Date: 2019-12-25 20:17:11 CET, cola version: 1.3.2
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All available functions which can be applied to this res_list object:
res_list
#> A 'ConsensusPartitionList' object with 24 methods.
#> On a matrix with 8229 rows and 84 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] 8229 84
The density distribution for each sample is visualized as in one column in the following heatmap. The clustering is based on the distance which is the Kolmogorov-Smirnov statistic between two distributions.
library(ComplexHeatmap)
densityHeatmap(mat, top_annotation = HeatmapAnnotation(df = get_anno(res_list),
col = get_anno_col(res_list)), ylab = "value", cluster_columns = TRUE, show_column_names = FALSE,
mc.cores = 4)
Folowing table shows the best k (number of partitions) for each combination
of top-value methods and partition methods. Clicking on the method name in
the table goes to the section for a single combination of methods.
The cola vignette explains the definition of the metrics used for determining the best number of partitions.
suggest_best_k(res_list)
| The best k | 1-PAC | Mean silhouette | Concordance | Optional k | ||
|---|---|---|---|---|---|---|
| SD:pam | 3 | 1.000 | 0.964 | 0.988 | ** | 2 |
| ATC:hclust | 2 | 1.000 | 0.987 | 0.995 | ** | |
| MAD:mclust | 3 | 0.981 | 0.919 | 0.954 | ** | |
| CV:NMF | 4 | 0.974 | 0.925 | 0.967 | ** | 2 |
| ATC:skmeans | 4 | 0.973 | 0.946 | 0.978 | ** | 2,3 |
| ATC:pam | 6 | 0.973 | 0.901 | 0.951 | ** | 4,5 |
| SD:skmeans | 4 | 0.964 | 0.964 | 0.983 | ** | 2 |
| ATC:NMF | 4 | 0.961 | 0.948 | 0.977 | ** | 3 |
| CV:mclust | 3 | 0.958 | 0.900 | 0.957 | ** | |
| MAD:NMF | 4 | 0.941 | 0.926 | 0.963 | * | 3 |
| SD:NMF | 4 | 0.938 | 0.919 | 0.963 | * | |
| SD:mclust | 3 | 0.937 | 0.893 | 0.947 | * | |
| MAD:hclust | 6 | 0.935 | 0.884 | 0.903 | * | 4 |
| MAD:pam | 5 | 0.925 | 0.831 | 0.932 | * | 3 |
| MAD:skmeans | 5 | 0.916 | 0.893 | 0.896 | * | 4 |
| CV:skmeans | 5 | 0.910 | 0.810 | 0.899 | * | 2,4 |
| CV:pam | 4 | 0.904 | 0.884 | 0.948 | * | 3 |
| CV:hclust | 5 | 0.903 | 0.897 | 0.926 | * | 4 |
| ATC:mclust | 6 | 0.901 | 0.844 | 0.910 | * | |
| SD:hclust | 4 | 0.891 | 0.939 | 0.965 | ||
| CV:kmeans | 4 | 0.630 | 0.908 | 0.854 | ||
| SD:kmeans | 4 | 0.613 | 0.901 | 0.834 | ||
| MAD:kmeans | 4 | 0.603 | 0.896 | 0.853 | ||
| ATC:kmeans | 3 | 0.592 | 0.878 | 0.871 |
**: 1-PAC > 0.95, *: 1-PAC > 0.9
Cumulative distribution function curves of consensus matrix for all methods.
collect_plots(res_list, fun = plot_ecdf)
Consensus heatmaps for all methods. (What is a consensus heatmap?)
collect_plots(res_list, k = 2, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = consensus_heatmap, mc.cores = 4)
Membership heatmaps for all methods. (What is a membership heatmap?)
collect_plots(res_list, k = 2, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = membership_heatmap, mc.cores = 4)
Signature heatmaps for all methods. (What is a signature heatmap?)
Note in following heatmaps, rows are scaled.
collect_plots(res_list, k = 2, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 3, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 4, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 5, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 6, fun = get_signatures, mc.cores = 4)
The statistics used for measuring the stability of consensus partitioning. (How are they defined?)
get_stats(res_list, k = 2)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 2 0.892 0.896 0.935 0.437 0.577 0.577
#> CV:NMF 2 0.910 0.917 0.960 0.456 0.550 0.550
#> MAD:NMF 2 0.861 0.883 0.937 0.447 0.550 0.550
#> ATC:NMF 2 0.894 0.912 0.961 0.453 0.535 0.535
#> SD:skmeans 2 1.000 0.937 0.949 0.506 0.494 0.494
#> CV:skmeans 2 1.000 0.980 0.991 0.506 0.494 0.494
#> MAD:skmeans 2 0.494 0.926 0.943 0.506 0.494 0.494
#> ATC:skmeans 2 1.000 0.954 0.966 0.504 0.497 0.497
#> SD:mclust 2 0.221 0.373 0.679 0.503 0.559 0.559
#> CV:mclust 2 0.220 0.484 0.677 0.503 0.620 0.620
#> MAD:mclust 2 0.279 0.886 0.894 0.505 0.497 0.497
#> ATC:mclust 2 0.532 0.919 0.924 0.498 0.501 0.501
#> SD:kmeans 2 0.229 0.504 0.653 0.396 0.494 0.494
#> CV:kmeans 2 0.242 0.524 0.644 0.385 0.598 0.598
#> MAD:kmeans 2 0.189 0.502 0.686 0.399 0.508 0.508
#> ATC:kmeans 2 0.223 0.681 0.723 0.381 0.646 0.646
#> SD:pam 2 1.000 0.982 0.979 0.350 0.646 0.646
#> CV:pam 2 0.485 0.834 0.851 0.342 0.646 0.646
#> MAD:pam 2 0.491 0.806 0.827 0.346 0.646 0.646
#> ATC:pam 2 0.510 0.893 0.895 0.335 0.659 0.659
#> SD:hclust 2 0.371 0.728 0.810 0.355 0.512 0.512
#> CV:hclust 2 0.405 0.359 0.691 0.361 0.620 0.620
#> MAD:hclust 2 0.280 0.598 0.791 0.398 0.703 0.703
#> ATC:hclust 2 1.000 0.987 0.995 0.347 0.659 0.659
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.821 0.869 0.937 0.427 0.648 0.465
#> CV:NMF 3 0.778 0.887 0.939 0.377 0.616 0.419
#> MAD:NMF 3 0.945 0.932 0.969 0.387 0.626 0.430
#> ATC:NMF 3 1.000 0.966 0.984 0.396 0.793 0.626
#> SD:skmeans 3 0.609 0.786 0.870 0.272 0.598 0.364
#> CV:skmeans 3 0.589 0.604 0.776 0.274 0.572 0.319
#> MAD:skmeans 3 0.564 0.699 0.859 0.283 0.687 0.453
#> ATC:skmeans 3 1.000 0.973 0.988 0.271 0.804 0.627
#> SD:mclust 3 0.937 0.893 0.947 0.273 0.551 0.339
#> CV:mclust 3 0.958 0.900 0.957 0.279 0.690 0.519
#> MAD:mclust 3 0.981 0.919 0.954 0.265 0.824 0.659
#> ATC:mclust 3 0.585 0.814 0.777 0.273 0.579 0.345
#> SD:kmeans 3 0.391 0.764 0.780 0.499 0.592 0.375
#> CV:kmeans 3 0.382 0.778 0.781 0.544 0.685 0.521
#> MAD:kmeans 3 0.478 0.636 0.634 0.511 0.641 0.408
#> ATC:kmeans 3 0.592 0.878 0.871 0.559 0.739 0.604
#> SD:pam 3 1.000 0.964 0.988 0.653 0.785 0.667
#> CV:pam 3 1.000 0.996 0.999 0.719 0.766 0.637
#> MAD:pam 3 1.000 0.984 0.994 0.701 0.766 0.637
#> ATC:pam 3 0.676 0.906 0.861 0.705 0.771 0.652
#> SD:hclust 3 0.639 0.808 0.813 0.588 0.918 0.840
#> CV:hclust 3 0.640 0.832 0.829 0.550 0.659 0.510
#> MAD:hclust 3 0.657 0.816 0.821 0.392 0.727 0.612
#> ATC:hclust 3 0.626 0.483 0.769 0.700 0.673 0.508
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.938 0.919 0.963 0.202 0.834 0.589
#> CV:NMF 4 0.974 0.925 0.967 0.199 0.861 0.640
#> MAD:NMF 4 0.941 0.926 0.963 0.212 0.850 0.618
#> ATC:NMF 4 0.961 0.948 0.977 0.187 0.820 0.546
#> SD:skmeans 4 0.964 0.964 0.983 0.173 0.876 0.664
#> CV:skmeans 4 0.964 0.967 0.985 0.172 0.865 0.621
#> MAD:skmeans 4 1.000 0.968 0.912 0.164 0.837 0.563
#> ATC:skmeans 4 0.973 0.946 0.978 0.181 0.849 0.599
#> SD:mclust 4 0.659 0.817 0.838 0.145 0.857 0.613
#> CV:mclust 4 0.783 0.859 0.915 0.153 0.818 0.533
#> MAD:mclust 4 0.718 0.779 0.886 0.138 0.803 0.517
#> ATC:mclust 4 0.820 0.807 0.897 0.166 0.880 0.669
#> SD:kmeans 4 0.613 0.901 0.834 0.175 0.850 0.628
#> CV:kmeans 4 0.630 0.908 0.854 0.189 0.850 0.628
#> MAD:kmeans 4 0.603 0.896 0.853 0.163 0.899 0.711
#> ATC:kmeans 4 0.828 0.956 0.909 0.200 0.849 0.632
#> SD:pam 4 0.880 0.867 0.939 0.272 0.813 0.573
#> CV:pam 4 0.904 0.884 0.948 0.260 0.849 0.633
#> MAD:pam 4 0.862 0.805 0.930 0.262 0.837 0.605
#> ATC:pam 4 1.000 0.969 0.989 0.279 0.839 0.626
#> SD:hclust 4 0.891 0.939 0.965 0.287 0.849 0.650
#> CV:hclust 4 0.938 0.963 0.972 0.292 0.849 0.650
#> MAD:hclust 4 0.914 0.954 0.973 0.305 0.849 0.650
#> ATC:hclust 4 0.869 0.921 0.961 0.241 0.757 0.435
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.878 0.825 0.887 0.0483 0.944 0.787
#> CV:NMF 5 0.852 0.743 0.822 0.0499 0.943 0.780
#> MAD:NMF 5 0.888 0.799 0.893 0.0473 0.977 0.908
#> ATC:NMF 5 0.853 0.872 0.902 0.0434 0.987 0.948
#> SD:skmeans 5 0.891 0.879 0.896 0.0463 0.971 0.880
#> CV:skmeans 5 0.910 0.810 0.899 0.0470 0.983 0.930
#> MAD:skmeans 5 0.916 0.893 0.896 0.0471 0.971 0.880
#> ATC:skmeans 5 0.892 0.863 0.927 0.0434 0.962 0.847
#> SD:mclust 5 0.780 0.658 0.834 0.0748 0.913 0.680
#> CV:mclust 5 0.813 0.780 0.889 0.0654 0.882 0.572
#> MAD:mclust 5 0.830 0.643 0.827 0.0875 0.936 0.761
#> ATC:mclust 5 0.875 0.840 0.916 0.0731 0.917 0.682
#> SD:kmeans 5 0.765 0.836 0.841 0.0871 1.000 1.000
#> CV:kmeans 5 0.790 0.853 0.853 0.0823 1.000 1.000
#> MAD:kmeans 5 0.806 0.831 0.852 0.0904 0.987 0.949
#> ATC:kmeans 5 0.743 0.892 0.877 0.0643 1.000 1.000
#> SD:pam 5 0.795 0.810 0.873 0.0382 0.971 0.888
#> CV:pam 5 0.828 0.806 0.890 0.0326 0.974 0.899
#> MAD:pam 5 0.925 0.831 0.932 0.0346 0.917 0.707
#> ATC:pam 5 1.000 0.958 0.983 0.0278 0.981 0.931
#> SD:hclust 5 0.855 0.869 0.914 0.0461 0.964 0.873
#> CV:hclust 5 0.903 0.897 0.926 0.0492 0.964 0.873
#> MAD:hclust 5 0.889 0.902 0.945 0.0539 0.964 0.873
#> ATC:hclust 5 0.866 0.894 0.941 0.0371 0.977 0.916
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.868 0.803 0.857 0.0381 0.968 0.853
#> CV:NMF 6 0.869 0.738 0.859 0.0371 0.949 0.771
#> MAD:NMF 6 0.858 0.785 0.872 0.0392 0.955 0.807
#> ATC:NMF 6 0.826 0.797 0.851 0.0316 0.964 0.857
#> SD:skmeans 6 0.869 0.757 0.839 0.0389 0.961 0.823
#> CV:skmeans 6 0.858 0.761 0.780 0.0377 0.930 0.704
#> MAD:skmeans 6 0.871 0.799 0.836 0.0380 0.943 0.744
#> ATC:skmeans 6 0.879 0.776 0.864 0.0333 0.990 0.954
#> SD:mclust 6 0.839 0.822 0.856 0.0442 0.884 0.541
#> CV:mclust 6 0.840 0.778 0.869 0.0398 0.940 0.715
#> MAD:mclust 6 0.849 0.672 0.846 0.0387 0.906 0.607
#> ATC:mclust 6 0.901 0.844 0.910 0.0395 0.916 0.628
#> SD:kmeans 6 0.764 0.731 0.811 0.0533 0.978 0.914
#> CV:kmeans 6 0.765 0.755 0.800 0.0445 0.987 0.949
#> MAD:kmeans 6 0.776 0.728 0.816 0.0494 0.991 0.963
#> ATC:kmeans 6 0.810 0.821 0.822 0.0438 1.000 1.000
#> SD:pam 6 0.856 0.861 0.916 0.0268 0.987 0.946
#> CV:pam 6 0.878 0.869 0.917 0.0243 0.987 0.947
#> MAD:pam 6 0.876 0.820 0.914 0.0199 0.987 0.946
#> ATC:pam 6 0.973 0.901 0.951 0.0250 0.968 0.879
#> SD:hclust 6 0.873 0.877 0.917 0.0438 0.974 0.894
#> CV:hclust 6 0.870 0.887 0.910 0.0393 0.974 0.894
#> MAD:hclust 6 0.935 0.884 0.903 0.0427 0.955 0.819
#> ATC:hclust 6 0.874 0.867 0.936 0.0490 0.952 0.808
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 = 823, method = "euler")
top_rows_overlap(res_list, top_n = 1646, method = "euler")
top_rows_overlap(res_list, top_n = 2468, method = "euler")
top_rows_overlap(res_list, top_n = 3291, method = "euler")
top_rows_overlap(res_list, top_n = 4114, method = "euler")
Also visualize the correspondance of rankings between different top-row methods:
top_rows_overlap(res_list, top_n = 823, method = "correspondance")
top_rows_overlap(res_list, top_n = 1646, method = "correspondance")
top_rows_overlap(res_list, top_n = 2468, method = "correspondance")
top_rows_overlap(res_list, top_n = 3291, method = "correspondance")
top_rows_overlap(res_list, top_n = 4114, method = "correspondance")
Heatmaps of the top rows:
top_rows_heatmap(res_list, top_n = 823)
top_rows_heatmap(res_list, top_n = 1646)
top_rows_heatmap(res_list, top_n = 2468)
top_rows_heatmap(res_list, top_n = 3291)
top_rows_heatmap(res_list, top_n = 4114)
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 tissue(p) k
#> SD:NMF 79 4.66e-05 2
#> CV:NMF 81 6.04e-05 2
#> MAD:NMF 80 5.31e-05 2
#> ATC:NMF 81 6.04e-05 2
#> SD:skmeans 83 3.39e-05 2
#> CV:skmeans 83 3.39e-05 2
#> MAD:skmeans 83 3.39e-05 2
#> ATC:skmeans 84 4.54e-05 2
#> SD:mclust 19 NA 2
#> CV:mclust 19 NA 2
#> MAD:mclust 84 2.53e-05 2
#> ATC:mclust 84 4.57e-05 2
#> SD:kmeans 60 1.68e-04 2
#> CV:kmeans 61 1.95e-04 2
#> MAD:kmeans 45 NA 2
#> ATC:kmeans 64 3.97e-04 2
#> SD:pam 84 2.53e-05 2
#> CV:pam 84 2.53e-05 2
#> MAD:pam 84 2.53e-05 2
#> ATC:pam 84 2.53e-05 2
#> SD:hclust 67 1.21e-04 2
#> CV:hclust 15 NA 2
#> MAD:hclust 65 1.42e-04 2
#> ATC:hclust 83 3.39e-05 2
test_to_known_factors(res_list, k = 3)
#> n tissue(p) k
#> SD:NMF 77 2.99e-08 3
#> CV:NMF 79 2.19e-08 3
#> MAD:NMF 82 9.10e-09 3
#> ATC:NMF 84 1.72e-08 3
#> SD:skmeans 81 6.98e-09 3
#> CV:skmeans 64 1.46e-07 3
#> MAD:skmeans 64 1.46e-07 3
#> ATC:skmeans 84 6.67e-09 3
#> SD:mclust 78 1.69e-08 3
#> CV:mclust 79 2.19e-08 3
#> MAD:mclust 80 1.24e-08 3
#> ATC:mclust 83 5.13e-09 3
#> SD:kmeans 84 6.67e-09 3
#> CV:kmeans 84 6.67e-09 3
#> MAD:kmeans 61 8.31e-07 3
#> ATC:kmeans 84 1.65e-08 3
#> SD:pam 82 2.06e-08 3
#> CV:pam 84 2.34e-08 3
#> MAD:pam 84 2.34e-08 3
#> ATC:pam 84 1.63e-07 3
#> SD:hclust 84 6.67e-09 3
#> CV:hclust 84 6.67e-09 3
#> MAD:hclust 84 6.67e-09 3
#> ATC:hclust 50 1.60e-05 3
test_to_known_factors(res_list, k = 4)
#> n tissue(p) k
#> SD:NMF 81 2.10e-11 4
#> CV:NMF 80 1.46e-11 4
#> MAD:NMF 82 9.12e-12 4
#> ATC:NMF 83 4.06e-12 4
#> SD:skmeans 83 4.22e-12 4
#> CV:skmeans 83 4.22e-12 4
#> MAD:skmeans 83 4.22e-12 4
#> ATC:skmeans 81 6.79e-12 4
#> SD:mclust 76 3.70e-11 4
#> CV:mclust 79 1.16e-11 4
#> MAD:mclust 74 6.77e-11 4
#> ATC:mclust 77 1.70e-11 4
#> SD:kmeans 82 8.86e-12 4
#> CV:kmeans 84 5.71e-12 4
#> MAD:kmeans 82 8.86e-12 4
#> ATC:kmeans 84 5.57e-12 4
#> SD:pam 81 2.66e-10 4
#> CV:pam 80 6.57e-11 4
#> MAD:pam 73 4.97e-10 4
#> ATC:pam 83 1.77e-10 4
#> SD:hclust 84 1.99e-12 4
#> CV:hclust 84 1.99e-12 4
#> MAD:hclust 84 1.99e-12 4
#> ATC:hclust 81 7.31e-12 4
test_to_known_factors(res_list, k = 5)
#> n tissue(p) k
#> SD:NMF 77 3.38e-14 5
#> CV:NMF 61 8.46e-07 5
#> MAD:NMF 76 2.03e-14 5
#> ATC:NMF 83 4.06e-12 5
#> SD:skmeans 82 3.49e-15 5
#> CV:skmeans 79 1.87e-14 5
#> MAD:skmeans 82 3.49e-15 5
#> ATC:skmeans 78 3.91e-15 5
#> SD:mclust 64 1.46e-12 5
#> CV:mclust 74 6.72e-14 5
#> MAD:mclust 63 8.71e-13 5
#> ATC:mclust 79 4.10e-15 5
#> SD:kmeans 79 3.12e-11 5
#> CV:kmeans 82 8.86e-12 5
#> MAD:kmeans 79 3.61e-15 5
#> ATC:kmeans 84 5.57e-12 5
#> SD:pam 75 3.07e-10 5
#> CV:pam 76 1.38e-10 5
#> MAD:pam 74 3.22e-13 5
#> ATC:pam 83 4.01e-12 5
#> SD:hclust 78 3.91e-15 5
#> CV:hclust 84 6.24e-16 5
#> MAD:hclust 82 1.15e-15 5
#> ATC:hclust 79 6.48e-15 5
test_to_known_factors(res_list, k = 6)
#> n tissue(p) k
#> SD:NMF 78 5.97e-18 6
#> CV:NMF 75 5.30e-17 6
#> MAD:NMF 78 5.97e-18 6
#> ATC:NMF 80 6.28e-15 6
#> SD:skmeans 67 6.10e-12 6
#> CV:skmeans 73 3.70e-17 6
#> MAD:skmeans 77 8.02e-18 6
#> ATC:skmeans 74 9.11e-18 6
#> SD:mclust 78 4.67e-17 6
#> CV:mclust 78 2.87e-16 6
#> MAD:mclust 61 1.60e-12 6
#> ATC:mclust 73 3.70e-17 6
#> SD:kmeans 77 6.70e-15 6
#> CV:kmeans 77 6.70e-15 6
#> MAD:kmeans 77 6.70e-15 6
#> ATC:kmeans 84 5.57e-12 6
#> SD:pam 80 1.42e-16 6
#> CV:pam 81 1.23e-17 6
#> MAD:pam 74 4.81e-16 6
#> ATC:pam 80 8.33e-17 6
#> SD:hclust 78 1.99e-18 6
#> CV:hclust 80 9.28e-19 6
#> MAD:hclust 78 1.99e-18 6
#> ATC:hclust 79 3.73e-18 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 8229 rows and 84 columns.
#> Top rows (823, 1646, 2468, 3291, 4114) 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.371 0.728 0.810 0.3549 0.512 0.512
#> 3 3 0.639 0.808 0.813 0.5876 0.918 0.840
#> 4 4 0.891 0.939 0.965 0.2867 0.849 0.650
#> 5 5 0.855 0.869 0.914 0.0461 0.964 0.873
#> 6 6 0.873 0.877 0.917 0.0438 0.974 0.894
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM2819 2 0.6048 0.730 0.148 0.852
#> GSM2820 2 0.1633 0.946 0.024 0.976
#> GSM2822 2 0.0672 0.951 0.008 0.992
#> GSM2832 2 0.0672 0.951 0.008 0.992
#> GSM2823 2 0.4161 0.846 0.084 0.916
#> GSM2824 2 0.4161 0.846 0.084 0.916
#> GSM2825 2 0.0672 0.951 0.008 0.992
#> GSM2826 2 0.0672 0.951 0.008 0.992
#> GSM2829 1 0.9775 0.532 0.588 0.412
#> GSM2856 1 0.9775 0.532 0.588 0.412
#> GSM2830 1 0.9775 0.532 0.588 0.412
#> GSM2843 1 0.9775 0.532 0.588 0.412
#> GSM2871 1 0.9775 0.532 0.588 0.412
#> GSM2831 1 0.9775 0.532 0.588 0.412
#> GSM2844 1 0.9775 0.532 0.588 0.412
#> GSM2833 1 0.9775 0.532 0.588 0.412
#> GSM2846 1 0.9775 0.532 0.588 0.412
#> GSM2835 1 0.9775 0.532 0.588 0.412
#> GSM2858 1 0.9775 0.532 0.588 0.412
#> GSM2836 2 0.0000 0.959 0.000 1.000
#> GSM2848 2 0.0000 0.959 0.000 1.000
#> GSM2828 2 0.1633 0.946 0.024 0.976
#> GSM2837 2 0.1633 0.946 0.024 0.976
#> GSM2839 1 0.9983 0.303 0.524 0.476
#> GSM2841 1 0.9983 0.303 0.524 0.476
#> GSM2827 2 0.0000 0.959 0.000 1.000
#> GSM2842 2 0.0000 0.959 0.000 1.000
#> GSM2845 1 0.9775 0.532 0.588 0.412
#> GSM2872 1 0.9775 0.532 0.588 0.412
#> GSM2834 1 0.9775 0.532 0.588 0.412
#> GSM2847 1 0.9775 0.532 0.588 0.412
#> GSM2849 2 0.1633 0.946 0.024 0.976
#> GSM2850 2 0.1633 0.946 0.024 0.976
#> GSM2838 2 0.0000 0.959 0.000 1.000
#> GSM2853 2 0.0000 0.959 0.000 1.000
#> GSM2852 2 0.0000 0.959 0.000 1.000
#> GSM2855 2 0.0000 0.959 0.000 1.000
#> GSM2840 1 0.9983 0.303 0.524 0.476
#> GSM2857 1 0.9983 0.303 0.524 0.476
#> GSM2859 2 0.0000 0.959 0.000 1.000
#> GSM2860 2 0.0000 0.959 0.000 1.000
#> GSM2861 2 0.0000 0.959 0.000 1.000
#> GSM2862 2 0.0000 0.959 0.000 1.000
#> GSM2863 2 0.0000 0.959 0.000 1.000
#> GSM2864 2 0.0000 0.959 0.000 1.000
#> GSM2865 2 0.0000 0.959 0.000 1.000
#> GSM2866 2 0.0000 0.959 0.000 1.000
#> GSM2868 2 0.0000 0.959 0.000 1.000
#> GSM2869 2 0.0000 0.959 0.000 1.000
#> GSM2851 2 0.0000 0.959 0.000 1.000
#> GSM2867 2 0.0000 0.959 0.000 1.000
#> GSM2870 2 0.0000 0.959 0.000 1.000
#> GSM2854 1 0.9909 0.490 0.556 0.444
#> GSM2873 1 0.9909 0.490 0.556 0.444
#> GSM2874 2 0.1633 0.946 0.024 0.976
#> GSM2884 2 0.1633 0.946 0.024 0.976
#> GSM2875 1 0.9983 0.303 0.524 0.476
#> GSM2890 1 0.9983 0.303 0.524 0.476
#> GSM2877 1 0.9983 0.303 0.524 0.476
#> GSM2892 1 0.9983 0.303 0.524 0.476
#> GSM2902 1 0.9983 0.303 0.524 0.476
#> GSM2878 1 0.9983 0.303 0.524 0.476
#> GSM2901 1 0.9983 0.303 0.524 0.476
#> GSM2879 2 0.0000 0.959 0.000 1.000
#> GSM2898 2 0.0000 0.959 0.000 1.000
#> GSM2881 2 0.1633 0.946 0.024 0.976
#> GSM2897 2 0.1633 0.946 0.024 0.976
#> GSM2882 1 0.9775 0.532 0.588 0.412
#> GSM2894 1 0.9775 0.532 0.588 0.412
#> GSM2883 2 0.1633 0.946 0.024 0.976
#> GSM2895 2 0.1633 0.946 0.024 0.976
#> GSM2885 2 0.1633 0.946 0.024 0.976
#> GSM2886 2 0.1633 0.946 0.024 0.976
#> GSM2887 2 0.1633 0.946 0.024 0.976
#> GSM2896 2 0.1633 0.946 0.024 0.976
#> GSM2888 2 0.0000 0.959 0.000 1.000
#> GSM2889 2 0.0000 0.959 0.000 1.000
#> GSM2876 1 0.9983 0.303 0.524 0.476
#> GSM2891 1 0.9983 0.303 0.524 0.476
#> GSM2880 1 0.9983 0.303 0.524 0.476
#> GSM2893 1 0.9983 0.303 0.524 0.476
#> GSM2821 2 0.6048 0.730 0.148 0.852
#> GSM2900 2 0.6048 0.730 0.148 0.852
#> GSM2903 2 0.6048 0.730 0.148 0.852
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM2819 3 0.9497 0.572 0.200 0.332 0.468
#> GSM2820 3 0.0000 0.601 0.000 0.000 1.000
#> GSM2822 3 0.6192 0.737 0.000 0.420 0.580
#> GSM2832 3 0.6192 0.737 0.000 0.420 0.580
#> GSM2823 3 0.8887 0.641 0.128 0.368 0.504
#> GSM2824 3 0.8887 0.641 0.128 0.368 0.504
#> GSM2825 3 0.6192 0.737 0.000 0.420 0.580
#> GSM2826 3 0.6192 0.737 0.000 0.420 0.580
#> GSM2829 2 0.0000 0.994 0.000 1.000 0.000
#> GSM2856 2 0.0000 0.994 0.000 1.000 0.000
#> GSM2830 2 0.0000 0.994 0.000 1.000 0.000
#> GSM2843 2 0.0000 0.994 0.000 1.000 0.000
#> GSM2871 2 0.0000 0.994 0.000 1.000 0.000
#> GSM2831 2 0.0000 0.994 0.000 1.000 0.000
#> GSM2844 2 0.0000 0.994 0.000 1.000 0.000
#> GSM2833 2 0.0000 0.994 0.000 1.000 0.000
#> GSM2846 2 0.0000 0.994 0.000 1.000 0.000
#> GSM2835 2 0.0000 0.994 0.000 1.000 0.000
#> GSM2858 2 0.0000 0.994 0.000 1.000 0.000
#> GSM2836 3 0.6168 0.745 0.000 0.412 0.588
#> GSM2848 3 0.6168 0.745 0.000 0.412 0.588
#> GSM2828 3 0.0000 0.601 0.000 0.000 1.000
#> GSM2837 3 0.0000 0.601 0.000 0.000 1.000
#> GSM2839 1 0.0000 0.998 1.000 0.000 0.000
#> GSM2841 1 0.0000 0.998 1.000 0.000 0.000
#> GSM2827 3 0.6168 0.745 0.000 0.412 0.588
#> GSM2842 3 0.6168 0.745 0.000 0.412 0.588
#> GSM2845 2 0.0000 0.994 0.000 1.000 0.000
#> GSM2872 2 0.0000 0.994 0.000 1.000 0.000
#> GSM2834 2 0.0000 0.994 0.000 1.000 0.000
#> GSM2847 2 0.0000 0.994 0.000 1.000 0.000
#> GSM2849 3 0.0000 0.601 0.000 0.000 1.000
#> GSM2850 3 0.0000 0.601 0.000 0.000 1.000
#> GSM2838 3 0.6168 0.745 0.000 0.412 0.588
#> GSM2853 3 0.6168 0.745 0.000 0.412 0.588
#> GSM2852 3 0.6008 0.737 0.000 0.372 0.628
#> GSM2855 3 0.6008 0.737 0.000 0.372 0.628
#> GSM2840 1 0.0000 0.998 1.000 0.000 0.000
#> GSM2857 1 0.0000 0.998 1.000 0.000 0.000
#> GSM2859 3 0.6168 0.745 0.000 0.412 0.588
#> GSM2860 3 0.6168 0.745 0.000 0.412 0.588
#> GSM2861 3 0.6168 0.745 0.000 0.412 0.588
#> GSM2862 3 0.6168 0.745 0.000 0.412 0.588
#> GSM2863 3 0.6168 0.745 0.000 0.412 0.588
#> GSM2864 3 0.6168 0.745 0.000 0.412 0.588
#> GSM2865 3 0.6168 0.745 0.000 0.412 0.588
#> GSM2866 3 0.6168 0.745 0.000 0.412 0.588
#> GSM2868 3 0.6168 0.745 0.000 0.412 0.588
#> GSM2869 3 0.6168 0.745 0.000 0.412 0.588
#> GSM2851 3 0.6168 0.745 0.000 0.412 0.588
#> GSM2867 3 0.6168 0.745 0.000 0.412 0.588
#> GSM2870 3 0.6168 0.745 0.000 0.412 0.588
#> GSM2854 2 0.1289 0.950 0.000 0.968 0.032
#> GSM2873 2 0.1289 0.950 0.000 0.968 0.032
#> GSM2874 3 0.0000 0.601 0.000 0.000 1.000
#> GSM2884 3 0.0000 0.601 0.000 0.000 1.000
#> GSM2875 1 0.0000 0.998 1.000 0.000 0.000
#> GSM2890 1 0.0000 0.998 1.000 0.000 0.000
#> GSM2877 1 0.0000 0.998 1.000 0.000 0.000
#> GSM2892 1 0.0000 0.998 1.000 0.000 0.000
#> GSM2902 1 0.0000 0.998 1.000 0.000 0.000
#> GSM2878 1 0.0000 0.998 1.000 0.000 0.000
#> GSM2901 1 0.0000 0.998 1.000 0.000 0.000
#> GSM2879 3 0.6095 0.743 0.000 0.392 0.608
#> GSM2898 3 0.6095 0.743 0.000 0.392 0.608
#> GSM2881 3 0.0000 0.601 0.000 0.000 1.000
#> GSM2897 3 0.0000 0.601 0.000 0.000 1.000
#> GSM2882 2 0.0000 0.994 0.000 1.000 0.000
#> GSM2894 2 0.0000 0.994 0.000 1.000 0.000
#> GSM2883 3 0.0000 0.601 0.000 0.000 1.000
#> GSM2895 3 0.0000 0.601 0.000 0.000 1.000
#> GSM2885 3 0.0000 0.601 0.000 0.000 1.000
#> GSM2886 3 0.0000 0.601 0.000 0.000 1.000
#> GSM2887 3 0.0000 0.601 0.000 0.000 1.000
#> GSM2896 3 0.0000 0.601 0.000 0.000 1.000
#> GSM2888 3 0.6168 0.745 0.000 0.412 0.588
#> GSM2889 3 0.6168 0.745 0.000 0.412 0.588
#> GSM2876 1 0.0592 0.985 0.988 0.000 0.012
#> GSM2891 1 0.0592 0.985 0.988 0.000 0.012
#> GSM2880 1 0.0000 0.998 1.000 0.000 0.000
#> GSM2893 1 0.0000 0.998 1.000 0.000 0.000
#> GSM2821 3 0.9497 0.572 0.200 0.332 0.468
#> GSM2900 3 0.9497 0.572 0.200 0.332 0.468
#> GSM2903 3 0.9497 0.572 0.200 0.332 0.468
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM2819 2 0.4284 0.761 0.200 0.780 0.000 0.020
#> GSM2820 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM2822 2 0.3688 0.755 0.000 0.792 0.000 0.208
#> GSM2832 2 0.3688 0.755 0.000 0.792 0.000 0.208
#> GSM2823 2 0.3088 0.847 0.128 0.864 0.000 0.008
#> GSM2824 2 0.3088 0.847 0.128 0.864 0.000 0.008
#> GSM2825 2 0.3688 0.755 0.000 0.792 0.000 0.208
#> GSM2826 2 0.3688 0.755 0.000 0.792 0.000 0.208
#> GSM2829 4 0.0336 0.965 0.000 0.008 0.000 0.992
#> GSM2856 4 0.0336 0.965 0.000 0.008 0.000 0.992
#> GSM2830 4 0.0921 0.962 0.000 0.028 0.000 0.972
#> GSM2843 4 0.0921 0.962 0.000 0.028 0.000 0.972
#> GSM2871 4 0.0921 0.962 0.000 0.028 0.000 0.972
#> GSM2831 4 0.0336 0.965 0.000 0.008 0.000 0.992
#> GSM2844 4 0.0336 0.965 0.000 0.008 0.000 0.992
#> GSM2833 4 0.0336 0.965 0.000 0.008 0.000 0.992
#> GSM2846 4 0.0336 0.965 0.000 0.008 0.000 0.992
#> GSM2835 4 0.0336 0.965 0.000 0.008 0.000 0.992
#> GSM2858 4 0.0336 0.965 0.000 0.008 0.000 0.992
#> GSM2836 2 0.0336 0.932 0.000 0.992 0.000 0.008
#> GSM2848 2 0.0336 0.932 0.000 0.992 0.000 0.008
#> GSM2828 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM2837 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM2839 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM2841 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM2827 2 0.0336 0.932 0.000 0.992 0.000 0.008
#> GSM2842 2 0.0336 0.932 0.000 0.992 0.000 0.008
#> GSM2845 4 0.0921 0.962 0.000 0.028 0.000 0.972
#> GSM2872 4 0.0921 0.962 0.000 0.028 0.000 0.972
#> GSM2834 4 0.0921 0.962 0.000 0.028 0.000 0.972
#> GSM2847 4 0.0921 0.962 0.000 0.028 0.000 0.972
#> GSM2849 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM2850 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM2838 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM2853 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM2852 2 0.1557 0.905 0.000 0.944 0.056 0.000
#> GSM2855 2 0.1557 0.905 0.000 0.944 0.056 0.000
#> GSM2840 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM2857 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM2859 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM2860 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM2861 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM2862 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM2863 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM2864 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM2865 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM2866 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM2868 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM2869 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM2851 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM2867 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM2870 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM2854 4 0.3528 0.774 0.000 0.192 0.000 0.808
#> GSM2873 4 0.3528 0.774 0.000 0.192 0.000 0.808
#> GSM2874 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM2884 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM2875 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM2890 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM2877 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM2892 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM2902 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM2878 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM2901 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM2879 2 0.1042 0.925 0.000 0.972 0.020 0.008
#> GSM2898 2 0.1042 0.925 0.000 0.972 0.020 0.008
#> GSM2881 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM2897 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM2882 4 0.0336 0.965 0.000 0.008 0.000 0.992
#> GSM2894 4 0.0336 0.965 0.000 0.008 0.000 0.992
#> GSM2883 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM2895 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM2885 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM2886 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM2887 3 0.0188 0.995 0.000 0.004 0.996 0.000
#> GSM2896 3 0.0188 0.995 0.000 0.004 0.996 0.000
#> GSM2888 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM2889 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM2876 1 0.0469 0.986 0.988 0.012 0.000 0.000
#> GSM2891 1 0.0469 0.986 0.988 0.012 0.000 0.000
#> GSM2880 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM2893 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM2821 2 0.4284 0.761 0.200 0.780 0.000 0.020
#> GSM2900 2 0.4284 0.761 0.200 0.780 0.000 0.020
#> GSM2903 2 0.4284 0.761 0.200 0.780 0.000 0.020
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM2819 5 0.4045 1.000 0.000 0.356 0.000 0.000 0.644
#> GSM2820 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2822 2 0.4073 0.498 0.000 0.752 0.000 0.216 0.032
#> GSM2832 2 0.4073 0.498 0.000 0.752 0.000 0.216 0.032
#> GSM2823 2 0.3582 0.429 0.000 0.768 0.000 0.008 0.224
#> GSM2824 2 0.3582 0.429 0.000 0.768 0.000 0.008 0.224
#> GSM2825 2 0.4073 0.498 0.000 0.752 0.000 0.216 0.032
#> GSM2826 2 0.4073 0.498 0.000 0.752 0.000 0.216 0.032
#> GSM2829 4 0.0000 0.811 0.000 0.000 0.000 1.000 0.000
#> GSM2856 4 0.0000 0.811 0.000 0.000 0.000 1.000 0.000
#> GSM2830 4 0.4599 0.768 0.000 0.020 0.000 0.624 0.356
#> GSM2843 4 0.4599 0.768 0.000 0.020 0.000 0.624 0.356
#> GSM2871 4 0.4599 0.768 0.000 0.020 0.000 0.624 0.356
#> GSM2831 4 0.0000 0.811 0.000 0.000 0.000 1.000 0.000
#> GSM2844 4 0.0000 0.811 0.000 0.000 0.000 1.000 0.000
#> GSM2833 4 0.0000 0.811 0.000 0.000 0.000 1.000 0.000
#> GSM2846 4 0.0000 0.811 0.000 0.000 0.000 1.000 0.000
#> GSM2835 4 0.0000 0.811 0.000 0.000 0.000 1.000 0.000
#> GSM2858 4 0.0000 0.811 0.000 0.000 0.000 1.000 0.000
#> GSM2836 2 0.0290 0.897 0.000 0.992 0.000 0.008 0.000
#> GSM2848 2 0.0290 0.897 0.000 0.992 0.000 0.008 0.000
#> GSM2828 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2837 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2839 1 0.0000 0.971 1.000 0.000 0.000 0.000 0.000
#> GSM2841 1 0.0000 0.971 1.000 0.000 0.000 0.000 0.000
#> GSM2827 2 0.0290 0.897 0.000 0.992 0.000 0.008 0.000
#> GSM2842 2 0.0290 0.897 0.000 0.992 0.000 0.008 0.000
#> GSM2845 4 0.4599 0.768 0.000 0.020 0.000 0.624 0.356
#> GSM2872 4 0.4599 0.768 0.000 0.020 0.000 0.624 0.356
#> GSM2834 4 0.4599 0.768 0.000 0.020 0.000 0.624 0.356
#> GSM2847 4 0.4599 0.768 0.000 0.020 0.000 0.624 0.356
#> GSM2849 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2850 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2838 2 0.0000 0.902 0.000 1.000 0.000 0.000 0.000
#> GSM2853 2 0.0000 0.902 0.000 1.000 0.000 0.000 0.000
#> GSM2852 2 0.1341 0.837 0.000 0.944 0.056 0.000 0.000
#> GSM2855 2 0.1341 0.837 0.000 0.944 0.056 0.000 0.000
#> GSM2840 1 0.0000 0.971 1.000 0.000 0.000 0.000 0.000
#> GSM2857 1 0.0000 0.971 1.000 0.000 0.000 0.000 0.000
#> GSM2859 2 0.0000 0.902 0.000 1.000 0.000 0.000 0.000
#> GSM2860 2 0.0000 0.902 0.000 1.000 0.000 0.000 0.000
#> GSM2861 2 0.0000 0.902 0.000 1.000 0.000 0.000 0.000
#> GSM2862 2 0.0000 0.902 0.000 1.000 0.000 0.000 0.000
#> GSM2863 2 0.0000 0.902 0.000 1.000 0.000 0.000 0.000
#> GSM2864 2 0.0000 0.902 0.000 1.000 0.000 0.000 0.000
#> GSM2865 2 0.0000 0.902 0.000 1.000 0.000 0.000 0.000
#> GSM2866 2 0.0000 0.902 0.000 1.000 0.000 0.000 0.000
#> GSM2868 2 0.0000 0.902 0.000 1.000 0.000 0.000 0.000
#> GSM2869 2 0.0000 0.902 0.000 1.000 0.000 0.000 0.000
#> GSM2851 2 0.0000 0.902 0.000 1.000 0.000 0.000 0.000
#> GSM2867 2 0.0000 0.902 0.000 1.000 0.000 0.000 0.000
#> GSM2870 2 0.0000 0.902 0.000 1.000 0.000 0.000 0.000
#> GSM2854 4 0.6326 0.563 0.000 0.160 0.000 0.460 0.380
#> GSM2873 4 0.6326 0.563 0.000 0.160 0.000 0.460 0.380
#> GSM2874 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2884 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2875 1 0.0000 0.971 1.000 0.000 0.000 0.000 0.000
#> GSM2890 1 0.0000 0.971 1.000 0.000 0.000 0.000 0.000
#> GSM2877 1 0.0000 0.971 1.000 0.000 0.000 0.000 0.000
#> GSM2892 1 0.0000 0.971 1.000 0.000 0.000 0.000 0.000
#> GSM2902 1 0.0000 0.971 1.000 0.000 0.000 0.000 0.000
#> GSM2878 1 0.0000 0.971 1.000 0.000 0.000 0.000 0.000
#> GSM2901 1 0.0000 0.971 1.000 0.000 0.000 0.000 0.000
#> GSM2879 2 0.0898 0.882 0.000 0.972 0.020 0.008 0.000
#> GSM2898 2 0.0898 0.882 0.000 0.972 0.020 0.008 0.000
#> GSM2881 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2897 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2882 4 0.0000 0.811 0.000 0.000 0.000 1.000 0.000
#> GSM2894 4 0.0000 0.811 0.000 0.000 0.000 1.000 0.000
#> GSM2883 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2895 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2885 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2886 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2887 3 0.0162 0.995 0.000 0.004 0.996 0.000 0.000
#> GSM2896 3 0.0162 0.995 0.000 0.004 0.996 0.000 0.000
#> GSM2888 2 0.0000 0.902 0.000 1.000 0.000 0.000 0.000
#> GSM2889 2 0.0000 0.902 0.000 1.000 0.000 0.000 0.000
#> GSM2876 1 0.3210 0.780 0.788 0.000 0.000 0.000 0.212
#> GSM2891 1 0.3210 0.780 0.788 0.000 0.000 0.000 0.212
#> GSM2880 1 0.0000 0.971 1.000 0.000 0.000 0.000 0.000
#> GSM2893 1 0.0000 0.971 1.000 0.000 0.000 0.000 0.000
#> GSM2821 5 0.4045 1.000 0.000 0.356 0.000 0.000 0.644
#> GSM2900 5 0.4045 1.000 0.000 0.356 0.000 0.000 0.644
#> GSM2903 5 0.4045 1.000 0.000 0.356 0.000 0.000 0.644
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM2819 5 0.1957 1.000 0.000 0.112 0.000 0.000 0.888 0.000
#> GSM2820 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2822 2 0.5321 0.442 0.000 0.596 0.000 0.136 0.004 0.264
#> GSM2832 2 0.5321 0.442 0.000 0.596 0.000 0.136 0.004 0.264
#> GSM2823 2 0.4300 0.259 0.000 0.608 0.000 0.000 0.364 0.028
#> GSM2824 2 0.4300 0.259 0.000 0.608 0.000 0.000 0.364 0.028
#> GSM2825 2 0.5321 0.442 0.000 0.596 0.000 0.136 0.004 0.264
#> GSM2826 2 0.5321 0.442 0.000 0.596 0.000 0.136 0.004 0.264
#> GSM2829 4 0.0000 0.957 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2856 4 0.0000 0.957 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2830 6 0.3244 0.871 0.000 0.000 0.000 0.268 0.000 0.732
#> GSM2843 6 0.3244 0.871 0.000 0.000 0.000 0.268 0.000 0.732
#> GSM2871 6 0.3244 0.871 0.000 0.000 0.000 0.268 0.000 0.732
#> GSM2831 4 0.1267 0.934 0.000 0.000 0.000 0.940 0.000 0.060
#> GSM2844 4 0.1267 0.934 0.000 0.000 0.000 0.940 0.000 0.060
#> GSM2833 4 0.0000 0.957 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2846 4 0.0000 0.957 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2835 4 0.0000 0.957 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2858 4 0.0000 0.957 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2836 2 0.0632 0.884 0.000 0.976 0.000 0.000 0.000 0.024
#> GSM2848 2 0.0632 0.884 0.000 0.976 0.000 0.000 0.000 0.024
#> GSM2828 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2837 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2839 1 0.1957 0.897 0.888 0.000 0.000 0.000 0.112 0.000
#> GSM2841 1 0.1957 0.897 0.888 0.000 0.000 0.000 0.112 0.000
#> GSM2827 2 0.0632 0.884 0.000 0.976 0.000 0.000 0.000 0.024
#> GSM2842 2 0.0632 0.884 0.000 0.976 0.000 0.000 0.000 0.024
#> GSM2845 6 0.3244 0.871 0.000 0.000 0.000 0.268 0.000 0.732
#> GSM2872 6 0.3244 0.871 0.000 0.000 0.000 0.268 0.000 0.732
#> GSM2834 6 0.3244 0.871 0.000 0.000 0.000 0.268 0.000 0.732
#> GSM2847 6 0.3244 0.871 0.000 0.000 0.000 0.268 0.000 0.732
#> GSM2849 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2850 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2838 2 0.0000 0.894 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2853 2 0.0000 0.894 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2852 2 0.1349 0.852 0.000 0.940 0.056 0.000 0.000 0.004
#> GSM2855 2 0.1349 0.852 0.000 0.940 0.056 0.000 0.000 0.004
#> GSM2840 1 0.1957 0.897 0.888 0.000 0.000 0.000 0.112 0.000
#> GSM2857 1 0.1957 0.897 0.888 0.000 0.000 0.000 0.112 0.000
#> GSM2859 2 0.0146 0.894 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM2860 2 0.0146 0.894 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM2861 2 0.0146 0.894 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM2862 2 0.0146 0.894 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM2863 2 0.0146 0.894 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM2864 2 0.0146 0.894 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM2865 2 0.0146 0.894 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM2866 2 0.0146 0.894 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM2868 2 0.0000 0.894 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2869 2 0.0000 0.894 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2851 2 0.0000 0.894 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2867 2 0.0000 0.894 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2870 2 0.0000 0.894 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2854 6 0.3388 0.564 0.000 0.036 0.000 0.172 0.000 0.792
#> GSM2873 6 0.3388 0.564 0.000 0.036 0.000 0.172 0.000 0.792
#> GSM2874 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2884 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2875 1 0.0000 0.938 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2890 1 0.0000 0.938 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2877 1 0.0000 0.938 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2892 1 0.0000 0.938 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2902 1 0.0000 0.938 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2878 1 0.0000 0.938 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2901 1 0.0000 0.938 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2879 2 0.1257 0.873 0.000 0.952 0.020 0.000 0.000 0.028
#> GSM2898 2 0.1257 0.873 0.000 0.952 0.020 0.000 0.000 0.028
#> GSM2881 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2897 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2882 4 0.1267 0.934 0.000 0.000 0.000 0.940 0.000 0.060
#> GSM2894 4 0.1267 0.934 0.000 0.000 0.000 0.940 0.000 0.060
#> GSM2883 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2895 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2885 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2886 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2887 3 0.0146 0.994 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM2896 3 0.0146 0.994 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM2888 2 0.0146 0.894 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM2889 2 0.0146 0.894 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM2876 1 0.2883 0.742 0.788 0.000 0.000 0.000 0.212 0.000
#> GSM2891 1 0.2883 0.742 0.788 0.000 0.000 0.000 0.212 0.000
#> GSM2880 1 0.0000 0.938 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2893 1 0.0000 0.938 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2821 5 0.1957 1.000 0.000 0.112 0.000 0.000 0.888 0.000
#> GSM2900 5 0.1957 1.000 0.000 0.112 0.000 0.000 0.888 0.000
#> GSM2903 5 0.1957 1.000 0.000 0.112 0.000 0.000 0.888 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 tissue(p) k
#> SD:hclust 67 1.21e-04 2
#> SD:hclust 84 6.67e-09 3
#> SD:hclust 84 1.99e-12 4
#> SD:hclust 78 3.91e-15 5
#> SD:hclust 78 1.99e-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["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 8229 rows and 84 columns.
#> Top rows (823, 1646, 2468, 3291, 4114) 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.229 0.504 0.653 0.3958 0.494 0.494
#> 3 3 0.391 0.764 0.780 0.4991 0.592 0.375
#> 4 4 0.613 0.901 0.834 0.1754 0.850 0.628
#> 5 5 0.765 0.836 0.841 0.0871 1.000 1.000
#> 6 6 0.764 0.731 0.811 0.0533 0.978 0.914
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM2819 1 0.9933 0.136 0.548 0.452
#> GSM2820 2 0.0938 0.618 0.012 0.988
#> GSM2822 1 0.9896 0.180 0.560 0.440
#> GSM2832 1 0.9896 0.180 0.560 0.440
#> GSM2823 2 0.8555 0.537 0.280 0.720
#> GSM2824 2 0.8555 0.537 0.280 0.720
#> GSM2825 1 0.9881 0.182 0.564 0.436
#> GSM2826 1 0.9881 0.182 0.564 0.436
#> GSM2829 1 0.9635 0.368 0.612 0.388
#> GSM2856 1 0.9635 0.368 0.612 0.388
#> GSM2830 1 0.9635 0.368 0.612 0.388
#> GSM2843 1 0.9635 0.368 0.612 0.388
#> GSM2871 1 0.9635 0.368 0.612 0.388
#> GSM2831 1 0.9635 0.368 0.612 0.388
#> GSM2844 1 0.9635 0.368 0.612 0.388
#> GSM2833 1 0.9635 0.368 0.612 0.388
#> GSM2846 1 0.9635 0.368 0.612 0.388
#> GSM2835 1 0.9635 0.368 0.612 0.388
#> GSM2858 1 0.9635 0.368 0.612 0.388
#> GSM2836 2 0.9427 0.595 0.360 0.640
#> GSM2848 2 0.9427 0.595 0.360 0.640
#> GSM2828 2 0.0938 0.618 0.012 0.988
#> GSM2837 2 0.0938 0.618 0.012 0.988
#> GSM2839 1 0.6801 0.514 0.820 0.180
#> GSM2841 1 0.6801 0.514 0.820 0.180
#> GSM2827 2 0.9427 0.595 0.360 0.640
#> GSM2842 2 0.9427 0.595 0.360 0.640
#> GSM2845 1 0.9635 0.368 0.612 0.388
#> GSM2872 1 0.9635 0.368 0.612 0.388
#> GSM2834 1 0.9635 0.368 0.612 0.388
#> GSM2847 1 0.9635 0.368 0.612 0.388
#> GSM2849 2 0.0938 0.618 0.012 0.988
#> GSM2850 2 0.0938 0.618 0.012 0.988
#> GSM2838 2 0.9460 0.595 0.364 0.636
#> GSM2853 2 0.9460 0.595 0.364 0.636
#> GSM2852 2 0.3733 0.608 0.072 0.928
#> GSM2855 2 0.3733 0.608 0.072 0.928
#> GSM2840 1 0.6801 0.514 0.820 0.180
#> GSM2857 1 0.6801 0.514 0.820 0.180
#> GSM2859 2 0.9460 0.595 0.364 0.636
#> GSM2860 2 0.9460 0.595 0.364 0.636
#> GSM2861 2 0.9460 0.595 0.364 0.636
#> GSM2862 2 0.9460 0.595 0.364 0.636
#> GSM2863 2 0.9460 0.595 0.364 0.636
#> GSM2864 2 0.9460 0.595 0.364 0.636
#> GSM2865 2 0.9460 0.595 0.364 0.636
#> GSM2866 2 0.9460 0.595 0.364 0.636
#> GSM2868 2 0.9460 0.595 0.364 0.636
#> GSM2869 2 0.9460 0.595 0.364 0.636
#> GSM2851 2 0.9460 0.595 0.364 0.636
#> GSM2867 2 0.9460 0.595 0.364 0.636
#> GSM2870 2 0.9460 0.595 0.364 0.636
#> GSM2854 1 0.9710 0.345 0.600 0.400
#> GSM2873 2 0.9850 0.413 0.428 0.572
#> GSM2874 2 0.0938 0.618 0.012 0.988
#> GSM2884 2 0.0938 0.618 0.012 0.988
#> GSM2875 1 0.7299 0.507 0.796 0.204
#> GSM2890 1 0.7299 0.507 0.796 0.204
#> GSM2877 1 0.7299 0.507 0.796 0.204
#> GSM2892 1 0.7299 0.507 0.796 0.204
#> GSM2902 1 0.7299 0.507 0.796 0.204
#> GSM2878 1 0.7299 0.507 0.796 0.204
#> GSM2901 1 0.7299 0.507 0.796 0.204
#> GSM2879 2 0.3733 0.612 0.072 0.928
#> GSM2898 2 0.3733 0.612 0.072 0.928
#> GSM2881 2 0.0938 0.618 0.012 0.988
#> GSM2897 2 0.0938 0.618 0.012 0.988
#> GSM2882 1 0.9635 0.368 0.612 0.388
#> GSM2894 1 0.9635 0.368 0.612 0.388
#> GSM2883 2 0.0938 0.618 0.012 0.988
#> GSM2895 2 0.0938 0.618 0.012 0.988
#> GSM2885 2 0.0938 0.618 0.012 0.988
#> GSM2886 2 0.0938 0.618 0.012 0.988
#> GSM2887 2 0.0938 0.618 0.012 0.988
#> GSM2896 2 0.0938 0.618 0.012 0.988
#> GSM2888 2 0.9209 0.603 0.336 0.664
#> GSM2889 2 0.9209 0.603 0.336 0.664
#> GSM2876 1 0.7139 0.510 0.804 0.196
#> GSM2891 1 0.7139 0.510 0.804 0.196
#> GSM2880 1 0.7299 0.507 0.796 0.204
#> GSM2893 1 0.7299 0.507 0.796 0.204
#> GSM2821 1 0.7674 0.501 0.776 0.224
#> GSM2900 1 0.7674 0.501 0.776 0.224
#> GSM2903 1 0.7674 0.501 0.776 0.224
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM2819 2 0.802 0.679 0.160 0.656 0.184
#> GSM2820 3 0.380 0.954 0.052 0.056 0.892
#> GSM2822 2 0.679 0.690 0.100 0.740 0.160
#> GSM2832 2 0.679 0.690 0.100 0.740 0.160
#> GSM2823 2 0.891 0.597 0.176 0.564 0.260
#> GSM2824 2 0.891 0.597 0.176 0.564 0.260
#> GSM2825 2 0.760 0.649 0.228 0.672 0.100
#> GSM2826 2 0.760 0.649 0.228 0.672 0.100
#> GSM2829 2 0.492 0.614 0.108 0.840 0.052
#> GSM2856 2 0.492 0.614 0.108 0.840 0.052
#> GSM2830 2 0.484 0.614 0.104 0.844 0.052
#> GSM2843 2 0.484 0.614 0.104 0.844 0.052
#> GSM2871 2 0.436 0.623 0.080 0.868 0.052
#> GSM2831 2 0.484 0.614 0.104 0.844 0.052
#> GSM2844 2 0.484 0.614 0.104 0.844 0.052
#> GSM2833 2 0.492 0.614 0.108 0.840 0.052
#> GSM2846 2 0.492 0.614 0.108 0.840 0.052
#> GSM2835 2 0.492 0.614 0.108 0.840 0.052
#> GSM2858 2 0.492 0.614 0.108 0.840 0.052
#> GSM2836 2 0.788 0.683 0.100 0.640 0.260
#> GSM2848 2 0.788 0.683 0.100 0.640 0.260
#> GSM2828 3 0.380 0.954 0.052 0.056 0.892
#> GSM2837 3 0.380 0.954 0.052 0.056 0.892
#> GSM2839 1 0.175 0.928 0.960 0.012 0.028
#> GSM2841 1 0.175 0.928 0.960 0.012 0.028
#> GSM2827 2 0.798 0.679 0.100 0.628 0.272
#> GSM2842 2 0.798 0.679 0.100 0.628 0.272
#> GSM2845 2 0.484 0.614 0.104 0.844 0.052
#> GSM2872 2 0.484 0.614 0.104 0.844 0.052
#> GSM2834 2 0.477 0.616 0.100 0.848 0.052
#> GSM2847 2 0.484 0.614 0.104 0.844 0.052
#> GSM2849 3 0.380 0.954 0.052 0.056 0.892
#> GSM2850 3 0.380 0.954 0.052 0.056 0.892
#> GSM2838 2 0.801 0.678 0.100 0.624 0.276
#> GSM2853 2 0.801 0.678 0.100 0.624 0.276
#> GSM2852 3 0.311 0.861 0.004 0.096 0.900
#> GSM2855 3 0.311 0.861 0.004 0.096 0.900
#> GSM2840 1 0.175 0.928 0.960 0.012 0.028
#> GSM2857 1 0.175 0.928 0.960 0.012 0.028
#> GSM2859 2 0.801 0.678 0.100 0.624 0.276
#> GSM2860 2 0.801 0.678 0.100 0.624 0.276
#> GSM2861 2 0.801 0.678 0.100 0.624 0.276
#> GSM2862 2 0.801 0.678 0.100 0.624 0.276
#> GSM2863 2 0.801 0.678 0.100 0.624 0.276
#> GSM2864 2 0.801 0.678 0.100 0.624 0.276
#> GSM2865 2 0.801 0.678 0.100 0.624 0.276
#> GSM2866 2 0.785 0.683 0.100 0.644 0.256
#> GSM2868 2 0.801 0.678 0.100 0.624 0.276
#> GSM2869 2 0.801 0.678 0.100 0.624 0.276
#> GSM2851 2 0.801 0.678 0.100 0.624 0.276
#> GSM2867 2 0.801 0.678 0.100 0.624 0.276
#> GSM2870 2 0.801 0.678 0.100 0.624 0.276
#> GSM2854 2 0.304 0.628 0.044 0.920 0.036
#> GSM2873 2 0.672 0.690 0.096 0.744 0.160
#> GSM2874 3 0.380 0.954 0.052 0.056 0.892
#> GSM2884 3 0.380 0.954 0.052 0.056 0.892
#> GSM2875 1 0.195 0.936 0.952 0.008 0.040
#> GSM2890 1 0.195 0.936 0.952 0.008 0.040
#> GSM2877 1 0.195 0.936 0.952 0.008 0.040
#> GSM2892 1 0.195 0.936 0.952 0.008 0.040
#> GSM2902 1 0.195 0.936 0.952 0.008 0.040
#> GSM2878 1 0.145 0.936 0.968 0.008 0.024
#> GSM2901 1 0.145 0.936 0.968 0.008 0.024
#> GSM2879 3 0.706 0.693 0.068 0.236 0.696
#> GSM2898 3 0.706 0.693 0.068 0.236 0.696
#> GSM2881 3 0.380 0.954 0.052 0.056 0.892
#> GSM2897 3 0.380 0.954 0.052 0.056 0.892
#> GSM2882 2 0.484 0.614 0.104 0.844 0.052
#> GSM2894 2 0.484 0.614 0.104 0.844 0.052
#> GSM2883 3 0.379 0.943 0.060 0.048 0.892
#> GSM2895 3 0.379 0.943 0.060 0.048 0.892
#> GSM2885 3 0.380 0.954 0.052 0.056 0.892
#> GSM2886 3 0.380 0.954 0.052 0.056 0.892
#> GSM2887 3 0.380 0.954 0.052 0.056 0.892
#> GSM2896 3 0.380 0.954 0.052 0.056 0.892
#> GSM2888 2 0.797 0.674 0.096 0.624 0.280
#> GSM2889 2 0.797 0.674 0.096 0.624 0.280
#> GSM2876 1 0.195 0.933 0.952 0.008 0.040
#> GSM2891 1 0.195 0.933 0.952 0.008 0.040
#> GSM2880 1 0.195 0.936 0.952 0.008 0.040
#> GSM2893 1 0.195 0.936 0.952 0.008 0.040
#> GSM2821 1 0.601 0.728 0.768 0.184 0.048
#> GSM2900 1 0.601 0.728 0.768 0.184 0.048
#> GSM2903 1 0.601 0.728 0.768 0.184 0.048
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM2819 2 0.4807 0.773 0.008 0.800 0.104 0.088
#> GSM2820 3 0.4217 0.940 0.016 0.152 0.816 0.016
#> GSM2822 2 0.4055 0.792 0.000 0.832 0.060 0.108
#> GSM2832 2 0.4055 0.792 0.000 0.832 0.060 0.108
#> GSM2823 2 0.3705 0.852 0.016 0.868 0.040 0.076
#> GSM2824 2 0.3705 0.852 0.016 0.868 0.040 0.076
#> GSM2825 2 0.5518 0.681 0.020 0.752 0.064 0.164
#> GSM2826 2 0.5518 0.681 0.020 0.752 0.064 0.164
#> GSM2829 4 0.5234 0.975 0.024 0.208 0.024 0.744
#> GSM2856 4 0.5234 0.975 0.024 0.208 0.024 0.744
#> GSM2830 4 0.5520 0.974 0.028 0.208 0.032 0.732
#> GSM2843 4 0.5520 0.974 0.028 0.208 0.032 0.732
#> GSM2871 4 0.5394 0.969 0.020 0.216 0.032 0.732
#> GSM2831 4 0.4808 0.976 0.020 0.208 0.012 0.760
#> GSM2844 4 0.4808 0.976 0.020 0.208 0.012 0.760
#> GSM2833 4 0.5424 0.973 0.024 0.208 0.032 0.736
#> GSM2846 4 0.5424 0.973 0.024 0.208 0.032 0.736
#> GSM2835 4 0.5387 0.971 0.024 0.204 0.032 0.740
#> GSM2858 4 0.5387 0.971 0.024 0.204 0.032 0.740
#> GSM2836 2 0.0188 0.936 0.000 0.996 0.000 0.004
#> GSM2848 2 0.0188 0.936 0.000 0.996 0.000 0.004
#> GSM2828 3 0.4217 0.940 0.016 0.152 0.816 0.016
#> GSM2837 3 0.4217 0.940 0.016 0.152 0.816 0.016
#> GSM2839 1 0.4653 0.882 0.820 0.020 0.080 0.080
#> GSM2841 1 0.4653 0.882 0.820 0.020 0.080 0.080
#> GSM2827 2 0.0188 0.936 0.000 0.996 0.000 0.004
#> GSM2842 2 0.0188 0.936 0.000 0.996 0.000 0.004
#> GSM2845 4 0.5520 0.974 0.028 0.208 0.032 0.732
#> GSM2872 4 0.5520 0.974 0.028 0.208 0.032 0.732
#> GSM2834 4 0.5608 0.974 0.028 0.208 0.036 0.728
#> GSM2847 4 0.5608 0.974 0.028 0.208 0.036 0.728
#> GSM2849 3 0.4217 0.940 0.016 0.152 0.816 0.016
#> GSM2850 3 0.4217 0.940 0.016 0.152 0.816 0.016
#> GSM2838 2 0.0336 0.937 0.000 0.992 0.008 0.000
#> GSM2853 2 0.0336 0.937 0.000 0.992 0.008 0.000
#> GSM2852 3 0.4467 0.920 0.000 0.172 0.788 0.040
#> GSM2855 3 0.4467 0.920 0.000 0.172 0.788 0.040
#> GSM2840 1 0.4653 0.882 0.820 0.020 0.080 0.080
#> GSM2857 1 0.4653 0.882 0.820 0.020 0.080 0.080
#> GSM2859 2 0.0000 0.937 0.000 1.000 0.000 0.000
#> GSM2860 2 0.0000 0.937 0.000 1.000 0.000 0.000
#> GSM2861 2 0.0000 0.937 0.000 1.000 0.000 0.000
#> GSM2862 2 0.0000 0.937 0.000 1.000 0.000 0.000
#> GSM2863 2 0.0000 0.937 0.000 1.000 0.000 0.000
#> GSM2864 2 0.0000 0.937 0.000 1.000 0.000 0.000
#> GSM2865 2 0.0000 0.937 0.000 1.000 0.000 0.000
#> GSM2866 2 0.0188 0.936 0.000 0.996 0.004 0.000
#> GSM2868 2 0.0336 0.937 0.000 0.992 0.008 0.000
#> GSM2869 2 0.0336 0.937 0.000 0.992 0.008 0.000
#> GSM2851 2 0.0336 0.937 0.000 0.992 0.008 0.000
#> GSM2867 2 0.0336 0.937 0.000 0.992 0.008 0.000
#> GSM2870 2 0.0336 0.937 0.000 0.992 0.008 0.000
#> GSM2854 4 0.5217 0.952 0.012 0.232 0.028 0.728
#> GSM2873 2 0.2867 0.834 0.000 0.884 0.012 0.104
#> GSM2874 3 0.4217 0.940 0.016 0.152 0.816 0.016
#> GSM2884 3 0.4217 0.940 0.016 0.152 0.816 0.016
#> GSM2875 1 0.1516 0.901 0.960 0.016 0.008 0.016
#> GSM2890 1 0.1516 0.901 0.960 0.016 0.008 0.016
#> GSM2877 1 0.1516 0.901 0.960 0.016 0.008 0.016
#> GSM2892 1 0.1516 0.901 0.960 0.016 0.008 0.016
#> GSM2902 1 0.1516 0.901 0.960 0.016 0.008 0.016
#> GSM2878 1 0.0967 0.902 0.976 0.016 0.004 0.004
#> GSM2901 1 0.0967 0.902 0.976 0.016 0.004 0.004
#> GSM2879 3 0.6152 0.425 0.008 0.464 0.496 0.032
#> GSM2898 3 0.6152 0.425 0.008 0.464 0.496 0.032
#> GSM2881 3 0.3982 0.940 0.012 0.152 0.824 0.012
#> GSM2897 3 0.3982 0.940 0.012 0.152 0.824 0.012
#> GSM2882 4 0.4732 0.974 0.020 0.200 0.012 0.768
#> GSM2894 4 0.4732 0.974 0.020 0.200 0.012 0.768
#> GSM2883 3 0.5159 0.921 0.020 0.152 0.776 0.052
#> GSM2895 3 0.5159 0.921 0.020 0.152 0.776 0.052
#> GSM2885 3 0.3982 0.940 0.012 0.152 0.824 0.012
#> GSM2886 3 0.3982 0.940 0.012 0.152 0.824 0.012
#> GSM2887 3 0.4258 0.937 0.012 0.156 0.812 0.020
#> GSM2896 3 0.4258 0.937 0.012 0.156 0.812 0.020
#> GSM2888 2 0.0921 0.919 0.000 0.972 0.000 0.028
#> GSM2889 2 0.0921 0.919 0.000 0.972 0.000 0.028
#> GSM2876 1 0.3959 0.889 0.856 0.016 0.052 0.076
#> GSM2891 1 0.3959 0.889 0.856 0.016 0.052 0.076
#> GSM2880 1 0.1516 0.901 0.960 0.016 0.008 0.016
#> GSM2893 1 0.1516 0.901 0.960 0.016 0.008 0.016
#> GSM2821 1 0.8107 0.695 0.584 0.176 0.096 0.144
#> GSM2900 1 0.8107 0.695 0.584 0.176 0.096 0.144
#> GSM2903 1 0.8107 0.695 0.584 0.176 0.096 0.144
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM2819 2 0.4608 0.699 0.000 0.644 0.008 0.012 0.336
#> GSM2820 3 0.1996 0.905 0.000 0.036 0.928 0.004 0.032
#> GSM2822 2 0.4269 0.767 0.000 0.780 0.004 0.076 0.140
#> GSM2832 2 0.4269 0.767 0.000 0.780 0.004 0.076 0.140
#> GSM2823 2 0.5177 0.743 0.004 0.660 0.020 0.028 0.288
#> GSM2824 2 0.5177 0.743 0.004 0.660 0.020 0.028 0.288
#> GSM2825 2 0.5689 0.591 0.000 0.644 0.004 0.160 0.192
#> GSM2826 2 0.5689 0.591 0.000 0.644 0.004 0.160 0.192
#> GSM2829 4 0.4089 0.920 0.000 0.100 0.008 0.804 0.088
#> GSM2856 4 0.4089 0.920 0.000 0.100 0.008 0.804 0.088
#> GSM2830 4 0.3908 0.922 0.000 0.088 0.016 0.824 0.072
#> GSM2843 4 0.3908 0.922 0.000 0.088 0.016 0.824 0.072
#> GSM2871 4 0.3908 0.922 0.000 0.088 0.016 0.824 0.072
#> GSM2831 4 0.2532 0.931 0.000 0.088 0.008 0.892 0.012
#> GSM2844 4 0.2532 0.931 0.000 0.088 0.008 0.892 0.012
#> GSM2833 4 0.4195 0.918 0.000 0.104 0.008 0.796 0.092
#> GSM2846 4 0.4195 0.918 0.000 0.104 0.008 0.796 0.092
#> GSM2835 4 0.4351 0.914 0.000 0.104 0.008 0.784 0.104
#> GSM2858 4 0.4351 0.914 0.000 0.104 0.008 0.784 0.104
#> GSM2836 2 0.1799 0.879 0.000 0.940 0.012 0.020 0.028
#> GSM2848 2 0.1799 0.879 0.000 0.940 0.012 0.020 0.028
#> GSM2828 3 0.1996 0.905 0.000 0.036 0.928 0.004 0.032
#> GSM2837 3 0.1996 0.905 0.000 0.036 0.928 0.004 0.032
#> GSM2839 1 0.4915 0.796 0.700 0.000 0.012 0.048 0.240
#> GSM2841 1 0.4915 0.796 0.700 0.000 0.012 0.048 0.240
#> GSM2827 2 0.2859 0.880 0.000 0.876 0.012 0.016 0.096
#> GSM2842 2 0.2859 0.880 0.000 0.876 0.012 0.016 0.096
#> GSM2845 4 0.3852 0.920 0.000 0.084 0.016 0.828 0.072
#> GSM2872 4 0.3852 0.920 0.000 0.084 0.016 0.828 0.072
#> GSM2834 4 0.4121 0.923 0.000 0.088 0.020 0.812 0.080
#> GSM2847 4 0.4121 0.923 0.000 0.088 0.020 0.812 0.080
#> GSM2849 3 0.2122 0.904 0.000 0.036 0.924 0.008 0.032
#> GSM2850 3 0.2122 0.904 0.000 0.036 0.924 0.008 0.032
#> GSM2838 2 0.2305 0.881 0.000 0.896 0.012 0.000 0.092
#> GSM2853 2 0.2305 0.881 0.000 0.896 0.012 0.000 0.092
#> GSM2852 3 0.4031 0.861 0.004 0.044 0.804 0.008 0.140
#> GSM2855 3 0.4031 0.861 0.004 0.044 0.804 0.008 0.140
#> GSM2840 1 0.4915 0.796 0.700 0.000 0.012 0.048 0.240
#> GSM2857 1 0.4915 0.796 0.700 0.000 0.012 0.048 0.240
#> GSM2859 2 0.1074 0.884 0.000 0.968 0.012 0.004 0.016
#> GSM2860 2 0.1074 0.884 0.000 0.968 0.012 0.004 0.016
#> GSM2861 2 0.1364 0.885 0.000 0.952 0.012 0.000 0.036
#> GSM2862 2 0.1074 0.884 0.000 0.968 0.012 0.004 0.016
#> GSM2863 2 0.1074 0.884 0.000 0.968 0.012 0.004 0.016
#> GSM2864 2 0.1074 0.884 0.000 0.968 0.012 0.004 0.016
#> GSM2865 2 0.1074 0.884 0.000 0.968 0.012 0.004 0.016
#> GSM2866 2 0.0671 0.882 0.000 0.980 0.000 0.004 0.016
#> GSM2868 2 0.2574 0.878 0.000 0.876 0.012 0.000 0.112
#> GSM2869 2 0.2574 0.878 0.000 0.876 0.012 0.000 0.112
#> GSM2851 2 0.2522 0.878 0.000 0.880 0.012 0.000 0.108
#> GSM2867 2 0.2574 0.878 0.000 0.876 0.012 0.000 0.112
#> GSM2870 2 0.2574 0.878 0.000 0.876 0.012 0.000 0.112
#> GSM2854 4 0.4455 0.912 0.000 0.112 0.012 0.780 0.096
#> GSM2873 2 0.3448 0.805 0.000 0.852 0.012 0.072 0.064
#> GSM2874 3 0.1412 0.906 0.000 0.036 0.952 0.004 0.008
#> GSM2884 3 0.1412 0.906 0.000 0.036 0.952 0.004 0.008
#> GSM2875 1 0.0162 0.847 0.996 0.000 0.000 0.004 0.000
#> GSM2890 1 0.0162 0.847 0.996 0.000 0.000 0.004 0.000
#> GSM2877 1 0.0162 0.847 0.996 0.000 0.000 0.004 0.000
#> GSM2892 1 0.0162 0.847 0.996 0.000 0.000 0.004 0.000
#> GSM2902 1 0.0162 0.847 0.996 0.000 0.000 0.004 0.000
#> GSM2878 1 0.1646 0.846 0.944 0.000 0.004 0.020 0.032
#> GSM2901 1 0.1646 0.846 0.944 0.000 0.004 0.020 0.032
#> GSM2879 3 0.6695 0.247 0.004 0.388 0.468 0.020 0.120
#> GSM2898 3 0.6695 0.247 0.004 0.388 0.468 0.020 0.120
#> GSM2881 3 0.1630 0.906 0.000 0.036 0.944 0.004 0.016
#> GSM2897 3 0.1630 0.906 0.000 0.036 0.944 0.004 0.016
#> GSM2882 4 0.2532 0.932 0.000 0.088 0.008 0.892 0.012
#> GSM2894 4 0.2532 0.932 0.000 0.088 0.008 0.892 0.012
#> GSM2883 3 0.3058 0.880 0.004 0.032 0.884 0.024 0.056
#> GSM2895 3 0.3058 0.880 0.004 0.032 0.884 0.024 0.056
#> GSM2885 3 0.1630 0.906 0.000 0.036 0.944 0.004 0.016
#> GSM2886 3 0.1630 0.906 0.000 0.036 0.944 0.004 0.016
#> GSM2887 3 0.2853 0.890 0.000 0.040 0.880 0.004 0.076
#> GSM2896 3 0.2853 0.890 0.000 0.040 0.880 0.004 0.076
#> GSM2888 2 0.3067 0.868 0.000 0.844 0.012 0.004 0.140
#> GSM2889 2 0.3067 0.868 0.000 0.844 0.012 0.004 0.140
#> GSM2876 1 0.3360 0.826 0.816 0.000 0.004 0.012 0.168
#> GSM2891 1 0.3360 0.826 0.816 0.000 0.004 0.012 0.168
#> GSM2880 1 0.0162 0.847 0.996 0.000 0.000 0.004 0.000
#> GSM2893 1 0.0162 0.847 0.996 0.000 0.000 0.004 0.000
#> GSM2821 1 0.7352 0.434 0.384 0.216 0.008 0.020 0.372
#> GSM2900 1 0.7337 0.441 0.388 0.212 0.008 0.020 0.372
#> GSM2903 1 0.7337 0.441 0.388 0.212 0.008 0.020 0.372
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM2819 5 0.4528 0.0195 0.000 0.428 0.000 0.008 0.544 NA
#> GSM2820 3 0.1718 0.8621 0.000 0.024 0.936 0.000 0.020 NA
#> GSM2822 2 0.5709 0.5324 0.000 0.652 0.000 0.088 0.124 NA
#> GSM2832 2 0.5709 0.5324 0.000 0.652 0.000 0.088 0.124 NA
#> GSM2823 2 0.5700 0.0358 0.000 0.464 0.004 0.020 0.432 NA
#> GSM2824 2 0.5700 0.0358 0.000 0.464 0.004 0.020 0.432 NA
#> GSM2825 2 0.6628 0.3464 0.000 0.544 0.000 0.152 0.132 NA
#> GSM2826 2 0.6628 0.3464 0.000 0.544 0.000 0.152 0.132 NA
#> GSM2829 4 0.3152 0.8596 0.000 0.020 0.000 0.832 0.016 NA
#> GSM2856 4 0.3152 0.8596 0.000 0.020 0.000 0.832 0.016 NA
#> GSM2830 4 0.2592 0.8584 0.000 0.016 0.000 0.864 0.004 NA
#> GSM2843 4 0.2592 0.8584 0.000 0.016 0.000 0.864 0.004 NA
#> GSM2871 4 0.3111 0.8425 0.000 0.016 0.000 0.820 0.008 NA
#> GSM2831 4 0.1672 0.8748 0.000 0.016 0.000 0.932 0.048 NA
#> GSM2844 4 0.1672 0.8748 0.000 0.016 0.000 0.932 0.048 NA
#> GSM2833 4 0.3357 0.8538 0.000 0.020 0.000 0.816 0.020 NA
#> GSM2846 4 0.3357 0.8538 0.000 0.020 0.000 0.816 0.020 NA
#> GSM2835 4 0.3438 0.8532 0.000 0.020 0.000 0.812 0.024 NA
#> GSM2858 4 0.3438 0.8532 0.000 0.020 0.000 0.812 0.024 NA
#> GSM2836 2 0.2556 0.7084 0.000 0.888 0.000 0.012 0.052 NA
#> GSM2848 2 0.2556 0.7084 0.000 0.888 0.000 0.012 0.052 NA
#> GSM2828 3 0.1802 0.8615 0.000 0.024 0.932 0.000 0.020 NA
#> GSM2837 3 0.1802 0.8615 0.000 0.024 0.932 0.000 0.020 NA
#> GSM2839 1 0.4828 0.7094 0.676 0.000 0.004 0.000 0.196 NA
#> GSM2841 1 0.4828 0.7094 0.676 0.000 0.004 0.000 0.196 NA
#> GSM2827 2 0.3955 0.7004 0.000 0.772 0.000 0.004 0.132 NA
#> GSM2842 2 0.3955 0.7004 0.000 0.772 0.000 0.004 0.132 NA
#> GSM2845 4 0.3406 0.8429 0.000 0.016 0.012 0.820 0.012 NA
#> GSM2872 4 0.3406 0.8429 0.000 0.016 0.012 0.820 0.012 NA
#> GSM2834 4 0.2704 0.8595 0.000 0.016 0.000 0.844 0.000 NA
#> GSM2847 4 0.2664 0.8606 0.000 0.016 0.000 0.848 0.000 NA
#> GSM2849 3 0.2172 0.8591 0.000 0.024 0.912 0.000 0.020 NA
#> GSM2850 3 0.2172 0.8591 0.000 0.024 0.912 0.000 0.020 NA
#> GSM2838 2 0.3686 0.6987 0.000 0.788 0.000 0.000 0.088 NA
#> GSM2853 2 0.3686 0.6987 0.000 0.788 0.000 0.000 0.088 NA
#> GSM2852 3 0.5226 0.7264 0.000 0.032 0.676 0.000 0.140 NA
#> GSM2855 3 0.5226 0.7264 0.000 0.032 0.676 0.000 0.140 NA
#> GSM2840 1 0.4828 0.7094 0.676 0.000 0.004 0.000 0.196 NA
#> GSM2857 1 0.4828 0.7094 0.676 0.000 0.004 0.000 0.196 NA
#> GSM2859 2 0.1462 0.7189 0.000 0.936 0.000 0.000 0.008 NA
#> GSM2860 2 0.1462 0.7189 0.000 0.936 0.000 0.000 0.008 NA
#> GSM2861 2 0.2147 0.7178 0.000 0.896 0.000 0.000 0.020 NA
#> GSM2862 2 0.1462 0.7189 0.000 0.936 0.000 0.000 0.008 NA
#> GSM2863 2 0.1462 0.7189 0.000 0.936 0.000 0.000 0.008 NA
#> GSM2864 2 0.1462 0.7189 0.000 0.936 0.000 0.000 0.008 NA
#> GSM2865 2 0.1462 0.7189 0.000 0.936 0.000 0.000 0.008 NA
#> GSM2866 2 0.1524 0.7173 0.000 0.932 0.000 0.000 0.008 NA
#> GSM2868 2 0.4074 0.6814 0.000 0.748 0.000 0.000 0.092 NA
#> GSM2869 2 0.4074 0.6814 0.000 0.748 0.000 0.000 0.092 NA
#> GSM2851 2 0.4050 0.6843 0.000 0.752 0.000 0.000 0.096 NA
#> GSM2867 2 0.4074 0.6814 0.000 0.748 0.000 0.000 0.092 NA
#> GSM2870 2 0.4074 0.6814 0.000 0.748 0.000 0.000 0.092 NA
#> GSM2854 4 0.3969 0.8278 0.000 0.032 0.000 0.760 0.020 NA
#> GSM2873 2 0.4747 0.6054 0.000 0.736 0.000 0.084 0.052 NA
#> GSM2874 3 0.0922 0.8643 0.000 0.024 0.968 0.000 0.004 NA
#> GSM2884 3 0.0632 0.8644 0.000 0.024 0.976 0.000 0.000 NA
#> GSM2875 1 0.0146 0.8540 0.996 0.000 0.000 0.000 0.000 NA
#> GSM2890 1 0.0146 0.8540 0.996 0.000 0.000 0.000 0.000 NA
#> GSM2877 1 0.0146 0.8540 0.996 0.000 0.000 0.000 0.000 NA
#> GSM2892 1 0.0146 0.8540 0.996 0.000 0.000 0.000 0.000 NA
#> GSM2902 1 0.0146 0.8540 0.996 0.000 0.000 0.000 0.000 NA
#> GSM2878 1 0.1562 0.8452 0.940 0.000 0.000 0.004 0.032 NA
#> GSM2901 1 0.1562 0.8452 0.940 0.000 0.000 0.004 0.032 NA
#> GSM2879 3 0.7330 0.1321 0.000 0.340 0.360 0.004 0.184 NA
#> GSM2898 3 0.7330 0.1321 0.000 0.340 0.360 0.004 0.184 NA
#> GSM2881 3 0.1138 0.8650 0.000 0.024 0.960 0.000 0.004 NA
#> GSM2897 3 0.1138 0.8650 0.000 0.024 0.960 0.000 0.004 NA
#> GSM2882 4 0.1913 0.8749 0.000 0.016 0.000 0.924 0.044 NA
#> GSM2894 4 0.1913 0.8749 0.000 0.016 0.000 0.924 0.044 NA
#> GSM2883 3 0.3150 0.8314 0.000 0.024 0.848 0.000 0.032 NA
#> GSM2895 3 0.3150 0.8314 0.000 0.024 0.848 0.000 0.032 NA
#> GSM2885 3 0.1138 0.8650 0.000 0.024 0.960 0.000 0.004 NA
#> GSM2886 3 0.1138 0.8650 0.000 0.024 0.960 0.000 0.004 NA
#> GSM2887 3 0.3467 0.8249 0.000 0.024 0.832 0.000 0.068 NA
#> GSM2896 3 0.3467 0.8249 0.000 0.024 0.832 0.000 0.068 NA
#> GSM2888 2 0.4465 0.6728 0.000 0.712 0.000 0.000 0.144 NA
#> GSM2889 2 0.4465 0.6728 0.000 0.712 0.000 0.000 0.144 NA
#> GSM2876 1 0.3817 0.7533 0.780 0.000 0.008 0.008 0.172 NA
#> GSM2891 1 0.3817 0.7533 0.780 0.000 0.008 0.008 0.172 NA
#> GSM2880 1 0.0146 0.8538 0.996 0.000 0.000 0.004 0.000 NA
#> GSM2893 1 0.0146 0.8538 0.996 0.000 0.000 0.004 0.000 NA
#> GSM2821 5 0.5430 0.7519 0.260 0.128 0.000 0.012 0.600 NA
#> GSM2900 5 0.5430 0.7519 0.260 0.128 0.000 0.012 0.600 NA
#> GSM2903 5 0.5430 0.7519 0.260 0.128 0.000 0.012 0.600 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> SD:kmeans 60 1.68e-04 2
#> SD:kmeans 84 6.67e-09 3
#> SD:kmeans 82 8.86e-12 4
#> SD:kmeans 79 3.12e-11 5
#> SD:kmeans 77 6.70e-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["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 8229 rows and 84 columns.
#> Top rows (823, 1646, 2468, 3291, 4114) 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 0.937 0.949 0.5061 0.494 0.494
#> 3 3 0.609 0.786 0.870 0.2723 0.598 0.364
#> 4 4 0.964 0.964 0.983 0.1733 0.876 0.664
#> 5 5 0.891 0.879 0.896 0.0463 0.971 0.880
#> 6 6 0.869 0.757 0.839 0.0389 0.961 0.823
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM2819 1 0.0000 0.952 1.000 0.000
#> GSM2820 2 0.0000 0.937 0.000 1.000
#> GSM2822 1 0.0000 0.952 1.000 0.000
#> GSM2832 1 0.0000 0.952 1.000 0.000
#> GSM2823 2 0.0938 0.933 0.012 0.988
#> GSM2824 2 0.0938 0.933 0.012 0.988
#> GSM2825 1 0.0000 0.952 1.000 0.000
#> GSM2826 1 0.0000 0.952 1.000 0.000
#> GSM2829 1 0.0376 0.954 0.996 0.004
#> GSM2856 1 0.0376 0.954 0.996 0.004
#> GSM2830 1 0.0376 0.954 0.996 0.004
#> GSM2843 1 0.0376 0.954 0.996 0.004
#> GSM2871 1 0.0376 0.954 0.996 0.004
#> GSM2831 1 0.0376 0.954 0.996 0.004
#> GSM2844 1 0.0376 0.954 0.996 0.004
#> GSM2833 1 0.0376 0.954 0.996 0.004
#> GSM2846 1 0.0376 0.954 0.996 0.004
#> GSM2835 1 0.0376 0.954 0.996 0.004
#> GSM2858 1 0.0376 0.954 0.996 0.004
#> GSM2836 2 0.4562 0.942 0.096 0.904
#> GSM2848 2 0.4562 0.942 0.096 0.904
#> GSM2828 2 0.0000 0.937 0.000 1.000
#> GSM2837 2 0.0000 0.937 0.000 1.000
#> GSM2839 1 0.4431 0.941 0.908 0.092
#> GSM2841 1 0.4431 0.941 0.908 0.092
#> GSM2827 2 0.4562 0.942 0.096 0.904
#> GSM2842 2 0.4562 0.942 0.096 0.904
#> GSM2845 1 0.0376 0.954 0.996 0.004
#> GSM2872 1 0.0376 0.954 0.996 0.004
#> GSM2834 1 0.0376 0.954 0.996 0.004
#> GSM2847 1 0.0376 0.954 0.996 0.004
#> GSM2849 2 0.0000 0.937 0.000 1.000
#> GSM2850 2 0.0000 0.937 0.000 1.000
#> GSM2838 2 0.4562 0.942 0.096 0.904
#> GSM2853 2 0.4562 0.942 0.096 0.904
#> GSM2852 2 0.2423 0.941 0.040 0.960
#> GSM2855 2 0.2423 0.941 0.040 0.960
#> GSM2840 1 0.4431 0.941 0.908 0.092
#> GSM2857 1 0.4431 0.941 0.908 0.092
#> GSM2859 2 0.4562 0.942 0.096 0.904
#> GSM2860 2 0.4562 0.942 0.096 0.904
#> GSM2861 2 0.4562 0.942 0.096 0.904
#> GSM2862 2 0.4562 0.942 0.096 0.904
#> GSM2863 2 0.4562 0.942 0.096 0.904
#> GSM2864 2 0.4562 0.942 0.096 0.904
#> GSM2865 2 0.4562 0.942 0.096 0.904
#> GSM2866 2 0.4562 0.942 0.096 0.904
#> GSM2868 2 0.4562 0.942 0.096 0.904
#> GSM2869 2 0.4562 0.942 0.096 0.904
#> GSM2851 2 0.4562 0.942 0.096 0.904
#> GSM2867 2 0.4562 0.942 0.096 0.904
#> GSM2870 2 0.4562 0.942 0.096 0.904
#> GSM2854 1 0.0376 0.954 0.996 0.004
#> GSM2873 2 0.9909 0.363 0.444 0.556
#> GSM2874 2 0.0000 0.937 0.000 1.000
#> GSM2884 2 0.0000 0.937 0.000 1.000
#> GSM2875 1 0.4431 0.941 0.908 0.092
#> GSM2890 1 0.4431 0.941 0.908 0.092
#> GSM2877 1 0.4431 0.941 0.908 0.092
#> GSM2892 1 0.4431 0.941 0.908 0.092
#> GSM2902 1 0.4431 0.941 0.908 0.092
#> GSM2878 1 0.4431 0.941 0.908 0.092
#> GSM2901 1 0.4431 0.941 0.908 0.092
#> GSM2879 2 0.0000 0.937 0.000 1.000
#> GSM2898 2 0.0000 0.937 0.000 1.000
#> GSM2881 2 0.0000 0.937 0.000 1.000
#> GSM2897 2 0.0000 0.937 0.000 1.000
#> GSM2882 1 0.0376 0.954 0.996 0.004
#> GSM2894 1 0.0376 0.954 0.996 0.004
#> GSM2883 2 0.0000 0.937 0.000 1.000
#> GSM2895 2 0.0000 0.937 0.000 1.000
#> GSM2885 2 0.0000 0.937 0.000 1.000
#> GSM2886 2 0.0000 0.937 0.000 1.000
#> GSM2887 2 0.0000 0.937 0.000 1.000
#> GSM2896 2 0.0000 0.937 0.000 1.000
#> GSM2888 2 0.4562 0.942 0.096 0.904
#> GSM2889 2 0.4562 0.942 0.096 0.904
#> GSM2876 1 0.4431 0.941 0.908 0.092
#> GSM2891 1 0.4431 0.941 0.908 0.092
#> GSM2880 1 0.4431 0.941 0.908 0.092
#> GSM2893 1 0.4431 0.941 0.908 0.092
#> GSM2821 1 0.4431 0.941 0.908 0.092
#> GSM2900 1 0.4431 0.941 0.908 0.092
#> GSM2903 1 0.4431 0.941 0.908 0.092
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM2819 1 0.6045 0.329 0.620 0.380 0.00
#> GSM2820 3 0.5560 1.000 0.000 0.300 0.70
#> GSM2822 2 0.5560 0.704 0.000 0.700 0.30
#> GSM2832 2 0.5560 0.704 0.000 0.700 0.30
#> GSM2823 1 0.5506 0.692 0.764 0.016 0.22
#> GSM2824 1 0.5506 0.692 0.764 0.016 0.22
#> GSM2825 1 0.2165 0.901 0.936 0.064 0.00
#> GSM2826 1 0.2165 0.901 0.936 0.064 0.00
#> GSM2829 2 0.8362 0.684 0.112 0.588 0.30
#> GSM2856 2 0.8362 0.684 0.112 0.588 0.30
#> GSM2830 2 0.8362 0.684 0.112 0.588 0.30
#> GSM2843 2 0.8301 0.686 0.108 0.592 0.30
#> GSM2871 2 0.7749 0.697 0.076 0.624 0.30
#> GSM2831 2 0.9800 0.537 0.268 0.432 0.30
#> GSM2844 2 0.9800 0.537 0.268 0.432 0.30
#> GSM2833 2 0.8362 0.684 0.112 0.588 0.30
#> GSM2846 2 0.8362 0.684 0.112 0.588 0.30
#> GSM2835 2 0.9800 0.537 0.268 0.432 0.30
#> GSM2858 2 0.9800 0.537 0.268 0.432 0.30
#> GSM2836 2 0.0000 0.673 0.000 1.000 0.00
#> GSM2848 2 0.0000 0.673 0.000 1.000 0.00
#> GSM2828 3 0.5560 1.000 0.000 0.300 0.70
#> GSM2837 3 0.5560 1.000 0.000 0.300 0.70
#> GSM2839 1 0.0000 0.950 1.000 0.000 0.00
#> GSM2841 1 0.0000 0.950 1.000 0.000 0.00
#> GSM2827 2 0.0000 0.673 0.000 1.000 0.00
#> GSM2842 2 0.0000 0.673 0.000 1.000 0.00
#> GSM2845 2 0.9783 0.542 0.264 0.436 0.30
#> GSM2872 2 0.9833 0.525 0.276 0.424 0.30
#> GSM2834 2 0.8301 0.686 0.108 0.592 0.30
#> GSM2847 2 0.8362 0.684 0.112 0.588 0.30
#> GSM2849 3 0.5560 1.000 0.000 0.300 0.70
#> GSM2850 3 0.5560 1.000 0.000 0.300 0.70
#> GSM2838 2 0.0000 0.673 0.000 1.000 0.00
#> GSM2853 2 0.0000 0.673 0.000 1.000 0.00
#> GSM2852 3 0.5560 1.000 0.000 0.300 0.70
#> GSM2855 3 0.5560 1.000 0.000 0.300 0.70
#> GSM2840 1 0.0000 0.950 1.000 0.000 0.00
#> GSM2857 1 0.0000 0.950 1.000 0.000 0.00
#> GSM2859 2 0.0000 0.673 0.000 1.000 0.00
#> GSM2860 2 0.0000 0.673 0.000 1.000 0.00
#> GSM2861 2 0.0000 0.673 0.000 1.000 0.00
#> GSM2862 2 0.0000 0.673 0.000 1.000 0.00
#> GSM2863 2 0.0000 0.673 0.000 1.000 0.00
#> GSM2864 2 0.0000 0.673 0.000 1.000 0.00
#> GSM2865 2 0.0000 0.673 0.000 1.000 0.00
#> GSM2866 2 0.0000 0.673 0.000 1.000 0.00
#> GSM2868 2 0.0000 0.673 0.000 1.000 0.00
#> GSM2869 2 0.0000 0.673 0.000 1.000 0.00
#> GSM2851 2 0.0000 0.673 0.000 1.000 0.00
#> GSM2867 2 0.0000 0.673 0.000 1.000 0.00
#> GSM2870 2 0.0000 0.673 0.000 1.000 0.00
#> GSM2854 2 0.6744 0.706 0.032 0.668 0.30
#> GSM2873 2 0.5560 0.704 0.000 0.700 0.30
#> GSM2874 3 0.5560 1.000 0.000 0.300 0.70
#> GSM2884 3 0.5560 1.000 0.000 0.300 0.70
#> GSM2875 1 0.0000 0.950 1.000 0.000 0.00
#> GSM2890 1 0.0000 0.950 1.000 0.000 0.00
#> GSM2877 1 0.0000 0.950 1.000 0.000 0.00
#> GSM2892 1 0.0000 0.950 1.000 0.000 0.00
#> GSM2902 1 0.0000 0.950 1.000 0.000 0.00
#> GSM2878 1 0.0000 0.950 1.000 0.000 0.00
#> GSM2901 1 0.0000 0.950 1.000 0.000 0.00
#> GSM2879 3 0.5560 1.000 0.000 0.300 0.70
#> GSM2898 3 0.5560 1.000 0.000 0.300 0.70
#> GSM2881 3 0.5560 1.000 0.000 0.300 0.70
#> GSM2897 3 0.5560 1.000 0.000 0.300 0.70
#> GSM2882 2 0.9817 0.531 0.272 0.428 0.30
#> GSM2894 2 0.9817 0.531 0.272 0.428 0.30
#> GSM2883 3 0.5560 1.000 0.000 0.300 0.70
#> GSM2895 3 0.5560 1.000 0.000 0.300 0.70
#> GSM2885 3 0.5560 1.000 0.000 0.300 0.70
#> GSM2886 3 0.5560 1.000 0.000 0.300 0.70
#> GSM2887 3 0.5560 1.000 0.000 0.300 0.70
#> GSM2896 3 0.5560 1.000 0.000 0.300 0.70
#> GSM2888 2 0.4796 0.199 0.000 0.780 0.22
#> GSM2889 2 0.4796 0.199 0.000 0.780 0.22
#> GSM2876 1 0.0000 0.950 1.000 0.000 0.00
#> GSM2891 1 0.0000 0.950 1.000 0.000 0.00
#> GSM2880 1 0.0000 0.950 1.000 0.000 0.00
#> GSM2893 1 0.0000 0.950 1.000 0.000 0.00
#> GSM2821 1 0.0237 0.948 0.996 0.004 0.00
#> GSM2900 1 0.0237 0.948 0.996 0.004 0.00
#> GSM2903 1 0.0237 0.948 0.996 0.004 0.00
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM2819 1 0.480 0.415 0.616 0.384 0 0.00
#> GSM2820 3 0.000 1.000 0.000 0.000 1 0.00
#> GSM2822 2 0.265 0.871 0.000 0.880 0 0.12
#> GSM2832 2 0.265 0.871 0.000 0.880 0 0.12
#> GSM2823 1 0.139 0.918 0.952 0.048 0 0.00
#> GSM2824 1 0.139 0.918 0.952 0.048 0 0.00
#> GSM2825 1 0.596 0.655 0.692 0.128 0 0.18
#> GSM2826 1 0.596 0.655 0.692 0.128 0 0.18
#> GSM2829 4 0.000 1.000 0.000 0.000 0 1.00
#> GSM2856 4 0.000 1.000 0.000 0.000 0 1.00
#> GSM2830 4 0.000 1.000 0.000 0.000 0 1.00
#> GSM2843 4 0.000 1.000 0.000 0.000 0 1.00
#> GSM2871 4 0.000 1.000 0.000 0.000 0 1.00
#> GSM2831 4 0.000 1.000 0.000 0.000 0 1.00
#> GSM2844 4 0.000 1.000 0.000 0.000 0 1.00
#> GSM2833 4 0.000 1.000 0.000 0.000 0 1.00
#> GSM2846 4 0.000 1.000 0.000 0.000 0 1.00
#> GSM2835 4 0.000 1.000 0.000 0.000 0 1.00
#> GSM2858 4 0.000 1.000 0.000 0.000 0 1.00
#> GSM2836 2 0.000 0.983 0.000 1.000 0 0.00
#> GSM2848 2 0.000 0.983 0.000 1.000 0 0.00
#> GSM2828 3 0.000 1.000 0.000 0.000 1 0.00
#> GSM2837 3 0.000 1.000 0.000 0.000 1 0.00
#> GSM2839 1 0.000 0.951 1.000 0.000 0 0.00
#> GSM2841 1 0.000 0.951 1.000 0.000 0 0.00
#> GSM2827 2 0.000 0.983 0.000 1.000 0 0.00
#> GSM2842 2 0.000 0.983 0.000 1.000 0 0.00
#> GSM2845 4 0.000 1.000 0.000 0.000 0 1.00
#> GSM2872 4 0.000 1.000 0.000 0.000 0 1.00
#> GSM2834 4 0.000 1.000 0.000 0.000 0 1.00
#> GSM2847 4 0.000 1.000 0.000 0.000 0 1.00
#> GSM2849 3 0.000 1.000 0.000 0.000 1 0.00
#> GSM2850 3 0.000 1.000 0.000 0.000 1 0.00
#> GSM2838 2 0.000 0.983 0.000 1.000 0 0.00
#> GSM2853 2 0.000 0.983 0.000 1.000 0 0.00
#> GSM2852 3 0.000 1.000 0.000 0.000 1 0.00
#> GSM2855 3 0.000 1.000 0.000 0.000 1 0.00
#> GSM2840 1 0.000 0.951 1.000 0.000 0 0.00
#> GSM2857 1 0.000 0.951 1.000 0.000 0 0.00
#> GSM2859 2 0.000 0.983 0.000 1.000 0 0.00
#> GSM2860 2 0.000 0.983 0.000 1.000 0 0.00
#> GSM2861 2 0.000 0.983 0.000 1.000 0 0.00
#> GSM2862 2 0.000 0.983 0.000 1.000 0 0.00
#> GSM2863 2 0.000 0.983 0.000 1.000 0 0.00
#> GSM2864 2 0.000 0.983 0.000 1.000 0 0.00
#> GSM2865 2 0.000 0.983 0.000 1.000 0 0.00
#> GSM2866 2 0.000 0.983 0.000 1.000 0 0.00
#> GSM2868 2 0.000 0.983 0.000 1.000 0 0.00
#> GSM2869 2 0.000 0.983 0.000 1.000 0 0.00
#> GSM2851 2 0.000 0.983 0.000 1.000 0 0.00
#> GSM2867 2 0.000 0.983 0.000 1.000 0 0.00
#> GSM2870 2 0.000 0.983 0.000 1.000 0 0.00
#> GSM2854 4 0.000 1.000 0.000 0.000 0 1.00
#> GSM2873 2 0.265 0.871 0.000 0.880 0 0.12
#> GSM2874 3 0.000 1.000 0.000 0.000 1 0.00
#> GSM2884 3 0.000 1.000 0.000 0.000 1 0.00
#> GSM2875 1 0.000 0.951 1.000 0.000 0 0.00
#> GSM2890 1 0.000 0.951 1.000 0.000 0 0.00
#> GSM2877 1 0.000 0.951 1.000 0.000 0 0.00
#> GSM2892 1 0.000 0.951 1.000 0.000 0 0.00
#> GSM2902 1 0.000 0.951 1.000 0.000 0 0.00
#> GSM2878 1 0.000 0.951 1.000 0.000 0 0.00
#> GSM2901 1 0.000 0.951 1.000 0.000 0 0.00
#> GSM2879 3 0.000 1.000 0.000 0.000 1 0.00
#> GSM2898 3 0.000 1.000 0.000 0.000 1 0.00
#> GSM2881 3 0.000 1.000 0.000 0.000 1 0.00
#> GSM2897 3 0.000 1.000 0.000 0.000 1 0.00
#> GSM2882 4 0.000 1.000 0.000 0.000 0 1.00
#> GSM2894 4 0.000 1.000 0.000 0.000 0 1.00
#> GSM2883 3 0.000 1.000 0.000 0.000 1 0.00
#> GSM2895 3 0.000 1.000 0.000 0.000 1 0.00
#> GSM2885 3 0.000 1.000 0.000 0.000 1 0.00
#> GSM2886 3 0.000 1.000 0.000 0.000 1 0.00
#> GSM2887 3 0.000 1.000 0.000 0.000 1 0.00
#> GSM2896 3 0.000 1.000 0.000 0.000 1 0.00
#> GSM2888 2 0.000 0.983 0.000 1.000 0 0.00
#> GSM2889 2 0.000 0.983 0.000 1.000 0 0.00
#> GSM2876 1 0.000 0.951 1.000 0.000 0 0.00
#> GSM2891 1 0.000 0.951 1.000 0.000 0 0.00
#> GSM2880 1 0.000 0.951 1.000 0.000 0 0.00
#> GSM2893 1 0.000 0.951 1.000 0.000 0 0.00
#> GSM2821 1 0.000 0.951 1.000 0.000 0 0.00
#> GSM2900 1 0.000 0.951 1.000 0.000 0 0.00
#> GSM2903 1 0.000 0.951 1.000 0.000 0 0.00
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM2819 5 0.6332 0.612 0.264 0.212 0.000 0.000 0.524
#> GSM2820 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2822 2 0.4768 0.667 0.000 0.592 0.000 0.024 0.384
#> GSM2832 2 0.4768 0.667 0.000 0.592 0.000 0.024 0.384
#> GSM2823 5 0.5227 0.845 0.448 0.044 0.000 0.000 0.508
#> GSM2824 5 0.5227 0.845 0.448 0.044 0.000 0.000 0.508
#> GSM2825 1 0.5620 0.279 0.504 0.020 0.000 0.036 0.440
#> GSM2826 1 0.5620 0.279 0.504 0.020 0.000 0.036 0.440
#> GSM2829 4 0.2329 0.920 0.000 0.000 0.000 0.876 0.124
#> GSM2856 4 0.2329 0.920 0.000 0.000 0.000 0.876 0.124
#> GSM2830 4 0.0000 0.950 0.000 0.000 0.000 1.000 0.000
#> GSM2843 4 0.0000 0.950 0.000 0.000 0.000 1.000 0.000
#> GSM2871 4 0.0000 0.950 0.000 0.000 0.000 1.000 0.000
#> GSM2831 4 0.0000 0.950 0.000 0.000 0.000 1.000 0.000
#> GSM2844 4 0.0000 0.950 0.000 0.000 0.000 1.000 0.000
#> GSM2833 4 0.2329 0.920 0.000 0.000 0.000 0.876 0.124
#> GSM2846 4 0.2329 0.920 0.000 0.000 0.000 0.876 0.124
#> GSM2835 4 0.2329 0.920 0.000 0.000 0.000 0.876 0.124
#> GSM2858 4 0.2329 0.920 0.000 0.000 0.000 0.876 0.124
#> GSM2836 2 0.3177 0.866 0.000 0.792 0.000 0.000 0.208
#> GSM2848 2 0.3177 0.866 0.000 0.792 0.000 0.000 0.208
#> GSM2828 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2837 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2839 1 0.2471 0.743 0.864 0.000 0.000 0.000 0.136
#> GSM2841 1 0.2471 0.743 0.864 0.000 0.000 0.000 0.136
#> GSM2827 2 0.1270 0.881 0.000 0.948 0.000 0.000 0.052
#> GSM2842 2 0.1043 0.878 0.000 0.960 0.000 0.000 0.040
#> GSM2845 4 0.0000 0.950 0.000 0.000 0.000 1.000 0.000
#> GSM2872 4 0.0000 0.950 0.000 0.000 0.000 1.000 0.000
#> GSM2834 4 0.0000 0.950 0.000 0.000 0.000 1.000 0.000
#> GSM2847 4 0.0000 0.950 0.000 0.000 0.000 1.000 0.000
#> GSM2849 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2850 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2838 2 0.0404 0.883 0.000 0.988 0.000 0.000 0.012
#> GSM2853 2 0.0404 0.883 0.000 0.988 0.000 0.000 0.012
#> GSM2852 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2855 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2840 1 0.2471 0.743 0.864 0.000 0.000 0.000 0.136
#> GSM2857 1 0.2471 0.743 0.864 0.000 0.000 0.000 0.136
#> GSM2859 2 0.2773 0.882 0.000 0.836 0.000 0.000 0.164
#> GSM2860 2 0.2773 0.882 0.000 0.836 0.000 0.000 0.164
#> GSM2861 2 0.2074 0.886 0.000 0.896 0.000 0.000 0.104
#> GSM2862 2 0.2773 0.882 0.000 0.836 0.000 0.000 0.164
#> GSM2863 2 0.2773 0.882 0.000 0.836 0.000 0.000 0.164
#> GSM2864 2 0.2773 0.882 0.000 0.836 0.000 0.000 0.164
#> GSM2865 2 0.2773 0.882 0.000 0.836 0.000 0.000 0.164
#> GSM2866 2 0.2773 0.882 0.000 0.836 0.000 0.000 0.164
#> GSM2868 2 0.0404 0.883 0.000 0.988 0.000 0.000 0.012
#> GSM2869 2 0.0404 0.883 0.000 0.988 0.000 0.000 0.012
#> GSM2851 2 0.0404 0.883 0.000 0.988 0.000 0.000 0.012
#> GSM2867 2 0.0404 0.883 0.000 0.988 0.000 0.000 0.012
#> GSM2870 2 0.0404 0.883 0.000 0.988 0.000 0.000 0.012
#> GSM2854 4 0.2516 0.909 0.000 0.000 0.000 0.860 0.140
#> GSM2873 2 0.4456 0.750 0.000 0.660 0.000 0.020 0.320
#> GSM2874 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2884 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2875 1 0.0000 0.824 1.000 0.000 0.000 0.000 0.000
#> GSM2890 1 0.0000 0.824 1.000 0.000 0.000 0.000 0.000
#> GSM2877 1 0.0000 0.824 1.000 0.000 0.000 0.000 0.000
#> GSM2892 1 0.0000 0.824 1.000 0.000 0.000 0.000 0.000
#> GSM2902 1 0.0000 0.824 1.000 0.000 0.000 0.000 0.000
#> GSM2878 1 0.0000 0.824 1.000 0.000 0.000 0.000 0.000
#> GSM2901 1 0.0000 0.824 1.000 0.000 0.000 0.000 0.000
#> GSM2879 3 0.0290 0.993 0.000 0.000 0.992 0.000 0.008
#> GSM2898 3 0.0290 0.993 0.000 0.000 0.992 0.000 0.008
#> GSM2881 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2897 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2882 4 0.0000 0.950 0.000 0.000 0.000 1.000 0.000
#> GSM2894 4 0.0000 0.950 0.000 0.000 0.000 1.000 0.000
#> GSM2883 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2895 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2885 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2886 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2887 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2896 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2888 2 0.0609 0.883 0.000 0.980 0.000 0.000 0.020
#> GSM2889 2 0.0609 0.883 0.000 0.980 0.000 0.000 0.020
#> GSM2876 1 0.0162 0.820 0.996 0.000 0.000 0.000 0.004
#> GSM2891 1 0.0162 0.820 0.996 0.000 0.000 0.000 0.004
#> GSM2880 1 0.0000 0.824 1.000 0.000 0.000 0.000 0.000
#> GSM2893 1 0.0000 0.824 1.000 0.000 0.000 0.000 0.000
#> GSM2821 5 0.4307 0.839 0.496 0.000 0.000 0.000 0.504
#> GSM2900 5 0.4307 0.839 0.496 0.000 0.000 0.000 0.504
#> GSM2903 5 0.4307 0.839 0.496 0.000 0.000 0.000 0.504
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM2819 5 0.5183 0.744 0.128 0.160 0.000 0.000 0.680 0.032
#> GSM2820 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2822 6 0.3487 0.483 0.000 0.224 0.000 0.000 0.020 0.756
#> GSM2832 6 0.3487 0.483 0.000 0.224 0.000 0.000 0.020 0.756
#> GSM2823 5 0.4389 0.830 0.208 0.076 0.004 0.000 0.712 0.000
#> GSM2824 5 0.4389 0.830 0.208 0.076 0.004 0.000 0.712 0.000
#> GSM2825 6 0.4862 0.287 0.216 0.020 0.000 0.000 0.080 0.684
#> GSM2826 6 0.4862 0.287 0.216 0.020 0.000 0.000 0.080 0.684
#> GSM2829 4 0.3104 0.852 0.000 0.000 0.000 0.800 0.016 0.184
#> GSM2856 4 0.3104 0.852 0.000 0.000 0.000 0.800 0.016 0.184
#> GSM2830 4 0.0146 0.908 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM2843 4 0.0146 0.908 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM2871 4 0.0146 0.908 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM2831 4 0.0146 0.909 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM2844 4 0.0146 0.909 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM2833 4 0.3104 0.852 0.000 0.000 0.000 0.800 0.016 0.184
#> GSM2846 4 0.3104 0.852 0.000 0.000 0.000 0.800 0.016 0.184
#> GSM2835 4 0.3168 0.847 0.000 0.000 0.000 0.792 0.016 0.192
#> GSM2858 4 0.3168 0.847 0.000 0.000 0.000 0.792 0.016 0.192
#> GSM2836 6 0.5658 -0.203 0.000 0.380 0.000 0.000 0.156 0.464
#> GSM2848 6 0.5662 -0.208 0.000 0.384 0.000 0.000 0.156 0.460
#> GSM2828 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2837 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2839 1 0.3871 0.751 0.768 0.000 0.000 0.000 0.084 0.148
#> GSM2841 1 0.3871 0.751 0.768 0.000 0.000 0.000 0.084 0.148
#> GSM2827 2 0.4079 0.456 0.000 0.744 0.000 0.000 0.084 0.172
#> GSM2842 2 0.3978 0.461 0.000 0.756 0.000 0.000 0.084 0.160
#> GSM2845 4 0.0260 0.907 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM2872 4 0.0146 0.908 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM2834 4 0.0717 0.906 0.000 0.000 0.000 0.976 0.008 0.016
#> GSM2847 4 0.0622 0.907 0.000 0.000 0.000 0.980 0.008 0.012
#> GSM2849 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2850 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2838 2 0.0146 0.628 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM2853 2 0.0146 0.628 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM2852 3 0.0520 0.978 0.000 0.000 0.984 0.000 0.008 0.008
#> GSM2855 3 0.0520 0.978 0.000 0.000 0.984 0.000 0.008 0.008
#> GSM2840 1 0.3871 0.751 0.768 0.000 0.000 0.000 0.084 0.148
#> GSM2857 1 0.3871 0.751 0.768 0.000 0.000 0.000 0.084 0.148
#> GSM2859 2 0.5583 0.394 0.000 0.508 0.000 0.000 0.156 0.336
#> GSM2860 2 0.5583 0.394 0.000 0.508 0.000 0.000 0.156 0.336
#> GSM2861 2 0.5411 0.421 0.000 0.560 0.000 0.000 0.152 0.288
#> GSM2862 2 0.5583 0.394 0.000 0.508 0.000 0.000 0.156 0.336
#> GSM2863 2 0.5583 0.394 0.000 0.508 0.000 0.000 0.156 0.336
#> GSM2864 2 0.5583 0.394 0.000 0.508 0.000 0.000 0.156 0.336
#> GSM2865 2 0.5583 0.394 0.000 0.508 0.000 0.000 0.156 0.336
#> GSM2866 2 0.5583 0.394 0.000 0.508 0.000 0.000 0.156 0.336
#> GSM2868 2 0.0260 0.628 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM2869 2 0.0260 0.628 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM2851 2 0.0260 0.628 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM2867 2 0.0260 0.628 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM2870 2 0.0260 0.628 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM2854 4 0.3314 0.797 0.000 0.000 0.000 0.740 0.004 0.256
#> GSM2873 6 0.3853 0.403 0.000 0.196 0.000 0.004 0.044 0.756
#> GSM2874 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2884 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2875 1 0.0000 0.911 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2890 1 0.0000 0.911 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2877 1 0.0000 0.911 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2892 1 0.0000 0.911 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2902 1 0.0000 0.911 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2878 1 0.0000 0.911 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2901 1 0.0000 0.911 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2879 3 0.2039 0.908 0.000 0.000 0.904 0.000 0.076 0.020
#> GSM2898 3 0.2039 0.908 0.000 0.000 0.904 0.000 0.076 0.020
#> GSM2881 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2897 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2882 4 0.0291 0.909 0.000 0.000 0.000 0.992 0.004 0.004
#> GSM2894 4 0.0291 0.909 0.000 0.000 0.000 0.992 0.004 0.004
#> GSM2883 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2895 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2885 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2886 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2887 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2896 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2888 2 0.1625 0.592 0.000 0.928 0.000 0.000 0.012 0.060
#> GSM2889 2 0.1625 0.592 0.000 0.928 0.000 0.000 0.012 0.060
#> GSM2876 1 0.0458 0.900 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM2891 1 0.0458 0.900 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM2880 1 0.0000 0.911 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2893 1 0.0000 0.911 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2821 5 0.3871 0.836 0.308 0.000 0.000 0.000 0.676 0.016
#> GSM2900 5 0.3871 0.836 0.308 0.000 0.000 0.000 0.676 0.016
#> GSM2903 5 0.3871 0.836 0.308 0.000 0.000 0.000 0.676 0.016
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> SD:skmeans 83 3.39e-05 2
#> SD:skmeans 81 6.98e-09 3
#> SD:skmeans 83 4.22e-12 4
#> SD:skmeans 82 3.49e-15 5
#> SD:skmeans 67 6.10e-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["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 8229 rows and 84 columns.
#> Top rows (823, 1646, 2468, 3291, 4114) are extracted by 'SD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.982 0.979 0.3503 0.646 0.646
#> 3 3 1.000 0.964 0.988 0.6525 0.785 0.667
#> 4 4 0.880 0.867 0.939 0.2722 0.813 0.573
#> 5 5 0.795 0.810 0.873 0.0382 0.971 0.888
#> 6 6 0.856 0.861 0.916 0.0268 0.987 0.946
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
#> GSM2819 1 0.000 0.989 1.000 0.000
#> GSM2820 2 0.260 0.988 0.044 0.956
#> GSM2822 1 0.000 0.989 1.000 0.000
#> GSM2832 1 0.000 0.989 1.000 0.000
#> GSM2823 1 0.000 0.989 1.000 0.000
#> GSM2824 1 0.000 0.989 1.000 0.000
#> GSM2825 1 0.000 0.989 1.000 0.000
#> GSM2826 1 0.000 0.989 1.000 0.000
#> GSM2829 1 0.000 0.989 1.000 0.000
#> GSM2856 1 0.000 0.989 1.000 0.000
#> GSM2830 1 0.000 0.989 1.000 0.000
#> GSM2843 1 0.000 0.989 1.000 0.000
#> GSM2871 1 0.000 0.989 1.000 0.000
#> GSM2831 1 0.000 0.989 1.000 0.000
#> GSM2844 1 0.000 0.989 1.000 0.000
#> GSM2833 1 0.000 0.989 1.000 0.000
#> GSM2846 1 0.000 0.989 1.000 0.000
#> GSM2835 1 0.000 0.989 1.000 0.000
#> GSM2858 1 0.000 0.989 1.000 0.000
#> GSM2836 1 0.000 0.989 1.000 0.000
#> GSM2848 1 0.000 0.989 1.000 0.000
#> GSM2828 2 0.260 0.988 0.044 0.956
#> GSM2837 2 0.260 0.988 0.044 0.956
#> GSM2839 1 0.260 0.964 0.956 0.044
#> GSM2841 1 0.260 0.964 0.956 0.044
#> GSM2827 1 0.000 0.989 1.000 0.000
#> GSM2842 1 0.000 0.989 1.000 0.000
#> GSM2845 1 0.000 0.989 1.000 0.000
#> GSM2872 1 0.000 0.989 1.000 0.000
#> GSM2834 1 0.000 0.989 1.000 0.000
#> GSM2847 1 0.000 0.989 1.000 0.000
#> GSM2849 2 0.260 0.988 0.044 0.956
#> GSM2850 2 0.260 0.988 0.044 0.956
#> GSM2838 1 0.000 0.989 1.000 0.000
#> GSM2853 1 0.000 0.989 1.000 0.000
#> GSM2852 2 0.260 0.988 0.044 0.956
#> GSM2855 2 0.260 0.988 0.044 0.956
#> GSM2840 1 0.260 0.964 0.956 0.044
#> GSM2857 1 0.260 0.964 0.956 0.044
#> GSM2859 1 0.000 0.989 1.000 0.000
#> GSM2860 1 0.000 0.989 1.000 0.000
#> GSM2861 1 0.000 0.989 1.000 0.000
#> GSM2862 1 0.000 0.989 1.000 0.000
#> GSM2863 1 0.000 0.989 1.000 0.000
#> GSM2864 1 0.000 0.989 1.000 0.000
#> GSM2865 1 0.000 0.989 1.000 0.000
#> GSM2866 1 0.000 0.989 1.000 0.000
#> GSM2868 1 0.000 0.989 1.000 0.000
#> GSM2869 1 0.000 0.989 1.000 0.000
#> GSM2851 1 0.000 0.989 1.000 0.000
#> GSM2867 1 0.000 0.989 1.000 0.000
#> GSM2870 1 0.000 0.989 1.000 0.000
#> GSM2854 1 0.000 0.989 1.000 0.000
#> GSM2873 1 0.000 0.989 1.000 0.000
#> GSM2874 2 0.260 0.988 0.044 0.956
#> GSM2884 2 0.260 0.988 0.044 0.956
#> GSM2875 1 0.260 0.964 0.956 0.044
#> GSM2890 1 0.260 0.964 0.956 0.044
#> GSM2877 1 0.260 0.964 0.956 0.044
#> GSM2892 1 0.260 0.964 0.956 0.044
#> GSM2902 1 0.260 0.964 0.956 0.044
#> GSM2878 1 0.260 0.964 0.956 0.044
#> GSM2901 1 0.260 0.964 0.956 0.044
#> GSM2879 2 0.574 0.898 0.136 0.864
#> GSM2898 2 0.615 0.879 0.152 0.848
#> GSM2881 2 0.260 0.988 0.044 0.956
#> GSM2897 2 0.260 0.988 0.044 0.956
#> GSM2882 1 0.000 0.989 1.000 0.000
#> GSM2894 1 0.000 0.989 1.000 0.000
#> GSM2883 2 0.260 0.988 0.044 0.956
#> GSM2895 2 0.260 0.988 0.044 0.956
#> GSM2885 2 0.260 0.988 0.044 0.956
#> GSM2886 2 0.260 0.988 0.044 0.956
#> GSM2887 2 0.260 0.988 0.044 0.956
#> GSM2896 2 0.260 0.988 0.044 0.956
#> GSM2888 1 0.000 0.989 1.000 0.000
#> GSM2889 1 0.000 0.989 1.000 0.000
#> GSM2876 1 0.260 0.964 0.956 0.044
#> GSM2891 1 0.260 0.964 0.956 0.044
#> GSM2880 1 0.260 0.964 0.956 0.044
#> GSM2893 1 0.260 0.964 0.956 0.044
#> GSM2821 1 0.000 0.989 1.000 0.000
#> GSM2900 1 0.141 0.978 0.980 0.020
#> GSM2903 1 0.141 0.978 0.980 0.020
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM2819 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2820 3 0.0000 0.9969 0.000 0.000 1.00
#> GSM2822 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2832 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2823 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2824 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2825 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2826 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2829 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2856 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2830 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2843 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2871 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2831 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2844 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2833 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2846 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2835 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2858 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2836 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2848 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2828 3 0.0000 0.9969 0.000 0.000 1.00
#> GSM2837 3 0.0000 0.9969 0.000 0.000 1.00
#> GSM2839 1 0.0000 1.0000 1.000 0.000 0.00
#> GSM2841 1 0.0000 1.0000 1.000 0.000 0.00
#> GSM2827 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2842 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2845 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2872 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2834 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2847 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2849 3 0.0000 0.9969 0.000 0.000 1.00
#> GSM2850 3 0.0000 0.9969 0.000 0.000 1.00
#> GSM2838 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2853 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2852 3 0.0000 0.9969 0.000 0.000 1.00
#> GSM2855 3 0.0000 0.9969 0.000 0.000 1.00
#> GSM2840 1 0.0000 1.0000 1.000 0.000 0.00
#> GSM2857 1 0.0000 1.0000 1.000 0.000 0.00
#> GSM2859 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2860 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2861 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2862 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2863 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2864 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2865 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2866 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2868 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2869 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2851 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2867 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2870 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2854 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2873 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2874 3 0.0000 0.9969 0.000 0.000 1.00
#> GSM2884 3 0.0000 0.9969 0.000 0.000 1.00
#> GSM2875 1 0.0000 1.0000 1.000 0.000 0.00
#> GSM2890 1 0.0000 1.0000 1.000 0.000 0.00
#> GSM2877 1 0.0000 1.0000 1.000 0.000 0.00
#> GSM2892 1 0.0000 1.0000 1.000 0.000 0.00
#> GSM2902 1 0.0000 1.0000 1.000 0.000 0.00
#> GSM2878 1 0.0000 1.0000 1.000 0.000 0.00
#> GSM2901 1 0.0000 1.0000 1.000 0.000 0.00
#> GSM2879 3 0.0892 0.9731 0.000 0.020 0.98
#> GSM2898 3 0.0892 0.9731 0.000 0.020 0.98
#> GSM2881 3 0.0000 0.9969 0.000 0.000 1.00
#> GSM2897 3 0.0000 0.9969 0.000 0.000 1.00
#> GSM2882 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2894 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2883 3 0.0000 0.9969 0.000 0.000 1.00
#> GSM2895 3 0.0000 0.9969 0.000 0.000 1.00
#> GSM2885 3 0.0000 0.9969 0.000 0.000 1.00
#> GSM2886 3 0.0000 0.9969 0.000 0.000 1.00
#> GSM2887 3 0.0000 0.9969 0.000 0.000 1.00
#> GSM2896 3 0.0000 0.9969 0.000 0.000 1.00
#> GSM2888 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2889 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2876 1 0.0000 1.0000 1.000 0.000 0.00
#> GSM2891 1 0.0000 1.0000 1.000 0.000 0.00
#> GSM2880 1 0.0000 1.0000 1.000 0.000 0.00
#> GSM2893 1 0.0000 1.0000 1.000 0.000 0.00
#> GSM2821 2 0.0000 0.9797 0.000 1.000 0.00
#> GSM2900 2 0.6309 0.0356 0.496 0.504 0.00
#> GSM2903 2 0.6307 0.0653 0.488 0.512 0.00
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM2819 2 0.1867 0.8559 0.000 0.928 0 0.072
#> GSM2820 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM2822 2 0.4605 0.6260 0.000 0.664 0 0.336
#> GSM2832 2 0.4605 0.6260 0.000 0.664 0 0.336
#> GSM2823 2 0.4454 0.6638 0.000 0.692 0 0.308
#> GSM2824 2 0.4164 0.7144 0.000 0.736 0 0.264
#> GSM2825 2 0.4605 0.6260 0.000 0.664 0 0.336
#> GSM2826 2 0.4605 0.6260 0.000 0.664 0 0.336
#> GSM2829 4 0.0000 0.9416 0.000 0.000 0 1.000
#> GSM2856 4 0.0000 0.9416 0.000 0.000 0 1.000
#> GSM2830 4 0.0000 0.9416 0.000 0.000 0 1.000
#> GSM2843 4 0.0000 0.9416 0.000 0.000 0 1.000
#> GSM2871 2 0.4830 0.5080 0.000 0.608 0 0.392
#> GSM2831 4 0.0000 0.9416 0.000 0.000 0 1.000
#> GSM2844 4 0.0000 0.9416 0.000 0.000 0 1.000
#> GSM2833 4 0.0000 0.9416 0.000 0.000 0 1.000
#> GSM2846 4 0.0000 0.9416 0.000 0.000 0 1.000
#> GSM2835 4 0.0000 0.9416 0.000 0.000 0 1.000
#> GSM2858 4 0.0000 0.9416 0.000 0.000 0 1.000
#> GSM2836 2 0.2868 0.8207 0.000 0.864 0 0.136
#> GSM2848 2 0.3444 0.7872 0.000 0.816 0 0.184
#> GSM2828 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM2837 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM2839 1 0.0000 0.9312 1.000 0.000 0 0.000
#> GSM2841 1 0.0000 0.9312 1.000 0.000 0 0.000
#> GSM2827 2 0.0336 0.8755 0.000 0.992 0 0.008
#> GSM2842 2 0.1389 0.8654 0.000 0.952 0 0.048
#> GSM2845 4 0.4925 0.0293 0.000 0.428 0 0.572
#> GSM2872 4 0.0000 0.9416 0.000 0.000 0 1.000
#> GSM2834 4 0.4250 0.5207 0.000 0.276 0 0.724
#> GSM2847 4 0.0000 0.9416 0.000 0.000 0 1.000
#> GSM2849 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM2850 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM2838 2 0.0000 0.8764 0.000 1.000 0 0.000
#> GSM2853 2 0.0000 0.8764 0.000 1.000 0 0.000
#> GSM2852 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM2855 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM2840 1 0.0000 0.9312 1.000 0.000 0 0.000
#> GSM2857 1 0.0000 0.9312 1.000 0.000 0 0.000
#> GSM2859 2 0.0000 0.8764 0.000 1.000 0 0.000
#> GSM2860 2 0.0000 0.8764 0.000 1.000 0 0.000
#> GSM2861 2 0.0000 0.8764 0.000 1.000 0 0.000
#> GSM2862 2 0.0000 0.8764 0.000 1.000 0 0.000
#> GSM2863 2 0.0000 0.8764 0.000 1.000 0 0.000
#> GSM2864 2 0.0000 0.8764 0.000 1.000 0 0.000
#> GSM2865 2 0.0000 0.8764 0.000 1.000 0 0.000
#> GSM2866 2 0.0000 0.8764 0.000 1.000 0 0.000
#> GSM2868 2 0.0000 0.8764 0.000 1.000 0 0.000
#> GSM2869 2 0.0000 0.8764 0.000 1.000 0 0.000
#> GSM2851 2 0.0000 0.8764 0.000 1.000 0 0.000
#> GSM2867 2 0.0000 0.8764 0.000 1.000 0 0.000
#> GSM2870 2 0.0000 0.8764 0.000 1.000 0 0.000
#> GSM2854 4 0.1302 0.9005 0.000 0.044 0 0.956
#> GSM2873 2 0.4605 0.6260 0.000 0.664 0 0.336
#> GSM2874 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM2884 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM2875 1 0.0000 0.9312 1.000 0.000 0 0.000
#> GSM2890 1 0.0000 0.9312 1.000 0.000 0 0.000
#> GSM2877 1 0.0000 0.9312 1.000 0.000 0 0.000
#> GSM2892 1 0.0000 0.9312 1.000 0.000 0 0.000
#> GSM2902 1 0.0000 0.9312 1.000 0.000 0 0.000
#> GSM2878 1 0.0000 0.9312 1.000 0.000 0 0.000
#> GSM2901 1 0.0000 0.9312 1.000 0.000 0 0.000
#> GSM2879 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM2898 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM2881 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM2897 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM2882 4 0.0000 0.9416 0.000 0.000 0 1.000
#> GSM2894 4 0.0000 0.9416 0.000 0.000 0 1.000
#> GSM2883 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM2895 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM2885 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM2886 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM2887 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM2896 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM2888 2 0.1022 0.8708 0.000 0.968 0 0.032
#> GSM2889 2 0.1118 0.8697 0.000 0.964 0 0.036
#> GSM2876 1 0.0000 0.9312 1.000 0.000 0 0.000
#> GSM2891 1 0.0000 0.9312 1.000 0.000 0 0.000
#> GSM2880 1 0.0000 0.9312 1.000 0.000 0 0.000
#> GSM2893 1 0.0000 0.9312 1.000 0.000 0 0.000
#> GSM2821 2 0.3074 0.8102 0.000 0.848 0 0.152
#> GSM2900 1 0.7098 0.1108 0.472 0.400 0 0.128
#> GSM2903 1 0.7464 0.1942 0.480 0.328 0 0.192
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM2819 2 0.457 0.44844 0.000 0.664 0 0.028 0.308
#> GSM2820 3 0.000 1.00000 0.000 0.000 1 0.000 0.000
#> GSM2822 2 0.389 0.64018 0.000 0.680 0 0.320 0.000
#> GSM2832 2 0.389 0.64018 0.000 0.680 0 0.320 0.000
#> GSM2823 2 0.345 0.72993 0.000 0.784 0 0.208 0.008
#> GSM2824 2 0.477 0.63633 0.000 0.728 0 0.108 0.164
#> GSM2825 2 0.431 0.62105 0.000 0.660 0 0.328 0.012
#> GSM2826 2 0.408 0.62754 0.000 0.668 0 0.328 0.004
#> GSM2829 4 0.000 0.93073 0.000 0.000 0 1.000 0.000
#> GSM2856 4 0.000 0.93073 0.000 0.000 0 1.000 0.000
#> GSM2830 4 0.000 0.93073 0.000 0.000 0 1.000 0.000
#> GSM2843 4 0.000 0.93073 0.000 0.000 0 1.000 0.000
#> GSM2871 2 0.416 0.50923 0.000 0.608 0 0.392 0.000
#> GSM2831 4 0.000 0.93073 0.000 0.000 0 1.000 0.000
#> GSM2844 4 0.000 0.93073 0.000 0.000 0 1.000 0.000
#> GSM2833 4 0.000 0.93073 0.000 0.000 0 1.000 0.000
#> GSM2846 4 0.000 0.93073 0.000 0.000 0 1.000 0.000
#> GSM2835 4 0.000 0.93073 0.000 0.000 0 1.000 0.000
#> GSM2858 4 0.000 0.93073 0.000 0.000 0 1.000 0.000
#> GSM2836 2 0.364 0.78208 0.000 0.812 0 0.144 0.044
#> GSM2848 2 0.357 0.76837 0.000 0.800 0 0.176 0.024
#> GSM2828 3 0.000 1.00000 0.000 0.000 1 0.000 0.000
#> GSM2837 3 0.000 1.00000 0.000 0.000 1 0.000 0.000
#> GSM2839 5 0.429 0.32406 0.468 0.000 0 0.000 0.532
#> GSM2841 5 0.429 0.32406 0.468 0.000 0 0.000 0.532
#> GSM2827 2 0.000 0.81829 0.000 1.000 0 0.000 0.000
#> GSM2842 2 0.029 0.81748 0.000 0.992 0 0.008 0.000
#> GSM2845 4 0.424 0.00988 0.000 0.428 0 0.572 0.000
#> GSM2872 4 0.000 0.93073 0.000 0.000 0 1.000 0.000
#> GSM2834 4 0.366 0.50981 0.000 0.276 0 0.724 0.000
#> GSM2847 4 0.000 0.93073 0.000 0.000 0 1.000 0.000
#> GSM2849 3 0.000 1.00000 0.000 0.000 1 0.000 0.000
#> GSM2850 3 0.000 1.00000 0.000 0.000 1 0.000 0.000
#> GSM2838 2 0.000 0.81829 0.000 1.000 0 0.000 0.000
#> GSM2853 2 0.000 0.81829 0.000 1.000 0 0.000 0.000
#> GSM2852 3 0.000 1.00000 0.000 0.000 1 0.000 0.000
#> GSM2855 3 0.000 1.00000 0.000 0.000 1 0.000 0.000
#> GSM2840 5 0.429 0.32406 0.468 0.000 0 0.000 0.532
#> GSM2857 5 0.429 0.32406 0.468 0.000 0 0.000 0.532
#> GSM2859 2 0.273 0.79951 0.000 0.840 0 0.000 0.160
#> GSM2860 2 0.273 0.79951 0.000 0.840 0 0.000 0.160
#> GSM2861 2 0.273 0.79951 0.000 0.840 0 0.000 0.160
#> GSM2862 2 0.273 0.79951 0.000 0.840 0 0.000 0.160
#> GSM2863 2 0.273 0.79951 0.000 0.840 0 0.000 0.160
#> GSM2864 2 0.273 0.79951 0.000 0.840 0 0.000 0.160
#> GSM2865 2 0.273 0.79951 0.000 0.840 0 0.000 0.160
#> GSM2866 2 0.273 0.79951 0.000 0.840 0 0.000 0.160
#> GSM2868 2 0.000 0.81829 0.000 1.000 0 0.000 0.000
#> GSM2869 2 0.000 0.81829 0.000 1.000 0 0.000 0.000
#> GSM2851 2 0.000 0.81829 0.000 1.000 0 0.000 0.000
#> GSM2867 2 0.000 0.81829 0.000 1.000 0 0.000 0.000
#> GSM2870 2 0.000 0.81829 0.000 1.000 0 0.000 0.000
#> GSM2854 4 0.120 0.87932 0.000 0.048 0 0.952 0.000
#> GSM2873 2 0.437 0.63713 0.000 0.664 0 0.320 0.016
#> GSM2874 3 0.000 1.00000 0.000 0.000 1 0.000 0.000
#> GSM2884 3 0.000 1.00000 0.000 0.000 1 0.000 0.000
#> GSM2875 1 0.000 0.96455 1.000 0.000 0 0.000 0.000
#> GSM2890 1 0.000 0.96455 1.000 0.000 0 0.000 0.000
#> GSM2877 1 0.000 0.96455 1.000 0.000 0 0.000 0.000
#> GSM2892 1 0.000 0.96455 1.000 0.000 0 0.000 0.000
#> GSM2902 1 0.000 0.96455 1.000 0.000 0 0.000 0.000
#> GSM2878 1 0.000 0.96455 1.000 0.000 0 0.000 0.000
#> GSM2901 1 0.000 0.96455 1.000 0.000 0 0.000 0.000
#> GSM2879 3 0.000 1.00000 0.000 0.000 1 0.000 0.000
#> GSM2898 3 0.000 1.00000 0.000 0.000 1 0.000 0.000
#> GSM2881 3 0.000 1.00000 0.000 0.000 1 0.000 0.000
#> GSM2897 3 0.000 1.00000 0.000 0.000 1 0.000 0.000
#> GSM2882 4 0.000 0.93073 0.000 0.000 0 1.000 0.000
#> GSM2894 4 0.000 0.93073 0.000 0.000 0 1.000 0.000
#> GSM2883 3 0.000 1.00000 0.000 0.000 1 0.000 0.000
#> GSM2895 3 0.000 1.00000 0.000 0.000 1 0.000 0.000
#> GSM2885 3 0.000 1.00000 0.000 0.000 1 0.000 0.000
#> GSM2886 3 0.000 1.00000 0.000 0.000 1 0.000 0.000
#> GSM2887 3 0.000 1.00000 0.000 0.000 1 0.000 0.000
#> GSM2896 3 0.000 1.00000 0.000 0.000 1 0.000 0.000
#> GSM2888 2 0.000 0.81829 0.000 1.000 0 0.000 0.000
#> GSM2889 2 0.000 0.81829 0.000 1.000 0 0.000 0.000
#> GSM2876 1 0.223 0.81779 0.884 0.000 0 0.000 0.116
#> GSM2891 1 0.223 0.81773 0.884 0.000 0 0.000 0.116
#> GSM2880 1 0.000 0.96455 1.000 0.000 0 0.000 0.000
#> GSM2893 1 0.000 0.96455 1.000 0.000 0 0.000 0.000
#> GSM2821 5 0.466 -0.13345 0.000 0.488 0 0.012 0.500
#> GSM2900 5 0.676 0.34765 0.244 0.116 0 0.064 0.576
#> GSM2903 5 0.666 0.36227 0.220 0.100 0 0.080 0.600
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM2819 5 0.1863 0.86454 0.000 0.104 0 0.000 0.896 0.000
#> GSM2820 3 0.0000 1.00000 0.000 0.000 1 0.000 0.000 0.000
#> GSM2822 2 0.3619 0.64155 0.000 0.680 0 0.316 0.004 0.000
#> GSM2832 2 0.3619 0.64155 0.000 0.680 0 0.316 0.004 0.000
#> GSM2823 2 0.3189 0.74492 0.000 0.796 0 0.184 0.020 0.000
#> GSM2824 2 0.4565 0.01576 0.000 0.532 0 0.036 0.432 0.000
#> GSM2825 2 0.3515 0.63181 0.000 0.676 0 0.324 0.000 0.000
#> GSM2826 2 0.3515 0.63181 0.000 0.676 0 0.324 0.000 0.000
#> GSM2829 4 0.0000 0.93012 0.000 0.000 0 1.000 0.000 0.000
#> GSM2856 4 0.0000 0.93012 0.000 0.000 0 1.000 0.000 0.000
#> GSM2830 4 0.0000 0.93012 0.000 0.000 0 1.000 0.000 0.000
#> GSM2843 4 0.0000 0.93012 0.000 0.000 0 1.000 0.000 0.000
#> GSM2871 2 0.3747 0.49962 0.000 0.604 0 0.396 0.000 0.000
#> GSM2831 4 0.0000 0.93012 0.000 0.000 0 1.000 0.000 0.000
#> GSM2844 4 0.0000 0.93012 0.000 0.000 0 1.000 0.000 0.000
#> GSM2833 4 0.0000 0.93012 0.000 0.000 0 1.000 0.000 0.000
#> GSM2846 4 0.0000 0.93012 0.000 0.000 0 1.000 0.000 0.000
#> GSM2835 4 0.0000 0.93012 0.000 0.000 0 1.000 0.000 0.000
#> GSM2858 4 0.0000 0.93012 0.000 0.000 0 1.000 0.000 0.000
#> GSM2836 2 0.3820 0.78303 0.000 0.784 0 0.144 0.008 0.064
#> GSM2848 2 0.3602 0.77350 0.000 0.784 0 0.176 0.008 0.032
#> GSM2828 3 0.0000 1.00000 0.000 0.000 1 0.000 0.000 0.000
#> GSM2837 3 0.0000 1.00000 0.000 0.000 1 0.000 0.000 0.000
#> GSM2839 6 0.3514 1.00000 0.108 0.000 0 0.000 0.088 0.804
#> GSM2841 6 0.3514 1.00000 0.108 0.000 0 0.000 0.088 0.804
#> GSM2827 2 0.0146 0.81032 0.000 0.996 0 0.000 0.004 0.000
#> GSM2842 2 0.0146 0.81032 0.000 0.996 0 0.000 0.004 0.000
#> GSM2845 4 0.3810 0.00917 0.000 0.428 0 0.572 0.000 0.000
#> GSM2872 4 0.0000 0.93012 0.000 0.000 0 1.000 0.000 0.000
#> GSM2834 4 0.3309 0.49739 0.000 0.280 0 0.720 0.000 0.000
#> GSM2847 4 0.0000 0.93012 0.000 0.000 0 1.000 0.000 0.000
#> GSM2849 3 0.0000 1.00000 0.000 0.000 1 0.000 0.000 0.000
#> GSM2850 3 0.0000 1.00000 0.000 0.000 1 0.000 0.000 0.000
#> GSM2838 2 0.0146 0.81032 0.000 0.996 0 0.000 0.004 0.000
#> GSM2853 2 0.0146 0.81032 0.000 0.996 0 0.000 0.004 0.000
#> GSM2852 3 0.0000 1.00000 0.000 0.000 1 0.000 0.000 0.000
#> GSM2855 3 0.0000 1.00000 0.000 0.000 1 0.000 0.000 0.000
#> GSM2840 6 0.3514 1.00000 0.108 0.000 0 0.000 0.088 0.804
#> GSM2857 6 0.3514 1.00000 0.108 0.000 0 0.000 0.088 0.804
#> GSM2859 2 0.3200 0.78909 0.000 0.788 0 0.000 0.016 0.196
#> GSM2860 2 0.3200 0.78909 0.000 0.788 0 0.000 0.016 0.196
#> GSM2861 2 0.3200 0.78909 0.000 0.788 0 0.000 0.016 0.196
#> GSM2862 2 0.3200 0.78909 0.000 0.788 0 0.000 0.016 0.196
#> GSM2863 2 0.3200 0.78909 0.000 0.788 0 0.000 0.016 0.196
#> GSM2864 2 0.3200 0.78909 0.000 0.788 0 0.000 0.016 0.196
#> GSM2865 2 0.3200 0.78909 0.000 0.788 0 0.000 0.016 0.196
#> GSM2866 2 0.3200 0.78909 0.000 0.788 0 0.000 0.016 0.196
#> GSM2868 2 0.0146 0.81032 0.000 0.996 0 0.000 0.004 0.000
#> GSM2869 2 0.0146 0.81032 0.000 0.996 0 0.000 0.004 0.000
#> GSM2851 2 0.0146 0.81032 0.000 0.996 0 0.000 0.004 0.000
#> GSM2867 2 0.0146 0.81032 0.000 0.996 0 0.000 0.004 0.000
#> GSM2870 2 0.0146 0.81032 0.000 0.996 0 0.000 0.004 0.000
#> GSM2854 4 0.1075 0.87878 0.000 0.048 0 0.952 0.000 0.000
#> GSM2873 2 0.3986 0.63740 0.000 0.664 0 0.316 0.000 0.020
#> GSM2874 3 0.0000 1.00000 0.000 0.000 1 0.000 0.000 0.000
#> GSM2884 3 0.0000 1.00000 0.000 0.000 1 0.000 0.000 0.000
#> GSM2875 1 0.0000 0.95158 1.000 0.000 0 0.000 0.000 0.000
#> GSM2890 1 0.0000 0.95158 1.000 0.000 0 0.000 0.000 0.000
#> GSM2877 1 0.0000 0.95158 1.000 0.000 0 0.000 0.000 0.000
#> GSM2892 1 0.0000 0.95158 1.000 0.000 0 0.000 0.000 0.000
#> GSM2902 1 0.0000 0.95158 1.000 0.000 0 0.000 0.000 0.000
#> GSM2878 1 0.0000 0.95158 1.000 0.000 0 0.000 0.000 0.000
#> GSM2901 1 0.0000 0.95158 1.000 0.000 0 0.000 0.000 0.000
#> GSM2879 3 0.0000 1.00000 0.000 0.000 1 0.000 0.000 0.000
#> GSM2898 3 0.0000 1.00000 0.000 0.000 1 0.000 0.000 0.000
#> GSM2881 3 0.0000 1.00000 0.000 0.000 1 0.000 0.000 0.000
#> GSM2897 3 0.0000 1.00000 0.000 0.000 1 0.000 0.000 0.000
#> GSM2882 4 0.0000 0.93012 0.000 0.000 0 1.000 0.000 0.000
#> GSM2894 4 0.0000 0.93012 0.000 0.000 0 1.000 0.000 0.000
#> GSM2883 3 0.0000 1.00000 0.000 0.000 1 0.000 0.000 0.000
#> GSM2895 3 0.0000 1.00000 0.000 0.000 1 0.000 0.000 0.000
#> GSM2885 3 0.0000 1.00000 0.000 0.000 1 0.000 0.000 0.000
#> GSM2886 3 0.0000 1.00000 0.000 0.000 1 0.000 0.000 0.000
#> GSM2887 3 0.0000 1.00000 0.000 0.000 1 0.000 0.000 0.000
#> GSM2896 3 0.0000 1.00000 0.000 0.000 1 0.000 0.000 0.000
#> GSM2888 2 0.0146 0.81032 0.000 0.996 0 0.000 0.004 0.000
#> GSM2889 2 0.0146 0.81032 0.000 0.996 0 0.000 0.004 0.000
#> GSM2876 1 0.3877 0.72581 0.764 0.000 0 0.000 0.160 0.076
#> GSM2891 1 0.3694 0.73974 0.784 0.000 0 0.000 0.140 0.076
#> GSM2880 1 0.0000 0.95158 1.000 0.000 0 0.000 0.000 0.000
#> GSM2893 1 0.0000 0.95158 1.000 0.000 0 0.000 0.000 0.000
#> GSM2821 5 0.1082 0.92957 0.000 0.040 0 0.004 0.956 0.000
#> GSM2900 5 0.0458 0.92983 0.000 0.016 0 0.000 0.984 0.000
#> GSM2903 5 0.0508 0.92549 0.000 0.012 0 0.000 0.984 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> SD:pam 84 2.53e-05 2
#> SD:pam 82 2.06e-08 3
#> SD:pam 81 2.66e-10 4
#> SD:pam 75 3.07e-10 5
#> SD:pam 80 1.42e-16 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 8229 rows and 84 columns.
#> Top rows (823, 1646, 2468, 3291, 4114) are extracted by 'SD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.221 0.373 0.679 0.5030 0.559 0.559
#> 3 3 0.937 0.893 0.947 0.2735 0.551 0.339
#> 4 4 0.659 0.817 0.838 0.1447 0.857 0.613
#> 5 5 0.780 0.658 0.834 0.0748 0.913 0.680
#> 6 6 0.839 0.822 0.856 0.0442 0.884 0.541
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM2819 2 0.997 -0.1865 0.468 0.532
#> GSM2820 2 0.909 0.4134 0.324 0.676
#> GSM2822 1 0.925 0.4433 0.660 0.340
#> GSM2832 1 0.925 0.4433 0.660 0.340
#> GSM2823 2 0.141 0.4278 0.020 0.980
#> GSM2824 2 0.141 0.4278 0.020 0.980
#> GSM2825 1 0.992 0.2569 0.552 0.448
#> GSM2826 1 0.992 0.2569 0.552 0.448
#> GSM2829 1 0.000 0.7722 1.000 0.000
#> GSM2856 1 0.000 0.7722 1.000 0.000
#> GSM2830 1 0.000 0.7722 1.000 0.000
#> GSM2843 1 0.000 0.7722 1.000 0.000
#> GSM2871 1 0.000 0.7722 1.000 0.000
#> GSM2831 1 0.000 0.7722 1.000 0.000
#> GSM2844 1 0.000 0.7722 1.000 0.000
#> GSM2833 1 0.000 0.7722 1.000 0.000
#> GSM2846 1 0.000 0.7722 1.000 0.000
#> GSM2835 1 0.000 0.7722 1.000 0.000
#> GSM2858 1 0.000 0.7722 1.000 0.000
#> GSM2836 1 0.961 0.4101 0.616 0.384
#> GSM2848 1 0.961 0.4102 0.616 0.384
#> GSM2828 2 0.909 0.4134 0.324 0.676
#> GSM2837 2 0.909 0.4134 0.324 0.676
#> GSM2839 2 0.767 0.4166 0.224 0.776
#> GSM2841 2 0.767 0.4166 0.224 0.776
#> GSM2827 1 0.871 0.5107 0.708 0.292
#> GSM2842 1 0.961 0.4103 0.616 0.384
#> GSM2845 1 0.000 0.7722 1.000 0.000
#> GSM2872 1 0.000 0.7722 1.000 0.000
#> GSM2834 1 0.000 0.7722 1.000 0.000
#> GSM2847 1 0.000 0.7722 1.000 0.000
#> GSM2849 2 0.909 0.4134 0.324 0.676
#> GSM2850 2 0.909 0.4134 0.324 0.676
#> GSM2838 2 0.993 -0.1423 0.452 0.548
#> GSM2853 2 0.993 -0.1423 0.452 0.548
#> GSM2852 2 0.909 0.4134 0.324 0.676
#> GSM2855 2 0.909 0.4134 0.324 0.676
#> GSM2840 2 0.767 0.4166 0.224 0.776
#> GSM2857 2 0.767 0.4166 0.224 0.776
#> GSM2859 2 0.993 -0.1423 0.452 0.548
#> GSM2860 2 0.993 -0.1423 0.452 0.548
#> GSM2861 2 0.993 -0.1423 0.452 0.548
#> GSM2862 2 0.993 -0.1423 0.452 0.548
#> GSM2863 2 0.993 -0.1423 0.452 0.548
#> GSM2864 2 0.993 -0.1423 0.452 0.548
#> GSM2865 2 0.993 -0.1423 0.452 0.548
#> GSM2866 2 0.993 -0.1423 0.452 0.548
#> GSM2868 2 0.993 -0.1423 0.452 0.548
#> GSM2869 2 0.993 -0.1423 0.452 0.548
#> GSM2851 2 0.993 -0.1423 0.452 0.548
#> GSM2867 2 0.993 -0.1423 0.452 0.548
#> GSM2870 2 0.993 -0.1423 0.452 0.548
#> GSM2854 1 0.000 0.7722 1.000 0.000
#> GSM2873 1 0.913 0.4505 0.672 0.328
#> GSM2874 2 0.909 0.4134 0.324 0.676
#> GSM2884 2 0.909 0.4134 0.324 0.676
#> GSM2875 2 0.767 0.4166 0.224 0.776
#> GSM2890 2 0.767 0.4166 0.224 0.776
#> GSM2877 2 0.767 0.4166 0.224 0.776
#> GSM2892 2 0.767 0.4166 0.224 0.776
#> GSM2902 2 0.767 0.4166 0.224 0.776
#> GSM2878 2 0.767 0.4166 0.224 0.776
#> GSM2901 2 0.767 0.4166 0.224 0.776
#> GSM2879 2 0.909 0.4134 0.324 0.676
#> GSM2898 2 0.909 0.4134 0.324 0.676
#> GSM2881 2 0.909 0.4134 0.324 0.676
#> GSM2897 2 0.909 0.4134 0.324 0.676
#> GSM2882 1 0.000 0.7722 1.000 0.000
#> GSM2894 1 0.000 0.7722 1.000 0.000
#> GSM2883 2 0.909 0.4134 0.324 0.676
#> GSM2895 2 0.909 0.4134 0.324 0.676
#> GSM2885 2 0.909 0.4134 0.324 0.676
#> GSM2886 2 0.909 0.4134 0.324 0.676
#> GSM2887 2 0.909 0.4134 0.324 0.676
#> GSM2896 2 0.909 0.4134 0.324 0.676
#> GSM2888 2 0.952 -0.0258 0.372 0.628
#> GSM2889 2 0.952 -0.0258 0.372 0.628
#> GSM2876 2 0.767 0.4166 0.224 0.776
#> GSM2891 2 0.767 0.4166 0.224 0.776
#> GSM2880 2 0.767 0.4166 0.224 0.776
#> GSM2893 2 0.767 0.4166 0.224 0.776
#> GSM2821 2 0.767 0.4166 0.224 0.776
#> GSM2900 2 0.767 0.4166 0.224 0.776
#> GSM2903 2 0.767 0.4166 0.224 0.776
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM2819 1 0.0661 0.917 0.988 0.008 0.004
#> GSM2820 3 0.0747 0.936 0.016 0.000 0.984
#> GSM2822 1 0.6432 0.219 0.568 0.428 0.004
#> GSM2832 2 0.6169 0.440 0.360 0.636 0.004
#> GSM2823 1 0.6410 0.277 0.576 0.004 0.420
#> GSM2824 1 0.6410 0.277 0.576 0.004 0.420
#> GSM2825 1 0.3644 0.810 0.872 0.124 0.004
#> GSM2826 1 0.3644 0.810 0.872 0.124 0.004
#> GSM2829 2 0.0747 0.966 0.016 0.984 0.000
#> GSM2856 2 0.0747 0.966 0.016 0.984 0.000
#> GSM2830 2 0.0747 0.966 0.016 0.984 0.000
#> GSM2843 2 0.0747 0.966 0.016 0.984 0.000
#> GSM2871 2 0.0747 0.966 0.016 0.984 0.000
#> GSM2831 2 0.0747 0.966 0.016 0.984 0.000
#> GSM2844 2 0.0747 0.966 0.016 0.984 0.000
#> GSM2833 2 0.0747 0.966 0.016 0.984 0.000
#> GSM2846 2 0.0747 0.966 0.016 0.984 0.000
#> GSM2835 2 0.0747 0.966 0.016 0.984 0.000
#> GSM2858 2 0.0747 0.966 0.016 0.984 0.000
#> GSM2836 2 0.1337 0.965 0.016 0.972 0.012
#> GSM2848 2 0.1337 0.965 0.016 0.972 0.012
#> GSM2828 3 0.0747 0.936 0.016 0.000 0.984
#> GSM2837 3 0.0747 0.936 0.016 0.000 0.984
#> GSM2839 1 0.0000 0.924 1.000 0.000 0.000
#> GSM2841 1 0.0000 0.924 1.000 0.000 0.000
#> GSM2827 2 0.1163 0.962 0.028 0.972 0.000
#> GSM2842 2 0.1163 0.962 0.028 0.972 0.000
#> GSM2845 2 0.0747 0.966 0.016 0.984 0.000
#> GSM2872 2 0.0747 0.966 0.016 0.984 0.000
#> GSM2834 2 0.0747 0.966 0.016 0.984 0.000
#> GSM2847 2 0.0747 0.966 0.016 0.984 0.000
#> GSM2849 3 0.0747 0.936 0.016 0.000 0.984
#> GSM2850 3 0.0747 0.936 0.016 0.000 0.984
#> GSM2838 2 0.2229 0.948 0.012 0.944 0.044
#> GSM2853 2 0.1620 0.955 0.012 0.964 0.024
#> GSM2852 3 0.1289 0.930 0.032 0.000 0.968
#> GSM2855 3 0.1289 0.930 0.032 0.000 0.968
#> GSM2840 1 0.0000 0.924 1.000 0.000 0.000
#> GSM2857 1 0.0000 0.924 1.000 0.000 0.000
#> GSM2859 2 0.1620 0.955 0.012 0.964 0.024
#> GSM2860 2 0.2446 0.944 0.012 0.936 0.052
#> GSM2861 2 0.2550 0.941 0.012 0.932 0.056
#> GSM2862 2 0.2446 0.944 0.012 0.936 0.052
#> GSM2863 2 0.1751 0.954 0.012 0.960 0.028
#> GSM2864 2 0.2229 0.948 0.012 0.944 0.044
#> GSM2865 2 0.1999 0.952 0.012 0.952 0.036
#> GSM2866 2 0.1751 0.961 0.028 0.960 0.012
#> GSM2868 2 0.2681 0.945 0.040 0.932 0.028
#> GSM2869 2 0.2339 0.946 0.012 0.940 0.048
#> GSM2851 2 0.2446 0.944 0.012 0.936 0.052
#> GSM2867 2 0.2527 0.949 0.020 0.936 0.044
#> GSM2870 2 0.2939 0.928 0.012 0.916 0.072
#> GSM2854 2 0.0747 0.966 0.016 0.984 0.000
#> GSM2873 2 0.1267 0.964 0.024 0.972 0.004
#> GSM2874 3 0.0747 0.936 0.016 0.000 0.984
#> GSM2884 3 0.0747 0.936 0.016 0.000 0.984
#> GSM2875 1 0.0000 0.924 1.000 0.000 0.000
#> GSM2890 1 0.0000 0.924 1.000 0.000 0.000
#> GSM2877 1 0.0000 0.924 1.000 0.000 0.000
#> GSM2892 1 0.0000 0.924 1.000 0.000 0.000
#> GSM2902 1 0.0000 0.924 1.000 0.000 0.000
#> GSM2878 1 0.0000 0.924 1.000 0.000 0.000
#> GSM2901 1 0.0000 0.924 1.000 0.000 0.000
#> GSM2879 3 0.1289 0.930 0.032 0.000 0.968
#> GSM2898 3 0.1289 0.930 0.032 0.000 0.968
#> GSM2881 3 0.0747 0.936 0.016 0.000 0.984
#> GSM2897 3 0.0747 0.936 0.016 0.000 0.984
#> GSM2882 2 0.0747 0.966 0.016 0.984 0.000
#> GSM2894 2 0.0747 0.966 0.016 0.984 0.000
#> GSM2883 3 0.1411 0.928 0.036 0.000 0.964
#> GSM2895 3 0.1411 0.928 0.036 0.000 0.964
#> GSM2885 3 0.0747 0.936 0.016 0.000 0.984
#> GSM2886 3 0.0747 0.936 0.016 0.000 0.984
#> GSM2887 3 0.0892 0.935 0.020 0.000 0.980
#> GSM2896 3 0.0892 0.935 0.020 0.000 0.980
#> GSM2888 3 0.7102 0.227 0.024 0.420 0.556
#> GSM2889 3 0.7102 0.227 0.024 0.420 0.556
#> GSM2876 1 0.0000 0.924 1.000 0.000 0.000
#> GSM2891 1 0.0000 0.924 1.000 0.000 0.000
#> GSM2880 1 0.0000 0.924 1.000 0.000 0.000
#> GSM2893 1 0.0000 0.924 1.000 0.000 0.000
#> GSM2821 1 0.0000 0.924 1.000 0.000 0.000
#> GSM2900 1 0.0000 0.924 1.000 0.000 0.000
#> GSM2903 1 0.0000 0.924 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM2819 1 0.5389 0.616 0.660 0.308 0.000 0.032
#> GSM2820 3 0.0000 0.882 0.000 0.000 1.000 0.000
#> GSM2822 1 0.7516 0.169 0.496 0.240 0.000 0.264
#> GSM2832 1 0.7516 0.169 0.496 0.240 0.000 0.264
#> GSM2823 1 0.8413 0.118 0.416 0.264 0.296 0.024
#> GSM2824 1 0.8413 0.118 0.416 0.264 0.296 0.024
#> GSM2825 1 0.6732 0.495 0.612 0.220 0.000 0.168
#> GSM2826 1 0.6732 0.495 0.612 0.220 0.000 0.168
#> GSM2829 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM2856 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM2830 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM2843 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM2871 4 0.0188 0.995 0.000 0.004 0.000 0.996
#> GSM2831 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM2844 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM2833 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM2846 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM2835 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM2858 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM2836 2 0.6265 0.799 0.124 0.656 0.000 0.220
#> GSM2848 2 0.6265 0.799 0.124 0.656 0.000 0.220
#> GSM2828 3 0.0000 0.882 0.000 0.000 1.000 0.000
#> GSM2837 3 0.0000 0.882 0.000 0.000 1.000 0.000
#> GSM2839 1 0.0921 0.833 0.972 0.028 0.000 0.000
#> GSM2841 1 0.0921 0.833 0.972 0.028 0.000 0.000
#> GSM2827 2 0.6374 0.791 0.128 0.644 0.000 0.228
#> GSM2842 2 0.6344 0.793 0.128 0.648 0.000 0.224
#> GSM2845 4 0.0188 0.995 0.000 0.004 0.000 0.996
#> GSM2872 4 0.0188 0.995 0.000 0.004 0.000 0.996
#> GSM2834 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM2847 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM2849 3 0.0000 0.882 0.000 0.000 1.000 0.000
#> GSM2850 3 0.0000 0.882 0.000 0.000 1.000 0.000
#> GSM2838 2 0.2704 0.889 0.000 0.876 0.000 0.124
#> GSM2853 2 0.2704 0.889 0.000 0.876 0.000 0.124
#> GSM2852 3 0.7797 0.481 0.148 0.320 0.508 0.024
#> GSM2855 3 0.7797 0.481 0.148 0.320 0.508 0.024
#> GSM2840 1 0.0921 0.833 0.972 0.028 0.000 0.000
#> GSM2857 1 0.0921 0.833 0.972 0.028 0.000 0.000
#> GSM2859 2 0.3311 0.875 0.000 0.828 0.000 0.172
#> GSM2860 2 0.2704 0.889 0.000 0.876 0.000 0.124
#> GSM2861 2 0.4669 0.868 0.052 0.780 0.000 0.168
#> GSM2862 2 0.2760 0.889 0.000 0.872 0.000 0.128
#> GSM2863 2 0.2760 0.889 0.000 0.872 0.000 0.128
#> GSM2864 2 0.2760 0.889 0.000 0.872 0.000 0.128
#> GSM2865 2 0.2760 0.889 0.000 0.872 0.000 0.128
#> GSM2866 2 0.5184 0.851 0.060 0.736 0.000 0.204
#> GSM2868 2 0.3907 0.879 0.032 0.828 0.000 0.140
#> GSM2869 2 0.2704 0.889 0.000 0.876 0.000 0.124
#> GSM2851 2 0.2704 0.889 0.000 0.876 0.000 0.124
#> GSM2867 2 0.3088 0.889 0.008 0.864 0.000 0.128
#> GSM2870 2 0.2921 0.887 0.000 0.860 0.000 0.140
#> GSM2854 4 0.0524 0.984 0.004 0.008 0.000 0.988
#> GSM2873 2 0.6432 0.632 0.076 0.552 0.000 0.372
#> GSM2874 3 0.0000 0.882 0.000 0.000 1.000 0.000
#> GSM2884 3 0.0000 0.882 0.000 0.000 1.000 0.000
#> GSM2875 1 0.0336 0.831 0.992 0.008 0.000 0.000
#> GSM2890 1 0.0336 0.831 0.992 0.008 0.000 0.000
#> GSM2877 1 0.0336 0.831 0.992 0.008 0.000 0.000
#> GSM2892 1 0.0336 0.831 0.992 0.008 0.000 0.000
#> GSM2902 1 0.0336 0.831 0.992 0.008 0.000 0.000
#> GSM2878 1 0.0336 0.831 0.992 0.008 0.000 0.000
#> GSM2901 1 0.0336 0.831 0.992 0.008 0.000 0.000
#> GSM2879 3 0.7047 0.620 0.148 0.192 0.636 0.024
#> GSM2898 3 0.7047 0.620 0.148 0.192 0.636 0.024
#> GSM2881 3 0.0000 0.882 0.000 0.000 1.000 0.000
#> GSM2897 3 0.0000 0.882 0.000 0.000 1.000 0.000
#> GSM2882 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM2894 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM2883 3 0.5369 0.759 0.084 0.116 0.776 0.024
#> GSM2895 3 0.5369 0.759 0.084 0.116 0.776 0.024
#> GSM2885 3 0.0000 0.882 0.000 0.000 1.000 0.000
#> GSM2886 3 0.0000 0.882 0.000 0.000 1.000 0.000
#> GSM2887 3 0.0469 0.878 0.012 0.000 0.988 0.000
#> GSM2896 3 0.0469 0.878 0.012 0.000 0.988 0.000
#> GSM2888 2 0.6455 0.711 0.132 0.716 0.060 0.092
#> GSM2889 2 0.6443 0.706 0.136 0.716 0.060 0.088
#> GSM2876 1 0.0921 0.833 0.972 0.028 0.000 0.000
#> GSM2891 1 0.0921 0.833 0.972 0.028 0.000 0.000
#> GSM2880 1 0.0000 0.831 1.000 0.000 0.000 0.000
#> GSM2893 1 0.0336 0.831 0.992 0.008 0.000 0.000
#> GSM2821 1 0.3711 0.780 0.836 0.140 0.000 0.024
#> GSM2900 1 0.3711 0.780 0.836 0.140 0.000 0.024
#> GSM2903 1 0.3711 0.780 0.836 0.140 0.000 0.024
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM2819 5 0.6726 0.6096 0.348 0.176 0.000 0.012 0.464
#> GSM2820 3 0.0000 0.9567 0.000 0.000 1.000 0.000 0.000
#> GSM2822 2 0.8217 0.1826 0.304 0.368 0.000 0.172 0.156
#> GSM2832 2 0.8212 0.1907 0.300 0.372 0.000 0.172 0.156
#> GSM2823 5 0.4300 0.8798 0.476 0.000 0.000 0.000 0.524
#> GSM2824 5 0.4300 0.8798 0.476 0.000 0.000 0.000 0.524
#> GSM2825 1 0.8140 -0.5076 0.364 0.176 0.000 0.136 0.324
#> GSM2826 1 0.8140 -0.5076 0.364 0.176 0.000 0.136 0.324
#> GSM2829 4 0.0000 0.9958 0.000 0.000 0.000 1.000 0.000
#> GSM2856 4 0.0000 0.9958 0.000 0.000 0.000 1.000 0.000
#> GSM2830 4 0.0000 0.9958 0.000 0.000 0.000 1.000 0.000
#> GSM2843 4 0.0000 0.9958 0.000 0.000 0.000 1.000 0.000
#> GSM2871 4 0.0162 0.9920 0.004 0.000 0.000 0.996 0.000
#> GSM2831 4 0.0000 0.9958 0.000 0.000 0.000 1.000 0.000
#> GSM2844 4 0.0000 0.9958 0.000 0.000 0.000 1.000 0.000
#> GSM2833 4 0.0162 0.9924 0.000 0.004 0.000 0.996 0.000
#> GSM2846 4 0.0162 0.9924 0.000 0.004 0.000 0.996 0.000
#> GSM2835 4 0.0000 0.9958 0.000 0.000 0.000 1.000 0.000
#> GSM2858 4 0.0000 0.9958 0.000 0.000 0.000 1.000 0.000
#> GSM2836 2 0.7426 0.3816 0.268 0.488 0.000 0.172 0.072
#> GSM2848 2 0.7447 0.3799 0.268 0.488 0.000 0.168 0.076
#> GSM2828 3 0.0000 0.9567 0.000 0.000 1.000 0.000 0.000
#> GSM2837 3 0.0000 0.9567 0.000 0.000 1.000 0.000 0.000
#> GSM2839 1 0.0000 0.3016 1.000 0.000 0.000 0.000 0.000
#> GSM2841 1 0.0000 0.3016 1.000 0.000 0.000 0.000 0.000
#> GSM2827 2 0.8090 0.2580 0.276 0.408 0.000 0.176 0.140
#> GSM2842 2 0.8095 0.2550 0.276 0.408 0.000 0.172 0.144
#> GSM2845 4 0.0000 0.9958 0.000 0.000 0.000 1.000 0.000
#> GSM2872 4 0.0000 0.9958 0.000 0.000 0.000 1.000 0.000
#> GSM2834 4 0.0000 0.9958 0.000 0.000 0.000 1.000 0.000
#> GSM2847 4 0.0000 0.9958 0.000 0.000 0.000 1.000 0.000
#> GSM2849 3 0.0000 0.9567 0.000 0.000 1.000 0.000 0.000
#> GSM2850 3 0.0000 0.9567 0.000 0.000 1.000 0.000 0.000
#> GSM2838 2 0.0000 0.7015 0.000 1.000 0.000 0.000 0.000
#> GSM2853 2 0.0000 0.7015 0.000 1.000 0.000 0.000 0.000
#> GSM2852 1 0.6777 -0.6108 0.372 0.000 0.276 0.000 0.352
#> GSM2855 1 0.6777 -0.6108 0.372 0.000 0.276 0.000 0.352
#> GSM2840 1 0.0000 0.3016 1.000 0.000 0.000 0.000 0.000
#> GSM2857 1 0.0000 0.3016 1.000 0.000 0.000 0.000 0.000
#> GSM2859 2 0.1082 0.6981 0.000 0.964 0.000 0.028 0.008
#> GSM2860 2 0.0000 0.7015 0.000 1.000 0.000 0.000 0.000
#> GSM2861 2 0.2732 0.6590 0.088 0.884 0.000 0.008 0.020
#> GSM2862 2 0.0000 0.7015 0.000 1.000 0.000 0.000 0.000
#> GSM2863 2 0.0000 0.7015 0.000 1.000 0.000 0.000 0.000
#> GSM2864 2 0.0000 0.7015 0.000 1.000 0.000 0.000 0.000
#> GSM2865 2 0.0000 0.7015 0.000 1.000 0.000 0.000 0.000
#> GSM2866 2 0.7125 0.4771 0.140 0.576 0.000 0.132 0.152
#> GSM2868 2 0.2784 0.6774 0.012 0.888 0.000 0.072 0.028
#> GSM2869 2 0.0000 0.7015 0.000 1.000 0.000 0.000 0.000
#> GSM2851 2 0.0000 0.7015 0.000 1.000 0.000 0.000 0.000
#> GSM2867 2 0.2390 0.6840 0.008 0.908 0.000 0.060 0.024
#> GSM2870 2 0.0290 0.7010 0.000 0.992 0.000 0.008 0.000
#> GSM2854 4 0.1538 0.9423 0.008 0.008 0.000 0.948 0.036
#> GSM2873 2 0.8063 0.3052 0.200 0.412 0.000 0.264 0.124
#> GSM2874 3 0.0000 0.9567 0.000 0.000 1.000 0.000 0.000
#> GSM2884 3 0.0000 0.9567 0.000 0.000 1.000 0.000 0.000
#> GSM2875 1 0.4297 0.5952 0.528 0.000 0.000 0.000 0.472
#> GSM2890 1 0.4297 0.5952 0.528 0.000 0.000 0.000 0.472
#> GSM2877 1 0.4297 0.5952 0.528 0.000 0.000 0.000 0.472
#> GSM2892 1 0.4297 0.5952 0.528 0.000 0.000 0.000 0.472
#> GSM2902 1 0.4297 0.5952 0.528 0.000 0.000 0.000 0.472
#> GSM2878 1 0.4297 0.5952 0.528 0.000 0.000 0.000 0.472
#> GSM2901 1 0.4297 0.5952 0.528 0.000 0.000 0.000 0.472
#> GSM2879 5 0.5812 0.8131 0.372 0.000 0.100 0.000 0.528
#> GSM2898 5 0.5812 0.8131 0.372 0.000 0.100 0.000 0.528
#> GSM2881 3 0.0000 0.9567 0.000 0.000 1.000 0.000 0.000
#> GSM2897 3 0.0000 0.9567 0.000 0.000 1.000 0.000 0.000
#> GSM2882 4 0.0000 0.9958 0.000 0.000 0.000 1.000 0.000
#> GSM2894 4 0.0000 0.9958 0.000 0.000 0.000 1.000 0.000
#> GSM2883 3 0.4434 0.6526 0.056 0.000 0.736 0.000 0.208
#> GSM2895 3 0.4434 0.6526 0.056 0.000 0.736 0.000 0.208
#> GSM2885 3 0.0000 0.9567 0.000 0.000 1.000 0.000 0.000
#> GSM2886 3 0.0000 0.9567 0.000 0.000 1.000 0.000 0.000
#> GSM2887 3 0.0579 0.9470 0.008 0.000 0.984 0.000 0.008
#> GSM2896 3 0.0579 0.9470 0.008 0.000 0.984 0.000 0.008
#> GSM2888 2 0.7473 -0.0378 0.280 0.392 0.000 0.036 0.292
#> GSM2889 2 0.7473 -0.0378 0.280 0.392 0.000 0.036 0.292
#> GSM2876 1 0.0609 0.3142 0.980 0.000 0.000 0.000 0.020
#> GSM2891 1 0.0609 0.3142 0.980 0.000 0.000 0.000 0.020
#> GSM2880 1 0.4294 0.5938 0.532 0.000 0.000 0.000 0.468
#> GSM2893 1 0.4297 0.5952 0.528 0.000 0.000 0.000 0.472
#> GSM2821 5 0.4302 0.8785 0.480 0.000 0.000 0.000 0.520
#> GSM2900 5 0.4302 0.8785 0.480 0.000 0.000 0.000 0.520
#> GSM2903 5 0.4305 0.8711 0.488 0.000 0.000 0.000 0.512
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM2819 5 0.1391 0.6047 0.000 0.016 0.000 0.000 0.944 0.040
#> GSM2820 3 0.0000 0.8995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2822 5 0.5114 0.6642 0.000 0.128 0.000 0.028 0.684 0.160
#> GSM2832 5 0.5114 0.6642 0.000 0.128 0.000 0.028 0.684 0.160
#> GSM2823 5 0.2340 0.5969 0.000 0.000 0.000 0.000 0.852 0.148
#> GSM2824 5 0.2340 0.5969 0.000 0.000 0.000 0.000 0.852 0.148
#> GSM2825 5 0.4297 0.4993 0.068 0.000 0.000 0.044 0.772 0.116
#> GSM2826 5 0.4297 0.4993 0.068 0.000 0.000 0.044 0.772 0.116
#> GSM2829 4 0.0000 0.9674 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2856 4 0.0000 0.9674 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2830 4 0.0000 0.9674 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2843 4 0.0000 0.9674 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2871 4 0.0993 0.9520 0.000 0.000 0.000 0.964 0.024 0.012
#> GSM2831 4 0.0000 0.9674 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2844 4 0.0000 0.9674 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2833 4 0.1434 0.9359 0.000 0.000 0.000 0.940 0.012 0.048
#> GSM2846 4 0.1367 0.9392 0.000 0.000 0.000 0.944 0.012 0.044
#> GSM2835 4 0.0000 0.9674 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2858 4 0.0000 0.9674 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2836 5 0.5967 0.6315 0.000 0.228 0.000 0.020 0.548 0.204
#> GSM2848 5 0.5904 0.6380 0.000 0.220 0.000 0.020 0.560 0.200
#> GSM2828 3 0.0000 0.8995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2837 3 0.0000 0.8995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2839 6 0.5787 0.9922 0.248 0.000 0.000 0.000 0.248 0.504
#> GSM2841 6 0.5787 0.9922 0.248 0.000 0.000 0.000 0.248 0.504
#> GSM2827 5 0.6282 0.6411 0.000 0.204 0.000 0.048 0.544 0.204
#> GSM2842 5 0.6282 0.6411 0.000 0.204 0.000 0.048 0.544 0.204
#> GSM2845 4 0.0622 0.9599 0.000 0.000 0.000 0.980 0.008 0.012
#> GSM2872 4 0.0622 0.9599 0.000 0.000 0.000 0.980 0.008 0.012
#> GSM2834 4 0.0146 0.9664 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM2847 4 0.0520 0.9620 0.000 0.000 0.000 0.984 0.008 0.008
#> GSM2849 3 0.0000 0.8995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2850 3 0.0000 0.8995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2838 2 0.0000 0.9372 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2853 2 0.0146 0.9352 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM2852 5 0.3802 0.6196 0.000 0.000 0.012 0.000 0.676 0.312
#> GSM2855 5 0.3802 0.6196 0.000 0.000 0.012 0.000 0.676 0.312
#> GSM2840 6 0.5787 0.9922 0.248 0.000 0.000 0.000 0.248 0.504
#> GSM2857 6 0.5787 0.9922 0.248 0.000 0.000 0.000 0.248 0.504
#> GSM2859 2 0.0922 0.9192 0.000 0.968 0.000 0.004 0.004 0.024
#> GSM2860 2 0.0000 0.9372 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2861 2 0.1970 0.8639 0.000 0.912 0.000 0.000 0.028 0.060
#> GSM2862 2 0.0000 0.9372 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2863 2 0.0000 0.9372 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2864 2 0.0000 0.9372 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2865 2 0.0000 0.9372 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2866 5 0.5771 0.3894 0.000 0.396 0.000 0.012 0.468 0.124
#> GSM2868 2 0.4516 -0.0872 0.000 0.564 0.000 0.000 0.400 0.036
#> GSM2869 2 0.0508 0.9298 0.000 0.984 0.000 0.000 0.004 0.012
#> GSM2851 2 0.0000 0.9372 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2867 2 0.1789 0.8768 0.000 0.924 0.000 0.000 0.044 0.032
#> GSM2870 2 0.0000 0.9372 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2854 4 0.4855 0.5121 0.000 0.000 0.000 0.660 0.204 0.136
#> GSM2873 5 0.6683 0.6095 0.000 0.200 0.000 0.112 0.528 0.160
#> GSM2874 3 0.0000 0.8995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2884 3 0.0000 0.8995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2875 1 0.0000 0.9828 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2890 1 0.0000 0.9828 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2877 1 0.0000 0.9828 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2892 1 0.0000 0.9828 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2902 1 0.0000 0.9828 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2878 1 0.0405 0.9736 0.988 0.000 0.000 0.000 0.008 0.004
#> GSM2901 1 0.0692 0.9644 0.976 0.000 0.000 0.000 0.020 0.004
#> GSM2879 5 0.3636 0.6197 0.000 0.000 0.004 0.000 0.676 0.320
#> GSM2898 5 0.3636 0.6197 0.000 0.000 0.004 0.000 0.676 0.320
#> GSM2881 3 0.0000 0.8995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2897 3 0.0000 0.8995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2882 4 0.0000 0.9674 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2894 4 0.0000 0.9674 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2883 3 0.5651 0.4933 0.000 0.000 0.532 0.000 0.208 0.260
#> GSM2895 3 0.5651 0.4933 0.000 0.000 0.532 0.000 0.208 0.260
#> GSM2885 3 0.0000 0.8995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2886 3 0.0000 0.8995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2887 3 0.3670 0.7401 0.000 0.000 0.736 0.000 0.024 0.240
#> GSM2896 3 0.3645 0.7429 0.000 0.000 0.740 0.000 0.024 0.236
#> GSM2888 5 0.5430 0.6526 0.000 0.224 0.000 0.016 0.620 0.140
#> GSM2889 5 0.5430 0.6526 0.000 0.224 0.000 0.016 0.620 0.140
#> GSM2876 6 0.5784 0.9842 0.260 0.000 0.000 0.000 0.236 0.504
#> GSM2891 6 0.5784 0.9842 0.260 0.000 0.000 0.000 0.236 0.504
#> GSM2880 1 0.1219 0.9116 0.948 0.000 0.000 0.000 0.048 0.004
#> GSM2893 1 0.0000 0.9828 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2821 5 0.1757 0.5754 0.000 0.008 0.000 0.000 0.916 0.076
#> GSM2900 5 0.1967 0.5681 0.000 0.012 0.000 0.000 0.904 0.084
#> GSM2903 5 0.1866 0.5675 0.000 0.008 0.000 0.000 0.908 0.084
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> SD:mclust 19 NA 2
#> SD:mclust 78 1.69e-08 3
#> SD:mclust 76 3.70e-11 4
#> SD:mclust 64 1.46e-12 5
#> SD:mclust 78 4.67e-17 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 8229 rows and 84 columns.
#> Top rows (823, 1646, 2468, 3291, 4114) 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.892 0.896 0.935 0.4374 0.577 0.577
#> 3 3 0.821 0.869 0.937 0.4272 0.648 0.465
#> 4 4 0.938 0.919 0.963 0.2023 0.834 0.589
#> 5 5 0.878 0.825 0.887 0.0483 0.944 0.787
#> 6 6 0.868 0.803 0.857 0.0381 0.968 0.853
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM2819 1 0.9129 0.465 0.672 0.328
#> GSM2820 2 0.2043 0.908 0.032 0.968
#> GSM2822 2 0.9998 0.150 0.492 0.508
#> GSM2832 2 0.7453 0.784 0.212 0.788
#> GSM2823 2 0.7950 0.712 0.240 0.760
#> GSM2824 2 0.9552 0.483 0.376 0.624
#> GSM2825 1 0.2043 0.960 0.968 0.032
#> GSM2826 1 0.2043 0.960 0.968 0.032
#> GSM2829 2 0.3274 0.929 0.060 0.940
#> GSM2856 2 0.3431 0.927 0.064 0.936
#> GSM2830 2 0.3274 0.929 0.060 0.940
#> GSM2843 2 0.3274 0.929 0.060 0.940
#> GSM2871 2 0.3274 0.929 0.060 0.940
#> GSM2831 2 0.9661 0.455 0.392 0.608
#> GSM2844 2 0.9866 0.347 0.432 0.568
#> GSM2833 2 0.5408 0.881 0.124 0.876
#> GSM2846 2 0.3431 0.927 0.064 0.936
#> GSM2835 1 0.2043 0.960 0.968 0.032
#> GSM2858 1 0.2043 0.960 0.968 0.032
#> GSM2836 2 0.3274 0.929 0.060 0.940
#> GSM2848 2 0.3274 0.929 0.060 0.940
#> GSM2828 2 0.2043 0.908 0.032 0.968
#> GSM2837 2 0.2043 0.908 0.032 0.968
#> GSM2839 1 0.0000 0.972 1.000 0.000
#> GSM2841 1 0.0000 0.972 1.000 0.000
#> GSM2827 2 0.3274 0.929 0.060 0.940
#> GSM2842 2 0.3274 0.929 0.060 0.940
#> GSM2845 2 0.3274 0.929 0.060 0.940
#> GSM2872 2 0.7376 0.790 0.208 0.792
#> GSM2834 2 0.3274 0.929 0.060 0.940
#> GSM2847 2 0.3274 0.929 0.060 0.940
#> GSM2849 2 0.2043 0.908 0.032 0.968
#> GSM2850 2 0.2043 0.908 0.032 0.968
#> GSM2838 2 0.3274 0.929 0.060 0.940
#> GSM2853 2 0.3274 0.929 0.060 0.940
#> GSM2852 2 0.1633 0.910 0.024 0.976
#> GSM2855 2 0.1633 0.910 0.024 0.976
#> GSM2840 1 0.0000 0.972 1.000 0.000
#> GSM2857 1 0.0000 0.972 1.000 0.000
#> GSM2859 2 0.3274 0.929 0.060 0.940
#> GSM2860 2 0.3274 0.929 0.060 0.940
#> GSM2861 2 0.3274 0.929 0.060 0.940
#> GSM2862 2 0.3274 0.929 0.060 0.940
#> GSM2863 2 0.3274 0.929 0.060 0.940
#> GSM2864 2 0.3274 0.929 0.060 0.940
#> GSM2865 2 0.3274 0.929 0.060 0.940
#> GSM2866 2 0.3274 0.929 0.060 0.940
#> GSM2868 2 0.3274 0.929 0.060 0.940
#> GSM2869 2 0.3274 0.929 0.060 0.940
#> GSM2851 2 0.3274 0.929 0.060 0.940
#> GSM2867 2 0.3274 0.929 0.060 0.940
#> GSM2870 2 0.3274 0.929 0.060 0.940
#> GSM2854 2 0.3431 0.927 0.064 0.936
#> GSM2873 2 0.3274 0.929 0.060 0.940
#> GSM2874 2 0.2043 0.908 0.032 0.968
#> GSM2884 2 0.2043 0.908 0.032 0.968
#> GSM2875 1 0.0000 0.972 1.000 0.000
#> GSM2890 1 0.0000 0.972 1.000 0.000
#> GSM2877 1 0.0000 0.972 1.000 0.000
#> GSM2892 1 0.0000 0.972 1.000 0.000
#> GSM2902 1 0.0000 0.972 1.000 0.000
#> GSM2878 1 0.0000 0.972 1.000 0.000
#> GSM2901 1 0.0000 0.972 1.000 0.000
#> GSM2879 2 0.1414 0.911 0.020 0.980
#> GSM2898 2 0.1184 0.911 0.016 0.984
#> GSM2881 2 0.2043 0.908 0.032 0.968
#> GSM2897 2 0.2043 0.908 0.032 0.968
#> GSM2882 1 0.2778 0.949 0.952 0.048
#> GSM2894 1 0.2778 0.949 0.952 0.048
#> GSM2883 2 0.2043 0.908 0.032 0.968
#> GSM2895 2 0.2043 0.908 0.032 0.968
#> GSM2885 2 0.2043 0.908 0.032 0.968
#> GSM2886 2 0.2043 0.908 0.032 0.968
#> GSM2887 2 0.2043 0.908 0.032 0.968
#> GSM2896 2 0.2043 0.908 0.032 0.968
#> GSM2888 2 0.0672 0.915 0.008 0.992
#> GSM2889 2 0.0672 0.915 0.008 0.992
#> GSM2876 1 0.0000 0.972 1.000 0.000
#> GSM2891 1 0.0000 0.972 1.000 0.000
#> GSM2880 1 0.0000 0.972 1.000 0.000
#> GSM2893 1 0.0000 0.972 1.000 0.000
#> GSM2821 1 0.1843 0.962 0.972 0.028
#> GSM2900 1 0.1414 0.966 0.980 0.020
#> GSM2903 1 0.1414 0.966 0.980 0.020
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM2819 2 0.0000 0.9083 0.000 1.000 0.000
#> GSM2820 3 0.0000 0.9673 0.000 0.000 1.000
#> GSM2822 2 0.0000 0.9083 0.000 1.000 0.000
#> GSM2832 2 0.0000 0.9083 0.000 1.000 0.000
#> GSM2823 3 0.9949 -0.0397 0.356 0.284 0.360
#> GSM2824 1 0.8853 0.4225 0.568 0.264 0.168
#> GSM2825 2 0.6079 0.4020 0.388 0.612 0.000
#> GSM2826 2 0.6126 0.3788 0.400 0.600 0.000
#> GSM2829 2 0.0000 0.9083 0.000 1.000 0.000
#> GSM2856 2 0.0000 0.9083 0.000 1.000 0.000
#> GSM2830 2 0.0000 0.9083 0.000 1.000 0.000
#> GSM2843 2 0.0000 0.9083 0.000 1.000 0.000
#> GSM2871 2 0.0000 0.9083 0.000 1.000 0.000
#> GSM2831 2 0.0000 0.9083 0.000 1.000 0.000
#> GSM2844 2 0.0000 0.9083 0.000 1.000 0.000
#> GSM2833 2 0.0000 0.9083 0.000 1.000 0.000
#> GSM2846 2 0.0000 0.9083 0.000 1.000 0.000
#> GSM2835 2 0.0892 0.8984 0.020 0.980 0.000
#> GSM2858 2 0.0747 0.9007 0.016 0.984 0.000
#> GSM2836 2 0.2448 0.8837 0.000 0.924 0.076
#> GSM2848 2 0.1529 0.8984 0.000 0.960 0.040
#> GSM2828 3 0.0000 0.9673 0.000 0.000 1.000
#> GSM2837 3 0.0000 0.9673 0.000 0.000 1.000
#> GSM2839 1 0.0000 0.9596 1.000 0.000 0.000
#> GSM2841 1 0.0000 0.9596 1.000 0.000 0.000
#> GSM2827 2 0.2261 0.8883 0.000 0.932 0.068
#> GSM2842 2 0.4121 0.8172 0.000 0.832 0.168
#> GSM2845 2 0.0000 0.9083 0.000 1.000 0.000
#> GSM2872 2 0.0000 0.9083 0.000 1.000 0.000
#> GSM2834 2 0.0000 0.9083 0.000 1.000 0.000
#> GSM2847 2 0.0000 0.9083 0.000 1.000 0.000
#> GSM2849 3 0.0000 0.9673 0.000 0.000 1.000
#> GSM2850 3 0.0000 0.9673 0.000 0.000 1.000
#> GSM2838 2 0.0237 0.9077 0.000 0.996 0.004
#> GSM2853 2 0.0000 0.9083 0.000 1.000 0.000
#> GSM2852 3 0.0000 0.9673 0.000 0.000 1.000
#> GSM2855 3 0.0000 0.9673 0.000 0.000 1.000
#> GSM2840 1 0.0000 0.9596 1.000 0.000 0.000
#> GSM2857 1 0.0000 0.9596 1.000 0.000 0.000
#> GSM2859 2 0.1411 0.8995 0.000 0.964 0.036
#> GSM2860 2 0.2625 0.8798 0.000 0.916 0.084
#> GSM2861 2 0.4654 0.7756 0.000 0.792 0.208
#> GSM2862 2 0.1753 0.8954 0.000 0.952 0.048
#> GSM2863 2 0.3038 0.8681 0.000 0.896 0.104
#> GSM2864 2 0.4002 0.8240 0.000 0.840 0.160
#> GSM2865 2 0.2878 0.8731 0.000 0.904 0.096
#> GSM2866 2 0.0000 0.9083 0.000 1.000 0.000
#> GSM2868 2 0.6111 0.4729 0.000 0.604 0.396
#> GSM2869 2 0.4931 0.7476 0.000 0.768 0.232
#> GSM2851 2 0.2878 0.8734 0.000 0.904 0.096
#> GSM2867 2 0.5327 0.6945 0.000 0.728 0.272
#> GSM2870 2 0.3116 0.8654 0.000 0.892 0.108
#> GSM2854 2 0.0000 0.9083 0.000 1.000 0.000
#> GSM2873 2 0.0000 0.9083 0.000 1.000 0.000
#> GSM2874 3 0.0000 0.9673 0.000 0.000 1.000
#> GSM2884 3 0.0000 0.9673 0.000 0.000 1.000
#> GSM2875 1 0.0000 0.9596 1.000 0.000 0.000
#> GSM2890 1 0.0000 0.9596 1.000 0.000 0.000
#> GSM2877 1 0.0000 0.9596 1.000 0.000 0.000
#> GSM2892 1 0.0000 0.9596 1.000 0.000 0.000
#> GSM2902 1 0.0000 0.9596 1.000 0.000 0.000
#> GSM2878 1 0.0000 0.9596 1.000 0.000 0.000
#> GSM2901 1 0.0000 0.9596 1.000 0.000 0.000
#> GSM2879 3 0.0000 0.9673 0.000 0.000 1.000
#> GSM2898 3 0.0000 0.9673 0.000 0.000 1.000
#> GSM2881 3 0.0000 0.9673 0.000 0.000 1.000
#> GSM2897 3 0.0000 0.9673 0.000 0.000 1.000
#> GSM2882 2 0.0424 0.9049 0.008 0.992 0.000
#> GSM2894 2 0.0424 0.9049 0.008 0.992 0.000
#> GSM2883 3 0.0000 0.9673 0.000 0.000 1.000
#> GSM2895 3 0.0000 0.9673 0.000 0.000 1.000
#> GSM2885 3 0.0000 0.9673 0.000 0.000 1.000
#> GSM2886 3 0.0000 0.9673 0.000 0.000 1.000
#> GSM2887 3 0.0000 0.9673 0.000 0.000 1.000
#> GSM2896 3 0.0000 0.9673 0.000 0.000 1.000
#> GSM2888 2 0.6286 0.3016 0.000 0.536 0.464
#> GSM2889 2 0.6302 0.2540 0.000 0.520 0.480
#> GSM2876 1 0.0000 0.9596 1.000 0.000 0.000
#> GSM2891 1 0.0000 0.9596 1.000 0.000 0.000
#> GSM2880 1 0.0000 0.9596 1.000 0.000 0.000
#> GSM2893 1 0.0000 0.9596 1.000 0.000 0.000
#> GSM2821 1 0.3816 0.7927 0.852 0.148 0.000
#> GSM2900 1 0.1163 0.9356 0.972 0.028 0.000
#> GSM2903 1 0.1289 0.9317 0.968 0.032 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM2819 2 0.0524 0.903 0.008 0.988 0.000 0.004
#> GSM2820 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM2822 2 0.3400 0.768 0.000 0.820 0.000 0.180
#> GSM2832 2 0.3400 0.768 0.000 0.820 0.000 0.180
#> GSM2823 2 0.4967 0.138 0.452 0.548 0.000 0.000
#> GSM2824 2 0.4843 0.312 0.396 0.604 0.000 0.000
#> GSM2825 2 0.7430 0.423 0.228 0.512 0.000 0.260
#> GSM2826 2 0.6680 0.542 0.136 0.604 0.000 0.260
#> GSM2829 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM2856 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM2830 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM2843 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM2871 4 0.0188 0.995 0.000 0.004 0.000 0.996
#> GSM2831 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM2844 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM2833 4 0.0188 0.995 0.000 0.004 0.000 0.996
#> GSM2846 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM2835 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM2858 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM2836 2 0.1211 0.891 0.000 0.960 0.000 0.040
#> GSM2848 2 0.1022 0.895 0.000 0.968 0.000 0.032
#> GSM2828 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM2837 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM2839 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM2841 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM2827 2 0.1211 0.891 0.000 0.960 0.000 0.040
#> GSM2842 2 0.0817 0.899 0.000 0.976 0.000 0.024
#> GSM2845 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM2872 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM2834 4 0.0188 0.995 0.000 0.004 0.000 0.996
#> GSM2847 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM2849 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM2850 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM2838 2 0.0000 0.907 0.000 1.000 0.000 0.000
#> GSM2853 2 0.0000 0.907 0.000 1.000 0.000 0.000
#> GSM2852 3 0.0336 0.991 0.000 0.008 0.992 0.000
#> GSM2855 3 0.0188 0.995 0.000 0.004 0.996 0.000
#> GSM2840 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM2857 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM2859 2 0.0000 0.907 0.000 1.000 0.000 0.000
#> GSM2860 2 0.0000 0.907 0.000 1.000 0.000 0.000
#> GSM2861 2 0.0000 0.907 0.000 1.000 0.000 0.000
#> GSM2862 2 0.0000 0.907 0.000 1.000 0.000 0.000
#> GSM2863 2 0.0000 0.907 0.000 1.000 0.000 0.000
#> GSM2864 2 0.0000 0.907 0.000 1.000 0.000 0.000
#> GSM2865 2 0.0000 0.907 0.000 1.000 0.000 0.000
#> GSM2866 2 0.0000 0.907 0.000 1.000 0.000 0.000
#> GSM2868 2 0.0000 0.907 0.000 1.000 0.000 0.000
#> GSM2869 2 0.0000 0.907 0.000 1.000 0.000 0.000
#> GSM2851 2 0.0000 0.907 0.000 1.000 0.000 0.000
#> GSM2867 2 0.0000 0.907 0.000 1.000 0.000 0.000
#> GSM2870 2 0.0000 0.907 0.000 1.000 0.000 0.000
#> GSM2854 4 0.0707 0.979 0.000 0.020 0.000 0.980
#> GSM2873 2 0.4277 0.637 0.000 0.720 0.000 0.280
#> GSM2874 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM2884 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM2875 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM2890 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM2877 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM2892 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM2902 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM2878 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM2901 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM2879 3 0.0469 0.988 0.000 0.012 0.988 0.000
#> GSM2898 3 0.0817 0.977 0.000 0.024 0.976 0.000
#> GSM2881 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM2897 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM2882 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM2894 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM2883 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM2895 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM2885 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM2886 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM2887 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM2896 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM2888 2 0.0524 0.905 0.000 0.988 0.004 0.008
#> GSM2889 2 0.0376 0.906 0.000 0.992 0.004 0.004
#> GSM2876 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM2891 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM2880 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM2893 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM2821 1 0.4222 0.634 0.728 0.272 0.000 0.000
#> GSM2900 1 0.2647 0.864 0.880 0.120 0.000 0.000
#> GSM2903 1 0.2647 0.864 0.880 0.120 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM2819 2 0.6446 0.288 0.388 0.464 0.000 0.008 0.140
#> GSM2820 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000
#> GSM2822 2 0.5390 0.733 0.056 0.724 0.000 0.072 0.148
#> GSM2832 2 0.5308 0.723 0.036 0.728 0.000 0.108 0.128
#> GSM2823 1 0.5584 0.198 0.584 0.324 0.000 0.000 0.092
#> GSM2824 1 0.5289 0.204 0.616 0.312 0.000 0.000 0.072
#> GSM2825 5 0.6858 0.525 0.124 0.184 0.000 0.096 0.596
#> GSM2826 5 0.6803 0.476 0.104 0.256 0.000 0.072 0.568
#> GSM2829 4 0.0609 0.967 0.000 0.000 0.000 0.980 0.020
#> GSM2856 4 0.0703 0.967 0.000 0.000 0.000 0.976 0.024
#> GSM2830 4 0.0451 0.969 0.004 0.000 0.000 0.988 0.008
#> GSM2843 4 0.0451 0.969 0.000 0.004 0.000 0.988 0.008
#> GSM2871 4 0.1267 0.963 0.004 0.012 0.000 0.960 0.024
#> GSM2831 4 0.0162 0.969 0.004 0.000 0.000 0.996 0.000
#> GSM2844 4 0.0162 0.969 0.004 0.000 0.000 0.996 0.000
#> GSM2833 4 0.2236 0.937 0.024 0.000 0.000 0.908 0.068
#> GSM2846 4 0.2079 0.941 0.020 0.000 0.000 0.916 0.064
#> GSM2835 4 0.1270 0.956 0.000 0.000 0.000 0.948 0.052
#> GSM2858 4 0.1732 0.938 0.000 0.000 0.000 0.920 0.080
#> GSM2836 2 0.0865 0.900 0.004 0.972 0.000 0.000 0.024
#> GSM2848 2 0.0510 0.903 0.000 0.984 0.000 0.000 0.016
#> GSM2828 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000
#> GSM2837 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000
#> GSM2839 5 0.2648 0.663 0.152 0.000 0.000 0.000 0.848
#> GSM2841 5 0.2813 0.631 0.168 0.000 0.000 0.000 0.832
#> GSM2827 2 0.1012 0.906 0.020 0.968 0.000 0.000 0.012
#> GSM2842 2 0.1386 0.905 0.032 0.952 0.000 0.000 0.016
#> GSM2845 4 0.0609 0.968 0.000 0.000 0.000 0.980 0.020
#> GSM2872 4 0.0566 0.969 0.004 0.000 0.000 0.984 0.012
#> GSM2834 4 0.1568 0.948 0.000 0.020 0.000 0.944 0.036
#> GSM2847 4 0.0609 0.968 0.000 0.000 0.000 0.980 0.020
#> GSM2849 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000
#> GSM2850 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000
#> GSM2838 2 0.2359 0.896 0.060 0.904 0.000 0.000 0.036
#> GSM2853 2 0.2359 0.896 0.060 0.904 0.000 0.000 0.036
#> GSM2852 3 0.0162 0.994 0.000 0.004 0.996 0.000 0.000
#> GSM2855 3 0.0162 0.994 0.000 0.004 0.996 0.000 0.000
#> GSM2840 5 0.2439 0.676 0.120 0.000 0.000 0.004 0.876
#> GSM2857 5 0.2536 0.676 0.128 0.000 0.000 0.004 0.868
#> GSM2859 2 0.0912 0.903 0.012 0.972 0.000 0.000 0.016
#> GSM2860 2 0.0510 0.903 0.000 0.984 0.000 0.000 0.016
#> GSM2861 2 0.0693 0.906 0.012 0.980 0.000 0.000 0.008
#> GSM2862 2 0.0671 0.902 0.004 0.980 0.000 0.000 0.016
#> GSM2863 2 0.0798 0.902 0.008 0.976 0.000 0.000 0.016
#> GSM2864 2 0.0912 0.903 0.012 0.972 0.000 0.000 0.016
#> GSM2865 2 0.0798 0.902 0.008 0.976 0.000 0.000 0.016
#> GSM2866 2 0.0609 0.902 0.000 0.980 0.000 0.000 0.020
#> GSM2868 2 0.3075 0.875 0.092 0.860 0.000 0.000 0.048
#> GSM2869 2 0.2889 0.884 0.084 0.872 0.000 0.000 0.044
#> GSM2851 2 0.2426 0.894 0.064 0.900 0.000 0.000 0.036
#> GSM2867 2 0.2770 0.887 0.076 0.880 0.000 0.000 0.044
#> GSM2870 2 0.2554 0.891 0.072 0.892 0.000 0.000 0.036
#> GSM2854 4 0.1568 0.955 0.000 0.020 0.000 0.944 0.036
#> GSM2873 2 0.3019 0.816 0.000 0.864 0.000 0.088 0.048
#> GSM2874 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000
#> GSM2884 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000
#> GSM2875 1 0.3999 0.625 0.656 0.000 0.000 0.000 0.344
#> GSM2890 1 0.3999 0.625 0.656 0.000 0.000 0.000 0.344
#> GSM2877 1 0.4015 0.621 0.652 0.000 0.000 0.000 0.348
#> GSM2892 1 0.3999 0.625 0.656 0.000 0.000 0.000 0.344
#> GSM2902 1 0.3999 0.625 0.656 0.000 0.000 0.000 0.344
#> GSM2878 1 0.3949 0.623 0.668 0.000 0.000 0.000 0.332
#> GSM2901 1 0.3949 0.623 0.668 0.000 0.000 0.000 0.332
#> GSM2879 3 0.0771 0.976 0.000 0.020 0.976 0.000 0.004
#> GSM2898 3 0.0609 0.978 0.000 0.020 0.980 0.000 0.000
#> GSM2881 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000
#> GSM2897 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000
#> GSM2882 4 0.0693 0.967 0.012 0.000 0.000 0.980 0.008
#> GSM2894 4 0.0912 0.965 0.016 0.000 0.000 0.972 0.012
#> GSM2883 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000
#> GSM2895 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000
#> GSM2885 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000
#> GSM2886 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000
#> GSM2887 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000
#> GSM2896 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000
#> GSM2888 2 0.2536 0.897 0.044 0.900 0.004 0.000 0.052
#> GSM2889 2 0.2536 0.897 0.044 0.900 0.004 0.000 0.052
#> GSM2876 1 0.3508 0.548 0.748 0.000 0.000 0.000 0.252
#> GSM2891 1 0.3452 0.545 0.756 0.000 0.000 0.000 0.244
#> GSM2880 1 0.4045 0.612 0.644 0.000 0.000 0.000 0.356
#> GSM2893 1 0.4045 0.612 0.644 0.000 0.000 0.000 0.356
#> GSM2821 1 0.4525 0.263 0.740 0.056 0.000 0.004 0.200
#> GSM2900 1 0.3174 0.379 0.844 0.020 0.000 0.004 0.132
#> GSM2903 1 0.3219 0.375 0.840 0.020 0.000 0.004 0.136
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM2819 5 0.2324 0.5743 0.016 0.048 0.000 0.020 0.908 0.008
#> GSM2820 3 0.0000 0.9919 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2822 6 0.5879 -0.3229 0.000 0.396 0.000 0.016 0.128 0.460
#> GSM2832 2 0.6099 0.3270 0.000 0.440 0.000 0.024 0.140 0.396
#> GSM2823 5 0.5082 0.3999 0.460 0.056 0.000 0.000 0.476 0.008
#> GSM2824 5 0.5108 0.4821 0.424 0.060 0.000 0.000 0.508 0.008
#> GSM2825 6 0.3311 0.6374 0.092 0.024 0.000 0.016 0.020 0.848
#> GSM2826 6 0.3298 0.6167 0.064 0.044 0.000 0.016 0.020 0.856
#> GSM2829 4 0.1471 0.9091 0.000 0.000 0.000 0.932 0.004 0.064
#> GSM2856 4 0.1753 0.9017 0.000 0.000 0.000 0.912 0.004 0.084
#> GSM2830 4 0.0725 0.9211 0.000 0.000 0.000 0.976 0.012 0.012
#> GSM2843 4 0.0820 0.9206 0.000 0.000 0.000 0.972 0.012 0.016
#> GSM2871 4 0.1798 0.9070 0.000 0.028 0.000 0.932 0.020 0.020
#> GSM2831 4 0.0146 0.9231 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM2844 4 0.0291 0.9233 0.000 0.000 0.000 0.992 0.004 0.004
#> GSM2833 4 0.3426 0.8393 0.000 0.000 0.000 0.808 0.124 0.068
#> GSM2846 4 0.3261 0.8531 0.000 0.000 0.000 0.824 0.104 0.072
#> GSM2835 4 0.3440 0.8043 0.000 0.000 0.000 0.776 0.028 0.196
#> GSM2858 4 0.3470 0.8000 0.000 0.000 0.000 0.772 0.028 0.200
#> GSM2836 2 0.1148 0.7854 0.000 0.960 0.000 0.004 0.016 0.020
#> GSM2848 2 0.0436 0.7988 0.000 0.988 0.000 0.004 0.004 0.004
#> GSM2828 3 0.0000 0.9919 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2837 3 0.0000 0.9919 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2839 6 0.4520 0.6782 0.220 0.000 0.000 0.000 0.092 0.688
#> GSM2841 6 0.4614 0.6692 0.228 0.000 0.000 0.000 0.096 0.676
#> GSM2827 2 0.2724 0.8013 0.000 0.864 0.000 0.000 0.052 0.084
#> GSM2842 2 0.3321 0.7953 0.000 0.820 0.000 0.000 0.080 0.100
#> GSM2845 4 0.1350 0.9176 0.000 0.008 0.000 0.952 0.020 0.020
#> GSM2872 4 0.1059 0.9191 0.000 0.004 0.000 0.964 0.016 0.016
#> GSM2834 4 0.2816 0.8561 0.000 0.088 0.000 0.868 0.020 0.024
#> GSM2847 4 0.1369 0.9163 0.000 0.016 0.000 0.952 0.016 0.016
#> GSM2849 3 0.0000 0.9919 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2850 3 0.0000 0.9919 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2838 2 0.4780 0.7511 0.000 0.660 0.000 0.000 0.228 0.112
#> GSM2853 2 0.4866 0.7450 0.000 0.648 0.000 0.000 0.236 0.116
#> GSM2852 3 0.0000 0.9919 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2855 3 0.0000 0.9919 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2840 6 0.4156 0.6972 0.188 0.000 0.000 0.000 0.080 0.732
#> GSM2857 6 0.4186 0.6969 0.192 0.000 0.000 0.000 0.080 0.728
#> GSM2859 2 0.0748 0.7966 0.000 0.976 0.000 0.004 0.004 0.016
#> GSM2860 2 0.0363 0.7969 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM2861 2 0.1984 0.8050 0.000 0.912 0.000 0.000 0.056 0.032
#> GSM2862 2 0.0363 0.7969 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM2863 2 0.0603 0.7944 0.000 0.980 0.000 0.000 0.004 0.016
#> GSM2864 2 0.0951 0.7898 0.000 0.968 0.000 0.004 0.008 0.020
#> GSM2865 2 0.0748 0.7931 0.000 0.976 0.000 0.004 0.004 0.016
#> GSM2866 2 0.0725 0.7928 0.000 0.976 0.000 0.000 0.012 0.012
#> GSM2868 2 0.4873 0.7283 0.000 0.632 0.000 0.000 0.268 0.100
#> GSM2869 2 0.4834 0.7394 0.000 0.644 0.000 0.000 0.252 0.104
#> GSM2851 2 0.4625 0.7582 0.000 0.680 0.000 0.000 0.216 0.104
#> GSM2867 2 0.4769 0.7467 0.000 0.656 0.000 0.000 0.240 0.104
#> GSM2870 2 0.4914 0.7314 0.000 0.628 0.000 0.000 0.268 0.104
#> GSM2854 4 0.1555 0.9141 0.000 0.004 0.000 0.932 0.004 0.060
#> GSM2873 2 0.2084 0.7734 0.000 0.916 0.000 0.044 0.016 0.024
#> GSM2874 3 0.0000 0.9919 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2884 3 0.0000 0.9919 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2875 1 0.0000 0.8781 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2890 1 0.0000 0.8781 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2877 1 0.0291 0.8751 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM2892 1 0.0000 0.8781 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2902 1 0.0146 0.8769 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM2878 1 0.0458 0.8689 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM2901 1 0.0458 0.8689 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM2879 3 0.1588 0.9132 0.000 0.072 0.924 0.000 0.004 0.000
#> GSM2898 3 0.1219 0.9396 0.000 0.048 0.948 0.000 0.004 0.000
#> GSM2881 3 0.0000 0.9919 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2897 3 0.0000 0.9919 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2882 4 0.0363 0.9231 0.000 0.000 0.000 0.988 0.012 0.000
#> GSM2894 4 0.0603 0.9228 0.000 0.000 0.000 0.980 0.016 0.004
#> GSM2883 3 0.0000 0.9919 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2895 3 0.0000 0.9919 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2885 3 0.0000 0.9919 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2886 3 0.0000 0.9919 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2887 3 0.0000 0.9919 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2896 3 0.0000 0.9919 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2888 2 0.5008 0.7246 0.000 0.644 0.000 0.000 0.168 0.188
#> GSM2889 2 0.5088 0.7302 0.000 0.648 0.004 0.000 0.168 0.180
#> GSM2876 1 0.3899 0.1325 0.628 0.000 0.000 0.000 0.364 0.008
#> GSM2891 1 0.3945 0.0706 0.612 0.000 0.000 0.000 0.380 0.008
#> GSM2880 1 0.0405 0.8733 0.988 0.000 0.000 0.000 0.004 0.008
#> GSM2893 1 0.0405 0.8733 0.988 0.000 0.000 0.000 0.004 0.008
#> GSM2821 5 0.3025 0.7149 0.132 0.012 0.000 0.004 0.840 0.012
#> GSM2900 5 0.3368 0.7174 0.232 0.000 0.000 0.000 0.756 0.012
#> GSM2903 5 0.3398 0.7236 0.216 0.004 0.000 0.000 0.768 0.012
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> SD:NMF 79 4.66e-05 2
#> SD:NMF 77 2.99e-08 3
#> SD:NMF 81 2.10e-11 4
#> SD:NMF 77 3.38e-14 5
#> SD:NMF 78 5.97e-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["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 8229 rows and 84 columns.
#> Top rows (823, 1646, 2468, 3291, 4114) are extracted by 'CV' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.405 0.359 0.691 0.3610 0.620 0.620
#> 3 3 0.640 0.832 0.829 0.5497 0.659 0.510
#> 4 4 0.938 0.963 0.972 0.2916 0.849 0.650
#> 5 5 0.903 0.897 0.926 0.0492 0.964 0.873
#> 6 6 0.870 0.887 0.910 0.0393 0.974 0.894
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] 4
There is also optional best \(k\) = 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
#> GSM2819 1 0.993 -0.318 0.548 0.452
#> GSM2820 2 0.978 0.384 0.412 0.588
#> GSM2822 2 1.000 0.414 0.496 0.504
#> GSM2832 2 1.000 0.414 0.496 0.504
#> GSM2823 1 1.000 -0.425 0.508 0.492
#> GSM2824 1 1.000 -0.425 0.508 0.492
#> GSM2825 2 1.000 0.414 0.496 0.504
#> GSM2826 2 1.000 0.414 0.496 0.504
#> GSM2829 2 0.855 0.195 0.280 0.720
#> GSM2856 2 0.855 0.195 0.280 0.720
#> GSM2830 2 0.855 0.195 0.280 0.720
#> GSM2843 2 0.855 0.195 0.280 0.720
#> GSM2871 2 0.855 0.195 0.280 0.720
#> GSM2831 2 0.855 0.195 0.280 0.720
#> GSM2844 2 0.855 0.195 0.280 0.720
#> GSM2833 2 0.855 0.195 0.280 0.720
#> GSM2846 2 0.855 0.195 0.280 0.720
#> GSM2835 2 0.855 0.195 0.280 0.720
#> GSM2858 2 0.855 0.195 0.280 0.720
#> GSM2836 2 1.000 0.414 0.496 0.504
#> GSM2848 2 1.000 0.414 0.496 0.504
#> GSM2828 2 0.978 0.384 0.412 0.588
#> GSM2837 2 0.978 0.384 0.412 0.588
#> GSM2839 1 0.000 0.725 1.000 0.000
#> GSM2841 1 0.000 0.725 1.000 0.000
#> GSM2827 2 1.000 0.414 0.496 0.504
#> GSM2842 2 1.000 0.414 0.496 0.504
#> GSM2845 2 0.855 0.195 0.280 0.720
#> GSM2872 2 0.855 0.195 0.280 0.720
#> GSM2834 2 0.855 0.195 0.280 0.720
#> GSM2847 2 0.855 0.195 0.280 0.720
#> GSM2849 2 0.978 0.384 0.412 0.588
#> GSM2850 2 0.978 0.384 0.412 0.588
#> GSM2838 2 1.000 0.414 0.496 0.504
#> GSM2853 2 1.000 0.414 0.496 0.504
#> GSM2852 2 0.998 0.405 0.472 0.528
#> GSM2855 2 0.998 0.405 0.472 0.528
#> GSM2840 1 0.000 0.725 1.000 0.000
#> GSM2857 1 0.000 0.725 1.000 0.000
#> GSM2859 2 1.000 0.414 0.496 0.504
#> GSM2860 2 1.000 0.414 0.496 0.504
#> GSM2861 2 1.000 0.414 0.496 0.504
#> GSM2862 2 1.000 0.414 0.496 0.504
#> GSM2863 2 1.000 0.414 0.496 0.504
#> GSM2864 2 1.000 0.414 0.496 0.504
#> GSM2865 2 1.000 0.414 0.496 0.504
#> GSM2866 2 1.000 0.414 0.496 0.504
#> GSM2868 2 1.000 0.414 0.496 0.504
#> GSM2869 2 1.000 0.414 0.496 0.504
#> GSM2851 2 1.000 0.414 0.496 0.504
#> GSM2867 2 1.000 0.414 0.496 0.504
#> GSM2870 2 1.000 0.414 0.496 0.504
#> GSM2854 2 0.886 0.184 0.304 0.696
#> GSM2873 2 0.886 0.184 0.304 0.696
#> GSM2874 2 0.978 0.384 0.412 0.588
#> GSM2884 2 0.978 0.384 0.412 0.588
#> GSM2875 1 0.000 0.725 1.000 0.000
#> GSM2890 1 0.000 0.725 1.000 0.000
#> GSM2877 1 0.000 0.725 1.000 0.000
#> GSM2892 1 0.000 0.725 1.000 0.000
#> GSM2902 1 0.000 0.725 1.000 0.000
#> GSM2878 1 0.000 0.725 1.000 0.000
#> GSM2901 1 0.000 0.725 1.000 0.000
#> GSM2879 2 1.000 0.414 0.496 0.504
#> GSM2898 2 1.000 0.414 0.496 0.504
#> GSM2881 2 0.978 0.384 0.412 0.588
#> GSM2897 2 0.978 0.384 0.412 0.588
#> GSM2882 2 0.855 0.195 0.280 0.720
#> GSM2894 2 0.855 0.195 0.280 0.720
#> GSM2883 2 0.978 0.384 0.412 0.588
#> GSM2895 2 0.978 0.384 0.412 0.588
#> GSM2885 2 0.978 0.384 0.412 0.588
#> GSM2886 2 0.978 0.384 0.412 0.588
#> GSM2887 2 0.978 0.384 0.412 0.588
#> GSM2896 2 0.978 0.384 0.412 0.588
#> GSM2888 2 1.000 0.414 0.496 0.504
#> GSM2889 2 1.000 0.414 0.496 0.504
#> GSM2876 1 0.000 0.725 1.000 0.000
#> GSM2891 1 0.000 0.725 1.000 0.000
#> GSM2880 1 0.000 0.725 1.000 0.000
#> GSM2893 1 0.000 0.725 1.000 0.000
#> GSM2821 1 0.993 -0.318 0.548 0.452
#> GSM2900 1 0.993 -0.318 0.548 0.452
#> GSM2903 1 0.993 -0.318 0.548 0.452
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM2819 3 0.2448 0.730 0.076 0.000 0.924
#> GSM2820 3 0.6126 0.621 0.000 0.400 0.600
#> GSM2822 3 0.0000 0.776 0.000 0.000 1.000
#> GSM2832 3 0.0000 0.776 0.000 0.000 1.000
#> GSM2823 3 0.1411 0.749 0.036 0.000 0.964
#> GSM2824 3 0.1411 0.749 0.036 0.000 0.964
#> GSM2825 3 0.0000 0.776 0.000 0.000 1.000
#> GSM2826 3 0.0000 0.776 0.000 0.000 1.000
#> GSM2829 2 0.6126 0.996 0.000 0.600 0.400
#> GSM2856 2 0.6126 0.996 0.000 0.600 0.400
#> GSM2830 2 0.6126 0.996 0.000 0.600 0.400
#> GSM2843 2 0.6126 0.996 0.000 0.600 0.400
#> GSM2871 2 0.6126 0.996 0.000 0.600 0.400
#> GSM2831 2 0.6126 0.996 0.000 0.600 0.400
#> GSM2844 2 0.6126 0.996 0.000 0.600 0.400
#> GSM2833 2 0.6126 0.996 0.000 0.600 0.400
#> GSM2846 2 0.6126 0.996 0.000 0.600 0.400
#> GSM2835 2 0.6126 0.996 0.000 0.600 0.400
#> GSM2858 2 0.6126 0.996 0.000 0.600 0.400
#> GSM2836 3 0.0000 0.776 0.000 0.000 1.000
#> GSM2848 3 0.0000 0.776 0.000 0.000 1.000
#> GSM2828 3 0.6126 0.621 0.000 0.400 0.600
#> GSM2837 3 0.6126 0.621 0.000 0.400 0.600
#> GSM2839 1 0.0000 0.996 1.000 0.000 0.000
#> GSM2841 1 0.0000 0.996 1.000 0.000 0.000
#> GSM2827 3 0.0000 0.776 0.000 0.000 1.000
#> GSM2842 3 0.0000 0.776 0.000 0.000 1.000
#> GSM2845 2 0.6126 0.996 0.000 0.600 0.400
#> GSM2872 2 0.6126 0.996 0.000 0.600 0.400
#> GSM2834 2 0.6126 0.996 0.000 0.600 0.400
#> GSM2847 2 0.6126 0.996 0.000 0.600 0.400
#> GSM2849 3 0.6126 0.621 0.000 0.400 0.600
#> GSM2850 3 0.6126 0.621 0.000 0.400 0.600
#> GSM2838 3 0.0000 0.776 0.000 0.000 1.000
#> GSM2853 3 0.0000 0.776 0.000 0.000 1.000
#> GSM2852 3 0.3752 0.720 0.000 0.144 0.856
#> GSM2855 3 0.3752 0.720 0.000 0.144 0.856
#> GSM2840 1 0.0000 0.996 1.000 0.000 0.000
#> GSM2857 1 0.0000 0.996 1.000 0.000 0.000
#> GSM2859 3 0.0000 0.776 0.000 0.000 1.000
#> GSM2860 3 0.0000 0.776 0.000 0.000 1.000
#> GSM2861 3 0.0000 0.776 0.000 0.000 1.000
#> GSM2862 3 0.0000 0.776 0.000 0.000 1.000
#> GSM2863 3 0.0000 0.776 0.000 0.000 1.000
#> GSM2864 3 0.0000 0.776 0.000 0.000 1.000
#> GSM2865 3 0.0000 0.776 0.000 0.000 1.000
#> GSM2866 3 0.0000 0.776 0.000 0.000 1.000
#> GSM2868 3 0.0000 0.776 0.000 0.000 1.000
#> GSM2869 3 0.0000 0.776 0.000 0.000 1.000
#> GSM2851 3 0.0000 0.776 0.000 0.000 1.000
#> GSM2867 3 0.0000 0.776 0.000 0.000 1.000
#> GSM2870 3 0.0000 0.776 0.000 0.000 1.000
#> GSM2854 2 0.6204 0.963 0.000 0.576 0.424
#> GSM2873 2 0.6204 0.963 0.000 0.576 0.424
#> GSM2874 3 0.6126 0.621 0.000 0.400 0.600
#> GSM2884 3 0.6126 0.621 0.000 0.400 0.600
#> GSM2875 1 0.0000 0.996 1.000 0.000 0.000
#> GSM2890 1 0.0000 0.996 1.000 0.000 0.000
#> GSM2877 1 0.0000 0.996 1.000 0.000 0.000
#> GSM2892 1 0.0000 0.996 1.000 0.000 0.000
#> GSM2902 1 0.0000 0.996 1.000 0.000 0.000
#> GSM2878 1 0.0000 0.996 1.000 0.000 0.000
#> GSM2901 1 0.0000 0.996 1.000 0.000 0.000
#> GSM2879 3 0.0000 0.776 0.000 0.000 1.000
#> GSM2898 3 0.0000 0.776 0.000 0.000 1.000
#> GSM2881 3 0.6126 0.621 0.000 0.400 0.600
#> GSM2897 3 0.6126 0.621 0.000 0.400 0.600
#> GSM2882 2 0.6126 0.996 0.000 0.600 0.400
#> GSM2894 2 0.6126 0.996 0.000 0.600 0.400
#> GSM2883 3 0.6126 0.621 0.000 0.400 0.600
#> GSM2895 3 0.6126 0.621 0.000 0.400 0.600
#> GSM2885 3 0.6126 0.621 0.000 0.400 0.600
#> GSM2886 3 0.6126 0.621 0.000 0.400 0.600
#> GSM2887 3 0.6126 0.621 0.000 0.400 0.600
#> GSM2896 3 0.6126 0.621 0.000 0.400 0.600
#> GSM2888 3 0.0000 0.776 0.000 0.000 1.000
#> GSM2889 3 0.0000 0.776 0.000 0.000 1.000
#> GSM2876 1 0.0892 0.976 0.980 0.000 0.020
#> GSM2891 1 0.0892 0.976 0.980 0.000 0.020
#> GSM2880 1 0.0000 0.996 1.000 0.000 0.000
#> GSM2893 1 0.0000 0.996 1.000 0.000 0.000
#> GSM2821 3 0.2448 0.730 0.076 0.000 0.924
#> GSM2900 3 0.2448 0.730 0.076 0.000 0.924
#> GSM2903 3 0.2448 0.730 0.076 0.000 0.924
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM2819 2 0.3621 0.881 0.072 0.860 0.000 0.068
#> GSM2820 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM2822 2 0.3356 0.824 0.000 0.824 0.000 0.176
#> GSM2832 2 0.3356 0.824 0.000 0.824 0.000 0.176
#> GSM2823 2 0.1305 0.934 0.036 0.960 0.000 0.004
#> GSM2824 2 0.1305 0.934 0.036 0.960 0.000 0.004
#> GSM2825 2 0.3356 0.824 0.000 0.824 0.000 0.176
#> GSM2826 2 0.3356 0.824 0.000 0.824 0.000 0.176
#> GSM2829 4 0.0592 0.990 0.000 0.016 0.000 0.984
#> GSM2856 4 0.0592 0.990 0.000 0.016 0.000 0.984
#> GSM2830 4 0.0707 0.989 0.000 0.020 0.000 0.980
#> GSM2843 4 0.0707 0.989 0.000 0.020 0.000 0.980
#> GSM2871 4 0.0707 0.989 0.000 0.020 0.000 0.980
#> GSM2831 4 0.0592 0.990 0.000 0.016 0.000 0.984
#> GSM2844 4 0.0592 0.990 0.000 0.016 0.000 0.984
#> GSM2833 4 0.0592 0.990 0.000 0.016 0.000 0.984
#> GSM2846 4 0.0592 0.990 0.000 0.016 0.000 0.984
#> GSM2835 4 0.0592 0.990 0.000 0.016 0.000 0.984
#> GSM2858 4 0.0592 0.990 0.000 0.016 0.000 0.984
#> GSM2836 2 0.0188 0.952 0.000 0.996 0.000 0.004
#> GSM2848 2 0.0188 0.952 0.000 0.996 0.000 0.004
#> GSM2828 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM2837 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM2839 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM2841 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM2827 2 0.0188 0.952 0.000 0.996 0.000 0.004
#> GSM2842 2 0.0188 0.952 0.000 0.996 0.000 0.004
#> GSM2845 4 0.0707 0.989 0.000 0.020 0.000 0.980
#> GSM2872 4 0.0707 0.989 0.000 0.020 0.000 0.980
#> GSM2834 4 0.0817 0.986 0.000 0.024 0.000 0.976
#> GSM2847 4 0.0817 0.986 0.000 0.024 0.000 0.976
#> GSM2849 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM2850 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM2838 2 0.0188 0.953 0.000 0.996 0.000 0.004
#> GSM2853 2 0.0188 0.953 0.000 0.996 0.000 0.004
#> GSM2852 2 0.2973 0.840 0.000 0.856 0.144 0.000
#> GSM2855 2 0.2973 0.840 0.000 0.856 0.144 0.000
#> GSM2840 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM2857 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM2859 2 0.0188 0.953 0.000 0.996 0.000 0.004
#> GSM2860 2 0.0188 0.953 0.000 0.996 0.000 0.004
#> GSM2861 2 0.0188 0.953 0.000 0.996 0.000 0.004
#> GSM2862 2 0.0188 0.953 0.000 0.996 0.000 0.004
#> GSM2863 2 0.0188 0.953 0.000 0.996 0.000 0.004
#> GSM2864 2 0.0188 0.953 0.000 0.996 0.000 0.004
#> GSM2865 2 0.0188 0.953 0.000 0.996 0.000 0.004
#> GSM2866 2 0.0188 0.953 0.000 0.996 0.000 0.004
#> GSM2868 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM2869 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM2851 2 0.0188 0.953 0.000 0.996 0.000 0.004
#> GSM2867 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM2870 2 0.0188 0.953 0.000 0.996 0.000 0.004
#> GSM2854 4 0.1940 0.933 0.000 0.076 0.000 0.924
#> GSM2873 4 0.1940 0.933 0.000 0.076 0.000 0.924
#> GSM2874 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM2884 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM2875 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM2890 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM2877 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM2892 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM2902 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM2878 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM2901 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM2879 2 0.0376 0.951 0.000 0.992 0.004 0.004
#> GSM2898 2 0.0376 0.951 0.000 0.992 0.004 0.004
#> GSM2881 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM2897 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM2882 4 0.0592 0.990 0.000 0.016 0.000 0.984
#> GSM2894 4 0.0592 0.990 0.000 0.016 0.000 0.984
#> GSM2883 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM2895 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM2885 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM2886 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM2887 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM2896 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM2888 2 0.0188 0.953 0.000 0.996 0.000 0.004
#> GSM2889 2 0.0188 0.953 0.000 0.996 0.000 0.004
#> GSM2876 1 0.0707 0.976 0.980 0.020 0.000 0.000
#> GSM2891 1 0.0707 0.976 0.980 0.020 0.000 0.000
#> GSM2880 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM2893 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM2821 2 0.3621 0.881 0.072 0.860 0.000 0.068
#> GSM2900 2 0.3621 0.881 0.072 0.860 0.000 0.068
#> GSM2903 2 0.3621 0.881 0.072 0.860 0.000 0.068
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM2819 5 0.3949 1.000 0.000 0.332 0.000 0.000 0.668
#> GSM2820 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2822 2 0.4395 0.511 0.000 0.748 0.000 0.188 0.064
#> GSM2832 2 0.4395 0.511 0.000 0.748 0.000 0.188 0.064
#> GSM2823 2 0.2124 0.800 0.000 0.900 0.000 0.004 0.096
#> GSM2824 2 0.2124 0.800 0.000 0.900 0.000 0.004 0.096
#> GSM2825 2 0.4395 0.511 0.000 0.748 0.000 0.188 0.064
#> GSM2826 2 0.4395 0.511 0.000 0.748 0.000 0.188 0.064
#> GSM2829 4 0.0000 0.843 0.000 0.000 0.000 1.000 0.000
#> GSM2856 4 0.0000 0.843 0.000 0.000 0.000 1.000 0.000
#> GSM2830 4 0.4288 0.817 0.000 0.012 0.000 0.664 0.324
#> GSM2843 4 0.4288 0.817 0.000 0.012 0.000 0.664 0.324
#> GSM2871 4 0.4288 0.817 0.000 0.012 0.000 0.664 0.324
#> GSM2831 4 0.0609 0.842 0.000 0.000 0.000 0.980 0.020
#> GSM2844 4 0.0609 0.842 0.000 0.000 0.000 0.980 0.020
#> GSM2833 4 0.0000 0.843 0.000 0.000 0.000 1.000 0.000
#> GSM2846 4 0.0000 0.843 0.000 0.000 0.000 1.000 0.000
#> GSM2835 4 0.0000 0.843 0.000 0.000 0.000 1.000 0.000
#> GSM2858 4 0.0000 0.843 0.000 0.000 0.000 1.000 0.000
#> GSM2836 2 0.0566 0.905 0.000 0.984 0.000 0.004 0.012
#> GSM2848 2 0.0566 0.905 0.000 0.984 0.000 0.004 0.012
#> GSM2828 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2837 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2839 1 0.0000 0.991 1.000 0.000 0.000 0.000 0.000
#> GSM2841 1 0.0000 0.991 1.000 0.000 0.000 0.000 0.000
#> GSM2827 2 0.0566 0.905 0.000 0.984 0.000 0.004 0.012
#> GSM2842 2 0.0566 0.905 0.000 0.984 0.000 0.004 0.012
#> GSM2845 4 0.4288 0.817 0.000 0.012 0.000 0.664 0.324
#> GSM2872 4 0.4288 0.817 0.000 0.012 0.000 0.664 0.324
#> GSM2834 4 0.4290 0.815 0.000 0.016 0.000 0.680 0.304
#> GSM2847 4 0.4290 0.815 0.000 0.016 0.000 0.680 0.304
#> GSM2849 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2850 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2838 2 0.0000 0.909 0.000 1.000 0.000 0.000 0.000
#> GSM2853 2 0.0000 0.909 0.000 1.000 0.000 0.000 0.000
#> GSM2852 2 0.2561 0.701 0.000 0.856 0.144 0.000 0.000
#> GSM2855 2 0.2561 0.701 0.000 0.856 0.144 0.000 0.000
#> GSM2840 1 0.0000 0.991 1.000 0.000 0.000 0.000 0.000
#> GSM2857 1 0.0000 0.991 1.000 0.000 0.000 0.000 0.000
#> GSM2859 2 0.0000 0.909 0.000 1.000 0.000 0.000 0.000
#> GSM2860 2 0.0000 0.909 0.000 1.000 0.000 0.000 0.000
#> GSM2861 2 0.0000 0.909 0.000 1.000 0.000 0.000 0.000
#> GSM2862 2 0.0000 0.909 0.000 1.000 0.000 0.000 0.000
#> GSM2863 2 0.0000 0.909 0.000 1.000 0.000 0.000 0.000
#> GSM2864 2 0.0000 0.909 0.000 1.000 0.000 0.000 0.000
#> GSM2865 2 0.0000 0.909 0.000 1.000 0.000 0.000 0.000
#> GSM2866 2 0.0000 0.909 0.000 1.000 0.000 0.000 0.000
#> GSM2868 2 0.0404 0.905 0.000 0.988 0.000 0.000 0.012
#> GSM2869 2 0.0404 0.905 0.000 0.988 0.000 0.000 0.012
#> GSM2851 2 0.0000 0.909 0.000 1.000 0.000 0.000 0.000
#> GSM2867 2 0.0404 0.905 0.000 0.988 0.000 0.000 0.012
#> GSM2870 2 0.0000 0.909 0.000 1.000 0.000 0.000 0.000
#> GSM2854 4 0.5126 0.774 0.000 0.064 0.000 0.636 0.300
#> GSM2873 4 0.5126 0.774 0.000 0.064 0.000 0.636 0.300
#> GSM2874 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2884 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2875 1 0.0000 0.991 1.000 0.000 0.000 0.000 0.000
#> GSM2890 1 0.0000 0.991 1.000 0.000 0.000 0.000 0.000
#> GSM2877 1 0.0000 0.991 1.000 0.000 0.000 0.000 0.000
#> GSM2892 1 0.0000 0.991 1.000 0.000 0.000 0.000 0.000
#> GSM2902 1 0.0000 0.991 1.000 0.000 0.000 0.000 0.000
#> GSM2878 1 0.0000 0.991 1.000 0.000 0.000 0.000 0.000
#> GSM2901 1 0.0000 0.991 1.000 0.000 0.000 0.000 0.000
#> GSM2879 2 0.0727 0.903 0.000 0.980 0.004 0.004 0.012
#> GSM2898 2 0.0727 0.903 0.000 0.980 0.004 0.004 0.012
#> GSM2881 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2897 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2882 4 0.0609 0.842 0.000 0.000 0.000 0.980 0.020
#> GSM2894 4 0.0609 0.842 0.000 0.000 0.000 0.980 0.020
#> GSM2883 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2895 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2885 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2886 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2887 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2896 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2888 2 0.0000 0.909 0.000 1.000 0.000 0.000 0.000
#> GSM2889 2 0.0000 0.909 0.000 1.000 0.000 0.000 0.000
#> GSM2876 1 0.1478 0.940 0.936 0.000 0.000 0.000 0.064
#> GSM2891 1 0.1478 0.940 0.936 0.000 0.000 0.000 0.064
#> GSM2880 1 0.0000 0.991 1.000 0.000 0.000 0.000 0.000
#> GSM2893 1 0.0000 0.991 1.000 0.000 0.000 0.000 0.000
#> GSM2821 5 0.3949 1.000 0.000 0.332 0.000 0.000 0.668
#> GSM2900 5 0.3949 1.000 0.000 0.332 0.000 0.000 0.668
#> GSM2903 5 0.3949 1.000 0.000 0.332 0.000 0.000 0.668
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM2819 5 0.2260 1.000 0.000 0.140 0.000 0.000 0.860 0.000
#> GSM2820 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2822 2 0.5709 0.396 0.000 0.584 0.000 0.152 0.020 0.244
#> GSM2832 2 0.5709 0.396 0.000 0.584 0.000 0.152 0.020 0.244
#> GSM2823 2 0.3168 0.705 0.000 0.804 0.000 0.000 0.172 0.024
#> GSM2824 2 0.3168 0.705 0.000 0.804 0.000 0.000 0.172 0.024
#> GSM2825 2 0.5709 0.396 0.000 0.584 0.000 0.152 0.020 0.244
#> GSM2826 2 0.5709 0.396 0.000 0.584 0.000 0.152 0.020 0.244
#> GSM2829 4 0.0000 0.901 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2856 4 0.0000 0.901 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2830 6 0.3244 0.885 0.000 0.000 0.000 0.268 0.000 0.732
#> GSM2843 6 0.3244 0.885 0.000 0.000 0.000 0.268 0.000 0.732
#> GSM2871 6 0.3244 0.885 0.000 0.000 0.000 0.268 0.000 0.732
#> GSM2831 4 0.2219 0.843 0.000 0.000 0.000 0.864 0.000 0.136
#> GSM2844 4 0.2219 0.843 0.000 0.000 0.000 0.864 0.000 0.136
#> GSM2833 4 0.0000 0.901 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2846 4 0.0000 0.901 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2835 4 0.0000 0.901 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2858 4 0.0000 0.901 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2836 2 0.0777 0.890 0.000 0.972 0.000 0.000 0.004 0.024
#> GSM2848 2 0.0777 0.890 0.000 0.972 0.000 0.000 0.004 0.024
#> GSM2828 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2837 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2839 1 0.2531 0.891 0.856 0.000 0.000 0.000 0.132 0.012
#> GSM2841 1 0.2531 0.891 0.856 0.000 0.000 0.000 0.132 0.012
#> GSM2827 2 0.0777 0.890 0.000 0.972 0.000 0.000 0.004 0.024
#> GSM2842 2 0.0777 0.890 0.000 0.972 0.000 0.000 0.004 0.024
#> GSM2845 6 0.3244 0.885 0.000 0.000 0.000 0.268 0.000 0.732
#> GSM2872 6 0.3244 0.885 0.000 0.000 0.000 0.268 0.000 0.732
#> GSM2834 6 0.3830 0.846 0.000 0.004 0.000 0.376 0.000 0.620
#> GSM2847 6 0.3830 0.846 0.000 0.004 0.000 0.376 0.000 0.620
#> GSM2849 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2850 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2838 2 0.0146 0.895 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM2853 2 0.0146 0.895 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM2852 2 0.2300 0.758 0.000 0.856 0.144 0.000 0.000 0.000
#> GSM2855 2 0.2300 0.758 0.000 0.856 0.144 0.000 0.000 0.000
#> GSM2840 1 0.2531 0.891 0.856 0.000 0.000 0.000 0.132 0.012
#> GSM2857 1 0.2531 0.891 0.856 0.000 0.000 0.000 0.132 0.012
#> GSM2859 2 0.0260 0.895 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM2860 2 0.0260 0.895 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM2861 2 0.0260 0.895 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM2862 2 0.0260 0.895 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM2863 2 0.0260 0.895 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM2864 2 0.0260 0.895 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM2865 2 0.0260 0.895 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM2866 2 0.0260 0.895 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM2868 2 0.0717 0.890 0.000 0.976 0.000 0.000 0.008 0.016
#> GSM2869 2 0.0717 0.890 0.000 0.976 0.000 0.000 0.008 0.016
#> GSM2851 2 0.0000 0.895 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2867 2 0.0717 0.890 0.000 0.976 0.000 0.000 0.008 0.016
#> GSM2870 2 0.0000 0.895 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2854 6 0.4444 0.793 0.000 0.024 0.000 0.356 0.008 0.612
#> GSM2873 6 0.4444 0.793 0.000 0.024 0.000 0.356 0.008 0.612
#> GSM2874 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2884 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2875 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2890 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2877 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2892 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2902 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2878 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2901 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2879 2 0.0922 0.888 0.000 0.968 0.004 0.000 0.004 0.024
#> GSM2898 2 0.0922 0.888 0.000 0.968 0.004 0.000 0.004 0.024
#> GSM2881 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2897 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2882 4 0.2219 0.843 0.000 0.000 0.000 0.864 0.000 0.136
#> GSM2894 4 0.2219 0.843 0.000 0.000 0.000 0.864 0.000 0.136
#> GSM2883 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2895 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2885 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2886 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2887 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2896 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2888 2 0.0000 0.895 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2889 2 0.0000 0.895 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2876 1 0.1327 0.913 0.936 0.000 0.000 0.000 0.064 0.000
#> GSM2891 1 0.1327 0.913 0.936 0.000 0.000 0.000 0.064 0.000
#> GSM2880 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2893 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2821 5 0.2260 1.000 0.000 0.140 0.000 0.000 0.860 0.000
#> GSM2900 5 0.2260 1.000 0.000 0.140 0.000 0.000 0.860 0.000
#> GSM2903 5 0.2260 1.000 0.000 0.140 0.000 0.000 0.860 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 tissue(p) k
#> CV:hclust 15 NA 2
#> CV:hclust 84 6.67e-09 3
#> CV:hclust 84 1.99e-12 4
#> CV:hclust 84 6.24e-16 5
#> CV:hclust 80 9.28e-19 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 8229 rows and 84 columns.
#> Top rows (823, 1646, 2468, 3291, 4114) 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.242 0.524 0.644 0.3847 0.598 0.598
#> 3 3 0.382 0.778 0.781 0.5444 0.685 0.521
#> 4 4 0.630 0.908 0.854 0.1890 0.850 0.628
#> 5 5 0.790 0.853 0.853 0.0823 1.000 1.000
#> 6 6 0.765 0.755 0.800 0.0445 0.987 0.949
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM2819 1 0.9954 -0.396 0.540 0.460
#> GSM2820 2 0.6973 0.537 0.188 0.812
#> GSM2822 1 0.9988 -0.429 0.520 0.480
#> GSM2832 1 0.9988 -0.429 0.520 0.480
#> GSM2823 2 0.9933 0.565 0.452 0.548
#> GSM2824 2 0.9933 0.565 0.452 0.548
#> GSM2825 1 0.9922 -0.373 0.552 0.448
#> GSM2826 1 0.9922 -0.373 0.552 0.448
#> GSM2829 2 0.9833 0.405 0.424 0.576
#> GSM2856 2 0.9833 0.405 0.424 0.576
#> GSM2830 2 0.9833 0.405 0.424 0.576
#> GSM2843 2 0.9833 0.405 0.424 0.576
#> GSM2871 2 0.9833 0.405 0.424 0.576
#> GSM2831 2 0.9850 0.398 0.428 0.572
#> GSM2844 2 0.9850 0.398 0.428 0.572
#> GSM2833 2 0.9815 0.405 0.420 0.580
#> GSM2846 2 0.9815 0.405 0.420 0.580
#> GSM2835 2 0.9881 0.381 0.436 0.564
#> GSM2858 2 0.9881 0.381 0.436 0.564
#> GSM2836 2 0.9686 0.603 0.396 0.604
#> GSM2848 2 0.9686 0.603 0.396 0.604
#> GSM2828 2 0.6973 0.537 0.188 0.812
#> GSM2837 2 0.6973 0.537 0.188 0.812
#> GSM2839 1 0.0000 0.793 1.000 0.000
#> GSM2841 1 0.0000 0.793 1.000 0.000
#> GSM2827 2 0.9635 0.605 0.388 0.612
#> GSM2842 2 0.9635 0.605 0.388 0.612
#> GSM2845 2 0.9833 0.405 0.424 0.576
#> GSM2872 2 0.9833 0.405 0.424 0.576
#> GSM2834 2 0.9833 0.405 0.424 0.576
#> GSM2847 2 0.9833 0.405 0.424 0.576
#> GSM2849 2 0.6973 0.537 0.188 0.812
#> GSM2850 2 0.6973 0.537 0.188 0.812
#> GSM2838 2 0.9686 0.603 0.396 0.604
#> GSM2853 2 0.9686 0.603 0.396 0.604
#> GSM2852 2 0.5408 0.547 0.124 0.876
#> GSM2855 2 0.5408 0.547 0.124 0.876
#> GSM2840 1 0.0000 0.793 1.000 0.000
#> GSM2857 1 0.0000 0.793 1.000 0.000
#> GSM2859 2 0.9686 0.603 0.396 0.604
#> GSM2860 2 0.9686 0.603 0.396 0.604
#> GSM2861 2 0.9686 0.603 0.396 0.604
#> GSM2862 2 0.9686 0.603 0.396 0.604
#> GSM2863 2 0.9686 0.603 0.396 0.604
#> GSM2864 2 0.9686 0.603 0.396 0.604
#> GSM2865 2 0.9686 0.603 0.396 0.604
#> GSM2866 2 0.9686 0.603 0.396 0.604
#> GSM2868 2 0.9686 0.603 0.396 0.604
#> GSM2869 2 0.9686 0.603 0.396 0.604
#> GSM2851 2 0.9686 0.603 0.396 0.604
#> GSM2867 2 0.9686 0.603 0.396 0.604
#> GSM2870 2 0.9686 0.603 0.396 0.604
#> GSM2854 2 0.9710 0.404 0.400 0.600
#> GSM2873 2 0.9795 0.571 0.416 0.584
#> GSM2874 2 0.6973 0.537 0.188 0.812
#> GSM2884 2 0.6973 0.537 0.188 0.812
#> GSM2875 1 0.0672 0.793 0.992 0.008
#> GSM2890 1 0.0672 0.793 0.992 0.008
#> GSM2877 1 0.0672 0.793 0.992 0.008
#> GSM2892 1 0.0672 0.793 0.992 0.008
#> GSM2902 1 0.0672 0.793 0.992 0.008
#> GSM2878 1 0.0672 0.793 0.992 0.008
#> GSM2901 1 0.0672 0.793 0.992 0.008
#> GSM2879 2 0.7376 0.541 0.208 0.792
#> GSM2898 2 0.7376 0.541 0.208 0.792
#> GSM2881 2 0.6973 0.537 0.188 0.812
#> GSM2897 2 0.6973 0.537 0.188 0.812
#> GSM2882 2 0.9881 0.381 0.436 0.564
#> GSM2894 2 0.9881 0.381 0.436 0.564
#> GSM2883 2 0.6973 0.537 0.188 0.812
#> GSM2895 2 0.6973 0.537 0.188 0.812
#> GSM2885 2 0.6973 0.537 0.188 0.812
#> GSM2886 2 0.6973 0.537 0.188 0.812
#> GSM2887 2 0.6887 0.537 0.184 0.816
#> GSM2896 2 0.6887 0.537 0.184 0.816
#> GSM2888 2 0.9323 0.606 0.348 0.652
#> GSM2889 2 0.9323 0.606 0.348 0.652
#> GSM2876 1 0.0000 0.793 1.000 0.000
#> GSM2891 1 0.0000 0.793 1.000 0.000
#> GSM2880 1 0.0672 0.793 0.992 0.008
#> GSM2893 1 0.0672 0.793 0.992 0.008
#> GSM2821 1 0.1843 0.770 0.972 0.028
#> GSM2900 1 0.1843 0.770 0.972 0.028
#> GSM2903 1 0.1843 0.770 0.972 0.028
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM2819 2 0.780 0.673 0.140 0.672 0.188
#> GSM2820 3 0.298 0.973 0.024 0.056 0.920
#> GSM2822 2 0.672 0.681 0.096 0.744 0.160
#> GSM2832 2 0.672 0.681 0.096 0.744 0.160
#> GSM2823 2 0.835 0.650 0.120 0.600 0.280
#> GSM2824 2 0.835 0.650 0.120 0.600 0.280
#> GSM2825 2 0.780 0.612 0.276 0.636 0.088
#> GSM2826 2 0.780 0.612 0.276 0.636 0.088
#> GSM2829 2 0.466 0.602 0.124 0.844 0.032
#> GSM2856 2 0.466 0.602 0.124 0.844 0.032
#> GSM2830 2 0.473 0.602 0.128 0.840 0.032
#> GSM2843 2 0.473 0.602 0.128 0.840 0.032
#> GSM2871 2 0.473 0.602 0.128 0.840 0.032
#> GSM2831 2 0.466 0.602 0.124 0.844 0.032
#> GSM2844 2 0.466 0.602 0.124 0.844 0.032
#> GSM2833 2 0.454 0.603 0.124 0.848 0.028
#> GSM2846 2 0.454 0.603 0.124 0.848 0.028
#> GSM2835 2 0.454 0.603 0.124 0.848 0.028
#> GSM2858 2 0.454 0.603 0.124 0.848 0.028
#> GSM2836 2 0.807 0.671 0.104 0.620 0.276
#> GSM2848 2 0.807 0.671 0.104 0.620 0.276
#> GSM2828 3 0.298 0.973 0.024 0.056 0.920
#> GSM2837 3 0.298 0.973 0.024 0.056 0.920
#> GSM2839 1 0.241 0.954 0.940 0.020 0.040
#> GSM2841 1 0.241 0.954 0.940 0.020 0.040
#> GSM2827 2 0.807 0.671 0.104 0.620 0.276
#> GSM2842 2 0.807 0.671 0.104 0.620 0.276
#> GSM2845 2 0.473 0.602 0.128 0.840 0.032
#> GSM2872 2 0.473 0.602 0.128 0.840 0.032
#> GSM2834 2 0.454 0.605 0.124 0.848 0.028
#> GSM2847 2 0.473 0.602 0.128 0.840 0.032
#> GSM2849 3 0.298 0.973 0.024 0.056 0.920
#> GSM2850 3 0.298 0.973 0.024 0.056 0.920
#> GSM2838 2 0.807 0.671 0.104 0.620 0.276
#> GSM2853 2 0.807 0.671 0.104 0.620 0.276
#> GSM2852 3 0.268 0.942 0.008 0.068 0.924
#> GSM2855 3 0.268 0.942 0.008 0.068 0.924
#> GSM2840 1 0.241 0.954 0.940 0.020 0.040
#> GSM2857 1 0.241 0.954 0.940 0.020 0.040
#> GSM2859 2 0.807 0.671 0.104 0.620 0.276
#> GSM2860 2 0.807 0.671 0.104 0.620 0.276
#> GSM2861 2 0.807 0.671 0.104 0.620 0.276
#> GSM2862 2 0.807 0.671 0.104 0.620 0.276
#> GSM2863 2 0.807 0.671 0.104 0.620 0.276
#> GSM2864 2 0.807 0.671 0.104 0.620 0.276
#> GSM2865 2 0.807 0.671 0.104 0.620 0.276
#> GSM2866 2 0.792 0.675 0.104 0.640 0.256
#> GSM2868 2 0.807 0.671 0.104 0.620 0.276
#> GSM2869 2 0.807 0.671 0.104 0.620 0.276
#> GSM2851 2 0.807 0.671 0.104 0.620 0.276
#> GSM2867 2 0.807 0.671 0.104 0.620 0.276
#> GSM2870 2 0.807 0.671 0.104 0.620 0.276
#> GSM2854 2 0.165 0.631 0.036 0.960 0.004
#> GSM2873 2 0.666 0.681 0.096 0.748 0.156
#> GSM2874 3 0.285 0.973 0.020 0.056 0.924
#> GSM2884 3 0.285 0.973 0.020 0.056 0.924
#> GSM2875 1 0.132 0.965 0.972 0.008 0.020
#> GSM2890 1 0.132 0.965 0.972 0.008 0.020
#> GSM2877 1 0.132 0.965 0.972 0.008 0.020
#> GSM2892 1 0.132 0.965 0.972 0.008 0.020
#> GSM2902 1 0.132 0.965 0.972 0.008 0.020
#> GSM2878 1 0.117 0.965 0.976 0.008 0.016
#> GSM2901 1 0.117 0.965 0.976 0.008 0.016
#> GSM2879 3 0.551 0.812 0.044 0.156 0.800
#> GSM2898 3 0.551 0.812 0.044 0.156 0.800
#> GSM2881 3 0.285 0.973 0.020 0.056 0.924
#> GSM2897 3 0.285 0.973 0.020 0.056 0.924
#> GSM2882 2 0.478 0.598 0.124 0.840 0.036
#> GSM2894 2 0.478 0.598 0.124 0.840 0.036
#> GSM2883 3 0.311 0.972 0.028 0.056 0.916
#> GSM2895 3 0.311 0.972 0.028 0.056 0.916
#> GSM2885 3 0.285 0.973 0.020 0.056 0.924
#> GSM2886 3 0.285 0.973 0.020 0.056 0.924
#> GSM2887 3 0.285 0.973 0.020 0.056 0.924
#> GSM2896 3 0.285 0.973 0.020 0.056 0.924
#> GSM2888 2 0.807 0.659 0.100 0.616 0.284
#> GSM2889 2 0.807 0.659 0.100 0.616 0.284
#> GSM2876 1 0.206 0.961 0.948 0.008 0.044
#> GSM2891 1 0.206 0.961 0.948 0.008 0.044
#> GSM2880 1 0.132 0.965 0.972 0.008 0.020
#> GSM2893 1 0.132 0.965 0.972 0.008 0.020
#> GSM2821 1 0.440 0.882 0.864 0.092 0.044
#> GSM2900 1 0.440 0.882 0.864 0.092 0.044
#> GSM2903 1 0.440 0.882 0.864 0.092 0.044
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM2819 2 0.4758 0.806 0.024 0.816 0.080 0.080
#> GSM2820 3 0.4526 0.952 0.016 0.160 0.800 0.024
#> GSM2822 2 0.4370 0.767 0.000 0.800 0.044 0.156
#> GSM2832 2 0.4370 0.767 0.000 0.800 0.044 0.156
#> GSM2823 2 0.3471 0.860 0.016 0.880 0.036 0.068
#> GSM2824 2 0.3471 0.860 0.016 0.880 0.036 0.068
#> GSM2825 2 0.6410 0.625 0.040 0.688 0.064 0.208
#> GSM2826 2 0.6410 0.625 0.040 0.688 0.064 0.208
#> GSM2829 4 0.4400 0.971 0.012 0.136 0.036 0.816
#> GSM2856 4 0.4400 0.971 0.012 0.136 0.036 0.816
#> GSM2830 4 0.4853 0.971 0.024 0.132 0.044 0.800
#> GSM2843 4 0.4853 0.971 0.024 0.132 0.044 0.800
#> GSM2871 4 0.4853 0.971 0.024 0.132 0.044 0.800
#> GSM2831 4 0.4606 0.973 0.016 0.136 0.040 0.808
#> GSM2844 4 0.4606 0.973 0.016 0.136 0.040 0.808
#> GSM2833 4 0.4360 0.969 0.012 0.140 0.032 0.816
#> GSM2846 4 0.4360 0.969 0.012 0.140 0.032 0.816
#> GSM2835 4 0.4348 0.966 0.012 0.132 0.036 0.820
#> GSM2858 4 0.4348 0.966 0.012 0.132 0.036 0.820
#> GSM2836 2 0.1296 0.921 0.004 0.964 0.004 0.028
#> GSM2848 2 0.1296 0.921 0.004 0.964 0.004 0.028
#> GSM2828 3 0.4526 0.952 0.016 0.160 0.800 0.024
#> GSM2837 3 0.4526 0.952 0.016 0.160 0.800 0.024
#> GSM2839 1 0.4185 0.906 0.848 0.024 0.072 0.056
#> GSM2841 1 0.4185 0.906 0.848 0.024 0.072 0.056
#> GSM2827 2 0.1151 0.920 0.000 0.968 0.008 0.024
#> GSM2842 2 0.1151 0.920 0.000 0.968 0.008 0.024
#> GSM2845 4 0.4853 0.971 0.024 0.132 0.044 0.800
#> GSM2872 4 0.4853 0.971 0.024 0.132 0.044 0.800
#> GSM2834 4 0.4640 0.971 0.024 0.136 0.032 0.808
#> GSM2847 4 0.4680 0.972 0.024 0.132 0.036 0.808
#> GSM2849 3 0.4625 0.952 0.016 0.160 0.796 0.028
#> GSM2850 3 0.4625 0.952 0.016 0.160 0.796 0.028
#> GSM2838 2 0.0672 0.922 0.000 0.984 0.008 0.008
#> GSM2853 2 0.0672 0.922 0.000 0.984 0.008 0.008
#> GSM2852 3 0.4776 0.920 0.004 0.184 0.772 0.040
#> GSM2855 3 0.4776 0.920 0.004 0.184 0.772 0.040
#> GSM2840 1 0.4185 0.906 0.848 0.024 0.072 0.056
#> GSM2857 1 0.4185 0.906 0.848 0.024 0.072 0.056
#> GSM2859 2 0.1229 0.921 0.008 0.968 0.004 0.020
#> GSM2860 2 0.1229 0.921 0.008 0.968 0.004 0.020
#> GSM2861 2 0.1114 0.921 0.004 0.972 0.008 0.016
#> GSM2862 2 0.1229 0.921 0.008 0.968 0.004 0.020
#> GSM2863 2 0.1229 0.921 0.008 0.968 0.004 0.020
#> GSM2864 2 0.1229 0.921 0.008 0.968 0.004 0.020
#> GSM2865 2 0.1229 0.921 0.008 0.968 0.004 0.020
#> GSM2866 2 0.2057 0.911 0.008 0.940 0.020 0.032
#> GSM2868 2 0.0524 0.921 0.000 0.988 0.008 0.004
#> GSM2869 2 0.0524 0.921 0.000 0.988 0.008 0.004
#> GSM2851 2 0.0524 0.921 0.000 0.988 0.008 0.004
#> GSM2867 2 0.0524 0.921 0.000 0.988 0.008 0.004
#> GSM2870 2 0.0524 0.921 0.000 0.988 0.008 0.004
#> GSM2854 4 0.4418 0.941 0.008 0.172 0.024 0.796
#> GSM2873 2 0.4232 0.763 0.004 0.804 0.024 0.168
#> GSM2874 3 0.4305 0.952 0.012 0.160 0.808 0.020
#> GSM2884 3 0.4305 0.952 0.012 0.160 0.808 0.020
#> GSM2875 1 0.1749 0.927 0.952 0.024 0.012 0.012
#> GSM2890 1 0.1749 0.927 0.952 0.024 0.012 0.012
#> GSM2877 1 0.1749 0.927 0.952 0.024 0.012 0.012
#> GSM2892 1 0.1749 0.927 0.952 0.024 0.012 0.012
#> GSM2902 1 0.1749 0.927 0.952 0.024 0.012 0.012
#> GSM2878 1 0.1339 0.927 0.964 0.024 0.004 0.008
#> GSM2901 1 0.1339 0.927 0.964 0.024 0.004 0.008
#> GSM2879 3 0.5907 0.613 0.004 0.392 0.572 0.032
#> GSM2898 3 0.5907 0.613 0.004 0.392 0.572 0.032
#> GSM2881 3 0.4178 0.953 0.008 0.160 0.812 0.020
#> GSM2897 3 0.4178 0.953 0.008 0.160 0.812 0.020
#> GSM2882 4 0.4308 0.972 0.012 0.136 0.032 0.820
#> GSM2894 4 0.4308 0.972 0.012 0.136 0.032 0.820
#> GSM2883 3 0.5251 0.942 0.020 0.160 0.768 0.052
#> GSM2895 3 0.5251 0.942 0.020 0.160 0.768 0.052
#> GSM2885 3 0.4178 0.953 0.008 0.160 0.812 0.020
#> GSM2886 3 0.4178 0.953 0.008 0.160 0.812 0.020
#> GSM2887 3 0.4567 0.949 0.008 0.160 0.796 0.036
#> GSM2896 3 0.4567 0.949 0.008 0.160 0.796 0.036
#> GSM2888 2 0.1584 0.912 0.000 0.952 0.012 0.036
#> GSM2889 2 0.1584 0.912 0.000 0.952 0.012 0.036
#> GSM2876 1 0.3379 0.917 0.888 0.024 0.052 0.036
#> GSM2891 1 0.3379 0.917 0.888 0.024 0.052 0.036
#> GSM2880 1 0.1749 0.927 0.952 0.024 0.012 0.012
#> GSM2893 1 0.1749 0.927 0.952 0.024 0.012 0.012
#> GSM2821 1 0.6791 0.765 0.684 0.172 0.072 0.072
#> GSM2900 1 0.6791 0.765 0.684 0.172 0.072 0.072
#> GSM2903 1 0.6791 0.765 0.684 0.172 0.072 0.072
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM2819 2 0.4329 0.697 0.000 0.672 0.000 0.016 NA
#> GSM2820 3 0.2663 0.912 0.004 0.064 0.896 0.004 NA
#> GSM2822 2 0.4944 0.751 0.000 0.724 0.004 0.116 NA
#> GSM2832 2 0.4944 0.751 0.000 0.724 0.004 0.116 NA
#> GSM2823 2 0.4468 0.736 0.000 0.696 0.004 0.024 NA
#> GSM2824 2 0.4468 0.736 0.000 0.696 0.004 0.024 NA
#> GSM2825 2 0.6093 0.638 0.000 0.608 0.012 0.156 NA
#> GSM2826 2 0.6093 0.638 0.000 0.608 0.012 0.156 NA
#> GSM2829 4 0.3522 0.923 0.000 0.032 0.020 0.844 NA
#> GSM2856 4 0.3522 0.923 0.000 0.032 0.020 0.844 NA
#> GSM2830 4 0.2386 0.929 0.004 0.032 0.004 0.912 NA
#> GSM2843 4 0.2386 0.929 0.004 0.032 0.004 0.912 NA
#> GSM2871 4 0.2722 0.925 0.004 0.032 0.008 0.896 NA
#> GSM2831 4 0.2045 0.934 0.004 0.032 0.012 0.932 NA
#> GSM2844 4 0.2045 0.934 0.004 0.032 0.012 0.932 NA
#> GSM2833 4 0.3452 0.925 0.000 0.032 0.024 0.852 NA
#> GSM2846 4 0.3452 0.925 0.000 0.032 0.024 0.852 NA
#> GSM2835 4 0.3640 0.916 0.000 0.028 0.020 0.832 NA
#> GSM2858 4 0.3640 0.916 0.000 0.028 0.020 0.832 NA
#> GSM2836 2 0.1818 0.877 0.000 0.932 0.000 0.024 NA
#> GSM2848 2 0.1818 0.877 0.000 0.932 0.000 0.024 NA
#> GSM2828 3 0.2663 0.912 0.004 0.064 0.896 0.004 NA
#> GSM2837 3 0.2663 0.912 0.004 0.064 0.896 0.004 NA
#> GSM2839 1 0.4163 0.839 0.772 0.004 0.020 0.012 NA
#> GSM2841 1 0.4163 0.839 0.772 0.004 0.020 0.012 NA
#> GSM2827 2 0.1725 0.878 0.000 0.936 0.000 0.020 NA
#> GSM2842 2 0.1725 0.878 0.000 0.936 0.000 0.020 NA
#> GSM2845 4 0.2741 0.924 0.000 0.032 0.012 0.892 NA
#> GSM2872 4 0.2741 0.924 0.000 0.032 0.012 0.892 NA
#> GSM2834 4 0.2632 0.930 0.000 0.032 0.004 0.892 NA
#> GSM2847 4 0.2569 0.931 0.000 0.032 0.004 0.896 NA
#> GSM2849 3 0.2972 0.911 0.004 0.064 0.880 0.004 NA
#> GSM2850 3 0.2972 0.911 0.004 0.064 0.880 0.004 NA
#> GSM2838 2 0.1697 0.874 0.000 0.932 0.000 0.008 NA
#> GSM2853 2 0.1697 0.874 0.000 0.932 0.000 0.008 NA
#> GSM2852 3 0.4643 0.856 0.000 0.068 0.736 0.004 NA
#> GSM2855 3 0.4643 0.856 0.000 0.068 0.736 0.004 NA
#> GSM2840 1 0.4163 0.839 0.772 0.004 0.020 0.012 NA
#> GSM2857 1 0.4163 0.839 0.772 0.004 0.020 0.012 NA
#> GSM2859 2 0.1205 0.880 0.000 0.956 0.000 0.004 NA
#> GSM2860 2 0.1205 0.880 0.000 0.956 0.000 0.004 NA
#> GSM2861 2 0.1638 0.879 0.000 0.932 0.000 0.004 NA
#> GSM2862 2 0.1205 0.880 0.000 0.956 0.000 0.004 NA
#> GSM2863 2 0.1205 0.880 0.000 0.956 0.000 0.004 NA
#> GSM2864 2 0.1205 0.880 0.000 0.956 0.000 0.004 NA
#> GSM2865 2 0.1205 0.880 0.000 0.956 0.000 0.004 NA
#> GSM2866 2 0.1484 0.880 0.000 0.944 0.000 0.008 NA
#> GSM2868 2 0.2011 0.867 0.000 0.908 0.000 0.004 NA
#> GSM2869 2 0.2011 0.867 0.000 0.908 0.000 0.004 NA
#> GSM2851 2 0.1952 0.868 0.000 0.912 0.000 0.004 NA
#> GSM2867 2 0.2011 0.867 0.000 0.908 0.000 0.004 NA
#> GSM2870 2 0.2011 0.867 0.000 0.908 0.000 0.004 NA
#> GSM2854 4 0.3781 0.915 0.000 0.040 0.020 0.828 NA
#> GSM2873 2 0.4280 0.776 0.000 0.772 0.000 0.140 NA
#> GSM2874 3 0.1924 0.914 0.000 0.064 0.924 0.004 NA
#> GSM2884 3 0.1638 0.914 0.000 0.064 0.932 0.000 NA
#> GSM2875 1 0.0486 0.878 0.988 0.004 0.004 0.004 NA
#> GSM2890 1 0.0486 0.878 0.988 0.004 0.004 0.004 NA
#> GSM2877 1 0.0486 0.878 0.988 0.004 0.004 0.004 NA
#> GSM2892 1 0.0486 0.878 0.988 0.004 0.004 0.004 NA
#> GSM2902 1 0.0486 0.878 0.988 0.004 0.004 0.004 NA
#> GSM2878 1 0.0613 0.878 0.984 0.004 0.008 0.004 NA
#> GSM2901 1 0.0613 0.878 0.984 0.004 0.008 0.004 NA
#> GSM2879 3 0.6471 0.437 0.000 0.336 0.488 0.004 NA
#> GSM2898 3 0.6471 0.437 0.000 0.336 0.488 0.004 NA
#> GSM2881 3 0.1981 0.915 0.000 0.064 0.920 0.000 NA
#> GSM2897 3 0.1981 0.915 0.000 0.064 0.920 0.000 NA
#> GSM2882 4 0.2312 0.934 0.004 0.032 0.012 0.920 NA
#> GSM2894 4 0.2312 0.934 0.004 0.032 0.012 0.920 NA
#> GSM2883 3 0.3275 0.899 0.000 0.064 0.860 0.008 NA
#> GSM2895 3 0.3275 0.899 0.000 0.064 0.860 0.008 NA
#> GSM2885 3 0.1981 0.915 0.000 0.064 0.920 0.000 NA
#> GSM2886 3 0.1981 0.915 0.000 0.064 0.920 0.000 NA
#> GSM2887 3 0.3334 0.900 0.000 0.064 0.852 0.004 NA
#> GSM2896 3 0.3334 0.900 0.000 0.064 0.852 0.004 NA
#> GSM2888 2 0.2783 0.854 0.000 0.868 0.004 0.012 NA
#> GSM2889 2 0.2783 0.854 0.000 0.868 0.004 0.012 NA
#> GSM2876 1 0.3180 0.855 0.844 0.004 0.012 0.004 NA
#> GSM2891 1 0.3180 0.855 0.844 0.004 0.012 0.004 NA
#> GSM2880 1 0.0486 0.878 0.988 0.004 0.004 0.004 NA
#> GSM2893 1 0.0486 0.878 0.988 0.004 0.004 0.004 NA
#> GSM2821 1 0.6660 0.572 0.480 0.168 0.000 0.012 NA
#> GSM2900 1 0.6660 0.572 0.480 0.168 0.000 0.012 NA
#> GSM2903 1 0.6660 0.572 0.480 0.168 0.000 0.012 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM2819 2 0.4095 0.139 0.000 0.512 0.000 0.008 0.480 NA
#> GSM2820 3 0.2135 0.857 0.000 0.024 0.916 0.004 0.012 NA
#> GSM2822 2 0.5419 0.595 0.000 0.688 0.004 0.124 0.116 NA
#> GSM2832 2 0.5419 0.595 0.000 0.688 0.004 0.124 0.116 NA
#> GSM2823 2 0.5187 0.306 0.000 0.524 0.012 0.012 0.416 NA
#> GSM2824 2 0.5187 0.306 0.000 0.524 0.012 0.012 0.416 NA
#> GSM2825 2 0.6517 0.466 0.004 0.584 0.004 0.152 0.148 NA
#> GSM2826 2 0.6517 0.466 0.004 0.584 0.004 0.152 0.148 NA
#> GSM2829 4 0.1148 0.864 0.000 0.016 0.004 0.960 0.020 NA
#> GSM2856 4 0.1148 0.864 0.000 0.016 0.004 0.960 0.020 NA
#> GSM2830 4 0.3876 0.866 0.000 0.012 0.000 0.728 0.016 NA
#> GSM2843 4 0.3876 0.866 0.000 0.012 0.000 0.728 0.016 NA
#> GSM2871 4 0.4039 0.863 0.004 0.012 0.000 0.720 0.016 NA
#> GSM2831 4 0.3457 0.878 0.000 0.012 0.016 0.820 0.016 NA
#> GSM2844 4 0.3457 0.878 0.000 0.012 0.016 0.820 0.016 NA
#> GSM2833 4 0.1266 0.868 0.004 0.016 0.004 0.960 0.008 NA
#> GSM2846 4 0.1266 0.868 0.004 0.016 0.004 0.960 0.008 NA
#> GSM2835 4 0.1779 0.855 0.000 0.020 0.004 0.936 0.020 NA
#> GSM2858 4 0.1779 0.855 0.000 0.020 0.004 0.936 0.020 NA
#> GSM2836 2 0.2145 0.736 0.000 0.912 0.004 0.008 0.056 NA
#> GSM2848 2 0.2145 0.736 0.000 0.912 0.004 0.008 0.056 NA
#> GSM2828 3 0.2135 0.857 0.000 0.024 0.916 0.004 0.012 NA
#> GSM2837 3 0.2135 0.857 0.000 0.024 0.916 0.004 0.012 NA
#> GSM2839 1 0.5007 0.635 0.680 0.008 0.004 0.000 0.136 NA
#> GSM2841 1 0.5007 0.635 0.680 0.008 0.004 0.000 0.136 NA
#> GSM2827 2 0.3218 0.732 0.000 0.836 0.004 0.004 0.112 NA
#> GSM2842 2 0.3218 0.732 0.000 0.836 0.004 0.004 0.112 NA
#> GSM2845 4 0.3746 0.861 0.004 0.012 0.000 0.712 0.000 NA
#> GSM2872 4 0.3746 0.861 0.004 0.012 0.000 0.712 0.000 NA
#> GSM2834 4 0.3507 0.868 0.000 0.012 0.000 0.752 0.004 NA
#> GSM2847 4 0.3507 0.868 0.000 0.012 0.000 0.752 0.004 NA
#> GSM2849 3 0.2666 0.854 0.000 0.024 0.892 0.008 0.032 NA
#> GSM2850 3 0.2666 0.854 0.000 0.024 0.892 0.008 0.032 NA
#> GSM2838 2 0.3751 0.719 0.000 0.792 0.004 0.000 0.108 NA
#> GSM2853 2 0.3751 0.719 0.000 0.792 0.004 0.000 0.108 NA
#> GSM2852 3 0.5741 0.713 0.000 0.052 0.612 0.000 0.232 NA
#> GSM2855 3 0.5741 0.713 0.000 0.052 0.612 0.000 0.232 NA
#> GSM2840 1 0.5007 0.635 0.680 0.008 0.004 0.000 0.136 NA
#> GSM2857 1 0.5007 0.635 0.680 0.008 0.004 0.000 0.136 NA
#> GSM2859 2 0.2485 0.732 0.000 0.884 0.004 0.004 0.020 NA
#> GSM2860 2 0.2485 0.732 0.000 0.884 0.004 0.004 0.020 NA
#> GSM2861 2 0.3172 0.731 0.000 0.840 0.004 0.004 0.044 NA
#> GSM2862 2 0.2485 0.732 0.000 0.884 0.004 0.004 0.020 NA
#> GSM2863 2 0.2485 0.732 0.000 0.884 0.004 0.004 0.020 NA
#> GSM2864 2 0.2485 0.732 0.000 0.884 0.004 0.004 0.020 NA
#> GSM2865 2 0.2485 0.732 0.000 0.884 0.004 0.004 0.020 NA
#> GSM2866 2 0.2425 0.730 0.000 0.884 0.000 0.004 0.024 NA
#> GSM2868 2 0.4218 0.700 0.000 0.748 0.004 0.000 0.112 NA
#> GSM2869 2 0.4218 0.700 0.000 0.748 0.004 0.000 0.112 NA
#> GSM2851 2 0.4141 0.704 0.000 0.756 0.004 0.000 0.112 NA
#> GSM2867 2 0.4218 0.700 0.000 0.748 0.004 0.000 0.112 NA
#> GSM2870 2 0.4218 0.700 0.000 0.748 0.004 0.000 0.112 NA
#> GSM2854 4 0.2399 0.851 0.000 0.024 0.004 0.904 0.024 NA
#> GSM2873 2 0.4756 0.635 0.000 0.732 0.000 0.144 0.060 NA
#> GSM2874 3 0.1232 0.859 0.000 0.024 0.956 0.004 0.000 NA
#> GSM2884 3 0.1138 0.859 0.000 0.024 0.960 0.004 0.000 NA
#> GSM2875 1 0.0405 0.832 0.988 0.008 0.004 0.000 0.000 NA
#> GSM2890 1 0.0405 0.832 0.988 0.008 0.004 0.000 0.000 NA
#> GSM2877 1 0.0405 0.832 0.988 0.008 0.004 0.000 0.000 NA
#> GSM2892 1 0.0405 0.832 0.988 0.008 0.004 0.000 0.000 NA
#> GSM2902 1 0.0405 0.832 0.988 0.008 0.004 0.000 0.000 NA
#> GSM2878 1 0.1406 0.825 0.952 0.008 0.004 0.000 0.016 NA
#> GSM2901 1 0.1406 0.825 0.952 0.008 0.004 0.000 0.016 NA
#> GSM2879 3 0.7140 0.341 0.000 0.268 0.396 0.000 0.248 NA
#> GSM2898 3 0.7140 0.341 0.000 0.268 0.396 0.000 0.248 NA
#> GSM2881 3 0.1743 0.860 0.000 0.024 0.936 0.004 0.008 NA
#> GSM2897 3 0.1743 0.860 0.000 0.024 0.936 0.004 0.008 NA
#> GSM2882 4 0.3110 0.878 0.000 0.012 0.016 0.852 0.016 NA
#> GSM2894 4 0.3110 0.878 0.000 0.012 0.016 0.852 0.016 NA
#> GSM2883 3 0.3573 0.829 0.000 0.024 0.824 0.004 0.040 NA
#> GSM2895 3 0.3573 0.829 0.000 0.024 0.824 0.004 0.040 NA
#> GSM2885 3 0.1743 0.860 0.000 0.024 0.936 0.004 0.008 NA
#> GSM2886 3 0.1743 0.860 0.000 0.024 0.936 0.004 0.008 NA
#> GSM2887 3 0.3972 0.820 0.000 0.024 0.800 0.004 0.092 NA
#> GSM2896 3 0.3972 0.820 0.000 0.024 0.800 0.004 0.092 NA
#> GSM2888 2 0.4326 0.695 0.000 0.732 0.004 0.000 0.168 NA
#> GSM2889 2 0.4326 0.695 0.000 0.732 0.004 0.000 0.168 NA
#> GSM2876 1 0.3853 0.692 0.788 0.008 0.008 0.004 0.160 NA
#> GSM2891 1 0.3853 0.692 0.788 0.008 0.008 0.004 0.160 NA
#> GSM2880 1 0.0405 0.832 0.988 0.008 0.004 0.000 0.000 NA
#> GSM2893 1 0.0405 0.832 0.988 0.008 0.004 0.000 0.000 NA
#> GSM2821 5 0.5829 1.000 0.332 0.160 0.000 0.008 0.500 NA
#> GSM2900 5 0.5829 1.000 0.332 0.160 0.000 0.008 0.500 NA
#> GSM2903 5 0.5829 1.000 0.332 0.160 0.000 0.008 0.500 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> CV:kmeans 61 1.95e-04 2
#> CV:kmeans 84 6.67e-09 3
#> CV:kmeans 84 5.71e-12 4
#> CV:kmeans 82 8.86e-12 5
#> CV:kmeans 77 6.70e-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["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 8229 rows and 84 columns.
#> Top rows (823, 1646, 2468, 3291, 4114) 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 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.980 0.991 0.5064 0.494 0.494
#> 3 3 0.589 0.604 0.776 0.2736 0.572 0.319
#> 4 4 0.964 0.967 0.985 0.1718 0.865 0.621
#> 5 5 0.910 0.810 0.899 0.0470 0.983 0.930
#> 6 6 0.858 0.761 0.780 0.0377 0.930 0.704
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
#> attr(,"optional")
#> [1] 2 4
There is also optional best \(k\) = 2 4 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM2819 1 0.0000 0.985 1.000 0.000
#> GSM2820 2 0.0000 0.996 0.000 1.000
#> GSM2822 1 0.0000 0.985 1.000 0.000
#> GSM2832 1 0.0000 0.985 1.000 0.000
#> GSM2823 2 0.0000 0.996 0.000 1.000
#> GSM2824 2 0.0000 0.996 0.000 1.000
#> GSM2825 1 0.0000 0.985 1.000 0.000
#> GSM2826 1 0.0000 0.985 1.000 0.000
#> GSM2829 1 0.0000 0.985 1.000 0.000
#> GSM2856 1 0.0000 0.985 1.000 0.000
#> GSM2830 1 0.0000 0.985 1.000 0.000
#> GSM2843 1 0.0000 0.985 1.000 0.000
#> GSM2871 1 0.0000 0.985 1.000 0.000
#> GSM2831 1 0.0000 0.985 1.000 0.000
#> GSM2844 1 0.0000 0.985 1.000 0.000
#> GSM2833 1 0.0000 0.985 1.000 0.000
#> GSM2846 1 0.0000 0.985 1.000 0.000
#> GSM2835 1 0.0000 0.985 1.000 0.000
#> GSM2858 1 0.0000 0.985 1.000 0.000
#> GSM2836 2 0.0672 0.996 0.008 0.992
#> GSM2848 2 0.0672 0.996 0.008 0.992
#> GSM2828 2 0.0000 0.996 0.000 1.000
#> GSM2837 2 0.0000 0.996 0.000 1.000
#> GSM2839 1 0.0672 0.984 0.992 0.008
#> GSM2841 1 0.0672 0.984 0.992 0.008
#> GSM2827 2 0.0672 0.996 0.008 0.992
#> GSM2842 2 0.0672 0.996 0.008 0.992
#> GSM2845 1 0.0000 0.985 1.000 0.000
#> GSM2872 1 0.0000 0.985 1.000 0.000
#> GSM2834 1 0.0000 0.985 1.000 0.000
#> GSM2847 1 0.0000 0.985 1.000 0.000
#> GSM2849 2 0.0000 0.996 0.000 1.000
#> GSM2850 2 0.0000 0.996 0.000 1.000
#> GSM2838 2 0.0672 0.996 0.008 0.992
#> GSM2853 2 0.0672 0.996 0.008 0.992
#> GSM2852 2 0.0000 0.996 0.000 1.000
#> GSM2855 2 0.0000 0.996 0.000 1.000
#> GSM2840 1 0.0672 0.984 0.992 0.008
#> GSM2857 1 0.0672 0.984 0.992 0.008
#> GSM2859 2 0.0672 0.996 0.008 0.992
#> GSM2860 2 0.0672 0.996 0.008 0.992
#> GSM2861 2 0.0672 0.996 0.008 0.992
#> GSM2862 2 0.0672 0.996 0.008 0.992
#> GSM2863 2 0.0672 0.996 0.008 0.992
#> GSM2864 2 0.0672 0.996 0.008 0.992
#> GSM2865 2 0.0672 0.996 0.008 0.992
#> GSM2866 2 0.0672 0.996 0.008 0.992
#> GSM2868 2 0.0672 0.996 0.008 0.992
#> GSM2869 2 0.0672 0.996 0.008 0.992
#> GSM2851 2 0.0672 0.996 0.008 0.992
#> GSM2867 2 0.0672 0.996 0.008 0.992
#> GSM2870 2 0.0672 0.996 0.008 0.992
#> GSM2854 1 0.0000 0.985 1.000 0.000
#> GSM2873 1 0.9970 0.108 0.532 0.468
#> GSM2874 2 0.0000 0.996 0.000 1.000
#> GSM2884 2 0.0000 0.996 0.000 1.000
#> GSM2875 1 0.0672 0.984 0.992 0.008
#> GSM2890 1 0.0672 0.984 0.992 0.008
#> GSM2877 1 0.0672 0.984 0.992 0.008
#> GSM2892 1 0.0672 0.984 0.992 0.008
#> GSM2902 1 0.0672 0.984 0.992 0.008
#> GSM2878 1 0.0672 0.984 0.992 0.008
#> GSM2901 1 0.0672 0.984 0.992 0.008
#> GSM2879 2 0.0000 0.996 0.000 1.000
#> GSM2898 2 0.0000 0.996 0.000 1.000
#> GSM2881 2 0.0000 0.996 0.000 1.000
#> GSM2897 2 0.0000 0.996 0.000 1.000
#> GSM2882 1 0.0000 0.985 1.000 0.000
#> GSM2894 1 0.0000 0.985 1.000 0.000
#> GSM2883 2 0.0000 0.996 0.000 1.000
#> GSM2895 2 0.0000 0.996 0.000 1.000
#> GSM2885 2 0.0000 0.996 0.000 1.000
#> GSM2886 2 0.0000 0.996 0.000 1.000
#> GSM2887 2 0.0000 0.996 0.000 1.000
#> GSM2896 2 0.0000 0.996 0.000 1.000
#> GSM2888 2 0.0672 0.996 0.008 0.992
#> GSM2889 2 0.0672 0.996 0.008 0.992
#> GSM2876 1 0.0672 0.984 0.992 0.008
#> GSM2891 1 0.0672 0.984 0.992 0.008
#> GSM2880 1 0.0672 0.984 0.992 0.008
#> GSM2893 1 0.0672 0.984 0.992 0.008
#> GSM2821 1 0.0672 0.984 0.992 0.008
#> GSM2900 1 0.0672 0.984 0.992 0.008
#> GSM2903 1 0.0672 0.984 0.992 0.008
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM2819 1 0.6215 0.267 0.572 0.428 0.000
#> GSM2820 3 0.5905 0.628 0.000 0.352 0.648
#> GSM2822 2 0.6252 0.556 0.008 0.648 0.344
#> GSM2832 2 0.6252 0.556 0.008 0.648 0.344
#> GSM2823 1 0.5954 0.748 0.792 0.116 0.092
#> GSM2824 1 0.5954 0.748 0.792 0.116 0.092
#> GSM2825 1 0.1643 0.921 0.956 0.044 0.000
#> GSM2826 1 0.1643 0.921 0.956 0.044 0.000
#> GSM2829 2 0.9241 0.471 0.164 0.484 0.352
#> GSM2856 2 0.9241 0.471 0.164 0.484 0.352
#> GSM2830 2 0.9241 0.471 0.164 0.484 0.352
#> GSM2843 2 0.9241 0.471 0.164 0.484 0.352
#> GSM2871 2 0.9241 0.471 0.164 0.484 0.352
#> GSM2831 3 0.9993 -0.266 0.324 0.324 0.352
#> GSM2844 3 0.9993 -0.266 0.324 0.324 0.352
#> GSM2833 2 0.9241 0.471 0.164 0.484 0.352
#> GSM2846 2 0.9241 0.471 0.164 0.484 0.352
#> GSM2835 3 0.9989 -0.253 0.336 0.312 0.352
#> GSM2858 3 0.9989 -0.253 0.336 0.312 0.352
#> GSM2836 2 0.0000 0.686 0.000 1.000 0.000
#> GSM2848 2 0.0000 0.686 0.000 1.000 0.000
#> GSM2828 3 0.5905 0.628 0.000 0.352 0.648
#> GSM2837 3 0.5905 0.628 0.000 0.352 0.648
#> GSM2839 1 0.0000 0.949 1.000 0.000 0.000
#> GSM2841 1 0.0000 0.949 1.000 0.000 0.000
#> GSM2827 2 0.0000 0.686 0.000 1.000 0.000
#> GSM2842 2 0.0000 0.686 0.000 1.000 0.000
#> GSM2845 3 0.9992 -0.272 0.320 0.328 0.352
#> GSM2872 3 0.9992 -0.272 0.320 0.328 0.352
#> GSM2834 2 0.9241 0.471 0.164 0.484 0.352
#> GSM2847 2 0.9241 0.471 0.164 0.484 0.352
#> GSM2849 3 0.5905 0.628 0.000 0.352 0.648
#> GSM2850 3 0.5905 0.628 0.000 0.352 0.648
#> GSM2838 2 0.0000 0.686 0.000 1.000 0.000
#> GSM2853 2 0.0000 0.686 0.000 1.000 0.000
#> GSM2852 3 0.5905 0.628 0.000 0.352 0.648
#> GSM2855 3 0.5905 0.628 0.000 0.352 0.648
#> GSM2840 1 0.0000 0.949 1.000 0.000 0.000
#> GSM2857 1 0.0000 0.949 1.000 0.000 0.000
#> GSM2859 2 0.0000 0.686 0.000 1.000 0.000
#> GSM2860 2 0.0000 0.686 0.000 1.000 0.000
#> GSM2861 2 0.0000 0.686 0.000 1.000 0.000
#> GSM2862 2 0.0000 0.686 0.000 1.000 0.000
#> GSM2863 2 0.0000 0.686 0.000 1.000 0.000
#> GSM2864 2 0.0000 0.686 0.000 1.000 0.000
#> GSM2865 2 0.0000 0.686 0.000 1.000 0.000
#> GSM2866 2 0.0000 0.686 0.000 1.000 0.000
#> GSM2868 2 0.0000 0.686 0.000 1.000 0.000
#> GSM2869 2 0.0000 0.686 0.000 1.000 0.000
#> GSM2851 2 0.0000 0.686 0.000 1.000 0.000
#> GSM2867 2 0.0000 0.686 0.000 1.000 0.000
#> GSM2870 2 0.0000 0.686 0.000 1.000 0.000
#> GSM2854 2 0.7462 0.535 0.048 0.600 0.352
#> GSM2873 2 0.5905 0.555 0.000 0.648 0.352
#> GSM2874 3 0.5905 0.628 0.000 0.352 0.648
#> GSM2884 3 0.5905 0.628 0.000 0.352 0.648
#> GSM2875 1 0.0000 0.949 1.000 0.000 0.000
#> GSM2890 1 0.0000 0.949 1.000 0.000 0.000
#> GSM2877 1 0.0000 0.949 1.000 0.000 0.000
#> GSM2892 1 0.0000 0.949 1.000 0.000 0.000
#> GSM2902 1 0.0000 0.949 1.000 0.000 0.000
#> GSM2878 1 0.0000 0.949 1.000 0.000 0.000
#> GSM2901 1 0.0000 0.949 1.000 0.000 0.000
#> GSM2879 3 0.5905 0.628 0.000 0.352 0.648
#> GSM2898 3 0.5905 0.628 0.000 0.352 0.648
#> GSM2881 3 0.5905 0.628 0.000 0.352 0.648
#> GSM2897 3 0.5905 0.628 0.000 0.352 0.648
#> GSM2882 3 0.9986 -0.250 0.340 0.308 0.352
#> GSM2894 3 0.9986 -0.250 0.340 0.308 0.352
#> GSM2883 3 0.5905 0.628 0.000 0.352 0.648
#> GSM2895 3 0.5905 0.628 0.000 0.352 0.648
#> GSM2885 3 0.5905 0.628 0.000 0.352 0.648
#> GSM2886 3 0.5905 0.628 0.000 0.352 0.648
#> GSM2887 3 0.5905 0.628 0.000 0.352 0.648
#> GSM2896 3 0.5905 0.628 0.000 0.352 0.648
#> GSM2888 2 0.4235 0.362 0.000 0.824 0.176
#> GSM2889 2 0.4235 0.362 0.000 0.824 0.176
#> GSM2876 1 0.0000 0.949 1.000 0.000 0.000
#> GSM2891 1 0.0000 0.949 1.000 0.000 0.000
#> GSM2880 1 0.0000 0.949 1.000 0.000 0.000
#> GSM2893 1 0.0000 0.949 1.000 0.000 0.000
#> GSM2821 1 0.0892 0.937 0.980 0.020 0.000
#> GSM2900 1 0.0892 0.937 0.980 0.020 0.000
#> GSM2903 1 0.0892 0.937 0.980 0.020 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM2819 1 0.4790 0.415 0.620 0.380 0 0.000
#> GSM2820 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM2822 2 0.2973 0.841 0.000 0.856 0 0.144
#> GSM2832 2 0.2973 0.841 0.000 0.856 0 0.144
#> GSM2823 1 0.0592 0.950 0.984 0.016 0 0.000
#> GSM2824 1 0.0592 0.950 0.984 0.016 0 0.000
#> GSM2825 1 0.4638 0.742 0.776 0.044 0 0.180
#> GSM2826 1 0.4638 0.742 0.776 0.044 0 0.180
#> GSM2829 4 0.0000 1.000 0.000 0.000 0 1.000
#> GSM2856 4 0.0000 1.000 0.000 0.000 0 1.000
#> GSM2830 4 0.0000 1.000 0.000 0.000 0 1.000
#> GSM2843 4 0.0000 1.000 0.000 0.000 0 1.000
#> GSM2871 4 0.0000 1.000 0.000 0.000 0 1.000
#> GSM2831 4 0.0000 1.000 0.000 0.000 0 1.000
#> GSM2844 4 0.0000 1.000 0.000 0.000 0 1.000
#> GSM2833 4 0.0000 1.000 0.000 0.000 0 1.000
#> GSM2846 4 0.0000 1.000 0.000 0.000 0 1.000
#> GSM2835 4 0.0000 1.000 0.000 0.000 0 1.000
#> GSM2858 4 0.0000 1.000 0.000 0.000 0 1.000
#> GSM2836 2 0.0000 0.980 0.000 1.000 0 0.000
#> GSM2848 2 0.0000 0.980 0.000 1.000 0 0.000
#> GSM2828 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM2837 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM2839 1 0.0000 0.961 1.000 0.000 0 0.000
#> GSM2841 1 0.0000 0.961 1.000 0.000 0 0.000
#> GSM2827 2 0.0000 0.980 0.000 1.000 0 0.000
#> GSM2842 2 0.0000 0.980 0.000 1.000 0 0.000
#> GSM2845 4 0.0000 1.000 0.000 0.000 0 1.000
#> GSM2872 4 0.0000 1.000 0.000 0.000 0 1.000
#> GSM2834 4 0.0000 1.000 0.000 0.000 0 1.000
#> GSM2847 4 0.0000 1.000 0.000 0.000 0 1.000
#> GSM2849 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM2850 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM2838 2 0.0000 0.980 0.000 1.000 0 0.000
#> GSM2853 2 0.0000 0.980 0.000 1.000 0 0.000
#> GSM2852 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM2855 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM2840 1 0.0000 0.961 1.000 0.000 0 0.000
#> GSM2857 1 0.0000 0.961 1.000 0.000 0 0.000
#> GSM2859 2 0.0000 0.980 0.000 1.000 0 0.000
#> GSM2860 2 0.0000 0.980 0.000 1.000 0 0.000
#> GSM2861 2 0.0000 0.980 0.000 1.000 0 0.000
#> GSM2862 2 0.0000 0.980 0.000 1.000 0 0.000
#> GSM2863 2 0.0000 0.980 0.000 1.000 0 0.000
#> GSM2864 2 0.0000 0.980 0.000 1.000 0 0.000
#> GSM2865 2 0.0000 0.980 0.000 1.000 0 0.000
#> GSM2866 2 0.0000 0.980 0.000 1.000 0 0.000
#> GSM2868 2 0.0000 0.980 0.000 1.000 0 0.000
#> GSM2869 2 0.0000 0.980 0.000 1.000 0 0.000
#> GSM2851 2 0.0000 0.980 0.000 1.000 0 0.000
#> GSM2867 2 0.0000 0.980 0.000 1.000 0 0.000
#> GSM2870 2 0.0000 0.980 0.000 1.000 0 0.000
#> GSM2854 4 0.0000 1.000 0.000 0.000 0 1.000
#> GSM2873 2 0.2973 0.841 0.000 0.856 0 0.144
#> GSM2874 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM2884 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM2875 1 0.0000 0.961 1.000 0.000 0 0.000
#> GSM2890 1 0.0000 0.961 1.000 0.000 0 0.000
#> GSM2877 1 0.0000 0.961 1.000 0.000 0 0.000
#> GSM2892 1 0.0000 0.961 1.000 0.000 0 0.000
#> GSM2902 1 0.0000 0.961 1.000 0.000 0 0.000
#> GSM2878 1 0.0000 0.961 1.000 0.000 0 0.000
#> GSM2901 1 0.0000 0.961 1.000 0.000 0 0.000
#> GSM2879 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM2898 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM2881 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM2897 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM2882 4 0.0000 1.000 0.000 0.000 0 1.000
#> GSM2894 4 0.0000 1.000 0.000 0.000 0 1.000
#> GSM2883 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM2895 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM2885 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM2886 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM2887 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM2896 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM2888 2 0.0000 0.980 0.000 1.000 0 0.000
#> GSM2889 2 0.0000 0.980 0.000 1.000 0 0.000
#> GSM2876 1 0.0000 0.961 1.000 0.000 0 0.000
#> GSM2891 1 0.0000 0.961 1.000 0.000 0 0.000
#> GSM2880 1 0.0000 0.961 1.000 0.000 0 0.000
#> GSM2893 1 0.0000 0.961 1.000 0.000 0 0.000
#> GSM2821 1 0.0000 0.961 1.000 0.000 0 0.000
#> GSM2900 1 0.0000 0.961 1.000 0.000 0 0.000
#> GSM2903 1 0.0000 0.961 1.000 0.000 0 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM2819 5 0.6319 0.646 0.216 0.256 0.000 0.000 0.528
#> GSM2820 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2822 2 0.5151 0.641 0.000 0.560 0.000 0.044 0.396
#> GSM2832 2 0.5151 0.641 0.000 0.560 0.000 0.044 0.396
#> GSM2823 5 0.5795 0.772 0.412 0.092 0.000 0.000 0.496
#> GSM2824 5 0.5795 0.772 0.412 0.092 0.000 0.000 0.496
#> GSM2825 1 0.5494 0.276 0.556 0.012 0.000 0.044 0.388
#> GSM2826 1 0.5494 0.276 0.556 0.012 0.000 0.044 0.388
#> GSM2829 4 0.1608 0.952 0.000 0.000 0.000 0.928 0.072
#> GSM2856 4 0.1608 0.952 0.000 0.000 0.000 0.928 0.072
#> GSM2830 4 0.0162 0.967 0.000 0.000 0.000 0.996 0.004
#> GSM2843 4 0.0162 0.967 0.000 0.000 0.000 0.996 0.004
#> GSM2871 4 0.0162 0.967 0.000 0.000 0.000 0.996 0.004
#> GSM2831 4 0.0000 0.968 0.000 0.000 0.000 1.000 0.000
#> GSM2844 4 0.0000 0.968 0.000 0.000 0.000 1.000 0.000
#> GSM2833 4 0.1544 0.954 0.000 0.000 0.000 0.932 0.068
#> GSM2846 4 0.1544 0.954 0.000 0.000 0.000 0.932 0.068
#> GSM2835 4 0.1732 0.948 0.000 0.000 0.000 0.920 0.080
#> GSM2858 4 0.1732 0.948 0.000 0.000 0.000 0.920 0.080
#> GSM2836 2 0.3684 0.825 0.000 0.720 0.000 0.000 0.280
#> GSM2848 2 0.3684 0.825 0.000 0.720 0.000 0.000 0.280
#> GSM2828 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2837 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2839 1 0.1851 0.723 0.912 0.000 0.000 0.000 0.088
#> GSM2841 1 0.1851 0.723 0.912 0.000 0.000 0.000 0.088
#> GSM2827 2 0.1341 0.824 0.000 0.944 0.000 0.000 0.056
#> GSM2842 2 0.1197 0.821 0.000 0.952 0.000 0.000 0.048
#> GSM2845 4 0.0162 0.967 0.000 0.000 0.000 0.996 0.004
#> GSM2872 4 0.0162 0.967 0.000 0.000 0.000 0.996 0.004
#> GSM2834 4 0.0510 0.968 0.000 0.000 0.000 0.984 0.016
#> GSM2847 4 0.0510 0.968 0.000 0.000 0.000 0.984 0.016
#> GSM2849 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2850 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2838 2 0.0000 0.827 0.000 1.000 0.000 0.000 0.000
#> GSM2853 2 0.0000 0.827 0.000 1.000 0.000 0.000 0.000
#> GSM2852 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2855 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2840 1 0.1851 0.723 0.912 0.000 0.000 0.000 0.088
#> GSM2857 1 0.1851 0.723 0.912 0.000 0.000 0.000 0.088
#> GSM2859 2 0.3452 0.834 0.000 0.756 0.000 0.000 0.244
#> GSM2860 2 0.3452 0.834 0.000 0.756 0.000 0.000 0.244
#> GSM2861 2 0.3177 0.837 0.000 0.792 0.000 0.000 0.208
#> GSM2862 2 0.3452 0.834 0.000 0.756 0.000 0.000 0.244
#> GSM2863 2 0.3452 0.834 0.000 0.756 0.000 0.000 0.244
#> GSM2864 2 0.3452 0.834 0.000 0.756 0.000 0.000 0.244
#> GSM2865 2 0.3452 0.834 0.000 0.756 0.000 0.000 0.244
#> GSM2866 2 0.3452 0.834 0.000 0.756 0.000 0.000 0.244
#> GSM2868 2 0.0290 0.824 0.000 0.992 0.000 0.000 0.008
#> GSM2869 2 0.0290 0.824 0.000 0.992 0.000 0.000 0.008
#> GSM2851 2 0.0162 0.826 0.000 0.996 0.000 0.000 0.004
#> GSM2867 2 0.0290 0.824 0.000 0.992 0.000 0.000 0.008
#> GSM2870 2 0.0162 0.826 0.000 0.996 0.000 0.000 0.004
#> GSM2854 4 0.2074 0.934 0.000 0.000 0.000 0.896 0.104
#> GSM2873 2 0.5176 0.693 0.000 0.572 0.000 0.048 0.380
#> GSM2874 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2884 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2875 1 0.0000 0.769 1.000 0.000 0.000 0.000 0.000
#> GSM2890 1 0.0000 0.769 1.000 0.000 0.000 0.000 0.000
#> GSM2877 1 0.0000 0.769 1.000 0.000 0.000 0.000 0.000
#> GSM2892 1 0.0000 0.769 1.000 0.000 0.000 0.000 0.000
#> GSM2902 1 0.0000 0.769 1.000 0.000 0.000 0.000 0.000
#> GSM2878 1 0.0000 0.769 1.000 0.000 0.000 0.000 0.000
#> GSM2901 1 0.0000 0.769 1.000 0.000 0.000 0.000 0.000
#> GSM2879 3 0.0162 0.997 0.000 0.000 0.996 0.000 0.004
#> GSM2898 3 0.0162 0.997 0.000 0.000 0.996 0.000 0.004
#> GSM2881 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2897 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2882 4 0.0000 0.968 0.000 0.000 0.000 1.000 0.000
#> GSM2894 4 0.0000 0.968 0.000 0.000 0.000 1.000 0.000
#> GSM2883 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2895 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2885 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2886 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2887 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2896 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2888 2 0.0963 0.823 0.000 0.964 0.000 0.000 0.036
#> GSM2889 2 0.0963 0.823 0.000 0.964 0.000 0.000 0.036
#> GSM2876 1 0.0000 0.769 1.000 0.000 0.000 0.000 0.000
#> GSM2891 1 0.0000 0.769 1.000 0.000 0.000 0.000 0.000
#> GSM2880 1 0.0000 0.769 1.000 0.000 0.000 0.000 0.000
#> GSM2893 1 0.0000 0.769 1.000 0.000 0.000 0.000 0.000
#> GSM2821 1 0.4306 -0.574 0.508 0.000 0.000 0.000 0.492
#> GSM2900 1 0.4306 -0.574 0.508 0.000 0.000 0.000 0.492
#> GSM2903 1 0.4306 -0.574 0.508 0.000 0.000 0.000 0.492
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM2819 5 0.7329 -0.0845 0.128 0.192 0.000 0.000 0.352 0.328
#> GSM2820 3 0.0000 0.9912 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2822 6 0.6178 0.5092 0.000 0.280 0.000 0.016 0.220 0.484
#> GSM2832 6 0.6178 0.5092 0.000 0.280 0.000 0.016 0.220 0.484
#> GSM2823 5 0.7260 -0.1046 0.192 0.120 0.000 0.000 0.384 0.304
#> GSM2824 5 0.7260 -0.1046 0.192 0.120 0.000 0.000 0.384 0.304
#> GSM2825 6 0.4648 0.4147 0.276 0.004 0.000 0.016 0.036 0.668
#> GSM2826 6 0.4648 0.4147 0.276 0.004 0.000 0.016 0.036 0.668
#> GSM2829 4 0.2730 0.8709 0.000 0.000 0.000 0.836 0.012 0.152
#> GSM2856 4 0.2730 0.8709 0.000 0.000 0.000 0.836 0.012 0.152
#> GSM2830 4 0.0520 0.9115 0.000 0.000 0.000 0.984 0.008 0.008
#> GSM2843 4 0.0520 0.9115 0.000 0.000 0.000 0.984 0.008 0.008
#> GSM2871 4 0.0520 0.9115 0.000 0.000 0.000 0.984 0.008 0.008
#> GSM2831 4 0.0000 0.9141 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2844 4 0.0000 0.9141 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2833 4 0.2768 0.8684 0.000 0.000 0.000 0.832 0.012 0.156
#> GSM2846 4 0.2768 0.8684 0.000 0.000 0.000 0.832 0.012 0.156
#> GSM2835 4 0.2948 0.8479 0.000 0.000 0.000 0.804 0.008 0.188
#> GSM2858 4 0.2948 0.8479 0.000 0.000 0.000 0.804 0.008 0.188
#> GSM2836 5 0.4948 0.4658 0.000 0.360 0.000 0.000 0.564 0.076
#> GSM2848 5 0.4948 0.4658 0.000 0.360 0.000 0.000 0.564 0.076
#> GSM2828 3 0.0000 0.9912 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2837 3 0.0000 0.9912 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2839 1 0.3023 0.6732 0.784 0.000 0.000 0.000 0.004 0.212
#> GSM2841 1 0.3023 0.6732 0.784 0.000 0.000 0.000 0.004 0.212
#> GSM2827 2 0.3611 0.7727 0.000 0.796 0.000 0.000 0.108 0.096
#> GSM2842 2 0.3167 0.8017 0.000 0.832 0.000 0.000 0.072 0.096
#> GSM2845 4 0.0520 0.9115 0.000 0.000 0.000 0.984 0.008 0.008
#> GSM2872 4 0.0520 0.9115 0.000 0.000 0.000 0.984 0.008 0.008
#> GSM2834 4 0.1225 0.9111 0.000 0.000 0.000 0.952 0.012 0.036
#> GSM2847 4 0.1225 0.9111 0.000 0.000 0.000 0.952 0.012 0.036
#> GSM2849 3 0.0000 0.9912 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2850 3 0.0000 0.9912 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2838 2 0.0790 0.8999 0.000 0.968 0.000 0.000 0.032 0.000
#> GSM2853 2 0.0790 0.8999 0.000 0.968 0.000 0.000 0.032 0.000
#> GSM2852 3 0.0692 0.9777 0.000 0.000 0.976 0.000 0.004 0.020
#> GSM2855 3 0.0692 0.9777 0.000 0.000 0.976 0.000 0.004 0.020
#> GSM2840 1 0.3023 0.6732 0.784 0.000 0.000 0.000 0.004 0.212
#> GSM2857 1 0.3023 0.6732 0.784 0.000 0.000 0.000 0.004 0.212
#> GSM2859 5 0.3804 0.5664 0.000 0.424 0.000 0.000 0.576 0.000
#> GSM2860 5 0.3804 0.5664 0.000 0.424 0.000 0.000 0.576 0.000
#> GSM2861 5 0.3838 0.5253 0.000 0.448 0.000 0.000 0.552 0.000
#> GSM2862 5 0.3804 0.5664 0.000 0.424 0.000 0.000 0.576 0.000
#> GSM2863 5 0.3804 0.5664 0.000 0.424 0.000 0.000 0.576 0.000
#> GSM2864 5 0.3804 0.5664 0.000 0.424 0.000 0.000 0.576 0.000
#> GSM2865 5 0.3804 0.5664 0.000 0.424 0.000 0.000 0.576 0.000
#> GSM2866 5 0.3804 0.5664 0.000 0.424 0.000 0.000 0.576 0.000
#> GSM2868 2 0.0000 0.9194 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2869 2 0.0000 0.9194 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2851 2 0.0000 0.9194 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2867 2 0.0000 0.9194 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2870 2 0.0000 0.9194 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2854 4 0.3487 0.8041 0.000 0.000 0.000 0.756 0.020 0.224
#> GSM2873 6 0.6433 0.3057 0.000 0.196 0.000 0.028 0.364 0.412
#> GSM2874 3 0.0000 0.9912 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2884 3 0.0000 0.9912 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2875 1 0.0000 0.8086 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2890 1 0.0000 0.8086 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2877 1 0.0000 0.8086 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2892 1 0.0000 0.8086 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2902 1 0.0000 0.8086 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2878 1 0.0000 0.8086 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2901 1 0.0000 0.8086 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2879 3 0.1434 0.9476 0.000 0.000 0.940 0.000 0.048 0.012
#> GSM2898 3 0.1434 0.9476 0.000 0.000 0.940 0.000 0.048 0.012
#> GSM2881 3 0.0000 0.9912 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2897 3 0.0000 0.9912 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2882 4 0.0000 0.9141 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2894 4 0.0000 0.9141 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2883 3 0.0000 0.9912 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2895 3 0.0000 0.9912 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2885 3 0.0000 0.9912 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2886 3 0.0000 0.9912 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2887 3 0.0146 0.9895 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM2896 3 0.0146 0.9895 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM2888 2 0.2325 0.8800 0.000 0.892 0.000 0.000 0.048 0.060
#> GSM2889 2 0.2325 0.8800 0.000 0.892 0.000 0.000 0.048 0.060
#> GSM2876 1 0.0146 0.8068 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM2891 1 0.0146 0.8068 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM2880 1 0.0000 0.8086 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2893 1 0.0000 0.8086 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2821 1 0.6123 0.2086 0.352 0.000 0.000 0.000 0.340 0.308
#> GSM2900 1 0.6123 0.2086 0.352 0.000 0.000 0.000 0.340 0.308
#> GSM2903 1 0.6123 0.2086 0.352 0.000 0.000 0.000 0.340 0.308
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 tissue(p) k
#> CV:skmeans 83 3.39e-05 2
#> CV:skmeans 64 1.46e-07 3
#> CV:skmeans 83 4.22e-12 4
#> CV:skmeans 79 1.87e-14 5
#> CV:skmeans 73 3.70e-17 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 8229 rows and 84 columns.
#> Top rows (823, 1646, 2468, 3291, 4114) 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.485 0.834 0.851 0.3419 0.646 0.646
#> 3 3 1.000 0.996 0.999 0.7189 0.766 0.637
#> 4 4 0.904 0.884 0.948 0.2603 0.849 0.633
#> 5 5 0.828 0.806 0.890 0.0326 0.974 0.899
#> 6 6 0.878 0.869 0.917 0.0243 0.987 0.947
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 3
There is also optional best \(k\) = 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM2819 1 0.9248 0.859 0.660 0.340
#> GSM2820 2 0.0000 0.978 0.000 1.000
#> GSM2822 1 0.9248 0.859 0.660 0.340
#> GSM2832 1 0.9248 0.859 0.660 0.340
#> GSM2823 1 0.9248 0.859 0.660 0.340
#> GSM2824 1 0.9248 0.859 0.660 0.340
#> GSM2825 1 0.9248 0.859 0.660 0.340
#> GSM2826 1 0.9248 0.859 0.660 0.340
#> GSM2829 1 0.9248 0.859 0.660 0.340
#> GSM2856 1 0.9248 0.859 0.660 0.340
#> GSM2830 1 0.9248 0.859 0.660 0.340
#> GSM2843 1 0.9248 0.859 0.660 0.340
#> GSM2871 1 0.9248 0.859 0.660 0.340
#> GSM2831 1 0.9248 0.859 0.660 0.340
#> GSM2844 1 0.9248 0.859 0.660 0.340
#> GSM2833 1 0.9248 0.859 0.660 0.340
#> GSM2846 1 0.9248 0.859 0.660 0.340
#> GSM2835 1 0.9248 0.859 0.660 0.340
#> GSM2858 1 0.9248 0.859 0.660 0.340
#> GSM2836 1 0.9248 0.859 0.660 0.340
#> GSM2848 1 0.9248 0.859 0.660 0.340
#> GSM2828 2 0.0000 0.978 0.000 1.000
#> GSM2837 2 0.0000 0.978 0.000 1.000
#> GSM2839 1 0.0000 0.625 1.000 0.000
#> GSM2841 1 0.0000 0.625 1.000 0.000
#> GSM2827 1 0.9248 0.859 0.660 0.340
#> GSM2842 1 0.9248 0.859 0.660 0.340
#> GSM2845 1 0.9248 0.859 0.660 0.340
#> GSM2872 1 0.9248 0.859 0.660 0.340
#> GSM2834 1 0.9248 0.859 0.660 0.340
#> GSM2847 1 0.9248 0.859 0.660 0.340
#> GSM2849 2 0.0000 0.978 0.000 1.000
#> GSM2850 2 0.0000 0.978 0.000 1.000
#> GSM2838 1 0.9248 0.859 0.660 0.340
#> GSM2853 1 0.9248 0.859 0.660 0.340
#> GSM2852 2 0.0000 0.978 0.000 1.000
#> GSM2855 2 0.0000 0.978 0.000 1.000
#> GSM2840 1 0.0000 0.625 1.000 0.000
#> GSM2857 1 0.0000 0.625 1.000 0.000
#> GSM2859 1 0.9248 0.859 0.660 0.340
#> GSM2860 1 0.9248 0.859 0.660 0.340
#> GSM2861 1 0.9248 0.859 0.660 0.340
#> GSM2862 1 0.9248 0.859 0.660 0.340
#> GSM2863 1 0.9248 0.859 0.660 0.340
#> GSM2864 1 0.9248 0.859 0.660 0.340
#> GSM2865 1 0.9248 0.859 0.660 0.340
#> GSM2866 1 0.9248 0.859 0.660 0.340
#> GSM2868 1 0.9248 0.859 0.660 0.340
#> GSM2869 1 0.9248 0.859 0.660 0.340
#> GSM2851 1 0.9248 0.859 0.660 0.340
#> GSM2867 1 0.9248 0.859 0.660 0.340
#> GSM2870 1 0.9248 0.859 0.660 0.340
#> GSM2854 1 0.9248 0.859 0.660 0.340
#> GSM2873 1 0.9248 0.859 0.660 0.340
#> GSM2874 2 0.0000 0.978 0.000 1.000
#> GSM2884 2 0.0000 0.978 0.000 1.000
#> GSM2875 1 0.0000 0.625 1.000 0.000
#> GSM2890 1 0.0000 0.625 1.000 0.000
#> GSM2877 1 0.0000 0.625 1.000 0.000
#> GSM2892 1 0.0000 0.625 1.000 0.000
#> GSM2902 1 0.0000 0.625 1.000 0.000
#> GSM2878 1 0.0000 0.625 1.000 0.000
#> GSM2901 1 0.0000 0.625 1.000 0.000
#> GSM2879 2 0.5519 0.778 0.128 0.872
#> GSM2898 2 0.5737 0.761 0.136 0.864
#> GSM2881 2 0.0000 0.978 0.000 1.000
#> GSM2897 2 0.0000 0.978 0.000 1.000
#> GSM2882 1 0.9248 0.859 0.660 0.340
#> GSM2894 1 0.9248 0.859 0.660 0.340
#> GSM2883 2 0.0000 0.978 0.000 1.000
#> GSM2895 2 0.0000 0.978 0.000 1.000
#> GSM2885 2 0.0000 0.978 0.000 1.000
#> GSM2886 2 0.0000 0.978 0.000 1.000
#> GSM2887 2 0.0000 0.978 0.000 1.000
#> GSM2896 2 0.0000 0.978 0.000 1.000
#> GSM2888 1 0.9248 0.859 0.660 0.340
#> GSM2889 1 0.9248 0.859 0.660 0.340
#> GSM2876 1 0.0000 0.625 1.000 0.000
#> GSM2891 1 0.0000 0.625 1.000 0.000
#> GSM2880 1 0.0000 0.625 1.000 0.000
#> GSM2893 1 0.0000 0.625 1.000 0.000
#> GSM2821 1 0.9129 0.851 0.672 0.328
#> GSM2900 1 0.0376 0.627 0.996 0.004
#> GSM2903 1 0.0672 0.630 0.992 0.008
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM2819 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2820 3 0.0000 0.996 0.000 0.000 1.000
#> GSM2822 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2832 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2823 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2824 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2825 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2826 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2829 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2856 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2830 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2843 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2871 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2831 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2844 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2833 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2846 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2835 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2858 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2836 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2848 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2828 3 0.0000 0.996 0.000 0.000 1.000
#> GSM2837 3 0.0000 0.996 0.000 0.000 1.000
#> GSM2839 1 0.0000 0.995 1.000 0.000 0.000
#> GSM2841 1 0.0000 0.995 1.000 0.000 0.000
#> GSM2827 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2842 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2845 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2872 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2834 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2847 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2849 3 0.0000 0.996 0.000 0.000 1.000
#> GSM2850 3 0.0000 0.996 0.000 0.000 1.000
#> GSM2838 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2853 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2852 3 0.0000 0.996 0.000 0.000 1.000
#> GSM2855 3 0.0000 0.996 0.000 0.000 1.000
#> GSM2840 1 0.0000 0.995 1.000 0.000 0.000
#> GSM2857 1 0.0000 0.995 1.000 0.000 0.000
#> GSM2859 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2860 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2861 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2862 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2863 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2864 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2865 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2866 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2868 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2869 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2851 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2867 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2870 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2854 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2873 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2874 3 0.0000 0.996 0.000 0.000 1.000
#> GSM2884 3 0.0000 0.996 0.000 0.000 1.000
#> GSM2875 1 0.0000 0.995 1.000 0.000 0.000
#> GSM2890 1 0.0000 0.995 1.000 0.000 0.000
#> GSM2877 1 0.0000 0.995 1.000 0.000 0.000
#> GSM2892 1 0.0000 0.995 1.000 0.000 0.000
#> GSM2902 1 0.0000 0.995 1.000 0.000 0.000
#> GSM2878 1 0.0000 0.995 1.000 0.000 0.000
#> GSM2901 1 0.0000 0.995 1.000 0.000 0.000
#> GSM2879 3 0.1163 0.963 0.000 0.028 0.972
#> GSM2898 3 0.1163 0.963 0.000 0.028 0.972
#> GSM2881 3 0.0000 0.996 0.000 0.000 1.000
#> GSM2897 3 0.0000 0.996 0.000 0.000 1.000
#> GSM2882 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2894 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2883 3 0.0000 0.996 0.000 0.000 1.000
#> GSM2895 3 0.0000 0.996 0.000 0.000 1.000
#> GSM2885 3 0.0000 0.996 0.000 0.000 1.000
#> GSM2886 3 0.0000 0.996 0.000 0.000 1.000
#> GSM2887 3 0.0000 0.996 0.000 0.000 1.000
#> GSM2896 3 0.0000 0.996 0.000 0.000 1.000
#> GSM2888 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2889 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2876 1 0.0000 0.995 1.000 0.000 0.000
#> GSM2891 1 0.0000 0.995 1.000 0.000 0.000
#> GSM2880 1 0.0000 0.995 1.000 0.000 0.000
#> GSM2893 1 0.0000 0.995 1.000 0.000 0.000
#> GSM2821 2 0.0000 1.000 0.000 1.000 0.000
#> GSM2900 1 0.0747 0.977 0.984 0.016 0.000
#> GSM2903 1 0.1643 0.941 0.956 0.044 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM2819 2 0.3024 0.785 0.000 0.852 0 0.148
#> GSM2820 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM2822 2 0.4761 0.522 0.000 0.628 0 0.372
#> GSM2832 2 0.4776 0.515 0.000 0.624 0 0.376
#> GSM2823 2 0.4679 0.556 0.000 0.648 0 0.352
#> GSM2824 2 0.4454 0.619 0.000 0.692 0 0.308
#> GSM2825 2 0.4790 0.507 0.000 0.620 0 0.380
#> GSM2826 2 0.4713 0.543 0.000 0.640 0 0.360
#> GSM2829 4 0.0000 0.934 0.000 0.000 0 1.000
#> GSM2856 4 0.0000 0.934 0.000 0.000 0 1.000
#> GSM2830 4 0.0000 0.934 0.000 0.000 0 1.000
#> GSM2843 4 0.0000 0.934 0.000 0.000 0 1.000
#> GSM2871 2 0.4994 0.225 0.000 0.520 0 0.480
#> GSM2831 4 0.0000 0.934 0.000 0.000 0 1.000
#> GSM2844 4 0.0000 0.934 0.000 0.000 0 1.000
#> GSM2833 4 0.0000 0.934 0.000 0.000 0 1.000
#> GSM2846 4 0.0000 0.934 0.000 0.000 0 1.000
#> GSM2835 4 0.0000 0.934 0.000 0.000 0 1.000
#> GSM2858 4 0.0000 0.934 0.000 0.000 0 1.000
#> GSM2836 2 0.0707 0.865 0.000 0.980 0 0.020
#> GSM2848 2 0.2647 0.809 0.000 0.880 0 0.120
#> GSM2828 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM2837 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM2839 1 0.0000 0.996 1.000 0.000 0 0.000
#> GSM2841 1 0.0000 0.996 1.000 0.000 0 0.000
#> GSM2827 2 0.0817 0.864 0.000 0.976 0 0.024
#> GSM2842 2 0.0817 0.864 0.000 0.976 0 0.024
#> GSM2845 4 0.4605 0.396 0.000 0.336 0 0.664
#> GSM2872 4 0.0000 0.934 0.000 0.000 0 1.000
#> GSM2834 4 0.3688 0.679 0.000 0.208 0 0.792
#> GSM2847 4 0.0000 0.934 0.000 0.000 0 1.000
#> GSM2849 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM2850 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM2838 2 0.0000 0.869 0.000 1.000 0 0.000
#> GSM2853 2 0.0000 0.869 0.000 1.000 0 0.000
#> GSM2852 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM2855 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM2840 1 0.0000 0.996 1.000 0.000 0 0.000
#> GSM2857 1 0.0000 0.996 1.000 0.000 0 0.000
#> GSM2859 2 0.0000 0.869 0.000 1.000 0 0.000
#> GSM2860 2 0.0000 0.869 0.000 1.000 0 0.000
#> GSM2861 2 0.0000 0.869 0.000 1.000 0 0.000
#> GSM2862 2 0.0000 0.869 0.000 1.000 0 0.000
#> GSM2863 2 0.0000 0.869 0.000 1.000 0 0.000
#> GSM2864 2 0.0000 0.869 0.000 1.000 0 0.000
#> GSM2865 2 0.0000 0.869 0.000 1.000 0 0.000
#> GSM2866 2 0.0000 0.869 0.000 1.000 0 0.000
#> GSM2868 2 0.0000 0.869 0.000 1.000 0 0.000
#> GSM2869 2 0.0000 0.869 0.000 1.000 0 0.000
#> GSM2851 2 0.0000 0.869 0.000 1.000 0 0.000
#> GSM2867 2 0.0000 0.869 0.000 1.000 0 0.000
#> GSM2870 2 0.0000 0.869 0.000 1.000 0 0.000
#> GSM2854 4 0.4477 0.466 0.000 0.312 0 0.688
#> GSM2873 2 0.4804 0.499 0.000 0.616 0 0.384
#> GSM2874 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM2884 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM2875 1 0.0000 0.996 1.000 0.000 0 0.000
#> GSM2890 1 0.0000 0.996 1.000 0.000 0 0.000
#> GSM2877 1 0.0000 0.996 1.000 0.000 0 0.000
#> GSM2892 1 0.0000 0.996 1.000 0.000 0 0.000
#> GSM2902 1 0.0000 0.996 1.000 0.000 0 0.000
#> GSM2878 1 0.0000 0.996 1.000 0.000 0 0.000
#> GSM2901 1 0.0000 0.996 1.000 0.000 0 0.000
#> GSM2879 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM2898 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM2881 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM2897 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM2882 4 0.0000 0.934 0.000 0.000 0 1.000
#> GSM2894 4 0.0000 0.934 0.000 0.000 0 1.000
#> GSM2883 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM2895 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM2885 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM2886 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM2887 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM2896 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM2888 2 0.1557 0.850 0.000 0.944 0 0.056
#> GSM2889 2 0.0188 0.869 0.000 0.996 0 0.004
#> GSM2876 1 0.0000 0.996 1.000 0.000 0 0.000
#> GSM2891 1 0.0000 0.996 1.000 0.000 0 0.000
#> GSM2880 1 0.0000 0.996 1.000 0.000 0 0.000
#> GSM2893 1 0.0000 0.996 1.000 0.000 0 0.000
#> GSM2821 2 0.1302 0.856 0.000 0.956 0 0.044
#> GSM2900 1 0.0657 0.982 0.984 0.012 0 0.004
#> GSM2903 1 0.1356 0.956 0.960 0.032 0 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM2819 5 0.4256 0.411 0.000 0.436 0 0.000 0.564
#> GSM2820 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM2822 2 0.4088 0.531 0.000 0.632 0 0.368 0.000
#> GSM2832 2 0.4101 0.524 0.000 0.628 0 0.372 0.000
#> GSM2823 2 0.3861 0.588 0.000 0.712 0 0.284 0.004
#> GSM2824 2 0.5158 0.439 0.000 0.676 0 0.100 0.224
#> GSM2825 2 0.4114 0.517 0.000 0.624 0 0.376 0.000
#> GSM2826 2 0.4045 0.545 0.000 0.644 0 0.356 0.000
#> GSM2829 4 0.0000 0.921 0.000 0.000 0 1.000 0.000
#> GSM2856 4 0.0000 0.921 0.000 0.000 0 1.000 0.000
#> GSM2830 4 0.0000 0.921 0.000 0.000 0 1.000 0.000
#> GSM2843 4 0.0000 0.921 0.000 0.000 0 1.000 0.000
#> GSM2871 2 0.4448 0.230 0.000 0.516 0 0.480 0.004
#> GSM2831 4 0.0000 0.921 0.000 0.000 0 1.000 0.000
#> GSM2844 4 0.0000 0.921 0.000 0.000 0 1.000 0.000
#> GSM2833 4 0.0000 0.921 0.000 0.000 0 1.000 0.000
#> GSM2846 4 0.0000 0.921 0.000 0.000 0 1.000 0.000
#> GSM2835 4 0.0000 0.921 0.000 0.000 0 1.000 0.000
#> GSM2858 4 0.0000 0.921 0.000 0.000 0 1.000 0.000
#> GSM2836 2 0.2669 0.781 0.000 0.876 0 0.020 0.104
#> GSM2848 2 0.2540 0.767 0.000 0.888 0 0.088 0.024
#> GSM2828 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM2837 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM2839 1 0.3876 0.689 0.684 0.000 0 0.000 0.316
#> GSM2841 1 0.3876 0.689 0.684 0.000 0 0.000 0.316
#> GSM2827 2 0.0000 0.790 0.000 1.000 0 0.000 0.000
#> GSM2842 2 0.0290 0.789 0.000 0.992 0 0.008 0.000
#> GSM2845 4 0.3966 0.383 0.000 0.336 0 0.664 0.000
#> GSM2872 4 0.0000 0.921 0.000 0.000 0 1.000 0.000
#> GSM2834 4 0.3177 0.665 0.000 0.208 0 0.792 0.000
#> GSM2847 4 0.0000 0.921 0.000 0.000 0 1.000 0.000
#> GSM2849 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM2850 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM2838 2 0.0000 0.790 0.000 1.000 0 0.000 0.000
#> GSM2853 2 0.0000 0.790 0.000 1.000 0 0.000 0.000
#> GSM2852 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM2855 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM2840 1 0.3876 0.689 0.684 0.000 0 0.000 0.316
#> GSM2857 1 0.3876 0.689 0.684 0.000 0 0.000 0.316
#> GSM2859 2 0.2280 0.780 0.000 0.880 0 0.000 0.120
#> GSM2860 2 0.2280 0.780 0.000 0.880 0 0.000 0.120
#> GSM2861 2 0.2280 0.780 0.000 0.880 0 0.000 0.120
#> GSM2862 2 0.2280 0.780 0.000 0.880 0 0.000 0.120
#> GSM2863 2 0.2280 0.780 0.000 0.880 0 0.000 0.120
#> GSM2864 2 0.2280 0.780 0.000 0.880 0 0.000 0.120
#> GSM2865 2 0.2280 0.780 0.000 0.880 0 0.000 0.120
#> GSM2866 2 0.2280 0.780 0.000 0.880 0 0.000 0.120
#> GSM2868 2 0.0000 0.790 0.000 1.000 0 0.000 0.000
#> GSM2869 2 0.0000 0.790 0.000 1.000 0 0.000 0.000
#> GSM2851 2 0.0000 0.790 0.000 1.000 0 0.000 0.000
#> GSM2867 2 0.0000 0.790 0.000 1.000 0 0.000 0.000
#> GSM2870 2 0.0000 0.790 0.000 1.000 0 0.000 0.000
#> GSM2854 4 0.3876 0.448 0.000 0.316 0 0.684 0.000
#> GSM2873 2 0.4126 0.508 0.000 0.620 0 0.380 0.000
#> GSM2874 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM2884 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM2875 1 0.0000 0.890 1.000 0.000 0 0.000 0.000
#> GSM2890 1 0.0000 0.890 1.000 0.000 0 0.000 0.000
#> GSM2877 1 0.0000 0.890 1.000 0.000 0 0.000 0.000
#> GSM2892 1 0.0000 0.890 1.000 0.000 0 0.000 0.000
#> GSM2902 1 0.0000 0.890 1.000 0.000 0 0.000 0.000
#> GSM2878 1 0.0000 0.890 1.000 0.000 0 0.000 0.000
#> GSM2901 1 0.0000 0.890 1.000 0.000 0 0.000 0.000
#> GSM2879 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM2898 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM2881 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM2897 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM2882 4 0.0000 0.921 0.000 0.000 0 1.000 0.000
#> GSM2894 4 0.0000 0.921 0.000 0.000 0 1.000 0.000
#> GSM2883 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM2895 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM2885 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM2886 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM2887 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM2896 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM2888 2 0.0404 0.788 0.000 0.988 0 0.012 0.000
#> GSM2889 2 0.0000 0.790 0.000 1.000 0 0.000 0.000
#> GSM2876 1 0.1121 0.855 0.956 0.000 0 0.000 0.044
#> GSM2891 1 0.0404 0.883 0.988 0.000 0 0.000 0.012
#> GSM2880 1 0.0000 0.890 1.000 0.000 0 0.000 0.000
#> GSM2893 1 0.0000 0.890 1.000 0.000 0 0.000 0.000
#> GSM2821 5 0.4242 0.425 0.000 0.428 0 0.000 0.572
#> GSM2900 5 0.4331 0.302 0.400 0.004 0 0.000 0.596
#> GSM2903 5 0.4770 0.336 0.384 0.012 0 0.008 0.596
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM2819 5 0.0260 0.987 0.000 0.008 0 0.000 0.992 0.000
#> GSM2820 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM2822 2 0.3911 0.537 0.000 0.624 0 0.368 0.000 0.008
#> GSM2832 2 0.3923 0.530 0.000 0.620 0 0.372 0.000 0.008
#> GSM2823 2 0.3855 0.644 0.000 0.704 0 0.276 0.004 0.016
#> GSM2824 2 0.4361 0.603 0.000 0.700 0 0.060 0.236 0.004
#> GSM2825 2 0.3695 0.523 0.000 0.624 0 0.376 0.000 0.000
#> GSM2826 2 0.3874 0.557 0.000 0.636 0 0.356 0.000 0.008
#> GSM2829 4 0.0000 0.921 0.000 0.000 0 1.000 0.000 0.000
#> GSM2856 4 0.0000 0.921 0.000 0.000 0 1.000 0.000 0.000
#> GSM2830 4 0.0000 0.921 0.000 0.000 0 1.000 0.000 0.000
#> GSM2843 4 0.0000 0.921 0.000 0.000 0 1.000 0.000 0.000
#> GSM2871 2 0.4183 0.242 0.000 0.508 0 0.480 0.000 0.012
#> GSM2831 4 0.0000 0.921 0.000 0.000 0 1.000 0.000 0.000
#> GSM2844 4 0.0000 0.921 0.000 0.000 0 1.000 0.000 0.000
#> GSM2833 4 0.0000 0.921 0.000 0.000 0 1.000 0.000 0.000
#> GSM2846 4 0.0000 0.921 0.000 0.000 0 1.000 0.000 0.000
#> GSM2835 4 0.0000 0.921 0.000 0.000 0 1.000 0.000 0.000
#> GSM2858 4 0.0000 0.921 0.000 0.000 0 1.000 0.000 0.000
#> GSM2836 2 0.3284 0.794 0.000 0.784 0 0.020 0.000 0.196
#> GSM2848 2 0.3123 0.799 0.000 0.836 0 0.088 0.000 0.076
#> GSM2828 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM2837 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM2839 6 0.3133 1.000 0.212 0.000 0 0.000 0.008 0.780
#> GSM2841 6 0.3133 1.000 0.212 0.000 0 0.000 0.008 0.780
#> GSM2827 2 0.0363 0.807 0.000 0.988 0 0.000 0.000 0.012
#> GSM2842 2 0.0146 0.807 0.000 0.996 0 0.000 0.000 0.004
#> GSM2845 4 0.3563 0.374 0.000 0.336 0 0.664 0.000 0.000
#> GSM2872 4 0.0000 0.921 0.000 0.000 0 1.000 0.000 0.000
#> GSM2834 4 0.2854 0.668 0.000 0.208 0 0.792 0.000 0.000
#> GSM2847 4 0.0000 0.921 0.000 0.000 0 1.000 0.000 0.000
#> GSM2849 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM2850 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM2838 2 0.0146 0.807 0.000 0.996 0 0.000 0.000 0.004
#> GSM2853 2 0.0146 0.807 0.000 0.996 0 0.000 0.000 0.004
#> GSM2852 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM2855 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM2840 6 0.3133 1.000 0.212 0.000 0 0.000 0.008 0.780
#> GSM2857 6 0.3133 1.000 0.212 0.000 0 0.000 0.008 0.780
#> GSM2859 2 0.2912 0.792 0.000 0.784 0 0.000 0.000 0.216
#> GSM2860 2 0.2912 0.792 0.000 0.784 0 0.000 0.000 0.216
#> GSM2861 2 0.2912 0.792 0.000 0.784 0 0.000 0.000 0.216
#> GSM2862 2 0.2912 0.792 0.000 0.784 0 0.000 0.000 0.216
#> GSM2863 2 0.2912 0.792 0.000 0.784 0 0.000 0.000 0.216
#> GSM2864 2 0.2912 0.792 0.000 0.784 0 0.000 0.000 0.216
#> GSM2865 2 0.2912 0.792 0.000 0.784 0 0.000 0.000 0.216
#> GSM2866 2 0.2912 0.792 0.000 0.784 0 0.000 0.000 0.216
#> GSM2868 2 0.0146 0.807 0.000 0.996 0 0.000 0.000 0.004
#> GSM2869 2 0.0146 0.807 0.000 0.996 0 0.000 0.000 0.004
#> GSM2851 2 0.0146 0.807 0.000 0.996 0 0.000 0.000 0.004
#> GSM2867 2 0.0146 0.807 0.000 0.996 0 0.000 0.000 0.004
#> GSM2870 2 0.0146 0.807 0.000 0.996 0 0.000 0.000 0.004
#> GSM2854 4 0.3601 0.443 0.000 0.312 0 0.684 0.000 0.004
#> GSM2873 2 0.3945 0.514 0.000 0.612 0 0.380 0.000 0.008
#> GSM2874 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM2884 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM2875 1 0.0000 0.984 1.000 0.000 0 0.000 0.000 0.000
#> GSM2890 1 0.0000 0.984 1.000 0.000 0 0.000 0.000 0.000
#> GSM2877 1 0.0000 0.984 1.000 0.000 0 0.000 0.000 0.000
#> GSM2892 1 0.0000 0.984 1.000 0.000 0 0.000 0.000 0.000
#> GSM2902 1 0.0000 0.984 1.000 0.000 0 0.000 0.000 0.000
#> GSM2878 1 0.0000 0.984 1.000 0.000 0 0.000 0.000 0.000
#> GSM2901 1 0.0000 0.984 1.000 0.000 0 0.000 0.000 0.000
#> GSM2879 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM2898 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM2881 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM2897 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM2882 4 0.0000 0.921 0.000 0.000 0 1.000 0.000 0.000
#> GSM2894 4 0.0000 0.921 0.000 0.000 0 1.000 0.000 0.000
#> GSM2883 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM2895 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM2885 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM2886 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM2887 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM2896 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM2888 2 0.0146 0.807 0.000 0.996 0 0.000 0.000 0.004
#> GSM2889 2 0.0146 0.807 0.000 0.996 0 0.000 0.000 0.004
#> GSM2876 1 0.1714 0.875 0.908 0.000 0 0.000 0.092 0.000
#> GSM2891 1 0.0632 0.961 0.976 0.000 0 0.000 0.024 0.000
#> GSM2880 1 0.0000 0.984 1.000 0.000 0 0.000 0.000 0.000
#> GSM2893 1 0.0000 0.984 1.000 0.000 0 0.000 0.000 0.000
#> GSM2821 5 0.0000 0.996 0.000 0.000 0 0.000 1.000 0.000
#> GSM2900 5 0.0000 0.996 0.000 0.000 0 0.000 1.000 0.000
#> GSM2903 5 0.0000 0.996 0.000 0.000 0 0.000 1.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> CV:pam 84 2.53e-05 2
#> CV:pam 84 2.34e-08 3
#> CV:pam 80 6.57e-11 4
#> CV:pam 76 1.38e-10 5
#> CV:pam 81 1.23e-17 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 8229 rows and 84 columns.
#> Top rows (823, 1646, 2468, 3291, 4114) 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 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.220 0.484 0.677 0.5035 0.620 0.620
#> 3 3 0.958 0.900 0.957 0.2795 0.690 0.519
#> 4 4 0.783 0.859 0.915 0.1531 0.818 0.533
#> 5 5 0.813 0.780 0.889 0.0654 0.882 0.572
#> 6 6 0.840 0.778 0.869 0.0398 0.940 0.715
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM2819 1 0.625 0.463 0.844 0.156
#> GSM2820 2 0.000 0.944 0.000 1.000
#> GSM2822 1 0.469 0.492 0.900 0.100
#> GSM2832 1 0.469 0.492 0.900 0.100
#> GSM2823 2 0.866 0.385 0.288 0.712
#> GSM2824 2 0.866 0.385 0.288 0.712
#> GSM2825 1 0.430 0.467 0.912 0.088
#> GSM2826 1 0.430 0.467 0.912 0.088
#> GSM2829 1 0.850 0.431 0.724 0.276
#> GSM2856 1 0.850 0.431 0.724 0.276
#> GSM2830 1 0.850 0.431 0.724 0.276
#> GSM2843 1 0.850 0.431 0.724 0.276
#> GSM2871 1 0.850 0.431 0.724 0.276
#> GSM2831 1 0.850 0.431 0.724 0.276
#> GSM2844 1 0.850 0.431 0.724 0.276
#> GSM2833 1 0.850 0.431 0.724 0.276
#> GSM2846 1 0.850 0.431 0.724 0.276
#> GSM2835 1 0.850 0.431 0.724 0.276
#> GSM2858 1 0.850 0.431 0.724 0.276
#> GSM2836 1 0.861 0.434 0.716 0.284
#> GSM2848 1 0.861 0.434 0.716 0.284
#> GSM2828 2 0.000 0.944 0.000 1.000
#> GSM2837 2 0.000 0.944 0.000 1.000
#> GSM2839 1 0.980 0.148 0.584 0.416
#> GSM2841 1 0.980 0.148 0.584 0.416
#> GSM2827 1 0.952 0.369 0.628 0.372
#> GSM2842 1 0.909 0.412 0.676 0.324
#> GSM2845 1 0.850 0.431 0.724 0.276
#> GSM2872 1 0.850 0.431 0.724 0.276
#> GSM2834 1 0.850 0.431 0.724 0.276
#> GSM2847 1 0.850 0.431 0.724 0.276
#> GSM2849 2 0.000 0.944 0.000 1.000
#> GSM2850 2 0.000 0.944 0.000 1.000
#> GSM2838 1 0.886 0.421 0.696 0.304
#> GSM2853 1 0.886 0.421 0.696 0.304
#> GSM2852 2 0.000 0.944 0.000 1.000
#> GSM2855 2 0.000 0.944 0.000 1.000
#> GSM2840 1 0.980 0.148 0.584 0.416
#> GSM2857 1 0.980 0.148 0.584 0.416
#> GSM2859 1 0.886 0.421 0.696 0.304
#> GSM2860 1 0.886 0.421 0.696 0.304
#> GSM2861 1 0.886 0.421 0.696 0.304
#> GSM2862 1 0.886 0.421 0.696 0.304
#> GSM2863 1 0.886 0.421 0.696 0.304
#> GSM2864 1 0.886 0.421 0.696 0.304
#> GSM2865 1 0.886 0.421 0.696 0.304
#> GSM2866 1 0.886 0.421 0.696 0.304
#> GSM2868 1 0.886 0.421 0.696 0.304
#> GSM2869 1 0.886 0.421 0.696 0.304
#> GSM2851 1 0.886 0.421 0.696 0.304
#> GSM2867 1 0.886 0.421 0.696 0.304
#> GSM2870 1 0.886 0.421 0.696 0.304
#> GSM2854 1 0.850 0.431 0.724 0.276
#> GSM2873 1 0.141 0.490 0.980 0.020
#> GSM2874 2 0.000 0.944 0.000 1.000
#> GSM2884 2 0.000 0.944 0.000 1.000
#> GSM2875 1 0.980 0.148 0.584 0.416
#> GSM2890 1 0.980 0.148 0.584 0.416
#> GSM2877 1 0.980 0.148 0.584 0.416
#> GSM2892 1 0.980 0.148 0.584 0.416
#> GSM2902 1 0.980 0.148 0.584 0.416
#> GSM2878 1 0.980 0.148 0.584 0.416
#> GSM2901 1 0.980 0.148 0.584 0.416
#> GSM2879 2 0.000 0.944 0.000 1.000
#> GSM2898 2 0.000 0.944 0.000 1.000
#> GSM2881 2 0.000 0.944 0.000 1.000
#> GSM2897 2 0.000 0.944 0.000 1.000
#> GSM2882 1 0.850 0.431 0.724 0.276
#> GSM2894 1 0.850 0.431 0.724 0.276
#> GSM2883 2 0.000 0.944 0.000 1.000
#> GSM2895 2 0.000 0.944 0.000 1.000
#> GSM2885 2 0.000 0.944 0.000 1.000
#> GSM2886 2 0.000 0.944 0.000 1.000
#> GSM2887 2 0.000 0.944 0.000 1.000
#> GSM2896 2 0.000 0.944 0.000 1.000
#> GSM2888 1 0.943 0.365 0.640 0.360
#> GSM2889 1 0.946 0.360 0.636 0.364
#> GSM2876 1 0.980 0.148 0.584 0.416
#> GSM2891 1 0.980 0.148 0.584 0.416
#> GSM2880 1 0.980 0.148 0.584 0.416
#> GSM2893 1 0.980 0.148 0.584 0.416
#> GSM2821 1 0.980 0.148 0.584 0.416
#> GSM2900 1 0.980 0.148 0.584 0.416
#> GSM2903 1 0.980 0.148 0.584 0.416
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM2819 1 0.0237 0.9491 0.996 0.004 0.000
#> GSM2820 3 0.0237 0.9443 0.004 0.000 0.996
#> GSM2822 2 0.6308 0.0551 0.492 0.508 0.000
#> GSM2832 2 0.5650 0.5527 0.312 0.688 0.000
#> GSM2823 1 0.6386 0.3334 0.584 0.004 0.412
#> GSM2824 1 0.6386 0.3334 0.584 0.004 0.412
#> GSM2825 1 0.2261 0.8855 0.932 0.068 0.000
#> GSM2826 1 0.2356 0.8839 0.928 0.072 0.000
#> GSM2829 2 0.0424 0.9579 0.008 0.992 0.000
#> GSM2856 2 0.0424 0.9579 0.008 0.992 0.000
#> GSM2830 2 0.0424 0.9579 0.008 0.992 0.000
#> GSM2843 2 0.0424 0.9579 0.008 0.992 0.000
#> GSM2871 2 0.0424 0.9579 0.008 0.992 0.000
#> GSM2831 2 0.0424 0.9579 0.008 0.992 0.000
#> GSM2844 2 0.0424 0.9579 0.008 0.992 0.000
#> GSM2833 2 0.0424 0.9579 0.008 0.992 0.000
#> GSM2846 2 0.0424 0.9579 0.008 0.992 0.000
#> GSM2835 2 0.0424 0.9579 0.008 0.992 0.000
#> GSM2858 2 0.0424 0.9579 0.008 0.992 0.000
#> GSM2836 2 0.0237 0.9559 0.000 0.996 0.004
#> GSM2848 2 0.0237 0.9559 0.000 0.996 0.004
#> GSM2828 3 0.0237 0.9443 0.004 0.000 0.996
#> GSM2837 3 0.0237 0.9443 0.004 0.000 0.996
#> GSM2839 1 0.0000 0.9529 1.000 0.000 0.000
#> GSM2841 1 0.0000 0.9529 1.000 0.000 0.000
#> GSM2827 2 0.0237 0.9566 0.004 0.996 0.000
#> GSM2842 2 0.0237 0.9566 0.004 0.996 0.000
#> GSM2845 2 0.0424 0.9579 0.008 0.992 0.000
#> GSM2872 2 0.0424 0.9579 0.008 0.992 0.000
#> GSM2834 2 0.0424 0.9579 0.008 0.992 0.000
#> GSM2847 2 0.0424 0.9579 0.008 0.992 0.000
#> GSM2849 3 0.0237 0.9443 0.004 0.000 0.996
#> GSM2850 3 0.0237 0.9443 0.004 0.000 0.996
#> GSM2838 2 0.1163 0.9478 0.000 0.972 0.028
#> GSM2853 2 0.0424 0.9554 0.000 0.992 0.008
#> GSM2852 3 0.0661 0.9408 0.004 0.008 0.988
#> GSM2855 3 0.0661 0.9408 0.004 0.008 0.988
#> GSM2840 1 0.0000 0.9529 1.000 0.000 0.000
#> GSM2857 1 0.0000 0.9529 1.000 0.000 0.000
#> GSM2859 2 0.0892 0.9516 0.000 0.980 0.020
#> GSM2860 2 0.1860 0.9327 0.000 0.948 0.052
#> GSM2861 2 0.3349 0.8737 0.004 0.888 0.108
#> GSM2862 2 0.1860 0.9327 0.000 0.948 0.052
#> GSM2863 2 0.0592 0.9544 0.000 0.988 0.012
#> GSM2864 2 0.1411 0.9436 0.000 0.964 0.036
#> GSM2865 2 0.0892 0.9517 0.000 0.980 0.020
#> GSM2866 2 0.0237 0.9566 0.004 0.996 0.000
#> GSM2868 2 0.3528 0.8873 0.016 0.892 0.092
#> GSM2869 2 0.1529 0.9411 0.000 0.960 0.040
#> GSM2851 2 0.1411 0.9435 0.000 0.964 0.036
#> GSM2867 2 0.2749 0.9174 0.012 0.924 0.064
#> GSM2870 2 0.2537 0.9095 0.000 0.920 0.080
#> GSM2854 2 0.0424 0.9579 0.008 0.992 0.000
#> GSM2873 2 0.0237 0.9572 0.004 0.996 0.000
#> GSM2874 3 0.0237 0.9443 0.004 0.000 0.996
#> GSM2884 3 0.0237 0.9443 0.004 0.000 0.996
#> GSM2875 1 0.0000 0.9529 1.000 0.000 0.000
#> GSM2890 1 0.0000 0.9529 1.000 0.000 0.000
#> GSM2877 1 0.0000 0.9529 1.000 0.000 0.000
#> GSM2892 1 0.0000 0.9529 1.000 0.000 0.000
#> GSM2902 1 0.0000 0.9529 1.000 0.000 0.000
#> GSM2878 1 0.0000 0.9529 1.000 0.000 0.000
#> GSM2901 1 0.0000 0.9529 1.000 0.000 0.000
#> GSM2879 3 0.0661 0.9408 0.004 0.008 0.988
#> GSM2898 3 0.0661 0.9408 0.004 0.008 0.988
#> GSM2881 3 0.0237 0.9443 0.004 0.000 0.996
#> GSM2897 3 0.0237 0.9443 0.004 0.000 0.996
#> GSM2882 2 0.0424 0.9579 0.008 0.992 0.000
#> GSM2894 2 0.0424 0.9579 0.008 0.992 0.000
#> GSM2883 3 0.0237 0.9443 0.004 0.000 0.996
#> GSM2895 3 0.0237 0.9443 0.004 0.000 0.996
#> GSM2885 3 0.0237 0.9443 0.004 0.000 0.996
#> GSM2886 3 0.0237 0.9443 0.004 0.000 0.996
#> GSM2887 3 0.0475 0.9429 0.004 0.004 0.992
#> GSM2896 3 0.0475 0.9429 0.004 0.004 0.992
#> GSM2888 3 0.6421 0.2599 0.004 0.424 0.572
#> GSM2889 3 0.6421 0.2599 0.004 0.424 0.572
#> GSM2876 1 0.0000 0.9529 1.000 0.000 0.000
#> GSM2891 1 0.0000 0.9529 1.000 0.000 0.000
#> GSM2880 1 0.0000 0.9529 1.000 0.000 0.000
#> GSM2893 1 0.0000 0.9529 1.000 0.000 0.000
#> GSM2821 1 0.0000 0.9529 1.000 0.000 0.000
#> GSM2900 1 0.0000 0.9529 1.000 0.000 0.000
#> GSM2903 1 0.0000 0.9529 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM2819 1 0.228 0.897 0.904 0.096 0.000 0.000
#> GSM2820 3 0.000 0.826 0.000 0.000 1.000 0.000
#> GSM2822 1 0.447 0.778 0.784 0.036 0.000 0.180
#> GSM2832 1 0.451 0.773 0.780 0.036 0.000 0.184
#> GSM2823 3 0.744 0.343 0.172 0.384 0.444 0.000
#> GSM2824 3 0.744 0.343 0.172 0.384 0.444 0.000
#> GSM2825 1 0.280 0.875 0.884 0.008 0.000 0.108
#> GSM2826 1 0.280 0.875 0.884 0.008 0.000 0.108
#> GSM2829 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM2856 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM2830 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM2843 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM2871 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM2831 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM2844 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM2833 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM2846 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM2835 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM2858 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM2836 2 0.542 0.778 0.148 0.740 0.000 0.112
#> GSM2848 2 0.542 0.778 0.148 0.740 0.000 0.112
#> GSM2828 3 0.000 0.826 0.000 0.000 1.000 0.000
#> GSM2837 3 0.000 0.826 0.000 0.000 1.000 0.000
#> GSM2839 1 0.000 0.951 1.000 0.000 0.000 0.000
#> GSM2841 1 0.000 0.951 1.000 0.000 0.000 0.000
#> GSM2827 2 0.557 0.770 0.148 0.728 0.000 0.124
#> GSM2842 2 0.547 0.776 0.148 0.736 0.000 0.116
#> GSM2845 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM2872 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM2834 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM2847 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM2849 3 0.000 0.826 0.000 0.000 1.000 0.000
#> GSM2850 3 0.000 0.826 0.000 0.000 1.000 0.000
#> GSM2838 2 0.112 0.895 0.000 0.964 0.000 0.036
#> GSM2853 2 0.121 0.894 0.000 0.960 0.000 0.040
#> GSM2852 3 0.734 0.390 0.164 0.360 0.476 0.000
#> GSM2855 3 0.734 0.390 0.164 0.360 0.476 0.000
#> GSM2840 1 0.000 0.951 1.000 0.000 0.000 0.000
#> GSM2857 1 0.000 0.951 1.000 0.000 0.000 0.000
#> GSM2859 2 0.139 0.891 0.000 0.952 0.000 0.048
#> GSM2860 2 0.112 0.895 0.000 0.964 0.000 0.036
#> GSM2861 2 0.139 0.891 0.000 0.952 0.000 0.048
#> GSM2862 2 0.112 0.895 0.000 0.964 0.000 0.036
#> GSM2863 2 0.112 0.895 0.000 0.964 0.000 0.036
#> GSM2864 2 0.112 0.895 0.000 0.964 0.000 0.036
#> GSM2865 2 0.112 0.895 0.000 0.964 0.000 0.036
#> GSM2866 2 0.309 0.865 0.060 0.888 0.000 0.052
#> GSM2868 2 0.112 0.895 0.000 0.964 0.000 0.036
#> GSM2869 2 0.112 0.895 0.000 0.964 0.000 0.036
#> GSM2851 2 0.102 0.893 0.000 0.968 0.000 0.032
#> GSM2867 2 0.102 0.893 0.000 0.968 0.000 0.032
#> GSM2870 2 0.112 0.895 0.000 0.964 0.000 0.036
#> GSM2854 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM2873 2 0.724 0.379 0.148 0.476 0.000 0.376
#> GSM2874 3 0.000 0.826 0.000 0.000 1.000 0.000
#> GSM2884 3 0.000 0.826 0.000 0.000 1.000 0.000
#> GSM2875 1 0.000 0.951 1.000 0.000 0.000 0.000
#> GSM2890 1 0.000 0.951 1.000 0.000 0.000 0.000
#> GSM2877 1 0.000 0.951 1.000 0.000 0.000 0.000
#> GSM2892 1 0.000 0.951 1.000 0.000 0.000 0.000
#> GSM2902 1 0.000 0.951 1.000 0.000 0.000 0.000
#> GSM2878 1 0.000 0.951 1.000 0.000 0.000 0.000
#> GSM2901 1 0.000 0.951 1.000 0.000 0.000 0.000
#> GSM2879 3 0.698 0.551 0.164 0.264 0.572 0.000
#> GSM2898 3 0.698 0.551 0.164 0.264 0.572 0.000
#> GSM2881 3 0.000 0.826 0.000 0.000 1.000 0.000
#> GSM2897 3 0.000 0.826 0.000 0.000 1.000 0.000
#> GSM2882 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM2894 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM2883 3 0.512 0.705 0.164 0.080 0.756 0.000
#> GSM2895 3 0.512 0.705 0.164 0.080 0.756 0.000
#> GSM2885 3 0.000 0.826 0.000 0.000 1.000 0.000
#> GSM2886 3 0.000 0.826 0.000 0.000 1.000 0.000
#> GSM2887 3 0.000 0.826 0.000 0.000 1.000 0.000
#> GSM2896 3 0.000 0.826 0.000 0.000 1.000 0.000
#> GSM2888 2 0.508 0.721 0.148 0.780 0.056 0.016
#> GSM2889 2 0.508 0.721 0.148 0.780 0.056 0.016
#> GSM2876 1 0.000 0.951 1.000 0.000 0.000 0.000
#> GSM2891 1 0.000 0.951 1.000 0.000 0.000 0.000
#> GSM2880 1 0.000 0.951 1.000 0.000 0.000 0.000
#> GSM2893 1 0.000 0.951 1.000 0.000 0.000 0.000
#> GSM2821 1 0.208 0.905 0.916 0.084 0.000 0.000
#> GSM2900 1 0.208 0.905 0.916 0.084 0.000 0.000
#> GSM2903 1 0.208 0.905 0.916 0.084 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM2819 5 0.5038 0.6389 0.132 0.164 0.000 0.000 0.704
#> GSM2820 3 0.0000 0.9501 0.000 0.000 1.000 0.000 0.000
#> GSM2822 5 0.7069 0.4641 0.076 0.340 0.000 0.096 0.488
#> GSM2832 5 0.7069 0.4641 0.076 0.340 0.000 0.096 0.488
#> GSM2823 5 0.0404 0.6698 0.012 0.000 0.000 0.000 0.988
#> GSM2824 5 0.0404 0.6698 0.012 0.000 0.000 0.000 0.988
#> GSM2825 5 0.6819 0.6051 0.152 0.164 0.000 0.084 0.600
#> GSM2826 5 0.6819 0.6051 0.152 0.164 0.000 0.084 0.600
#> GSM2829 4 0.0000 0.9937 0.000 0.000 0.000 1.000 0.000
#> GSM2856 4 0.0000 0.9937 0.000 0.000 0.000 1.000 0.000
#> GSM2830 4 0.0000 0.9937 0.000 0.000 0.000 1.000 0.000
#> GSM2843 4 0.0000 0.9937 0.000 0.000 0.000 1.000 0.000
#> GSM2871 4 0.0000 0.9937 0.000 0.000 0.000 1.000 0.000
#> GSM2831 4 0.0000 0.9937 0.000 0.000 0.000 1.000 0.000
#> GSM2844 4 0.0000 0.9937 0.000 0.000 0.000 1.000 0.000
#> GSM2833 4 0.0162 0.9901 0.000 0.004 0.000 0.996 0.000
#> GSM2846 4 0.0162 0.9901 0.000 0.004 0.000 0.996 0.000
#> GSM2835 4 0.0000 0.9937 0.000 0.000 0.000 1.000 0.000
#> GSM2858 4 0.0000 0.9937 0.000 0.000 0.000 1.000 0.000
#> GSM2836 2 0.5646 -0.1210 0.000 0.520 0.000 0.080 0.400
#> GSM2848 2 0.5562 -0.1277 0.000 0.520 0.000 0.072 0.408
#> GSM2828 3 0.0000 0.9501 0.000 0.000 1.000 0.000 0.000
#> GSM2837 3 0.0000 0.9501 0.000 0.000 1.000 0.000 0.000
#> GSM2839 1 0.3885 0.7481 0.724 0.008 0.000 0.000 0.268
#> GSM2841 1 0.3885 0.7481 0.724 0.008 0.000 0.000 0.268
#> GSM2827 5 0.5867 0.3665 0.000 0.404 0.000 0.100 0.496
#> GSM2842 5 0.5867 0.3665 0.000 0.404 0.000 0.100 0.496
#> GSM2845 4 0.0000 0.9937 0.000 0.000 0.000 1.000 0.000
#> GSM2872 4 0.0000 0.9937 0.000 0.000 0.000 1.000 0.000
#> GSM2834 4 0.0000 0.9937 0.000 0.000 0.000 1.000 0.000
#> GSM2847 4 0.0000 0.9937 0.000 0.000 0.000 1.000 0.000
#> GSM2849 3 0.0000 0.9501 0.000 0.000 1.000 0.000 0.000
#> GSM2850 3 0.0000 0.9501 0.000 0.000 1.000 0.000 0.000
#> GSM2838 2 0.0000 0.8588 0.000 1.000 0.000 0.000 0.000
#> GSM2853 2 0.0404 0.8536 0.000 0.988 0.000 0.000 0.012
#> GSM2852 5 0.3452 0.5550 0.000 0.000 0.244 0.000 0.756
#> GSM2855 5 0.3452 0.5550 0.000 0.000 0.244 0.000 0.756
#> GSM2840 1 0.3885 0.7481 0.724 0.008 0.000 0.000 0.268
#> GSM2857 1 0.3885 0.7481 0.724 0.008 0.000 0.000 0.268
#> GSM2859 2 0.0162 0.8566 0.000 0.996 0.000 0.004 0.000
#> GSM2860 2 0.0000 0.8588 0.000 1.000 0.000 0.000 0.000
#> GSM2861 2 0.3010 0.6641 0.000 0.824 0.000 0.004 0.172
#> GSM2862 2 0.0000 0.8588 0.000 1.000 0.000 0.000 0.000
#> GSM2863 2 0.0000 0.8588 0.000 1.000 0.000 0.000 0.000
#> GSM2864 2 0.0000 0.8588 0.000 1.000 0.000 0.000 0.000
#> GSM2865 2 0.0000 0.8588 0.000 1.000 0.000 0.000 0.000
#> GSM2866 2 0.5500 0.0265 0.000 0.552 0.000 0.072 0.376
#> GSM2868 2 0.1341 0.8150 0.000 0.944 0.000 0.000 0.056
#> GSM2869 2 0.0000 0.8588 0.000 1.000 0.000 0.000 0.000
#> GSM2851 2 0.0000 0.8588 0.000 1.000 0.000 0.000 0.000
#> GSM2867 2 0.0703 0.8444 0.000 0.976 0.000 0.000 0.024
#> GSM2870 2 0.0000 0.8588 0.000 1.000 0.000 0.000 0.000
#> GSM2854 4 0.2266 0.8943 0.008 0.016 0.000 0.912 0.064
#> GSM2873 5 0.7073 0.2787 0.012 0.348 0.000 0.260 0.380
#> GSM2874 3 0.0000 0.9501 0.000 0.000 1.000 0.000 0.000
#> GSM2884 3 0.0000 0.9501 0.000 0.000 1.000 0.000 0.000
#> GSM2875 1 0.0000 0.8591 1.000 0.000 0.000 0.000 0.000
#> GSM2890 1 0.0000 0.8591 1.000 0.000 0.000 0.000 0.000
#> GSM2877 1 0.0000 0.8591 1.000 0.000 0.000 0.000 0.000
#> GSM2892 1 0.0000 0.8591 1.000 0.000 0.000 0.000 0.000
#> GSM2902 1 0.0000 0.8591 1.000 0.000 0.000 0.000 0.000
#> GSM2878 1 0.0000 0.8591 1.000 0.000 0.000 0.000 0.000
#> GSM2901 1 0.0000 0.8591 1.000 0.000 0.000 0.000 0.000
#> GSM2879 5 0.1270 0.6692 0.000 0.000 0.052 0.000 0.948
#> GSM2898 5 0.1270 0.6692 0.000 0.000 0.052 0.000 0.948
#> GSM2881 3 0.0000 0.9501 0.000 0.000 1.000 0.000 0.000
#> GSM2897 3 0.0000 0.9501 0.000 0.000 1.000 0.000 0.000
#> GSM2882 4 0.0000 0.9937 0.000 0.000 0.000 1.000 0.000
#> GSM2894 4 0.0000 0.9937 0.000 0.000 0.000 1.000 0.000
#> GSM2883 3 0.3816 0.5436 0.000 0.000 0.696 0.000 0.304
#> GSM2895 3 0.3816 0.5436 0.000 0.000 0.696 0.000 0.304
#> GSM2885 3 0.0000 0.9501 0.000 0.000 1.000 0.000 0.000
#> GSM2886 3 0.0000 0.9501 0.000 0.000 1.000 0.000 0.000
#> GSM2887 3 0.0000 0.9501 0.000 0.000 1.000 0.000 0.000
#> GSM2896 3 0.0000 0.9501 0.000 0.000 1.000 0.000 0.000
#> GSM2888 5 0.4491 0.4815 0.000 0.364 0.004 0.008 0.624
#> GSM2889 5 0.4491 0.4815 0.000 0.364 0.004 0.008 0.624
#> GSM2876 1 0.3612 0.7514 0.732 0.000 0.000 0.000 0.268
#> GSM2891 1 0.3612 0.7514 0.732 0.000 0.000 0.000 0.268
#> GSM2880 1 0.1121 0.8474 0.956 0.000 0.000 0.000 0.044
#> GSM2893 1 0.0000 0.8591 1.000 0.000 0.000 0.000 0.000
#> GSM2821 5 0.1331 0.6619 0.040 0.008 0.000 0.000 0.952
#> GSM2900 5 0.1331 0.6619 0.040 0.008 0.000 0.000 0.952
#> GSM2903 5 0.1331 0.6619 0.040 0.008 0.000 0.000 0.952
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM2819 6 0.4387 0.533 0.004 0.020 0.000 0.000 0.404 0.572
#> GSM2820 3 0.0146 0.921 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM2822 6 0.4130 0.708 0.000 0.164 0.000 0.016 0.060 0.760
#> GSM2832 6 0.4073 0.709 0.000 0.164 0.000 0.016 0.056 0.764
#> GSM2823 6 0.3727 0.516 0.000 0.000 0.000 0.000 0.388 0.612
#> GSM2824 6 0.3737 0.515 0.000 0.000 0.000 0.000 0.392 0.608
#> GSM2825 6 0.5198 0.513 0.048 0.020 0.000 0.020 0.260 0.652
#> GSM2826 6 0.5177 0.516 0.048 0.020 0.000 0.020 0.256 0.656
#> GSM2829 4 0.0260 0.971 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM2856 4 0.0260 0.971 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM2830 4 0.0260 0.971 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM2843 4 0.0146 0.970 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM2871 4 0.0858 0.950 0.000 0.000 0.000 0.968 0.004 0.028
#> GSM2831 4 0.0146 0.971 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM2844 4 0.0146 0.971 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM2833 4 0.0603 0.964 0.000 0.000 0.000 0.980 0.004 0.016
#> GSM2846 4 0.0508 0.966 0.000 0.000 0.000 0.984 0.004 0.012
#> GSM2835 4 0.0405 0.968 0.000 0.000 0.000 0.988 0.008 0.004
#> GSM2858 4 0.0405 0.968 0.000 0.000 0.000 0.988 0.008 0.004
#> GSM2836 6 0.3559 0.693 0.000 0.240 0.000 0.004 0.012 0.744
#> GSM2848 6 0.3596 0.700 0.000 0.232 0.000 0.004 0.016 0.748
#> GSM2828 3 0.0000 0.923 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2837 3 0.0000 0.923 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2839 5 0.3390 0.543 0.296 0.000 0.000 0.000 0.704 0.000
#> GSM2841 5 0.3390 0.543 0.296 0.000 0.000 0.000 0.704 0.000
#> GSM2827 6 0.3231 0.709 0.000 0.200 0.000 0.016 0.000 0.784
#> GSM2842 6 0.3231 0.709 0.000 0.200 0.000 0.016 0.000 0.784
#> GSM2845 4 0.0146 0.970 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM2872 4 0.0146 0.970 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM2834 4 0.0291 0.969 0.000 0.000 0.000 0.992 0.004 0.004
#> GSM2847 4 0.0291 0.971 0.000 0.000 0.000 0.992 0.004 0.004
#> GSM2849 3 0.0000 0.923 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2850 3 0.0000 0.923 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2838 2 0.0000 0.942 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2853 2 0.1204 0.899 0.000 0.944 0.000 0.000 0.000 0.056
#> GSM2852 6 0.2805 0.605 0.000 0.004 0.000 0.000 0.184 0.812
#> GSM2855 6 0.2805 0.605 0.000 0.004 0.000 0.000 0.184 0.812
#> GSM2840 5 0.3175 0.558 0.256 0.000 0.000 0.000 0.744 0.000
#> GSM2857 5 0.3175 0.558 0.256 0.000 0.000 0.000 0.744 0.000
#> GSM2859 2 0.0260 0.937 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM2860 2 0.0000 0.942 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2861 2 0.2300 0.788 0.000 0.856 0.000 0.000 0.000 0.144
#> GSM2862 2 0.0000 0.942 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2863 2 0.0000 0.942 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2864 2 0.0000 0.942 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2865 2 0.0000 0.942 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2866 6 0.4124 0.573 0.000 0.332 0.000 0.008 0.012 0.648
#> GSM2868 2 0.3448 0.461 0.000 0.716 0.000 0.000 0.004 0.280
#> GSM2869 2 0.0000 0.942 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2851 2 0.0000 0.942 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2867 2 0.1610 0.867 0.000 0.916 0.000 0.000 0.000 0.084
#> GSM2870 2 0.0000 0.942 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2854 4 0.3741 0.533 0.000 0.000 0.000 0.672 0.008 0.320
#> GSM2873 6 0.5198 0.606 0.000 0.200 0.000 0.140 0.012 0.648
#> GSM2874 3 0.0000 0.923 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2884 3 0.0000 0.923 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2875 1 0.0000 0.991 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2890 1 0.0000 0.991 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2877 1 0.0000 0.991 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2892 1 0.0000 0.991 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2902 1 0.0000 0.991 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2878 1 0.0458 0.982 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM2901 1 0.0458 0.982 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM2879 6 0.2882 0.603 0.000 0.000 0.008 0.000 0.180 0.812
#> GSM2898 6 0.2882 0.603 0.000 0.000 0.008 0.000 0.180 0.812
#> GSM2881 3 0.0000 0.923 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2897 3 0.0000 0.923 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2882 4 0.0405 0.968 0.000 0.000 0.000 0.988 0.008 0.004
#> GSM2894 4 0.0405 0.968 0.000 0.000 0.000 0.988 0.008 0.004
#> GSM2883 3 0.5480 0.486 0.000 0.000 0.564 0.000 0.184 0.252
#> GSM2895 3 0.5461 0.491 0.000 0.000 0.568 0.000 0.184 0.248
#> GSM2885 3 0.0000 0.923 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2886 3 0.0000 0.923 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2887 3 0.2146 0.856 0.000 0.000 0.880 0.000 0.004 0.116
#> GSM2896 3 0.2006 0.863 0.000 0.000 0.892 0.000 0.004 0.104
#> GSM2888 6 0.4628 0.708 0.000 0.204 0.000 0.000 0.112 0.684
#> GSM2889 6 0.4628 0.708 0.000 0.204 0.000 0.000 0.112 0.684
#> GSM2876 5 0.3446 0.530 0.308 0.000 0.000 0.000 0.692 0.000
#> GSM2891 5 0.3446 0.530 0.308 0.000 0.000 0.000 0.692 0.000
#> GSM2880 1 0.0547 0.976 0.980 0.000 0.000 0.000 0.020 0.000
#> GSM2893 1 0.0146 0.990 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM2821 5 0.3847 -0.367 0.000 0.000 0.000 0.000 0.544 0.456
#> GSM2900 5 0.3789 -0.269 0.000 0.000 0.000 0.000 0.584 0.416
#> GSM2903 5 0.3789 -0.269 0.000 0.000 0.000 0.000 0.584 0.416
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 tissue(p) k
#> CV:mclust 19 NA 2
#> CV:mclust 79 2.19e-08 3
#> CV:mclust 79 1.16e-11 4
#> CV:mclust 74 6.72e-14 5
#> CV:mclust 78 2.87e-16 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 8229 rows and 84 columns.
#> Top rows (823, 1646, 2468, 3291, 4114) 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.910 0.917 0.960 0.4559 0.550 0.550
#> 3 3 0.778 0.887 0.939 0.3772 0.616 0.419
#> 4 4 0.974 0.925 0.967 0.1987 0.861 0.640
#> 5 5 0.852 0.743 0.822 0.0499 0.943 0.780
#> 6 6 0.869 0.738 0.859 0.0371 0.949 0.771
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM2819 1 0.6887 0.774 0.816 0.184
#> GSM2820 2 0.1184 0.951 0.016 0.984
#> GSM2822 2 0.9963 0.157 0.464 0.536
#> GSM2832 2 0.5842 0.844 0.140 0.860
#> GSM2823 2 0.8327 0.650 0.264 0.736
#> GSM2824 2 0.9970 0.149 0.468 0.532
#> GSM2825 1 0.1184 0.960 0.984 0.016
#> GSM2826 1 0.1184 0.960 0.984 0.016
#> GSM2829 2 0.1633 0.954 0.024 0.976
#> GSM2856 2 0.2043 0.949 0.032 0.968
#> GSM2830 2 0.1633 0.954 0.024 0.976
#> GSM2843 2 0.1414 0.955 0.020 0.980
#> GSM2871 2 0.1414 0.955 0.020 0.980
#> GSM2831 1 0.5519 0.851 0.872 0.128
#> GSM2844 1 0.2948 0.932 0.948 0.052
#> GSM2833 2 0.8144 0.683 0.252 0.748
#> GSM2846 2 0.4939 0.880 0.108 0.892
#> GSM2835 1 0.0938 0.962 0.988 0.012
#> GSM2858 1 0.1184 0.960 0.984 0.016
#> GSM2836 2 0.1184 0.956 0.016 0.984
#> GSM2848 2 0.1184 0.956 0.016 0.984
#> GSM2828 2 0.1184 0.951 0.016 0.984
#> GSM2837 2 0.1184 0.951 0.016 0.984
#> GSM2839 1 0.0000 0.967 1.000 0.000
#> GSM2841 1 0.0000 0.967 1.000 0.000
#> GSM2827 2 0.1184 0.956 0.016 0.984
#> GSM2842 2 0.0938 0.956 0.012 0.988
#> GSM2845 2 0.2603 0.941 0.044 0.956
#> GSM2872 1 0.9754 0.286 0.592 0.408
#> GSM2834 2 0.1633 0.954 0.024 0.976
#> GSM2847 2 0.2603 0.941 0.044 0.956
#> GSM2849 2 0.1184 0.951 0.016 0.984
#> GSM2850 2 0.1184 0.951 0.016 0.984
#> GSM2838 2 0.1184 0.956 0.016 0.984
#> GSM2853 2 0.1184 0.956 0.016 0.984
#> GSM2852 2 0.0376 0.954 0.004 0.996
#> GSM2855 2 0.0376 0.954 0.004 0.996
#> GSM2840 1 0.0000 0.967 1.000 0.000
#> GSM2857 1 0.0000 0.967 1.000 0.000
#> GSM2859 2 0.1414 0.955 0.020 0.980
#> GSM2860 2 0.1184 0.956 0.016 0.984
#> GSM2861 2 0.0672 0.956 0.008 0.992
#> GSM2862 2 0.0672 0.956 0.008 0.992
#> GSM2863 2 0.1184 0.956 0.016 0.984
#> GSM2864 2 0.1184 0.956 0.016 0.984
#> GSM2865 2 0.1184 0.956 0.016 0.984
#> GSM2866 2 0.1414 0.955 0.020 0.980
#> GSM2868 2 0.0938 0.956 0.012 0.988
#> GSM2869 2 0.1184 0.956 0.016 0.984
#> GSM2851 2 0.1184 0.956 0.016 0.984
#> GSM2867 2 0.1184 0.956 0.016 0.984
#> GSM2870 2 0.1184 0.956 0.016 0.984
#> GSM2854 2 0.1843 0.952 0.028 0.972
#> GSM2873 2 0.1414 0.955 0.020 0.980
#> GSM2874 2 0.1184 0.951 0.016 0.984
#> GSM2884 2 0.1184 0.951 0.016 0.984
#> GSM2875 1 0.0000 0.967 1.000 0.000
#> GSM2890 1 0.0000 0.967 1.000 0.000
#> GSM2877 1 0.0000 0.967 1.000 0.000
#> GSM2892 1 0.0000 0.967 1.000 0.000
#> GSM2902 1 0.0000 0.967 1.000 0.000
#> GSM2878 1 0.0000 0.967 1.000 0.000
#> GSM2901 1 0.0000 0.967 1.000 0.000
#> GSM2879 2 0.0672 0.953 0.008 0.992
#> GSM2898 2 0.0376 0.954 0.004 0.996
#> GSM2881 2 0.1184 0.951 0.016 0.984
#> GSM2897 2 0.1184 0.951 0.016 0.984
#> GSM2882 1 0.0938 0.962 0.988 0.012
#> GSM2894 1 0.0938 0.962 0.988 0.012
#> GSM2883 2 0.1184 0.951 0.016 0.984
#> GSM2895 2 0.1184 0.951 0.016 0.984
#> GSM2885 2 0.1184 0.951 0.016 0.984
#> GSM2886 2 0.1184 0.951 0.016 0.984
#> GSM2887 2 0.0938 0.952 0.012 0.988
#> GSM2896 2 0.0938 0.952 0.012 0.988
#> GSM2888 2 0.0000 0.953 0.000 1.000
#> GSM2889 2 0.0000 0.953 0.000 1.000
#> GSM2876 1 0.0000 0.967 1.000 0.000
#> GSM2891 1 0.0000 0.967 1.000 0.000
#> GSM2880 1 0.0000 0.967 1.000 0.000
#> GSM2893 1 0.0000 0.967 1.000 0.000
#> GSM2821 1 0.0672 0.964 0.992 0.008
#> GSM2900 1 0.0000 0.967 1.000 0.000
#> GSM2903 1 0.0000 0.967 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM2819 2 0.0237 0.898 0.004 0.996 0.000
#> GSM2820 3 0.0000 1.000 0.000 0.000 1.000
#> GSM2822 2 0.0000 0.898 0.000 1.000 0.000
#> GSM2832 2 0.0000 0.898 0.000 1.000 0.000
#> GSM2823 1 0.9236 0.379 0.532 0.248 0.220
#> GSM2824 1 0.6158 0.700 0.760 0.188 0.052
#> GSM2825 2 0.6026 0.443 0.376 0.624 0.000
#> GSM2826 2 0.6062 0.424 0.384 0.616 0.000
#> GSM2829 2 0.0000 0.898 0.000 1.000 0.000
#> GSM2856 2 0.0000 0.898 0.000 1.000 0.000
#> GSM2830 2 0.0000 0.898 0.000 1.000 0.000
#> GSM2843 2 0.0000 0.898 0.000 1.000 0.000
#> GSM2871 2 0.0000 0.898 0.000 1.000 0.000
#> GSM2831 2 0.0000 0.898 0.000 1.000 0.000
#> GSM2844 2 0.0237 0.897 0.004 0.996 0.000
#> GSM2833 2 0.0000 0.898 0.000 1.000 0.000
#> GSM2846 2 0.0000 0.898 0.000 1.000 0.000
#> GSM2835 2 0.1964 0.867 0.056 0.944 0.000
#> GSM2858 2 0.0892 0.890 0.020 0.980 0.000
#> GSM2836 2 0.3340 0.864 0.000 0.880 0.120
#> GSM2848 2 0.2625 0.882 0.000 0.916 0.084
#> GSM2828 3 0.0000 1.000 0.000 0.000 1.000
#> GSM2837 3 0.0000 1.000 0.000 0.000 1.000
#> GSM2839 1 0.0000 0.961 1.000 0.000 0.000
#> GSM2841 1 0.0000 0.961 1.000 0.000 0.000
#> GSM2827 2 0.2537 0.884 0.000 0.920 0.080
#> GSM2842 2 0.4346 0.816 0.000 0.816 0.184
#> GSM2845 2 0.0000 0.898 0.000 1.000 0.000
#> GSM2872 2 0.0000 0.898 0.000 1.000 0.000
#> GSM2834 2 0.0000 0.898 0.000 1.000 0.000
#> GSM2847 2 0.0000 0.898 0.000 1.000 0.000
#> GSM2849 3 0.0000 1.000 0.000 0.000 1.000
#> GSM2850 3 0.0000 1.000 0.000 0.000 1.000
#> GSM2838 2 0.1289 0.895 0.000 0.968 0.032
#> GSM2853 2 0.0747 0.897 0.000 0.984 0.016
#> GSM2852 3 0.0000 1.000 0.000 0.000 1.000
#> GSM2855 3 0.0000 1.000 0.000 0.000 1.000
#> GSM2840 1 0.0000 0.961 1.000 0.000 0.000
#> GSM2857 1 0.0000 0.961 1.000 0.000 0.000
#> GSM2859 2 0.3192 0.869 0.000 0.888 0.112
#> GSM2860 2 0.2711 0.880 0.000 0.912 0.088
#> GSM2861 2 0.4555 0.800 0.000 0.800 0.200
#> GSM2862 2 0.2537 0.883 0.000 0.920 0.080
#> GSM2863 2 0.2959 0.875 0.000 0.900 0.100
#> GSM2864 2 0.4121 0.829 0.000 0.832 0.168
#> GSM2865 2 0.3038 0.874 0.000 0.896 0.104
#> GSM2866 2 0.0000 0.898 0.000 1.000 0.000
#> GSM2868 2 0.6079 0.524 0.000 0.612 0.388
#> GSM2869 2 0.5216 0.732 0.000 0.740 0.260
#> GSM2851 2 0.3192 0.869 0.000 0.888 0.112
#> GSM2867 2 0.5529 0.683 0.000 0.704 0.296
#> GSM2870 2 0.3551 0.857 0.000 0.868 0.132
#> GSM2854 2 0.0000 0.898 0.000 1.000 0.000
#> GSM2873 2 0.0000 0.898 0.000 1.000 0.000
#> GSM2874 3 0.0000 1.000 0.000 0.000 1.000
#> GSM2884 3 0.0000 1.000 0.000 0.000 1.000
#> GSM2875 1 0.0000 0.961 1.000 0.000 0.000
#> GSM2890 1 0.0000 0.961 1.000 0.000 0.000
#> GSM2877 1 0.0000 0.961 1.000 0.000 0.000
#> GSM2892 1 0.0000 0.961 1.000 0.000 0.000
#> GSM2902 1 0.0000 0.961 1.000 0.000 0.000
#> GSM2878 1 0.0000 0.961 1.000 0.000 0.000
#> GSM2901 1 0.0000 0.961 1.000 0.000 0.000
#> GSM2879 3 0.0000 1.000 0.000 0.000 1.000
#> GSM2898 3 0.0000 1.000 0.000 0.000 1.000
#> GSM2881 3 0.0000 1.000 0.000 0.000 1.000
#> GSM2897 3 0.0000 1.000 0.000 0.000 1.000
#> GSM2882 2 0.3116 0.823 0.108 0.892 0.000
#> GSM2894 2 0.2625 0.845 0.084 0.916 0.000
#> GSM2883 3 0.0000 1.000 0.000 0.000 1.000
#> GSM2895 3 0.0000 1.000 0.000 0.000 1.000
#> GSM2885 3 0.0000 1.000 0.000 0.000 1.000
#> GSM2886 3 0.0000 1.000 0.000 0.000 1.000
#> GSM2887 3 0.0000 1.000 0.000 0.000 1.000
#> GSM2896 3 0.0000 1.000 0.000 0.000 1.000
#> GSM2888 2 0.6180 0.463 0.000 0.584 0.416
#> GSM2889 2 0.6215 0.435 0.000 0.572 0.428
#> GSM2876 1 0.0000 0.961 1.000 0.000 0.000
#> GSM2891 1 0.0000 0.961 1.000 0.000 0.000
#> GSM2880 1 0.0000 0.961 1.000 0.000 0.000
#> GSM2893 1 0.0000 0.961 1.000 0.000 0.000
#> GSM2821 1 0.0592 0.949 0.988 0.012 0.000
#> GSM2900 1 0.0000 0.961 1.000 0.000 0.000
#> GSM2903 1 0.0000 0.961 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM2819 2 0.0188 0.932 0.000 0.996 0.000 0.004
#> GSM2820 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM2822 2 0.3400 0.773 0.000 0.820 0.000 0.180
#> GSM2832 2 0.3528 0.759 0.000 0.808 0.000 0.192
#> GSM2823 1 0.5080 0.304 0.576 0.420 0.004 0.000
#> GSM2824 1 0.4804 0.402 0.616 0.384 0.000 0.000
#> GSM2825 2 0.7790 0.140 0.340 0.408 0.000 0.252
#> GSM2826 2 0.7322 0.433 0.224 0.532 0.000 0.244
#> GSM2829 4 0.0000 0.995 0.000 0.000 0.000 1.000
#> GSM2856 4 0.0000 0.995 0.000 0.000 0.000 1.000
#> GSM2830 4 0.0000 0.995 0.000 0.000 0.000 1.000
#> GSM2843 4 0.0000 0.995 0.000 0.000 0.000 1.000
#> GSM2871 4 0.0336 0.988 0.000 0.008 0.000 0.992
#> GSM2831 4 0.0000 0.995 0.000 0.000 0.000 1.000
#> GSM2844 4 0.0000 0.995 0.000 0.000 0.000 1.000
#> GSM2833 4 0.0000 0.995 0.000 0.000 0.000 1.000
#> GSM2846 4 0.0000 0.995 0.000 0.000 0.000 1.000
#> GSM2835 4 0.0000 0.995 0.000 0.000 0.000 1.000
#> GSM2858 4 0.0000 0.995 0.000 0.000 0.000 1.000
#> GSM2836 2 0.0188 0.932 0.000 0.996 0.000 0.004
#> GSM2848 2 0.0188 0.932 0.000 0.996 0.000 0.004
#> GSM2828 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM2837 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM2839 1 0.0000 0.951 1.000 0.000 0.000 0.000
#> GSM2841 1 0.0000 0.951 1.000 0.000 0.000 0.000
#> GSM2827 2 0.0817 0.920 0.000 0.976 0.000 0.024
#> GSM2842 2 0.0592 0.925 0.000 0.984 0.000 0.016
#> GSM2845 4 0.0000 0.995 0.000 0.000 0.000 1.000
#> GSM2872 4 0.0000 0.995 0.000 0.000 0.000 1.000
#> GSM2834 4 0.0336 0.988 0.000 0.008 0.000 0.992
#> GSM2847 4 0.0000 0.995 0.000 0.000 0.000 1.000
#> GSM2849 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM2850 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM2838 2 0.0188 0.932 0.000 0.996 0.000 0.004
#> GSM2853 2 0.0188 0.932 0.000 0.996 0.000 0.004
#> GSM2852 3 0.0336 0.993 0.000 0.008 0.992 0.000
#> GSM2855 3 0.0188 0.997 0.000 0.004 0.996 0.000
#> GSM2840 1 0.0188 0.949 0.996 0.000 0.000 0.004
#> GSM2857 1 0.0000 0.951 1.000 0.000 0.000 0.000
#> GSM2859 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM2860 2 0.0188 0.932 0.000 0.996 0.000 0.004
#> GSM2861 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM2862 2 0.0188 0.932 0.000 0.996 0.000 0.004
#> GSM2863 2 0.0188 0.932 0.000 0.996 0.000 0.004
#> GSM2864 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM2865 2 0.0188 0.932 0.000 0.996 0.000 0.004
#> GSM2866 2 0.0188 0.932 0.000 0.996 0.000 0.004
#> GSM2868 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM2869 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM2851 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM2867 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM2870 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM2854 4 0.1792 0.922 0.000 0.068 0.000 0.932
#> GSM2873 2 0.4406 0.601 0.000 0.700 0.000 0.300
#> GSM2874 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM2884 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM2875 1 0.0000 0.951 1.000 0.000 0.000 0.000
#> GSM2890 1 0.0000 0.951 1.000 0.000 0.000 0.000
#> GSM2877 1 0.0000 0.951 1.000 0.000 0.000 0.000
#> GSM2892 1 0.0000 0.951 1.000 0.000 0.000 0.000
#> GSM2902 1 0.0000 0.951 1.000 0.000 0.000 0.000
#> GSM2878 1 0.0000 0.951 1.000 0.000 0.000 0.000
#> GSM2901 1 0.0000 0.951 1.000 0.000 0.000 0.000
#> GSM2879 3 0.0188 0.997 0.000 0.004 0.996 0.000
#> GSM2898 3 0.0336 0.993 0.000 0.008 0.992 0.000
#> GSM2881 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM2897 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM2882 4 0.0000 0.995 0.000 0.000 0.000 1.000
#> GSM2894 4 0.0000 0.995 0.000 0.000 0.000 1.000
#> GSM2883 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM2895 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM2885 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM2886 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM2887 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM2896 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM2888 2 0.0336 0.927 0.000 0.992 0.008 0.000
#> GSM2889 2 0.0336 0.927 0.000 0.992 0.008 0.000
#> GSM2876 1 0.0000 0.951 1.000 0.000 0.000 0.000
#> GSM2891 1 0.0000 0.951 1.000 0.000 0.000 0.000
#> GSM2880 1 0.0000 0.951 1.000 0.000 0.000 0.000
#> GSM2893 1 0.0000 0.951 1.000 0.000 0.000 0.000
#> GSM2821 1 0.1389 0.913 0.952 0.048 0.000 0.000
#> GSM2900 1 0.0188 0.949 0.996 0.004 0.000 0.000
#> GSM2903 1 0.0000 0.951 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
#> GSM2819 5 0.5071 -0.3167 0.012 0.440 0.000 0.016 0.532
#> GSM2820 3 0.0000 0.9978 0.000 0.000 1.000 0.000 0.000
#> GSM2822 2 0.6725 0.6402 0.104 0.608 0.000 0.100 0.188
#> GSM2832 2 0.6319 0.6670 0.076 0.648 0.000 0.108 0.168
#> GSM2823 5 0.5673 0.4117 0.156 0.216 0.000 0.000 0.628
#> GSM2824 5 0.5218 0.4356 0.136 0.180 0.000 0.000 0.684
#> GSM2825 1 0.6803 0.0893 0.604 0.176 0.000 0.120 0.100
#> GSM2826 1 0.7166 0.0386 0.536 0.256 0.000 0.112 0.096
#> GSM2829 4 0.0963 0.9568 0.000 0.000 0.000 0.964 0.036
#> GSM2856 4 0.1043 0.9558 0.000 0.000 0.000 0.960 0.040
#> GSM2830 4 0.0451 0.9589 0.000 0.000 0.004 0.988 0.008
#> GSM2843 4 0.0579 0.9587 0.000 0.008 0.000 0.984 0.008
#> GSM2871 4 0.1211 0.9516 0.000 0.024 0.000 0.960 0.016
#> GSM2831 4 0.0451 0.9602 0.004 0.000 0.000 0.988 0.008
#> GSM2844 4 0.0566 0.9601 0.004 0.000 0.000 0.984 0.012
#> GSM2833 4 0.2349 0.9402 0.012 0.004 0.000 0.900 0.084
#> GSM2846 4 0.2331 0.9381 0.020 0.000 0.000 0.900 0.080
#> GSM2835 4 0.2632 0.9261 0.040 0.000 0.000 0.888 0.072
#> GSM2858 4 0.2989 0.9116 0.060 0.000 0.000 0.868 0.072
#> GSM2836 2 0.0693 0.8630 0.000 0.980 0.000 0.012 0.008
#> GSM2848 2 0.0771 0.8699 0.000 0.976 0.000 0.004 0.020
#> GSM2828 3 0.0000 0.9978 0.000 0.000 1.000 0.000 0.000
#> GSM2837 3 0.0000 0.9978 0.000 0.000 1.000 0.000 0.000
#> GSM2839 1 0.1638 0.3579 0.932 0.000 0.000 0.004 0.064
#> GSM2841 1 0.1831 0.3591 0.920 0.000 0.000 0.004 0.076
#> GSM2827 2 0.2136 0.8709 0.000 0.904 0.000 0.008 0.088
#> GSM2842 2 0.2127 0.8676 0.000 0.892 0.000 0.000 0.108
#> GSM2845 4 0.0566 0.9594 0.004 0.000 0.000 0.984 0.012
#> GSM2872 4 0.0510 0.9589 0.000 0.000 0.000 0.984 0.016
#> GSM2834 4 0.2284 0.9241 0.004 0.056 0.000 0.912 0.028
#> GSM2847 4 0.1074 0.9574 0.004 0.012 0.000 0.968 0.016
#> GSM2849 3 0.0000 0.9978 0.000 0.000 1.000 0.000 0.000
#> GSM2850 3 0.0000 0.9978 0.000 0.000 1.000 0.000 0.000
#> GSM2838 2 0.2605 0.8539 0.000 0.852 0.000 0.000 0.148
#> GSM2853 2 0.2891 0.8441 0.000 0.824 0.000 0.000 0.176
#> GSM2852 3 0.0162 0.9952 0.004 0.000 0.996 0.000 0.000
#> GSM2855 3 0.0162 0.9952 0.004 0.000 0.996 0.000 0.000
#> GSM2840 1 0.1597 0.3379 0.940 0.000 0.000 0.012 0.048
#> GSM2857 1 0.1484 0.3451 0.944 0.000 0.000 0.008 0.048
#> GSM2859 2 0.0000 0.8697 0.000 1.000 0.000 0.000 0.000
#> GSM2860 2 0.0000 0.8697 0.000 1.000 0.000 0.000 0.000
#> GSM2861 2 0.1121 0.8723 0.000 0.956 0.000 0.000 0.044
#> GSM2862 2 0.0000 0.8697 0.000 1.000 0.000 0.000 0.000
#> GSM2863 2 0.0000 0.8697 0.000 1.000 0.000 0.000 0.000
#> GSM2864 2 0.0162 0.8689 0.000 0.996 0.000 0.000 0.004
#> GSM2865 2 0.0000 0.8697 0.000 1.000 0.000 0.000 0.000
#> GSM2866 2 0.0451 0.8658 0.000 0.988 0.000 0.004 0.008
#> GSM2868 2 0.4475 0.7419 0.032 0.692 0.000 0.000 0.276
#> GSM2869 2 0.3988 0.7814 0.016 0.732 0.000 0.000 0.252
#> GSM2851 2 0.3231 0.8327 0.004 0.800 0.000 0.000 0.196
#> GSM2867 2 0.4404 0.7552 0.032 0.704 0.000 0.000 0.264
#> GSM2870 2 0.3551 0.8140 0.008 0.772 0.000 0.000 0.220
#> GSM2854 4 0.1978 0.9447 0.004 0.024 0.000 0.928 0.044
#> GSM2873 2 0.3273 0.7694 0.004 0.848 0.000 0.112 0.036
#> GSM2874 3 0.0000 0.9978 0.000 0.000 1.000 0.000 0.000
#> GSM2884 3 0.0000 0.9978 0.000 0.000 1.000 0.000 0.000
#> GSM2875 1 0.4268 0.4196 0.556 0.000 0.000 0.000 0.444
#> GSM2890 1 0.4268 0.4196 0.556 0.000 0.000 0.000 0.444
#> GSM2877 1 0.4262 0.4219 0.560 0.000 0.000 0.000 0.440
#> GSM2892 1 0.4268 0.4196 0.556 0.000 0.000 0.000 0.444
#> GSM2902 1 0.4268 0.4196 0.556 0.000 0.000 0.000 0.444
#> GSM2878 1 0.4278 0.4067 0.548 0.000 0.000 0.000 0.452
#> GSM2901 1 0.4283 0.3972 0.544 0.000 0.000 0.000 0.456
#> GSM2879 3 0.0566 0.9849 0.004 0.012 0.984 0.000 0.000
#> GSM2898 3 0.0566 0.9842 0.004 0.012 0.984 0.000 0.000
#> GSM2881 3 0.0000 0.9978 0.000 0.000 1.000 0.000 0.000
#> GSM2897 3 0.0000 0.9978 0.000 0.000 1.000 0.000 0.000
#> GSM2882 4 0.0955 0.9570 0.004 0.000 0.000 0.968 0.028
#> GSM2894 4 0.1251 0.9557 0.008 0.000 0.000 0.956 0.036
#> GSM2883 3 0.0000 0.9978 0.000 0.000 1.000 0.000 0.000
#> GSM2895 3 0.0000 0.9978 0.000 0.000 1.000 0.000 0.000
#> GSM2885 3 0.0000 0.9978 0.000 0.000 1.000 0.000 0.000
#> GSM2886 3 0.0000 0.9978 0.000 0.000 1.000 0.000 0.000
#> GSM2887 3 0.0000 0.9978 0.000 0.000 1.000 0.000 0.000
#> GSM2896 3 0.0000 0.9978 0.000 0.000 1.000 0.000 0.000
#> GSM2888 2 0.3243 0.8487 0.004 0.812 0.000 0.004 0.180
#> GSM2889 2 0.3243 0.8487 0.004 0.812 0.000 0.004 0.180
#> GSM2876 5 0.4273 -0.2485 0.448 0.000 0.000 0.000 0.552
#> GSM2891 5 0.4256 -0.2189 0.436 0.000 0.000 0.000 0.564
#> GSM2880 1 0.4262 0.4219 0.560 0.000 0.000 0.000 0.440
#> GSM2893 1 0.4262 0.4219 0.560 0.000 0.000 0.000 0.440
#> GSM2821 5 0.2969 0.4420 0.128 0.020 0.000 0.000 0.852
#> GSM2900 5 0.3427 0.4114 0.192 0.012 0.000 0.000 0.796
#> GSM2903 5 0.3439 0.4083 0.188 0.008 0.000 0.004 0.800
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM2819 5 0.2077 0.5081 0.032 0.032 0.000 0.012 0.920 0.004
#> GSM2820 3 0.0000 0.9941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2822 6 0.5543 -0.0406 0.000 0.364 0.000 0.008 0.112 0.516
#> GSM2832 6 0.5558 -0.1249 0.000 0.396 0.000 0.008 0.108 0.488
#> GSM2823 1 0.4985 -0.3263 0.472 0.056 0.000 0.000 0.468 0.004
#> GSM2824 5 0.4775 0.1844 0.456 0.040 0.000 0.000 0.500 0.004
#> GSM2825 6 0.2519 0.5444 0.068 0.044 0.000 0.000 0.004 0.884
#> GSM2826 6 0.2766 0.5363 0.060 0.060 0.000 0.000 0.008 0.872
#> GSM2829 4 0.1745 0.8940 0.000 0.000 0.000 0.920 0.012 0.068
#> GSM2856 4 0.2218 0.8775 0.000 0.000 0.000 0.884 0.012 0.104
#> GSM2830 4 0.0291 0.9121 0.000 0.000 0.000 0.992 0.004 0.004
#> GSM2843 4 0.0291 0.9121 0.000 0.000 0.000 0.992 0.004 0.004
#> GSM2871 4 0.0881 0.9080 0.000 0.012 0.000 0.972 0.008 0.008
#> GSM2831 4 0.0146 0.9127 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM2844 4 0.0146 0.9127 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM2833 4 0.3268 0.8502 0.000 0.000 0.000 0.824 0.100 0.076
#> GSM2846 4 0.3277 0.8520 0.000 0.000 0.000 0.824 0.084 0.092
#> GSM2835 4 0.4165 0.6795 0.000 0.000 0.000 0.672 0.036 0.292
#> GSM2858 4 0.4551 0.5925 0.000 0.000 0.000 0.608 0.048 0.344
#> GSM2836 2 0.0508 0.7732 0.000 0.984 0.000 0.000 0.004 0.012
#> GSM2848 2 0.0508 0.7752 0.000 0.984 0.000 0.000 0.012 0.004
#> GSM2828 3 0.0000 0.9941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2837 3 0.0000 0.9941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2839 6 0.4893 0.4886 0.340 0.000 0.000 0.000 0.076 0.584
#> GSM2841 6 0.4950 0.4815 0.344 0.000 0.000 0.000 0.080 0.576
#> GSM2827 2 0.3272 0.7439 0.000 0.824 0.000 0.004 0.124 0.048
#> GSM2842 2 0.4074 0.7166 0.000 0.748 0.000 0.000 0.160 0.092
#> GSM2845 4 0.0551 0.9110 0.000 0.004 0.000 0.984 0.004 0.008
#> GSM2872 4 0.0551 0.9118 0.000 0.004 0.000 0.984 0.008 0.004
#> GSM2834 4 0.1793 0.8865 0.000 0.048 0.000 0.928 0.012 0.012
#> GSM2847 4 0.0984 0.9086 0.000 0.012 0.000 0.968 0.008 0.012
#> GSM2849 3 0.0000 0.9941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2850 3 0.0000 0.9941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2838 2 0.4548 0.6687 0.000 0.672 0.000 0.000 0.248 0.080
#> GSM2853 2 0.4969 0.6288 0.000 0.616 0.000 0.000 0.280 0.104
#> GSM2852 3 0.0000 0.9941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2855 3 0.0000 0.9941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2840 6 0.4507 0.5515 0.268 0.000 0.000 0.000 0.068 0.664
#> GSM2857 6 0.4682 0.5403 0.284 0.000 0.000 0.000 0.076 0.640
#> GSM2859 2 0.0622 0.7740 0.000 0.980 0.000 0.000 0.008 0.012
#> GSM2860 2 0.0508 0.7732 0.000 0.984 0.000 0.000 0.004 0.012
#> GSM2861 2 0.1196 0.7743 0.000 0.952 0.000 0.000 0.040 0.008
#> GSM2862 2 0.0508 0.7732 0.000 0.984 0.000 0.000 0.004 0.012
#> GSM2863 2 0.0508 0.7732 0.000 0.984 0.000 0.000 0.004 0.012
#> GSM2864 2 0.0508 0.7732 0.000 0.984 0.000 0.000 0.004 0.012
#> GSM2865 2 0.0508 0.7732 0.000 0.984 0.000 0.000 0.004 0.012
#> GSM2866 2 0.0717 0.7730 0.000 0.976 0.000 0.000 0.008 0.016
#> GSM2868 5 0.4991 -0.4428 0.000 0.456 0.000 0.000 0.476 0.068
#> GSM2869 2 0.5181 0.4067 0.000 0.484 0.000 0.000 0.428 0.088
#> GSM2851 2 0.5197 0.5621 0.000 0.560 0.000 0.000 0.332 0.108
#> GSM2867 2 0.5105 0.3987 0.000 0.488 0.000 0.000 0.432 0.080
#> GSM2870 2 0.5152 0.5144 0.000 0.532 0.000 0.000 0.376 0.092
#> GSM2854 4 0.2958 0.8637 0.000 0.012 0.000 0.852 0.028 0.108
#> GSM2873 2 0.1785 0.7524 0.000 0.928 0.000 0.016 0.008 0.048
#> GSM2874 3 0.0000 0.9941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2884 3 0.0000 0.9941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2875 1 0.0000 0.8625 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2890 1 0.0000 0.8625 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2877 1 0.0000 0.8625 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2892 1 0.0000 0.8625 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2902 1 0.0000 0.8625 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2878 1 0.0405 0.8590 0.988 0.000 0.000 0.000 0.008 0.004
#> GSM2901 1 0.0508 0.8570 0.984 0.000 0.000 0.000 0.012 0.004
#> GSM2879 3 0.1219 0.9409 0.000 0.048 0.948 0.000 0.004 0.000
#> GSM2898 3 0.1010 0.9542 0.000 0.036 0.960 0.000 0.004 0.000
#> GSM2881 3 0.0000 0.9941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2897 3 0.0000 0.9941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2882 4 0.0458 0.9122 0.000 0.000 0.000 0.984 0.016 0.000
#> GSM2894 4 0.1074 0.9085 0.000 0.000 0.000 0.960 0.028 0.012
#> GSM2883 3 0.0000 0.9941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2895 3 0.0000 0.9941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2885 3 0.0000 0.9941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2886 3 0.0000 0.9941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2887 3 0.0000 0.9941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2896 3 0.0000 0.9941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2888 2 0.5557 0.5434 0.000 0.552 0.000 0.000 0.200 0.248
#> GSM2889 2 0.5619 0.5484 0.000 0.560 0.004 0.000 0.188 0.248
#> GSM2876 1 0.3360 0.5562 0.732 0.000 0.000 0.000 0.264 0.004
#> GSM2891 1 0.3534 0.5302 0.716 0.000 0.000 0.000 0.276 0.008
#> GSM2880 1 0.0458 0.8525 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM2893 1 0.0547 0.8493 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM2821 5 0.3056 0.5833 0.184 0.000 0.000 0.004 0.804 0.008
#> GSM2900 5 0.3586 0.5439 0.280 0.000 0.000 0.004 0.712 0.004
#> GSM2903 5 0.3606 0.5410 0.284 0.000 0.000 0.004 0.708 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> CV:NMF 81 6.04e-05 2
#> CV:NMF 79 2.19e-08 3
#> CV:NMF 80 1.46e-11 4
#> CV:NMF 61 8.46e-07 5
#> CV:NMF 75 5.30e-17 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 8229 rows and 84 columns.
#> Top rows (823, 1646, 2468, 3291, 4114) 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 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.280 0.598 0.791 0.3981 0.703 0.703
#> 3 3 0.657 0.816 0.821 0.3915 0.727 0.612
#> 4 4 0.914 0.954 0.973 0.3046 0.849 0.650
#> 5 5 0.889 0.902 0.945 0.0539 0.964 0.873
#> 6 6 0.935 0.884 0.903 0.0427 0.955 0.819
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] 4
There is also optional best \(k\) = 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
#> GSM2819 2 0.8267 0.695 0.260 0.740
#> GSM2820 2 0.9850 0.540 0.428 0.572
#> GSM2822 2 0.8267 0.695 0.260 0.740
#> GSM2832 2 0.8267 0.695 0.260 0.740
#> GSM2823 2 0.8267 0.695 0.260 0.740
#> GSM2824 2 0.8267 0.695 0.260 0.740
#> GSM2825 2 0.9170 0.641 0.332 0.668
#> GSM2826 2 0.9170 0.641 0.332 0.668
#> GSM2829 2 0.8909 0.148 0.308 0.692
#> GSM2856 2 0.8909 0.148 0.308 0.692
#> GSM2830 2 0.8909 0.148 0.308 0.692
#> GSM2843 2 0.8909 0.148 0.308 0.692
#> GSM2871 2 0.8909 0.148 0.308 0.692
#> GSM2831 2 0.8909 0.148 0.308 0.692
#> GSM2844 2 0.8909 0.148 0.308 0.692
#> GSM2833 2 0.8909 0.148 0.308 0.692
#> GSM2846 2 0.8909 0.148 0.308 0.692
#> GSM2835 2 0.8909 0.148 0.308 0.692
#> GSM2858 2 0.8909 0.148 0.308 0.692
#> GSM2836 2 0.8267 0.695 0.260 0.740
#> GSM2848 2 0.8267 0.695 0.260 0.740
#> GSM2828 2 0.9850 0.540 0.428 0.572
#> GSM2837 2 0.9850 0.540 0.428 0.572
#> GSM2839 1 0.0938 1.000 0.988 0.012
#> GSM2841 1 0.0938 1.000 0.988 0.012
#> GSM2827 2 0.8267 0.695 0.260 0.740
#> GSM2842 2 0.8267 0.695 0.260 0.740
#> GSM2845 2 0.8909 0.148 0.308 0.692
#> GSM2872 2 0.8909 0.148 0.308 0.692
#> GSM2834 2 0.8909 0.148 0.308 0.692
#> GSM2847 2 0.8909 0.148 0.308 0.692
#> GSM2849 2 0.9850 0.540 0.428 0.572
#> GSM2850 2 0.9850 0.540 0.428 0.572
#> GSM2838 2 0.8267 0.695 0.260 0.740
#> GSM2853 2 0.8267 0.695 0.260 0.740
#> GSM2852 2 0.8327 0.692 0.264 0.736
#> GSM2855 2 0.8327 0.692 0.264 0.736
#> GSM2840 1 0.0938 1.000 0.988 0.012
#> GSM2857 1 0.0938 1.000 0.988 0.012
#> GSM2859 2 0.8267 0.695 0.260 0.740
#> GSM2860 2 0.8267 0.695 0.260 0.740
#> GSM2861 2 0.8267 0.695 0.260 0.740
#> GSM2862 2 0.8267 0.695 0.260 0.740
#> GSM2863 2 0.8267 0.695 0.260 0.740
#> GSM2864 2 0.8267 0.695 0.260 0.740
#> GSM2865 2 0.8267 0.695 0.260 0.740
#> GSM2866 2 0.8267 0.695 0.260 0.740
#> GSM2868 2 0.8267 0.695 0.260 0.740
#> GSM2869 2 0.8267 0.695 0.260 0.740
#> GSM2851 2 0.8267 0.695 0.260 0.740
#> GSM2867 2 0.8267 0.695 0.260 0.740
#> GSM2870 2 0.8267 0.695 0.260 0.740
#> GSM2854 2 0.8386 0.203 0.268 0.732
#> GSM2873 2 0.8386 0.203 0.268 0.732
#> GSM2874 2 0.9850 0.540 0.428 0.572
#> GSM2884 2 0.9850 0.540 0.428 0.572
#> GSM2875 1 0.0938 1.000 0.988 0.012
#> GSM2890 1 0.0938 1.000 0.988 0.012
#> GSM2877 1 0.0938 1.000 0.988 0.012
#> GSM2892 1 0.0938 1.000 0.988 0.012
#> GSM2902 1 0.0938 1.000 0.988 0.012
#> GSM2878 1 0.0938 1.000 0.988 0.012
#> GSM2901 1 0.0938 1.000 0.988 0.012
#> GSM2879 2 0.8267 0.695 0.260 0.740
#> GSM2898 2 0.8267 0.695 0.260 0.740
#> GSM2881 2 0.9850 0.540 0.428 0.572
#> GSM2897 2 0.9850 0.540 0.428 0.572
#> GSM2882 2 0.8909 0.148 0.308 0.692
#> GSM2894 2 0.8909 0.148 0.308 0.692
#> GSM2883 2 0.9850 0.540 0.428 0.572
#> GSM2895 2 0.9850 0.540 0.428 0.572
#> GSM2885 2 0.9850 0.540 0.428 0.572
#> GSM2886 2 0.9850 0.540 0.428 0.572
#> GSM2887 2 0.9850 0.540 0.428 0.572
#> GSM2896 2 0.9850 0.540 0.428 0.572
#> GSM2888 2 0.8267 0.695 0.260 0.740
#> GSM2889 2 0.8267 0.695 0.260 0.740
#> GSM2876 1 0.0938 1.000 0.988 0.012
#> GSM2891 1 0.0938 1.000 0.988 0.012
#> GSM2880 1 0.0938 1.000 0.988 0.012
#> GSM2893 1 0.0938 1.000 0.988 0.012
#> GSM2821 2 0.8267 0.695 0.260 0.740
#> GSM2900 2 0.8267 0.695 0.260 0.740
#> GSM2903 2 0.8267 0.695 0.260 0.740
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM2819 3 0.622 0.757 0.432 0.000 0.568
#> GSM2820 3 0.000 0.568 0.000 0.000 1.000
#> GSM2822 3 0.622 0.757 0.432 0.000 0.568
#> GSM2832 3 0.622 0.757 0.432 0.000 0.568
#> GSM2823 3 0.619 0.754 0.420 0.000 0.580
#> GSM2824 3 0.619 0.754 0.420 0.000 0.580
#> GSM2825 3 0.788 0.689 0.392 0.060 0.548
#> GSM2826 3 0.788 0.689 0.392 0.060 0.548
#> GSM2829 2 0.622 0.990 0.432 0.568 0.000
#> GSM2856 2 0.622 0.990 0.432 0.568 0.000
#> GSM2830 2 0.622 0.990 0.432 0.568 0.000
#> GSM2843 2 0.622 0.990 0.432 0.568 0.000
#> GSM2871 2 0.622 0.990 0.432 0.568 0.000
#> GSM2831 2 0.622 0.990 0.432 0.568 0.000
#> GSM2844 2 0.622 0.990 0.432 0.568 0.000
#> GSM2833 2 0.622 0.990 0.432 0.568 0.000
#> GSM2846 2 0.622 0.990 0.432 0.568 0.000
#> GSM2835 2 0.622 0.990 0.432 0.568 0.000
#> GSM2858 2 0.622 0.990 0.432 0.568 0.000
#> GSM2836 3 0.622 0.757 0.432 0.000 0.568
#> GSM2848 3 0.622 0.757 0.432 0.000 0.568
#> GSM2828 3 0.000 0.568 0.000 0.000 1.000
#> GSM2837 3 0.000 0.568 0.000 0.000 1.000
#> GSM2839 1 0.622 1.000 0.568 0.432 0.000
#> GSM2841 1 0.622 1.000 0.568 0.432 0.000
#> GSM2827 3 0.622 0.757 0.432 0.000 0.568
#> GSM2842 3 0.622 0.757 0.432 0.000 0.568
#> GSM2845 2 0.622 0.990 0.432 0.568 0.000
#> GSM2872 2 0.622 0.990 0.432 0.568 0.000
#> GSM2834 2 0.622 0.990 0.432 0.568 0.000
#> GSM2847 2 0.622 0.990 0.432 0.568 0.000
#> GSM2849 3 0.000 0.568 0.000 0.000 1.000
#> GSM2850 3 0.000 0.568 0.000 0.000 1.000
#> GSM2838 3 0.622 0.757 0.432 0.000 0.568
#> GSM2853 3 0.622 0.757 0.432 0.000 0.568
#> GSM2852 3 0.617 0.750 0.412 0.000 0.588
#> GSM2855 3 0.617 0.750 0.412 0.000 0.588
#> GSM2840 1 0.622 1.000 0.568 0.432 0.000
#> GSM2857 1 0.622 1.000 0.568 0.432 0.000
#> GSM2859 3 0.622 0.757 0.432 0.000 0.568
#> GSM2860 3 0.622 0.757 0.432 0.000 0.568
#> GSM2861 3 0.622 0.757 0.432 0.000 0.568
#> GSM2862 3 0.622 0.757 0.432 0.000 0.568
#> GSM2863 3 0.622 0.757 0.432 0.000 0.568
#> GSM2864 3 0.622 0.757 0.432 0.000 0.568
#> GSM2865 3 0.622 0.757 0.432 0.000 0.568
#> GSM2866 3 0.622 0.757 0.432 0.000 0.568
#> GSM2868 3 0.622 0.757 0.432 0.000 0.568
#> GSM2869 3 0.622 0.757 0.432 0.000 0.568
#> GSM2851 3 0.622 0.757 0.432 0.000 0.568
#> GSM2867 3 0.622 0.757 0.432 0.000 0.568
#> GSM2870 3 0.622 0.757 0.432 0.000 0.568
#> GSM2854 2 0.789 0.906 0.432 0.512 0.056
#> GSM2873 2 0.789 0.906 0.432 0.512 0.056
#> GSM2874 3 0.000 0.568 0.000 0.000 1.000
#> GSM2884 3 0.000 0.568 0.000 0.000 1.000
#> GSM2875 1 0.622 1.000 0.568 0.432 0.000
#> GSM2890 1 0.622 1.000 0.568 0.432 0.000
#> GSM2877 1 0.622 1.000 0.568 0.432 0.000
#> GSM2892 1 0.622 1.000 0.568 0.432 0.000
#> GSM2902 1 0.622 1.000 0.568 0.432 0.000
#> GSM2878 1 0.622 1.000 0.568 0.432 0.000
#> GSM2901 1 0.622 1.000 0.568 0.432 0.000
#> GSM2879 3 0.620 0.755 0.424 0.000 0.576
#> GSM2898 3 0.620 0.755 0.424 0.000 0.576
#> GSM2881 3 0.000 0.568 0.000 0.000 1.000
#> GSM2897 3 0.000 0.568 0.000 0.000 1.000
#> GSM2882 2 0.622 0.990 0.432 0.568 0.000
#> GSM2894 2 0.622 0.990 0.432 0.568 0.000
#> GSM2883 3 0.000 0.568 0.000 0.000 1.000
#> GSM2895 3 0.000 0.568 0.000 0.000 1.000
#> GSM2885 3 0.000 0.568 0.000 0.000 1.000
#> GSM2886 3 0.000 0.568 0.000 0.000 1.000
#> GSM2887 3 0.000 0.568 0.000 0.000 1.000
#> GSM2896 3 0.000 0.568 0.000 0.000 1.000
#> GSM2888 3 0.622 0.757 0.432 0.000 0.568
#> GSM2889 3 0.622 0.757 0.432 0.000 0.568
#> GSM2876 1 0.622 1.000 0.568 0.432 0.000
#> GSM2891 1 0.622 1.000 0.568 0.432 0.000
#> GSM2880 1 0.622 1.000 0.568 0.432 0.000
#> GSM2893 1 0.622 1.000 0.568 0.432 0.000
#> GSM2821 3 0.622 0.757 0.432 0.000 0.568
#> GSM2900 3 0.622 0.757 0.432 0.000 0.568
#> GSM2903 3 0.622 0.757 0.432 0.000 0.568
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM2819 2 0.2973 0.861 0.00 0.856 0.000 0.144
#> GSM2820 3 0.0000 1.000 0.00 0.000 1.000 0.000
#> GSM2822 2 0.3486 0.803 0.00 0.812 0.000 0.188
#> GSM2832 2 0.3486 0.803 0.00 0.812 0.000 0.188
#> GSM2823 2 0.1059 0.942 0.00 0.972 0.012 0.016
#> GSM2824 2 0.1059 0.942 0.00 0.972 0.012 0.016
#> GSM2825 2 0.5593 0.701 0.08 0.708 0.000 0.212
#> GSM2826 2 0.5593 0.701 0.08 0.708 0.000 0.212
#> GSM2829 4 0.0336 0.973 0.00 0.008 0.000 0.992
#> GSM2856 4 0.0336 0.973 0.00 0.008 0.000 0.992
#> GSM2830 4 0.0592 0.972 0.00 0.016 0.000 0.984
#> GSM2843 4 0.0592 0.972 0.00 0.016 0.000 0.984
#> GSM2871 4 0.0592 0.972 0.00 0.016 0.000 0.984
#> GSM2831 4 0.0336 0.973 0.00 0.008 0.000 0.992
#> GSM2844 4 0.0336 0.973 0.00 0.008 0.000 0.992
#> GSM2833 4 0.0336 0.973 0.00 0.008 0.000 0.992
#> GSM2846 4 0.0336 0.973 0.00 0.008 0.000 0.992
#> GSM2835 4 0.0336 0.973 0.00 0.008 0.000 0.992
#> GSM2858 4 0.0336 0.973 0.00 0.008 0.000 0.992
#> GSM2836 2 0.0336 0.949 0.00 0.992 0.000 0.008
#> GSM2848 2 0.0336 0.949 0.00 0.992 0.000 0.008
#> GSM2828 3 0.0000 1.000 0.00 0.000 1.000 0.000
#> GSM2837 3 0.0000 1.000 0.00 0.000 1.000 0.000
#> GSM2839 1 0.0000 1.000 1.00 0.000 0.000 0.000
#> GSM2841 1 0.0000 1.000 1.00 0.000 0.000 0.000
#> GSM2827 2 0.0336 0.949 0.00 0.992 0.000 0.008
#> GSM2842 2 0.0336 0.949 0.00 0.992 0.000 0.008
#> GSM2845 4 0.0592 0.972 0.00 0.016 0.000 0.984
#> GSM2872 4 0.0592 0.972 0.00 0.016 0.000 0.984
#> GSM2834 4 0.0592 0.972 0.00 0.016 0.000 0.984
#> GSM2847 4 0.0592 0.972 0.00 0.016 0.000 0.984
#> GSM2849 3 0.0000 1.000 0.00 0.000 1.000 0.000
#> GSM2850 3 0.0000 1.000 0.00 0.000 1.000 0.000
#> GSM2838 2 0.0000 0.951 0.00 1.000 0.000 0.000
#> GSM2853 2 0.0000 0.951 0.00 1.000 0.000 0.000
#> GSM2852 2 0.1302 0.925 0.00 0.956 0.044 0.000
#> GSM2855 2 0.1302 0.925 0.00 0.956 0.044 0.000
#> GSM2840 1 0.0000 1.000 1.00 0.000 0.000 0.000
#> GSM2857 1 0.0000 1.000 1.00 0.000 0.000 0.000
#> GSM2859 2 0.0000 0.951 0.00 1.000 0.000 0.000
#> GSM2860 2 0.0000 0.951 0.00 1.000 0.000 0.000
#> GSM2861 2 0.0000 0.951 0.00 1.000 0.000 0.000
#> GSM2862 2 0.0000 0.951 0.00 1.000 0.000 0.000
#> GSM2863 2 0.0000 0.951 0.00 1.000 0.000 0.000
#> GSM2864 2 0.0000 0.951 0.00 1.000 0.000 0.000
#> GSM2865 2 0.0000 0.951 0.00 1.000 0.000 0.000
#> GSM2866 2 0.0000 0.951 0.00 1.000 0.000 0.000
#> GSM2868 2 0.0000 0.951 0.00 1.000 0.000 0.000
#> GSM2869 2 0.0000 0.951 0.00 1.000 0.000 0.000
#> GSM2851 2 0.0000 0.951 0.00 1.000 0.000 0.000
#> GSM2867 2 0.0000 0.951 0.00 1.000 0.000 0.000
#> GSM2870 2 0.0000 0.951 0.00 1.000 0.000 0.000
#> GSM2854 4 0.3400 0.795 0.00 0.180 0.000 0.820
#> GSM2873 4 0.3400 0.795 0.00 0.180 0.000 0.820
#> GSM2874 3 0.0000 1.000 0.00 0.000 1.000 0.000
#> GSM2884 3 0.0000 1.000 0.00 0.000 1.000 0.000
#> GSM2875 1 0.0000 1.000 1.00 0.000 0.000 0.000
#> GSM2890 1 0.0000 1.000 1.00 0.000 0.000 0.000
#> GSM2877 1 0.0000 1.000 1.00 0.000 0.000 0.000
#> GSM2892 1 0.0000 1.000 1.00 0.000 0.000 0.000
#> GSM2902 1 0.0000 1.000 1.00 0.000 0.000 0.000
#> GSM2878 1 0.0000 1.000 1.00 0.000 0.000 0.000
#> GSM2901 1 0.0000 1.000 1.00 0.000 0.000 0.000
#> GSM2879 2 0.0336 0.948 0.00 0.992 0.008 0.000
#> GSM2898 2 0.0336 0.948 0.00 0.992 0.008 0.000
#> GSM2881 3 0.0000 1.000 0.00 0.000 1.000 0.000
#> GSM2897 3 0.0000 1.000 0.00 0.000 1.000 0.000
#> GSM2882 4 0.0336 0.973 0.00 0.008 0.000 0.992
#> GSM2894 4 0.0336 0.973 0.00 0.008 0.000 0.992
#> GSM2883 3 0.0000 1.000 0.00 0.000 1.000 0.000
#> GSM2895 3 0.0000 1.000 0.00 0.000 1.000 0.000
#> GSM2885 3 0.0000 1.000 0.00 0.000 1.000 0.000
#> GSM2886 3 0.0000 1.000 0.00 0.000 1.000 0.000
#> GSM2887 3 0.0000 1.000 0.00 0.000 1.000 0.000
#> GSM2896 3 0.0000 1.000 0.00 0.000 1.000 0.000
#> GSM2888 2 0.0000 0.951 0.00 1.000 0.000 0.000
#> GSM2889 2 0.0000 0.951 0.00 1.000 0.000 0.000
#> GSM2876 1 0.0000 1.000 1.00 0.000 0.000 0.000
#> GSM2891 1 0.0000 1.000 1.00 0.000 0.000 0.000
#> GSM2880 1 0.0000 1.000 1.00 0.000 0.000 0.000
#> GSM2893 1 0.0000 1.000 1.00 0.000 0.000 0.000
#> GSM2821 2 0.2973 0.861 0.00 0.856 0.000 0.144
#> GSM2900 2 0.2973 0.861 0.00 0.856 0.000 0.144
#> GSM2903 2 0.2973 0.861 0.00 0.856 0.000 0.144
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM2819 5 0.285 1.000 0.00 0.172 0.000 0.000 0.828
#> GSM2820 3 0.000 1.000 0.00 0.000 1.000 0.000 0.000
#> GSM2822 2 0.356 0.655 0.00 0.788 0.000 0.196 0.016
#> GSM2832 2 0.356 0.655 0.00 0.788 0.000 0.196 0.016
#> GSM2823 2 0.462 0.149 0.00 0.612 0.012 0.004 0.372
#> GSM2824 2 0.462 0.149 0.00 0.612 0.012 0.004 0.372
#> GSM2825 2 0.535 0.507 0.08 0.684 0.000 0.220 0.016
#> GSM2826 2 0.535 0.507 0.08 0.684 0.000 0.220 0.016
#> GSM2829 4 0.000 0.898 0.00 0.000 0.000 1.000 0.000
#> GSM2856 4 0.000 0.898 0.00 0.000 0.000 1.000 0.000
#> GSM2830 4 0.313 0.876 0.00 0.008 0.000 0.820 0.172
#> GSM2843 4 0.313 0.876 0.00 0.008 0.000 0.820 0.172
#> GSM2871 4 0.313 0.876 0.00 0.008 0.000 0.820 0.172
#> GSM2831 4 0.000 0.898 0.00 0.000 0.000 1.000 0.000
#> GSM2844 4 0.000 0.898 0.00 0.000 0.000 1.000 0.000
#> GSM2833 4 0.000 0.898 0.00 0.000 0.000 1.000 0.000
#> GSM2846 4 0.000 0.898 0.00 0.000 0.000 1.000 0.000
#> GSM2835 4 0.000 0.898 0.00 0.000 0.000 1.000 0.000
#> GSM2858 4 0.000 0.898 0.00 0.000 0.000 1.000 0.000
#> GSM2836 2 0.029 0.908 0.00 0.992 0.000 0.008 0.000
#> GSM2848 2 0.029 0.908 0.00 0.992 0.000 0.008 0.000
#> GSM2828 3 0.000 1.000 0.00 0.000 1.000 0.000 0.000
#> GSM2837 3 0.000 1.000 0.00 0.000 1.000 0.000 0.000
#> GSM2839 1 0.000 1.000 1.00 0.000 0.000 0.000 0.000
#> GSM2841 1 0.000 1.000 1.00 0.000 0.000 0.000 0.000
#> GSM2827 2 0.029 0.908 0.00 0.992 0.000 0.008 0.000
#> GSM2842 2 0.029 0.908 0.00 0.992 0.000 0.008 0.000
#> GSM2845 4 0.313 0.876 0.00 0.008 0.000 0.820 0.172
#> GSM2872 4 0.313 0.876 0.00 0.008 0.000 0.820 0.172
#> GSM2834 4 0.313 0.876 0.00 0.008 0.000 0.820 0.172
#> GSM2847 4 0.313 0.876 0.00 0.008 0.000 0.820 0.172
#> GSM2849 3 0.000 1.000 0.00 0.000 1.000 0.000 0.000
#> GSM2850 3 0.000 1.000 0.00 0.000 1.000 0.000 0.000
#> GSM2838 2 0.000 0.912 0.00 1.000 0.000 0.000 0.000
#> GSM2853 2 0.000 0.912 0.00 1.000 0.000 0.000 0.000
#> GSM2852 2 0.112 0.872 0.00 0.956 0.044 0.000 0.000
#> GSM2855 2 0.112 0.872 0.00 0.956 0.044 0.000 0.000
#> GSM2840 1 0.000 1.000 1.00 0.000 0.000 0.000 0.000
#> GSM2857 1 0.000 1.000 1.00 0.000 0.000 0.000 0.000
#> GSM2859 2 0.000 0.912 0.00 1.000 0.000 0.000 0.000
#> GSM2860 2 0.000 0.912 0.00 1.000 0.000 0.000 0.000
#> GSM2861 2 0.000 0.912 0.00 1.000 0.000 0.000 0.000
#> GSM2862 2 0.000 0.912 0.00 1.000 0.000 0.000 0.000
#> GSM2863 2 0.000 0.912 0.00 1.000 0.000 0.000 0.000
#> GSM2864 2 0.000 0.912 0.00 1.000 0.000 0.000 0.000
#> GSM2865 2 0.000 0.912 0.00 1.000 0.000 0.000 0.000
#> GSM2866 2 0.000 0.912 0.00 1.000 0.000 0.000 0.000
#> GSM2868 2 0.000 0.912 0.00 1.000 0.000 0.000 0.000
#> GSM2869 2 0.000 0.912 0.00 1.000 0.000 0.000 0.000
#> GSM2851 2 0.000 0.912 0.00 1.000 0.000 0.000 0.000
#> GSM2867 2 0.000 0.912 0.00 1.000 0.000 0.000 0.000
#> GSM2870 2 0.000 0.912 0.00 1.000 0.000 0.000 0.000
#> GSM2854 4 0.545 0.681 0.00 0.172 0.000 0.660 0.168
#> GSM2873 4 0.545 0.681 0.00 0.172 0.000 0.660 0.168
#> GSM2874 3 0.000 1.000 0.00 0.000 1.000 0.000 0.000
#> GSM2884 3 0.000 1.000 0.00 0.000 1.000 0.000 0.000
#> GSM2875 1 0.000 1.000 1.00 0.000 0.000 0.000 0.000
#> GSM2890 1 0.000 1.000 1.00 0.000 0.000 0.000 0.000
#> GSM2877 1 0.000 1.000 1.00 0.000 0.000 0.000 0.000
#> GSM2892 1 0.000 1.000 1.00 0.000 0.000 0.000 0.000
#> GSM2902 1 0.000 1.000 1.00 0.000 0.000 0.000 0.000
#> GSM2878 1 0.000 1.000 1.00 0.000 0.000 0.000 0.000
#> GSM2901 1 0.000 1.000 1.00 0.000 0.000 0.000 0.000
#> GSM2879 2 0.029 0.907 0.00 0.992 0.008 0.000 0.000
#> GSM2898 2 0.029 0.907 0.00 0.992 0.008 0.000 0.000
#> GSM2881 3 0.000 1.000 0.00 0.000 1.000 0.000 0.000
#> GSM2897 3 0.000 1.000 0.00 0.000 1.000 0.000 0.000
#> GSM2882 4 0.000 0.898 0.00 0.000 0.000 1.000 0.000
#> GSM2894 4 0.000 0.898 0.00 0.000 0.000 1.000 0.000
#> GSM2883 3 0.000 1.000 0.00 0.000 1.000 0.000 0.000
#> GSM2895 3 0.000 1.000 0.00 0.000 1.000 0.000 0.000
#> GSM2885 3 0.000 1.000 0.00 0.000 1.000 0.000 0.000
#> GSM2886 3 0.000 1.000 0.00 0.000 1.000 0.000 0.000
#> GSM2887 3 0.000 1.000 0.00 0.000 1.000 0.000 0.000
#> GSM2896 3 0.000 1.000 0.00 0.000 1.000 0.000 0.000
#> GSM2888 2 0.000 0.912 0.00 1.000 0.000 0.000 0.000
#> GSM2889 2 0.000 0.912 0.00 1.000 0.000 0.000 0.000
#> GSM2876 1 0.000 1.000 1.00 0.000 0.000 0.000 0.000
#> GSM2891 1 0.000 1.000 1.00 0.000 0.000 0.000 0.000
#> GSM2880 1 0.000 1.000 1.00 0.000 0.000 0.000 0.000
#> GSM2893 1 0.000 1.000 1.00 0.000 0.000 0.000 0.000
#> GSM2821 5 0.285 1.000 0.00 0.172 0.000 0.000 0.828
#> GSM2900 5 0.285 1.000 0.00 0.172 0.000 0.000 0.828
#> GSM2903 5 0.285 1.000 0.00 0.172 0.000 0.000 0.828
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM2819 5 0.0000 0.746 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM2820 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2822 2 0.4920 0.452 0.000 0.580 0.000 0.064 0.004 0.352
#> GSM2832 2 0.4920 0.452 0.000 0.580 0.000 0.064 0.004 0.352
#> GSM2823 5 0.5265 0.385 0.000 0.404 0.008 0.000 0.512 0.076
#> GSM2824 5 0.5265 0.385 0.000 0.404 0.008 0.000 0.512 0.076
#> GSM2825 2 0.5649 0.296 0.016 0.488 0.000 0.084 0.004 0.408
#> GSM2826 2 0.5649 0.296 0.016 0.488 0.000 0.084 0.004 0.408
#> GSM2829 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2856 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2830 6 0.3868 0.841 0.000 0.000 0.000 0.492 0.000 0.508
#> GSM2843 6 0.3868 0.841 0.000 0.000 0.000 0.492 0.000 0.508
#> GSM2871 6 0.3868 0.841 0.000 0.000 0.000 0.492 0.000 0.508
#> GSM2831 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2844 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2833 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2846 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2835 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2858 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2836 2 0.1075 0.894 0.000 0.952 0.000 0.000 0.000 0.048
#> GSM2848 2 0.1075 0.894 0.000 0.952 0.000 0.000 0.000 0.048
#> GSM2828 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2837 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2839 1 0.1327 0.953 0.936 0.000 0.000 0.000 0.000 0.064
#> GSM2841 1 0.1327 0.953 0.936 0.000 0.000 0.000 0.000 0.064
#> GSM2827 2 0.1075 0.894 0.000 0.952 0.000 0.000 0.000 0.048
#> GSM2842 2 0.1075 0.894 0.000 0.952 0.000 0.000 0.000 0.048
#> GSM2845 6 0.3868 0.841 0.000 0.000 0.000 0.492 0.000 0.508
#> GSM2872 6 0.3868 0.841 0.000 0.000 0.000 0.492 0.000 0.508
#> GSM2834 6 0.3868 0.841 0.000 0.000 0.000 0.492 0.000 0.508
#> GSM2847 6 0.3868 0.841 0.000 0.000 0.000 0.492 0.000 0.508
#> GSM2849 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2850 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2838 2 0.0146 0.902 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM2853 2 0.0146 0.902 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM2852 2 0.1633 0.871 0.000 0.932 0.044 0.000 0.000 0.024
#> GSM2855 2 0.1633 0.871 0.000 0.932 0.044 0.000 0.000 0.024
#> GSM2840 1 0.1327 0.953 0.936 0.000 0.000 0.000 0.000 0.064
#> GSM2857 1 0.1327 0.953 0.936 0.000 0.000 0.000 0.000 0.064
#> GSM2859 2 0.0458 0.901 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM2860 2 0.0458 0.901 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM2861 2 0.0458 0.901 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM2862 2 0.0458 0.901 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM2863 2 0.0458 0.901 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM2864 2 0.0458 0.901 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM2865 2 0.0458 0.901 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM2866 2 0.0458 0.901 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM2868 2 0.0547 0.899 0.000 0.980 0.000 0.000 0.000 0.020
#> GSM2869 2 0.0547 0.899 0.000 0.980 0.000 0.000 0.000 0.020
#> GSM2851 2 0.0547 0.900 0.000 0.980 0.000 0.000 0.000 0.020
#> GSM2867 2 0.0547 0.899 0.000 0.980 0.000 0.000 0.000 0.020
#> GSM2870 2 0.0547 0.900 0.000 0.980 0.000 0.000 0.000 0.020
#> GSM2854 6 0.4968 0.559 0.000 0.120 0.000 0.248 0.000 0.632
#> GSM2873 6 0.4968 0.559 0.000 0.120 0.000 0.248 0.000 0.632
#> GSM2874 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2884 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2875 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2890 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2877 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2892 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2902 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2878 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2901 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2879 2 0.1471 0.881 0.000 0.932 0.004 0.000 0.000 0.064
#> GSM2898 2 0.1471 0.881 0.000 0.932 0.004 0.000 0.000 0.064
#> GSM2881 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2897 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2882 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2894 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2883 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2895 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2885 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2886 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2887 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2896 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2888 2 0.0632 0.899 0.000 0.976 0.000 0.000 0.000 0.024
#> GSM2889 2 0.0632 0.899 0.000 0.976 0.000 0.000 0.000 0.024
#> GSM2876 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2891 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2880 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2893 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2821 5 0.0000 0.746 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM2900 5 0.0000 0.746 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM2903 5 0.0000 0.746 0.000 0.000 0.000 0.000 1.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> MAD:hclust 65 1.42e-04 2
#> MAD:hclust 84 6.67e-09 3
#> MAD:hclust 84 1.99e-12 4
#> MAD:hclust 82 1.15e-15 5
#> MAD:hclust 78 1.99e-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["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 8229 rows and 84 columns.
#> Top rows (823, 1646, 2468, 3291, 4114) 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.189 0.502 0.686 0.3992 0.508 0.508
#> 3 3 0.478 0.636 0.634 0.5109 0.641 0.408
#> 4 4 0.603 0.896 0.853 0.1630 0.899 0.711
#> 5 5 0.806 0.831 0.852 0.0904 0.987 0.949
#> 6 6 0.776 0.728 0.816 0.0494 0.991 0.963
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM2819 2 0.5737 0.6684 0.136 0.864
#> GSM2820 1 0.9850 0.1594 0.572 0.428
#> GSM2822 2 0.4939 0.6811 0.108 0.892
#> GSM2832 2 0.4939 0.6811 0.108 0.892
#> GSM2823 2 0.9732 0.4737 0.404 0.596
#> GSM2824 2 0.9732 0.4737 0.404 0.596
#> GSM2825 2 0.5629 0.6679 0.132 0.868
#> GSM2826 2 0.5629 0.6679 0.132 0.868
#> GSM2829 2 0.2948 0.6594 0.052 0.948
#> GSM2856 2 0.2948 0.6594 0.052 0.948
#> GSM2830 2 0.2423 0.6692 0.040 0.960
#> GSM2843 2 0.2423 0.6692 0.040 0.960
#> GSM2871 2 0.2423 0.6692 0.040 0.960
#> GSM2831 2 0.2948 0.6594 0.052 0.948
#> GSM2844 2 0.2948 0.6594 0.052 0.948
#> GSM2833 2 0.2236 0.6656 0.036 0.964
#> GSM2846 2 0.2236 0.6656 0.036 0.964
#> GSM2835 2 0.2948 0.6594 0.052 0.948
#> GSM2858 2 0.2948 0.6594 0.052 0.948
#> GSM2836 2 0.8207 0.7190 0.256 0.744
#> GSM2848 2 0.8207 0.7190 0.256 0.744
#> GSM2828 1 0.9850 0.1594 0.572 0.428
#> GSM2837 1 0.9850 0.1594 0.572 0.428
#> GSM2839 1 0.9608 0.4033 0.616 0.384
#> GSM2841 1 0.9608 0.4033 0.616 0.384
#> GSM2827 2 0.7950 0.7155 0.240 0.760
#> GSM2842 2 0.7950 0.7155 0.240 0.760
#> GSM2845 2 0.2423 0.6692 0.040 0.960
#> GSM2872 2 0.2948 0.6594 0.052 0.948
#> GSM2834 2 0.2043 0.6723 0.032 0.968
#> GSM2847 2 0.2423 0.6692 0.040 0.960
#> GSM2849 1 0.9850 0.1594 0.572 0.428
#> GSM2850 1 0.9850 0.1594 0.572 0.428
#> GSM2838 2 0.8327 0.7139 0.264 0.736
#> GSM2853 2 0.8327 0.7139 0.264 0.736
#> GSM2852 2 0.9909 0.1615 0.444 0.556
#> GSM2855 2 0.9909 0.1615 0.444 0.556
#> GSM2840 1 0.9608 0.4033 0.616 0.384
#> GSM2857 1 0.9608 0.4033 0.616 0.384
#> GSM2859 2 0.8207 0.7190 0.256 0.744
#> GSM2860 2 0.8207 0.7190 0.256 0.744
#> GSM2861 2 0.8327 0.7139 0.264 0.736
#> GSM2862 2 0.8207 0.7190 0.256 0.744
#> GSM2863 2 0.8207 0.7190 0.256 0.744
#> GSM2864 2 0.8207 0.7190 0.256 0.744
#> GSM2865 2 0.8207 0.7190 0.256 0.744
#> GSM2866 2 0.8207 0.7190 0.256 0.744
#> GSM2868 2 0.8327 0.7139 0.264 0.736
#> GSM2869 2 0.8327 0.7139 0.264 0.736
#> GSM2851 2 0.8327 0.7139 0.264 0.736
#> GSM2867 2 0.8327 0.7139 0.264 0.736
#> GSM2870 2 0.8327 0.7139 0.264 0.736
#> GSM2854 2 0.0672 0.6754 0.008 0.992
#> GSM2873 2 0.6712 0.7191 0.176 0.824
#> GSM2874 1 0.9850 0.1594 0.572 0.428
#> GSM2884 1 0.9850 0.1594 0.572 0.428
#> GSM2875 1 0.9248 0.4385 0.660 0.340
#> GSM2890 1 0.9248 0.4385 0.660 0.340
#> GSM2877 1 0.9248 0.4385 0.660 0.340
#> GSM2892 1 0.9248 0.4385 0.660 0.340
#> GSM2902 1 0.9248 0.4385 0.660 0.340
#> GSM2878 1 0.9248 0.4385 0.660 0.340
#> GSM2901 1 0.9248 0.4385 0.660 0.340
#> GSM2879 1 0.9922 0.0169 0.552 0.448
#> GSM2898 1 0.9922 0.0169 0.552 0.448
#> GSM2881 1 0.9850 0.1594 0.572 0.428
#> GSM2897 1 0.9850 0.1594 0.572 0.428
#> GSM2882 2 0.2948 0.6594 0.052 0.948
#> GSM2894 2 0.2948 0.6594 0.052 0.948
#> GSM2883 1 0.9850 0.1594 0.572 0.428
#> GSM2895 1 0.9850 0.1594 0.572 0.428
#> GSM2885 1 0.9850 0.1594 0.572 0.428
#> GSM2886 1 0.9850 0.1594 0.572 0.428
#> GSM2887 1 0.9850 0.1594 0.572 0.428
#> GSM2896 1 0.9850 0.1594 0.572 0.428
#> GSM2888 2 0.8081 0.7079 0.248 0.752
#> GSM2889 2 0.8081 0.7079 0.248 0.752
#> GSM2876 1 0.9323 0.4333 0.652 0.348
#> GSM2891 1 0.9323 0.4333 0.652 0.348
#> GSM2880 1 0.9248 0.4385 0.660 0.340
#> GSM2893 1 0.9248 0.4385 0.660 0.340
#> GSM2821 1 0.9954 0.3111 0.540 0.460
#> GSM2900 1 0.9954 0.3111 0.540 0.460
#> GSM2903 1 0.9954 0.3111 0.540 0.460
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM2819 2 0.5681 0.6216 0.236 0.748 0.016
#> GSM2820 3 0.5982 0.9617 0.004 0.328 0.668
#> GSM2822 2 0.4121 0.7251 0.168 0.832 0.000
#> GSM2832 2 0.4121 0.7251 0.168 0.832 0.000
#> GSM2823 2 0.3888 0.7889 0.048 0.888 0.064
#> GSM2824 2 0.3888 0.7889 0.048 0.888 0.064
#> GSM2825 2 0.7300 0.4360 0.272 0.664 0.064
#> GSM2826 2 0.7300 0.4360 0.272 0.664 0.064
#> GSM2829 1 0.7715 0.1688 0.524 0.428 0.048
#> GSM2856 1 0.7715 0.1688 0.524 0.428 0.048
#> GSM2830 1 0.7715 0.1688 0.524 0.428 0.048
#> GSM2843 1 0.7722 0.1574 0.520 0.432 0.048
#> GSM2871 1 0.7758 0.0441 0.484 0.468 0.048
#> GSM2831 1 0.7715 0.1688 0.524 0.428 0.048
#> GSM2844 1 0.7715 0.1688 0.524 0.428 0.048
#> GSM2833 1 0.7715 0.1688 0.524 0.428 0.048
#> GSM2846 1 0.7715 0.1688 0.524 0.428 0.048
#> GSM2835 1 0.7715 0.1688 0.524 0.428 0.048
#> GSM2858 1 0.7715 0.1688 0.524 0.428 0.048
#> GSM2836 2 0.0892 0.8792 0.020 0.980 0.000
#> GSM2848 2 0.0892 0.8792 0.020 0.980 0.000
#> GSM2828 3 0.5982 0.9617 0.004 0.328 0.668
#> GSM2837 3 0.5982 0.9617 0.004 0.328 0.668
#> GSM2839 1 0.7613 0.5110 0.620 0.064 0.316
#> GSM2841 1 0.7613 0.5110 0.620 0.064 0.316
#> GSM2827 2 0.0892 0.8792 0.020 0.980 0.000
#> GSM2842 2 0.0892 0.8792 0.020 0.980 0.000
#> GSM2845 1 0.7715 0.1688 0.524 0.428 0.048
#> GSM2872 1 0.7715 0.1688 0.524 0.428 0.048
#> GSM2834 1 0.7715 0.1688 0.524 0.428 0.048
#> GSM2847 1 0.7715 0.1688 0.524 0.428 0.048
#> GSM2849 3 0.5982 0.9617 0.004 0.328 0.668
#> GSM2850 3 0.5982 0.9617 0.004 0.328 0.668
#> GSM2838 2 0.0000 0.8833 0.000 1.000 0.000
#> GSM2853 2 0.0000 0.8833 0.000 1.000 0.000
#> GSM2852 3 0.6154 0.8824 0.000 0.408 0.592
#> GSM2855 3 0.6154 0.8824 0.000 0.408 0.592
#> GSM2840 1 0.7613 0.5110 0.620 0.064 0.316
#> GSM2857 1 0.7613 0.5110 0.620 0.064 0.316
#> GSM2859 2 0.0424 0.8822 0.008 0.992 0.000
#> GSM2860 2 0.0000 0.8833 0.000 1.000 0.000
#> GSM2861 2 0.0000 0.8833 0.000 1.000 0.000
#> GSM2862 2 0.0000 0.8833 0.000 1.000 0.000
#> GSM2863 2 0.0000 0.8833 0.000 1.000 0.000
#> GSM2864 2 0.0000 0.8833 0.000 1.000 0.000
#> GSM2865 2 0.0000 0.8833 0.000 1.000 0.000
#> GSM2866 2 0.0892 0.8792 0.020 0.980 0.000
#> GSM2868 2 0.0000 0.8833 0.000 1.000 0.000
#> GSM2869 2 0.0000 0.8833 0.000 1.000 0.000
#> GSM2851 2 0.0000 0.8833 0.000 1.000 0.000
#> GSM2867 2 0.0000 0.8833 0.000 1.000 0.000
#> GSM2870 2 0.0000 0.8833 0.000 1.000 0.000
#> GSM2854 2 0.6836 0.2050 0.412 0.572 0.016
#> GSM2873 2 0.4235 0.7105 0.176 0.824 0.000
#> GSM2874 3 0.5982 0.9617 0.004 0.328 0.668
#> GSM2884 3 0.5982 0.9617 0.004 0.328 0.668
#> GSM2875 1 0.7571 0.5008 0.592 0.052 0.356
#> GSM2890 1 0.7571 0.5008 0.592 0.052 0.356
#> GSM2877 1 0.7571 0.5008 0.592 0.052 0.356
#> GSM2892 1 0.7571 0.5008 0.592 0.052 0.356
#> GSM2902 1 0.7571 0.5008 0.592 0.052 0.356
#> GSM2878 1 0.7552 0.5008 0.596 0.052 0.352
#> GSM2901 1 0.7552 0.5008 0.596 0.052 0.352
#> GSM2879 3 0.6299 0.7765 0.000 0.476 0.524
#> GSM2898 3 0.6299 0.7765 0.000 0.476 0.524
#> GSM2881 3 0.5760 0.9614 0.000 0.328 0.672
#> GSM2897 3 0.5760 0.9614 0.000 0.328 0.672
#> GSM2882 1 0.7715 0.1688 0.524 0.428 0.048
#> GSM2894 1 0.7715 0.1688 0.524 0.428 0.048
#> GSM2883 3 0.6008 0.9606 0.004 0.332 0.664
#> GSM2895 3 0.6008 0.9606 0.004 0.332 0.664
#> GSM2885 3 0.5760 0.9614 0.000 0.328 0.672
#> GSM2886 3 0.5760 0.9614 0.000 0.328 0.672
#> GSM2887 3 0.5785 0.9602 0.000 0.332 0.668
#> GSM2896 3 0.5785 0.9602 0.000 0.332 0.668
#> GSM2888 2 0.0000 0.8833 0.000 1.000 0.000
#> GSM2889 2 0.0000 0.8833 0.000 1.000 0.000
#> GSM2876 1 0.7448 0.5075 0.616 0.052 0.332
#> GSM2891 1 0.7448 0.5075 0.616 0.052 0.332
#> GSM2880 1 0.7571 0.5008 0.592 0.052 0.356
#> GSM2893 1 0.7571 0.5008 0.592 0.052 0.356
#> GSM2821 1 0.9184 0.4655 0.528 0.188 0.284
#> GSM2900 1 0.9145 0.4682 0.532 0.184 0.284
#> GSM2903 1 0.9145 0.4682 0.532 0.184 0.284
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM2819 2 0.4932 0.783 0.012 0.792 0.068 0.128
#> GSM2820 3 0.3272 0.937 0.008 0.128 0.860 0.004
#> GSM2822 2 0.3889 0.812 0.004 0.844 0.040 0.112
#> GSM2832 2 0.3889 0.812 0.004 0.844 0.040 0.112
#> GSM2823 2 0.3552 0.841 0.000 0.848 0.024 0.128
#> GSM2824 2 0.3552 0.841 0.000 0.848 0.024 0.128
#> GSM2825 2 0.5967 0.602 0.028 0.708 0.052 0.212
#> GSM2826 2 0.5967 0.602 0.028 0.708 0.052 0.212
#> GSM2829 4 0.4898 0.982 0.024 0.184 0.020 0.772
#> GSM2856 4 0.4898 0.982 0.024 0.184 0.020 0.772
#> GSM2830 4 0.5281 0.980 0.036 0.184 0.024 0.756
#> GSM2843 4 0.5232 0.979 0.032 0.188 0.024 0.756
#> GSM2871 4 0.5369 0.973 0.032 0.192 0.028 0.748
#> GSM2831 4 0.4673 0.983 0.024 0.184 0.012 0.780
#> GSM2844 4 0.4673 0.983 0.024 0.184 0.012 0.780
#> GSM2833 4 0.5098 0.979 0.024 0.184 0.028 0.764
#> GSM2846 4 0.5098 0.979 0.024 0.184 0.028 0.764
#> GSM2835 4 0.5015 0.975 0.024 0.176 0.028 0.772
#> GSM2858 4 0.5015 0.975 0.024 0.176 0.028 0.772
#> GSM2836 2 0.1118 0.915 0.000 0.964 0.000 0.036
#> GSM2848 2 0.1118 0.915 0.000 0.964 0.000 0.036
#> GSM2828 3 0.3272 0.937 0.008 0.128 0.860 0.004
#> GSM2837 3 0.3272 0.937 0.008 0.128 0.860 0.004
#> GSM2839 1 0.4161 0.894 0.852 0.032 0.056 0.060
#> GSM2841 1 0.4161 0.894 0.852 0.032 0.056 0.060
#> GSM2827 2 0.0921 0.920 0.000 0.972 0.000 0.028
#> GSM2842 2 0.0921 0.920 0.000 0.972 0.000 0.028
#> GSM2845 4 0.5378 0.979 0.036 0.184 0.028 0.752
#> GSM2872 4 0.5378 0.979 0.036 0.184 0.028 0.752
#> GSM2834 4 0.5139 0.980 0.028 0.188 0.024 0.760
#> GSM2847 4 0.5192 0.981 0.032 0.184 0.024 0.760
#> GSM2849 3 0.3272 0.937 0.008 0.128 0.860 0.004
#> GSM2850 3 0.3272 0.937 0.008 0.128 0.860 0.004
#> GSM2838 2 0.0188 0.928 0.000 0.996 0.004 0.000
#> GSM2853 2 0.0188 0.928 0.000 0.996 0.004 0.000
#> GSM2852 3 0.4764 0.912 0.008 0.136 0.796 0.060
#> GSM2855 3 0.4764 0.912 0.008 0.136 0.796 0.060
#> GSM2840 1 0.4161 0.894 0.852 0.032 0.056 0.060
#> GSM2857 1 0.4161 0.894 0.852 0.032 0.056 0.060
#> GSM2859 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> GSM2860 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> GSM2861 2 0.0188 0.928 0.000 0.996 0.004 0.000
#> GSM2862 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> GSM2863 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> GSM2864 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> GSM2865 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> GSM2866 2 0.0804 0.922 0.000 0.980 0.012 0.008
#> GSM2868 2 0.0564 0.927 0.004 0.988 0.004 0.004
#> GSM2869 2 0.0564 0.927 0.004 0.988 0.004 0.004
#> GSM2851 2 0.0564 0.927 0.004 0.988 0.004 0.004
#> GSM2867 2 0.0564 0.927 0.004 0.988 0.004 0.004
#> GSM2870 2 0.0564 0.927 0.004 0.988 0.004 0.004
#> GSM2854 4 0.4754 0.943 0.004 0.220 0.024 0.752
#> GSM2873 2 0.3325 0.823 0.000 0.864 0.024 0.112
#> GSM2874 3 0.3415 0.937 0.008 0.128 0.856 0.008
#> GSM2884 3 0.3415 0.937 0.008 0.128 0.856 0.008
#> GSM2875 1 0.1953 0.911 0.944 0.032 0.012 0.012
#> GSM2890 1 0.1953 0.911 0.944 0.032 0.012 0.012
#> GSM2877 1 0.1953 0.911 0.944 0.032 0.012 0.012
#> GSM2892 1 0.1953 0.911 0.944 0.032 0.012 0.012
#> GSM2902 1 0.1953 0.911 0.944 0.032 0.012 0.012
#> GSM2878 1 0.1543 0.911 0.956 0.032 0.008 0.004
#> GSM2901 1 0.1543 0.911 0.956 0.032 0.008 0.004
#> GSM2879 3 0.6542 0.422 0.000 0.428 0.496 0.076
#> GSM2898 3 0.6542 0.422 0.000 0.428 0.496 0.076
#> GSM2881 3 0.3272 0.937 0.004 0.128 0.860 0.008
#> GSM2897 3 0.3272 0.937 0.004 0.128 0.860 0.008
#> GSM2882 4 0.4673 0.983 0.024 0.184 0.012 0.780
#> GSM2894 4 0.4673 0.983 0.024 0.184 0.012 0.780
#> GSM2883 3 0.4903 0.916 0.016 0.128 0.796 0.060
#> GSM2895 3 0.4903 0.916 0.016 0.128 0.796 0.060
#> GSM2885 3 0.3272 0.937 0.004 0.128 0.860 0.008
#> GSM2886 3 0.3272 0.937 0.004 0.128 0.860 0.008
#> GSM2887 3 0.3932 0.932 0.004 0.128 0.836 0.032
#> GSM2896 3 0.3932 0.932 0.004 0.128 0.836 0.032
#> GSM2888 2 0.1443 0.909 0.004 0.960 0.008 0.028
#> GSM2889 2 0.1443 0.909 0.004 0.960 0.008 0.028
#> GSM2876 1 0.3921 0.894 0.864 0.032 0.048 0.056
#> GSM2891 1 0.3921 0.894 0.864 0.032 0.048 0.056
#> GSM2880 1 0.1953 0.911 0.944 0.032 0.012 0.012
#> GSM2893 1 0.1953 0.911 0.944 0.032 0.012 0.012
#> GSM2821 1 0.8064 0.640 0.568 0.216 0.068 0.148
#> GSM2900 1 0.8064 0.640 0.568 0.216 0.068 0.148
#> GSM2903 1 0.8064 0.640 0.568 0.216 0.068 0.148
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM2819 2 0.5012 0.388 0.000 0.600 0.004 0.032 0.364
#> GSM2820 3 0.2053 0.904 0.000 0.048 0.924 0.004 0.024
#> GSM2822 2 0.4764 0.695 0.000 0.756 0.016 0.088 0.140
#> GSM2832 2 0.4764 0.695 0.000 0.756 0.016 0.088 0.140
#> GSM2823 2 0.5041 0.514 0.004 0.636 0.000 0.044 0.316
#> GSM2824 2 0.5041 0.514 0.004 0.636 0.000 0.044 0.316
#> GSM2825 2 0.6362 0.418 0.000 0.584 0.016 0.204 0.196
#> GSM2826 2 0.6362 0.418 0.000 0.584 0.016 0.204 0.196
#> GSM2829 4 0.2772 0.943 0.000 0.052 0.012 0.892 0.044
#> GSM2856 4 0.2772 0.943 0.000 0.052 0.012 0.892 0.044
#> GSM2830 4 0.3046 0.943 0.000 0.052 0.020 0.880 0.048
#> GSM2843 4 0.3046 0.943 0.000 0.052 0.020 0.880 0.048
#> GSM2871 4 0.3254 0.938 0.000 0.052 0.020 0.868 0.060
#> GSM2831 4 0.1591 0.951 0.000 0.052 0.004 0.940 0.004
#> GSM2844 4 0.1591 0.951 0.000 0.052 0.004 0.940 0.004
#> GSM2833 4 0.2987 0.940 0.000 0.052 0.012 0.880 0.056
#> GSM2846 4 0.2987 0.940 0.000 0.052 0.012 0.880 0.056
#> GSM2835 4 0.2983 0.937 0.000 0.048 0.012 0.880 0.060
#> GSM2858 4 0.2983 0.937 0.000 0.048 0.012 0.880 0.060
#> GSM2836 2 0.1661 0.822 0.000 0.940 0.000 0.036 0.024
#> GSM2848 2 0.1661 0.822 0.000 0.940 0.000 0.036 0.024
#> GSM2828 3 0.2053 0.904 0.000 0.048 0.924 0.004 0.024
#> GSM2837 3 0.2053 0.904 0.000 0.048 0.924 0.004 0.024
#> GSM2839 1 0.4463 0.721 0.764 0.004 0.024 0.024 0.184
#> GSM2841 1 0.4463 0.721 0.764 0.004 0.024 0.024 0.184
#> GSM2827 2 0.2036 0.823 0.000 0.920 0.000 0.024 0.056
#> GSM2842 2 0.2036 0.823 0.000 0.920 0.000 0.024 0.056
#> GSM2845 4 0.3248 0.937 0.000 0.048 0.020 0.868 0.064
#> GSM2872 4 0.3248 0.937 0.000 0.048 0.020 0.868 0.064
#> GSM2834 4 0.3117 0.943 0.000 0.052 0.020 0.876 0.052
#> GSM2847 4 0.3117 0.943 0.000 0.052 0.020 0.876 0.052
#> GSM2849 3 0.2053 0.904 0.000 0.048 0.924 0.004 0.024
#> GSM2850 3 0.2053 0.904 0.000 0.048 0.924 0.004 0.024
#> GSM2838 2 0.2329 0.818 0.000 0.876 0.000 0.000 0.124
#> GSM2853 2 0.2329 0.818 0.000 0.876 0.000 0.000 0.124
#> GSM2852 3 0.4272 0.846 0.000 0.060 0.780 0.008 0.152
#> GSM2855 3 0.4272 0.846 0.000 0.060 0.780 0.008 0.152
#> GSM2840 1 0.4463 0.721 0.764 0.004 0.024 0.024 0.184
#> GSM2857 1 0.4463 0.721 0.764 0.004 0.024 0.024 0.184
#> GSM2859 2 0.0510 0.835 0.000 0.984 0.000 0.000 0.016
#> GSM2860 2 0.0510 0.835 0.000 0.984 0.000 0.000 0.016
#> GSM2861 2 0.1270 0.833 0.000 0.948 0.000 0.000 0.052
#> GSM2862 2 0.0510 0.835 0.000 0.984 0.000 0.000 0.016
#> GSM2863 2 0.0510 0.835 0.000 0.984 0.000 0.000 0.016
#> GSM2864 2 0.0510 0.835 0.000 0.984 0.000 0.000 0.016
#> GSM2865 2 0.0510 0.835 0.000 0.984 0.000 0.000 0.016
#> GSM2866 2 0.0609 0.835 0.000 0.980 0.000 0.000 0.020
#> GSM2868 2 0.2377 0.816 0.000 0.872 0.000 0.000 0.128
#> GSM2869 2 0.2377 0.816 0.000 0.872 0.000 0.000 0.128
#> GSM2851 2 0.2329 0.818 0.000 0.876 0.000 0.000 0.124
#> GSM2867 2 0.2377 0.816 0.000 0.872 0.000 0.000 0.128
#> GSM2870 2 0.2377 0.816 0.000 0.872 0.000 0.000 0.128
#> GSM2854 4 0.3388 0.936 0.000 0.056 0.020 0.860 0.064
#> GSM2873 2 0.3495 0.762 0.000 0.852 0.020 0.080 0.048
#> GSM2874 3 0.1805 0.905 0.004 0.048 0.936 0.004 0.008
#> GSM2884 3 0.1679 0.905 0.004 0.048 0.940 0.004 0.004
#> GSM2875 1 0.0162 0.869 0.996 0.004 0.000 0.000 0.000
#> GSM2890 1 0.0162 0.869 0.996 0.004 0.000 0.000 0.000
#> GSM2877 1 0.0162 0.869 0.996 0.004 0.000 0.000 0.000
#> GSM2892 1 0.0162 0.869 0.996 0.004 0.000 0.000 0.000
#> GSM2902 1 0.0162 0.869 0.996 0.004 0.000 0.000 0.000
#> GSM2878 1 0.0775 0.865 0.980 0.004 0.004 0.004 0.008
#> GSM2901 1 0.0775 0.865 0.980 0.004 0.004 0.004 0.008
#> GSM2879 3 0.6545 0.403 0.000 0.344 0.484 0.008 0.164
#> GSM2898 3 0.6545 0.403 0.000 0.344 0.484 0.008 0.164
#> GSM2881 3 0.2120 0.905 0.004 0.048 0.924 0.004 0.020
#> GSM2897 3 0.2120 0.905 0.004 0.048 0.924 0.004 0.020
#> GSM2882 4 0.1430 0.951 0.000 0.052 0.004 0.944 0.000
#> GSM2894 4 0.1430 0.951 0.000 0.052 0.004 0.944 0.000
#> GSM2883 3 0.3514 0.880 0.000 0.048 0.848 0.016 0.088
#> GSM2895 3 0.3514 0.880 0.000 0.048 0.848 0.016 0.088
#> GSM2885 3 0.2120 0.905 0.004 0.048 0.924 0.004 0.020
#> GSM2886 3 0.2120 0.905 0.004 0.048 0.924 0.004 0.020
#> GSM2887 3 0.3395 0.889 0.004 0.048 0.860 0.012 0.076
#> GSM2896 3 0.3395 0.889 0.004 0.048 0.860 0.012 0.076
#> GSM2888 2 0.2563 0.815 0.000 0.872 0.000 0.008 0.120
#> GSM2889 2 0.2563 0.815 0.000 0.872 0.000 0.008 0.120
#> GSM2876 1 0.3088 0.734 0.828 0.004 0.000 0.004 0.164
#> GSM2891 1 0.3088 0.734 0.828 0.004 0.000 0.004 0.164
#> GSM2880 1 0.0162 0.869 0.996 0.004 0.000 0.000 0.000
#> GSM2893 1 0.0162 0.869 0.996 0.004 0.000 0.000 0.000
#> GSM2821 5 0.7293 1.000 0.372 0.196 0.000 0.036 0.396
#> GSM2900 5 0.7293 1.000 0.372 0.196 0.000 0.036 0.396
#> GSM2903 5 0.7293 1.000 0.372 0.196 0.000 0.036 0.396
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM2819 5 0.5298 -0.0733 0.000 0.420 0.000 0.020 0.504 NA
#> GSM2820 3 0.2195 0.8581 0.000 0.012 0.904 0.000 0.068 NA
#> GSM2822 2 0.5401 0.5638 0.000 0.688 0.004 0.068 0.140 NA
#> GSM2832 2 0.5401 0.5638 0.000 0.688 0.004 0.068 0.140 NA
#> GSM2823 2 0.6606 0.0157 0.008 0.416 0.004 0.016 0.352 NA
#> GSM2824 2 0.6606 0.0157 0.008 0.416 0.004 0.016 0.352 NA
#> GSM2825 2 0.6952 0.2332 0.000 0.488 0.000 0.136 0.216 NA
#> GSM2826 2 0.6952 0.2332 0.000 0.488 0.000 0.136 0.216 NA
#> GSM2829 4 0.2010 0.8751 0.000 0.004 0.004 0.920 0.036 NA
#> GSM2856 4 0.2010 0.8751 0.000 0.004 0.004 0.920 0.036 NA
#> GSM2830 4 0.2955 0.8573 0.000 0.008 0.000 0.816 0.004 NA
#> GSM2843 4 0.2955 0.8573 0.000 0.008 0.000 0.816 0.004 NA
#> GSM2871 4 0.3198 0.8485 0.000 0.008 0.000 0.796 0.008 NA
#> GSM2831 4 0.0870 0.8852 0.000 0.004 0.000 0.972 0.012 NA
#> GSM2844 4 0.0870 0.8852 0.000 0.004 0.000 0.972 0.012 NA
#> GSM2833 4 0.2483 0.8669 0.000 0.004 0.004 0.892 0.056 NA
#> GSM2846 4 0.2483 0.8669 0.000 0.004 0.004 0.892 0.056 NA
#> GSM2835 4 0.2856 0.8555 0.000 0.004 0.004 0.868 0.060 NA
#> GSM2858 4 0.2856 0.8555 0.000 0.004 0.004 0.868 0.060 NA
#> GSM2836 2 0.2898 0.7028 0.000 0.868 0.000 0.020 0.040 NA
#> GSM2848 2 0.2898 0.7028 0.000 0.868 0.000 0.020 0.040 NA
#> GSM2828 3 0.2195 0.8581 0.000 0.012 0.904 0.000 0.068 NA
#> GSM2837 3 0.2195 0.8581 0.000 0.012 0.904 0.000 0.068 NA
#> GSM2839 1 0.4857 0.6817 0.668 0.000 0.000 0.004 0.212 NA
#> GSM2841 1 0.4857 0.6817 0.668 0.000 0.000 0.004 0.212 NA
#> GSM2827 2 0.3583 0.6966 0.000 0.800 0.000 0.008 0.048 NA
#> GSM2842 2 0.3583 0.6966 0.000 0.800 0.000 0.008 0.048 NA
#> GSM2845 4 0.3404 0.8480 0.000 0.008 0.004 0.792 0.012 NA
#> GSM2872 4 0.3404 0.8480 0.000 0.008 0.004 0.792 0.012 NA
#> GSM2834 4 0.3065 0.8562 0.000 0.008 0.000 0.812 0.008 NA
#> GSM2847 4 0.3065 0.8562 0.000 0.008 0.000 0.812 0.008 NA
#> GSM2849 3 0.2395 0.8569 0.000 0.012 0.892 0.000 0.076 NA
#> GSM2850 3 0.2395 0.8569 0.000 0.012 0.892 0.000 0.076 NA
#> GSM2838 2 0.3695 0.6934 0.000 0.772 0.000 0.004 0.040 NA
#> GSM2853 2 0.3695 0.6934 0.000 0.772 0.000 0.004 0.040 NA
#> GSM2852 3 0.4375 0.7396 0.000 0.020 0.700 0.000 0.032 NA
#> GSM2855 3 0.4375 0.7396 0.000 0.020 0.700 0.000 0.032 NA
#> GSM2840 1 0.4857 0.6817 0.668 0.000 0.000 0.004 0.212 NA
#> GSM2857 1 0.4857 0.6817 0.668 0.000 0.000 0.004 0.212 NA
#> GSM2859 2 0.1334 0.7293 0.000 0.948 0.000 0.000 0.032 NA
#> GSM2860 2 0.1334 0.7293 0.000 0.948 0.000 0.000 0.032 NA
#> GSM2861 2 0.2046 0.7287 0.000 0.908 0.000 0.000 0.032 NA
#> GSM2862 2 0.1334 0.7293 0.000 0.948 0.000 0.000 0.032 NA
#> GSM2863 2 0.1334 0.7293 0.000 0.948 0.000 0.000 0.032 NA
#> GSM2864 2 0.1334 0.7293 0.000 0.948 0.000 0.000 0.032 NA
#> GSM2865 2 0.1334 0.7293 0.000 0.948 0.000 0.000 0.032 NA
#> GSM2866 2 0.1334 0.7293 0.000 0.948 0.000 0.000 0.032 NA
#> GSM2868 2 0.4059 0.6760 0.000 0.732 0.000 0.004 0.048 NA
#> GSM2869 2 0.4059 0.6760 0.000 0.732 0.000 0.004 0.048 NA
#> GSM2851 2 0.3969 0.6790 0.000 0.740 0.000 0.004 0.044 NA
#> GSM2867 2 0.4059 0.6760 0.000 0.732 0.000 0.004 0.048 NA
#> GSM2870 2 0.3969 0.6790 0.000 0.740 0.000 0.004 0.044 NA
#> GSM2854 4 0.2907 0.8635 0.000 0.008 0.004 0.868 0.056 NA
#> GSM2873 2 0.3830 0.6667 0.000 0.816 0.004 0.056 0.040 NA
#> GSM2874 3 0.1225 0.8601 0.000 0.012 0.952 0.000 0.036 NA
#> GSM2884 3 0.0993 0.8607 0.000 0.012 0.964 0.000 0.024 NA
#> GSM2875 1 0.0146 0.8492 0.996 0.000 0.000 0.004 0.000 NA
#> GSM2890 1 0.0146 0.8492 0.996 0.000 0.000 0.004 0.000 NA
#> GSM2877 1 0.0146 0.8492 0.996 0.000 0.000 0.004 0.000 NA
#> GSM2892 1 0.0146 0.8492 0.996 0.000 0.000 0.004 0.000 NA
#> GSM2902 1 0.0146 0.8492 0.996 0.000 0.000 0.004 0.000 NA
#> GSM2878 1 0.1312 0.8421 0.956 0.000 0.004 0.008 0.012 NA
#> GSM2901 1 0.1312 0.8421 0.956 0.000 0.004 0.008 0.012 NA
#> GSM2879 3 0.7351 0.1691 0.000 0.288 0.388 0.004 0.108 NA
#> GSM2898 3 0.7351 0.1691 0.000 0.288 0.388 0.004 0.108 NA
#> GSM2881 3 0.0725 0.8608 0.000 0.012 0.976 0.000 0.000 NA
#> GSM2897 3 0.0725 0.8608 0.000 0.012 0.976 0.000 0.000 NA
#> GSM2882 4 0.0748 0.8850 0.000 0.004 0.000 0.976 0.016 NA
#> GSM2894 4 0.0748 0.8850 0.000 0.004 0.000 0.976 0.016 NA
#> GSM2883 3 0.3767 0.8226 0.004 0.012 0.808 0.000 0.092 NA
#> GSM2895 3 0.3767 0.8226 0.004 0.012 0.808 0.000 0.092 NA
#> GSM2885 3 0.0725 0.8608 0.000 0.012 0.976 0.000 0.000 NA
#> GSM2886 3 0.0725 0.8608 0.000 0.012 0.976 0.000 0.000 NA
#> GSM2887 3 0.2518 0.8373 0.000 0.012 0.880 0.000 0.016 NA
#> GSM2896 3 0.2518 0.8373 0.000 0.012 0.880 0.000 0.016 NA
#> GSM2888 2 0.3997 0.6882 0.000 0.736 0.000 0.004 0.044 NA
#> GSM2889 2 0.3997 0.6882 0.000 0.736 0.000 0.004 0.044 NA
#> GSM2876 1 0.3777 0.7265 0.776 0.000 0.000 0.004 0.164 NA
#> GSM2891 1 0.3777 0.7265 0.776 0.000 0.000 0.004 0.164 NA
#> GSM2880 1 0.0146 0.8492 0.996 0.000 0.000 0.004 0.000 NA
#> GSM2893 1 0.0146 0.8492 0.996 0.000 0.000 0.004 0.000 NA
#> GSM2821 5 0.5703 0.7141 0.316 0.108 0.000 0.024 0.552 NA
#> GSM2900 5 0.5703 0.7141 0.316 0.108 0.000 0.024 0.552 NA
#> GSM2903 5 0.5703 0.7141 0.316 0.108 0.000 0.024 0.552 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> MAD:kmeans 45 NA 2
#> MAD:kmeans 61 8.31e-07 3
#> MAD:kmeans 82 8.86e-12 4
#> MAD:kmeans 79 3.61e-15 5
#> MAD:kmeans 77 6.70e-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["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 8229 rows and 84 columns.
#> Top rows (823, 1646, 2468, 3291, 4114) 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 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.494 0.926 0.943 0.5056 0.494 0.494
#> 3 3 0.564 0.699 0.859 0.2831 0.687 0.453
#> 4 4 1.000 0.968 0.912 0.1639 0.837 0.563
#> 5 5 0.916 0.893 0.896 0.0471 0.971 0.880
#> 6 6 0.871 0.799 0.836 0.0380 0.943 0.744
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] 4
There is also optional best \(k\) = 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
#> GSM2819 1 0.494 0.937 0.892 0.108
#> GSM2820 2 0.494 0.931 0.108 0.892
#> GSM2822 1 0.494 0.937 0.892 0.108
#> GSM2832 1 0.494 0.937 0.892 0.108
#> GSM2823 2 0.494 0.931 0.108 0.892
#> GSM2824 2 0.494 0.931 0.108 0.892
#> GSM2825 1 0.494 0.937 0.892 0.108
#> GSM2826 1 0.494 0.937 0.892 0.108
#> GSM2829 1 0.494 0.937 0.892 0.108
#> GSM2856 1 0.494 0.937 0.892 0.108
#> GSM2830 1 0.494 0.937 0.892 0.108
#> GSM2843 1 0.494 0.937 0.892 0.108
#> GSM2871 1 0.494 0.937 0.892 0.108
#> GSM2831 1 0.494 0.937 0.892 0.108
#> GSM2844 1 0.494 0.937 0.892 0.108
#> GSM2833 1 0.494 0.937 0.892 0.108
#> GSM2846 1 0.494 0.937 0.892 0.108
#> GSM2835 1 0.494 0.937 0.892 0.108
#> GSM2858 1 0.494 0.937 0.892 0.108
#> GSM2836 2 0.000 0.943 0.000 1.000
#> GSM2848 2 0.000 0.943 0.000 1.000
#> GSM2828 2 0.494 0.931 0.108 0.892
#> GSM2837 2 0.494 0.931 0.108 0.892
#> GSM2839 1 0.000 0.921 1.000 0.000
#> GSM2841 1 0.000 0.921 1.000 0.000
#> GSM2827 2 0.000 0.943 0.000 1.000
#> GSM2842 2 0.000 0.943 0.000 1.000
#> GSM2845 1 0.494 0.937 0.892 0.108
#> GSM2872 1 0.494 0.937 0.892 0.108
#> GSM2834 1 0.494 0.937 0.892 0.108
#> GSM2847 1 0.494 0.937 0.892 0.108
#> GSM2849 2 0.494 0.931 0.108 0.892
#> GSM2850 2 0.494 0.931 0.108 0.892
#> GSM2838 2 0.000 0.943 0.000 1.000
#> GSM2853 2 0.000 0.943 0.000 1.000
#> GSM2852 2 0.000 0.943 0.000 1.000
#> GSM2855 2 0.000 0.943 0.000 1.000
#> GSM2840 1 0.000 0.921 1.000 0.000
#> GSM2857 1 0.000 0.921 1.000 0.000
#> GSM2859 2 0.000 0.943 0.000 1.000
#> GSM2860 2 0.000 0.943 0.000 1.000
#> GSM2861 2 0.000 0.943 0.000 1.000
#> GSM2862 2 0.000 0.943 0.000 1.000
#> GSM2863 2 0.000 0.943 0.000 1.000
#> GSM2864 2 0.000 0.943 0.000 1.000
#> GSM2865 2 0.000 0.943 0.000 1.000
#> GSM2866 2 0.000 0.943 0.000 1.000
#> GSM2868 2 0.000 0.943 0.000 1.000
#> GSM2869 2 0.000 0.943 0.000 1.000
#> GSM2851 2 0.000 0.943 0.000 1.000
#> GSM2867 2 0.000 0.943 0.000 1.000
#> GSM2870 2 0.000 0.943 0.000 1.000
#> GSM2854 1 0.494 0.937 0.892 0.108
#> GSM2873 1 0.998 0.293 0.524 0.476
#> GSM2874 2 0.494 0.931 0.108 0.892
#> GSM2884 2 0.494 0.931 0.108 0.892
#> GSM2875 1 0.000 0.921 1.000 0.000
#> GSM2890 1 0.000 0.921 1.000 0.000
#> GSM2877 1 0.000 0.921 1.000 0.000
#> GSM2892 1 0.000 0.921 1.000 0.000
#> GSM2902 1 0.000 0.921 1.000 0.000
#> GSM2878 1 0.000 0.921 1.000 0.000
#> GSM2901 1 0.000 0.921 1.000 0.000
#> GSM2879 2 0.494 0.931 0.108 0.892
#> GSM2898 2 0.494 0.931 0.108 0.892
#> GSM2881 2 0.494 0.931 0.108 0.892
#> GSM2897 2 0.494 0.931 0.108 0.892
#> GSM2882 1 0.494 0.937 0.892 0.108
#> GSM2894 1 0.494 0.937 0.892 0.108
#> GSM2883 2 0.494 0.931 0.108 0.892
#> GSM2895 2 0.494 0.931 0.108 0.892
#> GSM2885 2 0.494 0.931 0.108 0.892
#> GSM2886 2 0.494 0.931 0.108 0.892
#> GSM2887 2 0.494 0.931 0.108 0.892
#> GSM2896 2 0.494 0.931 0.108 0.892
#> GSM2888 2 0.000 0.943 0.000 1.000
#> GSM2889 2 0.000 0.943 0.000 1.000
#> GSM2876 1 0.000 0.921 1.000 0.000
#> GSM2891 1 0.000 0.921 1.000 0.000
#> GSM2880 1 0.000 0.921 1.000 0.000
#> GSM2893 1 0.000 0.921 1.000 0.000
#> GSM2821 1 0.000 0.921 1.000 0.000
#> GSM2900 1 0.000 0.921 1.000 0.000
#> GSM2903 1 0.000 0.921 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM2819 1 0.6267 0.111 0.548 0.452 0.000
#> GSM2820 3 0.0000 0.958 0.000 0.000 1.000
#> GSM2822 2 0.0237 0.712 0.004 0.996 0.000
#> GSM2832 2 0.0237 0.712 0.004 0.996 0.000
#> GSM2823 3 0.6045 0.471 0.380 0.000 0.620
#> GSM2824 3 0.6045 0.471 0.380 0.000 0.620
#> GSM2825 1 0.5254 0.511 0.736 0.264 0.000
#> GSM2826 1 0.5254 0.511 0.736 0.264 0.000
#> GSM2829 2 0.6140 0.127 0.404 0.596 0.000
#> GSM2856 2 0.6140 0.127 0.404 0.596 0.000
#> GSM2830 2 0.6140 0.127 0.404 0.596 0.000
#> GSM2843 2 0.6140 0.127 0.404 0.596 0.000
#> GSM2871 2 0.5882 0.250 0.348 0.652 0.000
#> GSM2831 1 0.6192 0.414 0.580 0.420 0.000
#> GSM2844 1 0.6192 0.414 0.580 0.420 0.000
#> GSM2833 2 0.6140 0.127 0.404 0.596 0.000
#> GSM2846 2 0.6140 0.127 0.404 0.596 0.000
#> GSM2835 1 0.6168 0.429 0.588 0.412 0.000
#> GSM2858 1 0.6168 0.429 0.588 0.412 0.000
#> GSM2836 2 0.3686 0.794 0.000 0.860 0.140
#> GSM2848 2 0.3686 0.794 0.000 0.860 0.140
#> GSM2828 3 0.0000 0.958 0.000 0.000 1.000
#> GSM2837 3 0.0000 0.958 0.000 0.000 1.000
#> GSM2839 1 0.0000 0.809 1.000 0.000 0.000
#> GSM2841 1 0.0000 0.809 1.000 0.000 0.000
#> GSM2827 2 0.3686 0.794 0.000 0.860 0.140
#> GSM2842 2 0.3686 0.794 0.000 0.860 0.140
#> GSM2845 1 0.6286 0.300 0.536 0.464 0.000
#> GSM2872 1 0.6204 0.405 0.576 0.424 0.000
#> GSM2834 2 0.6140 0.127 0.404 0.596 0.000
#> GSM2847 2 0.6140 0.127 0.404 0.596 0.000
#> GSM2849 3 0.0000 0.958 0.000 0.000 1.000
#> GSM2850 3 0.0000 0.958 0.000 0.000 1.000
#> GSM2838 2 0.3686 0.794 0.000 0.860 0.140
#> GSM2853 2 0.3686 0.794 0.000 0.860 0.140
#> GSM2852 3 0.0000 0.958 0.000 0.000 1.000
#> GSM2855 3 0.0000 0.958 0.000 0.000 1.000
#> GSM2840 1 0.0000 0.809 1.000 0.000 0.000
#> GSM2857 1 0.0000 0.809 1.000 0.000 0.000
#> GSM2859 2 0.3686 0.794 0.000 0.860 0.140
#> GSM2860 2 0.3686 0.794 0.000 0.860 0.140
#> GSM2861 2 0.3686 0.794 0.000 0.860 0.140
#> GSM2862 2 0.3686 0.794 0.000 0.860 0.140
#> GSM2863 2 0.3686 0.794 0.000 0.860 0.140
#> GSM2864 2 0.3686 0.794 0.000 0.860 0.140
#> GSM2865 2 0.3686 0.794 0.000 0.860 0.140
#> GSM2866 2 0.3686 0.794 0.000 0.860 0.140
#> GSM2868 2 0.3686 0.794 0.000 0.860 0.140
#> GSM2869 2 0.3686 0.794 0.000 0.860 0.140
#> GSM2851 2 0.3686 0.794 0.000 0.860 0.140
#> GSM2867 2 0.3686 0.794 0.000 0.860 0.140
#> GSM2870 2 0.3686 0.794 0.000 0.860 0.140
#> GSM2854 2 0.2356 0.659 0.072 0.928 0.000
#> GSM2873 2 0.0000 0.711 0.000 1.000 0.000
#> GSM2874 3 0.0000 0.958 0.000 0.000 1.000
#> GSM2884 3 0.0000 0.958 0.000 0.000 1.000
#> GSM2875 1 0.0000 0.809 1.000 0.000 0.000
#> GSM2890 1 0.0000 0.809 1.000 0.000 0.000
#> GSM2877 1 0.0000 0.809 1.000 0.000 0.000
#> GSM2892 1 0.0000 0.809 1.000 0.000 0.000
#> GSM2902 1 0.0000 0.809 1.000 0.000 0.000
#> GSM2878 1 0.0000 0.809 1.000 0.000 0.000
#> GSM2901 1 0.0000 0.809 1.000 0.000 0.000
#> GSM2879 3 0.0000 0.958 0.000 0.000 1.000
#> GSM2898 3 0.0000 0.958 0.000 0.000 1.000
#> GSM2881 3 0.0000 0.958 0.000 0.000 1.000
#> GSM2897 3 0.0000 0.958 0.000 0.000 1.000
#> GSM2882 1 0.6180 0.422 0.584 0.416 0.000
#> GSM2894 1 0.6180 0.422 0.584 0.416 0.000
#> GSM2883 3 0.0000 0.958 0.000 0.000 1.000
#> GSM2895 3 0.0000 0.958 0.000 0.000 1.000
#> GSM2885 3 0.0000 0.958 0.000 0.000 1.000
#> GSM2886 3 0.0000 0.958 0.000 0.000 1.000
#> GSM2887 3 0.0000 0.958 0.000 0.000 1.000
#> GSM2896 3 0.0000 0.958 0.000 0.000 1.000
#> GSM2888 2 0.4605 0.727 0.000 0.796 0.204
#> GSM2889 2 0.4605 0.727 0.000 0.796 0.204
#> GSM2876 1 0.0000 0.809 1.000 0.000 0.000
#> GSM2891 1 0.0000 0.809 1.000 0.000 0.000
#> GSM2880 1 0.0000 0.809 1.000 0.000 0.000
#> GSM2893 1 0.0000 0.809 1.000 0.000 0.000
#> GSM2821 1 0.0000 0.809 1.000 0.000 0.000
#> GSM2900 1 0.0000 0.809 1.000 0.000 0.000
#> GSM2903 1 0.0000 0.809 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM2819 1 0.492 0.295 0.576 0.424 0.000 0.00
#> GSM2820 3 0.000 1.000 0.000 0.000 1.000 0.00
#> GSM2822 2 0.000 1.000 0.000 1.000 0.000 0.00
#> GSM2832 2 0.000 1.000 0.000 1.000 0.000 0.00
#> GSM2823 1 0.344 0.768 0.816 0.000 0.184 0.00
#> GSM2824 1 0.344 0.768 0.816 0.000 0.184 0.00
#> GSM2825 1 0.455 0.752 0.780 0.180 0.000 0.04
#> GSM2826 1 0.455 0.752 0.780 0.180 0.000 0.04
#> GSM2829 4 0.000 1.000 0.000 0.000 0.000 1.00
#> GSM2856 4 0.000 1.000 0.000 0.000 0.000 1.00
#> GSM2830 4 0.000 1.000 0.000 0.000 0.000 1.00
#> GSM2843 4 0.000 1.000 0.000 0.000 0.000 1.00
#> GSM2871 4 0.000 1.000 0.000 0.000 0.000 1.00
#> GSM2831 4 0.000 1.000 0.000 0.000 0.000 1.00
#> GSM2844 4 0.000 1.000 0.000 0.000 0.000 1.00
#> GSM2833 4 0.000 1.000 0.000 0.000 0.000 1.00
#> GSM2846 4 0.000 1.000 0.000 0.000 0.000 1.00
#> GSM2835 4 0.000 1.000 0.000 0.000 0.000 1.00
#> GSM2858 4 0.000 1.000 0.000 0.000 0.000 1.00
#> GSM2836 2 0.000 1.000 0.000 1.000 0.000 0.00
#> GSM2848 2 0.000 1.000 0.000 1.000 0.000 0.00
#> GSM2828 3 0.000 1.000 0.000 0.000 1.000 0.00
#> GSM2837 3 0.000 1.000 0.000 0.000 1.000 0.00
#> GSM2839 1 0.000 0.942 1.000 0.000 0.000 0.00
#> GSM2841 1 0.000 0.942 1.000 0.000 0.000 0.00
#> GSM2827 2 0.000 1.000 0.000 1.000 0.000 0.00
#> GSM2842 2 0.000 1.000 0.000 1.000 0.000 0.00
#> GSM2845 4 0.000 1.000 0.000 0.000 0.000 1.00
#> GSM2872 4 0.000 1.000 0.000 0.000 0.000 1.00
#> GSM2834 4 0.000 1.000 0.000 0.000 0.000 1.00
#> GSM2847 4 0.000 1.000 0.000 0.000 0.000 1.00
#> GSM2849 3 0.000 1.000 0.000 0.000 1.000 0.00
#> GSM2850 3 0.000 1.000 0.000 0.000 1.000 0.00
#> GSM2838 2 0.000 1.000 0.000 1.000 0.000 0.00
#> GSM2853 2 0.000 1.000 0.000 1.000 0.000 0.00
#> GSM2852 3 0.000 1.000 0.000 0.000 1.000 0.00
#> GSM2855 3 0.000 1.000 0.000 0.000 1.000 0.00
#> GSM2840 1 0.000 0.942 1.000 0.000 0.000 0.00
#> GSM2857 1 0.000 0.942 1.000 0.000 0.000 0.00
#> GSM2859 2 0.000 1.000 0.000 1.000 0.000 0.00
#> GSM2860 2 0.000 1.000 0.000 1.000 0.000 0.00
#> GSM2861 2 0.000 1.000 0.000 1.000 0.000 0.00
#> GSM2862 2 0.000 1.000 0.000 1.000 0.000 0.00
#> GSM2863 2 0.000 1.000 0.000 1.000 0.000 0.00
#> GSM2864 2 0.000 1.000 0.000 1.000 0.000 0.00
#> GSM2865 2 0.000 1.000 0.000 1.000 0.000 0.00
#> GSM2866 2 0.000 1.000 0.000 1.000 0.000 0.00
#> GSM2868 2 0.000 1.000 0.000 1.000 0.000 0.00
#> GSM2869 2 0.000 1.000 0.000 1.000 0.000 0.00
#> GSM2851 2 0.000 1.000 0.000 1.000 0.000 0.00
#> GSM2867 2 0.000 1.000 0.000 1.000 0.000 0.00
#> GSM2870 2 0.000 1.000 0.000 1.000 0.000 0.00
#> GSM2854 4 0.000 1.000 0.000 0.000 0.000 1.00
#> GSM2873 2 0.000 1.000 0.000 1.000 0.000 0.00
#> GSM2874 3 0.000 1.000 0.000 0.000 1.000 0.00
#> GSM2884 3 0.000 1.000 0.000 0.000 1.000 0.00
#> GSM2875 1 0.000 0.942 1.000 0.000 0.000 0.00
#> GSM2890 1 0.000 0.942 1.000 0.000 0.000 0.00
#> GSM2877 1 0.000 0.942 1.000 0.000 0.000 0.00
#> GSM2892 1 0.000 0.942 1.000 0.000 0.000 0.00
#> GSM2902 1 0.000 0.942 1.000 0.000 0.000 0.00
#> GSM2878 1 0.000 0.942 1.000 0.000 0.000 0.00
#> GSM2901 1 0.000 0.942 1.000 0.000 0.000 0.00
#> GSM2879 3 0.000 1.000 0.000 0.000 1.000 0.00
#> GSM2898 3 0.000 1.000 0.000 0.000 1.000 0.00
#> GSM2881 3 0.000 1.000 0.000 0.000 1.000 0.00
#> GSM2897 3 0.000 1.000 0.000 0.000 1.000 0.00
#> GSM2882 4 0.000 1.000 0.000 0.000 0.000 1.00
#> GSM2894 4 0.000 1.000 0.000 0.000 0.000 1.00
#> GSM2883 3 0.000 1.000 0.000 0.000 1.000 0.00
#> GSM2895 3 0.000 1.000 0.000 0.000 1.000 0.00
#> GSM2885 3 0.000 1.000 0.000 0.000 1.000 0.00
#> GSM2886 3 0.000 1.000 0.000 0.000 1.000 0.00
#> GSM2887 3 0.000 1.000 0.000 0.000 1.000 0.00
#> GSM2896 3 0.000 1.000 0.000 0.000 1.000 0.00
#> GSM2888 2 0.000 1.000 0.000 1.000 0.000 0.00
#> GSM2889 2 0.000 1.000 0.000 1.000 0.000 0.00
#> GSM2876 1 0.000 0.942 1.000 0.000 0.000 0.00
#> GSM2891 1 0.000 0.942 1.000 0.000 0.000 0.00
#> GSM2880 1 0.000 0.942 1.000 0.000 0.000 0.00
#> GSM2893 1 0.000 0.942 1.000 0.000 0.000 0.00
#> GSM2821 1 0.000 0.942 1.000 0.000 0.000 0.00
#> GSM2900 1 0.000 0.942 1.000 0.000 0.000 0.00
#> GSM2903 1 0.000 0.942 1.000 0.000 0.000 0.00
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM2819 5 0.5158 0.632 0.224 0.100 0.000 0.000 0.676
#> GSM2820 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2822 2 0.3707 0.741 0.000 0.716 0.000 0.000 0.284
#> GSM2832 2 0.3707 0.741 0.000 0.716 0.000 0.000 0.284
#> GSM2823 5 0.5510 0.804 0.380 0.000 0.072 0.000 0.548
#> GSM2824 5 0.5510 0.804 0.380 0.000 0.072 0.000 0.548
#> GSM2825 1 0.5975 0.363 0.572 0.124 0.000 0.004 0.300
#> GSM2826 1 0.5975 0.363 0.572 0.124 0.000 0.004 0.300
#> GSM2829 4 0.1341 0.963 0.000 0.000 0.000 0.944 0.056
#> GSM2856 4 0.1341 0.963 0.000 0.000 0.000 0.944 0.056
#> GSM2830 4 0.0000 0.976 0.000 0.000 0.000 1.000 0.000
#> GSM2843 4 0.0000 0.976 0.000 0.000 0.000 1.000 0.000
#> GSM2871 4 0.0000 0.976 0.000 0.000 0.000 1.000 0.000
#> GSM2831 4 0.0000 0.976 0.000 0.000 0.000 1.000 0.000
#> GSM2844 4 0.0000 0.976 0.000 0.000 0.000 1.000 0.000
#> GSM2833 4 0.1341 0.963 0.000 0.000 0.000 0.944 0.056
#> GSM2846 4 0.1341 0.963 0.000 0.000 0.000 0.944 0.056
#> GSM2835 4 0.1410 0.961 0.000 0.000 0.000 0.940 0.060
#> GSM2858 4 0.1410 0.961 0.000 0.000 0.000 0.940 0.060
#> GSM2836 2 0.1270 0.854 0.000 0.948 0.000 0.000 0.052
#> GSM2848 2 0.1270 0.854 0.000 0.948 0.000 0.000 0.052
#> GSM2828 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2837 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2839 1 0.2127 0.802 0.892 0.000 0.000 0.000 0.108
#> GSM2841 1 0.2127 0.802 0.892 0.000 0.000 0.000 0.108
#> GSM2827 2 0.3452 0.868 0.000 0.756 0.000 0.000 0.244
#> GSM2842 2 0.3452 0.868 0.000 0.756 0.000 0.000 0.244
#> GSM2845 4 0.0162 0.975 0.000 0.000 0.000 0.996 0.004
#> GSM2872 4 0.0162 0.975 0.000 0.000 0.000 0.996 0.004
#> GSM2834 4 0.0162 0.975 0.000 0.000 0.000 0.996 0.004
#> GSM2847 4 0.0162 0.975 0.000 0.000 0.000 0.996 0.004
#> GSM2849 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2850 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2838 2 0.3274 0.872 0.000 0.780 0.000 0.000 0.220
#> GSM2853 2 0.3274 0.872 0.000 0.780 0.000 0.000 0.220
#> GSM2852 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2855 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2840 1 0.2127 0.802 0.892 0.000 0.000 0.000 0.108
#> GSM2857 1 0.2127 0.802 0.892 0.000 0.000 0.000 0.108
#> GSM2859 2 0.0000 0.870 0.000 1.000 0.000 0.000 0.000
#> GSM2860 2 0.0000 0.870 0.000 1.000 0.000 0.000 0.000
#> GSM2861 2 0.1965 0.874 0.000 0.904 0.000 0.000 0.096
#> GSM2862 2 0.0000 0.870 0.000 1.000 0.000 0.000 0.000
#> GSM2863 2 0.0000 0.870 0.000 1.000 0.000 0.000 0.000
#> GSM2864 2 0.0000 0.870 0.000 1.000 0.000 0.000 0.000
#> GSM2865 2 0.0000 0.870 0.000 1.000 0.000 0.000 0.000
#> GSM2866 2 0.0000 0.870 0.000 1.000 0.000 0.000 0.000
#> GSM2868 2 0.3242 0.872 0.000 0.784 0.000 0.000 0.216
#> GSM2869 2 0.3242 0.872 0.000 0.784 0.000 0.000 0.216
#> GSM2851 2 0.3274 0.872 0.000 0.780 0.000 0.000 0.220
#> GSM2867 2 0.3242 0.872 0.000 0.784 0.000 0.000 0.216
#> GSM2870 2 0.3274 0.872 0.000 0.780 0.000 0.000 0.220
#> GSM2854 4 0.1732 0.948 0.000 0.000 0.000 0.920 0.080
#> GSM2873 2 0.2605 0.801 0.000 0.852 0.000 0.000 0.148
#> GSM2874 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2884 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2875 1 0.0000 0.864 1.000 0.000 0.000 0.000 0.000
#> GSM2890 1 0.0000 0.864 1.000 0.000 0.000 0.000 0.000
#> GSM2877 1 0.0000 0.864 1.000 0.000 0.000 0.000 0.000
#> GSM2892 1 0.0000 0.864 1.000 0.000 0.000 0.000 0.000
#> GSM2902 1 0.0000 0.864 1.000 0.000 0.000 0.000 0.000
#> GSM2878 1 0.0000 0.864 1.000 0.000 0.000 0.000 0.000
#> GSM2901 1 0.0000 0.864 1.000 0.000 0.000 0.000 0.000
#> GSM2879 3 0.0290 0.993 0.000 0.000 0.992 0.000 0.008
#> GSM2898 3 0.0290 0.993 0.000 0.000 0.992 0.000 0.008
#> GSM2881 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2897 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2882 4 0.0000 0.976 0.000 0.000 0.000 1.000 0.000
#> GSM2894 4 0.0000 0.976 0.000 0.000 0.000 1.000 0.000
#> GSM2883 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2895 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2885 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2886 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2887 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2896 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> GSM2888 2 0.3305 0.873 0.000 0.776 0.000 0.000 0.224
#> GSM2889 2 0.3305 0.873 0.000 0.776 0.000 0.000 0.224
#> GSM2876 1 0.0290 0.855 0.992 0.000 0.000 0.000 0.008
#> GSM2891 1 0.0290 0.855 0.992 0.000 0.000 0.000 0.008
#> GSM2880 1 0.0000 0.864 1.000 0.000 0.000 0.000 0.000
#> GSM2893 1 0.0000 0.864 1.000 0.000 0.000 0.000 0.000
#> GSM2821 5 0.4287 0.809 0.460 0.000 0.000 0.000 0.540
#> GSM2900 5 0.4287 0.809 0.460 0.000 0.000 0.000 0.540
#> GSM2903 5 0.4287 0.809 0.460 0.000 0.000 0.000 0.540
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM2819 5 0.5341 0.7312 0.140 0.136 0.000 0.000 0.676 0.048
#> GSM2820 3 0.0000 0.9872 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2822 2 0.5972 -0.0427 0.000 0.452 0.000 0.004 0.200 0.344
#> GSM2832 2 0.5972 -0.0427 0.000 0.452 0.000 0.004 0.200 0.344
#> GSM2823 5 0.4839 0.8125 0.228 0.072 0.020 0.000 0.680 0.000
#> GSM2824 5 0.4839 0.8125 0.228 0.072 0.020 0.000 0.680 0.000
#> GSM2825 2 0.7446 -0.1377 0.244 0.396 0.000 0.008 0.244 0.108
#> GSM2826 2 0.7446 -0.1377 0.244 0.396 0.000 0.008 0.244 0.108
#> GSM2829 4 0.1921 0.9249 0.000 0.052 0.000 0.916 0.032 0.000
#> GSM2856 4 0.1921 0.9249 0.000 0.052 0.000 0.916 0.032 0.000
#> GSM2830 4 0.1092 0.9368 0.000 0.020 0.000 0.960 0.020 0.000
#> GSM2843 4 0.1092 0.9368 0.000 0.020 0.000 0.960 0.020 0.000
#> GSM2871 4 0.1176 0.9357 0.000 0.024 0.000 0.956 0.020 0.000
#> GSM2831 4 0.0146 0.9399 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM2844 4 0.0146 0.9399 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM2833 4 0.2308 0.9152 0.000 0.068 0.000 0.892 0.040 0.000
#> GSM2846 4 0.2308 0.9152 0.000 0.068 0.000 0.892 0.040 0.000
#> GSM2835 4 0.2442 0.9112 0.000 0.068 0.000 0.884 0.048 0.000
#> GSM2858 4 0.2442 0.9112 0.000 0.068 0.000 0.884 0.048 0.000
#> GSM2836 6 0.3042 0.7294 0.000 0.128 0.000 0.004 0.032 0.836
#> GSM2848 6 0.3155 0.7260 0.000 0.132 0.000 0.004 0.036 0.828
#> GSM2828 3 0.0000 0.9872 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2837 3 0.0000 0.9872 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2839 1 0.4237 0.7066 0.736 0.144 0.000 0.000 0.120 0.000
#> GSM2841 1 0.4237 0.7066 0.736 0.144 0.000 0.000 0.120 0.000
#> GSM2827 2 0.5044 0.3898 0.000 0.536 0.000 0.000 0.080 0.384
#> GSM2842 2 0.4905 0.4455 0.000 0.580 0.000 0.000 0.076 0.344
#> GSM2845 4 0.1176 0.9357 0.000 0.024 0.000 0.956 0.020 0.000
#> GSM2872 4 0.1176 0.9357 0.000 0.024 0.000 0.956 0.020 0.000
#> GSM2834 4 0.1261 0.9366 0.000 0.024 0.000 0.952 0.024 0.000
#> GSM2847 4 0.1261 0.9366 0.000 0.024 0.000 0.952 0.024 0.000
#> GSM2849 3 0.0000 0.9872 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2850 3 0.0000 0.9872 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2838 2 0.3843 0.5745 0.000 0.548 0.000 0.000 0.000 0.452
#> GSM2853 2 0.3843 0.5745 0.000 0.548 0.000 0.000 0.000 0.452
#> GSM2852 3 0.0146 0.9846 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM2855 3 0.0146 0.9846 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM2840 1 0.4237 0.7066 0.736 0.144 0.000 0.000 0.120 0.000
#> GSM2857 1 0.4237 0.7066 0.736 0.144 0.000 0.000 0.120 0.000
#> GSM2859 6 0.0000 0.8714 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM2860 6 0.0000 0.8714 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM2861 6 0.1610 0.7267 0.000 0.084 0.000 0.000 0.000 0.916
#> GSM2862 6 0.0000 0.8714 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM2863 6 0.0000 0.8714 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM2864 6 0.0000 0.8714 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM2865 6 0.0000 0.8714 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM2866 6 0.0000 0.8714 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM2868 2 0.3843 0.5745 0.000 0.548 0.000 0.000 0.000 0.452
#> GSM2869 2 0.3843 0.5745 0.000 0.548 0.000 0.000 0.000 0.452
#> GSM2851 2 0.3843 0.5745 0.000 0.548 0.000 0.000 0.000 0.452
#> GSM2867 2 0.3843 0.5745 0.000 0.548 0.000 0.000 0.000 0.452
#> GSM2870 2 0.3843 0.5745 0.000 0.548 0.000 0.000 0.000 0.452
#> GSM2854 4 0.3123 0.8705 0.000 0.112 0.000 0.832 0.056 0.000
#> GSM2873 6 0.4796 0.4559 0.000 0.260 0.000 0.004 0.084 0.652
#> GSM2874 3 0.0000 0.9872 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2884 3 0.0000 0.9872 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2875 1 0.0000 0.8961 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2890 1 0.0000 0.8961 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2877 1 0.0000 0.8961 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2892 1 0.0000 0.8961 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2902 1 0.0000 0.8961 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2878 1 0.0000 0.8961 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2901 1 0.0000 0.8961 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2879 3 0.2361 0.8860 0.000 0.028 0.884 0.000 0.088 0.000
#> GSM2898 3 0.2361 0.8860 0.000 0.028 0.884 0.000 0.088 0.000
#> GSM2881 3 0.0000 0.9872 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2897 3 0.0000 0.9872 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2882 4 0.0291 0.9400 0.000 0.004 0.000 0.992 0.004 0.000
#> GSM2894 4 0.0291 0.9400 0.000 0.004 0.000 0.992 0.004 0.000
#> GSM2883 3 0.0000 0.9872 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2895 3 0.0000 0.9872 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2885 3 0.0000 0.9872 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2886 3 0.0000 0.9872 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2887 3 0.0000 0.9872 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2896 3 0.0000 0.9872 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2888 2 0.4157 0.5611 0.000 0.544 0.000 0.000 0.012 0.444
#> GSM2889 2 0.4157 0.5611 0.000 0.544 0.000 0.000 0.012 0.444
#> GSM2876 1 0.0260 0.8911 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM2891 1 0.0260 0.8911 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM2880 1 0.0000 0.8961 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2893 1 0.0000 0.8961 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2821 5 0.3547 0.8237 0.332 0.000 0.000 0.000 0.668 0.000
#> GSM2900 5 0.3547 0.8237 0.332 0.000 0.000 0.000 0.668 0.000
#> GSM2903 5 0.3547 0.8237 0.332 0.000 0.000 0.000 0.668 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 tissue(p) k
#> MAD:skmeans 83 3.39e-05 2
#> MAD:skmeans 64 1.46e-07 3
#> MAD:skmeans 83 4.22e-12 4
#> MAD:skmeans 82 3.49e-15 5
#> MAD:skmeans 77 8.02e-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["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 8229 rows and 84 columns.
#> Top rows (823, 1646, 2468, 3291, 4114) 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 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.491 0.806 0.827 0.3457 0.646 0.646
#> 3 3 1.000 0.984 0.994 0.7006 0.766 0.637
#> 4 4 0.862 0.805 0.930 0.2623 0.837 0.605
#> 5 5 0.925 0.831 0.932 0.0346 0.917 0.707
#> 6 6 0.876 0.820 0.914 0.0199 0.987 0.946
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] 3
There is also optional best \(k\) = 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM2819 1 0.9710 0.820 0.600 0.400
#> GSM2820 2 0.0000 0.999 0.000 1.000
#> GSM2822 1 0.9710 0.820 0.600 0.400
#> GSM2832 1 0.9710 0.820 0.600 0.400
#> GSM2823 1 0.9710 0.820 0.600 0.400
#> GSM2824 1 0.9710 0.820 0.600 0.400
#> GSM2825 1 0.9686 0.817 0.604 0.396
#> GSM2826 1 0.9686 0.817 0.604 0.396
#> GSM2829 1 0.9710 0.820 0.600 0.400
#> GSM2856 1 0.9710 0.820 0.600 0.400
#> GSM2830 1 0.9710 0.820 0.600 0.400
#> GSM2843 1 0.9710 0.820 0.600 0.400
#> GSM2871 1 0.9710 0.820 0.600 0.400
#> GSM2831 1 0.9710 0.820 0.600 0.400
#> GSM2844 1 0.9710 0.820 0.600 0.400
#> GSM2833 1 0.9710 0.820 0.600 0.400
#> GSM2846 1 0.9710 0.820 0.600 0.400
#> GSM2835 1 0.9710 0.820 0.600 0.400
#> GSM2858 1 0.9710 0.820 0.600 0.400
#> GSM2836 1 0.9710 0.820 0.600 0.400
#> GSM2848 1 0.9710 0.820 0.600 0.400
#> GSM2828 2 0.0000 0.999 0.000 1.000
#> GSM2837 2 0.0000 0.999 0.000 1.000
#> GSM2839 1 0.0000 0.560 1.000 0.000
#> GSM2841 1 0.0000 0.560 1.000 0.000
#> GSM2827 1 0.9710 0.820 0.600 0.400
#> GSM2842 1 0.9710 0.820 0.600 0.400
#> GSM2845 1 0.9710 0.820 0.600 0.400
#> GSM2872 1 0.9710 0.820 0.600 0.400
#> GSM2834 1 0.9710 0.820 0.600 0.400
#> GSM2847 1 0.9710 0.820 0.600 0.400
#> GSM2849 2 0.0000 0.999 0.000 1.000
#> GSM2850 2 0.0000 0.999 0.000 1.000
#> GSM2838 1 0.9710 0.820 0.600 0.400
#> GSM2853 1 0.9710 0.820 0.600 0.400
#> GSM2852 2 0.0000 0.999 0.000 1.000
#> GSM2855 2 0.0000 0.999 0.000 1.000
#> GSM2840 1 0.0000 0.560 1.000 0.000
#> GSM2857 1 0.0000 0.560 1.000 0.000
#> GSM2859 1 0.9710 0.820 0.600 0.400
#> GSM2860 1 0.9710 0.820 0.600 0.400
#> GSM2861 1 0.9710 0.820 0.600 0.400
#> GSM2862 1 0.9710 0.820 0.600 0.400
#> GSM2863 1 0.9710 0.820 0.600 0.400
#> GSM2864 1 0.9710 0.820 0.600 0.400
#> GSM2865 1 0.9710 0.820 0.600 0.400
#> GSM2866 1 0.9710 0.820 0.600 0.400
#> GSM2868 1 0.9710 0.820 0.600 0.400
#> GSM2869 1 0.9710 0.820 0.600 0.400
#> GSM2851 1 0.9710 0.820 0.600 0.400
#> GSM2867 1 0.9710 0.820 0.600 0.400
#> GSM2870 1 0.9710 0.820 0.600 0.400
#> GSM2854 1 0.9710 0.820 0.600 0.400
#> GSM2873 1 0.9710 0.820 0.600 0.400
#> GSM2874 2 0.0000 0.999 0.000 1.000
#> GSM2884 2 0.0000 0.999 0.000 1.000
#> GSM2875 1 0.0000 0.560 1.000 0.000
#> GSM2890 1 0.0000 0.560 1.000 0.000
#> GSM2877 1 0.0000 0.560 1.000 0.000
#> GSM2892 1 0.0000 0.560 1.000 0.000
#> GSM2902 1 0.0000 0.560 1.000 0.000
#> GSM2878 1 0.0000 0.560 1.000 0.000
#> GSM2901 1 0.0000 0.560 1.000 0.000
#> GSM2879 2 0.0376 0.993 0.004 0.996
#> GSM2898 2 0.0938 0.981 0.012 0.988
#> GSM2881 2 0.0000 0.999 0.000 1.000
#> GSM2897 2 0.0000 0.999 0.000 1.000
#> GSM2882 1 0.9710 0.820 0.600 0.400
#> GSM2894 1 0.9710 0.820 0.600 0.400
#> GSM2883 2 0.0000 0.999 0.000 1.000
#> GSM2895 2 0.0000 0.999 0.000 1.000
#> GSM2885 2 0.0000 0.999 0.000 1.000
#> GSM2886 2 0.0000 0.999 0.000 1.000
#> GSM2887 2 0.0000 0.999 0.000 1.000
#> GSM2896 2 0.0000 0.999 0.000 1.000
#> GSM2888 1 0.9710 0.820 0.600 0.400
#> GSM2889 1 0.9710 0.820 0.600 0.400
#> GSM2876 1 0.0000 0.560 1.000 0.000
#> GSM2891 1 0.0000 0.560 1.000 0.000
#> GSM2880 1 0.0000 0.560 1.000 0.000
#> GSM2893 1 0.0000 0.560 1.000 0.000
#> GSM2821 1 0.8016 0.702 0.756 0.244
#> GSM2900 1 0.0672 0.564 0.992 0.008
#> GSM2903 1 0.0938 0.566 0.988 0.012
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM2819 2 0.000 0.995 0.000 1.000 0
#> GSM2820 3 0.000 1.000 0.000 0.000 1
#> GSM2822 2 0.000 0.995 0.000 1.000 0
#> GSM2832 2 0.000 0.995 0.000 1.000 0
#> GSM2823 2 0.000 0.995 0.000 1.000 0
#> GSM2824 2 0.000 0.995 0.000 1.000 0
#> GSM2825 2 0.000 0.995 0.000 1.000 0
#> GSM2826 2 0.000 0.995 0.000 1.000 0
#> GSM2829 2 0.000 0.995 0.000 1.000 0
#> GSM2856 2 0.000 0.995 0.000 1.000 0
#> GSM2830 2 0.000 0.995 0.000 1.000 0
#> GSM2843 2 0.000 0.995 0.000 1.000 0
#> GSM2871 2 0.000 0.995 0.000 1.000 0
#> GSM2831 2 0.000 0.995 0.000 1.000 0
#> GSM2844 2 0.000 0.995 0.000 1.000 0
#> GSM2833 2 0.000 0.995 0.000 1.000 0
#> GSM2846 2 0.000 0.995 0.000 1.000 0
#> GSM2835 2 0.000 0.995 0.000 1.000 0
#> GSM2858 2 0.000 0.995 0.000 1.000 0
#> GSM2836 2 0.000 0.995 0.000 1.000 0
#> GSM2848 2 0.000 0.995 0.000 1.000 0
#> GSM2828 3 0.000 1.000 0.000 0.000 1
#> GSM2837 3 0.000 1.000 0.000 0.000 1
#> GSM2839 1 0.000 0.974 1.000 0.000 0
#> GSM2841 1 0.000 0.974 1.000 0.000 0
#> GSM2827 2 0.000 0.995 0.000 1.000 0
#> GSM2842 2 0.000 0.995 0.000 1.000 0
#> GSM2845 2 0.000 0.995 0.000 1.000 0
#> GSM2872 2 0.000 0.995 0.000 1.000 0
#> GSM2834 2 0.000 0.995 0.000 1.000 0
#> GSM2847 2 0.000 0.995 0.000 1.000 0
#> GSM2849 3 0.000 1.000 0.000 0.000 1
#> GSM2850 3 0.000 1.000 0.000 0.000 1
#> GSM2838 2 0.000 0.995 0.000 1.000 0
#> GSM2853 2 0.000 0.995 0.000 1.000 0
#> GSM2852 3 0.000 1.000 0.000 0.000 1
#> GSM2855 3 0.000 1.000 0.000 0.000 1
#> GSM2840 1 0.000 0.974 1.000 0.000 0
#> GSM2857 1 0.000 0.974 1.000 0.000 0
#> GSM2859 2 0.000 0.995 0.000 1.000 0
#> GSM2860 2 0.000 0.995 0.000 1.000 0
#> GSM2861 2 0.000 0.995 0.000 1.000 0
#> GSM2862 2 0.000 0.995 0.000 1.000 0
#> GSM2863 2 0.000 0.995 0.000 1.000 0
#> GSM2864 2 0.000 0.995 0.000 1.000 0
#> GSM2865 2 0.000 0.995 0.000 1.000 0
#> GSM2866 2 0.000 0.995 0.000 1.000 0
#> GSM2868 2 0.000 0.995 0.000 1.000 0
#> GSM2869 2 0.000 0.995 0.000 1.000 0
#> GSM2851 2 0.000 0.995 0.000 1.000 0
#> GSM2867 2 0.000 0.995 0.000 1.000 0
#> GSM2870 2 0.000 0.995 0.000 1.000 0
#> GSM2854 2 0.000 0.995 0.000 1.000 0
#> GSM2873 2 0.000 0.995 0.000 1.000 0
#> GSM2874 3 0.000 1.000 0.000 0.000 1
#> GSM2884 3 0.000 1.000 0.000 0.000 1
#> GSM2875 1 0.000 0.974 1.000 0.000 0
#> GSM2890 1 0.000 0.974 1.000 0.000 0
#> GSM2877 1 0.000 0.974 1.000 0.000 0
#> GSM2892 1 0.000 0.974 1.000 0.000 0
#> GSM2902 1 0.000 0.974 1.000 0.000 0
#> GSM2878 1 0.000 0.974 1.000 0.000 0
#> GSM2901 1 0.000 0.974 1.000 0.000 0
#> GSM2879 3 0.000 1.000 0.000 0.000 1
#> GSM2898 3 0.000 1.000 0.000 0.000 1
#> GSM2881 3 0.000 1.000 0.000 0.000 1
#> GSM2897 3 0.000 1.000 0.000 0.000 1
#> GSM2882 2 0.000 0.995 0.000 1.000 0
#> GSM2894 2 0.000 0.995 0.000 1.000 0
#> GSM2883 3 0.000 1.000 0.000 0.000 1
#> GSM2895 3 0.000 1.000 0.000 0.000 1
#> GSM2885 3 0.000 1.000 0.000 0.000 1
#> GSM2886 3 0.000 1.000 0.000 0.000 1
#> GSM2887 3 0.000 1.000 0.000 0.000 1
#> GSM2896 3 0.000 1.000 0.000 0.000 1
#> GSM2888 2 0.000 0.995 0.000 1.000 0
#> GSM2889 2 0.000 0.995 0.000 1.000 0
#> GSM2876 1 0.000 0.974 1.000 0.000 0
#> GSM2891 1 0.000 0.974 1.000 0.000 0
#> GSM2880 1 0.000 0.974 1.000 0.000 0
#> GSM2893 1 0.000 0.974 1.000 0.000 0
#> GSM2821 2 0.484 0.702 0.224 0.776 0
#> GSM2900 1 0.348 0.828 0.872 0.128 0
#> GSM2903 1 0.424 0.765 0.824 0.176 0
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM2819 2 0.2704 0.7654 0.000 0.876 0 0.124
#> GSM2820 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM2822 4 0.5000 0.0517 0.000 0.496 0 0.504
#> GSM2832 2 0.5000 -0.1150 0.000 0.500 0 0.500
#> GSM2823 4 0.5000 0.0517 0.000 0.496 0 0.504
#> GSM2824 2 0.4992 -0.0271 0.000 0.524 0 0.476
#> GSM2825 4 0.5000 0.0517 0.000 0.496 0 0.504
#> GSM2826 2 0.5000 -0.1008 0.000 0.504 0 0.496
#> GSM2829 4 0.0000 0.8289 0.000 0.000 0 1.000
#> GSM2856 4 0.0000 0.8289 0.000 0.000 0 1.000
#> GSM2830 4 0.0000 0.8289 0.000 0.000 0 1.000
#> GSM2843 4 0.0000 0.8289 0.000 0.000 0 1.000
#> GSM2871 2 0.4992 -0.0236 0.000 0.524 0 0.476
#> GSM2831 4 0.0000 0.8289 0.000 0.000 0 1.000
#> GSM2844 4 0.0000 0.8289 0.000 0.000 0 1.000
#> GSM2833 4 0.0000 0.8289 0.000 0.000 0 1.000
#> GSM2846 4 0.0000 0.8289 0.000 0.000 0 1.000
#> GSM2835 4 0.0000 0.8289 0.000 0.000 0 1.000
#> GSM2858 4 0.0000 0.8289 0.000 0.000 0 1.000
#> GSM2836 2 0.2081 0.8041 0.000 0.916 0 0.084
#> GSM2848 2 0.3266 0.7100 0.000 0.832 0 0.168
#> GSM2828 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM2837 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM2839 1 0.0000 0.9777 1.000 0.000 0 0.000
#> GSM2841 1 0.0000 0.9777 1.000 0.000 0 0.000
#> GSM2827 2 0.0000 0.8699 0.000 1.000 0 0.000
#> GSM2842 2 0.0188 0.8676 0.000 0.996 0 0.004
#> GSM2845 4 0.4679 0.4225 0.000 0.352 0 0.648
#> GSM2872 4 0.0000 0.8289 0.000 0.000 0 1.000
#> GSM2834 4 0.4761 0.3827 0.000 0.372 0 0.628
#> GSM2847 4 0.0000 0.8289 0.000 0.000 0 1.000
#> GSM2849 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM2850 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM2838 2 0.0000 0.8699 0.000 1.000 0 0.000
#> GSM2853 2 0.0000 0.8699 0.000 1.000 0 0.000
#> GSM2852 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM2855 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM2840 1 0.0000 0.9777 1.000 0.000 0 0.000
#> GSM2857 1 0.0000 0.9777 1.000 0.000 0 0.000
#> GSM2859 2 0.0000 0.8699 0.000 1.000 0 0.000
#> GSM2860 2 0.0000 0.8699 0.000 1.000 0 0.000
#> GSM2861 2 0.0000 0.8699 0.000 1.000 0 0.000
#> GSM2862 2 0.0000 0.8699 0.000 1.000 0 0.000
#> GSM2863 2 0.0000 0.8699 0.000 1.000 0 0.000
#> GSM2864 2 0.0000 0.8699 0.000 1.000 0 0.000
#> GSM2865 2 0.0000 0.8699 0.000 1.000 0 0.000
#> GSM2866 2 0.0000 0.8699 0.000 1.000 0 0.000
#> GSM2868 2 0.0000 0.8699 0.000 1.000 0 0.000
#> GSM2869 2 0.0000 0.8699 0.000 1.000 0 0.000
#> GSM2851 2 0.0000 0.8699 0.000 1.000 0 0.000
#> GSM2867 2 0.0000 0.8699 0.000 1.000 0 0.000
#> GSM2870 2 0.0000 0.8699 0.000 1.000 0 0.000
#> GSM2854 4 0.1389 0.7966 0.000 0.048 0 0.952
#> GSM2873 4 0.5000 0.0517 0.000 0.496 0 0.504
#> GSM2874 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM2884 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM2875 1 0.0000 0.9777 1.000 0.000 0 0.000
#> GSM2890 1 0.0000 0.9777 1.000 0.000 0 0.000
#> GSM2877 1 0.0000 0.9777 1.000 0.000 0 0.000
#> GSM2892 1 0.0000 0.9777 1.000 0.000 0 0.000
#> GSM2902 1 0.0000 0.9777 1.000 0.000 0 0.000
#> GSM2878 1 0.0000 0.9777 1.000 0.000 0 0.000
#> GSM2901 1 0.0000 0.9777 1.000 0.000 0 0.000
#> GSM2879 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM2898 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM2881 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM2897 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM2882 4 0.0000 0.8289 0.000 0.000 0 1.000
#> GSM2894 4 0.0000 0.8289 0.000 0.000 0 1.000
#> GSM2883 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM2895 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM2885 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM2886 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM2887 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM2896 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM2888 2 0.0188 0.8676 0.000 0.996 0 0.004
#> GSM2889 2 0.0000 0.8699 0.000 1.000 0 0.000
#> GSM2876 1 0.0000 0.9777 1.000 0.000 0 0.000
#> GSM2891 1 0.0000 0.9777 1.000 0.000 0 0.000
#> GSM2880 1 0.0000 0.9777 1.000 0.000 0 0.000
#> GSM2893 1 0.0000 0.9777 1.000 0.000 0 0.000
#> GSM2821 2 0.7010 0.3863 0.184 0.576 0 0.240
#> GSM2900 1 0.4259 0.8129 0.816 0.128 0 0.056
#> GSM2903 1 0.4410 0.7885 0.808 0.064 0 0.128
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM2819 5 0.1741 0.920 0.000 0.040 0 0.024 0.936
#> GSM2820 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM2822 2 0.4304 0.191 0.000 0.516 0 0.484 0.000
#> GSM2832 2 0.4302 0.202 0.000 0.520 0 0.480 0.000
#> GSM2823 2 0.4560 0.175 0.000 0.508 0 0.484 0.008
#> GSM2824 4 0.6779 0.113 0.000 0.300 0 0.392 0.308
#> GSM2825 2 0.4304 0.191 0.000 0.516 0 0.484 0.000
#> GSM2826 2 0.4300 0.212 0.000 0.524 0 0.476 0.000
#> GSM2829 4 0.0000 0.896 0.000 0.000 0 1.000 0.000
#> GSM2856 4 0.0000 0.896 0.000 0.000 0 1.000 0.000
#> GSM2830 4 0.0000 0.896 0.000 0.000 0 1.000 0.000
#> GSM2843 4 0.0000 0.896 0.000 0.000 0 1.000 0.000
#> GSM2871 2 0.4294 0.227 0.000 0.532 0 0.468 0.000
#> GSM2831 4 0.0000 0.896 0.000 0.000 0 1.000 0.000
#> GSM2844 4 0.0000 0.896 0.000 0.000 0 1.000 0.000
#> GSM2833 4 0.0000 0.896 0.000 0.000 0 1.000 0.000
#> GSM2846 4 0.0000 0.896 0.000 0.000 0 1.000 0.000
#> GSM2835 4 0.0000 0.896 0.000 0.000 0 1.000 0.000
#> GSM2858 4 0.0000 0.896 0.000 0.000 0 1.000 0.000
#> GSM2836 2 0.1792 0.773 0.000 0.916 0 0.084 0.000
#> GSM2848 2 0.2690 0.718 0.000 0.844 0 0.156 0.000
#> GSM2828 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM2837 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM2839 1 0.1478 0.957 0.936 0.000 0 0.000 0.064
#> GSM2841 1 0.1478 0.957 0.936 0.000 0 0.000 0.064
#> GSM2827 2 0.0162 0.819 0.000 0.996 0 0.000 0.004
#> GSM2842 2 0.0771 0.818 0.000 0.976 0 0.004 0.020
#> GSM2845 4 0.4015 0.341 0.000 0.348 0 0.652 0.000
#> GSM2872 4 0.0000 0.896 0.000 0.000 0 1.000 0.000
#> GSM2834 4 0.4138 0.229 0.000 0.384 0 0.616 0.000
#> GSM2847 4 0.0000 0.896 0.000 0.000 0 1.000 0.000
#> GSM2849 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM2850 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM2838 2 0.0609 0.818 0.000 0.980 0 0.000 0.020
#> GSM2853 2 0.0609 0.818 0.000 0.980 0 0.000 0.020
#> GSM2852 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM2855 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM2840 1 0.1478 0.957 0.936 0.000 0 0.000 0.064
#> GSM2857 1 0.1478 0.957 0.936 0.000 0 0.000 0.064
#> GSM2859 2 0.0000 0.818 0.000 1.000 0 0.000 0.000
#> GSM2860 2 0.0000 0.818 0.000 1.000 0 0.000 0.000
#> GSM2861 2 0.0000 0.818 0.000 1.000 0 0.000 0.000
#> GSM2862 2 0.0000 0.818 0.000 1.000 0 0.000 0.000
#> GSM2863 2 0.0000 0.818 0.000 1.000 0 0.000 0.000
#> GSM2864 2 0.0000 0.818 0.000 1.000 0 0.000 0.000
#> GSM2865 2 0.0000 0.818 0.000 1.000 0 0.000 0.000
#> GSM2866 2 0.0000 0.818 0.000 1.000 0 0.000 0.000
#> GSM2868 2 0.0609 0.818 0.000 0.980 0 0.000 0.020
#> GSM2869 2 0.0609 0.818 0.000 0.980 0 0.000 0.020
#> GSM2851 2 0.0609 0.818 0.000 0.980 0 0.000 0.020
#> GSM2867 2 0.0609 0.818 0.000 0.980 0 0.000 0.020
#> GSM2870 2 0.0609 0.818 0.000 0.980 0 0.000 0.020
#> GSM2854 4 0.1197 0.850 0.000 0.048 0 0.952 0.000
#> GSM2873 2 0.4304 0.191 0.000 0.516 0 0.484 0.000
#> GSM2874 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM2884 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM2875 1 0.0000 0.972 1.000 0.000 0 0.000 0.000
#> GSM2890 1 0.0000 0.972 1.000 0.000 0 0.000 0.000
#> GSM2877 1 0.0000 0.972 1.000 0.000 0 0.000 0.000
#> GSM2892 1 0.0000 0.972 1.000 0.000 0 0.000 0.000
#> GSM2902 1 0.0000 0.972 1.000 0.000 0 0.000 0.000
#> GSM2878 1 0.0000 0.972 1.000 0.000 0 0.000 0.000
#> GSM2901 1 0.0000 0.972 1.000 0.000 0 0.000 0.000
#> GSM2879 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM2898 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM2881 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM2897 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM2882 4 0.0000 0.896 0.000 0.000 0 1.000 0.000
#> GSM2894 4 0.0000 0.896 0.000 0.000 0 1.000 0.000
#> GSM2883 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM2895 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM2885 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM2886 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM2887 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM2896 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM2888 2 0.0771 0.818 0.000 0.976 0 0.004 0.020
#> GSM2889 2 0.0609 0.818 0.000 0.980 0 0.000 0.020
#> GSM2876 1 0.1478 0.957 0.936 0.000 0 0.000 0.064
#> GSM2891 1 0.1478 0.957 0.936 0.000 0 0.000 0.064
#> GSM2880 1 0.0000 0.972 1.000 0.000 0 0.000 0.000
#> GSM2893 1 0.0000 0.972 1.000 0.000 0 0.000 0.000
#> GSM2821 5 0.0000 0.962 0.000 0.000 0 0.000 1.000
#> GSM2900 5 0.0510 0.964 0.016 0.000 0 0.000 0.984
#> GSM2903 5 0.0510 0.964 0.016 0.000 0 0.000 0.984
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM2819 5 0.0363 0.9824 0.000 0.012 0.000 0.000 0.988 0.000
#> GSM2820 3 0.0000 0.9995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2822 2 0.3997 0.2049 0.000 0.508 0.000 0.488 0.000 0.004
#> GSM2832 2 0.3866 0.2160 0.000 0.516 0.000 0.484 0.000 0.000
#> GSM2823 2 0.4097 0.1912 0.000 0.504 0.000 0.488 0.008 0.000
#> GSM2824 4 0.6317 0.0319 0.000 0.308 0.000 0.376 0.308 0.008
#> GSM2825 2 0.4184 0.1844 0.000 0.500 0.000 0.488 0.000 0.012
#> GSM2826 2 0.4183 0.2080 0.000 0.508 0.000 0.480 0.000 0.012
#> GSM2829 4 0.0000 0.8958 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2856 4 0.0000 0.8958 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2830 4 0.0000 0.8958 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2843 4 0.0000 0.8958 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2871 2 0.4175 0.2547 0.000 0.524 0.000 0.464 0.000 0.012
#> GSM2831 4 0.0000 0.8958 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2844 4 0.0000 0.8958 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2833 4 0.0000 0.8958 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2846 4 0.0000 0.8958 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2835 4 0.0000 0.8958 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2858 4 0.0000 0.8958 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2836 2 0.3372 0.7582 0.000 0.816 0.000 0.084 0.000 0.100
#> GSM2848 2 0.3920 0.7162 0.000 0.764 0.000 0.148 0.000 0.088
#> GSM2828 3 0.0000 0.9995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2837 3 0.0000 0.9995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2839 6 0.2346 1.0000 0.124 0.000 0.000 0.000 0.008 0.868
#> GSM2841 6 0.2346 1.0000 0.124 0.000 0.000 0.000 0.008 0.868
#> GSM2827 2 0.1663 0.7853 0.000 0.912 0.000 0.000 0.000 0.088
#> GSM2842 2 0.0405 0.7843 0.000 0.988 0.000 0.004 0.000 0.008
#> GSM2845 4 0.3620 0.3050 0.000 0.352 0.000 0.648 0.000 0.000
#> GSM2872 4 0.0000 0.8958 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2834 4 0.3717 0.1959 0.000 0.384 0.000 0.616 0.000 0.000
#> GSM2847 4 0.0000 0.8958 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2849 3 0.0000 0.9995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2850 3 0.0000 0.9995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2838 2 0.0363 0.7837 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM2853 2 0.0363 0.7837 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM2852 3 0.0260 0.9907 0.000 0.008 0.992 0.000 0.000 0.000
#> GSM2855 3 0.0000 0.9995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2840 6 0.2346 1.0000 0.124 0.000 0.000 0.000 0.008 0.868
#> GSM2857 6 0.2346 1.0000 0.124 0.000 0.000 0.000 0.008 0.868
#> GSM2859 2 0.2048 0.7832 0.000 0.880 0.000 0.000 0.000 0.120
#> GSM2860 2 0.2048 0.7832 0.000 0.880 0.000 0.000 0.000 0.120
#> GSM2861 2 0.2048 0.7832 0.000 0.880 0.000 0.000 0.000 0.120
#> GSM2862 2 0.2048 0.7832 0.000 0.880 0.000 0.000 0.000 0.120
#> GSM2863 2 0.2048 0.7832 0.000 0.880 0.000 0.000 0.000 0.120
#> GSM2864 2 0.2048 0.7832 0.000 0.880 0.000 0.000 0.000 0.120
#> GSM2865 2 0.2048 0.7832 0.000 0.880 0.000 0.000 0.000 0.120
#> GSM2866 2 0.2048 0.7832 0.000 0.880 0.000 0.000 0.000 0.120
#> GSM2868 2 0.0363 0.7837 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM2869 2 0.0363 0.7837 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM2851 2 0.0363 0.7837 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM2867 2 0.0363 0.7837 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM2870 2 0.0363 0.7837 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM2854 4 0.1075 0.8510 0.000 0.048 0.000 0.952 0.000 0.000
#> GSM2873 2 0.3867 0.2051 0.000 0.512 0.000 0.488 0.000 0.000
#> GSM2874 3 0.0000 0.9995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2884 3 0.0000 0.9995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2875 1 0.0000 0.9605 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2890 1 0.0000 0.9605 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2877 1 0.0000 0.9605 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2892 1 0.0000 0.9605 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2902 1 0.0000 0.9605 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2878 1 0.0000 0.9605 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2901 1 0.0000 0.9605 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2879 3 0.0000 0.9995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2898 3 0.0000 0.9995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2881 3 0.0000 0.9995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2897 3 0.0000 0.9995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2882 4 0.0000 0.8958 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2894 4 0.0000 0.8958 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2883 3 0.0000 0.9995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2895 3 0.0000 0.9995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2885 3 0.0000 0.9995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2886 3 0.0000 0.9995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2887 3 0.0000 0.9995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2896 3 0.0000 0.9995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2888 2 0.0363 0.7837 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM2889 2 0.0363 0.7837 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM2876 1 0.2669 0.7919 0.836 0.000 0.000 0.000 0.008 0.156
#> GSM2891 1 0.2706 0.7865 0.832 0.000 0.000 0.000 0.008 0.160
#> GSM2880 1 0.0000 0.9605 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2893 1 0.0000 0.9605 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2821 5 0.0000 0.9941 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM2900 5 0.0000 0.9941 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM2903 5 0.0000 0.9941 0.000 0.000 0.000 0.000 1.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> MAD:pam 84 2.53e-05 2
#> MAD:pam 84 2.34e-08 3
#> MAD:pam 73 4.97e-10 4
#> MAD:pam 74 3.22e-13 5
#> MAD:pam 74 4.81e-16 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 8229 rows and 84 columns.
#> Top rows (823, 1646, 2468, 3291, 4114) are extracted by 'MAD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.279 0.886 0.894 0.5045 0.497 0.497
#> 3 3 0.981 0.919 0.954 0.2655 0.824 0.659
#> 4 4 0.718 0.779 0.886 0.1384 0.803 0.517
#> 5 5 0.830 0.643 0.827 0.0875 0.936 0.761
#> 6 6 0.849 0.672 0.846 0.0387 0.906 0.607
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM2819 1 0.7674 0.815 0.776 0.224
#> GSM2820 2 0.5178 0.897 0.116 0.884
#> GSM2822 1 0.5629 0.877 0.868 0.132
#> GSM2832 1 0.5629 0.877 0.868 0.132
#> GSM2823 2 0.0376 0.867 0.004 0.996
#> GSM2824 2 0.0376 0.867 0.004 0.996
#> GSM2825 1 0.8555 0.711 0.720 0.280
#> GSM2826 1 0.8555 0.711 0.720 0.280
#> GSM2829 1 0.0000 0.893 1.000 0.000
#> GSM2856 1 0.0000 0.893 1.000 0.000
#> GSM2830 1 0.0000 0.893 1.000 0.000
#> GSM2843 1 0.0000 0.893 1.000 0.000
#> GSM2871 1 0.0000 0.893 1.000 0.000
#> GSM2831 1 0.0000 0.893 1.000 0.000
#> GSM2844 1 0.0000 0.893 1.000 0.000
#> GSM2833 1 0.0000 0.893 1.000 0.000
#> GSM2846 1 0.0000 0.893 1.000 0.000
#> GSM2835 1 0.0000 0.893 1.000 0.000
#> GSM2858 1 0.0000 0.893 1.000 0.000
#> GSM2836 1 0.6048 0.883 0.852 0.148
#> GSM2848 1 0.6247 0.885 0.844 0.156
#> GSM2828 2 0.5178 0.897 0.116 0.884
#> GSM2837 2 0.5178 0.897 0.116 0.884
#> GSM2839 2 0.4815 0.891 0.104 0.896
#> GSM2841 2 0.4815 0.891 0.104 0.896
#> GSM2827 1 0.2948 0.890 0.948 0.052
#> GSM2842 1 0.4690 0.894 0.900 0.100
#> GSM2845 1 0.0000 0.893 1.000 0.000
#> GSM2872 1 0.0000 0.893 1.000 0.000
#> GSM2834 1 0.0000 0.893 1.000 0.000
#> GSM2847 1 0.0000 0.893 1.000 0.000
#> GSM2849 2 0.5178 0.897 0.116 0.884
#> GSM2850 2 0.5178 0.897 0.116 0.884
#> GSM2838 1 0.7602 0.889 0.780 0.220
#> GSM2853 1 0.7602 0.889 0.780 0.220
#> GSM2852 2 0.5178 0.897 0.116 0.884
#> GSM2855 2 0.5178 0.897 0.116 0.884
#> GSM2840 2 0.4815 0.891 0.104 0.896
#> GSM2857 2 0.4815 0.891 0.104 0.896
#> GSM2859 1 0.7602 0.889 0.780 0.220
#> GSM2860 1 0.7602 0.889 0.780 0.220
#> GSM2861 1 0.7602 0.889 0.780 0.220
#> GSM2862 1 0.7602 0.889 0.780 0.220
#> GSM2863 1 0.7602 0.889 0.780 0.220
#> GSM2864 1 0.7602 0.889 0.780 0.220
#> GSM2865 1 0.7602 0.889 0.780 0.220
#> GSM2866 1 0.7602 0.889 0.780 0.220
#> GSM2868 1 0.7602 0.889 0.780 0.220
#> GSM2869 1 0.7602 0.889 0.780 0.220
#> GSM2851 1 0.7602 0.889 0.780 0.220
#> GSM2867 1 0.7602 0.889 0.780 0.220
#> GSM2870 1 0.7602 0.889 0.780 0.220
#> GSM2854 1 0.0000 0.893 1.000 0.000
#> GSM2873 1 0.3114 0.890 0.944 0.056
#> GSM2874 2 0.5178 0.897 0.116 0.884
#> GSM2884 2 0.5178 0.897 0.116 0.884
#> GSM2875 2 0.4815 0.891 0.104 0.896
#> GSM2890 2 0.4815 0.891 0.104 0.896
#> GSM2877 2 0.4815 0.891 0.104 0.896
#> GSM2892 2 0.4815 0.891 0.104 0.896
#> GSM2902 2 0.4815 0.891 0.104 0.896
#> GSM2878 2 0.4815 0.891 0.104 0.896
#> GSM2901 2 0.4815 0.891 0.104 0.896
#> GSM2879 2 0.5178 0.897 0.116 0.884
#> GSM2898 2 0.5178 0.897 0.116 0.884
#> GSM2881 2 0.5178 0.897 0.116 0.884
#> GSM2897 2 0.5178 0.897 0.116 0.884
#> GSM2882 1 0.0000 0.893 1.000 0.000
#> GSM2894 1 0.0000 0.893 1.000 0.000
#> GSM2883 2 0.5178 0.897 0.116 0.884
#> GSM2895 2 0.5178 0.897 0.116 0.884
#> GSM2885 2 0.5178 0.897 0.116 0.884
#> GSM2886 2 0.5178 0.897 0.116 0.884
#> GSM2887 2 0.5178 0.897 0.116 0.884
#> GSM2896 2 0.5178 0.897 0.116 0.884
#> GSM2888 1 0.7602 0.889 0.780 0.220
#> GSM2889 1 0.7602 0.889 0.780 0.220
#> GSM2876 2 0.4815 0.891 0.104 0.896
#> GSM2891 2 0.4815 0.891 0.104 0.896
#> GSM2880 2 0.4815 0.891 0.104 0.896
#> GSM2893 2 0.4815 0.891 0.104 0.896
#> GSM2821 2 0.4815 0.891 0.104 0.896
#> GSM2900 2 0.4815 0.891 0.104 0.896
#> GSM2903 2 0.4815 0.891 0.104 0.896
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM2819 1 0.1860 0.9149 0.948 0.052 0.000
#> GSM2820 3 0.1031 0.9402 0.024 0.000 0.976
#> GSM2822 1 0.6008 0.4148 0.628 0.372 0.000
#> GSM2832 2 0.6302 0.0193 0.480 0.520 0.000
#> GSM2823 3 0.6330 0.4748 0.396 0.004 0.600
#> GSM2824 3 0.6330 0.4748 0.396 0.004 0.600
#> GSM2825 1 0.2165 0.9041 0.936 0.064 0.000
#> GSM2826 1 0.2165 0.9041 0.936 0.064 0.000
#> GSM2829 2 0.0983 0.9632 0.004 0.980 0.016
#> GSM2856 2 0.0983 0.9632 0.004 0.980 0.016
#> GSM2830 2 0.0983 0.9632 0.004 0.980 0.016
#> GSM2843 2 0.0983 0.9632 0.004 0.980 0.016
#> GSM2871 2 0.0983 0.9632 0.004 0.980 0.016
#> GSM2831 2 0.0983 0.9632 0.004 0.980 0.016
#> GSM2844 2 0.0983 0.9632 0.004 0.980 0.016
#> GSM2833 2 0.0983 0.9632 0.004 0.980 0.016
#> GSM2846 2 0.0983 0.9632 0.004 0.980 0.016
#> GSM2835 2 0.0983 0.9632 0.004 0.980 0.016
#> GSM2858 2 0.0983 0.9632 0.004 0.980 0.016
#> GSM2836 2 0.0475 0.9620 0.004 0.992 0.004
#> GSM2848 2 0.0475 0.9620 0.004 0.992 0.004
#> GSM2828 3 0.1031 0.9402 0.024 0.000 0.976
#> GSM2837 3 0.1031 0.9402 0.024 0.000 0.976
#> GSM2839 1 0.0000 0.9630 1.000 0.000 0.000
#> GSM2841 1 0.0000 0.9630 1.000 0.000 0.000
#> GSM2827 2 0.0892 0.9573 0.020 0.980 0.000
#> GSM2842 2 0.0892 0.9573 0.020 0.980 0.000
#> GSM2845 2 0.0983 0.9632 0.004 0.980 0.016
#> GSM2872 2 0.0983 0.9632 0.004 0.980 0.016
#> GSM2834 2 0.0983 0.9632 0.004 0.980 0.016
#> GSM2847 2 0.0983 0.9632 0.004 0.980 0.016
#> GSM2849 3 0.1031 0.9402 0.024 0.000 0.976
#> GSM2850 3 0.1031 0.9402 0.024 0.000 0.976
#> GSM2838 2 0.0848 0.9613 0.008 0.984 0.008
#> GSM2853 2 0.1015 0.9601 0.012 0.980 0.008
#> GSM2852 3 0.3670 0.9079 0.092 0.020 0.888
#> GSM2855 3 0.3670 0.9079 0.092 0.020 0.888
#> GSM2840 1 0.0000 0.9630 1.000 0.000 0.000
#> GSM2857 1 0.0000 0.9630 1.000 0.000 0.000
#> GSM2859 2 0.0848 0.9613 0.008 0.984 0.008
#> GSM2860 2 0.0848 0.9613 0.008 0.984 0.008
#> GSM2861 2 0.1170 0.9589 0.008 0.976 0.016
#> GSM2862 2 0.0848 0.9613 0.008 0.984 0.008
#> GSM2863 2 0.0848 0.9613 0.008 0.984 0.008
#> GSM2864 2 0.0848 0.9613 0.008 0.984 0.008
#> GSM2865 2 0.0848 0.9613 0.008 0.984 0.008
#> GSM2866 2 0.0848 0.9613 0.008 0.984 0.008
#> GSM2868 2 0.2229 0.9367 0.012 0.944 0.044
#> GSM2869 2 0.0848 0.9613 0.008 0.984 0.008
#> GSM2851 2 0.0848 0.9613 0.008 0.984 0.008
#> GSM2867 2 0.1182 0.9589 0.012 0.976 0.012
#> GSM2870 2 0.1015 0.9604 0.008 0.980 0.012
#> GSM2854 2 0.0983 0.9632 0.004 0.980 0.016
#> GSM2873 2 0.0424 0.9615 0.008 0.992 0.000
#> GSM2874 3 0.1031 0.9402 0.024 0.000 0.976
#> GSM2884 3 0.1031 0.9402 0.024 0.000 0.976
#> GSM2875 1 0.0237 0.9630 0.996 0.000 0.004
#> GSM2890 1 0.0237 0.9630 0.996 0.000 0.004
#> GSM2877 1 0.0237 0.9630 0.996 0.000 0.004
#> GSM2892 1 0.0237 0.9630 0.996 0.000 0.004
#> GSM2902 1 0.0237 0.9630 0.996 0.000 0.004
#> GSM2878 1 0.0237 0.9630 0.996 0.000 0.004
#> GSM2901 1 0.0237 0.9630 0.996 0.000 0.004
#> GSM2879 3 0.3112 0.9121 0.096 0.004 0.900
#> GSM2898 3 0.3112 0.9121 0.096 0.004 0.900
#> GSM2881 3 0.1031 0.9402 0.024 0.000 0.976
#> GSM2897 3 0.1031 0.9402 0.024 0.000 0.976
#> GSM2882 2 0.0983 0.9632 0.004 0.980 0.016
#> GSM2894 2 0.0983 0.9632 0.004 0.980 0.016
#> GSM2883 3 0.2625 0.9188 0.084 0.000 0.916
#> GSM2895 3 0.2625 0.9188 0.084 0.000 0.916
#> GSM2885 3 0.1031 0.9402 0.024 0.000 0.976
#> GSM2886 3 0.1031 0.9402 0.024 0.000 0.976
#> GSM2887 3 0.1163 0.9389 0.028 0.000 0.972
#> GSM2896 3 0.1163 0.9389 0.028 0.000 0.972
#> GSM2888 2 0.4700 0.7681 0.008 0.812 0.180
#> GSM2889 2 0.4755 0.7623 0.008 0.808 0.184
#> GSM2876 1 0.0000 0.9630 1.000 0.000 0.000
#> GSM2891 1 0.0000 0.9630 1.000 0.000 0.000
#> GSM2880 1 0.0237 0.9630 0.996 0.000 0.004
#> GSM2893 1 0.0237 0.9630 0.996 0.000 0.004
#> GSM2821 1 0.0000 0.9630 1.000 0.000 0.000
#> GSM2900 1 0.0000 0.9630 1.000 0.000 0.000
#> GSM2903 1 0.0000 0.9630 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM2819 1 0.4214 0.7095 0.780 0.204 0.000 0.016
#> GSM2820 3 0.0000 0.8777 0.000 0.000 1.000 0.000
#> GSM2822 1 0.6156 0.3521 0.592 0.344 0.000 0.064
#> GSM2832 1 0.6263 0.3107 0.576 0.356 0.000 0.068
#> GSM2823 1 0.5873 0.6090 0.668 0.256 0.076 0.000
#> GSM2824 1 0.5873 0.6090 0.668 0.256 0.076 0.000
#> GSM2825 1 0.3610 0.7180 0.800 0.200 0.000 0.000
#> GSM2826 1 0.3610 0.7180 0.800 0.200 0.000 0.000
#> GSM2829 4 0.0000 0.9978 0.000 0.000 0.000 1.000
#> GSM2856 4 0.0000 0.9978 0.000 0.000 0.000 1.000
#> GSM2830 4 0.0000 0.9978 0.000 0.000 0.000 1.000
#> GSM2843 4 0.0000 0.9978 0.000 0.000 0.000 1.000
#> GSM2871 4 0.0000 0.9978 0.000 0.000 0.000 1.000
#> GSM2831 4 0.0000 0.9978 0.000 0.000 0.000 1.000
#> GSM2844 4 0.0000 0.9978 0.000 0.000 0.000 1.000
#> GSM2833 4 0.0000 0.9978 0.000 0.000 0.000 1.000
#> GSM2846 4 0.0000 0.9978 0.000 0.000 0.000 1.000
#> GSM2835 4 0.0000 0.9978 0.000 0.000 0.000 1.000
#> GSM2858 4 0.0000 0.9978 0.000 0.000 0.000 1.000
#> GSM2836 2 0.5383 0.7351 0.160 0.740 0.000 0.100
#> GSM2848 2 0.5339 0.7395 0.156 0.744 0.000 0.100
#> GSM2828 3 0.0000 0.8777 0.000 0.000 1.000 0.000
#> GSM2837 3 0.0000 0.8777 0.000 0.000 1.000 0.000
#> GSM2839 1 0.0000 0.8100 1.000 0.000 0.000 0.000
#> GSM2841 1 0.0000 0.8100 1.000 0.000 0.000 0.000
#> GSM2827 2 0.7121 0.4482 0.300 0.540 0.000 0.160
#> GSM2842 2 0.6792 0.5341 0.272 0.588 0.000 0.140
#> GSM2845 4 0.0000 0.9978 0.000 0.000 0.000 1.000
#> GSM2872 4 0.0000 0.9978 0.000 0.000 0.000 1.000
#> GSM2834 4 0.0000 0.9978 0.000 0.000 0.000 1.000
#> GSM2847 4 0.0000 0.9978 0.000 0.000 0.000 1.000
#> GSM2849 3 0.0000 0.8777 0.000 0.000 1.000 0.000
#> GSM2850 3 0.0000 0.8777 0.000 0.000 1.000 0.000
#> GSM2838 2 0.1118 0.8674 0.000 0.964 0.000 0.036
#> GSM2853 2 0.1305 0.8671 0.004 0.960 0.000 0.036
#> GSM2852 1 0.7722 0.2812 0.428 0.336 0.236 0.000
#> GSM2855 1 0.7722 0.2812 0.428 0.336 0.236 0.000
#> GSM2840 1 0.0000 0.8100 1.000 0.000 0.000 0.000
#> GSM2857 1 0.0000 0.8100 1.000 0.000 0.000 0.000
#> GSM2859 2 0.1792 0.8590 0.000 0.932 0.000 0.068
#> GSM2860 2 0.1118 0.8674 0.000 0.964 0.000 0.036
#> GSM2861 2 0.2549 0.8554 0.024 0.916 0.004 0.056
#> GSM2862 2 0.1118 0.8674 0.000 0.964 0.000 0.036
#> GSM2863 2 0.1211 0.8688 0.000 0.960 0.000 0.040
#> GSM2864 2 0.1211 0.8688 0.000 0.960 0.000 0.040
#> GSM2865 2 0.1211 0.8688 0.000 0.960 0.000 0.040
#> GSM2866 2 0.3082 0.8433 0.032 0.884 0.000 0.084
#> GSM2868 2 0.1211 0.8688 0.000 0.960 0.000 0.040
#> GSM2869 2 0.1211 0.8688 0.000 0.960 0.000 0.040
#> GSM2851 2 0.1302 0.8683 0.000 0.956 0.000 0.044
#> GSM2867 2 0.1211 0.8688 0.000 0.960 0.000 0.040
#> GSM2870 2 0.1302 0.8683 0.000 0.956 0.000 0.044
#> GSM2854 4 0.1022 0.9614 0.000 0.032 0.000 0.968
#> GSM2873 2 0.7421 0.4463 0.268 0.512 0.000 0.220
#> GSM2874 3 0.0000 0.8777 0.000 0.000 1.000 0.000
#> GSM2884 3 0.0000 0.8777 0.000 0.000 1.000 0.000
#> GSM2875 1 0.0592 0.8092 0.984 0.016 0.000 0.000
#> GSM2890 1 0.0592 0.8092 0.984 0.016 0.000 0.000
#> GSM2877 1 0.0592 0.8092 0.984 0.016 0.000 0.000
#> GSM2892 1 0.0592 0.8092 0.984 0.016 0.000 0.000
#> GSM2902 1 0.0592 0.8092 0.984 0.016 0.000 0.000
#> GSM2878 1 0.0592 0.8092 0.984 0.016 0.000 0.000
#> GSM2901 1 0.0592 0.8092 0.984 0.016 0.000 0.000
#> GSM2879 1 0.7711 0.2377 0.428 0.232 0.340 0.000
#> GSM2898 1 0.7711 0.2377 0.428 0.232 0.340 0.000
#> GSM2881 3 0.0000 0.8777 0.000 0.000 1.000 0.000
#> GSM2897 3 0.0000 0.8777 0.000 0.000 1.000 0.000
#> GSM2882 4 0.0000 0.9978 0.000 0.000 0.000 1.000
#> GSM2894 4 0.0000 0.9978 0.000 0.000 0.000 1.000
#> GSM2883 3 0.7210 -0.0782 0.404 0.140 0.456 0.000
#> GSM2895 3 0.7210 -0.0782 0.404 0.140 0.456 0.000
#> GSM2885 3 0.0000 0.8777 0.000 0.000 1.000 0.000
#> GSM2886 3 0.0000 0.8777 0.000 0.000 1.000 0.000
#> GSM2887 3 0.3626 0.6983 0.184 0.004 0.812 0.000
#> GSM2896 3 0.3626 0.6983 0.184 0.004 0.812 0.000
#> GSM2888 2 0.5992 0.5834 0.264 0.672 0.016 0.048
#> GSM2889 2 0.6044 0.5676 0.272 0.664 0.016 0.048
#> GSM2876 1 0.0000 0.8100 1.000 0.000 0.000 0.000
#> GSM2891 1 0.0000 0.8100 1.000 0.000 0.000 0.000
#> GSM2880 1 0.0469 0.8093 0.988 0.012 0.000 0.000
#> GSM2893 1 0.0592 0.8092 0.984 0.016 0.000 0.000
#> GSM2821 1 0.2345 0.7841 0.900 0.100 0.000 0.000
#> GSM2900 1 0.2345 0.7841 0.900 0.100 0.000 0.000
#> GSM2903 1 0.2345 0.7841 0.900 0.100 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM2819 1 0.6808 -0.437 0.368 0.308 0.000 0.000 0.324
#> GSM2820 3 0.0000 0.953 0.000 0.000 1.000 0.000 0.000
#> GSM2822 2 0.6909 0.299 0.224 0.448 0.000 0.012 0.316
#> GSM2832 2 0.6909 0.299 0.224 0.448 0.000 0.012 0.316
#> GSM2823 5 0.4300 0.898 0.476 0.000 0.000 0.000 0.524
#> GSM2824 5 0.4300 0.898 0.476 0.000 0.000 0.000 0.524
#> GSM2825 1 0.6939 -0.437 0.368 0.300 0.000 0.004 0.328
#> GSM2826 1 0.6942 -0.438 0.364 0.300 0.000 0.004 0.332
#> GSM2829 4 0.4294 0.996 0.000 0.000 0.000 0.532 0.468
#> GSM2856 4 0.4294 0.996 0.000 0.000 0.000 0.532 0.468
#> GSM2830 4 0.4294 0.996 0.000 0.000 0.000 0.532 0.468
#> GSM2843 4 0.4294 0.996 0.000 0.000 0.000 0.532 0.468
#> GSM2871 4 0.4546 0.988 0.008 0.000 0.000 0.532 0.460
#> GSM2831 4 0.4294 0.996 0.000 0.000 0.000 0.532 0.468
#> GSM2844 4 0.4294 0.996 0.000 0.000 0.000 0.532 0.468
#> GSM2833 4 0.4294 0.996 0.000 0.000 0.000 0.532 0.468
#> GSM2846 4 0.4294 0.996 0.000 0.000 0.000 0.532 0.468
#> GSM2835 4 0.4294 0.996 0.000 0.000 0.000 0.532 0.468
#> GSM2858 4 0.4294 0.996 0.000 0.000 0.000 0.532 0.468
#> GSM2836 2 0.6643 0.413 0.196 0.516 0.000 0.012 0.276
#> GSM2848 2 0.6603 0.424 0.192 0.524 0.000 0.012 0.272
#> GSM2828 3 0.0000 0.953 0.000 0.000 1.000 0.000 0.000
#> GSM2837 3 0.0000 0.953 0.000 0.000 1.000 0.000 0.000
#> GSM2839 1 0.0162 0.294 0.996 0.004 0.000 0.000 0.000
#> GSM2841 1 0.0162 0.294 0.996 0.004 0.000 0.000 0.000
#> GSM2827 2 0.6824 0.332 0.204 0.464 0.000 0.012 0.320
#> GSM2842 2 0.6814 0.340 0.204 0.468 0.000 0.012 0.316
#> GSM2845 4 0.4294 0.996 0.000 0.000 0.000 0.532 0.468
#> GSM2872 4 0.4294 0.996 0.000 0.000 0.000 0.532 0.468
#> GSM2834 4 0.4294 0.996 0.000 0.000 0.000 0.532 0.468
#> GSM2847 4 0.4294 0.996 0.000 0.000 0.000 0.532 0.468
#> GSM2849 3 0.0000 0.953 0.000 0.000 1.000 0.000 0.000
#> GSM2850 3 0.0000 0.953 0.000 0.000 1.000 0.000 0.000
#> GSM2838 2 0.0000 0.745 0.000 1.000 0.000 0.000 0.000
#> GSM2853 2 0.0000 0.745 0.000 1.000 0.000 0.000 0.000
#> GSM2852 5 0.5889 0.893 0.428 0.000 0.100 0.000 0.472
#> GSM2855 5 0.5889 0.893 0.428 0.000 0.100 0.000 0.472
#> GSM2840 1 0.0162 0.294 0.996 0.004 0.000 0.000 0.000
#> GSM2857 1 0.0162 0.294 0.996 0.004 0.000 0.000 0.000
#> GSM2859 2 0.0912 0.740 0.000 0.972 0.000 0.012 0.016
#> GSM2860 2 0.0000 0.745 0.000 1.000 0.000 0.000 0.000
#> GSM2861 2 0.2472 0.726 0.036 0.908 0.000 0.012 0.044
#> GSM2862 2 0.0000 0.745 0.000 1.000 0.000 0.000 0.000
#> GSM2863 2 0.0000 0.745 0.000 1.000 0.000 0.000 0.000
#> GSM2864 2 0.0000 0.745 0.000 1.000 0.000 0.000 0.000
#> GSM2865 2 0.0000 0.745 0.000 1.000 0.000 0.000 0.000
#> GSM2866 2 0.3556 0.697 0.036 0.836 0.000 0.012 0.116
#> GSM2868 2 0.2293 0.717 0.016 0.900 0.000 0.000 0.084
#> GSM2869 2 0.0000 0.745 0.000 1.000 0.000 0.000 0.000
#> GSM2851 2 0.0290 0.745 0.000 0.992 0.000 0.000 0.008
#> GSM2867 2 0.1364 0.737 0.012 0.952 0.000 0.000 0.036
#> GSM2870 2 0.0290 0.745 0.000 0.992 0.000 0.000 0.008
#> GSM2854 4 0.5097 0.947 0.012 0.016 0.000 0.496 0.476
#> GSM2873 2 0.7440 0.369 0.160 0.472 0.000 0.072 0.296
#> GSM2874 3 0.0000 0.953 0.000 0.000 1.000 0.000 0.000
#> GSM2884 3 0.0000 0.953 0.000 0.000 1.000 0.000 0.000
#> GSM2875 1 0.4294 0.540 0.532 0.000 0.000 0.468 0.000
#> GSM2890 1 0.4294 0.540 0.532 0.000 0.000 0.468 0.000
#> GSM2877 1 0.4294 0.540 0.532 0.000 0.000 0.468 0.000
#> GSM2892 1 0.4294 0.540 0.532 0.000 0.000 0.468 0.000
#> GSM2902 1 0.4294 0.540 0.532 0.000 0.000 0.468 0.000
#> GSM2878 1 0.4291 0.539 0.536 0.000 0.000 0.464 0.000
#> GSM2901 1 0.4291 0.539 0.536 0.000 0.000 0.464 0.000
#> GSM2879 5 0.5143 0.928 0.428 0.000 0.040 0.000 0.532
#> GSM2898 5 0.5143 0.928 0.428 0.000 0.040 0.000 0.532
#> GSM2881 3 0.0000 0.953 0.000 0.000 1.000 0.000 0.000
#> GSM2897 3 0.0000 0.953 0.000 0.000 1.000 0.000 0.000
#> GSM2882 4 0.4294 0.996 0.000 0.000 0.000 0.532 0.468
#> GSM2894 4 0.4294 0.996 0.000 0.000 0.000 0.532 0.468
#> GSM2883 3 0.4618 0.591 0.068 0.000 0.724 0.000 0.208
#> GSM2895 3 0.4649 0.584 0.068 0.000 0.720 0.000 0.212
#> GSM2885 3 0.0000 0.953 0.000 0.000 1.000 0.000 0.000
#> GSM2886 3 0.0000 0.953 0.000 0.000 1.000 0.000 0.000
#> GSM2887 3 0.0162 0.951 0.000 0.000 0.996 0.000 0.004
#> GSM2896 3 0.0162 0.951 0.000 0.000 0.996 0.000 0.004
#> GSM2888 2 0.7036 0.339 0.200 0.468 0.008 0.012 0.312
#> GSM2889 2 0.7036 0.339 0.200 0.468 0.008 0.012 0.312
#> GSM2876 1 0.0000 0.296 1.000 0.000 0.000 0.000 0.000
#> GSM2891 1 0.0000 0.296 1.000 0.000 0.000 0.000 0.000
#> GSM2880 1 0.4283 0.537 0.544 0.000 0.000 0.456 0.000
#> GSM2893 1 0.4294 0.540 0.532 0.000 0.000 0.468 0.000
#> GSM2821 1 0.4522 -0.786 0.552 0.008 0.000 0.000 0.440
#> GSM2900 1 0.4522 -0.786 0.552 0.008 0.000 0.000 0.440
#> GSM2903 1 0.4522 -0.786 0.552 0.008 0.000 0.000 0.440
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM2819 5 0.5198 -0.1387 0.016 0.052 0.000 0.000 0.476 0.456
#> GSM2820 3 0.0000 0.9569 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2822 5 0.6477 0.3207 0.000 0.272 0.000 0.020 0.404 0.304
#> GSM2832 5 0.6477 0.3207 0.000 0.272 0.000 0.020 0.404 0.304
#> GSM2823 5 0.3804 -0.0816 0.000 0.000 0.000 0.000 0.576 0.424
#> GSM2824 5 0.3828 -0.0953 0.000 0.000 0.000 0.000 0.560 0.440
#> GSM2825 6 0.5569 0.1273 0.056 0.040 0.000 0.000 0.384 0.520
#> GSM2826 6 0.5569 0.1273 0.056 0.040 0.000 0.000 0.384 0.520
#> GSM2829 4 0.0000 0.9893 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2856 4 0.0000 0.9893 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2830 4 0.0000 0.9893 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2843 4 0.0000 0.9893 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2871 4 0.0260 0.9818 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM2831 4 0.0000 0.9893 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2844 4 0.0000 0.9893 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2833 4 0.0146 0.9870 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM2846 4 0.0146 0.9870 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM2835 4 0.0000 0.9893 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2858 4 0.0000 0.9893 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2836 2 0.6358 -0.1794 0.000 0.408 0.000 0.032 0.396 0.164
#> GSM2848 2 0.6371 -0.1599 0.000 0.416 0.000 0.036 0.392 0.156
#> GSM2828 3 0.0000 0.9569 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2837 3 0.0000 0.9569 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2839 6 0.3076 0.6007 0.240 0.000 0.000 0.000 0.000 0.760
#> GSM2841 6 0.3076 0.6007 0.240 0.000 0.000 0.000 0.000 0.760
#> GSM2827 5 0.6373 0.1308 0.000 0.380 0.000 0.048 0.440 0.132
#> GSM2842 5 0.6373 0.1308 0.000 0.380 0.000 0.048 0.440 0.132
#> GSM2845 4 0.0000 0.9893 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2872 4 0.0000 0.9893 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2834 4 0.0000 0.9893 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2847 4 0.0000 0.9893 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2849 3 0.0000 0.9569 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2850 3 0.0000 0.9569 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2838 2 0.0000 0.8184 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2853 2 0.0000 0.8184 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2852 5 0.1572 0.3897 0.000 0.000 0.028 0.000 0.936 0.036
#> GSM2855 5 0.1572 0.3897 0.000 0.000 0.028 0.000 0.936 0.036
#> GSM2840 6 0.3076 0.6007 0.240 0.000 0.000 0.000 0.000 0.760
#> GSM2857 6 0.3076 0.6007 0.240 0.000 0.000 0.000 0.000 0.760
#> GSM2859 2 0.0806 0.8030 0.000 0.972 0.000 0.020 0.008 0.000
#> GSM2860 2 0.0000 0.8184 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2861 2 0.2339 0.7543 0.000 0.896 0.000 0.020 0.072 0.012
#> GSM2862 2 0.0000 0.8184 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2863 2 0.0000 0.8184 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2864 2 0.0000 0.8184 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2865 2 0.0000 0.8184 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2866 2 0.3724 0.6269 0.000 0.780 0.000 0.020 0.176 0.024
#> GSM2868 2 0.2996 0.5564 0.000 0.772 0.000 0.000 0.228 0.000
#> GSM2869 2 0.0000 0.8184 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2851 2 0.0000 0.8184 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2867 2 0.1267 0.7776 0.000 0.940 0.000 0.000 0.060 0.000
#> GSM2870 2 0.0000 0.8184 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2854 4 0.2860 0.8103 0.000 0.000 0.000 0.852 0.100 0.048
#> GSM2873 2 0.7061 -0.1564 0.000 0.380 0.000 0.120 0.360 0.140
#> GSM2874 3 0.0000 0.9569 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2884 3 0.0000 0.9569 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2875 1 0.0000 0.9914 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2890 1 0.0000 0.9914 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2877 1 0.0000 0.9914 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2892 1 0.0000 0.9914 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2902 1 0.0000 0.9914 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2878 1 0.0260 0.9872 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM2901 1 0.0260 0.9872 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM2879 5 0.1492 0.3900 0.000 0.000 0.024 0.000 0.940 0.036
#> GSM2898 5 0.1492 0.3900 0.000 0.000 0.024 0.000 0.940 0.036
#> GSM2881 3 0.0000 0.9569 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2897 3 0.0000 0.9569 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2882 4 0.0000 0.9893 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2894 4 0.0000 0.9893 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2883 5 0.4039 -0.1392 0.000 0.000 0.424 0.000 0.568 0.008
#> GSM2895 5 0.3993 -0.0901 0.000 0.000 0.400 0.000 0.592 0.008
#> GSM2885 3 0.0000 0.9569 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2886 3 0.0000 0.9569 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2887 3 0.3198 0.7195 0.000 0.000 0.740 0.000 0.260 0.000
#> GSM2896 3 0.3175 0.7241 0.000 0.000 0.744 0.000 0.256 0.000
#> GSM2888 5 0.5343 0.1267 0.000 0.440 0.004 0.020 0.488 0.048
#> GSM2889 5 0.5343 0.1267 0.000 0.440 0.004 0.020 0.488 0.048
#> GSM2876 6 0.3371 0.5425 0.292 0.000 0.000 0.000 0.000 0.708
#> GSM2891 6 0.3351 0.5472 0.288 0.000 0.000 0.000 0.000 0.712
#> GSM2880 1 0.0865 0.9488 0.964 0.000 0.000 0.000 0.000 0.036
#> GSM2893 1 0.0000 0.9914 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2821 6 0.4245 0.2974 0.016 0.004 0.000 0.000 0.376 0.604
#> GSM2900 6 0.4234 0.3044 0.016 0.004 0.000 0.000 0.372 0.608
#> GSM2903 6 0.4234 0.3044 0.016 0.004 0.000 0.000 0.372 0.608
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 tissue(p) k
#> MAD:mclust 84 2.53e-05 2
#> MAD:mclust 80 1.24e-08 3
#> MAD:mclust 74 6.77e-11 4
#> MAD:mclust 63 8.71e-13 5
#> MAD:mclust 61 1.60e-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["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 8229 rows and 84 columns.
#> Top rows (823, 1646, 2468, 3291, 4114) 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.861 0.883 0.937 0.4465 0.550 0.550
#> 3 3 0.945 0.932 0.969 0.3872 0.626 0.430
#> 4 4 0.941 0.926 0.963 0.2123 0.850 0.618
#> 5 5 0.888 0.799 0.893 0.0473 0.977 0.908
#> 6 6 0.858 0.785 0.872 0.0392 0.955 0.807
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 3
There is also optional best \(k\) = 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM2819 1 0.8499 0.594 0.724 0.276
#> GSM2820 2 0.0000 0.923 0.000 1.000
#> GSM2822 1 0.7745 0.680 0.772 0.228
#> GSM2832 2 0.9963 0.219 0.464 0.536
#> GSM2823 2 0.6438 0.778 0.164 0.836
#> GSM2824 2 0.8661 0.571 0.288 0.712
#> GSM2825 1 0.0000 0.943 1.000 0.000
#> GSM2826 1 0.0000 0.943 1.000 0.000
#> GSM2829 2 0.4022 0.927 0.080 0.920
#> GSM2856 2 0.4431 0.919 0.092 0.908
#> GSM2830 2 0.3733 0.931 0.072 0.928
#> GSM2843 2 0.3274 0.933 0.060 0.940
#> GSM2871 2 0.2778 0.931 0.048 0.952
#> GSM2831 1 0.9427 0.397 0.640 0.360
#> GSM2844 1 0.9635 0.315 0.612 0.388
#> GSM2833 2 0.9795 0.369 0.416 0.584
#> GSM2846 2 0.6531 0.842 0.168 0.832
#> GSM2835 1 0.0000 0.943 1.000 0.000
#> GSM2858 1 0.0000 0.943 1.000 0.000
#> GSM2836 2 0.3584 0.933 0.068 0.932
#> GSM2848 2 0.3584 0.933 0.068 0.932
#> GSM2828 2 0.0000 0.923 0.000 1.000
#> GSM2837 2 0.0000 0.923 0.000 1.000
#> GSM2839 1 0.0000 0.943 1.000 0.000
#> GSM2841 1 0.0000 0.943 1.000 0.000
#> GSM2827 2 0.3584 0.933 0.068 0.932
#> GSM2842 2 0.3584 0.933 0.068 0.932
#> GSM2845 2 0.4298 0.922 0.088 0.912
#> GSM2872 2 0.9460 0.507 0.364 0.636
#> GSM2834 2 0.4431 0.919 0.092 0.908
#> GSM2847 2 0.4022 0.927 0.080 0.920
#> GSM2849 2 0.0000 0.923 0.000 1.000
#> GSM2850 2 0.0000 0.923 0.000 1.000
#> GSM2838 2 0.3584 0.933 0.068 0.932
#> GSM2853 2 0.3584 0.933 0.068 0.932
#> GSM2852 2 0.0000 0.923 0.000 1.000
#> GSM2855 2 0.0000 0.923 0.000 1.000
#> GSM2840 1 0.0000 0.943 1.000 0.000
#> GSM2857 1 0.0000 0.943 1.000 0.000
#> GSM2859 2 0.3733 0.931 0.072 0.928
#> GSM2860 2 0.3584 0.933 0.068 0.932
#> GSM2861 2 0.3431 0.933 0.064 0.936
#> GSM2862 2 0.3584 0.933 0.068 0.932
#> GSM2863 2 0.3584 0.933 0.068 0.932
#> GSM2864 2 0.3584 0.933 0.068 0.932
#> GSM2865 2 0.3584 0.933 0.068 0.932
#> GSM2866 2 0.3733 0.931 0.072 0.928
#> GSM2868 2 0.3584 0.933 0.068 0.932
#> GSM2869 2 0.3584 0.933 0.068 0.932
#> GSM2851 2 0.3584 0.933 0.068 0.932
#> GSM2867 2 0.3584 0.933 0.068 0.932
#> GSM2870 2 0.3584 0.933 0.068 0.932
#> GSM2854 2 0.4022 0.927 0.080 0.920
#> GSM2873 2 0.3733 0.931 0.072 0.928
#> GSM2874 2 0.0000 0.923 0.000 1.000
#> GSM2884 2 0.0000 0.923 0.000 1.000
#> GSM2875 1 0.0000 0.943 1.000 0.000
#> GSM2890 1 0.0000 0.943 1.000 0.000
#> GSM2877 1 0.0000 0.943 1.000 0.000
#> GSM2892 1 0.0000 0.943 1.000 0.000
#> GSM2902 1 0.0000 0.943 1.000 0.000
#> GSM2878 1 0.0000 0.943 1.000 0.000
#> GSM2901 1 0.0000 0.943 1.000 0.000
#> GSM2879 2 0.0000 0.923 0.000 1.000
#> GSM2898 2 0.0000 0.923 0.000 1.000
#> GSM2881 2 0.0000 0.923 0.000 1.000
#> GSM2897 2 0.0000 0.923 0.000 1.000
#> GSM2882 1 0.2603 0.908 0.956 0.044
#> GSM2894 1 0.3274 0.894 0.940 0.060
#> GSM2883 2 0.0000 0.923 0.000 1.000
#> GSM2895 2 0.0000 0.923 0.000 1.000
#> GSM2885 2 0.0000 0.923 0.000 1.000
#> GSM2886 2 0.0000 0.923 0.000 1.000
#> GSM2887 2 0.0000 0.923 0.000 1.000
#> GSM2896 2 0.0000 0.923 0.000 1.000
#> GSM2888 2 0.0376 0.924 0.004 0.996
#> GSM2889 2 0.0000 0.923 0.000 1.000
#> GSM2876 1 0.0000 0.943 1.000 0.000
#> GSM2891 1 0.0000 0.943 1.000 0.000
#> GSM2880 1 0.0000 0.943 1.000 0.000
#> GSM2893 1 0.0000 0.943 1.000 0.000
#> GSM2821 1 0.0000 0.943 1.000 0.000
#> GSM2900 1 0.0000 0.943 1.000 0.000
#> GSM2903 1 0.0000 0.943 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM2819 2 0.0000 0.964 0.000 1.000 0.000
#> GSM2820 3 0.0000 0.977 0.000 0.000 1.000
#> GSM2822 2 0.0000 0.964 0.000 1.000 0.000
#> GSM2832 2 0.0000 0.964 0.000 1.000 0.000
#> GSM2823 3 0.7905 0.260 0.376 0.064 0.560
#> GSM2824 1 0.8238 0.426 0.596 0.104 0.300
#> GSM2825 2 0.4702 0.738 0.212 0.788 0.000
#> GSM2826 2 0.4974 0.704 0.236 0.764 0.000
#> GSM2829 2 0.0000 0.964 0.000 1.000 0.000
#> GSM2856 2 0.0000 0.964 0.000 1.000 0.000
#> GSM2830 2 0.0000 0.964 0.000 1.000 0.000
#> GSM2843 2 0.0000 0.964 0.000 1.000 0.000
#> GSM2871 2 0.0000 0.964 0.000 1.000 0.000
#> GSM2831 2 0.0000 0.964 0.000 1.000 0.000
#> GSM2844 2 0.0000 0.964 0.000 1.000 0.000
#> GSM2833 2 0.0000 0.964 0.000 1.000 0.000
#> GSM2846 2 0.0000 0.964 0.000 1.000 0.000
#> GSM2835 2 0.0000 0.964 0.000 1.000 0.000
#> GSM2858 2 0.0000 0.964 0.000 1.000 0.000
#> GSM2836 2 0.0237 0.962 0.000 0.996 0.004
#> GSM2848 2 0.0237 0.962 0.000 0.996 0.004
#> GSM2828 3 0.0000 0.977 0.000 0.000 1.000
#> GSM2837 3 0.0000 0.977 0.000 0.000 1.000
#> GSM2839 1 0.0000 0.968 1.000 0.000 0.000
#> GSM2841 1 0.0000 0.968 1.000 0.000 0.000
#> GSM2827 2 0.0592 0.958 0.000 0.988 0.012
#> GSM2842 2 0.1289 0.946 0.000 0.968 0.032
#> GSM2845 2 0.0000 0.964 0.000 1.000 0.000
#> GSM2872 2 0.0000 0.964 0.000 1.000 0.000
#> GSM2834 2 0.0000 0.964 0.000 1.000 0.000
#> GSM2847 2 0.0000 0.964 0.000 1.000 0.000
#> GSM2849 3 0.0000 0.977 0.000 0.000 1.000
#> GSM2850 3 0.0000 0.977 0.000 0.000 1.000
#> GSM2838 2 0.0000 0.964 0.000 1.000 0.000
#> GSM2853 2 0.0000 0.964 0.000 1.000 0.000
#> GSM2852 3 0.0000 0.977 0.000 0.000 1.000
#> GSM2855 3 0.0000 0.977 0.000 0.000 1.000
#> GSM2840 1 0.0000 0.968 1.000 0.000 0.000
#> GSM2857 1 0.0000 0.968 1.000 0.000 0.000
#> GSM2859 2 0.0000 0.964 0.000 1.000 0.000
#> GSM2860 2 0.0237 0.962 0.000 0.996 0.004
#> GSM2861 2 0.2165 0.921 0.000 0.936 0.064
#> GSM2862 2 0.0000 0.964 0.000 1.000 0.000
#> GSM2863 2 0.1031 0.951 0.000 0.976 0.024
#> GSM2864 2 0.1411 0.943 0.000 0.964 0.036
#> GSM2865 2 0.0237 0.962 0.000 0.996 0.004
#> GSM2866 2 0.0000 0.964 0.000 1.000 0.000
#> GSM2868 2 0.4555 0.774 0.000 0.800 0.200
#> GSM2869 2 0.1860 0.931 0.000 0.948 0.052
#> GSM2851 2 0.0000 0.964 0.000 1.000 0.000
#> GSM2867 2 0.3116 0.881 0.000 0.892 0.108
#> GSM2870 2 0.0000 0.964 0.000 1.000 0.000
#> GSM2854 2 0.0000 0.964 0.000 1.000 0.000
#> GSM2873 2 0.0000 0.964 0.000 1.000 0.000
#> GSM2874 3 0.0000 0.977 0.000 0.000 1.000
#> GSM2884 3 0.0000 0.977 0.000 0.000 1.000
#> GSM2875 1 0.0000 0.968 1.000 0.000 0.000
#> GSM2890 1 0.0000 0.968 1.000 0.000 0.000
#> GSM2877 1 0.0000 0.968 1.000 0.000 0.000
#> GSM2892 1 0.0000 0.968 1.000 0.000 0.000
#> GSM2902 1 0.0000 0.968 1.000 0.000 0.000
#> GSM2878 1 0.0000 0.968 1.000 0.000 0.000
#> GSM2901 1 0.0000 0.968 1.000 0.000 0.000
#> GSM2879 3 0.0000 0.977 0.000 0.000 1.000
#> GSM2898 3 0.0000 0.977 0.000 0.000 1.000
#> GSM2881 3 0.0000 0.977 0.000 0.000 1.000
#> GSM2897 3 0.0000 0.977 0.000 0.000 1.000
#> GSM2882 2 0.0000 0.964 0.000 1.000 0.000
#> GSM2894 2 0.0000 0.964 0.000 1.000 0.000
#> GSM2883 3 0.0000 0.977 0.000 0.000 1.000
#> GSM2895 3 0.0000 0.977 0.000 0.000 1.000
#> GSM2885 3 0.0000 0.977 0.000 0.000 1.000
#> GSM2886 3 0.0000 0.977 0.000 0.000 1.000
#> GSM2887 3 0.0000 0.977 0.000 0.000 1.000
#> GSM2896 3 0.0000 0.977 0.000 0.000 1.000
#> GSM2888 2 0.5529 0.625 0.000 0.704 0.296
#> GSM2889 2 0.5560 0.617 0.000 0.700 0.300
#> GSM2876 1 0.0000 0.968 1.000 0.000 0.000
#> GSM2891 1 0.0000 0.968 1.000 0.000 0.000
#> GSM2880 1 0.0000 0.968 1.000 0.000 0.000
#> GSM2893 1 0.0000 0.968 1.000 0.000 0.000
#> GSM2821 1 0.2878 0.861 0.904 0.096 0.000
#> GSM2900 1 0.0747 0.954 0.984 0.016 0.000
#> GSM2903 1 0.1163 0.942 0.972 0.028 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM2819 2 0.1118 0.928 0.000 0.964 0.000 0.036
#> GSM2820 3 0.0000 0.995 0.000 0.000 1.000 0.000
#> GSM2822 2 0.2647 0.868 0.000 0.880 0.000 0.120
#> GSM2832 2 0.3123 0.832 0.000 0.844 0.000 0.156
#> GSM2823 1 0.6038 0.304 0.532 0.424 0.044 0.000
#> GSM2824 1 0.5581 0.264 0.532 0.448 0.020 0.000
#> GSM2825 2 0.6585 0.605 0.180 0.632 0.000 0.188
#> GSM2826 2 0.6393 0.624 0.188 0.652 0.000 0.160
#> GSM2829 4 0.0000 0.997 0.000 0.000 0.000 1.000
#> GSM2856 4 0.0000 0.997 0.000 0.000 0.000 1.000
#> GSM2830 4 0.0000 0.997 0.000 0.000 0.000 1.000
#> GSM2843 4 0.0188 0.994 0.000 0.004 0.000 0.996
#> GSM2871 4 0.0188 0.994 0.000 0.004 0.000 0.996
#> GSM2831 4 0.0000 0.997 0.000 0.000 0.000 1.000
#> GSM2844 4 0.0000 0.997 0.000 0.000 0.000 1.000
#> GSM2833 4 0.0000 0.997 0.000 0.000 0.000 1.000
#> GSM2846 4 0.0000 0.997 0.000 0.000 0.000 1.000
#> GSM2835 4 0.0000 0.997 0.000 0.000 0.000 1.000
#> GSM2858 4 0.0000 0.997 0.000 0.000 0.000 1.000
#> GSM2836 2 0.1716 0.910 0.000 0.936 0.000 0.064
#> GSM2848 2 0.1792 0.908 0.000 0.932 0.000 0.068
#> GSM2828 3 0.0000 0.995 0.000 0.000 1.000 0.000
#> GSM2837 3 0.0000 0.995 0.000 0.000 1.000 0.000
#> GSM2839 1 0.0188 0.925 0.996 0.000 0.000 0.004
#> GSM2841 1 0.0000 0.925 1.000 0.000 0.000 0.000
#> GSM2827 2 0.1302 0.924 0.000 0.956 0.000 0.044
#> GSM2842 2 0.1022 0.929 0.000 0.968 0.000 0.032
#> GSM2845 4 0.0000 0.997 0.000 0.000 0.000 1.000
#> GSM2872 4 0.0000 0.997 0.000 0.000 0.000 1.000
#> GSM2834 4 0.0188 0.994 0.000 0.004 0.000 0.996
#> GSM2847 4 0.0000 0.997 0.000 0.000 0.000 1.000
#> GSM2849 3 0.0000 0.995 0.000 0.000 1.000 0.000
#> GSM2850 3 0.0000 0.995 0.000 0.000 1.000 0.000
#> GSM2838 2 0.0188 0.939 0.000 0.996 0.000 0.004
#> GSM2853 2 0.0188 0.939 0.000 0.996 0.000 0.004
#> GSM2852 3 0.0707 0.982 0.000 0.020 0.980 0.000
#> GSM2855 3 0.0592 0.985 0.000 0.016 0.984 0.000
#> GSM2840 1 0.0188 0.925 0.996 0.000 0.000 0.004
#> GSM2857 1 0.0188 0.925 0.996 0.000 0.000 0.004
#> GSM2859 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM2860 2 0.0188 0.939 0.000 0.996 0.000 0.004
#> GSM2861 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM2862 2 0.0188 0.939 0.000 0.996 0.000 0.004
#> GSM2863 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM2864 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM2865 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM2866 2 0.0336 0.938 0.000 0.992 0.000 0.008
#> GSM2868 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM2869 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM2851 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM2867 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM2870 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM2854 4 0.0921 0.969 0.000 0.028 0.000 0.972
#> GSM2873 2 0.4477 0.610 0.000 0.688 0.000 0.312
#> GSM2874 3 0.0000 0.995 0.000 0.000 1.000 0.000
#> GSM2884 3 0.0000 0.995 0.000 0.000 1.000 0.000
#> GSM2875 1 0.0188 0.925 0.996 0.000 0.000 0.004
#> GSM2890 1 0.0000 0.925 1.000 0.000 0.000 0.000
#> GSM2877 1 0.0188 0.925 0.996 0.000 0.000 0.004
#> GSM2892 1 0.0000 0.925 1.000 0.000 0.000 0.000
#> GSM2902 1 0.0000 0.925 1.000 0.000 0.000 0.000
#> GSM2878 1 0.0000 0.925 1.000 0.000 0.000 0.000
#> GSM2901 1 0.0000 0.925 1.000 0.000 0.000 0.000
#> GSM2879 3 0.0707 0.982 0.000 0.020 0.980 0.000
#> GSM2898 3 0.1211 0.963 0.000 0.040 0.960 0.000
#> GSM2881 3 0.0000 0.995 0.000 0.000 1.000 0.000
#> GSM2897 3 0.0000 0.995 0.000 0.000 1.000 0.000
#> GSM2882 4 0.0000 0.997 0.000 0.000 0.000 1.000
#> GSM2894 4 0.0000 0.997 0.000 0.000 0.000 1.000
#> GSM2883 3 0.0000 0.995 0.000 0.000 1.000 0.000
#> GSM2895 3 0.0188 0.993 0.000 0.004 0.996 0.000
#> GSM2885 3 0.0000 0.995 0.000 0.000 1.000 0.000
#> GSM2886 3 0.0000 0.995 0.000 0.000 1.000 0.000
#> GSM2887 3 0.0000 0.995 0.000 0.000 1.000 0.000
#> GSM2896 3 0.0000 0.995 0.000 0.000 1.000 0.000
#> GSM2888 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM2889 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM2876 1 0.0000 0.925 1.000 0.000 0.000 0.000
#> GSM2891 1 0.0000 0.925 1.000 0.000 0.000 0.000
#> GSM2880 1 0.0188 0.925 0.996 0.000 0.000 0.004
#> GSM2893 1 0.0188 0.925 0.996 0.000 0.000 0.004
#> GSM2821 1 0.3311 0.794 0.828 0.172 0.000 0.000
#> GSM2900 1 0.2647 0.847 0.880 0.120 0.000 0.000
#> GSM2903 1 0.2704 0.843 0.876 0.124 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM2819 5 0.4581 0.3447 0.032 0.268 0.000 0.004 0.696
#> GSM2820 3 0.0000 0.9942 0.000 0.000 1.000 0.000 0.000
#> GSM2822 2 0.4221 0.7381 0.000 0.732 0.000 0.032 0.236
#> GSM2832 2 0.4587 0.7180 0.000 0.728 0.000 0.068 0.204
#> GSM2823 1 0.7270 -0.2101 0.504 0.260 0.060 0.000 0.176
#> GSM2824 1 0.6843 -0.2553 0.496 0.260 0.016 0.000 0.228
#> GSM2825 2 0.7750 -0.0862 0.244 0.360 0.000 0.060 0.336
#> GSM2826 2 0.7666 -0.0816 0.248 0.364 0.000 0.052 0.336
#> GSM2829 4 0.0510 0.9626 0.000 0.000 0.000 0.984 0.016
#> GSM2856 4 0.0510 0.9626 0.000 0.000 0.000 0.984 0.016
#> GSM2830 4 0.0000 0.9630 0.000 0.000 0.000 1.000 0.000
#> GSM2843 4 0.0000 0.9630 0.000 0.000 0.000 1.000 0.000
#> GSM2871 4 0.0898 0.9533 0.000 0.020 0.000 0.972 0.008
#> GSM2831 4 0.0162 0.9631 0.000 0.000 0.000 0.996 0.004
#> GSM2844 4 0.0162 0.9631 0.000 0.000 0.000 0.996 0.004
#> GSM2833 4 0.2471 0.9001 0.000 0.000 0.000 0.864 0.136
#> GSM2846 4 0.2329 0.9091 0.000 0.000 0.000 0.876 0.124
#> GSM2835 4 0.2280 0.9095 0.000 0.000 0.000 0.880 0.120
#> GSM2858 4 0.2536 0.9005 0.004 0.000 0.000 0.868 0.128
#> GSM2836 2 0.0693 0.8534 0.000 0.980 0.000 0.008 0.012
#> GSM2848 2 0.0451 0.8559 0.000 0.988 0.000 0.004 0.008
#> GSM2828 3 0.0000 0.9942 0.000 0.000 1.000 0.000 0.000
#> GSM2837 3 0.0000 0.9942 0.000 0.000 1.000 0.000 0.000
#> GSM2839 1 0.3796 0.5461 0.700 0.000 0.000 0.000 0.300
#> GSM2841 1 0.3906 0.5479 0.704 0.004 0.000 0.000 0.292
#> GSM2827 2 0.0912 0.8567 0.000 0.972 0.000 0.012 0.016
#> GSM2842 2 0.0955 0.8592 0.000 0.968 0.000 0.004 0.028
#> GSM2845 4 0.0162 0.9627 0.000 0.004 0.000 0.996 0.000
#> GSM2872 4 0.0162 0.9627 0.000 0.004 0.000 0.996 0.000
#> GSM2834 4 0.0898 0.9532 0.000 0.020 0.000 0.972 0.008
#> GSM2847 4 0.0451 0.9607 0.000 0.008 0.000 0.988 0.004
#> GSM2849 3 0.0000 0.9942 0.000 0.000 1.000 0.000 0.000
#> GSM2850 3 0.0000 0.9942 0.000 0.000 1.000 0.000 0.000
#> GSM2838 2 0.2648 0.8269 0.000 0.848 0.000 0.000 0.152
#> GSM2853 2 0.2773 0.8215 0.000 0.836 0.000 0.000 0.164
#> GSM2852 3 0.0162 0.9910 0.000 0.004 0.996 0.000 0.000
#> GSM2855 3 0.0162 0.9910 0.000 0.004 0.996 0.000 0.000
#> GSM2840 1 0.4302 0.4979 0.648 0.004 0.000 0.004 0.344
#> GSM2857 1 0.4268 0.5003 0.648 0.008 0.000 0.000 0.344
#> GSM2859 2 0.0162 0.8576 0.000 0.996 0.000 0.000 0.004
#> GSM2860 2 0.0000 0.8583 0.000 1.000 0.000 0.000 0.000
#> GSM2861 2 0.0880 0.8579 0.000 0.968 0.000 0.000 0.032
#> GSM2862 2 0.0000 0.8583 0.000 1.000 0.000 0.000 0.000
#> GSM2863 2 0.0162 0.8576 0.000 0.996 0.000 0.000 0.004
#> GSM2864 2 0.0290 0.8567 0.000 0.992 0.000 0.000 0.008
#> GSM2865 2 0.0162 0.8576 0.000 0.996 0.000 0.000 0.004
#> GSM2866 2 0.0000 0.8583 0.000 1.000 0.000 0.000 0.000
#> GSM2868 2 0.3003 0.8048 0.000 0.812 0.000 0.000 0.188
#> GSM2869 2 0.2929 0.8111 0.000 0.820 0.000 0.000 0.180
#> GSM2851 2 0.2605 0.8279 0.000 0.852 0.000 0.000 0.148
#> GSM2867 2 0.2966 0.8094 0.000 0.816 0.000 0.000 0.184
#> GSM2870 2 0.2852 0.8159 0.000 0.828 0.000 0.000 0.172
#> GSM2854 4 0.1012 0.9546 0.000 0.020 0.000 0.968 0.012
#> GSM2873 2 0.2069 0.8072 0.000 0.912 0.000 0.076 0.012
#> GSM2874 3 0.0000 0.9942 0.000 0.000 1.000 0.000 0.000
#> GSM2884 3 0.0000 0.9942 0.000 0.000 1.000 0.000 0.000
#> GSM2875 1 0.0000 0.7296 1.000 0.000 0.000 0.000 0.000
#> GSM2890 1 0.0000 0.7296 1.000 0.000 0.000 0.000 0.000
#> GSM2877 1 0.0000 0.7296 1.000 0.000 0.000 0.000 0.000
#> GSM2892 1 0.0000 0.7296 1.000 0.000 0.000 0.000 0.000
#> GSM2902 1 0.0000 0.7296 1.000 0.000 0.000 0.000 0.000
#> GSM2878 1 0.0162 0.7276 0.996 0.000 0.000 0.000 0.004
#> GSM2901 1 0.0404 0.7232 0.988 0.000 0.000 0.000 0.012
#> GSM2879 3 0.1282 0.9486 0.000 0.044 0.952 0.000 0.004
#> GSM2898 3 0.0963 0.9599 0.000 0.036 0.964 0.000 0.000
#> GSM2881 3 0.0000 0.9942 0.000 0.000 1.000 0.000 0.000
#> GSM2897 3 0.0000 0.9942 0.000 0.000 1.000 0.000 0.000
#> GSM2882 4 0.0880 0.9589 0.000 0.000 0.000 0.968 0.032
#> GSM2894 4 0.0963 0.9578 0.000 0.000 0.000 0.964 0.036
#> GSM2883 3 0.0000 0.9942 0.000 0.000 1.000 0.000 0.000
#> GSM2895 3 0.0000 0.9942 0.000 0.000 1.000 0.000 0.000
#> GSM2885 3 0.0000 0.9942 0.000 0.000 1.000 0.000 0.000
#> GSM2886 3 0.0000 0.9942 0.000 0.000 1.000 0.000 0.000
#> GSM2887 3 0.0000 0.9942 0.000 0.000 1.000 0.000 0.000
#> GSM2896 3 0.0000 0.9942 0.000 0.000 1.000 0.000 0.000
#> GSM2888 2 0.1965 0.8459 0.000 0.904 0.000 0.000 0.096
#> GSM2889 2 0.1851 0.8478 0.000 0.912 0.000 0.000 0.088
#> GSM2876 1 0.3177 0.4583 0.792 0.000 0.000 0.000 0.208
#> GSM2891 1 0.3305 0.4246 0.776 0.000 0.000 0.000 0.224
#> GSM2880 1 0.0000 0.7296 1.000 0.000 0.000 0.000 0.000
#> GSM2893 1 0.0000 0.7296 1.000 0.000 0.000 0.000 0.000
#> GSM2821 5 0.4341 0.6771 0.364 0.008 0.000 0.000 0.628
#> GSM2900 5 0.4464 0.6669 0.408 0.008 0.000 0.000 0.584
#> GSM2903 5 0.4464 0.6669 0.408 0.008 0.000 0.000 0.584
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM2819 5 0.1995 0.7049 0.036 0.024 0.000 0.004 0.924 0.012
#> GSM2820 3 0.0000 0.9847 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2822 6 0.5781 0.0379 0.000 0.336 0.000 0.016 0.128 0.520
#> GSM2832 6 0.6019 -0.1554 0.000 0.396 0.000 0.024 0.128 0.452
#> GSM2823 1 0.5651 -0.0750 0.512 0.088 0.016 0.000 0.380 0.004
#> GSM2824 1 0.5355 -0.2421 0.468 0.060 0.008 0.000 0.456 0.008
#> GSM2825 6 0.3058 0.6265 0.136 0.016 0.000 0.004 0.008 0.836
#> GSM2826 6 0.3043 0.6282 0.140 0.020 0.000 0.000 0.008 0.832
#> GSM2829 4 0.1649 0.8968 0.000 0.000 0.000 0.932 0.032 0.036
#> GSM2856 4 0.1995 0.8913 0.000 0.000 0.000 0.912 0.036 0.052
#> GSM2830 4 0.0146 0.9030 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM2843 4 0.0405 0.9028 0.000 0.008 0.000 0.988 0.004 0.000
#> GSM2871 4 0.1850 0.8787 0.000 0.052 0.000 0.924 0.008 0.016
#> GSM2831 4 0.0260 0.9036 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM2844 4 0.0146 0.9034 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM2833 4 0.4171 0.7743 0.004 0.000 0.000 0.736 0.192 0.068
#> GSM2846 4 0.3877 0.8001 0.000 0.000 0.000 0.764 0.160 0.076
#> GSM2835 4 0.4513 0.7377 0.004 0.000 0.000 0.700 0.084 0.212
#> GSM2858 4 0.4790 0.6712 0.004 0.000 0.000 0.648 0.080 0.268
#> GSM2836 2 0.0665 0.8141 0.000 0.980 0.000 0.008 0.004 0.008
#> GSM2848 2 0.0665 0.8179 0.000 0.980 0.000 0.008 0.004 0.008
#> GSM2828 3 0.0000 0.9847 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2837 3 0.0000 0.9847 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2839 6 0.4118 0.5987 0.312 0.000 0.000 0.000 0.028 0.660
#> GSM2841 6 0.3969 0.5976 0.312 0.000 0.000 0.000 0.020 0.668
#> GSM2827 2 0.1851 0.8232 0.000 0.928 0.000 0.012 0.024 0.036
#> GSM2842 2 0.2994 0.8171 0.000 0.852 0.000 0.004 0.080 0.064
#> GSM2845 4 0.1577 0.8890 0.000 0.036 0.000 0.940 0.008 0.016
#> GSM2872 4 0.1149 0.8962 0.000 0.024 0.000 0.960 0.008 0.008
#> GSM2834 4 0.2418 0.8477 0.000 0.092 0.000 0.884 0.008 0.016
#> GSM2847 4 0.1307 0.8934 0.000 0.032 0.000 0.952 0.008 0.008
#> GSM2849 3 0.0000 0.9847 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2850 3 0.0000 0.9847 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2838 2 0.4641 0.7578 0.000 0.668 0.000 0.000 0.240 0.092
#> GSM2853 2 0.5020 0.7320 0.000 0.628 0.000 0.000 0.244 0.128
#> GSM2852 3 0.0000 0.9847 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2855 3 0.0000 0.9847 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2840 6 0.3758 0.6473 0.232 0.000 0.000 0.004 0.024 0.740
#> GSM2857 6 0.3956 0.6443 0.252 0.000 0.000 0.004 0.028 0.716
#> GSM2859 2 0.0767 0.8207 0.000 0.976 0.000 0.004 0.012 0.008
#> GSM2860 2 0.0508 0.8233 0.000 0.984 0.000 0.000 0.012 0.004
#> GSM2861 2 0.2680 0.8172 0.000 0.860 0.000 0.000 0.108 0.032
#> GSM2862 2 0.0653 0.8170 0.000 0.980 0.000 0.004 0.004 0.012
#> GSM2863 2 0.0665 0.8176 0.000 0.980 0.000 0.004 0.008 0.008
#> GSM2864 2 0.0551 0.8155 0.000 0.984 0.000 0.004 0.004 0.008
#> GSM2865 2 0.0405 0.8171 0.000 0.988 0.000 0.004 0.000 0.008
#> GSM2866 2 0.0622 0.8226 0.000 0.980 0.000 0.000 0.012 0.008
#> GSM2868 2 0.4686 0.7478 0.000 0.660 0.000 0.000 0.248 0.092
#> GSM2869 2 0.4793 0.7442 0.000 0.648 0.000 0.000 0.252 0.100
#> GSM2851 2 0.4855 0.7407 0.000 0.640 0.000 0.000 0.256 0.104
#> GSM2867 2 0.4699 0.7537 0.000 0.668 0.000 0.000 0.228 0.104
#> GSM2870 2 0.4914 0.7324 0.000 0.628 0.000 0.000 0.268 0.104
#> GSM2854 4 0.2257 0.8902 0.000 0.008 0.000 0.904 0.040 0.048
#> GSM2873 2 0.1442 0.7985 0.000 0.944 0.000 0.040 0.004 0.012
#> GSM2874 3 0.0000 0.9847 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2884 3 0.0000 0.9847 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2875 1 0.0000 0.8116 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2890 1 0.0146 0.8114 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM2877 1 0.0000 0.8116 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2892 1 0.0146 0.8114 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM2902 1 0.0146 0.8114 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM2878 1 0.0146 0.8103 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM2901 1 0.0260 0.8088 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM2879 3 0.2553 0.8192 0.000 0.144 0.848 0.000 0.000 0.008
#> GSM2898 3 0.1714 0.8887 0.000 0.092 0.908 0.000 0.000 0.000
#> GSM2881 3 0.0000 0.9847 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2897 3 0.0000 0.9847 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2882 4 0.0909 0.9033 0.000 0.000 0.000 0.968 0.020 0.012
#> GSM2894 4 0.1176 0.9025 0.000 0.000 0.000 0.956 0.024 0.020
#> GSM2883 3 0.0000 0.9847 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2895 3 0.0000 0.9847 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2885 3 0.0000 0.9847 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2886 3 0.0000 0.9847 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2887 3 0.0000 0.9847 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2896 3 0.0000 0.9847 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2888 2 0.4980 0.7324 0.000 0.648 0.000 0.000 0.184 0.168
#> GSM2889 2 0.5008 0.7300 0.000 0.644 0.000 0.000 0.188 0.168
#> GSM2876 1 0.3634 0.4451 0.696 0.000 0.000 0.000 0.296 0.008
#> GSM2891 1 0.3672 0.4297 0.688 0.000 0.000 0.000 0.304 0.008
#> GSM2880 1 0.0405 0.8067 0.988 0.000 0.000 0.000 0.004 0.008
#> GSM2893 1 0.0405 0.8067 0.988 0.000 0.000 0.000 0.004 0.008
#> GSM2821 5 0.2902 0.8550 0.196 0.000 0.000 0.000 0.800 0.004
#> GSM2900 5 0.3240 0.8307 0.244 0.000 0.000 0.000 0.752 0.004
#> GSM2903 5 0.3136 0.8508 0.228 0.000 0.000 0.000 0.768 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> MAD:NMF 80 5.31e-05 2
#> MAD:NMF 82 9.10e-09 3
#> MAD:NMF 82 9.12e-12 4
#> MAD:NMF 76 2.03e-14 5
#> MAD:NMF 78 5.97e-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", "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 8229 rows and 84 columns.
#> Top rows (823, 1646, 2468, 3291, 4114) are extracted by 'ATC' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.987 0.995 0.3467 0.659 0.659
#> 3 3 0.626 0.483 0.769 0.7001 0.673 0.508
#> 4 4 0.869 0.921 0.961 0.2415 0.757 0.435
#> 5 5 0.866 0.894 0.941 0.0371 0.977 0.916
#> 6 6 0.874 0.867 0.936 0.0490 0.952 0.808
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
#> GSM2819 2 0.0376 0.990 0.004 0.996
#> GSM2820 2 0.0000 0.994 0.000 1.000
#> GSM2822 2 0.0000 0.994 0.000 1.000
#> GSM2832 2 0.0000 0.994 0.000 1.000
#> GSM2823 2 0.0000 0.994 0.000 1.000
#> GSM2824 2 0.0000 0.994 0.000 1.000
#> GSM2825 2 0.0000 0.994 0.000 1.000
#> GSM2826 2 0.0000 0.994 0.000 1.000
#> GSM2829 1 0.0000 1.000 1.000 0.000
#> GSM2856 1 0.0000 1.000 1.000 0.000
#> GSM2830 1 0.0000 1.000 1.000 0.000
#> GSM2843 1 0.0000 1.000 1.000 0.000
#> GSM2871 1 0.0000 1.000 1.000 0.000
#> GSM2831 1 0.0000 1.000 1.000 0.000
#> GSM2844 1 0.0000 1.000 1.000 0.000
#> GSM2833 1 0.0000 1.000 1.000 0.000
#> GSM2846 1 0.0000 1.000 1.000 0.000
#> GSM2835 1 0.0000 1.000 1.000 0.000
#> GSM2858 1 0.0000 1.000 1.000 0.000
#> GSM2836 2 0.0000 0.994 0.000 1.000
#> GSM2848 2 0.0000 0.994 0.000 1.000
#> GSM2828 2 0.0000 0.994 0.000 1.000
#> GSM2837 2 0.0000 0.994 0.000 1.000
#> GSM2839 2 0.0000 0.994 0.000 1.000
#> GSM2841 2 0.0000 0.994 0.000 1.000
#> GSM2827 2 0.0000 0.994 0.000 1.000
#> GSM2842 2 0.0000 0.994 0.000 1.000
#> GSM2845 1 0.0000 1.000 1.000 0.000
#> GSM2872 1 0.0000 1.000 1.000 0.000
#> GSM2834 1 0.0000 1.000 1.000 0.000
#> GSM2847 1 0.0000 1.000 1.000 0.000
#> GSM2849 2 0.0000 0.994 0.000 1.000
#> GSM2850 2 0.0000 0.994 0.000 1.000
#> GSM2838 2 0.0000 0.994 0.000 1.000
#> GSM2853 2 0.0000 0.994 0.000 1.000
#> GSM2852 2 0.0000 0.994 0.000 1.000
#> GSM2855 2 0.0000 0.994 0.000 1.000
#> GSM2840 2 0.0000 0.994 0.000 1.000
#> GSM2857 2 0.0000 0.994 0.000 1.000
#> GSM2859 2 0.0000 0.994 0.000 1.000
#> GSM2860 2 0.0000 0.994 0.000 1.000
#> GSM2861 2 0.0000 0.994 0.000 1.000
#> GSM2862 2 0.0000 0.994 0.000 1.000
#> GSM2863 2 0.0000 0.994 0.000 1.000
#> GSM2864 2 0.0000 0.994 0.000 1.000
#> GSM2865 2 0.0000 0.994 0.000 1.000
#> GSM2866 2 0.0000 0.994 0.000 1.000
#> GSM2868 2 0.0000 0.994 0.000 1.000
#> GSM2869 2 0.0000 0.994 0.000 1.000
#> GSM2851 2 0.0000 0.994 0.000 1.000
#> GSM2867 2 0.0000 0.994 0.000 1.000
#> GSM2870 2 0.0000 0.994 0.000 1.000
#> GSM2854 1 0.0672 0.992 0.992 0.008
#> GSM2873 2 0.9661 0.355 0.392 0.608
#> GSM2874 2 0.0000 0.994 0.000 1.000
#> GSM2884 2 0.0000 0.994 0.000 1.000
#> GSM2875 2 0.0000 0.994 0.000 1.000
#> GSM2890 2 0.0000 0.994 0.000 1.000
#> GSM2877 2 0.0000 0.994 0.000 1.000
#> GSM2892 2 0.0000 0.994 0.000 1.000
#> GSM2902 2 0.0000 0.994 0.000 1.000
#> GSM2878 2 0.0000 0.994 0.000 1.000
#> GSM2901 2 0.0000 0.994 0.000 1.000
#> GSM2879 2 0.0000 0.994 0.000 1.000
#> GSM2898 2 0.0000 0.994 0.000 1.000
#> GSM2881 2 0.0000 0.994 0.000 1.000
#> GSM2897 2 0.0000 0.994 0.000 1.000
#> GSM2882 1 0.0000 1.000 1.000 0.000
#> GSM2894 1 0.0000 1.000 1.000 0.000
#> GSM2883 2 0.0000 0.994 0.000 1.000
#> GSM2895 2 0.0000 0.994 0.000 1.000
#> GSM2885 2 0.0000 0.994 0.000 1.000
#> GSM2886 2 0.0000 0.994 0.000 1.000
#> GSM2887 2 0.0000 0.994 0.000 1.000
#> GSM2896 2 0.0000 0.994 0.000 1.000
#> GSM2888 2 0.0000 0.994 0.000 1.000
#> GSM2889 2 0.0000 0.994 0.000 1.000
#> GSM2876 2 0.0000 0.994 0.000 1.000
#> GSM2891 2 0.0000 0.994 0.000 1.000
#> GSM2880 2 0.0000 0.994 0.000 1.000
#> GSM2893 2 0.0000 0.994 0.000 1.000
#> GSM2821 2 0.0000 0.994 0.000 1.000
#> GSM2900 2 0.0000 0.994 0.000 1.000
#> GSM2903 2 0.0000 0.994 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM2819 1 0.6345 0.311 0.596 0.004 0.400
#> GSM2820 3 0.0000 0.652 0.000 0.000 1.000
#> GSM2822 1 0.6299 0.181 0.524 0.000 0.476
#> GSM2832 1 0.6299 0.181 0.524 0.000 0.476
#> GSM2823 1 0.6286 0.208 0.536 0.000 0.464
#> GSM2824 1 0.6286 0.208 0.536 0.000 0.464
#> GSM2825 1 0.6295 0.191 0.528 0.000 0.472
#> GSM2826 1 0.6295 0.191 0.528 0.000 0.472
#> GSM2829 2 0.0000 0.963 0.000 1.000 0.000
#> GSM2856 2 0.0000 0.963 0.000 1.000 0.000
#> GSM2830 2 0.0000 0.963 0.000 1.000 0.000
#> GSM2843 2 0.0000 0.963 0.000 1.000 0.000
#> GSM2871 2 0.0000 0.963 0.000 1.000 0.000
#> GSM2831 2 0.0000 0.963 0.000 1.000 0.000
#> GSM2844 2 0.0000 0.963 0.000 1.000 0.000
#> GSM2833 2 0.0000 0.963 0.000 1.000 0.000
#> GSM2846 2 0.0000 0.963 0.000 1.000 0.000
#> GSM2835 2 0.0000 0.963 0.000 1.000 0.000
#> GSM2858 2 0.0000 0.963 0.000 1.000 0.000
#> GSM2836 3 0.6309 -0.160 0.500 0.000 0.500
#> GSM2848 1 0.6309 0.106 0.500 0.000 0.500
#> GSM2828 3 0.0000 0.652 0.000 0.000 1.000
#> GSM2837 3 0.0000 0.652 0.000 0.000 1.000
#> GSM2839 1 0.0000 0.605 1.000 0.000 0.000
#> GSM2841 1 0.0000 0.605 1.000 0.000 0.000
#> GSM2827 1 0.6309 0.106 0.500 0.000 0.500
#> GSM2842 3 0.6309 -0.160 0.500 0.000 0.500
#> GSM2845 2 0.0000 0.963 0.000 1.000 0.000
#> GSM2872 2 0.0000 0.963 0.000 1.000 0.000
#> GSM2834 2 0.0000 0.963 0.000 1.000 0.000
#> GSM2847 2 0.0000 0.963 0.000 1.000 0.000
#> GSM2849 3 0.0000 0.652 0.000 0.000 1.000
#> GSM2850 3 0.0000 0.652 0.000 0.000 1.000
#> GSM2838 3 0.6309 -0.160 0.500 0.000 0.500
#> GSM2853 1 0.6309 0.106 0.500 0.000 0.500
#> GSM2852 3 0.0000 0.652 0.000 0.000 1.000
#> GSM2855 3 0.0000 0.652 0.000 0.000 1.000
#> GSM2840 1 0.0000 0.605 1.000 0.000 0.000
#> GSM2857 1 0.0000 0.605 1.000 0.000 0.000
#> GSM2859 1 0.6309 0.106 0.500 0.000 0.500
#> GSM2860 3 0.6309 -0.160 0.500 0.000 0.500
#> GSM2861 3 0.6309 -0.160 0.500 0.000 0.500
#> GSM2862 1 0.6309 0.106 0.500 0.000 0.500
#> GSM2863 3 0.6309 -0.160 0.500 0.000 0.500
#> GSM2864 1 0.6309 0.106 0.500 0.000 0.500
#> GSM2865 3 0.6309 -0.160 0.500 0.000 0.500
#> GSM2866 3 0.6309 -0.160 0.500 0.000 0.500
#> GSM2868 1 0.6309 0.106 0.500 0.000 0.500
#> GSM2869 3 0.6309 -0.160 0.500 0.000 0.500
#> GSM2851 3 0.6309 -0.160 0.500 0.000 0.500
#> GSM2867 3 0.6309 -0.160 0.500 0.000 0.500
#> GSM2870 1 0.6309 0.106 0.500 0.000 0.500
#> GSM2854 2 0.0424 0.955 0.000 0.992 0.008
#> GSM2873 2 0.9883 -0.301 0.344 0.392 0.264
#> GSM2874 3 0.0000 0.652 0.000 0.000 1.000
#> GSM2884 3 0.0000 0.652 0.000 0.000 1.000
#> GSM2875 1 0.0000 0.605 1.000 0.000 0.000
#> GSM2890 1 0.0000 0.605 1.000 0.000 0.000
#> GSM2877 1 0.0000 0.605 1.000 0.000 0.000
#> GSM2892 1 0.0000 0.605 1.000 0.000 0.000
#> GSM2902 1 0.0000 0.605 1.000 0.000 0.000
#> GSM2878 1 0.0000 0.605 1.000 0.000 0.000
#> GSM2901 1 0.0000 0.605 1.000 0.000 0.000
#> GSM2879 3 0.4605 0.489 0.204 0.000 0.796
#> GSM2898 3 0.4605 0.489 0.204 0.000 0.796
#> GSM2881 3 0.0000 0.652 0.000 0.000 1.000
#> GSM2897 3 0.0000 0.652 0.000 0.000 1.000
#> GSM2882 2 0.0000 0.963 0.000 1.000 0.000
#> GSM2894 2 0.0000 0.963 0.000 1.000 0.000
#> GSM2883 3 0.0000 0.652 0.000 0.000 1.000
#> GSM2895 3 0.0000 0.652 0.000 0.000 1.000
#> GSM2885 3 0.0000 0.652 0.000 0.000 1.000
#> GSM2886 3 0.0000 0.652 0.000 0.000 1.000
#> GSM2887 3 0.0000 0.652 0.000 0.000 1.000
#> GSM2896 3 0.0000 0.652 0.000 0.000 1.000
#> GSM2888 3 0.6008 0.203 0.372 0.000 0.628
#> GSM2889 3 0.6008 0.203 0.372 0.000 0.628
#> GSM2876 1 0.0000 0.605 1.000 0.000 0.000
#> GSM2891 1 0.0000 0.605 1.000 0.000 0.000
#> GSM2880 1 0.0000 0.605 1.000 0.000 0.000
#> GSM2893 1 0.0000 0.605 1.000 0.000 0.000
#> GSM2821 1 0.5291 0.471 0.732 0.000 0.268
#> GSM2900 1 0.5291 0.471 0.732 0.000 0.268
#> GSM2903 1 0.5291 0.471 0.732 0.000 0.268
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM2819 2 0.2466 0.856 0.096 0.900 0.004 0.000
#> GSM2820 3 0.0188 0.947 0.000 0.004 0.996 0.000
#> GSM2822 2 0.0817 0.910 0.024 0.976 0.000 0.000
#> GSM2832 2 0.0817 0.910 0.024 0.976 0.000 0.000
#> GSM2823 2 0.1118 0.905 0.036 0.964 0.000 0.000
#> GSM2824 2 0.1118 0.905 0.036 0.964 0.000 0.000
#> GSM2825 2 0.0921 0.909 0.028 0.972 0.000 0.000
#> GSM2826 2 0.0921 0.909 0.028 0.972 0.000 0.000
#> GSM2829 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM2856 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM2830 4 0.0188 0.998 0.000 0.000 0.004 0.996
#> GSM2843 4 0.0188 0.998 0.000 0.000 0.004 0.996
#> GSM2871 4 0.0188 0.998 0.000 0.000 0.004 0.996
#> GSM2831 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM2844 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM2833 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM2846 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM2835 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM2858 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM2836 2 0.0000 0.919 0.000 1.000 0.000 0.000
#> GSM2848 2 0.0000 0.919 0.000 1.000 0.000 0.000
#> GSM2828 3 0.0188 0.947 0.000 0.004 0.996 0.000
#> GSM2837 3 0.0188 0.947 0.000 0.004 0.996 0.000
#> GSM2839 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM2841 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM2827 2 0.0000 0.919 0.000 1.000 0.000 0.000
#> GSM2842 2 0.0000 0.919 0.000 1.000 0.000 0.000
#> GSM2845 4 0.0188 0.998 0.000 0.000 0.004 0.996
#> GSM2872 4 0.0188 0.998 0.000 0.000 0.004 0.996
#> GSM2834 4 0.0188 0.998 0.000 0.000 0.004 0.996
#> GSM2847 4 0.0188 0.998 0.000 0.000 0.004 0.996
#> GSM2849 3 0.0188 0.947 0.000 0.004 0.996 0.000
#> GSM2850 3 0.0188 0.947 0.000 0.004 0.996 0.000
#> GSM2838 2 0.0000 0.919 0.000 1.000 0.000 0.000
#> GSM2853 2 0.0000 0.919 0.000 1.000 0.000 0.000
#> GSM2852 3 0.2589 0.903 0.000 0.116 0.884 0.000
#> GSM2855 3 0.2589 0.903 0.000 0.116 0.884 0.000
#> GSM2840 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM2857 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM2859 2 0.0000 0.919 0.000 1.000 0.000 0.000
#> GSM2860 2 0.0000 0.919 0.000 1.000 0.000 0.000
#> GSM2861 2 0.0000 0.919 0.000 1.000 0.000 0.000
#> GSM2862 2 0.0000 0.919 0.000 1.000 0.000 0.000
#> GSM2863 2 0.0000 0.919 0.000 1.000 0.000 0.000
#> GSM2864 2 0.0000 0.919 0.000 1.000 0.000 0.000
#> GSM2865 2 0.0000 0.919 0.000 1.000 0.000 0.000
#> GSM2866 2 0.0000 0.919 0.000 1.000 0.000 0.000
#> GSM2868 2 0.0000 0.919 0.000 1.000 0.000 0.000
#> GSM2869 2 0.0000 0.919 0.000 1.000 0.000 0.000
#> GSM2851 2 0.0000 0.919 0.000 1.000 0.000 0.000
#> GSM2867 2 0.0000 0.919 0.000 1.000 0.000 0.000
#> GSM2870 2 0.0000 0.919 0.000 1.000 0.000 0.000
#> GSM2854 4 0.0524 0.990 0.000 0.008 0.004 0.988
#> GSM2873 2 0.4991 0.342 0.000 0.608 0.004 0.388
#> GSM2874 3 0.0188 0.947 0.000 0.004 0.996 0.000
#> GSM2884 3 0.0188 0.947 0.000 0.004 0.996 0.000
#> GSM2875 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM2890 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM2877 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM2892 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM2902 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM2878 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM2901 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM2879 2 0.4713 0.416 0.000 0.640 0.360 0.000
#> GSM2898 2 0.4713 0.416 0.000 0.640 0.360 0.000
#> GSM2881 3 0.0188 0.947 0.000 0.004 0.996 0.000
#> GSM2897 3 0.0188 0.947 0.000 0.004 0.996 0.000
#> GSM2882 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM2894 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM2883 3 0.2921 0.881 0.000 0.140 0.860 0.000
#> GSM2895 3 0.2921 0.881 0.000 0.140 0.860 0.000
#> GSM2885 3 0.0188 0.947 0.000 0.004 0.996 0.000
#> GSM2886 3 0.0188 0.947 0.000 0.004 0.996 0.000
#> GSM2887 3 0.2589 0.903 0.000 0.116 0.884 0.000
#> GSM2896 3 0.2589 0.903 0.000 0.116 0.884 0.000
#> GSM2888 2 0.3400 0.751 0.000 0.820 0.180 0.000
#> GSM2889 2 0.3400 0.751 0.000 0.820 0.180 0.000
#> GSM2876 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM2891 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM2880 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM2893 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM2821 2 0.3907 0.716 0.232 0.768 0.000 0.000
#> GSM2900 2 0.3907 0.716 0.232 0.768 0.000 0.000
#> GSM2903 2 0.3907 0.716 0.232 0.768 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM2819 2 0.306 0.836 0.068 0.864 0.000 0.000 0.068
#> GSM2820 3 0.000 0.942 0.000 0.000 1.000 0.000 0.000
#> GSM2822 2 0.141 0.889 0.000 0.940 0.000 0.000 0.060
#> GSM2832 2 0.141 0.889 0.000 0.940 0.000 0.000 0.060
#> GSM2823 2 0.181 0.884 0.012 0.928 0.000 0.000 0.060
#> GSM2824 2 0.181 0.884 0.012 0.928 0.000 0.000 0.060
#> GSM2825 2 0.148 0.887 0.000 0.936 0.000 0.000 0.064
#> GSM2826 2 0.148 0.887 0.000 0.936 0.000 0.000 0.064
#> GSM2829 4 0.000 0.914 0.000 0.000 0.000 1.000 0.000
#> GSM2856 4 0.000 0.914 0.000 0.000 0.000 1.000 0.000
#> GSM2830 5 0.167 0.989 0.000 0.000 0.000 0.076 0.924
#> GSM2843 5 0.167 0.989 0.000 0.000 0.000 0.076 0.924
#> GSM2871 5 0.154 0.993 0.000 0.000 0.000 0.068 0.932
#> GSM2831 4 0.000 0.914 0.000 0.000 0.000 1.000 0.000
#> GSM2844 4 0.000 0.914 0.000 0.000 0.000 1.000 0.000
#> GSM2833 4 0.000 0.914 0.000 0.000 0.000 1.000 0.000
#> GSM2846 4 0.000 0.914 0.000 0.000 0.000 1.000 0.000
#> GSM2835 4 0.000 0.914 0.000 0.000 0.000 1.000 0.000
#> GSM2858 4 0.000 0.914 0.000 0.000 0.000 1.000 0.000
#> GSM2836 2 0.000 0.910 0.000 1.000 0.000 0.000 0.000
#> GSM2848 2 0.000 0.910 0.000 1.000 0.000 0.000 0.000
#> GSM2828 3 0.000 0.942 0.000 0.000 1.000 0.000 0.000
#> GSM2837 3 0.000 0.942 0.000 0.000 1.000 0.000 0.000
#> GSM2839 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM2841 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM2827 2 0.000 0.910 0.000 1.000 0.000 0.000 0.000
#> GSM2842 2 0.000 0.910 0.000 1.000 0.000 0.000 0.000
#> GSM2845 5 0.154 0.993 0.000 0.000 0.000 0.068 0.932
#> GSM2872 5 0.154 0.993 0.000 0.000 0.000 0.068 0.932
#> GSM2834 5 0.154 0.993 0.000 0.000 0.000 0.068 0.932
#> GSM2847 5 0.154 0.993 0.000 0.000 0.000 0.068 0.932
#> GSM2849 3 0.000 0.942 0.000 0.000 1.000 0.000 0.000
#> GSM2850 3 0.000 0.942 0.000 0.000 1.000 0.000 0.000
#> GSM2838 2 0.000 0.910 0.000 1.000 0.000 0.000 0.000
#> GSM2853 2 0.000 0.910 0.000 1.000 0.000 0.000 0.000
#> GSM2852 3 0.218 0.893 0.000 0.112 0.888 0.000 0.000
#> GSM2855 3 0.218 0.893 0.000 0.112 0.888 0.000 0.000
#> GSM2840 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM2857 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM2859 2 0.000 0.910 0.000 1.000 0.000 0.000 0.000
#> GSM2860 2 0.000 0.910 0.000 1.000 0.000 0.000 0.000
#> GSM2861 2 0.000 0.910 0.000 1.000 0.000 0.000 0.000
#> GSM2862 2 0.000 0.910 0.000 1.000 0.000 0.000 0.000
#> GSM2863 2 0.000 0.910 0.000 1.000 0.000 0.000 0.000
#> GSM2864 2 0.000 0.910 0.000 1.000 0.000 0.000 0.000
#> GSM2865 2 0.000 0.910 0.000 1.000 0.000 0.000 0.000
#> GSM2866 2 0.000 0.910 0.000 1.000 0.000 0.000 0.000
#> GSM2868 2 0.000 0.910 0.000 1.000 0.000 0.000 0.000
#> GSM2869 2 0.000 0.910 0.000 1.000 0.000 0.000 0.000
#> GSM2851 2 0.000 0.910 0.000 1.000 0.000 0.000 0.000
#> GSM2867 2 0.000 0.910 0.000 1.000 0.000 0.000 0.000
#> GSM2870 2 0.000 0.910 0.000 1.000 0.000 0.000 0.000
#> GSM2854 5 0.195 0.972 0.000 0.004 0.000 0.084 0.912
#> GSM2873 2 0.421 0.318 0.000 0.588 0.000 0.000 0.412
#> GSM2874 3 0.000 0.942 0.000 0.000 1.000 0.000 0.000
#> GSM2884 3 0.000 0.942 0.000 0.000 1.000 0.000 0.000
#> GSM2875 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM2890 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM2877 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM2892 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM2902 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM2878 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM2901 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM2879 2 0.406 0.417 0.000 0.640 0.360 0.000 0.000
#> GSM2898 2 0.406 0.417 0.000 0.640 0.360 0.000 0.000
#> GSM2881 3 0.000 0.942 0.000 0.000 1.000 0.000 0.000
#> GSM2897 3 0.000 0.942 0.000 0.000 1.000 0.000 0.000
#> GSM2882 4 0.400 0.484 0.000 0.000 0.000 0.656 0.344
#> GSM2894 4 0.400 0.484 0.000 0.000 0.000 0.656 0.344
#> GSM2883 3 0.247 0.868 0.000 0.136 0.864 0.000 0.000
#> GSM2895 3 0.247 0.868 0.000 0.136 0.864 0.000 0.000
#> GSM2885 3 0.000 0.942 0.000 0.000 1.000 0.000 0.000
#> GSM2886 3 0.000 0.942 0.000 0.000 1.000 0.000 0.000
#> GSM2887 3 0.218 0.893 0.000 0.112 0.888 0.000 0.000
#> GSM2896 3 0.218 0.893 0.000 0.112 0.888 0.000 0.000
#> GSM2888 2 0.293 0.750 0.000 0.820 0.180 0.000 0.000
#> GSM2889 2 0.293 0.750 0.000 0.820 0.180 0.000 0.000
#> GSM2876 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM2891 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM2880 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM2893 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM2821 2 0.447 0.711 0.204 0.736 0.000 0.000 0.060
#> GSM2900 2 0.447 0.711 0.204 0.736 0.000 0.000 0.060
#> GSM2903 2 0.447 0.711 0.204 0.736 0.000 0.000 0.060
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM2819 5 0.2320 0.701 0.000 0.132 0.000 0.000 0.864 0.004
#> GSM2820 3 0.0000 0.908 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2822 2 0.1444 0.849 0.000 0.928 0.000 0.000 0.072 0.000
#> GSM2832 2 0.1444 0.849 0.000 0.928 0.000 0.000 0.072 0.000
#> GSM2823 5 0.3727 0.517 0.000 0.388 0.000 0.000 0.612 0.000
#> GSM2824 5 0.3727 0.517 0.000 0.388 0.000 0.000 0.612 0.000
#> GSM2825 2 0.1501 0.845 0.000 0.924 0.000 0.000 0.076 0.000
#> GSM2826 2 0.1501 0.845 0.000 0.924 0.000 0.000 0.076 0.000
#> GSM2829 4 0.0000 0.900 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2856 4 0.0000 0.900 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2830 6 0.0260 0.989 0.000 0.000 0.000 0.008 0.000 0.992
#> GSM2843 6 0.0260 0.989 0.000 0.000 0.000 0.008 0.000 0.992
#> GSM2871 6 0.0000 0.993 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM2831 4 0.0000 0.900 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2844 4 0.0000 0.900 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2833 4 0.0000 0.900 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2846 4 0.0000 0.900 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2835 4 0.0000 0.900 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2858 4 0.0000 0.900 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2836 2 0.0000 0.908 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2848 2 0.0000 0.908 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2828 3 0.1141 0.893 0.000 0.000 0.948 0.000 0.052 0.000
#> GSM2837 3 0.1141 0.893 0.000 0.000 0.948 0.000 0.052 0.000
#> GSM2839 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2841 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2827 2 0.0000 0.908 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2842 2 0.0000 0.908 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2845 6 0.0000 0.993 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM2872 6 0.0000 0.993 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM2834 6 0.0000 0.993 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM2847 6 0.0000 0.993 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM2849 3 0.1141 0.893 0.000 0.000 0.948 0.000 0.052 0.000
#> GSM2850 3 0.1141 0.893 0.000 0.000 0.948 0.000 0.052 0.000
#> GSM2838 2 0.0000 0.908 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2853 2 0.0000 0.908 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2852 3 0.3196 0.844 0.000 0.108 0.828 0.000 0.064 0.000
#> GSM2855 3 0.3196 0.844 0.000 0.108 0.828 0.000 0.064 0.000
#> GSM2840 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2857 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2859 2 0.0000 0.908 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2860 2 0.0000 0.908 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2861 2 0.0146 0.907 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM2862 2 0.0000 0.908 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2863 2 0.0000 0.908 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2864 2 0.0000 0.908 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2865 2 0.0000 0.908 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2866 2 0.0000 0.908 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2868 2 0.0146 0.907 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM2869 2 0.0146 0.907 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM2851 2 0.0146 0.907 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM2867 2 0.0146 0.907 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM2870 2 0.0146 0.907 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM2854 6 0.0891 0.968 0.000 0.000 0.000 0.024 0.008 0.968
#> GSM2873 2 0.4301 0.231 0.000 0.584 0.000 0.000 0.024 0.392
#> GSM2874 3 0.0000 0.908 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2884 3 0.0000 0.908 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2875 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2890 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2877 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2892 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2902 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2878 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2901 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2879 2 0.4621 0.423 0.000 0.632 0.304 0.000 0.064 0.000
#> GSM2898 2 0.4621 0.423 0.000 0.632 0.304 0.000 0.064 0.000
#> GSM2881 3 0.0000 0.908 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2897 3 0.0000 0.908 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2882 4 0.3765 0.400 0.000 0.000 0.000 0.596 0.000 0.404
#> GSM2894 4 0.3765 0.400 0.000 0.000 0.000 0.596 0.000 0.404
#> GSM2883 3 0.3522 0.816 0.000 0.128 0.800 0.000 0.072 0.000
#> GSM2895 3 0.3522 0.816 0.000 0.128 0.800 0.000 0.072 0.000
#> GSM2885 3 0.0000 0.908 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2886 3 0.0000 0.908 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2887 3 0.3196 0.844 0.000 0.108 0.828 0.000 0.064 0.000
#> GSM2896 3 0.3196 0.844 0.000 0.108 0.828 0.000 0.064 0.000
#> GSM2888 2 0.3354 0.710 0.000 0.812 0.128 0.000 0.060 0.000
#> GSM2889 2 0.3354 0.710 0.000 0.812 0.128 0.000 0.060 0.000
#> GSM2876 1 0.0146 0.996 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM2891 1 0.0146 0.996 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM2880 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2893 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2821 5 0.2489 0.717 0.128 0.012 0.000 0.000 0.860 0.000
#> GSM2900 5 0.2489 0.717 0.128 0.012 0.000 0.000 0.860 0.000
#> GSM2903 5 0.2489 0.717 0.128 0.012 0.000 0.000 0.860 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 tissue(p) k
#> ATC:hclust 83 3.39e-05 2
#> ATC:hclust 50 1.60e-05 3
#> ATC:hclust 81 7.31e-12 4
#> ATC:hclust 79 6.48e-15 5
#> ATC:hclust 79 3.73e-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", "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 8229 rows and 84 columns.
#> Top rows (823, 1646, 2468, 3291, 4114) are extracted by 'ATC' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.223 0.681 0.723 0.3811 0.646 0.646
#> 3 3 0.592 0.878 0.871 0.5595 0.739 0.604
#> 4 4 0.828 0.956 0.909 0.1998 0.849 0.632
#> 5 5 0.743 0.892 0.877 0.0643 1.000 1.000
#> 6 6 0.810 0.821 0.822 0.0438 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] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM2819 1 0.999 -0.584 0.516 0.484
#> GSM2820 2 0.891 0.647 0.308 0.692
#> GSM2822 2 0.958 0.712 0.380 0.620
#> GSM2832 2 0.958 0.712 0.380 0.620
#> GSM2823 2 0.844 0.680 0.272 0.728
#> GSM2824 2 0.844 0.680 0.272 0.728
#> GSM2825 2 1.000 0.555 0.496 0.504
#> GSM2826 2 1.000 0.555 0.496 0.504
#> GSM2829 1 0.000 0.951 1.000 0.000
#> GSM2856 1 0.000 0.951 1.000 0.000
#> GSM2830 1 0.000 0.951 1.000 0.000
#> GSM2843 1 0.000 0.951 1.000 0.000
#> GSM2871 1 0.000 0.951 1.000 0.000
#> GSM2831 1 0.000 0.951 1.000 0.000
#> GSM2844 1 0.000 0.951 1.000 0.000
#> GSM2833 1 0.000 0.951 1.000 0.000
#> GSM2846 1 0.000 0.951 1.000 0.000
#> GSM2835 1 0.000 0.951 1.000 0.000
#> GSM2858 1 0.000 0.951 1.000 0.000
#> GSM2836 2 0.955 0.715 0.376 0.624
#> GSM2848 2 0.955 0.715 0.376 0.624
#> GSM2828 2 0.891 0.647 0.308 0.692
#> GSM2837 2 0.973 0.480 0.404 0.596
#> GSM2839 2 0.827 0.482 0.260 0.740
#> GSM2841 2 0.827 0.482 0.260 0.740
#> GSM2827 2 0.955 0.715 0.376 0.624
#> GSM2842 2 0.955 0.715 0.376 0.624
#> GSM2845 1 0.000 0.951 1.000 0.000
#> GSM2872 1 0.000 0.951 1.000 0.000
#> GSM2834 1 0.000 0.951 1.000 0.000
#> GSM2847 1 0.000 0.951 1.000 0.000
#> GSM2849 2 0.891 0.647 0.308 0.692
#> GSM2850 2 0.891 0.647 0.308 0.692
#> GSM2838 2 0.955 0.715 0.376 0.624
#> GSM2853 2 0.955 0.715 0.376 0.624
#> GSM2852 2 0.839 0.682 0.268 0.732
#> GSM2855 2 0.839 0.682 0.268 0.732
#> GSM2840 2 0.827 0.482 0.260 0.740
#> GSM2857 2 0.827 0.482 0.260 0.740
#> GSM2859 2 0.955 0.715 0.376 0.624
#> GSM2860 2 0.955 0.715 0.376 0.624
#> GSM2861 2 0.917 0.710 0.332 0.668
#> GSM2862 2 0.955 0.715 0.376 0.624
#> GSM2863 2 0.955 0.715 0.376 0.624
#> GSM2864 2 0.955 0.715 0.376 0.624
#> GSM2865 2 0.955 0.715 0.376 0.624
#> GSM2866 2 0.955 0.715 0.376 0.624
#> GSM2868 2 0.955 0.715 0.376 0.624
#> GSM2869 2 0.955 0.715 0.376 0.624
#> GSM2851 2 0.955 0.715 0.376 0.624
#> GSM2867 2 0.955 0.715 0.376 0.624
#> GSM2870 2 0.955 0.715 0.376 0.624
#> GSM2854 1 0.000 0.951 1.000 0.000
#> GSM2873 2 0.955 0.715 0.376 0.624
#> GSM2874 2 0.891 0.647 0.308 0.692
#> GSM2884 2 0.891 0.647 0.308 0.692
#> GSM2875 2 0.827 0.482 0.260 0.740
#> GSM2890 2 0.827 0.482 0.260 0.740
#> GSM2877 2 0.827 0.482 0.260 0.740
#> GSM2892 2 0.827 0.482 0.260 0.740
#> GSM2902 2 0.827 0.482 0.260 0.740
#> GSM2878 2 0.827 0.482 0.260 0.740
#> GSM2901 2 0.827 0.482 0.260 0.740
#> GSM2879 2 0.814 0.689 0.252 0.748
#> GSM2898 2 0.814 0.689 0.252 0.748
#> GSM2881 2 0.891 0.647 0.308 0.692
#> GSM2897 2 0.891 0.647 0.308 0.692
#> GSM2882 1 0.000 0.951 1.000 0.000
#> GSM2894 1 0.000 0.951 1.000 0.000
#> GSM2883 2 0.814 0.689 0.252 0.748
#> GSM2895 2 0.814 0.689 0.252 0.748
#> GSM2885 2 0.891 0.647 0.308 0.692
#> GSM2886 2 0.891 0.647 0.308 0.692
#> GSM2887 2 0.833 0.683 0.264 0.736
#> GSM2896 2 0.833 0.683 0.264 0.736
#> GSM2888 2 0.821 0.688 0.256 0.744
#> GSM2889 2 0.821 0.688 0.256 0.744
#> GSM2876 2 0.827 0.482 0.260 0.740
#> GSM2891 2 0.827 0.482 0.260 0.740
#> GSM2880 2 0.827 0.482 0.260 0.740
#> GSM2893 2 0.827 0.482 0.260 0.740
#> GSM2821 2 0.827 0.482 0.260 0.740
#> GSM2900 2 0.827 0.482 0.260 0.740
#> GSM2903 2 0.827 0.482 0.260 0.740
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM2819 3 0.832 0.674 0.284 0.116 0.600
#> GSM2820 3 0.270 0.794 0.016 0.056 0.928
#> GSM2822 3 0.650 0.827 0.140 0.100 0.760
#> GSM2832 3 0.650 0.827 0.140 0.100 0.760
#> GSM2823 3 0.663 0.581 0.360 0.016 0.624
#> GSM2824 3 0.663 0.581 0.360 0.016 0.624
#> GSM2825 3 0.795 0.703 0.252 0.108 0.640
#> GSM2826 3 0.795 0.703 0.252 0.108 0.640
#> GSM2829 2 0.341 0.989 0.080 0.900 0.020
#> GSM2856 2 0.341 0.989 0.080 0.900 0.020
#> GSM2830 2 0.295 0.991 0.060 0.920 0.020
#> GSM2843 2 0.285 0.991 0.056 0.924 0.020
#> GSM2871 2 0.295 0.990 0.060 0.920 0.020
#> GSM2831 2 0.333 0.990 0.076 0.904 0.020
#> GSM2844 2 0.333 0.990 0.076 0.904 0.020
#> GSM2833 2 0.341 0.989 0.080 0.900 0.020
#> GSM2846 2 0.341 0.989 0.080 0.900 0.020
#> GSM2835 2 0.341 0.989 0.080 0.900 0.020
#> GSM2858 2 0.341 0.989 0.080 0.900 0.020
#> GSM2836 3 0.650 0.827 0.140 0.100 0.760
#> GSM2848 3 0.650 0.827 0.140 0.100 0.760
#> GSM2828 3 0.270 0.794 0.016 0.056 0.928
#> GSM2837 3 0.300 0.786 0.016 0.068 0.916
#> GSM2839 1 0.231 0.988 0.944 0.024 0.032
#> GSM2841 1 0.231 0.988 0.944 0.024 0.032
#> GSM2827 3 0.650 0.827 0.140 0.100 0.760
#> GSM2842 3 0.650 0.827 0.140 0.100 0.760
#> GSM2845 2 0.295 0.990 0.060 0.920 0.020
#> GSM2872 2 0.295 0.990 0.060 0.920 0.020
#> GSM2834 2 0.295 0.990 0.060 0.920 0.020
#> GSM2847 2 0.295 0.990 0.060 0.920 0.020
#> GSM2849 3 0.270 0.794 0.016 0.056 0.928
#> GSM2850 3 0.270 0.794 0.016 0.056 0.928
#> GSM2838 3 0.650 0.827 0.140 0.100 0.760
#> GSM2853 3 0.650 0.827 0.140 0.100 0.760
#> GSM2852 3 0.270 0.794 0.016 0.056 0.928
#> GSM2855 3 0.270 0.794 0.016 0.056 0.928
#> GSM2840 1 0.231 0.988 0.944 0.024 0.032
#> GSM2857 1 0.231 0.988 0.944 0.024 0.032
#> GSM2859 3 0.650 0.827 0.140 0.100 0.760
#> GSM2860 3 0.650 0.827 0.140 0.100 0.760
#> GSM2861 3 0.534 0.826 0.092 0.084 0.824
#> GSM2862 3 0.650 0.827 0.140 0.100 0.760
#> GSM2863 3 0.650 0.827 0.140 0.100 0.760
#> GSM2864 3 0.650 0.827 0.140 0.100 0.760
#> GSM2865 3 0.650 0.827 0.140 0.100 0.760
#> GSM2866 3 0.650 0.827 0.140 0.100 0.760
#> GSM2868 3 0.650 0.827 0.140 0.100 0.760
#> GSM2869 3 0.650 0.827 0.140 0.100 0.760
#> GSM2851 3 0.650 0.827 0.140 0.100 0.760
#> GSM2867 3 0.650 0.827 0.140 0.100 0.760
#> GSM2870 3 0.650 0.827 0.140 0.100 0.760
#> GSM2854 2 0.295 0.991 0.060 0.920 0.020
#> GSM2873 3 0.650 0.827 0.140 0.100 0.760
#> GSM2874 3 0.270 0.794 0.016 0.056 0.928
#> GSM2884 3 0.270 0.794 0.016 0.056 0.928
#> GSM2875 1 0.175 0.992 0.960 0.012 0.028
#> GSM2890 1 0.175 0.992 0.960 0.012 0.028
#> GSM2877 1 0.175 0.992 0.960 0.012 0.028
#> GSM2892 1 0.175 0.992 0.960 0.012 0.028
#> GSM2902 1 0.175 0.992 0.960 0.012 0.028
#> GSM2878 1 0.175 0.992 0.960 0.012 0.028
#> GSM2901 1 0.175 0.992 0.960 0.012 0.028
#> GSM2879 3 0.116 0.811 0.028 0.000 0.972
#> GSM2898 3 0.116 0.811 0.028 0.000 0.972
#> GSM2881 3 0.270 0.794 0.016 0.056 0.928
#> GSM2897 3 0.270 0.794 0.016 0.056 0.928
#> GSM2882 2 0.285 0.991 0.056 0.924 0.020
#> GSM2894 2 0.285 0.991 0.056 0.924 0.020
#> GSM2883 3 0.270 0.794 0.016 0.056 0.928
#> GSM2895 3 0.270 0.794 0.016 0.056 0.928
#> GSM2885 3 0.270 0.794 0.016 0.056 0.928
#> GSM2886 3 0.270 0.794 0.016 0.056 0.928
#> GSM2887 3 0.270 0.794 0.016 0.056 0.928
#> GSM2896 3 0.270 0.794 0.016 0.056 0.928
#> GSM2888 3 0.103 0.812 0.024 0.000 0.976
#> GSM2889 3 0.103 0.812 0.024 0.000 0.976
#> GSM2876 1 0.175 0.992 0.960 0.012 0.028
#> GSM2891 1 0.175 0.992 0.960 0.012 0.028
#> GSM2880 1 0.175 0.992 0.960 0.012 0.028
#> GSM2893 1 0.175 0.992 0.960 0.012 0.028
#> GSM2821 1 0.223 0.977 0.944 0.012 0.044
#> GSM2900 1 0.223 0.977 0.944 0.012 0.044
#> GSM2903 1 0.223 0.977 0.944 0.012 0.044
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM2819 2 0.3626 0.833 0.016 0.844 0.136 0.004
#> GSM2820 3 0.3801 0.998 0.000 0.220 0.780 0.000
#> GSM2822 2 0.1867 0.911 0.000 0.928 0.072 0.000
#> GSM2832 2 0.1867 0.911 0.000 0.928 0.072 0.000
#> GSM2823 2 0.3006 0.878 0.012 0.888 0.092 0.008
#> GSM2824 2 0.3006 0.878 0.012 0.888 0.092 0.008
#> GSM2825 2 0.2593 0.879 0.004 0.892 0.104 0.000
#> GSM2826 2 0.2593 0.879 0.004 0.892 0.104 0.000
#> GSM2829 4 0.2465 0.963 0.020 0.012 0.044 0.924
#> GSM2856 4 0.2465 0.963 0.020 0.012 0.044 0.924
#> GSM2830 4 0.1749 0.964 0.024 0.012 0.012 0.952
#> GSM2843 4 0.1471 0.963 0.024 0.012 0.004 0.960
#> GSM2871 4 0.2956 0.950 0.036 0.012 0.048 0.904
#> GSM2831 4 0.2284 0.963 0.020 0.012 0.036 0.932
#> GSM2844 4 0.2284 0.963 0.020 0.012 0.036 0.932
#> GSM2833 4 0.2465 0.963 0.020 0.012 0.044 0.924
#> GSM2846 4 0.2465 0.963 0.020 0.012 0.044 0.924
#> GSM2835 4 0.2465 0.963 0.020 0.012 0.044 0.924
#> GSM2858 4 0.2465 0.963 0.020 0.012 0.044 0.924
#> GSM2836 2 0.0000 0.955 0.000 1.000 0.000 0.000
#> GSM2848 2 0.0000 0.955 0.000 1.000 0.000 0.000
#> GSM2828 3 0.3982 0.997 0.000 0.220 0.776 0.004
#> GSM2837 3 0.3982 0.997 0.000 0.220 0.776 0.004
#> GSM2839 1 0.3752 0.947 0.864 0.036 0.084 0.016
#> GSM2841 1 0.3752 0.947 0.864 0.036 0.084 0.016
#> GSM2827 2 0.0336 0.953 0.000 0.992 0.008 0.000
#> GSM2842 2 0.0188 0.954 0.000 0.996 0.004 0.000
#> GSM2845 4 0.2956 0.950 0.036 0.012 0.048 0.904
#> GSM2872 4 0.2956 0.950 0.036 0.012 0.048 0.904
#> GSM2834 4 0.2956 0.950 0.036 0.012 0.048 0.904
#> GSM2847 4 0.2781 0.952 0.036 0.012 0.040 0.912
#> GSM2849 3 0.3982 0.997 0.000 0.220 0.776 0.004
#> GSM2850 3 0.3982 0.997 0.000 0.220 0.776 0.004
#> GSM2838 2 0.0336 0.954 0.008 0.992 0.000 0.000
#> GSM2853 2 0.0336 0.954 0.008 0.992 0.000 0.000
#> GSM2852 3 0.3982 0.997 0.000 0.220 0.776 0.004
#> GSM2855 3 0.3982 0.997 0.000 0.220 0.776 0.004
#> GSM2840 1 0.3752 0.947 0.864 0.036 0.084 0.016
#> GSM2857 1 0.3752 0.947 0.864 0.036 0.084 0.016
#> GSM2859 2 0.0000 0.955 0.000 1.000 0.000 0.000
#> GSM2860 2 0.0000 0.955 0.000 1.000 0.000 0.000
#> GSM2861 2 0.0524 0.950 0.004 0.988 0.008 0.000
#> GSM2862 2 0.0000 0.955 0.000 1.000 0.000 0.000
#> GSM2863 2 0.0000 0.955 0.000 1.000 0.000 0.000
#> GSM2864 2 0.0000 0.955 0.000 1.000 0.000 0.000
#> GSM2865 2 0.0000 0.955 0.000 1.000 0.000 0.000
#> GSM2866 2 0.0188 0.954 0.000 0.996 0.004 0.000
#> GSM2868 2 0.0524 0.953 0.008 0.988 0.000 0.004
#> GSM2869 2 0.0524 0.953 0.008 0.988 0.000 0.004
#> GSM2851 2 0.0524 0.953 0.008 0.988 0.000 0.004
#> GSM2867 2 0.0524 0.953 0.008 0.988 0.000 0.004
#> GSM2870 2 0.0524 0.953 0.008 0.988 0.000 0.004
#> GSM2854 4 0.2686 0.957 0.032 0.012 0.040 0.916
#> GSM2873 2 0.1004 0.943 0.004 0.972 0.024 0.000
#> GSM2874 3 0.3801 0.998 0.000 0.220 0.780 0.000
#> GSM2884 3 0.3801 0.998 0.000 0.220 0.780 0.000
#> GSM2875 1 0.1452 0.969 0.956 0.036 0.000 0.008
#> GSM2890 1 0.1452 0.969 0.956 0.036 0.000 0.008
#> GSM2877 1 0.1452 0.969 0.956 0.036 0.000 0.008
#> GSM2892 1 0.1452 0.969 0.956 0.036 0.000 0.008
#> GSM2902 1 0.1452 0.969 0.956 0.036 0.000 0.008
#> GSM2878 1 0.1452 0.969 0.956 0.036 0.000 0.008
#> GSM2901 1 0.1452 0.969 0.956 0.036 0.000 0.008
#> GSM2879 2 0.1389 0.912 0.000 0.952 0.048 0.000
#> GSM2898 2 0.1389 0.912 0.000 0.952 0.048 0.000
#> GSM2881 3 0.3801 0.998 0.000 0.220 0.780 0.000
#> GSM2897 3 0.3801 0.998 0.000 0.220 0.780 0.000
#> GSM2882 4 0.0937 0.965 0.012 0.012 0.000 0.976
#> GSM2894 4 0.0937 0.965 0.012 0.012 0.000 0.976
#> GSM2883 3 0.4163 0.995 0.004 0.220 0.772 0.004
#> GSM2895 3 0.4163 0.995 0.004 0.220 0.772 0.004
#> GSM2885 3 0.3801 0.998 0.000 0.220 0.780 0.000
#> GSM2886 3 0.3801 0.998 0.000 0.220 0.780 0.000
#> GSM2887 3 0.3982 0.997 0.000 0.220 0.776 0.004
#> GSM2896 3 0.3982 0.997 0.000 0.220 0.776 0.004
#> GSM2888 2 0.1762 0.908 0.004 0.944 0.048 0.004
#> GSM2889 2 0.1762 0.908 0.004 0.944 0.048 0.004
#> GSM2876 1 0.1584 0.968 0.952 0.036 0.000 0.012
#> GSM2891 1 0.1584 0.968 0.952 0.036 0.000 0.012
#> GSM2880 1 0.1452 0.969 0.956 0.036 0.000 0.008
#> GSM2893 1 0.1452 0.969 0.956 0.036 0.000 0.008
#> GSM2821 1 0.3877 0.931 0.852 0.044 0.096 0.008
#> GSM2900 1 0.3919 0.933 0.852 0.040 0.096 0.012
#> GSM2903 1 0.3919 0.933 0.852 0.040 0.096 0.012
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM2819 2 0.4401 0.694 0.000 0.656 0.016 0.000 NA
#> GSM2820 3 0.2488 0.948 0.000 0.124 0.872 0.000 NA
#> GSM2822 2 0.2612 0.867 0.000 0.868 0.008 0.000 NA
#> GSM2832 2 0.2612 0.867 0.000 0.868 0.008 0.000 NA
#> GSM2823 2 0.4422 0.730 0.004 0.680 0.016 0.000 NA
#> GSM2824 2 0.4422 0.730 0.004 0.680 0.016 0.000 NA
#> GSM2825 2 0.3562 0.818 0.000 0.788 0.016 0.000 NA
#> GSM2826 2 0.3562 0.818 0.000 0.788 0.016 0.000 NA
#> GSM2829 4 0.0807 0.909 0.000 0.000 0.012 0.976 NA
#> GSM2856 4 0.0807 0.909 0.000 0.000 0.012 0.976 NA
#> GSM2830 4 0.2389 0.914 0.000 0.000 0.004 0.880 NA
#> GSM2843 4 0.2909 0.909 0.000 0.000 0.012 0.848 NA
#> GSM2871 4 0.4193 0.873 0.000 0.000 0.024 0.720 NA
#> GSM2831 4 0.0566 0.911 0.000 0.000 0.012 0.984 NA
#> GSM2844 4 0.0566 0.911 0.000 0.000 0.012 0.984 NA
#> GSM2833 4 0.0693 0.911 0.000 0.000 0.012 0.980 NA
#> GSM2846 4 0.0693 0.911 0.000 0.000 0.012 0.980 NA
#> GSM2835 4 0.0451 0.911 0.000 0.000 0.004 0.988 NA
#> GSM2858 4 0.0451 0.911 0.000 0.000 0.004 0.988 NA
#> GSM2836 2 0.0794 0.906 0.000 0.972 0.000 0.000 NA
#> GSM2848 2 0.0794 0.906 0.000 0.972 0.000 0.000 NA
#> GSM2828 3 0.3339 0.941 0.000 0.124 0.836 0.000 NA
#> GSM2837 3 0.3339 0.941 0.000 0.124 0.836 0.000 NA
#> GSM2839 1 0.4411 0.858 0.756 0.004 0.044 0.004 NA
#> GSM2841 1 0.4411 0.858 0.756 0.004 0.044 0.004 NA
#> GSM2827 2 0.1121 0.904 0.000 0.956 0.000 0.000 NA
#> GSM2842 2 0.1121 0.904 0.000 0.956 0.000 0.000 NA
#> GSM2845 4 0.4223 0.875 0.000 0.000 0.028 0.724 NA
#> GSM2872 4 0.4223 0.875 0.000 0.000 0.028 0.724 NA
#> GSM2834 4 0.4141 0.876 0.000 0.000 0.024 0.728 NA
#> GSM2847 4 0.4026 0.879 0.000 0.000 0.020 0.736 NA
#> GSM2849 3 0.3339 0.941 0.000 0.124 0.836 0.000 NA
#> GSM2850 3 0.3339 0.941 0.000 0.124 0.836 0.000 NA
#> GSM2838 2 0.1357 0.904 0.004 0.948 0.000 0.000 NA
#> GSM2853 2 0.1357 0.904 0.004 0.948 0.000 0.000 NA
#> GSM2852 3 0.4679 0.914 0.000 0.124 0.740 0.000 NA
#> GSM2855 3 0.4679 0.914 0.000 0.124 0.740 0.000 NA
#> GSM2840 1 0.4481 0.857 0.752 0.004 0.048 0.004 NA
#> GSM2857 1 0.4481 0.857 0.752 0.004 0.048 0.004 NA
#> GSM2859 2 0.0162 0.908 0.000 0.996 0.000 0.000 NA
#> GSM2860 2 0.0162 0.908 0.000 0.996 0.000 0.000 NA
#> GSM2861 2 0.0955 0.905 0.004 0.968 0.000 0.000 NA
#> GSM2862 2 0.0162 0.908 0.000 0.996 0.000 0.000 NA
#> GSM2863 2 0.0162 0.908 0.000 0.996 0.000 0.000 NA
#> GSM2864 2 0.0162 0.908 0.000 0.996 0.000 0.000 NA
#> GSM2865 2 0.0162 0.908 0.000 0.996 0.000 0.000 NA
#> GSM2866 2 0.0162 0.908 0.000 0.996 0.000 0.000 NA
#> GSM2868 2 0.1831 0.898 0.004 0.920 0.000 0.000 NA
#> GSM2869 2 0.1831 0.898 0.004 0.920 0.000 0.000 NA
#> GSM2851 2 0.1831 0.898 0.004 0.920 0.000 0.000 NA
#> GSM2867 2 0.1831 0.898 0.004 0.920 0.000 0.000 NA
#> GSM2870 2 0.1831 0.898 0.004 0.920 0.000 0.000 NA
#> GSM2854 4 0.3769 0.900 0.000 0.000 0.032 0.788 NA
#> GSM2873 2 0.1386 0.903 0.000 0.952 0.016 0.000 NA
#> GSM2874 3 0.2329 0.948 0.000 0.124 0.876 0.000 NA
#> GSM2884 3 0.2329 0.948 0.000 0.124 0.876 0.000 NA
#> GSM2875 1 0.0324 0.921 0.992 0.004 0.000 0.004 NA
#> GSM2890 1 0.0324 0.921 0.992 0.004 0.000 0.004 NA
#> GSM2877 1 0.0324 0.921 0.992 0.004 0.000 0.004 NA
#> GSM2892 1 0.0324 0.921 0.992 0.004 0.000 0.004 NA
#> GSM2902 1 0.0324 0.921 0.992 0.004 0.000 0.004 NA
#> GSM2878 1 0.0324 0.921 0.992 0.004 0.000 0.004 NA
#> GSM2901 1 0.0324 0.921 0.992 0.004 0.000 0.004 NA
#> GSM2879 2 0.3086 0.811 0.000 0.816 0.004 0.000 NA
#> GSM2898 2 0.3086 0.811 0.000 0.816 0.004 0.000 NA
#> GSM2881 3 0.2329 0.948 0.000 0.124 0.876 0.000 NA
#> GSM2897 3 0.2329 0.948 0.000 0.124 0.876 0.000 NA
#> GSM2882 4 0.2331 0.915 0.000 0.000 0.020 0.900 NA
#> GSM2894 4 0.2331 0.915 0.000 0.000 0.020 0.900 NA
#> GSM2883 3 0.5332 0.883 0.004 0.120 0.680 0.000 NA
#> GSM2895 3 0.5332 0.883 0.004 0.120 0.680 0.000 NA
#> GSM2885 3 0.2329 0.948 0.000 0.124 0.876 0.000 NA
#> GSM2886 3 0.2329 0.948 0.000 0.124 0.876 0.000 NA
#> GSM2887 3 0.4593 0.915 0.000 0.124 0.748 0.000 NA
#> GSM2896 3 0.4593 0.915 0.000 0.124 0.748 0.000 NA
#> GSM2888 2 0.2763 0.842 0.000 0.848 0.004 0.000 NA
#> GSM2889 2 0.2763 0.842 0.000 0.848 0.004 0.000 NA
#> GSM2876 1 0.0833 0.919 0.976 0.004 0.000 0.004 NA
#> GSM2891 1 0.0833 0.919 0.976 0.004 0.000 0.004 NA
#> GSM2880 1 0.0486 0.921 0.988 0.004 0.004 0.004 NA
#> GSM2893 1 0.0486 0.921 0.988 0.004 0.004 0.004 NA
#> GSM2821 1 0.4025 0.811 0.700 0.008 0.000 0.000 NA
#> GSM2900 1 0.3885 0.826 0.724 0.008 0.000 0.000 NA
#> GSM2903 1 0.3885 0.826 0.724 0.008 0.000 0.000 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM2819 2 0.4721 0.586 0.008 0.540 0.000 0.000 NA 0.032
#> GSM2820 3 0.1785 0.892 0.000 0.048 0.928 0.000 NA 0.016
#> GSM2822 2 0.3175 0.816 0.000 0.808 0.000 0.000 NA 0.028
#> GSM2832 2 0.3175 0.816 0.000 0.808 0.000 0.000 NA 0.028
#> GSM2823 2 0.5150 0.607 0.004 0.528 0.008 0.004 NA 0.044
#> GSM2824 2 0.5150 0.607 0.004 0.528 0.008 0.004 NA 0.044
#> GSM2825 2 0.4164 0.776 0.000 0.728 0.012 0.000 NA 0.040
#> GSM2826 2 0.4164 0.776 0.000 0.728 0.012 0.000 NA 0.040
#> GSM2829 4 0.0810 0.828 0.008 0.000 0.008 0.976 NA 0.004
#> GSM2856 4 0.0810 0.828 0.008 0.000 0.008 0.976 NA 0.004
#> GSM2830 4 0.3759 0.839 0.008 0.000 0.008 0.732 NA 0.248
#> GSM2843 4 0.3997 0.831 0.008 0.000 0.008 0.688 NA 0.292
#> GSM2871 4 0.4348 0.778 0.004 0.004 0.000 0.520 NA 0.464
#> GSM2831 4 0.1129 0.829 0.008 0.000 0.012 0.964 NA 0.012
#> GSM2844 4 0.1129 0.829 0.008 0.000 0.012 0.964 NA 0.012
#> GSM2833 4 0.0972 0.829 0.008 0.000 0.000 0.964 NA 0.000
#> GSM2846 4 0.0972 0.829 0.008 0.000 0.000 0.964 NA 0.000
#> GSM2835 4 0.0806 0.829 0.008 0.000 0.000 0.972 NA 0.000
#> GSM2858 4 0.0806 0.829 0.008 0.000 0.000 0.972 NA 0.000
#> GSM2836 2 0.1686 0.852 0.000 0.924 0.000 0.000 NA 0.012
#> GSM2848 2 0.1686 0.852 0.000 0.924 0.000 0.000 NA 0.012
#> GSM2828 3 0.3899 0.867 0.000 0.048 0.804 0.004 NA 0.112
#> GSM2837 3 0.3899 0.867 0.000 0.048 0.804 0.004 NA 0.112
#> GSM2839 1 0.5634 0.771 0.636 0.004 0.020 0.004 NA 0.164
#> GSM2841 1 0.5634 0.771 0.636 0.004 0.020 0.004 NA 0.164
#> GSM2827 2 0.2199 0.849 0.000 0.892 0.000 0.000 NA 0.020
#> GSM2842 2 0.2199 0.849 0.000 0.892 0.000 0.000 NA 0.020
#> GSM2845 4 0.4393 0.786 0.012 0.000 0.000 0.532 NA 0.448
#> GSM2872 4 0.4393 0.786 0.012 0.000 0.000 0.532 NA 0.448
#> GSM2834 4 0.4083 0.786 0.008 0.000 0.000 0.532 NA 0.460
#> GSM2847 4 0.4072 0.791 0.008 0.000 0.000 0.544 NA 0.448
#> GSM2849 3 0.3899 0.867 0.000 0.048 0.804 0.004 NA 0.112
#> GSM2850 3 0.3899 0.867 0.000 0.048 0.804 0.004 NA 0.112
#> GSM2838 2 0.2309 0.842 0.000 0.888 0.000 0.000 NA 0.028
#> GSM2853 2 0.2309 0.842 0.000 0.888 0.000 0.000 NA 0.028
#> GSM2852 3 0.5133 0.838 0.000 0.048 0.696 0.000 NA 0.104
#> GSM2855 3 0.5133 0.838 0.000 0.048 0.696 0.000 NA 0.104
#> GSM2840 1 0.5634 0.771 0.636 0.004 0.020 0.004 NA 0.164
#> GSM2857 1 0.5634 0.771 0.636 0.004 0.020 0.004 NA 0.164
#> GSM2859 2 0.0146 0.857 0.000 0.996 0.000 0.000 NA 0.000
#> GSM2860 2 0.0146 0.857 0.000 0.996 0.000 0.000 NA 0.000
#> GSM2861 2 0.1643 0.848 0.000 0.924 0.000 0.000 NA 0.008
#> GSM2862 2 0.0146 0.857 0.000 0.996 0.000 0.000 NA 0.000
#> GSM2863 2 0.0146 0.857 0.000 0.996 0.000 0.000 NA 0.000
#> GSM2864 2 0.0146 0.857 0.000 0.996 0.000 0.000 NA 0.000
#> GSM2865 2 0.0146 0.857 0.000 0.996 0.000 0.000 NA 0.000
#> GSM2866 2 0.0405 0.857 0.000 0.988 0.000 0.000 NA 0.004
#> GSM2868 2 0.3332 0.824 0.000 0.808 0.000 0.000 NA 0.048
#> GSM2869 2 0.3332 0.824 0.000 0.808 0.000 0.000 NA 0.048
#> GSM2851 2 0.3213 0.827 0.000 0.820 0.000 0.000 NA 0.048
#> GSM2867 2 0.3332 0.824 0.000 0.808 0.000 0.000 NA 0.048
#> GSM2870 2 0.3254 0.826 0.000 0.816 0.000 0.000 NA 0.048
#> GSM2854 4 0.4264 0.809 0.008 0.000 0.000 0.604 NA 0.376
#> GSM2873 2 0.2250 0.846 0.000 0.896 0.000 0.000 NA 0.040
#> GSM2874 3 0.1477 0.892 0.000 0.048 0.940 0.000 NA 0.008
#> GSM2884 3 0.1075 0.894 0.000 0.048 0.952 0.000 NA 0.000
#> GSM2875 1 0.0291 0.871 0.992 0.004 0.000 0.004 NA 0.000
#> GSM2890 1 0.0291 0.871 0.992 0.004 0.000 0.004 NA 0.000
#> GSM2877 1 0.0291 0.871 0.992 0.004 0.000 0.004 NA 0.000
#> GSM2892 1 0.0291 0.871 0.992 0.004 0.000 0.004 NA 0.000
#> GSM2902 1 0.0291 0.871 0.992 0.004 0.000 0.004 NA 0.000
#> GSM2878 1 0.0291 0.871 0.992 0.004 0.000 0.004 NA 0.000
#> GSM2901 1 0.0291 0.871 0.992 0.004 0.000 0.004 NA 0.000
#> GSM2879 2 0.4656 0.717 0.000 0.684 0.004 0.004 NA 0.072
#> GSM2898 2 0.4656 0.717 0.000 0.684 0.004 0.004 NA 0.072
#> GSM2881 3 0.1075 0.894 0.000 0.048 0.952 0.000 NA 0.000
#> GSM2897 3 0.1075 0.894 0.000 0.048 0.952 0.000 NA 0.000
#> GSM2882 4 0.3521 0.841 0.008 0.000 0.008 0.768 NA 0.212
#> GSM2894 4 0.3521 0.841 0.008 0.000 0.008 0.768 NA 0.212
#> GSM2883 3 0.5903 0.795 0.004 0.052 0.620 0.000 NA 0.136
#> GSM2895 3 0.5903 0.795 0.004 0.052 0.620 0.000 NA 0.136
#> GSM2885 3 0.1075 0.894 0.000 0.048 0.952 0.000 NA 0.000
#> GSM2886 3 0.1075 0.894 0.000 0.048 0.952 0.000 NA 0.000
#> GSM2887 3 0.4811 0.844 0.000 0.048 0.728 0.000 NA 0.088
#> GSM2896 3 0.4811 0.844 0.000 0.048 0.728 0.000 NA 0.088
#> GSM2888 2 0.4438 0.725 0.000 0.708 0.004 0.000 NA 0.080
#> GSM2889 2 0.4438 0.725 0.000 0.708 0.004 0.000 NA 0.080
#> GSM2876 1 0.2016 0.861 0.916 0.004 0.008 0.004 NA 0.004
#> GSM2891 1 0.2016 0.861 0.916 0.004 0.008 0.004 NA 0.004
#> GSM2880 1 0.0436 0.871 0.988 0.004 0.000 0.004 NA 0.004
#> GSM2893 1 0.0436 0.871 0.988 0.004 0.000 0.004 NA 0.004
#> GSM2821 1 0.4522 0.694 0.548 0.008 0.000 0.000 NA 0.020
#> GSM2900 1 0.4473 0.715 0.576 0.008 0.000 0.000 NA 0.020
#> GSM2903 1 0.4473 0.715 0.576 0.008 0.000 0.000 NA 0.020
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> ATC:kmeans 64 3.97e-04 2
#> ATC:kmeans 84 1.65e-08 3
#> ATC:kmeans 84 5.57e-12 4
#> ATC:kmeans 84 5.57e-12 5
#> ATC:kmeans 84 5.57e-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", "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 8229 rows and 84 columns.
#> Top rows (823, 1646, 2468, 3291, 4114) are extracted by 'ATC' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.954 0.966 0.5036 0.497 0.497
#> 3 3 1.000 0.973 0.988 0.2712 0.804 0.627
#> 4 4 0.973 0.946 0.978 0.1806 0.849 0.599
#> 5 5 0.892 0.863 0.927 0.0434 0.962 0.847
#> 6 6 0.879 0.776 0.864 0.0333 0.990 0.954
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
#> GSM2819 1 0.3431 0.967 0.936 0.064
#> GSM2820 2 0.3431 0.948 0.064 0.936
#> GSM2822 2 0.7745 0.685 0.228 0.772
#> GSM2832 2 0.7745 0.685 0.228 0.772
#> GSM2823 2 0.0000 0.963 0.000 1.000
#> GSM2824 2 0.0000 0.963 0.000 1.000
#> GSM2825 1 0.3431 0.967 0.936 0.064
#> GSM2826 1 0.3431 0.967 0.936 0.064
#> GSM2829 1 0.0000 0.962 1.000 0.000
#> GSM2856 1 0.0000 0.962 1.000 0.000
#> GSM2830 1 0.0000 0.962 1.000 0.000
#> GSM2843 1 0.0000 0.962 1.000 0.000
#> GSM2871 1 0.0000 0.962 1.000 0.000
#> GSM2831 1 0.0000 0.962 1.000 0.000
#> GSM2844 1 0.0000 0.962 1.000 0.000
#> GSM2833 1 0.0000 0.962 1.000 0.000
#> GSM2846 1 0.0000 0.962 1.000 0.000
#> GSM2835 1 0.0000 0.962 1.000 0.000
#> GSM2858 1 0.0000 0.962 1.000 0.000
#> GSM2836 2 0.0000 0.963 0.000 1.000
#> GSM2848 2 0.0000 0.963 0.000 1.000
#> GSM2828 2 0.3431 0.948 0.064 0.936
#> GSM2837 2 0.3431 0.948 0.064 0.936
#> GSM2839 1 0.3431 0.967 0.936 0.064
#> GSM2841 1 0.3431 0.967 0.936 0.064
#> GSM2827 2 0.0000 0.963 0.000 1.000
#> GSM2842 2 0.0000 0.963 0.000 1.000
#> GSM2845 1 0.0000 0.962 1.000 0.000
#> GSM2872 1 0.0000 0.962 1.000 0.000
#> GSM2834 1 0.0000 0.962 1.000 0.000
#> GSM2847 1 0.0000 0.962 1.000 0.000
#> GSM2849 2 0.3431 0.948 0.064 0.936
#> GSM2850 2 0.3431 0.948 0.064 0.936
#> GSM2838 2 0.0000 0.963 0.000 1.000
#> GSM2853 2 0.2043 0.957 0.032 0.968
#> GSM2852 2 0.3431 0.948 0.064 0.936
#> GSM2855 2 0.3431 0.948 0.064 0.936
#> GSM2840 1 0.3431 0.967 0.936 0.064
#> GSM2857 1 0.3431 0.967 0.936 0.064
#> GSM2859 2 0.0000 0.963 0.000 1.000
#> GSM2860 2 0.0000 0.963 0.000 1.000
#> GSM2861 2 0.0000 0.963 0.000 1.000
#> GSM2862 2 0.0000 0.963 0.000 1.000
#> GSM2863 2 0.0000 0.963 0.000 1.000
#> GSM2864 2 0.0000 0.963 0.000 1.000
#> GSM2865 2 0.0000 0.963 0.000 1.000
#> GSM2866 2 0.0000 0.963 0.000 1.000
#> GSM2868 2 0.0000 0.963 0.000 1.000
#> GSM2869 2 0.0000 0.963 0.000 1.000
#> GSM2851 2 0.0000 0.963 0.000 1.000
#> GSM2867 2 0.0000 0.963 0.000 1.000
#> GSM2870 2 0.0000 0.963 0.000 1.000
#> GSM2854 1 0.0000 0.962 1.000 0.000
#> GSM2873 2 0.3114 0.950 0.056 0.944
#> GSM2874 2 0.3431 0.948 0.064 0.936
#> GSM2884 2 0.3431 0.948 0.064 0.936
#> GSM2875 1 0.3431 0.967 0.936 0.064
#> GSM2890 1 0.3431 0.967 0.936 0.064
#> GSM2877 1 0.3431 0.967 0.936 0.064
#> GSM2892 1 0.3431 0.967 0.936 0.064
#> GSM2902 1 0.3431 0.967 0.936 0.064
#> GSM2878 1 0.3431 0.967 0.936 0.064
#> GSM2901 1 0.3431 0.967 0.936 0.064
#> GSM2879 2 0.0000 0.963 0.000 1.000
#> GSM2898 2 0.0000 0.963 0.000 1.000
#> GSM2881 2 0.3431 0.948 0.064 0.936
#> GSM2897 2 0.3431 0.948 0.064 0.936
#> GSM2882 1 0.0000 0.962 1.000 0.000
#> GSM2894 1 0.0000 0.962 1.000 0.000
#> GSM2883 2 0.0938 0.961 0.012 0.988
#> GSM2895 2 0.0376 0.963 0.004 0.996
#> GSM2885 2 0.3431 0.948 0.064 0.936
#> GSM2886 2 0.3431 0.948 0.064 0.936
#> GSM2887 2 0.3431 0.948 0.064 0.936
#> GSM2896 2 0.3431 0.948 0.064 0.936
#> GSM2888 2 0.0000 0.963 0.000 1.000
#> GSM2889 2 0.0000 0.963 0.000 1.000
#> GSM2876 1 0.3431 0.967 0.936 0.064
#> GSM2891 1 0.3431 0.967 0.936 0.064
#> GSM2880 1 0.3431 0.967 0.936 0.064
#> GSM2893 1 0.3431 0.967 0.936 0.064
#> GSM2821 1 0.3431 0.967 0.936 0.064
#> GSM2900 1 0.3431 0.967 0.936 0.064
#> GSM2903 1 0.3431 0.967 0.936 0.064
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM2819 1 0.435 0.770 0.816 0.184 0.000
#> GSM2820 3 0.000 0.995 0.000 0.000 1.000
#> GSM2822 1 0.617 0.685 0.740 0.036 0.224
#> GSM2832 1 0.617 0.685 0.740 0.036 0.224
#> GSM2823 1 0.000 0.968 1.000 0.000 0.000
#> GSM2824 1 0.000 0.968 1.000 0.000 0.000
#> GSM2825 1 0.000 0.968 1.000 0.000 0.000
#> GSM2826 1 0.000 0.968 1.000 0.000 0.000
#> GSM2829 2 0.000 0.994 0.000 1.000 0.000
#> GSM2856 2 0.000 0.994 0.000 1.000 0.000
#> GSM2830 2 0.000 0.994 0.000 1.000 0.000
#> GSM2843 2 0.000 0.994 0.000 1.000 0.000
#> GSM2871 2 0.000 0.994 0.000 1.000 0.000
#> GSM2831 2 0.000 0.994 0.000 1.000 0.000
#> GSM2844 2 0.000 0.994 0.000 1.000 0.000
#> GSM2833 2 0.000 0.994 0.000 1.000 0.000
#> GSM2846 2 0.000 0.994 0.000 1.000 0.000
#> GSM2835 2 0.000 0.994 0.000 1.000 0.000
#> GSM2858 2 0.000 0.994 0.000 1.000 0.000
#> GSM2836 3 0.000 0.995 0.000 0.000 1.000
#> GSM2848 3 0.000 0.995 0.000 0.000 1.000
#> GSM2828 3 0.000 0.995 0.000 0.000 1.000
#> GSM2837 3 0.465 0.738 0.000 0.208 0.792
#> GSM2839 1 0.000 0.968 1.000 0.000 0.000
#> GSM2841 1 0.000 0.968 1.000 0.000 0.000
#> GSM2827 3 0.000 0.995 0.000 0.000 1.000
#> GSM2842 3 0.000 0.995 0.000 0.000 1.000
#> GSM2845 2 0.000 0.994 0.000 1.000 0.000
#> GSM2872 2 0.000 0.994 0.000 1.000 0.000
#> GSM2834 2 0.000 0.994 0.000 1.000 0.000
#> GSM2847 2 0.000 0.994 0.000 1.000 0.000
#> GSM2849 3 0.000 0.995 0.000 0.000 1.000
#> GSM2850 3 0.000 0.995 0.000 0.000 1.000
#> GSM2838 3 0.000 0.995 0.000 0.000 1.000
#> GSM2853 3 0.000 0.995 0.000 0.000 1.000
#> GSM2852 3 0.000 0.995 0.000 0.000 1.000
#> GSM2855 3 0.000 0.995 0.000 0.000 1.000
#> GSM2840 1 0.000 0.968 1.000 0.000 0.000
#> GSM2857 1 0.000 0.968 1.000 0.000 0.000
#> GSM2859 3 0.000 0.995 0.000 0.000 1.000
#> GSM2860 3 0.000 0.995 0.000 0.000 1.000
#> GSM2861 3 0.000 0.995 0.000 0.000 1.000
#> GSM2862 3 0.000 0.995 0.000 0.000 1.000
#> GSM2863 3 0.000 0.995 0.000 0.000 1.000
#> GSM2864 3 0.000 0.995 0.000 0.000 1.000
#> GSM2865 3 0.000 0.995 0.000 0.000 1.000
#> GSM2866 3 0.000 0.995 0.000 0.000 1.000
#> GSM2868 3 0.000 0.995 0.000 0.000 1.000
#> GSM2869 3 0.000 0.995 0.000 0.000 1.000
#> GSM2851 3 0.000 0.995 0.000 0.000 1.000
#> GSM2867 3 0.000 0.995 0.000 0.000 1.000
#> GSM2870 3 0.000 0.995 0.000 0.000 1.000
#> GSM2854 2 0.000 0.994 0.000 1.000 0.000
#> GSM2873 2 0.288 0.879 0.000 0.904 0.096
#> GSM2874 3 0.000 0.995 0.000 0.000 1.000
#> GSM2884 3 0.000 0.995 0.000 0.000 1.000
#> GSM2875 1 0.000 0.968 1.000 0.000 0.000
#> GSM2890 1 0.000 0.968 1.000 0.000 0.000
#> GSM2877 1 0.000 0.968 1.000 0.000 0.000
#> GSM2892 1 0.000 0.968 1.000 0.000 0.000
#> GSM2902 1 0.000 0.968 1.000 0.000 0.000
#> GSM2878 1 0.000 0.968 1.000 0.000 0.000
#> GSM2901 1 0.000 0.968 1.000 0.000 0.000
#> GSM2879 3 0.000 0.995 0.000 0.000 1.000
#> GSM2898 3 0.000 0.995 0.000 0.000 1.000
#> GSM2881 3 0.000 0.995 0.000 0.000 1.000
#> GSM2897 3 0.000 0.995 0.000 0.000 1.000
#> GSM2882 2 0.000 0.994 0.000 1.000 0.000
#> GSM2894 2 0.000 0.994 0.000 1.000 0.000
#> GSM2883 3 0.000 0.995 0.000 0.000 1.000
#> GSM2895 3 0.000 0.995 0.000 0.000 1.000
#> GSM2885 3 0.000 0.995 0.000 0.000 1.000
#> GSM2886 3 0.000 0.995 0.000 0.000 1.000
#> GSM2887 3 0.000 0.995 0.000 0.000 1.000
#> GSM2896 3 0.000 0.995 0.000 0.000 1.000
#> GSM2888 3 0.000 0.995 0.000 0.000 1.000
#> GSM2889 3 0.000 0.995 0.000 0.000 1.000
#> GSM2876 1 0.000 0.968 1.000 0.000 0.000
#> GSM2891 1 0.000 0.968 1.000 0.000 0.000
#> GSM2880 1 0.000 0.968 1.000 0.000 0.000
#> GSM2893 1 0.000 0.968 1.000 0.000 0.000
#> GSM2821 1 0.000 0.968 1.000 0.000 0.000
#> GSM2900 1 0.000 0.968 1.000 0.000 0.000
#> GSM2903 1 0.000 0.968 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM2819 1 0.484 0.358 0.604 0.000 0.000 0.396
#> GSM2820 3 0.000 0.973 0.000 0.000 1.000 0.000
#> GSM2822 2 0.000 0.966 0.000 1.000 0.000 0.000
#> GSM2832 2 0.000 0.966 0.000 1.000 0.000 0.000
#> GSM2823 1 0.000 0.968 1.000 0.000 0.000 0.000
#> GSM2824 1 0.000 0.968 1.000 0.000 0.000 0.000
#> GSM2825 1 0.297 0.827 0.856 0.144 0.000 0.000
#> GSM2826 1 0.297 0.827 0.856 0.144 0.000 0.000
#> GSM2829 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM2856 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM2830 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM2843 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM2871 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM2831 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM2844 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM2833 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM2846 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM2835 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM2858 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM2836 2 0.000 0.966 0.000 1.000 0.000 0.000
#> GSM2848 2 0.000 0.966 0.000 1.000 0.000 0.000
#> GSM2828 3 0.000 0.973 0.000 0.000 1.000 0.000
#> GSM2837 3 0.000 0.973 0.000 0.000 1.000 0.000
#> GSM2839 1 0.000 0.968 1.000 0.000 0.000 0.000
#> GSM2841 1 0.000 0.968 1.000 0.000 0.000 0.000
#> GSM2827 2 0.000 0.966 0.000 1.000 0.000 0.000
#> GSM2842 2 0.000 0.966 0.000 1.000 0.000 0.000
#> GSM2845 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM2872 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM2834 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM2847 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM2849 3 0.000 0.973 0.000 0.000 1.000 0.000
#> GSM2850 3 0.000 0.973 0.000 0.000 1.000 0.000
#> GSM2838 2 0.000 0.966 0.000 1.000 0.000 0.000
#> GSM2853 2 0.000 0.966 0.000 1.000 0.000 0.000
#> GSM2852 3 0.000 0.973 0.000 0.000 1.000 0.000
#> GSM2855 3 0.000 0.973 0.000 0.000 1.000 0.000
#> GSM2840 1 0.000 0.968 1.000 0.000 0.000 0.000
#> GSM2857 1 0.000 0.968 1.000 0.000 0.000 0.000
#> GSM2859 2 0.000 0.966 0.000 1.000 0.000 0.000
#> GSM2860 2 0.000 0.966 0.000 1.000 0.000 0.000
#> GSM2861 2 0.000 0.966 0.000 1.000 0.000 0.000
#> GSM2862 2 0.000 0.966 0.000 1.000 0.000 0.000
#> GSM2863 2 0.000 0.966 0.000 1.000 0.000 0.000
#> GSM2864 2 0.000 0.966 0.000 1.000 0.000 0.000
#> GSM2865 2 0.000 0.966 0.000 1.000 0.000 0.000
#> GSM2866 2 0.000 0.966 0.000 1.000 0.000 0.000
#> GSM2868 2 0.000 0.966 0.000 1.000 0.000 0.000
#> GSM2869 2 0.000 0.966 0.000 1.000 0.000 0.000
#> GSM2851 2 0.000 0.966 0.000 1.000 0.000 0.000
#> GSM2867 2 0.000 0.966 0.000 1.000 0.000 0.000
#> GSM2870 2 0.000 0.966 0.000 1.000 0.000 0.000
#> GSM2854 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM2873 2 0.000 0.966 0.000 1.000 0.000 0.000
#> GSM2874 3 0.000 0.973 0.000 0.000 1.000 0.000
#> GSM2884 3 0.000 0.973 0.000 0.000 1.000 0.000
#> GSM2875 1 0.000 0.968 1.000 0.000 0.000 0.000
#> GSM2890 1 0.000 0.968 1.000 0.000 0.000 0.000
#> GSM2877 1 0.000 0.968 1.000 0.000 0.000 0.000
#> GSM2892 1 0.000 0.968 1.000 0.000 0.000 0.000
#> GSM2902 1 0.000 0.968 1.000 0.000 0.000 0.000
#> GSM2878 1 0.000 0.968 1.000 0.000 0.000 0.000
#> GSM2901 1 0.000 0.968 1.000 0.000 0.000 0.000
#> GSM2879 3 0.387 0.710 0.000 0.228 0.772 0.000
#> GSM2898 3 0.387 0.710 0.000 0.228 0.772 0.000
#> GSM2881 3 0.000 0.973 0.000 0.000 1.000 0.000
#> GSM2897 3 0.000 0.973 0.000 0.000 1.000 0.000
#> GSM2882 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM2894 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM2883 3 0.000 0.973 0.000 0.000 1.000 0.000
#> GSM2895 3 0.000 0.973 0.000 0.000 1.000 0.000
#> GSM2885 3 0.000 0.973 0.000 0.000 1.000 0.000
#> GSM2886 3 0.000 0.973 0.000 0.000 1.000 0.000
#> GSM2887 3 0.000 0.973 0.000 0.000 1.000 0.000
#> GSM2896 3 0.000 0.973 0.000 0.000 1.000 0.000
#> GSM2888 2 0.476 0.428 0.000 0.628 0.372 0.000
#> GSM2889 2 0.476 0.428 0.000 0.628 0.372 0.000
#> GSM2876 1 0.000 0.968 1.000 0.000 0.000 0.000
#> GSM2891 1 0.000 0.968 1.000 0.000 0.000 0.000
#> GSM2880 1 0.000 0.968 1.000 0.000 0.000 0.000
#> GSM2893 1 0.000 0.968 1.000 0.000 0.000 0.000
#> GSM2821 1 0.000 0.968 1.000 0.000 0.000 0.000
#> GSM2900 1 0.000 0.968 1.000 0.000 0.000 0.000
#> GSM2903 1 0.000 0.968 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
#> GSM2819 5 0.6124 0.090 0.412 0.000 0.000 0.128 0.460
#> GSM2820 3 0.0000 0.944 0.000 0.000 1.000 0.000 0.000
#> GSM2822 5 0.3661 0.572 0.000 0.276 0.000 0.000 0.724
#> GSM2832 5 0.3661 0.572 0.000 0.276 0.000 0.000 0.724
#> GSM2823 1 0.2732 0.839 0.840 0.000 0.000 0.000 0.160
#> GSM2824 1 0.2732 0.839 0.840 0.000 0.000 0.000 0.160
#> GSM2825 5 0.3727 0.630 0.216 0.016 0.000 0.000 0.768
#> GSM2826 5 0.3727 0.630 0.216 0.016 0.000 0.000 0.768
#> GSM2829 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM2856 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM2830 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM2843 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM2871 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM2831 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM2844 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM2833 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM2846 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM2835 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM2858 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM2836 2 0.2732 0.800 0.000 0.840 0.000 0.000 0.160
#> GSM2848 2 0.2732 0.800 0.000 0.840 0.000 0.000 0.160
#> GSM2828 3 0.0000 0.944 0.000 0.000 1.000 0.000 0.000
#> GSM2837 3 0.0000 0.944 0.000 0.000 1.000 0.000 0.000
#> GSM2839 1 0.1671 0.903 0.924 0.000 0.000 0.000 0.076
#> GSM2841 1 0.1671 0.903 0.924 0.000 0.000 0.000 0.076
#> GSM2827 2 0.3752 0.657 0.000 0.708 0.000 0.000 0.292
#> GSM2842 2 0.3752 0.657 0.000 0.708 0.000 0.000 0.292
#> GSM2845 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM2872 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM2834 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM2847 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM2849 3 0.0000 0.944 0.000 0.000 1.000 0.000 0.000
#> GSM2850 3 0.0000 0.944 0.000 0.000 1.000 0.000 0.000
#> GSM2838 2 0.1270 0.837 0.000 0.948 0.000 0.000 0.052
#> GSM2853 2 0.1270 0.837 0.000 0.948 0.000 0.000 0.052
#> GSM2852 3 0.0162 0.943 0.000 0.000 0.996 0.000 0.004
#> GSM2855 3 0.0162 0.943 0.000 0.000 0.996 0.000 0.004
#> GSM2840 1 0.1671 0.903 0.924 0.000 0.000 0.000 0.076
#> GSM2857 1 0.1671 0.903 0.924 0.000 0.000 0.000 0.076
#> GSM2859 2 0.1732 0.847 0.000 0.920 0.000 0.000 0.080
#> GSM2860 2 0.1732 0.847 0.000 0.920 0.000 0.000 0.080
#> GSM2861 2 0.0000 0.844 0.000 1.000 0.000 0.000 0.000
#> GSM2862 2 0.1732 0.847 0.000 0.920 0.000 0.000 0.080
#> GSM2863 2 0.1732 0.847 0.000 0.920 0.000 0.000 0.080
#> GSM2864 2 0.1732 0.847 0.000 0.920 0.000 0.000 0.080
#> GSM2865 2 0.1732 0.847 0.000 0.920 0.000 0.000 0.080
#> GSM2866 2 0.1732 0.847 0.000 0.920 0.000 0.000 0.080
#> GSM2868 2 0.1270 0.837 0.000 0.948 0.000 0.000 0.052
#> GSM2869 2 0.1270 0.837 0.000 0.948 0.000 0.000 0.052
#> GSM2851 2 0.1270 0.837 0.000 0.948 0.000 0.000 0.052
#> GSM2867 2 0.1270 0.837 0.000 0.948 0.000 0.000 0.052
#> GSM2870 2 0.1270 0.837 0.000 0.948 0.000 0.000 0.052
#> GSM2854 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM2873 5 0.3999 0.442 0.000 0.344 0.000 0.000 0.656
#> GSM2874 3 0.0000 0.944 0.000 0.000 1.000 0.000 0.000
#> GSM2884 3 0.0000 0.944 0.000 0.000 1.000 0.000 0.000
#> GSM2875 1 0.0000 0.946 1.000 0.000 0.000 0.000 0.000
#> GSM2890 1 0.0000 0.946 1.000 0.000 0.000 0.000 0.000
#> GSM2877 1 0.0000 0.946 1.000 0.000 0.000 0.000 0.000
#> GSM2892 1 0.0000 0.946 1.000 0.000 0.000 0.000 0.000
#> GSM2902 1 0.0000 0.946 1.000 0.000 0.000 0.000 0.000
#> GSM2878 1 0.0000 0.946 1.000 0.000 0.000 0.000 0.000
#> GSM2901 1 0.0000 0.946 1.000 0.000 0.000 0.000 0.000
#> GSM2879 3 0.5580 0.370 0.000 0.336 0.576 0.000 0.088
#> GSM2898 3 0.5593 0.360 0.000 0.340 0.572 0.000 0.088
#> GSM2881 3 0.0000 0.944 0.000 0.000 1.000 0.000 0.000
#> GSM2897 3 0.0000 0.944 0.000 0.000 1.000 0.000 0.000
#> GSM2882 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM2894 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM2883 3 0.0162 0.943 0.000 0.000 0.996 0.000 0.004
#> GSM2895 3 0.0162 0.943 0.000 0.000 0.996 0.000 0.004
#> GSM2885 3 0.0000 0.944 0.000 0.000 1.000 0.000 0.000
#> GSM2886 3 0.0000 0.944 0.000 0.000 1.000 0.000 0.000
#> GSM2887 3 0.0162 0.943 0.000 0.000 0.996 0.000 0.004
#> GSM2896 3 0.0162 0.943 0.000 0.000 0.996 0.000 0.004
#> GSM2888 2 0.4290 0.443 0.000 0.680 0.304 0.000 0.016
#> GSM2889 2 0.4290 0.443 0.000 0.680 0.304 0.000 0.016
#> GSM2876 1 0.0000 0.946 1.000 0.000 0.000 0.000 0.000
#> GSM2891 1 0.0000 0.946 1.000 0.000 0.000 0.000 0.000
#> GSM2880 1 0.0000 0.946 1.000 0.000 0.000 0.000 0.000
#> GSM2893 1 0.0000 0.946 1.000 0.000 0.000 0.000 0.000
#> GSM2821 1 0.2020 0.892 0.900 0.000 0.000 0.000 0.100
#> GSM2900 1 0.2020 0.892 0.900 0.000 0.000 0.000 0.100
#> GSM2903 1 0.2020 0.892 0.900 0.000 0.000 0.000 0.100
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM2819 5 0.6921 0.0732 0.336 0.000 0.000 0.080 0.408 0.176
#> GSM2820 3 0.0000 0.9691 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2822 5 0.4239 0.5957 0.000 0.248 0.000 0.000 0.696 0.056
#> GSM2832 5 0.4239 0.5957 0.000 0.248 0.000 0.000 0.696 0.056
#> GSM2823 1 0.5629 0.2483 0.448 0.000 0.000 0.000 0.148 0.404
#> GSM2824 1 0.5629 0.2483 0.448 0.000 0.000 0.000 0.148 0.404
#> GSM2825 5 0.3874 0.6030 0.136 0.060 0.000 0.000 0.788 0.016
#> GSM2826 5 0.3874 0.6030 0.136 0.060 0.000 0.000 0.788 0.016
#> GSM2829 4 0.0000 0.9983 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2856 4 0.0000 0.9983 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2830 4 0.0000 0.9983 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2843 4 0.0000 0.9983 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2871 4 0.0291 0.9941 0.000 0.000 0.000 0.992 0.004 0.004
#> GSM2831 4 0.0000 0.9983 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2844 4 0.0000 0.9983 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2833 4 0.0000 0.9983 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2846 4 0.0000 0.9983 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2835 4 0.0000 0.9983 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2858 4 0.0000 0.9983 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2836 2 0.3514 0.4195 0.000 0.752 0.000 0.000 0.020 0.228
#> GSM2848 2 0.3514 0.4195 0.000 0.752 0.000 0.000 0.020 0.228
#> GSM2828 3 0.0000 0.9691 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2837 3 0.0000 0.9691 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2839 1 0.2868 0.7654 0.840 0.000 0.000 0.000 0.132 0.028
#> GSM2841 1 0.2868 0.7654 0.840 0.000 0.000 0.000 0.132 0.028
#> GSM2827 2 0.5582 -0.1216 0.000 0.476 0.000 0.000 0.144 0.380
#> GSM2842 2 0.5582 -0.1216 0.000 0.476 0.000 0.000 0.144 0.380
#> GSM2845 4 0.0291 0.9941 0.000 0.000 0.000 0.992 0.004 0.004
#> GSM2872 4 0.0291 0.9941 0.000 0.000 0.000 0.992 0.004 0.004
#> GSM2834 4 0.0146 0.9965 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM2847 4 0.0146 0.9965 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM2849 3 0.0000 0.9691 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2850 3 0.0000 0.9691 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2838 2 0.3619 0.6526 0.000 0.680 0.000 0.000 0.004 0.316
#> GSM2853 2 0.3619 0.6526 0.000 0.680 0.000 0.000 0.004 0.316
#> GSM2852 3 0.1461 0.9379 0.000 0.000 0.940 0.000 0.016 0.044
#> GSM2855 3 0.1461 0.9379 0.000 0.000 0.940 0.000 0.016 0.044
#> GSM2840 1 0.2868 0.7654 0.840 0.000 0.000 0.000 0.132 0.028
#> GSM2857 1 0.2868 0.7654 0.840 0.000 0.000 0.000 0.132 0.028
#> GSM2859 2 0.0146 0.6746 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM2860 2 0.0146 0.6746 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM2861 2 0.1957 0.6736 0.000 0.888 0.000 0.000 0.000 0.112
#> GSM2862 2 0.0146 0.6746 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM2863 2 0.0146 0.6746 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM2864 2 0.0146 0.6746 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM2865 2 0.0146 0.6746 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM2866 2 0.0260 0.6724 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM2868 2 0.3953 0.6497 0.000 0.656 0.000 0.000 0.016 0.328
#> GSM2869 2 0.3953 0.6497 0.000 0.656 0.000 0.000 0.016 0.328
#> GSM2851 2 0.3953 0.6497 0.000 0.656 0.000 0.000 0.016 0.328
#> GSM2867 2 0.3953 0.6497 0.000 0.656 0.000 0.000 0.016 0.328
#> GSM2870 2 0.3953 0.6497 0.000 0.656 0.000 0.000 0.016 0.328
#> GSM2854 4 0.0000 0.9983 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2873 5 0.5469 0.4048 0.000 0.324 0.000 0.000 0.532 0.144
#> GSM2874 3 0.0000 0.9691 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2884 3 0.0000 0.9691 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2875 1 0.0000 0.8544 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2890 1 0.0000 0.8544 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2877 1 0.0000 0.8544 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2892 1 0.0000 0.8544 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2902 1 0.0000 0.8544 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2878 1 0.0000 0.8544 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2901 1 0.0000 0.8544 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2879 6 0.6838 1.0000 0.000 0.212 0.288 0.000 0.064 0.436
#> GSM2898 6 0.6838 1.0000 0.000 0.212 0.288 0.000 0.064 0.436
#> GSM2881 3 0.0000 0.9691 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2897 3 0.0000 0.9691 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2882 4 0.0000 0.9983 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2894 4 0.0000 0.9983 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2883 3 0.1500 0.9352 0.000 0.000 0.936 0.000 0.012 0.052
#> GSM2895 3 0.1563 0.9314 0.000 0.000 0.932 0.000 0.012 0.056
#> GSM2885 3 0.0000 0.9691 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2886 3 0.0000 0.9691 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2887 3 0.1461 0.9379 0.000 0.000 0.940 0.000 0.016 0.044
#> GSM2896 3 0.1461 0.9379 0.000 0.000 0.940 0.000 0.016 0.044
#> GSM2888 2 0.6183 0.2440 0.000 0.488 0.252 0.000 0.016 0.244
#> GSM2889 2 0.6183 0.2440 0.000 0.488 0.252 0.000 0.016 0.244
#> GSM2876 1 0.0000 0.8544 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2891 1 0.0000 0.8544 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2880 1 0.0000 0.8544 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2893 1 0.0000 0.8544 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2821 1 0.4094 0.6850 0.744 0.000 0.000 0.000 0.088 0.168
#> GSM2900 1 0.4094 0.6850 0.744 0.000 0.000 0.000 0.088 0.168
#> GSM2903 1 0.4094 0.6850 0.744 0.000 0.000 0.000 0.088 0.168
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 tissue(p) k
#> ATC:skmeans 84 4.54e-05 2
#> ATC:skmeans 84 6.67e-09 3
#> ATC:skmeans 81 6.79e-12 4
#> ATC:skmeans 78 3.91e-15 5
#> ATC:skmeans 74 9.11e-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", "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 8229 rows and 84 columns.
#> Top rows (823, 1646, 2468, 3291, 4114) are extracted by 'ATC' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.510 0.893 0.895 0.3347 0.659 0.659
#> 3 3 0.676 0.906 0.861 0.7047 0.771 0.652
#> 4 4 1.000 0.969 0.989 0.2790 0.839 0.626
#> 5 5 1.000 0.958 0.983 0.0278 0.981 0.931
#> 6 6 0.973 0.901 0.951 0.0250 0.968 0.879
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] 4 5
There is also optional best \(k\) = 4 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
#> GSM2819 2 0.000 0.914 0.000 1.000
#> GSM2820 2 0.000 0.914 0.000 1.000
#> GSM2822 2 0.000 0.914 0.000 1.000
#> GSM2832 2 0.000 0.914 0.000 1.000
#> GSM2823 2 0.000 0.914 0.000 1.000
#> GSM2824 2 0.000 0.914 0.000 1.000
#> GSM2825 2 0.000 0.914 0.000 1.000
#> GSM2826 2 0.000 0.914 0.000 1.000
#> GSM2829 2 0.808 0.746 0.248 0.752
#> GSM2856 2 0.808 0.746 0.248 0.752
#> GSM2830 2 0.808 0.746 0.248 0.752
#> GSM2843 2 0.808 0.746 0.248 0.752
#> GSM2871 2 0.000 0.914 0.000 1.000
#> GSM2831 2 0.808 0.746 0.248 0.752
#> GSM2844 2 0.808 0.746 0.248 0.752
#> GSM2833 2 0.808 0.746 0.248 0.752
#> GSM2846 2 0.808 0.746 0.248 0.752
#> GSM2835 2 0.808 0.746 0.248 0.752
#> GSM2858 2 0.808 0.746 0.248 0.752
#> GSM2836 2 0.000 0.914 0.000 1.000
#> GSM2848 2 0.000 0.914 0.000 1.000
#> GSM2828 2 0.000 0.914 0.000 1.000
#> GSM2837 2 0.000 0.914 0.000 1.000
#> GSM2839 1 0.808 0.986 0.752 0.248
#> GSM2841 1 0.808 0.986 0.752 0.248
#> GSM2827 2 0.000 0.914 0.000 1.000
#> GSM2842 2 0.000 0.914 0.000 1.000
#> GSM2845 2 0.745 0.771 0.212 0.788
#> GSM2872 2 0.808 0.746 0.248 0.752
#> GSM2834 2 0.767 0.763 0.224 0.776
#> GSM2847 2 0.808 0.746 0.248 0.752
#> GSM2849 2 0.000 0.914 0.000 1.000
#> GSM2850 2 0.000 0.914 0.000 1.000
#> GSM2838 2 0.000 0.914 0.000 1.000
#> GSM2853 2 0.000 0.914 0.000 1.000
#> GSM2852 2 0.000 0.914 0.000 1.000
#> GSM2855 2 0.000 0.914 0.000 1.000
#> GSM2840 1 0.808 0.986 0.752 0.248
#> GSM2857 1 0.808 0.986 0.752 0.248
#> GSM2859 2 0.000 0.914 0.000 1.000
#> GSM2860 2 0.000 0.914 0.000 1.000
#> GSM2861 2 0.000 0.914 0.000 1.000
#> GSM2862 2 0.000 0.914 0.000 1.000
#> GSM2863 2 0.000 0.914 0.000 1.000
#> GSM2864 2 0.000 0.914 0.000 1.000
#> GSM2865 2 0.000 0.914 0.000 1.000
#> GSM2866 2 0.000 0.914 0.000 1.000
#> GSM2868 2 0.000 0.914 0.000 1.000
#> GSM2869 2 0.000 0.914 0.000 1.000
#> GSM2851 2 0.000 0.914 0.000 1.000
#> GSM2867 2 0.000 0.914 0.000 1.000
#> GSM2870 2 0.000 0.914 0.000 1.000
#> GSM2854 2 0.808 0.746 0.248 0.752
#> GSM2873 2 0.000 0.914 0.000 1.000
#> GSM2874 2 0.000 0.914 0.000 1.000
#> GSM2884 2 0.000 0.914 0.000 1.000
#> GSM2875 1 0.808 0.986 0.752 0.248
#> GSM2890 1 0.808 0.986 0.752 0.248
#> GSM2877 1 0.808 0.986 0.752 0.248
#> GSM2892 1 0.808 0.986 0.752 0.248
#> GSM2902 1 0.808 0.986 0.752 0.248
#> GSM2878 1 0.808 0.986 0.752 0.248
#> GSM2901 1 0.808 0.986 0.752 0.248
#> GSM2879 2 0.000 0.914 0.000 1.000
#> GSM2898 2 0.000 0.914 0.000 1.000
#> GSM2881 2 0.000 0.914 0.000 1.000
#> GSM2897 2 0.000 0.914 0.000 1.000
#> GSM2882 2 0.808 0.746 0.248 0.752
#> GSM2894 2 0.808 0.746 0.248 0.752
#> GSM2883 2 0.000 0.914 0.000 1.000
#> GSM2895 2 0.000 0.914 0.000 1.000
#> GSM2885 2 0.000 0.914 0.000 1.000
#> GSM2886 2 0.000 0.914 0.000 1.000
#> GSM2887 2 0.000 0.914 0.000 1.000
#> GSM2896 2 0.000 0.914 0.000 1.000
#> GSM2888 2 0.000 0.914 0.000 1.000
#> GSM2889 2 0.000 0.914 0.000 1.000
#> GSM2876 1 0.808 0.986 0.752 0.248
#> GSM2891 1 0.808 0.986 0.752 0.248
#> GSM2880 1 0.808 0.986 0.752 0.248
#> GSM2893 1 0.808 0.986 0.752 0.248
#> GSM2821 1 0.981 0.705 0.580 0.420
#> GSM2900 1 0.808 0.986 0.752 0.248
#> GSM2903 1 0.808 0.986 0.752 0.248
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM2819 3 0.460 0.902 0.000 0.204 0.796
#> GSM2820 3 0.000 0.831 0.000 0.000 1.000
#> GSM2822 3 0.460 0.902 0.000 0.204 0.796
#> GSM2832 3 0.460 0.902 0.000 0.204 0.796
#> GSM2823 3 0.460 0.902 0.000 0.204 0.796
#> GSM2824 3 0.460 0.902 0.000 0.204 0.796
#> GSM2825 3 0.460 0.902 0.000 0.204 0.796
#> GSM2826 3 0.460 0.902 0.000 0.204 0.796
#> GSM2829 2 0.000 0.982 0.000 1.000 0.000
#> GSM2856 2 0.000 0.982 0.000 1.000 0.000
#> GSM2830 2 0.000 0.982 0.000 1.000 0.000
#> GSM2843 2 0.000 0.982 0.000 1.000 0.000
#> GSM2871 3 0.475 0.891 0.000 0.216 0.784
#> GSM2831 2 0.000 0.982 0.000 1.000 0.000
#> GSM2844 2 0.000 0.982 0.000 1.000 0.000
#> GSM2833 2 0.000 0.982 0.000 1.000 0.000
#> GSM2846 2 0.000 0.982 0.000 1.000 0.000
#> GSM2835 2 0.000 0.982 0.000 1.000 0.000
#> GSM2858 2 0.000 0.982 0.000 1.000 0.000
#> GSM2836 3 0.460 0.902 0.000 0.204 0.796
#> GSM2848 3 0.460 0.902 0.000 0.204 0.796
#> GSM2828 3 0.000 0.831 0.000 0.000 1.000
#> GSM2837 3 0.000 0.831 0.000 0.000 1.000
#> GSM2839 1 0.000 0.975 1.000 0.000 0.000
#> GSM2841 1 0.000 0.975 1.000 0.000 0.000
#> GSM2827 3 0.460 0.902 0.000 0.204 0.796
#> GSM2842 3 0.460 0.902 0.000 0.204 0.796
#> GSM2845 3 0.604 0.653 0.000 0.380 0.620
#> GSM2872 2 0.000 0.982 0.000 1.000 0.000
#> GSM2834 2 0.450 0.676 0.000 0.804 0.196
#> GSM2847 2 0.000 0.982 0.000 1.000 0.000
#> GSM2849 3 0.000 0.831 0.000 0.000 1.000
#> GSM2850 3 0.000 0.831 0.000 0.000 1.000
#> GSM2838 3 0.460 0.902 0.000 0.204 0.796
#> GSM2853 3 0.460 0.902 0.000 0.204 0.796
#> GSM2852 3 0.000 0.831 0.000 0.000 1.000
#> GSM2855 3 0.000 0.831 0.000 0.000 1.000
#> GSM2840 1 0.382 0.760 0.852 0.148 0.000
#> GSM2857 1 0.000 0.975 1.000 0.000 0.000
#> GSM2859 3 0.460 0.902 0.000 0.204 0.796
#> GSM2860 3 0.460 0.902 0.000 0.204 0.796
#> GSM2861 3 0.460 0.902 0.000 0.204 0.796
#> GSM2862 3 0.460 0.902 0.000 0.204 0.796
#> GSM2863 3 0.460 0.902 0.000 0.204 0.796
#> GSM2864 3 0.460 0.902 0.000 0.204 0.796
#> GSM2865 3 0.460 0.902 0.000 0.204 0.796
#> GSM2866 3 0.460 0.902 0.000 0.204 0.796
#> GSM2868 3 0.460 0.902 0.000 0.204 0.796
#> GSM2869 3 0.460 0.902 0.000 0.204 0.796
#> GSM2851 3 0.460 0.902 0.000 0.204 0.796
#> GSM2867 3 0.460 0.902 0.000 0.204 0.796
#> GSM2870 3 0.460 0.902 0.000 0.204 0.796
#> GSM2854 2 0.000 0.982 0.000 1.000 0.000
#> GSM2873 3 0.460 0.902 0.000 0.204 0.796
#> GSM2874 3 0.000 0.831 0.000 0.000 1.000
#> GSM2884 3 0.000 0.831 0.000 0.000 1.000
#> GSM2875 1 0.000 0.975 1.000 0.000 0.000
#> GSM2890 1 0.000 0.975 1.000 0.000 0.000
#> GSM2877 1 0.000 0.975 1.000 0.000 0.000
#> GSM2892 1 0.000 0.975 1.000 0.000 0.000
#> GSM2902 1 0.000 0.975 1.000 0.000 0.000
#> GSM2878 1 0.000 0.975 1.000 0.000 0.000
#> GSM2901 1 0.000 0.975 1.000 0.000 0.000
#> GSM2879 3 0.440 0.898 0.000 0.188 0.812
#> GSM2898 3 0.375 0.884 0.000 0.144 0.856
#> GSM2881 3 0.000 0.831 0.000 0.000 1.000
#> GSM2897 3 0.000 0.831 0.000 0.000 1.000
#> GSM2882 2 0.000 0.982 0.000 1.000 0.000
#> GSM2894 2 0.000 0.982 0.000 1.000 0.000
#> GSM2883 3 0.000 0.831 0.000 0.000 1.000
#> GSM2895 3 0.000 0.831 0.000 0.000 1.000
#> GSM2885 3 0.000 0.831 0.000 0.000 1.000
#> GSM2886 3 0.000 0.831 0.000 0.000 1.000
#> GSM2887 3 0.000 0.831 0.000 0.000 1.000
#> GSM2896 3 0.000 0.831 0.000 0.000 1.000
#> GSM2888 3 0.450 0.900 0.000 0.196 0.804
#> GSM2889 3 0.429 0.896 0.000 0.180 0.820
#> GSM2876 1 0.000 0.975 1.000 0.000 0.000
#> GSM2891 1 0.000 0.975 1.000 0.000 0.000
#> GSM2880 1 0.000 0.975 1.000 0.000 0.000
#> GSM2893 1 0.000 0.975 1.000 0.000 0.000
#> GSM2821 1 0.462 0.761 0.840 0.024 0.136
#> GSM2900 1 0.000 0.975 1.000 0.000 0.000
#> GSM2903 1 0.000 0.975 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM2819 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM2820 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM2822 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM2832 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM2823 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM2824 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM2825 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM2826 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM2829 4 0.0000 0.962 0.000 0.000 0.000 1.000
#> GSM2856 4 0.0000 0.962 0.000 0.000 0.000 1.000
#> GSM2830 4 0.0000 0.962 0.000 0.000 0.000 1.000
#> GSM2843 4 0.0000 0.962 0.000 0.000 0.000 1.000
#> GSM2871 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM2831 4 0.0000 0.962 0.000 0.000 0.000 1.000
#> GSM2844 4 0.0000 0.962 0.000 0.000 0.000 1.000
#> GSM2833 4 0.0000 0.962 0.000 0.000 0.000 1.000
#> GSM2846 4 0.0000 0.962 0.000 0.000 0.000 1.000
#> GSM2835 4 0.0000 0.962 0.000 0.000 0.000 1.000
#> GSM2858 4 0.0000 0.962 0.000 0.000 0.000 1.000
#> GSM2836 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM2848 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM2828 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM2837 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM2839 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM2841 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM2827 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM2842 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM2845 2 0.4331 0.575 0.000 0.712 0.000 0.288
#> GSM2872 4 0.0000 0.962 0.000 0.000 0.000 1.000
#> GSM2834 4 0.4981 0.114 0.000 0.464 0.000 0.536
#> GSM2847 4 0.0000 0.962 0.000 0.000 0.000 1.000
#> GSM2849 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM2850 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM2838 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM2853 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM2852 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM2855 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM2840 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM2857 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM2859 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM2860 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM2861 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM2862 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM2863 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM2864 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM2865 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM2866 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM2868 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM2869 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM2851 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM2867 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM2870 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM2854 4 0.0188 0.958 0.000 0.004 0.000 0.996
#> GSM2873 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM2874 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM2884 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM2875 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM2890 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM2877 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM2892 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM2902 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM2878 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM2901 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM2879 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM2898 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM2881 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM2897 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM2882 4 0.0000 0.962 0.000 0.000 0.000 1.000
#> GSM2894 4 0.0000 0.962 0.000 0.000 0.000 1.000
#> GSM2883 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM2895 3 0.0188 0.995 0.000 0.004 0.996 0.000
#> GSM2885 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM2886 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM2887 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM2896 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM2888 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM2889 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM2876 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM2891 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM2880 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM2893 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM2821 1 0.3074 0.799 0.848 0.152 0.000 0.000
#> GSM2900 1 0.0000 0.989 1.000 0.000 0.000 0.000
#> GSM2903 1 0.0000 0.989 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
#> GSM2819 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000
#> GSM2820 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2822 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000
#> GSM2832 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000
#> GSM2823 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000
#> GSM2824 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000
#> GSM2825 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000
#> GSM2826 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000
#> GSM2829 4 0.0000 0.946 0.000 0.000 0.000 1.000 0.000
#> GSM2856 4 0.0000 0.946 0.000 0.000 0.000 1.000 0.000
#> GSM2830 4 0.0000 0.946 0.000 0.000 0.000 1.000 0.000
#> GSM2843 4 0.0290 0.944 0.000 0.000 0.000 0.992 0.008
#> GSM2871 2 0.0609 0.970 0.000 0.980 0.000 0.000 0.020
#> GSM2831 4 0.0000 0.946 0.000 0.000 0.000 1.000 0.000
#> GSM2844 4 0.0000 0.946 0.000 0.000 0.000 1.000 0.000
#> GSM2833 4 0.0000 0.946 0.000 0.000 0.000 1.000 0.000
#> GSM2846 4 0.0000 0.946 0.000 0.000 0.000 1.000 0.000
#> GSM2835 4 0.0000 0.946 0.000 0.000 0.000 1.000 0.000
#> GSM2858 4 0.0000 0.946 0.000 0.000 0.000 1.000 0.000
#> GSM2836 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000
#> GSM2848 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000
#> GSM2828 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2837 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2839 5 0.0609 0.998 0.020 0.000 0.000 0.000 0.980
#> GSM2841 5 0.0609 0.998 0.020 0.000 0.000 0.000 0.980
#> GSM2827 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000
#> GSM2842 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000
#> GSM2845 2 0.4206 0.576 0.000 0.708 0.000 0.272 0.020
#> GSM2872 4 0.0609 0.939 0.000 0.000 0.000 0.980 0.020
#> GSM2834 4 0.4821 0.100 0.000 0.464 0.000 0.516 0.020
#> GSM2847 4 0.0609 0.939 0.000 0.000 0.000 0.980 0.020
#> GSM2849 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2850 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2838 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000
#> GSM2853 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000
#> GSM2852 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2855 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2840 5 0.0609 0.998 0.020 0.000 0.000 0.000 0.980
#> GSM2857 5 0.0609 0.998 0.020 0.000 0.000 0.000 0.980
#> GSM2859 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000
#> GSM2860 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000
#> GSM2861 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000
#> GSM2862 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000
#> GSM2863 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000
#> GSM2864 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000
#> GSM2865 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000
#> GSM2866 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000
#> GSM2868 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000
#> GSM2869 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000
#> GSM2851 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000
#> GSM2867 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000
#> GSM2870 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000
#> GSM2854 4 0.0771 0.936 0.000 0.004 0.000 0.976 0.020
#> GSM2873 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000
#> GSM2874 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2884 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2875 1 0.0000 0.962 1.000 0.000 0.000 0.000 0.000
#> GSM2890 1 0.0000 0.962 1.000 0.000 0.000 0.000 0.000
#> GSM2877 1 0.0000 0.962 1.000 0.000 0.000 0.000 0.000
#> GSM2892 1 0.0000 0.962 1.000 0.000 0.000 0.000 0.000
#> GSM2902 1 0.0000 0.962 1.000 0.000 0.000 0.000 0.000
#> GSM2878 1 0.0000 0.962 1.000 0.000 0.000 0.000 0.000
#> GSM2901 1 0.0000 0.962 1.000 0.000 0.000 0.000 0.000
#> GSM2879 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000
#> GSM2898 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000
#> GSM2881 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2897 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2882 4 0.0290 0.944 0.000 0.000 0.000 0.992 0.008
#> GSM2894 4 0.0609 0.939 0.000 0.000 0.000 0.980 0.020
#> GSM2883 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2895 3 0.0162 0.994 0.000 0.004 0.996 0.000 0.000
#> GSM2885 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2886 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2887 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2896 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2888 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000
#> GSM2889 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000
#> GSM2876 1 0.0000 0.962 1.000 0.000 0.000 0.000 0.000
#> GSM2891 1 0.0000 0.962 1.000 0.000 0.000 0.000 0.000
#> GSM2880 1 0.0000 0.962 1.000 0.000 0.000 0.000 0.000
#> GSM2893 1 0.0000 0.962 1.000 0.000 0.000 0.000 0.000
#> GSM2821 5 0.0671 0.993 0.016 0.004 0.000 0.000 0.980
#> GSM2900 1 0.2516 0.829 0.860 0.000 0.000 0.000 0.140
#> GSM2903 1 0.3774 0.596 0.704 0.000 0.000 0.000 0.296
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM2819 5 0.3620 0.2941 0.000 0.352 0.000 0.000 0.648 0.000
#> GSM2820 3 0.0000 0.9996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2822 2 0.0000 0.9503 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2832 2 0.0000 0.9503 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2823 2 0.0000 0.9503 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2824 2 0.1327 0.8837 0.000 0.936 0.000 0.000 0.064 0.000
#> GSM2825 2 0.0000 0.9503 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2826 2 0.0000 0.9503 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2829 4 0.0000 0.8935 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2856 4 0.0000 0.8935 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2830 4 0.0000 0.8935 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2843 4 0.2300 0.8525 0.000 0.000 0.000 0.856 0.144 0.000
#> GSM2871 2 0.3428 0.5520 0.000 0.696 0.000 0.000 0.304 0.000
#> GSM2831 4 0.0000 0.8935 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2844 4 0.0000 0.8935 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2833 4 0.0000 0.8935 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2846 4 0.0000 0.8935 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2835 4 0.0000 0.8935 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2858 4 0.0000 0.8935 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2836 2 0.0000 0.9503 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2848 2 0.0000 0.9503 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2828 3 0.0000 0.9996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2837 3 0.0000 0.9996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2839 6 0.0000 1.0000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM2841 6 0.0000 1.0000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM2827 2 0.0000 0.9503 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2842 2 0.0000 0.9503 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2845 2 0.5104 0.3522 0.000 0.588 0.000 0.108 0.304 0.000
#> GSM2872 4 0.3428 0.7685 0.000 0.000 0.000 0.696 0.304 0.000
#> GSM2834 2 0.6062 -0.0989 0.000 0.408 0.000 0.288 0.304 0.000
#> GSM2847 4 0.3428 0.7685 0.000 0.000 0.000 0.696 0.304 0.000
#> GSM2849 3 0.0000 0.9996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2850 3 0.0000 0.9996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2838 2 0.0000 0.9503 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2853 2 0.0000 0.9503 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2852 3 0.0000 0.9996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2855 3 0.0000 0.9996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2840 6 0.0000 1.0000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM2857 6 0.0000 1.0000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM2859 2 0.0000 0.9503 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2860 2 0.0000 0.9503 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2861 2 0.0000 0.9503 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2862 2 0.0000 0.9503 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2863 2 0.0000 0.9503 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2864 2 0.0000 0.9503 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2865 2 0.0000 0.9503 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2866 2 0.0000 0.9503 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2868 2 0.0000 0.9503 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2869 2 0.0000 0.9503 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2851 2 0.0000 0.9503 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2867 2 0.0000 0.9503 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2870 2 0.0000 0.9503 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2854 4 0.3565 0.7648 0.000 0.004 0.000 0.692 0.304 0.000
#> GSM2873 2 0.0000 0.9503 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2874 3 0.0000 0.9996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2884 3 0.0000 0.9996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2875 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2890 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2877 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2892 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2902 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2878 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2901 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2879 2 0.0000 0.9503 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2898 2 0.0000 0.9503 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2881 3 0.0000 0.9996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2897 3 0.0000 0.9996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2882 4 0.2300 0.8525 0.000 0.000 0.000 0.856 0.144 0.000
#> GSM2894 4 0.3409 0.7712 0.000 0.000 0.000 0.700 0.300 0.000
#> GSM2883 3 0.0000 0.9996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2895 3 0.0146 0.9939 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM2885 3 0.0000 0.9996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2886 3 0.0000 0.9996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2887 3 0.0000 0.9996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2896 3 0.0000 0.9996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2888 2 0.0000 0.9503 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2889 2 0.0000 0.9503 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2876 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2891 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2880 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2893 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM2821 5 0.3428 0.2042 0.000 0.000 0.000 0.000 0.696 0.304
#> GSM2900 5 0.3428 0.5591 0.304 0.000 0.000 0.000 0.696 0.000
#> GSM2903 5 0.3428 0.5591 0.304 0.000 0.000 0.000 0.696 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 tissue(p) k
#> ATC:pam 84 2.53e-05 2
#> ATC:pam 84 1.63e-07 3
#> ATC:pam 83 1.77e-10 4
#> ATC:pam 83 4.01e-12 5
#> ATC:pam 80 8.33e-17 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 8229 rows and 84 columns.
#> Top rows (823, 1646, 2468, 3291, 4114) 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 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.532 0.919 0.924 0.4978 0.501 0.501
#> 3 3 0.585 0.814 0.777 0.2734 0.579 0.345
#> 4 4 0.820 0.807 0.897 0.1657 0.880 0.669
#> 5 5 0.875 0.840 0.916 0.0731 0.917 0.682
#> 6 6 0.901 0.844 0.910 0.0395 0.916 0.628
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM2819 1 0.311 0.915 0.944 0.056
#> GSM2820 2 0.506 0.915 0.112 0.888
#> GSM2822 2 0.242 0.934 0.040 0.960
#> GSM2832 2 0.242 0.934 0.040 0.960
#> GSM2823 2 0.662 0.887 0.172 0.828
#> GSM2824 2 0.662 0.887 0.172 0.828
#> GSM2825 2 0.529 0.895 0.120 0.880
#> GSM2826 2 0.373 0.928 0.072 0.928
#> GSM2829 1 0.662 0.914 0.828 0.172
#> GSM2856 1 0.662 0.914 0.828 0.172
#> GSM2830 1 0.662 0.914 0.828 0.172
#> GSM2843 1 0.662 0.914 0.828 0.172
#> GSM2871 1 0.821 0.828 0.744 0.256
#> GSM2831 1 0.662 0.914 0.828 0.172
#> GSM2844 1 0.662 0.914 0.828 0.172
#> GSM2833 1 0.662 0.914 0.828 0.172
#> GSM2846 1 0.662 0.914 0.828 0.172
#> GSM2835 1 0.662 0.914 0.828 0.172
#> GSM2858 1 0.662 0.914 0.828 0.172
#> GSM2836 2 0.224 0.936 0.036 0.964
#> GSM2848 2 0.224 0.936 0.036 0.964
#> GSM2828 2 0.506 0.915 0.112 0.888
#> GSM2837 2 0.506 0.915 0.112 0.888
#> GSM2839 1 0.000 0.918 1.000 0.000
#> GSM2841 1 0.000 0.918 1.000 0.000
#> GSM2827 2 0.224 0.936 0.036 0.964
#> GSM2842 2 0.224 0.936 0.036 0.964
#> GSM2845 1 0.662 0.914 0.828 0.172
#> GSM2872 1 0.662 0.914 0.828 0.172
#> GSM2834 1 0.662 0.914 0.828 0.172
#> GSM2847 1 0.662 0.914 0.828 0.172
#> GSM2849 2 0.506 0.915 0.112 0.888
#> GSM2850 2 0.506 0.915 0.112 0.888
#> GSM2838 2 0.224 0.936 0.036 0.964
#> GSM2853 2 0.224 0.936 0.036 0.964
#> GSM2852 2 0.506 0.915 0.112 0.888
#> GSM2855 2 0.506 0.915 0.112 0.888
#> GSM2840 1 0.000 0.918 1.000 0.000
#> GSM2857 1 0.000 0.918 1.000 0.000
#> GSM2859 2 0.224 0.936 0.036 0.964
#> GSM2860 2 0.224 0.936 0.036 0.964
#> GSM2861 2 0.224 0.936 0.036 0.964
#> GSM2862 2 0.224 0.936 0.036 0.964
#> GSM2863 2 0.224 0.936 0.036 0.964
#> GSM2864 2 0.224 0.936 0.036 0.964
#> GSM2865 2 0.224 0.936 0.036 0.964
#> GSM2866 2 0.224 0.936 0.036 0.964
#> GSM2868 2 0.224 0.936 0.036 0.964
#> GSM2869 2 0.224 0.936 0.036 0.964
#> GSM2851 2 0.224 0.936 0.036 0.964
#> GSM2867 2 0.224 0.936 0.036 0.964
#> GSM2870 2 0.224 0.936 0.036 0.964
#> GSM2854 1 0.662 0.914 0.828 0.172
#> GSM2873 2 0.224 0.936 0.036 0.964
#> GSM2874 2 0.506 0.915 0.112 0.888
#> GSM2884 2 0.506 0.915 0.112 0.888
#> GSM2875 1 0.000 0.918 1.000 0.000
#> GSM2890 1 0.000 0.918 1.000 0.000
#> GSM2877 1 0.000 0.918 1.000 0.000
#> GSM2892 1 0.000 0.918 1.000 0.000
#> GSM2902 1 0.000 0.918 1.000 0.000
#> GSM2878 1 0.000 0.918 1.000 0.000
#> GSM2901 1 0.000 0.918 1.000 0.000
#> GSM2879 2 0.118 0.925 0.016 0.984
#> GSM2898 2 0.118 0.925 0.016 0.984
#> GSM2881 2 0.506 0.915 0.112 0.888
#> GSM2897 2 0.506 0.915 0.112 0.888
#> GSM2882 1 0.662 0.914 0.828 0.172
#> GSM2894 1 0.662 0.914 0.828 0.172
#> GSM2883 2 0.541 0.906 0.124 0.876
#> GSM2895 2 0.574 0.897 0.136 0.864
#> GSM2885 2 0.506 0.915 0.112 0.888
#> GSM2886 2 0.506 0.915 0.112 0.888
#> GSM2887 2 0.506 0.915 0.112 0.888
#> GSM2896 2 0.506 0.915 0.112 0.888
#> GSM2888 2 0.118 0.925 0.016 0.984
#> GSM2889 2 0.118 0.925 0.016 0.984
#> GSM2876 1 0.000 0.918 1.000 0.000
#> GSM2891 1 0.000 0.918 1.000 0.000
#> GSM2880 1 0.000 0.918 1.000 0.000
#> GSM2893 1 0.000 0.918 1.000 0.000
#> GSM2821 1 0.000 0.918 1.000 0.000
#> GSM2900 1 0.000 0.918 1.000 0.000
#> GSM2903 1 0.000 0.918 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM2819 2 0.9701 -0.168 0.284 0.456 0.260
#> GSM2820 3 0.0000 0.933 0.000 0.000 1.000
#> GSM2822 2 0.3192 0.745 0.112 0.888 0.000
#> GSM2832 2 0.2796 0.755 0.092 0.908 0.000
#> GSM2823 1 0.5591 0.898 0.696 0.000 0.304
#> GSM2824 1 0.5591 0.898 0.696 0.000 0.304
#> GSM2825 1 0.9258 0.607 0.528 0.216 0.256
#> GSM2826 1 0.9258 0.607 0.528 0.216 0.256
#> GSM2829 2 0.5443 0.784 0.260 0.736 0.004
#> GSM2856 2 0.5443 0.784 0.260 0.736 0.004
#> GSM2830 2 0.5443 0.784 0.260 0.736 0.004
#> GSM2843 2 0.5443 0.784 0.260 0.736 0.004
#> GSM2871 2 0.5443 0.784 0.260 0.736 0.004
#> GSM2831 2 0.5443 0.784 0.260 0.736 0.004
#> GSM2844 2 0.5443 0.784 0.260 0.736 0.004
#> GSM2833 2 0.5443 0.784 0.260 0.736 0.004
#> GSM2846 2 0.5443 0.784 0.260 0.736 0.004
#> GSM2835 2 0.5443 0.784 0.260 0.736 0.004
#> GSM2858 2 0.5443 0.784 0.260 0.736 0.004
#> GSM2836 2 0.4281 0.758 0.056 0.872 0.072
#> GSM2848 2 0.3637 0.766 0.024 0.892 0.084
#> GSM2828 3 0.0000 0.933 0.000 0.000 1.000
#> GSM2837 3 0.0000 0.933 0.000 0.000 1.000
#> GSM2839 1 0.5216 0.939 0.740 0.000 0.260
#> GSM2841 1 0.5216 0.939 0.740 0.000 0.260
#> GSM2827 2 0.5845 0.564 0.004 0.688 0.308
#> GSM2842 2 0.6102 0.549 0.008 0.672 0.320
#> GSM2845 2 0.6735 0.762 0.260 0.696 0.044
#> GSM2872 2 0.6633 0.764 0.260 0.700 0.040
#> GSM2834 2 0.5443 0.784 0.260 0.736 0.004
#> GSM2847 2 0.6053 0.776 0.260 0.720 0.020
#> GSM2849 3 0.0000 0.933 0.000 0.000 1.000
#> GSM2850 3 0.0000 0.933 0.000 0.000 1.000
#> GSM2838 2 0.3965 0.754 0.008 0.860 0.132
#> GSM2853 2 0.4137 0.760 0.032 0.872 0.096
#> GSM2852 3 0.1163 0.922 0.028 0.000 0.972
#> GSM2855 3 0.1163 0.922 0.028 0.000 0.972
#> GSM2840 1 0.5216 0.939 0.740 0.000 0.260
#> GSM2857 1 0.5216 0.939 0.740 0.000 0.260
#> GSM2859 2 0.3686 0.752 0.000 0.860 0.140
#> GSM2860 2 0.4842 0.676 0.000 0.776 0.224
#> GSM2861 2 0.5397 0.605 0.000 0.720 0.280
#> GSM2862 2 0.3816 0.748 0.000 0.852 0.148
#> GSM2863 2 0.4002 0.739 0.000 0.840 0.160
#> GSM2864 2 0.3752 0.750 0.000 0.856 0.144
#> GSM2865 2 0.3686 0.752 0.000 0.860 0.140
#> GSM2866 2 0.4269 0.754 0.076 0.872 0.052
#> GSM2868 2 0.3752 0.750 0.000 0.856 0.144
#> GSM2869 2 0.3941 0.742 0.000 0.844 0.156
#> GSM2851 2 0.3619 0.754 0.000 0.864 0.136
#> GSM2867 2 0.3816 0.748 0.000 0.852 0.148
#> GSM2870 2 0.3816 0.748 0.000 0.852 0.148
#> GSM2854 2 0.5443 0.784 0.260 0.736 0.004
#> GSM2873 2 0.0661 0.780 0.008 0.988 0.004
#> GSM2874 3 0.0000 0.933 0.000 0.000 1.000
#> GSM2884 3 0.0000 0.933 0.000 0.000 1.000
#> GSM2875 1 0.5465 0.937 0.712 0.000 0.288
#> GSM2890 1 0.5465 0.937 0.712 0.000 0.288
#> GSM2877 1 0.5465 0.937 0.712 0.000 0.288
#> GSM2892 1 0.5465 0.937 0.712 0.000 0.288
#> GSM2902 1 0.5465 0.937 0.712 0.000 0.288
#> GSM2878 1 0.5465 0.937 0.712 0.000 0.288
#> GSM2901 1 0.5465 0.937 0.712 0.000 0.288
#> GSM2879 3 0.4504 0.728 0.196 0.000 0.804
#> GSM2898 3 0.4452 0.735 0.192 0.000 0.808
#> GSM2881 3 0.0000 0.933 0.000 0.000 1.000
#> GSM2897 3 0.0000 0.933 0.000 0.000 1.000
#> GSM2882 2 0.5443 0.784 0.260 0.736 0.004
#> GSM2894 2 0.5443 0.784 0.260 0.736 0.004
#> GSM2883 3 0.4235 0.717 0.176 0.000 0.824
#> GSM2895 3 0.4235 0.717 0.176 0.000 0.824
#> GSM2885 3 0.0000 0.933 0.000 0.000 1.000
#> GSM2886 3 0.0000 0.933 0.000 0.000 1.000
#> GSM2887 3 0.1163 0.922 0.028 0.000 0.972
#> GSM2896 3 0.1163 0.922 0.028 0.000 0.972
#> GSM2888 3 0.2599 0.900 0.052 0.016 0.932
#> GSM2889 3 0.2599 0.900 0.052 0.016 0.932
#> GSM2876 1 0.5216 0.939 0.740 0.000 0.260
#> GSM2891 1 0.5216 0.939 0.740 0.000 0.260
#> GSM2880 1 0.5465 0.937 0.712 0.000 0.288
#> GSM2893 1 0.5465 0.937 0.712 0.000 0.288
#> GSM2821 1 0.5216 0.939 0.740 0.000 0.260
#> GSM2900 1 0.5216 0.939 0.740 0.000 0.260
#> GSM2903 1 0.5216 0.939 0.740 0.000 0.260
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM2819 4 0.9602 -0.0761 0.296 0.248 0.124 0.332
#> GSM2820 3 0.0000 0.7755 0.000 0.000 1.000 0.000
#> GSM2822 2 0.5738 0.7328 0.164 0.744 0.060 0.032
#> GSM2832 2 0.5738 0.7328 0.164 0.744 0.060 0.032
#> GSM2823 1 0.5956 0.4519 0.680 0.100 0.220 0.000
#> GSM2824 1 0.5956 0.4519 0.680 0.100 0.220 0.000
#> GSM2825 1 0.7131 0.2658 0.520 0.352 0.124 0.004
#> GSM2826 1 0.7119 0.2767 0.524 0.348 0.124 0.004
#> GSM2829 4 0.0000 0.9647 0.000 0.000 0.000 1.000
#> GSM2856 4 0.0000 0.9647 0.000 0.000 0.000 1.000
#> GSM2830 4 0.0000 0.9647 0.000 0.000 0.000 1.000
#> GSM2843 4 0.0000 0.9647 0.000 0.000 0.000 1.000
#> GSM2871 4 0.0188 0.9607 0.000 0.004 0.000 0.996
#> GSM2831 4 0.0000 0.9647 0.000 0.000 0.000 1.000
#> GSM2844 4 0.0000 0.9647 0.000 0.000 0.000 1.000
#> GSM2833 4 0.0000 0.9647 0.000 0.000 0.000 1.000
#> GSM2846 4 0.0000 0.9647 0.000 0.000 0.000 1.000
#> GSM2835 4 0.0000 0.9647 0.000 0.000 0.000 1.000
#> GSM2858 4 0.0000 0.9647 0.000 0.000 0.000 1.000
#> GSM2836 2 0.1610 0.9015 0.016 0.952 0.000 0.032
#> GSM2848 2 0.1022 0.9125 0.000 0.968 0.000 0.032
#> GSM2828 3 0.0000 0.7755 0.000 0.000 1.000 0.000
#> GSM2837 3 0.0000 0.7755 0.000 0.000 1.000 0.000
#> GSM2839 1 0.0000 0.9074 1.000 0.000 0.000 0.000
#> GSM2841 1 0.0000 0.9074 1.000 0.000 0.000 0.000
#> GSM2827 2 0.8444 0.1997 0.320 0.472 0.148 0.060
#> GSM2842 2 0.7761 0.2156 0.320 0.512 0.144 0.024
#> GSM2845 4 0.0000 0.9647 0.000 0.000 0.000 1.000
#> GSM2872 4 0.0000 0.9647 0.000 0.000 0.000 1.000
#> GSM2834 4 0.0000 0.9647 0.000 0.000 0.000 1.000
#> GSM2847 4 0.0000 0.9647 0.000 0.000 0.000 1.000
#> GSM2849 3 0.0000 0.7755 0.000 0.000 1.000 0.000
#> GSM2850 3 0.0000 0.7755 0.000 0.000 1.000 0.000
#> GSM2838 2 0.1022 0.9125 0.000 0.968 0.000 0.032
#> GSM2853 2 0.1022 0.9125 0.000 0.968 0.000 0.032
#> GSM2852 3 0.6685 0.5942 0.324 0.108 0.568 0.000
#> GSM2855 3 0.6685 0.5942 0.324 0.108 0.568 0.000
#> GSM2840 1 0.0000 0.9074 1.000 0.000 0.000 0.000
#> GSM2857 1 0.0000 0.9074 1.000 0.000 0.000 0.000
#> GSM2859 2 0.1022 0.9125 0.000 0.968 0.000 0.032
#> GSM2860 2 0.0921 0.9097 0.000 0.972 0.000 0.028
#> GSM2861 2 0.1284 0.8996 0.000 0.964 0.012 0.024
#> GSM2862 2 0.1022 0.9125 0.000 0.968 0.000 0.032
#> GSM2863 2 0.1022 0.9125 0.000 0.968 0.000 0.032
#> GSM2864 2 0.1022 0.9125 0.000 0.968 0.000 0.032
#> GSM2865 2 0.1022 0.9125 0.000 0.968 0.000 0.032
#> GSM2866 2 0.1022 0.9125 0.000 0.968 0.000 0.032
#> GSM2868 2 0.1022 0.9125 0.000 0.968 0.000 0.032
#> GSM2869 2 0.1022 0.9125 0.000 0.968 0.000 0.032
#> GSM2851 2 0.1022 0.9125 0.000 0.968 0.000 0.032
#> GSM2867 2 0.1022 0.9125 0.000 0.968 0.000 0.032
#> GSM2870 2 0.1022 0.9125 0.000 0.968 0.000 0.032
#> GSM2854 4 0.0000 0.9647 0.000 0.000 0.000 1.000
#> GSM2873 2 0.6196 0.7435 0.072 0.736 0.072 0.120
#> GSM2874 3 0.0000 0.7755 0.000 0.000 1.000 0.000
#> GSM2884 3 0.0000 0.7755 0.000 0.000 1.000 0.000
#> GSM2875 1 0.0000 0.9074 1.000 0.000 0.000 0.000
#> GSM2890 1 0.0000 0.9074 1.000 0.000 0.000 0.000
#> GSM2877 1 0.0000 0.9074 1.000 0.000 0.000 0.000
#> GSM2892 1 0.0000 0.9074 1.000 0.000 0.000 0.000
#> GSM2902 1 0.0000 0.9074 1.000 0.000 0.000 0.000
#> GSM2878 1 0.0000 0.9074 1.000 0.000 0.000 0.000
#> GSM2901 1 0.0000 0.9074 1.000 0.000 0.000 0.000
#> GSM2879 3 0.6685 0.5942 0.324 0.108 0.568 0.000
#> GSM2898 3 0.6685 0.5942 0.324 0.108 0.568 0.000
#> GSM2881 3 0.0000 0.7755 0.000 0.000 1.000 0.000
#> GSM2897 3 0.0000 0.7755 0.000 0.000 1.000 0.000
#> GSM2882 4 0.0000 0.9647 0.000 0.000 0.000 1.000
#> GSM2894 4 0.0000 0.9647 0.000 0.000 0.000 1.000
#> GSM2883 3 0.5793 0.6176 0.324 0.048 0.628 0.000
#> GSM2895 3 0.5793 0.6176 0.324 0.048 0.628 0.000
#> GSM2885 3 0.0000 0.7755 0.000 0.000 1.000 0.000
#> GSM2886 3 0.0000 0.7755 0.000 0.000 1.000 0.000
#> GSM2887 3 0.5537 0.6746 0.256 0.056 0.688 0.000
#> GSM2896 3 0.5537 0.6746 0.256 0.056 0.688 0.000
#> GSM2888 3 0.7142 0.5475 0.324 0.152 0.524 0.000
#> GSM2889 3 0.7142 0.5475 0.324 0.152 0.524 0.000
#> GSM2876 1 0.0000 0.9074 1.000 0.000 0.000 0.000
#> GSM2891 1 0.0000 0.9074 1.000 0.000 0.000 0.000
#> GSM2880 1 0.0000 0.9074 1.000 0.000 0.000 0.000
#> GSM2893 1 0.0000 0.9074 1.000 0.000 0.000 0.000
#> GSM2821 1 0.0000 0.9074 1.000 0.000 0.000 0.000
#> GSM2900 1 0.0000 0.9074 1.000 0.000 0.000 0.000
#> GSM2903 1 0.0000 0.9074 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
#> GSM2819 5 0.8595 0.155 0.240 0.228 0.000 0.252 0.280
#> GSM2820 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2822 2 0.4364 0.647 0.048 0.736 0.000 0.000 0.216
#> GSM2832 2 0.4364 0.647 0.048 0.736 0.000 0.000 0.216
#> GSM2823 5 0.3177 0.550 0.208 0.000 0.000 0.000 0.792
#> GSM2824 5 0.3177 0.550 0.208 0.000 0.000 0.000 0.792
#> GSM2825 5 0.5069 0.435 0.052 0.328 0.000 0.000 0.620
#> GSM2826 5 0.5069 0.435 0.052 0.328 0.000 0.000 0.620
#> GSM2829 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM2856 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM2830 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM2843 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM2871 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM2831 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM2844 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM2833 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM2846 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM2835 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM2858 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM2836 2 0.1544 0.880 0.000 0.932 0.000 0.000 0.068
#> GSM2848 2 0.1043 0.900 0.000 0.960 0.000 0.000 0.040
#> GSM2828 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2837 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2839 1 0.3661 0.734 0.724 0.000 0.000 0.000 0.276
#> GSM2841 1 0.3661 0.734 0.724 0.000 0.000 0.000 0.276
#> GSM2827 2 0.5047 -0.146 0.000 0.496 0.000 0.032 0.472
#> GSM2842 5 0.4451 0.084 0.000 0.492 0.000 0.004 0.504
#> GSM2845 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM2872 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM2834 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM2847 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM2849 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2850 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2838 2 0.0000 0.918 0.000 1.000 0.000 0.000 0.000
#> GSM2853 2 0.0000 0.918 0.000 1.000 0.000 0.000 0.000
#> GSM2852 5 0.1732 0.759 0.000 0.000 0.080 0.000 0.920
#> GSM2855 5 0.1732 0.759 0.000 0.000 0.080 0.000 0.920
#> GSM2840 1 0.3661 0.734 0.724 0.000 0.000 0.000 0.276
#> GSM2857 1 0.3661 0.734 0.724 0.000 0.000 0.000 0.276
#> GSM2859 2 0.0000 0.918 0.000 1.000 0.000 0.000 0.000
#> GSM2860 2 0.0000 0.918 0.000 1.000 0.000 0.000 0.000
#> GSM2861 2 0.2127 0.851 0.000 0.892 0.000 0.000 0.108
#> GSM2862 2 0.0000 0.918 0.000 1.000 0.000 0.000 0.000
#> GSM2863 2 0.0000 0.918 0.000 1.000 0.000 0.000 0.000
#> GSM2864 2 0.0000 0.918 0.000 1.000 0.000 0.000 0.000
#> GSM2865 2 0.0000 0.918 0.000 1.000 0.000 0.000 0.000
#> GSM2866 2 0.1197 0.895 0.000 0.952 0.000 0.000 0.048
#> GSM2868 2 0.0000 0.918 0.000 1.000 0.000 0.000 0.000
#> GSM2869 2 0.0000 0.918 0.000 1.000 0.000 0.000 0.000
#> GSM2851 2 0.0000 0.918 0.000 1.000 0.000 0.000 0.000
#> GSM2867 2 0.0000 0.918 0.000 1.000 0.000 0.000 0.000
#> GSM2870 2 0.0000 0.918 0.000 1.000 0.000 0.000 0.000
#> GSM2854 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM2873 2 0.2863 0.836 0.000 0.876 0.000 0.060 0.064
#> GSM2874 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2884 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2875 1 0.0000 0.853 1.000 0.000 0.000 0.000 0.000
#> GSM2890 1 0.0000 0.853 1.000 0.000 0.000 0.000 0.000
#> GSM2877 1 0.0000 0.853 1.000 0.000 0.000 0.000 0.000
#> GSM2892 1 0.0000 0.853 1.000 0.000 0.000 0.000 0.000
#> GSM2902 1 0.0000 0.853 1.000 0.000 0.000 0.000 0.000
#> GSM2878 1 0.0000 0.853 1.000 0.000 0.000 0.000 0.000
#> GSM2901 1 0.0000 0.853 1.000 0.000 0.000 0.000 0.000
#> GSM2879 5 0.1043 0.756 0.000 0.000 0.040 0.000 0.960
#> GSM2898 5 0.1043 0.756 0.000 0.000 0.040 0.000 0.960
#> GSM2881 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2897 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2882 4 0.0162 0.995 0.000 0.004 0.000 0.996 0.000
#> GSM2894 4 0.0162 0.995 0.000 0.004 0.000 0.996 0.000
#> GSM2883 5 0.2605 0.735 0.000 0.000 0.148 0.000 0.852
#> GSM2895 5 0.2605 0.735 0.000 0.000 0.148 0.000 0.852
#> GSM2885 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2886 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM2887 5 0.2852 0.724 0.000 0.000 0.172 0.000 0.828
#> GSM2896 5 0.2891 0.722 0.000 0.000 0.176 0.000 0.824
#> GSM2888 5 0.3058 0.751 0.000 0.096 0.044 0.000 0.860
#> GSM2889 5 0.3058 0.751 0.000 0.096 0.044 0.000 0.860
#> GSM2876 1 0.1121 0.846 0.956 0.000 0.000 0.000 0.044
#> GSM2891 1 0.1121 0.846 0.956 0.000 0.000 0.000 0.044
#> GSM2880 1 0.0000 0.853 1.000 0.000 0.000 0.000 0.000
#> GSM2893 1 0.0000 0.853 1.000 0.000 0.000 0.000 0.000
#> GSM2821 1 0.3816 0.702 0.696 0.000 0.000 0.000 0.304
#> GSM2900 1 0.3636 0.736 0.728 0.000 0.000 0.000 0.272
#> GSM2903 1 0.3636 0.736 0.728 0.000 0.000 0.000 0.272
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM2819 5 0.5451 0.5931 0.000 0.156 0.000 0.140 0.660 0.044
#> GSM2820 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2822 5 0.5711 0.4086 0.000 0.392 0.000 0.008 0.472 0.128
#> GSM2832 5 0.5735 0.4151 0.000 0.388 0.000 0.008 0.472 0.132
#> GSM2823 5 0.3531 0.4777 0.000 0.000 0.000 0.000 0.672 0.328
#> GSM2824 5 0.3547 0.4718 0.000 0.000 0.000 0.000 0.668 0.332
#> GSM2825 5 0.5641 0.4970 0.000 0.328 0.000 0.000 0.504 0.168
#> GSM2826 5 0.5641 0.4970 0.000 0.328 0.000 0.000 0.504 0.168
#> GSM2829 4 0.0260 0.9816 0.008 0.000 0.000 0.992 0.000 0.000
#> GSM2856 4 0.0260 0.9816 0.008 0.000 0.000 0.992 0.000 0.000
#> GSM2830 4 0.0260 0.9816 0.008 0.000 0.000 0.992 0.000 0.000
#> GSM2843 4 0.0260 0.9816 0.008 0.000 0.000 0.992 0.000 0.000
#> GSM2871 4 0.2000 0.9496 0.048 0.004 0.000 0.916 0.032 0.000
#> GSM2831 4 0.0000 0.9820 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2844 4 0.0000 0.9820 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2833 4 0.0000 0.9820 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM2846 4 0.0260 0.9816 0.008 0.000 0.000 0.992 0.000 0.000
#> GSM2835 4 0.0146 0.9820 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM2858 4 0.0146 0.9820 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM2836 2 0.0260 0.9413 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM2848 2 0.0260 0.9413 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM2828 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2837 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2839 5 0.0790 0.6305 0.032 0.000 0.000 0.000 0.968 0.000
#> GSM2841 5 0.0790 0.6305 0.032 0.000 0.000 0.000 0.968 0.000
#> GSM2827 5 0.5899 0.4386 0.000 0.372 0.000 0.008 0.460 0.160
#> GSM2842 5 0.5719 0.4373 0.000 0.372 0.000 0.000 0.460 0.168
#> GSM2845 4 0.1265 0.9667 0.044 0.000 0.000 0.948 0.008 0.000
#> GSM2872 4 0.1265 0.9667 0.044 0.000 0.000 0.948 0.008 0.000
#> GSM2834 4 0.1265 0.9667 0.044 0.000 0.000 0.948 0.008 0.000
#> GSM2847 4 0.1152 0.9683 0.044 0.000 0.000 0.952 0.004 0.000
#> GSM2849 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2850 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2838 2 0.0000 0.9451 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2853 2 0.0291 0.9409 0.000 0.992 0.000 0.000 0.004 0.004
#> GSM2852 6 0.0865 0.9647 0.000 0.000 0.036 0.000 0.000 0.964
#> GSM2855 6 0.0865 0.9647 0.000 0.000 0.036 0.000 0.000 0.964
#> GSM2840 5 0.0790 0.6305 0.032 0.000 0.000 0.000 0.968 0.000
#> GSM2857 5 0.0790 0.6305 0.032 0.000 0.000 0.000 0.968 0.000
#> GSM2859 2 0.0000 0.9451 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2860 2 0.0146 0.9444 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM2861 2 0.3081 0.6911 0.000 0.776 0.000 0.000 0.004 0.220
#> GSM2862 2 0.0146 0.9444 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM2863 2 0.0146 0.9444 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM2864 2 0.0146 0.9444 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM2865 2 0.0000 0.9451 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2866 2 0.0520 0.9356 0.000 0.984 0.000 0.000 0.008 0.008
#> GSM2868 2 0.0000 0.9451 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2869 2 0.0000 0.9451 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2851 2 0.0000 0.9451 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2867 2 0.0000 0.9451 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2870 2 0.0000 0.9451 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM2854 4 0.1010 0.9713 0.036 0.000 0.000 0.960 0.004 0.000
#> GSM2873 2 0.5668 -0.1947 0.016 0.500 0.000 0.028 0.412 0.044
#> GSM2874 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2884 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2875 1 0.1141 0.9544 0.948 0.000 0.000 0.000 0.052 0.000
#> GSM2890 1 0.1141 0.9544 0.948 0.000 0.000 0.000 0.052 0.000
#> GSM2877 1 0.1141 0.9544 0.948 0.000 0.000 0.000 0.052 0.000
#> GSM2892 1 0.1141 0.9544 0.948 0.000 0.000 0.000 0.052 0.000
#> GSM2902 1 0.1141 0.9544 0.948 0.000 0.000 0.000 0.052 0.000
#> GSM2878 1 0.1765 0.9404 0.904 0.000 0.000 0.000 0.096 0.000
#> GSM2901 1 0.1765 0.9404 0.904 0.000 0.000 0.000 0.096 0.000
#> GSM2879 6 0.0000 0.9734 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM2898 6 0.0000 0.9734 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM2881 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2897 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2882 4 0.0146 0.9814 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM2894 4 0.0146 0.9814 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM2883 6 0.0000 0.9734 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM2895 6 0.0000 0.9734 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM2885 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2886 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM2887 6 0.1267 0.9463 0.000 0.000 0.060 0.000 0.000 0.940
#> GSM2896 6 0.1444 0.9348 0.000 0.000 0.072 0.000 0.000 0.928
#> GSM2888 6 0.0146 0.9739 0.000 0.000 0.004 0.000 0.000 0.996
#> GSM2889 6 0.0146 0.9739 0.000 0.000 0.004 0.000 0.000 0.996
#> GSM2876 5 0.3838 0.0642 0.448 0.000 0.000 0.000 0.552 0.000
#> GSM2891 5 0.3838 0.0642 0.448 0.000 0.000 0.000 0.552 0.000
#> GSM2880 1 0.2969 0.7210 0.776 0.000 0.000 0.000 0.224 0.000
#> GSM2893 1 0.1610 0.9460 0.916 0.000 0.000 0.000 0.084 0.000
#> GSM2821 5 0.0790 0.6305 0.032 0.000 0.000 0.000 0.968 0.000
#> GSM2900 5 0.1141 0.6196 0.052 0.000 0.000 0.000 0.948 0.000
#> GSM2903 5 0.1075 0.6216 0.048 0.000 0.000 0.000 0.952 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 tissue(p) k
#> ATC:mclust 84 4.57e-05 2
#> ATC:mclust 83 5.13e-09 3
#> ATC:mclust 77 1.70e-11 4
#> ATC:mclust 79 4.10e-15 5
#> ATC:mclust 73 3.70e-17 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 8229 rows and 84 columns.
#> Top rows (823, 1646, 2468, 3291, 4114) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.894 0.912 0.961 0.4531 0.535 0.535
#> 3 3 1.000 0.966 0.984 0.3958 0.793 0.626
#> 4 4 0.961 0.948 0.977 0.1871 0.820 0.546
#> 5 5 0.853 0.872 0.902 0.0434 0.987 0.948
#> 6 6 0.826 0.797 0.851 0.0316 0.964 0.857
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 3
There is also optional best \(k\) = 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM2819 1 0.0000 0.921 1.000 0.000
#> GSM2820 2 0.0000 0.978 0.000 1.000
#> GSM2822 1 0.9323 0.520 0.652 0.348
#> GSM2832 1 0.9881 0.303 0.564 0.436
#> GSM2823 1 0.0376 0.920 0.996 0.004
#> GSM2824 1 0.0376 0.920 0.996 0.004
#> GSM2825 1 0.0376 0.920 0.996 0.004
#> GSM2826 1 0.0376 0.920 0.996 0.004
#> GSM2829 2 0.0376 0.976 0.004 0.996
#> GSM2856 2 0.0376 0.976 0.004 0.996
#> GSM2830 2 0.0376 0.976 0.004 0.996
#> GSM2843 2 0.0376 0.976 0.004 0.996
#> GSM2871 2 0.0376 0.976 0.004 0.996
#> GSM2831 2 0.7602 0.707 0.220 0.780
#> GSM2844 2 0.4431 0.893 0.092 0.908
#> GSM2833 2 0.1184 0.969 0.016 0.984
#> GSM2846 2 0.0376 0.976 0.004 0.996
#> GSM2835 1 0.8081 0.686 0.752 0.248
#> GSM2858 1 0.9460 0.483 0.636 0.364
#> GSM2836 2 0.1184 0.968 0.016 0.984
#> GSM2848 2 0.0000 0.978 0.000 1.000
#> GSM2828 2 0.0000 0.978 0.000 1.000
#> GSM2837 2 0.0000 0.978 0.000 1.000
#> GSM2839 1 0.0000 0.921 1.000 0.000
#> GSM2841 1 0.0000 0.921 1.000 0.000
#> GSM2827 2 0.0000 0.978 0.000 1.000
#> GSM2842 2 0.0000 0.978 0.000 1.000
#> GSM2845 2 0.3584 0.921 0.068 0.932
#> GSM2872 1 0.9944 0.234 0.544 0.456
#> GSM2834 2 0.8955 0.515 0.312 0.688
#> GSM2847 2 0.0938 0.972 0.012 0.988
#> GSM2849 2 0.0000 0.978 0.000 1.000
#> GSM2850 2 0.0000 0.978 0.000 1.000
#> GSM2838 2 0.0000 0.978 0.000 1.000
#> GSM2853 2 0.0000 0.978 0.000 1.000
#> GSM2852 2 0.0000 0.978 0.000 1.000
#> GSM2855 2 0.0000 0.978 0.000 1.000
#> GSM2840 1 0.0000 0.921 1.000 0.000
#> GSM2857 1 0.0000 0.921 1.000 0.000
#> GSM2859 2 0.0000 0.978 0.000 1.000
#> GSM2860 2 0.0000 0.978 0.000 1.000
#> GSM2861 2 0.0000 0.978 0.000 1.000
#> GSM2862 2 0.0000 0.978 0.000 1.000
#> GSM2863 2 0.0000 0.978 0.000 1.000
#> GSM2864 2 0.0000 0.978 0.000 1.000
#> GSM2865 2 0.0000 0.978 0.000 1.000
#> GSM2866 2 0.0376 0.976 0.004 0.996
#> GSM2868 2 0.5629 0.843 0.132 0.868
#> GSM2869 2 0.1843 0.958 0.028 0.972
#> GSM2851 2 0.0938 0.971 0.012 0.988
#> GSM2867 2 0.2423 0.948 0.040 0.960
#> GSM2870 2 0.0376 0.976 0.004 0.996
#> GSM2854 2 0.4022 0.908 0.080 0.920
#> GSM2873 2 0.0000 0.978 0.000 1.000
#> GSM2874 2 0.0000 0.978 0.000 1.000
#> GSM2884 2 0.0000 0.978 0.000 1.000
#> GSM2875 1 0.0000 0.921 1.000 0.000
#> GSM2890 1 0.0000 0.921 1.000 0.000
#> GSM2877 1 0.0000 0.921 1.000 0.000
#> GSM2892 1 0.0000 0.921 1.000 0.000
#> GSM2902 1 0.0000 0.921 1.000 0.000
#> GSM2878 1 0.0000 0.921 1.000 0.000
#> GSM2901 1 0.0000 0.921 1.000 0.000
#> GSM2879 2 0.0000 0.978 0.000 1.000
#> GSM2898 2 0.0000 0.978 0.000 1.000
#> GSM2881 2 0.0000 0.978 0.000 1.000
#> GSM2897 2 0.0000 0.978 0.000 1.000
#> GSM2882 1 0.7376 0.738 0.792 0.208
#> GSM2894 1 0.4562 0.851 0.904 0.096
#> GSM2883 2 0.0000 0.978 0.000 1.000
#> GSM2895 2 0.0000 0.978 0.000 1.000
#> GSM2885 2 0.0000 0.978 0.000 1.000
#> GSM2886 2 0.0000 0.978 0.000 1.000
#> GSM2887 2 0.0000 0.978 0.000 1.000
#> GSM2896 2 0.0000 0.978 0.000 1.000
#> GSM2888 2 0.0000 0.978 0.000 1.000
#> GSM2889 2 0.0000 0.978 0.000 1.000
#> GSM2876 1 0.0000 0.921 1.000 0.000
#> GSM2891 1 0.0000 0.921 1.000 0.000
#> GSM2880 1 0.0000 0.921 1.000 0.000
#> GSM2893 1 0.0000 0.921 1.000 0.000
#> GSM2821 1 0.0376 0.920 0.996 0.004
#> GSM2900 1 0.0000 0.921 1.000 0.000
#> GSM2903 1 0.0000 0.921 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM2819 1 0.2165 0.910 0.936 0.064 0.000
#> GSM2820 3 0.0000 0.989 0.000 0.000 1.000
#> GSM2822 1 0.5138 0.669 0.748 0.000 0.252
#> GSM2832 1 0.5397 0.622 0.720 0.000 0.280
#> GSM2823 1 0.0747 0.954 0.984 0.000 0.016
#> GSM2824 1 0.0747 0.954 0.984 0.000 0.016
#> GSM2825 1 0.0000 0.968 1.000 0.000 0.000
#> GSM2826 1 0.0000 0.968 1.000 0.000 0.000
#> GSM2829 2 0.0000 0.985 0.000 1.000 0.000
#> GSM2856 2 0.0000 0.985 0.000 1.000 0.000
#> GSM2830 2 0.0000 0.985 0.000 1.000 0.000
#> GSM2843 2 0.0000 0.985 0.000 1.000 0.000
#> GSM2871 2 0.4452 0.763 0.000 0.808 0.192
#> GSM2831 2 0.0000 0.985 0.000 1.000 0.000
#> GSM2844 2 0.0000 0.985 0.000 1.000 0.000
#> GSM2833 2 0.0000 0.985 0.000 1.000 0.000
#> GSM2846 2 0.0000 0.985 0.000 1.000 0.000
#> GSM2835 2 0.0000 0.985 0.000 1.000 0.000
#> GSM2858 2 0.0000 0.985 0.000 1.000 0.000
#> GSM2836 3 0.1289 0.969 0.032 0.000 0.968
#> GSM2848 3 0.0592 0.983 0.012 0.000 0.988
#> GSM2828 3 0.0000 0.989 0.000 0.000 1.000
#> GSM2837 3 0.0000 0.989 0.000 0.000 1.000
#> GSM2839 1 0.0000 0.968 1.000 0.000 0.000
#> GSM2841 1 0.0000 0.968 1.000 0.000 0.000
#> GSM2827 3 0.0237 0.987 0.004 0.000 0.996
#> GSM2842 3 0.0000 0.989 0.000 0.000 1.000
#> GSM2845 2 0.1711 0.951 0.032 0.960 0.008
#> GSM2872 2 0.0000 0.985 0.000 1.000 0.000
#> GSM2834 2 0.0000 0.985 0.000 1.000 0.000
#> GSM2847 2 0.0000 0.985 0.000 1.000 0.000
#> GSM2849 3 0.0000 0.989 0.000 0.000 1.000
#> GSM2850 3 0.0000 0.989 0.000 0.000 1.000
#> GSM2838 3 0.0237 0.987 0.004 0.000 0.996
#> GSM2853 3 0.0000 0.989 0.000 0.000 1.000
#> GSM2852 3 0.0000 0.989 0.000 0.000 1.000
#> GSM2855 3 0.0000 0.989 0.000 0.000 1.000
#> GSM2840 1 0.0000 0.968 1.000 0.000 0.000
#> GSM2857 1 0.0000 0.968 1.000 0.000 0.000
#> GSM2859 3 0.0892 0.978 0.020 0.000 0.980
#> GSM2860 3 0.0000 0.989 0.000 0.000 1.000
#> GSM2861 3 0.0000 0.989 0.000 0.000 1.000
#> GSM2862 3 0.0424 0.985 0.008 0.000 0.992
#> GSM2863 3 0.0000 0.989 0.000 0.000 1.000
#> GSM2864 3 0.0424 0.985 0.008 0.000 0.992
#> GSM2865 3 0.0424 0.985 0.008 0.000 0.992
#> GSM2866 3 0.0892 0.978 0.020 0.000 0.980
#> GSM2868 3 0.2878 0.901 0.096 0.000 0.904
#> GSM2869 3 0.1163 0.972 0.028 0.000 0.972
#> GSM2851 3 0.1031 0.975 0.024 0.000 0.976
#> GSM2867 3 0.1753 0.953 0.048 0.000 0.952
#> GSM2870 3 0.0892 0.978 0.020 0.000 0.980
#> GSM2854 2 0.0000 0.985 0.000 1.000 0.000
#> GSM2873 3 0.3695 0.873 0.012 0.108 0.880
#> GSM2874 3 0.0000 0.989 0.000 0.000 1.000
#> GSM2884 3 0.0000 0.989 0.000 0.000 1.000
#> GSM2875 1 0.0000 0.968 1.000 0.000 0.000
#> GSM2890 1 0.0000 0.968 1.000 0.000 0.000
#> GSM2877 1 0.0000 0.968 1.000 0.000 0.000
#> GSM2892 1 0.0000 0.968 1.000 0.000 0.000
#> GSM2902 1 0.0000 0.968 1.000 0.000 0.000
#> GSM2878 1 0.0000 0.968 1.000 0.000 0.000
#> GSM2901 1 0.0000 0.968 1.000 0.000 0.000
#> GSM2879 3 0.0000 0.989 0.000 0.000 1.000
#> GSM2898 3 0.0000 0.989 0.000 0.000 1.000
#> GSM2881 3 0.0000 0.989 0.000 0.000 1.000
#> GSM2897 3 0.0000 0.989 0.000 0.000 1.000
#> GSM2882 2 0.0000 0.985 0.000 1.000 0.000
#> GSM2894 2 0.0000 0.985 0.000 1.000 0.000
#> GSM2883 3 0.0000 0.989 0.000 0.000 1.000
#> GSM2895 3 0.0000 0.989 0.000 0.000 1.000
#> GSM2885 3 0.0000 0.989 0.000 0.000 1.000
#> GSM2886 3 0.0000 0.989 0.000 0.000 1.000
#> GSM2887 3 0.0000 0.989 0.000 0.000 1.000
#> GSM2896 3 0.0000 0.989 0.000 0.000 1.000
#> GSM2888 3 0.0000 0.989 0.000 0.000 1.000
#> GSM2889 3 0.0000 0.989 0.000 0.000 1.000
#> GSM2876 1 0.0000 0.968 1.000 0.000 0.000
#> GSM2891 1 0.0000 0.968 1.000 0.000 0.000
#> GSM2880 1 0.0000 0.968 1.000 0.000 0.000
#> GSM2893 1 0.0000 0.968 1.000 0.000 0.000
#> GSM2821 1 0.0000 0.968 1.000 0.000 0.000
#> GSM2900 1 0.0000 0.968 1.000 0.000 0.000
#> GSM2903 1 0.0000 0.968 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM2819 2 0.5244 0.356 0.388 0.600 0.000 0.012
#> GSM2820 3 0.0000 0.979 0.000 0.000 1.000 0.000
#> GSM2822 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM2832 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM2823 1 0.0188 0.996 0.996 0.004 0.000 0.000
#> GSM2824 1 0.0707 0.979 0.980 0.020 0.000 0.000
#> GSM2825 2 0.0707 0.947 0.020 0.980 0.000 0.000
#> GSM2826 2 0.0707 0.947 0.020 0.980 0.000 0.000
#> GSM2829 4 0.0000 0.958 0.000 0.000 0.000 1.000
#> GSM2856 4 0.0000 0.958 0.000 0.000 0.000 1.000
#> GSM2830 4 0.0000 0.958 0.000 0.000 0.000 1.000
#> GSM2843 4 0.0000 0.958 0.000 0.000 0.000 1.000
#> GSM2871 4 0.3528 0.795 0.000 0.192 0.000 0.808
#> GSM2831 4 0.0000 0.958 0.000 0.000 0.000 1.000
#> GSM2844 4 0.0000 0.958 0.000 0.000 0.000 1.000
#> GSM2833 4 0.0000 0.958 0.000 0.000 0.000 1.000
#> GSM2846 4 0.0000 0.958 0.000 0.000 0.000 1.000
#> GSM2835 4 0.0000 0.958 0.000 0.000 0.000 1.000
#> GSM2858 4 0.0000 0.958 0.000 0.000 0.000 1.000
#> GSM2836 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM2848 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM2828 3 0.0000 0.979 0.000 0.000 1.000 0.000
#> GSM2837 3 0.0000 0.979 0.000 0.000 1.000 0.000
#> GSM2839 1 0.0188 0.996 0.996 0.004 0.000 0.000
#> GSM2841 1 0.0188 0.996 0.996 0.004 0.000 0.000
#> GSM2827 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM2842 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM2845 4 0.3907 0.739 0.000 0.232 0.000 0.768
#> GSM2872 4 0.3219 0.827 0.000 0.164 0.000 0.836
#> GSM2834 4 0.1302 0.932 0.000 0.044 0.000 0.956
#> GSM2847 4 0.0000 0.958 0.000 0.000 0.000 1.000
#> GSM2849 3 0.0000 0.979 0.000 0.000 1.000 0.000
#> GSM2850 3 0.0000 0.979 0.000 0.000 1.000 0.000
#> GSM2838 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM2853 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM2852 3 0.0188 0.975 0.000 0.004 0.996 0.000
#> GSM2855 3 0.0000 0.979 0.000 0.000 1.000 0.000
#> GSM2840 1 0.0336 0.992 0.992 0.008 0.000 0.000
#> GSM2857 1 0.0188 0.996 0.996 0.004 0.000 0.000
#> GSM2859 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM2860 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM2861 2 0.0469 0.952 0.000 0.988 0.012 0.000
#> GSM2862 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM2863 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM2864 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM2865 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM2866 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM2868 2 0.0188 0.959 0.004 0.996 0.000 0.000
#> GSM2869 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM2851 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM2867 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM2870 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM2854 4 0.0817 0.944 0.000 0.024 0.000 0.976
#> GSM2873 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM2874 3 0.0000 0.979 0.000 0.000 1.000 0.000
#> GSM2884 3 0.0000 0.979 0.000 0.000 1.000 0.000
#> GSM2875 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM2890 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM2877 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM2892 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM2902 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM2878 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM2901 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM2879 3 0.2868 0.842 0.000 0.136 0.864 0.000
#> GSM2898 3 0.3610 0.753 0.000 0.200 0.800 0.000
#> GSM2881 3 0.0000 0.979 0.000 0.000 1.000 0.000
#> GSM2897 3 0.0000 0.979 0.000 0.000 1.000 0.000
#> GSM2882 4 0.0000 0.958 0.000 0.000 0.000 1.000
#> GSM2894 4 0.0000 0.958 0.000 0.000 0.000 1.000
#> GSM2883 3 0.0000 0.979 0.000 0.000 1.000 0.000
#> GSM2895 3 0.0000 0.979 0.000 0.000 1.000 0.000
#> GSM2885 3 0.0000 0.979 0.000 0.000 1.000 0.000
#> GSM2886 3 0.0000 0.979 0.000 0.000 1.000 0.000
#> GSM2887 3 0.0000 0.979 0.000 0.000 1.000 0.000
#> GSM2896 3 0.0000 0.979 0.000 0.000 1.000 0.000
#> GSM2888 2 0.3907 0.693 0.000 0.768 0.232 0.000
#> GSM2889 2 0.3942 0.687 0.000 0.764 0.236 0.000
#> GSM2876 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM2891 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM2880 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM2893 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM2821 1 0.0188 0.996 0.996 0.004 0.000 0.000
#> GSM2900 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM2903 1 0.0000 0.997 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM2819 1 0.7751 0.0808 0.392 0.304 0.000 0.064 NA
#> GSM2820 3 0.0000 0.9703 0.000 0.000 1.000 0.000 NA
#> GSM2822 2 0.3508 0.8038 0.000 0.748 0.000 0.000 NA
#> GSM2832 2 0.3837 0.7613 0.000 0.692 0.000 0.000 NA
#> GSM2823 1 0.0798 0.9260 0.976 0.016 0.000 0.000 NA
#> GSM2824 1 0.1682 0.9034 0.940 0.044 0.004 0.000 NA
#> GSM2825 2 0.4418 0.7113 0.016 0.652 0.000 0.000 NA
#> GSM2826 2 0.3934 0.7895 0.016 0.740 0.000 0.000 NA
#> GSM2829 4 0.0000 0.9077 0.000 0.000 0.000 1.000 NA
#> GSM2856 4 0.0162 0.9074 0.000 0.000 0.000 0.996 NA
#> GSM2830 4 0.1121 0.9017 0.000 0.000 0.000 0.956 NA
#> GSM2843 4 0.1270 0.9002 0.000 0.000 0.000 0.948 NA
#> GSM2871 4 0.5191 0.7449 0.000 0.088 0.000 0.660 NA
#> GSM2831 4 0.0000 0.9077 0.000 0.000 0.000 1.000 NA
#> GSM2844 4 0.0162 0.9075 0.000 0.000 0.000 0.996 NA
#> GSM2833 4 0.2648 0.8506 0.000 0.000 0.000 0.848 NA
#> GSM2846 4 0.1792 0.8880 0.000 0.000 0.000 0.916 NA
#> GSM2835 4 0.1197 0.8994 0.000 0.000 0.000 0.952 NA
#> GSM2858 4 0.1544 0.8942 0.000 0.000 0.000 0.932 NA
#> GSM2836 2 0.1792 0.8696 0.000 0.916 0.000 0.000 NA
#> GSM2848 2 0.1341 0.8778 0.000 0.944 0.000 0.000 NA
#> GSM2828 3 0.0000 0.9703 0.000 0.000 1.000 0.000 NA
#> GSM2837 3 0.0162 0.9697 0.000 0.000 0.996 0.000 NA
#> GSM2839 1 0.2516 0.8682 0.860 0.000 0.000 0.000 NA
#> GSM2841 1 0.2648 0.8611 0.848 0.000 0.000 0.000 NA
#> GSM2827 2 0.3305 0.8036 0.000 0.776 0.000 0.000 NA
#> GSM2842 2 0.2966 0.8306 0.000 0.816 0.000 0.000 NA
#> GSM2845 4 0.6054 0.5824 0.000 0.124 0.000 0.496 NA
#> GSM2872 4 0.5498 0.6846 0.000 0.080 0.000 0.580 NA
#> GSM2834 4 0.2970 0.8584 0.000 0.004 0.000 0.828 NA
#> GSM2847 4 0.2773 0.8620 0.000 0.000 0.000 0.836 NA
#> GSM2849 3 0.0162 0.9697 0.000 0.000 0.996 0.000 NA
#> GSM2850 3 0.0162 0.9697 0.000 0.000 0.996 0.000 NA
#> GSM2838 2 0.3876 0.7660 0.000 0.684 0.000 0.000 NA
#> GSM2853 2 0.3586 0.8026 0.000 0.736 0.000 0.000 NA
#> GSM2852 3 0.0162 0.9697 0.000 0.000 0.996 0.000 NA
#> GSM2855 3 0.0162 0.9697 0.000 0.000 0.996 0.000 NA
#> GSM2840 1 0.4178 0.7425 0.696 0.008 0.000 0.004 NA
#> GSM2857 1 0.3143 0.8274 0.796 0.000 0.000 0.000 NA
#> GSM2859 2 0.2074 0.8680 0.000 0.896 0.000 0.000 NA
#> GSM2860 2 0.0510 0.8797 0.000 0.984 0.000 0.000 NA
#> GSM2861 2 0.2230 0.8662 0.000 0.884 0.000 0.000 NA
#> GSM2862 2 0.0609 0.8812 0.000 0.980 0.000 0.000 NA
#> GSM2863 2 0.0162 0.8804 0.000 0.996 0.000 0.000 NA
#> GSM2864 2 0.1478 0.8737 0.000 0.936 0.000 0.000 NA
#> GSM2865 2 0.0880 0.8782 0.000 0.968 0.000 0.000 NA
#> GSM2866 2 0.0609 0.8817 0.000 0.980 0.000 0.000 NA
#> GSM2868 2 0.2280 0.8769 0.000 0.880 0.000 0.000 NA
#> GSM2869 2 0.2127 0.8780 0.000 0.892 0.000 0.000 NA
#> GSM2851 2 0.1671 0.8750 0.000 0.924 0.000 0.000 NA
#> GSM2867 2 0.1908 0.8759 0.000 0.908 0.000 0.000 NA
#> GSM2870 2 0.2280 0.8659 0.000 0.880 0.000 0.000 NA
#> GSM2854 4 0.1671 0.8914 0.000 0.000 0.000 0.924 NA
#> GSM2873 2 0.2929 0.8303 0.000 0.820 0.000 0.000 NA
#> GSM2874 3 0.0000 0.9703 0.000 0.000 1.000 0.000 NA
#> GSM2884 3 0.0000 0.9703 0.000 0.000 1.000 0.000 NA
#> GSM2875 1 0.0000 0.9317 1.000 0.000 0.000 0.000 NA
#> GSM2890 1 0.0162 0.9315 0.996 0.000 0.000 0.000 NA
#> GSM2877 1 0.0404 0.9309 0.988 0.000 0.000 0.000 NA
#> GSM2892 1 0.0290 0.9319 0.992 0.000 0.000 0.000 NA
#> GSM2902 1 0.0162 0.9315 0.996 0.000 0.000 0.000 NA
#> GSM2878 1 0.0404 0.9313 0.988 0.000 0.000 0.000 NA
#> GSM2901 1 0.0290 0.9314 0.992 0.000 0.000 0.000 NA
#> GSM2879 3 0.3264 0.7801 0.000 0.164 0.820 0.000 NA
#> GSM2898 3 0.4268 0.5945 0.000 0.268 0.708 0.000 NA
#> GSM2881 3 0.0000 0.9703 0.000 0.000 1.000 0.000 NA
#> GSM2897 3 0.0000 0.9703 0.000 0.000 1.000 0.000 NA
#> GSM2882 4 0.0000 0.9077 0.000 0.000 0.000 1.000 NA
#> GSM2894 4 0.0000 0.9077 0.000 0.000 0.000 1.000 NA
#> GSM2883 3 0.0162 0.9697 0.000 0.000 0.996 0.000 NA
#> GSM2895 3 0.0324 0.9675 0.000 0.004 0.992 0.000 NA
#> GSM2885 3 0.0000 0.9703 0.000 0.000 1.000 0.000 NA
#> GSM2886 3 0.0000 0.9703 0.000 0.000 1.000 0.000 NA
#> GSM2887 3 0.0000 0.9703 0.000 0.000 1.000 0.000 NA
#> GSM2896 3 0.0000 0.9703 0.000 0.000 1.000 0.000 NA
#> GSM2888 2 0.5102 0.7324 0.000 0.696 0.176 0.000 NA
#> GSM2889 2 0.4968 0.7581 0.000 0.712 0.152 0.000 NA
#> GSM2876 1 0.0510 0.9311 0.984 0.000 0.000 0.000 NA
#> GSM2891 1 0.0290 0.9311 0.992 0.000 0.000 0.000 NA
#> GSM2880 1 0.0290 0.9311 0.992 0.000 0.000 0.000 NA
#> GSM2893 1 0.0162 0.9318 0.996 0.000 0.000 0.000 NA
#> GSM2821 1 0.0880 0.9263 0.968 0.000 0.000 0.000 NA
#> GSM2900 1 0.0703 0.9285 0.976 0.000 0.000 0.000 NA
#> GSM2903 1 0.0703 0.9285 0.976 0.000 0.000 0.000 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM2819 1 0.7065 0.280 0.516 0.108 0.000 0.048 0.072 NA
#> GSM2820 3 0.0146 0.938 0.000 0.000 0.996 0.000 0.004 NA
#> GSM2822 2 0.3487 0.767 0.000 0.756 0.000 0.000 0.020 NA
#> GSM2832 2 0.4462 0.678 0.000 0.660 0.000 0.000 0.060 NA
#> GSM2823 1 0.2263 0.881 0.896 0.000 0.000 0.000 0.056 NA
#> GSM2824 1 0.2375 0.880 0.896 0.008 0.000 0.000 0.060 NA
#> GSM2825 5 0.3596 0.529 0.008 0.244 0.000 0.000 0.740 NA
#> GSM2826 5 0.3861 0.390 0.004 0.316 0.000 0.000 0.672 NA
#> GSM2829 4 0.1007 0.797 0.000 0.000 0.000 0.956 0.000 NA
#> GSM2856 4 0.1010 0.798 0.000 0.000 0.000 0.960 0.004 NA
#> GSM2830 4 0.2340 0.777 0.000 0.000 0.000 0.852 0.000 NA
#> GSM2843 4 0.2805 0.764 0.000 0.000 0.000 0.812 0.004 NA
#> GSM2871 4 0.5470 0.556 0.000 0.060 0.000 0.504 0.028 NA
#> GSM2831 4 0.0363 0.803 0.000 0.000 0.000 0.988 0.000 NA
#> GSM2844 4 0.0632 0.803 0.000 0.000 0.000 0.976 0.000 NA
#> GSM2833 4 0.3564 0.695 0.000 0.000 0.000 0.724 0.012 NA
#> GSM2846 4 0.3342 0.722 0.000 0.000 0.000 0.760 0.012 NA
#> GSM2835 4 0.2772 0.751 0.000 0.000 0.000 0.816 0.004 NA
#> GSM2858 4 0.2838 0.747 0.000 0.000 0.000 0.808 0.004 NA
#> GSM2836 2 0.2560 0.810 0.000 0.872 0.000 0.000 0.036 NA
#> GSM2848 2 0.2106 0.824 0.000 0.904 0.000 0.000 0.032 NA
#> GSM2828 3 0.0146 0.938 0.000 0.000 0.996 0.000 0.000 NA
#> GSM2837 3 0.0291 0.937 0.000 0.000 0.992 0.000 0.004 NA
#> GSM2839 5 0.3741 0.663 0.320 0.000 0.000 0.000 0.672 NA
#> GSM2841 5 0.3409 0.691 0.300 0.000 0.000 0.000 0.700 NA
#> GSM2827 2 0.4404 0.650 0.004 0.696 0.000 0.008 0.040 NA
#> GSM2842 2 0.3347 0.771 0.004 0.812 0.000 0.004 0.028 NA
#> GSM2845 4 0.6180 0.512 0.000 0.076 0.000 0.472 0.072 NA
#> GSM2872 4 0.5759 0.583 0.004 0.040 0.000 0.528 0.064 NA
#> GSM2834 4 0.4639 0.681 0.000 0.016 0.000 0.644 0.036 NA
#> GSM2847 4 0.3812 0.718 0.000 0.000 0.000 0.712 0.024 NA
#> GSM2849 3 0.0291 0.938 0.000 0.000 0.992 0.000 0.004 NA
#> GSM2850 3 0.0291 0.938 0.000 0.000 0.992 0.000 0.004 NA
#> GSM2838 2 0.3518 0.747 0.000 0.732 0.000 0.000 0.012 NA
#> GSM2853 2 0.3719 0.749 0.000 0.728 0.000 0.000 0.024 NA
#> GSM2852 3 0.0146 0.938 0.000 0.000 0.996 0.000 0.004 NA
#> GSM2855 3 0.0146 0.938 0.000 0.000 0.996 0.000 0.004 NA
#> GSM2840 5 0.3110 0.738 0.196 0.000 0.000 0.000 0.792 NA
#> GSM2857 5 0.3076 0.734 0.240 0.000 0.000 0.000 0.760 NA
#> GSM2859 2 0.1657 0.839 0.000 0.928 0.000 0.000 0.016 NA
#> GSM2860 2 0.0508 0.839 0.000 0.984 0.000 0.000 0.012 NA
#> GSM2861 2 0.2039 0.833 0.000 0.904 0.000 0.000 0.020 NA
#> GSM2862 2 0.0806 0.838 0.000 0.972 0.000 0.000 0.020 NA
#> GSM2863 2 0.0405 0.839 0.000 0.988 0.000 0.000 0.004 NA
#> GSM2864 2 0.1908 0.825 0.000 0.916 0.000 0.000 0.028 NA
#> GSM2865 2 0.1176 0.836 0.000 0.956 0.000 0.000 0.020 NA
#> GSM2866 2 0.0520 0.839 0.000 0.984 0.000 0.000 0.008 NA
#> GSM2868 2 0.3743 0.697 0.000 0.724 0.000 0.000 0.252 NA
#> GSM2869 2 0.3746 0.752 0.000 0.760 0.000 0.000 0.192 NA
#> GSM2851 2 0.2956 0.818 0.000 0.848 0.000 0.000 0.088 NA
#> GSM2867 2 0.3778 0.677 0.000 0.708 0.000 0.000 0.272 NA
#> GSM2870 2 0.3341 0.813 0.000 0.816 0.000 0.000 0.068 NA
#> GSM2854 4 0.2980 0.756 0.000 0.000 0.000 0.808 0.012 NA
#> GSM2873 2 0.3163 0.776 0.000 0.820 0.000 0.000 0.040 NA
#> GSM2874 3 0.0146 0.938 0.000 0.000 0.996 0.000 0.000 NA
#> GSM2884 3 0.0146 0.938 0.000 0.000 0.996 0.000 0.000 NA
#> GSM2875 1 0.0363 0.925 0.988 0.000 0.000 0.000 0.012 NA
#> GSM2890 1 0.0363 0.925 0.988 0.000 0.000 0.000 0.012 NA
#> GSM2877 1 0.0146 0.926 0.996 0.000 0.000 0.000 0.000 NA
#> GSM2892 1 0.0146 0.927 0.996 0.000 0.000 0.000 0.004 NA
#> GSM2902 1 0.0146 0.927 0.996 0.000 0.000 0.000 0.004 NA
#> GSM2878 1 0.0458 0.924 0.984 0.000 0.000 0.000 0.016 NA
#> GSM2901 1 0.0547 0.922 0.980 0.000 0.000 0.000 0.020 NA
#> GSM2879 3 0.4908 0.351 0.000 0.348 0.584 0.000 0.004 NA
#> GSM2898 3 0.5040 0.169 0.000 0.408 0.528 0.000 0.008 NA
#> GSM2881 3 0.0146 0.938 0.000 0.000 0.996 0.000 0.000 NA
#> GSM2897 3 0.0146 0.938 0.000 0.000 0.996 0.000 0.000 NA
#> GSM2882 4 0.0458 0.803 0.000 0.000 0.000 0.984 0.000 NA
#> GSM2894 4 0.0547 0.803 0.000 0.000 0.000 0.980 0.000 NA
#> GSM2883 3 0.0146 0.938 0.000 0.000 0.996 0.000 0.004 NA
#> GSM2895 3 0.0146 0.938 0.000 0.000 0.996 0.000 0.004 NA
#> GSM2885 3 0.0000 0.939 0.000 0.000 1.000 0.000 0.000 NA
#> GSM2886 3 0.0000 0.939 0.000 0.000 1.000 0.000 0.000 NA
#> GSM2887 3 0.0000 0.939 0.000 0.000 1.000 0.000 0.000 NA
#> GSM2896 3 0.0000 0.939 0.000 0.000 1.000 0.000 0.000 NA
#> GSM2888 2 0.4103 0.747 0.000 0.764 0.136 0.000 0.008 NA
#> GSM2889 2 0.3784 0.765 0.000 0.792 0.124 0.000 0.008 NA
#> GSM2876 1 0.0622 0.925 0.980 0.000 0.000 0.000 0.008 NA
#> GSM2891 1 0.0622 0.925 0.980 0.000 0.000 0.000 0.008 NA
#> GSM2880 1 0.0820 0.921 0.972 0.000 0.000 0.000 0.016 NA
#> GSM2893 1 0.0508 0.926 0.984 0.000 0.000 0.000 0.004 NA
#> GSM2821 1 0.2058 0.890 0.908 0.000 0.000 0.000 0.056 NA
#> GSM2900 1 0.1765 0.897 0.924 0.000 0.000 0.000 0.052 NA
#> GSM2903 1 0.1829 0.898 0.920 0.000 0.000 0.000 0.056 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> ATC:NMF 81 6.04e-05 2
#> ATC:NMF 84 1.72e-08 3
#> ATC:NMF 83 4.06e-12 4
#> ATC:NMF 83 4.06e-12 5
#> ATC:NMF 80 6.28e-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.
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