Date: 2019-12-25 20:17:18 CET, cola version: 1.3.2
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All available functions which can be applied to this res_list object:
res_list
#> A 'ConsensusPartitionList' object with 24 methods.
#> On a matrix with 21168 rows and 71 columns.
#> Top rows are extracted by 'SD, CV, MAD, ATC' methods.
#> Subgroups are detected by 'hclust, kmeans, skmeans, pam, mclust, NMF' method.
#> Number of partitions are tried for k = 2, 3, 4, 5, 6.
#> Performed in total 30000 partitions by row resampling.
#>
#> Following methods can be applied to this 'ConsensusPartitionList' object:
#> [1] "cola_report" "collect_classes" "collect_plots" "collect_stats"
#> [5] "colnames" "functional_enrichment" "get_anno_col" "get_anno"
#> [9] "get_classes" "get_matrix" "get_membership" "get_stats"
#> [13] "is_best_k" "is_stable_k" "ncol" "nrow"
#> [17] "rownames" "show" "suggest_best_k" "test_to_known_factors"
#> [21] "top_rows_heatmap" "top_rows_overlap"
#>
#> You can get result for a single method by, e.g. object["SD", "hclust"] or object["SD:hclust"]
#> or a subset of methods by object[c("SD", "CV")], c("hclust", "kmeans")]
The call of run_all_consensus_partition_methods() was:
#> run_all_consensus_partition_methods(data = mat, mc.cores = 4, anno = anno)
Dimension of the input matrix:
mat = get_matrix(res_list)
dim(mat)
#> [1] 21168 71
The density distribution for each sample is visualized as in one column in the following heatmap. The clustering is based on the distance which is the Kolmogorov-Smirnov statistic between two distributions.
library(ComplexHeatmap)
densityHeatmap(mat, top_annotation = HeatmapAnnotation(df = get_anno(res_list),
col = get_anno_col(res_list)), ylab = "value", cluster_columns = TRUE, show_column_names = FALSE,
mc.cores = 4)
Folowing table shows the best k (number of partitions) for each combination
of top-value methods and partition methods. Clicking on the method name in
the table goes to the section for a single combination of methods.
The cola vignette explains the definition of the metrics used for determining the best number of partitions.
suggest_best_k(res_list)
| The best k | 1-PAC | Mean silhouette | Concordance | Optional k | ||
|---|---|---|---|---|---|---|
| SD:kmeans | 2 | 1.000 | 0.984 | 0.994 | ** | |
| SD:NMF | 2 | 1.000 | 0.983 | 0.993 | ** | |
| CV:kmeans | 2 | 1.000 | 0.987 | 0.995 | ** | |
| CV:skmeans | 2 | 1.000 | 1.000 | 1.000 | ** | |
| CV:NMF | 2 | 1.000 | 0.992 | 0.997 | ** | |
| MAD:kmeans | 2 | 1.000 | 1.000 | 1.000 | ** | |
| MAD:skmeans | 2 | 1.000 | 0.999 | 0.999 | ** | |
| MAD:pam | 3 | 1.000 | 0.971 | 0.987 | ** | 2 |
| MAD:NMF | 2 | 1.000 | 0.987 | 0.995 | ** | |
| ATC:kmeans | 2 | 1.000 | 1.000 | 1.000 | ** | |
| ATC:skmeans | 2 | 1.000 | 1.000 | 1.000 | ** | |
| ATC:mclust | 4 | 1.000 | 0.980 | 0.985 | ** | 2,3 |
| ATC:NMF | 2 | 1.000 | 0.952 | 0.983 | ** | |
| SD:pam | 3 | 0.982 | 0.943 | 0.979 | ** | 2 |
| ATC:pam | 5 | 0.956 | 0.932 | 0.966 | ** | 2 |
| MAD:mclust | 3 | 0.948 | 0.937 | 0.970 | * | 2 |
| SD:skmeans | 3 | 0.946 | 0.934 | 0.971 | * | 2 |
| SD:mclust | 4 | 0.940 | 0.919 | 0.966 | * | 2,3 |
| CV:mclust | 5 | 0.938 | 0.895 | 0.941 | * | 2,4 |
| CV:pam | 3 | 0.915 | 0.940 | 0.965 | * | |
| ATC:hclust | 4 | 0.871 | 0.880 | 0.941 | ||
| SD:hclust | 6 | 0.724 | 0.736 | 0.846 | ||
| MAD:hclust | 2 | 0.559 | 0.874 | 0.899 | ||
| CV:hclust | 3 | 0.532 | 0.798 | 0.892 |
**: 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 0.983 0.993 0.480 0.522 0.522
#> CV:NMF 2 1.000 0.992 0.997 0.477 0.522 0.522
#> MAD:NMF 2 1.000 0.987 0.995 0.481 0.522 0.522
#> ATC:NMF 2 1.000 0.952 0.983 0.491 0.505 0.505
#> SD:skmeans 2 1.000 0.999 1.000 0.479 0.522 0.522
#> CV:skmeans 2 1.000 1.000 1.000 0.479 0.522 0.522
#> MAD:skmeans 2 1.000 0.999 0.999 0.479 0.522 0.522
#> ATC:skmeans 2 1.000 1.000 1.000 0.485 0.515 0.515
#> SD:mclust 2 1.000 0.999 1.000 0.471 0.529 0.529
#> CV:mclust 2 1.000 0.994 0.997 0.464 0.537 0.537
#> MAD:mclust 2 1.000 1.000 1.000 0.471 0.529 0.529
#> ATC:mclust 2 1.000 1.000 1.000 0.471 0.529 0.529
#> SD:kmeans 2 1.000 0.984 0.994 0.476 0.522 0.522
#> CV:kmeans 2 1.000 0.987 0.995 0.476 0.522 0.522
#> MAD:kmeans 2 1.000 1.000 1.000 0.479 0.522 0.522
#> ATC:kmeans 2 1.000 1.000 1.000 0.471 0.529 0.529
#> SD:pam 2 1.000 0.993 0.997 0.478 0.522 0.522
#> CV:pam 2 0.862 0.953 0.974 0.486 0.522 0.522
#> MAD:pam 2 1.000 0.985 0.993 0.482 0.522 0.522
#> ATC:pam 2 1.000 0.984 0.994 0.475 0.529 0.529
#> SD:hclust 2 0.232 0.641 0.815 0.385 0.566 0.566
#> CV:hclust 2 0.499 0.750 0.856 0.263 0.892 0.892
#> MAD:hclust 2 0.559 0.874 0.899 0.467 0.522 0.522
#> ATC:hclust 2 0.370 0.260 0.690 0.409 0.820 0.820
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.865 0.877 0.939 0.384 0.794 0.611
#> CV:NMF 3 0.883 0.893 0.944 0.390 0.794 0.611
#> MAD:NMF 3 0.711 0.813 0.887 0.355 0.808 0.637
#> ATC:NMF 3 0.816 0.847 0.916 0.344 0.776 0.582
#> SD:skmeans 3 0.946 0.934 0.971 0.407 0.786 0.597
#> CV:skmeans 3 0.848 0.871 0.941 0.402 0.806 0.628
#> MAD:skmeans 3 0.826 0.870 0.933 0.402 0.806 0.628
#> ATC:skmeans 3 0.819 0.863 0.895 0.379 0.801 0.619
#> SD:mclust 3 1.000 0.969 0.987 0.311 0.849 0.716
#> CV:mclust 3 0.849 0.896 0.938 0.316 0.855 0.730
#> MAD:mclust 3 0.948 0.937 0.970 0.280 0.859 0.734
#> ATC:mclust 3 1.000 0.998 0.999 0.336 0.841 0.699
#> SD:kmeans 3 0.796 0.833 0.897 0.393 0.791 0.605
#> CV:kmeans 3 0.723 0.803 0.877 0.363 0.806 0.628
#> MAD:kmeans 3 0.716 0.819 0.854 0.368 0.805 0.627
#> ATC:kmeans 3 0.710 0.737 0.865 0.333 0.849 0.716
#> SD:pam 3 0.982 0.943 0.979 0.382 0.820 0.655
#> CV:pam 3 0.915 0.940 0.965 0.357 0.825 0.665
#> MAD:pam 3 1.000 0.971 0.987 0.374 0.815 0.646
#> ATC:pam 3 0.850 0.945 0.966 0.399 0.801 0.624
#> SD:hclust 3 0.309 0.535 0.778 0.378 0.870 0.781
#> CV:hclust 3 0.532 0.798 0.892 0.817 0.602 0.553
#> MAD:hclust 3 0.479 0.695 0.827 0.195 0.858 0.745
#> ATC:hclust 3 0.806 0.835 0.896 0.450 0.585 0.503
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.784 0.833 0.887 0.1023 0.899 0.706
#> CV:NMF 4 0.786 0.793 0.882 0.1052 0.908 0.731
#> MAD:NMF 4 0.825 0.780 0.890 0.1111 0.901 0.721
#> ATC:NMF 4 0.757 0.808 0.886 0.1114 0.862 0.628
#> SD:skmeans 4 0.815 0.848 0.909 0.0910 0.886 0.675
#> CV:skmeans 4 0.753 0.729 0.850 0.0940 0.882 0.666
#> MAD:skmeans 4 0.765 0.773 0.870 0.0885 0.911 0.741
#> ATC:skmeans 4 0.898 0.872 0.943 0.0990 0.860 0.618
#> SD:mclust 4 0.940 0.919 0.966 0.1549 0.895 0.727
#> CV:mclust 4 0.900 0.846 0.935 0.2002 0.826 0.580
#> MAD:mclust 4 0.865 0.853 0.920 0.1860 0.878 0.693
#> ATC:mclust 4 1.000 0.980 0.985 0.1391 0.913 0.765
#> SD:kmeans 4 0.755 0.864 0.882 0.1000 0.920 0.762
#> CV:kmeans 4 0.855 0.813 0.898 0.1164 0.899 0.714
#> MAD:kmeans 4 0.671 0.786 0.829 0.1152 0.893 0.695
#> ATC:kmeans 4 0.731 0.871 0.854 0.1282 0.850 0.628
#> SD:pam 4 0.889 0.856 0.944 0.0343 0.989 0.968
#> CV:pam 4 0.880 0.864 0.938 0.0388 0.989 0.968
#> MAD:pam 4 0.943 0.901 0.950 0.0338 0.990 0.969
#> ATC:pam 4 0.899 0.836 0.897 0.0844 0.948 0.845
#> SD:hclust 4 0.403 0.371 0.697 0.1061 0.942 0.883
#> CV:hclust 4 0.562 0.737 0.865 0.1245 0.999 0.998
#> MAD:hclust 4 0.654 0.720 0.811 0.2003 0.813 0.606
#> ATC:hclust 4 0.871 0.880 0.941 0.1351 0.870 0.700
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.722 0.682 0.815 0.0525 0.934 0.766
#> CV:NMF 5 0.773 0.758 0.844 0.0497 0.948 0.810
#> MAD:NMF 5 0.711 0.697 0.817 0.0588 0.945 0.802
#> ATC:NMF 5 0.771 0.705 0.831 0.0496 0.960 0.854
#> SD:skmeans 5 0.731 0.744 0.811 0.0490 1.000 1.000
#> CV:skmeans 5 0.712 0.548 0.762 0.0482 0.963 0.867
#> MAD:skmeans 5 0.739 0.702 0.789 0.0483 1.000 1.000
#> ATC:skmeans 5 0.884 0.822 0.896 0.0435 0.926 0.739
#> SD:mclust 5 0.897 0.855 0.905 0.0686 0.933 0.768
#> CV:mclust 5 0.938 0.895 0.941 0.0446 0.948 0.810
#> MAD:mclust 5 0.844 0.766 0.882 0.0561 0.930 0.761
#> ATC:mclust 5 0.825 0.841 0.889 0.0798 0.957 0.846
#> SD:kmeans 5 0.746 0.709 0.823 0.0555 0.982 0.933
#> CV:kmeans 5 0.774 0.759 0.836 0.0506 0.937 0.794
#> MAD:kmeans 5 0.722 0.720 0.793 0.0592 0.959 0.850
#> ATC:kmeans 5 0.767 0.835 0.858 0.0735 1.000 1.000
#> SD:pam 5 0.859 0.830 0.926 0.0212 0.994 0.982
#> CV:pam 5 0.846 0.843 0.915 0.0131 0.994 0.983
#> MAD:pam 5 0.886 0.860 0.933 0.0184 0.994 0.980
#> ATC:pam 5 0.956 0.932 0.966 0.0480 0.938 0.790
#> SD:hclust 5 0.469 0.624 0.738 0.1172 0.779 0.541
#> CV:hclust 5 0.520 0.607 0.836 0.0732 0.913 0.825
#> MAD:hclust 5 0.692 0.714 0.854 0.0539 0.947 0.840
#> ATC:hclust 5 0.853 0.816 0.923 0.0452 0.990 0.966
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.746 0.639 0.787 0.03139 0.958 0.829
#> CV:NMF 6 0.779 0.675 0.801 0.02638 0.966 0.858
#> MAD:NMF 6 0.704 0.660 0.773 0.03537 0.990 0.959
#> ATC:NMF 6 0.821 0.743 0.851 0.02695 0.959 0.837
#> SD:skmeans 6 0.696 0.596 0.725 0.03552 0.962 0.861
#> CV:skmeans 6 0.649 0.535 0.699 0.03517 0.976 0.906
#> MAD:skmeans 6 0.662 0.592 0.712 0.03857 0.972 0.896
#> ATC:skmeans 6 0.878 0.773 0.853 0.02645 0.984 0.932
#> SD:mclust 6 0.814 0.851 0.889 0.03525 0.956 0.820
#> CV:mclust 6 0.864 0.850 0.893 0.03114 0.973 0.885
#> MAD:mclust 6 0.719 0.634 0.796 0.04523 0.973 0.891
#> ATC:mclust 6 0.832 0.838 0.898 0.05782 0.909 0.638
#> SD:kmeans 6 0.766 0.675 0.791 0.03873 0.986 0.945
#> CV:kmeans 6 0.761 0.705 0.801 0.03992 0.947 0.810
#> MAD:kmeans 6 0.754 0.735 0.799 0.03346 0.994 0.977
#> ATC:kmeans 6 0.799 0.658 0.791 0.04717 0.925 0.731
#> SD:pam 6 0.842 0.791 0.914 0.01345 0.994 0.983
#> CV:pam 6 0.829 0.846 0.927 0.00937 0.995 0.984
#> MAD:pam 6 0.884 0.859 0.932 0.00926 0.994 0.981
#> ATC:pam 6 0.932 0.898 0.932 0.01133 0.998 0.990
#> SD:hclust 6 0.724 0.736 0.846 0.08175 0.965 0.885
#> CV:hclust 6 0.573 0.578 0.802 0.08546 0.915 0.797
#> MAD:hclust 6 0.775 0.656 0.824 0.03400 0.989 0.961
#> ATC:hclust 6 0.899 0.837 0.925 0.08264 0.938 0.791
Following heatmap plots the partition for each combination of methods and the lightness correspond to the silhouette scores for samples in each method. On top the consensus subgroup is inferred from all methods by taking the mean silhouette scores as weight.
collect_stats(res_list, k = 2)
collect_stats(res_list, k = 3)
collect_stats(res_list, k = 4)
collect_stats(res_list, k = 5)
collect_stats(res_list, k = 6)
Collect partitions from all methods:
collect_classes(res_list, k = 2)
collect_classes(res_list, k = 3)
collect_classes(res_list, k = 4)
collect_classes(res_list, k = 5)
collect_classes(res_list, k = 6)
Overlap of top rows from different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "euler")
top_rows_overlap(res_list, top_n = 2000, method = "euler")
top_rows_overlap(res_list, top_n = 3000, method = "euler")
top_rows_overlap(res_list, top_n = 4000, method = "euler")
top_rows_overlap(res_list, top_n = 5000, method = "euler")
Also visualize the correspondance of rankings between different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "correspondance")
top_rows_overlap(res_list, top_n = 2000, method = "correspondance")
top_rows_overlap(res_list, top_n = 3000, method = "correspondance")
top_rows_overlap(res_list, top_n = 4000, method = "correspondance")
top_rows_overlap(res_list, top_n = 5000, method = "correspondance")
Heatmaps of the top rows:
top_rows_heatmap(res_list, top_n = 1000)
top_rows_heatmap(res_list, top_n = 2000)
top_rows_heatmap(res_list, top_n = 3000)
top_rows_heatmap(res_list, top_n = 4000)
top_rows_heatmap(res_list, top_n = 5000)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res_list, k = 2)
#> n disease.state(p) infection(p) agent(p) k
#> SD:NMF 70 6.31e-16 6.31e-16 7.57e-06 2
#> CV:NMF 71 3.82e-16 3.82e-16 6.04e-06 2
#> MAD:NMF 70 6.31e-16 6.31e-16 7.57e-06 2
#> ATC:NMF 69 7.45e-15 7.45e-15 1.80e-05 2
#> SD:skmeans 71 3.82e-16 3.82e-16 6.04e-06 2
#> CV:skmeans 71 3.82e-16 3.82e-16 6.04e-06 2
#> MAD:skmeans 71 3.82e-16 3.82e-16 6.04e-06 2
#> ATC:skmeans 71 2.82e-15 2.82e-15 1.16e-05 2
#> SD:mclust 71 3.04e-15 3.04e-15 5.99e-05 2
#> CV:mclust 71 2.21e-14 2.21e-14 4.70e-04 2
#> MAD:mclust 71 3.04e-15 3.04e-15 5.99e-05 2
#> ATC:mclust 71 3.04e-15 3.04e-15 5.99e-05 2
#> SD:kmeans 70 6.31e-16 6.31e-16 1.30e-05 2
#> CV:kmeans 70 6.31e-16 6.31e-16 1.30e-05 2
#> MAD:kmeans 71 3.82e-16 3.82e-16 6.04e-06 2
#> ATC:kmeans 71 3.04e-15 3.04e-15 5.99e-05 2
#> SD:pam 71 3.82e-16 3.82e-16 6.04e-06 2
#> CV:pam 71 3.82e-16 3.82e-16 6.04e-06 2
#> MAD:pam 71 3.82e-16 3.82e-16 6.04e-06 2
#> ATC:pam 70 6.31e-16 6.31e-16 1.30e-05 2
#> SD:hclust 58 6.76e-07 6.76e-07 1.31e-02 2
#> CV:hclust 71 8.91e-03 8.91e-03 8.09e-01 2
#> MAD:hclust 68 1.71e-15 1.71e-15 1.19e-05 2
#> ATC:hclust 33 6.83e-08 6.83e-08 9.77e-02 2
test_to_known_factors(res_list, k = 3)
#> n disease.state(p) infection(p) agent(p) k
#> SD:NMF 68 3.48e-13 3.48e-13 1.34e-04 3
#> CV:NMF 69 2.55e-13 2.55e-13 1.10e-04 3
#> MAD:NMF 66 1.87e-14 1.87e-14 3.89e-05 3
#> ATC:NMF 66 2.39e-15 2.39e-15 3.89e-05 3
#> SD:skmeans 69 2.33e-14 2.33e-14 2.00e-05 3
#> CV:skmeans 65 1.81e-13 1.81e-13 3.18e-05 3
#> MAD:skmeans 68 2.27e-14 2.27e-14 1.57e-05 3
#> ATC:skmeans 71 4.65e-26 4.65e-26 7.76e-06 3
#> SD:mclust 70 1.59e-16 1.59e-16 9.67e-05 3
#> CV:mclust 68 9.72e-16 9.72e-16 2.49e-04 3
#> MAD:mclust 68 1.89e-15 1.89e-15 1.47e-04 3
#> ATC:mclust 71 1.36e-17 1.36e-17 7.83e-05 3
#> SD:kmeans 67 3.52e-14 3.52e-14 3.11e-05 3
#> CV:kmeans 65 2.11e-13 2.11e-13 4.87e-05 3
#> MAD:kmeans 71 1.05e-14 1.05e-14 7.76e-06 3
#> ATC:kmeans 64 7.70e-15 7.70e-15 3.36e-04 3
#> SD:pam 69 6.35e-16 6.35e-16 1.24e-05 3
#> CV:pam 71 2.84e-16 2.84e-16 7.76e-06 3
#> MAD:pam 70 8.95e-17 8.95e-17 9.81e-06 3
#> ATC:pam 70 7.72e-15 7.72e-15 8.91e-05 3
#> SD:hclust 44 1.84e-09 1.84e-09 1.40e-02 3
#> CV:hclust 65 6.35e-07 6.35e-07 1.01e-02 3
#> MAD:hclust 59 5.77e-16 5.77e-16 1.33e-04 3
#> ATC:hclust 70 1.22e-14 1.22e-14 9.77e-05 3
test_to_known_factors(res_list, k = 4)
#> n disease.state(p) infection(p) agent(p) k
#> SD:NMF 68 1.48e-19 1.48e-19 4.65e-04 4
#> CV:NMF 64 1.54e-16 1.54e-16 1.04e-03 4
#> MAD:NMF 63 5.50e-18 5.50e-18 1.23e-03 4
#> ATC:NMF 66 6.20e-19 6.20e-19 6.63e-04 4
#> SD:skmeans 66 2.65e-19 2.65e-19 1.47e-04 4
#> CV:skmeans 61 8.44e-17 8.44e-17 4.26e-04 4
#> MAD:skmeans 62 2.04e-18 2.04e-18 2.38e-04 4
#> ATC:skmeans 66 3.18e-19 3.18e-19 1.47e-04 4
#> SD:mclust 70 4.14e-18 4.14e-18 3.33e-04 4
#> CV:mclust 65 9.70e-17 9.70e-17 8.58e-04 4
#> MAD:mclust 66 7.76e-17 7.76e-17 7.28e-04 4
#> ATC:mclust 71 2.80e-18 2.80e-18 2.74e-04 4
#> SD:kmeans 68 3.09e-20 3.09e-20 9.57e-05 4
#> CV:kmeans 66 5.12e-14 5.12e-14 1.47e-04 4
#> MAD:kmeans 66 1.35e-19 1.35e-19 9.64e-05 4
#> ATC:kmeans 70 4.19e-24 4.19e-24 3.28e-04 4
#> SD:pam 67 1.38e-15 1.38e-15 1.98e-05 4
#> CV:pam 68 7.80e-16 7.80e-16 1.57e-05 4
#> MAD:pam 69 7.37e-17 7.37e-17 1.24e-05 4
#> ATC:pam 67 1.04e-15 1.04e-15 5.81e-04 4
#> SD:hclust 27 NA NA NA 4
#> CV:hclust 65 9.68e-07 9.68e-07 1.01e-02 4
#> MAD:hclust 60 1.90e-16 1.90e-16 3.75e-04 4
#> ATC:hclust 69 6.33e-18 6.33e-18 4.11e-04 4
test_to_known_factors(res_list, k = 5)
#> n disease.state(p) infection(p) agent(p) k
#> SD:NMF 60 1.21e-16 1.21e-16 5.34e-03 5
#> CV:NMF 64 8.87e-16 8.87e-16 2.61e-03 5
#> MAD:NMF 58 1.09e-15 1.09e-15 7.82e-03 5
#> ATC:NMF 57 1.80e-17 1.80e-17 3.72e-03 5
#> SD:skmeans 64 8.56e-19 8.56e-19 2.25e-04 5
#> CV:skmeans 42 6.21e-09 6.21e-09 1.02e-02 5
#> MAD:skmeans 61 6.26e-18 6.26e-18 2.99e-04 5
#> ATC:skmeans 63 5.94e-18 5.94e-18 7.98e-04 5
#> SD:mclust 70 5.03e-21 5.03e-21 8.80e-04 5
#> CV:mclust 68 1.85e-17 1.85e-17 1.24e-03 5
#> MAD:mclust 60 1.36e-19 1.36e-19 1.47e-03 5
#> ATC:mclust 68 4.03e-20 4.03e-20 1.28e-03 5
#> SD:kmeans 62 1.60e-19 1.60e-19 3.44e-04 5
#> CV:kmeans 60 2.17e-16 2.17e-16 1.47e-03 5
#> MAD:kmeans 61 7.87e-18 7.87e-18 2.99e-04 5
#> ATC:kmeans 70 2.59e-25 2.59e-25 6.26e-05 5
#> SD:pam 66 3.88e-15 3.88e-15 2.51e-05 5
#> CV:pam 67 2.36e-15 2.36e-15 1.98e-05 5
#> MAD:pam 68 2.23e-16 2.23e-16 1.57e-05 5
#> ATC:pam 70 1.17e-20 1.17e-20 8.51e-04 5
#> SD:hclust 49 3.46e-10 3.46e-10 1.54e-03 5
#> CV:hclust 47 2.63e-06 2.63e-06 3.50e-02 5
#> MAD:hclust 56 5.29e-15 5.29e-15 2.74e-04 5
#> ATC:hclust 63 2.54e-17 2.54e-17 4.06e-04 5
test_to_known_factors(res_list, k = 6)
#> n disease.state(p) infection(p) agent(p) k
#> SD:NMF 53 2.41e-13 2.41e-13 2.03e-02 6
#> CV:NMF 55 1.63e-12 1.63e-12 4.05e-03 6
#> MAD:NMF 57 2.94e-15 2.94e-15 9.47e-03 6
#> ATC:NMF 64 3.05e-17 3.05e-17 5.53e-03 6
#> SD:skmeans 50 1.20e-13 1.20e-13 4.60e-03 6
#> CV:skmeans 41 2.70e-09 2.70e-09 1.31e-02 6
#> MAD:skmeans 46 6.15e-11 6.15e-11 3.30e-03 6
#> ATC:skmeans 61 6.91e-20 6.91e-20 1.20e-03 6
#> SD:mclust 69 3.18e-21 3.18e-21 2.44e-03 6
#> CV:mclust 69 4.89e-17 4.89e-17 2.48e-03 6
#> MAD:mclust 50 9.85e-17 9.85e-17 1.65e-02 6
#> ATC:mclust 66 1.85e-18 1.85e-18 2.27e-03 6
#> SD:kmeans 56 2.41e-18 2.41e-18 3.31e-03 6
#> CV:kmeans 62 1.40e-14 1.40e-14 2.36e-03 6
#> MAD:kmeans 66 4.79e-18 4.79e-18 2.91e-04 6
#> ATC:kmeans 60 8.10e-19 8.10e-19 4.61e-03 6
#> SD:pam 65 1.11e-14 1.11e-14 3.18e-05 6
#> CV:pam 67 2.36e-15 2.36e-15 1.98e-05 6
#> MAD:pam 67 6.88e-16 6.88e-16 1.98e-05 6
#> ATC:pam 69 2.96e-20 2.96e-20 1.03e-03 6
#> SD:hclust 62 4.60e-19 4.60e-19 6.90e-04 6
#> CV:hclust 49 3.96e-10 3.96e-10 9.91e-03 6
#> MAD:hclust 55 1.94e-18 1.94e-18 1.18e-03 6
#> ATC:hclust 67 9.96e-23 9.96e-23 1.23e-03 6
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "hclust"]
# you can also extract it by
# res = res_list["SD:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 71 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 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.232 0.641 0.815 0.3849 0.566 0.566
#> 3 3 0.309 0.535 0.778 0.3781 0.870 0.781
#> 4 4 0.403 0.371 0.697 0.1061 0.942 0.883
#> 5 5 0.469 0.624 0.738 0.1172 0.779 0.541
#> 6 6 0.724 0.736 0.846 0.0818 0.965 0.885
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM123732 2 0.909 0.4947 0.324 0.676
#> GSM123736 2 0.932 0.4578 0.348 0.652
#> GSM123740 2 0.932 0.4578 0.348 0.652
#> GSM123744 2 1.000 -0.1277 0.492 0.508
#> GSM123746 1 0.998 0.2579 0.528 0.472
#> GSM123750 2 1.000 -0.1277 0.492 0.508
#> GSM123752 2 0.996 -0.0185 0.464 0.536
#> GSM123756 1 0.689 0.8282 0.816 0.184
#> GSM123758 2 0.946 0.3960 0.364 0.636
#> GSM123761 1 0.730 0.8265 0.796 0.204
#> GSM123763 1 0.697 0.8290 0.812 0.188
#> GSM123765 2 0.900 0.5070 0.316 0.684
#> GSM123769 1 0.689 0.8282 0.816 0.184
#> GSM123771 1 0.689 0.8282 0.816 0.184
#> GSM123774 1 0.689 0.8282 0.816 0.184
#> GSM123778 2 0.900 0.5070 0.316 0.684
#> GSM123780 2 0.900 0.5070 0.316 0.684
#> GSM123784 2 0.900 0.5070 0.316 0.684
#> GSM123787 2 0.900 0.5070 0.316 0.684
#> GSM123791 2 0.900 0.5070 0.316 0.684
#> GSM123795 2 0.932 0.4578 0.348 0.652
#> GSM123799 2 0.932 0.4578 0.348 0.652
#> GSM123730 2 0.850 0.5671 0.276 0.724
#> GSM123734 1 0.000 0.6551 1.000 0.000
#> GSM123738 1 0.745 0.7226 0.788 0.212
#> GSM123742 1 0.932 0.6965 0.652 0.348
#> GSM123745 1 0.802 0.8290 0.756 0.244
#> GSM123748 1 0.876 0.7768 0.704 0.296
#> GSM123751 1 0.821 0.8200 0.744 0.256
#> GSM123754 1 0.802 0.8290 0.756 0.244
#> GSM123757 1 0.998 0.2579 0.528 0.472
#> GSM123760 1 0.932 0.6965 0.652 0.348
#> GSM123762 1 0.689 0.8282 0.816 0.184
#> GSM123764 2 0.971 0.2036 0.400 0.600
#> GSM123767 1 0.802 0.8290 0.756 0.244
#> GSM123770 1 0.802 0.8290 0.756 0.244
#> GSM123773 1 0.802 0.8290 0.756 0.244
#> GSM123777 2 0.850 0.5671 0.276 0.724
#> GSM123779 2 0.767 0.6098 0.224 0.776
#> GSM123782 2 0.966 0.2378 0.392 0.608
#> GSM123786 2 0.900 0.5070 0.316 0.684
#> GSM123789 2 0.767 0.6098 0.224 0.776
#> GSM123793 1 0.416 0.6971 0.916 0.084
#> GSM123797 1 0.745 0.7226 0.788 0.212
#> GSM123729 2 0.000 0.7622 0.000 1.000
#> GSM123733 2 0.000 0.7622 0.000 1.000
#> GSM123737 2 0.000 0.7622 0.000 1.000
#> GSM123741 2 0.000 0.7622 0.000 1.000
#> GSM123747 2 0.000 0.7622 0.000 1.000
#> GSM123753 2 0.000 0.7622 0.000 1.000
#> GSM123759 2 0.000 0.7622 0.000 1.000
#> GSM123766 2 0.000 0.7622 0.000 1.000
#> GSM123772 2 0.000 0.7622 0.000 1.000
#> GSM123775 2 0.000 0.7622 0.000 1.000
#> GSM123781 2 0.000 0.7622 0.000 1.000
#> GSM123785 2 0.000 0.7622 0.000 1.000
#> GSM123788 2 0.000 0.7622 0.000 1.000
#> GSM123792 2 0.000 0.7622 0.000 1.000
#> GSM123796 2 0.000 0.7622 0.000 1.000
#> GSM123731 2 0.000 0.7622 0.000 1.000
#> GSM123735 2 0.000 0.7622 0.000 1.000
#> GSM123739 2 0.000 0.7622 0.000 1.000
#> GSM123743 2 0.000 0.7622 0.000 1.000
#> GSM123749 2 0.000 0.7622 0.000 1.000
#> GSM123755 2 0.000 0.7622 0.000 1.000
#> GSM123768 2 0.000 0.7622 0.000 1.000
#> GSM123776 2 0.671 0.6652 0.176 0.824
#> GSM123783 2 0.000 0.7622 0.000 1.000
#> GSM123790 2 0.000 0.7622 0.000 1.000
#> GSM123794 2 0.000 0.7622 0.000 1.000
#> GSM123798 2 0.000 0.7622 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM123732 2 0.8876 0.1193 0.412 0.468 0.120
#> GSM123736 2 0.9241 0.1036 0.388 0.456 0.156
#> GSM123740 2 0.9241 0.1036 0.388 0.456 0.156
#> GSM123744 1 0.7872 0.4210 0.620 0.296 0.084
#> GSM123746 1 0.8233 0.4886 0.616 0.264 0.120
#> GSM123750 1 0.7872 0.4210 0.620 0.296 0.084
#> GSM123752 1 0.8582 0.3791 0.568 0.308 0.124
#> GSM123756 1 0.0592 0.5473 0.988 0.000 0.012
#> GSM123758 1 0.8774 0.0448 0.476 0.412 0.112
#> GSM123761 1 0.1529 0.5456 0.960 0.000 0.040
#> GSM123763 1 0.0747 0.5473 0.984 0.000 0.016
#> GSM123765 2 0.8836 0.1828 0.388 0.492 0.120
#> GSM123769 1 0.0592 0.5473 0.988 0.000 0.012
#> GSM123771 1 0.0592 0.5473 0.988 0.000 0.012
#> GSM123774 1 0.0592 0.5473 0.988 0.000 0.012
#> GSM123778 2 0.8836 0.1828 0.388 0.492 0.120
#> GSM123780 2 0.8836 0.1828 0.388 0.492 0.120
#> GSM123784 2 0.8836 0.1828 0.388 0.492 0.120
#> GSM123787 2 0.8836 0.1828 0.388 0.492 0.120
#> GSM123791 2 0.8808 0.1552 0.400 0.484 0.116
#> GSM123795 2 0.9241 0.1036 0.388 0.456 0.156
#> GSM123799 2 0.9241 0.1036 0.388 0.456 0.156
#> GSM123730 2 0.6404 0.4490 0.012 0.644 0.344
#> GSM123734 3 0.3192 0.7247 0.112 0.000 0.888
#> GSM123738 3 0.3771 0.8070 0.012 0.112 0.876
#> GSM123742 1 0.9441 0.4011 0.484 0.200 0.316
#> GSM123745 1 0.8196 0.4732 0.624 0.124 0.252
#> GSM123748 1 0.8823 0.4685 0.564 0.156 0.280
#> GSM123751 1 0.8343 0.4759 0.612 0.132 0.256
#> GSM123754 1 0.7824 0.5296 0.664 0.124 0.212
#> GSM123757 1 0.8349 0.4909 0.608 0.264 0.128
#> GSM123760 1 0.9372 0.4302 0.500 0.200 0.300
#> GSM123762 1 0.0892 0.5445 0.980 0.000 0.020
#> GSM123764 2 0.9212 0.1967 0.180 0.516 0.304
#> GSM123767 1 0.7824 0.5296 0.664 0.124 0.212
#> GSM123770 1 0.7824 0.5296 0.664 0.124 0.212
#> GSM123773 1 0.7824 0.5296 0.664 0.124 0.212
#> GSM123777 2 0.6404 0.4490 0.012 0.644 0.344
#> GSM123779 2 0.7078 0.5456 0.088 0.712 0.200
#> GSM123782 2 0.9172 0.2167 0.180 0.524 0.296
#> GSM123786 2 0.8836 0.1828 0.388 0.492 0.120
#> GSM123789 2 0.7078 0.5456 0.088 0.712 0.200
#> GSM123793 3 0.2050 0.8085 0.028 0.020 0.952
#> GSM123797 3 0.3771 0.8070 0.012 0.112 0.876
#> GSM123729 2 0.0000 0.7531 0.000 1.000 0.000
#> GSM123733 2 0.0000 0.7531 0.000 1.000 0.000
#> GSM123737 2 0.0000 0.7531 0.000 1.000 0.000
#> GSM123741 2 0.0000 0.7531 0.000 1.000 0.000
#> GSM123747 2 0.0000 0.7531 0.000 1.000 0.000
#> GSM123753 2 0.0000 0.7531 0.000 1.000 0.000
#> GSM123759 2 0.0000 0.7531 0.000 1.000 0.000
#> GSM123766 2 0.0000 0.7531 0.000 1.000 0.000
#> GSM123772 2 0.0000 0.7531 0.000 1.000 0.000
#> GSM123775 2 0.0000 0.7531 0.000 1.000 0.000
#> GSM123781 2 0.0000 0.7531 0.000 1.000 0.000
#> GSM123785 2 0.0000 0.7531 0.000 1.000 0.000
#> GSM123788 2 0.0000 0.7531 0.000 1.000 0.000
#> GSM123792 2 0.0000 0.7531 0.000 1.000 0.000
#> GSM123796 2 0.0000 0.7531 0.000 1.000 0.000
#> GSM123731 2 0.0000 0.7531 0.000 1.000 0.000
#> GSM123735 2 0.0000 0.7531 0.000 1.000 0.000
#> GSM123739 2 0.0000 0.7531 0.000 1.000 0.000
#> GSM123743 2 0.0000 0.7531 0.000 1.000 0.000
#> GSM123749 2 0.0000 0.7531 0.000 1.000 0.000
#> GSM123755 2 0.0000 0.7531 0.000 1.000 0.000
#> GSM123768 2 0.0000 0.7531 0.000 1.000 0.000
#> GSM123776 2 0.4634 0.6366 0.164 0.824 0.012
#> GSM123783 2 0.0000 0.7531 0.000 1.000 0.000
#> GSM123790 2 0.0000 0.7531 0.000 1.000 0.000
#> GSM123794 2 0.0000 0.7531 0.000 1.000 0.000
#> GSM123798 2 0.0000 0.7531 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM123732 2 0.788 0.0880 0.304 0.384 0.000 0.312
#> GSM123736 2 0.825 0.0794 0.284 0.376 0.012 0.328
#> GSM123740 2 0.825 0.0794 0.284 0.376 0.012 0.328
#> GSM123744 1 0.744 0.2442 0.512 0.244 0.000 0.244
#> GSM123746 1 0.759 0.2530 0.504 0.212 0.004 0.280
#> GSM123750 1 0.744 0.2442 0.512 0.244 0.000 0.244
#> GSM123752 1 0.765 0.2157 0.460 0.240 0.000 0.300
#> GSM123756 1 0.000 0.4507 1.000 0.000 0.000 0.000
#> GSM123758 1 0.790 0.0279 0.368 0.336 0.000 0.296
#> GSM123761 1 0.253 0.4094 0.888 0.000 0.000 0.112
#> GSM123763 1 0.288 0.4115 0.892 0.000 0.024 0.084
#> GSM123765 2 0.783 0.1452 0.280 0.408 0.000 0.312
#> GSM123769 1 0.000 0.4507 1.000 0.000 0.000 0.000
#> GSM123771 1 0.000 0.4507 1.000 0.000 0.000 0.000
#> GSM123774 1 0.000 0.4507 1.000 0.000 0.000 0.000
#> GSM123778 2 0.783 0.1452 0.280 0.408 0.000 0.312
#> GSM123780 2 0.783 0.1452 0.280 0.408 0.000 0.312
#> GSM123784 2 0.783 0.1452 0.280 0.408 0.000 0.312
#> GSM123787 2 0.783 0.1452 0.280 0.408 0.000 0.312
#> GSM123791 2 0.785 0.1226 0.292 0.400 0.000 0.308
#> GSM123795 2 0.825 0.0794 0.284 0.376 0.012 0.328
#> GSM123799 2 0.825 0.0794 0.284 0.376 0.012 0.328
#> GSM123730 2 0.654 0.0864 0.000 0.528 0.080 0.392
#> GSM123734 3 0.292 0.0000 0.028 0.000 0.892 0.080
#> GSM123738 4 0.531 -0.1489 0.000 0.036 0.280 0.684
#> GSM123742 4 0.800 -0.0454 0.336 0.116 0.048 0.500
#> GSM123745 1 0.759 0.2025 0.528 0.080 0.048 0.344
#> GSM123748 1 0.790 0.1132 0.460 0.096 0.048 0.396
#> GSM123751 1 0.762 0.1923 0.516 0.080 0.048 0.356
#> GSM123754 1 0.738 0.2618 0.568 0.080 0.044 0.308
#> GSM123757 1 0.763 0.2480 0.496 0.212 0.004 0.288
#> GSM123760 4 0.798 -0.0766 0.356 0.116 0.044 0.484
#> GSM123762 1 0.301 0.4042 0.888 0.000 0.032 0.080
#> GSM123764 4 0.778 0.1825 0.096 0.424 0.040 0.440
#> GSM123767 1 0.738 0.2618 0.568 0.080 0.044 0.308
#> GSM123770 1 0.738 0.2618 0.568 0.080 0.044 0.308
#> GSM123773 1 0.738 0.2618 0.568 0.080 0.044 0.308
#> GSM123777 2 0.654 0.0864 0.000 0.528 0.080 0.392
#> GSM123779 2 0.657 0.2723 0.052 0.632 0.032 0.284
#> GSM123782 4 0.778 0.1576 0.096 0.432 0.040 0.432
#> GSM123786 2 0.783 0.1452 0.280 0.408 0.000 0.312
#> GSM123789 2 0.657 0.2723 0.052 0.632 0.032 0.284
#> GSM123793 4 0.490 -0.4506 0.000 0.000 0.416 0.584
#> GSM123797 4 0.531 -0.1489 0.000 0.036 0.280 0.684
#> GSM123729 2 0.000 0.7060 0.000 1.000 0.000 0.000
#> GSM123733 2 0.000 0.7060 0.000 1.000 0.000 0.000
#> GSM123737 2 0.000 0.7060 0.000 1.000 0.000 0.000
#> GSM123741 2 0.000 0.7060 0.000 1.000 0.000 0.000
#> GSM123747 2 0.000 0.7060 0.000 1.000 0.000 0.000
#> GSM123753 2 0.000 0.7060 0.000 1.000 0.000 0.000
#> GSM123759 2 0.000 0.7060 0.000 1.000 0.000 0.000
#> GSM123766 2 0.000 0.7060 0.000 1.000 0.000 0.000
#> GSM123772 2 0.000 0.7060 0.000 1.000 0.000 0.000
#> GSM123775 2 0.000 0.7060 0.000 1.000 0.000 0.000
#> GSM123781 2 0.000 0.7060 0.000 1.000 0.000 0.000
#> GSM123785 2 0.000 0.7060 0.000 1.000 0.000 0.000
#> GSM123788 2 0.000 0.7060 0.000 1.000 0.000 0.000
#> GSM123792 2 0.000 0.7060 0.000 1.000 0.000 0.000
#> GSM123796 2 0.000 0.7060 0.000 1.000 0.000 0.000
#> GSM123731 2 0.000 0.7060 0.000 1.000 0.000 0.000
#> GSM123735 2 0.000 0.7060 0.000 1.000 0.000 0.000
#> GSM123739 2 0.000 0.7060 0.000 1.000 0.000 0.000
#> GSM123743 2 0.000 0.7060 0.000 1.000 0.000 0.000
#> GSM123749 2 0.000 0.7060 0.000 1.000 0.000 0.000
#> GSM123755 2 0.000 0.7060 0.000 1.000 0.000 0.000
#> GSM123768 2 0.000 0.7060 0.000 1.000 0.000 0.000
#> GSM123776 2 0.359 0.5675 0.168 0.824 0.000 0.008
#> GSM123783 2 0.000 0.7060 0.000 1.000 0.000 0.000
#> GSM123790 2 0.000 0.7060 0.000 1.000 0.000 0.000
#> GSM123794 2 0.000 0.7060 0.000 1.000 0.000 0.000
#> GSM123798 2 0.000 0.7060 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM123732 3 0.415 0.8686 0.020 0.240 0.736 0.004 0.000
#> GSM123736 3 0.394 0.8633 0.000 0.232 0.748 0.020 0.000
#> GSM123740 3 0.394 0.8633 0.000 0.232 0.748 0.020 0.000
#> GSM123744 3 0.585 0.7173 0.220 0.156 0.620 0.004 0.000
#> GSM123746 3 0.668 0.6560 0.220 0.140 0.588 0.052 0.000
#> GSM123750 3 0.585 0.7173 0.220 0.156 0.620 0.004 0.000
#> GSM123752 3 0.577 0.7388 0.160 0.144 0.672 0.024 0.000
#> GSM123756 1 0.297 0.5318 0.816 0.000 0.184 0.000 0.000
#> GSM123758 3 0.461 0.8374 0.072 0.200 0.728 0.000 0.000
#> GSM123761 1 0.465 0.2934 0.600 0.000 0.384 0.012 0.004
#> GSM123763 1 0.270 0.4930 0.884 0.000 0.088 0.024 0.004
#> GSM123765 3 0.374 0.8674 0.000 0.264 0.732 0.004 0.000
#> GSM123769 1 0.297 0.5318 0.816 0.000 0.184 0.000 0.000
#> GSM123771 1 0.297 0.5318 0.816 0.000 0.184 0.000 0.000
#> GSM123774 1 0.297 0.5318 0.816 0.000 0.184 0.000 0.000
#> GSM123778 3 0.374 0.8674 0.000 0.264 0.732 0.004 0.000
#> GSM123780 3 0.374 0.8674 0.000 0.264 0.732 0.004 0.000
#> GSM123784 3 0.374 0.8674 0.000 0.264 0.732 0.004 0.000
#> GSM123787 3 0.374 0.8674 0.000 0.264 0.732 0.004 0.000
#> GSM123791 3 0.353 0.8701 0.000 0.256 0.744 0.000 0.000
#> GSM123795 3 0.394 0.8633 0.000 0.232 0.748 0.020 0.000
#> GSM123799 3 0.394 0.8633 0.000 0.232 0.748 0.020 0.000
#> GSM123730 2 0.779 -0.0371 0.008 0.428 0.252 0.260 0.052
#> GSM123734 5 0.154 0.0000 0.000 0.000 0.000 0.068 0.932
#> GSM123738 4 0.531 -0.1317 0.004 0.000 0.284 0.640 0.072
#> GSM123742 4 0.728 0.0369 0.264 0.036 0.240 0.460 0.000
#> GSM123745 1 0.564 0.3387 0.488 0.024 0.032 0.456 0.000
#> GSM123748 4 0.674 -0.2913 0.400 0.032 0.116 0.452 0.000
#> GSM123751 1 0.583 0.3188 0.476 0.024 0.044 0.456 0.000
#> GSM123754 1 0.593 0.3950 0.500 0.024 0.052 0.424 0.000
#> GSM123757 3 0.672 0.6474 0.228 0.140 0.580 0.052 0.000
#> GSM123760 4 0.733 0.0187 0.272 0.036 0.248 0.444 0.000
#> GSM123762 1 0.240 0.4818 0.904 0.000 0.068 0.024 0.004
#> GSM123764 4 0.771 0.1754 0.052 0.292 0.296 0.360 0.000
#> GSM123767 1 0.593 0.3950 0.500 0.024 0.052 0.424 0.000
#> GSM123770 1 0.593 0.3950 0.500 0.024 0.052 0.424 0.000
#> GSM123773 1 0.593 0.3950 0.500 0.024 0.052 0.424 0.000
#> GSM123777 2 0.779 -0.0371 0.008 0.428 0.252 0.260 0.052
#> GSM123779 2 0.718 0.0692 0.044 0.500 0.204 0.252 0.000
#> GSM123782 4 0.773 0.1465 0.052 0.308 0.296 0.344 0.000
#> GSM123786 3 0.374 0.8674 0.000 0.264 0.732 0.004 0.000
#> GSM123789 2 0.718 0.0692 0.044 0.500 0.204 0.252 0.000
#> GSM123793 4 0.622 -0.3262 0.004 0.000 0.232 0.568 0.196
#> GSM123797 4 0.531 -0.1317 0.004 0.000 0.284 0.640 0.072
#> GSM123729 2 0.000 0.9117 0.000 1.000 0.000 0.000 0.000
#> GSM123733 2 0.000 0.9117 0.000 1.000 0.000 0.000 0.000
#> GSM123737 2 0.000 0.9117 0.000 1.000 0.000 0.000 0.000
#> GSM123741 2 0.000 0.9117 0.000 1.000 0.000 0.000 0.000
#> GSM123747 2 0.000 0.9117 0.000 1.000 0.000 0.000 0.000
#> GSM123753 2 0.000 0.9117 0.000 1.000 0.000 0.000 0.000
#> GSM123759 2 0.000 0.9117 0.000 1.000 0.000 0.000 0.000
#> GSM123766 2 0.000 0.9117 0.000 1.000 0.000 0.000 0.000
#> GSM123772 2 0.000 0.9117 0.000 1.000 0.000 0.000 0.000
#> GSM123775 2 0.000 0.9117 0.000 1.000 0.000 0.000 0.000
#> GSM123781 2 0.000 0.9117 0.000 1.000 0.000 0.000 0.000
#> GSM123785 2 0.000 0.9117 0.000 1.000 0.000 0.000 0.000
#> GSM123788 2 0.000 0.9117 0.000 1.000 0.000 0.000 0.000
#> GSM123792 2 0.000 0.9117 0.000 1.000 0.000 0.000 0.000
#> GSM123796 2 0.000 0.9117 0.000 1.000 0.000 0.000 0.000
#> GSM123731 2 0.000 0.9117 0.000 1.000 0.000 0.000 0.000
#> GSM123735 2 0.000 0.9117 0.000 1.000 0.000 0.000 0.000
#> GSM123739 2 0.000 0.9117 0.000 1.000 0.000 0.000 0.000
#> GSM123743 2 0.000 0.9117 0.000 1.000 0.000 0.000 0.000
#> GSM123749 2 0.000 0.9117 0.000 1.000 0.000 0.000 0.000
#> GSM123755 2 0.000 0.9117 0.000 1.000 0.000 0.000 0.000
#> GSM123768 2 0.000 0.9117 0.000 1.000 0.000 0.000 0.000
#> GSM123776 2 0.370 0.7176 0.128 0.824 0.036 0.012 0.000
#> GSM123783 2 0.000 0.9117 0.000 1.000 0.000 0.000 0.000
#> GSM123790 2 0.000 0.9117 0.000 1.000 0.000 0.000 0.000
#> GSM123794 2 0.000 0.9117 0.000 1.000 0.000 0.000 0.000
#> GSM123798 2 0.000 0.9117 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM123732 3 0.164 0.8816 0.000 0.076 0.920 0.000 0.004 0.000
#> GSM123736 3 0.259 0.8800 0.000 0.084 0.872 0.044 0.000 0.000
#> GSM123740 3 0.259 0.8800 0.000 0.084 0.872 0.044 0.000 0.000
#> GSM123744 3 0.437 0.7113 0.024 0.056 0.740 0.000 0.000 0.180
#> GSM123746 3 0.525 0.6612 0.104 0.056 0.688 0.000 0.000 0.152
#> GSM123750 3 0.440 0.7061 0.024 0.056 0.736 0.000 0.000 0.184
#> GSM123752 3 0.429 0.7635 0.064 0.056 0.776 0.000 0.000 0.104
#> GSM123756 6 0.541 0.7921 0.260 0.000 0.168 0.000 0.000 0.572
#> GSM123758 3 0.263 0.8517 0.016 0.064 0.884 0.000 0.000 0.036
#> GSM123761 6 0.536 0.4754 0.080 0.000 0.380 0.000 0.012 0.528
#> GSM123763 6 0.384 0.5773 0.148 0.000 0.056 0.000 0.012 0.784
#> GSM123765 3 0.196 0.8863 0.000 0.100 0.896 0.000 0.004 0.000
#> GSM123769 6 0.541 0.7921 0.260 0.000 0.168 0.000 0.000 0.572
#> GSM123771 6 0.541 0.7921 0.260 0.000 0.168 0.000 0.000 0.572
#> GSM123774 6 0.541 0.7921 0.260 0.000 0.168 0.000 0.000 0.572
#> GSM123778 3 0.196 0.8863 0.000 0.100 0.896 0.000 0.004 0.000
#> GSM123780 3 0.196 0.8863 0.000 0.100 0.896 0.000 0.004 0.000
#> GSM123784 3 0.196 0.8863 0.000 0.100 0.896 0.000 0.004 0.000
#> GSM123787 3 0.196 0.8863 0.000 0.100 0.896 0.000 0.004 0.000
#> GSM123791 3 0.171 0.8871 0.000 0.092 0.908 0.000 0.000 0.000
#> GSM123795 3 0.259 0.8800 0.000 0.084 0.872 0.044 0.000 0.000
#> GSM123799 3 0.259 0.8800 0.000 0.084 0.872 0.044 0.000 0.000
#> GSM123730 2 0.770 -0.1768 0.052 0.364 0.148 0.084 0.352 0.000
#> GSM123734 5 0.613 0.0000 0.028 0.000 0.064 0.168 0.636 0.104
#> GSM123738 4 0.395 0.7954 0.008 0.000 0.008 0.672 0.312 0.000
#> GSM123742 1 0.440 0.5881 0.748 0.004 0.180 0.004 0.024 0.040
#> GSM123745 1 0.081 0.6991 0.976 0.004 0.008 0.000 0.004 0.008
#> GSM123748 1 0.226 0.6831 0.892 0.004 0.092 0.000 0.004 0.008
#> GSM123751 1 0.110 0.7021 0.964 0.004 0.020 0.000 0.004 0.008
#> GSM123754 1 0.158 0.6908 0.936 0.004 0.012 0.000 0.000 0.048
#> GSM123757 3 0.533 0.6516 0.112 0.056 0.680 0.000 0.000 0.152
#> GSM123760 1 0.483 0.5805 0.716 0.004 0.180 0.004 0.020 0.076
#> GSM123762 6 0.370 0.5547 0.160 0.000 0.040 0.000 0.012 0.788
#> GSM123764 1 0.727 0.2823 0.424 0.252 0.256 0.004 0.028 0.036
#> GSM123767 1 0.158 0.6908 0.936 0.004 0.012 0.000 0.000 0.048
#> GSM123770 1 0.158 0.6908 0.936 0.004 0.012 0.000 0.000 0.048
#> GSM123773 1 0.158 0.6908 0.936 0.004 0.012 0.000 0.000 0.048
#> GSM123777 2 0.770 -0.1768 0.052 0.364 0.148 0.084 0.352 0.000
#> GSM123779 2 0.702 -0.0605 0.288 0.424 0.216 0.000 0.068 0.004
#> GSM123782 1 0.725 0.2686 0.412 0.264 0.260 0.004 0.024 0.036
#> GSM123786 3 0.196 0.8863 0.000 0.100 0.896 0.000 0.004 0.000
#> GSM123789 2 0.704 -0.0707 0.288 0.420 0.220 0.000 0.068 0.004
#> GSM123793 4 0.026 0.4844 0.008 0.000 0.000 0.992 0.000 0.000
#> GSM123797 4 0.395 0.7954 0.008 0.000 0.008 0.672 0.312 0.000
#> GSM123729 2 0.000 0.9087 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123733 2 0.000 0.9087 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123737 2 0.000 0.9087 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123741 2 0.000 0.9087 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123747 2 0.000 0.9087 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123753 2 0.000 0.9087 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123759 2 0.000 0.9087 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123766 2 0.000 0.9087 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123772 2 0.000 0.9087 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123775 2 0.000 0.9087 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123781 2 0.000 0.9087 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123785 2 0.000 0.9087 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123788 2 0.000 0.9087 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123792 2 0.000 0.9087 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123796 2 0.000 0.9087 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123731 2 0.000 0.9087 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123735 2 0.000 0.9087 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123739 2 0.000 0.9087 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123743 2 0.000 0.9087 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123749 2 0.000 0.9087 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123755 2 0.000 0.9087 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123768 2 0.000 0.9087 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123776 2 0.334 0.7335 0.048 0.824 0.008 0.000 0.000 0.120
#> GSM123783 2 0.000 0.9087 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123790 2 0.000 0.9087 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123794 2 0.000 0.9087 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123798 2 0.000 0.9087 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) infection(p) agent(p) k
#> SD:hclust 58 6.76e-07 6.76e-07 0.01310 2
#> SD:hclust 44 1.84e-09 1.84e-09 0.01402 3
#> SD:hclust 27 NA NA NA 4
#> SD:hclust 49 3.46e-10 3.46e-10 0.00154 5
#> SD:hclust 62 4.60e-19 4.60e-19 0.00069 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "kmeans"]
# you can also extract it by
# res = res_list["SD:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.984 0.994 0.4756 0.522 0.522
#> 3 3 0.796 0.833 0.897 0.3934 0.791 0.605
#> 4 4 0.755 0.864 0.882 0.1000 0.920 0.762
#> 5 5 0.746 0.709 0.823 0.0555 0.982 0.933
#> 6 6 0.766 0.675 0.791 0.0387 0.986 0.945
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
#> GSM123732 1 0.00 1.000 1.000 0.000
#> GSM123736 1 0.00 1.000 1.000 0.000
#> GSM123740 1 0.00 1.000 1.000 0.000
#> GSM123744 1 0.00 1.000 1.000 0.000
#> GSM123746 1 0.00 1.000 1.000 0.000
#> GSM123750 1 0.00 1.000 1.000 0.000
#> GSM123752 1 0.00 1.000 1.000 0.000
#> GSM123756 1 0.00 1.000 1.000 0.000
#> GSM123758 1 0.00 1.000 1.000 0.000
#> GSM123761 1 0.00 1.000 1.000 0.000
#> GSM123763 1 0.00 1.000 1.000 0.000
#> GSM123765 1 0.00 1.000 1.000 0.000
#> GSM123769 1 0.00 1.000 1.000 0.000
#> GSM123771 1 0.00 1.000 1.000 0.000
#> GSM123774 1 0.00 1.000 1.000 0.000
#> GSM123778 1 0.00 1.000 1.000 0.000
#> GSM123780 1 0.00 1.000 1.000 0.000
#> GSM123784 1 0.00 1.000 1.000 0.000
#> GSM123787 1 0.00 1.000 1.000 0.000
#> GSM123791 1 0.00 1.000 1.000 0.000
#> GSM123795 1 0.00 1.000 1.000 0.000
#> GSM123799 1 0.00 1.000 1.000 0.000
#> GSM123730 1 0.00 1.000 1.000 0.000
#> GSM123734 1 0.00 1.000 1.000 0.000
#> GSM123738 1 0.00 1.000 1.000 0.000
#> GSM123742 1 0.00 1.000 1.000 0.000
#> GSM123745 1 0.00 1.000 1.000 0.000
#> GSM123748 1 0.00 1.000 1.000 0.000
#> GSM123751 1 0.00 1.000 1.000 0.000
#> GSM123754 1 0.00 1.000 1.000 0.000
#> GSM123757 1 0.00 1.000 1.000 0.000
#> GSM123760 1 0.00 1.000 1.000 0.000
#> GSM123762 1 0.00 1.000 1.000 0.000
#> GSM123764 1 0.00 1.000 1.000 0.000
#> GSM123767 1 0.00 1.000 1.000 0.000
#> GSM123770 1 0.00 1.000 1.000 0.000
#> GSM123773 1 0.00 1.000 1.000 0.000
#> GSM123777 1 0.00 1.000 1.000 0.000
#> GSM123779 1 0.00 1.000 1.000 0.000
#> GSM123782 1 0.00 1.000 1.000 0.000
#> GSM123786 1 0.00 1.000 1.000 0.000
#> GSM123789 1 0.00 1.000 1.000 0.000
#> GSM123793 1 0.00 1.000 1.000 0.000
#> GSM123797 1 0.00 1.000 1.000 0.000
#> GSM123729 2 0.00 0.984 0.000 1.000
#> GSM123733 2 0.00 0.984 0.000 1.000
#> GSM123737 2 0.00 0.984 0.000 1.000
#> GSM123741 2 0.00 0.984 0.000 1.000
#> GSM123747 2 0.00 0.984 0.000 1.000
#> GSM123753 2 0.00 0.984 0.000 1.000
#> GSM123759 2 0.00 0.984 0.000 1.000
#> GSM123766 2 0.00 0.984 0.000 1.000
#> GSM123772 2 0.00 0.984 0.000 1.000
#> GSM123775 2 0.00 0.984 0.000 1.000
#> GSM123781 2 0.00 0.984 0.000 1.000
#> GSM123785 2 0.00 0.984 0.000 1.000
#> GSM123788 2 0.00 0.984 0.000 1.000
#> GSM123792 2 0.00 0.984 0.000 1.000
#> GSM123796 2 0.00 0.984 0.000 1.000
#> GSM123731 2 0.00 0.984 0.000 1.000
#> GSM123735 2 0.00 0.984 0.000 1.000
#> GSM123739 2 0.00 0.984 0.000 1.000
#> GSM123743 2 0.00 0.984 0.000 1.000
#> GSM123749 2 0.00 0.984 0.000 1.000
#> GSM123755 2 0.00 0.984 0.000 1.000
#> GSM123768 2 0.00 0.984 0.000 1.000
#> GSM123776 2 0.98 0.288 0.416 0.584
#> GSM123783 2 0.00 0.984 0.000 1.000
#> GSM123790 2 0.00 0.984 0.000 1.000
#> GSM123794 2 0.00 0.984 0.000 1.000
#> GSM123798 2 0.00 0.984 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM123732 3 0.0424 0.822 0.008 0.000 0.992
#> GSM123736 3 0.0237 0.820 0.004 0.000 0.996
#> GSM123740 3 0.0237 0.820 0.004 0.000 0.996
#> GSM123744 3 0.5706 0.306 0.320 0.000 0.680
#> GSM123746 1 0.5529 0.769 0.704 0.000 0.296
#> GSM123750 3 0.5810 0.254 0.336 0.000 0.664
#> GSM123752 3 0.5591 0.352 0.304 0.000 0.696
#> GSM123756 1 0.5529 0.769 0.704 0.000 0.296
#> GSM123758 3 0.0592 0.820 0.012 0.000 0.988
#> GSM123761 1 0.5529 0.769 0.704 0.000 0.296
#> GSM123763 1 0.5497 0.772 0.708 0.000 0.292
#> GSM123765 3 0.0424 0.822 0.008 0.000 0.992
#> GSM123769 1 0.5529 0.769 0.704 0.000 0.296
#> GSM123771 1 0.5529 0.769 0.704 0.000 0.296
#> GSM123774 1 0.5497 0.771 0.708 0.000 0.292
#> GSM123778 3 0.0424 0.822 0.008 0.000 0.992
#> GSM123780 3 0.0892 0.821 0.020 0.000 0.980
#> GSM123784 3 0.0424 0.822 0.008 0.000 0.992
#> GSM123787 3 0.0424 0.822 0.008 0.000 0.992
#> GSM123791 3 0.0592 0.820 0.012 0.000 0.988
#> GSM123795 3 0.0237 0.820 0.004 0.000 0.996
#> GSM123799 3 0.0237 0.820 0.004 0.000 0.996
#> GSM123730 3 0.5138 0.734 0.252 0.000 0.748
#> GSM123734 1 0.1964 0.784 0.944 0.000 0.056
#> GSM123738 3 0.5138 0.734 0.252 0.000 0.748
#> GSM123742 1 0.2537 0.819 0.920 0.000 0.080
#> GSM123745 1 0.2537 0.819 0.920 0.000 0.080
#> GSM123748 1 0.2537 0.819 0.920 0.000 0.080
#> GSM123751 1 0.2537 0.819 0.920 0.000 0.080
#> GSM123754 1 0.2537 0.819 0.920 0.000 0.080
#> GSM123757 1 0.5291 0.782 0.732 0.000 0.268
#> GSM123760 1 0.2537 0.819 0.920 0.000 0.080
#> GSM123762 1 0.4504 0.802 0.804 0.000 0.196
#> GSM123764 3 0.4887 0.743 0.228 0.000 0.772
#> GSM123767 1 0.2537 0.819 0.920 0.000 0.080
#> GSM123770 1 0.2448 0.819 0.924 0.000 0.076
#> GSM123773 1 0.2537 0.819 0.920 0.000 0.080
#> GSM123777 3 0.5138 0.734 0.252 0.000 0.748
#> GSM123779 3 0.5465 0.686 0.288 0.000 0.712
#> GSM123782 3 0.4887 0.743 0.228 0.000 0.772
#> GSM123786 3 0.0424 0.822 0.008 0.000 0.992
#> GSM123789 3 0.4887 0.743 0.228 0.000 0.772
#> GSM123793 3 0.5138 0.734 0.252 0.000 0.748
#> GSM123797 3 0.5138 0.734 0.252 0.000 0.748
#> GSM123729 2 0.1529 0.979 0.040 0.960 0.000
#> GSM123733 2 0.0892 0.989 0.020 0.980 0.000
#> GSM123737 2 0.1529 0.979 0.040 0.960 0.000
#> GSM123741 2 0.0000 0.991 0.000 1.000 0.000
#> GSM123747 2 0.0237 0.990 0.004 0.996 0.000
#> GSM123753 2 0.0000 0.991 0.000 1.000 0.000
#> GSM123759 2 0.0000 0.991 0.000 1.000 0.000
#> GSM123766 2 0.0000 0.991 0.000 1.000 0.000
#> GSM123772 2 0.0000 0.991 0.000 1.000 0.000
#> GSM123775 2 0.1411 0.981 0.036 0.964 0.000
#> GSM123781 2 0.0000 0.991 0.000 1.000 0.000
#> GSM123785 2 0.0892 0.989 0.020 0.980 0.000
#> GSM123788 2 0.0892 0.989 0.020 0.980 0.000
#> GSM123792 2 0.0747 0.989 0.016 0.984 0.000
#> GSM123796 2 0.0747 0.989 0.016 0.984 0.000
#> GSM123731 2 0.0237 0.990 0.004 0.996 0.000
#> GSM123735 2 0.1163 0.986 0.028 0.972 0.000
#> GSM123739 2 0.1529 0.979 0.040 0.960 0.000
#> GSM123743 2 0.0000 0.991 0.000 1.000 0.000
#> GSM123749 2 0.0000 0.991 0.000 1.000 0.000
#> GSM123755 2 0.0000 0.991 0.000 1.000 0.000
#> GSM123768 2 0.0000 0.991 0.000 1.000 0.000
#> GSM123776 1 0.7446 0.147 0.532 0.432 0.036
#> GSM123783 2 0.0424 0.990 0.008 0.992 0.000
#> GSM123790 2 0.1163 0.986 0.028 0.972 0.000
#> GSM123794 2 0.0747 0.989 0.016 0.984 0.000
#> GSM123798 2 0.0000 0.991 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM123732 3 0.0376 0.942 0.004 0.000 0.992 0.004
#> GSM123736 3 0.1356 0.931 0.008 0.000 0.960 0.032
#> GSM123740 3 0.1356 0.931 0.008 0.000 0.960 0.032
#> GSM123744 3 0.3858 0.819 0.100 0.000 0.844 0.056
#> GSM123746 1 0.4037 0.803 0.832 0.000 0.112 0.056
#> GSM123750 3 0.4037 0.804 0.112 0.000 0.832 0.056
#> GSM123752 3 0.3464 0.834 0.108 0.000 0.860 0.032
#> GSM123756 1 0.2530 0.817 0.896 0.000 0.100 0.004
#> GSM123758 3 0.0804 0.940 0.012 0.000 0.980 0.008
#> GSM123761 1 0.4055 0.801 0.832 0.000 0.108 0.060
#> GSM123763 1 0.3894 0.802 0.844 0.000 0.088 0.068
#> GSM123765 3 0.0524 0.941 0.004 0.000 0.988 0.008
#> GSM123769 1 0.2530 0.817 0.896 0.000 0.100 0.004
#> GSM123771 1 0.2530 0.817 0.896 0.000 0.100 0.004
#> GSM123774 1 0.2466 0.818 0.900 0.000 0.096 0.004
#> GSM123778 3 0.0376 0.942 0.004 0.000 0.992 0.004
#> GSM123780 3 0.0657 0.938 0.004 0.000 0.984 0.012
#> GSM123784 3 0.0524 0.941 0.004 0.000 0.988 0.008
#> GSM123787 3 0.0524 0.941 0.004 0.000 0.988 0.008
#> GSM123791 3 0.0524 0.941 0.004 0.000 0.988 0.008
#> GSM123795 3 0.1356 0.931 0.008 0.000 0.960 0.032
#> GSM123799 3 0.1256 0.933 0.008 0.000 0.964 0.028
#> GSM123730 4 0.4053 0.870 0.004 0.000 0.228 0.768
#> GSM123734 4 0.3881 0.632 0.172 0.000 0.016 0.812
#> GSM123738 4 0.3801 0.865 0.000 0.000 0.220 0.780
#> GSM123742 1 0.5776 0.342 0.504 0.000 0.028 0.468
#> GSM123745 1 0.4399 0.767 0.768 0.000 0.020 0.212
#> GSM123748 1 0.4675 0.760 0.736 0.000 0.020 0.244
#> GSM123751 1 0.4610 0.751 0.744 0.000 0.020 0.236
#> GSM123754 1 0.4323 0.773 0.776 0.000 0.020 0.204
#> GSM123757 1 0.2949 0.822 0.888 0.000 0.088 0.024
#> GSM123760 4 0.5078 0.403 0.272 0.000 0.028 0.700
#> GSM123762 1 0.3758 0.808 0.848 0.000 0.048 0.104
#> GSM123764 4 0.5047 0.806 0.016 0.000 0.316 0.668
#> GSM123767 1 0.4535 0.742 0.744 0.000 0.016 0.240
#> GSM123770 1 0.3037 0.810 0.880 0.000 0.020 0.100
#> GSM123773 1 0.4323 0.773 0.776 0.000 0.020 0.204
#> GSM123777 4 0.4252 0.865 0.004 0.000 0.252 0.744
#> GSM123779 4 0.4609 0.867 0.024 0.000 0.224 0.752
#> GSM123782 4 0.5110 0.792 0.016 0.000 0.328 0.656
#> GSM123786 3 0.0524 0.941 0.004 0.000 0.988 0.008
#> GSM123789 4 0.4776 0.852 0.016 0.000 0.272 0.712
#> GSM123793 4 0.3668 0.863 0.004 0.000 0.188 0.808
#> GSM123797 4 0.3688 0.868 0.000 0.000 0.208 0.792
#> GSM123729 2 0.4203 0.882 0.068 0.824 0.000 0.108
#> GSM123733 2 0.1913 0.952 0.020 0.940 0.000 0.040
#> GSM123737 2 0.4203 0.882 0.068 0.824 0.000 0.108
#> GSM123741 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> GSM123747 2 0.0592 0.958 0.000 0.984 0.000 0.016
#> GSM123753 2 0.0188 0.960 0.004 0.996 0.000 0.000
#> GSM123759 2 0.0188 0.960 0.004 0.996 0.000 0.000
#> GSM123766 2 0.0188 0.960 0.004 0.996 0.000 0.000
#> GSM123772 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> GSM123775 2 0.4274 0.882 0.072 0.820 0.000 0.108
#> GSM123781 2 0.0188 0.960 0.004 0.996 0.000 0.000
#> GSM123785 2 0.1913 0.952 0.020 0.940 0.000 0.040
#> GSM123788 2 0.1913 0.952 0.020 0.940 0.000 0.040
#> GSM123792 2 0.1305 0.956 0.004 0.960 0.000 0.036
#> GSM123796 2 0.1452 0.955 0.008 0.956 0.000 0.036
#> GSM123731 2 0.0524 0.960 0.008 0.988 0.000 0.004
#> GSM123735 2 0.2521 0.943 0.024 0.912 0.000 0.064
#> GSM123739 2 0.4203 0.882 0.068 0.824 0.000 0.108
#> GSM123743 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> GSM123749 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> GSM123755 2 0.0188 0.960 0.004 0.996 0.000 0.000
#> GSM123768 2 0.0188 0.960 0.004 0.996 0.000 0.000
#> GSM123776 1 0.6303 0.445 0.660 0.228 0.004 0.108
#> GSM123783 2 0.1406 0.952 0.016 0.960 0.000 0.024
#> GSM123790 2 0.2722 0.939 0.032 0.904 0.000 0.064
#> GSM123794 2 0.1677 0.954 0.012 0.948 0.000 0.040
#> GSM123798 2 0.0188 0.960 0.004 0.996 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM123732 3 0.0579 0.9395 0.000 0.000 0.984 0.008 0.008
#> GSM123736 3 0.1525 0.9293 0.004 0.000 0.948 0.036 0.012
#> GSM123740 3 0.1525 0.9293 0.004 0.000 0.948 0.036 0.012
#> GSM123744 3 0.3617 0.8298 0.060 0.000 0.836 0.008 0.096
#> GSM123746 1 0.4722 0.2142 0.716 0.000 0.040 0.012 0.232
#> GSM123750 3 0.4014 0.7974 0.060 0.000 0.804 0.008 0.128
#> GSM123752 3 0.2681 0.8833 0.052 0.000 0.892 0.004 0.052
#> GSM123756 1 0.3099 0.5082 0.848 0.000 0.028 0.000 0.124
#> GSM123758 3 0.1205 0.9306 0.004 0.000 0.956 0.000 0.040
#> GSM123761 1 0.5614 -0.4861 0.476 0.000 0.040 0.016 0.468
#> GSM123763 5 0.5781 0.3511 0.452 0.000 0.032 0.032 0.484
#> GSM123765 3 0.0451 0.9393 0.000 0.000 0.988 0.008 0.004
#> GSM123769 1 0.3099 0.5082 0.848 0.000 0.028 0.000 0.124
#> GSM123771 1 0.3099 0.5082 0.848 0.000 0.028 0.000 0.124
#> GSM123774 1 0.3099 0.5082 0.848 0.000 0.028 0.000 0.124
#> GSM123778 3 0.0579 0.9395 0.000 0.000 0.984 0.008 0.008
#> GSM123780 3 0.0451 0.9393 0.000 0.000 0.988 0.008 0.004
#> GSM123784 3 0.0451 0.9393 0.000 0.000 0.988 0.008 0.004
#> GSM123787 3 0.0579 0.9395 0.000 0.000 0.984 0.008 0.008
#> GSM123791 3 0.0290 0.9393 0.000 0.000 0.992 0.000 0.008
#> GSM123795 3 0.1525 0.9293 0.004 0.000 0.948 0.036 0.012
#> GSM123799 3 0.1525 0.9293 0.004 0.000 0.948 0.036 0.012
#> GSM123730 4 0.3981 0.7794 0.004 0.000 0.136 0.800 0.060
#> GSM123734 4 0.3547 0.6224 0.100 0.000 0.004 0.836 0.060
#> GSM123738 4 0.2304 0.7596 0.000 0.000 0.100 0.892 0.008
#> GSM123742 1 0.6999 -0.4036 0.408 0.000 0.016 0.208 0.368
#> GSM123745 1 0.4030 0.5211 0.808 0.000 0.012 0.120 0.060
#> GSM123748 1 0.5258 0.3442 0.704 0.000 0.012 0.108 0.176
#> GSM123751 1 0.4322 0.4987 0.788 0.000 0.012 0.124 0.076
#> GSM123754 1 0.2805 0.5669 0.872 0.000 0.012 0.108 0.008
#> GSM123757 1 0.2769 0.5492 0.892 0.000 0.024 0.020 0.064
#> GSM123760 5 0.7093 0.0482 0.240 0.000 0.016 0.340 0.404
#> GSM123762 5 0.5731 0.3592 0.456 0.000 0.016 0.048 0.480
#> GSM123764 4 0.7485 0.5766 0.056 0.000 0.216 0.456 0.272
#> GSM123767 1 0.3216 0.5519 0.852 0.000 0.012 0.116 0.020
#> GSM123770 1 0.1978 0.5678 0.932 0.000 0.012 0.032 0.024
#> GSM123773 1 0.2805 0.5669 0.872 0.000 0.012 0.108 0.008
#> GSM123777 4 0.4214 0.7753 0.004 0.000 0.152 0.780 0.064
#> GSM123779 4 0.6156 0.7313 0.052 0.000 0.132 0.656 0.160
#> GSM123782 4 0.7625 0.5541 0.064 0.000 0.228 0.440 0.268
#> GSM123786 3 0.0579 0.9395 0.000 0.000 0.984 0.008 0.008
#> GSM123789 4 0.6588 0.7069 0.036 0.000 0.184 0.588 0.192
#> GSM123793 4 0.2460 0.7544 0.004 0.000 0.072 0.900 0.024
#> GSM123797 4 0.2249 0.7609 0.000 0.000 0.096 0.896 0.008
#> GSM123729 2 0.5103 0.7687 0.020 0.692 0.000 0.048 0.240
#> GSM123733 2 0.3582 0.8490 0.000 0.768 0.000 0.008 0.224
#> GSM123737 2 0.5076 0.7720 0.020 0.696 0.000 0.048 0.236
#> GSM123741 2 0.0324 0.8881 0.000 0.992 0.000 0.004 0.004
#> GSM123747 2 0.2753 0.8683 0.000 0.856 0.000 0.008 0.136
#> GSM123753 2 0.0324 0.8870 0.004 0.992 0.000 0.000 0.004
#> GSM123759 2 0.0451 0.8869 0.004 0.988 0.000 0.000 0.008
#> GSM123766 2 0.0324 0.8870 0.004 0.992 0.000 0.000 0.004
#> GSM123772 2 0.0324 0.8881 0.000 0.992 0.000 0.004 0.004
#> GSM123775 2 0.5089 0.7658 0.016 0.684 0.000 0.048 0.252
#> GSM123781 2 0.0324 0.8870 0.004 0.992 0.000 0.000 0.004
#> GSM123785 2 0.3582 0.8490 0.000 0.768 0.000 0.008 0.224
#> GSM123788 2 0.3582 0.8490 0.000 0.768 0.000 0.008 0.224
#> GSM123792 2 0.3388 0.8571 0.000 0.792 0.000 0.008 0.200
#> GSM123796 2 0.3388 0.8571 0.000 0.792 0.000 0.008 0.200
#> GSM123731 2 0.0771 0.8893 0.004 0.976 0.000 0.000 0.020
#> GSM123735 2 0.3988 0.8372 0.000 0.732 0.000 0.016 0.252
#> GSM123739 2 0.5076 0.7720 0.020 0.696 0.000 0.048 0.236
#> GSM123743 2 0.0451 0.8885 0.000 0.988 0.000 0.004 0.008
#> GSM123749 2 0.0324 0.8881 0.000 0.992 0.000 0.004 0.004
#> GSM123755 2 0.0324 0.8870 0.004 0.992 0.000 0.000 0.004
#> GSM123768 2 0.0324 0.8870 0.004 0.992 0.000 0.000 0.004
#> GSM123776 1 0.6903 0.1121 0.552 0.164 0.000 0.048 0.236
#> GSM123783 2 0.1569 0.8767 0.004 0.944 0.000 0.008 0.044
#> GSM123790 2 0.4065 0.8335 0.000 0.720 0.000 0.016 0.264
#> GSM123794 2 0.3563 0.8557 0.000 0.780 0.000 0.012 0.208
#> GSM123798 2 0.0324 0.8870 0.004 0.992 0.000 0.000 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM123732 3 0.0291 0.9188 0.000 0.000 0.992 0.004 NA 0.000
#> GSM123736 3 0.2737 0.8917 0.004 0.000 0.876 0.056 NA 0.004
#> GSM123740 3 0.2737 0.8917 0.004 0.000 0.876 0.056 NA 0.004
#> GSM123744 3 0.3718 0.8001 0.004 0.000 0.780 0.000 NA 0.164
#> GSM123746 1 0.5675 0.0101 0.584 0.000 0.052 0.000 NA 0.292
#> GSM123750 3 0.4348 0.7178 0.012 0.000 0.716 0.000 NA 0.220
#> GSM123752 3 0.2872 0.8736 0.008 0.000 0.864 0.000 NA 0.076
#> GSM123756 1 0.4227 0.4822 0.692 0.000 0.000 0.000 NA 0.256
#> GSM123758 3 0.1511 0.9096 0.004 0.000 0.940 0.000 NA 0.012
#> GSM123761 6 0.3881 0.4916 0.252 0.000 0.004 0.000 NA 0.720
#> GSM123763 6 0.4230 0.5729 0.224 0.000 0.000 0.004 NA 0.716
#> GSM123765 3 0.0291 0.9188 0.000 0.000 0.992 0.004 NA 0.000
#> GSM123769 1 0.4227 0.4822 0.692 0.000 0.000 0.000 NA 0.256
#> GSM123771 1 0.4227 0.4822 0.692 0.000 0.000 0.000 NA 0.256
#> GSM123774 1 0.4227 0.4822 0.692 0.000 0.000 0.000 NA 0.256
#> GSM123778 3 0.0291 0.9188 0.000 0.000 0.992 0.004 NA 0.000
#> GSM123780 3 0.0520 0.9149 0.000 0.000 0.984 0.008 NA 0.000
#> GSM123784 3 0.0291 0.9188 0.000 0.000 0.992 0.004 NA 0.000
#> GSM123787 3 0.0291 0.9188 0.000 0.000 0.992 0.004 NA 0.000
#> GSM123791 3 0.0000 0.9187 0.000 0.000 1.000 0.000 NA 0.000
#> GSM123795 3 0.2737 0.8917 0.004 0.000 0.876 0.056 NA 0.004
#> GSM123799 3 0.2737 0.8917 0.004 0.000 0.876 0.056 NA 0.004
#> GSM123730 4 0.3807 0.6429 0.016 0.000 0.040 0.824 NA 0.036
#> GSM123734 4 0.5982 0.4630 0.144 0.000 0.000 0.624 NA 0.104
#> GSM123738 4 0.0862 0.6156 0.000 0.000 0.016 0.972 NA 0.008
#> GSM123742 6 0.6606 0.3422 0.372 0.000 0.000 0.084 NA 0.432
#> GSM123745 1 0.3720 0.4836 0.816 0.000 0.000 0.036 NA 0.092
#> GSM123748 1 0.5079 0.1692 0.652 0.000 0.000 0.024 NA 0.248
#> GSM123751 1 0.4379 0.4210 0.764 0.000 0.000 0.040 NA 0.120
#> GSM123754 1 0.1152 0.5855 0.952 0.000 0.000 0.044 NA 0.004
#> GSM123757 1 0.2721 0.5301 0.868 0.000 0.000 0.004 NA 0.088
#> GSM123760 6 0.7004 0.2535 0.228 0.000 0.000 0.160 NA 0.476
#> GSM123762 6 0.4255 0.5743 0.228 0.000 0.000 0.004 NA 0.712
#> GSM123764 4 0.8601 0.3863 0.084 0.000 0.180 0.300 NA 0.232
#> GSM123767 1 0.2146 0.5629 0.908 0.000 0.000 0.060 NA 0.024
#> GSM123770 1 0.2173 0.5740 0.904 0.000 0.000 0.004 NA 0.064
#> GSM123773 1 0.1152 0.5855 0.952 0.000 0.000 0.044 NA 0.004
#> GSM123777 4 0.4301 0.6401 0.012 0.000 0.080 0.788 NA 0.036
#> GSM123779 4 0.7951 0.5080 0.136 0.000 0.080 0.448 NA 0.132
#> GSM123782 4 0.8636 0.3841 0.088 0.000 0.184 0.296 NA 0.224
#> GSM123786 3 0.0291 0.9188 0.000 0.000 0.992 0.004 NA 0.000
#> GSM123789 4 0.8149 0.5076 0.068 0.000 0.164 0.408 NA 0.160
#> GSM123793 4 0.2164 0.5991 0.000 0.000 0.008 0.908 NA 0.028
#> GSM123797 4 0.0520 0.6167 0.000 0.000 0.008 0.984 NA 0.008
#> GSM123729 2 0.5317 0.6392 0.000 0.568 0.000 0.004 NA 0.112
#> GSM123733 2 0.3634 0.7551 0.000 0.644 0.000 0.000 NA 0.000
#> GSM123737 2 0.5317 0.6392 0.000 0.568 0.000 0.004 NA 0.112
#> GSM123741 2 0.0363 0.8256 0.000 0.988 0.000 0.000 NA 0.000
#> GSM123747 2 0.2883 0.7886 0.000 0.788 0.000 0.000 NA 0.000
#> GSM123753 2 0.0000 0.8243 0.000 1.000 0.000 0.000 NA 0.000
#> GSM123759 2 0.0146 0.8242 0.000 0.996 0.000 0.000 NA 0.000
#> GSM123766 2 0.0146 0.8248 0.000 0.996 0.000 0.000 NA 0.000
#> GSM123772 2 0.0363 0.8256 0.000 0.988 0.000 0.000 NA 0.000
#> GSM123775 2 0.5136 0.6554 0.000 0.584 0.000 0.004 NA 0.092
#> GSM123781 2 0.0000 0.8243 0.000 1.000 0.000 0.000 NA 0.000
#> GSM123785 2 0.3634 0.7551 0.000 0.644 0.000 0.000 NA 0.000
#> GSM123788 2 0.3620 0.7571 0.000 0.648 0.000 0.000 NA 0.000
#> GSM123792 2 0.3499 0.7687 0.000 0.680 0.000 0.000 NA 0.000
#> GSM123796 2 0.3515 0.7675 0.000 0.676 0.000 0.000 NA 0.000
#> GSM123731 2 0.0713 0.8258 0.000 0.972 0.000 0.000 NA 0.000
#> GSM123735 2 0.3747 0.7405 0.000 0.604 0.000 0.000 NA 0.000
#> GSM123739 2 0.5317 0.6392 0.000 0.568 0.000 0.004 NA 0.112
#> GSM123743 2 0.0547 0.8260 0.000 0.980 0.000 0.000 NA 0.000
#> GSM123749 2 0.0260 0.8256 0.000 0.992 0.000 0.000 NA 0.000
#> GSM123755 2 0.0146 0.8242 0.000 0.996 0.000 0.000 NA 0.000
#> GSM123768 2 0.0146 0.8242 0.000 0.996 0.000 0.000 NA 0.000
#> GSM123776 1 0.7329 0.1248 0.416 0.136 0.000 0.004 NA 0.168
#> GSM123783 2 0.1007 0.8156 0.000 0.956 0.000 0.000 NA 0.000
#> GSM123790 2 0.3782 0.7319 0.000 0.588 0.000 0.000 NA 0.000
#> GSM123794 2 0.3607 0.7630 0.000 0.652 0.000 0.000 NA 0.000
#> GSM123798 2 0.0146 0.8242 0.000 0.996 0.000 0.000 NA 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) infection(p) agent(p) k
#> SD:kmeans 70 6.31e-16 6.31e-16 1.30e-05 2
#> SD:kmeans 67 3.52e-14 3.52e-14 3.11e-05 3
#> SD:kmeans 68 3.09e-20 3.09e-20 9.57e-05 4
#> SD:kmeans 62 1.60e-19 1.60e-19 3.44e-04 5
#> SD:kmeans 56 2.41e-18 2.41e-18 3.31e-03 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "skmeans"]
# you can also extract it by
# res = res_list["SD:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.999 1.000 0.4787 0.522 0.522
#> 3 3 0.946 0.934 0.971 0.4068 0.786 0.597
#> 4 4 0.815 0.848 0.909 0.0910 0.886 0.675
#> 5 5 0.731 0.744 0.811 0.0490 1.000 1.000
#> 6 6 0.696 0.596 0.725 0.0355 0.962 0.861
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
#> GSM123732 1 0.0000 1.000 1.000 0.000
#> GSM123736 1 0.0000 1.000 1.000 0.000
#> GSM123740 1 0.0000 1.000 1.000 0.000
#> GSM123744 1 0.0000 1.000 1.000 0.000
#> GSM123746 1 0.0000 1.000 1.000 0.000
#> GSM123750 1 0.0000 1.000 1.000 0.000
#> GSM123752 1 0.0000 1.000 1.000 0.000
#> GSM123756 1 0.0000 1.000 1.000 0.000
#> GSM123758 1 0.0000 1.000 1.000 0.000
#> GSM123761 1 0.0000 1.000 1.000 0.000
#> GSM123763 1 0.0000 1.000 1.000 0.000
#> GSM123765 1 0.0000 1.000 1.000 0.000
#> GSM123769 1 0.0000 1.000 1.000 0.000
#> GSM123771 1 0.0000 1.000 1.000 0.000
#> GSM123774 1 0.0000 1.000 1.000 0.000
#> GSM123778 1 0.0000 1.000 1.000 0.000
#> GSM123780 1 0.0000 1.000 1.000 0.000
#> GSM123784 1 0.0000 1.000 1.000 0.000
#> GSM123787 1 0.0000 1.000 1.000 0.000
#> GSM123791 1 0.0000 1.000 1.000 0.000
#> GSM123795 1 0.0000 1.000 1.000 0.000
#> GSM123799 1 0.0000 1.000 1.000 0.000
#> GSM123730 1 0.1184 0.984 0.984 0.016
#> GSM123734 1 0.0000 1.000 1.000 0.000
#> GSM123738 1 0.0000 1.000 1.000 0.000
#> GSM123742 1 0.0000 1.000 1.000 0.000
#> GSM123745 1 0.0000 1.000 1.000 0.000
#> GSM123748 1 0.0000 1.000 1.000 0.000
#> GSM123751 1 0.0000 1.000 1.000 0.000
#> GSM123754 1 0.0000 1.000 1.000 0.000
#> GSM123757 1 0.0000 1.000 1.000 0.000
#> GSM123760 1 0.0000 1.000 1.000 0.000
#> GSM123762 1 0.0000 1.000 1.000 0.000
#> GSM123764 1 0.0000 1.000 1.000 0.000
#> GSM123767 1 0.0000 1.000 1.000 0.000
#> GSM123770 1 0.0000 1.000 1.000 0.000
#> GSM123773 1 0.0000 1.000 1.000 0.000
#> GSM123777 1 0.0000 1.000 1.000 0.000
#> GSM123779 1 0.0000 1.000 1.000 0.000
#> GSM123782 1 0.0000 1.000 1.000 0.000
#> GSM123786 1 0.0000 1.000 1.000 0.000
#> GSM123789 1 0.0000 1.000 1.000 0.000
#> GSM123793 1 0.0000 1.000 1.000 0.000
#> GSM123797 1 0.0000 1.000 1.000 0.000
#> GSM123729 2 0.0000 1.000 0.000 1.000
#> GSM123733 2 0.0000 1.000 0.000 1.000
#> GSM123737 2 0.0000 1.000 0.000 1.000
#> GSM123741 2 0.0000 1.000 0.000 1.000
#> GSM123747 2 0.0000 1.000 0.000 1.000
#> GSM123753 2 0.0000 1.000 0.000 1.000
#> GSM123759 2 0.0000 1.000 0.000 1.000
#> GSM123766 2 0.0000 1.000 0.000 1.000
#> GSM123772 2 0.0000 1.000 0.000 1.000
#> GSM123775 2 0.0000 1.000 0.000 1.000
#> GSM123781 2 0.0000 1.000 0.000 1.000
#> GSM123785 2 0.0000 1.000 0.000 1.000
#> GSM123788 2 0.0000 1.000 0.000 1.000
#> GSM123792 2 0.0000 1.000 0.000 1.000
#> GSM123796 2 0.0000 1.000 0.000 1.000
#> GSM123731 2 0.0000 1.000 0.000 1.000
#> GSM123735 2 0.0000 1.000 0.000 1.000
#> GSM123739 2 0.0000 1.000 0.000 1.000
#> GSM123743 2 0.0000 1.000 0.000 1.000
#> GSM123749 2 0.0000 1.000 0.000 1.000
#> GSM123755 2 0.0000 1.000 0.000 1.000
#> GSM123768 2 0.0000 1.000 0.000 1.000
#> GSM123776 2 0.0376 0.996 0.004 0.996
#> GSM123783 2 0.0000 1.000 0.000 1.000
#> GSM123790 2 0.0000 1.000 0.000 1.000
#> GSM123794 2 0.0000 1.000 0.000 1.000
#> GSM123798 2 0.0000 1.000 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM123732 3 0.0000 0.9730 0.000 0.000 1.000
#> GSM123736 3 0.0000 0.9730 0.000 0.000 1.000
#> GSM123740 3 0.0000 0.9730 0.000 0.000 1.000
#> GSM123744 1 0.5497 0.6023 0.708 0.000 0.292
#> GSM123746 1 0.0424 0.9261 0.992 0.000 0.008
#> GSM123750 1 0.3816 0.8112 0.852 0.000 0.148
#> GSM123752 1 0.3340 0.8389 0.880 0.000 0.120
#> GSM123756 1 0.0000 0.9296 1.000 0.000 0.000
#> GSM123758 3 0.2165 0.9266 0.064 0.000 0.936
#> GSM123761 1 0.0237 0.9281 0.996 0.000 0.004
#> GSM123763 1 0.0237 0.9284 0.996 0.000 0.004
#> GSM123765 3 0.0000 0.9730 0.000 0.000 1.000
#> GSM123769 1 0.0000 0.9296 1.000 0.000 0.000
#> GSM123771 1 0.0000 0.9296 1.000 0.000 0.000
#> GSM123774 1 0.0000 0.9296 1.000 0.000 0.000
#> GSM123778 3 0.0000 0.9730 0.000 0.000 1.000
#> GSM123780 3 0.0000 0.9730 0.000 0.000 1.000
#> GSM123784 3 0.0000 0.9730 0.000 0.000 1.000
#> GSM123787 3 0.0000 0.9730 0.000 0.000 1.000
#> GSM123791 3 0.0000 0.9730 0.000 0.000 1.000
#> GSM123795 3 0.0000 0.9730 0.000 0.000 1.000
#> GSM123799 3 0.0000 0.9730 0.000 0.000 1.000
#> GSM123730 3 0.1129 0.9636 0.020 0.004 0.976
#> GSM123734 1 0.1411 0.9076 0.964 0.000 0.036
#> GSM123738 3 0.0592 0.9687 0.012 0.000 0.988
#> GSM123742 1 0.0237 0.9284 0.996 0.000 0.004
#> GSM123745 1 0.0000 0.9296 1.000 0.000 0.000
#> GSM123748 1 0.0000 0.9296 1.000 0.000 0.000
#> GSM123751 1 0.0000 0.9296 1.000 0.000 0.000
#> GSM123754 1 0.0000 0.9296 1.000 0.000 0.000
#> GSM123757 1 0.0000 0.9296 1.000 0.000 0.000
#> GSM123760 1 0.0892 0.9198 0.980 0.000 0.020
#> GSM123762 1 0.0237 0.9284 0.996 0.000 0.004
#> GSM123764 3 0.1411 0.9551 0.036 0.000 0.964
#> GSM123767 1 0.0000 0.9296 1.000 0.000 0.000
#> GSM123770 1 0.0000 0.9296 1.000 0.000 0.000
#> GSM123773 1 0.0000 0.9296 1.000 0.000 0.000
#> GSM123777 3 0.0237 0.9717 0.004 0.000 0.996
#> GSM123779 1 0.6095 0.3388 0.608 0.000 0.392
#> GSM123782 3 0.4235 0.7917 0.176 0.000 0.824
#> GSM123786 3 0.0000 0.9730 0.000 0.000 1.000
#> GSM123789 3 0.3340 0.8748 0.120 0.000 0.880
#> GSM123793 3 0.2356 0.9264 0.072 0.000 0.928
#> GSM123797 3 0.0747 0.9671 0.016 0.000 0.984
#> GSM123729 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM123733 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM123737 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM123741 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM123747 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM123753 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM123759 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM123766 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM123772 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM123775 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM123781 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM123785 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM123788 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM123792 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM123796 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM123731 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM123735 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM123739 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM123743 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM123749 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM123755 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM123768 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM123776 1 0.6308 0.0469 0.508 0.492 0.000
#> GSM123783 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM123790 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM123794 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM123798 2 0.0000 1.0000 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM123732 3 0.1118 0.859 0.000 0.000 0.964 0.036
#> GSM123736 3 0.1743 0.856 0.004 0.000 0.940 0.056
#> GSM123740 3 0.1576 0.857 0.004 0.000 0.948 0.048
#> GSM123744 3 0.5109 0.666 0.212 0.000 0.736 0.052
#> GSM123746 1 0.2926 0.809 0.896 0.000 0.056 0.048
#> GSM123750 3 0.6278 0.296 0.408 0.000 0.532 0.060
#> GSM123752 3 0.5869 0.463 0.360 0.000 0.596 0.044
#> GSM123756 1 0.0000 0.846 1.000 0.000 0.000 0.000
#> GSM123758 3 0.2032 0.839 0.036 0.000 0.936 0.028
#> GSM123761 1 0.3144 0.799 0.884 0.000 0.072 0.044
#> GSM123763 1 0.4105 0.753 0.812 0.000 0.032 0.156
#> GSM123765 3 0.2011 0.854 0.000 0.000 0.920 0.080
#> GSM123769 1 0.0000 0.846 1.000 0.000 0.000 0.000
#> GSM123771 1 0.0000 0.846 1.000 0.000 0.000 0.000
#> GSM123774 1 0.0469 0.845 0.988 0.000 0.000 0.012
#> GSM123778 3 0.1118 0.860 0.000 0.000 0.964 0.036
#> GSM123780 3 0.2921 0.785 0.000 0.000 0.860 0.140
#> GSM123784 3 0.2011 0.847 0.000 0.000 0.920 0.080
#> GSM123787 3 0.1302 0.859 0.000 0.000 0.956 0.044
#> GSM123791 3 0.1151 0.861 0.008 0.000 0.968 0.024
#> GSM123795 3 0.2799 0.831 0.008 0.000 0.884 0.108
#> GSM123799 3 0.1576 0.858 0.004 0.000 0.948 0.048
#> GSM123730 4 0.2342 0.822 0.008 0.000 0.080 0.912
#> GSM123734 4 0.4560 0.529 0.296 0.000 0.004 0.700
#> GSM123738 4 0.3539 0.783 0.004 0.000 0.176 0.820
#> GSM123742 1 0.5523 0.400 0.596 0.000 0.024 0.380
#> GSM123745 1 0.3172 0.798 0.840 0.000 0.000 0.160
#> GSM123748 1 0.2760 0.825 0.872 0.000 0.000 0.128
#> GSM123751 1 0.3688 0.759 0.792 0.000 0.000 0.208
#> GSM123754 1 0.2345 0.836 0.900 0.000 0.000 0.100
#> GSM123757 1 0.0921 0.848 0.972 0.000 0.000 0.028
#> GSM123760 4 0.5313 0.301 0.376 0.000 0.016 0.608
#> GSM123762 1 0.2662 0.826 0.900 0.000 0.016 0.084
#> GSM123764 4 0.4171 0.819 0.060 0.000 0.116 0.824
#> GSM123767 1 0.4304 0.635 0.716 0.000 0.000 0.284
#> GSM123770 1 0.1118 0.845 0.964 0.000 0.000 0.036
#> GSM123773 1 0.2760 0.820 0.872 0.000 0.000 0.128
#> GSM123777 4 0.3356 0.771 0.000 0.000 0.176 0.824
#> GSM123779 4 0.3325 0.780 0.112 0.000 0.024 0.864
#> GSM123782 4 0.4906 0.775 0.084 0.000 0.140 0.776
#> GSM123786 3 0.1716 0.855 0.000 0.000 0.936 0.064
#> GSM123789 4 0.4285 0.821 0.076 0.000 0.104 0.820
#> GSM123793 4 0.3143 0.826 0.024 0.000 0.100 0.876
#> GSM123797 4 0.3032 0.815 0.008 0.000 0.124 0.868
#> GSM123729 2 0.0188 0.998 0.000 0.996 0.000 0.004
#> GSM123733 2 0.0188 0.998 0.000 0.996 0.000 0.004
#> GSM123737 2 0.0188 0.998 0.000 0.996 0.000 0.004
#> GSM123741 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM123747 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM123753 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM123759 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM123766 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM123772 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM123775 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM123781 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM123785 2 0.0188 0.998 0.000 0.996 0.000 0.004
#> GSM123788 2 0.0188 0.998 0.000 0.996 0.000 0.004
#> GSM123792 2 0.0188 0.998 0.000 0.996 0.000 0.004
#> GSM123796 2 0.0188 0.998 0.000 0.996 0.000 0.004
#> GSM123731 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM123735 2 0.0188 0.998 0.000 0.996 0.000 0.004
#> GSM123739 2 0.0188 0.998 0.000 0.996 0.000 0.004
#> GSM123743 2 0.0188 0.998 0.000 0.996 0.000 0.004
#> GSM123749 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM123755 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM123768 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM123776 1 0.5254 0.459 0.672 0.300 0.000 0.028
#> GSM123783 2 0.0188 0.996 0.000 0.996 0.000 0.004
#> GSM123790 2 0.0188 0.998 0.000 0.996 0.000 0.004
#> GSM123794 2 0.0188 0.998 0.000 0.996 0.000 0.004
#> GSM123798 2 0.0000 0.998 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM123732 3 0.2104 0.752 0.000 0.000 0.916 0.024 0.060
#> GSM123736 3 0.4172 0.735 0.004 0.000 0.792 0.092 0.112
#> GSM123740 3 0.4158 0.733 0.000 0.000 0.784 0.092 0.124
#> GSM123744 3 0.6719 0.459 0.204 0.000 0.472 0.008 0.316
#> GSM123746 1 0.4973 0.625 0.692 0.000 0.068 0.004 0.236
#> GSM123750 3 0.7047 0.180 0.300 0.000 0.348 0.008 0.344
#> GSM123752 3 0.6700 0.222 0.356 0.000 0.400 0.000 0.244
#> GSM123756 1 0.1341 0.726 0.944 0.000 0.000 0.000 0.056
#> GSM123758 3 0.3615 0.730 0.036 0.000 0.808 0.000 0.156
#> GSM123761 1 0.5550 0.572 0.636 0.000 0.068 0.016 0.280
#> GSM123763 1 0.6636 0.464 0.544 0.000 0.032 0.132 0.292
#> GSM123765 3 0.1914 0.754 0.000 0.000 0.924 0.060 0.016
#> GSM123769 1 0.1608 0.726 0.928 0.000 0.000 0.000 0.072
#> GSM123771 1 0.1478 0.727 0.936 0.000 0.000 0.000 0.064
#> GSM123774 1 0.0794 0.728 0.972 0.000 0.000 0.000 0.028
#> GSM123778 3 0.2370 0.750 0.000 0.000 0.904 0.040 0.056
#> GSM123780 3 0.4164 0.682 0.000 0.000 0.784 0.120 0.096
#> GSM123784 3 0.3043 0.748 0.000 0.000 0.864 0.080 0.056
#> GSM123787 3 0.2124 0.757 0.000 0.000 0.916 0.028 0.056
#> GSM123791 3 0.4901 0.703 0.004 0.000 0.716 0.084 0.196
#> GSM123795 3 0.5309 0.686 0.012 0.000 0.704 0.140 0.144
#> GSM123799 3 0.4203 0.738 0.000 0.000 0.780 0.092 0.128
#> GSM123730 4 0.2228 0.720 0.000 0.000 0.048 0.912 0.040
#> GSM123734 4 0.6269 0.521 0.196 0.000 0.012 0.588 0.204
#> GSM123738 4 0.4197 0.664 0.000 0.000 0.148 0.776 0.076
#> GSM123742 1 0.6968 0.117 0.380 0.000 0.008 0.252 0.360
#> GSM123745 1 0.5083 0.622 0.700 0.000 0.000 0.140 0.160
#> GSM123748 1 0.4869 0.651 0.712 0.000 0.000 0.096 0.192
#> GSM123751 1 0.5575 0.573 0.644 0.000 0.000 0.168 0.188
#> GSM123754 1 0.3608 0.691 0.824 0.000 0.000 0.112 0.064
#> GSM123757 1 0.2621 0.727 0.876 0.000 0.004 0.008 0.112
#> GSM123760 4 0.6864 0.238 0.252 0.000 0.004 0.384 0.360
#> GSM123762 1 0.5636 0.600 0.652 0.000 0.016 0.092 0.240
#> GSM123764 4 0.6604 0.638 0.052 0.000 0.088 0.544 0.316
#> GSM123767 1 0.5531 0.519 0.632 0.000 0.000 0.248 0.120
#> GSM123770 1 0.1830 0.723 0.932 0.000 0.000 0.028 0.040
#> GSM123773 1 0.3994 0.672 0.792 0.000 0.000 0.140 0.068
#> GSM123777 4 0.3863 0.661 0.000 0.000 0.152 0.796 0.052
#> GSM123779 4 0.5095 0.668 0.104 0.000 0.032 0.744 0.120
#> GSM123782 4 0.7174 0.589 0.064 0.000 0.124 0.476 0.336
#> GSM123786 3 0.2628 0.749 0.000 0.000 0.884 0.028 0.088
#> GSM123789 4 0.5861 0.697 0.036 0.000 0.088 0.656 0.220
#> GSM123793 4 0.3960 0.729 0.008 0.000 0.044 0.800 0.148
#> GSM123797 4 0.3346 0.712 0.000 0.000 0.092 0.844 0.064
#> GSM123729 2 0.2377 0.917 0.000 0.872 0.000 0.000 0.128
#> GSM123733 2 0.1341 0.953 0.000 0.944 0.000 0.000 0.056
#> GSM123737 2 0.2020 0.933 0.000 0.900 0.000 0.000 0.100
#> GSM123741 2 0.0510 0.959 0.000 0.984 0.000 0.000 0.016
#> GSM123747 2 0.0703 0.960 0.000 0.976 0.000 0.000 0.024
#> GSM123753 2 0.0963 0.958 0.000 0.964 0.000 0.000 0.036
#> GSM123759 2 0.1121 0.959 0.000 0.956 0.000 0.000 0.044
#> GSM123766 2 0.1043 0.958 0.000 0.960 0.000 0.000 0.040
#> GSM123772 2 0.0609 0.960 0.000 0.980 0.000 0.000 0.020
#> GSM123775 2 0.2329 0.929 0.000 0.876 0.000 0.000 0.124
#> GSM123781 2 0.0880 0.956 0.000 0.968 0.000 0.000 0.032
#> GSM123785 2 0.1544 0.949 0.000 0.932 0.000 0.000 0.068
#> GSM123788 2 0.1270 0.954 0.000 0.948 0.000 0.000 0.052
#> GSM123792 2 0.0794 0.958 0.000 0.972 0.000 0.000 0.028
#> GSM123796 2 0.1043 0.958 0.000 0.960 0.000 0.000 0.040
#> GSM123731 2 0.1410 0.959 0.000 0.940 0.000 0.000 0.060
#> GSM123735 2 0.1851 0.947 0.000 0.912 0.000 0.000 0.088
#> GSM123739 2 0.2329 0.921 0.000 0.876 0.000 0.000 0.124
#> GSM123743 2 0.0609 0.961 0.000 0.980 0.000 0.000 0.020
#> GSM123749 2 0.0510 0.960 0.000 0.984 0.000 0.000 0.016
#> GSM123755 2 0.0963 0.956 0.000 0.964 0.000 0.000 0.036
#> GSM123768 2 0.1121 0.956 0.000 0.956 0.000 0.000 0.044
#> GSM123776 1 0.5850 0.442 0.624 0.176 0.000 0.004 0.196
#> GSM123783 2 0.2127 0.939 0.000 0.892 0.000 0.000 0.108
#> GSM123790 2 0.2233 0.934 0.000 0.892 0.000 0.004 0.104
#> GSM123794 2 0.1478 0.953 0.000 0.936 0.000 0.000 0.064
#> GSM123798 2 0.1043 0.957 0.000 0.960 0.000 0.000 0.040
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM123732 3 0.2058 0.70008 0.000 0.000 0.916 0.012 0.048 0.024
#> GSM123736 3 0.5642 0.63434 0.004 0.000 0.644 0.208 0.072 0.072
#> GSM123740 3 0.5765 0.64517 0.004 0.000 0.644 0.184 0.088 0.080
#> GSM123744 3 0.7994 -0.07414 0.248 0.000 0.284 0.016 0.180 0.272
#> GSM123746 1 0.5831 0.36274 0.604 0.000 0.024 0.008 0.144 0.220
#> GSM123750 6 0.7730 -0.03918 0.308 0.000 0.196 0.008 0.168 0.320
#> GSM123752 1 0.7964 -0.10502 0.320 0.000 0.256 0.016 0.220 0.188
#> GSM123756 1 0.1461 0.57214 0.940 0.000 0.000 0.000 0.016 0.044
#> GSM123758 3 0.5832 0.55107 0.060 0.000 0.632 0.004 0.188 0.116
#> GSM123761 1 0.6290 0.17086 0.484 0.000 0.036 0.008 0.116 0.356
#> GSM123763 1 0.6873 0.00491 0.408 0.000 0.024 0.080 0.084 0.404
#> GSM123765 3 0.2901 0.70804 0.000 0.000 0.872 0.040 0.056 0.032
#> GSM123769 1 0.1867 0.56826 0.916 0.000 0.000 0.000 0.020 0.064
#> GSM123771 1 0.2147 0.55986 0.896 0.000 0.000 0.000 0.020 0.084
#> GSM123774 1 0.0909 0.57722 0.968 0.000 0.000 0.000 0.020 0.012
#> GSM123778 3 0.2908 0.69489 0.000 0.000 0.864 0.012 0.076 0.048
#> GSM123780 3 0.4784 0.62362 0.000 0.000 0.736 0.112 0.096 0.056
#> GSM123784 3 0.3240 0.70235 0.004 0.000 0.856 0.056 0.032 0.052
#> GSM123787 3 0.3530 0.69304 0.000 0.000 0.824 0.028 0.104 0.044
#> GSM123791 3 0.6103 0.58078 0.020 0.000 0.628 0.056 0.124 0.172
#> GSM123795 3 0.6481 0.52158 0.004 0.000 0.532 0.272 0.088 0.104
#> GSM123799 3 0.5649 0.65501 0.004 0.000 0.656 0.176 0.068 0.096
#> GSM123730 4 0.2926 0.56272 0.004 0.000 0.040 0.876 0.040 0.040
#> GSM123734 4 0.6212 0.16696 0.144 0.000 0.004 0.500 0.028 0.324
#> GSM123738 4 0.4199 0.51017 0.000 0.000 0.108 0.780 0.040 0.072
#> GSM123742 6 0.6047 0.25066 0.200 0.000 0.008 0.180 0.028 0.584
#> GSM123745 1 0.5895 0.42058 0.592 0.000 0.000 0.136 0.044 0.228
#> GSM123748 1 0.5617 0.32681 0.516 0.000 0.000 0.060 0.040 0.384
#> GSM123751 1 0.5933 0.33321 0.528 0.000 0.000 0.152 0.020 0.300
#> GSM123754 1 0.4756 0.53119 0.736 0.000 0.000 0.108 0.048 0.108
#> GSM123757 1 0.3764 0.55651 0.804 0.000 0.004 0.008 0.084 0.100
#> GSM123760 6 0.6291 0.21297 0.116 0.000 0.008 0.276 0.052 0.548
#> GSM123762 1 0.5646 0.22956 0.504 0.000 0.000 0.048 0.052 0.396
#> GSM123764 6 0.6842 -0.01576 0.012 0.000 0.088 0.336 0.104 0.460
#> GSM123767 1 0.5959 0.39274 0.584 0.000 0.000 0.228 0.044 0.144
#> GSM123770 1 0.2764 0.56935 0.872 0.000 0.000 0.024 0.020 0.084
#> GSM123773 1 0.4962 0.51706 0.716 0.000 0.000 0.124 0.048 0.112
#> GSM123777 4 0.4421 0.49953 0.000 0.000 0.152 0.752 0.048 0.048
#> GSM123779 4 0.6947 0.34732 0.104 0.000 0.048 0.560 0.092 0.196
#> GSM123782 6 0.8010 0.00596 0.040 0.000 0.132 0.296 0.184 0.348
#> GSM123786 3 0.3222 0.68440 0.000 0.000 0.844 0.024 0.096 0.036
#> GSM123789 4 0.6808 0.18379 0.008 0.000 0.080 0.476 0.128 0.308
#> GSM123793 4 0.4640 0.45835 0.004 0.000 0.032 0.692 0.028 0.244
#> GSM123797 4 0.2467 0.56996 0.000 0.000 0.048 0.896 0.020 0.036
#> GSM123729 2 0.3314 0.83569 0.000 0.764 0.000 0.000 0.224 0.012
#> GSM123733 2 0.2527 0.89169 0.000 0.832 0.000 0.000 0.168 0.000
#> GSM123737 2 0.3014 0.86604 0.000 0.804 0.000 0.000 0.184 0.012
#> GSM123741 2 0.0603 0.92133 0.000 0.980 0.000 0.000 0.016 0.004
#> GSM123747 2 0.1387 0.92180 0.000 0.932 0.000 0.000 0.068 0.000
#> GSM123753 2 0.0790 0.91985 0.000 0.968 0.000 0.000 0.032 0.000
#> GSM123759 2 0.0777 0.91947 0.000 0.972 0.000 0.000 0.024 0.004
#> GSM123766 2 0.1152 0.92091 0.000 0.952 0.000 0.000 0.044 0.004
#> GSM123772 2 0.1010 0.92197 0.000 0.960 0.000 0.000 0.036 0.004
#> GSM123775 2 0.3052 0.85510 0.000 0.780 0.000 0.000 0.216 0.004
#> GSM123781 2 0.1082 0.91795 0.000 0.956 0.000 0.000 0.040 0.004
#> GSM123785 2 0.2135 0.90528 0.000 0.872 0.000 0.000 0.128 0.000
#> GSM123788 2 0.2092 0.90638 0.000 0.876 0.000 0.000 0.124 0.000
#> GSM123792 2 0.1714 0.91753 0.000 0.908 0.000 0.000 0.092 0.000
#> GSM123796 2 0.1910 0.91101 0.000 0.892 0.000 0.000 0.108 0.000
#> GSM123731 2 0.1556 0.91858 0.000 0.920 0.000 0.000 0.080 0.000
#> GSM123735 2 0.2632 0.89410 0.000 0.832 0.000 0.000 0.164 0.004
#> GSM123739 2 0.3342 0.83559 0.000 0.760 0.000 0.000 0.228 0.012
#> GSM123743 2 0.1141 0.92225 0.000 0.948 0.000 0.000 0.052 0.000
#> GSM123749 2 0.0405 0.92070 0.000 0.988 0.000 0.000 0.008 0.004
#> GSM123755 2 0.0937 0.91846 0.000 0.960 0.000 0.000 0.040 0.000
#> GSM123768 2 0.1285 0.91400 0.000 0.944 0.000 0.000 0.052 0.004
#> GSM123776 1 0.6228 0.25315 0.528 0.100 0.000 0.008 0.316 0.048
#> GSM123783 2 0.2558 0.88211 0.000 0.840 0.000 0.000 0.156 0.004
#> GSM123790 2 0.3192 0.86043 0.000 0.776 0.000 0.004 0.216 0.004
#> GSM123794 2 0.2300 0.90433 0.000 0.856 0.000 0.000 0.144 0.000
#> GSM123798 2 0.1349 0.91455 0.000 0.940 0.000 0.000 0.056 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) infection(p) agent(p) k
#> SD:skmeans 71 3.82e-16 3.82e-16 6.04e-06 2
#> SD:skmeans 69 2.33e-14 2.33e-14 2.00e-05 3
#> SD:skmeans 66 2.65e-19 2.65e-19 1.47e-04 4
#> SD:skmeans 64 8.56e-19 8.56e-19 2.25e-04 5
#> SD:skmeans 50 1.20e-13 1.20e-13 4.60e-03 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "pam"]
# you can also extract it by
# res = res_list["SD:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 71 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 0.993 0.997 0.4780 0.522 0.522
#> 3 3 0.982 0.943 0.979 0.3821 0.820 0.655
#> 4 4 0.889 0.856 0.944 0.0343 0.989 0.968
#> 5 5 0.859 0.830 0.926 0.0212 0.994 0.982
#> 6 6 0.842 0.791 0.914 0.0134 0.994 0.983
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
#> GSM123732 1 0.0000 0.998 1.000 0.000
#> GSM123736 1 0.0000 0.998 1.000 0.000
#> GSM123740 1 0.0000 0.998 1.000 0.000
#> GSM123744 1 0.0000 0.998 1.000 0.000
#> GSM123746 1 0.0000 0.998 1.000 0.000
#> GSM123750 1 0.0000 0.998 1.000 0.000
#> GSM123752 1 0.0000 0.998 1.000 0.000
#> GSM123756 1 0.0000 0.998 1.000 0.000
#> GSM123758 1 0.0000 0.998 1.000 0.000
#> GSM123761 1 0.0000 0.998 1.000 0.000
#> GSM123763 1 0.0000 0.998 1.000 0.000
#> GSM123765 1 0.0000 0.998 1.000 0.000
#> GSM123769 1 0.0000 0.998 1.000 0.000
#> GSM123771 1 0.0000 0.998 1.000 0.000
#> GSM123774 1 0.0000 0.998 1.000 0.000
#> GSM123778 1 0.0000 0.998 1.000 0.000
#> GSM123780 1 0.0000 0.998 1.000 0.000
#> GSM123784 1 0.0000 0.998 1.000 0.000
#> GSM123787 1 0.0000 0.998 1.000 0.000
#> GSM123791 1 0.0000 0.998 1.000 0.000
#> GSM123795 1 0.0000 0.998 1.000 0.000
#> GSM123799 1 0.0000 0.998 1.000 0.000
#> GSM123730 1 0.0376 0.994 0.996 0.004
#> GSM123734 1 0.0000 0.998 1.000 0.000
#> GSM123738 1 0.0000 0.998 1.000 0.000
#> GSM123742 1 0.0000 0.998 1.000 0.000
#> GSM123745 1 0.3733 0.922 0.928 0.072
#> GSM123748 1 0.0000 0.998 1.000 0.000
#> GSM123751 1 0.0000 0.998 1.000 0.000
#> GSM123754 1 0.0000 0.998 1.000 0.000
#> GSM123757 1 0.0000 0.998 1.000 0.000
#> GSM123760 1 0.0000 0.998 1.000 0.000
#> GSM123762 1 0.0000 0.998 1.000 0.000
#> GSM123764 1 0.0000 0.998 1.000 0.000
#> GSM123767 1 0.0672 0.991 0.992 0.008
#> GSM123770 1 0.0000 0.998 1.000 0.000
#> GSM123773 1 0.0000 0.998 1.000 0.000
#> GSM123777 1 0.0000 0.998 1.000 0.000
#> GSM123779 1 0.0000 0.998 1.000 0.000
#> GSM123782 1 0.0000 0.998 1.000 0.000
#> GSM123786 1 0.0000 0.998 1.000 0.000
#> GSM123789 1 0.0000 0.998 1.000 0.000
#> GSM123793 1 0.0000 0.998 1.000 0.000
#> GSM123797 1 0.0000 0.998 1.000 0.000
#> GSM123729 2 0.0000 0.994 0.000 1.000
#> GSM123733 2 0.0000 0.994 0.000 1.000
#> GSM123737 2 0.0000 0.994 0.000 1.000
#> GSM123741 2 0.0000 0.994 0.000 1.000
#> GSM123747 2 0.0000 0.994 0.000 1.000
#> GSM123753 2 0.0000 0.994 0.000 1.000
#> GSM123759 2 0.0000 0.994 0.000 1.000
#> GSM123766 2 0.0000 0.994 0.000 1.000
#> GSM123772 2 0.0000 0.994 0.000 1.000
#> GSM123775 2 0.0000 0.994 0.000 1.000
#> GSM123781 2 0.0000 0.994 0.000 1.000
#> GSM123785 2 0.0000 0.994 0.000 1.000
#> GSM123788 2 0.0000 0.994 0.000 1.000
#> GSM123792 2 0.0000 0.994 0.000 1.000
#> GSM123796 2 0.0000 0.994 0.000 1.000
#> GSM123731 2 0.0000 0.994 0.000 1.000
#> GSM123735 2 0.0000 0.994 0.000 1.000
#> GSM123739 2 0.0000 0.994 0.000 1.000
#> GSM123743 2 0.0000 0.994 0.000 1.000
#> GSM123749 2 0.0000 0.994 0.000 1.000
#> GSM123755 2 0.0000 0.994 0.000 1.000
#> GSM123768 2 0.0000 0.994 0.000 1.000
#> GSM123776 2 0.6048 0.826 0.148 0.852
#> GSM123783 2 0.0000 0.994 0.000 1.000
#> GSM123790 2 0.0000 0.994 0.000 1.000
#> GSM123794 2 0.0000 0.994 0.000 1.000
#> GSM123798 2 0.0000 0.994 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM123732 3 0.0000 0.9709 0.000 0.000 1.000
#> GSM123736 3 0.0000 0.9709 0.000 0.000 1.000
#> GSM123740 3 0.0000 0.9709 0.000 0.000 1.000
#> GSM123744 3 0.0000 0.9709 0.000 0.000 1.000
#> GSM123746 3 0.0000 0.9709 0.000 0.000 1.000
#> GSM123750 3 0.0000 0.9709 0.000 0.000 1.000
#> GSM123752 3 0.0000 0.9709 0.000 0.000 1.000
#> GSM123756 1 0.0000 0.9666 1.000 0.000 0.000
#> GSM123758 3 0.0000 0.9709 0.000 0.000 1.000
#> GSM123761 3 0.3619 0.8318 0.136 0.000 0.864
#> GSM123763 3 0.6204 0.2542 0.424 0.000 0.576
#> GSM123765 3 0.0000 0.9709 0.000 0.000 1.000
#> GSM123769 1 0.0000 0.9666 1.000 0.000 0.000
#> GSM123771 1 0.0000 0.9666 1.000 0.000 0.000
#> GSM123774 1 0.0000 0.9666 1.000 0.000 0.000
#> GSM123778 3 0.0000 0.9709 0.000 0.000 1.000
#> GSM123780 3 0.0000 0.9709 0.000 0.000 1.000
#> GSM123784 3 0.0000 0.9709 0.000 0.000 1.000
#> GSM123787 3 0.0000 0.9709 0.000 0.000 1.000
#> GSM123791 3 0.0000 0.9709 0.000 0.000 1.000
#> GSM123795 3 0.0000 0.9709 0.000 0.000 1.000
#> GSM123799 3 0.0000 0.9709 0.000 0.000 1.000
#> GSM123730 3 0.0000 0.9709 0.000 0.000 1.000
#> GSM123734 1 0.0000 0.9666 1.000 0.000 0.000
#> GSM123738 3 0.0000 0.9709 0.000 0.000 1.000
#> GSM123742 1 0.0237 0.9629 0.996 0.000 0.004
#> GSM123745 1 0.0000 0.9666 1.000 0.000 0.000
#> GSM123748 1 0.0000 0.9666 1.000 0.000 0.000
#> GSM123751 1 0.0000 0.9666 1.000 0.000 0.000
#> GSM123754 1 0.0000 0.9666 1.000 0.000 0.000
#> GSM123757 1 0.0000 0.9666 1.000 0.000 0.000
#> GSM123760 1 0.6302 0.0402 0.520 0.000 0.480
#> GSM123762 1 0.0000 0.9666 1.000 0.000 0.000
#> GSM123764 3 0.0000 0.9709 0.000 0.000 1.000
#> GSM123767 1 0.0000 0.9666 1.000 0.000 0.000
#> GSM123770 1 0.0000 0.9666 1.000 0.000 0.000
#> GSM123773 1 0.0000 0.9666 1.000 0.000 0.000
#> GSM123777 3 0.0000 0.9709 0.000 0.000 1.000
#> GSM123779 3 0.4452 0.7529 0.192 0.000 0.808
#> GSM123782 3 0.0000 0.9709 0.000 0.000 1.000
#> GSM123786 3 0.0000 0.9709 0.000 0.000 1.000
#> GSM123789 3 0.0000 0.9709 0.000 0.000 1.000
#> GSM123793 3 0.0000 0.9709 0.000 0.000 1.000
#> GSM123797 3 0.0000 0.9709 0.000 0.000 1.000
#> GSM123729 2 0.0000 0.9887 0.000 1.000 0.000
#> GSM123733 2 0.0000 0.9887 0.000 1.000 0.000
#> GSM123737 2 0.0000 0.9887 0.000 1.000 0.000
#> GSM123741 2 0.0000 0.9887 0.000 1.000 0.000
#> GSM123747 2 0.0000 0.9887 0.000 1.000 0.000
#> GSM123753 2 0.0000 0.9887 0.000 1.000 0.000
#> GSM123759 2 0.0000 0.9887 0.000 1.000 0.000
#> GSM123766 2 0.0000 0.9887 0.000 1.000 0.000
#> GSM123772 2 0.0000 0.9887 0.000 1.000 0.000
#> GSM123775 2 0.0000 0.9887 0.000 1.000 0.000
#> GSM123781 2 0.0000 0.9887 0.000 1.000 0.000
#> GSM123785 2 0.0000 0.9887 0.000 1.000 0.000
#> GSM123788 2 0.0000 0.9887 0.000 1.000 0.000
#> GSM123792 2 0.0000 0.9887 0.000 1.000 0.000
#> GSM123796 2 0.0000 0.9887 0.000 1.000 0.000
#> GSM123731 2 0.0000 0.9887 0.000 1.000 0.000
#> GSM123735 2 0.0000 0.9887 0.000 1.000 0.000
#> GSM123739 2 0.0000 0.9887 0.000 1.000 0.000
#> GSM123743 2 0.0000 0.9887 0.000 1.000 0.000
#> GSM123749 2 0.0000 0.9887 0.000 1.000 0.000
#> GSM123755 2 0.0000 0.9887 0.000 1.000 0.000
#> GSM123768 2 0.0000 0.9887 0.000 1.000 0.000
#> GSM123776 2 0.5465 0.5926 0.288 0.712 0.000
#> GSM123783 2 0.0000 0.9887 0.000 1.000 0.000
#> GSM123790 2 0.0000 0.9887 0.000 1.000 0.000
#> GSM123794 2 0.0000 0.9887 0.000 1.000 0.000
#> GSM123798 2 0.0000 0.9887 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM123732 3 0.0000 0.8785 0.000 0.00 1.000 0.000
#> GSM123736 3 0.1118 0.8587 0.000 0.00 0.964 0.036
#> GSM123740 3 0.1211 0.8586 0.000 0.00 0.960 0.040
#> GSM123744 3 0.2647 0.7850 0.000 0.00 0.880 0.120
#> GSM123746 3 0.4405 0.6786 0.048 0.00 0.800 0.152
#> GSM123750 3 0.2469 0.7981 0.000 0.00 0.892 0.108
#> GSM123752 3 0.3370 0.7689 0.048 0.00 0.872 0.080
#> GSM123756 1 0.1716 0.8949 0.936 0.00 0.000 0.064
#> GSM123758 3 0.0469 0.8749 0.000 0.00 0.988 0.012
#> GSM123761 3 0.6215 0.4212 0.140 0.00 0.668 0.192
#> GSM123763 3 0.7302 -0.0500 0.332 0.00 0.500 0.168
#> GSM123765 3 0.0000 0.8785 0.000 0.00 1.000 0.000
#> GSM123769 1 0.1716 0.8949 0.936 0.00 0.000 0.064
#> GSM123771 1 0.1716 0.8949 0.936 0.00 0.000 0.064
#> GSM123774 1 0.1716 0.8949 0.936 0.00 0.000 0.064
#> GSM123778 3 0.0000 0.8785 0.000 0.00 1.000 0.000
#> GSM123780 3 0.0000 0.8785 0.000 0.00 1.000 0.000
#> GSM123784 3 0.0000 0.8785 0.000 0.00 1.000 0.000
#> GSM123787 3 0.0000 0.8785 0.000 0.00 1.000 0.000
#> GSM123791 3 0.0000 0.8785 0.000 0.00 1.000 0.000
#> GSM123795 3 0.1118 0.8587 0.000 0.00 0.964 0.036
#> GSM123799 3 0.0000 0.8785 0.000 0.00 1.000 0.000
#> GSM123730 3 0.0592 0.8709 0.016 0.00 0.984 0.000
#> GSM123734 1 0.2760 0.8298 0.872 0.00 0.000 0.128
#> GSM123738 3 0.2868 0.7377 0.000 0.00 0.864 0.136
#> GSM123742 1 0.2469 0.8616 0.892 0.00 0.000 0.108
#> GSM123745 1 0.0000 0.9071 1.000 0.00 0.000 0.000
#> GSM123748 1 0.1389 0.8973 0.952 0.00 0.000 0.048
#> GSM123751 1 0.1022 0.9034 0.968 0.00 0.000 0.032
#> GSM123754 1 0.1302 0.9011 0.956 0.00 0.000 0.044
#> GSM123757 1 0.2741 0.8674 0.892 0.00 0.012 0.096
#> GSM123760 1 0.6946 -0.0455 0.504 0.00 0.380 0.116
#> GSM123762 1 0.1940 0.8988 0.924 0.00 0.000 0.076
#> GSM123764 3 0.0000 0.8785 0.000 0.00 1.000 0.000
#> GSM123767 1 0.0000 0.9071 1.000 0.00 0.000 0.000
#> GSM123770 1 0.0000 0.9071 1.000 0.00 0.000 0.000
#> GSM123773 1 0.0000 0.9071 1.000 0.00 0.000 0.000
#> GSM123777 3 0.0000 0.8785 0.000 0.00 1.000 0.000
#> GSM123779 3 0.4086 0.5713 0.216 0.00 0.776 0.008
#> GSM123782 3 0.1174 0.8610 0.020 0.00 0.968 0.012
#> GSM123786 3 0.0000 0.8785 0.000 0.00 1.000 0.000
#> GSM123789 3 0.0188 0.8775 0.000 0.00 0.996 0.004
#> GSM123793 4 0.5090 0.0000 0.016 0.00 0.324 0.660
#> GSM123797 3 0.3324 0.7220 0.012 0.00 0.852 0.136
#> GSM123729 2 0.0000 0.9875 0.000 1.00 0.000 0.000
#> GSM123733 2 0.0000 0.9875 0.000 1.00 0.000 0.000
#> GSM123737 2 0.0000 0.9875 0.000 1.00 0.000 0.000
#> GSM123741 2 0.0000 0.9875 0.000 1.00 0.000 0.000
#> GSM123747 2 0.0000 0.9875 0.000 1.00 0.000 0.000
#> GSM123753 2 0.0000 0.9875 0.000 1.00 0.000 0.000
#> GSM123759 2 0.0000 0.9875 0.000 1.00 0.000 0.000
#> GSM123766 2 0.0000 0.9875 0.000 1.00 0.000 0.000
#> GSM123772 2 0.0000 0.9875 0.000 1.00 0.000 0.000
#> GSM123775 2 0.0000 0.9875 0.000 1.00 0.000 0.000
#> GSM123781 2 0.0000 0.9875 0.000 1.00 0.000 0.000
#> GSM123785 2 0.0000 0.9875 0.000 1.00 0.000 0.000
#> GSM123788 2 0.0000 0.9875 0.000 1.00 0.000 0.000
#> GSM123792 2 0.0000 0.9875 0.000 1.00 0.000 0.000
#> GSM123796 2 0.0000 0.9875 0.000 1.00 0.000 0.000
#> GSM123731 2 0.0000 0.9875 0.000 1.00 0.000 0.000
#> GSM123735 2 0.0000 0.9875 0.000 1.00 0.000 0.000
#> GSM123739 2 0.0000 0.9875 0.000 1.00 0.000 0.000
#> GSM123743 2 0.0000 0.9875 0.000 1.00 0.000 0.000
#> GSM123749 2 0.0000 0.9875 0.000 1.00 0.000 0.000
#> GSM123755 2 0.0000 0.9875 0.000 1.00 0.000 0.000
#> GSM123768 2 0.0000 0.9875 0.000 1.00 0.000 0.000
#> GSM123776 2 0.4428 0.5890 0.276 0.72 0.000 0.004
#> GSM123783 2 0.0000 0.9875 0.000 1.00 0.000 0.000
#> GSM123790 2 0.0000 0.9875 0.000 1.00 0.000 0.000
#> GSM123794 2 0.0000 0.9875 0.000 1.00 0.000 0.000
#> GSM123798 2 0.0000 0.9875 0.000 1.00 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM123732 3 0.0000 0.8812 0.000 0.000 1.000 0.000 0.000
#> GSM123736 3 0.1121 0.8681 0.000 0.000 0.956 0.044 0.000
#> GSM123740 3 0.1282 0.8675 0.000 0.000 0.952 0.044 0.004
#> GSM123744 3 0.2732 0.7992 0.000 0.000 0.840 0.000 0.160
#> GSM123746 3 0.5073 0.6460 0.100 0.000 0.688 0.000 0.212
#> GSM123750 3 0.2605 0.8082 0.000 0.000 0.852 0.000 0.148
#> GSM123752 3 0.4072 0.7437 0.100 0.000 0.792 0.000 0.108
#> GSM123756 1 0.2708 0.7928 0.884 0.000 0.000 0.044 0.072
#> GSM123758 3 0.0404 0.8798 0.000 0.000 0.988 0.000 0.012
#> GSM123761 3 0.5948 0.4732 0.156 0.000 0.580 0.000 0.264
#> GSM123763 3 0.7027 0.1726 0.296 0.000 0.460 0.020 0.224
#> GSM123765 3 0.0000 0.8812 0.000 0.000 1.000 0.000 0.000
#> GSM123769 1 0.2708 0.7928 0.884 0.000 0.000 0.044 0.072
#> GSM123771 1 0.2708 0.7928 0.884 0.000 0.000 0.044 0.072
#> GSM123774 1 0.2708 0.7928 0.884 0.000 0.000 0.044 0.072
#> GSM123778 3 0.0000 0.8812 0.000 0.000 1.000 0.000 0.000
#> GSM123780 3 0.0000 0.8812 0.000 0.000 1.000 0.000 0.000
#> GSM123784 3 0.0000 0.8812 0.000 0.000 1.000 0.000 0.000
#> GSM123787 3 0.0000 0.8812 0.000 0.000 1.000 0.000 0.000
#> GSM123791 3 0.0000 0.8812 0.000 0.000 1.000 0.000 0.000
#> GSM123795 3 0.1121 0.8681 0.000 0.000 0.956 0.044 0.000
#> GSM123799 3 0.0000 0.8812 0.000 0.000 1.000 0.000 0.000
#> GSM123730 3 0.1197 0.8633 0.000 0.000 0.952 0.048 0.000
#> GSM123734 5 0.5594 0.0000 0.232 0.000 0.000 0.136 0.632
#> GSM123738 3 0.3561 0.6769 0.000 0.000 0.740 0.260 0.000
#> GSM123742 1 0.2674 0.7402 0.856 0.000 0.004 0.000 0.140
#> GSM123745 1 0.1121 0.8221 0.956 0.000 0.000 0.044 0.000
#> GSM123748 1 0.1608 0.8022 0.928 0.000 0.000 0.000 0.072
#> GSM123751 1 0.1444 0.8191 0.948 0.000 0.000 0.012 0.040
#> GSM123754 1 0.1571 0.8105 0.936 0.000 0.000 0.004 0.060
#> GSM123757 1 0.2230 0.7687 0.884 0.000 0.000 0.000 0.116
#> GSM123760 1 0.6282 0.0901 0.524 0.000 0.336 0.008 0.132
#> GSM123762 1 0.3214 0.7557 0.844 0.000 0.000 0.036 0.120
#> GSM123764 3 0.0000 0.8812 0.000 0.000 1.000 0.000 0.000
#> GSM123767 1 0.1121 0.8221 0.956 0.000 0.000 0.044 0.000
#> GSM123770 1 0.1121 0.8221 0.956 0.000 0.000 0.044 0.000
#> GSM123773 1 0.1121 0.8221 0.956 0.000 0.000 0.044 0.000
#> GSM123777 3 0.0000 0.8812 0.000 0.000 1.000 0.000 0.000
#> GSM123779 3 0.4134 0.6768 0.196 0.000 0.760 0.044 0.000
#> GSM123782 3 0.1469 0.8624 0.036 0.000 0.948 0.000 0.016
#> GSM123786 3 0.0000 0.8812 0.000 0.000 1.000 0.000 0.000
#> GSM123789 3 0.0510 0.8776 0.016 0.000 0.984 0.000 0.000
#> GSM123793 4 0.1768 0.0000 0.004 0.000 0.072 0.924 0.000
#> GSM123797 3 0.3906 0.6340 0.004 0.000 0.704 0.292 0.000
#> GSM123729 2 0.0000 0.9878 0.000 1.000 0.000 0.000 0.000
#> GSM123733 2 0.0000 0.9878 0.000 1.000 0.000 0.000 0.000
#> GSM123737 2 0.0000 0.9878 0.000 1.000 0.000 0.000 0.000
#> GSM123741 2 0.0000 0.9878 0.000 1.000 0.000 0.000 0.000
#> GSM123747 2 0.0000 0.9878 0.000 1.000 0.000 0.000 0.000
#> GSM123753 2 0.0000 0.9878 0.000 1.000 0.000 0.000 0.000
#> GSM123759 2 0.0000 0.9878 0.000 1.000 0.000 0.000 0.000
#> GSM123766 2 0.0000 0.9878 0.000 1.000 0.000 0.000 0.000
#> GSM123772 2 0.0000 0.9878 0.000 1.000 0.000 0.000 0.000
#> GSM123775 2 0.0000 0.9878 0.000 1.000 0.000 0.000 0.000
#> GSM123781 2 0.0000 0.9878 0.000 1.000 0.000 0.000 0.000
#> GSM123785 2 0.0000 0.9878 0.000 1.000 0.000 0.000 0.000
#> GSM123788 2 0.0000 0.9878 0.000 1.000 0.000 0.000 0.000
#> GSM123792 2 0.0000 0.9878 0.000 1.000 0.000 0.000 0.000
#> GSM123796 2 0.0000 0.9878 0.000 1.000 0.000 0.000 0.000
#> GSM123731 2 0.0000 0.9878 0.000 1.000 0.000 0.000 0.000
#> GSM123735 2 0.0000 0.9878 0.000 1.000 0.000 0.000 0.000
#> GSM123739 2 0.0000 0.9878 0.000 1.000 0.000 0.000 0.000
#> GSM123743 2 0.0000 0.9878 0.000 1.000 0.000 0.000 0.000
#> GSM123749 2 0.0000 0.9878 0.000 1.000 0.000 0.000 0.000
#> GSM123755 2 0.0000 0.9878 0.000 1.000 0.000 0.000 0.000
#> GSM123768 2 0.0000 0.9878 0.000 1.000 0.000 0.000 0.000
#> GSM123776 2 0.3741 0.5733 0.264 0.732 0.000 0.000 0.004
#> GSM123783 2 0.0000 0.9878 0.000 1.000 0.000 0.000 0.000
#> GSM123790 2 0.0000 0.9878 0.000 1.000 0.000 0.000 0.000
#> GSM123794 2 0.0000 0.9878 0.000 1.000 0.000 0.000 0.000
#> GSM123798 2 0.0000 0.9878 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM123732 3 0.0000 0.8725 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM123736 3 0.1349 0.8565 0.000 0.000 0.940 0.000 0.056 0.004
#> GSM123740 3 0.1462 0.8558 0.000 0.000 0.936 0.000 0.056 0.008
#> GSM123744 3 0.2738 0.7861 0.000 0.000 0.820 0.004 0.000 0.176
#> GSM123746 3 0.5239 0.5398 0.152 0.000 0.600 0.000 0.000 0.248
#> GSM123750 3 0.2632 0.7946 0.000 0.000 0.832 0.004 0.000 0.164
#> GSM123752 3 0.4464 0.6600 0.148 0.000 0.712 0.000 0.000 0.140
#> GSM123756 1 0.2884 0.6506 0.824 0.000 0.000 0.008 0.004 0.164
#> GSM123758 3 0.0363 0.8715 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM123761 3 0.5751 0.3710 0.168 0.000 0.508 0.004 0.000 0.320
#> GSM123763 3 0.6269 0.1158 0.244 0.000 0.432 0.012 0.000 0.312
#> GSM123765 3 0.0000 0.8725 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM123769 1 0.2884 0.6506 0.824 0.000 0.000 0.008 0.004 0.164
#> GSM123771 1 0.2884 0.6506 0.824 0.000 0.000 0.008 0.004 0.164
#> GSM123774 1 0.2884 0.6506 0.824 0.000 0.000 0.008 0.004 0.164
#> GSM123778 3 0.0000 0.8725 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM123780 3 0.0000 0.8725 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM123784 3 0.0000 0.8725 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM123787 3 0.0000 0.8725 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM123791 3 0.0000 0.8725 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM123795 3 0.1349 0.8565 0.000 0.000 0.940 0.000 0.056 0.004
#> GSM123799 3 0.0146 0.8721 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM123730 3 0.1194 0.8612 0.008 0.000 0.956 0.032 0.004 0.000
#> GSM123734 4 0.1075 0.0000 0.048 0.000 0.000 0.952 0.000 0.000
#> GSM123738 3 0.4676 0.6561 0.000 0.000 0.696 0.036 0.228 0.040
#> GSM123742 1 0.2632 0.6212 0.832 0.000 0.000 0.000 0.004 0.164
#> GSM123745 1 0.0858 0.7496 0.968 0.000 0.000 0.028 0.004 0.000
#> GSM123748 1 0.1663 0.7163 0.912 0.000 0.000 0.000 0.000 0.088
#> GSM123751 1 0.1411 0.7345 0.936 0.000 0.000 0.004 0.000 0.060
#> GSM123754 1 0.1444 0.7272 0.928 0.000 0.000 0.000 0.000 0.072
#> GSM123757 1 0.2340 0.6515 0.852 0.000 0.000 0.000 0.000 0.148
#> GSM123760 1 0.5843 -0.0147 0.532 0.000 0.288 0.000 0.012 0.168
#> GSM123762 6 0.3728 0.0000 0.344 0.000 0.000 0.004 0.000 0.652
#> GSM123764 3 0.0000 0.8725 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM123767 1 0.0858 0.7496 0.968 0.000 0.000 0.028 0.004 0.000
#> GSM123770 1 0.1003 0.7487 0.964 0.000 0.000 0.028 0.004 0.004
#> GSM123773 1 0.0858 0.7496 0.968 0.000 0.000 0.028 0.004 0.000
#> GSM123777 3 0.0000 0.8725 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM123779 3 0.3837 0.6836 0.212 0.000 0.752 0.028 0.004 0.004
#> GSM123782 3 0.1349 0.8514 0.056 0.000 0.940 0.000 0.000 0.004
#> GSM123786 3 0.0000 0.8725 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM123789 3 0.0603 0.8684 0.016 0.000 0.980 0.000 0.000 0.004
#> GSM123793 5 0.0748 0.0000 0.004 0.000 0.004 0.016 0.976 0.000
#> GSM123797 3 0.4887 0.6404 0.000 0.000 0.680 0.048 0.232 0.040
#> GSM123729 2 0.0000 0.9874 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123733 2 0.0146 0.9859 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM123737 2 0.0000 0.9874 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123741 2 0.0000 0.9874 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123747 2 0.0000 0.9874 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123753 2 0.0000 0.9874 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123759 2 0.0000 0.9874 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123766 2 0.0000 0.9874 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123772 2 0.0000 0.9874 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123775 2 0.0146 0.9859 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM123781 2 0.0000 0.9874 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123785 2 0.0146 0.9859 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM123788 2 0.0146 0.9859 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM123792 2 0.0000 0.9874 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123796 2 0.0146 0.9859 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM123731 2 0.0000 0.9874 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123735 2 0.0146 0.9859 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM123739 2 0.0000 0.9874 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123743 2 0.0000 0.9874 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123749 2 0.0000 0.9874 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123755 2 0.0000 0.9874 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123768 2 0.0000 0.9874 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123776 2 0.3380 0.6121 0.244 0.748 0.000 0.004 0.000 0.004
#> GSM123783 2 0.0000 0.9874 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123790 2 0.0146 0.9859 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM123794 2 0.0146 0.9859 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM123798 2 0.0000 0.9874 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) infection(p) agent(p) k
#> SD:pam 71 3.82e-16 3.82e-16 6.04e-06 2
#> SD:pam 69 6.35e-16 6.35e-16 1.24e-05 3
#> SD:pam 67 1.38e-15 1.38e-15 1.98e-05 4
#> SD:pam 66 3.88e-15 3.88e-15 2.51e-05 5
#> SD:pam 65 1.11e-14 1.11e-14 3.18e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "mclust"]
# you can also extract it by
# res = res_list["SD:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.999 1.000 0.4711 0.529 0.529
#> 3 3 1.000 0.969 0.987 0.3107 0.849 0.716
#> 4 4 0.940 0.919 0.966 0.1549 0.895 0.727
#> 5 5 0.897 0.855 0.905 0.0686 0.933 0.768
#> 6 6 0.814 0.851 0.889 0.0353 0.956 0.820
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
#> GSM123732 1 0.0000 1.000 1.000 0.000
#> GSM123736 1 0.0000 1.000 1.000 0.000
#> GSM123740 1 0.0000 1.000 1.000 0.000
#> GSM123744 1 0.0000 1.000 1.000 0.000
#> GSM123746 1 0.0000 1.000 1.000 0.000
#> GSM123750 1 0.0000 1.000 1.000 0.000
#> GSM123752 1 0.0000 1.000 1.000 0.000
#> GSM123756 1 0.0000 1.000 1.000 0.000
#> GSM123758 1 0.0000 1.000 1.000 0.000
#> GSM123761 1 0.0000 1.000 1.000 0.000
#> GSM123763 1 0.0000 1.000 1.000 0.000
#> GSM123765 1 0.0000 1.000 1.000 0.000
#> GSM123769 1 0.0000 1.000 1.000 0.000
#> GSM123771 1 0.0000 1.000 1.000 0.000
#> GSM123774 1 0.0000 1.000 1.000 0.000
#> GSM123778 1 0.0000 1.000 1.000 0.000
#> GSM123780 1 0.0000 1.000 1.000 0.000
#> GSM123784 1 0.0000 1.000 1.000 0.000
#> GSM123787 1 0.0000 1.000 1.000 0.000
#> GSM123791 1 0.0000 1.000 1.000 0.000
#> GSM123795 1 0.0000 1.000 1.000 0.000
#> GSM123799 1 0.0000 1.000 1.000 0.000
#> GSM123730 1 0.0000 1.000 1.000 0.000
#> GSM123734 1 0.0000 1.000 1.000 0.000
#> GSM123738 1 0.0000 1.000 1.000 0.000
#> GSM123742 1 0.0000 1.000 1.000 0.000
#> GSM123745 1 0.0000 1.000 1.000 0.000
#> GSM123748 1 0.0000 1.000 1.000 0.000
#> GSM123751 1 0.0000 1.000 1.000 0.000
#> GSM123754 1 0.0000 1.000 1.000 0.000
#> GSM123757 1 0.0000 1.000 1.000 0.000
#> GSM123760 1 0.0000 1.000 1.000 0.000
#> GSM123762 1 0.0000 1.000 1.000 0.000
#> GSM123764 1 0.0000 1.000 1.000 0.000
#> GSM123767 1 0.0000 1.000 1.000 0.000
#> GSM123770 1 0.0000 1.000 1.000 0.000
#> GSM123773 1 0.0000 1.000 1.000 0.000
#> GSM123777 1 0.0000 1.000 1.000 0.000
#> GSM123779 1 0.0000 1.000 1.000 0.000
#> GSM123782 1 0.0000 1.000 1.000 0.000
#> GSM123786 1 0.0000 1.000 1.000 0.000
#> GSM123789 1 0.0000 1.000 1.000 0.000
#> GSM123793 1 0.0000 1.000 1.000 0.000
#> GSM123797 1 0.0000 1.000 1.000 0.000
#> GSM123729 2 0.0000 0.999 0.000 1.000
#> GSM123733 2 0.0000 0.999 0.000 1.000
#> GSM123737 2 0.0000 0.999 0.000 1.000
#> GSM123741 2 0.0000 0.999 0.000 1.000
#> GSM123747 2 0.0000 0.999 0.000 1.000
#> GSM123753 2 0.0000 0.999 0.000 1.000
#> GSM123759 2 0.0000 0.999 0.000 1.000
#> GSM123766 2 0.0000 0.999 0.000 1.000
#> GSM123772 2 0.0000 0.999 0.000 1.000
#> GSM123775 2 0.0000 0.999 0.000 1.000
#> GSM123781 2 0.0000 0.999 0.000 1.000
#> GSM123785 2 0.0000 0.999 0.000 1.000
#> GSM123788 2 0.0000 0.999 0.000 1.000
#> GSM123792 2 0.0000 0.999 0.000 1.000
#> GSM123796 2 0.0000 0.999 0.000 1.000
#> GSM123731 2 0.0000 0.999 0.000 1.000
#> GSM123735 2 0.0000 0.999 0.000 1.000
#> GSM123739 2 0.0000 0.999 0.000 1.000
#> GSM123743 2 0.0000 0.999 0.000 1.000
#> GSM123749 2 0.0000 0.999 0.000 1.000
#> GSM123755 2 0.0000 0.999 0.000 1.000
#> GSM123768 2 0.0000 0.999 0.000 1.000
#> GSM123776 1 0.0000 1.000 1.000 0.000
#> GSM123783 2 0.0672 0.992 0.008 0.992
#> GSM123790 2 0.1414 0.980 0.020 0.980
#> GSM123794 2 0.0000 0.999 0.000 1.000
#> GSM123798 2 0.0000 0.999 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM123732 3 0.153 0.909 0.040 0 0.960
#> GSM123736 3 0.319 0.865 0.112 0 0.888
#> GSM123740 3 0.000 0.926 0.000 0 1.000
#> GSM123744 1 0.000 0.991 1.000 0 0.000
#> GSM123746 1 0.000 0.991 1.000 0 0.000
#> GSM123750 1 0.000 0.991 1.000 0 0.000
#> GSM123752 1 0.000 0.991 1.000 0 0.000
#> GSM123756 1 0.000 0.991 1.000 0 0.000
#> GSM123758 1 0.000 0.991 1.000 0 0.000
#> GSM123761 1 0.000 0.991 1.000 0 0.000
#> GSM123763 1 0.000 0.991 1.000 0 0.000
#> GSM123765 3 0.000 0.926 0.000 0 1.000
#> GSM123769 1 0.000 0.991 1.000 0 0.000
#> GSM123771 1 0.000 0.991 1.000 0 0.000
#> GSM123774 1 0.000 0.991 1.000 0 0.000
#> GSM123778 3 0.000 0.926 0.000 0 1.000
#> GSM123780 3 0.604 0.435 0.380 0 0.620
#> GSM123784 3 0.000 0.926 0.000 0 1.000
#> GSM123787 3 0.000 0.926 0.000 0 1.000
#> GSM123791 3 0.375 0.834 0.144 0 0.856
#> GSM123795 1 0.536 0.583 0.724 0 0.276
#> GSM123799 3 0.000 0.926 0.000 0 1.000
#> GSM123730 1 0.000 0.991 1.000 0 0.000
#> GSM123734 1 0.000 0.991 1.000 0 0.000
#> GSM123738 1 0.000 0.991 1.000 0 0.000
#> GSM123742 1 0.000 0.991 1.000 0 0.000
#> GSM123745 1 0.000 0.991 1.000 0 0.000
#> GSM123748 1 0.000 0.991 1.000 0 0.000
#> GSM123751 1 0.000 0.991 1.000 0 0.000
#> GSM123754 1 0.000 0.991 1.000 0 0.000
#> GSM123757 1 0.000 0.991 1.000 0 0.000
#> GSM123760 1 0.000 0.991 1.000 0 0.000
#> GSM123762 1 0.000 0.991 1.000 0 0.000
#> GSM123764 1 0.000 0.991 1.000 0 0.000
#> GSM123767 1 0.000 0.991 1.000 0 0.000
#> GSM123770 1 0.000 0.991 1.000 0 0.000
#> GSM123773 1 0.000 0.991 1.000 0 0.000
#> GSM123777 1 0.000 0.991 1.000 0 0.000
#> GSM123779 1 0.000 0.991 1.000 0 0.000
#> GSM123782 1 0.000 0.991 1.000 0 0.000
#> GSM123786 3 0.000 0.926 0.000 0 1.000
#> GSM123789 1 0.000 0.991 1.000 0 0.000
#> GSM123793 1 0.000 0.991 1.000 0 0.000
#> GSM123797 1 0.000 0.991 1.000 0 0.000
#> GSM123729 2 0.000 1.000 0.000 1 0.000
#> GSM123733 2 0.000 1.000 0.000 1 0.000
#> GSM123737 2 0.000 1.000 0.000 1 0.000
#> GSM123741 2 0.000 1.000 0.000 1 0.000
#> GSM123747 2 0.000 1.000 0.000 1 0.000
#> GSM123753 2 0.000 1.000 0.000 1 0.000
#> GSM123759 2 0.000 1.000 0.000 1 0.000
#> GSM123766 2 0.000 1.000 0.000 1 0.000
#> GSM123772 2 0.000 1.000 0.000 1 0.000
#> GSM123775 2 0.000 1.000 0.000 1 0.000
#> GSM123781 2 0.000 1.000 0.000 1 0.000
#> GSM123785 2 0.000 1.000 0.000 1 0.000
#> GSM123788 2 0.000 1.000 0.000 1 0.000
#> GSM123792 2 0.000 1.000 0.000 1 0.000
#> GSM123796 2 0.000 1.000 0.000 1 0.000
#> GSM123731 2 0.000 1.000 0.000 1 0.000
#> GSM123735 2 0.000 1.000 0.000 1 0.000
#> GSM123739 2 0.000 1.000 0.000 1 0.000
#> GSM123743 2 0.000 1.000 0.000 1 0.000
#> GSM123749 2 0.000 1.000 0.000 1 0.000
#> GSM123755 2 0.000 1.000 0.000 1 0.000
#> GSM123768 2 0.000 1.000 0.000 1 0.000
#> GSM123776 1 0.000 0.991 1.000 0 0.000
#> GSM123783 2 0.000 1.000 0.000 1 0.000
#> GSM123790 2 0.000 1.000 0.000 1 0.000
#> GSM123794 2 0.000 1.000 0.000 1 0.000
#> GSM123798 2 0.000 1.000 0.000 1 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM123732 3 0.0000 0.963 0.000 0 1.000 0.000
#> GSM123736 3 0.0188 0.961 0.000 0 0.996 0.004
#> GSM123740 3 0.0000 0.963 0.000 0 1.000 0.000
#> GSM123744 1 0.1118 0.925 0.964 0 0.036 0.000
#> GSM123746 1 0.0000 0.949 1.000 0 0.000 0.000
#> GSM123750 1 0.1022 0.929 0.968 0 0.032 0.000
#> GSM123752 1 0.1022 0.929 0.968 0 0.032 0.000
#> GSM123756 1 0.0000 0.949 1.000 0 0.000 0.000
#> GSM123758 1 0.2345 0.854 0.900 0 0.100 0.000
#> GSM123761 1 0.0000 0.949 1.000 0 0.000 0.000
#> GSM123763 1 0.0000 0.949 1.000 0 0.000 0.000
#> GSM123765 3 0.0000 0.963 0.000 0 1.000 0.000
#> GSM123769 1 0.0000 0.949 1.000 0 0.000 0.000
#> GSM123771 1 0.0000 0.949 1.000 0 0.000 0.000
#> GSM123774 1 0.0000 0.949 1.000 0 0.000 0.000
#> GSM123778 3 0.0000 0.963 0.000 0 1.000 0.000
#> GSM123780 3 0.3494 0.784 0.004 0 0.824 0.172
#> GSM123784 3 0.0000 0.963 0.000 0 1.000 0.000
#> GSM123787 3 0.0000 0.963 0.000 0 1.000 0.000
#> GSM123791 3 0.1022 0.936 0.032 0 0.968 0.000
#> GSM123795 3 0.3616 0.808 0.112 0 0.852 0.036
#> GSM123799 3 0.0000 0.963 0.000 0 1.000 0.000
#> GSM123730 4 0.0000 0.820 0.000 0 0.000 1.000
#> GSM123734 4 0.4277 0.701 0.280 0 0.000 0.720
#> GSM123738 4 0.0000 0.820 0.000 0 0.000 1.000
#> GSM123742 1 0.0592 0.942 0.984 0 0.000 0.016
#> GSM123745 1 0.0336 0.946 0.992 0 0.000 0.008
#> GSM123748 1 0.0000 0.949 1.000 0 0.000 0.000
#> GSM123751 1 0.0469 0.944 0.988 0 0.000 0.012
#> GSM123754 1 0.0000 0.949 1.000 0 0.000 0.000
#> GSM123757 1 0.0000 0.949 1.000 0 0.000 0.000
#> GSM123760 1 0.4989 -0.119 0.528 0 0.000 0.472
#> GSM123762 1 0.0000 0.949 1.000 0 0.000 0.000
#> GSM123764 4 0.3751 0.779 0.196 0 0.004 0.800
#> GSM123767 1 0.0592 0.942 0.984 0 0.000 0.016
#> GSM123770 1 0.0000 0.949 1.000 0 0.000 0.000
#> GSM123773 1 0.0336 0.946 0.992 0 0.000 0.008
#> GSM123777 4 0.0000 0.820 0.000 0 0.000 1.000
#> GSM123779 4 0.4713 0.553 0.360 0 0.000 0.640
#> GSM123782 1 0.4283 0.584 0.740 0 0.004 0.256
#> GSM123786 3 0.0000 0.963 0.000 0 1.000 0.000
#> GSM123789 4 0.4072 0.735 0.252 0 0.000 0.748
#> GSM123793 4 0.0000 0.820 0.000 0 0.000 1.000
#> GSM123797 4 0.0000 0.820 0.000 0 0.000 1.000
#> GSM123729 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123733 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123737 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123741 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123747 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123753 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123759 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123766 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123772 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123775 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123781 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123785 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123788 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123792 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123796 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123731 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123735 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123739 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123743 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123749 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123755 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123768 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123776 1 0.0000 0.949 1.000 0 0.000 0.000
#> GSM123783 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123790 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123794 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123798 2 0.0000 1.000 0.000 1 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM123732 3 0.0000 0.9578 0.000 0.000 1.000 0.000 0.000
#> GSM123736 3 0.0404 0.9518 0.000 0.000 0.988 0.012 0.000
#> GSM123740 3 0.0000 0.9578 0.000 0.000 1.000 0.000 0.000
#> GSM123744 1 0.0771 0.5846 0.976 0.000 0.020 0.000 0.004
#> GSM123746 1 0.2471 0.6373 0.864 0.000 0.000 0.000 0.136
#> GSM123750 1 0.0771 0.5846 0.976 0.000 0.020 0.000 0.004
#> GSM123752 1 0.0771 0.5846 0.976 0.000 0.020 0.000 0.004
#> GSM123756 1 0.4171 0.6553 0.604 0.000 0.000 0.000 0.396
#> GSM123758 1 0.1357 0.5598 0.948 0.000 0.048 0.000 0.004
#> GSM123761 1 0.1965 0.6269 0.904 0.000 0.000 0.000 0.096
#> GSM123763 1 0.5185 0.5866 0.568 0.000 0.000 0.048 0.384
#> GSM123765 3 0.0000 0.9578 0.000 0.000 1.000 0.000 0.000
#> GSM123769 1 0.4171 0.6553 0.604 0.000 0.000 0.000 0.396
#> GSM123771 1 0.4171 0.6553 0.604 0.000 0.000 0.000 0.396
#> GSM123774 1 0.4171 0.6553 0.604 0.000 0.000 0.000 0.396
#> GSM123778 3 0.0000 0.9578 0.000 0.000 1.000 0.000 0.000
#> GSM123780 3 0.3160 0.7790 0.000 0.000 0.808 0.188 0.004
#> GSM123784 3 0.0000 0.9578 0.000 0.000 1.000 0.000 0.000
#> GSM123787 3 0.0000 0.9578 0.000 0.000 1.000 0.000 0.000
#> GSM123791 3 0.2179 0.8858 0.112 0.000 0.888 0.000 0.000
#> GSM123795 3 0.2516 0.8427 0.000 0.000 0.860 0.140 0.000
#> GSM123799 3 0.0000 0.9578 0.000 0.000 1.000 0.000 0.000
#> GSM123730 4 0.0000 0.9053 0.000 0.000 0.000 1.000 0.000
#> GSM123734 4 0.2970 0.8787 0.004 0.000 0.000 0.828 0.168
#> GSM123738 4 0.0000 0.9053 0.000 0.000 0.000 1.000 0.000
#> GSM123742 5 0.5953 -0.0712 0.384 0.000 0.000 0.112 0.504
#> GSM123745 5 0.1357 0.8160 0.004 0.000 0.000 0.048 0.948
#> GSM123748 5 0.4170 0.6246 0.192 0.000 0.000 0.048 0.760
#> GSM123751 5 0.2054 0.8164 0.028 0.000 0.000 0.052 0.920
#> GSM123754 5 0.2903 0.7848 0.080 0.000 0.000 0.048 0.872
#> GSM123757 1 0.5107 0.6252 0.596 0.000 0.000 0.048 0.356
#> GSM123760 4 0.3013 0.8831 0.008 0.000 0.000 0.832 0.160
#> GSM123762 1 0.5176 0.5958 0.572 0.000 0.000 0.048 0.380
#> GSM123764 4 0.2124 0.9079 0.004 0.000 0.000 0.900 0.096
#> GSM123767 5 0.1502 0.8106 0.004 0.000 0.000 0.056 0.940
#> GSM123770 1 0.5256 0.5145 0.532 0.000 0.000 0.048 0.420
#> GSM123773 5 0.1357 0.8160 0.004 0.000 0.000 0.048 0.948
#> GSM123777 4 0.0000 0.9053 0.000 0.000 0.000 1.000 0.000
#> GSM123779 4 0.2848 0.8881 0.004 0.000 0.000 0.840 0.156
#> GSM123782 4 0.3495 0.8838 0.036 0.000 0.008 0.836 0.120
#> GSM123786 3 0.0000 0.9578 0.000 0.000 1.000 0.000 0.000
#> GSM123789 4 0.2646 0.9019 0.004 0.000 0.004 0.868 0.124
#> GSM123793 4 0.0000 0.9053 0.000 0.000 0.000 1.000 0.000
#> GSM123797 4 0.0000 0.9053 0.000 0.000 0.000 1.000 0.000
#> GSM123729 2 0.0162 0.9975 0.000 0.996 0.000 0.000 0.004
#> GSM123733 2 0.0000 0.9989 0.000 1.000 0.000 0.000 0.000
#> GSM123737 2 0.0162 0.9975 0.000 0.996 0.000 0.000 0.004
#> GSM123741 2 0.0000 0.9989 0.000 1.000 0.000 0.000 0.000
#> GSM123747 2 0.0000 0.9989 0.000 1.000 0.000 0.000 0.000
#> GSM123753 2 0.0000 0.9989 0.000 1.000 0.000 0.000 0.000
#> GSM123759 2 0.0000 0.9989 0.000 1.000 0.000 0.000 0.000
#> GSM123766 2 0.0000 0.9989 0.000 1.000 0.000 0.000 0.000
#> GSM123772 2 0.0000 0.9989 0.000 1.000 0.000 0.000 0.000
#> GSM123775 2 0.0162 0.9975 0.000 0.996 0.000 0.000 0.004
#> GSM123781 2 0.0000 0.9989 0.000 1.000 0.000 0.000 0.000
#> GSM123785 2 0.0000 0.9989 0.000 1.000 0.000 0.000 0.000
#> GSM123788 2 0.0000 0.9989 0.000 1.000 0.000 0.000 0.000
#> GSM123792 2 0.0000 0.9989 0.000 1.000 0.000 0.000 0.000
#> GSM123796 2 0.0000 0.9989 0.000 1.000 0.000 0.000 0.000
#> GSM123731 2 0.0000 0.9989 0.000 1.000 0.000 0.000 0.000
#> GSM123735 2 0.0162 0.9975 0.000 0.996 0.000 0.000 0.004
#> GSM123739 2 0.0162 0.9975 0.000 0.996 0.000 0.000 0.004
#> GSM123743 2 0.0000 0.9989 0.000 1.000 0.000 0.000 0.000
#> GSM123749 2 0.0000 0.9989 0.000 1.000 0.000 0.000 0.000
#> GSM123755 2 0.0000 0.9989 0.000 1.000 0.000 0.000 0.000
#> GSM123768 2 0.0000 0.9989 0.000 1.000 0.000 0.000 0.000
#> GSM123776 1 0.5107 0.6252 0.596 0.000 0.000 0.048 0.356
#> GSM123783 2 0.0162 0.9975 0.000 0.996 0.000 0.000 0.004
#> GSM123790 2 0.0162 0.9975 0.000 0.996 0.000 0.000 0.004
#> GSM123794 2 0.0162 0.9975 0.000 0.996 0.000 0.000 0.004
#> GSM123798 2 0.0000 0.9989 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM123732 3 0.0000 0.959 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM123736 3 0.0603 0.951 0.000 0.000 0.980 0.016 0.004 0.000
#> GSM123740 3 0.0146 0.958 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM123744 5 0.3288 0.895 0.000 0.000 0.016 0.008 0.800 0.176
#> GSM123746 5 0.3713 0.815 0.008 0.000 0.000 0.004 0.704 0.284
#> GSM123750 5 0.3288 0.895 0.000 0.000 0.016 0.008 0.800 0.176
#> GSM123752 5 0.3288 0.895 0.000 0.000 0.016 0.008 0.800 0.176
#> GSM123756 6 0.1007 1.000 0.044 0.000 0.000 0.000 0.000 0.956
#> GSM123758 5 0.4490 0.794 0.000 0.000 0.108 0.004 0.716 0.172
#> GSM123761 5 0.3595 0.811 0.008 0.000 0.000 0.000 0.704 0.288
#> GSM123763 1 0.4918 0.677 0.612 0.000 0.000 0.004 0.076 0.308
#> GSM123765 3 0.0000 0.959 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM123769 6 0.1007 1.000 0.044 0.000 0.000 0.000 0.000 0.956
#> GSM123771 6 0.1007 1.000 0.044 0.000 0.000 0.000 0.000 0.956
#> GSM123774 6 0.1007 1.000 0.044 0.000 0.000 0.000 0.000 0.956
#> GSM123778 3 0.0000 0.959 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM123780 3 0.2454 0.825 0.000 0.000 0.840 0.160 0.000 0.000
#> GSM123784 3 0.0000 0.959 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM123787 3 0.0000 0.959 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM123791 3 0.2234 0.864 0.000 0.000 0.872 0.004 0.124 0.000
#> GSM123795 3 0.2325 0.878 0.000 0.000 0.884 0.100 0.008 0.008
#> GSM123799 3 0.0146 0.958 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM123730 4 0.0000 0.763 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM123734 4 0.3804 0.633 0.336 0.000 0.000 0.656 0.000 0.008
#> GSM123738 4 0.0000 0.763 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM123742 1 0.4981 0.702 0.680 0.000 0.000 0.116 0.016 0.188
#> GSM123745 1 0.0260 0.747 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM123748 1 0.2653 0.770 0.844 0.000 0.000 0.000 0.012 0.144
#> GSM123751 1 0.0692 0.753 0.976 0.000 0.000 0.004 0.000 0.020
#> GSM123754 1 0.1501 0.766 0.924 0.000 0.000 0.000 0.000 0.076
#> GSM123757 1 0.4809 0.652 0.600 0.000 0.000 0.000 0.072 0.328
#> GSM123760 4 0.4400 0.462 0.428 0.000 0.004 0.552 0.004 0.012
#> GSM123762 1 0.4062 0.710 0.660 0.000 0.000 0.000 0.024 0.316
#> GSM123764 4 0.3329 0.751 0.180 0.000 0.012 0.796 0.000 0.012
#> GSM123767 1 0.0260 0.747 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM123770 1 0.3482 0.720 0.684 0.000 0.000 0.000 0.000 0.316
#> GSM123773 1 0.0260 0.747 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM123777 4 0.0000 0.763 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM123779 4 0.4178 0.483 0.428 0.000 0.004 0.560 0.000 0.008
#> GSM123782 4 0.4710 0.687 0.260 0.000 0.028 0.680 0.012 0.020
#> GSM123786 3 0.0000 0.959 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM123789 4 0.3702 0.733 0.224 0.000 0.008 0.752 0.004 0.012
#> GSM123793 4 0.0000 0.763 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM123797 4 0.0000 0.763 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM123729 2 0.2595 0.893 0.000 0.836 0.000 0.000 0.160 0.004
#> GSM123733 2 0.1498 0.920 0.000 0.940 0.000 0.000 0.028 0.032
#> GSM123737 2 0.2482 0.900 0.000 0.848 0.000 0.000 0.148 0.004
#> GSM123741 2 0.0000 0.937 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123747 2 0.0000 0.937 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123753 2 0.0000 0.937 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123759 2 0.0000 0.937 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123766 2 0.2815 0.904 0.000 0.848 0.000 0.000 0.120 0.032
#> GSM123772 2 0.1341 0.919 0.000 0.948 0.000 0.000 0.024 0.028
#> GSM123775 2 0.2595 0.893 0.000 0.836 0.000 0.000 0.160 0.004
#> GSM123781 2 0.0000 0.937 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123785 2 0.3176 0.888 0.000 0.812 0.000 0.000 0.156 0.032
#> GSM123788 2 0.1341 0.919 0.000 0.948 0.000 0.000 0.024 0.028
#> GSM123792 2 0.0000 0.937 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123796 2 0.1341 0.919 0.000 0.948 0.000 0.000 0.024 0.028
#> GSM123731 2 0.0000 0.937 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123735 2 0.0260 0.936 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM123739 2 0.2595 0.893 0.000 0.836 0.000 0.000 0.160 0.004
#> GSM123743 2 0.0000 0.937 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123749 2 0.0000 0.937 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123755 2 0.0000 0.937 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123768 2 0.2402 0.902 0.000 0.856 0.000 0.000 0.140 0.004
#> GSM123776 1 0.4224 0.687 0.632 0.000 0.000 0.000 0.028 0.340
#> GSM123783 2 0.2482 0.899 0.000 0.848 0.000 0.000 0.148 0.004
#> GSM123790 2 0.2482 0.899 0.000 0.848 0.000 0.000 0.148 0.004
#> GSM123794 2 0.2191 0.910 0.000 0.876 0.000 0.000 0.120 0.004
#> GSM123798 2 0.0000 0.937 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) infection(p) agent(p) k
#> SD:mclust 71 3.04e-15 3.04e-15 5.99e-05 2
#> SD:mclust 70 1.59e-16 1.59e-16 9.67e-05 3
#> SD:mclust 70 4.14e-18 4.14e-18 3.33e-04 4
#> SD:mclust 70 5.03e-21 5.03e-21 8.80e-04 5
#> SD:mclust 69 3.18e-21 3.18e-21 2.44e-03 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "NMF"]
# you can also extract it by
# res = res_list["SD:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 71 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 0.983 0.993 0.4800 0.522 0.522
#> 3 3 0.865 0.877 0.939 0.3840 0.794 0.611
#> 4 4 0.784 0.833 0.887 0.1023 0.899 0.706
#> 5 5 0.722 0.682 0.815 0.0525 0.934 0.766
#> 6 6 0.746 0.639 0.787 0.0314 0.958 0.829
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
#> GSM123732 1 0.0000 0.992 1.000 0.000
#> GSM123736 1 0.0000 0.992 1.000 0.000
#> GSM123740 1 0.0000 0.992 1.000 0.000
#> GSM123744 1 0.0000 0.992 1.000 0.000
#> GSM123746 1 0.0000 0.992 1.000 0.000
#> GSM123750 1 0.0000 0.992 1.000 0.000
#> GSM123752 1 0.0000 0.992 1.000 0.000
#> GSM123756 1 0.0000 0.992 1.000 0.000
#> GSM123758 1 0.0000 0.992 1.000 0.000
#> GSM123761 1 0.0000 0.992 1.000 0.000
#> GSM123763 1 0.0000 0.992 1.000 0.000
#> GSM123765 1 0.0000 0.992 1.000 0.000
#> GSM123769 1 0.0000 0.992 1.000 0.000
#> GSM123771 1 0.0000 0.992 1.000 0.000
#> GSM123774 1 0.0000 0.992 1.000 0.000
#> GSM123778 1 0.0000 0.992 1.000 0.000
#> GSM123780 1 0.0000 0.992 1.000 0.000
#> GSM123784 1 0.0000 0.992 1.000 0.000
#> GSM123787 1 0.0000 0.992 1.000 0.000
#> GSM123791 1 0.0000 0.992 1.000 0.000
#> GSM123795 1 0.0000 0.992 1.000 0.000
#> GSM123799 1 0.0000 0.992 1.000 0.000
#> GSM123730 1 0.9393 0.442 0.644 0.356
#> GSM123734 1 0.0000 0.992 1.000 0.000
#> GSM123738 1 0.0000 0.992 1.000 0.000
#> GSM123742 1 0.0000 0.992 1.000 0.000
#> GSM123745 1 0.0000 0.992 1.000 0.000
#> GSM123748 1 0.0000 0.992 1.000 0.000
#> GSM123751 1 0.0000 0.992 1.000 0.000
#> GSM123754 1 0.0000 0.992 1.000 0.000
#> GSM123757 1 0.0000 0.992 1.000 0.000
#> GSM123760 1 0.0000 0.992 1.000 0.000
#> GSM123762 1 0.0000 0.992 1.000 0.000
#> GSM123764 1 0.0000 0.992 1.000 0.000
#> GSM123767 1 0.0000 0.992 1.000 0.000
#> GSM123770 1 0.0000 0.992 1.000 0.000
#> GSM123773 1 0.0000 0.992 1.000 0.000
#> GSM123777 1 0.0000 0.992 1.000 0.000
#> GSM123779 1 0.0000 0.992 1.000 0.000
#> GSM123782 1 0.0376 0.988 0.996 0.004
#> GSM123786 1 0.0000 0.992 1.000 0.000
#> GSM123789 1 0.0000 0.992 1.000 0.000
#> GSM123793 1 0.0000 0.992 1.000 0.000
#> GSM123797 1 0.0000 0.992 1.000 0.000
#> GSM123729 2 0.0000 0.995 0.000 1.000
#> GSM123733 2 0.0000 0.995 0.000 1.000
#> GSM123737 2 0.0000 0.995 0.000 1.000
#> GSM123741 2 0.0000 0.995 0.000 1.000
#> GSM123747 2 0.0000 0.995 0.000 1.000
#> GSM123753 2 0.0000 0.995 0.000 1.000
#> GSM123759 2 0.0000 0.995 0.000 1.000
#> GSM123766 2 0.0000 0.995 0.000 1.000
#> GSM123772 2 0.0000 0.995 0.000 1.000
#> GSM123775 2 0.0000 0.995 0.000 1.000
#> GSM123781 2 0.0000 0.995 0.000 1.000
#> GSM123785 2 0.0000 0.995 0.000 1.000
#> GSM123788 2 0.0000 0.995 0.000 1.000
#> GSM123792 2 0.0000 0.995 0.000 1.000
#> GSM123796 2 0.0000 0.995 0.000 1.000
#> GSM123731 2 0.0000 0.995 0.000 1.000
#> GSM123735 2 0.0000 0.995 0.000 1.000
#> GSM123739 2 0.0000 0.995 0.000 1.000
#> GSM123743 2 0.0000 0.995 0.000 1.000
#> GSM123749 2 0.0000 0.995 0.000 1.000
#> GSM123755 2 0.0000 0.995 0.000 1.000
#> GSM123768 2 0.0000 0.995 0.000 1.000
#> GSM123776 2 0.5629 0.846 0.132 0.868
#> GSM123783 2 0.0000 0.995 0.000 1.000
#> GSM123790 2 0.0000 0.995 0.000 1.000
#> GSM123794 2 0.0000 0.995 0.000 1.000
#> GSM123798 2 0.0000 0.995 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM123732 3 0.0000 0.8983 0.000 0.000 1.000
#> GSM123736 3 0.1031 0.9035 0.024 0.000 0.976
#> GSM123740 3 0.1031 0.9035 0.024 0.000 0.976
#> GSM123744 3 0.5529 0.5917 0.296 0.000 0.704
#> GSM123746 1 0.2066 0.8898 0.940 0.000 0.060
#> GSM123750 3 0.6008 0.4205 0.372 0.000 0.628
#> GSM123752 1 0.5138 0.6705 0.748 0.000 0.252
#> GSM123756 1 0.1031 0.9006 0.976 0.000 0.024
#> GSM123758 3 0.4521 0.7537 0.180 0.004 0.816
#> GSM123761 1 0.3816 0.8201 0.852 0.000 0.148
#> GSM123763 1 0.5785 0.5112 0.668 0.000 0.332
#> GSM123765 3 0.0424 0.9015 0.008 0.000 0.992
#> GSM123769 1 0.1163 0.9011 0.972 0.000 0.028
#> GSM123771 1 0.0424 0.8934 0.992 0.000 0.008
#> GSM123774 1 0.0237 0.8872 0.996 0.004 0.000
#> GSM123778 3 0.0237 0.8959 0.000 0.004 0.996
#> GSM123780 3 0.0237 0.9000 0.004 0.000 0.996
#> GSM123784 3 0.0592 0.9024 0.012 0.000 0.988
#> GSM123787 3 0.0000 0.8983 0.000 0.000 1.000
#> GSM123791 3 0.1289 0.9023 0.032 0.000 0.968
#> GSM123795 3 0.1163 0.9031 0.028 0.000 0.972
#> GSM123799 3 0.1163 0.9031 0.028 0.000 0.972
#> GSM123730 3 0.1636 0.8879 0.016 0.020 0.964
#> GSM123734 3 0.6307 0.0168 0.488 0.000 0.512
#> GSM123738 3 0.0747 0.9030 0.016 0.000 0.984
#> GSM123742 1 0.6235 0.2104 0.564 0.000 0.436
#> GSM123745 1 0.0892 0.8995 0.980 0.000 0.020
#> GSM123748 1 0.1529 0.8996 0.960 0.000 0.040
#> GSM123751 1 0.1529 0.9000 0.960 0.000 0.040
#> GSM123754 1 0.1643 0.8984 0.956 0.000 0.044
#> GSM123757 1 0.0592 0.8960 0.988 0.000 0.012
#> GSM123760 3 0.5016 0.6937 0.240 0.000 0.760
#> GSM123762 1 0.3879 0.8102 0.848 0.000 0.152
#> GSM123764 3 0.1411 0.9011 0.036 0.000 0.964
#> GSM123767 1 0.1129 0.8982 0.976 0.004 0.020
#> GSM123770 1 0.1031 0.9007 0.976 0.000 0.024
#> GSM123773 1 0.1289 0.9009 0.968 0.000 0.032
#> GSM123777 3 0.0592 0.9022 0.012 0.000 0.988
#> GSM123779 3 0.5497 0.5993 0.292 0.000 0.708
#> GSM123782 3 0.1753 0.8942 0.048 0.000 0.952
#> GSM123786 3 0.0000 0.8983 0.000 0.000 1.000
#> GSM123789 3 0.1860 0.8935 0.052 0.000 0.948
#> GSM123793 3 0.1529 0.8995 0.040 0.000 0.960
#> GSM123797 3 0.1411 0.9011 0.036 0.000 0.964
#> GSM123729 2 0.1129 0.9844 0.020 0.976 0.004
#> GSM123733 2 0.0237 0.9923 0.004 0.996 0.000
#> GSM123737 2 0.0592 0.9902 0.012 0.988 0.000
#> GSM123741 2 0.0000 0.9930 0.000 1.000 0.000
#> GSM123747 2 0.0237 0.9924 0.000 0.996 0.004
#> GSM123753 2 0.0475 0.9914 0.004 0.992 0.004
#> GSM123759 2 0.0237 0.9928 0.004 0.996 0.000
#> GSM123766 2 0.0237 0.9923 0.004 0.996 0.000
#> GSM123772 2 0.0237 0.9923 0.004 0.996 0.000
#> GSM123775 2 0.1289 0.9772 0.032 0.968 0.000
#> GSM123781 2 0.0000 0.9930 0.000 1.000 0.000
#> GSM123785 2 0.0475 0.9909 0.004 0.992 0.004
#> GSM123788 2 0.0000 0.9930 0.000 1.000 0.000
#> GSM123792 2 0.0000 0.9930 0.000 1.000 0.000
#> GSM123796 2 0.0237 0.9923 0.004 0.996 0.000
#> GSM123731 2 0.0237 0.9928 0.004 0.996 0.000
#> GSM123735 2 0.0237 0.9928 0.004 0.996 0.000
#> GSM123739 2 0.1031 0.9833 0.024 0.976 0.000
#> GSM123743 2 0.0000 0.9930 0.000 1.000 0.000
#> GSM123749 2 0.0237 0.9928 0.004 0.996 0.000
#> GSM123755 2 0.0237 0.9928 0.004 0.996 0.000
#> GSM123768 2 0.0829 0.9890 0.004 0.984 0.012
#> GSM123776 1 0.3340 0.7814 0.880 0.120 0.000
#> GSM123783 2 0.0829 0.9890 0.004 0.984 0.012
#> GSM123790 2 0.1399 0.9737 0.004 0.968 0.028
#> GSM123794 2 0.0475 0.9923 0.004 0.992 0.004
#> GSM123798 2 0.0475 0.9920 0.004 0.992 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM123732 3 0.1256 0.844 0.000 0.028 0.964 0.008
#> GSM123736 3 0.1940 0.844 0.000 0.000 0.924 0.076
#> GSM123740 3 0.1452 0.864 0.008 0.000 0.956 0.036
#> GSM123744 3 0.2799 0.794 0.108 0.000 0.884 0.008
#> GSM123746 1 0.2737 0.837 0.888 0.000 0.104 0.008
#> GSM123750 3 0.4049 0.672 0.212 0.000 0.780 0.008
#> GSM123752 3 0.6602 0.238 0.388 0.040 0.548 0.024
#> GSM123756 1 0.0376 0.888 0.992 0.000 0.004 0.004
#> GSM123758 3 0.3562 0.761 0.016 0.084 0.872 0.028
#> GSM123761 1 0.4284 0.707 0.764 0.000 0.224 0.012
#> GSM123763 1 0.4692 0.713 0.756 0.000 0.212 0.032
#> GSM123765 3 0.1557 0.857 0.000 0.000 0.944 0.056
#> GSM123769 1 0.0657 0.889 0.984 0.000 0.004 0.012
#> GSM123771 1 0.0188 0.887 0.996 0.000 0.004 0.000
#> GSM123774 1 0.0188 0.887 0.996 0.000 0.004 0.000
#> GSM123778 3 0.1004 0.850 0.000 0.024 0.972 0.004
#> GSM123780 3 0.2266 0.834 0.004 0.000 0.912 0.084
#> GSM123784 3 0.1557 0.857 0.000 0.000 0.944 0.056
#> GSM123787 3 0.0336 0.859 0.000 0.008 0.992 0.000
#> GSM123791 3 0.1256 0.864 0.008 0.000 0.964 0.028
#> GSM123795 3 0.2466 0.820 0.004 0.000 0.900 0.096
#> GSM123799 3 0.1722 0.861 0.008 0.000 0.944 0.048
#> GSM123730 4 0.2313 0.701 0.000 0.032 0.044 0.924
#> GSM123734 4 0.4261 0.755 0.068 0.000 0.112 0.820
#> GSM123738 4 0.4872 0.681 0.004 0.000 0.356 0.640
#> GSM123742 4 0.7165 0.369 0.372 0.000 0.140 0.488
#> GSM123745 1 0.3356 0.802 0.824 0.000 0.000 0.176
#> GSM123748 1 0.1978 0.876 0.928 0.000 0.004 0.068
#> GSM123751 1 0.4220 0.697 0.748 0.000 0.004 0.248
#> GSM123754 1 0.2469 0.857 0.892 0.000 0.000 0.108
#> GSM123757 1 0.0188 0.887 0.996 0.000 0.004 0.000
#> GSM123760 4 0.5687 0.762 0.068 0.000 0.248 0.684
#> GSM123762 1 0.2722 0.870 0.904 0.000 0.064 0.032
#> GSM123764 4 0.5372 0.529 0.012 0.000 0.444 0.544
#> GSM123767 4 0.4877 0.145 0.408 0.000 0.000 0.592
#> GSM123770 1 0.0895 0.888 0.976 0.000 0.004 0.020
#> GSM123773 1 0.3219 0.814 0.836 0.000 0.000 0.164
#> GSM123777 4 0.3873 0.769 0.000 0.000 0.228 0.772
#> GSM123779 4 0.3013 0.742 0.032 0.000 0.080 0.888
#> GSM123782 4 0.5352 0.738 0.020 0.008 0.296 0.676
#> GSM123786 3 0.0524 0.859 0.004 0.008 0.988 0.000
#> GSM123789 4 0.5465 0.630 0.020 0.000 0.392 0.588
#> GSM123793 4 0.4364 0.776 0.016 0.000 0.220 0.764
#> GSM123797 4 0.4011 0.775 0.008 0.000 0.208 0.784
#> GSM123729 2 0.1786 0.952 0.008 0.948 0.008 0.036
#> GSM123733 2 0.1716 0.951 0.000 0.936 0.000 0.064
#> GSM123737 2 0.1022 0.960 0.000 0.968 0.000 0.032
#> GSM123741 2 0.0592 0.963 0.000 0.984 0.000 0.016
#> GSM123747 2 0.0992 0.960 0.004 0.976 0.008 0.012
#> GSM123753 2 0.1042 0.959 0.000 0.972 0.008 0.020
#> GSM123759 2 0.1042 0.959 0.000 0.972 0.008 0.020
#> GSM123766 2 0.1867 0.947 0.000 0.928 0.000 0.072
#> GSM123772 2 0.1211 0.959 0.000 0.960 0.000 0.040
#> GSM123775 2 0.1677 0.959 0.012 0.948 0.000 0.040
#> GSM123781 2 0.0895 0.963 0.000 0.976 0.004 0.020
#> GSM123785 2 0.3074 0.886 0.000 0.848 0.000 0.152
#> GSM123788 2 0.1557 0.954 0.000 0.944 0.000 0.056
#> GSM123792 2 0.0188 0.963 0.000 0.996 0.000 0.004
#> GSM123796 2 0.1716 0.951 0.000 0.936 0.000 0.064
#> GSM123731 2 0.0927 0.960 0.000 0.976 0.008 0.016
#> GSM123735 2 0.1022 0.960 0.000 0.968 0.000 0.032
#> GSM123739 2 0.1824 0.955 0.004 0.936 0.000 0.060
#> GSM123743 2 0.0336 0.963 0.000 0.992 0.000 0.008
#> GSM123749 2 0.1109 0.959 0.000 0.968 0.004 0.028
#> GSM123755 2 0.1151 0.958 0.000 0.968 0.008 0.024
#> GSM123768 2 0.2494 0.930 0.000 0.916 0.048 0.036
#> GSM123776 1 0.1706 0.859 0.948 0.036 0.000 0.016
#> GSM123783 2 0.3016 0.916 0.004 0.896 0.060 0.040
#> GSM123790 2 0.1762 0.957 0.004 0.944 0.004 0.048
#> GSM123794 2 0.1339 0.957 0.004 0.964 0.008 0.024
#> GSM123798 2 0.1388 0.956 0.000 0.960 0.012 0.028
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM123732 3 0.1836 0.7664 0.008 0.000 0.936 0.016 0.040
#> GSM123736 3 0.4627 0.7131 0.020 0.000 0.760 0.056 0.164
#> GSM123740 3 0.4245 0.7515 0.028 0.000 0.800 0.048 0.124
#> GSM123744 3 0.5049 0.6400 0.148 0.000 0.732 0.104 0.016
#> GSM123746 1 0.4555 0.6198 0.776 0.000 0.112 0.096 0.016
#> GSM123750 3 0.6151 0.5076 0.232 0.000 0.620 0.120 0.028
#> GSM123752 1 0.6234 0.0340 0.476 0.012 0.436 0.016 0.060
#> GSM123756 1 0.0727 0.7168 0.980 0.000 0.004 0.012 0.004
#> GSM123758 3 0.4669 0.6677 0.052 0.024 0.792 0.020 0.112
#> GSM123761 1 0.6433 0.3004 0.516 0.000 0.184 0.296 0.004
#> GSM123763 1 0.6886 0.0595 0.436 0.000 0.144 0.392 0.028
#> GSM123765 3 0.3190 0.7522 0.012 0.000 0.840 0.008 0.140
#> GSM123769 1 0.1074 0.7157 0.968 0.000 0.012 0.016 0.004
#> GSM123771 1 0.0955 0.7168 0.968 0.000 0.004 0.028 0.000
#> GSM123774 1 0.0566 0.7157 0.984 0.000 0.000 0.012 0.004
#> GSM123778 3 0.1087 0.7713 0.008 0.000 0.968 0.016 0.008
#> GSM123780 3 0.3086 0.7119 0.000 0.000 0.816 0.004 0.180
#> GSM123784 3 0.3001 0.7510 0.004 0.000 0.844 0.008 0.144
#> GSM123787 3 0.2491 0.7598 0.004 0.004 0.904 0.064 0.024
#> GSM123791 3 0.3658 0.7496 0.016 0.000 0.832 0.116 0.036
#> GSM123795 3 0.5591 0.6034 0.016 0.000 0.668 0.104 0.212
#> GSM123799 3 0.3734 0.7588 0.020 0.000 0.824 0.028 0.128
#> GSM123730 5 0.5326 0.6054 0.000 0.028 0.064 0.212 0.696
#> GSM123734 4 0.4691 0.2057 0.004 0.000 0.020 0.636 0.340
#> GSM123738 5 0.5909 0.5245 0.004 0.000 0.352 0.100 0.544
#> GSM123742 4 0.2707 0.5873 0.080 0.000 0.024 0.888 0.008
#> GSM123745 4 0.5345 0.3284 0.404 0.000 0.000 0.540 0.056
#> GSM123748 4 0.4101 0.3801 0.372 0.000 0.000 0.628 0.000
#> GSM123751 4 0.5341 0.3773 0.376 0.000 0.000 0.564 0.060
#> GSM123754 1 0.3133 0.6692 0.864 0.000 0.004 0.052 0.080
#> GSM123757 1 0.2054 0.6998 0.916 0.000 0.004 0.072 0.008
#> GSM123760 4 0.2599 0.5752 0.044 0.000 0.024 0.904 0.028
#> GSM123762 4 0.5050 -0.0663 0.476 0.000 0.024 0.496 0.004
#> GSM123764 4 0.2899 0.5321 0.008 0.000 0.076 0.880 0.036
#> GSM123767 1 0.6889 -0.1478 0.396 0.000 0.004 0.272 0.328
#> GSM123770 1 0.1124 0.7130 0.960 0.000 0.000 0.036 0.004
#> GSM123773 1 0.3705 0.6312 0.816 0.000 0.000 0.064 0.120
#> GSM123777 5 0.5386 0.6884 0.000 0.008 0.276 0.072 0.644
#> GSM123779 5 0.6024 0.5590 0.016 0.016 0.080 0.252 0.636
#> GSM123782 4 0.3727 0.5219 0.004 0.000 0.068 0.824 0.104
#> GSM123786 3 0.3012 0.7347 0.000 0.004 0.872 0.052 0.072
#> GSM123789 4 0.5811 0.1719 0.004 0.000 0.120 0.604 0.272
#> GSM123793 4 0.5448 0.0450 0.000 0.000 0.076 0.584 0.340
#> GSM123797 5 0.5818 0.7064 0.004 0.000 0.196 0.172 0.628
#> GSM123729 2 0.0898 0.9412 0.008 0.972 0.000 0.000 0.020
#> GSM123733 2 0.1671 0.9238 0.000 0.924 0.000 0.000 0.076
#> GSM123737 2 0.1124 0.9377 0.004 0.960 0.000 0.000 0.036
#> GSM123741 2 0.1121 0.9376 0.000 0.956 0.000 0.000 0.044
#> GSM123747 2 0.1538 0.9405 0.000 0.948 0.008 0.008 0.036
#> GSM123753 2 0.2179 0.9236 0.000 0.912 0.008 0.008 0.072
#> GSM123759 2 0.1731 0.9298 0.000 0.932 0.004 0.004 0.060
#> GSM123766 2 0.1597 0.9394 0.000 0.940 0.000 0.012 0.048
#> GSM123772 2 0.1251 0.9391 0.000 0.956 0.000 0.008 0.036
#> GSM123775 2 0.0771 0.9422 0.004 0.976 0.000 0.000 0.020
#> GSM123781 2 0.2722 0.9014 0.000 0.872 0.000 0.020 0.108
#> GSM123785 2 0.2411 0.9015 0.000 0.884 0.000 0.008 0.108
#> GSM123788 2 0.1410 0.9307 0.000 0.940 0.000 0.000 0.060
#> GSM123792 2 0.0703 0.9390 0.000 0.976 0.000 0.000 0.024
#> GSM123796 2 0.1341 0.9321 0.000 0.944 0.000 0.000 0.056
#> GSM123731 2 0.1059 0.9420 0.000 0.968 0.004 0.008 0.020
#> GSM123735 2 0.1410 0.9306 0.000 0.940 0.000 0.000 0.060
#> GSM123739 2 0.1484 0.9354 0.008 0.944 0.000 0.000 0.048
#> GSM123743 2 0.0510 0.9414 0.000 0.984 0.000 0.000 0.016
#> GSM123749 2 0.1502 0.9319 0.000 0.940 0.000 0.004 0.056
#> GSM123755 2 0.2228 0.9238 0.000 0.912 0.008 0.012 0.068
#> GSM123768 2 0.3632 0.8603 0.000 0.816 0.016 0.016 0.152
#> GSM123776 1 0.2908 0.6170 0.868 0.108 0.000 0.008 0.016
#> GSM123783 2 0.4311 0.8318 0.000 0.788 0.044 0.024 0.144
#> GSM123790 2 0.3022 0.8725 0.000 0.848 0.012 0.004 0.136
#> GSM123794 2 0.1699 0.9396 0.004 0.944 0.008 0.008 0.036
#> GSM123798 2 0.2574 0.9175 0.004 0.896 0.008 0.012 0.080
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM123732 3 0.2089 0.6163 0.000 0.004 0.908 0.072 0.012 0.004
#> GSM123736 5 0.5723 0.1286 0.024 0.000 0.376 0.072 0.520 0.008
#> GSM123740 5 0.5343 -0.0822 0.012 0.000 0.456 0.060 0.468 0.004
#> GSM123744 3 0.5638 0.4153 0.052 0.000 0.616 0.000 0.244 0.088
#> GSM123746 1 0.5708 0.5659 0.668 0.000 0.144 0.012 0.064 0.112
#> GSM123750 3 0.6307 0.3410 0.108 0.000 0.568 0.000 0.220 0.104
#> GSM123752 3 0.6412 0.2950 0.296 0.008 0.552 0.036 0.080 0.028
#> GSM123756 1 0.1003 0.8332 0.964 0.000 0.004 0.000 0.028 0.004
#> GSM123758 3 0.3458 0.5670 0.016 0.004 0.844 0.052 0.076 0.008
#> GSM123761 5 0.6708 0.1367 0.176 0.000 0.076 0.000 0.488 0.260
#> GSM123763 5 0.5727 0.1937 0.084 0.000 0.056 0.000 0.600 0.260
#> GSM123765 3 0.5135 0.4505 0.004 0.000 0.656 0.164 0.172 0.004
#> GSM123769 1 0.1429 0.8286 0.940 0.000 0.004 0.000 0.052 0.004
#> GSM123771 1 0.1296 0.8297 0.948 0.000 0.004 0.000 0.044 0.004
#> GSM123774 1 0.0405 0.8326 0.988 0.000 0.000 0.000 0.008 0.004
#> GSM123778 3 0.1690 0.6229 0.000 0.004 0.940 0.020 0.020 0.016
#> GSM123780 3 0.4039 0.5128 0.000 0.000 0.724 0.232 0.040 0.004
#> GSM123784 3 0.4275 0.5573 0.004 0.000 0.756 0.156 0.072 0.012
#> GSM123787 3 0.2978 0.6007 0.000 0.000 0.856 0.008 0.084 0.052
#> GSM123791 3 0.5693 0.0761 0.004 0.000 0.476 0.020 0.420 0.080
#> GSM123795 5 0.5654 0.2534 0.016 0.000 0.296 0.084 0.588 0.016
#> GSM123799 3 0.5337 0.1422 0.016 0.000 0.540 0.072 0.372 0.000
#> GSM123730 4 0.3387 0.6340 0.000 0.004 0.024 0.836 0.032 0.104
#> GSM123734 6 0.6039 0.1052 0.004 0.000 0.000 0.228 0.316 0.452
#> GSM123738 4 0.6556 0.3002 0.000 0.000 0.156 0.428 0.364 0.052
#> GSM123742 6 0.2360 0.6143 0.024 0.000 0.008 0.020 0.040 0.908
#> GSM123745 6 0.5410 0.5068 0.224 0.000 0.000 0.148 0.012 0.616
#> GSM123748 6 0.3720 0.5887 0.196 0.000 0.000 0.016 0.020 0.768
#> GSM123751 6 0.5995 0.4473 0.268 0.000 0.000 0.140 0.036 0.556
#> GSM123754 1 0.2587 0.8021 0.888 0.000 0.004 0.068 0.012 0.028
#> GSM123757 1 0.2638 0.8066 0.888 0.000 0.012 0.012 0.020 0.068
#> GSM123760 6 0.2734 0.5948 0.024 0.000 0.008 0.000 0.104 0.864
#> GSM123762 6 0.6404 0.1736 0.236 0.000 0.020 0.000 0.320 0.424
#> GSM123764 6 0.3059 0.5948 0.000 0.000 0.072 0.028 0.040 0.860
#> GSM123767 1 0.5913 0.2222 0.480 0.000 0.000 0.356 0.012 0.152
#> GSM123770 1 0.0551 0.8336 0.984 0.000 0.000 0.004 0.004 0.008
#> GSM123773 1 0.3314 0.7489 0.816 0.000 0.000 0.144 0.008 0.032
#> GSM123777 4 0.4366 0.6255 0.000 0.000 0.168 0.748 0.048 0.036
#> GSM123779 4 0.4318 0.5456 0.012 0.004 0.028 0.756 0.020 0.180
#> GSM123782 6 0.4960 0.5531 0.004 0.004 0.100 0.072 0.080 0.740
#> GSM123786 3 0.2252 0.6055 0.000 0.000 0.908 0.028 0.020 0.044
#> GSM123789 6 0.6729 0.2571 0.000 0.000 0.116 0.252 0.128 0.504
#> GSM123793 5 0.5830 -0.0833 0.000 0.000 0.008 0.156 0.492 0.344
#> GSM123797 4 0.6090 0.5929 0.000 0.000 0.064 0.572 0.248 0.116
#> GSM123729 2 0.1313 0.9405 0.004 0.952 0.000 0.016 0.028 0.000
#> GSM123733 2 0.2493 0.9076 0.004 0.884 0.000 0.076 0.036 0.000
#> GSM123737 2 0.1080 0.9385 0.004 0.960 0.000 0.004 0.032 0.000
#> GSM123741 2 0.0665 0.9390 0.000 0.980 0.000 0.008 0.008 0.004
#> GSM123747 2 0.0717 0.9413 0.000 0.976 0.000 0.016 0.008 0.000
#> GSM123753 2 0.1485 0.9283 0.000 0.944 0.000 0.024 0.028 0.004
#> GSM123759 2 0.1138 0.9348 0.000 0.960 0.000 0.024 0.012 0.004
#> GSM123766 2 0.1232 0.9387 0.000 0.956 0.000 0.016 0.024 0.004
#> GSM123772 2 0.0767 0.9396 0.000 0.976 0.000 0.008 0.012 0.004
#> GSM123775 2 0.1346 0.9397 0.016 0.952 0.000 0.008 0.024 0.000
#> GSM123781 2 0.3052 0.8897 0.000 0.868 0.008 0.048 0.056 0.020
#> GSM123785 2 0.2487 0.9010 0.000 0.876 0.000 0.092 0.032 0.000
#> GSM123788 2 0.2119 0.9182 0.000 0.904 0.000 0.060 0.036 0.000
#> GSM123792 2 0.0891 0.9397 0.000 0.968 0.000 0.008 0.024 0.000
#> GSM123796 2 0.1498 0.9334 0.000 0.940 0.000 0.032 0.028 0.000
#> GSM123731 2 0.0508 0.9409 0.000 0.984 0.000 0.004 0.012 0.000
#> GSM123735 2 0.2078 0.9236 0.004 0.912 0.000 0.044 0.040 0.000
#> GSM123739 2 0.1296 0.9377 0.004 0.952 0.000 0.012 0.032 0.000
#> GSM123743 2 0.0260 0.9400 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM123749 2 0.0914 0.9353 0.000 0.968 0.000 0.016 0.016 0.000
#> GSM123755 2 0.1710 0.9249 0.000 0.936 0.004 0.028 0.028 0.004
#> GSM123768 2 0.4022 0.8314 0.000 0.808 0.044 0.072 0.068 0.008
#> GSM123776 1 0.3434 0.7261 0.840 0.084 0.004 0.008 0.056 0.008
#> GSM123783 2 0.4743 0.7603 0.000 0.748 0.112 0.072 0.064 0.004
#> GSM123790 2 0.3382 0.8538 0.000 0.820 0.008 0.124 0.048 0.000
#> GSM123794 2 0.1492 0.9357 0.000 0.940 0.000 0.024 0.036 0.000
#> GSM123798 2 0.1977 0.9184 0.000 0.920 0.008 0.040 0.032 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) infection(p) agent(p) k
#> SD:NMF 70 6.31e-16 6.31e-16 7.57e-06 2
#> SD:NMF 68 3.48e-13 3.48e-13 1.34e-04 3
#> SD:NMF 68 1.48e-19 1.48e-19 4.65e-04 4
#> SD:NMF 60 1.21e-16 1.21e-16 5.34e-03 5
#> SD:NMF 53 2.41e-13 2.41e-13 2.03e-02 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "hclust"]
# you can also extract it by
# res = res_list["CV:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.499 0.750 0.856 0.2633 0.892 0.892
#> 3 3 0.532 0.798 0.892 0.8167 0.602 0.553
#> 4 4 0.562 0.737 0.865 0.1245 0.999 0.998
#> 5 5 0.520 0.607 0.836 0.0732 0.913 0.825
#> 6 6 0.573 0.578 0.802 0.0855 0.915 0.797
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
#> GSM123732 1 0.3274 0.818 0.940 0.060
#> GSM123736 1 0.9710 0.504 0.600 0.400
#> GSM123740 1 0.9710 0.504 0.600 0.400
#> GSM123744 1 0.8267 0.714 0.740 0.260
#> GSM123746 1 0.8813 0.684 0.700 0.300
#> GSM123750 1 0.8813 0.685 0.700 0.300
#> GSM123752 1 0.8555 0.700 0.720 0.280
#> GSM123756 1 0.9710 0.576 0.600 0.400
#> GSM123758 1 0.8555 0.700 0.720 0.280
#> GSM123761 1 0.9552 0.608 0.624 0.376
#> GSM123763 1 0.8661 0.694 0.712 0.288
#> GSM123765 1 0.2778 0.820 0.952 0.048
#> GSM123769 1 0.9710 0.576 0.600 0.400
#> GSM123771 1 0.9710 0.576 0.600 0.400
#> GSM123774 1 0.9710 0.576 0.600 0.400
#> GSM123778 1 0.2778 0.820 0.952 0.048
#> GSM123780 1 0.2236 0.823 0.964 0.036
#> GSM123784 1 0.2778 0.820 0.952 0.048
#> GSM123787 1 0.3274 0.817 0.940 0.060
#> GSM123791 1 0.4161 0.808 0.916 0.084
#> GSM123795 1 0.9710 0.504 0.600 0.400
#> GSM123799 1 0.9710 0.504 0.600 0.400
#> GSM123730 1 0.0672 0.824 0.992 0.008
#> GSM123734 2 0.0000 0.937 0.000 1.000
#> GSM123738 2 0.3879 0.930 0.076 0.924
#> GSM123742 1 0.9427 0.627 0.640 0.360
#> GSM123745 1 0.9710 0.576 0.600 0.400
#> GSM123748 1 0.9552 0.608 0.624 0.376
#> GSM123751 1 0.9710 0.576 0.600 0.400
#> GSM123754 1 0.9661 0.587 0.608 0.392
#> GSM123757 1 0.8763 0.688 0.704 0.296
#> GSM123760 1 0.9460 0.622 0.636 0.364
#> GSM123762 1 0.9732 0.570 0.596 0.404
#> GSM123764 1 0.2948 0.820 0.948 0.052
#> GSM123767 1 0.9661 0.587 0.608 0.392
#> GSM123770 1 0.9661 0.587 0.608 0.392
#> GSM123773 1 0.9661 0.587 0.608 0.392
#> GSM123777 1 0.0672 0.824 0.992 0.008
#> GSM123779 1 0.0672 0.824 0.992 0.008
#> GSM123782 1 0.2778 0.821 0.952 0.048
#> GSM123786 1 0.2778 0.820 0.952 0.048
#> GSM123789 1 0.1414 0.825 0.980 0.020
#> GSM123793 2 0.0376 0.938 0.004 0.996
#> GSM123797 2 0.3733 0.933 0.072 0.928
#> GSM123729 1 0.0000 0.825 1.000 0.000
#> GSM123733 1 0.0000 0.825 1.000 0.000
#> GSM123737 1 0.0000 0.825 1.000 0.000
#> GSM123741 1 0.0000 0.825 1.000 0.000
#> GSM123747 1 0.0000 0.825 1.000 0.000
#> GSM123753 1 0.0000 0.825 1.000 0.000
#> GSM123759 1 0.0000 0.825 1.000 0.000
#> GSM123766 1 0.0000 0.825 1.000 0.000
#> GSM123772 1 0.0000 0.825 1.000 0.000
#> GSM123775 1 0.0000 0.825 1.000 0.000
#> GSM123781 1 0.0000 0.825 1.000 0.000
#> GSM123785 1 0.0000 0.825 1.000 0.000
#> GSM123788 1 0.0000 0.825 1.000 0.000
#> GSM123792 1 0.0000 0.825 1.000 0.000
#> GSM123796 1 0.0000 0.825 1.000 0.000
#> GSM123731 1 0.0000 0.825 1.000 0.000
#> GSM123735 1 0.0000 0.825 1.000 0.000
#> GSM123739 1 0.0000 0.825 1.000 0.000
#> GSM123743 1 0.0000 0.825 1.000 0.000
#> GSM123749 1 0.0000 0.825 1.000 0.000
#> GSM123755 1 0.0000 0.825 1.000 0.000
#> GSM123768 1 0.0000 0.825 1.000 0.000
#> GSM123776 1 0.1633 0.824 0.976 0.024
#> GSM123783 1 0.0000 0.825 1.000 0.000
#> GSM123790 1 0.0000 0.825 1.000 0.000
#> GSM123794 1 0.0000 0.825 1.000 0.000
#> GSM123798 1 0.0000 0.825 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM123732 2 0.5760 0.378 0.328 0.672 0.000
#> GSM123736 2 0.8705 0.289 0.116 0.524 0.360
#> GSM123740 2 0.8705 0.289 0.116 0.524 0.360
#> GSM123744 1 0.6252 0.450 0.556 0.444 0.000
#> GSM123746 1 0.6111 0.561 0.604 0.396 0.000
#> GSM123750 1 0.6140 0.546 0.596 0.404 0.000
#> GSM123752 1 0.6180 0.520 0.584 0.416 0.000
#> GSM123756 1 0.2711 0.800 0.912 0.088 0.000
#> GSM123758 1 0.6192 0.512 0.580 0.420 0.000
#> GSM123761 1 0.3116 0.806 0.892 0.108 0.000
#> GSM123763 1 0.4605 0.705 0.796 0.204 0.000
#> GSM123765 2 0.3192 0.824 0.112 0.888 0.000
#> GSM123769 1 0.2625 0.797 0.916 0.084 0.000
#> GSM123771 1 0.2625 0.797 0.916 0.084 0.000
#> GSM123774 1 0.2711 0.800 0.912 0.088 0.000
#> GSM123778 2 0.3192 0.824 0.112 0.888 0.000
#> GSM123780 2 0.2772 0.855 0.080 0.916 0.004
#> GSM123784 2 0.3192 0.824 0.112 0.888 0.000
#> GSM123787 2 0.3551 0.800 0.132 0.868 0.000
#> GSM123791 2 0.4121 0.749 0.168 0.832 0.000
#> GSM123795 2 0.8705 0.289 0.116 0.524 0.360
#> GSM123799 2 0.8745 0.293 0.120 0.524 0.356
#> GSM123730 2 0.0661 0.907 0.004 0.988 0.008
#> GSM123734 3 0.0237 0.928 0.004 0.000 0.996
#> GSM123738 3 0.3234 0.922 0.020 0.072 0.908
#> GSM123742 1 0.4110 0.791 0.844 0.152 0.004
#> GSM123745 1 0.2878 0.801 0.904 0.096 0.000
#> GSM123748 1 0.3340 0.806 0.880 0.120 0.000
#> GSM123751 1 0.2711 0.798 0.912 0.088 0.000
#> GSM123754 1 0.3038 0.807 0.896 0.104 0.000
#> GSM123757 1 0.6126 0.553 0.600 0.400 0.000
#> GSM123760 1 0.4351 0.778 0.828 0.168 0.004
#> GSM123762 1 0.0424 0.653 0.992 0.000 0.008
#> GSM123764 2 0.1964 0.879 0.056 0.944 0.000
#> GSM123767 1 0.3038 0.807 0.896 0.104 0.000
#> GSM123770 1 0.3038 0.807 0.896 0.104 0.000
#> GSM123773 1 0.3038 0.807 0.896 0.104 0.000
#> GSM123777 2 0.0661 0.907 0.004 0.988 0.008
#> GSM123779 2 0.0829 0.904 0.012 0.984 0.004
#> GSM123782 2 0.2066 0.877 0.060 0.940 0.000
#> GSM123786 2 0.2878 0.840 0.096 0.904 0.000
#> GSM123789 2 0.1163 0.899 0.028 0.972 0.000
#> GSM123793 3 0.0000 0.928 0.000 0.000 1.000
#> GSM123797 3 0.3141 0.927 0.020 0.068 0.912
#> GSM123729 2 0.0000 0.913 0.000 1.000 0.000
#> GSM123733 2 0.0000 0.913 0.000 1.000 0.000
#> GSM123737 2 0.0000 0.913 0.000 1.000 0.000
#> GSM123741 2 0.0000 0.913 0.000 1.000 0.000
#> GSM123747 2 0.0000 0.913 0.000 1.000 0.000
#> GSM123753 2 0.0000 0.913 0.000 1.000 0.000
#> GSM123759 2 0.0000 0.913 0.000 1.000 0.000
#> GSM123766 2 0.0000 0.913 0.000 1.000 0.000
#> GSM123772 2 0.0000 0.913 0.000 1.000 0.000
#> GSM123775 2 0.0000 0.913 0.000 1.000 0.000
#> GSM123781 2 0.0000 0.913 0.000 1.000 0.000
#> GSM123785 2 0.0000 0.913 0.000 1.000 0.000
#> GSM123788 2 0.0000 0.913 0.000 1.000 0.000
#> GSM123792 2 0.0000 0.913 0.000 1.000 0.000
#> GSM123796 2 0.0000 0.913 0.000 1.000 0.000
#> GSM123731 2 0.0000 0.913 0.000 1.000 0.000
#> GSM123735 2 0.0000 0.913 0.000 1.000 0.000
#> GSM123739 2 0.0000 0.913 0.000 1.000 0.000
#> GSM123743 2 0.0000 0.913 0.000 1.000 0.000
#> GSM123749 2 0.0000 0.913 0.000 1.000 0.000
#> GSM123755 2 0.0000 0.913 0.000 1.000 0.000
#> GSM123768 2 0.0000 0.913 0.000 1.000 0.000
#> GSM123776 2 0.1163 0.898 0.028 0.972 0.000
#> GSM123783 2 0.0000 0.913 0.000 1.000 0.000
#> GSM123790 2 0.0000 0.913 0.000 1.000 0.000
#> GSM123794 2 0.0000 0.913 0.000 1.000 0.000
#> GSM123798 2 0.0000 0.913 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM123732 2 0.7045 0.191 0.352 0.528 0.116 0.004
#> GSM123736 2 0.8466 0.154 0.120 0.436 0.072 0.372
#> GSM123740 2 0.8466 0.154 0.120 0.436 0.072 0.372
#> GSM123744 1 0.6979 0.504 0.556 0.320 0.120 0.004
#> GSM123746 1 0.6618 0.573 0.608 0.284 0.104 0.004
#> GSM123750 1 0.6661 0.564 0.600 0.292 0.104 0.004
#> GSM123752 1 0.6751 0.555 0.588 0.300 0.108 0.004
#> GSM123756 1 0.1042 0.765 0.972 0.020 0.008 0.000
#> GSM123758 1 0.6770 0.551 0.584 0.304 0.108 0.004
#> GSM123761 1 0.2861 0.748 0.888 0.016 0.096 0.000
#> GSM123763 1 0.5971 0.624 0.704 0.124 0.168 0.004
#> GSM123765 2 0.5193 0.726 0.116 0.768 0.112 0.004
#> GSM123769 1 0.0927 0.761 0.976 0.016 0.008 0.000
#> GSM123771 1 0.1059 0.762 0.972 0.016 0.012 0.000
#> GSM123774 1 0.1042 0.765 0.972 0.020 0.008 0.000
#> GSM123778 2 0.5193 0.726 0.116 0.768 0.112 0.004
#> GSM123780 2 0.4496 0.777 0.084 0.820 0.088 0.008
#> GSM123784 2 0.5193 0.726 0.116 0.768 0.112 0.004
#> GSM123787 2 0.5613 0.691 0.128 0.736 0.132 0.004
#> GSM123791 2 0.6248 0.610 0.172 0.680 0.144 0.004
#> GSM123795 2 0.8466 0.154 0.120 0.436 0.072 0.372
#> GSM123799 2 0.8513 0.158 0.120 0.436 0.076 0.368
#> GSM123730 2 0.2040 0.852 0.004 0.936 0.012 0.048
#> GSM123734 3 0.4585 0.000 0.000 0.000 0.668 0.332
#> GSM123738 4 0.1296 0.876 0.004 0.028 0.004 0.964
#> GSM123742 1 0.3944 0.750 0.848 0.068 0.080 0.004
#> GSM123745 1 0.2111 0.752 0.932 0.044 0.024 0.000
#> GSM123748 1 0.2578 0.767 0.912 0.036 0.052 0.000
#> GSM123751 1 0.1624 0.760 0.952 0.028 0.020 0.000
#> GSM123754 1 0.1302 0.770 0.956 0.044 0.000 0.000
#> GSM123757 1 0.6503 0.570 0.612 0.292 0.092 0.004
#> GSM123760 1 0.4783 0.730 0.804 0.072 0.112 0.012
#> GSM123762 1 0.3925 0.573 0.808 0.000 0.176 0.016
#> GSM123764 2 0.3462 0.815 0.020 0.860 0.116 0.004
#> GSM123767 1 0.1302 0.770 0.956 0.044 0.000 0.000
#> GSM123770 1 0.1302 0.770 0.956 0.044 0.000 0.000
#> GSM123773 1 0.1302 0.770 0.956 0.044 0.000 0.000
#> GSM123777 2 0.2040 0.852 0.004 0.936 0.012 0.048
#> GSM123779 2 0.1139 0.873 0.012 0.972 0.008 0.008
#> GSM123782 2 0.3619 0.816 0.036 0.860 0.100 0.004
#> GSM123786 2 0.4844 0.750 0.092 0.792 0.112 0.004
#> GSM123789 2 0.2500 0.847 0.040 0.916 0.044 0.000
#> GSM123793 4 0.2216 0.725 0.000 0.000 0.092 0.908
#> GSM123797 4 0.1109 0.877 0.004 0.028 0.000 0.968
#> GSM123729 2 0.0000 0.884 0.000 1.000 0.000 0.000
#> GSM123733 2 0.0000 0.884 0.000 1.000 0.000 0.000
#> GSM123737 2 0.0000 0.884 0.000 1.000 0.000 0.000
#> GSM123741 2 0.0000 0.884 0.000 1.000 0.000 0.000
#> GSM123747 2 0.0000 0.884 0.000 1.000 0.000 0.000
#> GSM123753 2 0.0000 0.884 0.000 1.000 0.000 0.000
#> GSM123759 2 0.0000 0.884 0.000 1.000 0.000 0.000
#> GSM123766 2 0.0000 0.884 0.000 1.000 0.000 0.000
#> GSM123772 2 0.0000 0.884 0.000 1.000 0.000 0.000
#> GSM123775 2 0.0000 0.884 0.000 1.000 0.000 0.000
#> GSM123781 2 0.0000 0.884 0.000 1.000 0.000 0.000
#> GSM123785 2 0.0000 0.884 0.000 1.000 0.000 0.000
#> GSM123788 2 0.0000 0.884 0.000 1.000 0.000 0.000
#> GSM123792 2 0.0000 0.884 0.000 1.000 0.000 0.000
#> GSM123796 2 0.0000 0.884 0.000 1.000 0.000 0.000
#> GSM123731 2 0.0000 0.884 0.000 1.000 0.000 0.000
#> GSM123735 2 0.0000 0.884 0.000 1.000 0.000 0.000
#> GSM123739 2 0.0000 0.884 0.000 1.000 0.000 0.000
#> GSM123743 2 0.0000 0.884 0.000 1.000 0.000 0.000
#> GSM123749 2 0.0000 0.884 0.000 1.000 0.000 0.000
#> GSM123755 2 0.0000 0.884 0.000 1.000 0.000 0.000
#> GSM123768 2 0.0000 0.884 0.000 1.000 0.000 0.000
#> GSM123776 2 0.1109 0.869 0.028 0.968 0.000 0.004
#> GSM123783 2 0.0336 0.881 0.000 0.992 0.008 0.000
#> GSM123790 2 0.0000 0.884 0.000 1.000 0.000 0.000
#> GSM123794 2 0.0000 0.884 0.000 1.000 0.000 0.000
#> GSM123798 2 0.0000 0.884 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM123732 2 0.6820 -0.139 0.348 0.408 0.000 0.004 0.240
#> GSM123736 3 0.7857 0.496 0.116 0.364 0.376 0.000 0.144
#> GSM123740 3 0.7857 0.496 0.116 0.364 0.376 0.000 0.144
#> GSM123744 1 0.6353 0.280 0.544 0.252 0.000 0.004 0.200
#> GSM123746 1 0.5957 0.351 0.604 0.232 0.000 0.004 0.160
#> GSM123750 1 0.5918 0.335 0.592 0.240 0.000 0.000 0.168
#> GSM123752 1 0.6113 0.336 0.584 0.232 0.000 0.004 0.180
#> GSM123756 1 0.0510 0.614 0.984 0.000 0.000 0.000 0.016
#> GSM123758 1 0.6135 0.332 0.580 0.236 0.000 0.004 0.180
#> GSM123761 1 0.3039 0.520 0.836 0.000 0.000 0.012 0.152
#> GSM123763 5 0.5890 0.287 0.400 0.076 0.004 0.004 0.516
#> GSM123765 2 0.5530 0.453 0.108 0.644 0.000 0.004 0.244
#> GSM123769 1 0.0609 0.612 0.980 0.000 0.000 0.000 0.020
#> GSM123771 1 0.0771 0.612 0.976 0.000 0.000 0.004 0.020
#> GSM123774 1 0.0510 0.614 0.984 0.000 0.000 0.000 0.016
#> GSM123778 2 0.5530 0.453 0.108 0.644 0.000 0.004 0.244
#> GSM123780 2 0.4921 0.582 0.084 0.724 0.008 0.000 0.184
#> GSM123784 2 0.5530 0.453 0.108 0.644 0.000 0.004 0.244
#> GSM123787 2 0.5810 0.375 0.124 0.608 0.000 0.004 0.264
#> GSM123791 2 0.6097 0.241 0.168 0.556 0.000 0.000 0.276
#> GSM123795 3 0.7857 0.496 0.116 0.364 0.376 0.000 0.144
#> GSM123799 3 0.7881 0.493 0.116 0.364 0.372 0.000 0.148
#> GSM123730 2 0.2208 0.802 0.000 0.908 0.072 0.000 0.020
#> GSM123734 4 0.0794 0.000 0.000 0.000 0.028 0.972 0.000
#> GSM123738 3 0.0404 -0.118 0.000 0.012 0.988 0.000 0.000
#> GSM123742 1 0.3415 0.550 0.840 0.028 0.004 0.004 0.124
#> GSM123745 1 0.1741 0.569 0.936 0.024 0.000 0.000 0.040
#> GSM123748 1 0.2110 0.600 0.912 0.016 0.000 0.000 0.072
#> GSM123751 1 0.1267 0.601 0.960 0.012 0.000 0.004 0.024
#> GSM123754 1 0.0703 0.621 0.976 0.024 0.000 0.000 0.000
#> GSM123757 1 0.5933 0.350 0.608 0.228 0.000 0.004 0.160
#> GSM123760 1 0.4279 0.465 0.772 0.028 0.008 0.008 0.184
#> GSM123762 5 0.4774 0.212 0.308 0.000 0.012 0.020 0.660
#> GSM123764 2 0.3737 0.659 0.008 0.764 0.000 0.004 0.224
#> GSM123767 1 0.0703 0.621 0.976 0.024 0.000 0.000 0.000
#> GSM123770 1 0.0703 0.621 0.976 0.024 0.000 0.000 0.000
#> GSM123773 1 0.0703 0.621 0.976 0.024 0.000 0.000 0.000
#> GSM123777 2 0.2208 0.802 0.000 0.908 0.072 0.000 0.020
#> GSM123779 2 0.1200 0.850 0.012 0.964 0.008 0.000 0.016
#> GSM123782 2 0.4052 0.660 0.028 0.764 0.000 0.004 0.204
#> GSM123786 2 0.5269 0.497 0.088 0.668 0.000 0.004 0.240
#> GSM123789 2 0.3130 0.760 0.048 0.856 0.000 0.000 0.096
#> GSM123793 3 0.2905 -0.225 0.000 0.000 0.868 0.096 0.036
#> GSM123797 3 0.0566 -0.119 0.000 0.012 0.984 0.004 0.000
#> GSM123729 2 0.0000 0.869 0.000 1.000 0.000 0.000 0.000
#> GSM123733 2 0.0000 0.869 0.000 1.000 0.000 0.000 0.000
#> GSM123737 2 0.0000 0.869 0.000 1.000 0.000 0.000 0.000
#> GSM123741 2 0.0000 0.869 0.000 1.000 0.000 0.000 0.000
#> GSM123747 2 0.0000 0.869 0.000 1.000 0.000 0.000 0.000
#> GSM123753 2 0.0000 0.869 0.000 1.000 0.000 0.000 0.000
#> GSM123759 2 0.0000 0.869 0.000 1.000 0.000 0.000 0.000
#> GSM123766 2 0.0000 0.869 0.000 1.000 0.000 0.000 0.000
#> GSM123772 2 0.0000 0.869 0.000 1.000 0.000 0.000 0.000
#> GSM123775 2 0.0000 0.869 0.000 1.000 0.000 0.000 0.000
#> GSM123781 2 0.0000 0.869 0.000 1.000 0.000 0.000 0.000
#> GSM123785 2 0.0000 0.869 0.000 1.000 0.000 0.000 0.000
#> GSM123788 2 0.0000 0.869 0.000 1.000 0.000 0.000 0.000
#> GSM123792 2 0.0000 0.869 0.000 1.000 0.000 0.000 0.000
#> GSM123796 2 0.0000 0.869 0.000 1.000 0.000 0.000 0.000
#> GSM123731 2 0.0000 0.869 0.000 1.000 0.000 0.000 0.000
#> GSM123735 2 0.0000 0.869 0.000 1.000 0.000 0.000 0.000
#> GSM123739 2 0.0000 0.869 0.000 1.000 0.000 0.000 0.000
#> GSM123743 2 0.0000 0.869 0.000 1.000 0.000 0.000 0.000
#> GSM123749 2 0.0000 0.869 0.000 1.000 0.000 0.000 0.000
#> GSM123755 2 0.0000 0.869 0.000 1.000 0.000 0.000 0.000
#> GSM123768 2 0.0000 0.869 0.000 1.000 0.000 0.000 0.000
#> GSM123776 2 0.1041 0.843 0.032 0.964 0.000 0.000 0.004
#> GSM123783 2 0.0609 0.857 0.000 0.980 0.000 0.000 0.020
#> GSM123790 2 0.0000 0.869 0.000 1.000 0.000 0.000 0.000
#> GSM123794 2 0.0000 0.869 0.000 1.000 0.000 0.000 0.000
#> GSM123798 2 0.0000 0.869 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM123732 3 0.6077 0.4032 0.300 0.248 0.448 0.000 0.000 0.004
#> GSM123736 4 0.7037 0.2176 0.072 0.232 0.320 0.376 0.000 0.000
#> GSM123740 4 0.7037 0.2176 0.072 0.232 0.320 0.376 0.000 0.000
#> GSM123744 1 0.6224 0.2601 0.488 0.156 0.324 0.000 0.000 0.032
#> GSM123746 1 0.6022 0.3883 0.548 0.152 0.268 0.000 0.000 0.032
#> GSM123750 1 0.6157 0.3521 0.528 0.156 0.280 0.000 0.000 0.036
#> GSM123752 1 0.5978 0.3541 0.532 0.152 0.292 0.000 0.000 0.024
#> GSM123756 1 0.1007 0.6609 0.956 0.000 0.044 0.000 0.000 0.000
#> GSM123758 1 0.6005 0.3433 0.528 0.156 0.292 0.000 0.000 0.024
#> GSM123761 1 0.4162 0.5327 0.744 0.000 0.120 0.000 0.000 0.136
#> GSM123763 6 0.6525 0.2024 0.320 0.024 0.216 0.004 0.000 0.436
#> GSM123765 3 0.5117 0.8124 0.068 0.448 0.480 0.000 0.000 0.004
#> GSM123769 1 0.0937 0.6600 0.960 0.000 0.040 0.000 0.000 0.000
#> GSM123771 1 0.1082 0.6601 0.956 0.000 0.040 0.000 0.000 0.004
#> GSM123774 1 0.1007 0.6609 0.956 0.000 0.044 0.000 0.000 0.000
#> GSM123778 3 0.4988 0.8128 0.068 0.448 0.484 0.000 0.000 0.000
#> GSM123780 2 0.4923 -0.6192 0.048 0.544 0.400 0.008 0.000 0.000
#> GSM123784 3 0.4988 0.8128 0.068 0.448 0.484 0.000 0.000 0.000
#> GSM123787 3 0.4893 0.7903 0.064 0.400 0.536 0.000 0.000 0.000
#> GSM123791 3 0.5726 0.7110 0.100 0.352 0.524 0.000 0.000 0.024
#> GSM123795 4 0.7037 0.2176 0.072 0.232 0.320 0.376 0.000 0.000
#> GSM123799 4 0.7040 0.2090 0.072 0.232 0.324 0.372 0.000 0.000
#> GSM123730 2 0.2230 0.7705 0.000 0.892 0.024 0.084 0.000 0.000
#> GSM123734 5 0.0000 0.0000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM123738 4 0.0000 -0.0164 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM123742 1 0.4200 0.5342 0.764 0.016 0.156 0.004 0.000 0.060
#> GSM123745 1 0.1950 0.5961 0.924 0.016 0.028 0.000 0.000 0.032
#> GSM123748 1 0.2344 0.6383 0.896 0.008 0.068 0.000 0.000 0.028
#> GSM123751 1 0.1059 0.6402 0.964 0.004 0.016 0.000 0.000 0.016
#> GSM123754 1 0.0603 0.6603 0.980 0.016 0.004 0.000 0.000 0.000
#> GSM123757 1 0.5889 0.3907 0.556 0.152 0.268 0.000 0.000 0.024
#> GSM123760 1 0.5488 0.2558 0.584 0.000 0.264 0.008 0.000 0.144
#> GSM123762 6 0.1644 -0.1356 0.076 0.000 0.004 0.000 0.000 0.920
#> GSM123764 2 0.3955 -0.1964 0.008 0.608 0.384 0.000 0.000 0.000
#> GSM123767 1 0.0603 0.6603 0.980 0.016 0.004 0.000 0.000 0.000
#> GSM123770 1 0.0603 0.6603 0.980 0.016 0.004 0.000 0.000 0.000
#> GSM123773 1 0.0603 0.6603 0.980 0.016 0.004 0.000 0.000 0.000
#> GSM123777 2 0.2230 0.7705 0.000 0.892 0.024 0.084 0.000 0.000
#> GSM123779 2 0.1251 0.8543 0.012 0.956 0.024 0.008 0.000 0.000
#> GSM123782 2 0.4230 -0.0710 0.024 0.648 0.324 0.000 0.000 0.004
#> GSM123786 2 0.4853 -0.7675 0.056 0.488 0.456 0.000 0.000 0.000
#> GSM123789 2 0.3242 0.5990 0.032 0.816 0.148 0.000 0.000 0.004
#> GSM123793 4 0.5074 -0.2343 0.000 0.000 0.252 0.652 0.068 0.028
#> GSM123797 4 0.0146 -0.0176 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM123729 2 0.0000 0.8953 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123733 2 0.0000 0.8953 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123737 2 0.0000 0.8953 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123741 2 0.0000 0.8953 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123747 2 0.0000 0.8953 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123753 2 0.0000 0.8953 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123759 2 0.0000 0.8953 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123766 2 0.0000 0.8953 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123772 2 0.0000 0.8953 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123775 2 0.0000 0.8953 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123781 2 0.0000 0.8953 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123785 2 0.0000 0.8953 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123788 2 0.0000 0.8953 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123792 2 0.0000 0.8953 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123796 2 0.0000 0.8953 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123731 2 0.0000 0.8953 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123735 2 0.0000 0.8953 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123739 2 0.0000 0.8953 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123743 2 0.0000 0.8953 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123749 2 0.0000 0.8953 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123755 2 0.0000 0.8953 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123768 2 0.0000 0.8953 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123776 2 0.1003 0.8533 0.028 0.964 0.004 0.000 0.000 0.004
#> GSM123783 2 0.0547 0.8724 0.000 0.980 0.020 0.000 0.000 0.000
#> GSM123790 2 0.0000 0.8953 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123794 2 0.0000 0.8953 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123798 2 0.0000 0.8953 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) infection(p) agent(p) k
#> CV:hclust 71 8.91e-03 8.91e-03 0.80894 2
#> CV:hclust 65 6.35e-07 6.35e-07 0.01006 3
#> CV:hclust 65 9.68e-07 9.68e-07 0.01006 4
#> CV:hclust 47 2.63e-06 2.63e-06 0.03501 5
#> CV:hclust 49 3.96e-10 3.96e-10 0.00991 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "kmeans"]
# you can also extract it by
# res = res_list["CV:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.987 0.995 0.4760 0.522 0.522
#> 3 3 0.723 0.803 0.877 0.3629 0.806 0.628
#> 4 4 0.855 0.813 0.898 0.1164 0.899 0.714
#> 5 5 0.774 0.759 0.836 0.0506 0.937 0.794
#> 6 6 0.761 0.705 0.801 0.0399 0.947 0.810
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
#> GSM123732 1 0.000 1.000 1.000 0.000
#> GSM123736 1 0.000 1.000 1.000 0.000
#> GSM123740 1 0.000 1.000 1.000 0.000
#> GSM123744 1 0.000 1.000 1.000 0.000
#> GSM123746 1 0.000 1.000 1.000 0.000
#> GSM123750 1 0.000 1.000 1.000 0.000
#> GSM123752 1 0.000 1.000 1.000 0.000
#> GSM123756 1 0.000 1.000 1.000 0.000
#> GSM123758 1 0.000 1.000 1.000 0.000
#> GSM123761 1 0.000 1.000 1.000 0.000
#> GSM123763 1 0.000 1.000 1.000 0.000
#> GSM123765 1 0.000 1.000 1.000 0.000
#> GSM123769 1 0.000 1.000 1.000 0.000
#> GSM123771 1 0.000 1.000 1.000 0.000
#> GSM123774 1 0.000 1.000 1.000 0.000
#> GSM123778 1 0.000 1.000 1.000 0.000
#> GSM123780 1 0.000 1.000 1.000 0.000
#> GSM123784 1 0.000 1.000 1.000 0.000
#> GSM123787 1 0.000 1.000 1.000 0.000
#> GSM123791 1 0.000 1.000 1.000 0.000
#> GSM123795 1 0.000 1.000 1.000 0.000
#> GSM123799 1 0.000 1.000 1.000 0.000
#> GSM123730 1 0.000 1.000 1.000 0.000
#> GSM123734 1 0.000 1.000 1.000 0.000
#> GSM123738 1 0.000 1.000 1.000 0.000
#> GSM123742 1 0.000 1.000 1.000 0.000
#> GSM123745 1 0.000 1.000 1.000 0.000
#> GSM123748 1 0.000 1.000 1.000 0.000
#> GSM123751 1 0.000 1.000 1.000 0.000
#> GSM123754 1 0.000 1.000 1.000 0.000
#> GSM123757 1 0.000 1.000 1.000 0.000
#> GSM123760 1 0.000 1.000 1.000 0.000
#> GSM123762 1 0.000 1.000 1.000 0.000
#> GSM123764 1 0.000 1.000 1.000 0.000
#> GSM123767 1 0.000 1.000 1.000 0.000
#> GSM123770 1 0.000 1.000 1.000 0.000
#> GSM123773 1 0.000 1.000 1.000 0.000
#> GSM123777 1 0.000 1.000 1.000 0.000
#> GSM123779 1 0.000 1.000 1.000 0.000
#> GSM123782 1 0.000 1.000 1.000 0.000
#> GSM123786 1 0.000 1.000 1.000 0.000
#> GSM123789 1 0.000 1.000 1.000 0.000
#> GSM123793 1 0.000 1.000 1.000 0.000
#> GSM123797 1 0.000 1.000 1.000 0.000
#> GSM123729 2 0.000 0.986 0.000 1.000
#> GSM123733 2 0.000 0.986 0.000 1.000
#> GSM123737 2 0.000 0.986 0.000 1.000
#> GSM123741 2 0.000 0.986 0.000 1.000
#> GSM123747 2 0.000 0.986 0.000 1.000
#> GSM123753 2 0.000 0.986 0.000 1.000
#> GSM123759 2 0.000 0.986 0.000 1.000
#> GSM123766 2 0.000 0.986 0.000 1.000
#> GSM123772 2 0.000 0.986 0.000 1.000
#> GSM123775 2 0.000 0.986 0.000 1.000
#> GSM123781 2 0.000 0.986 0.000 1.000
#> GSM123785 2 0.000 0.986 0.000 1.000
#> GSM123788 2 0.000 0.986 0.000 1.000
#> GSM123792 2 0.000 0.986 0.000 1.000
#> GSM123796 2 0.000 0.986 0.000 1.000
#> GSM123731 2 0.000 0.986 0.000 1.000
#> GSM123735 2 0.000 0.986 0.000 1.000
#> GSM123739 2 0.000 0.986 0.000 1.000
#> GSM123743 2 0.000 0.986 0.000 1.000
#> GSM123749 2 0.000 0.986 0.000 1.000
#> GSM123755 2 0.000 0.986 0.000 1.000
#> GSM123768 2 0.000 0.986 0.000 1.000
#> GSM123776 2 0.946 0.428 0.364 0.636
#> GSM123783 2 0.000 0.986 0.000 1.000
#> GSM123790 2 0.000 0.986 0.000 1.000
#> GSM123794 2 0.000 0.986 0.000 1.000
#> GSM123798 2 0.000 0.986 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM123732 3 0.5948 0.7626 0.360 0.000 0.640
#> GSM123736 3 0.5254 0.7585 0.264 0.000 0.736
#> GSM123740 3 0.5291 0.7597 0.268 0.000 0.732
#> GSM123744 1 0.4931 0.4917 0.768 0.000 0.232
#> GSM123746 1 0.0000 0.8604 1.000 0.000 0.000
#> GSM123750 1 0.2165 0.8173 0.936 0.000 0.064
#> GSM123752 1 0.1643 0.8319 0.956 0.000 0.044
#> GSM123756 1 0.0000 0.8604 1.000 0.000 0.000
#> GSM123758 1 0.6244 -0.3170 0.560 0.000 0.440
#> GSM123761 1 0.2165 0.8330 0.936 0.000 0.064
#> GSM123763 3 0.6168 0.2860 0.412 0.000 0.588
#> GSM123765 3 0.5948 0.7626 0.360 0.000 0.640
#> GSM123769 1 0.0000 0.8604 1.000 0.000 0.000
#> GSM123771 1 0.0000 0.8604 1.000 0.000 0.000
#> GSM123774 1 0.0000 0.8604 1.000 0.000 0.000
#> GSM123778 3 0.5948 0.7626 0.360 0.000 0.640
#> GSM123780 3 0.5948 0.7626 0.360 0.000 0.640
#> GSM123784 3 0.5948 0.7626 0.360 0.000 0.640
#> GSM123787 3 0.5948 0.7626 0.360 0.000 0.640
#> GSM123791 3 0.5948 0.7626 0.360 0.000 0.640
#> GSM123795 3 0.5216 0.7577 0.260 0.000 0.740
#> GSM123799 3 0.5291 0.7597 0.268 0.000 0.732
#> GSM123730 3 0.3412 0.7329 0.124 0.000 0.876
#> GSM123734 3 0.5859 0.1998 0.344 0.000 0.656
#> GSM123738 3 0.1860 0.6686 0.052 0.000 0.948
#> GSM123742 1 0.4002 0.7553 0.840 0.000 0.160
#> GSM123745 1 0.2878 0.7974 0.904 0.000 0.096
#> GSM123748 1 0.1031 0.8597 0.976 0.000 0.024
#> GSM123751 1 0.1163 0.8582 0.972 0.000 0.028
#> GSM123754 1 0.1289 0.8569 0.968 0.000 0.032
#> GSM123757 1 0.0000 0.8604 1.000 0.000 0.000
#> GSM123760 1 0.6307 -0.0347 0.512 0.000 0.488
#> GSM123762 1 0.5254 0.6337 0.736 0.000 0.264
#> GSM123764 3 0.5016 0.7675 0.240 0.000 0.760
#> GSM123767 1 0.1289 0.8569 0.968 0.000 0.032
#> GSM123770 1 0.0592 0.8612 0.988 0.000 0.012
#> GSM123773 1 0.1289 0.8569 0.968 0.000 0.032
#> GSM123777 3 0.3482 0.7345 0.128 0.000 0.872
#> GSM123779 3 0.5178 0.7678 0.256 0.000 0.744
#> GSM123782 3 0.5397 0.7719 0.280 0.000 0.720
#> GSM123786 3 0.5948 0.7626 0.360 0.000 0.640
#> GSM123789 3 0.5178 0.7698 0.256 0.000 0.744
#> GSM123793 3 0.1860 0.6686 0.052 0.000 0.948
#> GSM123797 3 0.1860 0.6686 0.052 0.000 0.948
#> GSM123729 2 0.0592 0.9768 0.000 0.988 0.012
#> GSM123733 2 0.0747 0.9759 0.000 0.984 0.016
#> GSM123737 2 0.0592 0.9768 0.000 0.988 0.012
#> GSM123741 2 0.0000 0.9789 0.000 1.000 0.000
#> GSM123747 2 0.0237 0.9781 0.000 0.996 0.004
#> GSM123753 2 0.0000 0.9789 0.000 1.000 0.000
#> GSM123759 2 0.0000 0.9789 0.000 1.000 0.000
#> GSM123766 2 0.0000 0.9789 0.000 1.000 0.000
#> GSM123772 2 0.0000 0.9789 0.000 1.000 0.000
#> GSM123775 2 0.0747 0.9755 0.000 0.984 0.016
#> GSM123781 2 0.0000 0.9789 0.000 1.000 0.000
#> GSM123785 2 0.0747 0.9759 0.000 0.984 0.016
#> GSM123788 2 0.0592 0.9771 0.000 0.988 0.012
#> GSM123792 2 0.0237 0.9781 0.000 0.996 0.004
#> GSM123796 2 0.0237 0.9781 0.000 0.996 0.004
#> GSM123731 2 0.0000 0.9789 0.000 1.000 0.000
#> GSM123735 2 0.0747 0.9755 0.000 0.984 0.016
#> GSM123739 2 0.0592 0.9768 0.000 0.988 0.012
#> GSM123743 2 0.0000 0.9789 0.000 1.000 0.000
#> GSM123749 2 0.0000 0.9789 0.000 1.000 0.000
#> GSM123755 2 0.0000 0.9789 0.000 1.000 0.000
#> GSM123768 2 0.0000 0.9789 0.000 1.000 0.000
#> GSM123776 2 0.7192 0.2690 0.412 0.560 0.028
#> GSM123783 2 0.0237 0.9783 0.000 0.996 0.004
#> GSM123790 2 0.0892 0.9745 0.000 0.980 0.020
#> GSM123794 2 0.0747 0.9762 0.000 0.984 0.016
#> GSM123798 2 0.0000 0.9789 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM123732 3 0.0817 0.825 0.024 0.000 0.976 0.000
#> GSM123736 3 0.4675 0.659 0.020 0.000 0.736 0.244
#> GSM123740 3 0.4675 0.659 0.020 0.000 0.736 0.244
#> GSM123744 3 0.4792 0.472 0.312 0.000 0.680 0.008
#> GSM123746 1 0.1042 0.841 0.972 0.000 0.020 0.008
#> GSM123750 1 0.5281 0.160 0.528 0.000 0.464 0.008
#> GSM123752 1 0.5112 0.377 0.608 0.000 0.384 0.008
#> GSM123756 1 0.0707 0.843 0.980 0.000 0.020 0.000
#> GSM123758 3 0.2334 0.777 0.088 0.000 0.908 0.004
#> GSM123761 1 0.5070 0.592 0.748 0.000 0.060 0.192
#> GSM123763 4 0.5815 0.767 0.152 0.000 0.140 0.708
#> GSM123765 3 0.0817 0.825 0.024 0.000 0.976 0.000
#> GSM123769 1 0.0707 0.843 0.980 0.000 0.020 0.000
#> GSM123771 1 0.0707 0.843 0.980 0.000 0.020 0.000
#> GSM123774 1 0.0707 0.843 0.980 0.000 0.020 0.000
#> GSM123778 3 0.0817 0.825 0.024 0.000 0.976 0.000
#> GSM123780 3 0.0707 0.825 0.020 0.000 0.980 0.000
#> GSM123784 3 0.0707 0.825 0.020 0.000 0.980 0.000
#> GSM123787 3 0.0707 0.825 0.020 0.000 0.980 0.000
#> GSM123791 3 0.0817 0.825 0.024 0.000 0.976 0.000
#> GSM123795 3 0.4737 0.648 0.020 0.000 0.728 0.252
#> GSM123799 3 0.4610 0.669 0.020 0.000 0.744 0.236
#> GSM123730 3 0.4567 0.592 0.008 0.000 0.716 0.276
#> GSM123734 4 0.2751 0.816 0.040 0.000 0.056 0.904
#> GSM123738 4 0.2345 0.808 0.000 0.000 0.100 0.900
#> GSM123742 1 0.5810 0.409 0.660 0.000 0.064 0.276
#> GSM123745 1 0.0779 0.832 0.980 0.000 0.016 0.004
#> GSM123748 1 0.0804 0.834 0.980 0.000 0.012 0.008
#> GSM123751 1 0.0657 0.840 0.984 0.000 0.012 0.004
#> GSM123754 1 0.0592 0.843 0.984 0.000 0.016 0.000
#> GSM123757 1 0.0707 0.843 0.980 0.000 0.020 0.000
#> GSM123760 4 0.6295 0.732 0.196 0.000 0.144 0.660
#> GSM123762 4 0.5673 0.605 0.288 0.000 0.052 0.660
#> GSM123764 3 0.3647 0.727 0.016 0.000 0.832 0.152
#> GSM123767 1 0.0707 0.841 0.980 0.000 0.020 0.000
#> GSM123770 1 0.0592 0.843 0.984 0.000 0.016 0.000
#> GSM123773 1 0.0707 0.841 0.980 0.000 0.020 0.000
#> GSM123777 3 0.4123 0.673 0.008 0.000 0.772 0.220
#> GSM123779 3 0.4365 0.694 0.028 0.000 0.784 0.188
#> GSM123782 3 0.2522 0.793 0.016 0.000 0.908 0.076
#> GSM123786 3 0.0817 0.825 0.024 0.000 0.976 0.000
#> GSM123789 3 0.3969 0.712 0.016 0.000 0.804 0.180
#> GSM123793 4 0.2216 0.811 0.000 0.000 0.092 0.908
#> GSM123797 4 0.2345 0.808 0.000 0.000 0.100 0.900
#> GSM123729 2 0.2010 0.960 0.004 0.932 0.004 0.060
#> GSM123733 2 0.1305 0.972 0.004 0.960 0.000 0.036
#> GSM123737 2 0.1930 0.961 0.004 0.936 0.004 0.056
#> GSM123741 2 0.0188 0.975 0.000 0.996 0.000 0.004
#> GSM123747 2 0.0469 0.975 0.000 0.988 0.000 0.012
#> GSM123753 2 0.0188 0.975 0.000 0.996 0.000 0.004
#> GSM123759 2 0.0188 0.975 0.000 0.996 0.000 0.004
#> GSM123766 2 0.0188 0.975 0.000 0.996 0.000 0.004
#> GSM123772 2 0.0469 0.975 0.000 0.988 0.000 0.012
#> GSM123775 2 0.2088 0.958 0.004 0.928 0.004 0.064
#> GSM123781 2 0.0336 0.975 0.000 0.992 0.000 0.008
#> GSM123785 2 0.1305 0.972 0.004 0.960 0.000 0.036
#> GSM123788 2 0.1305 0.972 0.004 0.960 0.000 0.036
#> GSM123792 2 0.1209 0.973 0.004 0.964 0.000 0.032
#> GSM123796 2 0.1305 0.972 0.004 0.960 0.000 0.036
#> GSM123731 2 0.0188 0.976 0.000 0.996 0.000 0.004
#> GSM123735 2 0.1847 0.967 0.004 0.940 0.004 0.052
#> GSM123739 2 0.1930 0.961 0.004 0.936 0.004 0.056
#> GSM123743 2 0.0336 0.976 0.000 0.992 0.000 0.008
#> GSM123749 2 0.0188 0.975 0.000 0.996 0.000 0.004
#> GSM123755 2 0.0336 0.975 0.000 0.992 0.000 0.008
#> GSM123768 2 0.0336 0.975 0.000 0.992 0.000 0.008
#> GSM123776 1 0.6891 0.022 0.484 0.436 0.016 0.064
#> GSM123783 2 0.1305 0.968 0.000 0.960 0.004 0.036
#> GSM123790 2 0.2384 0.955 0.008 0.916 0.004 0.072
#> GSM123794 2 0.1847 0.967 0.004 0.940 0.004 0.052
#> GSM123798 2 0.0336 0.975 0.000 0.992 0.000 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM123732 3 0.0290 0.713 0.008 0.000 0.992 0.000 0.000
#> GSM123736 3 0.4549 0.574 0.004 0.000 0.728 0.220 0.048
#> GSM123740 3 0.4518 0.577 0.004 0.000 0.732 0.216 0.048
#> GSM123744 3 0.4630 0.559 0.140 0.000 0.744 0.000 0.116
#> GSM123746 1 0.2464 0.879 0.888 0.000 0.016 0.000 0.096
#> GSM123750 3 0.5680 0.390 0.240 0.000 0.620 0.000 0.140
#> GSM123752 3 0.5126 0.403 0.300 0.000 0.636 0.000 0.064
#> GSM123756 1 0.0798 0.955 0.976 0.000 0.008 0.000 0.016
#> GSM123758 3 0.2291 0.688 0.036 0.000 0.908 0.000 0.056
#> GSM123761 5 0.6509 0.390 0.420 0.000 0.020 0.112 0.448
#> GSM123763 5 0.5715 0.398 0.032 0.000 0.032 0.396 0.540
#> GSM123765 3 0.0290 0.713 0.008 0.000 0.992 0.000 0.000
#> GSM123769 1 0.0798 0.955 0.976 0.000 0.008 0.000 0.016
#> GSM123771 1 0.0798 0.955 0.976 0.000 0.008 0.000 0.016
#> GSM123774 1 0.0798 0.955 0.976 0.000 0.008 0.000 0.016
#> GSM123778 3 0.0290 0.713 0.008 0.000 0.992 0.000 0.000
#> GSM123780 3 0.2722 0.674 0.008 0.000 0.868 0.004 0.120
#> GSM123784 3 0.0451 0.712 0.008 0.000 0.988 0.004 0.000
#> GSM123787 3 0.0290 0.713 0.008 0.000 0.992 0.000 0.000
#> GSM123791 3 0.0451 0.712 0.008 0.000 0.988 0.000 0.004
#> GSM123795 3 0.4481 0.565 0.000 0.000 0.720 0.232 0.048
#> GSM123799 3 0.4457 0.585 0.004 0.000 0.740 0.208 0.048
#> GSM123730 3 0.7095 0.130 0.012 0.000 0.388 0.316 0.284
#> GSM123734 4 0.2102 0.915 0.004 0.000 0.012 0.916 0.068
#> GSM123738 4 0.0912 0.933 0.000 0.000 0.016 0.972 0.012
#> GSM123742 5 0.6341 0.501 0.384 0.000 0.012 0.116 0.488
#> GSM123745 1 0.1197 0.940 0.952 0.000 0.000 0.000 0.048
#> GSM123748 1 0.2179 0.867 0.888 0.000 0.000 0.000 0.112
#> GSM123751 1 0.1205 0.944 0.956 0.000 0.004 0.000 0.040
#> GSM123754 1 0.0798 0.956 0.976 0.000 0.008 0.000 0.016
#> GSM123757 1 0.0898 0.955 0.972 0.000 0.008 0.000 0.020
#> GSM123760 5 0.6044 0.506 0.076 0.000 0.024 0.332 0.568
#> GSM123762 5 0.5940 0.519 0.100 0.000 0.004 0.364 0.532
#> GSM123764 3 0.5892 0.334 0.004 0.000 0.500 0.088 0.408
#> GSM123767 1 0.0798 0.956 0.976 0.000 0.008 0.000 0.016
#> GSM123770 1 0.0290 0.956 0.992 0.000 0.008 0.000 0.000
#> GSM123773 1 0.0798 0.956 0.976 0.000 0.008 0.000 0.016
#> GSM123777 3 0.6751 0.275 0.004 0.000 0.456 0.256 0.284
#> GSM123779 3 0.6838 0.298 0.020 0.000 0.456 0.164 0.360
#> GSM123782 3 0.5256 0.455 0.004 0.000 0.592 0.048 0.356
#> GSM123786 3 0.0290 0.713 0.008 0.000 0.992 0.000 0.000
#> GSM123789 3 0.6020 0.382 0.004 0.000 0.524 0.108 0.364
#> GSM123793 4 0.1757 0.932 0.004 0.000 0.012 0.936 0.048
#> GSM123797 4 0.0798 0.936 0.000 0.000 0.016 0.976 0.008
#> GSM123729 2 0.3023 0.891 0.004 0.852 0.004 0.008 0.132
#> GSM123733 2 0.2629 0.902 0.000 0.860 0.000 0.004 0.136
#> GSM123737 2 0.3023 0.891 0.004 0.852 0.004 0.008 0.132
#> GSM123741 2 0.0000 0.920 0.000 1.000 0.000 0.000 0.000
#> GSM123747 2 0.1430 0.914 0.000 0.944 0.000 0.004 0.052
#> GSM123753 2 0.0162 0.919 0.000 0.996 0.000 0.000 0.004
#> GSM123759 2 0.0566 0.919 0.000 0.984 0.000 0.004 0.012
#> GSM123766 2 0.0162 0.919 0.000 0.996 0.000 0.000 0.004
#> GSM123772 2 0.0771 0.920 0.000 0.976 0.000 0.004 0.020
#> GSM123775 2 0.3023 0.887 0.004 0.852 0.004 0.008 0.132
#> GSM123781 2 0.0162 0.919 0.000 0.996 0.000 0.000 0.004
#> GSM123785 2 0.2629 0.902 0.000 0.860 0.000 0.004 0.136
#> GSM123788 2 0.2583 0.903 0.000 0.864 0.000 0.004 0.132
#> GSM123792 2 0.2338 0.909 0.000 0.884 0.000 0.004 0.112
#> GSM123796 2 0.2536 0.904 0.000 0.868 0.000 0.004 0.128
#> GSM123731 2 0.0162 0.920 0.000 0.996 0.000 0.000 0.004
#> GSM123735 2 0.2741 0.904 0.000 0.860 0.004 0.004 0.132
#> GSM123739 2 0.3023 0.891 0.004 0.852 0.004 0.008 0.132
#> GSM123743 2 0.0510 0.921 0.000 0.984 0.000 0.000 0.016
#> GSM123749 2 0.0162 0.919 0.000 0.996 0.000 0.000 0.004
#> GSM123755 2 0.0162 0.919 0.000 0.996 0.000 0.000 0.004
#> GSM123768 2 0.0162 0.919 0.000 0.996 0.000 0.000 0.004
#> GSM123776 2 0.6942 0.150 0.400 0.428 0.016 0.008 0.148
#> GSM123783 2 0.0609 0.917 0.000 0.980 0.000 0.000 0.020
#> GSM123790 2 0.3160 0.879 0.000 0.808 0.000 0.004 0.188
#> GSM123794 2 0.2583 0.904 0.000 0.864 0.000 0.004 0.132
#> GSM123798 2 0.0162 0.919 0.000 0.996 0.000 0.000 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM123732 3 0.0146 0.66913 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM123736 3 0.5981 0.48616 0.008 0.000 0.568 0.112 0.280 0.032
#> GSM123740 3 0.5981 0.48616 0.008 0.000 0.568 0.112 0.280 0.032
#> GSM123744 3 0.5228 0.59447 0.084 0.000 0.728 0.044 0.036 0.108
#> GSM123746 1 0.3926 0.74259 0.816 0.000 0.040 0.040 0.016 0.088
#> GSM123750 3 0.6305 0.47656 0.164 0.000 0.600 0.044 0.024 0.168
#> GSM123752 3 0.5318 0.52883 0.216 0.000 0.676 0.044 0.036 0.028
#> GSM123756 1 0.1010 0.85619 0.960 0.000 0.000 0.000 0.004 0.036
#> GSM123758 3 0.3010 0.65644 0.028 0.000 0.876 0.044 0.036 0.016
#> GSM123761 6 0.3836 0.72358 0.176 0.000 0.000 0.040 0.012 0.772
#> GSM123763 6 0.1078 0.76461 0.012 0.000 0.000 0.016 0.008 0.964
#> GSM123765 3 0.0146 0.66913 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM123769 1 0.1010 0.85619 0.960 0.000 0.000 0.000 0.004 0.036
#> GSM123771 1 0.1010 0.85619 0.960 0.000 0.000 0.000 0.004 0.036
#> GSM123774 1 0.0935 0.85735 0.964 0.000 0.000 0.000 0.004 0.032
#> GSM123778 3 0.0146 0.66913 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM123780 3 0.2838 0.41525 0.004 0.000 0.808 0.188 0.000 0.000
#> GSM123784 3 0.0405 0.66585 0.004 0.000 0.988 0.008 0.000 0.000
#> GSM123787 3 0.0146 0.66913 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM123791 3 0.0508 0.66994 0.004 0.000 0.984 0.000 0.000 0.012
#> GSM123795 3 0.5981 0.48616 0.008 0.000 0.568 0.112 0.280 0.032
#> GSM123799 3 0.5981 0.48616 0.008 0.000 0.568 0.112 0.280 0.032
#> GSM123730 4 0.5103 0.66432 0.008 0.000 0.308 0.616 0.012 0.056
#> GSM123734 4 0.6082 -0.86377 0.000 0.000 0.004 0.392 0.384 0.220
#> GSM123738 5 0.5701 0.89630 0.000 0.000 0.004 0.356 0.492 0.148
#> GSM123742 6 0.4720 0.68385 0.228 0.000 0.000 0.076 0.012 0.684
#> GSM123745 1 0.1984 0.84007 0.912 0.000 0.000 0.032 0.000 0.056
#> GSM123748 1 0.3739 0.67405 0.768 0.000 0.000 0.056 0.000 0.176
#> GSM123751 1 0.1789 0.84516 0.924 0.000 0.000 0.032 0.000 0.044
#> GSM123754 1 0.0865 0.86039 0.964 0.000 0.000 0.036 0.000 0.000
#> GSM123757 1 0.1586 0.84987 0.940 0.000 0.004 0.040 0.004 0.012
#> GSM123760 6 0.2197 0.76884 0.044 0.000 0.000 0.056 0.000 0.900
#> GSM123762 6 0.1116 0.78009 0.028 0.000 0.000 0.008 0.004 0.960
#> GSM123764 4 0.6091 0.60729 0.004 0.000 0.404 0.416 0.008 0.168
#> GSM123767 1 0.0865 0.86039 0.964 0.000 0.000 0.036 0.000 0.000
#> GSM123770 1 0.0291 0.86214 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM123773 1 0.0865 0.86039 0.964 0.000 0.000 0.036 0.000 0.000
#> GSM123777 4 0.5147 0.66516 0.008 0.000 0.336 0.592 0.012 0.052
#> GSM123779 4 0.5814 0.67200 0.020 0.000 0.332 0.524 0.000 0.124
#> GSM123782 3 0.5608 -0.61483 0.004 0.000 0.468 0.416 0.004 0.108
#> GSM123786 3 0.0146 0.66913 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM123789 4 0.5928 0.62513 0.008 0.000 0.400 0.448 0.004 0.140
#> GSM123793 5 0.5997 0.79451 0.000 0.000 0.004 0.396 0.404 0.196
#> GSM123797 5 0.5715 0.89942 0.000 0.000 0.004 0.364 0.484 0.148
#> GSM123729 2 0.4290 0.75650 0.000 0.668 0.000 0.028 0.296 0.008
#> GSM123733 2 0.2883 0.84173 0.000 0.788 0.000 0.000 0.212 0.000
#> GSM123737 2 0.4213 0.76965 0.000 0.684 0.000 0.028 0.280 0.008
#> GSM123741 2 0.0000 0.87590 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123747 2 0.1714 0.86556 0.000 0.908 0.000 0.000 0.092 0.000
#> GSM123753 2 0.0146 0.87534 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM123759 2 0.0547 0.87522 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM123766 2 0.0146 0.87534 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM123772 2 0.0632 0.87507 0.000 0.976 0.000 0.000 0.024 0.000
#> GSM123775 2 0.4397 0.74643 0.000 0.664 0.000 0.024 0.296 0.016
#> GSM123781 2 0.0260 0.87508 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM123785 2 0.2912 0.84041 0.000 0.784 0.000 0.000 0.216 0.000
#> GSM123788 2 0.2854 0.84312 0.000 0.792 0.000 0.000 0.208 0.000
#> GSM123792 2 0.2697 0.84916 0.000 0.812 0.000 0.000 0.188 0.000
#> GSM123796 2 0.2762 0.84636 0.000 0.804 0.000 0.000 0.196 0.000
#> GSM123731 2 0.0260 0.87665 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM123735 2 0.3288 0.82111 0.000 0.724 0.000 0.000 0.276 0.000
#> GSM123739 2 0.4193 0.77080 0.000 0.688 0.000 0.028 0.276 0.008
#> GSM123743 2 0.0713 0.87811 0.000 0.972 0.000 0.000 0.028 0.000
#> GSM123749 2 0.0146 0.87534 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM123755 2 0.0260 0.87508 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM123768 2 0.0260 0.87508 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM123776 1 0.7296 0.00861 0.372 0.276 0.004 0.044 0.288 0.016
#> GSM123783 2 0.2278 0.83865 0.000 0.868 0.000 0.000 0.128 0.004
#> GSM123790 2 0.3934 0.75018 0.000 0.616 0.000 0.000 0.376 0.008
#> GSM123794 2 0.3351 0.81509 0.000 0.712 0.000 0.000 0.288 0.000
#> GSM123798 2 0.0260 0.87508 0.000 0.992 0.000 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 disease.state(p) infection(p) agent(p) k
#> CV:kmeans 70 6.31e-16 6.31e-16 1.30e-05 2
#> CV:kmeans 65 2.11e-13 2.11e-13 4.87e-05 3
#> CV:kmeans 66 5.12e-14 5.12e-14 1.47e-04 4
#> CV:kmeans 60 2.17e-16 2.17e-16 1.47e-03 5
#> CV:kmeans 62 1.40e-14 1.40e-14 2.36e-03 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "skmeans"]
# you can also extract it by
# res = res_list["CV:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4787 0.522 0.522
#> 3 3 0.848 0.871 0.941 0.4023 0.806 0.628
#> 4 4 0.753 0.729 0.850 0.0940 0.882 0.666
#> 5 5 0.712 0.548 0.762 0.0482 0.963 0.867
#> 6 6 0.649 0.535 0.699 0.0352 0.976 0.906
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
#> GSM123732 1 0.000 1.000 1.000 0.000
#> GSM123736 1 0.000 1.000 1.000 0.000
#> GSM123740 1 0.000 1.000 1.000 0.000
#> GSM123744 1 0.000 1.000 1.000 0.000
#> GSM123746 1 0.000 1.000 1.000 0.000
#> GSM123750 1 0.000 1.000 1.000 0.000
#> GSM123752 1 0.000 1.000 1.000 0.000
#> GSM123756 1 0.000 1.000 1.000 0.000
#> GSM123758 1 0.000 1.000 1.000 0.000
#> GSM123761 1 0.000 1.000 1.000 0.000
#> GSM123763 1 0.000 1.000 1.000 0.000
#> GSM123765 1 0.000 1.000 1.000 0.000
#> GSM123769 1 0.000 1.000 1.000 0.000
#> GSM123771 1 0.000 1.000 1.000 0.000
#> GSM123774 1 0.000 1.000 1.000 0.000
#> GSM123778 1 0.000 1.000 1.000 0.000
#> GSM123780 1 0.000 1.000 1.000 0.000
#> GSM123784 1 0.000 1.000 1.000 0.000
#> GSM123787 1 0.000 1.000 1.000 0.000
#> GSM123791 1 0.000 1.000 1.000 0.000
#> GSM123795 1 0.000 1.000 1.000 0.000
#> GSM123799 1 0.000 1.000 1.000 0.000
#> GSM123730 1 0.118 0.984 0.984 0.016
#> GSM123734 1 0.000 1.000 1.000 0.000
#> GSM123738 1 0.000 1.000 1.000 0.000
#> GSM123742 1 0.000 1.000 1.000 0.000
#> GSM123745 1 0.000 1.000 1.000 0.000
#> GSM123748 1 0.000 1.000 1.000 0.000
#> GSM123751 1 0.000 1.000 1.000 0.000
#> GSM123754 1 0.000 1.000 1.000 0.000
#> GSM123757 1 0.000 1.000 1.000 0.000
#> GSM123760 1 0.000 1.000 1.000 0.000
#> GSM123762 1 0.000 1.000 1.000 0.000
#> GSM123764 1 0.000 1.000 1.000 0.000
#> GSM123767 1 0.000 1.000 1.000 0.000
#> GSM123770 1 0.000 1.000 1.000 0.000
#> GSM123773 1 0.000 1.000 1.000 0.000
#> GSM123777 1 0.000 1.000 1.000 0.000
#> GSM123779 1 0.000 1.000 1.000 0.000
#> GSM123782 1 0.000 1.000 1.000 0.000
#> GSM123786 1 0.000 1.000 1.000 0.000
#> GSM123789 1 0.000 1.000 1.000 0.000
#> GSM123793 1 0.000 1.000 1.000 0.000
#> GSM123797 1 0.000 1.000 1.000 0.000
#> GSM123729 2 0.000 1.000 0.000 1.000
#> GSM123733 2 0.000 1.000 0.000 1.000
#> GSM123737 2 0.000 1.000 0.000 1.000
#> GSM123741 2 0.000 1.000 0.000 1.000
#> GSM123747 2 0.000 1.000 0.000 1.000
#> GSM123753 2 0.000 1.000 0.000 1.000
#> GSM123759 2 0.000 1.000 0.000 1.000
#> GSM123766 2 0.000 1.000 0.000 1.000
#> GSM123772 2 0.000 1.000 0.000 1.000
#> GSM123775 2 0.000 1.000 0.000 1.000
#> GSM123781 2 0.000 1.000 0.000 1.000
#> GSM123785 2 0.000 1.000 0.000 1.000
#> GSM123788 2 0.000 1.000 0.000 1.000
#> GSM123792 2 0.000 1.000 0.000 1.000
#> GSM123796 2 0.000 1.000 0.000 1.000
#> GSM123731 2 0.000 1.000 0.000 1.000
#> GSM123735 2 0.000 1.000 0.000 1.000
#> GSM123739 2 0.000 1.000 0.000 1.000
#> GSM123743 2 0.000 1.000 0.000 1.000
#> GSM123749 2 0.000 1.000 0.000 1.000
#> GSM123755 2 0.000 1.000 0.000 1.000
#> GSM123768 2 0.000 1.000 0.000 1.000
#> GSM123776 2 0.000 1.000 0.000 1.000
#> GSM123783 2 0.000 1.000 0.000 1.000
#> GSM123790 2 0.000 1.000 0.000 1.000
#> GSM123794 2 0.000 1.000 0.000 1.000
#> GSM123798 2 0.000 1.000 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM123732 3 0.0892 0.895 0.020 0.00 0.980
#> GSM123736 3 0.0892 0.900 0.020 0.00 0.980
#> GSM123740 3 0.0747 0.900 0.016 0.00 0.984
#> GSM123744 1 0.6192 0.347 0.580 0.00 0.420
#> GSM123746 1 0.0747 0.897 0.984 0.00 0.016
#> GSM123750 1 0.3816 0.815 0.852 0.00 0.148
#> GSM123752 1 0.3267 0.833 0.884 0.00 0.116
#> GSM123756 1 0.0424 0.899 0.992 0.00 0.008
#> GSM123758 1 0.6225 0.295 0.568 0.00 0.432
#> GSM123761 1 0.1964 0.878 0.944 0.00 0.056
#> GSM123763 3 0.6267 0.226 0.452 0.00 0.548
#> GSM123765 3 0.0000 0.898 0.000 0.00 1.000
#> GSM123769 1 0.0424 0.899 0.992 0.00 0.008
#> GSM123771 1 0.0424 0.899 0.992 0.00 0.008
#> GSM123774 1 0.0424 0.899 0.992 0.00 0.008
#> GSM123778 3 0.0237 0.898 0.004 0.00 0.996
#> GSM123780 3 0.0000 0.898 0.000 0.00 1.000
#> GSM123784 3 0.0000 0.898 0.000 0.00 1.000
#> GSM123787 3 0.0237 0.898 0.004 0.00 0.996
#> GSM123791 3 0.0747 0.900 0.016 0.00 0.984
#> GSM123795 3 0.1031 0.900 0.024 0.00 0.976
#> GSM123799 3 0.1031 0.900 0.024 0.00 0.976
#> GSM123730 3 0.2537 0.877 0.080 0.00 0.920
#> GSM123734 3 0.6299 0.160 0.476 0.00 0.524
#> GSM123738 3 0.2261 0.885 0.068 0.00 0.932
#> GSM123742 1 0.2537 0.858 0.920 0.00 0.080
#> GSM123745 1 0.0237 0.898 0.996 0.00 0.004
#> GSM123748 1 0.0237 0.899 0.996 0.00 0.004
#> GSM123751 1 0.0424 0.897 0.992 0.00 0.008
#> GSM123754 1 0.0000 0.899 1.000 0.00 0.000
#> GSM123757 1 0.0424 0.899 0.992 0.00 0.008
#> GSM123760 1 0.6008 0.376 0.628 0.00 0.372
#> GSM123762 1 0.3879 0.782 0.848 0.00 0.152
#> GSM123764 3 0.1753 0.893 0.048 0.00 0.952
#> GSM123767 1 0.0000 0.899 1.000 0.00 0.000
#> GSM123770 1 0.0000 0.899 1.000 0.00 0.000
#> GSM123773 1 0.0000 0.899 1.000 0.00 0.000
#> GSM123777 3 0.0747 0.899 0.016 0.00 0.984
#> GSM123779 3 0.6215 0.312 0.428 0.00 0.572
#> GSM123782 3 0.3038 0.855 0.104 0.00 0.896
#> GSM123786 3 0.0237 0.898 0.004 0.00 0.996
#> GSM123789 3 0.3192 0.847 0.112 0.00 0.888
#> GSM123793 3 0.3412 0.845 0.124 0.00 0.876
#> GSM123797 3 0.2165 0.887 0.064 0.00 0.936
#> GSM123729 2 0.0000 0.991 0.000 1.00 0.000
#> GSM123733 2 0.0000 0.991 0.000 1.00 0.000
#> GSM123737 2 0.0000 0.991 0.000 1.00 0.000
#> GSM123741 2 0.0000 0.991 0.000 1.00 0.000
#> GSM123747 2 0.0000 0.991 0.000 1.00 0.000
#> GSM123753 2 0.0000 0.991 0.000 1.00 0.000
#> GSM123759 2 0.0000 0.991 0.000 1.00 0.000
#> GSM123766 2 0.0000 0.991 0.000 1.00 0.000
#> GSM123772 2 0.0000 0.991 0.000 1.00 0.000
#> GSM123775 2 0.0000 0.991 0.000 1.00 0.000
#> GSM123781 2 0.0000 0.991 0.000 1.00 0.000
#> GSM123785 2 0.0000 0.991 0.000 1.00 0.000
#> GSM123788 2 0.0000 0.991 0.000 1.00 0.000
#> GSM123792 2 0.0000 0.991 0.000 1.00 0.000
#> GSM123796 2 0.0000 0.991 0.000 1.00 0.000
#> GSM123731 2 0.0000 0.991 0.000 1.00 0.000
#> GSM123735 2 0.0000 0.991 0.000 1.00 0.000
#> GSM123739 2 0.0000 0.991 0.000 1.00 0.000
#> GSM123743 2 0.0000 0.991 0.000 1.00 0.000
#> GSM123749 2 0.0000 0.991 0.000 1.00 0.000
#> GSM123755 2 0.0000 0.991 0.000 1.00 0.000
#> GSM123768 2 0.0000 0.991 0.000 1.00 0.000
#> GSM123776 2 0.4796 0.717 0.220 0.78 0.000
#> GSM123783 2 0.0000 0.991 0.000 1.00 0.000
#> GSM123790 2 0.0000 0.991 0.000 1.00 0.000
#> GSM123794 2 0.0000 0.991 0.000 1.00 0.000
#> GSM123798 2 0.0000 0.991 0.000 1.00 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM123732 3 0.1807 0.7116 0.008 0.000 0.940 0.052
#> GSM123736 3 0.5152 0.5900 0.020 0.000 0.664 0.316
#> GSM123740 3 0.4776 0.6450 0.016 0.000 0.712 0.272
#> GSM123744 3 0.6894 0.2717 0.320 0.000 0.552 0.128
#> GSM123746 1 0.3787 0.7007 0.840 0.000 0.124 0.036
#> GSM123750 1 0.7526 0.1078 0.468 0.000 0.332 0.200
#> GSM123752 1 0.5512 0.4877 0.660 0.000 0.300 0.040
#> GSM123756 1 0.0188 0.7718 0.996 0.000 0.000 0.004
#> GSM123758 3 0.4741 0.5163 0.228 0.000 0.744 0.028
#> GSM123761 1 0.6894 0.2473 0.552 0.000 0.128 0.320
#> GSM123763 4 0.6157 0.5729 0.232 0.000 0.108 0.660
#> GSM123765 3 0.3725 0.7105 0.008 0.000 0.812 0.180
#> GSM123769 1 0.0336 0.7720 0.992 0.000 0.000 0.008
#> GSM123771 1 0.0188 0.7717 0.996 0.000 0.000 0.004
#> GSM123774 1 0.0000 0.7716 1.000 0.000 0.000 0.000
#> GSM123778 3 0.2149 0.7107 0.000 0.000 0.912 0.088
#> GSM123780 3 0.4175 0.6746 0.012 0.000 0.776 0.212
#> GSM123784 3 0.3123 0.7157 0.000 0.000 0.844 0.156
#> GSM123787 3 0.2714 0.7121 0.004 0.000 0.884 0.112
#> GSM123791 3 0.4220 0.6092 0.004 0.000 0.748 0.248
#> GSM123795 3 0.5793 0.4281 0.036 0.000 0.580 0.384
#> GSM123799 3 0.4690 0.6566 0.016 0.000 0.724 0.260
#> GSM123730 4 0.4057 0.6031 0.028 0.000 0.160 0.812
#> GSM123734 4 0.5314 0.6221 0.176 0.000 0.084 0.740
#> GSM123738 4 0.4744 0.5151 0.024 0.000 0.240 0.736
#> GSM123742 1 0.6921 -0.0227 0.468 0.000 0.108 0.424
#> GSM123745 1 0.3355 0.7029 0.836 0.000 0.004 0.160
#> GSM123748 1 0.3672 0.6999 0.824 0.000 0.012 0.164
#> GSM123751 1 0.3196 0.7225 0.856 0.000 0.008 0.136
#> GSM123754 1 0.1716 0.7619 0.936 0.000 0.000 0.064
#> GSM123757 1 0.0895 0.7714 0.976 0.000 0.004 0.020
#> GSM123760 4 0.6013 0.5970 0.196 0.000 0.120 0.684
#> GSM123762 4 0.6330 0.0661 0.448 0.000 0.060 0.492
#> GSM123764 4 0.5668 0.5313 0.048 0.000 0.300 0.652
#> GSM123767 1 0.2345 0.7476 0.900 0.000 0.000 0.100
#> GSM123770 1 0.0592 0.7714 0.984 0.000 0.000 0.016
#> GSM123773 1 0.1557 0.7643 0.944 0.000 0.000 0.056
#> GSM123777 4 0.5339 0.3669 0.016 0.000 0.384 0.600
#> GSM123779 4 0.5863 0.5848 0.180 0.000 0.120 0.700
#> GSM123782 4 0.5915 0.3547 0.040 0.000 0.400 0.560
#> GSM123786 3 0.1637 0.7090 0.000 0.000 0.940 0.060
#> GSM123789 4 0.6013 0.5522 0.072 0.000 0.288 0.640
#> GSM123793 4 0.3606 0.6139 0.024 0.000 0.132 0.844
#> GSM123797 4 0.3978 0.5772 0.012 0.000 0.192 0.796
#> GSM123729 2 0.0524 0.9928 0.000 0.988 0.004 0.008
#> GSM123733 2 0.0188 0.9950 0.000 0.996 0.000 0.004
#> GSM123737 2 0.0336 0.9945 0.000 0.992 0.000 0.008
#> GSM123741 2 0.0188 0.9951 0.000 0.996 0.000 0.004
#> GSM123747 2 0.0188 0.9950 0.000 0.996 0.000 0.004
#> GSM123753 2 0.0000 0.9954 0.000 1.000 0.000 0.000
#> GSM123759 2 0.0469 0.9946 0.000 0.988 0.000 0.012
#> GSM123766 2 0.0188 0.9950 0.000 0.996 0.000 0.004
#> GSM123772 2 0.0188 0.9950 0.000 0.996 0.000 0.004
#> GSM123775 2 0.0376 0.9937 0.000 0.992 0.004 0.004
#> GSM123781 2 0.0188 0.9951 0.000 0.996 0.000 0.004
#> GSM123785 2 0.0336 0.9942 0.000 0.992 0.000 0.008
#> GSM123788 2 0.0336 0.9942 0.000 0.992 0.000 0.008
#> GSM123792 2 0.0000 0.9954 0.000 1.000 0.000 0.000
#> GSM123796 2 0.0336 0.9942 0.000 0.992 0.000 0.008
#> GSM123731 2 0.0188 0.9951 0.000 0.996 0.000 0.004
#> GSM123735 2 0.0524 0.9929 0.000 0.988 0.004 0.008
#> GSM123739 2 0.0336 0.9945 0.000 0.992 0.000 0.008
#> GSM123743 2 0.0000 0.9954 0.000 1.000 0.000 0.000
#> GSM123749 2 0.0188 0.9951 0.000 0.996 0.000 0.004
#> GSM123755 2 0.0188 0.9950 0.000 0.996 0.000 0.004
#> GSM123768 2 0.0188 0.9951 0.000 0.996 0.000 0.004
#> GSM123776 1 0.6639 0.1516 0.500 0.436 0.016 0.048
#> GSM123783 2 0.0188 0.9951 0.000 0.996 0.000 0.004
#> GSM123790 2 0.0707 0.9862 0.000 0.980 0.000 0.020
#> GSM123794 2 0.0188 0.9950 0.000 0.996 0.000 0.004
#> GSM123798 2 0.0188 0.9951 0.000 0.996 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM123732 3 0.2628 0.5131 0.000 0.000 0.884 0.028 0.088
#> GSM123736 4 0.6350 -0.2628 0.008 0.000 0.432 0.436 0.124
#> GSM123740 3 0.6225 0.2492 0.004 0.000 0.472 0.400 0.124
#> GSM123744 3 0.7813 0.1555 0.200 0.000 0.436 0.092 0.272
#> GSM123746 1 0.5340 0.6320 0.716 0.000 0.060 0.048 0.176
#> GSM123750 1 0.8226 -0.0769 0.356 0.000 0.264 0.120 0.260
#> GSM123752 1 0.6862 0.3207 0.524 0.000 0.256 0.028 0.192
#> GSM123756 1 0.0898 0.7391 0.972 0.000 0.000 0.008 0.020
#> GSM123758 3 0.6204 0.3102 0.196 0.000 0.620 0.024 0.160
#> GSM123761 1 0.8008 -0.0973 0.352 0.000 0.084 0.296 0.268
#> GSM123763 4 0.6422 0.1611 0.100 0.000 0.064 0.620 0.216
#> GSM123765 3 0.4393 0.4930 0.004 0.000 0.768 0.152 0.076
#> GSM123769 1 0.1845 0.7392 0.928 0.000 0.000 0.016 0.056
#> GSM123771 1 0.1549 0.7406 0.944 0.000 0.000 0.016 0.040
#> GSM123774 1 0.0451 0.7379 0.988 0.000 0.000 0.004 0.008
#> GSM123778 3 0.3065 0.5125 0.008 0.000 0.872 0.048 0.072
#> GSM123780 3 0.5969 0.2726 0.008 0.000 0.620 0.184 0.188
#> GSM123784 3 0.4892 0.4776 0.016 0.000 0.748 0.112 0.124
#> GSM123787 3 0.4203 0.4607 0.000 0.000 0.780 0.128 0.092
#> GSM123791 3 0.6215 0.2901 0.012 0.000 0.596 0.192 0.200
#> GSM123795 4 0.6548 -0.0369 0.032 0.000 0.332 0.528 0.108
#> GSM123799 3 0.6357 0.2698 0.012 0.000 0.496 0.372 0.120
#> GSM123730 4 0.6644 -0.0404 0.040 0.000 0.140 0.572 0.248
#> GSM123734 4 0.5111 0.2750 0.152 0.000 0.044 0.740 0.064
#> GSM123738 4 0.4652 0.2677 0.008 0.000 0.144 0.756 0.092
#> GSM123742 4 0.7483 0.0297 0.264 0.000 0.048 0.440 0.248
#> GSM123745 1 0.4634 0.6317 0.744 0.000 0.000 0.136 0.120
#> GSM123748 1 0.5847 0.5546 0.664 0.000 0.024 0.152 0.160
#> GSM123751 1 0.4149 0.6885 0.792 0.000 0.004 0.124 0.080
#> GSM123754 1 0.2654 0.7317 0.884 0.000 0.000 0.032 0.084
#> GSM123757 1 0.2712 0.7178 0.880 0.000 0.032 0.000 0.088
#> GSM123760 4 0.6711 0.0798 0.156 0.000 0.052 0.588 0.204
#> GSM123762 4 0.7534 0.0498 0.312 0.000 0.052 0.420 0.216
#> GSM123764 4 0.6513 -0.3069 0.012 0.000 0.208 0.548 0.232
#> GSM123767 1 0.2645 0.7178 0.888 0.000 0.000 0.068 0.044
#> GSM123770 1 0.0693 0.7380 0.980 0.000 0.000 0.008 0.012
#> GSM123773 1 0.2074 0.7317 0.920 0.000 0.000 0.036 0.044
#> GSM123777 4 0.7114 -0.2479 0.020 0.000 0.320 0.428 0.232
#> GSM123779 4 0.7661 -0.1240 0.164 0.000 0.096 0.464 0.276
#> GSM123782 5 0.7629 0.0000 0.044 0.000 0.284 0.332 0.340
#> GSM123786 3 0.2903 0.5091 0.000 0.000 0.872 0.048 0.080
#> GSM123789 4 0.7023 -0.2827 0.032 0.000 0.228 0.508 0.232
#> GSM123793 4 0.3191 0.2696 0.012 0.000 0.060 0.868 0.060
#> GSM123797 4 0.4156 0.2807 0.012 0.000 0.120 0.800 0.068
#> GSM123729 2 0.1671 0.9541 0.000 0.924 0.000 0.000 0.076
#> GSM123733 2 0.1270 0.9629 0.000 0.948 0.000 0.000 0.052
#> GSM123737 2 0.1671 0.9580 0.000 0.924 0.000 0.000 0.076
#> GSM123741 2 0.0880 0.9627 0.000 0.968 0.000 0.000 0.032
#> GSM123747 2 0.0963 0.9663 0.000 0.964 0.000 0.000 0.036
#> GSM123753 2 0.1121 0.9607 0.000 0.956 0.000 0.000 0.044
#> GSM123759 2 0.1341 0.9643 0.000 0.944 0.000 0.000 0.056
#> GSM123766 2 0.1270 0.9627 0.000 0.948 0.000 0.000 0.052
#> GSM123772 2 0.0963 0.9649 0.000 0.964 0.000 0.000 0.036
#> GSM123775 2 0.1908 0.9468 0.000 0.908 0.000 0.000 0.092
#> GSM123781 2 0.1043 0.9620 0.000 0.960 0.000 0.000 0.040
#> GSM123785 2 0.1410 0.9609 0.000 0.940 0.000 0.000 0.060
#> GSM123788 2 0.1197 0.9619 0.000 0.952 0.000 0.000 0.048
#> GSM123792 2 0.0963 0.9627 0.000 0.964 0.000 0.000 0.036
#> GSM123796 2 0.0794 0.9661 0.000 0.972 0.000 0.000 0.028
#> GSM123731 2 0.0963 0.9661 0.000 0.964 0.000 0.000 0.036
#> GSM123735 2 0.1410 0.9606 0.000 0.940 0.000 0.000 0.060
#> GSM123739 2 0.1671 0.9584 0.000 0.924 0.000 0.000 0.076
#> GSM123743 2 0.0963 0.9646 0.000 0.964 0.000 0.000 0.036
#> GSM123749 2 0.0794 0.9664 0.000 0.972 0.000 0.000 0.028
#> GSM123755 2 0.1121 0.9597 0.000 0.956 0.000 0.000 0.044
#> GSM123768 2 0.1197 0.9629 0.000 0.952 0.000 0.000 0.048
#> GSM123776 1 0.7099 0.0924 0.416 0.348 0.008 0.008 0.220
#> GSM123783 2 0.1908 0.9517 0.000 0.908 0.000 0.000 0.092
#> GSM123790 2 0.2942 0.8927 0.000 0.856 0.008 0.008 0.128
#> GSM123794 2 0.1478 0.9591 0.000 0.936 0.000 0.000 0.064
#> GSM123798 2 0.1043 0.9632 0.000 0.960 0.000 0.000 0.040
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM123732 3 0.4127 0.5165 0.008 0.000 0.784 0.016 0.072 0.120
#> GSM123736 4 0.6295 -0.2138 0.004 0.000 0.356 0.428 0.012 0.200
#> GSM123740 3 0.6844 0.1835 0.004 0.000 0.372 0.364 0.044 0.216
#> GSM123744 6 0.7559 0.1526 0.176 0.000 0.244 0.084 0.044 0.452
#> GSM123746 1 0.6104 0.2861 0.572 0.000 0.056 0.020 0.064 0.288
#> GSM123750 6 0.7247 0.2628 0.336 0.000 0.136 0.060 0.040 0.428
#> GSM123752 1 0.7321 -0.2370 0.380 0.000 0.164 0.016 0.088 0.352
#> GSM123756 1 0.1844 0.7197 0.924 0.000 0.000 0.004 0.024 0.048
#> GSM123758 3 0.7090 0.1341 0.116 0.000 0.452 0.028 0.076 0.328
#> GSM123761 6 0.7393 0.2080 0.308 0.000 0.032 0.216 0.052 0.392
#> GSM123763 4 0.6979 0.2211 0.088 0.000 0.056 0.512 0.064 0.280
#> GSM123765 3 0.4822 0.5294 0.004 0.000 0.740 0.076 0.060 0.120
#> GSM123769 1 0.2344 0.7169 0.896 0.000 0.000 0.008 0.028 0.068
#> GSM123771 1 0.2796 0.7052 0.868 0.000 0.000 0.008 0.044 0.080
#> GSM123774 1 0.0717 0.7221 0.976 0.000 0.000 0.000 0.016 0.008
#> GSM123778 3 0.5317 0.4900 0.008 0.000 0.700 0.072 0.076 0.144
#> GSM123780 3 0.6385 0.4243 0.000 0.000 0.568 0.096 0.184 0.152
#> GSM123784 3 0.4930 0.5219 0.000 0.000 0.728 0.088 0.084 0.100
#> GSM123787 3 0.5391 0.4751 0.004 0.000 0.688 0.064 0.104 0.140
#> GSM123791 3 0.7770 0.2310 0.016 0.000 0.356 0.176 0.160 0.292
#> GSM123795 4 0.6790 -0.0385 0.020 0.000 0.296 0.492 0.052 0.140
#> GSM123799 3 0.7020 0.2615 0.016 0.000 0.408 0.316 0.040 0.220
#> GSM123730 4 0.7505 0.2940 0.044 0.004 0.108 0.492 0.228 0.124
#> GSM123734 4 0.4625 0.3649 0.120 0.000 0.016 0.760 0.032 0.072
#> GSM123738 4 0.4905 0.3580 0.008 0.000 0.112 0.740 0.068 0.072
#> GSM123742 4 0.7923 -0.0764 0.228 0.000 0.048 0.332 0.084 0.308
#> GSM123745 1 0.5107 0.5934 0.708 0.000 0.000 0.132 0.088 0.072
#> GSM123748 1 0.6249 0.3345 0.576 0.000 0.004 0.092 0.092 0.236
#> GSM123751 1 0.5482 0.5649 0.692 0.000 0.008 0.116 0.092 0.092
#> GSM123754 1 0.3347 0.7046 0.848 0.000 0.004 0.040 0.072 0.036
#> GSM123757 1 0.3964 0.6552 0.792 0.000 0.016 0.004 0.068 0.120
#> GSM123760 4 0.7153 0.1362 0.136 0.000 0.028 0.456 0.072 0.308
#> GSM123762 4 0.7586 -0.1162 0.268 0.000 0.044 0.364 0.048 0.276
#> GSM123764 4 0.8062 0.1474 0.028 0.000 0.200 0.328 0.172 0.272
#> GSM123767 1 0.3798 0.6704 0.812 0.000 0.000 0.060 0.088 0.040
#> GSM123770 1 0.0622 0.7218 0.980 0.000 0.000 0.012 0.008 0.000
#> GSM123773 1 0.2965 0.6867 0.864 0.000 0.000 0.036 0.076 0.024
#> GSM123777 4 0.7803 0.0936 0.020 0.000 0.248 0.368 0.232 0.132
#> GSM123779 4 0.8228 0.2245 0.104 0.000 0.092 0.376 0.256 0.172
#> GSM123782 6 0.8203 -0.1382 0.040 0.000 0.280 0.228 0.152 0.300
#> GSM123786 3 0.4370 0.5042 0.000 0.000 0.748 0.040 0.044 0.168
#> GSM123789 4 0.7860 0.2597 0.040 0.000 0.164 0.428 0.160 0.208
#> GSM123793 4 0.3010 0.4126 0.008 0.000 0.036 0.872 0.028 0.056
#> GSM123797 4 0.3784 0.4120 0.016 0.000 0.072 0.828 0.044 0.040
#> GSM123729 2 0.2442 0.8710 0.000 0.852 0.000 0.000 0.144 0.004
#> GSM123733 2 0.2219 0.8779 0.000 0.864 0.000 0.000 0.136 0.000
#> GSM123737 2 0.2320 0.8819 0.000 0.864 0.000 0.000 0.132 0.004
#> GSM123741 2 0.1082 0.9049 0.000 0.956 0.000 0.000 0.040 0.004
#> GSM123747 2 0.1204 0.9055 0.000 0.944 0.000 0.000 0.056 0.000
#> GSM123753 2 0.1219 0.8971 0.000 0.948 0.000 0.000 0.048 0.004
#> GSM123759 2 0.1285 0.8990 0.000 0.944 0.000 0.000 0.052 0.004
#> GSM123766 2 0.1265 0.9023 0.000 0.948 0.000 0.000 0.044 0.008
#> GSM123772 2 0.1349 0.9071 0.000 0.940 0.000 0.000 0.056 0.004
#> GSM123775 2 0.2527 0.8356 0.000 0.832 0.000 0.000 0.168 0.000
#> GSM123781 2 0.1584 0.8897 0.000 0.928 0.000 0.000 0.064 0.008
#> GSM123785 2 0.1765 0.8983 0.000 0.904 0.000 0.000 0.096 0.000
#> GSM123788 2 0.2212 0.8914 0.000 0.880 0.000 0.000 0.112 0.008
#> GSM123792 2 0.1910 0.8905 0.000 0.892 0.000 0.000 0.108 0.000
#> GSM123796 2 0.2053 0.8895 0.000 0.888 0.000 0.000 0.108 0.004
#> GSM123731 2 0.1531 0.9062 0.000 0.928 0.000 0.000 0.068 0.004
#> GSM123735 2 0.2219 0.8766 0.000 0.864 0.000 0.000 0.136 0.000
#> GSM123739 2 0.2300 0.8741 0.000 0.856 0.000 0.000 0.144 0.000
#> GSM123743 2 0.1387 0.9049 0.000 0.932 0.000 0.000 0.068 0.000
#> GSM123749 2 0.1075 0.8992 0.000 0.952 0.000 0.000 0.048 0.000
#> GSM123755 2 0.1700 0.8953 0.000 0.916 0.000 0.000 0.080 0.004
#> GSM123768 2 0.1584 0.8900 0.000 0.928 0.000 0.000 0.064 0.008
#> GSM123776 5 0.7306 0.0000 0.344 0.236 0.008 0.016 0.356 0.040
#> GSM123783 2 0.2377 0.8640 0.000 0.868 0.004 0.000 0.124 0.004
#> GSM123790 2 0.4002 0.7109 0.000 0.736 0.016 0.004 0.228 0.016
#> GSM123794 2 0.2520 0.8608 0.000 0.844 0.000 0.000 0.152 0.004
#> GSM123798 2 0.1462 0.8971 0.000 0.936 0.000 0.000 0.056 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) infection(p) agent(p) k
#> CV:skmeans 71 3.82e-16 3.82e-16 6.04e-06 2
#> CV:skmeans 65 1.81e-13 1.81e-13 3.18e-05 3
#> CV:skmeans 61 8.44e-17 8.44e-17 4.26e-04 4
#> CV:skmeans 42 6.21e-09 6.21e-09 1.02e-02 5
#> CV:skmeans 41 2.70e-09 2.70e-09 1.31e-02 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "pam"]
# you can also extract it by
# res = res_list["CV:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.862 0.953 0.974 0.48594 0.522 0.522
#> 3 3 0.915 0.940 0.965 0.35676 0.825 0.665
#> 4 4 0.880 0.864 0.938 0.03884 0.989 0.968
#> 5 5 0.846 0.843 0.915 0.01308 0.994 0.983
#> 6 6 0.829 0.846 0.927 0.00937 0.995 0.984
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
#> GSM123732 1 0.6887 0.816 0.816 0.184
#> GSM123736 1 0.0000 0.957 1.000 0.000
#> GSM123740 1 0.0000 0.957 1.000 0.000
#> GSM123744 1 0.0000 0.957 1.000 0.000
#> GSM123746 1 0.0000 0.957 1.000 0.000
#> GSM123750 1 0.0000 0.957 1.000 0.000
#> GSM123752 1 0.0000 0.957 1.000 0.000
#> GSM123756 1 0.0000 0.957 1.000 0.000
#> GSM123758 1 0.0000 0.957 1.000 0.000
#> GSM123761 1 0.0000 0.957 1.000 0.000
#> GSM123763 1 0.0000 0.957 1.000 0.000
#> GSM123765 1 0.5946 0.860 0.856 0.144
#> GSM123769 1 0.0000 0.957 1.000 0.000
#> GSM123771 1 0.0000 0.957 1.000 0.000
#> GSM123774 1 0.0000 0.957 1.000 0.000
#> GSM123778 1 0.5294 0.881 0.880 0.120
#> GSM123780 1 0.6247 0.848 0.844 0.156
#> GSM123784 1 0.0376 0.955 0.996 0.004
#> GSM123787 1 0.4562 0.900 0.904 0.096
#> GSM123791 1 0.0000 0.957 1.000 0.000
#> GSM123795 1 0.0376 0.955 0.996 0.004
#> GSM123799 1 0.1633 0.946 0.976 0.024
#> GSM123730 1 0.8207 0.718 0.744 0.256
#> GSM123734 1 0.0000 0.957 1.000 0.000
#> GSM123738 1 0.0000 0.957 1.000 0.000
#> GSM123742 1 0.0000 0.957 1.000 0.000
#> GSM123745 1 0.7219 0.761 0.800 0.200
#> GSM123748 1 0.0000 0.957 1.000 0.000
#> GSM123751 1 0.0000 0.957 1.000 0.000
#> GSM123754 1 0.0000 0.957 1.000 0.000
#> GSM123757 1 0.0000 0.957 1.000 0.000
#> GSM123760 1 0.0000 0.957 1.000 0.000
#> GSM123762 1 0.0000 0.957 1.000 0.000
#> GSM123764 1 0.3274 0.926 0.940 0.060
#> GSM123767 1 0.2423 0.934 0.960 0.040
#> GSM123770 1 0.0000 0.957 1.000 0.000
#> GSM123773 1 0.0000 0.957 1.000 0.000
#> GSM123777 1 0.8207 0.718 0.744 0.256
#> GSM123779 1 0.1843 0.945 0.972 0.028
#> GSM123782 1 0.5842 0.864 0.860 0.140
#> GSM123786 1 0.5737 0.868 0.864 0.136
#> GSM123789 1 0.0000 0.957 1.000 0.000
#> GSM123793 1 0.0000 0.957 1.000 0.000
#> GSM123797 1 0.0000 0.957 1.000 0.000
#> GSM123729 2 0.0000 0.999 0.000 1.000
#> GSM123733 2 0.0000 0.999 0.000 1.000
#> GSM123737 2 0.0000 0.999 0.000 1.000
#> GSM123741 2 0.0000 0.999 0.000 1.000
#> GSM123747 2 0.0000 0.999 0.000 1.000
#> GSM123753 2 0.0000 0.999 0.000 1.000
#> GSM123759 2 0.0000 0.999 0.000 1.000
#> GSM123766 2 0.0000 0.999 0.000 1.000
#> GSM123772 2 0.0000 0.999 0.000 1.000
#> GSM123775 2 0.0000 0.999 0.000 1.000
#> GSM123781 2 0.0000 0.999 0.000 1.000
#> GSM123785 2 0.0000 0.999 0.000 1.000
#> GSM123788 2 0.0000 0.999 0.000 1.000
#> GSM123792 2 0.0000 0.999 0.000 1.000
#> GSM123796 2 0.0000 0.999 0.000 1.000
#> GSM123731 2 0.0000 0.999 0.000 1.000
#> GSM123735 2 0.0000 0.999 0.000 1.000
#> GSM123739 2 0.0000 0.999 0.000 1.000
#> GSM123743 2 0.0000 0.999 0.000 1.000
#> GSM123749 2 0.0000 0.999 0.000 1.000
#> GSM123755 2 0.0000 0.999 0.000 1.000
#> GSM123768 2 0.0000 0.999 0.000 1.000
#> GSM123776 2 0.1184 0.983 0.016 0.984
#> GSM123783 2 0.0000 0.999 0.000 1.000
#> GSM123790 2 0.0000 0.999 0.000 1.000
#> GSM123794 2 0.0000 0.999 0.000 1.000
#> GSM123798 2 0.0000 0.999 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM123732 3 0.0000 0.919 0.000 0.000 1.000
#> GSM123736 3 0.0000 0.919 0.000 0.000 1.000
#> GSM123740 3 0.2796 0.885 0.092 0.000 0.908
#> GSM123744 3 0.1860 0.903 0.052 0.000 0.948
#> GSM123746 3 0.5363 0.724 0.276 0.000 0.724
#> GSM123750 3 0.0747 0.916 0.016 0.000 0.984
#> GSM123752 3 0.5098 0.759 0.248 0.000 0.752
#> GSM123756 1 0.0000 0.988 1.000 0.000 0.000
#> GSM123758 3 0.4931 0.776 0.232 0.000 0.768
#> GSM123761 3 0.5760 0.644 0.328 0.000 0.672
#> GSM123763 3 0.5058 0.763 0.244 0.000 0.756
#> GSM123765 3 0.0000 0.919 0.000 0.000 1.000
#> GSM123769 1 0.1163 0.968 0.972 0.000 0.028
#> GSM123771 1 0.0000 0.988 1.000 0.000 0.000
#> GSM123774 1 0.0000 0.988 1.000 0.000 0.000
#> GSM123778 3 0.0000 0.919 0.000 0.000 1.000
#> GSM123780 3 0.0000 0.919 0.000 0.000 1.000
#> GSM123784 3 0.0000 0.919 0.000 0.000 1.000
#> GSM123787 3 0.0000 0.919 0.000 0.000 1.000
#> GSM123791 3 0.0000 0.919 0.000 0.000 1.000
#> GSM123795 3 0.0237 0.919 0.004 0.000 0.996
#> GSM123799 3 0.0000 0.919 0.000 0.000 1.000
#> GSM123730 3 0.0000 0.919 0.000 0.000 1.000
#> GSM123734 1 0.1643 0.953 0.956 0.000 0.044
#> GSM123738 3 0.3752 0.855 0.144 0.000 0.856
#> GSM123742 1 0.2165 0.928 0.936 0.000 0.064
#> GSM123745 1 0.0000 0.988 1.000 0.000 0.000
#> GSM123748 1 0.0000 0.988 1.000 0.000 0.000
#> GSM123751 1 0.0000 0.988 1.000 0.000 0.000
#> GSM123754 1 0.0000 0.988 1.000 0.000 0.000
#> GSM123757 1 0.0592 0.980 0.988 0.000 0.012
#> GSM123760 3 0.5760 0.622 0.328 0.000 0.672
#> GSM123762 1 0.0237 0.986 0.996 0.000 0.004
#> GSM123764 3 0.0237 0.919 0.004 0.000 0.996
#> GSM123767 1 0.0000 0.988 1.000 0.000 0.000
#> GSM123770 1 0.0000 0.988 1.000 0.000 0.000
#> GSM123773 1 0.0000 0.988 1.000 0.000 0.000
#> GSM123777 3 0.0000 0.919 0.000 0.000 1.000
#> GSM123779 3 0.3551 0.863 0.132 0.000 0.868
#> GSM123782 3 0.0237 0.919 0.004 0.000 0.996
#> GSM123786 3 0.0000 0.919 0.000 0.000 1.000
#> GSM123789 3 0.3879 0.848 0.152 0.000 0.848
#> GSM123793 3 0.0424 0.917 0.008 0.000 0.992
#> GSM123797 3 0.0592 0.916 0.012 0.000 0.988
#> GSM123729 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123733 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123737 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123741 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123747 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123753 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123759 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123766 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123772 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123775 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123781 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123785 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123788 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123792 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123796 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123731 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123735 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123739 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123743 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123749 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123755 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123768 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123776 2 0.2096 0.941 0.052 0.944 0.004
#> GSM123783 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123790 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123794 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123798 2 0.0000 0.998 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM123732 3 0.0000 0.862 0.000 0.000 1.000 0.000
#> GSM123736 3 0.1302 0.848 0.000 0.000 0.956 0.044
#> GSM123740 3 0.3354 0.818 0.084 0.000 0.872 0.044
#> GSM123744 3 0.1389 0.850 0.048 0.000 0.952 0.000
#> GSM123746 3 0.4594 0.654 0.280 0.000 0.712 0.008
#> GSM123750 3 0.0895 0.859 0.020 0.000 0.976 0.004
#> GSM123752 3 0.4040 0.700 0.248 0.000 0.752 0.000
#> GSM123756 1 0.0817 0.918 0.976 0.000 0.000 0.024
#> GSM123758 3 0.3837 0.727 0.224 0.000 0.776 0.000
#> GSM123761 3 0.6873 0.502 0.252 0.000 0.588 0.160
#> GSM123763 3 0.6079 0.532 0.072 0.000 0.628 0.300
#> GSM123765 3 0.0000 0.862 0.000 0.000 1.000 0.000
#> GSM123769 1 0.1913 0.903 0.940 0.000 0.020 0.040
#> GSM123771 1 0.0817 0.918 0.976 0.000 0.000 0.024
#> GSM123774 1 0.0921 0.918 0.972 0.000 0.000 0.028
#> GSM123778 3 0.0000 0.862 0.000 0.000 1.000 0.000
#> GSM123780 3 0.0000 0.862 0.000 0.000 1.000 0.000
#> GSM123784 3 0.0000 0.862 0.000 0.000 1.000 0.000
#> GSM123787 3 0.0000 0.862 0.000 0.000 1.000 0.000
#> GSM123791 3 0.0000 0.862 0.000 0.000 1.000 0.000
#> GSM123795 3 0.1489 0.848 0.004 0.000 0.952 0.044
#> GSM123799 3 0.0188 0.861 0.000 0.000 0.996 0.004
#> GSM123730 3 0.0657 0.860 0.004 0.000 0.984 0.012
#> GSM123734 1 0.4877 0.375 0.592 0.000 0.000 0.408
#> GSM123738 3 0.5050 0.653 0.028 0.000 0.704 0.268
#> GSM123742 1 0.1474 0.871 0.948 0.000 0.052 0.000
#> GSM123745 1 0.0592 0.921 0.984 0.000 0.000 0.016
#> GSM123748 1 0.0000 0.920 1.000 0.000 0.000 0.000
#> GSM123751 1 0.0188 0.922 0.996 0.000 0.000 0.004
#> GSM123754 1 0.0336 0.922 0.992 0.000 0.000 0.008
#> GSM123757 1 0.0657 0.913 0.984 0.000 0.012 0.004
#> GSM123760 3 0.7554 0.213 0.244 0.000 0.488 0.268
#> GSM123762 1 0.4632 0.550 0.688 0.000 0.004 0.308
#> GSM123764 3 0.0524 0.862 0.004 0.000 0.988 0.008
#> GSM123767 1 0.0592 0.921 0.984 0.000 0.000 0.016
#> GSM123770 1 0.0817 0.920 0.976 0.000 0.000 0.024
#> GSM123773 1 0.0592 0.921 0.984 0.000 0.000 0.016
#> GSM123777 3 0.0000 0.862 0.000 0.000 1.000 0.000
#> GSM123779 3 0.3529 0.784 0.152 0.000 0.836 0.012
#> GSM123782 3 0.0188 0.862 0.004 0.000 0.996 0.000
#> GSM123786 3 0.0000 0.862 0.000 0.000 1.000 0.000
#> GSM123789 3 0.4605 0.771 0.108 0.000 0.800 0.092
#> GSM123793 4 0.2124 0.000 0.008 0.000 0.068 0.924
#> GSM123797 3 0.4360 0.692 0.008 0.000 0.744 0.248
#> GSM123729 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM123733 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM123737 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM123741 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM123747 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM123753 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM123759 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM123766 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM123772 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM123775 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM123781 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM123785 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM123788 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM123792 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM123796 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM123731 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM123735 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM123739 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM123743 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM123749 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM123755 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM123768 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM123776 2 0.1545 0.942 0.040 0.952 0.008 0.000
#> GSM123783 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM123790 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM123794 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM123798 2 0.0000 0.998 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM123732 3 0.0000 0.861 0.000 0.00 1.000 0.000 0.000
#> GSM123736 3 0.2707 0.814 0.000 0.00 0.860 0.008 0.132
#> GSM123740 3 0.3857 0.801 0.048 0.00 0.812 0.008 0.132
#> GSM123744 3 0.1197 0.852 0.048 0.00 0.952 0.000 0.000
#> GSM123746 3 0.4088 0.652 0.304 0.00 0.688 0.000 0.008
#> GSM123750 3 0.0771 0.859 0.020 0.00 0.976 0.000 0.004
#> GSM123752 3 0.3661 0.691 0.276 0.00 0.724 0.000 0.000
#> GSM123756 1 0.2172 0.862 0.908 0.00 0.000 0.076 0.016
#> GSM123758 3 0.3480 0.721 0.248 0.00 0.752 0.000 0.000
#> GSM123761 3 0.6540 0.515 0.276 0.00 0.572 0.044 0.108
#> GSM123763 3 0.6487 0.577 0.064 0.00 0.620 0.116 0.200
#> GSM123765 3 0.0000 0.861 0.000 0.00 1.000 0.000 0.000
#> GSM123769 1 0.2930 0.847 0.880 0.00 0.012 0.076 0.032
#> GSM123771 1 0.2046 0.867 0.916 0.00 0.000 0.068 0.016
#> GSM123774 1 0.2270 0.861 0.904 0.00 0.000 0.076 0.020
#> GSM123778 3 0.0000 0.861 0.000 0.00 1.000 0.000 0.000
#> GSM123780 3 0.0000 0.861 0.000 0.00 1.000 0.000 0.000
#> GSM123784 3 0.0000 0.861 0.000 0.00 1.000 0.000 0.000
#> GSM123787 3 0.0000 0.861 0.000 0.00 1.000 0.000 0.000
#> GSM123791 3 0.0000 0.861 0.000 0.00 1.000 0.000 0.000
#> GSM123795 3 0.2865 0.814 0.004 0.00 0.856 0.008 0.132
#> GSM123799 3 0.0162 0.861 0.000 0.00 0.996 0.000 0.004
#> GSM123730 3 0.0566 0.859 0.004 0.00 0.984 0.000 0.012
#> GSM123734 5 0.4577 0.000 0.176 0.00 0.000 0.084 0.740
#> GSM123738 3 0.4676 0.709 0.032 0.00 0.696 0.008 0.264
#> GSM123742 1 0.1270 0.839 0.948 0.00 0.052 0.000 0.000
#> GSM123745 1 0.0510 0.897 0.984 0.00 0.000 0.000 0.016
#> GSM123748 1 0.0000 0.895 1.000 0.00 0.000 0.000 0.000
#> GSM123751 1 0.0162 0.897 0.996 0.00 0.000 0.000 0.004
#> GSM123754 1 0.0290 0.898 0.992 0.00 0.000 0.000 0.008
#> GSM123757 1 0.0566 0.887 0.984 0.00 0.012 0.000 0.004
#> GSM123760 3 0.7621 0.228 0.264 0.00 0.468 0.084 0.184
#> GSM123762 1 0.6315 -0.148 0.484 0.00 0.004 0.140 0.372
#> GSM123764 3 0.0451 0.861 0.004 0.00 0.988 0.000 0.008
#> GSM123767 1 0.0671 0.897 0.980 0.00 0.000 0.004 0.016
#> GSM123770 1 0.1018 0.896 0.968 0.00 0.000 0.016 0.016
#> GSM123773 1 0.0510 0.897 0.984 0.00 0.000 0.000 0.016
#> GSM123777 3 0.0000 0.861 0.000 0.00 1.000 0.000 0.000
#> GSM123779 3 0.3039 0.796 0.152 0.00 0.836 0.000 0.012
#> GSM123782 3 0.0162 0.861 0.004 0.00 0.996 0.000 0.000
#> GSM123786 3 0.0000 0.861 0.000 0.00 1.000 0.000 0.000
#> GSM123789 3 0.4338 0.789 0.112 0.00 0.800 0.040 0.048
#> GSM123793 4 0.2077 0.000 0.000 0.00 0.008 0.908 0.084
#> GSM123797 3 0.4209 0.735 0.008 0.00 0.732 0.016 0.244
#> GSM123729 2 0.0000 0.997 0.000 1.00 0.000 0.000 0.000
#> GSM123733 2 0.0000 0.997 0.000 1.00 0.000 0.000 0.000
#> GSM123737 2 0.0000 0.997 0.000 1.00 0.000 0.000 0.000
#> GSM123741 2 0.0000 0.997 0.000 1.00 0.000 0.000 0.000
#> GSM123747 2 0.0000 0.997 0.000 1.00 0.000 0.000 0.000
#> GSM123753 2 0.0000 0.997 0.000 1.00 0.000 0.000 0.000
#> GSM123759 2 0.0000 0.997 0.000 1.00 0.000 0.000 0.000
#> GSM123766 2 0.0000 0.997 0.000 1.00 0.000 0.000 0.000
#> GSM123772 2 0.0000 0.997 0.000 1.00 0.000 0.000 0.000
#> GSM123775 2 0.0000 0.997 0.000 1.00 0.000 0.000 0.000
#> GSM123781 2 0.0000 0.997 0.000 1.00 0.000 0.000 0.000
#> GSM123785 2 0.0000 0.997 0.000 1.00 0.000 0.000 0.000
#> GSM123788 2 0.0000 0.997 0.000 1.00 0.000 0.000 0.000
#> GSM123792 2 0.0000 0.997 0.000 1.00 0.000 0.000 0.000
#> GSM123796 2 0.0000 0.997 0.000 1.00 0.000 0.000 0.000
#> GSM123731 2 0.0000 0.997 0.000 1.00 0.000 0.000 0.000
#> GSM123735 2 0.0000 0.997 0.000 1.00 0.000 0.000 0.000
#> GSM123739 2 0.0000 0.997 0.000 1.00 0.000 0.000 0.000
#> GSM123743 2 0.0000 0.997 0.000 1.00 0.000 0.000 0.000
#> GSM123749 2 0.0000 0.997 0.000 1.00 0.000 0.000 0.000
#> GSM123755 2 0.0000 0.997 0.000 1.00 0.000 0.000 0.000
#> GSM123768 2 0.0000 0.997 0.000 1.00 0.000 0.000 0.000
#> GSM123776 2 0.2201 0.906 0.040 0.92 0.008 0.032 0.000
#> GSM123783 2 0.0000 0.997 0.000 1.00 0.000 0.000 0.000
#> GSM123790 2 0.0000 0.997 0.000 1.00 0.000 0.000 0.000
#> GSM123794 2 0.0000 0.997 0.000 1.00 0.000 0.000 0.000
#> GSM123798 2 0.0000 0.997 0.000 1.00 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM123732 3 0.0000 0.861 0.000 0.00 1.000 0.000 0.000 0.000
#> GSM123736 3 0.2680 0.815 0.000 0.00 0.856 0.124 0.016 0.004
#> GSM123740 3 0.3712 0.802 0.048 0.00 0.808 0.124 0.016 0.004
#> GSM123744 3 0.1075 0.852 0.048 0.00 0.952 0.000 0.000 0.000
#> GSM123746 3 0.3714 0.629 0.340 0.00 0.656 0.000 0.000 0.004
#> GSM123750 3 0.0692 0.859 0.020 0.00 0.976 0.000 0.000 0.004
#> GSM123752 3 0.3482 0.660 0.316 0.00 0.684 0.000 0.000 0.000
#> GSM123756 1 0.2697 0.822 0.812 0.00 0.000 0.000 0.000 0.188
#> GSM123758 3 0.3309 0.699 0.280 0.00 0.720 0.000 0.000 0.000
#> GSM123761 3 0.5424 0.551 0.288 0.00 0.580 0.008 0.000 0.124
#> GSM123763 3 0.5953 0.606 0.072 0.00 0.632 0.060 0.024 0.212
#> GSM123765 3 0.0000 0.861 0.000 0.00 1.000 0.000 0.000 0.000
#> GSM123769 1 0.3515 0.804 0.780 0.00 0.012 0.016 0.000 0.192
#> GSM123771 1 0.2416 0.843 0.844 0.00 0.000 0.000 0.000 0.156
#> GSM123774 1 0.2697 0.822 0.812 0.00 0.000 0.000 0.000 0.188
#> GSM123778 3 0.0000 0.861 0.000 0.00 1.000 0.000 0.000 0.000
#> GSM123780 3 0.0000 0.861 0.000 0.00 1.000 0.000 0.000 0.000
#> GSM123784 3 0.0000 0.861 0.000 0.00 1.000 0.000 0.000 0.000
#> GSM123787 3 0.0000 0.861 0.000 0.00 1.000 0.000 0.000 0.000
#> GSM123791 3 0.0000 0.861 0.000 0.00 1.000 0.000 0.000 0.000
#> GSM123795 3 0.2822 0.814 0.004 0.00 0.852 0.124 0.016 0.004
#> GSM123799 3 0.0260 0.860 0.000 0.00 0.992 0.008 0.000 0.000
#> GSM123730 3 0.0458 0.859 0.000 0.00 0.984 0.016 0.000 0.000
#> GSM123734 4 0.2662 0.000 0.000 0.00 0.000 0.856 0.024 0.120
#> GSM123738 3 0.4602 0.743 0.028 0.00 0.724 0.204 0.016 0.028
#> GSM123742 1 0.1010 0.880 0.960 0.00 0.036 0.000 0.000 0.004
#> GSM123745 1 0.0717 0.913 0.976 0.00 0.000 0.016 0.000 0.008
#> GSM123748 1 0.0000 0.909 1.000 0.00 0.000 0.000 0.000 0.000
#> GSM123751 1 0.0405 0.912 0.988 0.00 0.000 0.008 0.000 0.004
#> GSM123754 1 0.0291 0.911 0.992 0.00 0.000 0.004 0.000 0.004
#> GSM123757 1 0.0363 0.903 0.988 0.00 0.012 0.000 0.000 0.000
#> GSM123760 3 0.7024 0.302 0.292 0.00 0.472 0.060 0.024 0.152
#> GSM123762 6 0.2510 0.000 0.024 0.00 0.000 0.060 0.024 0.892
#> GSM123764 3 0.0405 0.861 0.004 0.00 0.988 0.008 0.000 0.000
#> GSM123767 1 0.0820 0.912 0.972 0.00 0.000 0.016 0.000 0.012
#> GSM123770 1 0.1461 0.904 0.940 0.00 0.000 0.016 0.000 0.044
#> GSM123773 1 0.0717 0.912 0.976 0.00 0.000 0.016 0.000 0.008
#> GSM123777 3 0.0000 0.861 0.000 0.00 1.000 0.000 0.000 0.000
#> GSM123779 3 0.2945 0.793 0.156 0.00 0.824 0.020 0.000 0.000
#> GSM123782 3 0.0146 0.861 0.004 0.00 0.996 0.000 0.000 0.000
#> GSM123786 3 0.0000 0.861 0.000 0.00 1.000 0.000 0.000 0.000
#> GSM123789 3 0.4146 0.785 0.120 0.00 0.792 0.028 0.016 0.044
#> GSM123793 5 0.0146 0.000 0.000 0.00 0.000 0.000 0.996 0.004
#> GSM123797 3 0.3945 0.767 0.000 0.00 0.764 0.184 0.024 0.028
#> GSM123729 2 0.0000 0.995 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM123733 2 0.0000 0.995 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM123737 2 0.0000 0.995 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM123741 2 0.0000 0.995 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM123747 2 0.0000 0.995 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM123753 2 0.0000 0.995 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM123759 2 0.0000 0.995 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM123766 2 0.0000 0.995 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM123772 2 0.0000 0.995 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM123775 2 0.0000 0.995 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM123781 2 0.0000 0.995 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM123785 2 0.0000 0.995 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM123788 2 0.0000 0.995 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM123792 2 0.0000 0.995 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM123796 2 0.0000 0.995 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM123731 2 0.0000 0.995 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM123735 2 0.0000 0.995 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM123739 2 0.0000 0.995 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM123743 2 0.0000 0.995 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM123749 2 0.0000 0.995 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM123755 2 0.0000 0.995 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM123768 2 0.0000 0.995 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM123776 2 0.2586 0.858 0.032 0.88 0.008 0.000 0.000 0.080
#> GSM123783 2 0.0000 0.995 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM123790 2 0.0000 0.995 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM123794 2 0.0000 0.995 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM123798 2 0.0000 0.995 0.000 1.00 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) infection(p) agent(p) k
#> CV:pam 71 3.82e-16 3.82e-16 6.04e-06 2
#> CV:pam 71 2.84e-16 2.84e-16 7.76e-06 3
#> CV:pam 68 7.80e-16 7.80e-16 1.57e-05 4
#> CV:pam 67 2.36e-15 2.36e-15 1.98e-05 5
#> CV:pam 67 2.36e-15 2.36e-15 1.98e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "mclust"]
# you can also extract it by
# res = res_list["CV:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 71 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 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 0.994 0.997 0.4636 0.537 0.537
#> 3 3 0.849 0.896 0.938 0.3158 0.855 0.730
#> 4 4 0.900 0.846 0.935 0.2002 0.826 0.580
#> 5 5 0.938 0.895 0.941 0.0446 0.948 0.810
#> 6 6 0.864 0.850 0.893 0.0311 0.973 0.885
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
#> GSM123732 1 0.0000 0.997 1.000 0.000
#> GSM123736 1 0.0000 0.997 1.000 0.000
#> GSM123740 1 0.0000 0.997 1.000 0.000
#> GSM123744 1 0.0000 0.997 1.000 0.000
#> GSM123746 1 0.0000 0.997 1.000 0.000
#> GSM123750 1 0.0000 0.997 1.000 0.000
#> GSM123752 1 0.0000 0.997 1.000 0.000
#> GSM123756 1 0.0000 0.997 1.000 0.000
#> GSM123758 1 0.0000 0.997 1.000 0.000
#> GSM123761 1 0.0000 0.997 1.000 0.000
#> GSM123763 1 0.0000 0.997 1.000 0.000
#> GSM123765 1 0.0000 0.997 1.000 0.000
#> GSM123769 1 0.0000 0.997 1.000 0.000
#> GSM123771 1 0.0000 0.997 1.000 0.000
#> GSM123774 1 0.0000 0.997 1.000 0.000
#> GSM123778 1 0.0000 0.997 1.000 0.000
#> GSM123780 1 0.0000 0.997 1.000 0.000
#> GSM123784 1 0.0000 0.997 1.000 0.000
#> GSM123787 1 0.0000 0.997 1.000 0.000
#> GSM123791 1 0.0000 0.997 1.000 0.000
#> GSM123795 1 0.0000 0.997 1.000 0.000
#> GSM123799 1 0.0000 0.997 1.000 0.000
#> GSM123730 1 0.0000 0.997 1.000 0.000
#> GSM123734 1 0.0000 0.997 1.000 0.000
#> GSM123738 1 0.0000 0.997 1.000 0.000
#> GSM123742 1 0.0000 0.997 1.000 0.000
#> GSM123745 1 0.0000 0.997 1.000 0.000
#> GSM123748 1 0.0000 0.997 1.000 0.000
#> GSM123751 1 0.0000 0.997 1.000 0.000
#> GSM123754 1 0.0000 0.997 1.000 0.000
#> GSM123757 1 0.0000 0.997 1.000 0.000
#> GSM123760 1 0.0000 0.997 1.000 0.000
#> GSM123762 1 0.0000 0.997 1.000 0.000
#> GSM123764 1 0.0000 0.997 1.000 0.000
#> GSM123767 1 0.0000 0.997 1.000 0.000
#> GSM123770 1 0.0000 0.997 1.000 0.000
#> GSM123773 1 0.0000 0.997 1.000 0.000
#> GSM123777 1 0.0000 0.997 1.000 0.000
#> GSM123779 1 0.0000 0.997 1.000 0.000
#> GSM123782 1 0.0000 0.997 1.000 0.000
#> GSM123786 1 0.0000 0.997 1.000 0.000
#> GSM123789 1 0.0000 0.997 1.000 0.000
#> GSM123793 1 0.0000 0.997 1.000 0.000
#> GSM123797 1 0.0000 0.997 1.000 0.000
#> GSM123729 2 0.0000 0.996 0.000 1.000
#> GSM123733 2 0.0000 0.996 0.000 1.000
#> GSM123737 2 0.0000 0.996 0.000 1.000
#> GSM123741 2 0.0000 0.996 0.000 1.000
#> GSM123747 2 0.0000 0.996 0.000 1.000
#> GSM123753 2 0.0000 0.996 0.000 1.000
#> GSM123759 2 0.0000 0.996 0.000 1.000
#> GSM123766 2 0.0000 0.996 0.000 1.000
#> GSM123772 2 0.0000 0.996 0.000 1.000
#> GSM123775 2 0.0672 0.989 0.008 0.992
#> GSM123781 2 0.0000 0.996 0.000 1.000
#> GSM123785 2 0.0000 0.996 0.000 1.000
#> GSM123788 2 0.0000 0.996 0.000 1.000
#> GSM123792 2 0.0000 0.996 0.000 1.000
#> GSM123796 2 0.0000 0.996 0.000 1.000
#> GSM123731 2 0.0000 0.996 0.000 1.000
#> GSM123735 2 0.0000 0.996 0.000 1.000
#> GSM123739 2 0.0000 0.996 0.000 1.000
#> GSM123743 2 0.0000 0.996 0.000 1.000
#> GSM123749 2 0.0000 0.996 0.000 1.000
#> GSM123755 2 0.0000 0.996 0.000 1.000
#> GSM123768 2 0.0000 0.996 0.000 1.000
#> GSM123776 1 0.0000 0.997 1.000 0.000
#> GSM123783 2 0.3879 0.918 0.076 0.924
#> GSM123790 1 0.5408 0.858 0.876 0.124
#> GSM123794 2 0.0000 0.996 0.000 1.000
#> GSM123798 2 0.0000 0.996 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM123732 3 0.6062 0.594 0.384 0.000 0.616
#> GSM123736 3 0.6280 0.398 0.460 0.000 0.540
#> GSM123740 3 0.3619 0.916 0.136 0.000 0.864
#> GSM123744 1 0.1753 0.882 0.952 0.000 0.048
#> GSM123746 1 0.2261 0.900 0.932 0.000 0.068
#> GSM123750 1 0.1529 0.888 0.960 0.000 0.040
#> GSM123752 1 0.1753 0.882 0.952 0.000 0.048
#> GSM123756 1 0.3482 0.861 0.872 0.000 0.128
#> GSM123758 1 0.1753 0.882 0.952 0.000 0.048
#> GSM123761 1 0.0237 0.910 0.996 0.000 0.004
#> GSM123763 1 0.0000 0.910 1.000 0.000 0.000
#> GSM123765 3 0.3551 0.916 0.132 0.000 0.868
#> GSM123769 1 0.3482 0.861 0.872 0.000 0.128
#> GSM123771 1 0.3482 0.861 0.872 0.000 0.128
#> GSM123774 1 0.3482 0.861 0.872 0.000 0.128
#> GSM123778 3 0.3482 0.916 0.128 0.000 0.872
#> GSM123780 1 0.6299 -0.271 0.524 0.000 0.476
#> GSM123784 3 0.3482 0.916 0.128 0.000 0.872
#> GSM123787 3 0.3482 0.916 0.128 0.000 0.872
#> GSM123791 3 0.3619 0.916 0.136 0.000 0.864
#> GSM123795 1 0.2356 0.857 0.928 0.000 0.072
#> GSM123799 3 0.3752 0.911 0.144 0.000 0.856
#> GSM123730 1 0.0000 0.910 1.000 0.000 0.000
#> GSM123734 1 0.0000 0.910 1.000 0.000 0.000
#> GSM123738 1 0.0000 0.910 1.000 0.000 0.000
#> GSM123742 1 0.0000 0.910 1.000 0.000 0.000
#> GSM123745 1 0.2796 0.886 0.908 0.000 0.092
#> GSM123748 1 0.2796 0.886 0.908 0.000 0.092
#> GSM123751 1 0.2711 0.888 0.912 0.000 0.088
#> GSM123754 1 0.2959 0.881 0.900 0.000 0.100
#> GSM123757 1 0.2537 0.891 0.920 0.000 0.080
#> GSM123760 1 0.0000 0.910 1.000 0.000 0.000
#> GSM123762 1 0.0237 0.910 0.996 0.000 0.004
#> GSM123764 1 0.1289 0.894 0.968 0.000 0.032
#> GSM123767 1 0.2356 0.895 0.928 0.000 0.072
#> GSM123770 1 0.3412 0.864 0.876 0.000 0.124
#> GSM123773 1 0.2878 0.883 0.904 0.000 0.096
#> GSM123777 1 0.0000 0.910 1.000 0.000 0.000
#> GSM123779 1 0.0000 0.910 1.000 0.000 0.000
#> GSM123782 1 0.0592 0.905 0.988 0.000 0.012
#> GSM123786 3 0.3482 0.916 0.128 0.000 0.872
#> GSM123789 1 0.0237 0.909 0.996 0.000 0.004
#> GSM123793 1 0.0000 0.910 1.000 0.000 0.000
#> GSM123797 1 0.0000 0.910 1.000 0.000 0.000
#> GSM123729 2 0.0000 0.997 0.000 1.000 0.000
#> GSM123733 2 0.0000 0.997 0.000 1.000 0.000
#> GSM123737 2 0.0000 0.997 0.000 1.000 0.000
#> GSM123741 2 0.0000 0.997 0.000 1.000 0.000
#> GSM123747 2 0.0000 0.997 0.000 1.000 0.000
#> GSM123753 2 0.0000 0.997 0.000 1.000 0.000
#> GSM123759 2 0.0000 0.997 0.000 1.000 0.000
#> GSM123766 2 0.0000 0.997 0.000 1.000 0.000
#> GSM123772 2 0.0000 0.997 0.000 1.000 0.000
#> GSM123775 2 0.0424 0.989 0.008 0.992 0.000
#> GSM123781 2 0.0000 0.997 0.000 1.000 0.000
#> GSM123785 2 0.0237 0.993 0.004 0.996 0.000
#> GSM123788 2 0.0000 0.997 0.000 1.000 0.000
#> GSM123792 2 0.0000 0.997 0.000 1.000 0.000
#> GSM123796 2 0.0000 0.997 0.000 1.000 0.000
#> GSM123731 2 0.0000 0.997 0.000 1.000 0.000
#> GSM123735 2 0.0000 0.997 0.000 1.000 0.000
#> GSM123739 2 0.0000 0.997 0.000 1.000 0.000
#> GSM123743 2 0.0000 0.997 0.000 1.000 0.000
#> GSM123749 2 0.0000 0.997 0.000 1.000 0.000
#> GSM123755 2 0.0000 0.997 0.000 1.000 0.000
#> GSM123768 2 0.0000 0.997 0.000 1.000 0.000
#> GSM123776 1 0.0747 0.909 0.984 0.000 0.016
#> GSM123783 2 0.1411 0.953 0.036 0.964 0.000
#> GSM123790 1 0.6008 0.318 0.628 0.372 0.000
#> GSM123794 2 0.0000 0.997 0.000 1.000 0.000
#> GSM123798 2 0.0000 0.997 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM123732 3 0.0188 0.87811 0.000 0.000 0.996 0.004
#> GSM123736 3 0.1211 0.85003 0.000 0.000 0.960 0.040
#> GSM123740 3 0.0188 0.87811 0.000 0.000 0.996 0.004
#> GSM123744 3 0.5143 0.08783 0.456 0.000 0.540 0.004
#> GSM123746 1 0.0817 0.88316 0.976 0.000 0.024 0.000
#> GSM123750 1 0.5167 -0.00594 0.508 0.000 0.488 0.004
#> GSM123752 1 0.5004 0.32781 0.604 0.000 0.392 0.004
#> GSM123756 1 0.0000 0.89205 1.000 0.000 0.000 0.000
#> GSM123758 3 0.5147 0.07432 0.460 0.000 0.536 0.004
#> GSM123761 1 0.3542 0.79300 0.852 0.000 0.120 0.028
#> GSM123763 4 0.4656 0.72078 0.160 0.000 0.056 0.784
#> GSM123765 3 0.0000 0.87806 0.000 0.000 1.000 0.000
#> GSM123769 1 0.0000 0.89205 1.000 0.000 0.000 0.000
#> GSM123771 1 0.0000 0.89205 1.000 0.000 0.000 0.000
#> GSM123774 1 0.0000 0.89205 1.000 0.000 0.000 0.000
#> GSM123778 3 0.0000 0.87806 0.000 0.000 1.000 0.000
#> GSM123780 3 0.2345 0.78163 0.000 0.000 0.900 0.100
#> GSM123784 3 0.0000 0.87806 0.000 0.000 1.000 0.000
#> GSM123787 3 0.0000 0.87806 0.000 0.000 1.000 0.000
#> GSM123791 3 0.0188 0.87811 0.000 0.000 0.996 0.004
#> GSM123795 4 0.5229 0.35833 0.008 0.000 0.428 0.564
#> GSM123799 3 0.0188 0.87811 0.000 0.000 0.996 0.004
#> GSM123730 4 0.0000 0.85092 0.000 0.000 0.000 1.000
#> GSM123734 4 0.0000 0.85092 0.000 0.000 0.000 1.000
#> GSM123738 4 0.0000 0.85092 0.000 0.000 0.000 1.000
#> GSM123742 1 0.5454 0.68713 0.732 0.000 0.096 0.172
#> GSM123745 1 0.0817 0.89105 0.976 0.000 0.000 0.024
#> GSM123748 1 0.0592 0.89266 0.984 0.000 0.000 0.016
#> GSM123751 1 0.0817 0.89105 0.976 0.000 0.000 0.024
#> GSM123754 1 0.0188 0.89253 0.996 0.000 0.000 0.004
#> GSM123757 1 0.0000 0.89205 1.000 0.000 0.000 0.000
#> GSM123760 4 0.2174 0.83695 0.020 0.000 0.052 0.928
#> GSM123762 1 0.5003 0.55194 0.676 0.000 0.016 0.308
#> GSM123764 4 0.3649 0.74336 0.000 0.000 0.204 0.796
#> GSM123767 1 0.0817 0.89105 0.976 0.000 0.000 0.024
#> GSM123770 1 0.0000 0.89205 1.000 0.000 0.000 0.000
#> GSM123773 1 0.0592 0.89266 0.984 0.000 0.000 0.016
#> GSM123777 4 0.0707 0.84979 0.000 0.000 0.020 0.980
#> GSM123779 4 0.1209 0.84340 0.032 0.000 0.004 0.964
#> GSM123782 4 0.6366 0.26993 0.064 0.000 0.424 0.512
#> GSM123786 3 0.0000 0.87806 0.000 0.000 1.000 0.000
#> GSM123789 4 0.3726 0.73586 0.000 0.000 0.212 0.788
#> GSM123793 4 0.0000 0.85092 0.000 0.000 0.000 1.000
#> GSM123797 4 0.0000 0.85092 0.000 0.000 0.000 1.000
#> GSM123729 2 0.0000 0.99791 0.000 1.000 0.000 0.000
#> GSM123733 2 0.0000 0.99791 0.000 1.000 0.000 0.000
#> GSM123737 2 0.0000 0.99791 0.000 1.000 0.000 0.000
#> GSM123741 2 0.0000 0.99791 0.000 1.000 0.000 0.000
#> GSM123747 2 0.0000 0.99791 0.000 1.000 0.000 0.000
#> GSM123753 2 0.0000 0.99791 0.000 1.000 0.000 0.000
#> GSM123759 2 0.0000 0.99791 0.000 1.000 0.000 0.000
#> GSM123766 2 0.0000 0.99791 0.000 1.000 0.000 0.000
#> GSM123772 2 0.0000 0.99791 0.000 1.000 0.000 0.000
#> GSM123775 2 0.0000 0.99791 0.000 1.000 0.000 0.000
#> GSM123781 2 0.0000 0.99791 0.000 1.000 0.000 0.000
#> GSM123785 2 0.0000 0.99791 0.000 1.000 0.000 0.000
#> GSM123788 2 0.0000 0.99791 0.000 1.000 0.000 0.000
#> GSM123792 2 0.0000 0.99791 0.000 1.000 0.000 0.000
#> GSM123796 2 0.0000 0.99791 0.000 1.000 0.000 0.000
#> GSM123731 2 0.0000 0.99791 0.000 1.000 0.000 0.000
#> GSM123735 2 0.0000 0.99791 0.000 1.000 0.000 0.000
#> GSM123739 2 0.0000 0.99791 0.000 1.000 0.000 0.000
#> GSM123743 2 0.0000 0.99791 0.000 1.000 0.000 0.000
#> GSM123749 2 0.0000 0.99791 0.000 1.000 0.000 0.000
#> GSM123755 2 0.0000 0.99791 0.000 1.000 0.000 0.000
#> GSM123768 2 0.0000 0.99791 0.000 1.000 0.000 0.000
#> GSM123776 1 0.0921 0.88925 0.972 0.000 0.000 0.028
#> GSM123783 2 0.0000 0.99791 0.000 1.000 0.000 0.000
#> GSM123790 2 0.1389 0.94517 0.000 0.952 0.000 0.048
#> GSM123794 2 0.0000 0.99791 0.000 1.000 0.000 0.000
#> GSM123798 2 0.0000 0.99791 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM123732 3 0.0703 0.930 0.000 0.000 0.976 0.000 0.024
#> GSM123736 3 0.2825 0.800 0.000 0.000 0.860 0.124 0.016
#> GSM123740 3 0.0000 0.945 0.000 0.000 1.000 0.000 0.000
#> GSM123744 5 0.3011 0.868 0.016 0.000 0.140 0.000 0.844
#> GSM123746 5 0.4045 0.431 0.356 0.000 0.000 0.000 0.644
#> GSM123750 5 0.3532 0.868 0.048 0.000 0.128 0.000 0.824
#> GSM123752 5 0.3060 0.876 0.024 0.000 0.128 0.000 0.848
#> GSM123756 1 0.0510 0.937 0.984 0.000 0.000 0.000 0.016
#> GSM123758 5 0.3016 0.874 0.020 0.000 0.132 0.000 0.848
#> GSM123761 1 0.5708 -0.173 0.480 0.000 0.024 0.036 0.460
#> GSM123763 4 0.1393 0.883 0.012 0.000 0.008 0.956 0.024
#> GSM123765 3 0.0162 0.943 0.000 0.000 0.996 0.000 0.004
#> GSM123769 1 0.0510 0.937 0.984 0.000 0.000 0.000 0.016
#> GSM123771 1 0.0510 0.937 0.984 0.000 0.000 0.000 0.016
#> GSM123774 1 0.0510 0.937 0.984 0.000 0.000 0.000 0.016
#> GSM123778 3 0.0000 0.945 0.000 0.000 1.000 0.000 0.000
#> GSM123780 3 0.3877 0.673 0.000 0.000 0.764 0.212 0.024
#> GSM123784 3 0.0000 0.945 0.000 0.000 1.000 0.000 0.000
#> GSM123787 3 0.0000 0.945 0.000 0.000 1.000 0.000 0.000
#> GSM123791 3 0.0000 0.945 0.000 0.000 1.000 0.000 0.000
#> GSM123795 4 0.3381 0.770 0.000 0.000 0.176 0.808 0.016
#> GSM123799 3 0.0324 0.941 0.000 0.000 0.992 0.004 0.004
#> GSM123730 4 0.0963 0.883 0.000 0.000 0.000 0.964 0.036
#> GSM123734 4 0.1270 0.878 0.000 0.000 0.000 0.948 0.052
#> GSM123738 4 0.0609 0.883 0.000 0.000 0.000 0.980 0.020
#> GSM123742 4 0.4565 0.648 0.240 0.000 0.016 0.720 0.024
#> GSM123745 1 0.1041 0.926 0.964 0.000 0.000 0.004 0.032
#> GSM123748 1 0.0510 0.936 0.984 0.000 0.000 0.000 0.016
#> GSM123751 1 0.0693 0.932 0.980 0.000 0.000 0.008 0.012
#> GSM123754 1 0.0290 0.935 0.992 0.000 0.000 0.000 0.008
#> GSM123757 1 0.0609 0.934 0.980 0.000 0.000 0.000 0.020
#> GSM123760 4 0.1117 0.884 0.000 0.000 0.016 0.964 0.020
#> GSM123762 4 0.5015 0.359 0.392 0.000 0.004 0.576 0.028
#> GSM123764 4 0.2450 0.858 0.000 0.000 0.076 0.896 0.028
#> GSM123767 1 0.1041 0.926 0.964 0.000 0.000 0.004 0.032
#> GSM123770 1 0.0404 0.937 0.988 0.000 0.000 0.000 0.012
#> GSM123773 1 0.0880 0.927 0.968 0.000 0.000 0.000 0.032
#> GSM123777 4 0.0912 0.885 0.000 0.000 0.012 0.972 0.016
#> GSM123779 4 0.1329 0.885 0.008 0.000 0.004 0.956 0.032
#> GSM123782 4 0.3278 0.792 0.000 0.000 0.156 0.824 0.020
#> GSM123786 3 0.0000 0.945 0.000 0.000 1.000 0.000 0.000
#> GSM123789 4 0.1992 0.873 0.000 0.000 0.044 0.924 0.032
#> GSM123793 4 0.1270 0.878 0.000 0.000 0.000 0.948 0.052
#> GSM123797 4 0.1270 0.878 0.000 0.000 0.000 0.948 0.052
#> GSM123729 2 0.1043 0.971 0.000 0.960 0.000 0.000 0.040
#> GSM123733 2 0.0000 0.987 0.000 1.000 0.000 0.000 0.000
#> GSM123737 2 0.0510 0.982 0.000 0.984 0.000 0.000 0.016
#> GSM123741 2 0.0000 0.987 0.000 1.000 0.000 0.000 0.000
#> GSM123747 2 0.0000 0.987 0.000 1.000 0.000 0.000 0.000
#> GSM123753 2 0.0000 0.987 0.000 1.000 0.000 0.000 0.000
#> GSM123759 2 0.0000 0.987 0.000 1.000 0.000 0.000 0.000
#> GSM123766 2 0.0000 0.987 0.000 1.000 0.000 0.000 0.000
#> GSM123772 2 0.0000 0.987 0.000 1.000 0.000 0.000 0.000
#> GSM123775 2 0.1043 0.971 0.000 0.960 0.000 0.000 0.040
#> GSM123781 2 0.0000 0.987 0.000 1.000 0.000 0.000 0.000
#> GSM123785 2 0.1121 0.969 0.000 0.956 0.000 0.000 0.044
#> GSM123788 2 0.0000 0.987 0.000 1.000 0.000 0.000 0.000
#> GSM123792 2 0.0000 0.987 0.000 1.000 0.000 0.000 0.000
#> GSM123796 2 0.0000 0.987 0.000 1.000 0.000 0.000 0.000
#> GSM123731 2 0.0000 0.987 0.000 1.000 0.000 0.000 0.000
#> GSM123735 2 0.0162 0.986 0.000 0.996 0.000 0.000 0.004
#> GSM123739 2 0.1043 0.971 0.000 0.960 0.000 0.000 0.040
#> GSM123743 2 0.0000 0.987 0.000 1.000 0.000 0.000 0.000
#> GSM123749 2 0.0000 0.987 0.000 1.000 0.000 0.000 0.000
#> GSM123755 2 0.0000 0.987 0.000 1.000 0.000 0.000 0.000
#> GSM123768 2 0.1043 0.971 0.000 0.960 0.000 0.000 0.040
#> GSM123776 1 0.1195 0.925 0.960 0.000 0.000 0.012 0.028
#> GSM123783 2 0.1043 0.971 0.000 0.960 0.000 0.000 0.040
#> GSM123790 2 0.2304 0.921 0.000 0.908 0.000 0.048 0.044
#> GSM123794 2 0.0404 0.983 0.000 0.988 0.000 0.000 0.012
#> GSM123798 2 0.0000 0.987 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM123732 3 0.1082 0.907 0.000 0.000 0.956 0.000 0.040 0.004
#> GSM123736 3 0.3023 0.705 0.000 0.000 0.768 0.000 0.000 0.232
#> GSM123740 3 0.0363 0.928 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM123744 5 0.1757 0.796 0.012 0.000 0.052 0.000 0.928 0.008
#> GSM123746 5 0.3601 0.574 0.312 0.000 0.000 0.000 0.684 0.004
#> GSM123750 5 0.1977 0.800 0.032 0.000 0.040 0.000 0.920 0.008
#> GSM123752 5 0.1555 0.799 0.012 0.000 0.040 0.000 0.940 0.008
#> GSM123756 1 0.2201 0.908 0.896 0.000 0.000 0.076 0.028 0.000
#> GSM123758 5 0.1624 0.800 0.012 0.000 0.044 0.000 0.936 0.008
#> GSM123761 5 0.5188 0.337 0.388 0.000 0.008 0.004 0.540 0.060
#> GSM123763 6 0.1010 0.719 0.004 0.000 0.000 0.036 0.000 0.960
#> GSM123765 3 0.0363 0.928 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM123769 1 0.2201 0.908 0.896 0.000 0.000 0.076 0.028 0.000
#> GSM123771 1 0.2201 0.908 0.896 0.000 0.000 0.076 0.028 0.000
#> GSM123774 1 0.2201 0.908 0.896 0.000 0.000 0.076 0.028 0.000
#> GSM123778 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM123780 3 0.3448 0.616 0.000 0.000 0.716 0.004 0.000 0.280
#> GSM123784 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM123787 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM123791 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM123795 6 0.2597 0.621 0.000 0.000 0.176 0.000 0.000 0.824
#> GSM123799 3 0.0865 0.915 0.000 0.000 0.964 0.000 0.000 0.036
#> GSM123730 4 0.3955 0.799 0.004 0.000 0.000 0.560 0.000 0.436
#> GSM123734 4 0.3371 0.891 0.000 0.000 0.000 0.708 0.000 0.292
#> GSM123738 4 0.3817 0.781 0.000 0.000 0.000 0.568 0.000 0.432
#> GSM123742 6 0.3161 0.594 0.156 0.000 0.012 0.004 0.008 0.820
#> GSM123745 1 0.1714 0.911 0.936 0.000 0.000 0.024 0.024 0.016
#> GSM123748 1 0.1369 0.921 0.952 0.000 0.000 0.016 0.016 0.016
#> GSM123751 1 0.1452 0.915 0.948 0.000 0.000 0.020 0.012 0.020
#> GSM123754 1 0.0520 0.923 0.984 0.000 0.000 0.008 0.000 0.008
#> GSM123757 1 0.2100 0.869 0.884 0.000 0.000 0.000 0.112 0.004
#> GSM123760 6 0.1155 0.720 0.000 0.000 0.004 0.036 0.004 0.956
#> GSM123762 6 0.5020 0.142 0.428 0.000 0.000 0.040 0.016 0.516
#> GSM123764 6 0.1556 0.714 0.000 0.000 0.080 0.000 0.000 0.920
#> GSM123767 1 0.1620 0.913 0.940 0.000 0.000 0.024 0.024 0.012
#> GSM123770 1 0.1408 0.919 0.944 0.000 0.000 0.036 0.020 0.000
#> GSM123773 1 0.1518 0.914 0.944 0.000 0.000 0.024 0.024 0.008
#> GSM123777 6 0.2053 0.614 0.000 0.000 0.004 0.108 0.000 0.888
#> GSM123779 6 0.1633 0.691 0.024 0.000 0.000 0.044 0.000 0.932
#> GSM123782 6 0.2520 0.641 0.000 0.000 0.152 0.004 0.000 0.844
#> GSM123786 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM123789 6 0.0547 0.726 0.000 0.000 0.020 0.000 0.000 0.980
#> GSM123793 4 0.3371 0.892 0.000 0.000 0.000 0.708 0.000 0.292
#> GSM123797 4 0.3351 0.890 0.000 0.000 0.000 0.712 0.000 0.288
#> GSM123729 2 0.2212 0.916 0.000 0.880 0.000 0.112 0.008 0.000
#> GSM123733 2 0.0777 0.949 0.000 0.972 0.000 0.024 0.004 0.000
#> GSM123737 2 0.1196 0.946 0.000 0.952 0.000 0.040 0.008 0.000
#> GSM123741 2 0.0508 0.950 0.000 0.984 0.000 0.012 0.004 0.000
#> GSM123747 2 0.0146 0.950 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM123753 2 0.0603 0.949 0.000 0.980 0.000 0.016 0.004 0.000
#> GSM123759 2 0.0405 0.950 0.000 0.988 0.000 0.008 0.004 0.000
#> GSM123766 2 0.0790 0.947 0.000 0.968 0.000 0.032 0.000 0.000
#> GSM123772 2 0.0713 0.946 0.000 0.972 0.000 0.028 0.000 0.000
#> GSM123775 2 0.2257 0.913 0.000 0.876 0.000 0.116 0.008 0.000
#> GSM123781 2 0.0603 0.949 0.000 0.980 0.000 0.016 0.004 0.000
#> GSM123785 2 0.2706 0.893 0.000 0.832 0.000 0.160 0.008 0.000
#> GSM123788 2 0.1152 0.946 0.000 0.952 0.000 0.044 0.004 0.000
#> GSM123792 2 0.0405 0.950 0.000 0.988 0.000 0.008 0.004 0.000
#> GSM123796 2 0.0865 0.947 0.000 0.964 0.000 0.036 0.000 0.000
#> GSM123731 2 0.0777 0.947 0.000 0.972 0.000 0.024 0.004 0.000
#> GSM123735 2 0.1010 0.947 0.000 0.960 0.000 0.036 0.004 0.000
#> GSM123739 2 0.2118 0.920 0.000 0.888 0.000 0.104 0.008 0.000
#> GSM123743 2 0.0603 0.949 0.000 0.980 0.000 0.016 0.004 0.000
#> GSM123749 2 0.0777 0.947 0.000 0.972 0.000 0.024 0.004 0.000
#> GSM123755 2 0.0777 0.947 0.000 0.972 0.000 0.024 0.004 0.000
#> GSM123768 2 0.2146 0.915 0.000 0.880 0.000 0.116 0.004 0.000
#> GSM123776 1 0.2726 0.884 0.884 0.004 0.000 0.044 0.016 0.052
#> GSM123783 2 0.2288 0.913 0.000 0.876 0.000 0.116 0.004 0.004
#> GSM123790 2 0.3164 0.879 0.000 0.824 0.000 0.140 0.004 0.032
#> GSM123794 2 0.1471 0.939 0.000 0.932 0.000 0.064 0.004 0.000
#> GSM123798 2 0.0777 0.947 0.000 0.972 0.000 0.024 0.004 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) infection(p) agent(p) k
#> CV:mclust 71 2.21e-14 2.21e-14 0.000470 2
#> CV:mclust 68 9.72e-16 9.72e-16 0.000249 3
#> CV:mclust 65 9.70e-17 9.70e-17 0.000858 4
#> CV:mclust 68 1.85e-17 1.85e-17 0.001245 5
#> CV:mclust 69 4.89e-17 4.89e-17 0.002482 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "NMF"]
# you can also extract it by
# res = res_list["CV:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.992 0.997 0.4770 0.522 0.522
#> 3 3 0.883 0.893 0.944 0.3903 0.794 0.611
#> 4 4 0.786 0.793 0.882 0.1052 0.908 0.731
#> 5 5 0.773 0.758 0.844 0.0497 0.948 0.810
#> 6 6 0.779 0.675 0.801 0.0264 0.966 0.858
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
#> GSM123732 1 0.0000 1.000 1.000 0.000
#> GSM123736 1 0.0000 1.000 1.000 0.000
#> GSM123740 1 0.0000 1.000 1.000 0.000
#> GSM123744 1 0.0000 1.000 1.000 0.000
#> GSM123746 1 0.0000 1.000 1.000 0.000
#> GSM123750 1 0.0000 1.000 1.000 0.000
#> GSM123752 1 0.0000 1.000 1.000 0.000
#> GSM123756 1 0.0000 1.000 1.000 0.000
#> GSM123758 1 0.0000 1.000 1.000 0.000
#> GSM123761 1 0.0000 1.000 1.000 0.000
#> GSM123763 1 0.0000 1.000 1.000 0.000
#> GSM123765 1 0.0000 1.000 1.000 0.000
#> GSM123769 1 0.0000 1.000 1.000 0.000
#> GSM123771 1 0.0000 1.000 1.000 0.000
#> GSM123774 1 0.0000 1.000 1.000 0.000
#> GSM123778 1 0.0000 1.000 1.000 0.000
#> GSM123780 1 0.0000 1.000 1.000 0.000
#> GSM123784 1 0.0000 1.000 1.000 0.000
#> GSM123787 1 0.0000 1.000 1.000 0.000
#> GSM123791 1 0.0000 1.000 1.000 0.000
#> GSM123795 1 0.0000 1.000 1.000 0.000
#> GSM123799 1 0.0000 1.000 1.000 0.000
#> GSM123730 1 0.0938 0.988 0.988 0.012
#> GSM123734 1 0.0000 1.000 1.000 0.000
#> GSM123738 1 0.0000 1.000 1.000 0.000
#> GSM123742 1 0.0000 1.000 1.000 0.000
#> GSM123745 1 0.0000 1.000 1.000 0.000
#> GSM123748 1 0.0000 1.000 1.000 0.000
#> GSM123751 1 0.0000 1.000 1.000 0.000
#> GSM123754 1 0.0000 1.000 1.000 0.000
#> GSM123757 1 0.0000 1.000 1.000 0.000
#> GSM123760 1 0.0000 1.000 1.000 0.000
#> GSM123762 1 0.0000 1.000 1.000 0.000
#> GSM123764 1 0.0000 1.000 1.000 0.000
#> GSM123767 1 0.0000 1.000 1.000 0.000
#> GSM123770 1 0.0000 1.000 1.000 0.000
#> GSM123773 1 0.0000 1.000 1.000 0.000
#> GSM123777 1 0.0000 1.000 1.000 0.000
#> GSM123779 1 0.0000 1.000 1.000 0.000
#> GSM123782 1 0.0000 1.000 1.000 0.000
#> GSM123786 1 0.0000 1.000 1.000 0.000
#> GSM123789 1 0.0000 1.000 1.000 0.000
#> GSM123793 1 0.0000 1.000 1.000 0.000
#> GSM123797 1 0.0000 1.000 1.000 0.000
#> GSM123729 2 0.0000 0.991 0.000 1.000
#> GSM123733 2 0.0000 0.991 0.000 1.000
#> GSM123737 2 0.0000 0.991 0.000 1.000
#> GSM123741 2 0.0000 0.991 0.000 1.000
#> GSM123747 2 0.0000 0.991 0.000 1.000
#> GSM123753 2 0.0000 0.991 0.000 1.000
#> GSM123759 2 0.0000 0.991 0.000 1.000
#> GSM123766 2 0.0000 0.991 0.000 1.000
#> GSM123772 2 0.0000 0.991 0.000 1.000
#> GSM123775 2 0.0000 0.991 0.000 1.000
#> GSM123781 2 0.0000 0.991 0.000 1.000
#> GSM123785 2 0.0000 0.991 0.000 1.000
#> GSM123788 2 0.0000 0.991 0.000 1.000
#> GSM123792 2 0.0000 0.991 0.000 1.000
#> GSM123796 2 0.0000 0.991 0.000 1.000
#> GSM123731 2 0.0000 0.991 0.000 1.000
#> GSM123735 2 0.0000 0.991 0.000 1.000
#> GSM123739 2 0.0000 0.991 0.000 1.000
#> GSM123743 2 0.0000 0.991 0.000 1.000
#> GSM123749 2 0.0000 0.991 0.000 1.000
#> GSM123755 2 0.0000 0.991 0.000 1.000
#> GSM123768 2 0.0000 0.991 0.000 1.000
#> GSM123776 2 0.7745 0.705 0.228 0.772
#> GSM123783 2 0.0000 0.991 0.000 1.000
#> GSM123790 2 0.0000 0.991 0.000 1.000
#> GSM123794 2 0.0000 0.991 0.000 1.000
#> GSM123798 2 0.0000 0.991 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM123732 3 0.0747 0.91514 0.016 0.000 0.984
#> GSM123736 3 0.1411 0.91651 0.036 0.000 0.964
#> GSM123740 3 0.1411 0.91646 0.036 0.000 0.964
#> GSM123744 3 0.6305 0.00995 0.484 0.000 0.516
#> GSM123746 1 0.1643 0.91190 0.956 0.000 0.044
#> GSM123750 1 0.5058 0.71238 0.756 0.000 0.244
#> GSM123752 1 0.1163 0.91497 0.972 0.000 0.028
#> GSM123756 1 0.0892 0.91441 0.980 0.000 0.020
#> GSM123758 1 0.5291 0.67641 0.732 0.000 0.268
#> GSM123761 1 0.4702 0.75916 0.788 0.000 0.212
#> GSM123763 3 0.4750 0.73455 0.216 0.000 0.784
#> GSM123765 3 0.0892 0.91779 0.020 0.000 0.980
#> GSM123769 1 0.1031 0.91597 0.976 0.000 0.024
#> GSM123771 1 0.0747 0.91239 0.984 0.000 0.016
#> GSM123774 1 0.0848 0.90057 0.984 0.008 0.008
#> GSM123778 3 0.0592 0.91328 0.012 0.000 0.988
#> GSM123780 3 0.0237 0.91300 0.004 0.000 0.996
#> GSM123784 3 0.0892 0.91789 0.020 0.000 0.980
#> GSM123787 3 0.0424 0.91472 0.008 0.000 0.992
#> GSM123791 3 0.1411 0.91651 0.036 0.000 0.964
#> GSM123795 3 0.1753 0.91059 0.048 0.000 0.952
#> GSM123799 3 0.1529 0.91476 0.040 0.000 0.960
#> GSM123730 3 0.0661 0.90085 0.004 0.008 0.988
#> GSM123734 3 0.3941 0.81771 0.156 0.000 0.844
#> GSM123738 3 0.1289 0.91733 0.032 0.000 0.968
#> GSM123742 3 0.6308 -0.00569 0.492 0.000 0.508
#> GSM123745 1 0.1031 0.91597 0.976 0.000 0.024
#> GSM123748 1 0.2165 0.90253 0.936 0.000 0.064
#> GSM123751 1 0.2537 0.89217 0.920 0.000 0.080
#> GSM123754 1 0.1860 0.90867 0.948 0.000 0.052
#> GSM123757 1 0.0592 0.90983 0.988 0.000 0.012
#> GSM123760 3 0.2959 0.87198 0.100 0.000 0.900
#> GSM123762 1 0.5835 0.51373 0.660 0.000 0.340
#> GSM123764 3 0.0424 0.91472 0.008 0.000 0.992
#> GSM123767 1 0.1031 0.91597 0.976 0.000 0.024
#> GSM123770 1 0.1031 0.91597 0.976 0.000 0.024
#> GSM123773 1 0.1031 0.91597 0.976 0.000 0.024
#> GSM123777 3 0.0237 0.90765 0.004 0.000 0.996
#> GSM123779 3 0.4452 0.77354 0.192 0.000 0.808
#> GSM123782 3 0.1129 0.91655 0.020 0.004 0.976
#> GSM123786 3 0.0000 0.91049 0.000 0.000 1.000
#> GSM123789 3 0.1411 0.91642 0.036 0.000 0.964
#> GSM123793 3 0.1031 0.91818 0.024 0.000 0.976
#> GSM123797 3 0.1031 0.91817 0.024 0.000 0.976
#> GSM123729 2 0.0747 0.98656 0.016 0.984 0.000
#> GSM123733 2 0.0424 0.99102 0.000 0.992 0.008
#> GSM123737 2 0.0424 0.98991 0.008 0.992 0.000
#> GSM123741 2 0.0237 0.99099 0.004 0.996 0.000
#> GSM123747 2 0.0661 0.99047 0.004 0.988 0.008
#> GSM123753 2 0.0661 0.99047 0.004 0.988 0.008
#> GSM123759 2 0.0475 0.99125 0.004 0.992 0.004
#> GSM123766 2 0.0661 0.99047 0.004 0.988 0.008
#> GSM123772 2 0.0829 0.98913 0.004 0.984 0.012
#> GSM123775 2 0.1031 0.98158 0.024 0.976 0.000
#> GSM123781 2 0.0237 0.99152 0.000 0.996 0.004
#> GSM123785 2 0.1170 0.98522 0.008 0.976 0.016
#> GSM123788 2 0.0000 0.99140 0.000 1.000 0.000
#> GSM123792 2 0.0424 0.99102 0.000 0.992 0.008
#> GSM123796 2 0.0829 0.98866 0.004 0.984 0.012
#> GSM123731 2 0.0237 0.99098 0.004 0.996 0.000
#> GSM123735 2 0.0424 0.98991 0.008 0.992 0.000
#> GSM123739 2 0.0892 0.98432 0.020 0.980 0.000
#> GSM123743 2 0.0237 0.99099 0.004 0.996 0.000
#> GSM123749 2 0.0237 0.99099 0.004 0.996 0.000
#> GSM123755 2 0.0000 0.99140 0.000 1.000 0.000
#> GSM123768 2 0.0424 0.99116 0.008 0.992 0.000
#> GSM123776 1 0.3425 0.80621 0.884 0.112 0.004
#> GSM123783 2 0.0592 0.99016 0.012 0.988 0.000
#> GSM123790 2 0.1711 0.97294 0.008 0.960 0.032
#> GSM123794 2 0.0829 0.98913 0.004 0.984 0.012
#> GSM123798 2 0.0237 0.99144 0.004 0.996 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM123732 3 0.1124 0.7567 0.004 0.012 0.972 0.012
#> GSM123736 3 0.3688 0.7045 0.000 0.000 0.792 0.208
#> GSM123740 3 0.2921 0.7686 0.000 0.000 0.860 0.140
#> GSM123744 3 0.3335 0.7164 0.120 0.000 0.860 0.020
#> GSM123746 1 0.3048 0.8011 0.876 0.000 0.108 0.016
#> GSM123750 3 0.5237 0.3936 0.356 0.000 0.628 0.016
#> GSM123752 1 0.5615 0.2510 0.556 0.004 0.424 0.016
#> GSM123756 1 0.0804 0.8589 0.980 0.000 0.008 0.012
#> GSM123758 3 0.3791 0.6753 0.092 0.032 0.860 0.016
#> GSM123761 1 0.4904 0.6668 0.744 0.000 0.216 0.040
#> GSM123763 4 0.6112 0.6310 0.096 0.000 0.248 0.656
#> GSM123765 3 0.2216 0.7898 0.000 0.000 0.908 0.092
#> GSM123769 1 0.1151 0.8610 0.968 0.000 0.008 0.024
#> GSM123771 1 0.0657 0.8588 0.984 0.000 0.004 0.012
#> GSM123774 1 0.0188 0.8570 0.996 0.000 0.000 0.004
#> GSM123778 3 0.0376 0.7749 0.000 0.004 0.992 0.004
#> GSM123780 3 0.2589 0.7825 0.000 0.000 0.884 0.116
#> GSM123784 3 0.2216 0.7892 0.000 0.000 0.908 0.092
#> GSM123787 3 0.0895 0.7806 0.004 0.000 0.976 0.020
#> GSM123791 3 0.2266 0.7906 0.004 0.000 0.912 0.084
#> GSM123795 3 0.4955 0.1898 0.000 0.000 0.556 0.444
#> GSM123799 3 0.2760 0.7764 0.000 0.000 0.872 0.128
#> GSM123730 4 0.2010 0.7369 0.008 0.040 0.012 0.940
#> GSM123734 4 0.2908 0.7856 0.040 0.000 0.064 0.896
#> GSM123738 4 0.3852 0.7549 0.012 0.000 0.180 0.808
#> GSM123742 4 0.6965 0.0654 0.428 0.000 0.112 0.460
#> GSM123745 1 0.3486 0.7985 0.812 0.000 0.000 0.188
#> GSM123748 1 0.2546 0.8533 0.900 0.000 0.008 0.092
#> GSM123751 1 0.3356 0.8079 0.824 0.000 0.000 0.176
#> GSM123754 1 0.2149 0.8543 0.912 0.000 0.000 0.088
#> GSM123757 1 0.0804 0.8497 0.980 0.000 0.012 0.008
#> GSM123760 4 0.4197 0.7704 0.036 0.000 0.156 0.808
#> GSM123762 1 0.5690 0.5918 0.672 0.000 0.060 0.268
#> GSM123764 3 0.4994 0.0482 0.000 0.000 0.520 0.480
#> GSM123767 1 0.3355 0.8171 0.836 0.000 0.004 0.160
#> GSM123770 1 0.1022 0.8603 0.968 0.000 0.000 0.032
#> GSM123773 1 0.2530 0.8455 0.888 0.000 0.000 0.112
#> GSM123777 4 0.3852 0.7220 0.000 0.008 0.192 0.800
#> GSM123779 4 0.2399 0.7661 0.048 0.000 0.032 0.920
#> GSM123782 3 0.4713 0.4388 0.000 0.000 0.640 0.360
#> GSM123786 3 0.0672 0.7742 0.000 0.008 0.984 0.008
#> GSM123789 4 0.5050 0.3003 0.004 0.000 0.408 0.588
#> GSM123793 4 0.2924 0.7918 0.016 0.000 0.100 0.884
#> GSM123797 4 0.2662 0.7905 0.016 0.000 0.084 0.900
#> GSM123729 2 0.2210 0.9536 0.016 0.936 0.020 0.028
#> GSM123733 2 0.1209 0.9649 0.000 0.964 0.004 0.032
#> GSM123737 2 0.0712 0.9713 0.004 0.984 0.004 0.008
#> GSM123741 2 0.0336 0.9714 0.000 0.992 0.000 0.008
#> GSM123747 2 0.0657 0.9721 0.000 0.984 0.004 0.012
#> GSM123753 2 0.0672 0.9716 0.000 0.984 0.008 0.008
#> GSM123759 2 0.0657 0.9715 0.000 0.984 0.004 0.012
#> GSM123766 2 0.1109 0.9669 0.000 0.968 0.004 0.028
#> GSM123772 2 0.0336 0.9719 0.000 0.992 0.000 0.008
#> GSM123775 2 0.1674 0.9641 0.012 0.952 0.004 0.032
#> GSM123781 2 0.0524 0.9716 0.000 0.988 0.004 0.008
#> GSM123785 2 0.2053 0.9433 0.000 0.924 0.004 0.072
#> GSM123788 2 0.1209 0.9650 0.000 0.964 0.004 0.032
#> GSM123792 2 0.0188 0.9721 0.000 0.996 0.004 0.000
#> GSM123796 2 0.1398 0.9617 0.000 0.956 0.004 0.040
#> GSM123731 2 0.0657 0.9714 0.000 0.984 0.004 0.012
#> GSM123735 2 0.0469 0.9712 0.000 0.988 0.000 0.012
#> GSM123739 2 0.1484 0.9673 0.016 0.960 0.004 0.020
#> GSM123743 2 0.0000 0.9721 0.000 1.000 0.000 0.000
#> GSM123749 2 0.0844 0.9712 0.004 0.980 0.004 0.012
#> GSM123755 2 0.1484 0.9642 0.004 0.960 0.020 0.016
#> GSM123768 2 0.2809 0.9282 0.004 0.904 0.064 0.028
#> GSM123776 1 0.2998 0.7929 0.892 0.080 0.004 0.024
#> GSM123783 2 0.3301 0.9029 0.004 0.876 0.092 0.028
#> GSM123790 2 0.1637 0.9532 0.000 0.940 0.000 0.060
#> GSM123794 2 0.0804 0.9705 0.000 0.980 0.008 0.012
#> GSM123798 2 0.1624 0.9594 0.000 0.952 0.028 0.020
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM123732 3 0.2016 0.72929 0.020 0.012 0.936 0.020 0.012
#> GSM123736 3 0.6042 0.45167 0.028 0.000 0.576 0.324 0.072
#> GSM123740 3 0.5793 0.56630 0.032 0.000 0.636 0.264 0.068
#> GSM123744 3 0.4726 0.67824 0.108 0.000 0.752 0.008 0.132
#> GSM123746 1 0.3080 0.79214 0.872 0.000 0.060 0.008 0.060
#> GSM123750 3 0.6486 0.25329 0.324 0.000 0.472 0.000 0.204
#> GSM123752 1 0.5066 0.25287 0.584 0.004 0.384 0.004 0.024
#> GSM123756 1 0.0451 0.83173 0.988 0.000 0.000 0.004 0.008
#> GSM123758 3 0.3846 0.67284 0.100 0.036 0.836 0.016 0.012
#> GSM123761 5 0.5375 0.51441 0.276 0.000 0.080 0.004 0.640
#> GSM123763 5 0.4014 0.69607 0.024 0.000 0.060 0.096 0.820
#> GSM123765 3 0.3400 0.72160 0.000 0.000 0.828 0.136 0.036
#> GSM123769 1 0.1278 0.83334 0.960 0.000 0.004 0.020 0.016
#> GSM123771 1 0.0609 0.83138 0.980 0.000 0.000 0.000 0.020
#> GSM123774 1 0.0290 0.83195 0.992 0.000 0.000 0.000 0.008
#> GSM123778 3 0.2356 0.74030 0.004 0.004 0.912 0.024 0.056
#> GSM123780 3 0.4062 0.67466 0.000 0.000 0.764 0.196 0.040
#> GSM123784 3 0.2959 0.73635 0.000 0.000 0.864 0.100 0.036
#> GSM123787 3 0.3239 0.70714 0.004 0.000 0.828 0.012 0.156
#> GSM123791 3 0.4220 0.69969 0.004 0.000 0.768 0.048 0.180
#> GSM123795 4 0.6572 0.00519 0.016 0.000 0.392 0.460 0.132
#> GSM123799 3 0.5520 0.58955 0.028 0.000 0.656 0.260 0.056
#> GSM123730 4 0.3283 0.64367 0.000 0.008 0.028 0.848 0.116
#> GSM123734 4 0.5176 0.53102 0.012 0.000 0.032 0.608 0.348
#> GSM123738 4 0.4930 0.65013 0.000 0.000 0.144 0.716 0.140
#> GSM123742 5 0.4203 0.69903 0.108 0.000 0.032 0.052 0.808
#> GSM123745 1 0.5478 0.42450 0.592 0.000 0.004 0.068 0.336
#> GSM123748 1 0.4666 0.36994 0.596 0.000 0.004 0.012 0.388
#> GSM123751 1 0.3882 0.73381 0.788 0.000 0.000 0.044 0.168
#> GSM123754 1 0.1901 0.82612 0.928 0.000 0.004 0.056 0.012
#> GSM123757 1 0.0898 0.83092 0.972 0.000 0.008 0.000 0.020
#> GSM123760 5 0.3256 0.72236 0.012 0.000 0.060 0.064 0.864
#> GSM123762 5 0.4312 0.66215 0.176 0.000 0.020 0.032 0.772
#> GSM123764 5 0.3386 0.70586 0.000 0.000 0.128 0.040 0.832
#> GSM123767 1 0.3431 0.77542 0.828 0.000 0.008 0.144 0.020
#> GSM123770 1 0.0671 0.83125 0.980 0.000 0.000 0.016 0.004
#> GSM123773 1 0.2629 0.80674 0.880 0.000 0.004 0.104 0.012
#> GSM123777 4 0.4796 0.64072 0.000 0.000 0.120 0.728 0.152
#> GSM123779 4 0.4758 0.57303 0.012 0.000 0.032 0.696 0.260
#> GSM123782 5 0.4413 0.61423 0.000 0.000 0.232 0.044 0.724
#> GSM123786 3 0.2575 0.73040 0.004 0.000 0.884 0.012 0.100
#> GSM123789 5 0.4801 0.63327 0.000 0.000 0.148 0.124 0.728
#> GSM123793 4 0.5325 0.40195 0.000 0.000 0.052 0.520 0.428
#> GSM123797 4 0.3934 0.68140 0.000 0.000 0.076 0.800 0.124
#> GSM123729 2 0.1095 0.96572 0.000 0.968 0.008 0.012 0.012
#> GSM123733 2 0.1282 0.95748 0.000 0.952 0.000 0.044 0.004
#> GSM123737 2 0.0992 0.96291 0.000 0.968 0.000 0.024 0.008
#> GSM123741 2 0.0566 0.96641 0.000 0.984 0.000 0.004 0.012
#> GSM123747 2 0.0740 0.96477 0.000 0.980 0.008 0.004 0.008
#> GSM123753 2 0.1095 0.96198 0.000 0.968 0.008 0.012 0.012
#> GSM123759 2 0.1074 0.96693 0.000 0.968 0.004 0.016 0.012
#> GSM123766 2 0.1195 0.96274 0.000 0.960 0.000 0.028 0.012
#> GSM123772 2 0.0693 0.96565 0.000 0.980 0.000 0.012 0.008
#> GSM123775 2 0.1356 0.96357 0.000 0.956 0.004 0.028 0.012
#> GSM123781 2 0.0854 0.96601 0.000 0.976 0.004 0.012 0.008
#> GSM123785 2 0.2470 0.91142 0.000 0.884 0.000 0.104 0.012
#> GSM123788 2 0.1205 0.95915 0.000 0.956 0.000 0.040 0.004
#> GSM123792 2 0.0162 0.96653 0.000 0.996 0.000 0.004 0.000
#> GSM123796 2 0.1251 0.95995 0.000 0.956 0.000 0.036 0.008
#> GSM123731 2 0.0613 0.96527 0.000 0.984 0.004 0.008 0.004
#> GSM123735 2 0.1041 0.96350 0.000 0.964 0.000 0.032 0.004
#> GSM123739 2 0.1267 0.96220 0.000 0.960 0.004 0.024 0.012
#> GSM123743 2 0.0162 0.96648 0.000 0.996 0.000 0.000 0.004
#> GSM123749 2 0.0867 0.96383 0.000 0.976 0.008 0.008 0.008
#> GSM123755 2 0.1200 0.96078 0.000 0.964 0.008 0.016 0.012
#> GSM123768 2 0.2606 0.92001 0.000 0.900 0.056 0.032 0.012
#> GSM123776 1 0.3755 0.71077 0.828 0.116 0.008 0.004 0.044
#> GSM123783 2 0.2938 0.89595 0.000 0.876 0.084 0.032 0.008
#> GSM123790 2 0.2629 0.91196 0.000 0.880 0.004 0.104 0.012
#> GSM123794 2 0.0981 0.96583 0.000 0.972 0.008 0.008 0.012
#> GSM123798 2 0.1503 0.95516 0.000 0.952 0.020 0.020 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM123732 3 0.2194 0.6926 0.008 0.000 0.912 0.040 0.036 0.004
#> GSM123736 4 0.4796 0.3813 0.032 0.000 0.352 0.600 0.004 0.012
#> GSM123740 4 0.5061 0.2804 0.048 0.000 0.404 0.536 0.004 0.008
#> GSM123744 3 0.5641 0.5717 0.124 0.000 0.696 0.080 0.040 0.060
#> GSM123746 1 0.4602 0.6631 0.756 0.000 0.056 0.008 0.048 0.132
#> GSM123750 3 0.7384 0.2506 0.268 0.000 0.448 0.056 0.044 0.184
#> GSM123752 1 0.6012 0.1573 0.536 0.004 0.340 0.076 0.036 0.008
#> GSM123756 1 0.0806 0.7712 0.972 0.000 0.000 0.008 0.020 0.000
#> GSM123758 3 0.6039 0.4875 0.144 0.024 0.668 0.084 0.068 0.012
#> GSM123761 6 0.6055 0.5505 0.164 0.000 0.052 0.052 0.080 0.652
#> GSM123763 6 0.5845 0.5149 0.012 0.000 0.048 0.156 0.140 0.644
#> GSM123765 3 0.3854 0.6539 0.000 0.000 0.788 0.140 0.056 0.016
#> GSM123769 1 0.1086 0.7730 0.964 0.000 0.000 0.012 0.012 0.012
#> GSM123771 1 0.1693 0.7720 0.936 0.000 0.000 0.012 0.032 0.020
#> GSM123774 1 0.0665 0.7745 0.980 0.000 0.000 0.004 0.008 0.008
#> GSM123778 3 0.2266 0.7119 0.000 0.000 0.908 0.028 0.040 0.024
#> GSM123780 3 0.4747 0.5660 0.000 0.000 0.712 0.132 0.140 0.016
#> GSM123784 3 0.4002 0.6783 0.004 0.000 0.792 0.088 0.100 0.016
#> GSM123787 3 0.3332 0.6843 0.000 0.000 0.832 0.016 0.044 0.108
#> GSM123791 3 0.5408 0.5907 0.000 0.000 0.668 0.060 0.096 0.176
#> GSM123795 4 0.4138 0.4598 0.020 0.000 0.184 0.752 0.000 0.044
#> GSM123799 4 0.4999 0.1811 0.040 0.000 0.448 0.500 0.004 0.008
#> GSM123730 5 0.5751 0.5989 0.004 0.008 0.040 0.372 0.532 0.044
#> GSM123734 4 0.4620 0.2133 0.012 0.000 0.000 0.696 0.072 0.220
#> GSM123738 4 0.3041 0.3156 0.000 0.000 0.036 0.864 0.056 0.044
#> GSM123742 6 0.4821 0.5679 0.060 0.000 0.024 0.108 0.052 0.756
#> GSM123745 1 0.6175 0.0950 0.452 0.000 0.000 0.056 0.092 0.400
#> GSM123748 6 0.5583 -0.0454 0.428 0.000 0.008 0.040 0.036 0.488
#> GSM123751 1 0.5590 0.5158 0.636 0.000 0.000 0.088 0.060 0.216
#> GSM123754 1 0.3033 0.7452 0.856 0.000 0.004 0.032 0.096 0.012
#> GSM123757 1 0.1755 0.7700 0.932 0.000 0.008 0.000 0.028 0.032
#> GSM123760 6 0.2656 0.6142 0.008 0.000 0.044 0.036 0.020 0.892
#> GSM123762 6 0.4744 0.6098 0.056 0.000 0.032 0.044 0.104 0.764
#> GSM123764 6 0.4786 0.5526 0.000 0.000 0.160 0.028 0.096 0.716
#> GSM123767 1 0.4441 0.6828 0.752 0.000 0.004 0.080 0.144 0.020
#> GSM123770 1 0.0748 0.7749 0.976 0.000 0.000 0.004 0.016 0.004
#> GSM123773 1 0.3569 0.7330 0.824 0.000 0.004 0.056 0.100 0.016
#> GSM123777 5 0.6329 0.6491 0.000 0.004 0.184 0.260 0.520 0.032
#> GSM123779 5 0.6036 0.6395 0.012 0.000 0.088 0.144 0.640 0.116
#> GSM123782 6 0.5211 0.4955 0.004 0.000 0.224 0.008 0.120 0.644
#> GSM123786 3 0.1957 0.7090 0.000 0.000 0.920 0.008 0.024 0.048
#> GSM123789 6 0.6651 0.2095 0.000 0.000 0.276 0.040 0.248 0.436
#> GSM123793 4 0.4843 0.1455 0.004 0.000 0.004 0.592 0.048 0.352
#> GSM123797 4 0.4399 0.0913 0.000 0.000 0.024 0.728 0.200 0.048
#> GSM123729 2 0.0790 0.9601 0.000 0.968 0.000 0.000 0.032 0.000
#> GSM123733 2 0.1225 0.9522 0.000 0.952 0.000 0.012 0.036 0.000
#> GSM123737 2 0.0777 0.9597 0.000 0.972 0.000 0.004 0.024 0.000
#> GSM123741 2 0.0858 0.9586 0.000 0.968 0.000 0.000 0.028 0.004
#> GSM123747 2 0.0653 0.9617 0.000 0.980 0.004 0.000 0.012 0.004
#> GSM123753 2 0.1225 0.9548 0.000 0.956 0.004 0.004 0.032 0.004
#> GSM123759 2 0.1080 0.9568 0.000 0.960 0.004 0.004 0.032 0.000
#> GSM123766 2 0.1116 0.9608 0.000 0.960 0.000 0.004 0.028 0.008
#> GSM123772 2 0.0837 0.9609 0.000 0.972 0.000 0.004 0.020 0.004
#> GSM123775 2 0.1307 0.9585 0.000 0.952 0.000 0.008 0.032 0.008
#> GSM123781 2 0.1440 0.9511 0.000 0.944 0.004 0.004 0.044 0.004
#> GSM123785 2 0.2525 0.8952 0.000 0.876 0.000 0.012 0.100 0.012
#> GSM123788 2 0.1074 0.9550 0.000 0.960 0.000 0.012 0.028 0.000
#> GSM123792 2 0.0547 0.9608 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM123796 2 0.1074 0.9550 0.000 0.960 0.000 0.012 0.028 0.000
#> GSM123731 2 0.0551 0.9614 0.000 0.984 0.004 0.000 0.008 0.004
#> GSM123735 2 0.1049 0.9566 0.000 0.960 0.000 0.008 0.032 0.000
#> GSM123739 2 0.1036 0.9605 0.000 0.964 0.000 0.008 0.024 0.004
#> GSM123743 2 0.0692 0.9599 0.000 0.976 0.000 0.004 0.020 0.000
#> GSM123749 2 0.0748 0.9590 0.000 0.976 0.004 0.000 0.016 0.004
#> GSM123755 2 0.1299 0.9534 0.000 0.952 0.004 0.004 0.036 0.004
#> GSM123768 2 0.2291 0.9258 0.000 0.904 0.016 0.008 0.064 0.008
#> GSM123776 1 0.6106 0.4518 0.600 0.152 0.000 0.012 0.196 0.040
#> GSM123783 2 0.2369 0.9214 0.000 0.900 0.028 0.004 0.060 0.008
#> GSM123790 2 0.3086 0.8283 0.000 0.820 0.004 0.020 0.156 0.000
#> GSM123794 2 0.1080 0.9617 0.000 0.960 0.004 0.000 0.032 0.004
#> GSM123798 2 0.1452 0.9521 0.000 0.948 0.008 0.004 0.032 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) infection(p) agent(p) k
#> CV:NMF 71 3.82e-16 3.82e-16 6.04e-06 2
#> CV:NMF 69 2.55e-13 2.55e-13 1.10e-04 3
#> CV:NMF 64 1.54e-16 1.54e-16 1.04e-03 4
#> CV:NMF 64 8.87e-16 8.87e-16 2.61e-03 5
#> CV:NMF 55 1.63e-12 1.63e-12 4.05e-03 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "hclust"]
# you can also extract it by
# res = res_list["MAD:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.559 0.874 0.899 0.4669 0.522 0.522
#> 3 3 0.479 0.695 0.827 0.1946 0.858 0.745
#> 4 4 0.654 0.720 0.811 0.2003 0.813 0.606
#> 5 5 0.692 0.714 0.854 0.0539 0.947 0.840
#> 6 6 0.775 0.656 0.824 0.0340 0.989 0.961
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 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
#> GSM123732 1 0.8386 0.802 0.732 0.268
#> GSM123736 1 0.7376 0.837 0.792 0.208
#> GSM123740 1 0.7376 0.837 0.792 0.208
#> GSM123744 1 0.6887 0.844 0.816 0.184
#> GSM123746 1 0.6887 0.844 0.816 0.184
#> GSM123750 1 0.6801 0.845 0.820 0.180
#> GSM123752 1 0.6887 0.844 0.816 0.184
#> GSM123756 1 0.0000 0.828 1.000 0.000
#> GSM123758 1 0.7056 0.842 0.808 0.192
#> GSM123761 1 0.0000 0.828 1.000 0.000
#> GSM123763 1 0.0376 0.830 0.996 0.004
#> GSM123765 1 0.8386 0.802 0.732 0.268
#> GSM123769 1 0.0000 0.828 1.000 0.000
#> GSM123771 1 0.0000 0.828 1.000 0.000
#> GSM123774 1 0.0000 0.828 1.000 0.000
#> GSM123778 1 0.8386 0.802 0.732 0.268
#> GSM123780 1 0.8386 0.802 0.732 0.268
#> GSM123784 1 0.8386 0.802 0.732 0.268
#> GSM123787 1 0.8386 0.802 0.732 0.268
#> GSM123791 1 0.8267 0.808 0.740 0.260
#> GSM123795 1 0.7376 0.837 0.792 0.208
#> GSM123799 1 0.7376 0.837 0.792 0.208
#> GSM123730 1 0.9944 0.495 0.544 0.456
#> GSM123734 1 0.0000 0.828 1.000 0.000
#> GSM123738 1 0.4562 0.848 0.904 0.096
#> GSM123742 1 0.3879 0.846 0.924 0.076
#> GSM123745 1 0.2236 0.841 0.964 0.036
#> GSM123748 1 0.2423 0.842 0.960 0.040
#> GSM123751 1 0.2236 0.841 0.964 0.036
#> GSM123754 1 0.2236 0.841 0.964 0.036
#> GSM123757 1 0.6887 0.844 0.816 0.184
#> GSM123760 1 0.3879 0.846 0.924 0.076
#> GSM123762 1 0.0000 0.828 1.000 0.000
#> GSM123764 1 0.9248 0.711 0.660 0.340
#> GSM123767 1 0.2236 0.841 0.964 0.036
#> GSM123770 1 0.2236 0.841 0.964 0.036
#> GSM123773 1 0.2236 0.841 0.964 0.036
#> GSM123777 1 0.9944 0.495 0.544 0.456
#> GSM123779 1 0.9977 0.473 0.528 0.472
#> GSM123782 1 0.9323 0.695 0.652 0.348
#> GSM123786 1 0.8386 0.802 0.732 0.268
#> GSM123789 1 0.9815 0.585 0.580 0.420
#> GSM123793 1 0.0672 0.832 0.992 0.008
#> GSM123797 1 0.4431 0.848 0.908 0.092
#> GSM123729 2 0.0000 1.000 0.000 1.000
#> GSM123733 2 0.0000 1.000 0.000 1.000
#> GSM123737 2 0.0000 1.000 0.000 1.000
#> GSM123741 2 0.0000 1.000 0.000 1.000
#> GSM123747 2 0.0000 1.000 0.000 1.000
#> GSM123753 2 0.0000 1.000 0.000 1.000
#> GSM123759 2 0.0000 1.000 0.000 1.000
#> GSM123766 2 0.0000 1.000 0.000 1.000
#> GSM123772 2 0.0000 1.000 0.000 1.000
#> GSM123775 2 0.0000 1.000 0.000 1.000
#> GSM123781 2 0.0000 1.000 0.000 1.000
#> GSM123785 2 0.0000 1.000 0.000 1.000
#> GSM123788 2 0.0000 1.000 0.000 1.000
#> GSM123792 2 0.0000 1.000 0.000 1.000
#> GSM123796 2 0.0000 1.000 0.000 1.000
#> GSM123731 2 0.0000 1.000 0.000 1.000
#> GSM123735 2 0.0000 1.000 0.000 1.000
#> GSM123739 2 0.0000 1.000 0.000 1.000
#> GSM123743 2 0.0000 1.000 0.000 1.000
#> GSM123749 2 0.0000 1.000 0.000 1.000
#> GSM123755 2 0.0000 1.000 0.000 1.000
#> GSM123768 2 0.0000 1.000 0.000 1.000
#> GSM123776 2 0.0000 1.000 0.000 1.000
#> GSM123783 2 0.0000 1.000 0.000 1.000
#> GSM123790 2 0.0000 1.000 0.000 1.000
#> GSM123794 2 0.0000 1.000 0.000 1.000
#> GSM123798 2 0.0000 1.000 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM123732 1 0.5881 0.660 0.728 0.256 0.016
#> GSM123736 1 0.5406 0.692 0.780 0.200 0.020
#> GSM123740 1 0.5406 0.692 0.780 0.200 0.020
#> GSM123744 1 0.4805 0.697 0.812 0.176 0.012
#> GSM123746 1 0.5348 0.698 0.796 0.176 0.028
#> GSM123750 1 0.5412 0.695 0.796 0.172 0.032
#> GSM123752 1 0.4645 0.696 0.816 0.176 0.008
#> GSM123756 1 0.4121 0.534 0.832 0.000 0.168
#> GSM123758 1 0.4861 0.695 0.808 0.180 0.012
#> GSM123761 1 0.2711 0.576 0.912 0.000 0.088
#> GSM123763 1 0.2066 0.587 0.940 0.000 0.060
#> GSM123765 1 0.5881 0.660 0.728 0.256 0.016
#> GSM123769 1 0.4121 0.534 0.832 0.000 0.168
#> GSM123771 1 0.4121 0.534 0.832 0.000 0.168
#> GSM123774 1 0.4121 0.534 0.832 0.000 0.168
#> GSM123778 1 0.6143 0.659 0.720 0.256 0.024
#> GSM123780 1 0.6143 0.659 0.720 0.256 0.024
#> GSM123784 1 0.6143 0.659 0.720 0.256 0.024
#> GSM123787 1 0.6143 0.659 0.720 0.256 0.024
#> GSM123791 1 0.6187 0.667 0.724 0.248 0.028
#> GSM123795 1 0.5406 0.692 0.780 0.200 0.020
#> GSM123799 1 0.5406 0.692 0.780 0.200 0.020
#> GSM123730 2 0.9616 -0.165 0.212 0.444 0.344
#> GSM123734 3 0.0892 0.700 0.020 0.000 0.980
#> GSM123738 3 0.7169 0.766 0.208 0.088 0.704
#> GSM123742 1 0.6933 0.555 0.716 0.076 0.208
#> GSM123745 1 0.7084 0.449 0.628 0.036 0.336
#> GSM123748 1 0.5850 0.570 0.772 0.040 0.188
#> GSM123751 1 0.7037 0.459 0.636 0.036 0.328
#> GSM123754 1 0.7061 0.454 0.632 0.036 0.332
#> GSM123757 1 0.5348 0.698 0.796 0.176 0.028
#> GSM123760 1 0.6794 0.569 0.728 0.076 0.196
#> GSM123762 1 0.3038 0.570 0.896 0.000 0.104
#> GSM123764 1 0.8808 0.458 0.536 0.332 0.132
#> GSM123767 1 0.7037 0.455 0.636 0.036 0.328
#> GSM123770 1 0.7061 0.454 0.632 0.036 0.332
#> GSM123773 1 0.7061 0.454 0.632 0.036 0.332
#> GSM123777 2 0.9616 -0.165 0.212 0.444 0.344
#> GSM123779 2 0.9479 -0.215 0.348 0.460 0.192
#> GSM123782 1 0.8891 0.424 0.524 0.340 0.136
#> GSM123786 1 0.6143 0.659 0.720 0.256 0.024
#> GSM123789 1 0.9299 0.268 0.432 0.408 0.160
#> GSM123793 3 0.4002 0.786 0.160 0.000 0.840
#> GSM123797 3 0.7092 0.770 0.208 0.084 0.708
#> GSM123729 2 0.0000 0.933 0.000 1.000 0.000
#> GSM123733 2 0.0000 0.933 0.000 1.000 0.000
#> GSM123737 2 0.0000 0.933 0.000 1.000 0.000
#> GSM123741 2 0.0000 0.933 0.000 1.000 0.000
#> GSM123747 2 0.0000 0.933 0.000 1.000 0.000
#> GSM123753 2 0.0000 0.933 0.000 1.000 0.000
#> GSM123759 2 0.0000 0.933 0.000 1.000 0.000
#> GSM123766 2 0.0000 0.933 0.000 1.000 0.000
#> GSM123772 2 0.0000 0.933 0.000 1.000 0.000
#> GSM123775 2 0.0000 0.933 0.000 1.000 0.000
#> GSM123781 2 0.0000 0.933 0.000 1.000 0.000
#> GSM123785 2 0.0000 0.933 0.000 1.000 0.000
#> GSM123788 2 0.0000 0.933 0.000 1.000 0.000
#> GSM123792 2 0.0000 0.933 0.000 1.000 0.000
#> GSM123796 2 0.0000 0.933 0.000 1.000 0.000
#> GSM123731 2 0.0000 0.933 0.000 1.000 0.000
#> GSM123735 2 0.0000 0.933 0.000 1.000 0.000
#> GSM123739 2 0.0000 0.933 0.000 1.000 0.000
#> GSM123743 2 0.0000 0.933 0.000 1.000 0.000
#> GSM123749 2 0.0000 0.933 0.000 1.000 0.000
#> GSM123755 2 0.0000 0.933 0.000 1.000 0.000
#> GSM123768 2 0.0000 0.933 0.000 1.000 0.000
#> GSM123776 2 0.0000 0.933 0.000 1.000 0.000
#> GSM123783 2 0.0000 0.933 0.000 1.000 0.000
#> GSM123790 2 0.0000 0.933 0.000 1.000 0.000
#> GSM123794 2 0.0000 0.933 0.000 1.000 0.000
#> GSM123798 2 0.0000 0.933 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM123732 3 0.123 0.692 0.004 0.020 0.968 0.008
#> GSM123736 3 0.342 0.672 0.088 0.016 0.876 0.020
#> GSM123740 3 0.342 0.672 0.088 0.016 0.876 0.020
#> GSM123744 3 0.420 0.610 0.160 0.012 0.812 0.016
#> GSM123746 3 0.434 0.596 0.184 0.012 0.792 0.012
#> GSM123750 3 0.465 0.568 0.192 0.012 0.776 0.020
#> GSM123752 3 0.412 0.609 0.164 0.012 0.812 0.012
#> GSM123756 1 0.413 0.743 0.740 0.000 0.260 0.000
#> GSM123758 3 0.402 0.622 0.156 0.016 0.820 0.008
#> GSM123761 3 0.621 -0.289 0.460 0.000 0.488 0.052
#> GSM123763 1 0.620 0.415 0.508 0.000 0.440 0.052
#> GSM123765 3 0.123 0.692 0.004 0.020 0.968 0.008
#> GSM123769 1 0.413 0.743 0.740 0.000 0.260 0.000
#> GSM123771 1 0.413 0.743 0.740 0.000 0.260 0.000
#> GSM123774 1 0.413 0.743 0.740 0.000 0.260 0.000
#> GSM123778 3 0.148 0.691 0.004 0.020 0.960 0.016
#> GSM123780 3 0.160 0.690 0.004 0.020 0.956 0.020
#> GSM123784 3 0.148 0.691 0.004 0.020 0.960 0.016
#> GSM123787 3 0.160 0.690 0.004 0.020 0.956 0.020
#> GSM123791 3 0.176 0.691 0.012 0.016 0.952 0.020
#> GSM123795 3 0.342 0.672 0.088 0.016 0.876 0.020
#> GSM123799 3 0.342 0.672 0.088 0.016 0.876 0.020
#> GSM123730 3 0.898 -0.216 0.068 0.228 0.412 0.292
#> GSM123734 4 0.482 0.476 0.296 0.000 0.012 0.692
#> GSM123738 4 0.589 0.720 0.072 0.000 0.268 0.660
#> GSM123742 3 0.719 -0.140 0.404 0.004 0.472 0.120
#> GSM123745 1 0.551 0.758 0.736 0.004 0.172 0.088
#> GSM123748 1 0.687 0.545 0.540 0.004 0.356 0.100
#> GSM123751 1 0.581 0.759 0.708 0.004 0.196 0.092
#> GSM123754 1 0.556 0.762 0.732 0.004 0.176 0.088
#> GSM123757 3 0.430 0.588 0.192 0.012 0.788 0.008
#> GSM123760 3 0.708 -0.102 0.388 0.000 0.484 0.128
#> GSM123762 1 0.601 0.673 0.652 0.000 0.268 0.080
#> GSM123764 3 0.676 0.489 0.108 0.112 0.700 0.080
#> GSM123767 1 0.560 0.760 0.728 0.004 0.180 0.088
#> GSM123770 1 0.556 0.762 0.732 0.004 0.176 0.088
#> GSM123773 1 0.556 0.762 0.732 0.004 0.176 0.088
#> GSM123777 3 0.898 -0.216 0.068 0.228 0.412 0.292
#> GSM123779 3 0.807 0.182 0.072 0.232 0.564 0.132
#> GSM123782 3 0.732 0.449 0.124 0.136 0.656 0.084
#> GSM123786 3 0.160 0.690 0.004 0.020 0.956 0.020
#> GSM123789 3 0.732 0.346 0.076 0.172 0.648 0.104
#> GSM123793 4 0.485 0.731 0.072 0.000 0.152 0.776
#> GSM123797 4 0.593 0.725 0.076 0.000 0.264 0.660
#> GSM123729 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM123733 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM123737 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM123741 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM123747 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM123753 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM123759 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM123766 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM123772 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM123775 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM123781 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM123785 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM123788 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM123792 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM123796 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM123731 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM123735 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM123739 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM123743 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM123749 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM123755 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM123768 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM123776 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM123783 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM123790 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM123794 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM123798 2 0.000 1.000 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM123732 3 0.123 0.7551 0.004 0.004 0.964 0.016 0.012
#> GSM123736 3 0.288 0.7596 0.060 0.000 0.888 0.028 0.024
#> GSM123740 3 0.288 0.7596 0.060 0.000 0.888 0.028 0.024
#> GSM123744 3 0.356 0.7172 0.136 0.000 0.824 0.004 0.036
#> GSM123746 3 0.373 0.7037 0.160 0.000 0.804 0.004 0.032
#> GSM123750 3 0.410 0.6849 0.160 0.000 0.784 0.004 0.052
#> GSM123752 3 0.352 0.7159 0.140 0.000 0.824 0.004 0.032
#> GSM123756 1 0.444 0.6029 0.756 0.000 0.156 0.000 0.088
#> GSM123758 3 0.351 0.7260 0.132 0.004 0.832 0.004 0.028
#> GSM123761 3 0.646 -0.1373 0.400 0.000 0.440 0.004 0.156
#> GSM123763 1 0.680 0.4097 0.476 0.000 0.328 0.016 0.180
#> GSM123765 3 0.107 0.7536 0.000 0.004 0.968 0.016 0.012
#> GSM123769 1 0.444 0.6029 0.756 0.000 0.156 0.000 0.088
#> GSM123771 1 0.444 0.6029 0.756 0.000 0.156 0.000 0.088
#> GSM123774 1 0.444 0.6029 0.756 0.000 0.156 0.000 0.088
#> GSM123778 3 0.128 0.7509 0.000 0.004 0.960 0.020 0.016
#> GSM123780 3 0.137 0.7489 0.000 0.004 0.956 0.024 0.016
#> GSM123784 3 0.128 0.7509 0.000 0.004 0.960 0.020 0.016
#> GSM123787 3 0.137 0.7489 0.000 0.004 0.956 0.024 0.016
#> GSM123791 3 0.118 0.7560 0.004 0.000 0.964 0.016 0.016
#> GSM123795 3 0.288 0.7596 0.060 0.000 0.888 0.028 0.024
#> GSM123799 3 0.288 0.7596 0.060 0.000 0.888 0.028 0.024
#> GSM123730 4 0.772 0.4819 0.040 0.208 0.268 0.464 0.020
#> GSM123734 5 0.550 0.0000 0.212 0.000 0.000 0.140 0.648
#> GSM123738 4 0.301 0.4637 0.036 0.000 0.104 0.860 0.000
#> GSM123742 1 0.745 0.2652 0.444 0.000 0.348 0.108 0.100
#> GSM123745 1 0.295 0.6232 0.884 0.000 0.044 0.056 0.016
#> GSM123748 1 0.605 0.5395 0.652 0.000 0.212 0.068 0.068
#> GSM123751 1 0.326 0.6259 0.868 0.000 0.056 0.056 0.020
#> GSM123754 1 0.299 0.6307 0.880 0.000 0.052 0.056 0.012
#> GSM123757 3 0.377 0.6949 0.172 0.000 0.796 0.004 0.028
#> GSM123760 1 0.777 0.2165 0.400 0.000 0.352 0.112 0.136
#> GSM123762 1 0.513 0.4603 0.664 0.000 0.036 0.020 0.280
#> GSM123764 3 0.752 0.3357 0.116 0.096 0.608 0.100 0.080
#> GSM123767 1 0.305 0.6283 0.876 0.000 0.052 0.060 0.012
#> GSM123770 1 0.299 0.6307 0.880 0.000 0.052 0.056 0.012
#> GSM123773 1 0.299 0.6307 0.880 0.000 0.052 0.056 0.012
#> GSM123777 4 0.772 0.4819 0.040 0.208 0.268 0.464 0.020
#> GSM123779 3 0.797 -0.1882 0.072 0.204 0.476 0.228 0.020
#> GSM123782 3 0.781 0.2940 0.128 0.120 0.576 0.112 0.064
#> GSM123786 3 0.137 0.7489 0.000 0.004 0.956 0.024 0.016
#> GSM123789 3 0.767 0.1207 0.072 0.144 0.568 0.168 0.048
#> GSM123793 4 0.468 0.0266 0.036 0.000 0.036 0.756 0.172
#> GSM123797 4 0.304 0.4582 0.040 0.000 0.100 0.860 0.000
#> GSM123729 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM123733 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM123737 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM123741 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM123747 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM123753 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM123759 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM123766 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM123772 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM123775 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM123781 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM123785 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM123788 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM123792 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM123796 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM123731 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM123735 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM123739 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM123743 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM123749 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM123755 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM123768 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM123776 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM123783 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM123790 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM123794 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM123798 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM123732 3 0.1444 0.7278 0.000 0.000 0.928 0.000 NA 0.000
#> GSM123736 3 0.2180 0.7213 0.048 0.000 0.912 0.028 NA 0.008
#> GSM123740 3 0.2180 0.7213 0.048 0.000 0.912 0.028 NA 0.008
#> GSM123744 3 0.3089 0.6837 0.092 0.000 0.844 0.000 NA 0.060
#> GSM123746 3 0.3324 0.6710 0.112 0.000 0.824 0.000 NA 0.060
#> GSM123750 3 0.3817 0.6536 0.104 0.000 0.796 0.000 NA 0.088
#> GSM123752 3 0.2948 0.6841 0.092 0.000 0.848 0.000 NA 0.060
#> GSM123756 1 0.5219 0.2850 0.612 0.000 0.176 0.000 NA 0.212
#> GSM123758 3 0.2876 0.6945 0.080 0.000 0.860 0.000 NA 0.056
#> GSM123761 3 0.6016 -0.1272 0.220 0.000 0.456 0.000 NA 0.320
#> GSM123763 6 0.6711 0.0150 0.308 0.000 0.304 0.000 NA 0.356
#> GSM123765 3 0.1501 0.7269 0.000 0.000 0.924 0.000 NA 0.000
#> GSM123769 1 0.5219 0.2850 0.612 0.000 0.176 0.000 NA 0.212
#> GSM123771 1 0.5219 0.2850 0.612 0.000 0.176 0.000 NA 0.212
#> GSM123774 1 0.5219 0.2850 0.612 0.000 0.176 0.000 NA 0.212
#> GSM123778 3 0.1610 0.7245 0.000 0.000 0.916 0.000 NA 0.000
#> GSM123780 3 0.1918 0.7198 0.000 0.000 0.904 0.008 NA 0.000
#> GSM123784 3 0.1610 0.7245 0.000 0.000 0.916 0.000 NA 0.000
#> GSM123787 3 0.1908 0.7202 0.000 0.000 0.900 0.004 NA 0.000
#> GSM123791 3 0.2202 0.7265 0.008 0.000 0.904 0.004 NA 0.012
#> GSM123795 3 0.2180 0.7213 0.048 0.000 0.912 0.028 NA 0.008
#> GSM123799 3 0.2180 0.7213 0.048 0.000 0.912 0.028 NA 0.008
#> GSM123730 4 0.7580 0.5076 0.024 0.160 0.208 0.468 NA 0.004
#> GSM123734 6 0.6416 -0.0330 0.208 0.000 0.000 0.024 NA 0.408
#> GSM123738 4 0.1643 0.5707 0.008 0.000 0.068 0.924 NA 0.000
#> GSM123742 1 0.7251 0.0428 0.452 0.000 0.180 0.016 NA 0.088
#> GSM123745 1 0.0260 0.5520 0.992 0.000 0.008 0.000 NA 0.000
#> GSM123748 1 0.5580 0.2751 0.680 0.000 0.136 0.008 NA 0.084
#> GSM123751 1 0.1129 0.5465 0.964 0.000 0.012 0.004 NA 0.008
#> GSM123754 1 0.0458 0.5585 0.984 0.000 0.016 0.000 NA 0.000
#> GSM123757 3 0.3395 0.6630 0.124 0.000 0.816 0.000 NA 0.056
#> GSM123760 1 0.7552 -0.0363 0.380 0.000 0.164 0.016 NA 0.124
#> GSM123762 6 0.5310 0.0237 0.376 0.000 0.020 0.004 NA 0.548
#> GSM123764 3 0.7014 0.0798 0.128 0.060 0.412 0.012 NA 0.008
#> GSM123767 1 0.0603 0.5566 0.980 0.000 0.016 0.004 NA 0.000
#> GSM123770 1 0.0458 0.5585 0.984 0.000 0.016 0.000 NA 0.000
#> GSM123773 1 0.0458 0.5585 0.984 0.000 0.016 0.000 NA 0.000
#> GSM123777 4 0.7580 0.5076 0.024 0.160 0.208 0.468 NA 0.004
#> GSM123779 3 0.8719 -0.2766 0.128 0.156 0.320 0.140 NA 0.004
#> GSM123782 3 0.7418 0.0529 0.148 0.084 0.400 0.016 NA 0.008
#> GSM123786 3 0.1858 0.7205 0.000 0.000 0.904 0.004 NA 0.000
#> GSM123789 3 0.7914 -0.0795 0.128 0.104 0.388 0.072 NA 0.000
#> GSM123793 4 0.5110 0.3040 0.012 0.000 0.004 0.656 NA 0.096
#> GSM123797 4 0.1686 0.5688 0.012 0.000 0.064 0.924 NA 0.000
#> GSM123729 2 0.0000 1.0000 0.000 1.000 0.000 0.000 NA 0.000
#> GSM123733 2 0.0000 1.0000 0.000 1.000 0.000 0.000 NA 0.000
#> GSM123737 2 0.0000 1.0000 0.000 1.000 0.000 0.000 NA 0.000
#> GSM123741 2 0.0000 1.0000 0.000 1.000 0.000 0.000 NA 0.000
#> GSM123747 2 0.0000 1.0000 0.000 1.000 0.000 0.000 NA 0.000
#> GSM123753 2 0.0000 1.0000 0.000 1.000 0.000 0.000 NA 0.000
#> GSM123759 2 0.0000 1.0000 0.000 1.000 0.000 0.000 NA 0.000
#> GSM123766 2 0.0000 1.0000 0.000 1.000 0.000 0.000 NA 0.000
#> GSM123772 2 0.0000 1.0000 0.000 1.000 0.000 0.000 NA 0.000
#> GSM123775 2 0.0000 1.0000 0.000 1.000 0.000 0.000 NA 0.000
#> GSM123781 2 0.0000 1.0000 0.000 1.000 0.000 0.000 NA 0.000
#> GSM123785 2 0.0000 1.0000 0.000 1.000 0.000 0.000 NA 0.000
#> GSM123788 2 0.0000 1.0000 0.000 1.000 0.000 0.000 NA 0.000
#> GSM123792 2 0.0000 1.0000 0.000 1.000 0.000 0.000 NA 0.000
#> GSM123796 2 0.0000 1.0000 0.000 1.000 0.000 0.000 NA 0.000
#> GSM123731 2 0.0000 1.0000 0.000 1.000 0.000 0.000 NA 0.000
#> GSM123735 2 0.0000 1.0000 0.000 1.000 0.000 0.000 NA 0.000
#> GSM123739 2 0.0000 1.0000 0.000 1.000 0.000 0.000 NA 0.000
#> GSM123743 2 0.0000 1.0000 0.000 1.000 0.000 0.000 NA 0.000
#> GSM123749 2 0.0000 1.0000 0.000 1.000 0.000 0.000 NA 0.000
#> GSM123755 2 0.0000 1.0000 0.000 1.000 0.000 0.000 NA 0.000
#> GSM123768 2 0.0000 1.0000 0.000 1.000 0.000 0.000 NA 0.000
#> GSM123776 2 0.0000 1.0000 0.000 1.000 0.000 0.000 NA 0.000
#> GSM123783 2 0.0000 1.0000 0.000 1.000 0.000 0.000 NA 0.000
#> GSM123790 2 0.0000 1.0000 0.000 1.000 0.000 0.000 NA 0.000
#> GSM123794 2 0.0000 1.0000 0.000 1.000 0.000 0.000 NA 0.000
#> GSM123798 2 0.0000 1.0000 0.000 1.000 0.000 0.000 NA 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) infection(p) agent(p) k
#> MAD:hclust 68 1.71e-15 1.71e-15 1.19e-05 2
#> MAD:hclust 59 5.77e-16 5.77e-16 1.33e-04 3
#> MAD:hclust 60 1.90e-16 1.90e-16 3.75e-04 4
#> MAD:hclust 56 5.29e-15 5.29e-15 2.74e-04 5
#> MAD:hclust 55 1.94e-18 1.94e-18 1.18e-03 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "kmeans"]
# you can also extract it by
# res = res_list["MAD:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4786 0.522 0.522
#> 3 3 0.716 0.819 0.854 0.3684 0.805 0.627
#> 4 4 0.671 0.786 0.829 0.1152 0.893 0.695
#> 5 5 0.722 0.720 0.793 0.0592 0.959 0.850
#> 6 6 0.754 0.735 0.799 0.0335 0.994 0.977
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM123732 1 0 1 1 0
#> GSM123736 1 0 1 1 0
#> GSM123740 1 0 1 1 0
#> GSM123744 1 0 1 1 0
#> GSM123746 1 0 1 1 0
#> GSM123750 1 0 1 1 0
#> GSM123752 1 0 1 1 0
#> GSM123756 1 0 1 1 0
#> GSM123758 1 0 1 1 0
#> GSM123761 1 0 1 1 0
#> GSM123763 1 0 1 1 0
#> GSM123765 1 0 1 1 0
#> GSM123769 1 0 1 1 0
#> GSM123771 1 0 1 1 0
#> GSM123774 1 0 1 1 0
#> GSM123778 1 0 1 1 0
#> GSM123780 1 0 1 1 0
#> GSM123784 1 0 1 1 0
#> GSM123787 1 0 1 1 0
#> GSM123791 1 0 1 1 0
#> GSM123795 1 0 1 1 0
#> GSM123799 1 0 1 1 0
#> GSM123730 1 0 1 1 0
#> GSM123734 1 0 1 1 0
#> GSM123738 1 0 1 1 0
#> GSM123742 1 0 1 1 0
#> GSM123745 1 0 1 1 0
#> GSM123748 1 0 1 1 0
#> GSM123751 1 0 1 1 0
#> GSM123754 1 0 1 1 0
#> GSM123757 1 0 1 1 0
#> GSM123760 1 0 1 1 0
#> GSM123762 1 0 1 1 0
#> GSM123764 1 0 1 1 0
#> GSM123767 1 0 1 1 0
#> GSM123770 1 0 1 1 0
#> GSM123773 1 0 1 1 0
#> GSM123777 1 0 1 1 0
#> GSM123779 1 0 1 1 0
#> GSM123782 1 0 1 1 0
#> GSM123786 1 0 1 1 0
#> GSM123789 1 0 1 1 0
#> GSM123793 1 0 1 1 0
#> GSM123797 1 0 1 1 0
#> GSM123729 2 0 1 0 1
#> GSM123733 2 0 1 0 1
#> GSM123737 2 0 1 0 1
#> GSM123741 2 0 1 0 1
#> GSM123747 2 0 1 0 1
#> GSM123753 2 0 1 0 1
#> GSM123759 2 0 1 0 1
#> GSM123766 2 0 1 0 1
#> GSM123772 2 0 1 0 1
#> GSM123775 2 0 1 0 1
#> GSM123781 2 0 1 0 1
#> GSM123785 2 0 1 0 1
#> GSM123788 2 0 1 0 1
#> GSM123792 2 0 1 0 1
#> GSM123796 2 0 1 0 1
#> GSM123731 2 0 1 0 1
#> GSM123735 2 0 1 0 1
#> GSM123739 2 0 1 0 1
#> GSM123743 2 0 1 0 1
#> GSM123749 2 0 1 0 1
#> GSM123755 2 0 1 0 1
#> GSM123768 2 0 1 0 1
#> GSM123776 2 0 1 0 1
#> GSM123783 2 0 1 0 1
#> GSM123790 2 0 1 0 1
#> GSM123794 2 0 1 0 1
#> GSM123798 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM123732 3 0.5560 0.792 0.300 0.000 0.700
#> GSM123736 3 0.5621 0.788 0.308 0.000 0.692
#> GSM123740 3 0.5621 0.788 0.308 0.000 0.692
#> GSM123744 1 0.5138 0.541 0.748 0.000 0.252
#> GSM123746 1 0.3267 0.727 0.884 0.000 0.116
#> GSM123750 1 0.4235 0.674 0.824 0.000 0.176
#> GSM123752 1 0.4931 0.583 0.768 0.000 0.232
#> GSM123756 1 0.3267 0.727 0.884 0.000 0.116
#> GSM123758 3 0.5560 0.792 0.300 0.000 0.700
#> GSM123761 1 0.3879 0.701 0.848 0.000 0.152
#> GSM123763 1 0.4346 0.704 0.816 0.000 0.184
#> GSM123765 3 0.5560 0.792 0.300 0.000 0.700
#> GSM123769 1 0.3267 0.727 0.884 0.000 0.116
#> GSM123771 1 0.3267 0.727 0.884 0.000 0.116
#> GSM123774 1 0.3340 0.729 0.880 0.000 0.120
#> GSM123778 3 0.5560 0.792 0.300 0.000 0.700
#> GSM123780 3 0.5363 0.788 0.276 0.000 0.724
#> GSM123784 3 0.5560 0.792 0.300 0.000 0.700
#> GSM123787 3 0.5560 0.792 0.300 0.000 0.700
#> GSM123791 3 0.5560 0.792 0.300 0.000 0.700
#> GSM123795 3 0.5621 0.788 0.308 0.000 0.692
#> GSM123799 3 0.5621 0.788 0.308 0.000 0.692
#> GSM123730 3 0.0592 0.671 0.012 0.000 0.988
#> GSM123734 1 0.6180 0.726 0.584 0.000 0.416
#> GSM123738 3 0.0424 0.677 0.008 0.000 0.992
#> GSM123742 1 0.6140 0.732 0.596 0.000 0.404
#> GSM123745 1 0.6140 0.737 0.596 0.000 0.404
#> GSM123748 1 0.6008 0.744 0.628 0.000 0.372
#> GSM123751 1 0.6140 0.737 0.596 0.000 0.404
#> GSM123754 1 0.6140 0.737 0.596 0.000 0.404
#> GSM123757 1 0.3412 0.731 0.876 0.000 0.124
#> GSM123760 1 0.6168 0.726 0.588 0.000 0.412
#> GSM123762 1 0.5760 0.752 0.672 0.000 0.328
#> GSM123764 3 0.1753 0.692 0.048 0.000 0.952
#> GSM123767 1 0.6180 0.726 0.584 0.000 0.416
#> GSM123770 1 0.6140 0.737 0.596 0.000 0.404
#> GSM123773 1 0.6140 0.737 0.596 0.000 0.404
#> GSM123777 3 0.0000 0.679 0.000 0.000 1.000
#> GSM123779 3 0.0592 0.671 0.012 0.000 0.988
#> GSM123782 3 0.1753 0.688 0.048 0.000 0.952
#> GSM123786 3 0.5560 0.792 0.300 0.000 0.700
#> GSM123789 3 0.1860 0.691 0.052 0.000 0.948
#> GSM123793 3 0.0892 0.667 0.020 0.000 0.980
#> GSM123797 3 0.0892 0.667 0.020 0.000 0.980
#> GSM123729 2 0.2066 0.965 0.060 0.940 0.000
#> GSM123733 2 0.1753 0.965 0.048 0.952 0.000
#> GSM123737 2 0.1860 0.965 0.052 0.948 0.000
#> GSM123741 2 0.0892 0.970 0.020 0.980 0.000
#> GSM123747 2 0.1411 0.968 0.036 0.964 0.000
#> GSM123753 2 0.1031 0.970 0.024 0.976 0.000
#> GSM123759 2 0.1163 0.969 0.028 0.972 0.000
#> GSM123766 2 0.0892 0.970 0.020 0.980 0.000
#> GSM123772 2 0.0892 0.970 0.020 0.980 0.000
#> GSM123775 2 0.2261 0.963 0.068 0.932 0.000
#> GSM123781 2 0.1163 0.969 0.028 0.972 0.000
#> GSM123785 2 0.1753 0.965 0.048 0.952 0.000
#> GSM123788 2 0.1643 0.966 0.044 0.956 0.000
#> GSM123792 2 0.1529 0.966 0.040 0.960 0.000
#> GSM123796 2 0.1643 0.966 0.044 0.956 0.000
#> GSM123731 2 0.1289 0.969 0.032 0.968 0.000
#> GSM123735 2 0.2711 0.955 0.088 0.912 0.000
#> GSM123739 2 0.1860 0.965 0.052 0.948 0.000
#> GSM123743 2 0.0000 0.971 0.000 1.000 0.000
#> GSM123749 2 0.1031 0.970 0.024 0.976 0.000
#> GSM123755 2 0.1163 0.969 0.028 0.972 0.000
#> GSM123768 2 0.1163 0.969 0.028 0.972 0.000
#> GSM123776 2 0.2356 0.961 0.072 0.928 0.000
#> GSM123783 2 0.2261 0.963 0.068 0.932 0.000
#> GSM123790 2 0.2711 0.955 0.088 0.912 0.000
#> GSM123794 2 0.2625 0.956 0.084 0.916 0.000
#> GSM123798 2 0.1163 0.969 0.028 0.972 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM123732 3 0.0469 0.860 0.000 0.000 0.988 0.012
#> GSM123736 3 0.2174 0.841 0.020 0.000 0.928 0.052
#> GSM123740 3 0.2174 0.841 0.020 0.000 0.928 0.052
#> GSM123744 3 0.5249 0.552 0.248 0.000 0.708 0.044
#> GSM123746 1 0.3946 0.760 0.812 0.000 0.168 0.020
#> GSM123750 3 0.6009 0.191 0.380 0.000 0.572 0.048
#> GSM123752 3 0.4452 0.576 0.260 0.000 0.732 0.008
#> GSM123756 1 0.3208 0.773 0.848 0.000 0.148 0.004
#> GSM123758 3 0.0469 0.858 0.012 0.000 0.988 0.000
#> GSM123761 1 0.6000 0.460 0.592 0.000 0.356 0.052
#> GSM123763 1 0.7105 0.501 0.556 0.000 0.176 0.268
#> GSM123765 3 0.0469 0.860 0.000 0.000 0.988 0.012
#> GSM123769 1 0.3208 0.773 0.848 0.000 0.148 0.004
#> GSM123771 1 0.3208 0.773 0.848 0.000 0.148 0.004
#> GSM123774 1 0.3157 0.775 0.852 0.000 0.144 0.004
#> GSM123778 3 0.0592 0.858 0.000 0.000 0.984 0.016
#> GSM123780 3 0.1059 0.844 0.012 0.000 0.972 0.016
#> GSM123784 3 0.0592 0.858 0.000 0.000 0.984 0.016
#> GSM123787 3 0.0592 0.858 0.000 0.000 0.984 0.016
#> GSM123791 3 0.0188 0.860 0.000 0.000 0.996 0.004
#> GSM123795 3 0.2174 0.841 0.020 0.000 0.928 0.052
#> GSM123799 3 0.2174 0.841 0.020 0.000 0.928 0.052
#> GSM123730 4 0.6794 0.815 0.136 0.000 0.280 0.584
#> GSM123734 4 0.5244 0.394 0.388 0.000 0.012 0.600
#> GSM123738 4 0.6479 0.810 0.140 0.000 0.224 0.636
#> GSM123742 1 0.6453 0.265 0.560 0.000 0.080 0.360
#> GSM123745 1 0.2255 0.745 0.920 0.000 0.012 0.068
#> GSM123748 1 0.3149 0.758 0.880 0.000 0.032 0.088
#> GSM123751 1 0.2402 0.740 0.912 0.000 0.012 0.076
#> GSM123754 1 0.2402 0.742 0.912 0.000 0.012 0.076
#> GSM123757 1 0.2973 0.775 0.856 0.000 0.144 0.000
#> GSM123760 4 0.6696 0.102 0.428 0.000 0.088 0.484
#> GSM123762 1 0.5292 0.621 0.724 0.000 0.060 0.216
#> GSM123764 4 0.6837 0.729 0.104 0.000 0.392 0.504
#> GSM123767 1 0.3718 0.640 0.820 0.000 0.012 0.168
#> GSM123770 1 0.1059 0.763 0.972 0.000 0.012 0.016
#> GSM123773 1 0.2402 0.742 0.912 0.000 0.012 0.076
#> GSM123777 4 0.6813 0.810 0.132 0.000 0.292 0.576
#> GSM123779 4 0.6815 0.814 0.136 0.000 0.284 0.580
#> GSM123782 4 0.6830 0.737 0.104 0.000 0.388 0.508
#> GSM123786 3 0.0592 0.858 0.000 0.000 0.984 0.016
#> GSM123789 4 0.6766 0.746 0.100 0.000 0.380 0.520
#> GSM123793 4 0.6084 0.805 0.120 0.000 0.204 0.676
#> GSM123797 4 0.6479 0.810 0.140 0.000 0.224 0.636
#> GSM123729 2 0.3978 0.887 0.012 0.796 0.000 0.192
#> GSM123733 2 0.3311 0.895 0.000 0.828 0.000 0.172
#> GSM123737 2 0.3764 0.893 0.012 0.816 0.000 0.172
#> GSM123741 2 0.0000 0.912 0.000 1.000 0.000 0.000
#> GSM123747 2 0.2216 0.904 0.000 0.908 0.000 0.092
#> GSM123753 2 0.0188 0.912 0.000 0.996 0.000 0.004
#> GSM123759 2 0.0336 0.911 0.000 0.992 0.000 0.008
#> GSM123766 2 0.0188 0.912 0.000 0.996 0.000 0.004
#> GSM123772 2 0.0188 0.912 0.000 0.996 0.000 0.004
#> GSM123775 2 0.4137 0.877 0.012 0.780 0.000 0.208
#> GSM123781 2 0.0336 0.911 0.000 0.992 0.000 0.008
#> GSM123785 2 0.3311 0.895 0.000 0.828 0.000 0.172
#> GSM123788 2 0.3311 0.895 0.000 0.828 0.000 0.172
#> GSM123792 2 0.3266 0.896 0.000 0.832 0.000 0.168
#> GSM123796 2 0.3311 0.895 0.000 0.828 0.000 0.172
#> GSM123731 2 0.0336 0.911 0.000 0.992 0.000 0.008
#> GSM123735 2 0.4134 0.868 0.000 0.740 0.000 0.260
#> GSM123739 2 0.3764 0.893 0.012 0.816 0.000 0.172
#> GSM123743 2 0.1389 0.914 0.000 0.952 0.000 0.048
#> GSM123749 2 0.0188 0.912 0.000 0.996 0.000 0.004
#> GSM123755 2 0.0336 0.911 0.000 0.992 0.000 0.008
#> GSM123768 2 0.0336 0.911 0.000 0.992 0.000 0.008
#> GSM123776 2 0.4284 0.873 0.012 0.764 0.000 0.224
#> GSM123783 2 0.3032 0.883 0.008 0.868 0.000 0.124
#> GSM123790 2 0.4277 0.859 0.000 0.720 0.000 0.280
#> GSM123794 2 0.4222 0.863 0.000 0.728 0.000 0.272
#> GSM123798 2 0.0336 0.911 0.000 0.992 0.000 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM123732 3 0.0451 0.893721 0.000 0.000 0.988 0.004 0.008
#> GSM123736 3 0.2694 0.867945 0.008 0.000 0.892 0.032 0.068
#> GSM123740 3 0.2694 0.867945 0.008 0.000 0.892 0.032 0.068
#> GSM123744 3 0.4394 0.723320 0.100 0.000 0.764 0.000 0.136
#> GSM123746 1 0.3336 0.789368 0.844 0.000 0.060 0.000 0.096
#> GSM123750 3 0.5927 0.403613 0.236 0.000 0.592 0.000 0.172
#> GSM123752 3 0.3670 0.784878 0.112 0.000 0.820 0.000 0.068
#> GSM123756 1 0.2708 0.829501 0.884 0.000 0.044 0.000 0.072
#> GSM123758 3 0.0992 0.889103 0.008 0.000 0.968 0.000 0.024
#> GSM123761 5 0.6844 0.092503 0.376 0.000 0.212 0.008 0.404
#> GSM123763 5 0.5611 0.322968 0.344 0.000 0.060 0.012 0.584
#> GSM123765 3 0.0451 0.893721 0.000 0.000 0.988 0.004 0.008
#> GSM123769 1 0.2708 0.829501 0.884 0.000 0.044 0.000 0.072
#> GSM123771 1 0.2708 0.829501 0.884 0.000 0.044 0.000 0.072
#> GSM123774 1 0.2370 0.838613 0.904 0.000 0.040 0.000 0.056
#> GSM123778 3 0.0451 0.893721 0.000 0.000 0.988 0.004 0.008
#> GSM123780 3 0.0968 0.883172 0.004 0.000 0.972 0.012 0.012
#> GSM123784 3 0.0451 0.893721 0.000 0.000 0.988 0.004 0.008
#> GSM123787 3 0.0451 0.893721 0.000 0.000 0.988 0.004 0.008
#> GSM123791 3 0.0162 0.893675 0.000 0.000 0.996 0.000 0.004
#> GSM123795 3 0.2775 0.866054 0.008 0.000 0.888 0.036 0.068
#> GSM123799 3 0.2694 0.867945 0.008 0.000 0.892 0.032 0.068
#> GSM123730 4 0.6865 0.807196 0.044 0.000 0.108 0.440 0.408
#> GSM123734 4 0.6460 0.593852 0.180 0.000 0.000 0.412 0.408
#> GSM123738 4 0.6318 0.782215 0.044 0.000 0.056 0.468 0.432
#> GSM123742 5 0.4854 0.406766 0.340 0.000 0.028 0.004 0.628
#> GSM123745 1 0.1907 0.837325 0.928 0.000 0.000 0.028 0.044
#> GSM123748 1 0.2864 0.770455 0.852 0.000 0.012 0.000 0.136
#> GSM123751 1 0.2209 0.826991 0.912 0.000 0.000 0.032 0.056
#> GSM123754 1 0.1907 0.837325 0.928 0.000 0.000 0.028 0.044
#> GSM123757 1 0.1043 0.849185 0.960 0.000 0.040 0.000 0.000
#> GSM123760 5 0.4829 0.369884 0.272 0.000 0.032 0.012 0.684
#> GSM123762 5 0.5146 0.219045 0.432 0.000 0.020 0.012 0.536
#> GSM123764 5 0.6331 0.018704 0.040 0.000 0.240 0.112 0.608
#> GSM123767 1 0.3780 0.681322 0.808 0.000 0.000 0.060 0.132
#> GSM123770 1 0.0451 0.850608 0.988 0.000 0.000 0.004 0.008
#> GSM123773 1 0.1907 0.837325 0.928 0.000 0.000 0.028 0.044
#> GSM123777 4 0.6961 0.799303 0.044 0.000 0.120 0.436 0.400
#> GSM123779 4 0.7133 0.780688 0.052 0.000 0.128 0.412 0.408
#> GSM123782 5 0.6342 -0.000315 0.040 0.000 0.228 0.120 0.612
#> GSM123786 3 0.0451 0.893721 0.000 0.000 0.988 0.004 0.008
#> GSM123789 5 0.6239 -0.036085 0.040 0.000 0.212 0.120 0.628
#> GSM123793 5 0.6204 -0.803349 0.040 0.000 0.052 0.432 0.476
#> GSM123797 4 0.6313 0.786120 0.044 0.000 0.056 0.476 0.424
#> GSM123729 2 0.4878 0.793725 0.000 0.676 0.000 0.264 0.060
#> GSM123733 2 0.3816 0.806007 0.000 0.696 0.000 0.304 0.000
#> GSM123737 2 0.4878 0.795913 0.000 0.676 0.000 0.264 0.060
#> GSM123741 2 0.0162 0.840416 0.000 0.996 0.000 0.004 0.000
#> GSM123747 2 0.3210 0.821717 0.000 0.788 0.000 0.212 0.000
#> GSM123753 2 0.0000 0.840028 0.000 1.000 0.000 0.000 0.000
#> GSM123759 2 0.0162 0.839297 0.000 0.996 0.000 0.004 0.000
#> GSM123766 2 0.0162 0.840416 0.000 0.996 0.000 0.004 0.000
#> GSM123772 2 0.0290 0.840557 0.000 0.992 0.000 0.008 0.000
#> GSM123775 2 0.4983 0.778573 0.000 0.664 0.000 0.272 0.064
#> GSM123781 2 0.0162 0.839297 0.000 0.996 0.000 0.004 0.000
#> GSM123785 2 0.3816 0.806007 0.000 0.696 0.000 0.304 0.000
#> GSM123788 2 0.3816 0.806007 0.000 0.696 0.000 0.304 0.000
#> GSM123792 2 0.3816 0.806007 0.000 0.696 0.000 0.304 0.000
#> GSM123796 2 0.3816 0.806007 0.000 0.696 0.000 0.304 0.000
#> GSM123731 2 0.0451 0.839166 0.000 0.988 0.000 0.008 0.004
#> GSM123735 2 0.4331 0.772137 0.000 0.596 0.000 0.400 0.004
#> GSM123739 2 0.4878 0.795913 0.000 0.676 0.000 0.264 0.060
#> GSM123743 2 0.1608 0.844337 0.000 0.928 0.000 0.072 0.000
#> GSM123749 2 0.0000 0.840028 0.000 1.000 0.000 0.000 0.000
#> GSM123755 2 0.0162 0.839297 0.000 0.996 0.000 0.004 0.000
#> GSM123768 2 0.0162 0.839297 0.000 0.996 0.000 0.004 0.000
#> GSM123776 2 0.5342 0.754873 0.000 0.612 0.000 0.312 0.076
#> GSM123783 2 0.3284 0.800764 0.000 0.828 0.000 0.148 0.024
#> GSM123790 2 0.4268 0.748717 0.000 0.556 0.000 0.444 0.000
#> GSM123794 2 0.4182 0.773629 0.000 0.600 0.000 0.400 0.000
#> GSM123798 2 0.0162 0.839297 0.000 0.996 0.000 0.004 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM123732 3 0.0000 0.841 0.000 0.000 1.000 0.000 NA 0.000
#> GSM123736 3 0.4403 0.797 0.000 0.000 0.760 0.096 NA 0.032
#> GSM123740 3 0.4403 0.797 0.000 0.000 0.760 0.096 NA 0.032
#> GSM123744 3 0.5673 0.655 0.044 0.000 0.632 0.000 NA 0.152
#> GSM123746 1 0.4483 0.728 0.728 0.000 0.008 0.000 NA 0.144
#> GSM123750 3 0.6698 0.457 0.096 0.000 0.516 0.000 NA 0.216
#> GSM123752 3 0.5274 0.713 0.076 0.000 0.688 0.000 NA 0.080
#> GSM123756 1 0.3791 0.801 0.788 0.000 0.004 0.000 NA 0.116
#> GSM123758 3 0.2398 0.828 0.000 0.000 0.876 0.000 NA 0.020
#> GSM123761 6 0.5612 0.475 0.148 0.000 0.044 0.000 NA 0.640
#> GSM123763 6 0.4990 0.566 0.132 0.000 0.012 0.040 NA 0.728
#> GSM123765 3 0.0000 0.841 0.000 0.000 1.000 0.000 NA 0.000
#> GSM123769 1 0.3791 0.801 0.788 0.000 0.004 0.000 NA 0.116
#> GSM123771 1 0.3791 0.801 0.788 0.000 0.004 0.000 NA 0.116
#> GSM123774 1 0.3554 0.810 0.808 0.000 0.004 0.000 NA 0.108
#> GSM123778 3 0.0000 0.841 0.000 0.000 1.000 0.000 NA 0.000
#> GSM123780 3 0.1592 0.797 0.000 0.000 0.940 0.008 NA 0.032
#> GSM123784 3 0.0000 0.841 0.000 0.000 1.000 0.000 NA 0.000
#> GSM123787 3 0.0000 0.841 0.000 0.000 1.000 0.000 NA 0.000
#> GSM123791 3 0.0260 0.841 0.000 0.000 0.992 0.000 NA 0.000
#> GSM123795 3 0.4448 0.795 0.000 0.000 0.756 0.100 NA 0.032
#> GSM123799 3 0.4403 0.797 0.000 0.000 0.760 0.096 NA 0.032
#> GSM123730 4 0.5144 0.704 0.020 0.000 0.068 0.732 NA 0.080
#> GSM123734 4 0.4672 0.591 0.168 0.000 0.000 0.728 NA 0.044
#> GSM123738 4 0.1078 0.736 0.000 0.000 0.016 0.964 NA 0.012
#> GSM123742 6 0.5031 0.551 0.224 0.000 0.008 0.064 NA 0.680
#> GSM123745 1 0.1780 0.826 0.932 0.000 0.000 0.028 NA 0.028
#> GSM123748 1 0.3374 0.681 0.772 0.000 0.000 0.000 NA 0.208
#> GSM123751 1 0.1760 0.829 0.936 0.000 0.004 0.028 NA 0.020
#> GSM123754 1 0.1116 0.838 0.960 0.000 0.004 0.028 NA 0.000
#> GSM123757 1 0.1793 0.841 0.928 0.000 0.004 0.000 NA 0.036
#> GSM123760 6 0.4528 0.554 0.168 0.000 0.012 0.084 NA 0.732
#> GSM123762 6 0.4795 0.563 0.148 0.000 0.000 0.040 NA 0.724
#> GSM123764 6 0.7129 0.332 0.016 0.000 0.196 0.160 NA 0.508
#> GSM123767 1 0.2114 0.796 0.904 0.000 0.000 0.076 NA 0.008
#> GSM123770 1 0.0291 0.844 0.992 0.000 0.004 0.000 NA 0.004
#> GSM123773 1 0.1116 0.838 0.960 0.000 0.004 0.028 NA 0.000
#> GSM123777 4 0.5536 0.662 0.004 0.000 0.144 0.676 NA 0.076
#> GSM123779 4 0.6822 0.560 0.032 0.000 0.136 0.576 NA 0.148
#> GSM123782 6 0.7264 0.312 0.016 0.000 0.212 0.164 NA 0.484
#> GSM123786 3 0.0000 0.841 0.000 0.000 1.000 0.000 NA 0.000
#> GSM123789 6 0.7269 0.299 0.016 0.000 0.220 0.164 NA 0.480
#> GSM123793 4 0.3146 0.685 0.000 0.000 0.012 0.848 NA 0.080
#> GSM123797 4 0.0748 0.738 0.000 0.000 0.016 0.976 NA 0.004
#> GSM123729 2 0.5067 0.735 0.004 0.612 0.000 0.012 NA 0.060
#> GSM123733 2 0.3531 0.769 0.000 0.672 0.000 0.000 NA 0.000
#> GSM123737 2 0.5020 0.743 0.004 0.624 0.000 0.012 NA 0.060
#> GSM123741 2 0.0000 0.812 0.000 1.000 0.000 0.000 NA 0.000
#> GSM123747 2 0.2762 0.789 0.000 0.804 0.000 0.000 NA 0.000
#> GSM123753 2 0.0000 0.812 0.000 1.000 0.000 0.000 NA 0.000
#> GSM123759 2 0.0146 0.812 0.000 0.996 0.000 0.000 NA 0.004
#> GSM123766 2 0.0000 0.812 0.000 1.000 0.000 0.000 NA 0.000
#> GSM123772 2 0.0146 0.812 0.000 0.996 0.000 0.000 NA 0.000
#> GSM123775 2 0.5133 0.718 0.004 0.604 0.000 0.012 NA 0.064
#> GSM123781 2 0.0000 0.812 0.000 1.000 0.000 0.000 NA 0.000
#> GSM123785 2 0.3515 0.769 0.000 0.676 0.000 0.000 NA 0.000
#> GSM123788 2 0.3531 0.769 0.000 0.672 0.000 0.000 NA 0.000
#> GSM123792 2 0.3515 0.770 0.000 0.676 0.000 0.000 NA 0.000
#> GSM123796 2 0.3515 0.770 0.000 0.676 0.000 0.000 NA 0.000
#> GSM123731 2 0.0725 0.812 0.000 0.976 0.000 0.000 NA 0.012
#> GSM123735 2 0.4311 0.729 0.004 0.556 0.000 0.008 NA 0.004
#> GSM123739 2 0.5020 0.743 0.004 0.624 0.000 0.012 NA 0.060
#> GSM123743 2 0.1610 0.816 0.000 0.916 0.000 0.000 NA 0.000
#> GSM123749 2 0.0000 0.812 0.000 1.000 0.000 0.000 NA 0.000
#> GSM123755 2 0.0146 0.812 0.000 0.996 0.000 0.000 NA 0.004
#> GSM123768 2 0.0146 0.812 0.000 0.996 0.000 0.000 NA 0.004
#> GSM123776 2 0.5217 0.700 0.004 0.564 0.000 0.012 NA 0.060
#> GSM123783 2 0.3637 0.760 0.000 0.788 0.000 0.008 NA 0.040
#> GSM123790 2 0.3867 0.700 0.000 0.512 0.000 0.000 NA 0.000
#> GSM123794 2 0.3854 0.715 0.000 0.536 0.000 0.000 NA 0.000
#> GSM123798 2 0.0000 0.812 0.000 1.000 0.000 0.000 NA 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) infection(p) agent(p) k
#> MAD:kmeans 71 3.82e-16 3.82e-16 6.04e-06 2
#> MAD:kmeans 71 1.05e-14 1.05e-14 7.76e-06 3
#> MAD:kmeans 66 1.35e-19 1.35e-19 9.64e-05 4
#> MAD:kmeans 61 7.87e-18 7.87e-18 2.99e-04 5
#> MAD:kmeans 66 4.79e-18 4.79e-18 2.91e-04 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "skmeans"]
# you can also extract it by
# res = res_list["MAD:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.999 0.999 0.4789 0.522 0.522
#> 3 3 0.826 0.870 0.933 0.4017 0.806 0.628
#> 4 4 0.765 0.773 0.870 0.0885 0.911 0.741
#> 5 5 0.739 0.702 0.789 0.0483 1.000 1.000
#> 6 6 0.662 0.592 0.712 0.0386 0.972 0.896
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
#> GSM123732 1 0.00 0.999 1.000 0.000
#> GSM123736 1 0.00 0.999 1.000 0.000
#> GSM123740 1 0.00 0.999 1.000 0.000
#> GSM123744 1 0.00 0.999 1.000 0.000
#> GSM123746 1 0.00 0.999 1.000 0.000
#> GSM123750 1 0.00 0.999 1.000 0.000
#> GSM123752 1 0.00 0.999 1.000 0.000
#> GSM123756 1 0.00 0.999 1.000 0.000
#> GSM123758 1 0.00 0.999 1.000 0.000
#> GSM123761 1 0.00 0.999 1.000 0.000
#> GSM123763 1 0.00 0.999 1.000 0.000
#> GSM123765 1 0.00 0.999 1.000 0.000
#> GSM123769 1 0.00 0.999 1.000 0.000
#> GSM123771 1 0.00 0.999 1.000 0.000
#> GSM123774 1 0.00 0.999 1.000 0.000
#> GSM123778 1 0.00 0.999 1.000 0.000
#> GSM123780 1 0.00 0.999 1.000 0.000
#> GSM123784 1 0.00 0.999 1.000 0.000
#> GSM123787 1 0.00 0.999 1.000 0.000
#> GSM123791 1 0.00 0.999 1.000 0.000
#> GSM123795 1 0.00 0.999 1.000 0.000
#> GSM123799 1 0.00 0.999 1.000 0.000
#> GSM123730 1 0.26 0.954 0.956 0.044
#> GSM123734 1 0.00 0.999 1.000 0.000
#> GSM123738 1 0.00 0.999 1.000 0.000
#> GSM123742 1 0.00 0.999 1.000 0.000
#> GSM123745 1 0.00 0.999 1.000 0.000
#> GSM123748 1 0.00 0.999 1.000 0.000
#> GSM123751 1 0.00 0.999 1.000 0.000
#> GSM123754 1 0.00 0.999 1.000 0.000
#> GSM123757 1 0.00 0.999 1.000 0.000
#> GSM123760 1 0.00 0.999 1.000 0.000
#> GSM123762 1 0.00 0.999 1.000 0.000
#> GSM123764 1 0.00 0.999 1.000 0.000
#> GSM123767 1 0.00 0.999 1.000 0.000
#> GSM123770 1 0.00 0.999 1.000 0.000
#> GSM123773 1 0.00 0.999 1.000 0.000
#> GSM123777 1 0.00 0.999 1.000 0.000
#> GSM123779 1 0.00 0.999 1.000 0.000
#> GSM123782 1 0.00 0.999 1.000 0.000
#> GSM123786 1 0.00 0.999 1.000 0.000
#> GSM123789 1 0.00 0.999 1.000 0.000
#> GSM123793 1 0.00 0.999 1.000 0.000
#> GSM123797 1 0.00 0.999 1.000 0.000
#> GSM123729 2 0.00 1.000 0.000 1.000
#> GSM123733 2 0.00 1.000 0.000 1.000
#> GSM123737 2 0.00 1.000 0.000 1.000
#> GSM123741 2 0.00 1.000 0.000 1.000
#> GSM123747 2 0.00 1.000 0.000 1.000
#> GSM123753 2 0.00 1.000 0.000 1.000
#> GSM123759 2 0.00 1.000 0.000 1.000
#> GSM123766 2 0.00 1.000 0.000 1.000
#> GSM123772 2 0.00 1.000 0.000 1.000
#> GSM123775 2 0.00 1.000 0.000 1.000
#> GSM123781 2 0.00 1.000 0.000 1.000
#> GSM123785 2 0.00 1.000 0.000 1.000
#> GSM123788 2 0.00 1.000 0.000 1.000
#> GSM123792 2 0.00 1.000 0.000 1.000
#> GSM123796 2 0.00 1.000 0.000 1.000
#> GSM123731 2 0.00 1.000 0.000 1.000
#> GSM123735 2 0.00 1.000 0.000 1.000
#> GSM123739 2 0.00 1.000 0.000 1.000
#> GSM123743 2 0.00 1.000 0.000 1.000
#> GSM123749 2 0.00 1.000 0.000 1.000
#> GSM123755 2 0.00 1.000 0.000 1.000
#> GSM123768 2 0.00 1.000 0.000 1.000
#> GSM123776 2 0.00 1.000 0.000 1.000
#> GSM123783 2 0.00 1.000 0.000 1.000
#> GSM123790 2 0.00 1.000 0.000 1.000
#> GSM123794 2 0.00 1.000 0.000 1.000
#> GSM123798 2 0.00 1.000 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM123732 3 0.0000 0.866 0.000 0 1.000
#> GSM123736 3 0.0892 0.862 0.020 0 0.980
#> GSM123740 3 0.0592 0.864 0.012 0 0.988
#> GSM123744 1 0.6215 0.384 0.572 0 0.428
#> GSM123746 1 0.2959 0.856 0.900 0 0.100
#> GSM123750 1 0.5363 0.673 0.724 0 0.276
#> GSM123752 1 0.5678 0.613 0.684 0 0.316
#> GSM123756 1 0.2066 0.879 0.940 0 0.060
#> GSM123758 3 0.3412 0.778 0.124 0 0.876
#> GSM123761 1 0.3879 0.816 0.848 0 0.152
#> GSM123763 1 0.3619 0.838 0.864 0 0.136
#> GSM123765 3 0.0000 0.866 0.000 0 1.000
#> GSM123769 1 0.2066 0.879 0.940 0 0.060
#> GSM123771 1 0.2066 0.879 0.940 0 0.060
#> GSM123774 1 0.1860 0.882 0.948 0 0.052
#> GSM123778 3 0.0000 0.866 0.000 0 1.000
#> GSM123780 3 0.0892 0.861 0.020 0 0.980
#> GSM123784 3 0.0000 0.866 0.000 0 1.000
#> GSM123787 3 0.0000 0.866 0.000 0 1.000
#> GSM123791 3 0.0000 0.866 0.000 0 1.000
#> GSM123795 3 0.1753 0.849 0.048 0 0.952
#> GSM123799 3 0.0747 0.863 0.016 0 0.984
#> GSM123730 3 0.5397 0.706 0.280 0 0.720
#> GSM123734 1 0.1529 0.862 0.960 0 0.040
#> GSM123738 3 0.4452 0.788 0.192 0 0.808
#> GSM123742 1 0.0747 0.883 0.984 0 0.016
#> GSM123745 1 0.0000 0.880 1.000 0 0.000
#> GSM123748 1 0.0424 0.882 0.992 0 0.008
#> GSM123751 1 0.0000 0.880 1.000 0 0.000
#> GSM123754 1 0.0000 0.880 1.000 0 0.000
#> GSM123757 1 0.1860 0.882 0.948 0 0.052
#> GSM123760 1 0.2066 0.848 0.940 0 0.060
#> GSM123762 1 0.1163 0.884 0.972 0 0.028
#> GSM123764 3 0.5363 0.706 0.276 0 0.724
#> GSM123767 1 0.0000 0.880 1.000 0 0.000
#> GSM123770 1 0.0237 0.881 0.996 0 0.004
#> GSM123773 1 0.0000 0.880 1.000 0 0.000
#> GSM123777 3 0.3192 0.829 0.112 0 0.888
#> GSM123779 3 0.6168 0.487 0.412 0 0.588
#> GSM123782 1 0.6291 -0.103 0.532 0 0.468
#> GSM123786 3 0.0000 0.866 0.000 0 1.000
#> GSM123789 3 0.5650 0.665 0.312 0 0.688
#> GSM123793 3 0.5968 0.595 0.364 0 0.636
#> GSM123797 3 0.5431 0.707 0.284 0 0.716
#> GSM123729 2 0.0000 1.000 0.000 1 0.000
#> GSM123733 2 0.0000 1.000 0.000 1 0.000
#> GSM123737 2 0.0000 1.000 0.000 1 0.000
#> GSM123741 2 0.0000 1.000 0.000 1 0.000
#> GSM123747 2 0.0000 1.000 0.000 1 0.000
#> GSM123753 2 0.0000 1.000 0.000 1 0.000
#> GSM123759 2 0.0000 1.000 0.000 1 0.000
#> GSM123766 2 0.0000 1.000 0.000 1 0.000
#> GSM123772 2 0.0000 1.000 0.000 1 0.000
#> GSM123775 2 0.0000 1.000 0.000 1 0.000
#> GSM123781 2 0.0000 1.000 0.000 1 0.000
#> GSM123785 2 0.0000 1.000 0.000 1 0.000
#> GSM123788 2 0.0000 1.000 0.000 1 0.000
#> GSM123792 2 0.0000 1.000 0.000 1 0.000
#> GSM123796 2 0.0000 1.000 0.000 1 0.000
#> GSM123731 2 0.0000 1.000 0.000 1 0.000
#> GSM123735 2 0.0000 1.000 0.000 1 0.000
#> GSM123739 2 0.0000 1.000 0.000 1 0.000
#> GSM123743 2 0.0000 1.000 0.000 1 0.000
#> GSM123749 2 0.0000 1.000 0.000 1 0.000
#> GSM123755 2 0.0000 1.000 0.000 1 0.000
#> GSM123768 2 0.0000 1.000 0.000 1 0.000
#> GSM123776 2 0.0000 1.000 0.000 1 0.000
#> GSM123783 2 0.0000 1.000 0.000 1 0.000
#> GSM123790 2 0.0000 1.000 0.000 1 0.000
#> GSM123794 2 0.0000 1.000 0.000 1 0.000
#> GSM123798 2 0.0000 1.000 0.000 1 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM123732 3 0.1489 0.8404 0.004 0.000 0.952 0.044
#> GSM123736 3 0.3229 0.8207 0.048 0.000 0.880 0.072
#> GSM123740 3 0.2996 0.8244 0.044 0.000 0.892 0.064
#> GSM123744 3 0.6426 0.3018 0.352 0.000 0.568 0.080
#> GSM123746 1 0.3088 0.7147 0.888 0.000 0.060 0.052
#> GSM123750 1 0.6374 0.3245 0.556 0.000 0.372 0.072
#> GSM123752 1 0.6235 0.1603 0.524 0.000 0.420 0.056
#> GSM123756 1 0.0657 0.7410 0.984 0.000 0.012 0.004
#> GSM123758 3 0.3107 0.8011 0.080 0.000 0.884 0.036
#> GSM123761 1 0.6298 0.4542 0.632 0.000 0.268 0.100
#> GSM123763 1 0.6873 0.3383 0.580 0.000 0.148 0.272
#> GSM123765 3 0.2480 0.8347 0.008 0.000 0.904 0.088
#> GSM123769 1 0.0927 0.7403 0.976 0.000 0.016 0.008
#> GSM123771 1 0.0524 0.7414 0.988 0.000 0.008 0.004
#> GSM123774 1 0.0188 0.7413 0.996 0.000 0.000 0.004
#> GSM123778 3 0.1743 0.8406 0.004 0.000 0.940 0.056
#> GSM123780 3 0.4072 0.6568 0.000 0.000 0.748 0.252
#> GSM123784 3 0.2814 0.8072 0.000 0.000 0.868 0.132
#> GSM123787 3 0.1557 0.8403 0.000 0.000 0.944 0.056
#> GSM123791 3 0.2124 0.8354 0.008 0.000 0.924 0.068
#> GSM123795 3 0.4990 0.7022 0.060 0.000 0.756 0.184
#> GSM123799 3 0.2830 0.8287 0.040 0.000 0.900 0.060
#> GSM123730 4 0.3700 0.6986 0.036 0.008 0.096 0.860
#> GSM123734 4 0.5353 0.1518 0.432 0.000 0.012 0.556
#> GSM123738 4 0.5478 0.6275 0.056 0.000 0.248 0.696
#> GSM123742 1 0.6264 0.3014 0.560 0.000 0.064 0.376
#> GSM123745 1 0.3649 0.6551 0.796 0.000 0.000 0.204
#> GSM123748 1 0.2654 0.7263 0.888 0.000 0.004 0.108
#> GSM123751 1 0.3528 0.6729 0.808 0.000 0.000 0.192
#> GSM123754 1 0.3074 0.6973 0.848 0.000 0.000 0.152
#> GSM123757 1 0.1109 0.7415 0.968 0.000 0.004 0.028
#> GSM123760 4 0.6655 0.0507 0.440 0.000 0.084 0.476
#> GSM123762 1 0.5144 0.5851 0.732 0.000 0.052 0.216
#> GSM123764 4 0.5935 0.5709 0.080 0.000 0.256 0.664
#> GSM123767 1 0.4477 0.4934 0.688 0.000 0.000 0.312
#> GSM123770 1 0.1302 0.7377 0.956 0.000 0.000 0.044
#> GSM123773 1 0.3123 0.6889 0.844 0.000 0.000 0.156
#> GSM123777 4 0.4621 0.5479 0.008 0.000 0.284 0.708
#> GSM123779 4 0.4599 0.6906 0.112 0.000 0.088 0.800
#> GSM123782 4 0.5994 0.6433 0.152 0.000 0.156 0.692
#> GSM123786 3 0.2345 0.8272 0.000 0.000 0.900 0.100
#> GSM123789 4 0.5454 0.6746 0.096 0.000 0.172 0.732
#> GSM123793 4 0.5113 0.7085 0.088 0.000 0.152 0.760
#> GSM123797 4 0.5143 0.6963 0.076 0.000 0.172 0.752
#> GSM123729 2 0.0336 0.9930 0.000 0.992 0.000 0.008
#> GSM123733 2 0.0188 0.9942 0.000 0.996 0.000 0.004
#> GSM123737 2 0.0188 0.9942 0.000 0.996 0.000 0.004
#> GSM123741 2 0.0000 0.9948 0.000 1.000 0.000 0.000
#> GSM123747 2 0.0336 0.9941 0.000 0.992 0.000 0.008
#> GSM123753 2 0.0188 0.9946 0.000 0.996 0.000 0.004
#> GSM123759 2 0.0188 0.9946 0.000 0.996 0.000 0.004
#> GSM123766 2 0.0000 0.9948 0.000 1.000 0.000 0.000
#> GSM123772 2 0.0000 0.9948 0.000 1.000 0.000 0.000
#> GSM123775 2 0.0336 0.9940 0.000 0.992 0.000 0.008
#> GSM123781 2 0.0336 0.9940 0.000 0.992 0.000 0.008
#> GSM123785 2 0.0188 0.9942 0.000 0.996 0.000 0.004
#> GSM123788 2 0.0188 0.9942 0.000 0.996 0.000 0.004
#> GSM123792 2 0.0336 0.9937 0.000 0.992 0.000 0.008
#> GSM123796 2 0.0188 0.9942 0.000 0.996 0.000 0.004
#> GSM123731 2 0.0188 0.9946 0.000 0.996 0.000 0.004
#> GSM123735 2 0.0188 0.9941 0.000 0.996 0.000 0.004
#> GSM123739 2 0.0336 0.9930 0.000 0.992 0.000 0.008
#> GSM123743 2 0.0000 0.9948 0.000 1.000 0.000 0.000
#> GSM123749 2 0.0188 0.9946 0.000 0.996 0.000 0.004
#> GSM123755 2 0.0188 0.9946 0.000 0.996 0.000 0.004
#> GSM123768 2 0.0188 0.9946 0.000 0.996 0.000 0.004
#> GSM123776 2 0.1388 0.9629 0.028 0.960 0.000 0.012
#> GSM123783 2 0.0336 0.9940 0.000 0.992 0.000 0.008
#> GSM123790 2 0.0336 0.9924 0.000 0.992 0.000 0.008
#> GSM123794 2 0.0336 0.9932 0.000 0.992 0.000 0.008
#> GSM123798 2 0.0336 0.9940 0.000 0.992 0.000 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM123732 3 0.1393 0.74881 0.008 0.000 0.956 0.012 NA
#> GSM123736 3 0.5684 0.68174 0.048 0.000 0.700 0.108 NA
#> GSM123740 3 0.5307 0.69741 0.032 0.000 0.716 0.080 NA
#> GSM123744 3 0.7326 0.14034 0.332 0.000 0.408 0.032 NA
#> GSM123746 1 0.4791 0.60918 0.748 0.000 0.064 0.020 NA
#> GSM123750 1 0.7159 0.33586 0.476 0.000 0.228 0.032 NA
#> GSM123752 1 0.6642 0.22815 0.492 0.000 0.304 0.008 NA
#> GSM123756 1 0.1041 0.66639 0.964 0.000 0.004 0.000 NA
#> GSM123758 3 0.4363 0.71591 0.072 0.000 0.792 0.020 NA
#> GSM123761 1 0.6824 0.44311 0.536 0.000 0.116 0.052 NA
#> GSM123763 1 0.7990 0.15975 0.396 0.000 0.116 0.176 NA
#> GSM123765 3 0.3504 0.74283 0.004 0.000 0.840 0.064 NA
#> GSM123769 1 0.2054 0.66620 0.916 0.000 0.008 0.004 NA
#> GSM123771 1 0.2237 0.66354 0.904 0.000 0.004 0.008 NA
#> GSM123774 1 0.0510 0.66412 0.984 0.000 0.000 0.000 NA
#> GSM123778 3 0.2459 0.74406 0.004 0.000 0.904 0.052 NA
#> GSM123780 3 0.5470 0.61210 0.012 0.000 0.684 0.180 NA
#> GSM123784 3 0.3390 0.72028 0.000 0.000 0.840 0.100 NA
#> GSM123787 3 0.3432 0.73426 0.000 0.000 0.828 0.040 NA
#> GSM123791 3 0.4923 0.69266 0.020 0.000 0.736 0.068 NA
#> GSM123795 3 0.6820 0.59342 0.072 0.000 0.592 0.152 NA
#> GSM123799 3 0.5297 0.70451 0.040 0.000 0.716 0.064 NA
#> GSM123730 4 0.3445 0.62673 0.048 0.000 0.032 0.860 NA
#> GSM123734 4 0.6232 0.30596 0.300 0.000 0.008 0.552 NA
#> GSM123738 4 0.5941 0.53577 0.032 0.000 0.180 0.660 NA
#> GSM123742 1 0.7627 0.00107 0.352 0.000 0.044 0.316 NA
#> GSM123745 1 0.4930 0.53788 0.696 0.000 0.000 0.220 NA
#> GSM123748 1 0.5148 0.59868 0.688 0.000 0.000 0.120 NA
#> GSM123751 1 0.5553 0.53590 0.664 0.000 0.008 0.204 NA
#> GSM123754 1 0.3752 0.61766 0.804 0.000 0.000 0.148 NA
#> GSM123757 1 0.2332 0.66705 0.904 0.000 0.004 0.016 NA
#> GSM123760 4 0.7277 0.09659 0.292 0.000 0.020 0.360 NA
#> GSM123762 1 0.6079 0.50391 0.604 0.000 0.016 0.124 NA
#> GSM123764 4 0.6997 0.54013 0.048 0.000 0.120 0.456 NA
#> GSM123767 1 0.5273 0.33572 0.588 0.000 0.000 0.352 NA
#> GSM123770 1 0.2708 0.64492 0.884 0.000 0.000 0.072 NA
#> GSM123773 1 0.4303 0.56585 0.752 0.000 0.000 0.192 NA
#> GSM123777 4 0.5602 0.46601 0.008 0.000 0.244 0.644 NA
#> GSM123779 4 0.5177 0.62001 0.068 0.000 0.040 0.732 NA
#> GSM123782 4 0.7390 0.52527 0.076 0.000 0.128 0.432 NA
#> GSM123786 3 0.3180 0.73304 0.000 0.000 0.856 0.068 NA
#> GSM123789 4 0.7466 0.51580 0.084 0.000 0.172 0.500 NA
#> GSM123793 4 0.5496 0.63112 0.036 0.000 0.076 0.696 NA
#> GSM123797 4 0.5194 0.61737 0.060 0.000 0.096 0.748 NA
#> GSM123729 2 0.1671 0.95138 0.000 0.924 0.000 0.000 NA
#> GSM123733 2 0.1502 0.95330 0.000 0.940 0.000 0.004 NA
#> GSM123737 2 0.1197 0.95797 0.000 0.952 0.000 0.000 NA
#> GSM123741 2 0.0510 0.96045 0.000 0.984 0.000 0.000 NA
#> GSM123747 2 0.1121 0.96096 0.000 0.956 0.000 0.000 NA
#> GSM123753 2 0.1043 0.95831 0.000 0.960 0.000 0.000 NA
#> GSM123759 2 0.1043 0.96033 0.000 0.960 0.000 0.000 NA
#> GSM123766 2 0.1197 0.95912 0.000 0.952 0.000 0.000 NA
#> GSM123772 2 0.0794 0.96016 0.000 0.972 0.000 0.000 NA
#> GSM123775 2 0.1908 0.94091 0.000 0.908 0.000 0.000 NA
#> GSM123781 2 0.1270 0.95473 0.000 0.948 0.000 0.000 NA
#> GSM123785 2 0.1430 0.95719 0.000 0.944 0.000 0.004 NA
#> GSM123788 2 0.1043 0.95802 0.000 0.960 0.000 0.000 NA
#> GSM123792 2 0.1124 0.95897 0.000 0.960 0.000 0.004 NA
#> GSM123796 2 0.1502 0.95428 0.000 0.940 0.000 0.004 NA
#> GSM123731 2 0.1043 0.96123 0.000 0.960 0.000 0.000 NA
#> GSM123735 2 0.1768 0.95110 0.000 0.924 0.000 0.004 NA
#> GSM123739 2 0.1270 0.95466 0.000 0.948 0.000 0.000 NA
#> GSM123743 2 0.0963 0.96106 0.000 0.964 0.000 0.000 NA
#> GSM123749 2 0.0510 0.96005 0.000 0.984 0.000 0.000 NA
#> GSM123755 2 0.1341 0.95433 0.000 0.944 0.000 0.000 NA
#> GSM123768 2 0.1410 0.95358 0.000 0.940 0.000 0.000 NA
#> GSM123776 2 0.4499 0.79860 0.060 0.764 0.000 0.012 NA
#> GSM123783 2 0.1965 0.94133 0.000 0.904 0.000 0.000 NA
#> GSM123790 2 0.2304 0.93355 0.000 0.892 0.000 0.008 NA
#> GSM123794 2 0.1671 0.95327 0.000 0.924 0.000 0.000 NA
#> GSM123798 2 0.1197 0.95553 0.000 0.952 0.000 0.000 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM123732 3 0.447 0.6570 0.008 0.000 0.768 0.064 NA 0.040
#> GSM123736 3 0.584 0.6034 0.040 0.000 0.684 0.092 NA 0.100
#> GSM123740 3 0.534 0.6322 0.028 0.000 0.720 0.072 NA 0.076
#> GSM123744 3 0.725 0.0930 0.352 0.000 0.400 0.016 NA 0.128
#> GSM123746 1 0.497 0.4879 0.728 0.000 0.068 0.004 NA 0.124
#> GSM123750 1 0.726 0.1534 0.456 0.000 0.212 0.012 NA 0.224
#> GSM123752 1 0.725 0.1902 0.468 0.000 0.256 0.020 NA 0.092
#> GSM123756 1 0.100 0.5877 0.964 0.000 0.000 0.000 NA 0.016
#> GSM123758 3 0.585 0.5660 0.140 0.000 0.652 0.012 NA 0.060
#> GSM123761 1 0.699 0.1874 0.492 0.000 0.128 0.016 NA 0.272
#> GSM123763 6 0.783 0.1302 0.356 0.000 0.108 0.096 NA 0.360
#> GSM123765 3 0.463 0.6532 0.008 0.000 0.764 0.088 NA 0.072
#> GSM123769 1 0.248 0.5786 0.900 0.000 0.028 0.004 NA 0.044
#> GSM123771 1 0.210 0.5785 0.912 0.000 0.008 0.000 NA 0.052
#> GSM123774 1 0.148 0.5907 0.944 0.000 0.000 0.008 NA 0.036
#> GSM123778 3 0.503 0.6429 0.004 0.000 0.720 0.076 NA 0.064
#> GSM123780 3 0.629 0.5240 0.004 0.000 0.596 0.172 NA 0.100
#> GSM123784 3 0.465 0.6199 0.000 0.000 0.744 0.128 NA 0.052
#> GSM123787 3 0.537 0.6414 0.016 0.000 0.700 0.052 NA 0.088
#> GSM123791 3 0.617 0.5983 0.032 0.000 0.644 0.076 NA 0.108
#> GSM123795 3 0.699 0.4836 0.072 0.000 0.572 0.148 NA 0.136
#> GSM123799 3 0.575 0.6205 0.060 0.000 0.696 0.068 NA 0.080
#> GSM123730 4 0.365 0.4300 0.020 0.000 0.024 0.836 NA 0.056
#> GSM123734 4 0.641 0.1154 0.152 0.000 0.008 0.464 NA 0.348
#> GSM123738 4 0.674 0.3729 0.024 0.000 0.212 0.540 NA 0.172
#> GSM123742 6 0.644 0.3110 0.240 0.000 0.028 0.112 NA 0.572
#> GSM123745 1 0.654 0.3170 0.480 0.000 0.000 0.216 NA 0.260
#> GSM123748 1 0.588 0.3275 0.516 0.000 0.004 0.064 NA 0.368
#> GSM123751 1 0.654 0.3404 0.516 0.000 0.008 0.160 NA 0.268
#> GSM123754 1 0.502 0.5033 0.696 0.000 0.000 0.164 NA 0.108
#> GSM123757 1 0.316 0.5815 0.856 0.000 0.008 0.016 NA 0.084
#> GSM123760 6 0.587 0.3261 0.160 0.000 0.016 0.168 NA 0.628
#> GSM123762 1 0.665 0.0408 0.460 0.000 0.040 0.060 NA 0.380
#> GSM123764 6 0.682 0.2341 0.044 0.000 0.092 0.204 NA 0.568
#> GSM123767 1 0.618 0.2869 0.492 0.000 0.000 0.340 NA 0.128
#> GSM123770 1 0.362 0.5609 0.820 0.000 0.000 0.068 NA 0.088
#> GSM123773 1 0.559 0.4467 0.632 0.000 0.000 0.212 NA 0.112
#> GSM123777 4 0.509 0.3421 0.000 0.000 0.164 0.696 NA 0.044
#> GSM123779 4 0.633 0.2869 0.048 0.000 0.032 0.588 NA 0.236
#> GSM123782 6 0.720 0.1639 0.044 0.000 0.060 0.248 NA 0.492
#> GSM123786 3 0.540 0.6263 0.008 0.000 0.672 0.048 NA 0.076
#> GSM123789 6 0.732 0.0892 0.040 0.000 0.104 0.284 NA 0.468
#> GSM123793 4 0.617 0.2464 0.024 0.000 0.084 0.484 NA 0.384
#> GSM123797 4 0.587 0.4400 0.036 0.000 0.096 0.640 NA 0.200
#> GSM123729 2 0.273 0.8877 0.000 0.808 0.000 0.000 NA 0.000
#> GSM123733 2 0.226 0.8962 0.000 0.860 0.000 0.000 NA 0.000
#> GSM123737 2 0.256 0.8905 0.000 0.828 0.000 0.000 NA 0.000
#> GSM123741 2 0.133 0.9098 0.000 0.936 0.000 0.000 NA 0.000
#> GSM123747 2 0.133 0.9079 0.000 0.936 0.000 0.000 NA 0.000
#> GSM123753 2 0.120 0.9019 0.000 0.944 0.000 0.000 NA 0.000
#> GSM123759 2 0.161 0.8957 0.000 0.916 0.000 0.000 NA 0.000
#> GSM123766 2 0.156 0.9044 0.000 0.920 0.000 0.000 NA 0.000
#> GSM123772 2 0.139 0.9079 0.000 0.932 0.000 0.000 NA 0.000
#> GSM123775 2 0.285 0.8587 0.000 0.792 0.000 0.000 NA 0.000
#> GSM123781 2 0.161 0.8956 0.000 0.916 0.000 0.000 NA 0.000
#> GSM123785 2 0.205 0.9003 0.000 0.880 0.000 0.000 NA 0.000
#> GSM123788 2 0.218 0.8960 0.000 0.868 0.000 0.000 NA 0.000
#> GSM123792 2 0.209 0.9018 0.000 0.876 0.000 0.000 NA 0.000
#> GSM123796 2 0.214 0.8982 0.000 0.872 0.000 0.000 NA 0.000
#> GSM123731 2 0.150 0.9083 0.000 0.924 0.000 0.000 NA 0.000
#> GSM123735 2 0.226 0.8982 0.000 0.860 0.000 0.000 NA 0.000
#> GSM123739 2 0.273 0.8860 0.000 0.808 0.000 0.000 NA 0.000
#> GSM123743 2 0.181 0.9098 0.000 0.900 0.000 0.000 NA 0.000
#> GSM123749 2 0.144 0.9059 0.000 0.928 0.000 0.000 NA 0.000
#> GSM123755 2 0.139 0.8983 0.000 0.932 0.000 0.000 NA 0.000
#> GSM123768 2 0.205 0.8838 0.000 0.880 0.000 0.000 NA 0.000
#> GSM123776 2 0.565 0.5722 0.060 0.540 0.000 0.024 NA 0.012
#> GSM123783 2 0.290 0.8640 0.000 0.800 0.000 0.004 NA 0.000
#> GSM123790 2 0.326 0.8561 0.000 0.780 0.000 0.016 NA 0.000
#> GSM123794 2 0.260 0.8868 0.000 0.836 0.000 0.004 NA 0.000
#> GSM123798 2 0.171 0.8970 0.000 0.908 0.000 0.000 NA 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) infection(p) agent(p) k
#> MAD:skmeans 71 3.82e-16 3.82e-16 6.04e-06 2
#> MAD:skmeans 68 2.27e-14 2.27e-14 1.57e-05 3
#> MAD:skmeans 62 2.04e-18 2.04e-18 2.38e-04 4
#> MAD:skmeans 61 6.26e-18 6.26e-18 2.99e-04 5
#> MAD:skmeans 46 6.15e-11 6.15e-11 3.30e-03 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "pam"]
# you can also extract it by
# res = res_list["MAD:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.985 0.993 0.48151 0.522 0.522
#> 3 3 1.000 0.971 0.987 0.37383 0.815 0.646
#> 4 4 0.943 0.901 0.950 0.03376 0.990 0.969
#> 5 5 0.886 0.860 0.933 0.01836 0.994 0.980
#> 6 6 0.884 0.859 0.932 0.00926 0.994 0.981
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
#> GSM123732 1 0.000 0.989 1.000 0.000
#> GSM123736 1 0.000 0.989 1.000 0.000
#> GSM123740 1 0.000 0.989 1.000 0.000
#> GSM123744 1 0.000 0.989 1.000 0.000
#> GSM123746 1 0.000 0.989 1.000 0.000
#> GSM123750 1 0.000 0.989 1.000 0.000
#> GSM123752 1 0.000 0.989 1.000 0.000
#> GSM123756 1 0.000 0.989 1.000 0.000
#> GSM123758 1 0.000 0.989 1.000 0.000
#> GSM123761 1 0.000 0.989 1.000 0.000
#> GSM123763 1 0.000 0.989 1.000 0.000
#> GSM123765 1 0.000 0.989 1.000 0.000
#> GSM123769 1 0.000 0.989 1.000 0.000
#> GSM123771 1 0.000 0.989 1.000 0.000
#> GSM123774 1 0.000 0.989 1.000 0.000
#> GSM123778 1 0.000 0.989 1.000 0.000
#> GSM123780 1 0.000 0.989 1.000 0.000
#> GSM123784 1 0.000 0.989 1.000 0.000
#> GSM123787 1 0.000 0.989 1.000 0.000
#> GSM123791 1 0.000 0.989 1.000 0.000
#> GSM123795 1 0.000 0.989 1.000 0.000
#> GSM123799 1 0.000 0.989 1.000 0.000
#> GSM123730 1 0.327 0.933 0.940 0.060
#> GSM123734 1 0.000 0.989 1.000 0.000
#> GSM123738 1 0.000 0.989 1.000 0.000
#> GSM123742 1 0.000 0.989 1.000 0.000
#> GSM123745 1 0.855 0.618 0.720 0.280
#> GSM123748 1 0.000 0.989 1.000 0.000
#> GSM123751 1 0.000 0.989 1.000 0.000
#> GSM123754 1 0.000 0.989 1.000 0.000
#> GSM123757 1 0.000 0.989 1.000 0.000
#> GSM123760 1 0.000 0.989 1.000 0.000
#> GSM123762 1 0.000 0.989 1.000 0.000
#> GSM123764 1 0.000 0.989 1.000 0.000
#> GSM123767 1 0.469 0.888 0.900 0.100
#> GSM123770 1 0.000 0.989 1.000 0.000
#> GSM123773 1 0.000 0.989 1.000 0.000
#> GSM123777 1 0.204 0.960 0.968 0.032
#> GSM123779 1 0.000 0.989 1.000 0.000
#> GSM123782 1 0.000 0.989 1.000 0.000
#> GSM123786 1 0.000 0.989 1.000 0.000
#> GSM123789 1 0.000 0.989 1.000 0.000
#> GSM123793 1 0.000 0.989 1.000 0.000
#> GSM123797 1 0.000 0.989 1.000 0.000
#> GSM123729 2 0.000 1.000 0.000 1.000
#> GSM123733 2 0.000 1.000 0.000 1.000
#> GSM123737 2 0.000 1.000 0.000 1.000
#> GSM123741 2 0.000 1.000 0.000 1.000
#> GSM123747 2 0.000 1.000 0.000 1.000
#> GSM123753 2 0.000 1.000 0.000 1.000
#> GSM123759 2 0.000 1.000 0.000 1.000
#> GSM123766 2 0.000 1.000 0.000 1.000
#> GSM123772 2 0.000 1.000 0.000 1.000
#> GSM123775 2 0.000 1.000 0.000 1.000
#> GSM123781 2 0.000 1.000 0.000 1.000
#> GSM123785 2 0.000 1.000 0.000 1.000
#> GSM123788 2 0.000 1.000 0.000 1.000
#> GSM123792 2 0.000 1.000 0.000 1.000
#> GSM123796 2 0.000 1.000 0.000 1.000
#> GSM123731 2 0.000 1.000 0.000 1.000
#> GSM123735 2 0.000 1.000 0.000 1.000
#> GSM123739 2 0.000 1.000 0.000 1.000
#> GSM123743 2 0.000 1.000 0.000 1.000
#> GSM123749 2 0.000 1.000 0.000 1.000
#> GSM123755 2 0.000 1.000 0.000 1.000
#> GSM123768 2 0.000 1.000 0.000 1.000
#> GSM123776 2 0.000 1.000 0.000 1.000
#> GSM123783 2 0.000 1.000 0.000 1.000
#> GSM123790 2 0.000 1.000 0.000 1.000
#> GSM123794 2 0.000 1.000 0.000 1.000
#> GSM123798 2 0.000 1.000 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM123732 3 0.0000 0.987 0.000 0 1.000
#> GSM123736 3 0.0000 0.987 0.000 0 1.000
#> GSM123740 3 0.0000 0.987 0.000 0 1.000
#> GSM123744 3 0.0237 0.985 0.004 0 0.996
#> GSM123746 3 0.3752 0.837 0.144 0 0.856
#> GSM123750 3 0.0000 0.987 0.000 0 1.000
#> GSM123752 3 0.0747 0.978 0.016 0 0.984
#> GSM123756 1 0.0000 0.962 1.000 0 0.000
#> GSM123758 3 0.0747 0.978 0.016 0 0.984
#> GSM123761 3 0.1163 0.969 0.028 0 0.972
#> GSM123763 3 0.2066 0.940 0.060 0 0.940
#> GSM123765 3 0.0000 0.987 0.000 0 1.000
#> GSM123769 1 0.0000 0.962 1.000 0 0.000
#> GSM123771 1 0.0000 0.962 1.000 0 0.000
#> GSM123774 1 0.0000 0.962 1.000 0 0.000
#> GSM123778 3 0.0000 0.987 0.000 0 1.000
#> GSM123780 3 0.0000 0.987 0.000 0 1.000
#> GSM123784 3 0.0000 0.987 0.000 0 1.000
#> GSM123787 3 0.0000 0.987 0.000 0 1.000
#> GSM123791 3 0.0000 0.987 0.000 0 1.000
#> GSM123795 3 0.0000 0.987 0.000 0 1.000
#> GSM123799 3 0.0000 0.987 0.000 0 1.000
#> GSM123730 3 0.0000 0.987 0.000 0 1.000
#> GSM123734 1 0.0000 0.962 1.000 0 0.000
#> GSM123738 3 0.1411 0.960 0.036 0 0.964
#> GSM123742 1 0.1031 0.945 0.976 0 0.024
#> GSM123745 1 0.0000 0.962 1.000 0 0.000
#> GSM123748 1 0.0000 0.962 1.000 0 0.000
#> GSM123751 1 0.0000 0.962 1.000 0 0.000
#> GSM123754 1 0.0000 0.962 1.000 0 0.000
#> GSM123757 1 0.0592 0.954 0.988 0 0.012
#> GSM123760 1 0.4178 0.790 0.828 0 0.172
#> GSM123762 1 0.0000 0.962 1.000 0 0.000
#> GSM123764 3 0.0000 0.987 0.000 0 1.000
#> GSM123767 1 0.0000 0.962 1.000 0 0.000
#> GSM123770 1 0.0000 0.962 1.000 0 0.000
#> GSM123773 1 0.0000 0.962 1.000 0 0.000
#> GSM123777 3 0.0000 0.987 0.000 0 1.000
#> GSM123779 3 0.0424 0.983 0.008 0 0.992
#> GSM123782 3 0.0000 0.987 0.000 0 1.000
#> GSM123786 3 0.0000 0.987 0.000 0 1.000
#> GSM123789 3 0.0237 0.985 0.004 0 0.996
#> GSM123793 3 0.0747 0.977 0.016 0 0.984
#> GSM123797 1 0.6111 0.373 0.604 0 0.396
#> GSM123729 2 0.0000 1.000 0.000 1 0.000
#> GSM123733 2 0.0000 1.000 0.000 1 0.000
#> GSM123737 2 0.0000 1.000 0.000 1 0.000
#> GSM123741 2 0.0000 1.000 0.000 1 0.000
#> GSM123747 2 0.0000 1.000 0.000 1 0.000
#> GSM123753 2 0.0000 1.000 0.000 1 0.000
#> GSM123759 2 0.0000 1.000 0.000 1 0.000
#> GSM123766 2 0.0000 1.000 0.000 1 0.000
#> GSM123772 2 0.0000 1.000 0.000 1 0.000
#> GSM123775 2 0.0000 1.000 0.000 1 0.000
#> GSM123781 2 0.0000 1.000 0.000 1 0.000
#> GSM123785 2 0.0000 1.000 0.000 1 0.000
#> GSM123788 2 0.0000 1.000 0.000 1 0.000
#> GSM123792 2 0.0000 1.000 0.000 1 0.000
#> GSM123796 2 0.0000 1.000 0.000 1 0.000
#> GSM123731 2 0.0000 1.000 0.000 1 0.000
#> GSM123735 2 0.0000 1.000 0.000 1 0.000
#> GSM123739 2 0.0000 1.000 0.000 1 0.000
#> GSM123743 2 0.0000 1.000 0.000 1 0.000
#> GSM123749 2 0.0000 1.000 0.000 1 0.000
#> GSM123755 2 0.0000 1.000 0.000 1 0.000
#> GSM123768 2 0.0000 1.000 0.000 1 0.000
#> GSM123776 2 0.0000 1.000 0.000 1 0.000
#> GSM123783 2 0.0000 1.000 0.000 1 0.000
#> GSM123790 2 0.0000 1.000 0.000 1 0.000
#> GSM123794 2 0.0000 1.000 0.000 1 0.000
#> GSM123798 2 0.0000 1.000 0.000 1 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM123732 3 0.0000 0.930 0.000 0 1.000 0.000
#> GSM123736 3 0.1557 0.903 0.000 0 0.944 0.056
#> GSM123740 3 0.1557 0.903 0.000 0 0.944 0.056
#> GSM123744 3 0.1356 0.918 0.008 0 0.960 0.032
#> GSM123746 3 0.5653 0.544 0.096 0 0.712 0.192
#> GSM123750 3 0.0469 0.928 0.012 0 0.988 0.000
#> GSM123752 3 0.1975 0.891 0.016 0 0.936 0.048
#> GSM123756 1 0.3610 0.848 0.800 0 0.000 0.200
#> GSM123758 3 0.2412 0.857 0.008 0 0.908 0.084
#> GSM123761 3 0.4182 0.707 0.024 0 0.796 0.180
#> GSM123763 3 0.3962 0.767 0.044 0 0.832 0.124
#> GSM123765 3 0.0000 0.930 0.000 0 1.000 0.000
#> GSM123769 1 0.1867 0.870 0.928 0 0.000 0.072
#> GSM123771 1 0.1867 0.872 0.928 0 0.000 0.072
#> GSM123774 1 0.1940 0.872 0.924 0 0.000 0.076
#> GSM123778 3 0.0000 0.930 0.000 0 1.000 0.000
#> GSM123780 3 0.0000 0.930 0.000 0 1.000 0.000
#> GSM123784 3 0.0000 0.930 0.000 0 1.000 0.000
#> GSM123787 3 0.0000 0.930 0.000 0 1.000 0.000
#> GSM123791 3 0.0000 0.930 0.000 0 1.000 0.000
#> GSM123795 3 0.1557 0.903 0.000 0 0.944 0.056
#> GSM123799 3 0.1389 0.908 0.000 0 0.952 0.048
#> GSM123730 3 0.0895 0.921 0.020 0 0.976 0.004
#> GSM123734 1 0.0921 0.870 0.972 0 0.000 0.028
#> GSM123738 3 0.3587 0.822 0.052 0 0.860 0.088
#> GSM123742 1 0.2868 0.858 0.864 0 0.000 0.136
#> GSM123745 1 0.0469 0.879 0.988 0 0.000 0.012
#> GSM123748 1 0.2921 0.856 0.860 0 0.000 0.140
#> GSM123751 1 0.2081 0.875 0.916 0 0.000 0.084
#> GSM123754 1 0.3569 0.848 0.804 0 0.000 0.196
#> GSM123757 1 0.3024 0.856 0.852 0 0.000 0.148
#> GSM123760 1 0.4514 0.803 0.800 0 0.064 0.136
#> GSM123762 1 0.2011 0.867 0.920 0 0.000 0.080
#> GSM123764 3 0.0000 0.930 0.000 0 1.000 0.000
#> GSM123767 1 0.0336 0.876 0.992 0 0.000 0.008
#> GSM123770 1 0.0336 0.876 0.992 0 0.000 0.008
#> GSM123773 1 0.0188 0.877 0.996 0 0.000 0.004
#> GSM123777 3 0.0000 0.930 0.000 0 1.000 0.000
#> GSM123779 3 0.1109 0.916 0.028 0 0.968 0.004
#> GSM123782 3 0.0524 0.928 0.008 0 0.988 0.004
#> GSM123786 3 0.0000 0.930 0.000 0 1.000 0.000
#> GSM123789 3 0.0937 0.923 0.012 0 0.976 0.012
#> GSM123793 4 0.4542 0.000 0.020 0 0.228 0.752
#> GSM123797 1 0.6568 0.128 0.572 0 0.332 0.096
#> GSM123729 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123733 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123737 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123741 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123747 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123753 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123759 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123766 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123772 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123775 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123781 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123785 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123788 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123792 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123796 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123731 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123735 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123739 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123743 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123749 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123755 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123768 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123776 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123783 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123790 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123794 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123798 2 0.0000 1.000 0.000 1 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM123732 3 0.0000 0.923 0.000 0 1.000 0.000 0.000
#> GSM123736 3 0.2020 0.882 0.000 0 0.900 0.100 0.000
#> GSM123740 3 0.2020 0.882 0.000 0 0.900 0.100 0.000
#> GSM123744 3 0.1569 0.915 0.008 0 0.948 0.032 0.012
#> GSM123746 3 0.5433 0.568 0.084 0 0.652 0.008 0.256
#> GSM123750 3 0.0960 0.919 0.016 0 0.972 0.004 0.008
#> GSM123752 3 0.2478 0.883 0.028 0 0.904 0.008 0.060
#> GSM123756 1 0.3766 0.712 0.728 0 0.000 0.004 0.268
#> GSM123758 3 0.2304 0.866 0.008 0 0.892 0.000 0.100
#> GSM123761 3 0.4625 0.669 0.036 0 0.712 0.008 0.244
#> GSM123763 3 0.4181 0.760 0.032 0 0.780 0.016 0.172
#> GSM123765 3 0.0000 0.923 0.000 0 1.000 0.000 0.000
#> GSM123769 1 0.2389 0.726 0.880 0 0.000 0.004 0.116
#> GSM123771 1 0.2439 0.731 0.876 0 0.000 0.004 0.120
#> GSM123774 1 0.2488 0.732 0.872 0 0.000 0.004 0.124
#> GSM123778 3 0.0000 0.923 0.000 0 1.000 0.000 0.000
#> GSM123780 3 0.0000 0.923 0.000 0 1.000 0.000 0.000
#> GSM123784 3 0.0000 0.923 0.000 0 1.000 0.000 0.000
#> GSM123787 3 0.0000 0.923 0.000 0 1.000 0.000 0.000
#> GSM123791 3 0.0000 0.923 0.000 0 1.000 0.000 0.000
#> GSM123795 3 0.2020 0.882 0.000 0 0.900 0.100 0.000
#> GSM123799 3 0.1671 0.896 0.000 0 0.924 0.076 0.000
#> GSM123730 3 0.0833 0.919 0.016 0 0.976 0.004 0.004
#> GSM123734 1 0.3051 0.637 0.852 0 0.000 0.028 0.120
#> GSM123738 3 0.4015 0.786 0.024 0 0.788 0.172 0.016
#> GSM123742 1 0.3093 0.755 0.824 0 0.000 0.008 0.168
#> GSM123745 1 0.0566 0.770 0.984 0 0.000 0.004 0.012
#> GSM123748 1 0.2929 0.762 0.840 0 0.000 0.008 0.152
#> GSM123751 1 0.1908 0.781 0.908 0 0.000 0.000 0.092
#> GSM123754 1 0.3715 0.717 0.736 0 0.000 0.004 0.260
#> GSM123757 1 0.3132 0.754 0.820 0 0.000 0.008 0.172
#> GSM123760 1 0.3928 0.728 0.788 0 0.028 0.008 0.176
#> GSM123762 5 0.3876 0.000 0.316 0 0.000 0.000 0.684
#> GSM123764 3 0.0324 0.923 0.000 0 0.992 0.004 0.004
#> GSM123767 1 0.0451 0.765 0.988 0 0.000 0.004 0.008
#> GSM123770 1 0.0451 0.765 0.988 0 0.000 0.004 0.008
#> GSM123773 1 0.0324 0.766 0.992 0 0.000 0.004 0.004
#> GSM123777 3 0.0000 0.923 0.000 0 1.000 0.000 0.000
#> GSM123779 3 0.1026 0.916 0.024 0 0.968 0.004 0.004
#> GSM123782 3 0.0613 0.922 0.008 0 0.984 0.004 0.004
#> GSM123786 3 0.0000 0.923 0.000 0 1.000 0.000 0.000
#> GSM123789 3 0.1018 0.919 0.016 0 0.968 0.000 0.016
#> GSM123793 4 0.1670 0.000 0.012 0 0.052 0.936 0.000
#> GSM123797 1 0.6602 0.143 0.560 0 0.240 0.176 0.024
#> GSM123729 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM123733 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM123737 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM123741 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM123747 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM123753 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM123759 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM123766 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM123772 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM123775 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM123781 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM123785 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM123788 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM123792 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM123796 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM123731 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM123735 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM123739 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM123743 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM123749 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM123755 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM123768 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM123776 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM123783 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM123790 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM123794 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM123798 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM123732 3 0.0000 0.924 0.000 0 1.000 0.000 0.000 0.000
#> GSM123736 3 0.2069 0.892 0.000 0 0.908 0.020 0.068 0.004
#> GSM123740 3 0.2069 0.892 0.000 0 0.908 0.020 0.068 0.004
#> GSM123744 3 0.1448 0.917 0.016 0 0.948 0.000 0.024 0.012
#> GSM123746 3 0.4954 0.552 0.260 0 0.628 0.000 0.000 0.112
#> GSM123750 3 0.1010 0.915 0.036 0 0.960 0.000 0.000 0.004
#> GSM123752 3 0.2006 0.877 0.104 0 0.892 0.000 0.000 0.004
#> GSM123756 1 0.2491 0.749 0.836 0 0.000 0.000 0.000 0.164
#> GSM123758 3 0.2118 0.868 0.104 0 0.888 0.000 0.000 0.008
#> GSM123761 3 0.4503 0.668 0.204 0 0.696 0.000 0.000 0.100
#> GSM123763 3 0.4175 0.759 0.100 0 0.768 0.008 0.004 0.120
#> GSM123765 3 0.0000 0.924 0.000 0 1.000 0.000 0.000 0.000
#> GSM123769 1 0.3595 0.749 0.704 0 0.000 0.008 0.000 0.288
#> GSM123771 1 0.3555 0.753 0.712 0 0.000 0.008 0.000 0.280
#> GSM123774 1 0.3534 0.755 0.716 0 0.000 0.008 0.000 0.276
#> GSM123778 3 0.0000 0.924 0.000 0 1.000 0.000 0.000 0.000
#> GSM123780 3 0.0000 0.924 0.000 0 1.000 0.000 0.000 0.000
#> GSM123784 3 0.0000 0.924 0.000 0 1.000 0.000 0.000 0.000
#> GSM123787 3 0.0000 0.924 0.000 0 1.000 0.000 0.000 0.000
#> GSM123791 3 0.0000 0.924 0.000 0 1.000 0.000 0.000 0.000
#> GSM123795 3 0.2069 0.892 0.000 0 0.908 0.020 0.068 0.004
#> GSM123799 3 0.1826 0.900 0.000 0 0.924 0.020 0.052 0.004
#> GSM123730 3 0.0508 0.923 0.004 0 0.984 0.012 0.000 0.000
#> GSM123734 4 0.3041 0.000 0.040 0 0.000 0.832 0.000 0.128
#> GSM123738 3 0.4256 0.760 0.004 0 0.756 0.160 0.068 0.012
#> GSM123742 1 0.0547 0.788 0.980 0 0.000 0.000 0.000 0.020
#> GSM123745 1 0.2704 0.798 0.844 0 0.000 0.016 0.000 0.140
#> GSM123748 1 0.0146 0.794 0.996 0 0.000 0.000 0.000 0.004
#> GSM123751 1 0.1838 0.808 0.916 0 0.000 0.016 0.000 0.068
#> GSM123754 1 0.2320 0.752 0.864 0 0.000 0.004 0.000 0.132
#> GSM123757 1 0.0458 0.787 0.984 0 0.000 0.000 0.000 0.016
#> GSM123760 1 0.1176 0.773 0.956 0 0.020 0.000 0.000 0.024
#> GSM123762 6 0.1563 0.000 0.056 0 0.000 0.012 0.000 0.932
#> GSM123764 3 0.0291 0.925 0.004 0 0.992 0.000 0.004 0.000
#> GSM123767 1 0.2869 0.794 0.832 0 0.000 0.020 0.000 0.148
#> GSM123770 1 0.2907 0.792 0.828 0 0.000 0.020 0.000 0.152
#> GSM123773 1 0.2821 0.794 0.832 0 0.000 0.016 0.000 0.152
#> GSM123777 3 0.0000 0.924 0.000 0 1.000 0.000 0.000 0.000
#> GSM123779 3 0.0725 0.921 0.012 0 0.976 0.012 0.000 0.000
#> GSM123782 3 0.0632 0.922 0.024 0 0.976 0.000 0.000 0.000
#> GSM123786 3 0.0000 0.924 0.000 0 1.000 0.000 0.000 0.000
#> GSM123789 3 0.0790 0.921 0.032 0 0.968 0.000 0.000 0.000
#> GSM123793 5 0.0000 0.000 0.000 0 0.000 0.000 1.000 0.000
#> GSM123797 1 0.6660 0.250 0.544 0 0.208 0.168 0.068 0.012
#> GSM123729 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123733 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123737 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123741 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123747 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123753 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123759 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123766 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123772 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123775 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123781 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123785 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123788 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123792 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123796 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123731 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123735 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123739 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123743 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123749 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123755 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123768 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123776 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123783 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123790 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123794 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123798 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) infection(p) agent(p) k
#> MAD:pam 71 3.82e-16 3.82e-16 6.04e-06 2
#> MAD:pam 70 8.95e-17 8.95e-17 9.81e-06 3
#> MAD:pam 69 7.37e-17 7.37e-17 1.24e-05 4
#> MAD:pam 68 2.23e-16 2.23e-16 1.57e-05 5
#> MAD:pam 67 6.88e-16 6.88e-16 1.98e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "mclust"]
# you can also extract it by
# res = res_list["MAD:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 71 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 1.000 1.000 0.4714 0.529 0.529
#> 3 3 0.948 0.937 0.970 0.2802 0.859 0.734
#> 4 4 0.865 0.853 0.920 0.1860 0.878 0.693
#> 5 5 0.844 0.766 0.882 0.0561 0.930 0.761
#> 6 6 0.719 0.634 0.796 0.0452 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] 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
#> GSM123732 1 0 1 1 0
#> GSM123736 1 0 1 1 0
#> GSM123740 1 0 1 1 0
#> GSM123744 1 0 1 1 0
#> GSM123746 1 0 1 1 0
#> GSM123750 1 0 1 1 0
#> GSM123752 1 0 1 1 0
#> GSM123756 1 0 1 1 0
#> GSM123758 1 0 1 1 0
#> GSM123761 1 0 1 1 0
#> GSM123763 1 0 1 1 0
#> GSM123765 1 0 1 1 0
#> GSM123769 1 0 1 1 0
#> GSM123771 1 0 1 1 0
#> GSM123774 1 0 1 1 0
#> GSM123778 1 0 1 1 0
#> GSM123780 1 0 1 1 0
#> GSM123784 1 0 1 1 0
#> GSM123787 1 0 1 1 0
#> GSM123791 1 0 1 1 0
#> GSM123795 1 0 1 1 0
#> GSM123799 1 0 1 1 0
#> GSM123730 1 0 1 1 0
#> GSM123734 1 0 1 1 0
#> GSM123738 1 0 1 1 0
#> GSM123742 1 0 1 1 0
#> GSM123745 1 0 1 1 0
#> GSM123748 1 0 1 1 0
#> GSM123751 1 0 1 1 0
#> GSM123754 1 0 1 1 0
#> GSM123757 1 0 1 1 0
#> GSM123760 1 0 1 1 0
#> GSM123762 1 0 1 1 0
#> GSM123764 1 0 1 1 0
#> GSM123767 1 0 1 1 0
#> GSM123770 1 0 1 1 0
#> GSM123773 1 0 1 1 0
#> GSM123777 1 0 1 1 0
#> GSM123779 1 0 1 1 0
#> GSM123782 1 0 1 1 0
#> GSM123786 1 0 1 1 0
#> GSM123789 1 0 1 1 0
#> GSM123793 1 0 1 1 0
#> GSM123797 1 0 1 1 0
#> GSM123729 2 0 1 0 1
#> GSM123733 2 0 1 0 1
#> GSM123737 2 0 1 0 1
#> GSM123741 2 0 1 0 1
#> GSM123747 2 0 1 0 1
#> GSM123753 2 0 1 0 1
#> GSM123759 2 0 1 0 1
#> GSM123766 2 0 1 0 1
#> GSM123772 2 0 1 0 1
#> GSM123775 2 0 1 0 1
#> GSM123781 2 0 1 0 1
#> GSM123785 2 0 1 0 1
#> GSM123788 2 0 1 0 1
#> GSM123792 2 0 1 0 1
#> GSM123796 2 0 1 0 1
#> GSM123731 2 0 1 0 1
#> GSM123735 2 0 1 0 1
#> GSM123739 2 0 1 0 1
#> GSM123743 2 0 1 0 1
#> GSM123749 2 0 1 0 1
#> GSM123755 2 0 1 0 1
#> GSM123768 2 0 1 0 1
#> GSM123776 1 0 1 1 0
#> GSM123783 2 0 1 0 1
#> GSM123790 2 0 1 0 1
#> GSM123794 2 0 1 0 1
#> GSM123798 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM123732 3 0.0000 0.838 0.000 0 1.000
#> GSM123736 1 0.5859 0.369 0.656 0 0.344
#> GSM123740 3 0.5058 0.718 0.244 0 0.756
#> GSM123744 1 0.1031 0.963 0.976 0 0.024
#> GSM123746 1 0.0000 0.973 1.000 0 0.000
#> GSM123750 1 0.0424 0.972 0.992 0 0.008
#> GSM123752 1 0.0000 0.973 1.000 0 0.000
#> GSM123756 1 0.0000 0.973 1.000 0 0.000
#> GSM123758 1 0.4235 0.759 0.824 0 0.176
#> GSM123761 1 0.0000 0.973 1.000 0 0.000
#> GSM123763 1 0.0424 0.972 0.992 0 0.008
#> GSM123765 3 0.0237 0.839 0.004 0 0.996
#> GSM123769 1 0.0000 0.973 1.000 0 0.000
#> GSM123771 1 0.0000 0.973 1.000 0 0.000
#> GSM123774 1 0.0000 0.973 1.000 0 0.000
#> GSM123778 3 0.0000 0.838 0.000 0 1.000
#> GSM123780 3 0.6235 0.354 0.436 0 0.564
#> GSM123784 3 0.2959 0.828 0.100 0 0.900
#> GSM123787 3 0.0000 0.838 0.000 0 1.000
#> GSM123791 3 0.3619 0.811 0.136 0 0.864
#> GSM123795 1 0.2261 0.916 0.932 0 0.068
#> GSM123799 3 0.6095 0.475 0.392 0 0.608
#> GSM123730 1 0.0592 0.971 0.988 0 0.012
#> GSM123734 1 0.0000 0.973 1.000 0 0.000
#> GSM123738 1 0.0747 0.969 0.984 0 0.016
#> GSM123742 1 0.0592 0.971 0.988 0 0.012
#> GSM123745 1 0.0000 0.973 1.000 0 0.000
#> GSM123748 1 0.0000 0.973 1.000 0 0.000
#> GSM123751 1 0.0000 0.973 1.000 0 0.000
#> GSM123754 1 0.0000 0.973 1.000 0 0.000
#> GSM123757 1 0.0000 0.973 1.000 0 0.000
#> GSM123760 1 0.0592 0.971 0.988 0 0.012
#> GSM123762 1 0.0000 0.973 1.000 0 0.000
#> GSM123764 1 0.1163 0.959 0.972 0 0.028
#> GSM123767 1 0.0000 0.973 1.000 0 0.000
#> GSM123770 1 0.0000 0.973 1.000 0 0.000
#> GSM123773 1 0.0000 0.973 1.000 0 0.000
#> GSM123777 1 0.0747 0.969 0.984 0 0.016
#> GSM123779 1 0.0592 0.971 0.988 0 0.012
#> GSM123782 1 0.0592 0.971 0.988 0 0.012
#> GSM123786 3 0.0000 0.838 0.000 0 1.000
#> GSM123789 1 0.1031 0.963 0.976 0 0.024
#> GSM123793 1 0.0747 0.969 0.984 0 0.016
#> GSM123797 1 0.0592 0.971 0.988 0 0.012
#> GSM123729 2 0.0000 1.000 0.000 1 0.000
#> GSM123733 2 0.0000 1.000 0.000 1 0.000
#> GSM123737 2 0.0000 1.000 0.000 1 0.000
#> GSM123741 2 0.0000 1.000 0.000 1 0.000
#> GSM123747 2 0.0000 1.000 0.000 1 0.000
#> GSM123753 2 0.0000 1.000 0.000 1 0.000
#> GSM123759 2 0.0000 1.000 0.000 1 0.000
#> GSM123766 2 0.0000 1.000 0.000 1 0.000
#> GSM123772 2 0.0000 1.000 0.000 1 0.000
#> GSM123775 2 0.0000 1.000 0.000 1 0.000
#> GSM123781 2 0.0000 1.000 0.000 1 0.000
#> GSM123785 2 0.0000 1.000 0.000 1 0.000
#> GSM123788 2 0.0000 1.000 0.000 1 0.000
#> GSM123792 2 0.0000 1.000 0.000 1 0.000
#> GSM123796 2 0.0000 1.000 0.000 1 0.000
#> GSM123731 2 0.0000 1.000 0.000 1 0.000
#> GSM123735 2 0.0000 1.000 0.000 1 0.000
#> GSM123739 2 0.0000 1.000 0.000 1 0.000
#> GSM123743 2 0.0000 1.000 0.000 1 0.000
#> GSM123749 2 0.0000 1.000 0.000 1 0.000
#> GSM123755 2 0.0000 1.000 0.000 1 0.000
#> GSM123768 2 0.0000 1.000 0.000 1 0.000
#> GSM123776 1 0.0000 0.973 1.000 0 0.000
#> GSM123783 2 0.0000 1.000 0.000 1 0.000
#> GSM123790 2 0.0000 1.000 0.000 1 0.000
#> GSM123794 2 0.0000 1.000 0.000 1 0.000
#> GSM123798 2 0.0000 1.000 0.000 1 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM123732 3 0.0336 0.8389 0.000 0.000 0.992 0.008
#> GSM123736 3 0.5188 0.7045 0.044 0.000 0.716 0.240
#> GSM123740 3 0.3636 0.8017 0.008 0.000 0.820 0.172
#> GSM123744 1 0.5312 0.6675 0.712 0.000 0.052 0.236
#> GSM123746 1 0.0336 0.8452 0.992 0.000 0.000 0.008
#> GSM123750 1 0.3881 0.7748 0.812 0.000 0.016 0.172
#> GSM123752 1 0.3636 0.7804 0.820 0.000 0.008 0.172
#> GSM123756 1 0.0817 0.8336 0.976 0.000 0.000 0.024
#> GSM123758 1 0.7702 0.0369 0.416 0.000 0.360 0.224
#> GSM123761 1 0.2999 0.8100 0.864 0.000 0.004 0.132
#> GSM123763 1 0.4053 0.7286 0.768 0.000 0.004 0.228
#> GSM123765 3 0.0707 0.8420 0.000 0.000 0.980 0.020
#> GSM123769 1 0.0707 0.8344 0.980 0.000 0.000 0.020
#> GSM123771 1 0.0817 0.8336 0.976 0.000 0.000 0.024
#> GSM123774 1 0.0817 0.8336 0.976 0.000 0.000 0.024
#> GSM123778 3 0.0188 0.8370 0.000 0.000 0.996 0.004
#> GSM123780 3 0.4609 0.7509 0.024 0.000 0.752 0.224
#> GSM123784 3 0.2412 0.8401 0.008 0.000 0.908 0.084
#> GSM123787 3 0.0188 0.8370 0.000 0.000 0.996 0.004
#> GSM123791 3 0.1716 0.8444 0.000 0.000 0.936 0.064
#> GSM123795 3 0.6992 0.4579 0.156 0.000 0.564 0.280
#> GSM123799 3 0.4540 0.7671 0.032 0.000 0.772 0.196
#> GSM123730 4 0.0921 0.9143 0.028 0.000 0.000 0.972
#> GSM123734 1 0.4713 0.4783 0.640 0.000 0.000 0.360
#> GSM123738 4 0.1004 0.9141 0.024 0.000 0.004 0.972
#> GSM123742 1 0.3975 0.7203 0.760 0.000 0.000 0.240
#> GSM123745 1 0.1022 0.8500 0.968 0.000 0.000 0.032
#> GSM123748 1 0.0592 0.8490 0.984 0.000 0.000 0.016
#> GSM123751 1 0.1211 0.8496 0.960 0.000 0.000 0.040
#> GSM123754 1 0.0921 0.8501 0.972 0.000 0.000 0.028
#> GSM123757 1 0.0188 0.8440 0.996 0.000 0.000 0.004
#> GSM123760 1 0.5295 0.1632 0.504 0.000 0.008 0.488
#> GSM123762 1 0.1118 0.8508 0.964 0.000 0.000 0.036
#> GSM123764 4 0.2036 0.8918 0.032 0.000 0.032 0.936
#> GSM123767 1 0.2216 0.8349 0.908 0.000 0.000 0.092
#> GSM123770 1 0.0707 0.8493 0.980 0.000 0.000 0.020
#> GSM123773 1 0.1022 0.8500 0.968 0.000 0.000 0.032
#> GSM123777 4 0.1004 0.9141 0.024 0.000 0.004 0.972
#> GSM123779 4 0.0921 0.9143 0.028 0.000 0.000 0.972
#> GSM123782 4 0.4855 0.1788 0.400 0.000 0.000 0.600
#> GSM123786 3 0.0188 0.8370 0.000 0.000 0.996 0.004
#> GSM123789 4 0.2443 0.8778 0.060 0.000 0.024 0.916
#> GSM123793 4 0.1004 0.9141 0.024 0.000 0.004 0.972
#> GSM123797 4 0.0921 0.9143 0.028 0.000 0.000 0.972
#> GSM123729 2 0.0000 0.9988 0.000 1.000 0.000 0.000
#> GSM123733 2 0.0000 0.9988 0.000 1.000 0.000 0.000
#> GSM123737 2 0.0000 0.9988 0.000 1.000 0.000 0.000
#> GSM123741 2 0.0000 0.9988 0.000 1.000 0.000 0.000
#> GSM123747 2 0.0000 0.9988 0.000 1.000 0.000 0.000
#> GSM123753 2 0.0000 0.9988 0.000 1.000 0.000 0.000
#> GSM123759 2 0.0000 0.9988 0.000 1.000 0.000 0.000
#> GSM123766 2 0.0000 0.9988 0.000 1.000 0.000 0.000
#> GSM123772 2 0.0000 0.9988 0.000 1.000 0.000 0.000
#> GSM123775 2 0.0376 0.9941 0.000 0.992 0.004 0.004
#> GSM123781 2 0.0000 0.9988 0.000 1.000 0.000 0.000
#> GSM123785 2 0.0000 0.9988 0.000 1.000 0.000 0.000
#> GSM123788 2 0.0000 0.9988 0.000 1.000 0.000 0.000
#> GSM123792 2 0.0000 0.9988 0.000 1.000 0.000 0.000
#> GSM123796 2 0.0000 0.9988 0.000 1.000 0.000 0.000
#> GSM123731 2 0.0000 0.9988 0.000 1.000 0.000 0.000
#> GSM123735 2 0.0000 0.9988 0.000 1.000 0.000 0.000
#> GSM123739 2 0.0188 0.9965 0.000 0.996 0.004 0.000
#> GSM123743 2 0.0000 0.9988 0.000 1.000 0.000 0.000
#> GSM123749 2 0.0000 0.9988 0.000 1.000 0.000 0.000
#> GSM123755 2 0.0000 0.9988 0.000 1.000 0.000 0.000
#> GSM123768 2 0.0000 0.9988 0.000 1.000 0.000 0.000
#> GSM123776 1 0.2773 0.8255 0.880 0.000 0.004 0.116
#> GSM123783 2 0.0376 0.9941 0.000 0.992 0.004 0.004
#> GSM123790 2 0.0376 0.9941 0.000 0.992 0.004 0.004
#> GSM123794 2 0.0376 0.9941 0.000 0.992 0.004 0.004
#> GSM123798 2 0.0000 0.9988 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM123732 3 0.0000 0.9234 0.000 0.000 1.000 0.000 0.000
#> GSM123736 3 0.1591 0.9145 0.004 0.000 0.940 0.052 0.004
#> GSM123740 3 0.1124 0.9238 0.000 0.000 0.960 0.036 0.004
#> GSM123744 1 0.7149 0.4036 0.452 0.000 0.308 0.028 0.212
#> GSM123746 1 0.2629 0.5579 0.860 0.000 0.000 0.004 0.136
#> GSM123750 1 0.6419 0.5031 0.584 0.000 0.188 0.020 0.208
#> GSM123752 1 0.6669 0.4812 0.552 0.000 0.232 0.024 0.192
#> GSM123756 1 0.0000 0.5689 1.000 0.000 0.000 0.000 0.000
#> GSM123758 3 0.6739 0.0702 0.324 0.000 0.508 0.028 0.140
#> GSM123761 1 0.5263 0.5364 0.696 0.000 0.080 0.016 0.208
#> GSM123763 1 0.6382 0.4682 0.616 0.000 0.228 0.056 0.100
#> GSM123765 3 0.0162 0.9244 0.000 0.000 0.996 0.004 0.000
#> GSM123769 1 0.0000 0.5689 1.000 0.000 0.000 0.000 0.000
#> GSM123771 1 0.0000 0.5689 1.000 0.000 0.000 0.000 0.000
#> GSM123774 1 0.0000 0.5689 1.000 0.000 0.000 0.000 0.000
#> GSM123778 3 0.0000 0.9234 0.000 0.000 1.000 0.000 0.000
#> GSM123780 3 0.1608 0.8983 0.000 0.000 0.928 0.072 0.000
#> GSM123784 3 0.0865 0.9260 0.000 0.000 0.972 0.024 0.004
#> GSM123787 3 0.0000 0.9234 0.000 0.000 1.000 0.000 0.000
#> GSM123791 3 0.0703 0.9263 0.000 0.000 0.976 0.024 0.000
#> GSM123795 3 0.2517 0.8661 0.008 0.000 0.884 0.104 0.004
#> GSM123799 3 0.1285 0.9229 0.004 0.000 0.956 0.036 0.004
#> GSM123730 4 0.0162 0.8422 0.000 0.000 0.004 0.996 0.000
#> GSM123734 4 0.6733 -0.2192 0.288 0.000 0.000 0.416 0.296
#> GSM123738 4 0.0000 0.8417 0.000 0.000 0.000 1.000 0.000
#> GSM123742 1 0.7117 0.1917 0.548 0.000 0.068 0.180 0.204
#> GSM123745 5 0.3491 0.7656 0.228 0.000 0.000 0.004 0.768
#> GSM123748 1 0.4225 -0.2135 0.632 0.000 0.000 0.004 0.364
#> GSM123751 5 0.4425 0.6470 0.452 0.000 0.000 0.004 0.544
#> GSM123754 5 0.4430 0.6386 0.456 0.000 0.000 0.004 0.540
#> GSM123757 1 0.0162 0.5694 0.996 0.000 0.000 0.004 0.000
#> GSM123760 4 0.6926 0.4190 0.180 0.000 0.080 0.584 0.156
#> GSM123762 1 0.3509 0.3595 0.792 0.000 0.004 0.008 0.196
#> GSM123764 4 0.2230 0.7980 0.000 0.000 0.116 0.884 0.000
#> GSM123767 5 0.4067 0.7762 0.300 0.000 0.000 0.008 0.692
#> GSM123770 1 0.3983 -0.0825 0.660 0.000 0.000 0.000 0.340
#> GSM123773 5 0.3491 0.7656 0.228 0.000 0.000 0.004 0.768
#> GSM123777 4 0.0162 0.8422 0.000 0.000 0.004 0.996 0.000
#> GSM123779 4 0.0162 0.8422 0.000 0.000 0.004 0.996 0.000
#> GSM123782 4 0.3547 0.7709 0.060 0.000 0.100 0.836 0.004
#> GSM123786 3 0.0000 0.9234 0.000 0.000 1.000 0.000 0.000
#> GSM123789 4 0.2377 0.7895 0.000 0.000 0.128 0.872 0.000
#> GSM123793 4 0.0000 0.8417 0.000 0.000 0.000 1.000 0.000
#> GSM123797 4 0.0000 0.8417 0.000 0.000 0.000 1.000 0.000
#> GSM123729 2 0.0000 0.9971 0.000 1.000 0.000 0.000 0.000
#> GSM123733 2 0.0162 0.9958 0.000 0.996 0.000 0.000 0.004
#> GSM123737 2 0.0000 0.9971 0.000 1.000 0.000 0.000 0.000
#> GSM123741 2 0.0000 0.9971 0.000 1.000 0.000 0.000 0.000
#> GSM123747 2 0.0000 0.9971 0.000 1.000 0.000 0.000 0.000
#> GSM123753 2 0.0000 0.9971 0.000 1.000 0.000 0.000 0.000
#> GSM123759 2 0.0000 0.9971 0.000 1.000 0.000 0.000 0.000
#> GSM123766 2 0.0162 0.9958 0.000 0.996 0.000 0.000 0.004
#> GSM123772 2 0.0162 0.9958 0.000 0.996 0.000 0.000 0.004
#> GSM123775 2 0.0404 0.9902 0.000 0.988 0.000 0.000 0.012
#> GSM123781 2 0.0000 0.9971 0.000 1.000 0.000 0.000 0.000
#> GSM123785 2 0.0162 0.9958 0.000 0.996 0.000 0.000 0.004
#> GSM123788 2 0.0162 0.9958 0.000 0.996 0.000 0.000 0.004
#> GSM123792 2 0.0000 0.9971 0.000 1.000 0.000 0.000 0.000
#> GSM123796 2 0.0162 0.9958 0.000 0.996 0.000 0.000 0.004
#> GSM123731 2 0.0000 0.9971 0.000 1.000 0.000 0.000 0.000
#> GSM123735 2 0.0000 0.9971 0.000 1.000 0.000 0.000 0.000
#> GSM123739 2 0.0000 0.9971 0.000 1.000 0.000 0.000 0.000
#> GSM123743 2 0.0000 0.9971 0.000 1.000 0.000 0.000 0.000
#> GSM123749 2 0.0000 0.9971 0.000 1.000 0.000 0.000 0.000
#> GSM123755 2 0.0000 0.9971 0.000 1.000 0.000 0.000 0.000
#> GSM123768 2 0.0000 0.9971 0.000 1.000 0.000 0.000 0.000
#> GSM123776 1 0.4684 0.2153 0.664 0.308 0.000 0.012 0.016
#> GSM123783 2 0.0510 0.9872 0.000 0.984 0.000 0.000 0.016
#> GSM123790 2 0.0510 0.9872 0.000 0.984 0.000 0.000 0.016
#> GSM123794 2 0.0404 0.9902 0.000 0.988 0.000 0.000 0.012
#> GSM123798 2 0.0000 0.9971 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM123732 3 0.0291 0.82804 0.000 0.000 0.992 0.004 0.004 0.000
#> GSM123736 3 0.3714 0.77817 0.000 0.000 0.760 0.196 0.044 0.000
#> GSM123740 3 0.2912 0.80835 0.000 0.000 0.816 0.172 0.012 0.000
#> GSM123744 6 0.6511 0.31277 0.000 0.000 0.252 0.156 0.072 0.520
#> GSM123746 6 0.3133 0.50660 0.072 0.000 0.008 0.016 0.044 0.860
#> GSM123750 6 0.5663 0.46360 0.000 0.000 0.144 0.132 0.072 0.652
#> GSM123752 6 0.6334 0.44945 0.012 0.000 0.156 0.176 0.064 0.592
#> GSM123756 6 0.4127 0.47125 0.172 0.000 0.000 0.000 0.088 0.740
#> GSM123758 3 0.5772 0.41201 0.000 0.000 0.556 0.152 0.016 0.276
#> GSM123761 6 0.4339 0.49752 0.000 0.000 0.076 0.080 0.068 0.776
#> GSM123763 6 0.8200 0.32077 0.108 0.000 0.136 0.200 0.136 0.420
#> GSM123765 3 0.0146 0.82891 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM123769 6 0.4127 0.47125 0.172 0.000 0.000 0.000 0.088 0.740
#> GSM123771 6 0.4127 0.47125 0.172 0.000 0.000 0.000 0.088 0.740
#> GSM123774 6 0.4159 0.46702 0.176 0.000 0.000 0.000 0.088 0.736
#> GSM123778 3 0.0146 0.82592 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM123780 3 0.3962 0.77624 0.004 0.000 0.772 0.128 0.096 0.000
#> GSM123784 3 0.1890 0.83560 0.000 0.000 0.916 0.060 0.024 0.000
#> GSM123787 3 0.0146 0.82592 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM123791 3 0.2191 0.83147 0.000 0.000 0.876 0.120 0.004 0.000
#> GSM123795 3 0.4948 0.68012 0.004 0.000 0.664 0.224 0.104 0.004
#> GSM123799 3 0.3037 0.80645 0.000 0.000 0.808 0.176 0.016 0.000
#> GSM123730 4 0.0260 0.84920 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM123734 4 0.5315 -0.04948 0.436 0.000 0.000 0.472 0.004 0.088
#> GSM123738 4 0.0000 0.85010 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM123742 1 0.7635 -0.00171 0.328 0.000 0.012 0.312 0.112 0.236
#> GSM123745 1 0.0000 0.63066 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM123748 1 0.3852 0.45217 0.612 0.000 0.000 0.000 0.004 0.384
#> GSM123751 1 0.3459 0.63095 0.768 0.000 0.000 0.016 0.004 0.212
#> GSM123754 1 0.3314 0.61421 0.740 0.000 0.000 0.000 0.004 0.256
#> GSM123757 6 0.2772 0.47310 0.180 0.000 0.000 0.000 0.004 0.816
#> GSM123760 4 0.6288 0.55464 0.180 0.000 0.020 0.612 0.116 0.072
#> GSM123762 6 0.4802 -0.00900 0.404 0.000 0.000 0.028 0.016 0.552
#> GSM123764 4 0.3185 0.80392 0.004 0.000 0.048 0.832 0.116 0.000
#> GSM123767 1 0.0964 0.63902 0.968 0.000 0.000 0.016 0.004 0.012
#> GSM123770 1 0.4228 0.41666 0.588 0.000 0.000 0.000 0.020 0.392
#> GSM123773 1 0.0146 0.62846 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM123777 4 0.0260 0.84920 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM123779 4 0.0363 0.84994 0.000 0.000 0.000 0.988 0.012 0.000
#> GSM123782 4 0.3515 0.80062 0.008 0.000 0.040 0.824 0.116 0.012
#> GSM123786 3 0.0146 0.82592 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM123789 4 0.3309 0.79914 0.004 0.000 0.056 0.824 0.116 0.000
#> GSM123793 4 0.0260 0.84967 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM123797 4 0.0260 0.84920 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM123729 2 0.2912 0.62532 0.000 0.784 0.000 0.000 0.216 0.000
#> GSM123733 2 0.2762 0.67013 0.000 0.804 0.000 0.000 0.196 0.000
#> GSM123737 2 0.0000 0.81457 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123741 2 0.0000 0.81457 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123747 2 0.0000 0.81457 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123753 2 0.0000 0.81457 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123759 2 0.0000 0.81457 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123766 2 0.3050 0.64306 0.000 0.764 0.000 0.000 0.236 0.000
#> GSM123772 2 0.2823 0.66194 0.000 0.796 0.000 0.000 0.204 0.000
#> GSM123775 2 0.3634 0.34405 0.000 0.644 0.000 0.000 0.356 0.000
#> GSM123781 2 0.0000 0.81457 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123785 2 0.3371 0.60350 0.000 0.708 0.000 0.000 0.292 0.000
#> GSM123788 2 0.2883 0.65292 0.000 0.788 0.000 0.000 0.212 0.000
#> GSM123792 2 0.0000 0.81457 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123796 2 0.2883 0.65292 0.000 0.788 0.000 0.000 0.212 0.000
#> GSM123731 2 0.0000 0.81457 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123735 2 0.0000 0.81457 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123739 2 0.2730 0.65919 0.000 0.808 0.000 0.000 0.192 0.000
#> GSM123743 2 0.0000 0.81457 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123749 2 0.0000 0.81457 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123755 2 0.0000 0.81457 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123768 2 0.2378 0.70262 0.000 0.848 0.000 0.000 0.152 0.000
#> GSM123776 5 0.6886 0.00000 0.128 0.232 0.000 0.000 0.492 0.148
#> GSM123783 2 0.3578 0.38741 0.000 0.660 0.000 0.000 0.340 0.000
#> GSM123790 2 0.3563 0.39713 0.000 0.664 0.000 0.000 0.336 0.000
#> GSM123794 2 0.3428 0.46603 0.000 0.696 0.000 0.000 0.304 0.000
#> GSM123798 2 0.0000 0.81457 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) infection(p) agent(p) k
#> MAD:mclust 71 3.04e-15 3.04e-15 5.99e-05 2
#> MAD:mclust 68 1.89e-15 1.89e-15 1.47e-04 3
#> MAD:mclust 66 7.76e-17 7.76e-17 7.28e-04 4
#> MAD:mclust 60 1.36e-19 1.36e-19 1.47e-03 5
#> MAD:mclust 50 9.85e-17 9.85e-17 1.65e-02 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "NMF"]
# you can also extract it by
# res = res_list["MAD:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.987 0.995 0.4809 0.522 0.522
#> 3 3 0.711 0.813 0.887 0.3554 0.808 0.637
#> 4 4 0.825 0.780 0.890 0.1111 0.901 0.721
#> 5 5 0.711 0.697 0.817 0.0588 0.945 0.802
#> 6 6 0.704 0.660 0.773 0.0354 0.990 0.959
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
#> GSM123732 1 0.000 0.992 1.000 0.000
#> GSM123736 1 0.000 0.992 1.000 0.000
#> GSM123740 1 0.000 0.992 1.000 0.000
#> GSM123744 1 0.000 0.992 1.000 0.000
#> GSM123746 1 0.000 0.992 1.000 0.000
#> GSM123750 1 0.000 0.992 1.000 0.000
#> GSM123752 1 0.000 0.992 1.000 0.000
#> GSM123756 1 0.000 0.992 1.000 0.000
#> GSM123758 1 0.000 0.992 1.000 0.000
#> GSM123761 1 0.000 0.992 1.000 0.000
#> GSM123763 1 0.000 0.992 1.000 0.000
#> GSM123765 1 0.000 0.992 1.000 0.000
#> GSM123769 1 0.000 0.992 1.000 0.000
#> GSM123771 1 0.000 0.992 1.000 0.000
#> GSM123774 1 0.000 0.992 1.000 0.000
#> GSM123778 1 0.000 0.992 1.000 0.000
#> GSM123780 1 0.000 0.992 1.000 0.000
#> GSM123784 1 0.000 0.992 1.000 0.000
#> GSM123787 1 0.000 0.992 1.000 0.000
#> GSM123791 1 0.000 0.992 1.000 0.000
#> GSM123795 1 0.000 0.992 1.000 0.000
#> GSM123799 1 0.000 0.992 1.000 0.000
#> GSM123730 1 0.936 0.457 0.648 0.352
#> GSM123734 1 0.000 0.992 1.000 0.000
#> GSM123738 1 0.000 0.992 1.000 0.000
#> GSM123742 1 0.000 0.992 1.000 0.000
#> GSM123745 1 0.000 0.992 1.000 0.000
#> GSM123748 1 0.000 0.992 1.000 0.000
#> GSM123751 1 0.000 0.992 1.000 0.000
#> GSM123754 1 0.000 0.992 1.000 0.000
#> GSM123757 1 0.000 0.992 1.000 0.000
#> GSM123760 1 0.000 0.992 1.000 0.000
#> GSM123762 1 0.000 0.992 1.000 0.000
#> GSM123764 1 0.000 0.992 1.000 0.000
#> GSM123767 1 0.000 0.992 1.000 0.000
#> GSM123770 1 0.000 0.992 1.000 0.000
#> GSM123773 1 0.000 0.992 1.000 0.000
#> GSM123777 1 0.000 0.992 1.000 0.000
#> GSM123779 1 0.000 0.992 1.000 0.000
#> GSM123782 1 0.000 0.992 1.000 0.000
#> GSM123786 1 0.000 0.992 1.000 0.000
#> GSM123789 1 0.000 0.992 1.000 0.000
#> GSM123793 1 0.000 0.992 1.000 0.000
#> GSM123797 1 0.000 0.992 1.000 0.000
#> GSM123729 2 0.000 1.000 0.000 1.000
#> GSM123733 2 0.000 1.000 0.000 1.000
#> GSM123737 2 0.000 1.000 0.000 1.000
#> GSM123741 2 0.000 1.000 0.000 1.000
#> GSM123747 2 0.000 1.000 0.000 1.000
#> GSM123753 2 0.000 1.000 0.000 1.000
#> GSM123759 2 0.000 1.000 0.000 1.000
#> GSM123766 2 0.000 1.000 0.000 1.000
#> GSM123772 2 0.000 1.000 0.000 1.000
#> GSM123775 2 0.000 1.000 0.000 1.000
#> GSM123781 2 0.000 1.000 0.000 1.000
#> GSM123785 2 0.000 1.000 0.000 1.000
#> GSM123788 2 0.000 1.000 0.000 1.000
#> GSM123792 2 0.000 1.000 0.000 1.000
#> GSM123796 2 0.000 1.000 0.000 1.000
#> GSM123731 2 0.000 1.000 0.000 1.000
#> GSM123735 2 0.000 1.000 0.000 1.000
#> GSM123739 2 0.000 1.000 0.000 1.000
#> GSM123743 2 0.000 1.000 0.000 1.000
#> GSM123749 2 0.000 1.000 0.000 1.000
#> GSM123755 2 0.000 1.000 0.000 1.000
#> GSM123768 2 0.000 1.000 0.000 1.000
#> GSM123776 2 0.000 1.000 0.000 1.000
#> GSM123783 2 0.000 1.000 0.000 1.000
#> GSM123790 2 0.000 1.000 0.000 1.000
#> GSM123794 2 0.000 1.000 0.000 1.000
#> GSM123798 2 0.000 1.000 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM123732 3 0.0829 0.8166 0.004 0.012 0.984
#> GSM123736 3 0.1031 0.8204 0.024 0.000 0.976
#> GSM123740 3 0.0592 0.8214 0.012 0.000 0.988
#> GSM123744 3 0.3340 0.7685 0.120 0.000 0.880
#> GSM123746 1 0.5835 0.6647 0.660 0.000 0.340
#> GSM123750 3 0.5254 0.5634 0.264 0.000 0.736
#> GSM123752 3 0.6489 -0.0888 0.456 0.004 0.540
#> GSM123756 1 0.4796 0.8276 0.780 0.000 0.220
#> GSM123758 3 0.2280 0.8052 0.052 0.008 0.940
#> GSM123761 3 0.5968 0.3010 0.364 0.000 0.636
#> GSM123763 3 0.4796 0.6608 0.220 0.000 0.780
#> GSM123765 3 0.0237 0.8207 0.004 0.000 0.996
#> GSM123769 1 0.4887 0.8208 0.772 0.000 0.228
#> GSM123771 1 0.4504 0.8402 0.804 0.000 0.196
#> GSM123774 1 0.3752 0.8398 0.856 0.000 0.144
#> GSM123778 3 0.0661 0.8162 0.004 0.008 0.988
#> GSM123780 3 0.1163 0.8144 0.028 0.000 0.972
#> GSM123784 3 0.0424 0.8212 0.008 0.000 0.992
#> GSM123787 3 0.0237 0.8190 0.004 0.000 0.996
#> GSM123791 3 0.0424 0.8212 0.008 0.000 0.992
#> GSM123795 3 0.1643 0.8164 0.044 0.000 0.956
#> GSM123799 3 0.1289 0.8198 0.032 0.000 0.968
#> GSM123730 3 0.8143 0.4384 0.360 0.080 0.560
#> GSM123734 1 0.5178 0.6164 0.744 0.000 0.256
#> GSM123738 3 0.3686 0.7853 0.140 0.000 0.860
#> GSM123742 3 0.6235 0.1221 0.436 0.000 0.564
#> GSM123745 1 0.2537 0.8118 0.920 0.000 0.080
#> GSM123748 1 0.4654 0.8375 0.792 0.000 0.208
#> GSM123751 1 0.4002 0.8414 0.840 0.000 0.160
#> GSM123754 1 0.4235 0.8457 0.824 0.000 0.176
#> GSM123757 1 0.4399 0.8439 0.812 0.000 0.188
#> GSM123760 3 0.5138 0.6501 0.252 0.000 0.748
#> GSM123762 1 0.6045 0.5595 0.620 0.000 0.380
#> GSM123764 3 0.1964 0.8185 0.056 0.000 0.944
#> GSM123767 1 0.2301 0.7934 0.936 0.004 0.060
#> GSM123770 1 0.3752 0.8416 0.856 0.000 0.144
#> GSM123773 1 0.2537 0.8136 0.920 0.000 0.080
#> GSM123777 3 0.4413 0.7460 0.160 0.008 0.832
#> GSM123779 3 0.5926 0.5715 0.356 0.000 0.644
#> GSM123782 3 0.4931 0.7226 0.212 0.004 0.784
#> GSM123786 3 0.0848 0.8143 0.008 0.008 0.984
#> GSM123789 3 0.2711 0.8086 0.088 0.000 0.912
#> GSM123793 3 0.4842 0.7346 0.224 0.000 0.776
#> GSM123797 3 0.5098 0.7142 0.248 0.000 0.752
#> GSM123729 2 0.0592 0.9841 0.012 0.988 0.000
#> GSM123733 2 0.1031 0.9828 0.024 0.976 0.000
#> GSM123737 2 0.0747 0.9845 0.016 0.984 0.000
#> GSM123741 2 0.0592 0.9857 0.012 0.988 0.000
#> GSM123747 2 0.0475 0.9860 0.004 0.992 0.004
#> GSM123753 2 0.0848 0.9848 0.008 0.984 0.008
#> GSM123759 2 0.0237 0.9860 0.000 0.996 0.004
#> GSM123766 2 0.1031 0.9828 0.024 0.976 0.000
#> GSM123772 2 0.0983 0.9838 0.016 0.980 0.004
#> GSM123775 2 0.1964 0.9577 0.056 0.944 0.000
#> GSM123781 2 0.0424 0.9864 0.008 0.992 0.000
#> GSM123785 2 0.2066 0.9603 0.060 0.940 0.000
#> GSM123788 2 0.0892 0.9841 0.020 0.980 0.000
#> GSM123792 2 0.0000 0.9866 0.000 1.000 0.000
#> GSM123796 2 0.1163 0.9814 0.028 0.972 0.000
#> GSM123731 2 0.0000 0.9866 0.000 1.000 0.000
#> GSM123735 2 0.0237 0.9865 0.004 0.996 0.000
#> GSM123739 2 0.1031 0.9813 0.024 0.976 0.000
#> GSM123743 2 0.0592 0.9857 0.012 0.988 0.000
#> GSM123749 2 0.0000 0.9866 0.000 1.000 0.000
#> GSM123755 2 0.0000 0.9866 0.000 1.000 0.000
#> GSM123768 2 0.0829 0.9828 0.004 0.984 0.012
#> GSM123776 1 0.5678 0.4375 0.684 0.316 0.000
#> GSM123783 2 0.0983 0.9809 0.004 0.980 0.016
#> GSM123790 2 0.2297 0.9609 0.036 0.944 0.020
#> GSM123794 2 0.0000 0.9866 0.000 1.000 0.000
#> GSM123798 2 0.0424 0.9852 0.000 0.992 0.008
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM123732 3 0.0592 0.807 0.000 0.000 0.984 0.016
#> GSM123736 3 0.0376 0.810 0.004 0.000 0.992 0.004
#> GSM123740 3 0.0000 0.811 0.000 0.000 1.000 0.000
#> GSM123744 3 0.2401 0.746 0.092 0.000 0.904 0.004
#> GSM123746 1 0.2125 0.850 0.920 0.000 0.076 0.004
#> GSM123750 3 0.4509 0.507 0.288 0.000 0.708 0.004
#> GSM123752 1 0.5339 0.313 0.600 0.000 0.384 0.016
#> GSM123756 1 0.0657 0.887 0.984 0.000 0.012 0.004
#> GSM123758 3 0.2634 0.763 0.028 0.020 0.920 0.032
#> GSM123761 3 0.5132 0.164 0.448 0.000 0.548 0.004
#> GSM123763 3 0.4103 0.556 0.256 0.000 0.744 0.000
#> GSM123765 3 0.0000 0.811 0.000 0.000 1.000 0.000
#> GSM123769 1 0.1004 0.885 0.972 0.000 0.024 0.004
#> GSM123771 1 0.0376 0.885 0.992 0.000 0.004 0.004
#> GSM123774 1 0.0000 0.885 1.000 0.000 0.000 0.000
#> GSM123778 3 0.0336 0.810 0.000 0.000 0.992 0.008
#> GSM123780 3 0.0921 0.796 0.000 0.000 0.972 0.028
#> GSM123784 3 0.0188 0.810 0.000 0.000 0.996 0.004
#> GSM123787 3 0.0469 0.809 0.000 0.000 0.988 0.012
#> GSM123791 3 0.0188 0.811 0.000 0.000 0.996 0.004
#> GSM123795 3 0.0592 0.804 0.000 0.000 0.984 0.016
#> GSM123799 3 0.0188 0.810 0.000 0.000 0.996 0.004
#> GSM123730 4 0.1796 0.632 0.004 0.016 0.032 0.948
#> GSM123734 4 0.4898 0.608 0.156 0.000 0.072 0.772
#> GSM123738 4 0.5000 0.393 0.000 0.000 0.496 0.504
#> GSM123742 3 0.7920 -0.376 0.340 0.000 0.344 0.316
#> GSM123745 1 0.3266 0.794 0.832 0.000 0.000 0.168
#> GSM123748 1 0.1211 0.884 0.960 0.000 0.000 0.040
#> GSM123751 1 0.3649 0.744 0.796 0.000 0.000 0.204
#> GSM123754 1 0.2149 0.864 0.912 0.000 0.000 0.088
#> GSM123757 1 0.0188 0.886 0.996 0.000 0.004 0.000
#> GSM123760 4 0.6885 0.452 0.104 0.000 0.436 0.460
#> GSM123762 1 0.3367 0.819 0.864 0.000 0.108 0.028
#> GSM123764 3 0.3801 0.488 0.000 0.000 0.780 0.220
#> GSM123767 4 0.5000 -0.155 0.496 0.000 0.000 0.504
#> GSM123770 1 0.0921 0.887 0.972 0.000 0.000 0.028
#> GSM123773 1 0.2011 0.870 0.920 0.000 0.000 0.080
#> GSM123777 4 0.4730 0.614 0.000 0.000 0.364 0.636
#> GSM123779 4 0.2861 0.670 0.016 0.000 0.096 0.888
#> GSM123782 4 0.6158 0.572 0.056 0.000 0.384 0.560
#> GSM123786 3 0.0336 0.810 0.000 0.000 0.992 0.008
#> GSM123789 3 0.4040 0.413 0.000 0.000 0.752 0.248
#> GSM123793 4 0.4781 0.643 0.004 0.000 0.336 0.660
#> GSM123797 4 0.3908 0.683 0.004 0.000 0.212 0.784
#> GSM123729 2 0.1109 0.971 0.004 0.968 0.000 0.028
#> GSM123733 2 0.1302 0.959 0.000 0.956 0.000 0.044
#> GSM123737 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> GSM123741 2 0.0336 0.974 0.000 0.992 0.000 0.008
#> GSM123747 2 0.0592 0.974 0.000 0.984 0.000 0.016
#> GSM123753 2 0.0592 0.974 0.000 0.984 0.000 0.016
#> GSM123759 2 0.0817 0.973 0.000 0.976 0.000 0.024
#> GSM123766 2 0.1389 0.957 0.000 0.952 0.000 0.048
#> GSM123772 2 0.0592 0.971 0.000 0.984 0.000 0.016
#> GSM123775 2 0.0937 0.971 0.012 0.976 0.000 0.012
#> GSM123781 2 0.0188 0.974 0.000 0.996 0.000 0.004
#> GSM123785 2 0.3726 0.796 0.000 0.788 0.000 0.212
#> GSM123788 2 0.1211 0.961 0.000 0.960 0.000 0.040
#> GSM123792 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> GSM123796 2 0.1211 0.962 0.000 0.960 0.000 0.040
#> GSM123731 2 0.0817 0.973 0.000 0.976 0.000 0.024
#> GSM123735 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> GSM123739 2 0.0592 0.973 0.000 0.984 0.000 0.016
#> GSM123743 2 0.0469 0.975 0.000 0.988 0.000 0.012
#> GSM123749 2 0.0817 0.973 0.000 0.976 0.000 0.024
#> GSM123755 2 0.0817 0.973 0.000 0.976 0.000 0.024
#> GSM123768 2 0.1118 0.969 0.000 0.964 0.000 0.036
#> GSM123776 1 0.2124 0.825 0.924 0.068 0.000 0.008
#> GSM123783 2 0.1211 0.967 0.000 0.960 0.000 0.040
#> GSM123790 2 0.1867 0.942 0.000 0.928 0.000 0.072
#> GSM123794 2 0.0336 0.975 0.000 0.992 0.000 0.008
#> GSM123798 2 0.0817 0.973 0.000 0.976 0.000 0.024
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM123732 3 0.1869 0.8057 0.016 0.000 0.936 0.012 0.036
#> GSM123736 3 0.3385 0.7935 0.036 0.000 0.864 0.056 0.044
#> GSM123740 3 0.2768 0.8046 0.040 0.000 0.896 0.024 0.040
#> GSM123744 3 0.4364 0.7225 0.112 0.000 0.768 0.000 0.120
#> GSM123746 1 0.3734 0.6891 0.812 0.000 0.060 0.000 0.128
#> GSM123750 3 0.6139 0.3304 0.260 0.000 0.556 0.000 0.184
#> GSM123752 1 0.4812 0.4132 0.652 0.000 0.312 0.004 0.032
#> GSM123756 1 0.2110 0.7306 0.912 0.000 0.072 0.000 0.016
#> GSM123758 3 0.3747 0.7718 0.052 0.000 0.844 0.044 0.060
#> GSM123761 5 0.6932 0.2197 0.348 0.000 0.288 0.004 0.360
#> GSM123763 3 0.6598 -0.1558 0.216 0.000 0.428 0.000 0.356
#> GSM123765 3 0.1653 0.8155 0.004 0.000 0.944 0.024 0.028
#> GSM123769 1 0.2473 0.7355 0.896 0.000 0.072 0.000 0.032
#> GSM123771 1 0.1915 0.7484 0.928 0.000 0.040 0.000 0.032
#> GSM123774 1 0.0898 0.7527 0.972 0.000 0.008 0.000 0.020
#> GSM123778 3 0.1704 0.8083 0.000 0.000 0.928 0.004 0.068
#> GSM123780 3 0.3142 0.7641 0.004 0.000 0.856 0.108 0.032
#> GSM123784 3 0.1818 0.8084 0.000 0.000 0.932 0.044 0.024
#> GSM123787 3 0.2976 0.7817 0.004 0.000 0.852 0.012 0.132
#> GSM123791 3 0.2074 0.8002 0.000 0.000 0.896 0.000 0.104
#> GSM123795 3 0.4513 0.7433 0.044 0.000 0.792 0.104 0.060
#> GSM123799 3 0.2523 0.8082 0.040 0.000 0.908 0.028 0.024
#> GSM123730 4 0.3259 0.5861 0.004 0.028 0.028 0.872 0.068
#> GSM123734 4 0.5954 0.3335 0.068 0.000 0.024 0.572 0.336
#> GSM123738 4 0.5724 0.2710 0.004 0.000 0.420 0.504 0.072
#> GSM123742 5 0.4981 0.6068 0.132 0.000 0.056 0.056 0.756
#> GSM123745 1 0.5872 0.0558 0.492 0.000 0.000 0.100 0.408
#> GSM123748 5 0.4528 0.0851 0.444 0.000 0.000 0.008 0.548
#> GSM123751 1 0.5973 0.2295 0.552 0.000 0.004 0.112 0.332
#> GSM123754 1 0.3301 0.7155 0.848 0.000 0.000 0.072 0.080
#> GSM123757 1 0.1908 0.7376 0.908 0.000 0.000 0.000 0.092
#> GSM123760 5 0.4858 0.6042 0.100 0.000 0.064 0.064 0.772
#> GSM123762 5 0.4969 0.4870 0.292 0.000 0.056 0.000 0.652
#> GSM123764 5 0.4245 0.5393 0.024 0.004 0.180 0.016 0.776
#> GSM123767 4 0.5714 0.1019 0.412 0.004 0.000 0.512 0.072
#> GSM123770 1 0.1618 0.7537 0.944 0.000 0.008 0.008 0.040
#> GSM123773 1 0.3731 0.6986 0.816 0.000 0.000 0.112 0.072
#> GSM123777 4 0.4936 0.5339 0.000 0.008 0.284 0.668 0.040
#> GSM123779 4 0.4378 0.5880 0.012 0.004 0.048 0.780 0.156
#> GSM123782 5 0.4747 0.5730 0.060 0.004 0.076 0.072 0.788
#> GSM123786 3 0.3688 0.7662 0.004 0.000 0.812 0.036 0.148
#> GSM123789 5 0.5821 0.4279 0.020 0.000 0.308 0.072 0.600
#> GSM123793 5 0.6603 -0.0979 0.016 0.000 0.140 0.368 0.476
#> GSM123797 4 0.5220 0.6026 0.012 0.000 0.124 0.712 0.152
#> GSM123729 2 0.2253 0.9343 0.016 0.920 0.000 0.036 0.028
#> GSM123733 2 0.2393 0.9120 0.004 0.900 0.000 0.080 0.016
#> GSM123737 2 0.1461 0.9365 0.004 0.952 0.000 0.028 0.016
#> GSM123741 2 0.0912 0.9419 0.000 0.972 0.000 0.012 0.016
#> GSM123747 2 0.1012 0.9433 0.000 0.968 0.000 0.020 0.012
#> GSM123753 2 0.1750 0.9380 0.000 0.936 0.000 0.036 0.028
#> GSM123759 2 0.1981 0.9346 0.000 0.924 0.000 0.048 0.028
#> GSM123766 2 0.1992 0.9376 0.000 0.924 0.000 0.032 0.044
#> GSM123772 2 0.1399 0.9423 0.000 0.952 0.000 0.028 0.020
#> GSM123775 2 0.1989 0.9409 0.016 0.932 0.000 0.020 0.032
#> GSM123781 2 0.2378 0.9283 0.000 0.904 0.000 0.048 0.048
#> GSM123785 2 0.3381 0.8353 0.000 0.808 0.000 0.176 0.016
#> GSM123788 2 0.1662 0.9291 0.004 0.936 0.000 0.056 0.004
#> GSM123792 2 0.0566 0.9416 0.000 0.984 0.000 0.012 0.004
#> GSM123796 2 0.1768 0.9228 0.000 0.924 0.000 0.072 0.004
#> GSM123731 2 0.1012 0.9422 0.000 0.968 0.000 0.020 0.012
#> GSM123735 2 0.1471 0.9363 0.004 0.952 0.000 0.024 0.020
#> GSM123739 2 0.1419 0.9397 0.012 0.956 0.000 0.016 0.016
#> GSM123743 2 0.0854 0.9423 0.004 0.976 0.000 0.012 0.008
#> GSM123749 2 0.1582 0.9384 0.000 0.944 0.000 0.028 0.028
#> GSM123755 2 0.2193 0.9308 0.000 0.912 0.000 0.060 0.028
#> GSM123768 2 0.3384 0.8991 0.000 0.848 0.004 0.088 0.060
#> GSM123776 1 0.4220 0.5483 0.768 0.180 0.004 0.000 0.048
#> GSM123783 2 0.3407 0.9014 0.004 0.864 0.020 0.064 0.048
#> GSM123790 2 0.3745 0.8019 0.000 0.780 0.000 0.196 0.024
#> GSM123794 2 0.1564 0.9376 0.004 0.948 0.000 0.024 0.024
#> GSM123798 2 0.2193 0.9307 0.000 0.912 0.000 0.060 0.028
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM123732 3 0.2302 0.69058 0.012 0.000 0.900 0.012 NA 0.004
#> GSM123736 3 0.5869 0.57796 0.032 0.000 0.584 0.044 NA 0.040
#> GSM123740 3 0.5476 0.60868 0.032 0.000 0.624 0.032 NA 0.032
#> GSM123744 3 0.6394 0.55744 0.080 0.000 0.568 0.004 NA 0.136
#> GSM123746 1 0.4013 0.70305 0.800 0.000 0.060 0.000 NA 0.076
#> GSM123750 3 0.7656 0.10572 0.212 0.000 0.356 0.004 NA 0.252
#> GSM123752 1 0.5913 0.29386 0.532 0.000 0.256 0.000 NA 0.012
#> GSM123756 1 0.1261 0.76151 0.956 0.000 0.008 0.004 NA 0.004
#> GSM123758 3 0.4416 0.63987 0.048 0.004 0.724 0.004 NA 0.008
#> GSM123761 6 0.7238 0.43506 0.156 0.000 0.136 0.008 NA 0.464
#> GSM123763 6 0.7100 0.43998 0.112 0.000 0.136 0.012 NA 0.480
#> GSM123765 3 0.3253 0.69448 0.008 0.000 0.852 0.032 NA 0.024
#> GSM123769 1 0.2973 0.74168 0.864 0.000 0.032 0.004 NA 0.016
#> GSM123771 1 0.1718 0.75908 0.932 0.000 0.008 0.000 NA 0.016
#> GSM123774 1 0.0725 0.75981 0.976 0.000 0.000 0.000 NA 0.012
#> GSM123778 3 0.2186 0.68057 0.000 0.000 0.908 0.008 NA 0.036
#> GSM123780 3 0.3050 0.64830 0.000 0.000 0.852 0.092 NA 0.012
#> GSM123784 3 0.2411 0.68487 0.000 0.000 0.900 0.044 NA 0.024
#> GSM123787 3 0.3768 0.63302 0.000 0.000 0.796 0.008 NA 0.104
#> GSM123791 3 0.3716 0.64406 0.000 0.000 0.792 0.004 NA 0.128
#> GSM123795 3 0.6723 0.47521 0.028 0.000 0.496 0.080 NA 0.072
#> GSM123799 3 0.5225 0.62523 0.040 0.000 0.652 0.020 NA 0.028
#> GSM123730 4 0.2466 0.54053 0.004 0.012 0.024 0.908 NA 0.028
#> GSM123734 4 0.6437 0.29206 0.028 0.000 0.016 0.528 NA 0.260
#> GSM123738 4 0.6982 0.25422 0.004 0.000 0.280 0.448 NA 0.076
#> GSM123742 6 0.3689 0.56523 0.028 0.000 0.016 0.048 NA 0.832
#> GSM123745 1 0.6606 0.09507 0.432 0.000 0.000 0.112 NA 0.372
#> GSM123748 6 0.5441 0.28214 0.304 0.000 0.000 0.036 NA 0.592
#> GSM123751 1 0.6676 0.33998 0.504 0.000 0.004 0.152 NA 0.268
#> GSM123754 1 0.2202 0.74240 0.904 0.000 0.004 0.072 NA 0.012
#> GSM123757 1 0.2857 0.75351 0.880 0.000 0.020 0.008 NA 0.052
#> GSM123760 6 0.2319 0.58577 0.012 0.000 0.020 0.028 NA 0.912
#> GSM123762 6 0.5128 0.56295 0.160 0.000 0.024 0.008 NA 0.696
#> GSM123764 6 0.4631 0.55268 0.000 0.004 0.108 0.052 NA 0.756
#> GSM123767 4 0.5249 -0.15967 0.460 0.000 0.000 0.472 NA 0.040
#> GSM123770 1 0.1542 0.76333 0.944 0.000 0.000 0.016 NA 0.016
#> GSM123773 1 0.3476 0.68626 0.808 0.000 0.000 0.148 NA 0.024
#> GSM123777 4 0.4876 0.48444 0.000 0.004 0.276 0.656 NA 0.028
#> GSM123779 4 0.4757 0.53211 0.004 0.012 0.084 0.764 NA 0.080
#> GSM123782 6 0.5766 0.50178 0.016 0.004 0.092 0.104 NA 0.684
#> GSM123786 3 0.3566 0.64810 0.000 0.000 0.812 0.008 NA 0.076
#> GSM123789 6 0.6102 0.36427 0.000 0.000 0.320 0.072 NA 0.528
#> GSM123793 6 0.6785 0.00883 0.000 0.000 0.044 0.300 NA 0.396
#> GSM123797 4 0.5471 0.53311 0.008 0.000 0.100 0.688 NA 0.068
#> GSM123729 2 0.1204 0.91971 0.000 0.944 0.000 0.000 NA 0.000
#> GSM123733 2 0.2390 0.88968 0.000 0.888 0.000 0.056 NA 0.000
#> GSM123737 2 0.1257 0.91456 0.000 0.952 0.000 0.020 NA 0.000
#> GSM123741 2 0.1387 0.91296 0.000 0.932 0.000 0.000 NA 0.000
#> GSM123747 2 0.1074 0.91989 0.000 0.960 0.000 0.012 NA 0.000
#> GSM123753 2 0.1765 0.90579 0.000 0.904 0.000 0.000 NA 0.000
#> GSM123759 2 0.2048 0.89570 0.000 0.880 0.000 0.000 NA 0.000
#> GSM123766 2 0.1349 0.91684 0.000 0.940 0.000 0.000 NA 0.004
#> GSM123772 2 0.0937 0.91985 0.000 0.960 0.000 0.000 NA 0.000
#> GSM123775 2 0.2203 0.90929 0.000 0.896 0.000 0.004 NA 0.016
#> GSM123781 2 0.2527 0.86981 0.000 0.832 0.000 0.000 NA 0.000
#> GSM123785 2 0.3355 0.83933 0.000 0.816 0.000 0.132 NA 0.004
#> GSM123788 2 0.1863 0.90604 0.000 0.920 0.000 0.044 NA 0.000
#> GSM123792 2 0.1003 0.91614 0.000 0.964 0.000 0.016 NA 0.000
#> GSM123796 2 0.1930 0.90232 0.000 0.916 0.000 0.048 NA 0.000
#> GSM123731 2 0.0790 0.91943 0.000 0.968 0.000 0.000 NA 0.000
#> GSM123735 2 0.2119 0.90092 0.000 0.904 0.000 0.036 NA 0.000
#> GSM123739 2 0.1168 0.91788 0.000 0.956 0.000 0.016 NA 0.000
#> GSM123743 2 0.0725 0.91870 0.000 0.976 0.000 0.012 NA 0.000
#> GSM123749 2 0.1444 0.91065 0.000 0.928 0.000 0.000 NA 0.000
#> GSM123755 2 0.2092 0.89420 0.000 0.876 0.000 0.000 NA 0.000
#> GSM123768 2 0.2902 0.84586 0.000 0.800 0.000 0.000 NA 0.004
#> GSM123776 1 0.5496 0.52703 0.692 0.148 0.004 0.016 NA 0.040
#> GSM123783 2 0.4050 0.80177 0.000 0.756 0.056 0.004 NA 0.004
#> GSM123790 2 0.3993 0.81601 0.000 0.792 0.016 0.108 NA 0.004
#> GSM123794 2 0.1970 0.90542 0.000 0.912 0.000 0.028 NA 0.000
#> GSM123798 2 0.2092 0.89591 0.000 0.876 0.000 0.000 NA 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) infection(p) agent(p) k
#> MAD:NMF 70 6.31e-16 6.31e-16 7.57e-06 2
#> MAD:NMF 66 1.87e-14 1.87e-14 3.89e-05 3
#> MAD:NMF 63 5.50e-18 5.50e-18 1.23e-03 4
#> MAD:NMF 58 1.09e-15 1.09e-15 7.82e-03 5
#> MAD:NMF 57 2.94e-15 2.94e-15 9.47e-03 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "hclust"]
# you can also extract it by
# res = res_list["ATC:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.370 0.260 0.690 0.4093 0.820 0.820
#> 3 3 0.806 0.835 0.896 0.4496 0.585 0.503
#> 4 4 0.871 0.880 0.941 0.1351 0.870 0.700
#> 5 5 0.853 0.816 0.923 0.0452 0.990 0.966
#> 6 6 0.899 0.837 0.925 0.0826 0.938 0.791
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM123732 1 0.9460 -0.267 0.636 0.364
#> GSM123736 1 0.9460 -0.267 0.636 0.364
#> GSM123740 1 0.9460 -0.267 0.636 0.364
#> GSM123744 1 0.9460 -0.267 0.636 0.364
#> GSM123746 1 0.9460 -0.267 0.636 0.364
#> GSM123750 1 0.9460 -0.267 0.636 0.364
#> GSM123752 1 0.9460 -0.267 0.636 0.364
#> GSM123756 2 0.9580 1.000 0.380 0.620
#> GSM123758 1 0.9460 -0.267 0.636 0.364
#> GSM123761 2 0.9580 1.000 0.380 0.620
#> GSM123763 2 0.9580 1.000 0.380 0.620
#> GSM123765 1 0.9460 -0.267 0.636 0.364
#> GSM123769 2 0.9580 1.000 0.380 0.620
#> GSM123771 2 0.9580 1.000 0.380 0.620
#> GSM123774 2 0.9580 1.000 0.380 0.620
#> GSM123778 1 0.9460 -0.267 0.636 0.364
#> GSM123780 1 0.9460 -0.267 0.636 0.364
#> GSM123784 1 0.9460 -0.267 0.636 0.364
#> GSM123787 1 0.9460 -0.267 0.636 0.364
#> GSM123791 1 0.9460 -0.267 0.636 0.364
#> GSM123795 1 0.9460 -0.267 0.636 0.364
#> GSM123799 1 0.9460 -0.267 0.636 0.364
#> GSM123730 1 0.0000 0.384 1.000 0.000
#> GSM123734 1 0.0000 0.384 1.000 0.000
#> GSM123738 1 0.0000 0.384 1.000 0.000
#> GSM123742 1 0.0000 0.384 1.000 0.000
#> GSM123745 1 0.9460 -0.267 0.636 0.364
#> GSM123748 1 0.0376 0.380 0.996 0.004
#> GSM123751 1 0.9286 -0.240 0.656 0.344
#> GSM123754 1 0.9460 -0.267 0.636 0.364
#> GSM123757 1 0.9460 -0.267 0.636 0.364
#> GSM123760 1 0.0000 0.384 1.000 0.000
#> GSM123762 2 0.9580 1.000 0.380 0.620
#> GSM123764 1 0.0000 0.384 1.000 0.000
#> GSM123767 1 0.9460 -0.267 0.636 0.364
#> GSM123770 1 0.9460 -0.267 0.636 0.364
#> GSM123773 1 0.9460 -0.267 0.636 0.364
#> GSM123777 1 0.0000 0.384 1.000 0.000
#> GSM123779 1 0.9427 -0.262 0.640 0.360
#> GSM123782 1 0.0000 0.384 1.000 0.000
#> GSM123786 1 0.9460 -0.267 0.636 0.364
#> GSM123789 1 0.0000 0.384 1.000 0.000
#> GSM123793 1 0.0000 0.384 1.000 0.000
#> GSM123797 1 0.0000 0.384 1.000 0.000
#> GSM123729 1 0.9580 0.530 0.620 0.380
#> GSM123733 1 0.9580 0.530 0.620 0.380
#> GSM123737 1 0.9580 0.530 0.620 0.380
#> GSM123741 1 0.9580 0.530 0.620 0.380
#> GSM123747 1 0.9580 0.530 0.620 0.380
#> GSM123753 1 0.9580 0.530 0.620 0.380
#> GSM123759 1 0.9580 0.530 0.620 0.380
#> GSM123766 1 0.9580 0.530 0.620 0.380
#> GSM123772 1 0.9580 0.530 0.620 0.380
#> GSM123775 1 0.9580 0.530 0.620 0.380
#> GSM123781 1 0.9580 0.530 0.620 0.380
#> GSM123785 1 0.9580 0.530 0.620 0.380
#> GSM123788 1 0.9580 0.530 0.620 0.380
#> GSM123792 1 0.9580 0.530 0.620 0.380
#> GSM123796 1 0.9580 0.530 0.620 0.380
#> GSM123731 1 0.9580 0.530 0.620 0.380
#> GSM123735 1 0.9580 0.530 0.620 0.380
#> GSM123739 1 0.9580 0.530 0.620 0.380
#> GSM123743 1 0.9580 0.530 0.620 0.380
#> GSM123749 1 0.9580 0.530 0.620 0.380
#> GSM123755 1 0.9580 0.530 0.620 0.380
#> GSM123768 1 0.9580 0.530 0.620 0.380
#> GSM123776 1 0.9460 -0.267 0.636 0.364
#> GSM123783 1 0.9580 0.530 0.620 0.380
#> GSM123790 1 0.9580 0.530 0.620 0.380
#> GSM123794 1 0.9580 0.530 0.620 0.380
#> GSM123798 1 0.9580 0.530 0.620 0.380
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM123732 3 0.0424 0.797 0.000 0.008 0.992
#> GSM123736 3 0.0424 0.797 0.000 0.008 0.992
#> GSM123740 3 0.0424 0.797 0.000 0.008 0.992
#> GSM123744 3 0.0424 0.797 0.000 0.008 0.992
#> GSM123746 3 0.0424 0.797 0.000 0.008 0.992
#> GSM123750 3 0.0424 0.797 0.000 0.008 0.992
#> GSM123752 3 0.0424 0.797 0.000 0.008 0.992
#> GSM123756 1 0.5968 0.999 0.636 0.000 0.364
#> GSM123758 3 0.0424 0.797 0.000 0.008 0.992
#> GSM123761 1 0.5988 0.994 0.632 0.000 0.368
#> GSM123763 1 0.5968 0.999 0.636 0.000 0.364
#> GSM123765 3 0.0424 0.797 0.000 0.008 0.992
#> GSM123769 1 0.5968 0.999 0.636 0.000 0.364
#> GSM123771 1 0.5968 0.999 0.636 0.000 0.364
#> GSM123774 3 0.6274 -0.626 0.456 0.000 0.544
#> GSM123778 3 0.0424 0.797 0.000 0.008 0.992
#> GSM123780 3 0.0424 0.797 0.000 0.008 0.992
#> GSM123784 3 0.0424 0.797 0.000 0.008 0.992
#> GSM123787 3 0.0424 0.797 0.000 0.008 0.992
#> GSM123791 3 0.0424 0.797 0.000 0.008 0.992
#> GSM123795 3 0.0424 0.797 0.000 0.008 0.992
#> GSM123799 3 0.0424 0.797 0.000 0.008 0.992
#> GSM123730 3 0.5968 0.601 0.364 0.000 0.636
#> GSM123734 3 0.5968 0.601 0.364 0.000 0.636
#> GSM123738 3 0.5968 0.601 0.364 0.000 0.636
#> GSM123742 3 0.6359 0.607 0.364 0.008 0.628
#> GSM123745 3 0.0424 0.797 0.000 0.008 0.992
#> GSM123748 3 0.6339 0.609 0.360 0.008 0.632
#> GSM123751 3 0.1315 0.786 0.020 0.008 0.972
#> GSM123754 3 0.0424 0.797 0.000 0.008 0.992
#> GSM123757 3 0.0424 0.797 0.000 0.008 0.992
#> GSM123760 3 0.6359 0.607 0.364 0.008 0.628
#> GSM123762 1 0.5968 0.999 0.636 0.000 0.364
#> GSM123764 3 0.6359 0.607 0.364 0.008 0.628
#> GSM123767 3 0.0424 0.797 0.000 0.008 0.992
#> GSM123770 3 0.0424 0.797 0.000 0.008 0.992
#> GSM123773 3 0.0424 0.797 0.000 0.008 0.992
#> GSM123777 3 0.5968 0.601 0.364 0.000 0.636
#> GSM123779 3 0.0661 0.795 0.004 0.008 0.988
#> GSM123782 3 0.6359 0.607 0.364 0.008 0.628
#> GSM123786 3 0.0424 0.797 0.000 0.008 0.992
#> GSM123789 3 0.6359 0.607 0.364 0.008 0.628
#> GSM123793 3 0.5968 0.601 0.364 0.000 0.636
#> GSM123797 3 0.5968 0.601 0.364 0.000 0.636
#> GSM123729 2 0.0000 1.000 0.000 1.000 0.000
#> GSM123733 2 0.0000 1.000 0.000 1.000 0.000
#> GSM123737 2 0.0000 1.000 0.000 1.000 0.000
#> GSM123741 2 0.0000 1.000 0.000 1.000 0.000
#> GSM123747 2 0.0000 1.000 0.000 1.000 0.000
#> GSM123753 2 0.0000 1.000 0.000 1.000 0.000
#> GSM123759 2 0.0000 1.000 0.000 1.000 0.000
#> GSM123766 2 0.0000 1.000 0.000 1.000 0.000
#> GSM123772 2 0.0000 1.000 0.000 1.000 0.000
#> GSM123775 2 0.0000 1.000 0.000 1.000 0.000
#> GSM123781 2 0.0000 1.000 0.000 1.000 0.000
#> GSM123785 2 0.0000 1.000 0.000 1.000 0.000
#> GSM123788 2 0.0000 1.000 0.000 1.000 0.000
#> GSM123792 2 0.0000 1.000 0.000 1.000 0.000
#> GSM123796 2 0.0000 1.000 0.000 1.000 0.000
#> GSM123731 2 0.0000 1.000 0.000 1.000 0.000
#> GSM123735 2 0.0000 1.000 0.000 1.000 0.000
#> GSM123739 2 0.0000 1.000 0.000 1.000 0.000
#> GSM123743 2 0.0000 1.000 0.000 1.000 0.000
#> GSM123749 2 0.0000 1.000 0.000 1.000 0.000
#> GSM123755 2 0.0000 1.000 0.000 1.000 0.000
#> GSM123768 2 0.0000 1.000 0.000 1.000 0.000
#> GSM123776 3 0.0424 0.797 0.000 0.008 0.992
#> GSM123783 2 0.0000 1.000 0.000 1.000 0.000
#> GSM123790 2 0.0000 1.000 0.000 1.000 0.000
#> GSM123794 2 0.0000 1.000 0.000 1.000 0.000
#> GSM123798 2 0.0000 1.000 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM123732 3 0.0188 0.9459 0.000 0 0.996 0.004
#> GSM123736 3 0.0000 0.9469 0.000 0 1.000 0.000
#> GSM123740 3 0.0000 0.9469 0.000 0 1.000 0.000
#> GSM123744 3 0.0000 0.9469 0.000 0 1.000 0.000
#> GSM123746 3 0.0336 0.9421 0.000 0 0.992 0.008
#> GSM123750 3 0.0000 0.9469 0.000 0 1.000 0.000
#> GSM123752 3 0.0000 0.9469 0.000 0 1.000 0.000
#> GSM123756 1 0.4730 0.7642 0.636 0 0.364 0.000
#> GSM123758 3 0.0000 0.9469 0.000 0 1.000 0.000
#> GSM123761 1 0.4746 0.7583 0.632 0 0.368 0.000
#> GSM123763 1 0.0000 0.5501 1.000 0 0.000 0.000
#> GSM123765 3 0.0188 0.9459 0.000 0 0.996 0.004
#> GSM123769 1 0.4730 0.7642 0.636 0 0.364 0.000
#> GSM123771 1 0.4730 0.7642 0.636 0 0.364 0.000
#> GSM123774 3 0.4972 -0.3856 0.456 0 0.544 0.000
#> GSM123778 3 0.0188 0.9459 0.000 0 0.996 0.004
#> GSM123780 3 0.0188 0.9459 0.000 0 0.996 0.004
#> GSM123784 3 0.0188 0.9459 0.000 0 0.996 0.004
#> GSM123787 3 0.0188 0.9459 0.000 0 0.996 0.004
#> GSM123791 3 0.0000 0.9469 0.000 0 1.000 0.000
#> GSM123795 3 0.0000 0.9469 0.000 0 1.000 0.000
#> GSM123799 3 0.0000 0.9469 0.000 0 1.000 0.000
#> GSM123730 4 0.0000 0.7577 0.000 0 0.000 1.000
#> GSM123734 4 0.0000 0.7577 0.000 0 0.000 1.000
#> GSM123738 4 0.0000 0.7577 0.000 0 0.000 1.000
#> GSM123742 4 0.4356 0.7440 0.000 0 0.292 0.708
#> GSM123745 3 0.0000 0.9469 0.000 0 1.000 0.000
#> GSM123748 4 0.4454 0.7222 0.000 0 0.308 0.692
#> GSM123751 3 0.0817 0.9208 0.000 0 0.976 0.024
#> GSM123754 3 0.0336 0.9421 0.000 0 0.992 0.008
#> GSM123757 3 0.0336 0.9421 0.000 0 0.992 0.008
#> GSM123760 4 0.4356 0.7440 0.000 0 0.292 0.708
#> GSM123762 1 0.0592 0.5679 0.984 0 0.016 0.000
#> GSM123764 4 0.4331 0.7461 0.000 0 0.288 0.712
#> GSM123767 3 0.0000 0.9469 0.000 0 1.000 0.000
#> GSM123770 3 0.0336 0.9421 0.000 0 0.992 0.008
#> GSM123773 3 0.0000 0.9469 0.000 0 1.000 0.000
#> GSM123777 4 0.0000 0.7577 0.000 0 0.000 1.000
#> GSM123779 3 0.4948 0.0591 0.000 0 0.560 0.440
#> GSM123782 4 0.4331 0.7461 0.000 0 0.288 0.712
#> GSM123786 3 0.0188 0.9459 0.000 0 0.996 0.004
#> GSM123789 4 0.4356 0.7440 0.000 0 0.292 0.708
#> GSM123793 4 0.0000 0.7577 0.000 0 0.000 1.000
#> GSM123797 4 0.0000 0.7577 0.000 0 0.000 1.000
#> GSM123729 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM123733 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM123737 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM123741 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM123747 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM123753 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM123759 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM123766 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM123772 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM123775 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM123781 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM123785 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM123788 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM123792 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM123796 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM123731 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM123735 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM123739 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM123743 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM123749 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM123755 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM123768 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM123776 3 0.0000 0.9469 0.000 0 1.000 0.000
#> GSM123783 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM123790 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM123794 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM123798 2 0.0000 1.0000 0.000 1 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM123732 3 0.0162 0.9308 0.000 0 0.996 0.004 0.000
#> GSM123736 3 0.0000 0.9310 0.000 0 1.000 0.000 0.000
#> GSM123740 3 0.0000 0.9310 0.000 0 1.000 0.000 0.000
#> GSM123744 3 0.0000 0.9310 0.000 0 1.000 0.000 0.000
#> GSM123746 3 0.0579 0.9275 0.000 0 0.984 0.008 0.008
#> GSM123750 3 0.0000 0.9310 0.000 0 1.000 0.000 0.000
#> GSM123752 3 0.0290 0.9292 0.000 0 0.992 0.000 0.008
#> GSM123756 1 0.4182 0.0420 0.600 0 0.000 0.000 0.400
#> GSM123758 3 0.0290 0.9292 0.000 0 0.992 0.000 0.008
#> GSM123761 1 0.4299 0.0242 0.608 0 0.004 0.000 0.388
#> GSM123763 1 0.4227 0.0701 0.580 0 0.000 0.000 0.420
#> GSM123765 3 0.0162 0.9308 0.000 0 0.996 0.004 0.000
#> GSM123769 1 0.4182 0.0420 0.600 0 0.000 0.000 0.400
#> GSM123771 1 0.4182 0.0420 0.600 0 0.000 0.000 0.400
#> GSM123774 5 0.4227 0.0000 0.420 0 0.000 0.000 0.580
#> GSM123778 3 0.0162 0.9308 0.000 0 0.996 0.004 0.000
#> GSM123780 3 0.0162 0.9308 0.000 0 0.996 0.004 0.000
#> GSM123784 3 0.0162 0.9308 0.000 0 0.996 0.004 0.000
#> GSM123787 3 0.0162 0.9308 0.000 0 0.996 0.004 0.000
#> GSM123791 3 0.0000 0.9310 0.000 0 1.000 0.000 0.000
#> GSM123795 3 0.0000 0.9310 0.000 0 1.000 0.000 0.000
#> GSM123799 3 0.0000 0.9310 0.000 0 1.000 0.000 0.000
#> GSM123730 4 0.0000 0.7375 0.000 0 0.000 1.000 0.000
#> GSM123734 4 0.0000 0.7375 0.000 0 0.000 1.000 0.000
#> GSM123738 4 0.0000 0.7375 0.000 0 0.000 1.000 0.000
#> GSM123742 4 0.3752 0.7490 0.000 0 0.292 0.708 0.000
#> GSM123745 3 0.2929 0.8321 0.000 0 0.820 0.000 0.180
#> GSM123748 4 0.3837 0.7292 0.000 0 0.308 0.692 0.000
#> GSM123751 3 0.3565 0.8142 0.000 0 0.800 0.024 0.176
#> GSM123754 3 0.0898 0.9233 0.000 0 0.972 0.008 0.020
#> GSM123757 3 0.0898 0.9233 0.000 0 0.972 0.008 0.020
#> GSM123760 4 0.3752 0.7490 0.000 0 0.292 0.708 0.000
#> GSM123762 1 0.0000 0.0994 1.000 0 0.000 0.000 0.000
#> GSM123764 4 0.3730 0.7503 0.000 0 0.288 0.712 0.000
#> GSM123767 3 0.2929 0.8321 0.000 0 0.820 0.000 0.180
#> GSM123770 3 0.3053 0.8387 0.000 0 0.828 0.008 0.164
#> GSM123773 3 0.2929 0.8321 0.000 0 0.820 0.000 0.180
#> GSM123777 4 0.0000 0.7375 0.000 0 0.000 1.000 0.000
#> GSM123779 3 0.4262 0.1034 0.000 0 0.560 0.440 0.000
#> GSM123782 4 0.3730 0.7503 0.000 0 0.288 0.712 0.000
#> GSM123786 3 0.0162 0.9308 0.000 0 0.996 0.004 0.000
#> GSM123789 4 0.3752 0.7490 0.000 0 0.292 0.708 0.000
#> GSM123793 4 0.0000 0.7375 0.000 0 0.000 1.000 0.000
#> GSM123797 4 0.0000 0.7375 0.000 0 0.000 1.000 0.000
#> GSM123729 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM123733 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM123737 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM123741 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM123747 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM123753 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM123759 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM123766 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM123772 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM123775 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM123781 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM123785 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM123788 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM123792 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM123796 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM123731 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM123735 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM123739 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM123743 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM123749 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM123755 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM123768 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM123776 3 0.2929 0.8321 0.000 0 0.820 0.000 0.180
#> GSM123783 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM123790 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM123794 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM123798 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM123732 3 0.0146 0.9099 0.000 0 0.996 0.004 0.000 0.000
#> GSM123736 3 0.0000 0.9103 0.000 0 1.000 0.000 0.000 0.000
#> GSM123740 3 0.0000 0.9103 0.000 0 1.000 0.000 0.000 0.000
#> GSM123744 3 0.0000 0.9103 0.000 0 1.000 0.000 0.000 0.000
#> GSM123746 3 0.3468 0.6338 0.264 0 0.728 0.000 0.000 0.008
#> GSM123750 3 0.0000 0.9103 0.000 0 1.000 0.000 0.000 0.000
#> GSM123752 3 0.3221 0.6409 0.264 0 0.736 0.000 0.000 0.000
#> GSM123756 5 0.0000 0.8322 0.000 0 0.000 0.000 1.000 0.000
#> GSM123758 3 0.3221 0.6409 0.264 0 0.736 0.000 0.000 0.000
#> GSM123761 5 0.0405 0.8257 0.000 0 0.004 0.000 0.988 0.008
#> GSM123763 6 0.2631 0.0000 0.000 0 0.000 0.000 0.180 0.820
#> GSM123765 3 0.0146 0.9099 0.000 0 0.996 0.004 0.000 0.000
#> GSM123769 5 0.0000 0.8322 0.000 0 0.000 0.000 1.000 0.000
#> GSM123771 5 0.0000 0.8322 0.000 0 0.000 0.000 1.000 0.000
#> GSM123774 5 0.3101 0.6363 0.148 0 0.000 0.000 0.820 0.032
#> GSM123778 3 0.0146 0.9099 0.000 0 0.996 0.004 0.000 0.000
#> GSM123780 3 0.0146 0.9099 0.000 0 0.996 0.004 0.000 0.000
#> GSM123784 3 0.0146 0.9099 0.000 0 0.996 0.004 0.000 0.000
#> GSM123787 3 0.0146 0.9099 0.000 0 0.996 0.004 0.000 0.000
#> GSM123791 3 0.0000 0.9103 0.000 0 1.000 0.000 0.000 0.000
#> GSM123795 3 0.0000 0.9103 0.000 0 1.000 0.000 0.000 0.000
#> GSM123799 3 0.0000 0.9103 0.000 0 1.000 0.000 0.000 0.000
#> GSM123730 4 0.0000 0.6825 0.000 0 0.000 1.000 0.000 0.000
#> GSM123734 4 0.2340 0.6719 0.000 0 0.000 0.852 0.000 0.148
#> GSM123738 4 0.0000 0.6825 0.000 0 0.000 1.000 0.000 0.000
#> GSM123742 4 0.5169 0.7041 0.000 0 0.292 0.588 0.000 0.120
#> GSM123745 1 0.0000 0.8615 1.000 0 0.000 0.000 0.000 0.000
#> GSM123748 4 0.6256 0.6686 0.088 0 0.220 0.572 0.000 0.120
#> GSM123751 1 0.1053 0.8412 0.964 0 0.012 0.020 0.000 0.004
#> GSM123754 1 0.2882 0.6466 0.812 0 0.180 0.000 0.000 0.008
#> GSM123757 3 0.3934 0.4266 0.376 0 0.616 0.000 0.000 0.008
#> GSM123760 4 0.5169 0.7041 0.000 0 0.292 0.588 0.000 0.120
#> GSM123762 5 0.3756 0.0401 0.000 0 0.000 0.000 0.600 0.400
#> GSM123764 4 0.5153 0.7062 0.000 0 0.288 0.592 0.000 0.120
#> GSM123767 1 0.0000 0.8615 1.000 0 0.000 0.000 0.000 0.000
#> GSM123770 1 0.0622 0.8543 0.980 0 0.012 0.000 0.000 0.008
#> GSM123773 1 0.0000 0.8615 1.000 0 0.000 0.000 0.000 0.000
#> GSM123777 4 0.0000 0.6825 0.000 0 0.000 1.000 0.000 0.000
#> GSM123779 1 0.4617 0.3037 0.544 0 0.016 0.424 0.000 0.016
#> GSM123782 4 0.5153 0.7062 0.000 0 0.288 0.592 0.000 0.120
#> GSM123786 3 0.0146 0.9099 0.000 0 0.996 0.004 0.000 0.000
#> GSM123789 4 0.5169 0.7041 0.000 0 0.292 0.588 0.000 0.120
#> GSM123793 4 0.0000 0.6825 0.000 0 0.000 1.000 0.000 0.000
#> GSM123797 4 0.0000 0.6825 0.000 0 0.000 1.000 0.000 0.000
#> GSM123729 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123733 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123737 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123741 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123747 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123753 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123759 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123766 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123772 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123775 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123781 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123785 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123788 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123792 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123796 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123731 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123735 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123739 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123743 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123749 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123755 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123768 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123776 1 0.0000 0.8615 1.000 0 0.000 0.000 0.000 0.000
#> GSM123783 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123790 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123794 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM123798 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) infection(p) agent(p) k
#> ATC:hclust 33 6.83e-08 6.83e-08 9.77e-02 2
#> ATC:hclust 70 1.22e-14 1.22e-14 9.77e-05 3
#> ATC:hclust 69 6.33e-18 6.33e-18 4.11e-04 4
#> ATC:hclust 63 2.54e-17 2.54e-17 4.06e-04 5
#> ATC:hclust 67 9.96e-23 9.96e-23 1.23e-03 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "kmeans"]
# you can also extract it by
# res = res_list["ATC:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 71 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 0.4714 0.529 0.529
#> 3 3 0.710 0.737 0.865 0.3327 0.849 0.716
#> 4 4 0.731 0.871 0.854 0.1282 0.850 0.628
#> 5 5 0.767 0.835 0.858 0.0735 1.000 1.000
#> 6 6 0.799 0.658 0.791 0.0472 0.925 0.731
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
#> GSM123732 1 0.0000 1.000 1.000 0.000
#> GSM123736 1 0.0000 1.000 1.000 0.000
#> GSM123740 1 0.0000 1.000 1.000 0.000
#> GSM123744 1 0.0000 1.000 1.000 0.000
#> GSM123746 1 0.0000 1.000 1.000 0.000
#> GSM123750 1 0.0000 1.000 1.000 0.000
#> GSM123752 1 0.0000 1.000 1.000 0.000
#> GSM123756 1 0.0000 1.000 1.000 0.000
#> GSM123758 1 0.0000 1.000 1.000 0.000
#> GSM123761 1 0.0000 1.000 1.000 0.000
#> GSM123763 1 0.0000 1.000 1.000 0.000
#> GSM123765 1 0.0000 1.000 1.000 0.000
#> GSM123769 1 0.0000 1.000 1.000 0.000
#> GSM123771 1 0.0000 1.000 1.000 0.000
#> GSM123774 1 0.0000 1.000 1.000 0.000
#> GSM123778 1 0.0000 1.000 1.000 0.000
#> GSM123780 1 0.0000 1.000 1.000 0.000
#> GSM123784 1 0.0000 1.000 1.000 0.000
#> GSM123787 1 0.0000 1.000 1.000 0.000
#> GSM123791 1 0.0000 1.000 1.000 0.000
#> GSM123795 1 0.0000 1.000 1.000 0.000
#> GSM123799 1 0.0000 1.000 1.000 0.000
#> GSM123730 1 0.0000 1.000 1.000 0.000
#> GSM123734 1 0.0000 1.000 1.000 0.000
#> GSM123738 1 0.0000 1.000 1.000 0.000
#> GSM123742 1 0.0000 1.000 1.000 0.000
#> GSM123745 1 0.0000 1.000 1.000 0.000
#> GSM123748 1 0.0000 1.000 1.000 0.000
#> GSM123751 1 0.0000 1.000 1.000 0.000
#> GSM123754 1 0.0000 1.000 1.000 0.000
#> GSM123757 1 0.0000 1.000 1.000 0.000
#> GSM123760 1 0.0000 1.000 1.000 0.000
#> GSM123762 1 0.0000 1.000 1.000 0.000
#> GSM123764 1 0.0000 1.000 1.000 0.000
#> GSM123767 1 0.0000 1.000 1.000 0.000
#> GSM123770 1 0.0000 1.000 1.000 0.000
#> GSM123773 1 0.0000 1.000 1.000 0.000
#> GSM123777 1 0.0000 1.000 1.000 0.000
#> GSM123779 1 0.0000 1.000 1.000 0.000
#> GSM123782 1 0.0000 1.000 1.000 0.000
#> GSM123786 1 0.0000 1.000 1.000 0.000
#> GSM123789 1 0.0000 1.000 1.000 0.000
#> GSM123793 1 0.0000 1.000 1.000 0.000
#> GSM123797 1 0.0000 1.000 1.000 0.000
#> GSM123729 2 0.0000 1.000 0.000 1.000
#> GSM123733 2 0.0000 1.000 0.000 1.000
#> GSM123737 2 0.0000 1.000 0.000 1.000
#> GSM123741 2 0.0000 1.000 0.000 1.000
#> GSM123747 2 0.0000 1.000 0.000 1.000
#> GSM123753 2 0.0000 1.000 0.000 1.000
#> GSM123759 2 0.0000 1.000 0.000 1.000
#> GSM123766 2 0.0000 1.000 0.000 1.000
#> GSM123772 2 0.0000 1.000 0.000 1.000
#> GSM123775 2 0.0000 1.000 0.000 1.000
#> GSM123781 2 0.0000 1.000 0.000 1.000
#> GSM123785 2 0.0000 1.000 0.000 1.000
#> GSM123788 2 0.0000 1.000 0.000 1.000
#> GSM123792 2 0.0000 1.000 0.000 1.000
#> GSM123796 2 0.0000 1.000 0.000 1.000
#> GSM123731 2 0.0000 1.000 0.000 1.000
#> GSM123735 2 0.0000 1.000 0.000 1.000
#> GSM123739 2 0.0000 1.000 0.000 1.000
#> GSM123743 2 0.0000 1.000 0.000 1.000
#> GSM123749 2 0.0000 1.000 0.000 1.000
#> GSM123755 2 0.0000 1.000 0.000 1.000
#> GSM123768 2 0.0000 1.000 0.000 1.000
#> GSM123776 1 0.0376 0.996 0.996 0.004
#> GSM123783 2 0.0000 1.000 0.000 1.000
#> GSM123790 2 0.0000 1.000 0.000 1.000
#> GSM123794 2 0.0000 1.000 0.000 1.000
#> GSM123798 2 0.0000 1.000 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM123732 3 0.5733 0.5214 0.324 0.000 0.676
#> GSM123736 3 0.5785 0.5081 0.332 0.000 0.668
#> GSM123740 3 0.5785 0.5081 0.332 0.000 0.668
#> GSM123744 1 0.3192 0.8292 0.888 0.000 0.112
#> GSM123746 1 0.5988 0.3440 0.632 0.000 0.368
#> GSM123750 1 0.6299 -0.1089 0.524 0.000 0.476
#> GSM123752 3 0.6305 0.1679 0.484 0.000 0.516
#> GSM123756 1 0.3116 0.8333 0.892 0.000 0.108
#> GSM123758 3 0.6215 0.2927 0.428 0.000 0.572
#> GSM123761 1 0.3116 0.8333 0.892 0.000 0.108
#> GSM123763 1 0.3116 0.8333 0.892 0.000 0.108
#> GSM123765 3 0.5733 0.5214 0.324 0.000 0.676
#> GSM123769 1 0.3116 0.8333 0.892 0.000 0.108
#> GSM123771 1 0.3116 0.8333 0.892 0.000 0.108
#> GSM123774 1 0.3116 0.8333 0.892 0.000 0.108
#> GSM123778 3 0.5733 0.5214 0.324 0.000 0.676
#> GSM123780 3 0.2537 0.6944 0.080 0.000 0.920
#> GSM123784 3 0.5733 0.5214 0.324 0.000 0.676
#> GSM123787 3 0.5733 0.5214 0.324 0.000 0.676
#> GSM123791 3 0.5882 0.4749 0.348 0.000 0.652
#> GSM123795 3 0.5760 0.5150 0.328 0.000 0.672
#> GSM123799 3 0.5785 0.5081 0.332 0.000 0.668
#> GSM123730 3 0.2313 0.6635 0.032 0.024 0.944
#> GSM123734 3 0.2261 0.6936 0.068 0.000 0.932
#> GSM123738 3 0.0000 0.7098 0.000 0.000 1.000
#> GSM123742 3 0.2448 0.6896 0.076 0.000 0.924
#> GSM123745 3 0.3482 0.6539 0.128 0.000 0.872
#> GSM123748 3 0.3482 0.6539 0.128 0.000 0.872
#> GSM123751 3 0.3482 0.6539 0.128 0.000 0.872
#> GSM123754 3 0.3482 0.6539 0.128 0.000 0.872
#> GSM123757 3 0.6008 0.4186 0.372 0.000 0.628
#> GSM123760 3 0.2261 0.6936 0.068 0.000 0.932
#> GSM123762 1 0.3116 0.8333 0.892 0.000 0.108
#> GSM123764 3 0.0000 0.7098 0.000 0.000 1.000
#> GSM123767 3 0.1964 0.6986 0.056 0.000 0.944
#> GSM123770 1 0.6309 0.0587 0.500 0.000 0.500
#> GSM123773 3 0.3192 0.6668 0.112 0.000 0.888
#> GSM123777 3 0.0000 0.7098 0.000 0.000 1.000
#> GSM123779 3 0.0000 0.7098 0.000 0.000 1.000
#> GSM123782 3 0.0000 0.7098 0.000 0.000 1.000
#> GSM123786 3 0.5733 0.5214 0.324 0.000 0.676
#> GSM123789 3 0.0000 0.7098 0.000 0.000 1.000
#> GSM123793 3 0.0000 0.7098 0.000 0.000 1.000
#> GSM123797 3 0.0000 0.7098 0.000 0.000 1.000
#> GSM123729 2 0.2448 0.9539 0.076 0.924 0.000
#> GSM123733 2 0.1031 0.9736 0.024 0.976 0.000
#> GSM123737 2 0.1529 0.9709 0.040 0.960 0.000
#> GSM123741 2 0.0000 0.9774 0.000 1.000 0.000
#> GSM123747 2 0.0000 0.9774 0.000 1.000 0.000
#> GSM123753 2 0.0000 0.9774 0.000 1.000 0.000
#> GSM123759 2 0.1163 0.9744 0.028 0.972 0.000
#> GSM123766 2 0.1289 0.9708 0.032 0.968 0.000
#> GSM123772 2 0.1289 0.9708 0.032 0.968 0.000
#> GSM123775 2 0.2448 0.9539 0.076 0.924 0.000
#> GSM123781 2 0.1289 0.9727 0.032 0.968 0.000
#> GSM123785 2 0.1289 0.9708 0.032 0.968 0.000
#> GSM123788 2 0.1031 0.9736 0.024 0.976 0.000
#> GSM123792 2 0.0237 0.9773 0.004 0.996 0.000
#> GSM123796 2 0.1031 0.9736 0.024 0.976 0.000
#> GSM123731 2 0.1163 0.9744 0.028 0.972 0.000
#> GSM123735 2 0.0237 0.9773 0.004 0.996 0.000
#> GSM123739 2 0.1529 0.9709 0.040 0.960 0.000
#> GSM123743 2 0.0000 0.9774 0.000 1.000 0.000
#> GSM123749 2 0.1163 0.9744 0.028 0.972 0.000
#> GSM123755 2 0.1163 0.9744 0.028 0.972 0.000
#> GSM123768 2 0.2165 0.9602 0.064 0.936 0.000
#> GSM123776 3 0.6075 0.5094 0.316 0.008 0.676
#> GSM123783 2 0.2448 0.9539 0.076 0.924 0.000
#> GSM123790 2 0.1031 0.9736 0.024 0.976 0.000
#> GSM123794 2 0.0237 0.9773 0.004 0.996 0.000
#> GSM123798 2 0.1163 0.9744 0.028 0.972 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM123732 3 0.0469 0.908 0.000 0.000 0.988 0.012
#> GSM123736 3 0.0336 0.910 0.000 0.000 0.992 0.008
#> GSM123740 3 0.0336 0.910 0.000 0.000 0.992 0.008
#> GSM123744 3 0.5997 -0.101 0.376 0.000 0.576 0.048
#> GSM123746 3 0.4656 0.686 0.072 0.000 0.792 0.136
#> GSM123750 3 0.2197 0.846 0.024 0.000 0.928 0.048
#> GSM123752 3 0.3048 0.812 0.016 0.000 0.876 0.108
#> GSM123756 1 0.4719 0.990 0.772 0.000 0.180 0.048
#> GSM123758 3 0.2142 0.865 0.016 0.000 0.928 0.056
#> GSM123761 1 0.4801 0.988 0.764 0.000 0.188 0.048
#> GSM123763 1 0.4990 0.984 0.756 0.000 0.184 0.060
#> GSM123765 3 0.0336 0.910 0.000 0.000 0.992 0.008
#> GSM123769 1 0.4719 0.990 0.772 0.000 0.180 0.048
#> GSM123771 1 0.4719 0.990 0.772 0.000 0.180 0.048
#> GSM123774 1 0.4789 0.978 0.772 0.000 0.172 0.056
#> GSM123778 3 0.0469 0.908 0.000 0.000 0.988 0.012
#> GSM123780 3 0.2999 0.721 0.004 0.000 0.864 0.132
#> GSM123784 3 0.0336 0.910 0.000 0.000 0.992 0.008
#> GSM123787 3 0.0336 0.910 0.000 0.000 0.992 0.008
#> GSM123791 3 0.0336 0.898 0.008 0.000 0.992 0.000
#> GSM123795 3 0.0336 0.910 0.000 0.000 0.992 0.008
#> GSM123799 3 0.0336 0.910 0.000 0.000 0.992 0.008
#> GSM123730 4 0.5291 0.847 0.032 0.004 0.264 0.700
#> GSM123734 4 0.3610 0.866 0.000 0.000 0.200 0.800
#> GSM123738 4 0.5182 0.845 0.028 0.000 0.288 0.684
#> GSM123742 4 0.4194 0.865 0.008 0.000 0.228 0.764
#> GSM123745 4 0.3479 0.849 0.012 0.000 0.148 0.840
#> GSM123748 4 0.3925 0.849 0.016 0.000 0.176 0.808
#> GSM123751 4 0.3836 0.850 0.016 0.000 0.168 0.816
#> GSM123754 4 0.3764 0.850 0.012 0.000 0.172 0.816
#> GSM123757 4 0.5322 0.652 0.028 0.000 0.312 0.660
#> GSM123760 4 0.4194 0.865 0.008 0.000 0.228 0.764
#> GSM123762 1 0.4990 0.984 0.756 0.000 0.184 0.060
#> GSM123764 4 0.4632 0.845 0.004 0.000 0.308 0.688
#> GSM123767 4 0.3725 0.862 0.008 0.000 0.180 0.812
#> GSM123770 4 0.6078 0.610 0.152 0.000 0.164 0.684
#> GSM123773 4 0.3401 0.852 0.008 0.000 0.152 0.840
#> GSM123777 4 0.5157 0.846 0.028 0.000 0.284 0.688
#> GSM123779 4 0.4456 0.854 0.004 0.000 0.280 0.716
#> GSM123782 4 0.4608 0.848 0.004 0.000 0.304 0.692
#> GSM123786 3 0.0469 0.908 0.000 0.000 0.988 0.012
#> GSM123789 4 0.4677 0.842 0.004 0.000 0.316 0.680
#> GSM123793 4 0.5157 0.846 0.028 0.000 0.284 0.688
#> GSM123797 4 0.5157 0.846 0.028 0.000 0.284 0.688
#> GSM123729 2 0.4805 0.815 0.132 0.784 0.000 0.084
#> GSM123733 2 0.0927 0.947 0.016 0.976 0.000 0.008
#> GSM123737 2 0.1174 0.943 0.012 0.968 0.000 0.020
#> GSM123741 2 0.0000 0.947 0.000 1.000 0.000 0.000
#> GSM123747 2 0.0804 0.947 0.012 0.980 0.000 0.008
#> GSM123753 2 0.0336 0.947 0.008 0.992 0.000 0.000
#> GSM123759 2 0.1151 0.944 0.024 0.968 0.000 0.008
#> GSM123766 2 0.1388 0.939 0.028 0.960 0.000 0.012
#> GSM123772 2 0.1388 0.939 0.028 0.960 0.000 0.012
#> GSM123775 2 0.5423 0.775 0.144 0.740 0.000 0.116
#> GSM123781 2 0.1677 0.938 0.040 0.948 0.000 0.012
#> GSM123785 2 0.1820 0.934 0.036 0.944 0.000 0.020
#> GSM123788 2 0.0927 0.947 0.016 0.976 0.000 0.008
#> GSM123792 2 0.0804 0.947 0.012 0.980 0.000 0.008
#> GSM123796 2 0.0927 0.947 0.016 0.976 0.000 0.008
#> GSM123731 2 0.0927 0.945 0.016 0.976 0.000 0.008
#> GSM123735 2 0.0804 0.947 0.012 0.980 0.000 0.008
#> GSM123739 2 0.1174 0.943 0.012 0.968 0.000 0.020
#> GSM123743 2 0.0336 0.948 0.008 0.992 0.000 0.000
#> GSM123749 2 0.1151 0.944 0.024 0.968 0.000 0.008
#> GSM123755 2 0.0592 0.947 0.016 0.984 0.000 0.000
#> GSM123768 2 0.5080 0.801 0.144 0.764 0.000 0.092
#> GSM123776 4 0.5900 0.555 0.148 0.052 0.056 0.744
#> GSM123783 2 0.5462 0.775 0.152 0.736 0.000 0.112
#> GSM123790 2 0.0927 0.947 0.016 0.976 0.000 0.008
#> GSM123794 2 0.0804 0.947 0.012 0.980 0.000 0.008
#> GSM123798 2 0.1284 0.943 0.024 0.964 0.000 0.012
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM123732 3 0.0324 0.950 0.000 0.000 0.992 0.004 0.004
#> GSM123736 3 0.0324 0.950 0.000 0.000 0.992 0.004 0.004
#> GSM123740 3 0.0324 0.950 0.000 0.000 0.992 0.004 0.004
#> GSM123744 3 0.4318 0.536 0.296 0.000 0.688 0.008 0.008
#> GSM123746 3 0.3120 0.846 0.048 0.000 0.864 0.084 0.004
#> GSM123750 3 0.1267 0.929 0.024 0.000 0.960 0.012 0.004
#> GSM123752 3 0.2429 0.884 0.020 0.000 0.900 0.076 0.004
#> GSM123756 1 0.1981 0.970 0.920 0.000 0.064 0.016 0.000
#> GSM123758 3 0.1646 0.917 0.020 0.000 0.944 0.032 0.004
#> GSM123761 1 0.2141 0.969 0.916 0.000 0.064 0.016 0.004
#> GSM123763 1 0.3845 0.943 0.824 0.000 0.064 0.012 0.100
#> GSM123765 3 0.0162 0.950 0.000 0.000 0.996 0.004 0.000
#> GSM123769 1 0.1981 0.970 0.920 0.000 0.064 0.016 0.000
#> GSM123771 1 0.1981 0.970 0.920 0.000 0.064 0.016 0.000
#> GSM123774 1 0.2153 0.941 0.916 0.000 0.040 0.044 0.000
#> GSM123778 3 0.0324 0.950 0.000 0.000 0.992 0.004 0.004
#> GSM123780 3 0.1444 0.910 0.000 0.000 0.948 0.040 0.012
#> GSM123784 3 0.0162 0.950 0.000 0.000 0.996 0.004 0.000
#> GSM123787 3 0.0162 0.950 0.000 0.000 0.996 0.004 0.000
#> GSM123791 3 0.0324 0.950 0.000 0.000 0.992 0.004 0.004
#> GSM123795 3 0.0324 0.950 0.000 0.000 0.992 0.004 0.004
#> GSM123799 3 0.0324 0.950 0.000 0.000 0.992 0.004 0.004
#> GSM123730 4 0.5980 0.758 0.016 0.000 0.092 0.584 0.308
#> GSM123734 4 0.4234 0.808 0.000 0.000 0.056 0.760 0.184
#> GSM123738 4 0.5933 0.758 0.012 0.000 0.096 0.584 0.308
#> GSM123742 4 0.3159 0.804 0.000 0.000 0.056 0.856 0.088
#> GSM123745 4 0.1216 0.777 0.020 0.000 0.020 0.960 0.000
#> GSM123748 4 0.1211 0.777 0.016 0.000 0.024 0.960 0.000
#> GSM123751 4 0.1211 0.777 0.016 0.000 0.024 0.960 0.000
#> GSM123754 4 0.1310 0.776 0.020 0.000 0.024 0.956 0.000
#> GSM123757 4 0.4039 0.615 0.036 0.000 0.184 0.776 0.004
#> GSM123760 4 0.4114 0.808 0.000 0.000 0.060 0.776 0.164
#> GSM123762 1 0.3845 0.943 0.824 0.000 0.064 0.012 0.100
#> GSM123764 4 0.4867 0.804 0.000 0.000 0.104 0.716 0.180
#> GSM123767 4 0.1211 0.779 0.016 0.000 0.024 0.960 0.000
#> GSM123770 4 0.3183 0.643 0.156 0.000 0.016 0.828 0.000
#> GSM123773 4 0.1211 0.779 0.016 0.000 0.024 0.960 0.000
#> GSM123777 4 0.5933 0.758 0.012 0.000 0.096 0.584 0.308
#> GSM123779 4 0.4964 0.800 0.000 0.000 0.096 0.700 0.204
#> GSM123782 4 0.4948 0.803 0.000 0.000 0.108 0.708 0.184
#> GSM123786 3 0.0324 0.950 0.000 0.000 0.992 0.004 0.004
#> GSM123789 4 0.4879 0.804 0.000 0.000 0.108 0.716 0.176
#> GSM123793 4 0.5933 0.758 0.012 0.000 0.096 0.584 0.308
#> GSM123797 4 0.5933 0.758 0.012 0.000 0.096 0.584 0.308
#> GSM123729 2 0.5189 0.649 0.020 0.584 0.004 0.012 0.380
#> GSM123733 2 0.1525 0.873 0.012 0.948 0.000 0.004 0.036
#> GSM123737 2 0.2633 0.862 0.012 0.892 0.004 0.008 0.084
#> GSM123741 2 0.0404 0.877 0.000 0.988 0.000 0.000 0.012
#> GSM123747 2 0.1251 0.874 0.008 0.956 0.000 0.000 0.036
#> GSM123753 2 0.1197 0.876 0.000 0.952 0.000 0.000 0.048
#> GSM123759 2 0.2648 0.854 0.000 0.848 0.000 0.000 0.152
#> GSM123766 2 0.2959 0.856 0.016 0.864 0.000 0.008 0.112
#> GSM123772 2 0.2857 0.856 0.012 0.868 0.000 0.008 0.112
#> GSM123775 2 0.5316 0.565 0.020 0.508 0.004 0.012 0.456
#> GSM123781 2 0.3403 0.845 0.012 0.820 0.000 0.008 0.160
#> GSM123785 2 0.2692 0.849 0.016 0.884 0.000 0.008 0.092
#> GSM123788 2 0.1525 0.873 0.012 0.948 0.000 0.004 0.036
#> GSM123792 2 0.1251 0.874 0.008 0.956 0.000 0.000 0.036
#> GSM123796 2 0.1525 0.873 0.012 0.948 0.000 0.004 0.036
#> GSM123731 2 0.2074 0.868 0.000 0.896 0.000 0.000 0.104
#> GSM123735 2 0.1251 0.874 0.008 0.956 0.000 0.000 0.036
#> GSM123739 2 0.2633 0.862 0.012 0.892 0.004 0.008 0.084
#> GSM123743 2 0.0162 0.877 0.000 0.996 0.000 0.000 0.004
#> GSM123749 2 0.2648 0.854 0.000 0.848 0.000 0.000 0.152
#> GSM123755 2 0.2329 0.862 0.000 0.876 0.000 0.000 0.124
#> GSM123768 2 0.4350 0.658 0.004 0.588 0.000 0.000 0.408
#> GSM123776 4 0.5998 0.293 0.048 0.016 0.012 0.540 0.384
#> GSM123783 2 0.4809 0.581 0.008 0.516 0.000 0.008 0.468
#> GSM123790 2 0.1525 0.873 0.012 0.948 0.000 0.004 0.036
#> GSM123794 2 0.1251 0.874 0.008 0.956 0.000 0.000 0.036
#> GSM123798 2 0.2732 0.852 0.000 0.840 0.000 0.000 0.160
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM123732 3 0.0767 0.9541 0.004 0.000 0.976 0.012 0.008 0.000
#> GSM123736 3 0.0146 0.9546 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM123740 3 0.0146 0.9546 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM123744 3 0.3884 0.6595 0.012 0.000 0.736 0.000 0.020 0.232
#> GSM123746 3 0.2594 0.8903 0.084 0.000 0.880 0.004 0.028 0.004
#> GSM123750 3 0.0914 0.9457 0.016 0.000 0.968 0.000 0.016 0.000
#> GSM123752 3 0.2199 0.8958 0.088 0.000 0.892 0.000 0.020 0.000
#> GSM123756 6 0.0547 0.9318 0.000 0.000 0.020 0.000 0.000 0.980
#> GSM123758 3 0.1616 0.9245 0.048 0.000 0.932 0.000 0.020 0.000
#> GSM123761 6 0.1262 0.9295 0.008 0.000 0.020 0.000 0.016 0.956
#> GSM123763 6 0.4431 0.8628 0.148 0.000 0.020 0.008 0.068 0.756
#> GSM123765 3 0.0653 0.9542 0.004 0.000 0.980 0.012 0.004 0.000
#> GSM123769 6 0.0547 0.9318 0.000 0.000 0.020 0.000 0.000 0.980
#> GSM123771 6 0.0837 0.9304 0.004 0.000 0.020 0.000 0.004 0.972
#> GSM123774 6 0.1985 0.8877 0.064 0.000 0.008 0.008 0.004 0.916
#> GSM123778 3 0.0767 0.9541 0.004 0.000 0.976 0.012 0.008 0.000
#> GSM123780 3 0.0951 0.9506 0.004 0.000 0.968 0.020 0.008 0.000
#> GSM123784 3 0.0653 0.9542 0.004 0.000 0.980 0.012 0.004 0.000
#> GSM123787 3 0.0653 0.9542 0.004 0.000 0.980 0.012 0.004 0.000
#> GSM123791 3 0.0146 0.9546 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM123795 3 0.0146 0.9546 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM123799 3 0.0146 0.9546 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM123730 4 0.5461 0.5742 0.108 0.000 0.024 0.648 0.212 0.008
#> GSM123734 4 0.2118 0.5587 0.048 0.000 0.020 0.916 0.012 0.004
#> GSM123738 4 0.5405 0.5777 0.096 0.000 0.024 0.660 0.208 0.012
#> GSM123742 4 0.3971 0.0170 0.268 0.000 0.024 0.704 0.004 0.000
#> GSM123745 1 0.3950 0.7361 0.564 0.000 0.004 0.432 0.000 0.000
#> GSM123748 4 0.4089 -0.6295 0.468 0.000 0.008 0.524 0.000 0.000
#> GSM123751 4 0.3997 -0.6639 0.488 0.000 0.004 0.508 0.000 0.000
#> GSM123754 1 0.4018 0.7451 0.580 0.000 0.008 0.412 0.000 0.000
#> GSM123757 1 0.5548 0.6298 0.580 0.000 0.108 0.292 0.020 0.000
#> GSM123760 4 0.2760 0.4652 0.116 0.000 0.024 0.856 0.004 0.000
#> GSM123762 6 0.4431 0.8628 0.148 0.000 0.020 0.008 0.068 0.756
#> GSM123764 4 0.1511 0.5785 0.012 0.000 0.044 0.940 0.004 0.000
#> GSM123767 1 0.4189 0.7312 0.552 0.000 0.004 0.436 0.008 0.000
#> GSM123770 1 0.4987 0.7017 0.584 0.000 0.000 0.328 0.000 0.088
#> GSM123773 1 0.4184 0.7351 0.556 0.000 0.004 0.432 0.008 0.000
#> GSM123777 4 0.5461 0.5742 0.108 0.000 0.024 0.648 0.212 0.008
#> GSM123779 4 0.1718 0.5836 0.020 0.000 0.024 0.936 0.020 0.000
#> GSM123782 4 0.1887 0.5734 0.016 0.000 0.048 0.924 0.012 0.000
#> GSM123786 3 0.0767 0.9541 0.004 0.000 0.976 0.012 0.008 0.000
#> GSM123789 4 0.1888 0.5638 0.012 0.000 0.068 0.916 0.004 0.000
#> GSM123793 4 0.5405 0.5777 0.096 0.000 0.024 0.660 0.208 0.012
#> GSM123797 4 0.5405 0.5777 0.096 0.000 0.024 0.660 0.208 0.012
#> GSM123729 5 0.4671 0.8227 0.044 0.424 0.000 0.000 0.532 0.000
#> GSM123733 2 0.0146 0.7249 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM123737 2 0.3409 0.5797 0.044 0.808 0.000 0.000 0.144 0.004
#> GSM123741 2 0.1508 0.7147 0.004 0.940 0.000 0.004 0.048 0.004
#> GSM123747 2 0.0146 0.7252 0.004 0.996 0.000 0.000 0.000 0.000
#> GSM123753 2 0.2519 0.6699 0.004 0.864 0.000 0.004 0.124 0.004
#> GSM123759 2 0.3717 0.0332 0.000 0.616 0.000 0.000 0.384 0.000
#> GSM123766 2 0.4219 0.5862 0.060 0.764 0.000 0.012 0.156 0.008
#> GSM123772 2 0.4219 0.5862 0.060 0.764 0.000 0.012 0.156 0.008
#> GSM123775 5 0.4736 0.8510 0.060 0.352 0.000 0.000 0.588 0.000
#> GSM123781 2 0.5124 0.2576 0.060 0.620 0.000 0.012 0.300 0.008
#> GSM123785 2 0.2007 0.6609 0.044 0.916 0.000 0.004 0.036 0.000
#> GSM123788 2 0.0146 0.7249 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM123792 2 0.0146 0.7252 0.004 0.996 0.000 0.000 0.000 0.000
#> GSM123796 2 0.0146 0.7249 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM123731 2 0.3464 0.2444 0.000 0.688 0.000 0.000 0.312 0.000
#> GSM123735 2 0.0291 0.7241 0.004 0.992 0.000 0.000 0.004 0.000
#> GSM123739 2 0.3409 0.5797 0.044 0.808 0.000 0.000 0.144 0.004
#> GSM123743 2 0.1080 0.7198 0.004 0.960 0.000 0.000 0.032 0.004
#> GSM123749 2 0.3717 0.0332 0.000 0.616 0.000 0.000 0.384 0.000
#> GSM123755 2 0.3659 0.1188 0.000 0.636 0.000 0.000 0.364 0.000
#> GSM123768 5 0.3765 0.8258 0.000 0.404 0.000 0.000 0.596 0.000
#> GSM123776 1 0.5549 0.4127 0.556 0.008 0.000 0.132 0.304 0.000
#> GSM123783 5 0.3954 0.8695 0.012 0.352 0.000 0.000 0.636 0.000
#> GSM123790 2 0.0405 0.7236 0.004 0.988 0.000 0.000 0.008 0.000
#> GSM123794 2 0.0291 0.7241 0.004 0.992 0.000 0.000 0.004 0.000
#> GSM123798 2 0.3717 0.0332 0.000 0.616 0.000 0.000 0.384 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) infection(p) agent(p) k
#> ATC:kmeans 71 3.04e-15 3.04e-15 5.99e-05 2
#> ATC:kmeans 64 7.70e-15 7.70e-15 3.36e-04 3
#> ATC:kmeans 70 4.19e-24 4.19e-24 3.28e-04 4
#> ATC:kmeans 70 2.59e-25 2.59e-25 6.26e-05 5
#> ATC:kmeans 60 8.10e-19 8.10e-19 4.61e-03 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "skmeans"]
# you can also extract it by
# res = res_list["ATC:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4850 0.515 0.515
#> 3 3 0.819 0.863 0.895 0.3793 0.801 0.619
#> 4 4 0.898 0.872 0.943 0.0990 0.860 0.618
#> 5 5 0.884 0.822 0.896 0.0435 0.926 0.739
#> 6 6 0.878 0.773 0.853 0.0265 0.984 0.932
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
#> GSM123732 1 0 1 1 0
#> GSM123736 1 0 1 1 0
#> GSM123740 1 0 1 1 0
#> GSM123744 1 0 1 1 0
#> GSM123746 1 0 1 1 0
#> GSM123750 1 0 1 1 0
#> GSM123752 1 0 1 1 0
#> GSM123756 1 0 1 1 0
#> GSM123758 1 0 1 1 0
#> GSM123761 1 0 1 1 0
#> GSM123763 1 0 1 1 0
#> GSM123765 1 0 1 1 0
#> GSM123769 1 0 1 1 0
#> GSM123771 1 0 1 1 0
#> GSM123774 1 0 1 1 0
#> GSM123778 1 0 1 1 0
#> GSM123780 1 0 1 1 0
#> GSM123784 1 0 1 1 0
#> GSM123787 1 0 1 1 0
#> GSM123791 1 0 1 1 0
#> GSM123795 1 0 1 1 0
#> GSM123799 1 0 1 1 0
#> GSM123730 2 0 1 0 1
#> GSM123734 1 0 1 1 0
#> GSM123738 1 0 1 1 0
#> GSM123742 1 0 1 1 0
#> GSM123745 1 0 1 1 0
#> GSM123748 1 0 1 1 0
#> GSM123751 1 0 1 1 0
#> GSM123754 1 0 1 1 0
#> GSM123757 1 0 1 1 0
#> GSM123760 1 0 1 1 0
#> GSM123762 1 0 1 1 0
#> GSM123764 1 0 1 1 0
#> GSM123767 1 0 1 1 0
#> GSM123770 1 0 1 1 0
#> GSM123773 1 0 1 1 0
#> GSM123777 1 0 1 1 0
#> GSM123779 1 0 1 1 0
#> GSM123782 1 0 1 1 0
#> GSM123786 1 0 1 1 0
#> GSM123789 1 0 1 1 0
#> GSM123793 1 0 1 1 0
#> GSM123797 1 0 1 1 0
#> GSM123729 2 0 1 0 1
#> GSM123733 2 0 1 0 1
#> GSM123737 2 0 1 0 1
#> GSM123741 2 0 1 0 1
#> GSM123747 2 0 1 0 1
#> GSM123753 2 0 1 0 1
#> GSM123759 2 0 1 0 1
#> GSM123766 2 0 1 0 1
#> GSM123772 2 0 1 0 1
#> GSM123775 2 0 1 0 1
#> GSM123781 2 0 1 0 1
#> GSM123785 2 0 1 0 1
#> GSM123788 2 0 1 0 1
#> GSM123792 2 0 1 0 1
#> GSM123796 2 0 1 0 1
#> GSM123731 2 0 1 0 1
#> GSM123735 2 0 1 0 1
#> GSM123739 2 0 1 0 1
#> GSM123743 2 0 1 0 1
#> GSM123749 2 0 1 0 1
#> GSM123755 2 0 1 0 1
#> GSM123768 2 0 1 0 1
#> GSM123776 2 0 1 0 1
#> GSM123783 2 0 1 0 1
#> GSM123790 2 0 1 0 1
#> GSM123794 2 0 1 0 1
#> GSM123798 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM123732 3 0.5397 0.793 0.280 0.000 0.720
#> GSM123736 3 0.5397 0.793 0.280 0.000 0.720
#> GSM123740 3 0.5397 0.793 0.280 0.000 0.720
#> GSM123744 3 0.0000 0.807 0.000 0.000 1.000
#> GSM123746 3 0.0000 0.807 0.000 0.000 1.000
#> GSM123750 3 0.0000 0.807 0.000 0.000 1.000
#> GSM123752 3 0.0000 0.807 0.000 0.000 1.000
#> GSM123756 3 0.0000 0.807 0.000 0.000 1.000
#> GSM123758 3 0.0237 0.807 0.004 0.000 0.996
#> GSM123761 3 0.0000 0.807 0.000 0.000 1.000
#> GSM123763 3 0.0000 0.807 0.000 0.000 1.000
#> GSM123765 3 0.5397 0.793 0.280 0.000 0.720
#> GSM123769 3 0.0000 0.807 0.000 0.000 1.000
#> GSM123771 3 0.0000 0.807 0.000 0.000 1.000
#> GSM123774 3 0.0000 0.807 0.000 0.000 1.000
#> GSM123778 3 0.5397 0.793 0.280 0.000 0.720
#> GSM123780 3 0.5397 0.793 0.280 0.000 0.720
#> GSM123784 3 0.5397 0.793 0.280 0.000 0.720
#> GSM123787 3 0.5397 0.793 0.280 0.000 0.720
#> GSM123791 3 0.5397 0.793 0.280 0.000 0.720
#> GSM123795 3 0.5397 0.793 0.280 0.000 0.720
#> GSM123799 3 0.5397 0.793 0.280 0.000 0.720
#> GSM123730 1 0.4235 0.697 0.824 0.176 0.000
#> GSM123734 1 0.5327 0.790 0.728 0.000 0.272
#> GSM123738 1 0.0000 0.771 1.000 0.000 0.000
#> GSM123742 1 0.5431 0.786 0.716 0.000 0.284
#> GSM123745 1 0.5397 0.788 0.720 0.000 0.280
#> GSM123748 1 0.5431 0.786 0.716 0.000 0.284
#> GSM123751 1 0.5397 0.788 0.720 0.000 0.280
#> GSM123754 1 0.6154 0.652 0.592 0.000 0.408
#> GSM123757 3 0.0000 0.807 0.000 0.000 1.000
#> GSM123760 1 0.5327 0.790 0.728 0.000 0.272
#> GSM123762 3 0.0000 0.807 0.000 0.000 1.000
#> GSM123764 1 0.0000 0.771 1.000 0.000 0.000
#> GSM123767 1 0.5397 0.788 0.720 0.000 0.280
#> GSM123770 1 0.6286 0.555 0.536 0.000 0.464
#> GSM123773 1 0.5397 0.788 0.720 0.000 0.280
#> GSM123777 1 0.0000 0.771 1.000 0.000 0.000
#> GSM123779 1 0.0000 0.771 1.000 0.000 0.000
#> GSM123782 1 0.0000 0.771 1.000 0.000 0.000
#> GSM123786 3 0.5397 0.793 0.280 0.000 0.720
#> GSM123789 1 0.0237 0.768 0.996 0.000 0.004
#> GSM123793 1 0.0000 0.771 1.000 0.000 0.000
#> GSM123797 1 0.0000 0.771 1.000 0.000 0.000
#> GSM123729 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123733 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123737 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123741 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123747 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123753 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123759 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123766 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123772 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123775 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123781 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123785 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123788 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123792 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123796 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123731 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123735 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123739 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123743 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123749 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123755 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123768 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123776 2 0.1753 0.945 0.000 0.952 0.048
#> GSM123783 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123790 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123794 2 0.0000 0.998 0.000 1.000 0.000
#> GSM123798 2 0.0000 0.998 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM123732 3 0.0000 0.922 0.000 0.00 1.000 0.000
#> GSM123736 3 0.0000 0.922 0.000 0.00 1.000 0.000
#> GSM123740 3 0.0000 0.922 0.000 0.00 1.000 0.000
#> GSM123744 3 0.4925 0.278 0.428 0.00 0.572 0.000
#> GSM123746 1 0.1118 0.862 0.964 0.00 0.036 0.000
#> GSM123750 3 0.4941 0.256 0.436 0.00 0.564 0.000
#> GSM123752 1 0.3873 0.648 0.772 0.00 0.228 0.000
#> GSM123756 1 0.1022 0.863 0.968 0.00 0.032 0.000
#> GSM123758 3 0.1389 0.883 0.048 0.00 0.952 0.000
#> GSM123761 1 0.1211 0.860 0.960 0.00 0.040 0.000
#> GSM123763 1 0.1118 0.862 0.964 0.00 0.036 0.000
#> GSM123765 3 0.0000 0.922 0.000 0.00 1.000 0.000
#> GSM123769 1 0.1022 0.863 0.968 0.00 0.032 0.000
#> GSM123771 1 0.1022 0.863 0.968 0.00 0.032 0.000
#> GSM123774 1 0.0000 0.858 1.000 0.00 0.000 0.000
#> GSM123778 3 0.0000 0.922 0.000 0.00 1.000 0.000
#> GSM123780 3 0.0469 0.910 0.000 0.00 0.988 0.012
#> GSM123784 3 0.0000 0.922 0.000 0.00 1.000 0.000
#> GSM123787 3 0.0000 0.922 0.000 0.00 1.000 0.000
#> GSM123791 3 0.0000 0.922 0.000 0.00 1.000 0.000
#> GSM123795 3 0.0000 0.922 0.000 0.00 1.000 0.000
#> GSM123799 3 0.0000 0.922 0.000 0.00 1.000 0.000
#> GSM123730 4 0.0000 0.893 0.000 0.00 0.000 1.000
#> GSM123734 4 0.0817 0.884 0.024 0.00 0.000 0.976
#> GSM123738 4 0.0188 0.893 0.000 0.00 0.004 0.996
#> GSM123742 1 0.5038 0.578 0.684 0.00 0.020 0.296
#> GSM123745 1 0.3266 0.751 0.832 0.00 0.000 0.168
#> GSM123748 1 0.3123 0.761 0.844 0.00 0.000 0.156
#> GSM123751 1 0.3266 0.751 0.832 0.00 0.000 0.168
#> GSM123754 1 0.0000 0.858 1.000 0.00 0.000 0.000
#> GSM123757 1 0.0000 0.858 1.000 0.00 0.000 0.000
#> GSM123760 4 0.4843 0.277 0.396 0.00 0.000 0.604
#> GSM123762 1 0.1118 0.862 0.964 0.00 0.036 0.000
#> GSM123764 4 0.3450 0.807 0.008 0.00 0.156 0.836
#> GSM123767 4 0.1302 0.872 0.044 0.00 0.000 0.956
#> GSM123770 1 0.0000 0.858 1.000 0.00 0.000 0.000
#> GSM123773 1 0.4888 0.338 0.588 0.00 0.000 0.412
#> GSM123777 4 0.0188 0.893 0.000 0.00 0.004 0.996
#> GSM123779 4 0.0188 0.893 0.000 0.00 0.004 0.996
#> GSM123782 4 0.3852 0.774 0.008 0.00 0.192 0.800
#> GSM123786 3 0.0000 0.922 0.000 0.00 1.000 0.000
#> GSM123789 4 0.4988 0.708 0.036 0.00 0.236 0.728
#> GSM123793 4 0.0000 0.893 0.000 0.00 0.000 1.000
#> GSM123797 4 0.0000 0.893 0.000 0.00 0.000 1.000
#> GSM123729 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM123733 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM123737 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM123741 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM123747 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM123753 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM123759 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM123766 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM123772 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM123775 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM123781 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM123785 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM123788 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM123792 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM123796 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM123731 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM123735 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM123739 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM123743 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM123749 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM123755 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM123768 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM123776 1 0.4624 0.463 0.660 0.34 0.000 0.000
#> GSM123783 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM123790 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM123794 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM123798 2 0.0000 1.000 0.000 1.00 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM123732 3 0.0000 0.967 0.000 0.000 1.000 0.000 0.000
#> GSM123736 3 0.0000 0.967 0.000 0.000 1.000 0.000 0.000
#> GSM123740 3 0.0000 0.967 0.000 0.000 1.000 0.000 0.000
#> GSM123744 1 0.3759 0.638 0.764 0.000 0.220 0.000 0.016
#> GSM123746 1 0.1205 0.808 0.956 0.000 0.004 0.000 0.040
#> GSM123750 1 0.4010 0.645 0.760 0.000 0.208 0.000 0.032
#> GSM123752 1 0.3119 0.770 0.860 0.000 0.072 0.000 0.068
#> GSM123756 1 0.0000 0.816 1.000 0.000 0.000 0.000 0.000
#> GSM123758 3 0.4681 0.567 0.252 0.000 0.696 0.000 0.052
#> GSM123761 1 0.0566 0.814 0.984 0.000 0.004 0.000 0.012
#> GSM123763 1 0.1544 0.789 0.932 0.000 0.000 0.000 0.068
#> GSM123765 3 0.0000 0.967 0.000 0.000 1.000 0.000 0.000
#> GSM123769 1 0.0000 0.816 1.000 0.000 0.000 0.000 0.000
#> GSM123771 1 0.0000 0.816 1.000 0.000 0.000 0.000 0.000
#> GSM123774 1 0.0963 0.808 0.964 0.000 0.000 0.000 0.036
#> GSM123778 3 0.0000 0.967 0.000 0.000 1.000 0.000 0.000
#> GSM123780 3 0.0451 0.959 0.000 0.000 0.988 0.004 0.008
#> GSM123784 3 0.0000 0.967 0.000 0.000 1.000 0.000 0.000
#> GSM123787 3 0.0000 0.967 0.000 0.000 1.000 0.000 0.000
#> GSM123791 3 0.0798 0.949 0.016 0.000 0.976 0.000 0.008
#> GSM123795 3 0.0451 0.959 0.008 0.000 0.988 0.000 0.004
#> GSM123799 3 0.0000 0.967 0.000 0.000 1.000 0.000 0.000
#> GSM123730 4 0.0290 0.790 0.000 0.000 0.000 0.992 0.008
#> GSM123734 5 0.4976 0.380 0.028 0.000 0.000 0.468 0.504
#> GSM123738 4 0.0290 0.790 0.000 0.000 0.000 0.992 0.008
#> GSM123742 5 0.5470 0.593 0.268 0.000 0.000 0.104 0.628
#> GSM123745 5 0.4305 0.478 0.200 0.000 0.000 0.052 0.748
#> GSM123748 5 0.4594 0.542 0.284 0.000 0.000 0.036 0.680
#> GSM123751 5 0.4477 0.537 0.252 0.000 0.000 0.040 0.708
#> GSM123754 1 0.3838 0.606 0.716 0.000 0.000 0.004 0.280
#> GSM123757 1 0.3210 0.723 0.788 0.000 0.000 0.000 0.212
#> GSM123760 5 0.5983 0.589 0.168 0.000 0.000 0.252 0.580
#> GSM123762 1 0.1608 0.787 0.928 0.000 0.000 0.000 0.072
#> GSM123764 5 0.5476 0.425 0.008 0.000 0.044 0.440 0.508
#> GSM123767 4 0.4264 0.435 0.004 0.000 0.000 0.620 0.376
#> GSM123770 1 0.3508 0.645 0.748 0.000 0.000 0.000 0.252
#> GSM123773 4 0.5856 0.257 0.100 0.000 0.000 0.504 0.396
#> GSM123777 4 0.0000 0.792 0.000 0.000 0.000 1.000 0.000
#> GSM123779 4 0.2011 0.710 0.000 0.000 0.004 0.908 0.088
#> GSM123782 5 0.5876 0.449 0.000 0.000 0.104 0.384 0.512
#> GSM123786 3 0.0000 0.967 0.000 0.000 1.000 0.000 0.000
#> GSM123789 5 0.6525 0.500 0.044 0.000 0.080 0.364 0.512
#> GSM123793 4 0.0963 0.769 0.000 0.000 0.000 0.964 0.036
#> GSM123797 4 0.0000 0.792 0.000 0.000 0.000 1.000 0.000
#> GSM123729 2 0.1043 0.974 0.000 0.960 0.000 0.000 0.040
#> GSM123733 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000
#> GSM123737 2 0.0404 0.988 0.000 0.988 0.000 0.000 0.012
#> GSM123741 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000
#> GSM123747 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000
#> GSM123753 2 0.0162 0.990 0.000 0.996 0.000 0.000 0.004
#> GSM123759 2 0.0609 0.985 0.000 0.980 0.000 0.000 0.020
#> GSM123766 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000
#> GSM123772 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000
#> GSM123775 2 0.1341 0.963 0.000 0.944 0.000 0.000 0.056
#> GSM123781 2 0.0162 0.990 0.000 0.996 0.000 0.000 0.004
#> GSM123785 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000
#> GSM123788 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000
#> GSM123792 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000
#> GSM123796 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000
#> GSM123731 2 0.0290 0.989 0.000 0.992 0.000 0.000 0.008
#> GSM123735 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000
#> GSM123739 2 0.0404 0.988 0.000 0.988 0.000 0.000 0.012
#> GSM123743 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000
#> GSM123749 2 0.0609 0.985 0.000 0.980 0.000 0.000 0.020
#> GSM123755 2 0.0510 0.986 0.000 0.984 0.000 0.000 0.016
#> GSM123768 2 0.0963 0.977 0.000 0.964 0.000 0.000 0.036
#> GSM123776 1 0.6422 0.281 0.508 0.256 0.000 0.000 0.236
#> GSM123783 2 0.1121 0.971 0.000 0.956 0.000 0.000 0.044
#> GSM123790 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000
#> GSM123794 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000
#> GSM123798 2 0.0609 0.985 0.000 0.980 0.000 0.000 0.020
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM123732 3 0.0260 0.9199 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM123736 3 0.0870 0.9199 0.004 0.000 0.972 0.000 0.012 0.012
#> GSM123740 3 0.0870 0.9199 0.004 0.000 0.972 0.000 0.012 0.012
#> GSM123744 1 0.3713 0.7038 0.812 0.000 0.108 0.000 0.032 0.048
#> GSM123746 1 0.2766 0.7251 0.852 0.000 0.004 0.000 0.124 0.020
#> GSM123750 1 0.3873 0.7055 0.804 0.000 0.104 0.000 0.044 0.048
#> GSM123752 1 0.3966 0.6738 0.776 0.000 0.020 0.000 0.156 0.048
#> GSM123756 1 0.0291 0.7744 0.992 0.000 0.004 0.000 0.004 0.000
#> GSM123758 3 0.6569 -0.1128 0.388 0.000 0.404 0.000 0.156 0.052
#> GSM123761 1 0.1592 0.7708 0.940 0.000 0.008 0.000 0.020 0.032
#> GSM123763 1 0.2425 0.7525 0.884 0.000 0.004 0.000 0.024 0.088
#> GSM123765 3 0.0146 0.9220 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM123769 1 0.0653 0.7750 0.980 0.000 0.004 0.000 0.004 0.012
#> GSM123771 1 0.0291 0.7744 0.992 0.000 0.004 0.000 0.004 0.000
#> GSM123774 1 0.1152 0.7569 0.952 0.000 0.000 0.000 0.044 0.004
#> GSM123778 3 0.0508 0.9182 0.000 0.000 0.984 0.000 0.004 0.012
#> GSM123780 3 0.0653 0.9160 0.000 0.000 0.980 0.004 0.004 0.012
#> GSM123784 3 0.0405 0.9222 0.004 0.000 0.988 0.000 0.000 0.008
#> GSM123787 3 0.0520 0.9219 0.000 0.000 0.984 0.000 0.008 0.008
#> GSM123791 3 0.2335 0.8684 0.044 0.000 0.904 0.000 0.024 0.028
#> GSM123795 3 0.1616 0.9016 0.012 0.000 0.940 0.000 0.020 0.028
#> GSM123799 3 0.0767 0.9206 0.004 0.000 0.976 0.000 0.008 0.012
#> GSM123730 4 0.0000 0.9042 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM123734 6 0.5218 0.5011 0.012 0.000 0.000 0.312 0.084 0.592
#> GSM123738 4 0.0865 0.9028 0.000 0.000 0.000 0.964 0.000 0.036
#> GSM123742 6 0.3461 0.5776 0.152 0.000 0.000 0.008 0.036 0.804
#> GSM123745 5 0.5595 0.0748 0.100 0.000 0.000 0.012 0.472 0.416
#> GSM123748 6 0.4701 0.4396 0.168 0.000 0.000 0.000 0.148 0.684
#> GSM123751 6 0.5309 0.1227 0.128 0.000 0.000 0.000 0.312 0.560
#> GSM123754 1 0.5524 -0.0431 0.464 0.000 0.000 0.000 0.404 0.132
#> GSM123757 1 0.4957 0.4320 0.584 0.000 0.000 0.000 0.332 0.084
#> GSM123760 6 0.3668 0.6486 0.088 0.000 0.000 0.084 0.016 0.812
#> GSM123762 1 0.2526 0.7481 0.876 0.000 0.004 0.000 0.024 0.096
#> GSM123764 6 0.3965 0.5975 0.000 0.000 0.024 0.248 0.008 0.720
#> GSM123767 5 0.5790 0.3875 0.008 0.000 0.000 0.388 0.464 0.140
#> GSM123770 1 0.5221 0.1682 0.560 0.000 0.000 0.000 0.328 0.112
#> GSM123773 5 0.6456 0.4991 0.060 0.000 0.000 0.300 0.496 0.144
#> GSM123777 4 0.0000 0.9042 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM123779 4 0.3635 0.7097 0.000 0.000 0.008 0.780 0.032 0.180
#> GSM123782 6 0.4341 0.6182 0.000 0.000 0.048 0.192 0.024 0.736
#> GSM123786 3 0.0508 0.9182 0.000 0.000 0.984 0.000 0.004 0.012
#> GSM123789 6 0.4383 0.6389 0.020 0.000 0.040 0.192 0.008 0.740
#> GSM123793 4 0.1957 0.8480 0.000 0.000 0.000 0.888 0.000 0.112
#> GSM123797 4 0.0260 0.9067 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM123729 2 0.1444 0.9455 0.000 0.928 0.000 0.000 0.072 0.000
#> GSM123733 2 0.0508 0.9647 0.000 0.984 0.000 0.000 0.004 0.012
#> GSM123737 2 0.0632 0.9646 0.000 0.976 0.000 0.000 0.024 0.000
#> GSM123741 2 0.0000 0.9664 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123747 2 0.0146 0.9663 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM123753 2 0.0858 0.9636 0.000 0.968 0.000 0.000 0.028 0.004
#> GSM123759 2 0.1411 0.9548 0.000 0.936 0.000 0.000 0.060 0.004
#> GSM123766 2 0.0777 0.9647 0.000 0.972 0.000 0.000 0.024 0.004
#> GSM123772 2 0.0603 0.9659 0.000 0.980 0.000 0.000 0.016 0.004
#> GSM123775 2 0.2378 0.8706 0.000 0.848 0.000 0.000 0.152 0.000
#> GSM123781 2 0.1124 0.9612 0.000 0.956 0.000 0.000 0.036 0.008
#> GSM123785 2 0.0622 0.9636 0.000 0.980 0.000 0.000 0.008 0.012
#> GSM123788 2 0.0508 0.9647 0.000 0.984 0.000 0.000 0.004 0.012
#> GSM123792 2 0.0405 0.9654 0.000 0.988 0.000 0.000 0.004 0.008
#> GSM123796 2 0.0508 0.9647 0.000 0.984 0.000 0.000 0.004 0.012
#> GSM123731 2 0.0865 0.9631 0.000 0.964 0.000 0.000 0.036 0.000
#> GSM123735 2 0.0405 0.9654 0.000 0.988 0.000 0.000 0.004 0.008
#> GSM123739 2 0.0790 0.9626 0.000 0.968 0.000 0.000 0.032 0.000
#> GSM123743 2 0.0000 0.9664 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123749 2 0.1285 0.9580 0.000 0.944 0.000 0.000 0.052 0.004
#> GSM123755 2 0.1349 0.9564 0.000 0.940 0.000 0.000 0.056 0.004
#> GSM123768 2 0.1753 0.9430 0.000 0.912 0.000 0.000 0.084 0.004
#> GSM123776 5 0.5899 0.1196 0.324 0.120 0.000 0.000 0.528 0.028
#> GSM123783 2 0.1958 0.9322 0.000 0.896 0.000 0.000 0.100 0.004
#> GSM123790 2 0.0508 0.9647 0.000 0.984 0.000 0.000 0.004 0.012
#> GSM123794 2 0.0405 0.9654 0.000 0.988 0.000 0.000 0.004 0.008
#> GSM123798 2 0.1531 0.9521 0.000 0.928 0.000 0.000 0.068 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) infection(p) agent(p) k
#> ATC:skmeans 71 2.82e-15 2.82e-15 1.16e-05 2
#> ATC:skmeans 71 4.65e-26 4.65e-26 7.76e-06 3
#> ATC:skmeans 66 3.18e-19 3.18e-19 1.47e-04 4
#> ATC:skmeans 63 5.94e-18 5.94e-18 7.98e-04 5
#> ATC:skmeans 61 6.91e-20 6.91e-20 1.20e-03 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "pam"]
# you can also extract it by
# res = res_list["ATC:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 71 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 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 0.984 0.994 0.4745 0.529 0.529
#> 3 3 0.850 0.945 0.966 0.3990 0.801 0.624
#> 4 4 0.899 0.836 0.897 0.0844 0.948 0.845
#> 5 5 0.956 0.932 0.966 0.0480 0.938 0.790
#> 6 6 0.932 0.898 0.932 0.0113 0.998 0.990
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM123732 1 0.0000 0.990 1.000 0.000
#> GSM123736 1 0.0000 0.990 1.000 0.000
#> GSM123740 1 0.0000 0.990 1.000 0.000
#> GSM123744 1 0.0000 0.990 1.000 0.000
#> GSM123746 1 0.0000 0.990 1.000 0.000
#> GSM123750 1 0.0000 0.990 1.000 0.000
#> GSM123752 1 0.0000 0.990 1.000 0.000
#> GSM123756 1 0.0000 0.990 1.000 0.000
#> GSM123758 1 0.0000 0.990 1.000 0.000
#> GSM123761 1 0.0000 0.990 1.000 0.000
#> GSM123763 1 0.0000 0.990 1.000 0.000
#> GSM123765 1 0.0000 0.990 1.000 0.000
#> GSM123769 1 0.0000 0.990 1.000 0.000
#> GSM123771 1 0.0000 0.990 1.000 0.000
#> GSM123774 1 0.0000 0.990 1.000 0.000
#> GSM123778 1 0.0000 0.990 1.000 0.000
#> GSM123780 1 0.0000 0.990 1.000 0.000
#> GSM123784 1 0.0000 0.990 1.000 0.000
#> GSM123787 1 0.0000 0.990 1.000 0.000
#> GSM123791 1 0.0000 0.990 1.000 0.000
#> GSM123795 1 0.0000 0.990 1.000 0.000
#> GSM123799 1 0.0000 0.990 1.000 0.000
#> GSM123730 1 0.2423 0.951 0.960 0.040
#> GSM123734 1 0.0000 0.990 1.000 0.000
#> GSM123738 1 0.0000 0.990 1.000 0.000
#> GSM123742 1 0.0000 0.990 1.000 0.000
#> GSM123745 1 0.0000 0.990 1.000 0.000
#> GSM123748 1 0.0000 0.990 1.000 0.000
#> GSM123751 1 0.0000 0.990 1.000 0.000
#> GSM123754 1 0.0000 0.990 1.000 0.000
#> GSM123757 1 0.0000 0.990 1.000 0.000
#> GSM123760 1 0.0000 0.990 1.000 0.000
#> GSM123762 1 0.0000 0.990 1.000 0.000
#> GSM123764 1 0.0000 0.990 1.000 0.000
#> GSM123767 1 0.0376 0.986 0.996 0.004
#> GSM123770 1 0.0000 0.990 1.000 0.000
#> GSM123773 1 0.0000 0.990 1.000 0.000
#> GSM123777 1 0.0000 0.990 1.000 0.000
#> GSM123779 1 0.0000 0.990 1.000 0.000
#> GSM123782 1 0.0000 0.990 1.000 0.000
#> GSM123786 1 0.0000 0.990 1.000 0.000
#> GSM123789 1 0.0000 0.990 1.000 0.000
#> GSM123793 1 0.0000 0.990 1.000 0.000
#> GSM123797 1 0.0000 0.990 1.000 0.000
#> GSM123729 2 0.0000 1.000 0.000 1.000
#> GSM123733 2 0.0000 1.000 0.000 1.000
#> GSM123737 2 0.0000 1.000 0.000 1.000
#> GSM123741 2 0.0000 1.000 0.000 1.000
#> GSM123747 2 0.0000 1.000 0.000 1.000
#> GSM123753 2 0.0000 1.000 0.000 1.000
#> GSM123759 2 0.0000 1.000 0.000 1.000
#> GSM123766 2 0.0000 1.000 0.000 1.000
#> GSM123772 2 0.0000 1.000 0.000 1.000
#> GSM123775 2 0.0000 1.000 0.000 1.000
#> GSM123781 2 0.0000 1.000 0.000 1.000
#> GSM123785 2 0.0000 1.000 0.000 1.000
#> GSM123788 2 0.0000 1.000 0.000 1.000
#> GSM123792 2 0.0000 1.000 0.000 1.000
#> GSM123796 2 0.0000 1.000 0.000 1.000
#> GSM123731 2 0.0000 1.000 0.000 1.000
#> GSM123735 2 0.0000 1.000 0.000 1.000
#> GSM123739 2 0.0000 1.000 0.000 1.000
#> GSM123743 2 0.0000 1.000 0.000 1.000
#> GSM123749 2 0.0000 1.000 0.000 1.000
#> GSM123755 2 0.0000 1.000 0.000 1.000
#> GSM123768 2 0.0000 1.000 0.000 1.000
#> GSM123776 1 0.9710 0.337 0.600 0.400
#> GSM123783 2 0.0000 1.000 0.000 1.000
#> GSM123790 2 0.0000 1.000 0.000 1.000
#> GSM123794 2 0.0000 1.000 0.000 1.000
#> GSM123798 2 0.0000 1.000 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM123732 3 0.000 0.960 0.000 0 1.000
#> GSM123736 3 0.000 0.960 0.000 0 1.000
#> GSM123740 3 0.000 0.960 0.000 0 1.000
#> GSM123744 3 0.465 0.760 0.208 0 0.792
#> GSM123746 3 0.536 0.659 0.276 0 0.724
#> GSM123750 3 0.175 0.922 0.048 0 0.952
#> GSM123752 3 0.000 0.960 0.000 0 1.000
#> GSM123756 1 0.000 0.909 1.000 0 0.000
#> GSM123758 3 0.000 0.960 0.000 0 1.000
#> GSM123761 1 0.000 0.909 1.000 0 0.000
#> GSM123763 1 0.000 0.909 1.000 0 0.000
#> GSM123765 3 0.000 0.960 0.000 0 1.000
#> GSM123769 1 0.000 0.909 1.000 0 0.000
#> GSM123771 1 0.000 0.909 1.000 0 0.000
#> GSM123774 1 0.000 0.909 1.000 0 0.000
#> GSM123778 3 0.000 0.960 0.000 0 1.000
#> GSM123780 3 0.000 0.960 0.000 0 1.000
#> GSM123784 3 0.000 0.960 0.000 0 1.000
#> GSM123787 3 0.000 0.960 0.000 0 1.000
#> GSM123791 3 0.000 0.960 0.000 0 1.000
#> GSM123795 3 0.000 0.960 0.000 0 1.000
#> GSM123799 3 0.000 0.960 0.000 0 1.000
#> GSM123730 3 0.000 0.960 0.000 0 1.000
#> GSM123734 1 0.355 0.929 0.868 0 0.132
#> GSM123738 3 0.000 0.960 0.000 0 1.000
#> GSM123742 1 0.355 0.929 0.868 0 0.132
#> GSM123745 1 0.355 0.929 0.868 0 0.132
#> GSM123748 1 0.355 0.929 0.868 0 0.132
#> GSM123751 1 0.355 0.929 0.868 0 0.132
#> GSM123754 1 0.355 0.929 0.868 0 0.132
#> GSM123757 1 0.355 0.929 0.868 0 0.132
#> GSM123760 1 0.355 0.929 0.868 0 0.132
#> GSM123762 1 0.000 0.909 1.000 0 0.000
#> GSM123764 3 0.000 0.960 0.000 0 1.000
#> GSM123767 1 0.355 0.929 0.868 0 0.132
#> GSM123770 1 0.000 0.909 1.000 0 0.000
#> GSM123773 1 0.355 0.929 0.868 0 0.132
#> GSM123777 3 0.000 0.960 0.000 0 1.000
#> GSM123779 3 0.000 0.960 0.000 0 1.000
#> GSM123782 3 0.000 0.960 0.000 0 1.000
#> GSM123786 3 0.000 0.960 0.000 0 1.000
#> GSM123789 3 0.000 0.960 0.000 0 1.000
#> GSM123793 3 0.619 0.128 0.420 0 0.580
#> GSM123797 3 0.000 0.960 0.000 0 1.000
#> GSM123729 2 0.000 1.000 0.000 1 0.000
#> GSM123733 2 0.000 1.000 0.000 1 0.000
#> GSM123737 2 0.000 1.000 0.000 1 0.000
#> GSM123741 2 0.000 1.000 0.000 1 0.000
#> GSM123747 2 0.000 1.000 0.000 1 0.000
#> GSM123753 2 0.000 1.000 0.000 1 0.000
#> GSM123759 2 0.000 1.000 0.000 1 0.000
#> GSM123766 2 0.000 1.000 0.000 1 0.000
#> GSM123772 2 0.000 1.000 0.000 1 0.000
#> GSM123775 2 0.000 1.000 0.000 1 0.000
#> GSM123781 2 0.000 1.000 0.000 1 0.000
#> GSM123785 2 0.000 1.000 0.000 1 0.000
#> GSM123788 2 0.000 1.000 0.000 1 0.000
#> GSM123792 2 0.000 1.000 0.000 1 0.000
#> GSM123796 2 0.000 1.000 0.000 1 0.000
#> GSM123731 2 0.000 1.000 0.000 1 0.000
#> GSM123735 2 0.000 1.000 0.000 1 0.000
#> GSM123739 2 0.000 1.000 0.000 1 0.000
#> GSM123743 2 0.000 1.000 0.000 1 0.000
#> GSM123749 2 0.000 1.000 0.000 1 0.000
#> GSM123755 2 0.000 1.000 0.000 1 0.000
#> GSM123768 2 0.000 1.000 0.000 1 0.000
#> GSM123776 1 0.375 0.917 0.856 0 0.144
#> GSM123783 2 0.000 1.000 0.000 1 0.000
#> GSM123790 2 0.000 1.000 0.000 1 0.000
#> GSM123794 2 0.000 1.000 0.000 1 0.000
#> GSM123798 2 0.000 1.000 0.000 1 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM123732 3 0.0707 0.902 0.000 0 0.980 0.020
#> GSM123736 3 0.0000 0.905 0.000 0 1.000 0.000
#> GSM123740 3 0.0000 0.905 0.000 0 1.000 0.000
#> GSM123744 3 0.4697 0.397 0.356 0 0.644 0.000
#> GSM123746 3 0.1004 0.885 0.024 0 0.972 0.004
#> GSM123750 3 0.0000 0.905 0.000 0 1.000 0.000
#> GSM123752 3 0.0188 0.903 0.000 0 0.996 0.004
#> GSM123756 1 0.0000 0.656 1.000 0 0.000 0.000
#> GSM123758 3 0.0188 0.903 0.000 0 0.996 0.004
#> GSM123761 1 0.0000 0.656 1.000 0 0.000 0.000
#> GSM123763 1 0.0000 0.656 1.000 0 0.000 0.000
#> GSM123765 3 0.0707 0.902 0.000 0 0.980 0.020
#> GSM123769 1 0.0000 0.656 1.000 0 0.000 0.000
#> GSM123771 1 0.0000 0.656 1.000 0 0.000 0.000
#> GSM123774 1 0.0000 0.656 1.000 0 0.000 0.000
#> GSM123778 3 0.0707 0.902 0.000 0 0.980 0.020
#> GSM123780 3 0.0707 0.902 0.000 0 0.980 0.020
#> GSM123784 3 0.0707 0.902 0.000 0 0.980 0.020
#> GSM123787 3 0.0000 0.905 0.000 0 1.000 0.000
#> GSM123791 3 0.0000 0.905 0.000 0 1.000 0.000
#> GSM123795 3 0.0000 0.905 0.000 0 1.000 0.000
#> GSM123799 3 0.0000 0.905 0.000 0 1.000 0.000
#> GSM123730 4 0.4916 0.526 0.000 0 0.424 0.576
#> GSM123734 4 0.0657 0.437 0.012 0 0.004 0.984
#> GSM123738 4 0.4925 0.517 0.000 0 0.428 0.572
#> GSM123742 1 0.4933 0.768 0.568 0 0.000 0.432
#> GSM123745 1 0.4933 0.768 0.568 0 0.000 0.432
#> GSM123748 1 0.4933 0.768 0.568 0 0.000 0.432
#> GSM123751 1 0.4933 0.768 0.568 0 0.000 0.432
#> GSM123754 1 0.4933 0.768 0.568 0 0.000 0.432
#> GSM123757 1 0.5220 0.763 0.568 0 0.008 0.424
#> GSM123760 1 0.5366 0.739 0.548 0 0.012 0.440
#> GSM123762 1 0.0000 0.656 1.000 0 0.000 0.000
#> GSM123764 3 0.2973 0.750 0.000 0 0.856 0.144
#> GSM123767 1 0.4933 0.768 0.568 0 0.000 0.432
#> GSM123770 1 0.4933 0.768 0.568 0 0.000 0.432
#> GSM123773 1 0.4933 0.768 0.568 0 0.000 0.432
#> GSM123777 4 0.4916 0.526 0.000 0 0.424 0.576
#> GSM123779 3 0.3907 0.592 0.000 0 0.768 0.232
#> GSM123782 3 0.0707 0.902 0.000 0 0.980 0.020
#> GSM123786 3 0.0469 0.904 0.000 0 0.988 0.012
#> GSM123789 3 0.4830 0.242 0.000 0 0.608 0.392
#> GSM123793 4 0.0188 0.455 0.000 0 0.004 0.996
#> GSM123797 4 0.2814 0.594 0.000 0 0.132 0.868
#> GSM123729 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123733 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123737 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123741 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123747 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123753 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123759 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123766 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123772 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123775 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123781 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123785 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123788 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123792 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123796 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123731 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123735 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123739 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123743 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123749 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123755 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123768 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123776 1 0.4933 0.768 0.568 0 0.000 0.432
#> GSM123783 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123790 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123794 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123798 2 0.0000 1.000 0.000 1 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM123732 3 0.2377 0.890 0.000 0.000 0.872 0.128 0.000
#> GSM123736 3 0.0000 0.913 0.000 0.000 1.000 0.000 0.000
#> GSM123740 3 0.0000 0.913 0.000 0.000 1.000 0.000 0.000
#> GSM123744 3 0.3661 0.590 0.000 0.000 0.724 0.000 0.276
#> GSM123746 3 0.0579 0.911 0.008 0.000 0.984 0.000 0.008
#> GSM123750 3 0.0000 0.913 0.000 0.000 1.000 0.000 0.000
#> GSM123752 3 0.1041 0.904 0.032 0.000 0.964 0.004 0.000
#> GSM123756 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> GSM123758 3 0.0162 0.912 0.004 0.000 0.996 0.000 0.000
#> GSM123761 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> GSM123763 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> GSM123765 3 0.2280 0.893 0.000 0.000 0.880 0.120 0.000
#> GSM123769 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> GSM123771 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> GSM123774 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> GSM123778 3 0.2377 0.890 0.000 0.000 0.872 0.128 0.000
#> GSM123780 3 0.2377 0.890 0.000 0.000 0.872 0.128 0.000
#> GSM123784 3 0.2377 0.890 0.000 0.000 0.872 0.128 0.000
#> GSM123787 3 0.0162 0.913 0.000 0.000 0.996 0.004 0.000
#> GSM123791 3 0.0000 0.913 0.000 0.000 1.000 0.000 0.000
#> GSM123795 3 0.0000 0.913 0.000 0.000 1.000 0.000 0.000
#> GSM123799 3 0.0000 0.913 0.000 0.000 1.000 0.000 0.000
#> GSM123730 4 0.0000 0.964 0.000 0.000 0.000 1.000 0.000
#> GSM123734 1 0.0162 0.920 0.996 0.000 0.000 0.004 0.000
#> GSM123738 4 0.0404 0.957 0.000 0.000 0.012 0.988 0.000
#> GSM123742 1 0.0000 0.922 1.000 0.000 0.000 0.000 0.000
#> GSM123745 1 0.0000 0.922 1.000 0.000 0.000 0.000 0.000
#> GSM123748 1 0.0000 0.922 1.000 0.000 0.000 0.000 0.000
#> GSM123751 1 0.0000 0.922 1.000 0.000 0.000 0.000 0.000
#> GSM123754 1 0.0000 0.922 1.000 0.000 0.000 0.000 0.000
#> GSM123757 1 0.0000 0.922 1.000 0.000 0.000 0.000 0.000
#> GSM123760 1 0.0162 0.920 0.996 0.000 0.000 0.004 0.000
#> GSM123762 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> GSM123764 3 0.4637 0.761 0.128 0.000 0.744 0.128 0.000
#> GSM123767 1 0.0000 0.922 1.000 0.000 0.000 0.000 0.000
#> GSM123770 1 0.0000 0.922 1.000 0.000 0.000 0.000 0.000
#> GSM123773 1 0.0000 0.922 1.000 0.000 0.000 0.000 0.000
#> GSM123777 4 0.0000 0.964 0.000 0.000 0.000 1.000 0.000
#> GSM123779 1 0.6455 0.219 0.500 0.000 0.236 0.264 0.000
#> GSM123782 3 0.2377 0.890 0.000 0.000 0.872 0.128 0.000
#> GSM123786 3 0.2329 0.892 0.000 0.000 0.876 0.124 0.000
#> GSM123789 1 0.5025 0.566 0.704 0.000 0.172 0.124 0.000
#> GSM123793 4 0.1851 0.869 0.088 0.000 0.000 0.912 0.000
#> GSM123797 4 0.0000 0.964 0.000 0.000 0.000 1.000 0.000
#> GSM123729 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM123733 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM123737 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM123741 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM123747 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM123753 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM123759 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM123766 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM123772 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM123775 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM123781 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM123785 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM123788 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM123792 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM123796 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM123731 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM123735 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM123739 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM123743 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM123749 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM123755 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM123768 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM123776 1 0.1484 0.862 0.944 0.048 0.000 0.008 0.000
#> GSM123783 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM123790 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM123794 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM123798 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM123732 3 0.1267 0.898 0.000 0.000 0.940 0.060 0.000 0.000
#> GSM123736 3 0.1584 0.891 0.000 0.000 0.928 0.008 0.064 0.000
#> GSM123740 3 0.1584 0.891 0.000 0.000 0.928 0.008 0.064 0.000
#> GSM123744 3 0.4917 0.591 0.000 0.000 0.664 0.008 0.104 0.224
#> GSM123746 3 0.3043 0.820 0.004 0.000 0.796 0.000 0.196 0.004
#> GSM123750 3 0.3816 0.800 0.096 0.000 0.792 0.008 0.104 0.000
#> GSM123752 3 0.1584 0.890 0.008 0.000 0.928 0.000 0.064 0.000
#> GSM123756 6 0.0000 0.976 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM123758 3 0.1471 0.891 0.004 0.000 0.932 0.000 0.064 0.000
#> GSM123761 6 0.0713 0.957 0.000 0.000 0.000 0.000 0.028 0.972
#> GSM123763 5 0.3482 0.000 0.000 0.000 0.000 0.000 0.684 0.316
#> GSM123765 3 0.2136 0.903 0.000 0.000 0.904 0.048 0.048 0.000
#> GSM123769 6 0.0000 0.976 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM123771 6 0.0000 0.976 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM123774 6 0.0260 0.968 0.000 0.000 0.000 0.000 0.008 0.992
#> GSM123778 3 0.1267 0.898 0.000 0.000 0.940 0.060 0.000 0.000
#> GSM123780 3 0.1267 0.898 0.000 0.000 0.940 0.060 0.000 0.000
#> GSM123784 3 0.2451 0.901 0.000 0.000 0.884 0.060 0.056 0.000
#> GSM123787 3 0.0458 0.903 0.000 0.000 0.984 0.016 0.000 0.000
#> GSM123791 3 0.2118 0.873 0.000 0.000 0.888 0.008 0.104 0.000
#> GSM123795 3 0.1701 0.888 0.000 0.000 0.920 0.008 0.072 0.000
#> GSM123799 3 0.1462 0.893 0.000 0.000 0.936 0.008 0.056 0.000
#> GSM123730 4 0.0260 0.958 0.000 0.000 0.008 0.992 0.000 0.000
#> GSM123734 1 0.1765 0.845 0.924 0.000 0.000 0.024 0.052 0.000
#> GSM123738 4 0.0632 0.930 0.000 0.000 0.024 0.976 0.000 0.000
#> GSM123742 1 0.0260 0.845 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM123745 1 0.0260 0.847 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM123748 1 0.0146 0.845 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM123751 1 0.0000 0.846 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM123754 1 0.2762 0.821 0.804 0.000 0.000 0.000 0.196 0.000
#> GSM123757 1 0.2260 0.830 0.860 0.000 0.000 0.000 0.140 0.000
#> GSM123760 1 0.0146 0.845 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM123762 6 0.0790 0.952 0.000 0.000 0.000 0.000 0.032 0.968
#> GSM123764 3 0.3368 0.801 0.116 0.000 0.820 0.060 0.004 0.000
#> GSM123767 1 0.2597 0.827 0.824 0.000 0.000 0.000 0.176 0.000
#> GSM123770 1 0.2562 0.828 0.828 0.000 0.000 0.000 0.172 0.000
#> GSM123773 1 0.2597 0.827 0.824 0.000 0.000 0.000 0.176 0.000
#> GSM123777 4 0.0260 0.958 0.000 0.000 0.008 0.992 0.000 0.000
#> GSM123779 1 0.5911 0.256 0.464 0.000 0.296 0.240 0.000 0.000
#> GSM123782 3 0.1267 0.898 0.000 0.000 0.940 0.060 0.000 0.000
#> GSM123786 3 0.1267 0.898 0.000 0.000 0.940 0.060 0.000 0.000
#> GSM123789 1 0.4005 0.593 0.748 0.000 0.192 0.056 0.004 0.000
#> GSM123793 4 0.1501 0.886 0.076 0.000 0.000 0.924 0.000 0.000
#> GSM123797 4 0.0260 0.958 0.000 0.000 0.008 0.992 0.000 0.000
#> GSM123729 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123733 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123737 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123741 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123747 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123753 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123759 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123766 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123772 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123775 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123781 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123785 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123788 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123792 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123796 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123731 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123735 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123739 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123743 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123749 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123755 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123768 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123776 1 0.3481 0.775 0.792 0.048 0.000 0.000 0.160 0.000
#> GSM123783 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123790 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123794 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123798 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) infection(p) agent(p) k
#> ATC:pam 70 6.31e-16 6.31e-16 1.30e-05 2
#> ATC:pam 70 7.72e-15 7.72e-15 8.91e-05 3
#> ATC:pam 67 1.04e-15 1.04e-15 5.81e-04 4
#> ATC:pam 70 1.17e-20 1.17e-20 8.51e-04 5
#> ATC:pam 69 2.96e-20 2.96e-20 1.03e-03 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "mclust"]
# you can also extract it by
# res = res_list["ATC:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 71 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 0.4713 0.529 0.529
#> 3 3 1.000 0.998 0.999 0.3363 0.841 0.699
#> 4 4 1.000 0.980 0.985 0.1391 0.913 0.765
#> 5 5 0.825 0.841 0.889 0.0798 0.957 0.846
#> 6 6 0.832 0.838 0.898 0.0578 0.909 0.638
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
#> GSM123732 1 0.0000 1.000 1.000 0.000
#> GSM123736 1 0.0000 1.000 1.000 0.000
#> GSM123740 1 0.0000 1.000 1.000 0.000
#> GSM123744 1 0.0000 1.000 1.000 0.000
#> GSM123746 1 0.0000 1.000 1.000 0.000
#> GSM123750 1 0.0000 1.000 1.000 0.000
#> GSM123752 1 0.0000 1.000 1.000 0.000
#> GSM123756 1 0.0000 1.000 1.000 0.000
#> GSM123758 1 0.0000 1.000 1.000 0.000
#> GSM123761 1 0.0000 1.000 1.000 0.000
#> GSM123763 1 0.0000 1.000 1.000 0.000
#> GSM123765 1 0.0000 1.000 1.000 0.000
#> GSM123769 1 0.0000 1.000 1.000 0.000
#> GSM123771 1 0.0000 1.000 1.000 0.000
#> GSM123774 1 0.0000 1.000 1.000 0.000
#> GSM123778 1 0.0000 1.000 1.000 0.000
#> GSM123780 1 0.0000 1.000 1.000 0.000
#> GSM123784 1 0.0000 1.000 1.000 0.000
#> GSM123787 1 0.0000 1.000 1.000 0.000
#> GSM123791 1 0.0000 1.000 1.000 0.000
#> GSM123795 1 0.0000 1.000 1.000 0.000
#> GSM123799 1 0.0000 1.000 1.000 0.000
#> GSM123730 1 0.0000 1.000 1.000 0.000
#> GSM123734 1 0.0000 1.000 1.000 0.000
#> GSM123738 1 0.0000 1.000 1.000 0.000
#> GSM123742 1 0.0000 1.000 1.000 0.000
#> GSM123745 1 0.0000 1.000 1.000 0.000
#> GSM123748 1 0.0000 1.000 1.000 0.000
#> GSM123751 1 0.0000 1.000 1.000 0.000
#> GSM123754 1 0.0000 1.000 1.000 0.000
#> GSM123757 1 0.0000 1.000 1.000 0.000
#> GSM123760 1 0.0000 1.000 1.000 0.000
#> GSM123762 1 0.0000 1.000 1.000 0.000
#> GSM123764 1 0.0000 1.000 1.000 0.000
#> GSM123767 1 0.0000 1.000 1.000 0.000
#> GSM123770 1 0.0000 1.000 1.000 0.000
#> GSM123773 1 0.0000 1.000 1.000 0.000
#> GSM123777 1 0.0000 1.000 1.000 0.000
#> GSM123779 1 0.0000 1.000 1.000 0.000
#> GSM123782 1 0.0000 1.000 1.000 0.000
#> GSM123786 1 0.0000 1.000 1.000 0.000
#> GSM123789 1 0.0000 1.000 1.000 0.000
#> GSM123793 1 0.0000 1.000 1.000 0.000
#> GSM123797 1 0.0000 1.000 1.000 0.000
#> GSM123729 2 0.0000 1.000 0.000 1.000
#> GSM123733 2 0.0000 1.000 0.000 1.000
#> GSM123737 2 0.0000 1.000 0.000 1.000
#> GSM123741 2 0.0000 1.000 0.000 1.000
#> GSM123747 2 0.0000 1.000 0.000 1.000
#> GSM123753 2 0.0000 1.000 0.000 1.000
#> GSM123759 2 0.0000 1.000 0.000 1.000
#> GSM123766 2 0.0000 1.000 0.000 1.000
#> GSM123772 2 0.0000 1.000 0.000 1.000
#> GSM123775 2 0.0000 1.000 0.000 1.000
#> GSM123781 2 0.0000 1.000 0.000 1.000
#> GSM123785 2 0.0000 1.000 0.000 1.000
#> GSM123788 2 0.0000 1.000 0.000 1.000
#> GSM123792 2 0.0000 1.000 0.000 1.000
#> GSM123796 2 0.0000 1.000 0.000 1.000
#> GSM123731 2 0.0000 1.000 0.000 1.000
#> GSM123735 2 0.0000 1.000 0.000 1.000
#> GSM123739 2 0.0000 1.000 0.000 1.000
#> GSM123743 2 0.0000 1.000 0.000 1.000
#> GSM123749 2 0.0000 1.000 0.000 1.000
#> GSM123755 2 0.0000 1.000 0.000 1.000
#> GSM123768 2 0.0000 1.000 0.000 1.000
#> GSM123776 1 0.0000 1.000 1.000 0.000
#> GSM123783 2 0.0376 0.996 0.004 0.996
#> GSM123790 2 0.0000 1.000 0.000 1.000
#> GSM123794 2 0.0000 1.000 0.000 1.000
#> GSM123798 2 0.0000 1.000 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM123732 3 0.0000 0.992 0.000 0 1.000
#> GSM123736 3 0.0000 0.992 0.000 0 1.000
#> GSM123740 3 0.0000 0.992 0.000 0 1.000
#> GSM123744 1 0.0000 1.000 1.000 0 0.000
#> GSM123746 1 0.0000 1.000 1.000 0 0.000
#> GSM123750 1 0.0000 1.000 1.000 0 0.000
#> GSM123752 1 0.0000 1.000 1.000 0 0.000
#> GSM123756 1 0.0000 1.000 1.000 0 0.000
#> GSM123758 1 0.0000 1.000 1.000 0 0.000
#> GSM123761 1 0.0000 1.000 1.000 0 0.000
#> GSM123763 1 0.0000 1.000 1.000 0 0.000
#> GSM123765 3 0.0000 0.992 0.000 0 1.000
#> GSM123769 1 0.0000 1.000 1.000 0 0.000
#> GSM123771 1 0.0000 1.000 1.000 0 0.000
#> GSM123774 1 0.0000 1.000 1.000 0 0.000
#> GSM123778 3 0.0000 0.992 0.000 0 1.000
#> GSM123780 3 0.2356 0.921 0.072 0 0.928
#> GSM123784 3 0.0000 0.992 0.000 0 1.000
#> GSM123787 3 0.0000 0.992 0.000 0 1.000
#> GSM123791 3 0.0000 0.992 0.000 0 1.000
#> GSM123795 3 0.0424 0.986 0.008 0 0.992
#> GSM123799 3 0.0000 0.992 0.000 0 1.000
#> GSM123730 1 0.0000 1.000 1.000 0 0.000
#> GSM123734 1 0.0000 1.000 1.000 0 0.000
#> GSM123738 1 0.0000 1.000 1.000 0 0.000
#> GSM123742 1 0.0000 1.000 1.000 0 0.000
#> GSM123745 1 0.0000 1.000 1.000 0 0.000
#> GSM123748 1 0.0000 1.000 1.000 0 0.000
#> GSM123751 1 0.0000 1.000 1.000 0 0.000
#> GSM123754 1 0.0000 1.000 1.000 0 0.000
#> GSM123757 1 0.0000 1.000 1.000 0 0.000
#> GSM123760 1 0.0000 1.000 1.000 0 0.000
#> GSM123762 1 0.0000 1.000 1.000 0 0.000
#> GSM123764 1 0.0000 1.000 1.000 0 0.000
#> GSM123767 1 0.0000 1.000 1.000 0 0.000
#> GSM123770 1 0.0000 1.000 1.000 0 0.000
#> GSM123773 1 0.0000 1.000 1.000 0 0.000
#> GSM123777 1 0.0000 1.000 1.000 0 0.000
#> GSM123779 1 0.0000 1.000 1.000 0 0.000
#> GSM123782 1 0.0000 1.000 1.000 0 0.000
#> GSM123786 3 0.0000 0.992 0.000 0 1.000
#> GSM123789 1 0.0000 1.000 1.000 0 0.000
#> GSM123793 1 0.0000 1.000 1.000 0 0.000
#> GSM123797 1 0.0000 1.000 1.000 0 0.000
#> GSM123729 2 0.0000 1.000 0.000 1 0.000
#> GSM123733 2 0.0000 1.000 0.000 1 0.000
#> GSM123737 2 0.0000 1.000 0.000 1 0.000
#> GSM123741 2 0.0000 1.000 0.000 1 0.000
#> GSM123747 2 0.0000 1.000 0.000 1 0.000
#> GSM123753 2 0.0000 1.000 0.000 1 0.000
#> GSM123759 2 0.0000 1.000 0.000 1 0.000
#> GSM123766 2 0.0000 1.000 0.000 1 0.000
#> GSM123772 2 0.0000 1.000 0.000 1 0.000
#> GSM123775 2 0.0000 1.000 0.000 1 0.000
#> GSM123781 2 0.0000 1.000 0.000 1 0.000
#> GSM123785 2 0.0000 1.000 0.000 1 0.000
#> GSM123788 2 0.0000 1.000 0.000 1 0.000
#> GSM123792 2 0.0000 1.000 0.000 1 0.000
#> GSM123796 2 0.0000 1.000 0.000 1 0.000
#> GSM123731 2 0.0000 1.000 0.000 1 0.000
#> GSM123735 2 0.0000 1.000 0.000 1 0.000
#> GSM123739 2 0.0000 1.000 0.000 1 0.000
#> GSM123743 2 0.0000 1.000 0.000 1 0.000
#> GSM123749 2 0.0000 1.000 0.000 1 0.000
#> GSM123755 2 0.0000 1.000 0.000 1 0.000
#> GSM123768 2 0.0000 1.000 0.000 1 0.000
#> GSM123776 1 0.0000 1.000 1.000 0 0.000
#> GSM123783 2 0.0000 1.000 0.000 1 0.000
#> GSM123790 2 0.0000 1.000 0.000 1 0.000
#> GSM123794 2 0.0000 1.000 0.000 1 0.000
#> GSM123798 2 0.0000 1.000 0.000 1 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM123732 3 0.0000 0.994 0.000 0 1.000 0.000
#> GSM123736 3 0.0000 0.994 0.000 0 1.000 0.000
#> GSM123740 3 0.0000 0.994 0.000 0 1.000 0.000
#> GSM123744 1 0.0336 0.961 0.992 0 0.000 0.008
#> GSM123746 1 0.0817 0.968 0.976 0 0.000 0.024
#> GSM123750 1 0.1022 0.967 0.968 0 0.000 0.032
#> GSM123752 1 0.1022 0.967 0.968 0 0.000 0.032
#> GSM123756 1 0.0000 0.962 1.000 0 0.000 0.000
#> GSM123758 1 0.1022 0.967 0.968 0 0.000 0.032
#> GSM123761 1 0.0000 0.962 1.000 0 0.000 0.000
#> GSM123763 1 0.0000 0.962 1.000 0 0.000 0.000
#> GSM123765 3 0.0000 0.994 0.000 0 1.000 0.000
#> GSM123769 1 0.0000 0.962 1.000 0 0.000 0.000
#> GSM123771 1 0.0000 0.962 1.000 0 0.000 0.000
#> GSM123774 1 0.0000 0.962 1.000 0 0.000 0.000
#> GSM123778 3 0.0000 0.994 0.000 0 1.000 0.000
#> GSM123780 3 0.1557 0.937 0.000 0 0.944 0.056
#> GSM123784 3 0.0000 0.994 0.000 0 1.000 0.000
#> GSM123787 3 0.0000 0.994 0.000 0 1.000 0.000
#> GSM123791 3 0.0000 0.994 0.000 0 1.000 0.000
#> GSM123795 3 0.0188 0.991 0.000 0 0.996 0.004
#> GSM123799 3 0.0000 0.994 0.000 0 1.000 0.000
#> GSM123730 4 0.0000 0.978 0.000 0 0.000 1.000
#> GSM123734 1 0.1940 0.956 0.924 0 0.000 0.076
#> GSM123738 4 0.0000 0.978 0.000 0 0.000 1.000
#> GSM123742 1 0.1940 0.956 0.924 0 0.000 0.076
#> GSM123745 1 0.1940 0.956 0.924 0 0.000 0.076
#> GSM123748 1 0.1940 0.956 0.924 0 0.000 0.076
#> GSM123751 1 0.1940 0.956 0.924 0 0.000 0.076
#> GSM123754 1 0.1867 0.957 0.928 0 0.000 0.072
#> GSM123757 1 0.0817 0.968 0.976 0 0.000 0.024
#> GSM123760 1 0.1940 0.956 0.924 0 0.000 0.076
#> GSM123762 1 0.0000 0.962 1.000 0 0.000 0.000
#> GSM123764 4 0.0000 0.978 0.000 0 0.000 1.000
#> GSM123767 1 0.1940 0.956 0.924 0 0.000 0.076
#> GSM123770 1 0.0817 0.968 0.976 0 0.000 0.024
#> GSM123773 1 0.1940 0.956 0.924 0 0.000 0.076
#> GSM123777 4 0.0000 0.978 0.000 0 0.000 1.000
#> GSM123779 4 0.0707 0.962 0.020 0 0.000 0.980
#> GSM123782 4 0.2589 0.851 0.116 0 0.000 0.884
#> GSM123786 3 0.0000 0.994 0.000 0 1.000 0.000
#> GSM123789 4 0.0000 0.978 0.000 0 0.000 1.000
#> GSM123793 4 0.0000 0.978 0.000 0 0.000 1.000
#> GSM123797 4 0.0000 0.978 0.000 0 0.000 1.000
#> GSM123729 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123733 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123737 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123741 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123747 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123753 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123759 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123766 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123772 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123775 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123781 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123785 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123788 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123792 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123796 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123731 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123735 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123739 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123743 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123749 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123755 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123768 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123776 1 0.0817 0.968 0.976 0 0.000 0.024
#> GSM123783 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123790 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123794 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM123798 2 0.0000 1.000 0.000 1 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM123732 3 0.0162 0.986 0.000 0.000 0.996 0.000 0.004
#> GSM123736 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000
#> GSM123740 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000
#> GSM123744 1 0.2230 0.784 0.884 0.000 0.000 0.116 0.000
#> GSM123746 1 0.0963 0.817 0.964 0.000 0.000 0.000 0.036
#> GSM123750 1 0.3242 0.773 0.844 0.000 0.000 0.116 0.040
#> GSM123752 1 0.1364 0.817 0.952 0.000 0.000 0.012 0.036
#> GSM123756 1 0.0000 0.812 1.000 0.000 0.000 0.000 0.000
#> GSM123758 1 0.1364 0.817 0.952 0.000 0.000 0.012 0.036
#> GSM123761 1 0.0000 0.812 1.000 0.000 0.000 0.000 0.000
#> GSM123763 1 0.2230 0.784 0.884 0.000 0.000 0.116 0.000
#> GSM123765 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000
#> GSM123769 1 0.0000 0.812 1.000 0.000 0.000 0.000 0.000
#> GSM123771 1 0.0000 0.812 1.000 0.000 0.000 0.000 0.000
#> GSM123774 1 0.0510 0.816 0.984 0.000 0.000 0.000 0.016
#> GSM123778 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000
#> GSM123780 3 0.2291 0.886 0.000 0.000 0.908 0.036 0.056
#> GSM123784 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000
#> GSM123787 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000
#> GSM123791 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000
#> GSM123795 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000
#> GSM123799 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000
#> GSM123730 4 0.3857 0.976 0.000 0.000 0.000 0.688 0.312
#> GSM123734 1 0.6783 -0.196 0.388 0.000 0.000 0.296 0.316
#> GSM123738 4 0.3752 0.966 0.000 0.000 0.000 0.708 0.292
#> GSM123742 1 0.6783 -0.196 0.388 0.000 0.000 0.296 0.316
#> GSM123745 5 0.0290 0.979 0.008 0.000 0.000 0.000 0.992
#> GSM123748 5 0.0000 0.981 0.000 0.000 0.000 0.000 1.000
#> GSM123751 5 0.0000 0.981 0.000 0.000 0.000 0.000 1.000
#> GSM123754 5 0.0880 0.935 0.032 0.000 0.000 0.000 0.968
#> GSM123757 1 0.1197 0.815 0.952 0.000 0.000 0.000 0.048
#> GSM123760 1 0.6820 -0.307 0.352 0.000 0.000 0.332 0.316
#> GSM123762 1 0.2230 0.784 0.884 0.000 0.000 0.116 0.000
#> GSM123764 4 0.3876 0.975 0.000 0.000 0.000 0.684 0.316
#> GSM123767 5 0.0162 0.983 0.004 0.000 0.000 0.000 0.996
#> GSM123770 1 0.3210 0.698 0.788 0.000 0.000 0.000 0.212
#> GSM123773 5 0.0162 0.983 0.004 0.000 0.000 0.000 0.996
#> GSM123777 4 0.3837 0.975 0.000 0.000 0.000 0.692 0.308
#> GSM123779 4 0.3876 0.975 0.000 0.000 0.000 0.684 0.316
#> GSM123782 4 0.4522 0.941 0.024 0.000 0.000 0.660 0.316
#> GSM123786 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000
#> GSM123789 4 0.3876 0.975 0.000 0.000 0.000 0.684 0.316
#> GSM123793 4 0.3752 0.966 0.000 0.000 0.000 0.708 0.292
#> GSM123797 4 0.3752 0.966 0.000 0.000 0.000 0.708 0.292
#> GSM123729 2 0.5659 0.714 0.116 0.604 0.000 0.280 0.000
#> GSM123733 2 0.0000 0.894 0.000 1.000 0.000 0.000 0.000
#> GSM123737 2 0.4219 0.813 0.116 0.780 0.000 0.104 0.000
#> GSM123741 2 0.0000 0.894 0.000 1.000 0.000 0.000 0.000
#> GSM123747 2 0.0000 0.894 0.000 1.000 0.000 0.000 0.000
#> GSM123753 2 0.0000 0.894 0.000 1.000 0.000 0.000 0.000
#> GSM123759 2 0.3586 0.808 0.000 0.736 0.000 0.264 0.000
#> GSM123766 2 0.0000 0.894 0.000 1.000 0.000 0.000 0.000
#> GSM123772 2 0.0000 0.894 0.000 1.000 0.000 0.000 0.000
#> GSM123775 2 0.5659 0.714 0.116 0.604 0.000 0.280 0.000
#> GSM123781 2 0.0000 0.894 0.000 1.000 0.000 0.000 0.000
#> GSM123785 2 0.0000 0.894 0.000 1.000 0.000 0.000 0.000
#> GSM123788 2 0.0000 0.894 0.000 1.000 0.000 0.000 0.000
#> GSM123792 2 0.0000 0.894 0.000 1.000 0.000 0.000 0.000
#> GSM123796 2 0.0000 0.894 0.000 1.000 0.000 0.000 0.000
#> GSM123731 2 0.2773 0.853 0.000 0.836 0.000 0.164 0.000
#> GSM123735 2 0.0000 0.894 0.000 1.000 0.000 0.000 0.000
#> GSM123739 2 0.4457 0.807 0.116 0.760 0.000 0.124 0.000
#> GSM123743 2 0.0000 0.894 0.000 1.000 0.000 0.000 0.000
#> GSM123749 2 0.3366 0.825 0.000 0.768 0.000 0.232 0.000
#> GSM123755 2 0.2891 0.849 0.000 0.824 0.000 0.176 0.000
#> GSM123768 2 0.3684 0.799 0.000 0.720 0.000 0.280 0.000
#> GSM123776 1 0.1197 0.815 0.952 0.000 0.000 0.000 0.048
#> GSM123783 2 0.5659 0.714 0.116 0.604 0.000 0.280 0.000
#> GSM123790 2 0.0000 0.894 0.000 1.000 0.000 0.000 0.000
#> GSM123794 2 0.0000 0.894 0.000 1.000 0.000 0.000 0.000
#> GSM123798 2 0.3684 0.799 0.000 0.720 0.000 0.280 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM123732 3 0.0146 0.9565 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM123736 3 0.0000 0.9609 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM123740 3 0.0000 0.9609 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM123744 1 0.1821 0.8960 0.928 0.000 0.000 0.040 0.024 0.008
#> GSM123746 1 0.2146 0.8970 0.880 0.000 0.000 0.000 0.116 0.004
#> GSM123750 1 0.3560 0.8717 0.816 0.000 0.004 0.056 0.116 0.008
#> GSM123752 1 0.2573 0.8932 0.856 0.000 0.004 0.000 0.132 0.008
#> GSM123756 1 0.0547 0.8860 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM123758 1 0.2876 0.8917 0.844 0.000 0.016 0.000 0.132 0.008
#> GSM123761 1 0.0520 0.8901 0.984 0.000 0.000 0.000 0.008 0.008
#> GSM123763 1 0.1826 0.8861 0.924 0.000 0.000 0.052 0.020 0.004
#> GSM123765 3 0.0000 0.9609 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM123769 1 0.0547 0.8860 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM123771 1 0.0547 0.8860 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM123774 1 0.2039 0.9033 0.904 0.000 0.000 0.000 0.076 0.020
#> GSM123778 3 0.0000 0.9609 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM123780 3 0.4934 0.4244 0.000 0.000 0.628 0.264 0.108 0.000
#> GSM123784 3 0.0000 0.9609 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM123787 3 0.0000 0.9609 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM123791 3 0.0000 0.9609 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM123795 3 0.0000 0.9609 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM123799 3 0.0000 0.9609 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM123730 4 0.1007 0.9025 0.000 0.000 0.000 0.956 0.044 0.000
#> GSM123734 4 0.3141 0.8276 0.012 0.000 0.000 0.788 0.200 0.000
#> GSM123738 4 0.0000 0.8796 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM123742 4 0.3333 0.8247 0.024 0.000 0.000 0.784 0.192 0.000
#> GSM123745 5 0.0820 0.9447 0.012 0.000 0.000 0.016 0.972 0.000
#> GSM123748 5 0.0458 0.9443 0.000 0.000 0.000 0.016 0.984 0.000
#> GSM123751 5 0.0458 0.9443 0.000 0.000 0.000 0.016 0.984 0.000
#> GSM123754 5 0.1168 0.9300 0.028 0.000 0.000 0.016 0.956 0.000
#> GSM123757 1 0.3068 0.8830 0.840 0.000 0.000 0.016 0.124 0.020
#> GSM123760 4 0.2946 0.8503 0.012 0.000 0.000 0.812 0.176 0.000
#> GSM123762 1 0.1826 0.8861 0.924 0.000 0.000 0.052 0.020 0.004
#> GSM123764 4 0.1663 0.9073 0.000 0.000 0.000 0.912 0.088 0.000
#> GSM123767 5 0.2980 0.7357 0.008 0.000 0.000 0.192 0.800 0.000
#> GSM123770 1 0.3231 0.8347 0.784 0.000 0.000 0.016 0.200 0.000
#> GSM123773 5 0.0717 0.9457 0.008 0.000 0.000 0.016 0.976 0.000
#> GSM123777 4 0.0713 0.8965 0.000 0.000 0.000 0.972 0.028 0.000
#> GSM123779 4 0.1663 0.9079 0.000 0.000 0.000 0.912 0.088 0.000
#> GSM123782 4 0.2053 0.8997 0.000 0.000 0.004 0.888 0.108 0.000
#> GSM123786 3 0.0000 0.9609 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM123789 4 0.1910 0.9005 0.000 0.000 0.000 0.892 0.108 0.000
#> GSM123793 4 0.0000 0.8796 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM123797 4 0.0000 0.8796 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM123729 6 0.0713 0.7848 0.000 0.028 0.000 0.000 0.000 0.972
#> GSM123733 2 0.0000 0.8547 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123737 2 0.3810 0.1930 0.000 0.572 0.000 0.000 0.000 0.428
#> GSM123741 2 0.1814 0.8671 0.000 0.900 0.000 0.000 0.000 0.100
#> GSM123747 2 0.1714 0.8677 0.000 0.908 0.000 0.000 0.000 0.092
#> GSM123753 2 0.1863 0.8653 0.000 0.896 0.000 0.000 0.000 0.104
#> GSM123759 6 0.2969 0.7589 0.000 0.224 0.000 0.000 0.000 0.776
#> GSM123766 2 0.0146 0.8539 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM123772 2 0.0146 0.8539 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM123775 6 0.0858 0.7841 0.004 0.028 0.000 0.000 0.000 0.968
#> GSM123781 2 0.1327 0.8692 0.000 0.936 0.000 0.000 0.000 0.064
#> GSM123785 2 0.0146 0.8539 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM123788 2 0.0000 0.8547 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123792 2 0.1863 0.8653 0.000 0.896 0.000 0.000 0.000 0.104
#> GSM123796 2 0.0000 0.8547 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM123731 6 0.3782 0.4509 0.000 0.412 0.000 0.000 0.000 0.588
#> GSM123735 2 0.1714 0.8677 0.000 0.908 0.000 0.000 0.000 0.092
#> GSM123739 2 0.3868 -0.0986 0.000 0.508 0.000 0.000 0.000 0.492
#> GSM123743 2 0.1714 0.8677 0.000 0.908 0.000 0.000 0.000 0.092
#> GSM123749 6 0.3198 0.7214 0.000 0.260 0.000 0.000 0.000 0.740
#> GSM123755 6 0.3804 0.4261 0.000 0.424 0.000 0.000 0.000 0.576
#> GSM123768 6 0.1700 0.7975 0.004 0.080 0.000 0.000 0.000 0.916
#> GSM123776 1 0.3068 0.8830 0.840 0.000 0.000 0.016 0.124 0.020
#> GSM123783 6 0.1168 0.7795 0.016 0.028 0.000 0.000 0.000 0.956
#> GSM123790 2 0.2092 0.8525 0.000 0.876 0.000 0.000 0.000 0.124
#> GSM123794 2 0.2416 0.8267 0.000 0.844 0.000 0.000 0.000 0.156
#> GSM123798 6 0.2178 0.7963 0.000 0.132 0.000 0.000 0.000 0.868
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) infection(p) agent(p) k
#> ATC:mclust 71 3.04e-15 3.04e-15 5.99e-05 2
#> ATC:mclust 71 1.36e-17 1.36e-17 7.83e-05 3
#> ATC:mclust 71 2.80e-18 2.80e-18 2.74e-04 4
#> ATC:mclust 68 4.03e-20 4.03e-20 1.28e-03 5
#> ATC:mclust 66 1.85e-18 1.85e-18 2.27e-03 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "NMF"]
# you can also extract it by
# res = res_list["ATC:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 71 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.952 0.983 0.4914 0.505 0.505
#> 3 3 0.816 0.847 0.916 0.3444 0.776 0.582
#> 4 4 0.757 0.808 0.886 0.1114 0.862 0.628
#> 5 5 0.771 0.705 0.831 0.0496 0.960 0.854
#> 6 6 0.821 0.743 0.851 0.0270 0.959 0.837
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM123732 1 0.0376 0.99094 0.996 0.004
#> GSM123736 1 0.0000 0.99345 1.000 0.000
#> GSM123740 1 0.0000 0.99345 1.000 0.000
#> GSM123744 1 0.0000 0.99345 1.000 0.000
#> GSM123746 1 0.0000 0.99345 1.000 0.000
#> GSM123750 1 0.0000 0.99345 1.000 0.000
#> GSM123752 1 0.0000 0.99345 1.000 0.000
#> GSM123756 1 0.0000 0.99345 1.000 0.000
#> GSM123758 1 0.0000 0.99345 1.000 0.000
#> GSM123761 1 0.0000 0.99345 1.000 0.000
#> GSM123763 1 0.0000 0.99345 1.000 0.000
#> GSM123765 1 0.0000 0.99345 1.000 0.000
#> GSM123769 1 0.0000 0.99345 1.000 0.000
#> GSM123771 1 0.0000 0.99345 1.000 0.000
#> GSM123774 1 0.0000 0.99345 1.000 0.000
#> GSM123778 1 0.0376 0.99094 0.996 0.004
#> GSM123780 1 0.0672 0.98763 0.992 0.008
#> GSM123784 1 0.0000 0.99345 1.000 0.000
#> GSM123787 1 0.0000 0.99345 1.000 0.000
#> GSM123791 1 0.0000 0.99345 1.000 0.000
#> GSM123795 1 0.0000 0.99345 1.000 0.000
#> GSM123799 1 0.0000 0.99345 1.000 0.000
#> GSM123730 2 0.0000 0.96583 0.000 1.000
#> GSM123734 1 0.0000 0.99345 1.000 0.000
#> GSM123738 1 0.0000 0.99345 1.000 0.000
#> GSM123742 1 0.0000 0.99345 1.000 0.000
#> GSM123745 1 0.0000 0.99345 1.000 0.000
#> GSM123748 1 0.0000 0.99345 1.000 0.000
#> GSM123751 1 0.0000 0.99345 1.000 0.000
#> GSM123754 1 0.0000 0.99345 1.000 0.000
#> GSM123757 1 0.0000 0.99345 1.000 0.000
#> GSM123760 1 0.0000 0.99345 1.000 0.000
#> GSM123762 1 0.0000 0.99345 1.000 0.000
#> GSM123764 1 0.0672 0.98763 0.992 0.008
#> GSM123767 2 0.9977 0.11506 0.472 0.528
#> GSM123770 1 0.0000 0.99345 1.000 0.000
#> GSM123773 1 0.0000 0.99345 1.000 0.000
#> GSM123777 2 1.0000 0.00876 0.500 0.500
#> GSM123779 1 0.1843 0.96780 0.972 0.028
#> GSM123782 1 0.6973 0.76007 0.812 0.188
#> GSM123786 1 0.0376 0.99094 0.996 0.004
#> GSM123789 1 0.0000 0.99345 1.000 0.000
#> GSM123793 1 0.0376 0.99094 0.996 0.004
#> GSM123797 1 0.0376 0.99094 0.996 0.004
#> GSM123729 2 0.0000 0.96583 0.000 1.000
#> GSM123733 2 0.0000 0.96583 0.000 1.000
#> GSM123737 2 0.0000 0.96583 0.000 1.000
#> GSM123741 2 0.0000 0.96583 0.000 1.000
#> GSM123747 2 0.0000 0.96583 0.000 1.000
#> GSM123753 2 0.0000 0.96583 0.000 1.000
#> GSM123759 2 0.0000 0.96583 0.000 1.000
#> GSM123766 2 0.0000 0.96583 0.000 1.000
#> GSM123772 2 0.0000 0.96583 0.000 1.000
#> GSM123775 2 0.0000 0.96583 0.000 1.000
#> GSM123781 2 0.0000 0.96583 0.000 1.000
#> GSM123785 2 0.0000 0.96583 0.000 1.000
#> GSM123788 2 0.0000 0.96583 0.000 1.000
#> GSM123792 2 0.0000 0.96583 0.000 1.000
#> GSM123796 2 0.0000 0.96583 0.000 1.000
#> GSM123731 2 0.0000 0.96583 0.000 1.000
#> GSM123735 2 0.0000 0.96583 0.000 1.000
#> GSM123739 2 0.0000 0.96583 0.000 1.000
#> GSM123743 2 0.0000 0.96583 0.000 1.000
#> GSM123749 2 0.0000 0.96583 0.000 1.000
#> GSM123755 2 0.0000 0.96583 0.000 1.000
#> GSM123768 2 0.0000 0.96583 0.000 1.000
#> GSM123776 2 0.0000 0.96583 0.000 1.000
#> GSM123783 2 0.0000 0.96583 0.000 1.000
#> GSM123790 2 0.0000 0.96583 0.000 1.000
#> GSM123794 2 0.0000 0.96583 0.000 1.000
#> GSM123798 2 0.0000 0.96583 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM123732 3 0.5115 0.7202 0.228 0.004 0.768
#> GSM123736 3 0.2878 0.8412 0.096 0.000 0.904
#> GSM123740 3 0.6225 0.3414 0.432 0.000 0.568
#> GSM123744 1 0.1964 0.9271 0.944 0.000 0.056
#> GSM123746 1 0.1411 0.9311 0.964 0.000 0.036
#> GSM123750 1 0.2261 0.9206 0.932 0.000 0.068
#> GSM123752 1 0.0983 0.9026 0.980 0.016 0.004
#> GSM123756 1 0.1411 0.9311 0.964 0.000 0.036
#> GSM123758 1 0.1636 0.9044 0.964 0.020 0.016
#> GSM123761 1 0.1529 0.9315 0.960 0.000 0.040
#> GSM123763 1 0.2448 0.9149 0.924 0.000 0.076
#> GSM123765 3 0.1860 0.8518 0.052 0.000 0.948
#> GSM123769 1 0.1643 0.9312 0.956 0.000 0.044
#> GSM123771 1 0.1163 0.9283 0.972 0.000 0.028
#> GSM123774 1 0.0475 0.9112 0.992 0.004 0.004
#> GSM123778 3 0.4575 0.7711 0.184 0.004 0.812
#> GSM123780 3 0.1267 0.8467 0.004 0.024 0.972
#> GSM123784 3 0.2165 0.8499 0.064 0.000 0.936
#> GSM123787 3 0.2959 0.8381 0.100 0.000 0.900
#> GSM123791 3 0.6299 0.2075 0.476 0.000 0.524
#> GSM123795 3 0.2356 0.8490 0.072 0.000 0.928
#> GSM123799 3 0.5968 0.5039 0.364 0.000 0.636
#> GSM123730 3 0.2066 0.8227 0.000 0.060 0.940
#> GSM123734 3 0.1289 0.8523 0.032 0.000 0.968
#> GSM123738 3 0.1315 0.8478 0.008 0.020 0.972
#> GSM123742 3 0.2356 0.8491 0.072 0.000 0.928
#> GSM123745 1 0.6386 0.2856 0.584 0.004 0.412
#> GSM123748 3 0.6308 0.0793 0.492 0.000 0.508
#> GSM123751 3 0.3816 0.8058 0.148 0.000 0.852
#> GSM123754 1 0.4796 0.7198 0.780 0.000 0.220
#> GSM123757 1 0.1163 0.9287 0.972 0.000 0.028
#> GSM123760 3 0.1643 0.8522 0.044 0.000 0.956
#> GSM123762 1 0.2448 0.9149 0.924 0.000 0.076
#> GSM123764 3 0.1399 0.8453 0.004 0.028 0.968
#> GSM123767 3 0.2878 0.7942 0.000 0.096 0.904
#> GSM123770 1 0.1643 0.9312 0.956 0.000 0.044
#> GSM123773 3 0.5024 0.6969 0.220 0.004 0.776
#> GSM123777 3 0.1643 0.8348 0.000 0.044 0.956
#> GSM123779 3 0.1647 0.8398 0.004 0.036 0.960
#> GSM123782 3 0.1289 0.8416 0.000 0.032 0.968
#> GSM123786 3 0.3715 0.8190 0.128 0.004 0.868
#> GSM123789 3 0.1289 0.8523 0.032 0.000 0.968
#> GSM123793 3 0.1399 0.8441 0.004 0.028 0.968
#> GSM123797 3 0.1399 0.8441 0.004 0.028 0.968
#> GSM123729 2 0.1031 0.9541 0.024 0.976 0.000
#> GSM123733 2 0.1411 0.9603 0.000 0.964 0.036
#> GSM123737 2 0.0747 0.9584 0.016 0.984 0.000
#> GSM123741 2 0.0747 0.9644 0.000 0.984 0.016
#> GSM123747 2 0.1031 0.9644 0.000 0.976 0.024
#> GSM123753 2 0.1031 0.9644 0.000 0.976 0.024
#> GSM123759 2 0.0592 0.9598 0.012 0.988 0.000
#> GSM123766 2 0.1860 0.9503 0.000 0.948 0.052
#> GSM123772 2 0.1289 0.9620 0.000 0.968 0.032
#> GSM123775 2 0.1289 0.9495 0.032 0.968 0.000
#> GSM123781 2 0.1163 0.9634 0.000 0.972 0.028
#> GSM123785 2 0.1860 0.9503 0.000 0.948 0.052
#> GSM123788 2 0.1163 0.9634 0.000 0.972 0.028
#> GSM123792 2 0.1031 0.9644 0.000 0.976 0.024
#> GSM123796 2 0.1411 0.9603 0.000 0.964 0.036
#> GSM123731 2 0.0237 0.9618 0.004 0.996 0.000
#> GSM123735 2 0.1031 0.9644 0.000 0.976 0.024
#> GSM123739 2 0.0747 0.9584 0.016 0.984 0.000
#> GSM123743 2 0.0892 0.9645 0.000 0.980 0.020
#> GSM123749 2 0.0747 0.9584 0.016 0.984 0.000
#> GSM123755 2 0.0000 0.9624 0.000 1.000 0.000
#> GSM123768 2 0.1267 0.9527 0.024 0.972 0.004
#> GSM123776 2 0.6204 0.3129 0.424 0.576 0.000
#> GSM123783 2 0.0829 0.9589 0.012 0.984 0.004
#> GSM123790 2 0.1529 0.9583 0.000 0.960 0.040
#> GSM123794 2 0.1031 0.9644 0.000 0.976 0.024
#> GSM123798 2 0.0747 0.9584 0.016 0.984 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM123732 3 0.0927 0.843 0.000 0.016 0.976 0.008
#> GSM123736 3 0.1151 0.855 0.008 0.000 0.968 0.024
#> GSM123740 3 0.0524 0.856 0.004 0.000 0.988 0.008
#> GSM123744 3 0.4222 0.542 0.272 0.000 0.728 0.000
#> GSM123746 1 0.2530 0.856 0.896 0.000 0.100 0.004
#> GSM123750 3 0.3074 0.738 0.152 0.000 0.848 0.000
#> GSM123752 1 0.4551 0.802 0.796 0.004 0.156 0.044
#> GSM123756 1 0.1211 0.869 0.960 0.000 0.040 0.000
#> GSM123758 3 0.8052 0.314 0.220 0.144 0.568 0.068
#> GSM123761 1 0.3052 0.839 0.860 0.000 0.136 0.004
#> GSM123763 1 0.4632 0.611 0.688 0.000 0.308 0.004
#> GSM123765 3 0.1109 0.855 0.004 0.000 0.968 0.028
#> GSM123769 1 0.1398 0.869 0.956 0.000 0.040 0.004
#> GSM123771 1 0.0817 0.866 0.976 0.000 0.024 0.000
#> GSM123774 1 0.0712 0.854 0.984 0.008 0.004 0.004
#> GSM123778 3 0.0937 0.844 0.000 0.012 0.976 0.012
#> GSM123780 3 0.1732 0.847 0.008 0.004 0.948 0.040
#> GSM123784 3 0.1256 0.854 0.008 0.000 0.964 0.028
#> GSM123787 3 0.0000 0.853 0.000 0.000 1.000 0.000
#> GSM123791 3 0.1042 0.856 0.008 0.000 0.972 0.020
#> GSM123795 3 0.1545 0.849 0.008 0.000 0.952 0.040
#> GSM123799 3 0.0524 0.856 0.004 0.000 0.988 0.008
#> GSM123730 4 0.2660 0.755 0.000 0.056 0.036 0.908
#> GSM123734 4 0.3659 0.784 0.024 0.000 0.136 0.840
#> GSM123738 4 0.5050 0.406 0.000 0.004 0.408 0.588
#> GSM123742 4 0.5949 0.623 0.068 0.000 0.288 0.644
#> GSM123745 4 0.4193 0.609 0.268 0.000 0.000 0.732
#> GSM123748 4 0.5273 0.235 0.456 0.000 0.008 0.536
#> GSM123751 4 0.4277 0.606 0.280 0.000 0.000 0.720
#> GSM123754 1 0.4456 0.501 0.716 0.000 0.004 0.280
#> GSM123757 1 0.0657 0.862 0.984 0.000 0.012 0.004
#> GSM123760 4 0.4818 0.731 0.036 0.000 0.216 0.748
#> GSM123762 1 0.3626 0.798 0.812 0.000 0.184 0.004
#> GSM123764 3 0.4872 0.345 0.004 0.000 0.640 0.356
#> GSM123767 4 0.3051 0.709 0.028 0.088 0.000 0.884
#> GSM123770 1 0.0707 0.852 0.980 0.000 0.000 0.020
#> GSM123773 4 0.3172 0.702 0.160 0.000 0.000 0.840
#> GSM123777 4 0.3852 0.755 0.000 0.008 0.192 0.800
#> GSM123779 4 0.3280 0.782 0.000 0.016 0.124 0.860
#> GSM123782 3 0.4392 0.641 0.004 0.012 0.768 0.216
#> GSM123786 3 0.0336 0.851 0.000 0.008 0.992 0.000
#> GSM123789 3 0.4914 0.459 0.012 0.000 0.676 0.312
#> GSM123793 4 0.3208 0.779 0.000 0.004 0.148 0.848
#> GSM123797 4 0.3355 0.775 0.000 0.004 0.160 0.836
#> GSM123729 2 0.1042 0.952 0.008 0.972 0.000 0.020
#> GSM123733 2 0.2149 0.936 0.000 0.912 0.000 0.088
#> GSM123737 2 0.1545 0.955 0.008 0.952 0.000 0.040
#> GSM123741 2 0.1118 0.956 0.000 0.964 0.000 0.036
#> GSM123747 2 0.0564 0.958 0.004 0.988 0.004 0.004
#> GSM123753 2 0.0188 0.958 0.000 0.996 0.004 0.000
#> GSM123759 2 0.0804 0.954 0.000 0.980 0.008 0.012
#> GSM123766 2 0.3219 0.871 0.000 0.836 0.000 0.164
#> GSM123772 2 0.1867 0.945 0.000 0.928 0.000 0.072
#> GSM123775 2 0.0937 0.954 0.012 0.976 0.000 0.012
#> GSM123781 2 0.1474 0.953 0.000 0.948 0.000 0.052
#> GSM123785 2 0.3402 0.869 0.004 0.832 0.000 0.164
#> GSM123788 2 0.2011 0.941 0.000 0.920 0.000 0.080
#> GSM123792 2 0.0376 0.959 0.000 0.992 0.004 0.004
#> GSM123796 2 0.1474 0.953 0.000 0.948 0.000 0.052
#> GSM123731 2 0.0188 0.958 0.000 0.996 0.000 0.004
#> GSM123735 2 0.0336 0.959 0.000 0.992 0.000 0.008
#> GSM123739 2 0.1888 0.952 0.016 0.940 0.000 0.044
#> GSM123743 2 0.0921 0.957 0.000 0.972 0.000 0.028
#> GSM123749 2 0.0188 0.958 0.000 0.996 0.000 0.004
#> GSM123755 2 0.0376 0.957 0.000 0.992 0.004 0.004
#> GSM123768 2 0.2722 0.907 0.000 0.904 0.032 0.064
#> GSM123776 1 0.2799 0.767 0.884 0.108 0.000 0.008
#> GSM123783 2 0.3189 0.895 0.004 0.888 0.048 0.060
#> GSM123790 2 0.1743 0.952 0.004 0.940 0.000 0.056
#> GSM123794 2 0.0524 0.958 0.004 0.988 0.008 0.000
#> GSM123798 2 0.0779 0.954 0.000 0.980 0.004 0.016
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM123732 3 0.1894 0.763 0.000 0.008 0.920 0.000 0.072
#> GSM123736 3 0.2970 0.761 0.000 0.000 0.828 0.004 0.168
#> GSM123740 3 0.2020 0.787 0.000 0.000 0.900 0.000 0.100
#> GSM123744 3 0.6361 0.172 0.176 0.000 0.484 0.000 0.340
#> GSM123746 1 0.1597 0.757 0.940 0.000 0.012 0.000 0.048
#> GSM123750 3 0.4888 0.614 0.064 0.000 0.700 0.004 0.232
#> GSM123752 1 0.6015 0.336 0.584 0.004 0.268 0.000 0.144
#> GSM123756 1 0.2017 0.752 0.912 0.000 0.008 0.000 0.080
#> GSM123758 3 0.5985 0.487 0.096 0.044 0.656 0.000 0.204
#> GSM123761 1 0.4421 0.502 0.704 0.000 0.024 0.004 0.268
#> GSM123763 5 0.6189 0.448 0.216 0.000 0.188 0.008 0.588
#> GSM123765 3 0.3016 0.773 0.000 0.000 0.848 0.020 0.132
#> GSM123769 1 0.3087 0.698 0.836 0.000 0.008 0.004 0.152
#> GSM123771 1 0.0963 0.768 0.964 0.000 0.000 0.000 0.036
#> GSM123774 1 0.0162 0.769 0.996 0.000 0.000 0.000 0.004
#> GSM123778 3 0.1557 0.772 0.000 0.008 0.940 0.000 0.052
#> GSM123780 3 0.2446 0.781 0.000 0.000 0.900 0.044 0.056
#> GSM123784 3 0.2873 0.777 0.000 0.000 0.860 0.020 0.120
#> GSM123787 3 0.0510 0.789 0.000 0.000 0.984 0.000 0.016
#> GSM123791 3 0.4151 0.564 0.004 0.000 0.652 0.000 0.344
#> GSM123795 3 0.3724 0.724 0.000 0.000 0.776 0.020 0.204
#> GSM123799 3 0.0404 0.790 0.000 0.000 0.988 0.000 0.012
#> GSM123730 4 0.1913 0.627 0.000 0.024 0.020 0.936 0.020
#> GSM123734 4 0.3278 0.631 0.000 0.000 0.020 0.824 0.156
#> GSM123738 4 0.5714 0.288 0.000 0.000 0.312 0.580 0.108
#> GSM123742 4 0.5586 0.266 0.012 0.000 0.044 0.480 0.464
#> GSM123745 4 0.5405 0.514 0.204 0.000 0.000 0.660 0.136
#> GSM123748 4 0.6649 0.378 0.192 0.000 0.012 0.512 0.284
#> GSM123751 4 0.4647 0.598 0.092 0.000 0.000 0.736 0.172
#> GSM123754 1 0.4235 0.366 0.656 0.000 0.000 0.336 0.008
#> GSM123757 1 0.3008 0.723 0.868 0.000 0.004 0.036 0.092
#> GSM123760 4 0.5001 0.499 0.004 0.000 0.036 0.620 0.340
#> GSM123762 5 0.5673 0.214 0.388 0.000 0.056 0.012 0.544
#> GSM123764 4 0.5757 0.315 0.000 0.000 0.088 0.496 0.416
#> GSM123767 4 0.1299 0.630 0.008 0.020 0.000 0.960 0.012
#> GSM123770 1 0.1106 0.768 0.964 0.000 0.000 0.024 0.012
#> GSM123773 4 0.3531 0.559 0.152 0.016 0.000 0.820 0.012
#> GSM123777 4 0.4677 0.482 0.000 0.008 0.204 0.732 0.056
#> GSM123779 4 0.2353 0.632 0.000 0.004 0.060 0.908 0.028
#> GSM123782 4 0.6651 0.203 0.000 0.000 0.256 0.444 0.300
#> GSM123786 3 0.2280 0.737 0.000 0.000 0.880 0.000 0.120
#> GSM123789 5 0.6261 -0.252 0.000 0.000 0.156 0.356 0.488
#> GSM123793 4 0.3291 0.645 0.000 0.000 0.064 0.848 0.088
#> GSM123797 4 0.3134 0.602 0.000 0.000 0.120 0.848 0.032
#> GSM123729 2 0.0703 0.953 0.000 0.976 0.000 0.000 0.024
#> GSM123733 2 0.1965 0.934 0.000 0.924 0.000 0.052 0.024
#> GSM123737 2 0.1386 0.946 0.000 0.952 0.000 0.032 0.016
#> GSM123741 2 0.0693 0.955 0.000 0.980 0.000 0.008 0.012
#> GSM123747 2 0.0566 0.954 0.000 0.984 0.004 0.000 0.012
#> GSM123753 2 0.0880 0.951 0.000 0.968 0.000 0.000 0.032
#> GSM123759 2 0.1502 0.942 0.000 0.940 0.004 0.000 0.056
#> GSM123766 2 0.1579 0.949 0.000 0.944 0.000 0.024 0.032
#> GSM123772 2 0.1082 0.955 0.000 0.964 0.000 0.008 0.028
#> GSM123775 2 0.0703 0.952 0.000 0.976 0.000 0.000 0.024
#> GSM123781 2 0.2733 0.908 0.000 0.872 0.004 0.012 0.112
#> GSM123785 2 0.2171 0.926 0.000 0.912 0.000 0.064 0.024
#> GSM123788 2 0.1725 0.941 0.000 0.936 0.000 0.044 0.020
#> GSM123792 2 0.0290 0.954 0.000 0.992 0.000 0.000 0.008
#> GSM123796 2 0.1399 0.947 0.000 0.952 0.000 0.028 0.020
#> GSM123731 2 0.0290 0.954 0.000 0.992 0.000 0.000 0.008
#> GSM123735 2 0.0579 0.954 0.000 0.984 0.000 0.008 0.008
#> GSM123739 2 0.1386 0.946 0.000 0.952 0.000 0.032 0.016
#> GSM123743 2 0.0566 0.954 0.000 0.984 0.000 0.004 0.012
#> GSM123749 2 0.1124 0.949 0.000 0.960 0.004 0.000 0.036
#> GSM123755 2 0.1502 0.942 0.000 0.940 0.004 0.000 0.056
#> GSM123768 2 0.3656 0.824 0.000 0.800 0.032 0.000 0.168
#> GSM123776 1 0.2536 0.650 0.868 0.128 0.000 0.000 0.004
#> GSM123783 2 0.2864 0.879 0.000 0.852 0.012 0.000 0.136
#> GSM123790 2 0.2390 0.913 0.000 0.896 0.000 0.084 0.020
#> GSM123794 2 0.0290 0.954 0.000 0.992 0.000 0.000 0.008
#> GSM123798 2 0.1502 0.942 0.000 0.940 0.004 0.000 0.056
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM123732 3 0.1269 0.806 0.000 0.000 0.956 0.020 0.012 0.012
#> GSM123736 3 0.3321 0.779 0.000 0.000 0.820 0.080 0.100 0.000
#> GSM123740 3 0.1616 0.810 0.000 0.000 0.932 0.020 0.048 0.000
#> GSM123744 5 0.4859 0.319 0.084 0.000 0.304 0.000 0.612 0.000
#> GSM123746 1 0.1082 0.771 0.956 0.000 0.040 0.000 0.004 0.000
#> GSM123750 3 0.5377 0.473 0.036 0.000 0.608 0.000 0.288 0.068
#> GSM123752 1 0.5391 0.131 0.516 0.000 0.400 0.004 0.012 0.068
#> GSM123756 1 0.1663 0.764 0.912 0.000 0.000 0.000 0.088 0.000
#> GSM123758 3 0.4924 0.575 0.144 0.000 0.720 0.012 0.020 0.104
#> GSM123761 5 0.4067 0.107 0.444 0.000 0.008 0.000 0.548 0.000
#> GSM123763 5 0.1275 0.617 0.012 0.000 0.016 0.000 0.956 0.016
#> GSM123765 3 0.3092 0.785 0.000 0.000 0.836 0.104 0.060 0.000
#> GSM123769 1 0.2969 0.625 0.776 0.000 0.000 0.000 0.224 0.000
#> GSM123771 1 0.0632 0.785 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM123774 1 0.0146 0.785 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM123778 3 0.0881 0.806 0.000 0.000 0.972 0.008 0.012 0.008
#> GSM123780 3 0.2092 0.789 0.000 0.000 0.876 0.124 0.000 0.000
#> GSM123784 3 0.3017 0.756 0.000 0.000 0.816 0.164 0.020 0.000
#> GSM123787 3 0.1624 0.799 0.000 0.000 0.936 0.004 0.020 0.040
#> GSM123791 3 0.4098 0.150 0.000 0.000 0.496 0.000 0.496 0.008
#> GSM123795 3 0.4024 0.718 0.000 0.000 0.744 0.072 0.184 0.000
#> GSM123799 3 0.0951 0.810 0.000 0.000 0.968 0.004 0.020 0.008
#> GSM123730 4 0.1265 0.709 0.000 0.000 0.008 0.948 0.000 0.044
#> GSM123734 4 0.4344 0.187 0.000 0.000 0.000 0.612 0.032 0.356
#> GSM123738 4 0.3559 0.614 0.000 0.000 0.240 0.744 0.012 0.004
#> GSM123742 6 0.4294 0.693 0.000 0.000 0.000 0.048 0.280 0.672
#> GSM123745 6 0.4945 0.511 0.084 0.000 0.000 0.328 0.000 0.588
#> GSM123748 6 0.4321 0.739 0.008 0.000 0.000 0.140 0.108 0.744
#> GSM123751 6 0.4456 0.487 0.028 0.000 0.000 0.372 0.004 0.596
#> GSM123754 1 0.3018 0.680 0.816 0.000 0.000 0.168 0.004 0.012
#> GSM123757 1 0.2584 0.718 0.848 0.000 0.000 0.004 0.004 0.144
#> GSM123760 6 0.4945 0.676 0.000 0.000 0.000 0.084 0.328 0.588
#> GSM123762 5 0.1364 0.619 0.020 0.000 0.012 0.000 0.952 0.016
#> GSM123764 6 0.4087 0.734 0.000 0.000 0.016 0.116 0.092 0.776
#> GSM123767 4 0.2909 0.630 0.012 0.004 0.000 0.828 0.000 0.156
#> GSM123770 1 0.1599 0.783 0.940 0.000 0.000 0.024 0.028 0.008
#> GSM123773 4 0.3536 0.516 0.252 0.004 0.000 0.736 0.000 0.008
#> GSM123777 4 0.2793 0.649 0.000 0.000 0.200 0.800 0.000 0.000
#> GSM123779 4 0.2257 0.720 0.000 0.000 0.048 0.904 0.008 0.040
#> GSM123782 6 0.2001 0.662 0.000 0.000 0.040 0.048 0.000 0.912
#> GSM123786 3 0.2262 0.773 0.000 0.000 0.896 0.008 0.016 0.080
#> GSM123789 6 0.5540 0.600 0.000 0.000 0.012 0.100 0.372 0.516
#> GSM123793 4 0.3577 0.597 0.000 0.000 0.016 0.772 0.012 0.200
#> GSM123797 4 0.2611 0.707 0.000 0.000 0.116 0.864 0.008 0.012
#> GSM123729 2 0.0665 0.954 0.000 0.980 0.000 0.008 0.008 0.004
#> GSM123733 2 0.0713 0.953 0.000 0.972 0.000 0.028 0.000 0.000
#> GSM123737 2 0.0891 0.954 0.000 0.968 0.000 0.024 0.008 0.000
#> GSM123741 2 0.0260 0.955 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM123747 2 0.0260 0.955 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM123753 2 0.0862 0.951 0.000 0.972 0.000 0.008 0.004 0.016
#> GSM123759 2 0.1442 0.942 0.000 0.944 0.000 0.012 0.004 0.040
#> GSM123766 2 0.1668 0.934 0.000 0.928 0.000 0.008 0.004 0.060
#> GSM123772 2 0.0820 0.953 0.000 0.972 0.000 0.012 0.000 0.016
#> GSM123775 2 0.0779 0.953 0.000 0.976 0.000 0.008 0.008 0.008
#> GSM123781 2 0.4241 0.583 0.000 0.644 0.004 0.016 0.004 0.332
#> GSM123785 2 0.0865 0.950 0.000 0.964 0.000 0.036 0.000 0.000
#> GSM123788 2 0.0713 0.953 0.000 0.972 0.000 0.028 0.000 0.000
#> GSM123792 2 0.0547 0.954 0.000 0.980 0.000 0.020 0.000 0.000
#> GSM123796 2 0.0632 0.953 0.000 0.976 0.000 0.024 0.000 0.000
#> GSM123731 2 0.0405 0.956 0.000 0.988 0.000 0.008 0.004 0.000
#> GSM123735 2 0.0547 0.954 0.000 0.980 0.000 0.020 0.000 0.000
#> GSM123739 2 0.0806 0.954 0.000 0.972 0.000 0.020 0.008 0.000
#> GSM123743 2 0.0363 0.955 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM123749 2 0.1223 0.949 0.000 0.960 0.004 0.008 0.012 0.016
#> GSM123755 2 0.1729 0.938 0.000 0.936 0.004 0.012 0.012 0.036
#> GSM123768 2 0.3770 0.836 0.000 0.812 0.036 0.016 0.016 0.120
#> GSM123776 1 0.2805 0.616 0.828 0.160 0.000 0.000 0.012 0.000
#> GSM123783 2 0.2665 0.909 0.000 0.892 0.024 0.016 0.016 0.052
#> GSM123790 2 0.1075 0.945 0.000 0.952 0.000 0.048 0.000 0.000
#> GSM123794 2 0.0547 0.954 0.000 0.980 0.000 0.020 0.000 0.000
#> GSM123798 2 0.1555 0.941 0.000 0.940 0.000 0.012 0.008 0.040
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) infection(p) agent(p) k
#> ATC:NMF 69 7.45e-15 7.45e-15 1.80e-05 2
#> ATC:NMF 66 2.39e-15 2.39e-15 3.89e-05 3
#> ATC:NMF 66 6.20e-19 6.20e-19 6.63e-04 4
#> ATC:NMF 57 1.80e-17 1.80e-17 3.72e-03 5
#> ATC:NMF 64 3.05e-17 3.05e-17 5.53e-03 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
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