Date: 2019-12-25 20:45:56 CET, cola version: 1.3.2
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All available functions which can be applied to this res_list object:
res_list
#> A 'ConsensusPartitionList' object with 24 methods.
#> On a matrix with 51941 rows and 67 columns.
#> Top rows are extracted by 'SD, CV, MAD, ATC' methods.
#> Subgroups are detected by 'hclust, kmeans, skmeans, pam, mclust, NMF' method.
#> Number of partitions are tried for k = 2, 3, 4, 5, 6.
#> Performed in total 30000 partitions by row resampling.
#>
#> Following methods can be applied to this 'ConsensusPartitionList' object:
#> [1] "cola_report" "collect_classes" "collect_plots" "collect_stats"
#> [5] "colnames" "functional_enrichment" "get_anno_col" "get_anno"
#> [9] "get_classes" "get_matrix" "get_membership" "get_stats"
#> [13] "is_best_k" "is_stable_k" "ncol" "nrow"
#> [17] "rownames" "show" "suggest_best_k" "test_to_known_factors"
#> [21] "top_rows_heatmap" "top_rows_overlap"
#>
#> You can get result for a single method by, e.g. object["SD", "hclust"] or object["SD:hclust"]
#> or a subset of methods by object[c("SD", "CV")], c("hclust", "kmeans")]
The call of run_all_consensus_partition_methods() was:
#> run_all_consensus_partition_methods(data = mat, mc.cores = 4, anno = anno)
Dimension of the input matrix:
mat = get_matrix(res_list)
dim(mat)
#> [1] 51941 67
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 | 0.996 | 0.996 | ** | |
| CV:kmeans | 2 | 1.000 | 0.994 | 0.997 | ** | |
| CV:skmeans | 3 | 1.000 | 0.950 | 0.967 | ** | 2 |
| MAD:hclust | 5 | 1.000 | 0.962 | 0.977 | ** | 2 |
| MAD:kmeans | 2 | 1.000 | 0.998 | 0.998 | ** | |
| MAD:mclust | 2 | 1.000 | 0.999 | 0.999 | ** | |
| ATC:hclust | 4 | 1.000 | 0.961 | 0.971 | ** | 2,3 |
| ATC:kmeans | 2 | 1.000 | 0.991 | 0.996 | ** | |
| ATC:pam | 2 | 1.000 | 0.974 | 0.990 | ** | |
| ATC:mclust | 2 | 1.000 | 1.000 | 1.000 | ** | |
| SD:mclust | 6 | 0.997 | 0.952 | 0.980 | ** | 2 |
| SD:hclust | 6 | 0.986 | 0.943 | 0.970 | ** | 2,5 |
| MAD:pam | 6 | 0.959 | 0.907 | 0.967 | ** | 2,3 |
| CV:NMF | 6 | 0.956 | 0.897 | 0.955 | ** | 2,3 |
| CV:hclust | 6 | 0.950 | 0.923 | 0.943 | ** | 2,5 |
| MAD:NMF | 6 | 0.950 | 0.891 | 0.950 | * | 2,3 |
| CV:mclust | 6 | 0.947 | 0.929 | 0.968 | * | 2 |
| SD:NMF | 6 | 0.943 | 0.893 | 0.953 | * | 2,3 |
| CV:pam | 6 | 0.917 | 0.859 | 0.945 | * | 2,3,4 |
| SD:skmeans | 4 | 0.915 | 0.898 | 0.938 | * | 2,3 |
| ATC:skmeans | 3 | 0.912 | 0.927 | 0.965 | * | 2 |
| SD:pam | 6 | 0.910 | 0.883 | 0.956 | * | 2,3,4 |
| MAD:skmeans | 4 | 0.904 | 0.898 | 0.929 | * | 2,3 |
| ATC:NMF | 3 | 0.901 | 0.915 | 0.963 | * | 2 |
**: 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 0.968 0.988 0.481 0.518 0.518
#> CV:NMF 2 1 0.973 0.988 0.484 0.518 0.518
#> MAD:NMF 2 1 0.974 0.990 0.481 0.518 0.518
#> ATC:NMF 2 1 0.994 0.997 0.495 0.506 0.506
#> SD:skmeans 2 1 0.987 0.994 0.482 0.518 0.518
#> CV:skmeans 2 1 0.992 0.996 0.483 0.518 0.518
#> MAD:skmeans 2 1 0.990 0.996 0.481 0.518 0.518
#> ATC:skmeans 2 1 0.999 0.999 0.494 0.506 0.506
#> SD:mclust 2 1 0.998 0.998 0.473 0.525 0.525
#> CV:mclust 2 1 0.997 0.997 0.473 0.525 0.525
#> MAD:mclust 2 1 0.999 0.999 0.475 0.525 0.525
#> ATC:mclust 2 1 1.000 1.000 0.476 0.525 0.525
#> SD:kmeans 2 1 0.996 0.996 0.476 0.525 0.525
#> CV:kmeans 2 1 0.994 0.997 0.477 0.525 0.525
#> MAD:kmeans 2 1 0.998 0.998 0.475 0.525 0.525
#> ATC:kmeans 2 1 0.991 0.996 0.490 0.512 0.512
#> SD:pam 2 1 1.000 1.000 0.475 0.525 0.525
#> CV:pam 2 1 0.998 0.999 0.476 0.525 0.525
#> MAD:pam 2 1 1.000 1.000 0.475 0.525 0.525
#> ATC:pam 2 1 0.974 0.990 0.483 0.518 0.518
#> SD:hclust 2 1 1.000 1.000 0.475 0.525 0.525
#> CV:hclust 2 1 1.000 1.000 0.475 0.525 0.525
#> MAD:hclust 2 1 1.000 1.000 0.475 0.525 0.525
#> ATC:hclust 2 1 1.000 1.000 0.494 0.506 0.506
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.947 0.924 0.969 0.277 0.811 0.656
#> CV:NMF 3 0.935 0.919 0.966 0.275 0.810 0.656
#> MAD:NMF 3 0.948 0.911 0.964 0.282 0.819 0.667
#> ATC:NMF 3 0.901 0.915 0.963 0.237 0.844 0.702
#> SD:skmeans 3 1.000 0.935 0.967 0.382 0.801 0.620
#> CV:skmeans 3 1.000 0.950 0.967 0.384 0.796 0.613
#> MAD:skmeans 3 1.000 0.939 0.970 0.390 0.801 0.620
#> ATC:skmeans 3 0.912 0.927 0.965 0.240 0.855 0.719
#> SD:mclust 3 0.575 0.722 0.866 0.281 0.909 0.828
#> CV:mclust 3 0.676 0.786 0.880 0.280 0.866 0.751
#> MAD:mclust 3 0.715 0.769 0.879 0.256 0.826 0.682
#> ATC:mclust 3 0.667 0.733 0.794 0.228 0.912 0.834
#> SD:kmeans 3 0.625 0.427 0.700 0.284 0.889 0.789
#> CV:kmeans 3 0.640 0.812 0.797 0.256 1.000 1.000
#> MAD:kmeans 3 0.615 0.501 0.772 0.280 0.902 0.814
#> ATC:kmeans 3 0.750 0.783 0.885 0.214 0.924 0.853
#> SD:pam 3 1.000 0.991 0.996 0.138 0.935 0.876
#> CV:pam 3 0.962 0.941 0.958 0.158 0.935 0.876
#> MAD:pam 3 0.954 0.955 0.974 0.143 0.935 0.876
#> ATC:pam 3 0.744 0.886 0.876 0.221 0.931 0.866
#> SD:hclust 3 0.801 0.923 0.935 0.201 0.931 0.869
#> CV:hclust 3 0.801 0.854 0.892 0.239 0.931 0.869
#> MAD:hclust 3 0.801 0.927 0.935 0.200 0.931 0.869
#> ATC:hclust 3 1.000 0.942 0.958 0.110 0.934 0.869
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.671 0.563 0.745 0.1413 0.796 0.554
#> CV:NMF 4 0.656 0.643 0.809 0.1383 0.857 0.654
#> MAD:NMF 4 0.667 0.702 0.839 0.1577 0.817 0.563
#> ATC:NMF 4 0.598 0.599 0.767 0.1496 0.907 0.771
#> SD:skmeans 4 0.915 0.898 0.938 0.1048 0.932 0.796
#> CV:skmeans 4 0.827 0.883 0.923 0.1043 0.932 0.794
#> MAD:skmeans 4 0.904 0.898 0.929 0.1001 0.932 0.796
#> ATC:skmeans 4 0.846 0.832 0.923 0.2006 0.802 0.528
#> SD:mclust 4 0.561 0.779 0.816 0.0783 0.954 0.901
#> CV:mclust 4 0.648 0.809 0.844 0.1057 0.903 0.771
#> MAD:mclust 4 0.720 0.746 0.870 0.1631 0.867 0.683
#> ATC:mclust 4 0.659 0.759 0.881 0.1577 0.828 0.633
#> SD:kmeans 4 0.608 0.809 0.765 0.1425 0.740 0.444
#> CV:kmeans 4 0.614 0.786 0.757 0.1655 0.737 0.499
#> MAD:kmeans 4 0.599 0.734 0.741 0.1441 0.764 0.491
#> ATC:kmeans 4 0.696 0.816 0.792 0.1342 0.930 0.842
#> SD:pam 4 1.000 0.960 0.986 0.0534 0.975 0.946
#> CV:pam 4 0.907 0.946 0.949 0.0682 0.973 0.941
#> MAD:pam 4 0.717 0.904 0.895 0.1333 0.973 0.941
#> ATC:pam 4 0.792 0.781 0.896 0.2137 0.852 0.673
#> SD:hclust 4 0.795 0.908 0.929 0.1157 0.935 0.857
#> CV:hclust 4 0.795 0.837 0.885 0.1127 0.935 0.857
#> MAD:hclust 4 0.732 0.911 0.905 0.1197 0.935 0.857
#> ATC:hclust 4 1.000 0.961 0.971 0.0969 0.953 0.893
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.740 0.779 0.865 0.0931 0.859 0.590
#> CV:NMF 5 0.697 0.773 0.865 0.0889 0.878 0.615
#> MAD:NMF 5 0.800 0.786 0.872 0.0791 0.860 0.550
#> ATC:NMF 5 0.592 0.645 0.784 0.1040 0.762 0.388
#> SD:skmeans 5 0.866 0.815 0.871 0.0557 1.000 1.000
#> CV:skmeans 5 0.817 0.756 0.839 0.0589 0.964 0.871
#> MAD:skmeans 5 0.802 0.668 0.845 0.0685 0.971 0.894
#> ATC:skmeans 5 0.800 0.764 0.875 0.0464 0.976 0.910
#> SD:mclust 5 0.715 0.509 0.761 0.1449 0.823 0.595
#> CV:mclust 5 0.710 0.714 0.847 0.1179 0.798 0.476
#> MAD:mclust 5 0.707 0.794 0.849 0.1030 0.871 0.604
#> ATC:mclust 5 0.716 0.660 0.790 0.1081 0.958 0.873
#> SD:kmeans 5 0.676 0.779 0.794 0.0833 0.964 0.862
#> CV:kmeans 5 0.691 0.785 0.808 0.0887 0.964 0.862
#> MAD:kmeans 5 0.684 0.764 0.771 0.0851 0.914 0.700
#> ATC:kmeans 5 0.666 0.738 0.775 0.1166 0.834 0.570
#> SD:pam 5 0.897 0.903 0.955 0.3279 0.805 0.554
#> CV:pam 5 0.827 0.843 0.931 0.2856 0.801 0.540
#> MAD:pam 5 0.835 0.877 0.938 0.2170 0.801 0.544
#> ATC:pam 5 0.805 0.847 0.906 0.0652 0.888 0.665
#> SD:hclust 5 0.935 0.947 0.966 0.2064 0.841 0.593
#> CV:hclust 5 0.939 0.947 0.965 0.1769 0.837 0.584
#> MAD:hclust 5 1.000 0.962 0.977 0.2037 0.841 0.593
#> ATC:hclust 5 0.687 0.708 0.792 0.2204 0.842 0.597
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.943 0.893 0.953 0.0481 0.954 0.805
#> CV:NMF 6 0.956 0.897 0.955 0.0536 0.949 0.786
#> MAD:NMF 6 0.950 0.891 0.950 0.0388 0.970 0.862
#> ATC:NMF 6 0.573 0.524 0.717 0.0383 0.957 0.806
#> SD:skmeans 6 0.832 0.688 0.753 0.0506 0.846 0.490
#> CV:skmeans 6 0.838 0.794 0.845 0.0462 0.877 0.564
#> MAD:skmeans 6 0.849 0.811 0.838 0.0427 0.907 0.642
#> ATC:skmeans 6 0.856 0.816 0.913 0.0369 0.943 0.773
#> SD:mclust 6 0.997 0.952 0.980 0.0631 0.793 0.387
#> CV:mclust 6 0.947 0.929 0.968 0.0664 0.906 0.647
#> MAD:mclust 6 0.771 0.754 0.859 0.0438 0.918 0.667
#> ATC:mclust 6 0.698 0.271 0.681 0.0652 0.828 0.506
#> SD:kmeans 6 0.746 0.748 0.767 0.0578 0.939 0.740
#> CV:kmeans 6 0.763 0.754 0.773 0.0583 0.960 0.823
#> MAD:kmeans 6 0.738 0.736 0.760 0.0536 0.959 0.819
#> ATC:kmeans 6 0.664 0.677 0.745 0.0592 0.941 0.756
#> SD:pam 6 0.910 0.883 0.956 0.0596 0.953 0.806
#> CV:pam 6 0.917 0.859 0.945 0.0607 0.919 0.681
#> MAD:pam 6 0.959 0.907 0.967 0.0671 0.953 0.804
#> ATC:pam 6 0.806 0.805 0.830 0.0516 0.967 0.869
#> SD:hclust 6 0.986 0.943 0.970 0.0370 0.967 0.858
#> CV:hclust 6 0.950 0.923 0.943 0.0347 0.967 0.856
#> MAD:hclust 6 0.884 0.859 0.900 0.0396 1.000 1.000
#> ATC:hclust 6 0.756 0.759 0.867 0.0604 0.905 0.651
Following heatmap plots the partition for each combination of methods and the lightness correspond to the silhouette scores for samples in each method. On top the consensus subgroup is inferred from all methods by taking the mean silhouette scores as weight.
collect_stats(res_list, k = 2)
collect_stats(res_list, k = 3)
collect_stats(res_list, k = 4)
collect_stats(res_list, k = 5)
collect_stats(res_list, k = 6)
Collect partitions from all methods:
collect_classes(res_list, k = 2)
collect_classes(res_list, k = 3)
collect_classes(res_list, k = 4)
collect_classes(res_list, k = 5)
collect_classes(res_list, k = 6)
Overlap of top rows from different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "euler")
top_rows_overlap(res_list, top_n = 2000, method = "euler")
top_rows_overlap(res_list, top_n = 3000, method = "euler")
top_rows_overlap(res_list, top_n = 4000, method = "euler")
top_rows_overlap(res_list, top_n = 5000, method = "euler")
Also visualize the correspondance of rankings between different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "correspondance")
top_rows_overlap(res_list, top_n = 2000, method = "correspondance")
top_rows_overlap(res_list, top_n = 3000, method = "correspondance")
top_rows_overlap(res_list, top_n = 4000, method = "correspondance")
top_rows_overlap(res_list, top_n = 5000, method = "correspondance")
Heatmaps of the top rows:
top_rows_heatmap(res_list, top_n = 1000)
top_rows_heatmap(res_list, top_n = 2000)
top_rows_heatmap(res_list, top_n = 3000)
top_rows_heatmap(res_list, top_n = 4000)
top_rows_heatmap(res_list, top_n = 5000)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res_list, k = 2)
#> n disease.state(p) k
#> SD:NMF 66 2.61e-10 2
#> CV:NMF 67 7.40e-10 2
#> MAD:NMF 66 2.61e-10 2
#> ATC:NMF 67 9.63e-09 2
#> SD:skmeans 67 7.40e-10 2
#> CV:skmeans 67 7.40e-10 2
#> MAD:skmeans 67 7.40e-10 2
#> ATC:skmeans 67 9.63e-09 2
#> SD:mclust 67 1.68e-10 2
#> CV:mclust 67 1.68e-10 2
#> MAD:mclust 67 1.68e-10 2
#> ATC:mclust 67 1.68e-10 2
#> SD:kmeans 67 1.68e-10 2
#> CV:kmeans 67 1.68e-10 2
#> MAD:kmeans 67 1.68e-10 2
#> ATC:kmeans 67 3.51e-09 2
#> SD:pam 67 1.68e-10 2
#> CV:pam 67 1.68e-10 2
#> MAD:pam 67 1.68e-10 2
#> ATC:pam 66 1.39e-09 2
#> SD:hclust 67 1.68e-10 2
#> CV:hclust 67 1.68e-10 2
#> MAD:hclust 67 1.68e-10 2
#> ATC:hclust 67 9.63e-09 2
test_to_known_factors(res_list, k = 3)
#> n disease.state(p) k
#> SD:NMF 65 2.26e-14 3
#> CV:NMF 64 4.83e-14 3
#> MAD:NMF 64 1.08e-13 3
#> ATC:NMF 65 1.12e-08 3
#> SD:skmeans 65 4.05e-15 3
#> CV:skmeans 66 4.75e-15 3
#> MAD:skmeans 65 9.56e-15 3
#> ATC:skmeans 67 3.11e-12 3
#> SD:mclust 61 1.21e-16 3
#> CV:mclust 63 2.18e-17 3
#> MAD:mclust 60 2.85e-16 3
#> ATC:mclust 61 1.06e-13 3
#> SD:kmeans 32 5.94e-06 3
#> CV:kmeans 67 1.68e-10 3
#> MAD:kmeans 44 2.94e-10 3
#> ATC:kmeans 62 1.92e-09 3
#> SD:pam 67 3.83e-17 3
#> CV:pam 66 1.64e-18 3
#> MAD:pam 67 3.83e-17 3
#> ATC:pam 67 8.42e-15 3
#> SD:hclust 67 6.34e-10 3
#> CV:hclust 67 6.34e-10 3
#> MAD:hclust 67 6.34e-10 3
#> ATC:hclust 67 4.21e-07 3
test_to_known_factors(res_list, k = 4)
#> n disease.state(p) k
#> SD:NMF 40 4.13e-12 4
#> CV:NMF 52 1.98e-13 4
#> MAD:NMF 55 7.43e-16 4
#> ATC:NMF 50 9.27e-09 4
#> SD:skmeans 65 4.31e-23 4
#> CV:skmeans 66 3.31e-23 4
#> MAD:skmeans 65 1.02e-22 4
#> ATC:skmeans 62 3.29e-12 4
#> SD:mclust 66 1.17e-26 4
#> CV:mclust 61 6.65e-20 4
#> MAD:mclust 65 4.09e-21 4
#> ATC:mclust 61 5.18e-12 4
#> SD:kmeans 66 3.31e-23 4
#> CV:kmeans 61 6.59e-22 4
#> MAD:kmeans 56 3.78e-19 4
#> ATC:kmeans 62 8.66e-13 4
#> SD:pam 66 1.17e-26 4
#> CV:pam 66 1.17e-26 4
#> MAD:pam 67 1.90e-24 4
#> ATC:pam 64 1.22e-17 4
#> SD:hclust 66 8.68e-18 4
#> CV:hclust 66 8.68e-18 4
#> MAD:hclust 67 1.51e-16 4
#> ATC:hclust 67 1.87e-12 4
test_to_known_factors(res_list, k = 5)
#> n disease.state(p) k
#> SD:NMF 59 5.26e-25 5
#> CV:NMF 59 5.26e-25 5
#> MAD:NMF 57 6.95e-18 5
#> ATC:NMF 53 7.16e-12 5
#> SD:skmeans 64 4.92e-23 5
#> CV:skmeans 61 1.85e-20 5
#> MAD:skmeans 56 3.57e-19 5
#> ATC:skmeans 57 2.08e-12 5
#> SD:mclust 32 2.51e-10 5
#> CV:mclust 55 1.18e-21 5
#> MAD:mclust 65 1.81e-22 5
#> ATC:mclust 49 1.64e-10 5
#> SD:kmeans 59 7.92e-20 5
#> CV:kmeans 59 7.92e-20 5
#> MAD:kmeans 61 2.43e-20 5
#> ATC:kmeans 58 4.73e-11 5
#> SD:pam 65 1.21e-28 5
#> CV:pam 62 1.19e-24 5
#> MAD:pam 67 4.23e-26 5
#> ATC:pam 66 2.13e-16 5
#> SD:hclust 66 7.60e-22 5
#> CV:hclust 66 4.32e-21 5
#> MAD:hclust 67 9.85e-21 5
#> ATC:hclust 59 2.62e-14 5
test_to_known_factors(res_list, k = 6)
#> n disease.state(p) k
#> SD:NMF 65 4.06e-24 6
#> CV:NMF 64 1.23e-23 6
#> MAD:NMF 63 5.00e-25 6
#> ATC:NMF 44 5.37e-13 6
#> SD:skmeans 54 2.21e-27 6
#> CV:skmeans 52 2.31e-27 6
#> MAD:skmeans 63 3.27e-26 6
#> ATC:skmeans 60 4.69e-12 6
#> SD:mclust 66 3.45e-27 6
#> CV:mclust 66 3.45e-27 6
#> MAD:mclust 56 3.24e-22 6
#> ATC:mclust 27 1.12e-06 6
#> SD:kmeans 55 2.17e-25 6
#> CV:kmeans 57 6.84e-26 6
#> MAD:kmeans 59 8.96e-25 6
#> ATC:kmeans 57 1.71e-15 6
#> SD:pam 63 2.66e-26 6
#> CV:pam 62 2.10e-26 6
#> MAD:pam 64 4.35e-23 6
#> ATC:pam 60 2.63e-18 6
#> SD:hclust 66 6.69e-30 6
#> CV:hclust 65 7.90e-29 6
#> MAD:hclust 66 1.57e-20 6
#> ATC:hclust 60 9.93e-14 6
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "hclust"]
# you can also extract it by
# res = res_list["SD:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 67 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 1.000 1.000 1.000 0.475 0.525 0.525
#> 3 3 0.801 0.923 0.935 0.201 0.931 0.869
#> 4 4 0.795 0.908 0.929 0.116 0.935 0.857
#> 5 5 0.935 0.947 0.966 0.206 0.841 0.593
#> 6 6 0.986 0.943 0.970 0.037 0.967 0.858
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 5
There is also optional best \(k\) = 2 5 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM312811 2 0 1 0 1
#> GSM312812 2 0 1 0 1
#> GSM312813 2 0 1 0 1
#> GSM312814 2 0 1 0 1
#> GSM312815 2 0 1 0 1
#> GSM312816 2 0 1 0 1
#> GSM312817 2 0 1 0 1
#> GSM312818 2 0 1 0 1
#> GSM312819 2 0 1 0 1
#> GSM312820 2 0 1 0 1
#> GSM312821 2 0 1 0 1
#> GSM312822 2 0 1 0 1
#> GSM312823 2 0 1 0 1
#> GSM312824 2 0 1 0 1
#> GSM312825 2 0 1 0 1
#> GSM312826 2 0 1 0 1
#> GSM312839 2 0 1 0 1
#> GSM312840 2 0 1 0 1
#> GSM312841 2 0 1 0 1
#> GSM312843 2 0 1 0 1
#> GSM312844 2 0 1 0 1
#> GSM312845 2 0 1 0 1
#> GSM312846 2 0 1 0 1
#> GSM312847 2 0 1 0 1
#> GSM312848 2 0 1 0 1
#> GSM312849 2 0 1 0 1
#> GSM312851 2 0 1 0 1
#> GSM312853 2 0 1 0 1
#> GSM312854 2 0 1 0 1
#> GSM312856 2 0 1 0 1
#> GSM312857 2 0 1 0 1
#> GSM312858 2 0 1 0 1
#> GSM312859 2 0 1 0 1
#> GSM312860 2 0 1 0 1
#> GSM312861 2 0 1 0 1
#> GSM312862 2 0 1 0 1
#> GSM312863 2 0 1 0 1
#> GSM312864 2 0 1 0 1
#> GSM312865 2 0 1 0 1
#> GSM312867 2 0 1 0 1
#> GSM312868 2 0 1 0 1
#> GSM312869 2 0 1 0 1
#> GSM312870 1 0 1 1 0
#> GSM312872 1 0 1 1 0
#> GSM312874 1 0 1 1 0
#> GSM312875 1 0 1 1 0
#> GSM312876 1 0 1 1 0
#> GSM312877 1 0 1 1 0
#> GSM312879 1 0 1 1 0
#> GSM312882 1 0 1 1 0
#> GSM312883 1 0 1 1 0
#> GSM312886 1 0 1 1 0
#> GSM312887 1 0 1 1 0
#> GSM312890 1 0 1 1 0
#> GSM312893 1 0 1 1 0
#> GSM312894 1 0 1 1 0
#> GSM312895 1 0 1 1 0
#> GSM312937 1 0 1 1 0
#> GSM312938 1 0 1 1 0
#> GSM312939 1 0 1 1 0
#> GSM312940 1 0 1 1 0
#> GSM312941 1 0 1 1 0
#> GSM312942 1 0 1 1 0
#> GSM312943 1 0 1 1 0
#> GSM312944 1 0 1 1 0
#> GSM312945 1 0 1 1 0
#> GSM312946 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM312811 2 0.0000 0.870 0 1.000 0.000
#> GSM312812 2 0.0000 0.870 0 1.000 0.000
#> GSM312813 2 0.0000 0.870 0 1.000 0.000
#> GSM312814 2 0.0000 0.870 0 1.000 0.000
#> GSM312815 2 0.0000 0.870 0 1.000 0.000
#> GSM312816 3 0.4750 1.000 0 0.216 0.784
#> GSM312817 2 0.0000 0.870 0 1.000 0.000
#> GSM312818 3 0.4750 1.000 0 0.216 0.784
#> GSM312819 2 0.0000 0.870 0 1.000 0.000
#> GSM312820 3 0.4750 1.000 0 0.216 0.784
#> GSM312821 3 0.4750 1.000 0 0.216 0.784
#> GSM312822 2 0.0000 0.870 0 1.000 0.000
#> GSM312823 2 0.0000 0.870 0 1.000 0.000
#> GSM312824 2 0.0000 0.870 0 1.000 0.000
#> GSM312825 2 0.0000 0.870 0 1.000 0.000
#> GSM312826 2 0.0000 0.870 0 1.000 0.000
#> GSM312839 2 0.0000 0.870 0 1.000 0.000
#> GSM312840 2 0.0000 0.870 0 1.000 0.000
#> GSM312841 2 0.0000 0.870 0 1.000 0.000
#> GSM312843 2 0.4291 0.862 0 0.820 0.180
#> GSM312844 2 0.0000 0.870 0 1.000 0.000
#> GSM312845 2 0.4750 0.858 0 0.784 0.216
#> GSM312846 2 0.4750 0.858 0 0.784 0.216
#> GSM312847 2 0.4750 0.858 0 0.784 0.216
#> GSM312848 2 0.4750 0.858 0 0.784 0.216
#> GSM312849 2 0.4750 0.858 0 0.784 0.216
#> GSM312851 2 0.4750 0.858 0 0.784 0.216
#> GSM312853 2 0.4750 0.858 0 0.784 0.216
#> GSM312854 2 0.4750 0.858 0 0.784 0.216
#> GSM312856 2 0.4750 0.858 0 0.784 0.216
#> GSM312857 2 0.4750 0.858 0 0.784 0.216
#> GSM312858 2 0.4750 0.858 0 0.784 0.216
#> GSM312859 2 0.0000 0.870 0 1.000 0.000
#> GSM312860 2 0.0424 0.870 0 0.992 0.008
#> GSM312861 2 0.4750 0.858 0 0.784 0.216
#> GSM312862 2 0.4291 0.862 0 0.820 0.180
#> GSM312863 2 0.4750 0.858 0 0.784 0.216
#> GSM312864 2 0.0424 0.870 0 0.992 0.008
#> GSM312865 2 0.4750 0.858 0 0.784 0.216
#> GSM312867 2 0.4750 0.858 0 0.784 0.216
#> GSM312868 2 0.4750 0.858 0 0.784 0.216
#> GSM312869 2 0.0000 0.870 0 1.000 0.000
#> GSM312870 1 0.0000 1.000 1 0.000 0.000
#> GSM312872 1 0.0000 1.000 1 0.000 0.000
#> GSM312874 1 0.0000 1.000 1 0.000 0.000
#> GSM312875 1 0.0000 1.000 1 0.000 0.000
#> GSM312876 1 0.0000 1.000 1 0.000 0.000
#> GSM312877 1 0.0000 1.000 1 0.000 0.000
#> GSM312879 1 0.0000 1.000 1 0.000 0.000
#> GSM312882 1 0.0000 1.000 1 0.000 0.000
#> GSM312883 1 0.0000 1.000 1 0.000 0.000
#> GSM312886 1 0.0000 1.000 1 0.000 0.000
#> GSM312887 1 0.0000 1.000 1 0.000 0.000
#> GSM312890 1 0.0000 1.000 1 0.000 0.000
#> GSM312893 1 0.0000 1.000 1 0.000 0.000
#> GSM312894 1 0.0000 1.000 1 0.000 0.000
#> GSM312895 1 0.0000 1.000 1 0.000 0.000
#> GSM312937 1 0.0000 1.000 1 0.000 0.000
#> GSM312938 1 0.0000 1.000 1 0.000 0.000
#> GSM312939 1 0.0000 1.000 1 0.000 0.000
#> GSM312940 1 0.0000 1.000 1 0.000 0.000
#> GSM312941 1 0.0000 1.000 1 0.000 0.000
#> GSM312942 1 0.0000 1.000 1 0.000 0.000
#> GSM312943 1 0.0000 1.000 1 0.000 0.000
#> GSM312944 1 0.0000 1.000 1 0.000 0.000
#> GSM312945 1 0.0000 1.000 1 0.000 0.000
#> GSM312946 1 0.0000 1.000 1 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM312811 2 0.0000 0.870 0.00 1.000 0.00 0.000
#> GSM312812 2 0.0000 0.870 0.00 1.000 0.00 0.000
#> GSM312813 2 0.0000 0.870 0.00 1.000 0.00 0.000
#> GSM312814 2 0.0000 0.870 0.00 1.000 0.00 0.000
#> GSM312815 2 0.0000 0.870 0.00 1.000 0.00 0.000
#> GSM312816 4 0.3764 1.000 0.00 0.216 0.00 0.784
#> GSM312817 2 0.0000 0.870 0.00 1.000 0.00 0.000
#> GSM312818 4 0.3764 1.000 0.00 0.216 0.00 0.784
#> GSM312819 2 0.0000 0.870 0.00 1.000 0.00 0.000
#> GSM312820 4 0.3764 1.000 0.00 0.216 0.00 0.784
#> GSM312821 4 0.3764 1.000 0.00 0.216 0.00 0.784
#> GSM312822 2 0.0000 0.870 0.00 1.000 0.00 0.000
#> GSM312823 2 0.0000 0.870 0.00 1.000 0.00 0.000
#> GSM312824 2 0.0000 0.870 0.00 1.000 0.00 0.000
#> GSM312825 2 0.0000 0.870 0.00 1.000 0.00 0.000
#> GSM312826 2 0.0000 0.870 0.00 1.000 0.00 0.000
#> GSM312839 2 0.0000 0.870 0.00 1.000 0.00 0.000
#> GSM312840 2 0.0000 0.870 0.00 1.000 0.00 0.000
#> GSM312841 2 0.0000 0.870 0.00 1.000 0.00 0.000
#> GSM312843 2 0.3400 0.862 0.00 0.820 0.00 0.180
#> GSM312844 2 0.0000 0.870 0.00 1.000 0.00 0.000
#> GSM312845 2 0.3764 0.858 0.00 0.784 0.00 0.216
#> GSM312846 2 0.3764 0.858 0.00 0.784 0.00 0.216
#> GSM312847 2 0.3764 0.858 0.00 0.784 0.00 0.216
#> GSM312848 2 0.3764 0.858 0.00 0.784 0.00 0.216
#> GSM312849 2 0.3764 0.858 0.00 0.784 0.00 0.216
#> GSM312851 2 0.3764 0.858 0.00 0.784 0.00 0.216
#> GSM312853 2 0.3764 0.858 0.00 0.784 0.00 0.216
#> GSM312854 2 0.3764 0.858 0.00 0.784 0.00 0.216
#> GSM312856 2 0.3764 0.858 0.00 0.784 0.00 0.216
#> GSM312857 2 0.3764 0.858 0.00 0.784 0.00 0.216
#> GSM312858 2 0.3764 0.858 0.00 0.784 0.00 0.216
#> GSM312859 2 0.0000 0.870 0.00 1.000 0.00 0.000
#> GSM312860 2 0.0336 0.870 0.00 0.992 0.00 0.008
#> GSM312861 2 0.3764 0.858 0.00 0.784 0.00 0.216
#> GSM312862 2 0.3400 0.862 0.00 0.820 0.00 0.180
#> GSM312863 2 0.3764 0.858 0.00 0.784 0.00 0.216
#> GSM312864 2 0.0336 0.870 0.00 0.992 0.00 0.008
#> GSM312865 2 0.3764 0.858 0.00 0.784 0.00 0.216
#> GSM312867 2 0.3764 0.858 0.00 0.784 0.00 0.216
#> GSM312868 2 0.3764 0.858 0.00 0.784 0.00 0.216
#> GSM312869 2 0.0000 0.870 0.00 1.000 0.00 0.000
#> GSM312870 3 0.0000 1.000 0.00 0.000 1.00 0.000
#> GSM312872 3 0.0000 1.000 0.00 0.000 1.00 0.000
#> GSM312874 3 0.0000 1.000 0.00 0.000 1.00 0.000
#> GSM312875 3 0.0000 1.000 0.00 0.000 1.00 0.000
#> GSM312876 3 0.0000 1.000 0.00 0.000 1.00 0.000
#> GSM312877 1 0.4790 0.387 0.62 0.000 0.38 0.000
#> GSM312879 3 0.0000 1.000 0.00 0.000 1.00 0.000
#> GSM312882 3 0.0000 1.000 0.00 0.000 1.00 0.000
#> GSM312883 3 0.0000 1.000 0.00 0.000 1.00 0.000
#> GSM312886 3 0.0000 1.000 0.00 0.000 1.00 0.000
#> GSM312887 1 0.0000 0.972 1.00 0.000 0.00 0.000
#> GSM312890 1 0.0000 0.972 1.00 0.000 0.00 0.000
#> GSM312893 1 0.0000 0.972 1.00 0.000 0.00 0.000
#> GSM312894 1 0.0000 0.972 1.00 0.000 0.00 0.000
#> GSM312895 1 0.0000 0.972 1.00 0.000 0.00 0.000
#> GSM312937 1 0.0000 0.972 1.00 0.000 0.00 0.000
#> GSM312938 1 0.0000 0.972 1.00 0.000 0.00 0.000
#> GSM312939 1 0.0000 0.972 1.00 0.000 0.00 0.000
#> GSM312940 1 0.0000 0.972 1.00 0.000 0.00 0.000
#> GSM312941 1 0.0000 0.972 1.00 0.000 0.00 0.000
#> GSM312942 1 0.0000 0.972 1.00 0.000 0.00 0.000
#> GSM312943 1 0.0000 0.972 1.00 0.000 0.00 0.000
#> GSM312944 1 0.0000 0.972 1.00 0.000 0.00 0.000
#> GSM312945 1 0.0000 0.972 1.00 0.000 0.00 0.000
#> GSM312946 1 0.0000 0.972 1.00 0.000 0.00 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM312811 2 0.0000 0.953 0.000 1.000 0.00 0.000 0.000
#> GSM312812 2 0.0000 0.953 0.000 1.000 0.00 0.000 0.000
#> GSM312813 2 0.0000 0.953 0.000 1.000 0.00 0.000 0.000
#> GSM312814 2 0.0162 0.953 0.000 0.996 0.00 0.004 0.000
#> GSM312815 2 0.0000 0.953 0.000 1.000 0.00 0.000 0.000
#> GSM312816 5 0.2471 1.000 0.000 0.136 0.00 0.000 0.864
#> GSM312817 2 0.0162 0.953 0.000 0.996 0.00 0.000 0.004
#> GSM312818 5 0.2471 1.000 0.000 0.136 0.00 0.000 0.864
#> GSM312819 2 0.0404 0.951 0.000 0.988 0.00 0.000 0.012
#> GSM312820 5 0.2471 1.000 0.000 0.136 0.00 0.000 0.864
#> GSM312821 5 0.2471 1.000 0.000 0.136 0.00 0.000 0.864
#> GSM312822 2 0.0162 0.953 0.000 0.996 0.00 0.004 0.000
#> GSM312823 2 0.0404 0.948 0.000 0.988 0.00 0.012 0.000
#> GSM312824 2 0.0290 0.953 0.000 0.992 0.00 0.000 0.008
#> GSM312825 2 0.0290 0.953 0.000 0.992 0.00 0.000 0.008
#> GSM312826 2 0.0290 0.953 0.000 0.992 0.00 0.000 0.008
#> GSM312839 2 0.0000 0.953 0.000 1.000 0.00 0.000 0.000
#> GSM312840 2 0.0290 0.953 0.000 0.992 0.00 0.000 0.008
#> GSM312841 2 0.0404 0.951 0.000 0.988 0.00 0.000 0.012
#> GSM312843 2 0.3274 0.673 0.000 0.780 0.00 0.220 0.000
#> GSM312844 2 0.0000 0.953 0.000 1.000 0.00 0.000 0.000
#> GSM312845 4 0.0000 1.000 0.000 0.000 0.00 1.000 0.000
#> GSM312846 4 0.0000 1.000 0.000 0.000 0.00 1.000 0.000
#> GSM312847 4 0.0000 1.000 0.000 0.000 0.00 1.000 0.000
#> GSM312848 4 0.0000 1.000 0.000 0.000 0.00 1.000 0.000
#> GSM312849 4 0.0000 1.000 0.000 0.000 0.00 1.000 0.000
#> GSM312851 4 0.0000 1.000 0.000 0.000 0.00 1.000 0.000
#> GSM312853 4 0.0000 1.000 0.000 0.000 0.00 1.000 0.000
#> GSM312854 4 0.0000 1.000 0.000 0.000 0.00 1.000 0.000
#> GSM312856 4 0.0000 1.000 0.000 0.000 0.00 1.000 0.000
#> GSM312857 4 0.0000 1.000 0.000 0.000 0.00 1.000 0.000
#> GSM312858 4 0.0000 1.000 0.000 0.000 0.00 1.000 0.000
#> GSM312859 2 0.1270 0.911 0.000 0.948 0.00 0.052 0.000
#> GSM312860 2 0.1410 0.902 0.000 0.940 0.00 0.060 0.000
#> GSM312861 4 0.0000 1.000 0.000 0.000 0.00 1.000 0.000
#> GSM312862 2 0.3274 0.673 0.000 0.780 0.00 0.220 0.000
#> GSM312863 4 0.0000 1.000 0.000 0.000 0.00 1.000 0.000
#> GSM312864 2 0.1410 0.900 0.000 0.940 0.00 0.060 0.000
#> GSM312865 4 0.0000 1.000 0.000 0.000 0.00 1.000 0.000
#> GSM312867 4 0.0000 1.000 0.000 0.000 0.00 1.000 0.000
#> GSM312868 4 0.0000 1.000 0.000 0.000 0.00 1.000 0.000
#> GSM312869 2 0.0290 0.953 0.000 0.992 0.00 0.000 0.008
#> GSM312870 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM312872 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM312874 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM312875 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM312876 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM312877 1 0.4126 0.437 0.620 0.000 0.38 0.000 0.000
#> GSM312879 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM312882 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM312883 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM312886 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM312887 1 0.0000 0.932 1.000 0.000 0.00 0.000 0.000
#> GSM312890 1 0.0000 0.932 1.000 0.000 0.00 0.000 0.000
#> GSM312893 1 0.0000 0.932 1.000 0.000 0.00 0.000 0.000
#> GSM312894 1 0.0000 0.932 1.000 0.000 0.00 0.000 0.000
#> GSM312895 1 0.0000 0.932 1.000 0.000 0.00 0.000 0.000
#> GSM312937 1 0.0000 0.932 1.000 0.000 0.00 0.000 0.000
#> GSM312938 1 0.0000 0.932 1.000 0.000 0.00 0.000 0.000
#> GSM312939 1 0.0000 0.932 1.000 0.000 0.00 0.000 0.000
#> GSM312940 1 0.0000 0.932 1.000 0.000 0.00 0.000 0.000
#> GSM312941 1 0.0000 0.932 1.000 0.000 0.00 0.000 0.000
#> GSM312942 1 0.2471 0.889 0.864 0.000 0.00 0.000 0.136
#> GSM312943 1 0.2471 0.889 0.864 0.000 0.00 0.000 0.136
#> GSM312944 1 0.2471 0.889 0.864 0.000 0.00 0.000 0.136
#> GSM312945 1 0.2471 0.889 0.864 0.000 0.00 0.000 0.136
#> GSM312946 1 0.2471 0.889 0.864 0.000 0.00 0.000 0.136
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM312811 2 0.0000 0.941 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM312812 2 0.0000 0.941 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM312813 2 0.0000 0.941 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM312814 2 0.0146 0.942 0.000 0.996 0.00 0.004 0.000 0.000
#> GSM312815 2 0.0146 0.942 0.000 0.996 0.00 0.000 0.004 0.000
#> GSM312816 5 0.0000 1.000 0.000 0.000 0.00 0.000 1.000 0.000
#> GSM312817 2 0.0146 0.942 0.000 0.996 0.00 0.000 0.004 0.000
#> GSM312818 5 0.0000 1.000 0.000 0.000 0.00 0.000 1.000 0.000
#> GSM312819 2 0.2448 0.893 0.000 0.884 0.00 0.000 0.064 0.052
#> GSM312820 5 0.0000 1.000 0.000 0.000 0.00 0.000 1.000 0.000
#> GSM312821 5 0.0000 1.000 0.000 0.000 0.00 0.000 1.000 0.000
#> GSM312822 2 0.0146 0.942 0.000 0.996 0.00 0.004 0.000 0.000
#> GSM312823 2 0.0363 0.939 0.000 0.988 0.00 0.012 0.000 0.000
#> GSM312824 2 0.0806 0.938 0.000 0.972 0.00 0.000 0.020 0.008
#> GSM312825 2 0.0806 0.938 0.000 0.972 0.00 0.000 0.020 0.008
#> GSM312826 2 0.0806 0.938 0.000 0.972 0.00 0.000 0.020 0.008
#> GSM312839 2 0.0146 0.942 0.000 0.996 0.00 0.000 0.004 0.000
#> GSM312840 2 0.1995 0.909 0.000 0.912 0.00 0.000 0.036 0.052
#> GSM312841 2 0.2448 0.893 0.000 0.884 0.00 0.000 0.064 0.052
#> GSM312843 2 0.2941 0.717 0.000 0.780 0.00 0.220 0.000 0.000
#> GSM312844 2 0.0000 0.941 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM312845 4 0.0000 1.000 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM312846 4 0.0000 1.000 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM312847 4 0.0000 1.000 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM312848 4 0.0000 1.000 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM312849 4 0.0000 1.000 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM312851 4 0.0000 1.000 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM312853 4 0.0000 1.000 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM312854 4 0.0000 1.000 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM312856 4 0.0000 1.000 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM312857 4 0.0000 1.000 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM312858 4 0.0000 1.000 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM312859 2 0.1398 0.915 0.000 0.940 0.00 0.052 0.000 0.008
#> GSM312860 2 0.1267 0.908 0.000 0.940 0.00 0.060 0.000 0.000
#> GSM312861 4 0.0000 1.000 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM312862 2 0.2941 0.717 0.000 0.780 0.00 0.220 0.000 0.000
#> GSM312863 4 0.0000 1.000 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM312864 2 0.3005 0.868 0.000 0.864 0.00 0.060 0.024 0.052
#> GSM312865 4 0.0000 1.000 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM312867 4 0.0000 1.000 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM312868 4 0.0000 1.000 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM312869 2 0.0806 0.938 0.000 0.972 0.00 0.000 0.020 0.008
#> GSM312870 3 0.0000 0.929 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM312872 3 0.0000 0.929 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM312874 3 0.0000 0.929 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM312875 3 0.0000 0.929 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM312876 3 0.0000 0.929 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM312877 3 0.6059 -0.158 0.260 0.000 0.38 0.000 0.000 0.360
#> GSM312879 3 0.0000 0.929 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM312882 3 0.0000 0.929 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM312883 3 0.0000 0.929 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM312886 3 0.0000 0.929 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM312887 1 0.0000 1.000 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM312890 1 0.0000 1.000 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM312893 1 0.0000 1.000 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM312894 1 0.0000 1.000 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM312895 1 0.0000 1.000 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM312937 1 0.0000 1.000 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM312938 1 0.0000 1.000 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM312939 1 0.0000 1.000 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM312940 1 0.0000 1.000 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM312941 1 0.0000 1.000 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM312942 6 0.1141 1.000 0.052 0.000 0.00 0.000 0.000 0.948
#> GSM312943 6 0.1141 1.000 0.052 0.000 0.00 0.000 0.000 0.948
#> GSM312944 6 0.1141 1.000 0.052 0.000 0.00 0.000 0.000 0.948
#> GSM312945 6 0.1141 1.000 0.052 0.000 0.00 0.000 0.000 0.948
#> GSM312946 6 0.1141 1.000 0.052 0.000 0.00 0.000 0.000 0.948
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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 5)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 6)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:hclust 67 1.68e-10 2
#> SD:hclust 67 6.34e-10 3
#> SD:hclust 66 8.68e-18 4
#> SD:hclust 66 7.60e-22 5
#> SD:hclust 66 6.69e-30 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "kmeans"]
# you can also extract it by
# res = res_list["SD:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 67 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 0.996 0.996 0.4757 0.525 0.525
#> 3 3 0.625 0.427 0.700 0.2845 0.889 0.789
#> 4 4 0.608 0.809 0.765 0.1425 0.740 0.444
#> 5 5 0.676 0.779 0.794 0.0833 0.964 0.862
#> 6 6 0.746 0.748 0.767 0.0578 0.939 0.740
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
#> GSM312811 2 0.0000 0.996 0.000 1.000
#> GSM312812 2 0.0000 0.996 0.000 1.000
#> GSM312813 2 0.0000 0.996 0.000 1.000
#> GSM312814 2 0.0000 0.996 0.000 1.000
#> GSM312815 2 0.0000 0.996 0.000 1.000
#> GSM312816 2 0.0000 0.996 0.000 1.000
#> GSM312817 2 0.0000 0.996 0.000 1.000
#> GSM312818 2 0.0000 0.996 0.000 1.000
#> GSM312819 2 0.0000 0.996 0.000 1.000
#> GSM312820 2 0.0000 0.996 0.000 1.000
#> GSM312821 2 0.0000 0.996 0.000 1.000
#> GSM312822 2 0.0000 0.996 0.000 1.000
#> GSM312823 2 0.0000 0.996 0.000 1.000
#> GSM312824 2 0.0000 0.996 0.000 1.000
#> GSM312825 2 0.0000 0.996 0.000 1.000
#> GSM312826 2 0.0000 0.996 0.000 1.000
#> GSM312839 2 0.0000 0.996 0.000 1.000
#> GSM312840 2 0.0000 0.996 0.000 1.000
#> GSM312841 2 0.0000 0.996 0.000 1.000
#> GSM312843 2 0.0376 0.996 0.004 0.996
#> GSM312844 2 0.0000 0.996 0.000 1.000
#> GSM312845 2 0.1843 0.978 0.028 0.972
#> GSM312846 2 0.0672 0.995 0.008 0.992
#> GSM312847 2 0.0672 0.995 0.008 0.992
#> GSM312848 2 0.0672 0.995 0.008 0.992
#> GSM312849 2 0.0672 0.995 0.008 0.992
#> GSM312851 2 0.0672 0.995 0.008 0.992
#> GSM312853 2 0.0672 0.995 0.008 0.992
#> GSM312854 2 0.0672 0.995 0.008 0.992
#> GSM312856 2 0.0672 0.995 0.008 0.992
#> GSM312857 2 0.0672 0.995 0.008 0.992
#> GSM312858 2 0.0672 0.995 0.008 0.992
#> GSM312859 2 0.0000 0.996 0.000 1.000
#> GSM312860 2 0.0376 0.996 0.004 0.996
#> GSM312861 2 0.0672 0.995 0.008 0.992
#> GSM312862 2 0.0000 0.996 0.000 1.000
#> GSM312863 2 0.0672 0.995 0.008 0.992
#> GSM312864 2 0.0000 0.996 0.000 1.000
#> GSM312865 2 0.0672 0.995 0.008 0.992
#> GSM312867 2 0.0672 0.995 0.008 0.992
#> GSM312868 2 0.0672 0.995 0.008 0.992
#> GSM312869 2 0.0000 0.996 0.000 1.000
#> GSM312870 1 0.0672 0.997 0.992 0.008
#> GSM312872 1 0.0672 0.997 0.992 0.008
#> GSM312874 1 0.0672 0.997 0.992 0.008
#> GSM312875 1 0.0672 0.997 0.992 0.008
#> GSM312876 1 0.0672 0.997 0.992 0.008
#> GSM312877 1 0.0672 0.997 0.992 0.008
#> GSM312879 1 0.0672 0.997 0.992 0.008
#> GSM312882 1 0.0672 0.997 0.992 0.008
#> GSM312883 1 0.0672 0.997 0.992 0.008
#> GSM312886 1 0.0672 0.997 0.992 0.008
#> GSM312887 1 0.0000 0.995 1.000 0.000
#> GSM312890 1 0.0000 0.995 1.000 0.000
#> GSM312893 1 0.0000 0.995 1.000 0.000
#> GSM312894 1 0.0000 0.995 1.000 0.000
#> GSM312895 1 0.0000 0.995 1.000 0.000
#> GSM312937 1 0.0000 0.995 1.000 0.000
#> GSM312938 1 0.0000 0.995 1.000 0.000
#> GSM312939 1 0.0000 0.995 1.000 0.000
#> GSM312940 1 0.0000 0.995 1.000 0.000
#> GSM312941 1 0.0000 0.995 1.000 0.000
#> GSM312942 1 0.0672 0.997 0.992 0.008
#> GSM312943 1 0.0672 0.997 0.992 0.008
#> GSM312944 1 0.0672 0.997 0.992 0.008
#> GSM312945 1 0.0672 0.997 0.992 0.008
#> GSM312946 1 0.0672 0.997 0.992 0.008
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM312811 3 0.6302 0.8415 0.000 0.480 0.520
#> GSM312812 2 0.6192 -0.4610 0.000 0.580 0.420
#> GSM312813 2 0.6126 -0.3952 0.000 0.600 0.400
#> GSM312814 3 0.6299 0.8474 0.000 0.476 0.524
#> GSM312815 2 0.6192 -0.4610 0.000 0.580 0.420
#> GSM312816 3 0.6168 0.8955 0.000 0.412 0.588
#> GSM312817 2 0.6192 -0.4793 0.000 0.580 0.420
#> GSM312818 3 0.6168 0.8955 0.000 0.412 0.588
#> GSM312819 2 0.6309 -0.7977 0.000 0.500 0.500
#> GSM312820 3 0.6168 0.8955 0.000 0.412 0.588
#> GSM312821 3 0.6168 0.8955 0.000 0.412 0.588
#> GSM312822 3 0.6302 0.8415 0.000 0.480 0.520
#> GSM312823 2 0.6126 -0.3952 0.000 0.600 0.400
#> GSM312824 2 0.6126 -0.3952 0.000 0.600 0.400
#> GSM312825 2 0.6126 -0.3952 0.000 0.600 0.400
#> GSM312826 2 0.6126 -0.3952 0.000 0.600 0.400
#> GSM312839 2 0.6140 -0.4070 0.000 0.596 0.404
#> GSM312840 2 0.6140 -0.4081 0.000 0.596 0.404
#> GSM312841 2 0.6204 -0.4772 0.000 0.576 0.424
#> GSM312843 2 0.1753 0.4627 0.000 0.952 0.048
#> GSM312844 2 0.6140 -0.4070 0.000 0.596 0.404
#> GSM312845 2 0.0747 0.4773 0.016 0.984 0.000
#> GSM312846 2 0.0000 0.4886 0.000 1.000 0.000
#> GSM312847 2 0.0000 0.4886 0.000 1.000 0.000
#> GSM312848 2 0.0000 0.4886 0.000 1.000 0.000
#> GSM312849 2 0.0000 0.4886 0.000 1.000 0.000
#> GSM312851 2 0.3752 0.3870 0.000 0.856 0.144
#> GSM312853 2 0.3752 0.3870 0.000 0.856 0.144
#> GSM312854 2 0.3686 0.3912 0.000 0.860 0.140
#> GSM312856 2 0.3686 0.3912 0.000 0.860 0.140
#> GSM312857 2 0.3752 0.3870 0.000 0.856 0.144
#> GSM312858 2 0.0000 0.4886 0.000 1.000 0.000
#> GSM312859 2 0.5905 -0.3126 0.000 0.648 0.352
#> GSM312860 2 0.5178 -0.0211 0.000 0.744 0.256
#> GSM312861 2 0.0000 0.4886 0.000 1.000 0.000
#> GSM312862 2 0.0237 0.4863 0.000 0.996 0.004
#> GSM312863 2 0.3551 0.3974 0.000 0.868 0.132
#> GSM312864 2 0.6215 -0.5059 0.000 0.572 0.428
#> GSM312865 2 0.0237 0.4870 0.000 0.996 0.004
#> GSM312867 2 0.0000 0.4886 0.000 1.000 0.000
#> GSM312868 2 0.0000 0.4886 0.000 1.000 0.000
#> GSM312869 2 0.6126 -0.3952 0.000 0.600 0.400
#> GSM312870 1 0.6062 0.8463 0.616 0.000 0.384
#> GSM312872 1 0.6062 0.8463 0.616 0.000 0.384
#> GSM312874 1 0.6062 0.8463 0.616 0.000 0.384
#> GSM312875 1 0.6062 0.8463 0.616 0.000 0.384
#> GSM312876 1 0.6062 0.8463 0.616 0.000 0.384
#> GSM312877 1 0.5810 0.8548 0.664 0.000 0.336
#> GSM312879 1 0.6062 0.8463 0.616 0.000 0.384
#> GSM312882 1 0.6062 0.8463 0.616 0.000 0.384
#> GSM312883 1 0.6062 0.8463 0.616 0.000 0.384
#> GSM312886 1 0.6062 0.8463 0.616 0.000 0.384
#> GSM312887 1 0.0000 0.8618 1.000 0.000 0.000
#> GSM312890 1 0.0000 0.8618 1.000 0.000 0.000
#> GSM312893 1 0.0000 0.8618 1.000 0.000 0.000
#> GSM312894 1 0.0000 0.8618 1.000 0.000 0.000
#> GSM312895 1 0.0000 0.8618 1.000 0.000 0.000
#> GSM312937 1 0.0000 0.8618 1.000 0.000 0.000
#> GSM312938 1 0.0000 0.8618 1.000 0.000 0.000
#> GSM312939 1 0.0000 0.8618 1.000 0.000 0.000
#> GSM312940 1 0.0000 0.8618 1.000 0.000 0.000
#> GSM312941 1 0.0000 0.8618 1.000 0.000 0.000
#> GSM312942 1 0.4346 0.8711 0.816 0.000 0.184
#> GSM312943 1 0.4346 0.8711 0.816 0.000 0.184
#> GSM312944 1 0.4346 0.8711 0.816 0.000 0.184
#> GSM312945 1 0.4346 0.8711 0.816 0.000 0.184
#> GSM312946 1 0.4346 0.8711 0.816 0.000 0.184
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM312811 2 0.3885 0.773 0.000 0.844 0.064 0.092
#> GSM312812 2 0.0707 0.824 0.000 0.980 0.020 0.000
#> GSM312813 2 0.1724 0.827 0.000 0.948 0.020 0.032
#> GSM312814 2 0.4605 0.753 0.000 0.800 0.108 0.092
#> GSM312815 2 0.1389 0.818 0.000 0.952 0.048 0.000
#> GSM312816 2 0.6764 0.602 0.000 0.596 0.260 0.144
#> GSM312817 2 0.1929 0.828 0.000 0.940 0.024 0.036
#> GSM312818 2 0.6788 0.599 0.000 0.592 0.264 0.144
#> GSM312819 2 0.3160 0.801 0.000 0.872 0.020 0.108
#> GSM312820 2 0.6764 0.602 0.000 0.596 0.260 0.144
#> GSM312821 2 0.6764 0.602 0.000 0.596 0.260 0.144
#> GSM312822 2 0.4605 0.753 0.000 0.800 0.108 0.092
#> GSM312823 2 0.1022 0.824 0.000 0.968 0.000 0.032
#> GSM312824 2 0.1022 0.824 0.000 0.968 0.000 0.032
#> GSM312825 2 0.1022 0.824 0.000 0.968 0.000 0.032
#> GSM312826 2 0.1022 0.824 0.000 0.968 0.000 0.032
#> GSM312839 2 0.0921 0.826 0.000 0.972 0.000 0.028
#> GSM312840 2 0.1356 0.826 0.000 0.960 0.008 0.032
#> GSM312841 2 0.0707 0.825 0.000 0.980 0.020 0.000
#> GSM312843 4 0.4744 0.881 0.000 0.284 0.012 0.704
#> GSM312844 2 0.0592 0.827 0.000 0.984 0.000 0.016
#> GSM312845 4 0.4746 0.895 0.008 0.304 0.000 0.688
#> GSM312846 4 0.4477 0.898 0.000 0.312 0.000 0.688
#> GSM312847 4 0.4454 0.900 0.000 0.308 0.000 0.692
#> GSM312848 4 0.4454 0.900 0.000 0.308 0.000 0.692
#> GSM312849 4 0.4500 0.895 0.000 0.316 0.000 0.684
#> GSM312851 4 0.4789 0.820 0.000 0.172 0.056 0.772
#> GSM312853 4 0.4789 0.820 0.000 0.172 0.056 0.772
#> GSM312854 4 0.4832 0.824 0.000 0.176 0.056 0.768
#> GSM312856 4 0.4832 0.824 0.000 0.176 0.056 0.768
#> GSM312857 4 0.4789 0.820 0.000 0.172 0.056 0.772
#> GSM312858 4 0.4431 0.900 0.000 0.304 0.000 0.696
#> GSM312859 2 0.2345 0.753 0.000 0.900 0.000 0.100
#> GSM312860 2 0.3649 0.556 0.000 0.796 0.000 0.204
#> GSM312861 4 0.4522 0.893 0.000 0.320 0.000 0.680
#> GSM312862 4 0.4522 0.892 0.000 0.320 0.000 0.680
#> GSM312863 4 0.4511 0.831 0.000 0.176 0.040 0.784
#> GSM312864 2 0.5686 0.363 0.000 0.592 0.032 0.376
#> GSM312865 4 0.4406 0.900 0.000 0.300 0.000 0.700
#> GSM312867 4 0.4500 0.895 0.000 0.316 0.000 0.684
#> GSM312868 4 0.4406 0.900 0.000 0.300 0.000 0.700
#> GSM312869 2 0.1022 0.824 0.000 0.968 0.000 0.032
#> GSM312870 3 0.4605 0.973 0.336 0.000 0.664 0.000
#> GSM312872 3 0.4605 0.973 0.336 0.000 0.664 0.000
#> GSM312874 3 0.4605 0.973 0.336 0.000 0.664 0.000
#> GSM312875 3 0.4781 0.973 0.336 0.000 0.660 0.004
#> GSM312876 3 0.4781 0.973 0.336 0.000 0.660 0.004
#> GSM312877 3 0.5535 0.817 0.420 0.000 0.560 0.020
#> GSM312879 3 0.5038 0.972 0.336 0.000 0.652 0.012
#> GSM312882 3 0.5252 0.971 0.336 0.000 0.644 0.020
#> GSM312883 3 0.5252 0.971 0.336 0.000 0.644 0.020
#> GSM312886 3 0.5149 0.971 0.336 0.000 0.648 0.016
#> GSM312887 1 0.0000 0.830 1.000 0.000 0.000 0.000
#> GSM312890 1 0.0000 0.830 1.000 0.000 0.000 0.000
#> GSM312893 1 0.0000 0.830 1.000 0.000 0.000 0.000
#> GSM312894 1 0.0000 0.830 1.000 0.000 0.000 0.000
#> GSM312895 1 0.0000 0.830 1.000 0.000 0.000 0.000
#> GSM312937 1 0.0000 0.830 1.000 0.000 0.000 0.000
#> GSM312938 1 0.0000 0.830 1.000 0.000 0.000 0.000
#> GSM312939 1 0.0000 0.830 1.000 0.000 0.000 0.000
#> GSM312940 1 0.0000 0.830 1.000 0.000 0.000 0.000
#> GSM312941 1 0.0000 0.830 1.000 0.000 0.000 0.000
#> GSM312942 1 0.6262 0.549 0.660 0.000 0.208 0.132
#> GSM312943 1 0.6262 0.549 0.660 0.000 0.208 0.132
#> GSM312944 1 0.6262 0.549 0.660 0.000 0.208 0.132
#> GSM312945 1 0.6262 0.549 0.660 0.000 0.208 0.132
#> GSM312946 1 0.6262 0.549 0.660 0.000 0.208 0.132
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM312811 2 0.454 0.602 0.000 0.768 0.048 0.024 0.160
#> GSM312812 2 0.215 0.787 0.000 0.916 0.036 0.000 0.048
#> GSM312813 2 0.315 0.806 0.000 0.876 0.052 0.028 0.044
#> GSM312814 2 0.518 0.386 0.000 0.676 0.040 0.024 0.260
#> GSM312815 2 0.315 0.705 0.000 0.844 0.028 0.000 0.128
#> GSM312816 5 0.430 1.000 0.000 0.260 0.000 0.028 0.712
#> GSM312817 2 0.343 0.803 0.000 0.860 0.064 0.028 0.048
#> GSM312818 5 0.430 1.000 0.000 0.260 0.000 0.028 0.712
#> GSM312819 2 0.254 0.807 0.000 0.904 0.052 0.032 0.012
#> GSM312820 5 0.430 1.000 0.000 0.260 0.000 0.028 0.712
#> GSM312821 5 0.430 1.000 0.000 0.260 0.000 0.028 0.712
#> GSM312822 2 0.518 0.386 0.000 0.676 0.040 0.024 0.260
#> GSM312823 2 0.128 0.830 0.000 0.956 0.012 0.032 0.000
#> GSM312824 2 0.117 0.829 0.000 0.960 0.008 0.032 0.000
#> GSM312825 2 0.117 0.829 0.000 0.960 0.008 0.032 0.000
#> GSM312826 2 0.117 0.829 0.000 0.960 0.008 0.032 0.000
#> GSM312839 2 0.149 0.830 0.000 0.948 0.024 0.028 0.000
#> GSM312840 2 0.131 0.828 0.000 0.956 0.020 0.024 0.000
#> GSM312841 2 0.101 0.812 0.000 0.968 0.020 0.000 0.012
#> GSM312843 4 0.468 0.828 0.000 0.176 0.072 0.744 0.008
#> GSM312844 2 0.101 0.830 0.000 0.968 0.012 0.020 0.000
#> GSM312845 4 0.286 0.884 0.000 0.132 0.004 0.856 0.008
#> GSM312846 4 0.286 0.884 0.000 0.132 0.004 0.856 0.008
#> GSM312847 4 0.286 0.884 0.000 0.132 0.004 0.856 0.008
#> GSM312848 4 0.286 0.884 0.000 0.132 0.004 0.856 0.008
#> GSM312849 4 0.286 0.884 0.000 0.132 0.004 0.856 0.008
#> GSM312851 4 0.570 0.779 0.000 0.068 0.116 0.708 0.108
#> GSM312853 4 0.570 0.779 0.000 0.068 0.116 0.708 0.108
#> GSM312854 4 0.570 0.779 0.000 0.068 0.116 0.708 0.108
#> GSM312856 4 0.570 0.779 0.000 0.068 0.116 0.708 0.108
#> GSM312857 4 0.570 0.779 0.000 0.068 0.116 0.708 0.108
#> GSM312858 4 0.242 0.884 0.000 0.132 0.000 0.868 0.000
#> GSM312859 2 0.271 0.766 0.000 0.876 0.024 0.100 0.000
#> GSM312860 2 0.310 0.708 0.000 0.836 0.016 0.148 0.000
#> GSM312861 4 0.313 0.869 0.000 0.156 0.008 0.832 0.004
#> GSM312862 4 0.331 0.869 0.000 0.144 0.020 0.832 0.004
#> GSM312863 4 0.540 0.791 0.000 0.068 0.116 0.732 0.084
#> GSM312864 2 0.661 0.150 0.000 0.520 0.092 0.344 0.044
#> GSM312865 4 0.233 0.883 0.000 0.124 0.000 0.876 0.000
#> GSM312867 4 0.286 0.884 0.000 0.132 0.004 0.856 0.008
#> GSM312868 4 0.254 0.884 0.000 0.128 0.004 0.868 0.000
#> GSM312869 2 0.117 0.829 0.000 0.960 0.008 0.032 0.000
#> GSM312870 3 0.361 0.964 0.268 0.000 0.732 0.000 0.000
#> GSM312872 3 0.361 0.964 0.268 0.000 0.732 0.000 0.000
#> GSM312874 3 0.361 0.964 0.268 0.000 0.732 0.000 0.000
#> GSM312875 3 0.361 0.964 0.268 0.000 0.732 0.000 0.000
#> GSM312876 3 0.361 0.964 0.268 0.000 0.732 0.000 0.000
#> GSM312877 3 0.530 0.861 0.332 0.000 0.616 0.020 0.032
#> GSM312879 3 0.465 0.960 0.268 0.000 0.696 0.012 0.024
#> GSM312882 3 0.499 0.954 0.268 0.000 0.680 0.020 0.032
#> GSM312883 3 0.499 0.954 0.268 0.000 0.680 0.020 0.032
#> GSM312886 3 0.473 0.959 0.268 0.000 0.692 0.012 0.028
#> GSM312887 1 0.029 0.759 0.992 0.000 0.000 0.000 0.008
#> GSM312890 1 0.000 0.762 1.000 0.000 0.000 0.000 0.000
#> GSM312893 1 0.000 0.762 1.000 0.000 0.000 0.000 0.000
#> GSM312894 1 0.000 0.762 1.000 0.000 0.000 0.000 0.000
#> GSM312895 1 0.000 0.762 1.000 0.000 0.000 0.000 0.000
#> GSM312937 1 0.000 0.762 1.000 0.000 0.000 0.000 0.000
#> GSM312938 1 0.029 0.759 0.992 0.000 0.000 0.000 0.008
#> GSM312939 1 0.000 0.762 1.000 0.000 0.000 0.000 0.000
#> GSM312940 1 0.000 0.762 1.000 0.000 0.000 0.000 0.000
#> GSM312941 1 0.000 0.762 1.000 0.000 0.000 0.000 0.000
#> GSM312942 1 0.717 0.299 0.476 0.000 0.320 0.048 0.156
#> GSM312943 1 0.717 0.299 0.476 0.000 0.320 0.048 0.156
#> GSM312944 1 0.717 0.299 0.476 0.000 0.320 0.048 0.156
#> GSM312945 1 0.717 0.299 0.476 0.000 0.320 0.048 0.156
#> GSM312946 1 0.717 0.299 0.476 0.000 0.320 0.048 0.156
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM312811 2 0.5278 0.725 0.056 0.676 0.000 0.000 0.184 0.084
#> GSM312812 2 0.2395 0.835 0.012 0.892 0.000 0.000 0.076 0.020
#> GSM312813 2 0.3997 0.814 0.040 0.796 0.000 0.012 0.128 0.024
#> GSM312814 2 0.5846 0.639 0.052 0.612 0.000 0.000 0.200 0.136
#> GSM312815 2 0.3397 0.805 0.024 0.836 0.000 0.000 0.084 0.056
#> GSM312816 6 0.5438 0.308 0.000 0.172 0.000 0.000 0.260 0.568
#> GSM312817 2 0.4927 0.790 0.076 0.724 0.000 0.012 0.156 0.032
#> GSM312818 6 0.5438 0.308 0.000 0.172 0.000 0.000 0.260 0.568
#> GSM312819 2 0.3752 0.807 0.076 0.804 0.000 0.004 0.108 0.008
#> GSM312820 6 0.5438 0.308 0.000 0.172 0.000 0.000 0.260 0.568
#> GSM312821 6 0.5438 0.308 0.000 0.172 0.000 0.000 0.260 0.568
#> GSM312822 2 0.5846 0.639 0.052 0.612 0.000 0.000 0.200 0.136
#> GSM312823 2 0.1774 0.848 0.020 0.936 0.000 0.024 0.016 0.004
#> GSM312824 2 0.0692 0.848 0.004 0.976 0.000 0.020 0.000 0.000
#> GSM312825 2 0.0692 0.848 0.004 0.976 0.000 0.020 0.000 0.000
#> GSM312826 2 0.0692 0.848 0.004 0.976 0.000 0.020 0.000 0.000
#> GSM312839 2 0.1882 0.848 0.024 0.928 0.000 0.020 0.028 0.000
#> GSM312840 2 0.1599 0.843 0.028 0.940 0.000 0.008 0.024 0.000
#> GSM312841 2 0.1788 0.839 0.040 0.928 0.000 0.000 0.028 0.004
#> GSM312843 4 0.6033 0.155 0.072 0.180 0.000 0.624 0.116 0.008
#> GSM312844 2 0.1690 0.849 0.020 0.940 0.000 0.020 0.016 0.004
#> GSM312845 4 0.0717 0.813 0.008 0.016 0.000 0.976 0.000 0.000
#> GSM312846 4 0.0806 0.812 0.008 0.020 0.000 0.972 0.000 0.000
#> GSM312847 4 0.0717 0.813 0.008 0.016 0.000 0.976 0.000 0.000
#> GSM312848 4 0.0717 0.813 0.008 0.016 0.000 0.976 0.000 0.000
#> GSM312849 4 0.0806 0.812 0.008 0.020 0.000 0.972 0.000 0.000
#> GSM312851 5 0.4179 1.000 0.000 0.012 0.000 0.472 0.516 0.000
#> GSM312853 5 0.4179 1.000 0.000 0.012 0.000 0.472 0.516 0.000
#> GSM312854 5 0.4179 1.000 0.000 0.012 0.000 0.472 0.516 0.000
#> GSM312856 5 0.4179 1.000 0.000 0.012 0.000 0.472 0.516 0.000
#> GSM312857 5 0.4179 1.000 0.000 0.012 0.000 0.472 0.516 0.000
#> GSM312858 4 0.2014 0.781 0.024 0.016 0.000 0.924 0.032 0.004
#> GSM312859 2 0.2577 0.828 0.024 0.896 0.000 0.048 0.024 0.008
#> GSM312860 2 0.2726 0.761 0.008 0.848 0.000 0.136 0.000 0.008
#> GSM312861 4 0.1699 0.785 0.012 0.040 0.000 0.936 0.004 0.008
#> GSM312862 4 0.2485 0.746 0.032 0.040 0.000 0.900 0.024 0.004
#> GSM312863 4 0.4410 -0.903 0.008 0.012 0.000 0.508 0.472 0.000
#> GSM312864 2 0.7115 0.288 0.084 0.464 0.000 0.176 0.264 0.012
#> GSM312865 4 0.1511 0.782 0.012 0.012 0.000 0.944 0.032 0.000
#> GSM312867 4 0.0458 0.813 0.000 0.016 0.000 0.984 0.000 0.000
#> GSM312868 4 0.2127 0.769 0.024 0.016 0.000 0.920 0.032 0.008
#> GSM312869 2 0.0837 0.847 0.004 0.972 0.000 0.020 0.004 0.000
#> GSM312870 3 0.0146 0.943 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM312872 3 0.0146 0.943 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM312874 3 0.0146 0.943 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM312875 3 0.0146 0.943 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM312876 3 0.0146 0.943 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM312877 3 0.3490 0.868 0.056 0.000 0.836 0.012 0.084 0.012
#> GSM312879 3 0.1606 0.939 0.000 0.000 0.932 0.004 0.056 0.008
#> GSM312882 3 0.2323 0.927 0.000 0.000 0.892 0.012 0.084 0.012
#> GSM312883 3 0.2323 0.927 0.000 0.000 0.892 0.012 0.084 0.012
#> GSM312886 3 0.1888 0.935 0.000 0.000 0.916 0.004 0.068 0.012
#> GSM312887 1 0.3651 0.955 0.792 0.000 0.160 0.000 0.032 0.016
#> GSM312890 1 0.2454 0.989 0.840 0.000 0.160 0.000 0.000 0.000
#> GSM312893 1 0.2454 0.989 0.840 0.000 0.160 0.000 0.000 0.000
#> GSM312894 1 0.2454 0.989 0.840 0.000 0.160 0.000 0.000 0.000
#> GSM312895 1 0.2454 0.989 0.840 0.000 0.160 0.000 0.000 0.000
#> GSM312937 1 0.2454 0.989 0.840 0.000 0.160 0.000 0.000 0.000
#> GSM312938 1 0.3651 0.955 0.792 0.000 0.160 0.000 0.032 0.016
#> GSM312939 1 0.2454 0.989 0.840 0.000 0.160 0.000 0.000 0.000
#> GSM312940 1 0.2454 0.989 0.840 0.000 0.160 0.000 0.000 0.000
#> GSM312941 1 0.2454 0.989 0.840 0.000 0.160 0.000 0.000 0.000
#> GSM312942 6 0.6094 0.243 0.312 0.000 0.300 0.000 0.000 0.388
#> GSM312943 6 0.6094 0.243 0.312 0.000 0.300 0.000 0.000 0.388
#> GSM312944 6 0.6094 0.243 0.312 0.000 0.300 0.000 0.000 0.388
#> GSM312945 6 0.6094 0.243 0.312 0.000 0.300 0.000 0.000 0.388
#> GSM312946 6 0.6094 0.243 0.312 0.000 0.300 0.000 0.000 0.388
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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:kmeans 67 1.68e-10 2
#> SD:kmeans 32 5.94e-06 3
#> SD:kmeans 66 3.31e-23 4
#> SD:kmeans 59 7.92e-20 5
#> SD:kmeans 55 2.17e-25 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "skmeans"]
# you can also extract it by
# res = res_list["SD:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 67 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 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 0.987 0.994 0.4821 0.518 0.518
#> 3 3 1.000 0.935 0.967 0.3816 0.801 0.620
#> 4 4 0.915 0.898 0.938 0.1048 0.932 0.796
#> 5 5 0.866 0.815 0.871 0.0557 1.000 1.000
#> 6 6 0.832 0.688 0.753 0.0506 0.846 0.490
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
#> GSM312811 2 0.000 0.996 0.000 1.000
#> GSM312812 2 0.000 0.996 0.000 1.000
#> GSM312813 2 0.000 0.996 0.000 1.000
#> GSM312814 2 0.000 0.996 0.000 1.000
#> GSM312815 2 0.000 0.996 0.000 1.000
#> GSM312816 2 0.000 0.996 0.000 1.000
#> GSM312817 2 0.000 0.996 0.000 1.000
#> GSM312818 2 0.000 0.996 0.000 1.000
#> GSM312819 2 0.000 0.996 0.000 1.000
#> GSM312820 2 0.000 0.996 0.000 1.000
#> GSM312821 2 0.000 0.996 0.000 1.000
#> GSM312822 2 0.000 0.996 0.000 1.000
#> GSM312823 2 0.000 0.996 0.000 1.000
#> GSM312824 2 0.000 0.996 0.000 1.000
#> GSM312825 2 0.000 0.996 0.000 1.000
#> GSM312826 2 0.000 0.996 0.000 1.000
#> GSM312839 2 0.000 0.996 0.000 1.000
#> GSM312840 2 0.000 0.996 0.000 1.000
#> GSM312841 2 0.000 0.996 0.000 1.000
#> GSM312843 2 0.000 0.996 0.000 1.000
#> GSM312844 2 0.000 0.996 0.000 1.000
#> GSM312845 1 0.753 0.722 0.784 0.216
#> GSM312846 2 0.625 0.812 0.156 0.844
#> GSM312847 2 0.000 0.996 0.000 1.000
#> GSM312848 2 0.000 0.996 0.000 1.000
#> GSM312849 2 0.000 0.996 0.000 1.000
#> GSM312851 2 0.000 0.996 0.000 1.000
#> GSM312853 2 0.000 0.996 0.000 1.000
#> GSM312854 2 0.000 0.996 0.000 1.000
#> GSM312856 2 0.000 0.996 0.000 1.000
#> GSM312857 2 0.000 0.996 0.000 1.000
#> GSM312858 2 0.000 0.996 0.000 1.000
#> GSM312859 2 0.000 0.996 0.000 1.000
#> GSM312860 2 0.000 0.996 0.000 1.000
#> GSM312861 2 0.000 0.996 0.000 1.000
#> GSM312862 2 0.000 0.996 0.000 1.000
#> GSM312863 2 0.000 0.996 0.000 1.000
#> GSM312864 2 0.000 0.996 0.000 1.000
#> GSM312865 2 0.000 0.996 0.000 1.000
#> GSM312867 2 0.000 0.996 0.000 1.000
#> GSM312868 2 0.000 0.996 0.000 1.000
#> GSM312869 2 0.000 0.996 0.000 1.000
#> GSM312870 1 0.000 0.991 1.000 0.000
#> GSM312872 1 0.000 0.991 1.000 0.000
#> GSM312874 1 0.000 0.991 1.000 0.000
#> GSM312875 1 0.000 0.991 1.000 0.000
#> GSM312876 1 0.000 0.991 1.000 0.000
#> GSM312877 1 0.000 0.991 1.000 0.000
#> GSM312879 1 0.000 0.991 1.000 0.000
#> GSM312882 1 0.000 0.991 1.000 0.000
#> GSM312883 1 0.000 0.991 1.000 0.000
#> GSM312886 1 0.000 0.991 1.000 0.000
#> GSM312887 1 0.000 0.991 1.000 0.000
#> GSM312890 1 0.000 0.991 1.000 0.000
#> GSM312893 1 0.000 0.991 1.000 0.000
#> GSM312894 1 0.000 0.991 1.000 0.000
#> GSM312895 1 0.000 0.991 1.000 0.000
#> GSM312937 1 0.000 0.991 1.000 0.000
#> GSM312938 1 0.000 0.991 1.000 0.000
#> GSM312939 1 0.000 0.991 1.000 0.000
#> GSM312940 1 0.000 0.991 1.000 0.000
#> GSM312941 1 0.000 0.991 1.000 0.000
#> GSM312942 1 0.000 0.991 1.000 0.000
#> GSM312943 1 0.000 0.991 1.000 0.000
#> GSM312944 1 0.000 0.991 1.000 0.000
#> GSM312945 1 0.000 0.991 1.000 0.000
#> GSM312946 1 0.000 0.991 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM312811 2 0.1289 0.9433 0.000 0.968 0.032
#> GSM312812 2 0.0000 0.9544 0.000 1.000 0.000
#> GSM312813 2 0.0000 0.9544 0.000 1.000 0.000
#> GSM312814 2 0.1289 0.9433 0.000 0.968 0.032
#> GSM312815 2 0.0000 0.9544 0.000 1.000 0.000
#> GSM312816 2 0.1289 0.9433 0.000 0.968 0.032
#> GSM312817 2 0.0000 0.9544 0.000 1.000 0.000
#> GSM312818 2 0.1711 0.9387 0.008 0.960 0.032
#> GSM312819 2 0.0592 0.9510 0.000 0.988 0.012
#> GSM312820 2 0.1289 0.9433 0.000 0.968 0.032
#> GSM312821 2 0.1289 0.9433 0.000 0.968 0.032
#> GSM312822 2 0.1289 0.9433 0.000 0.968 0.032
#> GSM312823 2 0.0000 0.9544 0.000 1.000 0.000
#> GSM312824 2 0.0000 0.9544 0.000 1.000 0.000
#> GSM312825 2 0.0000 0.9544 0.000 1.000 0.000
#> GSM312826 2 0.0000 0.9544 0.000 1.000 0.000
#> GSM312839 2 0.0000 0.9544 0.000 1.000 0.000
#> GSM312840 2 0.0000 0.9544 0.000 1.000 0.000
#> GSM312841 2 0.0000 0.9544 0.000 1.000 0.000
#> GSM312843 3 0.6286 0.0432 0.000 0.464 0.536
#> GSM312844 2 0.0000 0.9544 0.000 1.000 0.000
#> GSM312845 3 0.1289 0.9448 0.000 0.032 0.968
#> GSM312846 3 0.1289 0.9448 0.000 0.032 0.968
#> GSM312847 3 0.1753 0.9525 0.000 0.048 0.952
#> GSM312848 3 0.1753 0.9525 0.000 0.048 0.952
#> GSM312849 3 0.1753 0.9525 0.000 0.048 0.952
#> GSM312851 3 0.0747 0.9462 0.000 0.016 0.984
#> GSM312853 3 0.0747 0.9462 0.000 0.016 0.984
#> GSM312854 3 0.0747 0.9462 0.000 0.016 0.984
#> GSM312856 3 0.0747 0.9462 0.000 0.016 0.984
#> GSM312857 3 0.0747 0.9462 0.000 0.016 0.984
#> GSM312858 3 0.1753 0.9525 0.000 0.048 0.952
#> GSM312859 2 0.0237 0.9524 0.000 0.996 0.004
#> GSM312860 2 0.1411 0.9279 0.000 0.964 0.036
#> GSM312861 3 0.1753 0.9525 0.000 0.048 0.952
#> GSM312862 2 0.6252 0.1184 0.000 0.556 0.444
#> GSM312863 3 0.0747 0.9462 0.000 0.016 0.984
#> GSM312864 2 0.5529 0.5982 0.000 0.704 0.296
#> GSM312865 3 0.1753 0.9525 0.000 0.048 0.952
#> GSM312867 3 0.1643 0.9513 0.000 0.044 0.956
#> GSM312868 3 0.1753 0.9525 0.000 0.048 0.952
#> GSM312869 2 0.0000 0.9544 0.000 1.000 0.000
#> GSM312870 1 0.0000 0.9945 1.000 0.000 0.000
#> GSM312872 1 0.0000 0.9945 1.000 0.000 0.000
#> GSM312874 1 0.0000 0.9945 1.000 0.000 0.000
#> GSM312875 1 0.0000 0.9945 1.000 0.000 0.000
#> GSM312876 1 0.0000 0.9945 1.000 0.000 0.000
#> GSM312877 1 0.0000 0.9945 1.000 0.000 0.000
#> GSM312879 1 0.0000 0.9945 1.000 0.000 0.000
#> GSM312882 1 0.0000 0.9945 1.000 0.000 0.000
#> GSM312883 1 0.0000 0.9945 1.000 0.000 0.000
#> GSM312886 1 0.0000 0.9945 1.000 0.000 0.000
#> GSM312887 1 0.0747 0.9918 0.984 0.000 0.016
#> GSM312890 1 0.0747 0.9918 0.984 0.000 0.016
#> GSM312893 1 0.0747 0.9918 0.984 0.000 0.016
#> GSM312894 1 0.0747 0.9918 0.984 0.000 0.016
#> GSM312895 1 0.0747 0.9918 0.984 0.000 0.016
#> GSM312937 1 0.0747 0.9918 0.984 0.000 0.016
#> GSM312938 1 0.0747 0.9918 0.984 0.000 0.016
#> GSM312939 1 0.0747 0.9918 0.984 0.000 0.016
#> GSM312940 1 0.0747 0.9918 0.984 0.000 0.016
#> GSM312941 1 0.0747 0.9918 0.984 0.000 0.016
#> GSM312942 1 0.0000 0.9945 1.000 0.000 0.000
#> GSM312943 1 0.0000 0.9945 1.000 0.000 0.000
#> GSM312944 1 0.0000 0.9945 1.000 0.000 0.000
#> GSM312945 1 0.0000 0.9945 1.000 0.000 0.000
#> GSM312946 1 0.0000 0.9945 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM312811 2 0.2313 0.91619 0.032 0.924 0.000 0.044
#> GSM312812 2 0.0000 0.93956 0.000 1.000 0.000 0.000
#> GSM312813 2 0.0000 0.93956 0.000 1.000 0.000 0.000
#> GSM312814 2 0.2313 0.91619 0.032 0.924 0.000 0.044
#> GSM312815 2 0.0336 0.93817 0.008 0.992 0.000 0.000
#> GSM312816 2 0.2313 0.91619 0.032 0.924 0.000 0.044
#> GSM312817 2 0.0188 0.93893 0.000 0.996 0.000 0.004
#> GSM312818 2 0.3756 0.88298 0.032 0.872 0.052 0.044
#> GSM312819 2 0.0469 0.93704 0.000 0.988 0.000 0.012
#> GSM312820 2 0.2313 0.91619 0.032 0.924 0.000 0.044
#> GSM312821 2 0.2313 0.91619 0.032 0.924 0.000 0.044
#> GSM312822 2 0.2313 0.91619 0.032 0.924 0.000 0.044
#> GSM312823 2 0.0000 0.93956 0.000 1.000 0.000 0.000
#> GSM312824 2 0.0000 0.93956 0.000 1.000 0.000 0.000
#> GSM312825 2 0.0000 0.93956 0.000 1.000 0.000 0.000
#> GSM312826 2 0.0000 0.93956 0.000 1.000 0.000 0.000
#> GSM312839 2 0.0000 0.93956 0.000 1.000 0.000 0.000
#> GSM312840 2 0.0000 0.93956 0.000 1.000 0.000 0.000
#> GSM312841 2 0.0000 0.93956 0.000 1.000 0.000 0.000
#> GSM312843 4 0.4889 0.33884 0.004 0.360 0.000 0.636
#> GSM312844 2 0.0000 0.93956 0.000 1.000 0.000 0.000
#> GSM312845 4 0.3708 0.81905 0.148 0.020 0.000 0.832
#> GSM312846 4 0.3862 0.81388 0.152 0.024 0.000 0.824
#> GSM312847 4 0.1489 0.92963 0.004 0.044 0.000 0.952
#> GSM312848 4 0.1398 0.93055 0.004 0.040 0.000 0.956
#> GSM312849 4 0.1489 0.92963 0.004 0.044 0.000 0.952
#> GSM312851 4 0.0188 0.92391 0.004 0.000 0.000 0.996
#> GSM312853 4 0.0188 0.92391 0.004 0.000 0.000 0.996
#> GSM312854 4 0.0188 0.92391 0.004 0.000 0.000 0.996
#> GSM312856 4 0.0188 0.92391 0.004 0.000 0.000 0.996
#> GSM312857 4 0.0188 0.92391 0.004 0.000 0.000 0.996
#> GSM312858 4 0.1302 0.92981 0.000 0.044 0.000 0.956
#> GSM312859 2 0.0336 0.93611 0.000 0.992 0.000 0.008
#> GSM312860 2 0.1474 0.90352 0.000 0.948 0.000 0.052
#> GSM312861 4 0.1389 0.92829 0.000 0.048 0.000 0.952
#> GSM312862 2 0.4994 0.00841 0.000 0.520 0.000 0.480
#> GSM312863 4 0.0188 0.92391 0.004 0.000 0.000 0.996
#> GSM312864 2 0.4543 0.56743 0.000 0.676 0.000 0.324
#> GSM312865 4 0.1211 0.93063 0.000 0.040 0.000 0.960
#> GSM312867 4 0.1489 0.92963 0.004 0.044 0.000 0.952
#> GSM312868 4 0.1211 0.93063 0.000 0.040 0.000 0.960
#> GSM312869 2 0.0000 0.93956 0.000 1.000 0.000 0.000
#> GSM312870 3 0.0707 0.91974 0.020 0.000 0.980 0.000
#> GSM312872 3 0.0707 0.91974 0.020 0.000 0.980 0.000
#> GSM312874 3 0.0707 0.91974 0.020 0.000 0.980 0.000
#> GSM312875 3 0.0707 0.91974 0.020 0.000 0.980 0.000
#> GSM312876 3 0.0707 0.91974 0.020 0.000 0.980 0.000
#> GSM312877 3 0.0707 0.91974 0.020 0.000 0.980 0.000
#> GSM312879 3 0.0707 0.91974 0.020 0.000 0.980 0.000
#> GSM312882 3 0.0707 0.91974 0.020 0.000 0.980 0.000
#> GSM312883 3 0.0707 0.91974 0.020 0.000 0.980 0.000
#> GSM312886 3 0.0707 0.91974 0.020 0.000 0.980 0.000
#> GSM312887 1 0.1211 1.00000 0.960 0.000 0.040 0.000
#> GSM312890 1 0.1211 1.00000 0.960 0.000 0.040 0.000
#> GSM312893 1 0.1211 1.00000 0.960 0.000 0.040 0.000
#> GSM312894 1 0.1211 1.00000 0.960 0.000 0.040 0.000
#> GSM312895 1 0.1211 1.00000 0.960 0.000 0.040 0.000
#> GSM312937 1 0.1211 1.00000 0.960 0.000 0.040 0.000
#> GSM312938 1 0.1211 1.00000 0.960 0.000 0.040 0.000
#> GSM312939 1 0.1211 1.00000 0.960 0.000 0.040 0.000
#> GSM312940 1 0.1211 1.00000 0.960 0.000 0.040 0.000
#> GSM312941 1 0.1211 1.00000 0.960 0.000 0.040 0.000
#> GSM312942 3 0.3528 0.81297 0.192 0.000 0.808 0.000
#> GSM312943 3 0.3528 0.81297 0.192 0.000 0.808 0.000
#> GSM312944 3 0.3528 0.81297 0.192 0.000 0.808 0.000
#> GSM312945 3 0.3528 0.81297 0.192 0.000 0.808 0.000
#> GSM312946 3 0.3528 0.81297 0.192 0.000 0.808 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM312811 2 0.3990 0.738 0.000 0.688 0.000 0.004 NA
#> GSM312812 2 0.0000 0.857 0.000 1.000 0.000 0.000 NA
#> GSM312813 2 0.0000 0.857 0.000 1.000 0.000 0.000 NA
#> GSM312814 2 0.4084 0.727 0.000 0.668 0.000 0.004 NA
#> GSM312815 2 0.1478 0.838 0.000 0.936 0.000 0.000 NA
#> GSM312816 2 0.4510 0.656 0.000 0.560 0.000 0.008 NA
#> GSM312817 2 0.0000 0.857 0.000 1.000 0.000 0.000 NA
#> GSM312818 2 0.5641 0.604 0.000 0.504 0.056 0.008 NA
#> GSM312819 2 0.0162 0.856 0.000 0.996 0.000 0.000 NA
#> GSM312820 2 0.4510 0.656 0.000 0.560 0.000 0.008 NA
#> GSM312821 2 0.4510 0.656 0.000 0.560 0.000 0.008 NA
#> GSM312822 2 0.4135 0.721 0.000 0.656 0.000 0.004 NA
#> GSM312823 2 0.0000 0.857 0.000 1.000 0.000 0.000 NA
#> GSM312824 2 0.0000 0.857 0.000 1.000 0.000 0.000 NA
#> GSM312825 2 0.0000 0.857 0.000 1.000 0.000 0.000 NA
#> GSM312826 2 0.0000 0.857 0.000 1.000 0.000 0.000 NA
#> GSM312839 2 0.0000 0.857 0.000 1.000 0.000 0.000 NA
#> GSM312840 2 0.0000 0.857 0.000 1.000 0.000 0.000 NA
#> GSM312841 2 0.0000 0.857 0.000 1.000 0.000 0.000 NA
#> GSM312843 4 0.5740 0.410 0.000 0.308 0.000 0.580 NA
#> GSM312844 2 0.0000 0.857 0.000 1.000 0.000 0.000 NA
#> GSM312845 4 0.3934 0.782 0.124 0.000 0.000 0.800 NA
#> GSM312846 4 0.4155 0.761 0.144 0.000 0.000 0.780 NA
#> GSM312847 4 0.1956 0.871 0.000 0.008 0.000 0.916 NA
#> GSM312848 4 0.1956 0.871 0.000 0.008 0.000 0.916 NA
#> GSM312849 4 0.2069 0.870 0.000 0.012 0.000 0.912 NA
#> GSM312851 4 0.3074 0.832 0.000 0.000 0.000 0.804 NA
#> GSM312853 4 0.2732 0.851 0.000 0.000 0.000 0.840 NA
#> GSM312854 4 0.2690 0.852 0.000 0.000 0.000 0.844 NA
#> GSM312856 4 0.2690 0.852 0.000 0.000 0.000 0.844 NA
#> GSM312857 4 0.2732 0.851 0.000 0.000 0.000 0.840 NA
#> GSM312858 4 0.0290 0.880 0.000 0.008 0.000 0.992 NA
#> GSM312859 2 0.0510 0.849 0.000 0.984 0.000 0.016 NA
#> GSM312860 2 0.1469 0.829 0.000 0.948 0.000 0.036 NA
#> GSM312861 4 0.1836 0.873 0.000 0.036 0.000 0.932 NA
#> GSM312862 2 0.5028 0.292 0.000 0.564 0.000 0.400 NA
#> GSM312863 4 0.1671 0.872 0.000 0.000 0.000 0.924 NA
#> GSM312864 2 0.6175 0.333 0.000 0.528 0.000 0.312 NA
#> GSM312865 4 0.0898 0.880 0.000 0.008 0.000 0.972 NA
#> GSM312867 4 0.1894 0.871 0.000 0.008 0.000 0.920 NA
#> GSM312868 4 0.0579 0.880 0.000 0.008 0.000 0.984 NA
#> GSM312869 2 0.0000 0.857 0.000 1.000 0.000 0.000 NA
#> GSM312870 3 0.0000 0.840 0.000 0.000 1.000 0.000 NA
#> GSM312872 3 0.0000 0.840 0.000 0.000 1.000 0.000 NA
#> GSM312874 3 0.0000 0.840 0.000 0.000 1.000 0.000 NA
#> GSM312875 3 0.0000 0.840 0.000 0.000 1.000 0.000 NA
#> GSM312876 3 0.0000 0.840 0.000 0.000 1.000 0.000 NA
#> GSM312877 3 0.0000 0.840 0.000 0.000 1.000 0.000 NA
#> GSM312879 3 0.0000 0.840 0.000 0.000 1.000 0.000 NA
#> GSM312882 3 0.0000 0.840 0.000 0.000 1.000 0.000 NA
#> GSM312883 3 0.0000 0.840 0.000 0.000 1.000 0.000 NA
#> GSM312886 3 0.0000 0.840 0.000 0.000 1.000 0.000 NA
#> GSM312887 1 0.0000 1.000 1.000 0.000 0.000 0.000 NA
#> GSM312890 1 0.0000 1.000 1.000 0.000 0.000 0.000 NA
#> GSM312893 1 0.0000 1.000 1.000 0.000 0.000 0.000 NA
#> GSM312894 1 0.0000 1.000 1.000 0.000 0.000 0.000 NA
#> GSM312895 1 0.0000 1.000 1.000 0.000 0.000 0.000 NA
#> GSM312937 1 0.0000 1.000 1.000 0.000 0.000 0.000 NA
#> GSM312938 1 0.0000 1.000 1.000 0.000 0.000 0.000 NA
#> GSM312939 1 0.0000 1.000 1.000 0.000 0.000 0.000 NA
#> GSM312940 1 0.0000 1.000 1.000 0.000 0.000 0.000 NA
#> GSM312941 1 0.0000 1.000 1.000 0.000 0.000 0.000 NA
#> GSM312942 3 0.5733 0.621 0.084 0.000 0.476 0.000 NA
#> GSM312943 3 0.5733 0.621 0.084 0.000 0.476 0.000 NA
#> GSM312944 3 0.5733 0.621 0.084 0.000 0.476 0.000 NA
#> GSM312945 3 0.5733 0.621 0.084 0.000 0.476 0.000 NA
#> GSM312946 3 0.5733 0.621 0.084 0.000 0.476 0.000 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM312811 1 0.6110 0.0298 0.416 0.344 0.000 0.004 0.000 0.236
#> GSM312812 2 0.1088 0.9279 0.024 0.960 0.000 0.000 0.000 0.016
#> GSM312813 2 0.1088 0.9279 0.024 0.960 0.000 0.000 0.000 0.016
#> GSM312814 1 0.6437 0.1370 0.444 0.284 0.000 0.024 0.000 0.248
#> GSM312815 2 0.3377 0.7644 0.136 0.808 0.000 0.000 0.000 0.056
#> GSM312816 1 0.6963 0.2400 0.464 0.192 0.000 0.100 0.000 0.244
#> GSM312817 2 0.1245 0.9224 0.032 0.952 0.000 0.000 0.000 0.016
#> GSM312818 1 0.7148 0.2349 0.464 0.184 0.008 0.100 0.000 0.244
#> GSM312819 2 0.0291 0.9440 0.004 0.992 0.000 0.004 0.000 0.000
#> GSM312820 1 0.6963 0.2400 0.464 0.192 0.000 0.100 0.000 0.244
#> GSM312821 1 0.6963 0.2400 0.464 0.192 0.000 0.100 0.000 0.244
#> GSM312822 1 0.6416 0.1482 0.452 0.276 0.000 0.024 0.000 0.248
#> GSM312823 2 0.0146 0.9461 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM312824 2 0.0000 0.9465 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312825 2 0.0000 0.9465 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312826 2 0.0000 0.9465 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312839 2 0.0291 0.9450 0.004 0.992 0.000 0.000 0.000 0.004
#> GSM312840 2 0.0000 0.9465 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312841 2 0.0000 0.9465 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312843 4 0.2633 0.5006 0.020 0.112 0.000 0.864 0.000 0.004
#> GSM312844 2 0.0146 0.9461 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM312845 5 0.3797 0.8836 0.000 0.000 0.000 0.420 0.580 0.000
#> GSM312846 5 0.3765 0.8504 0.000 0.000 0.000 0.404 0.596 0.000
#> GSM312847 5 0.3854 0.9294 0.000 0.000 0.000 0.464 0.536 0.000
#> GSM312848 5 0.3860 0.9206 0.000 0.000 0.000 0.472 0.528 0.000
#> GSM312849 5 0.3854 0.9294 0.000 0.000 0.000 0.464 0.536 0.000
#> GSM312851 4 0.1075 0.5776 0.048 0.000 0.000 0.952 0.000 0.000
#> GSM312853 4 0.0000 0.6152 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312854 4 0.0000 0.6152 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312856 4 0.0000 0.6152 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312857 4 0.0000 0.6152 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312858 4 0.3288 0.0256 0.000 0.000 0.000 0.724 0.276 0.000
#> GSM312859 2 0.0458 0.9367 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM312860 2 0.0865 0.9195 0.000 0.964 0.000 0.000 0.036 0.000
#> GSM312861 4 0.5271 -0.5340 0.000 0.104 0.000 0.516 0.380 0.000
#> GSM312862 2 0.5635 0.3907 0.012 0.612 0.000 0.216 0.152 0.008
#> GSM312863 4 0.1444 0.5428 0.000 0.000 0.000 0.928 0.072 0.000
#> GSM312864 4 0.4656 0.1825 0.036 0.404 0.000 0.556 0.000 0.004
#> GSM312865 4 0.3221 0.0851 0.000 0.000 0.000 0.736 0.264 0.000
#> GSM312867 5 0.3860 0.9209 0.000 0.000 0.000 0.472 0.528 0.000
#> GSM312868 4 0.3050 0.1912 0.000 0.000 0.000 0.764 0.236 0.000
#> GSM312869 2 0.0000 0.9465 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312870 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312872 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312874 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312875 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312876 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312877 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312879 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312882 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312883 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312886 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312887 1 0.3854 0.5139 0.536 0.000 0.000 0.000 0.464 0.000
#> GSM312890 1 0.3854 0.5139 0.536 0.000 0.000 0.000 0.464 0.000
#> GSM312893 1 0.3854 0.5139 0.536 0.000 0.000 0.000 0.464 0.000
#> GSM312894 1 0.3854 0.5139 0.536 0.000 0.000 0.000 0.464 0.000
#> GSM312895 1 0.3854 0.5139 0.536 0.000 0.000 0.000 0.464 0.000
#> GSM312937 1 0.3854 0.5139 0.536 0.000 0.000 0.000 0.464 0.000
#> GSM312938 1 0.3854 0.5139 0.536 0.000 0.000 0.000 0.464 0.000
#> GSM312939 1 0.3854 0.5139 0.536 0.000 0.000 0.000 0.464 0.000
#> GSM312940 1 0.3854 0.5139 0.536 0.000 0.000 0.000 0.464 0.000
#> GSM312941 1 0.3854 0.5139 0.536 0.000 0.000 0.000 0.464 0.000
#> GSM312942 6 0.3773 1.0000 0.044 0.000 0.204 0.000 0.000 0.752
#> GSM312943 6 0.3773 1.0000 0.044 0.000 0.204 0.000 0.000 0.752
#> GSM312944 6 0.3773 1.0000 0.044 0.000 0.204 0.000 0.000 0.752
#> GSM312945 6 0.3773 1.0000 0.044 0.000 0.204 0.000 0.000 0.752
#> GSM312946 6 0.3773 1.0000 0.044 0.000 0.204 0.000 0.000 0.752
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:skmeans 67 7.40e-10 2
#> SD:skmeans 65 4.05e-15 3
#> SD:skmeans 65 4.31e-23 4
#> SD:skmeans 64 4.92e-23 5
#> SD:skmeans 54 2.21e-27 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "pam"]
# you can also extract it by
# res = res_list["SD:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 67 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4754 0.525 0.525
#> 3 3 1.000 0.991 0.996 0.1384 0.935 0.876
#> 4 4 1.000 0.960 0.986 0.0534 0.975 0.946
#> 5 5 0.897 0.903 0.955 0.3279 0.805 0.554
#> 6 6 0.910 0.883 0.956 0.0596 0.953 0.806
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 3 4
There is also optional best \(k\) = 2 3 4 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM312811 2 0 1 0 1
#> GSM312812 2 0 1 0 1
#> GSM312813 2 0 1 0 1
#> GSM312814 2 0 1 0 1
#> GSM312815 2 0 1 0 1
#> GSM312816 2 0 1 0 1
#> GSM312817 2 0 1 0 1
#> GSM312818 2 0 1 0 1
#> GSM312819 2 0 1 0 1
#> GSM312820 2 0 1 0 1
#> GSM312821 2 0 1 0 1
#> GSM312822 2 0 1 0 1
#> GSM312823 2 0 1 0 1
#> GSM312824 2 0 1 0 1
#> GSM312825 2 0 1 0 1
#> GSM312826 2 0 1 0 1
#> GSM312839 2 0 1 0 1
#> GSM312840 2 0 1 0 1
#> GSM312841 2 0 1 0 1
#> GSM312843 2 0 1 0 1
#> GSM312844 2 0 1 0 1
#> GSM312845 2 0 1 0 1
#> GSM312846 2 0 1 0 1
#> GSM312847 2 0 1 0 1
#> GSM312848 2 0 1 0 1
#> GSM312849 2 0 1 0 1
#> GSM312851 2 0 1 0 1
#> GSM312853 2 0 1 0 1
#> GSM312854 2 0 1 0 1
#> GSM312856 2 0 1 0 1
#> GSM312857 2 0 1 0 1
#> GSM312858 2 0 1 0 1
#> GSM312859 2 0 1 0 1
#> GSM312860 2 0 1 0 1
#> GSM312861 2 0 1 0 1
#> GSM312862 2 0 1 0 1
#> GSM312863 2 0 1 0 1
#> GSM312864 2 0 1 0 1
#> GSM312865 2 0 1 0 1
#> GSM312867 2 0 1 0 1
#> GSM312868 2 0 1 0 1
#> GSM312869 2 0 1 0 1
#> GSM312870 1 0 1 1 0
#> GSM312872 1 0 1 1 0
#> GSM312874 1 0 1 1 0
#> GSM312875 1 0 1 1 0
#> GSM312876 1 0 1 1 0
#> GSM312877 1 0 1 1 0
#> GSM312879 1 0 1 1 0
#> GSM312882 1 0 1 1 0
#> GSM312883 1 0 1 1 0
#> GSM312886 1 0 1 1 0
#> GSM312887 1 0 1 1 0
#> GSM312890 1 0 1 1 0
#> GSM312893 1 0 1 1 0
#> GSM312894 1 0 1 1 0
#> GSM312895 1 0 1 1 0
#> GSM312937 1 0 1 1 0
#> GSM312938 1 0 1 1 0
#> GSM312939 1 0 1 1 0
#> GSM312940 1 0 1 1 0
#> GSM312941 1 0 1 1 0
#> GSM312942 1 0 1 1 0
#> GSM312943 1 0 1 1 0
#> GSM312944 1 0 1 1 0
#> GSM312945 1 0 1 1 0
#> GSM312946 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM312811 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312812 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312813 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312814 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312815 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312816 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312817 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312818 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312819 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312820 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312821 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312822 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312823 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312824 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312825 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312826 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312839 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312840 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312841 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312843 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312844 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312845 2 0.0424 0.992 0.008 0.992 0.000
#> GSM312846 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312847 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312848 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312849 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312851 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312853 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312854 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312856 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312857 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312858 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312859 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312860 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312861 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312862 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312863 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312864 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312865 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312867 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312868 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312869 2 0.0000 1.000 0.000 1.000 0.000
#> GSM312870 3 0.0000 1.000 0.000 0.000 1.000
#> GSM312872 3 0.0000 1.000 0.000 0.000 1.000
#> GSM312874 3 0.0000 1.000 0.000 0.000 1.000
#> GSM312875 3 0.0000 1.000 0.000 0.000 1.000
#> GSM312876 3 0.0000 1.000 0.000 0.000 1.000
#> GSM312877 1 0.4974 0.694 0.764 0.000 0.236
#> GSM312879 3 0.0000 1.000 0.000 0.000 1.000
#> GSM312882 3 0.0000 1.000 0.000 0.000 1.000
#> GSM312883 3 0.0000 1.000 0.000 0.000 1.000
#> GSM312886 3 0.0000 1.000 0.000 0.000 1.000
#> GSM312887 1 0.0000 0.983 1.000 0.000 0.000
#> GSM312890 1 0.0000 0.983 1.000 0.000 0.000
#> GSM312893 1 0.0000 0.983 1.000 0.000 0.000
#> GSM312894 1 0.0000 0.983 1.000 0.000 0.000
#> GSM312895 1 0.0000 0.983 1.000 0.000 0.000
#> GSM312937 1 0.0000 0.983 1.000 0.000 0.000
#> GSM312938 1 0.0000 0.983 1.000 0.000 0.000
#> GSM312939 1 0.0000 0.983 1.000 0.000 0.000
#> GSM312940 1 0.0000 0.983 1.000 0.000 0.000
#> GSM312941 1 0.0000 0.983 1.000 0.000 0.000
#> GSM312942 1 0.0237 0.981 0.996 0.000 0.004
#> GSM312943 1 0.0237 0.981 0.996 0.000 0.004
#> GSM312944 1 0.0237 0.981 0.996 0.000 0.004
#> GSM312945 1 0.0237 0.981 0.996 0.000 0.004
#> GSM312946 1 0.0237 0.981 0.996 0.000 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM312811 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312812 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312813 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312814 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312815 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312816 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312817 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312818 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312819 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312820 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312821 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312822 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312823 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312824 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312825 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312826 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312839 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312840 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312841 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312843 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312844 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312845 2 0.511 0.655 0.196 0.744 0.00 0.060
#> GSM312846 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312847 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312848 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312849 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312851 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312853 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312854 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312856 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312857 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312858 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312859 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312860 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312861 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312862 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312863 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312864 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312865 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312867 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312868 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312869 2 0.000 0.993 0.000 1.000 0.00 0.000
#> GSM312870 3 0.000 1.000 0.000 0.000 1.00 0.000
#> GSM312872 3 0.000 1.000 0.000 0.000 1.00 0.000
#> GSM312874 3 0.000 1.000 0.000 0.000 1.00 0.000
#> GSM312875 3 0.000 1.000 0.000 0.000 1.00 0.000
#> GSM312876 3 0.000 1.000 0.000 0.000 1.00 0.000
#> GSM312877 1 0.380 -0.361 0.780 0.000 0.22 0.000
#> GSM312879 3 0.000 1.000 0.000 0.000 1.00 0.000
#> GSM312882 3 0.000 1.000 0.000 0.000 1.00 0.000
#> GSM312883 3 0.000 1.000 0.000 0.000 1.00 0.000
#> GSM312886 3 0.000 1.000 0.000 0.000 1.00 0.000
#> GSM312887 1 0.500 0.931 0.516 0.000 0.00 0.484
#> GSM312890 1 0.500 0.931 0.516 0.000 0.00 0.484
#> GSM312893 1 0.500 0.931 0.516 0.000 0.00 0.484
#> GSM312894 1 0.500 0.931 0.516 0.000 0.00 0.484
#> GSM312895 1 0.500 0.931 0.516 0.000 0.00 0.484
#> GSM312937 1 0.500 0.931 0.516 0.000 0.00 0.484
#> GSM312938 1 0.500 0.931 0.516 0.000 0.00 0.484
#> GSM312939 1 0.500 0.931 0.516 0.000 0.00 0.484
#> GSM312940 1 0.500 0.931 0.516 0.000 0.00 0.484
#> GSM312941 1 0.500 0.931 0.516 0.000 0.00 0.484
#> GSM312942 4 0.500 1.000 0.484 0.000 0.00 0.516
#> GSM312943 4 0.500 1.000 0.484 0.000 0.00 0.516
#> GSM312944 4 0.500 1.000 0.484 0.000 0.00 0.516
#> GSM312945 4 0.500 1.000 0.484 0.000 0.00 0.516
#> GSM312946 4 0.500 1.000 0.484 0.000 0.00 0.516
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM312811 2 0.0000 0.937 0.000 1.000 0.00 0.000 0.000
#> GSM312812 2 0.0000 0.937 0.000 1.000 0.00 0.000 0.000
#> GSM312813 2 0.0000 0.937 0.000 1.000 0.00 0.000 0.000
#> GSM312814 2 0.0162 0.934 0.000 0.996 0.00 0.004 0.000
#> GSM312815 2 0.0000 0.937 0.000 1.000 0.00 0.000 0.000
#> GSM312816 2 0.1410 0.893 0.000 0.940 0.00 0.060 0.000
#> GSM312817 2 0.0000 0.937 0.000 1.000 0.00 0.000 0.000
#> GSM312818 2 0.2516 0.839 0.000 0.860 0.00 0.140 0.000
#> GSM312819 2 0.0000 0.937 0.000 1.000 0.00 0.000 0.000
#> GSM312820 2 0.3424 0.719 0.000 0.760 0.00 0.240 0.000
#> GSM312821 2 0.3913 0.573 0.000 0.676 0.00 0.324 0.000
#> GSM312822 2 0.0000 0.937 0.000 1.000 0.00 0.000 0.000
#> GSM312823 2 0.0000 0.937 0.000 1.000 0.00 0.000 0.000
#> GSM312824 2 0.0000 0.937 0.000 1.000 0.00 0.000 0.000
#> GSM312825 2 0.0000 0.937 0.000 1.000 0.00 0.000 0.000
#> GSM312826 2 0.0000 0.937 0.000 1.000 0.00 0.000 0.000
#> GSM312839 2 0.0000 0.937 0.000 1.000 0.00 0.000 0.000
#> GSM312840 2 0.0000 0.937 0.000 1.000 0.00 0.000 0.000
#> GSM312841 2 0.0000 0.937 0.000 1.000 0.00 0.000 0.000
#> GSM312843 4 0.1197 0.909 0.000 0.048 0.00 0.952 0.000
#> GSM312844 2 0.0000 0.937 0.000 1.000 0.00 0.000 0.000
#> GSM312845 4 0.4455 0.340 0.404 0.008 0.00 0.588 0.000
#> GSM312846 2 0.3561 0.649 0.000 0.740 0.00 0.260 0.000
#> GSM312847 4 0.1197 0.909 0.000 0.048 0.00 0.952 0.000
#> GSM312848 4 0.1197 0.909 0.000 0.048 0.00 0.952 0.000
#> GSM312849 2 0.2929 0.771 0.000 0.820 0.00 0.180 0.000
#> GSM312851 4 0.0000 0.906 0.000 0.000 0.00 1.000 0.000
#> GSM312853 4 0.0000 0.906 0.000 0.000 0.00 1.000 0.000
#> GSM312854 4 0.0000 0.906 0.000 0.000 0.00 1.000 0.000
#> GSM312856 4 0.0000 0.906 0.000 0.000 0.00 1.000 0.000
#> GSM312857 4 0.0000 0.906 0.000 0.000 0.00 1.000 0.000
#> GSM312858 4 0.1197 0.909 0.000 0.048 0.00 0.952 0.000
#> GSM312859 2 0.0000 0.937 0.000 1.000 0.00 0.000 0.000
#> GSM312860 2 0.0000 0.937 0.000 1.000 0.00 0.000 0.000
#> GSM312861 4 0.3039 0.755 0.000 0.192 0.00 0.808 0.000
#> GSM312862 2 0.3109 0.745 0.000 0.800 0.00 0.200 0.000
#> GSM312863 4 0.0000 0.906 0.000 0.000 0.00 1.000 0.000
#> GSM312864 4 0.0510 0.901 0.000 0.016 0.00 0.984 0.000
#> GSM312865 4 0.1197 0.909 0.000 0.048 0.00 0.952 0.000
#> GSM312867 4 0.3039 0.755 0.000 0.192 0.00 0.808 0.000
#> GSM312868 4 0.1197 0.909 0.000 0.048 0.00 0.952 0.000
#> GSM312869 2 0.0000 0.937 0.000 1.000 0.00 0.000 0.000
#> GSM312870 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM312872 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM312874 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM312875 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM312876 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM312877 5 0.6491 0.354 0.296 0.000 0.22 0.000 0.484
#> GSM312879 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM312882 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM312883 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM312886 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM312887 1 0.0000 1.000 1.000 0.000 0.00 0.000 0.000
#> GSM312890 1 0.0000 1.000 1.000 0.000 0.00 0.000 0.000
#> GSM312893 1 0.0000 1.000 1.000 0.000 0.00 0.000 0.000
#> GSM312894 1 0.0000 1.000 1.000 0.000 0.00 0.000 0.000
#> GSM312895 1 0.0000 1.000 1.000 0.000 0.00 0.000 0.000
#> GSM312937 1 0.0000 1.000 1.000 0.000 0.00 0.000 0.000
#> GSM312938 1 0.0000 1.000 1.000 0.000 0.00 0.000 0.000
#> GSM312939 1 0.0000 1.000 1.000 0.000 0.00 0.000 0.000
#> GSM312940 1 0.0000 1.000 1.000 0.000 0.00 0.000 0.000
#> GSM312941 1 0.0000 1.000 1.000 0.000 0.00 0.000 0.000
#> GSM312942 5 0.0000 0.908 0.000 0.000 0.00 0.000 1.000
#> GSM312943 5 0.0000 0.908 0.000 0.000 0.00 0.000 1.000
#> GSM312944 5 0.0000 0.908 0.000 0.000 0.00 0.000 1.000
#> GSM312945 5 0.0000 0.908 0.000 0.000 0.00 0.000 1.000
#> GSM312946 5 0.0000 0.908 0.000 0.000 0.00 0.000 1.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM312811 2 0.2823 0.717 0.000 0.796 0.00 0.000 0.204 0.000
#> GSM312812 2 0.0000 0.923 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM312813 2 0.0000 0.923 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM312814 2 0.3765 0.289 0.000 0.596 0.00 0.000 0.404 0.000
#> GSM312815 2 0.0000 0.923 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM312816 5 0.0000 0.828 0.000 0.000 0.00 0.000 1.000 0.000
#> GSM312817 2 0.0000 0.923 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM312818 5 0.0000 0.828 0.000 0.000 0.00 0.000 1.000 0.000
#> GSM312819 2 0.0000 0.923 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM312820 5 0.0000 0.828 0.000 0.000 0.00 0.000 1.000 0.000
#> GSM312821 5 0.0000 0.828 0.000 0.000 0.00 0.000 1.000 0.000
#> GSM312822 5 0.3782 0.187 0.000 0.412 0.00 0.000 0.588 0.000
#> GSM312823 2 0.0000 0.923 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM312824 2 0.0000 0.923 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM312825 2 0.0000 0.923 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM312826 2 0.0000 0.923 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM312839 2 0.0000 0.923 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM312840 2 0.0000 0.923 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM312841 2 0.0000 0.923 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM312843 4 0.0000 0.935 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM312844 2 0.0000 0.923 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM312845 4 0.4002 0.331 0.404 0.008 0.00 0.588 0.000 0.000
#> GSM312846 2 0.3198 0.633 0.000 0.740 0.00 0.260 0.000 0.000
#> GSM312847 4 0.0000 0.935 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM312848 4 0.0000 0.935 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM312849 2 0.2631 0.744 0.000 0.820 0.00 0.180 0.000 0.000
#> GSM312851 4 0.0000 0.935 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM312853 4 0.0000 0.935 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM312854 4 0.0000 0.935 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM312856 4 0.0000 0.935 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM312857 4 0.0000 0.935 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM312858 4 0.0000 0.935 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM312859 2 0.0000 0.923 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM312860 2 0.0000 0.923 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM312861 4 0.2631 0.730 0.000 0.180 0.00 0.820 0.000 0.000
#> GSM312862 2 0.2793 0.719 0.000 0.800 0.00 0.200 0.000 0.000
#> GSM312863 4 0.0000 0.935 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM312864 4 0.0458 0.922 0.000 0.016 0.00 0.984 0.000 0.000
#> GSM312865 4 0.0000 0.935 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM312867 4 0.2597 0.736 0.000 0.176 0.00 0.824 0.000 0.000
#> GSM312868 4 0.0000 0.935 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM312869 2 0.0000 0.923 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM312870 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM312872 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM312874 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM312875 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM312876 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM312877 6 0.5830 0.354 0.296 0.000 0.22 0.000 0.000 0.484
#> GSM312879 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM312882 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM312883 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM312886 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM312887 1 0.0000 1.000 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM312890 1 0.0000 1.000 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM312893 1 0.0000 1.000 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM312894 1 0.0000 1.000 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM312895 1 0.0000 1.000 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM312937 1 0.0000 1.000 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM312938 1 0.0000 1.000 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM312939 1 0.0000 1.000 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM312940 1 0.0000 1.000 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM312941 1 0.0000 1.000 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM312942 6 0.0000 0.892 0.000 0.000 0.00 0.000 0.000 1.000
#> GSM312943 6 0.0000 0.892 0.000 0.000 0.00 0.000 0.000 1.000
#> GSM312944 6 0.0000 0.892 0.000 0.000 0.00 0.000 0.000 1.000
#> GSM312945 6 0.0000 0.892 0.000 0.000 0.00 0.000 0.000 1.000
#> GSM312946 6 0.0000 0.892 0.000 0.000 0.00 0.000 0.000 1.000
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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:pam 67 1.68e-10 2
#> SD:pam 67 3.83e-17 3
#> SD:pam 66 1.17e-26 4
#> SD:pam 65 1.21e-28 5
#> SD:pam 63 2.66e-26 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "mclust"]
# you can also extract it by
# res = res_list["SD:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 67 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 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.998 0.998 0.4734 0.525 0.525
#> 3 3 0.575 0.722 0.866 0.2807 0.909 0.828
#> 4 4 0.561 0.779 0.816 0.0783 0.954 0.901
#> 5 5 0.715 0.509 0.761 0.1449 0.823 0.595
#> 6 6 0.997 0.952 0.980 0.0631 0.793 0.387
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2
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
#> GSM312811 2 0.0000 1.000 0.000 1.000
#> GSM312812 2 0.0000 1.000 0.000 1.000
#> GSM312813 2 0.0000 1.000 0.000 1.000
#> GSM312814 2 0.0000 1.000 0.000 1.000
#> GSM312815 2 0.0000 1.000 0.000 1.000
#> GSM312816 2 0.0000 1.000 0.000 1.000
#> GSM312817 2 0.0000 1.000 0.000 1.000
#> GSM312818 2 0.0000 1.000 0.000 1.000
#> GSM312819 2 0.0000 1.000 0.000 1.000
#> GSM312820 2 0.0000 1.000 0.000 1.000
#> GSM312821 2 0.0000 1.000 0.000 1.000
#> GSM312822 2 0.0000 1.000 0.000 1.000
#> GSM312823 2 0.0000 1.000 0.000 1.000
#> GSM312824 2 0.0000 1.000 0.000 1.000
#> GSM312825 2 0.0000 1.000 0.000 1.000
#> GSM312826 2 0.0000 1.000 0.000 1.000
#> GSM312839 2 0.0000 1.000 0.000 1.000
#> GSM312840 2 0.0000 1.000 0.000 1.000
#> GSM312841 2 0.0000 1.000 0.000 1.000
#> GSM312843 2 0.0000 1.000 0.000 1.000
#> GSM312844 2 0.0000 1.000 0.000 1.000
#> GSM312845 2 0.0000 1.000 0.000 1.000
#> GSM312846 2 0.0000 1.000 0.000 1.000
#> GSM312847 2 0.0000 1.000 0.000 1.000
#> GSM312848 2 0.0000 1.000 0.000 1.000
#> GSM312849 2 0.0000 1.000 0.000 1.000
#> GSM312851 2 0.0000 1.000 0.000 1.000
#> GSM312853 2 0.0000 1.000 0.000 1.000
#> GSM312854 2 0.0000 1.000 0.000 1.000
#> GSM312856 2 0.0000 1.000 0.000 1.000
#> GSM312857 2 0.0000 1.000 0.000 1.000
#> GSM312858 2 0.0000 1.000 0.000 1.000
#> GSM312859 2 0.0000 1.000 0.000 1.000
#> GSM312860 2 0.0000 1.000 0.000 1.000
#> GSM312861 2 0.0000 1.000 0.000 1.000
#> GSM312862 2 0.0000 1.000 0.000 1.000
#> GSM312863 2 0.0000 1.000 0.000 1.000
#> GSM312864 2 0.0000 1.000 0.000 1.000
#> GSM312865 2 0.0000 1.000 0.000 1.000
#> GSM312867 2 0.0000 1.000 0.000 1.000
#> GSM312868 2 0.0000 1.000 0.000 1.000
#> GSM312869 2 0.0000 1.000 0.000 1.000
#> GSM312870 1 0.0000 0.993 1.000 0.000
#> GSM312872 1 0.0000 0.993 1.000 0.000
#> GSM312874 1 0.0000 0.993 1.000 0.000
#> GSM312875 1 0.0000 0.993 1.000 0.000
#> GSM312876 1 0.0000 0.993 1.000 0.000
#> GSM312877 1 0.0000 0.993 1.000 0.000
#> GSM312879 1 0.0000 0.993 1.000 0.000
#> GSM312882 1 0.0000 0.993 1.000 0.000
#> GSM312883 1 0.0000 0.993 1.000 0.000
#> GSM312886 1 0.0000 0.993 1.000 0.000
#> GSM312887 1 0.0938 0.994 0.988 0.012
#> GSM312890 1 0.0938 0.994 0.988 0.012
#> GSM312893 1 0.0938 0.994 0.988 0.012
#> GSM312894 1 0.0938 0.994 0.988 0.012
#> GSM312895 1 0.0938 0.994 0.988 0.012
#> GSM312937 1 0.0938 0.994 0.988 0.012
#> GSM312938 1 0.0938 0.994 0.988 0.012
#> GSM312939 1 0.0938 0.994 0.988 0.012
#> GSM312940 1 0.0938 0.994 0.988 0.012
#> GSM312941 1 0.0938 0.994 0.988 0.012
#> GSM312942 1 0.0672 0.995 0.992 0.008
#> GSM312943 1 0.0672 0.995 0.992 0.008
#> GSM312944 1 0.0672 0.995 0.992 0.008
#> GSM312945 1 0.0672 0.995 0.992 0.008
#> GSM312946 1 0.0672 0.995 0.992 0.008
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM312811 2 0.0000 0.825 0.000 1.000 0.000
#> GSM312812 2 0.0000 0.825 0.000 1.000 0.000
#> GSM312813 2 0.0000 0.825 0.000 1.000 0.000
#> GSM312814 2 0.0000 0.825 0.000 1.000 0.000
#> GSM312815 2 0.0000 0.825 0.000 1.000 0.000
#> GSM312816 2 0.8561 0.134 0.096 0.484 0.420
#> GSM312817 2 0.0000 0.825 0.000 1.000 0.000
#> GSM312818 2 0.8561 0.134 0.096 0.484 0.420
#> GSM312819 2 0.6986 0.502 0.056 0.688 0.256
#> GSM312820 2 0.8561 0.134 0.096 0.484 0.420
#> GSM312821 2 0.8561 0.134 0.096 0.484 0.420
#> GSM312822 2 0.0000 0.825 0.000 1.000 0.000
#> GSM312823 2 0.0000 0.825 0.000 1.000 0.000
#> GSM312824 2 0.0000 0.825 0.000 1.000 0.000
#> GSM312825 2 0.0000 0.825 0.000 1.000 0.000
#> GSM312826 2 0.0000 0.825 0.000 1.000 0.000
#> GSM312839 2 0.0000 0.825 0.000 1.000 0.000
#> GSM312840 2 0.0000 0.825 0.000 1.000 0.000
#> GSM312841 2 0.0000 0.825 0.000 1.000 0.000
#> GSM312843 2 0.0000 0.825 0.000 1.000 0.000
#> GSM312844 2 0.0000 0.825 0.000 1.000 0.000
#> GSM312845 3 0.6291 -0.191 0.000 0.468 0.532
#> GSM312846 2 0.6192 0.422 0.000 0.580 0.420
#> GSM312847 2 0.5650 0.609 0.000 0.688 0.312
#> GSM312848 2 0.4702 0.724 0.000 0.788 0.212
#> GSM312849 2 0.5621 0.614 0.000 0.692 0.308
#> GSM312851 2 0.4796 0.719 0.000 0.780 0.220
#> GSM312853 2 0.4796 0.719 0.000 0.780 0.220
#> GSM312854 2 0.4796 0.719 0.000 0.780 0.220
#> GSM312856 2 0.4796 0.719 0.000 0.780 0.220
#> GSM312857 2 0.4796 0.719 0.000 0.780 0.220
#> GSM312858 2 0.4702 0.724 0.000 0.788 0.212
#> GSM312859 2 0.0000 0.825 0.000 1.000 0.000
#> GSM312860 2 0.0000 0.825 0.000 1.000 0.000
#> GSM312861 2 0.0000 0.825 0.000 1.000 0.000
#> GSM312862 2 0.0000 0.825 0.000 1.000 0.000
#> GSM312863 2 0.4750 0.722 0.000 0.784 0.216
#> GSM312864 2 0.0000 0.825 0.000 1.000 0.000
#> GSM312865 2 0.5650 0.609 0.000 0.688 0.312
#> GSM312867 2 0.5621 0.614 0.000 0.692 0.308
#> GSM312868 2 0.4702 0.724 0.000 0.788 0.212
#> GSM312869 2 0.0000 0.825 0.000 1.000 0.000
#> GSM312870 1 0.5968 0.796 0.636 0.000 0.364
#> GSM312872 1 0.5968 0.796 0.636 0.000 0.364
#> GSM312874 1 0.5968 0.796 0.636 0.000 0.364
#> GSM312875 1 0.5968 0.796 0.636 0.000 0.364
#> GSM312876 1 0.5968 0.796 0.636 0.000 0.364
#> GSM312877 1 0.0592 0.635 0.988 0.000 0.012
#> GSM312879 1 0.5968 0.796 0.636 0.000 0.364
#> GSM312882 1 0.5968 0.796 0.636 0.000 0.364
#> GSM312883 1 0.5138 0.773 0.748 0.000 0.252
#> GSM312886 1 0.6305 0.708 0.516 0.000 0.484
#> GSM312887 3 0.5988 0.911 0.368 0.000 0.632
#> GSM312890 3 0.5968 0.914 0.364 0.000 0.636
#> GSM312893 3 0.5968 0.914 0.364 0.000 0.636
#> GSM312894 3 0.5988 0.911 0.368 0.000 0.632
#> GSM312895 3 0.5968 0.914 0.364 0.000 0.636
#> GSM312937 3 0.5968 0.914 0.364 0.000 0.636
#> GSM312938 3 0.5988 0.911 0.368 0.000 0.632
#> GSM312939 3 0.5968 0.914 0.364 0.000 0.636
#> GSM312940 3 0.5968 0.914 0.364 0.000 0.636
#> GSM312941 3 0.5968 0.914 0.364 0.000 0.636
#> GSM312942 1 0.1163 0.647 0.972 0.000 0.028
#> GSM312943 1 0.0747 0.636 0.984 0.000 0.016
#> GSM312944 1 0.0747 0.636 0.984 0.000 0.016
#> GSM312945 1 0.0747 0.636 0.984 0.000 0.016
#> GSM312946 1 0.0747 0.636 0.984 0.000 0.016
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM312811 2 0.2589 0.783 0.000 0.884 0.000 0.116
#> GSM312812 2 0.0000 0.804 0.000 1.000 0.000 0.000
#> GSM312813 2 0.2530 0.768 0.112 0.888 0.000 0.000
#> GSM312814 2 0.2345 0.789 0.000 0.900 0.000 0.100
#> GSM312815 2 0.0000 0.804 0.000 1.000 0.000 0.000
#> GSM312816 2 0.8469 0.547 0.112 0.504 0.096 0.288
#> GSM312817 2 0.2714 0.768 0.112 0.884 0.000 0.004
#> GSM312818 2 0.8469 0.547 0.112 0.504 0.096 0.288
#> GSM312819 2 0.4586 0.747 0.112 0.812 0.068 0.008
#> GSM312820 2 0.8469 0.547 0.112 0.504 0.096 0.288
#> GSM312821 2 0.8469 0.547 0.112 0.504 0.096 0.288
#> GSM312822 2 0.2868 0.774 0.000 0.864 0.000 0.136
#> GSM312823 2 0.0707 0.802 0.020 0.980 0.000 0.000
#> GSM312824 2 0.0000 0.804 0.000 1.000 0.000 0.000
#> GSM312825 2 0.0000 0.804 0.000 1.000 0.000 0.000
#> GSM312826 2 0.0000 0.804 0.000 1.000 0.000 0.000
#> GSM312839 2 0.0000 0.804 0.000 1.000 0.000 0.000
#> GSM312840 2 0.0336 0.804 0.000 0.992 0.000 0.008
#> GSM312841 2 0.1940 0.795 0.000 0.924 0.000 0.076
#> GSM312843 2 0.0921 0.805 0.000 0.972 0.000 0.028
#> GSM312844 2 0.0000 0.804 0.000 1.000 0.000 0.000
#> GSM312845 2 0.6621 0.683 0.188 0.628 0.000 0.184
#> GSM312846 2 0.6437 0.703 0.168 0.648 0.000 0.184
#> GSM312847 2 0.4916 0.745 0.056 0.760 0.000 0.184
#> GSM312848 2 0.4789 0.748 0.056 0.772 0.000 0.172
#> GSM312849 2 0.6437 0.703 0.168 0.648 0.000 0.184
#> GSM312851 2 0.6277 0.584 0.056 0.476 0.000 0.468
#> GSM312853 2 0.6277 0.584 0.056 0.476 0.000 0.468
#> GSM312854 2 0.6276 0.588 0.056 0.480 0.000 0.464
#> GSM312856 2 0.5898 0.706 0.056 0.628 0.000 0.316
#> GSM312857 2 0.6277 0.584 0.056 0.476 0.000 0.468
#> GSM312858 2 0.4789 0.748 0.056 0.772 0.000 0.172
#> GSM312859 2 0.0000 0.804 0.000 1.000 0.000 0.000
#> GSM312860 2 0.2469 0.770 0.108 0.892 0.000 0.000
#> GSM312861 2 0.1389 0.803 0.000 0.952 0.000 0.048
#> GSM312862 2 0.2530 0.768 0.112 0.888 0.000 0.000
#> GSM312863 2 0.5857 0.711 0.056 0.636 0.000 0.308
#> GSM312864 2 0.4257 0.769 0.048 0.812 0.000 0.140
#> GSM312865 2 0.4789 0.748 0.056 0.772 0.000 0.172
#> GSM312867 2 0.6437 0.703 0.168 0.648 0.000 0.184
#> GSM312868 2 0.6284 0.712 0.164 0.664 0.000 0.172
#> GSM312869 2 0.0000 0.804 0.000 1.000 0.000 0.000
#> GSM312870 3 0.0000 0.870 0.000 0.000 1.000 0.000
#> GSM312872 3 0.0000 0.870 0.000 0.000 1.000 0.000
#> GSM312874 3 0.0000 0.870 0.000 0.000 1.000 0.000
#> GSM312875 3 0.0000 0.870 0.000 0.000 1.000 0.000
#> GSM312876 3 0.0000 0.870 0.000 0.000 1.000 0.000
#> GSM312877 3 0.6616 -0.484 0.108 0.000 0.584 0.308
#> GSM312879 3 0.0000 0.870 0.000 0.000 1.000 0.000
#> GSM312882 3 0.1211 0.838 0.000 0.000 0.960 0.040
#> GSM312883 3 0.1867 0.798 0.000 0.000 0.928 0.072
#> GSM312886 3 0.3521 0.674 0.084 0.000 0.864 0.052
#> GSM312887 1 0.2081 0.925 0.916 0.000 0.000 0.084
#> GSM312890 1 0.0000 0.970 1.000 0.000 0.000 0.000
#> GSM312893 1 0.0000 0.970 1.000 0.000 0.000 0.000
#> GSM312894 1 0.2011 0.927 0.920 0.000 0.000 0.080
#> GSM312895 1 0.0000 0.970 1.000 0.000 0.000 0.000
#> GSM312937 1 0.0000 0.970 1.000 0.000 0.000 0.000
#> GSM312938 1 0.2081 0.925 0.916 0.000 0.000 0.084
#> GSM312939 1 0.0000 0.970 1.000 0.000 0.000 0.000
#> GSM312940 1 0.0000 0.970 1.000 0.000 0.000 0.000
#> GSM312941 1 0.0000 0.970 1.000 0.000 0.000 0.000
#> GSM312942 4 0.6867 0.977 0.108 0.000 0.384 0.508
#> GSM312943 4 0.6727 0.994 0.096 0.000 0.384 0.520
#> GSM312944 4 0.6727 0.994 0.096 0.000 0.384 0.520
#> GSM312945 4 0.6727 0.994 0.096 0.000 0.384 0.520
#> GSM312946 4 0.6727 0.994 0.096 0.000 0.384 0.520
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM312811 4 0.1908 0.272 0.00 0.092 0.000 0.908 0.000
#> GSM312812 2 0.4304 0.503 0.00 0.516 0.000 0.484 0.000
#> GSM312813 4 0.4307 -0.527 0.00 0.496 0.000 0.504 0.000
#> GSM312814 4 0.2516 0.206 0.00 0.140 0.000 0.860 0.000
#> GSM312815 2 0.4304 0.503 0.00 0.516 0.000 0.484 0.000
#> GSM312816 4 0.1892 0.430 0.00 0.004 0.000 0.916 0.080
#> GSM312817 4 0.0880 0.384 0.00 0.032 0.000 0.968 0.000
#> GSM312818 4 0.1952 0.431 0.00 0.004 0.000 0.912 0.084
#> GSM312819 4 0.0703 0.390 0.00 0.024 0.000 0.976 0.000
#> GSM312820 4 0.1952 0.431 0.00 0.004 0.000 0.912 0.084
#> GSM312821 4 0.1952 0.431 0.00 0.004 0.000 0.912 0.084
#> GSM312822 4 0.0609 0.382 0.00 0.020 0.000 0.980 0.000
#> GSM312823 4 0.2329 0.253 0.00 0.124 0.000 0.876 0.000
#> GSM312824 2 0.4304 0.503 0.00 0.516 0.000 0.484 0.000
#> GSM312825 2 0.4304 0.503 0.00 0.516 0.000 0.484 0.000
#> GSM312826 2 0.4304 0.503 0.00 0.516 0.000 0.484 0.000
#> GSM312839 2 0.4304 0.503 0.00 0.516 0.000 0.484 0.000
#> GSM312840 2 0.4307 0.485 0.00 0.500 0.000 0.500 0.000
#> GSM312841 4 0.4101 -0.344 0.00 0.372 0.000 0.628 0.000
#> GSM312843 4 0.3774 0.434 0.00 0.296 0.000 0.704 0.000
#> GSM312844 4 0.4306 -0.530 0.00 0.492 0.000 0.508 0.000
#> GSM312845 4 0.4307 0.393 0.00 0.500 0.000 0.500 0.000
#> GSM312846 4 0.4307 0.393 0.00 0.500 0.000 0.500 0.000
#> GSM312847 2 0.4307 -0.459 0.00 0.500 0.000 0.500 0.000
#> GSM312848 2 0.4307 -0.459 0.00 0.500 0.000 0.500 0.000
#> GSM312849 4 0.4307 0.393 0.00 0.500 0.000 0.500 0.000
#> GSM312851 4 0.5691 0.419 0.00 0.400 0.000 0.516 0.084
#> GSM312853 4 0.5691 0.419 0.00 0.400 0.000 0.516 0.084
#> GSM312854 4 0.5691 0.419 0.00 0.400 0.000 0.516 0.084
#> GSM312856 4 0.4448 0.399 0.00 0.480 0.000 0.516 0.004
#> GSM312857 4 0.5691 0.419 0.00 0.400 0.000 0.516 0.084
#> GSM312858 4 0.4307 0.393 0.00 0.500 0.000 0.500 0.000
#> GSM312859 2 0.4307 0.483 0.00 0.504 0.000 0.496 0.000
#> GSM312860 4 0.4300 -0.498 0.00 0.476 0.000 0.524 0.000
#> GSM312861 4 0.3612 0.357 0.00 0.268 0.000 0.732 0.000
#> GSM312862 4 0.3816 0.385 0.00 0.304 0.000 0.696 0.000
#> GSM312863 4 0.4448 0.399 0.00 0.480 0.000 0.516 0.004
#> GSM312864 4 0.2017 0.432 0.00 0.008 0.000 0.912 0.080
#> GSM312865 2 0.4307 -0.459 0.00 0.500 0.000 0.500 0.000
#> GSM312867 4 0.4307 0.393 0.00 0.500 0.000 0.500 0.000
#> GSM312868 2 0.4307 -0.459 0.00 0.500 0.000 0.500 0.000
#> GSM312869 2 0.4304 0.503 0.00 0.516 0.000 0.484 0.000
#> GSM312870 3 0.0000 0.994 0.00 0.000 1.000 0.000 0.000
#> GSM312872 3 0.0000 0.994 0.00 0.000 1.000 0.000 0.000
#> GSM312874 3 0.0000 0.994 0.00 0.000 1.000 0.000 0.000
#> GSM312875 3 0.0000 0.994 0.00 0.000 1.000 0.000 0.000
#> GSM312876 3 0.0000 0.994 0.00 0.000 1.000 0.000 0.000
#> GSM312877 5 0.3707 0.720 0.00 0.000 0.284 0.000 0.716
#> GSM312879 3 0.0000 0.994 0.00 0.000 1.000 0.000 0.000
#> GSM312882 3 0.0000 0.994 0.00 0.000 1.000 0.000 0.000
#> GSM312883 3 0.0963 0.953 0.00 0.000 0.964 0.000 0.036
#> GSM312886 3 0.0000 0.994 0.00 0.000 1.000 0.000 0.000
#> GSM312887 1 0.3161 0.838 0.86 0.000 0.008 0.100 0.032
#> GSM312890 1 0.0000 0.956 1.00 0.000 0.000 0.000 0.000
#> GSM312893 1 0.0000 0.956 1.00 0.000 0.000 0.000 0.000
#> GSM312894 1 0.1043 0.930 0.96 0.000 0.000 0.000 0.040
#> GSM312895 1 0.0000 0.956 1.00 0.000 0.000 0.000 0.000
#> GSM312937 1 0.0000 0.956 1.00 0.000 0.000 0.000 0.000
#> GSM312938 1 0.2984 0.831 0.86 0.000 0.000 0.108 0.032
#> GSM312939 1 0.0000 0.956 1.00 0.000 0.000 0.000 0.000
#> GSM312940 1 0.0000 0.956 1.00 0.000 0.000 0.000 0.000
#> GSM312941 1 0.0000 0.956 1.00 0.000 0.000 0.000 0.000
#> GSM312942 5 0.2020 0.942 0.00 0.000 0.100 0.000 0.900
#> GSM312943 5 0.1792 0.951 0.00 0.000 0.084 0.000 0.916
#> GSM312944 5 0.1792 0.951 0.00 0.000 0.084 0.000 0.916
#> GSM312945 5 0.1792 0.951 0.00 0.000 0.084 0.000 0.916
#> GSM312946 5 0.1792 0.951 0.00 0.000 0.084 0.000 0.916
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM312811 2 0.1204 0.942 0.000 0.944 0.000 0.000 0.056 0.000
#> GSM312812 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312813 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312814 2 0.0937 0.952 0.000 0.960 0.000 0.000 0.040 0.000
#> GSM312815 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312816 5 0.1267 0.904 0.000 0.060 0.000 0.000 0.940 0.000
#> GSM312817 2 0.0713 0.957 0.000 0.972 0.000 0.000 0.028 0.000
#> GSM312818 5 0.0000 0.968 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM312819 2 0.1327 0.936 0.000 0.936 0.000 0.000 0.064 0.000
#> GSM312820 5 0.0000 0.968 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM312821 5 0.0000 0.968 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM312822 2 0.1267 0.939 0.000 0.940 0.000 0.000 0.060 0.000
#> GSM312823 2 0.0790 0.945 0.000 0.968 0.000 0.032 0.000 0.000
#> GSM312824 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312825 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312826 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312839 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312840 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312841 2 0.1075 0.947 0.000 0.952 0.000 0.000 0.048 0.000
#> GSM312843 4 0.3695 0.388 0.000 0.376 0.000 0.624 0.000 0.000
#> GSM312844 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312845 4 0.0000 0.960 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312846 4 0.0000 0.960 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312847 4 0.0000 0.960 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312848 4 0.0000 0.960 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312849 4 0.0146 0.958 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM312851 4 0.0146 0.959 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM312853 4 0.0146 0.959 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM312854 4 0.0146 0.959 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM312856 4 0.0146 0.959 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM312857 4 0.0146 0.959 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM312858 4 0.0458 0.947 0.000 0.016 0.000 0.984 0.000 0.000
#> GSM312859 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312860 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312861 2 0.2260 0.822 0.000 0.860 0.000 0.140 0.000 0.000
#> GSM312862 2 0.2340 0.811 0.000 0.852 0.000 0.148 0.000 0.000
#> GSM312863 4 0.0146 0.959 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM312864 2 0.0790 0.956 0.000 0.968 0.000 0.000 0.032 0.000
#> GSM312865 4 0.0000 0.960 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312867 4 0.0000 0.960 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312868 4 0.0713 0.935 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM312869 2 0.0000 0.966 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312870 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312872 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312874 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312875 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312876 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312877 6 0.2793 0.734 0.000 0.000 0.200 0.000 0.000 0.800
#> GSM312879 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312882 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312883 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312886 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312887 1 0.0146 0.995 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM312890 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312893 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312894 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312895 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312937 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312938 1 0.0146 0.995 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM312939 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312940 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312941 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312942 6 0.0146 0.946 0.000 0.000 0.004 0.000 0.000 0.996
#> GSM312943 6 0.0000 0.949 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM312944 6 0.0000 0.949 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM312945 6 0.0000 0.949 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM312946 6 0.0000 0.949 0.000 0.000 0.000 0.000 0.000 1.000
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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 5)
get_signatures(res, k = 6)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:mclust 67 1.68e-10 2
#> SD:mclust 61 1.21e-16 3
#> SD:mclust 66 1.17e-26 4
#> SD:mclust 32 2.51e-10 5
#> SD:mclust 66 3.45e-27 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "NMF"]
# you can also extract it by
# res = res_list["SD:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 67 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 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.968 0.988 0.4810 0.518 0.518
#> 3 3 0.947 0.924 0.969 0.2771 0.811 0.656
#> 4 4 0.671 0.563 0.745 0.1413 0.796 0.554
#> 5 5 0.740 0.779 0.865 0.0931 0.859 0.590
#> 6 6 0.943 0.893 0.953 0.0481 0.954 0.805
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM312811 2 0.000 0.9924 0.000 1.000
#> GSM312812 2 0.000 0.9924 0.000 1.000
#> GSM312813 2 0.000 0.9924 0.000 1.000
#> GSM312814 2 0.000 0.9924 0.000 1.000
#> GSM312815 2 0.000 0.9924 0.000 1.000
#> GSM312816 2 0.000 0.9924 0.000 1.000
#> GSM312817 2 0.000 0.9924 0.000 1.000
#> GSM312818 2 0.529 0.8607 0.120 0.880
#> GSM312819 2 0.000 0.9924 0.000 1.000
#> GSM312820 2 0.000 0.9924 0.000 1.000
#> GSM312821 2 0.000 0.9924 0.000 1.000
#> GSM312822 2 0.000 0.9924 0.000 1.000
#> GSM312823 2 0.000 0.9924 0.000 1.000
#> GSM312824 2 0.000 0.9924 0.000 1.000
#> GSM312825 2 0.000 0.9924 0.000 1.000
#> GSM312826 2 0.000 0.9924 0.000 1.000
#> GSM312839 2 0.000 0.9924 0.000 1.000
#> GSM312840 2 0.000 0.9924 0.000 1.000
#> GSM312841 2 0.000 0.9924 0.000 1.000
#> GSM312843 2 0.000 0.9924 0.000 1.000
#> GSM312844 2 0.000 0.9924 0.000 1.000
#> GSM312845 1 1.000 -0.0011 0.504 0.496
#> GSM312846 2 0.671 0.7819 0.176 0.824
#> GSM312847 2 0.000 0.9924 0.000 1.000
#> GSM312848 2 0.000 0.9924 0.000 1.000
#> GSM312849 2 0.000 0.9924 0.000 1.000
#> GSM312851 2 0.000 0.9924 0.000 1.000
#> GSM312853 2 0.000 0.9924 0.000 1.000
#> GSM312854 2 0.000 0.9924 0.000 1.000
#> GSM312856 2 0.000 0.9924 0.000 1.000
#> GSM312857 2 0.000 0.9924 0.000 1.000
#> GSM312858 2 0.000 0.9924 0.000 1.000
#> GSM312859 2 0.000 0.9924 0.000 1.000
#> GSM312860 2 0.000 0.9924 0.000 1.000
#> GSM312861 2 0.000 0.9924 0.000 1.000
#> GSM312862 2 0.000 0.9924 0.000 1.000
#> GSM312863 2 0.000 0.9924 0.000 1.000
#> GSM312864 2 0.000 0.9924 0.000 1.000
#> GSM312865 2 0.000 0.9924 0.000 1.000
#> GSM312867 2 0.000 0.9924 0.000 1.000
#> GSM312868 2 0.000 0.9924 0.000 1.000
#> GSM312869 2 0.000 0.9924 0.000 1.000
#> GSM312870 1 0.000 0.9798 1.000 0.000
#> GSM312872 1 0.000 0.9798 1.000 0.000
#> GSM312874 1 0.000 0.9798 1.000 0.000
#> GSM312875 1 0.000 0.9798 1.000 0.000
#> GSM312876 1 0.000 0.9798 1.000 0.000
#> GSM312877 1 0.000 0.9798 1.000 0.000
#> GSM312879 1 0.000 0.9798 1.000 0.000
#> GSM312882 1 0.000 0.9798 1.000 0.000
#> GSM312883 1 0.000 0.9798 1.000 0.000
#> GSM312886 1 0.000 0.9798 1.000 0.000
#> GSM312887 1 0.000 0.9798 1.000 0.000
#> GSM312890 1 0.000 0.9798 1.000 0.000
#> GSM312893 1 0.000 0.9798 1.000 0.000
#> GSM312894 1 0.000 0.9798 1.000 0.000
#> GSM312895 1 0.000 0.9798 1.000 0.000
#> GSM312937 1 0.000 0.9798 1.000 0.000
#> GSM312938 1 0.000 0.9798 1.000 0.000
#> GSM312939 1 0.000 0.9798 1.000 0.000
#> GSM312940 1 0.000 0.9798 1.000 0.000
#> GSM312941 1 0.000 0.9798 1.000 0.000
#> GSM312942 1 0.000 0.9798 1.000 0.000
#> GSM312943 1 0.000 0.9798 1.000 0.000
#> GSM312944 1 0.000 0.9798 1.000 0.000
#> GSM312945 1 0.000 0.9798 1.000 0.000
#> GSM312946 1 0.000 0.9798 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM312811 2 0.0000 0.9791 0.000 1.000 0.000
#> GSM312812 2 0.0000 0.9791 0.000 1.000 0.000
#> GSM312813 2 0.0000 0.9791 0.000 1.000 0.000
#> GSM312814 2 0.0000 0.9791 0.000 1.000 0.000
#> GSM312815 2 0.0000 0.9791 0.000 1.000 0.000
#> GSM312816 2 0.0000 0.9791 0.000 1.000 0.000
#> GSM312817 2 0.0000 0.9791 0.000 1.000 0.000
#> GSM312818 2 0.5678 0.5409 0.000 0.684 0.316
#> GSM312819 2 0.0000 0.9791 0.000 1.000 0.000
#> GSM312820 2 0.0237 0.9762 0.000 0.996 0.004
#> GSM312821 2 0.0237 0.9762 0.000 0.996 0.004
#> GSM312822 2 0.0000 0.9791 0.000 1.000 0.000
#> GSM312823 2 0.0000 0.9791 0.000 1.000 0.000
#> GSM312824 2 0.0000 0.9791 0.000 1.000 0.000
#> GSM312825 2 0.0000 0.9791 0.000 1.000 0.000
#> GSM312826 2 0.0000 0.9791 0.000 1.000 0.000
#> GSM312839 2 0.0000 0.9791 0.000 1.000 0.000
#> GSM312840 2 0.0000 0.9791 0.000 1.000 0.000
#> GSM312841 2 0.0000 0.9791 0.000 1.000 0.000
#> GSM312843 2 0.0000 0.9791 0.000 1.000 0.000
#> GSM312844 2 0.0000 0.9791 0.000 1.000 0.000
#> GSM312845 1 0.0000 0.9481 1.000 0.000 0.000
#> GSM312846 1 0.0000 0.9481 1.000 0.000 0.000
#> GSM312847 1 0.0237 0.9452 0.996 0.004 0.000
#> GSM312848 2 0.3340 0.8643 0.120 0.880 0.000
#> GSM312849 1 0.1031 0.9249 0.976 0.024 0.000
#> GSM312851 2 0.0000 0.9791 0.000 1.000 0.000
#> GSM312853 2 0.0000 0.9791 0.000 1.000 0.000
#> GSM312854 2 0.2796 0.8951 0.092 0.908 0.000
#> GSM312856 2 0.0000 0.9791 0.000 1.000 0.000
#> GSM312857 2 0.1163 0.9557 0.028 0.972 0.000
#> GSM312858 2 0.3619 0.8452 0.136 0.864 0.000
#> GSM312859 2 0.0000 0.9791 0.000 1.000 0.000
#> GSM312860 2 0.0000 0.9791 0.000 1.000 0.000
#> GSM312861 2 0.0000 0.9791 0.000 1.000 0.000
#> GSM312862 2 0.0000 0.9791 0.000 1.000 0.000
#> GSM312863 2 0.0000 0.9791 0.000 1.000 0.000
#> GSM312864 2 0.0000 0.9791 0.000 1.000 0.000
#> GSM312865 1 0.0237 0.9452 0.996 0.004 0.000
#> GSM312867 1 0.0000 0.9481 1.000 0.000 0.000
#> GSM312868 2 0.0000 0.9791 0.000 1.000 0.000
#> GSM312869 2 0.0000 0.9791 0.000 1.000 0.000
#> GSM312870 3 0.0000 0.9527 0.000 0.000 1.000
#> GSM312872 3 0.0000 0.9527 0.000 0.000 1.000
#> GSM312874 3 0.0000 0.9527 0.000 0.000 1.000
#> GSM312875 3 0.0000 0.9527 0.000 0.000 1.000
#> GSM312876 3 0.0000 0.9527 0.000 0.000 1.000
#> GSM312877 3 0.0592 0.9448 0.012 0.000 0.988
#> GSM312879 3 0.0000 0.9527 0.000 0.000 1.000
#> GSM312882 3 0.0000 0.9527 0.000 0.000 1.000
#> GSM312883 3 0.0000 0.9527 0.000 0.000 1.000
#> GSM312886 3 0.0000 0.9527 0.000 0.000 1.000
#> GSM312887 3 0.6252 0.1914 0.444 0.000 0.556
#> GSM312890 1 0.0000 0.9481 1.000 0.000 0.000
#> GSM312893 1 0.0000 0.9481 1.000 0.000 0.000
#> GSM312894 1 0.0000 0.9481 1.000 0.000 0.000
#> GSM312895 1 0.0000 0.9481 1.000 0.000 0.000
#> GSM312937 1 0.0000 0.9481 1.000 0.000 0.000
#> GSM312938 1 0.0000 0.9481 1.000 0.000 0.000
#> GSM312939 1 0.0000 0.9481 1.000 0.000 0.000
#> GSM312940 1 0.0000 0.9481 1.000 0.000 0.000
#> GSM312941 1 0.0000 0.9481 1.000 0.000 0.000
#> GSM312942 3 0.1529 0.9195 0.040 0.000 0.960
#> GSM312943 1 0.4235 0.7821 0.824 0.000 0.176
#> GSM312944 1 0.2625 0.8848 0.916 0.000 0.084
#> GSM312945 1 0.2878 0.8743 0.904 0.000 0.096
#> GSM312946 1 0.6305 0.0776 0.516 0.000 0.484
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM312811 2 0.0707 0.8837 0.000 0.980 0.000 0.020
#> GSM312812 2 0.0000 0.8906 0.000 1.000 0.000 0.000
#> GSM312813 2 0.0000 0.8906 0.000 1.000 0.000 0.000
#> GSM312814 2 0.1118 0.8765 0.000 0.964 0.000 0.036
#> GSM312815 2 0.0336 0.8876 0.000 0.992 0.000 0.008
#> GSM312816 2 0.3447 0.8026 0.020 0.852 0.000 0.128
#> GSM312817 2 0.0000 0.8906 0.000 1.000 0.000 0.000
#> GSM312818 2 0.7870 0.2171 0.012 0.452 0.352 0.184
#> GSM312819 2 0.0000 0.8906 0.000 1.000 0.000 0.000
#> GSM312820 2 0.4646 0.7549 0.028 0.780 0.008 0.184
#> GSM312821 2 0.5206 0.7320 0.012 0.756 0.048 0.184
#> GSM312822 2 0.2081 0.8480 0.000 0.916 0.000 0.084
#> GSM312823 2 0.0000 0.8906 0.000 1.000 0.000 0.000
#> GSM312824 2 0.0000 0.8906 0.000 1.000 0.000 0.000
#> GSM312825 2 0.1211 0.8653 0.000 0.960 0.000 0.040
#> GSM312826 2 0.0000 0.8906 0.000 1.000 0.000 0.000
#> GSM312839 2 0.0336 0.8876 0.000 0.992 0.000 0.008
#> GSM312840 2 0.0000 0.8906 0.000 1.000 0.000 0.000
#> GSM312841 2 0.0000 0.8906 0.000 1.000 0.000 0.000
#> GSM312843 2 0.6706 0.4770 0.288 0.588 0.000 0.124
#> GSM312844 2 0.0000 0.8906 0.000 1.000 0.000 0.000
#> GSM312845 1 0.4477 0.2064 0.688 0.000 0.000 0.312
#> GSM312846 1 0.5070 0.1876 0.580 0.004 0.000 0.416
#> GSM312847 1 0.2089 0.2316 0.932 0.020 0.000 0.048
#> GSM312848 1 0.4855 0.0763 0.644 0.352 0.000 0.004
#> GSM312849 1 0.7423 0.0444 0.428 0.168 0.000 0.404
#> GSM312851 1 0.7081 -0.1989 0.452 0.424 0.000 0.124
#> GSM312853 1 0.7078 -0.1901 0.456 0.420 0.000 0.124
#> GSM312854 1 0.6726 0.0862 0.584 0.292 0.000 0.124
#> GSM312856 1 0.7078 -0.1901 0.456 0.420 0.000 0.124
#> GSM312857 1 0.7042 -0.1231 0.488 0.388 0.000 0.124
#> GSM312858 1 0.5250 -0.1300 0.552 0.440 0.000 0.008
#> GSM312859 2 0.0000 0.8906 0.000 1.000 0.000 0.000
#> GSM312860 2 0.0336 0.8876 0.000 0.992 0.000 0.008
#> GSM312861 2 0.2921 0.7778 0.140 0.860 0.000 0.000
#> GSM312862 2 0.0779 0.8832 0.004 0.980 0.000 0.016
#> GSM312863 1 0.7081 -0.1989 0.452 0.424 0.000 0.124
#> GSM312864 2 0.6377 0.5409 0.256 0.632 0.000 0.112
#> GSM312865 1 0.1042 0.2325 0.972 0.020 0.000 0.008
#> GSM312867 1 0.4522 0.2068 0.680 0.000 0.000 0.320
#> GSM312868 2 0.4955 0.3241 0.444 0.556 0.000 0.000
#> GSM312869 2 0.0000 0.8906 0.000 1.000 0.000 0.000
#> GSM312870 3 0.0000 0.9595 0.000 0.000 1.000 0.000
#> GSM312872 3 0.0000 0.9595 0.000 0.000 1.000 0.000
#> GSM312874 3 0.0188 0.9578 0.004 0.000 0.996 0.000
#> GSM312875 3 0.0188 0.9605 0.000 0.000 0.996 0.004
#> GSM312876 3 0.0188 0.9605 0.000 0.000 0.996 0.004
#> GSM312877 3 0.4134 0.5333 0.000 0.000 0.740 0.260
#> GSM312879 3 0.0188 0.9605 0.000 0.000 0.996 0.004
#> GSM312882 3 0.0188 0.9605 0.000 0.000 0.996 0.004
#> GSM312883 3 0.0336 0.9574 0.000 0.000 0.992 0.008
#> GSM312886 3 0.0336 0.9585 0.000 0.000 0.992 0.008
#> GSM312887 1 0.7743 -0.2363 0.436 0.000 0.308 0.256
#> GSM312890 1 0.4972 0.1681 0.544 0.000 0.000 0.456
#> GSM312893 1 0.4972 0.1681 0.544 0.000 0.000 0.456
#> GSM312894 1 0.4972 0.1681 0.544 0.000 0.000 0.456
#> GSM312895 1 0.4972 0.1681 0.544 0.000 0.000 0.456
#> GSM312937 1 0.4972 0.1681 0.544 0.000 0.000 0.456
#> GSM312938 1 0.5060 0.1776 0.584 0.000 0.004 0.412
#> GSM312939 1 0.4972 0.1681 0.544 0.000 0.000 0.456
#> GSM312940 1 0.4972 0.1681 0.544 0.000 0.000 0.456
#> GSM312941 1 0.4972 0.1681 0.544 0.000 0.000 0.456
#> GSM312942 4 0.3764 0.8646 0.000 0.000 0.216 0.784
#> GSM312943 4 0.2999 0.9553 0.004 0.000 0.132 0.864
#> GSM312944 4 0.3217 0.9530 0.012 0.000 0.128 0.860
#> GSM312945 4 0.3217 0.9530 0.012 0.000 0.128 0.860
#> GSM312946 4 0.3157 0.9504 0.004 0.000 0.144 0.852
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM312811 2 0.1725 0.858409 0.000 0.936 0.000 0.020 0.044
#> GSM312812 2 0.0162 0.892225 0.000 0.996 0.000 0.000 0.004
#> GSM312813 2 0.0162 0.892225 0.000 0.996 0.000 0.000 0.004
#> GSM312814 2 0.3359 0.790765 0.000 0.844 0.000 0.072 0.084
#> GSM312815 2 0.0671 0.883587 0.000 0.980 0.000 0.004 0.016
#> GSM312816 2 0.5025 0.651907 0.000 0.704 0.000 0.124 0.172
#> GSM312817 2 0.0162 0.891304 0.000 0.996 0.000 0.004 0.000
#> GSM312818 5 0.8218 -0.149431 0.000 0.320 0.136 0.196 0.348
#> GSM312819 2 0.0162 0.891304 0.000 0.996 0.000 0.004 0.000
#> GSM312820 2 0.6577 0.364832 0.000 0.500 0.012 0.160 0.328
#> GSM312821 2 0.6772 0.326042 0.000 0.480 0.016 0.176 0.328
#> GSM312822 2 0.3691 0.771404 0.000 0.820 0.000 0.076 0.104
#> GSM312823 2 0.0000 0.891978 0.000 1.000 0.000 0.000 0.000
#> GSM312824 2 0.0162 0.892225 0.000 0.996 0.000 0.000 0.004
#> GSM312825 2 0.0162 0.892225 0.000 0.996 0.000 0.000 0.004
#> GSM312826 2 0.0162 0.892225 0.000 0.996 0.000 0.000 0.004
#> GSM312839 2 0.0162 0.892225 0.000 0.996 0.000 0.000 0.004
#> GSM312840 2 0.0000 0.891978 0.000 1.000 0.000 0.000 0.000
#> GSM312841 2 0.0000 0.891978 0.000 1.000 0.000 0.000 0.000
#> GSM312843 4 0.3055 0.814489 0.000 0.144 0.000 0.840 0.016
#> GSM312844 2 0.0000 0.891978 0.000 1.000 0.000 0.000 0.000
#> GSM312845 4 0.4774 0.274222 0.424 0.000 0.020 0.556 0.000
#> GSM312846 1 0.1124 0.842682 0.960 0.004 0.000 0.036 0.000
#> GSM312847 4 0.4166 0.473788 0.348 0.004 0.000 0.648 0.000
#> GSM312848 4 0.4035 0.810577 0.060 0.156 0.000 0.784 0.000
#> GSM312849 1 0.5379 0.372794 0.632 0.300 0.000 0.056 0.012
#> GSM312851 4 0.3410 0.799919 0.000 0.092 0.000 0.840 0.068
#> GSM312853 4 0.2193 0.834632 0.000 0.092 0.000 0.900 0.008
#> GSM312854 4 0.2077 0.834108 0.008 0.084 0.000 0.908 0.000
#> GSM312856 4 0.2068 0.835123 0.000 0.092 0.000 0.904 0.004
#> GSM312857 4 0.2237 0.834230 0.008 0.084 0.000 0.904 0.004
#> GSM312858 4 0.4113 0.810252 0.076 0.140 0.000 0.784 0.000
#> GSM312859 2 0.0290 0.890474 0.000 0.992 0.000 0.000 0.008
#> GSM312860 2 0.0703 0.879858 0.000 0.976 0.000 0.000 0.024
#> GSM312861 4 0.4182 0.531446 0.000 0.400 0.000 0.600 0.000
#> GSM312862 2 0.5165 0.095796 0.000 0.512 0.000 0.040 0.448
#> GSM312863 4 0.1908 0.835517 0.000 0.092 0.000 0.908 0.000
#> GSM312864 4 0.3048 0.806162 0.000 0.176 0.000 0.820 0.004
#> GSM312865 4 0.3650 0.724502 0.176 0.028 0.000 0.796 0.000
#> GSM312867 1 0.4533 0.000552 0.544 0.008 0.000 0.448 0.000
#> GSM312868 4 0.3210 0.787657 0.000 0.212 0.000 0.788 0.000
#> GSM312869 2 0.0162 0.892225 0.000 0.996 0.000 0.000 0.004
#> GSM312870 3 0.0404 0.969037 0.000 0.000 0.988 0.000 0.012
#> GSM312872 3 0.0290 0.970600 0.000 0.000 0.992 0.000 0.008
#> GSM312874 3 0.0510 0.967212 0.000 0.000 0.984 0.000 0.016
#> GSM312875 3 0.0404 0.969412 0.000 0.000 0.988 0.000 0.012
#> GSM312876 3 0.0290 0.970238 0.000 0.000 0.992 0.000 0.008
#> GSM312877 3 0.2727 0.848426 0.016 0.000 0.868 0.000 0.116
#> GSM312879 3 0.0404 0.971197 0.000 0.000 0.988 0.000 0.012
#> GSM312882 3 0.0703 0.964402 0.000 0.000 0.976 0.000 0.024
#> GSM312883 3 0.0703 0.964402 0.000 0.000 0.976 0.000 0.024
#> GSM312886 3 0.0404 0.969754 0.000 0.000 0.988 0.000 0.012
#> GSM312887 1 0.3165 0.709313 0.848 0.000 0.116 0.000 0.036
#> GSM312890 1 0.0000 0.874308 1.000 0.000 0.000 0.000 0.000
#> GSM312893 1 0.0000 0.874308 1.000 0.000 0.000 0.000 0.000
#> GSM312894 1 0.0404 0.865185 0.988 0.000 0.012 0.000 0.000
#> GSM312895 1 0.0000 0.874308 1.000 0.000 0.000 0.000 0.000
#> GSM312937 1 0.0000 0.874308 1.000 0.000 0.000 0.000 0.000
#> GSM312938 1 0.0162 0.872061 0.996 0.000 0.000 0.004 0.000
#> GSM312939 1 0.0000 0.874308 1.000 0.000 0.000 0.000 0.000
#> GSM312940 1 0.0000 0.874308 1.000 0.000 0.000 0.000 0.000
#> GSM312941 1 0.0000 0.874308 1.000 0.000 0.000 0.000 0.000
#> GSM312942 5 0.5177 0.767501 0.180 0.000 0.132 0.000 0.688
#> GSM312943 5 0.5284 0.779519 0.216 0.000 0.116 0.000 0.668
#> GSM312944 5 0.5337 0.767663 0.228 0.000 0.100 0.004 0.668
#> GSM312945 5 0.5295 0.775544 0.224 0.000 0.112 0.000 0.664
#> GSM312946 5 0.5295 0.779199 0.200 0.000 0.128 0.000 0.672
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM312811 2 0.1765 0.841 0.000 0.904 0.000 0.000 0.096 0.000
#> GSM312812 2 0.0000 0.931 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312813 2 0.0000 0.931 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312814 2 0.2697 0.713 0.000 0.812 0.000 0.000 0.188 0.000
#> GSM312815 2 0.0865 0.904 0.000 0.964 0.000 0.000 0.036 0.000
#> GSM312816 2 0.3756 0.145 0.000 0.600 0.000 0.000 0.400 0.000
#> GSM312817 2 0.0146 0.929 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM312818 5 0.1461 0.650 0.000 0.044 0.016 0.000 0.940 0.000
#> GSM312819 2 0.0291 0.928 0.000 0.992 0.000 0.000 0.004 0.004
#> GSM312820 5 0.3244 0.803 0.000 0.268 0.000 0.000 0.732 0.000
#> GSM312821 5 0.3076 0.828 0.000 0.240 0.000 0.000 0.760 0.000
#> GSM312822 2 0.3126 0.601 0.000 0.752 0.000 0.000 0.248 0.000
#> GSM312823 2 0.0146 0.931 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM312824 2 0.0146 0.931 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM312825 2 0.0146 0.931 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM312826 2 0.0146 0.931 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM312839 2 0.0000 0.931 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312840 2 0.0000 0.931 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312841 2 0.0000 0.931 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312843 4 0.0000 0.929 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312844 2 0.0000 0.931 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312845 4 0.4136 0.662 0.192 0.000 0.076 0.732 0.000 0.000
#> GSM312846 1 0.0146 0.964 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM312847 4 0.0260 0.925 0.008 0.000 0.000 0.992 0.000 0.000
#> GSM312848 4 0.0405 0.923 0.000 0.008 0.000 0.988 0.004 0.000
#> GSM312849 1 0.3990 0.592 0.736 0.232 0.004 0.012 0.012 0.004
#> GSM312851 4 0.1610 0.863 0.000 0.000 0.000 0.916 0.084 0.000
#> GSM312853 4 0.0000 0.929 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312854 4 0.0000 0.929 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312856 4 0.0000 0.929 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312857 4 0.0000 0.929 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312858 4 0.0000 0.929 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312859 2 0.0146 0.931 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM312860 2 0.0291 0.928 0.000 0.992 0.000 0.000 0.004 0.004
#> GSM312861 4 0.1700 0.854 0.000 0.080 0.000 0.916 0.004 0.000
#> GSM312862 6 0.2445 0.800 0.000 0.108 0.000 0.020 0.000 0.872
#> GSM312863 4 0.0000 0.929 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312864 4 0.1010 0.902 0.000 0.036 0.000 0.960 0.004 0.000
#> GSM312865 4 0.0000 0.929 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312867 4 0.4018 0.307 0.412 0.008 0.000 0.580 0.000 0.000
#> GSM312868 4 0.0000 0.929 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312869 2 0.0146 0.931 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM312870 3 0.0865 0.975 0.000 0.000 0.964 0.000 0.036 0.000
#> GSM312872 3 0.0632 0.979 0.000 0.000 0.976 0.000 0.024 0.000
#> GSM312874 3 0.1075 0.971 0.000 0.000 0.952 0.000 0.048 0.000
#> GSM312875 3 0.0146 0.979 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM312876 3 0.0000 0.980 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312877 3 0.0458 0.975 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM312879 3 0.0632 0.979 0.000 0.000 0.976 0.000 0.024 0.000
#> GSM312882 3 0.0260 0.978 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM312883 3 0.0458 0.975 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM312886 3 0.1075 0.970 0.000 0.000 0.952 0.000 0.048 0.000
#> GSM312887 1 0.0547 0.951 0.980 0.000 0.000 0.000 0.020 0.000
#> GSM312890 1 0.0000 0.967 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312893 1 0.0000 0.967 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312894 1 0.0000 0.967 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312895 1 0.0000 0.967 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312937 1 0.0000 0.967 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312938 1 0.0000 0.967 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312939 1 0.0000 0.967 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312940 1 0.0000 0.967 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312941 1 0.0000 0.967 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312942 6 0.0146 0.964 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM312943 6 0.0146 0.964 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM312944 6 0.0146 0.964 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM312945 6 0.0146 0.964 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM312946 6 0.0146 0.964 0.004 0.000 0.000 0.000 0.000 0.996
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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:NMF 66 2.61e-10 2
#> SD:NMF 65 2.26e-14 3
#> SD:NMF 40 4.13e-12 4
#> SD:NMF 59 5.26e-25 5
#> SD:NMF 65 4.06e-24 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "hclust"]
# you can also extract it by
# res = res_list["CV:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 67 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 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4754 0.525 0.525
#> 3 3 0.801 0.854 0.892 0.2394 0.931 0.869
#> 4 4 0.795 0.837 0.885 0.1127 0.935 0.857
#> 5 5 0.939 0.947 0.965 0.1769 0.837 0.584
#> 6 6 0.950 0.923 0.943 0.0347 0.967 0.856
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 5
There is also optional best \(k\) = 2 5 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM312811 2 0 1 0 1
#> GSM312812 2 0 1 0 1
#> GSM312813 2 0 1 0 1
#> GSM312814 2 0 1 0 1
#> GSM312815 2 0 1 0 1
#> GSM312816 2 0 1 0 1
#> GSM312817 2 0 1 0 1
#> GSM312818 2 0 1 0 1
#> GSM312819 2 0 1 0 1
#> GSM312820 2 0 1 0 1
#> GSM312821 2 0 1 0 1
#> GSM312822 2 0 1 0 1
#> GSM312823 2 0 1 0 1
#> GSM312824 2 0 1 0 1
#> GSM312825 2 0 1 0 1
#> GSM312826 2 0 1 0 1
#> GSM312839 2 0 1 0 1
#> GSM312840 2 0 1 0 1
#> GSM312841 2 0 1 0 1
#> GSM312843 2 0 1 0 1
#> GSM312844 2 0 1 0 1
#> GSM312845 2 0 1 0 1
#> GSM312846 2 0 1 0 1
#> GSM312847 2 0 1 0 1
#> GSM312848 2 0 1 0 1
#> GSM312849 2 0 1 0 1
#> GSM312851 2 0 1 0 1
#> GSM312853 2 0 1 0 1
#> GSM312854 2 0 1 0 1
#> GSM312856 2 0 1 0 1
#> GSM312857 2 0 1 0 1
#> GSM312858 2 0 1 0 1
#> GSM312859 2 0 1 0 1
#> GSM312860 2 0 1 0 1
#> GSM312861 2 0 1 0 1
#> GSM312862 2 0 1 0 1
#> GSM312863 2 0 1 0 1
#> GSM312864 2 0 1 0 1
#> GSM312865 2 0 1 0 1
#> GSM312867 2 0 1 0 1
#> GSM312868 2 0 1 0 1
#> GSM312869 2 0 1 0 1
#> GSM312870 1 0 1 1 0
#> GSM312872 1 0 1 1 0
#> GSM312874 1 0 1 1 0
#> GSM312875 1 0 1 1 0
#> GSM312876 1 0 1 1 0
#> GSM312877 1 0 1 1 0
#> GSM312879 1 0 1 1 0
#> GSM312882 1 0 1 1 0
#> GSM312883 1 0 1 1 0
#> GSM312886 1 0 1 1 0
#> GSM312887 1 0 1 1 0
#> GSM312890 1 0 1 1 0
#> GSM312893 1 0 1 1 0
#> GSM312894 1 0 1 1 0
#> GSM312895 1 0 1 1 0
#> GSM312937 1 0 1 1 0
#> GSM312938 1 0 1 1 0
#> GSM312939 1 0 1 1 0
#> GSM312940 1 0 1 1 0
#> GSM312941 1 0 1 1 0
#> GSM312942 1 0 1 1 0
#> GSM312943 1 0 1 1 0
#> GSM312944 1 0 1 1 0
#> GSM312945 1 0 1 1 0
#> GSM312946 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM312811 2 0.0000 0.737 0 1.000 0.000
#> GSM312812 2 0.0000 0.737 0 1.000 0.000
#> GSM312813 2 0.0000 0.737 0 1.000 0.000
#> GSM312814 2 0.0237 0.738 0 0.996 0.004
#> GSM312815 2 0.0000 0.737 0 1.000 0.000
#> GSM312816 3 0.5926 1.000 0 0.356 0.644
#> GSM312817 2 0.0000 0.737 0 1.000 0.000
#> GSM312818 3 0.5926 1.000 0 0.356 0.644
#> GSM312819 2 0.0424 0.731 0 0.992 0.008
#> GSM312820 3 0.5926 1.000 0 0.356 0.644
#> GSM312821 3 0.5926 1.000 0 0.356 0.644
#> GSM312822 2 0.0237 0.738 0 0.996 0.004
#> GSM312823 2 0.0237 0.738 0 0.996 0.004
#> GSM312824 2 0.0000 0.737 0 1.000 0.000
#> GSM312825 2 0.0000 0.737 0 1.000 0.000
#> GSM312826 2 0.0000 0.737 0 1.000 0.000
#> GSM312839 2 0.0000 0.737 0 1.000 0.000
#> GSM312840 2 0.0000 0.737 0 1.000 0.000
#> GSM312841 2 0.0424 0.731 0 0.992 0.008
#> GSM312843 2 0.5785 0.754 0 0.668 0.332
#> GSM312844 2 0.0000 0.737 0 1.000 0.000
#> GSM312845 2 0.5926 0.747 0 0.644 0.356
#> GSM312846 2 0.5926 0.747 0 0.644 0.356
#> GSM312847 2 0.5926 0.747 0 0.644 0.356
#> GSM312848 2 0.5926 0.747 0 0.644 0.356
#> GSM312849 2 0.5926 0.747 0 0.644 0.356
#> GSM312851 2 0.5859 0.751 0 0.656 0.344
#> GSM312853 2 0.5859 0.751 0 0.656 0.344
#> GSM312854 2 0.5859 0.751 0 0.656 0.344
#> GSM312856 2 0.5859 0.751 0 0.656 0.344
#> GSM312857 2 0.5859 0.751 0 0.656 0.344
#> GSM312858 2 0.5926 0.747 0 0.644 0.356
#> GSM312859 2 0.0237 0.738 0 0.996 0.004
#> GSM312860 2 0.0237 0.738 0 0.996 0.004
#> GSM312861 2 0.5926 0.747 0 0.644 0.356
#> GSM312862 2 0.5785 0.754 0 0.668 0.332
#> GSM312863 2 0.5926 0.747 0 0.644 0.356
#> GSM312864 2 0.3192 0.741 0 0.888 0.112
#> GSM312865 2 0.5926 0.747 0 0.644 0.356
#> GSM312867 2 0.5926 0.747 0 0.644 0.356
#> GSM312868 2 0.5926 0.747 0 0.644 0.356
#> GSM312869 2 0.0000 0.737 0 1.000 0.000
#> GSM312870 1 0.0000 1.000 1 0.000 0.000
#> GSM312872 1 0.0000 1.000 1 0.000 0.000
#> GSM312874 1 0.0000 1.000 1 0.000 0.000
#> GSM312875 1 0.0000 1.000 1 0.000 0.000
#> GSM312876 1 0.0000 1.000 1 0.000 0.000
#> GSM312877 1 0.0000 1.000 1 0.000 0.000
#> GSM312879 1 0.0000 1.000 1 0.000 0.000
#> GSM312882 1 0.0000 1.000 1 0.000 0.000
#> GSM312883 1 0.0000 1.000 1 0.000 0.000
#> GSM312886 1 0.0000 1.000 1 0.000 0.000
#> GSM312887 1 0.0000 1.000 1 0.000 0.000
#> GSM312890 1 0.0000 1.000 1 0.000 0.000
#> GSM312893 1 0.0000 1.000 1 0.000 0.000
#> GSM312894 1 0.0000 1.000 1 0.000 0.000
#> GSM312895 1 0.0000 1.000 1 0.000 0.000
#> GSM312937 1 0.0000 1.000 1 0.000 0.000
#> GSM312938 1 0.0000 1.000 1 0.000 0.000
#> GSM312939 1 0.0000 1.000 1 0.000 0.000
#> GSM312940 1 0.0000 1.000 1 0.000 0.000
#> GSM312941 1 0.0000 1.000 1 0.000 0.000
#> GSM312942 1 0.0000 1.000 1 0.000 0.000
#> GSM312943 1 0.0000 1.000 1 0.000 0.000
#> GSM312944 1 0.0000 1.000 1 0.000 0.000
#> GSM312945 1 0.0000 1.000 1 0.000 0.000
#> GSM312946 1 0.0000 1.000 1 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM312811 2 0.0000 0.737 0.000 1.000 0.000 0.000
#> GSM312812 2 0.0000 0.737 0.000 1.000 0.000 0.000
#> GSM312813 2 0.0000 0.737 0.000 1.000 0.000 0.000
#> GSM312814 2 0.0188 0.738 0.000 0.996 0.004 0.000
#> GSM312815 2 0.0000 0.737 0.000 1.000 0.000 0.000
#> GSM312816 4 0.4679 1.000 0.000 0.352 0.000 0.648
#> GSM312817 2 0.0000 0.737 0.000 1.000 0.000 0.000
#> GSM312818 4 0.4679 1.000 0.000 0.352 0.000 0.648
#> GSM312819 2 0.0336 0.730 0.000 0.992 0.000 0.008
#> GSM312820 4 0.4679 1.000 0.000 0.352 0.000 0.648
#> GSM312821 4 0.4679 1.000 0.000 0.352 0.000 0.648
#> GSM312822 2 0.0188 0.738 0.000 0.996 0.004 0.000
#> GSM312823 2 0.0188 0.738 0.000 0.996 0.004 0.000
#> GSM312824 2 0.0000 0.737 0.000 1.000 0.000 0.000
#> GSM312825 2 0.0000 0.737 0.000 1.000 0.000 0.000
#> GSM312826 2 0.0000 0.737 0.000 1.000 0.000 0.000
#> GSM312839 2 0.0000 0.737 0.000 1.000 0.000 0.000
#> GSM312840 2 0.0000 0.737 0.000 1.000 0.000 0.000
#> GSM312841 2 0.0336 0.730 0.000 0.992 0.000 0.008
#> GSM312843 2 0.4761 0.753 0.000 0.664 0.332 0.004
#> GSM312844 2 0.0000 0.737 0.000 1.000 0.000 0.000
#> GSM312845 2 0.4697 0.748 0.000 0.644 0.356 0.000
#> GSM312846 2 0.4697 0.748 0.000 0.644 0.356 0.000
#> GSM312847 2 0.4697 0.748 0.000 0.644 0.356 0.000
#> GSM312848 2 0.4697 0.748 0.000 0.644 0.356 0.000
#> GSM312849 2 0.4697 0.748 0.000 0.644 0.356 0.000
#> GSM312851 2 0.5038 0.750 0.000 0.652 0.336 0.012
#> GSM312853 2 0.5038 0.750 0.000 0.652 0.336 0.012
#> GSM312854 2 0.5038 0.750 0.000 0.652 0.336 0.012
#> GSM312856 2 0.5038 0.750 0.000 0.652 0.336 0.012
#> GSM312857 2 0.5038 0.750 0.000 0.652 0.336 0.012
#> GSM312858 2 0.4697 0.748 0.000 0.644 0.356 0.000
#> GSM312859 2 0.0188 0.738 0.000 0.996 0.004 0.000
#> GSM312860 2 0.0188 0.738 0.000 0.996 0.004 0.000
#> GSM312861 2 0.4697 0.748 0.000 0.644 0.356 0.000
#> GSM312862 2 0.4761 0.753 0.000 0.664 0.332 0.004
#> GSM312863 2 0.4697 0.748 0.000 0.644 0.356 0.000
#> GSM312864 2 0.2867 0.740 0.000 0.884 0.104 0.012
#> GSM312865 2 0.4697 0.748 0.000 0.644 0.356 0.000
#> GSM312867 2 0.4697 0.748 0.000 0.644 0.356 0.000
#> GSM312868 2 0.4697 0.748 0.000 0.644 0.356 0.000
#> GSM312869 2 0.0000 0.737 0.000 1.000 0.000 0.000
#> GSM312870 3 0.4855 1.000 0.004 0.000 0.644 0.352
#> GSM312872 3 0.4855 1.000 0.004 0.000 0.644 0.352
#> GSM312874 3 0.4855 1.000 0.004 0.000 0.644 0.352
#> GSM312875 3 0.4855 1.000 0.004 0.000 0.644 0.352
#> GSM312876 3 0.4855 1.000 0.004 0.000 0.644 0.352
#> GSM312877 1 0.6171 0.295 0.588 0.000 0.064 0.348
#> GSM312879 3 0.4855 1.000 0.004 0.000 0.644 0.352
#> GSM312882 3 0.4855 1.000 0.004 0.000 0.644 0.352
#> GSM312883 3 0.4855 1.000 0.004 0.000 0.644 0.352
#> GSM312886 3 0.4855 1.000 0.004 0.000 0.644 0.352
#> GSM312887 1 0.0000 0.971 1.000 0.000 0.000 0.000
#> GSM312890 1 0.0000 0.971 1.000 0.000 0.000 0.000
#> GSM312893 1 0.0000 0.971 1.000 0.000 0.000 0.000
#> GSM312894 1 0.0000 0.971 1.000 0.000 0.000 0.000
#> GSM312895 1 0.0000 0.971 1.000 0.000 0.000 0.000
#> GSM312937 1 0.0000 0.971 1.000 0.000 0.000 0.000
#> GSM312938 1 0.0000 0.971 1.000 0.000 0.000 0.000
#> GSM312939 1 0.0000 0.971 1.000 0.000 0.000 0.000
#> GSM312940 1 0.0000 0.971 1.000 0.000 0.000 0.000
#> GSM312941 1 0.0000 0.971 1.000 0.000 0.000 0.000
#> GSM312942 1 0.0000 0.971 1.000 0.000 0.000 0.000
#> GSM312943 1 0.0000 0.971 1.000 0.000 0.000 0.000
#> GSM312944 1 0.0000 0.971 1.000 0.000 0.000 0.000
#> GSM312945 1 0.0000 0.971 1.000 0.000 0.000 0.000
#> GSM312946 1 0.0000 0.971 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM312811 2 0.0162 0.964 0.000 0.996 0.000 0.000 0.004
#> GSM312812 2 0.0162 0.964 0.000 0.996 0.000 0.000 0.004
#> GSM312813 2 0.0162 0.964 0.000 0.996 0.000 0.000 0.004
#> GSM312814 2 0.0451 0.961 0.000 0.988 0.000 0.004 0.008
#> GSM312815 2 0.0162 0.964 0.000 0.996 0.000 0.000 0.004
#> GSM312816 5 0.2127 1.000 0.000 0.108 0.000 0.000 0.892
#> GSM312817 2 0.1041 0.939 0.000 0.964 0.000 0.032 0.004
#> GSM312818 5 0.2127 1.000 0.000 0.108 0.000 0.000 0.892
#> GSM312819 2 0.0798 0.950 0.000 0.976 0.000 0.008 0.016
#> GSM312820 5 0.2127 1.000 0.000 0.108 0.000 0.000 0.892
#> GSM312821 5 0.2127 1.000 0.000 0.108 0.000 0.000 0.892
#> GSM312822 2 0.0451 0.961 0.000 0.988 0.000 0.004 0.008
#> GSM312823 2 0.2127 0.840 0.000 0.892 0.000 0.108 0.000
#> GSM312824 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM312825 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM312826 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM312839 2 0.0162 0.964 0.000 0.996 0.000 0.000 0.004
#> GSM312840 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM312841 2 0.0798 0.950 0.000 0.976 0.000 0.008 0.016
#> GSM312843 4 0.1740 0.942 0.000 0.056 0.000 0.932 0.012
#> GSM312844 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM312845 4 0.0290 0.978 0.000 0.008 0.000 0.992 0.000
#> GSM312846 4 0.0290 0.978 0.000 0.008 0.000 0.992 0.000
#> GSM312847 4 0.0290 0.978 0.000 0.008 0.000 0.992 0.000
#> GSM312848 4 0.0609 0.976 0.000 0.020 0.000 0.980 0.000
#> GSM312849 4 0.0290 0.978 0.000 0.008 0.000 0.992 0.000
#> GSM312851 4 0.0898 0.969 0.000 0.008 0.000 0.972 0.020
#> GSM312853 4 0.0898 0.969 0.000 0.008 0.000 0.972 0.020
#> GSM312854 4 0.0898 0.969 0.000 0.008 0.000 0.972 0.020
#> GSM312856 4 0.0898 0.969 0.000 0.008 0.000 0.972 0.020
#> GSM312857 4 0.0898 0.969 0.000 0.008 0.000 0.972 0.020
#> GSM312858 4 0.0609 0.976 0.000 0.020 0.000 0.980 0.000
#> GSM312859 2 0.0703 0.948 0.000 0.976 0.000 0.024 0.000
#> GSM312860 2 0.0703 0.948 0.000 0.976 0.000 0.024 0.000
#> GSM312861 4 0.0290 0.978 0.000 0.008 0.000 0.992 0.000
#> GSM312862 4 0.1740 0.942 0.000 0.056 0.000 0.932 0.012
#> GSM312863 4 0.0609 0.976 0.000 0.020 0.000 0.980 0.000
#> GSM312864 2 0.3909 0.629 0.000 0.760 0.000 0.216 0.024
#> GSM312865 4 0.0609 0.976 0.000 0.020 0.000 0.980 0.000
#> GSM312867 4 0.0290 0.978 0.000 0.008 0.000 0.992 0.000
#> GSM312868 4 0.0609 0.976 0.000 0.020 0.000 0.980 0.000
#> GSM312869 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM312870 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312872 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312874 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312875 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312876 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312877 1 0.4219 0.332 0.584 0.000 0.416 0.000 0.000
#> GSM312879 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312882 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312883 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312886 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312887 1 0.0000 0.937 1.000 0.000 0.000 0.000 0.000
#> GSM312890 1 0.0000 0.937 1.000 0.000 0.000 0.000 0.000
#> GSM312893 1 0.0000 0.937 1.000 0.000 0.000 0.000 0.000
#> GSM312894 1 0.0000 0.937 1.000 0.000 0.000 0.000 0.000
#> GSM312895 1 0.0000 0.937 1.000 0.000 0.000 0.000 0.000
#> GSM312937 1 0.0000 0.937 1.000 0.000 0.000 0.000 0.000
#> GSM312938 1 0.0000 0.937 1.000 0.000 0.000 0.000 0.000
#> GSM312939 1 0.0000 0.937 1.000 0.000 0.000 0.000 0.000
#> GSM312940 1 0.0000 0.937 1.000 0.000 0.000 0.000 0.000
#> GSM312941 1 0.0000 0.937 1.000 0.000 0.000 0.000 0.000
#> GSM312942 1 0.2127 0.903 0.892 0.000 0.000 0.000 0.108
#> GSM312943 1 0.2127 0.903 0.892 0.000 0.000 0.000 0.108
#> GSM312944 1 0.2127 0.903 0.892 0.000 0.000 0.000 0.108
#> GSM312945 1 0.2127 0.903 0.892 0.000 0.000 0.000 0.108
#> GSM312946 1 0.2127 0.903 0.892 0.000 0.000 0.000 0.108
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM312811 2 0.0547 0.921 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM312812 2 0.0547 0.921 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM312813 2 0.0547 0.921 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM312814 2 0.0777 0.919 0.000 0.972 0.000 0.004 0.024 0.000
#> GSM312815 2 0.0547 0.921 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM312816 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM312817 2 0.1334 0.908 0.000 0.948 0.000 0.032 0.020 0.000
#> GSM312818 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM312819 2 0.3956 0.713 0.000 0.712 0.000 0.000 0.036 0.252
#> GSM312820 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM312821 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM312822 2 0.0777 0.919 0.000 0.972 0.000 0.004 0.024 0.000
#> GSM312823 2 0.1910 0.840 0.000 0.892 0.000 0.108 0.000 0.000
#> GSM312824 2 0.0146 0.921 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM312825 2 0.0146 0.921 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM312826 2 0.0146 0.921 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM312839 2 0.0547 0.921 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM312840 2 0.2595 0.827 0.000 0.836 0.000 0.000 0.004 0.160
#> GSM312841 2 0.3909 0.721 0.000 0.720 0.000 0.000 0.036 0.244
#> GSM312843 4 0.1563 0.941 0.000 0.056 0.000 0.932 0.012 0.000
#> GSM312844 2 0.0000 0.921 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312845 4 0.0260 0.978 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM312846 4 0.0260 0.978 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM312847 4 0.0260 0.978 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM312848 4 0.0547 0.976 0.000 0.020 0.000 0.980 0.000 0.000
#> GSM312849 4 0.0260 0.978 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM312851 4 0.0806 0.967 0.000 0.000 0.000 0.972 0.020 0.008
#> GSM312853 4 0.0806 0.967 0.000 0.000 0.000 0.972 0.020 0.008
#> GSM312854 4 0.0806 0.967 0.000 0.000 0.000 0.972 0.020 0.008
#> GSM312856 4 0.0806 0.967 0.000 0.000 0.000 0.972 0.020 0.008
#> GSM312857 4 0.0806 0.967 0.000 0.000 0.000 0.972 0.020 0.008
#> GSM312858 4 0.0547 0.976 0.000 0.020 0.000 0.980 0.000 0.000
#> GSM312859 2 0.0632 0.913 0.000 0.976 0.000 0.024 0.000 0.000
#> GSM312860 2 0.0632 0.913 0.000 0.976 0.000 0.024 0.000 0.000
#> GSM312861 4 0.0260 0.978 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM312862 4 0.1563 0.941 0.000 0.056 0.000 0.932 0.012 0.000
#> GSM312863 4 0.0547 0.976 0.000 0.020 0.000 0.980 0.000 0.000
#> GSM312864 2 0.5880 0.495 0.000 0.580 0.000 0.212 0.028 0.180
#> GSM312865 4 0.0547 0.976 0.000 0.020 0.000 0.980 0.000 0.000
#> GSM312867 4 0.0260 0.978 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM312868 4 0.0547 0.976 0.000 0.020 0.000 0.980 0.000 0.000
#> GSM312869 2 0.0146 0.921 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM312870 3 0.0000 0.927 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312872 3 0.0000 0.927 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312874 3 0.0000 0.927 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312875 3 0.0000 0.927 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312876 3 0.0000 0.927 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312877 3 0.6041 -0.314 0.272 0.000 0.416 0.000 0.000 0.312
#> GSM312879 3 0.0000 0.927 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312882 3 0.0000 0.927 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312883 3 0.0000 0.927 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312886 3 0.0000 0.927 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312887 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312890 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312893 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312894 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312895 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312937 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312938 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312939 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312940 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312941 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312942 6 0.3151 1.000 0.252 0.000 0.000 0.000 0.000 0.748
#> GSM312943 6 0.3151 1.000 0.252 0.000 0.000 0.000 0.000 0.748
#> GSM312944 6 0.3151 1.000 0.252 0.000 0.000 0.000 0.000 0.748
#> GSM312945 6 0.3151 1.000 0.252 0.000 0.000 0.000 0.000 0.748
#> GSM312946 6 0.3151 1.000 0.252 0.000 0.000 0.000 0.000 0.748
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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 5)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:hclust 67 1.68e-10 2
#> CV:hclust 67 6.34e-10 3
#> CV:hclust 66 8.68e-18 4
#> CV:hclust 66 4.32e-21 5
#> CV:hclust 65 7.90e-29 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "kmeans"]
# you can also extract it by
# res = res_list["CV:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 67 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 0.994 0.997 0.4767 0.525 0.525
#> 3 3 0.640 0.812 0.797 0.2559 1.000 1.000
#> 4 4 0.614 0.786 0.757 0.1655 0.737 0.499
#> 5 5 0.691 0.785 0.808 0.0887 0.964 0.862
#> 6 6 0.763 0.754 0.773 0.0583 0.960 0.823
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
#> GSM312811 2 0.00 0.996 0.00 1.00
#> GSM312812 2 0.00 0.996 0.00 1.00
#> GSM312813 2 0.00 0.996 0.00 1.00
#> GSM312814 2 0.00 0.996 0.00 1.00
#> GSM312815 2 0.00 0.996 0.00 1.00
#> GSM312816 2 0.00 0.996 0.00 1.00
#> GSM312817 2 0.00 0.996 0.00 1.00
#> GSM312818 2 0.00 0.996 0.00 1.00
#> GSM312819 2 0.00 0.996 0.00 1.00
#> GSM312820 2 0.00 0.996 0.00 1.00
#> GSM312821 2 0.00 0.996 0.00 1.00
#> GSM312822 2 0.00 0.996 0.00 1.00
#> GSM312823 2 0.00 0.996 0.00 1.00
#> GSM312824 2 0.00 0.996 0.00 1.00
#> GSM312825 2 0.00 0.996 0.00 1.00
#> GSM312826 2 0.00 0.996 0.00 1.00
#> GSM312839 2 0.00 0.996 0.00 1.00
#> GSM312840 2 0.00 0.996 0.00 1.00
#> GSM312841 2 0.00 0.996 0.00 1.00
#> GSM312843 2 0.00 0.996 0.00 1.00
#> GSM312844 2 0.00 0.996 0.00 1.00
#> GSM312845 2 0.68 0.780 0.18 0.82
#> GSM312846 2 0.00 0.996 0.00 1.00
#> GSM312847 2 0.00 0.996 0.00 1.00
#> GSM312848 2 0.00 0.996 0.00 1.00
#> GSM312849 2 0.00 0.996 0.00 1.00
#> GSM312851 2 0.00 0.996 0.00 1.00
#> GSM312853 2 0.00 0.996 0.00 1.00
#> GSM312854 2 0.00 0.996 0.00 1.00
#> GSM312856 2 0.00 0.996 0.00 1.00
#> GSM312857 2 0.00 0.996 0.00 1.00
#> GSM312858 2 0.00 0.996 0.00 1.00
#> GSM312859 2 0.00 0.996 0.00 1.00
#> GSM312860 2 0.00 0.996 0.00 1.00
#> GSM312861 2 0.00 0.996 0.00 1.00
#> GSM312862 2 0.00 0.996 0.00 1.00
#> GSM312863 2 0.00 0.996 0.00 1.00
#> GSM312864 2 0.00 0.996 0.00 1.00
#> GSM312865 2 0.00 0.996 0.00 1.00
#> GSM312867 2 0.00 0.996 0.00 1.00
#> GSM312868 2 0.00 0.996 0.00 1.00
#> GSM312869 2 0.00 0.996 0.00 1.00
#> GSM312870 1 0.00 1.000 1.00 0.00
#> GSM312872 1 0.00 1.000 1.00 0.00
#> GSM312874 1 0.00 1.000 1.00 0.00
#> GSM312875 1 0.00 1.000 1.00 0.00
#> GSM312876 1 0.00 1.000 1.00 0.00
#> GSM312877 1 0.00 1.000 1.00 0.00
#> GSM312879 1 0.00 1.000 1.00 0.00
#> GSM312882 1 0.00 1.000 1.00 0.00
#> GSM312883 1 0.00 1.000 1.00 0.00
#> GSM312886 1 0.00 1.000 1.00 0.00
#> GSM312887 1 0.00 1.000 1.00 0.00
#> GSM312890 1 0.00 1.000 1.00 0.00
#> GSM312893 1 0.00 1.000 1.00 0.00
#> GSM312894 1 0.00 1.000 1.00 0.00
#> GSM312895 1 0.00 1.000 1.00 0.00
#> GSM312937 1 0.00 1.000 1.00 0.00
#> GSM312938 1 0.00 1.000 1.00 0.00
#> GSM312939 1 0.00 1.000 1.00 0.00
#> GSM312940 1 0.00 1.000 1.00 0.00
#> GSM312941 1 0.00 1.000 1.00 0.00
#> GSM312942 1 0.00 1.000 1.00 0.00
#> GSM312943 1 0.00 1.000 1.00 0.00
#> GSM312944 1 0.00 1.000 1.00 0.00
#> GSM312945 1 0.00 1.000 1.00 0.00
#> GSM312946 1 0.00 1.000 1.00 0.00
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM312811 2 0.341 0.805 0.000 0.876 0.124
#> GSM312812 2 0.116 0.826 0.000 0.972 0.028
#> GSM312813 2 0.000 0.834 0.000 1.000 0.000
#> GSM312814 2 0.341 0.805 0.000 0.876 0.124
#> GSM312815 2 0.116 0.826 0.000 0.972 0.028
#> GSM312816 2 0.424 0.784 0.000 0.824 0.176
#> GSM312817 2 0.000 0.834 0.000 1.000 0.000
#> GSM312818 2 0.424 0.784 0.000 0.824 0.176
#> GSM312819 2 0.362 0.802 0.000 0.864 0.136
#> GSM312820 2 0.424 0.784 0.000 0.824 0.176
#> GSM312821 2 0.424 0.784 0.000 0.824 0.176
#> GSM312822 2 0.341 0.805 0.000 0.876 0.124
#> GSM312823 2 0.000 0.834 0.000 1.000 0.000
#> GSM312824 2 0.000 0.834 0.000 1.000 0.000
#> GSM312825 2 0.000 0.834 0.000 1.000 0.000
#> GSM312826 2 0.000 0.834 0.000 1.000 0.000
#> GSM312839 2 0.000 0.834 0.000 1.000 0.000
#> GSM312840 2 0.000 0.834 0.000 1.000 0.000
#> GSM312841 2 0.141 0.824 0.000 0.964 0.036
#> GSM312843 2 0.562 0.797 0.000 0.692 0.308
#> GSM312844 2 0.000 0.834 0.000 1.000 0.000
#> GSM312845 2 0.795 0.737 0.084 0.608 0.308
#> GSM312846 2 0.562 0.797 0.000 0.692 0.308
#> GSM312847 2 0.562 0.797 0.000 0.692 0.308
#> GSM312848 2 0.562 0.797 0.000 0.692 0.308
#> GSM312849 2 0.562 0.797 0.000 0.692 0.308
#> GSM312851 2 0.623 0.766 0.000 0.564 0.436
#> GSM312853 2 0.622 0.767 0.000 0.568 0.432
#> GSM312854 2 0.620 0.770 0.000 0.576 0.424
#> GSM312856 2 0.620 0.770 0.000 0.576 0.424
#> GSM312857 2 0.622 0.767 0.000 0.568 0.432
#> GSM312858 2 0.562 0.797 0.000 0.692 0.308
#> GSM312859 2 0.103 0.835 0.000 0.976 0.024
#> GSM312860 2 0.116 0.836 0.000 0.972 0.028
#> GSM312861 2 0.562 0.797 0.000 0.692 0.308
#> GSM312862 2 0.562 0.797 0.000 0.692 0.308
#> GSM312863 2 0.620 0.770 0.000 0.576 0.424
#> GSM312864 2 0.450 0.817 0.000 0.804 0.196
#> GSM312865 2 0.562 0.797 0.000 0.692 0.308
#> GSM312867 2 0.562 0.797 0.000 0.692 0.308
#> GSM312868 2 0.562 0.797 0.000 0.692 0.308
#> GSM312869 2 0.000 0.834 0.000 1.000 0.000
#> GSM312870 1 0.630 0.812 0.516 0.000 0.484
#> GSM312872 1 0.630 0.812 0.516 0.000 0.484
#> GSM312874 1 0.630 0.812 0.516 0.000 0.484
#> GSM312875 1 0.630 0.812 0.516 0.000 0.484
#> GSM312876 1 0.630 0.812 0.516 0.000 0.484
#> GSM312877 1 0.617 0.824 0.588 0.000 0.412
#> GSM312879 1 0.630 0.812 0.516 0.000 0.484
#> GSM312882 1 0.630 0.812 0.516 0.000 0.484
#> GSM312883 1 0.630 0.812 0.516 0.000 0.484
#> GSM312886 1 0.630 0.812 0.516 0.000 0.484
#> GSM312887 1 0.000 0.829 1.000 0.000 0.000
#> GSM312890 1 0.000 0.829 1.000 0.000 0.000
#> GSM312893 1 0.000 0.829 1.000 0.000 0.000
#> GSM312894 1 0.000 0.829 1.000 0.000 0.000
#> GSM312895 1 0.000 0.829 1.000 0.000 0.000
#> GSM312937 1 0.000 0.829 1.000 0.000 0.000
#> GSM312938 1 0.000 0.829 1.000 0.000 0.000
#> GSM312939 1 0.000 0.829 1.000 0.000 0.000
#> GSM312940 1 0.000 0.829 1.000 0.000 0.000
#> GSM312941 1 0.000 0.829 1.000 0.000 0.000
#> GSM312942 1 0.497 0.842 0.764 0.000 0.236
#> GSM312943 1 0.497 0.842 0.764 0.000 0.236
#> GSM312944 1 0.497 0.842 0.764 0.000 0.236
#> GSM312945 1 0.497 0.842 0.764 0.000 0.236
#> GSM312946 1 0.497 0.842 0.764 0.000 0.236
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM312811 2 0.3764 0.771 0.000 0.852 0.072 0.076
#> GSM312812 2 0.1022 0.815 0.000 0.968 0.032 0.000
#> GSM312813 2 0.2131 0.819 0.000 0.932 0.032 0.036
#> GSM312814 2 0.4621 0.741 0.000 0.796 0.128 0.076
#> GSM312815 2 0.1398 0.812 0.000 0.956 0.040 0.004
#> GSM312816 2 0.7048 0.541 0.000 0.556 0.284 0.160
#> GSM312817 2 0.2565 0.818 0.000 0.912 0.032 0.056
#> GSM312818 2 0.7048 0.541 0.000 0.556 0.284 0.160
#> GSM312819 2 0.2654 0.785 0.000 0.888 0.004 0.108
#> GSM312820 2 0.7048 0.541 0.000 0.556 0.284 0.160
#> GSM312821 2 0.7048 0.541 0.000 0.556 0.284 0.160
#> GSM312822 2 0.4621 0.741 0.000 0.796 0.128 0.076
#> GSM312823 2 0.1118 0.821 0.000 0.964 0.000 0.036
#> GSM312824 2 0.1118 0.821 0.000 0.964 0.000 0.036
#> GSM312825 2 0.1118 0.821 0.000 0.964 0.000 0.036
#> GSM312826 2 0.1118 0.821 0.000 0.964 0.000 0.036
#> GSM312839 2 0.1022 0.822 0.000 0.968 0.000 0.032
#> GSM312840 2 0.1118 0.821 0.000 0.964 0.000 0.036
#> GSM312841 2 0.0188 0.819 0.000 0.996 0.004 0.000
#> GSM312843 4 0.4988 0.868 0.000 0.288 0.020 0.692
#> GSM312844 2 0.1022 0.822 0.000 0.968 0.000 0.032
#> GSM312845 4 0.5309 0.857 0.028 0.280 0.004 0.688
#> GSM312846 4 0.4632 0.878 0.000 0.308 0.004 0.688
#> GSM312847 4 0.4632 0.878 0.000 0.308 0.004 0.688
#> GSM312848 4 0.4632 0.878 0.000 0.308 0.004 0.688
#> GSM312849 4 0.4677 0.872 0.000 0.316 0.004 0.680
#> GSM312851 4 0.5637 0.765 0.000 0.168 0.112 0.720
#> GSM312853 4 0.5637 0.765 0.000 0.168 0.112 0.720
#> GSM312854 4 0.5582 0.768 0.000 0.168 0.108 0.724
#> GSM312856 4 0.5582 0.768 0.000 0.168 0.108 0.724
#> GSM312857 4 0.5637 0.765 0.000 0.168 0.112 0.720
#> GSM312858 4 0.4454 0.879 0.000 0.308 0.000 0.692
#> GSM312859 2 0.1637 0.801 0.000 0.940 0.000 0.060
#> GSM312860 2 0.2149 0.770 0.000 0.912 0.000 0.088
#> GSM312861 4 0.4677 0.872 0.000 0.316 0.004 0.680
#> GSM312862 4 0.4454 0.879 0.000 0.308 0.000 0.692
#> GSM312863 4 0.4789 0.796 0.000 0.172 0.056 0.772
#> GSM312864 2 0.6357 0.215 0.000 0.544 0.068 0.388
#> GSM312865 4 0.4454 0.879 0.000 0.308 0.000 0.692
#> GSM312867 4 0.4677 0.872 0.000 0.316 0.004 0.680
#> GSM312868 4 0.4454 0.879 0.000 0.308 0.000 0.692
#> GSM312869 2 0.1118 0.821 0.000 0.964 0.000 0.036
#> GSM312870 3 0.4804 0.978 0.384 0.000 0.616 0.000
#> GSM312872 3 0.4804 0.978 0.384 0.000 0.616 0.000
#> GSM312874 3 0.4804 0.978 0.384 0.000 0.616 0.000
#> GSM312875 3 0.4804 0.978 0.384 0.000 0.616 0.000
#> GSM312876 3 0.4804 0.978 0.384 0.000 0.616 0.000
#> GSM312877 3 0.5472 0.871 0.440 0.000 0.544 0.016
#> GSM312879 3 0.5339 0.976 0.384 0.000 0.600 0.016
#> GSM312882 3 0.5339 0.976 0.384 0.000 0.600 0.016
#> GSM312883 3 0.5339 0.976 0.384 0.000 0.600 0.016
#> GSM312886 3 0.5339 0.976 0.384 0.000 0.600 0.016
#> GSM312887 1 0.0000 0.803 1.000 0.000 0.000 0.000
#> GSM312890 1 0.0000 0.803 1.000 0.000 0.000 0.000
#> GSM312893 1 0.0000 0.803 1.000 0.000 0.000 0.000
#> GSM312894 1 0.0000 0.803 1.000 0.000 0.000 0.000
#> GSM312895 1 0.0000 0.803 1.000 0.000 0.000 0.000
#> GSM312937 1 0.0000 0.803 1.000 0.000 0.000 0.000
#> GSM312938 1 0.0000 0.803 1.000 0.000 0.000 0.000
#> GSM312939 1 0.0000 0.803 1.000 0.000 0.000 0.000
#> GSM312940 1 0.0000 0.803 1.000 0.000 0.000 0.000
#> GSM312941 1 0.0000 0.803 1.000 0.000 0.000 0.000
#> GSM312942 1 0.6449 0.440 0.636 0.000 0.232 0.132
#> GSM312943 1 0.6449 0.440 0.636 0.000 0.232 0.132
#> GSM312944 1 0.6449 0.440 0.636 0.000 0.232 0.132
#> GSM312945 1 0.6449 0.440 0.636 0.000 0.232 0.132
#> GSM312946 1 0.6449 0.440 0.636 0.000 0.232 0.132
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM312811 2 0.4819 0.6691 0.000 0.768 0.112 0.036 0.084
#> GSM312812 2 0.2529 0.8013 0.000 0.900 0.056 0.004 0.040
#> GSM312813 2 0.3709 0.7879 0.000 0.832 0.108 0.016 0.044
#> GSM312814 2 0.6032 0.2948 0.000 0.624 0.084 0.036 0.256
#> GSM312815 2 0.2153 0.8003 0.000 0.916 0.040 0.000 0.044
#> GSM312816 5 0.4890 1.0000 0.000 0.256 0.000 0.064 0.680
#> GSM312817 2 0.3809 0.7853 0.000 0.824 0.116 0.016 0.044
#> GSM312818 5 0.4890 1.0000 0.000 0.256 0.000 0.064 0.680
#> GSM312819 2 0.3373 0.7610 0.000 0.848 0.092 0.056 0.004
#> GSM312820 5 0.4890 1.0000 0.000 0.256 0.000 0.064 0.680
#> GSM312821 5 0.4890 1.0000 0.000 0.256 0.000 0.064 0.680
#> GSM312822 2 0.6032 0.2948 0.000 0.624 0.084 0.036 0.256
#> GSM312823 2 0.1012 0.8369 0.000 0.968 0.012 0.020 0.000
#> GSM312824 2 0.0609 0.8362 0.000 0.980 0.000 0.020 0.000
#> GSM312825 2 0.0609 0.8362 0.000 0.980 0.000 0.020 0.000
#> GSM312826 2 0.0609 0.8362 0.000 0.980 0.000 0.020 0.000
#> GSM312839 2 0.1216 0.8363 0.000 0.960 0.020 0.020 0.000
#> GSM312840 2 0.1630 0.8302 0.000 0.944 0.036 0.016 0.004
#> GSM312841 2 0.0955 0.8301 0.000 0.968 0.028 0.004 0.000
#> GSM312843 4 0.3773 0.8625 0.000 0.108 0.060 0.824 0.008
#> GSM312844 2 0.1012 0.8369 0.000 0.968 0.012 0.020 0.000
#> GSM312845 4 0.2858 0.8753 0.008 0.100 0.012 0.876 0.004
#> GSM312846 4 0.2733 0.8779 0.000 0.112 0.012 0.872 0.004
#> GSM312847 4 0.2681 0.8788 0.000 0.108 0.012 0.876 0.004
#> GSM312848 4 0.2629 0.8794 0.000 0.104 0.012 0.880 0.004
#> GSM312849 4 0.2783 0.8763 0.000 0.116 0.012 0.868 0.004
#> GSM312851 4 0.5371 0.7266 0.000 0.032 0.124 0.720 0.124
#> GSM312853 4 0.5431 0.7356 0.000 0.040 0.124 0.720 0.116
#> GSM312854 4 0.5290 0.7461 0.000 0.040 0.124 0.732 0.104
#> GSM312856 4 0.5290 0.7461 0.000 0.040 0.124 0.732 0.104
#> GSM312857 4 0.5431 0.7356 0.000 0.040 0.124 0.720 0.116
#> GSM312858 4 0.2233 0.8797 0.000 0.104 0.000 0.892 0.004
#> GSM312859 2 0.1743 0.8251 0.000 0.940 0.028 0.028 0.004
#> GSM312860 2 0.1644 0.8126 0.000 0.940 0.008 0.048 0.004
#> GSM312861 4 0.3107 0.8699 0.000 0.124 0.016 0.852 0.008
#> GSM312862 4 0.2548 0.8770 0.000 0.116 0.004 0.876 0.004
#> GSM312863 4 0.4101 0.7926 0.000 0.040 0.124 0.808 0.028
#> GSM312864 2 0.7581 -0.0871 0.000 0.420 0.152 0.348 0.080
#> GSM312865 4 0.2074 0.8798 0.000 0.104 0.000 0.896 0.000
#> GSM312867 4 0.2783 0.8763 0.000 0.116 0.012 0.868 0.004
#> GSM312868 4 0.2517 0.8788 0.000 0.104 0.008 0.884 0.004
#> GSM312869 2 0.0771 0.8359 0.000 0.976 0.004 0.020 0.000
#> GSM312870 3 0.3774 0.9635 0.296 0.000 0.704 0.000 0.000
#> GSM312872 3 0.3774 0.9635 0.296 0.000 0.704 0.000 0.000
#> GSM312874 3 0.3774 0.9635 0.296 0.000 0.704 0.000 0.000
#> GSM312875 3 0.3774 0.9635 0.296 0.000 0.704 0.000 0.000
#> GSM312876 3 0.3774 0.9635 0.296 0.000 0.704 0.000 0.000
#> GSM312877 3 0.5396 0.8579 0.360 0.000 0.588 0.020 0.032
#> GSM312879 3 0.4811 0.9596 0.296 0.000 0.668 0.016 0.020
#> GSM312882 3 0.5142 0.9537 0.296 0.000 0.652 0.020 0.032
#> GSM312883 3 0.5142 0.9537 0.296 0.000 0.652 0.020 0.032
#> GSM312886 3 0.4901 0.9585 0.296 0.000 0.664 0.020 0.020
#> GSM312887 1 0.0510 0.7747 0.984 0.000 0.000 0.000 0.016
#> GSM312890 1 0.0000 0.7807 1.000 0.000 0.000 0.000 0.000
#> GSM312893 1 0.0000 0.7807 1.000 0.000 0.000 0.000 0.000
#> GSM312894 1 0.0000 0.7807 1.000 0.000 0.000 0.000 0.000
#> GSM312895 1 0.0000 0.7807 1.000 0.000 0.000 0.000 0.000
#> GSM312937 1 0.0000 0.7807 1.000 0.000 0.000 0.000 0.000
#> GSM312938 1 0.0510 0.7747 0.984 0.000 0.000 0.000 0.016
#> GSM312939 1 0.0000 0.7807 1.000 0.000 0.000 0.000 0.000
#> GSM312940 1 0.0000 0.7807 1.000 0.000 0.000 0.000 0.000
#> GSM312941 1 0.0000 0.7807 1.000 0.000 0.000 0.000 0.000
#> GSM312942 1 0.6733 0.4116 0.532 0.000 0.212 0.020 0.236
#> GSM312943 1 0.6733 0.4116 0.532 0.000 0.212 0.020 0.236
#> GSM312944 1 0.6733 0.4116 0.532 0.000 0.212 0.020 0.236
#> GSM312945 1 0.6733 0.4116 0.532 0.000 0.212 0.020 0.236
#> GSM312946 1 0.6733 0.4116 0.532 0.000 0.212 0.020 0.236
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM312811 2 0.6000 0.632 0.000 0.620 0.096 0.000 0.152 0.132
#> GSM312812 2 0.3489 0.792 0.000 0.836 0.052 0.000 0.064 0.048
#> GSM312813 2 0.5083 0.738 0.000 0.712 0.096 0.000 0.072 0.120
#> GSM312814 2 0.6275 0.283 0.000 0.496 0.076 0.000 0.340 0.088
#> GSM312815 2 0.3474 0.789 0.000 0.836 0.048 0.000 0.072 0.044
#> GSM312816 5 0.1910 1.000 0.000 0.108 0.000 0.000 0.892 0.000
#> GSM312817 2 0.5216 0.733 0.000 0.700 0.100 0.000 0.076 0.124
#> GSM312818 5 0.1910 1.000 0.000 0.108 0.000 0.000 0.892 0.000
#> GSM312819 2 0.4006 0.769 0.000 0.796 0.060 0.004 0.028 0.112
#> GSM312820 5 0.1910 1.000 0.000 0.108 0.000 0.000 0.892 0.000
#> GSM312821 5 0.1910 1.000 0.000 0.108 0.000 0.000 0.892 0.000
#> GSM312822 2 0.6275 0.283 0.000 0.496 0.076 0.000 0.340 0.088
#> GSM312823 2 0.1409 0.832 0.000 0.948 0.012 0.008 0.000 0.032
#> GSM312824 2 0.0260 0.832 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM312825 2 0.0260 0.832 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM312826 2 0.0260 0.832 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM312839 2 0.1890 0.830 0.000 0.924 0.024 0.008 0.000 0.044
#> GSM312840 2 0.1821 0.823 0.000 0.928 0.024 0.000 0.008 0.040
#> GSM312841 2 0.1624 0.825 0.000 0.936 0.020 0.000 0.004 0.040
#> GSM312843 4 0.5191 0.469 0.000 0.064 0.044 0.696 0.012 0.184
#> GSM312844 2 0.1426 0.832 0.000 0.948 0.016 0.008 0.000 0.028
#> GSM312845 4 0.1408 0.860 0.000 0.036 0.020 0.944 0.000 0.000
#> GSM312846 4 0.1480 0.860 0.000 0.040 0.020 0.940 0.000 0.000
#> GSM312847 4 0.1408 0.860 0.000 0.036 0.020 0.944 0.000 0.000
#> GSM312848 4 0.1552 0.859 0.000 0.036 0.020 0.940 0.000 0.004
#> GSM312849 4 0.1480 0.860 0.000 0.040 0.020 0.940 0.000 0.000
#> GSM312851 6 0.5516 0.784 0.000 0.004 0.000 0.424 0.112 0.460
#> GSM312853 6 0.5634 0.796 0.000 0.012 0.000 0.424 0.104 0.460
#> GSM312854 6 0.5602 0.793 0.000 0.012 0.000 0.428 0.100 0.460
#> GSM312856 6 0.5602 0.793 0.000 0.012 0.000 0.428 0.100 0.460
#> GSM312857 6 0.5634 0.796 0.000 0.012 0.000 0.424 0.104 0.460
#> GSM312858 4 0.1867 0.846 0.000 0.036 0.000 0.924 0.004 0.036
#> GSM312859 2 0.2402 0.813 0.000 0.908 0.024 0.028 0.012 0.028
#> GSM312860 2 0.1723 0.805 0.000 0.932 0.004 0.048 0.012 0.004
#> GSM312861 4 0.1964 0.838 0.000 0.056 0.004 0.920 0.012 0.008
#> GSM312862 4 0.2569 0.825 0.000 0.044 0.012 0.892 0.004 0.048
#> GSM312863 4 0.4555 -0.593 0.000 0.012 0.000 0.532 0.016 0.440
#> GSM312864 6 0.8100 0.184 0.000 0.308 0.056 0.208 0.104 0.324
#> GSM312865 4 0.1572 0.848 0.000 0.036 0.000 0.936 0.000 0.028
#> GSM312867 4 0.1480 0.860 0.000 0.040 0.020 0.940 0.000 0.000
#> GSM312868 4 0.2224 0.839 0.000 0.036 0.004 0.912 0.012 0.036
#> GSM312869 2 0.0405 0.832 0.000 0.988 0.000 0.008 0.000 0.004
#> GSM312870 3 0.2491 0.952 0.164 0.000 0.836 0.000 0.000 0.000
#> GSM312872 3 0.2491 0.952 0.164 0.000 0.836 0.000 0.000 0.000
#> GSM312874 3 0.2491 0.952 0.164 0.000 0.836 0.000 0.000 0.000
#> GSM312875 3 0.2491 0.952 0.164 0.000 0.836 0.000 0.000 0.000
#> GSM312876 3 0.2491 0.952 0.164 0.000 0.836 0.000 0.000 0.000
#> GSM312877 3 0.5184 0.863 0.228 0.000 0.676 0.028 0.024 0.044
#> GSM312879 3 0.3846 0.948 0.164 0.000 0.784 0.008 0.012 0.032
#> GSM312882 3 0.4724 0.936 0.164 0.000 0.740 0.028 0.024 0.044
#> GSM312883 3 0.4724 0.936 0.164 0.000 0.740 0.028 0.024 0.044
#> GSM312886 3 0.4356 0.943 0.164 0.000 0.760 0.016 0.024 0.036
#> GSM312887 1 0.0806 0.761 0.972 0.000 0.000 0.000 0.020 0.008
#> GSM312890 1 0.0000 0.770 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312893 1 0.0000 0.770 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312894 1 0.0000 0.770 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312895 1 0.0000 0.770 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312937 1 0.0000 0.770 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312938 1 0.0806 0.761 0.972 0.000 0.000 0.000 0.020 0.008
#> GSM312939 1 0.0000 0.770 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312940 1 0.0000 0.770 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312941 1 0.0000 0.770 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312942 1 0.6739 0.393 0.420 0.000 0.204 0.000 0.052 0.324
#> GSM312943 1 0.6739 0.393 0.420 0.000 0.204 0.000 0.052 0.324
#> GSM312944 1 0.6739 0.393 0.420 0.000 0.204 0.000 0.052 0.324
#> GSM312945 1 0.6739 0.393 0.420 0.000 0.204 0.000 0.052 0.324
#> GSM312946 1 0.6739 0.393 0.420 0.000 0.204 0.000 0.052 0.324
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:kmeans 67 1.68e-10 2
#> CV:kmeans 67 1.68e-10 3
#> CV:kmeans 61 6.59e-22 4
#> CV:kmeans 59 7.92e-20 5
#> CV:kmeans 57 6.84e-26 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "skmeans"]
# you can also extract it by
# res = res_list["CV:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 67 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.992 0.996 0.4832 0.518 0.518
#> 3 3 1.000 0.950 0.967 0.3837 0.796 0.613
#> 4 4 0.827 0.883 0.923 0.1043 0.932 0.794
#> 5 5 0.817 0.756 0.839 0.0589 0.964 0.871
#> 6 6 0.838 0.794 0.845 0.0462 0.877 0.564
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
#> GSM312811 2 0.000 0.996 0.000 1.000
#> GSM312812 2 0.000 0.996 0.000 1.000
#> GSM312813 2 0.000 0.996 0.000 1.000
#> GSM312814 2 0.000 0.996 0.000 1.000
#> GSM312815 2 0.000 0.996 0.000 1.000
#> GSM312816 2 0.000 0.996 0.000 1.000
#> GSM312817 2 0.000 0.996 0.000 1.000
#> GSM312818 2 0.000 0.996 0.000 1.000
#> GSM312819 2 0.000 0.996 0.000 1.000
#> GSM312820 2 0.000 0.996 0.000 1.000
#> GSM312821 2 0.000 0.996 0.000 1.000
#> GSM312822 2 0.000 0.996 0.000 1.000
#> GSM312823 2 0.000 0.996 0.000 1.000
#> GSM312824 2 0.000 0.996 0.000 1.000
#> GSM312825 2 0.000 0.996 0.000 1.000
#> GSM312826 2 0.000 0.996 0.000 1.000
#> GSM312839 2 0.000 0.996 0.000 1.000
#> GSM312840 2 0.000 0.996 0.000 1.000
#> GSM312841 2 0.000 0.996 0.000 1.000
#> GSM312843 2 0.000 0.996 0.000 1.000
#> GSM312844 2 0.000 0.996 0.000 1.000
#> GSM312845 1 0.373 0.922 0.928 0.072
#> GSM312846 2 0.671 0.785 0.176 0.824
#> GSM312847 2 0.000 0.996 0.000 1.000
#> GSM312848 2 0.000 0.996 0.000 1.000
#> GSM312849 2 0.000 0.996 0.000 1.000
#> GSM312851 2 0.000 0.996 0.000 1.000
#> GSM312853 2 0.000 0.996 0.000 1.000
#> GSM312854 2 0.000 0.996 0.000 1.000
#> GSM312856 2 0.000 0.996 0.000 1.000
#> GSM312857 2 0.000 0.996 0.000 1.000
#> GSM312858 2 0.000 0.996 0.000 1.000
#> GSM312859 2 0.000 0.996 0.000 1.000
#> GSM312860 2 0.000 0.996 0.000 1.000
#> GSM312861 2 0.000 0.996 0.000 1.000
#> GSM312862 2 0.000 0.996 0.000 1.000
#> GSM312863 2 0.000 0.996 0.000 1.000
#> GSM312864 2 0.000 0.996 0.000 1.000
#> GSM312865 2 0.000 0.996 0.000 1.000
#> GSM312867 2 0.000 0.996 0.000 1.000
#> GSM312868 2 0.000 0.996 0.000 1.000
#> GSM312869 2 0.000 0.996 0.000 1.000
#> GSM312870 1 0.000 0.997 1.000 0.000
#> GSM312872 1 0.000 0.997 1.000 0.000
#> GSM312874 1 0.000 0.997 1.000 0.000
#> GSM312875 1 0.000 0.997 1.000 0.000
#> GSM312876 1 0.000 0.997 1.000 0.000
#> GSM312877 1 0.000 0.997 1.000 0.000
#> GSM312879 1 0.000 0.997 1.000 0.000
#> GSM312882 1 0.000 0.997 1.000 0.000
#> GSM312883 1 0.000 0.997 1.000 0.000
#> GSM312886 1 0.000 0.997 1.000 0.000
#> GSM312887 1 0.000 0.997 1.000 0.000
#> GSM312890 1 0.000 0.997 1.000 0.000
#> GSM312893 1 0.000 0.997 1.000 0.000
#> GSM312894 1 0.000 0.997 1.000 0.000
#> GSM312895 1 0.000 0.997 1.000 0.000
#> GSM312937 1 0.000 0.997 1.000 0.000
#> GSM312938 1 0.000 0.997 1.000 0.000
#> GSM312939 1 0.000 0.997 1.000 0.000
#> GSM312940 1 0.000 0.997 1.000 0.000
#> GSM312941 1 0.000 0.997 1.000 0.000
#> GSM312942 1 0.000 0.997 1.000 0.000
#> GSM312943 1 0.000 0.997 1.000 0.000
#> GSM312944 1 0.000 0.997 1.000 0.000
#> GSM312945 1 0.000 0.997 1.000 0.000
#> GSM312946 1 0.000 0.997 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM312811 2 0.1964 0.939 0.000 0.944 0.056
#> GSM312812 2 0.0000 0.959 0.000 1.000 0.000
#> GSM312813 2 0.0000 0.959 0.000 1.000 0.000
#> GSM312814 2 0.1964 0.939 0.000 0.944 0.056
#> GSM312815 2 0.0000 0.959 0.000 1.000 0.000
#> GSM312816 2 0.1964 0.939 0.000 0.944 0.056
#> GSM312817 2 0.0000 0.959 0.000 1.000 0.000
#> GSM312818 2 0.1964 0.939 0.000 0.944 0.056
#> GSM312819 2 0.1529 0.946 0.000 0.960 0.040
#> GSM312820 2 0.1964 0.939 0.000 0.944 0.056
#> GSM312821 2 0.1964 0.939 0.000 0.944 0.056
#> GSM312822 2 0.1964 0.939 0.000 0.944 0.056
#> GSM312823 2 0.0000 0.959 0.000 1.000 0.000
#> GSM312824 2 0.0000 0.959 0.000 1.000 0.000
#> GSM312825 2 0.0000 0.959 0.000 1.000 0.000
#> GSM312826 2 0.0000 0.959 0.000 1.000 0.000
#> GSM312839 2 0.0000 0.959 0.000 1.000 0.000
#> GSM312840 2 0.0000 0.959 0.000 1.000 0.000
#> GSM312841 2 0.0000 0.959 0.000 1.000 0.000
#> GSM312843 3 0.3038 0.906 0.000 0.104 0.896
#> GSM312844 2 0.0000 0.959 0.000 1.000 0.000
#> GSM312845 3 0.1964 0.949 0.000 0.056 0.944
#> GSM312846 3 0.1964 0.949 0.000 0.056 0.944
#> GSM312847 3 0.2261 0.954 0.000 0.068 0.932
#> GSM312848 3 0.2356 0.954 0.000 0.072 0.928
#> GSM312849 3 0.2261 0.954 0.000 0.068 0.932
#> GSM312851 3 0.0747 0.942 0.000 0.016 0.984
#> GSM312853 3 0.0747 0.942 0.000 0.016 0.984
#> GSM312854 3 0.0747 0.942 0.000 0.016 0.984
#> GSM312856 3 0.0747 0.942 0.000 0.016 0.984
#> GSM312857 3 0.0747 0.942 0.000 0.016 0.984
#> GSM312858 3 0.2356 0.954 0.000 0.072 0.928
#> GSM312859 2 0.0000 0.959 0.000 1.000 0.000
#> GSM312860 2 0.0000 0.959 0.000 1.000 0.000
#> GSM312861 3 0.2356 0.954 0.000 0.072 0.928
#> GSM312862 3 0.5678 0.634 0.000 0.316 0.684
#> GSM312863 3 0.0747 0.942 0.000 0.016 0.984
#> GSM312864 2 0.6286 0.175 0.000 0.536 0.464
#> GSM312865 3 0.2261 0.954 0.000 0.068 0.932
#> GSM312867 3 0.2066 0.951 0.000 0.060 0.940
#> GSM312868 3 0.2356 0.954 0.000 0.072 0.928
#> GSM312869 2 0.0000 0.959 0.000 1.000 0.000
#> GSM312870 1 0.0000 0.995 1.000 0.000 0.000
#> GSM312872 1 0.0000 0.995 1.000 0.000 0.000
#> GSM312874 1 0.0000 0.995 1.000 0.000 0.000
#> GSM312875 1 0.0000 0.995 1.000 0.000 0.000
#> GSM312876 1 0.0000 0.995 1.000 0.000 0.000
#> GSM312877 1 0.0000 0.995 1.000 0.000 0.000
#> GSM312879 1 0.0000 0.995 1.000 0.000 0.000
#> GSM312882 1 0.0000 0.995 1.000 0.000 0.000
#> GSM312883 1 0.0000 0.995 1.000 0.000 0.000
#> GSM312886 1 0.0000 0.995 1.000 0.000 0.000
#> GSM312887 1 0.0747 0.992 0.984 0.000 0.016
#> GSM312890 1 0.0747 0.992 0.984 0.000 0.016
#> GSM312893 1 0.0747 0.992 0.984 0.000 0.016
#> GSM312894 1 0.0747 0.992 0.984 0.000 0.016
#> GSM312895 1 0.0747 0.992 0.984 0.000 0.016
#> GSM312937 1 0.0747 0.992 0.984 0.000 0.016
#> GSM312938 1 0.0747 0.992 0.984 0.000 0.016
#> GSM312939 1 0.0747 0.992 0.984 0.000 0.016
#> GSM312940 1 0.0747 0.992 0.984 0.000 0.016
#> GSM312941 1 0.0747 0.992 0.984 0.000 0.016
#> GSM312942 1 0.0000 0.995 1.000 0.000 0.000
#> GSM312943 1 0.0000 0.995 1.000 0.000 0.000
#> GSM312944 1 0.0000 0.995 1.000 0.000 0.000
#> GSM312945 1 0.0000 0.995 1.000 0.000 0.000
#> GSM312946 1 0.0000 0.995 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM312811 2 0.2676 0.894 0.012 0.896 0.000 0.092
#> GSM312812 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> GSM312813 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> GSM312814 2 0.2676 0.894 0.012 0.896 0.000 0.092
#> GSM312815 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> GSM312816 2 0.3404 0.875 0.032 0.864 0.000 0.104
#> GSM312817 2 0.0188 0.937 0.000 0.996 0.000 0.004
#> GSM312818 2 0.4975 0.833 0.032 0.804 0.060 0.104
#> GSM312819 2 0.0469 0.934 0.000 0.988 0.000 0.012
#> GSM312820 2 0.3404 0.875 0.032 0.864 0.000 0.104
#> GSM312821 2 0.3404 0.875 0.032 0.864 0.000 0.104
#> GSM312822 2 0.2676 0.894 0.012 0.896 0.000 0.092
#> GSM312823 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> GSM312824 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> GSM312825 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> GSM312826 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> GSM312839 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> GSM312840 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> GSM312841 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> GSM312843 4 0.2775 0.883 0.020 0.084 0.000 0.896
#> GSM312844 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> GSM312845 4 0.4008 0.703 0.244 0.000 0.000 0.756
#> GSM312846 4 0.4764 0.731 0.220 0.032 0.000 0.748
#> GSM312847 4 0.2466 0.897 0.004 0.096 0.000 0.900
#> GSM312848 4 0.2401 0.898 0.004 0.092 0.000 0.904
#> GSM312849 4 0.2593 0.894 0.004 0.104 0.000 0.892
#> GSM312851 4 0.1022 0.876 0.032 0.000 0.000 0.968
#> GSM312853 4 0.0921 0.878 0.028 0.000 0.000 0.972
#> GSM312854 4 0.0921 0.878 0.028 0.000 0.000 0.972
#> GSM312856 4 0.0921 0.878 0.028 0.000 0.000 0.972
#> GSM312857 4 0.0921 0.878 0.028 0.000 0.000 0.972
#> GSM312858 4 0.2281 0.898 0.000 0.096 0.000 0.904
#> GSM312859 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> GSM312860 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> GSM312861 4 0.2593 0.894 0.004 0.104 0.000 0.892
#> GSM312862 4 0.4950 0.521 0.004 0.376 0.000 0.620
#> GSM312863 4 0.0707 0.879 0.020 0.000 0.000 0.980
#> GSM312864 2 0.5695 0.159 0.024 0.500 0.000 0.476
#> GSM312865 4 0.2281 0.898 0.000 0.096 0.000 0.904
#> GSM312867 4 0.2593 0.894 0.004 0.104 0.000 0.892
#> GSM312868 4 0.2281 0.898 0.000 0.096 0.000 0.904
#> GSM312869 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> GSM312870 3 0.0188 0.893 0.004 0.000 0.996 0.000
#> GSM312872 3 0.0188 0.893 0.004 0.000 0.996 0.000
#> GSM312874 3 0.0188 0.893 0.004 0.000 0.996 0.000
#> GSM312875 3 0.0188 0.893 0.004 0.000 0.996 0.000
#> GSM312876 3 0.0188 0.893 0.004 0.000 0.996 0.000
#> GSM312877 3 0.0188 0.893 0.004 0.000 0.996 0.000
#> GSM312879 3 0.0188 0.893 0.004 0.000 0.996 0.000
#> GSM312882 3 0.0188 0.893 0.004 0.000 0.996 0.000
#> GSM312883 3 0.0188 0.893 0.004 0.000 0.996 0.000
#> GSM312886 3 0.0188 0.893 0.004 0.000 0.996 0.000
#> GSM312887 1 0.1302 1.000 0.956 0.000 0.044 0.000
#> GSM312890 1 0.1302 1.000 0.956 0.000 0.044 0.000
#> GSM312893 1 0.1302 1.000 0.956 0.000 0.044 0.000
#> GSM312894 1 0.1302 1.000 0.956 0.000 0.044 0.000
#> GSM312895 1 0.1302 1.000 0.956 0.000 0.044 0.000
#> GSM312937 1 0.1302 1.000 0.956 0.000 0.044 0.000
#> GSM312938 1 0.1302 1.000 0.956 0.000 0.044 0.000
#> GSM312939 1 0.1302 1.000 0.956 0.000 0.044 0.000
#> GSM312940 1 0.1302 1.000 0.956 0.000 0.044 0.000
#> GSM312941 1 0.1302 1.000 0.956 0.000 0.044 0.000
#> GSM312942 3 0.4134 0.732 0.260 0.000 0.740 0.000
#> GSM312943 3 0.4134 0.732 0.260 0.000 0.740 0.000
#> GSM312944 3 0.4134 0.732 0.260 0.000 0.740 0.000
#> GSM312945 3 0.4134 0.732 0.260 0.000 0.740 0.000
#> GSM312946 3 0.4134 0.732 0.260 0.000 0.740 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM312811 2 0.4243 0.708 0.000 0.712 0.000 0.024 0.264
#> GSM312812 2 0.0703 0.837 0.000 0.976 0.000 0.000 0.024
#> GSM312813 2 0.0703 0.837 0.000 0.976 0.000 0.000 0.024
#> GSM312814 2 0.4622 0.691 0.000 0.684 0.000 0.040 0.276
#> GSM312815 2 0.0703 0.837 0.000 0.976 0.000 0.000 0.024
#> GSM312816 2 0.6650 0.471 0.000 0.448 0.000 0.272 0.280
#> GSM312817 2 0.0703 0.837 0.000 0.976 0.000 0.000 0.024
#> GSM312818 2 0.6994 0.457 0.000 0.436 0.012 0.272 0.280
#> GSM312819 2 0.0510 0.837 0.000 0.984 0.000 0.016 0.000
#> GSM312820 2 0.6650 0.471 0.000 0.448 0.000 0.272 0.280
#> GSM312821 2 0.6650 0.471 0.000 0.448 0.000 0.272 0.280
#> GSM312822 2 0.4691 0.688 0.000 0.680 0.000 0.044 0.276
#> GSM312823 2 0.0000 0.840 0.000 1.000 0.000 0.000 0.000
#> GSM312824 2 0.0000 0.840 0.000 1.000 0.000 0.000 0.000
#> GSM312825 2 0.0000 0.840 0.000 1.000 0.000 0.000 0.000
#> GSM312826 2 0.0000 0.840 0.000 1.000 0.000 0.000 0.000
#> GSM312839 2 0.0000 0.840 0.000 1.000 0.000 0.000 0.000
#> GSM312840 2 0.0000 0.840 0.000 1.000 0.000 0.000 0.000
#> GSM312841 2 0.0000 0.840 0.000 1.000 0.000 0.000 0.000
#> GSM312843 4 0.3810 0.681 0.000 0.176 0.000 0.788 0.036
#> GSM312844 2 0.0000 0.840 0.000 1.000 0.000 0.000 0.000
#> GSM312845 4 0.6206 0.692 0.152 0.000 0.000 0.504 0.344
#> GSM312846 4 0.6400 0.698 0.144 0.008 0.000 0.504 0.344
#> GSM312847 4 0.4467 0.799 0.000 0.016 0.000 0.640 0.344
#> GSM312848 4 0.4467 0.799 0.000 0.016 0.000 0.640 0.344
#> GSM312849 4 0.4794 0.795 0.000 0.032 0.000 0.624 0.344
#> GSM312851 4 0.2891 0.602 0.000 0.000 0.000 0.824 0.176
#> GSM312853 4 0.0000 0.735 0.000 0.000 0.000 1.000 0.000
#> GSM312854 4 0.0000 0.735 0.000 0.000 0.000 1.000 0.000
#> GSM312856 4 0.0000 0.735 0.000 0.000 0.000 1.000 0.000
#> GSM312857 4 0.0000 0.735 0.000 0.000 0.000 1.000 0.000
#> GSM312858 4 0.4348 0.801 0.000 0.016 0.000 0.668 0.316
#> GSM312859 2 0.0000 0.840 0.000 1.000 0.000 0.000 0.000
#> GSM312860 2 0.0510 0.831 0.000 0.984 0.000 0.000 0.016
#> GSM312861 4 0.5099 0.791 0.000 0.052 0.000 0.612 0.336
#> GSM312862 2 0.6478 -0.304 0.000 0.420 0.000 0.396 0.184
#> GSM312863 4 0.2280 0.772 0.000 0.000 0.000 0.880 0.120
#> GSM312864 4 0.5731 -0.276 0.000 0.436 0.000 0.480 0.084
#> GSM312865 4 0.4366 0.801 0.000 0.016 0.000 0.664 0.320
#> GSM312867 4 0.4467 0.799 0.000 0.016 0.000 0.640 0.344
#> GSM312868 4 0.4269 0.801 0.000 0.016 0.000 0.684 0.300
#> GSM312869 2 0.0000 0.840 0.000 1.000 0.000 0.000 0.000
#> GSM312870 3 0.0000 0.828 0.000 0.000 1.000 0.000 0.000
#> GSM312872 3 0.0000 0.828 0.000 0.000 1.000 0.000 0.000
#> GSM312874 3 0.0000 0.828 0.000 0.000 1.000 0.000 0.000
#> GSM312875 3 0.0000 0.828 0.000 0.000 1.000 0.000 0.000
#> GSM312876 3 0.0000 0.828 0.000 0.000 1.000 0.000 0.000
#> GSM312877 3 0.0000 0.828 0.000 0.000 1.000 0.000 0.000
#> GSM312879 3 0.0000 0.828 0.000 0.000 1.000 0.000 0.000
#> GSM312882 3 0.0000 0.828 0.000 0.000 1.000 0.000 0.000
#> GSM312883 3 0.0000 0.828 0.000 0.000 1.000 0.000 0.000
#> GSM312886 3 0.0000 0.828 0.000 0.000 1.000 0.000 0.000
#> GSM312887 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM312890 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM312893 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM312894 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM312895 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM312937 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM312938 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM312939 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM312940 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM312941 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM312942 3 0.6372 0.561 0.168 0.000 0.456 0.000 0.376
#> GSM312943 3 0.6372 0.561 0.168 0.000 0.456 0.000 0.376
#> GSM312944 3 0.6372 0.561 0.168 0.000 0.456 0.000 0.376
#> GSM312945 3 0.6372 0.561 0.168 0.000 0.456 0.000 0.376
#> GSM312946 3 0.6372 0.561 0.168 0.000 0.456 0.000 0.376
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM312811 2 0.5579 0.399 0.000 0.544 0.000 0.000 0.264 0.192
#> GSM312812 2 0.1564 0.863 0.000 0.936 0.000 0.000 0.040 0.024
#> GSM312813 2 0.1644 0.862 0.000 0.932 0.000 0.000 0.040 0.028
#> GSM312814 2 0.5819 0.299 0.000 0.488 0.000 0.000 0.292 0.220
#> GSM312815 2 0.1970 0.848 0.000 0.912 0.000 0.000 0.060 0.028
#> GSM312816 5 0.5242 0.440 0.000 0.176 0.000 0.000 0.608 0.216
#> GSM312817 2 0.2074 0.852 0.000 0.912 0.000 0.004 0.048 0.036
#> GSM312818 5 0.5242 0.440 0.000 0.176 0.000 0.000 0.608 0.216
#> GSM312819 2 0.0551 0.884 0.000 0.984 0.000 0.004 0.004 0.008
#> GSM312820 5 0.5242 0.440 0.000 0.176 0.000 0.000 0.608 0.216
#> GSM312821 5 0.5242 0.440 0.000 0.176 0.000 0.000 0.608 0.216
#> GSM312822 2 0.5830 0.290 0.000 0.484 0.000 0.000 0.296 0.220
#> GSM312823 2 0.0000 0.889 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312824 2 0.0000 0.889 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312825 2 0.0000 0.889 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312826 2 0.0000 0.889 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312839 2 0.0000 0.889 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312840 2 0.0146 0.888 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM312841 2 0.0146 0.889 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM312843 5 0.5869 0.321 0.000 0.172 0.000 0.288 0.528 0.012
#> GSM312844 2 0.0000 0.889 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312845 4 0.1588 0.775 0.072 0.004 0.000 0.924 0.000 0.000
#> GSM312846 4 0.1644 0.772 0.076 0.004 0.000 0.920 0.000 0.000
#> GSM312847 4 0.0146 0.809 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM312848 4 0.0458 0.806 0.000 0.000 0.000 0.984 0.016 0.000
#> GSM312849 4 0.0865 0.802 0.000 0.036 0.000 0.964 0.000 0.000
#> GSM312851 5 0.2527 0.527 0.000 0.000 0.000 0.168 0.832 0.000
#> GSM312853 5 0.3288 0.496 0.000 0.000 0.000 0.276 0.724 0.000
#> GSM312854 5 0.3309 0.492 0.000 0.000 0.000 0.280 0.720 0.000
#> GSM312856 5 0.3309 0.492 0.000 0.000 0.000 0.280 0.720 0.000
#> GSM312857 5 0.3288 0.496 0.000 0.000 0.000 0.276 0.724 0.000
#> GSM312858 4 0.2558 0.729 0.000 0.000 0.000 0.840 0.156 0.004
#> GSM312859 2 0.0146 0.887 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM312860 2 0.0458 0.878 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM312861 4 0.2544 0.741 0.000 0.120 0.000 0.864 0.012 0.004
#> GSM312862 4 0.5986 0.149 0.000 0.416 0.000 0.416 0.156 0.012
#> GSM312863 5 0.3899 0.254 0.000 0.000 0.000 0.404 0.592 0.004
#> GSM312864 5 0.5184 0.467 0.000 0.284 0.000 0.100 0.608 0.008
#> GSM312865 4 0.2482 0.735 0.000 0.000 0.000 0.848 0.148 0.004
#> GSM312867 4 0.0260 0.810 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM312868 4 0.2933 0.678 0.000 0.000 0.000 0.796 0.200 0.004
#> GSM312869 2 0.0000 0.889 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312870 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312872 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312874 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312875 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312876 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312877 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312879 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312882 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312883 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312886 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312887 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312890 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312893 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312894 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312895 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312937 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312938 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312939 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312940 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312941 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312942 6 0.3672 1.000 0.056 0.000 0.168 0.000 0.000 0.776
#> GSM312943 6 0.3672 1.000 0.056 0.000 0.168 0.000 0.000 0.776
#> GSM312944 6 0.3672 1.000 0.056 0.000 0.168 0.000 0.000 0.776
#> GSM312945 6 0.3672 1.000 0.056 0.000 0.168 0.000 0.000 0.776
#> GSM312946 6 0.3672 1.000 0.056 0.000 0.168 0.000 0.000 0.776
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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 4)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:skmeans 67 7.40e-10 2
#> CV:skmeans 66 4.75e-15 3
#> CV:skmeans 66 3.31e-23 4
#> CV:skmeans 61 1.85e-20 5
#> CV:skmeans 52 2.31e-27 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "pam"]
# you can also extract it by
# res = res_list["CV:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 67 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.998 0.999 0.4758 0.525 0.525
#> 3 3 0.962 0.941 0.958 0.1582 0.935 0.876
#> 4 4 0.907 0.946 0.949 0.0682 0.973 0.941
#> 5 5 0.827 0.843 0.931 0.2856 0.801 0.540
#> 6 6 0.917 0.859 0.945 0.0607 0.919 0.681
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 3 4
There is also optional best \(k\) = 2 3 4 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM312811 2 0.000 0.999 0.000 1.000
#> GSM312812 2 0.000 0.999 0.000 1.000
#> GSM312813 2 0.000 0.999 0.000 1.000
#> GSM312814 2 0.000 0.999 0.000 1.000
#> GSM312815 2 0.000 0.999 0.000 1.000
#> GSM312816 2 0.000 0.999 0.000 1.000
#> GSM312817 2 0.000 0.999 0.000 1.000
#> GSM312818 2 0.000 0.999 0.000 1.000
#> GSM312819 2 0.000 0.999 0.000 1.000
#> GSM312820 2 0.000 0.999 0.000 1.000
#> GSM312821 2 0.000 0.999 0.000 1.000
#> GSM312822 2 0.000 0.999 0.000 1.000
#> GSM312823 2 0.000 0.999 0.000 1.000
#> GSM312824 2 0.000 0.999 0.000 1.000
#> GSM312825 2 0.000 0.999 0.000 1.000
#> GSM312826 2 0.000 0.999 0.000 1.000
#> GSM312839 2 0.000 0.999 0.000 1.000
#> GSM312840 2 0.000 0.999 0.000 1.000
#> GSM312841 2 0.000 0.999 0.000 1.000
#> GSM312843 2 0.000 0.999 0.000 1.000
#> GSM312844 2 0.000 0.999 0.000 1.000
#> GSM312845 2 0.311 0.941 0.056 0.944
#> GSM312846 2 0.000 0.999 0.000 1.000
#> GSM312847 2 0.000 0.999 0.000 1.000
#> GSM312848 2 0.000 0.999 0.000 1.000
#> GSM312849 2 0.000 0.999 0.000 1.000
#> GSM312851 2 0.000 0.999 0.000 1.000
#> GSM312853 2 0.000 0.999 0.000 1.000
#> GSM312854 2 0.000 0.999 0.000 1.000
#> GSM312856 2 0.000 0.999 0.000 1.000
#> GSM312857 2 0.000 0.999 0.000 1.000
#> GSM312858 2 0.000 0.999 0.000 1.000
#> GSM312859 2 0.000 0.999 0.000 1.000
#> GSM312860 2 0.000 0.999 0.000 1.000
#> GSM312861 2 0.000 0.999 0.000 1.000
#> GSM312862 2 0.000 0.999 0.000 1.000
#> GSM312863 2 0.000 0.999 0.000 1.000
#> GSM312864 2 0.000 0.999 0.000 1.000
#> GSM312865 2 0.000 0.999 0.000 1.000
#> GSM312867 2 0.000 0.999 0.000 1.000
#> GSM312868 2 0.000 0.999 0.000 1.000
#> GSM312869 2 0.000 0.999 0.000 1.000
#> GSM312870 1 0.000 1.000 1.000 0.000
#> GSM312872 1 0.000 1.000 1.000 0.000
#> GSM312874 1 0.000 1.000 1.000 0.000
#> GSM312875 1 0.000 1.000 1.000 0.000
#> GSM312876 1 0.000 1.000 1.000 0.000
#> GSM312877 1 0.000 1.000 1.000 0.000
#> GSM312879 1 0.000 1.000 1.000 0.000
#> GSM312882 1 0.000 1.000 1.000 0.000
#> GSM312883 1 0.000 1.000 1.000 0.000
#> GSM312886 1 0.000 1.000 1.000 0.000
#> GSM312887 1 0.000 1.000 1.000 0.000
#> GSM312890 1 0.000 1.000 1.000 0.000
#> GSM312893 1 0.000 1.000 1.000 0.000
#> GSM312894 1 0.000 1.000 1.000 0.000
#> GSM312895 1 0.000 1.000 1.000 0.000
#> GSM312937 1 0.000 1.000 1.000 0.000
#> GSM312938 1 0.000 1.000 1.000 0.000
#> GSM312939 1 0.000 1.000 1.000 0.000
#> GSM312940 1 0.000 1.000 1.000 0.000
#> GSM312941 1 0.000 1.000 1.000 0.000
#> GSM312942 1 0.000 1.000 1.000 0.000
#> GSM312943 1 0.000 1.000 1.000 0.000
#> GSM312944 1 0.000 1.000 1.000 0.000
#> GSM312945 1 0.000 1.000 1.000 0.000
#> GSM312946 1 0.000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM312811 2 0.0892 0.973 0.000 0.980 0.020
#> GSM312812 2 0.0892 0.973 0.000 0.980 0.020
#> GSM312813 2 0.0892 0.973 0.000 0.980 0.020
#> GSM312814 2 0.0892 0.973 0.000 0.980 0.020
#> GSM312815 2 0.0892 0.973 0.000 0.980 0.020
#> GSM312816 2 0.0892 0.973 0.000 0.980 0.020
#> GSM312817 2 0.0892 0.973 0.000 0.980 0.020
#> GSM312818 2 0.0592 0.973 0.000 0.988 0.012
#> GSM312819 2 0.0892 0.973 0.000 0.980 0.020
#> GSM312820 2 0.0000 0.973 0.000 1.000 0.000
#> GSM312821 2 0.0592 0.973 0.000 0.988 0.012
#> GSM312822 2 0.0892 0.973 0.000 0.980 0.020
#> GSM312823 2 0.0892 0.973 0.000 0.980 0.020
#> GSM312824 2 0.0892 0.973 0.000 0.980 0.020
#> GSM312825 2 0.0892 0.973 0.000 0.980 0.020
#> GSM312826 2 0.0892 0.973 0.000 0.980 0.020
#> GSM312839 2 0.0892 0.973 0.000 0.980 0.020
#> GSM312840 2 0.0892 0.973 0.000 0.980 0.020
#> GSM312841 2 0.0892 0.973 0.000 0.980 0.020
#> GSM312843 2 0.1031 0.972 0.000 0.976 0.024
#> GSM312844 2 0.0892 0.973 0.000 0.980 0.020
#> GSM312845 2 0.6541 0.557 0.304 0.672 0.024
#> GSM312846 2 0.1031 0.972 0.000 0.976 0.024
#> GSM312847 2 0.1031 0.972 0.000 0.976 0.024
#> GSM312848 2 0.1031 0.972 0.000 0.976 0.024
#> GSM312849 2 0.1031 0.972 0.000 0.976 0.024
#> GSM312851 2 0.1031 0.972 0.000 0.976 0.024
#> GSM312853 2 0.1031 0.972 0.000 0.976 0.024
#> GSM312854 2 0.1031 0.972 0.000 0.976 0.024
#> GSM312856 2 0.1031 0.972 0.000 0.976 0.024
#> GSM312857 2 0.1031 0.972 0.000 0.976 0.024
#> GSM312858 2 0.1031 0.972 0.000 0.976 0.024
#> GSM312859 2 0.0892 0.973 0.000 0.980 0.020
#> GSM312860 2 0.0892 0.973 0.000 0.980 0.020
#> GSM312861 2 0.1031 0.972 0.000 0.976 0.024
#> GSM312862 2 0.1031 0.972 0.000 0.976 0.024
#> GSM312863 2 0.1031 0.972 0.000 0.976 0.024
#> GSM312864 2 0.1031 0.972 0.000 0.976 0.024
#> GSM312865 2 0.1031 0.972 0.000 0.976 0.024
#> GSM312867 2 0.1031 0.972 0.000 0.976 0.024
#> GSM312868 2 0.1031 0.972 0.000 0.976 0.024
#> GSM312869 2 0.0892 0.973 0.000 0.980 0.020
#> GSM312870 3 0.1643 1.000 0.044 0.000 0.956
#> GSM312872 3 0.1643 1.000 0.044 0.000 0.956
#> GSM312874 3 0.1643 1.000 0.044 0.000 0.956
#> GSM312875 3 0.1643 1.000 0.044 0.000 0.956
#> GSM312876 3 0.1643 1.000 0.044 0.000 0.956
#> GSM312877 1 0.6192 0.367 0.580 0.000 0.420
#> GSM312879 3 0.1643 1.000 0.044 0.000 0.956
#> GSM312882 3 0.1643 1.000 0.044 0.000 0.956
#> GSM312883 3 0.1643 1.000 0.044 0.000 0.956
#> GSM312886 3 0.1643 1.000 0.044 0.000 0.956
#> GSM312887 1 0.0000 0.907 1.000 0.000 0.000
#> GSM312890 1 0.0000 0.907 1.000 0.000 0.000
#> GSM312893 1 0.0000 0.907 1.000 0.000 0.000
#> GSM312894 1 0.0000 0.907 1.000 0.000 0.000
#> GSM312895 1 0.0000 0.907 1.000 0.000 0.000
#> GSM312937 1 0.0000 0.907 1.000 0.000 0.000
#> GSM312938 1 0.0000 0.907 1.000 0.000 0.000
#> GSM312939 1 0.0000 0.907 1.000 0.000 0.000
#> GSM312940 1 0.0000 0.907 1.000 0.000 0.000
#> GSM312941 1 0.0000 0.907 1.000 0.000 0.000
#> GSM312942 1 0.4178 0.829 0.828 0.000 0.172
#> GSM312943 1 0.4121 0.832 0.832 0.000 0.168
#> GSM312944 1 0.4121 0.832 0.832 0.000 0.168
#> GSM312945 1 0.4121 0.832 0.832 0.000 0.168
#> GSM312946 1 0.4121 0.832 0.832 0.000 0.168
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM312811 2 0.000 0.953 0.000 1.000 0.000 0.000
#> GSM312812 2 0.000 0.953 0.000 1.000 0.000 0.000
#> GSM312813 2 0.000 0.953 0.000 1.000 0.000 0.000
#> GSM312814 2 0.000 0.953 0.000 1.000 0.000 0.000
#> GSM312815 2 0.000 0.953 0.000 1.000 0.000 0.000
#> GSM312816 2 0.194 0.929 0.000 0.924 0.000 0.076
#> GSM312817 2 0.000 0.953 0.000 1.000 0.000 0.000
#> GSM312818 2 0.253 0.927 0.000 0.888 0.000 0.112
#> GSM312819 2 0.000 0.953 0.000 1.000 0.000 0.000
#> GSM312820 2 0.228 0.929 0.000 0.904 0.000 0.096
#> GSM312821 2 0.247 0.928 0.000 0.892 0.000 0.108
#> GSM312822 2 0.000 0.953 0.000 1.000 0.000 0.000
#> GSM312823 2 0.000 0.953 0.000 1.000 0.000 0.000
#> GSM312824 2 0.000 0.953 0.000 1.000 0.000 0.000
#> GSM312825 2 0.000 0.953 0.000 1.000 0.000 0.000
#> GSM312826 2 0.000 0.953 0.000 1.000 0.000 0.000
#> GSM312839 2 0.000 0.953 0.000 1.000 0.000 0.000
#> GSM312840 2 0.000 0.953 0.000 1.000 0.000 0.000
#> GSM312841 2 0.000 0.953 0.000 1.000 0.000 0.000
#> GSM312843 2 0.164 0.949 0.000 0.940 0.000 0.060
#> GSM312844 2 0.000 0.953 0.000 1.000 0.000 0.000
#> GSM312845 2 0.515 0.743 0.200 0.740 0.000 0.060
#> GSM312846 2 0.164 0.949 0.000 0.940 0.000 0.060
#> GSM312847 2 0.164 0.949 0.000 0.940 0.000 0.060
#> GSM312848 2 0.164 0.949 0.000 0.940 0.000 0.060
#> GSM312849 2 0.156 0.950 0.000 0.944 0.000 0.056
#> GSM312851 2 0.281 0.922 0.000 0.868 0.000 0.132
#> GSM312853 2 0.281 0.922 0.000 0.868 0.000 0.132
#> GSM312854 2 0.281 0.922 0.000 0.868 0.000 0.132
#> GSM312856 2 0.281 0.922 0.000 0.868 0.000 0.132
#> GSM312857 2 0.281 0.922 0.000 0.868 0.000 0.132
#> GSM312858 2 0.164 0.949 0.000 0.940 0.000 0.060
#> GSM312859 2 0.000 0.953 0.000 1.000 0.000 0.000
#> GSM312860 2 0.000 0.953 0.000 1.000 0.000 0.000
#> GSM312861 2 0.164 0.949 0.000 0.940 0.000 0.060
#> GSM312862 2 0.164 0.949 0.000 0.940 0.000 0.060
#> GSM312863 2 0.281 0.922 0.000 0.868 0.000 0.132
#> GSM312864 2 0.281 0.922 0.000 0.868 0.000 0.132
#> GSM312865 2 0.164 0.949 0.000 0.940 0.000 0.060
#> GSM312867 2 0.164 0.949 0.000 0.940 0.000 0.060
#> GSM312868 2 0.164 0.949 0.000 0.940 0.000 0.060
#> GSM312869 2 0.000 0.953 0.000 1.000 0.000 0.000
#> GSM312870 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM312872 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM312874 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM312875 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM312876 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM312877 4 0.762 0.376 0.208 0.000 0.356 0.436
#> GSM312879 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM312882 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM312883 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM312886 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM312887 1 0.000 1.000 1.000 0.000 0.000 0.000
#> GSM312890 1 0.000 1.000 1.000 0.000 0.000 0.000
#> GSM312893 1 0.000 1.000 1.000 0.000 0.000 0.000
#> GSM312894 1 0.000 1.000 1.000 0.000 0.000 0.000
#> GSM312895 1 0.000 1.000 1.000 0.000 0.000 0.000
#> GSM312937 1 0.000 1.000 1.000 0.000 0.000 0.000
#> GSM312938 1 0.000 1.000 1.000 0.000 0.000 0.000
#> GSM312939 1 0.000 1.000 1.000 0.000 0.000 0.000
#> GSM312940 1 0.000 1.000 1.000 0.000 0.000 0.000
#> GSM312941 1 0.000 1.000 1.000 0.000 0.000 0.000
#> GSM312942 4 0.340 0.915 0.092 0.000 0.040 0.868
#> GSM312943 4 0.340 0.915 0.092 0.000 0.040 0.868
#> GSM312944 4 0.340 0.915 0.092 0.000 0.040 0.868
#> GSM312945 4 0.340 0.915 0.092 0.000 0.040 0.868
#> GSM312946 4 0.340 0.915 0.092 0.000 0.040 0.868
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM312811 2 0.000 0.940 0.000 1.000 0.000 0.000 0.000
#> GSM312812 2 0.000 0.940 0.000 1.000 0.000 0.000 0.000
#> GSM312813 2 0.000 0.940 0.000 1.000 0.000 0.000 0.000
#> GSM312814 2 0.000 0.940 0.000 1.000 0.000 0.000 0.000
#> GSM312815 2 0.000 0.940 0.000 1.000 0.000 0.000 0.000
#> GSM312816 4 0.386 0.518 0.000 0.312 0.000 0.688 0.000
#> GSM312817 2 0.120 0.887 0.000 0.952 0.000 0.048 0.000
#> GSM312818 4 0.148 0.764 0.000 0.064 0.000 0.936 0.000
#> GSM312819 2 0.000 0.940 0.000 1.000 0.000 0.000 0.000
#> GSM312820 4 0.260 0.707 0.000 0.148 0.000 0.852 0.000
#> GSM312821 4 0.191 0.750 0.000 0.092 0.000 0.908 0.000
#> GSM312822 2 0.000 0.940 0.000 1.000 0.000 0.000 0.000
#> GSM312823 2 0.000 0.940 0.000 1.000 0.000 0.000 0.000
#> GSM312824 2 0.000 0.940 0.000 1.000 0.000 0.000 0.000
#> GSM312825 2 0.000 0.940 0.000 1.000 0.000 0.000 0.000
#> GSM312826 2 0.000 0.940 0.000 1.000 0.000 0.000 0.000
#> GSM312839 2 0.000 0.940 0.000 1.000 0.000 0.000 0.000
#> GSM312840 2 0.000 0.940 0.000 1.000 0.000 0.000 0.000
#> GSM312841 2 0.000 0.940 0.000 1.000 0.000 0.000 0.000
#> GSM312843 4 0.318 0.762 0.000 0.208 0.000 0.792 0.000
#> GSM312844 2 0.000 0.940 0.000 1.000 0.000 0.000 0.000
#> GSM312845 4 0.369 0.676 0.200 0.020 0.000 0.780 0.000
#> GSM312846 2 0.421 0.141 0.000 0.588 0.000 0.412 0.000
#> GSM312847 4 0.318 0.762 0.000 0.208 0.000 0.792 0.000
#> GSM312848 4 0.318 0.762 0.000 0.208 0.000 0.792 0.000
#> GSM312849 2 0.311 0.682 0.000 0.800 0.000 0.200 0.000
#> GSM312851 4 0.000 0.780 0.000 0.000 0.000 1.000 0.000
#> GSM312853 4 0.000 0.780 0.000 0.000 0.000 1.000 0.000
#> GSM312854 4 0.000 0.780 0.000 0.000 0.000 1.000 0.000
#> GSM312856 4 0.000 0.780 0.000 0.000 0.000 1.000 0.000
#> GSM312857 4 0.000 0.780 0.000 0.000 0.000 1.000 0.000
#> GSM312858 4 0.318 0.762 0.000 0.208 0.000 0.792 0.000
#> GSM312859 2 0.000 0.940 0.000 1.000 0.000 0.000 0.000
#> GSM312860 2 0.000 0.940 0.000 1.000 0.000 0.000 0.000
#> GSM312861 4 0.431 0.145 0.000 0.500 0.000 0.500 0.000
#> GSM312862 2 0.400 0.366 0.000 0.656 0.000 0.344 0.000
#> GSM312863 4 0.000 0.780 0.000 0.000 0.000 1.000 0.000
#> GSM312864 4 0.000 0.780 0.000 0.000 0.000 1.000 0.000
#> GSM312865 4 0.318 0.762 0.000 0.208 0.000 0.792 0.000
#> GSM312867 4 0.430 0.201 0.000 0.484 0.000 0.516 0.000
#> GSM312868 4 0.318 0.762 0.000 0.208 0.000 0.792 0.000
#> GSM312869 2 0.000 0.940 0.000 1.000 0.000 0.000 0.000
#> GSM312870 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312872 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312874 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312875 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312876 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312877 5 0.654 0.221 0.204 0.000 0.352 0.000 0.444
#> GSM312879 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312882 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312883 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312886 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312887 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM312890 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM312893 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM312894 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM312895 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM312937 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM312938 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM312939 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM312940 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM312941 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM312942 5 0.000 0.901 0.000 0.000 0.000 0.000 1.000
#> GSM312943 5 0.000 0.901 0.000 0.000 0.000 0.000 1.000
#> GSM312944 5 0.000 0.901 0.000 0.000 0.000 0.000 1.000
#> GSM312945 5 0.000 0.901 0.000 0.000 0.000 0.000 1.000
#> GSM312946 5 0.000 0.901 0.000 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM312811 2 0.3198 0.546 0.000 0.740 0.000 0.000 0.260 0.000
#> GSM312812 2 0.0000 0.856 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312813 2 0.0000 0.856 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312814 5 0.3782 0.300 0.000 0.412 0.000 0.000 0.588 0.000
#> GSM312815 2 0.0146 0.853 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM312816 5 0.0000 0.775 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM312817 2 0.1471 0.800 0.000 0.932 0.000 0.064 0.004 0.000
#> GSM312818 5 0.0000 0.775 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM312819 2 0.0000 0.856 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312820 5 0.0000 0.775 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM312821 5 0.0000 0.775 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM312822 5 0.3221 0.608 0.000 0.264 0.000 0.000 0.736 0.000
#> GSM312823 2 0.0000 0.856 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312824 2 0.0000 0.856 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312825 2 0.0000 0.856 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312826 2 0.0000 0.856 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312839 2 0.0000 0.856 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312840 2 0.0000 0.856 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312841 2 0.0000 0.856 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312843 4 0.0000 0.984 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312844 2 0.0000 0.856 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312845 4 0.3037 0.763 0.176 0.016 0.000 0.808 0.000 0.000
#> GSM312846 2 0.3782 0.413 0.000 0.588 0.000 0.412 0.000 0.000
#> GSM312847 4 0.0000 0.984 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312848 4 0.0000 0.984 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312849 2 0.2793 0.684 0.000 0.800 0.000 0.200 0.000 0.000
#> GSM312851 4 0.0000 0.984 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312853 4 0.0000 0.984 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312854 4 0.0000 0.984 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312856 4 0.0000 0.984 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312857 4 0.0000 0.984 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312858 4 0.0000 0.984 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312859 2 0.0000 0.856 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312860 2 0.0000 0.856 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312861 2 0.3857 0.274 0.000 0.532 0.000 0.468 0.000 0.000
#> GSM312862 2 0.3592 0.524 0.000 0.656 0.000 0.344 0.000 0.000
#> GSM312863 4 0.0000 0.984 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312864 4 0.0000 0.984 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312865 4 0.0000 0.984 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312867 2 0.3866 0.228 0.000 0.516 0.000 0.484 0.000 0.000
#> GSM312868 4 0.0000 0.984 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312869 2 0.0000 0.856 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312870 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312872 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312874 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312875 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312876 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312877 6 0.5873 0.221 0.204 0.000 0.352 0.000 0.000 0.444
#> GSM312879 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312882 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312883 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312886 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312887 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312890 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312893 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312894 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312895 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312937 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312938 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312939 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312940 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312941 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312942 6 0.0000 0.887 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM312943 6 0.0000 0.887 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM312944 6 0.0000 0.887 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM312945 6 0.0000 0.887 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM312946 6 0.0000 0.887 0.000 0.000 0.000 0.000 0.000 1.000
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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 4)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:pam 67 1.68e-10 2
#> CV:pam 66 1.64e-18 3
#> CV:pam 66 1.17e-26 4
#> CV:pam 62 1.19e-24 5
#> CV:pam 62 2.10e-26 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "mclust"]
# you can also extract it by
# res = res_list["CV:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 67 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 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.997 0.997 0.4728 0.525 0.525
#> 3 3 0.676 0.786 0.880 0.2796 0.866 0.751
#> 4 4 0.648 0.809 0.844 0.1057 0.903 0.771
#> 5 5 0.710 0.714 0.847 0.1179 0.798 0.476
#> 6 6 0.947 0.929 0.968 0.0664 0.906 0.647
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2
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
#> GSM312811 2 0.0000 1.000 0.000 1.000
#> GSM312812 2 0.0000 1.000 0.000 1.000
#> GSM312813 2 0.0000 1.000 0.000 1.000
#> GSM312814 2 0.0000 1.000 0.000 1.000
#> GSM312815 2 0.0000 1.000 0.000 1.000
#> GSM312816 2 0.0000 1.000 0.000 1.000
#> GSM312817 2 0.0000 1.000 0.000 1.000
#> GSM312818 2 0.0000 1.000 0.000 1.000
#> GSM312819 2 0.0000 1.000 0.000 1.000
#> GSM312820 2 0.0000 1.000 0.000 1.000
#> GSM312821 2 0.0000 1.000 0.000 1.000
#> GSM312822 2 0.0000 1.000 0.000 1.000
#> GSM312823 2 0.0000 1.000 0.000 1.000
#> GSM312824 2 0.0000 1.000 0.000 1.000
#> GSM312825 2 0.0000 1.000 0.000 1.000
#> GSM312826 2 0.0000 1.000 0.000 1.000
#> GSM312839 2 0.0000 1.000 0.000 1.000
#> GSM312840 2 0.0000 1.000 0.000 1.000
#> GSM312841 2 0.0000 1.000 0.000 1.000
#> GSM312843 2 0.0000 1.000 0.000 1.000
#> GSM312844 2 0.0000 1.000 0.000 1.000
#> GSM312845 2 0.0000 1.000 0.000 1.000
#> GSM312846 2 0.0000 1.000 0.000 1.000
#> GSM312847 2 0.0000 1.000 0.000 1.000
#> GSM312848 2 0.0000 1.000 0.000 1.000
#> GSM312849 2 0.0000 1.000 0.000 1.000
#> GSM312851 2 0.0000 1.000 0.000 1.000
#> GSM312853 2 0.0000 1.000 0.000 1.000
#> GSM312854 2 0.0000 1.000 0.000 1.000
#> GSM312856 2 0.0000 1.000 0.000 1.000
#> GSM312857 2 0.0000 1.000 0.000 1.000
#> GSM312858 2 0.0000 1.000 0.000 1.000
#> GSM312859 2 0.0000 1.000 0.000 1.000
#> GSM312860 2 0.0000 1.000 0.000 1.000
#> GSM312861 2 0.0000 1.000 0.000 1.000
#> GSM312862 2 0.0000 1.000 0.000 1.000
#> GSM312863 2 0.0000 1.000 0.000 1.000
#> GSM312864 2 0.0000 1.000 0.000 1.000
#> GSM312865 2 0.0000 1.000 0.000 1.000
#> GSM312867 2 0.0000 1.000 0.000 1.000
#> GSM312868 2 0.0000 1.000 0.000 1.000
#> GSM312869 2 0.0000 1.000 0.000 1.000
#> GSM312870 1 0.0000 0.991 1.000 0.000
#> GSM312872 1 0.0000 0.991 1.000 0.000
#> GSM312874 1 0.0000 0.991 1.000 0.000
#> GSM312875 1 0.0000 0.991 1.000 0.000
#> GSM312876 1 0.0000 0.991 1.000 0.000
#> GSM312877 1 0.0000 0.991 1.000 0.000
#> GSM312879 1 0.0000 0.991 1.000 0.000
#> GSM312882 1 0.0000 0.991 1.000 0.000
#> GSM312883 1 0.0000 0.991 1.000 0.000
#> GSM312886 1 0.1184 0.992 0.984 0.016
#> GSM312887 1 0.1184 0.992 0.984 0.016
#> GSM312890 1 0.1184 0.992 0.984 0.016
#> GSM312893 1 0.1184 0.992 0.984 0.016
#> GSM312894 1 0.1184 0.992 0.984 0.016
#> GSM312895 1 0.1184 0.992 0.984 0.016
#> GSM312937 1 0.1184 0.992 0.984 0.016
#> GSM312938 1 0.1184 0.992 0.984 0.016
#> GSM312939 1 0.1184 0.992 0.984 0.016
#> GSM312940 1 0.1184 0.992 0.984 0.016
#> GSM312941 1 0.1184 0.992 0.984 0.016
#> GSM312942 1 0.0000 0.991 1.000 0.000
#> GSM312943 1 0.0672 0.992 0.992 0.008
#> GSM312944 1 0.0672 0.992 0.992 0.008
#> GSM312945 1 0.0000 0.991 1.000 0.000
#> GSM312946 1 0.1184 0.992 0.984 0.016
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM312811 2 0.1860 0.821 0.000 0.948 0.052
#> GSM312812 2 0.0000 0.843 0.000 1.000 0.000
#> GSM312813 2 0.0000 0.843 0.000 1.000 0.000
#> GSM312814 2 0.1860 0.821 0.000 0.948 0.052
#> GSM312815 2 0.0000 0.843 0.000 1.000 0.000
#> GSM312816 2 0.7944 0.444 0.144 0.660 0.196
#> GSM312817 2 0.0000 0.843 0.000 1.000 0.000
#> GSM312818 3 0.9152 0.238 0.144 0.424 0.432
#> GSM312819 2 0.1163 0.825 0.028 0.972 0.000
#> GSM312820 3 0.9152 0.238 0.144 0.424 0.432
#> GSM312821 3 0.9152 0.238 0.144 0.424 0.432
#> GSM312822 2 0.2165 0.815 0.000 0.936 0.064
#> GSM312823 2 0.0000 0.843 0.000 1.000 0.000
#> GSM312824 2 0.0000 0.843 0.000 1.000 0.000
#> GSM312825 2 0.0000 0.843 0.000 1.000 0.000
#> GSM312826 2 0.0000 0.843 0.000 1.000 0.000
#> GSM312839 2 0.0000 0.843 0.000 1.000 0.000
#> GSM312840 2 0.0000 0.843 0.000 1.000 0.000
#> GSM312841 2 0.0000 0.843 0.000 1.000 0.000
#> GSM312843 2 0.0000 0.843 0.000 1.000 0.000
#> GSM312844 2 0.0000 0.843 0.000 1.000 0.000
#> GSM312845 2 0.5968 0.574 0.000 0.636 0.364
#> GSM312846 2 0.4931 0.740 0.000 0.768 0.232
#> GSM312847 2 0.4887 0.742 0.000 0.772 0.228
#> GSM312848 2 0.4842 0.745 0.000 0.776 0.224
#> GSM312849 2 0.4887 0.742 0.000 0.772 0.228
#> GSM312851 2 0.6111 0.583 0.000 0.604 0.396
#> GSM312853 2 0.6111 0.583 0.000 0.604 0.396
#> GSM312854 2 0.6111 0.583 0.000 0.604 0.396
#> GSM312856 2 0.6111 0.583 0.000 0.604 0.396
#> GSM312857 2 0.6111 0.583 0.000 0.604 0.396
#> GSM312858 2 0.4842 0.745 0.000 0.776 0.224
#> GSM312859 2 0.0000 0.843 0.000 1.000 0.000
#> GSM312860 2 0.0000 0.843 0.000 1.000 0.000
#> GSM312861 2 0.0000 0.843 0.000 1.000 0.000
#> GSM312862 2 0.0000 0.843 0.000 1.000 0.000
#> GSM312863 2 0.5650 0.692 0.000 0.688 0.312
#> GSM312864 2 0.2165 0.815 0.000 0.936 0.064
#> GSM312865 2 0.4887 0.742 0.000 0.772 0.228
#> GSM312867 2 0.4887 0.742 0.000 0.772 0.228
#> GSM312868 2 0.4842 0.745 0.000 0.776 0.224
#> GSM312869 2 0.0000 0.843 0.000 1.000 0.000
#> GSM312870 1 0.0000 0.951 1.000 0.000 0.000
#> GSM312872 1 0.0000 0.951 1.000 0.000 0.000
#> GSM312874 1 0.0000 0.951 1.000 0.000 0.000
#> GSM312875 1 0.0000 0.951 1.000 0.000 0.000
#> GSM312876 1 0.0000 0.951 1.000 0.000 0.000
#> GSM312877 1 0.2200 0.942 0.940 0.004 0.056
#> GSM312879 1 0.0000 0.951 1.000 0.000 0.000
#> GSM312882 1 0.0000 0.951 1.000 0.000 0.000
#> GSM312883 1 0.0237 0.951 0.996 0.000 0.004
#> GSM312886 1 0.5024 0.679 0.776 0.004 0.220
#> GSM312887 3 0.2400 0.820 0.064 0.004 0.932
#> GSM312890 3 0.2165 0.821 0.064 0.000 0.936
#> GSM312893 3 0.2165 0.821 0.064 0.000 0.936
#> GSM312894 3 0.2400 0.820 0.064 0.004 0.932
#> GSM312895 3 0.2165 0.821 0.064 0.000 0.936
#> GSM312937 3 0.2165 0.821 0.064 0.000 0.936
#> GSM312938 3 0.2400 0.820 0.064 0.004 0.932
#> GSM312939 3 0.2165 0.821 0.064 0.000 0.936
#> GSM312940 3 0.2165 0.821 0.064 0.000 0.936
#> GSM312941 3 0.2165 0.821 0.064 0.000 0.936
#> GSM312942 1 0.2301 0.940 0.936 0.004 0.060
#> GSM312943 1 0.2400 0.939 0.932 0.004 0.064
#> GSM312944 1 0.2400 0.939 0.932 0.004 0.064
#> GSM312945 1 0.2400 0.939 0.932 0.004 0.064
#> GSM312946 1 0.2400 0.939 0.932 0.004 0.064
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM312811 2 0.4277 0.411 0.000 0.720 0.000 0.280
#> GSM312812 2 0.0000 0.834 0.000 1.000 0.000 0.000
#> GSM312813 2 0.0592 0.827 0.016 0.984 0.000 0.000
#> GSM312814 2 0.4250 0.422 0.000 0.724 0.000 0.276
#> GSM312815 2 0.0000 0.834 0.000 1.000 0.000 0.000
#> GSM312816 4 0.6009 0.835 0.040 0.312 0.012 0.636
#> GSM312817 2 0.1118 0.821 0.036 0.964 0.000 0.000
#> GSM312818 4 0.6397 0.855 0.072 0.280 0.012 0.636
#> GSM312819 2 0.1590 0.814 0.028 0.956 0.008 0.008
#> GSM312820 4 0.6397 0.855 0.072 0.280 0.012 0.636
#> GSM312821 4 0.6397 0.855 0.072 0.280 0.012 0.636
#> GSM312822 2 0.4456 0.408 0.004 0.716 0.000 0.280
#> GSM312823 2 0.0000 0.834 0.000 1.000 0.000 0.000
#> GSM312824 2 0.0000 0.834 0.000 1.000 0.000 0.000
#> GSM312825 2 0.0000 0.834 0.000 1.000 0.000 0.000
#> GSM312826 2 0.0000 0.834 0.000 1.000 0.000 0.000
#> GSM312839 2 0.0000 0.834 0.000 1.000 0.000 0.000
#> GSM312840 2 0.0000 0.834 0.000 1.000 0.000 0.000
#> GSM312841 2 0.3528 0.606 0.000 0.808 0.000 0.192
#> GSM312843 2 0.0817 0.829 0.000 0.976 0.000 0.024
#> GSM312844 2 0.0000 0.834 0.000 1.000 0.000 0.000
#> GSM312845 2 0.3999 0.741 0.140 0.824 0.000 0.036
#> GSM312846 2 0.3948 0.745 0.136 0.828 0.000 0.036
#> GSM312847 2 0.3435 0.767 0.100 0.864 0.000 0.036
#> GSM312848 2 0.3435 0.767 0.100 0.864 0.000 0.036
#> GSM312849 2 0.3842 0.752 0.128 0.836 0.000 0.036
#> GSM312851 4 0.6019 0.862 0.100 0.228 0.000 0.672
#> GSM312853 4 0.6019 0.862 0.100 0.228 0.000 0.672
#> GSM312854 4 0.6019 0.862 0.100 0.228 0.000 0.672
#> GSM312856 2 0.6553 0.260 0.100 0.584 0.000 0.316
#> GSM312857 4 0.6019 0.862 0.100 0.228 0.000 0.672
#> GSM312858 2 0.3435 0.767 0.100 0.864 0.000 0.036
#> GSM312859 2 0.0000 0.834 0.000 1.000 0.000 0.000
#> GSM312860 2 0.0188 0.834 0.004 0.996 0.000 0.000
#> GSM312861 2 0.0336 0.833 0.000 0.992 0.000 0.008
#> GSM312862 2 0.0921 0.820 0.028 0.972 0.000 0.000
#> GSM312863 2 0.6553 0.260 0.100 0.584 0.000 0.316
#> GSM312864 2 0.4509 0.388 0.004 0.708 0.000 0.288
#> GSM312865 2 0.3435 0.767 0.100 0.864 0.000 0.036
#> GSM312867 2 0.3842 0.752 0.128 0.836 0.000 0.036
#> GSM312868 2 0.3342 0.769 0.100 0.868 0.000 0.032
#> GSM312869 2 0.0000 0.834 0.000 1.000 0.000 0.000
#> GSM312870 3 0.0000 0.893 0.000 0.000 1.000 0.000
#> GSM312872 3 0.0000 0.893 0.000 0.000 1.000 0.000
#> GSM312874 3 0.0000 0.893 0.000 0.000 1.000 0.000
#> GSM312875 3 0.0000 0.893 0.000 0.000 1.000 0.000
#> GSM312876 3 0.0000 0.893 0.000 0.000 1.000 0.000
#> GSM312877 3 0.3634 0.855 0.048 0.000 0.856 0.096
#> GSM312879 3 0.0000 0.893 0.000 0.000 1.000 0.000
#> GSM312882 3 0.0000 0.893 0.000 0.000 1.000 0.000
#> GSM312883 3 0.0000 0.893 0.000 0.000 1.000 0.000
#> GSM312886 3 0.0188 0.892 0.004 0.000 0.996 0.000
#> GSM312887 1 0.0188 0.997 0.996 0.000 0.000 0.004
#> GSM312890 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM312893 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM312894 1 0.0188 0.997 0.996 0.000 0.000 0.004
#> GSM312895 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM312937 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM312938 1 0.0188 0.997 0.996 0.000 0.000 0.004
#> GSM312939 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM312940 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM312941 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM312942 3 0.5646 0.788 0.048 0.000 0.656 0.296
#> GSM312943 3 0.5110 0.795 0.016 0.000 0.656 0.328
#> GSM312944 3 0.5110 0.795 0.016 0.000 0.656 0.328
#> GSM312945 3 0.5110 0.795 0.016 0.000 0.656 0.328
#> GSM312946 3 0.5110 0.795 0.016 0.000 0.656 0.328
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM312811 4 0.4256 0.1087 0.000 0.436 0.000 0.564 0.000
#> GSM312812 2 0.0000 0.7748 0.000 1.000 0.000 0.000 0.000
#> GSM312813 2 0.1012 0.7712 0.000 0.968 0.000 0.020 0.012
#> GSM312814 2 0.4262 0.2167 0.000 0.560 0.000 0.440 0.000
#> GSM312815 2 0.0000 0.7748 0.000 1.000 0.000 0.000 0.000
#> GSM312816 4 0.4806 0.4235 0.000 0.252 0.000 0.688 0.060
#> GSM312817 2 0.4306 0.4211 0.000 0.660 0.000 0.328 0.012
#> GSM312818 4 0.4728 0.4348 0.000 0.240 0.000 0.700 0.060
#> GSM312819 2 0.5550 0.1244 0.000 0.528 0.000 0.400 0.072
#> GSM312820 4 0.4728 0.4348 0.000 0.240 0.000 0.700 0.060
#> GSM312821 4 0.4728 0.4348 0.000 0.240 0.000 0.700 0.060
#> GSM312822 4 0.4304 -0.0608 0.000 0.484 0.000 0.516 0.000
#> GSM312823 2 0.3752 0.5083 0.000 0.708 0.000 0.292 0.000
#> GSM312824 2 0.0000 0.7748 0.000 1.000 0.000 0.000 0.000
#> GSM312825 2 0.0000 0.7748 0.000 1.000 0.000 0.000 0.000
#> GSM312826 2 0.0000 0.7748 0.000 1.000 0.000 0.000 0.000
#> GSM312839 2 0.0000 0.7748 0.000 1.000 0.000 0.000 0.000
#> GSM312840 2 0.1478 0.7583 0.000 0.936 0.000 0.064 0.000
#> GSM312841 2 0.2813 0.6745 0.000 0.832 0.000 0.168 0.000
#> GSM312843 2 0.5176 0.2006 0.000 0.572 0.000 0.380 0.048
#> GSM312844 2 0.0000 0.7748 0.000 1.000 0.000 0.000 0.000
#> GSM312845 4 0.5130 0.6236 0.000 0.220 0.000 0.680 0.100
#> GSM312846 4 0.5130 0.6236 0.000 0.220 0.000 0.680 0.100
#> GSM312847 4 0.5130 0.6236 0.000 0.220 0.000 0.680 0.100
#> GSM312848 4 0.5130 0.6236 0.000 0.220 0.000 0.680 0.100
#> GSM312849 4 0.5130 0.6236 0.000 0.220 0.000 0.680 0.100
#> GSM312851 4 0.0000 0.6389 0.000 0.000 0.000 1.000 0.000
#> GSM312853 4 0.0000 0.6389 0.000 0.000 0.000 1.000 0.000
#> GSM312854 4 0.0609 0.6454 0.000 0.020 0.000 0.980 0.000
#> GSM312856 4 0.2448 0.6499 0.000 0.020 0.000 0.892 0.088
#> GSM312857 4 0.0290 0.6421 0.000 0.008 0.000 0.992 0.000
#> GSM312858 4 0.5130 0.6236 0.000 0.220 0.000 0.680 0.100
#> GSM312859 2 0.0693 0.7723 0.000 0.980 0.000 0.008 0.012
#> GSM312860 2 0.2006 0.7519 0.000 0.916 0.000 0.072 0.012
#> GSM312861 2 0.4016 0.5338 0.000 0.716 0.000 0.272 0.012
#> GSM312862 2 0.3876 0.4638 0.000 0.684 0.000 0.316 0.000
#> GSM312863 4 0.2540 0.6509 0.000 0.024 0.000 0.888 0.088
#> GSM312864 4 0.4616 0.3940 0.000 0.288 0.000 0.676 0.036
#> GSM312865 4 0.5130 0.6236 0.000 0.220 0.000 0.680 0.100
#> GSM312867 4 0.5130 0.6236 0.000 0.220 0.000 0.680 0.100
#> GSM312868 4 0.5425 0.5701 0.000 0.268 0.000 0.632 0.100
#> GSM312869 2 0.0000 0.7748 0.000 1.000 0.000 0.000 0.000
#> GSM312870 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM312872 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM312874 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM312875 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM312876 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM312877 5 0.4731 0.7179 0.032 0.000 0.328 0.000 0.640
#> GSM312879 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM312882 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM312883 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM312886 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM312887 1 0.1671 0.8950 0.924 0.000 0.000 0.076 0.000
#> GSM312890 1 0.0000 0.9744 1.000 0.000 0.000 0.000 0.000
#> GSM312893 1 0.0000 0.9744 1.000 0.000 0.000 0.000 0.000
#> GSM312894 1 0.0000 0.9744 1.000 0.000 0.000 0.000 0.000
#> GSM312895 1 0.0000 0.9744 1.000 0.000 0.000 0.000 0.000
#> GSM312937 1 0.0000 0.9744 1.000 0.000 0.000 0.000 0.000
#> GSM312938 1 0.1671 0.8950 0.924 0.000 0.000 0.076 0.000
#> GSM312939 1 0.0000 0.9744 1.000 0.000 0.000 0.000 0.000
#> GSM312940 1 0.0000 0.9744 1.000 0.000 0.000 0.000 0.000
#> GSM312941 1 0.0000 0.9744 1.000 0.000 0.000 0.000 0.000
#> GSM312942 5 0.4192 0.8540 0.032 0.000 0.232 0.000 0.736
#> GSM312943 5 0.3055 0.9240 0.016 0.000 0.144 0.000 0.840
#> GSM312944 5 0.3055 0.9240 0.016 0.000 0.144 0.000 0.840
#> GSM312945 5 0.3229 0.9121 0.032 0.000 0.128 0.000 0.840
#> GSM312946 5 0.3055 0.9240 0.016 0.000 0.144 0.000 0.840
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM312811 2 0.1957 0.8977 0.000 0.888 0.000 0.000 0.112 0.000
#> GSM312812 2 0.0547 0.9534 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM312813 2 0.0000 0.9583 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312814 2 0.2135 0.8852 0.000 0.872 0.000 0.000 0.128 0.000
#> GSM312815 2 0.0713 0.9512 0.000 0.972 0.000 0.000 0.028 0.000
#> GSM312816 5 0.1387 0.8848 0.000 0.068 0.000 0.000 0.932 0.000
#> GSM312817 2 0.1327 0.9273 0.000 0.936 0.000 0.000 0.064 0.000
#> GSM312818 5 0.0000 0.9617 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM312819 2 0.2300 0.8511 0.000 0.856 0.000 0.000 0.144 0.000
#> GSM312820 5 0.0000 0.9617 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM312821 5 0.0000 0.9617 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM312822 2 0.2092 0.8880 0.000 0.876 0.000 0.000 0.124 0.000
#> GSM312823 2 0.0000 0.9583 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312824 2 0.0000 0.9583 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312825 2 0.0146 0.9580 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM312826 2 0.0000 0.9583 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312839 2 0.0000 0.9583 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312840 2 0.0000 0.9583 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312841 2 0.1075 0.9404 0.000 0.952 0.000 0.000 0.048 0.000
#> GSM312843 4 0.3868 0.0955 0.000 0.492 0.000 0.508 0.000 0.000
#> GSM312844 2 0.0000 0.9583 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312845 4 0.0000 0.9245 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312846 4 0.0000 0.9245 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312847 4 0.0000 0.9245 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312848 4 0.0000 0.9245 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312849 4 0.0146 0.9227 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM312851 4 0.0790 0.9121 0.000 0.000 0.000 0.968 0.032 0.000
#> GSM312853 4 0.0790 0.9121 0.000 0.000 0.000 0.968 0.032 0.000
#> GSM312854 4 0.0790 0.9121 0.000 0.000 0.000 0.968 0.032 0.000
#> GSM312856 4 0.0146 0.9237 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM312857 4 0.0790 0.9121 0.000 0.000 0.000 0.968 0.032 0.000
#> GSM312858 4 0.0000 0.9245 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312859 2 0.0000 0.9583 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312860 2 0.0260 0.9563 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM312861 2 0.0260 0.9553 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM312862 2 0.0458 0.9506 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM312863 4 0.0291 0.9228 0.000 0.004 0.000 0.992 0.004 0.000
#> GSM312864 2 0.2520 0.8512 0.000 0.844 0.000 0.004 0.152 0.000
#> GSM312865 4 0.0000 0.9245 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312867 4 0.0000 0.9245 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312868 4 0.2941 0.6423 0.000 0.220 0.000 0.780 0.000 0.000
#> GSM312869 2 0.0146 0.9580 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM312870 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312872 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312874 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312875 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312876 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312877 6 0.2793 0.7483 0.000 0.000 0.200 0.000 0.000 0.800
#> GSM312879 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312882 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312883 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312886 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312887 1 0.0146 0.9952 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM312890 1 0.0000 0.9995 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312893 1 0.0000 0.9995 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312894 1 0.0000 0.9995 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312895 1 0.0000 0.9995 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312937 1 0.0000 0.9995 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312938 1 0.0000 0.9995 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312939 1 0.0000 0.9995 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312940 1 0.0000 0.9995 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312941 1 0.0000 0.9995 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312942 6 0.2092 0.8328 0.000 0.000 0.124 0.000 0.000 0.876
#> GSM312943 6 0.0000 0.9180 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM312944 6 0.0000 0.9180 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM312945 6 0.0000 0.9180 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM312946 6 0.0000 0.9180 0.000 0.000 0.000 0.000 0.000 1.000
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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:mclust 67 1.68e-10 2
#> CV:mclust 63 2.18e-17 3
#> CV:mclust 61 6.65e-20 4
#> CV:mclust 55 1.18e-21 5
#> CV:mclust 66 3.45e-27 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "NMF"]
# you can also extract it by
# res = res_list["CV:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 67 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 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.973 0.988 0.4838 0.518 0.518
#> 3 3 0.935 0.919 0.966 0.2748 0.810 0.656
#> 4 4 0.656 0.643 0.809 0.1383 0.857 0.654
#> 5 5 0.697 0.773 0.865 0.0889 0.878 0.615
#> 6 6 0.956 0.897 0.955 0.0536 0.949 0.786
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM312811 2 0.0000 0.987 0.000 1.000
#> GSM312812 2 0.0000 0.987 0.000 1.000
#> GSM312813 2 0.0000 0.987 0.000 1.000
#> GSM312814 2 0.0000 0.987 0.000 1.000
#> GSM312815 2 0.0000 0.987 0.000 1.000
#> GSM312816 2 0.0000 0.987 0.000 1.000
#> GSM312817 2 0.0000 0.987 0.000 1.000
#> GSM312818 2 0.5629 0.846 0.132 0.868
#> GSM312819 2 0.0000 0.987 0.000 1.000
#> GSM312820 2 0.0000 0.987 0.000 1.000
#> GSM312821 2 0.0000 0.987 0.000 1.000
#> GSM312822 2 0.0000 0.987 0.000 1.000
#> GSM312823 2 0.0000 0.987 0.000 1.000
#> GSM312824 2 0.0000 0.987 0.000 1.000
#> GSM312825 2 0.0000 0.987 0.000 1.000
#> GSM312826 2 0.0000 0.987 0.000 1.000
#> GSM312839 2 0.0000 0.987 0.000 1.000
#> GSM312840 2 0.0000 0.987 0.000 1.000
#> GSM312841 2 0.0000 0.987 0.000 1.000
#> GSM312843 2 0.0000 0.987 0.000 1.000
#> GSM312844 2 0.0000 0.987 0.000 1.000
#> GSM312845 1 0.8555 0.603 0.720 0.280
#> GSM312846 2 0.8499 0.619 0.276 0.724
#> GSM312847 2 0.0376 0.984 0.004 0.996
#> GSM312848 2 0.0000 0.987 0.000 1.000
#> GSM312849 2 0.0000 0.987 0.000 1.000
#> GSM312851 2 0.0000 0.987 0.000 1.000
#> GSM312853 2 0.0000 0.987 0.000 1.000
#> GSM312854 2 0.0000 0.987 0.000 1.000
#> GSM312856 2 0.0000 0.987 0.000 1.000
#> GSM312857 2 0.0000 0.987 0.000 1.000
#> GSM312858 2 0.0000 0.987 0.000 1.000
#> GSM312859 2 0.0000 0.987 0.000 1.000
#> GSM312860 2 0.0000 0.987 0.000 1.000
#> GSM312861 2 0.0000 0.987 0.000 1.000
#> GSM312862 2 0.0000 0.987 0.000 1.000
#> GSM312863 2 0.0000 0.987 0.000 1.000
#> GSM312864 2 0.0000 0.987 0.000 1.000
#> GSM312865 2 0.0000 0.987 0.000 1.000
#> GSM312867 2 0.4431 0.894 0.092 0.908
#> GSM312868 2 0.0000 0.987 0.000 1.000
#> GSM312869 2 0.0000 0.987 0.000 1.000
#> GSM312870 1 0.0000 0.989 1.000 0.000
#> GSM312872 1 0.0000 0.989 1.000 0.000
#> GSM312874 1 0.0000 0.989 1.000 0.000
#> GSM312875 1 0.0000 0.989 1.000 0.000
#> GSM312876 1 0.0000 0.989 1.000 0.000
#> GSM312877 1 0.0000 0.989 1.000 0.000
#> GSM312879 1 0.0000 0.989 1.000 0.000
#> GSM312882 1 0.0000 0.989 1.000 0.000
#> GSM312883 1 0.0000 0.989 1.000 0.000
#> GSM312886 1 0.0000 0.989 1.000 0.000
#> GSM312887 1 0.0000 0.989 1.000 0.000
#> GSM312890 1 0.0000 0.989 1.000 0.000
#> GSM312893 1 0.0000 0.989 1.000 0.000
#> GSM312894 1 0.0000 0.989 1.000 0.000
#> GSM312895 1 0.0000 0.989 1.000 0.000
#> GSM312937 1 0.0000 0.989 1.000 0.000
#> GSM312938 1 0.0000 0.989 1.000 0.000
#> GSM312939 1 0.0000 0.989 1.000 0.000
#> GSM312940 1 0.0000 0.989 1.000 0.000
#> GSM312941 1 0.0000 0.989 1.000 0.000
#> GSM312942 1 0.0000 0.989 1.000 0.000
#> GSM312943 1 0.0000 0.989 1.000 0.000
#> GSM312944 1 0.0000 0.989 1.000 0.000
#> GSM312945 1 0.0000 0.989 1.000 0.000
#> GSM312946 1 0.0000 0.989 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM312811 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312812 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312813 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312814 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312815 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312816 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312817 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312818 2 0.5988 0.421 0.000 0.632 0.368
#> GSM312819 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312820 2 0.0237 0.961 0.000 0.996 0.004
#> GSM312821 2 0.0747 0.952 0.000 0.984 0.016
#> GSM312822 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312823 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312824 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312825 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312826 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312839 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312840 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312841 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312843 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312844 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312845 1 0.0000 0.946 1.000 0.000 0.000
#> GSM312846 1 0.0000 0.946 1.000 0.000 0.000
#> GSM312847 1 0.0000 0.946 1.000 0.000 0.000
#> GSM312848 2 0.5216 0.667 0.260 0.740 0.000
#> GSM312849 1 0.0000 0.946 1.000 0.000 0.000
#> GSM312851 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312853 2 0.0237 0.961 0.004 0.996 0.000
#> GSM312854 2 0.3879 0.819 0.152 0.848 0.000
#> GSM312856 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312857 2 0.2356 0.901 0.072 0.928 0.000
#> GSM312858 2 0.5650 0.571 0.312 0.688 0.000
#> GSM312859 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312860 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312861 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312862 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312863 2 0.0424 0.958 0.008 0.992 0.000
#> GSM312864 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312865 1 0.0000 0.946 1.000 0.000 0.000
#> GSM312867 1 0.0000 0.946 1.000 0.000 0.000
#> GSM312868 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312869 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312870 3 0.0000 0.990 0.000 0.000 1.000
#> GSM312872 3 0.0000 0.990 0.000 0.000 1.000
#> GSM312874 3 0.0000 0.990 0.000 0.000 1.000
#> GSM312875 3 0.0000 0.990 0.000 0.000 1.000
#> GSM312876 3 0.0000 0.990 0.000 0.000 1.000
#> GSM312877 3 0.1289 0.964 0.032 0.000 0.968
#> GSM312879 3 0.0000 0.990 0.000 0.000 1.000
#> GSM312882 3 0.0000 0.990 0.000 0.000 1.000
#> GSM312883 3 0.0000 0.990 0.000 0.000 1.000
#> GSM312886 3 0.0000 0.990 0.000 0.000 1.000
#> GSM312887 1 0.6235 0.232 0.564 0.000 0.436
#> GSM312890 1 0.0000 0.946 1.000 0.000 0.000
#> GSM312893 1 0.0000 0.946 1.000 0.000 0.000
#> GSM312894 1 0.0000 0.946 1.000 0.000 0.000
#> GSM312895 1 0.0000 0.946 1.000 0.000 0.000
#> GSM312937 1 0.0000 0.946 1.000 0.000 0.000
#> GSM312938 1 0.0000 0.946 1.000 0.000 0.000
#> GSM312939 1 0.0000 0.946 1.000 0.000 0.000
#> GSM312940 1 0.0000 0.946 1.000 0.000 0.000
#> GSM312941 1 0.0000 0.946 1.000 0.000 0.000
#> GSM312942 3 0.1964 0.938 0.056 0.000 0.944
#> GSM312943 1 0.2959 0.861 0.900 0.000 0.100
#> GSM312944 1 0.0592 0.938 0.988 0.000 0.012
#> GSM312945 1 0.1643 0.914 0.956 0.000 0.044
#> GSM312946 1 0.6126 0.361 0.600 0.000 0.400
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM312811 2 0.1118 0.8328 0.000 0.964 0.000 0.036
#> GSM312812 2 0.0000 0.8492 0.000 1.000 0.000 0.000
#> GSM312813 2 0.0000 0.8492 0.000 1.000 0.000 0.000
#> GSM312814 2 0.1557 0.8213 0.000 0.944 0.000 0.056
#> GSM312815 2 0.0336 0.8461 0.000 0.992 0.000 0.008
#> GSM312816 2 0.3311 0.7249 0.000 0.828 0.000 0.172
#> GSM312817 2 0.0000 0.8492 0.000 1.000 0.000 0.000
#> GSM312818 2 0.7569 0.1004 0.000 0.436 0.368 0.196
#> GSM312819 2 0.0000 0.8492 0.000 1.000 0.000 0.000
#> GSM312820 2 0.4716 0.6662 0.000 0.764 0.040 0.196
#> GSM312821 2 0.6205 0.5298 0.000 0.668 0.136 0.196
#> GSM312822 2 0.3074 0.7453 0.000 0.848 0.000 0.152
#> GSM312823 2 0.0000 0.8492 0.000 1.000 0.000 0.000
#> GSM312824 2 0.0000 0.8492 0.000 1.000 0.000 0.000
#> GSM312825 2 0.0469 0.8419 0.000 0.988 0.000 0.012
#> GSM312826 2 0.0000 0.8492 0.000 1.000 0.000 0.000
#> GSM312839 2 0.0000 0.8492 0.000 1.000 0.000 0.000
#> GSM312840 2 0.0000 0.8492 0.000 1.000 0.000 0.000
#> GSM312841 2 0.0000 0.8492 0.000 1.000 0.000 0.000
#> GSM312843 2 0.3907 0.6452 0.000 0.768 0.000 0.232
#> GSM312844 2 0.0000 0.8492 0.000 1.000 0.000 0.000
#> GSM312845 1 0.2647 0.8065 0.880 0.000 0.000 0.120
#> GSM312846 1 0.1867 0.8340 0.928 0.000 0.000 0.072
#> GSM312847 1 0.4741 0.5718 0.668 0.004 0.000 0.328
#> GSM312848 4 0.7921 0.1722 0.320 0.332 0.000 0.348
#> GSM312849 1 0.5495 0.6022 0.728 0.176 0.000 0.096
#> GSM312851 4 0.5500 -0.0425 0.016 0.464 0.000 0.520
#> GSM312853 4 0.5917 0.0186 0.036 0.444 0.000 0.520
#> GSM312854 4 0.7285 0.1244 0.308 0.176 0.000 0.516
#> GSM312856 4 0.6242 0.0649 0.056 0.424 0.000 0.520
#> GSM312857 4 0.6554 0.1102 0.080 0.400 0.000 0.520
#> GSM312858 2 0.7272 -0.0460 0.160 0.496 0.000 0.344
#> GSM312859 2 0.0000 0.8492 0.000 1.000 0.000 0.000
#> GSM312860 2 0.0188 0.8471 0.000 0.996 0.000 0.004
#> GSM312861 2 0.2589 0.7492 0.000 0.884 0.000 0.116
#> GSM312862 2 0.4103 0.5253 0.000 0.744 0.000 0.256
#> GSM312863 4 0.5696 -0.0607 0.024 0.480 0.000 0.496
#> GSM312864 2 0.4522 0.5185 0.000 0.680 0.000 0.320
#> GSM312865 1 0.4837 0.5411 0.648 0.004 0.000 0.348
#> GSM312867 1 0.2888 0.8090 0.872 0.004 0.000 0.124
#> GSM312868 2 0.4072 0.5584 0.000 0.748 0.000 0.252
#> GSM312869 2 0.0000 0.8492 0.000 1.000 0.000 0.000
#> GSM312870 3 0.0188 0.9475 0.000 0.000 0.996 0.004
#> GSM312872 3 0.0188 0.9475 0.000 0.000 0.996 0.004
#> GSM312874 3 0.0188 0.9475 0.000 0.000 0.996 0.004
#> GSM312875 3 0.0188 0.9482 0.000 0.000 0.996 0.004
#> GSM312876 3 0.0188 0.9482 0.000 0.000 0.996 0.004
#> GSM312877 3 0.6885 0.4558 0.164 0.000 0.588 0.248
#> GSM312879 3 0.0000 0.9484 0.000 0.000 1.000 0.000
#> GSM312882 3 0.0188 0.9482 0.000 0.000 0.996 0.004
#> GSM312883 3 0.0592 0.9403 0.000 0.000 0.984 0.016
#> GSM312886 3 0.0000 0.9484 0.000 0.000 1.000 0.000
#> GSM312887 1 0.4509 0.5732 0.708 0.000 0.288 0.004
#> GSM312890 1 0.0592 0.8506 0.984 0.000 0.000 0.016
#> GSM312893 1 0.0336 0.8464 0.992 0.000 0.000 0.008
#> GSM312894 1 0.1297 0.8285 0.964 0.000 0.020 0.016
#> GSM312895 1 0.0336 0.8464 0.992 0.000 0.000 0.008
#> GSM312937 1 0.0000 0.8496 1.000 0.000 0.000 0.000
#> GSM312938 1 0.2530 0.8004 0.888 0.000 0.000 0.112
#> GSM312939 1 0.0188 0.8503 0.996 0.000 0.000 0.004
#> GSM312940 1 0.0592 0.8506 0.984 0.000 0.000 0.016
#> GSM312941 1 0.0000 0.8496 1.000 0.000 0.000 0.000
#> GSM312942 4 0.7660 0.0676 0.324 0.000 0.228 0.448
#> GSM312943 4 0.7478 0.1025 0.344 0.000 0.188 0.468
#> GSM312944 4 0.7460 0.0966 0.348 0.000 0.184 0.468
#> GSM312945 4 0.7478 0.1025 0.344 0.000 0.188 0.468
#> GSM312946 4 0.7478 0.1025 0.344 0.000 0.188 0.468
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM312811 2 0.1364 0.8595 0.000 0.952 0.000 0.036 0.012
#> GSM312812 2 0.0000 0.8896 0.000 1.000 0.000 0.000 0.000
#> GSM312813 2 0.0000 0.8896 0.000 1.000 0.000 0.000 0.000
#> GSM312814 2 0.2694 0.8102 0.000 0.884 0.000 0.076 0.040
#> GSM312815 2 0.0000 0.8896 0.000 1.000 0.000 0.000 0.000
#> GSM312816 2 0.4696 0.6699 0.000 0.736 0.000 0.156 0.108
#> GSM312817 2 0.0000 0.8896 0.000 1.000 0.000 0.000 0.000
#> GSM312818 2 0.8495 0.0971 0.000 0.328 0.192 0.248 0.232
#> GSM312819 2 0.0000 0.8896 0.000 1.000 0.000 0.000 0.000
#> GSM312820 2 0.7037 0.4517 0.000 0.536 0.048 0.196 0.220
#> GSM312821 2 0.7832 0.3066 0.000 0.440 0.092 0.236 0.232
#> GSM312822 2 0.3670 0.7551 0.000 0.820 0.000 0.112 0.068
#> GSM312823 2 0.0000 0.8896 0.000 1.000 0.000 0.000 0.000
#> GSM312824 2 0.0000 0.8896 0.000 1.000 0.000 0.000 0.000
#> GSM312825 2 0.0000 0.8896 0.000 1.000 0.000 0.000 0.000
#> GSM312826 2 0.0000 0.8896 0.000 1.000 0.000 0.000 0.000
#> GSM312839 2 0.0000 0.8896 0.000 1.000 0.000 0.000 0.000
#> GSM312840 2 0.0000 0.8896 0.000 1.000 0.000 0.000 0.000
#> GSM312841 2 0.0000 0.8896 0.000 1.000 0.000 0.000 0.000
#> GSM312843 4 0.3461 0.7976 0.000 0.224 0.000 0.772 0.004
#> GSM312844 2 0.0000 0.8896 0.000 1.000 0.000 0.000 0.000
#> GSM312845 1 0.4816 -0.0470 0.496 0.000 0.008 0.488 0.008
#> GSM312846 1 0.0955 0.8394 0.968 0.004 0.000 0.028 0.000
#> GSM312847 4 0.4235 0.2087 0.424 0.000 0.000 0.576 0.000
#> GSM312848 4 0.4734 0.7934 0.088 0.188 0.000 0.724 0.000
#> GSM312849 1 0.5447 0.4791 0.672 0.244 0.000 0.048 0.036
#> GSM312851 4 0.3616 0.8011 0.004 0.116 0.000 0.828 0.052
#> GSM312853 4 0.2886 0.8162 0.004 0.116 0.000 0.864 0.016
#> GSM312854 4 0.2754 0.8020 0.040 0.080 0.000 0.880 0.000
#> GSM312856 4 0.2672 0.8180 0.004 0.116 0.000 0.872 0.008
#> GSM312857 4 0.3113 0.8136 0.020 0.100 0.000 0.864 0.016
#> GSM312858 4 0.4871 0.7849 0.084 0.212 0.000 0.704 0.000
#> GSM312859 2 0.0000 0.8896 0.000 1.000 0.000 0.000 0.000
#> GSM312860 2 0.0162 0.8866 0.000 0.996 0.000 0.000 0.004
#> GSM312861 4 0.4249 0.5382 0.000 0.432 0.000 0.568 0.000
#> GSM312862 5 0.4680 0.1575 0.000 0.448 0.004 0.008 0.540
#> GSM312863 4 0.3106 0.8246 0.020 0.140 0.000 0.840 0.000
#> GSM312864 4 0.3789 0.7968 0.000 0.224 0.000 0.760 0.016
#> GSM312865 4 0.3636 0.5421 0.272 0.000 0.000 0.728 0.000
#> GSM312867 1 0.4201 0.2390 0.592 0.000 0.000 0.408 0.000
#> GSM312868 4 0.3752 0.7525 0.000 0.292 0.000 0.708 0.000
#> GSM312869 2 0.0000 0.8896 0.000 1.000 0.000 0.000 0.000
#> GSM312870 3 0.0510 0.9465 0.000 0.000 0.984 0.016 0.000
#> GSM312872 3 0.0162 0.9495 0.000 0.000 0.996 0.004 0.000
#> GSM312874 3 0.0609 0.9449 0.000 0.000 0.980 0.020 0.000
#> GSM312875 3 0.0703 0.9510 0.000 0.000 0.976 0.000 0.024
#> GSM312876 3 0.0703 0.9510 0.000 0.000 0.976 0.000 0.024
#> GSM312877 3 0.3944 0.6777 0.016 0.000 0.756 0.004 0.224
#> GSM312879 3 0.0566 0.9520 0.000 0.000 0.984 0.004 0.012
#> GSM312882 3 0.0794 0.9495 0.000 0.000 0.972 0.000 0.028
#> GSM312883 3 0.1205 0.9401 0.000 0.000 0.956 0.004 0.040
#> GSM312886 3 0.0671 0.9486 0.000 0.000 0.980 0.016 0.004
#> GSM312887 1 0.2833 0.7308 0.864 0.000 0.120 0.004 0.012
#> GSM312890 1 0.0000 0.8560 1.000 0.000 0.000 0.000 0.000
#> GSM312893 1 0.0000 0.8560 1.000 0.000 0.000 0.000 0.000
#> GSM312894 1 0.0771 0.8408 0.976 0.000 0.020 0.004 0.000
#> GSM312895 1 0.0000 0.8560 1.000 0.000 0.000 0.000 0.000
#> GSM312937 1 0.0000 0.8560 1.000 0.000 0.000 0.000 0.000
#> GSM312938 1 0.0290 0.8524 0.992 0.000 0.000 0.008 0.000
#> GSM312939 1 0.0000 0.8560 1.000 0.000 0.000 0.000 0.000
#> GSM312940 1 0.0000 0.8560 1.000 0.000 0.000 0.000 0.000
#> GSM312941 1 0.0000 0.8560 1.000 0.000 0.000 0.000 0.000
#> GSM312942 5 0.4069 0.8353 0.096 0.000 0.112 0.000 0.792
#> GSM312943 5 0.4123 0.8453 0.108 0.000 0.104 0.000 0.788
#> GSM312944 5 0.4169 0.8438 0.116 0.000 0.100 0.000 0.784
#> GSM312945 5 0.4262 0.8382 0.124 0.000 0.100 0.000 0.776
#> GSM312946 5 0.4073 0.8443 0.104 0.000 0.104 0.000 0.792
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM312811 2 0.1444 0.872 0.000 0.928 0.000 0.000 0.072 0.000
#> GSM312812 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312813 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312814 2 0.2730 0.722 0.000 0.808 0.000 0.000 0.192 0.000
#> GSM312815 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312816 2 0.3765 0.225 0.000 0.596 0.000 0.000 0.404 0.000
#> GSM312817 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312818 5 0.1333 0.806 0.000 0.048 0.008 0.000 0.944 0.000
#> GSM312819 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312820 5 0.2762 0.844 0.000 0.196 0.000 0.000 0.804 0.000
#> GSM312821 5 0.2260 0.883 0.000 0.140 0.000 0.000 0.860 0.000
#> GSM312822 2 0.3244 0.590 0.000 0.732 0.000 0.000 0.268 0.000
#> GSM312823 2 0.0363 0.932 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM312824 2 0.0146 0.935 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM312825 2 0.0363 0.932 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM312826 2 0.0363 0.932 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM312839 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312840 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312841 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312843 4 0.0000 0.918 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312844 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312845 4 0.5231 0.495 0.260 0.000 0.116 0.616 0.008 0.000
#> GSM312846 1 0.0363 0.965 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM312847 4 0.0891 0.902 0.024 0.000 0.000 0.968 0.008 0.000
#> GSM312848 4 0.0260 0.916 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM312849 1 0.3507 0.715 0.800 0.164 0.012 0.004 0.020 0.000
#> GSM312851 4 0.1501 0.856 0.000 0.000 0.000 0.924 0.076 0.000
#> GSM312853 4 0.0000 0.918 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312854 4 0.0000 0.918 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312856 4 0.0000 0.918 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312857 4 0.0000 0.918 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312858 4 0.0146 0.918 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM312859 2 0.0363 0.932 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM312860 2 0.0363 0.932 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM312861 4 0.0820 0.905 0.000 0.016 0.000 0.972 0.012 0.000
#> GSM312862 6 0.1714 0.838 0.000 0.092 0.000 0.000 0.000 0.908
#> GSM312863 4 0.0000 0.918 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312864 4 0.0937 0.886 0.000 0.040 0.000 0.960 0.000 0.000
#> GSM312865 4 0.0146 0.918 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM312867 4 0.4091 0.133 0.472 0.000 0.000 0.520 0.008 0.000
#> GSM312868 4 0.0146 0.918 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM312869 2 0.0146 0.935 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM312870 3 0.0865 0.978 0.000 0.000 0.964 0.000 0.036 0.000
#> GSM312872 3 0.0790 0.979 0.000 0.000 0.968 0.000 0.032 0.000
#> GSM312874 3 0.0865 0.978 0.000 0.000 0.964 0.000 0.036 0.000
#> GSM312875 3 0.0146 0.978 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM312876 3 0.0146 0.979 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM312877 3 0.0260 0.977 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM312879 3 0.0790 0.979 0.000 0.000 0.968 0.000 0.032 0.000
#> GSM312882 3 0.0260 0.977 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM312883 3 0.0260 0.977 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM312886 3 0.1007 0.974 0.000 0.000 0.956 0.000 0.044 0.000
#> GSM312887 1 0.0458 0.962 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM312890 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312893 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312894 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312895 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312937 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312938 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312939 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312940 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312941 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312942 6 0.0000 0.970 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM312943 6 0.0000 0.970 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM312944 6 0.0000 0.970 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM312945 6 0.0000 0.970 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM312946 6 0.0000 0.970 0.000 0.000 0.000 0.000 0.000 1.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:NMF 67 7.40e-10 2
#> CV:NMF 64 4.83e-14 3
#> CV:NMF 52 1.98e-13 4
#> CV:NMF 59 5.26e-25 5
#> CV:NMF 64 1.23e-23 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "hclust"]
# you can also extract it by
# res = res_list["MAD:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 67 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4754 0.525 0.525
#> 3 3 0.801 0.927 0.935 0.1996 0.931 0.869
#> 4 4 0.732 0.911 0.905 0.1197 0.935 0.857
#> 5 5 1.000 0.962 0.977 0.2037 0.841 0.593
#> 6 6 0.884 0.859 0.900 0.0396 1.000 1.000
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
#> GSM312811 2 0 1 0 1
#> GSM312812 2 0 1 0 1
#> GSM312813 2 0 1 0 1
#> GSM312814 2 0 1 0 1
#> GSM312815 2 0 1 0 1
#> GSM312816 2 0 1 0 1
#> GSM312817 2 0 1 0 1
#> GSM312818 2 0 1 0 1
#> GSM312819 2 0 1 0 1
#> GSM312820 2 0 1 0 1
#> GSM312821 2 0 1 0 1
#> GSM312822 2 0 1 0 1
#> GSM312823 2 0 1 0 1
#> GSM312824 2 0 1 0 1
#> GSM312825 2 0 1 0 1
#> GSM312826 2 0 1 0 1
#> GSM312839 2 0 1 0 1
#> GSM312840 2 0 1 0 1
#> GSM312841 2 0 1 0 1
#> GSM312843 2 0 1 0 1
#> GSM312844 2 0 1 0 1
#> GSM312845 2 0 1 0 1
#> GSM312846 2 0 1 0 1
#> GSM312847 2 0 1 0 1
#> GSM312848 2 0 1 0 1
#> GSM312849 2 0 1 0 1
#> GSM312851 2 0 1 0 1
#> GSM312853 2 0 1 0 1
#> GSM312854 2 0 1 0 1
#> GSM312856 2 0 1 0 1
#> GSM312857 2 0 1 0 1
#> GSM312858 2 0 1 0 1
#> GSM312859 2 0 1 0 1
#> GSM312860 2 0 1 0 1
#> GSM312861 2 0 1 0 1
#> GSM312862 2 0 1 0 1
#> GSM312863 2 0 1 0 1
#> GSM312864 2 0 1 0 1
#> GSM312865 2 0 1 0 1
#> GSM312867 2 0 1 0 1
#> GSM312868 2 0 1 0 1
#> GSM312869 2 0 1 0 1
#> GSM312870 1 0 1 1 0
#> GSM312872 1 0 1 1 0
#> GSM312874 1 0 1 1 0
#> GSM312875 1 0 1 1 0
#> GSM312876 1 0 1 1 0
#> GSM312877 1 0 1 1 0
#> GSM312879 1 0 1 1 0
#> GSM312882 1 0 1 1 0
#> GSM312883 1 0 1 1 0
#> GSM312886 1 0 1 1 0
#> GSM312887 1 0 1 1 0
#> GSM312890 1 0 1 1 0
#> GSM312893 1 0 1 1 0
#> GSM312894 1 0 1 1 0
#> GSM312895 1 0 1 1 0
#> GSM312937 1 0 1 1 0
#> GSM312938 1 0 1 1 0
#> GSM312939 1 0 1 1 0
#> GSM312940 1 0 1 1 0
#> GSM312941 1 0 1 1 0
#> GSM312942 1 0 1 1 0
#> GSM312943 1 0 1 1 0
#> GSM312944 1 0 1 1 0
#> GSM312945 1 0 1 1 0
#> GSM312946 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM312811 2 0.460 0.882 0 0.796 0.204
#> GSM312812 2 0.470 0.879 0 0.788 0.212
#> GSM312813 2 0.470 0.879 0 0.788 0.212
#> GSM312814 2 0.445 0.885 0 0.808 0.192
#> GSM312815 2 0.470 0.879 0 0.788 0.212
#> GSM312816 3 0.000 1.000 0 0.000 1.000
#> GSM312817 2 0.470 0.879 0 0.788 0.212
#> GSM312818 3 0.000 1.000 0 0.000 1.000
#> GSM312819 2 0.484 0.871 0 0.776 0.224
#> GSM312820 3 0.000 1.000 0 0.000 1.000
#> GSM312821 3 0.000 1.000 0 0.000 1.000
#> GSM312822 2 0.445 0.885 0 0.808 0.192
#> GSM312823 2 0.445 0.885 0 0.808 0.192
#> GSM312824 2 0.470 0.879 0 0.788 0.212
#> GSM312825 2 0.470 0.879 0 0.788 0.212
#> GSM312826 2 0.470 0.879 0 0.788 0.212
#> GSM312839 2 0.470 0.879 0 0.788 0.212
#> GSM312840 2 0.484 0.871 0 0.776 0.224
#> GSM312841 2 0.484 0.871 0 0.776 0.224
#> GSM312843 2 0.400 0.885 0 0.840 0.160
#> GSM312844 2 0.445 0.885 0 0.808 0.192
#> GSM312845 2 0.000 0.859 0 1.000 0.000
#> GSM312846 2 0.000 0.859 0 1.000 0.000
#> GSM312847 2 0.000 0.859 0 1.000 0.000
#> GSM312848 2 0.000 0.859 0 1.000 0.000
#> GSM312849 2 0.000 0.859 0 1.000 0.000
#> GSM312851 2 0.000 0.859 0 1.000 0.000
#> GSM312853 2 0.000 0.859 0 1.000 0.000
#> GSM312854 2 0.000 0.859 0 1.000 0.000
#> GSM312856 2 0.000 0.859 0 1.000 0.000
#> GSM312857 2 0.000 0.859 0 1.000 0.000
#> GSM312858 2 0.000 0.859 0 1.000 0.000
#> GSM312859 2 0.440 0.885 0 0.812 0.188
#> GSM312860 2 0.435 0.885 0 0.816 0.184
#> GSM312861 2 0.000 0.859 0 1.000 0.000
#> GSM312862 2 0.400 0.885 0 0.840 0.160
#> GSM312863 2 0.000 0.859 0 1.000 0.000
#> GSM312864 2 0.465 0.879 0 0.792 0.208
#> GSM312865 2 0.000 0.859 0 1.000 0.000
#> GSM312867 2 0.000 0.859 0 1.000 0.000
#> GSM312868 2 0.000 0.859 0 1.000 0.000
#> GSM312869 2 0.470 0.879 0 0.788 0.212
#> GSM312870 1 0.000 1.000 1 0.000 0.000
#> GSM312872 1 0.000 1.000 1 0.000 0.000
#> GSM312874 1 0.000 1.000 1 0.000 0.000
#> GSM312875 1 0.000 1.000 1 0.000 0.000
#> GSM312876 1 0.000 1.000 1 0.000 0.000
#> GSM312877 1 0.000 1.000 1 0.000 0.000
#> GSM312879 1 0.000 1.000 1 0.000 0.000
#> GSM312882 1 0.000 1.000 1 0.000 0.000
#> GSM312883 1 0.000 1.000 1 0.000 0.000
#> GSM312886 1 0.000 1.000 1 0.000 0.000
#> GSM312887 1 0.000 1.000 1 0.000 0.000
#> GSM312890 1 0.000 1.000 1 0.000 0.000
#> GSM312893 1 0.000 1.000 1 0.000 0.000
#> GSM312894 1 0.000 1.000 1 0.000 0.000
#> GSM312895 1 0.000 1.000 1 0.000 0.000
#> GSM312937 1 0.000 1.000 1 0.000 0.000
#> GSM312938 1 0.000 1.000 1 0.000 0.000
#> GSM312939 1 0.000 1.000 1 0.000 0.000
#> GSM312940 1 0.000 1.000 1 0.000 0.000
#> GSM312941 1 0.000 1.000 1 0.000 0.000
#> GSM312942 1 0.000 1.000 1 0.000 0.000
#> GSM312943 1 0.000 1.000 1 0.000 0.000
#> GSM312944 1 0.000 1.000 1 0.000 0.000
#> GSM312945 1 0.000 1.000 1 0.000 0.000
#> GSM312946 1 0.000 1.000 1 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM312811 2 0.0707 0.865 0.000 0.980 0.000 0.020
#> GSM312812 2 0.0921 0.864 0.000 0.972 0.000 0.028
#> GSM312813 2 0.0921 0.864 0.000 0.972 0.000 0.028
#> GSM312814 2 0.0469 0.868 0.000 0.988 0.000 0.012
#> GSM312815 2 0.1022 0.864 0.000 0.968 0.000 0.032
#> GSM312816 4 0.2704 1.000 0.000 0.124 0.000 0.876
#> GSM312817 2 0.0817 0.864 0.000 0.976 0.000 0.024
#> GSM312818 4 0.2704 1.000 0.000 0.124 0.000 0.876
#> GSM312819 2 0.1118 0.857 0.000 0.964 0.000 0.036
#> GSM312820 4 0.2704 1.000 0.000 0.124 0.000 0.876
#> GSM312821 4 0.2704 1.000 0.000 0.124 0.000 0.876
#> GSM312822 2 0.0469 0.868 0.000 0.988 0.000 0.012
#> GSM312823 2 0.0469 0.868 0.000 0.988 0.000 0.012
#> GSM312824 2 0.0817 0.864 0.000 0.976 0.000 0.024
#> GSM312825 2 0.0817 0.864 0.000 0.976 0.000 0.024
#> GSM312826 2 0.0817 0.864 0.000 0.976 0.000 0.024
#> GSM312839 2 0.1022 0.864 0.000 0.968 0.000 0.032
#> GSM312840 2 0.1118 0.857 0.000 0.964 0.000 0.036
#> GSM312841 2 0.1118 0.857 0.000 0.964 0.000 0.036
#> GSM312843 2 0.1388 0.868 0.000 0.960 0.012 0.028
#> GSM312844 2 0.0469 0.868 0.000 0.988 0.000 0.012
#> GSM312845 2 0.5174 0.834 0.000 0.760 0.116 0.124
#> GSM312846 2 0.5174 0.834 0.000 0.760 0.116 0.124
#> GSM312847 2 0.5174 0.834 0.000 0.760 0.116 0.124
#> GSM312848 2 0.5174 0.834 0.000 0.760 0.116 0.124
#> GSM312849 2 0.5174 0.834 0.000 0.760 0.116 0.124
#> GSM312851 2 0.5063 0.835 0.000 0.768 0.108 0.124
#> GSM312853 2 0.5063 0.835 0.000 0.768 0.108 0.124
#> GSM312854 2 0.5063 0.835 0.000 0.768 0.108 0.124
#> GSM312856 2 0.5063 0.835 0.000 0.768 0.108 0.124
#> GSM312857 2 0.5063 0.835 0.000 0.768 0.108 0.124
#> GSM312858 2 0.5174 0.834 0.000 0.760 0.116 0.124
#> GSM312859 2 0.0000 0.869 0.000 1.000 0.000 0.000
#> GSM312860 2 0.0188 0.869 0.000 0.996 0.000 0.004
#> GSM312861 2 0.5174 0.834 0.000 0.760 0.116 0.124
#> GSM312862 2 0.1388 0.868 0.000 0.960 0.012 0.028
#> GSM312863 2 0.5174 0.834 0.000 0.760 0.116 0.124
#> GSM312864 2 0.1545 0.864 0.000 0.952 0.008 0.040
#> GSM312865 2 0.5174 0.834 0.000 0.760 0.116 0.124
#> GSM312867 2 0.5174 0.834 0.000 0.760 0.116 0.124
#> GSM312868 2 0.5174 0.834 0.000 0.760 0.116 0.124
#> GSM312869 2 0.0817 0.864 0.000 0.976 0.000 0.024
#> GSM312870 3 0.2589 1.000 0.116 0.000 0.884 0.000
#> GSM312872 3 0.2589 1.000 0.116 0.000 0.884 0.000
#> GSM312874 3 0.2589 1.000 0.116 0.000 0.884 0.000
#> GSM312875 3 0.2589 1.000 0.116 0.000 0.884 0.000
#> GSM312876 3 0.2589 1.000 0.116 0.000 0.884 0.000
#> GSM312877 1 0.2814 0.824 0.868 0.000 0.132 0.000
#> GSM312879 3 0.2589 1.000 0.116 0.000 0.884 0.000
#> GSM312882 3 0.2589 1.000 0.116 0.000 0.884 0.000
#> GSM312883 3 0.2589 1.000 0.116 0.000 0.884 0.000
#> GSM312886 3 0.2589 1.000 0.116 0.000 0.884 0.000
#> GSM312887 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM312890 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM312893 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM312894 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM312895 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM312937 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM312938 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM312939 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM312940 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM312941 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM312942 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM312943 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM312944 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM312945 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM312946 1 0.0000 0.990 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM312811 2 0.0807 0.945 0.000 0.976 0.000 0.012 0.012
#> GSM312812 2 0.0566 0.944 0.000 0.984 0.000 0.012 0.004
#> GSM312813 2 0.0566 0.944 0.000 0.984 0.000 0.012 0.004
#> GSM312814 2 0.1469 0.941 0.000 0.948 0.000 0.036 0.016
#> GSM312815 2 0.0992 0.946 0.000 0.968 0.000 0.024 0.008
#> GSM312816 5 0.0290 1.000 0.000 0.008 0.000 0.000 0.992
#> GSM312817 2 0.0404 0.944 0.000 0.988 0.000 0.012 0.000
#> GSM312818 5 0.0290 1.000 0.000 0.008 0.000 0.000 0.992
#> GSM312819 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000
#> GSM312820 5 0.0290 1.000 0.000 0.008 0.000 0.000 0.992
#> GSM312821 5 0.0290 1.000 0.000 0.008 0.000 0.000 0.992
#> GSM312822 2 0.1469 0.941 0.000 0.948 0.000 0.036 0.016
#> GSM312823 2 0.1701 0.934 0.000 0.936 0.000 0.048 0.016
#> GSM312824 2 0.0703 0.946 0.000 0.976 0.000 0.024 0.000
#> GSM312825 2 0.0703 0.946 0.000 0.976 0.000 0.024 0.000
#> GSM312826 2 0.0703 0.946 0.000 0.976 0.000 0.024 0.000
#> GSM312839 2 0.0992 0.946 0.000 0.968 0.000 0.024 0.008
#> GSM312840 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000
#> GSM312841 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000
#> GSM312843 2 0.4309 0.605 0.000 0.676 0.000 0.308 0.016
#> GSM312844 2 0.1469 0.941 0.000 0.948 0.000 0.036 0.016
#> GSM312845 4 0.0000 0.997 0.000 0.000 0.000 1.000 0.000
#> GSM312846 4 0.0000 0.997 0.000 0.000 0.000 1.000 0.000
#> GSM312847 4 0.0000 0.997 0.000 0.000 0.000 1.000 0.000
#> GSM312848 4 0.0000 0.997 0.000 0.000 0.000 1.000 0.000
#> GSM312849 4 0.0000 0.997 0.000 0.000 0.000 1.000 0.000
#> GSM312851 4 0.0290 0.993 0.000 0.000 0.000 0.992 0.008
#> GSM312853 4 0.0290 0.993 0.000 0.000 0.000 0.992 0.008
#> GSM312854 4 0.0290 0.993 0.000 0.000 0.000 0.992 0.008
#> GSM312856 4 0.0290 0.993 0.000 0.000 0.000 0.992 0.008
#> GSM312857 4 0.0290 0.993 0.000 0.000 0.000 0.992 0.008
#> GSM312858 4 0.0000 0.997 0.000 0.000 0.000 1.000 0.000
#> GSM312859 2 0.1408 0.938 0.000 0.948 0.000 0.044 0.008
#> GSM312860 2 0.1557 0.933 0.000 0.940 0.000 0.052 0.008
#> GSM312861 4 0.0000 0.997 0.000 0.000 0.000 1.000 0.000
#> GSM312862 2 0.4309 0.605 0.000 0.676 0.000 0.308 0.016
#> GSM312863 4 0.0000 0.997 0.000 0.000 0.000 1.000 0.000
#> GSM312864 2 0.0963 0.923 0.000 0.964 0.000 0.036 0.000
#> GSM312865 4 0.0000 0.997 0.000 0.000 0.000 1.000 0.000
#> GSM312867 4 0.0000 0.997 0.000 0.000 0.000 1.000 0.000
#> GSM312868 4 0.0000 0.997 0.000 0.000 0.000 1.000 0.000
#> GSM312869 2 0.0404 0.944 0.000 0.988 0.000 0.012 0.000
#> GSM312870 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312872 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312874 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312875 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312876 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312877 1 0.3177 0.730 0.792 0.000 0.208 0.000 0.000
#> GSM312879 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312882 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312883 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312886 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312887 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM312890 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM312893 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM312894 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM312895 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM312937 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM312938 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM312939 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM312940 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM312941 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM312942 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM312943 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM312944 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM312945 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
#> GSM312946 1 0.0000 0.984 1.000 0.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM312811 2 0.0858 0.867 0.000 0.968 0.000 0.000 0.004 NA
#> GSM312812 2 0.0692 0.866 0.000 0.976 0.000 0.000 0.004 NA
#> GSM312813 2 0.0692 0.866 0.000 0.976 0.000 0.000 0.004 NA
#> GSM312814 2 0.0862 0.865 0.000 0.972 0.000 0.004 0.008 NA
#> GSM312815 2 0.0260 0.868 0.000 0.992 0.000 0.000 0.008 NA
#> GSM312816 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 NA
#> GSM312817 2 0.0547 0.865 0.000 0.980 0.000 0.000 0.000 NA
#> GSM312818 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 NA
#> GSM312819 2 0.3851 0.506 0.000 0.540 0.000 0.000 0.000 NA
#> GSM312820 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 NA
#> GSM312821 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 NA
#> GSM312822 2 0.0862 0.865 0.000 0.972 0.000 0.004 0.008 NA
#> GSM312823 2 0.1173 0.861 0.000 0.960 0.000 0.016 0.008 NA
#> GSM312824 2 0.0000 0.868 0.000 1.000 0.000 0.000 0.000 NA
#> GSM312825 2 0.0000 0.868 0.000 1.000 0.000 0.000 0.000 NA
#> GSM312826 2 0.0000 0.868 0.000 1.000 0.000 0.000 0.000 NA
#> GSM312839 2 0.0260 0.868 0.000 0.992 0.000 0.000 0.008 NA
#> GSM312840 2 0.3843 0.513 0.000 0.548 0.000 0.000 0.000 NA
#> GSM312841 2 0.3847 0.508 0.000 0.544 0.000 0.000 0.000 NA
#> GSM312843 2 0.4130 0.602 0.000 0.700 0.000 0.264 0.008 NA
#> GSM312844 2 0.0862 0.865 0.000 0.972 0.000 0.004 0.008 NA
#> GSM312845 4 0.2662 0.820 0.000 0.024 0.000 0.856 0.000 NA
#> GSM312846 4 0.2662 0.820 0.000 0.024 0.000 0.856 0.000 NA
#> GSM312847 4 0.2662 0.820 0.000 0.024 0.000 0.856 0.000 NA
#> GSM312848 4 0.0547 0.837 0.000 0.020 0.000 0.980 0.000 NA
#> GSM312849 4 0.2662 0.820 0.000 0.024 0.000 0.856 0.000 NA
#> GSM312851 4 0.3351 0.743 0.000 0.000 0.000 0.712 0.000 NA
#> GSM312853 4 0.3351 0.743 0.000 0.000 0.000 0.712 0.000 NA
#> GSM312854 4 0.3351 0.743 0.000 0.000 0.000 0.712 0.000 NA
#> GSM312856 4 0.3351 0.743 0.000 0.000 0.000 0.712 0.000 NA
#> GSM312857 4 0.3351 0.743 0.000 0.000 0.000 0.712 0.000 NA
#> GSM312858 4 0.0547 0.837 0.000 0.020 0.000 0.980 0.000 NA
#> GSM312859 2 0.0806 0.865 0.000 0.972 0.000 0.008 0.000 NA
#> GSM312860 2 0.1003 0.861 0.000 0.964 0.000 0.016 0.000 NA
#> GSM312861 4 0.2662 0.820 0.000 0.024 0.000 0.856 0.000 NA
#> GSM312862 2 0.4130 0.602 0.000 0.700 0.000 0.264 0.008 NA
#> GSM312863 4 0.2743 0.795 0.000 0.008 0.000 0.828 0.000 NA
#> GSM312864 2 0.3998 0.462 0.000 0.504 0.000 0.004 0.000 NA
#> GSM312865 4 0.0547 0.837 0.000 0.020 0.000 0.980 0.000 NA
#> GSM312867 4 0.2662 0.820 0.000 0.024 0.000 0.856 0.000 NA
#> GSM312868 4 0.0547 0.837 0.000 0.020 0.000 0.980 0.000 NA
#> GSM312869 2 0.0547 0.865 0.000 0.980 0.000 0.000 0.000 NA
#> GSM312870 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 NA
#> GSM312872 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 NA
#> GSM312874 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 NA
#> GSM312875 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 NA
#> GSM312876 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 NA
#> GSM312877 1 0.3103 0.758 0.784 0.000 0.208 0.000 0.000 NA
#> GSM312879 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 NA
#> GSM312882 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 NA
#> GSM312883 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 NA
#> GSM312886 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 NA
#> GSM312887 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000 NA
#> GSM312890 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000 NA
#> GSM312893 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000 NA
#> GSM312894 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000 NA
#> GSM312895 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000 NA
#> GSM312937 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000 NA
#> GSM312938 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000 NA
#> GSM312939 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000 NA
#> GSM312940 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000 NA
#> GSM312941 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000 NA
#> GSM312942 1 0.2178 0.904 0.868 0.000 0.000 0.000 0.000 NA
#> GSM312943 1 0.2178 0.904 0.868 0.000 0.000 0.000 0.000 NA
#> GSM312944 1 0.2178 0.904 0.868 0.000 0.000 0.000 0.000 NA
#> GSM312945 1 0.2178 0.904 0.868 0.000 0.000 0.000 0.000 NA
#> GSM312946 1 0.2178 0.904 0.868 0.000 0.000 0.000 0.000 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:hclust 67 1.68e-10 2
#> MAD:hclust 67 6.34e-10 3
#> MAD:hclust 67 1.51e-16 4
#> MAD:hclust 67 9.85e-21 5
#> MAD:hclust 66 1.57e-20 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "kmeans"]
# you can also extract it by
# res = res_list["MAD:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 67 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 0.998 0.998 0.4754 0.525 0.525
#> 3 3 0.615 0.501 0.772 0.2796 0.902 0.814
#> 4 4 0.599 0.734 0.741 0.1441 0.764 0.491
#> 5 5 0.684 0.764 0.771 0.0851 0.914 0.700
#> 6 6 0.738 0.736 0.760 0.0536 0.959 0.819
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
#> GSM312811 2 0.0000 0.998 0.000 1.000
#> GSM312812 2 0.0000 0.998 0.000 1.000
#> GSM312813 2 0.0000 0.998 0.000 1.000
#> GSM312814 2 0.0000 0.998 0.000 1.000
#> GSM312815 2 0.0000 0.998 0.000 1.000
#> GSM312816 2 0.0000 0.998 0.000 1.000
#> GSM312817 2 0.0000 0.998 0.000 1.000
#> GSM312818 2 0.0000 0.998 0.000 1.000
#> GSM312819 2 0.0000 0.998 0.000 1.000
#> GSM312820 2 0.0000 0.998 0.000 1.000
#> GSM312821 2 0.0000 0.998 0.000 1.000
#> GSM312822 2 0.0000 0.998 0.000 1.000
#> GSM312823 2 0.0000 0.998 0.000 1.000
#> GSM312824 2 0.0000 0.998 0.000 1.000
#> GSM312825 2 0.0000 0.998 0.000 1.000
#> GSM312826 2 0.0000 0.998 0.000 1.000
#> GSM312839 2 0.0000 0.998 0.000 1.000
#> GSM312840 2 0.0000 0.998 0.000 1.000
#> GSM312841 2 0.0000 0.998 0.000 1.000
#> GSM312843 2 0.0000 0.998 0.000 1.000
#> GSM312844 2 0.0000 0.998 0.000 1.000
#> GSM312845 2 0.0376 0.997 0.004 0.996
#> GSM312846 2 0.0376 0.997 0.004 0.996
#> GSM312847 2 0.0376 0.997 0.004 0.996
#> GSM312848 2 0.0376 0.997 0.004 0.996
#> GSM312849 2 0.0376 0.997 0.004 0.996
#> GSM312851 2 0.0376 0.997 0.004 0.996
#> GSM312853 2 0.0376 0.997 0.004 0.996
#> GSM312854 2 0.0376 0.997 0.004 0.996
#> GSM312856 2 0.0376 0.997 0.004 0.996
#> GSM312857 2 0.0376 0.997 0.004 0.996
#> GSM312858 2 0.0376 0.997 0.004 0.996
#> GSM312859 2 0.0000 0.998 0.000 1.000
#> GSM312860 2 0.0000 0.998 0.000 1.000
#> GSM312861 2 0.0376 0.997 0.004 0.996
#> GSM312862 2 0.0000 0.998 0.000 1.000
#> GSM312863 2 0.0376 0.997 0.004 0.996
#> GSM312864 2 0.0000 0.998 0.000 1.000
#> GSM312865 2 0.0376 0.997 0.004 0.996
#> GSM312867 2 0.0376 0.997 0.004 0.996
#> GSM312868 2 0.0376 0.997 0.004 0.996
#> GSM312869 2 0.0000 0.998 0.000 1.000
#> GSM312870 1 0.0376 0.998 0.996 0.004
#> GSM312872 1 0.0376 0.998 0.996 0.004
#> GSM312874 1 0.0376 0.998 0.996 0.004
#> GSM312875 1 0.0376 0.998 0.996 0.004
#> GSM312876 1 0.0376 0.998 0.996 0.004
#> GSM312877 1 0.0376 0.998 0.996 0.004
#> GSM312879 1 0.0376 0.998 0.996 0.004
#> GSM312882 1 0.0376 0.998 0.996 0.004
#> GSM312883 1 0.0376 0.998 0.996 0.004
#> GSM312886 1 0.0376 0.998 0.996 0.004
#> GSM312887 1 0.0000 0.997 1.000 0.000
#> GSM312890 1 0.0000 0.997 1.000 0.000
#> GSM312893 1 0.0000 0.997 1.000 0.000
#> GSM312894 1 0.0000 0.997 1.000 0.000
#> GSM312895 1 0.0000 0.997 1.000 0.000
#> GSM312937 1 0.0000 0.997 1.000 0.000
#> GSM312938 1 0.0000 0.997 1.000 0.000
#> GSM312939 1 0.0000 0.997 1.000 0.000
#> GSM312940 1 0.0000 0.997 1.000 0.000
#> GSM312941 1 0.0000 0.997 1.000 0.000
#> GSM312942 1 0.0376 0.998 0.996 0.004
#> GSM312943 1 0.0376 0.998 0.996 0.004
#> GSM312944 1 0.0376 0.998 0.996 0.004
#> GSM312945 1 0.0376 0.998 0.996 0.004
#> GSM312946 1 0.0376 0.998 0.996 0.004
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM312811 2 0.3267 0.492 0.000 0.884 0.116
#> GSM312812 2 0.0592 0.566 0.000 0.988 0.012
#> GSM312813 2 0.0000 0.568 0.000 1.000 0.000
#> GSM312814 2 0.3267 0.492 0.000 0.884 0.116
#> GSM312815 2 0.0592 0.566 0.000 0.988 0.012
#> GSM312816 2 0.4452 0.415 0.000 0.808 0.192
#> GSM312817 2 0.0747 0.563 0.000 0.984 0.016
#> GSM312818 2 0.4452 0.415 0.000 0.808 0.192
#> GSM312819 2 0.3619 0.469 0.000 0.864 0.136
#> GSM312820 2 0.4452 0.415 0.000 0.808 0.192
#> GSM312821 2 0.4452 0.415 0.000 0.808 0.192
#> GSM312822 2 0.3267 0.492 0.000 0.884 0.116
#> GSM312823 2 0.0000 0.568 0.000 1.000 0.000
#> GSM312824 2 0.0000 0.568 0.000 1.000 0.000
#> GSM312825 2 0.0000 0.568 0.000 1.000 0.000
#> GSM312826 2 0.0000 0.568 0.000 1.000 0.000
#> GSM312839 2 0.0000 0.568 0.000 1.000 0.000
#> GSM312840 2 0.0424 0.567 0.000 0.992 0.008
#> GSM312841 2 0.0747 0.565 0.000 0.984 0.016
#> GSM312843 2 0.6140 -0.549 0.000 0.596 0.404
#> GSM312844 2 0.0000 0.568 0.000 1.000 0.000
#> GSM312845 2 0.6451 -0.485 0.008 0.608 0.384
#> GSM312846 2 0.6062 -0.471 0.000 0.616 0.384
#> GSM312847 2 0.6062 -0.471 0.000 0.616 0.384
#> GSM312848 2 0.6062 -0.471 0.000 0.616 0.384
#> GSM312849 2 0.6062 -0.471 0.000 0.616 0.384
#> GSM312851 3 0.6291 0.980 0.000 0.468 0.532
#> GSM312853 3 0.6295 0.989 0.000 0.472 0.528
#> GSM312854 3 0.6299 0.990 0.000 0.476 0.524
#> GSM312856 3 0.6299 0.990 0.000 0.476 0.524
#> GSM312857 3 0.6295 0.989 0.000 0.472 0.528
#> GSM312858 2 0.6062 -0.471 0.000 0.616 0.384
#> GSM312859 2 0.2448 0.475 0.000 0.924 0.076
#> GSM312860 2 0.3816 0.317 0.000 0.852 0.148
#> GSM312861 2 0.6062 -0.471 0.000 0.616 0.384
#> GSM312862 2 0.6062 -0.471 0.000 0.616 0.384
#> GSM312863 3 0.6299 0.990 0.000 0.476 0.524
#> GSM312864 2 0.5291 0.218 0.000 0.732 0.268
#> GSM312865 2 0.6062 -0.471 0.000 0.616 0.384
#> GSM312867 2 0.6062 -0.471 0.000 0.616 0.384
#> GSM312868 2 0.6062 -0.471 0.000 0.616 0.384
#> GSM312869 2 0.0000 0.568 0.000 1.000 0.000
#> GSM312870 1 0.6062 0.840 0.616 0.000 0.384
#> GSM312872 1 0.6062 0.840 0.616 0.000 0.384
#> GSM312874 1 0.6062 0.840 0.616 0.000 0.384
#> GSM312875 1 0.6062 0.840 0.616 0.000 0.384
#> GSM312876 1 0.6062 0.840 0.616 0.000 0.384
#> GSM312877 1 0.5529 0.856 0.704 0.000 0.296
#> GSM312879 1 0.6062 0.840 0.616 0.000 0.384
#> GSM312882 1 0.6062 0.840 0.616 0.000 0.384
#> GSM312883 1 0.6062 0.840 0.616 0.000 0.384
#> GSM312886 1 0.6062 0.840 0.616 0.000 0.384
#> GSM312887 1 0.0000 0.862 1.000 0.000 0.000
#> GSM312890 1 0.0000 0.862 1.000 0.000 0.000
#> GSM312893 1 0.0000 0.862 1.000 0.000 0.000
#> GSM312894 1 0.0000 0.862 1.000 0.000 0.000
#> GSM312895 1 0.0000 0.862 1.000 0.000 0.000
#> GSM312937 1 0.0000 0.862 1.000 0.000 0.000
#> GSM312938 1 0.0000 0.862 1.000 0.000 0.000
#> GSM312939 1 0.0000 0.862 1.000 0.000 0.000
#> GSM312940 1 0.0000 0.862 1.000 0.000 0.000
#> GSM312941 1 0.0000 0.862 1.000 0.000 0.000
#> GSM312942 1 0.4346 0.867 0.816 0.000 0.184
#> GSM312943 1 0.4346 0.867 0.816 0.000 0.184
#> GSM312944 1 0.4346 0.867 0.816 0.000 0.184
#> GSM312945 1 0.4346 0.867 0.816 0.000 0.184
#> GSM312946 1 0.4346 0.867 0.816 0.000 0.184
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM312811 2 0.5935 0.744 0.000 0.664 0.080 0.256
#> GSM312812 2 0.3356 0.812 0.000 0.824 0.000 0.176
#> GSM312813 2 0.3486 0.811 0.000 0.812 0.000 0.188
#> GSM312814 2 0.6326 0.730 0.000 0.636 0.108 0.256
#> GSM312815 2 0.3356 0.812 0.000 0.824 0.000 0.176
#> GSM312816 2 0.7830 0.465 0.000 0.404 0.324 0.272
#> GSM312817 2 0.3801 0.804 0.000 0.780 0.000 0.220
#> GSM312818 2 0.7830 0.465 0.000 0.404 0.324 0.272
#> GSM312819 2 0.5207 0.741 0.000 0.680 0.028 0.292
#> GSM312820 2 0.7830 0.465 0.000 0.404 0.324 0.272
#> GSM312821 2 0.7830 0.465 0.000 0.404 0.324 0.272
#> GSM312822 2 0.6326 0.730 0.000 0.636 0.108 0.256
#> GSM312823 2 0.3569 0.810 0.000 0.804 0.000 0.196
#> GSM312824 2 0.3569 0.810 0.000 0.804 0.000 0.196
#> GSM312825 2 0.3569 0.810 0.000 0.804 0.000 0.196
#> GSM312826 2 0.3569 0.810 0.000 0.804 0.000 0.196
#> GSM312839 2 0.3569 0.810 0.000 0.804 0.000 0.196
#> GSM312840 2 0.3356 0.812 0.000 0.824 0.000 0.176
#> GSM312841 2 0.4238 0.805 0.000 0.796 0.028 0.176
#> GSM312843 4 0.3606 0.831 0.000 0.140 0.020 0.840
#> GSM312844 2 0.3569 0.810 0.000 0.804 0.000 0.196
#> GSM312845 4 0.3311 0.837 0.000 0.172 0.000 0.828
#> GSM312846 4 0.3311 0.837 0.000 0.172 0.000 0.828
#> GSM312847 4 0.3172 0.842 0.000 0.160 0.000 0.840
#> GSM312848 4 0.3074 0.844 0.000 0.152 0.000 0.848
#> GSM312849 4 0.3311 0.837 0.000 0.172 0.000 0.828
#> GSM312851 4 0.2216 0.754 0.000 0.000 0.092 0.908
#> GSM312853 4 0.2216 0.754 0.000 0.000 0.092 0.908
#> GSM312854 4 0.2216 0.754 0.000 0.000 0.092 0.908
#> GSM312856 4 0.2216 0.754 0.000 0.000 0.092 0.908
#> GSM312857 4 0.2216 0.754 0.000 0.000 0.092 0.908
#> GSM312858 4 0.3074 0.844 0.000 0.152 0.000 0.848
#> GSM312859 2 0.4454 0.657 0.000 0.692 0.000 0.308
#> GSM312860 2 0.4697 0.555 0.000 0.644 0.000 0.356
#> GSM312861 4 0.3311 0.837 0.000 0.172 0.000 0.828
#> GSM312862 4 0.3356 0.834 0.000 0.176 0.000 0.824
#> GSM312863 4 0.1792 0.763 0.000 0.000 0.068 0.932
#> GSM312864 4 0.5815 0.158 0.000 0.288 0.060 0.652
#> GSM312865 4 0.3401 0.844 0.000 0.152 0.008 0.840
#> GSM312867 4 0.3311 0.837 0.000 0.172 0.000 0.828
#> GSM312868 4 0.3529 0.843 0.000 0.152 0.012 0.836
#> GSM312869 2 0.3569 0.810 0.000 0.804 0.000 0.196
#> GSM312870 3 0.4907 0.995 0.420 0.000 0.580 0.000
#> GSM312872 3 0.4907 0.995 0.420 0.000 0.580 0.000
#> GSM312874 3 0.4907 0.995 0.420 0.000 0.580 0.000
#> GSM312875 3 0.4907 0.995 0.420 0.000 0.580 0.000
#> GSM312876 3 0.4907 0.995 0.420 0.000 0.580 0.000
#> GSM312877 1 0.5288 -0.728 0.520 0.008 0.472 0.000
#> GSM312879 3 0.5080 0.994 0.420 0.004 0.576 0.000
#> GSM312882 3 0.5212 0.992 0.420 0.008 0.572 0.000
#> GSM312883 3 0.5212 0.992 0.420 0.008 0.572 0.000
#> GSM312886 3 0.5212 0.992 0.420 0.008 0.572 0.000
#> GSM312887 1 0.0336 0.755 0.992 0.008 0.000 0.000
#> GSM312890 1 0.0000 0.758 1.000 0.000 0.000 0.000
#> GSM312893 1 0.0000 0.758 1.000 0.000 0.000 0.000
#> GSM312894 1 0.0000 0.758 1.000 0.000 0.000 0.000
#> GSM312895 1 0.0000 0.758 1.000 0.000 0.000 0.000
#> GSM312937 1 0.0000 0.758 1.000 0.000 0.000 0.000
#> GSM312938 1 0.0336 0.755 0.992 0.008 0.000 0.000
#> GSM312939 1 0.0000 0.758 1.000 0.000 0.000 0.000
#> GSM312940 1 0.0000 0.758 1.000 0.000 0.000 0.000
#> GSM312941 1 0.0000 0.758 1.000 0.000 0.000 0.000
#> GSM312942 1 0.6216 0.409 0.660 0.120 0.220 0.000
#> GSM312943 1 0.6216 0.409 0.660 0.120 0.220 0.000
#> GSM312944 1 0.6216 0.409 0.660 0.120 0.220 0.000
#> GSM312945 1 0.6216 0.409 0.660 0.120 0.220 0.000
#> GSM312946 1 0.6216 0.409 0.660 0.120 0.220 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM312811 2 0.4723 0.654 0.076 0.772 0.000 0.032 0.120
#> GSM312812 2 0.0486 0.877 0.004 0.988 0.000 0.004 0.004
#> GSM312813 2 0.1731 0.870 0.040 0.940 0.000 0.012 0.008
#> GSM312814 2 0.4615 0.620 0.052 0.772 0.000 0.032 0.144
#> GSM312815 2 0.1059 0.875 0.020 0.968 0.000 0.004 0.008
#> GSM312816 5 0.5139 1.000 0.000 0.316 0.000 0.060 0.624
#> GSM312817 2 0.2569 0.854 0.076 0.896 0.000 0.016 0.012
#> GSM312818 5 0.5139 1.000 0.000 0.316 0.000 0.060 0.624
#> GSM312819 2 0.3595 0.754 0.064 0.852 0.000 0.044 0.040
#> GSM312820 5 0.5139 1.000 0.000 0.316 0.000 0.060 0.624
#> GSM312821 5 0.5139 1.000 0.000 0.316 0.000 0.060 0.624
#> GSM312822 2 0.4615 0.620 0.052 0.772 0.000 0.032 0.144
#> GSM312823 2 0.1267 0.875 0.024 0.960 0.000 0.012 0.004
#> GSM312824 2 0.0404 0.879 0.000 0.988 0.000 0.012 0.000
#> GSM312825 2 0.0404 0.879 0.000 0.988 0.000 0.012 0.000
#> GSM312826 2 0.0404 0.879 0.000 0.988 0.000 0.012 0.000
#> GSM312839 2 0.1012 0.877 0.020 0.968 0.000 0.012 0.000
#> GSM312840 2 0.1116 0.871 0.028 0.964 0.000 0.004 0.004
#> GSM312841 2 0.1750 0.844 0.028 0.936 0.000 0.000 0.036
#> GSM312843 4 0.6178 0.718 0.128 0.212 0.000 0.628 0.032
#> GSM312844 2 0.1012 0.877 0.020 0.968 0.000 0.012 0.000
#> GSM312845 4 0.2648 0.809 0.000 0.152 0.000 0.848 0.000
#> GSM312846 4 0.2648 0.809 0.000 0.152 0.000 0.848 0.000
#> GSM312847 4 0.2605 0.809 0.000 0.148 0.000 0.852 0.000
#> GSM312848 4 0.2516 0.810 0.000 0.140 0.000 0.860 0.000
#> GSM312849 4 0.2648 0.809 0.000 0.152 0.000 0.848 0.000
#> GSM312851 4 0.6191 0.677 0.164 0.052 0.000 0.652 0.132
#> GSM312853 4 0.6191 0.677 0.164 0.052 0.000 0.652 0.132
#> GSM312854 4 0.6127 0.681 0.164 0.048 0.000 0.656 0.132
#> GSM312856 4 0.6127 0.681 0.164 0.048 0.000 0.656 0.132
#> GSM312857 4 0.6191 0.677 0.164 0.052 0.000 0.652 0.132
#> GSM312858 4 0.3099 0.810 0.012 0.132 0.000 0.848 0.008
#> GSM312859 2 0.2828 0.759 0.020 0.872 0.000 0.104 0.004
#> GSM312860 2 0.3128 0.660 0.004 0.824 0.000 0.168 0.004
#> GSM312861 4 0.2648 0.809 0.000 0.152 0.000 0.848 0.000
#> GSM312862 4 0.3850 0.776 0.032 0.172 0.000 0.792 0.004
#> GSM312863 4 0.5576 0.706 0.164 0.048 0.000 0.704 0.084
#> GSM312864 4 0.7876 0.153 0.188 0.308 0.000 0.408 0.096
#> GSM312865 4 0.2865 0.810 0.008 0.132 0.000 0.856 0.004
#> GSM312867 4 0.2648 0.809 0.000 0.152 0.000 0.848 0.000
#> GSM312868 4 0.4268 0.802 0.060 0.132 0.000 0.792 0.016
#> GSM312869 2 0.0404 0.879 0.000 0.988 0.000 0.012 0.000
#> GSM312870 3 0.0000 0.723 0.000 0.000 1.000 0.000 0.000
#> GSM312872 3 0.0000 0.723 0.000 0.000 1.000 0.000 0.000
#> GSM312874 3 0.0000 0.723 0.000 0.000 1.000 0.000 0.000
#> GSM312875 3 0.0000 0.723 0.000 0.000 1.000 0.000 0.000
#> GSM312876 3 0.0000 0.723 0.000 0.000 1.000 0.000 0.000
#> GSM312877 3 0.3696 0.647 0.092 0.000 0.840 0.028 0.040
#> GSM312879 3 0.1117 0.720 0.000 0.000 0.964 0.020 0.016
#> GSM312882 3 0.1830 0.715 0.000 0.000 0.932 0.028 0.040
#> GSM312883 3 0.1830 0.715 0.000 0.000 0.932 0.028 0.040
#> GSM312886 3 0.1493 0.718 0.000 0.000 0.948 0.024 0.028
#> GSM312887 1 0.4442 0.969 0.688 0.000 0.284 0.000 0.028
#> GSM312890 1 0.3707 0.992 0.716 0.000 0.284 0.000 0.000
#> GSM312893 1 0.3707 0.992 0.716 0.000 0.284 0.000 0.000
#> GSM312894 1 0.3707 0.992 0.716 0.000 0.284 0.000 0.000
#> GSM312895 1 0.3707 0.992 0.716 0.000 0.284 0.000 0.000
#> GSM312937 1 0.3707 0.992 0.716 0.000 0.284 0.000 0.000
#> GSM312938 1 0.4442 0.969 0.688 0.000 0.284 0.000 0.028
#> GSM312939 1 0.3707 0.992 0.716 0.000 0.284 0.000 0.000
#> GSM312940 1 0.3707 0.992 0.716 0.000 0.284 0.000 0.000
#> GSM312941 1 0.3707 0.992 0.716 0.000 0.284 0.000 0.000
#> GSM312942 3 0.7031 0.195 0.312 0.000 0.452 0.020 0.216
#> GSM312943 3 0.7031 0.195 0.312 0.000 0.452 0.020 0.216
#> GSM312944 3 0.7031 0.195 0.312 0.000 0.452 0.020 0.216
#> GSM312945 3 0.7031 0.195 0.312 0.000 0.452 0.020 0.216
#> GSM312946 3 0.7031 0.195 0.312 0.000 0.452 0.020 0.216
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM312811 2 0.6260 0.6191 0.136 0.632 0.000 0.024 0.104 0.104
#> GSM312812 2 0.0777 0.8457 0.024 0.972 0.000 0.000 0.000 0.004
#> GSM312813 2 0.3647 0.7929 0.100 0.820 0.000 0.008 0.012 0.060
#> GSM312814 2 0.6056 0.5982 0.096 0.652 0.000 0.028 0.144 0.080
#> GSM312815 2 0.1649 0.8411 0.032 0.932 0.000 0.000 0.000 0.036
#> GSM312816 5 0.3841 1.0000 0.000 0.168 0.000 0.068 0.764 0.000
#> GSM312817 2 0.4937 0.7497 0.144 0.720 0.000 0.008 0.028 0.100
#> GSM312818 5 0.3841 1.0000 0.000 0.168 0.000 0.068 0.764 0.000
#> GSM312819 2 0.4945 0.7221 0.116 0.744 0.000 0.032 0.032 0.076
#> GSM312820 5 0.3841 1.0000 0.000 0.168 0.000 0.068 0.764 0.000
#> GSM312821 5 0.3841 1.0000 0.000 0.168 0.000 0.068 0.764 0.000
#> GSM312822 2 0.6056 0.5982 0.096 0.652 0.000 0.028 0.144 0.080
#> GSM312823 2 0.2562 0.8383 0.032 0.896 0.000 0.008 0.016 0.048
#> GSM312824 2 0.0622 0.8443 0.000 0.980 0.000 0.008 0.000 0.012
#> GSM312825 2 0.0622 0.8443 0.000 0.980 0.000 0.008 0.000 0.012
#> GSM312826 2 0.0622 0.8443 0.000 0.980 0.000 0.008 0.000 0.012
#> GSM312839 2 0.1933 0.8414 0.032 0.920 0.000 0.004 0.000 0.044
#> GSM312840 2 0.1485 0.8347 0.028 0.944 0.000 0.004 0.000 0.024
#> GSM312841 2 0.1882 0.8246 0.028 0.928 0.000 0.000 0.020 0.024
#> GSM312843 4 0.7446 0.0826 0.112 0.252 0.000 0.452 0.024 0.160
#> GSM312844 2 0.2000 0.8410 0.032 0.916 0.000 0.004 0.000 0.048
#> GSM312845 6 0.5128 0.9347 0.008 0.072 0.000 0.356 0.000 0.564
#> GSM312846 6 0.5128 0.9347 0.008 0.072 0.000 0.356 0.000 0.564
#> GSM312847 6 0.5081 0.9340 0.008 0.068 0.000 0.356 0.000 0.568
#> GSM312848 6 0.5014 0.9238 0.008 0.060 0.000 0.368 0.000 0.564
#> GSM312849 6 0.5128 0.9347 0.008 0.072 0.000 0.356 0.000 0.564
#> GSM312851 4 0.0547 0.6889 0.000 0.020 0.000 0.980 0.000 0.000
#> GSM312853 4 0.0458 0.6927 0.000 0.016 0.000 0.984 0.000 0.000
#> GSM312854 4 0.0458 0.6927 0.000 0.016 0.000 0.984 0.000 0.000
#> GSM312856 4 0.0458 0.6927 0.000 0.016 0.000 0.984 0.000 0.000
#> GSM312857 4 0.0458 0.6927 0.000 0.016 0.000 0.984 0.000 0.000
#> GSM312858 6 0.5598 0.8582 0.016 0.056 0.000 0.400 0.016 0.512
#> GSM312859 2 0.2562 0.8048 0.008 0.892 0.000 0.012 0.024 0.064
#> GSM312860 2 0.3433 0.6894 0.000 0.808 0.000 0.020 0.020 0.152
#> GSM312861 6 0.5026 0.9327 0.000 0.072 0.000 0.356 0.004 0.568
#> GSM312862 6 0.6357 0.7248 0.044 0.100 0.000 0.296 0.020 0.540
#> GSM312863 4 0.1536 0.6407 0.004 0.016 0.000 0.940 0.000 0.040
#> GSM312864 4 0.7080 0.2584 0.128 0.236 0.000 0.520 0.040 0.076
#> GSM312865 6 0.5034 0.8731 0.008 0.056 0.000 0.404 0.000 0.532
#> GSM312867 6 0.4893 0.9342 0.000 0.072 0.000 0.356 0.000 0.572
#> GSM312868 4 0.5707 -0.7591 0.016 0.056 0.000 0.464 0.020 0.444
#> GSM312869 2 0.0622 0.8443 0.000 0.980 0.000 0.008 0.000 0.012
#> GSM312870 3 0.0000 0.7011 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312872 3 0.0000 0.7011 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312874 3 0.0000 0.7011 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312875 3 0.0000 0.7011 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312876 3 0.0000 0.7011 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312877 3 0.4082 0.6422 0.072 0.000 0.792 0.008 0.020 0.108
#> GSM312879 3 0.1333 0.6983 0.000 0.000 0.944 0.000 0.008 0.048
#> GSM312882 3 0.2699 0.6847 0.000 0.000 0.864 0.008 0.020 0.108
#> GSM312883 3 0.2699 0.6847 0.000 0.000 0.864 0.008 0.020 0.108
#> GSM312886 3 0.2095 0.6933 0.000 0.000 0.904 0.004 0.016 0.076
#> GSM312887 1 0.4317 0.9462 0.728 0.000 0.216 0.008 0.012 0.036
#> GSM312890 1 0.2912 0.9852 0.784 0.000 0.216 0.000 0.000 0.000
#> GSM312893 1 0.3052 0.9852 0.780 0.000 0.216 0.000 0.004 0.000
#> GSM312894 1 0.3052 0.9852 0.780 0.000 0.216 0.000 0.004 0.000
#> GSM312895 1 0.2912 0.9852 0.784 0.000 0.216 0.000 0.000 0.000
#> GSM312937 1 0.2912 0.9852 0.784 0.000 0.216 0.000 0.000 0.000
#> GSM312938 1 0.4317 0.9462 0.728 0.000 0.216 0.008 0.012 0.036
#> GSM312939 1 0.2912 0.9852 0.784 0.000 0.216 0.000 0.000 0.000
#> GSM312940 1 0.3052 0.9852 0.780 0.000 0.216 0.000 0.004 0.000
#> GSM312941 1 0.3052 0.9852 0.780 0.000 0.216 0.000 0.004 0.000
#> GSM312942 3 0.7417 0.2351 0.304 0.000 0.360 0.000 0.172 0.164
#> GSM312943 3 0.7417 0.2351 0.304 0.000 0.360 0.000 0.172 0.164
#> GSM312944 3 0.7417 0.2351 0.304 0.000 0.360 0.000 0.172 0.164
#> GSM312945 3 0.7417 0.2351 0.304 0.000 0.360 0.000 0.172 0.164
#> GSM312946 3 0.7417 0.2351 0.304 0.000 0.360 0.000 0.172 0.164
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:kmeans 67 1.68e-10 2
#> MAD:kmeans 44 2.94e-10 3
#> MAD:kmeans 56 3.78e-19 4
#> MAD:kmeans 61 2.43e-20 5
#> MAD:kmeans 59 8.96e-25 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "skmeans"]
# you can also extract it by
# res = res_list["MAD:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 67 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.990 0.996 0.4808 0.518 0.518
#> 3 3 1.000 0.939 0.970 0.3905 0.801 0.620
#> 4 4 0.904 0.898 0.929 0.1001 0.932 0.796
#> 5 5 0.802 0.668 0.845 0.0685 0.971 0.894
#> 6 6 0.849 0.811 0.838 0.0427 0.907 0.642
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
#> GSM312811 2 0.000 0.999 0.000 1.000
#> GSM312812 2 0.000 0.999 0.000 1.000
#> GSM312813 2 0.000 0.999 0.000 1.000
#> GSM312814 2 0.000 0.999 0.000 1.000
#> GSM312815 2 0.000 0.999 0.000 1.000
#> GSM312816 2 0.000 0.999 0.000 1.000
#> GSM312817 2 0.000 0.999 0.000 1.000
#> GSM312818 2 0.000 0.999 0.000 1.000
#> GSM312819 2 0.000 0.999 0.000 1.000
#> GSM312820 2 0.000 0.999 0.000 1.000
#> GSM312821 2 0.000 0.999 0.000 1.000
#> GSM312822 2 0.000 0.999 0.000 1.000
#> GSM312823 2 0.000 0.999 0.000 1.000
#> GSM312824 2 0.000 0.999 0.000 1.000
#> GSM312825 2 0.000 0.999 0.000 1.000
#> GSM312826 2 0.000 0.999 0.000 1.000
#> GSM312839 2 0.000 0.999 0.000 1.000
#> GSM312840 2 0.000 0.999 0.000 1.000
#> GSM312841 2 0.000 0.999 0.000 1.000
#> GSM312843 2 0.000 0.999 0.000 1.000
#> GSM312844 2 0.000 0.999 0.000 1.000
#> GSM312845 1 0.844 0.626 0.728 0.272
#> GSM312846 2 0.141 0.979 0.020 0.980
#> GSM312847 2 0.000 0.999 0.000 1.000
#> GSM312848 2 0.000 0.999 0.000 1.000
#> GSM312849 2 0.000 0.999 0.000 1.000
#> GSM312851 2 0.000 0.999 0.000 1.000
#> GSM312853 2 0.000 0.999 0.000 1.000
#> GSM312854 2 0.000 0.999 0.000 1.000
#> GSM312856 2 0.000 0.999 0.000 1.000
#> GSM312857 2 0.000 0.999 0.000 1.000
#> GSM312858 2 0.000 0.999 0.000 1.000
#> GSM312859 2 0.000 0.999 0.000 1.000
#> GSM312860 2 0.000 0.999 0.000 1.000
#> GSM312861 2 0.000 0.999 0.000 1.000
#> GSM312862 2 0.000 0.999 0.000 1.000
#> GSM312863 2 0.000 0.999 0.000 1.000
#> GSM312864 2 0.000 0.999 0.000 1.000
#> GSM312865 2 0.000 0.999 0.000 1.000
#> GSM312867 2 0.000 0.999 0.000 1.000
#> GSM312868 2 0.000 0.999 0.000 1.000
#> GSM312869 2 0.000 0.999 0.000 1.000
#> GSM312870 1 0.000 0.989 1.000 0.000
#> GSM312872 1 0.000 0.989 1.000 0.000
#> GSM312874 1 0.000 0.989 1.000 0.000
#> GSM312875 1 0.000 0.989 1.000 0.000
#> GSM312876 1 0.000 0.989 1.000 0.000
#> GSM312877 1 0.000 0.989 1.000 0.000
#> GSM312879 1 0.000 0.989 1.000 0.000
#> GSM312882 1 0.000 0.989 1.000 0.000
#> GSM312883 1 0.000 0.989 1.000 0.000
#> GSM312886 1 0.000 0.989 1.000 0.000
#> GSM312887 1 0.000 0.989 1.000 0.000
#> GSM312890 1 0.000 0.989 1.000 0.000
#> GSM312893 1 0.000 0.989 1.000 0.000
#> GSM312894 1 0.000 0.989 1.000 0.000
#> GSM312895 1 0.000 0.989 1.000 0.000
#> GSM312937 1 0.000 0.989 1.000 0.000
#> GSM312938 1 0.000 0.989 1.000 0.000
#> GSM312939 1 0.000 0.989 1.000 0.000
#> GSM312940 1 0.000 0.989 1.000 0.000
#> GSM312941 1 0.000 0.989 1.000 0.000
#> GSM312942 1 0.000 0.989 1.000 0.000
#> GSM312943 1 0.000 0.989 1.000 0.000
#> GSM312944 1 0.000 0.989 1.000 0.000
#> GSM312945 1 0.000 0.989 1.000 0.000
#> GSM312946 1 0.000 0.989 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM312811 2 0.1529 0.931 0 0.960 0.040
#> GSM312812 2 0.0000 0.942 0 1.000 0.000
#> GSM312813 2 0.0000 0.942 0 1.000 0.000
#> GSM312814 2 0.1529 0.931 0 0.960 0.040
#> GSM312815 2 0.0000 0.942 0 1.000 0.000
#> GSM312816 2 0.1529 0.931 0 0.960 0.040
#> GSM312817 2 0.0237 0.940 0 0.996 0.004
#> GSM312818 2 0.1529 0.931 0 0.960 0.040
#> GSM312819 2 0.1031 0.936 0 0.976 0.024
#> GSM312820 2 0.1529 0.931 0 0.960 0.040
#> GSM312821 2 0.1529 0.931 0 0.960 0.040
#> GSM312822 2 0.1529 0.931 0 0.960 0.040
#> GSM312823 2 0.0000 0.942 0 1.000 0.000
#> GSM312824 2 0.0000 0.942 0 1.000 0.000
#> GSM312825 2 0.0000 0.942 0 1.000 0.000
#> GSM312826 2 0.0000 0.942 0 1.000 0.000
#> GSM312839 2 0.0000 0.942 0 1.000 0.000
#> GSM312840 2 0.0000 0.942 0 1.000 0.000
#> GSM312841 2 0.0000 0.942 0 1.000 0.000
#> GSM312843 3 0.5291 0.578 0 0.268 0.732
#> GSM312844 2 0.0000 0.942 0 1.000 0.000
#> GSM312845 3 0.1529 0.964 0 0.040 0.960
#> GSM312846 3 0.1529 0.964 0 0.040 0.960
#> GSM312847 3 0.1529 0.964 0 0.040 0.960
#> GSM312848 3 0.1529 0.964 0 0.040 0.960
#> GSM312849 3 0.1529 0.964 0 0.040 0.960
#> GSM312851 3 0.0000 0.953 0 0.000 1.000
#> GSM312853 3 0.0000 0.953 0 0.000 1.000
#> GSM312854 3 0.0000 0.953 0 0.000 1.000
#> GSM312856 3 0.0000 0.953 0 0.000 1.000
#> GSM312857 3 0.0000 0.953 0 0.000 1.000
#> GSM312858 3 0.1529 0.964 0 0.040 0.960
#> GSM312859 2 0.1289 0.922 0 0.968 0.032
#> GSM312860 2 0.3340 0.834 0 0.880 0.120
#> GSM312861 3 0.1529 0.964 0 0.040 0.960
#> GSM312862 2 0.6204 0.235 0 0.576 0.424
#> GSM312863 3 0.0000 0.953 0 0.000 1.000
#> GSM312864 2 0.6235 0.307 0 0.564 0.436
#> GSM312865 3 0.1529 0.964 0 0.040 0.960
#> GSM312867 3 0.1529 0.964 0 0.040 0.960
#> GSM312868 3 0.1529 0.964 0 0.040 0.960
#> GSM312869 2 0.0000 0.942 0 1.000 0.000
#> GSM312870 1 0.0000 1.000 1 0.000 0.000
#> GSM312872 1 0.0000 1.000 1 0.000 0.000
#> GSM312874 1 0.0000 1.000 1 0.000 0.000
#> GSM312875 1 0.0000 1.000 1 0.000 0.000
#> GSM312876 1 0.0000 1.000 1 0.000 0.000
#> GSM312877 1 0.0000 1.000 1 0.000 0.000
#> GSM312879 1 0.0000 1.000 1 0.000 0.000
#> GSM312882 1 0.0000 1.000 1 0.000 0.000
#> GSM312883 1 0.0000 1.000 1 0.000 0.000
#> GSM312886 1 0.0000 1.000 1 0.000 0.000
#> GSM312887 1 0.0000 1.000 1 0.000 0.000
#> GSM312890 1 0.0000 1.000 1 0.000 0.000
#> GSM312893 1 0.0000 1.000 1 0.000 0.000
#> GSM312894 1 0.0000 1.000 1 0.000 0.000
#> GSM312895 1 0.0000 1.000 1 0.000 0.000
#> GSM312937 1 0.0000 1.000 1 0.000 0.000
#> GSM312938 1 0.0000 1.000 1 0.000 0.000
#> GSM312939 1 0.0000 1.000 1 0.000 0.000
#> GSM312940 1 0.0000 1.000 1 0.000 0.000
#> GSM312941 1 0.0000 1.000 1 0.000 0.000
#> GSM312942 1 0.0000 1.000 1 0.000 0.000
#> GSM312943 1 0.0000 1.000 1 0.000 0.000
#> GSM312944 1 0.0000 1.000 1 0.000 0.000
#> GSM312945 1 0.0000 1.000 1 0.000 0.000
#> GSM312946 1 0.0000 1.000 1 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM312811 2 0.2500 0.902 0.044 0.916 0.000 0.040
#> GSM312812 2 0.0000 0.926 0.000 1.000 0.000 0.000
#> GSM312813 2 0.0000 0.926 0.000 1.000 0.000 0.000
#> GSM312814 2 0.2675 0.899 0.048 0.908 0.000 0.044
#> GSM312815 2 0.0000 0.926 0.000 1.000 0.000 0.000
#> GSM312816 2 0.3398 0.881 0.068 0.872 0.000 0.060
#> GSM312817 2 0.0657 0.923 0.004 0.984 0.000 0.012
#> GSM312818 2 0.4387 0.862 0.068 0.840 0.032 0.060
#> GSM312819 2 0.0469 0.923 0.000 0.988 0.000 0.012
#> GSM312820 2 0.3398 0.881 0.068 0.872 0.000 0.060
#> GSM312821 2 0.3398 0.881 0.068 0.872 0.000 0.060
#> GSM312822 2 0.2761 0.897 0.048 0.904 0.000 0.048
#> GSM312823 2 0.0000 0.926 0.000 1.000 0.000 0.000
#> GSM312824 2 0.0000 0.926 0.000 1.000 0.000 0.000
#> GSM312825 2 0.0000 0.926 0.000 1.000 0.000 0.000
#> GSM312826 2 0.0000 0.926 0.000 1.000 0.000 0.000
#> GSM312839 2 0.0000 0.926 0.000 1.000 0.000 0.000
#> GSM312840 2 0.0000 0.926 0.000 1.000 0.000 0.000
#> GSM312841 2 0.0000 0.926 0.000 1.000 0.000 0.000
#> GSM312843 4 0.4722 0.521 0.008 0.300 0.000 0.692
#> GSM312844 2 0.0000 0.926 0.000 1.000 0.000 0.000
#> GSM312845 4 0.2125 0.907 0.076 0.004 0.000 0.920
#> GSM312846 4 0.2255 0.912 0.068 0.012 0.000 0.920
#> GSM312847 4 0.1938 0.935 0.012 0.052 0.000 0.936
#> GSM312848 4 0.1854 0.936 0.012 0.048 0.000 0.940
#> GSM312849 4 0.2101 0.932 0.012 0.060 0.000 0.928
#> GSM312851 4 0.1118 0.918 0.036 0.000 0.000 0.964
#> GSM312853 4 0.0707 0.926 0.020 0.000 0.000 0.980
#> GSM312854 4 0.0707 0.926 0.020 0.000 0.000 0.980
#> GSM312856 4 0.0707 0.926 0.020 0.000 0.000 0.980
#> GSM312857 4 0.0707 0.926 0.020 0.000 0.000 0.980
#> GSM312858 4 0.1474 0.936 0.000 0.052 0.000 0.948
#> GSM312859 2 0.0921 0.911 0.000 0.972 0.000 0.028
#> GSM312860 2 0.2149 0.861 0.000 0.912 0.000 0.088
#> GSM312861 4 0.2101 0.932 0.012 0.060 0.000 0.928
#> GSM312862 2 0.5060 0.280 0.004 0.584 0.000 0.412
#> GSM312863 4 0.0592 0.927 0.016 0.000 0.000 0.984
#> GSM312864 2 0.6005 0.194 0.040 0.500 0.000 0.460
#> GSM312865 4 0.1389 0.937 0.000 0.048 0.000 0.952
#> GSM312867 4 0.2101 0.932 0.012 0.060 0.000 0.928
#> GSM312868 4 0.1389 0.937 0.000 0.048 0.000 0.952
#> GSM312869 2 0.0000 0.926 0.000 1.000 0.000 0.000
#> GSM312870 3 0.0336 0.926 0.008 0.000 0.992 0.000
#> GSM312872 3 0.0336 0.926 0.008 0.000 0.992 0.000
#> GSM312874 3 0.0336 0.926 0.008 0.000 0.992 0.000
#> GSM312875 3 0.0336 0.926 0.008 0.000 0.992 0.000
#> GSM312876 3 0.0336 0.926 0.008 0.000 0.992 0.000
#> GSM312877 3 0.0336 0.926 0.008 0.000 0.992 0.000
#> GSM312879 3 0.0336 0.926 0.008 0.000 0.992 0.000
#> GSM312882 3 0.0336 0.926 0.008 0.000 0.992 0.000
#> GSM312883 3 0.0336 0.926 0.008 0.000 0.992 0.000
#> GSM312886 3 0.0336 0.926 0.008 0.000 0.992 0.000
#> GSM312887 1 0.2011 1.000 0.920 0.000 0.080 0.000
#> GSM312890 1 0.2011 1.000 0.920 0.000 0.080 0.000
#> GSM312893 1 0.2011 1.000 0.920 0.000 0.080 0.000
#> GSM312894 1 0.2011 1.000 0.920 0.000 0.080 0.000
#> GSM312895 1 0.2011 1.000 0.920 0.000 0.080 0.000
#> GSM312937 1 0.2011 1.000 0.920 0.000 0.080 0.000
#> GSM312938 1 0.2011 1.000 0.920 0.000 0.080 0.000
#> GSM312939 1 0.2011 1.000 0.920 0.000 0.080 0.000
#> GSM312940 1 0.2011 1.000 0.920 0.000 0.080 0.000
#> GSM312941 1 0.2011 1.000 0.920 0.000 0.080 0.000
#> GSM312942 3 0.3356 0.828 0.176 0.000 0.824 0.000
#> GSM312943 3 0.3356 0.828 0.176 0.000 0.824 0.000
#> GSM312944 3 0.3356 0.828 0.176 0.000 0.824 0.000
#> GSM312945 3 0.3356 0.828 0.176 0.000 0.824 0.000
#> GSM312946 3 0.3356 0.828 0.176 0.000 0.824 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM312811 2 0.029 0.2604 0.000 0.992 0.000 0.008 0.000
#> GSM312812 2 0.395 0.6311 0.000 0.668 0.000 0.000 0.332
#> GSM312813 2 0.395 0.6311 0.000 0.668 0.000 0.000 0.332
#> GSM312814 2 0.184 0.2142 0.000 0.932 0.000 0.036 0.032
#> GSM312815 2 0.395 0.6311 0.000 0.668 0.000 0.000 0.332
#> GSM312816 2 0.454 0.0347 0.000 0.712 0.000 0.240 0.048
#> GSM312817 2 0.407 0.6195 0.000 0.672 0.000 0.004 0.324
#> GSM312818 2 0.501 0.0180 0.000 0.696 0.016 0.240 0.048
#> GSM312819 2 0.393 0.6281 0.000 0.672 0.000 0.000 0.328
#> GSM312820 2 0.454 0.0347 0.000 0.712 0.000 0.240 0.048
#> GSM312821 2 0.454 0.0347 0.000 0.712 0.000 0.240 0.048
#> GSM312822 2 0.200 0.2076 0.000 0.924 0.000 0.036 0.040
#> GSM312823 2 0.395 0.6311 0.000 0.668 0.000 0.000 0.332
#> GSM312824 2 0.395 0.6311 0.000 0.668 0.000 0.000 0.332
#> GSM312825 2 0.395 0.6311 0.000 0.668 0.000 0.000 0.332
#> GSM312826 2 0.395 0.6311 0.000 0.668 0.000 0.000 0.332
#> GSM312839 2 0.395 0.6311 0.000 0.668 0.000 0.000 0.332
#> GSM312840 2 0.395 0.6311 0.000 0.668 0.000 0.000 0.332
#> GSM312841 2 0.395 0.6311 0.000 0.668 0.000 0.000 0.332
#> GSM312843 4 0.316 0.3777 0.000 0.188 0.000 0.808 0.004
#> GSM312844 2 0.395 0.6311 0.000 0.668 0.000 0.000 0.332
#> GSM312845 4 0.475 0.6474 0.016 0.000 0.000 0.500 0.484
#> GSM312846 4 0.491 0.6414 0.024 0.000 0.000 0.492 0.484
#> GSM312847 4 0.430 0.6569 0.000 0.000 0.000 0.516 0.484
#> GSM312848 4 0.430 0.6569 0.000 0.000 0.000 0.516 0.484
#> GSM312849 4 0.431 0.6496 0.000 0.000 0.000 0.508 0.492
#> GSM312851 4 0.281 0.5212 0.000 0.108 0.000 0.868 0.024
#> GSM312853 4 0.000 0.6365 0.000 0.000 0.000 1.000 0.000
#> GSM312854 4 0.000 0.6365 0.000 0.000 0.000 1.000 0.000
#> GSM312856 4 0.000 0.6365 0.000 0.000 0.000 1.000 0.000
#> GSM312857 4 0.000 0.6365 0.000 0.000 0.000 1.000 0.000
#> GSM312858 4 0.393 0.6847 0.000 0.000 0.000 0.672 0.328
#> GSM312859 2 0.403 0.5887 0.000 0.648 0.000 0.000 0.352
#> GSM312860 2 0.425 0.3480 0.000 0.568 0.000 0.000 0.432
#> GSM312861 4 0.425 0.6712 0.000 0.000 0.000 0.568 0.432
#> GSM312862 5 0.641 0.0000 0.000 0.396 0.000 0.172 0.432
#> GSM312863 4 0.112 0.6491 0.000 0.000 0.000 0.956 0.044
#> GSM312864 4 0.404 0.2081 0.000 0.276 0.000 0.712 0.012
#> GSM312865 4 0.391 0.6853 0.000 0.000 0.000 0.676 0.324
#> GSM312867 4 0.430 0.6585 0.000 0.000 0.000 0.520 0.480
#> GSM312868 4 0.388 0.6850 0.000 0.000 0.000 0.684 0.316
#> GSM312869 2 0.395 0.6311 0.000 0.668 0.000 0.000 0.332
#> GSM312870 3 0.000 0.9191 0.000 0.000 1.000 0.000 0.000
#> GSM312872 3 0.000 0.9191 0.000 0.000 1.000 0.000 0.000
#> GSM312874 3 0.000 0.9191 0.000 0.000 1.000 0.000 0.000
#> GSM312875 3 0.000 0.9191 0.000 0.000 1.000 0.000 0.000
#> GSM312876 3 0.000 0.9191 0.000 0.000 1.000 0.000 0.000
#> GSM312877 3 0.000 0.9191 0.000 0.000 1.000 0.000 0.000
#> GSM312879 3 0.000 0.9191 0.000 0.000 1.000 0.000 0.000
#> GSM312882 3 0.000 0.9191 0.000 0.000 1.000 0.000 0.000
#> GSM312883 3 0.000 0.9191 0.000 0.000 1.000 0.000 0.000
#> GSM312886 3 0.000 0.9191 0.000 0.000 1.000 0.000 0.000
#> GSM312887 1 0.000 1.0000 1.000 0.000 0.000 0.000 0.000
#> GSM312890 1 0.000 1.0000 1.000 0.000 0.000 0.000 0.000
#> GSM312893 1 0.000 1.0000 1.000 0.000 0.000 0.000 0.000
#> GSM312894 1 0.000 1.0000 1.000 0.000 0.000 0.000 0.000
#> GSM312895 1 0.000 1.0000 1.000 0.000 0.000 0.000 0.000
#> GSM312937 1 0.000 1.0000 1.000 0.000 0.000 0.000 0.000
#> GSM312938 1 0.000 1.0000 1.000 0.000 0.000 0.000 0.000
#> GSM312939 1 0.000 1.0000 1.000 0.000 0.000 0.000 0.000
#> GSM312940 1 0.000 1.0000 1.000 0.000 0.000 0.000 0.000
#> GSM312941 1 0.000 1.0000 1.000 0.000 0.000 0.000 0.000
#> GSM312942 3 0.463 0.8169 0.120 0.000 0.744 0.000 0.136
#> GSM312943 3 0.463 0.8169 0.120 0.000 0.744 0.000 0.136
#> GSM312944 3 0.463 0.8169 0.120 0.000 0.744 0.000 0.136
#> GSM312945 3 0.463 0.8169 0.120 0.000 0.744 0.000 0.136
#> GSM312946 3 0.463 0.8169 0.120 0.000 0.744 0.000 0.136
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM312811 5 0.3804 0.6539 0.000 0.424 0.00 0.000 0.576 0.000
#> GSM312812 2 0.0000 0.9415 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM312813 2 0.0000 0.9415 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM312814 5 0.4039 0.7713 0.000 0.352 0.00 0.016 0.632 0.000
#> GSM312815 2 0.1007 0.8949 0.000 0.956 0.00 0.000 0.044 0.000
#> GSM312816 5 0.5039 0.8460 0.000 0.180 0.00 0.180 0.640 0.000
#> GSM312817 2 0.0891 0.9146 0.000 0.968 0.00 0.008 0.024 0.000
#> GSM312818 5 0.5039 0.8460 0.000 0.180 0.00 0.180 0.640 0.000
#> GSM312819 2 0.0260 0.9367 0.000 0.992 0.00 0.000 0.008 0.000
#> GSM312820 5 0.5039 0.8460 0.000 0.180 0.00 0.180 0.640 0.000
#> GSM312821 5 0.5039 0.8460 0.000 0.180 0.00 0.180 0.640 0.000
#> GSM312822 5 0.3927 0.7776 0.000 0.344 0.00 0.012 0.644 0.000
#> GSM312823 2 0.0000 0.9415 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM312824 2 0.0000 0.9415 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM312825 2 0.0000 0.9415 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM312826 2 0.0000 0.9415 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM312839 2 0.0146 0.9398 0.000 0.996 0.00 0.000 0.004 0.000
#> GSM312840 2 0.0000 0.9415 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM312841 2 0.0146 0.9395 0.000 0.996 0.00 0.000 0.004 0.000
#> GSM312843 4 0.2771 0.6719 0.000 0.116 0.00 0.852 0.032 0.000
#> GSM312844 2 0.0146 0.9398 0.000 0.996 0.00 0.000 0.004 0.000
#> GSM312845 6 0.2597 0.9676 0.000 0.000 0.00 0.176 0.000 0.824
#> GSM312846 6 0.2597 0.9676 0.000 0.000 0.00 0.176 0.000 0.824
#> GSM312847 6 0.2597 0.9676 0.000 0.000 0.00 0.176 0.000 0.824
#> GSM312848 6 0.2912 0.9265 0.000 0.000 0.00 0.216 0.000 0.784
#> GSM312849 6 0.2703 0.9630 0.000 0.004 0.00 0.172 0.000 0.824
#> GSM312851 4 0.1327 0.7300 0.000 0.000 0.00 0.936 0.064 0.000
#> GSM312853 4 0.0000 0.7698 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM312854 4 0.0000 0.7698 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM312856 4 0.0000 0.7698 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM312857 4 0.0000 0.7698 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM312858 4 0.3961 -0.0176 0.000 0.000 0.00 0.556 0.004 0.440
#> GSM312859 2 0.0405 0.9317 0.000 0.988 0.00 0.000 0.004 0.008
#> GSM312860 2 0.1531 0.8564 0.000 0.928 0.00 0.000 0.004 0.068
#> GSM312861 6 0.4024 0.8702 0.000 0.044 0.00 0.220 0.004 0.732
#> GSM312862 2 0.6150 0.1277 0.000 0.520 0.00 0.160 0.032 0.288
#> GSM312863 4 0.0547 0.7597 0.000 0.000 0.00 0.980 0.000 0.020
#> GSM312864 4 0.3227 0.6331 0.000 0.088 0.00 0.828 0.084 0.000
#> GSM312865 4 0.3930 0.0644 0.000 0.000 0.00 0.576 0.004 0.420
#> GSM312867 6 0.2597 0.9676 0.000 0.000 0.00 0.176 0.000 0.824
#> GSM312868 4 0.3807 0.2300 0.000 0.000 0.00 0.628 0.004 0.368
#> GSM312869 2 0.0000 0.9415 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM312870 3 0.0000 0.8109 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM312872 3 0.0000 0.8109 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM312874 3 0.0000 0.8109 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM312875 3 0.0000 0.8109 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM312876 3 0.0000 0.8109 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM312877 3 0.0000 0.8109 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM312879 3 0.0000 0.8109 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM312882 3 0.0000 0.8109 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM312883 3 0.0000 0.8109 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM312886 3 0.0000 0.8109 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM312887 1 0.0000 1.0000 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM312890 1 0.0000 1.0000 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM312893 1 0.0000 1.0000 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM312894 1 0.0000 1.0000 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM312895 1 0.0000 1.0000 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM312937 1 0.0000 1.0000 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM312938 1 0.0000 1.0000 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM312939 1 0.0000 1.0000 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM312940 1 0.0000 1.0000 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM312941 1 0.0000 1.0000 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM312942 3 0.6649 0.5700 0.052 0.000 0.42 0.000 0.352 0.176
#> GSM312943 3 0.6649 0.5700 0.052 0.000 0.42 0.000 0.352 0.176
#> GSM312944 3 0.6649 0.5700 0.052 0.000 0.42 0.000 0.352 0.176
#> GSM312945 3 0.6649 0.5700 0.052 0.000 0.42 0.000 0.352 0.176
#> GSM312946 3 0.6649 0.5700 0.052 0.000 0.42 0.000 0.352 0.176
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:skmeans 67 7.40e-10 2
#> MAD:skmeans 65 9.56e-15 3
#> MAD:skmeans 65 1.02e-22 4
#> MAD:skmeans 56 3.57e-19 5
#> MAD:skmeans 63 3.27e-26 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "pam"]
# you can also extract it by
# res = res_list["MAD:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 67 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 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4754 0.525 0.525
#> 3 3 0.954 0.955 0.974 0.1434 0.935 0.876
#> 4 4 0.717 0.904 0.895 0.1333 0.973 0.941
#> 5 5 0.835 0.877 0.938 0.2170 0.801 0.544
#> 6 6 0.959 0.907 0.967 0.0671 0.953 0.804
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM312811 2 0 1 0 1
#> GSM312812 2 0 1 0 1
#> GSM312813 2 0 1 0 1
#> GSM312814 2 0 1 0 1
#> GSM312815 2 0 1 0 1
#> GSM312816 2 0 1 0 1
#> GSM312817 2 0 1 0 1
#> GSM312818 2 0 1 0 1
#> GSM312819 2 0 1 0 1
#> GSM312820 2 0 1 0 1
#> GSM312821 2 0 1 0 1
#> GSM312822 2 0 1 0 1
#> GSM312823 2 0 1 0 1
#> GSM312824 2 0 1 0 1
#> GSM312825 2 0 1 0 1
#> GSM312826 2 0 1 0 1
#> GSM312839 2 0 1 0 1
#> GSM312840 2 0 1 0 1
#> GSM312841 2 0 1 0 1
#> GSM312843 2 0 1 0 1
#> GSM312844 2 0 1 0 1
#> GSM312845 2 0 1 0 1
#> GSM312846 2 0 1 0 1
#> GSM312847 2 0 1 0 1
#> GSM312848 2 0 1 0 1
#> GSM312849 2 0 1 0 1
#> GSM312851 2 0 1 0 1
#> GSM312853 2 0 1 0 1
#> GSM312854 2 0 1 0 1
#> GSM312856 2 0 1 0 1
#> GSM312857 2 0 1 0 1
#> GSM312858 2 0 1 0 1
#> GSM312859 2 0 1 0 1
#> GSM312860 2 0 1 0 1
#> GSM312861 2 0 1 0 1
#> GSM312862 2 0 1 0 1
#> GSM312863 2 0 1 0 1
#> GSM312864 2 0 1 0 1
#> GSM312865 2 0 1 0 1
#> GSM312867 2 0 1 0 1
#> GSM312868 2 0 1 0 1
#> GSM312869 2 0 1 0 1
#> GSM312870 1 0 1 1 0
#> GSM312872 1 0 1 1 0
#> GSM312874 1 0 1 1 0
#> GSM312875 1 0 1 1 0
#> GSM312876 1 0 1 1 0
#> GSM312877 1 0 1 1 0
#> GSM312879 1 0 1 1 0
#> GSM312882 1 0 1 1 0
#> GSM312883 1 0 1 1 0
#> GSM312886 1 0 1 1 0
#> GSM312887 1 0 1 1 0
#> GSM312890 1 0 1 1 0
#> GSM312893 1 0 1 1 0
#> GSM312894 1 0 1 1 0
#> GSM312895 1 0 1 1 0
#> GSM312937 1 0 1 1 0
#> GSM312938 1 0 1 1 0
#> GSM312939 1 0 1 1 0
#> GSM312940 1 0 1 1 0
#> GSM312941 1 0 1 1 0
#> GSM312942 1 0 1 1 0
#> GSM312943 1 0 1 1 0
#> GSM312944 1 0 1 1 0
#> GSM312945 1 0 1 1 0
#> GSM312946 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM312811 2 0.000 0.996 0.000 1.000 0.000
#> GSM312812 2 0.000 0.996 0.000 1.000 0.000
#> GSM312813 2 0.000 0.996 0.000 1.000 0.000
#> GSM312814 2 0.000 0.996 0.000 1.000 0.000
#> GSM312815 2 0.000 0.996 0.000 1.000 0.000
#> GSM312816 2 0.000 0.996 0.000 1.000 0.000
#> GSM312817 2 0.000 0.996 0.000 1.000 0.000
#> GSM312818 2 0.000 0.996 0.000 1.000 0.000
#> GSM312819 2 0.000 0.996 0.000 1.000 0.000
#> GSM312820 2 0.000 0.996 0.000 1.000 0.000
#> GSM312821 2 0.000 0.996 0.000 1.000 0.000
#> GSM312822 2 0.000 0.996 0.000 1.000 0.000
#> GSM312823 2 0.000 0.996 0.000 1.000 0.000
#> GSM312824 2 0.000 0.996 0.000 1.000 0.000
#> GSM312825 2 0.000 0.996 0.000 1.000 0.000
#> GSM312826 2 0.000 0.996 0.000 1.000 0.000
#> GSM312839 2 0.000 0.996 0.000 1.000 0.000
#> GSM312840 2 0.000 0.996 0.000 1.000 0.000
#> GSM312841 2 0.000 0.996 0.000 1.000 0.000
#> GSM312843 2 0.000 0.996 0.000 1.000 0.000
#> GSM312844 2 0.000 0.996 0.000 1.000 0.000
#> GSM312845 2 0.412 0.802 0.168 0.832 0.000
#> GSM312846 2 0.000 0.996 0.000 1.000 0.000
#> GSM312847 2 0.000 0.996 0.000 1.000 0.000
#> GSM312848 2 0.000 0.996 0.000 1.000 0.000
#> GSM312849 2 0.000 0.996 0.000 1.000 0.000
#> GSM312851 2 0.000 0.996 0.000 1.000 0.000
#> GSM312853 2 0.000 0.996 0.000 1.000 0.000
#> GSM312854 2 0.000 0.996 0.000 1.000 0.000
#> GSM312856 2 0.000 0.996 0.000 1.000 0.000
#> GSM312857 2 0.000 0.996 0.000 1.000 0.000
#> GSM312858 2 0.000 0.996 0.000 1.000 0.000
#> GSM312859 2 0.000 0.996 0.000 1.000 0.000
#> GSM312860 2 0.000 0.996 0.000 1.000 0.000
#> GSM312861 2 0.000 0.996 0.000 1.000 0.000
#> GSM312862 2 0.000 0.996 0.000 1.000 0.000
#> GSM312863 2 0.000 0.996 0.000 1.000 0.000
#> GSM312864 2 0.000 0.996 0.000 1.000 0.000
#> GSM312865 2 0.000 0.996 0.000 1.000 0.000
#> GSM312867 2 0.000 0.996 0.000 1.000 0.000
#> GSM312868 2 0.000 0.996 0.000 1.000 0.000
#> GSM312869 2 0.000 0.996 0.000 1.000 0.000
#> GSM312870 3 0.000 1.000 0.000 0.000 1.000
#> GSM312872 3 0.000 1.000 0.000 0.000 1.000
#> GSM312874 3 0.000 1.000 0.000 0.000 1.000
#> GSM312875 3 0.000 1.000 0.000 0.000 1.000
#> GSM312876 3 0.000 1.000 0.000 0.000 1.000
#> GSM312877 1 0.576 0.660 0.672 0.000 0.328
#> GSM312879 3 0.000 1.000 0.000 0.000 1.000
#> GSM312882 3 0.000 1.000 0.000 0.000 1.000
#> GSM312883 3 0.000 1.000 0.000 0.000 1.000
#> GSM312886 3 0.000 1.000 0.000 0.000 1.000
#> GSM312887 1 0.000 0.885 1.000 0.000 0.000
#> GSM312890 1 0.000 0.885 1.000 0.000 0.000
#> GSM312893 1 0.000 0.885 1.000 0.000 0.000
#> GSM312894 1 0.000 0.885 1.000 0.000 0.000
#> GSM312895 1 0.000 0.885 1.000 0.000 0.000
#> GSM312937 1 0.000 0.885 1.000 0.000 0.000
#> GSM312938 1 0.000 0.885 1.000 0.000 0.000
#> GSM312939 1 0.000 0.885 1.000 0.000 0.000
#> GSM312940 1 0.000 0.885 1.000 0.000 0.000
#> GSM312941 1 0.000 0.885 1.000 0.000 0.000
#> GSM312942 1 0.525 0.751 0.736 0.000 0.264
#> GSM312943 1 0.514 0.763 0.748 0.000 0.252
#> GSM312944 1 0.502 0.773 0.760 0.000 0.240
#> GSM312945 1 0.502 0.773 0.760 0.000 0.240
#> GSM312946 1 0.525 0.751 0.736 0.000 0.264
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM312811 2 0.000 0.900 0.000 1.000 0.000 0.000
#> GSM312812 2 0.000 0.900 0.000 1.000 0.000 0.000
#> GSM312813 2 0.000 0.900 0.000 1.000 0.000 0.000
#> GSM312814 2 0.000 0.900 0.000 1.000 0.000 0.000
#> GSM312815 2 0.000 0.900 0.000 1.000 0.000 0.000
#> GSM312816 2 0.340 0.821 0.000 0.820 0.000 0.180
#> GSM312817 2 0.000 0.900 0.000 1.000 0.000 0.000
#> GSM312818 2 0.344 0.821 0.000 0.816 0.000 0.184
#> GSM312819 2 0.000 0.900 0.000 1.000 0.000 0.000
#> GSM312820 2 0.357 0.817 0.000 0.804 0.000 0.196
#> GSM312821 2 0.361 0.816 0.000 0.800 0.000 0.200
#> GSM312822 2 0.000 0.900 0.000 1.000 0.000 0.000
#> GSM312823 2 0.000 0.900 0.000 1.000 0.000 0.000
#> GSM312824 2 0.000 0.900 0.000 1.000 0.000 0.000
#> GSM312825 2 0.000 0.900 0.000 1.000 0.000 0.000
#> GSM312826 2 0.000 0.900 0.000 1.000 0.000 0.000
#> GSM312839 2 0.000 0.900 0.000 1.000 0.000 0.000
#> GSM312840 2 0.000 0.900 0.000 1.000 0.000 0.000
#> GSM312841 2 0.000 0.900 0.000 1.000 0.000 0.000
#> GSM312843 2 0.302 0.861 0.000 0.852 0.000 0.148
#> GSM312844 2 0.000 0.900 0.000 1.000 0.000 0.000
#> GSM312845 2 0.520 0.690 0.232 0.720 0.000 0.048
#> GSM312846 2 0.000 0.900 0.000 1.000 0.000 0.000
#> GSM312847 2 0.302 0.861 0.000 0.852 0.000 0.148
#> GSM312848 2 0.302 0.861 0.000 0.852 0.000 0.148
#> GSM312849 2 0.000 0.900 0.000 1.000 0.000 0.000
#> GSM312851 2 0.456 0.767 0.000 0.672 0.000 0.328
#> GSM312853 2 0.456 0.767 0.000 0.672 0.000 0.328
#> GSM312854 2 0.456 0.767 0.000 0.672 0.000 0.328
#> GSM312856 2 0.456 0.767 0.000 0.672 0.000 0.328
#> GSM312857 2 0.456 0.767 0.000 0.672 0.000 0.328
#> GSM312858 2 0.302 0.861 0.000 0.852 0.000 0.148
#> GSM312859 2 0.000 0.900 0.000 1.000 0.000 0.000
#> GSM312860 2 0.000 0.900 0.000 1.000 0.000 0.000
#> GSM312861 2 0.253 0.873 0.000 0.888 0.000 0.112
#> GSM312862 2 0.000 0.900 0.000 1.000 0.000 0.000
#> GSM312863 2 0.456 0.767 0.000 0.672 0.000 0.328
#> GSM312864 2 0.454 0.769 0.000 0.676 0.000 0.324
#> GSM312865 2 0.302 0.861 0.000 0.852 0.000 0.148
#> GSM312867 2 0.276 0.868 0.000 0.872 0.000 0.128
#> GSM312868 2 0.302 0.861 0.000 0.852 0.000 0.148
#> GSM312869 2 0.000 0.900 0.000 1.000 0.000 0.000
#> GSM312870 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM312872 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM312874 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM312875 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM312876 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM312877 4 0.740 0.793 0.300 0.000 0.196 0.504
#> GSM312879 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM312882 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM312883 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM312886 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM312887 1 0.000 1.000 1.000 0.000 0.000 0.000
#> GSM312890 1 0.000 1.000 1.000 0.000 0.000 0.000
#> GSM312893 1 0.000 1.000 1.000 0.000 0.000 0.000
#> GSM312894 1 0.000 1.000 1.000 0.000 0.000 0.000
#> GSM312895 1 0.000 1.000 1.000 0.000 0.000 0.000
#> GSM312937 1 0.000 1.000 1.000 0.000 0.000 0.000
#> GSM312938 1 0.000 1.000 1.000 0.000 0.000 0.000
#> GSM312939 1 0.000 1.000 1.000 0.000 0.000 0.000
#> GSM312940 1 0.000 1.000 1.000 0.000 0.000 0.000
#> GSM312941 1 0.000 1.000 1.000 0.000 0.000 0.000
#> GSM312942 4 0.594 0.951 0.240 0.000 0.088 0.672
#> GSM312943 4 0.591 0.951 0.244 0.000 0.084 0.672
#> GSM312944 4 0.581 0.946 0.256 0.000 0.072 0.672
#> GSM312945 4 0.581 0.946 0.256 0.000 0.072 0.672
#> GSM312946 4 0.594 0.951 0.240 0.000 0.088 0.672
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM312811 2 0.000 0.933 0.000 1.000 0.000 0.000 0.000
#> GSM312812 2 0.000 0.933 0.000 1.000 0.000 0.000 0.000
#> GSM312813 2 0.000 0.933 0.000 1.000 0.000 0.000 0.000
#> GSM312814 2 0.000 0.933 0.000 1.000 0.000 0.000 0.000
#> GSM312815 2 0.000 0.933 0.000 1.000 0.000 0.000 0.000
#> GSM312816 2 0.340 0.679 0.000 0.764 0.000 0.236 0.000
#> GSM312817 2 0.000 0.933 0.000 1.000 0.000 0.000 0.000
#> GSM312818 2 0.342 0.675 0.000 0.760 0.000 0.240 0.000
#> GSM312819 2 0.000 0.933 0.000 1.000 0.000 0.000 0.000
#> GSM312820 2 0.402 0.518 0.000 0.652 0.000 0.348 0.000
#> GSM312821 2 0.397 0.538 0.000 0.664 0.000 0.336 0.000
#> GSM312822 2 0.000 0.933 0.000 1.000 0.000 0.000 0.000
#> GSM312823 2 0.000 0.933 0.000 1.000 0.000 0.000 0.000
#> GSM312824 2 0.000 0.933 0.000 1.000 0.000 0.000 0.000
#> GSM312825 2 0.000 0.933 0.000 1.000 0.000 0.000 0.000
#> GSM312826 2 0.000 0.933 0.000 1.000 0.000 0.000 0.000
#> GSM312839 2 0.000 0.933 0.000 1.000 0.000 0.000 0.000
#> GSM312840 2 0.000 0.933 0.000 1.000 0.000 0.000 0.000
#> GSM312841 2 0.000 0.933 0.000 1.000 0.000 0.000 0.000
#> GSM312843 4 0.359 0.781 0.000 0.264 0.000 0.736 0.000
#> GSM312844 2 0.000 0.933 0.000 1.000 0.000 0.000 0.000
#> GSM312845 1 0.297 0.754 0.828 0.004 0.000 0.168 0.000
#> GSM312846 2 0.260 0.746 0.000 0.852 0.000 0.148 0.000
#> GSM312847 4 0.359 0.781 0.000 0.264 0.000 0.736 0.000
#> GSM312848 4 0.359 0.781 0.000 0.264 0.000 0.736 0.000
#> GSM312849 2 0.000 0.933 0.000 1.000 0.000 0.000 0.000
#> GSM312851 4 0.000 0.757 0.000 0.000 0.000 1.000 0.000
#> GSM312853 4 0.000 0.757 0.000 0.000 0.000 1.000 0.000
#> GSM312854 4 0.000 0.757 0.000 0.000 0.000 1.000 0.000
#> GSM312856 4 0.000 0.757 0.000 0.000 0.000 1.000 0.000
#> GSM312857 4 0.000 0.757 0.000 0.000 0.000 1.000 0.000
#> GSM312858 4 0.359 0.781 0.000 0.264 0.000 0.736 0.000
#> GSM312859 2 0.000 0.933 0.000 1.000 0.000 0.000 0.000
#> GSM312860 2 0.000 0.933 0.000 1.000 0.000 0.000 0.000
#> GSM312861 4 0.414 0.607 0.000 0.384 0.000 0.616 0.000
#> GSM312862 2 0.134 0.875 0.000 0.944 0.000 0.056 0.000
#> GSM312863 4 0.000 0.757 0.000 0.000 0.000 1.000 0.000
#> GSM312864 4 0.088 0.754 0.000 0.032 0.000 0.968 0.000
#> GSM312865 4 0.340 0.784 0.000 0.236 0.000 0.764 0.000
#> GSM312867 4 0.402 0.671 0.000 0.348 0.000 0.652 0.000
#> GSM312868 4 0.340 0.784 0.000 0.236 0.000 0.764 0.000
#> GSM312869 2 0.000 0.933 0.000 1.000 0.000 0.000 0.000
#> GSM312870 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312872 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312874 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312875 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312876 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312877 5 0.530 0.618 0.224 0.000 0.112 0.000 0.664
#> GSM312879 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312882 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312883 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312886 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312887 1 0.000 0.977 1.000 0.000 0.000 0.000 0.000
#> GSM312890 1 0.000 0.977 1.000 0.000 0.000 0.000 0.000
#> GSM312893 1 0.000 0.977 1.000 0.000 0.000 0.000 0.000
#> GSM312894 1 0.000 0.977 1.000 0.000 0.000 0.000 0.000
#> GSM312895 1 0.000 0.977 1.000 0.000 0.000 0.000 0.000
#> GSM312937 1 0.000 0.977 1.000 0.000 0.000 0.000 0.000
#> GSM312938 1 0.000 0.977 1.000 0.000 0.000 0.000 0.000
#> GSM312939 1 0.000 0.977 1.000 0.000 0.000 0.000 0.000
#> GSM312940 1 0.000 0.977 1.000 0.000 0.000 0.000 0.000
#> GSM312941 1 0.000 0.977 1.000 0.000 0.000 0.000 0.000
#> GSM312942 5 0.000 0.939 0.000 0.000 0.000 0.000 1.000
#> GSM312943 5 0.000 0.939 0.000 0.000 0.000 0.000 1.000
#> GSM312944 5 0.000 0.939 0.000 0.000 0.000 0.000 1.000
#> GSM312945 5 0.000 0.939 0.000 0.000 0.000 0.000 1.000
#> GSM312946 5 0.000 0.939 0.000 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM312811 2 0.1007 0.932 0.000 0.956 0.000 0.000 0.044 0.000
#> GSM312812 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312813 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312814 2 0.3023 0.679 0.000 0.768 0.000 0.000 0.232 0.000
#> GSM312815 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312816 5 0.0000 0.832 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM312817 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312818 5 0.0000 0.832 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM312819 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312820 5 0.0000 0.832 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM312821 5 0.0000 0.832 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM312822 5 0.3756 0.270 0.000 0.400 0.000 0.000 0.600 0.000
#> GSM312823 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312824 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312825 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312826 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312839 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312840 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312841 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312843 4 0.0000 0.921 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312844 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312845 1 0.2668 0.751 0.828 0.004 0.000 0.168 0.000 0.000
#> GSM312846 2 0.2562 0.755 0.000 0.828 0.000 0.172 0.000 0.000
#> GSM312847 4 0.0000 0.921 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312848 4 0.0000 0.921 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312849 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312851 4 0.0000 0.921 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312853 4 0.0000 0.921 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312854 4 0.0000 0.921 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312856 4 0.0000 0.921 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312857 4 0.0000 0.921 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312858 4 0.0000 0.921 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312859 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312860 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312861 4 0.3782 0.309 0.000 0.412 0.000 0.588 0.000 0.000
#> GSM312862 2 0.1267 0.907 0.000 0.940 0.000 0.060 0.000 0.000
#> GSM312863 4 0.0000 0.921 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312864 4 0.0146 0.917 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM312865 4 0.0000 0.921 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312867 4 0.3695 0.401 0.000 0.376 0.000 0.624 0.000 0.000
#> GSM312868 4 0.0000 0.921 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312869 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312870 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312872 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312874 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312875 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312876 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312877 6 0.4756 0.607 0.224 0.000 0.112 0.000 0.000 0.664
#> GSM312879 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312882 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312883 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312886 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312887 1 0.0000 0.977 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312890 1 0.0000 0.977 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312893 1 0.0000 0.977 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312894 1 0.0000 0.977 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312895 1 0.0000 0.977 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312937 1 0.0000 0.977 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312938 1 0.0000 0.977 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312939 1 0.0000 0.977 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312940 1 0.0000 0.977 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312941 1 0.0000 0.977 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312942 6 0.0000 0.928 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM312943 6 0.0000 0.928 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM312944 6 0.0000 0.928 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM312945 6 0.0000 0.928 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM312946 6 0.0000 0.928 0.000 0.000 0.000 0.000 0.000 1.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:pam 67 1.68e-10 2
#> MAD:pam 67 3.83e-17 3
#> MAD:pam 67 1.90e-24 4
#> MAD:pam 67 4.23e-26 5
#> MAD:pam 64 4.35e-23 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "mclust"]
# you can also extract it by
# res = res_list["MAD:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 67 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 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 0.4747 0.525 0.525
#> 3 3 0.715 0.769 0.879 0.2563 0.826 0.682
#> 4 4 0.720 0.746 0.870 0.1631 0.867 0.683
#> 5 5 0.707 0.794 0.849 0.1030 0.871 0.604
#> 6 6 0.771 0.754 0.859 0.0438 0.918 0.667
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
#> GSM312811 2 0.0000 1.000 0.000 1.000
#> GSM312812 2 0.0000 1.000 0.000 1.000
#> GSM312813 2 0.0000 1.000 0.000 1.000
#> GSM312814 2 0.0000 1.000 0.000 1.000
#> GSM312815 2 0.0000 1.000 0.000 1.000
#> GSM312816 2 0.0000 1.000 0.000 1.000
#> GSM312817 2 0.0000 1.000 0.000 1.000
#> GSM312818 2 0.0000 1.000 0.000 1.000
#> GSM312819 2 0.0000 1.000 0.000 1.000
#> GSM312820 2 0.0000 1.000 0.000 1.000
#> GSM312821 2 0.0000 1.000 0.000 1.000
#> GSM312822 2 0.0000 1.000 0.000 1.000
#> GSM312823 2 0.0000 1.000 0.000 1.000
#> GSM312824 2 0.0000 1.000 0.000 1.000
#> GSM312825 2 0.0000 1.000 0.000 1.000
#> GSM312826 2 0.0000 1.000 0.000 1.000
#> GSM312839 2 0.0000 1.000 0.000 1.000
#> GSM312840 2 0.0000 1.000 0.000 1.000
#> GSM312841 2 0.0000 1.000 0.000 1.000
#> GSM312843 2 0.0000 1.000 0.000 1.000
#> GSM312844 2 0.0000 1.000 0.000 1.000
#> GSM312845 2 0.0000 1.000 0.000 1.000
#> GSM312846 2 0.0000 1.000 0.000 1.000
#> GSM312847 2 0.0000 1.000 0.000 1.000
#> GSM312848 2 0.0000 1.000 0.000 1.000
#> GSM312849 2 0.0000 1.000 0.000 1.000
#> GSM312851 2 0.0000 1.000 0.000 1.000
#> GSM312853 2 0.0000 1.000 0.000 1.000
#> GSM312854 2 0.0000 1.000 0.000 1.000
#> GSM312856 2 0.0000 1.000 0.000 1.000
#> GSM312857 2 0.0000 1.000 0.000 1.000
#> GSM312858 2 0.0000 1.000 0.000 1.000
#> GSM312859 2 0.0000 1.000 0.000 1.000
#> GSM312860 2 0.0000 1.000 0.000 1.000
#> GSM312861 2 0.0000 1.000 0.000 1.000
#> GSM312862 2 0.0000 1.000 0.000 1.000
#> GSM312863 2 0.0000 1.000 0.000 1.000
#> GSM312864 2 0.0000 1.000 0.000 1.000
#> GSM312865 2 0.0000 1.000 0.000 1.000
#> GSM312867 2 0.0000 1.000 0.000 1.000
#> GSM312868 2 0.0000 1.000 0.000 1.000
#> GSM312869 2 0.0000 1.000 0.000 1.000
#> GSM312870 1 0.0000 0.997 1.000 0.000
#> GSM312872 1 0.0000 0.997 1.000 0.000
#> GSM312874 1 0.0000 0.997 1.000 0.000
#> GSM312875 1 0.0000 0.997 1.000 0.000
#> GSM312876 1 0.0000 0.997 1.000 0.000
#> GSM312877 1 0.0376 0.998 0.996 0.004
#> GSM312879 1 0.0000 0.997 1.000 0.000
#> GSM312882 1 0.0000 0.997 1.000 0.000
#> GSM312883 1 0.0000 0.997 1.000 0.000
#> GSM312886 1 0.0376 0.998 0.996 0.004
#> GSM312887 1 0.0376 0.998 0.996 0.004
#> GSM312890 1 0.0376 0.998 0.996 0.004
#> GSM312893 1 0.0376 0.998 0.996 0.004
#> GSM312894 1 0.0376 0.998 0.996 0.004
#> GSM312895 1 0.0376 0.998 0.996 0.004
#> GSM312937 1 0.0376 0.998 0.996 0.004
#> GSM312938 1 0.0376 0.998 0.996 0.004
#> GSM312939 1 0.0376 0.998 0.996 0.004
#> GSM312940 1 0.0376 0.998 0.996 0.004
#> GSM312941 1 0.0376 0.998 0.996 0.004
#> GSM312942 1 0.0376 0.998 0.996 0.004
#> GSM312943 1 0.0376 0.998 0.996 0.004
#> GSM312944 1 0.0376 0.998 0.996 0.004
#> GSM312945 1 0.0376 0.998 0.996 0.004
#> GSM312946 1 0.0000 0.997 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM312811 2 0.0661 0.919 0.004 0.988 0.008
#> GSM312812 2 0.0000 0.921 0.000 1.000 0.000
#> GSM312813 2 0.4121 0.776 0.000 0.832 0.168
#> GSM312814 2 0.0424 0.920 0.000 0.992 0.008
#> GSM312815 2 0.0000 0.921 0.000 1.000 0.000
#> GSM312816 3 0.8361 0.416 0.092 0.364 0.544
#> GSM312817 2 0.4178 0.775 0.000 0.828 0.172
#> GSM312818 3 0.8330 0.434 0.092 0.356 0.552
#> GSM312819 2 0.5412 0.741 0.032 0.796 0.172
#> GSM312820 3 0.8330 0.434 0.092 0.356 0.552
#> GSM312821 3 0.8330 0.434 0.092 0.356 0.552
#> GSM312822 2 0.1031 0.915 0.000 0.976 0.024
#> GSM312823 2 0.1411 0.909 0.000 0.964 0.036
#> GSM312824 2 0.0000 0.921 0.000 1.000 0.000
#> GSM312825 2 0.0000 0.921 0.000 1.000 0.000
#> GSM312826 2 0.0000 0.921 0.000 1.000 0.000
#> GSM312839 2 0.0000 0.921 0.000 1.000 0.000
#> GSM312840 2 0.0000 0.921 0.000 1.000 0.000
#> GSM312841 2 0.0424 0.920 0.000 0.992 0.008
#> GSM312843 2 0.0237 0.920 0.000 0.996 0.004
#> GSM312844 2 0.0000 0.921 0.000 1.000 0.000
#> GSM312845 3 0.6274 0.198 0.000 0.456 0.544
#> GSM312846 2 0.6309 -0.100 0.000 0.504 0.496
#> GSM312847 2 0.1411 0.913 0.000 0.964 0.036
#> GSM312848 2 0.1289 0.913 0.000 0.968 0.032
#> GSM312849 2 0.4555 0.761 0.000 0.800 0.200
#> GSM312851 2 0.3267 0.870 0.000 0.884 0.116
#> GSM312853 2 0.3267 0.870 0.000 0.884 0.116
#> GSM312854 2 0.2448 0.900 0.000 0.924 0.076
#> GSM312856 2 0.2448 0.900 0.000 0.924 0.076
#> GSM312857 2 0.3267 0.870 0.000 0.884 0.116
#> GSM312858 2 0.1289 0.913 0.000 0.968 0.032
#> GSM312859 2 0.0000 0.921 0.000 1.000 0.000
#> GSM312860 2 0.0000 0.921 0.000 1.000 0.000
#> GSM312861 2 0.0237 0.920 0.000 0.996 0.004
#> GSM312862 2 0.4178 0.775 0.000 0.828 0.172
#> GSM312863 2 0.2625 0.895 0.000 0.916 0.084
#> GSM312864 2 0.1753 0.910 0.000 0.952 0.048
#> GSM312865 2 0.1289 0.913 0.000 0.968 0.032
#> GSM312867 2 0.4605 0.756 0.000 0.796 0.204
#> GSM312868 2 0.1643 0.911 0.000 0.956 0.044
#> GSM312869 2 0.0000 0.921 0.000 1.000 0.000
#> GSM312870 1 0.0000 0.792 1.000 0.000 0.000
#> GSM312872 1 0.0000 0.792 1.000 0.000 0.000
#> GSM312874 1 0.0000 0.792 1.000 0.000 0.000
#> GSM312875 1 0.0000 0.792 1.000 0.000 0.000
#> GSM312876 1 0.0000 0.792 1.000 0.000 0.000
#> GSM312877 1 0.5810 0.723 0.664 0.000 0.336
#> GSM312879 1 0.0000 0.792 1.000 0.000 0.000
#> GSM312882 1 0.0237 0.792 0.996 0.000 0.004
#> GSM312883 1 0.3752 0.776 0.856 0.000 0.144
#> GSM312886 1 0.6252 0.244 0.556 0.000 0.444
#> GSM312887 3 0.2537 0.675 0.080 0.000 0.920
#> GSM312890 3 0.1643 0.698 0.044 0.000 0.956
#> GSM312893 3 0.1860 0.694 0.052 0.000 0.948
#> GSM312894 3 0.2537 0.675 0.080 0.000 0.920
#> GSM312895 3 0.1643 0.698 0.044 0.000 0.956
#> GSM312937 3 0.1643 0.698 0.044 0.000 0.956
#> GSM312938 3 0.2537 0.675 0.080 0.000 0.920
#> GSM312939 3 0.1643 0.698 0.044 0.000 0.956
#> GSM312940 3 0.1643 0.698 0.044 0.000 0.956
#> GSM312941 3 0.1643 0.698 0.044 0.000 0.956
#> GSM312942 1 0.5810 0.723 0.664 0.000 0.336
#> GSM312943 1 0.5810 0.723 0.664 0.000 0.336
#> GSM312944 1 0.5810 0.723 0.664 0.000 0.336
#> GSM312945 1 0.5810 0.723 0.664 0.000 0.336
#> GSM312946 1 0.5810 0.723 0.664 0.000 0.336
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM312811 2 0.3610 0.698 0.000 0.800 0.000 0.200
#> GSM312812 2 0.0000 0.803 0.000 1.000 0.000 0.000
#> GSM312813 2 0.0592 0.805 0.000 0.984 0.000 0.016
#> GSM312814 2 0.3311 0.733 0.000 0.828 0.000 0.172
#> GSM312815 2 0.0000 0.803 0.000 1.000 0.000 0.000
#> GSM312816 4 0.4642 0.656 0.000 0.240 0.020 0.740
#> GSM312817 2 0.2081 0.796 0.000 0.916 0.000 0.084
#> GSM312818 4 0.4610 0.660 0.000 0.236 0.020 0.744
#> GSM312819 2 0.2909 0.789 0.000 0.888 0.020 0.092
#> GSM312820 4 0.4610 0.660 0.000 0.236 0.020 0.744
#> GSM312821 4 0.4610 0.660 0.000 0.236 0.020 0.744
#> GSM312822 2 0.3649 0.691 0.000 0.796 0.000 0.204
#> GSM312823 2 0.2216 0.795 0.000 0.908 0.000 0.092
#> GSM312824 2 0.0000 0.803 0.000 1.000 0.000 0.000
#> GSM312825 2 0.0000 0.803 0.000 1.000 0.000 0.000
#> GSM312826 2 0.0000 0.803 0.000 1.000 0.000 0.000
#> GSM312839 2 0.0000 0.803 0.000 1.000 0.000 0.000
#> GSM312840 2 0.0336 0.802 0.000 0.992 0.000 0.008
#> GSM312841 2 0.1022 0.794 0.000 0.968 0.000 0.032
#> GSM312843 2 0.3172 0.776 0.000 0.840 0.000 0.160
#> GSM312844 2 0.0000 0.803 0.000 1.000 0.000 0.000
#> GSM312845 2 0.4605 0.632 0.000 0.664 0.000 0.336
#> GSM312846 2 0.4605 0.632 0.000 0.664 0.000 0.336
#> GSM312847 2 0.4605 0.632 0.000 0.664 0.000 0.336
#> GSM312848 2 0.4643 0.625 0.000 0.656 0.000 0.344
#> GSM312849 2 0.4564 0.640 0.000 0.672 0.000 0.328
#> GSM312851 4 0.0000 0.686 0.000 0.000 0.000 1.000
#> GSM312853 4 0.0000 0.686 0.000 0.000 0.000 1.000
#> GSM312854 4 0.0188 0.686 0.000 0.004 0.000 0.996
#> GSM312856 4 0.4961 -0.223 0.000 0.448 0.000 0.552
#> GSM312857 4 0.0000 0.686 0.000 0.000 0.000 1.000
#> GSM312858 2 0.4605 0.632 0.000 0.664 0.000 0.336
#> GSM312859 2 0.0188 0.804 0.000 0.996 0.000 0.004
#> GSM312860 2 0.0188 0.804 0.000 0.996 0.000 0.004
#> GSM312861 2 0.3123 0.775 0.000 0.844 0.000 0.156
#> GSM312862 2 0.2216 0.795 0.000 0.908 0.000 0.092
#> GSM312863 4 0.4998 -0.341 0.000 0.488 0.000 0.512
#> GSM312864 2 0.4040 0.619 0.000 0.752 0.000 0.248
#> GSM312865 2 0.4605 0.632 0.000 0.664 0.000 0.336
#> GSM312867 2 0.4605 0.632 0.000 0.664 0.000 0.336
#> GSM312868 2 0.4605 0.632 0.000 0.664 0.000 0.336
#> GSM312869 2 0.0000 0.803 0.000 1.000 0.000 0.000
#> GSM312870 3 0.0000 0.832 0.000 0.000 1.000 0.000
#> GSM312872 3 0.0000 0.832 0.000 0.000 1.000 0.000
#> GSM312874 3 0.0000 0.832 0.000 0.000 1.000 0.000
#> GSM312875 3 0.0000 0.832 0.000 0.000 1.000 0.000
#> GSM312876 3 0.0000 0.832 0.000 0.000 1.000 0.000
#> GSM312877 3 0.4605 0.686 0.336 0.000 0.664 0.000
#> GSM312879 3 0.0000 0.832 0.000 0.000 1.000 0.000
#> GSM312882 3 0.0000 0.832 0.000 0.000 1.000 0.000
#> GSM312883 3 0.1474 0.823 0.052 0.000 0.948 0.000
#> GSM312886 3 0.0817 0.830 0.024 0.000 0.976 0.000
#> GSM312887 1 0.0188 0.996 0.996 0.000 0.004 0.000
#> GSM312890 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM312893 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM312894 1 0.0188 0.996 0.996 0.000 0.004 0.000
#> GSM312895 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM312937 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM312938 1 0.0188 0.996 0.996 0.000 0.004 0.000
#> GSM312939 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM312940 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM312941 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM312942 3 0.4605 0.686 0.336 0.000 0.664 0.000
#> GSM312943 3 0.4605 0.686 0.336 0.000 0.664 0.000
#> GSM312944 3 0.4605 0.686 0.336 0.000 0.664 0.000
#> GSM312945 3 0.4605 0.686 0.336 0.000 0.664 0.000
#> GSM312946 3 0.4605 0.686 0.336 0.000 0.664 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM312811 2 0.3888 0.791 0.000 0.796 0.000 0.148 0.056
#> GSM312812 2 0.0290 0.820 0.000 0.992 0.000 0.000 0.008
#> GSM312813 2 0.3327 0.809 0.000 0.828 0.000 0.144 0.028
#> GSM312814 2 0.3888 0.791 0.000 0.796 0.000 0.148 0.056
#> GSM312815 2 0.0000 0.819 0.000 1.000 0.000 0.000 0.000
#> GSM312816 5 0.6215 0.584 0.000 0.336 0.000 0.156 0.508
#> GSM312817 2 0.3983 0.782 0.000 0.784 0.000 0.164 0.052
#> GSM312818 5 0.6205 0.590 0.000 0.332 0.000 0.156 0.512
#> GSM312819 2 0.4772 0.711 0.000 0.728 0.000 0.164 0.108
#> GSM312820 5 0.6205 0.590 0.000 0.332 0.000 0.156 0.512
#> GSM312821 5 0.6205 0.590 0.000 0.332 0.000 0.156 0.512
#> GSM312822 2 0.3888 0.791 0.000 0.796 0.000 0.148 0.056
#> GSM312823 2 0.3141 0.801 0.000 0.832 0.000 0.152 0.016
#> GSM312824 2 0.0000 0.819 0.000 1.000 0.000 0.000 0.000
#> GSM312825 2 0.0290 0.820 0.000 0.992 0.000 0.000 0.008
#> GSM312826 2 0.0000 0.819 0.000 1.000 0.000 0.000 0.000
#> GSM312839 2 0.0000 0.819 0.000 1.000 0.000 0.000 0.000
#> GSM312840 2 0.1082 0.830 0.000 0.964 0.000 0.028 0.008
#> GSM312841 2 0.3098 0.804 0.000 0.836 0.000 0.148 0.016
#> GSM312843 4 0.3630 0.658 0.000 0.204 0.000 0.780 0.016
#> GSM312844 2 0.0898 0.828 0.000 0.972 0.000 0.020 0.008
#> GSM312845 4 0.1341 0.907 0.000 0.056 0.000 0.944 0.000
#> GSM312846 4 0.1341 0.907 0.000 0.056 0.000 0.944 0.000
#> GSM312847 4 0.1341 0.907 0.000 0.056 0.000 0.944 0.000
#> GSM312848 4 0.1697 0.902 0.000 0.060 0.000 0.932 0.008
#> GSM312849 4 0.1410 0.904 0.000 0.060 0.000 0.940 0.000
#> GSM312851 5 0.3990 0.506 0.000 0.004 0.000 0.308 0.688
#> GSM312853 5 0.3990 0.506 0.000 0.004 0.000 0.308 0.688
#> GSM312854 5 0.4108 0.505 0.000 0.008 0.000 0.308 0.684
#> GSM312856 4 0.4088 0.484 0.000 0.008 0.000 0.688 0.304
#> GSM312857 5 0.4108 0.505 0.000 0.008 0.000 0.308 0.684
#> GSM312858 4 0.1341 0.905 0.000 0.056 0.000 0.944 0.000
#> GSM312859 2 0.1197 0.831 0.000 0.952 0.000 0.048 0.000
#> GSM312860 2 0.2605 0.810 0.000 0.852 0.000 0.148 0.000
#> GSM312861 2 0.4410 0.317 0.000 0.556 0.000 0.440 0.004
#> GSM312862 2 0.3053 0.797 0.000 0.828 0.000 0.164 0.008
#> GSM312863 4 0.2612 0.763 0.000 0.008 0.000 0.868 0.124
#> GSM312864 5 0.6557 0.539 0.000 0.368 0.000 0.204 0.428
#> GSM312865 4 0.1557 0.904 0.000 0.052 0.000 0.940 0.008
#> GSM312867 4 0.1341 0.907 0.000 0.056 0.000 0.944 0.000
#> GSM312868 4 0.1043 0.868 0.000 0.040 0.000 0.960 0.000
#> GSM312869 2 0.0000 0.819 0.000 1.000 0.000 0.000 0.000
#> GSM312870 3 0.0000 0.856 0.000 0.000 1.000 0.000 0.000
#> GSM312872 3 0.0000 0.856 0.000 0.000 1.000 0.000 0.000
#> GSM312874 3 0.0000 0.856 0.000 0.000 1.000 0.000 0.000
#> GSM312875 3 0.0000 0.856 0.000 0.000 1.000 0.000 0.000
#> GSM312876 3 0.0000 0.856 0.000 0.000 1.000 0.000 0.000
#> GSM312877 3 0.5772 0.750 0.148 0.000 0.652 0.012 0.188
#> GSM312879 3 0.0000 0.856 0.000 0.000 1.000 0.000 0.000
#> GSM312882 3 0.0000 0.856 0.000 0.000 1.000 0.000 0.000
#> GSM312883 3 0.0404 0.854 0.000 0.000 0.988 0.000 0.012
#> GSM312886 3 0.0000 0.856 0.000 0.000 1.000 0.000 0.000
#> GSM312887 1 0.1845 0.932 0.928 0.000 0.056 0.000 0.016
#> GSM312890 1 0.0000 0.979 1.000 0.000 0.000 0.000 0.000
#> GSM312893 1 0.0000 0.979 1.000 0.000 0.000 0.000 0.000
#> GSM312894 1 0.1701 0.939 0.936 0.000 0.048 0.000 0.016
#> GSM312895 1 0.0000 0.979 1.000 0.000 0.000 0.000 0.000
#> GSM312937 1 0.0000 0.979 1.000 0.000 0.000 0.000 0.000
#> GSM312938 1 0.1403 0.956 0.952 0.000 0.024 0.000 0.024
#> GSM312939 1 0.0000 0.979 1.000 0.000 0.000 0.000 0.000
#> GSM312940 1 0.0000 0.979 1.000 0.000 0.000 0.000 0.000
#> GSM312941 1 0.0000 0.979 1.000 0.000 0.000 0.000 0.000
#> GSM312942 3 0.5497 0.756 0.136 0.000 0.664 0.004 0.196
#> GSM312943 3 0.5972 0.735 0.164 0.000 0.628 0.012 0.196
#> GSM312944 3 0.5972 0.735 0.164 0.000 0.628 0.012 0.196
#> GSM312945 3 0.5972 0.735 0.164 0.000 0.628 0.012 0.196
#> GSM312946 3 0.5972 0.735 0.164 0.000 0.628 0.012 0.196
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM312811 2 0.2631 0.7679 0.000 0.820 0.000 0.000 0.180 0.000
#> GSM312812 2 0.0000 0.8596 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312813 2 0.0260 0.8595 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM312814 2 0.2562 0.7742 0.000 0.828 0.000 0.000 0.172 0.000
#> GSM312815 2 0.0000 0.8596 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312816 5 0.3151 0.8114 0.000 0.252 0.000 0.000 0.748 0.000
#> GSM312817 2 0.2823 0.7376 0.000 0.796 0.000 0.000 0.204 0.000
#> GSM312818 5 0.2260 0.9407 0.000 0.140 0.000 0.000 0.860 0.000
#> GSM312819 2 0.3578 0.4814 0.000 0.660 0.000 0.000 0.340 0.000
#> GSM312820 5 0.2260 0.9407 0.000 0.140 0.000 0.000 0.860 0.000
#> GSM312821 5 0.2260 0.9407 0.000 0.140 0.000 0.000 0.860 0.000
#> GSM312822 2 0.2562 0.7742 0.000 0.828 0.000 0.000 0.172 0.000
#> GSM312823 2 0.2070 0.8194 0.000 0.892 0.000 0.008 0.100 0.000
#> GSM312824 2 0.0000 0.8596 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312825 2 0.0000 0.8596 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312826 2 0.0000 0.8596 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312839 2 0.0000 0.8596 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312840 2 0.0260 0.8595 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM312841 2 0.3428 0.5467 0.000 0.696 0.000 0.000 0.304 0.000
#> GSM312843 4 0.5599 0.3056 0.000 0.276 0.000 0.572 0.140 0.012
#> GSM312844 2 0.0260 0.8595 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM312845 4 0.0806 0.6679 0.000 0.020 0.000 0.972 0.000 0.008
#> GSM312846 4 0.0806 0.6679 0.000 0.020 0.000 0.972 0.000 0.008
#> GSM312847 4 0.0547 0.6680 0.000 0.020 0.000 0.980 0.000 0.000
#> GSM312848 4 0.0865 0.6659 0.000 0.036 0.000 0.964 0.000 0.000
#> GSM312849 4 0.1714 0.6303 0.000 0.092 0.000 0.908 0.000 0.000
#> GSM312851 4 0.5031 0.4086 0.000 0.000 0.000 0.480 0.448 0.072
#> GSM312853 4 0.5031 0.4086 0.000 0.000 0.000 0.480 0.448 0.072
#> GSM312854 4 0.5031 0.4086 0.000 0.000 0.000 0.480 0.448 0.072
#> GSM312856 4 0.5031 0.4086 0.000 0.000 0.000 0.480 0.448 0.072
#> GSM312857 4 0.5031 0.4086 0.000 0.000 0.000 0.480 0.448 0.072
#> GSM312858 4 0.1265 0.6608 0.000 0.044 0.000 0.948 0.000 0.008
#> GSM312859 2 0.0260 0.8595 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM312860 2 0.0363 0.8555 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM312861 4 0.4320 -0.0324 0.000 0.468 0.000 0.516 0.008 0.008
#> GSM312862 2 0.3252 0.7735 0.000 0.824 0.000 0.068 0.108 0.000
#> GSM312863 4 0.5007 0.4239 0.000 0.000 0.000 0.512 0.416 0.072
#> GSM312864 2 0.3922 0.4871 0.000 0.664 0.000 0.000 0.320 0.016
#> GSM312865 4 0.0547 0.6680 0.000 0.020 0.000 0.980 0.000 0.000
#> GSM312867 4 0.0806 0.6679 0.000 0.020 0.000 0.972 0.000 0.008
#> GSM312868 4 0.4332 0.5546 0.000 0.128 0.000 0.744 0.120 0.008
#> GSM312869 2 0.0000 0.8596 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312870 3 0.0000 0.9595 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312872 3 0.0000 0.9595 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312874 3 0.0000 0.9595 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312875 3 0.0000 0.9595 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312876 3 0.0000 0.9595 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312877 6 0.2039 0.9090 0.076 0.000 0.020 0.000 0.000 0.904
#> GSM312879 3 0.0000 0.9595 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312882 3 0.0000 0.9595 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312883 3 0.3330 0.5460 0.000 0.000 0.716 0.000 0.000 0.284
#> GSM312886 3 0.0000 0.9595 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312887 1 0.4781 0.5728 0.672 0.000 0.188 0.000 0.000 0.140
#> GSM312890 1 0.0000 0.9209 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312893 1 0.0000 0.9209 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312894 1 0.2164 0.8542 0.900 0.000 0.032 0.000 0.000 0.068
#> GSM312895 1 0.0000 0.9209 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312937 1 0.0000 0.9209 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312938 1 0.4281 0.7196 0.764 0.000 0.032 0.000 0.140 0.064
#> GSM312939 1 0.0000 0.9209 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312940 1 0.0000 0.9209 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312941 1 0.0000 0.9209 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312942 6 0.4763 0.4543 0.064 0.000 0.344 0.000 0.000 0.592
#> GSM312943 6 0.1745 0.9186 0.068 0.000 0.012 0.000 0.000 0.920
#> GSM312944 6 0.1745 0.9186 0.068 0.000 0.012 0.000 0.000 0.920
#> GSM312945 6 0.1745 0.9186 0.068 0.000 0.012 0.000 0.000 0.920
#> GSM312946 6 0.1745 0.9186 0.068 0.000 0.012 0.000 0.000 0.920
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:mclust 67 1.68e-10 2
#> MAD:mclust 60 2.85e-16 3
#> MAD:mclust 65 4.09e-21 4
#> MAD:mclust 65 1.81e-22 5
#> MAD:mclust 56 3.24e-22 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "NMF"]
# you can also extract it by
# res = res_list["MAD:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 67 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 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.974 0.990 0.4807 0.518 0.518
#> 3 3 0.948 0.911 0.964 0.2824 0.819 0.667
#> 4 4 0.667 0.702 0.839 0.1577 0.817 0.563
#> 5 5 0.800 0.786 0.872 0.0791 0.860 0.550
#> 6 6 0.950 0.891 0.950 0.0388 0.970 0.862
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM312811 2 0.000 0.995 0.000 1.000
#> GSM312812 2 0.000 0.995 0.000 1.000
#> GSM312813 2 0.000 0.995 0.000 1.000
#> GSM312814 2 0.000 0.995 0.000 1.000
#> GSM312815 2 0.000 0.995 0.000 1.000
#> GSM312816 2 0.000 0.995 0.000 1.000
#> GSM312817 2 0.000 0.995 0.000 1.000
#> GSM312818 2 0.430 0.902 0.088 0.912
#> GSM312819 2 0.000 0.995 0.000 1.000
#> GSM312820 2 0.000 0.995 0.000 1.000
#> GSM312821 2 0.000 0.995 0.000 1.000
#> GSM312822 2 0.000 0.995 0.000 1.000
#> GSM312823 2 0.000 0.995 0.000 1.000
#> GSM312824 2 0.000 0.995 0.000 1.000
#> GSM312825 2 0.000 0.995 0.000 1.000
#> GSM312826 2 0.000 0.995 0.000 1.000
#> GSM312839 2 0.000 0.995 0.000 1.000
#> GSM312840 2 0.000 0.995 0.000 1.000
#> GSM312841 2 0.000 0.995 0.000 1.000
#> GSM312843 2 0.000 0.995 0.000 1.000
#> GSM312844 2 0.000 0.995 0.000 1.000
#> GSM312845 1 0.994 0.151 0.544 0.456
#> GSM312846 2 0.541 0.856 0.124 0.876
#> GSM312847 2 0.000 0.995 0.000 1.000
#> GSM312848 2 0.000 0.995 0.000 1.000
#> GSM312849 2 0.000 0.995 0.000 1.000
#> GSM312851 2 0.000 0.995 0.000 1.000
#> GSM312853 2 0.000 0.995 0.000 1.000
#> GSM312854 2 0.000 0.995 0.000 1.000
#> GSM312856 2 0.000 0.995 0.000 1.000
#> GSM312857 2 0.000 0.995 0.000 1.000
#> GSM312858 2 0.000 0.995 0.000 1.000
#> GSM312859 2 0.000 0.995 0.000 1.000
#> GSM312860 2 0.000 0.995 0.000 1.000
#> GSM312861 2 0.000 0.995 0.000 1.000
#> GSM312862 2 0.000 0.995 0.000 1.000
#> GSM312863 2 0.000 0.995 0.000 1.000
#> GSM312864 2 0.000 0.995 0.000 1.000
#> GSM312865 2 0.000 0.995 0.000 1.000
#> GSM312867 2 0.000 0.995 0.000 1.000
#> GSM312868 2 0.000 0.995 0.000 1.000
#> GSM312869 2 0.000 0.995 0.000 1.000
#> GSM312870 1 0.000 0.981 1.000 0.000
#> GSM312872 1 0.000 0.981 1.000 0.000
#> GSM312874 1 0.000 0.981 1.000 0.000
#> GSM312875 1 0.000 0.981 1.000 0.000
#> GSM312876 1 0.000 0.981 1.000 0.000
#> GSM312877 1 0.000 0.981 1.000 0.000
#> GSM312879 1 0.000 0.981 1.000 0.000
#> GSM312882 1 0.000 0.981 1.000 0.000
#> GSM312883 1 0.000 0.981 1.000 0.000
#> GSM312886 1 0.000 0.981 1.000 0.000
#> GSM312887 1 0.000 0.981 1.000 0.000
#> GSM312890 1 0.000 0.981 1.000 0.000
#> GSM312893 1 0.000 0.981 1.000 0.000
#> GSM312894 1 0.000 0.981 1.000 0.000
#> GSM312895 1 0.000 0.981 1.000 0.000
#> GSM312937 1 0.000 0.981 1.000 0.000
#> GSM312938 1 0.000 0.981 1.000 0.000
#> GSM312939 1 0.000 0.981 1.000 0.000
#> GSM312940 1 0.000 0.981 1.000 0.000
#> GSM312941 1 0.000 0.981 1.000 0.000
#> GSM312942 1 0.000 0.981 1.000 0.000
#> GSM312943 1 0.000 0.981 1.000 0.000
#> GSM312944 1 0.000 0.981 1.000 0.000
#> GSM312945 1 0.000 0.981 1.000 0.000
#> GSM312946 1 0.000 0.981 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM312811 2 0.0000 0.983 0.000 1.000 0.000
#> GSM312812 2 0.0000 0.983 0.000 1.000 0.000
#> GSM312813 2 0.0000 0.983 0.000 1.000 0.000
#> GSM312814 2 0.0000 0.983 0.000 1.000 0.000
#> GSM312815 2 0.0000 0.983 0.000 1.000 0.000
#> GSM312816 2 0.0000 0.983 0.000 1.000 0.000
#> GSM312817 2 0.0000 0.983 0.000 1.000 0.000
#> GSM312818 2 0.5327 0.638 0.272 0.728 0.000
#> GSM312819 2 0.0000 0.983 0.000 1.000 0.000
#> GSM312820 2 0.0000 0.983 0.000 1.000 0.000
#> GSM312821 2 0.0237 0.980 0.004 0.996 0.000
#> GSM312822 2 0.0000 0.983 0.000 1.000 0.000
#> GSM312823 2 0.0000 0.983 0.000 1.000 0.000
#> GSM312824 2 0.0000 0.983 0.000 1.000 0.000
#> GSM312825 2 0.0000 0.983 0.000 1.000 0.000
#> GSM312826 2 0.0000 0.983 0.000 1.000 0.000
#> GSM312839 2 0.0000 0.983 0.000 1.000 0.000
#> GSM312840 2 0.0000 0.983 0.000 1.000 0.000
#> GSM312841 2 0.0000 0.983 0.000 1.000 0.000
#> GSM312843 2 0.0000 0.983 0.000 1.000 0.000
#> GSM312844 2 0.0000 0.983 0.000 1.000 0.000
#> GSM312845 3 0.0000 0.960 0.000 0.000 1.000
#> GSM312846 3 0.0000 0.960 0.000 0.000 1.000
#> GSM312847 3 0.0000 0.960 0.000 0.000 1.000
#> GSM312848 2 0.2165 0.924 0.000 0.936 0.064
#> GSM312849 3 0.0237 0.956 0.000 0.004 0.996
#> GSM312851 2 0.0000 0.983 0.000 1.000 0.000
#> GSM312853 2 0.0000 0.983 0.000 1.000 0.000
#> GSM312854 2 0.0424 0.977 0.000 0.992 0.008
#> GSM312856 2 0.0000 0.983 0.000 1.000 0.000
#> GSM312857 2 0.0237 0.980 0.000 0.996 0.004
#> GSM312858 2 0.4842 0.716 0.000 0.776 0.224
#> GSM312859 2 0.0000 0.983 0.000 1.000 0.000
#> GSM312860 2 0.0000 0.983 0.000 1.000 0.000
#> GSM312861 2 0.0000 0.983 0.000 1.000 0.000
#> GSM312862 2 0.0000 0.983 0.000 1.000 0.000
#> GSM312863 2 0.0000 0.983 0.000 1.000 0.000
#> GSM312864 2 0.0000 0.983 0.000 1.000 0.000
#> GSM312865 3 0.0424 0.951 0.000 0.008 0.992
#> GSM312867 3 0.0000 0.960 0.000 0.000 1.000
#> GSM312868 2 0.0000 0.983 0.000 1.000 0.000
#> GSM312869 2 0.0000 0.983 0.000 1.000 0.000
#> GSM312870 1 0.0000 0.900 1.000 0.000 0.000
#> GSM312872 1 0.0000 0.900 1.000 0.000 0.000
#> GSM312874 1 0.0000 0.900 1.000 0.000 0.000
#> GSM312875 1 0.0000 0.900 1.000 0.000 0.000
#> GSM312876 1 0.0000 0.900 1.000 0.000 0.000
#> GSM312877 1 0.2165 0.865 0.936 0.000 0.064
#> GSM312879 1 0.0000 0.900 1.000 0.000 0.000
#> GSM312882 1 0.0000 0.900 1.000 0.000 0.000
#> GSM312883 1 0.0000 0.900 1.000 0.000 0.000
#> GSM312886 1 0.0000 0.900 1.000 0.000 0.000
#> GSM312887 1 0.2959 0.839 0.900 0.000 0.100
#> GSM312890 3 0.0000 0.960 0.000 0.000 1.000
#> GSM312893 3 0.0000 0.960 0.000 0.000 1.000
#> GSM312894 3 0.2625 0.870 0.084 0.000 0.916
#> GSM312895 3 0.0000 0.960 0.000 0.000 1.000
#> GSM312937 3 0.0000 0.960 0.000 0.000 1.000
#> GSM312938 3 0.0000 0.960 0.000 0.000 1.000
#> GSM312939 3 0.0000 0.960 0.000 0.000 1.000
#> GSM312940 3 0.0000 0.960 0.000 0.000 1.000
#> GSM312941 3 0.0000 0.960 0.000 0.000 1.000
#> GSM312942 1 0.0424 0.897 0.992 0.000 0.008
#> GSM312943 1 0.6180 0.341 0.584 0.000 0.416
#> GSM312944 3 0.6192 0.135 0.420 0.000 0.580
#> GSM312945 1 0.6291 0.187 0.532 0.000 0.468
#> GSM312946 1 0.4931 0.690 0.768 0.000 0.232
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM312811 2 0.0000 0.8904 0.000 1.000 0.000 0.000
#> GSM312812 2 0.0469 0.8860 0.000 0.988 0.000 0.012
#> GSM312813 2 0.0000 0.8904 0.000 1.000 0.000 0.000
#> GSM312814 2 0.1302 0.8626 0.000 0.956 0.000 0.044
#> GSM312815 2 0.0817 0.8791 0.000 0.976 0.000 0.024
#> GSM312816 2 0.3266 0.7298 0.000 0.832 0.000 0.168
#> GSM312817 2 0.0188 0.8893 0.000 0.996 0.000 0.004
#> GSM312818 3 0.7626 -0.0308 0.000 0.384 0.412 0.204
#> GSM312819 2 0.0188 0.8893 0.000 0.996 0.000 0.004
#> GSM312820 2 0.4692 0.6544 0.000 0.756 0.032 0.212
#> GSM312821 2 0.5288 0.6215 0.000 0.732 0.068 0.200
#> GSM312822 2 0.2408 0.8051 0.000 0.896 0.000 0.104
#> GSM312823 2 0.0000 0.8904 0.000 1.000 0.000 0.000
#> GSM312824 2 0.0000 0.8904 0.000 1.000 0.000 0.000
#> GSM312825 2 0.2011 0.8194 0.000 0.920 0.000 0.080
#> GSM312826 2 0.0188 0.8894 0.000 0.996 0.000 0.004
#> GSM312839 2 0.0817 0.8791 0.000 0.976 0.000 0.024
#> GSM312840 2 0.0000 0.8904 0.000 1.000 0.000 0.000
#> GSM312841 2 0.0000 0.8904 0.000 1.000 0.000 0.000
#> GSM312843 2 0.4981 -0.1713 0.000 0.536 0.000 0.464
#> GSM312844 2 0.0000 0.8904 0.000 1.000 0.000 0.000
#> GSM312845 1 0.2589 0.7365 0.884 0.000 0.000 0.116
#> GSM312846 1 0.0592 0.8129 0.984 0.000 0.000 0.016
#> GSM312847 4 0.5161 0.1662 0.476 0.004 0.000 0.520
#> GSM312848 4 0.6970 0.7308 0.168 0.256 0.000 0.576
#> GSM312849 1 0.4222 0.5022 0.728 0.272 0.000 0.000
#> GSM312851 4 0.4770 0.7630 0.012 0.288 0.000 0.700
#> GSM312853 4 0.4883 0.7659 0.016 0.288 0.000 0.696
#> GSM312854 4 0.5478 0.7687 0.056 0.248 0.000 0.696
#> GSM312856 4 0.4963 0.7688 0.020 0.284 0.000 0.696
#> GSM312857 4 0.4963 0.7690 0.020 0.284 0.000 0.696
#> GSM312858 4 0.7146 0.7246 0.176 0.276 0.000 0.548
#> GSM312859 2 0.0000 0.8904 0.000 1.000 0.000 0.000
#> GSM312860 2 0.0895 0.8805 0.004 0.976 0.000 0.020
#> GSM312861 2 0.2530 0.7677 0.000 0.888 0.000 0.112
#> GSM312862 2 0.0188 0.8893 0.000 0.996 0.000 0.004
#> GSM312863 4 0.4795 0.7610 0.012 0.292 0.000 0.696
#> GSM312864 2 0.4961 -0.0978 0.000 0.552 0.000 0.448
#> GSM312865 4 0.5126 0.2420 0.444 0.004 0.000 0.552
#> GSM312867 1 0.2408 0.7548 0.896 0.000 0.000 0.104
#> GSM312868 4 0.4996 0.4563 0.000 0.484 0.000 0.516
#> GSM312869 2 0.0707 0.8817 0.000 0.980 0.000 0.020
#> GSM312870 3 0.0336 0.8221 0.000 0.000 0.992 0.008
#> GSM312872 3 0.0188 0.8228 0.000 0.000 0.996 0.004
#> GSM312874 3 0.0336 0.8221 0.000 0.000 0.992 0.008
#> GSM312875 3 0.0524 0.8222 0.004 0.000 0.988 0.008
#> GSM312876 3 0.0524 0.8222 0.004 0.000 0.988 0.008
#> GSM312877 3 0.7133 0.1789 0.344 0.000 0.512 0.144
#> GSM312879 3 0.0000 0.8230 0.000 0.000 1.000 0.000
#> GSM312882 3 0.1151 0.8163 0.008 0.000 0.968 0.024
#> GSM312883 3 0.1510 0.8106 0.016 0.000 0.956 0.028
#> GSM312886 3 0.0336 0.8221 0.000 0.000 0.992 0.008
#> GSM312887 3 0.5150 0.2829 0.396 0.000 0.596 0.008
#> GSM312890 1 0.0469 0.8146 0.988 0.000 0.000 0.012
#> GSM312893 1 0.0336 0.8110 0.992 0.000 0.000 0.008
#> GSM312894 1 0.3105 0.7287 0.868 0.000 0.120 0.012
#> GSM312895 1 0.0336 0.8147 0.992 0.000 0.000 0.008
#> GSM312937 1 0.0469 0.8146 0.988 0.000 0.000 0.012
#> GSM312938 1 0.2654 0.7414 0.888 0.000 0.004 0.108
#> GSM312939 1 0.0469 0.8146 0.988 0.000 0.000 0.012
#> GSM312940 1 0.0469 0.8146 0.988 0.000 0.000 0.012
#> GSM312941 1 0.0000 0.8136 1.000 0.000 0.000 0.000
#> GSM312942 3 0.6613 0.5110 0.200 0.000 0.628 0.172
#> GSM312943 1 0.7198 0.4526 0.540 0.000 0.180 0.280
#> GSM312944 1 0.7133 0.4650 0.548 0.000 0.172 0.280
#> GSM312945 1 0.7179 0.4571 0.544 0.000 0.180 0.276
#> GSM312946 1 0.7497 0.3710 0.496 0.000 0.224 0.280
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM312811 2 0.0880 0.9237 0.000 0.968 0.000 0.000 0.032
#> GSM312812 2 0.0162 0.9418 0.000 0.996 0.000 0.000 0.004
#> GSM312813 2 0.0162 0.9414 0.000 0.996 0.000 0.004 0.000
#> GSM312814 2 0.2462 0.8419 0.000 0.880 0.000 0.008 0.112
#> GSM312815 2 0.0609 0.9297 0.000 0.980 0.000 0.000 0.020
#> GSM312816 2 0.4206 0.6059 0.000 0.708 0.000 0.020 0.272
#> GSM312817 2 0.0162 0.9414 0.000 0.996 0.000 0.004 0.000
#> GSM312818 5 0.6227 0.1765 0.000 0.288 0.076 0.044 0.592
#> GSM312819 2 0.0290 0.9399 0.000 0.992 0.000 0.008 0.000
#> GSM312820 5 0.5229 -0.0970 0.000 0.432 0.004 0.036 0.528
#> GSM312821 5 0.5477 -0.0468 0.000 0.412 0.012 0.040 0.536
#> GSM312822 2 0.3081 0.7874 0.000 0.832 0.000 0.012 0.156
#> GSM312823 2 0.0000 0.9427 0.000 1.000 0.000 0.000 0.000
#> GSM312824 2 0.0000 0.9427 0.000 1.000 0.000 0.000 0.000
#> GSM312825 2 0.0290 0.9397 0.000 0.992 0.000 0.000 0.008
#> GSM312826 2 0.0000 0.9427 0.000 1.000 0.000 0.000 0.000
#> GSM312839 2 0.0404 0.9369 0.000 0.988 0.000 0.000 0.012
#> GSM312840 2 0.0000 0.9427 0.000 1.000 0.000 0.000 0.000
#> GSM312841 2 0.0000 0.9427 0.000 1.000 0.000 0.000 0.000
#> GSM312843 4 0.2818 0.8246 0.000 0.132 0.000 0.856 0.012
#> GSM312844 2 0.0000 0.9427 0.000 1.000 0.000 0.000 0.000
#> GSM312845 4 0.3846 0.7288 0.200 0.000 0.020 0.776 0.004
#> GSM312846 1 0.1830 0.8579 0.932 0.012 0.000 0.052 0.004
#> GSM312847 4 0.2389 0.8202 0.116 0.000 0.000 0.880 0.004
#> GSM312848 4 0.1934 0.8815 0.016 0.052 0.000 0.928 0.004
#> GSM312849 1 0.5689 0.3501 0.604 0.316 0.000 0.060 0.020
#> GSM312851 4 0.2871 0.8409 0.000 0.040 0.000 0.872 0.088
#> GSM312853 4 0.1043 0.8834 0.000 0.040 0.000 0.960 0.000
#> GSM312854 4 0.1043 0.8834 0.000 0.040 0.000 0.960 0.000
#> GSM312856 4 0.1043 0.8834 0.000 0.040 0.000 0.960 0.000
#> GSM312857 4 0.1043 0.8834 0.000 0.040 0.000 0.960 0.000
#> GSM312858 4 0.1978 0.8809 0.024 0.044 0.000 0.928 0.004
#> GSM312859 2 0.0324 0.9398 0.000 0.992 0.000 0.004 0.004
#> GSM312860 2 0.0566 0.9357 0.000 0.984 0.000 0.004 0.012
#> GSM312861 4 0.3990 0.6150 0.000 0.308 0.000 0.688 0.004
#> GSM312862 2 0.3835 0.5778 0.000 0.732 0.000 0.008 0.260
#> GSM312863 4 0.1043 0.8834 0.000 0.040 0.000 0.960 0.000
#> GSM312864 4 0.3061 0.8167 0.000 0.136 0.000 0.844 0.020
#> GSM312865 4 0.1430 0.8568 0.052 0.004 0.000 0.944 0.000
#> GSM312867 4 0.4446 0.1454 0.476 0.000 0.000 0.520 0.004
#> GSM312868 4 0.1478 0.8782 0.000 0.064 0.000 0.936 0.000
#> GSM312869 2 0.0162 0.9418 0.000 0.996 0.000 0.000 0.004
#> GSM312870 3 0.0510 0.9489 0.000 0.000 0.984 0.000 0.016
#> GSM312872 3 0.0510 0.9489 0.000 0.000 0.984 0.000 0.016
#> GSM312874 3 0.0510 0.9489 0.000 0.000 0.984 0.000 0.016
#> GSM312875 3 0.0451 0.9469 0.000 0.000 0.988 0.004 0.008
#> GSM312876 3 0.0324 0.9483 0.000 0.000 0.992 0.004 0.004
#> GSM312877 3 0.3846 0.6804 0.020 0.000 0.776 0.004 0.200
#> GSM312879 3 0.0290 0.9499 0.000 0.000 0.992 0.000 0.008
#> GSM312882 3 0.0671 0.9432 0.000 0.000 0.980 0.004 0.016
#> GSM312883 3 0.1365 0.9218 0.004 0.000 0.952 0.004 0.040
#> GSM312886 3 0.0609 0.9470 0.000 0.000 0.980 0.000 0.020
#> GSM312887 1 0.4155 0.6895 0.780 0.000 0.076 0.000 0.144
#> GSM312890 1 0.0162 0.9140 0.996 0.000 0.000 0.004 0.000
#> GSM312893 1 0.0000 0.9143 1.000 0.000 0.000 0.000 0.000
#> GSM312894 1 0.0404 0.9056 0.988 0.000 0.012 0.000 0.000
#> GSM312895 1 0.0000 0.9143 1.000 0.000 0.000 0.000 0.000
#> GSM312937 1 0.0000 0.9143 1.000 0.000 0.000 0.000 0.000
#> GSM312938 1 0.0566 0.9088 0.984 0.000 0.000 0.012 0.004
#> GSM312939 1 0.0162 0.9140 0.996 0.000 0.000 0.004 0.000
#> GSM312940 1 0.0162 0.9140 0.996 0.000 0.000 0.004 0.000
#> GSM312941 1 0.0000 0.9143 1.000 0.000 0.000 0.000 0.000
#> GSM312942 5 0.6705 0.3441 0.244 0.000 0.364 0.000 0.392
#> GSM312943 5 0.6709 0.3652 0.248 0.000 0.352 0.000 0.400
#> GSM312944 5 0.6732 0.3733 0.260 0.000 0.340 0.000 0.400
#> GSM312945 5 0.6758 0.3702 0.272 0.000 0.336 0.000 0.392
#> GSM312946 5 0.6709 0.3652 0.248 0.000 0.352 0.000 0.400
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM312811 2 0.0713 0.9327 0.000 0.972 0.000 0.000 0.028 0.000
#> GSM312812 2 0.0363 0.9484 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM312813 2 0.0547 0.9467 0.000 0.980 0.000 0.000 0.000 0.020
#> GSM312814 2 0.2147 0.8685 0.000 0.896 0.000 0.000 0.084 0.020
#> GSM312815 2 0.0547 0.9467 0.000 0.980 0.000 0.000 0.000 0.020
#> GSM312816 2 0.3653 0.4179 0.000 0.692 0.000 0.000 0.300 0.008
#> GSM312817 2 0.0692 0.9449 0.000 0.976 0.000 0.004 0.000 0.020
#> GSM312818 5 0.2070 0.7171 0.000 0.092 0.012 0.000 0.896 0.000
#> GSM312819 2 0.0260 0.9479 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM312820 5 0.3244 0.8452 0.000 0.268 0.000 0.000 0.732 0.000
#> GSM312821 5 0.3126 0.8585 0.000 0.248 0.000 0.000 0.752 0.000
#> GSM312822 2 0.2581 0.8196 0.000 0.860 0.000 0.000 0.120 0.020
#> GSM312823 2 0.0458 0.9478 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM312824 2 0.0260 0.9479 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM312825 2 0.0260 0.9479 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM312826 2 0.0260 0.9479 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM312839 2 0.0547 0.9467 0.000 0.980 0.000 0.000 0.000 0.020
#> GSM312840 2 0.0260 0.9479 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM312841 2 0.0260 0.9479 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM312843 4 0.0622 0.9411 0.000 0.008 0.000 0.980 0.000 0.012
#> GSM312844 2 0.0692 0.9460 0.000 0.976 0.000 0.000 0.004 0.020
#> GSM312845 4 0.6044 0.3271 0.268 0.004 0.184 0.532 0.004 0.008
#> GSM312846 1 0.0146 0.9122 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM312847 4 0.0717 0.9389 0.016 0.000 0.000 0.976 0.000 0.008
#> GSM312848 4 0.0146 0.9503 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM312849 1 0.3909 0.5920 0.760 0.200 0.008 0.000 0.012 0.020
#> GSM312851 4 0.1007 0.9193 0.000 0.000 0.000 0.956 0.044 0.000
#> GSM312853 4 0.0000 0.9516 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312854 4 0.0000 0.9516 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312856 4 0.0000 0.9516 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312857 4 0.0000 0.9516 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312858 4 0.0291 0.9488 0.000 0.004 0.000 0.992 0.000 0.004
#> GSM312859 2 0.0000 0.9484 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312860 2 0.0692 0.9452 0.000 0.976 0.000 0.000 0.004 0.020
#> GSM312861 4 0.1075 0.9065 0.000 0.048 0.000 0.952 0.000 0.000
#> GSM312862 6 0.3622 0.4920 0.000 0.236 0.000 0.016 0.004 0.744
#> GSM312863 4 0.0000 0.9516 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312864 4 0.0146 0.9503 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM312865 4 0.0000 0.9516 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312867 1 0.3993 0.0461 0.520 0.000 0.000 0.476 0.004 0.000
#> GSM312868 4 0.0000 0.9516 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312869 2 0.0260 0.9479 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM312870 3 0.0632 0.9857 0.000 0.000 0.976 0.000 0.024 0.000
#> GSM312872 3 0.0458 0.9879 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM312874 3 0.0632 0.9857 0.000 0.000 0.976 0.000 0.024 0.000
#> GSM312875 3 0.0000 0.9880 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312876 3 0.0000 0.9880 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312877 3 0.0363 0.9824 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM312879 3 0.0458 0.9879 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM312882 3 0.0146 0.9869 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM312883 3 0.0146 0.9869 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM312886 3 0.0632 0.9857 0.000 0.000 0.976 0.000 0.024 0.000
#> GSM312887 1 0.1556 0.8476 0.920 0.000 0.000 0.000 0.080 0.000
#> GSM312890 1 0.0000 0.9147 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312893 1 0.0000 0.9147 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312894 1 0.0000 0.9147 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312895 1 0.0000 0.9147 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312937 1 0.0000 0.9147 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312938 1 0.0000 0.9147 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312939 1 0.0000 0.9147 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312940 1 0.0000 0.9147 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312941 1 0.0000 0.9147 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312942 6 0.0713 0.9076 0.000 0.000 0.028 0.000 0.000 0.972
#> GSM312943 6 0.0777 0.9089 0.004 0.000 0.024 0.000 0.000 0.972
#> GSM312944 6 0.0820 0.8998 0.016 0.000 0.012 0.000 0.000 0.972
#> GSM312945 6 0.0806 0.9076 0.008 0.000 0.020 0.000 0.000 0.972
#> GSM312946 6 0.0713 0.9076 0.000 0.000 0.028 0.000 0.000 0.972
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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:NMF 66 2.61e-10 2
#> MAD:NMF 64 1.08e-13 3
#> MAD:NMF 55 7.43e-16 4
#> MAD:NMF 57 6.95e-18 5
#> MAD:NMF 63 5.00e-25 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "hclust"]
# you can also extract it by
# res = res_list["ATC:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 67 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 1.000 1.000 1.000 0.4944 0.506 0.506
#> 3 3 1.000 0.942 0.958 0.1104 0.934 0.869
#> 4 4 1.000 0.961 0.971 0.0969 0.953 0.893
#> 5 5 0.687 0.708 0.792 0.2204 0.842 0.597
#> 6 6 0.756 0.759 0.867 0.0604 0.905 0.651
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
#> GSM312811 2 0 1 0 1
#> GSM312812 2 0 1 0 1
#> GSM312813 2 0 1 0 1
#> GSM312814 2 0 1 0 1
#> GSM312815 2 0 1 0 1
#> GSM312816 2 0 1 0 1
#> GSM312817 2 0 1 0 1
#> GSM312818 1 0 1 1 0
#> GSM312819 2 0 1 0 1
#> GSM312820 1 0 1 1 0
#> GSM312821 1 0 1 1 0
#> GSM312822 2 0 1 0 1
#> GSM312823 2 0 1 0 1
#> GSM312824 2 0 1 0 1
#> GSM312825 2 0 1 0 1
#> GSM312826 2 0 1 0 1
#> GSM312839 2 0 1 0 1
#> GSM312840 2 0 1 0 1
#> GSM312841 2 0 1 0 1
#> GSM312843 2 0 1 0 1
#> GSM312844 2 0 1 0 1
#> GSM312845 2 0 1 0 1
#> GSM312846 2 0 1 0 1
#> GSM312847 2 0 1 0 1
#> GSM312848 2 0 1 0 1
#> GSM312849 2 0 1 0 1
#> GSM312851 2 0 1 0 1
#> GSM312853 2 0 1 0 1
#> GSM312854 2 0 1 0 1
#> GSM312856 2 0 1 0 1
#> GSM312857 2 0 1 0 1
#> GSM312858 2 0 1 0 1
#> GSM312859 2 0 1 0 1
#> GSM312860 2 0 1 0 1
#> GSM312861 2 0 1 0 1
#> GSM312862 2 0 1 0 1
#> GSM312863 2 0 1 0 1
#> GSM312864 2 0 1 0 1
#> GSM312865 2 0 1 0 1
#> GSM312867 2 0 1 0 1
#> GSM312868 2 0 1 0 1
#> GSM312869 2 0 1 0 1
#> GSM312870 1 0 1 1 0
#> GSM312872 1 0 1 1 0
#> GSM312874 1 0 1 1 0
#> GSM312875 1 0 1 1 0
#> GSM312876 1 0 1 1 0
#> GSM312877 1 0 1 1 0
#> GSM312879 1 0 1 1 0
#> GSM312882 1 0 1 1 0
#> GSM312883 1 0 1 1 0
#> GSM312886 1 0 1 1 0
#> GSM312887 1 0 1 1 0
#> GSM312890 1 0 1 1 0
#> GSM312893 1 0 1 1 0
#> GSM312894 1 0 1 1 0
#> GSM312895 1 0 1 1 0
#> GSM312937 1 0 1 1 0
#> GSM312938 1 0 1 1 0
#> GSM312939 1 0 1 1 0
#> GSM312940 1 0 1 1 0
#> GSM312941 1 0 1 1 0
#> GSM312942 1 0 1 1 0
#> GSM312943 1 0 1 1 0
#> GSM312944 1 0 1 1 0
#> GSM312945 1 0 1 1 0
#> GSM312946 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM312811 2 0.000 1.000 0.000 1 0.000
#> GSM312812 2 0.000 1.000 0.000 1 0.000
#> GSM312813 2 0.000 1.000 0.000 1 0.000
#> GSM312814 2 0.000 1.000 0.000 1 0.000
#> GSM312815 2 0.000 1.000 0.000 1 0.000
#> GSM312816 2 0.000 1.000 0.000 1 0.000
#> GSM312817 2 0.000 1.000 0.000 1 0.000
#> GSM312818 3 0.254 0.687 0.080 0 0.920
#> GSM312819 2 0.000 1.000 0.000 1 0.000
#> GSM312820 3 0.254 0.687 0.080 0 0.920
#> GSM312821 3 0.254 0.687 0.080 0 0.920
#> GSM312822 2 0.000 1.000 0.000 1 0.000
#> GSM312823 2 0.000 1.000 0.000 1 0.000
#> GSM312824 2 0.000 1.000 0.000 1 0.000
#> GSM312825 2 0.000 1.000 0.000 1 0.000
#> GSM312826 2 0.000 1.000 0.000 1 0.000
#> GSM312839 2 0.000 1.000 0.000 1 0.000
#> GSM312840 2 0.000 1.000 0.000 1 0.000
#> GSM312841 2 0.000 1.000 0.000 1 0.000
#> GSM312843 2 0.000 1.000 0.000 1 0.000
#> GSM312844 2 0.000 1.000 0.000 1 0.000
#> GSM312845 2 0.000 1.000 0.000 1 0.000
#> GSM312846 2 0.000 1.000 0.000 1 0.000
#> GSM312847 2 0.000 1.000 0.000 1 0.000
#> GSM312848 2 0.000 1.000 0.000 1 0.000
#> GSM312849 2 0.000 1.000 0.000 1 0.000
#> GSM312851 2 0.000 1.000 0.000 1 0.000
#> GSM312853 2 0.000 1.000 0.000 1 0.000
#> GSM312854 2 0.000 1.000 0.000 1 0.000
#> GSM312856 2 0.000 1.000 0.000 1 0.000
#> GSM312857 2 0.000 1.000 0.000 1 0.000
#> GSM312858 2 0.000 1.000 0.000 1 0.000
#> GSM312859 2 0.000 1.000 0.000 1 0.000
#> GSM312860 2 0.000 1.000 0.000 1 0.000
#> GSM312861 2 0.000 1.000 0.000 1 0.000
#> GSM312862 2 0.000 1.000 0.000 1 0.000
#> GSM312863 2 0.000 1.000 0.000 1 0.000
#> GSM312864 2 0.000 1.000 0.000 1 0.000
#> GSM312865 2 0.000 1.000 0.000 1 0.000
#> GSM312867 2 0.000 1.000 0.000 1 0.000
#> GSM312868 2 0.000 1.000 0.000 1 0.000
#> GSM312869 2 0.000 1.000 0.000 1 0.000
#> GSM312870 1 0.280 0.917 0.908 0 0.092
#> GSM312872 1 0.280 0.917 0.908 0 0.092
#> GSM312874 1 0.280 0.917 0.908 0 0.092
#> GSM312875 1 0.280 0.917 0.908 0 0.092
#> GSM312876 1 0.280 0.917 0.908 0 0.092
#> GSM312877 1 0.000 0.949 1.000 0 0.000
#> GSM312879 1 0.280 0.917 0.908 0 0.092
#> GSM312882 1 0.280 0.917 0.908 0 0.092
#> GSM312883 1 0.280 0.917 0.908 0 0.092
#> GSM312886 3 0.623 0.594 0.436 0 0.564
#> GSM312887 3 0.627 0.605 0.456 0 0.544
#> GSM312890 1 0.000 0.949 1.000 0 0.000
#> GSM312893 1 0.000 0.949 1.000 0 0.000
#> GSM312894 1 0.000 0.949 1.000 0 0.000
#> GSM312895 1 0.000 0.949 1.000 0 0.000
#> GSM312937 1 0.000 0.949 1.000 0 0.000
#> GSM312938 3 0.630 0.593 0.476 0 0.524
#> GSM312939 1 0.000 0.949 1.000 0 0.000
#> GSM312940 1 0.000 0.949 1.000 0 0.000
#> GSM312941 1 0.000 0.949 1.000 0 0.000
#> GSM312942 3 0.628 0.604 0.460 0 0.540
#> GSM312943 1 0.000 0.949 1.000 0 0.000
#> GSM312944 1 0.000 0.949 1.000 0 0.000
#> GSM312945 1 0.000 0.949 1.000 0 0.000
#> GSM312946 1 0.000 0.949 1.000 0 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM312811 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM312812 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM312813 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM312814 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM312815 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM312816 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM312817 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM312818 4 0.000 0.674 0.000 0 0.000 1.000
#> GSM312819 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM312820 4 0.000 0.674 0.000 0 0.000 1.000
#> GSM312821 4 0.000 0.674 0.000 0 0.000 1.000
#> GSM312822 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM312823 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM312824 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM312825 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM312826 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM312839 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM312840 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM312841 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM312843 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM312844 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM312845 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM312846 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM312847 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM312848 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM312849 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM312851 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM312853 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM312854 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM312856 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM312857 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM312858 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM312859 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM312860 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM312861 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM312862 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM312863 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM312864 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM312865 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM312867 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM312868 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM312869 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM312870 3 0.000 1.000 0.000 0 1.000 0.000
#> GSM312872 3 0.000 1.000 0.000 0 1.000 0.000
#> GSM312874 3 0.000 1.000 0.000 0 1.000 0.000
#> GSM312875 3 0.000 1.000 0.000 0 1.000 0.000
#> GSM312876 3 0.000 1.000 0.000 0 1.000 0.000
#> GSM312877 1 0.000 1.000 1.000 0 0.000 0.000
#> GSM312879 3 0.000 1.000 0.000 0 1.000 0.000
#> GSM312882 3 0.000 1.000 0.000 0 1.000 0.000
#> GSM312883 3 0.000 1.000 0.000 0 1.000 0.000
#> GSM312886 4 0.677 0.553 0.100 0 0.384 0.516
#> GSM312887 4 0.710 0.605 0.140 0 0.344 0.516
#> GSM312890 1 0.000 1.000 1.000 0 0.000 0.000
#> GSM312893 1 0.000 1.000 1.000 0 0.000 0.000
#> GSM312894 1 0.000 1.000 1.000 0 0.000 0.000
#> GSM312895 1 0.000 1.000 1.000 0 0.000 0.000
#> GSM312937 1 0.000 1.000 1.000 0 0.000 0.000
#> GSM312938 4 0.735 0.583 0.288 0 0.196 0.516
#> GSM312939 1 0.000 1.000 1.000 0 0.000 0.000
#> GSM312940 1 0.000 1.000 1.000 0 0.000 0.000
#> GSM312941 1 0.000 1.000 1.000 0 0.000 0.000
#> GSM312942 4 0.712 0.607 0.144 0 0.340 0.516
#> GSM312943 1 0.000 1.000 1.000 0 0.000 0.000
#> GSM312944 1 0.000 1.000 1.000 0 0.000 0.000
#> GSM312945 1 0.000 1.000 1.000 0 0.000 0.000
#> GSM312946 1 0.000 1.000 1.000 0 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM312811 2 0.1043 0.622 0.000 0.960 0.000 0.040 0.000
#> GSM312812 2 0.4101 0.517 0.000 0.628 0.000 0.372 0.000
#> GSM312813 4 0.3730 0.868 0.000 0.288 0.000 0.712 0.000
#> GSM312814 2 0.0963 0.622 0.000 0.964 0.000 0.036 0.000
#> GSM312815 2 0.4060 0.531 0.000 0.640 0.000 0.360 0.000
#> GSM312816 2 0.0000 0.609 0.000 1.000 0.000 0.000 0.000
#> GSM312817 2 0.4283 -0.385 0.000 0.544 0.000 0.456 0.000
#> GSM312818 5 0.2966 0.596 0.000 0.000 0.000 0.184 0.816
#> GSM312819 2 0.4283 -0.385 0.000 0.544 0.000 0.456 0.000
#> GSM312820 5 0.2966 0.596 0.000 0.000 0.000 0.184 0.816
#> GSM312821 5 0.2966 0.596 0.000 0.000 0.000 0.184 0.816
#> GSM312822 2 0.3796 0.540 0.000 0.700 0.000 0.300 0.000
#> GSM312823 2 0.0963 0.622 0.000 0.964 0.000 0.036 0.000
#> GSM312824 2 0.4307 0.237 0.000 0.504 0.000 0.496 0.000
#> GSM312825 2 0.4307 0.237 0.000 0.504 0.000 0.496 0.000
#> GSM312826 2 0.4307 0.237 0.000 0.504 0.000 0.496 0.000
#> GSM312839 2 0.4060 0.531 0.000 0.640 0.000 0.360 0.000
#> GSM312840 2 0.3774 0.574 0.000 0.704 0.000 0.296 0.000
#> GSM312841 2 0.3636 0.588 0.000 0.728 0.000 0.272 0.000
#> GSM312843 2 0.3932 0.432 0.000 0.672 0.000 0.328 0.000
#> GSM312844 2 0.4060 0.531 0.000 0.640 0.000 0.360 0.000
#> GSM312845 4 0.3336 0.761 0.000 0.228 0.000 0.772 0.000
#> GSM312846 2 0.4256 0.418 0.000 0.564 0.000 0.436 0.000
#> GSM312847 4 0.3612 0.867 0.000 0.268 0.000 0.732 0.000
#> GSM312848 4 0.3966 0.840 0.000 0.336 0.000 0.664 0.000
#> GSM312849 4 0.3074 0.797 0.000 0.196 0.000 0.804 0.000
#> GSM312851 2 0.0000 0.609 0.000 1.000 0.000 0.000 0.000
#> GSM312853 2 0.0609 0.610 0.000 0.980 0.000 0.020 0.000
#> GSM312854 2 0.1908 0.545 0.000 0.908 0.000 0.092 0.000
#> GSM312856 2 0.0510 0.610 0.000 0.984 0.000 0.016 0.000
#> GSM312857 2 0.0510 0.610 0.000 0.984 0.000 0.016 0.000
#> GSM312858 4 0.3857 0.855 0.000 0.312 0.000 0.688 0.000
#> GSM312859 4 0.3636 0.872 0.000 0.272 0.000 0.728 0.000
#> GSM312860 4 0.3636 0.872 0.000 0.272 0.000 0.728 0.000
#> GSM312861 4 0.3452 0.860 0.000 0.244 0.000 0.756 0.000
#> GSM312862 2 0.4074 0.527 0.000 0.636 0.000 0.364 0.000
#> GSM312863 4 0.4278 0.596 0.000 0.452 0.000 0.548 0.000
#> GSM312864 2 0.0963 0.603 0.000 0.964 0.000 0.036 0.000
#> GSM312865 4 0.3895 0.854 0.000 0.320 0.000 0.680 0.000
#> GSM312867 4 0.2966 0.800 0.000 0.184 0.000 0.816 0.000
#> GSM312868 4 0.3857 0.855 0.000 0.312 0.000 0.688 0.000
#> GSM312869 4 0.3452 0.754 0.000 0.244 0.000 0.756 0.000
#> GSM312870 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312872 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312874 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312875 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312876 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312877 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM312879 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312882 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312883 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM312886 5 0.5836 0.448 0.100 0.000 0.384 0.000 0.516
#> GSM312887 5 0.6112 0.507 0.140 0.000 0.344 0.000 0.516
#> GSM312890 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM312893 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM312894 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM312895 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM312937 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM312938 5 0.6333 0.507 0.288 0.000 0.196 0.000 0.516
#> GSM312939 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM312940 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM312941 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM312942 5 0.6134 0.510 0.144 0.000 0.340 0.000 0.516
#> GSM312943 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM312944 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM312945 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM312946 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM312811 2 0.1124 0.736 0.000 0.956 0.000 0.036 0 0.008
#> GSM312812 2 0.4409 0.541 0.000 0.588 0.000 0.380 0 0.032
#> GSM312813 4 0.1970 0.735 0.000 0.092 0.000 0.900 0 0.008
#> GSM312814 2 0.1124 0.737 0.000 0.956 0.000 0.036 0 0.008
#> GSM312815 2 0.4443 0.569 0.000 0.596 0.000 0.368 0 0.036
#> GSM312816 2 0.0363 0.726 0.000 0.988 0.000 0.000 0 0.012
#> GSM312817 4 0.4155 0.445 0.000 0.364 0.000 0.616 0 0.020
#> GSM312818 5 0.0000 1.000 0.000 0.000 0.000 0.000 1 0.000
#> GSM312819 4 0.4155 0.445 0.000 0.364 0.000 0.616 0 0.020
#> GSM312820 5 0.0000 1.000 0.000 0.000 0.000 0.000 1 0.000
#> GSM312821 5 0.0000 1.000 0.000 0.000 0.000 0.000 1 0.000
#> GSM312822 2 0.3898 0.603 0.000 0.652 0.000 0.336 0 0.012
#> GSM312823 2 0.1124 0.737 0.000 0.956 0.000 0.036 0 0.008
#> GSM312824 4 0.4575 0.188 0.000 0.352 0.000 0.600 0 0.048
#> GSM312825 4 0.4575 0.188 0.000 0.352 0.000 0.600 0 0.048
#> GSM312826 4 0.4575 0.188 0.000 0.352 0.000 0.600 0 0.048
#> GSM312839 2 0.4443 0.569 0.000 0.596 0.000 0.368 0 0.036
#> GSM312840 2 0.4152 0.628 0.000 0.664 0.000 0.304 0 0.032
#> GSM312841 2 0.4020 0.649 0.000 0.692 0.000 0.276 0 0.032
#> GSM312843 2 0.3819 0.456 0.000 0.624 0.000 0.372 0 0.004
#> GSM312844 2 0.4443 0.569 0.000 0.596 0.000 0.368 0 0.036
#> GSM312845 4 0.3172 0.662 0.000 0.036 0.000 0.816 0 0.148
#> GSM312846 4 0.4666 -0.158 0.000 0.420 0.000 0.536 0 0.044
#> GSM312847 4 0.2745 0.732 0.000 0.068 0.000 0.864 0 0.068
#> GSM312848 4 0.2260 0.726 0.000 0.140 0.000 0.860 0 0.000
#> GSM312849 4 0.2613 0.680 0.000 0.012 0.000 0.848 0 0.140
#> GSM312851 2 0.0363 0.726 0.000 0.988 0.000 0.000 0 0.012
#> GSM312853 2 0.0820 0.724 0.000 0.972 0.000 0.016 0 0.012
#> GSM312854 2 0.1806 0.668 0.000 0.908 0.000 0.088 0 0.004
#> GSM312856 2 0.0725 0.725 0.000 0.976 0.000 0.012 0 0.012
#> GSM312857 2 0.0725 0.725 0.000 0.976 0.000 0.012 0 0.012
#> GSM312858 4 0.1957 0.729 0.000 0.112 0.000 0.888 0 0.000
#> GSM312859 4 0.1387 0.738 0.000 0.068 0.000 0.932 0 0.000
#> GSM312860 4 0.1531 0.737 0.000 0.068 0.000 0.928 0 0.004
#> GSM312861 4 0.1649 0.729 0.000 0.032 0.000 0.932 0 0.036
#> GSM312862 2 0.4482 0.543 0.000 0.580 0.000 0.384 0 0.036
#> GSM312863 4 0.3175 0.621 0.000 0.256 0.000 0.744 0 0.000
#> GSM312864 2 0.1010 0.718 0.000 0.960 0.000 0.036 0 0.004
#> GSM312865 4 0.2402 0.732 0.000 0.120 0.000 0.868 0 0.012
#> GSM312867 4 0.2300 0.683 0.000 0.000 0.000 0.856 0 0.144
#> GSM312868 4 0.2357 0.726 0.000 0.116 0.000 0.872 0 0.012
#> GSM312869 4 0.3439 0.667 0.000 0.072 0.000 0.808 0 0.120
#> GSM312870 3 0.0000 1.000 0.000 0.000 1.000 0.000 0 0.000
#> GSM312872 3 0.0000 1.000 0.000 0.000 1.000 0.000 0 0.000
#> GSM312874 3 0.0000 1.000 0.000 0.000 1.000 0.000 0 0.000
#> GSM312875 3 0.0000 1.000 0.000 0.000 1.000 0.000 0 0.000
#> GSM312876 3 0.0000 1.000 0.000 0.000 1.000 0.000 0 0.000
#> GSM312877 1 0.0000 1.000 1.000 0.000 0.000 0.000 0 0.000
#> GSM312879 3 0.0000 1.000 0.000 0.000 1.000 0.000 0 0.000
#> GSM312882 3 0.0000 1.000 0.000 0.000 1.000 0.000 0 0.000
#> GSM312883 3 0.0000 1.000 0.000 0.000 1.000 0.000 0 0.000
#> GSM312886 6 0.2697 0.837 0.000 0.000 0.188 0.000 0 0.812
#> GSM312887 6 0.3101 0.880 0.032 0.000 0.148 0.000 0 0.820
#> GSM312890 1 0.0000 1.000 1.000 0.000 0.000 0.000 0 0.000
#> GSM312893 1 0.0000 1.000 1.000 0.000 0.000 0.000 0 0.000
#> GSM312894 1 0.0000 1.000 1.000 0.000 0.000 0.000 0 0.000
#> GSM312895 1 0.0000 1.000 1.000 0.000 0.000 0.000 0 0.000
#> GSM312937 1 0.0000 1.000 1.000 0.000 0.000 0.000 0 0.000
#> GSM312938 6 0.2631 0.694 0.180 0.000 0.000 0.000 0 0.820
#> GSM312939 1 0.0000 1.000 1.000 0.000 0.000 0.000 0 0.000
#> GSM312940 1 0.0000 1.000 1.000 0.000 0.000 0.000 0 0.000
#> GSM312941 1 0.0000 1.000 1.000 0.000 0.000 0.000 0 0.000
#> GSM312942 6 0.3134 0.880 0.036 0.000 0.144 0.000 0 0.820
#> GSM312943 1 0.0000 1.000 1.000 0.000 0.000 0.000 0 0.000
#> GSM312944 1 0.0000 1.000 1.000 0.000 0.000 0.000 0 0.000
#> GSM312945 1 0.0000 1.000 1.000 0.000 0.000 0.000 0 0.000
#> GSM312946 1 0.0000 1.000 1.000 0.000 0.000 0.000 0 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:hclust 67 9.63e-09 2
#> ATC:hclust 67 4.21e-07 3
#> ATC:hclust 67 1.87e-12 4
#> ATC:hclust 59 2.62e-14 5
#> ATC:hclust 60 9.93e-14 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "kmeans"]
# you can also extract it by
# res = res_list["ATC:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 67 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.991 0.996 0.4904 0.512 0.512
#> 3 3 0.750 0.783 0.885 0.2143 0.924 0.853
#> 4 4 0.696 0.816 0.792 0.1342 0.930 0.842
#> 5 5 0.666 0.738 0.775 0.1166 0.834 0.570
#> 6 6 0.664 0.677 0.745 0.0592 0.941 0.756
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
#> GSM312811 2 0.000 0.993 0.000 1.000
#> GSM312812 2 0.000 0.993 0.000 1.000
#> GSM312813 2 0.000 0.993 0.000 1.000
#> GSM312814 2 0.000 0.993 0.000 1.000
#> GSM312815 2 0.000 0.993 0.000 1.000
#> GSM312816 2 0.000 0.993 0.000 1.000
#> GSM312817 2 0.000 0.993 0.000 1.000
#> GSM312818 1 0.000 1.000 1.000 0.000
#> GSM312819 2 0.000 0.993 0.000 1.000
#> GSM312820 2 0.821 0.656 0.256 0.744
#> GSM312821 1 0.000 1.000 1.000 0.000
#> GSM312822 2 0.000 0.993 0.000 1.000
#> GSM312823 2 0.000 0.993 0.000 1.000
#> GSM312824 2 0.000 0.993 0.000 1.000
#> GSM312825 2 0.000 0.993 0.000 1.000
#> GSM312826 2 0.000 0.993 0.000 1.000
#> GSM312839 2 0.000 0.993 0.000 1.000
#> GSM312840 2 0.000 0.993 0.000 1.000
#> GSM312841 2 0.000 0.993 0.000 1.000
#> GSM312843 2 0.000 0.993 0.000 1.000
#> GSM312844 2 0.000 0.993 0.000 1.000
#> GSM312845 2 0.000 0.993 0.000 1.000
#> GSM312846 2 0.000 0.993 0.000 1.000
#> GSM312847 2 0.000 0.993 0.000 1.000
#> GSM312848 2 0.000 0.993 0.000 1.000
#> GSM312849 2 0.000 0.993 0.000 1.000
#> GSM312851 2 0.000 0.993 0.000 1.000
#> GSM312853 2 0.000 0.993 0.000 1.000
#> GSM312854 2 0.000 0.993 0.000 1.000
#> GSM312856 2 0.000 0.993 0.000 1.000
#> GSM312857 2 0.000 0.993 0.000 1.000
#> GSM312858 2 0.000 0.993 0.000 1.000
#> GSM312859 2 0.000 0.993 0.000 1.000
#> GSM312860 2 0.000 0.993 0.000 1.000
#> GSM312861 2 0.000 0.993 0.000 1.000
#> GSM312862 2 0.000 0.993 0.000 1.000
#> GSM312863 2 0.000 0.993 0.000 1.000
#> GSM312864 2 0.000 0.993 0.000 1.000
#> GSM312865 2 0.000 0.993 0.000 1.000
#> GSM312867 2 0.000 0.993 0.000 1.000
#> GSM312868 2 0.000 0.993 0.000 1.000
#> GSM312869 2 0.000 0.993 0.000 1.000
#> GSM312870 1 0.000 1.000 1.000 0.000
#> GSM312872 1 0.000 1.000 1.000 0.000
#> GSM312874 1 0.000 1.000 1.000 0.000
#> GSM312875 1 0.000 1.000 1.000 0.000
#> GSM312876 1 0.000 1.000 1.000 0.000
#> GSM312877 1 0.000 1.000 1.000 0.000
#> GSM312879 1 0.000 1.000 1.000 0.000
#> GSM312882 1 0.000 1.000 1.000 0.000
#> GSM312883 1 0.000 1.000 1.000 0.000
#> GSM312886 1 0.000 1.000 1.000 0.000
#> GSM312887 1 0.000 1.000 1.000 0.000
#> GSM312890 1 0.000 1.000 1.000 0.000
#> GSM312893 1 0.000 1.000 1.000 0.000
#> GSM312894 1 0.000 1.000 1.000 0.000
#> GSM312895 1 0.000 1.000 1.000 0.000
#> GSM312937 1 0.000 1.000 1.000 0.000
#> GSM312938 1 0.000 1.000 1.000 0.000
#> GSM312939 1 0.000 1.000 1.000 0.000
#> GSM312940 1 0.000 1.000 1.000 0.000
#> GSM312941 1 0.000 1.000 1.000 0.000
#> GSM312942 1 0.000 1.000 1.000 0.000
#> GSM312943 1 0.000 1.000 1.000 0.000
#> GSM312944 1 0.000 1.000 1.000 0.000
#> GSM312945 1 0.000 1.000 1.000 0.000
#> GSM312946 1 0.000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM312811 2 0.5988 0.404 0.000 0.632 0.368
#> GSM312812 2 0.0000 0.914 0.000 1.000 0.000
#> GSM312813 2 0.0000 0.914 0.000 1.000 0.000
#> GSM312814 2 0.5988 0.404 0.000 0.632 0.368
#> GSM312815 2 0.4121 0.776 0.000 0.832 0.168
#> GSM312816 3 0.6095 0.322 0.000 0.392 0.608
#> GSM312817 2 0.0000 0.914 0.000 1.000 0.000
#> GSM312818 3 0.6095 0.610 0.392 0.000 0.608
#> GSM312819 2 0.0000 0.914 0.000 1.000 0.000
#> GSM312820 3 0.6587 0.629 0.352 0.016 0.632
#> GSM312821 3 0.5988 0.616 0.368 0.000 0.632
#> GSM312822 2 0.6008 0.394 0.000 0.628 0.372
#> GSM312823 2 0.3752 0.803 0.000 0.856 0.144
#> GSM312824 2 0.0000 0.914 0.000 1.000 0.000
#> GSM312825 2 0.0000 0.914 0.000 1.000 0.000
#> GSM312826 2 0.0000 0.914 0.000 1.000 0.000
#> GSM312839 2 0.3192 0.831 0.000 0.888 0.112
#> GSM312840 2 0.0000 0.914 0.000 1.000 0.000
#> GSM312841 2 0.0892 0.902 0.000 0.980 0.020
#> GSM312843 2 0.0000 0.914 0.000 1.000 0.000
#> GSM312844 2 0.4121 0.776 0.000 0.832 0.168
#> GSM312845 2 0.0000 0.914 0.000 1.000 0.000
#> GSM312846 2 0.3192 0.831 0.000 0.888 0.112
#> GSM312847 2 0.0000 0.914 0.000 1.000 0.000
#> GSM312848 2 0.0000 0.914 0.000 1.000 0.000
#> GSM312849 2 0.0000 0.914 0.000 1.000 0.000
#> GSM312851 3 0.6168 0.269 0.000 0.412 0.588
#> GSM312853 2 0.5178 0.610 0.000 0.744 0.256
#> GSM312854 2 0.0000 0.914 0.000 1.000 0.000
#> GSM312856 2 0.0237 0.911 0.000 0.996 0.004
#> GSM312857 2 0.5178 0.610 0.000 0.744 0.256
#> GSM312858 2 0.0000 0.914 0.000 1.000 0.000
#> GSM312859 2 0.0000 0.914 0.000 1.000 0.000
#> GSM312860 2 0.0000 0.914 0.000 1.000 0.000
#> GSM312861 2 0.0000 0.914 0.000 1.000 0.000
#> GSM312862 2 0.3816 0.799 0.000 0.852 0.148
#> GSM312863 2 0.0000 0.914 0.000 1.000 0.000
#> GSM312864 2 0.0237 0.911 0.000 0.996 0.004
#> GSM312865 2 0.0000 0.914 0.000 1.000 0.000
#> GSM312867 2 0.0000 0.914 0.000 1.000 0.000
#> GSM312868 2 0.0000 0.914 0.000 1.000 0.000
#> GSM312869 2 0.0000 0.914 0.000 1.000 0.000
#> GSM312870 1 0.0000 0.710 1.000 0.000 0.000
#> GSM312872 1 0.0000 0.710 1.000 0.000 0.000
#> GSM312874 1 0.0000 0.710 1.000 0.000 0.000
#> GSM312875 1 0.0000 0.710 1.000 0.000 0.000
#> GSM312876 1 0.0000 0.710 1.000 0.000 0.000
#> GSM312877 1 0.6095 0.802 0.608 0.000 0.392
#> GSM312879 1 0.0000 0.710 1.000 0.000 0.000
#> GSM312882 1 0.0000 0.710 1.000 0.000 0.000
#> GSM312883 1 0.0000 0.710 1.000 0.000 0.000
#> GSM312886 1 0.0000 0.710 1.000 0.000 0.000
#> GSM312887 1 0.0000 0.710 1.000 0.000 0.000
#> GSM312890 1 0.6095 0.802 0.608 0.000 0.392
#> GSM312893 1 0.6095 0.802 0.608 0.000 0.392
#> GSM312894 1 0.6095 0.802 0.608 0.000 0.392
#> GSM312895 1 0.6095 0.802 0.608 0.000 0.392
#> GSM312937 1 0.6095 0.802 0.608 0.000 0.392
#> GSM312938 1 0.6095 0.802 0.608 0.000 0.392
#> GSM312939 1 0.6095 0.802 0.608 0.000 0.392
#> GSM312940 1 0.6095 0.802 0.608 0.000 0.392
#> GSM312941 1 0.6095 0.802 0.608 0.000 0.392
#> GSM312942 1 0.0000 0.710 1.000 0.000 0.000
#> GSM312943 1 0.6095 0.802 0.608 0.000 0.392
#> GSM312944 1 0.6095 0.802 0.608 0.000 0.392
#> GSM312945 1 0.6095 0.802 0.608 0.000 0.392
#> GSM312946 1 0.6095 0.802 0.608 0.000 0.392
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM312811 2 0.7855 0.250 0.000 0.396 0.284 0.320
#> GSM312812 2 0.2647 0.791 0.000 0.880 0.120 0.000
#> GSM312813 2 0.0000 0.797 0.000 1.000 0.000 0.000
#> GSM312814 2 0.7916 0.221 0.000 0.356 0.316 0.328
#> GSM312815 2 0.6731 0.633 0.000 0.604 0.248 0.148
#> GSM312816 4 0.4502 0.794 0.000 0.016 0.236 0.748
#> GSM312817 2 0.1867 0.784 0.000 0.928 0.072 0.000
#> GSM312818 4 0.1118 0.833 0.000 0.000 0.036 0.964
#> GSM312819 2 0.1867 0.784 0.000 0.928 0.072 0.000
#> GSM312820 4 0.0592 0.851 0.000 0.000 0.016 0.984
#> GSM312821 4 0.0592 0.851 0.000 0.000 0.016 0.984
#> GSM312822 2 0.7916 0.221 0.000 0.356 0.316 0.328
#> GSM312823 2 0.6422 0.664 0.000 0.632 0.248 0.120
#> GSM312824 2 0.2647 0.791 0.000 0.880 0.120 0.000
#> GSM312825 2 0.2647 0.791 0.000 0.880 0.120 0.000
#> GSM312826 2 0.2647 0.791 0.000 0.880 0.120 0.000
#> GSM312839 2 0.5998 0.692 0.000 0.664 0.248 0.088
#> GSM312840 2 0.2408 0.793 0.000 0.896 0.104 0.000
#> GSM312841 2 0.5496 0.713 0.000 0.652 0.312 0.036
#> GSM312843 2 0.4319 0.742 0.000 0.760 0.228 0.012
#> GSM312844 2 0.6731 0.633 0.000 0.604 0.248 0.148
#> GSM312845 2 0.1716 0.795 0.000 0.936 0.064 0.000
#> GSM312846 2 0.5998 0.692 0.000 0.664 0.248 0.088
#> GSM312847 2 0.0000 0.797 0.000 1.000 0.000 0.000
#> GSM312848 2 0.1118 0.794 0.000 0.964 0.036 0.000
#> GSM312849 2 0.1118 0.798 0.000 0.964 0.036 0.000
#> GSM312851 4 0.5312 0.750 0.000 0.052 0.236 0.712
#> GSM312853 2 0.7347 0.440 0.000 0.528 0.228 0.244
#> GSM312854 2 0.2081 0.785 0.000 0.916 0.084 0.000
#> GSM312856 2 0.4644 0.734 0.000 0.748 0.228 0.024
#> GSM312857 2 0.7347 0.440 0.000 0.528 0.228 0.244
#> GSM312858 2 0.0000 0.797 0.000 1.000 0.000 0.000
#> GSM312859 2 0.0000 0.797 0.000 1.000 0.000 0.000
#> GSM312860 2 0.1022 0.798 0.000 0.968 0.032 0.000
#> GSM312861 2 0.0000 0.797 0.000 1.000 0.000 0.000
#> GSM312862 2 0.6422 0.664 0.000 0.632 0.248 0.120
#> GSM312863 2 0.1867 0.784 0.000 0.928 0.072 0.000
#> GSM312864 2 0.4319 0.742 0.000 0.760 0.228 0.012
#> GSM312865 2 0.0000 0.797 0.000 1.000 0.000 0.000
#> GSM312867 2 0.1118 0.798 0.000 0.964 0.036 0.000
#> GSM312868 2 0.0188 0.797 0.000 0.996 0.004 0.000
#> GSM312869 2 0.2647 0.791 0.000 0.880 0.120 0.000
#> GSM312870 3 0.4522 0.989 0.320 0.000 0.680 0.000
#> GSM312872 3 0.4522 0.989 0.320 0.000 0.680 0.000
#> GSM312874 3 0.4522 0.989 0.320 0.000 0.680 0.000
#> GSM312875 3 0.4522 0.989 0.320 0.000 0.680 0.000
#> GSM312876 3 0.4522 0.989 0.320 0.000 0.680 0.000
#> GSM312877 1 0.0000 0.993 1.000 0.000 0.000 0.000
#> GSM312879 3 0.4522 0.989 0.320 0.000 0.680 0.000
#> GSM312882 3 0.4522 0.989 0.320 0.000 0.680 0.000
#> GSM312883 3 0.5069 0.978 0.320 0.000 0.664 0.016
#> GSM312886 3 0.5334 0.942 0.284 0.000 0.680 0.036
#> GSM312887 3 0.4836 0.984 0.320 0.000 0.672 0.008
#> GSM312890 1 0.0000 0.993 1.000 0.000 0.000 0.000
#> GSM312893 1 0.0000 0.993 1.000 0.000 0.000 0.000
#> GSM312894 1 0.0000 0.993 1.000 0.000 0.000 0.000
#> GSM312895 1 0.0000 0.993 1.000 0.000 0.000 0.000
#> GSM312937 1 0.0000 0.993 1.000 0.000 0.000 0.000
#> GSM312938 1 0.0592 0.987 0.984 0.000 0.000 0.016
#> GSM312939 1 0.0000 0.993 1.000 0.000 0.000 0.000
#> GSM312940 1 0.0000 0.993 1.000 0.000 0.000 0.000
#> GSM312941 1 0.0000 0.993 1.000 0.000 0.000 0.000
#> GSM312942 3 0.5090 0.974 0.324 0.000 0.660 0.016
#> GSM312943 1 0.0592 0.987 0.984 0.000 0.000 0.016
#> GSM312944 1 0.0592 0.987 0.984 0.000 0.000 0.016
#> GSM312945 1 0.0592 0.987 0.984 0.000 0.000 0.016
#> GSM312946 1 0.0592 0.987 0.984 0.000 0.000 0.016
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM312811 2 0.2488 0.633 0.000 0.872 0.000 0.124 0.004
#> GSM312812 4 0.5984 0.426 0.000 0.208 0.204 0.588 0.000
#> GSM312813 4 0.0162 0.750 0.000 0.000 0.004 0.996 0.000
#> GSM312814 2 0.3796 0.660 0.000 0.820 0.100 0.076 0.004
#> GSM312815 2 0.6256 0.581 0.000 0.564 0.224 0.208 0.004
#> GSM312816 2 0.3274 0.391 0.000 0.780 0.000 0.000 0.220
#> GSM312817 4 0.3374 0.641 0.000 0.108 0.044 0.844 0.004
#> GSM312818 5 0.0880 1.000 0.000 0.032 0.000 0.000 0.968
#> GSM312819 4 0.4114 0.576 0.000 0.176 0.044 0.776 0.004
#> GSM312820 5 0.0880 1.000 0.000 0.032 0.000 0.000 0.968
#> GSM312821 5 0.0880 1.000 0.000 0.032 0.000 0.000 0.968
#> GSM312822 2 0.3796 0.660 0.000 0.820 0.100 0.076 0.004
#> GSM312823 2 0.6233 0.584 0.000 0.568 0.216 0.212 0.004
#> GSM312824 4 0.5984 0.426 0.000 0.208 0.204 0.588 0.000
#> GSM312825 4 0.5984 0.426 0.000 0.208 0.204 0.588 0.000
#> GSM312826 4 0.5984 0.426 0.000 0.208 0.204 0.588 0.000
#> GSM312839 2 0.6309 0.541 0.000 0.532 0.228 0.240 0.000
#> GSM312840 4 0.5375 0.528 0.000 0.156 0.176 0.668 0.000
#> GSM312841 2 0.5538 0.621 0.000 0.644 0.212 0.144 0.000
#> GSM312843 2 0.5638 0.402 0.000 0.532 0.068 0.396 0.004
#> GSM312844 2 0.6159 0.591 0.000 0.580 0.208 0.208 0.004
#> GSM312845 4 0.4169 0.645 0.000 0.100 0.116 0.784 0.000
#> GSM312846 2 0.6309 0.541 0.000 0.532 0.228 0.240 0.000
#> GSM312847 4 0.0000 0.750 0.000 0.000 0.000 1.000 0.000
#> GSM312848 4 0.1568 0.728 0.000 0.036 0.020 0.944 0.000
#> GSM312849 4 0.2300 0.726 0.000 0.052 0.040 0.908 0.000
#> GSM312851 2 0.3611 0.405 0.000 0.780 0.008 0.004 0.208
#> GSM312853 2 0.4756 0.554 0.000 0.704 0.052 0.240 0.004
#> GSM312854 4 0.5469 0.149 0.000 0.392 0.056 0.548 0.004
#> GSM312856 2 0.4883 0.545 0.000 0.684 0.052 0.260 0.004
#> GSM312857 2 0.4756 0.554 0.000 0.704 0.052 0.240 0.004
#> GSM312858 4 0.0162 0.750 0.000 0.000 0.004 0.996 0.000
#> GSM312859 4 0.0000 0.750 0.000 0.000 0.000 1.000 0.000
#> GSM312860 4 0.1197 0.739 0.000 0.048 0.000 0.952 0.000
#> GSM312861 4 0.0162 0.750 0.000 0.000 0.004 0.996 0.000
#> GSM312862 2 0.6209 0.587 0.000 0.572 0.212 0.212 0.004
#> GSM312863 4 0.3595 0.628 0.000 0.120 0.048 0.828 0.004
#> GSM312864 2 0.4969 0.536 0.000 0.676 0.056 0.264 0.004
#> GSM312865 4 0.0000 0.750 0.000 0.000 0.000 1.000 0.000
#> GSM312867 4 0.2221 0.727 0.000 0.052 0.036 0.912 0.000
#> GSM312868 4 0.1443 0.730 0.000 0.004 0.044 0.948 0.004
#> GSM312869 4 0.6084 0.397 0.000 0.208 0.220 0.572 0.000
#> GSM312870 3 0.3752 0.957 0.292 0.000 0.708 0.000 0.000
#> GSM312872 3 0.3752 0.957 0.292 0.000 0.708 0.000 0.000
#> GSM312874 3 0.3752 0.957 0.292 0.000 0.708 0.000 0.000
#> GSM312875 3 0.3752 0.957 0.292 0.000 0.708 0.000 0.000
#> GSM312876 3 0.3752 0.957 0.292 0.000 0.708 0.000 0.000
#> GSM312877 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000
#> GSM312879 3 0.3752 0.957 0.292 0.000 0.708 0.000 0.000
#> GSM312882 3 0.4380 0.951 0.292 0.016 0.688 0.000 0.004
#> GSM312883 3 0.5641 0.921 0.292 0.064 0.624 0.000 0.020
#> GSM312886 3 0.5472 0.876 0.220 0.024 0.680 0.000 0.076
#> GSM312887 3 0.5834 0.912 0.292 0.072 0.612 0.000 0.024
#> GSM312890 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000
#> GSM312893 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000
#> GSM312894 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000
#> GSM312895 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000
#> GSM312937 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000
#> GSM312938 1 0.2104 0.927 0.916 0.060 0.000 0.000 0.024
#> GSM312939 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000
#> GSM312940 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000
#> GSM312941 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000
#> GSM312942 3 0.5982 0.900 0.296 0.076 0.600 0.000 0.028
#> GSM312943 1 0.1965 0.934 0.924 0.052 0.000 0.000 0.024
#> GSM312944 1 0.1965 0.934 0.924 0.052 0.000 0.000 0.024
#> GSM312945 1 0.1965 0.934 0.924 0.052 0.000 0.000 0.024
#> GSM312946 1 0.1965 0.934 0.924 0.052 0.000 0.000 0.024
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM312811 6 0.5317 0.54974 0.024 0.376 0.000 0.040 0.008 0.552
#> GSM312812 4 0.5260 0.07820 0.072 0.456 0.000 0.464 0.000 0.008
#> GSM312813 4 0.1492 0.71298 0.036 0.000 0.000 0.940 0.000 0.024
#> GSM312814 2 0.4945 0.01493 0.020 0.608 0.000 0.028 0.008 0.336
#> GSM312815 2 0.2006 0.74633 0.004 0.892 0.000 0.104 0.000 0.000
#> GSM312816 6 0.5638 0.56493 0.024 0.332 0.000 0.000 0.096 0.548
#> GSM312817 4 0.3821 0.52628 0.040 0.000 0.000 0.740 0.000 0.220
#> GSM312818 5 0.0146 0.99400 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM312819 4 0.4348 0.36592 0.040 0.000 0.000 0.640 0.000 0.320
#> GSM312820 5 0.0260 0.99699 0.000 0.008 0.000 0.000 0.992 0.000
#> GSM312821 5 0.0260 0.99699 0.000 0.008 0.000 0.000 0.992 0.000
#> GSM312822 2 0.5089 0.00658 0.028 0.600 0.000 0.028 0.008 0.336
#> GSM312823 2 0.2527 0.74646 0.000 0.868 0.000 0.108 0.000 0.024
#> GSM312824 4 0.5260 0.07820 0.072 0.456 0.000 0.464 0.000 0.008
#> GSM312825 4 0.5260 0.07820 0.072 0.456 0.000 0.464 0.000 0.008
#> GSM312826 4 0.5260 0.07820 0.072 0.456 0.000 0.464 0.000 0.008
#> GSM312839 2 0.2389 0.73720 0.008 0.864 0.000 0.128 0.000 0.000
#> GSM312840 4 0.6182 0.33137 0.068 0.296 0.000 0.536 0.000 0.100
#> GSM312841 2 0.4180 0.63474 0.076 0.784 0.000 0.044 0.000 0.096
#> GSM312843 6 0.6088 0.48346 0.004 0.244 0.000 0.312 0.000 0.440
#> GSM312844 2 0.2622 0.74476 0.004 0.868 0.000 0.104 0.000 0.024
#> GSM312845 4 0.4601 0.53389 0.076 0.224 0.000 0.692 0.000 0.008
#> GSM312846 2 0.2581 0.73474 0.016 0.856 0.000 0.128 0.000 0.000
#> GSM312847 4 0.1285 0.71669 0.052 0.004 0.000 0.944 0.000 0.000
#> GSM312848 4 0.1700 0.68403 0.004 0.000 0.000 0.916 0.000 0.080
#> GSM312849 4 0.3161 0.67424 0.076 0.080 0.000 0.840 0.000 0.004
#> GSM312851 6 0.5343 0.63865 0.020 0.280 0.000 0.004 0.080 0.616
#> GSM312853 6 0.4510 0.77043 0.000 0.172 0.000 0.100 0.008 0.720
#> GSM312854 6 0.4365 0.54601 0.004 0.040 0.000 0.292 0.000 0.664
#> GSM312856 6 0.4351 0.76805 0.000 0.172 0.000 0.108 0.000 0.720
#> GSM312857 6 0.4510 0.77043 0.000 0.172 0.000 0.100 0.008 0.720
#> GSM312858 4 0.0260 0.72102 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM312859 4 0.0405 0.72294 0.008 0.004 0.000 0.988 0.000 0.000
#> GSM312860 4 0.1914 0.71328 0.056 0.016 0.000 0.920 0.000 0.008
#> GSM312861 4 0.0363 0.72049 0.000 0.000 0.000 0.988 0.000 0.012
#> GSM312862 2 0.2480 0.74518 0.000 0.872 0.000 0.104 0.000 0.024
#> GSM312863 4 0.3189 0.51693 0.004 0.000 0.000 0.760 0.000 0.236
#> GSM312864 6 0.4425 0.76479 0.004 0.164 0.000 0.108 0.000 0.724
#> GSM312865 4 0.0260 0.72243 0.008 0.000 0.000 0.992 0.000 0.000
#> GSM312867 4 0.2886 0.68335 0.064 0.072 0.000 0.860 0.000 0.004
#> GSM312868 4 0.2680 0.65732 0.032 0.000 0.000 0.860 0.000 0.108
#> GSM312869 2 0.5333 -0.11280 0.080 0.480 0.000 0.432 0.000 0.008
#> GSM312870 3 0.0291 0.89521 0.000 0.000 0.992 0.000 0.004 0.004
#> GSM312872 3 0.0291 0.89521 0.000 0.000 0.992 0.000 0.004 0.004
#> GSM312874 3 0.0291 0.89521 0.000 0.000 0.992 0.000 0.004 0.004
#> GSM312875 3 0.0146 0.89518 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM312876 3 0.0000 0.89531 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312877 1 0.2838 0.88768 0.808 0.004 0.188 0.000 0.000 0.000
#> GSM312879 3 0.0291 0.89521 0.000 0.000 0.992 0.000 0.004 0.004
#> GSM312882 3 0.1334 0.88506 0.000 0.020 0.948 0.000 0.000 0.032
#> GSM312883 3 0.4223 0.76492 0.000 0.072 0.732 0.000 0.004 0.192
#> GSM312886 3 0.2838 0.85671 0.000 0.024 0.872 0.000 0.032 0.072
#> GSM312887 3 0.4518 0.73236 0.000 0.080 0.696 0.000 0.004 0.220
#> GSM312890 1 0.2838 0.88768 0.808 0.004 0.188 0.000 0.000 0.000
#> GSM312893 1 0.2697 0.88786 0.812 0.000 0.188 0.000 0.000 0.000
#> GSM312894 1 0.2697 0.88786 0.812 0.000 0.188 0.000 0.000 0.000
#> GSM312895 1 0.2838 0.88768 0.808 0.004 0.188 0.000 0.000 0.000
#> GSM312937 1 0.2697 0.88786 0.812 0.000 0.188 0.000 0.000 0.000
#> GSM312938 1 0.6540 0.74691 0.532 0.060 0.188 0.000 0.004 0.216
#> GSM312939 1 0.2838 0.88768 0.808 0.004 0.188 0.000 0.000 0.000
#> GSM312940 1 0.2697 0.88786 0.812 0.000 0.188 0.000 0.000 0.000
#> GSM312941 1 0.2697 0.88786 0.812 0.000 0.188 0.000 0.000 0.000
#> GSM312942 3 0.4753 0.70939 0.004 0.080 0.676 0.000 0.004 0.236
#> GSM312943 1 0.6498 0.77732 0.556 0.076 0.188 0.000 0.004 0.176
#> GSM312944 1 0.6365 0.77981 0.560 0.076 0.188 0.000 0.000 0.176
#> GSM312945 1 0.6498 0.77732 0.556 0.076 0.188 0.000 0.004 0.176
#> GSM312946 1 0.6498 0.77732 0.556 0.076 0.188 0.000 0.004 0.176
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:kmeans 67 3.51e-09 2
#> ATC:kmeans 62 1.92e-09 3
#> ATC:kmeans 62 8.66e-13 4
#> ATC:kmeans 58 4.73e-11 5
#> ATC:kmeans 57 1.71e-15 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "skmeans"]
# you can also extract it by
# res = res_list["ATC:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 67 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 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 0.999 0.4942 0.506 0.506
#> 3 3 0.912 0.927 0.965 0.2398 0.855 0.719
#> 4 4 0.846 0.832 0.923 0.2006 0.802 0.528
#> 5 5 0.800 0.764 0.875 0.0464 0.976 0.910
#> 6 6 0.856 0.816 0.913 0.0369 0.943 0.773
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
#> GSM312811 2 0.00 1.000 0.000 1.000
#> GSM312812 2 0.00 1.000 0.000 1.000
#> GSM312813 2 0.00 1.000 0.000 1.000
#> GSM312814 2 0.00 1.000 0.000 1.000
#> GSM312815 2 0.00 1.000 0.000 1.000
#> GSM312816 2 0.00 1.000 0.000 1.000
#> GSM312817 2 0.00 1.000 0.000 1.000
#> GSM312818 1 0.00 0.998 1.000 0.000
#> GSM312819 2 0.00 1.000 0.000 1.000
#> GSM312820 1 0.26 0.954 0.956 0.044
#> GSM312821 1 0.00 0.998 1.000 0.000
#> GSM312822 2 0.00 1.000 0.000 1.000
#> GSM312823 2 0.00 1.000 0.000 1.000
#> GSM312824 2 0.00 1.000 0.000 1.000
#> GSM312825 2 0.00 1.000 0.000 1.000
#> GSM312826 2 0.00 1.000 0.000 1.000
#> GSM312839 2 0.00 1.000 0.000 1.000
#> GSM312840 2 0.00 1.000 0.000 1.000
#> GSM312841 2 0.00 1.000 0.000 1.000
#> GSM312843 2 0.00 1.000 0.000 1.000
#> GSM312844 2 0.00 1.000 0.000 1.000
#> GSM312845 2 0.00 1.000 0.000 1.000
#> GSM312846 2 0.00 1.000 0.000 1.000
#> GSM312847 2 0.00 1.000 0.000 1.000
#> GSM312848 2 0.00 1.000 0.000 1.000
#> GSM312849 2 0.00 1.000 0.000 1.000
#> GSM312851 2 0.00 1.000 0.000 1.000
#> GSM312853 2 0.00 1.000 0.000 1.000
#> GSM312854 2 0.00 1.000 0.000 1.000
#> GSM312856 2 0.00 1.000 0.000 1.000
#> GSM312857 2 0.00 1.000 0.000 1.000
#> GSM312858 2 0.00 1.000 0.000 1.000
#> GSM312859 2 0.00 1.000 0.000 1.000
#> GSM312860 2 0.00 1.000 0.000 1.000
#> GSM312861 2 0.00 1.000 0.000 1.000
#> GSM312862 2 0.00 1.000 0.000 1.000
#> GSM312863 2 0.00 1.000 0.000 1.000
#> GSM312864 2 0.00 1.000 0.000 1.000
#> GSM312865 2 0.00 1.000 0.000 1.000
#> GSM312867 2 0.00 1.000 0.000 1.000
#> GSM312868 2 0.00 1.000 0.000 1.000
#> GSM312869 2 0.00 1.000 0.000 1.000
#> GSM312870 1 0.00 0.998 1.000 0.000
#> GSM312872 1 0.00 0.998 1.000 0.000
#> GSM312874 1 0.00 0.998 1.000 0.000
#> GSM312875 1 0.00 0.998 1.000 0.000
#> GSM312876 1 0.00 0.998 1.000 0.000
#> GSM312877 1 0.00 0.998 1.000 0.000
#> GSM312879 1 0.00 0.998 1.000 0.000
#> GSM312882 1 0.00 0.998 1.000 0.000
#> GSM312883 1 0.00 0.998 1.000 0.000
#> GSM312886 1 0.00 0.998 1.000 0.000
#> GSM312887 1 0.00 0.998 1.000 0.000
#> GSM312890 1 0.00 0.998 1.000 0.000
#> GSM312893 1 0.00 0.998 1.000 0.000
#> GSM312894 1 0.00 0.998 1.000 0.000
#> GSM312895 1 0.00 0.998 1.000 0.000
#> GSM312937 1 0.00 0.998 1.000 0.000
#> GSM312938 1 0.00 0.998 1.000 0.000
#> GSM312939 1 0.00 0.998 1.000 0.000
#> GSM312940 1 0.00 0.998 1.000 0.000
#> GSM312941 1 0.00 0.998 1.000 0.000
#> GSM312942 1 0.00 0.998 1.000 0.000
#> GSM312943 1 0.00 0.998 1.000 0.000
#> GSM312944 1 0.00 0.998 1.000 0.000
#> GSM312945 1 0.00 0.998 1.000 0.000
#> GSM312946 1 0.00 0.998 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM312811 3 0.5431 0.683 0.000 0.284 0.716
#> GSM312812 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312813 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312814 3 0.5465 0.680 0.000 0.288 0.712
#> GSM312815 2 0.3192 0.844 0.000 0.888 0.112
#> GSM312816 3 0.0424 0.835 0.000 0.008 0.992
#> GSM312817 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312818 3 0.0237 0.830 0.004 0.000 0.996
#> GSM312819 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312820 3 0.0000 0.831 0.000 0.000 1.000
#> GSM312821 3 0.0237 0.830 0.004 0.000 0.996
#> GSM312822 3 0.0747 0.836 0.000 0.016 0.984
#> GSM312823 2 0.0237 0.962 0.000 0.996 0.004
#> GSM312824 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312825 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312826 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312839 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312840 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312841 2 0.0424 0.958 0.000 0.992 0.008
#> GSM312843 2 0.0237 0.962 0.000 0.996 0.004
#> GSM312844 2 0.3816 0.797 0.000 0.852 0.148
#> GSM312845 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312846 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312847 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312848 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312849 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312851 3 0.0424 0.835 0.000 0.008 0.992
#> GSM312853 3 0.6045 0.545 0.000 0.380 0.620
#> GSM312854 2 0.4605 0.702 0.000 0.796 0.204
#> GSM312856 2 0.4654 0.697 0.000 0.792 0.208
#> GSM312857 3 0.6045 0.545 0.000 0.380 0.620
#> GSM312858 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312859 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312860 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312861 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312862 2 0.0237 0.962 0.000 0.996 0.004
#> GSM312863 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312864 2 0.4654 0.697 0.000 0.792 0.208
#> GSM312865 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312867 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312868 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312869 2 0.0000 0.964 0.000 1.000 0.000
#> GSM312870 1 0.0424 0.996 0.992 0.000 0.008
#> GSM312872 1 0.0424 0.996 0.992 0.000 0.008
#> GSM312874 1 0.0424 0.996 0.992 0.000 0.008
#> GSM312875 1 0.0424 0.996 0.992 0.000 0.008
#> GSM312876 1 0.0424 0.996 0.992 0.000 0.008
#> GSM312877 1 0.0000 0.997 1.000 0.000 0.000
#> GSM312879 1 0.0424 0.996 0.992 0.000 0.008
#> GSM312882 1 0.0424 0.996 0.992 0.000 0.008
#> GSM312883 1 0.0424 0.996 0.992 0.000 0.008
#> GSM312886 1 0.0424 0.996 0.992 0.000 0.008
#> GSM312887 1 0.0424 0.996 0.992 0.000 0.008
#> GSM312890 1 0.0000 0.997 1.000 0.000 0.000
#> GSM312893 1 0.0000 0.997 1.000 0.000 0.000
#> GSM312894 1 0.0000 0.997 1.000 0.000 0.000
#> GSM312895 1 0.0000 0.997 1.000 0.000 0.000
#> GSM312937 1 0.0000 0.997 1.000 0.000 0.000
#> GSM312938 1 0.0000 0.997 1.000 0.000 0.000
#> GSM312939 1 0.0000 0.997 1.000 0.000 0.000
#> GSM312940 1 0.0000 0.997 1.000 0.000 0.000
#> GSM312941 1 0.0000 0.997 1.000 0.000 0.000
#> GSM312942 1 0.0424 0.996 0.992 0.000 0.008
#> GSM312943 1 0.0000 0.997 1.000 0.000 0.000
#> GSM312944 1 0.0000 0.997 1.000 0.000 0.000
#> GSM312945 1 0.0000 0.997 1.000 0.000 0.000
#> GSM312946 1 0.0000 0.997 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM312811 4 0.0336 0.835 0.000 0.008 0.000 0.992
#> GSM312812 2 0.0000 0.889 0.000 1.000 0.000 0.000
#> GSM312813 2 0.0000 0.889 0.000 1.000 0.000 0.000
#> GSM312814 4 0.0336 0.835 0.000 0.008 0.000 0.992
#> GSM312815 2 0.4730 0.266 0.000 0.636 0.000 0.364
#> GSM312816 4 0.1302 0.810 0.000 0.000 0.044 0.956
#> GSM312817 2 0.3907 0.673 0.000 0.768 0.000 0.232
#> GSM312818 3 0.0707 0.898 0.000 0.000 0.980 0.020
#> GSM312819 2 0.4277 0.600 0.000 0.720 0.000 0.280
#> GSM312820 3 0.4564 0.529 0.000 0.000 0.672 0.328
#> GSM312821 3 0.1716 0.869 0.000 0.000 0.936 0.064
#> GSM312822 4 0.0336 0.827 0.000 0.000 0.008 0.992
#> GSM312823 4 0.4522 0.543 0.000 0.320 0.000 0.680
#> GSM312824 2 0.0000 0.889 0.000 1.000 0.000 0.000
#> GSM312825 2 0.0000 0.889 0.000 1.000 0.000 0.000
#> GSM312826 2 0.0000 0.889 0.000 1.000 0.000 0.000
#> GSM312839 2 0.1389 0.850 0.000 0.952 0.000 0.048
#> GSM312840 2 0.4008 0.657 0.000 0.756 0.000 0.244
#> GSM312841 2 0.4888 0.282 0.000 0.588 0.000 0.412
#> GSM312843 4 0.4500 0.551 0.000 0.316 0.000 0.684
#> GSM312844 4 0.4989 0.220 0.000 0.472 0.000 0.528
#> GSM312845 2 0.0000 0.889 0.000 1.000 0.000 0.000
#> GSM312846 2 0.0000 0.889 0.000 1.000 0.000 0.000
#> GSM312847 2 0.0000 0.889 0.000 1.000 0.000 0.000
#> GSM312848 2 0.3907 0.673 0.000 0.768 0.000 0.232
#> GSM312849 2 0.0000 0.889 0.000 1.000 0.000 0.000
#> GSM312851 4 0.0336 0.827 0.000 0.000 0.008 0.992
#> GSM312853 4 0.0469 0.836 0.000 0.012 0.000 0.988
#> GSM312854 4 0.3975 0.629 0.000 0.240 0.000 0.760
#> GSM312856 4 0.0817 0.836 0.000 0.024 0.000 0.976
#> GSM312857 4 0.0469 0.836 0.000 0.012 0.000 0.988
#> GSM312858 2 0.0000 0.889 0.000 1.000 0.000 0.000
#> GSM312859 2 0.0000 0.889 0.000 1.000 0.000 0.000
#> GSM312860 2 0.0000 0.889 0.000 1.000 0.000 0.000
#> GSM312861 2 0.0000 0.889 0.000 1.000 0.000 0.000
#> GSM312862 4 0.4643 0.497 0.000 0.344 0.000 0.656
#> GSM312863 2 0.4103 0.641 0.000 0.744 0.000 0.256
#> GSM312864 4 0.0817 0.836 0.000 0.024 0.000 0.976
#> GSM312865 2 0.0188 0.888 0.000 0.996 0.000 0.004
#> GSM312867 2 0.0000 0.889 0.000 1.000 0.000 0.000
#> GSM312868 2 0.0336 0.885 0.000 0.992 0.000 0.008
#> GSM312869 2 0.0000 0.889 0.000 1.000 0.000 0.000
#> GSM312870 3 0.1302 0.938 0.044 0.000 0.956 0.000
#> GSM312872 3 0.1302 0.938 0.044 0.000 0.956 0.000
#> GSM312874 3 0.1302 0.938 0.044 0.000 0.956 0.000
#> GSM312875 3 0.1302 0.938 0.044 0.000 0.956 0.000
#> GSM312876 3 0.1302 0.938 0.044 0.000 0.956 0.000
#> GSM312877 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM312879 3 0.1302 0.938 0.044 0.000 0.956 0.000
#> GSM312882 3 0.1302 0.938 0.044 0.000 0.956 0.000
#> GSM312883 3 0.1302 0.938 0.044 0.000 0.956 0.000
#> GSM312886 3 0.1302 0.938 0.044 0.000 0.956 0.000
#> GSM312887 3 0.1302 0.938 0.044 0.000 0.956 0.000
#> GSM312890 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM312893 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM312894 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM312895 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM312937 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM312938 3 0.4776 0.456 0.376 0.000 0.624 0.000
#> GSM312939 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM312940 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM312941 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM312942 3 0.1302 0.938 0.044 0.000 0.956 0.000
#> GSM312943 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM312944 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM312945 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM312946 1 0.0000 1.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM312811 4 0.1310 0.7032 0.000 0.020 0.000 0.956 0.024
#> GSM312812 2 0.1399 0.7814 0.000 0.952 0.000 0.028 0.020
#> GSM312813 2 0.0290 0.7933 0.000 0.992 0.000 0.008 0.000
#> GSM312814 4 0.0794 0.6804 0.000 0.000 0.000 0.972 0.028
#> GSM312815 2 0.6845 -0.0833 0.000 0.420 0.008 0.356 0.216
#> GSM312816 5 0.3452 0.7300 0.000 0.000 0.000 0.244 0.756
#> GSM312817 2 0.4030 0.4704 0.000 0.648 0.000 0.352 0.000
#> GSM312818 5 0.3958 0.8449 0.000 0.000 0.184 0.040 0.776
#> GSM312819 2 0.4150 0.3990 0.000 0.612 0.000 0.388 0.000
#> GSM312820 5 0.4197 0.8435 0.000 0.000 0.076 0.148 0.776
#> GSM312821 5 0.4059 0.8565 0.000 0.000 0.172 0.052 0.776
#> GSM312822 4 0.3857 0.2230 0.000 0.000 0.000 0.688 0.312
#> GSM312823 4 0.3427 0.6669 0.000 0.192 0.000 0.796 0.012
#> GSM312824 2 0.1310 0.7802 0.000 0.956 0.000 0.024 0.020
#> GSM312825 2 0.1310 0.7802 0.000 0.956 0.000 0.024 0.020
#> GSM312826 2 0.1310 0.7802 0.000 0.956 0.000 0.024 0.020
#> GSM312839 2 0.6272 0.3156 0.000 0.576 0.008 0.204 0.212
#> GSM312840 2 0.4505 0.4479 0.000 0.604 0.000 0.384 0.012
#> GSM312841 2 0.4821 0.2488 0.000 0.516 0.000 0.464 0.020
#> GSM312843 4 0.3305 0.6640 0.000 0.224 0.000 0.776 0.000
#> GSM312844 4 0.6692 0.2501 0.000 0.292 0.008 0.488 0.212
#> GSM312845 2 0.0000 0.7939 0.000 1.000 0.000 0.000 0.000
#> GSM312846 2 0.0162 0.7928 0.000 0.996 0.000 0.000 0.004
#> GSM312847 2 0.0162 0.7938 0.000 0.996 0.000 0.004 0.000
#> GSM312848 2 0.3895 0.5200 0.000 0.680 0.000 0.320 0.000
#> GSM312849 2 0.0000 0.7939 0.000 1.000 0.000 0.000 0.000
#> GSM312851 4 0.4088 0.1026 0.000 0.000 0.000 0.632 0.368
#> GSM312853 4 0.1661 0.7135 0.000 0.036 0.000 0.940 0.024
#> GSM312854 4 0.3774 0.5066 0.000 0.296 0.000 0.704 0.000
#> GSM312856 4 0.2020 0.7271 0.000 0.100 0.000 0.900 0.000
#> GSM312857 4 0.1661 0.7135 0.000 0.036 0.000 0.940 0.024
#> GSM312858 2 0.0510 0.7909 0.000 0.984 0.000 0.016 0.000
#> GSM312859 2 0.0290 0.7933 0.000 0.992 0.000 0.008 0.000
#> GSM312860 2 0.0000 0.7939 0.000 1.000 0.000 0.000 0.000
#> GSM312861 2 0.0000 0.7939 0.000 1.000 0.000 0.000 0.000
#> GSM312862 4 0.4016 0.5906 0.000 0.272 0.000 0.716 0.012
#> GSM312863 2 0.4045 0.4640 0.000 0.644 0.000 0.356 0.000
#> GSM312864 4 0.2020 0.7271 0.000 0.100 0.000 0.900 0.000
#> GSM312865 2 0.2648 0.7038 0.000 0.848 0.000 0.152 0.000
#> GSM312867 2 0.0000 0.7939 0.000 1.000 0.000 0.000 0.000
#> GSM312868 2 0.3336 0.6330 0.000 0.772 0.000 0.228 0.000
#> GSM312869 2 0.1893 0.7625 0.000 0.928 0.000 0.024 0.048
#> GSM312870 3 0.0290 0.9930 0.008 0.000 0.992 0.000 0.000
#> GSM312872 3 0.0290 0.9930 0.008 0.000 0.992 0.000 0.000
#> GSM312874 3 0.0290 0.9930 0.008 0.000 0.992 0.000 0.000
#> GSM312875 3 0.0290 0.9930 0.008 0.000 0.992 0.000 0.000
#> GSM312876 3 0.0290 0.9930 0.008 0.000 0.992 0.000 0.000
#> GSM312877 1 0.0000 0.9940 1.000 0.000 0.000 0.000 0.000
#> GSM312879 3 0.0290 0.9930 0.008 0.000 0.992 0.000 0.000
#> GSM312882 3 0.0290 0.9930 0.008 0.000 0.992 0.000 0.000
#> GSM312883 3 0.0290 0.9930 0.008 0.000 0.992 0.000 0.000
#> GSM312886 3 0.0290 0.9930 0.008 0.000 0.992 0.000 0.000
#> GSM312887 3 0.0290 0.9930 0.008 0.000 0.992 0.000 0.000
#> GSM312890 1 0.0000 0.9940 1.000 0.000 0.000 0.000 0.000
#> GSM312893 1 0.0000 0.9940 1.000 0.000 0.000 0.000 0.000
#> GSM312894 1 0.0000 0.9940 1.000 0.000 0.000 0.000 0.000
#> GSM312895 1 0.0000 0.9940 1.000 0.000 0.000 0.000 0.000
#> GSM312937 1 0.0000 0.9940 1.000 0.000 0.000 0.000 0.000
#> GSM312938 3 0.1478 0.9205 0.064 0.000 0.936 0.000 0.000
#> GSM312939 1 0.0000 0.9940 1.000 0.000 0.000 0.000 0.000
#> GSM312940 1 0.0000 0.9940 1.000 0.000 0.000 0.000 0.000
#> GSM312941 1 0.0000 0.9940 1.000 0.000 0.000 0.000 0.000
#> GSM312942 3 0.0290 0.9930 0.008 0.000 0.992 0.000 0.000
#> GSM312943 1 0.0912 0.9773 0.972 0.000 0.016 0.000 0.012
#> GSM312944 1 0.0404 0.9887 0.988 0.000 0.000 0.000 0.012
#> GSM312945 1 0.0807 0.9811 0.976 0.000 0.012 0.000 0.012
#> GSM312946 1 0.0566 0.9870 0.984 0.000 0.004 0.000 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM312811 2 0.0291 0.7627 0.000 0.992 0.000 0.004 0.004 0.000
#> GSM312812 4 0.1858 0.8263 0.000 0.004 0.000 0.904 0.000 0.092
#> GSM312813 4 0.0405 0.8533 0.000 0.004 0.000 0.988 0.000 0.008
#> GSM312814 2 0.0291 0.7600 0.000 0.992 0.000 0.000 0.004 0.004
#> GSM312815 6 0.2122 0.9489 0.000 0.024 0.000 0.076 0.000 0.900
#> GSM312816 5 0.1501 0.9074 0.000 0.076 0.000 0.000 0.924 0.000
#> GSM312817 4 0.3647 0.4093 0.000 0.360 0.000 0.640 0.000 0.000
#> GSM312818 5 0.0717 0.9635 0.000 0.008 0.016 0.000 0.976 0.000
#> GSM312819 2 0.3869 -0.0874 0.000 0.500 0.000 0.500 0.000 0.000
#> GSM312820 5 0.0717 0.9620 0.000 0.016 0.008 0.000 0.976 0.000
#> GSM312821 5 0.0717 0.9635 0.000 0.008 0.016 0.000 0.976 0.000
#> GSM312822 2 0.5013 0.3234 0.000 0.636 0.000 0.000 0.140 0.224
#> GSM312823 2 0.2949 0.6971 0.000 0.832 0.000 0.140 0.000 0.028
#> GSM312824 4 0.2003 0.8200 0.000 0.000 0.000 0.884 0.000 0.116
#> GSM312825 4 0.2003 0.8200 0.000 0.000 0.000 0.884 0.000 0.116
#> GSM312826 4 0.2003 0.8200 0.000 0.000 0.000 0.884 0.000 0.116
#> GSM312839 6 0.2163 0.9373 0.000 0.016 0.000 0.092 0.000 0.892
#> GSM312840 4 0.4417 0.2407 0.000 0.416 0.000 0.556 0.000 0.028
#> GSM312841 2 0.4895 0.0239 0.000 0.496 0.000 0.444 0.000 0.060
#> GSM312843 2 0.1910 0.7352 0.000 0.892 0.000 0.108 0.000 0.000
#> GSM312844 6 0.2591 0.9156 0.000 0.064 0.000 0.052 0.004 0.880
#> GSM312845 4 0.1225 0.8443 0.000 0.000 0.000 0.952 0.012 0.036
#> GSM312846 4 0.1434 0.8378 0.000 0.000 0.000 0.940 0.012 0.048
#> GSM312847 4 0.0665 0.8520 0.000 0.004 0.000 0.980 0.008 0.008
#> GSM312848 4 0.2912 0.6725 0.000 0.216 0.000 0.784 0.000 0.000
#> GSM312849 4 0.1074 0.8468 0.000 0.000 0.000 0.960 0.012 0.028
#> GSM312851 2 0.3221 0.4504 0.000 0.736 0.000 0.000 0.264 0.000
#> GSM312853 2 0.0000 0.7625 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312854 2 0.1204 0.7525 0.000 0.944 0.000 0.056 0.000 0.000
#> GSM312856 2 0.0260 0.7641 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM312857 2 0.0000 0.7625 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312858 4 0.0260 0.8518 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM312859 4 0.0405 0.8533 0.000 0.004 0.000 0.988 0.000 0.008
#> GSM312860 4 0.0692 0.8508 0.000 0.000 0.000 0.976 0.004 0.020
#> GSM312861 4 0.0363 0.8527 0.000 0.000 0.000 0.988 0.000 0.012
#> GSM312862 2 0.3997 0.6196 0.000 0.736 0.000 0.216 0.004 0.044
#> GSM312863 4 0.3804 0.2447 0.000 0.424 0.000 0.576 0.000 0.000
#> GSM312864 2 0.0458 0.7642 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM312865 4 0.1204 0.8327 0.000 0.056 0.000 0.944 0.000 0.000
#> GSM312867 4 0.1074 0.8468 0.000 0.000 0.000 0.960 0.012 0.028
#> GSM312868 4 0.1765 0.8070 0.000 0.096 0.000 0.904 0.000 0.000
#> GSM312869 4 0.2219 0.8064 0.000 0.000 0.000 0.864 0.000 0.136
#> GSM312870 3 0.0000 0.9941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312872 3 0.0000 0.9941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312874 3 0.0000 0.9941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312875 3 0.0000 0.9941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312876 3 0.0000 0.9941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312877 1 0.0000 0.9645 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312879 3 0.0000 0.9941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312882 3 0.0000 0.9941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312883 3 0.0000 0.9941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312886 3 0.0000 0.9941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312887 3 0.0000 0.9941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312890 1 0.0000 0.9645 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312893 1 0.0000 0.9645 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312894 1 0.0000 0.9645 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312895 1 0.0000 0.9645 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312937 1 0.0000 0.9645 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312938 3 0.1141 0.9324 0.052 0.000 0.948 0.000 0.000 0.000
#> GSM312939 1 0.0000 0.9645 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312940 1 0.0000 0.9645 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312941 1 0.0000 0.9645 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312942 3 0.0000 0.9941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312943 1 0.2605 0.9092 0.876 0.000 0.020 0.000 0.012 0.092
#> GSM312944 1 0.2070 0.9201 0.896 0.000 0.000 0.000 0.012 0.092
#> GSM312945 1 0.2605 0.9092 0.876 0.000 0.020 0.000 0.012 0.092
#> GSM312946 1 0.2426 0.9145 0.884 0.000 0.012 0.000 0.012 0.092
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:skmeans 67 9.63e-09 2
#> ATC:skmeans 67 3.11e-12 3
#> ATC:skmeans 62 3.29e-12 4
#> ATC:skmeans 57 2.08e-12 5
#> ATC:skmeans 60 4.69e-12 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "pam"]
# you can also extract it by
# res = res_list["ATC:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 67 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.974 0.990 0.4830 0.518 0.518
#> 3 3 0.744 0.886 0.876 0.2207 0.931 0.866
#> 4 4 0.792 0.781 0.896 0.2137 0.852 0.673
#> 5 5 0.805 0.847 0.906 0.0652 0.888 0.665
#> 6 6 0.806 0.805 0.830 0.0516 0.967 0.869
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
#> GSM312811 2 0.000 0.990 0.000 1.000
#> GSM312812 2 0.000 0.990 0.000 1.000
#> GSM312813 2 0.000 0.990 0.000 1.000
#> GSM312814 2 0.000 0.990 0.000 1.000
#> GSM312815 2 0.000 0.990 0.000 1.000
#> GSM312816 2 0.000 0.990 0.000 1.000
#> GSM312817 2 0.000 0.990 0.000 1.000
#> GSM312818 1 0.871 0.579 0.708 0.292
#> GSM312819 2 0.000 0.990 0.000 1.000
#> GSM312820 2 0.000 0.990 0.000 1.000
#> GSM312821 2 0.961 0.360 0.384 0.616
#> GSM312822 2 0.000 0.990 0.000 1.000
#> GSM312823 2 0.000 0.990 0.000 1.000
#> GSM312824 2 0.000 0.990 0.000 1.000
#> GSM312825 2 0.000 0.990 0.000 1.000
#> GSM312826 2 0.000 0.990 0.000 1.000
#> GSM312839 2 0.000 0.990 0.000 1.000
#> GSM312840 2 0.000 0.990 0.000 1.000
#> GSM312841 2 0.000 0.990 0.000 1.000
#> GSM312843 2 0.000 0.990 0.000 1.000
#> GSM312844 2 0.000 0.990 0.000 1.000
#> GSM312845 2 0.000 0.990 0.000 1.000
#> GSM312846 2 0.000 0.990 0.000 1.000
#> GSM312847 2 0.000 0.990 0.000 1.000
#> GSM312848 2 0.000 0.990 0.000 1.000
#> GSM312849 2 0.000 0.990 0.000 1.000
#> GSM312851 2 0.000 0.990 0.000 1.000
#> GSM312853 2 0.000 0.990 0.000 1.000
#> GSM312854 2 0.000 0.990 0.000 1.000
#> GSM312856 2 0.000 0.990 0.000 1.000
#> GSM312857 2 0.000 0.990 0.000 1.000
#> GSM312858 2 0.000 0.990 0.000 1.000
#> GSM312859 2 0.000 0.990 0.000 1.000
#> GSM312860 2 0.000 0.990 0.000 1.000
#> GSM312861 2 0.000 0.990 0.000 1.000
#> GSM312862 2 0.000 0.990 0.000 1.000
#> GSM312863 2 0.000 0.990 0.000 1.000
#> GSM312864 2 0.000 0.990 0.000 1.000
#> GSM312865 2 0.000 0.990 0.000 1.000
#> GSM312867 2 0.000 0.990 0.000 1.000
#> GSM312868 2 0.000 0.990 0.000 1.000
#> GSM312869 2 0.000 0.990 0.000 1.000
#> GSM312870 1 0.000 0.988 1.000 0.000
#> GSM312872 1 0.000 0.988 1.000 0.000
#> GSM312874 1 0.000 0.988 1.000 0.000
#> GSM312875 1 0.000 0.988 1.000 0.000
#> GSM312876 1 0.000 0.988 1.000 0.000
#> GSM312877 1 0.000 0.988 1.000 0.000
#> GSM312879 1 0.000 0.988 1.000 0.000
#> GSM312882 1 0.000 0.988 1.000 0.000
#> GSM312883 1 0.000 0.988 1.000 0.000
#> GSM312886 1 0.000 0.988 1.000 0.000
#> GSM312887 1 0.000 0.988 1.000 0.000
#> GSM312890 1 0.000 0.988 1.000 0.000
#> GSM312893 1 0.000 0.988 1.000 0.000
#> GSM312894 1 0.000 0.988 1.000 0.000
#> GSM312895 1 0.000 0.988 1.000 0.000
#> GSM312937 1 0.000 0.988 1.000 0.000
#> GSM312938 1 0.000 0.988 1.000 0.000
#> GSM312939 1 0.000 0.988 1.000 0.000
#> GSM312940 1 0.000 0.988 1.000 0.000
#> GSM312941 1 0.000 0.988 1.000 0.000
#> GSM312942 1 0.000 0.988 1.000 0.000
#> GSM312943 1 0.000 0.988 1.000 0.000
#> GSM312944 1 0.000 0.988 1.000 0.000
#> GSM312945 1 0.000 0.988 1.000 0.000
#> GSM312946 1 0.000 0.988 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM312811 2 0.553 0.834 0.296 0.704 0.000
#> GSM312812 2 0.186 0.857 0.052 0.948 0.000
#> GSM312813 2 0.000 0.856 0.000 1.000 0.000
#> GSM312814 2 0.553 0.834 0.296 0.704 0.000
#> GSM312815 2 0.553 0.834 0.296 0.704 0.000
#> GSM312816 2 0.553 0.834 0.296 0.704 0.000
#> GSM312817 2 0.000 0.856 0.000 1.000 0.000
#> GSM312818 3 0.553 0.562 0.296 0.000 0.704
#> GSM312819 2 0.000 0.856 0.000 1.000 0.000
#> GSM312820 2 0.553 0.834 0.296 0.704 0.000
#> GSM312821 2 0.821 0.735 0.296 0.600 0.104
#> GSM312822 2 0.553 0.834 0.296 0.704 0.000
#> GSM312823 2 0.553 0.834 0.296 0.704 0.000
#> GSM312824 2 0.543 0.837 0.284 0.716 0.000
#> GSM312825 2 0.175 0.857 0.048 0.952 0.000
#> GSM312826 2 0.000 0.856 0.000 1.000 0.000
#> GSM312839 2 0.553 0.834 0.296 0.704 0.000
#> GSM312840 2 0.141 0.857 0.036 0.964 0.000
#> GSM312841 2 0.553 0.834 0.296 0.704 0.000
#> GSM312843 2 0.553 0.834 0.296 0.704 0.000
#> GSM312844 2 0.553 0.834 0.296 0.704 0.000
#> GSM312845 2 0.000 0.856 0.000 1.000 0.000
#> GSM312846 2 0.553 0.834 0.296 0.704 0.000
#> GSM312847 2 0.000 0.856 0.000 1.000 0.000
#> GSM312848 2 0.000 0.856 0.000 1.000 0.000
#> GSM312849 2 0.000 0.856 0.000 1.000 0.000
#> GSM312851 2 0.553 0.834 0.296 0.704 0.000
#> GSM312853 2 0.553 0.834 0.296 0.704 0.000
#> GSM312854 2 0.000 0.856 0.000 1.000 0.000
#> GSM312856 2 0.510 0.838 0.248 0.752 0.000
#> GSM312857 2 0.543 0.836 0.284 0.716 0.000
#> GSM312858 2 0.000 0.856 0.000 1.000 0.000
#> GSM312859 2 0.000 0.856 0.000 1.000 0.000
#> GSM312860 2 0.000 0.856 0.000 1.000 0.000
#> GSM312861 2 0.000 0.856 0.000 1.000 0.000
#> GSM312862 2 0.553 0.834 0.296 0.704 0.000
#> GSM312863 2 0.000 0.856 0.000 1.000 0.000
#> GSM312864 2 0.245 0.857 0.076 0.924 0.000
#> GSM312865 2 0.000 0.856 0.000 1.000 0.000
#> GSM312867 2 0.000 0.856 0.000 1.000 0.000
#> GSM312868 2 0.000 0.856 0.000 1.000 0.000
#> GSM312869 2 0.000 0.856 0.000 1.000 0.000
#> GSM312870 3 0.000 0.930 0.000 0.000 1.000
#> GSM312872 3 0.000 0.930 0.000 0.000 1.000
#> GSM312874 3 0.000 0.930 0.000 0.000 1.000
#> GSM312875 3 0.000 0.930 0.000 0.000 1.000
#> GSM312876 3 0.000 0.930 0.000 0.000 1.000
#> GSM312877 1 0.553 0.991 0.704 0.000 0.296
#> GSM312879 3 0.000 0.930 0.000 0.000 1.000
#> GSM312882 3 0.000 0.930 0.000 0.000 1.000
#> GSM312883 1 0.573 0.962 0.676 0.000 0.324
#> GSM312886 3 0.000 0.930 0.000 0.000 1.000
#> GSM312887 1 0.586 0.935 0.656 0.000 0.344
#> GSM312890 1 0.553 0.991 0.704 0.000 0.296
#> GSM312893 1 0.553 0.991 0.704 0.000 0.296
#> GSM312894 1 0.553 0.991 0.704 0.000 0.296
#> GSM312895 1 0.553 0.991 0.704 0.000 0.296
#> GSM312937 1 0.553 0.991 0.704 0.000 0.296
#> GSM312938 1 0.553 0.991 0.704 0.000 0.296
#> GSM312939 1 0.553 0.991 0.704 0.000 0.296
#> GSM312940 1 0.553 0.991 0.704 0.000 0.296
#> GSM312941 1 0.553 0.991 0.704 0.000 0.296
#> GSM312942 1 0.573 0.962 0.676 0.000 0.324
#> GSM312943 1 0.553 0.991 0.704 0.000 0.296
#> GSM312944 1 0.553 0.991 0.704 0.000 0.296
#> GSM312945 1 0.553 0.991 0.704 0.000 0.296
#> GSM312946 1 0.553 0.991 0.704 0.000 0.296
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM312811 4 0.4916 0.860 0 0.424 0.000 0.576
#> GSM312812 2 0.3688 0.674 0 0.792 0.000 0.208
#> GSM312813 2 0.4916 0.762 0 0.576 0.000 0.424
#> GSM312814 2 0.4972 -0.726 0 0.544 0.000 0.456
#> GSM312815 2 0.0000 0.521 0 1.000 0.000 0.000
#> GSM312816 4 0.4916 0.860 0 0.424 0.000 0.576
#> GSM312817 2 0.4916 0.762 0 0.576 0.000 0.424
#> GSM312818 4 0.5080 0.858 0 0.420 0.004 0.576
#> GSM312819 2 0.4916 0.762 0 0.576 0.000 0.424
#> GSM312820 4 0.4916 0.860 0 0.424 0.000 0.576
#> GSM312821 4 0.4916 0.860 0 0.424 0.000 0.576
#> GSM312822 2 0.3837 -0.137 0 0.776 0.000 0.224
#> GSM312823 2 0.0000 0.521 0 1.000 0.000 0.000
#> GSM312824 2 0.0469 0.532 0 0.988 0.000 0.012
#> GSM312825 2 0.3837 0.683 0 0.776 0.000 0.224
#> GSM312826 2 0.4916 0.762 0 0.576 0.000 0.424
#> GSM312839 2 0.0000 0.521 0 1.000 0.000 0.000
#> GSM312840 2 0.3801 0.681 0 0.780 0.000 0.220
#> GSM312841 2 0.0000 0.521 0 1.000 0.000 0.000
#> GSM312843 2 0.0000 0.521 0 1.000 0.000 0.000
#> GSM312844 2 0.0000 0.521 0 1.000 0.000 0.000
#> GSM312845 2 0.4916 0.762 0 0.576 0.000 0.424
#> GSM312846 2 0.0000 0.521 0 1.000 0.000 0.000
#> GSM312847 2 0.4916 0.762 0 0.576 0.000 0.424
#> GSM312848 2 0.4916 0.762 0 0.576 0.000 0.424
#> GSM312849 2 0.4916 0.762 0 0.576 0.000 0.424
#> GSM312851 4 0.4916 0.860 0 0.424 0.000 0.576
#> GSM312853 4 0.4916 0.860 0 0.424 0.000 0.576
#> GSM312854 4 0.0000 0.379 0 0.000 0.000 1.000
#> GSM312856 4 0.3726 0.701 0 0.212 0.000 0.788
#> GSM312857 4 0.4406 0.787 0 0.300 0.000 0.700
#> GSM312858 2 0.4916 0.762 0 0.576 0.000 0.424
#> GSM312859 2 0.4916 0.762 0 0.576 0.000 0.424
#> GSM312860 2 0.4916 0.762 0 0.576 0.000 0.424
#> GSM312861 2 0.4916 0.762 0 0.576 0.000 0.424
#> GSM312862 2 0.0000 0.521 0 1.000 0.000 0.000
#> GSM312863 2 0.4916 0.762 0 0.576 0.000 0.424
#> GSM312864 4 0.3311 0.642 0 0.172 0.000 0.828
#> GSM312865 2 0.4916 0.762 0 0.576 0.000 0.424
#> GSM312867 2 0.4916 0.762 0 0.576 0.000 0.424
#> GSM312868 2 0.4916 0.762 0 0.576 0.000 0.424
#> GSM312869 2 0.4916 0.762 0 0.576 0.000 0.424
#> GSM312870 3 0.0000 1.000 0 0.000 1.000 0.000
#> GSM312872 3 0.0000 1.000 0 0.000 1.000 0.000
#> GSM312874 3 0.0000 1.000 0 0.000 1.000 0.000
#> GSM312875 3 0.0000 1.000 0 0.000 1.000 0.000
#> GSM312876 3 0.0000 1.000 0 0.000 1.000 0.000
#> GSM312877 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM312879 3 0.0000 1.000 0 0.000 1.000 0.000
#> GSM312882 3 0.0000 1.000 0 0.000 1.000 0.000
#> GSM312883 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM312886 3 0.0000 1.000 0 0.000 1.000 0.000
#> GSM312887 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM312890 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM312893 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM312894 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM312895 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM312937 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM312938 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM312939 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM312940 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM312941 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM312942 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM312943 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM312944 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM312945 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM312946 1 0.0000 1.000 1 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM312811 4 0.0000 0.735 0.000 0.000 0 1.000 0.000
#> GSM312812 2 0.3209 0.832 0.000 0.812 0 0.008 0.180
#> GSM312813 2 0.0000 0.811 0.000 1.000 0 0.000 0.000
#> GSM312814 4 0.3882 0.592 0.000 0.168 0 0.788 0.044
#> GSM312815 2 0.5218 0.775 0.000 0.684 0 0.136 0.180
#> GSM312816 4 0.2891 0.546 0.000 0.000 0 0.824 0.176
#> GSM312817 4 0.3949 0.612 0.000 0.332 0 0.668 0.000
#> GSM312818 5 0.3039 1.000 0.000 0.000 0 0.192 0.808
#> GSM312819 4 0.3932 0.614 0.000 0.328 0 0.672 0.000
#> GSM312820 5 0.3039 1.000 0.000 0.000 0 0.192 0.808
#> GSM312821 5 0.3039 1.000 0.000 0.000 0 0.192 0.808
#> GSM312822 4 0.5610 0.494 0.000 0.180 0 0.640 0.180
#> GSM312823 2 0.5218 0.775 0.000 0.684 0 0.136 0.180
#> GSM312824 2 0.4325 0.814 0.000 0.756 0 0.064 0.180
#> GSM312825 2 0.3209 0.832 0.000 0.812 0 0.008 0.180
#> GSM312826 2 0.2929 0.833 0.000 0.820 0 0.000 0.180
#> GSM312839 2 0.5218 0.775 0.000 0.684 0 0.136 0.180
#> GSM312840 2 0.3209 0.832 0.000 0.812 0 0.008 0.180
#> GSM312841 2 0.5218 0.775 0.000 0.684 0 0.136 0.180
#> GSM312843 4 0.3381 0.664 0.000 0.016 0 0.808 0.176
#> GSM312844 2 0.5941 0.667 0.000 0.592 0 0.228 0.180
#> GSM312845 2 0.2605 0.834 0.000 0.852 0 0.000 0.148
#> GSM312846 2 0.5218 0.775 0.000 0.684 0 0.136 0.180
#> GSM312847 2 0.0000 0.811 0.000 1.000 0 0.000 0.000
#> GSM312848 2 0.2813 0.595 0.000 0.832 0 0.168 0.000
#> GSM312849 2 0.0000 0.811 0.000 1.000 0 0.000 0.000
#> GSM312851 4 0.0000 0.735 0.000 0.000 0 1.000 0.000
#> GSM312853 4 0.0000 0.735 0.000 0.000 0 1.000 0.000
#> GSM312854 4 0.0609 0.735 0.000 0.020 0 0.980 0.000
#> GSM312856 4 0.3003 0.710 0.000 0.188 0 0.812 0.000
#> GSM312857 4 0.0000 0.735 0.000 0.000 0 1.000 0.000
#> GSM312858 2 0.0000 0.811 0.000 1.000 0 0.000 0.000
#> GSM312859 2 0.0000 0.811 0.000 1.000 0 0.000 0.000
#> GSM312860 2 0.0000 0.811 0.000 1.000 0 0.000 0.000
#> GSM312861 2 0.0000 0.811 0.000 1.000 0 0.000 0.000
#> GSM312862 2 0.5759 0.707 0.000 0.620 0 0.200 0.180
#> GSM312863 4 0.3336 0.696 0.000 0.228 0 0.772 0.000
#> GSM312864 4 0.0404 0.736 0.000 0.012 0 0.988 0.000
#> GSM312865 2 0.0404 0.802 0.000 0.988 0 0.012 0.000
#> GSM312867 2 0.0000 0.811 0.000 1.000 0 0.000 0.000
#> GSM312868 4 0.4030 0.592 0.000 0.352 0 0.648 0.000
#> GSM312869 2 0.2929 0.833 0.000 0.820 0 0.000 0.180
#> GSM312870 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM312872 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM312874 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM312875 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM312876 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM312877 1 0.0000 0.994 1.000 0.000 0 0.000 0.000
#> GSM312879 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM312882 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM312883 1 0.0404 0.994 0.988 0.000 0 0.000 0.012
#> GSM312886 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM312887 1 0.0404 0.994 0.988 0.000 0 0.000 0.012
#> GSM312890 1 0.0000 0.994 1.000 0.000 0 0.000 0.000
#> GSM312893 1 0.0000 0.994 1.000 0.000 0 0.000 0.000
#> GSM312894 1 0.0000 0.994 1.000 0.000 0 0.000 0.000
#> GSM312895 1 0.0000 0.994 1.000 0.000 0 0.000 0.000
#> GSM312937 1 0.0000 0.994 1.000 0.000 0 0.000 0.000
#> GSM312938 1 0.0404 0.994 0.988 0.000 0 0.000 0.012
#> GSM312939 1 0.0000 0.994 1.000 0.000 0 0.000 0.000
#> GSM312940 1 0.0000 0.994 1.000 0.000 0 0.000 0.000
#> GSM312941 1 0.0000 0.994 1.000 0.000 0 0.000 0.000
#> GSM312942 1 0.0404 0.994 0.988 0.000 0 0.000 0.012
#> GSM312943 1 0.0404 0.994 0.988 0.000 0 0.000 0.012
#> GSM312944 1 0.0404 0.994 0.988 0.000 0 0.000 0.012
#> GSM312945 1 0.0404 0.994 0.988 0.000 0 0.000 0.012
#> GSM312946 1 0.0404 0.994 0.988 0.000 0 0.000 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM312811 4 0.0000 0.731 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312812 2 0.0000 0.776 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312813 2 0.3851 0.632 0.000 0.540 0.000 0.000 0.460 0.000
#> GSM312814 4 0.3309 0.493 0.000 0.280 0.000 0.720 0.000 0.000
#> GSM312815 2 0.0000 0.776 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312816 4 0.3221 0.418 0.000 0.000 0.000 0.736 0.264 0.000
#> GSM312817 4 0.3982 0.455 0.000 0.004 0.000 0.536 0.460 0.000
#> GSM312818 5 0.5195 1.000 0.000 0.000 0.000 0.100 0.540 0.360
#> GSM312819 4 0.3851 0.458 0.000 0.000 0.000 0.540 0.460 0.000
#> GSM312820 5 0.5195 1.000 0.000 0.000 0.000 0.100 0.540 0.360
#> GSM312821 5 0.5195 1.000 0.000 0.000 0.000 0.100 0.540 0.360
#> GSM312822 4 0.3592 0.451 0.000 0.344 0.000 0.656 0.000 0.000
#> GSM312823 2 0.0000 0.776 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312824 2 0.0000 0.776 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312825 2 0.0000 0.776 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312826 2 0.0000 0.776 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312839 2 0.0000 0.776 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312840 2 0.0000 0.776 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312841 2 0.0000 0.776 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312843 4 0.1908 0.695 0.000 0.096 0.000 0.900 0.004 0.000
#> GSM312844 2 0.2941 0.623 0.000 0.780 0.000 0.220 0.000 0.000
#> GSM312845 2 0.0632 0.773 0.000 0.976 0.000 0.000 0.024 0.000
#> GSM312846 2 0.0000 0.776 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312847 2 0.3851 0.632 0.000 0.540 0.000 0.000 0.460 0.000
#> GSM312848 2 0.5858 0.348 0.000 0.484 0.000 0.244 0.272 0.000
#> GSM312849 2 0.2527 0.738 0.000 0.832 0.000 0.000 0.168 0.000
#> GSM312851 4 0.0000 0.731 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312853 4 0.0000 0.731 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312854 4 0.0000 0.731 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312856 4 0.1814 0.714 0.000 0.000 0.000 0.900 0.100 0.000
#> GSM312857 4 0.0000 0.731 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312858 2 0.3851 0.632 0.000 0.540 0.000 0.000 0.460 0.000
#> GSM312859 2 0.3851 0.632 0.000 0.540 0.000 0.000 0.460 0.000
#> GSM312860 2 0.3851 0.632 0.000 0.540 0.000 0.000 0.460 0.000
#> GSM312861 2 0.3851 0.632 0.000 0.540 0.000 0.000 0.460 0.000
#> GSM312862 2 0.2378 0.691 0.000 0.848 0.000 0.152 0.000 0.000
#> GSM312863 4 0.2697 0.673 0.000 0.000 0.000 0.812 0.188 0.000
#> GSM312864 4 0.0000 0.731 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM312865 2 0.4589 0.589 0.000 0.504 0.000 0.036 0.460 0.000
#> GSM312867 2 0.3782 0.652 0.000 0.588 0.000 0.000 0.412 0.000
#> GSM312868 4 0.3982 0.455 0.000 0.004 0.000 0.536 0.460 0.000
#> GSM312869 2 0.0000 0.776 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM312870 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312872 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312874 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312875 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312876 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312877 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312879 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312882 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM312883 6 0.3647 0.999 0.360 0.000 0.000 0.000 0.000 0.640
#> GSM312886 3 0.0146 0.995 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM312887 6 0.3647 0.999 0.360 0.000 0.000 0.000 0.000 0.640
#> GSM312890 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312893 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312894 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312895 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312937 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312938 6 0.3659 0.994 0.364 0.000 0.000 0.000 0.000 0.636
#> GSM312939 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312940 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312941 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312942 6 0.3647 0.999 0.360 0.000 0.000 0.000 0.000 0.640
#> GSM312943 6 0.3647 0.999 0.360 0.000 0.000 0.000 0.000 0.640
#> GSM312944 6 0.3647 0.999 0.360 0.000 0.000 0.000 0.000 0.640
#> GSM312945 6 0.3647 0.999 0.360 0.000 0.000 0.000 0.000 0.640
#> GSM312946 6 0.3647 0.999 0.360 0.000 0.000 0.000 0.000 0.640
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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:pam 66 1.39e-09 2
#> ATC:pam 67 8.42e-15 3
#> ATC:pam 64 1.22e-17 4
#> ATC:pam 66 2.13e-16 5
#> ATC:pam 60 2.63e-18 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "mclust"]
# you can also extract it by
# res = res_list["ATC:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 67 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 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 0.4755 0.525 0.525
#> 3 3 0.667 0.733 0.794 0.2284 0.912 0.834
#> 4 4 0.659 0.759 0.881 0.1577 0.828 0.633
#> 5 5 0.716 0.660 0.790 0.1081 0.958 0.873
#> 6 6 0.698 0.271 0.681 0.0652 0.828 0.506
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
#> GSM312811 2 0.0000 1.000 0.000 1.000
#> GSM312812 2 0.0000 1.000 0.000 1.000
#> GSM312813 2 0.0000 1.000 0.000 1.000
#> GSM312814 2 0.0000 1.000 0.000 1.000
#> GSM312815 2 0.0000 1.000 0.000 1.000
#> GSM312816 2 0.0000 1.000 0.000 1.000
#> GSM312817 2 0.0000 1.000 0.000 1.000
#> GSM312818 2 0.0000 1.000 0.000 1.000
#> GSM312819 2 0.0000 1.000 0.000 1.000
#> GSM312820 2 0.0000 1.000 0.000 1.000
#> GSM312821 2 0.0000 1.000 0.000 1.000
#> GSM312822 2 0.0000 1.000 0.000 1.000
#> GSM312823 2 0.0000 1.000 0.000 1.000
#> GSM312824 2 0.0000 1.000 0.000 1.000
#> GSM312825 2 0.0000 1.000 0.000 1.000
#> GSM312826 2 0.0000 1.000 0.000 1.000
#> GSM312839 2 0.0000 1.000 0.000 1.000
#> GSM312840 2 0.0000 1.000 0.000 1.000
#> GSM312841 2 0.0000 1.000 0.000 1.000
#> GSM312843 2 0.0000 1.000 0.000 1.000
#> GSM312844 2 0.0000 1.000 0.000 1.000
#> GSM312845 2 0.0938 0.988 0.012 0.988
#> GSM312846 2 0.0000 1.000 0.000 1.000
#> GSM312847 2 0.0000 1.000 0.000 1.000
#> GSM312848 2 0.0000 1.000 0.000 1.000
#> GSM312849 2 0.0000 1.000 0.000 1.000
#> GSM312851 2 0.0000 1.000 0.000 1.000
#> GSM312853 2 0.0000 1.000 0.000 1.000
#> GSM312854 2 0.0000 1.000 0.000 1.000
#> GSM312856 2 0.0000 1.000 0.000 1.000
#> GSM312857 2 0.0000 1.000 0.000 1.000
#> GSM312858 2 0.0000 1.000 0.000 1.000
#> GSM312859 2 0.0000 1.000 0.000 1.000
#> GSM312860 2 0.0000 1.000 0.000 1.000
#> GSM312861 2 0.0000 1.000 0.000 1.000
#> GSM312862 2 0.0000 1.000 0.000 1.000
#> GSM312863 2 0.0000 1.000 0.000 1.000
#> GSM312864 2 0.0000 1.000 0.000 1.000
#> GSM312865 2 0.0000 1.000 0.000 1.000
#> GSM312867 2 0.0000 1.000 0.000 1.000
#> GSM312868 2 0.0000 1.000 0.000 1.000
#> GSM312869 2 0.0000 1.000 0.000 1.000
#> GSM312870 1 0.0000 1.000 1.000 0.000
#> GSM312872 1 0.0000 1.000 1.000 0.000
#> GSM312874 1 0.0000 1.000 1.000 0.000
#> GSM312875 1 0.0000 1.000 1.000 0.000
#> GSM312876 1 0.0000 1.000 1.000 0.000
#> GSM312877 1 0.0000 1.000 1.000 0.000
#> GSM312879 1 0.0000 1.000 1.000 0.000
#> GSM312882 1 0.0000 1.000 1.000 0.000
#> GSM312883 1 0.0000 1.000 1.000 0.000
#> GSM312886 1 0.0000 1.000 1.000 0.000
#> GSM312887 1 0.0000 1.000 1.000 0.000
#> GSM312890 1 0.0000 1.000 1.000 0.000
#> GSM312893 1 0.0000 1.000 1.000 0.000
#> GSM312894 1 0.0000 1.000 1.000 0.000
#> GSM312895 1 0.0000 1.000 1.000 0.000
#> GSM312937 1 0.0000 1.000 1.000 0.000
#> GSM312938 1 0.0000 1.000 1.000 0.000
#> GSM312939 1 0.0000 1.000 1.000 0.000
#> GSM312940 1 0.0000 1.000 1.000 0.000
#> GSM312941 1 0.0000 1.000 1.000 0.000
#> GSM312942 1 0.0000 1.000 1.000 0.000
#> GSM312943 1 0.0000 1.000 1.000 0.000
#> GSM312944 1 0.0000 1.000 1.000 0.000
#> GSM312945 1 0.0000 1.000 1.000 0.000
#> GSM312946 1 0.0000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM312811 2 0.4110 0.856 0.004 0.844 0.152
#> GSM312812 2 0.3686 0.858 0.000 0.860 0.140
#> GSM312813 2 0.0747 0.890 0.000 0.984 0.016
#> GSM312814 2 0.5815 0.769 0.004 0.692 0.304
#> GSM312815 2 0.6345 0.685 0.004 0.596 0.400
#> GSM312816 2 0.5158 0.813 0.004 0.764 0.232
#> GSM312817 2 0.1289 0.888 0.000 0.968 0.032
#> GSM312818 2 0.7410 0.641 0.040 0.576 0.384
#> GSM312819 2 0.1289 0.888 0.000 0.968 0.032
#> GSM312820 2 0.7397 0.543 0.032 0.484 0.484
#> GSM312821 3 0.7397 -0.599 0.032 0.484 0.484
#> GSM312822 2 0.6410 0.667 0.004 0.576 0.420
#> GSM312823 2 0.1267 0.892 0.004 0.972 0.024
#> GSM312824 2 0.4062 0.848 0.000 0.836 0.164
#> GSM312825 2 0.4062 0.849 0.000 0.836 0.164
#> GSM312826 2 0.3267 0.869 0.000 0.884 0.116
#> GSM312839 2 0.6345 0.685 0.004 0.596 0.400
#> GSM312840 2 0.0592 0.891 0.000 0.988 0.012
#> GSM312841 2 0.4002 0.848 0.000 0.840 0.160
#> GSM312843 2 0.0892 0.891 0.000 0.980 0.020
#> GSM312844 2 0.6345 0.685 0.004 0.596 0.400
#> GSM312845 2 0.2681 0.870 0.028 0.932 0.040
#> GSM312846 2 0.1163 0.887 0.000 0.972 0.028
#> GSM312847 2 0.1031 0.888 0.000 0.976 0.024
#> GSM312848 2 0.1267 0.891 0.004 0.972 0.024
#> GSM312849 2 0.1031 0.886 0.000 0.976 0.024
#> GSM312851 2 0.1878 0.886 0.004 0.952 0.044
#> GSM312853 2 0.1399 0.890 0.004 0.968 0.028
#> GSM312854 2 0.0424 0.891 0.000 0.992 0.008
#> GSM312856 2 0.3112 0.871 0.004 0.900 0.096
#> GSM312857 2 0.1878 0.887 0.004 0.952 0.044
#> GSM312858 2 0.1031 0.886 0.000 0.976 0.024
#> GSM312859 2 0.0747 0.890 0.000 0.984 0.016
#> GSM312860 2 0.0892 0.891 0.000 0.980 0.020
#> GSM312861 2 0.0424 0.890 0.000 0.992 0.008
#> GSM312862 2 0.1031 0.888 0.000 0.976 0.024
#> GSM312863 2 0.0424 0.891 0.000 0.992 0.008
#> GSM312864 2 0.2096 0.890 0.004 0.944 0.052
#> GSM312865 2 0.1031 0.888 0.000 0.976 0.024
#> GSM312867 2 0.4233 0.842 0.004 0.836 0.160
#> GSM312868 2 0.0892 0.887 0.000 0.980 0.020
#> GSM312869 2 0.5929 0.752 0.004 0.676 0.320
#> GSM312870 1 0.1753 0.733 0.952 0.000 0.048
#> GSM312872 1 0.1753 0.733 0.952 0.000 0.048
#> GSM312874 1 0.1753 0.733 0.952 0.000 0.048
#> GSM312875 1 0.0000 0.766 1.000 0.000 0.000
#> GSM312876 1 0.0000 0.766 1.000 0.000 0.000
#> GSM312877 1 0.6286 -0.519 0.536 0.000 0.464
#> GSM312879 1 0.0592 0.760 0.988 0.000 0.012
#> GSM312882 1 0.0000 0.766 1.000 0.000 0.000
#> GSM312883 1 0.0747 0.765 0.984 0.000 0.016
#> GSM312886 1 0.1860 0.755 0.948 0.000 0.052
#> GSM312887 1 0.3116 0.697 0.892 0.000 0.108
#> GSM312890 3 0.6291 0.677 0.468 0.000 0.532
#> GSM312893 3 0.6291 0.677 0.468 0.000 0.532
#> GSM312894 3 0.6291 0.677 0.468 0.000 0.532
#> GSM312895 3 0.6291 0.677 0.468 0.000 0.532
#> GSM312937 3 0.6291 0.677 0.468 0.000 0.532
#> GSM312938 1 0.5327 0.405 0.728 0.000 0.272
#> GSM312939 3 0.6291 0.677 0.468 0.000 0.532
#> GSM312940 3 0.6291 0.677 0.468 0.000 0.532
#> GSM312941 3 0.6291 0.677 0.468 0.000 0.532
#> GSM312942 1 0.1753 0.753 0.952 0.000 0.048
#> GSM312943 1 0.5327 0.405 0.728 0.000 0.272
#> GSM312944 1 0.5397 0.381 0.720 0.000 0.280
#> GSM312945 1 0.5397 0.381 0.720 0.000 0.280
#> GSM312946 3 0.6309 0.584 0.500 0.000 0.500
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM312811 2 0.4624 0.5654 0.000 0.660 0.000 0.340
#> GSM312812 2 0.3528 0.7910 0.000 0.808 0.000 0.192
#> GSM312813 2 0.3311 0.8035 0.000 0.828 0.000 0.172
#> GSM312814 4 0.4999 -0.0595 0.000 0.492 0.000 0.508
#> GSM312815 4 0.3074 0.7925 0.000 0.152 0.000 0.848
#> GSM312816 4 0.4898 0.2751 0.000 0.416 0.000 0.584
#> GSM312817 2 0.3444 0.8002 0.000 0.816 0.000 0.184
#> GSM312818 4 0.0336 0.7176 0.000 0.008 0.000 0.992
#> GSM312819 2 0.3444 0.8002 0.000 0.816 0.000 0.184
#> GSM312820 4 0.0336 0.7176 0.000 0.008 0.000 0.992
#> GSM312821 4 0.0336 0.7176 0.000 0.008 0.000 0.992
#> GSM312822 4 0.3172 0.7875 0.000 0.160 0.000 0.840
#> GSM312823 2 0.3356 0.8030 0.000 0.824 0.000 0.176
#> GSM312824 2 0.3688 0.7749 0.000 0.792 0.000 0.208
#> GSM312825 2 0.3801 0.7609 0.000 0.780 0.000 0.220
#> GSM312826 2 0.3486 0.7943 0.000 0.812 0.000 0.188
#> GSM312839 4 0.3074 0.7925 0.000 0.152 0.000 0.848
#> GSM312840 2 0.3311 0.8035 0.000 0.828 0.000 0.172
#> GSM312841 2 0.3942 0.7356 0.000 0.764 0.000 0.236
#> GSM312843 2 0.0921 0.8466 0.000 0.972 0.000 0.028
#> GSM312844 4 0.3074 0.7925 0.000 0.152 0.000 0.848
#> GSM312845 2 0.0000 0.8458 0.000 1.000 0.000 0.000
#> GSM312846 2 0.0000 0.8458 0.000 1.000 0.000 0.000
#> GSM312847 2 0.0000 0.8458 0.000 1.000 0.000 0.000
#> GSM312848 2 0.0188 0.8453 0.000 0.996 0.000 0.004
#> GSM312849 2 0.0000 0.8458 0.000 1.000 0.000 0.000
#> GSM312851 2 0.3172 0.7044 0.000 0.840 0.000 0.160
#> GSM312853 2 0.2973 0.7269 0.000 0.856 0.000 0.144
#> GSM312854 2 0.0188 0.8455 0.000 0.996 0.000 0.004
#> GSM312856 2 0.3172 0.7111 0.000 0.840 0.000 0.160
#> GSM312857 2 0.3123 0.7103 0.000 0.844 0.000 0.156
#> GSM312858 2 0.0000 0.8458 0.000 1.000 0.000 0.000
#> GSM312859 2 0.2760 0.8243 0.000 0.872 0.000 0.128
#> GSM312860 2 0.1474 0.8442 0.000 0.948 0.000 0.052
#> GSM312861 2 0.0592 0.8472 0.000 0.984 0.000 0.016
#> GSM312862 2 0.0000 0.8458 0.000 1.000 0.000 0.000
#> GSM312863 2 0.0000 0.8458 0.000 1.000 0.000 0.000
#> GSM312864 2 0.3444 0.8002 0.000 0.816 0.000 0.184
#> GSM312865 2 0.0000 0.8458 0.000 1.000 0.000 0.000
#> GSM312867 2 0.0188 0.8453 0.000 0.996 0.000 0.004
#> GSM312868 2 0.0188 0.8455 0.000 0.996 0.000 0.004
#> GSM312869 2 0.4040 0.7243 0.000 0.752 0.000 0.248
#> GSM312870 3 0.0000 0.9534 0.000 0.000 1.000 0.000
#> GSM312872 3 0.0000 0.9534 0.000 0.000 1.000 0.000
#> GSM312874 3 0.0000 0.9534 0.000 0.000 1.000 0.000
#> GSM312875 3 0.0000 0.9534 0.000 0.000 1.000 0.000
#> GSM312876 3 0.0000 0.9534 0.000 0.000 1.000 0.000
#> GSM312877 1 0.4343 0.6238 0.732 0.000 0.264 0.004
#> GSM312879 3 0.0000 0.9534 0.000 0.000 1.000 0.000
#> GSM312882 3 0.0000 0.9534 0.000 0.000 1.000 0.000
#> GSM312883 3 0.0000 0.9534 0.000 0.000 1.000 0.000
#> GSM312886 3 0.0000 0.9534 0.000 0.000 1.000 0.000
#> GSM312887 3 0.3356 0.7246 0.176 0.000 0.824 0.000
#> GSM312890 1 0.1022 0.7750 0.968 0.000 0.032 0.000
#> GSM312893 1 0.0188 0.7788 0.996 0.000 0.004 0.000
#> GSM312894 1 0.0000 0.7781 1.000 0.000 0.000 0.000
#> GSM312895 1 0.0000 0.7781 1.000 0.000 0.000 0.000
#> GSM312937 1 0.0000 0.7781 1.000 0.000 0.000 0.000
#> GSM312938 1 0.5163 0.3462 0.516 0.000 0.480 0.004
#> GSM312939 1 0.0188 0.7788 0.996 0.000 0.004 0.000
#> GSM312940 1 0.2593 0.7514 0.892 0.000 0.104 0.004
#> GSM312941 1 0.0000 0.7781 1.000 0.000 0.000 0.000
#> GSM312942 3 0.3172 0.7535 0.160 0.000 0.840 0.000
#> GSM312943 1 0.5163 0.3462 0.516 0.000 0.480 0.004
#> GSM312944 1 0.5163 0.3462 0.516 0.000 0.480 0.004
#> GSM312945 1 0.5163 0.3462 0.516 0.000 0.480 0.004
#> GSM312946 1 0.3219 0.7192 0.836 0.000 0.164 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM312811 2 0.4420 0.275 0.000 0.548 0.000 0.448 0.004
#> GSM312812 4 0.3910 0.485 0.000 0.272 0.000 0.720 0.008
#> GSM312813 4 0.2852 0.598 0.000 0.172 0.000 0.828 0.000
#> GSM312814 2 0.3790 0.609 0.000 0.724 0.000 0.272 0.004
#> GSM312815 2 0.0324 0.456 0.000 0.992 0.000 0.004 0.004
#> GSM312816 2 0.3766 0.612 0.000 0.728 0.000 0.268 0.004
#> GSM312817 4 0.2930 0.606 0.000 0.164 0.000 0.832 0.004
#> GSM312818 5 0.4273 1.000 0.000 0.448 0.000 0.000 0.552
#> GSM312819 4 0.2930 0.606 0.000 0.164 0.000 0.832 0.004
#> GSM312820 5 0.4273 1.000 0.000 0.448 0.000 0.000 0.552
#> GSM312821 5 0.4273 1.000 0.000 0.448 0.000 0.000 0.552
#> GSM312822 2 0.0324 0.456 0.000 0.992 0.000 0.004 0.004
#> GSM312823 2 0.4560 0.153 0.000 0.508 0.000 0.484 0.008
#> GSM312824 4 0.3910 0.485 0.000 0.272 0.000 0.720 0.008
#> GSM312825 4 0.3910 0.485 0.000 0.272 0.000 0.720 0.008
#> GSM312826 4 0.3910 0.485 0.000 0.272 0.000 0.720 0.008
#> GSM312839 2 0.0324 0.456 0.000 0.992 0.000 0.004 0.004
#> GSM312840 4 0.3109 0.573 0.000 0.200 0.000 0.800 0.000
#> GSM312841 4 0.3636 0.483 0.000 0.272 0.000 0.728 0.000
#> GSM312843 4 0.1965 0.610 0.000 0.096 0.000 0.904 0.000
#> GSM312844 2 0.0324 0.456 0.000 0.992 0.000 0.004 0.004
#> GSM312845 4 0.3636 0.593 0.000 0.000 0.000 0.728 0.272
#> GSM312846 4 0.3612 0.593 0.000 0.000 0.000 0.732 0.268
#> GSM312847 4 0.3636 0.593 0.000 0.000 0.000 0.728 0.272
#> GSM312848 4 0.3586 0.593 0.000 0.000 0.000 0.736 0.264
#> GSM312849 4 0.3636 0.593 0.000 0.000 0.000 0.728 0.272
#> GSM312851 4 0.4288 -0.106 0.000 0.384 0.000 0.612 0.004
#> GSM312853 4 0.5074 0.486 0.000 0.168 0.000 0.700 0.132
#> GSM312854 4 0.2929 0.621 0.000 0.008 0.000 0.840 0.152
#> GSM312856 4 0.3990 0.145 0.000 0.308 0.000 0.688 0.004
#> GSM312857 4 0.4066 0.097 0.000 0.324 0.000 0.672 0.004
#> GSM312858 4 0.2424 0.626 0.000 0.000 0.000 0.868 0.132
#> GSM312859 4 0.3081 0.609 0.000 0.156 0.000 0.832 0.012
#> GSM312860 4 0.2971 0.608 0.000 0.156 0.000 0.836 0.008
#> GSM312861 4 0.3039 0.612 0.000 0.152 0.000 0.836 0.012
#> GSM312862 4 0.5425 0.509 0.000 0.100 0.000 0.632 0.268
#> GSM312863 4 0.3586 0.593 0.000 0.000 0.000 0.736 0.264
#> GSM312864 4 0.2970 0.604 0.000 0.168 0.000 0.828 0.004
#> GSM312865 4 0.3636 0.593 0.000 0.000 0.000 0.728 0.272
#> GSM312867 4 0.3766 0.591 0.000 0.004 0.000 0.728 0.268
#> GSM312868 4 0.0324 0.626 0.000 0.004 0.000 0.992 0.004
#> GSM312869 4 0.4047 0.397 0.000 0.320 0.000 0.676 0.004
#> GSM312870 3 0.0000 0.899 0.000 0.000 1.000 0.000 0.000
#> GSM312872 3 0.0000 0.899 0.000 0.000 1.000 0.000 0.000
#> GSM312874 3 0.0000 0.899 0.000 0.000 1.000 0.000 0.000
#> GSM312875 3 0.0000 0.899 0.000 0.000 1.000 0.000 0.000
#> GSM312876 3 0.0000 0.899 0.000 0.000 1.000 0.000 0.000
#> GSM312877 1 0.3242 0.880 0.816 0.000 0.012 0.000 0.172
#> GSM312879 3 0.0000 0.899 0.000 0.000 1.000 0.000 0.000
#> GSM312882 3 0.0000 0.899 0.000 0.000 1.000 0.000 0.000
#> GSM312883 3 0.0290 0.896 0.000 0.000 0.992 0.000 0.008
#> GSM312886 3 0.0290 0.896 0.000 0.000 0.992 0.000 0.008
#> GSM312887 3 0.4626 0.414 0.364 0.000 0.616 0.000 0.020
#> GSM312890 1 0.0000 0.934 1.000 0.000 0.000 0.000 0.000
#> GSM312893 1 0.0000 0.934 1.000 0.000 0.000 0.000 0.000
#> GSM312894 1 0.0162 0.934 0.996 0.000 0.000 0.000 0.004
#> GSM312895 1 0.0000 0.934 1.000 0.000 0.000 0.000 0.000
#> GSM312937 1 0.0000 0.934 1.000 0.000 0.000 0.000 0.000
#> GSM312938 1 0.3242 0.880 0.816 0.000 0.012 0.000 0.172
#> GSM312939 1 0.0000 0.934 1.000 0.000 0.000 0.000 0.000
#> GSM312940 1 0.0000 0.934 1.000 0.000 0.000 0.000 0.000
#> GSM312941 1 0.0000 0.934 1.000 0.000 0.000 0.000 0.000
#> GSM312942 3 0.4555 0.460 0.344 0.000 0.636 0.000 0.020
#> GSM312943 1 0.3242 0.880 0.816 0.000 0.012 0.000 0.172
#> GSM312944 1 0.3242 0.880 0.816 0.000 0.012 0.000 0.172
#> GSM312945 1 0.3242 0.880 0.816 0.000 0.012 0.000 0.172
#> GSM312946 1 0.0404 0.932 0.988 0.000 0.000 0.000 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM312811 2 0.4356 -0.00927 0.000 0.608 0.000 0.360 0.000 0.032
#> GSM312812 2 0.1444 0.05687 0.000 0.928 0.000 0.072 0.000 0.000
#> GSM312813 2 0.4086 -0.19430 0.000 0.528 0.000 0.464 0.000 0.008
#> GSM312814 2 0.5336 0.01431 0.000 0.576 0.000 0.332 0.024 0.068
#> GSM312815 2 0.7167 -0.29306 0.000 0.400 0.000 0.212 0.288 0.100
#> GSM312816 2 0.6448 -0.05745 0.000 0.448 0.000 0.368 0.060 0.124
#> GSM312817 4 0.3489 0.27682 0.000 0.288 0.000 0.708 0.000 0.004
#> GSM312818 5 0.0000 0.78126 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM312819 4 0.3489 0.27682 0.000 0.288 0.000 0.708 0.000 0.004
#> GSM312820 5 0.0000 0.78126 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM312821 5 0.0000 0.78126 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM312822 5 0.7600 0.19162 0.000 0.276 0.000 0.268 0.296 0.160
#> GSM312823 4 0.5656 -0.18922 0.000 0.408 0.000 0.440 0.000 0.152
#> GSM312824 2 0.0363 0.07124 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM312825 2 0.0363 0.07124 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM312826 2 0.0790 0.06681 0.000 0.968 0.000 0.032 0.000 0.000
#> GSM312839 2 0.7103 -0.28587 0.000 0.408 0.000 0.212 0.288 0.092
#> GSM312840 2 0.3607 -0.09029 0.000 0.652 0.000 0.348 0.000 0.000
#> GSM312841 2 0.1753 0.04528 0.000 0.912 0.000 0.084 0.000 0.004
#> GSM312843 2 0.4129 -0.14268 0.000 0.564 0.000 0.424 0.000 0.012
#> GSM312844 2 0.7251 -0.31790 0.000 0.372 0.000 0.240 0.288 0.100
#> GSM312845 2 0.6095 -0.21286 0.000 0.376 0.000 0.340 0.000 0.284
#> GSM312846 2 0.5162 -0.67576 0.000 0.504 0.000 0.088 0.000 0.408
#> GSM312847 2 0.6104 -0.21253 0.000 0.372 0.000 0.336 0.000 0.292
#> GSM312848 2 0.6099 -0.22601 0.000 0.380 0.000 0.328 0.000 0.292
#> GSM312849 2 0.6087 -0.22033 0.000 0.392 0.000 0.316 0.000 0.292
#> GSM312851 4 0.6026 -0.22598 0.000 0.168 0.000 0.516 0.020 0.296
#> GSM312853 4 0.6095 -0.38681 0.000 0.224 0.000 0.464 0.008 0.304
#> GSM312854 2 0.6094 -0.31904 0.000 0.368 0.000 0.352 0.000 0.280
#> GSM312856 4 0.5575 -0.13476 0.000 0.304 0.000 0.528 0.000 0.168
#> GSM312857 4 0.5697 -0.17989 0.000 0.272 0.000 0.520 0.000 0.208
#> GSM312858 4 0.6035 -0.13133 0.000 0.376 0.000 0.376 0.000 0.248
#> GSM312859 4 0.3881 0.22268 0.000 0.396 0.000 0.600 0.000 0.004
#> GSM312860 2 0.3854 -0.19004 0.000 0.536 0.000 0.464 0.000 0.000
#> GSM312861 4 0.3930 0.20684 0.000 0.420 0.000 0.576 0.000 0.004
#> GSM312862 6 0.5862 0.00000 0.000 0.376 0.000 0.196 0.000 0.428
#> GSM312863 2 0.6106 -0.21864 0.000 0.368 0.000 0.340 0.000 0.292
#> GSM312864 4 0.3742 0.17763 0.000 0.348 0.000 0.648 0.000 0.004
#> GSM312865 2 0.6104 -0.21253 0.000 0.372 0.000 0.336 0.000 0.292
#> GSM312867 2 0.5366 -0.41439 0.000 0.564 0.000 0.144 0.000 0.292
#> GSM312868 4 0.5219 0.13372 0.000 0.296 0.000 0.580 0.000 0.124
#> GSM312869 2 0.2468 0.05053 0.000 0.880 0.000 0.096 0.016 0.008
#> GSM312870 3 0.0547 0.87644 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM312872 3 0.0547 0.87644 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM312874 3 0.0547 0.87644 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM312875 3 0.0260 0.87855 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM312876 3 0.0260 0.87855 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM312877 1 0.2631 0.70613 0.840 0.000 0.008 0.000 0.000 0.152
#> GSM312879 3 0.0547 0.87644 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM312882 3 0.0260 0.87855 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM312883 3 0.1588 0.85462 0.072 0.000 0.924 0.000 0.000 0.004
#> GSM312886 3 0.2350 0.82995 0.100 0.000 0.880 0.000 0.000 0.020
#> GSM312887 3 0.4237 0.44688 0.396 0.000 0.584 0.000 0.000 0.020
#> GSM312890 1 0.3857 0.83270 0.532 0.000 0.000 0.000 0.000 0.468
#> GSM312893 1 0.3857 0.83270 0.532 0.000 0.000 0.000 0.000 0.468
#> GSM312894 1 0.3857 0.83270 0.532 0.000 0.000 0.000 0.000 0.468
#> GSM312895 1 0.3857 0.83270 0.532 0.000 0.000 0.000 0.000 0.468
#> GSM312937 1 0.3857 0.83270 0.532 0.000 0.000 0.000 0.000 0.468
#> GSM312938 1 0.0909 0.61180 0.968 0.000 0.012 0.000 0.000 0.020
#> GSM312939 1 0.3857 0.83270 0.532 0.000 0.000 0.000 0.000 0.468
#> GSM312940 1 0.3857 0.83270 0.532 0.000 0.000 0.000 0.000 0.468
#> GSM312941 1 0.3857 0.83270 0.532 0.000 0.000 0.000 0.000 0.468
#> GSM312942 3 0.4155 0.51741 0.364 0.000 0.616 0.000 0.000 0.020
#> GSM312943 1 0.0725 0.61894 0.976 0.000 0.012 0.000 0.000 0.012
#> GSM312944 1 0.0405 0.63370 0.988 0.000 0.008 0.000 0.000 0.004
#> GSM312945 1 0.0260 0.63115 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM312946 1 0.3833 0.82429 0.556 0.000 0.000 0.000 0.000 0.444
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:mclust 67 1.68e-10 2
#> ATC:mclust 61 1.06e-13 3
#> ATC:mclust 61 5.18e-12 4
#> ATC:mclust 49 1.64e-10 5
#> ATC:mclust 27 1.12e-06 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "NMF"]
# you can also extract it by
# res = res_list["ATC:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 67 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.994 0.997 0.4951 0.506 0.506
#> 3 3 0.901 0.915 0.963 0.2371 0.844 0.702
#> 4 4 0.598 0.599 0.767 0.1496 0.907 0.771
#> 5 5 0.592 0.645 0.784 0.1040 0.762 0.388
#> 6 6 0.573 0.524 0.717 0.0383 0.957 0.806
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
#> GSM312811 2 0.0000 0.995 0.000 1.000
#> GSM312812 2 0.0000 0.995 0.000 1.000
#> GSM312813 2 0.0000 0.995 0.000 1.000
#> GSM312814 2 0.0000 0.995 0.000 1.000
#> GSM312815 2 0.4690 0.893 0.100 0.900
#> GSM312816 2 0.1184 0.981 0.016 0.984
#> GSM312817 2 0.0000 0.995 0.000 1.000
#> GSM312818 1 0.0000 1.000 1.000 0.000
#> GSM312819 2 0.0000 0.995 0.000 1.000
#> GSM312820 1 0.0376 0.996 0.996 0.004
#> GSM312821 1 0.0000 1.000 1.000 0.000
#> GSM312822 2 0.0000 0.995 0.000 1.000
#> GSM312823 2 0.0000 0.995 0.000 1.000
#> GSM312824 2 0.0000 0.995 0.000 1.000
#> GSM312825 2 0.0000 0.995 0.000 1.000
#> GSM312826 2 0.0000 0.995 0.000 1.000
#> GSM312839 2 0.0000 0.995 0.000 1.000
#> GSM312840 2 0.0000 0.995 0.000 1.000
#> GSM312841 2 0.0000 0.995 0.000 1.000
#> GSM312843 2 0.0000 0.995 0.000 1.000
#> GSM312844 2 0.0938 0.985 0.012 0.988
#> GSM312845 2 0.0000 0.995 0.000 1.000
#> GSM312846 2 0.3431 0.934 0.064 0.936
#> GSM312847 2 0.0000 0.995 0.000 1.000
#> GSM312848 2 0.0000 0.995 0.000 1.000
#> GSM312849 2 0.0000 0.995 0.000 1.000
#> GSM312851 2 0.0000 0.995 0.000 1.000
#> GSM312853 2 0.0000 0.995 0.000 1.000
#> GSM312854 2 0.0000 0.995 0.000 1.000
#> GSM312856 2 0.0000 0.995 0.000 1.000
#> GSM312857 2 0.0000 0.995 0.000 1.000
#> GSM312858 2 0.0000 0.995 0.000 1.000
#> GSM312859 2 0.0000 0.995 0.000 1.000
#> GSM312860 2 0.0000 0.995 0.000 1.000
#> GSM312861 2 0.0000 0.995 0.000 1.000
#> GSM312862 2 0.0000 0.995 0.000 1.000
#> GSM312863 2 0.0000 0.995 0.000 1.000
#> GSM312864 2 0.0000 0.995 0.000 1.000
#> GSM312865 2 0.0000 0.995 0.000 1.000
#> GSM312867 2 0.0000 0.995 0.000 1.000
#> GSM312868 2 0.0000 0.995 0.000 1.000
#> GSM312869 2 0.0000 0.995 0.000 1.000
#> GSM312870 1 0.0000 1.000 1.000 0.000
#> GSM312872 1 0.0000 1.000 1.000 0.000
#> GSM312874 1 0.0000 1.000 1.000 0.000
#> GSM312875 1 0.0000 1.000 1.000 0.000
#> GSM312876 1 0.0000 1.000 1.000 0.000
#> GSM312877 1 0.0000 1.000 1.000 0.000
#> GSM312879 1 0.0000 1.000 1.000 0.000
#> GSM312882 1 0.0000 1.000 1.000 0.000
#> GSM312883 1 0.0000 1.000 1.000 0.000
#> GSM312886 1 0.0000 1.000 1.000 0.000
#> GSM312887 1 0.0000 1.000 1.000 0.000
#> GSM312890 1 0.0000 1.000 1.000 0.000
#> GSM312893 1 0.0000 1.000 1.000 0.000
#> GSM312894 1 0.0000 1.000 1.000 0.000
#> GSM312895 1 0.0000 1.000 1.000 0.000
#> GSM312937 1 0.0000 1.000 1.000 0.000
#> GSM312938 1 0.0000 1.000 1.000 0.000
#> GSM312939 1 0.0000 1.000 1.000 0.000
#> GSM312940 1 0.0000 1.000 1.000 0.000
#> GSM312941 1 0.0000 1.000 1.000 0.000
#> GSM312942 1 0.0000 1.000 1.000 0.000
#> GSM312943 1 0.0000 1.000 1.000 0.000
#> GSM312944 1 0.0000 1.000 1.000 0.000
#> GSM312945 1 0.0000 1.000 1.000 0.000
#> GSM312946 1 0.0000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM312811 2 0.0237 0.974 0.000 0.996 0.004
#> GSM312812 2 0.0000 0.977 0.000 1.000 0.000
#> GSM312813 2 0.0000 0.977 0.000 1.000 0.000
#> GSM312814 2 0.0000 0.977 0.000 1.000 0.000
#> GSM312815 2 0.0848 0.965 0.008 0.984 0.008
#> GSM312816 3 0.6045 0.371 0.000 0.380 0.620
#> GSM312817 2 0.0000 0.977 0.000 1.000 0.000
#> GSM312818 3 0.0000 0.934 0.000 0.000 1.000
#> GSM312819 2 0.0000 0.977 0.000 1.000 0.000
#> GSM312820 3 0.0000 0.934 0.000 0.000 1.000
#> GSM312821 3 0.0000 0.934 0.000 0.000 1.000
#> GSM312822 2 0.0237 0.974 0.000 0.996 0.004
#> GSM312823 2 0.0000 0.977 0.000 1.000 0.000
#> GSM312824 2 0.0000 0.977 0.000 1.000 0.000
#> GSM312825 2 0.0000 0.977 0.000 1.000 0.000
#> GSM312826 2 0.0000 0.977 0.000 1.000 0.000
#> GSM312839 2 0.3816 0.822 0.148 0.852 0.000
#> GSM312840 2 0.0000 0.977 0.000 1.000 0.000
#> GSM312841 2 0.0000 0.977 0.000 1.000 0.000
#> GSM312843 2 0.0000 0.977 0.000 1.000 0.000
#> GSM312844 2 0.0000 0.977 0.000 1.000 0.000
#> GSM312845 1 0.1860 0.883 0.948 0.052 0.000
#> GSM312846 2 0.5327 0.626 0.272 0.728 0.000
#> GSM312847 2 0.0000 0.977 0.000 1.000 0.000
#> GSM312848 2 0.0000 0.977 0.000 1.000 0.000
#> GSM312849 2 0.3340 0.857 0.120 0.880 0.000
#> GSM312851 2 0.4796 0.714 0.000 0.780 0.220
#> GSM312853 2 0.0000 0.977 0.000 1.000 0.000
#> GSM312854 2 0.0000 0.977 0.000 1.000 0.000
#> GSM312856 2 0.0000 0.977 0.000 1.000 0.000
#> GSM312857 2 0.0000 0.977 0.000 1.000 0.000
#> GSM312858 2 0.0000 0.977 0.000 1.000 0.000
#> GSM312859 2 0.0000 0.977 0.000 1.000 0.000
#> GSM312860 2 0.0000 0.977 0.000 1.000 0.000
#> GSM312861 2 0.0000 0.977 0.000 1.000 0.000
#> GSM312862 2 0.0000 0.977 0.000 1.000 0.000
#> GSM312863 2 0.0000 0.977 0.000 1.000 0.000
#> GSM312864 2 0.0000 0.977 0.000 1.000 0.000
#> GSM312865 2 0.0000 0.977 0.000 1.000 0.000
#> GSM312867 1 0.5291 0.614 0.732 0.268 0.000
#> GSM312868 2 0.0000 0.977 0.000 1.000 0.000
#> GSM312869 2 0.0000 0.977 0.000 1.000 0.000
#> GSM312870 3 0.0000 0.934 0.000 0.000 1.000
#> GSM312872 3 0.0000 0.934 0.000 0.000 1.000
#> GSM312874 3 0.0000 0.934 0.000 0.000 1.000
#> GSM312875 3 0.1643 0.922 0.044 0.000 0.956
#> GSM312876 3 0.1643 0.922 0.044 0.000 0.956
#> GSM312877 1 0.0000 0.927 1.000 0.000 0.000
#> GSM312879 3 0.0000 0.934 0.000 0.000 1.000
#> GSM312882 3 0.2066 0.911 0.060 0.000 0.940
#> GSM312883 3 0.2448 0.898 0.076 0.000 0.924
#> GSM312886 3 0.0000 0.934 0.000 0.000 1.000
#> GSM312887 3 0.0424 0.933 0.008 0.000 0.992
#> GSM312890 1 0.0000 0.927 1.000 0.000 0.000
#> GSM312893 1 0.0000 0.927 1.000 0.000 0.000
#> GSM312894 1 0.0000 0.927 1.000 0.000 0.000
#> GSM312895 1 0.0000 0.927 1.000 0.000 0.000
#> GSM312937 1 0.0000 0.927 1.000 0.000 0.000
#> GSM312938 3 0.3752 0.822 0.144 0.000 0.856
#> GSM312939 1 0.0000 0.927 1.000 0.000 0.000
#> GSM312940 1 0.0000 0.927 1.000 0.000 0.000
#> GSM312941 1 0.0000 0.927 1.000 0.000 0.000
#> GSM312942 3 0.1643 0.922 0.044 0.000 0.956
#> GSM312943 1 0.5882 0.461 0.652 0.000 0.348
#> GSM312944 1 0.0000 0.927 1.000 0.000 0.000
#> GSM312945 1 0.3816 0.802 0.852 0.000 0.148
#> GSM312946 1 0.2165 0.884 0.936 0.000 0.064
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM312811 2 0.3726 0.7073 0.000 0.788 0.000 0.212
#> GSM312812 2 0.4741 0.6888 0.028 0.744 0.000 0.228
#> GSM312813 2 0.3266 0.7371 0.000 0.832 0.000 0.168
#> GSM312814 2 0.4936 0.4437 0.000 0.624 0.004 0.372
#> GSM312815 4 0.7660 0.3824 0.304 0.208 0.004 0.484
#> GSM312816 4 0.7485 -0.0831 0.000 0.180 0.380 0.440
#> GSM312817 2 0.1211 0.7769 0.000 0.960 0.000 0.040
#> GSM312818 3 0.4855 0.4025 0.000 0.000 0.600 0.400
#> GSM312819 2 0.1474 0.7761 0.000 0.948 0.000 0.052
#> GSM312820 3 0.4888 0.3821 0.000 0.000 0.588 0.412
#> GSM312821 3 0.4866 0.3955 0.000 0.000 0.596 0.404
#> GSM312822 2 0.5788 0.1398 0.012 0.532 0.012 0.444
#> GSM312823 2 0.3649 0.7168 0.000 0.796 0.000 0.204
#> GSM312824 2 0.3539 0.7297 0.004 0.820 0.000 0.176
#> GSM312825 2 0.5279 0.6685 0.072 0.736 0.000 0.192
#> GSM312826 2 0.5226 0.6750 0.076 0.744 0.000 0.180
#> GSM312839 1 0.6968 0.0407 0.552 0.140 0.000 0.308
#> GSM312840 2 0.3311 0.7363 0.000 0.828 0.000 0.172
#> GSM312841 2 0.3907 0.6996 0.000 0.768 0.000 0.232
#> GSM312843 2 0.1792 0.7607 0.000 0.932 0.000 0.068
#> GSM312844 4 0.7122 0.3149 0.144 0.340 0.000 0.516
#> GSM312845 1 0.5471 0.6394 0.720 0.060 0.004 0.216
#> GSM312846 2 0.6314 0.1016 0.372 0.560 0.000 0.068
#> GSM312847 2 0.1833 0.7522 0.024 0.944 0.000 0.032
#> GSM312848 2 0.1389 0.7589 0.000 0.952 0.000 0.048
#> GSM312849 2 0.5374 0.4651 0.244 0.704 0.000 0.052
#> GSM312851 2 0.6794 -0.0317 0.000 0.584 0.136 0.280
#> GSM312853 2 0.1474 0.7625 0.000 0.948 0.000 0.052
#> GSM312854 2 0.0592 0.7688 0.000 0.984 0.000 0.016
#> GSM312856 2 0.1211 0.7658 0.000 0.960 0.000 0.040
#> GSM312857 2 0.1716 0.7537 0.000 0.936 0.000 0.064
#> GSM312858 2 0.0927 0.7717 0.008 0.976 0.000 0.016
#> GSM312859 2 0.3074 0.7442 0.000 0.848 0.000 0.152
#> GSM312860 2 0.5874 0.5994 0.124 0.700 0.000 0.176
#> GSM312861 2 0.2053 0.7756 0.004 0.924 0.000 0.072
#> GSM312862 2 0.5330 0.5230 0.000 0.748 0.132 0.120
#> GSM312863 2 0.0592 0.7688 0.000 0.984 0.000 0.016
#> GSM312864 2 0.0188 0.7723 0.000 0.996 0.000 0.004
#> GSM312865 2 0.1256 0.7651 0.008 0.964 0.000 0.028
#> GSM312867 1 0.4780 0.5883 0.788 0.116 0.000 0.096
#> GSM312868 2 0.0336 0.7716 0.000 0.992 0.000 0.008
#> GSM312869 1 0.7170 -0.0479 0.548 0.268 0.000 0.184
#> GSM312870 3 0.0469 0.7216 0.000 0.000 0.988 0.012
#> GSM312872 3 0.2401 0.7097 0.004 0.000 0.904 0.092
#> GSM312874 3 0.0707 0.7220 0.000 0.000 0.980 0.020
#> GSM312875 3 0.4776 0.6581 0.024 0.000 0.732 0.244
#> GSM312876 3 0.4807 0.6568 0.024 0.000 0.728 0.248
#> GSM312877 1 0.7707 0.2010 0.440 0.000 0.240 0.320
#> GSM312879 3 0.0188 0.7215 0.000 0.000 0.996 0.004
#> GSM312882 3 0.4964 0.6552 0.032 0.000 0.724 0.244
#> GSM312883 3 0.5416 0.6362 0.048 0.000 0.692 0.260
#> GSM312886 3 0.2345 0.7000 0.000 0.000 0.900 0.100
#> GSM312887 3 0.2918 0.6961 0.008 0.000 0.876 0.116
#> GSM312890 1 0.0592 0.7628 0.984 0.000 0.000 0.016
#> GSM312893 1 0.2675 0.7592 0.908 0.000 0.048 0.044
#> GSM312894 1 0.4203 0.7283 0.824 0.000 0.108 0.068
#> GSM312895 1 0.1004 0.7640 0.972 0.000 0.004 0.024
#> GSM312937 1 0.1406 0.7658 0.960 0.000 0.024 0.016
#> GSM312938 3 0.7146 0.4481 0.228 0.000 0.560 0.212
#> GSM312939 1 0.0592 0.7628 0.984 0.000 0.000 0.016
#> GSM312940 1 0.0817 0.7618 0.976 0.000 0.000 0.024
#> GSM312941 1 0.0657 0.7654 0.984 0.000 0.004 0.012
#> GSM312942 3 0.3037 0.7049 0.020 0.000 0.880 0.100
#> GSM312943 3 0.6722 0.0548 0.408 0.000 0.500 0.092
#> GSM312944 1 0.4318 0.7193 0.816 0.000 0.116 0.068
#> GSM312945 1 0.5773 0.4253 0.620 0.000 0.336 0.044
#> GSM312946 1 0.3611 0.7444 0.860 0.000 0.080 0.060
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM312811 2 0.4342 0.723 0.000 0.728 0.000 0.232 0.040
#> GSM312812 2 0.2291 0.756 0.012 0.908 0.000 0.072 0.008
#> GSM312813 2 0.4015 0.664 0.000 0.652 0.000 0.348 0.000
#> GSM312814 2 0.4747 0.759 0.000 0.720 0.000 0.196 0.084
#> GSM312815 2 0.4246 0.654 0.088 0.800 0.008 0.004 0.100
#> GSM312816 5 0.4258 0.640 0.004 0.100 0.032 0.052 0.812
#> GSM312817 4 0.3424 0.643 0.000 0.240 0.000 0.760 0.000
#> GSM312818 5 0.3146 0.677 0.000 0.052 0.092 0.000 0.856
#> GSM312819 4 0.2891 0.759 0.000 0.176 0.000 0.824 0.000
#> GSM312820 5 0.3012 0.691 0.004 0.072 0.052 0.000 0.872
#> GSM312821 5 0.2734 0.690 0.008 0.052 0.048 0.000 0.892
#> GSM312822 2 0.6505 0.609 0.012 0.532 0.000 0.168 0.288
#> GSM312823 2 0.3816 0.713 0.000 0.696 0.000 0.304 0.000
#> GSM312824 2 0.3366 0.760 0.000 0.768 0.000 0.232 0.000
#> GSM312825 2 0.4167 0.747 0.136 0.788 0.000 0.072 0.004
#> GSM312826 2 0.4686 0.768 0.104 0.736 0.000 0.160 0.000
#> GSM312839 2 0.4964 0.634 0.228 0.712 0.004 0.020 0.036
#> GSM312840 2 0.3480 0.753 0.000 0.752 0.000 0.248 0.000
#> GSM312841 2 0.2286 0.765 0.000 0.888 0.000 0.108 0.004
#> GSM312843 4 0.3838 0.646 0.000 0.280 0.000 0.716 0.004
#> GSM312844 2 0.4312 0.657 0.048 0.792 0.004 0.016 0.140
#> GSM312845 1 0.5771 0.592 0.664 0.000 0.100 0.208 0.028
#> GSM312846 1 0.5341 0.432 0.600 0.036 0.000 0.348 0.016
#> GSM312847 4 0.1299 0.878 0.008 0.020 0.000 0.960 0.012
#> GSM312848 4 0.1282 0.875 0.000 0.044 0.000 0.952 0.004
#> GSM312849 1 0.6204 0.291 0.524 0.136 0.000 0.336 0.004
#> GSM312851 4 0.4356 0.653 0.000 0.020 0.024 0.756 0.200
#> GSM312853 4 0.0579 0.876 0.000 0.008 0.000 0.984 0.008
#> GSM312854 4 0.0579 0.878 0.000 0.008 0.000 0.984 0.008
#> GSM312856 4 0.1310 0.878 0.000 0.024 0.000 0.956 0.020
#> GSM312857 4 0.1568 0.865 0.000 0.020 0.000 0.944 0.036
#> GSM312858 4 0.1894 0.867 0.000 0.072 0.000 0.920 0.008
#> GSM312859 2 0.4192 0.580 0.000 0.596 0.000 0.404 0.000
#> GSM312860 2 0.4950 0.645 0.040 0.612 0.000 0.348 0.000
#> GSM312861 4 0.3475 0.745 0.012 0.180 0.000 0.804 0.004
#> GSM312862 3 0.6996 0.152 0.000 0.284 0.456 0.244 0.016
#> GSM312863 4 0.0609 0.881 0.000 0.020 0.000 0.980 0.000
#> GSM312864 4 0.1121 0.880 0.000 0.044 0.000 0.956 0.000
#> GSM312865 4 0.0963 0.880 0.000 0.036 0.000 0.964 0.000
#> GSM312867 1 0.2713 0.769 0.888 0.036 0.004 0.072 0.000
#> GSM312868 4 0.2193 0.852 0.000 0.092 0.000 0.900 0.008
#> GSM312869 2 0.5684 0.721 0.200 0.668 0.000 0.112 0.020
#> GSM312870 3 0.4066 0.478 0.000 0.004 0.672 0.000 0.324
#> GSM312872 3 0.3395 0.537 0.000 0.000 0.764 0.000 0.236
#> GSM312874 3 0.3983 0.462 0.000 0.000 0.660 0.000 0.340
#> GSM312875 3 0.0955 0.585 0.004 0.000 0.968 0.000 0.028
#> GSM312876 3 0.0609 0.580 0.000 0.000 0.980 0.000 0.020
#> GSM312877 3 0.4936 0.345 0.260 0.008 0.684 0.000 0.048
#> GSM312879 3 0.4084 0.472 0.000 0.004 0.668 0.000 0.328
#> GSM312882 3 0.0510 0.583 0.000 0.000 0.984 0.000 0.016
#> GSM312883 3 0.0865 0.576 0.024 0.000 0.972 0.000 0.004
#> GSM312886 3 0.4449 0.164 0.000 0.004 0.512 0.000 0.484
#> GSM312887 5 0.4504 -0.072 0.000 0.008 0.428 0.000 0.564
#> GSM312890 1 0.0740 0.813 0.980 0.000 0.008 0.004 0.008
#> GSM312893 1 0.1043 0.807 0.960 0.000 0.040 0.000 0.000
#> GSM312894 1 0.2519 0.776 0.884 0.000 0.100 0.000 0.016
#> GSM312895 1 0.0693 0.811 0.980 0.012 0.000 0.000 0.008
#> GSM312937 1 0.0451 0.813 0.988 0.004 0.008 0.000 0.000
#> GSM312938 5 0.8283 0.186 0.328 0.100 0.136 0.028 0.408
#> GSM312939 1 0.0613 0.813 0.984 0.004 0.004 0.000 0.008
#> GSM312940 1 0.1153 0.810 0.964 0.004 0.008 0.000 0.024
#> GSM312941 1 0.0579 0.813 0.984 0.000 0.008 0.000 0.008
#> GSM312942 3 0.4451 0.161 0.000 0.004 0.504 0.000 0.492
#> GSM312943 3 0.5987 0.441 0.248 0.036 0.632 0.000 0.084
#> GSM312944 1 0.5073 0.373 0.640 0.040 0.312 0.000 0.008
#> GSM312945 3 0.6287 0.223 0.408 0.028 0.488 0.000 0.076
#> GSM312946 1 0.3771 0.735 0.836 0.024 0.088 0.000 0.052
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM312811 2 0.6315 0.5684 0.000 0.580 0.000 0.184 0.112 0.124
#> GSM312812 2 0.3846 0.5789 0.004 0.776 0.000 0.040 0.008 0.172
#> GSM312813 2 0.3445 0.6715 0.000 0.744 0.000 0.244 0.000 0.012
#> GSM312814 2 0.5154 0.7039 0.000 0.680 0.000 0.156 0.136 0.028
#> GSM312815 2 0.5624 0.4659 0.056 0.648 0.000 0.000 0.156 0.140
#> GSM312816 5 0.6395 0.4953 0.000 0.128 0.056 0.092 0.636 0.088
#> GSM312817 4 0.4002 0.4744 0.000 0.320 0.000 0.660 0.000 0.020
#> GSM312818 5 0.4499 0.6892 0.000 0.032 0.108 0.004 0.760 0.096
#> GSM312819 4 0.3784 0.4983 0.000 0.308 0.000 0.680 0.000 0.012
#> GSM312820 5 0.2715 0.7091 0.000 0.028 0.088 0.000 0.872 0.012
#> GSM312821 5 0.2780 0.6946 0.000 0.016 0.092 0.000 0.868 0.024
#> GSM312822 2 0.6803 0.3755 0.020 0.436 0.008 0.104 0.388 0.044
#> GSM312823 2 0.3454 0.6976 0.000 0.760 0.000 0.224 0.012 0.004
#> GSM312824 2 0.2520 0.7309 0.000 0.844 0.000 0.152 0.000 0.004
#> GSM312825 2 0.2736 0.6969 0.020 0.880 0.000 0.052 0.000 0.048
#> GSM312826 2 0.3066 0.7337 0.016 0.836 0.000 0.132 0.000 0.016
#> GSM312839 2 0.6155 0.5181 0.120 0.644 0.000 0.024 0.100 0.112
#> GSM312840 2 0.3746 0.7165 0.000 0.760 0.000 0.192 0.000 0.048
#> GSM312841 2 0.3317 0.7065 0.000 0.836 0.000 0.080 0.012 0.072
#> GSM312843 4 0.6274 0.4187 0.012 0.184 0.000 0.556 0.028 0.220
#> GSM312844 2 0.6214 0.4267 0.056 0.576 0.000 0.004 0.220 0.144
#> GSM312845 1 0.6975 0.2940 0.544 0.016 0.040 0.236 0.036 0.128
#> GSM312846 1 0.6657 0.3244 0.564 0.044 0.000 0.196 0.036 0.160
#> GSM312847 4 0.4422 0.6661 0.104 0.044 0.000 0.764 0.000 0.088
#> GSM312848 4 0.2201 0.7375 0.000 0.028 0.000 0.896 0.000 0.076
#> GSM312849 4 0.7327 0.1215 0.320 0.216 0.000 0.348 0.000 0.116
#> GSM312851 4 0.4678 0.5386 0.004 0.004 0.016 0.736 0.148 0.092
#> GSM312853 4 0.2756 0.6849 0.000 0.016 0.000 0.872 0.028 0.084
#> GSM312854 4 0.1155 0.7437 0.004 0.004 0.000 0.956 0.000 0.036
#> GSM312856 4 0.1699 0.7596 0.016 0.032 0.000 0.936 0.000 0.016
#> GSM312857 4 0.2219 0.7436 0.012 0.020 0.000 0.916 0.016 0.036
#> GSM312858 4 0.3542 0.7042 0.000 0.160 0.000 0.788 0.000 0.052
#> GSM312859 2 0.3565 0.6027 0.000 0.692 0.000 0.304 0.000 0.004
#> GSM312860 2 0.4536 0.6101 0.008 0.664 0.000 0.280 0.000 0.048
#> GSM312861 4 0.4643 0.4901 0.008 0.304 0.000 0.640 0.000 0.048
#> GSM312862 6 0.7921 0.0401 0.004 0.200 0.164 0.164 0.036 0.432
#> GSM312863 4 0.1320 0.7611 0.000 0.036 0.000 0.948 0.000 0.016
#> GSM312864 4 0.2209 0.7550 0.000 0.072 0.000 0.900 0.004 0.024
#> GSM312865 4 0.2190 0.7590 0.000 0.060 0.000 0.900 0.000 0.040
#> GSM312867 1 0.4901 0.4954 0.736 0.112 0.004 0.072 0.000 0.076
#> GSM312868 4 0.3247 0.7118 0.000 0.156 0.000 0.808 0.000 0.036
#> GSM312869 2 0.5360 0.6952 0.088 0.716 0.000 0.116 0.040 0.040
#> GSM312870 3 0.4274 0.6111 0.000 0.000 0.676 0.000 0.276 0.048
#> GSM312872 3 0.3808 0.6403 0.000 0.000 0.736 0.000 0.228 0.036
#> GSM312874 3 0.4386 0.5895 0.000 0.000 0.652 0.000 0.300 0.048
#> GSM312875 3 0.1138 0.6595 0.004 0.000 0.960 0.000 0.024 0.012
#> GSM312876 3 0.1223 0.6550 0.008 0.004 0.960 0.000 0.016 0.012
#> GSM312877 3 0.5592 0.1494 0.196 0.000 0.644 0.000 0.060 0.100
#> GSM312879 3 0.4249 0.6174 0.000 0.000 0.688 0.000 0.260 0.052
#> GSM312882 3 0.0976 0.6542 0.008 0.000 0.968 0.000 0.008 0.016
#> GSM312883 3 0.0912 0.6425 0.008 0.004 0.972 0.000 0.004 0.012
#> GSM312886 3 0.5207 0.4542 0.000 0.000 0.560 0.008 0.352 0.080
#> GSM312887 5 0.5301 -0.2054 0.004 0.000 0.416 0.000 0.492 0.088
#> GSM312890 1 0.0000 0.6435 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM312893 1 0.1976 0.6284 0.916 0.000 0.060 0.000 0.008 0.016
#> GSM312894 1 0.5278 0.4349 0.672 0.000 0.192 0.000 0.052 0.084
#> GSM312895 1 0.1668 0.6359 0.928 0.008 0.004 0.000 0.000 0.060
#> GSM312937 1 0.1492 0.6425 0.940 0.000 0.036 0.000 0.000 0.024
#> GSM312938 1 0.7921 0.1558 0.468 0.028 0.112 0.032 0.220 0.140
#> GSM312939 1 0.0603 0.6427 0.980 0.004 0.000 0.000 0.000 0.016
#> GSM312940 1 0.1821 0.6387 0.928 0.000 0.008 0.000 0.040 0.024
#> GSM312941 1 0.1088 0.6429 0.960 0.000 0.016 0.000 0.000 0.024
#> GSM312942 3 0.6377 0.3394 0.020 0.008 0.484 0.004 0.332 0.152
#> GSM312943 6 0.7768 -0.1160 0.260 0.076 0.228 0.004 0.036 0.396
#> GSM312944 1 0.7325 -0.1141 0.400 0.108 0.128 0.004 0.012 0.348
#> GSM312945 1 0.7598 -0.2746 0.348 0.068 0.220 0.004 0.024 0.336
#> GSM312946 1 0.7691 -0.0374 0.436 0.084 0.152 0.000 0.060 0.268
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:NMF 67 9.63e-09 2
#> ATC:NMF 65 1.12e-08 3
#> ATC:NMF 50 9.27e-09 4
#> ATC:NMF 53 7.16e-12 5
#> ATC:NMF 44 5.37e-13 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