 0.884 0.076 0.000
#> GSM381197 3 0.7279 0.4046 0.324 0.000 0.360 0.296 0.020
#> GSM381202 1 0.6362 0.1482 0.496 0.000 0.184 0.320 0.000
#> GSM381207 1 0.2304 0.8046 0.892 0.000 0.008 0.100 0.000
#> GSM381208 5 0.5544 0.8274 0.000 0.452 0.008 0.048 0.492
#> GSM381210 1 0.0404 0.8460 0.988 0.000 0.000 0.012 0.000
#> GSM381215 3 0.3569 0.7143 0.068 0.000 0.828 0.104 0.000
#> GSM381219 5 0.5097 0.9531 0.000 0.476 0.016 0.012 0.496
#> GSM381221 2 0.4676 -0.5580 0.000 0.592 0.012 0.004 0.392
#> GSM381223 2 0.3009 0.6174 0.000 0.876 0.016 0.080 0.028
#> GSM381229 3 0.1557 0.6914 0.052 0.000 0.940 0.008 0.000
#> GSM381230 1 0.0000 0.8481 1.000 0.000 0.000 0.000 0.000
#> GSM381233 1 0.5117 0.6119 0.652 0.000 0.072 0.276 0.000
#> GSM381234 1 0.0162 0.8472 0.996 0.000 0.000 0.004 0.000
#> GSM381238 4 0.6656 0.7660 0.012 0.000 0.156 0.440 0.392
#> GSM381239 4 0.6659 0.7656 0.012 0.000 0.156 0.436 0.396
#> GSM381242 4 0.6972 -0.5494 0.200 0.000 0.384 0.400 0.016
#> GSM381247 2 0.0162 0.6408 0.000 0.996 0.004 0.000 0.000
#> GSM381248 1 0.1041 0.8403 0.964 0.000 0.000 0.032 0.004
#> GSM381249 1 0.4823 0.6353 0.672 0.000 0.052 0.276 0.000
#> GSM381253 3 0.4736 0.6989 0.216 0.000 0.712 0.072 0.000
#> GSM381255 5 0.4446 0.9633 0.000 0.476 0.004 0.000 0.520
#> GSM381258 3 0.5691 0.5529 0.084 0.000 0.516 0.400 0.000
#> GSM381262 3 0.1197 0.6923 0.048 0.000 0.952 0.000 0.000
#> GSM381266 3 0.1282 0.6896 0.044 0.000 0.952 0.004 0.000
#> GSM381267 2 0.5208 -0.1114 0.000 0.640 0.012 0.044 0.304
#> GSM381269 1 0.5691 0.4065 0.516 0.000 0.084 0.400 0.000
#> GSM381273 3 0.1717 0.6901 0.052 0.000 0.936 0.008 0.004
#> GSM381274 2 0.3093 0.6155 0.000 0.872 0.016 0.080 0.032
#> GSM381276 3 0.7051 0.5365 0.236 0.000 0.428 0.320 0.016
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM381194 3 0.1138 0.86476 0.012 0.000 0.960 0.024 0.004 0.000
#> GSM381199 2 0.3789 0.51506 0.000 0.784 0.016 0.004 0.028 0.168
#> GSM381205 6 0.3774 0.94592 0.000 0.328 0.000 0.000 0.008 0.664
#> GSM381211 6 0.4046 0.94305 0.000 0.328 0.004 0.008 0.004 0.656
#> GSM381220 2 0.3713 0.28080 0.000 0.704 0.000 0.004 0.008 0.284
#> GSM381222 1 0.5077 -0.04090 0.468 0.000 0.064 0.000 0.464 0.004
#> GSM381224 5 0.4821 -0.07412 0.468 0.000 0.008 0.000 0.488 0.036
#> GSM381232 4 0.1485 0.98890 0.000 0.000 0.024 0.944 0.004 0.028
#> GSM381240 1 0.2094 0.75139 0.900 0.000 0.000 0.000 0.020 0.080
#> GSM381250 3 0.4006 0.76370 0.084 0.000 0.792 0.000 0.096 0.028
#> GSM381252 6 0.3910 0.94413 0.000 0.328 0.008 0.000 0.004 0.660
#> GSM381254 1 0.0146 0.80193 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM381256 6 0.4438 0.93305 0.000 0.332 0.016 0.004 0.012 0.636
#> GSM381257 1 0.0146 0.80129 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM381259 1 0.0000 0.80301 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381260 5 0.7345 0.65708 0.176 0.000 0.208 0.000 0.420 0.196
#> GSM381261 2 0.3284 0.62797 0.000 0.784 0.000 0.000 0.196 0.020
#> GSM381263 3 0.3951 0.76957 0.076 0.000 0.796 0.000 0.100 0.028
#> GSM381265 1 0.0000 0.80301 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381268 3 0.1082 0.85852 0.040 0.000 0.956 0.000 0.004 0.000
#> GSM381270 2 0.0260 0.67307 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM381271 4 0.1176 0.98989 0.000 0.000 0.024 0.956 0.000 0.020
#> GSM381275 2 0.3512 0.62641 0.000 0.772 0.000 0.000 0.196 0.032
#> GSM381279 2 0.0260 0.67307 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM381195 1 0.0000 0.80301 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381196 3 0.4006 0.76370 0.084 0.000 0.792 0.000 0.096 0.028
#> GSM381198 6 0.3910 0.94525 0.000 0.328 0.004 0.000 0.008 0.660
#> GSM381200 2 0.4318 0.49306 0.000 0.740 0.016 0.004 0.048 0.192
#> GSM381201 3 0.2359 0.85892 0.012 0.000 0.908 0.028 0.012 0.040
#> GSM381203 1 0.5533 -0.17413 0.464 0.000 0.432 0.000 0.092 0.012
#> GSM381204 1 0.0000 0.80301 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381209 1 0.0000 0.80301 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381212 1 0.0000 0.80301 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381213 2 0.4132 -0.02919 0.000 0.632 0.004 0.008 0.004 0.352
#> GSM381214 6 0.4046 0.94305 0.000 0.328 0.004 0.008 0.004 0.656
#> GSM381216 5 0.4451 0.65775 0.072 0.000 0.248 0.000 0.680 0.000
#> GSM381225 3 0.2798 0.82533 0.048 0.000 0.876 0.000 0.020 0.056
#> GSM381231 4 0.1485 0.98890 0.000 0.000 0.024 0.944 0.004 0.028
#> GSM381235 5 0.4408 0.63010 0.056 0.000 0.280 0.000 0.664 0.000
#> GSM381237 1 0.0000 0.80301 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381241 6 0.3941 0.94560 0.000 0.328 0.004 0.004 0.004 0.660
#> GSM381243 2 0.0260 0.67307 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM381245 1 0.3616 0.65125 0.792 0.000 0.000 0.000 0.076 0.132
#> GSM381246 6 0.5493 0.76177 0.000 0.348 0.008 0.004 0.096 0.544
#> GSM381251 3 0.2258 0.85859 0.012 0.000 0.912 0.028 0.008 0.040
#> GSM381264 1 0.0000 0.80301 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381206 6 0.3774 0.94592 0.000 0.328 0.000 0.000 0.008 0.664
#> GSM381217 5 0.4537 0.65029 0.072 0.000 0.264 0.000 0.664 0.000
#> GSM381218 6 0.4151 0.94154 0.000 0.328 0.004 0.008 0.008 0.652
#> GSM381226 2 0.5714 -0.34017 0.000 0.480 0.012 0.004 0.100 0.404
#> GSM381227 2 0.0146 0.67187 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM381228 4 0.0632 0.98985 0.000 0.000 0.024 0.976 0.000 0.000
#> GSM381236 4 0.0922 0.98995 0.000 0.000 0.024 0.968 0.004 0.004
#> GSM381244 5 0.6925 0.68693 0.104 0.000 0.204 0.000 0.480 0.212
#> GSM381272 4 0.1176 0.98989 0.000 0.000 0.024 0.956 0.000 0.020
#> GSM381277 1 0.5955 -0.04654 0.476 0.000 0.004 0.000 0.308 0.212
#> GSM381278 3 0.3790 0.76029 0.012 0.000 0.812 0.020 0.116 0.040
#> GSM381197 5 0.7381 0.64260 0.180 0.000 0.208 0.000 0.412 0.200
#> GSM381202 5 0.6903 0.57741 0.288 0.000 0.116 0.000 0.460 0.136
#> GSM381207 1 0.4596 0.56338 0.728 0.000 0.016 0.000 0.128 0.128
#> GSM381208 6 0.5193 0.81083 0.000 0.300 0.016 0.012 0.052 0.620
#> GSM381210 1 0.0993 0.78987 0.964 0.000 0.000 0.000 0.024 0.012
#> GSM381215 3 0.2487 0.82247 0.032 0.000 0.876 0.000 0.092 0.000
#> GSM381219 6 0.4683 0.92206 0.000 0.328 0.012 0.008 0.024 0.628
#> GSM381221 2 0.4923 -0.46374 0.000 0.504 0.016 0.004 0.024 0.452
#> GSM381223 2 0.3512 0.62641 0.000 0.772 0.000 0.000 0.196 0.032
#> GSM381229 3 0.2187 0.85973 0.012 0.000 0.916 0.028 0.008 0.036
#> GSM381230 1 0.0146 0.80112 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM381233 1 0.5077 -0.04090 0.468 0.000 0.064 0.000 0.464 0.004
#> GSM381234 1 0.0146 0.80193 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM381238 4 0.0922 0.98995 0.000 0.000 0.024 0.968 0.004 0.004
#> GSM381239 4 0.0632 0.98985 0.000 0.000 0.024 0.976 0.000 0.000
#> GSM381242 5 0.6697 0.68595 0.084 0.000 0.216 0.000 0.508 0.192
#> GSM381247 2 0.0260 0.67307 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM381248 1 0.1745 0.76914 0.924 0.000 0.000 0.000 0.020 0.056
#> GSM381249 1 0.4885 -0.00318 0.484 0.000 0.048 0.000 0.464 0.004
#> GSM381253 3 0.4006 0.76370 0.084 0.000 0.792 0.000 0.096 0.028
#> GSM381255 6 0.3668 0.94608 0.000 0.328 0.000 0.004 0.000 0.668
#> GSM381258 5 0.4146 0.61057 0.036 0.000 0.288 0.000 0.676 0.000
#> GSM381262 3 0.0993 0.86433 0.012 0.000 0.964 0.024 0.000 0.000
#> GSM381266 3 0.2074 0.86061 0.012 0.000 0.920 0.028 0.004 0.036
#> GSM381267 2 0.5336 0.15608 0.000 0.592 0.016 0.012 0.056 0.324
#> GSM381269 5 0.4451 0.52384 0.248 0.000 0.072 0.000 0.680 0.000
#> GSM381273 3 0.2258 0.85859 0.012 0.000 0.912 0.028 0.008 0.040
#> GSM381274 2 0.3512 0.62641 0.000 0.772 0.000 0.000 0.196 0.032
#> GSM381276 5 0.7273 0.63062 0.124 0.000 0.264 0.000 0.404 0.208
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 other(p) k
#> SD:kmeans 86 0.744 2
#> SD:kmeans 83 0.592 3
#> SD:kmeans 82 0.556 4
#> SD:kmeans 71 0.683 5
#> SD:kmeans 74 0.375 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 86 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.829 0.910 0.962 0.4705 0.548 0.548
#> 3 3 0.940 0.926 0.969 0.4083 0.783 0.604
#> 4 4 0.871 0.886 0.938 0.0913 0.885 0.681
#> 5 5 0.895 0.854 0.921 0.0697 0.920 0.723
#> 6 6 0.846 0.798 0.880 0.0614 0.928 0.690
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
#> GSM381194 1 0.000 0.940 1.000 0.000
#> GSM381199 2 0.000 1.000 0.000 1.000
#> GSM381205 2 0.000 1.000 0.000 1.000
#> GSM381211 2 0.000 1.000 0.000 1.000
#> GSM381220 2 0.000 1.000 0.000 1.000
#> GSM381222 1 0.000 0.940 1.000 0.000
#> GSM381224 1 0.000 0.940 1.000 0.000
#> GSM381232 1 0.973 0.407 0.596 0.404
#> GSM381240 1 0.000 0.940 1.000 0.000
#> GSM381250 1 0.000 0.940 1.000 0.000
#> GSM381252 2 0.000 1.000 0.000 1.000
#> GSM381254 1 0.000 0.940 1.000 0.000
#> GSM381256 2 0.000 1.000 0.000 1.000
#> GSM381257 1 0.000 0.940 1.000 0.000
#> GSM381259 1 0.000 0.940 1.000 0.000
#> GSM381260 1 0.000 0.940 1.000 0.000
#> GSM381261 2 0.000 1.000 0.000 1.000
#> GSM381263 1 0.000 0.940 1.000 0.000
#> GSM381265 1 0.000 0.940 1.000 0.000
#> GSM381268 1 0.000 0.940 1.000 0.000
#> GSM381270 2 0.000 1.000 0.000 1.000
#> GSM381271 1 0.973 0.407 0.596 0.404
#> GSM381275 2 0.000 1.000 0.000 1.000
#> GSM381279 2 0.000 1.000 0.000 1.000
#> GSM381195 1 0.000 0.940 1.000 0.000
#> GSM381196 1 0.000 0.940 1.000 0.000
#> GSM381198 2 0.000 1.000 0.000 1.000
#> GSM381200 2 0.000 1.000 0.000 1.000
#> GSM381201 1 0.000 0.940 1.000 0.000
#> GSM381203 1 0.000 0.940 1.000 0.000
#> GSM381204 1 0.000 0.940 1.000 0.000
#> GSM381209 1 0.000 0.940 1.000 0.000
#> GSM381212 1 0.000 0.940 1.000 0.000
#> GSM381213 2 0.000 1.000 0.000 1.000
#> GSM381214 2 0.000 1.000 0.000 1.000
#> GSM381216 1 0.000 0.940 1.000 0.000
#> GSM381225 1 0.000 0.940 1.000 0.000
#> GSM381231 1 0.973 0.407 0.596 0.404
#> GSM381235 1 0.000 0.940 1.000 0.000
#> GSM381237 1 0.000 0.940 1.000 0.000
#> GSM381241 2 0.000 1.000 0.000 1.000
#> GSM381243 2 0.000 1.000 0.000 1.000
#> GSM381245 1 0.000 0.940 1.000 0.000
#> GSM381246 2 0.000 1.000 0.000 1.000
#> GSM381251 1 0.000 0.940 1.000 0.000
#> GSM381264 1 0.000 0.940 1.000 0.000
#> GSM381206 2 0.000 1.000 0.000 1.000
#> GSM381217 1 0.000 0.940 1.000 0.000
#> GSM381218 2 0.000 1.000 0.000 1.000
#> GSM381226 2 0.000 1.000 0.000 1.000
#> GSM381227 2 0.000 1.000 0.000 1.000
#> GSM381228 1 0.973 0.407 0.596 0.404
#> GSM381236 1 0.973 0.407 0.596 0.404
#> GSM381244 1 0.000 0.940 1.000 0.000
#> GSM381272 1 0.973 0.407 0.596 0.404
#> GSM381277 1 0.000 0.940 1.000 0.000
#> GSM381278 1 0.000 0.940 1.000 0.000
#> GSM381197 1 0.000 0.940 1.000 0.000
#> GSM381202 1 0.000 0.940 1.000 0.000
#> GSM381207 1 0.000 0.940 1.000 0.000
#> GSM381208 2 0.000 1.000 0.000 1.000
#> GSM381210 1 0.000 0.940 1.000 0.000
#> GSM381215 1 0.000 0.940 1.000 0.000
#> GSM381219 2 0.000 1.000 0.000 1.000
#> GSM381221 2 0.000 1.000 0.000 1.000
#> GSM381223 2 0.000 1.000 0.000 1.000
#> GSM381229 1 0.000 0.940 1.000 0.000
#> GSM381230 1 0.000 0.940 1.000 0.000
#> GSM381233 1 0.000 0.940 1.000 0.000
#> GSM381234 1 0.000 0.940 1.000 0.000
#> GSM381238 1 0.973 0.407 0.596 0.404
#> GSM381239 1 0.973 0.407 0.596 0.404
#> GSM381242 1 0.000 0.940 1.000 0.000
#> GSM381247 2 0.000 1.000 0.000 1.000
#> GSM381248 1 0.000 0.940 1.000 0.000
#> GSM381249 1 0.000 0.940 1.000 0.000
#> GSM381253 1 0.000 0.940 1.000 0.000
#> GSM381255 2 0.000 1.000 0.000 1.000
#> GSM381258 1 0.000 0.940 1.000 0.000
#> GSM381262 1 0.000 0.940 1.000 0.000
#> GSM381266 1 0.000 0.940 1.000 0.000
#> GSM381267 2 0.000 1.000 0.000 1.000
#> GSM381269 1 0.000 0.940 1.000 0.000
#> GSM381273 1 0.000 0.940 1.000 0.000
#> GSM381274 2 0.000 1.000 0.000 1.000
#> GSM381276 1 0.000 0.940 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM381194 3 0.0000 0.904 0.000 0 1.000
#> GSM381199 2 0.0000 1.000 0.000 1 0.000
#> GSM381205 2 0.0000 1.000 0.000 1 0.000
#> GSM381211 2 0.0000 1.000 0.000 1 0.000
#> GSM381220 2 0.0000 1.000 0.000 1 0.000
#> GSM381222 1 0.0000 0.977 1.000 0 0.000
#> GSM381224 1 0.0000 0.977 1.000 0 0.000
#> GSM381232 3 0.0000 0.904 0.000 0 1.000
#> GSM381240 1 0.0000 0.977 1.000 0 0.000
#> GSM381250 3 0.6126 0.420 0.400 0 0.600
#> GSM381252 2 0.0000 1.000 0.000 1 0.000
#> GSM381254 1 0.0000 0.977 1.000 0 0.000
#> GSM381256 2 0.0000 1.000 0.000 1 0.000
#> GSM381257 1 0.0000 0.977 1.000 0 0.000
#> GSM381259 1 0.0000 0.977 1.000 0 0.000
#> GSM381260 1 0.3412 0.844 0.876 0 0.124
#> GSM381261 2 0.0000 1.000 0.000 1 0.000
#> GSM381263 3 0.6126 0.420 0.400 0 0.600
#> GSM381265 1 0.0000 0.977 1.000 0 0.000
#> GSM381268 3 0.1031 0.888 0.024 0 0.976
#> GSM381270 2 0.0000 1.000 0.000 1 0.000
#> GSM381271 3 0.0000 0.904 0.000 0 1.000
#> GSM381275 2 0.0000 1.000 0.000 1 0.000
#> GSM381279 2 0.0000 1.000 0.000 1 0.000
#> GSM381195 1 0.0000 0.977 1.000 0 0.000
#> GSM381196 3 0.6126 0.420 0.400 0 0.600
#> GSM381198 2 0.0000 1.000 0.000 1 0.000
#> GSM381200 2 0.0000 1.000 0.000 1 0.000
#> GSM381201 3 0.0000 0.904 0.000 0 1.000
#> GSM381203 1 0.0000 0.977 1.000 0 0.000
#> GSM381204 1 0.0000 0.977 1.000 0 0.000
#> GSM381209 1 0.0000 0.977 1.000 0 0.000
#> GSM381212 1 0.0000 0.977 1.000 0 0.000
#> GSM381213 2 0.0000 1.000 0.000 1 0.000
#> GSM381214 2 0.0000 1.000 0.000 1 0.000
#> GSM381216 1 0.0000 0.977 1.000 0 0.000
#> GSM381225 3 0.6126 0.420 0.400 0 0.600
#> GSM381231 3 0.0000 0.904 0.000 0 1.000
#> GSM381235 1 0.0000 0.977 1.000 0 0.000
#> GSM381237 1 0.0000 0.977 1.000 0 0.000
#> GSM381241 2 0.0000 1.000 0.000 1 0.000
#> GSM381243 2 0.0000 1.000 0.000 1 0.000
#> GSM381245 1 0.0000 0.977 1.000 0 0.000
#> GSM381246 2 0.0000 1.000 0.000 1 0.000
#> GSM381251 3 0.0000 0.904 0.000 0 1.000
#> GSM381264 1 0.0000 0.977 1.000 0 0.000
#> GSM381206 2 0.0000 1.000 0.000 1 0.000
#> GSM381217 1 0.0000 0.977 1.000 0 0.000
#> GSM381218 2 0.0000 1.000 0.000 1 0.000
#> GSM381226 2 0.0000 1.000 0.000 1 0.000
#> GSM381227 2 0.0000 1.000 0.000 1 0.000
#> GSM381228 3 0.0000 0.904 0.000 0 1.000
#> GSM381236 3 0.0000 0.904 0.000 0 1.000
#> GSM381244 1 0.0000 0.977 1.000 0 0.000
#> GSM381272 3 0.0000 0.904 0.000 0 1.000
#> GSM381277 1 0.0000 0.977 1.000 0 0.000
#> GSM381278 3 0.0000 0.904 0.000 0 1.000
#> GSM381197 1 0.3412 0.844 0.876 0 0.124
#> GSM381202 1 0.0000 0.977 1.000 0 0.000
#> GSM381207 1 0.0000 0.977 1.000 0 0.000
#> GSM381208 2 0.0000 1.000 0.000 1 0.000
#> GSM381210 1 0.0000 0.977 1.000 0 0.000
#> GSM381215 3 0.0000 0.904 0.000 0 1.000
#> GSM381219 2 0.0000 1.000 0.000 1 0.000
#> GSM381221 2 0.0000 1.000 0.000 1 0.000
#> GSM381223 2 0.0000 1.000 0.000 1 0.000
#> GSM381229 3 0.0000 0.904 0.000 0 1.000
#> GSM381230 1 0.0000 0.977 1.000 0 0.000
#> GSM381233 1 0.0000 0.977 1.000 0 0.000
#> GSM381234 1 0.0000 0.977 1.000 0 0.000
#> GSM381238 3 0.0000 0.904 0.000 0 1.000
#> GSM381239 3 0.0000 0.904 0.000 0 1.000
#> GSM381242 1 0.3116 0.864 0.892 0 0.108
#> GSM381247 2 0.0000 1.000 0.000 1 0.000
#> GSM381248 1 0.0000 0.977 1.000 0 0.000
#> GSM381249 1 0.0000 0.977 1.000 0 0.000
#> GSM381253 1 0.5529 0.530 0.704 0 0.296
#> GSM381255 2 0.0000 1.000 0.000 1 0.000
#> GSM381258 3 0.0237 0.902 0.004 0 0.996
#> GSM381262 3 0.0000 0.904 0.000 0 1.000
#> GSM381266 3 0.0000 0.904 0.000 0 1.000
#> GSM381267 2 0.0000 1.000 0.000 1 0.000
#> GSM381269 1 0.0000 0.977 1.000 0 0.000
#> GSM381273 3 0.0000 0.904 0.000 0 1.000
#> GSM381274 2 0.0000 1.000 0.000 1 0.000
#> GSM381276 3 0.6126 0.420 0.400 0 0.600
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM381194 3 0.2081 0.807 0.000 0.000 0.916 0.084
#> GSM381199 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM381205 2 0.0469 0.994 0.000 0.988 0.000 0.012
#> GSM381211 2 0.0469 0.994 0.000 0.988 0.000 0.012
#> GSM381220 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM381222 1 0.3400 0.795 0.820 0.000 0.180 0.000
#> GSM381224 1 0.1940 0.882 0.924 0.000 0.076 0.000
#> GSM381232 4 0.0469 1.000 0.000 0.000 0.012 0.988
#> GSM381240 1 0.0000 0.928 1.000 0.000 0.000 0.000
#> GSM381250 3 0.3172 0.794 0.160 0.000 0.840 0.000
#> GSM381252 2 0.0469 0.994 0.000 0.988 0.000 0.012
#> GSM381254 1 0.0000 0.928 1.000 0.000 0.000 0.000
#> GSM381256 2 0.0469 0.994 0.000 0.988 0.000 0.012
#> GSM381257 1 0.0000 0.928 1.000 0.000 0.000 0.000
#> GSM381259 1 0.0000 0.928 1.000 0.000 0.000 0.000
#> GSM381260 3 0.4500 0.654 0.316 0.000 0.684 0.000
#> GSM381261 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM381263 3 0.3172 0.794 0.160 0.000 0.840 0.000
#> GSM381265 1 0.0000 0.928 1.000 0.000 0.000 0.000
#> GSM381268 3 0.0469 0.812 0.000 0.000 0.988 0.012
#> GSM381270 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM381271 4 0.0469 1.000 0.000 0.000 0.012 0.988
#> GSM381275 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM381279 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM381195 1 0.0000 0.928 1.000 0.000 0.000 0.000
#> GSM381196 3 0.3402 0.792 0.164 0.000 0.832 0.004
#> GSM381198 2 0.0469 0.994 0.000 0.988 0.000 0.012
#> GSM381200 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM381201 3 0.2081 0.807 0.000 0.000 0.916 0.084
#> GSM381203 3 0.4989 0.332 0.472 0.000 0.528 0.000
#> GSM381204 1 0.0000 0.928 1.000 0.000 0.000 0.000
#> GSM381209 1 0.0000 0.928 1.000 0.000 0.000 0.000
#> GSM381212 1 0.0000 0.928 1.000 0.000 0.000 0.000
#> GSM381213 2 0.0469 0.994 0.000 0.988 0.000 0.012
#> GSM381214 2 0.0469 0.994 0.000 0.988 0.000 0.012
#> GSM381216 3 0.4843 0.239 0.396 0.000 0.604 0.000
#> GSM381225 3 0.0657 0.812 0.012 0.000 0.984 0.004
#> GSM381231 4 0.0469 1.000 0.000 0.000 0.012 0.988
#> GSM381235 3 0.1940 0.792 0.076 0.000 0.924 0.000
#> GSM381237 1 0.0000 0.928 1.000 0.000 0.000 0.000
#> GSM381241 2 0.0469 0.994 0.000 0.988 0.000 0.012
#> GSM381243 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM381245 1 0.0000 0.928 1.000 0.000 0.000 0.000
#> GSM381246 2 0.0469 0.994 0.000 0.988 0.000 0.012
#> GSM381251 3 0.2081 0.807 0.000 0.000 0.916 0.084
#> GSM381264 1 0.0000 0.928 1.000 0.000 0.000 0.000
#> GSM381206 2 0.0469 0.994 0.000 0.988 0.000 0.012
#> GSM381217 1 0.4992 0.201 0.524 0.000 0.476 0.000
#> GSM381218 2 0.0469 0.994 0.000 0.988 0.000 0.012
#> GSM381226 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM381227 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM381228 4 0.0469 1.000 0.000 0.000 0.012 0.988
#> GSM381236 4 0.0469 1.000 0.000 0.000 0.012 0.988
#> GSM381244 1 0.4406 0.622 0.700 0.000 0.300 0.000
#> GSM381272 4 0.0469 1.000 0.000 0.000 0.012 0.988
#> GSM381277 1 0.0000 0.928 1.000 0.000 0.000 0.000
#> GSM381278 3 0.1557 0.803 0.000 0.000 0.944 0.056
#> GSM381197 3 0.4543 0.647 0.324 0.000 0.676 0.000
#> GSM381202 1 0.1867 0.873 0.928 0.000 0.072 0.000
#> GSM381207 1 0.0000 0.928 1.000 0.000 0.000 0.000
#> GSM381208 2 0.0469 0.994 0.000 0.988 0.000 0.012
#> GSM381210 1 0.0000 0.928 1.000 0.000 0.000 0.000
#> GSM381215 3 0.0336 0.812 0.000 0.000 0.992 0.008
#> GSM381219 2 0.0469 0.994 0.000 0.988 0.000 0.012
#> GSM381221 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM381223 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM381229 3 0.2081 0.807 0.000 0.000 0.916 0.084
#> GSM381230 1 0.0000 0.928 1.000 0.000 0.000 0.000
#> GSM381233 1 0.3486 0.788 0.812 0.000 0.188 0.000
#> GSM381234 1 0.0000 0.928 1.000 0.000 0.000 0.000
#> GSM381238 4 0.0469 1.000 0.000 0.000 0.012 0.988
#> GSM381239 4 0.0469 1.000 0.000 0.000 0.012 0.988
#> GSM381242 3 0.3688 0.713 0.208 0.000 0.792 0.000
#> GSM381247 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM381248 1 0.0000 0.928 1.000 0.000 0.000 0.000
#> GSM381249 1 0.3074 0.820 0.848 0.000 0.152 0.000
#> GSM381253 3 0.3266 0.791 0.168 0.000 0.832 0.000
#> GSM381255 2 0.0469 0.994 0.000 0.988 0.000 0.012
#> GSM381258 3 0.0000 0.811 0.000 0.000 1.000 0.000
#> GSM381262 3 0.2011 0.808 0.000 0.000 0.920 0.080
#> GSM381266 3 0.2704 0.783 0.000 0.000 0.876 0.124
#> GSM381267 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM381269 1 0.3610 0.779 0.800 0.000 0.200 0.000
#> GSM381273 3 0.2704 0.783 0.000 0.000 0.876 0.124
#> GSM381274 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM381276 3 0.4283 0.725 0.256 0.000 0.740 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM381194 5 0.0290 0.932 0.000 0.000 0.000 0.008 0.992
#> GSM381199 2 0.1628 0.960 0.000 0.936 0.056 0.000 0.008
#> GSM381205 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000
#> GSM381211 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000
#> GSM381220 2 0.1357 0.962 0.000 0.948 0.048 0.000 0.004
#> GSM381222 3 0.4747 0.221 0.484 0.000 0.500 0.000 0.016
#> GSM381224 1 0.4305 -0.237 0.512 0.000 0.488 0.000 0.000
#> GSM381232 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM381240 1 0.0000 0.935 1.000 0.000 0.000 0.000 0.000
#> GSM381250 5 0.1195 0.917 0.028 0.000 0.012 0.000 0.960
#> GSM381252 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000
#> GSM381254 1 0.0000 0.935 1.000 0.000 0.000 0.000 0.000
#> GSM381256 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000
#> GSM381257 1 0.0000 0.935 1.000 0.000 0.000 0.000 0.000
#> GSM381259 1 0.0000 0.935 1.000 0.000 0.000 0.000 0.000
#> GSM381260 3 0.5082 0.638 0.220 0.000 0.684 0.000 0.096
#> GSM381261 2 0.2193 0.951 0.000 0.900 0.092 0.000 0.008
#> GSM381263 5 0.1018 0.924 0.016 0.000 0.016 0.000 0.968
#> GSM381265 1 0.0000 0.935 1.000 0.000 0.000 0.000 0.000
#> GSM381268 5 0.0290 0.931 0.000 0.000 0.008 0.000 0.992
#> GSM381270 2 0.2193 0.951 0.000 0.900 0.092 0.000 0.008
#> GSM381271 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM381275 2 0.2193 0.951 0.000 0.900 0.092 0.000 0.008
#> GSM381279 2 0.2193 0.951 0.000 0.900 0.092 0.000 0.008
#> GSM381195 1 0.0000 0.935 1.000 0.000 0.000 0.000 0.000
#> GSM381196 5 0.0912 0.925 0.016 0.000 0.012 0.000 0.972
#> GSM381198 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000
#> GSM381200 2 0.1697 0.959 0.000 0.932 0.060 0.000 0.008
#> GSM381201 5 0.0290 0.932 0.000 0.000 0.000 0.008 0.992
#> GSM381203 5 0.4557 0.135 0.476 0.000 0.008 0.000 0.516
#> GSM381204 1 0.0000 0.935 1.000 0.000 0.000 0.000 0.000
#> GSM381209 1 0.0000 0.935 1.000 0.000 0.000 0.000 0.000
#> GSM381212 1 0.0000 0.935 1.000 0.000 0.000 0.000 0.000
#> GSM381213 2 0.1197 0.959 0.000 0.952 0.048 0.000 0.000
#> GSM381214 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000
#> GSM381216 3 0.2304 0.721 0.044 0.000 0.908 0.000 0.048
#> GSM381225 5 0.0404 0.930 0.000 0.000 0.012 0.000 0.988
#> GSM381231 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM381235 3 0.2488 0.689 0.004 0.000 0.872 0.000 0.124
#> GSM381237 1 0.0000 0.935 1.000 0.000 0.000 0.000 0.000
#> GSM381241 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000
#> GSM381243 2 0.2193 0.951 0.000 0.900 0.092 0.000 0.008
#> GSM381245 1 0.0000 0.935 1.000 0.000 0.000 0.000 0.000
#> GSM381246 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000
#> GSM381251 5 0.0290 0.932 0.000 0.000 0.000 0.008 0.992
#> GSM381264 1 0.0000 0.935 1.000 0.000 0.000 0.000 0.000
#> GSM381206 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000
#> GSM381217 3 0.3075 0.723 0.092 0.000 0.860 0.000 0.048
#> GSM381218 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000
#> GSM381226 2 0.0865 0.964 0.000 0.972 0.024 0.000 0.004
#> GSM381227 2 0.2193 0.951 0.000 0.900 0.092 0.000 0.008
#> GSM381228 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM381236 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM381244 3 0.2450 0.727 0.076 0.000 0.896 0.000 0.028
#> GSM381272 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM381277 1 0.3837 0.365 0.692 0.000 0.308 0.000 0.000
#> GSM381278 5 0.2890 0.767 0.000 0.000 0.160 0.004 0.836
#> GSM381197 3 0.6471 0.462 0.296 0.000 0.488 0.000 0.216
#> GSM381202 3 0.4196 0.502 0.356 0.000 0.640 0.000 0.004
#> GSM381207 1 0.0510 0.924 0.984 0.000 0.016 0.000 0.000
#> GSM381208 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000
#> GSM381210 1 0.0703 0.913 0.976 0.000 0.024 0.000 0.000
#> GSM381215 5 0.1197 0.908 0.000 0.000 0.048 0.000 0.952
#> GSM381219 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000
#> GSM381221 2 0.0865 0.964 0.000 0.972 0.024 0.000 0.004
#> GSM381223 2 0.2193 0.951 0.000 0.900 0.092 0.000 0.008
#> GSM381229 5 0.0290 0.932 0.000 0.000 0.000 0.008 0.992
#> GSM381230 1 0.0510 0.922 0.984 0.000 0.016 0.000 0.000
#> GSM381233 3 0.4746 0.230 0.480 0.000 0.504 0.000 0.016
#> GSM381234 1 0.0000 0.935 1.000 0.000 0.000 0.000 0.000
#> GSM381238 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM381239 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM381242 3 0.2260 0.714 0.028 0.000 0.908 0.000 0.064
#> GSM381247 2 0.2193 0.951 0.000 0.900 0.092 0.000 0.008
#> GSM381248 1 0.0404 0.925 0.988 0.000 0.012 0.000 0.000
#> GSM381249 3 0.4450 0.217 0.488 0.000 0.508 0.000 0.004
#> GSM381253 5 0.1364 0.910 0.036 0.000 0.012 0.000 0.952
#> GSM381255 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000
#> GSM381258 3 0.1965 0.695 0.000 0.000 0.904 0.000 0.096
#> GSM381262 5 0.0324 0.931 0.000 0.000 0.004 0.004 0.992
#> GSM381266 5 0.0451 0.931 0.000 0.000 0.004 0.008 0.988
#> GSM381267 2 0.1484 0.961 0.000 0.944 0.048 0.000 0.008
#> GSM381269 3 0.2172 0.723 0.076 0.000 0.908 0.000 0.016
#> GSM381273 5 0.0290 0.932 0.000 0.000 0.000 0.008 0.992
#> GSM381274 2 0.2193 0.951 0.000 0.900 0.092 0.000 0.008
#> GSM381276 3 0.5867 0.574 0.180 0.000 0.604 0.000 0.216
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM381194 3 0.0291 0.9716 0.000 0.000 0.992 0.004 0.004 0.000
#> GSM381199 6 0.3986 0.4518 0.000 0.464 0.000 0.000 0.004 0.532
#> GSM381205 2 0.0000 0.8446 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381211 2 0.0000 0.8446 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381220 2 0.3890 -0.0123 0.000 0.596 0.000 0.000 0.004 0.400
#> GSM381222 5 0.3515 0.5397 0.324 0.000 0.000 0.000 0.676 0.000
#> GSM381224 5 0.4209 0.4249 0.396 0.000 0.004 0.000 0.588 0.012
#> GSM381232 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381240 1 0.0405 0.9210 0.988 0.000 0.004 0.000 0.000 0.008
#> GSM381250 3 0.0653 0.9685 0.004 0.000 0.980 0.000 0.004 0.012
#> GSM381252 2 0.0000 0.8446 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381254 1 0.0000 0.9273 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381256 2 0.0865 0.8203 0.000 0.964 0.000 0.000 0.000 0.036
#> GSM381257 1 0.0146 0.9247 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM381259 1 0.0000 0.9273 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381260 5 0.5764 0.6072 0.180 0.000 0.024 0.000 0.592 0.204
#> GSM381261 6 0.2941 0.9159 0.000 0.220 0.000 0.000 0.000 0.780
#> GSM381263 3 0.0964 0.9630 0.004 0.000 0.968 0.000 0.016 0.012
#> GSM381265 1 0.0000 0.9273 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381268 3 0.0146 0.9719 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM381270 6 0.3081 0.9156 0.000 0.220 0.000 0.000 0.004 0.776
#> GSM381271 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381275 6 0.3023 0.9116 0.000 0.232 0.000 0.000 0.000 0.768
#> GSM381279 6 0.2941 0.9159 0.000 0.220 0.000 0.000 0.000 0.780
#> GSM381195 1 0.0000 0.9273 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381196 3 0.0653 0.9685 0.004 0.000 0.980 0.000 0.004 0.012
#> GSM381198 2 0.0000 0.8446 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381200 6 0.3950 0.5615 0.000 0.432 0.000 0.000 0.004 0.564
#> GSM381201 3 0.0405 0.9720 0.000 0.000 0.988 0.004 0.000 0.008
#> GSM381203 1 0.4284 0.1494 0.544 0.000 0.440 0.000 0.004 0.012
#> GSM381204 1 0.0000 0.9273 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381209 1 0.0000 0.9273 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381212 1 0.0000 0.9273 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381213 2 0.3765 -0.0364 0.000 0.596 0.000 0.000 0.000 0.404
#> GSM381214 2 0.0000 0.8446 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381216 5 0.0146 0.7025 0.000 0.000 0.004 0.000 0.996 0.000
#> GSM381225 3 0.1082 0.9509 0.000 0.000 0.956 0.000 0.004 0.040
#> GSM381231 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381235 5 0.0858 0.6970 0.000 0.000 0.028 0.000 0.968 0.004
#> GSM381237 1 0.0000 0.9273 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381241 2 0.0000 0.8446 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381243 6 0.3081 0.9156 0.000 0.220 0.000 0.000 0.004 0.776
#> GSM381245 1 0.0935 0.9018 0.964 0.000 0.004 0.000 0.000 0.032
#> GSM381246 2 0.1814 0.7566 0.000 0.900 0.000 0.000 0.000 0.100
#> GSM381251 3 0.0291 0.9719 0.000 0.000 0.992 0.004 0.000 0.004
#> GSM381264 1 0.0000 0.9273 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381206 2 0.0000 0.8446 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381217 5 0.1531 0.7025 0.068 0.000 0.004 0.000 0.928 0.000
#> GSM381218 2 0.0000 0.8446 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381226 2 0.3371 0.4161 0.000 0.708 0.000 0.000 0.000 0.292
#> GSM381227 6 0.2941 0.9159 0.000 0.220 0.000 0.000 0.000 0.780
#> GSM381228 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381236 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381244 5 0.3643 0.6748 0.024 0.000 0.008 0.000 0.768 0.200
#> GSM381272 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381277 1 0.5634 0.1694 0.560 0.000 0.004 0.000 0.236 0.200
#> GSM381278 3 0.3121 0.7665 0.000 0.000 0.804 0.004 0.180 0.012
#> GSM381197 5 0.7454 0.4381 0.224 0.000 0.184 0.000 0.392 0.200
#> GSM381202 5 0.5067 0.5557 0.268 0.000 0.000 0.000 0.612 0.120
#> GSM381207 1 0.1552 0.8798 0.940 0.000 0.004 0.000 0.020 0.036
#> GSM381208 2 0.0000 0.8446 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381210 1 0.0260 0.9218 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM381215 3 0.1010 0.9559 0.000 0.000 0.960 0.000 0.036 0.004
#> GSM381219 2 0.0000 0.8446 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381221 2 0.3221 0.4945 0.000 0.736 0.000 0.000 0.000 0.264
#> GSM381223 6 0.3023 0.9116 0.000 0.232 0.000 0.000 0.000 0.768
#> GSM381229 3 0.0405 0.9714 0.000 0.000 0.988 0.004 0.000 0.008
#> GSM381230 1 0.0000 0.9273 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381233 5 0.3499 0.5451 0.320 0.000 0.000 0.000 0.680 0.000
#> GSM381234 1 0.0000 0.9273 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381238 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381239 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381242 5 0.3043 0.6731 0.000 0.000 0.008 0.000 0.792 0.200
#> GSM381247 6 0.3081 0.9156 0.000 0.220 0.000 0.000 0.004 0.776
#> GSM381248 1 0.0405 0.9210 0.988 0.000 0.004 0.000 0.000 0.008
#> GSM381249 5 0.3464 0.5541 0.312 0.000 0.000 0.000 0.688 0.000
#> GSM381253 3 0.0862 0.9624 0.016 0.000 0.972 0.000 0.004 0.008
#> GSM381255 2 0.0000 0.8446 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381258 5 0.0146 0.7025 0.000 0.000 0.004 0.000 0.996 0.000
#> GSM381262 3 0.0291 0.9719 0.000 0.000 0.992 0.004 0.000 0.004
#> GSM381266 3 0.0405 0.9714 0.000 0.000 0.988 0.004 0.000 0.008
#> GSM381267 2 0.3636 0.3249 0.000 0.676 0.000 0.000 0.004 0.320
#> GSM381269 5 0.0146 0.7033 0.004 0.000 0.000 0.000 0.996 0.000
#> GSM381273 3 0.0405 0.9714 0.000 0.000 0.988 0.004 0.000 0.008
#> GSM381274 6 0.3101 0.8999 0.000 0.244 0.000 0.000 0.000 0.756
#> GSM381276 5 0.6909 0.5612 0.172 0.000 0.128 0.000 0.496 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 other(p) k
#> SD:skmeans 78 0.572 2
#> SD:skmeans 81 0.677 3
#> SD:skmeans 83 0.490 4
#> SD:skmeans 79 0.418 5
#> SD:skmeans 76 0.545 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 86 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4528 0.548 0.548
#> 3 3 1.000 1.000 1.000 0.2366 0.893 0.804
#> 4 4 0.823 0.964 0.953 0.2335 0.856 0.672
#> 5 5 0.884 0.918 0.952 0.0764 0.954 0.845
#> 6 6 0.830 0.866 0.922 0.0456 0.982 0.930
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
#> GSM381194 1 0 1 1 0
#> GSM381199 2 0 1 0 1
#> GSM381205 2 0 1 0 1
#> GSM381211 2 0 1 0 1
#> GSM381220 2 0 1 0 1
#> GSM381222 1 0 1 1 0
#> GSM381224 1 0 1 1 0
#> GSM381232 1 0 1 1 0
#> GSM381240 1 0 1 1 0
#> GSM381250 1 0 1 1 0
#> GSM381252 2 0 1 0 1
#> GSM381254 1 0 1 1 0
#> GSM381256 2 0 1 0 1
#> GSM381257 1 0 1 1 0
#> GSM381259 1 0 1 1 0
#> GSM381260 1 0 1 1 0
#> GSM381261 2 0 1 0 1
#> GSM381263 1 0 1 1 0
#> GSM381265 1 0 1 1 0
#> GSM381268 1 0 1 1 0
#> GSM381270 2 0 1 0 1
#> GSM381271 1 0 1 1 0
#> GSM381275 2 0 1 0 1
#> GSM381279 2 0 1 0 1
#> GSM381195 1 0 1 1 0
#> GSM381196 1 0 1 1 0
#> GSM381198 2 0 1 0 1
#> GSM381200 2 0 1 0 1
#> GSM381201 1 0 1 1 0
#> GSM381203 1 0 1 1 0
#> GSM381204 1 0 1 1 0
#> GSM381209 1 0 1 1 0
#> GSM381212 1 0 1 1 0
#> GSM381213 2 0 1 0 1
#> GSM381214 2 0 1 0 1
#> GSM381216 1 0 1 1 0
#> GSM381225 1 0 1 1 0
#> GSM381231 1 0 1 1 0
#> GSM381235 1 0 1 1 0
#> GSM381237 1 0 1 1 0
#> GSM381241 2 0 1 0 1
#> GSM381243 2 0 1 0 1
#> GSM381245 1 0 1 1 0
#> GSM381246 2 0 1 0 1
#> GSM381251 1 0 1 1 0
#> GSM381264 1 0 1 1 0
#> GSM381206 2 0 1 0 1
#> GSM381217 1 0 1 1 0
#> GSM381218 2 0 1 0 1
#> GSM381226 2 0 1 0 1
#> GSM381227 2 0 1 0 1
#> GSM381228 1 0 1 1 0
#> GSM381236 1 0 1 1 0
#> GSM381244 1 0 1 1 0
#> GSM381272 1 0 1 1 0
#> GSM381277 1 0 1 1 0
#> GSM381278 1 0 1 1 0
#> GSM381197 1 0 1 1 0
#> GSM381202 1 0 1 1 0
#> GSM381207 1 0 1 1 0
#> GSM381208 2 0 1 0 1
#> GSM381210 1 0 1 1 0
#> GSM381215 1 0 1 1 0
#> GSM381219 2 0 1 0 1
#> GSM381221 2 0 1 0 1
#> GSM381223 2 0 1 0 1
#> GSM381229 1 0 1 1 0
#> GSM381230 1 0 1 1 0
#> GSM381233 1 0 1 1 0
#> GSM381234 1 0 1 1 0
#> GSM381238 1 0 1 1 0
#> GSM381239 1 0 1 1 0
#> GSM381242 1 0 1 1 0
#> GSM381247 2 0 1 0 1
#> GSM381248 1 0 1 1 0
#> GSM381249 1 0 1 1 0
#> GSM381253 1 0 1 1 0
#> GSM381255 2 0 1 0 1
#> GSM381258 1 0 1 1 0
#> GSM381262 1 0 1 1 0
#> GSM381266 1 0 1 1 0
#> GSM381267 2 0 1 0 1
#> GSM381269 1 0 1 1 0
#> GSM381273 1 0 1 1 0
#> GSM381274 2 0 1 0 1
#> GSM381276 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM381194 1 0 1 1 0 0
#> GSM381199 2 0 1 0 1 0
#> GSM381205 2 0 1 0 1 0
#> GSM381211 2 0 1 0 1 0
#> GSM381220 2 0 1 0 1 0
#> GSM381222 1 0 1 1 0 0
#> GSM381224 1 0 1 1 0 0
#> GSM381232 3 0 1 0 0 1
#> GSM381240 1 0 1 1 0 0
#> GSM381250 1 0 1 1 0 0
#> GSM381252 2 0 1 0 1 0
#> GSM381254 1 0 1 1 0 0
#> GSM381256 2 0 1 0 1 0
#> GSM381257 1 0 1 1 0 0
#> GSM381259 1 0 1 1 0 0
#> GSM381260 1 0 1 1 0 0
#> GSM381261 2 0 1 0 1 0
#> GSM381263 1 0 1 1 0 0
#> GSM381265 1 0 1 1 0 0
#> GSM381268 1 0 1 1 0 0
#> GSM381270 2 0 1 0 1 0
#> GSM381271 3 0 1 0 0 1
#> GSM381275 2 0 1 0 1 0
#> GSM381279 2 0 1 0 1 0
#> GSM381195 1 0 1 1 0 0
#> GSM381196 1 0 1 1 0 0
#> GSM381198 2 0 1 0 1 0
#> GSM381200 2 0 1 0 1 0
#> GSM381201 1 0 1 1 0 0
#> GSM381203 1 0 1 1 0 0
#> GSM381204 1 0 1 1 0 0
#> GSM381209 1 0 1 1 0 0
#> GSM381212 1 0 1 1 0 0
#> GSM381213 2 0 1 0 1 0
#> GSM381214 2 0 1 0 1 0
#> GSM381216 1 0 1 1 0 0
#> GSM381225 1 0 1 1 0 0
#> GSM381231 3 0 1 0 0 1
#> GSM381235 1 0 1 1 0 0
#> GSM381237 1 0 1 1 0 0
#> GSM381241 2 0 1 0 1 0
#> GSM381243 2 0 1 0 1 0
#> GSM381245 1 0 1 1 0 0
#> GSM381246 2 0 1 0 1 0
#> GSM381251 1 0 1 1 0 0
#> GSM381264 1 0 1 1 0 0
#> GSM381206 2 0 1 0 1 0
#> GSM381217 1 0 1 1 0 0
#> GSM381218 2 0 1 0 1 0
#> GSM381226 2 0 1 0 1 0
#> GSM381227 2 0 1 0 1 0
#> GSM381228 3 0 1 0 0 1
#> GSM381236 3 0 1 0 0 1
#> GSM381244 1 0 1 1 0 0
#> GSM381272 3 0 1 0 0 1
#> GSM381277 1 0 1 1 0 0
#> GSM381278 1 0 1 1 0 0
#> GSM381197 1 0 1 1 0 0
#> GSM381202 1 0 1 1 0 0
#> GSM381207 1 0 1 1 0 0
#> GSM381208 2 0 1 0 1 0
#> GSM381210 1 0 1 1 0 0
#> GSM381215 1 0 1 1 0 0
#> GSM381219 2 0 1 0 1 0
#> GSM381221 2 0 1 0 1 0
#> GSM381223 2 0 1 0 1 0
#> GSM381229 1 0 1 1 0 0
#> GSM381230 1 0 1 1 0 0
#> GSM381233 1 0 1 1 0 0
#> GSM381234 1 0 1 1 0 0
#> GSM381238 3 0 1 0 0 1
#> GSM381239 3 0 1 0 0 1
#> GSM381242 1 0 1 1 0 0
#> GSM381247 2 0 1 0 1 0
#> GSM381248 1 0 1 1 0 0
#> GSM381249 1 0 1 1 0 0
#> GSM381253 1 0 1 1 0 0
#> GSM381255 2 0 1 0 1 0
#> GSM381258 1 0 1 1 0 0
#> GSM381262 1 0 1 1 0 0
#> GSM381266 1 0 1 1 0 0
#> GSM381267 2 0 1 0 1 0
#> GSM381269 1 0 1 1 0 0
#> GSM381273 1 0 1 1 0 0
#> GSM381274 2 0 1 0 1 0
#> GSM381276 1 0 1 1 0 0
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM381194 3 0.0000 0.990 0.000 0.000 1.000 0.000
#> GSM381199 2 0.2921 0.908 0.140 0.860 0.000 0.000
#> GSM381205 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> GSM381211 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> GSM381220 2 0.1716 0.938 0.064 0.936 0.000 0.000
#> GSM381222 3 0.0000 0.990 0.000 0.000 1.000 0.000
#> GSM381224 1 0.3942 0.884 0.764 0.000 0.236 0.000
#> GSM381232 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM381240 1 0.2921 0.973 0.860 0.000 0.140 0.000
#> GSM381250 3 0.0000 0.990 0.000 0.000 1.000 0.000
#> GSM381252 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> GSM381254 1 0.2921 0.973 0.860 0.000 0.140 0.000
#> GSM381256 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> GSM381257 3 0.0000 0.990 0.000 0.000 1.000 0.000
#> GSM381259 1 0.2921 0.973 0.860 0.000 0.140 0.000
#> GSM381260 3 0.0000 0.990 0.000 0.000 1.000 0.000
#> GSM381261 2 0.2921 0.908 0.140 0.860 0.000 0.000
#> GSM381263 3 0.0000 0.990 0.000 0.000 1.000 0.000
#> GSM381265 1 0.2921 0.973 0.860 0.000 0.140 0.000
#> GSM381268 3 0.0000 0.990 0.000 0.000 1.000 0.000
#> GSM381270 2 0.2921 0.908 0.140 0.860 0.000 0.000
#> GSM381271 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM381275 2 0.2216 0.927 0.092 0.908 0.000 0.000
#> GSM381279 2 0.2921 0.908 0.140 0.860 0.000 0.000
#> GSM381195 1 0.3074 0.965 0.848 0.000 0.152 0.000
#> GSM381196 3 0.0000 0.990 0.000 0.000 1.000 0.000
#> GSM381198 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> GSM381200 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> GSM381201 3 0.0000 0.990 0.000 0.000 1.000 0.000
#> GSM381203 3 0.0000 0.990 0.000 0.000 1.000 0.000
#> GSM381204 1 0.2921 0.973 0.860 0.000 0.140 0.000
#> GSM381209 1 0.2921 0.973 0.860 0.000 0.140 0.000
#> GSM381212 1 0.2921 0.973 0.860 0.000 0.140 0.000
#> GSM381213 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> GSM381214 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> GSM381216 3 0.0000 0.990 0.000 0.000 1.000 0.000
#> GSM381225 3 0.0000 0.990 0.000 0.000 1.000 0.000
#> GSM381231 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM381235 3 0.0000 0.990 0.000 0.000 1.000 0.000
#> GSM381237 1 0.2921 0.973 0.860 0.000 0.140 0.000
#> GSM381241 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> GSM381243 2 0.2921 0.908 0.140 0.860 0.000 0.000
#> GSM381245 3 0.0000 0.990 0.000 0.000 1.000 0.000
#> GSM381246 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> GSM381251 3 0.0000 0.990 0.000 0.000 1.000 0.000
#> GSM381264 1 0.2921 0.973 0.860 0.000 0.140 0.000
#> GSM381206 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> GSM381217 3 0.0000 0.990 0.000 0.000 1.000 0.000
#> GSM381218 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> GSM381226 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> GSM381227 2 0.2921 0.908 0.140 0.860 0.000 0.000
#> GSM381228 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM381236 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM381244 3 0.0000 0.990 0.000 0.000 1.000 0.000
#> GSM381272 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM381277 1 0.3356 0.947 0.824 0.000 0.176 0.000
#> GSM381278 3 0.0188 0.985 0.004 0.000 0.996 0.000
#> GSM381197 3 0.0000 0.990 0.000 0.000 1.000 0.000
#> GSM381202 3 0.1389 0.934 0.048 0.000 0.952 0.000
#> GSM381207 3 0.0000 0.990 0.000 0.000 1.000 0.000
#> GSM381208 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> GSM381210 1 0.2921 0.973 0.860 0.000 0.140 0.000
#> GSM381215 3 0.0000 0.990 0.000 0.000 1.000 0.000
#> GSM381219 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> GSM381221 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> GSM381223 2 0.2921 0.908 0.140 0.860 0.000 0.000
#> GSM381229 3 0.0000 0.990 0.000 0.000 1.000 0.000
#> GSM381230 1 0.2921 0.973 0.860 0.000 0.140 0.000
#> GSM381233 3 0.0000 0.990 0.000 0.000 1.000 0.000
#> GSM381234 1 0.3873 0.895 0.772 0.000 0.228 0.000
#> GSM381238 4 0.0188 0.997 0.004 0.000 0.000 0.996
#> GSM381239 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM381242 3 0.0000 0.990 0.000 0.000 1.000 0.000
#> GSM381247 2 0.2921 0.908 0.140 0.860 0.000 0.000
#> GSM381248 3 0.3726 0.660 0.212 0.000 0.788 0.000
#> GSM381249 1 0.3610 0.925 0.800 0.000 0.200 0.000
#> GSM381253 3 0.0000 0.990 0.000 0.000 1.000 0.000
#> GSM381255 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> GSM381258 3 0.0000 0.990 0.000 0.000 1.000 0.000
#> GSM381262 3 0.0000 0.990 0.000 0.000 1.000 0.000
#> GSM381266 3 0.0000 0.990 0.000 0.000 1.000 0.000
#> GSM381267 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> GSM381269 3 0.0188 0.986 0.004 0.000 0.996 0.000
#> GSM381273 3 0.0000 0.990 0.000 0.000 1.000 0.000
#> GSM381274 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> GSM381276 3 0.0000 0.990 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM381194 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000
#> GSM381199 5 0.4171 0.661 0.000 0.396 0.000 0.000 0.604
#> GSM381205 2 0.0000 0.935 0.000 1.000 0.000 0.000 0.000
#> GSM381211 2 0.0000 0.935 0.000 1.000 0.000 0.000 0.000
#> GSM381220 5 0.3949 0.778 0.000 0.332 0.000 0.000 0.668
#> GSM381222 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000
#> GSM381224 1 0.3395 0.704 0.764 0.000 0.236 0.000 0.000
#> GSM381232 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM381240 1 0.0000 0.918 1.000 0.000 0.000 0.000 0.000
#> GSM381250 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000
#> GSM381252 2 0.0000 0.935 0.000 1.000 0.000 0.000 0.000
#> GSM381254 1 0.0000 0.918 1.000 0.000 0.000 0.000 0.000
#> GSM381256 2 0.0162 0.935 0.000 0.996 0.000 0.000 0.004
#> GSM381257 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000
#> GSM381259 1 0.0000 0.918 1.000 0.000 0.000 0.000 0.000
#> GSM381260 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000
#> GSM381261 5 0.0162 0.644 0.000 0.004 0.000 0.000 0.996
#> GSM381263 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000
#> GSM381265 1 0.0000 0.918 1.000 0.000 0.000 0.000 0.000
#> GSM381268 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000
#> GSM381270 5 0.3336 0.888 0.000 0.228 0.000 0.000 0.772
#> GSM381271 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM381275 2 0.4015 0.502 0.000 0.652 0.000 0.000 0.348
#> GSM381279 5 0.3210 0.895 0.000 0.212 0.000 0.000 0.788
#> GSM381195 1 0.0404 0.910 0.988 0.000 0.012 0.000 0.000
#> GSM381196 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000
#> GSM381198 2 0.0000 0.935 0.000 1.000 0.000 0.000 0.000
#> GSM381200 2 0.0162 0.935 0.000 0.996 0.000 0.000 0.004
#> GSM381201 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000
#> GSM381203 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000
#> GSM381204 1 0.0000 0.918 1.000 0.000 0.000 0.000 0.000
#> GSM381209 1 0.0000 0.918 1.000 0.000 0.000 0.000 0.000
#> GSM381212 1 0.0000 0.918 1.000 0.000 0.000 0.000 0.000
#> GSM381213 2 0.0290 0.933 0.000 0.992 0.000 0.000 0.008
#> GSM381214 2 0.0162 0.935 0.000 0.996 0.000 0.000 0.004
#> GSM381216 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000
#> GSM381225 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000
#> GSM381231 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM381235 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000
#> GSM381237 1 0.0000 0.918 1.000 0.000 0.000 0.000 0.000
#> GSM381241 2 0.0000 0.935 0.000 1.000 0.000 0.000 0.000
#> GSM381243 5 0.3242 0.895 0.000 0.216 0.000 0.000 0.784
#> GSM381245 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000
#> GSM381246 2 0.0000 0.935 0.000 1.000 0.000 0.000 0.000
#> GSM381251 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000
#> GSM381264 1 0.0162 0.916 0.996 0.000 0.004 0.000 0.000
#> GSM381206 2 0.0000 0.935 0.000 1.000 0.000 0.000 0.000
#> GSM381217 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000
#> GSM381218 2 0.0162 0.935 0.000 0.996 0.000 0.000 0.004
#> GSM381226 2 0.0162 0.935 0.000 0.996 0.000 0.000 0.004
#> GSM381227 5 0.3242 0.895 0.000 0.216 0.000 0.000 0.784
#> GSM381228 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM381236 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM381244 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000
#> GSM381272 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM381277 1 0.2813 0.780 0.832 0.000 0.168 0.000 0.000
#> GSM381278 3 0.0162 0.984 0.000 0.000 0.996 0.000 0.004
#> GSM381197 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000
#> GSM381202 3 0.2561 0.821 0.144 0.000 0.856 0.000 0.000
#> GSM381207 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000
#> GSM381208 2 0.0000 0.935 0.000 1.000 0.000 0.000 0.000
#> GSM381210 1 0.0000 0.918 1.000 0.000 0.000 0.000 0.000
#> GSM381215 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000
#> GSM381219 2 0.0162 0.935 0.000 0.996 0.000 0.000 0.004
#> GSM381221 2 0.0162 0.935 0.000 0.996 0.000 0.000 0.004
#> GSM381223 2 0.4268 0.296 0.000 0.556 0.000 0.000 0.444
#> GSM381229 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000
#> GSM381230 1 0.0000 0.918 1.000 0.000 0.000 0.000 0.000
#> GSM381233 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000
#> GSM381234 1 0.3336 0.716 0.772 0.000 0.228 0.000 0.000
#> GSM381238 4 0.0162 0.996 0.000 0.000 0.000 0.996 0.004
#> GSM381239 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM381242 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000
#> GSM381247 5 0.3210 0.895 0.000 0.212 0.000 0.000 0.788
#> GSM381248 3 0.3210 0.705 0.212 0.000 0.788 0.000 0.000
#> GSM381249 1 0.3109 0.748 0.800 0.000 0.200 0.000 0.000
#> GSM381253 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000
#> GSM381255 2 0.0000 0.935 0.000 1.000 0.000 0.000 0.000
#> GSM381258 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000
#> GSM381262 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000
#> GSM381266 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000
#> GSM381267 2 0.0162 0.935 0.000 0.996 0.000 0.000 0.004
#> GSM381269 3 0.0162 0.984 0.004 0.000 0.996 0.000 0.000
#> GSM381273 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000
#> GSM381274 2 0.3366 0.670 0.000 0.768 0.000 0.000 0.232
#> GSM381276 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM381194 3 0.0000 0.927 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM381199 6 0.2527 0.661 0.000 0.168 0.000 0.000 0.000 0.832
#> GSM381205 2 0.0260 0.879 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM381211 2 0.0146 0.879 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM381220 6 0.1863 0.762 0.000 0.104 0.000 0.000 0.000 0.896
#> GSM381222 3 0.1610 0.900 0.000 0.000 0.916 0.000 0.084 0.000
#> GSM381224 1 0.3163 0.687 0.764 0.000 0.232 0.000 0.004 0.000
#> GSM381232 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381240 1 0.0000 0.921 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381250 3 0.0000 0.927 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM381252 2 0.0260 0.879 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM381254 1 0.0000 0.921 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381256 2 0.3431 0.780 0.000 0.756 0.000 0.000 0.016 0.228
#> GSM381257 3 0.0000 0.927 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM381259 1 0.0000 0.921 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381260 3 0.0260 0.926 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM381261 5 0.3636 0.505 0.000 0.004 0.000 0.000 0.676 0.320
#> GSM381263 3 0.0000 0.927 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM381265 1 0.0000 0.921 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381268 3 0.0000 0.927 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM381270 6 0.0000 0.861 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM381271 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381275 5 0.4707 0.731 0.000 0.204 0.000 0.000 0.676 0.120
#> GSM381279 6 0.0000 0.861 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM381195 1 0.0363 0.912 0.988 0.000 0.012 0.000 0.000 0.000
#> GSM381196 3 0.0000 0.927 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM381198 2 0.0260 0.879 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM381200 2 0.2805 0.841 0.000 0.828 0.000 0.000 0.012 0.160
#> GSM381201 3 0.1141 0.911 0.000 0.000 0.948 0.000 0.052 0.000
#> GSM381203 3 0.0000 0.927 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM381204 1 0.0000 0.921 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381209 1 0.0000 0.921 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381212 1 0.0000 0.921 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381213 2 0.3345 0.729 0.000 0.776 0.000 0.000 0.204 0.020
#> GSM381214 2 0.0909 0.879 0.000 0.968 0.000 0.000 0.012 0.020
#> GSM381216 3 0.3175 0.770 0.000 0.000 0.744 0.000 0.256 0.000
#> GSM381225 3 0.0000 0.927 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM381231 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381235 3 0.1957 0.884 0.000 0.000 0.888 0.000 0.112 0.000
#> GSM381237 1 0.0000 0.921 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381241 2 0.2513 0.849 0.000 0.852 0.000 0.000 0.008 0.140
#> GSM381243 6 0.0260 0.858 0.000 0.008 0.000 0.000 0.000 0.992
#> GSM381245 3 0.0000 0.927 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM381246 2 0.0363 0.879 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM381251 3 0.1141 0.911 0.000 0.000 0.948 0.000 0.052 0.000
#> GSM381264 1 0.0146 0.919 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM381206 2 0.0260 0.879 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM381217 3 0.1501 0.904 0.000 0.000 0.924 0.000 0.076 0.000
#> GSM381218 2 0.2805 0.841 0.000 0.828 0.000 0.000 0.012 0.160
#> GSM381226 2 0.1151 0.879 0.000 0.956 0.000 0.000 0.012 0.032
#> GSM381227 6 0.2454 0.665 0.000 0.160 0.000 0.000 0.000 0.840
#> GSM381228 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381236 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381244 3 0.1267 0.909 0.000 0.000 0.940 0.000 0.060 0.000
#> GSM381272 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381277 1 0.2778 0.762 0.824 0.000 0.168 0.000 0.008 0.000
#> GSM381278 3 0.2006 0.886 0.000 0.000 0.892 0.000 0.104 0.004
#> GSM381197 3 0.1267 0.909 0.000 0.000 0.940 0.000 0.060 0.000
#> GSM381202 3 0.2300 0.833 0.144 0.000 0.856 0.000 0.000 0.000
#> GSM381207 3 0.0000 0.927 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM381208 2 0.0146 0.879 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM381210 1 0.0000 0.921 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381215 3 0.0000 0.927 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM381219 2 0.2805 0.841 0.000 0.828 0.000 0.000 0.012 0.160
#> GSM381221 2 0.3046 0.822 0.000 0.800 0.000 0.000 0.012 0.188
#> GSM381223 5 0.4614 0.709 0.000 0.108 0.000 0.000 0.684 0.208
#> GSM381229 3 0.1141 0.911 0.000 0.000 0.948 0.000 0.052 0.000
#> GSM381230 1 0.0000 0.921 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381233 3 0.3126 0.775 0.000 0.000 0.752 0.000 0.248 0.000
#> GSM381234 1 0.2996 0.697 0.772 0.000 0.228 0.000 0.000 0.000
#> GSM381238 4 0.0146 0.995 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM381239 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381242 3 0.3023 0.788 0.000 0.000 0.768 0.000 0.232 0.000
#> GSM381247 6 0.0000 0.861 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM381248 3 0.2883 0.698 0.212 0.000 0.788 0.000 0.000 0.000
#> GSM381249 1 0.3713 0.707 0.744 0.000 0.032 0.000 0.224 0.000
#> GSM381253 3 0.0000 0.927 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM381255 2 0.0260 0.879 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM381258 3 0.3175 0.770 0.000 0.000 0.744 0.000 0.256 0.000
#> GSM381262 3 0.0000 0.927 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM381266 3 0.0632 0.921 0.000 0.000 0.976 0.000 0.024 0.000
#> GSM381267 2 0.3201 0.803 0.000 0.780 0.000 0.000 0.012 0.208
#> GSM381269 3 0.3314 0.767 0.004 0.000 0.740 0.000 0.256 0.000
#> GSM381273 3 0.1141 0.911 0.000 0.000 0.948 0.000 0.052 0.000
#> GSM381274 5 0.3482 0.597 0.000 0.316 0.000 0.000 0.684 0.000
#> GSM381276 3 0.0260 0.926 0.000 0.000 0.992 0.000 0.008 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 other(p) k
#> SD:pam 86 0.744 2
#> SD:pam 86 0.326 3
#> SD:pam 86 0.394 4
#> SD:pam 85 0.302 5
#> SD:pam 86 0.414 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 86 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.829 0.944 0.974 0.4652 0.548 0.548
#> 3 3 0.941 0.930 0.958 0.2604 0.893 0.804
#> 4 4 0.801 0.863 0.896 0.1989 0.839 0.635
#> 5 5 0.693 0.677 0.782 0.0831 0.874 0.598
#> 6 6 0.796 0.615 0.831 0.0748 0.895 0.587
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
#> GSM381194 1 0.000 0.958 1.000 0.000
#> GSM381199 2 0.000 1.000 0.000 1.000
#> GSM381205 2 0.000 1.000 0.000 1.000
#> GSM381211 2 0.000 1.000 0.000 1.000
#> GSM381220 2 0.000 1.000 0.000 1.000
#> GSM381222 1 0.000 0.958 1.000 0.000
#> GSM381224 1 0.000 0.958 1.000 0.000
#> GSM381232 1 0.861 0.653 0.716 0.284
#> GSM381240 1 0.000 0.958 1.000 0.000
#> GSM381250 1 0.000 0.958 1.000 0.000
#> GSM381252 2 0.000 1.000 0.000 1.000
#> GSM381254 1 0.000 0.958 1.000 0.000
#> GSM381256 2 0.000 1.000 0.000 1.000
#> GSM381257 1 0.000 0.958 1.000 0.000
#> GSM381259 1 0.000 0.958 1.000 0.000
#> GSM381260 1 0.000 0.958 1.000 0.000
#> GSM381261 2 0.000 1.000 0.000 1.000
#> GSM381263 1 0.000 0.958 1.000 0.000
#> GSM381265 1 0.000 0.958 1.000 0.000
#> GSM381268 1 0.000 0.958 1.000 0.000
#> GSM381270 2 0.000 1.000 0.000 1.000
#> GSM381271 1 0.861 0.653 0.716 0.284
#> GSM381275 2 0.000 1.000 0.000 1.000
#> GSM381279 2 0.000 1.000 0.000 1.000
#> GSM381195 1 0.000 0.958 1.000 0.000
#> GSM381196 1 0.000 0.958 1.000 0.000
#> GSM381198 2 0.000 1.000 0.000 1.000
#> GSM381200 2 0.000 1.000 0.000 1.000
#> GSM381201 1 0.000 0.958 1.000 0.000
#> GSM381203 1 0.000 0.958 1.000 0.000
#> GSM381204 1 0.000 0.958 1.000 0.000
#> GSM381209 1 0.000 0.958 1.000 0.000
#> GSM381212 1 0.000 0.958 1.000 0.000
#> GSM381213 2 0.000 1.000 0.000 1.000
#> GSM381214 2 0.000 1.000 0.000 1.000
#> GSM381216 1 0.000 0.958 1.000 0.000
#> GSM381225 1 0.000 0.958 1.000 0.000
#> GSM381231 1 0.861 0.653 0.716 0.284
#> GSM381235 1 0.000 0.958 1.000 0.000
#> GSM381237 1 0.000 0.958 1.000 0.000
#> GSM381241 2 0.000 1.000 0.000 1.000
#> GSM381243 2 0.000 1.000 0.000 1.000
#> GSM381245 1 0.000 0.958 1.000 0.000
#> GSM381246 2 0.000 1.000 0.000 1.000
#> GSM381251 1 0.000 0.958 1.000 0.000
#> GSM381264 1 0.000 0.958 1.000 0.000
#> GSM381206 2 0.000 1.000 0.000 1.000
#> GSM381217 1 0.000 0.958 1.000 0.000
#> GSM381218 2 0.000 1.000 0.000 1.000
#> GSM381226 2 0.000 1.000 0.000 1.000
#> GSM381227 2 0.000 1.000 0.000 1.000
#> GSM381228 1 0.861 0.653 0.716 0.284
#> GSM381236 1 0.861 0.653 0.716 0.284
#> GSM381244 1 0.000 0.958 1.000 0.000
#> GSM381272 1 0.861 0.653 0.716 0.284
#> GSM381277 1 0.000 0.958 1.000 0.000
#> GSM381278 1 0.000 0.958 1.000 0.000
#> GSM381197 1 0.000 0.958 1.000 0.000
#> GSM381202 1 0.000 0.958 1.000 0.000
#> GSM381207 1 0.000 0.958 1.000 0.000
#> GSM381208 2 0.000 1.000 0.000 1.000
#> GSM381210 1 0.000 0.958 1.000 0.000
#> GSM381215 1 0.000 0.958 1.000 0.000
#> GSM381219 2 0.000 1.000 0.000 1.000
#> GSM381221 2 0.000 1.000 0.000 1.000
#> GSM381223 2 0.000 1.000 0.000 1.000
#> GSM381229 1 0.000 0.958 1.000 0.000
#> GSM381230 1 0.000 0.958 1.000 0.000
#> GSM381233 1 0.000 0.958 1.000 0.000
#> GSM381234 1 0.000 0.958 1.000 0.000
#> GSM381238 1 0.861 0.653 0.716 0.284
#> GSM381239 1 0.861 0.653 0.716 0.284
#> GSM381242 1 0.000 0.958 1.000 0.000
#> GSM381247 2 0.000 1.000 0.000 1.000
#> GSM381248 1 0.000 0.958 1.000 0.000
#> GSM381249 1 0.000 0.958 1.000 0.000
#> GSM381253 1 0.000 0.958 1.000 0.000
#> GSM381255 2 0.000 1.000 0.000 1.000
#> GSM381258 1 0.000 0.958 1.000 0.000
#> GSM381262 1 0.000 0.958 1.000 0.000
#> GSM381266 1 0.000 0.958 1.000 0.000
#> GSM381267 2 0.000 1.000 0.000 1.000
#> GSM381269 1 0.000 0.958 1.000 0.000
#> GSM381273 1 0.000 0.958 1.000 0.000
#> GSM381274 2 0.000 1.000 0.000 1.000
#> GSM381276 1 0.000 0.958 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM381194 1 0.4842 0.759 0.776 0.000 0.224
#> GSM381199 2 0.0000 1.000 0.000 1.000 0.000
#> GSM381205 2 0.0000 1.000 0.000 1.000 0.000
#> GSM381211 2 0.0000 1.000 0.000 1.000 0.000
#> GSM381220 2 0.0000 1.000 0.000 1.000 0.000
#> GSM381222 1 0.0000 0.931 1.000 0.000 0.000
#> GSM381224 1 0.0000 0.931 1.000 0.000 0.000
#> GSM381232 3 0.0747 1.000 0.000 0.016 0.984
#> GSM381240 1 0.0747 0.930 0.984 0.000 0.016
#> GSM381250 1 0.1643 0.919 0.956 0.000 0.044
#> GSM381252 2 0.0000 1.000 0.000 1.000 0.000
#> GSM381254 1 0.0747 0.930 0.984 0.000 0.016
#> GSM381256 2 0.0000 1.000 0.000 1.000 0.000
#> GSM381257 1 0.0237 0.931 0.996 0.000 0.004
#> GSM381259 1 0.0747 0.930 0.984 0.000 0.016
#> GSM381260 1 0.0000 0.931 1.000 0.000 0.000
#> GSM381261 2 0.0000 1.000 0.000 1.000 0.000
#> GSM381263 1 0.1643 0.919 0.956 0.000 0.044
#> GSM381265 1 0.0747 0.930 0.984 0.000 0.016
#> GSM381268 1 0.1643 0.919 0.956 0.000 0.044
#> GSM381270 2 0.0000 1.000 0.000 1.000 0.000
#> GSM381271 3 0.0747 1.000 0.000 0.016 0.984
#> GSM381275 2 0.0000 1.000 0.000 1.000 0.000
#> GSM381279 2 0.0000 1.000 0.000 1.000 0.000
#> GSM381195 1 0.0747 0.930 0.984 0.000 0.016
#> GSM381196 1 0.1643 0.919 0.956 0.000 0.044
#> GSM381198 2 0.0000 1.000 0.000 1.000 0.000
#> GSM381200 2 0.0000 1.000 0.000 1.000 0.000
#> GSM381201 1 0.1643 0.919 0.956 0.000 0.044
#> GSM381203 1 0.1643 0.919 0.956 0.000 0.044
#> GSM381204 1 0.0747 0.930 0.984 0.000 0.016
#> GSM381209 1 0.0747 0.930 0.984 0.000 0.016
#> GSM381212 1 0.0747 0.930 0.984 0.000 0.016
#> GSM381213 2 0.0000 1.000 0.000 1.000 0.000
#> GSM381214 2 0.0000 1.000 0.000 1.000 0.000
#> GSM381216 1 0.1529 0.921 0.960 0.000 0.040
#> GSM381225 1 0.5905 0.564 0.648 0.000 0.352
#> GSM381231 3 0.0747 1.000 0.000 0.016 0.984
#> GSM381235 1 0.1643 0.919 0.956 0.000 0.044
#> GSM381237 1 0.0747 0.930 0.984 0.000 0.016
#> GSM381241 2 0.0000 1.000 0.000 1.000 0.000
#> GSM381243 2 0.0000 1.000 0.000 1.000 0.000
#> GSM381245 1 0.0747 0.930 0.984 0.000 0.016
#> GSM381246 2 0.0000 1.000 0.000 1.000 0.000
#> GSM381251 1 0.5497 0.666 0.708 0.000 0.292
#> GSM381264 1 0.0747 0.930 0.984 0.000 0.016
#> GSM381206 2 0.0000 1.000 0.000 1.000 0.000
#> GSM381217 1 0.1411 0.922 0.964 0.000 0.036
#> GSM381218 2 0.0000 1.000 0.000 1.000 0.000
#> GSM381226 2 0.0000 1.000 0.000 1.000 0.000
#> GSM381227 2 0.0000 1.000 0.000 1.000 0.000
#> GSM381228 3 0.0747 1.000 0.000 0.016 0.984
#> GSM381236 3 0.0747 1.000 0.000 0.016 0.984
#> GSM381244 1 0.0000 0.931 1.000 0.000 0.000
#> GSM381272 3 0.0747 1.000 0.000 0.016 0.984
#> GSM381277 1 0.0747 0.930 0.984 0.000 0.016
#> GSM381278 1 0.4931 0.749 0.768 0.000 0.232
#> GSM381197 1 0.0000 0.931 1.000 0.000 0.000
#> GSM381202 1 0.0000 0.931 1.000 0.000 0.000
#> GSM381207 1 0.0747 0.930 0.984 0.000 0.016
#> GSM381208 2 0.0000 1.000 0.000 1.000 0.000
#> GSM381210 1 0.0747 0.930 0.984 0.000 0.016
#> GSM381215 1 0.2537 0.898 0.920 0.000 0.080
#> GSM381219 2 0.0000 1.000 0.000 1.000 0.000
#> GSM381221 2 0.0000 1.000 0.000 1.000 0.000
#> GSM381223 2 0.0000 1.000 0.000 1.000 0.000
#> GSM381229 1 0.4931 0.749 0.768 0.000 0.232
#> GSM381230 1 0.0747 0.930 0.984 0.000 0.016
#> GSM381233 1 0.0000 0.931 1.000 0.000 0.000
#> GSM381234 1 0.0747 0.930 0.984 0.000 0.016
#> GSM381238 3 0.0747 1.000 0.000 0.016 0.984
#> GSM381239 3 0.0747 1.000 0.000 0.016 0.984
#> GSM381242 1 0.0000 0.931 1.000 0.000 0.000
#> GSM381247 2 0.0000 1.000 0.000 1.000 0.000
#> GSM381248 1 0.0747 0.930 0.984 0.000 0.016
#> GSM381249 1 0.0237 0.931 0.996 0.000 0.004
#> GSM381253 1 0.0000 0.931 1.000 0.000 0.000
#> GSM381255 2 0.0000 1.000 0.000 1.000 0.000
#> GSM381258 1 0.2356 0.903 0.928 0.000 0.072
#> GSM381262 1 0.4842 0.759 0.776 0.000 0.224
#> GSM381266 1 0.6008 0.520 0.628 0.000 0.372
#> GSM381267 2 0.0000 1.000 0.000 1.000 0.000
#> GSM381269 1 0.0000 0.931 1.000 0.000 0.000
#> GSM381273 1 0.6305 0.224 0.516 0.000 0.484
#> GSM381274 2 0.0000 1.000 0.000 1.000 0.000
#> GSM381276 1 0.2066 0.911 0.940 0.000 0.060
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM381194 3 0.3356 0.8865 0.176 0.000 0.824 0.000
#> GSM381199 2 0.0336 0.9877 0.000 0.992 0.008 0.000
#> GSM381205 2 0.0921 0.9809 0.000 0.972 0.028 0.000
#> GSM381211 2 0.0921 0.9809 0.000 0.972 0.028 0.000
#> GSM381220 2 0.0000 0.9873 0.000 1.000 0.000 0.000
#> GSM381222 1 0.2216 0.8424 0.908 0.000 0.092 0.000
#> GSM381224 1 0.2814 0.8154 0.868 0.000 0.132 0.000
#> GSM381232 4 0.0000 1.0000 0.000 0.000 0.000 1.000
#> GSM381240 1 0.0000 0.8617 1.000 0.000 0.000 0.000
#> GSM381250 3 0.3569 0.8949 0.196 0.000 0.804 0.000
#> GSM381252 2 0.0921 0.9809 0.000 0.972 0.028 0.000
#> GSM381254 1 0.1474 0.8476 0.948 0.000 0.052 0.000
#> GSM381256 2 0.0336 0.9861 0.000 0.992 0.008 0.000
#> GSM381257 1 0.1716 0.8427 0.936 0.000 0.064 0.000
#> GSM381259 1 0.0000 0.8617 1.000 0.000 0.000 0.000
#> GSM381260 1 0.4855 0.0693 0.600 0.000 0.400 0.000
#> GSM381261 2 0.0336 0.9877 0.000 0.992 0.008 0.000
#> GSM381263 3 0.3726 0.8844 0.212 0.000 0.788 0.000
#> GSM381265 1 0.0469 0.8605 0.988 0.000 0.012 0.000
#> GSM381268 3 0.3569 0.8949 0.196 0.000 0.804 0.000
#> GSM381270 2 0.0336 0.9877 0.000 0.992 0.008 0.000
#> GSM381271 4 0.0000 1.0000 0.000 0.000 0.000 1.000
#> GSM381275 2 0.0336 0.9877 0.000 0.992 0.008 0.000
#> GSM381279 2 0.0336 0.9877 0.000 0.992 0.008 0.000
#> GSM381195 1 0.0000 0.8617 1.000 0.000 0.000 0.000
#> GSM381196 3 0.3486 0.8924 0.188 0.000 0.812 0.000
#> GSM381198 2 0.0921 0.9809 0.000 0.972 0.028 0.000
#> GSM381200 2 0.0336 0.9877 0.000 0.992 0.008 0.000
#> GSM381201 3 0.3569 0.8949 0.196 0.000 0.804 0.000
#> GSM381203 3 0.3356 0.8865 0.176 0.000 0.824 0.000
#> GSM381204 1 0.0000 0.8617 1.000 0.000 0.000 0.000
#> GSM381209 1 0.0000 0.8617 1.000 0.000 0.000 0.000
#> GSM381212 1 0.0000 0.8617 1.000 0.000 0.000 0.000
#> GSM381213 2 0.0000 0.9873 0.000 1.000 0.000 0.000
#> GSM381214 2 0.0921 0.9809 0.000 0.972 0.028 0.000
#> GSM381216 3 0.4746 0.3327 0.368 0.000 0.632 0.000
#> GSM381225 3 0.4171 0.8348 0.116 0.000 0.824 0.060
#> GSM381231 4 0.0000 1.0000 0.000 0.000 0.000 1.000
#> GSM381235 3 0.4543 0.4563 0.324 0.000 0.676 0.000
#> GSM381237 1 0.0000 0.8617 1.000 0.000 0.000 0.000
#> GSM381241 2 0.0921 0.9809 0.000 0.972 0.028 0.000
#> GSM381243 2 0.0336 0.9877 0.000 0.992 0.008 0.000
#> GSM381245 1 0.2011 0.8334 0.920 0.000 0.080 0.000
#> GSM381246 2 0.0000 0.9873 0.000 1.000 0.000 0.000
#> GSM381251 3 0.3569 0.8949 0.196 0.000 0.804 0.000
#> GSM381264 1 0.0000 0.8617 1.000 0.000 0.000 0.000
#> GSM381206 2 0.0921 0.9809 0.000 0.972 0.028 0.000
#> GSM381217 3 0.4585 0.5825 0.332 0.000 0.668 0.000
#> GSM381218 2 0.0921 0.9809 0.000 0.972 0.028 0.000
#> GSM381226 2 0.0336 0.9877 0.000 0.992 0.008 0.000
#> GSM381227 2 0.0336 0.9877 0.000 0.992 0.008 0.000
#> GSM381228 4 0.0000 1.0000 0.000 0.000 0.000 1.000
#> GSM381236 4 0.0000 1.0000 0.000 0.000 0.000 1.000
#> GSM381244 1 0.1557 0.8454 0.944 0.000 0.056 0.000
#> GSM381272 4 0.0000 1.0000 0.000 0.000 0.000 1.000
#> GSM381277 1 0.1557 0.8454 0.944 0.000 0.056 0.000
#> GSM381278 3 0.2081 0.8107 0.084 0.000 0.916 0.000
#> GSM381197 1 0.3219 0.7306 0.836 0.000 0.164 0.000
#> GSM381202 1 0.4277 0.4957 0.720 0.000 0.280 0.000
#> GSM381207 1 0.4500 0.4387 0.684 0.000 0.316 0.000
#> GSM381208 2 0.0188 0.9868 0.000 0.996 0.004 0.000
#> GSM381210 1 0.0000 0.8617 1.000 0.000 0.000 0.000
#> GSM381215 3 0.3569 0.8949 0.196 0.000 0.804 0.000
#> GSM381219 2 0.0921 0.9809 0.000 0.972 0.028 0.000
#> GSM381221 2 0.0336 0.9877 0.000 0.992 0.008 0.000
#> GSM381223 2 0.0336 0.9877 0.000 0.992 0.008 0.000
#> GSM381229 3 0.3569 0.8949 0.196 0.000 0.804 0.000
#> GSM381230 1 0.0000 0.8617 1.000 0.000 0.000 0.000
#> GSM381233 1 0.3569 0.7610 0.804 0.000 0.196 0.000
#> GSM381234 1 0.0188 0.8616 0.996 0.000 0.004 0.000
#> GSM381238 4 0.0000 1.0000 0.000 0.000 0.000 1.000
#> GSM381239 4 0.0000 1.0000 0.000 0.000 0.000 1.000
#> GSM381242 1 0.4948 -0.1062 0.560 0.000 0.440 0.000
#> GSM381247 2 0.0336 0.9877 0.000 0.992 0.008 0.000
#> GSM381248 1 0.4500 0.4673 0.684 0.000 0.316 0.000
#> GSM381249 1 0.2408 0.7930 0.896 0.000 0.104 0.000
#> GSM381253 3 0.4222 0.8186 0.272 0.000 0.728 0.000
#> GSM381255 2 0.0921 0.9809 0.000 0.972 0.028 0.000
#> GSM381258 3 0.3528 0.6945 0.192 0.000 0.808 0.000
#> GSM381262 3 0.3569 0.8949 0.196 0.000 0.804 0.000
#> GSM381266 3 0.3569 0.8949 0.196 0.000 0.804 0.000
#> GSM381267 2 0.0336 0.9869 0.000 0.992 0.008 0.000
#> GSM381269 1 0.3688 0.7557 0.792 0.000 0.208 0.000
#> GSM381273 3 0.4136 0.8881 0.196 0.000 0.788 0.016
#> GSM381274 2 0.0336 0.9877 0.000 0.992 0.008 0.000
#> GSM381276 3 0.3356 0.8865 0.176 0.000 0.824 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM381194 3 0.4735 0.5711 0.048 0.000 0.680 0.000 0.272
#> GSM381199 5 0.3857 0.9350 0.000 0.312 0.000 0.000 0.688
#> GSM381205 2 0.0000 0.7948 0.000 1.000 0.000 0.000 0.000
#> GSM381211 2 0.0000 0.7948 0.000 1.000 0.000 0.000 0.000
#> GSM381220 2 0.1043 0.7890 0.000 0.960 0.000 0.000 0.040
#> GSM381222 1 0.4392 -0.1792 0.612 0.000 0.380 0.000 0.008
#> GSM381224 1 0.4354 -0.1601 0.624 0.000 0.368 0.000 0.008
#> GSM381232 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM381240 1 0.3752 0.8141 0.708 0.000 0.292 0.000 0.000
#> GSM381250 3 0.1341 0.6302 0.056 0.000 0.944 0.000 0.000
#> GSM381252 2 0.1732 0.7694 0.000 0.920 0.000 0.000 0.080
#> GSM381254 1 0.4030 0.7893 0.648 0.000 0.352 0.000 0.000
#> GSM381256 2 0.4268 -0.2366 0.000 0.556 0.000 0.000 0.444
#> GSM381257 1 0.4138 0.7699 0.616 0.000 0.384 0.000 0.000
#> GSM381259 1 0.3774 0.8138 0.704 0.000 0.296 0.000 0.000
#> GSM381260 3 0.2074 0.5792 0.104 0.000 0.896 0.000 0.000
#> GSM381261 5 0.3684 0.9336 0.000 0.280 0.000 0.000 0.720
#> GSM381263 3 0.1197 0.6344 0.048 0.000 0.952 0.000 0.000
#> GSM381265 1 0.3774 0.8138 0.704 0.000 0.296 0.000 0.000
#> GSM381268 3 0.1670 0.6342 0.052 0.000 0.936 0.000 0.012
#> GSM381270 5 0.3796 0.9398 0.000 0.300 0.000 0.000 0.700
#> GSM381271 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM381275 5 0.3684 0.9336 0.000 0.280 0.000 0.000 0.720
#> GSM381279 5 0.3796 0.9398 0.000 0.300 0.000 0.000 0.700
#> GSM381195 1 0.3752 0.8141 0.708 0.000 0.292 0.000 0.000
#> GSM381196 3 0.1638 0.6258 0.064 0.000 0.932 0.000 0.004
#> GSM381198 2 0.1197 0.7885 0.000 0.952 0.000 0.000 0.048
#> GSM381200 5 0.4015 0.9065 0.000 0.348 0.000 0.000 0.652
#> GSM381201 3 0.2974 0.6074 0.080 0.000 0.868 0.000 0.052
#> GSM381203 3 0.2179 0.5654 0.112 0.000 0.888 0.000 0.000
#> GSM381204 1 0.3752 0.8141 0.708 0.000 0.292 0.000 0.000
#> GSM381209 1 0.3752 0.8141 0.708 0.000 0.292 0.000 0.000
#> GSM381212 1 0.3752 0.8141 0.708 0.000 0.292 0.000 0.000
#> GSM381213 2 0.2773 0.6994 0.000 0.836 0.000 0.000 0.164
#> GSM381214 2 0.0000 0.7948 0.000 1.000 0.000 0.000 0.000
#> GSM381216 3 0.4025 0.5876 0.292 0.000 0.700 0.000 0.008
#> GSM381225 3 0.5954 0.5798 0.056 0.000 0.652 0.068 0.224
#> GSM381231 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM381235 3 0.4025 0.5876 0.292 0.000 0.700 0.000 0.008
#> GSM381237 1 0.3752 0.8141 0.708 0.000 0.292 0.000 0.000
#> GSM381241 2 0.1965 0.7559 0.000 0.904 0.000 0.000 0.096
#> GSM381243 5 0.4210 0.7667 0.000 0.412 0.000 0.000 0.588
#> GSM381245 1 0.4126 0.7732 0.620 0.000 0.380 0.000 0.000
#> GSM381246 2 0.4262 -0.3891 0.000 0.560 0.000 0.000 0.440
#> GSM381251 3 0.4800 0.5297 0.052 0.000 0.676 0.000 0.272
#> GSM381264 1 0.3752 0.8141 0.708 0.000 0.292 0.000 0.000
#> GSM381206 2 0.0000 0.7948 0.000 1.000 0.000 0.000 0.000
#> GSM381217 3 0.3796 0.5894 0.300 0.000 0.700 0.000 0.000
#> GSM381218 2 0.0963 0.7929 0.000 0.964 0.000 0.000 0.036
#> GSM381226 5 0.4045 0.8968 0.000 0.356 0.000 0.000 0.644
#> GSM381227 2 0.4305 -0.5723 0.000 0.512 0.000 0.000 0.488
#> GSM381228 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM381236 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM381244 1 0.4307 0.6049 0.504 0.000 0.496 0.000 0.000
#> GSM381272 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM381277 1 0.4161 0.7595 0.608 0.000 0.392 0.000 0.000
#> GSM381278 3 0.6683 0.4937 0.292 0.000 0.436 0.000 0.272
#> GSM381197 3 0.3684 0.0941 0.280 0.000 0.720 0.000 0.000
#> GSM381202 3 0.2852 0.4572 0.172 0.000 0.828 0.000 0.000
#> GSM381207 1 0.4235 0.7258 0.576 0.000 0.424 0.000 0.000
#> GSM381208 2 0.1043 0.7890 0.000 0.960 0.000 0.000 0.040
#> GSM381210 1 0.3752 0.8141 0.708 0.000 0.292 0.000 0.000
#> GSM381215 3 0.1012 0.6518 0.020 0.000 0.968 0.000 0.012
#> GSM381219 2 0.3366 0.5537 0.000 0.768 0.000 0.000 0.232
#> GSM381221 5 0.4030 0.9015 0.000 0.352 0.000 0.000 0.648
#> GSM381223 5 0.3707 0.9344 0.000 0.284 0.000 0.000 0.716
#> GSM381229 3 0.4735 0.5331 0.048 0.000 0.680 0.000 0.272
#> GSM381230 1 0.1043 0.5281 0.960 0.000 0.040 0.000 0.000
#> GSM381233 3 0.4446 0.5029 0.400 0.000 0.592 0.000 0.008
#> GSM381234 1 0.3816 0.8116 0.696 0.000 0.304 0.000 0.000
#> GSM381238 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM381239 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM381242 3 0.4067 0.5847 0.300 0.000 0.692 0.000 0.008
#> GSM381247 5 0.3774 0.9399 0.000 0.296 0.000 0.000 0.704
#> GSM381248 1 0.4201 0.7461 0.592 0.000 0.408 0.000 0.000
#> GSM381249 1 0.2462 0.3386 0.880 0.000 0.112 0.000 0.008
#> GSM381253 3 0.1410 0.6260 0.060 0.000 0.940 0.000 0.000
#> GSM381255 2 0.0000 0.7948 0.000 1.000 0.000 0.000 0.000
#> GSM381258 3 0.4130 0.5880 0.292 0.000 0.696 0.000 0.012
#> GSM381262 3 0.4167 0.5786 0.024 0.000 0.724 0.000 0.252
#> GSM381266 3 0.5987 0.5570 0.156 0.000 0.572 0.000 0.272
#> GSM381267 2 0.1410 0.7777 0.000 0.940 0.000 0.000 0.060
#> GSM381269 3 0.4183 0.5727 0.324 0.000 0.668 0.000 0.008
#> GSM381273 3 0.5271 0.5186 0.052 0.000 0.660 0.016 0.272
#> GSM381274 5 0.3684 0.9336 0.000 0.280 0.000 0.000 0.720
#> GSM381276 3 0.1430 0.6330 0.052 0.000 0.944 0.000 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM381194 6 0.3862 0.4295 0.000 0.000 0.476 0.000 0.000 0.524
#> GSM381199 2 0.1387 0.8284 0.000 0.932 0.000 0.000 0.068 0.000
#> GSM381205 5 0.0000 0.8683 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM381211 5 0.0000 0.8683 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM381220 5 0.1007 0.8532 0.000 0.044 0.000 0.000 0.956 0.000
#> GSM381222 3 0.5521 0.2218 0.132 0.000 0.468 0.000 0.000 0.400
#> GSM381224 3 0.5112 0.2922 0.084 0.000 0.516 0.000 0.000 0.400
#> GSM381232 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381240 1 0.0000 0.8692 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381250 3 0.0291 0.4968 0.004 0.000 0.992 0.000 0.000 0.004
#> GSM381252 5 0.2941 0.7285 0.000 0.220 0.000 0.000 0.780 0.000
#> GSM381254 1 0.1297 0.8601 0.948 0.000 0.040 0.000 0.000 0.012
#> GSM381256 2 0.3563 0.4660 0.000 0.664 0.000 0.000 0.336 0.000
#> GSM381257 1 0.1910 0.8221 0.892 0.000 0.108 0.000 0.000 0.000
#> GSM381259 1 0.0363 0.8650 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM381260 3 0.4246 0.2279 0.400 0.000 0.580 0.000 0.000 0.020
#> GSM381261 2 0.0865 0.8245 0.000 0.964 0.000 0.000 0.000 0.036
#> GSM381263 3 0.2006 0.4439 0.016 0.000 0.904 0.000 0.000 0.080
#> GSM381265 1 0.1297 0.8601 0.948 0.000 0.040 0.000 0.000 0.012
#> GSM381268 3 0.0146 0.4939 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM381270 2 0.0632 0.8312 0.000 0.976 0.000 0.000 0.024 0.000
#> GSM381271 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381275 2 0.0865 0.8245 0.000 0.964 0.000 0.000 0.000 0.036
#> GSM381279 2 0.0632 0.8312 0.000 0.976 0.000 0.000 0.024 0.000
#> GSM381195 1 0.0000 0.8692 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381196 3 0.0146 0.4941 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM381198 5 0.2454 0.7925 0.000 0.160 0.000 0.000 0.840 0.000
#> GSM381200 2 0.1501 0.8268 0.000 0.924 0.000 0.000 0.076 0.000
#> GSM381201 3 0.0146 0.4941 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM381203 3 0.0405 0.4922 0.004 0.000 0.988 0.000 0.000 0.008
#> GSM381204 1 0.0000 0.8692 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381209 1 0.0000 0.8692 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381212 1 0.0000 0.8692 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381213 5 0.3371 0.6775 0.000 0.292 0.000 0.000 0.708 0.000
#> GSM381214 5 0.0146 0.8680 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM381216 3 0.3843 0.3110 0.000 0.000 0.548 0.000 0.000 0.452
#> GSM381225 6 0.3995 0.4243 0.000 0.000 0.480 0.004 0.000 0.516
#> GSM381231 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381235 6 0.3789 -0.2241 0.000 0.000 0.416 0.000 0.000 0.584
#> GSM381237 1 0.0000 0.8692 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381241 5 0.3371 0.6038 0.000 0.292 0.000 0.000 0.708 0.000
#> GSM381243 2 0.1610 0.7970 0.000 0.916 0.000 0.000 0.084 0.000
#> GSM381245 1 0.2912 0.6959 0.784 0.000 0.216 0.000 0.000 0.000
#> GSM381246 2 0.3868 0.0875 0.000 0.508 0.000 0.000 0.492 0.000
#> GSM381251 3 0.3620 -0.2005 0.000 0.000 0.648 0.000 0.000 0.352
#> GSM381264 1 0.0000 0.8692 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381206 5 0.0000 0.8683 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM381217 3 0.3823 0.3255 0.000 0.000 0.564 0.000 0.000 0.436
#> GSM381218 5 0.2527 0.7862 0.000 0.168 0.000 0.000 0.832 0.000
#> GSM381226 2 0.1501 0.8268 0.000 0.924 0.000 0.000 0.076 0.000
#> GSM381227 2 0.3857 0.1850 0.000 0.532 0.000 0.000 0.468 0.000
#> GSM381228 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381236 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381244 1 0.2219 0.7897 0.864 0.000 0.136 0.000 0.000 0.000
#> GSM381272 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381277 1 0.1075 0.8571 0.952 0.000 0.048 0.000 0.000 0.000
#> GSM381278 6 0.2597 0.3281 0.000 0.000 0.176 0.000 0.000 0.824
#> GSM381197 1 0.4294 0.1284 0.552 0.000 0.428 0.000 0.000 0.020
#> GSM381202 3 0.4246 0.2279 0.400 0.000 0.580 0.000 0.000 0.020
#> GSM381207 1 0.3860 0.2174 0.528 0.000 0.472 0.000 0.000 0.000
#> GSM381208 5 0.1075 0.8520 0.000 0.048 0.000 0.000 0.952 0.000
#> GSM381210 1 0.0000 0.8692 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381215 3 0.2178 0.3272 0.000 0.000 0.868 0.000 0.000 0.132
#> GSM381219 2 0.3864 0.0427 0.000 0.520 0.000 0.000 0.480 0.000
#> GSM381221 2 0.1501 0.8268 0.000 0.924 0.000 0.000 0.076 0.000
#> GSM381223 2 0.0972 0.8266 0.000 0.964 0.000 0.000 0.008 0.028
#> GSM381229 6 0.3866 0.4247 0.000 0.000 0.484 0.000 0.000 0.516
#> GSM381230 1 0.1387 0.8281 0.932 0.000 0.000 0.000 0.000 0.068
#> GSM381233 3 0.4893 0.3104 0.064 0.000 0.536 0.000 0.000 0.400
#> GSM381234 1 0.1225 0.8613 0.952 0.000 0.036 0.000 0.000 0.012
#> GSM381238 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381239 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381242 3 0.3789 0.3383 0.000 0.000 0.584 0.000 0.000 0.416
#> GSM381247 2 0.0632 0.8312 0.000 0.976 0.000 0.000 0.024 0.000
#> GSM381248 1 0.4076 0.3569 0.592 0.000 0.396 0.000 0.000 0.012
#> GSM381249 6 0.5997 -0.0748 0.344 0.000 0.240 0.000 0.000 0.416
#> GSM381253 3 0.0260 0.4963 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM381255 5 0.0000 0.8683 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM381258 6 0.3409 -0.0142 0.000 0.000 0.300 0.000 0.000 0.700
#> GSM381262 6 0.3864 0.4275 0.000 0.000 0.480 0.000 0.000 0.520
#> GSM381266 3 0.2996 0.1494 0.000 0.000 0.772 0.000 0.000 0.228
#> GSM381267 5 0.1141 0.8501 0.000 0.052 0.000 0.000 0.948 0.000
#> GSM381269 3 0.4123 0.3324 0.012 0.000 0.568 0.000 0.000 0.420
#> GSM381273 3 0.3103 0.1801 0.000 0.000 0.784 0.008 0.000 0.208
#> GSM381274 2 0.0865 0.8245 0.000 0.964 0.000 0.000 0.000 0.036
#> GSM381276 3 0.0291 0.4953 0.004 0.000 0.992 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 other(p) k
#> SD:mclust 86 0.744 2
#> SD:mclust 85 0.356 3
#> SD:mclust 79 0.711 4
#> SD:mclust 77 0.555 5
#> SD:mclust 50 0.687 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 86 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 0.942 0.978 0.4650 0.540 0.540
#> 3 3 0.866 0.895 0.951 0.4253 0.785 0.607
#> 4 4 0.769 0.685 0.848 0.0739 0.933 0.809
#> 5 5 0.840 0.804 0.898 0.0607 0.905 0.706
#> 6 6 0.781 0.724 0.859 0.0342 0.919 0.709
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
#> GSM381194 1 0.000 0.9739 1.000 0.000
#> GSM381199 2 0.000 0.9823 0.000 1.000
#> GSM381205 2 0.000 0.9823 0.000 1.000
#> GSM381211 2 0.000 0.9823 0.000 1.000
#> GSM381220 2 0.000 0.9823 0.000 1.000
#> GSM381222 1 0.000 0.9739 1.000 0.000
#> GSM381224 1 0.000 0.9739 1.000 0.000
#> GSM381232 1 0.563 0.8428 0.868 0.132
#> GSM381240 1 0.000 0.9739 1.000 0.000
#> GSM381250 1 0.000 0.9739 1.000 0.000
#> GSM381252 2 0.000 0.9823 0.000 1.000
#> GSM381254 1 0.000 0.9739 1.000 0.000
#> GSM381256 2 0.000 0.9823 0.000 1.000
#> GSM381257 1 0.000 0.9739 1.000 0.000
#> GSM381259 1 0.000 0.9739 1.000 0.000
#> GSM381260 1 0.000 0.9739 1.000 0.000
#> GSM381261 2 0.000 0.9823 0.000 1.000
#> GSM381263 1 0.000 0.9739 1.000 0.000
#> GSM381265 1 0.000 0.9739 1.000 0.000
#> GSM381268 1 0.000 0.9739 1.000 0.000
#> GSM381270 2 0.000 0.9823 0.000 1.000
#> GSM381271 1 0.402 0.9015 0.920 0.080
#> GSM381275 2 0.000 0.9823 0.000 1.000
#> GSM381279 2 0.000 0.9823 0.000 1.000
#> GSM381195 1 0.000 0.9739 1.000 0.000
#> GSM381196 1 0.000 0.9739 1.000 0.000
#> GSM381198 2 0.000 0.9823 0.000 1.000
#> GSM381200 2 0.000 0.9823 0.000 1.000
#> GSM381201 1 0.000 0.9739 1.000 0.000
#> GSM381203 1 0.000 0.9739 1.000 0.000
#> GSM381204 1 0.000 0.9739 1.000 0.000
#> GSM381209 1 0.000 0.9739 1.000 0.000
#> GSM381212 1 0.000 0.9739 1.000 0.000
#> GSM381213 2 0.000 0.9823 0.000 1.000
#> GSM381214 2 0.000 0.9823 0.000 1.000
#> GSM381216 1 0.000 0.9739 1.000 0.000
#> GSM381225 1 0.000 0.9739 1.000 0.000
#> GSM381231 2 1.000 -0.0257 0.488 0.512
#> GSM381235 1 0.000 0.9739 1.000 0.000
#> GSM381237 1 0.000 0.9739 1.000 0.000
#> GSM381241 2 0.000 0.9823 0.000 1.000
#> GSM381243 2 0.000 0.9823 0.000 1.000
#> GSM381245 1 0.000 0.9739 1.000 0.000
#> GSM381246 2 0.000 0.9823 0.000 1.000
#> GSM381251 1 0.000 0.9739 1.000 0.000
#> GSM381264 1 0.000 0.9739 1.000 0.000
#> GSM381206 2 0.000 0.9823 0.000 1.000
#> GSM381217 1 0.000 0.9739 1.000 0.000
#> GSM381218 2 0.000 0.9823 0.000 1.000
#> GSM381226 2 0.000 0.9823 0.000 1.000
#> GSM381227 2 0.000 0.9823 0.000 1.000
#> GSM381228 1 0.996 0.1569 0.536 0.464
#> GSM381236 1 0.358 0.9137 0.932 0.068
#> GSM381244 1 0.000 0.9739 1.000 0.000
#> GSM381272 1 0.278 0.9324 0.952 0.048
#> GSM381277 1 0.000 0.9739 1.000 0.000
#> GSM381278 1 0.000 0.9739 1.000 0.000
#> GSM381197 1 0.000 0.9739 1.000 0.000
#> GSM381202 1 0.000 0.9739 1.000 0.000
#> GSM381207 1 0.000 0.9739 1.000 0.000
#> GSM381208 2 0.000 0.9823 0.000 1.000
#> GSM381210 1 0.000 0.9739 1.000 0.000
#> GSM381215 1 0.000 0.9739 1.000 0.000
#> GSM381219 2 0.000 0.9823 0.000 1.000
#> GSM381221 2 0.000 0.9823 0.000 1.000
#> GSM381223 2 0.000 0.9823 0.000 1.000
#> GSM381229 1 0.000 0.9739 1.000 0.000
#> GSM381230 1 0.000 0.9739 1.000 0.000
#> GSM381233 1 0.000 0.9739 1.000 0.000
#> GSM381234 1 0.000 0.9739 1.000 0.000
#> GSM381238 1 0.961 0.3943 0.616 0.384
#> GSM381239 1 0.767 0.7155 0.776 0.224
#> GSM381242 1 0.000 0.9739 1.000 0.000
#> GSM381247 2 0.000 0.9823 0.000 1.000
#> GSM381248 1 0.000 0.9739 1.000 0.000
#> GSM381249 1 0.000 0.9739 1.000 0.000
#> GSM381253 1 0.000 0.9739 1.000 0.000
#> GSM381255 2 0.000 0.9823 0.000 1.000
#> GSM381258 1 0.000 0.9739 1.000 0.000
#> GSM381262 1 0.000 0.9739 1.000 0.000
#> GSM381266 1 0.000 0.9739 1.000 0.000
#> GSM381267 2 0.000 0.9823 0.000 1.000
#> GSM381269 1 0.000 0.9739 1.000 0.000
#> GSM381273 1 0.000 0.9739 1.000 0.000
#> GSM381274 2 0.000 0.9823 0.000 1.000
#> GSM381276 1 0.000 0.9739 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM381194 3 0.0000 0.9231 0.000 0.000 1.000
#> GSM381199 2 0.0424 0.9870 0.000 0.992 0.008
#> GSM381205 2 0.0424 0.9859 0.008 0.992 0.000
#> GSM381211 2 0.0000 0.9908 0.000 1.000 0.000
#> GSM381220 2 0.0237 0.9894 0.000 0.996 0.004
#> GSM381222 1 0.1289 0.9187 0.968 0.000 0.032
#> GSM381224 1 0.0000 0.9231 1.000 0.000 0.000
#> GSM381232 3 0.0592 0.9162 0.000 0.012 0.988
#> GSM381240 1 0.0237 0.9236 0.996 0.000 0.004
#> GSM381250 1 0.3752 0.8388 0.856 0.000 0.144
#> GSM381252 2 0.0000 0.9908 0.000 1.000 0.000
#> GSM381254 1 0.0237 0.9237 0.996 0.000 0.004
#> GSM381256 2 0.0000 0.9908 0.000 1.000 0.000
#> GSM381257 1 0.0592 0.9231 0.988 0.000 0.012
#> GSM381259 1 0.0000 0.9231 1.000 0.000 0.000
#> GSM381260 1 0.3116 0.8702 0.892 0.000 0.108
#> GSM381261 2 0.0237 0.9894 0.000 0.996 0.004
#> GSM381263 3 0.5968 0.4254 0.364 0.000 0.636
#> GSM381265 1 0.0000 0.9231 1.000 0.000 0.000
#> GSM381268 3 0.3482 0.8079 0.128 0.000 0.872
#> GSM381270 2 0.0424 0.9871 0.000 0.992 0.008
#> GSM381271 3 0.0000 0.9231 0.000 0.000 1.000
#> GSM381275 2 0.0000 0.9908 0.000 1.000 0.000
#> GSM381279 2 0.0424 0.9871 0.000 0.992 0.008
#> GSM381195 1 0.0000 0.9231 1.000 0.000 0.000
#> GSM381196 1 0.5733 0.5582 0.676 0.000 0.324
#> GSM381198 2 0.0000 0.9908 0.000 1.000 0.000
#> GSM381200 2 0.0000 0.9908 0.000 1.000 0.000
#> GSM381201 3 0.0747 0.9157 0.016 0.000 0.984
#> GSM381203 1 0.0000 0.9231 1.000 0.000 0.000
#> GSM381204 1 0.0000 0.9231 1.000 0.000 0.000
#> GSM381209 1 0.0000 0.9231 1.000 0.000 0.000
#> GSM381212 1 0.0000 0.9231 1.000 0.000 0.000
#> GSM381213 2 0.0237 0.9894 0.000 0.996 0.004
#> GSM381214 2 0.0000 0.9908 0.000 1.000 0.000
#> GSM381216 1 0.5138 0.7101 0.748 0.000 0.252
#> GSM381225 3 0.6305 0.0595 0.484 0.000 0.516
#> GSM381231 3 0.0237 0.9203 0.000 0.004 0.996
#> GSM381235 1 0.4750 0.7600 0.784 0.000 0.216
#> GSM381237 1 0.0000 0.9231 1.000 0.000 0.000
#> GSM381241 2 0.0000 0.9908 0.000 1.000 0.000
#> GSM381243 2 0.1643 0.9547 0.000 0.956 0.044
#> GSM381245 1 0.0592 0.9231 0.988 0.000 0.012
#> GSM381246 2 0.0000 0.9908 0.000 1.000 0.000
#> GSM381251 3 0.0000 0.9231 0.000 0.000 1.000
#> GSM381264 1 0.0000 0.9231 1.000 0.000 0.000
#> GSM381206 2 0.0424 0.9859 0.008 0.992 0.000
#> GSM381217 1 0.2625 0.8908 0.916 0.000 0.084
#> GSM381218 2 0.0000 0.9908 0.000 1.000 0.000
#> GSM381226 2 0.0000 0.9908 0.000 1.000 0.000
#> GSM381227 2 0.0000 0.9908 0.000 1.000 0.000
#> GSM381228 3 0.0000 0.9231 0.000 0.000 1.000
#> GSM381236 3 0.0000 0.9231 0.000 0.000 1.000
#> GSM381244 1 0.5835 0.5575 0.660 0.000 0.340
#> GSM381272 3 0.0000 0.9231 0.000 0.000 1.000
#> GSM381277 1 0.1411 0.9161 0.964 0.000 0.036
#> GSM381278 3 0.0000 0.9231 0.000 0.000 1.000
#> GSM381197 1 0.6095 0.3688 0.608 0.000 0.392
#> GSM381202 1 0.0592 0.9231 0.988 0.000 0.012
#> GSM381207 1 0.1643 0.9136 0.956 0.000 0.044
#> GSM381208 2 0.0000 0.9908 0.000 1.000 0.000
#> GSM381210 1 0.0237 0.9236 0.996 0.000 0.004
#> GSM381215 3 0.0892 0.9125 0.020 0.000 0.980
#> GSM381219 2 0.0000 0.9908 0.000 1.000 0.000
#> GSM381221 2 0.0000 0.9908 0.000 1.000 0.000
#> GSM381223 2 0.0000 0.9908 0.000 1.000 0.000
#> GSM381229 3 0.0000 0.9231 0.000 0.000 1.000
#> GSM381230 1 0.0000 0.9231 1.000 0.000 0.000
#> GSM381233 1 0.3116 0.8695 0.892 0.000 0.108
#> GSM381234 1 0.0237 0.9236 0.996 0.000 0.004
#> GSM381238 3 0.0000 0.9231 0.000 0.000 1.000
#> GSM381239 3 0.1163 0.9049 0.000 0.028 0.972
#> GSM381242 1 0.2537 0.8917 0.920 0.000 0.080
#> GSM381247 2 0.4121 0.8103 0.000 0.832 0.168
#> GSM381248 1 0.1411 0.9176 0.964 0.000 0.036
#> GSM381249 1 0.0592 0.9234 0.988 0.000 0.012
#> GSM381253 1 0.2959 0.8797 0.900 0.000 0.100
#> GSM381255 2 0.0000 0.9908 0.000 1.000 0.000
#> GSM381258 3 0.0592 0.9178 0.012 0.000 0.988
#> GSM381262 3 0.0237 0.9216 0.004 0.000 0.996
#> GSM381266 3 0.0000 0.9231 0.000 0.000 1.000
#> GSM381267 2 0.0237 0.9894 0.000 0.996 0.004
#> GSM381269 1 0.3482 0.8596 0.872 0.000 0.128
#> GSM381273 3 0.0000 0.9231 0.000 0.000 1.000
#> GSM381274 2 0.0000 0.9908 0.000 1.000 0.000
#> GSM381276 3 0.6079 0.3771 0.388 0.000 0.612
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM381194 3 0.4999 -0.3374 0.000 0.000 0.508 0.492
#> GSM381199 2 0.0707 0.9670 0.000 0.980 0.020 0.000
#> GSM381205 2 0.0672 0.9690 0.008 0.984 0.008 0.000
#> GSM381211 2 0.0524 0.9693 0.000 0.988 0.004 0.008
#> GSM381220 2 0.0779 0.9673 0.000 0.980 0.004 0.016
#> GSM381222 1 0.3099 0.7472 0.876 0.000 0.104 0.020
#> GSM381224 1 0.2216 0.7605 0.908 0.000 0.092 0.000
#> GSM381232 4 0.0188 0.7204 0.000 0.000 0.004 0.996
#> GSM381240 1 0.1305 0.7760 0.960 0.000 0.036 0.004
#> GSM381250 1 0.7188 -0.2427 0.432 0.000 0.432 0.136
#> GSM381252 2 0.0188 0.9699 0.000 0.996 0.004 0.000
#> GSM381254 1 0.0895 0.7669 0.976 0.000 0.020 0.004
#> GSM381256 2 0.0336 0.9695 0.000 0.992 0.008 0.000
#> GSM381257 1 0.2596 0.7639 0.908 0.000 0.068 0.024
#> GSM381259 1 0.0336 0.7705 0.992 0.000 0.008 0.000
#> GSM381260 1 0.5599 0.4418 0.644 0.000 0.316 0.040
#> GSM381261 2 0.3123 0.8691 0.000 0.844 0.156 0.000
#> GSM381263 3 0.7270 0.4425 0.304 0.000 0.520 0.176
#> GSM381265 1 0.0592 0.7671 0.984 0.000 0.016 0.000
#> GSM381268 4 0.5626 0.4529 0.028 0.000 0.384 0.588
#> GSM381270 2 0.1807 0.9500 0.000 0.940 0.052 0.008
#> GSM381271 4 0.0000 0.7198 0.000 0.000 0.000 1.000
#> GSM381275 2 0.3356 0.8484 0.000 0.824 0.176 0.000
#> GSM381279 2 0.0336 0.9699 0.000 0.992 0.008 0.000
#> GSM381195 1 0.0707 0.7649 0.980 0.000 0.020 0.000
#> GSM381196 3 0.7900 0.3207 0.308 0.000 0.372 0.320
#> GSM381198 2 0.0564 0.9701 0.004 0.988 0.004 0.004
#> GSM381200 2 0.0336 0.9693 0.000 0.992 0.008 0.000
#> GSM381201 4 0.4252 0.6460 0.004 0.000 0.252 0.744
#> GSM381203 1 0.4477 0.4935 0.688 0.000 0.312 0.000
#> GSM381204 1 0.0817 0.7766 0.976 0.000 0.024 0.000
#> GSM381209 1 0.0000 0.7730 1.000 0.000 0.000 0.000
#> GSM381212 1 0.0188 0.7719 0.996 0.000 0.004 0.000
#> GSM381213 2 0.0469 0.9696 0.000 0.988 0.000 0.012
#> GSM381214 2 0.0524 0.9693 0.000 0.988 0.004 0.008
#> GSM381216 3 0.3743 0.5126 0.160 0.000 0.824 0.016
#> GSM381225 3 0.6425 0.1456 0.424 0.000 0.508 0.068
#> GSM381231 4 0.0376 0.7195 0.000 0.004 0.004 0.992
#> GSM381235 3 0.4248 0.5091 0.220 0.000 0.768 0.012
#> GSM381237 1 0.0707 0.7766 0.980 0.000 0.020 0.000
#> GSM381241 2 0.0376 0.9698 0.000 0.992 0.004 0.004
#> GSM381243 2 0.0188 0.9699 0.000 0.996 0.004 0.000
#> GSM381245 1 0.1174 0.7732 0.968 0.000 0.012 0.020
#> GSM381246 2 0.0657 0.9687 0.004 0.984 0.012 0.000
#> GSM381251 4 0.4679 0.5568 0.000 0.000 0.352 0.648
#> GSM381264 1 0.0707 0.7649 0.980 0.000 0.020 0.000
#> GSM381206 2 0.0779 0.9673 0.016 0.980 0.004 0.000
#> GSM381217 1 0.5345 0.2410 0.560 0.000 0.428 0.012
#> GSM381218 2 0.0524 0.9693 0.000 0.988 0.004 0.008
#> GSM381226 2 0.1022 0.9629 0.000 0.968 0.032 0.000
#> GSM381227 2 0.0707 0.9669 0.000 0.980 0.020 0.000
#> GSM381228 4 0.0336 0.7130 0.000 0.008 0.000 0.992
#> GSM381236 4 0.0000 0.7198 0.000 0.000 0.000 1.000
#> GSM381244 1 0.6474 0.0871 0.536 0.000 0.076 0.388
#> GSM381272 4 0.0188 0.7208 0.000 0.000 0.004 0.996
#> GSM381277 1 0.1584 0.7748 0.952 0.000 0.012 0.036
#> GSM381278 3 0.4500 0.0968 0.000 0.000 0.684 0.316
#> GSM381197 1 0.7806 -0.2946 0.408 0.000 0.332 0.260
#> GSM381202 1 0.3958 0.7028 0.816 0.000 0.160 0.024
#> GSM381207 1 0.1510 0.7734 0.956 0.000 0.016 0.028
#> GSM381208 2 0.1545 0.9510 0.000 0.952 0.008 0.040
#> GSM381210 1 0.2198 0.7678 0.920 0.000 0.072 0.008
#> GSM381215 4 0.5931 0.2177 0.036 0.000 0.460 0.504
#> GSM381219 2 0.0000 0.9699 0.000 1.000 0.000 0.000
#> GSM381221 2 0.0188 0.9696 0.000 0.996 0.004 0.000
#> GSM381223 2 0.1557 0.9514 0.000 0.944 0.056 0.000
#> GSM381229 4 0.4776 0.5255 0.000 0.000 0.376 0.624
#> GSM381230 1 0.0921 0.7766 0.972 0.000 0.028 0.000
#> GSM381233 1 0.3925 0.7007 0.808 0.000 0.176 0.016
#> GSM381234 1 0.1042 0.7684 0.972 0.000 0.020 0.008
#> GSM381238 4 0.0188 0.7208 0.000 0.000 0.004 0.996
#> GSM381239 4 0.1109 0.6849 0.000 0.028 0.004 0.968
#> GSM381242 1 0.5933 0.2394 0.552 0.000 0.408 0.040
#> GSM381247 2 0.3448 0.8399 0.000 0.828 0.168 0.004
#> GSM381248 1 0.1624 0.7714 0.952 0.000 0.028 0.020
#> GSM381249 1 0.2737 0.7552 0.888 0.000 0.104 0.008
#> GSM381253 1 0.5990 0.3447 0.608 0.000 0.336 0.056
#> GSM381255 2 0.0524 0.9693 0.000 0.988 0.004 0.008
#> GSM381258 3 0.2843 0.4197 0.020 0.000 0.892 0.088
#> GSM381262 4 0.5236 0.4047 0.008 0.000 0.432 0.560
#> GSM381266 4 0.4632 0.6014 0.004 0.000 0.308 0.688
#> GSM381267 2 0.1489 0.9509 0.000 0.952 0.004 0.044
#> GSM381269 1 0.5488 0.2377 0.532 0.000 0.452 0.016
#> GSM381273 4 0.4103 0.6473 0.000 0.000 0.256 0.744
#> GSM381274 2 0.1389 0.9556 0.000 0.952 0.048 0.000
#> GSM381276 1 0.7168 0.2641 0.556 0.000 0.236 0.208
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM381194 3 0.1845 0.833 0.000 0.000 0.928 0.016 0.056
#> GSM381199 2 0.0404 0.955 0.000 0.988 0.000 0.000 0.012
#> GSM381205 2 0.0613 0.954 0.004 0.984 0.000 0.004 0.008
#> GSM381211 2 0.0162 0.956 0.000 0.996 0.000 0.004 0.000
#> GSM381220 2 0.0880 0.944 0.000 0.968 0.000 0.032 0.000
#> GSM381222 1 0.3299 0.767 0.828 0.000 0.004 0.016 0.152
#> GSM381224 1 0.3582 0.691 0.768 0.000 0.000 0.008 0.224
#> GSM381232 4 0.0740 0.982 0.008 0.000 0.008 0.980 0.004
#> GSM381240 1 0.1892 0.809 0.916 0.000 0.000 0.004 0.080
#> GSM381250 3 0.1329 0.841 0.032 0.000 0.956 0.004 0.008
#> GSM381252 2 0.0162 0.956 0.000 0.996 0.000 0.004 0.000
#> GSM381254 1 0.1173 0.803 0.964 0.000 0.004 0.012 0.020
#> GSM381256 2 0.1043 0.937 0.000 0.960 0.040 0.000 0.000
#> GSM381257 1 0.3129 0.805 0.872 0.000 0.032 0.020 0.076
#> GSM381259 1 0.0613 0.814 0.984 0.000 0.004 0.008 0.004
#> GSM381260 1 0.5682 0.415 0.616 0.000 0.072 0.016 0.296
#> GSM381261 2 0.3895 0.613 0.000 0.680 0.000 0.000 0.320
#> GSM381263 3 0.3888 0.699 0.056 0.000 0.796 0.000 0.148
#> GSM381265 1 0.0510 0.812 0.984 0.000 0.000 0.000 0.016
#> GSM381268 3 0.0404 0.843 0.000 0.000 0.988 0.012 0.000
#> GSM381270 2 0.1544 0.926 0.000 0.932 0.000 0.000 0.068
#> GSM381271 4 0.0609 0.991 0.000 0.000 0.020 0.980 0.000
#> GSM381275 2 0.4150 0.487 0.000 0.612 0.000 0.000 0.388
#> GSM381279 2 0.0671 0.954 0.000 0.980 0.000 0.004 0.016
#> GSM381195 1 0.1405 0.799 0.956 0.000 0.008 0.016 0.020
#> GSM381196 3 0.0727 0.845 0.012 0.000 0.980 0.004 0.004
#> GSM381198 2 0.0162 0.956 0.004 0.996 0.000 0.000 0.000
#> GSM381200 2 0.0404 0.955 0.000 0.988 0.000 0.000 0.012
#> GSM381201 3 0.1908 0.822 0.000 0.000 0.908 0.092 0.000
#> GSM381203 3 0.4525 0.329 0.360 0.000 0.624 0.016 0.000
#> GSM381204 1 0.1628 0.818 0.936 0.000 0.000 0.008 0.056
#> GSM381209 1 0.0566 0.819 0.984 0.000 0.000 0.004 0.012
#> GSM381212 1 0.0324 0.818 0.992 0.000 0.000 0.004 0.004
#> GSM381213 2 0.0404 0.956 0.000 0.988 0.000 0.012 0.000
#> GSM381214 2 0.0290 0.956 0.000 0.992 0.000 0.008 0.000
#> GSM381216 5 0.2416 0.715 0.100 0.000 0.000 0.012 0.888
#> GSM381225 3 0.0771 0.841 0.020 0.000 0.976 0.004 0.000
#> GSM381231 4 0.0833 0.991 0.000 0.004 0.016 0.976 0.004
#> GSM381235 5 0.3650 0.722 0.176 0.000 0.028 0.000 0.796
#> GSM381237 1 0.1571 0.816 0.936 0.000 0.000 0.004 0.060
#> GSM381241 2 0.0162 0.956 0.000 0.996 0.000 0.004 0.000
#> GSM381243 2 0.0510 0.955 0.000 0.984 0.000 0.000 0.016
#> GSM381245 1 0.0566 0.813 0.984 0.000 0.000 0.004 0.012
#> GSM381246 2 0.0510 0.954 0.000 0.984 0.000 0.000 0.016
#> GSM381251 3 0.0290 0.843 0.000 0.000 0.992 0.008 0.000
#> GSM381264 1 0.1405 0.799 0.956 0.000 0.008 0.016 0.020
#> GSM381206 2 0.0162 0.956 0.000 0.996 0.000 0.004 0.000
#> GSM381217 1 0.4574 0.246 0.576 0.000 0.012 0.000 0.412
#> GSM381218 2 0.0162 0.956 0.000 0.996 0.000 0.004 0.000
#> GSM381226 2 0.0510 0.954 0.000 0.984 0.000 0.000 0.016
#> GSM381227 2 0.0290 0.955 0.000 0.992 0.000 0.000 0.008
#> GSM381228 4 0.0609 0.991 0.000 0.000 0.020 0.980 0.000
#> GSM381236 4 0.0693 0.988 0.008 0.000 0.012 0.980 0.000
#> GSM381244 1 0.5928 0.575 0.672 0.000 0.048 0.104 0.176
#> GSM381272 4 0.0771 0.990 0.000 0.000 0.020 0.976 0.004
#> GSM381277 1 0.2770 0.795 0.880 0.000 0.000 0.076 0.044
#> GSM381278 3 0.4527 0.515 0.000 0.000 0.596 0.012 0.392
#> GSM381197 3 0.5072 0.697 0.124 0.000 0.752 0.072 0.052
#> GSM381202 1 0.4064 0.616 0.716 0.000 0.004 0.008 0.272
#> GSM381207 1 0.1106 0.816 0.964 0.000 0.000 0.024 0.012
#> GSM381208 2 0.0290 0.955 0.000 0.992 0.008 0.000 0.000
#> GSM381210 1 0.2741 0.783 0.860 0.000 0.004 0.004 0.132
#> GSM381215 3 0.1408 0.838 0.000 0.000 0.948 0.008 0.044
#> GSM381219 2 0.0162 0.956 0.000 0.996 0.000 0.004 0.000
#> GSM381221 2 0.0000 0.956 0.000 1.000 0.000 0.000 0.000
#> GSM381223 2 0.1197 0.940 0.000 0.952 0.000 0.000 0.048
#> GSM381229 3 0.0290 0.843 0.000 0.000 0.992 0.008 0.000
#> GSM381230 1 0.1757 0.819 0.936 0.000 0.004 0.012 0.048
#> GSM381233 1 0.4015 0.633 0.708 0.000 0.004 0.004 0.284
#> GSM381234 1 0.1059 0.806 0.968 0.000 0.004 0.008 0.020
#> GSM381238 4 0.0798 0.990 0.000 0.000 0.016 0.976 0.008
#> GSM381239 4 0.0671 0.989 0.000 0.004 0.016 0.980 0.000
#> GSM381242 5 0.4821 0.116 0.464 0.000 0.000 0.020 0.516
#> GSM381247 2 0.2124 0.903 0.000 0.900 0.004 0.000 0.096
#> GSM381248 1 0.1106 0.811 0.964 0.000 0.000 0.012 0.024
#> GSM381249 1 0.3809 0.648 0.736 0.000 0.000 0.008 0.256
#> GSM381253 3 0.5175 0.178 0.408 0.000 0.548 0.000 0.044
#> GSM381255 2 0.0162 0.956 0.000 0.996 0.000 0.004 0.000
#> GSM381258 5 0.1299 0.620 0.020 0.000 0.008 0.012 0.960
#> GSM381262 3 0.0324 0.842 0.000 0.000 0.992 0.004 0.004
#> GSM381266 3 0.2124 0.820 0.000 0.000 0.900 0.096 0.004
#> GSM381267 2 0.0794 0.946 0.000 0.972 0.028 0.000 0.000
#> GSM381269 5 0.4046 0.620 0.296 0.000 0.000 0.008 0.696
#> GSM381273 3 0.1851 0.823 0.000 0.000 0.912 0.088 0.000
#> GSM381274 2 0.2377 0.868 0.000 0.872 0.000 0.000 0.128
#> GSM381276 1 0.6964 0.209 0.532 0.000 0.048 0.152 0.268
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM381194 3 0.1787 0.8342 0.000 0.000 0.920 0.008 0.068 0.004
#> GSM381199 2 0.0146 0.9581 0.004 0.996 0.000 0.000 0.000 0.000
#> GSM381205 2 0.0291 0.9575 0.004 0.992 0.000 0.004 0.000 0.000
#> GSM381211 2 0.0146 0.9578 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM381220 2 0.1765 0.9020 0.000 0.904 0.000 0.096 0.000 0.000
#> GSM381222 5 0.3998 -0.1627 0.492 0.000 0.000 0.000 0.504 0.004
#> GSM381224 5 0.2278 0.6117 0.128 0.000 0.000 0.000 0.868 0.004
#> GSM381232 4 0.0260 0.9914 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM381240 5 0.2882 0.5744 0.180 0.000 0.000 0.000 0.812 0.008
#> GSM381250 3 0.1152 0.8430 0.000 0.000 0.952 0.004 0.044 0.000
#> GSM381252 2 0.0000 0.9580 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381254 1 0.2340 0.7186 0.852 0.000 0.000 0.000 0.148 0.000
#> GSM381256 2 0.1970 0.9012 0.008 0.900 0.092 0.000 0.000 0.000
#> GSM381257 1 0.3996 0.1438 0.512 0.000 0.004 0.000 0.484 0.000
#> GSM381259 1 0.3309 0.6829 0.720 0.000 0.000 0.000 0.280 0.000
#> GSM381260 5 0.0837 0.6384 0.000 0.000 0.020 0.004 0.972 0.004
#> GSM381261 2 0.2446 0.8820 0.000 0.864 0.000 0.000 0.012 0.124
#> GSM381263 3 0.3668 0.4688 0.000 0.000 0.668 0.000 0.328 0.004
#> GSM381265 1 0.3409 0.6785 0.700 0.000 0.000 0.000 0.300 0.000
#> GSM381268 3 0.0000 0.8352 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM381270 2 0.0713 0.9538 0.000 0.972 0.000 0.000 0.000 0.028
#> GSM381271 4 0.0000 0.9956 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381275 2 0.2664 0.8667 0.000 0.848 0.000 0.000 0.016 0.136
#> GSM381279 2 0.1049 0.9473 0.000 0.960 0.000 0.032 0.000 0.008
#> GSM381195 1 0.2730 0.7152 0.808 0.000 0.000 0.000 0.192 0.000
#> GSM381196 3 0.1082 0.8432 0.000 0.000 0.956 0.000 0.040 0.004
#> GSM381198 2 0.0000 0.9580 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381200 2 0.0260 0.9573 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM381201 3 0.4613 0.7280 0.076 0.000 0.764 0.008 0.096 0.056
#> GSM381203 3 0.3991 0.6008 0.088 0.000 0.756 0.000 0.156 0.000
#> GSM381204 5 0.3620 0.2590 0.352 0.000 0.000 0.000 0.648 0.000
#> GSM381209 5 0.3371 0.4223 0.292 0.000 0.000 0.000 0.708 0.000
#> GSM381212 1 0.3851 0.3609 0.540 0.000 0.000 0.000 0.460 0.000
#> GSM381213 2 0.0458 0.9564 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM381214 2 0.0146 0.9578 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM381216 5 0.3302 0.4852 0.000 0.000 0.004 0.004 0.760 0.232
#> GSM381225 3 0.1327 0.8278 0.000 0.000 0.936 0.000 0.064 0.000
#> GSM381231 4 0.0146 0.9953 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM381235 6 0.4382 0.2570 0.012 0.000 0.020 0.000 0.332 0.636
#> GSM381237 5 0.3672 0.2065 0.368 0.000 0.000 0.000 0.632 0.000
#> GSM381241 2 0.0146 0.9578 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM381243 2 0.1700 0.9321 0.000 0.928 0.000 0.024 0.000 0.048
#> GSM381245 5 0.3871 0.3524 0.308 0.000 0.000 0.000 0.676 0.016
#> GSM381246 2 0.0363 0.9572 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM381251 3 0.0837 0.8414 0.004 0.000 0.972 0.000 0.020 0.004
#> GSM381264 1 0.2219 0.7084 0.864 0.000 0.000 0.000 0.136 0.000
#> GSM381206 2 0.0000 0.9580 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381217 5 0.3748 0.6086 0.092 0.000 0.004 0.000 0.792 0.112
#> GSM381218 2 0.0146 0.9578 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM381226 2 0.0260 0.9573 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM381227 2 0.0363 0.9570 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM381228 4 0.0000 0.9956 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381236 4 0.0000 0.9956 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381244 5 0.3935 0.5356 0.080 0.000 0.020 0.016 0.812 0.072
#> GSM381272 4 0.0146 0.9953 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM381277 5 0.4319 0.5210 0.052 0.000 0.000 0.148 0.760 0.040
#> GSM381278 6 0.3339 0.4066 0.008 0.000 0.188 0.004 0.008 0.792
#> GSM381197 5 0.4983 0.3769 0.076 0.000 0.152 0.000 0.712 0.060
#> GSM381202 5 0.1332 0.6434 0.028 0.000 0.008 0.000 0.952 0.012
#> GSM381207 5 0.5386 -0.1060 0.388 0.000 0.000 0.116 0.496 0.000
#> GSM381208 2 0.2420 0.8802 0.076 0.884 0.000 0.000 0.000 0.040
#> GSM381210 5 0.3515 0.4204 0.324 0.000 0.000 0.000 0.676 0.000
#> GSM381215 3 0.2937 0.7870 0.100 0.000 0.852 0.000 0.044 0.004
#> GSM381219 2 0.0000 0.9580 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381221 2 0.0146 0.9578 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM381223 2 0.1610 0.9232 0.000 0.916 0.000 0.000 0.000 0.084
#> GSM381229 3 0.0260 0.8333 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM381230 1 0.2772 0.7206 0.816 0.000 0.000 0.000 0.180 0.004
#> GSM381233 1 0.5552 0.1876 0.460 0.000 0.000 0.000 0.404 0.136
#> GSM381234 1 0.2883 0.7041 0.788 0.000 0.000 0.000 0.212 0.000
#> GSM381238 4 0.0146 0.9953 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM381239 4 0.0000 0.9956 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381242 5 0.1332 0.6306 0.000 0.000 0.012 0.008 0.952 0.028
#> GSM381247 2 0.2536 0.8852 0.000 0.864 0.020 0.000 0.000 0.116
#> GSM381248 1 0.3758 0.6574 0.764 0.004 0.000 0.000 0.192 0.040
#> GSM381249 5 0.2631 0.5992 0.152 0.000 0.000 0.000 0.840 0.008
#> GSM381253 3 0.4579 0.5021 0.092 0.000 0.696 0.004 0.208 0.000
#> GSM381255 2 0.0291 0.9582 0.000 0.992 0.000 0.004 0.000 0.004
#> GSM381258 5 0.4889 0.0779 0.044 0.000 0.008 0.004 0.592 0.352
#> GSM381262 3 0.0713 0.8332 0.028 0.000 0.972 0.000 0.000 0.000
#> GSM381266 3 0.1989 0.8302 0.016 0.000 0.928 0.012 0.020 0.024
#> GSM381267 2 0.3191 0.8474 0.072 0.852 0.028 0.000 0.000 0.048
#> GSM381269 5 0.2845 0.5774 0.004 0.000 0.000 0.004 0.820 0.172
#> GSM381273 3 0.3961 0.7534 0.068 0.000 0.804 0.000 0.060 0.068
#> GSM381274 2 0.1462 0.9360 0.000 0.936 0.000 0.000 0.008 0.056
#> GSM381276 5 0.2188 0.6252 0.000 0.000 0.020 0.032 0.912 0.036
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n other(p) k
#> SD:NMF 83 0.774 2
#> SD:NMF 82 0.645 3
#> SD:NMF 67 0.387 4
#> SD:NMF 79 0.703 5
#> SD:NMF 70 0.321 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 86 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 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 0.419 0.625 0.851 0.4562 0.495 0.495
#> 3 3 0.494 0.632 0.837 0.2395 0.877 0.763
#> 4 4 0.781 0.746 0.883 0.2707 0.754 0.476
#> 5 5 0.865 0.877 0.920 0.0544 0.904 0.685
#> 6 6 0.867 0.826 0.901 0.0140 0.973 0.891
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
#> GSM381194 2 0.9944 0.0975 0.456 0.544
#> GSM381199 2 0.0000 0.7927 0.000 1.000
#> GSM381205 2 0.0000 0.7927 0.000 1.000
#> GSM381211 2 0.0000 0.7927 0.000 1.000
#> GSM381220 2 0.0000 0.7927 0.000 1.000
#> GSM381222 1 0.9635 0.4112 0.612 0.388
#> GSM381224 1 0.6048 0.7343 0.852 0.148
#> GSM381232 2 0.9686 0.3060 0.396 0.604
#> GSM381240 1 0.0000 0.7904 1.000 0.000
#> GSM381250 1 0.9000 0.5512 0.684 0.316
#> GSM381252 2 0.0000 0.7927 0.000 1.000
#> GSM381254 1 0.0000 0.7904 1.000 0.000
#> GSM381256 2 0.0000 0.7927 0.000 1.000
#> GSM381257 1 0.0000 0.7904 1.000 0.000
#> GSM381259 1 0.0000 0.7904 1.000 0.000
#> GSM381260 1 0.7453 0.6886 0.788 0.212
#> GSM381261 2 0.0000 0.7927 0.000 1.000
#> GSM381263 1 0.9248 0.5115 0.660 0.340
#> GSM381265 1 0.0000 0.7904 1.000 0.000
#> GSM381268 2 0.9954 0.0807 0.460 0.540
#> GSM381270 2 0.0000 0.7927 0.000 1.000
#> GSM381271 2 0.9686 0.3060 0.396 0.604
#> GSM381275 2 0.0000 0.7927 0.000 1.000
#> GSM381279 2 0.0000 0.7927 0.000 1.000
#> GSM381195 1 0.0376 0.7897 0.996 0.004
#> GSM381196 1 0.9209 0.5190 0.664 0.336
#> GSM381198 2 0.0000 0.7927 0.000 1.000
#> GSM381200 2 0.0000 0.7927 0.000 1.000
#> GSM381201 1 0.0000 0.7904 1.000 0.000
#> GSM381203 1 0.7299 0.6883 0.796 0.204
#> GSM381204 1 0.0000 0.7904 1.000 0.000
#> GSM381209 1 0.0000 0.7904 1.000 0.000
#> GSM381212 1 0.0000 0.7904 1.000 0.000
#> GSM381213 2 0.0000 0.7927 0.000 1.000
#> GSM381214 2 0.0000 0.7927 0.000 1.000
#> GSM381216 1 0.9909 0.2703 0.556 0.444
#> GSM381225 2 0.9996 -0.0413 0.488 0.512
#> GSM381231 2 0.9686 0.3060 0.396 0.604
#> GSM381235 1 0.9933 0.2482 0.548 0.452
#> GSM381237 1 0.0000 0.7904 1.000 0.000
#> GSM381241 2 0.0000 0.7927 0.000 1.000
#> GSM381243 2 0.0000 0.7927 0.000 1.000
#> GSM381245 1 0.0000 0.7904 1.000 0.000
#> GSM381246 2 0.0000 0.7927 0.000 1.000
#> GSM381251 1 0.0000 0.7904 1.000 0.000
#> GSM381264 1 0.0000 0.7904 1.000 0.000
#> GSM381206 2 0.0000 0.7927 0.000 1.000
#> GSM381217 1 0.9944 0.2353 0.544 0.456
#> GSM381218 2 0.0000 0.7927 0.000 1.000
#> GSM381226 2 0.0000 0.7927 0.000 1.000
#> GSM381227 2 0.0000 0.7927 0.000 1.000
#> GSM381228 2 0.9686 0.3060 0.396 0.604
#> GSM381236 2 0.9686 0.3060 0.396 0.604
#> GSM381244 1 0.0000 0.7904 1.000 0.000
#> GSM381272 2 0.9686 0.3060 0.396 0.604
#> GSM381277 1 0.7219 0.6988 0.800 0.200
#> GSM381278 2 0.9686 0.3060 0.396 0.604
#> GSM381197 1 0.0000 0.7904 1.000 0.000
#> GSM381202 1 0.6343 0.7243 0.840 0.160
#> GSM381207 1 0.0000 0.7904 1.000 0.000
#> GSM381208 1 0.0000 0.7904 1.000 0.000
#> GSM381210 1 0.3431 0.7739 0.936 0.064
#> GSM381215 1 0.9993 0.1315 0.516 0.484
#> GSM381219 2 0.0000 0.7927 0.000 1.000
#> GSM381221 2 0.0000 0.7927 0.000 1.000
#> GSM381223 2 0.0000 0.7927 0.000 1.000
#> GSM381229 1 0.7950 0.6347 0.760 0.240
#> GSM381230 1 0.2423 0.7807 0.960 0.040
#> GSM381233 1 0.9635 0.4112 0.612 0.388
#> GSM381234 1 0.0000 0.7904 1.000 0.000
#> GSM381238 2 0.9686 0.3060 0.396 0.604
#> GSM381239 2 0.9686 0.3060 0.396 0.604
#> GSM381242 1 0.7453 0.6886 0.788 0.212
#> GSM381247 2 0.0000 0.7927 0.000 1.000
#> GSM381248 1 0.1633 0.7836 0.976 0.024
#> GSM381249 1 0.9909 0.2703 0.556 0.444
#> GSM381253 1 0.9000 0.5512 0.684 0.316
#> GSM381255 2 0.0000 0.7927 0.000 1.000
#> GSM381258 1 0.9988 0.1477 0.520 0.480
#> GSM381262 2 0.9944 0.0975 0.456 0.544
#> GSM381266 2 0.9686 0.3060 0.396 0.604
#> GSM381267 1 0.0000 0.7904 1.000 0.000
#> GSM381269 1 0.9909 0.2703 0.556 0.444
#> GSM381273 1 0.0000 0.7904 1.000 0.000
#> GSM381274 2 0.0000 0.7927 0.000 1.000
#> GSM381276 1 0.7219 0.6988 0.800 0.200
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM381194 2 0.8202 0.0942 0.376 0.544 0.080
#> GSM381199 2 0.0000 0.8000 0.000 1.000 0.000
#> GSM381205 2 0.0000 0.8000 0.000 1.000 0.000
#> GSM381211 2 0.0000 0.8000 0.000 1.000 0.000
#> GSM381220 2 0.0000 0.8000 0.000 1.000 0.000
#> GSM381222 1 0.7114 0.4346 0.584 0.388 0.028
#> GSM381224 1 0.5173 0.7128 0.816 0.148 0.036
#> GSM381232 2 0.6314 0.4770 0.004 0.604 0.392
#> GSM381240 1 0.0000 0.7216 1.000 0.000 0.000
#> GSM381250 1 0.7850 0.5311 0.608 0.316 0.076
#> GSM381252 2 0.0000 0.8000 0.000 1.000 0.000
#> GSM381254 1 0.0000 0.7216 1.000 0.000 0.000
#> GSM381256 2 0.0000 0.8000 0.000 1.000 0.000
#> GSM381257 1 0.0000 0.7216 1.000 0.000 0.000
#> GSM381259 1 0.0000 0.7216 1.000 0.000 0.000
#> GSM381260 1 0.6633 0.6688 0.728 0.212 0.060
#> GSM381261 2 0.0000 0.8000 0.000 1.000 0.000
#> GSM381263 1 0.7981 0.4924 0.584 0.340 0.076
#> GSM381265 1 0.0000 0.7216 1.000 0.000 0.000
#> GSM381268 2 0.8157 0.0719 0.384 0.540 0.076
#> GSM381270 2 0.0000 0.8000 0.000 1.000 0.000
#> GSM381271 2 0.6314 0.4770 0.004 0.604 0.392
#> GSM381275 2 0.0000 0.8000 0.000 1.000 0.000
#> GSM381279 2 0.0000 0.8000 0.000 1.000 0.000
#> GSM381195 1 0.0237 0.7222 0.996 0.004 0.000
#> GSM381196 1 0.7961 0.4999 0.588 0.336 0.076
#> GSM381198 2 0.0000 0.8000 0.000 1.000 0.000
#> GSM381200 2 0.0000 0.8000 0.000 1.000 0.000
#> GSM381201 3 0.0000 0.9542 0.000 0.000 1.000
#> GSM381203 1 0.6887 0.6595 0.720 0.204 0.076
#> GSM381204 1 0.0000 0.7216 1.000 0.000 0.000
#> GSM381209 1 0.0000 0.7216 1.000 0.000 0.000
#> GSM381212 1 0.0000 0.7216 1.000 0.000 0.000
#> GSM381213 2 0.0000 0.8000 0.000 1.000 0.000
#> GSM381214 2 0.0000 0.8000 0.000 1.000 0.000
#> GSM381216 1 0.8271 0.2508 0.480 0.444 0.076
#> GSM381225 2 0.8288 -0.0300 0.408 0.512 0.080
#> GSM381231 2 0.6314 0.4770 0.004 0.604 0.392
#> GSM381235 1 0.8275 0.2295 0.472 0.452 0.076
#> GSM381237 1 0.0000 0.7216 1.000 0.000 0.000
#> GSM381241 2 0.0000 0.8000 0.000 1.000 0.000
#> GSM381243 2 0.0000 0.8000 0.000 1.000 0.000
#> GSM381245 1 0.0000 0.7216 1.000 0.000 0.000
#> GSM381246 2 0.0000 0.8000 0.000 1.000 0.000
#> GSM381251 3 0.0000 0.9542 0.000 0.000 1.000
#> GSM381264 1 0.0000 0.7216 1.000 0.000 0.000
#> GSM381206 2 0.0000 0.8000 0.000 1.000 0.000
#> GSM381217 1 0.8277 0.2167 0.468 0.456 0.076
#> GSM381218 2 0.0000 0.8000 0.000 1.000 0.000
#> GSM381226 2 0.0000 0.8000 0.000 1.000 0.000
#> GSM381227 2 0.0000 0.8000 0.000 1.000 0.000
#> GSM381228 2 0.6314 0.4770 0.004 0.604 0.392
#> GSM381236 2 0.6314 0.4770 0.004 0.604 0.392
#> GSM381244 3 0.0000 0.9542 0.000 0.000 1.000
#> GSM381272 2 0.6314 0.4770 0.004 0.604 0.392
#> GSM381277 1 0.6495 0.6776 0.740 0.200 0.060
#> GSM381278 2 0.8020 0.2943 0.308 0.604 0.088
#> GSM381197 3 0.0000 0.9542 0.000 0.000 1.000
#> GSM381202 1 0.6324 0.6918 0.764 0.160 0.076
#> GSM381207 1 0.0000 0.7216 1.000 0.000 0.000
#> GSM381208 3 0.0000 0.9542 0.000 0.000 1.000
#> GSM381210 1 0.2165 0.7250 0.936 0.064 0.000
#> GSM381215 2 0.8268 -0.1568 0.440 0.484 0.076
#> GSM381219 2 0.0000 0.8000 0.000 1.000 0.000
#> GSM381221 2 0.0000 0.8000 0.000 1.000 0.000
#> GSM381223 2 0.0000 0.8000 0.000 1.000 0.000
#> GSM381229 3 0.5244 0.5735 0.004 0.240 0.756
#> GSM381230 1 0.1529 0.7235 0.960 0.040 0.000
#> GSM381233 1 0.7114 0.4346 0.584 0.388 0.028
#> GSM381234 1 0.0000 0.7216 1.000 0.000 0.000
#> GSM381238 2 0.6314 0.4770 0.004 0.604 0.392
#> GSM381239 2 0.6314 0.4770 0.004 0.604 0.392
#> GSM381242 1 0.6633 0.6688 0.728 0.212 0.060
#> GSM381247 2 0.0000 0.8000 0.000 1.000 0.000
#> GSM381248 1 0.1031 0.7192 0.976 0.024 0.000
#> GSM381249 1 0.8271 0.2508 0.480 0.444 0.076
#> GSM381253 1 0.7850 0.5311 0.608 0.316 0.076
#> GSM381255 2 0.0000 0.8000 0.000 1.000 0.000
#> GSM381258 2 0.8334 -0.1646 0.440 0.480 0.080
#> GSM381262 2 0.8202 0.0942 0.376 0.544 0.080
#> GSM381266 2 0.8020 0.2943 0.308 0.604 0.088
#> GSM381267 3 0.0000 0.9542 0.000 0.000 1.000
#> GSM381269 1 0.8271 0.2508 0.480 0.444 0.076
#> GSM381273 3 0.0000 0.9542 0.000 0.000 1.000
#> GSM381274 2 0.0000 0.8000 0.000 1.000 0.000
#> GSM381276 1 0.6495 0.6776 0.740 0.200 0.060
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM381194 3 0.2081 0.7023 0.084 0 0.916 0.000
#> GSM381199 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381205 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381211 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381220 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381222 3 0.4925 0.3391 0.428 0 0.572 0.000
#> GSM381224 1 0.4522 0.4301 0.680 0 0.320 0.000
#> GSM381232 3 0.4382 0.4516 0.000 0 0.704 0.296
#> GSM381240 1 0.0000 0.8283 1.000 0 0.000 0.000
#> GSM381250 3 0.4543 0.5159 0.324 0 0.676 0.000
#> GSM381252 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381254 1 0.0000 0.8283 1.000 0 0.000 0.000
#> GSM381256 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381257 1 0.0000 0.8283 1.000 0 0.000 0.000
#> GSM381259 1 0.0000 0.8283 1.000 0 0.000 0.000
#> GSM381260 1 0.5000 -0.0295 0.504 0 0.496 0.000
#> GSM381261 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381263 3 0.4406 0.5547 0.300 0 0.700 0.000
#> GSM381265 1 0.0000 0.8283 1.000 0 0.000 0.000
#> GSM381268 3 0.2469 0.7032 0.108 0 0.892 0.000
#> GSM381270 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381271 3 0.4382 0.4516 0.000 0 0.704 0.296
#> GSM381275 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381279 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381195 1 0.0188 0.8258 0.996 0 0.004 0.000
#> GSM381196 3 0.4522 0.5349 0.320 0 0.680 0.000
#> GSM381198 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381200 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381201 4 0.0336 0.9564 0.000 0 0.008 0.992
#> GSM381203 3 0.4972 0.1953 0.456 0 0.544 0.000
#> GSM381204 1 0.0000 0.8283 1.000 0 0.000 0.000
#> GSM381209 1 0.0000 0.8283 1.000 0 0.000 0.000
#> GSM381212 1 0.0000 0.8283 1.000 0 0.000 0.000
#> GSM381213 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381214 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381216 3 0.3873 0.6544 0.228 0 0.772 0.000
#> GSM381225 3 0.2589 0.7000 0.116 0 0.884 0.000
#> GSM381231 3 0.4382 0.4516 0.000 0 0.704 0.296
#> GSM381235 3 0.3801 0.6613 0.220 0 0.780 0.000
#> GSM381237 1 0.0000 0.8283 1.000 0 0.000 0.000
#> GSM381241 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381243 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381245 1 0.0000 0.8283 1.000 0 0.000 0.000
#> GSM381246 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381251 4 0.0336 0.9564 0.000 0 0.008 0.992
#> GSM381264 1 0.0000 0.8283 1.000 0 0.000 0.000
#> GSM381206 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381217 3 0.3726 0.6662 0.212 0 0.788 0.000
#> GSM381218 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381226 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381227 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381228 3 0.4382 0.4516 0.000 0 0.704 0.296
#> GSM381236 3 0.4382 0.4516 0.000 0 0.704 0.296
#> GSM381244 4 0.0000 0.9570 0.000 0 0.000 1.000
#> GSM381272 3 0.4382 0.4516 0.000 0 0.704 0.296
#> GSM381277 1 0.4996 0.0137 0.516 0 0.484 0.000
#> GSM381278 3 0.0336 0.6844 0.008 0 0.992 0.000
#> GSM381197 4 0.0000 0.9570 0.000 0 0.000 1.000
#> GSM381202 1 0.4996 -0.0525 0.516 0 0.484 0.000
#> GSM381207 1 0.0000 0.8283 1.000 0 0.000 0.000
#> GSM381208 4 0.0000 0.9570 0.000 0 0.000 1.000
#> GSM381210 1 0.1716 0.7804 0.936 0 0.064 0.000
#> GSM381215 3 0.3219 0.6884 0.164 0 0.836 0.000
#> GSM381219 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381221 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381223 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381229 4 0.4072 0.6449 0.000 0 0.252 0.748
#> GSM381230 1 0.1302 0.7976 0.956 0 0.044 0.000
#> GSM381233 3 0.4925 0.3391 0.428 0 0.572 0.000
#> GSM381234 1 0.0000 0.8283 1.000 0 0.000 0.000
#> GSM381238 3 0.4382 0.4516 0.000 0 0.704 0.296
#> GSM381239 3 0.4382 0.4516 0.000 0 0.704 0.296
#> GSM381242 1 0.5000 -0.0295 0.504 0 0.496 0.000
#> GSM381247 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381248 1 0.1022 0.8059 0.968 0 0.032 0.000
#> GSM381249 3 0.3873 0.6544 0.228 0 0.772 0.000
#> GSM381253 3 0.4543 0.5159 0.324 0 0.676 0.000
#> GSM381255 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381258 3 0.3024 0.6914 0.148 0 0.852 0.000
#> GSM381262 3 0.2081 0.7023 0.084 0 0.916 0.000
#> GSM381266 3 0.0336 0.6844 0.008 0 0.992 0.000
#> GSM381267 4 0.0000 0.9570 0.000 0 0.000 1.000
#> GSM381269 3 0.3873 0.6544 0.228 0 0.772 0.000
#> GSM381273 4 0.0336 0.9564 0.000 0 0.008 0.992
#> GSM381274 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381276 1 0.4996 0.0137 0.516 0 0.484 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM381194 3 0.0609 0.740 0.020 0 0.980 0.000 0.000
#> GSM381199 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM381205 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM381211 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM381220 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM381222 3 0.4126 0.585 0.380 0 0.620 0.000 0.000
#> GSM381224 1 0.3999 0.183 0.656 0 0.344 0.000 0.000
#> GSM381232 4 0.0162 1.000 0.000 0 0.004 0.996 0.000
#> GSM381240 1 0.0290 0.952 0.992 0 0.008 0.000 0.000
#> GSM381250 3 0.3561 0.737 0.260 0 0.740 0.000 0.000
#> GSM381252 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM381254 1 0.0000 0.955 1.000 0 0.000 0.000 0.000
#> GSM381256 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM381257 1 0.0000 0.955 1.000 0 0.000 0.000 0.000
#> GSM381259 1 0.0000 0.955 1.000 0 0.000 0.000 0.000
#> GSM381260 3 0.4302 0.435 0.480 0 0.520 0.000 0.000
#> GSM381261 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM381263 3 0.3395 0.752 0.236 0 0.764 0.000 0.000
#> GSM381265 1 0.0000 0.955 1.000 0 0.000 0.000 0.000
#> GSM381268 3 0.1121 0.756 0.044 0 0.956 0.000 0.000
#> GSM381270 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM381271 4 0.0162 1.000 0.000 0 0.004 0.996 0.000
#> GSM381275 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM381279 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM381195 1 0.0404 0.948 0.988 0 0.012 0.000 0.000
#> GSM381196 3 0.3534 0.746 0.256 0 0.744 0.000 0.000
#> GSM381198 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM381200 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM381201 5 0.0404 0.955 0.000 0 0.000 0.012 0.988
#> GSM381203 3 0.4161 0.604 0.392 0 0.608 0.000 0.000
#> GSM381204 1 0.0000 0.955 1.000 0 0.000 0.000 0.000
#> GSM381209 1 0.0000 0.955 1.000 0 0.000 0.000 0.000
#> GSM381212 1 0.0000 0.955 1.000 0 0.000 0.000 0.000
#> GSM381213 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM381214 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM381216 3 0.3535 0.779 0.164 0 0.808 0.028 0.000
#> GSM381225 3 0.1270 0.761 0.052 0 0.948 0.000 0.000
#> GSM381231 4 0.0162 1.000 0.000 0 0.004 0.996 0.000
#> GSM381235 3 0.2690 0.785 0.156 0 0.844 0.000 0.000
#> GSM381237 1 0.0290 0.952 0.992 0 0.008 0.000 0.000
#> GSM381241 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM381243 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM381245 1 0.0404 0.949 0.988 0 0.012 0.000 0.000
#> GSM381246 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM381251 5 0.0404 0.955 0.000 0 0.000 0.012 0.988
#> GSM381264 1 0.0000 0.955 1.000 0 0.000 0.000 0.000
#> GSM381206 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM381217 3 0.2763 0.786 0.148 0 0.848 0.004 0.000
#> GSM381218 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM381226 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM381227 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM381228 4 0.0162 1.000 0.000 0 0.004 0.996 0.000
#> GSM381236 4 0.0162 1.000 0.000 0 0.004 0.996 0.000
#> GSM381244 5 0.0000 0.956 0.000 0 0.000 0.000 1.000
#> GSM381272 4 0.0162 1.000 0.000 0 0.004 0.996 0.000
#> GSM381277 3 0.4306 0.409 0.492 0 0.508 0.000 0.000
#> GSM381278 3 0.1410 0.694 0.000 0 0.940 0.060 0.000
#> GSM381197 5 0.0000 0.956 0.000 0 0.000 0.000 1.000
#> GSM381202 3 0.4965 0.497 0.452 0 0.520 0.028 0.000
#> GSM381207 1 0.0404 0.949 0.988 0 0.012 0.000 0.000
#> GSM381208 5 0.0000 0.956 0.000 0 0.000 0.000 1.000
#> GSM381210 1 0.1792 0.868 0.916 0 0.084 0.000 0.000
#> GSM381215 3 0.2707 0.781 0.100 0 0.876 0.024 0.000
#> GSM381219 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM381221 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM381223 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM381229 5 0.3835 0.704 0.000 0 0.244 0.012 0.744
#> GSM381230 1 0.1121 0.916 0.956 0 0.044 0.000 0.000
#> GSM381233 3 0.4126 0.585 0.380 0 0.620 0.000 0.000
#> GSM381234 1 0.0000 0.955 1.000 0 0.000 0.000 0.000
#> GSM381238 4 0.0162 1.000 0.000 0 0.004 0.996 0.000
#> GSM381239 4 0.0162 1.000 0.000 0 0.004 0.996 0.000
#> GSM381242 3 0.4302 0.435 0.480 0 0.520 0.000 0.000
#> GSM381247 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM381248 1 0.0963 0.924 0.964 0 0.036 0.000 0.000
#> GSM381249 3 0.3535 0.779 0.164 0 0.808 0.028 0.000
#> GSM381253 3 0.3561 0.737 0.260 0 0.740 0.000 0.000
#> GSM381255 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM381258 3 0.2570 0.779 0.084 0 0.888 0.028 0.000
#> GSM381262 3 0.0609 0.740 0.020 0 0.980 0.000 0.000
#> GSM381266 3 0.1410 0.694 0.000 0 0.940 0.060 0.000
#> GSM381267 5 0.0000 0.956 0.000 0 0.000 0.000 1.000
#> GSM381269 3 0.3535 0.779 0.164 0 0.808 0.028 0.000
#> GSM381273 5 0.0404 0.955 0.000 0 0.000 0.012 0.988
#> GSM381274 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM381276 3 0.4306 0.409 0.492 0 0.508 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM381194 3 0.2744 0.702 0.016 0 0.840 0.000 0.000 0.144
#> GSM381199 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM381205 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM381211 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM381220 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM381222 3 0.3927 0.531 0.344 0 0.644 0.000 0.000 0.012
#> GSM381224 1 0.3620 0.283 0.648 0 0.352 0.000 0.000 0.000
#> GSM381232 4 0.0000 1.000 0.000 0 0.000 1.000 0.000 0.000
#> GSM381240 1 0.0260 0.885 0.992 0 0.008 0.000 0.000 0.000
#> GSM381250 3 0.3979 0.710 0.256 0 0.708 0.000 0.000 0.036
#> GSM381252 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM381254 1 0.0000 0.887 1.000 0 0.000 0.000 0.000 0.000
#> GSM381256 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM381257 1 0.0000 0.887 1.000 0 0.000 0.000 0.000 0.000
#> GSM381259 1 0.0000 0.887 1.000 0 0.000 0.000 0.000 0.000
#> GSM381260 3 0.4534 0.265 0.472 0 0.496 0.000 0.000 0.032
#> GSM381261 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM381263 3 0.4085 0.724 0.232 0 0.716 0.000 0.000 0.052
#> GSM381265 1 0.0000 0.887 1.000 0 0.000 0.000 0.000 0.000
#> GSM381268 3 0.3351 0.714 0.040 0 0.800 0.000 0.000 0.160
#> GSM381270 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM381271 4 0.0000 1.000 0.000 0 0.000 1.000 0.000 0.000
#> GSM381275 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM381279 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM381195 1 0.0363 0.881 0.988 0 0.012 0.000 0.000 0.000
#> GSM381196 3 0.4145 0.717 0.252 0 0.700 0.000 0.000 0.048
#> GSM381198 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM381200 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM381201 6 0.3737 0.562 0.000 0 0.000 0.000 0.392 0.608
#> GSM381203 3 0.3965 0.557 0.388 0 0.604 0.000 0.000 0.008
#> GSM381204 1 0.0000 0.887 1.000 0 0.000 0.000 0.000 0.000
#> GSM381209 1 0.0000 0.887 1.000 0 0.000 0.000 0.000 0.000
#> GSM381212 1 0.0000 0.887 1.000 0 0.000 0.000 0.000 0.000
#> GSM381213 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM381214 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM381216 3 0.3393 0.748 0.124 0 0.824 0.028 0.000 0.024
#> GSM381225 3 0.2629 0.731 0.040 0 0.868 0.000 0.000 0.092
#> GSM381231 4 0.0000 1.000 0.000 0 0.000 1.000 0.000 0.000
#> GSM381235 3 0.2494 0.766 0.120 0 0.864 0.000 0.000 0.016
#> GSM381237 1 0.0260 0.885 0.992 0 0.008 0.000 0.000 0.000
#> GSM381241 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM381243 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM381245 1 0.0363 0.883 0.988 0 0.012 0.000 0.000 0.000
#> GSM381246 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM381251 6 0.2883 0.778 0.000 0 0.000 0.000 0.212 0.788
#> GSM381264 1 0.0000 0.887 1.000 0 0.000 0.000 0.000 0.000
#> GSM381206 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM381217 3 0.2547 0.766 0.112 0 0.868 0.004 0.000 0.016
#> GSM381218 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM381226 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM381227 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM381228 4 0.0000 1.000 0.000 0 0.000 1.000 0.000 0.000
#> GSM381236 4 0.0000 1.000 0.000 0 0.000 1.000 0.000 0.000
#> GSM381244 5 0.0790 0.972 0.000 0 0.000 0.000 0.968 0.032
#> GSM381272 4 0.0000 1.000 0.000 0 0.000 1.000 0.000 0.000
#> GSM381277 1 0.4535 -0.298 0.484 0 0.484 0.000 0.000 0.032
#> GSM381278 3 0.3276 0.646 0.000 0 0.816 0.052 0.000 0.132
#> GSM381197 5 0.0790 0.972 0.000 0 0.000 0.000 0.968 0.032
#> GSM381202 3 0.4588 0.431 0.448 0 0.520 0.028 0.000 0.004
#> GSM381207 1 0.0363 0.883 0.988 0 0.012 0.000 0.000 0.000
#> GSM381208 5 0.0000 0.972 0.000 0 0.000 0.000 1.000 0.000
#> GSM381210 1 0.1663 0.812 0.912 0 0.088 0.000 0.000 0.000
#> GSM381215 3 0.2934 0.746 0.064 0 0.868 0.024 0.000 0.044
#> GSM381219 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM381221 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM381223 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM381229 6 0.1967 0.600 0.000 0 0.084 0.000 0.012 0.904
#> GSM381230 1 0.1075 0.852 0.952 0 0.048 0.000 0.000 0.000
#> GSM381233 3 0.3912 0.534 0.340 0 0.648 0.000 0.000 0.012
#> GSM381234 1 0.0000 0.887 1.000 0 0.000 0.000 0.000 0.000
#> GSM381238 4 0.0000 1.000 0.000 0 0.000 1.000 0.000 0.000
#> GSM381239 4 0.0000 1.000 0.000 0 0.000 1.000 0.000 0.000
#> GSM381242 3 0.4534 0.265 0.472 0 0.496 0.000 0.000 0.032
#> GSM381247 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM381248 1 0.1391 0.840 0.944 0 0.016 0.000 0.000 0.040
#> GSM381249 3 0.3393 0.748 0.124 0 0.824 0.028 0.000 0.024
#> GSM381253 3 0.3979 0.710 0.256 0 0.708 0.000 0.000 0.036
#> GSM381255 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM381258 3 0.2335 0.735 0.044 0 0.904 0.028 0.000 0.024
#> GSM381262 3 0.2744 0.702 0.016 0 0.840 0.000 0.000 0.144
#> GSM381266 3 0.3276 0.646 0.000 0 0.816 0.052 0.000 0.132
#> GSM381267 5 0.0000 0.972 0.000 0 0.000 0.000 1.000 0.000
#> GSM381269 3 0.3393 0.748 0.124 0 0.824 0.028 0.000 0.024
#> GSM381273 6 0.2883 0.778 0.000 0 0.000 0.000 0.212 0.788
#> GSM381274 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM381276 1 0.4535 -0.298 0.484 0 0.484 0.000 0.000 0.032
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 other(p) k
#> CV:hclust 63 0.309 2
#> CV:hclust 61 0.252 3
#> CV:hclust 69 0.334 4
#> CV:hclust 80 0.239 5
#> CV:hclust 80 0.250 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 86 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.799 0.887 0.928 0.4522 0.548 0.548
#> 3 3 0.714 0.937 0.934 0.3445 0.805 0.649
#> 4 4 0.745 0.824 0.844 0.1181 0.980 0.947
#> 5 5 0.747 0.847 0.817 0.0984 0.866 0.628
#> 6 6 0.754 0.807 0.839 0.0609 0.953 0.803
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
#> GSM381194 1 0.0376 0.926 0.996 0.004
#> GSM381199 2 0.3879 0.983 0.076 0.924
#> GSM381205 2 0.3879 0.983 0.076 0.924
#> GSM381211 2 0.3879 0.983 0.076 0.924
#> GSM381220 2 0.3733 0.981 0.072 0.928
#> GSM381222 1 0.0000 0.928 1.000 0.000
#> GSM381224 1 0.0000 0.928 1.000 0.000
#> GSM381232 1 0.9754 0.401 0.592 0.408
#> GSM381240 1 0.0000 0.928 1.000 0.000
#> GSM381250 1 0.0000 0.928 1.000 0.000
#> GSM381252 2 0.3879 0.983 0.076 0.924
#> GSM381254 1 0.0000 0.928 1.000 0.000
#> GSM381256 2 0.3879 0.983 0.076 0.924
#> GSM381257 1 0.0000 0.928 1.000 0.000
#> GSM381259 1 0.0000 0.928 1.000 0.000
#> GSM381260 1 0.0000 0.928 1.000 0.000
#> GSM381261 2 0.3879 0.983 0.076 0.924
#> GSM381263 1 0.0000 0.928 1.000 0.000
#> GSM381265 1 0.0000 0.928 1.000 0.000
#> GSM381268 1 0.0376 0.926 0.996 0.004
#> GSM381270 2 0.3733 0.981 0.072 0.928
#> GSM381271 1 0.9754 0.401 0.592 0.408
#> GSM381275 2 0.3879 0.983 0.076 0.924
#> GSM381279 2 0.3733 0.981 0.072 0.928
#> GSM381195 1 0.0000 0.928 1.000 0.000
#> GSM381196 1 0.0000 0.928 1.000 0.000
#> GSM381198 2 0.3879 0.983 0.076 0.924
#> GSM381200 2 0.3879 0.983 0.076 0.924
#> GSM381201 1 0.3879 0.878 0.924 0.076
#> GSM381203 1 0.0000 0.928 1.000 0.000
#> GSM381204 1 0.0000 0.928 1.000 0.000
#> GSM381209 1 0.0000 0.928 1.000 0.000
#> GSM381212 1 0.0000 0.928 1.000 0.000
#> GSM381213 2 0.3733 0.981 0.072 0.928
#> GSM381214 2 0.3879 0.983 0.076 0.924
#> GSM381216 1 0.0000 0.928 1.000 0.000
#> GSM381225 1 0.0000 0.928 1.000 0.000
#> GSM381231 1 0.9754 0.401 0.592 0.408
#> GSM381235 1 0.0000 0.928 1.000 0.000
#> GSM381237 1 0.0000 0.928 1.000 0.000
#> GSM381241 2 0.3879 0.983 0.076 0.924
#> GSM381243 2 0.3733 0.981 0.072 0.928
#> GSM381245 1 0.0000 0.928 1.000 0.000
#> GSM381246 2 0.3879 0.983 0.076 0.924
#> GSM381251 1 0.3879 0.878 0.924 0.076
#> GSM381264 1 0.0000 0.928 1.000 0.000
#> GSM381206 2 0.3879 0.983 0.076 0.924
#> GSM381217 1 0.0000 0.928 1.000 0.000
#> GSM381218 2 0.3879 0.983 0.076 0.924
#> GSM381226 2 0.3879 0.983 0.076 0.924
#> GSM381227 2 0.3879 0.983 0.076 0.924
#> GSM381228 1 0.9754 0.401 0.592 0.408
#> GSM381236 1 0.9754 0.401 0.592 0.408
#> GSM381244 1 0.3879 0.878 0.924 0.076
#> GSM381272 1 0.9754 0.401 0.592 0.408
#> GSM381277 1 0.0000 0.928 1.000 0.000
#> GSM381278 1 0.0376 0.926 0.996 0.004
#> GSM381197 1 0.3879 0.878 0.924 0.076
#> GSM381202 1 0.0000 0.928 1.000 0.000
#> GSM381207 1 0.0000 0.928 1.000 0.000
#> GSM381208 2 0.8499 0.526 0.276 0.724
#> GSM381210 1 0.0000 0.928 1.000 0.000
#> GSM381215 1 0.0376 0.926 0.996 0.004
#> GSM381219 2 0.3879 0.983 0.076 0.924
#> GSM381221 2 0.3879 0.983 0.076 0.924
#> GSM381223 2 0.3879 0.983 0.076 0.924
#> GSM381229 1 0.3879 0.878 0.924 0.076
#> GSM381230 1 0.0000 0.928 1.000 0.000
#> GSM381233 1 0.0000 0.928 1.000 0.000
#> GSM381234 1 0.0000 0.928 1.000 0.000
#> GSM381238 1 0.9754 0.401 0.592 0.408
#> GSM381239 1 0.9754 0.401 0.592 0.408
#> GSM381242 1 0.0000 0.928 1.000 0.000
#> GSM381247 2 0.3733 0.981 0.072 0.928
#> GSM381248 1 0.0000 0.928 1.000 0.000
#> GSM381249 1 0.0000 0.928 1.000 0.000
#> GSM381253 1 0.0000 0.928 1.000 0.000
#> GSM381255 2 0.3879 0.983 0.076 0.924
#> GSM381258 1 0.0376 0.926 0.996 0.004
#> GSM381262 1 0.0376 0.926 0.996 0.004
#> GSM381266 1 0.3114 0.891 0.944 0.056
#> GSM381267 2 0.2948 0.887 0.052 0.948
#> GSM381269 1 0.0000 0.928 1.000 0.000
#> GSM381273 1 0.3879 0.878 0.924 0.076
#> GSM381274 2 0.3879 0.983 0.076 0.924
#> GSM381276 1 0.0376 0.926 0.996 0.004
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM381194 1 0.3482 0.854 0.872 0.000 0.128
#> GSM381199 2 0.1878 0.969 0.004 0.952 0.044
#> GSM381205 2 0.0661 0.974 0.004 0.988 0.008
#> GSM381211 2 0.0661 0.974 0.004 0.988 0.008
#> GSM381220 2 0.1267 0.974 0.004 0.972 0.024
#> GSM381222 1 0.0424 0.968 0.992 0.000 0.008
#> GSM381224 1 0.0424 0.968 0.992 0.000 0.008
#> GSM381232 3 0.6793 0.882 0.160 0.100 0.740
#> GSM381240 1 0.0000 0.971 1.000 0.000 0.000
#> GSM381250 1 0.1289 0.951 0.968 0.000 0.032
#> GSM381252 2 0.0661 0.974 0.004 0.988 0.008
#> GSM381254 1 0.0000 0.971 1.000 0.000 0.000
#> GSM381256 2 0.0661 0.975 0.004 0.988 0.008
#> GSM381257 1 0.0000 0.971 1.000 0.000 0.000
#> GSM381259 1 0.0000 0.971 1.000 0.000 0.000
#> GSM381260 1 0.0424 0.967 0.992 0.000 0.008
#> GSM381261 2 0.2682 0.959 0.004 0.920 0.076
#> GSM381263 1 0.1289 0.951 0.968 0.000 0.032
#> GSM381265 1 0.0000 0.971 1.000 0.000 0.000
#> GSM381268 1 0.2878 0.885 0.904 0.000 0.096
#> GSM381270 2 0.2301 0.965 0.004 0.936 0.060
#> GSM381271 3 0.6793 0.882 0.160 0.100 0.740
#> GSM381275 2 0.2682 0.959 0.004 0.920 0.076
#> GSM381279 2 0.2301 0.965 0.004 0.936 0.060
#> GSM381195 1 0.0000 0.971 1.000 0.000 0.000
#> GSM381196 1 0.1289 0.951 0.968 0.000 0.032
#> GSM381198 2 0.0661 0.974 0.004 0.988 0.008
#> GSM381200 2 0.1525 0.972 0.004 0.964 0.032
#> GSM381201 3 0.4351 0.864 0.168 0.004 0.828
#> GSM381203 1 0.0000 0.971 1.000 0.000 0.000
#> GSM381204 1 0.0000 0.971 1.000 0.000 0.000
#> GSM381209 1 0.0000 0.971 1.000 0.000 0.000
#> GSM381212 1 0.0000 0.971 1.000 0.000 0.000
#> GSM381213 2 0.1267 0.974 0.004 0.972 0.024
#> GSM381214 2 0.0661 0.974 0.004 0.988 0.008
#> GSM381216 1 0.0424 0.968 0.992 0.000 0.008
#> GSM381225 1 0.1529 0.949 0.960 0.000 0.040
#> GSM381231 3 0.6737 0.880 0.156 0.100 0.744
#> GSM381235 1 0.0424 0.968 0.992 0.000 0.008
#> GSM381237 1 0.0000 0.971 1.000 0.000 0.000
#> GSM381241 2 0.0661 0.974 0.004 0.988 0.008
#> GSM381243 2 0.2301 0.965 0.004 0.936 0.060
#> GSM381245 1 0.0000 0.971 1.000 0.000 0.000
#> GSM381246 2 0.0983 0.973 0.004 0.980 0.016
#> GSM381251 3 0.4351 0.864 0.168 0.004 0.828
#> GSM381264 1 0.0000 0.971 1.000 0.000 0.000
#> GSM381206 2 0.0661 0.974 0.004 0.988 0.008
#> GSM381217 1 0.0424 0.968 0.992 0.000 0.008
#> GSM381218 2 0.0661 0.974 0.004 0.988 0.008
#> GSM381226 2 0.0983 0.974 0.004 0.980 0.016
#> GSM381227 2 0.2301 0.965 0.004 0.936 0.060
#> GSM381228 3 0.6793 0.882 0.160 0.100 0.740
#> GSM381236 3 0.6793 0.882 0.160 0.100 0.740
#> GSM381244 3 0.4409 0.863 0.172 0.004 0.824
#> GSM381272 3 0.6793 0.882 0.160 0.100 0.740
#> GSM381277 1 0.0000 0.971 1.000 0.000 0.000
#> GSM381278 1 0.4555 0.738 0.800 0.000 0.200
#> GSM381197 3 0.4409 0.863 0.172 0.004 0.824
#> GSM381202 1 0.0000 0.971 1.000 0.000 0.000
#> GSM381207 1 0.0000 0.971 1.000 0.000 0.000
#> GSM381208 3 0.4891 0.775 0.040 0.124 0.836
#> GSM381210 1 0.0000 0.971 1.000 0.000 0.000
#> GSM381215 1 0.3267 0.869 0.884 0.000 0.116
#> GSM381219 2 0.0661 0.974 0.004 0.988 0.008
#> GSM381221 2 0.0661 0.975 0.004 0.988 0.008
#> GSM381223 2 0.2682 0.959 0.004 0.920 0.076
#> GSM381229 3 0.4575 0.860 0.184 0.004 0.812
#> GSM381230 1 0.0000 0.971 1.000 0.000 0.000
#> GSM381233 1 0.0424 0.968 0.992 0.000 0.008
#> GSM381234 1 0.0000 0.971 1.000 0.000 0.000
#> GSM381238 3 0.6737 0.880 0.156 0.100 0.744
#> GSM381239 3 0.6793 0.882 0.160 0.100 0.740
#> GSM381242 1 0.0424 0.968 0.992 0.000 0.008
#> GSM381247 2 0.2301 0.965 0.004 0.936 0.060
#> GSM381248 1 0.0000 0.971 1.000 0.000 0.000
#> GSM381249 1 0.0424 0.968 0.992 0.000 0.008
#> GSM381253 1 0.0000 0.971 1.000 0.000 0.000
#> GSM381255 2 0.0661 0.974 0.004 0.988 0.008
#> GSM381258 1 0.3267 0.869 0.884 0.000 0.116
#> GSM381262 1 0.3340 0.865 0.880 0.000 0.120
#> GSM381266 3 0.5529 0.755 0.296 0.000 0.704
#> GSM381267 3 0.3752 0.724 0.000 0.144 0.856
#> GSM381269 1 0.0424 0.968 0.992 0.000 0.008
#> GSM381273 3 0.4351 0.864 0.168 0.004 0.828
#> GSM381274 2 0.2590 0.961 0.004 0.924 0.072
#> GSM381276 1 0.1289 0.951 0.968 0.000 0.032
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM381194 1 0.6106 0.657 0.604 0.000 0.332 0.064
#> GSM381199 2 0.3764 0.862 0.000 0.784 0.216 0.000
#> GSM381205 2 0.0188 0.890 0.000 0.996 0.000 0.004
#> GSM381211 2 0.0188 0.890 0.000 0.996 0.000 0.004
#> GSM381220 2 0.1743 0.883 0.000 0.940 0.056 0.004
#> GSM381222 1 0.1389 0.832 0.952 0.000 0.048 0.000
#> GSM381224 1 0.0592 0.838 0.984 0.000 0.016 0.000
#> GSM381232 4 0.1833 0.999 0.032 0.024 0.000 0.944
#> GSM381240 1 0.0000 0.839 1.000 0.000 0.000 0.000
#> GSM381250 1 0.5131 0.738 0.692 0.000 0.280 0.028
#> GSM381252 2 0.0188 0.890 0.000 0.996 0.000 0.004
#> GSM381254 1 0.0000 0.839 1.000 0.000 0.000 0.000
#> GSM381256 2 0.0469 0.891 0.000 0.988 0.012 0.000
#> GSM381257 1 0.0000 0.839 1.000 0.000 0.000 0.000
#> GSM381259 1 0.0000 0.839 1.000 0.000 0.000 0.000
#> GSM381260 1 0.4855 0.757 0.712 0.000 0.268 0.020
#> GSM381261 2 0.4690 0.843 0.000 0.724 0.260 0.016
#> GSM381263 1 0.5182 0.734 0.684 0.000 0.288 0.028
#> GSM381265 1 0.0000 0.839 1.000 0.000 0.000 0.000
#> GSM381268 1 0.5658 0.689 0.632 0.000 0.328 0.040
#> GSM381270 2 0.4304 0.841 0.000 0.716 0.284 0.000
#> GSM381271 4 0.1833 0.999 0.032 0.024 0.000 0.944
#> GSM381275 2 0.4661 0.845 0.000 0.728 0.256 0.016
#> GSM381279 2 0.4277 0.843 0.000 0.720 0.280 0.000
#> GSM381195 1 0.0000 0.839 1.000 0.000 0.000 0.000
#> GSM381196 1 0.5105 0.740 0.696 0.000 0.276 0.028
#> GSM381198 2 0.0188 0.890 0.000 0.996 0.000 0.004
#> GSM381200 2 0.3942 0.858 0.000 0.764 0.236 0.000
#> GSM381201 3 0.6315 0.770 0.064 0.000 0.540 0.396
#> GSM381203 1 0.3311 0.810 0.828 0.000 0.172 0.000
#> GSM381204 1 0.0000 0.839 1.000 0.000 0.000 0.000
#> GSM381209 1 0.0000 0.839 1.000 0.000 0.000 0.000
#> GSM381212 1 0.0000 0.839 1.000 0.000 0.000 0.000
#> GSM381213 2 0.1902 0.886 0.000 0.932 0.064 0.004
#> GSM381214 2 0.0188 0.890 0.000 0.996 0.000 0.004
#> GSM381216 1 0.3975 0.791 0.760 0.000 0.240 0.000
#> GSM381225 1 0.5343 0.719 0.656 0.000 0.316 0.028
#> GSM381231 4 0.1833 0.999 0.032 0.024 0.000 0.944
#> GSM381235 1 0.3975 0.791 0.760 0.000 0.240 0.000
#> GSM381237 1 0.0000 0.839 1.000 0.000 0.000 0.000
#> GSM381241 2 0.0188 0.890 0.000 0.996 0.000 0.004
#> GSM381243 2 0.4304 0.841 0.000 0.716 0.284 0.000
#> GSM381245 1 0.0000 0.839 1.000 0.000 0.000 0.000
#> GSM381246 2 0.0000 0.890 0.000 1.000 0.000 0.000
#> GSM381251 3 0.6315 0.770 0.064 0.000 0.540 0.396
#> GSM381264 1 0.0000 0.839 1.000 0.000 0.000 0.000
#> GSM381206 2 0.0188 0.890 0.000 0.996 0.000 0.004
#> GSM381217 1 0.3942 0.793 0.764 0.000 0.236 0.000
#> GSM381218 2 0.0188 0.890 0.000 0.996 0.000 0.004
#> GSM381226 2 0.2589 0.882 0.000 0.884 0.116 0.000
#> GSM381227 2 0.4193 0.848 0.000 0.732 0.268 0.000
#> GSM381228 4 0.1833 0.999 0.032 0.024 0.000 0.944
#> GSM381236 4 0.1833 0.999 0.032 0.024 0.000 0.944
#> GSM381244 3 0.6597 0.769 0.088 0.000 0.540 0.372
#> GSM381272 4 0.1833 0.999 0.032 0.024 0.000 0.944
#> GSM381277 1 0.0000 0.839 1.000 0.000 0.000 0.000
#> GSM381278 1 0.6547 0.601 0.568 0.000 0.340 0.092
#> GSM381197 3 0.6597 0.769 0.088 0.000 0.540 0.372
#> GSM381202 1 0.2530 0.825 0.888 0.000 0.112 0.000
#> GSM381207 1 0.0000 0.839 1.000 0.000 0.000 0.000
#> GSM381208 3 0.7086 0.570 0.008 0.108 0.532 0.352
#> GSM381210 1 0.0188 0.838 0.996 0.000 0.004 0.000
#> GSM381215 1 0.5677 0.688 0.628 0.000 0.332 0.040
#> GSM381219 2 0.0188 0.890 0.000 0.996 0.000 0.004
#> GSM381221 2 0.1118 0.891 0.000 0.964 0.036 0.000
#> GSM381223 2 0.4661 0.845 0.000 0.728 0.256 0.016
#> GSM381229 3 0.5900 0.649 0.076 0.000 0.664 0.260
#> GSM381230 1 0.0188 0.838 0.996 0.000 0.004 0.000
#> GSM381233 1 0.1474 0.832 0.948 0.000 0.052 0.000
#> GSM381234 1 0.0000 0.839 1.000 0.000 0.000 0.000
#> GSM381238 4 0.2019 0.992 0.032 0.024 0.004 0.940
#> GSM381239 4 0.1833 0.999 0.032 0.024 0.000 0.944
#> GSM381242 1 0.4535 0.759 0.704 0.000 0.292 0.004
#> GSM381247 2 0.4304 0.841 0.000 0.716 0.284 0.000
#> GSM381248 1 0.0000 0.839 1.000 0.000 0.000 0.000
#> GSM381249 1 0.0921 0.835 0.972 0.000 0.028 0.000
#> GSM381253 1 0.4502 0.778 0.748 0.000 0.236 0.016
#> GSM381255 2 0.0188 0.890 0.000 0.996 0.000 0.004
#> GSM381258 1 0.5677 0.688 0.628 0.000 0.332 0.040
#> GSM381262 1 0.6041 0.663 0.608 0.000 0.332 0.060
#> GSM381266 3 0.7137 0.475 0.188 0.000 0.556 0.256
#> GSM381267 3 0.6831 0.553 0.000 0.112 0.536 0.352
#> GSM381269 1 0.3528 0.808 0.808 0.000 0.192 0.000
#> GSM381273 3 0.6315 0.770 0.064 0.000 0.540 0.396
#> GSM381274 2 0.4661 0.845 0.000 0.728 0.256 0.016
#> GSM381276 1 0.5050 0.751 0.704 0.000 0.268 0.028
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM381194 3 0.4265 0.871 0.268 0.000 0.712 0.008 0.012
#> GSM381199 2 0.6184 0.761 0.000 0.656 0.180 0.084 0.080
#> GSM381205 2 0.0000 0.814 0.000 1.000 0.000 0.000 0.000
#> GSM381211 2 0.0000 0.814 0.000 1.000 0.000 0.000 0.000
#> GSM381220 2 0.1978 0.804 0.000 0.928 0.024 0.004 0.044
#> GSM381222 1 0.2570 0.806 0.880 0.000 0.108 0.008 0.004
#> GSM381224 1 0.1153 0.918 0.964 0.000 0.024 0.008 0.004
#> GSM381232 4 0.2929 0.998 0.004 0.008 0.004 0.860 0.124
#> GSM381240 1 0.0000 0.952 1.000 0.000 0.000 0.000 0.000
#> GSM381250 3 0.4114 0.838 0.376 0.000 0.624 0.000 0.000
#> GSM381252 2 0.0000 0.814 0.000 1.000 0.000 0.000 0.000
#> GSM381254 1 0.0000 0.952 1.000 0.000 0.000 0.000 0.000
#> GSM381256 2 0.0798 0.814 0.000 0.976 0.000 0.008 0.016
#> GSM381257 1 0.0000 0.952 1.000 0.000 0.000 0.000 0.000
#> GSM381259 1 0.0000 0.952 1.000 0.000 0.000 0.000 0.000
#> GSM381260 3 0.4264 0.841 0.376 0.000 0.620 0.000 0.004
#> GSM381261 2 0.7019 0.729 0.000 0.556 0.244 0.112 0.088
#> GSM381263 3 0.4030 0.857 0.352 0.000 0.648 0.000 0.000
#> GSM381265 1 0.0000 0.952 1.000 0.000 0.000 0.000 0.000
#> GSM381268 3 0.4170 0.873 0.272 0.000 0.712 0.004 0.012
#> GSM381270 2 0.7127 0.727 0.000 0.552 0.232 0.100 0.116
#> GSM381271 4 0.2929 0.998 0.004 0.008 0.004 0.860 0.124
#> GSM381275 2 0.6951 0.732 0.000 0.564 0.240 0.112 0.084
#> GSM381279 2 0.7064 0.728 0.000 0.552 0.244 0.092 0.112
#> GSM381195 1 0.0000 0.952 1.000 0.000 0.000 0.000 0.000
#> GSM381196 3 0.4126 0.834 0.380 0.000 0.620 0.000 0.000
#> GSM381198 2 0.0000 0.814 0.000 1.000 0.000 0.000 0.000
#> GSM381200 2 0.6567 0.752 0.000 0.612 0.212 0.092 0.084
#> GSM381201 5 0.2968 0.945 0.012 0.000 0.112 0.012 0.864
#> GSM381203 3 0.4307 0.624 0.500 0.000 0.500 0.000 0.000
#> GSM381204 1 0.0000 0.952 1.000 0.000 0.000 0.000 0.000
#> GSM381209 1 0.0000 0.952 1.000 0.000 0.000 0.000 0.000
#> GSM381212 1 0.0000 0.952 1.000 0.000 0.000 0.000 0.000
#> GSM381213 2 0.2910 0.801 0.000 0.888 0.052 0.024 0.036
#> GSM381214 2 0.0000 0.814 0.000 1.000 0.000 0.000 0.000
#> GSM381216 3 0.4353 0.862 0.328 0.000 0.660 0.008 0.004
#> GSM381225 3 0.3730 0.876 0.288 0.000 0.712 0.000 0.000
#> GSM381231 4 0.2929 0.998 0.004 0.008 0.004 0.860 0.124
#> GSM381235 3 0.4353 0.862 0.328 0.000 0.660 0.008 0.004
#> GSM381237 1 0.0000 0.952 1.000 0.000 0.000 0.000 0.000
#> GSM381241 2 0.0000 0.814 0.000 1.000 0.000 0.000 0.000
#> GSM381243 2 0.7127 0.727 0.000 0.552 0.232 0.100 0.116
#> GSM381245 1 0.0000 0.952 1.000 0.000 0.000 0.000 0.000
#> GSM381246 2 0.0566 0.814 0.000 0.984 0.004 0.012 0.000
#> GSM381251 5 0.2907 0.943 0.012 0.000 0.116 0.008 0.864
#> GSM381264 1 0.0000 0.952 1.000 0.000 0.000 0.000 0.000
#> GSM381206 2 0.0000 0.814 0.000 1.000 0.000 0.000 0.000
#> GSM381217 3 0.4370 0.858 0.332 0.000 0.656 0.008 0.004
#> GSM381218 2 0.0000 0.814 0.000 1.000 0.000 0.000 0.000
#> GSM381226 2 0.4552 0.790 0.000 0.780 0.132 0.056 0.032
#> GSM381227 2 0.6896 0.736 0.000 0.568 0.244 0.092 0.096
#> GSM381228 4 0.2929 0.998 0.004 0.008 0.004 0.860 0.124
#> GSM381236 4 0.2929 0.998 0.004 0.008 0.004 0.860 0.124
#> GSM381244 5 0.2967 0.943 0.016 0.000 0.104 0.012 0.868
#> GSM381272 4 0.2929 0.998 0.004 0.008 0.004 0.860 0.124
#> GSM381277 1 0.0000 0.952 1.000 0.000 0.000 0.000 0.000
#> GSM381278 3 0.4509 0.843 0.232 0.000 0.728 0.024 0.016
#> GSM381197 5 0.2967 0.943 0.016 0.000 0.104 0.012 0.868
#> GSM381202 1 0.4211 -0.185 0.636 0.000 0.360 0.000 0.004
#> GSM381207 1 0.0000 0.952 1.000 0.000 0.000 0.000 0.000
#> GSM381208 5 0.2679 0.872 0.000 0.048 0.056 0.004 0.892
#> GSM381210 1 0.0000 0.952 1.000 0.000 0.000 0.000 0.000
#> GSM381215 3 0.4170 0.873 0.272 0.000 0.712 0.004 0.012
#> GSM381219 2 0.0000 0.814 0.000 1.000 0.000 0.000 0.000
#> GSM381221 2 0.1419 0.814 0.000 0.956 0.012 0.016 0.016
#> GSM381223 2 0.6951 0.732 0.000 0.564 0.240 0.112 0.084
#> GSM381229 3 0.4609 0.367 0.024 0.000 0.688 0.008 0.280
#> GSM381230 1 0.0000 0.952 1.000 0.000 0.000 0.000 0.000
#> GSM381233 1 0.2672 0.793 0.872 0.000 0.116 0.008 0.004
#> GSM381234 1 0.0000 0.952 1.000 0.000 0.000 0.000 0.000
#> GSM381238 4 0.2831 0.989 0.004 0.008 0.004 0.868 0.116
#> GSM381239 4 0.2929 0.998 0.004 0.008 0.004 0.860 0.124
#> GSM381242 3 0.4220 0.873 0.300 0.000 0.688 0.008 0.004
#> GSM381247 2 0.7127 0.727 0.000 0.552 0.232 0.100 0.116
#> GSM381248 1 0.0162 0.947 0.996 0.000 0.000 0.004 0.000
#> GSM381249 1 0.1569 0.896 0.944 0.000 0.044 0.008 0.004
#> GSM381253 3 0.4192 0.811 0.404 0.000 0.596 0.000 0.000
#> GSM381255 2 0.0000 0.814 0.000 1.000 0.000 0.000 0.000
#> GSM381258 3 0.4419 0.873 0.276 0.000 0.700 0.012 0.012
#> GSM381262 3 0.4265 0.871 0.268 0.000 0.712 0.008 0.012
#> GSM381266 3 0.5126 0.565 0.084 0.000 0.708 0.012 0.196
#> GSM381267 5 0.2679 0.872 0.000 0.048 0.056 0.004 0.892
#> GSM381269 3 0.4464 0.832 0.356 0.000 0.632 0.008 0.004
#> GSM381273 5 0.2968 0.945 0.012 0.000 0.112 0.012 0.864
#> GSM381274 2 0.6951 0.732 0.000 0.564 0.240 0.112 0.084
#> GSM381276 3 0.4074 0.851 0.364 0.000 0.636 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM381194 3 0.3141 0.814 0.124 0.000 0.832 0.004 0.000 0.040
#> GSM381199 2 0.5841 -0.643 0.000 0.488 0.064 0.000 0.052 0.396
#> GSM381205 2 0.0146 0.867 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM381211 2 0.0260 0.867 0.000 0.992 0.008 0.000 0.000 0.000
#> GSM381220 2 0.3897 0.640 0.000 0.808 0.056 0.000 0.060 0.076
#> GSM381222 1 0.5362 0.513 0.636 0.000 0.156 0.000 0.016 0.192
#> GSM381224 1 0.3800 0.705 0.764 0.000 0.036 0.000 0.008 0.192
#> GSM381232 4 0.0291 0.996 0.000 0.000 0.004 0.992 0.000 0.004
#> GSM381240 1 0.0260 0.903 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM381250 3 0.3215 0.792 0.240 0.000 0.756 0.000 0.000 0.004
#> GSM381252 2 0.0146 0.867 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM381254 1 0.0146 0.904 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM381256 2 0.0862 0.860 0.000 0.972 0.016 0.000 0.008 0.004
#> GSM381257 1 0.1296 0.872 0.952 0.000 0.032 0.000 0.004 0.012
#> GSM381259 1 0.0000 0.904 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381260 3 0.5102 0.750 0.264 0.000 0.632 0.000 0.012 0.092
#> GSM381261 6 0.4406 0.837 0.000 0.316 0.028 0.004 0.004 0.648
#> GSM381263 3 0.2969 0.803 0.224 0.000 0.776 0.000 0.000 0.000
#> GSM381265 1 0.0000 0.904 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381268 3 0.3083 0.816 0.132 0.000 0.828 0.000 0.000 0.040
#> GSM381270 6 0.5799 0.853 0.000 0.344 0.060 0.000 0.060 0.536
#> GSM381271 4 0.0146 0.997 0.000 0.000 0.004 0.996 0.000 0.000
#> GSM381275 6 0.4521 0.833 0.000 0.348 0.028 0.004 0.004 0.616
#> GSM381279 6 0.5488 0.859 0.000 0.344 0.048 0.000 0.048 0.560
#> GSM381195 1 0.0000 0.904 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381196 3 0.3151 0.782 0.252 0.000 0.748 0.000 0.000 0.000
#> GSM381198 2 0.0146 0.867 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM381200 6 0.4772 0.731 0.000 0.452 0.004 0.000 0.040 0.504
#> GSM381201 5 0.2483 0.955 0.004 0.000 0.060 0.024 0.896 0.016
#> GSM381203 3 0.3862 0.592 0.388 0.000 0.608 0.000 0.000 0.004
#> GSM381204 1 0.0000 0.904 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381209 1 0.0000 0.904 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381212 1 0.0000 0.904 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381213 2 0.2944 0.650 0.000 0.832 0.012 0.000 0.008 0.148
#> GSM381214 2 0.0260 0.867 0.000 0.992 0.008 0.000 0.000 0.000
#> GSM381216 3 0.5291 0.768 0.144 0.000 0.644 0.000 0.016 0.196
#> GSM381225 3 0.3235 0.816 0.128 0.000 0.820 0.000 0.000 0.052
#> GSM381231 4 0.0291 0.996 0.000 0.000 0.004 0.992 0.000 0.004
#> GSM381235 3 0.5264 0.770 0.144 0.000 0.648 0.000 0.016 0.192
#> GSM381237 1 0.0000 0.904 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381241 2 0.0146 0.867 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM381243 6 0.5799 0.853 0.000 0.344 0.060 0.000 0.060 0.536
#> GSM381245 1 0.0260 0.903 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM381246 2 0.1615 0.809 0.000 0.928 0.004 0.000 0.004 0.064
#> GSM381251 5 0.2482 0.946 0.004 0.000 0.072 0.012 0.892 0.020
#> GSM381264 1 0.0000 0.904 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381206 2 0.0146 0.867 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM381217 3 0.5264 0.770 0.144 0.000 0.648 0.000 0.016 0.192
#> GSM381218 2 0.0260 0.867 0.000 0.992 0.008 0.000 0.000 0.000
#> GSM381226 2 0.3693 0.242 0.000 0.708 0.008 0.000 0.004 0.280
#> GSM381227 6 0.5374 0.861 0.000 0.344 0.040 0.000 0.048 0.568
#> GSM381228 4 0.0291 0.998 0.000 0.000 0.004 0.992 0.004 0.000
#> GSM381236 4 0.0291 0.998 0.000 0.000 0.004 0.992 0.004 0.000
#> GSM381244 5 0.2063 0.955 0.008 0.000 0.060 0.020 0.912 0.000
#> GSM381272 4 0.0146 0.997 0.000 0.000 0.004 0.996 0.000 0.000
#> GSM381277 1 0.0547 0.897 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM381278 3 0.2773 0.764 0.064 0.000 0.868 0.004 0.000 0.064
#> GSM381197 5 0.2063 0.955 0.008 0.000 0.060 0.020 0.912 0.000
#> GSM381202 1 0.5880 -0.105 0.512 0.000 0.328 0.000 0.016 0.144
#> GSM381207 1 0.0260 0.903 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM381208 5 0.2489 0.908 0.000 0.016 0.028 0.020 0.904 0.032
#> GSM381210 1 0.0146 0.904 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM381215 3 0.2278 0.820 0.128 0.000 0.868 0.000 0.000 0.004
#> GSM381219 2 0.0000 0.867 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381221 2 0.1410 0.824 0.000 0.944 0.004 0.000 0.008 0.044
#> GSM381223 6 0.4521 0.833 0.000 0.348 0.028 0.004 0.004 0.616
#> GSM381229 3 0.4084 0.595 0.004 0.000 0.764 0.008 0.164 0.060
#> GSM381230 1 0.0000 0.904 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381233 1 0.5507 0.474 0.616 0.000 0.172 0.000 0.016 0.196
#> GSM381234 1 0.0146 0.904 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM381238 4 0.0291 0.998 0.000 0.000 0.004 0.992 0.004 0.000
#> GSM381239 4 0.0291 0.998 0.000 0.000 0.004 0.992 0.004 0.000
#> GSM381242 3 0.5368 0.767 0.144 0.000 0.632 0.000 0.016 0.208
#> GSM381247 6 0.5799 0.853 0.000 0.344 0.060 0.000 0.060 0.536
#> GSM381248 1 0.0363 0.900 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM381249 1 0.4615 0.634 0.712 0.000 0.080 0.000 0.016 0.192
#> GSM381253 3 0.3290 0.785 0.252 0.000 0.744 0.000 0.000 0.004
#> GSM381255 2 0.0458 0.865 0.000 0.984 0.016 0.000 0.000 0.000
#> GSM381258 3 0.5124 0.774 0.128 0.000 0.664 0.000 0.016 0.192
#> GSM381262 3 0.3141 0.814 0.124 0.000 0.832 0.004 0.000 0.040
#> GSM381266 3 0.3381 0.671 0.008 0.000 0.836 0.008 0.096 0.052
#> GSM381267 5 0.2489 0.908 0.000 0.016 0.028 0.020 0.904 0.032
#> GSM381269 3 0.5507 0.741 0.172 0.000 0.616 0.000 0.016 0.196
#> GSM381273 5 0.2571 0.954 0.004 0.000 0.060 0.024 0.892 0.020
#> GSM381274 6 0.4521 0.833 0.000 0.348 0.028 0.004 0.004 0.616
#> GSM381276 3 0.4142 0.792 0.232 0.000 0.712 0.000 0.000 0.056
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 other(p) k
#> CV:kmeans 78 0.572 2
#> CV:kmeans 86 0.266 3
#> CV:kmeans 85 0.218 4
#> CV:kmeans 84 0.484 5
#> CV:kmeans 82 0.624 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 86 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.829 0.903 0.958 0.4768 0.504 0.504
#> 3 3 0.859 0.930 0.967 0.3930 0.763 0.560
#> 4 4 0.801 0.836 0.923 0.1094 0.843 0.587
#> 5 5 0.862 0.840 0.909 0.0468 0.957 0.842
#> 6 6 0.813 0.706 0.819 0.0495 0.945 0.772
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
#> GSM381194 1 0.000 1.000 1.000 0.000
#> GSM381199 2 0.000 0.895 0.000 1.000
#> GSM381205 2 0.000 0.895 0.000 1.000
#> GSM381211 2 0.000 0.895 0.000 1.000
#> GSM381220 2 0.000 0.895 0.000 1.000
#> GSM381222 1 0.000 1.000 1.000 0.000
#> GSM381224 1 0.000 1.000 1.000 0.000
#> GSM381232 2 0.993 0.336 0.452 0.548
#> GSM381240 1 0.000 1.000 1.000 0.000
#> GSM381250 1 0.000 1.000 1.000 0.000
#> GSM381252 2 0.000 0.895 0.000 1.000
#> GSM381254 1 0.000 1.000 1.000 0.000
#> GSM381256 2 0.000 0.895 0.000 1.000
#> GSM381257 1 0.000 1.000 1.000 0.000
#> GSM381259 1 0.000 1.000 1.000 0.000
#> GSM381260 1 0.000 1.000 1.000 0.000
#> GSM381261 2 0.000 0.895 0.000 1.000
#> GSM381263 1 0.000 1.000 1.000 0.000
#> GSM381265 1 0.000 1.000 1.000 0.000
#> GSM381268 1 0.000 1.000 1.000 0.000
#> GSM381270 2 0.000 0.895 0.000 1.000
#> GSM381271 2 0.993 0.336 0.452 0.548
#> GSM381275 2 0.000 0.895 0.000 1.000
#> GSM381279 2 0.000 0.895 0.000 1.000
#> GSM381195 1 0.000 1.000 1.000 0.000
#> GSM381196 1 0.000 1.000 1.000 0.000
#> GSM381198 2 0.000 0.895 0.000 1.000
#> GSM381200 2 0.000 0.895 0.000 1.000
#> GSM381201 1 0.000 1.000 1.000 0.000
#> GSM381203 1 0.000 1.000 1.000 0.000
#> GSM381204 1 0.000 1.000 1.000 0.000
#> GSM381209 1 0.000 1.000 1.000 0.000
#> GSM381212 1 0.000 1.000 1.000 0.000
#> GSM381213 2 0.000 0.895 0.000 1.000
#> GSM381214 2 0.000 0.895 0.000 1.000
#> GSM381216 1 0.000 1.000 1.000 0.000
#> GSM381225 1 0.000 1.000 1.000 0.000
#> GSM381231 2 0.993 0.336 0.452 0.548
#> GSM381235 1 0.000 1.000 1.000 0.000
#> GSM381237 1 0.000 1.000 1.000 0.000
#> GSM381241 2 0.000 0.895 0.000 1.000
#> GSM381243 2 0.000 0.895 0.000 1.000
#> GSM381245 1 0.000 1.000 1.000 0.000
#> GSM381246 2 0.000 0.895 0.000 1.000
#> GSM381251 1 0.000 1.000 1.000 0.000
#> GSM381264 1 0.000 1.000 1.000 0.000
#> GSM381206 2 0.000 0.895 0.000 1.000
#> GSM381217 1 0.000 1.000 1.000 0.000
#> GSM381218 2 0.000 0.895 0.000 1.000
#> GSM381226 2 0.000 0.895 0.000 1.000
#> GSM381227 2 0.000 0.895 0.000 1.000
#> GSM381228 2 0.993 0.336 0.452 0.548
#> GSM381236 2 0.993 0.336 0.452 0.548
#> GSM381244 1 0.000 1.000 1.000 0.000
#> GSM381272 2 0.993 0.336 0.452 0.548
#> GSM381277 1 0.000 1.000 1.000 0.000
#> GSM381278 1 0.000 1.000 1.000 0.000
#> GSM381197 1 0.000 1.000 1.000 0.000
#> GSM381202 1 0.000 1.000 1.000 0.000
#> GSM381207 1 0.000 1.000 1.000 0.000
#> GSM381208 2 0.000 0.895 0.000 1.000
#> GSM381210 1 0.000 1.000 1.000 0.000
#> GSM381215 1 0.000 1.000 1.000 0.000
#> GSM381219 2 0.000 0.895 0.000 1.000
#> GSM381221 2 0.000 0.895 0.000 1.000
#> GSM381223 2 0.000 0.895 0.000 1.000
#> GSM381229 1 0.000 1.000 1.000 0.000
#> GSM381230 1 0.000 1.000 1.000 0.000
#> GSM381233 1 0.000 1.000 1.000 0.000
#> GSM381234 1 0.000 1.000 1.000 0.000
#> GSM381238 2 0.993 0.336 0.452 0.548
#> GSM381239 2 0.993 0.336 0.452 0.548
#> GSM381242 1 0.000 1.000 1.000 0.000
#> GSM381247 2 0.000 0.895 0.000 1.000
#> GSM381248 1 0.000 1.000 1.000 0.000
#> GSM381249 1 0.000 1.000 1.000 0.000
#> GSM381253 1 0.000 1.000 1.000 0.000
#> GSM381255 2 0.000 0.895 0.000 1.000
#> GSM381258 1 0.000 1.000 1.000 0.000
#> GSM381262 1 0.000 1.000 1.000 0.000
#> GSM381266 1 0.000 1.000 1.000 0.000
#> GSM381267 2 0.000 0.895 0.000 1.000
#> GSM381269 1 0.000 1.000 1.000 0.000
#> GSM381273 1 0.000 1.000 1.000 0.000
#> GSM381274 2 0.000 0.895 0.000 1.000
#> GSM381276 1 0.000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM381194 3 0.000 0.951 0.000 0.000 1.000
#> GSM381199 2 0.000 1.000 0.000 1.000 0.000
#> GSM381205 2 0.000 1.000 0.000 1.000 0.000
#> GSM381211 2 0.000 1.000 0.000 1.000 0.000
#> GSM381220 2 0.000 1.000 0.000 1.000 0.000
#> GSM381222 1 0.000 0.943 1.000 0.000 0.000
#> GSM381224 1 0.000 0.943 1.000 0.000 0.000
#> GSM381232 3 0.000 0.951 0.000 0.000 1.000
#> GSM381240 1 0.000 0.943 1.000 0.000 0.000
#> GSM381250 1 0.536 0.678 0.724 0.000 0.276
#> GSM381252 2 0.000 1.000 0.000 1.000 0.000
#> GSM381254 1 0.000 0.943 1.000 0.000 0.000
#> GSM381256 2 0.000 1.000 0.000 1.000 0.000
#> GSM381257 1 0.000 0.943 1.000 0.000 0.000
#> GSM381259 1 0.000 0.943 1.000 0.000 0.000
#> GSM381260 1 0.450 0.774 0.804 0.000 0.196
#> GSM381261 2 0.000 1.000 0.000 1.000 0.000
#> GSM381263 1 0.536 0.678 0.724 0.000 0.276
#> GSM381265 1 0.000 0.943 1.000 0.000 0.000
#> GSM381268 3 0.429 0.755 0.180 0.000 0.820
#> GSM381270 2 0.000 1.000 0.000 1.000 0.000
#> GSM381271 3 0.000 0.951 0.000 0.000 1.000
#> GSM381275 2 0.000 1.000 0.000 1.000 0.000
#> GSM381279 2 0.000 1.000 0.000 1.000 0.000
#> GSM381195 1 0.000 0.943 1.000 0.000 0.000
#> GSM381196 1 0.536 0.678 0.724 0.000 0.276
#> GSM381198 2 0.000 1.000 0.000 1.000 0.000
#> GSM381200 2 0.000 1.000 0.000 1.000 0.000
#> GSM381201 3 0.000 0.951 0.000 0.000 1.000
#> GSM381203 1 0.000 0.943 1.000 0.000 0.000
#> GSM381204 1 0.000 0.943 1.000 0.000 0.000
#> GSM381209 1 0.000 0.943 1.000 0.000 0.000
#> GSM381212 1 0.000 0.943 1.000 0.000 0.000
#> GSM381213 2 0.000 1.000 0.000 1.000 0.000
#> GSM381214 2 0.000 1.000 0.000 1.000 0.000
#> GSM381216 1 0.000 0.943 1.000 0.000 0.000
#> GSM381225 1 0.536 0.678 0.724 0.000 0.276
#> GSM381231 3 0.000 0.951 0.000 0.000 1.000
#> GSM381235 1 0.000 0.943 1.000 0.000 0.000
#> GSM381237 1 0.000 0.943 1.000 0.000 0.000
#> GSM381241 2 0.000 1.000 0.000 1.000 0.000
#> GSM381243 2 0.000 1.000 0.000 1.000 0.000
#> GSM381245 1 0.000 0.943 1.000 0.000 0.000
#> GSM381246 2 0.000 1.000 0.000 1.000 0.000
#> GSM381251 3 0.000 0.951 0.000 0.000 1.000
#> GSM381264 1 0.000 0.943 1.000 0.000 0.000
#> GSM381206 2 0.000 1.000 0.000 1.000 0.000
#> GSM381217 1 0.000 0.943 1.000 0.000 0.000
#> GSM381218 2 0.000 1.000 0.000 1.000 0.000
#> GSM381226 2 0.000 1.000 0.000 1.000 0.000
#> GSM381227 2 0.000 1.000 0.000 1.000 0.000
#> GSM381228 3 0.000 0.951 0.000 0.000 1.000
#> GSM381236 3 0.000 0.951 0.000 0.000 1.000
#> GSM381244 3 0.000 0.951 0.000 0.000 1.000
#> GSM381272 3 0.000 0.951 0.000 0.000 1.000
#> GSM381277 1 0.000 0.943 1.000 0.000 0.000
#> GSM381278 3 0.000 0.951 0.000 0.000 1.000
#> GSM381197 3 0.000 0.951 0.000 0.000 1.000
#> GSM381202 1 0.000 0.943 1.000 0.000 0.000
#> GSM381207 1 0.000 0.943 1.000 0.000 0.000
#> GSM381208 3 0.536 0.605 0.000 0.276 0.724
#> GSM381210 1 0.000 0.943 1.000 0.000 0.000
#> GSM381215 3 0.000 0.951 0.000 0.000 1.000
#> GSM381219 2 0.000 1.000 0.000 1.000 0.000
#> GSM381221 2 0.000 1.000 0.000 1.000 0.000
#> GSM381223 2 0.000 1.000 0.000 1.000 0.000
#> GSM381229 3 0.000 0.951 0.000 0.000 1.000
#> GSM381230 1 0.000 0.943 1.000 0.000 0.000
#> GSM381233 1 0.000 0.943 1.000 0.000 0.000
#> GSM381234 1 0.000 0.943 1.000 0.000 0.000
#> GSM381238 3 0.000 0.951 0.000 0.000 1.000
#> GSM381239 3 0.000 0.951 0.000 0.000 1.000
#> GSM381242 1 0.103 0.927 0.976 0.000 0.024
#> GSM381247 2 0.000 1.000 0.000 1.000 0.000
#> GSM381248 1 0.000 0.943 1.000 0.000 0.000
#> GSM381249 1 0.000 0.943 1.000 0.000 0.000
#> GSM381253 1 0.522 0.699 0.740 0.000 0.260
#> GSM381255 2 0.000 1.000 0.000 1.000 0.000
#> GSM381258 3 0.355 0.823 0.132 0.000 0.868
#> GSM381262 3 0.319 0.847 0.112 0.000 0.888
#> GSM381266 3 0.000 0.951 0.000 0.000 1.000
#> GSM381267 3 0.536 0.605 0.000 0.276 0.724
#> GSM381269 1 0.000 0.943 1.000 0.000 0.000
#> GSM381273 3 0.000 0.951 0.000 0.000 1.000
#> GSM381274 2 0.000 1.000 0.000 1.000 0.000
#> GSM381276 1 0.536 0.678 0.724 0.000 0.276
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM381194 3 0.0336 0.7377 0.000 0.000 0.992 0.008
#> GSM381199 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM381205 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM381211 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM381220 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM381222 1 0.2647 0.8427 0.880 0.000 0.120 0.000
#> GSM381224 1 0.1118 0.9206 0.964 0.000 0.036 0.000
#> GSM381232 4 0.0000 0.9556 0.000 0.000 0.000 1.000
#> GSM381240 1 0.0000 0.9464 1.000 0.000 0.000 0.000
#> GSM381250 3 0.3356 0.7261 0.176 0.000 0.824 0.000
#> GSM381252 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM381254 1 0.0000 0.9464 1.000 0.000 0.000 0.000
#> GSM381256 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM381257 1 0.0000 0.9464 1.000 0.000 0.000 0.000
#> GSM381259 1 0.0000 0.9464 1.000 0.000 0.000 0.000
#> GSM381260 3 0.3907 0.6958 0.232 0.000 0.768 0.000
#> GSM381261 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM381263 3 0.3219 0.7321 0.164 0.000 0.836 0.000
#> GSM381265 1 0.0000 0.9464 1.000 0.000 0.000 0.000
#> GSM381268 3 0.0188 0.7394 0.004 0.000 0.996 0.000
#> GSM381270 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM381271 4 0.0000 0.9556 0.000 0.000 0.000 1.000
#> GSM381275 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM381279 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM381195 1 0.0000 0.9464 1.000 0.000 0.000 0.000
#> GSM381196 3 0.2814 0.7296 0.132 0.000 0.868 0.000
#> GSM381198 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM381200 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM381201 3 0.4977 0.2015 0.000 0.000 0.540 0.460
#> GSM381203 1 0.4877 0.1874 0.592 0.000 0.408 0.000
#> GSM381204 1 0.0000 0.9464 1.000 0.000 0.000 0.000
#> GSM381209 1 0.0000 0.9464 1.000 0.000 0.000 0.000
#> GSM381212 1 0.0000 0.9464 1.000 0.000 0.000 0.000
#> GSM381213 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM381214 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM381216 3 0.3266 0.7064 0.168 0.000 0.832 0.000
#> GSM381225 3 0.1302 0.7444 0.044 0.000 0.956 0.000
#> GSM381231 4 0.0000 0.9556 0.000 0.000 0.000 1.000
#> GSM381235 3 0.2973 0.7209 0.144 0.000 0.856 0.000
#> GSM381237 1 0.0000 0.9464 1.000 0.000 0.000 0.000
#> GSM381241 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM381243 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM381245 1 0.0000 0.9464 1.000 0.000 0.000 0.000
#> GSM381246 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM381251 3 0.4941 0.2570 0.000 0.000 0.564 0.436
#> GSM381264 1 0.0000 0.9464 1.000 0.000 0.000 0.000
#> GSM381206 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM381217 3 0.4382 0.5154 0.296 0.000 0.704 0.000
#> GSM381218 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM381226 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM381227 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM381228 4 0.0000 0.9556 0.000 0.000 0.000 1.000
#> GSM381236 4 0.0000 0.9556 0.000 0.000 0.000 1.000
#> GSM381244 3 0.4977 0.2015 0.000 0.000 0.540 0.460
#> GSM381272 4 0.0000 0.9556 0.000 0.000 0.000 1.000
#> GSM381277 1 0.0000 0.9464 1.000 0.000 0.000 0.000
#> GSM381278 3 0.0707 0.7366 0.000 0.000 0.980 0.020
#> GSM381197 3 0.4977 0.2015 0.000 0.000 0.540 0.460
#> GSM381202 1 0.3726 0.6791 0.788 0.000 0.212 0.000
#> GSM381207 1 0.0000 0.9464 1.000 0.000 0.000 0.000
#> GSM381208 4 0.4487 0.8084 0.000 0.100 0.092 0.808
#> GSM381210 1 0.0000 0.9464 1.000 0.000 0.000 0.000
#> GSM381215 3 0.0000 0.7375 0.000 0.000 1.000 0.000
#> GSM381219 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM381221 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM381223 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM381229 3 0.2469 0.6947 0.000 0.000 0.892 0.108
#> GSM381230 1 0.0000 0.9464 1.000 0.000 0.000 0.000
#> GSM381233 1 0.3123 0.8024 0.844 0.000 0.156 0.000
#> GSM381234 1 0.0000 0.9464 1.000 0.000 0.000 0.000
#> GSM381238 4 0.0000 0.9556 0.000 0.000 0.000 1.000
#> GSM381239 4 0.0000 0.9556 0.000 0.000 0.000 1.000
#> GSM381242 3 0.2530 0.7343 0.112 0.000 0.888 0.000
#> GSM381247 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM381248 1 0.0188 0.9430 0.996 0.000 0.004 0.000
#> GSM381249 1 0.2408 0.8588 0.896 0.000 0.104 0.000
#> GSM381253 3 0.3942 0.6899 0.236 0.000 0.764 0.000
#> GSM381255 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM381258 3 0.0592 0.7424 0.016 0.000 0.984 0.000
#> GSM381262 3 0.0188 0.7394 0.004 0.000 0.996 0.000
#> GSM381266 3 0.4500 0.4689 0.000 0.000 0.684 0.316
#> GSM381267 4 0.4547 0.8039 0.000 0.104 0.092 0.804
#> GSM381269 3 0.4998 -0.0467 0.488 0.000 0.512 0.000
#> GSM381273 3 0.4977 0.2015 0.000 0.000 0.540 0.460
#> GSM381274 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM381276 3 0.3942 0.6876 0.236 0.000 0.764 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM381194 3 0.3010 0.753 0.000 0.000 0.824 0.004 0.172
#> GSM381199 2 0.1124 0.977 0.000 0.960 0.004 0.000 0.036
#> GSM381205 2 0.0162 0.981 0.000 0.996 0.000 0.000 0.004
#> GSM381211 2 0.0162 0.981 0.000 0.996 0.000 0.000 0.004
#> GSM381220 2 0.0609 0.979 0.000 0.980 0.000 0.000 0.020
#> GSM381222 1 0.3999 0.548 0.656 0.000 0.344 0.000 0.000
#> GSM381224 1 0.2690 0.772 0.844 0.000 0.156 0.000 0.000
#> GSM381232 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM381240 1 0.0162 0.884 0.996 0.000 0.000 0.000 0.004
#> GSM381250 3 0.5756 0.670 0.204 0.000 0.620 0.000 0.176
#> GSM381252 2 0.0162 0.981 0.000 0.996 0.000 0.000 0.004
#> GSM381254 1 0.0162 0.884 0.996 0.000 0.000 0.000 0.004
#> GSM381256 2 0.0162 0.982 0.000 0.996 0.004 0.000 0.000
#> GSM381257 1 0.0865 0.873 0.972 0.000 0.024 0.000 0.004
#> GSM381259 1 0.0000 0.885 1.000 0.000 0.000 0.000 0.000
#> GSM381260 3 0.4679 0.687 0.216 0.000 0.716 0.000 0.068
#> GSM381261 2 0.1124 0.976 0.000 0.960 0.004 0.000 0.036
#> GSM381263 3 0.5339 0.707 0.176 0.000 0.672 0.000 0.152
#> GSM381265 1 0.0000 0.885 1.000 0.000 0.000 0.000 0.000
#> GSM381268 3 0.3816 0.633 0.000 0.000 0.696 0.000 0.304
#> GSM381270 2 0.1357 0.972 0.000 0.948 0.004 0.000 0.048
#> GSM381271 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM381275 2 0.1124 0.976 0.000 0.960 0.004 0.000 0.036
#> GSM381279 2 0.1357 0.972 0.000 0.948 0.004 0.000 0.048
#> GSM381195 1 0.0000 0.885 1.000 0.000 0.000 0.000 0.000
#> GSM381196 3 0.6059 0.621 0.184 0.000 0.572 0.000 0.244
#> GSM381198 2 0.0162 0.981 0.000 0.996 0.000 0.000 0.004
#> GSM381200 2 0.0865 0.979 0.000 0.972 0.004 0.000 0.024
#> GSM381201 5 0.1893 0.869 0.000 0.000 0.048 0.024 0.928
#> GSM381203 1 0.5680 -0.214 0.492 0.000 0.428 0.000 0.080
#> GSM381204 1 0.0000 0.885 1.000 0.000 0.000 0.000 0.000
#> GSM381209 1 0.0000 0.885 1.000 0.000 0.000 0.000 0.000
#> GSM381212 1 0.0000 0.885 1.000 0.000 0.000 0.000 0.000
#> GSM381213 2 0.0794 0.980 0.000 0.972 0.000 0.000 0.028
#> GSM381214 2 0.0162 0.981 0.000 0.996 0.000 0.000 0.004
#> GSM381216 3 0.1043 0.752 0.040 0.000 0.960 0.000 0.000
#> GSM381225 3 0.2763 0.762 0.004 0.000 0.848 0.000 0.148
#> GSM381231 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM381235 3 0.0771 0.755 0.020 0.000 0.976 0.000 0.004
#> GSM381237 1 0.0000 0.885 1.000 0.000 0.000 0.000 0.000
#> GSM381241 2 0.0162 0.981 0.000 0.996 0.000 0.000 0.004
#> GSM381243 2 0.1357 0.972 0.000 0.948 0.004 0.000 0.048
#> GSM381245 1 0.0162 0.884 0.996 0.000 0.000 0.000 0.004
#> GSM381246 2 0.0162 0.981 0.000 0.996 0.000 0.000 0.004
#> GSM381251 5 0.1484 0.860 0.000 0.000 0.048 0.008 0.944
#> GSM381264 1 0.0000 0.885 1.000 0.000 0.000 0.000 0.000
#> GSM381206 2 0.0162 0.981 0.000 0.996 0.000 0.000 0.004
#> GSM381217 3 0.1121 0.750 0.044 0.000 0.956 0.000 0.000
#> GSM381218 2 0.0162 0.981 0.000 0.996 0.000 0.000 0.004
#> GSM381226 2 0.0451 0.981 0.000 0.988 0.004 0.000 0.008
#> GSM381227 2 0.1282 0.974 0.000 0.952 0.004 0.000 0.044
#> GSM381228 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM381236 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM381244 5 0.2570 0.851 0.000 0.000 0.084 0.028 0.888
#> GSM381272 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM381277 1 0.0671 0.877 0.980 0.000 0.016 0.000 0.004
#> GSM381278 3 0.3197 0.754 0.000 0.000 0.836 0.024 0.140
#> GSM381197 5 0.2104 0.867 0.000 0.000 0.060 0.024 0.916
#> GSM381202 1 0.4256 0.169 0.564 0.000 0.436 0.000 0.000
#> GSM381207 1 0.0162 0.884 0.996 0.000 0.000 0.000 0.004
#> GSM381208 5 0.3323 0.764 0.000 0.056 0.000 0.100 0.844
#> GSM381210 1 0.0162 0.884 0.996 0.000 0.004 0.000 0.000
#> GSM381215 3 0.3242 0.726 0.000 0.000 0.784 0.000 0.216
#> GSM381219 2 0.0162 0.981 0.000 0.996 0.000 0.000 0.004
#> GSM381221 2 0.0162 0.982 0.000 0.996 0.004 0.000 0.000
#> GSM381223 2 0.1124 0.976 0.000 0.960 0.004 0.000 0.036
#> GSM381229 5 0.2124 0.821 0.000 0.000 0.096 0.004 0.900
#> GSM381230 1 0.0000 0.885 1.000 0.000 0.000 0.000 0.000
#> GSM381233 1 0.4126 0.487 0.620 0.000 0.380 0.000 0.000
#> GSM381234 1 0.0162 0.884 0.996 0.000 0.000 0.000 0.004
#> GSM381238 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM381239 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM381242 3 0.1357 0.751 0.048 0.000 0.948 0.000 0.004
#> GSM381247 2 0.1357 0.972 0.000 0.948 0.004 0.000 0.048
#> GSM381248 1 0.2230 0.798 0.884 0.000 0.000 0.000 0.116
#> GSM381249 1 0.4015 0.545 0.652 0.000 0.348 0.000 0.000
#> GSM381253 3 0.5754 0.642 0.260 0.000 0.604 0.000 0.136
#> GSM381255 2 0.0162 0.981 0.000 0.996 0.000 0.000 0.004
#> GSM381258 3 0.0451 0.756 0.004 0.000 0.988 0.000 0.008
#> GSM381262 3 0.3266 0.741 0.004 0.000 0.796 0.000 0.200
#> GSM381266 5 0.5000 0.171 0.000 0.000 0.388 0.036 0.576
#> GSM381267 5 0.3269 0.764 0.000 0.056 0.000 0.096 0.848
#> GSM381269 3 0.2561 0.671 0.144 0.000 0.856 0.000 0.000
#> GSM381273 5 0.1893 0.869 0.000 0.000 0.048 0.024 0.928
#> GSM381274 2 0.1124 0.976 0.000 0.960 0.004 0.000 0.036
#> GSM381276 3 0.4901 0.714 0.196 0.000 0.708 0.000 0.096
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM381194 6 0.4844 0.6757 0.000 0.000 0.440 0.000 0.056 0.504
#> GSM381199 2 0.2020 0.7785 0.000 0.896 0.000 0.000 0.008 0.096
#> GSM381205 2 0.3817 0.8084 0.000 0.568 0.000 0.000 0.000 0.432
#> GSM381211 2 0.3817 0.8084 0.000 0.568 0.000 0.000 0.000 0.432
#> GSM381220 2 0.3898 0.8097 0.000 0.652 0.000 0.000 0.012 0.336
#> GSM381222 3 0.4123 0.2269 0.420 0.000 0.568 0.000 0.000 0.012
#> GSM381224 1 0.3936 0.5021 0.688 0.000 0.288 0.000 0.000 0.024
#> GSM381232 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381240 1 0.0260 0.9300 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM381250 6 0.6363 0.7442 0.136 0.000 0.304 0.000 0.056 0.504
#> GSM381252 2 0.3817 0.8084 0.000 0.568 0.000 0.000 0.000 0.432
#> GSM381254 1 0.0260 0.9300 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM381256 2 0.3592 0.8164 0.000 0.656 0.000 0.000 0.000 0.344
#> GSM381257 1 0.1421 0.8920 0.944 0.000 0.028 0.000 0.000 0.028
#> GSM381259 1 0.0000 0.9321 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381260 3 0.6031 0.0255 0.216 0.000 0.568 0.000 0.036 0.180
#> GSM381261 2 0.0146 0.7566 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM381263 6 0.6267 0.7288 0.124 0.000 0.344 0.000 0.048 0.484
#> GSM381265 1 0.0000 0.9321 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381268 6 0.5258 0.7038 0.004 0.000 0.384 0.000 0.088 0.524
#> GSM381270 2 0.0725 0.7475 0.000 0.976 0.000 0.000 0.012 0.012
#> GSM381271 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381275 2 0.0146 0.7596 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM381279 2 0.0725 0.7475 0.000 0.976 0.000 0.000 0.012 0.012
#> GSM381195 1 0.0000 0.9321 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381196 6 0.6430 0.7425 0.132 0.000 0.276 0.000 0.072 0.520
#> GSM381198 2 0.3817 0.8084 0.000 0.568 0.000 0.000 0.000 0.432
#> GSM381200 2 0.2146 0.7873 0.000 0.880 0.000 0.000 0.004 0.116
#> GSM381201 5 0.0363 0.8449 0.000 0.000 0.000 0.000 0.988 0.012
#> GSM381203 6 0.6608 0.3899 0.352 0.000 0.200 0.000 0.040 0.408
#> GSM381204 1 0.0000 0.9321 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381209 1 0.0000 0.9321 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381212 1 0.0000 0.9321 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381213 2 0.3690 0.8026 0.000 0.684 0.000 0.000 0.008 0.308
#> GSM381214 2 0.3817 0.8084 0.000 0.568 0.000 0.000 0.000 0.432
#> GSM381216 3 0.0000 0.4967 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM381225 6 0.4802 0.6912 0.000 0.000 0.404 0.000 0.056 0.540
#> GSM381231 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381235 3 0.0937 0.4764 0.000 0.000 0.960 0.000 0.000 0.040
#> GSM381237 1 0.0000 0.9321 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381241 2 0.3817 0.8084 0.000 0.568 0.000 0.000 0.000 0.432
#> GSM381243 2 0.0725 0.7475 0.000 0.976 0.000 0.000 0.012 0.012
#> GSM381245 1 0.0363 0.9287 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM381246 2 0.3774 0.8118 0.000 0.592 0.000 0.000 0.000 0.408
#> GSM381251 5 0.0632 0.8404 0.000 0.000 0.000 0.000 0.976 0.024
#> GSM381264 1 0.0000 0.9321 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381206 2 0.3817 0.8084 0.000 0.568 0.000 0.000 0.000 0.432
#> GSM381217 3 0.1265 0.4754 0.008 0.000 0.948 0.000 0.000 0.044
#> GSM381218 2 0.3817 0.8084 0.000 0.568 0.000 0.000 0.000 0.432
#> GSM381226 2 0.2941 0.8050 0.000 0.780 0.000 0.000 0.000 0.220
#> GSM381227 2 0.0622 0.7493 0.000 0.980 0.000 0.000 0.008 0.012
#> GSM381228 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381236 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381244 5 0.0891 0.8361 0.000 0.000 0.024 0.000 0.968 0.008
#> GSM381272 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381277 1 0.1418 0.8978 0.944 0.000 0.024 0.000 0.000 0.032
#> GSM381278 3 0.4943 -0.4541 0.000 0.000 0.564 0.016 0.040 0.380
#> GSM381197 5 0.0508 0.8446 0.000 0.000 0.004 0.000 0.984 0.012
#> GSM381202 1 0.4592 -0.0811 0.496 0.000 0.468 0.000 0.000 0.036
#> GSM381207 1 0.0363 0.9288 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM381208 5 0.1010 0.8193 0.000 0.000 0.000 0.004 0.960 0.036
#> GSM381210 1 0.0458 0.9234 0.984 0.000 0.016 0.000 0.000 0.000
#> GSM381215 3 0.4872 -0.4840 0.000 0.000 0.548 0.000 0.064 0.388
#> GSM381219 2 0.3817 0.8084 0.000 0.568 0.000 0.000 0.000 0.432
#> GSM381221 2 0.3309 0.8138 0.000 0.720 0.000 0.000 0.000 0.280
#> GSM381223 2 0.0146 0.7596 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM381229 5 0.4396 0.3472 0.000 0.000 0.036 0.000 0.612 0.352
#> GSM381230 1 0.0000 0.9321 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381233 3 0.4057 0.2997 0.388 0.000 0.600 0.000 0.000 0.012
#> GSM381234 1 0.0146 0.9311 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM381238 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381239 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381242 3 0.1562 0.5036 0.032 0.000 0.940 0.000 0.004 0.024
#> GSM381247 2 0.0725 0.7475 0.000 0.976 0.000 0.000 0.012 0.012
#> GSM381248 1 0.2389 0.7962 0.864 0.000 0.000 0.000 0.128 0.008
#> GSM381249 3 0.4025 0.2422 0.416 0.000 0.576 0.000 0.000 0.008
#> GSM381253 6 0.6378 0.7206 0.164 0.000 0.280 0.000 0.048 0.508
#> GSM381255 2 0.3817 0.8084 0.000 0.568 0.000 0.000 0.000 0.432
#> GSM381258 3 0.0363 0.4925 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM381262 6 0.4868 0.6925 0.000 0.000 0.416 0.000 0.060 0.524
#> GSM381266 5 0.6684 -0.1889 0.000 0.000 0.212 0.044 0.412 0.332
#> GSM381267 5 0.1268 0.8152 0.000 0.008 0.000 0.004 0.952 0.036
#> GSM381269 3 0.1588 0.5093 0.072 0.000 0.924 0.000 0.000 0.004
#> GSM381273 5 0.0363 0.8449 0.000 0.000 0.000 0.000 0.988 0.012
#> GSM381274 2 0.0458 0.7635 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM381276 3 0.6129 -0.4619 0.160 0.000 0.452 0.000 0.020 0.368
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 other(p) k
#> CV:skmeans 78 0.572 2
#> CV:skmeans 86 0.153 3
#> CV:skmeans 78 0.630 4
#> CV:skmeans 82 0.401 5
#> CV:skmeans 71 0.266 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 86 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.992 0.997 0.451 0.548 0.548
#> 3 3 1.000 0.987 0.994 0.239 0.893 0.804
#> 4 4 0.832 0.935 0.950 0.158 0.922 0.825
#> 5 5 0.845 0.922 0.943 0.149 0.881 0.677
#> 6 6 0.959 0.916 0.968 0.067 0.962 0.846
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 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
#> GSM381194 1 0.00 1.000 1.000 0.000
#> GSM381199 2 0.00 0.990 0.000 1.000
#> GSM381205 2 0.00 0.990 0.000 1.000
#> GSM381211 2 0.00 0.990 0.000 1.000
#> GSM381220 2 0.00 0.990 0.000 1.000
#> GSM381222 1 0.00 1.000 1.000 0.000
#> GSM381224 1 0.00 1.000 1.000 0.000
#> GSM381232 1 0.00 1.000 1.000 0.000
#> GSM381240 1 0.00 1.000 1.000 0.000
#> GSM381250 1 0.00 1.000 1.000 0.000
#> GSM381252 2 0.00 0.990 0.000 1.000
#> GSM381254 1 0.00 1.000 1.000 0.000
#> GSM381256 2 0.00 0.990 0.000 1.000
#> GSM381257 1 0.00 1.000 1.000 0.000
#> GSM381259 1 0.00 1.000 1.000 0.000
#> GSM381260 1 0.00 1.000 1.000 0.000
#> GSM381261 2 0.00 0.990 0.000 1.000
#> GSM381263 1 0.00 1.000 1.000 0.000
#> GSM381265 1 0.00 1.000 1.000 0.000
#> GSM381268 1 0.00 1.000 1.000 0.000
#> GSM381270 2 0.00 0.990 0.000 1.000
#> GSM381271 1 0.00 1.000 1.000 0.000
#> GSM381275 2 0.00 0.990 0.000 1.000
#> GSM381279 2 0.00 0.990 0.000 1.000
#> GSM381195 1 0.00 1.000 1.000 0.000
#> GSM381196 1 0.00 1.000 1.000 0.000
#> GSM381198 2 0.00 0.990 0.000 1.000
#> GSM381200 2 0.00 0.990 0.000 1.000
#> GSM381201 1 0.00 1.000 1.000 0.000
#> GSM381203 1 0.00 1.000 1.000 0.000
#> GSM381204 1 0.00 1.000 1.000 0.000
#> GSM381209 1 0.00 1.000 1.000 0.000
#> GSM381212 1 0.00 1.000 1.000 0.000
#> GSM381213 2 0.00 0.990 0.000 1.000
#> GSM381214 2 0.00 0.990 0.000 1.000
#> GSM381216 1 0.00 1.000 1.000 0.000
#> GSM381225 1 0.00 1.000 1.000 0.000
#> GSM381231 1 0.00 1.000 1.000 0.000
#> GSM381235 1 0.00 1.000 1.000 0.000
#> GSM381237 1 0.00 1.000 1.000 0.000
#> GSM381241 2 0.00 0.990 0.000 1.000
#> GSM381243 2 0.00 0.990 0.000 1.000
#> GSM381245 1 0.00 1.000 1.000 0.000
#> GSM381246 2 0.00 0.990 0.000 1.000
#> GSM381251 1 0.00 1.000 1.000 0.000
#> GSM381264 1 0.00 1.000 1.000 0.000
#> GSM381206 2 0.00 0.990 0.000 1.000
#> GSM381217 1 0.00 1.000 1.000 0.000
#> GSM381218 2 0.00 0.990 0.000 1.000
#> GSM381226 2 0.00 0.990 0.000 1.000
#> GSM381227 2 0.00 0.990 0.000 1.000
#> GSM381228 1 0.00 1.000 1.000 0.000
#> GSM381236 1 0.00 1.000 1.000 0.000
#> GSM381244 1 0.00 1.000 1.000 0.000
#> GSM381272 1 0.00 1.000 1.000 0.000
#> GSM381277 1 0.00 1.000 1.000 0.000
#> GSM381278 1 0.00 1.000 1.000 0.000
#> GSM381197 1 0.00 1.000 1.000 0.000
#> GSM381202 1 0.00 1.000 1.000 0.000
#> GSM381207 1 0.00 1.000 1.000 0.000
#> GSM381208 2 0.85 0.619 0.276 0.724
#> GSM381210 1 0.00 1.000 1.000 0.000
#> GSM381215 1 0.00 1.000 1.000 0.000
#> GSM381219 2 0.00 0.990 0.000 1.000
#> GSM381221 2 0.00 0.990 0.000 1.000
#> GSM381223 2 0.00 0.990 0.000 1.000
#> GSM381229 1 0.00 1.000 1.000 0.000
#> GSM381230 1 0.00 1.000 1.000 0.000
#> GSM381233 1 0.00 1.000 1.000 0.000
#> GSM381234 1 0.00 1.000 1.000 0.000
#> GSM381238 1 0.00 1.000 1.000 0.000
#> GSM381239 1 0.00 1.000 1.000 0.000
#> GSM381242 1 0.00 1.000 1.000 0.000
#> GSM381247 2 0.00 0.990 0.000 1.000
#> GSM381248 1 0.00 1.000 1.000 0.000
#> GSM381249 1 0.00 1.000 1.000 0.000
#> GSM381253 1 0.00 1.000 1.000 0.000
#> GSM381255 2 0.00 0.990 0.000 1.000
#> GSM381258 1 0.00 1.000 1.000 0.000
#> GSM381262 1 0.00 1.000 1.000 0.000
#> GSM381266 1 0.00 1.000 1.000 0.000
#> GSM381267 2 0.00 0.990 0.000 1.000
#> GSM381269 1 0.00 1.000 1.000 0.000
#> GSM381273 1 0.00 1.000 1.000 0.000
#> GSM381274 2 0.00 0.990 0.000 1.000
#> GSM381276 1 0.00 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM381194 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381199 2 0.0000 0.985 0.000 1.000 0.000
#> GSM381205 2 0.0000 0.985 0.000 1.000 0.000
#> GSM381211 2 0.0000 0.985 0.000 1.000 0.000
#> GSM381220 2 0.0000 0.985 0.000 1.000 0.000
#> GSM381222 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381224 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381232 3 0.0747 1.000 0.016 0.000 0.984
#> GSM381240 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381250 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381252 2 0.0000 0.985 0.000 1.000 0.000
#> GSM381254 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381256 2 0.0000 0.985 0.000 1.000 0.000
#> GSM381257 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381259 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381260 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381261 2 0.0000 0.985 0.000 1.000 0.000
#> GSM381263 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381265 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381268 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381270 2 0.0000 0.985 0.000 1.000 0.000
#> GSM381271 3 0.0747 1.000 0.016 0.000 0.984
#> GSM381275 2 0.0000 0.985 0.000 1.000 0.000
#> GSM381279 2 0.0000 0.985 0.000 1.000 0.000
#> GSM381195 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381196 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381198 2 0.0000 0.985 0.000 1.000 0.000
#> GSM381200 2 0.0000 0.985 0.000 1.000 0.000
#> GSM381201 1 0.0747 0.985 0.984 0.000 0.016
#> GSM381203 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381204 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381209 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381212 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381213 2 0.0000 0.985 0.000 1.000 0.000
#> GSM381214 2 0.0000 0.985 0.000 1.000 0.000
#> GSM381216 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381225 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381231 3 0.0747 1.000 0.016 0.000 0.984
#> GSM381235 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381237 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381241 2 0.0000 0.985 0.000 1.000 0.000
#> GSM381243 2 0.0000 0.985 0.000 1.000 0.000
#> GSM381245 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381246 2 0.0000 0.985 0.000 1.000 0.000
#> GSM381251 1 0.0747 0.985 0.984 0.000 0.016
#> GSM381264 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381206 2 0.0000 0.985 0.000 1.000 0.000
#> GSM381217 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381218 2 0.0000 0.985 0.000 1.000 0.000
#> GSM381226 2 0.0000 0.985 0.000 1.000 0.000
#> GSM381227 2 0.0000 0.985 0.000 1.000 0.000
#> GSM381228 3 0.0747 1.000 0.016 0.000 0.984
#> GSM381236 3 0.0747 1.000 0.016 0.000 0.984
#> GSM381244 1 0.0747 0.985 0.984 0.000 0.016
#> GSM381272 3 0.0747 1.000 0.016 0.000 0.984
#> GSM381277 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381278 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381197 1 0.0747 0.985 0.984 0.000 0.016
#> GSM381202 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381207 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381208 2 0.6161 0.518 0.272 0.708 0.020
#> GSM381210 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381215 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381219 2 0.0000 0.985 0.000 1.000 0.000
#> GSM381221 2 0.0000 0.985 0.000 1.000 0.000
#> GSM381223 2 0.0000 0.985 0.000 1.000 0.000
#> GSM381229 1 0.0592 0.988 0.988 0.000 0.012
#> GSM381230 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381233 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381234 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381238 3 0.0747 1.000 0.016 0.000 0.984
#> GSM381239 3 0.0747 1.000 0.016 0.000 0.984
#> GSM381242 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381247 2 0.0000 0.985 0.000 1.000 0.000
#> GSM381248 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381249 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381253 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381255 2 0.0000 0.985 0.000 1.000 0.000
#> GSM381258 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381262 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381266 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381267 2 0.0747 0.970 0.000 0.984 0.016
#> GSM381269 1 0.0000 0.998 1.000 0.000 0.000
#> GSM381273 1 0.0747 0.985 0.984 0.000 0.016
#> GSM381274 2 0.0000 0.985 0.000 1.000 0.000
#> GSM381276 1 0.0000 0.998 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM381194 1 0.0000 0.918 1.000 0.000 0.000 0
#> GSM381199 2 0.0000 1.000 0.000 1.000 0.000 0
#> GSM381205 2 0.0000 1.000 0.000 1.000 0.000 0
#> GSM381211 2 0.0000 1.000 0.000 1.000 0.000 0
#> GSM381220 2 0.0000 1.000 0.000 1.000 0.000 0
#> GSM381222 1 0.0000 0.918 1.000 0.000 0.000 0
#> GSM381224 1 0.2973 0.881 0.856 0.000 0.144 0
#> GSM381232 4 0.0000 1.000 0.000 0.000 0.000 1
#> GSM381240 1 0.3356 0.870 0.824 0.000 0.176 0
#> GSM381250 1 0.0000 0.918 1.000 0.000 0.000 0
#> GSM381252 2 0.0000 1.000 0.000 1.000 0.000 0
#> GSM381254 1 0.3356 0.870 0.824 0.000 0.176 0
#> GSM381256 2 0.0000 1.000 0.000 1.000 0.000 0
#> GSM381257 1 0.0000 0.918 1.000 0.000 0.000 0
#> GSM381259 1 0.3356 0.870 0.824 0.000 0.176 0
#> GSM381260 1 0.0000 0.918 1.000 0.000 0.000 0
#> GSM381261 2 0.0000 1.000 0.000 1.000 0.000 0
#> GSM381263 1 0.0000 0.918 1.000 0.000 0.000 0
#> GSM381265 1 0.3356 0.870 0.824 0.000 0.176 0
#> GSM381268 1 0.0000 0.918 1.000 0.000 0.000 0
#> GSM381270 2 0.0000 1.000 0.000 1.000 0.000 0
#> GSM381271 4 0.0000 1.000 0.000 0.000 0.000 1
#> GSM381275 2 0.0000 1.000 0.000 1.000 0.000 0
#> GSM381279 2 0.0000 1.000 0.000 1.000 0.000 0
#> GSM381195 1 0.3356 0.870 0.824 0.000 0.176 0
#> GSM381196 1 0.0000 0.918 1.000 0.000 0.000 0
#> GSM381198 2 0.0000 1.000 0.000 1.000 0.000 0
#> GSM381200 2 0.0000 1.000 0.000 1.000 0.000 0
#> GSM381201 3 0.3356 0.897 0.176 0.000 0.824 0
#> GSM381203 1 0.0000 0.918 1.000 0.000 0.000 0
#> GSM381204 1 0.3356 0.870 0.824 0.000 0.176 0
#> GSM381209 1 0.3356 0.870 0.824 0.000 0.176 0
#> GSM381212 1 0.3356 0.870 0.824 0.000 0.176 0
#> GSM381213 2 0.0000 1.000 0.000 1.000 0.000 0
#> GSM381214 2 0.0000 1.000 0.000 1.000 0.000 0
#> GSM381216 1 0.0000 0.918 1.000 0.000 0.000 0
#> GSM381225 1 0.0000 0.918 1.000 0.000 0.000 0
#> GSM381231 4 0.0000 1.000 0.000 0.000 0.000 1
#> GSM381235 1 0.0000 0.918 1.000 0.000 0.000 0
#> GSM381237 1 0.3356 0.870 0.824 0.000 0.176 0
#> GSM381241 2 0.0000 1.000 0.000 1.000 0.000 0
#> GSM381243 2 0.0000 1.000 0.000 1.000 0.000 0
#> GSM381245 1 0.0000 0.918 1.000 0.000 0.000 0
#> GSM381246 2 0.0000 1.000 0.000 1.000 0.000 0
#> GSM381251 3 0.3356 0.897 0.176 0.000 0.824 0
#> GSM381264 1 0.3356 0.870 0.824 0.000 0.176 0
#> GSM381206 2 0.0000 1.000 0.000 1.000 0.000 0
#> GSM381217 1 0.0000 0.918 1.000 0.000 0.000 0
#> GSM381218 2 0.0000 1.000 0.000 1.000 0.000 0
#> GSM381226 2 0.0000 1.000 0.000 1.000 0.000 0
#> GSM381227 2 0.0000 1.000 0.000 1.000 0.000 0
#> GSM381228 4 0.0000 1.000 0.000 0.000 0.000 1
#> GSM381236 4 0.0000 1.000 0.000 0.000 0.000 1
#> GSM381244 3 0.3356 0.897 0.176 0.000 0.824 0
#> GSM381272 4 0.0000 1.000 0.000 0.000 0.000 1
#> GSM381277 1 0.3356 0.870 0.824 0.000 0.176 0
#> GSM381278 1 0.0000 0.918 1.000 0.000 0.000 0
#> GSM381197 3 0.3356 0.897 0.176 0.000 0.824 0
#> GSM381202 1 0.0000 0.918 1.000 0.000 0.000 0
#> GSM381207 1 0.0000 0.918 1.000 0.000 0.000 0
#> GSM381208 3 0.4037 0.752 0.040 0.136 0.824 0
#> GSM381210 1 0.3356 0.870 0.824 0.000 0.176 0
#> GSM381215 1 0.0000 0.918 1.000 0.000 0.000 0
#> GSM381219 2 0.0000 1.000 0.000 1.000 0.000 0
#> GSM381221 2 0.0000 1.000 0.000 1.000 0.000 0
#> GSM381223 2 0.0000 1.000 0.000 1.000 0.000 0
#> GSM381229 1 0.2704 0.787 0.876 0.000 0.124 0
#> GSM381230 1 0.3356 0.870 0.824 0.000 0.176 0
#> GSM381233 1 0.0000 0.918 1.000 0.000 0.000 0
#> GSM381234 1 0.3356 0.870 0.824 0.000 0.176 0
#> GSM381238 4 0.0000 1.000 0.000 0.000 0.000 1
#> GSM381239 4 0.0000 1.000 0.000 0.000 0.000 1
#> GSM381242 1 0.0000 0.918 1.000 0.000 0.000 0
#> GSM381247 2 0.0000 1.000 0.000 1.000 0.000 0
#> GSM381248 1 0.3172 0.876 0.840 0.000 0.160 0
#> GSM381249 1 0.3266 0.873 0.832 0.000 0.168 0
#> GSM381253 1 0.0000 0.918 1.000 0.000 0.000 0
#> GSM381255 2 0.0000 1.000 0.000 1.000 0.000 0
#> GSM381258 1 0.0000 0.918 1.000 0.000 0.000 0
#> GSM381262 1 0.0000 0.918 1.000 0.000 0.000 0
#> GSM381266 1 0.0000 0.918 1.000 0.000 0.000 0
#> GSM381267 3 0.3356 0.684 0.000 0.176 0.824 0
#> GSM381269 1 0.0188 0.917 0.996 0.000 0.004 0
#> GSM381273 3 0.3356 0.897 0.176 0.000 0.824 0
#> GSM381274 2 0.0000 1.000 0.000 1.000 0.000 0
#> GSM381276 1 0.0000 0.918 1.000 0.000 0.000 0
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM381194 3 0.0000 0.9475 0.000 0.000 1.000 0 0.000
#> GSM381199 2 0.2561 0.9019 0.144 0.856 0.000 0 0.000
#> GSM381205 2 0.0000 0.9600 0.000 1.000 0.000 0 0.000
#> GSM381211 2 0.0000 0.9600 0.000 1.000 0.000 0 0.000
#> GSM381220 2 0.2377 0.9100 0.128 0.872 0.000 0 0.000
#> GSM381222 3 0.0000 0.9475 0.000 0.000 1.000 0 0.000
#> GSM381224 3 0.4297 -0.2193 0.472 0.000 0.528 0 0.000
#> GSM381232 4 0.0000 1.0000 0.000 0.000 0.000 1 0.000
#> GSM381240 1 0.2561 0.9603 0.856 0.000 0.144 0 0.000
#> GSM381250 3 0.0000 0.9475 0.000 0.000 1.000 0 0.000
#> GSM381252 2 0.0000 0.9600 0.000 1.000 0.000 0 0.000
#> GSM381254 1 0.2561 0.9603 0.856 0.000 0.144 0 0.000
#> GSM381256 2 0.0000 0.9600 0.000 1.000 0.000 0 0.000
#> GSM381257 3 0.0290 0.9412 0.008 0.000 0.992 0 0.000
#> GSM381259 1 0.2561 0.9603 0.856 0.000 0.144 0 0.000
#> GSM381260 3 0.1478 0.8837 0.064 0.000 0.936 0 0.000
#> GSM381261 2 0.1121 0.9446 0.044 0.956 0.000 0 0.000
#> GSM381263 3 0.0000 0.9475 0.000 0.000 1.000 0 0.000
#> GSM381265 1 0.2561 0.9603 0.856 0.000 0.144 0 0.000
#> GSM381268 3 0.0000 0.9475 0.000 0.000 1.000 0 0.000
#> GSM381270 2 0.2561 0.9019 0.144 0.856 0.000 0 0.000
#> GSM381271 4 0.0000 1.0000 0.000 0.000 0.000 1 0.000
#> GSM381275 2 0.0000 0.9600 0.000 1.000 0.000 0 0.000
#> GSM381279 2 0.2561 0.9019 0.144 0.856 0.000 0 0.000
#> GSM381195 1 0.3274 0.8882 0.780 0.000 0.220 0 0.000
#> GSM381196 3 0.0000 0.9475 0.000 0.000 1.000 0 0.000
#> GSM381198 2 0.0000 0.9600 0.000 1.000 0.000 0 0.000
#> GSM381200 2 0.0000 0.9600 0.000 1.000 0.000 0 0.000
#> GSM381201 5 0.0000 1.0000 0.000 0.000 0.000 0 1.000
#> GSM381203 3 0.0000 0.9475 0.000 0.000 1.000 0 0.000
#> GSM381204 1 0.2561 0.9603 0.856 0.000 0.144 0 0.000
#> GSM381209 1 0.2561 0.9603 0.856 0.000 0.144 0 0.000
#> GSM381212 1 0.2561 0.9603 0.856 0.000 0.144 0 0.000
#> GSM381213 2 0.0000 0.9600 0.000 1.000 0.000 0 0.000
#> GSM381214 2 0.0000 0.9600 0.000 1.000 0.000 0 0.000
#> GSM381216 3 0.0000 0.9475 0.000 0.000 1.000 0 0.000
#> GSM381225 3 0.0000 0.9475 0.000 0.000 1.000 0 0.000
#> GSM381231 4 0.0000 1.0000 0.000 0.000 0.000 1 0.000
#> GSM381235 3 0.0000 0.9475 0.000 0.000 1.000 0 0.000
#> GSM381237 1 0.2561 0.9603 0.856 0.000 0.144 0 0.000
#> GSM381241 2 0.0000 0.9600 0.000 1.000 0.000 0 0.000
#> GSM381243 2 0.2561 0.9019 0.144 0.856 0.000 0 0.000
#> GSM381245 3 0.0000 0.9475 0.000 0.000 1.000 0 0.000
#> GSM381246 2 0.0000 0.9600 0.000 1.000 0.000 0 0.000
#> GSM381251 5 0.0000 1.0000 0.000 0.000 0.000 0 1.000
#> GSM381264 1 0.2561 0.9603 0.856 0.000 0.144 0 0.000
#> GSM381206 2 0.0000 0.9600 0.000 1.000 0.000 0 0.000
#> GSM381217 3 0.0000 0.9475 0.000 0.000 1.000 0 0.000
#> GSM381218 2 0.0000 0.9600 0.000 1.000 0.000 0 0.000
#> GSM381226 2 0.0000 0.9600 0.000 1.000 0.000 0 0.000
#> GSM381227 2 0.2561 0.9019 0.144 0.856 0.000 0 0.000
#> GSM381228 4 0.0000 1.0000 0.000 0.000 0.000 1 0.000
#> GSM381236 4 0.0000 1.0000 0.000 0.000 0.000 1 0.000
#> GSM381244 5 0.0000 1.0000 0.000 0.000 0.000 0 1.000
#> GSM381272 4 0.0000 1.0000 0.000 0.000 0.000 1 0.000
#> GSM381277 1 0.2605 0.9572 0.852 0.000 0.148 0 0.000
#> GSM381278 3 0.0290 0.9398 0.008 0.000 0.992 0 0.000
#> GSM381197 5 0.0000 1.0000 0.000 0.000 0.000 0 1.000
#> GSM381202 3 0.1792 0.8614 0.084 0.000 0.916 0 0.000
#> GSM381207 3 0.0000 0.9475 0.000 0.000 1.000 0 0.000
#> GSM381208 5 0.0000 1.0000 0.000 0.000 0.000 0 1.000
#> GSM381210 1 0.2561 0.9603 0.856 0.000 0.144 0 0.000
#> GSM381215 3 0.0000 0.9475 0.000 0.000 1.000 0 0.000
#> GSM381219 2 0.0000 0.9600 0.000 1.000 0.000 0 0.000
#> GSM381221 2 0.0000 0.9600 0.000 1.000 0.000 0 0.000
#> GSM381223 2 0.2377 0.9101 0.128 0.872 0.000 0 0.000
#> GSM381229 3 0.2329 0.8100 0.000 0.000 0.876 0 0.124
#> GSM381230 1 0.2561 0.9603 0.856 0.000 0.144 0 0.000
#> GSM381233 3 0.0000 0.9475 0.000 0.000 1.000 0 0.000
#> GSM381234 1 0.3210 0.8976 0.788 0.000 0.212 0 0.000
#> GSM381238 4 0.0000 1.0000 0.000 0.000 0.000 1 0.000
#> GSM381239 4 0.0000 1.0000 0.000 0.000 0.000 1 0.000
#> GSM381242 3 0.0000 0.9475 0.000 0.000 1.000 0 0.000
#> GSM381247 2 0.2561 0.9019 0.144 0.856 0.000 0 0.000
#> GSM381248 3 0.4242 -0.0433 0.428 0.000 0.572 0 0.000
#> GSM381249 1 0.4210 0.5348 0.588 0.000 0.412 0 0.000
#> GSM381253 3 0.0000 0.9475 0.000 0.000 1.000 0 0.000
#> GSM381255 2 0.0000 0.9600 0.000 1.000 0.000 0 0.000
#> GSM381258 3 0.0000 0.9475 0.000 0.000 1.000 0 0.000
#> GSM381262 3 0.0000 0.9475 0.000 0.000 1.000 0 0.000
#> GSM381266 3 0.0000 0.9475 0.000 0.000 1.000 0 0.000
#> GSM381267 5 0.0000 1.0000 0.000 0.000 0.000 0 1.000
#> GSM381269 3 0.0162 0.9444 0.004 0.000 0.996 0 0.000
#> GSM381273 5 0.0000 1.0000 0.000 0.000 0.000 0 1.000
#> GSM381274 2 0.0000 0.9600 0.000 1.000 0.000 0 0.000
#> GSM381276 3 0.0000 0.9475 0.000 0.000 1.000 0 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM381194 3 0.0000 0.9518 0.000 0.000 1.000 0 0.000 0.000
#> GSM381199 6 0.0937 0.9543 0.000 0.040 0.000 0 0.000 0.960
#> GSM381205 2 0.0000 0.9622 0.000 1.000 0.000 0 0.000 0.000
#> GSM381211 2 0.0000 0.9622 0.000 1.000 0.000 0 0.000 0.000
#> GSM381220 6 0.0632 0.9663 0.000 0.024 0.000 0 0.000 0.976
#> GSM381222 3 0.0000 0.9518 0.000 0.000 1.000 0 0.000 0.000
#> GSM381224 3 0.3862 0.0225 0.476 0.000 0.524 0 0.000 0.000
#> GSM381232 4 0.0000 1.0000 0.000 0.000 0.000 1 0.000 0.000
#> GSM381240 1 0.0000 0.9276 1.000 0.000 0.000 0 0.000 0.000
#> GSM381250 3 0.0000 0.9518 0.000 0.000 1.000 0 0.000 0.000
#> GSM381252 2 0.0000 0.9622 0.000 1.000 0.000 0 0.000 0.000
#> GSM381254 1 0.0260 0.9257 0.992 0.000 0.008 0 0.000 0.000
#> GSM381256 2 0.0363 0.9574 0.000 0.988 0.000 0 0.000 0.012
#> GSM381257 3 0.0260 0.9464 0.008 0.000 0.992 0 0.000 0.000
#> GSM381259 1 0.0000 0.9276 1.000 0.000 0.000 0 0.000 0.000
#> GSM381260 3 0.1387 0.8948 0.068 0.000 0.932 0 0.000 0.000
#> GSM381261 2 0.3804 0.2910 0.000 0.576 0.000 0 0.000 0.424
#> GSM381263 3 0.0000 0.9518 0.000 0.000 1.000 0 0.000 0.000
#> GSM381265 1 0.0000 0.9276 1.000 0.000 0.000 0 0.000 0.000
#> GSM381268 3 0.0000 0.9518 0.000 0.000 1.000 0 0.000 0.000
#> GSM381270 6 0.0000 0.9838 0.000 0.000 0.000 0 0.000 1.000
#> GSM381271 4 0.0000 1.0000 0.000 0.000 0.000 1 0.000 0.000
#> GSM381275 2 0.0000 0.9622 0.000 1.000 0.000 0 0.000 0.000
#> GSM381279 6 0.0000 0.9838 0.000 0.000 0.000 0 0.000 1.000
#> GSM381195 1 0.2300 0.7908 0.856 0.000 0.144 0 0.000 0.000
#> GSM381196 3 0.0000 0.9518 0.000 0.000 1.000 0 0.000 0.000
#> GSM381198 2 0.0000 0.9622 0.000 1.000 0.000 0 0.000 0.000
#> GSM381200 2 0.0000 0.9622 0.000 1.000 0.000 0 0.000 0.000
#> GSM381201 5 0.0000 1.0000 0.000 0.000 0.000 0 1.000 0.000
#> GSM381203 3 0.0000 0.9518 0.000 0.000 1.000 0 0.000 0.000
#> GSM381204 1 0.0000 0.9276 1.000 0.000 0.000 0 0.000 0.000
#> GSM381209 1 0.0000 0.9276 1.000 0.000 0.000 0 0.000 0.000
#> GSM381212 1 0.0000 0.9276 1.000 0.000 0.000 0 0.000 0.000
#> GSM381213 2 0.0790 0.9461 0.000 0.968 0.000 0 0.000 0.032
#> GSM381214 2 0.0146 0.9608 0.000 0.996 0.000 0 0.000 0.004
#> GSM381216 3 0.0000 0.9518 0.000 0.000 1.000 0 0.000 0.000
#> GSM381225 3 0.0000 0.9518 0.000 0.000 1.000 0 0.000 0.000
#> GSM381231 4 0.0000 1.0000 0.000 0.000 0.000 1 0.000 0.000
#> GSM381235 3 0.0000 0.9518 0.000 0.000 1.000 0 0.000 0.000
#> GSM381237 1 0.0000 0.9276 1.000 0.000 0.000 0 0.000 0.000
#> GSM381241 2 0.0000 0.9622 0.000 1.000 0.000 0 0.000 0.000
#> GSM381243 6 0.0000 0.9838 0.000 0.000 0.000 0 0.000 1.000
#> GSM381245 3 0.0000 0.9518 0.000 0.000 1.000 0 0.000 0.000
#> GSM381246 2 0.0000 0.9622 0.000 1.000 0.000 0 0.000 0.000
#> GSM381251 5 0.0000 1.0000 0.000 0.000 0.000 0 1.000 0.000
#> GSM381264 1 0.0146 0.9271 0.996 0.000 0.004 0 0.000 0.000
#> GSM381206 2 0.0000 0.9622 0.000 1.000 0.000 0 0.000 0.000
#> GSM381217 3 0.0000 0.9518 0.000 0.000 1.000 0 0.000 0.000
#> GSM381218 2 0.0363 0.9574 0.000 0.988 0.000 0 0.000 0.012
#> GSM381226 2 0.0000 0.9622 0.000 1.000 0.000 0 0.000 0.000
#> GSM381227 6 0.0363 0.9780 0.000 0.012 0.000 0 0.000 0.988
#> GSM381228 4 0.0000 1.0000 0.000 0.000 0.000 1 0.000 0.000
#> GSM381236 4 0.0000 1.0000 0.000 0.000 0.000 1 0.000 0.000
#> GSM381244 5 0.0000 1.0000 0.000 0.000 0.000 0 1.000 0.000
#> GSM381272 4 0.0000 1.0000 0.000 0.000 0.000 1 0.000 0.000
#> GSM381277 1 0.0632 0.9140 0.976 0.000 0.024 0 0.000 0.000
#> GSM381278 3 0.0260 0.9463 0.000 0.000 0.992 0 0.000 0.008
#> GSM381197 5 0.0000 1.0000 0.000 0.000 0.000 0 1.000 0.000
#> GSM381202 3 0.1957 0.8509 0.112 0.000 0.888 0 0.000 0.000
#> GSM381207 3 0.0000 0.9518 0.000 0.000 1.000 0 0.000 0.000
#> GSM381208 5 0.0000 1.0000 0.000 0.000 0.000 0 1.000 0.000
#> GSM381210 1 0.0260 0.9260 0.992 0.000 0.008 0 0.000 0.000
#> GSM381215 3 0.0000 0.9518 0.000 0.000 1.000 0 0.000 0.000
#> GSM381219 2 0.0000 0.9622 0.000 1.000 0.000 0 0.000 0.000
#> GSM381221 2 0.0000 0.9622 0.000 1.000 0.000 0 0.000 0.000
#> GSM381223 2 0.2562 0.7941 0.000 0.828 0.000 0 0.000 0.172
#> GSM381229 3 0.2092 0.8306 0.000 0.000 0.876 0 0.124 0.000
#> GSM381230 1 0.0260 0.9258 0.992 0.000 0.008 0 0.000 0.000
#> GSM381233 3 0.0000 0.9518 0.000 0.000 1.000 0 0.000 0.000
#> GSM381234 1 0.2300 0.7936 0.856 0.000 0.144 0 0.000 0.000
#> GSM381238 4 0.0000 1.0000 0.000 0.000 0.000 1 0.000 0.000
#> GSM381239 4 0.0000 1.0000 0.000 0.000 0.000 1 0.000 0.000
#> GSM381242 3 0.0000 0.9518 0.000 0.000 1.000 0 0.000 0.000
#> GSM381247 6 0.0000 0.9838 0.000 0.000 0.000 0 0.000 1.000
#> GSM381248 3 0.3823 0.1680 0.436 0.000 0.564 0 0.000 0.000
#> GSM381249 1 0.3756 0.3378 0.600 0.000 0.400 0 0.000 0.000
#> GSM381253 3 0.0000 0.9518 0.000 0.000 1.000 0 0.000 0.000
#> GSM381255 2 0.0713 0.9483 0.000 0.972 0.000 0 0.000 0.028
#> GSM381258 3 0.0000 0.9518 0.000 0.000 1.000 0 0.000 0.000
#> GSM381262 3 0.0000 0.9518 0.000 0.000 1.000 0 0.000 0.000
#> GSM381266 3 0.0000 0.9518 0.000 0.000 1.000 0 0.000 0.000
#> GSM381267 5 0.0000 1.0000 0.000 0.000 0.000 0 1.000 0.000
#> GSM381269 3 0.0146 0.9492 0.004 0.000 0.996 0 0.000 0.000
#> GSM381273 5 0.0000 1.0000 0.000 0.000 0.000 0 1.000 0.000
#> GSM381274 2 0.0790 0.9461 0.000 0.968 0.000 0 0.000 0.032
#> GSM381276 3 0.0000 0.9518 0.000 0.000 1.000 0 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 other(p) k
#> CV:pam 86 0.744 2
#> CV:pam 86 0.326 3
#> CV:pam 86 0.260 4
#> CV:pam 84 0.360 5
#> CV:pam 82 0.397 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 86 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 0.693 0.881 0.947 0.4821 0.504 0.504
#> 3 3 0.822 0.874 0.917 0.2285 0.852 0.715
#> 4 4 0.849 0.767 0.888 0.1636 0.935 0.833
#> 5 5 0.694 0.587 0.755 0.0751 0.952 0.859
#> 6 6 0.723 0.654 0.824 0.0691 0.812 0.448
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
#> GSM381194 1 0.0376 0.960 0.996 0.004
#> GSM381199 2 0.0000 0.907 0.000 1.000
#> GSM381205 2 0.0000 0.907 0.000 1.000
#> GSM381211 2 0.0000 0.907 0.000 1.000
#> GSM381220 2 0.0000 0.907 0.000 1.000
#> GSM381222 1 0.0000 0.963 1.000 0.000
#> GSM381224 1 0.0000 0.963 1.000 0.000
#> GSM381232 2 0.9460 0.502 0.364 0.636
#> GSM381240 1 0.0000 0.963 1.000 0.000
#> GSM381250 1 0.0000 0.963 1.000 0.000
#> GSM381252 2 0.0000 0.907 0.000 1.000
#> GSM381254 1 0.0000 0.963 1.000 0.000
#> GSM381256 2 0.0000 0.907 0.000 1.000
#> GSM381257 1 0.0000 0.963 1.000 0.000
#> GSM381259 1 0.0000 0.963 1.000 0.000
#> GSM381260 1 0.0000 0.963 1.000 0.000
#> GSM381261 2 0.0000 0.907 0.000 1.000
#> GSM381263 1 0.0000 0.963 1.000 0.000
#> GSM381265 1 0.0000 0.963 1.000 0.000
#> GSM381268 1 0.0000 0.963 1.000 0.000
#> GSM381270 2 0.0000 0.907 0.000 1.000
#> GSM381271 2 0.9460 0.502 0.364 0.636
#> GSM381275 2 0.0000 0.907 0.000 1.000
#> GSM381279 2 0.0000 0.907 0.000 1.000
#> GSM381195 1 0.0000 0.963 1.000 0.000
#> GSM381196 1 0.0000 0.963 1.000 0.000
#> GSM381198 2 0.0000 0.907 0.000 1.000
#> GSM381200 2 0.0000 0.907 0.000 1.000
#> GSM381201 1 0.7453 0.727 0.788 0.212
#> GSM381203 1 0.0000 0.963 1.000 0.000
#> GSM381204 1 0.0000 0.963 1.000 0.000
#> GSM381209 1 0.0000 0.963 1.000 0.000
#> GSM381212 1 0.0000 0.963 1.000 0.000
#> GSM381213 2 0.0000 0.907 0.000 1.000
#> GSM381214 2 0.0000 0.907 0.000 1.000
#> GSM381216 1 0.0000 0.963 1.000 0.000
#> GSM381225 1 0.0938 0.954 0.988 0.012
#> GSM381231 2 0.9460 0.502 0.364 0.636
#> GSM381235 1 0.0000 0.963 1.000 0.000
#> GSM381237 1 0.0000 0.963 1.000 0.000
#> GSM381241 2 0.0000 0.907 0.000 1.000
#> GSM381243 2 0.0000 0.907 0.000 1.000
#> GSM381245 1 0.0000 0.963 1.000 0.000
#> GSM381246 2 0.0000 0.907 0.000 1.000
#> GSM381251 1 0.7453 0.727 0.788 0.212
#> GSM381264 1 0.0000 0.963 1.000 0.000
#> GSM381206 2 0.0000 0.907 0.000 1.000
#> GSM381217 1 0.0000 0.963 1.000 0.000
#> GSM381218 2 0.0000 0.907 0.000 1.000
#> GSM381226 2 0.0000 0.907 0.000 1.000
#> GSM381227 2 0.0000 0.907 0.000 1.000
#> GSM381228 2 0.9460 0.502 0.364 0.636
#> GSM381236 2 0.9460 0.502 0.364 0.636
#> GSM381244 1 0.7453 0.727 0.788 0.212
#> GSM381272 2 0.9460 0.502 0.364 0.636
#> GSM381277 1 0.0000 0.963 1.000 0.000
#> GSM381278 1 0.0938 0.954 0.988 0.012
#> GSM381197 1 0.7453 0.727 0.788 0.212
#> GSM381202 1 0.0000 0.963 1.000 0.000
#> GSM381207 1 0.0000 0.963 1.000 0.000
#> GSM381208 2 0.2778 0.876 0.048 0.952
#> GSM381210 1 0.0000 0.963 1.000 0.000
#> GSM381215 1 0.0000 0.963 1.000 0.000
#> GSM381219 2 0.0000 0.907 0.000 1.000
#> GSM381221 2 0.0000 0.907 0.000 1.000
#> GSM381223 2 0.0000 0.907 0.000 1.000
#> GSM381229 1 0.7453 0.727 0.788 0.212
#> GSM381230 1 0.0000 0.963 1.000 0.000
#> GSM381233 1 0.0000 0.963 1.000 0.000
#> GSM381234 1 0.0000 0.963 1.000 0.000
#> GSM381238 2 0.9460 0.502 0.364 0.636
#> GSM381239 2 0.9460 0.502 0.364 0.636
#> GSM381242 1 0.0000 0.963 1.000 0.000
#> GSM381247 2 0.0000 0.907 0.000 1.000
#> GSM381248 1 0.0000 0.963 1.000 0.000
#> GSM381249 1 0.0000 0.963 1.000 0.000
#> GSM381253 1 0.0000 0.963 1.000 0.000
#> GSM381255 2 0.0000 0.907 0.000 1.000
#> GSM381258 1 0.0000 0.963 1.000 0.000
#> GSM381262 1 0.0000 0.963 1.000 0.000
#> GSM381266 1 0.7376 0.733 0.792 0.208
#> GSM381267 2 0.2778 0.876 0.048 0.952
#> GSM381269 1 0.0000 0.963 1.000 0.000
#> GSM381273 1 0.7453 0.727 0.788 0.212
#> GSM381274 2 0.0000 0.907 0.000 1.000
#> GSM381276 1 0.0000 0.963 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM381194 1 0.3340 0.810 0.880 0.000 0.120
#> GSM381199 2 0.0000 0.997 0.000 1.000 0.000
#> GSM381205 2 0.0000 0.997 0.000 1.000 0.000
#> GSM381211 2 0.0000 0.997 0.000 1.000 0.000
#> GSM381220 2 0.0000 0.997 0.000 1.000 0.000
#> GSM381222 1 0.0592 0.922 0.988 0.000 0.012
#> GSM381224 1 0.0237 0.922 0.996 0.000 0.004
#> GSM381232 3 0.6976 0.771 0.236 0.064 0.700
#> GSM381240 1 0.1529 0.919 0.960 0.000 0.040
#> GSM381250 1 0.1031 0.919 0.976 0.000 0.024
#> GSM381252 2 0.0000 0.997 0.000 1.000 0.000
#> GSM381254 1 0.1529 0.919 0.960 0.000 0.040
#> GSM381256 2 0.0000 0.997 0.000 1.000 0.000
#> GSM381257 1 0.0892 0.922 0.980 0.000 0.020
#> GSM381259 1 0.1529 0.919 0.960 0.000 0.040
#> GSM381260 1 0.1031 0.919 0.976 0.000 0.024
#> GSM381261 2 0.0000 0.997 0.000 1.000 0.000
#> GSM381263 1 0.1031 0.919 0.976 0.000 0.024
#> GSM381265 1 0.1529 0.919 0.960 0.000 0.040
#> GSM381268 1 0.1031 0.919 0.976 0.000 0.024
#> GSM381270 2 0.0000 0.997 0.000 1.000 0.000
#> GSM381271 3 0.6976 0.771 0.236 0.064 0.700
#> GSM381275 2 0.0000 0.997 0.000 1.000 0.000
#> GSM381279 2 0.0000 0.997 0.000 1.000 0.000
#> GSM381195 1 0.1529 0.919 0.960 0.000 0.040
#> GSM381196 1 0.1031 0.919 0.976 0.000 0.024
#> GSM381198 2 0.0000 0.997 0.000 1.000 0.000
#> GSM381200 2 0.0000 0.997 0.000 1.000 0.000
#> GSM381201 3 0.6026 0.529 0.376 0.000 0.624
#> GSM381203 1 0.1031 0.919 0.976 0.000 0.024
#> GSM381204 1 0.1529 0.919 0.960 0.000 0.040
#> GSM381209 1 0.1529 0.919 0.960 0.000 0.040
#> GSM381212 1 0.1529 0.919 0.960 0.000 0.040
#> GSM381213 2 0.0000 0.997 0.000 1.000 0.000
#> GSM381214 2 0.0000 0.997 0.000 1.000 0.000
#> GSM381216 1 0.1031 0.919 0.976 0.000 0.024
#> GSM381225 1 0.3340 0.810 0.880 0.000 0.120
#> GSM381231 3 0.6976 0.771 0.236 0.064 0.700
#> GSM381235 1 0.1163 0.917 0.972 0.000 0.028
#> GSM381237 1 0.1529 0.919 0.960 0.000 0.040
#> GSM381241 2 0.0000 0.997 0.000 1.000 0.000
#> GSM381243 2 0.0000 0.997 0.000 1.000 0.000
#> GSM381245 1 0.1529 0.919 0.960 0.000 0.040
#> GSM381246 2 0.0000 0.997 0.000 1.000 0.000
#> GSM381251 3 0.6111 0.489 0.396 0.000 0.604
#> GSM381264 1 0.1529 0.919 0.960 0.000 0.040
#> GSM381206 2 0.0000 0.997 0.000 1.000 0.000
#> GSM381217 1 0.1031 0.919 0.976 0.000 0.024
#> GSM381218 2 0.0000 0.997 0.000 1.000 0.000
#> GSM381226 2 0.0000 0.997 0.000 1.000 0.000
#> GSM381227 2 0.0000 0.997 0.000 1.000 0.000
#> GSM381228 3 0.6976 0.771 0.236 0.064 0.700
#> GSM381236 3 0.6976 0.771 0.236 0.064 0.700
#> GSM381244 3 0.6062 0.515 0.384 0.000 0.616
#> GSM381272 3 0.6976 0.771 0.236 0.064 0.700
#> GSM381277 1 0.1529 0.919 0.960 0.000 0.040
#> GSM381278 1 0.5431 0.441 0.716 0.000 0.284
#> GSM381197 3 0.6026 0.529 0.376 0.000 0.624
#> GSM381202 1 0.1031 0.919 0.976 0.000 0.024
#> GSM381207 1 0.1529 0.919 0.960 0.000 0.040
#> GSM381208 3 0.2680 0.627 0.008 0.068 0.924
#> GSM381210 1 0.1529 0.919 0.960 0.000 0.040
#> GSM381215 1 0.1031 0.919 0.976 0.000 0.024
#> GSM381219 2 0.0000 0.997 0.000 1.000 0.000
#> GSM381221 2 0.0000 0.997 0.000 1.000 0.000
#> GSM381223 2 0.0000 0.997 0.000 1.000 0.000
#> GSM381229 1 0.5835 0.256 0.660 0.000 0.340
#> GSM381230 1 0.1529 0.919 0.960 0.000 0.040
#> GSM381233 1 0.1031 0.919 0.976 0.000 0.024
#> GSM381234 1 0.1529 0.919 0.960 0.000 0.040
#> GSM381238 3 0.6976 0.771 0.236 0.064 0.700
#> GSM381239 3 0.6976 0.771 0.236 0.064 0.700
#> GSM381242 1 0.1031 0.919 0.976 0.000 0.024
#> GSM381247 2 0.2261 0.919 0.000 0.932 0.068
#> GSM381248 1 0.1529 0.919 0.960 0.000 0.040
#> GSM381249 1 0.1163 0.921 0.972 0.000 0.028
#> GSM381253 1 0.1031 0.919 0.976 0.000 0.024
#> GSM381255 2 0.0000 0.997 0.000 1.000 0.000
#> GSM381258 1 0.1753 0.901 0.952 0.000 0.048
#> GSM381262 1 0.2878 0.844 0.904 0.000 0.096
#> GSM381266 1 0.5835 0.252 0.660 0.000 0.340
#> GSM381267 3 0.2680 0.627 0.008 0.068 0.924
#> GSM381269 1 0.1163 0.917 0.972 0.000 0.028
#> GSM381273 3 0.6026 0.529 0.376 0.000 0.624
#> GSM381274 2 0.0000 0.997 0.000 1.000 0.000
#> GSM381276 1 0.0237 0.922 0.996 0.000 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM381194 1 0.7003 0.0789 0.460 0.000 0.424 0.116
#> GSM381199 2 0.0336 0.9689 0.000 0.992 0.008 0.000
#> GSM381205 2 0.1867 0.9603 0.000 0.928 0.072 0.000
#> GSM381211 2 0.1867 0.9603 0.000 0.928 0.072 0.000
#> GSM381220 2 0.0188 0.9693 0.000 0.996 0.004 0.000
#> GSM381222 1 0.1022 0.8214 0.968 0.000 0.032 0.000
#> GSM381224 1 0.1209 0.8199 0.964 0.000 0.032 0.004
#> GSM381232 4 0.0469 0.8260 0.012 0.000 0.000 0.988
#> GSM381240 1 0.0000 0.8261 1.000 0.000 0.000 0.000
#> GSM381250 1 0.4713 0.4779 0.640 0.000 0.360 0.000
#> GSM381252 2 0.1867 0.9603 0.000 0.928 0.072 0.000
#> GSM381254 1 0.0000 0.8261 1.000 0.000 0.000 0.000
#> GSM381256 2 0.0000 0.9693 0.000 1.000 0.000 0.000
#> GSM381257 1 0.0000 0.8261 1.000 0.000 0.000 0.000
#> GSM381259 1 0.0000 0.8261 1.000 0.000 0.000 0.000
#> GSM381260 1 0.5028 0.4168 0.596 0.000 0.400 0.004
#> GSM381261 2 0.0336 0.9689 0.000 0.992 0.008 0.000
#> GSM381263 1 0.4843 0.4459 0.604 0.000 0.396 0.000
#> GSM381265 1 0.0000 0.8261 1.000 0.000 0.000 0.000
#> GSM381268 1 0.4830 0.4520 0.608 0.000 0.392 0.000
#> GSM381270 2 0.0336 0.9689 0.000 0.992 0.008 0.000
#> GSM381271 4 0.0000 0.8341 0.000 0.000 0.000 1.000
#> GSM381275 2 0.0336 0.9689 0.000 0.992 0.008 0.000
#> GSM381279 2 0.0336 0.9689 0.000 0.992 0.008 0.000
#> GSM381195 1 0.0000 0.8261 1.000 0.000 0.000 0.000
#> GSM381196 1 0.0188 0.8254 0.996 0.000 0.004 0.000
#> GSM381198 2 0.1867 0.9603 0.000 0.928 0.072 0.000
#> GSM381200 2 0.0336 0.9689 0.000 0.992 0.008 0.000
#> GSM381201 3 0.2773 0.7290 0.004 0.000 0.880 0.116
#> GSM381203 1 0.0336 0.8241 0.992 0.000 0.008 0.000
#> GSM381204 1 0.0000 0.8261 1.000 0.000 0.000 0.000
#> GSM381209 1 0.0000 0.8261 1.000 0.000 0.000 0.000
#> GSM381212 1 0.0000 0.8261 1.000 0.000 0.000 0.000
#> GSM381213 2 0.1118 0.9660 0.000 0.964 0.036 0.000
#> GSM381214 2 0.1867 0.9603 0.000 0.928 0.072 0.000
#> GSM381216 1 0.5268 0.4394 0.592 0.000 0.396 0.012
#> GSM381225 3 0.7043 0.1829 0.368 0.000 0.504 0.128
#> GSM381231 4 0.0000 0.8341 0.000 0.000 0.000 1.000
#> GSM381235 1 0.4560 0.5938 0.700 0.000 0.296 0.004
#> GSM381237 1 0.0000 0.8261 1.000 0.000 0.000 0.000
#> GSM381241 2 0.1867 0.9603 0.000 0.928 0.072 0.000
#> GSM381243 2 0.0336 0.9689 0.000 0.992 0.008 0.000
#> GSM381245 1 0.0188 0.8243 0.996 0.000 0.004 0.000
#> GSM381246 2 0.1867 0.9603 0.000 0.928 0.072 0.000
#> GSM381251 3 0.2773 0.7290 0.004 0.000 0.880 0.116
#> GSM381264 1 0.0000 0.8261 1.000 0.000 0.000 0.000
#> GSM381206 2 0.1867 0.9603 0.000 0.928 0.072 0.000
#> GSM381217 1 0.4328 0.6505 0.748 0.000 0.244 0.008
#> GSM381218 2 0.1867 0.9603 0.000 0.928 0.072 0.000
#> GSM381226 2 0.0188 0.9693 0.000 0.996 0.004 0.000
#> GSM381227 2 0.0336 0.9689 0.000 0.992 0.008 0.000
#> GSM381228 4 0.0000 0.8341 0.000 0.000 0.000 1.000
#> GSM381236 4 0.0000 0.8341 0.000 0.000 0.000 1.000
#> GSM381244 3 0.2773 0.7290 0.004 0.000 0.880 0.116
#> GSM381272 4 0.0000 0.8341 0.000 0.000 0.000 1.000
#> GSM381277 1 0.0000 0.8261 1.000 0.000 0.000 0.000
#> GSM381278 4 0.7841 -0.3117 0.356 0.000 0.264 0.380
#> GSM381197 3 0.2773 0.7290 0.004 0.000 0.880 0.116
#> GSM381202 1 0.0592 0.8249 0.984 0.000 0.016 0.000
#> GSM381207 1 0.0817 0.8238 0.976 0.000 0.024 0.000
#> GSM381208 4 0.4585 0.5308 0.000 0.000 0.332 0.668
#> GSM381210 1 0.0817 0.8238 0.976 0.000 0.024 0.000
#> GSM381215 1 0.4877 0.4368 0.592 0.000 0.408 0.000
#> GSM381219 2 0.1792 0.9611 0.000 0.932 0.068 0.000
#> GSM381221 2 0.0188 0.9693 0.000 0.996 0.004 0.000
#> GSM381223 2 0.0336 0.9689 0.000 0.992 0.008 0.000
#> GSM381229 3 0.5434 0.6518 0.132 0.000 0.740 0.128
#> GSM381230 1 0.0921 0.8227 0.972 0.000 0.028 0.000
#> GSM381233 1 0.1022 0.8214 0.968 0.000 0.032 0.000
#> GSM381234 1 0.0000 0.8261 1.000 0.000 0.000 0.000
#> GSM381238 4 0.0592 0.8216 0.016 0.000 0.000 0.984
#> GSM381239 4 0.0336 0.8311 0.000 0.000 0.008 0.992
#> GSM381242 1 0.5080 0.4037 0.576 0.000 0.420 0.004
#> GSM381247 2 0.0336 0.9689 0.000 0.992 0.008 0.000
#> GSM381248 1 0.0188 0.8243 0.996 0.000 0.004 0.000
#> GSM381249 1 0.1022 0.8214 0.968 0.000 0.032 0.000
#> GSM381253 1 0.0817 0.8238 0.976 0.000 0.024 0.000
#> GSM381255 2 0.1867 0.9603 0.000 0.928 0.072 0.000
#> GSM381258 1 0.5550 0.3555 0.552 0.000 0.428 0.020
#> GSM381262 1 0.5888 0.3294 0.540 0.000 0.424 0.036
#> GSM381266 3 0.7527 0.3015 0.356 0.000 0.452 0.192
#> GSM381267 4 0.4585 0.5308 0.000 0.000 0.332 0.668
#> GSM381269 1 0.5435 0.3779 0.564 0.000 0.420 0.016
#> GSM381273 3 0.2831 0.7252 0.004 0.000 0.876 0.120
#> GSM381274 2 0.0336 0.9689 0.000 0.992 0.008 0.000
#> GSM381276 1 0.1118 0.8204 0.964 0.000 0.036 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM381194 3 0.7160 -0.051 0.388 0.000 0.436 0.108 0.068
#> GSM381199 2 0.1732 0.813 0.000 0.920 0.000 0.000 0.080
#> GSM381205 2 0.4210 0.794 0.000 0.588 0.000 0.000 0.412
#> GSM381211 2 0.4201 0.795 0.000 0.592 0.000 0.000 0.408
#> GSM381220 2 0.1851 0.817 0.000 0.912 0.000 0.000 0.088
#> GSM381222 1 0.2230 0.688 0.884 0.000 0.116 0.000 0.000
#> GSM381224 1 0.2612 0.683 0.868 0.000 0.124 0.008 0.000
#> GSM381232 4 0.0000 0.841 0.000 0.000 0.000 1.000 0.000
#> GSM381240 1 0.2074 0.667 0.896 0.000 0.000 0.000 0.104
#> GSM381250 1 0.4201 0.391 0.592 0.000 0.408 0.000 0.000
#> GSM381252 2 0.4192 0.797 0.000 0.596 0.000 0.000 0.404
#> GSM381254 1 0.0703 0.698 0.976 0.000 0.000 0.000 0.024
#> GSM381256 2 0.3305 0.820 0.000 0.776 0.000 0.000 0.224
#> GSM381257 1 0.0794 0.702 0.972 0.000 0.028 0.000 0.000
#> GSM381259 1 0.2074 0.667 0.896 0.000 0.000 0.000 0.104
#> GSM381260 1 0.4549 0.304 0.528 0.000 0.464 0.000 0.008
#> GSM381261 2 0.1410 0.778 0.000 0.940 0.000 0.000 0.060
#> GSM381263 1 0.4907 0.252 0.492 0.000 0.484 0.000 0.024
#> GSM381265 1 0.2074 0.667 0.896 0.000 0.000 0.000 0.104
#> GSM381268 1 0.5103 0.284 0.512 0.000 0.452 0.000 0.036
#> GSM381270 2 0.0880 0.792 0.000 0.968 0.000 0.000 0.032
#> GSM381271 4 0.0000 0.841 0.000 0.000 0.000 1.000 0.000
#> GSM381275 2 0.1121 0.788 0.000 0.956 0.000 0.000 0.044
#> GSM381279 2 0.0703 0.799 0.000 0.976 0.000 0.000 0.024
#> GSM381195 1 0.0992 0.698 0.968 0.000 0.008 0.000 0.024
#> GSM381196 1 0.3816 0.534 0.696 0.000 0.304 0.000 0.000
#> GSM381198 2 0.4210 0.794 0.000 0.588 0.000 0.000 0.412
#> GSM381200 2 0.3636 0.818 0.000 0.728 0.000 0.000 0.272
#> GSM381201 3 0.6222 0.192 0.016 0.000 0.528 0.100 0.356
#> GSM381203 1 0.3932 0.508 0.672 0.000 0.328 0.000 0.000
#> GSM381204 1 0.2074 0.667 0.896 0.000 0.000 0.000 0.104
#> GSM381209 1 0.2358 0.666 0.888 0.000 0.008 0.000 0.104
#> GSM381212 1 0.2358 0.666 0.888 0.000 0.008 0.000 0.104
#> GSM381213 2 0.2852 0.821 0.000 0.828 0.000 0.000 0.172
#> GSM381214 2 0.4201 0.795 0.000 0.592 0.000 0.000 0.408
#> GSM381216 1 0.4747 0.278 0.496 0.000 0.488 0.016 0.000
#> GSM381225 3 0.6650 0.117 0.324 0.000 0.536 0.060 0.080
#> GSM381231 4 0.0000 0.841 0.000 0.000 0.000 1.000 0.000
#> GSM381235 1 0.4989 0.336 0.520 0.000 0.456 0.016 0.008
#> GSM381237 1 0.2074 0.667 0.896 0.000 0.000 0.000 0.104
#> GSM381241 2 0.4201 0.795 0.000 0.592 0.000 0.000 0.408
#> GSM381243 2 0.0880 0.795 0.000 0.968 0.000 0.000 0.032
#> GSM381245 1 0.1041 0.702 0.964 0.000 0.032 0.000 0.004
#> GSM381246 2 0.4182 0.799 0.000 0.600 0.000 0.000 0.400
#> GSM381251 3 0.5783 0.198 0.000 0.000 0.540 0.100 0.360
#> GSM381264 1 0.2074 0.667 0.896 0.000 0.000 0.000 0.104
#> GSM381206 2 0.4182 0.798 0.000 0.600 0.000 0.000 0.400
#> GSM381217 1 0.4689 0.404 0.560 0.000 0.424 0.016 0.000
#> GSM381218 2 0.4210 0.794 0.000 0.588 0.000 0.000 0.412
#> GSM381226 2 0.1851 0.821 0.000 0.912 0.000 0.000 0.088
#> GSM381227 2 0.1043 0.809 0.000 0.960 0.000 0.000 0.040
#> GSM381228 4 0.0000 0.841 0.000 0.000 0.000 1.000 0.000
#> GSM381236 4 0.0000 0.841 0.000 0.000 0.000 1.000 0.000
#> GSM381244 3 0.6375 0.186 0.024 0.000 0.524 0.100 0.352
#> GSM381272 4 0.0000 0.841 0.000 0.000 0.000 1.000 0.000
#> GSM381277 1 0.0703 0.702 0.976 0.000 0.024 0.000 0.000
#> GSM381278 4 0.8026 -0.256 0.188 0.000 0.320 0.380 0.112
#> GSM381197 3 0.5986 0.195 0.016 0.000 0.596 0.100 0.288
#> GSM381202 1 0.3039 0.647 0.808 0.000 0.192 0.000 0.000
#> GSM381207 1 0.1671 0.697 0.924 0.000 0.076 0.000 0.000
#> GSM381208 4 0.5119 0.510 0.000 0.000 0.360 0.592 0.048
#> GSM381210 1 0.3255 0.675 0.848 0.000 0.052 0.000 0.100
#> GSM381215 1 0.5368 0.239 0.480 0.000 0.476 0.008 0.036
#> GSM381219 2 0.4126 0.802 0.000 0.620 0.000 0.000 0.380
#> GSM381221 2 0.2074 0.823 0.000 0.896 0.000 0.000 0.104
#> GSM381223 2 0.1270 0.788 0.000 0.948 0.000 0.000 0.052
#> GSM381229 3 0.6380 0.317 0.108 0.000 0.652 0.132 0.108
#> GSM381230 1 0.3506 0.669 0.832 0.000 0.064 0.000 0.104
#> GSM381233 1 0.2929 0.663 0.820 0.000 0.180 0.000 0.000
#> GSM381234 1 0.1197 0.691 0.952 0.000 0.000 0.000 0.048
#> GSM381238 4 0.0000 0.841 0.000 0.000 0.000 1.000 0.000
#> GSM381239 4 0.0510 0.833 0.000 0.000 0.016 0.984 0.000
#> GSM381242 3 0.4706 -0.331 0.492 0.000 0.496 0.004 0.008
#> GSM381247 2 0.1341 0.780 0.000 0.944 0.000 0.000 0.056
#> GSM381248 1 0.1357 0.700 0.948 0.000 0.048 0.004 0.000
#> GSM381249 1 0.2389 0.688 0.880 0.000 0.116 0.000 0.004
#> GSM381253 1 0.4015 0.514 0.652 0.000 0.348 0.000 0.000
#> GSM381255 2 0.4171 0.797 0.000 0.604 0.000 0.000 0.396
#> GSM381258 3 0.5898 -0.201 0.444 0.000 0.484 0.044 0.028
#> GSM381262 3 0.6362 -0.205 0.440 0.000 0.456 0.040 0.064
#> GSM381266 3 0.8380 0.315 0.272 0.000 0.352 0.172 0.204
#> GSM381267 4 0.5168 0.510 0.000 0.000 0.356 0.592 0.052
#> GSM381269 1 0.4989 0.303 0.520 0.000 0.456 0.016 0.008
#> GSM381273 3 0.6006 0.182 0.004 0.000 0.496 0.100 0.400
#> GSM381274 2 0.1197 0.790 0.000 0.952 0.000 0.000 0.048
#> GSM381276 1 0.4375 0.493 0.628 0.000 0.364 0.004 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM381194 3 0.2189 0.7249 0.028 0.000 0.916 0.024 0.028 0.004
#> GSM381199 6 0.3717 0.5384 0.000 0.384 0.000 0.000 0.000 0.616
#> GSM381205 2 0.0000 0.7906 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381211 2 0.0458 0.7863 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM381220 2 0.3851 -0.1302 0.000 0.540 0.000 0.000 0.000 0.460
#> GSM381222 3 0.3864 -0.1484 0.480 0.000 0.520 0.000 0.000 0.000
#> GSM381224 3 0.3804 -0.0612 0.424 0.000 0.576 0.000 0.000 0.000
#> GSM381232 4 0.0000 0.8854 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381240 1 0.0260 0.7939 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM381250 3 0.2969 0.7540 0.224 0.000 0.776 0.000 0.000 0.000
#> GSM381252 2 0.0000 0.7906 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381254 1 0.2454 0.7245 0.840 0.000 0.160 0.000 0.000 0.000
#> GSM381256 6 0.3854 0.2339 0.000 0.464 0.000 0.000 0.000 0.536
#> GSM381257 1 0.3684 0.4404 0.628 0.000 0.372 0.000 0.000 0.000
#> GSM381259 1 0.0458 0.7971 0.984 0.000 0.016 0.000 0.000 0.000
#> GSM381260 3 0.3078 0.7612 0.192 0.000 0.796 0.000 0.012 0.000
#> GSM381261 6 0.2135 0.6849 0.000 0.128 0.000 0.000 0.000 0.872
#> GSM381263 3 0.3230 0.7620 0.212 0.000 0.776 0.000 0.012 0.000
#> GSM381265 1 0.0260 0.7939 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM381268 3 0.2793 0.7626 0.200 0.000 0.800 0.000 0.000 0.000
#> GSM381270 6 0.3620 0.5547 0.000 0.352 0.000 0.000 0.000 0.648
#> GSM381271 4 0.0000 0.8854 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381275 6 0.2664 0.6908 0.000 0.184 0.000 0.000 0.000 0.816
#> GSM381279 6 0.3695 0.5287 0.000 0.376 0.000 0.000 0.000 0.624
#> GSM381195 1 0.2219 0.7429 0.864 0.000 0.136 0.000 0.000 0.000
#> GSM381196 3 0.2941 0.7581 0.220 0.000 0.780 0.000 0.000 0.000
#> GSM381198 2 0.1007 0.7493 0.000 0.956 0.000 0.000 0.000 0.044
#> GSM381200 2 0.2260 0.6632 0.000 0.860 0.000 0.000 0.000 0.140
#> GSM381201 5 0.0767 0.9872 0.012 0.000 0.008 0.004 0.976 0.000
#> GSM381203 3 0.2597 0.7664 0.176 0.000 0.824 0.000 0.000 0.000
#> GSM381204 1 0.0458 0.7971 0.984 0.000 0.016 0.000 0.000 0.000
#> GSM381209 1 0.0458 0.7960 0.984 0.000 0.016 0.000 0.000 0.000
#> GSM381212 1 0.0363 0.7961 0.988 0.000 0.012 0.000 0.000 0.000
#> GSM381213 2 0.3804 0.0105 0.000 0.576 0.000 0.000 0.000 0.424
#> GSM381214 2 0.0363 0.7872 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM381216 3 0.1511 0.7498 0.044 0.000 0.940 0.004 0.012 0.000
#> GSM381225 3 0.2711 0.7075 0.036 0.000 0.884 0.016 0.060 0.004
#> GSM381231 4 0.0000 0.8854 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381235 3 0.1578 0.7478 0.048 0.000 0.936 0.004 0.012 0.000
#> GSM381237 1 0.0458 0.7971 0.984 0.000 0.016 0.000 0.000 0.000
#> GSM381241 2 0.0000 0.7906 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381243 6 0.3620 0.5547 0.000 0.352 0.000 0.000 0.000 0.648
#> GSM381245 1 0.3515 0.5220 0.676 0.000 0.324 0.000 0.000 0.000
#> GSM381246 2 0.0146 0.7899 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM381251 5 0.0935 0.9754 0.000 0.000 0.032 0.004 0.964 0.000
#> GSM381264 1 0.0458 0.7971 0.984 0.000 0.016 0.000 0.000 0.000
#> GSM381206 2 0.0000 0.7906 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381217 3 0.1477 0.7492 0.048 0.000 0.940 0.004 0.008 0.000
#> GSM381218 2 0.0146 0.7903 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM381226 2 0.3737 -0.0468 0.000 0.608 0.000 0.000 0.000 0.392
#> GSM381227 6 0.3817 0.4283 0.000 0.432 0.000 0.000 0.000 0.568
#> GSM381228 4 0.0000 0.8854 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381236 4 0.0000 0.8854 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381244 5 0.0870 0.9857 0.012 0.000 0.012 0.004 0.972 0.000
#> GSM381272 4 0.0000 0.8854 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381277 1 0.3647 0.4618 0.640 0.000 0.360 0.000 0.000 0.000
#> GSM381278 3 0.5388 0.2923 0.024 0.000 0.612 0.284 0.076 0.004
#> GSM381197 5 0.0767 0.9872 0.012 0.000 0.008 0.004 0.976 0.000
#> GSM381202 3 0.3023 0.7381 0.232 0.000 0.768 0.000 0.000 0.000
#> GSM381207 1 0.3774 0.3943 0.592 0.000 0.408 0.000 0.000 0.000
#> GSM381208 4 0.5441 0.2512 0.008 0.000 0.008 0.516 0.396 0.072
#> GSM381210 1 0.1141 0.7920 0.948 0.000 0.052 0.000 0.000 0.000
#> GSM381215 3 0.2416 0.7745 0.156 0.000 0.844 0.000 0.000 0.000
#> GSM381219 2 0.1610 0.7272 0.000 0.916 0.000 0.000 0.000 0.084
#> GSM381221 2 0.3804 -0.1525 0.000 0.576 0.000 0.000 0.000 0.424
#> GSM381223 6 0.2664 0.6908 0.000 0.184 0.000 0.000 0.000 0.816
#> GSM381229 3 0.5780 0.2756 0.144 0.000 0.488 0.008 0.360 0.000
#> GSM381230 1 0.0790 0.7948 0.968 0.000 0.032 0.000 0.000 0.000
#> GSM381233 3 0.2996 0.7378 0.228 0.000 0.772 0.000 0.000 0.000
#> GSM381234 1 0.1267 0.7855 0.940 0.000 0.060 0.000 0.000 0.000
#> GSM381238 4 0.0146 0.8827 0.000 0.000 0.004 0.996 0.000 0.000
#> GSM381239 4 0.0547 0.8736 0.000 0.000 0.000 0.980 0.020 0.000
#> GSM381242 3 0.2980 0.7685 0.180 0.000 0.808 0.000 0.012 0.000
#> GSM381247 6 0.1700 0.6621 0.000 0.080 0.000 0.000 0.004 0.916
#> GSM381248 1 0.3728 0.4957 0.652 0.000 0.344 0.000 0.004 0.000
#> GSM381249 1 0.3867 0.1168 0.512 0.000 0.488 0.000 0.000 0.000
#> GSM381253 3 0.2996 0.7520 0.228 0.000 0.772 0.000 0.000 0.000
#> GSM381255 2 0.0363 0.7872 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM381258 3 0.2653 0.7733 0.100 0.000 0.868 0.004 0.028 0.000
#> GSM381262 3 0.2450 0.7555 0.064 0.000 0.896 0.012 0.024 0.004
#> GSM381266 3 0.5680 0.5304 0.144 0.000 0.572 0.016 0.268 0.000
#> GSM381267 4 0.5441 0.2512 0.008 0.000 0.008 0.516 0.396 0.072
#> GSM381269 3 0.2631 0.7772 0.128 0.000 0.856 0.004 0.012 0.000
#> GSM381273 5 0.1036 0.9830 0.008 0.000 0.024 0.004 0.964 0.000
#> GSM381274 6 0.2823 0.6828 0.000 0.204 0.000 0.000 0.000 0.796
#> GSM381276 3 0.2378 0.7643 0.152 0.000 0.848 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 other(p) k
#> CV:mclust 86 0.303 2
#> CV:mclust 82 0.168 3
#> CV:mclust 72 0.412 4
#> CV:mclust 63 0.268 5
#> CV:mclust 69 0.113 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 86 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.976 0.973 0.987 0.4446 0.564 0.564
#> 3 3 0.990 0.963 0.978 0.4845 0.773 0.598
#> 4 4 0.826 0.746 0.869 0.0810 0.958 0.876
#> 5 5 0.837 0.831 0.904 0.0525 0.937 0.796
#> 6 6 0.826 0.801 0.890 0.0457 0.922 0.720
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
#> GSM381194 1 0.0000 0.980 1.000 0.000
#> GSM381199 2 0.0000 1.000 0.000 1.000
#> GSM381205 2 0.0000 1.000 0.000 1.000
#> GSM381211 2 0.0000 1.000 0.000 1.000
#> GSM381220 2 0.0000 1.000 0.000 1.000
#> GSM381222 1 0.0000 0.980 1.000 0.000
#> GSM381224 1 0.0000 0.980 1.000 0.000
#> GSM381232 1 0.6531 0.815 0.832 0.168
#> GSM381240 1 0.0000 0.980 1.000 0.000
#> GSM381250 1 0.0000 0.980 1.000 0.000
#> GSM381252 2 0.0000 1.000 0.000 1.000
#> GSM381254 1 0.0000 0.980 1.000 0.000
#> GSM381256 2 0.0000 1.000 0.000 1.000
#> GSM381257 1 0.0000 0.980 1.000 0.000
#> GSM381259 1 0.0000 0.980 1.000 0.000
#> GSM381260 1 0.0000 0.980 1.000 0.000
#> GSM381261 2 0.0000 1.000 0.000 1.000
#> GSM381263 1 0.0000 0.980 1.000 0.000
#> GSM381265 1 0.0000 0.980 1.000 0.000
#> GSM381268 1 0.0000 0.980 1.000 0.000
#> GSM381270 2 0.0000 1.000 0.000 1.000
#> GSM381271 1 0.2043 0.955 0.968 0.032
#> GSM381275 2 0.0000 1.000 0.000 1.000
#> GSM381279 2 0.0000 1.000 0.000 1.000
#> GSM381195 1 0.0000 0.980 1.000 0.000
#> GSM381196 1 0.0000 0.980 1.000 0.000
#> GSM381198 2 0.0000 1.000 0.000 1.000
#> GSM381200 2 0.0000 1.000 0.000 1.000
#> GSM381201 1 0.0000 0.980 1.000 0.000
#> GSM381203 1 0.0000 0.980 1.000 0.000
#> GSM381204 1 0.0000 0.980 1.000 0.000
#> GSM381209 1 0.0000 0.980 1.000 0.000
#> GSM381212 1 0.0000 0.980 1.000 0.000
#> GSM381213 2 0.0000 1.000 0.000 1.000
#> GSM381214 2 0.0000 1.000 0.000 1.000
#> GSM381216 1 0.0000 0.980 1.000 0.000
#> GSM381225 1 0.0000 0.980 1.000 0.000
#> GSM381231 1 0.6887 0.795 0.816 0.184
#> GSM381235 1 0.0000 0.980 1.000 0.000
#> GSM381237 1 0.0000 0.980 1.000 0.000
#> GSM381241 2 0.0000 1.000 0.000 1.000
#> GSM381243 2 0.0000 1.000 0.000 1.000
#> GSM381245 1 0.0000 0.980 1.000 0.000
#> GSM381246 2 0.0000 1.000 0.000 1.000
#> GSM381251 1 0.0000 0.980 1.000 0.000
#> GSM381264 1 0.0000 0.980 1.000 0.000
#> GSM381206 2 0.0000 1.000 0.000 1.000
#> GSM381217 1 0.0000 0.980 1.000 0.000
#> GSM381218 2 0.0000 1.000 0.000 1.000
#> GSM381226 2 0.0000 1.000 0.000 1.000
#> GSM381227 2 0.0000 1.000 0.000 1.000
#> GSM381228 1 0.5519 0.863 0.872 0.128
#> GSM381236 1 0.5059 0.880 0.888 0.112
#> GSM381244 1 0.0000 0.980 1.000 0.000
#> GSM381272 1 0.2948 0.938 0.948 0.052
#> GSM381277 1 0.0000 0.980 1.000 0.000
#> GSM381278 1 0.0000 0.980 1.000 0.000
#> GSM381197 1 0.0000 0.980 1.000 0.000
#> GSM381202 1 0.0000 0.980 1.000 0.000
#> GSM381207 1 0.0000 0.980 1.000 0.000
#> GSM381208 1 0.0000 0.980 1.000 0.000
#> GSM381210 1 0.0000 0.980 1.000 0.000
#> GSM381215 1 0.0000 0.980 1.000 0.000
#> GSM381219 2 0.0000 1.000 0.000 1.000
#> GSM381221 2 0.0000 1.000 0.000 1.000
#> GSM381223 2 0.0000 1.000 0.000 1.000
#> GSM381229 1 0.0000 0.980 1.000 0.000
#> GSM381230 1 0.0000 0.980 1.000 0.000
#> GSM381233 1 0.0000 0.980 1.000 0.000
#> GSM381234 1 0.0000 0.980 1.000 0.000
#> GSM381238 1 0.8207 0.687 0.744 0.256
#> GSM381239 1 0.7139 0.779 0.804 0.196
#> GSM381242 1 0.0000 0.980 1.000 0.000
#> GSM381247 2 0.0000 1.000 0.000 1.000
#> GSM381248 1 0.0000 0.980 1.000 0.000
#> GSM381249 1 0.0000 0.980 1.000 0.000
#> GSM381253 1 0.0000 0.980 1.000 0.000
#> GSM381255 2 0.0000 1.000 0.000 1.000
#> GSM381258 1 0.0000 0.980 1.000 0.000
#> GSM381262 1 0.0000 0.980 1.000 0.000
#> GSM381266 1 0.0000 0.980 1.000 0.000
#> GSM381267 1 0.0938 0.971 0.988 0.012
#> GSM381269 1 0.0000 0.980 1.000 0.000
#> GSM381273 1 0.0000 0.980 1.000 0.000
#> GSM381274 2 0.0000 1.000 0.000 1.000
#> GSM381276 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
#> GSM381194 3 0.1529 0.946 0.040 0.000 0.960
#> GSM381199 2 0.0237 0.993 0.000 0.996 0.004
#> GSM381205 2 0.0237 0.994 0.004 0.996 0.000
#> GSM381211 2 0.0000 0.995 0.000 1.000 0.000
#> GSM381220 2 0.0000 0.995 0.000 1.000 0.000
#> GSM381222 1 0.0237 0.979 0.996 0.000 0.004
#> GSM381224 1 0.0000 0.978 1.000 0.000 0.000
#> GSM381232 3 0.0592 0.949 0.000 0.012 0.988
#> GSM381240 1 0.0000 0.978 1.000 0.000 0.000
#> GSM381250 1 0.1643 0.952 0.956 0.000 0.044
#> GSM381252 2 0.0237 0.994 0.004 0.996 0.000
#> GSM381254 1 0.0237 0.979 0.996 0.000 0.004
#> GSM381256 2 0.0000 0.995 0.000 1.000 0.000
#> GSM381257 1 0.0237 0.979 0.996 0.000 0.004
#> GSM381259 1 0.0000 0.978 1.000 0.000 0.000
#> GSM381260 1 0.0892 0.971 0.980 0.000 0.020
#> GSM381261 2 0.0000 0.995 0.000 1.000 0.000
#> GSM381263 1 0.1964 0.941 0.944 0.000 0.056
#> GSM381265 1 0.0237 0.979 0.996 0.000 0.004
#> GSM381268 3 0.1964 0.945 0.056 0.000 0.944
#> GSM381270 2 0.1163 0.976 0.000 0.972 0.028
#> GSM381271 3 0.0000 0.952 0.000 0.000 1.000
#> GSM381275 2 0.0237 0.994 0.004 0.996 0.000
#> GSM381279 2 0.1031 0.979 0.000 0.976 0.024
#> GSM381195 1 0.0237 0.979 0.996 0.000 0.004
#> GSM381196 1 0.4452 0.773 0.808 0.000 0.192
#> GSM381198 2 0.0237 0.994 0.004 0.996 0.000
#> GSM381200 2 0.0000 0.995 0.000 1.000 0.000
#> GSM381201 3 0.1289 0.956 0.032 0.000 0.968
#> GSM381203 1 0.0237 0.979 0.996 0.000 0.004
#> GSM381204 1 0.0000 0.978 1.000 0.000 0.000
#> GSM381209 1 0.0000 0.978 1.000 0.000 0.000
#> GSM381212 1 0.0000 0.978 1.000 0.000 0.000
#> GSM381213 2 0.0000 0.995 0.000 1.000 0.000
#> GSM381214 2 0.0000 0.995 0.000 1.000 0.000
#> GSM381216 1 0.0747 0.974 0.984 0.000 0.016
#> GSM381225 1 0.0592 0.976 0.988 0.000 0.012
#> GSM381231 3 0.0000 0.952 0.000 0.000 1.000
#> GSM381235 1 0.1163 0.964 0.972 0.000 0.028
#> GSM381237 1 0.0000 0.978 1.000 0.000 0.000
#> GSM381241 2 0.0000 0.995 0.000 1.000 0.000
#> GSM381243 2 0.1289 0.973 0.000 0.968 0.032
#> GSM381245 1 0.0237 0.979 0.996 0.000 0.004
#> GSM381246 2 0.0237 0.994 0.004 0.996 0.000
#> GSM381251 3 0.1289 0.956 0.032 0.000 0.968
#> GSM381264 1 0.0000 0.978 1.000 0.000 0.000
#> GSM381206 2 0.0237 0.994 0.004 0.996 0.000
#> GSM381217 1 0.0237 0.979 0.996 0.000 0.004
#> GSM381218 2 0.0000 0.995 0.000 1.000 0.000
#> GSM381226 2 0.0237 0.994 0.004 0.996 0.000
#> GSM381227 2 0.0000 0.995 0.000 1.000 0.000
#> GSM381228 3 0.0000 0.952 0.000 0.000 1.000
#> GSM381236 3 0.0000 0.952 0.000 0.000 1.000
#> GSM381244 3 0.1411 0.954 0.036 0.000 0.964
#> GSM381272 3 0.0237 0.951 0.000 0.004 0.996
#> GSM381277 1 0.0592 0.976 0.988 0.000 0.012
#> GSM381278 3 0.2796 0.907 0.092 0.000 0.908
#> GSM381197 3 0.1289 0.956 0.032 0.000 0.968
#> GSM381202 1 0.0237 0.979 0.996 0.000 0.004
#> GSM381207 1 0.0592 0.976 0.988 0.000 0.012
#> GSM381208 3 0.1289 0.956 0.032 0.000 0.968
#> GSM381210 1 0.0000 0.978 1.000 0.000 0.000
#> GSM381215 3 0.2448 0.923 0.076 0.000 0.924
#> GSM381219 2 0.0000 0.995 0.000 1.000 0.000
#> GSM381221 2 0.0000 0.995 0.000 1.000 0.000
#> GSM381223 2 0.0000 0.995 0.000 1.000 0.000
#> GSM381229 3 0.1289 0.956 0.032 0.000 0.968
#> GSM381230 1 0.0000 0.978 1.000 0.000 0.000
#> GSM381233 1 0.0237 0.979 0.996 0.000 0.004
#> GSM381234 1 0.0237 0.979 0.996 0.000 0.004
#> GSM381238 3 0.1289 0.938 0.000 0.032 0.968
#> GSM381239 3 0.0237 0.951 0.000 0.004 0.996
#> GSM381242 1 0.0747 0.974 0.984 0.000 0.016
#> GSM381247 2 0.1289 0.973 0.000 0.968 0.032
#> GSM381248 1 0.3192 0.882 0.888 0.000 0.112
#> GSM381249 1 0.0000 0.978 1.000 0.000 0.000
#> GSM381253 1 0.0747 0.974 0.984 0.000 0.016
#> GSM381255 2 0.0000 0.995 0.000 1.000 0.000
#> GSM381258 3 0.5058 0.705 0.244 0.000 0.756
#> GSM381262 3 0.4062 0.826 0.164 0.000 0.836
#> GSM381266 3 0.0000 0.952 0.000 0.000 1.000
#> GSM381267 3 0.1525 0.955 0.032 0.004 0.964
#> GSM381269 1 0.0424 0.977 0.992 0.000 0.008
#> GSM381273 3 0.1289 0.956 0.032 0.000 0.968
#> GSM381274 2 0.0000 0.995 0.000 1.000 0.000
#> GSM381276 1 0.4399 0.776 0.812 0.000 0.188
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM381194 3 0.0672 0.5080 0.008 0.000 0.984 0.008
#> GSM381199 2 0.0336 0.9681 0.000 0.992 0.008 0.000
#> GSM381205 2 0.0188 0.9688 0.000 0.996 0.004 0.000
#> GSM381211 2 0.0000 0.9704 0.000 1.000 0.000 0.000
#> GSM381220 2 0.0188 0.9691 0.000 0.996 0.004 0.000
#> GSM381222 1 0.1211 0.8867 0.960 0.000 0.040 0.000
#> GSM381224 1 0.0188 0.8947 0.996 0.000 0.004 0.000
#> GSM381232 4 0.4713 0.5268 0.000 0.000 0.360 0.640
#> GSM381240 1 0.0000 0.8950 1.000 0.000 0.000 0.000
#> GSM381250 1 0.5070 0.4183 0.620 0.000 0.372 0.008
#> GSM381252 2 0.0000 0.9704 0.000 1.000 0.000 0.000
#> GSM381254 1 0.0188 0.8943 0.996 0.000 0.004 0.000
#> GSM381256 2 0.0188 0.9693 0.000 0.996 0.004 0.000
#> GSM381257 1 0.0817 0.8904 0.976 0.000 0.024 0.000
#> GSM381259 1 0.0188 0.8943 0.996 0.000 0.004 0.000
#> GSM381260 1 0.2466 0.8517 0.900 0.000 0.096 0.004
#> GSM381261 2 0.0921 0.9564 0.000 0.972 0.028 0.000
#> GSM381263 1 0.5143 0.2095 0.540 0.000 0.456 0.004
#> GSM381265 1 0.0188 0.8943 0.996 0.000 0.004 0.000
#> GSM381268 3 0.7258 0.3476 0.328 0.000 0.508 0.164
#> GSM381270 2 0.2466 0.8916 0.000 0.900 0.096 0.004
#> GSM381271 4 0.4713 0.5268 0.000 0.000 0.360 0.640
#> GSM381275 2 0.0469 0.9661 0.000 0.988 0.012 0.000
#> GSM381279 2 0.1716 0.9266 0.000 0.936 0.064 0.000
#> GSM381195 1 0.0188 0.8943 0.996 0.000 0.004 0.000
#> GSM381196 1 0.5530 0.4275 0.632 0.000 0.336 0.032
#> GSM381198 2 0.0000 0.9704 0.000 1.000 0.000 0.000
#> GSM381200 2 0.0000 0.9704 0.000 1.000 0.000 0.000
#> GSM381201 4 0.3801 0.5172 0.000 0.000 0.220 0.780
#> GSM381203 1 0.1474 0.8796 0.948 0.000 0.052 0.000
#> GSM381204 1 0.0000 0.8950 1.000 0.000 0.000 0.000
#> GSM381209 1 0.0188 0.8943 0.996 0.000 0.004 0.000
#> GSM381212 1 0.0188 0.8943 0.996 0.000 0.004 0.000
#> GSM381213 2 0.0000 0.9704 0.000 1.000 0.000 0.000
#> GSM381214 2 0.0000 0.9704 0.000 1.000 0.000 0.000
#> GSM381216 1 0.4477 0.6138 0.688 0.000 0.312 0.000
#> GSM381225 3 0.5220 0.0766 0.424 0.000 0.568 0.008
#> GSM381231 4 0.4713 0.5268 0.000 0.000 0.360 0.640
#> GSM381235 1 0.4843 0.4419 0.604 0.000 0.396 0.000
#> GSM381237 1 0.0000 0.8950 1.000 0.000 0.000 0.000
#> GSM381241 2 0.0000 0.9704 0.000 1.000 0.000 0.000
#> GSM381243 2 0.2814 0.8522 0.000 0.868 0.132 0.000
#> GSM381245 1 0.0188 0.8943 0.996 0.000 0.004 0.000
#> GSM381246 2 0.0000 0.9704 0.000 1.000 0.000 0.000
#> GSM381251 4 0.3801 0.5172 0.000 0.000 0.220 0.780
#> GSM381264 1 0.0000 0.8950 1.000 0.000 0.000 0.000
#> GSM381206 2 0.0188 0.9688 0.000 0.996 0.004 0.000
#> GSM381217 1 0.3975 0.7171 0.760 0.000 0.240 0.000
#> GSM381218 2 0.0000 0.9704 0.000 1.000 0.000 0.000
#> GSM381226 2 0.0188 0.9693 0.000 0.996 0.004 0.000
#> GSM381227 2 0.0000 0.9704 0.000 1.000 0.000 0.000
#> GSM381228 4 0.4713 0.5268 0.000 0.000 0.360 0.640
#> GSM381236 4 0.4713 0.5268 0.000 0.000 0.360 0.640
#> GSM381244 4 0.3801 0.5172 0.000 0.000 0.220 0.780
#> GSM381272 4 0.4713 0.5268 0.000 0.000 0.360 0.640
#> GSM381277 1 0.0188 0.8943 0.996 0.000 0.004 0.000
#> GSM381278 3 0.2593 0.4394 0.004 0.000 0.892 0.104
#> GSM381197 4 0.3801 0.5172 0.000 0.000 0.220 0.780
#> GSM381202 1 0.1022 0.8881 0.968 0.000 0.032 0.000
#> GSM381207 1 0.0469 0.8930 0.988 0.000 0.012 0.000
#> GSM381208 4 0.3982 0.5137 0.000 0.004 0.220 0.776
#> GSM381210 1 0.0000 0.8950 1.000 0.000 0.000 0.000
#> GSM381215 3 0.3820 0.5099 0.064 0.000 0.848 0.088
#> GSM381219 2 0.0000 0.9704 0.000 1.000 0.000 0.000
#> GSM381221 2 0.0000 0.9704 0.000 1.000 0.000 0.000
#> GSM381223 2 0.1302 0.9467 0.000 0.956 0.044 0.000
#> GSM381229 4 0.4761 0.2218 0.000 0.000 0.372 0.628
#> GSM381230 1 0.0000 0.8950 1.000 0.000 0.000 0.000
#> GSM381233 1 0.1792 0.8752 0.932 0.000 0.068 0.000
#> GSM381234 1 0.0188 0.8943 0.996 0.000 0.004 0.000
#> GSM381238 4 0.4830 0.4830 0.000 0.000 0.392 0.608
#> GSM381239 4 0.4697 0.5265 0.000 0.000 0.356 0.644
#> GSM381242 1 0.3105 0.8192 0.856 0.000 0.140 0.004
#> GSM381247 2 0.4790 0.4950 0.000 0.620 0.380 0.000
#> GSM381248 1 0.1978 0.8468 0.928 0.000 0.004 0.068
#> GSM381249 1 0.0336 0.8941 0.992 0.000 0.008 0.000
#> GSM381253 1 0.2647 0.8382 0.880 0.000 0.120 0.000
#> GSM381255 2 0.0000 0.9704 0.000 1.000 0.000 0.000
#> GSM381258 3 0.2843 0.4682 0.020 0.000 0.892 0.088
#> GSM381262 3 0.2300 0.5081 0.016 0.000 0.920 0.064
#> GSM381266 3 0.4998 -0.4507 0.000 0.000 0.512 0.488
#> GSM381267 4 0.3801 0.5172 0.000 0.000 0.220 0.780
#> GSM381269 1 0.2921 0.8255 0.860 0.000 0.140 0.000
#> GSM381273 4 0.3801 0.5172 0.000 0.000 0.220 0.780
#> GSM381274 2 0.0336 0.9680 0.000 0.992 0.008 0.000
#> GSM381276 1 0.3577 0.7987 0.832 0.000 0.156 0.012
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM381194 3 0.2446 0.698 0.000 0.000 0.900 0.056 0.044
#> GSM381199 2 0.0290 0.962 0.000 0.992 0.008 0.000 0.000
#> GSM381205 2 0.0162 0.963 0.004 0.996 0.000 0.000 0.000
#> GSM381211 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM381220 2 0.0794 0.949 0.000 0.972 0.000 0.028 0.000
#> GSM381222 1 0.2416 0.826 0.888 0.000 0.100 0.000 0.012
#> GSM381224 1 0.1671 0.838 0.924 0.000 0.076 0.000 0.000
#> GSM381232 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM381240 1 0.0290 0.857 0.992 0.000 0.008 0.000 0.000
#> GSM381250 1 0.5353 0.390 0.600 0.000 0.328 0.000 0.072
#> GSM381252 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM381254 1 0.0865 0.853 0.972 0.000 0.000 0.004 0.024
#> GSM381256 2 0.0451 0.960 0.000 0.988 0.008 0.000 0.004
#> GSM381257 1 0.2953 0.819 0.868 0.000 0.100 0.028 0.004
#> GSM381259 1 0.0510 0.856 0.984 0.000 0.000 0.000 0.016
#> GSM381260 1 0.3336 0.716 0.772 0.000 0.228 0.000 0.000
#> GSM381261 2 0.2124 0.913 0.000 0.916 0.056 0.000 0.028
#> GSM381263 3 0.4893 0.309 0.404 0.000 0.568 0.000 0.028
#> GSM381265 1 0.0609 0.855 0.980 0.000 0.000 0.000 0.020
#> GSM381268 3 0.6400 0.539 0.292 0.000 0.544 0.012 0.152
#> GSM381270 2 0.2523 0.907 0.000 0.908 0.040 0.028 0.024
#> GSM381271 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM381275 2 0.1830 0.925 0.000 0.932 0.040 0.000 0.028
#> GSM381279 2 0.0162 0.963 0.000 0.996 0.004 0.000 0.000
#> GSM381195 1 0.0703 0.854 0.976 0.000 0.000 0.000 0.024
#> GSM381196 1 0.5309 0.542 0.656 0.000 0.240 0.000 0.104
#> GSM381198 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM381200 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM381201 5 0.2280 0.922 0.000 0.000 0.000 0.120 0.880
#> GSM381203 1 0.3954 0.722 0.772 0.000 0.192 0.000 0.036
#> GSM381204 1 0.0290 0.857 0.992 0.000 0.008 0.000 0.000
#> GSM381209 1 0.0162 0.858 0.996 0.000 0.000 0.000 0.004
#> GSM381212 1 0.0510 0.856 0.984 0.000 0.000 0.000 0.016
#> GSM381213 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM381214 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM381216 3 0.4114 0.701 0.176 0.000 0.776 0.004 0.044
#> GSM381225 3 0.4637 0.689 0.196 0.000 0.728 0.000 0.076
#> GSM381231 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM381235 3 0.2110 0.716 0.072 0.000 0.912 0.000 0.016
#> GSM381237 1 0.0162 0.858 0.996 0.000 0.004 0.000 0.000
#> GSM381241 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM381243 2 0.1399 0.937 0.000 0.952 0.020 0.028 0.000
#> GSM381245 1 0.0703 0.854 0.976 0.000 0.000 0.000 0.024
#> GSM381246 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM381251 5 0.1915 0.870 0.000 0.000 0.040 0.032 0.928
#> GSM381264 1 0.0703 0.854 0.976 0.000 0.000 0.000 0.024
#> GSM381206 2 0.0162 0.963 0.004 0.996 0.000 0.000 0.000
#> GSM381217 3 0.4210 0.309 0.412 0.000 0.588 0.000 0.000
#> GSM381218 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM381226 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM381227 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM381228 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM381236 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM381244 5 0.2280 0.922 0.000 0.000 0.000 0.120 0.880
#> GSM381272 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM381277 1 0.0404 0.857 0.988 0.000 0.000 0.012 0.000
#> GSM381278 3 0.2661 0.669 0.000 0.000 0.888 0.056 0.056
#> GSM381197 5 0.2280 0.922 0.000 0.000 0.000 0.120 0.880
#> GSM381202 1 0.2852 0.773 0.828 0.000 0.172 0.000 0.000
#> GSM381207 1 0.0609 0.855 0.980 0.000 0.000 0.000 0.020
#> GSM381208 5 0.2280 0.922 0.000 0.000 0.000 0.120 0.880
#> GSM381210 1 0.0880 0.853 0.968 0.000 0.032 0.000 0.000
#> GSM381215 3 0.3030 0.687 0.004 0.000 0.868 0.040 0.088
#> GSM381219 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM381221 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM381223 2 0.1877 0.917 0.000 0.924 0.064 0.000 0.012
#> GSM381229 5 0.2020 0.825 0.000 0.000 0.100 0.000 0.900
#> GSM381230 1 0.0566 0.858 0.984 0.000 0.004 0.000 0.012
#> GSM381233 1 0.3628 0.727 0.772 0.000 0.216 0.000 0.012
#> GSM381234 1 0.0703 0.854 0.976 0.000 0.000 0.000 0.024
#> GSM381238 4 0.0324 0.990 0.000 0.000 0.004 0.992 0.004
#> GSM381239 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM381242 1 0.4309 0.573 0.676 0.000 0.308 0.000 0.016
#> GSM381247 2 0.5051 0.146 0.000 0.492 0.480 0.024 0.004
#> GSM381248 1 0.1914 0.823 0.924 0.000 0.000 0.016 0.060
#> GSM381249 1 0.1732 0.836 0.920 0.000 0.080 0.000 0.000
#> GSM381253 1 0.4269 0.671 0.732 0.000 0.232 0.000 0.036
#> GSM381255 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM381258 3 0.2492 0.694 0.024 0.000 0.908 0.020 0.048
#> GSM381262 3 0.2408 0.681 0.000 0.000 0.892 0.016 0.092
#> GSM381266 5 0.5295 0.649 0.000 0.000 0.200 0.128 0.672
#> GSM381267 5 0.2280 0.922 0.000 0.000 0.000 0.120 0.880
#> GSM381269 1 0.5195 0.315 0.564 0.000 0.388 0.000 0.048
#> GSM381273 5 0.2280 0.922 0.000 0.000 0.000 0.120 0.880
#> GSM381274 2 0.0865 0.951 0.000 0.972 0.024 0.000 0.004
#> GSM381276 1 0.3878 0.692 0.748 0.000 0.236 0.016 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM381194 3 0.1225 0.728 0.000 0.000 0.952 0.012 0.000 0.036
#> GSM381199 2 0.0508 0.947 0.000 0.984 0.012 0.000 0.000 0.004
#> GSM381205 2 0.0146 0.953 0.004 0.996 0.000 0.000 0.000 0.000
#> GSM381211 2 0.0146 0.953 0.004 0.996 0.000 0.000 0.000 0.000
#> GSM381220 2 0.0713 0.940 0.000 0.972 0.000 0.028 0.000 0.000
#> GSM381222 1 0.3705 0.743 0.740 0.000 0.020 0.004 0.000 0.236
#> GSM381224 1 0.3217 0.728 0.768 0.000 0.008 0.000 0.000 0.224
#> GSM381232 4 0.0146 0.996 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM381240 1 0.2454 0.777 0.840 0.000 0.000 0.000 0.000 0.160
#> GSM381250 3 0.4858 0.524 0.228 0.000 0.652 0.000 0.000 0.120
#> GSM381252 2 0.0146 0.953 0.004 0.996 0.000 0.000 0.000 0.000
#> GSM381254 1 0.1625 0.763 0.928 0.000 0.012 0.000 0.000 0.060
#> GSM381256 2 0.0547 0.944 0.000 0.980 0.020 0.000 0.000 0.000
#> GSM381257 1 0.5189 0.611 0.652 0.000 0.152 0.012 0.000 0.184
#> GSM381259 1 0.1151 0.785 0.956 0.000 0.012 0.000 0.000 0.032
#> GSM381260 1 0.4569 0.525 0.624 0.000 0.036 0.008 0.000 0.332
#> GSM381261 2 0.3101 0.724 0.000 0.756 0.000 0.000 0.000 0.244
#> GSM381263 3 0.5362 0.396 0.184 0.000 0.588 0.000 0.000 0.228
#> GSM381265 1 0.0632 0.783 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM381268 3 0.1542 0.739 0.052 0.000 0.936 0.000 0.008 0.004
#> GSM381270 2 0.3488 0.720 0.000 0.744 0.000 0.004 0.008 0.244
#> GSM381271 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381275 2 0.3659 0.534 0.000 0.636 0.000 0.000 0.000 0.364
#> GSM381279 2 0.0291 0.952 0.000 0.992 0.000 0.004 0.000 0.004
#> GSM381195 1 0.0632 0.779 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM381196 3 0.3141 0.702 0.112 0.000 0.836 0.000 0.004 0.048
#> GSM381198 2 0.0146 0.953 0.004 0.996 0.000 0.000 0.000 0.000
#> GSM381200 2 0.0000 0.953 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381201 5 0.0405 0.991 0.000 0.000 0.004 0.008 0.988 0.000
#> GSM381203 3 0.4885 0.360 0.372 0.000 0.560 0.000 0.000 0.068
#> GSM381204 1 0.2178 0.789 0.868 0.000 0.000 0.000 0.000 0.132
#> GSM381209 1 0.1556 0.799 0.920 0.000 0.000 0.000 0.000 0.080
#> GSM381212 1 0.0547 0.796 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM381213 2 0.0146 0.953 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM381214 2 0.0146 0.953 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM381216 6 0.2579 0.727 0.088 0.004 0.032 0.000 0.000 0.876
#> GSM381225 3 0.1285 0.739 0.052 0.000 0.944 0.000 0.000 0.004
#> GSM381231 4 0.0146 0.996 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM381235 6 0.3672 0.628 0.056 0.000 0.168 0.000 0.000 0.776
#> GSM381237 1 0.2135 0.791 0.872 0.000 0.000 0.000 0.000 0.128
#> GSM381241 2 0.0146 0.953 0.004 0.996 0.000 0.000 0.000 0.000
#> GSM381243 2 0.0146 0.953 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM381245 1 0.0547 0.792 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM381246 2 0.0000 0.953 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381251 5 0.1007 0.955 0.000 0.000 0.044 0.000 0.956 0.000
#> GSM381264 1 0.1745 0.756 0.924 0.000 0.020 0.000 0.000 0.056
#> GSM381206 2 0.0146 0.953 0.004 0.996 0.000 0.000 0.000 0.000
#> GSM381217 1 0.4823 0.452 0.584 0.000 0.068 0.000 0.000 0.348
#> GSM381218 2 0.0146 0.953 0.004 0.996 0.000 0.000 0.000 0.000
#> GSM381226 2 0.0000 0.953 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381227 2 0.0146 0.953 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM381228 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381236 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381244 5 0.0363 0.989 0.000 0.000 0.000 0.012 0.988 0.000
#> GSM381272 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381277 1 0.2604 0.795 0.872 0.000 0.004 0.028 0.000 0.096
#> GSM381278 3 0.3650 0.533 0.000 0.000 0.708 0.000 0.012 0.280
#> GSM381197 5 0.0405 0.991 0.000 0.000 0.004 0.008 0.988 0.000
#> GSM381202 1 0.4011 0.610 0.672 0.000 0.024 0.000 0.000 0.304
#> GSM381207 1 0.0806 0.789 0.972 0.000 0.000 0.020 0.000 0.008
#> GSM381208 5 0.0363 0.989 0.000 0.000 0.000 0.012 0.988 0.000
#> GSM381210 1 0.3320 0.762 0.772 0.000 0.016 0.000 0.000 0.212
#> GSM381215 3 0.1674 0.727 0.000 0.000 0.924 0.004 0.004 0.068
#> GSM381219 2 0.0146 0.953 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM381221 2 0.0146 0.953 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM381223 2 0.1075 0.926 0.000 0.952 0.000 0.000 0.000 0.048
#> GSM381229 3 0.2092 0.694 0.000 0.000 0.876 0.000 0.124 0.000
#> GSM381230 1 0.1802 0.783 0.916 0.000 0.012 0.000 0.000 0.072
#> GSM381233 1 0.3990 0.677 0.676 0.000 0.016 0.000 0.004 0.304
#> GSM381234 1 0.0632 0.779 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM381238 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381239 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381242 6 0.4461 -0.124 0.464 0.000 0.020 0.004 0.000 0.512
#> GSM381247 2 0.2905 0.844 0.000 0.852 0.064 0.000 0.000 0.084
#> GSM381248 1 0.2882 0.651 0.848 0.000 0.004 0.000 0.120 0.028
#> GSM381249 1 0.3490 0.683 0.724 0.000 0.008 0.000 0.000 0.268
#> GSM381253 3 0.4601 0.472 0.312 0.000 0.628 0.000 0.000 0.060
#> GSM381255 2 0.0146 0.953 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM381258 6 0.1644 0.680 0.012 0.000 0.052 0.004 0.000 0.932
#> GSM381262 3 0.0935 0.723 0.000 0.000 0.964 0.000 0.004 0.032
#> GSM381266 3 0.3637 0.642 0.000 0.000 0.780 0.056 0.164 0.000
#> GSM381267 5 0.0405 0.991 0.000 0.000 0.004 0.008 0.988 0.000
#> GSM381269 6 0.2859 0.711 0.156 0.000 0.016 0.000 0.000 0.828
#> GSM381273 5 0.0405 0.991 0.000 0.000 0.004 0.008 0.988 0.000
#> GSM381274 2 0.1814 0.884 0.000 0.900 0.000 0.000 0.000 0.100
#> GSM381276 1 0.5312 0.563 0.632 0.000 0.068 0.040 0.000 0.260
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 other(p) k
#> CV:NMF 86 0.416 2
#> CV:NMF 86 0.153 3
#> CV:NMF 74 0.359 4
#> CV:NMF 81 0.199 5
#> CV:NMF 81 0.472 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 86 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.561 0.738 0.892 0.3856 0.583 0.583
#> 3 3 0.754 0.689 0.851 0.6701 0.590 0.411
#> 4 4 0.749 0.727 0.842 0.0876 0.791 0.528
#> 5 5 0.823 0.774 0.895 0.0829 0.873 0.606
#> 6 6 0.800 0.783 0.849 0.0483 0.925 0.705
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
#> GSM381194 2 0.1633 0.88985 0.024 0.976
#> GSM381199 2 0.0000 0.90200 0.000 1.000
#> GSM381205 2 0.0000 0.90200 0.000 1.000
#> GSM381211 2 0.0000 0.90200 0.000 1.000
#> GSM381220 2 0.0000 0.90200 0.000 1.000
#> GSM381222 1 0.9815 0.49412 0.580 0.420
#> GSM381224 1 0.9754 0.51941 0.592 0.408
#> GSM381232 2 0.0376 0.90129 0.004 0.996
#> GSM381240 1 0.8443 0.68602 0.728 0.272
#> GSM381250 2 0.4815 0.81396 0.104 0.896
#> GSM381252 2 0.0000 0.90200 0.000 1.000
#> GSM381254 1 0.3431 0.76088 0.936 0.064
#> GSM381256 2 0.0000 0.90200 0.000 1.000
#> GSM381257 1 0.4690 0.75023 0.900 0.100
#> GSM381259 1 0.0000 0.75652 1.000 0.000
#> GSM381260 2 0.9881 -0.02332 0.436 0.564
#> GSM381261 2 0.0000 0.90200 0.000 1.000
#> GSM381263 2 0.4815 0.81262 0.104 0.896
#> GSM381265 1 0.0000 0.75652 1.000 0.000
#> GSM381268 2 0.2236 0.88121 0.036 0.964
#> GSM381270 2 0.0000 0.90200 0.000 1.000
#> GSM381271 2 0.0376 0.90129 0.004 0.996
#> GSM381275 2 0.0000 0.90200 0.000 1.000
#> GSM381279 2 0.0000 0.90200 0.000 1.000
#> GSM381195 1 0.0000 0.75652 1.000 0.000
#> GSM381196 2 0.5294 0.79379 0.120 0.880
#> GSM381198 2 0.0000 0.90200 0.000 1.000
#> GSM381200 2 0.0000 0.90200 0.000 1.000
#> GSM381201 2 0.2236 0.88121 0.036 0.964
#> GSM381203 2 0.8861 0.48845 0.304 0.696
#> GSM381204 1 0.0000 0.75652 1.000 0.000
#> GSM381209 1 0.0672 0.75789 0.992 0.008
#> GSM381212 1 0.0000 0.75652 1.000 0.000
#> GSM381213 2 0.0000 0.90200 0.000 1.000
#> GSM381214 2 0.0000 0.90200 0.000 1.000
#> GSM381216 2 0.9866 -0.00741 0.432 0.568
#> GSM381225 2 0.2948 0.86758 0.052 0.948
#> GSM381231 2 0.0376 0.90129 0.004 0.996
#> GSM381235 2 0.9775 0.07072 0.412 0.588
#> GSM381237 1 0.0000 0.75652 1.000 0.000
#> GSM381241 2 0.0000 0.90200 0.000 1.000
#> GSM381243 2 0.0000 0.90200 0.000 1.000
#> GSM381245 1 0.8499 0.68352 0.724 0.276
#> GSM381246 2 0.0000 0.90200 0.000 1.000
#> GSM381251 2 0.1414 0.89243 0.020 0.980
#> GSM381264 1 0.0000 0.75652 1.000 0.000
#> GSM381206 2 0.0000 0.90200 0.000 1.000
#> GSM381217 2 0.8861 0.43656 0.304 0.696
#> GSM381218 2 0.0000 0.90200 0.000 1.000
#> GSM381226 2 0.0000 0.90200 0.000 1.000
#> GSM381227 2 0.0000 0.90200 0.000 1.000
#> GSM381228 2 0.0376 0.90129 0.004 0.996
#> GSM381236 2 0.0376 0.90129 0.004 0.996
#> GSM381244 1 0.9286 0.61358 0.656 0.344
#> GSM381272 2 0.0376 0.90129 0.004 0.996
#> GSM381277 1 0.9993 0.31809 0.516 0.484
#> GSM381278 2 0.0376 0.90129 0.004 0.996
#> GSM381197 2 0.9909 -0.05418 0.444 0.556
#> GSM381202 2 0.9909 -0.05724 0.444 0.556
#> GSM381207 1 0.8861 0.65884 0.696 0.304
#> GSM381208 2 0.0000 0.90200 0.000 1.000
#> GSM381210 1 0.8555 0.68041 0.720 0.280
#> GSM381215 2 0.4562 0.82351 0.096 0.904
#> GSM381219 2 0.0000 0.90200 0.000 1.000
#> GSM381221 2 0.0000 0.90200 0.000 1.000
#> GSM381223 2 0.0000 0.90200 0.000 1.000
#> GSM381229 2 0.1414 0.89243 0.020 0.980
#> GSM381230 1 0.0000 0.75652 1.000 0.000
#> GSM381233 1 0.9815 0.49412 0.580 0.420
#> GSM381234 1 0.3584 0.76058 0.932 0.068
#> GSM381238 2 0.0376 0.90129 0.004 0.996
#> GSM381239 2 0.0376 0.90129 0.004 0.996
#> GSM381242 2 0.9881 -0.02332 0.436 0.564
#> GSM381247 2 0.0000 0.90200 0.000 1.000
#> GSM381248 1 0.4431 0.75234 0.908 0.092
#> GSM381249 1 0.9866 0.46583 0.568 0.432
#> GSM381253 2 0.4815 0.81396 0.104 0.896
#> GSM381255 2 0.0000 0.90200 0.000 1.000
#> GSM381258 2 0.9710 0.11900 0.400 0.600
#> GSM381262 2 0.1414 0.89243 0.020 0.980
#> GSM381266 2 0.0376 0.90129 0.004 0.996
#> GSM381267 2 0.0000 0.90200 0.000 1.000
#> GSM381269 1 0.9881 0.45665 0.564 0.436
#> GSM381273 2 0.1414 0.89243 0.020 0.980
#> GSM381274 2 0.0000 0.90200 0.000 1.000
#> GSM381276 1 0.9993 0.31809 0.516 0.484
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM381194 1 0.6154 0.675 0.592 0 0.408
#> GSM381199 2 0.0000 1.000 0.000 1 0.000
#> GSM381205 2 0.0000 1.000 0.000 1 0.000
#> GSM381211 2 0.0000 1.000 0.000 1 0.000
#> GSM381220 2 0.0000 1.000 0.000 1 0.000
#> GSM381222 1 0.3879 0.157 0.848 0 0.152
#> GSM381224 1 0.4291 0.107 0.820 0 0.180
#> GSM381232 1 0.6215 0.670 0.572 0 0.428
#> GSM381240 1 0.5560 -0.378 0.700 0 0.300
#> GSM381250 1 0.5760 0.668 0.672 0 0.328
#> GSM381252 2 0.0000 1.000 0.000 1 0.000
#> GSM381254 3 0.6309 0.891 0.496 0 0.504
#> GSM381256 2 0.0000 1.000 0.000 1 0.000
#> GSM381257 1 0.6295 -0.845 0.528 0 0.472
#> GSM381259 3 0.6215 0.966 0.428 0 0.572
#> GSM381260 1 0.0592 0.458 0.988 0 0.012
#> GSM381261 2 0.0000 1.000 0.000 1 0.000
#> GSM381263 1 0.5760 0.668 0.672 0 0.328
#> GSM381265 3 0.6215 0.966 0.428 0 0.572
#> GSM381268 1 0.6111 0.675 0.604 0 0.396
#> GSM381270 2 0.0000 1.000 0.000 1 0.000
#> GSM381271 1 0.6215 0.670 0.572 0 0.428
#> GSM381275 2 0.0000 1.000 0.000 1 0.000
#> GSM381279 2 0.0000 1.000 0.000 1 0.000
#> GSM381195 3 0.6215 0.966 0.428 0 0.572
#> GSM381196 1 0.5650 0.664 0.688 0 0.312
#> GSM381198 2 0.0000 1.000 0.000 1 0.000
#> GSM381200 2 0.0000 1.000 0.000 1 0.000
#> GSM381201 1 0.6111 0.675 0.604 0 0.396
#> GSM381203 1 0.5529 0.566 0.704 0 0.296
#> GSM381204 3 0.6215 0.966 0.428 0 0.572
#> GSM381209 3 0.6235 0.961 0.436 0 0.564
#> GSM381212 3 0.6215 0.966 0.428 0 0.572
#> GSM381213 2 0.0000 1.000 0.000 1 0.000
#> GSM381214 2 0.0000 1.000 0.000 1 0.000
#> GSM381216 1 0.0000 0.463 1.000 0 0.000
#> GSM381225 1 0.6045 0.675 0.620 0 0.380
#> GSM381231 1 0.6215 0.670 0.572 0 0.428
#> GSM381235 1 0.1163 0.480 0.972 0 0.028
#> GSM381237 3 0.6215 0.966 0.428 0 0.572
#> GSM381241 2 0.0000 1.000 0.000 1 0.000
#> GSM381243 2 0.0000 1.000 0.000 1 0.000
#> GSM381245 1 0.5529 -0.366 0.704 0 0.296
#> GSM381246 2 0.0000 1.000 0.000 1 0.000
#> GSM381251 1 0.6168 0.674 0.588 0 0.412
#> GSM381264 3 0.6215 0.966 0.428 0 0.572
#> GSM381206 2 0.0000 1.000 0.000 1 0.000
#> GSM381217 1 0.3752 0.569 0.856 0 0.144
#> GSM381218 2 0.0000 1.000 0.000 1 0.000
#> GSM381226 2 0.0000 1.000 0.000 1 0.000
#> GSM381227 2 0.0000 1.000 0.000 1 0.000
#> GSM381228 1 0.6215 0.670 0.572 0 0.428
#> GSM381236 1 0.6215 0.670 0.572 0 0.428
#> GSM381244 1 0.4887 -0.129 0.772 0 0.228
#> GSM381272 1 0.6215 0.670 0.572 0 0.428
#> GSM381277 1 0.2959 0.321 0.900 0 0.100
#> GSM381278 1 0.6215 0.670 0.572 0 0.428
#> GSM381197 1 0.0892 0.450 0.980 0 0.020
#> GSM381202 1 0.0892 0.449 0.980 0 0.020
#> GSM381207 1 0.5291 -0.271 0.732 0 0.268
#> GSM381208 2 0.0000 1.000 0.000 1 0.000
#> GSM381210 1 0.5497 -0.351 0.708 0 0.292
#> GSM381215 1 0.5810 0.670 0.664 0 0.336
#> GSM381219 2 0.0000 1.000 0.000 1 0.000
#> GSM381221 2 0.0000 1.000 0.000 1 0.000
#> GSM381223 2 0.0000 1.000 0.000 1 0.000
#> GSM381229 1 0.6168 0.674 0.588 0 0.412
#> GSM381230 3 0.6215 0.966 0.428 0 0.572
#> GSM381233 1 0.3879 0.157 0.848 0 0.152
#> GSM381234 3 0.6309 0.885 0.500 0 0.500
#> GSM381238 1 0.6215 0.670 0.572 0 0.428
#> GSM381239 1 0.6215 0.670 0.572 0 0.428
#> GSM381242 1 0.0592 0.458 0.988 0 0.012
#> GSM381247 2 0.0000 1.000 0.000 1 0.000
#> GSM381248 3 0.6299 0.871 0.476 0 0.524
#> GSM381249 1 0.3686 0.195 0.860 0 0.140
#> GSM381253 1 0.5760 0.668 0.672 0 0.328
#> GSM381255 2 0.0000 1.000 0.000 1 0.000
#> GSM381258 1 0.1289 0.491 0.968 0 0.032
#> GSM381262 1 0.6168 0.674 0.588 0 0.412
#> GSM381266 1 0.6215 0.670 0.572 0 0.428
#> GSM381267 2 0.0000 1.000 0.000 1 0.000
#> GSM381269 1 0.3619 0.204 0.864 0 0.136
#> GSM381273 1 0.6168 0.674 0.588 0 0.412
#> GSM381274 2 0.0000 1.000 0.000 1 0.000
#> GSM381276 1 0.2959 0.321 0.900 0 0.100
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM381194 3 0.0376 0.6733 0.004 0 0.992 0.004
#> GSM381199 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381205 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381211 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381220 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381222 1 0.5435 0.3911 0.564 0 0.420 0.016
#> GSM381224 1 0.5310 0.4198 0.576 0 0.412 0.012
#> GSM381232 4 0.2760 1.0000 0.000 0 0.128 0.872
#> GSM381240 1 0.4594 0.6044 0.712 0 0.280 0.008
#> GSM381250 3 0.2266 0.6679 0.084 0 0.912 0.004
#> GSM381252 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381254 1 0.1902 0.6990 0.932 0 0.064 0.004
#> GSM381256 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381257 1 0.2345 0.6801 0.900 0 0.100 0.000
#> GSM381259 1 0.0000 0.6975 1.000 0 0.000 0.000
#> GSM381260 3 0.6292 0.0653 0.416 0 0.524 0.060
#> GSM381261 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381263 3 0.2266 0.6670 0.084 0 0.912 0.004
#> GSM381265 1 0.0000 0.6975 1.000 0 0.000 0.000
#> GSM381268 3 0.0779 0.6750 0.016 0 0.980 0.004
#> GSM381270 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381271 4 0.2760 1.0000 0.000 0 0.128 0.872
#> GSM381275 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381279 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381195 1 0.0000 0.6975 1.000 0 0.000 0.000
#> GSM381196 3 0.2530 0.6593 0.100 0 0.896 0.004
#> GSM381198 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381200 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381201 3 0.0779 0.6750 0.016 0 0.980 0.004
#> GSM381203 3 0.4844 0.4710 0.300 0 0.688 0.012
#> GSM381204 1 0.0000 0.6975 1.000 0 0.000 0.000
#> GSM381209 1 0.0817 0.7008 0.976 0 0.024 0.000
#> GSM381212 1 0.0000 0.6975 1.000 0 0.000 0.000
#> GSM381213 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381214 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381216 3 0.6285 0.0751 0.412 0 0.528 0.060
#> GSM381225 3 0.3694 0.6423 0.032 0 0.844 0.124
#> GSM381231 4 0.2760 1.0000 0.000 0 0.128 0.872
#> GSM381235 3 0.6179 0.1254 0.392 0 0.552 0.056
#> GSM381237 1 0.0000 0.6975 1.000 0 0.000 0.000
#> GSM381241 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381243 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381245 1 0.4621 0.6013 0.708 0 0.284 0.008
#> GSM381246 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381251 3 0.2704 0.6312 0.000 0 0.876 0.124
#> GSM381264 1 0.0000 0.6975 1.000 0 0.000 0.000
#> GSM381206 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381217 3 0.5649 0.3930 0.284 0 0.664 0.052
#> GSM381218 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381226 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381227 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381228 4 0.2760 1.0000 0.000 0 0.128 0.872
#> GSM381236 4 0.2760 1.0000 0.000 0 0.128 0.872
#> GSM381244 1 0.4990 0.5244 0.640 0 0.352 0.008
#> GSM381272 4 0.2760 1.0000 0.000 0 0.128 0.872
#> GSM381277 1 0.6268 0.2292 0.496 0 0.448 0.056
#> GSM381278 3 0.3266 0.5934 0.000 0 0.832 0.168
#> GSM381197 3 0.6305 0.0432 0.424 0 0.516 0.060
#> GSM381202 3 0.6305 0.0395 0.424 0 0.516 0.060
#> GSM381207 1 0.4792 0.5757 0.680 0 0.312 0.008
#> GSM381208 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381210 1 0.4647 0.5975 0.704 0 0.288 0.008
#> GSM381215 3 0.2125 0.6697 0.076 0 0.920 0.004
#> GSM381219 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381221 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381223 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381229 3 0.2760 0.6302 0.000 0 0.872 0.128
#> GSM381230 1 0.0000 0.6975 1.000 0 0.000 0.000
#> GSM381233 1 0.5435 0.3911 0.564 0 0.420 0.016
#> GSM381234 1 0.1978 0.6983 0.928 0 0.068 0.004
#> GSM381238 4 0.2760 1.0000 0.000 0 0.128 0.872
#> GSM381239 4 0.2760 1.0000 0.000 0 0.128 0.872
#> GSM381242 3 0.6292 0.0653 0.416 0 0.524 0.060
#> GSM381247 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381248 1 0.2759 0.6844 0.904 0 0.052 0.044
#> GSM381249 1 0.5865 0.3764 0.552 0 0.412 0.036
#> GSM381253 3 0.2266 0.6679 0.084 0 0.912 0.004
#> GSM381255 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381258 3 0.6212 0.1581 0.380 0 0.560 0.060
#> GSM381262 3 0.2081 0.6494 0.000 0 0.916 0.084
#> GSM381266 3 0.3266 0.5934 0.000 0 0.832 0.168
#> GSM381267 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381269 1 0.5873 0.3677 0.548 0 0.416 0.036
#> GSM381273 3 0.2760 0.6302 0.000 0 0.872 0.128
#> GSM381274 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM381276 1 0.6268 0.2292 0.496 0 0.448 0.056
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM381194 5 0.4249 0.4338 0.000 0.000 0.432 0.000 0.568
#> GSM381199 2 0.0000 0.9987 0.000 1.000 0.000 0.000 0.000
#> GSM381205 2 0.0000 0.9987 0.000 1.000 0.000 0.000 0.000
#> GSM381211 2 0.0000 0.9987 0.000 1.000 0.000 0.000 0.000
#> GSM381220 2 0.0000 0.9987 0.000 1.000 0.000 0.000 0.000
#> GSM381222 3 0.3231 0.6628 0.196 0.000 0.800 0.000 0.004
#> GSM381224 3 0.3878 0.6424 0.236 0.000 0.748 0.000 0.016
#> GSM381232 4 0.0290 1.0000 0.000 0.000 0.008 0.992 0.000
#> GSM381240 3 0.4235 0.3774 0.424 0.000 0.576 0.000 0.000
#> GSM381250 3 0.4242 -0.1141 0.000 0.000 0.572 0.000 0.428
#> GSM381252 2 0.0000 0.9987 0.000 1.000 0.000 0.000 0.000
#> GSM381254 1 0.2488 0.8425 0.872 0.000 0.124 0.000 0.004
#> GSM381256 2 0.0000 0.9987 0.000 1.000 0.000 0.000 0.000
#> GSM381257 1 0.2471 0.8280 0.864 0.000 0.136 0.000 0.000
#> GSM381259 1 0.0290 0.9350 0.992 0.000 0.008 0.000 0.000
#> GSM381260 3 0.0579 0.6559 0.008 0.000 0.984 0.000 0.008
#> GSM381261 2 0.0290 0.9939 0.000 0.992 0.000 0.008 0.000
#> GSM381263 3 0.4242 -0.0975 0.000 0.000 0.572 0.000 0.428
#> GSM381265 1 0.0290 0.9350 0.992 0.000 0.008 0.000 0.000
#> GSM381268 5 0.4192 0.5081 0.000 0.000 0.404 0.000 0.596
#> GSM381270 2 0.0000 0.9987 0.000 1.000 0.000 0.000 0.000
#> GSM381271 4 0.0290 1.0000 0.000 0.000 0.008 0.992 0.000
#> GSM381275 2 0.0290 0.9939 0.000 0.992 0.000 0.008 0.000
#> GSM381279 2 0.0000 0.9987 0.000 1.000 0.000 0.000 0.000
#> GSM381195 1 0.0290 0.9350 0.992 0.000 0.008 0.000 0.000
#> GSM381196 3 0.4367 -0.0763 0.004 0.000 0.580 0.000 0.416
#> GSM381198 2 0.0000 0.9987 0.000 1.000 0.000 0.000 0.000
#> GSM381200 2 0.0000 0.9987 0.000 1.000 0.000 0.000 0.000
#> GSM381201 5 0.4161 0.5279 0.000 0.000 0.392 0.000 0.608
#> GSM381203 3 0.6351 0.0612 0.192 0.000 0.508 0.000 0.300
#> GSM381204 1 0.0290 0.9350 0.992 0.000 0.008 0.000 0.000
#> GSM381209 1 0.1965 0.8796 0.904 0.000 0.096 0.000 0.000
#> GSM381212 1 0.0290 0.9350 0.992 0.000 0.008 0.000 0.000
#> GSM381213 2 0.0000 0.9987 0.000 1.000 0.000 0.000 0.000
#> GSM381214 2 0.0000 0.9987 0.000 1.000 0.000 0.000 0.000
#> GSM381216 3 0.0162 0.6528 0.000 0.000 0.996 0.000 0.004
#> GSM381225 5 0.2773 0.7429 0.000 0.000 0.164 0.000 0.836
#> GSM381231 4 0.0290 1.0000 0.000 0.000 0.008 0.992 0.000
#> GSM381235 3 0.1041 0.6482 0.004 0.000 0.964 0.000 0.032
#> GSM381237 1 0.0290 0.9350 0.992 0.000 0.008 0.000 0.000
#> GSM381241 2 0.0000 0.9987 0.000 1.000 0.000 0.000 0.000
#> GSM381243 2 0.0000 0.9987 0.000 1.000 0.000 0.000 0.000
#> GSM381245 3 0.4242 0.3702 0.428 0.000 0.572 0.000 0.000
#> GSM381246 2 0.0290 0.9939 0.000 0.992 0.000 0.008 0.000
#> GSM381251 5 0.1792 0.7760 0.000 0.000 0.084 0.000 0.916
#> GSM381264 1 0.0290 0.9350 0.992 0.000 0.008 0.000 0.000
#> GSM381206 2 0.0000 0.9987 0.000 1.000 0.000 0.000 0.000
#> GSM381217 3 0.3381 0.4997 0.016 0.000 0.808 0.000 0.176
#> GSM381218 2 0.0000 0.9987 0.000 1.000 0.000 0.000 0.000
#> GSM381226 2 0.0000 0.9987 0.000 1.000 0.000 0.000 0.000
#> GSM381227 2 0.0000 0.9987 0.000 1.000 0.000 0.000 0.000
#> GSM381228 4 0.0290 1.0000 0.000 0.000 0.008 0.992 0.000
#> GSM381236 4 0.0290 1.0000 0.000 0.000 0.008 0.992 0.000
#> GSM381244 3 0.3752 0.5847 0.292 0.000 0.708 0.000 0.000
#> GSM381272 4 0.0290 1.0000 0.000 0.000 0.008 0.992 0.000
#> GSM381277 3 0.2616 0.6745 0.100 0.000 0.880 0.000 0.020
#> GSM381278 5 0.1082 0.7230 0.008 0.000 0.028 0.000 0.964
#> GSM381197 3 0.1168 0.6578 0.032 0.000 0.960 0.000 0.008
#> GSM381202 3 0.0992 0.6603 0.024 0.000 0.968 0.000 0.008
#> GSM381207 3 0.4138 0.4581 0.384 0.000 0.616 0.000 0.000
#> GSM381208 2 0.0000 0.9987 0.000 1.000 0.000 0.000 0.000
#> GSM381210 3 0.4219 0.3939 0.416 0.000 0.584 0.000 0.000
#> GSM381215 3 0.4305 -0.2998 0.000 0.000 0.512 0.000 0.488
#> GSM381219 2 0.0000 0.9987 0.000 1.000 0.000 0.000 0.000
#> GSM381221 2 0.0000 0.9987 0.000 1.000 0.000 0.000 0.000
#> GSM381223 2 0.0290 0.9939 0.000 0.992 0.000 0.008 0.000
#> GSM381229 5 0.1732 0.7760 0.000 0.000 0.080 0.000 0.920
#> GSM381230 1 0.0510 0.9316 0.984 0.000 0.016 0.000 0.000
#> GSM381233 3 0.3231 0.6628 0.196 0.000 0.800 0.000 0.004
#> GSM381234 1 0.2536 0.8370 0.868 0.000 0.128 0.000 0.004
#> GSM381238 4 0.0290 1.0000 0.000 0.000 0.008 0.992 0.000
#> GSM381239 4 0.0290 1.0000 0.000 0.000 0.008 0.992 0.000
#> GSM381242 3 0.0579 0.6559 0.008 0.000 0.984 0.000 0.008
#> GSM381247 2 0.0000 0.9987 0.000 1.000 0.000 0.000 0.000
#> GSM381248 1 0.3536 0.8207 0.832 0.000 0.084 0.000 0.084
#> GSM381249 3 0.2674 0.6737 0.140 0.000 0.856 0.000 0.004
#> GSM381253 3 0.4242 -0.1141 0.000 0.000 0.572 0.000 0.428
#> GSM381255 2 0.0000 0.9987 0.000 1.000 0.000 0.000 0.000
#> GSM381258 3 0.0963 0.6423 0.000 0.000 0.964 0.000 0.036
#> GSM381262 5 0.3561 0.6879 0.000 0.000 0.260 0.000 0.740
#> GSM381266 5 0.0579 0.7201 0.008 0.000 0.008 0.000 0.984
#> GSM381267 2 0.0000 0.9987 0.000 1.000 0.000 0.000 0.000
#> GSM381269 3 0.2629 0.6733 0.136 0.000 0.860 0.000 0.004
#> GSM381273 5 0.1732 0.7760 0.000 0.000 0.080 0.000 0.920
#> GSM381274 2 0.0290 0.9939 0.000 0.992 0.000 0.008 0.000
#> GSM381276 3 0.2616 0.6745 0.100 0.000 0.880 0.000 0.020
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM381194 3 0.4971 0.664 0.000 0.000 0.604 0 0.300 0.096
#> GSM381199 2 0.1327 0.904 0.000 0.936 0.000 0 0.000 0.064
#> GSM381205 2 0.0000 0.926 0.000 1.000 0.000 0 0.000 0.000
#> GSM381211 2 0.0000 0.926 0.000 1.000 0.000 0 0.000 0.000
#> GSM381220 2 0.1267 0.907 0.000 0.940 0.000 0 0.000 0.060
#> GSM381222 5 0.3377 0.733 0.188 0.000 0.000 0 0.784 0.028
#> GSM381224 5 0.4500 0.689 0.224 0.000 0.000 0 0.688 0.088
#> GSM381232 4 0.0000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM381240 5 0.4537 0.464 0.412 0.000 0.000 0 0.552 0.036
#> GSM381250 3 0.5186 0.559 0.000 0.000 0.476 0 0.436 0.088
#> GSM381252 2 0.0000 0.926 0.000 1.000 0.000 0 0.000 0.000
#> GSM381254 1 0.2454 0.841 0.876 0.000 0.004 0 0.104 0.016
#> GSM381256 2 0.1075 0.912 0.000 0.952 0.000 0 0.000 0.048
#> GSM381257 1 0.2135 0.814 0.872 0.000 0.000 0 0.128 0.000
#> GSM381259 1 0.0000 0.932 1.000 0.000 0.000 0 0.000 0.000
#> GSM381260 5 0.1429 0.686 0.004 0.000 0.004 0 0.940 0.052
#> GSM381261 6 0.3774 0.996 0.000 0.408 0.000 0 0.000 0.592
#> GSM381263 3 0.5223 0.546 0.000 0.000 0.472 0 0.436 0.092
#> GSM381265 1 0.0000 0.932 1.000 0.000 0.000 0 0.000 0.000
#> GSM381268 3 0.4309 0.676 0.000 0.000 0.660 0 0.296 0.044
#> GSM381270 2 0.1327 0.904 0.000 0.936 0.000 0 0.000 0.064
#> GSM381271 4 0.0000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM381275 6 0.3774 0.996 0.000 0.408 0.000 0 0.000 0.592
#> GSM381279 2 0.1327 0.904 0.000 0.936 0.000 0 0.000 0.064
#> GSM381195 1 0.0000 0.932 1.000 0.000 0.000 0 0.000 0.000
#> GSM381196 3 0.5318 0.535 0.004 0.000 0.460 0 0.448 0.088
#> GSM381198 2 0.0000 0.926 0.000 1.000 0.000 0 0.000 0.000
#> GSM381200 2 0.1610 0.877 0.000 0.916 0.000 0 0.000 0.084
#> GSM381201 3 0.3835 0.676 0.000 0.000 0.684 0 0.300 0.016
#> GSM381203 5 0.7300 -0.266 0.200 0.000 0.232 0 0.420 0.148
#> GSM381204 1 0.0000 0.932 1.000 0.000 0.000 0 0.000 0.000
#> GSM381209 1 0.1951 0.875 0.908 0.000 0.000 0 0.076 0.016
#> GSM381212 1 0.0000 0.932 1.000 0.000 0.000 0 0.000 0.000
#> GSM381213 2 0.0000 0.926 0.000 1.000 0.000 0 0.000 0.000
#> GSM381214 2 0.0000 0.926 0.000 1.000 0.000 0 0.000 0.000
#> GSM381216 5 0.0458 0.693 0.000 0.000 0.000 0 0.984 0.016
#> GSM381225 3 0.2932 0.642 0.000 0.000 0.820 0 0.016 0.164
#> GSM381231 4 0.0000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM381235 5 0.1313 0.687 0.004 0.000 0.028 0 0.952 0.016
#> GSM381237 1 0.0146 0.931 0.996 0.000 0.000 0 0.000 0.004
#> GSM381241 2 0.0000 0.926 0.000 1.000 0.000 0 0.000 0.000
#> GSM381243 2 0.1327 0.904 0.000 0.936 0.000 0 0.000 0.064
#> GSM381245 5 0.4488 0.450 0.420 0.000 0.000 0 0.548 0.032
#> GSM381246 6 0.3789 0.985 0.000 0.416 0.000 0 0.000 0.584
#> GSM381251 3 0.0291 0.668 0.000 0.000 0.992 0 0.004 0.004
#> GSM381264 1 0.0000 0.932 1.000 0.000 0.000 0 0.000 0.000
#> GSM381206 2 0.0000 0.926 0.000 1.000 0.000 0 0.000 0.000
#> GSM381217 5 0.4297 0.439 0.016 0.000 0.132 0 0.756 0.096
#> GSM381218 2 0.0000 0.926 0.000 1.000 0.000 0 0.000 0.000
#> GSM381226 2 0.3634 -0.261 0.000 0.644 0.000 0 0.000 0.356
#> GSM381227 2 0.1327 0.904 0.000 0.936 0.000 0 0.000 0.064
#> GSM381228 4 0.0000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM381236 4 0.0000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM381244 5 0.4368 0.659 0.272 0.000 0.000 0 0.672 0.056
#> GSM381272 4 0.0000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM381277 5 0.3579 0.720 0.072 0.000 0.004 0 0.804 0.120
#> GSM381278 3 0.2703 0.595 0.000 0.000 0.824 0 0.004 0.172
#> GSM381197 5 0.1642 0.690 0.028 0.000 0.004 0 0.936 0.032
#> GSM381202 5 0.1485 0.693 0.024 0.000 0.004 0 0.944 0.028
#> GSM381207 5 0.4453 0.540 0.372 0.000 0.000 0 0.592 0.036
#> GSM381208 2 0.0000 0.926 0.000 1.000 0.000 0 0.000 0.000
#> GSM381210 5 0.4468 0.478 0.408 0.000 0.000 0 0.560 0.032
#> GSM381215 3 0.4808 0.577 0.000 0.000 0.536 0 0.408 0.056
#> GSM381219 2 0.0000 0.926 0.000 1.000 0.000 0 0.000 0.000
#> GSM381221 2 0.1141 0.911 0.000 0.948 0.000 0 0.000 0.052
#> GSM381223 6 0.3774 0.996 0.000 0.408 0.000 0 0.000 0.592
#> GSM381229 3 0.0713 0.658 0.000 0.000 0.972 0 0.000 0.028
#> GSM381230 1 0.0260 0.929 0.992 0.000 0.000 0 0.008 0.000
#> GSM381233 5 0.3377 0.733 0.188 0.000 0.000 0 0.784 0.028
#> GSM381234 1 0.2501 0.836 0.872 0.000 0.004 0 0.108 0.016
#> GSM381238 4 0.0000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM381239 4 0.0000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM381242 5 0.1429 0.686 0.004 0.000 0.004 0 0.940 0.052
#> GSM381247 2 0.1327 0.904 0.000 0.936 0.000 0 0.000 0.064
#> GSM381248 1 0.3633 0.791 0.800 0.000 0.004 0 0.076 0.120
#> GSM381249 5 0.2831 0.741 0.136 0.000 0.000 0 0.840 0.024
#> GSM381253 3 0.5186 0.559 0.000 0.000 0.476 0 0.436 0.088
#> GSM381255 2 0.0000 0.926 0.000 1.000 0.000 0 0.000 0.000
#> GSM381258 5 0.1245 0.679 0.000 0.000 0.032 0 0.952 0.016
#> GSM381262 3 0.3694 0.699 0.000 0.000 0.784 0 0.140 0.076
#> GSM381266 3 0.2191 0.615 0.000 0.000 0.876 0 0.004 0.120
#> GSM381267 2 0.0000 0.926 0.000 1.000 0.000 0 0.000 0.000
#> GSM381269 5 0.2790 0.741 0.132 0.000 0.000 0 0.844 0.024
#> GSM381273 3 0.0713 0.658 0.000 0.000 0.972 0 0.000 0.028
#> GSM381274 6 0.3774 0.996 0.000 0.408 0.000 0 0.000 0.592
#> GSM381276 5 0.3579 0.720 0.072 0.000 0.004 0 0.804 0.120
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n other(p) k
#> MAD:hclust 71 0.531 2
#> MAD:hclust 66 0.491 3
#> MAD:hclust 70 0.571 4
#> MAD:hclust 74 0.318 5
#> MAD:hclust 80 0.393 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 86 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 0.829 0.979 0.989 0.4580 0.548 0.548
#> 3 3 0.749 0.925 0.917 0.4001 0.781 0.600
#> 4 4 0.762 0.787 0.843 0.1153 0.903 0.723
#> 5 5 0.715 0.635 0.738 0.0708 0.925 0.742
#> 6 6 0.745 0.696 0.791 0.0483 0.923 0.680
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
#> GSM381194 1 0.000 0.983 1.00 0.00
#> GSM381199 2 0.000 1.000 0.00 1.00
#> GSM381205 2 0.000 1.000 0.00 1.00
#> GSM381211 2 0.000 1.000 0.00 1.00
#> GSM381220 2 0.000 1.000 0.00 1.00
#> GSM381222 1 0.000 0.983 1.00 0.00
#> GSM381224 1 0.000 0.983 1.00 0.00
#> GSM381232 1 0.529 0.881 0.88 0.12
#> GSM381240 1 0.000 0.983 1.00 0.00
#> GSM381250 1 0.000 0.983 1.00 0.00
#> GSM381252 2 0.000 1.000 0.00 1.00
#> GSM381254 1 0.000 0.983 1.00 0.00
#> GSM381256 2 0.000 1.000 0.00 1.00
#> GSM381257 1 0.000 0.983 1.00 0.00
#> GSM381259 1 0.000 0.983 1.00 0.00
#> GSM381260 1 0.000 0.983 1.00 0.00
#> GSM381261 2 0.000 1.000 0.00 1.00
#> GSM381263 1 0.000 0.983 1.00 0.00
#> GSM381265 1 0.000 0.983 1.00 0.00
#> GSM381268 1 0.000 0.983 1.00 0.00
#> GSM381270 2 0.000 1.000 0.00 1.00
#> GSM381271 1 0.529 0.881 0.88 0.12
#> GSM381275 2 0.000 1.000 0.00 1.00
#> GSM381279 2 0.000 1.000 0.00 1.00
#> GSM381195 1 0.000 0.983 1.00 0.00
#> GSM381196 1 0.000 0.983 1.00 0.00
#> GSM381198 2 0.000 1.000 0.00 1.00
#> GSM381200 2 0.000 1.000 0.00 1.00
#> GSM381201 1 0.000 0.983 1.00 0.00
#> GSM381203 1 0.000 0.983 1.00 0.00
#> GSM381204 1 0.000 0.983 1.00 0.00
#> GSM381209 1 0.000 0.983 1.00 0.00
#> GSM381212 1 0.000 0.983 1.00 0.00
#> GSM381213 2 0.000 1.000 0.00 1.00
#> GSM381214 2 0.000 1.000 0.00 1.00
#> GSM381216 1 0.000 0.983 1.00 0.00
#> GSM381225 1 0.000 0.983 1.00 0.00
#> GSM381231 1 0.529 0.881 0.88 0.12
#> GSM381235 1 0.000 0.983 1.00 0.00
#> GSM381237 1 0.000 0.983 1.00 0.00
#> GSM381241 2 0.000 1.000 0.00 1.00
#> GSM381243 2 0.000 1.000 0.00 1.00
#> GSM381245 1 0.000 0.983 1.00 0.00
#> GSM381246 2 0.000 1.000 0.00 1.00
#> GSM381251 1 0.000 0.983 1.00 0.00
#> GSM381264 1 0.000 0.983 1.00 0.00
#> GSM381206 2 0.000 1.000 0.00 1.00
#> GSM381217 1 0.000 0.983 1.00 0.00
#> GSM381218 2 0.000 1.000 0.00 1.00
#> GSM381226 2 0.000 1.000 0.00 1.00
#> GSM381227 2 0.000 1.000 0.00 1.00
#> GSM381228 1 0.529 0.881 0.88 0.12
#> GSM381236 1 0.529 0.881 0.88 0.12
#> GSM381244 1 0.000 0.983 1.00 0.00
#> GSM381272 1 0.529 0.881 0.88 0.12
#> GSM381277 1 0.000 0.983 1.00 0.00
#> GSM381278 1 0.000 0.983 1.00 0.00
#> GSM381197 1 0.000 0.983 1.00 0.00
#> GSM381202 1 0.000 0.983 1.00 0.00
#> GSM381207 1 0.000 0.983 1.00 0.00
#> GSM381208 2 0.000 1.000 0.00 1.00
#> GSM381210 1 0.000 0.983 1.00 0.00
#> GSM381215 1 0.000 0.983 1.00 0.00
#> GSM381219 2 0.000 1.000 0.00 1.00
#> GSM381221 2 0.000 1.000 0.00 1.00
#> GSM381223 2 0.000 1.000 0.00 1.00
#> GSM381229 1 0.000 0.983 1.00 0.00
#> GSM381230 1 0.000 0.983 1.00 0.00
#> GSM381233 1 0.000 0.983 1.00 0.00
#> GSM381234 1 0.000 0.983 1.00 0.00
#> GSM381238 1 0.529 0.881 0.88 0.12
#> GSM381239 1 0.529 0.881 0.88 0.12
#> GSM381242 1 0.000 0.983 1.00 0.00
#> GSM381247 2 0.000 1.000 0.00 1.00
#> GSM381248 1 0.000 0.983 1.00 0.00
#> GSM381249 1 0.000 0.983 1.00 0.00
#> GSM381253 1 0.000 0.983 1.00 0.00
#> GSM381255 2 0.000 1.000 0.00 1.00
#> GSM381258 1 0.000 0.983 1.00 0.00
#> GSM381262 1 0.000 0.983 1.00 0.00
#> GSM381266 1 0.000 0.983 1.00 0.00
#> GSM381267 2 0.000 1.000 0.00 1.00
#> GSM381269 1 0.000 0.983 1.00 0.00
#> GSM381273 1 0.000 0.983 1.00 0.00
#> GSM381274 2 0.000 1.000 0.00 1.00
#> GSM381276 1 0.000 0.983 1.00 0.00
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM381194 3 0.4235 0.881 0.176 0.000 0.824
#> GSM381199 2 0.1860 0.967 0.000 0.948 0.052
#> GSM381205 2 0.0237 0.970 0.000 0.996 0.004
#> GSM381211 2 0.0237 0.970 0.000 0.996 0.004
#> GSM381220 2 0.1289 0.970 0.000 0.968 0.032
#> GSM381222 1 0.1031 0.970 0.976 0.000 0.024
#> GSM381224 1 0.0424 0.978 0.992 0.000 0.008
#> GSM381232 3 0.4196 0.867 0.112 0.024 0.864
#> GSM381240 1 0.0000 0.980 1.000 0.000 0.000
#> GSM381250 3 0.6079 0.684 0.388 0.000 0.612
#> GSM381252 2 0.0237 0.970 0.000 0.996 0.004
#> GSM381254 1 0.0000 0.980 1.000 0.000 0.000
#> GSM381256 2 0.0000 0.970 0.000 1.000 0.000
#> GSM381257 1 0.0000 0.980 1.000 0.000 0.000
#> GSM381259 1 0.0000 0.980 1.000 0.000 0.000
#> GSM381260 1 0.3116 0.858 0.892 0.000 0.108
#> GSM381261 2 0.3116 0.952 0.000 0.892 0.108
#> GSM381263 3 0.6079 0.684 0.388 0.000 0.612
#> GSM381265 1 0.0000 0.980 1.000 0.000 0.000
#> GSM381268 3 0.4931 0.849 0.232 0.000 0.768
#> GSM381270 2 0.2878 0.956 0.000 0.904 0.096
#> GSM381271 3 0.4196 0.867 0.112 0.024 0.864
#> GSM381275 2 0.3038 0.954 0.000 0.896 0.104
#> GSM381279 2 0.2878 0.956 0.000 0.904 0.096
#> GSM381195 1 0.0000 0.980 1.000 0.000 0.000
#> GSM381196 3 0.6079 0.684 0.388 0.000 0.612
#> GSM381198 2 0.0237 0.970 0.000 0.996 0.004
#> GSM381200 2 0.2066 0.965 0.000 0.940 0.060
#> GSM381201 3 0.4235 0.881 0.176 0.000 0.824
#> GSM381203 1 0.0424 0.977 0.992 0.000 0.008
#> GSM381204 1 0.0000 0.980 1.000 0.000 0.000
#> GSM381209 1 0.0000 0.980 1.000 0.000 0.000
#> GSM381212 1 0.0000 0.980 1.000 0.000 0.000
#> GSM381213 2 0.1860 0.965 0.000 0.948 0.052
#> GSM381214 2 0.0237 0.970 0.000 0.996 0.004
#> GSM381216 1 0.1289 0.965 0.968 0.000 0.032
#> GSM381225 3 0.6045 0.696 0.380 0.000 0.620
#> GSM381231 3 0.4121 0.864 0.108 0.024 0.868
#> GSM381235 1 0.1289 0.965 0.968 0.000 0.032
#> GSM381237 1 0.0000 0.980 1.000 0.000 0.000
#> GSM381241 2 0.0237 0.970 0.000 0.996 0.004
#> GSM381243 2 0.2878 0.956 0.000 0.904 0.096
#> GSM381245 1 0.0000 0.980 1.000 0.000 0.000
#> GSM381246 2 0.0747 0.970 0.000 0.984 0.016
#> GSM381251 3 0.4235 0.881 0.176 0.000 0.824
#> GSM381264 1 0.0000 0.980 1.000 0.000 0.000
#> GSM381206 2 0.0237 0.970 0.000 0.996 0.004
#> GSM381217 1 0.1289 0.965 0.968 0.000 0.032
#> GSM381218 2 0.0237 0.970 0.000 0.996 0.004
#> GSM381226 2 0.1163 0.970 0.000 0.972 0.028
#> GSM381227 2 0.2959 0.955 0.000 0.900 0.100
#> GSM381228 3 0.4196 0.867 0.112 0.024 0.864
#> GSM381236 3 0.4196 0.867 0.112 0.024 0.864
#> GSM381244 1 0.0892 0.973 0.980 0.000 0.020
#> GSM381272 3 0.4196 0.867 0.112 0.024 0.864
#> GSM381277 1 0.0000 0.980 1.000 0.000 0.000
#> GSM381278 3 0.3752 0.880 0.144 0.000 0.856
#> GSM381197 1 0.2356 0.904 0.928 0.000 0.072
#> GSM381202 1 0.0424 0.978 0.992 0.000 0.008
#> GSM381207 1 0.0424 0.978 0.992 0.000 0.008
#> GSM381208 2 0.0237 0.970 0.000 0.996 0.004
#> GSM381210 1 0.0000 0.980 1.000 0.000 0.000
#> GSM381215 3 0.4235 0.881 0.176 0.000 0.824
#> GSM381219 2 0.0237 0.970 0.000 0.996 0.004
#> GSM381221 2 0.0892 0.970 0.000 0.980 0.020
#> GSM381223 2 0.3038 0.954 0.000 0.896 0.104
#> GSM381229 3 0.4235 0.881 0.176 0.000 0.824
#> GSM381230 1 0.0000 0.980 1.000 0.000 0.000
#> GSM381233 1 0.1031 0.970 0.976 0.000 0.024
#> GSM381234 1 0.0000 0.980 1.000 0.000 0.000
#> GSM381238 3 0.4121 0.864 0.108 0.024 0.868
#> GSM381239 3 0.4196 0.867 0.112 0.024 0.864
#> GSM381242 1 0.2796 0.890 0.908 0.000 0.092
#> GSM381247 2 0.2878 0.956 0.000 0.904 0.096
#> GSM381248 1 0.0000 0.980 1.000 0.000 0.000
#> GSM381249 1 0.0747 0.975 0.984 0.000 0.016
#> GSM381253 3 0.6180 0.628 0.416 0.000 0.584
#> GSM381255 2 0.0237 0.970 0.000 0.996 0.004
#> GSM381258 3 0.5327 0.817 0.272 0.000 0.728
#> GSM381262 3 0.4235 0.881 0.176 0.000 0.824
#> GSM381266 3 0.3752 0.880 0.144 0.000 0.856
#> GSM381267 2 0.1289 0.970 0.000 0.968 0.032
#> GSM381269 1 0.1031 0.970 0.976 0.000 0.024
#> GSM381273 3 0.3752 0.880 0.144 0.000 0.856
#> GSM381274 2 0.2959 0.955 0.000 0.900 0.100
#> GSM381276 3 0.6062 0.694 0.384 0.000 0.616
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM381194 3 0.5923 0.700 0.044 0.000 0.580 0.376
#> GSM381199 2 0.4040 0.845 0.000 0.752 0.248 0.000
#> GSM381205 2 0.0000 0.862 0.000 1.000 0.000 0.000
#> GSM381211 2 0.0000 0.862 0.000 1.000 0.000 0.000
#> GSM381220 2 0.3688 0.853 0.000 0.792 0.208 0.000
#> GSM381222 1 0.2216 0.848 0.908 0.000 0.092 0.000
#> GSM381224 1 0.0921 0.897 0.972 0.000 0.028 0.000
#> GSM381232 4 0.0592 1.000 0.016 0.000 0.000 0.984
#> GSM381240 1 0.0188 0.910 0.996 0.000 0.004 0.000
#> GSM381250 3 0.6950 0.744 0.180 0.000 0.584 0.236
#> GSM381252 2 0.0000 0.862 0.000 1.000 0.000 0.000
#> GSM381254 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM381256 2 0.0469 0.863 0.000 0.988 0.012 0.000
#> GSM381257 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM381259 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM381260 3 0.5853 0.350 0.460 0.000 0.508 0.032
#> GSM381261 2 0.5284 0.796 0.000 0.616 0.368 0.016
#> GSM381263 3 0.6950 0.744 0.180 0.000 0.584 0.236
#> GSM381265 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM381268 3 0.6407 0.727 0.084 0.000 0.584 0.332
#> GSM381270 2 0.4697 0.812 0.000 0.644 0.356 0.000
#> GSM381271 4 0.0592 1.000 0.016 0.000 0.000 0.984
#> GSM381275 2 0.5253 0.800 0.000 0.624 0.360 0.016
#> GSM381279 2 0.4697 0.812 0.000 0.644 0.356 0.000
#> GSM381195 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM381196 3 0.6950 0.744 0.180 0.000 0.584 0.236
#> GSM381198 2 0.0000 0.862 0.000 1.000 0.000 0.000
#> GSM381200 2 0.4252 0.844 0.000 0.744 0.252 0.004
#> GSM381201 3 0.5923 0.700 0.044 0.000 0.580 0.376
#> GSM381203 1 0.4998 -0.277 0.512 0.000 0.488 0.000
#> GSM381204 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM381209 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM381212 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM381213 2 0.3444 0.847 0.000 0.816 0.184 0.000
#> GSM381214 2 0.0000 0.862 0.000 1.000 0.000 0.000
#> GSM381216 3 0.4933 0.380 0.432 0.000 0.568 0.000
#> GSM381225 3 0.6823 0.744 0.160 0.000 0.596 0.244
#> GSM381231 4 0.0592 1.000 0.016 0.000 0.000 0.984
#> GSM381235 3 0.4830 0.465 0.392 0.000 0.608 0.000
#> GSM381237 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM381241 2 0.0000 0.862 0.000 1.000 0.000 0.000
#> GSM381243 2 0.4697 0.812 0.000 0.644 0.356 0.000
#> GSM381245 1 0.0336 0.909 0.992 0.000 0.008 0.000
#> GSM381246 2 0.0657 0.863 0.000 0.984 0.012 0.004
#> GSM381251 3 0.5923 0.700 0.044 0.000 0.580 0.376
#> GSM381264 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM381206 2 0.0000 0.862 0.000 1.000 0.000 0.000
#> GSM381217 3 0.4941 0.370 0.436 0.000 0.564 0.000
#> GSM381218 2 0.0000 0.862 0.000 1.000 0.000 0.000
#> GSM381226 2 0.2401 0.864 0.000 0.904 0.092 0.004
#> GSM381227 2 0.4697 0.812 0.000 0.644 0.356 0.000
#> GSM381228 4 0.0592 1.000 0.016 0.000 0.000 0.984
#> GSM381236 4 0.0592 1.000 0.016 0.000 0.000 0.984
#> GSM381244 1 0.2011 0.862 0.920 0.000 0.080 0.000
#> GSM381272 4 0.0592 1.000 0.016 0.000 0.000 0.984
#> GSM381277 1 0.0336 0.909 0.992 0.000 0.008 0.000
#> GSM381278 3 0.5660 0.668 0.028 0.000 0.576 0.396
#> GSM381197 1 0.5497 -0.226 0.524 0.000 0.460 0.016
#> GSM381202 1 0.4830 0.103 0.608 0.000 0.392 0.000
#> GSM381207 1 0.0469 0.908 0.988 0.000 0.012 0.000
#> GSM381208 2 0.0000 0.862 0.000 1.000 0.000 0.000
#> GSM381210 1 0.0188 0.910 0.996 0.000 0.004 0.000
#> GSM381215 3 0.5855 0.707 0.044 0.000 0.600 0.356
#> GSM381219 2 0.0000 0.862 0.000 1.000 0.000 0.000
#> GSM381221 2 0.2216 0.864 0.000 0.908 0.092 0.000
#> GSM381223 2 0.5253 0.800 0.000 0.624 0.360 0.016
#> GSM381229 3 0.5923 0.700 0.044 0.000 0.580 0.376
#> GSM381230 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM381233 1 0.2216 0.848 0.908 0.000 0.092 0.000
#> GSM381234 1 0.0000 0.911 1.000 0.000 0.000 0.000
#> GSM381238 4 0.0592 1.000 0.016 0.000 0.000 0.984
#> GSM381239 4 0.0592 1.000 0.016 0.000 0.000 0.984
#> GSM381242 3 0.5466 0.369 0.436 0.000 0.548 0.016
#> GSM381247 2 0.4697 0.812 0.000 0.644 0.356 0.000
#> GSM381248 1 0.0188 0.910 0.996 0.000 0.004 0.000
#> GSM381249 1 0.1118 0.894 0.964 0.000 0.036 0.000
#> GSM381253 3 0.6973 0.735 0.196 0.000 0.584 0.220
#> GSM381255 2 0.0000 0.862 0.000 1.000 0.000 0.000
#> GSM381258 3 0.6436 0.736 0.100 0.000 0.608 0.292
#> GSM381262 3 0.5923 0.700 0.044 0.000 0.580 0.376
#> GSM381266 3 0.5660 0.668 0.028 0.000 0.576 0.396
#> GSM381267 2 0.3688 0.853 0.000 0.792 0.208 0.000
#> GSM381269 1 0.2216 0.848 0.908 0.000 0.092 0.000
#> GSM381273 3 0.5660 0.668 0.028 0.000 0.576 0.396
#> GSM381274 2 0.5253 0.800 0.000 0.624 0.360 0.016
#> GSM381276 3 0.7129 0.732 0.196 0.000 0.560 0.244
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM381194 3 0.0867 0.8527 0.008 0.000 0.976 0.008 0.008
#> GSM381199 2 0.4570 0.5908 0.000 0.632 0.000 0.020 0.348
#> GSM381205 2 0.0404 0.7900 0.000 0.988 0.000 0.012 0.000
#> GSM381211 2 0.0324 0.7905 0.000 0.992 0.000 0.004 0.004
#> GSM381220 2 0.4196 0.5897 0.000 0.640 0.000 0.004 0.356
#> GSM381222 1 0.4639 0.6880 0.708 0.000 0.056 0.000 0.236
#> GSM381224 1 0.4096 0.7051 0.724 0.000 0.012 0.004 0.260
#> GSM381232 4 0.3328 0.9921 0.004 0.000 0.176 0.812 0.008
#> GSM381240 1 0.0566 0.8455 0.984 0.000 0.000 0.004 0.012
#> GSM381250 3 0.2983 0.8296 0.056 0.000 0.868 0.000 0.076
#> GSM381252 2 0.0162 0.7907 0.000 0.996 0.000 0.004 0.000
#> GSM381254 1 0.0451 0.8442 0.988 0.000 0.000 0.004 0.008
#> GSM381256 2 0.1106 0.7882 0.000 0.964 0.000 0.012 0.024
#> GSM381257 1 0.0880 0.8395 0.968 0.000 0.000 0.000 0.032
#> GSM381259 1 0.0000 0.8465 1.000 0.000 0.000 0.000 0.000
#> GSM381260 5 0.7006 -0.1174 0.272 0.000 0.344 0.008 0.376
#> GSM381261 2 0.6421 0.4168 0.000 0.464 0.008 0.136 0.392
#> GSM381263 3 0.2983 0.8296 0.056 0.000 0.868 0.000 0.076
#> GSM381265 1 0.0000 0.8465 1.000 0.000 0.000 0.000 0.000
#> GSM381268 3 0.0865 0.8541 0.024 0.000 0.972 0.004 0.000
#> GSM381270 5 0.4300 -0.4179 0.000 0.476 0.000 0.000 0.524
#> GSM381271 4 0.3365 0.9943 0.004 0.000 0.180 0.808 0.008
#> GSM381275 2 0.6315 0.4440 0.000 0.484 0.004 0.140 0.372
#> GSM381279 5 0.4300 -0.4179 0.000 0.476 0.000 0.000 0.524
#> GSM381195 1 0.0162 0.8456 0.996 0.000 0.000 0.000 0.004
#> GSM381196 3 0.3051 0.8293 0.060 0.000 0.864 0.000 0.076
#> GSM381198 2 0.0162 0.7907 0.000 0.996 0.000 0.004 0.000
#> GSM381200 2 0.5005 0.6255 0.000 0.660 0.000 0.064 0.276
#> GSM381201 3 0.0579 0.8522 0.008 0.000 0.984 0.008 0.000
#> GSM381203 3 0.5434 0.4276 0.336 0.000 0.588 0.000 0.076
#> GSM381204 1 0.0000 0.8465 1.000 0.000 0.000 0.000 0.000
#> GSM381209 1 0.0000 0.8465 1.000 0.000 0.000 0.000 0.000
#> GSM381212 1 0.0000 0.8465 1.000 0.000 0.000 0.000 0.000
#> GSM381213 2 0.3906 0.6302 0.000 0.704 0.000 0.004 0.292
#> GSM381214 2 0.0324 0.7905 0.000 0.992 0.000 0.004 0.004
#> GSM381216 5 0.6584 -0.1218 0.208 0.000 0.380 0.000 0.412
#> GSM381225 3 0.1830 0.8429 0.052 0.000 0.932 0.012 0.004
#> GSM381231 4 0.3365 0.9943 0.004 0.000 0.180 0.808 0.008
#> GSM381235 5 0.6460 -0.1759 0.180 0.000 0.408 0.000 0.412
#> GSM381237 1 0.0000 0.8465 1.000 0.000 0.000 0.000 0.000
#> GSM381241 2 0.0000 0.7905 0.000 1.000 0.000 0.000 0.000
#> GSM381243 5 0.4300 -0.4179 0.000 0.476 0.000 0.000 0.524
#> GSM381245 1 0.1168 0.8421 0.960 0.000 0.000 0.008 0.032
#> GSM381246 2 0.1831 0.7752 0.000 0.920 0.000 0.076 0.004
#> GSM381251 3 0.0579 0.8522 0.008 0.000 0.984 0.008 0.000
#> GSM381264 1 0.0162 0.8456 0.996 0.000 0.000 0.000 0.004
#> GSM381206 2 0.0404 0.7900 0.000 0.988 0.000 0.012 0.000
#> GSM381217 5 0.6536 -0.1423 0.196 0.000 0.392 0.000 0.412
#> GSM381218 2 0.0451 0.7899 0.000 0.988 0.000 0.004 0.008
#> GSM381226 2 0.3586 0.7432 0.000 0.828 0.000 0.076 0.096
#> GSM381227 5 0.4302 -0.4228 0.000 0.480 0.000 0.000 0.520
#> GSM381228 4 0.3086 0.9939 0.004 0.000 0.180 0.816 0.000
#> GSM381236 4 0.3048 0.9936 0.004 0.000 0.176 0.820 0.000
#> GSM381244 1 0.5594 0.4993 0.532 0.000 0.048 0.012 0.408
#> GSM381272 4 0.3365 0.9943 0.004 0.000 0.180 0.808 0.008
#> GSM381277 1 0.2361 0.8129 0.892 0.000 0.000 0.012 0.096
#> GSM381278 3 0.0740 0.8504 0.008 0.000 0.980 0.008 0.004
#> GSM381197 1 0.7056 -0.0866 0.348 0.000 0.316 0.008 0.328
#> GSM381202 1 0.6696 0.0991 0.388 0.000 0.240 0.000 0.372
#> GSM381207 1 0.2362 0.8218 0.900 0.000 0.008 0.008 0.084
#> GSM381208 2 0.0566 0.7904 0.000 0.984 0.000 0.012 0.004
#> GSM381210 1 0.1478 0.8308 0.936 0.000 0.000 0.000 0.064
#> GSM381215 3 0.1830 0.8410 0.008 0.000 0.924 0.000 0.068
#> GSM381219 2 0.0404 0.7901 0.000 0.988 0.000 0.012 0.000
#> GSM381221 2 0.2753 0.7504 0.000 0.856 0.000 0.008 0.136
#> GSM381223 2 0.6315 0.4440 0.000 0.484 0.004 0.140 0.372
#> GSM381229 3 0.0579 0.8522 0.008 0.000 0.984 0.008 0.000
#> GSM381230 1 0.0000 0.8465 1.000 0.000 0.000 0.000 0.000
#> GSM381233 1 0.4639 0.6880 0.708 0.000 0.056 0.000 0.236
#> GSM381234 1 0.0451 0.8442 0.988 0.000 0.000 0.004 0.008
#> GSM381238 4 0.3048 0.9936 0.004 0.000 0.176 0.820 0.000
#> GSM381239 4 0.3048 0.9936 0.004 0.000 0.176 0.820 0.000
#> GSM381242 5 0.6852 -0.1125 0.216 0.000 0.364 0.008 0.412
#> GSM381247 5 0.4300 -0.4179 0.000 0.476 0.000 0.000 0.524
#> GSM381248 1 0.0992 0.8432 0.968 0.000 0.000 0.008 0.024
#> GSM381249 1 0.4058 0.7144 0.740 0.000 0.024 0.000 0.236
#> GSM381253 3 0.3051 0.8261 0.060 0.000 0.864 0.000 0.076
#> GSM381255 2 0.0324 0.7905 0.000 0.992 0.000 0.004 0.004
#> GSM381258 3 0.4982 0.4189 0.032 0.000 0.556 0.000 0.412
#> GSM381262 3 0.0579 0.8522 0.008 0.000 0.984 0.008 0.000
#> GSM381266 3 0.0579 0.8522 0.008 0.000 0.984 0.008 0.000
#> GSM381267 2 0.4196 0.5897 0.000 0.640 0.000 0.004 0.356
#> GSM381269 1 0.5359 0.4843 0.532 0.000 0.056 0.000 0.412
#> GSM381273 3 0.0579 0.8522 0.008 0.000 0.984 0.008 0.000
#> GSM381274 2 0.6315 0.4440 0.000 0.484 0.004 0.140 0.372
#> GSM381276 3 0.5912 0.4176 0.088 0.000 0.544 0.008 0.360
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM381194 3 0.0696 0.8907 0.004 0.000 0.980 0.004 0.008 0.004
#> GSM381199 2 0.5133 -0.3127 0.000 0.480 0.000 0.032 0.028 0.460
#> GSM381205 2 0.0870 0.7432 0.000 0.972 0.004 0.012 0.012 0.000
#> GSM381211 2 0.0891 0.7446 0.000 0.968 0.000 0.008 0.024 0.000
#> GSM381220 2 0.4338 -0.2948 0.000 0.496 0.000 0.000 0.020 0.484
#> GSM381222 1 0.5051 0.2952 0.544 0.000 0.020 0.000 0.396 0.040
#> GSM381224 1 0.4995 0.2681 0.528 0.000 0.008 0.000 0.412 0.052
#> GSM381232 4 0.1411 0.9897 0.004 0.000 0.060 0.936 0.000 0.000
#> GSM381240 1 0.2630 0.7976 0.872 0.000 0.000 0.004 0.032 0.092
#> GSM381250 3 0.3074 0.8356 0.020 0.000 0.856 0.000 0.080 0.044
#> GSM381252 2 0.0405 0.7458 0.000 0.988 0.000 0.008 0.004 0.000
#> GSM381254 1 0.0547 0.8265 0.980 0.000 0.000 0.000 0.020 0.000
#> GSM381256 2 0.2274 0.7175 0.000 0.908 0.000 0.028 0.028 0.036
#> GSM381257 1 0.2988 0.7685 0.852 0.000 0.004 0.000 0.060 0.084
#> GSM381259 1 0.0000 0.8313 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381260 5 0.7060 0.7276 0.188 0.000 0.232 0.004 0.472 0.104
#> GSM381261 6 0.5809 0.7195 0.000 0.272 0.000 0.000 0.232 0.496
#> GSM381263 3 0.3228 0.8233 0.020 0.000 0.844 0.000 0.092 0.044
#> GSM381265 1 0.0000 0.8313 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381268 3 0.1074 0.8878 0.012 0.000 0.960 0.000 0.000 0.028
#> GSM381270 6 0.3409 0.7761 0.000 0.300 0.000 0.000 0.000 0.700
#> GSM381271 4 0.1411 0.9897 0.004 0.000 0.060 0.936 0.000 0.000
#> GSM381275 6 0.5901 0.7036 0.000 0.304 0.000 0.000 0.232 0.464
#> GSM381279 6 0.3409 0.7761 0.000 0.300 0.000 0.000 0.000 0.700
#> GSM381195 1 0.0146 0.8307 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM381196 3 0.3074 0.8356 0.020 0.000 0.856 0.000 0.080 0.044
#> GSM381198 2 0.0405 0.7458 0.000 0.988 0.000 0.008 0.004 0.000
#> GSM381200 2 0.5521 -0.2543 0.000 0.516 0.000 0.020 0.080 0.384
#> GSM381201 3 0.1003 0.8885 0.004 0.000 0.964 0.004 0.000 0.028
#> GSM381203 3 0.5476 0.3657 0.252 0.000 0.624 0.000 0.080 0.044
#> GSM381204 1 0.0000 0.8313 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381209 1 0.0000 0.8313 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381212 1 0.0000 0.8313 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381213 2 0.4537 -0.0589 0.000 0.576 0.000 0.008 0.024 0.392
#> GSM381214 2 0.0993 0.7441 0.000 0.964 0.000 0.012 0.024 0.000
#> GSM381216 5 0.4789 0.7280 0.092 0.000 0.268 0.000 0.640 0.000
#> GSM381225 3 0.1552 0.8787 0.020 0.000 0.940 0.004 0.000 0.036
#> GSM381231 4 0.1668 0.9878 0.004 0.000 0.060 0.928 0.008 0.000
#> GSM381235 5 0.5049 0.6897 0.060 0.000 0.300 0.000 0.620 0.020
#> GSM381237 1 0.0000 0.8313 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381241 2 0.0405 0.7458 0.000 0.988 0.000 0.008 0.004 0.000
#> GSM381243 6 0.3547 0.7758 0.000 0.300 0.000 0.004 0.000 0.696
#> GSM381245 1 0.3328 0.7763 0.832 0.000 0.008 0.004 0.044 0.112
#> GSM381246 2 0.3282 0.6754 0.000 0.836 0.004 0.028 0.116 0.016
#> GSM381251 3 0.0436 0.8884 0.004 0.000 0.988 0.004 0.000 0.004
#> GSM381264 1 0.0146 0.8307 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM381206 2 0.0870 0.7432 0.000 0.972 0.004 0.012 0.012 0.000
#> GSM381217 5 0.5235 0.7171 0.084 0.000 0.276 0.000 0.620 0.020
#> GSM381218 2 0.0972 0.7454 0.000 0.964 0.000 0.008 0.028 0.000
#> GSM381226 2 0.4609 0.5391 0.000 0.744 0.004 0.024 0.104 0.124
#> GSM381227 6 0.3409 0.7761 0.000 0.300 0.000 0.000 0.000 0.700
#> GSM381228 4 0.2094 0.9897 0.004 0.000 0.060 0.912 0.004 0.020
#> GSM381236 4 0.2094 0.9897 0.004 0.000 0.060 0.912 0.004 0.020
#> GSM381244 5 0.6011 0.3033 0.328 0.000 0.016 0.004 0.508 0.144
#> GSM381272 4 0.1411 0.9897 0.004 0.000 0.060 0.936 0.000 0.000
#> GSM381277 1 0.4845 0.6233 0.692 0.000 0.004 0.004 0.148 0.152
#> GSM381278 3 0.1194 0.8788 0.004 0.000 0.956 0.008 0.000 0.032
#> GSM381197 5 0.7402 0.6682 0.236 0.000 0.240 0.004 0.400 0.120
#> GSM381202 5 0.6848 0.7259 0.220 0.000 0.200 0.004 0.496 0.080
#> GSM381207 1 0.4175 0.7234 0.768 0.000 0.008 0.004 0.100 0.120
#> GSM381208 2 0.1924 0.7323 0.000 0.920 0.004 0.028 0.048 0.000
#> GSM381210 1 0.2909 0.7886 0.868 0.000 0.008 0.004 0.060 0.060
#> GSM381215 3 0.2474 0.8513 0.004 0.000 0.884 0.000 0.080 0.032
#> GSM381219 2 0.1549 0.7360 0.000 0.936 0.000 0.020 0.044 0.000
#> GSM381221 2 0.3955 0.5550 0.000 0.768 0.000 0.028 0.028 0.176
#> GSM381223 6 0.5901 0.7036 0.000 0.304 0.000 0.000 0.232 0.464
#> GSM381229 3 0.0922 0.8843 0.004 0.000 0.968 0.004 0.000 0.024
#> GSM381230 1 0.0146 0.8306 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM381233 1 0.5051 0.2952 0.544 0.000 0.020 0.000 0.396 0.040
#> GSM381234 1 0.0547 0.8265 0.980 0.000 0.000 0.000 0.020 0.000
#> GSM381238 4 0.2307 0.9878 0.004 0.000 0.060 0.904 0.012 0.020
#> GSM381239 4 0.2094 0.9897 0.004 0.000 0.060 0.912 0.004 0.020
#> GSM381242 5 0.6528 0.7464 0.120 0.000 0.240 0.004 0.544 0.092
#> GSM381247 6 0.3547 0.7758 0.000 0.300 0.000 0.004 0.000 0.696
#> GSM381248 1 0.2981 0.7955 0.856 0.000 0.004 0.004 0.044 0.092
#> GSM381249 1 0.4672 0.2875 0.548 0.000 0.012 0.000 0.416 0.024
#> GSM381253 3 0.3074 0.8356 0.020 0.000 0.856 0.000 0.080 0.044
#> GSM381255 2 0.0520 0.7457 0.000 0.984 0.000 0.008 0.008 0.000
#> GSM381258 5 0.3954 0.6030 0.012 0.000 0.352 0.000 0.636 0.000
#> GSM381262 3 0.0291 0.8897 0.004 0.000 0.992 0.000 0.000 0.004
#> GSM381266 3 0.1036 0.8822 0.004 0.000 0.964 0.008 0.000 0.024
#> GSM381267 2 0.4721 -0.2895 0.000 0.492 0.000 0.012 0.024 0.472
#> GSM381269 5 0.4274 0.3853 0.336 0.000 0.024 0.000 0.636 0.004
#> GSM381273 3 0.1036 0.8822 0.004 0.000 0.964 0.008 0.000 0.024
#> GSM381274 6 0.5910 0.6985 0.000 0.308 0.000 0.000 0.232 0.460
#> GSM381276 5 0.6597 0.5504 0.052 0.000 0.376 0.004 0.428 0.140
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 other(p) k
#> MAD:kmeans 86 0.744 2
#> MAD:kmeans 86 0.863 3
#> MAD:kmeans 78 0.590 4
#> MAD:kmeans 65 0.594 5
#> MAD:kmeans 74 0.695 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 86 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 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 0.827 0.953 0.977 0.4642 0.548 0.548
#> 3 3 0.984 0.972 0.984 0.4361 0.781 0.600
#> 4 4 0.929 0.881 0.949 0.0867 0.882 0.674
#> 5 5 0.894 0.884 0.931 0.0672 0.940 0.789
#> 6 6 0.858 0.790 0.882 0.0615 0.916 0.654
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] 3
There is also optional best \(k\) = 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM381194 1 0.000 0.963 1.000 0.000
#> GSM381199 2 0.000 1.000 0.000 1.000
#> GSM381205 2 0.000 1.000 0.000 1.000
#> GSM381211 2 0.000 1.000 0.000 1.000
#> GSM381220 2 0.000 1.000 0.000 1.000
#> GSM381222 1 0.000 0.963 1.000 0.000
#> GSM381224 1 0.000 0.963 1.000 0.000
#> GSM381232 1 0.730 0.774 0.796 0.204
#> GSM381240 1 0.000 0.963 1.000 0.000
#> GSM381250 1 0.000 0.963 1.000 0.000
#> GSM381252 2 0.000 1.000 0.000 1.000
#> GSM381254 1 0.000 0.963 1.000 0.000
#> GSM381256 2 0.000 1.000 0.000 1.000
#> GSM381257 1 0.000 0.963 1.000 0.000
#> GSM381259 1 0.000 0.963 1.000 0.000
#> GSM381260 1 0.000 0.963 1.000 0.000
#> GSM381261 2 0.000 1.000 0.000 1.000
#> GSM381263 1 0.000 0.963 1.000 0.000
#> GSM381265 1 0.000 0.963 1.000 0.000
#> GSM381268 1 0.000 0.963 1.000 0.000
#> GSM381270 2 0.000 1.000 0.000 1.000
#> GSM381271 1 0.730 0.774 0.796 0.204
#> GSM381275 2 0.000 1.000 0.000 1.000
#> GSM381279 2 0.000 1.000 0.000 1.000
#> GSM381195 1 0.000 0.963 1.000 0.000
#> GSM381196 1 0.000 0.963 1.000 0.000
#> GSM381198 2 0.000 1.000 0.000 1.000
#> GSM381200 2 0.000 1.000 0.000 1.000
#> GSM381201 1 0.000 0.963 1.000 0.000
#> GSM381203 1 0.000 0.963 1.000 0.000
#> GSM381204 1 0.000 0.963 1.000 0.000
#> GSM381209 1 0.000 0.963 1.000 0.000
#> GSM381212 1 0.000 0.963 1.000 0.000
#> GSM381213 2 0.000 1.000 0.000 1.000
#> GSM381214 2 0.000 1.000 0.000 1.000
#> GSM381216 1 0.000 0.963 1.000 0.000
#> GSM381225 1 0.929 0.481 0.656 0.344
#> GSM381231 1 0.730 0.774 0.796 0.204
#> GSM381235 1 0.000 0.963 1.000 0.000
#> GSM381237 1 0.000 0.963 1.000 0.000
#> GSM381241 2 0.000 1.000 0.000 1.000
#> GSM381243 2 0.000 1.000 0.000 1.000
#> GSM381245 1 0.000 0.963 1.000 0.000
#> GSM381246 2 0.000 1.000 0.000 1.000
#> GSM381251 1 0.000 0.963 1.000 0.000
#> GSM381264 1 0.000 0.963 1.000 0.000
#> GSM381206 2 0.000 1.000 0.000 1.000
#> GSM381217 1 0.000 0.963 1.000 0.000
#> GSM381218 2 0.000 1.000 0.000 1.000
#> GSM381226 2 0.000 1.000 0.000 1.000
#> GSM381227 2 0.000 1.000 0.000 1.000
#> GSM381228 1 0.730 0.774 0.796 0.204
#> GSM381236 1 0.730 0.774 0.796 0.204
#> GSM381244 1 0.000 0.963 1.000 0.000
#> GSM381272 1 0.730 0.774 0.796 0.204
#> GSM381277 1 0.000 0.963 1.000 0.000
#> GSM381278 1 0.000 0.963 1.000 0.000
#> GSM381197 1 0.000 0.963 1.000 0.000
#> GSM381202 1 0.000 0.963 1.000 0.000
#> GSM381207 1 0.000 0.963 1.000 0.000
#> GSM381208 2 0.000 1.000 0.000 1.000
#> GSM381210 1 0.000 0.963 1.000 0.000
#> GSM381215 1 0.000 0.963 1.000 0.000
#> GSM381219 2 0.000 1.000 0.000 1.000
#> GSM381221 2 0.000 1.000 0.000 1.000
#> GSM381223 2 0.000 1.000 0.000 1.000
#> GSM381229 1 0.000 0.963 1.000 0.000
#> GSM381230 1 0.000 0.963 1.000 0.000
#> GSM381233 1 0.000 0.963 1.000 0.000
#> GSM381234 1 0.000 0.963 1.000 0.000
#> GSM381238 1 0.730 0.774 0.796 0.204
#> GSM381239 1 0.730 0.774 0.796 0.204
#> GSM381242 1 0.000 0.963 1.000 0.000
#> GSM381247 2 0.000 1.000 0.000 1.000
#> GSM381248 1 0.000 0.963 1.000 0.000
#> GSM381249 1 0.000 0.963 1.000 0.000
#> GSM381253 1 0.000 0.963 1.000 0.000
#> GSM381255 2 0.000 1.000 0.000 1.000
#> GSM381258 1 0.000 0.963 1.000 0.000
#> GSM381262 1 0.000 0.963 1.000 0.000
#> GSM381266 1 0.000 0.963 1.000 0.000
#> GSM381267 2 0.000 1.000 0.000 1.000
#> GSM381269 1 0.000 0.963 1.000 0.000
#> GSM381273 1 0.000 0.963 1.000 0.000
#> GSM381274 2 0.000 1.000 0.000 1.000
#> GSM381276 1 0.000 0.963 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM381194 3 0.0000 0.943 0.000 0 1.000
#> GSM381199 2 0.0000 1.000 0.000 1 0.000
#> GSM381205 2 0.0000 1.000 0.000 1 0.000
#> GSM381211 2 0.0000 1.000 0.000 1 0.000
#> GSM381220 2 0.0000 1.000 0.000 1 0.000
#> GSM381222 1 0.0000 0.999 1.000 0 0.000
#> GSM381224 1 0.0000 0.999 1.000 0 0.000
#> GSM381232 3 0.0000 0.943 0.000 0 1.000
#> GSM381240 1 0.0000 0.999 1.000 0 0.000
#> GSM381250 3 0.4605 0.800 0.204 0 0.796
#> GSM381252 2 0.0000 1.000 0.000 1 0.000
#> GSM381254 1 0.0000 0.999 1.000 0 0.000
#> GSM381256 2 0.0000 1.000 0.000 1 0.000
#> GSM381257 1 0.0000 0.999 1.000 0 0.000
#> GSM381259 1 0.0000 0.999 1.000 0 0.000
#> GSM381260 1 0.1289 0.964 0.968 0 0.032
#> GSM381261 2 0.0000 1.000 0.000 1 0.000
#> GSM381263 3 0.4555 0.804 0.200 0 0.800
#> GSM381265 1 0.0000 0.999 1.000 0 0.000
#> GSM381268 3 0.0237 0.941 0.004 0 0.996
#> GSM381270 2 0.0000 1.000 0.000 1 0.000
#> GSM381271 3 0.0000 0.943 0.000 0 1.000
#> GSM381275 2 0.0000 1.000 0.000 1 0.000
#> GSM381279 2 0.0000 1.000 0.000 1 0.000
#> GSM381195 1 0.0000 0.999 1.000 0 0.000
#> GSM381196 3 0.4605 0.800 0.204 0 0.796
#> GSM381198 2 0.0000 1.000 0.000 1 0.000
#> GSM381200 2 0.0000 1.000 0.000 1 0.000
#> GSM381201 3 0.0000 0.943 0.000 0 1.000
#> GSM381203 1 0.0000 0.999 1.000 0 0.000
#> GSM381204 1 0.0000 0.999 1.000 0 0.000
#> GSM381209 1 0.0000 0.999 1.000 0 0.000
#> GSM381212 1 0.0000 0.999 1.000 0 0.000
#> GSM381213 2 0.0000 1.000 0.000 1 0.000
#> GSM381214 2 0.0000 1.000 0.000 1 0.000
#> GSM381216 1 0.0000 0.999 1.000 0 0.000
#> GSM381225 3 0.4504 0.808 0.196 0 0.804
#> GSM381231 3 0.0000 0.943 0.000 0 1.000
#> GSM381235 1 0.0000 0.999 1.000 0 0.000
#> GSM381237 1 0.0000 0.999 1.000 0 0.000
#> GSM381241 2 0.0000 1.000 0.000 1 0.000
#> GSM381243 2 0.0000 1.000 0.000 1 0.000
#> GSM381245 1 0.0000 0.999 1.000 0 0.000
#> GSM381246 2 0.0000 1.000 0.000 1 0.000
#> GSM381251 3 0.0000 0.943 0.000 0 1.000
#> GSM381264 1 0.0000 0.999 1.000 0 0.000
#> GSM381206 2 0.0000 1.000 0.000 1 0.000
#> GSM381217 1 0.0000 0.999 1.000 0 0.000
#> GSM381218 2 0.0000 1.000 0.000 1 0.000
#> GSM381226 2 0.0000 1.000 0.000 1 0.000
#> GSM381227 2 0.0000 1.000 0.000 1 0.000
#> GSM381228 3 0.0000 0.943 0.000 0 1.000
#> GSM381236 3 0.0000 0.943 0.000 0 1.000
#> GSM381244 1 0.0000 0.999 1.000 0 0.000
#> GSM381272 3 0.0000 0.943 0.000 0 1.000
#> GSM381277 1 0.0000 0.999 1.000 0 0.000
#> GSM381278 3 0.0000 0.943 0.000 0 1.000
#> GSM381197 1 0.0000 0.999 1.000 0 0.000
#> GSM381202 1 0.0000 0.999 1.000 0 0.000
#> GSM381207 1 0.0000 0.999 1.000 0 0.000
#> GSM381208 2 0.0000 1.000 0.000 1 0.000
#> GSM381210 1 0.0000 0.999 1.000 0 0.000
#> GSM381215 3 0.0000 0.943 0.000 0 1.000
#> GSM381219 2 0.0000 1.000 0.000 1 0.000
#> GSM381221 2 0.0000 1.000 0.000 1 0.000
#> GSM381223 2 0.0000 1.000 0.000 1 0.000
#> GSM381229 3 0.0000 0.943 0.000 0 1.000
#> GSM381230 1 0.0000 0.999 1.000 0 0.000
#> GSM381233 1 0.0000 0.999 1.000 0 0.000
#> GSM381234 1 0.0000 0.999 1.000 0 0.000
#> GSM381238 3 0.0000 0.943 0.000 0 1.000
#> GSM381239 3 0.0000 0.943 0.000 0 1.000
#> GSM381242 1 0.0000 0.999 1.000 0 0.000
#> GSM381247 2 0.0000 1.000 0.000 1 0.000
#> GSM381248 1 0.0000 0.999 1.000 0 0.000
#> GSM381249 1 0.0000 0.999 1.000 0 0.000
#> GSM381253 3 0.5058 0.745 0.244 0 0.756
#> GSM381255 2 0.0000 1.000 0.000 1 0.000
#> GSM381258 3 0.2537 0.898 0.080 0 0.920
#> GSM381262 3 0.0000 0.943 0.000 0 1.000
#> GSM381266 3 0.0000 0.943 0.000 0 1.000
#> GSM381267 2 0.0000 1.000 0.000 1 0.000
#> GSM381269 1 0.0000 0.999 1.000 0 0.000
#> GSM381273 3 0.0000 0.943 0.000 0 1.000
#> GSM381274 2 0.0000 1.000 0.000 1 0.000
#> GSM381276 3 0.4555 0.804 0.200 0 0.800
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM381194 3 0.0592 0.790 0.000 0 0.984 0.016
#> GSM381199 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381205 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381211 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381220 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381222 1 0.0707 0.965 0.980 0 0.020 0.000
#> GSM381224 1 0.0469 0.970 0.988 0 0.012 0.000
#> GSM381232 4 0.0000 1.000 0.000 0 0.000 1.000
#> GSM381240 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM381250 3 0.0336 0.791 0.008 0 0.992 0.000
#> GSM381252 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381254 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM381256 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381257 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM381259 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM381260 3 0.4855 0.404 0.400 0 0.600 0.000
#> GSM381261 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381263 3 0.0188 0.791 0.004 0 0.996 0.000
#> GSM381265 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM381268 3 0.0817 0.789 0.000 0 0.976 0.024
#> GSM381270 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381271 4 0.0000 1.000 0.000 0 0.000 1.000
#> GSM381275 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381279 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381195 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM381196 3 0.0592 0.790 0.016 0 0.984 0.000
#> GSM381198 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381200 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381201 3 0.1022 0.785 0.000 0 0.968 0.032
#> GSM381203 3 0.2868 0.728 0.136 0 0.864 0.000
#> GSM381204 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM381209 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM381212 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM381213 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381214 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381216 3 0.4992 0.173 0.476 0 0.524 0.000
#> GSM381225 3 0.0336 0.791 0.000 0 0.992 0.008
#> GSM381231 4 0.0000 1.000 0.000 0 0.000 1.000
#> GSM381235 3 0.0336 0.790 0.008 0 0.992 0.000
#> GSM381237 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM381241 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381243 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381245 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM381246 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381251 3 0.0817 0.789 0.000 0 0.976 0.024
#> GSM381264 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM381206 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381217 3 0.4941 0.290 0.436 0 0.564 0.000
#> GSM381218 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381226 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381227 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381228 4 0.0000 1.000 0.000 0 0.000 1.000
#> GSM381236 4 0.0000 1.000 0.000 0 0.000 1.000
#> GSM381244 1 0.0592 0.968 0.984 0 0.016 0.000
#> GSM381272 4 0.0000 1.000 0.000 0 0.000 1.000
#> GSM381277 1 0.0188 0.974 0.996 0 0.004 0.000
#> GSM381278 3 0.4713 0.379 0.000 0 0.640 0.360
#> GSM381197 3 0.4877 0.394 0.408 0 0.592 0.000
#> GSM381202 1 0.4790 0.265 0.620 0 0.380 0.000
#> GSM381207 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM381208 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381210 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM381215 3 0.0592 0.790 0.000 0 0.984 0.016
#> GSM381219 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381221 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381223 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381229 3 0.0921 0.787 0.000 0 0.972 0.028
#> GSM381230 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM381233 1 0.0707 0.965 0.980 0 0.020 0.000
#> GSM381234 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM381238 4 0.0000 1.000 0.000 0 0.000 1.000
#> GSM381239 4 0.0000 1.000 0.000 0 0.000 1.000
#> GSM381242 3 0.4948 0.301 0.440 0 0.560 0.000
#> GSM381247 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381248 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM381249 1 0.0469 0.970 0.988 0 0.012 0.000
#> GSM381253 3 0.0524 0.792 0.008 0 0.988 0.004
#> GSM381255 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381258 3 0.0000 0.790 0.000 0 1.000 0.000
#> GSM381262 3 0.0817 0.789 0.000 0 0.976 0.024
#> GSM381266 3 0.4713 0.379 0.000 0 0.640 0.360
#> GSM381267 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381269 1 0.1211 0.948 0.960 0 0.040 0.000
#> GSM381273 3 0.4697 0.387 0.000 0 0.644 0.356
#> GSM381274 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381276 3 0.5473 0.642 0.192 0 0.724 0.084
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM381194 5 0.0290 0.957 0.000 0.000 0.008 0.000 0.992
#> GSM381199 2 0.1270 0.958 0.000 0.948 0.052 0.000 0.000
#> GSM381205 2 0.0162 0.961 0.000 0.996 0.004 0.000 0.000
#> GSM381211 2 0.0162 0.961 0.000 0.996 0.004 0.000 0.000
#> GSM381220 2 0.0880 0.961 0.000 0.968 0.032 0.000 0.000
#> GSM381222 1 0.4192 0.328 0.596 0.000 0.404 0.000 0.000
#> GSM381224 1 0.4256 0.246 0.564 0.000 0.436 0.000 0.000
#> GSM381232 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM381240 1 0.0510 0.884 0.984 0.000 0.016 0.000 0.000
#> GSM381250 5 0.0404 0.955 0.000 0.000 0.012 0.000 0.988
#> GSM381252 2 0.0162 0.961 0.000 0.996 0.004 0.000 0.000
#> GSM381254 1 0.0000 0.892 1.000 0.000 0.000 0.000 0.000
#> GSM381256 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM381257 1 0.0000 0.892 1.000 0.000 0.000 0.000 0.000
#> GSM381259 1 0.0000 0.892 1.000 0.000 0.000 0.000 0.000
#> GSM381260 3 0.4421 0.787 0.184 0.000 0.748 0.000 0.068
#> GSM381261 2 0.2074 0.945 0.000 0.896 0.104 0.000 0.000
#> GSM381263 5 0.0963 0.938 0.000 0.000 0.036 0.000 0.964
#> GSM381265 1 0.0000 0.892 1.000 0.000 0.000 0.000 0.000
#> GSM381268 5 0.0000 0.959 0.000 0.000 0.000 0.000 1.000
#> GSM381270 2 0.2074 0.945 0.000 0.896 0.104 0.000 0.000
#> GSM381271 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM381275 2 0.2074 0.945 0.000 0.896 0.104 0.000 0.000
#> GSM381279 2 0.2074 0.945 0.000 0.896 0.104 0.000 0.000
#> GSM381195 1 0.0000 0.892 1.000 0.000 0.000 0.000 0.000
#> GSM381196 5 0.0404 0.955 0.000 0.000 0.012 0.000 0.988
#> GSM381198 2 0.0162 0.961 0.000 0.996 0.004 0.000 0.000
#> GSM381200 2 0.1608 0.954 0.000 0.928 0.072 0.000 0.000
#> GSM381201 5 0.0000 0.959 0.000 0.000 0.000 0.000 1.000
#> GSM381203 5 0.3779 0.620 0.236 0.000 0.012 0.000 0.752
#> GSM381204 1 0.0000 0.892 1.000 0.000 0.000 0.000 0.000
#> GSM381209 1 0.0000 0.892 1.000 0.000 0.000 0.000 0.000
#> GSM381212 1 0.0000 0.892 1.000 0.000 0.000 0.000 0.000
#> GSM381213 2 0.1671 0.951 0.000 0.924 0.076 0.000 0.000
#> GSM381214 2 0.0162 0.961 0.000 0.996 0.004 0.000 0.000
#> GSM381216 3 0.2708 0.837 0.072 0.000 0.884 0.000 0.044
#> GSM381225 5 0.0162 0.958 0.000 0.000 0.004 0.000 0.996
#> GSM381231 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM381235 3 0.2848 0.787 0.004 0.000 0.840 0.000 0.156
#> GSM381237 1 0.0000 0.892 1.000 0.000 0.000 0.000 0.000
#> GSM381241 2 0.0162 0.961 0.000 0.996 0.004 0.000 0.000
#> GSM381243 2 0.2074 0.945 0.000 0.896 0.104 0.000 0.000
#> GSM381245 1 0.0404 0.886 0.988 0.000 0.012 0.000 0.000
#> GSM381246 2 0.0404 0.962 0.000 0.988 0.012 0.000 0.000
#> GSM381251 5 0.0000 0.959 0.000 0.000 0.000 0.000 1.000
#> GSM381264 1 0.0000 0.892 1.000 0.000 0.000 0.000 0.000
#> GSM381206 2 0.0162 0.961 0.000 0.996 0.004 0.000 0.000
#> GSM381217 3 0.3110 0.837 0.080 0.000 0.860 0.000 0.060
#> GSM381218 2 0.0162 0.961 0.000 0.996 0.004 0.000 0.000
#> GSM381226 2 0.0794 0.961 0.000 0.972 0.028 0.000 0.000
#> GSM381227 2 0.2074 0.945 0.000 0.896 0.104 0.000 0.000
#> GSM381228 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM381236 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM381244 3 0.2471 0.800 0.136 0.000 0.864 0.000 0.000
#> GSM381272 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM381277 1 0.2020 0.803 0.900 0.000 0.100 0.000 0.000
#> GSM381278 5 0.1544 0.914 0.000 0.000 0.000 0.068 0.932
#> GSM381197 3 0.5874 0.477 0.364 0.000 0.528 0.000 0.108
#> GSM381202 3 0.4451 0.734 0.248 0.000 0.712 0.000 0.040
#> GSM381207 1 0.0703 0.878 0.976 0.000 0.024 0.000 0.000
#> GSM381208 2 0.0162 0.961 0.000 0.996 0.004 0.000 0.000
#> GSM381210 1 0.0609 0.878 0.980 0.000 0.020 0.000 0.000
#> GSM381215 5 0.0162 0.958 0.000 0.000 0.004 0.000 0.996
#> GSM381219 2 0.0162 0.961 0.000 0.996 0.004 0.000 0.000
#> GSM381221 2 0.0162 0.962 0.000 0.996 0.004 0.000 0.000
#> GSM381223 2 0.2074 0.945 0.000 0.896 0.104 0.000 0.000
#> GSM381229 5 0.0000 0.959 0.000 0.000 0.000 0.000 1.000
#> GSM381230 1 0.0000 0.892 1.000 0.000 0.000 0.000 0.000
#> GSM381233 1 0.4192 0.328 0.596 0.000 0.404 0.000 0.000
#> GSM381234 1 0.0000 0.892 1.000 0.000 0.000 0.000 0.000
#> GSM381238 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM381239 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM381242 3 0.2569 0.832 0.040 0.000 0.892 0.000 0.068
#> GSM381247 2 0.2074 0.945 0.000 0.896 0.104 0.000 0.000
#> GSM381248 1 0.0404 0.886 0.988 0.000 0.012 0.000 0.000
#> GSM381249 1 0.4256 0.241 0.564 0.000 0.436 0.000 0.000
#> GSM381253 5 0.0162 0.958 0.000 0.000 0.004 0.000 0.996
#> GSM381255 2 0.0162 0.961 0.000 0.996 0.004 0.000 0.000
#> GSM381258 3 0.2377 0.800 0.000 0.000 0.872 0.000 0.128
#> GSM381262 5 0.0000 0.959 0.000 0.000 0.000 0.000 1.000
#> GSM381266 5 0.1410 0.920 0.000 0.000 0.000 0.060 0.940
#> GSM381267 2 0.0963 0.960 0.000 0.964 0.036 0.000 0.000
#> GSM381269 3 0.2377 0.808 0.128 0.000 0.872 0.000 0.000
#> GSM381273 5 0.1341 0.923 0.000 0.000 0.000 0.056 0.944
#> GSM381274 2 0.2074 0.945 0.000 0.896 0.104 0.000 0.000
#> GSM381276 3 0.5152 0.744 0.104 0.000 0.696 0.004 0.196
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM381194 3 0.0935 0.944 0.000 0.000 0.964 0.000 0.032 0.004
#> GSM381199 2 0.3862 -0.207 0.000 0.524 0.000 0.000 0.000 0.476
#> GSM381205 2 0.0000 0.816 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381211 2 0.0000 0.816 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381220 2 0.3765 0.108 0.000 0.596 0.000 0.000 0.000 0.404
#> GSM381222 5 0.4095 0.219 0.480 0.000 0.000 0.000 0.512 0.008
#> GSM381224 5 0.4407 0.192 0.484 0.000 0.000 0.000 0.492 0.024
#> GSM381232 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381240 1 0.1285 0.940 0.944 0.000 0.000 0.000 0.004 0.052
#> GSM381250 3 0.1480 0.939 0.000 0.000 0.940 0.000 0.020 0.040
#> GSM381252 2 0.0000 0.816 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381254 1 0.0405 0.961 0.988 0.000 0.000 0.000 0.004 0.008
#> GSM381256 2 0.1765 0.751 0.000 0.904 0.000 0.000 0.000 0.096
#> GSM381257 1 0.0405 0.960 0.988 0.000 0.000 0.000 0.004 0.008
#> GSM381259 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381260 5 0.4393 0.651 0.140 0.000 0.000 0.000 0.720 0.140
#> GSM381261 6 0.2996 0.937 0.000 0.228 0.000 0.000 0.000 0.772
#> GSM381263 3 0.1970 0.918 0.000 0.000 0.912 0.000 0.060 0.028
#> GSM381265 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381268 3 0.0363 0.950 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM381270 6 0.2912 0.938 0.000 0.216 0.000 0.000 0.000 0.784
#> GSM381271 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381275 6 0.3050 0.933 0.000 0.236 0.000 0.000 0.000 0.764
#> GSM381279 6 0.2883 0.936 0.000 0.212 0.000 0.000 0.000 0.788
#> GSM381195 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381196 3 0.1391 0.941 0.000 0.000 0.944 0.000 0.016 0.040
#> GSM381198 2 0.0000 0.816 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381200 6 0.3843 0.426 0.000 0.452 0.000 0.000 0.000 0.548
#> GSM381201 3 0.0363 0.950 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM381203 3 0.4507 0.611 0.248 0.000 0.692 0.000 0.020 0.040
#> GSM381204 1 0.0146 0.964 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM381209 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381212 1 0.0146 0.964 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM381213 2 0.3866 -0.326 0.000 0.516 0.000 0.000 0.000 0.484
#> GSM381214 2 0.0146 0.815 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM381216 5 0.0291 0.696 0.004 0.000 0.000 0.000 0.992 0.004
#> GSM381225 3 0.0603 0.947 0.000 0.000 0.980 0.000 0.004 0.016
#> GSM381231 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381235 5 0.1218 0.688 0.004 0.000 0.028 0.000 0.956 0.012
#> GSM381237 1 0.0146 0.964 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM381241 2 0.0000 0.816 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381243 6 0.2912 0.938 0.000 0.216 0.000 0.000 0.000 0.784
#> GSM381245 1 0.1219 0.941 0.948 0.000 0.000 0.000 0.004 0.048
#> GSM381246 2 0.1007 0.789 0.000 0.956 0.000 0.000 0.000 0.044
#> GSM381251 3 0.0000 0.949 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM381264 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381206 2 0.0000 0.816 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381217 5 0.0692 0.695 0.004 0.000 0.000 0.000 0.976 0.020
#> GSM381218 2 0.0146 0.815 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM381226 2 0.2912 0.598 0.000 0.784 0.000 0.000 0.000 0.216
#> GSM381227 6 0.2912 0.936 0.000 0.216 0.000 0.000 0.000 0.784
#> GSM381228 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381236 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381244 5 0.3381 0.689 0.044 0.000 0.000 0.000 0.800 0.156
#> GSM381272 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381277 1 0.4061 0.668 0.748 0.000 0.000 0.000 0.088 0.164
#> GSM381278 3 0.1738 0.915 0.000 0.000 0.928 0.052 0.016 0.004
#> GSM381197 5 0.5691 0.487 0.284 0.000 0.012 0.000 0.556 0.148
#> GSM381202 5 0.4026 0.663 0.160 0.000 0.000 0.000 0.752 0.088
#> GSM381207 1 0.1745 0.923 0.920 0.000 0.000 0.000 0.012 0.068
#> GSM381208 2 0.0000 0.816 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381210 1 0.1297 0.927 0.948 0.000 0.000 0.000 0.040 0.012
#> GSM381215 3 0.1088 0.946 0.000 0.000 0.960 0.000 0.016 0.024
#> GSM381219 2 0.0146 0.815 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM381221 2 0.3101 0.557 0.000 0.756 0.000 0.000 0.000 0.244
#> GSM381223 6 0.3050 0.933 0.000 0.236 0.000 0.000 0.000 0.764
#> GSM381229 3 0.0146 0.949 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM381230 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381233 5 0.4093 0.229 0.476 0.000 0.000 0.000 0.516 0.008
#> GSM381234 1 0.0291 0.963 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM381238 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381239 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381242 5 0.2135 0.678 0.000 0.000 0.000 0.000 0.872 0.128
#> GSM381247 6 0.2912 0.938 0.000 0.216 0.000 0.000 0.000 0.784
#> GSM381248 1 0.1010 0.949 0.960 0.000 0.000 0.000 0.004 0.036
#> GSM381249 5 0.4086 0.258 0.464 0.000 0.000 0.000 0.528 0.008
#> GSM381253 3 0.1010 0.946 0.000 0.000 0.960 0.000 0.004 0.036
#> GSM381255 2 0.0000 0.816 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381258 5 0.0291 0.695 0.000 0.000 0.004 0.000 0.992 0.004
#> GSM381262 3 0.0000 0.949 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM381266 3 0.1285 0.923 0.000 0.000 0.944 0.052 0.000 0.004
#> GSM381267 2 0.3756 0.123 0.000 0.600 0.000 0.000 0.000 0.400
#> GSM381269 5 0.0363 0.698 0.012 0.000 0.000 0.000 0.988 0.000
#> GSM381273 3 0.0603 0.945 0.000 0.000 0.980 0.016 0.000 0.004
#> GSM381274 6 0.3151 0.915 0.000 0.252 0.000 0.000 0.000 0.748
#> GSM381276 5 0.6130 0.587 0.096 0.000 0.144 0.000 0.604 0.156
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 other(p) k
#> MAD:skmeans 85 0.756 2
#> MAD:skmeans 86 0.863 3
#> MAD:skmeans 77 0.435 4
#> MAD:skmeans 81 0.585 5
#> MAD:skmeans 76 0.705 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 86 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4528 0.548 0.548
#> 3 3 1.000 1.000 1.000 0.2366 0.893 0.804
#> 4 4 0.987 0.956 0.983 0.2571 0.856 0.672
#> 5 5 0.865 0.773 0.893 0.0682 0.962 0.872
#> 6 6 0.780 0.698 0.832 0.0486 0.945 0.794
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
#> GSM381194 1 0 1 1 0
#> GSM381199 2 0 1 0 1
#> GSM381205 2 0 1 0 1
#> GSM381211 2 0 1 0 1
#> GSM381220 2 0 1 0 1
#> GSM381222 1 0 1 1 0
#> GSM381224 1 0 1 1 0
#> GSM381232 1 0 1 1 0
#> GSM381240 1 0 1 1 0
#> GSM381250 1 0 1 1 0
#> GSM381252 2 0 1 0 1
#> GSM381254 1 0 1 1 0
#> GSM381256 2 0 1 0 1
#> GSM381257 1 0 1 1 0
#> GSM381259 1 0 1 1 0
#> GSM381260 1 0 1 1 0
#> GSM381261 2 0 1 0 1
#> GSM381263 1 0 1 1 0
#> GSM381265 1 0 1 1 0
#> GSM381268 1 0 1 1 0
#> GSM381270 2 0 1 0 1
#> GSM381271 1 0 1 1 0
#> GSM381275 2 0 1 0 1
#> GSM381279 2 0 1 0 1
#> GSM381195 1 0 1 1 0
#> GSM381196 1 0 1 1 0
#> GSM381198 2 0 1 0 1
#> GSM381200 2 0 1 0 1
#> GSM381201 1 0 1 1 0
#> GSM381203 1 0 1 1 0
#> GSM381204 1 0 1 1 0
#> GSM381209 1 0 1 1 0
#> GSM381212 1 0 1 1 0
#> GSM381213 2 0 1 0 1
#> GSM381214 2 0 1 0 1
#> GSM381216 1 0 1 1 0
#> GSM381225 1 0 1 1 0
#> GSM381231 1 0 1 1 0
#> GSM381235 1 0 1 1 0
#> GSM381237 1 0 1 1 0
#> GSM381241 2 0 1 0 1
#> GSM381243 2 0 1 0 1
#> GSM381245 1 0 1 1 0
#> GSM381246 2 0 1 0 1
#> GSM381251 1 0 1 1 0
#> GSM381264 1 0 1 1 0
#> GSM381206 2 0 1 0 1
#> GSM381217 1 0 1 1 0
#> GSM381218 2 0 1 0 1
#> GSM381226 2 0 1 0 1
#> GSM381227 2 0 1 0 1
#> GSM381228 1 0 1 1 0
#> GSM381236 1 0 1 1 0
#> GSM381244 1 0 1 1 0
#> GSM381272 1 0 1 1 0
#> GSM381277 1 0 1 1 0
#> GSM381278 1 0 1 1 0
#> GSM381197 1 0 1 1 0
#> GSM381202 1 0 1 1 0
#> GSM381207 1 0 1 1 0
#> GSM381208 2 0 1 0 1
#> GSM381210 1 0 1 1 0
#> GSM381215 1 0 1 1 0
#> GSM381219 2 0 1 0 1
#> GSM381221 2 0 1 0 1
#> GSM381223 2 0 1 0 1
#> GSM381229 1 0 1 1 0
#> GSM381230 1 0 1 1 0
#> GSM381233 1 0 1 1 0
#> GSM381234 1 0 1 1 0
#> GSM381238 1 0 1 1 0
#> GSM381239 1 0 1 1 0
#> GSM381242 1 0 1 1 0
#> GSM381247 2 0 1 0 1
#> GSM381248 1 0 1 1 0
#> GSM381249 1 0 1 1 0
#> GSM381253 1 0 1 1 0
#> GSM381255 2 0 1 0 1
#> GSM381258 1 0 1 1 0
#> GSM381262 1 0 1 1 0
#> GSM381266 1 0 1 1 0
#> GSM381267 2 0 1 0 1
#> GSM381269 1 0 1 1 0
#> GSM381273 1 0 1 1 0
#> GSM381274 2 0 1 0 1
#> GSM381276 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM381194 1 0 1 1 0 0
#> GSM381199 2 0 1 0 1 0
#> GSM381205 2 0 1 0 1 0
#> GSM381211 2 0 1 0 1 0
#> GSM381220 2 0 1 0 1 0
#> GSM381222 1 0 1 1 0 0
#> GSM381224 1 0 1 1 0 0
#> GSM381232 3 0 1 0 0 1
#> GSM381240 1 0 1 1 0 0
#> GSM381250 1 0 1 1 0 0
#> GSM381252 2 0 1 0 1 0
#> GSM381254 1 0 1 1 0 0
#> GSM381256 2 0 1 0 1 0
#> GSM381257 1 0 1 1 0 0
#> GSM381259 1 0 1 1 0 0
#> GSM381260 1 0 1 1 0 0
#> GSM381261 2 0 1 0 1 0
#> GSM381263 1 0 1 1 0 0
#> GSM381265 1 0 1 1 0 0
#> GSM381268 1 0 1 1 0 0
#> GSM381270 2 0 1 0 1 0
#> GSM381271 3 0 1 0 0 1
#> GSM381275 2 0 1 0 1 0
#> GSM381279 2 0 1 0 1 0
#> GSM381195 1 0 1 1 0 0
#> GSM381196 1 0 1 1 0 0
#> GSM381198 2 0 1 0 1 0
#> GSM381200 2 0 1 0 1 0
#> GSM381201 1 0 1 1 0 0
#> GSM381203 1 0 1 1 0 0
#> GSM381204 1 0 1 1 0 0
#> GSM381209 1 0 1 1 0 0
#> GSM381212 1 0 1 1 0 0
#> GSM381213 2 0 1 0 1 0
#> GSM381214 2 0 1 0 1 0
#> GSM381216 1 0 1 1 0 0
#> GSM381225 1 0 1 1 0 0
#> GSM381231 3 0 1 0 0 1
#> GSM381235 1 0 1 1 0 0
#> GSM381237 1 0 1 1 0 0
#> GSM381241 2 0 1 0 1 0
#> GSM381243 2 0 1 0 1 0
#> GSM381245 1 0 1 1 0 0
#> GSM381246 2 0 1 0 1 0
#> GSM381251 1 0 1 1 0 0
#> GSM381264 1 0 1 1 0 0
#> GSM381206 2 0 1 0 1 0
#> GSM381217 1 0 1 1 0 0
#> GSM381218 2 0 1 0 1 0
#> GSM381226 2 0 1 0 1 0
#> GSM381227 2 0 1 0 1 0
#> GSM381228 3 0 1 0 0 1
#> GSM381236 3 0 1 0 0 1
#> GSM381244 1 0 1 1 0 0
#> GSM381272 3 0 1 0 0 1
#> GSM381277 1 0 1 1 0 0
#> GSM381278 1 0 1 1 0 0
#> GSM381197 1 0 1 1 0 0
#> GSM381202 1 0 1 1 0 0
#> GSM381207 1 0 1 1 0 0
#> GSM381208 2 0 1 0 1 0
#> GSM381210 1 0 1 1 0 0
#> GSM381215 1 0 1 1 0 0
#> GSM381219 2 0 1 0 1 0
#> GSM381221 2 0 1 0 1 0
#> GSM381223 2 0 1 0 1 0
#> GSM381229 1 0 1 1 0 0
#> GSM381230 1 0 1 1 0 0
#> GSM381233 1 0 1 1 0 0
#> GSM381234 1 0 1 1 0 0
#> GSM381238 3 0 1 0 0 1
#> GSM381239 3 0 1 0 0 1
#> GSM381242 1 0 1 1 0 0
#> GSM381247 2 0 1 0 1 0
#> GSM381248 1 0 1 1 0 0
#> GSM381249 1 0 1 1 0 0
#> GSM381253 1 0 1 1 0 0
#> GSM381255 2 0 1 0 1 0
#> GSM381258 1 0 1 1 0 0
#> GSM381262 1 0 1 1 0 0
#> GSM381266 1 0 1 1 0 0
#> GSM381267 2 0 1 0 1 0
#> GSM381269 1 0 1 1 0 0
#> GSM381273 1 0 1 1 0 0
#> GSM381274 2 0 1 0 1 0
#> GSM381276 1 0 1 1 0 0
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM381194 3 0.0000 0.9741 0.000 0 1.000 0
#> GSM381199 2 0.0000 1.0000 0.000 1 0.000 0
#> GSM381205 2 0.0000 1.0000 0.000 1 0.000 0
#> GSM381211 2 0.0000 1.0000 0.000 1 0.000 0
#> GSM381220 2 0.0000 1.0000 0.000 1 0.000 0
#> GSM381222 3 0.0000 0.9741 0.000 0 1.000 0
#> GSM381224 1 0.3801 0.7179 0.780 0 0.220 0
#> GSM381232 4 0.0000 1.0000 0.000 0 0.000 1
#> GSM381240 1 0.0000 0.9348 1.000 0 0.000 0
#> GSM381250 3 0.0000 0.9741 0.000 0 1.000 0
#> GSM381252 2 0.0000 1.0000 0.000 1 0.000 0
#> GSM381254 1 0.0000 0.9348 1.000 0 0.000 0
#> GSM381256 2 0.0000 1.0000 0.000 1 0.000 0
#> GSM381257 3 0.0000 0.9741 0.000 0 1.000 0
#> GSM381259 1 0.0000 0.9348 1.000 0 0.000 0
#> GSM381260 3 0.0000 0.9741 0.000 0 1.000 0
#> GSM381261 2 0.0000 1.0000 0.000 1 0.000 0
#> GSM381263 3 0.0000 0.9741 0.000 0 1.000 0
#> GSM381265 1 0.0000 0.9348 1.000 0 0.000 0
#> GSM381268 3 0.0000 0.9741 0.000 0 1.000 0
#> GSM381270 2 0.0000 1.0000 0.000 1 0.000 0
#> GSM381271 4 0.0000 1.0000 0.000 0 0.000 1
#> GSM381275 2 0.0000 1.0000 0.000 1 0.000 0
#> GSM381279 2 0.0000 1.0000 0.000 1 0.000 0
#> GSM381195 1 0.2921 0.8208 0.860 0 0.140 0
#> GSM381196 3 0.0000 0.9741 0.000 0 1.000 0
#> GSM381198 2 0.0000 1.0000 0.000 1 0.000 0
#> GSM381200 2 0.0000 1.0000 0.000 1 0.000 0
#> GSM381201 3 0.0000 0.9741 0.000 0 1.000 0
#> GSM381203 3 0.0000 0.9741 0.000 0 1.000 0
#> GSM381204 1 0.0000 0.9348 1.000 0 0.000 0
#> GSM381209 1 0.0000 0.9348 1.000 0 0.000 0
#> GSM381212 1 0.0000 0.9348 1.000 0 0.000 0
#> GSM381213 2 0.0000 1.0000 0.000 1 0.000 0
#> GSM381214 2 0.0000 1.0000 0.000 1 0.000 0
#> GSM381216 3 0.0000 0.9741 0.000 0 1.000 0
#> GSM381225 3 0.0000 0.9741 0.000 0 1.000 0
#> GSM381231 4 0.0000 1.0000 0.000 0 0.000 1
#> GSM381235 3 0.0000 0.9741 0.000 0 1.000 0
#> GSM381237 1 0.0000 0.9348 1.000 0 0.000 0
#> GSM381241 2 0.0000 1.0000 0.000 1 0.000 0
#> GSM381243 2 0.0000 1.0000 0.000 1 0.000 0
#> GSM381245 3 0.0188 0.9708 0.004 0 0.996 0
#> GSM381246 2 0.0000 1.0000 0.000 1 0.000 0
#> GSM381251 3 0.0000 0.9741 0.000 0 1.000 0
#> GSM381264 1 0.0000 0.9348 1.000 0 0.000 0
#> GSM381206 2 0.0000 1.0000 0.000 1 0.000 0
#> GSM381217 3 0.0000 0.9741 0.000 0 1.000 0
#> GSM381218 2 0.0000 1.0000 0.000 1 0.000 0
#> GSM381226 2 0.0000 1.0000 0.000 1 0.000 0
#> GSM381227 2 0.0000 1.0000 0.000 1 0.000 0
#> GSM381228 4 0.0000 1.0000 0.000 0 0.000 1
#> GSM381236 4 0.0000 1.0000 0.000 0 0.000 1
#> GSM381244 3 0.0000 0.9741 0.000 0 1.000 0
#> GSM381272 4 0.0000 1.0000 0.000 0 0.000 1
#> GSM381277 1 0.0707 0.9244 0.980 0 0.020 0
#> GSM381278 3 0.0000 0.9741 0.000 0 1.000 0
#> GSM381197 3 0.0188 0.9708 0.004 0 0.996 0
#> GSM381202 3 0.0817 0.9510 0.024 0 0.976 0
#> GSM381207 3 0.0000 0.9741 0.000 0 1.000 0
#> GSM381208 2 0.0000 1.0000 0.000 1 0.000 0
#> GSM381210 1 0.1118 0.9150 0.964 0 0.036 0
#> GSM381215 3 0.0000 0.9741 0.000 0 1.000 0
#> GSM381219 2 0.0000 1.0000 0.000 1 0.000 0
#> GSM381221 2 0.0000 1.0000 0.000 1 0.000 0
#> GSM381223 2 0.0000 1.0000 0.000 1 0.000 0
#> GSM381229 3 0.0000 0.9741 0.000 0 1.000 0
#> GSM381230 1 0.0000 0.9348 1.000 0 0.000 0
#> GSM381233 3 0.0000 0.9741 0.000 0 1.000 0
#> GSM381234 1 0.2973 0.8087 0.856 0 0.144 0
#> GSM381238 4 0.0000 1.0000 0.000 0 0.000 1
#> GSM381239 4 0.0000 1.0000 0.000 0 0.000 1
#> GSM381242 3 0.0000 0.9741 0.000 0 1.000 0
#> GSM381247 2 0.0000 1.0000 0.000 1 0.000 0
#> GSM381248 3 0.4977 0.0594 0.460 0 0.540 0
#> GSM381249 1 0.2814 0.8291 0.868 0 0.132 0
#> GSM381253 3 0.0000 0.9741 0.000 0 1.000 0
#> GSM381255 2 0.0000 1.0000 0.000 1 0.000 0
#> GSM381258 3 0.0000 0.9741 0.000 0 1.000 0
#> GSM381262 3 0.0000 0.9741 0.000 0 1.000 0
#> GSM381266 3 0.0000 0.9741 0.000 0 1.000 0
#> GSM381267 2 0.0000 1.0000 0.000 1 0.000 0
#> GSM381269 3 0.4164 0.6138 0.264 0 0.736 0
#> GSM381273 3 0.0000 0.9741 0.000 0 1.000 0
#> GSM381274 2 0.0000 1.0000 0.000 1 0.000 0
#> GSM381276 3 0.0000 0.9741 0.000 0 1.000 0
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM381194 3 0.0000 0.9738 0.000 0.000 1.000 0 0.000
#> GSM381199 2 0.3480 0.1670 0.000 0.752 0.000 0 0.248
#> GSM381205 2 0.3949 0.5953 0.000 0.668 0.000 0 0.332
#> GSM381211 2 0.3949 0.5953 0.000 0.668 0.000 0 0.332
#> GSM381220 2 0.4300 0.1411 0.000 0.524 0.000 0 0.476
#> GSM381222 3 0.0000 0.9738 0.000 0.000 1.000 0 0.000
#> GSM381224 1 0.3274 0.7098 0.780 0.000 0.220 0 0.000
#> GSM381232 4 0.0000 1.0000 0.000 0.000 0.000 1 0.000
#> GSM381240 1 0.0000 0.9331 1.000 0.000 0.000 0 0.000
#> GSM381250 3 0.0000 0.9738 0.000 0.000 1.000 0 0.000
#> GSM381252 2 0.3949 0.5953 0.000 0.668 0.000 0 0.332
#> GSM381254 1 0.0000 0.9331 1.000 0.000 0.000 0 0.000
#> GSM381256 2 0.0000 0.6101 0.000 1.000 0.000 0 0.000
#> GSM381257 3 0.0000 0.9738 0.000 0.000 1.000 0 0.000
#> GSM381259 1 0.0000 0.9331 1.000 0.000 0.000 0 0.000
#> GSM381260 3 0.0000 0.9738 0.000 0.000 1.000 0 0.000
#> GSM381261 5 0.3949 0.6022 0.000 0.332 0.000 0 0.668
#> GSM381263 3 0.0000 0.9738 0.000 0.000 1.000 0 0.000
#> GSM381265 1 0.0000 0.9331 1.000 0.000 0.000 0 0.000
#> GSM381268 3 0.0000 0.9738 0.000 0.000 1.000 0 0.000
#> GSM381270 2 0.3752 0.0278 0.000 0.708 0.000 0 0.292
#> GSM381271 4 0.0000 1.0000 0.000 0.000 0.000 1 0.000
#> GSM381275 5 0.4249 0.1888 0.000 0.432 0.000 0 0.568
#> GSM381279 5 0.4273 0.5999 0.000 0.448 0.000 0 0.552
#> GSM381195 1 0.2516 0.8158 0.860 0.000 0.140 0 0.000
#> GSM381196 3 0.0000 0.9738 0.000 0.000 1.000 0 0.000
#> GSM381198 2 0.3949 0.5953 0.000 0.668 0.000 0 0.332
#> GSM381200 2 0.0000 0.6101 0.000 1.000 0.000 0 0.000
#> GSM381201 3 0.0000 0.9738 0.000 0.000 1.000 0 0.000
#> GSM381203 3 0.0000 0.9738 0.000 0.000 1.000 0 0.000
#> GSM381204 1 0.0000 0.9331 1.000 0.000 0.000 0 0.000
#> GSM381209 1 0.0000 0.9331 1.000 0.000 0.000 0 0.000
#> GSM381212 1 0.0000 0.9331 1.000 0.000 0.000 0 0.000
#> GSM381213 2 0.1908 0.5157 0.000 0.908 0.000 0 0.092
#> GSM381214 2 0.1965 0.6201 0.000 0.904 0.000 0 0.096
#> GSM381216 3 0.0000 0.9738 0.000 0.000 1.000 0 0.000
#> GSM381225 3 0.0000 0.9738 0.000 0.000 1.000 0 0.000
#> GSM381231 4 0.0000 1.0000 0.000 0.000 0.000 1 0.000
#> GSM381235 3 0.0000 0.9738 0.000 0.000 1.000 0 0.000
#> GSM381237 1 0.0000 0.9331 1.000 0.000 0.000 0 0.000
#> GSM381241 2 0.2127 0.6208 0.000 0.892 0.000 0 0.108
#> GSM381243 5 0.3003 0.5556 0.000 0.188 0.000 0 0.812
#> GSM381245 3 0.0162 0.9703 0.004 0.000 0.996 0 0.000
#> GSM381246 2 0.3895 0.5981 0.000 0.680 0.000 0 0.320
#> GSM381251 3 0.0000 0.9738 0.000 0.000 1.000 0 0.000
#> GSM381264 1 0.0000 0.9331 1.000 0.000 0.000 0 0.000
#> GSM381206 2 0.3949 0.5953 0.000 0.668 0.000 0 0.332
#> GSM381217 3 0.0000 0.9738 0.000 0.000 1.000 0 0.000
#> GSM381218 2 0.0000 0.6101 0.000 1.000 0.000 0 0.000
#> GSM381226 2 0.1792 0.6212 0.000 0.916 0.000 0 0.084
#> GSM381227 5 0.1908 0.4744 0.000 0.092 0.000 0 0.908
#> GSM381228 4 0.0000 1.0000 0.000 0.000 0.000 1 0.000
#> GSM381236 4 0.0000 1.0000 0.000 0.000 0.000 1 0.000
#> GSM381244 3 0.0000 0.9738 0.000 0.000 1.000 0 0.000
#> GSM381272 4 0.0000 1.0000 0.000 0.000 0.000 1 0.000
#> GSM381277 1 0.0609 0.9224 0.980 0.000 0.020 0 0.000
#> GSM381278 3 0.0000 0.9738 0.000 0.000 1.000 0 0.000
#> GSM381197 3 0.0162 0.9703 0.004 0.000 0.996 0 0.000
#> GSM381202 3 0.0703 0.9503 0.024 0.000 0.976 0 0.000
#> GSM381207 3 0.0000 0.9738 0.000 0.000 1.000 0 0.000
#> GSM381208 2 0.3949 0.5953 0.000 0.668 0.000 0 0.332
#> GSM381210 1 0.0963 0.9127 0.964 0.000 0.036 0 0.000
#> GSM381215 3 0.0000 0.9738 0.000 0.000 1.000 0 0.000
#> GSM381219 2 0.0000 0.6101 0.000 1.000 0.000 0 0.000
#> GSM381221 2 0.0290 0.6039 0.000 0.992 0.000 0 0.008
#> GSM381223 2 0.4306 -0.4945 0.000 0.508 0.000 0 0.492
#> GSM381229 3 0.0000 0.9738 0.000 0.000 1.000 0 0.000
#> GSM381230 1 0.0000 0.9331 1.000 0.000 0.000 0 0.000
#> GSM381233 3 0.0000 0.9738 0.000 0.000 1.000 0 0.000
#> GSM381234 1 0.2561 0.8031 0.856 0.000 0.144 0 0.000
#> GSM381238 4 0.0000 1.0000 0.000 0.000 0.000 1 0.000
#> GSM381239 4 0.0000 1.0000 0.000 0.000 0.000 1 0.000
#> GSM381242 3 0.0000 0.9738 0.000 0.000 1.000 0 0.000
#> GSM381247 5 0.4235 0.6209 0.000 0.424 0.000 0 0.576
#> GSM381248 3 0.4287 0.0594 0.460 0.000 0.540 0 0.000
#> GSM381249 1 0.2424 0.8244 0.868 0.000 0.132 0 0.000
#> GSM381253 3 0.0000 0.9738 0.000 0.000 1.000 0 0.000
#> GSM381255 2 0.3949 0.5953 0.000 0.668 0.000 0 0.332
#> GSM381258 3 0.0000 0.9738 0.000 0.000 1.000 0 0.000
#> GSM381262 3 0.0000 0.9738 0.000 0.000 1.000 0 0.000
#> GSM381266 3 0.0000 0.9738 0.000 0.000 1.000 0 0.000
#> GSM381267 2 0.0000 0.6101 0.000 1.000 0.000 0 0.000
#> GSM381269 3 0.3586 0.6138 0.264 0.000 0.736 0 0.000
#> GSM381273 3 0.0000 0.9738 0.000 0.000 1.000 0 0.000
#> GSM381274 2 0.4201 -0.3329 0.000 0.592 0.000 0 0.408
#> GSM381276 3 0.0000 0.9738 0.000 0.000 1.000 0 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM381194 3 0.0000 0.8943 0.000 0.000 1.000 0 0.000 0.000
#> GSM381199 2 0.4270 0.4598 0.000 0.684 0.000 0 0.052 0.264
#> GSM381205 6 0.3838 0.4679 0.000 0.448 0.000 0 0.000 0.552
#> GSM381211 6 0.3838 0.4679 0.000 0.448 0.000 0 0.000 0.552
#> GSM381220 2 0.4508 0.4386 0.000 0.632 0.000 0 0.052 0.316
#> GSM381222 3 0.2416 0.8211 0.000 0.000 0.844 0 0.156 0.000
#> GSM381224 1 0.4191 0.7009 0.732 0.000 0.180 0 0.088 0.000
#> GSM381232 4 0.0000 1.0000 0.000 0.000 0.000 1 0.000 0.000
#> GSM381240 1 0.0000 0.9267 1.000 0.000 0.000 0 0.000 0.000
#> GSM381250 3 0.0000 0.8943 0.000 0.000 1.000 0 0.000 0.000
#> GSM381252 6 0.3843 0.4629 0.000 0.452 0.000 0 0.000 0.548
#> GSM381254 1 0.0000 0.9267 1.000 0.000 0.000 0 0.000 0.000
#> GSM381256 2 0.1610 0.6404 0.000 0.916 0.000 0 0.000 0.084
#> GSM381257 3 0.0000 0.8943 0.000 0.000 1.000 0 0.000 0.000
#> GSM381259 1 0.0000 0.9267 1.000 0.000 0.000 0 0.000 0.000
#> GSM381260 3 0.2527 0.8182 0.000 0.000 0.832 0 0.168 0.000
#> GSM381261 5 0.3874 0.6206 0.000 0.008 0.000 0 0.636 0.356
#> GSM381263 3 0.0000 0.8943 0.000 0.000 1.000 0 0.000 0.000
#> GSM381265 1 0.0000 0.9267 1.000 0.000 0.000 0 0.000 0.000
#> GSM381268 3 0.0000 0.8943 0.000 0.000 1.000 0 0.000 0.000
#> GSM381270 2 0.4371 0.4359 0.000 0.664 0.000 0 0.052 0.284
#> GSM381271 4 0.0000 1.0000 0.000 0.000 0.000 1 0.000 0.000
#> GSM381275 5 0.5325 0.7183 0.000 0.156 0.000 0 0.584 0.260
#> GSM381279 6 0.5392 -0.2302 0.000 0.440 0.000 0 0.112 0.448
#> GSM381195 1 0.2178 0.8158 0.868 0.000 0.132 0 0.000 0.000
#> GSM381196 3 0.0000 0.8943 0.000 0.000 1.000 0 0.000 0.000
#> GSM381198 6 0.3838 0.4679 0.000 0.448 0.000 0 0.000 0.552
#> GSM381200 2 0.0000 0.6426 0.000 1.000 0.000 0 0.000 0.000
#> GSM381201 3 0.0000 0.8943 0.000 0.000 1.000 0 0.000 0.000
#> GSM381203 3 0.0000 0.8943 0.000 0.000 1.000 0 0.000 0.000
#> GSM381204 1 0.0000 0.9267 1.000 0.000 0.000 0 0.000 0.000
#> GSM381209 1 0.0000 0.9267 1.000 0.000 0.000 0 0.000 0.000
#> GSM381212 1 0.0000 0.9267 1.000 0.000 0.000 0 0.000 0.000
#> GSM381213 5 0.3868 0.2336 0.000 0.492 0.000 0 0.508 0.000
#> GSM381214 2 0.3804 -0.3446 0.000 0.576 0.000 0 0.000 0.424
#> GSM381216 3 0.3659 0.6757 0.000 0.000 0.636 0 0.364 0.000
#> GSM381225 3 0.0000 0.8943 0.000 0.000 1.000 0 0.000 0.000
#> GSM381231 4 0.0000 1.0000 0.000 0.000 0.000 1 0.000 0.000
#> GSM381235 3 0.2454 0.8185 0.000 0.000 0.840 0 0.160 0.000
#> GSM381237 1 0.0000 0.9267 1.000 0.000 0.000 0 0.000 0.000
#> GSM381241 2 0.1501 0.5772 0.000 0.924 0.000 0 0.000 0.076
#> GSM381243 6 0.5355 -0.2252 0.000 0.424 0.000 0 0.108 0.468
#> GSM381245 3 0.0260 0.8911 0.008 0.000 0.992 0 0.000 0.000
#> GSM381246 6 0.3869 0.3888 0.000 0.500 0.000 0 0.000 0.500
#> GSM381251 3 0.0000 0.8943 0.000 0.000 1.000 0 0.000 0.000
#> GSM381264 1 0.0000 0.9267 1.000 0.000 0.000 0 0.000 0.000
#> GSM381206 6 0.3838 0.4679 0.000 0.448 0.000 0 0.000 0.552
#> GSM381217 3 0.2003 0.8436 0.000 0.000 0.884 0 0.116 0.000
#> GSM381218 2 0.0000 0.6426 0.000 1.000 0.000 0 0.000 0.000
#> GSM381226 2 0.3695 -0.2395 0.000 0.624 0.000 0 0.000 0.376
#> GSM381227 6 0.1765 -0.1167 0.000 0.000 0.000 0 0.096 0.904
#> GSM381228 4 0.0000 1.0000 0.000 0.000 0.000 1 0.000 0.000
#> GSM381236 4 0.0000 1.0000 0.000 0.000 0.000 1 0.000 0.000
#> GSM381244 3 0.2730 0.8082 0.000 0.000 0.808 0 0.192 0.000
#> GSM381272 4 0.0000 1.0000 0.000 0.000 0.000 1 0.000 0.000
#> GSM381277 1 0.1333 0.8986 0.944 0.000 0.008 0 0.048 0.000
#> GSM381278 3 0.0000 0.8943 0.000 0.000 1.000 0 0.000 0.000
#> GSM381197 3 0.2778 0.8156 0.008 0.000 0.824 0 0.168 0.000
#> GSM381202 3 0.2506 0.8474 0.052 0.000 0.880 0 0.068 0.000
#> GSM381207 3 0.0000 0.8943 0.000 0.000 1.000 0 0.000 0.000
#> GSM381208 6 0.3838 0.4679 0.000 0.448 0.000 0 0.000 0.552
#> GSM381210 1 0.2257 0.8584 0.876 0.000 0.008 0 0.116 0.000
#> GSM381215 3 0.0000 0.8943 0.000 0.000 1.000 0 0.000 0.000
#> GSM381219 2 0.0000 0.6426 0.000 1.000 0.000 0 0.000 0.000
#> GSM381221 2 0.0713 0.6490 0.000 0.972 0.000 0 0.000 0.028
#> GSM381223 5 0.5257 0.7312 0.000 0.136 0.000 0 0.584 0.280
#> GSM381229 3 0.0000 0.8943 0.000 0.000 1.000 0 0.000 0.000
#> GSM381230 1 0.0547 0.9197 0.980 0.000 0.000 0 0.020 0.000
#> GSM381233 3 0.2762 0.7905 0.000 0.000 0.804 0 0.196 0.000
#> GSM381234 1 0.2378 0.7839 0.848 0.000 0.152 0 0.000 0.000
#> GSM381238 4 0.0000 1.0000 0.000 0.000 0.000 1 0.000 0.000
#> GSM381239 4 0.0000 1.0000 0.000 0.000 0.000 1 0.000 0.000
#> GSM381242 3 0.3464 0.7241 0.000 0.000 0.688 0 0.312 0.000
#> GSM381247 6 0.5392 -0.2302 0.000 0.440 0.000 0 0.112 0.448
#> GSM381248 3 0.3854 0.0263 0.464 0.000 0.536 0 0.000 0.000
#> GSM381249 1 0.2902 0.7924 0.800 0.000 0.004 0 0.196 0.000
#> GSM381253 3 0.0000 0.8943 0.000 0.000 1.000 0 0.000 0.000
#> GSM381255 6 0.3838 0.4679 0.000 0.448 0.000 0 0.000 0.552
#> GSM381258 3 0.3547 0.7068 0.000 0.000 0.668 0 0.332 0.000
#> GSM381262 3 0.0000 0.8943 0.000 0.000 1.000 0 0.000 0.000
#> GSM381266 3 0.0000 0.8943 0.000 0.000 1.000 0 0.000 0.000
#> GSM381267 2 0.1610 0.6404 0.000 0.916 0.000 0 0.000 0.084
#> GSM381269 3 0.5949 0.3240 0.220 0.000 0.416 0 0.364 0.000
#> GSM381273 3 0.0000 0.8943 0.000 0.000 1.000 0 0.000 0.000
#> GSM381274 5 0.5395 0.7309 0.000 0.220 0.000 0 0.584 0.196
#> GSM381276 3 0.2527 0.8182 0.000 0.000 0.832 0 0.168 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 other(p) k
#> MAD:pam 86 0.744 2
#> MAD:pam 86 0.326 3
#> MAD:pam 85 0.453 4
#> MAD:pam 78 0.614 5
#> MAD:pam 66 0.545 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 86 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.983 0.991 0.4570 0.548 0.548
#> 3 3 0.940 0.890 0.952 0.3026 0.871 0.765
#> 4 4 0.836 0.911 0.939 0.2047 0.835 0.616
#> 5 5 0.631 0.695 0.779 0.0571 0.916 0.717
#> 6 6 0.713 0.586 0.768 0.0678 0.917 0.663
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
#> GSM381194 1 0.000 0.986 1.000 0.000
#> GSM381199 2 0.000 1.000 0.000 1.000
#> GSM381205 2 0.000 1.000 0.000 1.000
#> GSM381211 2 0.000 1.000 0.000 1.000
#> GSM381220 2 0.000 1.000 0.000 1.000
#> GSM381222 1 0.000 0.986 1.000 0.000
#> GSM381224 1 0.000 0.986 1.000 0.000
#> GSM381232 1 0.456 0.907 0.904 0.096
#> GSM381240 1 0.000 0.986 1.000 0.000
#> GSM381250 1 0.000 0.986 1.000 0.000
#> GSM381252 2 0.000 1.000 0.000 1.000
#> GSM381254 1 0.000 0.986 1.000 0.000
#> GSM381256 2 0.000 1.000 0.000 1.000
#> GSM381257 1 0.000 0.986 1.000 0.000
#> GSM381259 1 0.000 0.986 1.000 0.000
#> GSM381260 1 0.000 0.986 1.000 0.000
#> GSM381261 2 0.000 1.000 0.000 1.000
#> GSM381263 1 0.000 0.986 1.000 0.000
#> GSM381265 1 0.000 0.986 1.000 0.000
#> GSM381268 1 0.000 0.986 1.000 0.000
#> GSM381270 2 0.000 1.000 0.000 1.000
#> GSM381271 1 0.456 0.907 0.904 0.096
#> GSM381275 2 0.000 1.000 0.000 1.000
#> GSM381279 2 0.000 1.000 0.000 1.000
#> GSM381195 1 0.000 0.986 1.000 0.000
#> GSM381196 1 0.000 0.986 1.000 0.000
#> GSM381198 2 0.000 1.000 0.000 1.000
#> GSM381200 2 0.000 1.000 0.000 1.000
#> GSM381201 1 0.000 0.986 1.000 0.000
#> GSM381203 1 0.000 0.986 1.000 0.000
#> GSM381204 1 0.000 0.986 1.000 0.000
#> GSM381209 1 0.000 0.986 1.000 0.000
#> GSM381212 1 0.000 0.986 1.000 0.000
#> GSM381213 2 0.000 1.000 0.000 1.000
#> GSM381214 2 0.000 1.000 0.000 1.000
#> GSM381216 1 0.000 0.986 1.000 0.000
#> GSM381225 1 0.000 0.986 1.000 0.000
#> GSM381231 1 0.456 0.907 0.904 0.096
#> GSM381235 1 0.000 0.986 1.000 0.000
#> GSM381237 1 0.000 0.986 1.000 0.000
#> GSM381241 2 0.000 1.000 0.000 1.000
#> GSM381243 2 0.000 1.000 0.000 1.000
#> GSM381245 1 0.000 0.986 1.000 0.000
#> GSM381246 2 0.000 1.000 0.000 1.000
#> GSM381251 1 0.000 0.986 1.000 0.000
#> GSM381264 1 0.000 0.986 1.000 0.000
#> GSM381206 2 0.000 1.000 0.000 1.000
#> GSM381217 1 0.000 0.986 1.000 0.000
#> GSM381218 2 0.000 1.000 0.000 1.000
#> GSM381226 2 0.000 1.000 0.000 1.000
#> GSM381227 2 0.000 1.000 0.000 1.000
#> GSM381228 1 0.456 0.907 0.904 0.096
#> GSM381236 1 0.456 0.907 0.904 0.096
#> GSM381244 1 0.000 0.986 1.000 0.000
#> GSM381272 1 0.456 0.907 0.904 0.096
#> GSM381277 1 0.000 0.986 1.000 0.000
#> GSM381278 1 0.000 0.986 1.000 0.000
#> GSM381197 1 0.000 0.986 1.000 0.000
#> GSM381202 1 0.000 0.986 1.000 0.000
#> GSM381207 1 0.000 0.986 1.000 0.000
#> GSM381208 2 0.000 1.000 0.000 1.000
#> GSM381210 1 0.000 0.986 1.000 0.000
#> GSM381215 1 0.000 0.986 1.000 0.000
#> GSM381219 2 0.000 1.000 0.000 1.000
#> GSM381221 2 0.000 1.000 0.000 1.000
#> GSM381223 2 0.000 1.000 0.000 1.000
#> GSM381229 1 0.000 0.986 1.000 0.000
#> GSM381230 1 0.000 0.986 1.000 0.000
#> GSM381233 1 0.000 0.986 1.000 0.000
#> GSM381234 1 0.000 0.986 1.000 0.000
#> GSM381238 1 0.456 0.907 0.904 0.096
#> GSM381239 1 0.456 0.907 0.904 0.096
#> GSM381242 1 0.000 0.986 1.000 0.000
#> GSM381247 2 0.000 1.000 0.000 1.000
#> GSM381248 1 0.000 0.986 1.000 0.000
#> GSM381249 1 0.000 0.986 1.000 0.000
#> GSM381253 1 0.000 0.986 1.000 0.000
#> GSM381255 2 0.000 1.000 0.000 1.000
#> GSM381258 1 0.000 0.986 1.000 0.000
#> GSM381262 1 0.000 0.986 1.000 0.000
#> GSM381266 1 0.000 0.986 1.000 0.000
#> GSM381267 2 0.000 1.000 0.000 1.000
#> GSM381269 1 0.000 0.986 1.000 0.000
#> GSM381273 1 0.000 0.986 1.000 0.000
#> GSM381274 2 0.000 1.000 0.000 1.000
#> GSM381276 1 0.000 0.986 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM381194 1 0.5216 0.6371 0.740 0.000 0.260
#> GSM381199 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM381205 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM381211 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM381220 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM381222 1 0.0237 0.9279 0.996 0.000 0.004
#> GSM381224 1 0.0000 0.9281 1.000 0.000 0.000
#> GSM381232 3 0.1163 0.8811 0.000 0.028 0.972
#> GSM381240 1 0.0892 0.9261 0.980 0.000 0.020
#> GSM381250 1 0.0892 0.9240 0.980 0.000 0.020
#> GSM381252 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM381254 1 0.0892 0.9261 0.980 0.000 0.020
#> GSM381256 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM381257 1 0.0592 0.9274 0.988 0.000 0.012
#> GSM381259 1 0.0892 0.9261 0.980 0.000 0.020
#> GSM381260 1 0.0424 0.9275 0.992 0.000 0.008
#> GSM381261 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM381263 1 0.0892 0.9240 0.980 0.000 0.020
#> GSM381265 1 0.0892 0.9261 0.980 0.000 0.020
#> GSM381268 1 0.2066 0.8971 0.940 0.000 0.060
#> GSM381270 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM381271 3 0.1163 0.8811 0.000 0.028 0.972
#> GSM381275 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM381279 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM381195 1 0.0892 0.9261 0.980 0.000 0.020
#> GSM381196 1 0.0892 0.9240 0.980 0.000 0.020
#> GSM381198 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM381200 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM381201 1 0.2066 0.8955 0.940 0.000 0.060
#> GSM381203 1 0.0892 0.9251 0.980 0.000 0.020
#> GSM381204 1 0.0892 0.9261 0.980 0.000 0.020
#> GSM381209 1 0.0892 0.9261 0.980 0.000 0.020
#> GSM381212 1 0.0892 0.9261 0.980 0.000 0.020
#> GSM381213 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM381214 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM381216 1 0.0747 0.9255 0.984 0.000 0.016
#> GSM381225 3 0.6140 0.2782 0.404 0.000 0.596
#> GSM381231 3 0.1163 0.8811 0.000 0.028 0.972
#> GSM381235 1 0.0747 0.9255 0.984 0.000 0.016
#> GSM381237 1 0.0892 0.9261 0.980 0.000 0.020
#> GSM381241 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM381243 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM381245 1 0.0892 0.9261 0.980 0.000 0.020
#> GSM381246 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM381251 1 0.5591 0.5569 0.696 0.000 0.304
#> GSM381264 1 0.0892 0.9261 0.980 0.000 0.020
#> GSM381206 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM381217 1 0.0747 0.9255 0.984 0.000 0.016
#> GSM381218 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM381226 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM381227 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM381228 3 0.1163 0.8811 0.000 0.028 0.972
#> GSM381236 3 0.1163 0.8811 0.000 0.028 0.972
#> GSM381244 1 0.0000 0.9281 1.000 0.000 0.000
#> GSM381272 3 0.1163 0.8811 0.000 0.028 0.972
#> GSM381277 1 0.0892 0.9261 0.980 0.000 0.020
#> GSM381278 1 0.6286 0.1132 0.536 0.000 0.464
#> GSM381197 1 0.0237 0.9279 0.996 0.000 0.004
#> GSM381202 1 0.0237 0.9279 0.996 0.000 0.004
#> GSM381207 1 0.0892 0.9261 0.980 0.000 0.020
#> GSM381208 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM381210 1 0.0747 0.9269 0.984 0.000 0.016
#> GSM381215 1 0.2165 0.8936 0.936 0.000 0.064
#> GSM381219 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM381221 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM381223 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM381229 1 0.6180 0.2757 0.584 0.000 0.416
#> GSM381230 1 0.0747 0.9269 0.984 0.000 0.016
#> GSM381233 1 0.0424 0.9275 0.992 0.000 0.008
#> GSM381234 1 0.0892 0.9261 0.980 0.000 0.020
#> GSM381238 3 0.1163 0.8811 0.000 0.028 0.972
#> GSM381239 3 0.1163 0.8811 0.000 0.028 0.972
#> GSM381242 1 0.0424 0.9275 0.992 0.000 0.008
#> GSM381247 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM381248 1 0.3340 0.8303 0.880 0.000 0.120
#> GSM381249 1 0.0000 0.9281 1.000 0.000 0.000
#> GSM381253 1 0.0424 0.9275 0.992 0.000 0.008
#> GSM381255 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM381258 1 0.1289 0.9175 0.968 0.000 0.032
#> GSM381262 1 0.5216 0.6371 0.740 0.000 0.260
#> GSM381266 1 0.6244 0.2006 0.560 0.000 0.440
#> GSM381267 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM381269 1 0.0424 0.9275 0.992 0.000 0.008
#> GSM381273 3 0.6299 0.0186 0.476 0.000 0.524
#> GSM381274 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM381276 1 0.0592 0.9267 0.988 0.000 0.012
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM381194 3 0.2654 0.875 0.108 0.000 0.888 0.004
#> GSM381199 2 0.0000 0.994 0.000 1.000 0.000 0.000
#> GSM381205 2 0.0592 0.991 0.000 0.984 0.016 0.000
#> GSM381211 2 0.0592 0.991 0.000 0.984 0.016 0.000
#> GSM381220 2 0.0000 0.994 0.000 1.000 0.000 0.000
#> GSM381222 1 0.0188 0.950 0.996 0.000 0.004 0.000
#> GSM381224 1 0.1716 0.904 0.936 0.000 0.064 0.000
#> GSM381232 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM381240 1 0.0000 0.951 1.000 0.000 0.000 0.000
#> GSM381250 3 0.2469 0.875 0.108 0.000 0.892 0.000
#> GSM381252 2 0.0592 0.991 0.000 0.984 0.016 0.000
#> GSM381254 1 0.0188 0.950 0.996 0.000 0.004 0.000
#> GSM381256 2 0.0592 0.991 0.000 0.984 0.016 0.000
#> GSM381257 1 0.0188 0.950 0.996 0.000 0.004 0.000
#> GSM381259 1 0.0000 0.951 1.000 0.000 0.000 0.000
#> GSM381260 3 0.4985 0.341 0.468 0.000 0.532 0.000
#> GSM381261 2 0.0000 0.994 0.000 1.000 0.000 0.000
#> GSM381263 3 0.2530 0.874 0.112 0.000 0.888 0.000
#> GSM381265 1 0.0000 0.951 1.000 0.000 0.000 0.000
#> GSM381268 3 0.2469 0.875 0.108 0.000 0.892 0.000
#> GSM381270 2 0.0000 0.994 0.000 1.000 0.000 0.000
#> GSM381271 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM381275 2 0.0000 0.994 0.000 1.000 0.000 0.000
#> GSM381279 2 0.0000 0.994 0.000 1.000 0.000 0.000
#> GSM381195 1 0.0000 0.951 1.000 0.000 0.000 0.000
#> GSM381196 3 0.2469 0.875 0.108 0.000 0.892 0.000
#> GSM381198 2 0.0592 0.991 0.000 0.984 0.016 0.000
#> GSM381200 2 0.0000 0.994 0.000 1.000 0.000 0.000
#> GSM381201 3 0.2654 0.875 0.108 0.000 0.888 0.004
#> GSM381203 3 0.2675 0.872 0.100 0.000 0.892 0.008
#> GSM381204 1 0.0000 0.951 1.000 0.000 0.000 0.000
#> GSM381209 1 0.0000 0.951 1.000 0.000 0.000 0.000
#> GSM381212 1 0.0000 0.951 1.000 0.000 0.000 0.000
#> GSM381213 2 0.0592 0.991 0.000 0.984 0.016 0.000
#> GSM381214 2 0.0592 0.991 0.000 0.984 0.016 0.000
#> GSM381216 3 0.3688 0.726 0.208 0.000 0.792 0.000
#> GSM381225 3 0.3311 0.736 0.000 0.000 0.828 0.172
#> GSM381231 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM381235 3 0.2814 0.791 0.132 0.000 0.868 0.000
#> GSM381237 1 0.0000 0.951 1.000 0.000 0.000 0.000
#> GSM381241 2 0.0592 0.991 0.000 0.984 0.016 0.000
#> GSM381243 2 0.0000 0.994 0.000 1.000 0.000 0.000
#> GSM381245 1 0.0188 0.950 0.996 0.000 0.004 0.000
#> GSM381246 2 0.0000 0.994 0.000 1.000 0.000 0.000
#> GSM381251 3 0.2928 0.872 0.108 0.000 0.880 0.012
#> GSM381264 1 0.0000 0.951 1.000 0.000 0.000 0.000
#> GSM381206 2 0.0592 0.991 0.000 0.984 0.016 0.000
#> GSM381217 3 0.2011 0.821 0.080 0.000 0.920 0.000
#> GSM381218 2 0.0592 0.991 0.000 0.984 0.016 0.000
#> GSM381226 2 0.0000 0.994 0.000 1.000 0.000 0.000
#> GSM381227 2 0.0000 0.994 0.000 1.000 0.000 0.000
#> GSM381228 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM381236 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM381244 1 0.0188 0.950 0.996 0.000 0.004 0.000
#> GSM381272 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM381277 1 0.0188 0.950 0.996 0.000 0.004 0.000
#> GSM381278 3 0.4574 0.628 0.024 0.000 0.756 0.220
#> GSM381197 1 0.3801 0.661 0.780 0.000 0.220 0.000
#> GSM381202 1 0.4331 0.501 0.712 0.000 0.288 0.000
#> GSM381207 1 0.2760 0.817 0.872 0.000 0.128 0.000
#> GSM381208 2 0.0000 0.994 0.000 1.000 0.000 0.000
#> GSM381210 1 0.0000 0.951 1.000 0.000 0.000 0.000
#> GSM381215 3 0.2469 0.875 0.108 0.000 0.892 0.000
#> GSM381219 2 0.0592 0.991 0.000 0.984 0.016 0.000
#> GSM381221 2 0.0000 0.994 0.000 1.000 0.000 0.000
#> GSM381223 2 0.0000 0.994 0.000 1.000 0.000 0.000
#> GSM381229 3 0.4667 0.824 0.108 0.000 0.796 0.096
#> GSM381230 1 0.0000 0.951 1.000 0.000 0.000 0.000
#> GSM381233 1 0.2281 0.873 0.904 0.000 0.096 0.000
#> GSM381234 1 0.0000 0.951 1.000 0.000 0.000 0.000
#> GSM381238 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM381239 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM381242 3 0.4933 0.444 0.432 0.000 0.568 0.000
#> GSM381247 2 0.0000 0.994 0.000 1.000 0.000 0.000
#> GSM381248 1 0.1716 0.896 0.936 0.000 0.064 0.000
#> GSM381249 1 0.1118 0.925 0.964 0.000 0.036 0.000
#> GSM381253 3 0.2760 0.868 0.128 0.000 0.872 0.000
#> GSM381255 2 0.0592 0.991 0.000 0.984 0.016 0.000
#> GSM381258 3 0.2216 0.813 0.092 0.000 0.908 0.000
#> GSM381262 3 0.2654 0.875 0.108 0.000 0.888 0.004
#> GSM381266 3 0.5857 0.728 0.108 0.000 0.696 0.196
#> GSM381267 2 0.0000 0.994 0.000 1.000 0.000 0.000
#> GSM381269 1 0.2345 0.872 0.900 0.000 0.100 0.000
#> GSM381273 3 0.6245 0.668 0.108 0.000 0.648 0.244
#> GSM381274 2 0.0000 0.994 0.000 1.000 0.000 0.000
#> GSM381276 3 0.2469 0.875 0.108 0.000 0.892 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM381194 3 0.5556 0.7739 0.184 0.000 0.660 0.004 0.152
#> GSM381199 2 0.4304 -0.5214 0.000 0.516 0.000 0.000 0.484
#> GSM381205 2 0.0000 0.6416 0.000 1.000 0.000 0.000 0.000
#> GSM381211 2 0.0162 0.6397 0.000 0.996 0.000 0.000 0.004
#> GSM381220 2 0.2377 0.5380 0.000 0.872 0.000 0.000 0.128
#> GSM381222 1 0.4227 0.5674 0.580 0.000 0.420 0.000 0.000
#> GSM381224 1 0.3612 0.6714 0.732 0.000 0.268 0.000 0.000
#> GSM381232 4 0.0000 0.9693 0.000 0.000 0.000 1.000 0.000
#> GSM381240 1 0.0000 0.8516 1.000 0.000 0.000 0.000 0.000
#> GSM381250 3 0.3231 0.7978 0.196 0.000 0.800 0.000 0.004
#> GSM381252 2 0.2127 0.6467 0.000 0.892 0.000 0.000 0.108
#> GSM381254 1 0.2677 0.8304 0.872 0.000 0.112 0.000 0.016
#> GSM381256 2 0.3983 0.1539 0.000 0.660 0.000 0.000 0.340
#> GSM381257 1 0.2516 0.8139 0.860 0.000 0.140 0.000 0.000
#> GSM381259 1 0.0963 0.8503 0.964 0.000 0.036 0.000 0.000
#> GSM381260 3 0.3689 0.7585 0.256 0.000 0.740 0.000 0.004
#> GSM381261 5 0.3913 0.8514 0.000 0.324 0.000 0.000 0.676
#> GSM381263 3 0.3427 0.7984 0.192 0.000 0.796 0.000 0.012
#> GSM381265 1 0.2416 0.8349 0.888 0.000 0.100 0.000 0.012
#> GSM381268 3 0.3795 0.8019 0.192 0.000 0.780 0.000 0.028
#> GSM381270 5 0.4150 0.8709 0.000 0.388 0.000 0.000 0.612
#> GSM381271 4 0.0000 0.9693 0.000 0.000 0.000 1.000 0.000
#> GSM381275 5 0.3913 0.8514 0.000 0.324 0.000 0.000 0.676
#> GSM381279 5 0.4150 0.8709 0.000 0.388 0.000 0.000 0.612
#> GSM381195 1 0.0000 0.8516 1.000 0.000 0.000 0.000 0.000
#> GSM381196 3 0.3656 0.8009 0.196 0.000 0.784 0.000 0.020
#> GSM381198 2 0.2127 0.6467 0.000 0.892 0.000 0.000 0.108
#> GSM381200 2 0.4045 0.1087 0.000 0.644 0.000 0.000 0.356
#> GSM381201 3 0.4170 0.8011 0.192 0.000 0.760 0.000 0.048
#> GSM381203 3 0.3665 0.7978 0.200 0.000 0.784 0.008 0.008
#> GSM381204 1 0.0000 0.8516 1.000 0.000 0.000 0.000 0.000
#> GSM381209 1 0.0000 0.8516 1.000 0.000 0.000 0.000 0.000
#> GSM381212 1 0.0000 0.8516 1.000 0.000 0.000 0.000 0.000
#> GSM381213 2 0.3612 0.4438 0.000 0.732 0.000 0.000 0.268
#> GSM381214 2 0.1043 0.6505 0.000 0.960 0.000 0.000 0.040
#> GSM381216 3 0.0510 0.7214 0.000 0.000 0.984 0.000 0.016
#> GSM381225 3 0.5482 0.6256 0.000 0.000 0.652 0.204 0.144
#> GSM381231 4 0.0000 0.9693 0.000 0.000 0.000 1.000 0.000
#> GSM381235 3 0.0510 0.7214 0.000 0.000 0.984 0.000 0.016
#> GSM381237 1 0.0000 0.8516 1.000 0.000 0.000 0.000 0.000
#> GSM381241 2 0.2127 0.6467 0.000 0.892 0.000 0.000 0.108
#> GSM381243 5 0.4287 0.7443 0.000 0.460 0.000 0.000 0.540
#> GSM381245 1 0.2677 0.8304 0.872 0.000 0.112 0.000 0.016
#> GSM381246 2 0.3661 0.3385 0.000 0.724 0.000 0.000 0.276
#> GSM381251 3 0.5838 0.7690 0.192 0.000 0.644 0.012 0.152
#> GSM381264 1 0.0000 0.8516 1.000 0.000 0.000 0.000 0.000
#> GSM381206 2 0.0000 0.6416 0.000 1.000 0.000 0.000 0.000
#> GSM381217 3 0.0290 0.7240 0.000 0.000 0.992 0.000 0.008
#> GSM381218 2 0.1965 0.6492 0.000 0.904 0.000 0.000 0.096
#> GSM381226 2 0.3983 0.1762 0.000 0.660 0.000 0.000 0.340
#> GSM381227 2 0.3913 0.0245 0.000 0.676 0.000 0.000 0.324
#> GSM381228 4 0.0000 0.9693 0.000 0.000 0.000 1.000 0.000
#> GSM381236 4 0.2020 0.9482 0.000 0.000 0.000 0.900 0.100
#> GSM381244 1 0.2690 0.7954 0.844 0.000 0.156 0.000 0.000
#> GSM381272 4 0.0000 0.9693 0.000 0.000 0.000 1.000 0.000
#> GSM381277 1 0.2677 0.8304 0.872 0.000 0.112 0.000 0.016
#> GSM381278 3 0.5583 0.4693 0.000 0.000 0.640 0.208 0.152
#> GSM381197 3 0.4273 0.4415 0.448 0.000 0.552 0.000 0.000
#> GSM381202 3 0.3816 0.7162 0.304 0.000 0.696 0.000 0.000
#> GSM381207 1 0.3264 0.7948 0.820 0.000 0.164 0.000 0.016
#> GSM381208 2 0.2424 0.5319 0.000 0.868 0.000 0.000 0.132
#> GSM381210 1 0.0000 0.8516 1.000 0.000 0.000 0.000 0.000
#> GSM381215 3 0.4031 0.8039 0.184 0.000 0.772 0.000 0.044
#> GSM381219 2 0.2179 0.6438 0.000 0.888 0.000 0.000 0.112
#> GSM381221 2 0.4074 0.0693 0.000 0.636 0.000 0.000 0.364
#> GSM381223 5 0.4192 0.8439 0.000 0.404 0.000 0.000 0.596
#> GSM381229 3 0.6769 0.7431 0.192 0.000 0.592 0.064 0.152
#> GSM381230 1 0.2329 0.7654 0.876 0.000 0.124 0.000 0.000
#> GSM381233 1 0.4298 0.5820 0.640 0.000 0.352 0.000 0.008
#> GSM381234 1 0.2625 0.8327 0.876 0.000 0.108 0.000 0.016
#> GSM381238 4 0.2020 0.9482 0.000 0.000 0.000 0.900 0.100
#> GSM381239 4 0.2020 0.9482 0.000 0.000 0.000 0.900 0.100
#> GSM381242 3 0.1628 0.7257 0.056 0.000 0.936 0.000 0.008
#> GSM381247 5 0.4150 0.8709 0.000 0.388 0.000 0.000 0.612
#> GSM381248 1 0.3241 0.8088 0.832 0.000 0.144 0.000 0.024
#> GSM381249 1 0.3774 0.6987 0.704 0.000 0.296 0.000 0.000
#> GSM381253 3 0.3196 0.7987 0.192 0.000 0.804 0.000 0.004
#> GSM381255 2 0.0162 0.6397 0.000 0.996 0.000 0.000 0.004
#> GSM381258 3 0.0404 0.7227 0.000 0.000 0.988 0.000 0.012
#> GSM381262 3 0.5618 0.7717 0.192 0.000 0.652 0.004 0.152
#> GSM381266 3 0.7814 0.6429 0.176 0.000 0.484 0.188 0.152
#> GSM381267 2 0.3816 0.1048 0.000 0.696 0.000 0.000 0.304
#> GSM381269 3 0.3700 0.4715 0.240 0.000 0.752 0.000 0.008
#> GSM381273 3 0.8181 0.5680 0.192 0.000 0.404 0.252 0.152
#> GSM381274 5 0.3913 0.8514 0.000 0.324 0.000 0.000 0.676
#> GSM381276 3 0.3795 0.8027 0.192 0.000 0.780 0.000 0.028
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM381194 6 0.3672 0.642 0.000 0.000 0.368 0.000 0.000 0.632
#> GSM381199 5 0.3428 0.601 0.000 0.304 0.000 0.000 0.696 0.000
#> GSM381205 2 0.0000 0.664 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381211 2 0.0146 0.665 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM381220 2 0.2597 0.561 0.000 0.824 0.000 0.000 0.176 0.000
#> GSM381222 1 0.3860 0.332 0.528 0.000 0.472 0.000 0.000 0.000
#> GSM381224 1 0.3695 0.466 0.624 0.000 0.376 0.000 0.000 0.000
#> GSM381232 4 0.1686 0.958 0.000 0.000 0.012 0.924 0.000 0.064
#> GSM381240 1 0.0000 0.819 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381250 3 0.3917 0.442 0.024 0.000 0.692 0.000 0.000 0.284
#> GSM381252 2 0.3076 0.570 0.000 0.760 0.000 0.000 0.240 0.000
#> GSM381254 1 0.4625 0.724 0.692 0.000 0.060 0.000 0.016 0.232
#> GSM381256 5 0.3843 0.223 0.000 0.452 0.000 0.000 0.548 0.000
#> GSM381257 1 0.2482 0.751 0.848 0.000 0.148 0.000 0.000 0.004
#> GSM381259 1 0.1501 0.799 0.924 0.000 0.000 0.000 0.000 0.076
#> GSM381260 3 0.3694 0.432 0.232 0.000 0.740 0.000 0.000 0.028
#> GSM381261 5 0.1225 0.657 0.000 0.036 0.000 0.000 0.952 0.012
#> GSM381263 3 0.3917 0.442 0.024 0.000 0.692 0.000 0.000 0.284
#> GSM381265 1 0.3586 0.774 0.796 0.000 0.080 0.000 0.000 0.124
#> GSM381268 3 0.3371 0.397 0.000 0.000 0.708 0.000 0.000 0.292
#> GSM381270 5 0.2491 0.673 0.000 0.164 0.000 0.000 0.836 0.000
#> GSM381271 4 0.1327 0.968 0.000 0.000 0.000 0.936 0.000 0.064
#> GSM381275 5 0.1225 0.657 0.000 0.036 0.000 0.000 0.952 0.012
#> GSM381279 5 0.2454 0.675 0.000 0.160 0.000 0.000 0.840 0.000
#> GSM381195 1 0.0146 0.818 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM381196 3 0.3351 0.403 0.000 0.000 0.712 0.000 0.000 0.288
#> GSM381198 2 0.3050 0.575 0.000 0.764 0.000 0.000 0.236 0.000
#> GSM381200 5 0.3866 0.243 0.000 0.484 0.000 0.000 0.516 0.000
#> GSM381201 3 0.3446 0.361 0.000 0.000 0.692 0.000 0.000 0.308
#> GSM381203 3 0.3555 0.410 0.008 0.000 0.712 0.000 0.000 0.280
#> GSM381204 1 0.0000 0.819 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381209 1 0.0000 0.819 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381212 1 0.0000 0.819 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381213 2 0.3833 0.310 0.000 0.556 0.000 0.000 0.444 0.000
#> GSM381214 2 0.1714 0.656 0.000 0.908 0.000 0.000 0.092 0.000
#> GSM381216 3 0.1088 0.497 0.024 0.000 0.960 0.000 0.000 0.016
#> GSM381225 6 0.5662 0.556 0.000 0.000 0.384 0.156 0.000 0.460
#> GSM381231 4 0.1327 0.968 0.000 0.000 0.000 0.936 0.000 0.064
#> GSM381235 3 0.0993 0.497 0.024 0.000 0.964 0.000 0.000 0.012
#> GSM381237 1 0.0000 0.819 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381241 2 0.3076 0.570 0.000 0.760 0.000 0.000 0.240 0.000
#> GSM381243 5 0.3515 0.468 0.000 0.324 0.000 0.000 0.676 0.000
#> GSM381245 1 0.3752 0.776 0.800 0.000 0.060 0.000 0.016 0.124
#> GSM381246 2 0.3647 0.186 0.000 0.640 0.000 0.000 0.360 0.000
#> GSM381251 6 0.3634 0.653 0.000 0.000 0.356 0.000 0.000 0.644
#> GSM381264 1 0.0000 0.819 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381206 2 0.0000 0.664 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381217 3 0.1176 0.498 0.024 0.000 0.956 0.000 0.000 0.020
#> GSM381218 2 0.2969 0.585 0.000 0.776 0.000 0.000 0.224 0.000
#> GSM381226 5 0.3868 0.201 0.000 0.496 0.000 0.000 0.504 0.000
#> GSM381227 2 0.3659 0.227 0.000 0.636 0.000 0.000 0.364 0.000
#> GSM381228 4 0.0865 0.967 0.000 0.000 0.000 0.964 0.000 0.036
#> GSM381236 4 0.0000 0.960 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381244 1 0.3351 0.717 0.800 0.000 0.168 0.000 0.004 0.028
#> GSM381272 4 0.1327 0.968 0.000 0.000 0.000 0.936 0.000 0.064
#> GSM381277 1 0.3950 0.768 0.780 0.000 0.060 0.000 0.016 0.144
#> GSM381278 6 0.5431 0.523 0.000 0.000 0.344 0.132 0.000 0.524
#> GSM381197 3 0.4396 0.165 0.456 0.000 0.520 0.000 0.000 0.024
#> GSM381202 3 0.3076 0.433 0.240 0.000 0.760 0.000 0.000 0.000
#> GSM381207 1 0.5173 0.537 0.576 0.000 0.064 0.000 0.016 0.344
#> GSM381208 2 0.2562 0.564 0.000 0.828 0.000 0.000 0.172 0.000
#> GSM381210 1 0.0146 0.818 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM381215 3 0.3578 0.256 0.000 0.000 0.660 0.000 0.000 0.340
#> GSM381219 2 0.3221 0.528 0.000 0.736 0.000 0.000 0.264 0.000
#> GSM381221 5 0.3717 0.490 0.000 0.384 0.000 0.000 0.616 0.000
#> GSM381223 5 0.2092 0.664 0.000 0.124 0.000 0.000 0.876 0.000
#> GSM381229 6 0.3871 0.684 0.000 0.000 0.308 0.016 0.000 0.676
#> GSM381230 1 0.1007 0.805 0.956 0.000 0.044 0.000 0.000 0.000
#> GSM381233 3 0.3868 -0.253 0.496 0.000 0.504 0.000 0.000 0.000
#> GSM381234 1 0.4108 0.760 0.756 0.000 0.060 0.000 0.012 0.172
#> GSM381238 4 0.0000 0.960 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381239 4 0.0000 0.960 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381242 3 0.1492 0.480 0.036 0.000 0.940 0.000 0.000 0.024
#> GSM381247 5 0.2378 0.678 0.000 0.152 0.000 0.000 0.848 0.000
#> GSM381248 1 0.5204 0.544 0.548 0.000 0.060 0.000 0.016 0.376
#> GSM381249 1 0.3838 0.396 0.552 0.000 0.448 0.000 0.000 0.000
#> GSM381253 3 0.3690 0.423 0.012 0.000 0.700 0.000 0.000 0.288
#> GSM381255 2 0.0000 0.664 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381258 3 0.2527 0.413 0.024 0.000 0.868 0.000 0.000 0.108
#> GSM381262 6 0.3647 0.650 0.000 0.000 0.360 0.000 0.000 0.640
#> GSM381266 6 0.5301 0.597 0.000 0.000 0.268 0.148 0.000 0.584
#> GSM381267 2 0.3647 0.264 0.000 0.640 0.000 0.000 0.360 0.000
#> GSM381269 3 0.3665 0.312 0.252 0.000 0.728 0.000 0.000 0.020
#> GSM381273 6 0.5395 0.569 0.000 0.000 0.196 0.220 0.000 0.584
#> GSM381274 5 0.1225 0.657 0.000 0.036 0.000 0.000 0.952 0.012
#> GSM381276 3 0.3330 0.406 0.000 0.000 0.716 0.000 0.000 0.284
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 other(p) k
#> MAD:mclust 86 0.744 2
#> MAD:mclust 81 0.322 3
#> MAD:mclust 84 0.600 4
#> MAD:mclust 74 0.453 5
#> MAD:mclust 55 0.356 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 86 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.905 0.932 0.972 0.4676 0.540 0.540
#> 3 3 0.913 0.906 0.945 0.4111 0.781 0.600
#> 4 4 0.688 0.756 0.839 0.0896 0.868 0.638
#> 5 5 0.809 0.772 0.865 0.0602 0.940 0.783
#> 6 6 0.847 0.779 0.885 0.0250 0.925 0.714
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
#> GSM381194 1 0.000 0.964 1.000 0.000
#> GSM381199 2 0.000 0.983 0.000 1.000
#> GSM381205 2 0.000 0.983 0.000 1.000
#> GSM381211 2 0.000 0.983 0.000 1.000
#> GSM381220 2 0.000 0.983 0.000 1.000
#> GSM381222 1 0.000 0.964 1.000 0.000
#> GSM381224 1 0.000 0.964 1.000 0.000
#> GSM381232 1 0.697 0.779 0.812 0.188
#> GSM381240 1 0.000 0.964 1.000 0.000
#> GSM381250 1 0.000 0.964 1.000 0.000
#> GSM381252 2 0.000 0.983 0.000 1.000
#> GSM381254 1 0.000 0.964 1.000 0.000
#> GSM381256 2 0.000 0.983 0.000 1.000
#> GSM381257 1 0.000 0.964 1.000 0.000
#> GSM381259 1 0.000 0.964 1.000 0.000
#> GSM381260 1 0.000 0.964 1.000 0.000
#> GSM381261 2 0.000 0.983 0.000 1.000
#> GSM381263 1 0.000 0.964 1.000 0.000
#> GSM381265 1 0.000 0.964 1.000 0.000
#> GSM381268 1 0.000 0.964 1.000 0.000
#> GSM381270 2 0.000 0.983 0.000 1.000
#> GSM381271 1 0.730 0.758 0.796 0.204
#> GSM381275 2 0.000 0.983 0.000 1.000
#> GSM381279 2 0.000 0.983 0.000 1.000
#> GSM381195 1 0.000 0.964 1.000 0.000
#> GSM381196 1 0.000 0.964 1.000 0.000
#> GSM381198 2 0.000 0.983 0.000 1.000
#> GSM381200 2 0.000 0.983 0.000 1.000
#> GSM381201 1 0.000 0.964 1.000 0.000
#> GSM381203 1 0.000 0.964 1.000 0.000
#> GSM381204 1 0.000 0.964 1.000 0.000
#> GSM381209 1 0.000 0.964 1.000 0.000
#> GSM381212 1 0.000 0.964 1.000 0.000
#> GSM381213 2 0.000 0.983 0.000 1.000
#> GSM381214 2 0.000 0.983 0.000 1.000
#> GSM381216 1 0.000 0.964 1.000 0.000
#> GSM381225 1 0.781 0.697 0.768 0.232
#> GSM381231 1 0.999 0.124 0.520 0.480
#> GSM381235 1 0.000 0.964 1.000 0.000
#> GSM381237 1 0.000 0.964 1.000 0.000
#> GSM381241 2 0.000 0.983 0.000 1.000
#> GSM381243 2 0.000 0.983 0.000 1.000
#> GSM381245 1 0.000 0.964 1.000 0.000
#> GSM381246 2 0.000 0.983 0.000 1.000
#> GSM381251 1 0.000 0.964 1.000 0.000
#> GSM381264 1 0.000 0.964 1.000 0.000
#> GSM381206 2 0.000 0.983 0.000 1.000
#> GSM381217 1 0.000 0.964 1.000 0.000
#> GSM381218 2 0.000 0.983 0.000 1.000
#> GSM381226 2 0.000 0.983 0.000 1.000
#> GSM381227 2 0.000 0.983 0.000 1.000
#> GSM381228 2 0.997 0.030 0.468 0.532
#> GSM381236 1 0.706 0.774 0.808 0.192
#> GSM381244 1 0.000 0.964 1.000 0.000
#> GSM381272 1 0.730 0.758 0.796 0.204
#> GSM381277 1 0.000 0.964 1.000 0.000
#> GSM381278 1 0.000 0.964 1.000 0.000
#> GSM381197 1 0.000 0.964 1.000 0.000
#> GSM381202 1 0.000 0.964 1.000 0.000
#> GSM381207 1 0.000 0.964 1.000 0.000
#> GSM381208 2 0.000 0.983 0.000 1.000
#> GSM381210 1 0.000 0.964 1.000 0.000
#> GSM381215 1 0.000 0.964 1.000 0.000
#> GSM381219 2 0.000 0.983 0.000 1.000
#> GSM381221 2 0.000 0.983 0.000 1.000
#> GSM381223 2 0.000 0.983 0.000 1.000
#> GSM381229 1 0.000 0.964 1.000 0.000
#> GSM381230 1 0.000 0.964 1.000 0.000
#> GSM381233 1 0.000 0.964 1.000 0.000
#> GSM381234 1 0.000 0.964 1.000 0.000
#> GSM381238 1 0.738 0.753 0.792 0.208
#> GSM381239 1 0.745 0.747 0.788 0.212
#> GSM381242 1 0.000 0.964 1.000 0.000
#> GSM381247 2 0.000 0.983 0.000 1.000
#> GSM381248 1 0.000 0.964 1.000 0.000
#> GSM381249 1 0.000 0.964 1.000 0.000
#> GSM381253 1 0.000 0.964 1.000 0.000
#> GSM381255 2 0.000 0.983 0.000 1.000
#> GSM381258 1 0.000 0.964 1.000 0.000
#> GSM381262 1 0.000 0.964 1.000 0.000
#> GSM381266 1 0.000 0.964 1.000 0.000
#> GSM381267 2 0.000 0.983 0.000 1.000
#> GSM381269 1 0.000 0.964 1.000 0.000
#> GSM381273 1 0.000 0.964 1.000 0.000
#> GSM381274 2 0.000 0.983 0.000 1.000
#> GSM381276 1 0.000 0.964 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM381194 3 0.1711 0.911 0.032 0.008 0.960
#> GSM381199 2 0.0747 0.978 0.000 0.984 0.016
#> GSM381205 2 0.1453 0.967 0.008 0.968 0.024
#> GSM381211 2 0.1031 0.970 0.000 0.976 0.024
#> GSM381220 2 0.1411 0.971 0.000 0.964 0.036
#> GSM381222 1 0.0892 0.945 0.980 0.000 0.020
#> GSM381224 1 0.0237 0.946 0.996 0.000 0.004
#> GSM381232 3 0.1182 0.905 0.012 0.012 0.976
#> GSM381240 1 0.0000 0.945 1.000 0.000 0.000
#> GSM381250 1 0.6244 0.126 0.560 0.000 0.440
#> GSM381252 2 0.0747 0.974 0.000 0.984 0.016
#> GSM381254 1 0.0592 0.946 0.988 0.000 0.012
#> GSM381256 2 0.0747 0.978 0.000 0.984 0.016
#> GSM381257 1 0.1031 0.944 0.976 0.000 0.024
#> GSM381259 1 0.1620 0.922 0.964 0.012 0.024
#> GSM381260 1 0.3482 0.858 0.872 0.000 0.128
#> GSM381261 2 0.0747 0.978 0.000 0.984 0.016
#> GSM381263 3 0.5785 0.569 0.332 0.000 0.668
#> GSM381265 1 0.0237 0.946 0.996 0.000 0.004
#> GSM381268 3 0.2878 0.880 0.096 0.000 0.904
#> GSM381270 2 0.2066 0.955 0.000 0.940 0.060
#> GSM381271 3 0.1182 0.905 0.012 0.012 0.976
#> GSM381275 2 0.0592 0.975 0.000 0.988 0.012
#> GSM381279 2 0.1964 0.958 0.000 0.944 0.056
#> GSM381195 1 0.0237 0.943 0.996 0.000 0.004
#> GSM381196 3 0.6307 0.121 0.488 0.000 0.512
#> GSM381198 2 0.1453 0.967 0.008 0.968 0.024
#> GSM381200 2 0.0747 0.978 0.000 0.984 0.016
#> GSM381201 3 0.2066 0.904 0.060 0.000 0.940
#> GSM381203 1 0.0829 0.942 0.984 0.004 0.012
#> GSM381204 1 0.0983 0.934 0.980 0.004 0.016
#> GSM381209 1 0.1774 0.919 0.960 0.016 0.024
#> GSM381212 1 0.1337 0.929 0.972 0.012 0.016
#> GSM381213 2 0.1289 0.973 0.000 0.968 0.032
#> GSM381214 2 0.0237 0.977 0.000 0.996 0.004
#> GSM381216 1 0.2448 0.916 0.924 0.000 0.076
#> GSM381225 3 0.6161 0.660 0.272 0.020 0.708
#> GSM381231 3 0.1163 0.893 0.000 0.028 0.972
#> GSM381235 1 0.2625 0.909 0.916 0.000 0.084
#> GSM381237 1 0.0237 0.943 0.996 0.000 0.004
#> GSM381241 2 0.0424 0.976 0.000 0.992 0.008
#> GSM381243 2 0.1964 0.958 0.000 0.944 0.056
#> GSM381245 1 0.0592 0.946 0.988 0.000 0.012
#> GSM381246 2 0.1170 0.971 0.008 0.976 0.016
#> GSM381251 3 0.1529 0.911 0.040 0.000 0.960
#> GSM381264 1 0.0661 0.940 0.988 0.004 0.008
#> GSM381206 2 0.1453 0.967 0.008 0.968 0.024
#> GSM381217 1 0.1031 0.944 0.976 0.000 0.024
#> GSM381218 2 0.0747 0.978 0.000 0.984 0.016
#> GSM381226 2 0.0892 0.977 0.000 0.980 0.020
#> GSM381227 2 0.0747 0.978 0.000 0.984 0.016
#> GSM381228 3 0.1031 0.896 0.000 0.024 0.976
#> GSM381236 3 0.1482 0.908 0.020 0.012 0.968
#> GSM381244 1 0.2625 0.908 0.916 0.000 0.084
#> GSM381272 3 0.1182 0.905 0.012 0.012 0.976
#> GSM381277 1 0.1163 0.942 0.972 0.000 0.028
#> GSM381278 3 0.1289 0.911 0.032 0.000 0.968
#> GSM381197 1 0.3412 0.863 0.876 0.000 0.124
#> GSM381202 1 0.0592 0.946 0.988 0.000 0.012
#> GSM381207 1 0.1753 0.933 0.952 0.000 0.048
#> GSM381208 2 0.0592 0.975 0.000 0.988 0.012
#> GSM381210 1 0.0237 0.946 0.996 0.000 0.004
#> GSM381215 3 0.2537 0.893 0.080 0.000 0.920
#> GSM381219 2 0.0747 0.978 0.000 0.984 0.016
#> GSM381221 2 0.0747 0.978 0.000 0.984 0.016
#> GSM381223 2 0.0747 0.978 0.000 0.984 0.016
#> GSM381229 3 0.1765 0.911 0.040 0.004 0.956
#> GSM381230 1 0.0000 0.945 1.000 0.000 0.000
#> GSM381233 1 0.0592 0.946 0.988 0.000 0.012
#> GSM381234 1 0.0237 0.946 0.996 0.000 0.004
#> GSM381238 3 0.1337 0.907 0.016 0.012 0.972
#> GSM381239 3 0.1781 0.904 0.020 0.020 0.960
#> GSM381242 1 0.2878 0.893 0.904 0.000 0.096
#> GSM381247 2 0.3551 0.881 0.000 0.868 0.132
#> GSM381248 1 0.1031 0.944 0.976 0.000 0.024
#> GSM381249 1 0.0424 0.946 0.992 0.000 0.008
#> GSM381253 1 0.4702 0.737 0.788 0.000 0.212
#> GSM381255 2 0.0592 0.975 0.000 0.988 0.012
#> GSM381258 3 0.2448 0.895 0.076 0.000 0.924
#> GSM381262 3 0.1529 0.911 0.040 0.000 0.960
#> GSM381266 3 0.1643 0.910 0.044 0.000 0.956
#> GSM381267 2 0.1163 0.975 0.000 0.972 0.028
#> GSM381269 1 0.1753 0.934 0.952 0.000 0.048
#> GSM381273 3 0.1529 0.911 0.040 0.000 0.960
#> GSM381274 2 0.0592 0.978 0.000 0.988 0.012
#> GSM381276 3 0.5733 0.585 0.324 0.000 0.676
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM381194 3 0.4387 0.4721 0.024 0.000 0.776 0.200
#> GSM381199 2 0.1724 0.9445 0.000 0.948 0.032 0.020
#> GSM381205 2 0.2409 0.9321 0.032 0.924 0.004 0.040
#> GSM381211 2 0.1743 0.9386 0.004 0.940 0.000 0.056
#> GSM381220 2 0.3831 0.8397 0.000 0.792 0.004 0.204
#> GSM381222 1 0.3123 0.8044 0.844 0.000 0.156 0.000
#> GSM381224 1 0.3024 0.8136 0.852 0.000 0.148 0.000
#> GSM381232 4 0.2921 0.8259 0.000 0.000 0.140 0.860
#> GSM381240 1 0.1211 0.8840 0.960 0.000 0.040 0.000
#> GSM381250 3 0.4420 0.6936 0.240 0.000 0.748 0.012
#> GSM381252 2 0.0524 0.9432 0.004 0.988 0.000 0.008
#> GSM381254 1 0.0336 0.8852 0.992 0.000 0.008 0.000
#> GSM381256 2 0.2048 0.9418 0.000 0.928 0.008 0.064
#> GSM381257 1 0.3123 0.8031 0.844 0.000 0.156 0.000
#> GSM381259 1 0.0707 0.8700 0.980 0.020 0.000 0.000
#> GSM381260 3 0.4741 0.6175 0.328 0.000 0.668 0.004
#> GSM381261 2 0.3691 0.8979 0.000 0.856 0.068 0.076
#> GSM381263 3 0.4638 0.6796 0.180 0.000 0.776 0.044
#> GSM381265 1 0.0188 0.8861 0.996 0.000 0.004 0.000
#> GSM381268 3 0.6097 0.1866 0.056 0.000 0.580 0.364
#> GSM381270 2 0.2376 0.9423 0.000 0.916 0.016 0.068
#> GSM381271 4 0.2469 0.8288 0.000 0.000 0.108 0.892
#> GSM381275 2 0.3439 0.8968 0.000 0.868 0.048 0.084
#> GSM381279 2 0.1940 0.9427 0.000 0.924 0.000 0.076
#> GSM381195 1 0.0000 0.8847 1.000 0.000 0.000 0.000
#> GSM381196 3 0.5657 0.6835 0.244 0.000 0.688 0.068
#> GSM381198 2 0.0376 0.9430 0.004 0.992 0.000 0.004
#> GSM381200 2 0.1824 0.9361 0.000 0.936 0.004 0.060
#> GSM381201 4 0.5856 0.4130 0.036 0.000 0.408 0.556
#> GSM381203 3 0.5143 0.3257 0.456 0.004 0.540 0.000
#> GSM381204 1 0.1256 0.8858 0.964 0.008 0.028 0.000
#> GSM381209 1 0.1174 0.8762 0.968 0.020 0.012 0.000
#> GSM381212 1 0.0672 0.8839 0.984 0.008 0.008 0.000
#> GSM381213 2 0.2345 0.9353 0.000 0.900 0.000 0.100
#> GSM381214 2 0.2197 0.9362 0.004 0.916 0.000 0.080
#> GSM381216 3 0.3991 0.6028 0.120 0.000 0.832 0.048
#> GSM381225 3 0.5662 0.6792 0.200 0.020 0.728 0.052
#> GSM381231 4 0.2921 0.8281 0.000 0.000 0.140 0.860
#> GSM381235 3 0.3610 0.6788 0.200 0.000 0.800 0.000
#> GSM381237 1 0.0707 0.8885 0.980 0.000 0.020 0.000
#> GSM381241 2 0.0779 0.9448 0.004 0.980 0.000 0.016
#> GSM381243 2 0.2530 0.9248 0.000 0.888 0.000 0.112
#> GSM381245 1 0.0469 0.8870 0.988 0.000 0.012 0.000
#> GSM381246 2 0.1792 0.9290 0.000 0.932 0.000 0.068
#> GSM381251 3 0.5660 0.0452 0.028 0.000 0.576 0.396
#> GSM381264 1 0.0188 0.8829 0.996 0.004 0.000 0.000
#> GSM381206 2 0.1174 0.9422 0.020 0.968 0.000 0.012
#> GSM381217 3 0.4936 0.5632 0.340 0.000 0.652 0.008
#> GSM381218 2 0.2081 0.9360 0.000 0.916 0.000 0.084
#> GSM381226 2 0.1118 0.9385 0.000 0.964 0.000 0.036
#> GSM381227 2 0.1722 0.9454 0.000 0.944 0.008 0.048
#> GSM381228 4 0.2654 0.8283 0.000 0.004 0.108 0.888
#> GSM381236 4 0.2466 0.8188 0.000 0.004 0.096 0.900
#> GSM381244 1 0.4018 0.6889 0.772 0.000 0.224 0.004
#> GSM381272 4 0.2868 0.8281 0.000 0.000 0.136 0.864
#> GSM381277 1 0.1929 0.8725 0.940 0.000 0.036 0.024
#> GSM381278 4 0.5168 0.4016 0.004 0.000 0.492 0.504
#> GSM381197 3 0.5080 0.4524 0.420 0.000 0.576 0.004
#> GSM381202 1 0.5163 -0.1540 0.516 0.000 0.480 0.004
#> GSM381207 1 0.1767 0.8739 0.944 0.000 0.044 0.012
#> GSM381208 2 0.2926 0.9233 0.012 0.888 0.004 0.096
#> GSM381210 1 0.2973 0.8192 0.856 0.000 0.144 0.000
#> GSM381215 3 0.5599 0.4057 0.052 0.000 0.672 0.276
#> GSM381219 2 0.1118 0.9456 0.000 0.964 0.000 0.036
#> GSM381221 2 0.1022 0.9454 0.000 0.968 0.000 0.032
#> GSM381223 2 0.2742 0.9215 0.000 0.900 0.024 0.076
#> GSM381229 3 0.5691 -0.0149 0.028 0.000 0.564 0.408
#> GSM381230 1 0.0707 0.8885 0.980 0.000 0.020 0.000
#> GSM381233 1 0.3852 0.7601 0.800 0.000 0.192 0.008
#> GSM381234 1 0.0592 0.8862 0.984 0.000 0.016 0.000
#> GSM381238 4 0.2593 0.8250 0.000 0.004 0.104 0.892
#> GSM381239 4 0.2483 0.7737 0.000 0.032 0.052 0.916
#> GSM381242 3 0.4632 0.6341 0.308 0.000 0.688 0.004
#> GSM381247 2 0.3497 0.9126 0.000 0.860 0.036 0.104
#> GSM381248 1 0.1059 0.8819 0.972 0.000 0.016 0.012
#> GSM381249 1 0.3688 0.7388 0.792 0.000 0.208 0.000
#> GSM381253 3 0.6362 0.6589 0.288 0.000 0.616 0.096
#> GSM381255 2 0.1576 0.9402 0.004 0.948 0.000 0.048
#> GSM381258 3 0.1209 0.5009 0.004 0.000 0.964 0.032
#> GSM381262 3 0.5565 0.2096 0.032 0.000 0.624 0.344
#> GSM381266 4 0.5645 0.5308 0.032 0.000 0.364 0.604
#> GSM381267 2 0.2469 0.9270 0.000 0.892 0.000 0.108
#> GSM381269 3 0.5055 0.3956 0.368 0.000 0.624 0.008
#> GSM381273 4 0.4995 0.7136 0.032 0.000 0.248 0.720
#> GSM381274 2 0.2402 0.9214 0.000 0.912 0.012 0.076
#> GSM381276 3 0.7269 0.6019 0.296 0.000 0.524 0.180
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM381194 5 0.0693 0.9288 0.000 0.000 0.012 0.008 0.980
#> GSM381199 2 0.1041 0.9539 0.000 0.964 0.032 0.000 0.004
#> GSM381205 2 0.2130 0.9414 0.016 0.924 0.044 0.016 0.000
#> GSM381211 2 0.1356 0.9524 0.004 0.956 0.012 0.028 0.000
#> GSM381220 2 0.3445 0.8583 0.000 0.824 0.036 0.140 0.000
#> GSM381222 1 0.4586 0.3901 0.644 0.000 0.336 0.004 0.016
#> GSM381224 1 0.4627 0.0467 0.544 0.000 0.444 0.000 0.012
#> GSM381232 4 0.0865 0.9700 0.000 0.000 0.024 0.972 0.004
#> GSM381240 1 0.3861 0.5487 0.728 0.000 0.264 0.000 0.008
#> GSM381250 5 0.0162 0.9279 0.004 0.000 0.000 0.000 0.996
#> GSM381252 2 0.0671 0.9545 0.004 0.980 0.016 0.000 0.000
#> GSM381254 1 0.0771 0.6864 0.976 0.000 0.020 0.000 0.004
#> GSM381256 2 0.1942 0.9298 0.000 0.920 0.012 0.000 0.068
#> GSM381257 1 0.3994 0.6187 0.772 0.000 0.188 0.000 0.040
#> GSM381259 1 0.1251 0.7034 0.956 0.008 0.036 0.000 0.000
#> GSM381260 3 0.6742 0.5587 0.344 0.000 0.512 0.056 0.088
#> GSM381261 2 0.2280 0.9059 0.000 0.880 0.120 0.000 0.000
#> GSM381263 5 0.2970 0.7500 0.004 0.000 0.168 0.000 0.828
#> GSM381265 1 0.0290 0.6979 0.992 0.000 0.008 0.000 0.000
#> GSM381268 5 0.0324 0.9296 0.004 0.000 0.000 0.004 0.992
#> GSM381270 2 0.1568 0.9511 0.000 0.944 0.020 0.036 0.000
#> GSM381271 4 0.0162 0.9803 0.000 0.000 0.000 0.996 0.004
#> GSM381275 2 0.2929 0.8467 0.000 0.820 0.180 0.000 0.000
#> GSM381279 2 0.1082 0.9546 0.000 0.964 0.008 0.028 0.000
#> GSM381195 1 0.0771 0.6833 0.976 0.000 0.020 0.000 0.004
#> GSM381196 5 0.0290 0.9289 0.008 0.000 0.000 0.000 0.992
#> GSM381198 2 0.0324 0.9542 0.004 0.992 0.004 0.000 0.000
#> GSM381200 2 0.1357 0.9462 0.000 0.948 0.048 0.004 0.000
#> GSM381201 5 0.1209 0.9259 0.012 0.000 0.012 0.012 0.964
#> GSM381203 5 0.1365 0.9091 0.040 0.004 0.004 0.000 0.952
#> GSM381204 1 0.3305 0.6098 0.776 0.000 0.224 0.000 0.000
#> GSM381209 1 0.2770 0.6907 0.864 0.008 0.124 0.000 0.004
#> GSM381212 1 0.1571 0.7063 0.936 0.004 0.060 0.000 0.000
#> GSM381213 2 0.1043 0.9526 0.000 0.960 0.000 0.040 0.000
#> GSM381214 2 0.1412 0.9517 0.004 0.952 0.008 0.036 0.000
#> GSM381216 3 0.3451 0.5945 0.080 0.000 0.856 0.032 0.032
#> GSM381225 5 0.0671 0.9220 0.000 0.016 0.004 0.000 0.980
#> GSM381231 4 0.0771 0.9744 0.000 0.000 0.020 0.976 0.004
#> GSM381235 3 0.6106 0.4355 0.080 0.000 0.560 0.024 0.336
#> GSM381237 1 0.2561 0.6811 0.856 0.000 0.144 0.000 0.000
#> GSM381241 2 0.0671 0.9546 0.000 0.980 0.016 0.000 0.004
#> GSM381243 2 0.1893 0.9476 0.000 0.928 0.024 0.048 0.000
#> GSM381245 1 0.1216 0.7017 0.960 0.000 0.020 0.000 0.020
#> GSM381246 2 0.1638 0.9377 0.004 0.932 0.064 0.000 0.000
#> GSM381251 5 0.0290 0.9278 0.000 0.000 0.000 0.008 0.992
#> GSM381264 1 0.0771 0.6833 0.976 0.000 0.020 0.000 0.004
#> GSM381206 2 0.0798 0.9541 0.016 0.976 0.008 0.000 0.000
#> GSM381217 3 0.5799 0.5189 0.360 0.000 0.548 0.004 0.088
#> GSM381218 2 0.1865 0.9490 0.000 0.936 0.024 0.032 0.008
#> GSM381226 2 0.0963 0.9487 0.000 0.964 0.036 0.000 0.000
#> GSM381227 2 0.1444 0.9513 0.000 0.948 0.012 0.040 0.000
#> GSM381228 4 0.0162 0.9803 0.000 0.000 0.000 0.996 0.004
#> GSM381236 4 0.0162 0.9803 0.000 0.000 0.000 0.996 0.004
#> GSM381244 1 0.6628 -0.1040 0.492 0.000 0.372 0.100 0.036
#> GSM381272 4 0.0771 0.9744 0.000 0.000 0.020 0.976 0.004
#> GSM381277 1 0.5245 0.3961 0.648 0.000 0.044 0.292 0.016
#> GSM381278 5 0.4946 0.6765 0.004 0.000 0.076 0.216 0.704
#> GSM381197 3 0.7008 0.4236 0.388 0.000 0.412 0.024 0.176
#> GSM381202 3 0.5519 0.3611 0.424 0.000 0.520 0.008 0.048
#> GSM381207 1 0.3354 0.6718 0.864 0.000 0.044 0.064 0.028
#> GSM381208 2 0.2104 0.9391 0.000 0.916 0.024 0.060 0.000
#> GSM381210 1 0.4505 0.2724 0.604 0.000 0.384 0.000 0.012
#> GSM381215 5 0.2766 0.8766 0.012 0.000 0.056 0.040 0.892
#> GSM381219 2 0.0324 0.9539 0.000 0.992 0.004 0.004 0.000
#> GSM381221 2 0.0693 0.9540 0.000 0.980 0.012 0.000 0.008
#> GSM381223 2 0.1732 0.9325 0.000 0.920 0.080 0.000 0.000
#> GSM381229 5 0.0486 0.9254 0.000 0.004 0.004 0.004 0.988
#> GSM381230 1 0.1851 0.7037 0.912 0.000 0.088 0.000 0.000
#> GSM381233 1 0.4585 0.2720 0.592 0.000 0.396 0.004 0.008
#> GSM381234 1 0.0865 0.6798 0.972 0.000 0.024 0.000 0.004
#> GSM381238 4 0.0324 0.9802 0.000 0.000 0.004 0.992 0.004
#> GSM381239 4 0.1041 0.9433 0.000 0.032 0.000 0.964 0.004
#> GSM381242 3 0.5942 0.6170 0.276 0.000 0.620 0.064 0.040
#> GSM381247 2 0.1173 0.9531 0.000 0.964 0.012 0.004 0.020
#> GSM381248 1 0.1365 0.6734 0.952 0.000 0.040 0.004 0.004
#> GSM381249 1 0.4656 -0.1215 0.508 0.000 0.480 0.000 0.012
#> GSM381253 5 0.1981 0.8866 0.048 0.000 0.028 0.000 0.924
#> GSM381255 2 0.1372 0.9519 0.004 0.956 0.016 0.024 0.000
#> GSM381258 3 0.3474 0.5697 0.024 0.000 0.856 0.068 0.052
#> GSM381262 5 0.0162 0.9273 0.000 0.004 0.000 0.000 0.996
#> GSM381266 5 0.3361 0.8415 0.012 0.000 0.020 0.128 0.840
#> GSM381267 2 0.1872 0.9453 0.000 0.928 0.020 0.052 0.000
#> GSM381269 3 0.4494 0.6217 0.164 0.000 0.768 0.048 0.020
#> GSM381273 5 0.1281 0.9202 0.000 0.000 0.012 0.032 0.956
#> GSM381274 2 0.1908 0.9234 0.000 0.908 0.092 0.000 0.000
#> GSM381276 3 0.7670 0.5591 0.292 0.000 0.452 0.164 0.092
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM381194 3 0.0508 0.9062 0.000 0.000 0.984 0.004 0.012 0.000
#> GSM381199 2 0.1155 0.9538 0.004 0.956 0.004 0.000 0.000 0.036
#> GSM381205 2 0.1757 0.9397 0.052 0.928 0.000 0.012 0.000 0.008
#> GSM381211 2 0.0935 0.9557 0.000 0.964 0.000 0.032 0.000 0.004
#> GSM381220 2 0.3301 0.7846 0.008 0.772 0.000 0.216 0.000 0.004
#> GSM381222 5 0.3804 0.5361 0.336 0.000 0.000 0.000 0.656 0.008
#> GSM381224 5 0.2487 0.7765 0.092 0.000 0.000 0.000 0.876 0.032
#> GSM381232 4 0.0632 0.8875 0.000 0.000 0.000 0.976 0.024 0.000
#> GSM381240 5 0.2907 0.7514 0.152 0.000 0.000 0.000 0.828 0.020
#> GSM381250 3 0.0260 0.9088 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM381252 2 0.0146 0.9554 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM381254 1 0.1152 0.7613 0.952 0.000 0.000 0.004 0.044 0.000
#> GSM381256 2 0.1957 0.8887 0.000 0.888 0.112 0.000 0.000 0.000
#> GSM381257 5 0.3956 0.6004 0.292 0.000 0.024 0.000 0.684 0.000
#> GSM381259 1 0.2597 0.7019 0.824 0.000 0.000 0.000 0.176 0.000
#> GSM381260 5 0.1121 0.7706 0.004 0.000 0.008 0.016 0.964 0.008
#> GSM381261 2 0.1863 0.9218 0.000 0.920 0.000 0.004 0.016 0.060
#> GSM381263 3 0.3240 0.3704 0.000 0.000 0.752 0.004 0.244 0.000
#> GSM381265 1 0.2260 0.7377 0.860 0.000 0.000 0.000 0.140 0.000
#> GSM381268 3 0.0000 0.9078 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM381270 2 0.1367 0.9521 0.000 0.944 0.000 0.044 0.000 0.012
#> GSM381271 4 0.0363 0.8968 0.000 0.000 0.000 0.988 0.012 0.000
#> GSM381275 2 0.2189 0.9088 0.000 0.904 0.000 0.004 0.032 0.060
#> GSM381279 2 0.1082 0.9548 0.000 0.956 0.000 0.040 0.000 0.004
#> GSM381195 1 0.0790 0.7545 0.968 0.000 0.000 0.000 0.032 0.000
#> GSM381196 3 0.0146 0.9085 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM381198 2 0.0405 0.9559 0.008 0.988 0.000 0.000 0.000 0.004
#> GSM381200 2 0.0146 0.9548 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM381201 3 0.1152 0.8870 0.000 0.000 0.952 0.004 0.044 0.000
#> GSM381203 3 0.0291 0.9084 0.004 0.000 0.992 0.000 0.004 0.000
#> GSM381204 5 0.3727 0.4325 0.388 0.000 0.000 0.000 0.612 0.000
#> GSM381209 5 0.3371 0.6273 0.292 0.000 0.000 0.000 0.708 0.000
#> GSM381212 1 0.3672 0.3152 0.632 0.000 0.000 0.000 0.368 0.000
#> GSM381213 2 0.0865 0.9562 0.000 0.964 0.000 0.036 0.000 0.000
#> GSM381214 2 0.0692 0.9569 0.000 0.976 0.000 0.020 0.000 0.004
#> GSM381216 5 0.0935 0.7696 0.000 0.000 0.000 0.004 0.964 0.032
#> GSM381225 3 0.2493 0.7636 0.000 0.004 0.884 0.000 0.076 0.036
#> GSM381231 4 0.0458 0.8958 0.000 0.000 0.000 0.984 0.016 0.000
#> GSM381235 6 0.6246 0.3754 0.004 0.000 0.312 0.000 0.332 0.352
#> GSM381237 5 0.3868 0.1076 0.496 0.000 0.000 0.000 0.504 0.000
#> GSM381241 2 0.0146 0.9554 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM381243 2 0.2697 0.9014 0.000 0.864 0.000 0.092 0.000 0.044
#> GSM381245 1 0.4407 -0.0600 0.496 0.000 0.000 0.000 0.480 0.024
#> GSM381246 2 0.0405 0.9536 0.000 0.988 0.000 0.004 0.008 0.000
#> GSM381251 3 0.0000 0.9078 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM381264 1 0.1387 0.7686 0.932 0.000 0.000 0.000 0.068 0.000
#> GSM381206 2 0.0653 0.9561 0.012 0.980 0.000 0.004 0.000 0.004
#> GSM381217 5 0.3590 0.7574 0.068 0.000 0.020 0.000 0.820 0.092
#> GSM381218 2 0.0972 0.9562 0.000 0.964 0.000 0.028 0.000 0.008
#> GSM381226 2 0.0146 0.9548 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM381227 2 0.1265 0.9527 0.000 0.948 0.000 0.044 0.000 0.008
#> GSM381228 4 0.0146 0.8964 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM381236 4 0.0146 0.8964 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM381244 5 0.2480 0.7658 0.028 0.000 0.000 0.028 0.896 0.048
#> GSM381272 4 0.0458 0.8958 0.000 0.000 0.000 0.984 0.016 0.000
#> GSM381277 4 0.6216 -0.0598 0.096 0.000 0.000 0.432 0.416 0.056
#> GSM381278 6 0.4989 0.2446 0.000 0.000 0.388 0.028 0.028 0.556
#> GSM381197 5 0.2095 0.7589 0.016 0.000 0.052 0.012 0.916 0.004
#> GSM381202 5 0.0964 0.7774 0.012 0.000 0.000 0.004 0.968 0.016
#> GSM381207 1 0.6231 0.1306 0.368 0.000 0.004 0.296 0.332 0.000
#> GSM381208 2 0.1668 0.9448 0.004 0.928 0.000 0.060 0.000 0.008
#> GSM381210 5 0.2340 0.7600 0.148 0.000 0.000 0.000 0.852 0.000
#> GSM381215 3 0.1429 0.8759 0.000 0.000 0.940 0.004 0.052 0.004
#> GSM381219 2 0.0146 0.9548 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM381221 2 0.0146 0.9560 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM381223 2 0.1194 0.9455 0.000 0.956 0.000 0.004 0.008 0.032
#> GSM381229 3 0.0146 0.9073 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM381230 1 0.1501 0.7691 0.924 0.000 0.000 0.000 0.076 0.000
#> GSM381233 5 0.5906 0.0354 0.368 0.000 0.000 0.000 0.424 0.208
#> GSM381234 1 0.0603 0.7396 0.980 0.000 0.000 0.000 0.016 0.004
#> GSM381238 4 0.0291 0.8923 0.000 0.004 0.000 0.992 0.000 0.004
#> GSM381239 4 0.0146 0.8929 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM381242 5 0.0520 0.7698 0.000 0.000 0.000 0.008 0.984 0.008
#> GSM381247 2 0.2100 0.9391 0.000 0.916 0.032 0.036 0.000 0.016
#> GSM381248 1 0.1644 0.6739 0.920 0.000 0.000 0.000 0.004 0.076
#> GSM381249 5 0.2201 0.7852 0.076 0.000 0.000 0.000 0.896 0.028
#> GSM381253 3 0.1267 0.8584 0.000 0.000 0.940 0.000 0.060 0.000
#> GSM381255 2 0.1296 0.9528 0.004 0.948 0.000 0.044 0.000 0.004
#> GSM381258 5 0.2103 0.7353 0.000 0.000 0.020 0.012 0.912 0.056
#> GSM381262 3 0.0146 0.9073 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM381266 3 0.2051 0.8437 0.000 0.000 0.916 0.040 0.008 0.036
#> GSM381267 2 0.1411 0.9469 0.000 0.936 0.000 0.060 0.000 0.004
#> GSM381269 5 0.1480 0.7786 0.020 0.000 0.000 0.000 0.940 0.040
#> GSM381273 3 0.1434 0.8809 0.000 0.000 0.948 0.020 0.008 0.024
#> GSM381274 2 0.1511 0.9357 0.000 0.940 0.000 0.004 0.012 0.044
#> GSM381276 5 0.2806 0.7154 0.000 0.000 0.012 0.056 0.872 0.060
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 other(p) k
#> MAD:NMF 84 0.728 2
#> MAD:NMF 84 0.788 3
#> MAD:NMF 74 0.823 4
#> MAD:NMF 76 0.384 5
#> MAD:NMF 76 0.454 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 86 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 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4528 0.548 0.548
#> 3 3 1.000 1.000 1.000 0.0326 0.985 0.973
#> 4 4 0.998 0.938 0.974 0.4519 0.793 0.612
#> 5 5 0.930 0.842 0.941 0.0686 0.937 0.814
#> 6 6 0.853 0.780 0.881 0.0432 0.976 0.918
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 4
There is also optional best \(k\) = 2 4 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
#> GSM381194 1 0 1 1 0
#> GSM381199 2 0 1 0 1
#> GSM381205 2 0 1 0 1
#> GSM381211 2 0 1 0 1
#> GSM381220 2 0 1 0 1
#> GSM381222 1 0 1 1 0
#> GSM381224 1 0 1 1 0
#> GSM381232 1 0 1 1 0
#> GSM381240 1 0 1 1 0
#> GSM381250 1 0 1 1 0
#> GSM381252 2 0 1 0 1
#> GSM381254 1 0 1 1 0
#> GSM381256 2 0 1 0 1
#> GSM381257 1 0 1 1 0
#> GSM381259 1 0 1 1 0
#> GSM381260 1 0 1 1 0
#> GSM381261 2 0 1 0 1
#> GSM381263 1 0 1 1 0
#> GSM381265 1 0 1 1 0
#> GSM381268 1 0 1 1 0
#> GSM381270 2 0 1 0 1
#> GSM381271 1 0 1 1 0
#> GSM381275 2 0 1 0 1
#> GSM381279 2 0 1 0 1
#> GSM381195 1 0 1 1 0
#> GSM381196 1 0 1 1 0
#> GSM381198 2 0 1 0 1
#> GSM381200 2 0 1 0 1
#> GSM381201 1 0 1 1 0
#> GSM381203 1 0 1 1 0
#> GSM381204 1 0 1 1 0
#> GSM381209 1 0 1 1 0
#> GSM381212 1 0 1 1 0
#> GSM381213 2 0 1 0 1
#> GSM381214 2 0 1 0 1
#> GSM381216 1 0 1 1 0
#> GSM381225 1 0 1 1 0
#> GSM381231 1 0 1 1 0
#> GSM381235 1 0 1 1 0
#> GSM381237 1 0 1 1 0
#> GSM381241 2 0 1 0 1
#> GSM381243 2 0 1 0 1
#> GSM381245 1 0 1 1 0
#> GSM381246 2 0 1 0 1
#> GSM381251 1 0 1 1 0
#> GSM381264 1 0 1 1 0
#> GSM381206 2 0 1 0 1
#> GSM381217 1 0 1 1 0
#> GSM381218 2 0 1 0 1
#> GSM381226 2 0 1 0 1
#> GSM381227 2 0 1 0 1
#> GSM381228 1 0 1 1 0
#> GSM381236 1 0 1 1 0
#> GSM381244 1 0 1 1 0
#> GSM381272 1 0 1 1 0
#> GSM381277 1 0 1 1 0
#> GSM381278 1 0 1 1 0
#> GSM381197 1 0 1 1 0
#> GSM381202 1 0 1 1 0
#> GSM381207 1 0 1 1 0
#> GSM381208 2 0 1 0 1
#> GSM381210 1 0 1 1 0
#> GSM381215 1 0 1 1 0
#> GSM381219 2 0 1 0 1
#> GSM381221 2 0 1 0 1
#> GSM381223 2 0 1 0 1
#> GSM381229 1 0 1 1 0
#> GSM381230 1 0 1 1 0
#> GSM381233 1 0 1 1 0
#> GSM381234 1 0 1 1 0
#> GSM381238 1 0 1 1 0
#> GSM381239 1 0 1 1 0
#> GSM381242 1 0 1 1 0
#> GSM381247 2 0 1 0 1
#> GSM381248 1 0 1 1 0
#> GSM381249 1 0 1 1 0
#> GSM381253 1 0 1 1 0
#> GSM381255 2 0 1 0 1
#> GSM381258 1 0 1 1 0
#> GSM381262 1 0 1 1 0
#> GSM381266 1 0 1 1 0
#> GSM381267 2 0 1 0 1
#> GSM381269 1 0 1 1 0
#> GSM381273 1 0 1 1 0
#> GSM381274 2 0 1 0 1
#> GSM381276 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM381194 1 0 1 1 0 0
#> GSM381199 2 0 1 0 1 0
#> GSM381205 2 0 1 0 1 0
#> GSM381211 2 0 1 0 1 0
#> GSM381220 2 0 1 0 1 0
#> GSM381222 1 0 1 1 0 0
#> GSM381224 1 0 1 1 0 0
#> GSM381232 1 0 1 1 0 0
#> GSM381240 1 0 1 1 0 0
#> GSM381250 1 0 1 1 0 0
#> GSM381252 2 0 1 0 1 0
#> GSM381254 1 0 1 1 0 0
#> GSM381256 2 0 1 0 1 0
#> GSM381257 1 0 1 1 0 0
#> GSM381259 1 0 1 1 0 0
#> GSM381260 1 0 1 1 0 0
#> GSM381261 2 0 1 0 1 0
#> GSM381263 1 0 1 1 0 0
#> GSM381265 1 0 1 1 0 0
#> GSM381268 1 0 1 1 0 0
#> GSM381270 2 0 1 0 1 0
#> GSM381271 1 0 1 1 0 0
#> GSM381275 2 0 1 0 1 0
#> GSM381279 2 0 1 0 1 0
#> GSM381195 1 0 1 1 0 0
#> GSM381196 1 0 1 1 0 0
#> GSM381198 2 0 1 0 1 0
#> GSM381200 2 0 1 0 1 0
#> GSM381201 1 0 1 1 0 0
#> GSM381203 1 0 1 1 0 0
#> GSM381204 1 0 1 1 0 0
#> GSM381209 1 0 1 1 0 0
#> GSM381212 1 0 1 1 0 0
#> GSM381213 2 0 1 0 1 0
#> GSM381214 2 0 1 0 1 0
#> GSM381216 1 0 1 1 0 0
#> GSM381225 1 0 1 1 0 0
#> GSM381231 1 0 1 1 0 0
#> GSM381235 1 0 1 1 0 0
#> GSM381237 1 0 1 1 0 0
#> GSM381241 2 0 1 0 1 0
#> GSM381243 2 0 1 0 1 0
#> GSM381245 1 0 1 1 0 0
#> GSM381246 2 0 1 0 1 0
#> GSM381251 1 0 1 1 0 0
#> GSM381264 1 0 1 1 0 0
#> GSM381206 2 0 1 0 1 0
#> GSM381217 1 0 1 1 0 0
#> GSM381218 2 0 1 0 1 0
#> GSM381226 2 0 1 0 1 0
#> GSM381227 2 0 1 0 1 0
#> GSM381228 1 0 1 1 0 0
#> GSM381236 1 0 1 1 0 0
#> GSM381244 1 0 1 1 0 0
#> GSM381272 1 0 1 1 0 0
#> GSM381277 1 0 1 1 0 0
#> GSM381278 1 0 1 1 0 0
#> GSM381197 1 0 1 1 0 0
#> GSM381202 1 0 1 1 0 0
#> GSM381207 1 0 1 1 0 0
#> GSM381208 3 0 1 0 0 1
#> GSM381210 1 0 1 1 0 0
#> GSM381215 1 0 1 1 0 0
#> GSM381219 2 0 1 0 1 0
#> GSM381221 2 0 1 0 1 0
#> GSM381223 2 0 1 0 1 0
#> GSM381229 1 0 1 1 0 0
#> GSM381230 1 0 1 1 0 0
#> GSM381233 1 0 1 1 0 0
#> GSM381234 1 0 1 1 0 0
#> GSM381238 1 0 1 1 0 0
#> GSM381239 1 0 1 1 0 0
#> GSM381242 1 0 1 1 0 0
#> GSM381247 2 0 1 0 1 0
#> GSM381248 1 0 1 1 0 0
#> GSM381249 1 0 1 1 0 0
#> GSM381253 1 0 1 1 0 0
#> GSM381255 2 0 1 0 1 0
#> GSM381258 1 0 1 1 0 0
#> GSM381262 1 0 1 1 0 0
#> GSM381266 1 0 1 1 0 0
#> GSM381267 3 0 1 0 0 1
#> GSM381269 1 0 1 1 0 0
#> GSM381273 1 0 1 1 0 0
#> GSM381274 2 0 1 0 1 0
#> GSM381276 1 0 1 1 0 0
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM381194 3 0.0000 0.926 0.000 0 1.000 0
#> GSM381199 2 0.0000 1.000 0.000 1 0.000 0
#> GSM381205 2 0.0000 1.000 0.000 1 0.000 0
#> GSM381211 2 0.0000 1.000 0.000 1 0.000 0
#> GSM381220 2 0.0000 1.000 0.000 1 0.000 0
#> GSM381222 1 0.0000 0.995 1.000 0 0.000 0
#> GSM381224 1 0.0000 0.995 1.000 0 0.000 0
#> GSM381232 3 0.0000 0.926 0.000 0 1.000 0
#> GSM381240 1 0.0000 0.995 1.000 0 0.000 0
#> GSM381250 3 0.0336 0.926 0.008 0 0.992 0
#> GSM381252 2 0.0000 1.000 0.000 1 0.000 0
#> GSM381254 1 0.0188 0.990 0.996 0 0.004 0
#> GSM381256 2 0.0000 1.000 0.000 1 0.000 0
#> GSM381257 1 0.1716 0.899 0.936 0 0.064 0
#> GSM381259 1 0.0000 0.995 1.000 0 0.000 0
#> GSM381260 3 0.1022 0.917 0.032 0 0.968 0
#> GSM381261 2 0.0000 1.000 0.000 1 0.000 0
#> GSM381263 3 0.0000 0.926 0.000 0 1.000 0
#> GSM381265 1 0.0000 0.995 1.000 0 0.000 0
#> GSM381268 3 0.0469 0.924 0.012 0 0.988 0
#> GSM381270 2 0.0000 1.000 0.000 1 0.000 0
#> GSM381271 3 0.0000 0.926 0.000 0 1.000 0
#> GSM381275 2 0.0000 1.000 0.000 1 0.000 0
#> GSM381279 2 0.0000 1.000 0.000 1 0.000 0
#> GSM381195 1 0.0000 0.995 1.000 0 0.000 0
#> GSM381196 3 0.0336 0.926 0.008 0 0.992 0
#> GSM381198 2 0.0000 1.000 0.000 1 0.000 0
#> GSM381200 2 0.0000 1.000 0.000 1 0.000 0
#> GSM381201 3 0.0000 0.926 0.000 0 1.000 0
#> GSM381203 3 0.0469 0.925 0.012 0 0.988 0
#> GSM381204 1 0.0000 0.995 1.000 0 0.000 0
#> GSM381209 1 0.0000 0.995 1.000 0 0.000 0
#> GSM381212 1 0.0000 0.995 1.000 0 0.000 0
#> GSM381213 2 0.0000 1.000 0.000 1 0.000 0
#> GSM381214 2 0.0000 1.000 0.000 1 0.000 0
#> GSM381216 3 0.0592 0.924 0.016 0 0.984 0
#> GSM381225 3 0.3486 0.759 0.188 0 0.812 0
#> GSM381231 3 0.0000 0.926 0.000 0 1.000 0
#> GSM381235 3 0.1637 0.899 0.060 0 0.940 0
#> GSM381237 1 0.0000 0.995 1.000 0 0.000 0
#> GSM381241 2 0.0000 1.000 0.000 1 0.000 0
#> GSM381243 2 0.0000 1.000 0.000 1 0.000 0
#> GSM381245 1 0.0000 0.995 1.000 0 0.000 0
#> GSM381246 2 0.0000 1.000 0.000 1 0.000 0
#> GSM381251 3 0.0000 0.926 0.000 0 1.000 0
#> GSM381264 1 0.0000 0.995 1.000 0 0.000 0
#> GSM381206 2 0.0000 1.000 0.000 1 0.000 0
#> GSM381217 3 0.0707 0.923 0.020 0 0.980 0
#> GSM381218 2 0.0000 1.000 0.000 1 0.000 0
#> GSM381226 2 0.0000 1.000 0.000 1 0.000 0
#> GSM381227 2 0.0000 1.000 0.000 1 0.000 0
#> GSM381228 3 0.0000 0.926 0.000 0 1.000 0
#> GSM381236 3 0.0000 0.926 0.000 0 1.000 0
#> GSM381244 3 0.4994 0.201 0.480 0 0.520 0
#> GSM381272 3 0.0000 0.926 0.000 0 1.000 0
#> GSM381277 3 0.4972 0.275 0.456 0 0.544 0
#> GSM381278 3 0.2011 0.882 0.080 0 0.920 0
#> GSM381197 3 0.0000 0.926 0.000 0 1.000 0
#> GSM381202 3 0.0592 0.924 0.016 0 0.984 0
#> GSM381207 1 0.0188 0.990 0.996 0 0.004 0
#> GSM381208 4 0.0000 1.000 0.000 0 0.000 1
#> GSM381210 1 0.0000 0.995 1.000 0 0.000 0
#> GSM381215 3 0.0336 0.926 0.008 0 0.992 0
#> GSM381219 2 0.0000 1.000 0.000 1 0.000 0
#> GSM381221 2 0.0000 1.000 0.000 1 0.000 0
#> GSM381223 2 0.0000 1.000 0.000 1 0.000 0
#> GSM381229 3 0.1940 0.885 0.076 0 0.924 0
#> GSM381230 1 0.0000 0.995 1.000 0 0.000 0
#> GSM381233 1 0.0000 0.995 1.000 0 0.000 0
#> GSM381234 1 0.0000 0.995 1.000 0 0.000 0
#> GSM381238 3 0.0000 0.926 0.000 0 1.000 0
#> GSM381239 3 0.0000 0.926 0.000 0 1.000 0
#> GSM381242 3 0.1022 0.917 0.032 0 0.968 0
#> GSM381247 2 0.0000 1.000 0.000 1 0.000 0
#> GSM381248 1 0.0000 0.995 1.000 0 0.000 0
#> GSM381249 1 0.0000 0.995 1.000 0 0.000 0
#> GSM381253 3 0.0336 0.926 0.008 0 0.992 0
#> GSM381255 2 0.0000 1.000 0.000 1 0.000 0
#> GSM381258 3 0.0000 0.926 0.000 0 1.000 0
#> GSM381262 3 0.0000 0.926 0.000 0 1.000 0
#> GSM381266 3 0.1557 0.901 0.056 0 0.944 0
#> GSM381267 4 0.0000 1.000 0.000 0 0.000 1
#> GSM381269 3 0.2345 0.862 0.100 0 0.900 0
#> GSM381273 3 0.1557 0.901 0.056 0 0.944 0
#> GSM381274 2 0.0000 1.000 0.000 1 0.000 0
#> GSM381276 3 0.4948 0.320 0.440 0 0.560 0
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM381194 3 0.0162 0.8805 0.000 0 0.996 0 0.004
#> GSM381199 2 0.0000 1.0000 0.000 1 0.000 0 0.000
#> GSM381205 2 0.0000 1.0000 0.000 1 0.000 0 0.000
#> GSM381211 2 0.0000 1.0000 0.000 1 0.000 0 0.000
#> GSM381220 2 0.0000 1.0000 0.000 1 0.000 0 0.000
#> GSM381222 1 0.0000 0.9370 1.000 0 0.000 0 0.000
#> GSM381224 1 0.0000 0.9370 1.000 0 0.000 0 0.000
#> GSM381232 3 0.0290 0.8813 0.000 0 0.992 0 0.008
#> GSM381240 1 0.0000 0.9370 1.000 0 0.000 0 0.000
#> GSM381250 3 0.1082 0.8746 0.008 0 0.964 0 0.028
#> GSM381252 2 0.0000 1.0000 0.000 1 0.000 0 0.000
#> GSM381254 1 0.0162 0.9329 0.996 0 0.004 0 0.000
#> GSM381256 2 0.0000 1.0000 0.000 1 0.000 0 0.000
#> GSM381257 1 0.1628 0.8536 0.936 0 0.056 0 0.008
#> GSM381259 1 0.0000 0.9370 1.000 0 0.000 0 0.000
#> GSM381260 3 0.4485 0.5121 0.028 0 0.680 0 0.292
#> GSM381261 2 0.0000 1.0000 0.000 1 0.000 0 0.000
#> GSM381263 3 0.0162 0.8805 0.000 0 0.996 0 0.004
#> GSM381265 1 0.0000 0.9370 1.000 0 0.000 0 0.000
#> GSM381268 3 0.0566 0.8773 0.012 0 0.984 0 0.004
#> GSM381270 2 0.0000 1.0000 0.000 1 0.000 0 0.000
#> GSM381271 3 0.0290 0.8813 0.000 0 0.992 0 0.008
#> GSM381275 2 0.0000 1.0000 0.000 1 0.000 0 0.000
#> GSM381279 2 0.0000 1.0000 0.000 1 0.000 0 0.000
#> GSM381195 1 0.0000 0.9370 1.000 0 0.000 0 0.000
#> GSM381196 3 0.0992 0.8762 0.008 0 0.968 0 0.024
#> GSM381198 2 0.0000 1.0000 0.000 1 0.000 0 0.000
#> GSM381200 2 0.0000 1.0000 0.000 1 0.000 0 0.000
#> GSM381201 3 0.2516 0.7597 0.000 0 0.860 0 0.140
#> GSM381203 3 0.1281 0.8717 0.012 0 0.956 0 0.032
#> GSM381204 1 0.0000 0.9370 1.000 0 0.000 0 0.000
#> GSM381209 1 0.0000 0.9370 1.000 0 0.000 0 0.000
#> GSM381212 1 0.0000 0.9370 1.000 0 0.000 0 0.000
#> GSM381213 2 0.0000 1.0000 0.000 1 0.000 0 0.000
#> GSM381214 2 0.0000 1.0000 0.000 1 0.000 0 0.000
#> GSM381216 3 0.1469 0.8693 0.016 0 0.948 0 0.036
#> GSM381225 5 0.0290 0.3097 0.000 0 0.008 0 0.992
#> GSM381231 3 0.0290 0.8813 0.000 0 0.992 0 0.008
#> GSM381235 3 0.4083 0.6401 0.028 0 0.744 0 0.228
#> GSM381237 1 0.0000 0.9370 1.000 0 0.000 0 0.000
#> GSM381241 2 0.0000 1.0000 0.000 1 0.000 0 0.000
#> GSM381243 2 0.0000 1.0000 0.000 1 0.000 0 0.000
#> GSM381245 1 0.0000 0.9370 1.000 0 0.000 0 0.000
#> GSM381246 2 0.0000 1.0000 0.000 1 0.000 0 0.000
#> GSM381251 3 0.3661 0.5415 0.000 0 0.724 0 0.276
#> GSM381264 1 0.0000 0.9370 1.000 0 0.000 0 0.000
#> GSM381206 2 0.0000 1.0000 0.000 1 0.000 0 0.000
#> GSM381217 3 0.1485 0.8672 0.020 0 0.948 0 0.032
#> GSM381218 2 0.0000 1.0000 0.000 1 0.000 0 0.000
#> GSM381226 2 0.0000 1.0000 0.000 1 0.000 0 0.000
#> GSM381227 2 0.0000 1.0000 0.000 1 0.000 0 0.000
#> GSM381228 3 0.0290 0.8813 0.000 0 0.992 0 0.008
#> GSM381236 3 0.0290 0.8813 0.000 0 0.992 0 0.008
#> GSM381244 1 0.6081 -0.1843 0.476 0 0.124 0 0.400
#> GSM381272 3 0.0290 0.8813 0.000 0 0.992 0 0.008
#> GSM381277 1 0.6100 -0.2639 0.448 0 0.124 0 0.428
#> GSM381278 5 0.2732 0.4780 0.000 0 0.160 0 0.840
#> GSM381197 3 0.0290 0.8798 0.000 0 0.992 0 0.008
#> GSM381202 3 0.1469 0.8693 0.016 0 0.948 0 0.036
#> GSM381207 1 0.0162 0.9329 0.996 0 0.004 0 0.000
#> GSM381208 4 0.0000 1.0000 0.000 0 0.000 1 0.000
#> GSM381210 1 0.0000 0.9370 1.000 0 0.000 0 0.000
#> GSM381215 3 0.0992 0.8762 0.008 0 0.968 0 0.024
#> GSM381219 2 0.0000 1.0000 0.000 1 0.000 0 0.000
#> GSM381221 2 0.0000 1.0000 0.000 1 0.000 0 0.000
#> GSM381223 2 0.0000 1.0000 0.000 1 0.000 0 0.000
#> GSM381229 5 0.3752 0.4193 0.000 0 0.292 0 0.708
#> GSM381230 1 0.0000 0.9370 1.000 0 0.000 0 0.000
#> GSM381233 1 0.0000 0.9370 1.000 0 0.000 0 0.000
#> GSM381234 1 0.0000 0.9370 1.000 0 0.000 0 0.000
#> GSM381238 3 0.0290 0.8813 0.000 0 0.992 0 0.008
#> GSM381239 3 0.0290 0.8813 0.000 0 0.992 0 0.008
#> GSM381242 3 0.4485 0.5121 0.028 0 0.680 0 0.292
#> GSM381247 2 0.0000 1.0000 0.000 1 0.000 0 0.000
#> GSM381248 1 0.0510 0.9216 0.984 0 0.000 0 0.016
#> GSM381249 1 0.0000 0.9370 1.000 0 0.000 0 0.000
#> GSM381253 3 0.0992 0.8762 0.008 0 0.968 0 0.024
#> GSM381255 2 0.0000 1.0000 0.000 1 0.000 0 0.000
#> GSM381258 3 0.0162 0.8805 0.000 0 0.996 0 0.004
#> GSM381262 3 0.0162 0.8805 0.000 0 0.996 0 0.004
#> GSM381266 3 0.4306 0.0185 0.000 0 0.508 0 0.492
#> GSM381267 4 0.0000 1.0000 0.000 0 0.000 1 0.000
#> GSM381269 3 0.2959 0.7737 0.100 0 0.864 0 0.036
#> GSM381273 3 0.4306 0.0185 0.000 0 0.508 0 0.492
#> GSM381274 2 0.0000 1.0000 0.000 1 0.000 0 0.000
#> GSM381276 5 0.6101 0.0337 0.432 0 0.124 0 0.444
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM381194 3 0.0777 0.7842 0.000 0.000 0.972 0.000 0.004 0.024
#> GSM381199 2 0.0000 0.9483 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381205 2 0.0363 0.9474 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM381211 2 0.0363 0.9474 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM381220 2 0.0632 0.9459 0.000 0.976 0.000 0.024 0.000 0.000
#> GSM381222 1 0.0000 0.8772 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381224 1 0.0000 0.8772 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381232 3 0.3531 0.6675 0.000 0.000 0.672 0.000 0.000 0.328
#> GSM381240 1 0.0000 0.8772 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381250 3 0.0405 0.7827 0.008 0.000 0.988 0.000 0.000 0.004
#> GSM381252 2 0.0363 0.9474 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM381254 1 0.0146 0.8755 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM381256 2 0.0632 0.9459 0.000 0.976 0.000 0.024 0.000 0.000
#> GSM381257 1 0.4117 0.6636 0.716 0.000 0.056 0.000 0.000 0.228
#> GSM381259 1 0.1204 0.8743 0.944 0.000 0.000 0.000 0.000 0.056
#> GSM381260 3 0.4181 0.5179 0.028 0.000 0.704 0.000 0.256 0.012
#> GSM381261 2 0.3221 0.7377 0.000 0.736 0.000 0.264 0.000 0.000
#> GSM381263 3 0.0777 0.7842 0.000 0.000 0.972 0.000 0.004 0.024
#> GSM381265 1 0.1204 0.8743 0.944 0.000 0.000 0.000 0.000 0.056
#> GSM381268 3 0.1010 0.7831 0.000 0.000 0.960 0.000 0.004 0.036
#> GSM381270 2 0.0632 0.9459 0.000 0.976 0.000 0.024 0.000 0.000
#> GSM381271 3 0.3531 0.6675 0.000 0.000 0.672 0.000 0.000 0.328
#> GSM381275 2 0.3221 0.7377 0.000 0.736 0.000 0.264 0.000 0.000
#> GSM381279 2 0.0632 0.9459 0.000 0.976 0.000 0.024 0.000 0.000
#> GSM381195 1 0.1204 0.8743 0.944 0.000 0.000 0.000 0.000 0.056
#> GSM381196 3 0.0260 0.7838 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM381198 2 0.0363 0.9474 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM381200 2 0.0363 0.9474 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM381201 3 0.3806 0.5981 0.000 0.000 0.776 0.000 0.136 0.088
#> GSM381203 3 0.0622 0.7807 0.012 0.000 0.980 0.000 0.000 0.008
#> GSM381204 1 0.1204 0.8743 0.944 0.000 0.000 0.000 0.000 0.056
#> GSM381209 1 0.1204 0.8743 0.944 0.000 0.000 0.000 0.000 0.056
#> GSM381212 1 0.1204 0.8743 0.944 0.000 0.000 0.000 0.000 0.056
#> GSM381213 2 0.0632 0.9459 0.000 0.976 0.000 0.024 0.000 0.000
#> GSM381214 2 0.0363 0.9474 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM381216 3 0.0820 0.7793 0.016 0.000 0.972 0.000 0.000 0.012
#> GSM381225 5 0.0000 0.4308 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM381231 3 0.3531 0.6675 0.000 0.000 0.672 0.000 0.000 0.328
#> GSM381235 3 0.4037 0.6072 0.028 0.000 0.752 0.000 0.196 0.024
#> GSM381237 1 0.0000 0.8772 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381241 2 0.0000 0.9483 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381243 2 0.0632 0.9459 0.000 0.976 0.000 0.024 0.000 0.000
#> GSM381245 1 0.0000 0.8772 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381246 2 0.0363 0.9474 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM381251 3 0.5826 -0.2393 0.000 0.000 0.492 0.000 0.272 0.236
#> GSM381264 1 0.1204 0.8743 0.944 0.000 0.000 0.000 0.000 0.056
#> GSM381206 2 0.0363 0.9474 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM381217 3 0.0806 0.7766 0.020 0.000 0.972 0.000 0.000 0.008
#> GSM381218 2 0.0000 0.9483 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381226 2 0.0363 0.9474 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM381227 2 0.0632 0.9459 0.000 0.976 0.000 0.024 0.000 0.000
#> GSM381228 3 0.3531 0.6675 0.000 0.000 0.672 0.000 0.000 0.328
#> GSM381236 3 0.3531 0.6675 0.000 0.000 0.672 0.000 0.000 0.328
#> GSM381244 1 0.5899 0.1310 0.476 0.000 0.148 0.000 0.364 0.012
#> GSM381272 3 0.3531 0.6675 0.000 0.000 0.672 0.000 0.000 0.328
#> GSM381277 1 0.5931 0.0626 0.448 0.000 0.148 0.000 0.392 0.012
#> GSM381278 5 0.2831 0.6600 0.000 0.000 0.136 0.000 0.840 0.024
#> GSM381197 3 0.1584 0.7710 0.000 0.000 0.928 0.000 0.008 0.064
#> GSM381202 3 0.0820 0.7793 0.016 0.000 0.972 0.000 0.000 0.012
#> GSM381207 1 0.0146 0.8755 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM381208 4 0.3221 1.0000 0.000 0.000 0.000 0.736 0.000 0.264
#> GSM381210 1 0.1204 0.8743 0.944 0.000 0.000 0.000 0.000 0.056
#> GSM381215 3 0.0260 0.7838 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM381219 2 0.0363 0.9474 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM381221 2 0.0000 0.9483 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381223 2 0.3221 0.7377 0.000 0.736 0.000 0.264 0.000 0.000
#> GSM381229 5 0.4474 0.7004 0.000 0.000 0.172 0.000 0.708 0.120
#> GSM381230 1 0.0000 0.8772 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381233 1 0.0000 0.8772 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381234 1 0.0000 0.8772 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381238 3 0.3531 0.6675 0.000 0.000 0.672 0.000 0.000 0.328
#> GSM381239 3 0.3531 0.6675 0.000 0.000 0.672 0.000 0.000 0.328
#> GSM381242 3 0.4181 0.5179 0.028 0.000 0.704 0.000 0.256 0.012
#> GSM381247 2 0.0632 0.9459 0.000 0.976 0.000 0.024 0.000 0.000
#> GSM381248 1 0.2793 0.7229 0.800 0.000 0.000 0.000 0.000 0.200
#> GSM381249 1 0.1204 0.8743 0.944 0.000 0.000 0.000 0.000 0.056
#> GSM381253 3 0.0260 0.7838 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM381255 2 0.0632 0.9459 0.000 0.976 0.000 0.024 0.000 0.000
#> GSM381258 3 0.0777 0.7842 0.000 0.000 0.972 0.000 0.004 0.024
#> GSM381262 3 0.0777 0.7842 0.000 0.000 0.972 0.000 0.004 0.024
#> GSM381266 5 0.5794 0.6657 0.000 0.000 0.296 0.000 0.492 0.212
#> GSM381267 4 0.3221 1.0000 0.000 0.000 0.000 0.736 0.000 0.264
#> GSM381269 3 0.2170 0.7006 0.100 0.000 0.888 0.000 0.000 0.012
#> GSM381273 5 0.5794 0.6657 0.000 0.000 0.296 0.000 0.492 0.212
#> GSM381274 2 0.3221 0.7377 0.000 0.736 0.000 0.264 0.000 0.000
#> GSM381276 1 0.5939 0.0199 0.432 0.000 0.148 0.000 0.408 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 other(p) k
#> ATC:hclust 86 0.744 2
#> ATC:hclust 86 0.390 3
#> ATC:hclust 83 0.318 4
#> ATC:hclust 78 0.402 5
#> ATC:hclust 81 0.286 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 86 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4528 0.548 0.548
#> 3 3 0.726 0.949 0.887 0.3619 0.789 0.615
#> 4 4 0.630 0.508 0.838 0.1251 0.982 0.946
#> 5 5 0.799 0.730 0.832 0.0811 0.917 0.750
#> 6 6 0.743 0.626 0.670 0.0362 0.890 0.596
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
#> GSM381194 1 0 1 1 0
#> GSM381199 2 0 1 0 1
#> GSM381205 2 0 1 0 1
#> GSM381211 2 0 1 0 1
#> GSM381220 2 0 1 0 1
#> GSM381222 1 0 1 1 0
#> GSM381224 1 0 1 1 0
#> GSM381232 1 0 1 1 0
#> GSM381240 1 0 1 1 0
#> GSM381250 1 0 1 1 0
#> GSM381252 2 0 1 0 1
#> GSM381254 1 0 1 1 0
#> GSM381256 2 0 1 0 1
#> GSM381257 1 0 1 1 0
#> GSM381259 1 0 1 1 0
#> GSM381260 1 0 1 1 0
#> GSM381261 2 0 1 0 1
#> GSM381263 1 0 1 1 0
#> GSM381265 1 0 1 1 0
#> GSM381268 1 0 1 1 0
#> GSM381270 2 0 1 0 1
#> GSM381271 1 0 1 1 0
#> GSM381275 2 0 1 0 1
#> GSM381279 2 0 1 0 1
#> GSM381195 1 0 1 1 0
#> GSM381196 1 0 1 1 0
#> GSM381198 2 0 1 0 1
#> GSM381200 2 0 1 0 1
#> GSM381201 1 0 1 1 0
#> GSM381203 1 0 1 1 0
#> GSM381204 1 0 1 1 0
#> GSM381209 1 0 1 1 0
#> GSM381212 1 0 1 1 0
#> GSM381213 2 0 1 0 1
#> GSM381214 2 0 1 0 1
#> GSM381216 1 0 1 1 0
#> GSM381225 1 0 1 1 0
#> GSM381231 1 0 1 1 0
#> GSM381235 1 0 1 1 0
#> GSM381237 1 0 1 1 0
#> GSM381241 2 0 1 0 1
#> GSM381243 2 0 1 0 1
#> GSM381245 1 0 1 1 0
#> GSM381246 2 0 1 0 1
#> GSM381251 1 0 1 1 0
#> GSM381264 1 0 1 1 0
#> GSM381206 2 0 1 0 1
#> GSM381217 1 0 1 1 0
#> GSM381218 2 0 1 0 1
#> GSM381226 2 0 1 0 1
#> GSM381227 2 0 1 0 1
#> GSM381228 1 0 1 1 0
#> GSM381236 1 0 1 1 0
#> GSM381244 1 0 1 1 0
#> GSM381272 1 0 1 1 0
#> GSM381277 1 0 1 1 0
#> GSM381278 1 0 1 1 0
#> GSM381197 1 0 1 1 0
#> GSM381202 1 0 1 1 0
#> GSM381207 1 0 1 1 0
#> GSM381208 2 0 1 0 1
#> GSM381210 1 0 1 1 0
#> GSM381215 1 0 1 1 0
#> GSM381219 2 0 1 0 1
#> GSM381221 2 0 1 0 1
#> GSM381223 2 0 1 0 1
#> GSM381229 1 0 1 1 0
#> GSM381230 1 0 1 1 0
#> GSM381233 1 0 1 1 0
#> GSM381234 1 0 1 1 0
#> GSM381238 1 0 1 1 0
#> GSM381239 1 0 1 1 0
#> GSM381242 1 0 1 1 0
#> GSM381247 2 0 1 0 1
#> GSM381248 1 0 1 1 0
#> GSM381249 1 0 1 1 0
#> GSM381253 1 0 1 1 0
#> GSM381255 2 0 1 0 1
#> GSM381258 1 0 1 1 0
#> GSM381262 1 0 1 1 0
#> GSM381266 1 0 1 1 0
#> GSM381267 2 0 1 0 1
#> GSM381269 1 0 1 1 0
#> GSM381273 1 0 1 1 0
#> GSM381274 2 0 1 0 1
#> GSM381276 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM381194 3 0.0000 0.964 0.000 0.000 1.000
#> GSM381199 2 0.0000 0.936 0.000 1.000 0.000
#> GSM381205 2 0.1031 0.932 0.024 0.976 0.000
#> GSM381211 2 0.1031 0.932 0.024 0.976 0.000
#> GSM381220 2 0.4178 0.922 0.172 0.828 0.000
#> GSM381222 1 0.5465 1.000 0.712 0.000 0.288
#> GSM381224 1 0.5465 1.000 0.712 0.000 0.288
#> GSM381232 3 0.0000 0.964 0.000 0.000 1.000
#> GSM381240 1 0.5465 1.000 0.712 0.000 0.288
#> GSM381250 3 0.0000 0.964 0.000 0.000 1.000
#> GSM381252 2 0.0000 0.936 0.000 1.000 0.000
#> GSM381254 1 0.5465 1.000 0.712 0.000 0.288
#> GSM381256 2 0.2066 0.936 0.060 0.940 0.000
#> GSM381257 3 0.2356 0.897 0.072 0.000 0.928
#> GSM381259 1 0.5465 1.000 0.712 0.000 0.288
#> GSM381260 3 0.0892 0.950 0.020 0.000 0.980
#> GSM381261 2 0.4235 0.921 0.176 0.824 0.000
#> GSM381263 3 0.0000 0.964 0.000 0.000 1.000
#> GSM381265 1 0.5465 1.000 0.712 0.000 0.288
#> GSM381268 3 0.0000 0.964 0.000 0.000 1.000
#> GSM381270 2 0.4178 0.922 0.172 0.828 0.000
#> GSM381271 3 0.0000 0.964 0.000 0.000 1.000
#> GSM381275 2 0.4002 0.925 0.160 0.840 0.000
#> GSM381279 2 0.4235 0.921 0.176 0.824 0.000
#> GSM381195 1 0.5465 1.000 0.712 0.000 0.288
#> GSM381196 3 0.0000 0.964 0.000 0.000 1.000
#> GSM381198 2 0.1031 0.932 0.024 0.976 0.000
#> GSM381200 2 0.1031 0.932 0.024 0.976 0.000
#> GSM381201 3 0.0000 0.964 0.000 0.000 1.000
#> GSM381203 3 0.0237 0.962 0.004 0.000 0.996
#> GSM381204 1 0.5465 1.000 0.712 0.000 0.288
#> GSM381209 1 0.5465 1.000 0.712 0.000 0.288
#> GSM381212 1 0.5465 1.000 0.712 0.000 0.288
#> GSM381213 2 0.4178 0.922 0.172 0.828 0.000
#> GSM381214 2 0.0000 0.936 0.000 1.000 0.000
#> GSM381216 3 0.3686 0.797 0.140 0.000 0.860
#> GSM381225 3 0.0237 0.962 0.004 0.000 0.996
#> GSM381231 3 0.0000 0.964 0.000 0.000 1.000
#> GSM381235 3 0.2448 0.891 0.076 0.000 0.924
#> GSM381237 1 0.5465 1.000 0.712 0.000 0.288
#> GSM381241 2 0.1031 0.932 0.024 0.976 0.000
#> GSM381243 2 0.4178 0.922 0.172 0.828 0.000
#> GSM381245 1 0.5465 1.000 0.712 0.000 0.288
#> GSM381246 2 0.0237 0.936 0.004 0.996 0.000
#> GSM381251 3 0.0000 0.964 0.000 0.000 1.000
#> GSM381264 1 0.5465 1.000 0.712 0.000 0.288
#> GSM381206 2 0.1031 0.932 0.024 0.976 0.000
#> GSM381217 3 0.3686 0.797 0.140 0.000 0.860
#> GSM381218 2 0.1031 0.932 0.024 0.976 0.000
#> GSM381226 2 0.0237 0.936 0.004 0.996 0.000
#> GSM381227 2 0.3941 0.925 0.156 0.844 0.000
#> GSM381228 3 0.0000 0.964 0.000 0.000 1.000
#> GSM381236 3 0.0000 0.964 0.000 0.000 1.000
#> GSM381244 1 0.5465 1.000 0.712 0.000 0.288
#> GSM381272 3 0.0000 0.964 0.000 0.000 1.000
#> GSM381277 1 0.5465 1.000 0.712 0.000 0.288
#> GSM381278 3 0.0000 0.964 0.000 0.000 1.000
#> GSM381197 3 0.0000 0.964 0.000 0.000 1.000
#> GSM381202 3 0.3686 0.797 0.140 0.000 0.860
#> GSM381207 1 0.5465 1.000 0.712 0.000 0.288
#> GSM381208 2 0.3551 0.891 0.132 0.868 0.000
#> GSM381210 1 0.5465 1.000 0.712 0.000 0.288
#> GSM381215 3 0.0000 0.964 0.000 0.000 1.000
#> GSM381219 2 0.0000 0.936 0.000 1.000 0.000
#> GSM381221 2 0.2066 0.936 0.060 0.940 0.000
#> GSM381223 2 0.3879 0.926 0.152 0.848 0.000
#> GSM381229 3 0.0000 0.964 0.000 0.000 1.000
#> GSM381230 1 0.5465 1.000 0.712 0.000 0.288
#> GSM381233 1 0.5465 1.000 0.712 0.000 0.288
#> GSM381234 1 0.5465 1.000 0.712 0.000 0.288
#> GSM381238 3 0.0000 0.964 0.000 0.000 1.000
#> GSM381239 3 0.2625 0.866 0.084 0.000 0.916
#> GSM381242 3 0.1031 0.947 0.024 0.000 0.976
#> GSM381247 2 0.4178 0.922 0.172 0.828 0.000
#> GSM381248 1 0.5431 0.994 0.716 0.000 0.284
#> GSM381249 1 0.5465 1.000 0.712 0.000 0.288
#> GSM381253 3 0.0237 0.962 0.004 0.000 0.996
#> GSM381255 2 0.3879 0.926 0.152 0.848 0.000
#> GSM381258 3 0.0000 0.964 0.000 0.000 1.000
#> GSM381262 3 0.0000 0.964 0.000 0.000 1.000
#> GSM381266 3 0.0000 0.964 0.000 0.000 1.000
#> GSM381267 2 0.3551 0.891 0.132 0.868 0.000
#> GSM381269 3 0.3686 0.797 0.140 0.000 0.860
#> GSM381273 3 0.0000 0.964 0.000 0.000 1.000
#> GSM381274 2 0.4002 0.925 0.160 0.840 0.000
#> GSM381276 3 0.0892 0.950 0.020 0.000 0.980
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM381194 3 0.6894 -0.1530 0.112 0.000 0.512 0.376
#> GSM381199 2 0.0000 0.8811 0.000 1.000 0.000 0.000
#> GSM381205 2 0.0707 0.8791 0.000 0.980 0.000 0.020
#> GSM381211 2 0.0469 0.8791 0.000 0.988 0.000 0.012
#> GSM381220 2 0.4356 0.8577 0.000 0.708 0.000 0.292
#> GSM381222 1 0.0000 0.9932 1.000 0.000 0.000 0.000
#> GSM381224 1 0.0336 0.9910 0.992 0.000 0.000 0.008
#> GSM381232 3 0.3219 0.2213 0.112 0.000 0.868 0.020
#> GSM381240 1 0.0188 0.9925 0.996 0.000 0.000 0.004
#> GSM381250 3 0.6843 -0.1816 0.112 0.000 0.532 0.356
#> GSM381252 2 0.0469 0.8811 0.000 0.988 0.000 0.012
#> GSM381254 1 0.0469 0.9900 0.988 0.000 0.000 0.012
#> GSM381256 2 0.1940 0.8813 0.000 0.924 0.000 0.076
#> GSM381257 3 0.7220 -0.3398 0.144 0.000 0.472 0.384
#> GSM381259 1 0.0188 0.9930 0.996 0.000 0.000 0.004
#> GSM381260 3 0.7098 -0.2615 0.132 0.000 0.492 0.376
#> GSM381261 2 0.4677 0.8513 0.000 0.680 0.004 0.316
#> GSM381263 3 0.6894 -0.1530 0.112 0.000 0.512 0.376
#> GSM381265 1 0.0188 0.9930 0.996 0.000 0.000 0.004
#> GSM381268 3 0.6843 -0.1816 0.112 0.000 0.532 0.356
#> GSM381270 2 0.4382 0.8566 0.000 0.704 0.000 0.296
#> GSM381271 3 0.3219 0.2213 0.112 0.000 0.868 0.020
#> GSM381275 2 0.4655 0.8527 0.000 0.684 0.004 0.312
#> GSM381279 2 0.4477 0.8520 0.000 0.688 0.000 0.312
#> GSM381195 1 0.0188 0.9930 0.996 0.000 0.000 0.004
#> GSM381196 3 0.6843 -0.1816 0.112 0.000 0.532 0.356
#> GSM381198 2 0.0707 0.8791 0.000 0.980 0.000 0.020
#> GSM381200 2 0.0469 0.8791 0.000 0.988 0.000 0.012
#> GSM381201 3 0.6403 -0.0573 0.112 0.000 0.628 0.260
#> GSM381203 3 0.6843 -0.1816 0.112 0.000 0.532 0.356
#> GSM381204 1 0.0188 0.9930 0.996 0.000 0.000 0.004
#> GSM381209 1 0.0188 0.9930 0.996 0.000 0.000 0.004
#> GSM381212 1 0.0000 0.9932 1.000 0.000 0.000 0.000
#> GSM381213 2 0.4382 0.8566 0.000 0.704 0.000 0.296
#> GSM381214 2 0.0000 0.8811 0.000 1.000 0.000 0.000
#> GSM381216 3 0.7534 -0.4157 0.188 0.000 0.432 0.380
#> GSM381225 3 0.6970 -0.6601 0.112 0.000 0.444 0.444
#> GSM381231 3 0.3219 0.2213 0.112 0.000 0.868 0.020
#> GSM381235 4 0.7458 0.6834 0.176 0.000 0.380 0.444
#> GSM381237 1 0.0000 0.9932 1.000 0.000 0.000 0.000
#> GSM381241 2 0.0469 0.8791 0.000 0.988 0.000 0.012
#> GSM381243 2 0.4382 0.8566 0.000 0.704 0.000 0.296
#> GSM381245 1 0.0707 0.9867 0.980 0.000 0.000 0.020
#> GSM381246 2 0.0592 0.8811 0.000 0.984 0.000 0.016
#> GSM381251 3 0.6476 -0.0880 0.112 0.000 0.616 0.272
#> GSM381264 1 0.0188 0.9930 0.996 0.000 0.000 0.004
#> GSM381206 2 0.0707 0.8791 0.000 0.980 0.000 0.020
#> GSM381217 3 0.7515 -0.4615 0.188 0.000 0.448 0.364
#> GSM381218 2 0.0469 0.8791 0.000 0.988 0.000 0.012
#> GSM381226 2 0.0592 0.8811 0.000 0.984 0.000 0.016
#> GSM381227 2 0.4331 0.8600 0.000 0.712 0.000 0.288
#> GSM381228 3 0.3523 0.2025 0.112 0.000 0.856 0.032
#> GSM381236 3 0.3793 0.1988 0.112 0.000 0.844 0.044
#> GSM381244 1 0.0707 0.9867 0.980 0.000 0.000 0.020
#> GSM381272 3 0.3219 0.2213 0.112 0.000 0.868 0.020
#> GSM381277 1 0.0707 0.9867 0.980 0.000 0.000 0.020
#> GSM381278 3 0.6764 -0.2127 0.112 0.000 0.556 0.332
#> GSM381197 3 0.6894 -0.1530 0.112 0.000 0.512 0.376
#> GSM381202 3 0.7534 -0.4157 0.188 0.000 0.432 0.380
#> GSM381207 1 0.0469 0.9900 0.988 0.000 0.000 0.012
#> GSM381208 2 0.6074 0.7374 0.000 0.668 0.104 0.228
#> GSM381210 1 0.0188 0.9930 0.996 0.000 0.000 0.004
#> GSM381215 3 0.6843 -0.1816 0.112 0.000 0.532 0.356
#> GSM381219 2 0.0000 0.8811 0.000 1.000 0.000 0.000
#> GSM381221 2 0.2081 0.8811 0.000 0.916 0.000 0.084
#> GSM381223 2 0.4483 0.8592 0.000 0.712 0.004 0.284
#> GSM381229 3 0.6764 -0.2185 0.112 0.000 0.556 0.332
#> GSM381230 1 0.0000 0.9932 1.000 0.000 0.000 0.000
#> GSM381233 1 0.0000 0.9932 1.000 0.000 0.000 0.000
#> GSM381234 1 0.0469 0.9900 0.988 0.000 0.000 0.012
#> GSM381238 3 0.3793 0.1988 0.112 0.000 0.844 0.044
#> GSM381239 3 0.4669 0.1390 0.168 0.000 0.780 0.052
#> GSM381242 3 0.7113 -0.3062 0.132 0.000 0.484 0.384
#> GSM381247 2 0.4382 0.8566 0.000 0.704 0.000 0.296
#> GSM381248 1 0.1004 0.9822 0.972 0.000 0.004 0.024
#> GSM381249 1 0.0188 0.9930 0.996 0.000 0.000 0.004
#> GSM381253 3 0.6843 -0.1816 0.112 0.000 0.532 0.356
#> GSM381255 2 0.4250 0.8615 0.000 0.724 0.000 0.276
#> GSM381258 3 0.6894 -0.1530 0.112 0.000 0.512 0.376
#> GSM381262 3 0.6843 -0.1816 0.112 0.000 0.532 0.356
#> GSM381266 3 0.6566 -0.1229 0.112 0.000 0.600 0.288
#> GSM381267 2 0.6074 0.7374 0.000 0.668 0.104 0.228
#> GSM381269 3 0.7534 -0.4157 0.188 0.000 0.432 0.380
#> GSM381273 3 0.6733 -0.1951 0.112 0.000 0.564 0.324
#> GSM381274 2 0.4655 0.8527 0.000 0.684 0.004 0.312
#> GSM381276 4 0.7153 0.6418 0.132 0.000 0.424 0.444
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM381194 3 0.0703 0.762 0.000 0.000 0.976 0.024 0.000
#> GSM381199 2 0.3983 0.577 0.000 0.660 0.000 0.000 0.340
#> GSM381205 2 0.4074 0.552 0.000 0.636 0.000 0.000 0.364
#> GSM381211 2 0.4074 0.552 0.000 0.636 0.000 0.000 0.364
#> GSM381220 2 0.0609 0.548 0.000 0.980 0.000 0.000 0.020
#> GSM381222 1 0.0703 0.960 0.976 0.000 0.024 0.000 0.000
#> GSM381224 1 0.1997 0.951 0.932 0.000 0.024 0.016 0.028
#> GSM381232 4 0.4060 0.907 0.000 0.000 0.360 0.640 0.000
#> GSM381240 1 0.1597 0.956 0.948 0.000 0.024 0.008 0.020
#> GSM381250 3 0.1357 0.768 0.000 0.000 0.948 0.004 0.048
#> GSM381252 2 0.3999 0.577 0.000 0.656 0.000 0.000 0.344
#> GSM381254 1 0.1393 0.959 0.956 0.000 0.024 0.008 0.012
#> GSM381256 2 0.3561 0.582 0.000 0.740 0.000 0.000 0.260
#> GSM381257 3 0.3761 0.673 0.028 0.000 0.840 0.068 0.064
#> GSM381259 1 0.2060 0.954 0.928 0.000 0.024 0.012 0.036
#> GSM381260 3 0.1710 0.757 0.012 0.000 0.944 0.024 0.020
#> GSM381261 2 0.2095 0.509 0.024 0.928 0.000 0.028 0.020
#> GSM381263 3 0.0992 0.755 0.000 0.000 0.968 0.024 0.008
#> GSM381265 1 0.2060 0.954 0.928 0.000 0.024 0.012 0.036
#> GSM381268 3 0.1357 0.768 0.000 0.000 0.948 0.004 0.048
#> GSM381270 2 0.0324 0.536 0.000 0.992 0.000 0.004 0.004
#> GSM381271 4 0.4060 0.907 0.000 0.000 0.360 0.640 0.000
#> GSM381275 2 0.1997 0.514 0.024 0.932 0.000 0.028 0.016
#> GSM381279 2 0.1012 0.518 0.000 0.968 0.000 0.012 0.020
#> GSM381195 1 0.2060 0.954 0.928 0.000 0.024 0.012 0.036
#> GSM381196 3 0.1197 0.769 0.000 0.000 0.952 0.000 0.048
#> GSM381198 2 0.4074 0.552 0.000 0.636 0.000 0.000 0.364
#> GSM381200 2 0.4074 0.552 0.000 0.636 0.000 0.000 0.364
#> GSM381201 3 0.4083 0.617 0.000 0.000 0.788 0.132 0.080
#> GSM381203 3 0.1270 0.769 0.000 0.000 0.948 0.000 0.052
#> GSM381204 1 0.2060 0.954 0.928 0.000 0.024 0.012 0.036
#> GSM381209 1 0.2060 0.954 0.928 0.000 0.024 0.012 0.036
#> GSM381212 1 0.0865 0.960 0.972 0.000 0.024 0.000 0.004
#> GSM381213 2 0.0324 0.536 0.000 0.992 0.000 0.004 0.004
#> GSM381214 2 0.3999 0.573 0.000 0.656 0.000 0.000 0.344
#> GSM381216 3 0.2581 0.725 0.048 0.000 0.904 0.020 0.028
#> GSM381225 3 0.5460 0.552 0.004 0.000 0.640 0.092 0.264
#> GSM381231 4 0.4060 0.907 0.000 0.000 0.360 0.640 0.000
#> GSM381235 3 0.5465 0.601 0.020 0.000 0.680 0.084 0.216
#> GSM381237 1 0.0703 0.960 0.976 0.000 0.024 0.000 0.000
#> GSM381241 2 0.4074 0.552 0.000 0.636 0.000 0.000 0.364
#> GSM381243 2 0.0162 0.540 0.000 0.996 0.000 0.000 0.004
#> GSM381245 1 0.2535 0.940 0.908 0.000 0.028 0.032 0.032
#> GSM381246 2 0.4045 0.574 0.000 0.644 0.000 0.000 0.356
#> GSM381251 3 0.5329 0.536 0.000 0.000 0.672 0.144 0.184
#> GSM381264 1 0.2060 0.954 0.928 0.000 0.024 0.012 0.036
#> GSM381206 2 0.4074 0.552 0.000 0.636 0.000 0.000 0.364
#> GSM381217 3 0.2086 0.741 0.048 0.000 0.924 0.008 0.020
#> GSM381218 2 0.4074 0.552 0.000 0.636 0.000 0.000 0.364
#> GSM381226 2 0.4030 0.576 0.000 0.648 0.000 0.000 0.352
#> GSM381227 2 0.1043 0.552 0.000 0.960 0.000 0.000 0.040
#> GSM381228 4 0.4624 0.896 0.000 0.000 0.340 0.636 0.024
#> GSM381236 4 0.4925 0.894 0.000 0.000 0.324 0.632 0.044
#> GSM381244 1 0.3054 0.924 0.880 0.000 0.028 0.032 0.060
#> GSM381272 4 0.4060 0.907 0.000 0.000 0.360 0.640 0.000
#> GSM381277 1 0.3054 0.924 0.880 0.000 0.028 0.032 0.060
#> GSM381278 3 0.6319 0.361 0.000 0.000 0.524 0.204 0.272
#> GSM381197 3 0.1281 0.754 0.000 0.000 0.956 0.032 0.012
#> GSM381202 3 0.2581 0.725 0.048 0.000 0.904 0.020 0.028
#> GSM381207 1 0.2450 0.946 0.912 0.000 0.028 0.028 0.032
#> GSM381208 5 0.6480 1.000 0.000 0.400 0.000 0.184 0.416
#> GSM381210 1 0.2060 0.954 0.928 0.000 0.024 0.012 0.036
#> GSM381215 3 0.1197 0.769 0.000 0.000 0.952 0.000 0.048
#> GSM381219 2 0.3983 0.577 0.000 0.660 0.000 0.000 0.340
#> GSM381221 2 0.3661 0.583 0.000 0.724 0.000 0.000 0.276
#> GSM381223 2 0.2355 0.532 0.024 0.916 0.000 0.024 0.036
#> GSM381229 3 0.6135 0.412 0.000 0.000 0.560 0.192 0.248
#> GSM381230 1 0.0703 0.960 0.976 0.000 0.024 0.000 0.000
#> GSM381233 1 0.1026 0.959 0.968 0.000 0.024 0.004 0.004
#> GSM381234 1 0.1904 0.952 0.936 0.000 0.028 0.020 0.016
#> GSM381238 4 0.4925 0.894 0.000 0.000 0.324 0.632 0.044
#> GSM381239 4 0.5768 0.809 0.052 0.000 0.264 0.640 0.044
#> GSM381242 3 0.2152 0.750 0.012 0.000 0.924 0.032 0.032
#> GSM381247 2 0.0324 0.536 0.000 0.992 0.000 0.004 0.004
#> GSM381248 1 0.4123 0.878 0.816 0.000 0.028 0.072 0.084
#> GSM381249 1 0.2060 0.954 0.928 0.000 0.024 0.012 0.036
#> GSM381253 3 0.1557 0.769 0.000 0.000 0.940 0.008 0.052
#> GSM381255 2 0.1270 0.556 0.000 0.948 0.000 0.000 0.052
#> GSM381258 3 0.1082 0.754 0.000 0.000 0.964 0.028 0.008
#> GSM381262 3 0.1484 0.768 0.000 0.000 0.944 0.008 0.048
#> GSM381266 3 0.5921 0.434 0.000 0.000 0.596 0.184 0.220
#> GSM381267 5 0.6480 1.000 0.000 0.400 0.000 0.184 0.416
#> GSM381269 3 0.2998 0.710 0.052 0.000 0.884 0.028 0.036
#> GSM381273 3 0.6236 0.380 0.000 0.000 0.544 0.208 0.248
#> GSM381274 2 0.1997 0.514 0.024 0.932 0.000 0.028 0.016
#> GSM381276 3 0.5726 0.553 0.016 0.000 0.632 0.088 0.264
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM381194 6 0.6680 0.4367 0.032 0.000 0.308 0.280 0.000 0.380
#> GSM381199 2 0.1621 0.7862 0.000 0.944 0.012 0.016 0.020 0.008
#> GSM381205 2 0.1059 0.7975 0.000 0.964 0.000 0.016 0.004 0.016
#> GSM381211 2 0.0603 0.7973 0.000 0.980 0.000 0.004 0.000 0.016
#> GSM381220 5 0.3971 0.8462 0.000 0.448 0.000 0.004 0.548 0.000
#> GSM381222 1 0.0000 0.9385 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381224 1 0.1718 0.9267 0.932 0.000 0.016 0.000 0.044 0.008
#> GSM381232 4 0.1642 0.8004 0.032 0.000 0.004 0.936 0.000 0.028
#> GSM381240 1 0.1707 0.9259 0.928 0.000 0.004 0.000 0.056 0.012
#> GSM381250 3 0.6627 -0.0634 0.032 0.000 0.408 0.260 0.000 0.300
#> GSM381252 2 0.1957 0.7827 0.000 0.928 0.012 0.024 0.028 0.008
#> GSM381254 1 0.2001 0.9305 0.920 0.000 0.000 0.020 0.044 0.016
#> GSM381256 2 0.3294 0.5658 0.000 0.820 0.012 0.012 0.148 0.008
#> GSM381257 6 0.7304 0.3978 0.044 0.000 0.228 0.196 0.056 0.476
#> GSM381259 1 0.1693 0.9300 0.932 0.000 0.004 0.000 0.044 0.020
#> GSM381260 6 0.6883 0.5841 0.048 0.000 0.268 0.256 0.004 0.424
#> GSM381261 5 0.6174 0.7733 0.000 0.404 0.132 0.000 0.432 0.032
#> GSM381263 6 0.6597 0.5509 0.032 0.000 0.264 0.280 0.000 0.424
#> GSM381265 1 0.1693 0.9300 0.932 0.000 0.004 0.000 0.044 0.020
#> GSM381268 3 0.6627 -0.0634 0.032 0.000 0.408 0.260 0.000 0.300
#> GSM381270 5 0.3804 0.8684 0.000 0.424 0.000 0.000 0.576 0.000
#> GSM381271 4 0.1699 0.8087 0.032 0.000 0.016 0.936 0.000 0.016
#> GSM381275 5 0.6231 0.7672 0.000 0.408 0.132 0.000 0.424 0.036
#> GSM381279 5 0.3737 0.8605 0.000 0.392 0.000 0.000 0.608 0.000
#> GSM381195 1 0.1693 0.9300 0.932 0.000 0.004 0.000 0.044 0.020
#> GSM381196 3 0.6627 -0.0634 0.032 0.000 0.408 0.260 0.000 0.300
#> GSM381198 2 0.0964 0.7981 0.000 0.968 0.000 0.012 0.004 0.016
#> GSM381200 2 0.0603 0.7973 0.000 0.980 0.000 0.004 0.000 0.016
#> GSM381201 4 0.7122 -0.4952 0.032 0.000 0.344 0.380 0.028 0.216
#> GSM381203 3 0.6627 -0.0634 0.032 0.000 0.408 0.260 0.000 0.300
#> GSM381204 1 0.1296 0.9334 0.952 0.000 0.004 0.000 0.032 0.012
#> GSM381209 1 0.1296 0.9334 0.952 0.000 0.004 0.000 0.032 0.012
#> GSM381212 1 0.0000 0.9385 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381213 5 0.3804 0.8684 0.000 0.424 0.000 0.000 0.576 0.000
#> GSM381214 2 0.0951 0.7966 0.000 0.968 0.000 0.004 0.020 0.008
#> GSM381216 6 0.6978 0.5907 0.080 0.000 0.252 0.232 0.000 0.436
#> GSM381225 3 0.3922 0.4292 0.036 0.000 0.792 0.144 0.016 0.012
#> GSM381231 4 0.1699 0.8087 0.032 0.000 0.016 0.936 0.000 0.016
#> GSM381235 3 0.5201 0.3643 0.072 0.000 0.724 0.108 0.016 0.080
#> GSM381237 1 0.0000 0.9385 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381241 2 0.0717 0.7981 0.000 0.976 0.000 0.008 0.000 0.016
#> GSM381243 5 0.3937 0.8683 0.000 0.424 0.000 0.004 0.572 0.000
#> GSM381245 1 0.2900 0.9033 0.876 0.000 0.020 0.024 0.068 0.012
#> GSM381246 2 0.2452 0.7544 0.000 0.900 0.008 0.020 0.056 0.016
#> GSM381251 3 0.6518 0.3821 0.032 0.000 0.488 0.344 0.028 0.108
#> GSM381264 1 0.1693 0.9300 0.932 0.000 0.004 0.000 0.044 0.020
#> GSM381206 2 0.1059 0.7975 0.000 0.964 0.000 0.016 0.004 0.016
#> GSM381217 6 0.7076 0.5097 0.084 0.000 0.304 0.216 0.000 0.396
#> GSM381218 2 0.0717 0.7981 0.000 0.976 0.000 0.008 0.000 0.016
#> GSM381226 2 0.2635 0.7516 0.000 0.892 0.012 0.024 0.056 0.016
#> GSM381227 5 0.4308 0.8343 0.000 0.452 0.008 0.008 0.532 0.000
#> GSM381228 4 0.3007 0.7890 0.032 0.000 0.080 0.864 0.020 0.004
#> GSM381236 4 0.2917 0.7942 0.032 0.000 0.048 0.876 0.040 0.004
#> GSM381244 1 0.3277 0.8900 0.852 0.000 0.024 0.028 0.084 0.012
#> GSM381272 4 0.1699 0.8087 0.032 0.000 0.016 0.936 0.000 0.016
#> GSM381277 1 0.3277 0.8900 0.852 0.000 0.024 0.028 0.084 0.012
#> GSM381278 3 0.4475 0.3346 0.032 0.000 0.692 0.252 0.024 0.000
#> GSM381197 6 0.6994 0.5174 0.032 0.000 0.268 0.284 0.016 0.400
#> GSM381202 6 0.6978 0.5907 0.080 0.000 0.252 0.232 0.000 0.436
#> GSM381207 1 0.2753 0.9069 0.876 0.000 0.004 0.028 0.080 0.012
#> GSM381208 2 0.6049 0.0761 0.000 0.416 0.012 0.000 0.168 0.404
#> GSM381210 1 0.1053 0.9359 0.964 0.000 0.004 0.000 0.020 0.012
#> GSM381215 3 0.6627 -0.0634 0.032 0.000 0.408 0.260 0.000 0.300
#> GSM381219 2 0.1425 0.7874 0.000 0.952 0.008 0.012 0.020 0.008
#> GSM381221 2 0.2964 0.6468 0.000 0.852 0.012 0.012 0.116 0.008
#> GSM381223 2 0.6333 -0.7685 0.000 0.424 0.140 0.000 0.396 0.040
#> GSM381229 3 0.4907 0.3622 0.032 0.000 0.672 0.256 0.028 0.012
#> GSM381230 1 0.0603 0.9384 0.980 0.000 0.000 0.000 0.016 0.004
#> GSM381233 1 0.0146 0.9384 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM381234 1 0.2196 0.9245 0.908 0.000 0.000 0.020 0.056 0.016
#> GSM381238 4 0.2917 0.7942 0.032 0.000 0.048 0.876 0.040 0.004
#> GSM381239 4 0.3548 0.7469 0.072 0.000 0.048 0.836 0.040 0.004
#> GSM381242 6 0.7106 0.5777 0.052 0.000 0.276 0.248 0.012 0.412
#> GSM381247 5 0.3804 0.8684 0.000 0.424 0.000 0.000 0.576 0.000
#> GSM381248 1 0.5303 0.7807 0.712 0.000 0.040 0.028 0.136 0.084
#> GSM381249 1 0.1296 0.9334 0.952 0.000 0.004 0.000 0.032 0.012
#> GSM381253 3 0.6672 -0.0808 0.036 0.000 0.408 0.256 0.000 0.300
#> GSM381255 5 0.4320 0.8137 0.000 0.468 0.008 0.008 0.516 0.000
#> GSM381258 6 0.6586 0.5545 0.032 0.000 0.260 0.280 0.000 0.428
#> GSM381262 3 0.6627 -0.0634 0.032 0.000 0.408 0.260 0.000 0.300
#> GSM381266 3 0.5899 0.3649 0.032 0.000 0.568 0.316 0.028 0.056
#> GSM381267 6 0.5903 -0.5126 0.000 0.416 0.008 0.000 0.156 0.420
#> GSM381269 6 0.7144 0.5679 0.080 0.000 0.248 0.220 0.008 0.444
#> GSM381273 3 0.5229 0.3284 0.032 0.000 0.640 0.276 0.036 0.016
#> GSM381274 5 0.6175 0.7712 0.000 0.408 0.132 0.000 0.428 0.032
#> GSM381276 3 0.5342 0.3869 0.060 0.000 0.716 0.128 0.064 0.032
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 other(p) k
#> ATC:kmeans 86 0.744 2
#> ATC:kmeans 86 0.889 3
#> ATC:kmeans 53 0.893 4
#> ATC:kmeans 82 0.374 5
#> ATC:kmeans 65 0.555 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 86 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 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4528 0.548 0.548
#> 3 3 1.000 0.991 0.996 0.4672 0.789 0.615
#> 4 4 1.000 0.977 0.983 0.0919 0.941 0.825
#> 5 5 0.943 0.937 0.939 0.0465 0.962 0.862
#> 6 6 0.849 0.856 0.894 0.0395 0.985 0.938
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
#> attr(,"optional")
#> [1] 2 3 4
There is also optional best \(k\) = 2 3 4 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
#> GSM381194 1 0 1 1 0
#> GSM381199 2 0 1 0 1
#> GSM381205 2 0 1 0 1
#> GSM381211 2 0 1 0 1
#> GSM381220 2 0 1 0 1
#> GSM381222 1 0 1 1 0
#> GSM381224 1 0 1 1 0
#> GSM381232 1 0 1 1 0
#> GSM381240 1 0 1 1 0
#> GSM381250 1 0 1 1 0
#> GSM381252 2 0 1 0 1
#> GSM381254 1 0 1 1 0
#> GSM381256 2 0 1 0 1
#> GSM381257 1 0 1 1 0
#> GSM381259 1 0 1 1 0
#> GSM381260 1 0 1 1 0
#> GSM381261 2 0 1 0 1
#> GSM381263 1 0 1 1 0
#> GSM381265 1 0 1 1 0
#> GSM381268 1 0 1 1 0
#> GSM381270 2 0 1 0 1
#> GSM381271 1 0 1 1 0
#> GSM381275 2 0 1 0 1
#> GSM381279 2 0 1 0 1
#> GSM381195 1 0 1 1 0
#> GSM381196 1 0 1 1 0
#> GSM381198 2 0 1 0 1
#> GSM381200 2 0 1 0 1
#> GSM381201 1 0 1 1 0
#> GSM381203 1 0 1 1 0
#> GSM381204 1 0 1 1 0
#> GSM381209 1 0 1 1 0
#> GSM381212 1 0 1 1 0
#> GSM381213 2 0 1 0 1
#> GSM381214 2 0 1 0 1
#> GSM381216 1 0 1 1 0
#> GSM381225 1 0 1 1 0
#> GSM381231 1 0 1 1 0
#> GSM381235 1 0 1 1 0
#> GSM381237 1 0 1 1 0
#> GSM381241 2 0 1 0 1
#> GSM381243 2 0 1 0 1
#> GSM381245 1 0 1 1 0
#> GSM381246 2 0 1 0 1
#> GSM381251 1 0 1 1 0
#> GSM381264 1 0 1 1 0
#> GSM381206 2 0 1 0 1
#> GSM381217 1 0 1 1 0
#> GSM381218 2 0 1 0 1
#> GSM381226 2 0 1 0 1
#> GSM381227 2 0 1 0 1
#> GSM381228 1 0 1 1 0
#> GSM381236 1 0 1 1 0
#> GSM381244 1 0 1 1 0
#> GSM381272 1 0 1 1 0
#> GSM381277 1 0 1 1 0
#> GSM381278 1 0 1 1 0
#> GSM381197 1 0 1 1 0
#> GSM381202 1 0 1 1 0
#> GSM381207 1 0 1 1 0
#> GSM381208 2 0 1 0 1
#> GSM381210 1 0 1 1 0
#> GSM381215 1 0 1 1 0
#> GSM381219 2 0 1 0 1
#> GSM381221 2 0 1 0 1
#> GSM381223 2 0 1 0 1
#> GSM381229 1 0 1 1 0
#> GSM381230 1 0 1 1 0
#> GSM381233 1 0 1 1 0
#> GSM381234 1 0 1 1 0
#> GSM381238 1 0 1 1 0
#> GSM381239 1 0 1 1 0
#> GSM381242 1 0 1 1 0
#> GSM381247 2 0 1 0 1
#> GSM381248 1 0 1 1 0
#> GSM381249 1 0 1 1 0
#> GSM381253 1 0 1 1 0
#> GSM381255 2 0 1 0 1
#> GSM381258 1 0 1 1 0
#> GSM381262 1 0 1 1 0
#> GSM381266 1 0 1 1 0
#> GSM381267 2 0 1 0 1
#> GSM381269 1 0 1 1 0
#> GSM381273 1 0 1 1 0
#> GSM381274 2 0 1 0 1
#> GSM381276 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM381194 3 0.0000 0.990 0.000 0 1.000
#> GSM381199 2 0.0000 1.000 0.000 1 0.000
#> GSM381205 2 0.0000 1.000 0.000 1 0.000
#> GSM381211 2 0.0000 1.000 0.000 1 0.000
#> GSM381220 2 0.0000 1.000 0.000 1 0.000
#> GSM381222 1 0.0000 1.000 1.000 0 0.000
#> GSM381224 1 0.0000 1.000 1.000 0 0.000
#> GSM381232 3 0.0000 0.990 0.000 0 1.000
#> GSM381240 1 0.0000 1.000 1.000 0 0.000
#> GSM381250 3 0.0000 0.990 0.000 0 1.000
#> GSM381252 2 0.0000 1.000 0.000 1 0.000
#> GSM381254 1 0.0000 1.000 1.000 0 0.000
#> GSM381256 2 0.0000 1.000 0.000 1 0.000
#> GSM381257 3 0.0000 0.990 0.000 0 1.000
#> GSM381259 1 0.0000 1.000 1.000 0 0.000
#> GSM381260 3 0.0000 0.990 0.000 0 1.000
#> GSM381261 2 0.0000 1.000 0.000 1 0.000
#> GSM381263 3 0.0000 0.990 0.000 0 1.000
#> GSM381265 1 0.0000 1.000 1.000 0 0.000
#> GSM381268 3 0.0000 0.990 0.000 0 1.000
#> GSM381270 2 0.0000 1.000 0.000 1 0.000
#> GSM381271 3 0.0000 0.990 0.000 0 1.000
#> GSM381275 2 0.0000 1.000 0.000 1 0.000
#> GSM381279 2 0.0000 1.000 0.000 1 0.000
#> GSM381195 1 0.0000 1.000 1.000 0 0.000
#> GSM381196 3 0.0000 0.990 0.000 0 1.000
#> GSM381198 2 0.0000 1.000 0.000 1 0.000
#> GSM381200 2 0.0000 1.000 0.000 1 0.000
#> GSM381201 3 0.0000 0.990 0.000 0 1.000
#> GSM381203 3 0.0000 0.990 0.000 0 1.000
#> GSM381204 1 0.0000 1.000 1.000 0 0.000
#> GSM381209 1 0.0000 1.000 1.000 0 0.000
#> GSM381212 1 0.0000 1.000 1.000 0 0.000
#> GSM381213 2 0.0000 1.000 0.000 1 0.000
#> GSM381214 2 0.0000 1.000 0.000 1 0.000
#> GSM381216 3 0.0000 0.990 0.000 0 1.000
#> GSM381225 3 0.0000 0.990 0.000 0 1.000
#> GSM381231 3 0.0000 0.990 0.000 0 1.000
#> GSM381235 3 0.0592 0.979 0.012 0 0.988
#> GSM381237 1 0.0000 1.000 1.000 0 0.000
#> GSM381241 2 0.0000 1.000 0.000 1 0.000
#> GSM381243 2 0.0000 1.000 0.000 1 0.000
#> GSM381245 1 0.0000 1.000 1.000 0 0.000
#> GSM381246 2 0.0000 1.000 0.000 1 0.000
#> GSM381251 3 0.0000 0.990 0.000 0 1.000
#> GSM381264 1 0.0000 1.000 1.000 0 0.000
#> GSM381206 2 0.0000 1.000 0.000 1 0.000
#> GSM381217 3 0.0000 0.990 0.000 0 1.000
#> GSM381218 2 0.0000 1.000 0.000 1 0.000
#> GSM381226 2 0.0000 1.000 0.000 1 0.000
#> GSM381227 2 0.0000 1.000 0.000 1 0.000
#> GSM381228 3 0.0000 0.990 0.000 0 1.000
#> GSM381236 3 0.0000 0.990 0.000 0 1.000
#> GSM381244 1 0.0000 1.000 1.000 0 0.000
#> GSM381272 3 0.0000 0.990 0.000 0 1.000
#> GSM381277 1 0.0000 1.000 1.000 0 0.000
#> GSM381278 3 0.0000 0.990 0.000 0 1.000
#> GSM381197 3 0.0000 0.990 0.000 0 1.000
#> GSM381202 3 0.0000 0.990 0.000 0 1.000
#> GSM381207 1 0.0000 1.000 1.000 0 0.000
#> GSM381208 2 0.0000 1.000 0.000 1 0.000
#> GSM381210 1 0.0000 1.000 1.000 0 0.000
#> GSM381215 3 0.0000 0.990 0.000 0 1.000
#> GSM381219 2 0.0000 1.000 0.000 1 0.000
#> GSM381221 2 0.0000 1.000 0.000 1 0.000
#> GSM381223 2 0.0000 1.000 0.000 1 0.000
#> GSM381229 3 0.0000 0.990 0.000 0 1.000
#> GSM381230 1 0.0000 1.000 1.000 0 0.000
#> GSM381233 1 0.0000 1.000 1.000 0 0.000
#> GSM381234 1 0.0000 1.000 1.000 0 0.000
#> GSM381238 3 0.0000 0.990 0.000 0 1.000
#> GSM381239 3 0.5706 0.530 0.320 0 0.680
#> GSM381242 3 0.0000 0.990 0.000 0 1.000
#> GSM381247 2 0.0000 1.000 0.000 1 0.000
#> GSM381248 1 0.0000 1.000 1.000 0 0.000
#> GSM381249 1 0.0000 1.000 1.000 0 0.000
#> GSM381253 3 0.0000 0.990 0.000 0 1.000
#> GSM381255 2 0.0000 1.000 0.000 1 0.000
#> GSM381258 3 0.0000 0.990 0.000 0 1.000
#> GSM381262 3 0.0000 0.990 0.000 0 1.000
#> GSM381266 3 0.0000 0.990 0.000 0 1.000
#> GSM381267 2 0.0000 1.000 0.000 1 0.000
#> GSM381269 3 0.0000 0.990 0.000 0 1.000
#> GSM381273 3 0.0000 0.990 0.000 0 1.000
#> GSM381274 2 0.0000 1.000 0.000 1 0.000
#> GSM381276 3 0.0000 0.990 0.000 0 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM381194 3 0.0000 0.958 0.000 0 1.000 0.000
#> GSM381199 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381205 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381211 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381220 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381222 1 0.0000 0.998 1.000 0 0.000 0.000
#> GSM381224 1 0.0000 0.998 1.000 0 0.000 0.000
#> GSM381232 4 0.1211 0.992 0.000 0 0.040 0.960
#> GSM381240 1 0.0000 0.998 1.000 0 0.000 0.000
#> GSM381250 3 0.0188 0.958 0.000 0 0.996 0.004
#> GSM381252 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381254 1 0.0188 0.996 0.996 0 0.000 0.004
#> GSM381256 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381257 3 0.0188 0.958 0.000 0 0.996 0.004
#> GSM381259 1 0.0000 0.998 1.000 0 0.000 0.000
#> GSM381260 3 0.0336 0.955 0.000 0 0.992 0.008
#> GSM381261 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381263 3 0.0000 0.958 0.000 0 1.000 0.000
#> GSM381265 1 0.0000 0.998 1.000 0 0.000 0.000
#> GSM381268 3 0.0469 0.956 0.000 0 0.988 0.012
#> GSM381270 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381271 4 0.1118 0.994 0.000 0 0.036 0.964
#> GSM381275 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381279 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381195 1 0.0000 0.998 1.000 0 0.000 0.000
#> GSM381196 3 0.0000 0.958 0.000 0 1.000 0.000
#> GSM381198 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381200 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381201 3 0.0707 0.953 0.000 0 0.980 0.020
#> GSM381203 3 0.0336 0.957 0.000 0 0.992 0.008
#> GSM381204 1 0.0000 0.998 1.000 0 0.000 0.000
#> GSM381209 1 0.0000 0.998 1.000 0 0.000 0.000
#> GSM381212 1 0.0000 0.998 1.000 0 0.000 0.000
#> GSM381213 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381214 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381216 3 0.0000 0.958 0.000 0 1.000 0.000
#> GSM381225 3 0.2216 0.915 0.000 0 0.908 0.092
#> GSM381231 4 0.1118 0.994 0.000 0 0.036 0.964
#> GSM381235 3 0.1022 0.944 0.000 0 0.968 0.032
#> GSM381237 1 0.0000 0.998 1.000 0 0.000 0.000
#> GSM381241 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381243 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381245 1 0.0336 0.994 0.992 0 0.000 0.008
#> GSM381246 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381251 3 0.0817 0.951 0.000 0 0.976 0.024
#> GSM381264 1 0.0000 0.998 1.000 0 0.000 0.000
#> GSM381206 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381217 3 0.0336 0.954 0.008 0 0.992 0.000
#> GSM381218 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381226 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381227 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381228 4 0.1118 0.994 0.000 0 0.036 0.964
#> GSM381236 4 0.0921 0.992 0.000 0 0.028 0.972
#> GSM381244 1 0.0469 0.992 0.988 0 0.000 0.012
#> GSM381272 4 0.1118 0.994 0.000 0 0.036 0.964
#> GSM381277 1 0.0469 0.992 0.988 0 0.000 0.012
#> GSM381278 3 0.3907 0.775 0.000 0 0.768 0.232
#> GSM381197 3 0.0000 0.958 0.000 0 1.000 0.000
#> GSM381202 3 0.0000 0.958 0.000 0 1.000 0.000
#> GSM381207 1 0.0336 0.994 0.992 0 0.000 0.008
#> GSM381208 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381210 1 0.0000 0.998 1.000 0 0.000 0.000
#> GSM381215 3 0.0336 0.957 0.000 0 0.992 0.008
#> GSM381219 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381221 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381223 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381229 3 0.2814 0.881 0.000 0 0.868 0.132
#> GSM381230 1 0.0000 0.998 1.000 0 0.000 0.000
#> GSM381233 1 0.0000 0.998 1.000 0 0.000 0.000
#> GSM381234 1 0.0188 0.996 0.996 0 0.000 0.004
#> GSM381238 4 0.0921 0.992 0.000 0 0.028 0.972
#> GSM381239 4 0.1042 0.984 0.008 0 0.020 0.972
#> GSM381242 3 0.0188 0.957 0.000 0 0.996 0.004
#> GSM381247 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381248 1 0.0336 0.994 0.992 0 0.000 0.008
#> GSM381249 1 0.0000 0.998 1.000 0 0.000 0.000
#> GSM381253 3 0.0336 0.957 0.000 0 0.992 0.008
#> GSM381255 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381258 3 0.0000 0.958 0.000 0 1.000 0.000
#> GSM381262 3 0.0336 0.957 0.000 0 0.992 0.008
#> GSM381266 3 0.3219 0.836 0.000 0 0.836 0.164
#> GSM381267 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381269 3 0.0336 0.954 0.008 0 0.992 0.000
#> GSM381273 3 0.3610 0.812 0.000 0 0.800 0.200
#> GSM381274 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM381276 3 0.3444 0.833 0.000 0 0.816 0.184
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM381194 3 0.0609 0.888 0.000 0.000 0.980 0.000 0.020
#> GSM381199 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> GSM381205 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> GSM381211 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> GSM381220 2 0.1478 0.957 0.000 0.936 0.000 0.000 0.064
#> GSM381222 1 0.0162 0.990 0.996 0.000 0.000 0.000 0.004
#> GSM381224 1 0.0162 0.990 0.996 0.000 0.000 0.000 0.004
#> GSM381232 4 0.0290 0.995 0.000 0.000 0.008 0.992 0.000
#> GSM381240 1 0.0609 0.984 0.980 0.000 0.000 0.000 0.020
#> GSM381250 3 0.2516 0.856 0.000 0.000 0.860 0.000 0.140
#> GSM381252 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> GSM381254 1 0.0162 0.990 0.996 0.000 0.000 0.000 0.004
#> GSM381256 2 0.0794 0.960 0.000 0.972 0.000 0.000 0.028
#> GSM381257 3 0.0865 0.886 0.004 0.000 0.972 0.000 0.024
#> GSM381259 1 0.0290 0.990 0.992 0.000 0.000 0.000 0.008
#> GSM381260 3 0.0162 0.883 0.000 0.000 0.996 0.000 0.004
#> GSM381261 2 0.1478 0.957 0.000 0.936 0.000 0.000 0.064
#> GSM381263 3 0.0162 0.886 0.000 0.000 0.996 0.000 0.004
#> GSM381265 1 0.0290 0.990 0.992 0.000 0.000 0.000 0.008
#> GSM381268 3 0.2690 0.841 0.000 0.000 0.844 0.000 0.156
#> GSM381270 2 0.1478 0.957 0.000 0.936 0.000 0.000 0.064
#> GSM381271 4 0.0290 0.995 0.000 0.000 0.008 0.992 0.000
#> GSM381275 2 0.1478 0.957 0.000 0.936 0.000 0.000 0.064
#> GSM381279 2 0.1478 0.957 0.000 0.936 0.000 0.000 0.064
#> GSM381195 1 0.0290 0.990 0.992 0.000 0.000 0.000 0.008
#> GSM381196 3 0.2329 0.863 0.000 0.000 0.876 0.000 0.124
#> GSM381198 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> GSM381200 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> GSM381201 3 0.2890 0.834 0.000 0.000 0.836 0.004 0.160
#> GSM381203 3 0.2516 0.856 0.000 0.000 0.860 0.000 0.140
#> GSM381204 1 0.0290 0.990 0.992 0.000 0.000 0.000 0.008
#> GSM381209 1 0.0290 0.990 0.992 0.000 0.000 0.000 0.008
#> GSM381212 1 0.0000 0.990 1.000 0.000 0.000 0.000 0.000
#> GSM381213 2 0.1478 0.957 0.000 0.936 0.000 0.000 0.064
#> GSM381214 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> GSM381216 3 0.0290 0.880 0.000 0.000 0.992 0.000 0.008
#> GSM381225 5 0.3814 0.903 0.000 0.000 0.276 0.004 0.720
#> GSM381231 4 0.0290 0.995 0.000 0.000 0.008 0.992 0.000
#> GSM381235 5 0.3990 0.884 0.004 0.000 0.308 0.000 0.688
#> GSM381237 1 0.0000 0.990 1.000 0.000 0.000 0.000 0.000
#> GSM381241 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> GSM381243 2 0.1478 0.957 0.000 0.936 0.000 0.000 0.064
#> GSM381245 1 0.0609 0.984 0.980 0.000 0.000 0.000 0.020
#> GSM381246 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> GSM381251 3 0.3123 0.798 0.000 0.000 0.812 0.004 0.184
#> GSM381264 1 0.0290 0.990 0.992 0.000 0.000 0.000 0.008
#> GSM381206 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> GSM381217 3 0.0609 0.886 0.000 0.000 0.980 0.000 0.020
#> GSM381218 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> GSM381226 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> GSM381227 2 0.1478 0.957 0.000 0.936 0.000 0.000 0.064
#> GSM381228 4 0.0324 0.994 0.000 0.000 0.004 0.992 0.004
#> GSM381236 4 0.0162 0.993 0.000 0.000 0.000 0.996 0.004
#> GSM381244 1 0.1243 0.972 0.960 0.000 0.008 0.004 0.028
#> GSM381272 4 0.0290 0.995 0.000 0.000 0.008 0.992 0.000
#> GSM381277 1 0.0865 0.980 0.972 0.000 0.000 0.004 0.024
#> GSM381278 5 0.4795 0.900 0.000 0.000 0.224 0.072 0.704
#> GSM381197 3 0.0703 0.889 0.000 0.000 0.976 0.000 0.024
#> GSM381202 3 0.0290 0.880 0.000 0.000 0.992 0.000 0.008
#> GSM381207 1 0.0771 0.982 0.976 0.000 0.000 0.004 0.020
#> GSM381208 2 0.3300 0.781 0.000 0.792 0.000 0.004 0.204
#> GSM381210 1 0.0290 0.990 0.992 0.000 0.000 0.000 0.008
#> GSM381215 3 0.2516 0.856 0.000 0.000 0.860 0.000 0.140
#> GSM381219 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> GSM381221 2 0.0963 0.960 0.000 0.964 0.000 0.000 0.036
#> GSM381223 2 0.1478 0.957 0.000 0.936 0.000 0.000 0.064
#> GSM381229 5 0.4615 0.917 0.000 0.000 0.252 0.048 0.700
#> GSM381230 1 0.0000 0.990 1.000 0.000 0.000 0.000 0.000
#> GSM381233 1 0.0000 0.990 1.000 0.000 0.000 0.000 0.000
#> GSM381234 1 0.0404 0.987 0.988 0.000 0.000 0.000 0.012
#> GSM381238 4 0.0162 0.993 0.000 0.000 0.000 0.996 0.004
#> GSM381239 4 0.0162 0.993 0.000 0.000 0.000 0.996 0.004
#> GSM381242 3 0.0162 0.883 0.000 0.000 0.996 0.000 0.004
#> GSM381247 2 0.1478 0.957 0.000 0.936 0.000 0.000 0.064
#> GSM381248 1 0.0771 0.982 0.976 0.000 0.000 0.004 0.020
#> GSM381249 1 0.0290 0.990 0.992 0.000 0.000 0.000 0.008
#> GSM381253 3 0.2516 0.856 0.000 0.000 0.860 0.000 0.140
#> GSM381255 2 0.1478 0.957 0.000 0.936 0.000 0.000 0.064
#> GSM381258 3 0.0000 0.884 0.000 0.000 1.000 0.000 0.000
#> GSM381262 3 0.2852 0.821 0.000 0.000 0.828 0.000 0.172
#> GSM381266 5 0.5341 0.739 0.000 0.000 0.376 0.060 0.564
#> GSM381267 2 0.3300 0.781 0.000 0.792 0.000 0.004 0.204
#> GSM381269 3 0.0290 0.880 0.000 0.000 0.992 0.000 0.008
#> GSM381273 5 0.4788 0.912 0.000 0.000 0.240 0.064 0.696
#> GSM381274 2 0.1478 0.957 0.000 0.936 0.000 0.000 0.064
#> GSM381276 5 0.4479 0.901 0.000 0.000 0.264 0.036 0.700
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM381194 3 0.2190 0.825 0.000 0.000 0.900 0.000 0.040 0.060
#> GSM381199 2 0.0000 0.810 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381205 2 0.0000 0.810 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381211 2 0.0000 0.810 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381220 2 0.2854 0.800 0.000 0.792 0.000 0.000 0.208 0.000
#> GSM381222 1 0.0713 0.935 0.972 0.000 0.000 0.000 0.028 0.000
#> GSM381224 1 0.1408 0.929 0.944 0.000 0.000 0.000 0.036 0.020
#> GSM381232 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381240 1 0.2605 0.900 0.864 0.000 0.000 0.000 0.108 0.028
#> GSM381250 3 0.3221 0.789 0.000 0.000 0.792 0.000 0.020 0.188
#> GSM381252 2 0.0000 0.810 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381254 1 0.1643 0.921 0.924 0.000 0.000 0.000 0.068 0.008
#> GSM381256 2 0.1501 0.814 0.000 0.924 0.000 0.000 0.076 0.000
#> GSM381257 3 0.1418 0.824 0.000 0.000 0.944 0.000 0.024 0.032
#> GSM381259 1 0.1124 0.931 0.956 0.000 0.000 0.000 0.036 0.008
#> GSM381260 3 0.2474 0.775 0.000 0.000 0.880 0.000 0.080 0.040
#> GSM381261 2 0.2969 0.795 0.000 0.776 0.000 0.000 0.224 0.000
#> GSM381263 3 0.1124 0.823 0.000 0.000 0.956 0.000 0.036 0.008
#> GSM381265 1 0.1049 0.932 0.960 0.000 0.000 0.000 0.032 0.008
#> GSM381268 3 0.3368 0.759 0.000 0.000 0.756 0.000 0.012 0.232
#> GSM381270 2 0.2969 0.795 0.000 0.776 0.000 0.000 0.224 0.000
#> GSM381271 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381275 2 0.2969 0.795 0.000 0.776 0.000 0.000 0.224 0.000
#> GSM381279 2 0.2969 0.795 0.000 0.776 0.000 0.000 0.224 0.000
#> GSM381195 1 0.1049 0.932 0.960 0.000 0.000 0.000 0.032 0.008
#> GSM381196 3 0.3017 0.799 0.000 0.000 0.816 0.000 0.020 0.164
#> GSM381198 2 0.0000 0.810 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381200 2 0.0000 0.810 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381201 3 0.3533 0.751 0.000 0.000 0.748 0.004 0.012 0.236
#> GSM381203 3 0.3189 0.791 0.000 0.000 0.796 0.000 0.020 0.184
#> GSM381204 1 0.1049 0.931 0.960 0.000 0.000 0.000 0.032 0.008
#> GSM381209 1 0.1049 0.931 0.960 0.000 0.000 0.000 0.032 0.008
#> GSM381212 1 0.0363 0.935 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM381213 2 0.2969 0.795 0.000 0.776 0.000 0.000 0.224 0.000
#> GSM381214 2 0.0000 0.810 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381216 3 0.1780 0.805 0.000 0.000 0.924 0.000 0.048 0.028
#> GSM381225 6 0.2255 0.902 0.000 0.000 0.088 0.004 0.016 0.892
#> GSM381231 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381235 6 0.2624 0.880 0.000 0.000 0.124 0.000 0.020 0.856
#> GSM381237 1 0.0146 0.935 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM381241 2 0.0000 0.810 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381243 2 0.2969 0.795 0.000 0.776 0.000 0.000 0.224 0.000
#> GSM381245 1 0.2752 0.895 0.856 0.000 0.000 0.000 0.108 0.036
#> GSM381246 2 0.0000 0.810 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381251 3 0.3724 0.713 0.000 0.000 0.716 0.004 0.012 0.268
#> GSM381264 1 0.1049 0.932 0.960 0.000 0.000 0.000 0.032 0.008
#> GSM381206 2 0.0000 0.810 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381217 3 0.1498 0.819 0.000 0.000 0.940 0.000 0.032 0.028
#> GSM381218 2 0.0000 0.810 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381226 2 0.0146 0.810 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM381227 2 0.2941 0.797 0.000 0.780 0.000 0.000 0.220 0.000
#> GSM381228 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381236 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381244 1 0.4241 0.816 0.756 0.000 0.016 0.000 0.152 0.076
#> GSM381272 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381277 1 0.3587 0.850 0.792 0.000 0.000 0.000 0.140 0.068
#> GSM381278 6 0.2362 0.899 0.000 0.000 0.080 0.016 0.012 0.892
#> GSM381197 3 0.1418 0.828 0.000 0.000 0.944 0.000 0.024 0.032
#> GSM381202 3 0.1856 0.802 0.000 0.000 0.920 0.000 0.048 0.032
#> GSM381207 1 0.2605 0.900 0.864 0.000 0.000 0.000 0.108 0.028
#> GSM381208 5 0.4520 1.000 0.000 0.448 0.000 0.000 0.520 0.032
#> GSM381210 1 0.0993 0.934 0.964 0.000 0.000 0.000 0.024 0.012
#> GSM381215 3 0.3284 0.784 0.000 0.000 0.784 0.000 0.020 0.196
#> GSM381219 2 0.0000 0.810 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381221 2 0.1714 0.814 0.000 0.908 0.000 0.000 0.092 0.000
#> GSM381223 2 0.2969 0.795 0.000 0.776 0.000 0.000 0.224 0.000
#> GSM381229 6 0.2313 0.901 0.000 0.000 0.100 0.012 0.004 0.884
#> GSM381230 1 0.0713 0.935 0.972 0.000 0.000 0.000 0.028 0.000
#> GSM381233 1 0.1010 0.934 0.960 0.000 0.000 0.000 0.036 0.004
#> GSM381234 1 0.2333 0.909 0.884 0.000 0.000 0.000 0.092 0.024
#> GSM381238 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381239 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM381242 3 0.2527 0.772 0.000 0.000 0.876 0.000 0.084 0.040
#> GSM381247 2 0.2969 0.795 0.000 0.776 0.000 0.000 0.224 0.000
#> GSM381248 1 0.2726 0.897 0.856 0.000 0.000 0.000 0.112 0.032
#> GSM381249 1 0.1049 0.931 0.960 0.000 0.000 0.000 0.032 0.008
#> GSM381253 3 0.3284 0.784 0.000 0.000 0.784 0.000 0.020 0.196
#> GSM381255 2 0.2793 0.802 0.000 0.800 0.000 0.000 0.200 0.000
#> GSM381258 3 0.1265 0.818 0.000 0.000 0.948 0.000 0.044 0.008
#> GSM381262 3 0.3582 0.736 0.000 0.000 0.732 0.000 0.016 0.252
#> GSM381266 6 0.4034 0.663 0.000 0.000 0.260 0.024 0.008 0.708
#> GSM381267 5 0.4520 1.000 0.000 0.448 0.000 0.000 0.520 0.032
#> GSM381269 3 0.1765 0.805 0.000 0.000 0.924 0.000 0.052 0.024
#> GSM381273 6 0.2383 0.900 0.000 0.000 0.096 0.024 0.000 0.880
#> GSM381274 2 0.2969 0.795 0.000 0.776 0.000 0.000 0.224 0.000
#> GSM381276 6 0.3321 0.786 0.008 0.000 0.088 0.000 0.072 0.832
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 other(p) k
#> ATC:skmeans 86 0.744 2
#> ATC:skmeans 86 0.889 3
#> ATC:skmeans 86 0.552 4
#> ATC:skmeans 86 0.588 5
#> ATC:skmeans 86 0.424 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 86 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4528 0.548 0.548
#> 3 3 0.827 0.932 0.949 0.1210 0.985 0.973
#> 4 4 0.700 0.785 0.890 0.2294 0.871 0.759
#> 5 5 0.728 0.809 0.883 0.1190 0.889 0.729
#> 6 6 0.855 0.846 0.930 0.0754 0.953 0.847
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
#> GSM381194 1 0 1 1 0
#> GSM381199 2 0 1 0 1
#> GSM381205 2 0 1 0 1
#> GSM381211 2 0 1 0 1
#> GSM381220 2 0 1 0 1
#> GSM381222 1 0 1 1 0
#> GSM381224 1 0 1 1 0
#> GSM381232 1 0 1 1 0
#> GSM381240 1 0 1 1 0
#> GSM381250 1 0 1 1 0
#> GSM381252 2 0 1 0 1
#> GSM381254 1 0 1 1 0
#> GSM381256 2 0 1 0 1
#> GSM381257 1 0 1 1 0
#> GSM381259 1 0 1 1 0
#> GSM381260 1 0 1 1 0
#> GSM381261 2 0 1 0 1
#> GSM381263 1 0 1 1 0
#> GSM381265 1 0 1 1 0
#> GSM381268 1 0 1 1 0
#> GSM381270 2 0 1 0 1
#> GSM381271 1 0 1 1 0
#> GSM381275 2 0 1 0 1
#> GSM381279 2 0 1 0 1
#> GSM381195 1 0 1 1 0
#> GSM381196 1 0 1 1 0
#> GSM381198 2 0 1 0 1
#> GSM381200 2 0 1 0 1
#> GSM381201 1 0 1 1 0
#> GSM381203 1 0 1 1 0
#> GSM381204 1 0 1 1 0
#> GSM381209 1 0 1 1 0
#> GSM381212 1 0 1 1 0
#> GSM381213 2 0 1 0 1
#> GSM381214 2 0 1 0 1
#> GSM381216 1 0 1 1 0
#> GSM381225 1 0 1 1 0
#> GSM381231 1 0 1 1 0
#> GSM381235 1 0 1 1 0
#> GSM381237 1 0 1 1 0
#> GSM381241 2 0 1 0 1
#> GSM381243 2 0 1 0 1
#> GSM381245 1 0 1 1 0
#> GSM381246 2 0 1 0 1
#> GSM381251 1 0 1 1 0
#> GSM381264 1 0 1 1 0
#> GSM381206 2 0 1 0 1
#> GSM381217 1 0 1 1 0
#> GSM381218 2 0 1 0 1
#> GSM381226 2 0 1 0 1
#> GSM381227 2 0 1 0 1
#> GSM381228 1 0 1 1 0
#> GSM381236 1 0 1 1 0
#> GSM381244 1 0 1 1 0
#> GSM381272 1 0 1 1 0
#> GSM381277 1 0 1 1 0
#> GSM381278 1 0 1 1 0
#> GSM381197 1 0 1 1 0
#> GSM381202 1 0 1 1 0
#> GSM381207 1 0 1 1 0
#> GSM381208 2 0 1 0 1
#> GSM381210 1 0 1 1 0
#> GSM381215 1 0 1 1 0
#> GSM381219 2 0 1 0 1
#> GSM381221 2 0 1 0 1
#> GSM381223 2 0 1 0 1
#> GSM381229 1 0 1 1 0
#> GSM381230 1 0 1 1 0
#> GSM381233 1 0 1 1 0
#> GSM381234 1 0 1 1 0
#> GSM381238 1 0 1 1 0
#> GSM381239 1 0 1 1 0
#> GSM381242 1 0 1 1 0
#> GSM381247 2 0 1 0 1
#> GSM381248 1 0 1 1 0
#> GSM381249 1 0 1 1 0
#> GSM381253 1 0 1 1 0
#> GSM381255 2 0 1 0 1
#> GSM381258 1 0 1 1 0
#> GSM381262 1 0 1 1 0
#> GSM381266 1 0 1 1 0
#> GSM381267 2 0 1 0 1
#> GSM381269 1 0 1 1 0
#> GSM381273 1 0 1 1 0
#> GSM381274 2 0 1 0 1
#> GSM381276 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM381194 1 0.0000 0.936 1.000 0.000 0.000
#> GSM381199 2 0.0000 0.996 0.000 1.000 0.000
#> GSM381205 2 0.0000 0.996 0.000 1.000 0.000
#> GSM381211 2 0.0000 0.996 0.000 1.000 0.000
#> GSM381220 2 0.0000 0.996 0.000 1.000 0.000
#> GSM381222 1 0.0747 0.933 0.984 0.000 0.016
#> GSM381224 1 0.1163 0.929 0.972 0.000 0.028
#> GSM381232 1 0.2356 0.900 0.928 0.000 0.072
#> GSM381240 1 0.1529 0.925 0.960 0.000 0.040
#> GSM381250 1 0.0000 0.936 1.000 0.000 0.000
#> GSM381252 2 0.0000 0.996 0.000 1.000 0.000
#> GSM381254 1 0.4702 0.808 0.788 0.000 0.212
#> GSM381256 2 0.0000 0.996 0.000 1.000 0.000
#> GSM381257 1 0.0000 0.936 1.000 0.000 0.000
#> GSM381259 1 0.5058 0.786 0.756 0.000 0.244
#> GSM381260 1 0.0000 0.936 1.000 0.000 0.000
#> GSM381261 2 0.0424 0.991 0.000 0.992 0.008
#> GSM381263 1 0.0000 0.936 1.000 0.000 0.000
#> GSM381265 1 0.4974 0.791 0.764 0.000 0.236
#> GSM381268 1 0.0000 0.936 1.000 0.000 0.000
#> GSM381270 2 0.0000 0.996 0.000 1.000 0.000
#> GSM381271 1 0.2356 0.900 0.928 0.000 0.072
#> GSM381275 2 0.0424 0.991 0.000 0.992 0.008
#> GSM381279 2 0.0424 0.991 0.000 0.992 0.008
#> GSM381195 1 0.4842 0.800 0.776 0.000 0.224
#> GSM381196 1 0.0000 0.936 1.000 0.000 0.000
#> GSM381198 2 0.0000 0.996 0.000 1.000 0.000
#> GSM381200 2 0.0000 0.996 0.000 1.000 0.000
#> GSM381201 1 0.0000 0.936 1.000 0.000 0.000
#> GSM381203 1 0.0000 0.936 1.000 0.000 0.000
#> GSM381204 1 0.5058 0.786 0.756 0.000 0.244
#> GSM381209 1 0.5058 0.786 0.756 0.000 0.244
#> GSM381212 1 0.5058 0.786 0.756 0.000 0.244
#> GSM381213 2 0.0000 0.996 0.000 1.000 0.000
#> GSM381214 2 0.0000 0.996 0.000 1.000 0.000
#> GSM381216 1 0.0000 0.936 1.000 0.000 0.000
#> GSM381225 1 0.0000 0.936 1.000 0.000 0.000
#> GSM381231 1 0.2356 0.900 0.928 0.000 0.072
#> GSM381235 1 0.0424 0.935 0.992 0.000 0.008
#> GSM381237 1 0.5058 0.786 0.756 0.000 0.244
#> GSM381241 2 0.0000 0.996 0.000 1.000 0.000
#> GSM381243 2 0.0000 0.996 0.000 1.000 0.000
#> GSM381245 1 0.1031 0.931 0.976 0.000 0.024
#> GSM381246 2 0.0424 0.991 0.000 0.992 0.008
#> GSM381251 1 0.0000 0.936 1.000 0.000 0.000
#> GSM381264 1 0.4654 0.809 0.792 0.000 0.208
#> GSM381206 2 0.0000 0.996 0.000 1.000 0.000
#> GSM381217 1 0.0000 0.936 1.000 0.000 0.000
#> GSM381218 2 0.0000 0.996 0.000 1.000 0.000
#> GSM381226 2 0.0424 0.991 0.000 0.992 0.008
#> GSM381227 2 0.0424 0.991 0.000 0.992 0.008
#> GSM381228 1 0.2356 0.900 0.928 0.000 0.072
#> GSM381236 1 0.2356 0.900 0.928 0.000 0.072
#> GSM381244 1 0.0592 0.934 0.988 0.000 0.012
#> GSM381272 1 0.2356 0.900 0.928 0.000 0.072
#> GSM381277 1 0.1163 0.929 0.972 0.000 0.028
#> GSM381278 1 0.0000 0.936 1.000 0.000 0.000
#> GSM381197 1 0.0000 0.936 1.000 0.000 0.000
#> GSM381202 1 0.0592 0.934 0.988 0.000 0.012
#> GSM381207 1 0.0000 0.936 1.000 0.000 0.000
#> GSM381208 3 0.5733 1.000 0.000 0.324 0.676
#> GSM381210 1 0.1529 0.925 0.960 0.000 0.040
#> GSM381215 1 0.0000 0.936 1.000 0.000 0.000
#> GSM381219 2 0.0000 0.996 0.000 1.000 0.000
#> GSM381221 2 0.0000 0.996 0.000 1.000 0.000
#> GSM381223 2 0.0424 0.991 0.000 0.992 0.008
#> GSM381229 1 0.0000 0.936 1.000 0.000 0.000
#> GSM381230 1 0.5058 0.786 0.756 0.000 0.244
#> GSM381233 1 0.0747 0.933 0.984 0.000 0.016
#> GSM381234 1 0.4750 0.806 0.784 0.000 0.216
#> GSM381238 1 0.2356 0.900 0.928 0.000 0.072
#> GSM381239 1 0.2356 0.900 0.928 0.000 0.072
#> GSM381242 1 0.0000 0.936 1.000 0.000 0.000
#> GSM381247 2 0.0000 0.996 0.000 1.000 0.000
#> GSM381248 1 0.1529 0.926 0.960 0.000 0.040
#> GSM381249 1 0.5058 0.786 0.756 0.000 0.244
#> GSM381253 1 0.0000 0.936 1.000 0.000 0.000
#> GSM381255 2 0.0000 0.996 0.000 1.000 0.000
#> GSM381258 1 0.0000 0.936 1.000 0.000 0.000
#> GSM381262 1 0.0000 0.936 1.000 0.000 0.000
#> GSM381266 1 0.0000 0.936 1.000 0.000 0.000
#> GSM381267 3 0.5733 1.000 0.000 0.324 0.676
#> GSM381269 1 0.0000 0.936 1.000 0.000 0.000
#> GSM381273 1 0.0000 0.936 1.000 0.000 0.000
#> GSM381274 2 0.0424 0.991 0.000 0.992 0.008
#> GSM381276 1 0.0000 0.936 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM381194 3 0.0000 0.817 0.000 0.000 1.000 0.000
#> GSM381199 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM381205 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM381211 2 0.0188 0.973 0.004 0.996 0.000 0.000
#> GSM381220 2 0.1211 0.964 0.040 0.960 0.000 0.000
#> GSM381222 3 0.3837 0.588 0.224 0.000 0.776 0.000
#> GSM381224 3 0.4500 0.416 0.316 0.000 0.684 0.000
#> GSM381232 3 0.5531 0.607 0.140 0.000 0.732 0.128
#> GSM381240 3 0.4697 0.312 0.356 0.000 0.644 0.000
#> GSM381250 3 0.0000 0.817 0.000 0.000 1.000 0.000
#> GSM381252 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM381254 3 0.4989 -0.385 0.472 0.000 0.528 0.000
#> GSM381256 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM381257 3 0.0000 0.817 0.000 0.000 1.000 0.000
#> GSM381259 1 0.3569 0.886 0.804 0.000 0.196 0.000
#> GSM381260 3 0.0000 0.817 0.000 0.000 1.000 0.000
#> GSM381261 2 0.2142 0.953 0.056 0.928 0.000 0.016
#> GSM381263 3 0.0000 0.817 0.000 0.000 1.000 0.000
#> GSM381265 1 0.4790 0.698 0.620 0.000 0.380 0.000
#> GSM381268 3 0.0000 0.817 0.000 0.000 1.000 0.000
#> GSM381270 2 0.1389 0.963 0.048 0.952 0.000 0.000
#> GSM381271 3 0.5531 0.607 0.140 0.000 0.732 0.128
#> GSM381275 2 0.1182 0.964 0.016 0.968 0.000 0.016
#> GSM381279 2 0.2142 0.953 0.056 0.928 0.000 0.016
#> GSM381195 1 0.4661 0.762 0.652 0.000 0.348 0.000
#> GSM381196 3 0.0000 0.817 0.000 0.000 1.000 0.000
#> GSM381198 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM381200 2 0.0188 0.973 0.004 0.996 0.000 0.000
#> GSM381201 3 0.0000 0.817 0.000 0.000 1.000 0.000
#> GSM381203 3 0.0000 0.817 0.000 0.000 1.000 0.000
#> GSM381204 1 0.3569 0.886 0.804 0.000 0.196 0.000
#> GSM381209 1 0.3649 0.885 0.796 0.000 0.204 0.000
#> GSM381212 1 0.3569 0.886 0.804 0.000 0.196 0.000
#> GSM381213 2 0.1211 0.964 0.040 0.960 0.000 0.000
#> GSM381214 2 0.0188 0.973 0.004 0.996 0.000 0.000
#> GSM381216 3 0.0000 0.817 0.000 0.000 1.000 0.000
#> GSM381225 3 0.2814 0.709 0.132 0.000 0.868 0.000
#> GSM381231 3 0.5531 0.607 0.140 0.000 0.732 0.128
#> GSM381235 3 0.3400 0.651 0.180 0.000 0.820 0.000
#> GSM381237 1 0.3569 0.886 0.804 0.000 0.196 0.000
#> GSM381241 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM381243 2 0.1211 0.964 0.040 0.960 0.000 0.000
#> GSM381245 3 0.4406 0.452 0.300 0.000 0.700 0.000
#> GSM381246 2 0.1182 0.964 0.016 0.968 0.000 0.016
#> GSM381251 3 0.0000 0.817 0.000 0.000 1.000 0.000
#> GSM381264 3 0.4981 -0.360 0.464 0.000 0.536 0.000
#> GSM381206 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM381217 3 0.0000 0.817 0.000 0.000 1.000 0.000
#> GSM381218 2 0.0188 0.973 0.004 0.996 0.000 0.000
#> GSM381226 2 0.1182 0.964 0.016 0.968 0.000 0.016
#> GSM381227 2 0.2142 0.953 0.056 0.928 0.000 0.016
#> GSM381228 3 0.5531 0.607 0.140 0.000 0.732 0.128
#> GSM381236 3 0.5531 0.607 0.140 0.000 0.732 0.128
#> GSM381244 3 0.2760 0.714 0.128 0.000 0.872 0.000
#> GSM381272 3 0.5531 0.607 0.140 0.000 0.732 0.128
#> GSM381277 3 0.4500 0.416 0.316 0.000 0.684 0.000
#> GSM381278 3 0.0000 0.817 0.000 0.000 1.000 0.000
#> GSM381197 3 0.0000 0.817 0.000 0.000 1.000 0.000
#> GSM381202 3 0.1211 0.789 0.040 0.000 0.960 0.000
#> GSM381207 3 0.0000 0.817 0.000 0.000 1.000 0.000
#> GSM381208 4 0.2973 1.000 0.000 0.144 0.000 0.856
#> GSM381210 3 0.4072 0.533 0.252 0.000 0.748 0.000
#> GSM381215 3 0.0000 0.817 0.000 0.000 1.000 0.000
#> GSM381219 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM381221 2 0.0336 0.972 0.000 0.992 0.000 0.008
#> GSM381223 2 0.1182 0.964 0.016 0.968 0.000 0.016
#> GSM381229 3 0.0000 0.817 0.000 0.000 1.000 0.000
#> GSM381230 1 0.3569 0.886 0.804 0.000 0.196 0.000
#> GSM381233 3 0.3688 0.614 0.208 0.000 0.792 0.000
#> GSM381234 1 0.4679 0.748 0.648 0.000 0.352 0.000
#> GSM381238 3 0.5483 0.611 0.136 0.000 0.736 0.128
#> GSM381239 3 0.5483 0.611 0.136 0.000 0.736 0.128
#> GSM381242 3 0.0000 0.817 0.000 0.000 1.000 0.000
#> GSM381247 2 0.1211 0.964 0.040 0.960 0.000 0.000
#> GSM381248 3 0.4697 0.284 0.356 0.000 0.644 0.000
#> GSM381249 1 0.4164 0.847 0.736 0.000 0.264 0.000
#> GSM381253 3 0.0000 0.817 0.000 0.000 1.000 0.000
#> GSM381255 2 0.1118 0.965 0.036 0.964 0.000 0.000
#> GSM381258 3 0.0000 0.817 0.000 0.000 1.000 0.000
#> GSM381262 3 0.0000 0.817 0.000 0.000 1.000 0.000
#> GSM381266 3 0.0000 0.817 0.000 0.000 1.000 0.000
#> GSM381267 4 0.2973 1.000 0.000 0.144 0.000 0.856
#> GSM381269 3 0.0000 0.817 0.000 0.000 1.000 0.000
#> GSM381273 3 0.0000 0.817 0.000 0.000 1.000 0.000
#> GSM381274 2 0.2142 0.953 0.056 0.928 0.000 0.016
#> GSM381276 3 0.0000 0.817 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM381194 3 0.0000 0.865 0.000 0.000 1.000 0.000 0
#> GSM381199 2 0.0000 0.898 0.000 1.000 0.000 0.000 0
#> GSM381205 2 0.0000 0.898 0.000 1.000 0.000 0.000 0
#> GSM381211 2 0.0290 0.899 0.000 0.992 0.000 0.008 0
#> GSM381220 2 0.3305 0.832 0.000 0.776 0.000 0.224 0
#> GSM381222 3 0.3636 0.632 0.272 0.000 0.728 0.000 0
#> GSM381224 3 0.4161 0.457 0.392 0.000 0.608 0.000 0
#> GSM381232 4 0.3636 0.991 0.000 0.000 0.272 0.728 0
#> GSM381240 3 0.4291 0.300 0.464 0.000 0.536 0.000 0
#> GSM381250 3 0.0000 0.865 0.000 0.000 1.000 0.000 0
#> GSM381252 2 0.0000 0.898 0.000 1.000 0.000 0.000 0
#> GSM381254 1 0.4268 0.382 0.556 0.000 0.444 0.000 0
#> GSM381256 2 0.0000 0.898 0.000 1.000 0.000 0.000 0
#> GSM381257 3 0.0000 0.865 0.000 0.000 1.000 0.000 0
#> GSM381259 1 0.0000 0.725 1.000 0.000 0.000 0.000 0
#> GSM381260 3 0.0000 0.865 0.000 0.000 1.000 0.000 0
#> GSM381261 2 0.3636 0.816 0.000 0.728 0.000 0.272 0
#> GSM381263 3 0.0000 0.865 0.000 0.000 1.000 0.000 0
#> GSM381265 1 0.3366 0.602 0.768 0.000 0.232 0.000 0
#> GSM381268 3 0.0000 0.865 0.000 0.000 1.000 0.000 0
#> GSM381270 2 0.3452 0.826 0.000 0.756 0.000 0.244 0
#> GSM381271 4 0.3636 0.991 0.000 0.000 0.272 0.728 0
#> GSM381275 2 0.1270 0.887 0.000 0.948 0.000 0.052 0
#> GSM381279 2 0.3636 0.816 0.000 0.728 0.000 0.272 0
#> GSM381195 1 0.3177 0.655 0.792 0.000 0.208 0.000 0
#> GSM381196 3 0.0000 0.865 0.000 0.000 1.000 0.000 0
#> GSM381198 2 0.0000 0.898 0.000 1.000 0.000 0.000 0
#> GSM381200 2 0.0290 0.899 0.000 0.992 0.000 0.008 0
#> GSM381201 3 0.0000 0.865 0.000 0.000 1.000 0.000 0
#> GSM381203 3 0.0000 0.865 0.000 0.000 1.000 0.000 0
#> GSM381204 1 0.0000 0.725 1.000 0.000 0.000 0.000 0
#> GSM381209 1 0.0703 0.725 0.976 0.000 0.024 0.000 0
#> GSM381212 1 0.0000 0.725 1.000 0.000 0.000 0.000 0
#> GSM381213 2 0.3305 0.832 0.000 0.776 0.000 0.224 0
#> GSM381214 2 0.0290 0.899 0.000 0.992 0.000 0.008 0
#> GSM381216 3 0.0000 0.865 0.000 0.000 1.000 0.000 0
#> GSM381225 3 0.2813 0.741 0.168 0.000 0.832 0.000 0
#> GSM381231 4 0.3636 0.991 0.000 0.000 0.272 0.728 0
#> GSM381235 3 0.3305 0.692 0.224 0.000 0.776 0.000 0
#> GSM381237 1 0.0000 0.725 1.000 0.000 0.000 0.000 0
#> GSM381241 2 0.0000 0.898 0.000 1.000 0.000 0.000 0
#> GSM381243 2 0.3305 0.832 0.000 0.776 0.000 0.224 0
#> GSM381245 3 0.4101 0.493 0.372 0.000 0.628 0.000 0
#> GSM381246 2 0.1121 0.888 0.000 0.956 0.000 0.044 0
#> GSM381251 3 0.0000 0.865 0.000 0.000 1.000 0.000 0
#> GSM381264 1 0.4262 0.379 0.560 0.000 0.440 0.000 0
#> GSM381206 2 0.0000 0.898 0.000 1.000 0.000 0.000 0
#> GSM381217 3 0.0000 0.865 0.000 0.000 1.000 0.000 0
#> GSM381218 2 0.0290 0.899 0.000 0.992 0.000 0.008 0
#> GSM381226 2 0.1121 0.888 0.000 0.956 0.000 0.044 0
#> GSM381227 2 0.3612 0.818 0.000 0.732 0.000 0.268 0
#> GSM381228 4 0.3636 0.991 0.000 0.000 0.272 0.728 0
#> GSM381236 4 0.3636 0.991 0.000 0.000 0.272 0.728 0
#> GSM381244 3 0.2561 0.765 0.144 0.000 0.856 0.000 0
#> GSM381272 4 0.3636 0.991 0.000 0.000 0.272 0.728 0
#> GSM381277 3 0.4161 0.457 0.392 0.000 0.608 0.000 0
#> GSM381278 3 0.0162 0.863 0.004 0.000 0.996 0.000 0
#> GSM381197 3 0.0000 0.865 0.000 0.000 1.000 0.000 0
#> GSM381202 3 0.1478 0.805 0.064 0.000 0.936 0.000 0
#> GSM381207 3 0.0000 0.865 0.000 0.000 1.000 0.000 0
#> GSM381208 5 0.0000 1.000 0.000 0.000 0.000 0.000 1
#> GSM381210 3 0.3913 0.540 0.324 0.000 0.676 0.000 0
#> GSM381215 3 0.0000 0.865 0.000 0.000 1.000 0.000 0
#> GSM381219 2 0.0000 0.898 0.000 1.000 0.000 0.000 0
#> GSM381221 2 0.0404 0.897 0.000 0.988 0.000 0.012 0
#> GSM381223 2 0.1197 0.887 0.000 0.952 0.000 0.048 0
#> GSM381229 3 0.0000 0.865 0.000 0.000 1.000 0.000 0
#> GSM381230 1 0.0000 0.725 1.000 0.000 0.000 0.000 0
#> GSM381233 3 0.3534 0.654 0.256 0.000 0.744 0.000 0
#> GSM381234 1 0.3305 0.633 0.776 0.000 0.224 0.000 0
#> GSM381238 4 0.3730 0.974 0.000 0.000 0.288 0.712 0
#> GSM381239 4 0.3730 0.974 0.000 0.000 0.288 0.712 0
#> GSM381242 3 0.0000 0.865 0.000 0.000 1.000 0.000 0
#> GSM381247 2 0.3395 0.829 0.000 0.764 0.000 0.236 0
#> GSM381248 3 0.4256 0.329 0.436 0.000 0.564 0.000 0
#> GSM381249 1 0.2020 0.695 0.900 0.000 0.100 0.000 0
#> GSM381253 3 0.0000 0.865 0.000 0.000 1.000 0.000 0
#> GSM381255 2 0.3242 0.834 0.000 0.784 0.000 0.216 0
#> GSM381258 3 0.0000 0.865 0.000 0.000 1.000 0.000 0
#> GSM381262 3 0.0000 0.865 0.000 0.000 1.000 0.000 0
#> GSM381266 3 0.0000 0.865 0.000 0.000 1.000 0.000 0
#> GSM381267 5 0.0000 1.000 0.000 0.000 0.000 0.000 1
#> GSM381269 3 0.0000 0.865 0.000 0.000 1.000 0.000 0
#> GSM381273 3 0.0000 0.865 0.000 0.000 1.000 0.000 0
#> GSM381274 2 0.3636 0.816 0.000 0.728 0.000 0.272 0
#> GSM381276 3 0.0162 0.863 0.004 0.000 0.996 0.000 0
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM381194 3 0.0000 0.883 0.000 0.000 1.000 0.000 0.000 0
#> GSM381199 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000 0
#> GSM381205 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000 0
#> GSM381211 2 0.0260 0.979 0.000 0.992 0.000 0.000 0.008 0
#> GSM381220 5 0.1267 0.943 0.000 0.060 0.000 0.000 0.940 0
#> GSM381222 3 0.3266 0.651 0.272 0.000 0.728 0.000 0.000 0
#> GSM381224 3 0.3737 0.474 0.392 0.000 0.608 0.000 0.000 0
#> GSM381232 4 0.0000 0.980 0.000 0.000 0.000 1.000 0.000 0
#> GSM381240 3 0.3854 0.318 0.464 0.000 0.536 0.000 0.000 0
#> GSM381250 3 0.0000 0.883 0.000 0.000 1.000 0.000 0.000 0
#> GSM381252 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000 0
#> GSM381254 1 0.3817 0.445 0.568 0.000 0.432 0.000 0.000 0
#> GSM381256 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000 0
#> GSM381257 3 0.0000 0.883 0.000 0.000 1.000 0.000 0.000 0
#> GSM381259 1 0.0000 0.738 1.000 0.000 0.000 0.000 0.000 0
#> GSM381260 3 0.0000 0.883 0.000 0.000 1.000 0.000 0.000 0
#> GSM381261 5 0.1204 0.920 0.000 0.056 0.000 0.000 0.944 0
#> GSM381263 3 0.0000 0.883 0.000 0.000 1.000 0.000 0.000 0
#> GSM381265 1 0.2941 0.630 0.780 0.000 0.220 0.000 0.000 0
#> GSM381268 3 0.0000 0.883 0.000 0.000 1.000 0.000 0.000 0
#> GSM381270 5 0.0865 0.945 0.000 0.036 0.000 0.000 0.964 0
#> GSM381271 4 0.0000 0.980 0.000 0.000 0.000 1.000 0.000 0
#> GSM381275 2 0.1327 0.942 0.000 0.936 0.000 0.000 0.064 0
#> GSM381279 5 0.0146 0.927 0.000 0.004 0.000 0.000 0.996 0
#> GSM381195 1 0.2854 0.667 0.792 0.000 0.208 0.000 0.000 0
#> GSM381196 3 0.0000 0.883 0.000 0.000 1.000 0.000 0.000 0
#> GSM381198 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000 0
#> GSM381200 2 0.0260 0.979 0.000 0.992 0.000 0.000 0.008 0
#> GSM381201 3 0.0146 0.882 0.000 0.000 0.996 0.000 0.004 0
#> GSM381203 3 0.0000 0.883 0.000 0.000 1.000 0.000 0.000 0
#> GSM381204 1 0.0000 0.738 1.000 0.000 0.000 0.000 0.000 0
#> GSM381209 1 0.0632 0.739 0.976 0.000 0.024 0.000 0.000 0
#> GSM381212 1 0.0000 0.738 1.000 0.000 0.000 0.000 0.000 0
#> GSM381213 5 0.1957 0.906 0.000 0.112 0.000 0.000 0.888 0
#> GSM381214 2 0.0260 0.979 0.000 0.992 0.000 0.000 0.008 0
#> GSM381216 3 0.0000 0.883 0.000 0.000 1.000 0.000 0.000 0
#> GSM381225 3 0.2527 0.762 0.168 0.000 0.832 0.000 0.000 0
#> GSM381231 4 0.0000 0.980 0.000 0.000 0.000 1.000 0.000 0
#> GSM381235 3 0.2969 0.707 0.224 0.000 0.776 0.000 0.000 0
#> GSM381237 1 0.0000 0.738 1.000 0.000 0.000 0.000 0.000 0
#> GSM381241 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000 0
#> GSM381243 5 0.1267 0.943 0.000 0.060 0.000 0.000 0.940 0
#> GSM381245 3 0.3684 0.509 0.372 0.000 0.628 0.000 0.000 0
#> GSM381246 2 0.1075 0.953 0.000 0.952 0.000 0.000 0.048 0
#> GSM381251 3 0.0146 0.882 0.000 0.000 0.996 0.000 0.004 0
#> GSM381264 1 0.3810 0.457 0.572 0.000 0.428 0.000 0.000 0
#> GSM381206 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000 0
#> GSM381217 3 0.0000 0.883 0.000 0.000 1.000 0.000 0.000 0
#> GSM381218 2 0.0260 0.979 0.000 0.992 0.000 0.000 0.008 0
#> GSM381226 2 0.1075 0.953 0.000 0.952 0.000 0.000 0.048 0
#> GSM381227 5 0.0260 0.931 0.000 0.008 0.000 0.000 0.992 0
#> GSM381228 4 0.0000 0.980 0.000 0.000 0.000 1.000 0.000 0
#> GSM381236 4 0.0260 0.975 0.000 0.000 0.008 0.992 0.000 0
#> GSM381244 3 0.2340 0.782 0.148 0.000 0.852 0.000 0.000 0
#> GSM381272 4 0.0000 0.980 0.000 0.000 0.000 1.000 0.000 0
#> GSM381277 3 0.3737 0.474 0.392 0.000 0.608 0.000 0.000 0
#> GSM381278 3 0.0458 0.875 0.016 0.000 0.984 0.000 0.000 0
#> GSM381197 3 0.0146 0.882 0.000 0.000 0.996 0.000 0.004 0
#> GSM381202 3 0.1327 0.832 0.064 0.000 0.936 0.000 0.000 0
#> GSM381207 3 0.0000 0.883 0.000 0.000 1.000 0.000 0.000 0
#> GSM381208 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1
#> GSM381210 3 0.3547 0.538 0.332 0.000 0.668 0.000 0.000 0
#> GSM381215 3 0.0000 0.883 0.000 0.000 1.000 0.000 0.000 0
#> GSM381219 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000 0
#> GSM381221 2 0.0363 0.977 0.000 0.988 0.000 0.000 0.012 0
#> GSM381223 2 0.1204 0.947 0.000 0.944 0.000 0.000 0.056 0
#> GSM381229 3 0.0146 0.882 0.000 0.000 0.996 0.000 0.004 0
#> GSM381230 1 0.0000 0.738 1.000 0.000 0.000 0.000 0.000 0
#> GSM381233 3 0.3175 0.672 0.256 0.000 0.744 0.000 0.000 0
#> GSM381234 1 0.2969 0.645 0.776 0.000 0.224 0.000 0.000 0
#> GSM381238 4 0.0790 0.948 0.000 0.000 0.032 0.968 0.000 0
#> GSM381239 4 0.0790 0.948 0.000 0.000 0.032 0.968 0.000 0
#> GSM381242 3 0.0000 0.883 0.000 0.000 1.000 0.000 0.000 0
#> GSM381247 5 0.1007 0.946 0.000 0.044 0.000 0.000 0.956 0
#> GSM381248 3 0.3823 0.350 0.436 0.000 0.564 0.000 0.000 0
#> GSM381249 1 0.1714 0.714 0.908 0.000 0.092 0.000 0.000 0
#> GSM381253 3 0.0000 0.883 0.000 0.000 1.000 0.000 0.000 0
#> GSM381255 5 0.1444 0.939 0.000 0.072 0.000 0.000 0.928 0
#> GSM381258 3 0.0000 0.883 0.000 0.000 1.000 0.000 0.000 0
#> GSM381262 3 0.0000 0.883 0.000 0.000 1.000 0.000 0.000 0
#> GSM381266 3 0.0146 0.882 0.000 0.000 0.996 0.000 0.004 0
#> GSM381267 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1
#> GSM381269 3 0.0000 0.883 0.000 0.000 1.000 0.000 0.000 0
#> GSM381273 3 0.0146 0.882 0.000 0.000 0.996 0.000 0.004 0
#> GSM381274 5 0.1204 0.920 0.000 0.056 0.000 0.000 0.944 0
#> GSM381276 3 0.0458 0.875 0.016 0.000 0.984 0.000 0.000 0
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n other(p) k
#> ATC:pam 86 0.744 2
#> ATC:pam 86 0.390 3
#> ATC:pam 79 0.241 4
#> ATC:pam 79 0.163 5
#> ATC:pam 80 0.304 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 86 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 1.000 1.000 1.000 0.4528 0.548 0.548
#> 3 3 0.740 0.766 0.864 0.2684 0.969 0.944
#> 4 4 0.923 0.963 0.961 0.1850 0.789 0.600
#> 5 5 0.832 0.756 0.863 0.0937 0.925 0.769
#> 6 6 0.787 0.687 0.826 0.0563 0.965 0.865
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM381194 1 0 1 1 0
#> GSM381199 2 0 1 0 1
#> GSM381205 2 0 1 0 1
#> GSM381211 2 0 1 0 1
#> GSM381220 2 0 1 0 1
#> GSM381222 1 0 1 1 0
#> GSM381224 1 0 1 1 0
#> GSM381232 1 0 1 1 0
#> GSM381240 1 0 1 1 0
#> GSM381250 1 0 1 1 0
#> GSM381252 2 0 1 0 1
#> GSM381254 1 0 1 1 0
#> GSM381256 2 0 1 0 1
#> GSM381257 1 0 1 1 0
#> GSM381259 1 0 1 1 0
#> GSM381260 1 0 1 1 0
#> GSM381261 2 0 1 0 1
#> GSM381263 1 0 1 1 0
#> GSM381265 1 0 1 1 0
#> GSM381268 1 0 1 1 0
#> GSM381270 2 0 1 0 1
#> GSM381271 1 0 1 1 0
#> GSM381275 2 0 1 0 1
#> GSM381279 2 0 1 0 1
#> GSM381195 1 0 1 1 0
#> GSM381196 1 0 1 1 0
#> GSM381198 2 0 1 0 1
#> GSM381200 2 0 1 0 1
#> GSM381201 1 0 1 1 0
#> GSM381203 1 0 1 1 0
#> GSM381204 1 0 1 1 0
#> GSM381209 1 0 1 1 0
#> GSM381212 1 0 1 1 0
#> GSM381213 2 0 1 0 1
#> GSM381214 2 0 1 0 1
#> GSM381216 1 0 1 1 0
#> GSM381225 1 0 1 1 0
#> GSM381231 1 0 1 1 0
#> GSM381235 1 0 1 1 0
#> GSM381237 1 0 1 1 0
#> GSM381241 2 0 1 0 1
#> GSM381243 2 0 1 0 1
#> GSM381245 1 0 1 1 0
#> GSM381246 2 0 1 0 1
#> GSM381251 1 0 1 1 0
#> GSM381264 1 0 1 1 0
#> GSM381206 2 0 1 0 1
#> GSM381217 1 0 1 1 0
#> GSM381218 2 0 1 0 1
#> GSM381226 2 0 1 0 1
#> GSM381227 2 0 1 0 1
#> GSM381228 1 0 1 1 0
#> GSM381236 1 0 1 1 0
#> GSM381244 1 0 1 1 0
#> GSM381272 1 0 1 1 0
#> GSM381277 1 0 1 1 0
#> GSM381278 1 0 1 1 0
#> GSM381197 1 0 1 1 0
#> GSM381202 1 0 1 1 0
#> GSM381207 1 0 1 1 0
#> GSM381208 2 0 1 0 1
#> GSM381210 1 0 1 1 0
#> GSM381215 1 0 1 1 0
#> GSM381219 2 0 1 0 1
#> GSM381221 2 0 1 0 1
#> GSM381223 2 0 1 0 1
#> GSM381229 1 0 1 1 0
#> GSM381230 1 0 1 1 0
#> GSM381233 1 0 1 1 0
#> GSM381234 1 0 1 1 0
#> GSM381238 1 0 1 1 0
#> GSM381239 1 0 1 1 0
#> GSM381242 1 0 1 1 0
#> GSM381247 2 0 1 0 1
#> GSM381248 1 0 1 1 0
#> GSM381249 1 0 1 1 0
#> GSM381253 1 0 1 1 0
#> GSM381255 2 0 1 0 1
#> GSM381258 1 0 1 1 0
#> GSM381262 1 0 1 1 0
#> GSM381266 1 0 1 1 0
#> GSM381267 2 0 1 0 1
#> GSM381269 1 0 1 1 0
#> GSM381273 1 0 1 1 0
#> GSM381274 2 0 1 0 1
#> GSM381276 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM381194 1 0.000 0.7511 1.000 0.000 0.000
#> GSM381199 2 0.000 1.0000 0.000 1.000 0.000
#> GSM381205 2 0.000 1.0000 0.000 1.000 0.000
#> GSM381211 2 0.000 1.0000 0.000 1.000 0.000
#> GSM381220 2 0.000 1.0000 0.000 1.000 0.000
#> GSM381222 1 0.620 0.6328 0.576 0.000 0.424
#> GSM381224 1 0.620 0.6328 0.576 0.000 0.424
#> GSM381232 1 0.000 0.7511 1.000 0.000 0.000
#> GSM381240 1 0.620 0.6328 0.576 0.000 0.424
#> GSM381250 1 0.000 0.7511 1.000 0.000 0.000
#> GSM381252 2 0.000 1.0000 0.000 1.000 0.000
#> GSM381254 1 0.620 0.6328 0.576 0.000 0.424
#> GSM381256 2 0.000 1.0000 0.000 1.000 0.000
#> GSM381257 1 0.000 0.7511 1.000 0.000 0.000
#> GSM381259 1 0.620 0.6328 0.576 0.000 0.424
#> GSM381260 1 0.000 0.7511 1.000 0.000 0.000
#> GSM381261 2 0.000 1.0000 0.000 1.000 0.000
#> GSM381263 1 0.000 0.7511 1.000 0.000 0.000
#> GSM381265 1 0.620 0.6328 0.576 0.000 0.424
#> GSM381268 1 0.000 0.7511 1.000 0.000 0.000
#> GSM381270 2 0.000 1.0000 0.000 1.000 0.000
#> GSM381271 1 0.000 0.7511 1.000 0.000 0.000
#> GSM381275 2 0.000 1.0000 0.000 1.000 0.000
#> GSM381279 2 0.000 1.0000 0.000 1.000 0.000
#> GSM381195 1 0.620 0.6328 0.576 0.000 0.424
#> GSM381196 1 0.000 0.7511 1.000 0.000 0.000
#> GSM381198 2 0.000 1.0000 0.000 1.000 0.000
#> GSM381200 2 0.000 1.0000 0.000 1.000 0.000
#> GSM381201 1 0.296 0.6650 0.900 0.000 0.100
#> GSM381203 1 0.000 0.7511 1.000 0.000 0.000
#> GSM381204 1 0.620 0.6328 0.576 0.000 0.424
#> GSM381209 1 0.620 0.6328 0.576 0.000 0.424
#> GSM381212 1 0.620 0.6328 0.576 0.000 0.424
#> GSM381213 2 0.000 1.0000 0.000 1.000 0.000
#> GSM381214 2 0.000 1.0000 0.000 1.000 0.000
#> GSM381216 1 0.000 0.7511 1.000 0.000 0.000
#> GSM381225 3 0.631 0.0222 0.496 0.000 0.504
#> GSM381231 1 0.000 0.7511 1.000 0.000 0.000
#> GSM381235 1 0.000 0.7511 1.000 0.000 0.000
#> GSM381237 1 0.620 0.6328 0.576 0.000 0.424
#> GSM381241 2 0.000 1.0000 0.000 1.000 0.000
#> GSM381243 2 0.000 1.0000 0.000 1.000 0.000
#> GSM381245 1 0.620 0.6328 0.576 0.000 0.424
#> GSM381246 2 0.000 1.0000 0.000 1.000 0.000
#> GSM381251 1 0.296 0.6650 0.900 0.000 0.100
#> GSM381264 1 0.620 0.6328 0.576 0.000 0.424
#> GSM381206 2 0.000 1.0000 0.000 1.000 0.000
#> GSM381217 1 0.000 0.7511 1.000 0.000 0.000
#> GSM381218 2 0.000 1.0000 0.000 1.000 0.000
#> GSM381226 2 0.000 1.0000 0.000 1.000 0.000
#> GSM381227 2 0.000 1.0000 0.000 1.000 0.000
#> GSM381228 1 0.000 0.7511 1.000 0.000 0.000
#> GSM381236 1 0.186 0.7114 0.948 0.000 0.052
#> GSM381244 1 0.226 0.7355 0.932 0.000 0.068
#> GSM381272 1 0.000 0.7511 1.000 0.000 0.000
#> GSM381277 1 0.620 0.6328 0.576 0.000 0.424
#> GSM381278 1 0.502 0.4498 0.760 0.000 0.240
#> GSM381197 1 0.296 0.6650 0.900 0.000 0.100
#> GSM381202 1 0.000 0.7511 1.000 0.000 0.000
#> GSM381207 1 0.619 0.6338 0.580 0.000 0.420
#> GSM381208 3 0.620 0.4147 0.000 0.424 0.576
#> GSM381210 1 0.620 0.6328 0.576 0.000 0.424
#> GSM381215 1 0.000 0.7511 1.000 0.000 0.000
#> GSM381219 2 0.000 1.0000 0.000 1.000 0.000
#> GSM381221 2 0.000 1.0000 0.000 1.000 0.000
#> GSM381223 2 0.000 1.0000 0.000 1.000 0.000
#> GSM381229 1 0.470 0.5077 0.788 0.000 0.212
#> GSM381230 1 0.620 0.6328 0.576 0.000 0.424
#> GSM381233 1 0.620 0.6328 0.576 0.000 0.424
#> GSM381234 1 0.620 0.6328 0.576 0.000 0.424
#> GSM381238 1 0.000 0.7511 1.000 0.000 0.000
#> GSM381239 1 0.226 0.6967 0.932 0.000 0.068
#> GSM381242 1 0.000 0.7511 1.000 0.000 0.000
#> GSM381247 2 0.000 1.0000 0.000 1.000 0.000
#> GSM381248 1 0.620 0.6328 0.576 0.000 0.424
#> GSM381249 1 0.620 0.6328 0.576 0.000 0.424
#> GSM381253 1 0.000 0.7511 1.000 0.000 0.000
#> GSM381255 2 0.000 1.0000 0.000 1.000 0.000
#> GSM381258 1 0.000 0.7511 1.000 0.000 0.000
#> GSM381262 1 0.000 0.7511 1.000 0.000 0.000
#> GSM381266 1 0.480 0.4936 0.780 0.000 0.220
#> GSM381267 3 0.620 0.4147 0.000 0.424 0.576
#> GSM381269 1 0.000 0.7511 1.000 0.000 0.000
#> GSM381273 1 0.536 0.3773 0.724 0.000 0.276
#> GSM381274 2 0.000 1.0000 0.000 1.000 0.000
#> GSM381276 1 0.000 0.7511 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM381194 3 0.1256 0.935 0.028 0.00 0.964 0.008
#> GSM381199 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM381205 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM381211 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM381220 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM381222 1 0.0188 0.989 0.996 0.00 0.004 0.000
#> GSM381224 1 0.0336 0.983 0.992 0.00 0.008 0.000
#> GSM381232 3 0.1256 0.935 0.028 0.00 0.964 0.008
#> GSM381240 1 0.0188 0.989 0.996 0.00 0.004 0.000
#> GSM381250 3 0.3088 0.926 0.060 0.00 0.888 0.052
#> GSM381252 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM381254 1 0.0921 0.963 0.972 0.00 0.028 0.000
#> GSM381256 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM381257 3 0.2926 0.922 0.048 0.00 0.896 0.056
#> GSM381259 1 0.0469 0.980 0.988 0.00 0.012 0.000
#> GSM381260 3 0.3323 0.923 0.064 0.00 0.876 0.060
#> GSM381261 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM381263 3 0.0921 0.936 0.028 0.00 0.972 0.000
#> GSM381265 1 0.0921 0.963 0.972 0.00 0.028 0.000
#> GSM381268 3 0.0817 0.936 0.024 0.00 0.976 0.000
#> GSM381270 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM381271 3 0.1042 0.933 0.020 0.00 0.972 0.008
#> GSM381275 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM381279 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM381195 1 0.0000 0.988 1.000 0.00 0.000 0.000
#> GSM381196 3 0.3164 0.925 0.064 0.00 0.884 0.052
#> GSM381198 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM381200 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM381201 3 0.0524 0.928 0.004 0.00 0.988 0.008
#> GSM381203 3 0.3312 0.921 0.072 0.00 0.876 0.052
#> GSM381204 1 0.0188 0.989 0.996 0.00 0.004 0.000
#> GSM381209 1 0.0188 0.989 0.996 0.00 0.004 0.000
#> GSM381212 1 0.0188 0.989 0.996 0.00 0.004 0.000
#> GSM381213 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM381214 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM381216 3 0.4462 0.879 0.064 0.00 0.804 0.132
#> GSM381225 3 0.2647 0.889 0.000 0.00 0.880 0.120
#> GSM381231 3 0.1256 0.935 0.028 0.00 0.964 0.008
#> GSM381235 3 0.3453 0.918 0.080 0.00 0.868 0.052
#> GSM381237 1 0.0469 0.980 0.988 0.00 0.012 0.000
#> GSM381241 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM381243 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM381245 1 0.0000 0.988 1.000 0.00 0.000 0.000
#> GSM381246 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM381251 3 0.0524 0.928 0.004 0.00 0.988 0.008
#> GSM381264 1 0.0336 0.983 0.992 0.00 0.008 0.000
#> GSM381206 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM381217 3 0.3667 0.912 0.088 0.00 0.856 0.056
#> GSM381218 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM381226 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM381227 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM381228 3 0.1256 0.935 0.028 0.00 0.964 0.008
#> GSM381236 3 0.1975 0.924 0.016 0.00 0.936 0.048
#> GSM381244 3 0.3239 0.910 0.068 0.00 0.880 0.052
#> GSM381272 3 0.0524 0.928 0.004 0.00 0.988 0.008
#> GSM381277 1 0.0188 0.989 0.996 0.00 0.004 0.000
#> GSM381278 3 0.1975 0.924 0.016 0.00 0.936 0.048
#> GSM381197 3 0.0524 0.928 0.004 0.00 0.988 0.008
#> GSM381202 3 0.4462 0.879 0.064 0.00 0.804 0.132
#> GSM381207 1 0.1388 0.958 0.960 0.00 0.012 0.028
#> GSM381208 4 0.2921 1.000 0.000 0.14 0.000 0.860
#> GSM381210 1 0.0188 0.989 0.996 0.00 0.004 0.000
#> GSM381215 3 0.3009 0.925 0.056 0.00 0.892 0.052
#> GSM381219 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM381221 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM381223 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM381229 3 0.1975 0.924 0.016 0.00 0.936 0.048
#> GSM381230 1 0.0000 0.988 1.000 0.00 0.000 0.000
#> GSM381233 1 0.0188 0.989 0.996 0.00 0.004 0.000
#> GSM381234 1 0.0188 0.989 0.996 0.00 0.004 0.000
#> GSM381238 3 0.2222 0.934 0.060 0.00 0.924 0.016
#> GSM381239 3 0.3071 0.923 0.068 0.00 0.888 0.044
#> GSM381242 3 0.3617 0.918 0.064 0.00 0.860 0.076
#> GSM381247 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM381248 1 0.0188 0.989 0.996 0.00 0.004 0.000
#> GSM381249 1 0.0188 0.989 0.996 0.00 0.004 0.000
#> GSM381253 3 0.3312 0.919 0.072 0.00 0.876 0.052
#> GSM381255 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM381258 3 0.1256 0.935 0.028 0.00 0.964 0.008
#> GSM381262 3 0.1256 0.935 0.028 0.00 0.964 0.008
#> GSM381266 3 0.1305 0.922 0.004 0.00 0.960 0.036
#> GSM381267 4 0.2921 1.000 0.000 0.14 0.000 0.860
#> GSM381269 3 0.2660 0.923 0.036 0.00 0.908 0.056
#> GSM381273 3 0.1474 0.914 0.000 0.00 0.948 0.052
#> GSM381274 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM381276 3 0.3164 0.925 0.064 0.00 0.884 0.052
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM381194 3 0.4659 -0.427 0.000 0.000 0.496 0.492 0.012
#> GSM381199 2 0.0000 0.931 0.000 1.000 0.000 0.000 0.000
#> GSM381205 2 0.0000 0.931 0.000 1.000 0.000 0.000 0.000
#> GSM381211 2 0.0000 0.931 0.000 1.000 0.000 0.000 0.000
#> GSM381220 2 0.1386 0.918 0.000 0.952 0.000 0.032 0.016
#> GSM381222 1 0.0290 0.983 0.992 0.000 0.008 0.000 0.000
#> GSM381224 1 0.0000 0.987 1.000 0.000 0.000 0.000 0.000
#> GSM381232 3 0.4656 -0.392 0.000 0.000 0.508 0.480 0.012
#> GSM381240 1 0.0000 0.987 1.000 0.000 0.000 0.000 0.000
#> GSM381250 3 0.1121 0.679 0.000 0.000 0.956 0.044 0.000
#> GSM381252 2 0.0000 0.931 0.000 1.000 0.000 0.000 0.000
#> GSM381254 1 0.0771 0.973 0.976 0.000 0.004 0.020 0.000
#> GSM381256 2 0.0404 0.928 0.000 0.988 0.000 0.000 0.012
#> GSM381257 3 0.2198 0.677 0.012 0.000 0.920 0.020 0.048
#> GSM381259 1 0.0510 0.979 0.984 0.000 0.016 0.000 0.000
#> GSM381260 3 0.1857 0.679 0.004 0.000 0.928 0.008 0.060
#> GSM381261 2 0.3656 0.827 0.000 0.784 0.000 0.196 0.020
#> GSM381263 3 0.4637 -0.290 0.000 0.000 0.536 0.452 0.012
#> GSM381265 1 0.1018 0.968 0.968 0.000 0.016 0.016 0.000
#> GSM381268 3 0.3949 0.313 0.004 0.000 0.696 0.300 0.000
#> GSM381270 2 0.3318 0.845 0.000 0.808 0.000 0.180 0.012
#> GSM381271 4 0.4126 0.774 0.000 0.000 0.380 0.620 0.000
#> GSM381275 2 0.3656 0.826 0.000 0.784 0.000 0.196 0.020
#> GSM381279 2 0.3355 0.843 0.000 0.804 0.000 0.184 0.012
#> GSM381195 1 0.0000 0.987 1.000 0.000 0.000 0.000 0.000
#> GSM381196 3 0.0404 0.688 0.012 0.000 0.988 0.000 0.000
#> GSM381198 2 0.0000 0.931 0.000 1.000 0.000 0.000 0.000
#> GSM381200 2 0.0000 0.931 0.000 1.000 0.000 0.000 0.000
#> GSM381201 4 0.3508 0.842 0.000 0.000 0.252 0.748 0.000
#> GSM381203 3 0.0609 0.685 0.020 0.000 0.980 0.000 0.000
#> GSM381204 1 0.0510 0.978 0.984 0.000 0.016 0.000 0.000
#> GSM381209 1 0.0000 0.987 1.000 0.000 0.000 0.000 0.000
#> GSM381212 1 0.0000 0.987 1.000 0.000 0.000 0.000 0.000
#> GSM381213 2 0.3318 0.845 0.000 0.808 0.000 0.180 0.012
#> GSM381214 2 0.0000 0.931 0.000 1.000 0.000 0.000 0.000
#> GSM381216 3 0.2597 0.660 0.004 0.000 0.896 0.040 0.060
#> GSM381225 3 0.5047 -0.377 0.000 0.000 0.496 0.472 0.032
#> GSM381231 4 0.4088 0.795 0.000 0.000 0.368 0.632 0.000
#> GSM381235 3 0.0404 0.688 0.012 0.000 0.988 0.000 0.000
#> GSM381237 1 0.0000 0.987 1.000 0.000 0.000 0.000 0.000
#> GSM381241 2 0.0000 0.931 0.000 1.000 0.000 0.000 0.000
#> GSM381243 2 0.1597 0.913 0.000 0.940 0.000 0.048 0.012
#> GSM381245 1 0.0000 0.987 1.000 0.000 0.000 0.000 0.000
#> GSM381246 2 0.0000 0.931 0.000 1.000 0.000 0.000 0.000
#> GSM381251 4 0.3508 0.842 0.000 0.000 0.252 0.748 0.000
#> GSM381264 1 0.0000 0.987 1.000 0.000 0.000 0.000 0.000
#> GSM381206 2 0.0000 0.931 0.000 1.000 0.000 0.000 0.000
#> GSM381217 3 0.0671 0.687 0.016 0.000 0.980 0.000 0.004
#> GSM381218 2 0.0000 0.931 0.000 1.000 0.000 0.000 0.000
#> GSM381226 2 0.0000 0.931 0.000 1.000 0.000 0.000 0.000
#> GSM381227 2 0.0703 0.925 0.000 0.976 0.000 0.024 0.000
#> GSM381228 4 0.4387 0.793 0.012 0.000 0.348 0.640 0.000
#> GSM381236 3 0.4262 0.387 0.012 0.000 0.696 0.288 0.004
#> GSM381244 3 0.3805 0.489 0.184 0.000 0.784 0.032 0.000
#> GSM381272 4 0.3730 0.847 0.000 0.000 0.288 0.712 0.000
#> GSM381277 1 0.0404 0.980 0.988 0.000 0.012 0.000 0.000
#> GSM381278 4 0.4803 0.358 0.012 0.000 0.488 0.496 0.004
#> GSM381197 4 0.3612 0.835 0.000 0.000 0.268 0.732 0.000
#> GSM381202 3 0.2597 0.660 0.004 0.000 0.896 0.040 0.060
#> GSM381207 1 0.1792 0.898 0.916 0.000 0.084 0.000 0.000
#> GSM381208 5 0.1872 1.000 0.000 0.052 0.000 0.020 0.928
#> GSM381210 1 0.0290 0.984 0.992 0.000 0.008 0.000 0.000
#> GSM381215 3 0.0162 0.687 0.004 0.000 0.996 0.000 0.000
#> GSM381219 2 0.0000 0.931 0.000 1.000 0.000 0.000 0.000
#> GSM381221 2 0.0000 0.931 0.000 1.000 0.000 0.000 0.000
#> GSM381223 2 0.3282 0.840 0.000 0.804 0.000 0.188 0.008
#> GSM381229 4 0.4251 0.823 0.012 0.000 0.316 0.672 0.000
#> GSM381230 1 0.0000 0.987 1.000 0.000 0.000 0.000 0.000
#> GSM381233 1 0.0000 0.987 1.000 0.000 0.000 0.000 0.000
#> GSM381234 1 0.0162 0.985 0.996 0.000 0.004 0.000 0.000
#> GSM381238 3 0.4016 0.420 0.012 0.000 0.716 0.272 0.000
#> GSM381239 3 0.4103 0.490 0.012 0.000 0.748 0.228 0.012
#> GSM381242 3 0.1857 0.679 0.004 0.000 0.928 0.008 0.060
#> GSM381247 2 0.3318 0.845 0.000 0.808 0.000 0.180 0.012
#> GSM381248 1 0.0290 0.983 0.992 0.000 0.008 0.000 0.000
#> GSM381249 1 0.0609 0.976 0.980 0.000 0.020 0.000 0.000
#> GSM381253 3 0.0290 0.688 0.008 0.000 0.992 0.000 0.000
#> GSM381255 2 0.0404 0.929 0.000 0.988 0.000 0.012 0.000
#> GSM381258 3 0.4653 -0.366 0.000 0.000 0.516 0.472 0.012
#> GSM381262 3 0.4597 -0.191 0.012 0.000 0.564 0.424 0.000
#> GSM381266 4 0.3395 0.834 0.000 0.000 0.236 0.764 0.000
#> GSM381267 5 0.1872 1.000 0.000 0.052 0.000 0.020 0.928
#> GSM381269 3 0.3494 0.650 0.012 0.000 0.848 0.084 0.056
#> GSM381273 4 0.3395 0.834 0.000 0.000 0.236 0.764 0.000
#> GSM381274 2 0.3745 0.823 0.000 0.780 0.000 0.196 0.024
#> GSM381276 3 0.0404 0.688 0.012 0.000 0.988 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM381194 3 0.5548 -0.1841 0.000 0.000 0.464 0.400 0.136 0.000
#> GSM381199 2 0.0000 0.7865 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381205 2 0.0000 0.7865 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381211 2 0.0000 0.7865 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381220 2 0.3371 0.2400 0.000 0.708 0.000 0.000 0.292 0.000
#> GSM381222 1 0.0547 0.9654 0.980 0.000 0.000 0.020 0.000 0.000
#> GSM381224 1 0.0000 0.9787 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381232 3 0.5271 0.1952 0.000 0.000 0.576 0.292 0.132 0.000
#> GSM381240 1 0.0000 0.9787 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381250 3 0.2234 0.6995 0.000 0.000 0.872 0.124 0.000 0.004
#> GSM381252 2 0.0000 0.7865 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381254 1 0.0146 0.9772 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM381256 2 0.2823 0.4771 0.000 0.796 0.000 0.000 0.204 0.000
#> GSM381257 3 0.2698 0.6971 0.008 0.000 0.860 0.120 0.008 0.004
#> GSM381259 1 0.1267 0.9301 0.940 0.000 0.000 0.060 0.000 0.000
#> GSM381260 3 0.2495 0.6717 0.000 0.000 0.892 0.060 0.032 0.016
#> GSM381261 5 0.3515 0.8721 0.000 0.324 0.000 0.000 0.676 0.000
#> GSM381263 3 0.4552 0.4764 0.000 0.000 0.700 0.172 0.128 0.000
#> GSM381265 1 0.1444 0.9189 0.928 0.000 0.000 0.072 0.000 0.000
#> GSM381268 3 0.3101 0.6636 0.000 0.000 0.756 0.244 0.000 0.000
#> GSM381270 2 0.3867 -0.5550 0.000 0.512 0.000 0.000 0.488 0.000
#> GSM381271 4 0.3563 0.7866 0.000 0.000 0.092 0.800 0.108 0.000
#> GSM381275 5 0.3706 0.8158 0.000 0.380 0.000 0.000 0.620 0.000
#> GSM381279 5 0.3817 0.7177 0.000 0.432 0.000 0.000 0.568 0.000
#> GSM381195 1 0.0000 0.9787 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381196 3 0.1957 0.7012 0.000 0.000 0.888 0.112 0.000 0.000
#> GSM381198 2 0.0000 0.7865 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381200 2 0.0000 0.7865 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381201 4 0.1814 0.8092 0.000 0.000 0.100 0.900 0.000 0.000
#> GSM381203 3 0.5293 0.6254 0.036 0.000 0.672 0.152 0.140 0.000
#> GSM381204 1 0.0000 0.9787 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381209 1 0.0000 0.9787 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381212 1 0.0000 0.9787 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381213 2 0.3867 -0.5550 0.000 0.512 0.000 0.000 0.488 0.000
#> GSM381214 2 0.0000 0.7865 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381216 3 0.2649 0.6685 0.000 0.000 0.884 0.052 0.048 0.016
#> GSM381225 3 0.5938 0.5605 0.000 0.000 0.620 0.164 0.140 0.076
#> GSM381231 4 0.3602 0.7844 0.000 0.000 0.088 0.796 0.116 0.000
#> GSM381235 3 0.5746 0.5987 0.088 0.000 0.648 0.128 0.136 0.000
#> GSM381237 1 0.0000 0.9787 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381241 2 0.0000 0.7865 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381243 2 0.3647 -0.0513 0.000 0.640 0.000 0.000 0.360 0.000
#> GSM381245 1 0.0000 0.9787 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381246 2 0.0146 0.7828 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM381251 4 0.1616 0.8066 0.000 0.000 0.048 0.932 0.000 0.020
#> GSM381264 1 0.0000 0.9787 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381206 2 0.0000 0.7865 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381217 3 0.2968 0.6886 0.052 0.000 0.852 0.092 0.000 0.004
#> GSM381218 2 0.0000 0.7865 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381226 2 0.0000 0.7865 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381227 2 0.0937 0.7461 0.000 0.960 0.000 0.000 0.040 0.000
#> GSM381228 4 0.5879 0.7072 0.000 0.000 0.084 0.612 0.216 0.088
#> GSM381236 3 0.5735 0.5437 0.000 0.000 0.632 0.196 0.104 0.068
#> GSM381244 3 0.5127 0.3466 0.384 0.000 0.528 0.088 0.000 0.000
#> GSM381272 4 0.3196 0.7939 0.000 0.000 0.064 0.828 0.108 0.000
#> GSM381277 1 0.1531 0.9188 0.928 0.000 0.004 0.068 0.000 0.000
#> GSM381278 3 0.6352 0.4193 0.000 0.000 0.540 0.252 0.140 0.068
#> GSM381197 4 0.2662 0.7859 0.000 0.000 0.152 0.840 0.004 0.004
#> GSM381202 3 0.2775 0.6654 0.000 0.000 0.876 0.052 0.056 0.016
#> GSM381207 1 0.2066 0.8931 0.904 0.000 0.024 0.072 0.000 0.000
#> GSM381208 6 0.0458 1.0000 0.000 0.016 0.000 0.000 0.000 0.984
#> GSM381210 1 0.0000 0.9787 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381215 3 0.2416 0.6919 0.000 0.000 0.844 0.156 0.000 0.000
#> GSM381219 2 0.0000 0.7865 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381221 2 0.0000 0.7865 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM381223 2 0.3810 -0.3533 0.000 0.572 0.000 0.000 0.428 0.000
#> GSM381229 4 0.5694 0.6344 0.000 0.000 0.224 0.624 0.084 0.068
#> GSM381230 1 0.0000 0.9787 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381233 1 0.0000 0.9787 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM381234 1 0.0146 0.9772 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM381238 3 0.5780 0.5646 0.000 0.000 0.636 0.156 0.140 0.068
#> GSM381239 3 0.5733 0.5721 0.000 0.000 0.644 0.144 0.140 0.072
#> GSM381242 3 0.2649 0.6680 0.000 0.000 0.884 0.052 0.048 0.016
#> GSM381247 2 0.3867 -0.5550 0.000 0.512 0.000 0.000 0.488 0.000
#> GSM381248 1 0.0146 0.9772 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM381249 1 0.0146 0.9772 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM381253 3 0.3125 0.6824 0.080 0.000 0.836 0.084 0.000 0.000
#> GSM381255 2 0.0260 0.7800 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM381258 3 0.4771 0.4088 0.000 0.000 0.664 0.220 0.116 0.000
#> GSM381262 3 0.4525 0.6587 0.000 0.000 0.684 0.228 0.088 0.000
#> GSM381266 4 0.3118 0.7908 0.000 0.000 0.092 0.836 0.000 0.072
#> GSM381267 6 0.0458 1.0000 0.000 0.016 0.000 0.000 0.000 0.984
#> GSM381269 3 0.2089 0.6833 0.004 0.000 0.908 0.072 0.012 0.004
#> GSM381273 4 0.3426 0.7792 0.000 0.000 0.124 0.808 0.000 0.068
#> GSM381274 5 0.3464 0.8649 0.000 0.312 0.000 0.000 0.688 0.000
#> GSM381276 3 0.3785 0.6813 0.004 0.000 0.780 0.152 0.064 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 other(p) k
#> ATC:mclust 86 0.744 2
#> ATC:mclust 80 0.591 3
#> ATC:mclust 86 0.463 4
#> ATC:mclust 74 0.615 5
#> ATC:mclust 73 0.348 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 86 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4528 0.548 0.548
#> 3 3 0.873 0.885 0.951 0.4727 0.778 0.595
#> 4 4 0.758 0.752 0.844 0.0831 0.904 0.718
#> 5 5 0.745 0.658 0.819 0.0407 0.879 0.617
#> 6 6 0.657 0.630 0.742 0.0351 0.951 0.817
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
#> GSM381194 1 0 1 1 0
#> GSM381199 2 0 1 0 1
#> GSM381205 2 0 1 0 1
#> GSM381211 2 0 1 0 1
#> GSM381220 2 0 1 0 1
#> GSM381222 1 0 1 1 0
#> GSM381224 1 0 1 1 0
#> GSM381232 1 0 1 1 0
#> GSM381240 1 0 1 1 0
#> GSM381250 1 0 1 1 0
#> GSM381252 2 0 1 0 1
#> GSM381254 1 0 1 1 0
#> GSM381256 2 0 1 0 1
#> GSM381257 1 0 1 1 0
#> GSM381259 1 0 1 1 0
#> GSM381260 1 0 1 1 0
#> GSM381261 2 0 1 0 1
#> GSM381263 1 0 1 1 0
#> GSM381265 1 0 1 1 0
#> GSM381268 1 0 1 1 0
#> GSM381270 2 0 1 0 1
#> GSM381271 1 0 1 1 0
#> GSM381275 2 0 1 0 1
#> GSM381279 2 0 1 0 1
#> GSM381195 1 0 1 1 0
#> GSM381196 1 0 1 1 0
#> GSM381198 2 0 1 0 1
#> GSM381200 2 0 1 0 1
#> GSM381201 1 0 1 1 0
#> GSM381203 1 0 1 1 0
#> GSM381204 1 0 1 1 0
#> GSM381209 1 0 1 1 0
#> GSM381212 1 0 1 1 0
#> GSM381213 2 0 1 0 1
#> GSM381214 2 0 1 0 1
#> GSM381216 1 0 1 1 0
#> GSM381225 1 0 1 1 0
#> GSM381231 1 0 1 1 0
#> GSM381235 1 0 1 1 0
#> GSM381237 1 0 1 1 0
#> GSM381241 2 0 1 0 1
#> GSM381243 2 0 1 0 1
#> GSM381245 1 0 1 1 0
#> GSM381246 2 0 1 0 1
#> GSM381251 1 0 1 1 0
#> GSM381264 1 0 1 1 0
#> GSM381206 2 0 1 0 1
#> GSM381217 1 0 1 1 0
#> GSM381218 2 0 1 0 1
#> GSM381226 2 0 1 0 1
#> GSM381227 2 0 1 0 1
#> GSM381228 1 0 1 1 0
#> GSM381236 1 0 1 1 0
#> GSM381244 1 0 1 1 0
#> GSM381272 1 0 1 1 0
#> GSM381277 1 0 1 1 0
#> GSM381278 1 0 1 1 0
#> GSM381197 1 0 1 1 0
#> GSM381202 1 0 1 1 0
#> GSM381207 1 0 1 1 0
#> GSM381208 2 0 1 0 1
#> GSM381210 1 0 1 1 0
#> GSM381215 1 0 1 1 0
#> GSM381219 2 0 1 0 1
#> GSM381221 2 0 1 0 1
#> GSM381223 2 0 1 0 1
#> GSM381229 1 0 1 1 0
#> GSM381230 1 0 1 1 0
#> GSM381233 1 0 1 1 0
#> GSM381234 1 0 1 1 0
#> GSM381238 1 0 1 1 0
#> GSM381239 1 0 1 1 0
#> GSM381242 1 0 1 1 0
#> GSM381247 2 0 1 0 1
#> GSM381248 1 0 1 1 0
#> GSM381249 1 0 1 1 0
#> GSM381253 1 0 1 1 0
#> GSM381255 2 0 1 0 1
#> GSM381258 1 0 1 1 0
#> GSM381262 1 0 1 1 0
#> GSM381266 1 0 1 1 0
#> GSM381267 2 0 1 0 1
#> GSM381269 1 0 1 1 0
#> GSM381273 1 0 1 1 0
#> GSM381274 2 0 1 0 1
#> GSM381276 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM381194 3 0.0000 0.89863 0.000 0.0 1.000
#> GSM381199 2 0.0000 0.99654 0.000 1.0 0.000
#> GSM381205 2 0.0000 0.99654 0.000 1.0 0.000
#> GSM381211 2 0.0000 0.99654 0.000 1.0 0.000
#> GSM381220 2 0.0000 0.99654 0.000 1.0 0.000
#> GSM381222 1 0.0000 0.92871 1.000 0.0 0.000
#> GSM381224 1 0.0000 0.92871 1.000 0.0 0.000
#> GSM381232 3 0.0000 0.89863 0.000 0.0 1.000
#> GSM381240 1 0.0000 0.92871 1.000 0.0 0.000
#> GSM381250 3 0.2878 0.83921 0.096 0.0 0.904
#> GSM381252 2 0.0000 0.99654 0.000 1.0 0.000
#> GSM381254 1 0.0237 0.92757 0.996 0.0 0.004
#> GSM381256 2 0.0000 0.99654 0.000 1.0 0.000
#> GSM381257 1 0.4555 0.76721 0.800 0.0 0.200
#> GSM381259 1 0.0000 0.92871 1.000 0.0 0.000
#> GSM381260 3 0.6309 -0.00269 0.500 0.0 0.500
#> GSM381261 2 0.0000 0.99654 0.000 1.0 0.000
#> GSM381263 3 0.0237 0.89841 0.004 0.0 0.996
#> GSM381265 1 0.0237 0.92757 0.996 0.0 0.004
#> GSM381268 3 0.0424 0.89744 0.008 0.0 0.992
#> GSM381270 2 0.0000 0.99654 0.000 1.0 0.000
#> GSM381271 3 0.0000 0.89863 0.000 0.0 1.000
#> GSM381275 2 0.0000 0.99654 0.000 1.0 0.000
#> GSM381279 2 0.0000 0.99654 0.000 1.0 0.000
#> GSM381195 1 0.0237 0.92757 0.996 0.0 0.004
#> GSM381196 3 0.2878 0.83935 0.096 0.0 0.904
#> GSM381198 2 0.0000 0.99654 0.000 1.0 0.000
#> GSM381200 2 0.0000 0.99654 0.000 1.0 0.000
#> GSM381201 3 0.0000 0.89863 0.000 0.0 1.000
#> GSM381203 3 0.6307 0.04858 0.488 0.0 0.512
#> GSM381204 1 0.0000 0.92871 1.000 0.0 0.000
#> GSM381209 1 0.0000 0.92871 1.000 0.0 0.000
#> GSM381212 1 0.0000 0.92871 1.000 0.0 0.000
#> GSM381213 2 0.0000 0.99654 0.000 1.0 0.000
#> GSM381214 2 0.0000 0.99654 0.000 1.0 0.000
#> GSM381216 1 0.4504 0.77274 0.804 0.0 0.196
#> GSM381225 3 0.0747 0.89421 0.016 0.0 0.984
#> GSM381231 3 0.0000 0.89863 0.000 0.0 1.000
#> GSM381235 1 0.4504 0.77252 0.804 0.0 0.196
#> GSM381237 1 0.0000 0.92871 1.000 0.0 0.000
#> GSM381241 2 0.0000 0.99654 0.000 1.0 0.000
#> GSM381243 2 0.0000 0.99654 0.000 1.0 0.000
#> GSM381245 1 0.0000 0.92871 1.000 0.0 0.000
#> GSM381246 2 0.0000 0.99654 0.000 1.0 0.000
#> GSM381251 3 0.0000 0.89863 0.000 0.0 1.000
#> GSM381264 1 0.0000 0.92871 1.000 0.0 0.000
#> GSM381206 2 0.0000 0.99654 0.000 1.0 0.000
#> GSM381217 1 0.3551 0.84122 0.868 0.0 0.132
#> GSM381218 2 0.0000 0.99654 0.000 1.0 0.000
#> GSM381226 2 0.0000 0.99654 0.000 1.0 0.000
#> GSM381227 2 0.0000 0.99654 0.000 1.0 0.000
#> GSM381228 3 0.0000 0.89863 0.000 0.0 1.000
#> GSM381236 3 0.0747 0.89440 0.016 0.0 0.984
#> GSM381244 1 0.1860 0.90192 0.948 0.0 0.052
#> GSM381272 3 0.0000 0.89863 0.000 0.0 1.000
#> GSM381277 1 0.0000 0.92871 1.000 0.0 0.000
#> GSM381278 3 0.0000 0.89863 0.000 0.0 1.000
#> GSM381197 3 0.0747 0.89404 0.016 0.0 0.984
#> GSM381202 1 0.4062 0.80996 0.836 0.0 0.164
#> GSM381207 1 0.1643 0.90678 0.956 0.0 0.044
#> GSM381208 2 0.0000 0.99654 0.000 1.0 0.000
#> GSM381210 1 0.0000 0.92871 1.000 0.0 0.000
#> GSM381215 3 0.5098 0.65478 0.248 0.0 0.752
#> GSM381219 2 0.0000 0.99654 0.000 1.0 0.000
#> GSM381221 2 0.0000 0.99654 0.000 1.0 0.000
#> GSM381223 2 0.0000 0.99654 0.000 1.0 0.000
#> GSM381229 3 0.0000 0.89863 0.000 0.0 1.000
#> GSM381230 1 0.0000 0.92871 1.000 0.0 0.000
#> GSM381233 1 0.0000 0.92871 1.000 0.0 0.000
#> GSM381234 1 0.0000 0.92871 1.000 0.0 0.000
#> GSM381238 3 0.2261 0.86179 0.068 0.0 0.932
#> GSM381239 3 0.5760 0.51267 0.328 0.0 0.672
#> GSM381242 1 0.5905 0.46749 0.648 0.0 0.352
#> GSM381247 2 0.0000 0.99654 0.000 1.0 0.000
#> GSM381248 1 0.0000 0.92871 1.000 0.0 0.000
#> GSM381249 1 0.0000 0.92871 1.000 0.0 0.000
#> GSM381253 1 0.5431 0.62469 0.716 0.0 0.284
#> GSM381255 2 0.0000 0.99654 0.000 1.0 0.000
#> GSM381258 3 0.0237 0.89841 0.004 0.0 0.996
#> GSM381262 3 0.0237 0.89841 0.004 0.0 0.996
#> GSM381266 3 0.0000 0.89863 0.000 0.0 1.000
#> GSM381267 2 0.2959 0.89357 0.000 0.9 0.100
#> GSM381269 1 0.3752 0.83025 0.856 0.0 0.144
#> GSM381273 3 0.0000 0.89863 0.000 0.0 1.000
#> GSM381274 2 0.0000 0.99654 0.000 1.0 0.000
#> GSM381276 3 0.6252 0.21006 0.444 0.0 0.556
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM381194 3 0.5026 0.271 0.016 0.000 0.672 0.312
#> GSM381199 2 0.0188 0.976 0.000 0.996 0.004 0.000
#> GSM381205 2 0.0469 0.973 0.000 0.988 0.012 0.000
#> GSM381211 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM381220 2 0.0336 0.975 0.000 0.992 0.008 0.000
#> GSM381222 1 0.1474 0.858 0.948 0.000 0.052 0.000
#> GSM381224 1 0.2469 0.822 0.892 0.000 0.108 0.000
#> GSM381232 4 0.2662 0.755 0.016 0.000 0.084 0.900
#> GSM381240 1 0.1302 0.860 0.956 0.000 0.044 0.000
#> GSM381250 3 0.6586 0.221 0.088 0.000 0.544 0.368
#> GSM381252 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM381254 1 0.1356 0.838 0.960 0.000 0.032 0.008
#> GSM381256 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM381257 3 0.5781 0.280 0.484 0.000 0.488 0.028
#> GSM381259 1 0.2011 0.845 0.920 0.000 0.080 0.000
#> GSM381260 3 0.4932 0.664 0.240 0.000 0.728 0.032
#> GSM381261 2 0.1474 0.954 0.000 0.948 0.052 0.000
#> GSM381263 3 0.4804 0.554 0.072 0.000 0.780 0.148
#> GSM381265 1 0.1576 0.859 0.948 0.000 0.048 0.004
#> GSM381268 4 0.4599 0.715 0.016 0.000 0.248 0.736
#> GSM381270 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM381271 4 0.1042 0.768 0.008 0.000 0.020 0.972
#> GSM381275 2 0.1211 0.962 0.000 0.960 0.040 0.000
#> GSM381279 2 0.0707 0.972 0.000 0.980 0.020 0.000
#> GSM381195 1 0.1489 0.859 0.952 0.000 0.044 0.004
#> GSM381196 4 0.6400 0.283 0.068 0.000 0.408 0.524
#> GSM381198 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM381200 2 0.0336 0.976 0.000 0.992 0.008 0.000
#> GSM381201 4 0.4328 0.726 0.008 0.000 0.244 0.748
#> GSM381203 3 0.7389 0.460 0.212 0.000 0.516 0.272
#> GSM381204 1 0.3610 0.706 0.800 0.000 0.200 0.000
#> GSM381209 1 0.3074 0.774 0.848 0.000 0.152 0.000
#> GSM381212 1 0.1211 0.861 0.960 0.000 0.040 0.000
#> GSM381213 2 0.0707 0.972 0.000 0.980 0.020 0.000
#> GSM381214 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM381216 3 0.4567 0.655 0.244 0.000 0.740 0.016
#> GSM381225 4 0.4826 0.708 0.020 0.000 0.264 0.716
#> GSM381231 4 0.0592 0.763 0.000 0.000 0.016 0.984
#> GSM381235 3 0.6009 0.332 0.468 0.000 0.492 0.040
#> GSM381237 1 0.1389 0.859 0.952 0.000 0.048 0.000
#> GSM381241 2 0.0188 0.976 0.000 0.996 0.004 0.000
#> GSM381243 2 0.0188 0.976 0.000 0.996 0.004 0.000
#> GSM381245 1 0.1474 0.822 0.948 0.000 0.052 0.000
#> GSM381246 2 0.0921 0.969 0.000 0.972 0.028 0.000
#> GSM381251 4 0.4456 0.701 0.004 0.000 0.280 0.716
#> GSM381264 1 0.0188 0.855 0.996 0.000 0.004 0.000
#> GSM381206 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM381217 3 0.5047 0.616 0.316 0.000 0.668 0.016
#> GSM381218 2 0.0188 0.976 0.000 0.996 0.004 0.000
#> GSM381226 2 0.0188 0.977 0.000 0.996 0.004 0.000
#> GSM381227 2 0.0188 0.977 0.000 0.996 0.004 0.000
#> GSM381228 4 0.0188 0.757 0.000 0.000 0.004 0.996
#> GSM381236 4 0.1452 0.752 0.036 0.000 0.008 0.956
#> GSM381244 1 0.2635 0.834 0.904 0.000 0.076 0.020
#> GSM381272 4 0.1042 0.768 0.008 0.000 0.020 0.972
#> GSM381277 1 0.1356 0.838 0.960 0.000 0.032 0.008
#> GSM381278 4 0.1661 0.772 0.004 0.000 0.052 0.944
#> GSM381197 3 0.6207 -0.129 0.052 0.000 0.496 0.452
#> GSM381202 3 0.4748 0.639 0.268 0.000 0.716 0.016
#> GSM381207 1 0.0895 0.850 0.976 0.000 0.004 0.020
#> GSM381208 2 0.4261 0.819 0.000 0.820 0.112 0.068
#> GSM381210 1 0.3873 0.655 0.772 0.000 0.228 0.000
#> GSM381215 4 0.7066 0.286 0.152 0.000 0.304 0.544
#> GSM381219 2 0.0336 0.976 0.000 0.992 0.008 0.000
#> GSM381221 2 0.0000 0.977 0.000 1.000 0.000 0.000
#> GSM381223 2 0.0921 0.969 0.000 0.972 0.028 0.000
#> GSM381229 4 0.3610 0.747 0.000 0.000 0.200 0.800
#> GSM381230 1 0.0336 0.849 0.992 0.000 0.008 0.000
#> GSM381233 1 0.0592 0.858 0.984 0.000 0.016 0.000
#> GSM381234 1 0.2466 0.781 0.900 0.000 0.096 0.004
#> GSM381238 4 0.1452 0.752 0.036 0.000 0.008 0.956
#> GSM381239 4 0.3441 0.651 0.120 0.000 0.024 0.856
#> GSM381242 3 0.5137 0.616 0.296 0.000 0.680 0.024
#> GSM381247 2 0.0336 0.976 0.000 0.992 0.008 0.000
#> GSM381248 1 0.3166 0.752 0.868 0.000 0.116 0.016
#> GSM381249 1 0.4679 0.365 0.648 0.000 0.352 0.000
#> GSM381253 1 0.7359 -0.155 0.508 0.000 0.188 0.304
#> GSM381255 2 0.0336 0.976 0.000 0.992 0.008 0.000
#> GSM381258 3 0.5632 0.542 0.092 0.000 0.712 0.196
#> GSM381262 4 0.4978 0.628 0.012 0.000 0.324 0.664
#> GSM381266 4 0.3401 0.766 0.008 0.000 0.152 0.840
#> GSM381267 2 0.5613 0.682 0.000 0.724 0.120 0.156
#> GSM381269 3 0.5496 0.535 0.372 0.000 0.604 0.024
#> GSM381273 4 0.2589 0.769 0.000 0.000 0.116 0.884
#> GSM381274 2 0.1118 0.965 0.000 0.964 0.036 0.000
#> GSM381276 4 0.7142 0.132 0.324 0.000 0.152 0.524
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM381194 3 0.5283 0.5780 0.048 0.000 0.712 0.048 0.192
#> GSM381199 2 0.0794 0.9665 0.000 0.972 0.000 0.000 0.028
#> GSM381205 2 0.1981 0.9433 0.000 0.920 0.000 0.016 0.064
#> GSM381211 2 0.0703 0.9672 0.000 0.976 0.000 0.000 0.024
#> GSM381220 2 0.1364 0.9675 0.000 0.952 0.000 0.012 0.036
#> GSM381222 1 0.0613 0.6525 0.984 0.000 0.004 0.004 0.008
#> GSM381224 1 0.1408 0.6295 0.948 0.000 0.008 0.000 0.044
#> GSM381232 4 0.2238 0.9533 0.020 0.000 0.064 0.912 0.004
#> GSM381240 1 0.0566 0.6517 0.984 0.000 0.000 0.004 0.012
#> GSM381250 3 0.4330 0.6389 0.116 0.000 0.796 0.024 0.064
#> GSM381252 2 0.0404 0.9692 0.000 0.988 0.000 0.000 0.012
#> GSM381254 1 0.3875 0.5725 0.804 0.000 0.000 0.072 0.124
#> GSM381256 2 0.0290 0.9696 0.000 0.992 0.000 0.000 0.008
#> GSM381257 1 0.6502 -0.4886 0.560 0.000 0.160 0.020 0.260
#> GSM381259 1 0.1205 0.6403 0.956 0.000 0.000 0.004 0.040
#> GSM381260 5 0.6990 0.8127 0.400 0.000 0.172 0.024 0.404
#> GSM381261 2 0.2563 0.9096 0.000 0.872 0.000 0.008 0.120
#> GSM381263 3 0.7281 -0.5253 0.228 0.000 0.392 0.028 0.352
#> GSM381265 1 0.0727 0.6527 0.980 0.000 0.004 0.004 0.012
#> GSM381268 3 0.3321 0.7265 0.040 0.000 0.856 0.092 0.012
#> GSM381270 2 0.1018 0.9689 0.000 0.968 0.000 0.016 0.016
#> GSM381271 4 0.2054 0.9577 0.008 0.000 0.072 0.916 0.004
#> GSM381275 2 0.1830 0.9498 0.000 0.924 0.000 0.008 0.068
#> GSM381279 2 0.1522 0.9615 0.000 0.944 0.000 0.012 0.044
#> GSM381195 1 0.1828 0.6461 0.936 0.000 0.028 0.004 0.032
#> GSM381196 3 0.4474 0.6134 0.140 0.000 0.780 0.024 0.056
#> GSM381198 2 0.1725 0.9520 0.000 0.936 0.000 0.020 0.044
#> GSM381200 2 0.0955 0.9690 0.000 0.968 0.000 0.004 0.028
#> GSM381201 3 0.2464 0.7272 0.016 0.000 0.888 0.096 0.000
#> GSM381203 3 0.3649 0.6288 0.152 0.000 0.808 0.000 0.040
#> GSM381204 1 0.3419 0.4455 0.804 0.000 0.016 0.000 0.180
#> GSM381209 1 0.2011 0.5979 0.908 0.000 0.004 0.000 0.088
#> GSM381212 1 0.0703 0.6515 0.976 0.000 0.000 0.000 0.024
#> GSM381213 2 0.1364 0.9640 0.000 0.952 0.000 0.012 0.036
#> GSM381214 2 0.0404 0.9698 0.000 0.988 0.000 0.000 0.012
#> GSM381216 5 0.6560 0.8108 0.416 0.000 0.140 0.012 0.432
#> GSM381225 3 0.2507 0.7085 0.028 0.000 0.908 0.020 0.044
#> GSM381231 4 0.1830 0.9590 0.008 0.000 0.068 0.924 0.000
#> GSM381235 3 0.4323 0.4854 0.240 0.000 0.728 0.004 0.028
#> GSM381237 1 0.0451 0.6532 0.988 0.000 0.000 0.004 0.008
#> GSM381241 2 0.0609 0.9677 0.000 0.980 0.000 0.000 0.020
#> GSM381243 2 0.1399 0.9678 0.000 0.952 0.000 0.020 0.028
#> GSM381245 1 0.3343 0.5756 0.812 0.000 0.000 0.016 0.172
#> GSM381246 2 0.1357 0.9618 0.000 0.948 0.000 0.004 0.048
#> GSM381251 3 0.1901 0.7273 0.012 0.000 0.928 0.056 0.004
#> GSM381264 1 0.0865 0.6515 0.972 0.000 0.000 0.004 0.024
#> GSM381206 2 0.1300 0.9621 0.000 0.956 0.000 0.016 0.028
#> GSM381217 1 0.6697 -0.7290 0.460 0.000 0.224 0.004 0.312
#> GSM381218 2 0.1043 0.9632 0.000 0.960 0.000 0.000 0.040
#> GSM381226 2 0.0000 0.9698 0.000 1.000 0.000 0.000 0.000
#> GSM381227 2 0.0912 0.9680 0.000 0.972 0.000 0.016 0.012
#> GSM381228 4 0.1831 0.9483 0.004 0.000 0.076 0.920 0.000
#> GSM381236 4 0.1893 0.9481 0.048 0.000 0.024 0.928 0.000
#> GSM381244 1 0.1949 0.6291 0.932 0.000 0.040 0.016 0.012
#> GSM381272 4 0.1990 0.9594 0.008 0.000 0.068 0.920 0.004
#> GSM381277 1 0.4290 0.5150 0.756 0.000 0.004 0.196 0.044
#> GSM381278 3 0.4904 0.5798 0.024 0.000 0.704 0.240 0.032
#> GSM381197 3 0.3064 0.7043 0.052 0.000 0.880 0.024 0.044
#> GSM381202 5 0.6474 0.7930 0.424 0.000 0.128 0.012 0.436
#> GSM381207 1 0.3752 0.5297 0.780 0.000 0.004 0.200 0.016
#> GSM381208 3 0.7178 0.1984 0.000 0.344 0.448 0.040 0.168
#> GSM381210 1 0.3841 0.3869 0.780 0.000 0.032 0.000 0.188
#> GSM381215 3 0.5742 0.4228 0.228 0.000 0.664 0.052 0.056
#> GSM381219 2 0.0404 0.9696 0.000 0.988 0.000 0.000 0.012
#> GSM381221 2 0.0451 0.9701 0.000 0.988 0.000 0.004 0.008
#> GSM381223 2 0.1502 0.9572 0.000 0.940 0.000 0.004 0.056
#> GSM381229 3 0.2576 0.7124 0.008 0.000 0.900 0.056 0.036
#> GSM381230 1 0.1768 0.6367 0.924 0.000 0.000 0.004 0.072
#> GSM381233 1 0.1525 0.6516 0.948 0.000 0.012 0.004 0.036
#> GSM381234 1 0.4090 0.4930 0.716 0.000 0.000 0.016 0.268
#> GSM381238 4 0.1893 0.9481 0.048 0.000 0.024 0.928 0.000
#> GSM381239 4 0.2012 0.9363 0.060 0.000 0.020 0.920 0.000
#> GSM381242 1 0.6618 -0.8503 0.424 0.000 0.136 0.016 0.424
#> GSM381247 2 0.1300 0.9651 0.000 0.956 0.000 0.016 0.028
#> GSM381248 1 0.4919 0.4334 0.652 0.000 0.004 0.040 0.304
#> GSM381249 1 0.4650 0.0675 0.684 0.000 0.032 0.004 0.280
#> GSM381253 1 0.5584 -0.0555 0.628 0.000 0.292 0.020 0.060
#> GSM381255 2 0.1018 0.9678 0.000 0.968 0.000 0.016 0.016
#> GSM381258 5 0.7735 0.6223 0.296 0.000 0.324 0.052 0.328
#> GSM381262 3 0.3138 0.7223 0.032 0.000 0.876 0.060 0.032
#> GSM381266 3 0.4000 0.6869 0.020 0.000 0.784 0.180 0.016
#> GSM381267 3 0.5494 0.5362 0.000 0.132 0.716 0.044 0.108
#> GSM381269 1 0.6585 -0.6367 0.512 0.000 0.152 0.016 0.320
#> GSM381273 3 0.3934 0.6720 0.008 0.000 0.792 0.168 0.032
#> GSM381274 2 0.1830 0.9498 0.000 0.924 0.000 0.008 0.068
#> GSM381276 1 0.7099 -0.1508 0.464 0.000 0.320 0.184 0.032
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM381194 3 0.5068 0.5878 0.028 0.000 0.708 0.012 0.164 NA
#> GSM381199 2 0.0713 0.9004 0.000 0.972 0.000 0.000 0.000 NA
#> GSM381205 2 0.3109 0.7838 0.000 0.772 0.000 0.000 0.004 NA
#> GSM381211 2 0.1610 0.8820 0.000 0.916 0.000 0.000 0.000 NA
#> GSM381220 2 0.1738 0.8996 0.000 0.928 0.000 0.016 0.004 NA
#> GSM381222 1 0.3504 0.5724 0.776 0.000 0.024 0.000 0.196 NA
#> GSM381224 1 0.3222 0.5945 0.844 0.000 0.024 0.000 0.096 NA
#> GSM381232 4 0.2957 0.9076 0.008 0.000 0.020 0.860 0.100 NA
#> GSM381240 1 0.2573 0.6002 0.864 0.000 0.000 0.000 0.112 NA
#> GSM381250 3 0.5235 0.4948 0.084 0.000 0.620 0.020 0.276 NA
#> GSM381252 2 0.0260 0.9002 0.000 0.992 0.000 0.000 0.000 NA
#> GSM381254 1 0.4359 0.5840 0.784 0.000 0.020 0.032 0.108 NA
#> GSM381256 2 0.1007 0.9016 0.000 0.956 0.000 0.000 0.000 NA
#> GSM381257 5 0.5596 0.5999 0.260 0.000 0.120 0.024 0.596 NA
#> GSM381259 1 0.4731 0.2226 0.532 0.000 0.008 0.000 0.428 NA
#> GSM381260 5 0.7553 0.5766 0.224 0.000 0.172 0.008 0.412 NA
#> GSM381261 2 0.4559 0.6514 0.000 0.628 0.000 0.004 0.044 NA
#> GSM381263 3 0.6936 0.1480 0.092 0.000 0.452 0.012 0.332 NA
#> GSM381265 1 0.5209 0.3395 0.564 0.000 0.032 0.004 0.368 NA
#> GSM381268 3 0.4430 0.6167 0.084 0.000 0.748 0.024 0.144 NA
#> GSM381270 2 0.1444 0.8958 0.000 0.928 0.000 0.000 0.000 NA
#> GSM381271 4 0.2715 0.8932 0.000 0.000 0.024 0.860 0.112 NA
#> GSM381275 2 0.3570 0.7914 0.000 0.752 0.000 0.004 0.016 NA
#> GSM381279 2 0.2613 0.8644 0.000 0.848 0.000 0.012 0.000 NA
#> GSM381195 1 0.5170 0.4373 0.612 0.000 0.032 0.000 0.304 NA
#> GSM381196 3 0.5089 0.5408 0.108 0.000 0.660 0.016 0.216 NA
#> GSM381198 2 0.2278 0.8591 0.000 0.868 0.000 0.004 0.000 NA
#> GSM381200 2 0.1753 0.8855 0.000 0.912 0.000 0.004 0.000 NA
#> GSM381201 3 0.4834 0.6065 0.024 0.000 0.708 0.076 0.188 NA
#> GSM381203 3 0.4710 0.5497 0.104 0.000 0.684 0.004 0.208 NA
#> GSM381204 1 0.4315 0.0510 0.492 0.000 0.004 0.000 0.492 NA
#> GSM381209 1 0.4242 0.2043 0.536 0.000 0.000 0.000 0.448 NA
#> GSM381212 1 0.3534 0.5351 0.740 0.000 0.000 0.000 0.244 NA
#> GSM381213 2 0.1594 0.8995 0.000 0.932 0.000 0.016 0.000 NA
#> GSM381214 2 0.0937 0.8966 0.000 0.960 0.000 0.000 0.000 NA
#> GSM381216 5 0.5547 0.6227 0.168 0.000 0.048 0.008 0.668 NA
#> GSM381225 3 0.3867 0.5542 0.176 0.000 0.768 0.000 0.008 NA
#> GSM381231 4 0.0976 0.9357 0.000 0.000 0.008 0.968 0.016 NA
#> GSM381235 3 0.4938 0.3708 0.344 0.000 0.596 0.000 0.024 NA
#> GSM381237 1 0.2491 0.5923 0.836 0.000 0.000 0.000 0.164 NA
#> GSM381241 2 0.0790 0.8977 0.000 0.968 0.000 0.000 0.000 NA
#> GSM381243 2 0.2255 0.8882 0.000 0.892 0.000 0.016 0.004 NA
#> GSM381245 1 0.2849 0.5545 0.876 0.000 0.016 0.004 0.044 NA
#> GSM381246 2 0.1204 0.9016 0.000 0.944 0.000 0.000 0.000 NA
#> GSM381251 3 0.2619 0.6442 0.008 0.000 0.884 0.032 0.072 NA
#> GSM381264 1 0.5020 0.4214 0.616 0.000 0.028 0.000 0.312 NA
#> GSM381206 2 0.2527 0.8344 0.000 0.832 0.000 0.000 0.000 NA
#> GSM381217 5 0.5658 0.6164 0.252 0.000 0.156 0.008 0.580 NA
#> GSM381218 2 0.1501 0.8869 0.000 0.924 0.000 0.000 0.000 NA
#> GSM381226 2 0.0260 0.9014 0.000 0.992 0.000 0.000 0.000 NA
#> GSM381227 2 0.1501 0.8954 0.000 0.924 0.000 0.000 0.000 NA
#> GSM381228 4 0.0914 0.9382 0.000 0.000 0.016 0.968 0.016 NA
#> GSM381236 4 0.1026 0.9393 0.008 0.000 0.004 0.968 0.012 NA
#> GSM381244 1 0.3951 0.5776 0.816 0.000 0.052 0.012 0.072 NA
#> GSM381272 4 0.2373 0.9160 0.004 0.000 0.024 0.888 0.084 NA
#> GSM381277 1 0.3078 0.5553 0.864 0.000 0.016 0.032 0.012 NA
#> GSM381278 3 0.5455 0.4604 0.248 0.000 0.636 0.048 0.004 NA
#> GSM381197 3 0.5593 0.4033 0.060 0.000 0.560 0.036 0.340 NA
#> GSM381202 5 0.5776 0.6400 0.208 0.000 0.052 0.004 0.628 NA
#> GSM381207 1 0.5004 0.5508 0.728 0.000 0.032 0.100 0.124 NA
#> GSM381208 2 0.6617 0.3237 0.000 0.460 0.140 0.036 0.016 NA
#> GSM381210 1 0.4412 0.0367 0.500 0.000 0.008 0.000 0.480 NA
#> GSM381215 3 0.6098 0.2707 0.156 0.000 0.516 0.028 0.300 NA
#> GSM381219 2 0.0260 0.9007 0.000 0.992 0.000 0.000 0.000 NA
#> GSM381221 2 0.0260 0.9015 0.000 0.992 0.000 0.000 0.000 NA
#> GSM381223 2 0.1910 0.8841 0.000 0.892 0.000 0.000 0.000 NA
#> GSM381229 3 0.1370 0.6349 0.036 0.000 0.948 0.004 0.000 NA
#> GSM381230 1 0.1970 0.6047 0.912 0.000 0.000 0.000 0.060 NA
#> GSM381233 1 0.2519 0.6106 0.888 0.000 0.020 0.000 0.072 NA
#> GSM381234 1 0.3260 0.5485 0.848 0.000 0.028 0.000 0.056 NA
#> GSM381238 4 0.0653 0.9402 0.004 0.000 0.004 0.980 0.012 NA
#> GSM381239 4 0.1294 0.9272 0.024 0.000 0.004 0.956 0.008 NA
#> GSM381242 5 0.7511 0.5259 0.260 0.000 0.120 0.008 0.388 NA
#> GSM381247 2 0.2100 0.8815 0.000 0.884 0.000 0.004 0.000 NA
#> GSM381248 1 0.4699 0.4748 0.760 0.000 0.044 0.016 0.072 NA
#> GSM381249 5 0.4306 -0.0120 0.464 0.000 0.004 0.000 0.520 NA
#> GSM381253 1 0.6376 -0.2901 0.368 0.000 0.348 0.012 0.272 NA
#> GSM381255 2 0.1327 0.8980 0.000 0.936 0.000 0.000 0.000 NA
#> GSM381258 5 0.6042 0.3339 0.124 0.000 0.296 0.032 0.544 NA
#> GSM381262 3 0.2920 0.6541 0.040 0.000 0.864 0.016 0.080 NA
#> GSM381266 3 0.3317 0.6486 0.036 0.000 0.852 0.072 0.032 NA
#> GSM381267 3 0.7238 0.1119 0.000 0.304 0.380 0.036 0.028 NA
#> GSM381269 5 0.5234 0.6200 0.240 0.000 0.088 0.020 0.648 NA
#> GSM381273 3 0.3530 0.6212 0.056 0.000 0.840 0.064 0.008 NA
#> GSM381274 2 0.3259 0.8075 0.000 0.772 0.000 0.000 0.012 NA
#> GSM381276 1 0.5752 0.1881 0.560 0.000 0.328 0.020 0.016 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n other(p) k
#> ATC:NMF 86 0.744 2
#> ATC:NMF 82 0.914 3
#> ATC:NMF 75 0.863 4
#> ATC:NMF 71 0.684 5
#> ATC:NMF 66 0.695 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