Date: 2019-12-25 21:48:35 CET, cola version: 1.3.2
Document is loading...
All available functions which can be applied to this res_list object:
res_list
#> A 'ConsensusPartitionList' object with 24 methods.
#> On a matrix with 31589 rows and 80 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] 31589 80
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:skmeans | 3 | 1.000 | 0.999 | 1.000 | ** | 2 |
| CV:skmeans | 3 | 1.000 | 1.000 | 1.000 | ** | 2 |
| MAD:hclust | 6 | 1.000 | 0.999 | 1.000 | ** | 3 |
| MAD:skmeans | 2 | 1.000 | 0.962 | 0.985 | ** | |
| MAD:pam | 6 | 1.000 | 0.961 | 0.980 | ** | 3,4,5 |
| ATC:kmeans | 2 | 1.000 | 1.000 | 1.000 | ** | |
| ATC:pam | 6 | 1.000 | 0.964 | 0.985 | ** | 2,4,5 |
| ATC:NMF | 2 | 1.000 | 0.994 | 0.997 | ** | |
| SD:NMF | 4 | 0.988 | 0.955 | 0.966 | ** | 2,3 |
| MAD:NMF | 2 | 0.974 | 0.975 | 0.988 | ** | |
| ATC:skmeans | 4 | 0.968 | 0.974 | 0.972 | ** | 2,3 |
| CV:pam | 3 | 0.962 | 0.957 | 0.982 | ** | |
| ATC:mclust | 6 | 0.958 | 0.956 | 0.945 | ** | 5 |
| SD:pam | 3 | 0.926 | 0.927 | 0.969 | * | |
| CV:NMF | 5 | 0.916 | 0.867 | 0.916 | * | 3,4 |
| SD:hclust | 6 | 0.915 | 0.883 | 0.939 | * | |
| ATC:hclust | 6 | 0.912 | 0.873 | 0.915 | * | 3,4 |
| MAD:kmeans | 2 | 0.902 | 0.947 | 0.966 | * | |
| MAD:mclust | 5 | 0.876 | 0.908 | 0.942 | ||
| SD:mclust | 5 | 0.817 | 0.798 | 0.888 | ||
| CV:mclust | 5 | 0.803 | 0.863 | 0.902 | ||
| CV:hclust | 3 | 0.795 | 0.879 | 0.946 | ||
| CV:kmeans | 3 | 0.666 | 0.899 | 0.878 | ||
| SD:kmeans | 2 | 0.487 | 0.784 | 0.874 |
**: 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 0.948 0.927 0.972 0.505 0.494 0.494
#> CV:NMF 2 0.866 0.928 0.961 0.496 0.499 0.499
#> MAD:NMF 2 0.974 0.975 0.988 0.506 0.495 0.495
#> ATC:NMF 2 1.000 0.994 0.997 0.492 0.509 0.509
#> SD:skmeans 2 0.924 0.955 0.981 0.505 0.494 0.494
#> CV:skmeans 2 1.000 0.957 0.983 0.505 0.494 0.494
#> MAD:skmeans 2 1.000 0.962 0.985 0.506 0.495 0.495
#> ATC:skmeans 2 1.000 1.000 1.000 0.491 0.509 0.509
#> SD:mclust 2 0.339 0.812 0.865 0.364 0.724 0.724
#> CV:mclust 2 0.379 0.891 0.893 0.441 0.556 0.556
#> MAD:mclust 2 0.357 0.817 0.871 0.456 0.509 0.509
#> ATC:mclust 2 0.519 0.874 0.868 0.435 0.509 0.509
#> SD:kmeans 2 0.487 0.784 0.874 0.475 0.494 0.494
#> CV:kmeans 2 0.452 0.319 0.726 0.476 0.539 0.539
#> MAD:kmeans 2 0.902 0.947 0.966 0.500 0.495 0.495
#> ATC:kmeans 2 1.000 1.000 1.000 0.491 0.509 0.509
#> SD:pam 2 0.814 0.918 0.964 0.504 0.495 0.495
#> CV:pam 2 0.810 0.896 0.954 0.504 0.495 0.495
#> MAD:pam 2 0.898 0.964 0.981 0.504 0.495 0.495
#> ATC:pam 2 1.000 1.000 1.000 0.491 0.509 0.509
#> SD:hclust 2 0.400 0.831 0.896 0.463 0.495 0.495
#> CV:hclust 2 0.473 0.862 0.905 0.471 0.495 0.495
#> MAD:hclust 2 0.838 0.914 0.959 0.500 0.502 0.502
#> ATC:hclust 2 0.624 0.914 0.957 0.483 0.509 0.509
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.927 0.922 0.969 0.323 0.710 0.480
#> CV:NMF 3 1.000 0.966 0.986 0.348 0.748 0.534
#> MAD:NMF 3 0.747 0.822 0.923 0.309 0.717 0.491
#> ATC:NMF 3 0.736 0.888 0.875 0.248 0.867 0.739
#> SD:skmeans 3 1.000 0.999 1.000 0.322 0.750 0.535
#> CV:skmeans 3 1.000 1.000 1.000 0.323 0.750 0.535
#> MAD:skmeans 3 0.641 0.734 0.792 0.283 0.830 0.669
#> ATC:skmeans 3 1.000 0.999 0.999 0.270 0.867 0.739
#> SD:mclust 3 0.685 0.740 0.880 0.832 0.478 0.335
#> CV:mclust 3 0.522 0.738 0.873 0.452 0.714 0.512
#> MAD:mclust 3 0.574 0.754 0.858 0.399 0.740 0.525
#> ATC:mclust 3 0.789 0.834 0.887 0.480 0.835 0.685
#> SD:kmeans 3 0.655 0.844 0.855 0.362 0.750 0.535
#> CV:kmeans 3 0.666 0.899 0.878 0.362 0.718 0.511
#> MAD:kmeans 3 0.566 0.657 0.739 0.274 0.836 0.679
#> ATC:kmeans 3 0.788 0.943 0.912 0.247 0.867 0.739
#> SD:pam 3 0.926 0.927 0.969 0.318 0.689 0.452
#> CV:pam 3 0.962 0.957 0.982 0.324 0.689 0.452
#> MAD:pam 3 0.906 0.941 0.975 0.278 0.796 0.612
#> ATC:pam 3 0.830 0.910 0.940 0.297 0.853 0.714
#> SD:hclust 3 0.703 0.860 0.929 0.381 0.862 0.721
#> CV:hclust 3 0.795 0.879 0.946 0.368 0.862 0.721
#> MAD:hclust 3 0.926 0.927 0.968 0.205 0.916 0.832
#> ATC:hclust 3 0.926 0.929 0.969 0.315 0.867 0.739
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.988 0.955 0.966 0.0880 0.893 0.701
#> CV:NMF 4 1.000 0.985 0.991 0.0835 0.893 0.701
#> MAD:NMF 4 0.744 0.829 0.895 0.1158 0.836 0.570
#> ATC:NMF 4 0.793 0.833 0.884 0.1693 0.862 0.647
#> SD:skmeans 4 0.777 0.451 0.613 0.1005 0.721 0.400
#> CV:skmeans 4 0.861 0.862 0.854 0.0974 0.947 0.840
#> MAD:skmeans 4 0.777 0.877 0.892 0.1293 0.853 0.621
#> ATC:skmeans 4 0.968 0.974 0.972 0.0855 0.949 0.864
#> SD:mclust 4 0.633 0.670 0.820 0.0848 0.767 0.434
#> CV:mclust 4 0.791 0.799 0.875 0.1451 0.797 0.485
#> MAD:mclust 4 0.656 0.694 0.832 0.1443 0.733 0.373
#> ATC:mclust 4 0.881 0.905 0.951 0.0936 0.902 0.749
#> SD:kmeans 4 0.728 0.774 0.804 0.1208 1.000 1.000
#> CV:kmeans 4 0.748 0.808 0.827 0.1168 1.000 1.000
#> MAD:kmeans 4 0.617 0.695 0.723 0.1256 0.851 0.613
#> ATC:kmeans 4 0.803 0.720 0.819 0.1369 0.949 0.864
#> SD:pam 4 0.840 0.919 0.916 0.1121 0.914 0.744
#> CV:pam 4 0.865 0.928 0.912 0.1070 0.914 0.744
#> MAD:pam 4 0.955 0.945 0.977 0.1449 0.894 0.705
#> ATC:pam 4 1.000 0.957 0.961 0.1330 0.903 0.738
#> SD:hclust 4 0.792 0.833 0.895 0.1273 0.939 0.830
#> CV:hclust 4 0.849 0.874 0.923 0.1130 0.939 0.830
#> MAD:hclust 4 0.785 0.825 0.849 0.1558 0.901 0.763
#> ATC:hclust 4 0.973 0.902 0.965 0.0869 0.932 0.818
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.892 0.866 0.906 0.0619 0.930 0.749
#> CV:NMF 5 0.916 0.867 0.916 0.0586 0.934 0.763
#> MAD:NMF 5 0.801 0.732 0.858 0.0450 0.935 0.760
#> ATC:NMF 5 0.660 0.615 0.767 0.0671 0.916 0.724
#> SD:skmeans 5 0.802 0.865 0.897 0.0773 0.850 0.554
#> CV:skmeans 5 0.813 0.861 0.894 0.0790 0.904 0.665
#> MAD:skmeans 5 0.874 0.866 0.911 0.0805 0.937 0.763
#> ATC:skmeans 5 0.829 0.963 0.938 0.1166 0.904 0.704
#> SD:mclust 5 0.817 0.798 0.888 0.0917 0.923 0.716
#> CV:mclust 5 0.803 0.863 0.902 0.0680 0.973 0.895
#> MAD:mclust 5 0.876 0.908 0.942 0.0846 0.891 0.616
#> ATC:mclust 5 0.938 0.955 0.974 0.1363 0.867 0.584
#> SD:kmeans 5 0.744 0.561 0.730 0.0607 0.891 0.676
#> CV:kmeans 5 0.728 0.676 0.715 0.0656 0.886 0.658
#> MAD:kmeans 5 0.693 0.782 0.787 0.0723 0.930 0.738
#> ATC:kmeans 5 0.768 0.673 0.745 0.0720 0.905 0.708
#> SD:pam 5 0.841 0.831 0.910 0.0683 0.938 0.765
#> CV:pam 5 0.840 0.782 0.864 0.0640 0.962 0.852
#> MAD:pam 5 1.000 1.000 1.000 0.0786 0.930 0.738
#> ATC:pam 5 1.000 0.963 0.985 0.0861 0.933 0.757
#> SD:hclust 5 0.792 0.797 0.885 0.0482 0.929 0.767
#> CV:hclust 5 0.798 0.789 0.831 0.0524 0.981 0.936
#> MAD:hclust 5 0.886 0.925 0.910 0.0831 0.913 0.726
#> ATC:hclust 5 0.864 0.893 0.870 0.0991 0.905 0.692
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.837 0.773 0.855 0.0393 0.981 0.914
#> CV:NMF 6 0.836 0.770 0.870 0.0493 0.981 0.916
#> MAD:NMF 6 0.789 0.740 0.822 0.0417 0.929 0.704
#> ATC:NMF 6 0.655 0.558 0.664 0.0362 0.896 0.618
#> SD:skmeans 6 0.848 0.817 0.891 0.0404 0.977 0.888
#> CV:skmeans 6 0.843 0.828 0.887 0.0431 0.937 0.704
#> MAD:skmeans 6 0.881 0.858 0.907 0.0358 0.974 0.877
#> ATC:skmeans 6 0.940 0.897 0.896 0.0422 0.990 0.956
#> SD:mclust 6 0.864 0.774 0.882 0.0371 0.939 0.727
#> CV:mclust 6 0.876 0.874 0.923 0.0506 0.920 0.666
#> MAD:mclust 6 0.885 0.905 0.919 0.0274 0.987 0.933
#> ATC:mclust 6 0.958 0.956 0.945 0.0236 0.987 0.933
#> SD:kmeans 6 0.721 0.616 0.718 0.0468 0.901 0.623
#> CV:kmeans 6 0.715 0.646 0.731 0.0468 0.952 0.785
#> MAD:kmeans 6 0.701 0.749 0.758 0.0466 0.992 0.963
#> ATC:kmeans 6 0.723 0.811 0.796 0.0604 0.903 0.631
#> SD:pam 6 0.891 0.897 0.946 0.0470 0.942 0.737
#> CV:pam 6 0.893 0.901 0.946 0.0512 0.938 0.726
#> MAD:pam 6 1.000 0.961 0.980 0.0347 0.952 0.774
#> ATC:pam 6 1.000 0.964 0.985 0.0577 0.957 0.798
#> SD:hclust 6 0.915 0.883 0.939 0.0786 0.910 0.658
#> CV:hclust 6 0.840 0.828 0.847 0.0515 0.949 0.820
#> MAD:hclust 6 1.000 0.999 1.000 0.0704 0.962 0.836
#> ATC:hclust 6 0.912 0.873 0.915 0.0616 0.965 0.839
Following heatmap plots the partition for each combination of methods and the lightness correspond to the silhouette scores for samples in each method. On top the consensus subgroup is inferred from all methods by taking the mean silhouette scores as weight.
collect_stats(res_list, k = 2)
collect_stats(res_list, k = 3)
collect_stats(res_list, k = 4)
collect_stats(res_list, k = 5)
collect_stats(res_list, k = 6)
Collect partitions from all methods:
collect_classes(res_list, k = 2)
collect_classes(res_list, k = 3)
collect_classes(res_list, k = 4)
collect_classes(res_list, k = 5)
collect_classes(res_list, k = 6)
Overlap of top rows from different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "euler")
top_rows_overlap(res_list, top_n = 2000, method = "euler")
top_rows_overlap(res_list, top_n = 3000, method = "euler")
top_rows_overlap(res_list, top_n = 4000, method = "euler")
top_rows_overlap(res_list, top_n = 5000, method = "euler")
Also visualize the correspondance of rankings between different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "correspondance")
top_rows_overlap(res_list, top_n = 2000, method = "correspondance")
top_rows_overlap(res_list, top_n = 3000, method = "correspondance")
top_rows_overlap(res_list, top_n = 4000, method = "correspondance")
top_rows_overlap(res_list, top_n = 5000, method = "correspondance")
Heatmaps of the top rows:
top_rows_heatmap(res_list, top_n = 1000)
top_rows_heatmap(res_list, top_n = 2000)
top_rows_heatmap(res_list, top_n = 3000)
top_rows_heatmap(res_list, top_n = 4000)
top_rows_heatmap(res_list, top_n = 5000)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res_list, k = 2)
#> n protocol(p) cell.type(p) k
#> SD:NMF 76 6.05e-07 3.68e-06 2
#> CV:NMF 79 3.39e-05 1.50e-08 2
#> MAD:NMF 80 1.22e-07 6.13e-05 2
#> ATC:NMF 80 1.10e-11 4.22e-01 2
#> SD:skmeans 80 1.36e-06 2.28e-06 2
#> CV:skmeans 77 4.63e-06 1.59e-07 2
#> MAD:skmeans 77 4.05e-07 8.12e-06 2
#> ATC:skmeans 80 1.10e-11 4.22e-01 2
#> SD:mclust 80 1.22e-07 8.06e-04 2
#> CV:mclust 80 9.82e-09 1.94e-03 2
#> MAD:mclust 80 1.10e-11 4.22e-01 2
#> ATC:mclust 80 1.10e-11 4.22e-01 2
#> SD:kmeans 73 2.04e-06 2.19e-07 2
#> CV:kmeans 50 1.35e-04 4.90e-09 2
#> MAD:kmeans 80 1.22e-07 6.13e-05 2
#> ATC:kmeans 80 1.10e-11 4.22e-01 2
#> SD:pam 74 1.36e-06 6.10e-07 2
#> CV:pam 72 3.06e-06 7.12e-08 2
#> MAD:pam 80 1.22e-07 6.13e-05 2
#> ATC:pam 80 1.10e-11 4.22e-01 2
#> SD:hclust 76 6.05e-07 3.68e-06 2
#> CV:hclust 80 3.07e-06 6.59e-07 2
#> MAD:hclust 73 1.81e-07 1.42e-05 2
#> ATC:hclust 80 1.10e-11 4.22e-01 2
test_to_known_factors(res_list, k = 3)
#> n protocol(p) cell.type(p) k
#> SD:NMF 77 5.49e-11 2.79e-10 3
#> CV:NMF 79 1.78e-10 2.17e-10 3
#> MAD:NMF 73 5.52e-12 1.39e-07 3
#> ATC:NMF 79 1.71e-14 1.03e-04 3
#> SD:skmeans 80 2.40e-10 5.36e-11 3
#> CV:skmeans 80 2.40e-10 5.36e-11 3
#> MAD:skmeans 70 7.45e-12 3.09e-09 3
#> ATC:skmeans 80 9.12e-15 1.26e-04 3
#> SD:mclust 65 3.09e-11 7.96e-10 3
#> CV:mclust 68 1.93e-10 2.24e-08 3
#> MAD:mclust 73 3.39e-15 1.25e-05 3
#> ATC:mclust 76 1.17e-12 3.47e-03 3
#> SD:kmeans 80 2.40e-10 5.36e-11 3
#> CV:kmeans 80 2.40e-10 5.36e-11 3
#> MAD:kmeans 70 1.92e-12 5.88e-08 3
#> ATC:kmeans 80 9.12e-15 1.26e-04 3
#> SD:pam 78 1.82e-10 2.94e-10 3
#> CV:pam 79 1.78e-10 2.17e-10 3
#> MAD:pam 79 4.03e-14 1.29e-05 3
#> ATC:pam 79 1.71e-14 1.03e-04 3
#> SD:hclust 76 5.29e-11 1.09e-07 3
#> CV:hclust 74 4.44e-09 1.12e-11 3
#> MAD:hclust 74 3.24e-08 4.57e-10 3
#> ATC:hclust 74 3.84e-13 1.93e-05 3
test_to_known_factors(res_list, k = 4)
#> n protocol(p) cell.type(p) k
#> SD:NMF 80 5.59e-11 3.07e-17 4
#> CV:NMF 80 5.59e-11 3.07e-17 4
#> MAD:NMF 78 6.04e-11 8.24e-17 4
#> ATC:NMF 73 8.77e-19 1.04e-06 4
#> SD:skmeans 35 5.66e-08 5.81e-06 4
#> CV:skmeans 77 6.46e-16 2.62e-14 4
#> MAD:skmeans 77 1.00e-19 7.99e-06 4
#> ATC:skmeans 80 8.27e-16 2.47e-06 4
#> SD:mclust 59 5.91e-12 9.61e-13 4
#> CV:mclust 73 6.10e-14 9.98e-13 4
#> MAD:mclust 76 1.02e-13 7.08e-08 4
#> ATC:mclust 76 3.99e-13 8.00e-10 4
#> SD:kmeans 80 2.40e-10 5.36e-11 4
#> CV:kmeans 80 2.40e-10 5.36e-11 4
#> MAD:kmeans 70 9.95e-17 1.58e-08 4
#> ATC:kmeans 73 4.00e-13 4.34e-09 4
#> SD:pam 78 2.64e-15 5.77e-10 4
#> CV:pam 80 2.97e-15 3.00e-10 4
#> MAD:pam 78 2.47e-19 6.14e-06 4
#> ATC:pam 79 5.15e-21 3.63e-04 4
#> SD:hclust 76 6.81e-12 2.19e-11 4
#> CV:hclust 80 8.66e-12 2.68e-12 4
#> MAD:hclust 74 3.92e-13 2.44e-09 4
#> ATC:hclust 73 4.00e-13 4.34e-09 4
test_to_known_factors(res_list, k = 5)
#> n protocol(p) cell.type(p) k
#> SD:NMF 77 1.74e-15 7.52e-16 5
#> CV:NMF 77 7.58e-16 7.52e-16 5
#> MAD:NMF 74 4.45e-13 3.24e-15 5
#> ATC:NMF 66 1.34e-18 3.00e-07 5
#> SD:skmeans 77 1.84e-20 1.36e-13 5
#> CV:skmeans 77 1.84e-20 1.36e-13 5
#> MAD:skmeans 80 7.64e-20 2.66e-10 5
#> ATC:skmeans 80 1.46e-23 6.83e-06 5
#> SD:mclust 73 1.85e-14 5.28e-15 5
#> CV:mclust 80 1.34e-16 1.37e-13 5
#> MAD:mclust 80 3.30e-17 1.92e-14 5
#> ATC:mclust 80 1.08e-20 3.36e-10 5
#> SD:kmeans 59 1.11e-14 1.26e-08 5
#> CV:kmeans 65 3.37e-18 4.76e-11 5
#> MAD:kmeans 74 1.38e-18 3.80e-11 5
#> ATC:kmeans 69 7.62e-19 1.51e-09 5
#> SD:pam 76 2.03e-19 2.15e-09 5
#> CV:pam 76 3.70e-19 2.02e-09 5
#> MAD:pam 80 7.64e-20 2.66e-10 5
#> ATC:pam 78 1.86e-20 7.15e-07 5
#> SD:hclust 69 2.12e-11 6.74e-10 5
#> CV:hclust 77 6.34e-15 6.01e-11 5
#> MAD:hclust 80 5.03e-20 9.50e-08 5
#> ATC:hclust 73 9.57e-20 9.15e-09 5
test_to_known_factors(res_list, k = 6)
#> n protocol(p) cell.type(p) k
#> SD:NMF 68 7.13e-15 6.00e-14 6
#> CV:NMF 66 2.67e-15 1.58e-13 6
#> MAD:NMF 71 1.25e-23 6.35e-14 6
#> ATC:NMF 54 3.20e-15 2.10e-09 6
#> SD:skmeans 73 2.24e-30 3.99e-10 6
#> CV:skmeans 74 8.39e-29 1.48e-11 6
#> MAD:skmeans 80 2.76e-23 8.50e-10 6
#> ATC:skmeans 77 2.26e-25 3.15e-06 6
#> SD:mclust 65 3.84e-21 5.29e-11 6
#> CV:mclust 77 2.13e-24 5.97e-13 6
#> MAD:mclust 79 1.54e-20 1.39e-13 6
#> ATC:mclust 80 2.52e-23 1.29e-09 6
#> SD:kmeans 52 1.51e-16 1.38e-10 6
#> CV:kmeans 58 3.59e-17 1.78e-09 6
#> MAD:kmeans 74 8.86e-21 1.52e-10 6
#> ATC:kmeans 80 1.08e-20 3.36e-10 6
#> SD:pam 79 6.42e-28 6.93e-08 6
#> CV:pam 80 1.08e-28 1.03e-07 6
#> MAD:pam 79 5.39e-26 2.50e-08 6
#> ATC:pam 78 1.97e-26 1.09e-06 6
#> SD:hclust 73 1.69e-24 1.43e-09 6
#> CV:hclust 80 8.72e-22 2.76e-13 6
#> MAD:hclust 80 3.12e-20 5.27e-11 6
#> ATC:hclust 73 9.57e-20 9.15e-09 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 31589 rows and 80 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.400 0.831 0.896 0.4626 0.495 0.495
#> 3 3 0.703 0.860 0.929 0.3811 0.862 0.721
#> 4 4 0.792 0.833 0.895 0.1273 0.939 0.830
#> 5 5 0.792 0.797 0.885 0.0482 0.929 0.767
#> 6 6 0.915 0.883 0.939 0.0786 0.910 0.658
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
#> GSM1022325 2 0.000 0.894 0.000 1.000
#> GSM1022326 2 0.000 0.894 0.000 1.000
#> GSM1022327 2 0.000 0.894 0.000 1.000
#> GSM1022331 1 0.000 0.844 1.000 0.000
#> GSM1022332 1 0.000 0.844 1.000 0.000
#> GSM1022333 1 0.000 0.844 1.000 0.000
#> GSM1022328 2 0.000 0.894 0.000 1.000
#> GSM1022329 2 0.000 0.894 0.000 1.000
#> GSM1022330 2 0.000 0.894 0.000 1.000
#> GSM1022337 2 0.278 0.872 0.048 0.952
#> GSM1022338 2 0.278 0.872 0.048 0.952
#> GSM1022339 2 0.278 0.872 0.048 0.952
#> GSM1022334 2 0.000 0.894 0.000 1.000
#> GSM1022335 2 0.000 0.894 0.000 1.000
#> GSM1022336 2 0.000 0.894 0.000 1.000
#> GSM1022340 1 0.615 0.884 0.848 0.152
#> GSM1022341 1 0.615 0.884 0.848 0.152
#> GSM1022342 1 0.615 0.884 0.848 0.152
#> GSM1022343 1 0.615 0.884 0.848 0.152
#> GSM1022347 1 0.000 0.844 1.000 0.000
#> GSM1022348 1 0.000 0.844 1.000 0.000
#> GSM1022349 1 0.000 0.844 1.000 0.000
#> GSM1022350 1 0.000 0.844 1.000 0.000
#> GSM1022344 1 0.615 0.884 0.848 0.152
#> GSM1022345 1 0.615 0.884 0.848 0.152
#> GSM1022346 1 0.615 0.884 0.848 0.152
#> GSM1022355 1 0.615 0.884 0.848 0.152
#> GSM1022356 1 0.615 0.884 0.848 0.152
#> GSM1022357 1 0.615 0.884 0.848 0.152
#> GSM1022358 1 0.615 0.884 0.848 0.152
#> GSM1022351 1 0.615 0.884 0.848 0.152
#> GSM1022352 1 0.615 0.884 0.848 0.152
#> GSM1022353 1 0.615 0.884 0.848 0.152
#> GSM1022354 1 0.615 0.884 0.848 0.152
#> GSM1022359 2 0.000 0.894 0.000 1.000
#> GSM1022360 2 0.000 0.894 0.000 1.000
#> GSM1022361 2 0.000 0.894 0.000 1.000
#> GSM1022362 2 0.000 0.894 0.000 1.000
#> GSM1022367 1 0.990 0.377 0.560 0.440
#> GSM1022368 1 0.990 0.377 0.560 0.440
#> GSM1022369 1 0.990 0.377 0.560 0.440
#> GSM1022370 1 0.990 0.377 0.560 0.440
#> GSM1022363 2 0.000 0.894 0.000 1.000
#> GSM1022364 2 0.000 0.894 0.000 1.000
#> GSM1022365 2 0.000 0.894 0.000 1.000
#> GSM1022366 2 0.000 0.894 0.000 1.000
#> GSM1022374 2 0.278 0.872 0.048 0.952
#> GSM1022375 2 0.278 0.872 0.048 0.952
#> GSM1022376 2 0.278 0.872 0.048 0.952
#> GSM1022371 2 0.000 0.894 0.000 1.000
#> GSM1022372 2 0.000 0.894 0.000 1.000
#> GSM1022373 2 0.000 0.894 0.000 1.000
#> GSM1022377 2 0.775 0.740 0.228 0.772
#> GSM1022378 2 0.775 0.740 0.228 0.772
#> GSM1022379 2 0.775 0.740 0.228 0.772
#> GSM1022380 2 0.775 0.740 0.228 0.772
#> GSM1022385 1 0.000 0.844 1.000 0.000
#> GSM1022386 1 0.000 0.844 1.000 0.000
#> GSM1022387 1 0.000 0.844 1.000 0.000
#> GSM1022388 1 0.000 0.844 1.000 0.000
#> GSM1022381 2 0.775 0.740 0.228 0.772
#> GSM1022382 2 0.775 0.740 0.228 0.772
#> GSM1022383 2 0.775 0.740 0.228 0.772
#> GSM1022384 2 0.775 0.740 0.228 0.772
#> GSM1022393 1 0.615 0.884 0.848 0.152
#> GSM1022394 1 0.615 0.884 0.848 0.152
#> GSM1022395 1 0.615 0.884 0.848 0.152
#> GSM1022396 1 0.615 0.884 0.848 0.152
#> GSM1022389 2 0.775 0.740 0.228 0.772
#> GSM1022390 2 0.775 0.740 0.228 0.772
#> GSM1022391 2 0.775 0.740 0.228 0.772
#> GSM1022392 2 0.775 0.740 0.228 0.772
#> GSM1022397 1 0.000 0.844 1.000 0.000
#> GSM1022398 1 0.000 0.844 1.000 0.000
#> GSM1022399 1 0.000 0.844 1.000 0.000
#> GSM1022400 1 0.000 0.844 1.000 0.000
#> GSM1022401 1 0.615 0.884 0.848 0.152
#> GSM1022402 1 0.615 0.884 0.848 0.152
#> GSM1022403 1 0.615 0.884 0.848 0.152
#> GSM1022404 1 0.615 0.884 0.848 0.152
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1022325 2 0.000 0.864 0.000 1.000 0.00
#> GSM1022326 2 0.000 0.864 0.000 1.000 0.00
#> GSM1022327 2 0.000 0.864 0.000 1.000 0.00
#> GSM1022331 3 0.000 0.889 0.000 0.000 1.00
#> GSM1022332 3 0.000 0.889 0.000 0.000 1.00
#> GSM1022333 3 0.000 0.889 0.000 0.000 1.00
#> GSM1022328 2 0.000 0.864 0.000 1.000 0.00
#> GSM1022329 2 0.000 0.864 0.000 1.000 0.00
#> GSM1022330 2 0.000 0.864 0.000 1.000 0.00
#> GSM1022337 2 0.455 0.743 0.200 0.800 0.00
#> GSM1022338 2 0.455 0.743 0.200 0.800 0.00
#> GSM1022339 2 0.455 0.743 0.200 0.800 0.00
#> GSM1022334 2 0.000 0.864 0.000 1.000 0.00
#> GSM1022335 2 0.000 0.864 0.000 1.000 0.00
#> GSM1022336 2 0.000 0.864 0.000 1.000 0.00
#> GSM1022340 1 0.000 1.000 1.000 0.000 0.00
#> GSM1022341 1 0.000 1.000 1.000 0.000 0.00
#> GSM1022342 1 0.000 1.000 1.000 0.000 0.00
#> GSM1022343 1 0.000 1.000 1.000 0.000 0.00
#> GSM1022347 3 0.000 0.889 0.000 0.000 1.00
#> GSM1022348 3 0.000 0.889 0.000 0.000 1.00
#> GSM1022349 3 0.000 0.889 0.000 0.000 1.00
#> GSM1022350 3 0.000 0.889 0.000 0.000 1.00
#> GSM1022344 1 0.000 1.000 1.000 0.000 0.00
#> GSM1022345 1 0.000 1.000 1.000 0.000 0.00
#> GSM1022346 1 0.000 1.000 1.000 0.000 0.00
#> GSM1022355 1 0.000 1.000 1.000 0.000 0.00
#> GSM1022356 1 0.000 1.000 1.000 0.000 0.00
#> GSM1022357 1 0.000 1.000 1.000 0.000 0.00
#> GSM1022358 1 0.000 1.000 1.000 0.000 0.00
#> GSM1022351 1 0.000 1.000 1.000 0.000 0.00
#> GSM1022352 1 0.000 1.000 1.000 0.000 0.00
#> GSM1022353 1 0.000 1.000 1.000 0.000 0.00
#> GSM1022354 1 0.000 1.000 1.000 0.000 0.00
#> GSM1022359 2 0.000 0.864 0.000 1.000 0.00
#> GSM1022360 2 0.000 0.864 0.000 1.000 0.00
#> GSM1022361 2 0.000 0.864 0.000 1.000 0.00
#> GSM1022362 2 0.000 0.864 0.000 1.000 0.00
#> GSM1022367 3 0.624 0.322 0.000 0.440 0.56
#> GSM1022368 3 0.624 0.322 0.000 0.440 0.56
#> GSM1022369 3 0.624 0.322 0.000 0.440 0.56
#> GSM1022370 3 0.624 0.322 0.000 0.440 0.56
#> GSM1022363 2 0.000 0.864 0.000 1.000 0.00
#> GSM1022364 2 0.000 0.864 0.000 1.000 0.00
#> GSM1022365 2 0.000 0.864 0.000 1.000 0.00
#> GSM1022366 2 0.000 0.864 0.000 1.000 0.00
#> GSM1022374 2 0.455 0.743 0.200 0.800 0.00
#> GSM1022375 2 0.455 0.743 0.200 0.800 0.00
#> GSM1022376 2 0.455 0.743 0.200 0.800 0.00
#> GSM1022371 2 0.000 0.864 0.000 1.000 0.00
#> GSM1022372 2 0.000 0.864 0.000 1.000 0.00
#> GSM1022373 2 0.000 0.864 0.000 1.000 0.00
#> GSM1022377 2 0.489 0.784 0.228 0.772 0.00
#> GSM1022378 2 0.489 0.784 0.228 0.772 0.00
#> GSM1022379 2 0.489 0.784 0.228 0.772 0.00
#> GSM1022380 2 0.489 0.784 0.228 0.772 0.00
#> GSM1022385 3 0.000 0.889 0.000 0.000 1.00
#> GSM1022386 3 0.000 0.889 0.000 0.000 1.00
#> GSM1022387 3 0.000 0.889 0.000 0.000 1.00
#> GSM1022388 3 0.000 0.889 0.000 0.000 1.00
#> GSM1022381 2 0.489 0.784 0.228 0.772 0.00
#> GSM1022382 2 0.489 0.784 0.228 0.772 0.00
#> GSM1022383 2 0.489 0.784 0.228 0.772 0.00
#> GSM1022384 2 0.489 0.784 0.228 0.772 0.00
#> GSM1022393 1 0.000 1.000 1.000 0.000 0.00
#> GSM1022394 1 0.000 1.000 1.000 0.000 0.00
#> GSM1022395 1 0.000 1.000 1.000 0.000 0.00
#> GSM1022396 1 0.000 1.000 1.000 0.000 0.00
#> GSM1022389 2 0.489 0.784 0.228 0.772 0.00
#> GSM1022390 2 0.489 0.784 0.228 0.772 0.00
#> GSM1022391 2 0.489 0.784 0.228 0.772 0.00
#> GSM1022392 2 0.489 0.784 0.228 0.772 0.00
#> GSM1022397 3 0.000 0.889 0.000 0.000 1.00
#> GSM1022398 3 0.000 0.889 0.000 0.000 1.00
#> GSM1022399 3 0.000 0.889 0.000 0.000 1.00
#> GSM1022400 3 0.000 0.889 0.000 0.000 1.00
#> GSM1022401 1 0.000 1.000 1.000 0.000 0.00
#> GSM1022402 1 0.000 1.000 1.000 0.000 0.00
#> GSM1022403 1 0.000 1.000 1.000 0.000 0.00
#> GSM1022404 1 0.000 1.000 1.000 0.000 0.00
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1022325 2 0.000 0.841 0.000 1.000 0.00 0.000
#> GSM1022326 2 0.000 0.841 0.000 1.000 0.00 0.000
#> GSM1022327 2 0.000 0.841 0.000 1.000 0.00 0.000
#> GSM1022331 3 0.000 0.887 0.000 0.000 1.00 0.000
#> GSM1022332 3 0.000 0.887 0.000 0.000 1.00 0.000
#> GSM1022333 3 0.000 0.887 0.000 0.000 1.00 0.000
#> GSM1022328 2 0.000 0.841 0.000 1.000 0.00 0.000
#> GSM1022329 2 0.000 0.841 0.000 1.000 0.00 0.000
#> GSM1022330 2 0.000 0.841 0.000 1.000 0.00 0.000
#> GSM1022337 4 0.419 1.000 0.008 0.228 0.00 0.764
#> GSM1022338 4 0.419 1.000 0.008 0.228 0.00 0.764
#> GSM1022339 4 0.419 1.000 0.008 0.228 0.00 0.764
#> GSM1022334 2 0.000 0.841 0.000 1.000 0.00 0.000
#> GSM1022335 2 0.000 0.841 0.000 1.000 0.00 0.000
#> GSM1022336 2 0.000 0.841 0.000 1.000 0.00 0.000
#> GSM1022340 1 0.000 0.925 1.000 0.000 0.00 0.000
#> GSM1022341 1 0.000 0.925 1.000 0.000 0.00 0.000
#> GSM1022342 1 0.000 0.925 1.000 0.000 0.00 0.000
#> GSM1022343 1 0.000 0.925 1.000 0.000 0.00 0.000
#> GSM1022347 3 0.000 0.887 0.000 0.000 1.00 0.000
#> GSM1022348 3 0.000 0.887 0.000 0.000 1.00 0.000
#> GSM1022349 3 0.000 0.887 0.000 0.000 1.00 0.000
#> GSM1022350 3 0.000 0.887 0.000 0.000 1.00 0.000
#> GSM1022344 1 0.000 0.925 1.000 0.000 0.00 0.000
#> GSM1022345 1 0.000 0.925 1.000 0.000 0.00 0.000
#> GSM1022346 1 0.000 0.925 1.000 0.000 0.00 0.000
#> GSM1022355 1 0.000 0.925 1.000 0.000 0.00 0.000
#> GSM1022356 1 0.000 0.925 1.000 0.000 0.00 0.000
#> GSM1022357 1 0.000 0.925 1.000 0.000 0.00 0.000
#> GSM1022358 1 0.000 0.925 1.000 0.000 0.00 0.000
#> GSM1022351 1 0.000 0.925 1.000 0.000 0.00 0.000
#> GSM1022352 1 0.000 0.925 1.000 0.000 0.00 0.000
#> GSM1022353 1 0.000 0.925 1.000 0.000 0.00 0.000
#> GSM1022354 1 0.000 0.925 1.000 0.000 0.00 0.000
#> GSM1022359 2 0.000 0.841 0.000 1.000 0.00 0.000
#> GSM1022360 2 0.000 0.841 0.000 1.000 0.00 0.000
#> GSM1022361 2 0.000 0.841 0.000 1.000 0.00 0.000
#> GSM1022362 2 0.000 0.841 0.000 1.000 0.00 0.000
#> GSM1022367 3 0.715 0.390 0.000 0.220 0.56 0.220
#> GSM1022368 3 0.715 0.390 0.000 0.220 0.56 0.220
#> GSM1022369 3 0.715 0.390 0.000 0.220 0.56 0.220
#> GSM1022370 3 0.715 0.390 0.000 0.220 0.56 0.220
#> GSM1022363 2 0.380 0.551 0.000 0.780 0.00 0.220
#> GSM1022364 2 0.380 0.551 0.000 0.780 0.00 0.220
#> GSM1022365 2 0.380 0.551 0.000 0.780 0.00 0.220
#> GSM1022366 2 0.380 0.551 0.000 0.780 0.00 0.220
#> GSM1022374 4 0.419 1.000 0.008 0.228 0.00 0.764
#> GSM1022375 4 0.419 1.000 0.008 0.228 0.00 0.764
#> GSM1022376 4 0.419 1.000 0.008 0.228 0.00 0.764
#> GSM1022371 2 0.000 0.841 0.000 1.000 0.00 0.000
#> GSM1022372 2 0.000 0.841 0.000 1.000 0.00 0.000
#> GSM1022373 2 0.000 0.841 0.000 1.000 0.00 0.000
#> GSM1022377 2 0.387 0.791 0.000 0.772 0.00 0.228
#> GSM1022378 2 0.387 0.791 0.000 0.772 0.00 0.228
#> GSM1022379 2 0.387 0.791 0.000 0.772 0.00 0.228
#> GSM1022380 2 0.387 0.791 0.000 0.772 0.00 0.228
#> GSM1022385 3 0.000 0.887 0.000 0.000 1.00 0.000
#> GSM1022386 3 0.000 0.887 0.000 0.000 1.00 0.000
#> GSM1022387 3 0.000 0.887 0.000 0.000 1.00 0.000
#> GSM1022388 3 0.000 0.887 0.000 0.000 1.00 0.000
#> GSM1022381 2 0.387 0.791 0.000 0.772 0.00 0.228
#> GSM1022382 2 0.387 0.791 0.000 0.772 0.00 0.228
#> GSM1022383 2 0.387 0.791 0.000 0.772 0.00 0.228
#> GSM1022384 2 0.387 0.791 0.000 0.772 0.00 0.228
#> GSM1022393 1 0.353 0.844 0.808 0.000 0.00 0.192
#> GSM1022394 1 0.353 0.844 0.808 0.000 0.00 0.192
#> GSM1022395 1 0.353 0.844 0.808 0.000 0.00 0.192
#> GSM1022396 1 0.353 0.844 0.808 0.000 0.00 0.192
#> GSM1022389 2 0.387 0.791 0.000 0.772 0.00 0.228
#> GSM1022390 2 0.387 0.791 0.000 0.772 0.00 0.228
#> GSM1022391 2 0.387 0.791 0.000 0.772 0.00 0.228
#> GSM1022392 2 0.387 0.791 0.000 0.772 0.00 0.228
#> GSM1022397 3 0.000 0.887 0.000 0.000 1.00 0.000
#> GSM1022398 3 0.000 0.887 0.000 0.000 1.00 0.000
#> GSM1022399 3 0.000 0.887 0.000 0.000 1.00 0.000
#> GSM1022400 3 0.000 0.887 0.000 0.000 1.00 0.000
#> GSM1022401 1 0.353 0.844 0.808 0.000 0.00 0.192
#> GSM1022402 1 0.353 0.844 0.808 0.000 0.00 0.192
#> GSM1022403 1 0.353 0.844 0.808 0.000 0.00 0.192
#> GSM1022404 1 0.353 0.844 0.808 0.000 0.00 0.192
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1022325 4 0.3366 0.8490 0.0 0.000 0.000 0.768 0.232
#> GSM1022326 4 0.3366 0.8490 0.0 0.000 0.000 0.768 0.232
#> GSM1022327 4 0.3366 0.8490 0.0 0.000 0.000 0.768 0.232
#> GSM1022331 2 0.4283 -0.0345 0.0 0.544 0.456 0.000 0.000
#> GSM1022332 2 0.4283 -0.0345 0.0 0.544 0.456 0.000 0.000
#> GSM1022333 2 0.4283 -0.0345 0.0 0.544 0.456 0.000 0.000
#> GSM1022328 4 0.3366 0.8490 0.0 0.000 0.000 0.768 0.232
#> GSM1022329 4 0.3366 0.8490 0.0 0.000 0.000 0.768 0.232
#> GSM1022330 4 0.3366 0.8490 0.0 0.000 0.000 0.768 0.232
#> GSM1022337 5 0.0162 1.0000 0.0 0.004 0.000 0.000 0.996
#> GSM1022338 5 0.0162 1.0000 0.0 0.004 0.000 0.000 0.996
#> GSM1022339 5 0.0162 1.0000 0.0 0.004 0.000 0.000 0.996
#> GSM1022334 4 0.3366 0.8490 0.0 0.000 0.000 0.768 0.232
#> GSM1022335 4 0.3366 0.8490 0.0 0.000 0.000 0.768 0.232
#> GSM1022336 4 0.3366 0.8490 0.0 0.000 0.000 0.768 0.232
#> GSM1022340 1 0.0000 0.9215 1.0 0.000 0.000 0.000 0.000
#> GSM1022341 1 0.0000 0.9215 1.0 0.000 0.000 0.000 0.000
#> GSM1022342 1 0.0000 0.9215 1.0 0.000 0.000 0.000 0.000
#> GSM1022343 1 0.0000 0.9215 1.0 0.000 0.000 0.000 0.000
#> GSM1022347 3 0.0000 1.0000 0.0 0.000 1.000 0.000 0.000
#> GSM1022348 3 0.0000 1.0000 0.0 0.000 1.000 0.000 0.000
#> GSM1022349 3 0.0000 1.0000 0.0 0.000 1.000 0.000 0.000
#> GSM1022350 3 0.0000 1.0000 0.0 0.000 1.000 0.000 0.000
#> GSM1022344 1 0.0000 0.9215 1.0 0.000 0.000 0.000 0.000
#> GSM1022345 1 0.0000 0.9215 1.0 0.000 0.000 0.000 0.000
#> GSM1022346 1 0.0000 0.9215 1.0 0.000 0.000 0.000 0.000
#> GSM1022355 1 0.0000 0.9215 1.0 0.000 0.000 0.000 0.000
#> GSM1022356 1 0.0000 0.9215 1.0 0.000 0.000 0.000 0.000
#> GSM1022357 1 0.0000 0.9215 1.0 0.000 0.000 0.000 0.000
#> GSM1022358 1 0.0000 0.9215 1.0 0.000 0.000 0.000 0.000
#> GSM1022351 1 0.0000 0.9215 1.0 0.000 0.000 0.000 0.000
#> GSM1022352 1 0.0000 0.9215 1.0 0.000 0.000 0.000 0.000
#> GSM1022353 1 0.0000 0.9215 1.0 0.000 0.000 0.000 0.000
#> GSM1022354 1 0.0000 0.9215 1.0 0.000 0.000 0.000 0.000
#> GSM1022359 4 0.3366 0.8490 0.0 0.000 0.000 0.768 0.232
#> GSM1022360 4 0.3366 0.8490 0.0 0.000 0.000 0.768 0.232
#> GSM1022361 4 0.3366 0.8490 0.0 0.000 0.000 0.768 0.232
#> GSM1022362 4 0.3366 0.8490 0.0 0.000 0.000 0.768 0.232
#> GSM1022367 2 0.0510 0.4551 0.0 0.984 0.016 0.000 0.000
#> GSM1022368 2 0.0510 0.4551 0.0 0.984 0.016 0.000 0.000
#> GSM1022369 2 0.0510 0.4551 0.0 0.984 0.016 0.000 0.000
#> GSM1022370 2 0.0510 0.4551 0.0 0.984 0.016 0.000 0.000
#> GSM1022363 2 0.6530 0.0884 0.0 0.440 0.000 0.360 0.200
#> GSM1022364 2 0.6530 0.0884 0.0 0.440 0.000 0.360 0.200
#> GSM1022365 2 0.6530 0.0884 0.0 0.440 0.000 0.360 0.200
#> GSM1022366 2 0.6530 0.0884 0.0 0.440 0.000 0.360 0.200
#> GSM1022374 5 0.0162 1.0000 0.0 0.004 0.000 0.000 0.996
#> GSM1022375 5 0.0162 1.0000 0.0 0.004 0.000 0.000 0.996
#> GSM1022376 5 0.0162 1.0000 0.0 0.004 0.000 0.000 0.996
#> GSM1022371 4 0.3366 0.8490 0.0 0.000 0.000 0.768 0.232
#> GSM1022372 4 0.3366 0.8490 0.0 0.000 0.000 0.768 0.232
#> GSM1022373 4 0.3366 0.8490 0.0 0.000 0.000 0.768 0.232
#> GSM1022377 4 0.0510 0.7977 0.0 0.016 0.000 0.984 0.000
#> GSM1022378 4 0.0510 0.7977 0.0 0.016 0.000 0.984 0.000
#> GSM1022379 4 0.0510 0.7977 0.0 0.016 0.000 0.984 0.000
#> GSM1022380 4 0.0510 0.7977 0.0 0.016 0.000 0.984 0.000
#> GSM1022385 3 0.0000 1.0000 0.0 0.000 1.000 0.000 0.000
#> GSM1022386 3 0.0000 1.0000 0.0 0.000 1.000 0.000 0.000
#> GSM1022387 3 0.0000 1.0000 0.0 0.000 1.000 0.000 0.000
#> GSM1022388 3 0.0000 1.0000 0.0 0.000 1.000 0.000 0.000
#> GSM1022381 4 0.0510 0.7977 0.0 0.016 0.000 0.984 0.000
#> GSM1022382 4 0.0510 0.7977 0.0 0.016 0.000 0.984 0.000
#> GSM1022383 4 0.0510 0.7977 0.0 0.016 0.000 0.984 0.000
#> GSM1022384 4 0.0510 0.7977 0.0 0.016 0.000 0.984 0.000
#> GSM1022393 1 0.3109 0.8340 0.8 0.000 0.000 0.000 0.200
#> GSM1022394 1 0.3109 0.8340 0.8 0.000 0.000 0.000 0.200
#> GSM1022395 1 0.3109 0.8340 0.8 0.000 0.000 0.000 0.200
#> GSM1022396 1 0.3109 0.8340 0.8 0.000 0.000 0.000 0.200
#> GSM1022389 4 0.0510 0.7977 0.0 0.016 0.000 0.984 0.000
#> GSM1022390 4 0.0510 0.7977 0.0 0.016 0.000 0.984 0.000
#> GSM1022391 4 0.0510 0.7977 0.0 0.016 0.000 0.984 0.000
#> GSM1022392 4 0.0510 0.7977 0.0 0.016 0.000 0.984 0.000
#> GSM1022397 3 0.0000 1.0000 0.0 0.000 1.000 0.000 0.000
#> GSM1022398 3 0.0000 1.0000 0.0 0.000 1.000 0.000 0.000
#> GSM1022399 3 0.0000 1.0000 0.0 0.000 1.000 0.000 0.000
#> GSM1022400 3 0.0000 1.0000 0.0 0.000 1.000 0.000 0.000
#> GSM1022401 1 0.3109 0.8340 0.8 0.000 0.000 0.000 0.200
#> GSM1022402 1 0.3109 0.8340 0.8 0.000 0.000 0.000 0.200
#> GSM1022403 1 0.3109 0.8340 0.8 0.000 0.000 0.000 0.200
#> GSM1022404 1 0.3109 0.8340 0.8 0.000 0.000 0.000 0.200
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1022325 2 0.3828 0.904 0.000 0.560 0.00 0.000 0.0 0.44
#> GSM1022326 2 0.3828 0.904 0.000 0.560 0.00 0.000 0.0 0.44
#> GSM1022327 2 0.3828 0.904 0.000 0.560 0.00 0.000 0.0 0.44
#> GSM1022331 6 0.3828 0.424 0.000 0.000 0.44 0.000 0.0 0.56
#> GSM1022332 6 0.3828 0.424 0.000 0.000 0.44 0.000 0.0 0.56
#> GSM1022333 6 0.3828 0.424 0.000 0.000 0.44 0.000 0.0 0.56
#> GSM1022328 2 0.3828 0.904 0.000 0.560 0.00 0.000 0.0 0.44
#> GSM1022329 2 0.3828 0.904 0.000 0.560 0.00 0.000 0.0 0.44
#> GSM1022330 2 0.3828 0.904 0.000 0.560 0.00 0.000 0.0 0.44
#> GSM1022337 5 0.0000 1.000 0.000 0.000 0.00 0.000 1.0 0.00
#> GSM1022338 5 0.0000 1.000 0.000 0.000 0.00 0.000 1.0 0.00
#> GSM1022339 5 0.0000 1.000 0.000 0.000 0.00 0.000 1.0 0.00
#> GSM1022334 2 0.3828 0.904 0.000 0.560 0.00 0.000 0.0 0.44
#> GSM1022335 2 0.3828 0.904 0.000 0.560 0.00 0.000 0.0 0.44
#> GSM1022336 2 0.3828 0.904 0.000 0.560 0.00 0.000 0.0 0.44
#> GSM1022340 1 0.0363 0.914 0.988 0.000 0.00 0.012 0.0 0.00
#> GSM1022341 1 0.0363 0.914 0.988 0.000 0.00 0.012 0.0 0.00
#> GSM1022342 1 0.0363 0.914 0.988 0.000 0.00 0.012 0.0 0.00
#> GSM1022343 1 0.0363 0.914 0.988 0.000 0.00 0.012 0.0 0.00
#> GSM1022347 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.0 0.00
#> GSM1022348 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.0 0.00
#> GSM1022349 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.0 0.00
#> GSM1022350 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.0 0.00
#> GSM1022344 1 0.0363 0.914 0.988 0.000 0.00 0.012 0.0 0.00
#> GSM1022345 1 0.0363 0.914 0.988 0.000 0.00 0.012 0.0 0.00
#> GSM1022346 1 0.0363 0.914 0.988 0.000 0.00 0.012 0.0 0.00
#> GSM1022355 1 0.0000 0.916 1.000 0.000 0.00 0.000 0.0 0.00
#> GSM1022356 1 0.0000 0.916 1.000 0.000 0.00 0.000 0.0 0.00
#> GSM1022357 1 0.0000 0.916 1.000 0.000 0.00 0.000 0.0 0.00
#> GSM1022358 1 0.0000 0.916 1.000 0.000 0.00 0.000 0.0 0.00
#> GSM1022351 1 0.0000 0.916 1.000 0.000 0.00 0.000 0.0 0.00
#> GSM1022352 1 0.0000 0.916 1.000 0.000 0.00 0.000 0.0 0.00
#> GSM1022353 1 0.0000 0.916 1.000 0.000 0.00 0.000 0.0 0.00
#> GSM1022354 1 0.0000 0.916 1.000 0.000 0.00 0.000 0.0 0.00
#> GSM1022359 2 0.3828 0.904 0.000 0.560 0.00 0.000 0.0 0.44
#> GSM1022360 2 0.3828 0.904 0.000 0.560 0.00 0.000 0.0 0.44
#> GSM1022361 2 0.3828 0.904 0.000 0.560 0.00 0.000 0.0 0.44
#> GSM1022362 2 0.3828 0.904 0.000 0.560 0.00 0.000 0.0 0.44
#> GSM1022367 6 0.3828 0.696 0.000 0.440 0.00 0.000 0.0 0.56
#> GSM1022368 6 0.3828 0.696 0.000 0.440 0.00 0.000 0.0 0.56
#> GSM1022369 6 0.3828 0.696 0.000 0.440 0.00 0.000 0.0 0.56
#> GSM1022370 6 0.3828 0.696 0.000 0.440 0.00 0.000 0.0 0.56
#> GSM1022363 2 0.0000 0.448 0.000 1.000 0.00 0.000 0.0 0.00
#> GSM1022364 2 0.0000 0.448 0.000 1.000 0.00 0.000 0.0 0.00
#> GSM1022365 2 0.0000 0.448 0.000 1.000 0.00 0.000 0.0 0.00
#> GSM1022366 2 0.0000 0.448 0.000 1.000 0.00 0.000 0.0 0.00
#> GSM1022374 5 0.0000 1.000 0.000 0.000 0.00 0.000 1.0 0.00
#> GSM1022375 5 0.0000 1.000 0.000 0.000 0.00 0.000 1.0 0.00
#> GSM1022376 5 0.0000 1.000 0.000 0.000 0.00 0.000 1.0 0.00
#> GSM1022371 2 0.3828 0.904 0.000 0.560 0.00 0.000 0.0 0.44
#> GSM1022372 2 0.3828 0.904 0.000 0.560 0.00 0.000 0.0 0.44
#> GSM1022373 2 0.3828 0.904 0.000 0.560 0.00 0.000 0.0 0.44
#> GSM1022377 4 0.0363 1.000 0.000 0.012 0.00 0.988 0.0 0.00
#> GSM1022378 4 0.0363 1.000 0.000 0.012 0.00 0.988 0.0 0.00
#> GSM1022379 4 0.0363 1.000 0.000 0.012 0.00 0.988 0.0 0.00
#> GSM1022380 4 0.0363 1.000 0.000 0.012 0.00 0.988 0.0 0.00
#> GSM1022385 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.0 0.00
#> GSM1022386 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.0 0.00
#> GSM1022387 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.0 0.00
#> GSM1022388 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.0 0.00
#> GSM1022381 4 0.0363 1.000 0.000 0.012 0.00 0.988 0.0 0.00
#> GSM1022382 4 0.0363 1.000 0.000 0.012 0.00 0.988 0.0 0.00
#> GSM1022383 4 0.0363 1.000 0.000 0.012 0.00 0.988 0.0 0.00
#> GSM1022384 4 0.0363 1.000 0.000 0.012 0.00 0.988 0.0 0.00
#> GSM1022393 1 0.2793 0.828 0.800 0.000 0.00 0.000 0.2 0.00
#> GSM1022394 1 0.2793 0.828 0.800 0.000 0.00 0.000 0.2 0.00
#> GSM1022395 1 0.2793 0.828 0.800 0.000 0.00 0.000 0.2 0.00
#> GSM1022396 1 0.2793 0.828 0.800 0.000 0.00 0.000 0.2 0.00
#> GSM1022389 4 0.0363 1.000 0.000 0.012 0.00 0.988 0.0 0.00
#> GSM1022390 4 0.0363 1.000 0.000 0.012 0.00 0.988 0.0 0.00
#> GSM1022391 4 0.0363 1.000 0.000 0.012 0.00 0.988 0.0 0.00
#> GSM1022392 4 0.0363 1.000 0.000 0.012 0.00 0.988 0.0 0.00
#> GSM1022397 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.0 0.00
#> GSM1022398 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.0 0.00
#> GSM1022399 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.0 0.00
#> GSM1022400 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.0 0.00
#> GSM1022401 1 0.2793 0.828 0.800 0.000 0.00 0.000 0.2 0.00
#> GSM1022402 1 0.2793 0.828 0.800 0.000 0.00 0.000 0.2 0.00
#> GSM1022403 1 0.2793 0.828 0.800 0.000 0.00 0.000 0.2 0.00
#> GSM1022404 1 0.2793 0.828 0.800 0.000 0.00 0.000 0.2 0.00
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 protocol(p) cell.type(p) k
#> SD:hclust 76 6.05e-07 3.68e-06 2
#> SD:hclust 76 5.29e-11 1.09e-07 3
#> SD:hclust 76 6.81e-12 2.19e-11 4
#> SD:hclust 69 2.12e-11 6.74e-10 5
#> SD:hclust 73 1.69e-24 1.43e-09 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 31589 rows and 80 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.487 0.784 0.874 0.4746 0.494 0.494
#> 3 3 0.655 0.844 0.855 0.3622 0.750 0.535
#> 4 4 0.728 0.774 0.804 0.1208 1.000 1.000
#> 5 5 0.744 0.561 0.730 0.0607 0.891 0.676
#> 6 6 0.721 0.616 0.718 0.0468 0.901 0.623
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
#> GSM1022325 2 0.000 0.902 0.000 1.000
#> GSM1022326 2 0.000 0.902 0.000 1.000
#> GSM1022327 2 0.000 0.902 0.000 1.000
#> GSM1022331 1 0.311 0.785 0.944 0.056
#> GSM1022332 1 0.311 0.785 0.944 0.056
#> GSM1022333 1 0.311 0.785 0.944 0.056
#> GSM1022328 2 0.000 0.902 0.000 1.000
#> GSM1022329 2 0.000 0.902 0.000 1.000
#> GSM1022330 2 0.000 0.902 0.000 1.000
#> GSM1022337 1 1.000 0.295 0.508 0.492
#> GSM1022338 1 1.000 0.295 0.508 0.492
#> GSM1022339 1 1.000 0.295 0.508 0.492
#> GSM1022334 2 0.000 0.902 0.000 1.000
#> GSM1022335 2 0.000 0.902 0.000 1.000
#> GSM1022336 2 0.000 0.902 0.000 1.000
#> GSM1022340 1 0.775 0.799 0.772 0.228
#> GSM1022341 1 0.775 0.799 0.772 0.228
#> GSM1022342 1 0.775 0.799 0.772 0.228
#> GSM1022343 1 0.775 0.799 0.772 0.228
#> GSM1022347 1 0.311 0.785 0.944 0.056
#> GSM1022348 1 0.311 0.785 0.944 0.056
#> GSM1022349 1 0.311 0.785 0.944 0.056
#> GSM1022350 1 0.311 0.785 0.944 0.056
#> GSM1022344 1 0.141 0.781 0.980 0.020
#> GSM1022345 1 0.141 0.781 0.980 0.020
#> GSM1022346 1 0.141 0.781 0.980 0.020
#> GSM1022355 1 0.788 0.797 0.764 0.236
#> GSM1022356 1 0.788 0.797 0.764 0.236
#> GSM1022357 1 0.788 0.797 0.764 0.236
#> GSM1022358 1 0.788 0.797 0.764 0.236
#> GSM1022351 1 0.788 0.797 0.764 0.236
#> GSM1022352 1 0.788 0.797 0.764 0.236
#> GSM1022353 1 0.788 0.797 0.764 0.236
#> GSM1022354 1 0.788 0.797 0.764 0.236
#> GSM1022359 2 0.000 0.902 0.000 1.000
#> GSM1022360 2 0.000 0.902 0.000 1.000
#> GSM1022361 2 0.000 0.902 0.000 1.000
#> GSM1022362 2 0.000 0.902 0.000 1.000
#> GSM1022367 2 0.981 0.371 0.420 0.580
#> GSM1022368 2 0.981 0.371 0.420 0.580
#> GSM1022369 2 0.981 0.371 0.420 0.580
#> GSM1022370 2 0.981 0.371 0.420 0.580
#> GSM1022363 2 0.000 0.902 0.000 1.000
#> GSM1022364 2 0.000 0.902 0.000 1.000
#> GSM1022365 2 0.000 0.902 0.000 1.000
#> GSM1022366 2 0.000 0.902 0.000 1.000
#> GSM1022374 2 0.861 0.516 0.284 0.716
#> GSM1022375 2 0.861 0.516 0.284 0.716
#> GSM1022376 2 0.861 0.516 0.284 0.716
#> GSM1022371 2 0.000 0.902 0.000 1.000
#> GSM1022372 2 0.000 0.902 0.000 1.000
#> GSM1022373 2 0.000 0.902 0.000 1.000
#> GSM1022377 2 0.242 0.890 0.040 0.960
#> GSM1022378 2 0.242 0.890 0.040 0.960
#> GSM1022379 2 0.242 0.890 0.040 0.960
#> GSM1022380 2 0.242 0.890 0.040 0.960
#> GSM1022385 1 0.311 0.785 0.944 0.056
#> GSM1022386 1 0.311 0.785 0.944 0.056
#> GSM1022387 1 0.311 0.785 0.944 0.056
#> GSM1022388 1 0.311 0.785 0.944 0.056
#> GSM1022381 2 0.242 0.890 0.040 0.960
#> GSM1022382 2 0.242 0.890 0.040 0.960
#> GSM1022383 2 0.242 0.890 0.040 0.960
#> GSM1022384 2 0.242 0.890 0.040 0.960
#> GSM1022393 1 0.788 0.797 0.764 0.236
#> GSM1022394 1 0.788 0.797 0.764 0.236
#> GSM1022395 1 0.788 0.797 0.764 0.236
#> GSM1022396 1 0.788 0.797 0.764 0.236
#> GSM1022389 2 0.242 0.890 0.040 0.960
#> GSM1022390 2 0.242 0.890 0.040 0.960
#> GSM1022391 2 0.242 0.890 0.040 0.960
#> GSM1022392 2 0.242 0.890 0.040 0.960
#> GSM1022397 1 0.311 0.785 0.944 0.056
#> GSM1022398 1 0.311 0.785 0.944 0.056
#> GSM1022399 1 0.311 0.785 0.944 0.056
#> GSM1022400 1 0.311 0.785 0.944 0.056
#> GSM1022401 1 0.788 0.797 0.764 0.236
#> GSM1022402 1 0.788 0.797 0.764 0.236
#> GSM1022403 1 0.788 0.797 0.764 0.236
#> GSM1022404 1 0.788 0.797 0.764 0.236
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1022325 2 0.0747 0.915 0.016 0.984 0.000
#> GSM1022326 2 0.0747 0.915 0.016 0.984 0.000
#> GSM1022327 2 0.0747 0.915 0.016 0.984 0.000
#> GSM1022331 3 0.4351 0.773 0.168 0.004 0.828
#> GSM1022332 3 0.4351 0.773 0.168 0.004 0.828
#> GSM1022333 3 0.4351 0.773 0.168 0.004 0.828
#> GSM1022328 2 0.0747 0.915 0.016 0.984 0.000
#> GSM1022329 2 0.0747 0.915 0.016 0.984 0.000
#> GSM1022330 2 0.0747 0.915 0.016 0.984 0.000
#> GSM1022337 1 0.6968 0.681 0.732 0.120 0.148
#> GSM1022338 1 0.6968 0.681 0.732 0.120 0.148
#> GSM1022339 1 0.6968 0.681 0.732 0.120 0.148
#> GSM1022334 2 0.0747 0.915 0.016 0.984 0.000
#> GSM1022335 2 0.0747 0.915 0.016 0.984 0.000
#> GSM1022336 2 0.0747 0.915 0.016 0.984 0.000
#> GSM1022340 1 0.0237 0.896 0.996 0.000 0.004
#> GSM1022341 1 0.0237 0.896 0.996 0.000 0.004
#> GSM1022342 1 0.0237 0.896 0.996 0.000 0.004
#> GSM1022343 1 0.0237 0.896 0.996 0.000 0.004
#> GSM1022347 3 0.5845 0.854 0.308 0.004 0.688
#> GSM1022348 3 0.5845 0.854 0.308 0.004 0.688
#> GSM1022349 3 0.5845 0.854 0.308 0.004 0.688
#> GSM1022350 3 0.5845 0.854 0.308 0.004 0.688
#> GSM1022344 3 0.5733 0.836 0.324 0.000 0.676
#> GSM1022345 3 0.5733 0.836 0.324 0.000 0.676
#> GSM1022346 3 0.5733 0.836 0.324 0.000 0.676
#> GSM1022355 1 0.0237 0.896 0.996 0.000 0.004
#> GSM1022356 1 0.0237 0.896 0.996 0.000 0.004
#> GSM1022357 1 0.0237 0.896 0.996 0.000 0.004
#> GSM1022358 1 0.0237 0.896 0.996 0.000 0.004
#> GSM1022351 1 0.0237 0.896 0.996 0.000 0.004
#> GSM1022352 1 0.0237 0.896 0.996 0.000 0.004
#> GSM1022353 1 0.0237 0.896 0.996 0.000 0.004
#> GSM1022354 1 0.0237 0.896 0.996 0.000 0.004
#> GSM1022359 2 0.2031 0.911 0.016 0.952 0.032
#> GSM1022360 2 0.2031 0.911 0.016 0.952 0.032
#> GSM1022361 2 0.2031 0.911 0.016 0.952 0.032
#> GSM1022362 2 0.2031 0.911 0.016 0.952 0.032
#> GSM1022367 3 0.5956 0.530 0.016 0.264 0.720
#> GSM1022368 3 0.5956 0.530 0.016 0.264 0.720
#> GSM1022369 3 0.5956 0.530 0.016 0.264 0.720
#> GSM1022370 3 0.5956 0.530 0.016 0.264 0.720
#> GSM1022363 2 0.2625 0.881 0.000 0.916 0.084
#> GSM1022364 2 0.2625 0.881 0.000 0.916 0.084
#> GSM1022365 2 0.2625 0.881 0.000 0.916 0.084
#> GSM1022366 2 0.2625 0.881 0.000 0.916 0.084
#> GSM1022374 1 0.8199 0.584 0.640 0.200 0.160
#> GSM1022375 1 0.8199 0.584 0.640 0.200 0.160
#> GSM1022376 1 0.8199 0.584 0.640 0.200 0.160
#> GSM1022371 2 0.0983 0.914 0.016 0.980 0.004
#> GSM1022372 2 0.0983 0.914 0.016 0.980 0.004
#> GSM1022373 2 0.0983 0.914 0.016 0.980 0.004
#> GSM1022377 2 0.6191 0.872 0.084 0.776 0.140
#> GSM1022378 2 0.6191 0.872 0.084 0.776 0.140
#> GSM1022379 2 0.6191 0.872 0.084 0.776 0.140
#> GSM1022380 2 0.6191 0.872 0.084 0.776 0.140
#> GSM1022385 3 0.5845 0.854 0.308 0.004 0.688
#> GSM1022386 3 0.5845 0.854 0.308 0.004 0.688
#> GSM1022387 3 0.5845 0.854 0.308 0.004 0.688
#> GSM1022388 3 0.5845 0.854 0.308 0.004 0.688
#> GSM1022381 2 0.6393 0.869 0.088 0.764 0.148
#> GSM1022382 2 0.6393 0.869 0.088 0.764 0.148
#> GSM1022383 2 0.6393 0.869 0.088 0.764 0.148
#> GSM1022384 2 0.6393 0.869 0.088 0.764 0.148
#> GSM1022393 1 0.0000 0.896 1.000 0.000 0.000
#> GSM1022394 1 0.0000 0.896 1.000 0.000 0.000
#> GSM1022395 1 0.0000 0.896 1.000 0.000 0.000
#> GSM1022396 1 0.0000 0.896 1.000 0.000 0.000
#> GSM1022389 2 0.5874 0.869 0.088 0.796 0.116
#> GSM1022390 2 0.5874 0.869 0.088 0.796 0.116
#> GSM1022391 2 0.5874 0.869 0.088 0.796 0.116
#> GSM1022392 2 0.5874 0.869 0.088 0.796 0.116
#> GSM1022397 3 0.5845 0.854 0.308 0.004 0.688
#> GSM1022398 3 0.5845 0.854 0.308 0.004 0.688
#> GSM1022399 3 0.5845 0.854 0.308 0.004 0.688
#> GSM1022400 3 0.5845 0.854 0.308 0.004 0.688
#> GSM1022401 1 0.0000 0.896 1.000 0.000 0.000
#> GSM1022402 1 0.0000 0.896 1.000 0.000 0.000
#> GSM1022403 1 0.0000 0.896 1.000 0.000 0.000
#> GSM1022404 1 0.0000 0.896 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1022325 2 0.000 0.821 0.000 1.000 0.000 NA
#> GSM1022326 2 0.000 0.821 0.000 1.000 0.000 NA
#> GSM1022327 2 0.000 0.821 0.000 1.000 0.000 NA
#> GSM1022331 3 0.332 0.774 0.012 0.000 0.852 NA
#> GSM1022332 3 0.332 0.774 0.012 0.000 0.852 NA
#> GSM1022333 3 0.332 0.774 0.012 0.000 0.852 NA
#> GSM1022328 2 0.000 0.821 0.000 1.000 0.000 NA
#> GSM1022329 2 0.000 0.821 0.000 1.000 0.000 NA
#> GSM1022330 2 0.000 0.821 0.000 1.000 0.000 NA
#> GSM1022337 1 0.701 0.708 0.600 0.040 0.064 NA
#> GSM1022338 1 0.701 0.708 0.600 0.040 0.064 NA
#> GSM1022339 1 0.701 0.708 0.600 0.040 0.064 NA
#> GSM1022334 2 0.000 0.821 0.000 1.000 0.000 NA
#> GSM1022335 2 0.000 0.821 0.000 1.000 0.000 NA
#> GSM1022336 2 0.000 0.821 0.000 1.000 0.000 NA
#> GSM1022340 1 0.238 0.810 0.920 0.000 0.028 NA
#> GSM1022341 1 0.238 0.810 0.920 0.000 0.028 NA
#> GSM1022342 1 0.238 0.810 0.920 0.000 0.028 NA
#> GSM1022343 1 0.238 0.810 0.920 0.000 0.028 NA
#> GSM1022347 3 0.215 0.840 0.088 0.000 0.912 NA
#> GSM1022348 3 0.215 0.840 0.088 0.000 0.912 NA
#> GSM1022349 3 0.215 0.840 0.088 0.000 0.912 NA
#> GSM1022350 3 0.215 0.840 0.088 0.000 0.912 NA
#> GSM1022344 3 0.564 0.664 0.260 0.000 0.680 NA
#> GSM1022345 3 0.564 0.664 0.260 0.000 0.680 NA
#> GSM1022346 3 0.564 0.664 0.260 0.000 0.680 NA
#> GSM1022355 1 0.000 0.839 1.000 0.000 0.000 NA
#> GSM1022356 1 0.000 0.839 1.000 0.000 0.000 NA
#> GSM1022357 1 0.000 0.839 1.000 0.000 0.000 NA
#> GSM1022358 1 0.000 0.839 1.000 0.000 0.000 NA
#> GSM1022351 1 0.158 0.825 0.948 0.000 0.004 NA
#> GSM1022352 1 0.158 0.825 0.948 0.000 0.004 NA
#> GSM1022353 1 0.158 0.825 0.948 0.000 0.004 NA
#> GSM1022354 1 0.158 0.825 0.948 0.000 0.004 NA
#> GSM1022359 2 0.215 0.811 0.000 0.912 0.000 NA
#> GSM1022360 2 0.215 0.811 0.000 0.912 0.000 NA
#> GSM1022361 2 0.215 0.811 0.000 0.912 0.000 NA
#> GSM1022362 2 0.215 0.811 0.000 0.912 0.000 NA
#> GSM1022367 3 0.703 0.523 0.000 0.136 0.528 NA
#> GSM1022368 3 0.703 0.523 0.000 0.136 0.528 NA
#> GSM1022369 3 0.703 0.523 0.000 0.136 0.528 NA
#> GSM1022370 3 0.703 0.523 0.000 0.136 0.528 NA
#> GSM1022363 2 0.410 0.755 0.000 0.784 0.012 NA
#> GSM1022364 2 0.410 0.755 0.000 0.784 0.012 NA
#> GSM1022365 2 0.410 0.755 0.000 0.784 0.012 NA
#> GSM1022366 2 0.410 0.755 0.000 0.784 0.012 NA
#> GSM1022374 1 0.779 0.655 0.540 0.084 0.064 NA
#> GSM1022375 1 0.779 0.655 0.540 0.084 0.064 NA
#> GSM1022376 1 0.779 0.655 0.540 0.084 0.064 NA
#> GSM1022371 2 0.156 0.809 0.000 0.944 0.000 NA
#> GSM1022372 2 0.156 0.809 0.000 0.944 0.000 NA
#> GSM1022373 2 0.156 0.809 0.000 0.944 0.000 NA
#> GSM1022377 2 0.565 0.726 0.028 0.580 0.000 NA
#> GSM1022378 2 0.565 0.726 0.028 0.580 0.000 NA
#> GSM1022379 2 0.565 0.726 0.028 0.580 0.000 NA
#> GSM1022380 2 0.565 0.726 0.028 0.580 0.000 NA
#> GSM1022385 3 0.273 0.840 0.088 0.000 0.896 NA
#> GSM1022386 3 0.273 0.840 0.088 0.000 0.896 NA
#> GSM1022387 3 0.273 0.840 0.088 0.000 0.896 NA
#> GSM1022388 3 0.273 0.840 0.088 0.000 0.896 NA
#> GSM1022381 2 0.573 0.714 0.028 0.544 0.000 NA
#> GSM1022382 2 0.573 0.714 0.028 0.544 0.000 NA
#> GSM1022383 2 0.573 0.714 0.028 0.544 0.000 NA
#> GSM1022384 2 0.573 0.714 0.028 0.544 0.000 NA
#> GSM1022393 1 0.297 0.841 0.856 0.000 0.000 NA
#> GSM1022394 1 0.297 0.841 0.856 0.000 0.000 NA
#> GSM1022395 1 0.297 0.841 0.856 0.000 0.000 NA
#> GSM1022396 1 0.297 0.841 0.856 0.000 0.000 NA
#> GSM1022389 2 0.567 0.728 0.028 0.620 0.004 NA
#> GSM1022390 2 0.567 0.728 0.028 0.620 0.004 NA
#> GSM1022391 2 0.567 0.728 0.028 0.620 0.004 NA
#> GSM1022392 2 0.567 0.728 0.028 0.620 0.004 NA
#> GSM1022397 3 0.215 0.840 0.088 0.000 0.912 NA
#> GSM1022398 3 0.215 0.840 0.088 0.000 0.912 NA
#> GSM1022399 3 0.215 0.840 0.088 0.000 0.912 NA
#> GSM1022400 3 0.215 0.840 0.088 0.000 0.912 NA
#> GSM1022401 1 0.297 0.841 0.856 0.000 0.000 NA
#> GSM1022402 1 0.297 0.841 0.856 0.000 0.000 NA
#> GSM1022403 1 0.297 0.841 0.856 0.000 0.000 NA
#> GSM1022404 1 0.297 0.841 0.856 0.000 0.000 NA
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1022325 2 0.0000 0.674 0.000 1.000 0.000 0.000 0.000
#> GSM1022326 2 0.0000 0.674 0.000 1.000 0.000 0.000 0.000
#> GSM1022327 2 0.0000 0.674 0.000 1.000 0.000 0.000 0.000
#> GSM1022331 3 0.4656 0.550 0.004 0.000 0.700 0.040 0.256
#> GSM1022332 3 0.4656 0.550 0.004 0.000 0.700 0.040 0.256
#> GSM1022333 3 0.4656 0.550 0.004 0.000 0.700 0.040 0.256
#> GSM1022328 2 0.0000 0.674 0.000 1.000 0.000 0.000 0.000
#> GSM1022329 2 0.0000 0.674 0.000 1.000 0.000 0.000 0.000
#> GSM1022330 2 0.0000 0.674 0.000 1.000 0.000 0.000 0.000
#> GSM1022337 1 0.6709 0.219 0.448 0.016 0.000 0.152 0.384
#> GSM1022338 1 0.6709 0.219 0.448 0.016 0.000 0.152 0.384
#> GSM1022339 1 0.6709 0.219 0.448 0.016 0.000 0.152 0.384
#> GSM1022334 2 0.0162 0.673 0.000 0.996 0.000 0.004 0.000
#> GSM1022335 2 0.0162 0.673 0.000 0.996 0.000 0.004 0.000
#> GSM1022336 2 0.0162 0.673 0.000 0.996 0.000 0.004 0.000
#> GSM1022340 1 0.4404 0.653 0.788 0.004 0.016 0.136 0.056
#> GSM1022341 1 0.4404 0.653 0.788 0.004 0.016 0.136 0.056
#> GSM1022342 1 0.4404 0.653 0.788 0.004 0.016 0.136 0.056
#> GSM1022343 1 0.4404 0.653 0.788 0.004 0.016 0.136 0.056
#> GSM1022347 3 0.1041 0.817 0.032 0.000 0.964 0.004 0.000
#> GSM1022348 3 0.1041 0.817 0.032 0.000 0.964 0.004 0.000
#> GSM1022349 3 0.1041 0.817 0.032 0.000 0.964 0.004 0.000
#> GSM1022350 3 0.1041 0.817 0.032 0.000 0.964 0.004 0.000
#> GSM1022344 3 0.6987 0.422 0.264 0.000 0.540 0.136 0.060
#> GSM1022345 3 0.6987 0.422 0.264 0.000 0.540 0.136 0.060
#> GSM1022346 3 0.6987 0.422 0.264 0.000 0.540 0.136 0.060
#> GSM1022355 1 0.0324 0.715 0.992 0.004 0.000 0.004 0.000
#> GSM1022356 1 0.0324 0.715 0.992 0.004 0.000 0.004 0.000
#> GSM1022357 1 0.0324 0.715 0.992 0.004 0.000 0.004 0.000
#> GSM1022358 1 0.0324 0.715 0.992 0.004 0.000 0.004 0.000
#> GSM1022351 1 0.2940 0.690 0.876 0.004 0.000 0.072 0.048
#> GSM1022352 1 0.2940 0.690 0.876 0.004 0.000 0.072 0.048
#> GSM1022353 1 0.2940 0.690 0.876 0.004 0.000 0.072 0.048
#> GSM1022354 1 0.2940 0.690 0.876 0.004 0.000 0.072 0.048
#> GSM1022359 2 0.2731 0.591 0.000 0.876 0.004 0.104 0.016
#> GSM1022360 2 0.2731 0.591 0.000 0.876 0.004 0.104 0.016
#> GSM1022361 2 0.2731 0.591 0.000 0.876 0.004 0.104 0.016
#> GSM1022362 2 0.2731 0.591 0.000 0.876 0.004 0.104 0.016
#> GSM1022367 5 0.5960 0.263 0.000 0.060 0.348 0.028 0.564
#> GSM1022368 5 0.5960 0.263 0.000 0.060 0.348 0.028 0.564
#> GSM1022369 5 0.5960 0.263 0.000 0.060 0.348 0.028 0.564
#> GSM1022370 5 0.5960 0.263 0.000 0.060 0.348 0.028 0.564
#> GSM1022363 2 0.5828 0.401 0.000 0.596 0.004 0.116 0.284
#> GSM1022364 2 0.5828 0.401 0.000 0.596 0.004 0.116 0.284
#> GSM1022365 2 0.5828 0.401 0.000 0.596 0.004 0.116 0.284
#> GSM1022366 2 0.5828 0.401 0.000 0.596 0.004 0.116 0.284
#> GSM1022374 5 0.6992 -0.253 0.404 0.028 0.000 0.160 0.408
#> GSM1022375 5 0.6992 -0.253 0.404 0.028 0.000 0.160 0.408
#> GSM1022376 5 0.6992 -0.253 0.404 0.028 0.000 0.160 0.408
#> GSM1022371 2 0.2529 0.643 0.000 0.900 0.004 0.056 0.040
#> GSM1022372 2 0.2529 0.643 0.000 0.900 0.004 0.056 0.040
#> GSM1022373 2 0.2529 0.643 0.000 0.900 0.004 0.056 0.040
#> GSM1022377 4 0.4779 0.952 0.004 0.448 0.000 0.536 0.012
#> GSM1022378 4 0.4779 0.952 0.004 0.448 0.000 0.536 0.012
#> GSM1022379 4 0.4779 0.952 0.004 0.448 0.000 0.536 0.012
#> GSM1022380 4 0.4779 0.952 0.004 0.448 0.000 0.536 0.012
#> GSM1022385 3 0.2499 0.804 0.036 0.000 0.908 0.040 0.016
#> GSM1022386 3 0.2499 0.804 0.036 0.000 0.908 0.040 0.016
#> GSM1022387 3 0.2499 0.804 0.036 0.000 0.908 0.040 0.016
#> GSM1022388 3 0.2499 0.804 0.036 0.000 0.908 0.040 0.016
#> GSM1022381 4 0.5071 0.953 0.004 0.420 0.000 0.548 0.028
#> GSM1022382 4 0.5071 0.953 0.004 0.420 0.000 0.548 0.028
#> GSM1022383 4 0.5071 0.953 0.004 0.420 0.000 0.548 0.028
#> GSM1022384 4 0.5071 0.953 0.004 0.420 0.000 0.548 0.028
#> GSM1022393 1 0.4741 0.671 0.740 0.004 0.000 0.096 0.160
#> GSM1022394 1 0.4741 0.671 0.740 0.004 0.000 0.096 0.160
#> GSM1022395 1 0.4741 0.671 0.740 0.004 0.000 0.096 0.160
#> GSM1022396 1 0.4741 0.671 0.740 0.004 0.000 0.096 0.160
#> GSM1022389 2 0.5939 -0.469 0.004 0.520 0.016 0.404 0.056
#> GSM1022390 2 0.5939 -0.469 0.004 0.520 0.016 0.404 0.056
#> GSM1022391 2 0.5939 -0.469 0.004 0.520 0.016 0.404 0.056
#> GSM1022392 2 0.5939 -0.469 0.004 0.520 0.016 0.404 0.056
#> GSM1022397 3 0.0880 0.818 0.032 0.000 0.968 0.000 0.000
#> GSM1022398 3 0.0880 0.818 0.032 0.000 0.968 0.000 0.000
#> GSM1022399 3 0.0880 0.818 0.032 0.000 0.968 0.000 0.000
#> GSM1022400 3 0.0880 0.818 0.032 0.000 0.968 0.000 0.000
#> GSM1022401 1 0.4741 0.671 0.740 0.004 0.000 0.096 0.160
#> GSM1022402 1 0.4741 0.671 0.740 0.004 0.000 0.096 0.160
#> GSM1022403 1 0.4741 0.671 0.740 0.004 0.000 0.096 0.160
#> GSM1022404 1 0.4741 0.671 0.740 0.004 0.000 0.096 0.160
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1022325 2 0.0000 0.8029 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022326 2 0.0000 0.8029 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022327 2 0.0000 0.8029 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022331 3 0.5775 0.3963 0.000 0.000 0.628 0.068 0.108 0.196
#> GSM1022332 3 0.5775 0.3963 0.000 0.000 0.628 0.068 0.108 0.196
#> GSM1022333 3 0.5775 0.3963 0.000 0.000 0.628 0.068 0.108 0.196
#> GSM1022328 2 0.0000 0.8029 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022329 2 0.0000 0.8029 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022330 2 0.0000 0.8029 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022337 1 0.4481 0.4152 0.520 0.016 0.000 0.008 0.000 0.456
#> GSM1022338 1 0.4481 0.4152 0.520 0.016 0.000 0.008 0.000 0.456
#> GSM1022339 1 0.4481 0.4152 0.520 0.016 0.000 0.008 0.000 0.456
#> GSM1022334 2 0.0146 0.8022 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM1022335 2 0.0146 0.8022 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM1022336 2 0.0146 0.8022 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM1022340 5 0.4588 0.3854 0.420 0.000 0.024 0.008 0.548 0.000
#> GSM1022341 5 0.4588 0.3854 0.420 0.000 0.024 0.008 0.548 0.000
#> GSM1022342 5 0.4588 0.3854 0.420 0.000 0.024 0.008 0.548 0.000
#> GSM1022343 5 0.4588 0.3854 0.420 0.000 0.024 0.008 0.548 0.000
#> GSM1022347 3 0.1879 0.8465 0.008 0.000 0.932 0.016 0.028 0.016
#> GSM1022348 3 0.1879 0.8465 0.008 0.000 0.932 0.016 0.028 0.016
#> GSM1022349 3 0.1879 0.8465 0.008 0.000 0.932 0.016 0.028 0.016
#> GSM1022350 3 0.1879 0.8465 0.008 0.000 0.932 0.016 0.028 0.016
#> GSM1022344 5 0.5548 0.3524 0.024 0.000 0.400 0.020 0.520 0.036
#> GSM1022345 5 0.5548 0.3524 0.024 0.000 0.400 0.020 0.520 0.036
#> GSM1022346 5 0.5548 0.3524 0.024 0.000 0.400 0.020 0.520 0.036
#> GSM1022355 1 0.5178 0.2020 0.624 0.000 0.000 0.064 0.284 0.028
#> GSM1022356 1 0.5178 0.2020 0.624 0.000 0.000 0.064 0.284 0.028
#> GSM1022357 1 0.5178 0.2020 0.624 0.000 0.000 0.064 0.284 0.028
#> GSM1022358 1 0.5178 0.2020 0.624 0.000 0.000 0.064 0.284 0.028
#> GSM1022351 1 0.5512 -0.0806 0.504 0.000 0.000 0.064 0.404 0.028
#> GSM1022352 1 0.5512 -0.0806 0.504 0.000 0.000 0.064 0.404 0.028
#> GSM1022353 1 0.5512 -0.0806 0.504 0.000 0.000 0.064 0.404 0.028
#> GSM1022354 1 0.5512 -0.0806 0.504 0.000 0.000 0.064 0.404 0.028
#> GSM1022359 2 0.2831 0.7599 0.000 0.872 0.000 0.048 0.064 0.016
#> GSM1022360 2 0.2831 0.7599 0.000 0.872 0.000 0.048 0.064 0.016
#> GSM1022361 2 0.2831 0.7599 0.000 0.872 0.000 0.048 0.064 0.016
#> GSM1022362 2 0.2831 0.7599 0.000 0.872 0.000 0.048 0.064 0.016
#> GSM1022367 6 0.7645 1.0000 0.000 0.060 0.196 0.128 0.132 0.484
#> GSM1022368 6 0.7645 1.0000 0.000 0.060 0.196 0.128 0.132 0.484
#> GSM1022369 6 0.7645 1.0000 0.000 0.060 0.196 0.128 0.132 0.484
#> GSM1022370 6 0.7645 1.0000 0.000 0.060 0.196 0.128 0.132 0.484
#> GSM1022363 2 0.6895 0.3849 0.000 0.484 0.000 0.140 0.128 0.248
#> GSM1022364 2 0.6895 0.3849 0.000 0.484 0.000 0.140 0.128 0.248
#> GSM1022365 2 0.6895 0.3849 0.000 0.484 0.000 0.140 0.128 0.248
#> GSM1022366 2 0.6895 0.3849 0.000 0.484 0.000 0.140 0.128 0.248
#> GSM1022374 1 0.4473 0.3993 0.492 0.028 0.000 0.000 0.000 0.480
#> GSM1022375 1 0.4473 0.3993 0.492 0.028 0.000 0.000 0.000 0.480
#> GSM1022376 1 0.4473 0.3993 0.492 0.028 0.000 0.000 0.000 0.480
#> GSM1022371 2 0.3199 0.7483 0.000 0.852 0.000 0.052 0.068 0.028
#> GSM1022372 2 0.3199 0.7483 0.000 0.852 0.000 0.052 0.068 0.028
#> GSM1022373 2 0.3199 0.7483 0.000 0.852 0.000 0.052 0.068 0.028
#> GSM1022377 4 0.4595 0.8566 0.004 0.280 0.004 0.672 0.024 0.016
#> GSM1022378 4 0.4595 0.8566 0.004 0.280 0.004 0.672 0.024 0.016
#> GSM1022379 4 0.4600 0.8566 0.004 0.280 0.004 0.672 0.020 0.020
#> GSM1022380 4 0.4600 0.8566 0.004 0.280 0.004 0.672 0.020 0.020
#> GSM1022385 3 0.1684 0.8550 0.008 0.000 0.940 0.016 0.028 0.008
#> GSM1022386 3 0.1684 0.8550 0.008 0.000 0.940 0.016 0.028 0.008
#> GSM1022387 3 0.1684 0.8550 0.008 0.000 0.940 0.016 0.028 0.008
#> GSM1022388 3 0.1684 0.8550 0.008 0.000 0.940 0.016 0.028 0.008
#> GSM1022381 4 0.3771 0.8568 0.004 0.252 0.000 0.728 0.004 0.012
#> GSM1022382 4 0.3771 0.8568 0.004 0.252 0.000 0.728 0.004 0.012
#> GSM1022383 4 0.3771 0.8568 0.004 0.252 0.000 0.728 0.004 0.012
#> GSM1022384 4 0.3771 0.8568 0.004 0.252 0.000 0.728 0.004 0.012
#> GSM1022393 1 0.0000 0.5515 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022394 1 0.0000 0.5515 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022395 1 0.0000 0.5515 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022396 1 0.0000 0.5515 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022389 4 0.6132 0.7539 0.004 0.304 0.000 0.528 0.132 0.032
#> GSM1022390 4 0.6132 0.7539 0.004 0.304 0.000 0.528 0.132 0.032
#> GSM1022391 4 0.6132 0.7539 0.004 0.304 0.000 0.528 0.132 0.032
#> GSM1022392 4 0.6132 0.7539 0.004 0.304 0.000 0.528 0.132 0.032
#> GSM1022397 3 0.0260 0.8635 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM1022398 3 0.0260 0.8635 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM1022399 3 0.0260 0.8635 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM1022400 3 0.0260 0.8635 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM1022401 1 0.0000 0.5515 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022402 1 0.0000 0.5515 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022403 1 0.0000 0.5515 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022404 1 0.0000 0.5515 1.000 0.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n protocol(p) cell.type(p) k
#> SD:kmeans 73 2.04e-06 2.19e-07 2
#> SD:kmeans 80 2.40e-10 5.36e-11 3
#> SD:kmeans 80 2.40e-10 5.36e-11 4
#> SD:kmeans 59 1.11e-14 1.26e-08 5
#> SD:kmeans 52 1.51e-16 1.38e-10 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 31589 rows and 80 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.924 0.955 0.981 0.5048 0.494 0.494
#> 3 3 1.000 0.999 1.000 0.3220 0.750 0.535
#> 4 4 0.777 0.451 0.613 0.1005 0.721 0.400
#> 5 5 0.802 0.865 0.897 0.0773 0.850 0.554
#> 6 6 0.848 0.817 0.891 0.0404 0.977 0.888
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
#> GSM1022325 2 0.000 0.974 0.000 1.000
#> GSM1022326 2 0.000 0.974 0.000 1.000
#> GSM1022327 2 0.000 0.974 0.000 1.000
#> GSM1022331 1 0.000 0.985 1.000 0.000
#> GSM1022332 1 0.000 0.985 1.000 0.000
#> GSM1022333 1 0.000 0.985 1.000 0.000
#> GSM1022328 2 0.000 0.974 0.000 1.000
#> GSM1022329 2 0.000 0.974 0.000 1.000
#> GSM1022330 2 0.000 0.974 0.000 1.000
#> GSM1022337 1 0.697 0.769 0.812 0.188
#> GSM1022338 1 0.697 0.769 0.812 0.188
#> GSM1022339 1 0.697 0.769 0.812 0.188
#> GSM1022334 2 0.000 0.974 0.000 1.000
#> GSM1022335 2 0.000 0.974 0.000 1.000
#> GSM1022336 2 0.000 0.974 0.000 1.000
#> GSM1022340 1 0.000 0.985 1.000 0.000
#> GSM1022341 1 0.000 0.985 1.000 0.000
#> GSM1022342 1 0.000 0.985 1.000 0.000
#> GSM1022343 1 0.000 0.985 1.000 0.000
#> GSM1022347 1 0.000 0.985 1.000 0.000
#> GSM1022348 1 0.000 0.985 1.000 0.000
#> GSM1022349 1 0.000 0.985 1.000 0.000
#> GSM1022350 1 0.000 0.985 1.000 0.000
#> GSM1022344 1 0.000 0.985 1.000 0.000
#> GSM1022345 1 0.000 0.985 1.000 0.000
#> GSM1022346 1 0.000 0.985 1.000 0.000
#> GSM1022355 1 0.000 0.985 1.000 0.000
#> GSM1022356 1 0.000 0.985 1.000 0.000
#> GSM1022357 1 0.000 0.985 1.000 0.000
#> GSM1022358 1 0.000 0.985 1.000 0.000
#> GSM1022351 1 0.000 0.985 1.000 0.000
#> GSM1022352 1 0.000 0.985 1.000 0.000
#> GSM1022353 1 0.000 0.985 1.000 0.000
#> GSM1022354 1 0.000 0.985 1.000 0.000
#> GSM1022359 2 0.000 0.974 0.000 1.000
#> GSM1022360 2 0.000 0.974 0.000 1.000
#> GSM1022361 2 0.000 0.974 0.000 1.000
#> GSM1022362 2 0.000 0.974 0.000 1.000
#> GSM1022367 2 0.000 0.974 0.000 1.000
#> GSM1022368 2 0.000 0.974 0.000 1.000
#> GSM1022369 2 0.000 0.974 0.000 1.000
#> GSM1022370 2 0.000 0.974 0.000 1.000
#> GSM1022363 2 0.000 0.974 0.000 1.000
#> GSM1022364 2 0.000 0.974 0.000 1.000
#> GSM1022365 2 0.000 0.974 0.000 1.000
#> GSM1022366 2 0.000 0.974 0.000 1.000
#> GSM1022374 2 0.904 0.538 0.320 0.680
#> GSM1022375 2 0.904 0.538 0.320 0.680
#> GSM1022376 2 0.904 0.538 0.320 0.680
#> GSM1022371 2 0.000 0.974 0.000 1.000
#> GSM1022372 2 0.000 0.974 0.000 1.000
#> GSM1022373 2 0.000 0.974 0.000 1.000
#> GSM1022377 2 0.000 0.974 0.000 1.000
#> GSM1022378 2 0.000 0.974 0.000 1.000
#> GSM1022379 2 0.000 0.974 0.000 1.000
#> GSM1022380 2 0.000 0.974 0.000 1.000
#> GSM1022385 1 0.000 0.985 1.000 0.000
#> GSM1022386 1 0.000 0.985 1.000 0.000
#> GSM1022387 1 0.000 0.985 1.000 0.000
#> GSM1022388 1 0.000 0.985 1.000 0.000
#> GSM1022381 2 0.000 0.974 0.000 1.000
#> GSM1022382 2 0.000 0.974 0.000 1.000
#> GSM1022383 2 0.000 0.974 0.000 1.000
#> GSM1022384 2 0.000 0.974 0.000 1.000
#> GSM1022393 1 0.000 0.985 1.000 0.000
#> GSM1022394 1 0.000 0.985 1.000 0.000
#> GSM1022395 1 0.000 0.985 1.000 0.000
#> GSM1022396 1 0.000 0.985 1.000 0.000
#> GSM1022389 2 0.000 0.974 0.000 1.000
#> GSM1022390 2 0.000 0.974 0.000 1.000
#> GSM1022391 2 0.000 0.974 0.000 1.000
#> GSM1022392 2 0.000 0.974 0.000 1.000
#> GSM1022397 1 0.000 0.985 1.000 0.000
#> GSM1022398 1 0.000 0.985 1.000 0.000
#> GSM1022399 1 0.000 0.985 1.000 0.000
#> GSM1022400 1 0.000 0.985 1.000 0.000
#> GSM1022401 1 0.000 0.985 1.000 0.000
#> GSM1022402 1 0.000 0.985 1.000 0.000
#> GSM1022403 1 0.000 0.985 1.000 0.000
#> GSM1022404 1 0.000 0.985 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1022325 2 0.0000 1.000 0.000 1.000 0.000
#> GSM1022326 2 0.0000 1.000 0.000 1.000 0.000
#> GSM1022327 2 0.0000 1.000 0.000 1.000 0.000
#> GSM1022331 3 0.0000 0.999 0.000 0.000 1.000
#> GSM1022332 3 0.0000 0.999 0.000 0.000 1.000
#> GSM1022333 3 0.0000 0.999 0.000 0.000 1.000
#> GSM1022328 2 0.0000 1.000 0.000 1.000 0.000
#> GSM1022329 2 0.0000 1.000 0.000 1.000 0.000
#> GSM1022330 2 0.0000 1.000 0.000 1.000 0.000
#> GSM1022337 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022338 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022339 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022334 2 0.0000 1.000 0.000 1.000 0.000
#> GSM1022335 2 0.0000 1.000 0.000 1.000 0.000
#> GSM1022336 2 0.0000 1.000 0.000 1.000 0.000
#> GSM1022340 1 0.0237 0.997 0.996 0.000 0.004
#> GSM1022341 1 0.0237 0.997 0.996 0.000 0.004
#> GSM1022342 1 0.0237 0.997 0.996 0.000 0.004
#> GSM1022343 1 0.0237 0.997 0.996 0.000 0.004
#> GSM1022347 3 0.0000 0.999 0.000 0.000 1.000
#> GSM1022348 3 0.0000 0.999 0.000 0.000 1.000
#> GSM1022349 3 0.0000 0.999 0.000 0.000 1.000
#> GSM1022350 3 0.0000 0.999 0.000 0.000 1.000
#> GSM1022344 3 0.0000 0.999 0.000 0.000 1.000
#> GSM1022345 3 0.0000 0.999 0.000 0.000 1.000
#> GSM1022346 3 0.0000 0.999 0.000 0.000 1.000
#> GSM1022355 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022356 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022357 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022358 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022351 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022352 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022353 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022354 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022359 2 0.0000 1.000 0.000 1.000 0.000
#> GSM1022360 2 0.0000 1.000 0.000 1.000 0.000
#> GSM1022361 2 0.0000 1.000 0.000 1.000 0.000
#> GSM1022362 2 0.0000 1.000 0.000 1.000 0.000
#> GSM1022367 3 0.0237 0.996 0.000 0.004 0.996
#> GSM1022368 3 0.0237 0.996 0.000 0.004 0.996
#> GSM1022369 3 0.0237 0.996 0.000 0.004 0.996
#> GSM1022370 3 0.0237 0.996 0.000 0.004 0.996
#> GSM1022363 2 0.0000 1.000 0.000 1.000 0.000
#> GSM1022364 2 0.0000 1.000 0.000 1.000 0.000
#> GSM1022365 2 0.0000 1.000 0.000 1.000 0.000
#> GSM1022366 2 0.0000 1.000 0.000 1.000 0.000
#> GSM1022374 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022375 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022376 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022371 2 0.0000 1.000 0.000 1.000 0.000
#> GSM1022372 2 0.0000 1.000 0.000 1.000 0.000
#> GSM1022373 2 0.0000 1.000 0.000 1.000 0.000
#> GSM1022377 2 0.0000 1.000 0.000 1.000 0.000
#> GSM1022378 2 0.0000 1.000 0.000 1.000 0.000
#> GSM1022379 2 0.0000 1.000 0.000 1.000 0.000
#> GSM1022380 2 0.0000 1.000 0.000 1.000 0.000
#> GSM1022385 3 0.0000 0.999 0.000 0.000 1.000
#> GSM1022386 3 0.0000 0.999 0.000 0.000 1.000
#> GSM1022387 3 0.0000 0.999 0.000 0.000 1.000
#> GSM1022388 3 0.0000 0.999 0.000 0.000 1.000
#> GSM1022381 2 0.0000 1.000 0.000 1.000 0.000
#> GSM1022382 2 0.0000 1.000 0.000 1.000 0.000
#> GSM1022383 2 0.0000 1.000 0.000 1.000 0.000
#> GSM1022384 2 0.0000 1.000 0.000 1.000 0.000
#> GSM1022393 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022394 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022395 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022396 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022389 2 0.0000 1.000 0.000 1.000 0.000
#> GSM1022390 2 0.0000 1.000 0.000 1.000 0.000
#> GSM1022391 2 0.0000 1.000 0.000 1.000 0.000
#> GSM1022392 2 0.0000 1.000 0.000 1.000 0.000
#> GSM1022397 3 0.0000 0.999 0.000 0.000 1.000
#> GSM1022398 3 0.0000 0.999 0.000 0.000 1.000
#> GSM1022399 3 0.0000 0.999 0.000 0.000 1.000
#> GSM1022400 3 0.0000 0.999 0.000 0.000 1.000
#> GSM1022401 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022402 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022403 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022404 1 0.0000 0.999 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1022325 2 0.491 0.1244 0.000 0.580 0.000 0.420
#> GSM1022326 2 0.491 0.1244 0.000 0.580 0.000 0.420
#> GSM1022327 2 0.491 0.1244 0.000 0.580 0.000 0.420
#> GSM1022331 2 0.785 0.2778 0.304 0.404 0.292 0.000
#> GSM1022332 2 0.785 0.2778 0.304 0.404 0.292 0.000
#> GSM1022333 2 0.785 0.2778 0.304 0.404 0.292 0.000
#> GSM1022328 2 0.491 0.1244 0.000 0.580 0.000 0.420
#> GSM1022329 2 0.491 0.1244 0.000 0.580 0.000 0.420
#> GSM1022330 2 0.491 0.1244 0.000 0.580 0.000 0.420
#> GSM1022337 1 0.480 0.7623 0.696 0.012 0.292 0.000
#> GSM1022338 1 0.480 0.7623 0.696 0.012 0.292 0.000
#> GSM1022339 1 0.480 0.7623 0.696 0.012 0.292 0.000
#> GSM1022334 2 0.491 0.1244 0.000 0.580 0.000 0.420
#> GSM1022335 2 0.491 0.1244 0.000 0.580 0.000 0.420
#> GSM1022336 2 0.491 0.1244 0.000 0.580 0.000 0.420
#> GSM1022340 3 0.425 0.5542 0.276 0.000 0.724 0.000
#> GSM1022341 3 0.425 0.5542 0.276 0.000 0.724 0.000
#> GSM1022342 3 0.425 0.5542 0.276 0.000 0.724 0.000
#> GSM1022343 3 0.425 0.5542 0.276 0.000 0.724 0.000
#> GSM1022347 2 0.785 0.2778 0.304 0.404 0.292 0.000
#> GSM1022348 2 0.785 0.2778 0.304 0.404 0.292 0.000
#> GSM1022349 2 0.785 0.2778 0.304 0.404 0.292 0.000
#> GSM1022350 2 0.785 0.2778 0.304 0.404 0.292 0.000
#> GSM1022344 3 0.714 -0.0481 0.304 0.160 0.536 0.000
#> GSM1022345 3 0.707 -0.0373 0.304 0.152 0.544 0.000
#> GSM1022346 3 0.710 -0.0423 0.304 0.156 0.540 0.000
#> GSM1022355 3 0.443 0.5358 0.304 0.000 0.696 0.000
#> GSM1022356 3 0.443 0.5358 0.304 0.000 0.696 0.000
#> GSM1022357 3 0.443 0.5358 0.304 0.000 0.696 0.000
#> GSM1022358 3 0.443 0.5358 0.304 0.000 0.696 0.000
#> GSM1022351 3 0.436 0.5514 0.292 0.000 0.708 0.000
#> GSM1022352 3 0.436 0.5514 0.292 0.000 0.708 0.000
#> GSM1022353 3 0.436 0.5514 0.292 0.000 0.708 0.000
#> GSM1022354 3 0.436 0.5514 0.292 0.000 0.708 0.000
#> GSM1022359 2 0.491 0.1244 0.000 0.580 0.000 0.420
#> GSM1022360 2 0.491 0.1244 0.000 0.580 0.000 0.420
#> GSM1022361 2 0.491 0.1244 0.000 0.580 0.000 0.420
#> GSM1022362 2 0.491 0.1244 0.000 0.580 0.000 0.420
#> GSM1022367 2 0.419 0.3160 0.000 0.732 0.268 0.000
#> GSM1022368 2 0.419 0.3160 0.000 0.732 0.268 0.000
#> GSM1022369 2 0.419 0.3160 0.000 0.732 0.268 0.000
#> GSM1022370 2 0.419 0.3160 0.000 0.732 0.268 0.000
#> GSM1022363 2 0.487 0.1249 0.000 0.596 0.000 0.404
#> GSM1022364 2 0.487 0.1249 0.000 0.596 0.000 0.404
#> GSM1022365 2 0.487 0.1249 0.000 0.596 0.000 0.404
#> GSM1022366 2 0.487 0.1249 0.000 0.596 0.000 0.404
#> GSM1022374 1 0.470 0.4252 0.644 0.356 0.000 0.000
#> GSM1022375 1 0.470 0.4252 0.644 0.356 0.000 0.000
#> GSM1022376 1 0.470 0.4252 0.644 0.356 0.000 0.000
#> GSM1022371 2 0.491 0.1244 0.000 0.580 0.000 0.420
#> GSM1022372 2 0.491 0.1244 0.000 0.580 0.000 0.420
#> GSM1022373 2 0.491 0.1244 0.000 0.580 0.000 0.420
#> GSM1022377 4 0.000 1.0000 0.000 0.000 0.000 1.000
#> GSM1022378 4 0.000 1.0000 0.000 0.000 0.000 1.000
#> GSM1022379 4 0.000 1.0000 0.000 0.000 0.000 1.000
#> GSM1022380 4 0.000 1.0000 0.000 0.000 0.000 1.000
#> GSM1022385 2 0.785 0.2778 0.304 0.404 0.292 0.000
#> GSM1022386 2 0.785 0.2778 0.304 0.404 0.292 0.000
#> GSM1022387 2 0.785 0.2778 0.304 0.404 0.292 0.000
#> GSM1022388 2 0.785 0.2778 0.304 0.404 0.292 0.000
#> GSM1022381 4 0.000 1.0000 0.000 0.000 0.000 1.000
#> GSM1022382 4 0.000 1.0000 0.000 0.000 0.000 1.000
#> GSM1022383 4 0.000 1.0000 0.000 0.000 0.000 1.000
#> GSM1022384 4 0.000 1.0000 0.000 0.000 0.000 1.000
#> GSM1022393 1 0.450 0.7701 0.684 0.000 0.316 0.000
#> GSM1022394 1 0.450 0.7701 0.684 0.000 0.316 0.000
#> GSM1022395 1 0.450 0.7701 0.684 0.000 0.316 0.000
#> GSM1022396 1 0.450 0.7701 0.684 0.000 0.316 0.000
#> GSM1022389 4 0.000 1.0000 0.000 0.000 0.000 1.000
#> GSM1022390 4 0.000 1.0000 0.000 0.000 0.000 1.000
#> GSM1022391 4 0.000 1.0000 0.000 0.000 0.000 1.000
#> GSM1022392 4 0.000 1.0000 0.000 0.000 0.000 1.000
#> GSM1022397 2 0.785 0.2778 0.304 0.404 0.292 0.000
#> GSM1022398 2 0.785 0.2778 0.304 0.404 0.292 0.000
#> GSM1022399 2 0.785 0.2778 0.304 0.404 0.292 0.000
#> GSM1022400 2 0.785 0.2778 0.304 0.404 0.292 0.000
#> GSM1022401 1 0.450 0.7701 0.684 0.000 0.316 0.000
#> GSM1022402 1 0.450 0.7701 0.684 0.000 0.316 0.000
#> GSM1022403 1 0.450 0.7701 0.684 0.000 0.316 0.000
#> GSM1022404 1 0.450 0.7701 0.684 0.000 0.316 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1022325 2 0.1851 0.971 0.000 0.912 0.000 0.088 0.000
#> GSM1022326 2 0.1851 0.971 0.000 0.912 0.000 0.088 0.000
#> GSM1022327 2 0.1851 0.971 0.000 0.912 0.000 0.088 0.000
#> GSM1022331 3 0.1216 0.853 0.020 0.000 0.960 0.000 0.020
#> GSM1022332 3 0.1216 0.853 0.020 0.000 0.960 0.000 0.020
#> GSM1022333 3 0.1216 0.853 0.020 0.000 0.960 0.000 0.020
#> GSM1022328 2 0.1851 0.971 0.000 0.912 0.000 0.088 0.000
#> GSM1022329 2 0.1851 0.971 0.000 0.912 0.000 0.088 0.000
#> GSM1022330 2 0.1851 0.971 0.000 0.912 0.000 0.088 0.000
#> GSM1022337 5 0.1168 0.761 0.032 0.008 0.000 0.000 0.960
#> GSM1022338 5 0.1168 0.761 0.032 0.008 0.000 0.000 0.960
#> GSM1022339 5 0.1168 0.761 0.032 0.008 0.000 0.000 0.960
#> GSM1022334 2 0.1851 0.971 0.000 0.912 0.000 0.088 0.000
#> GSM1022335 2 0.1851 0.971 0.000 0.912 0.000 0.088 0.000
#> GSM1022336 2 0.1851 0.971 0.000 0.912 0.000 0.088 0.000
#> GSM1022340 1 0.0992 0.955 0.968 0.000 0.024 0.008 0.000
#> GSM1022341 1 0.0992 0.955 0.968 0.000 0.024 0.008 0.000
#> GSM1022342 1 0.0992 0.955 0.968 0.000 0.024 0.008 0.000
#> GSM1022343 1 0.0992 0.955 0.968 0.000 0.024 0.008 0.000
#> GSM1022347 3 0.0000 0.866 0.000 0.000 1.000 0.000 0.000
#> GSM1022348 3 0.0000 0.866 0.000 0.000 1.000 0.000 0.000
#> GSM1022349 3 0.0000 0.866 0.000 0.000 1.000 0.000 0.000
#> GSM1022350 3 0.0000 0.866 0.000 0.000 1.000 0.000 0.000
#> GSM1022344 3 0.4455 0.340 0.404 0.000 0.588 0.008 0.000
#> GSM1022345 3 0.4481 0.312 0.416 0.000 0.576 0.008 0.000
#> GSM1022346 3 0.4464 0.331 0.408 0.000 0.584 0.008 0.000
#> GSM1022355 1 0.1357 0.956 0.948 0.000 0.000 0.004 0.048
#> GSM1022356 1 0.1357 0.956 0.948 0.000 0.000 0.004 0.048
#> GSM1022357 1 0.1357 0.956 0.948 0.000 0.000 0.004 0.048
#> GSM1022358 1 0.1357 0.956 0.948 0.000 0.000 0.004 0.048
#> GSM1022351 1 0.0703 0.968 0.976 0.000 0.000 0.000 0.024
#> GSM1022352 1 0.0703 0.968 0.976 0.000 0.000 0.000 0.024
#> GSM1022353 1 0.0703 0.968 0.976 0.000 0.000 0.000 0.024
#> GSM1022354 1 0.0703 0.968 0.976 0.000 0.000 0.000 0.024
#> GSM1022359 2 0.1908 0.970 0.000 0.908 0.000 0.092 0.000
#> GSM1022360 2 0.1908 0.970 0.000 0.908 0.000 0.092 0.000
#> GSM1022361 2 0.1908 0.970 0.000 0.908 0.000 0.092 0.000
#> GSM1022362 2 0.1908 0.970 0.000 0.908 0.000 0.092 0.000
#> GSM1022367 3 0.6100 0.635 0.024 0.196 0.632 0.000 0.148
#> GSM1022368 3 0.6100 0.635 0.024 0.196 0.632 0.000 0.148
#> GSM1022369 3 0.6100 0.635 0.024 0.196 0.632 0.000 0.148
#> GSM1022370 3 0.6100 0.635 0.024 0.196 0.632 0.000 0.148
#> GSM1022363 2 0.0932 0.889 0.004 0.972 0.000 0.004 0.020
#> GSM1022364 2 0.0932 0.889 0.004 0.972 0.000 0.004 0.020
#> GSM1022365 2 0.0932 0.889 0.004 0.972 0.000 0.004 0.020
#> GSM1022366 2 0.0932 0.889 0.004 0.972 0.000 0.004 0.020
#> GSM1022374 5 0.1117 0.753 0.016 0.020 0.000 0.000 0.964
#> GSM1022375 5 0.1117 0.753 0.016 0.020 0.000 0.000 0.964
#> GSM1022376 5 0.1117 0.753 0.016 0.020 0.000 0.000 0.964
#> GSM1022371 2 0.1851 0.971 0.000 0.912 0.000 0.088 0.000
#> GSM1022372 2 0.1851 0.971 0.000 0.912 0.000 0.088 0.000
#> GSM1022373 2 0.1851 0.971 0.000 0.912 0.000 0.088 0.000
#> GSM1022377 4 0.0404 0.960 0.000 0.012 0.000 0.988 0.000
#> GSM1022378 4 0.0404 0.960 0.000 0.012 0.000 0.988 0.000
#> GSM1022379 4 0.0404 0.960 0.000 0.012 0.000 0.988 0.000
#> GSM1022380 4 0.0404 0.960 0.000 0.012 0.000 0.988 0.000
#> GSM1022385 3 0.0000 0.866 0.000 0.000 1.000 0.000 0.000
#> GSM1022386 3 0.0000 0.866 0.000 0.000 1.000 0.000 0.000
#> GSM1022387 3 0.0000 0.866 0.000 0.000 1.000 0.000 0.000
#> GSM1022388 3 0.0000 0.866 0.000 0.000 1.000 0.000 0.000
#> GSM1022381 4 0.0404 0.960 0.000 0.012 0.000 0.988 0.000
#> GSM1022382 4 0.0404 0.960 0.000 0.012 0.000 0.988 0.000
#> GSM1022383 4 0.0404 0.960 0.000 0.012 0.000 0.988 0.000
#> GSM1022384 4 0.0404 0.960 0.000 0.012 0.000 0.988 0.000
#> GSM1022393 5 0.4101 0.777 0.332 0.000 0.000 0.004 0.664
#> GSM1022394 5 0.4101 0.777 0.332 0.000 0.000 0.004 0.664
#> GSM1022395 5 0.4101 0.777 0.332 0.000 0.000 0.004 0.664
#> GSM1022396 5 0.4101 0.777 0.332 0.000 0.000 0.004 0.664
#> GSM1022389 4 0.2233 0.917 0.000 0.104 0.000 0.892 0.004
#> GSM1022390 4 0.2233 0.917 0.000 0.104 0.000 0.892 0.004
#> GSM1022391 4 0.2233 0.917 0.000 0.104 0.000 0.892 0.004
#> GSM1022392 4 0.2233 0.917 0.000 0.104 0.000 0.892 0.004
#> GSM1022397 3 0.0000 0.866 0.000 0.000 1.000 0.000 0.000
#> GSM1022398 3 0.0000 0.866 0.000 0.000 1.000 0.000 0.000
#> GSM1022399 3 0.0000 0.866 0.000 0.000 1.000 0.000 0.000
#> GSM1022400 3 0.0000 0.866 0.000 0.000 1.000 0.000 0.000
#> GSM1022401 5 0.4101 0.777 0.332 0.000 0.000 0.004 0.664
#> GSM1022402 5 0.4101 0.777 0.332 0.000 0.000 0.004 0.664
#> GSM1022403 5 0.4101 0.777 0.332 0.000 0.000 0.004 0.664
#> GSM1022404 5 0.4101 0.777 0.332 0.000 0.000 0.004 0.664
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1022325 2 0.0000 0.901 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022326 2 0.0000 0.901 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022327 2 0.0000 0.901 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022331 3 0.3756 0.225 0.000 0.000 0.600 0.000 0.000 0.400
#> GSM1022332 3 0.3756 0.225 0.000 0.000 0.600 0.000 0.000 0.400
#> GSM1022333 3 0.3756 0.225 0.000 0.000 0.600 0.000 0.000 0.400
#> GSM1022328 2 0.0000 0.901 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022329 2 0.0000 0.901 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022330 2 0.0000 0.901 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022337 5 0.1267 0.734 0.000 0.000 0.000 0.000 0.940 0.060
#> GSM1022338 5 0.1267 0.734 0.000 0.000 0.000 0.000 0.940 0.060
#> GSM1022339 5 0.1267 0.734 0.000 0.000 0.000 0.000 0.940 0.060
#> GSM1022334 2 0.0000 0.901 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022335 2 0.0000 0.901 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022336 2 0.0000 0.901 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022340 1 0.1624 0.920 0.936 0.000 0.004 0.020 0.000 0.040
#> GSM1022341 1 0.1624 0.920 0.936 0.000 0.004 0.020 0.000 0.040
#> GSM1022342 1 0.1624 0.920 0.936 0.000 0.004 0.020 0.000 0.040
#> GSM1022343 1 0.1624 0.920 0.936 0.000 0.004 0.020 0.000 0.040
#> GSM1022347 3 0.0000 0.861 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022348 3 0.0000 0.861 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022349 3 0.0000 0.861 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022350 3 0.0000 0.861 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022344 3 0.3568 0.704 0.128 0.000 0.812 0.020 0.000 0.040
#> GSM1022345 3 0.3838 0.674 0.156 0.000 0.784 0.020 0.000 0.040
#> GSM1022346 3 0.3726 0.688 0.144 0.000 0.796 0.020 0.000 0.040
#> GSM1022355 1 0.1556 0.902 0.920 0.000 0.000 0.000 0.080 0.000
#> GSM1022356 1 0.1556 0.902 0.920 0.000 0.000 0.000 0.080 0.000
#> GSM1022357 1 0.1556 0.902 0.920 0.000 0.000 0.000 0.080 0.000
#> GSM1022358 1 0.1556 0.902 0.920 0.000 0.000 0.000 0.080 0.000
#> GSM1022351 1 0.0000 0.937 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022352 1 0.0000 0.937 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022353 1 0.0000 0.937 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022354 1 0.0000 0.937 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022359 2 0.0405 0.896 0.000 0.988 0.000 0.008 0.000 0.004
#> GSM1022360 2 0.0405 0.896 0.000 0.988 0.000 0.008 0.000 0.004
#> GSM1022361 2 0.0405 0.896 0.000 0.988 0.000 0.008 0.000 0.004
#> GSM1022362 2 0.0405 0.896 0.000 0.988 0.000 0.008 0.000 0.004
#> GSM1022367 6 0.2668 1.000 0.000 0.004 0.168 0.000 0.000 0.828
#> GSM1022368 6 0.2668 1.000 0.000 0.004 0.168 0.000 0.000 0.828
#> GSM1022369 6 0.2668 1.000 0.000 0.004 0.168 0.000 0.000 0.828
#> GSM1022370 6 0.2668 1.000 0.000 0.004 0.168 0.000 0.000 0.828
#> GSM1022363 2 0.3817 0.407 0.000 0.568 0.000 0.000 0.000 0.432
#> GSM1022364 2 0.3817 0.407 0.000 0.568 0.000 0.000 0.000 0.432
#> GSM1022365 2 0.3817 0.407 0.000 0.568 0.000 0.000 0.000 0.432
#> GSM1022366 2 0.3817 0.407 0.000 0.568 0.000 0.000 0.000 0.432
#> GSM1022374 5 0.1327 0.731 0.000 0.000 0.000 0.000 0.936 0.064
#> GSM1022375 5 0.1327 0.731 0.000 0.000 0.000 0.000 0.936 0.064
#> GSM1022376 5 0.1327 0.731 0.000 0.000 0.000 0.000 0.936 0.064
#> GSM1022371 2 0.0000 0.901 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022372 2 0.0000 0.901 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022373 2 0.0000 0.901 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022377 4 0.0547 0.919 0.000 0.020 0.000 0.980 0.000 0.000
#> GSM1022378 4 0.0547 0.919 0.000 0.020 0.000 0.980 0.000 0.000
#> GSM1022379 4 0.0547 0.919 0.000 0.020 0.000 0.980 0.000 0.000
#> GSM1022380 4 0.0547 0.919 0.000 0.020 0.000 0.980 0.000 0.000
#> GSM1022385 3 0.0000 0.861 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022386 3 0.0000 0.861 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022387 3 0.0000 0.861 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022388 3 0.0000 0.861 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022381 4 0.0547 0.919 0.000 0.020 0.000 0.980 0.000 0.000
#> GSM1022382 4 0.0547 0.919 0.000 0.020 0.000 0.980 0.000 0.000
#> GSM1022383 4 0.0547 0.919 0.000 0.020 0.000 0.980 0.000 0.000
#> GSM1022384 4 0.0547 0.919 0.000 0.020 0.000 0.980 0.000 0.000
#> GSM1022393 5 0.3371 0.766 0.292 0.000 0.000 0.000 0.708 0.000
#> GSM1022394 5 0.3371 0.766 0.292 0.000 0.000 0.000 0.708 0.000
#> GSM1022395 5 0.3371 0.766 0.292 0.000 0.000 0.000 0.708 0.000
#> GSM1022396 5 0.3371 0.766 0.292 0.000 0.000 0.000 0.708 0.000
#> GSM1022389 4 0.3772 0.832 0.000 0.160 0.000 0.772 0.000 0.068
#> GSM1022390 4 0.3772 0.832 0.000 0.160 0.000 0.772 0.000 0.068
#> GSM1022391 4 0.3772 0.832 0.000 0.160 0.000 0.772 0.000 0.068
#> GSM1022392 4 0.3772 0.832 0.000 0.160 0.000 0.772 0.000 0.068
#> GSM1022397 3 0.0000 0.861 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022398 3 0.0000 0.861 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022399 3 0.0000 0.861 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022400 3 0.0000 0.861 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022401 5 0.3371 0.766 0.292 0.000 0.000 0.000 0.708 0.000
#> GSM1022402 5 0.3371 0.766 0.292 0.000 0.000 0.000 0.708 0.000
#> GSM1022403 5 0.3371 0.766 0.292 0.000 0.000 0.000 0.708 0.000
#> GSM1022404 5 0.3371 0.766 0.292 0.000 0.000 0.000 0.708 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 protocol(p) cell.type(p) k
#> SD:skmeans 80 1.36e-06 2.28e-06 2
#> SD:skmeans 80 2.40e-10 5.36e-11 3
#> SD:skmeans 35 5.66e-08 5.81e-06 4
#> SD:skmeans 77 1.84e-20 1.36e-13 5
#> SD:skmeans 73 2.24e-30 3.99e-10 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 31589 rows and 80 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.814 0.918 0.964 0.5040 0.495 0.495
#> 3 3 0.926 0.927 0.969 0.3176 0.689 0.452
#> 4 4 0.840 0.919 0.916 0.1121 0.914 0.744
#> 5 5 0.841 0.831 0.910 0.0683 0.938 0.765
#> 6 6 0.891 0.897 0.946 0.0470 0.942 0.737
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
#> GSM1022325 2 0.0000 0.926 0.000 1.000
#> GSM1022326 2 0.0000 0.926 0.000 1.000
#> GSM1022327 2 0.0000 0.926 0.000 1.000
#> GSM1022331 1 0.0000 1.000 1.000 0.000
#> GSM1022332 1 0.0000 1.000 1.000 0.000
#> GSM1022333 1 0.0000 1.000 1.000 0.000
#> GSM1022328 2 0.0000 0.926 0.000 1.000
#> GSM1022329 2 0.0000 0.926 0.000 1.000
#> GSM1022330 2 0.0000 0.926 0.000 1.000
#> GSM1022337 2 0.9732 0.415 0.404 0.596
#> GSM1022338 2 0.9732 0.415 0.404 0.596
#> GSM1022339 2 0.9732 0.415 0.404 0.596
#> GSM1022334 2 0.0000 0.926 0.000 1.000
#> GSM1022335 2 0.0000 0.926 0.000 1.000
#> GSM1022336 2 0.0000 0.926 0.000 1.000
#> GSM1022340 1 0.0000 1.000 1.000 0.000
#> GSM1022341 1 0.0000 1.000 1.000 0.000
#> GSM1022342 1 0.0000 1.000 1.000 0.000
#> GSM1022343 1 0.0000 1.000 1.000 0.000
#> GSM1022347 1 0.0000 1.000 1.000 0.000
#> GSM1022348 1 0.0000 1.000 1.000 0.000
#> GSM1022349 1 0.0000 1.000 1.000 0.000
#> GSM1022350 1 0.0000 1.000 1.000 0.000
#> GSM1022344 1 0.0000 1.000 1.000 0.000
#> GSM1022345 1 0.0000 1.000 1.000 0.000
#> GSM1022346 1 0.0000 1.000 1.000 0.000
#> GSM1022355 1 0.0000 1.000 1.000 0.000
#> GSM1022356 1 0.0000 1.000 1.000 0.000
#> GSM1022357 1 0.0000 1.000 1.000 0.000
#> GSM1022358 1 0.0000 1.000 1.000 0.000
#> GSM1022351 1 0.0000 1.000 1.000 0.000
#> GSM1022352 1 0.0000 1.000 1.000 0.000
#> GSM1022353 1 0.0000 1.000 1.000 0.000
#> GSM1022354 1 0.0000 1.000 1.000 0.000
#> GSM1022359 2 0.0000 0.926 0.000 1.000
#> GSM1022360 2 0.0000 0.926 0.000 1.000
#> GSM1022361 2 0.0000 0.926 0.000 1.000
#> GSM1022362 2 0.0000 0.926 0.000 1.000
#> GSM1022367 2 0.0000 0.926 0.000 1.000
#> GSM1022368 2 0.6712 0.764 0.176 0.824
#> GSM1022369 2 0.7299 0.729 0.204 0.796
#> GSM1022370 2 0.0000 0.926 0.000 1.000
#> GSM1022363 2 0.0000 0.926 0.000 1.000
#> GSM1022364 2 0.0000 0.926 0.000 1.000
#> GSM1022365 2 0.0000 0.926 0.000 1.000
#> GSM1022366 2 0.0000 0.926 0.000 1.000
#> GSM1022374 2 0.9732 0.415 0.404 0.596
#> GSM1022375 2 0.9732 0.415 0.404 0.596
#> GSM1022376 2 0.9732 0.415 0.404 0.596
#> GSM1022371 2 0.0000 0.926 0.000 1.000
#> GSM1022372 2 0.0000 0.926 0.000 1.000
#> GSM1022373 2 0.0000 0.926 0.000 1.000
#> GSM1022377 2 0.0000 0.926 0.000 1.000
#> GSM1022378 2 0.0000 0.926 0.000 1.000
#> GSM1022379 2 0.0000 0.926 0.000 1.000
#> GSM1022380 2 0.0000 0.926 0.000 1.000
#> GSM1022385 1 0.0000 1.000 1.000 0.000
#> GSM1022386 1 0.0000 1.000 1.000 0.000
#> GSM1022387 1 0.0000 1.000 1.000 0.000
#> GSM1022388 1 0.0000 1.000 1.000 0.000
#> GSM1022381 2 0.0000 0.926 0.000 1.000
#> GSM1022382 2 0.0000 0.926 0.000 1.000
#> GSM1022383 2 0.0000 0.926 0.000 1.000
#> GSM1022384 2 0.0000 0.926 0.000 1.000
#> GSM1022393 1 0.0000 1.000 1.000 0.000
#> GSM1022394 1 0.0000 1.000 1.000 0.000
#> GSM1022395 1 0.0000 1.000 1.000 0.000
#> GSM1022396 1 0.0000 1.000 1.000 0.000
#> GSM1022389 2 0.0000 0.926 0.000 1.000
#> GSM1022390 2 0.0938 0.918 0.012 0.988
#> GSM1022391 2 0.0000 0.926 0.000 1.000
#> GSM1022392 2 0.4022 0.866 0.080 0.920
#> GSM1022397 1 0.0000 1.000 1.000 0.000
#> GSM1022398 1 0.0000 1.000 1.000 0.000
#> GSM1022399 1 0.0000 1.000 1.000 0.000
#> GSM1022400 1 0.0000 1.000 1.000 0.000
#> GSM1022401 1 0.0000 1.000 1.000 0.000
#> GSM1022402 1 0.0000 1.000 1.000 0.000
#> GSM1022403 1 0.0000 1.000 1.000 0.000
#> GSM1022404 1 0.0000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1022325 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022326 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022327 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022331 3 0.000 0.954 0.000 0.000 1.000
#> GSM1022332 3 0.000 0.954 0.000 0.000 1.000
#> GSM1022333 3 0.000 0.954 0.000 0.000 1.000
#> GSM1022328 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022329 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022330 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022337 1 0.000 0.933 1.000 0.000 0.000
#> GSM1022338 1 0.000 0.933 1.000 0.000 0.000
#> GSM1022339 1 0.000 0.933 1.000 0.000 0.000
#> GSM1022334 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022335 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022336 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022340 1 0.000 0.933 1.000 0.000 0.000
#> GSM1022341 1 0.000 0.933 1.000 0.000 0.000
#> GSM1022342 1 0.000 0.933 1.000 0.000 0.000
#> GSM1022343 1 0.000 0.933 1.000 0.000 0.000
#> GSM1022347 3 0.000 0.954 0.000 0.000 1.000
#> GSM1022348 3 0.000 0.954 0.000 0.000 1.000
#> GSM1022349 3 0.000 0.954 0.000 0.000 1.000
#> GSM1022350 3 0.000 0.954 0.000 0.000 1.000
#> GSM1022344 3 0.000 0.954 0.000 0.000 1.000
#> GSM1022345 3 0.000 0.954 0.000 0.000 1.000
#> GSM1022346 3 0.000 0.954 0.000 0.000 1.000
#> GSM1022355 1 0.000 0.933 1.000 0.000 0.000
#> GSM1022356 1 0.000 0.933 1.000 0.000 0.000
#> GSM1022357 1 0.000 0.933 1.000 0.000 0.000
#> GSM1022358 1 0.000 0.933 1.000 0.000 0.000
#> GSM1022351 1 0.000 0.933 1.000 0.000 0.000
#> GSM1022352 1 0.000 0.933 1.000 0.000 0.000
#> GSM1022353 1 0.000 0.933 1.000 0.000 0.000
#> GSM1022354 1 0.000 0.933 1.000 0.000 0.000
#> GSM1022359 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022360 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022361 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022362 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022367 3 0.588 0.506 0.000 0.348 0.652
#> GSM1022368 3 0.455 0.753 0.000 0.200 0.800
#> GSM1022369 3 0.103 0.936 0.000 0.024 0.976
#> GSM1022370 3 0.556 0.601 0.000 0.300 0.700
#> GSM1022363 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022364 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022365 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022366 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022374 1 0.593 0.484 0.644 0.356 0.000
#> GSM1022375 1 0.568 0.564 0.684 0.316 0.000
#> GSM1022376 1 0.455 0.741 0.800 0.200 0.000
#> GSM1022371 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022372 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022373 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022377 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022378 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022379 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022380 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022385 3 0.000 0.954 0.000 0.000 1.000
#> GSM1022386 3 0.000 0.954 0.000 0.000 1.000
#> GSM1022387 3 0.000 0.954 0.000 0.000 1.000
#> GSM1022388 3 0.000 0.954 0.000 0.000 1.000
#> GSM1022381 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022382 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022383 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022384 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022393 1 0.000 0.933 1.000 0.000 0.000
#> GSM1022394 1 0.000 0.933 1.000 0.000 0.000
#> GSM1022395 1 0.000 0.933 1.000 0.000 0.000
#> GSM1022396 1 0.000 0.933 1.000 0.000 0.000
#> GSM1022389 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022390 1 0.610 0.397 0.608 0.392 0.000
#> GSM1022391 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022392 1 0.573 0.546 0.676 0.324 0.000
#> GSM1022397 3 0.000 0.954 0.000 0.000 1.000
#> GSM1022398 3 0.000 0.954 0.000 0.000 1.000
#> GSM1022399 3 0.000 0.954 0.000 0.000 1.000
#> GSM1022400 3 0.000 0.954 0.000 0.000 1.000
#> GSM1022401 1 0.000 0.933 1.000 0.000 0.000
#> GSM1022402 1 0.000 0.933 1.000 0.000 0.000
#> GSM1022403 1 0.000 0.933 1.000 0.000 0.000
#> GSM1022404 1 0.000 0.933 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1022325 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022326 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022327 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022331 3 0.0000 0.953 0.000 0.000 1.000 0.000
#> GSM1022332 3 0.0000 0.953 0.000 0.000 1.000 0.000
#> GSM1022333 3 0.0000 0.953 0.000 0.000 1.000 0.000
#> GSM1022328 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022329 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022330 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022337 1 0.0000 0.869 1.000 0.000 0.000 0.000
#> GSM1022338 1 0.0000 0.869 1.000 0.000 0.000 0.000
#> GSM1022339 1 0.0000 0.869 1.000 0.000 0.000 0.000
#> GSM1022334 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022335 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022336 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022340 1 0.3688 0.869 0.792 0.000 0.000 0.208
#> GSM1022341 1 0.3688 0.869 0.792 0.000 0.000 0.208
#> GSM1022342 1 0.3688 0.869 0.792 0.000 0.000 0.208
#> GSM1022343 1 0.3688 0.869 0.792 0.000 0.000 0.208
#> GSM1022347 3 0.0000 0.953 0.000 0.000 1.000 0.000
#> GSM1022348 3 0.0000 0.953 0.000 0.000 1.000 0.000
#> GSM1022349 3 0.0000 0.953 0.000 0.000 1.000 0.000
#> GSM1022350 3 0.0000 0.953 0.000 0.000 1.000 0.000
#> GSM1022344 3 0.0000 0.953 0.000 0.000 1.000 0.000
#> GSM1022345 3 0.0000 0.953 0.000 0.000 1.000 0.000
#> GSM1022346 3 0.0000 0.953 0.000 0.000 1.000 0.000
#> GSM1022355 1 0.3688 0.869 0.792 0.000 0.000 0.208
#> GSM1022356 1 0.3688 0.869 0.792 0.000 0.000 0.208
#> GSM1022357 1 0.3688 0.869 0.792 0.000 0.000 0.208
#> GSM1022358 1 0.3688 0.869 0.792 0.000 0.000 0.208
#> GSM1022351 1 0.3688 0.869 0.792 0.000 0.000 0.208
#> GSM1022352 1 0.3688 0.869 0.792 0.000 0.000 0.208
#> GSM1022353 1 0.3688 0.869 0.792 0.000 0.000 0.208
#> GSM1022354 1 0.3688 0.869 0.792 0.000 0.000 0.208
#> GSM1022359 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022360 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022361 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022362 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022367 3 0.4661 0.510 0.000 0.348 0.652 0.000
#> GSM1022368 3 0.3610 0.753 0.000 0.200 0.800 0.000
#> GSM1022369 3 0.0817 0.933 0.000 0.024 0.976 0.000
#> GSM1022370 3 0.4406 0.603 0.000 0.300 0.700 0.000
#> GSM1022363 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022364 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022365 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022366 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022374 1 0.4697 0.409 0.644 0.356 0.000 0.000
#> GSM1022375 1 0.4500 0.496 0.684 0.316 0.000 0.000
#> GSM1022376 1 0.3610 0.689 0.800 0.200 0.000 0.000
#> GSM1022371 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022372 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022373 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022377 4 0.3688 1.000 0.000 0.208 0.000 0.792
#> GSM1022378 4 0.3688 1.000 0.000 0.208 0.000 0.792
#> GSM1022379 4 0.3688 1.000 0.000 0.208 0.000 0.792
#> GSM1022380 4 0.3688 1.000 0.000 0.208 0.000 0.792
#> GSM1022385 3 0.0000 0.953 0.000 0.000 1.000 0.000
#> GSM1022386 3 0.0000 0.953 0.000 0.000 1.000 0.000
#> GSM1022387 3 0.0000 0.953 0.000 0.000 1.000 0.000
#> GSM1022388 3 0.0000 0.953 0.000 0.000 1.000 0.000
#> GSM1022381 4 0.3688 1.000 0.000 0.208 0.000 0.792
#> GSM1022382 4 0.3688 1.000 0.000 0.208 0.000 0.792
#> GSM1022383 4 0.3688 1.000 0.000 0.208 0.000 0.792
#> GSM1022384 4 0.3688 1.000 0.000 0.208 0.000 0.792
#> GSM1022393 1 0.0000 0.869 1.000 0.000 0.000 0.000
#> GSM1022394 1 0.0000 0.869 1.000 0.000 0.000 0.000
#> GSM1022395 1 0.0000 0.869 1.000 0.000 0.000 0.000
#> GSM1022396 1 0.0000 0.869 1.000 0.000 0.000 0.000
#> GSM1022389 4 0.3688 1.000 0.000 0.208 0.000 0.792
#> GSM1022390 4 0.3688 1.000 0.000 0.208 0.000 0.792
#> GSM1022391 4 0.3688 1.000 0.000 0.208 0.000 0.792
#> GSM1022392 4 0.3688 1.000 0.000 0.208 0.000 0.792
#> GSM1022397 3 0.0000 0.953 0.000 0.000 1.000 0.000
#> GSM1022398 3 0.0000 0.953 0.000 0.000 1.000 0.000
#> GSM1022399 3 0.0000 0.953 0.000 0.000 1.000 0.000
#> GSM1022400 3 0.0000 0.953 0.000 0.000 1.000 0.000
#> GSM1022401 1 0.0000 0.869 1.000 0.000 0.000 0.000
#> GSM1022402 1 0.0000 0.869 1.000 0.000 0.000 0.000
#> GSM1022403 1 0.0000 0.869 1.000 0.000 0.000 0.000
#> GSM1022404 1 0.0000 0.869 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
#> GSM1022325 2 0.0000 0.9524 0.000 1.000 0.000 0.000 0.000
#> GSM1022326 2 0.0000 0.9524 0.000 1.000 0.000 0.000 0.000
#> GSM1022327 2 0.0000 0.9524 0.000 1.000 0.000 0.000 0.000
#> GSM1022331 3 0.3210 0.7368 0.000 0.000 0.788 0.000 0.212
#> GSM1022332 3 0.3210 0.7368 0.000 0.000 0.788 0.000 0.212
#> GSM1022333 3 0.3210 0.7368 0.000 0.000 0.788 0.000 0.212
#> GSM1022328 2 0.0000 0.9524 0.000 1.000 0.000 0.000 0.000
#> GSM1022329 2 0.0000 0.9524 0.000 1.000 0.000 0.000 0.000
#> GSM1022330 2 0.0000 0.9524 0.000 1.000 0.000 0.000 0.000
#> GSM1022337 5 0.3210 0.6280 0.212 0.000 0.000 0.000 0.788
#> GSM1022338 5 0.3210 0.6280 0.212 0.000 0.000 0.000 0.788
#> GSM1022339 5 0.3210 0.6280 0.212 0.000 0.000 0.000 0.788
#> GSM1022334 2 0.0000 0.9524 0.000 1.000 0.000 0.000 0.000
#> GSM1022335 2 0.0000 0.9524 0.000 1.000 0.000 0.000 0.000
#> GSM1022336 2 0.0000 0.9524 0.000 1.000 0.000 0.000 0.000
#> GSM1022340 1 0.0000 0.8903 1.000 0.000 0.000 0.000 0.000
#> GSM1022341 1 0.0000 0.8903 1.000 0.000 0.000 0.000 0.000
#> GSM1022342 1 0.0000 0.8903 1.000 0.000 0.000 0.000 0.000
#> GSM1022343 1 0.0000 0.8903 1.000 0.000 0.000 0.000 0.000
#> GSM1022347 3 0.0000 0.9198 0.000 0.000 1.000 0.000 0.000
#> GSM1022348 3 0.0000 0.9198 0.000 0.000 1.000 0.000 0.000
#> GSM1022349 3 0.0000 0.9198 0.000 0.000 1.000 0.000 0.000
#> GSM1022350 3 0.0000 0.9198 0.000 0.000 1.000 0.000 0.000
#> GSM1022344 3 0.0963 0.8961 0.036 0.000 0.964 0.000 0.000
#> GSM1022345 3 0.0963 0.8961 0.036 0.000 0.964 0.000 0.000
#> GSM1022346 3 0.0963 0.8961 0.036 0.000 0.964 0.000 0.000
#> GSM1022355 1 0.0000 0.8903 1.000 0.000 0.000 0.000 0.000
#> GSM1022356 1 0.0000 0.8903 1.000 0.000 0.000 0.000 0.000
#> GSM1022357 1 0.0000 0.8903 1.000 0.000 0.000 0.000 0.000
#> GSM1022358 1 0.0000 0.8903 1.000 0.000 0.000 0.000 0.000
#> GSM1022351 1 0.0000 0.8903 1.000 0.000 0.000 0.000 0.000
#> GSM1022352 1 0.0000 0.8903 1.000 0.000 0.000 0.000 0.000
#> GSM1022353 1 0.0000 0.8903 1.000 0.000 0.000 0.000 0.000
#> GSM1022354 1 0.0000 0.8903 1.000 0.000 0.000 0.000 0.000
#> GSM1022359 2 0.0000 0.9524 0.000 1.000 0.000 0.000 0.000
#> GSM1022360 2 0.0000 0.9524 0.000 1.000 0.000 0.000 0.000
#> GSM1022361 2 0.0000 0.9524 0.000 1.000 0.000 0.000 0.000
#> GSM1022362 2 0.0000 0.9524 0.000 1.000 0.000 0.000 0.000
#> GSM1022367 5 0.4990 0.1159 0.000 0.000 0.384 0.036 0.580
#> GSM1022368 5 0.5010 0.0971 0.000 0.000 0.392 0.036 0.572
#> GSM1022369 3 0.5111 0.1372 0.000 0.000 0.500 0.036 0.464
#> GSM1022370 5 0.5010 0.0971 0.000 0.000 0.392 0.036 0.572
#> GSM1022363 2 0.4119 0.7517 0.000 0.752 0.000 0.036 0.212
#> GSM1022364 2 0.4119 0.7517 0.000 0.752 0.000 0.036 0.212
#> GSM1022365 2 0.4119 0.7517 0.000 0.752 0.000 0.036 0.212
#> GSM1022366 2 0.3064 0.8471 0.000 0.856 0.000 0.036 0.108
#> GSM1022374 5 0.3848 0.6514 0.172 0.040 0.000 0.000 0.788
#> GSM1022375 5 0.3848 0.6514 0.172 0.040 0.000 0.000 0.788
#> GSM1022376 5 0.3848 0.6514 0.172 0.040 0.000 0.000 0.788
#> GSM1022371 2 0.0000 0.9524 0.000 1.000 0.000 0.000 0.000
#> GSM1022372 2 0.0000 0.9524 0.000 1.000 0.000 0.000 0.000
#> GSM1022373 2 0.0000 0.9524 0.000 1.000 0.000 0.000 0.000
#> GSM1022377 4 0.0963 0.9159 0.000 0.036 0.000 0.964 0.000
#> GSM1022378 4 0.0963 0.9159 0.000 0.036 0.000 0.964 0.000
#> GSM1022379 4 0.0963 0.9159 0.000 0.036 0.000 0.964 0.000
#> GSM1022380 4 0.0963 0.9159 0.000 0.036 0.000 0.964 0.000
#> GSM1022385 3 0.0000 0.9198 0.000 0.000 1.000 0.000 0.000
#> GSM1022386 3 0.0000 0.9198 0.000 0.000 1.000 0.000 0.000
#> GSM1022387 3 0.0000 0.9198 0.000 0.000 1.000 0.000 0.000
#> GSM1022388 3 0.0000 0.9198 0.000 0.000 1.000 0.000 0.000
#> GSM1022381 4 0.0000 0.9046 0.000 0.000 0.000 1.000 0.000
#> GSM1022382 4 0.0000 0.9046 0.000 0.000 0.000 1.000 0.000
#> GSM1022383 4 0.0000 0.9046 0.000 0.000 0.000 1.000 0.000
#> GSM1022384 4 0.0000 0.9046 0.000 0.000 0.000 1.000 0.000
#> GSM1022393 1 0.3177 0.8172 0.792 0.000 0.000 0.000 0.208
#> GSM1022394 1 0.3177 0.8172 0.792 0.000 0.000 0.000 0.208
#> GSM1022395 1 0.3177 0.8172 0.792 0.000 0.000 0.000 0.208
#> GSM1022396 1 0.3177 0.8172 0.792 0.000 0.000 0.000 0.208
#> GSM1022389 4 0.2966 0.8434 0.000 0.184 0.000 0.816 0.000
#> GSM1022390 4 0.2929 0.8477 0.000 0.180 0.000 0.820 0.000
#> GSM1022391 4 0.2813 0.8582 0.000 0.168 0.000 0.832 0.000
#> GSM1022392 4 0.2813 0.8582 0.000 0.168 0.000 0.832 0.000
#> GSM1022397 3 0.0000 0.9198 0.000 0.000 1.000 0.000 0.000
#> GSM1022398 3 0.0000 0.9198 0.000 0.000 1.000 0.000 0.000
#> GSM1022399 3 0.0000 0.9198 0.000 0.000 1.000 0.000 0.000
#> GSM1022400 3 0.0000 0.9198 0.000 0.000 1.000 0.000 0.000
#> GSM1022401 1 0.3177 0.8172 0.792 0.000 0.000 0.000 0.208
#> GSM1022402 1 0.3177 0.8172 0.792 0.000 0.000 0.000 0.208
#> GSM1022403 1 0.3177 0.8172 0.792 0.000 0.000 0.000 0.208
#> GSM1022404 1 0.3177 0.8172 0.792 0.000 0.000 0.000 0.208
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1022325 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022326 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022327 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022331 6 0.285 0.752 0.000 0.000 0.208 0.000 0.000 0.792
#> GSM1022332 6 0.297 0.738 0.000 0.000 0.224 0.000 0.000 0.776
#> GSM1022333 6 0.285 0.752 0.000 0.000 0.208 0.000 0.000 0.792
#> GSM1022328 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022329 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022330 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022337 5 0.000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1022338 5 0.000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1022339 5 0.000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1022334 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022335 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022336 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022340 1 0.000 0.879 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022341 1 0.000 0.879 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022342 1 0.000 0.879 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022343 1 0.000 0.879 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022347 3 0.000 0.949 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022348 3 0.000 0.949 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022349 3 0.000 0.949 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022350 3 0.000 0.949 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022344 3 0.276 0.781 0.196 0.000 0.804 0.000 0.000 0.000
#> GSM1022345 3 0.276 0.781 0.196 0.000 0.804 0.000 0.000 0.000
#> GSM1022346 3 0.276 0.781 0.196 0.000 0.804 0.000 0.000 0.000
#> GSM1022355 1 0.000 0.879 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022356 1 0.000 0.879 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022357 1 0.000 0.879 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022358 1 0.000 0.879 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022351 1 0.000 0.879 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022352 1 0.000 0.879 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022353 1 0.000 0.879 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022354 1 0.000 0.879 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022359 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022360 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022361 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022362 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022367 6 0.000 0.865 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1022368 6 0.000 0.865 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1022369 6 0.000 0.865 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1022370 6 0.000 0.865 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1022363 6 0.000 0.865 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1022364 6 0.000 0.865 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1022365 6 0.000 0.865 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1022366 6 0.383 0.186 0.000 0.440 0.000 0.000 0.000 0.560
#> GSM1022374 5 0.000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1022375 5 0.000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1022376 5 0.000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1022371 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022372 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022373 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022377 4 0.000 0.921 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022378 4 0.000 0.921 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022379 4 0.000 0.921 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022380 4 0.000 0.921 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022385 3 0.000 0.949 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022386 3 0.000 0.949 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022387 3 0.000 0.949 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022388 3 0.000 0.949 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022381 4 0.000 0.921 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022382 4 0.000 0.921 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022383 4 0.000 0.921 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022384 4 0.000 0.921 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022393 1 0.310 0.789 0.756 0.000 0.000 0.000 0.244 0.000
#> GSM1022394 1 0.310 0.789 0.756 0.000 0.000 0.000 0.244 0.000
#> GSM1022395 1 0.310 0.789 0.756 0.000 0.000 0.000 0.244 0.000
#> GSM1022396 1 0.310 0.789 0.756 0.000 0.000 0.000 0.244 0.000
#> GSM1022389 4 0.263 0.827 0.000 0.180 0.000 0.820 0.000 0.000
#> GSM1022390 4 0.263 0.827 0.000 0.180 0.000 0.820 0.000 0.000
#> GSM1022391 4 0.249 0.841 0.000 0.164 0.000 0.836 0.000 0.000
#> GSM1022392 4 0.249 0.841 0.000 0.164 0.000 0.836 0.000 0.000
#> GSM1022397 3 0.000 0.949 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022398 3 0.000 0.949 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022399 3 0.000 0.949 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022400 3 0.000 0.949 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022401 1 0.310 0.789 0.756 0.000 0.000 0.000 0.244 0.000
#> GSM1022402 1 0.310 0.789 0.756 0.000 0.000 0.000 0.244 0.000
#> GSM1022403 1 0.310 0.789 0.756 0.000 0.000 0.000 0.244 0.000
#> GSM1022404 1 0.310 0.789 0.756 0.000 0.000 0.000 0.244 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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n protocol(p) cell.type(p) k
#> SD:pam 74 1.36e-06 6.10e-07 2
#> SD:pam 78 1.82e-10 2.94e-10 3
#> SD:pam 78 2.64e-15 5.77e-10 4
#> SD:pam 76 2.03e-19 2.15e-09 5
#> SD:pam 79 6.42e-28 6.93e-08 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 31589 rows and 80 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.339 0.812 0.865 0.3636 0.724 0.724
#> 3 3 0.685 0.740 0.880 0.8322 0.478 0.335
#> 4 4 0.633 0.670 0.820 0.0848 0.767 0.434
#> 5 5 0.817 0.798 0.888 0.0917 0.923 0.716
#> 6 6 0.864 0.774 0.882 0.0371 0.939 0.727
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM1022325 2 0.584 0.915 0.140 0.860
#> GSM1022326 2 0.625 0.893 0.156 0.844
#> GSM1022327 2 0.416 0.969 0.084 0.916
#> GSM1022331 1 0.946 0.690 0.636 0.364
#> GSM1022332 1 0.946 0.690 0.636 0.364
#> GSM1022333 1 0.946 0.690 0.636 0.364
#> GSM1022328 2 0.469 0.959 0.100 0.900
#> GSM1022329 2 0.416 0.969 0.084 0.916
#> GSM1022330 2 0.388 0.968 0.076 0.924
#> GSM1022337 1 0.494 0.792 0.892 0.108
#> GSM1022338 1 0.494 0.792 0.892 0.108
#> GSM1022339 1 0.494 0.792 0.892 0.108
#> GSM1022334 2 0.430 0.968 0.088 0.912
#> GSM1022335 2 0.430 0.968 0.088 0.912
#> GSM1022336 2 0.402 0.968 0.080 0.920
#> GSM1022340 1 0.118 0.834 0.984 0.016
#> GSM1022341 1 0.118 0.834 0.984 0.016
#> GSM1022342 1 0.118 0.834 0.984 0.016
#> GSM1022343 1 0.118 0.834 0.984 0.016
#> GSM1022347 1 0.814 0.766 0.748 0.252
#> GSM1022348 1 0.814 0.766 0.748 0.252
#> GSM1022349 1 0.814 0.766 0.748 0.252
#> GSM1022350 1 0.814 0.766 0.748 0.252
#> GSM1022344 1 0.814 0.766 0.748 0.252
#> GSM1022345 1 0.814 0.766 0.748 0.252
#> GSM1022346 1 0.814 0.766 0.748 0.252
#> GSM1022355 1 0.000 0.834 1.000 0.000
#> GSM1022356 1 0.000 0.834 1.000 0.000
#> GSM1022357 1 0.000 0.834 1.000 0.000
#> GSM1022358 1 0.000 0.834 1.000 0.000
#> GSM1022351 1 0.000 0.834 1.000 0.000
#> GSM1022352 1 0.000 0.834 1.000 0.000
#> GSM1022353 1 0.000 0.834 1.000 0.000
#> GSM1022354 1 0.000 0.834 1.000 0.000
#> GSM1022359 2 0.311 0.954 0.056 0.944
#> GSM1022360 2 0.327 0.959 0.060 0.940
#> GSM1022361 2 0.343 0.961 0.064 0.936
#> GSM1022362 2 0.327 0.959 0.060 0.940
#> GSM1022367 1 0.946 0.690 0.636 0.364
#> GSM1022368 1 0.946 0.690 0.636 0.364
#> GSM1022369 1 0.946 0.690 0.636 0.364
#> GSM1022370 1 0.946 0.690 0.636 0.364
#> GSM1022363 1 0.971 0.664 0.600 0.400
#> GSM1022364 1 0.971 0.664 0.600 0.400
#> GSM1022365 1 0.971 0.664 0.600 0.400
#> GSM1022366 1 0.971 0.664 0.600 0.400
#> GSM1022374 1 0.494 0.792 0.892 0.108
#> GSM1022375 1 0.494 0.792 0.892 0.108
#> GSM1022376 1 0.494 0.792 0.892 0.108
#> GSM1022371 1 0.706 0.724 0.808 0.192
#> GSM1022372 1 0.706 0.724 0.808 0.192
#> GSM1022373 1 0.706 0.724 0.808 0.192
#> GSM1022377 1 0.242 0.827 0.960 0.040
#> GSM1022378 1 0.242 0.827 0.960 0.040
#> GSM1022379 1 0.242 0.827 0.960 0.040
#> GSM1022380 1 0.242 0.827 0.960 0.040
#> GSM1022385 1 0.814 0.766 0.748 0.252
#> GSM1022386 1 0.814 0.766 0.748 0.252
#> GSM1022387 1 0.814 0.766 0.748 0.252
#> GSM1022388 1 0.814 0.766 0.748 0.252
#> GSM1022381 1 0.343 0.831 0.936 0.064
#> GSM1022382 1 0.343 0.831 0.936 0.064
#> GSM1022383 1 0.343 0.831 0.936 0.064
#> GSM1022384 1 0.343 0.831 0.936 0.064
#> GSM1022393 1 0.000 0.834 1.000 0.000
#> GSM1022394 1 0.000 0.834 1.000 0.000
#> GSM1022395 1 0.000 0.834 1.000 0.000
#> GSM1022396 1 0.000 0.834 1.000 0.000
#> GSM1022389 1 0.242 0.827 0.960 0.040
#> GSM1022390 1 0.242 0.827 0.960 0.040
#> GSM1022391 1 0.242 0.827 0.960 0.040
#> GSM1022392 1 0.242 0.827 0.960 0.040
#> GSM1022397 1 0.814 0.766 0.748 0.252
#> GSM1022398 1 0.814 0.766 0.748 0.252
#> GSM1022399 1 0.814 0.766 0.748 0.252
#> GSM1022400 1 0.814 0.766 0.748 0.252
#> GSM1022401 1 0.000 0.834 1.000 0.000
#> GSM1022402 1 0.000 0.834 1.000 0.000
#> GSM1022403 1 0.000 0.834 1.000 0.000
#> GSM1022404 1 0.000 0.834 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1022325 2 0.0000 0.828 0.000 1.000 0.000
#> GSM1022326 2 0.0000 0.828 0.000 1.000 0.000
#> GSM1022327 2 0.0000 0.828 0.000 1.000 0.000
#> GSM1022331 3 0.6090 0.601 0.020 0.264 0.716
#> GSM1022332 3 0.6090 0.601 0.020 0.264 0.716
#> GSM1022333 3 0.6090 0.601 0.020 0.264 0.716
#> GSM1022328 2 0.0000 0.828 0.000 1.000 0.000
#> GSM1022329 2 0.0000 0.828 0.000 1.000 0.000
#> GSM1022330 2 0.0000 0.828 0.000 1.000 0.000
#> GSM1022337 1 0.0000 0.928 1.000 0.000 0.000
#> GSM1022338 1 0.0000 0.928 1.000 0.000 0.000
#> GSM1022339 1 0.0000 0.928 1.000 0.000 0.000
#> GSM1022334 2 0.0000 0.828 0.000 1.000 0.000
#> GSM1022335 2 0.0000 0.828 0.000 1.000 0.000
#> GSM1022336 2 0.0000 0.828 0.000 1.000 0.000
#> GSM1022340 3 0.6225 0.332 0.432 0.000 0.568
#> GSM1022341 3 0.6225 0.332 0.432 0.000 0.568
#> GSM1022342 3 0.6225 0.332 0.432 0.000 0.568
#> GSM1022343 3 0.6225 0.332 0.432 0.000 0.568
#> GSM1022347 3 0.0000 0.793 0.000 0.000 1.000
#> GSM1022348 3 0.0000 0.793 0.000 0.000 1.000
#> GSM1022349 3 0.0000 0.793 0.000 0.000 1.000
#> GSM1022350 3 0.0000 0.793 0.000 0.000 1.000
#> GSM1022344 3 0.2165 0.765 0.064 0.000 0.936
#> GSM1022345 3 0.2165 0.765 0.064 0.000 0.936
#> GSM1022346 3 0.2165 0.765 0.064 0.000 0.936
#> GSM1022355 1 0.0000 0.928 1.000 0.000 0.000
#> GSM1022356 1 0.0000 0.928 1.000 0.000 0.000
#> GSM1022357 1 0.0000 0.928 1.000 0.000 0.000
#> GSM1022358 1 0.0000 0.928 1.000 0.000 0.000
#> GSM1022351 1 0.0000 0.928 1.000 0.000 0.000
#> GSM1022352 1 0.0000 0.928 1.000 0.000 0.000
#> GSM1022353 1 0.0000 0.928 1.000 0.000 0.000
#> GSM1022354 1 0.0000 0.928 1.000 0.000 0.000
#> GSM1022359 2 0.0000 0.828 0.000 1.000 0.000
#> GSM1022360 2 0.0000 0.828 0.000 1.000 0.000
#> GSM1022361 2 0.0000 0.828 0.000 1.000 0.000
#> GSM1022362 2 0.0000 0.828 0.000 1.000 0.000
#> GSM1022367 3 0.6865 0.458 0.020 0.384 0.596
#> GSM1022368 3 0.6865 0.458 0.020 0.384 0.596
#> GSM1022369 3 0.6865 0.458 0.020 0.384 0.596
#> GSM1022370 3 0.6865 0.458 0.020 0.384 0.596
#> GSM1022363 2 0.0892 0.822 0.020 0.980 0.000
#> GSM1022364 2 0.0892 0.822 0.020 0.980 0.000
#> GSM1022365 2 0.0892 0.822 0.020 0.980 0.000
#> GSM1022366 2 0.0892 0.822 0.020 0.980 0.000
#> GSM1022374 1 0.0000 0.928 1.000 0.000 0.000
#> GSM1022375 1 0.0000 0.928 1.000 0.000 0.000
#> GSM1022376 1 0.0000 0.928 1.000 0.000 0.000
#> GSM1022371 2 0.6553 0.443 0.324 0.656 0.020
#> GSM1022372 2 0.6553 0.443 0.324 0.656 0.020
#> GSM1022373 2 0.6553 0.443 0.324 0.656 0.020
#> GSM1022377 2 0.7233 0.622 0.064 0.672 0.264
#> GSM1022378 2 0.7233 0.622 0.064 0.672 0.264
#> GSM1022379 2 0.7233 0.622 0.064 0.672 0.264
#> GSM1022380 2 0.7233 0.622 0.064 0.672 0.264
#> GSM1022385 3 0.0000 0.793 0.000 0.000 1.000
#> GSM1022386 3 0.0000 0.793 0.000 0.000 1.000
#> GSM1022387 3 0.0000 0.793 0.000 0.000 1.000
#> GSM1022388 3 0.0000 0.793 0.000 0.000 1.000
#> GSM1022381 2 0.7233 0.622 0.064 0.672 0.264
#> GSM1022382 2 0.7233 0.622 0.064 0.672 0.264
#> GSM1022383 2 0.7233 0.622 0.064 0.672 0.264
#> GSM1022384 2 0.7233 0.622 0.064 0.672 0.264
#> GSM1022393 1 0.0000 0.928 1.000 0.000 0.000
#> GSM1022394 1 0.0000 0.928 1.000 0.000 0.000
#> GSM1022395 1 0.0000 0.928 1.000 0.000 0.000
#> GSM1022396 1 0.0000 0.928 1.000 0.000 0.000
#> GSM1022389 1 0.7037 0.419 0.636 0.328 0.036
#> GSM1022390 1 0.7037 0.419 0.636 0.328 0.036
#> GSM1022391 1 0.7037 0.419 0.636 0.328 0.036
#> GSM1022392 1 0.7037 0.419 0.636 0.328 0.036
#> GSM1022397 3 0.0000 0.793 0.000 0.000 1.000
#> GSM1022398 3 0.0000 0.793 0.000 0.000 1.000
#> GSM1022399 3 0.0000 0.793 0.000 0.000 1.000
#> GSM1022400 3 0.0000 0.793 0.000 0.000 1.000
#> GSM1022401 1 0.0000 0.928 1.000 0.000 0.000
#> GSM1022402 1 0.0000 0.928 1.000 0.000 0.000
#> GSM1022403 1 0.0000 0.928 1.000 0.000 0.000
#> GSM1022404 1 0.0000 0.928 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1022325 2 0.0000 0.9173 0.000 1.000 0.000 0.000
#> GSM1022326 2 0.0000 0.9173 0.000 1.000 0.000 0.000
#> GSM1022327 2 0.0000 0.9173 0.000 1.000 0.000 0.000
#> GSM1022331 1 0.7856 0.2794 0.420 0.004 0.224 0.352
#> GSM1022332 1 0.7856 0.2794 0.420 0.004 0.224 0.352
#> GSM1022333 1 0.7856 0.2794 0.420 0.004 0.224 0.352
#> GSM1022328 2 0.0000 0.9173 0.000 1.000 0.000 0.000
#> GSM1022329 2 0.0000 0.9173 0.000 1.000 0.000 0.000
#> GSM1022330 2 0.0000 0.9173 0.000 1.000 0.000 0.000
#> GSM1022337 1 0.4382 0.4222 0.704 0.000 0.000 0.296
#> GSM1022338 1 0.4382 0.4222 0.704 0.000 0.000 0.296
#> GSM1022339 1 0.4382 0.4222 0.704 0.000 0.000 0.296
#> GSM1022334 2 0.0000 0.9173 0.000 1.000 0.000 0.000
#> GSM1022335 2 0.0000 0.9173 0.000 1.000 0.000 0.000
#> GSM1022336 2 0.0000 0.9173 0.000 1.000 0.000 0.000
#> GSM1022340 4 0.4719 0.7431 0.180 0.000 0.048 0.772
#> GSM1022341 4 0.4719 0.7431 0.180 0.000 0.048 0.772
#> GSM1022342 4 0.4719 0.7431 0.180 0.000 0.048 0.772
#> GSM1022343 4 0.4719 0.7431 0.180 0.000 0.048 0.772
#> GSM1022347 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM1022348 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM1022349 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM1022350 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM1022344 4 0.4955 0.7634 0.144 0.000 0.084 0.772
#> GSM1022345 4 0.4955 0.7634 0.144 0.000 0.084 0.772
#> GSM1022346 4 0.4955 0.7634 0.144 0.000 0.084 0.772
#> GSM1022355 1 0.4992 0.0408 0.524 0.000 0.000 0.476
#> GSM1022356 1 0.4992 0.0408 0.524 0.000 0.000 0.476
#> GSM1022357 1 0.4992 0.0408 0.524 0.000 0.000 0.476
#> GSM1022358 1 0.4992 0.0408 0.524 0.000 0.000 0.476
#> GSM1022351 1 0.4992 0.0408 0.524 0.000 0.000 0.476
#> GSM1022352 1 0.4992 0.0408 0.524 0.000 0.000 0.476
#> GSM1022353 1 0.4992 0.0408 0.524 0.000 0.000 0.476
#> GSM1022354 1 0.4992 0.0408 0.524 0.000 0.000 0.476
#> GSM1022359 2 0.0000 0.9173 0.000 1.000 0.000 0.000
#> GSM1022360 2 0.0000 0.9173 0.000 1.000 0.000 0.000
#> GSM1022361 2 0.0000 0.9173 0.000 1.000 0.000 0.000
#> GSM1022362 2 0.0000 0.9173 0.000 1.000 0.000 0.000
#> GSM1022367 1 0.8933 0.3053 0.420 0.072 0.200 0.308
#> GSM1022368 1 0.8933 0.3053 0.420 0.072 0.200 0.308
#> GSM1022369 1 0.8933 0.3053 0.420 0.072 0.200 0.308
#> GSM1022370 1 0.8933 0.3053 0.420 0.072 0.200 0.308
#> GSM1022363 2 0.5416 0.6095 0.048 0.692 0.000 0.260
#> GSM1022364 2 0.5416 0.6095 0.048 0.692 0.000 0.260
#> GSM1022365 2 0.5416 0.6095 0.048 0.692 0.000 0.260
#> GSM1022366 2 0.5416 0.6095 0.048 0.692 0.000 0.260
#> GSM1022374 1 0.4382 0.4222 0.704 0.000 0.000 0.296
#> GSM1022375 1 0.4382 0.4222 0.704 0.000 0.000 0.296
#> GSM1022376 1 0.4382 0.4222 0.704 0.000 0.000 0.296
#> GSM1022371 2 0.0469 0.9116 0.000 0.988 0.000 0.012
#> GSM1022372 2 0.0469 0.9116 0.000 0.988 0.000 0.012
#> GSM1022373 2 0.0469 0.9116 0.000 0.988 0.000 0.012
#> GSM1022377 4 0.0469 0.8399 0.000 0.000 0.012 0.988
#> GSM1022378 4 0.0469 0.8399 0.000 0.000 0.012 0.988
#> GSM1022379 4 0.0469 0.8399 0.000 0.000 0.012 0.988
#> GSM1022380 4 0.0469 0.8399 0.000 0.000 0.012 0.988
#> GSM1022385 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM1022386 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM1022387 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM1022388 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM1022381 4 0.0469 0.8399 0.000 0.000 0.012 0.988
#> GSM1022382 4 0.0469 0.8399 0.000 0.000 0.012 0.988
#> GSM1022383 4 0.0469 0.8399 0.000 0.000 0.012 0.988
#> GSM1022384 4 0.0469 0.8399 0.000 0.000 0.012 0.988
#> GSM1022393 1 0.1389 0.5241 0.952 0.000 0.000 0.048
#> GSM1022394 1 0.1389 0.5241 0.952 0.000 0.000 0.048
#> GSM1022395 1 0.1389 0.5241 0.952 0.000 0.000 0.048
#> GSM1022396 1 0.1389 0.5241 0.952 0.000 0.000 0.048
#> GSM1022389 4 0.1716 0.8423 0.064 0.000 0.000 0.936
#> GSM1022390 4 0.1716 0.8423 0.064 0.000 0.000 0.936
#> GSM1022391 4 0.1716 0.8423 0.064 0.000 0.000 0.936
#> GSM1022392 4 0.1716 0.8423 0.064 0.000 0.000 0.936
#> GSM1022397 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM1022398 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM1022399 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM1022400 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM1022401 1 0.1389 0.5241 0.952 0.000 0.000 0.048
#> GSM1022402 1 0.1389 0.5241 0.952 0.000 0.000 0.048
#> GSM1022403 1 0.1389 0.5241 0.952 0.000 0.000 0.048
#> GSM1022404 1 0.1389 0.5241 0.952 0.000 0.000 0.048
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1022325 2 0.000 0.941 0.000 1.000 0.000 0.000 0.000
#> GSM1022326 2 0.000 0.941 0.000 1.000 0.000 0.000 0.000
#> GSM1022327 2 0.000 0.941 0.000 1.000 0.000 0.000 0.000
#> GSM1022331 5 0.424 0.783 0.428 0.000 0.000 0.000 0.572
#> GSM1022332 5 0.424 0.783 0.428 0.000 0.000 0.000 0.572
#> GSM1022333 5 0.424 0.783 0.428 0.000 0.000 0.000 0.572
#> GSM1022328 2 0.000 0.941 0.000 1.000 0.000 0.000 0.000
#> GSM1022329 2 0.000 0.941 0.000 1.000 0.000 0.000 0.000
#> GSM1022330 2 0.000 0.941 0.000 1.000 0.000 0.000 0.000
#> GSM1022337 5 0.000 0.697 0.000 0.000 0.000 0.000 1.000
#> GSM1022338 5 0.000 0.697 0.000 0.000 0.000 0.000 1.000
#> GSM1022339 5 0.000 0.697 0.000 0.000 0.000 0.000 1.000
#> GSM1022334 2 0.000 0.941 0.000 1.000 0.000 0.000 0.000
#> GSM1022335 2 0.000 0.941 0.000 1.000 0.000 0.000 0.000
#> GSM1022336 2 0.000 0.941 0.000 1.000 0.000 0.000 0.000
#> GSM1022340 4 0.323 0.785 0.196 0.000 0.004 0.800 0.000
#> GSM1022341 4 0.323 0.785 0.196 0.000 0.004 0.800 0.000
#> GSM1022342 4 0.323 0.785 0.196 0.000 0.004 0.800 0.000
#> GSM1022343 4 0.323 0.785 0.196 0.000 0.004 0.800 0.000
#> GSM1022347 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022348 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022349 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022350 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022344 4 0.452 0.779 0.164 0.000 0.088 0.748 0.000
#> GSM1022345 4 0.452 0.779 0.164 0.000 0.088 0.748 0.000
#> GSM1022346 4 0.452 0.779 0.164 0.000 0.088 0.748 0.000
#> GSM1022355 1 0.424 0.413 0.572 0.000 0.000 0.428 0.000
#> GSM1022356 1 0.424 0.413 0.572 0.000 0.000 0.428 0.000
#> GSM1022357 1 0.424 0.413 0.572 0.000 0.000 0.428 0.000
#> GSM1022358 1 0.424 0.413 0.572 0.000 0.000 0.428 0.000
#> GSM1022351 4 0.311 0.781 0.200 0.000 0.000 0.800 0.000
#> GSM1022352 1 0.424 0.413 0.572 0.000 0.000 0.428 0.000
#> GSM1022353 1 0.424 0.413 0.572 0.000 0.000 0.428 0.000
#> GSM1022354 1 0.424 0.413 0.572 0.000 0.000 0.428 0.000
#> GSM1022359 2 0.000 0.941 0.000 1.000 0.000 0.000 0.000
#> GSM1022360 2 0.000 0.941 0.000 1.000 0.000 0.000 0.000
#> GSM1022361 2 0.000 0.941 0.000 1.000 0.000 0.000 0.000
#> GSM1022362 2 0.000 0.941 0.000 1.000 0.000 0.000 0.000
#> GSM1022367 5 0.424 0.783 0.428 0.000 0.000 0.000 0.572
#> GSM1022368 5 0.424 0.783 0.428 0.000 0.000 0.000 0.572
#> GSM1022369 5 0.424 0.783 0.428 0.000 0.000 0.000 0.572
#> GSM1022370 5 0.424 0.783 0.428 0.000 0.000 0.000 0.572
#> GSM1022363 2 0.437 0.699 0.052 0.740 0.000 0.000 0.208
#> GSM1022364 2 0.437 0.699 0.052 0.740 0.000 0.000 0.208
#> GSM1022365 2 0.437 0.699 0.052 0.740 0.000 0.000 0.208
#> GSM1022366 2 0.437 0.699 0.052 0.740 0.000 0.000 0.208
#> GSM1022374 5 0.000 0.697 0.000 0.000 0.000 0.000 1.000
#> GSM1022375 5 0.000 0.697 0.000 0.000 0.000 0.000 1.000
#> GSM1022376 5 0.000 0.697 0.000 0.000 0.000 0.000 1.000
#> GSM1022371 2 0.000 0.941 0.000 1.000 0.000 0.000 0.000
#> GSM1022372 2 0.000 0.941 0.000 1.000 0.000 0.000 0.000
#> GSM1022373 2 0.000 0.941 0.000 1.000 0.000 0.000 0.000
#> GSM1022377 4 0.029 0.841 0.008 0.000 0.000 0.992 0.000
#> GSM1022378 4 0.029 0.841 0.008 0.000 0.000 0.992 0.000
#> GSM1022379 4 0.029 0.841 0.008 0.000 0.000 0.992 0.000
#> GSM1022380 4 0.029 0.841 0.008 0.000 0.000 0.992 0.000
#> GSM1022385 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022386 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022387 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022388 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022381 4 0.141 0.821 0.044 0.008 0.000 0.948 0.000
#> GSM1022382 4 0.141 0.821 0.044 0.008 0.000 0.948 0.000
#> GSM1022383 4 0.141 0.821 0.044 0.008 0.000 0.948 0.000
#> GSM1022384 4 0.141 0.821 0.044 0.008 0.000 0.948 0.000
#> GSM1022393 1 0.424 0.639 0.572 0.000 0.000 0.000 0.428
#> GSM1022394 1 0.424 0.639 0.572 0.000 0.000 0.000 0.428
#> GSM1022395 1 0.424 0.639 0.572 0.000 0.000 0.000 0.428
#> GSM1022396 1 0.424 0.639 0.572 0.000 0.000 0.000 0.428
#> GSM1022389 4 0.173 0.853 0.080 0.000 0.000 0.920 0.000
#> GSM1022390 4 0.173 0.853 0.080 0.000 0.000 0.920 0.000
#> GSM1022391 4 0.173 0.853 0.080 0.000 0.000 0.920 0.000
#> GSM1022392 4 0.173 0.853 0.080 0.000 0.000 0.920 0.000
#> GSM1022397 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022398 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022399 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022400 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022401 1 0.424 0.639 0.572 0.000 0.000 0.000 0.428
#> GSM1022402 1 0.424 0.639 0.572 0.000 0.000 0.000 0.428
#> GSM1022403 1 0.424 0.639 0.572 0.000 0.000 0.000 0.428
#> GSM1022404 1 0.424 0.639 0.572 0.000 0.000 0.000 0.428
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1022325 2 0.000 0.9456 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022326 2 0.000 0.9456 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022327 2 0.000 0.9456 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022331 6 0.000 1.0000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1022332 6 0.000 1.0000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1022333 6 0.000 1.0000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1022328 2 0.000 0.9456 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022329 2 0.000 0.9456 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022330 2 0.000 0.9456 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022337 5 0.000 1.0000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1022338 5 0.000 1.0000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1022339 5 0.000 1.0000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1022334 2 0.000 0.9456 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022335 2 0.000 0.9456 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022336 2 0.000 0.9456 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022340 1 0.382 -0.0497 0.564 0.000 0.000 0.436 0.000 0.000
#> GSM1022341 1 0.382 -0.0497 0.564 0.000 0.000 0.436 0.000 0.000
#> GSM1022342 1 0.382 -0.0497 0.564 0.000 0.000 0.436 0.000 0.000
#> GSM1022343 1 0.382 -0.0497 0.564 0.000 0.000 0.436 0.000 0.000
#> GSM1022347 3 0.000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022348 3 0.000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022349 3 0.000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022350 3 0.000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022344 4 0.586 0.2361 0.368 0.000 0.196 0.436 0.000 0.000
#> GSM1022345 4 0.586 0.2361 0.368 0.000 0.196 0.436 0.000 0.000
#> GSM1022346 4 0.586 0.2361 0.368 0.000 0.196 0.436 0.000 0.000
#> GSM1022355 1 0.133 0.6439 0.936 0.000 0.000 0.064 0.000 0.000
#> GSM1022356 1 0.133 0.6439 0.936 0.000 0.000 0.064 0.000 0.000
#> GSM1022357 1 0.133 0.6439 0.936 0.000 0.000 0.064 0.000 0.000
#> GSM1022358 1 0.133 0.6439 0.936 0.000 0.000 0.064 0.000 0.000
#> GSM1022351 1 0.150 0.6338 0.924 0.000 0.000 0.076 0.000 0.000
#> GSM1022352 1 0.133 0.6439 0.936 0.000 0.000 0.064 0.000 0.000
#> GSM1022353 1 0.133 0.6439 0.936 0.000 0.000 0.064 0.000 0.000
#> GSM1022354 1 0.133 0.6439 0.936 0.000 0.000 0.064 0.000 0.000
#> GSM1022359 2 0.000 0.9456 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022360 2 0.000 0.9456 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022361 2 0.000 0.9456 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022362 2 0.000 0.9456 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022367 6 0.000 1.0000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1022368 6 0.000 1.0000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1022369 6 0.000 1.0000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1022370 6 0.000 1.0000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1022363 2 0.310 0.7282 0.000 0.756 0.000 0.000 0.000 0.244
#> GSM1022364 2 0.310 0.7282 0.000 0.756 0.000 0.000 0.000 0.244
#> GSM1022365 2 0.310 0.7282 0.000 0.756 0.000 0.000 0.000 0.244
#> GSM1022366 2 0.310 0.7282 0.000 0.756 0.000 0.000 0.000 0.244
#> GSM1022374 5 0.000 1.0000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1022375 5 0.000 1.0000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1022376 5 0.000 1.0000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1022371 2 0.000 0.9456 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022372 2 0.000 0.9456 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022373 2 0.000 0.9456 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022377 4 0.000 0.8241 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022378 4 0.000 0.8241 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022379 4 0.000 0.8241 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022380 4 0.000 0.8241 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022385 3 0.000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022386 3 0.000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022387 3 0.000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022388 3 0.000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022381 4 0.000 0.8241 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022382 4 0.000 0.8241 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022383 4 0.000 0.8241 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022384 4 0.000 0.8241 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022393 1 0.366 0.4386 0.636 0.000 0.000 0.000 0.364 0.000
#> GSM1022394 1 0.366 0.4386 0.636 0.000 0.000 0.000 0.364 0.000
#> GSM1022395 1 0.366 0.4386 0.636 0.000 0.000 0.000 0.364 0.000
#> GSM1022396 1 0.366 0.4386 0.636 0.000 0.000 0.000 0.364 0.000
#> GSM1022389 4 0.205 0.7816 0.120 0.000 0.000 0.880 0.000 0.000
#> GSM1022390 4 0.205 0.7816 0.120 0.000 0.000 0.880 0.000 0.000
#> GSM1022391 4 0.205 0.7816 0.120 0.000 0.000 0.880 0.000 0.000
#> GSM1022392 4 0.205 0.7816 0.120 0.000 0.000 0.880 0.000 0.000
#> GSM1022397 3 0.000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022398 3 0.000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022399 3 0.000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022400 3 0.000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022401 1 0.366 0.4386 0.636 0.000 0.000 0.000 0.364 0.000
#> GSM1022402 1 0.366 0.4386 0.636 0.000 0.000 0.000 0.364 0.000
#> GSM1022403 1 0.366 0.4386 0.636 0.000 0.000 0.000 0.364 0.000
#> GSM1022404 1 0.366 0.4386 0.636 0.000 0.000 0.000 0.364 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 protocol(p) cell.type(p) k
#> SD:mclust 80 1.22e-07 8.06e-04 2
#> SD:mclust 65 3.09e-11 7.96e-10 3
#> SD:mclust 59 5.91e-12 9.61e-13 4
#> SD:mclust 73 1.85e-14 5.28e-15 5
#> SD:mclust 65 3.84e-21 5.29e-11 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 31589 rows and 80 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.948 0.927 0.972 0.5050 0.494 0.494
#> 3 3 0.927 0.922 0.969 0.3228 0.710 0.480
#> 4 4 0.988 0.955 0.966 0.0880 0.893 0.701
#> 5 5 0.892 0.866 0.906 0.0619 0.930 0.749
#> 6 6 0.837 0.773 0.855 0.0393 0.981 0.914
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
#> GSM1022325 2 0.0000 0.9668 0.000 1.000
#> GSM1022326 2 0.0000 0.9668 0.000 1.000
#> GSM1022327 2 0.0000 0.9668 0.000 1.000
#> GSM1022331 1 0.0000 0.9740 1.000 0.000
#> GSM1022332 1 0.0000 0.9740 1.000 0.000
#> GSM1022333 1 0.0000 0.9740 1.000 0.000
#> GSM1022328 2 0.0000 0.9668 0.000 1.000
#> GSM1022329 2 0.0000 0.9668 0.000 1.000
#> GSM1022330 2 0.0000 0.9668 0.000 1.000
#> GSM1022337 2 0.6247 0.8088 0.156 0.844
#> GSM1022338 2 0.6343 0.8040 0.160 0.840
#> GSM1022339 2 0.3114 0.9180 0.056 0.944
#> GSM1022334 2 0.0000 0.9668 0.000 1.000
#> GSM1022335 2 0.0000 0.9668 0.000 1.000
#> GSM1022336 2 0.0000 0.9668 0.000 1.000
#> GSM1022340 1 0.0376 0.9727 0.996 0.004
#> GSM1022341 1 0.0000 0.9740 1.000 0.000
#> GSM1022342 1 0.0000 0.9740 1.000 0.000
#> GSM1022343 1 0.0000 0.9740 1.000 0.000
#> GSM1022347 1 0.0000 0.9740 1.000 0.000
#> GSM1022348 1 0.0000 0.9740 1.000 0.000
#> GSM1022349 1 0.0000 0.9740 1.000 0.000
#> GSM1022350 1 0.0000 0.9740 1.000 0.000
#> GSM1022344 1 0.0000 0.9740 1.000 0.000
#> GSM1022345 1 0.0000 0.9740 1.000 0.000
#> GSM1022346 1 0.0000 0.9740 1.000 0.000
#> GSM1022355 1 0.0376 0.9727 0.996 0.004
#> GSM1022356 1 0.0938 0.9668 0.988 0.012
#> GSM1022357 1 0.0376 0.9727 0.996 0.004
#> GSM1022358 1 0.0938 0.9668 0.988 0.012
#> GSM1022351 1 0.0672 0.9699 0.992 0.008
#> GSM1022352 1 0.0376 0.9727 0.996 0.004
#> GSM1022353 1 0.0000 0.9740 1.000 0.000
#> GSM1022354 1 0.0376 0.9727 0.996 0.004
#> GSM1022359 2 0.0000 0.9668 0.000 1.000
#> GSM1022360 2 0.0000 0.9668 0.000 1.000
#> GSM1022361 2 0.0000 0.9668 0.000 1.000
#> GSM1022362 2 0.0000 0.9668 0.000 1.000
#> GSM1022367 2 0.9661 0.3605 0.392 0.608
#> GSM1022368 1 0.9988 0.0267 0.520 0.480
#> GSM1022369 1 0.9608 0.3407 0.616 0.384
#> GSM1022370 2 0.9963 0.1412 0.464 0.536
#> GSM1022363 2 0.0000 0.9668 0.000 1.000
#> GSM1022364 2 0.0000 0.9668 0.000 1.000
#> GSM1022365 2 0.0000 0.9668 0.000 1.000
#> GSM1022366 2 0.0000 0.9668 0.000 1.000
#> GSM1022374 2 0.0672 0.9610 0.008 0.992
#> GSM1022375 2 0.0376 0.9640 0.004 0.996
#> GSM1022376 2 0.0672 0.9610 0.008 0.992
#> GSM1022371 2 0.0000 0.9668 0.000 1.000
#> GSM1022372 2 0.0000 0.9668 0.000 1.000
#> GSM1022373 2 0.0000 0.9668 0.000 1.000
#> GSM1022377 2 0.0000 0.9668 0.000 1.000
#> GSM1022378 2 0.0000 0.9668 0.000 1.000
#> GSM1022379 2 0.0000 0.9668 0.000 1.000
#> GSM1022380 2 0.0000 0.9668 0.000 1.000
#> GSM1022385 1 0.0000 0.9740 1.000 0.000
#> GSM1022386 1 0.0000 0.9740 1.000 0.000
#> GSM1022387 1 0.0000 0.9740 1.000 0.000
#> GSM1022388 1 0.0000 0.9740 1.000 0.000
#> GSM1022381 2 0.0000 0.9668 0.000 1.000
#> GSM1022382 2 0.0000 0.9668 0.000 1.000
#> GSM1022383 2 0.0000 0.9668 0.000 1.000
#> GSM1022384 2 0.0000 0.9668 0.000 1.000
#> GSM1022393 1 0.1184 0.9631 0.984 0.016
#> GSM1022394 1 0.0000 0.9740 1.000 0.000
#> GSM1022395 1 0.0938 0.9668 0.988 0.012
#> GSM1022396 1 0.0376 0.9727 0.996 0.004
#> GSM1022389 2 0.0000 0.9668 0.000 1.000
#> GSM1022390 2 0.0000 0.9668 0.000 1.000
#> GSM1022391 2 0.0000 0.9668 0.000 1.000
#> GSM1022392 2 0.0000 0.9668 0.000 1.000
#> GSM1022397 1 0.0000 0.9740 1.000 0.000
#> GSM1022398 1 0.0000 0.9740 1.000 0.000
#> GSM1022399 1 0.0000 0.9740 1.000 0.000
#> GSM1022400 1 0.0000 0.9740 1.000 0.000
#> GSM1022401 1 0.0000 0.9740 1.000 0.000
#> GSM1022402 1 0.0376 0.9727 0.996 0.004
#> GSM1022403 1 0.0376 0.9727 0.996 0.004
#> GSM1022404 1 0.0000 0.9740 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1022325 2 0.0000 0.9693 0.000 1.000 0.000
#> GSM1022326 2 0.0000 0.9693 0.000 1.000 0.000
#> GSM1022327 2 0.0000 0.9693 0.000 1.000 0.000
#> GSM1022331 3 0.0000 0.9805 0.000 0.000 1.000
#> GSM1022332 3 0.0000 0.9805 0.000 0.000 1.000
#> GSM1022333 3 0.0000 0.9805 0.000 0.000 1.000
#> GSM1022328 2 0.0000 0.9693 0.000 1.000 0.000
#> GSM1022329 2 0.0000 0.9693 0.000 1.000 0.000
#> GSM1022330 2 0.0000 0.9693 0.000 1.000 0.000
#> GSM1022337 1 0.0000 0.9485 1.000 0.000 0.000
#> GSM1022338 1 0.0000 0.9485 1.000 0.000 0.000
#> GSM1022339 1 0.0000 0.9485 1.000 0.000 0.000
#> GSM1022334 2 0.0000 0.9693 0.000 1.000 0.000
#> GSM1022335 2 0.0000 0.9693 0.000 1.000 0.000
#> GSM1022336 2 0.0000 0.9693 0.000 1.000 0.000
#> GSM1022340 1 0.0000 0.9485 1.000 0.000 0.000
#> GSM1022341 1 0.0000 0.9485 1.000 0.000 0.000
#> GSM1022342 1 0.0000 0.9485 1.000 0.000 0.000
#> GSM1022343 1 0.0000 0.9485 1.000 0.000 0.000
#> GSM1022347 3 0.0000 0.9805 0.000 0.000 1.000
#> GSM1022348 3 0.0000 0.9805 0.000 0.000 1.000
#> GSM1022349 3 0.0000 0.9805 0.000 0.000 1.000
#> GSM1022350 3 0.0000 0.9805 0.000 0.000 1.000
#> GSM1022344 3 0.0000 0.9805 0.000 0.000 1.000
#> GSM1022345 3 0.5810 0.4858 0.336 0.000 0.664
#> GSM1022346 3 0.2066 0.9219 0.060 0.000 0.940
#> GSM1022355 1 0.0000 0.9485 1.000 0.000 0.000
#> GSM1022356 1 0.0000 0.9485 1.000 0.000 0.000
#> GSM1022357 1 0.0000 0.9485 1.000 0.000 0.000
#> GSM1022358 1 0.0000 0.9485 1.000 0.000 0.000
#> GSM1022351 1 0.0000 0.9485 1.000 0.000 0.000
#> GSM1022352 1 0.0000 0.9485 1.000 0.000 0.000
#> GSM1022353 1 0.0000 0.9485 1.000 0.000 0.000
#> GSM1022354 1 0.0000 0.9485 1.000 0.000 0.000
#> GSM1022359 2 0.0000 0.9693 0.000 1.000 0.000
#> GSM1022360 2 0.0000 0.9693 0.000 1.000 0.000
#> GSM1022361 2 0.0000 0.9693 0.000 1.000 0.000
#> GSM1022362 2 0.0000 0.9693 0.000 1.000 0.000
#> GSM1022367 3 0.0000 0.9805 0.000 0.000 1.000
#> GSM1022368 3 0.0000 0.9805 0.000 0.000 1.000
#> GSM1022369 3 0.0000 0.9805 0.000 0.000 1.000
#> GSM1022370 3 0.0000 0.9805 0.000 0.000 1.000
#> GSM1022363 2 0.0000 0.9693 0.000 1.000 0.000
#> GSM1022364 2 0.0000 0.9693 0.000 1.000 0.000
#> GSM1022365 2 0.0000 0.9693 0.000 1.000 0.000
#> GSM1022366 2 0.0000 0.9693 0.000 1.000 0.000
#> GSM1022374 1 0.4654 0.7416 0.792 0.208 0.000
#> GSM1022375 1 0.4750 0.7307 0.784 0.216 0.000
#> GSM1022376 1 0.4291 0.7772 0.820 0.180 0.000
#> GSM1022371 2 0.0000 0.9693 0.000 1.000 0.000
#> GSM1022372 2 0.0000 0.9693 0.000 1.000 0.000
#> GSM1022373 2 0.0000 0.9693 0.000 1.000 0.000
#> GSM1022377 2 0.0000 0.9693 0.000 1.000 0.000
#> GSM1022378 2 0.0000 0.9693 0.000 1.000 0.000
#> GSM1022379 2 0.0000 0.9693 0.000 1.000 0.000
#> GSM1022380 2 0.0592 0.9578 0.012 0.988 0.000
#> GSM1022385 3 0.0000 0.9805 0.000 0.000 1.000
#> GSM1022386 3 0.0000 0.9805 0.000 0.000 1.000
#> GSM1022387 3 0.0000 0.9805 0.000 0.000 1.000
#> GSM1022388 3 0.0000 0.9805 0.000 0.000 1.000
#> GSM1022381 2 0.0000 0.9693 0.000 1.000 0.000
#> GSM1022382 2 0.0000 0.9693 0.000 1.000 0.000
#> GSM1022383 2 0.0000 0.9693 0.000 1.000 0.000
#> GSM1022384 2 0.0000 0.9693 0.000 1.000 0.000
#> GSM1022393 1 0.0000 0.9485 1.000 0.000 0.000
#> GSM1022394 1 0.0000 0.9485 1.000 0.000 0.000
#> GSM1022395 1 0.0000 0.9485 1.000 0.000 0.000
#> GSM1022396 1 0.0000 0.9485 1.000 0.000 0.000
#> GSM1022389 2 0.6302 0.0434 0.480 0.520 0.000
#> GSM1022390 1 0.5785 0.5021 0.668 0.332 0.000
#> GSM1022391 2 0.5859 0.4545 0.344 0.656 0.000
#> GSM1022392 1 0.5560 0.5697 0.700 0.300 0.000
#> GSM1022397 3 0.0000 0.9805 0.000 0.000 1.000
#> GSM1022398 3 0.0000 0.9805 0.000 0.000 1.000
#> GSM1022399 3 0.0000 0.9805 0.000 0.000 1.000
#> GSM1022400 3 0.0000 0.9805 0.000 0.000 1.000
#> GSM1022401 1 0.0000 0.9485 1.000 0.000 0.000
#> GSM1022402 1 0.0000 0.9485 1.000 0.000 0.000
#> GSM1022403 1 0.0000 0.9485 1.000 0.000 0.000
#> GSM1022404 1 0.0000 0.9485 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1022325 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM1022326 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM1022327 2 0.0469 0.971 0.012 0.988 0.000 0.000
#> GSM1022331 3 0.0000 0.985 0.000 0.000 1.000 0.000
#> GSM1022332 3 0.0000 0.985 0.000 0.000 1.000 0.000
#> GSM1022333 3 0.0000 0.985 0.000 0.000 1.000 0.000
#> GSM1022328 2 0.1022 0.968 0.032 0.968 0.000 0.000
#> GSM1022329 2 0.0592 0.971 0.016 0.984 0.000 0.000
#> GSM1022330 2 0.0592 0.971 0.016 0.984 0.000 0.000
#> GSM1022337 1 0.0336 0.927 0.992 0.000 0.000 0.008
#> GSM1022338 1 0.0336 0.927 0.992 0.000 0.000 0.008
#> GSM1022339 1 0.0000 0.922 1.000 0.000 0.000 0.000
#> GSM1022334 2 0.0336 0.970 0.008 0.992 0.000 0.000
#> GSM1022335 2 0.0469 0.971 0.012 0.988 0.000 0.000
#> GSM1022336 2 0.0469 0.971 0.012 0.988 0.000 0.000
#> GSM1022340 4 0.0188 0.973 0.004 0.000 0.000 0.996
#> GSM1022341 4 0.0188 0.973 0.004 0.000 0.000 0.996
#> GSM1022342 4 0.0188 0.973 0.004 0.000 0.000 0.996
#> GSM1022343 4 0.0188 0.973 0.004 0.000 0.000 0.996
#> GSM1022347 3 0.0000 0.985 0.000 0.000 1.000 0.000
#> GSM1022348 3 0.0000 0.985 0.000 0.000 1.000 0.000
#> GSM1022349 3 0.0000 0.985 0.000 0.000 1.000 0.000
#> GSM1022350 3 0.0000 0.985 0.000 0.000 1.000 0.000
#> GSM1022344 4 0.1867 0.922 0.000 0.000 0.072 0.928
#> GSM1022345 4 0.1389 0.944 0.000 0.000 0.048 0.952
#> GSM1022346 4 0.1637 0.934 0.000 0.000 0.060 0.940
#> GSM1022355 1 0.3444 0.865 0.816 0.000 0.000 0.184
#> GSM1022356 1 0.3172 0.887 0.840 0.000 0.000 0.160
#> GSM1022357 1 0.3528 0.856 0.808 0.000 0.000 0.192
#> GSM1022358 1 0.3219 0.884 0.836 0.000 0.000 0.164
#> GSM1022351 4 0.0469 0.971 0.012 0.000 0.000 0.988
#> GSM1022352 4 0.0469 0.971 0.012 0.000 0.000 0.988
#> GSM1022353 4 0.0469 0.971 0.012 0.000 0.000 0.988
#> GSM1022354 4 0.0592 0.968 0.016 0.000 0.000 0.984
#> GSM1022359 2 0.1302 0.965 0.044 0.956 0.000 0.000
#> GSM1022360 2 0.1302 0.965 0.044 0.956 0.000 0.000
#> GSM1022361 2 0.1302 0.965 0.044 0.956 0.000 0.000
#> GSM1022362 2 0.1302 0.965 0.044 0.956 0.000 0.000
#> GSM1022367 3 0.1743 0.943 0.056 0.000 0.940 0.004
#> GSM1022368 3 0.1743 0.943 0.056 0.000 0.940 0.004
#> GSM1022369 3 0.1743 0.943 0.056 0.000 0.940 0.004
#> GSM1022370 3 0.1743 0.943 0.056 0.000 0.940 0.004
#> GSM1022363 2 0.1743 0.959 0.056 0.940 0.000 0.004
#> GSM1022364 2 0.1743 0.959 0.056 0.940 0.000 0.004
#> GSM1022365 2 0.1743 0.959 0.056 0.940 0.000 0.004
#> GSM1022366 2 0.1743 0.959 0.056 0.940 0.000 0.004
#> GSM1022374 1 0.0000 0.922 1.000 0.000 0.000 0.000
#> GSM1022375 1 0.0000 0.922 1.000 0.000 0.000 0.000
#> GSM1022376 1 0.0000 0.922 1.000 0.000 0.000 0.000
#> GSM1022371 2 0.1557 0.960 0.056 0.944 0.000 0.000
#> GSM1022372 2 0.1474 0.962 0.052 0.948 0.000 0.000
#> GSM1022373 2 0.1557 0.960 0.056 0.944 0.000 0.000
#> GSM1022377 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM1022378 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM1022379 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM1022380 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM1022385 3 0.0000 0.985 0.000 0.000 1.000 0.000
#> GSM1022386 3 0.0000 0.985 0.000 0.000 1.000 0.000
#> GSM1022387 3 0.0000 0.985 0.000 0.000 1.000 0.000
#> GSM1022388 3 0.0000 0.985 0.000 0.000 1.000 0.000
#> GSM1022381 2 0.0707 0.961 0.000 0.980 0.000 0.020
#> GSM1022382 2 0.0707 0.961 0.000 0.980 0.000 0.020
#> GSM1022383 2 0.0817 0.959 0.000 0.976 0.000 0.024
#> GSM1022384 2 0.1389 0.942 0.000 0.952 0.000 0.048
#> GSM1022393 1 0.1792 0.944 0.932 0.000 0.000 0.068
#> GSM1022394 1 0.1867 0.943 0.928 0.000 0.000 0.072
#> GSM1022395 1 0.1792 0.944 0.932 0.000 0.000 0.068
#> GSM1022396 1 0.1792 0.944 0.932 0.000 0.000 0.068
#> GSM1022389 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM1022390 2 0.1940 0.917 0.000 0.924 0.000 0.076
#> GSM1022391 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM1022392 2 0.2814 0.854 0.000 0.868 0.000 0.132
#> GSM1022397 3 0.0000 0.985 0.000 0.000 1.000 0.000
#> GSM1022398 3 0.0000 0.985 0.000 0.000 1.000 0.000
#> GSM1022399 3 0.0000 0.985 0.000 0.000 1.000 0.000
#> GSM1022400 3 0.0000 0.985 0.000 0.000 1.000 0.000
#> GSM1022401 1 0.1792 0.944 0.932 0.000 0.000 0.068
#> GSM1022402 1 0.1792 0.944 0.932 0.000 0.000 0.068
#> GSM1022403 1 0.1792 0.944 0.932 0.000 0.000 0.068
#> GSM1022404 1 0.1792 0.944 0.932 0.000 0.000 0.068
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1022325 2 0.0000 0.889 0.000 1.000 0.000 0.000 0.000
#> GSM1022326 2 0.0000 0.889 0.000 1.000 0.000 0.000 0.000
#> GSM1022327 2 0.0000 0.889 0.000 1.000 0.000 0.000 0.000
#> GSM1022331 3 0.1121 0.961 0.000 0.000 0.956 0.044 0.000
#> GSM1022332 3 0.1043 0.962 0.000 0.000 0.960 0.040 0.000
#> GSM1022333 3 0.1197 0.959 0.000 0.000 0.952 0.048 0.000
#> GSM1022328 2 0.0000 0.889 0.000 1.000 0.000 0.000 0.000
#> GSM1022329 2 0.0000 0.889 0.000 1.000 0.000 0.000 0.000
#> GSM1022330 2 0.0000 0.889 0.000 1.000 0.000 0.000 0.000
#> GSM1022337 5 0.0162 0.930 0.000 0.000 0.000 0.004 0.996
#> GSM1022338 5 0.0162 0.930 0.000 0.000 0.000 0.004 0.996
#> GSM1022339 5 0.0162 0.930 0.000 0.000 0.000 0.004 0.996
#> GSM1022334 2 0.0162 0.886 0.000 0.996 0.000 0.004 0.000
#> GSM1022335 2 0.0162 0.886 0.000 0.996 0.000 0.004 0.000
#> GSM1022336 2 0.0000 0.889 0.000 1.000 0.000 0.000 0.000
#> GSM1022340 1 0.0000 0.996 1.000 0.000 0.000 0.000 0.000
#> GSM1022341 1 0.0000 0.996 1.000 0.000 0.000 0.000 0.000
#> GSM1022342 1 0.0000 0.996 1.000 0.000 0.000 0.000 0.000
#> GSM1022343 1 0.0000 0.996 1.000 0.000 0.000 0.000 0.000
#> GSM1022347 3 0.0000 0.974 0.000 0.000 1.000 0.000 0.000
#> GSM1022348 3 0.0000 0.974 0.000 0.000 1.000 0.000 0.000
#> GSM1022349 3 0.0000 0.974 0.000 0.000 1.000 0.000 0.000
#> GSM1022350 3 0.0000 0.974 0.000 0.000 1.000 0.000 0.000
#> GSM1022344 1 0.0703 0.975 0.976 0.000 0.024 0.000 0.000
#> GSM1022345 1 0.0162 0.993 0.996 0.000 0.004 0.000 0.000
#> GSM1022346 1 0.0290 0.990 0.992 0.000 0.008 0.000 0.000
#> GSM1022355 5 0.3508 0.694 0.252 0.000 0.000 0.000 0.748
#> GSM1022356 5 0.2424 0.829 0.132 0.000 0.000 0.000 0.868
#> GSM1022357 5 0.4242 0.353 0.428 0.000 0.000 0.000 0.572
#> GSM1022358 5 0.3876 0.596 0.316 0.000 0.000 0.000 0.684
#> GSM1022351 1 0.0000 0.996 1.000 0.000 0.000 0.000 0.000
#> GSM1022352 1 0.0000 0.996 1.000 0.000 0.000 0.000 0.000
#> GSM1022353 1 0.0000 0.996 1.000 0.000 0.000 0.000 0.000
#> GSM1022354 1 0.0000 0.996 1.000 0.000 0.000 0.000 0.000
#> GSM1022359 2 0.0162 0.887 0.000 0.996 0.000 0.004 0.000
#> GSM1022360 2 0.0162 0.887 0.000 0.996 0.000 0.004 0.000
#> GSM1022361 2 0.0162 0.887 0.000 0.996 0.000 0.004 0.000
#> GSM1022362 2 0.0162 0.887 0.000 0.996 0.000 0.004 0.000
#> GSM1022367 3 0.2708 0.918 0.000 0.044 0.884 0.072 0.000
#> GSM1022368 3 0.2473 0.928 0.000 0.032 0.896 0.072 0.000
#> GSM1022369 3 0.2208 0.936 0.000 0.020 0.908 0.072 0.000
#> GSM1022370 3 0.2708 0.918 0.000 0.044 0.884 0.072 0.000
#> GSM1022363 2 0.1478 0.820 0.000 0.936 0.000 0.064 0.000
#> GSM1022364 2 0.1410 0.825 0.000 0.940 0.000 0.060 0.000
#> GSM1022365 2 0.1478 0.820 0.000 0.936 0.000 0.064 0.000
#> GSM1022366 2 0.1410 0.825 0.000 0.940 0.000 0.060 0.000
#> GSM1022374 5 0.0324 0.927 0.000 0.004 0.000 0.004 0.992
#> GSM1022375 5 0.0324 0.927 0.000 0.004 0.000 0.004 0.992
#> GSM1022376 5 0.0162 0.930 0.000 0.000 0.000 0.004 0.996
#> GSM1022371 2 0.0000 0.889 0.000 1.000 0.000 0.000 0.000
#> GSM1022372 2 0.0000 0.889 0.000 1.000 0.000 0.000 0.000
#> GSM1022373 2 0.0000 0.889 0.000 1.000 0.000 0.000 0.000
#> GSM1022377 4 0.4302 0.863 0.000 0.480 0.000 0.520 0.000
#> GSM1022378 4 0.4446 0.869 0.004 0.476 0.000 0.520 0.000
#> GSM1022379 4 0.4446 0.869 0.004 0.476 0.000 0.520 0.000
#> GSM1022380 4 0.4555 0.872 0.008 0.472 0.000 0.520 0.000
#> GSM1022385 3 0.0000 0.974 0.000 0.000 1.000 0.000 0.000
#> GSM1022386 3 0.0000 0.974 0.000 0.000 1.000 0.000 0.000
#> GSM1022387 3 0.0000 0.974 0.000 0.000 1.000 0.000 0.000
#> GSM1022388 3 0.0000 0.974 0.000 0.000 1.000 0.000 0.000
#> GSM1022381 4 0.4630 0.902 0.016 0.396 0.000 0.588 0.000
#> GSM1022382 4 0.4707 0.901 0.020 0.392 0.000 0.588 0.000
#> GSM1022383 4 0.4748 0.897 0.016 0.384 0.004 0.596 0.000
#> GSM1022384 4 0.4714 0.885 0.016 0.372 0.004 0.608 0.000
#> GSM1022393 5 0.0000 0.930 0.000 0.000 0.000 0.000 1.000
#> GSM1022394 5 0.0000 0.930 0.000 0.000 0.000 0.000 1.000
#> GSM1022395 5 0.0000 0.930 0.000 0.000 0.000 0.000 1.000
#> GSM1022396 5 0.0000 0.930 0.000 0.000 0.000 0.000 1.000
#> GSM1022389 2 0.4655 -0.824 0.012 0.512 0.000 0.476 0.000
#> GSM1022390 4 0.5078 0.858 0.028 0.424 0.000 0.544 0.004
#> GSM1022391 2 0.4659 -0.853 0.012 0.496 0.000 0.492 0.000
#> GSM1022392 4 0.5118 0.858 0.036 0.376 0.000 0.584 0.004
#> GSM1022397 3 0.0000 0.974 0.000 0.000 1.000 0.000 0.000
#> GSM1022398 3 0.0000 0.974 0.000 0.000 1.000 0.000 0.000
#> GSM1022399 3 0.0000 0.974 0.000 0.000 1.000 0.000 0.000
#> GSM1022400 3 0.0000 0.974 0.000 0.000 1.000 0.000 0.000
#> GSM1022401 5 0.0000 0.930 0.000 0.000 0.000 0.000 1.000
#> GSM1022402 5 0.0000 0.930 0.000 0.000 0.000 0.000 1.000
#> GSM1022403 5 0.0000 0.930 0.000 0.000 0.000 0.000 1.000
#> GSM1022404 5 0.0000 0.930 0.000 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1022325 2 0.0547 0.7034 0.000 0.980 0.000 0.020 0.000 NA
#> GSM1022326 2 0.0458 0.7029 0.000 0.984 0.000 0.016 0.000 NA
#> GSM1022327 2 0.0632 0.7034 0.000 0.976 0.000 0.024 0.000 NA
#> GSM1022331 3 0.1501 0.8796 0.000 0.000 0.924 0.000 0.000 NA
#> GSM1022332 3 0.1327 0.8841 0.000 0.000 0.936 0.000 0.000 NA
#> GSM1022333 3 0.2048 0.8590 0.000 0.000 0.880 0.000 0.000 NA
#> GSM1022328 2 0.0508 0.7063 0.000 0.984 0.000 0.012 0.000 NA
#> GSM1022329 2 0.0622 0.7065 0.000 0.980 0.000 0.012 0.000 NA
#> GSM1022330 2 0.0806 0.7057 0.000 0.972 0.000 0.020 0.000 NA
#> GSM1022337 5 0.1204 0.8979 0.000 0.000 0.000 0.000 0.944 NA
#> GSM1022338 5 0.1204 0.8979 0.000 0.000 0.000 0.000 0.944 NA
#> GSM1022339 5 0.1204 0.8979 0.000 0.000 0.000 0.000 0.944 NA
#> GSM1022334 2 0.0405 0.7068 0.000 0.988 0.000 0.004 0.000 NA
#> GSM1022335 2 0.0520 0.7060 0.000 0.984 0.000 0.008 0.000 NA
#> GSM1022336 2 0.0520 0.7038 0.000 0.984 0.000 0.008 0.000 NA
#> GSM1022340 1 0.0260 0.9950 0.992 0.000 0.000 0.000 0.000 NA
#> GSM1022341 1 0.0260 0.9950 0.992 0.000 0.000 0.000 0.000 NA
#> GSM1022342 1 0.0260 0.9950 0.992 0.000 0.000 0.000 0.000 NA
#> GSM1022343 1 0.0260 0.9950 0.992 0.000 0.000 0.000 0.000 NA
#> GSM1022347 3 0.0291 0.8989 0.004 0.000 0.992 0.000 0.000 NA
#> GSM1022348 3 0.0000 0.8993 0.000 0.000 1.000 0.000 0.000 NA
#> GSM1022349 3 0.0291 0.8987 0.000 0.000 0.992 0.004 0.000 NA
#> GSM1022350 3 0.0291 0.8987 0.000 0.000 0.992 0.004 0.000 NA
#> GSM1022344 1 0.0000 0.9960 1.000 0.000 0.000 0.000 0.000 NA
#> GSM1022345 1 0.0000 0.9960 1.000 0.000 0.000 0.000 0.000 NA
#> GSM1022346 1 0.0000 0.9960 1.000 0.000 0.000 0.000 0.000 NA
#> GSM1022355 5 0.3636 0.5701 0.320 0.000 0.000 0.004 0.676 NA
#> GSM1022356 5 0.2320 0.8095 0.132 0.000 0.000 0.004 0.864 NA
#> GSM1022357 5 0.3923 0.3685 0.416 0.000 0.000 0.004 0.580 NA
#> GSM1022358 5 0.3769 0.5049 0.356 0.000 0.000 0.004 0.640 NA
#> GSM1022351 1 0.0146 0.9955 0.996 0.000 0.000 0.000 0.004 NA
#> GSM1022352 1 0.0146 0.9955 0.996 0.000 0.000 0.000 0.004 NA
#> GSM1022353 1 0.0146 0.9955 0.996 0.000 0.000 0.000 0.004 NA
#> GSM1022354 1 0.0146 0.9955 0.996 0.000 0.000 0.000 0.004 NA
#> GSM1022359 2 0.3394 0.5048 0.000 0.776 0.000 0.200 0.000 NA
#> GSM1022360 2 0.3460 0.4725 0.000 0.760 0.000 0.220 0.000 NA
#> GSM1022361 2 0.3190 0.4651 0.000 0.772 0.000 0.220 0.000 NA
#> GSM1022362 2 0.3541 0.4549 0.000 0.748 0.000 0.232 0.000 NA
#> GSM1022367 3 0.3950 0.6423 0.000 0.004 0.564 0.000 0.000 NA
#> GSM1022368 3 0.3782 0.6648 0.000 0.000 0.588 0.000 0.000 NA
#> GSM1022369 3 0.3765 0.6713 0.000 0.000 0.596 0.000 0.000 NA
#> GSM1022370 3 0.3797 0.6592 0.000 0.000 0.580 0.000 0.000 NA
#> GSM1022363 2 0.3930 0.4850 0.000 0.576 0.000 0.004 0.000 NA
#> GSM1022364 2 0.4018 0.4889 0.000 0.580 0.000 0.008 0.000 NA
#> GSM1022365 2 0.4018 0.4889 0.000 0.580 0.000 0.008 0.000 NA
#> GSM1022366 2 0.4018 0.4889 0.000 0.580 0.000 0.008 0.000 NA
#> GSM1022374 5 0.1327 0.8955 0.000 0.000 0.000 0.000 0.936 NA
#> GSM1022375 5 0.1327 0.8955 0.000 0.000 0.000 0.000 0.936 NA
#> GSM1022376 5 0.1327 0.8955 0.000 0.000 0.000 0.000 0.936 NA
#> GSM1022371 2 0.2070 0.6896 0.000 0.892 0.000 0.008 0.000 NA
#> GSM1022372 2 0.2070 0.6896 0.000 0.892 0.000 0.008 0.000 NA
#> GSM1022373 2 0.2070 0.6896 0.000 0.892 0.000 0.008 0.000 NA
#> GSM1022377 4 0.3615 0.9570 0.008 0.292 0.000 0.700 0.000 NA
#> GSM1022378 4 0.3615 0.9570 0.008 0.292 0.000 0.700 0.000 NA
#> GSM1022379 4 0.3595 0.9603 0.008 0.288 0.000 0.704 0.000 NA
#> GSM1022380 4 0.3575 0.9612 0.008 0.284 0.000 0.708 0.000 NA
#> GSM1022385 3 0.0260 0.8993 0.000 0.000 0.992 0.000 0.000 NA
#> GSM1022386 3 0.0260 0.8993 0.000 0.000 0.992 0.000 0.000 NA
#> GSM1022387 3 0.0260 0.8993 0.000 0.000 0.992 0.000 0.000 NA
#> GSM1022388 3 0.0260 0.8993 0.000 0.000 0.992 0.000 0.000 NA
#> GSM1022381 4 0.3398 0.9622 0.008 0.252 0.000 0.740 0.000 NA
#> GSM1022382 4 0.3398 0.9622 0.008 0.252 0.000 0.740 0.000 NA
#> GSM1022383 4 0.3373 0.9590 0.008 0.248 0.000 0.744 0.000 NA
#> GSM1022384 4 0.3298 0.9449 0.008 0.236 0.000 0.756 0.000 NA
#> GSM1022393 5 0.0146 0.9034 0.000 0.000 0.000 0.004 0.996 NA
#> GSM1022394 5 0.0146 0.9034 0.000 0.000 0.000 0.004 0.996 NA
#> GSM1022395 5 0.0000 0.9042 0.000 0.000 0.000 0.000 1.000 NA
#> GSM1022396 5 0.0146 0.9034 0.000 0.000 0.000 0.004 0.996 NA
#> GSM1022389 2 0.5056 0.0223 0.008 0.592 0.000 0.348 0.024 NA
#> GSM1022390 2 0.5423 0.0935 0.012 0.568 0.000 0.352 0.032 NA
#> GSM1022391 2 0.5051 0.0105 0.008 0.572 0.000 0.372 0.024 NA
#> GSM1022392 2 0.5480 -0.0293 0.008 0.528 0.000 0.392 0.032 NA
#> GSM1022397 3 0.0603 0.8962 0.000 0.000 0.980 0.004 0.000 NA
#> GSM1022398 3 0.0603 0.8962 0.000 0.000 0.980 0.004 0.000 NA
#> GSM1022399 3 0.0692 0.8949 0.000 0.000 0.976 0.004 0.000 NA
#> GSM1022400 3 0.0692 0.8949 0.000 0.000 0.976 0.004 0.000 NA
#> GSM1022401 5 0.0363 0.9041 0.000 0.000 0.000 0.000 0.988 NA
#> GSM1022402 5 0.0260 0.9043 0.000 0.000 0.000 0.000 0.992 NA
#> GSM1022403 5 0.0000 0.9042 0.000 0.000 0.000 0.000 1.000 NA
#> GSM1022404 5 0.0000 0.9042 0.000 0.000 0.000 0.000 1.000 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
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 protocol(p) cell.type(p) k
#> SD:NMF 76 6.05e-07 3.68e-06 2
#> SD:NMF 77 5.49e-11 2.79e-10 3
#> SD:NMF 80 5.59e-11 3.07e-17 4
#> SD:NMF 77 1.74e-15 7.52e-16 5
#> SD:NMF 68 7.13e-15 6.00e-14 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 31589 rows and 80 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.473 0.862 0.905 0.4713 0.495 0.495
#> 3 3 0.795 0.879 0.946 0.3681 0.862 0.721
#> 4 4 0.849 0.874 0.923 0.1130 0.939 0.830
#> 5 5 0.798 0.789 0.831 0.0524 0.981 0.936
#> 6 6 0.840 0.828 0.847 0.0515 0.949 0.820
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
#> GSM1022325 2 0.000 0.967 0.000 1.000
#> GSM1022326 2 0.000 0.967 0.000 1.000
#> GSM1022327 2 0.000 0.967 0.000 1.000
#> GSM1022331 1 0.000 0.811 1.000 0.000
#> GSM1022332 1 0.000 0.811 1.000 0.000
#> GSM1022333 1 0.000 0.811 1.000 0.000
#> GSM1022328 2 0.000 0.967 0.000 1.000
#> GSM1022329 2 0.000 0.967 0.000 1.000
#> GSM1022330 2 0.000 0.967 0.000 1.000
#> GSM1022337 2 0.625 0.786 0.156 0.844
#> GSM1022338 2 0.625 0.786 0.156 0.844
#> GSM1022339 2 0.625 0.786 0.156 0.844
#> GSM1022334 2 0.000 0.967 0.000 1.000
#> GSM1022335 2 0.000 0.967 0.000 1.000
#> GSM1022336 2 0.000 0.967 0.000 1.000
#> GSM1022340 1 0.714 0.827 0.804 0.196
#> GSM1022341 1 0.714 0.827 0.804 0.196
#> GSM1022342 1 0.714 0.827 0.804 0.196
#> GSM1022343 1 0.714 0.827 0.804 0.196
#> GSM1022347 1 0.000 0.811 1.000 0.000
#> GSM1022348 1 0.000 0.811 1.000 0.000
#> GSM1022349 1 0.000 0.811 1.000 0.000
#> GSM1022350 1 0.000 0.811 1.000 0.000
#> GSM1022344 1 0.671 0.829 0.824 0.176
#> GSM1022345 1 0.671 0.829 0.824 0.176
#> GSM1022346 1 0.671 0.829 0.824 0.176
#> GSM1022355 1 0.839 0.802 0.732 0.268
#> GSM1022356 1 0.839 0.802 0.732 0.268
#> GSM1022357 1 0.839 0.802 0.732 0.268
#> GSM1022358 1 0.839 0.802 0.732 0.268
#> GSM1022351 1 0.839 0.802 0.732 0.268
#> GSM1022352 1 0.839 0.802 0.732 0.268
#> GSM1022353 1 0.839 0.802 0.732 0.268
#> GSM1022354 1 0.839 0.802 0.732 0.268
#> GSM1022359 2 0.000 0.967 0.000 1.000
#> GSM1022360 2 0.000 0.967 0.000 1.000
#> GSM1022361 2 0.000 0.967 0.000 1.000
#> GSM1022362 2 0.000 0.967 0.000 1.000
#> GSM1022367 1 0.814 0.626 0.748 0.252
#> GSM1022368 1 0.814 0.626 0.748 0.252
#> GSM1022369 1 0.814 0.626 0.748 0.252
#> GSM1022370 1 0.814 0.626 0.748 0.252
#> GSM1022363 2 0.000 0.967 0.000 1.000
#> GSM1022364 2 0.000 0.967 0.000 1.000
#> GSM1022365 2 0.000 0.967 0.000 1.000
#> GSM1022366 2 0.000 0.967 0.000 1.000
#> GSM1022374 2 0.625 0.786 0.156 0.844
#> GSM1022375 2 0.625 0.786 0.156 0.844
#> GSM1022376 2 0.625 0.786 0.156 0.844
#> GSM1022371 2 0.000 0.967 0.000 1.000
#> GSM1022372 2 0.000 0.967 0.000 1.000
#> GSM1022373 2 0.000 0.967 0.000 1.000
#> GSM1022377 2 0.000 0.967 0.000 1.000
#> GSM1022378 2 0.000 0.967 0.000 1.000
#> GSM1022379 2 0.000 0.967 0.000 1.000
#> GSM1022380 2 0.000 0.967 0.000 1.000
#> GSM1022385 1 0.000 0.811 1.000 0.000
#> GSM1022386 1 0.000 0.811 1.000 0.000
#> GSM1022387 1 0.000 0.811 1.000 0.000
#> GSM1022388 1 0.000 0.811 1.000 0.000
#> GSM1022381 2 0.000 0.967 0.000 1.000
#> GSM1022382 2 0.000 0.967 0.000 1.000
#> GSM1022383 2 0.000 0.967 0.000 1.000
#> GSM1022384 2 0.000 0.967 0.000 1.000
#> GSM1022393 1 0.844 0.799 0.728 0.272
#> GSM1022394 1 0.844 0.799 0.728 0.272
#> GSM1022395 1 0.844 0.799 0.728 0.272
#> GSM1022396 1 0.844 0.799 0.728 0.272
#> GSM1022389 2 0.000 0.967 0.000 1.000
#> GSM1022390 2 0.000 0.967 0.000 1.000
#> GSM1022391 2 0.000 0.967 0.000 1.000
#> GSM1022392 2 0.000 0.967 0.000 1.000
#> GSM1022397 1 0.000 0.811 1.000 0.000
#> GSM1022398 1 0.000 0.811 1.000 0.000
#> GSM1022399 1 0.000 0.811 1.000 0.000
#> GSM1022400 1 0.000 0.811 1.000 0.000
#> GSM1022401 1 0.844 0.799 0.728 0.272
#> GSM1022402 1 0.844 0.799 0.728 0.272
#> GSM1022403 1 0.844 0.799 0.728 0.272
#> GSM1022404 1 0.844 0.799 0.728 0.272
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1022325 2 0.0000 0.921 0.000 1.000 0.000
#> GSM1022326 2 0.0000 0.921 0.000 1.000 0.000
#> GSM1022327 2 0.0000 0.921 0.000 1.000 0.000
#> GSM1022331 3 0.0000 0.932 0.000 0.000 1.000
#> GSM1022332 3 0.0000 0.932 0.000 0.000 1.000
#> GSM1022333 3 0.0000 0.932 0.000 0.000 1.000
#> GSM1022328 2 0.0000 0.921 0.000 1.000 0.000
#> GSM1022329 2 0.0000 0.921 0.000 1.000 0.000
#> GSM1022330 2 0.0000 0.921 0.000 1.000 0.000
#> GSM1022337 2 0.6215 0.371 0.428 0.572 0.000
#> GSM1022338 2 0.6215 0.371 0.428 0.572 0.000
#> GSM1022339 2 0.6215 0.371 0.428 0.572 0.000
#> GSM1022334 2 0.0000 0.921 0.000 1.000 0.000
#> GSM1022335 2 0.0000 0.921 0.000 1.000 0.000
#> GSM1022336 2 0.0000 0.921 0.000 1.000 0.000
#> GSM1022340 1 0.2711 0.922 0.912 0.000 0.088
#> GSM1022341 1 0.2711 0.922 0.912 0.000 0.088
#> GSM1022342 1 0.2711 0.922 0.912 0.000 0.088
#> GSM1022343 1 0.2711 0.922 0.912 0.000 0.088
#> GSM1022347 3 0.0000 0.932 0.000 0.000 1.000
#> GSM1022348 3 0.0000 0.932 0.000 0.000 1.000
#> GSM1022349 3 0.0000 0.932 0.000 0.000 1.000
#> GSM1022350 3 0.0000 0.932 0.000 0.000 1.000
#> GSM1022344 1 0.3192 0.900 0.888 0.000 0.112
#> GSM1022345 1 0.3192 0.900 0.888 0.000 0.112
#> GSM1022346 1 0.3192 0.900 0.888 0.000 0.112
#> GSM1022355 1 0.0237 0.965 0.996 0.000 0.004
#> GSM1022356 1 0.0237 0.965 0.996 0.000 0.004
#> GSM1022357 1 0.0237 0.965 0.996 0.000 0.004
#> GSM1022358 1 0.0237 0.965 0.996 0.000 0.004
#> GSM1022351 1 0.0237 0.965 0.996 0.000 0.004
#> GSM1022352 1 0.0237 0.965 0.996 0.000 0.004
#> GSM1022353 1 0.0237 0.965 0.996 0.000 0.004
#> GSM1022354 1 0.0237 0.965 0.996 0.000 0.004
#> GSM1022359 2 0.0000 0.921 0.000 1.000 0.000
#> GSM1022360 2 0.0000 0.921 0.000 1.000 0.000
#> GSM1022361 2 0.0000 0.921 0.000 1.000 0.000
#> GSM1022362 2 0.0000 0.921 0.000 1.000 0.000
#> GSM1022367 3 0.5138 0.707 0.000 0.252 0.748
#> GSM1022368 3 0.5138 0.707 0.000 0.252 0.748
#> GSM1022369 3 0.5138 0.707 0.000 0.252 0.748
#> GSM1022370 3 0.5138 0.707 0.000 0.252 0.748
#> GSM1022363 2 0.0000 0.921 0.000 1.000 0.000
#> GSM1022364 2 0.0000 0.921 0.000 1.000 0.000
#> GSM1022365 2 0.0000 0.921 0.000 1.000 0.000
#> GSM1022366 2 0.0000 0.921 0.000 1.000 0.000
#> GSM1022374 2 0.6215 0.371 0.428 0.572 0.000
#> GSM1022375 2 0.6215 0.371 0.428 0.572 0.000
#> GSM1022376 2 0.6215 0.371 0.428 0.572 0.000
#> GSM1022371 2 0.0000 0.921 0.000 1.000 0.000
#> GSM1022372 2 0.0000 0.921 0.000 1.000 0.000
#> GSM1022373 2 0.0000 0.921 0.000 1.000 0.000
#> GSM1022377 2 0.0000 0.921 0.000 1.000 0.000
#> GSM1022378 2 0.0000 0.921 0.000 1.000 0.000
#> GSM1022379 2 0.0000 0.921 0.000 1.000 0.000
#> GSM1022380 2 0.0000 0.921 0.000 1.000 0.000
#> GSM1022385 3 0.0000 0.932 0.000 0.000 1.000
#> GSM1022386 3 0.0000 0.932 0.000 0.000 1.000
#> GSM1022387 3 0.0000 0.932 0.000 0.000 1.000
#> GSM1022388 3 0.0000 0.932 0.000 0.000 1.000
#> GSM1022381 2 0.0000 0.921 0.000 1.000 0.000
#> GSM1022382 2 0.0000 0.921 0.000 1.000 0.000
#> GSM1022383 2 0.0000 0.921 0.000 1.000 0.000
#> GSM1022384 2 0.0000 0.921 0.000 1.000 0.000
#> GSM1022393 1 0.0000 0.964 1.000 0.000 0.000
#> GSM1022394 1 0.0000 0.964 1.000 0.000 0.000
#> GSM1022395 1 0.0000 0.964 1.000 0.000 0.000
#> GSM1022396 1 0.0000 0.964 1.000 0.000 0.000
#> GSM1022389 2 0.0000 0.921 0.000 1.000 0.000
#> GSM1022390 2 0.0000 0.921 0.000 1.000 0.000
#> GSM1022391 2 0.0000 0.921 0.000 1.000 0.000
#> GSM1022392 2 0.0000 0.921 0.000 1.000 0.000
#> GSM1022397 3 0.0000 0.932 0.000 0.000 1.000
#> GSM1022398 3 0.0000 0.932 0.000 0.000 1.000
#> GSM1022399 3 0.0000 0.932 0.000 0.000 1.000
#> GSM1022400 3 0.0000 0.932 0.000 0.000 1.000
#> GSM1022401 1 0.0000 0.964 1.000 0.000 0.000
#> GSM1022402 1 0.0000 0.964 1.000 0.000 0.000
#> GSM1022403 1 0.0000 0.964 1.000 0.000 0.000
#> GSM1022404 1 0.0000 0.964 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1022325 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM1022326 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM1022327 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM1022331 3 0.0817 0.923 0.000 0.000 0.976 0.024
#> GSM1022332 3 0.0817 0.923 0.000 0.000 0.976 0.024
#> GSM1022333 3 0.0817 0.923 0.000 0.000 0.976 0.024
#> GSM1022328 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM1022329 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM1022330 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM1022337 4 0.4925 1.000 0.428 0.000 0.000 0.572
#> GSM1022338 4 0.4925 1.000 0.428 0.000 0.000 0.572
#> GSM1022339 4 0.4925 1.000 0.428 0.000 0.000 0.572
#> GSM1022334 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM1022335 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM1022336 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM1022340 1 0.4866 0.787 0.596 0.000 0.000 0.404
#> GSM1022341 1 0.4866 0.787 0.596 0.000 0.000 0.404
#> GSM1022342 1 0.4866 0.787 0.596 0.000 0.000 0.404
#> GSM1022343 1 0.4866 0.787 0.596 0.000 0.000 0.404
#> GSM1022347 3 0.0000 0.932 0.000 0.000 1.000 0.000
#> GSM1022348 3 0.0000 0.932 0.000 0.000 1.000 0.000
#> GSM1022349 3 0.0000 0.932 0.000 0.000 1.000 0.000
#> GSM1022350 3 0.0000 0.932 0.000 0.000 1.000 0.000
#> GSM1022344 1 0.5592 0.771 0.572 0.000 0.024 0.404
#> GSM1022345 1 0.5592 0.771 0.572 0.000 0.024 0.404
#> GSM1022346 1 0.5592 0.771 0.572 0.000 0.024 0.404
#> GSM1022355 1 0.4500 0.812 0.684 0.000 0.000 0.316
#> GSM1022356 1 0.4500 0.812 0.684 0.000 0.000 0.316
#> GSM1022357 1 0.4500 0.812 0.684 0.000 0.000 0.316
#> GSM1022358 1 0.4500 0.812 0.684 0.000 0.000 0.316
#> GSM1022351 1 0.4500 0.812 0.684 0.000 0.000 0.316
#> GSM1022352 1 0.4500 0.812 0.684 0.000 0.000 0.316
#> GSM1022353 1 0.4500 0.812 0.684 0.000 0.000 0.316
#> GSM1022354 1 0.4500 0.812 0.684 0.000 0.000 0.316
#> GSM1022359 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM1022360 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM1022361 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM1022362 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM1022367 3 0.5213 0.712 0.000 0.052 0.724 0.224
#> GSM1022368 3 0.5213 0.712 0.000 0.052 0.724 0.224
#> GSM1022369 3 0.5213 0.712 0.000 0.052 0.724 0.224
#> GSM1022370 3 0.5213 0.712 0.000 0.052 0.724 0.224
#> GSM1022363 2 0.3610 0.770 0.000 0.800 0.000 0.200
#> GSM1022364 2 0.3610 0.770 0.000 0.800 0.000 0.200
#> GSM1022365 2 0.3610 0.770 0.000 0.800 0.000 0.200
#> GSM1022366 2 0.3610 0.770 0.000 0.800 0.000 0.200
#> GSM1022374 4 0.4925 1.000 0.428 0.000 0.000 0.572
#> GSM1022375 4 0.4925 1.000 0.428 0.000 0.000 0.572
#> GSM1022376 4 0.4925 1.000 0.428 0.000 0.000 0.572
#> GSM1022371 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM1022372 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM1022373 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM1022377 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM1022378 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM1022379 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM1022380 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM1022385 3 0.0000 0.932 0.000 0.000 1.000 0.000
#> GSM1022386 3 0.0000 0.932 0.000 0.000 1.000 0.000
#> GSM1022387 3 0.0000 0.932 0.000 0.000 1.000 0.000
#> GSM1022388 3 0.0000 0.932 0.000 0.000 1.000 0.000
#> GSM1022381 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM1022382 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM1022383 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM1022384 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM1022393 1 0.0000 0.601 1.000 0.000 0.000 0.000
#> GSM1022394 1 0.0000 0.601 1.000 0.000 0.000 0.000
#> GSM1022395 1 0.0000 0.601 1.000 0.000 0.000 0.000
#> GSM1022396 1 0.0000 0.601 1.000 0.000 0.000 0.000
#> GSM1022389 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM1022390 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM1022391 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM1022392 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM1022397 3 0.0000 0.932 0.000 0.000 1.000 0.000
#> GSM1022398 3 0.0000 0.932 0.000 0.000 1.000 0.000
#> GSM1022399 3 0.0000 0.932 0.000 0.000 1.000 0.000
#> GSM1022400 3 0.0000 0.932 0.000 0.000 1.000 0.000
#> GSM1022401 1 0.0000 0.601 1.000 0.000 0.000 0.000
#> GSM1022402 1 0.0000 0.601 1.000 0.000 0.000 0.000
#> GSM1022403 1 0.0000 0.601 1.000 0.000 0.000 0.000
#> GSM1022404 1 0.0000 0.601 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
#> GSM1022325 2 0.2471 0.8903 0.000 0.864 0.000 0.136 0.000
#> GSM1022326 2 0.2471 0.8903 0.000 0.864 0.000 0.136 0.000
#> GSM1022327 2 0.2471 0.8903 0.000 0.864 0.000 0.136 0.000
#> GSM1022331 3 0.3837 0.0474 0.000 0.000 0.692 0.308 0.000
#> GSM1022332 3 0.3837 0.0474 0.000 0.000 0.692 0.308 0.000
#> GSM1022333 3 0.3837 0.0474 0.000 0.000 0.692 0.308 0.000
#> GSM1022328 2 0.2471 0.8903 0.000 0.864 0.000 0.136 0.000
#> GSM1022329 2 0.2471 0.8903 0.000 0.864 0.000 0.136 0.000
#> GSM1022330 2 0.2471 0.8903 0.000 0.864 0.000 0.136 0.000
#> GSM1022337 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM1022338 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM1022339 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM1022334 2 0.2471 0.8903 0.000 0.864 0.000 0.136 0.000
#> GSM1022335 2 0.2471 0.8903 0.000 0.864 0.000 0.136 0.000
#> GSM1022336 2 0.2471 0.8903 0.000 0.864 0.000 0.136 0.000
#> GSM1022340 1 0.3707 0.6469 0.716 0.000 0.000 0.284 0.000
#> GSM1022341 1 0.3707 0.6469 0.716 0.000 0.000 0.284 0.000
#> GSM1022342 1 0.3707 0.6469 0.716 0.000 0.000 0.284 0.000
#> GSM1022343 1 0.3707 0.6469 0.716 0.000 0.000 0.284 0.000
#> GSM1022347 3 0.0000 0.8748 0.000 0.000 1.000 0.000 0.000
#> GSM1022348 3 0.0000 0.8748 0.000 0.000 1.000 0.000 0.000
#> GSM1022349 3 0.0000 0.8748 0.000 0.000 1.000 0.000 0.000
#> GSM1022350 3 0.0000 0.8748 0.000 0.000 1.000 0.000 0.000
#> GSM1022344 1 0.4360 0.6393 0.692 0.000 0.024 0.284 0.000
#> GSM1022345 1 0.4360 0.6393 0.692 0.000 0.024 0.284 0.000
#> GSM1022346 1 0.4360 0.6393 0.692 0.000 0.024 0.284 0.000
#> GSM1022355 1 0.0162 0.7403 0.996 0.000 0.000 0.000 0.004
#> GSM1022356 1 0.0162 0.7403 0.996 0.000 0.000 0.000 0.004
#> GSM1022357 1 0.0162 0.7403 0.996 0.000 0.000 0.000 0.004
#> GSM1022358 1 0.0162 0.7403 0.996 0.000 0.000 0.000 0.004
#> GSM1022351 1 0.0162 0.7403 0.996 0.000 0.000 0.000 0.004
#> GSM1022352 1 0.0162 0.7403 0.996 0.000 0.000 0.000 0.004
#> GSM1022353 1 0.0162 0.7403 0.996 0.000 0.000 0.000 0.004
#> GSM1022354 1 0.0162 0.7403 0.996 0.000 0.000 0.000 0.004
#> GSM1022359 2 0.0510 0.8980 0.000 0.984 0.000 0.016 0.000
#> GSM1022360 2 0.0510 0.8980 0.000 0.984 0.000 0.016 0.000
#> GSM1022361 2 0.0510 0.8980 0.000 0.984 0.000 0.016 0.000
#> GSM1022362 2 0.0510 0.8980 0.000 0.984 0.000 0.016 0.000
#> GSM1022367 4 0.4262 1.0000 0.000 0.000 0.440 0.560 0.000
#> GSM1022368 4 0.4262 1.0000 0.000 0.000 0.440 0.560 0.000
#> GSM1022369 4 0.4262 1.0000 0.000 0.000 0.440 0.560 0.000
#> GSM1022370 4 0.4262 1.0000 0.000 0.000 0.440 0.560 0.000
#> GSM1022363 2 0.4150 0.6598 0.000 0.612 0.000 0.388 0.000
#> GSM1022364 2 0.4150 0.6598 0.000 0.612 0.000 0.388 0.000
#> GSM1022365 2 0.4150 0.6598 0.000 0.612 0.000 0.388 0.000
#> GSM1022366 2 0.4150 0.6598 0.000 0.612 0.000 0.388 0.000
#> GSM1022374 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM1022375 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM1022376 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM1022371 2 0.2471 0.8903 0.000 0.864 0.000 0.136 0.000
#> GSM1022372 2 0.2471 0.8903 0.000 0.864 0.000 0.136 0.000
#> GSM1022373 2 0.2471 0.8903 0.000 0.864 0.000 0.136 0.000
#> GSM1022377 2 0.0609 0.8969 0.000 0.980 0.000 0.020 0.000
#> GSM1022378 2 0.0609 0.8969 0.000 0.980 0.000 0.020 0.000
#> GSM1022379 2 0.0609 0.8969 0.000 0.980 0.000 0.020 0.000
#> GSM1022380 2 0.0609 0.8969 0.000 0.980 0.000 0.020 0.000
#> GSM1022385 3 0.0000 0.8748 0.000 0.000 1.000 0.000 0.000
#> GSM1022386 3 0.0000 0.8748 0.000 0.000 1.000 0.000 0.000
#> GSM1022387 3 0.0000 0.8748 0.000 0.000 1.000 0.000 0.000
#> GSM1022388 3 0.0000 0.8748 0.000 0.000 1.000 0.000 0.000
#> GSM1022381 2 0.0609 0.8969 0.000 0.980 0.000 0.020 0.000
#> GSM1022382 2 0.0609 0.8969 0.000 0.980 0.000 0.020 0.000
#> GSM1022383 2 0.0609 0.8969 0.000 0.980 0.000 0.020 0.000
#> GSM1022384 2 0.0609 0.8969 0.000 0.980 0.000 0.020 0.000
#> GSM1022393 1 0.3999 0.5434 0.656 0.000 0.000 0.000 0.344
#> GSM1022394 1 0.3999 0.5434 0.656 0.000 0.000 0.000 0.344
#> GSM1022395 1 0.3999 0.5434 0.656 0.000 0.000 0.000 0.344
#> GSM1022396 1 0.3999 0.5434 0.656 0.000 0.000 0.000 0.344
#> GSM1022389 2 0.0162 0.8992 0.000 0.996 0.000 0.004 0.000
#> GSM1022390 2 0.0162 0.8992 0.000 0.996 0.000 0.004 0.000
#> GSM1022391 2 0.0162 0.8992 0.000 0.996 0.000 0.004 0.000
#> GSM1022392 2 0.0162 0.8992 0.000 0.996 0.000 0.004 0.000
#> GSM1022397 3 0.0000 0.8748 0.000 0.000 1.000 0.000 0.000
#> GSM1022398 3 0.0000 0.8748 0.000 0.000 1.000 0.000 0.000
#> GSM1022399 3 0.0000 0.8748 0.000 0.000 1.000 0.000 0.000
#> GSM1022400 3 0.0000 0.8748 0.000 0.000 1.000 0.000 0.000
#> GSM1022401 1 0.3999 0.5434 0.656 0.000 0.000 0.000 0.344
#> GSM1022402 1 0.3999 0.5434 0.656 0.000 0.000 0.000 0.344
#> GSM1022403 1 0.3999 0.5434 0.656 0.000 0.000 0.000 0.344
#> GSM1022404 1 0.3999 0.5434 0.656 0.000 0.000 0.000 0.344
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1022325 2 0.0000 0.810 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022326 2 0.0000 0.810 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022327 2 0.0000 0.810 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022331 6 0.3409 0.736 0.000 0.000 0.300 0.000 0.000 0.700
#> GSM1022332 6 0.3409 0.736 0.000 0.000 0.300 0.000 0.000 0.700
#> GSM1022333 6 0.3409 0.736 0.000 0.000 0.300 0.000 0.000 0.700
#> GSM1022328 2 0.0000 0.810 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022329 2 0.0000 0.810 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022330 2 0.0000 0.810 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022337 5 0.4227 1.000 0.344 0.000 0.000 0.020 0.632 0.004
#> GSM1022338 5 0.4227 1.000 0.344 0.000 0.000 0.020 0.632 0.004
#> GSM1022339 5 0.4227 1.000 0.344 0.000 0.000 0.020 0.632 0.004
#> GSM1022334 2 0.0000 0.810 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022335 2 0.0000 0.810 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022336 2 0.0000 0.810 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022340 4 0.0547 0.983 0.020 0.000 0.000 0.980 0.000 0.000
#> GSM1022341 4 0.0547 0.983 0.020 0.000 0.000 0.980 0.000 0.000
#> GSM1022342 4 0.0547 0.983 0.020 0.000 0.000 0.980 0.000 0.000
#> GSM1022343 4 0.0547 0.983 0.020 0.000 0.000 0.980 0.000 0.000
#> GSM1022347 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022348 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022349 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022350 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022344 4 0.1176 0.977 0.020 0.000 0.024 0.956 0.000 0.000
#> GSM1022345 4 0.1176 0.977 0.020 0.000 0.024 0.956 0.000 0.000
#> GSM1022346 4 0.1176 0.977 0.020 0.000 0.024 0.956 0.000 0.000
#> GSM1022355 1 0.4219 0.704 0.660 0.000 0.000 0.304 0.000 0.036
#> GSM1022356 1 0.4219 0.704 0.660 0.000 0.000 0.304 0.000 0.036
#> GSM1022357 1 0.4219 0.704 0.660 0.000 0.000 0.304 0.000 0.036
#> GSM1022358 1 0.4219 0.704 0.660 0.000 0.000 0.304 0.000 0.036
#> GSM1022351 1 0.4219 0.704 0.660 0.000 0.000 0.304 0.000 0.036
#> GSM1022352 1 0.4219 0.704 0.660 0.000 0.000 0.304 0.000 0.036
#> GSM1022353 1 0.4219 0.704 0.660 0.000 0.000 0.304 0.000 0.036
#> GSM1022354 1 0.4219 0.704 0.660 0.000 0.000 0.304 0.000 0.036
#> GSM1022359 2 0.2793 0.808 0.000 0.800 0.000 0.000 0.200 0.000
#> GSM1022360 2 0.2793 0.808 0.000 0.800 0.000 0.000 0.200 0.000
#> GSM1022361 2 0.2793 0.808 0.000 0.800 0.000 0.000 0.200 0.000
#> GSM1022362 2 0.2793 0.808 0.000 0.800 0.000 0.000 0.200 0.000
#> GSM1022367 6 0.1075 0.832 0.000 0.000 0.048 0.000 0.000 0.952
#> GSM1022368 6 0.1075 0.832 0.000 0.000 0.048 0.000 0.000 0.952
#> GSM1022369 6 0.1075 0.832 0.000 0.000 0.048 0.000 0.000 0.952
#> GSM1022370 6 0.1075 0.832 0.000 0.000 0.048 0.000 0.000 0.952
#> GSM1022363 2 0.3151 0.610 0.000 0.748 0.000 0.000 0.000 0.252
#> GSM1022364 2 0.3151 0.610 0.000 0.748 0.000 0.000 0.000 0.252
#> GSM1022365 2 0.3151 0.610 0.000 0.748 0.000 0.000 0.000 0.252
#> GSM1022366 2 0.3151 0.610 0.000 0.748 0.000 0.000 0.000 0.252
#> GSM1022374 5 0.4227 1.000 0.344 0.000 0.000 0.020 0.632 0.004
#> GSM1022375 5 0.4227 1.000 0.344 0.000 0.000 0.020 0.632 0.004
#> GSM1022376 5 0.4227 1.000 0.344 0.000 0.000 0.020 0.632 0.004
#> GSM1022371 2 0.0000 0.810 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022372 2 0.0000 0.810 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022373 2 0.0000 0.810 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022377 2 0.3672 0.768 0.000 0.632 0.000 0.000 0.368 0.000
#> GSM1022378 2 0.3672 0.768 0.000 0.632 0.000 0.000 0.368 0.000
#> GSM1022379 2 0.3672 0.768 0.000 0.632 0.000 0.000 0.368 0.000
#> GSM1022380 2 0.3672 0.768 0.000 0.632 0.000 0.000 0.368 0.000
#> GSM1022385 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022386 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022387 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022388 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022381 2 0.3672 0.768 0.000 0.632 0.000 0.000 0.368 0.000
#> GSM1022382 2 0.3672 0.768 0.000 0.632 0.000 0.000 0.368 0.000
#> GSM1022383 2 0.3672 0.768 0.000 0.632 0.000 0.000 0.368 0.000
#> GSM1022384 2 0.3672 0.768 0.000 0.632 0.000 0.000 0.368 0.000
#> GSM1022393 1 0.0000 0.693 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022394 1 0.0000 0.693 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022395 1 0.0000 0.693 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022396 1 0.0000 0.693 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022389 2 0.3653 0.781 0.000 0.692 0.000 0.000 0.300 0.008
#> GSM1022390 2 0.3653 0.781 0.000 0.692 0.000 0.000 0.300 0.008
#> GSM1022391 2 0.3653 0.781 0.000 0.692 0.000 0.000 0.300 0.008
#> GSM1022392 2 0.3653 0.781 0.000 0.692 0.000 0.000 0.300 0.008
#> GSM1022397 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022398 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022399 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022400 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022401 1 0.0000 0.693 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022402 1 0.0000 0.693 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022403 1 0.0000 0.693 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022404 1 0.0000 0.693 1.000 0.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n protocol(p) cell.type(p) k
#> CV:hclust 80 3.07e-06 6.59e-07 2
#> CV:hclust 74 4.44e-09 1.12e-11 3
#> CV:hclust 80 8.66e-12 2.68e-12 4
#> CV:hclust 77 6.34e-15 6.01e-11 5
#> CV:hclust 80 8.72e-22 2.76e-13 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
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 31589 rows and 80 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.452 0.319 0.726 0.4755 0.539 0.539
#> 3 3 0.666 0.899 0.878 0.3616 0.718 0.511
#> 4 4 0.748 0.808 0.827 0.1168 1.000 1.000
#> 5 5 0.728 0.676 0.715 0.0656 0.886 0.658
#> 6 6 0.715 0.646 0.731 0.0468 0.952 0.785
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
#> GSM1022325 2 0.993 0.5767 0.452 0.548
#> GSM1022326 2 0.993 0.5767 0.452 0.548
#> GSM1022327 2 0.993 0.5767 0.452 0.548
#> GSM1022331 1 0.955 0.7411 0.624 0.376
#> GSM1022332 1 0.955 0.7411 0.624 0.376
#> GSM1022333 1 0.955 0.7411 0.624 0.376
#> GSM1022328 2 0.993 0.5767 0.452 0.548
#> GSM1022329 2 0.993 0.5767 0.452 0.548
#> GSM1022330 2 0.993 0.5767 0.452 0.548
#> GSM1022337 1 0.995 0.3310 0.540 0.460
#> GSM1022338 1 0.995 0.3310 0.540 0.460
#> GSM1022339 1 0.995 0.3310 0.540 0.460
#> GSM1022334 2 0.993 0.5767 0.452 0.548
#> GSM1022335 2 0.993 0.5767 0.452 0.548
#> GSM1022336 2 0.993 0.5767 0.452 0.548
#> GSM1022340 2 0.932 -0.4267 0.348 0.652
#> GSM1022341 2 0.932 -0.4267 0.348 0.652
#> GSM1022342 2 0.932 -0.4267 0.348 0.652
#> GSM1022343 2 0.932 -0.4267 0.348 0.652
#> GSM1022347 1 0.955 0.7411 0.624 0.376
#> GSM1022348 1 0.955 0.7411 0.624 0.376
#> GSM1022349 1 0.955 0.7411 0.624 0.376
#> GSM1022350 1 0.955 0.7411 0.624 0.376
#> GSM1022344 1 0.980 0.7047 0.584 0.416
#> GSM1022345 1 0.980 0.7047 0.584 0.416
#> GSM1022346 1 0.980 0.7047 0.584 0.416
#> GSM1022355 2 0.932 -0.4267 0.348 0.652
#> GSM1022356 2 0.932 -0.4267 0.348 0.652
#> GSM1022357 2 0.932 -0.4267 0.348 0.652
#> GSM1022358 2 0.932 -0.4267 0.348 0.652
#> GSM1022351 2 0.932 -0.4267 0.348 0.652
#> GSM1022352 2 0.932 -0.4267 0.348 0.652
#> GSM1022353 2 0.932 -0.4267 0.348 0.652
#> GSM1022354 2 0.932 -0.4267 0.348 0.652
#> GSM1022359 2 0.993 0.5767 0.452 0.548
#> GSM1022360 2 0.993 0.5767 0.452 0.548
#> GSM1022361 2 0.993 0.5767 0.452 0.548
#> GSM1022362 2 0.993 0.5767 0.452 0.548
#> GSM1022367 1 0.000 0.3023 1.000 0.000
#> GSM1022368 1 0.000 0.3023 1.000 0.000
#> GSM1022369 1 0.000 0.3023 1.000 0.000
#> GSM1022370 1 0.000 0.3023 1.000 0.000
#> GSM1022363 2 0.993 0.5767 0.452 0.548
#> GSM1022364 2 0.993 0.5767 0.452 0.548
#> GSM1022365 2 0.993 0.5767 0.452 0.548
#> GSM1022366 2 0.993 0.5767 0.452 0.548
#> GSM1022374 1 0.871 0.0481 0.708 0.292
#> GSM1022375 1 0.871 0.0481 0.708 0.292
#> GSM1022376 1 0.871 0.0481 0.708 0.292
#> GSM1022371 2 0.993 0.5767 0.452 0.548
#> GSM1022372 2 0.993 0.5767 0.452 0.548
#> GSM1022373 2 0.993 0.5767 0.452 0.548
#> GSM1022377 2 0.993 0.5767 0.452 0.548
#> GSM1022378 2 0.993 0.5767 0.452 0.548
#> GSM1022379 2 0.993 0.5767 0.452 0.548
#> GSM1022380 2 0.993 0.5767 0.452 0.548
#> GSM1022385 1 0.955 0.7411 0.624 0.376
#> GSM1022386 1 0.955 0.7411 0.624 0.376
#> GSM1022387 1 0.955 0.7411 0.624 0.376
#> GSM1022388 1 0.955 0.7411 0.624 0.376
#> GSM1022381 2 0.993 0.5767 0.452 0.548
#> GSM1022382 2 0.993 0.5767 0.452 0.548
#> GSM1022383 2 0.993 0.5767 0.452 0.548
#> GSM1022384 2 0.993 0.5767 0.452 0.548
#> GSM1022393 2 0.932 -0.4267 0.348 0.652
#> GSM1022394 2 0.932 -0.4267 0.348 0.652
#> GSM1022395 2 0.932 -0.4267 0.348 0.652
#> GSM1022396 2 0.932 -0.4267 0.348 0.652
#> GSM1022389 2 0.993 0.5767 0.452 0.548
#> GSM1022390 2 0.993 0.5767 0.452 0.548
#> GSM1022391 2 0.993 0.5767 0.452 0.548
#> GSM1022392 2 0.993 0.5767 0.452 0.548
#> GSM1022397 1 0.955 0.7411 0.624 0.376
#> GSM1022398 1 0.955 0.7411 0.624 0.376
#> GSM1022399 1 0.955 0.7411 0.624 0.376
#> GSM1022400 1 0.955 0.7411 0.624 0.376
#> GSM1022401 2 0.932 -0.4267 0.348 0.652
#> GSM1022402 2 0.932 -0.4267 0.348 0.652
#> GSM1022403 2 0.932 -0.4267 0.348 0.652
#> GSM1022404 2 0.932 -0.4267 0.348 0.652
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1022325 2 0.0424 0.935 0.008 0.992 0.000
#> GSM1022326 2 0.0424 0.935 0.008 0.992 0.000
#> GSM1022327 2 0.0424 0.935 0.008 0.992 0.000
#> GSM1022331 3 0.3459 0.849 0.096 0.012 0.892
#> GSM1022332 3 0.3459 0.849 0.096 0.012 0.892
#> GSM1022333 3 0.3459 0.849 0.096 0.012 0.892
#> GSM1022328 2 0.0424 0.935 0.008 0.992 0.000
#> GSM1022329 2 0.0424 0.935 0.008 0.992 0.000
#> GSM1022330 2 0.0424 0.935 0.008 0.992 0.000
#> GSM1022337 1 0.5650 0.823 0.808 0.084 0.108
#> GSM1022338 1 0.5650 0.823 0.808 0.084 0.108
#> GSM1022339 1 0.5650 0.823 0.808 0.084 0.108
#> GSM1022334 2 0.0592 0.935 0.012 0.988 0.000
#> GSM1022335 2 0.0592 0.935 0.012 0.988 0.000
#> GSM1022336 2 0.0592 0.935 0.012 0.988 0.000
#> GSM1022340 1 0.6301 0.938 0.712 0.028 0.260
#> GSM1022341 1 0.6301 0.938 0.712 0.028 0.260
#> GSM1022342 1 0.6301 0.938 0.712 0.028 0.260
#> GSM1022343 1 0.6301 0.938 0.712 0.028 0.260
#> GSM1022347 3 0.1182 0.904 0.012 0.012 0.976
#> GSM1022348 3 0.1182 0.904 0.012 0.012 0.976
#> GSM1022349 3 0.1182 0.904 0.012 0.012 0.976
#> GSM1022350 3 0.1182 0.904 0.012 0.012 0.976
#> GSM1022344 3 0.0592 0.893 0.012 0.000 0.988
#> GSM1022345 3 0.0592 0.893 0.012 0.000 0.988
#> GSM1022346 3 0.0592 0.893 0.012 0.000 0.988
#> GSM1022355 1 0.6301 0.938 0.712 0.028 0.260
#> GSM1022356 1 0.6301 0.938 0.712 0.028 0.260
#> GSM1022357 1 0.6301 0.938 0.712 0.028 0.260
#> GSM1022358 1 0.6301 0.938 0.712 0.028 0.260
#> GSM1022351 1 0.6301 0.938 0.712 0.028 0.260
#> GSM1022352 1 0.6301 0.938 0.712 0.028 0.260
#> GSM1022353 1 0.6301 0.938 0.712 0.028 0.260
#> GSM1022354 1 0.6301 0.938 0.712 0.028 0.260
#> GSM1022359 2 0.1163 0.933 0.028 0.972 0.000
#> GSM1022360 2 0.1163 0.933 0.028 0.972 0.000
#> GSM1022361 2 0.1163 0.933 0.028 0.972 0.000
#> GSM1022362 2 0.1163 0.933 0.028 0.972 0.000
#> GSM1022367 3 0.7617 0.707 0.160 0.152 0.688
#> GSM1022368 3 0.7617 0.707 0.160 0.152 0.688
#> GSM1022369 3 0.7617 0.707 0.160 0.152 0.688
#> GSM1022370 3 0.7617 0.707 0.160 0.152 0.688
#> GSM1022363 2 0.3771 0.882 0.112 0.876 0.012
#> GSM1022364 2 0.3771 0.882 0.112 0.876 0.012
#> GSM1022365 2 0.3771 0.882 0.112 0.876 0.012
#> GSM1022366 2 0.3771 0.882 0.112 0.876 0.012
#> GSM1022374 1 0.5538 0.785 0.812 0.116 0.072
#> GSM1022375 1 0.5538 0.785 0.812 0.116 0.072
#> GSM1022376 1 0.5538 0.785 0.812 0.116 0.072
#> GSM1022371 2 0.0592 0.935 0.012 0.988 0.000
#> GSM1022372 2 0.0592 0.935 0.012 0.988 0.000
#> GSM1022373 2 0.0592 0.935 0.012 0.988 0.000
#> GSM1022377 2 0.3752 0.914 0.144 0.856 0.000
#> GSM1022378 2 0.3752 0.914 0.144 0.856 0.000
#> GSM1022379 2 0.3752 0.914 0.144 0.856 0.000
#> GSM1022380 2 0.3752 0.914 0.144 0.856 0.000
#> GSM1022385 3 0.1182 0.904 0.012 0.012 0.976
#> GSM1022386 3 0.1182 0.904 0.012 0.012 0.976
#> GSM1022387 3 0.1182 0.904 0.012 0.012 0.976
#> GSM1022388 3 0.1182 0.904 0.012 0.012 0.976
#> GSM1022381 2 0.4002 0.911 0.160 0.840 0.000
#> GSM1022382 2 0.4002 0.911 0.160 0.840 0.000
#> GSM1022383 2 0.4002 0.911 0.160 0.840 0.000
#> GSM1022384 2 0.4002 0.911 0.160 0.840 0.000
#> GSM1022393 1 0.6066 0.935 0.728 0.024 0.248
#> GSM1022394 1 0.6105 0.936 0.724 0.024 0.252
#> GSM1022395 1 0.6105 0.936 0.724 0.024 0.252
#> GSM1022396 1 0.6105 0.936 0.724 0.024 0.252
#> GSM1022389 2 0.3918 0.910 0.140 0.856 0.004
#> GSM1022390 2 0.3918 0.910 0.140 0.856 0.004
#> GSM1022391 2 0.3918 0.910 0.140 0.856 0.004
#> GSM1022392 2 0.3918 0.910 0.140 0.856 0.004
#> GSM1022397 3 0.1182 0.904 0.012 0.012 0.976
#> GSM1022398 3 0.1182 0.904 0.012 0.012 0.976
#> GSM1022399 3 0.1182 0.904 0.012 0.012 0.976
#> GSM1022400 3 0.1182 0.904 0.012 0.012 0.976
#> GSM1022401 1 0.6105 0.936 0.724 0.024 0.252
#> GSM1022402 1 0.6105 0.936 0.724 0.024 0.252
#> GSM1022403 1 0.6105 0.936 0.724 0.024 0.252
#> GSM1022404 1 0.6105 0.936 0.724 0.024 0.252
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1022325 2 0.0336 0.840 0.008 0.992 0.000 NA
#> GSM1022326 2 0.0336 0.840 0.008 0.992 0.000 NA
#> GSM1022327 2 0.0336 0.840 0.008 0.992 0.000 NA
#> GSM1022331 3 0.3969 0.796 0.016 0.000 0.804 NA
#> GSM1022332 3 0.3969 0.796 0.016 0.000 0.804 NA
#> GSM1022333 3 0.3969 0.796 0.016 0.000 0.804 NA
#> GSM1022328 2 0.0336 0.840 0.008 0.992 0.000 NA
#> GSM1022329 2 0.0336 0.840 0.008 0.992 0.000 NA
#> GSM1022330 2 0.0336 0.840 0.008 0.992 0.000 NA
#> GSM1022337 1 0.5788 0.777 0.700 0.016 0.048 NA
#> GSM1022338 1 0.5788 0.777 0.700 0.016 0.048 NA
#> GSM1022339 1 0.5788 0.777 0.700 0.016 0.048 NA
#> GSM1022334 2 0.0336 0.840 0.008 0.992 0.000 NA
#> GSM1022335 2 0.0336 0.840 0.008 0.992 0.000 NA
#> GSM1022336 2 0.0336 0.840 0.008 0.992 0.000 NA
#> GSM1022340 1 0.3367 0.822 0.864 0.000 0.028 NA
#> GSM1022341 1 0.3367 0.822 0.864 0.000 0.028 NA
#> GSM1022342 1 0.3367 0.822 0.864 0.000 0.028 NA
#> GSM1022343 1 0.3367 0.822 0.864 0.000 0.028 NA
#> GSM1022347 3 0.2053 0.859 0.072 0.000 0.924 NA
#> GSM1022348 3 0.2053 0.859 0.072 0.000 0.924 NA
#> GSM1022349 3 0.2053 0.859 0.072 0.000 0.924 NA
#> GSM1022350 3 0.2053 0.859 0.072 0.000 0.924 NA
#> GSM1022344 3 0.5495 0.725 0.176 0.000 0.728 NA
#> GSM1022345 3 0.5615 0.712 0.188 0.000 0.716 NA
#> GSM1022346 3 0.5615 0.712 0.188 0.000 0.716 NA
#> GSM1022355 1 0.0336 0.870 0.992 0.000 0.000 NA
#> GSM1022356 1 0.0336 0.870 0.992 0.000 0.000 NA
#> GSM1022357 1 0.0336 0.870 0.992 0.000 0.000 NA
#> GSM1022358 1 0.0336 0.870 0.992 0.000 0.000 NA
#> GSM1022351 1 0.2401 0.844 0.904 0.000 0.004 NA
#> GSM1022352 1 0.2401 0.844 0.904 0.000 0.004 NA
#> GSM1022353 1 0.2401 0.844 0.904 0.000 0.004 NA
#> GSM1022354 1 0.2401 0.844 0.904 0.000 0.004 NA
#> GSM1022359 2 0.1452 0.838 0.008 0.956 0.000 NA
#> GSM1022360 2 0.1452 0.838 0.008 0.956 0.000 NA
#> GSM1022361 2 0.1452 0.838 0.008 0.956 0.000 NA
#> GSM1022362 2 0.1452 0.838 0.008 0.956 0.000 NA
#> GSM1022367 3 0.6496 0.653 0.004 0.072 0.568 NA
#> GSM1022368 3 0.6496 0.653 0.004 0.072 0.568 NA
#> GSM1022369 3 0.6496 0.653 0.004 0.072 0.568 NA
#> GSM1022370 3 0.6496 0.653 0.004 0.072 0.568 NA
#> GSM1022363 2 0.3870 0.738 0.000 0.788 0.004 NA
#> GSM1022364 2 0.3870 0.738 0.000 0.788 0.004 NA
#> GSM1022365 2 0.3870 0.738 0.000 0.788 0.004 NA
#> GSM1022366 2 0.3870 0.738 0.000 0.788 0.004 NA
#> GSM1022374 1 0.5954 0.768 0.688 0.020 0.048 NA
#> GSM1022375 1 0.5954 0.768 0.688 0.020 0.048 NA
#> GSM1022376 1 0.5954 0.768 0.688 0.020 0.048 NA
#> GSM1022371 2 0.1639 0.833 0.008 0.952 0.004 NA
#> GSM1022372 2 0.1639 0.833 0.008 0.952 0.004 NA
#> GSM1022373 2 0.1639 0.833 0.008 0.952 0.004 NA
#> GSM1022377 2 0.5530 0.758 0.020 0.616 0.004 NA
#> GSM1022378 2 0.5530 0.758 0.020 0.616 0.004 NA
#> GSM1022379 2 0.5530 0.758 0.020 0.616 0.004 NA
#> GSM1022380 2 0.5530 0.758 0.020 0.616 0.004 NA
#> GSM1022385 3 0.2965 0.858 0.072 0.000 0.892 NA
#> GSM1022386 3 0.2965 0.858 0.072 0.000 0.892 NA
#> GSM1022387 3 0.2965 0.858 0.072 0.000 0.892 NA
#> GSM1022388 3 0.2965 0.858 0.072 0.000 0.892 NA
#> GSM1022381 2 0.5649 0.747 0.020 0.580 0.004 NA
#> GSM1022382 2 0.5649 0.747 0.020 0.580 0.004 NA
#> GSM1022383 2 0.5649 0.747 0.020 0.580 0.004 NA
#> GSM1022384 2 0.5649 0.747 0.020 0.580 0.004 NA
#> GSM1022393 1 0.2216 0.873 0.908 0.000 0.000 NA
#> GSM1022394 1 0.2216 0.873 0.908 0.000 0.000 NA
#> GSM1022395 1 0.2216 0.873 0.908 0.000 0.000 NA
#> GSM1022396 1 0.2216 0.873 0.908 0.000 0.000 NA
#> GSM1022389 2 0.5616 0.759 0.020 0.624 0.008 NA
#> GSM1022390 2 0.5616 0.759 0.020 0.624 0.008 NA
#> GSM1022391 2 0.5616 0.759 0.020 0.624 0.008 NA
#> GSM1022392 2 0.5616 0.759 0.020 0.624 0.008 NA
#> GSM1022397 3 0.1867 0.859 0.072 0.000 0.928 NA
#> GSM1022398 3 0.1867 0.859 0.072 0.000 0.928 NA
#> GSM1022399 3 0.1867 0.859 0.072 0.000 0.928 NA
#> GSM1022400 3 0.1867 0.859 0.072 0.000 0.928 NA
#> GSM1022401 1 0.2216 0.873 0.908 0.000 0.000 NA
#> GSM1022402 1 0.2216 0.873 0.908 0.000 0.000 NA
#> GSM1022403 1 0.2216 0.873 0.908 0.000 0.000 NA
#> GSM1022404 1 0.2216 0.873 0.908 0.000 0.000 NA
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1022325 2 0.4150 0.782 0.000 0.612 0.000 0.388 0.000
#> GSM1022326 2 0.4150 0.782 0.000 0.612 0.000 0.388 0.000
#> GSM1022327 2 0.4150 0.782 0.000 0.612 0.000 0.388 0.000
#> GSM1022331 3 0.4424 0.733 0.000 0.084 0.768 0.004 0.144
#> GSM1022332 3 0.4424 0.733 0.000 0.084 0.768 0.004 0.144
#> GSM1022333 3 0.4424 0.733 0.000 0.084 0.768 0.004 0.144
#> GSM1022328 2 0.4150 0.782 0.000 0.612 0.000 0.388 0.000
#> GSM1022329 2 0.4150 0.782 0.000 0.612 0.000 0.388 0.000
#> GSM1022330 2 0.4150 0.782 0.000 0.612 0.000 0.388 0.000
#> GSM1022337 5 0.4723 0.967 0.368 0.008 0.000 0.012 0.612
#> GSM1022338 5 0.4723 0.967 0.368 0.008 0.000 0.012 0.612
#> GSM1022339 5 0.4723 0.967 0.368 0.008 0.000 0.012 0.612
#> GSM1022334 2 0.4138 0.781 0.000 0.616 0.000 0.384 0.000
#> GSM1022335 2 0.4138 0.781 0.000 0.616 0.000 0.384 0.000
#> GSM1022336 2 0.4138 0.781 0.000 0.616 0.000 0.384 0.000
#> GSM1022340 1 0.2047 0.582 0.928 0.040 0.020 0.012 0.000
#> GSM1022341 1 0.2047 0.582 0.928 0.040 0.020 0.012 0.000
#> GSM1022342 1 0.2047 0.582 0.928 0.040 0.020 0.012 0.000
#> GSM1022343 1 0.2047 0.582 0.928 0.040 0.020 0.012 0.000
#> GSM1022347 3 0.1618 0.803 0.040 0.008 0.944 0.000 0.008
#> GSM1022348 3 0.1618 0.803 0.040 0.008 0.944 0.000 0.008
#> GSM1022349 3 0.1618 0.803 0.040 0.008 0.944 0.000 0.008
#> GSM1022350 3 0.1618 0.803 0.040 0.008 0.944 0.000 0.008
#> GSM1022344 3 0.5666 0.467 0.380 0.064 0.548 0.000 0.008
#> GSM1022345 3 0.5683 0.453 0.388 0.064 0.540 0.000 0.008
#> GSM1022346 3 0.5683 0.453 0.388 0.064 0.540 0.000 0.008
#> GSM1022355 1 0.3309 0.598 0.836 0.036 0.000 0.000 0.128
#> GSM1022356 1 0.3309 0.598 0.836 0.036 0.000 0.000 0.128
#> GSM1022357 1 0.3309 0.598 0.836 0.036 0.000 0.000 0.128
#> GSM1022358 1 0.3309 0.598 0.836 0.036 0.000 0.000 0.128
#> GSM1022351 1 0.0162 0.612 0.996 0.000 0.000 0.004 0.000
#> GSM1022352 1 0.0162 0.612 0.996 0.000 0.000 0.004 0.000
#> GSM1022353 1 0.0162 0.612 0.996 0.000 0.000 0.004 0.000
#> GSM1022354 1 0.0162 0.612 0.996 0.000 0.000 0.004 0.000
#> GSM1022359 2 0.5295 0.708 0.000 0.504 0.008 0.456 0.032
#> GSM1022360 2 0.5295 0.708 0.000 0.504 0.008 0.456 0.032
#> GSM1022361 2 0.5295 0.708 0.000 0.504 0.008 0.456 0.032
#> GSM1022362 2 0.5295 0.708 0.000 0.504 0.008 0.456 0.032
#> GSM1022367 3 0.7217 0.504 0.000 0.232 0.440 0.028 0.300
#> GSM1022368 3 0.7217 0.504 0.000 0.232 0.440 0.028 0.300
#> GSM1022369 3 0.7217 0.504 0.000 0.232 0.440 0.028 0.300
#> GSM1022370 3 0.7217 0.504 0.000 0.232 0.440 0.028 0.300
#> GSM1022363 2 0.6655 0.420 0.000 0.536 0.020 0.268 0.176
#> GSM1022364 2 0.6655 0.420 0.000 0.536 0.020 0.268 0.176
#> GSM1022365 2 0.6655 0.420 0.000 0.536 0.020 0.268 0.176
#> GSM1022366 2 0.6655 0.420 0.000 0.536 0.020 0.268 0.176
#> GSM1022374 5 0.4654 0.968 0.348 0.008 0.000 0.012 0.632
#> GSM1022375 5 0.4654 0.968 0.348 0.008 0.000 0.012 0.632
#> GSM1022376 5 0.4654 0.968 0.348 0.008 0.000 0.012 0.632
#> GSM1022371 2 0.5071 0.725 0.000 0.616 0.004 0.340 0.040
#> GSM1022372 2 0.5071 0.725 0.000 0.616 0.004 0.340 0.040
#> GSM1022373 2 0.5071 0.725 0.000 0.616 0.004 0.340 0.040
#> GSM1022377 4 0.1790 0.819 0.004 0.016 0.004 0.940 0.036
#> GSM1022378 4 0.1790 0.819 0.004 0.016 0.004 0.940 0.036
#> GSM1022379 4 0.1790 0.819 0.004 0.016 0.004 0.940 0.036
#> GSM1022380 4 0.1790 0.819 0.004 0.016 0.004 0.940 0.036
#> GSM1022385 3 0.2072 0.803 0.036 0.016 0.928 0.000 0.020
#> GSM1022386 3 0.2072 0.803 0.036 0.016 0.928 0.000 0.020
#> GSM1022387 3 0.2072 0.803 0.036 0.016 0.928 0.000 0.020
#> GSM1022388 3 0.2072 0.803 0.036 0.016 0.928 0.000 0.020
#> GSM1022381 4 0.1372 0.820 0.004 0.016 0.000 0.956 0.024
#> GSM1022382 4 0.1372 0.820 0.004 0.016 0.000 0.956 0.024
#> GSM1022383 4 0.1372 0.820 0.004 0.016 0.000 0.956 0.024
#> GSM1022384 4 0.1372 0.820 0.004 0.016 0.000 0.956 0.024
#> GSM1022393 1 0.5368 0.358 0.620 0.068 0.000 0.004 0.308
#> GSM1022394 1 0.5368 0.358 0.620 0.068 0.000 0.004 0.308
#> GSM1022395 1 0.5368 0.358 0.620 0.068 0.000 0.004 0.308
#> GSM1022396 1 0.5368 0.358 0.620 0.068 0.000 0.004 0.308
#> GSM1022389 4 0.4986 0.681 0.004 0.168 0.012 0.736 0.080
#> GSM1022390 4 0.4986 0.681 0.004 0.168 0.012 0.736 0.080
#> GSM1022391 4 0.4986 0.681 0.004 0.168 0.012 0.736 0.080
#> GSM1022392 4 0.4986 0.681 0.004 0.168 0.012 0.736 0.080
#> GSM1022397 3 0.1205 0.804 0.040 0.000 0.956 0.000 0.004
#> GSM1022398 3 0.1205 0.804 0.040 0.000 0.956 0.000 0.004
#> GSM1022399 3 0.1205 0.804 0.040 0.000 0.956 0.000 0.004
#> GSM1022400 3 0.1205 0.804 0.040 0.000 0.956 0.000 0.004
#> GSM1022401 1 0.5368 0.358 0.620 0.068 0.000 0.004 0.308
#> GSM1022402 1 0.5368 0.358 0.620 0.068 0.000 0.004 0.308
#> GSM1022403 1 0.5368 0.358 0.620 0.068 0.000 0.004 0.308
#> GSM1022404 1 0.5368 0.358 0.620 0.068 0.000 0.004 0.308
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1022325 2 0.0000 0.9259 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022326 2 0.0000 0.9259 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022327 2 0.0000 0.9259 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022331 3 0.4928 0.4684 0.000 0.000 0.640 0.032 0.040 0.288
#> GSM1022332 3 0.4928 0.4684 0.000 0.000 0.640 0.032 0.040 0.288
#> GSM1022333 3 0.4928 0.4684 0.000 0.000 0.640 0.032 0.040 0.288
#> GSM1022328 2 0.0000 0.9259 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022329 2 0.0000 0.9259 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022330 2 0.0000 0.9259 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022337 5 0.3767 0.9758 0.268 0.004 0.000 0.004 0.716 0.008
#> GSM1022338 5 0.3767 0.9758 0.268 0.004 0.000 0.004 0.716 0.008
#> GSM1022339 5 0.3767 0.9758 0.268 0.004 0.000 0.004 0.716 0.008
#> GSM1022334 2 0.0291 0.9240 0.000 0.992 0.000 0.004 0.004 0.000
#> GSM1022335 2 0.0291 0.9240 0.000 0.992 0.000 0.004 0.004 0.000
#> GSM1022336 2 0.0291 0.9240 0.000 0.992 0.000 0.004 0.004 0.000
#> GSM1022340 1 0.2759 0.5295 0.880 0.000 0.008 0.040 0.008 0.064
#> GSM1022341 1 0.2759 0.5295 0.880 0.000 0.008 0.040 0.008 0.064
#> GSM1022342 1 0.2759 0.5295 0.880 0.000 0.008 0.040 0.008 0.064
#> GSM1022343 1 0.2759 0.5295 0.880 0.000 0.008 0.040 0.008 0.064
#> GSM1022347 3 0.1232 0.7779 0.004 0.000 0.956 0.024 0.016 0.000
#> GSM1022348 3 0.1232 0.7779 0.004 0.000 0.956 0.024 0.016 0.000
#> GSM1022349 3 0.1232 0.7779 0.004 0.000 0.956 0.024 0.016 0.000
#> GSM1022350 3 0.1232 0.7779 0.004 0.000 0.956 0.024 0.016 0.000
#> GSM1022344 3 0.6684 0.3388 0.388 0.000 0.440 0.068 0.020 0.084
#> GSM1022345 3 0.6691 0.3139 0.400 0.000 0.428 0.068 0.020 0.084
#> GSM1022346 3 0.6691 0.3139 0.400 0.000 0.428 0.068 0.020 0.084
#> GSM1022355 1 0.2699 0.5510 0.864 0.000 0.000 0.008 0.108 0.020
#> GSM1022356 1 0.2699 0.5510 0.864 0.000 0.000 0.008 0.108 0.020
#> GSM1022357 1 0.2699 0.5510 0.864 0.000 0.000 0.008 0.108 0.020
#> GSM1022358 1 0.2699 0.5510 0.864 0.000 0.000 0.008 0.108 0.020
#> GSM1022351 1 0.0000 0.5734 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022352 1 0.0000 0.5734 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022353 1 0.0000 0.5734 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022354 1 0.0000 0.5734 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022359 2 0.2976 0.8583 0.000 0.872 0.004 0.048 0.028 0.048
#> GSM1022360 2 0.2976 0.8583 0.000 0.872 0.004 0.048 0.028 0.048
#> GSM1022361 2 0.2976 0.8583 0.000 0.872 0.004 0.048 0.028 0.048
#> GSM1022362 2 0.2976 0.8583 0.000 0.872 0.004 0.048 0.028 0.048
#> GSM1022367 6 0.4157 0.4454 0.000 0.004 0.276 0.000 0.032 0.688
#> GSM1022368 6 0.4157 0.4454 0.000 0.004 0.276 0.000 0.032 0.688
#> GSM1022369 6 0.4157 0.4454 0.000 0.004 0.276 0.000 0.032 0.688
#> GSM1022370 6 0.4157 0.4454 0.000 0.004 0.276 0.000 0.032 0.688
#> GSM1022363 6 0.6077 0.3602 0.000 0.412 0.000 0.076 0.060 0.452
#> GSM1022364 6 0.6077 0.3602 0.000 0.412 0.000 0.076 0.060 0.452
#> GSM1022365 6 0.6077 0.3602 0.000 0.412 0.000 0.076 0.060 0.452
#> GSM1022366 6 0.6077 0.3602 0.000 0.412 0.000 0.076 0.060 0.452
#> GSM1022374 5 0.3859 0.9763 0.252 0.004 0.000 0.004 0.724 0.016
#> GSM1022375 5 0.3859 0.9763 0.252 0.004 0.000 0.004 0.724 0.016
#> GSM1022376 5 0.3859 0.9763 0.252 0.004 0.000 0.004 0.724 0.016
#> GSM1022371 2 0.3041 0.8422 0.000 0.864 0.000 0.044 0.056 0.036
#> GSM1022372 2 0.3041 0.8422 0.000 0.864 0.000 0.044 0.056 0.036
#> GSM1022373 2 0.3041 0.8422 0.000 0.864 0.000 0.044 0.056 0.036
#> GSM1022377 4 0.4664 0.8338 0.000 0.248 0.000 0.680 0.016 0.056
#> GSM1022378 4 0.4664 0.8338 0.000 0.248 0.000 0.680 0.016 0.056
#> GSM1022379 4 0.4664 0.8338 0.000 0.248 0.000 0.680 0.016 0.056
#> GSM1022380 4 0.4664 0.8338 0.000 0.248 0.000 0.680 0.016 0.056
#> GSM1022385 3 0.1623 0.7728 0.004 0.000 0.940 0.020 0.032 0.004
#> GSM1022386 3 0.1623 0.7728 0.004 0.000 0.940 0.020 0.032 0.004
#> GSM1022387 3 0.1623 0.7728 0.004 0.000 0.940 0.020 0.032 0.004
#> GSM1022388 3 0.1623 0.7728 0.004 0.000 0.940 0.020 0.032 0.004
#> GSM1022381 4 0.3854 0.8292 0.000 0.188 0.000 0.760 0.004 0.048
#> GSM1022382 4 0.3854 0.8292 0.000 0.188 0.000 0.760 0.004 0.048
#> GSM1022383 4 0.3854 0.8292 0.000 0.188 0.000 0.760 0.004 0.048
#> GSM1022384 4 0.3854 0.8292 0.000 0.188 0.000 0.760 0.004 0.048
#> GSM1022393 1 0.5844 0.0441 0.480 0.000 0.000 0.048 0.404 0.068
#> GSM1022394 1 0.5844 0.0441 0.480 0.000 0.000 0.048 0.404 0.068
#> GSM1022395 1 0.5844 0.0441 0.480 0.000 0.000 0.048 0.404 0.068
#> GSM1022396 1 0.5844 0.0441 0.480 0.000 0.000 0.048 0.404 0.068
#> GSM1022389 4 0.6097 0.7453 0.000 0.292 0.000 0.544 0.108 0.056
#> GSM1022390 4 0.6097 0.7453 0.000 0.292 0.000 0.544 0.108 0.056
#> GSM1022391 4 0.6097 0.7453 0.000 0.292 0.000 0.544 0.108 0.056
#> GSM1022392 4 0.6097 0.7453 0.000 0.292 0.000 0.544 0.108 0.056
#> GSM1022397 3 0.0146 0.7826 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM1022398 3 0.0146 0.7826 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM1022399 3 0.0146 0.7826 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM1022400 3 0.0146 0.7826 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM1022401 1 0.5850 0.0416 0.480 0.000 0.000 0.052 0.404 0.064
#> GSM1022402 1 0.5850 0.0416 0.480 0.000 0.000 0.052 0.404 0.064
#> GSM1022403 1 0.5850 0.0416 0.480 0.000 0.000 0.052 0.404 0.064
#> GSM1022404 1 0.5850 0.0416 0.480 0.000 0.000 0.052 0.404 0.064
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 protocol(p) cell.type(p) k
#> CV:kmeans 50 1.35e-04 4.90e-09 2
#> CV:kmeans 80 2.40e-10 5.36e-11 3
#> CV:kmeans 80 2.40e-10 5.36e-11 4
#> CV:kmeans 65 3.37e-18 4.76e-11 5
#> CV:kmeans 58 3.59e-17 1.78e-09 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 31589 rows and 80 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.957 0.983 0.5045 0.494 0.494
#> 3 3 1.000 1.000 1.000 0.3229 0.750 0.535
#> 4 4 0.861 0.862 0.854 0.0974 0.947 0.840
#> 5 5 0.813 0.861 0.894 0.0790 0.904 0.665
#> 6 6 0.843 0.828 0.887 0.0431 0.937 0.704
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
#> GSM1022325 2 0.0000 0.967 0.000 1.000
#> GSM1022326 2 0.0000 0.967 0.000 1.000
#> GSM1022327 2 0.0000 0.967 0.000 1.000
#> GSM1022331 1 0.0000 0.996 1.000 0.000
#> GSM1022332 1 0.0000 0.996 1.000 0.000
#> GSM1022333 1 0.0000 0.996 1.000 0.000
#> GSM1022328 2 0.0000 0.967 0.000 1.000
#> GSM1022329 2 0.0000 0.967 0.000 1.000
#> GSM1022330 2 0.0000 0.967 0.000 1.000
#> GSM1022337 1 0.3114 0.941 0.944 0.056
#> GSM1022338 1 0.3114 0.941 0.944 0.056
#> GSM1022339 1 0.3114 0.941 0.944 0.056
#> GSM1022334 2 0.0000 0.967 0.000 1.000
#> GSM1022335 2 0.0000 0.967 0.000 1.000
#> GSM1022336 2 0.0000 0.967 0.000 1.000
#> GSM1022340 1 0.0000 0.996 1.000 0.000
#> GSM1022341 1 0.0000 0.996 1.000 0.000
#> GSM1022342 1 0.0000 0.996 1.000 0.000
#> GSM1022343 1 0.0000 0.996 1.000 0.000
#> GSM1022347 1 0.0000 0.996 1.000 0.000
#> GSM1022348 1 0.0000 0.996 1.000 0.000
#> GSM1022349 1 0.0000 0.996 1.000 0.000
#> GSM1022350 1 0.0000 0.996 1.000 0.000
#> GSM1022344 1 0.0000 0.996 1.000 0.000
#> GSM1022345 1 0.0000 0.996 1.000 0.000
#> GSM1022346 1 0.0000 0.996 1.000 0.000
#> GSM1022355 1 0.0000 0.996 1.000 0.000
#> GSM1022356 1 0.0000 0.996 1.000 0.000
#> GSM1022357 1 0.0000 0.996 1.000 0.000
#> GSM1022358 1 0.0000 0.996 1.000 0.000
#> GSM1022351 1 0.0000 0.996 1.000 0.000
#> GSM1022352 1 0.0000 0.996 1.000 0.000
#> GSM1022353 1 0.0000 0.996 1.000 0.000
#> GSM1022354 1 0.0000 0.996 1.000 0.000
#> GSM1022359 2 0.0000 0.967 0.000 1.000
#> GSM1022360 2 0.0000 0.967 0.000 1.000
#> GSM1022361 2 0.0000 0.967 0.000 1.000
#> GSM1022362 2 0.0000 0.967 0.000 1.000
#> GSM1022367 2 0.0376 0.964 0.004 0.996
#> GSM1022368 2 0.0376 0.964 0.004 0.996
#> GSM1022369 2 0.0376 0.964 0.004 0.996
#> GSM1022370 2 0.0376 0.964 0.004 0.996
#> GSM1022363 2 0.0000 0.967 0.000 1.000
#> GSM1022364 2 0.0000 0.967 0.000 1.000
#> GSM1022365 2 0.0000 0.967 0.000 1.000
#> GSM1022366 2 0.0000 0.967 0.000 1.000
#> GSM1022374 2 0.9710 0.362 0.400 0.600
#> GSM1022375 2 0.9710 0.362 0.400 0.600
#> GSM1022376 2 0.9710 0.362 0.400 0.600
#> GSM1022371 2 0.0000 0.967 0.000 1.000
#> GSM1022372 2 0.0000 0.967 0.000 1.000
#> GSM1022373 2 0.0000 0.967 0.000 1.000
#> GSM1022377 2 0.0000 0.967 0.000 1.000
#> GSM1022378 2 0.0000 0.967 0.000 1.000
#> GSM1022379 2 0.0000 0.967 0.000 1.000
#> GSM1022380 2 0.0000 0.967 0.000 1.000
#> GSM1022385 1 0.0000 0.996 1.000 0.000
#> GSM1022386 1 0.0000 0.996 1.000 0.000
#> GSM1022387 1 0.0000 0.996 1.000 0.000
#> GSM1022388 1 0.0000 0.996 1.000 0.000
#> GSM1022381 2 0.0000 0.967 0.000 1.000
#> GSM1022382 2 0.0000 0.967 0.000 1.000
#> GSM1022383 2 0.0000 0.967 0.000 1.000
#> GSM1022384 2 0.0000 0.967 0.000 1.000
#> GSM1022393 1 0.0000 0.996 1.000 0.000
#> GSM1022394 1 0.0000 0.996 1.000 0.000
#> GSM1022395 1 0.0000 0.996 1.000 0.000
#> GSM1022396 1 0.0000 0.996 1.000 0.000
#> GSM1022389 2 0.0000 0.967 0.000 1.000
#> GSM1022390 2 0.0000 0.967 0.000 1.000
#> GSM1022391 2 0.0000 0.967 0.000 1.000
#> GSM1022392 2 0.0000 0.967 0.000 1.000
#> GSM1022397 1 0.0000 0.996 1.000 0.000
#> GSM1022398 1 0.0000 0.996 1.000 0.000
#> GSM1022399 1 0.0000 0.996 1.000 0.000
#> GSM1022400 1 0.0000 0.996 1.000 0.000
#> GSM1022401 1 0.0000 0.996 1.000 0.000
#> GSM1022402 1 0.0000 0.996 1.000 0.000
#> GSM1022403 1 0.0000 0.996 1.000 0.000
#> GSM1022404 1 0.0000 0.996 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1022325 2 0 1 0 1 0
#> GSM1022326 2 0 1 0 1 0
#> GSM1022327 2 0 1 0 1 0
#> GSM1022331 3 0 1 0 0 1
#> GSM1022332 3 0 1 0 0 1
#> GSM1022333 3 0 1 0 0 1
#> GSM1022328 2 0 1 0 1 0
#> GSM1022329 2 0 1 0 1 0
#> GSM1022330 2 0 1 0 1 0
#> GSM1022337 1 0 1 1 0 0
#> GSM1022338 1 0 1 1 0 0
#> GSM1022339 1 0 1 1 0 0
#> GSM1022334 2 0 1 0 1 0
#> GSM1022335 2 0 1 0 1 0
#> GSM1022336 2 0 1 0 1 0
#> GSM1022340 1 0 1 1 0 0
#> GSM1022341 1 0 1 1 0 0
#> GSM1022342 1 0 1 1 0 0
#> GSM1022343 1 0 1 1 0 0
#> GSM1022347 3 0 1 0 0 1
#> GSM1022348 3 0 1 0 0 1
#> GSM1022349 3 0 1 0 0 1
#> GSM1022350 3 0 1 0 0 1
#> GSM1022344 3 0 1 0 0 1
#> GSM1022345 3 0 1 0 0 1
#> GSM1022346 3 0 1 0 0 1
#> GSM1022355 1 0 1 1 0 0
#> GSM1022356 1 0 1 1 0 0
#> GSM1022357 1 0 1 1 0 0
#> GSM1022358 1 0 1 1 0 0
#> GSM1022351 1 0 1 1 0 0
#> GSM1022352 1 0 1 1 0 0
#> GSM1022353 1 0 1 1 0 0
#> GSM1022354 1 0 1 1 0 0
#> GSM1022359 2 0 1 0 1 0
#> GSM1022360 2 0 1 0 1 0
#> GSM1022361 2 0 1 0 1 0
#> GSM1022362 2 0 1 0 1 0
#> GSM1022367 3 0 1 0 0 1
#> GSM1022368 3 0 1 0 0 1
#> GSM1022369 3 0 1 0 0 1
#> GSM1022370 3 0 1 0 0 1
#> GSM1022363 2 0 1 0 1 0
#> GSM1022364 2 0 1 0 1 0
#> GSM1022365 2 0 1 0 1 0
#> GSM1022366 2 0 1 0 1 0
#> GSM1022374 1 0 1 1 0 0
#> GSM1022375 1 0 1 1 0 0
#> GSM1022376 1 0 1 1 0 0
#> GSM1022371 2 0 1 0 1 0
#> GSM1022372 2 0 1 0 1 0
#> GSM1022373 2 0 1 0 1 0
#> GSM1022377 2 0 1 0 1 0
#> GSM1022378 2 0 1 0 1 0
#> GSM1022379 2 0 1 0 1 0
#> GSM1022380 2 0 1 0 1 0
#> GSM1022385 3 0 1 0 0 1
#> GSM1022386 3 0 1 0 0 1
#> GSM1022387 3 0 1 0 0 1
#> GSM1022388 3 0 1 0 0 1
#> GSM1022381 2 0 1 0 1 0
#> GSM1022382 2 0 1 0 1 0
#> GSM1022383 2 0 1 0 1 0
#> GSM1022384 2 0 1 0 1 0
#> GSM1022393 1 0 1 1 0 0
#> GSM1022394 1 0 1 1 0 0
#> GSM1022395 1 0 1 1 0 0
#> GSM1022396 1 0 1 1 0 0
#> GSM1022389 2 0 1 0 1 0
#> GSM1022390 2 0 1 0 1 0
#> GSM1022391 2 0 1 0 1 0
#> GSM1022392 2 0 1 0 1 0
#> GSM1022397 3 0 1 0 0 1
#> GSM1022398 3 0 1 0 0 1
#> GSM1022399 3 0 1 0 0 1
#> GSM1022400 3 0 1 0 0 1
#> GSM1022401 1 0 1 1 0 0
#> GSM1022402 1 0 1 1 0 0
#> GSM1022403 1 0 1 1 0 0
#> GSM1022404 1 0 1 1 0 0
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1022325 2 0.0000 0.859 0.000 1.000 0.000 0.000
#> GSM1022326 2 0.0000 0.859 0.000 1.000 0.000 0.000
#> GSM1022327 2 0.0000 0.859 0.000 1.000 0.000 0.000
#> GSM1022331 3 0.0188 0.924 0.004 0.000 0.996 0.000
#> GSM1022332 3 0.0188 0.924 0.004 0.000 0.996 0.000
#> GSM1022333 3 0.0188 0.924 0.004 0.000 0.996 0.000
#> GSM1022328 2 0.0000 0.859 0.000 1.000 0.000 0.000
#> GSM1022329 2 0.0000 0.859 0.000 1.000 0.000 0.000
#> GSM1022330 2 0.0000 0.859 0.000 1.000 0.000 0.000
#> GSM1022337 1 0.5050 0.954 0.588 0.004 0.000 0.408
#> GSM1022338 1 0.5050 0.954 0.588 0.004 0.000 0.408
#> GSM1022339 1 0.5050 0.954 0.588 0.004 0.000 0.408
#> GSM1022334 2 0.0000 0.859 0.000 1.000 0.000 0.000
#> GSM1022335 2 0.0000 0.859 0.000 1.000 0.000 0.000
#> GSM1022336 2 0.0000 0.859 0.000 1.000 0.000 0.000
#> GSM1022340 4 0.1302 0.923 0.000 0.000 0.044 0.956
#> GSM1022341 4 0.1302 0.923 0.000 0.000 0.044 0.956
#> GSM1022342 4 0.1302 0.923 0.000 0.000 0.044 0.956
#> GSM1022343 4 0.1302 0.923 0.000 0.000 0.044 0.956
#> GSM1022347 3 0.0000 0.925 0.000 0.000 1.000 0.000
#> GSM1022348 3 0.0000 0.925 0.000 0.000 1.000 0.000
#> GSM1022349 3 0.0000 0.925 0.000 0.000 1.000 0.000
#> GSM1022350 3 0.0000 0.925 0.000 0.000 1.000 0.000
#> GSM1022344 3 0.4916 0.369 0.000 0.000 0.576 0.424
#> GSM1022345 3 0.4933 0.351 0.000 0.000 0.568 0.432
#> GSM1022346 3 0.4933 0.351 0.000 0.000 0.568 0.432
#> GSM1022355 4 0.0817 0.937 0.024 0.000 0.000 0.976
#> GSM1022356 4 0.0817 0.937 0.024 0.000 0.000 0.976
#> GSM1022357 4 0.0817 0.937 0.024 0.000 0.000 0.976
#> GSM1022358 4 0.0817 0.937 0.024 0.000 0.000 0.976
#> GSM1022351 4 0.0000 0.950 0.000 0.000 0.000 1.000
#> GSM1022352 4 0.0000 0.950 0.000 0.000 0.000 1.000
#> GSM1022353 4 0.0000 0.950 0.000 0.000 0.000 1.000
#> GSM1022354 4 0.0000 0.950 0.000 0.000 0.000 1.000
#> GSM1022359 2 0.0000 0.859 0.000 1.000 0.000 0.000
#> GSM1022360 2 0.0000 0.859 0.000 1.000 0.000 0.000
#> GSM1022361 2 0.0000 0.859 0.000 1.000 0.000 0.000
#> GSM1022362 2 0.0000 0.859 0.000 1.000 0.000 0.000
#> GSM1022367 3 0.1635 0.894 0.008 0.044 0.948 0.000
#> GSM1022368 3 0.1635 0.894 0.008 0.044 0.948 0.000
#> GSM1022369 3 0.1635 0.894 0.008 0.044 0.948 0.000
#> GSM1022370 3 0.1635 0.894 0.008 0.044 0.948 0.000
#> GSM1022363 2 0.0336 0.855 0.008 0.992 0.000 0.000
#> GSM1022364 2 0.0336 0.855 0.008 0.992 0.000 0.000
#> GSM1022365 2 0.0336 0.855 0.008 0.992 0.000 0.000
#> GSM1022366 2 0.0336 0.855 0.008 0.992 0.000 0.000
#> GSM1022374 1 0.6309 0.862 0.588 0.076 0.000 0.336
#> GSM1022375 1 0.6309 0.862 0.588 0.076 0.000 0.336
#> GSM1022376 1 0.6309 0.862 0.588 0.076 0.000 0.336
#> GSM1022371 2 0.0000 0.859 0.000 1.000 0.000 0.000
#> GSM1022372 2 0.0000 0.859 0.000 1.000 0.000 0.000
#> GSM1022373 2 0.0000 0.859 0.000 1.000 0.000 0.000
#> GSM1022377 2 0.4866 0.743 0.404 0.596 0.000 0.000
#> GSM1022378 2 0.4866 0.743 0.404 0.596 0.000 0.000
#> GSM1022379 2 0.4866 0.743 0.404 0.596 0.000 0.000
#> GSM1022380 2 0.4866 0.743 0.404 0.596 0.000 0.000
#> GSM1022385 3 0.0000 0.925 0.000 0.000 1.000 0.000
#> GSM1022386 3 0.0000 0.925 0.000 0.000 1.000 0.000
#> GSM1022387 3 0.0000 0.925 0.000 0.000 1.000 0.000
#> GSM1022388 3 0.0000 0.925 0.000 0.000 1.000 0.000
#> GSM1022381 2 0.4866 0.743 0.404 0.596 0.000 0.000
#> GSM1022382 2 0.4866 0.743 0.404 0.596 0.000 0.000
#> GSM1022383 2 0.4866 0.743 0.404 0.596 0.000 0.000
#> GSM1022384 2 0.4866 0.743 0.404 0.596 0.000 0.000
#> GSM1022393 1 0.4898 0.957 0.584 0.000 0.000 0.416
#> GSM1022394 1 0.4898 0.957 0.584 0.000 0.000 0.416
#> GSM1022395 1 0.4898 0.957 0.584 0.000 0.000 0.416
#> GSM1022396 1 0.4898 0.957 0.584 0.000 0.000 0.416
#> GSM1022389 2 0.4804 0.751 0.384 0.616 0.000 0.000
#> GSM1022390 2 0.4804 0.751 0.384 0.616 0.000 0.000
#> GSM1022391 2 0.4804 0.751 0.384 0.616 0.000 0.000
#> GSM1022392 2 0.4804 0.751 0.384 0.616 0.000 0.000
#> GSM1022397 3 0.0000 0.925 0.000 0.000 1.000 0.000
#> GSM1022398 3 0.0000 0.925 0.000 0.000 1.000 0.000
#> GSM1022399 3 0.0000 0.925 0.000 0.000 1.000 0.000
#> GSM1022400 3 0.0000 0.925 0.000 0.000 1.000 0.000
#> GSM1022401 1 0.4898 0.957 0.584 0.000 0.000 0.416
#> GSM1022402 1 0.4898 0.957 0.584 0.000 0.000 0.416
#> GSM1022403 1 0.4898 0.957 0.584 0.000 0.000 0.416
#> GSM1022404 1 0.4898 0.957 0.584 0.000 0.000 0.416
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1022325 2 0.2891 0.936 0.000 0.824 0.000 0.176 0.000
#> GSM1022326 2 0.2891 0.936 0.000 0.824 0.000 0.176 0.000
#> GSM1022327 2 0.2891 0.936 0.000 0.824 0.000 0.176 0.000
#> GSM1022331 3 0.1205 0.899 0.040 0.000 0.956 0.004 0.000
#> GSM1022332 3 0.1205 0.899 0.040 0.000 0.956 0.004 0.000
#> GSM1022333 3 0.1205 0.899 0.040 0.000 0.956 0.004 0.000
#> GSM1022328 2 0.2891 0.936 0.000 0.824 0.000 0.176 0.000
#> GSM1022329 2 0.2891 0.936 0.000 0.824 0.000 0.176 0.000
#> GSM1022330 2 0.2891 0.936 0.000 0.824 0.000 0.176 0.000
#> GSM1022337 5 0.0162 0.874 0.004 0.000 0.000 0.000 0.996
#> GSM1022338 5 0.0162 0.874 0.004 0.000 0.000 0.000 0.996
#> GSM1022339 5 0.0162 0.874 0.004 0.000 0.000 0.000 0.996
#> GSM1022334 2 0.2891 0.936 0.000 0.824 0.000 0.176 0.000
#> GSM1022335 2 0.2891 0.936 0.000 0.824 0.000 0.176 0.000
#> GSM1022336 2 0.2891 0.936 0.000 0.824 0.000 0.176 0.000
#> GSM1022340 1 0.1630 0.864 0.944 0.000 0.036 0.004 0.016
#> GSM1022341 1 0.1630 0.864 0.944 0.000 0.036 0.004 0.016
#> GSM1022342 1 0.1630 0.864 0.944 0.000 0.036 0.004 0.016
#> GSM1022343 1 0.1630 0.864 0.944 0.000 0.036 0.004 0.016
#> GSM1022347 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000
#> GSM1022348 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000
#> GSM1022349 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000
#> GSM1022350 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000
#> GSM1022344 3 0.4452 -0.159 0.496 0.000 0.500 0.004 0.000
#> GSM1022345 1 0.4415 0.237 0.552 0.000 0.444 0.004 0.000
#> GSM1022346 1 0.4420 0.225 0.548 0.000 0.448 0.004 0.000
#> GSM1022355 1 0.2020 0.845 0.900 0.000 0.000 0.000 0.100
#> GSM1022356 1 0.2127 0.836 0.892 0.000 0.000 0.000 0.108
#> GSM1022357 1 0.2020 0.845 0.900 0.000 0.000 0.000 0.100
#> GSM1022358 1 0.2020 0.845 0.900 0.000 0.000 0.000 0.100
#> GSM1022351 1 0.1270 0.869 0.948 0.000 0.000 0.000 0.052
#> GSM1022352 1 0.1270 0.869 0.948 0.000 0.000 0.000 0.052
#> GSM1022353 1 0.1270 0.869 0.948 0.000 0.000 0.000 0.052
#> GSM1022354 1 0.1270 0.869 0.948 0.000 0.000 0.000 0.052
#> GSM1022359 2 0.3003 0.930 0.000 0.812 0.000 0.188 0.000
#> GSM1022360 2 0.3003 0.930 0.000 0.812 0.000 0.188 0.000
#> GSM1022361 2 0.3003 0.930 0.000 0.812 0.000 0.188 0.000
#> GSM1022362 2 0.3003 0.930 0.000 0.812 0.000 0.188 0.000
#> GSM1022367 3 0.4735 0.778 0.052 0.176 0.752 0.004 0.016
#> GSM1022368 3 0.4735 0.778 0.052 0.176 0.752 0.004 0.016
#> GSM1022369 3 0.4735 0.778 0.052 0.176 0.752 0.004 0.016
#> GSM1022370 3 0.4735 0.778 0.052 0.176 0.752 0.004 0.016
#> GSM1022363 2 0.1087 0.769 0.016 0.968 0.000 0.008 0.008
#> GSM1022364 2 0.1087 0.769 0.016 0.968 0.000 0.008 0.008
#> GSM1022365 2 0.1087 0.769 0.016 0.968 0.000 0.008 0.008
#> GSM1022366 2 0.1087 0.769 0.016 0.968 0.000 0.008 0.008
#> GSM1022374 5 0.0162 0.872 0.000 0.004 0.000 0.000 0.996
#> GSM1022375 5 0.0162 0.872 0.000 0.004 0.000 0.000 0.996
#> GSM1022376 5 0.0162 0.872 0.000 0.004 0.000 0.000 0.996
#> GSM1022371 2 0.2966 0.932 0.000 0.816 0.000 0.184 0.000
#> GSM1022372 2 0.2966 0.932 0.000 0.816 0.000 0.184 0.000
#> GSM1022373 2 0.2966 0.932 0.000 0.816 0.000 0.184 0.000
#> GSM1022377 4 0.0609 0.945 0.000 0.020 0.000 0.980 0.000
#> GSM1022378 4 0.0609 0.945 0.000 0.020 0.000 0.980 0.000
#> GSM1022379 4 0.0609 0.945 0.000 0.020 0.000 0.980 0.000
#> GSM1022380 4 0.0609 0.945 0.000 0.020 0.000 0.980 0.000
#> GSM1022385 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000
#> GSM1022386 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000
#> GSM1022387 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000
#> GSM1022388 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000
#> GSM1022381 4 0.0510 0.945 0.000 0.016 0.000 0.984 0.000
#> GSM1022382 4 0.0510 0.945 0.000 0.016 0.000 0.984 0.000
#> GSM1022383 4 0.0510 0.945 0.000 0.016 0.000 0.984 0.000
#> GSM1022384 4 0.0510 0.945 0.000 0.016 0.000 0.984 0.000
#> GSM1022393 5 0.2891 0.898 0.176 0.000 0.000 0.000 0.824
#> GSM1022394 5 0.2891 0.898 0.176 0.000 0.000 0.000 0.824
#> GSM1022395 5 0.2891 0.898 0.176 0.000 0.000 0.000 0.824
#> GSM1022396 5 0.2891 0.898 0.176 0.000 0.000 0.000 0.824
#> GSM1022389 4 0.2377 0.881 0.000 0.128 0.000 0.872 0.000
#> GSM1022390 4 0.2377 0.881 0.000 0.128 0.000 0.872 0.000
#> GSM1022391 4 0.2377 0.881 0.000 0.128 0.000 0.872 0.000
#> GSM1022392 4 0.2377 0.881 0.000 0.128 0.000 0.872 0.000
#> GSM1022397 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000
#> GSM1022398 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000
#> GSM1022399 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000
#> GSM1022400 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000
#> GSM1022401 5 0.2891 0.898 0.176 0.000 0.000 0.000 0.824
#> GSM1022402 5 0.2891 0.898 0.176 0.000 0.000 0.000 0.824
#> GSM1022403 5 0.2891 0.898 0.176 0.000 0.000 0.000 0.824
#> GSM1022404 5 0.2891 0.898 0.176 0.000 0.000 0.000 0.824
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1022325 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022326 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022327 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022331 3 0.2597 0.736 0.000 0.000 0.824 0.000 0.000 0.176
#> GSM1022332 3 0.2597 0.736 0.000 0.000 0.824 0.000 0.000 0.176
#> GSM1022333 3 0.2597 0.736 0.000 0.000 0.824 0.000 0.000 0.176
#> GSM1022328 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022329 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022330 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022337 5 0.0000 0.816 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1022338 5 0.0000 0.816 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1022339 5 0.0000 0.816 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1022334 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022335 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022336 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022340 1 0.1500 0.896 0.936 0.000 0.012 0.000 0.000 0.052
#> GSM1022341 1 0.1500 0.896 0.936 0.000 0.012 0.000 0.000 0.052
#> GSM1022342 1 0.1500 0.896 0.936 0.000 0.012 0.000 0.000 0.052
#> GSM1022343 1 0.1500 0.896 0.936 0.000 0.012 0.000 0.000 0.052
#> GSM1022347 3 0.0000 0.879 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022348 3 0.0000 0.879 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022349 3 0.0000 0.879 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022350 3 0.0000 0.879 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022344 3 0.4181 0.601 0.248 0.000 0.700 0.000 0.000 0.052
#> GSM1022345 3 0.4684 0.379 0.372 0.000 0.576 0.000 0.000 0.052
#> GSM1022346 3 0.4653 0.406 0.360 0.000 0.588 0.000 0.000 0.052
#> GSM1022355 1 0.3095 0.833 0.840 0.000 0.000 0.008 0.036 0.116
#> GSM1022356 1 0.3165 0.828 0.836 0.000 0.000 0.008 0.040 0.116
#> GSM1022357 1 0.3095 0.833 0.840 0.000 0.000 0.008 0.036 0.116
#> GSM1022358 1 0.3095 0.833 0.840 0.000 0.000 0.008 0.036 0.116
#> GSM1022351 1 0.0000 0.909 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022352 1 0.0000 0.909 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022353 1 0.0000 0.909 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022354 1 0.0000 0.909 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022359 2 0.0458 0.978 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM1022360 2 0.0458 0.978 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM1022361 2 0.0458 0.978 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM1022362 2 0.0458 0.978 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM1022367 6 0.3309 0.540 0.000 0.000 0.280 0.000 0.000 0.720
#> GSM1022368 6 0.3309 0.540 0.000 0.000 0.280 0.000 0.000 0.720
#> GSM1022369 6 0.3309 0.540 0.000 0.000 0.280 0.000 0.000 0.720
#> GSM1022370 6 0.3309 0.540 0.000 0.000 0.280 0.000 0.000 0.720
#> GSM1022363 6 0.3847 0.449 0.000 0.456 0.000 0.000 0.000 0.544
#> GSM1022364 6 0.3847 0.449 0.000 0.456 0.000 0.000 0.000 0.544
#> GSM1022365 6 0.3847 0.449 0.000 0.456 0.000 0.000 0.000 0.544
#> GSM1022366 6 0.3847 0.449 0.000 0.456 0.000 0.000 0.000 0.544
#> GSM1022374 5 0.0000 0.816 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1022375 5 0.0000 0.816 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1022376 5 0.0000 0.816 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1022371 2 0.0458 0.976 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM1022372 2 0.0458 0.976 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM1022373 2 0.0458 0.976 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM1022377 4 0.0713 0.894 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM1022378 4 0.0713 0.894 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM1022379 4 0.0713 0.894 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM1022380 4 0.0713 0.894 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM1022385 3 0.0000 0.879 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022386 3 0.0000 0.879 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022387 3 0.0000 0.879 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022388 3 0.0000 0.879 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022381 4 0.0713 0.894 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM1022382 4 0.0713 0.894 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM1022383 4 0.0713 0.894 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM1022384 4 0.0713 0.894 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM1022393 5 0.4548 0.847 0.156 0.000 0.000 0.008 0.720 0.116
#> GSM1022394 5 0.4548 0.847 0.156 0.000 0.000 0.008 0.720 0.116
#> GSM1022395 5 0.4548 0.847 0.156 0.000 0.000 0.008 0.720 0.116
#> GSM1022396 5 0.4548 0.847 0.156 0.000 0.000 0.008 0.720 0.116
#> GSM1022389 4 0.4456 0.767 0.000 0.180 0.000 0.708 0.000 0.112
#> GSM1022390 4 0.4456 0.767 0.000 0.180 0.000 0.708 0.000 0.112
#> GSM1022391 4 0.4456 0.767 0.000 0.180 0.000 0.708 0.000 0.112
#> GSM1022392 4 0.4456 0.767 0.000 0.180 0.000 0.708 0.000 0.112
#> GSM1022397 3 0.0000 0.879 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022398 3 0.0000 0.879 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022399 3 0.0000 0.879 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022400 3 0.0000 0.879 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022401 5 0.4548 0.847 0.156 0.000 0.000 0.008 0.720 0.116
#> GSM1022402 5 0.4548 0.847 0.156 0.000 0.000 0.008 0.720 0.116
#> GSM1022403 5 0.4548 0.847 0.156 0.000 0.000 0.008 0.720 0.116
#> GSM1022404 5 0.4548 0.847 0.156 0.000 0.000 0.008 0.720 0.116
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 protocol(p) cell.type(p) k
#> CV:skmeans 77 4.63e-06 1.59e-07 2
#> CV:skmeans 80 2.40e-10 5.36e-11 3
#> CV:skmeans 77 6.46e-16 2.62e-14 4
#> CV:skmeans 77 1.84e-20 1.36e-13 5
#> CV:skmeans 74 8.39e-29 1.48e-11 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 31589 rows and 80 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.810 0.896 0.954 0.5040 0.495 0.495
#> 3 3 0.962 0.957 0.982 0.3238 0.689 0.452
#> 4 4 0.865 0.928 0.912 0.1070 0.914 0.744
#> 5 5 0.840 0.782 0.864 0.0640 0.962 0.852
#> 6 6 0.893 0.901 0.946 0.0512 0.938 0.726
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
#> GSM1022325 2 0.000 0.905 0.000 1.000
#> GSM1022326 2 0.000 0.905 0.000 1.000
#> GSM1022327 2 0.000 0.905 0.000 1.000
#> GSM1022331 1 0.000 1.000 1.000 0.000
#> GSM1022332 1 0.000 1.000 1.000 0.000
#> GSM1022333 1 0.000 1.000 1.000 0.000
#> GSM1022328 2 0.000 0.905 0.000 1.000
#> GSM1022329 2 0.000 0.905 0.000 1.000
#> GSM1022330 2 0.000 0.905 0.000 1.000
#> GSM1022337 2 0.971 0.429 0.400 0.600
#> GSM1022338 2 0.971 0.429 0.400 0.600
#> GSM1022339 2 0.971 0.429 0.400 0.600
#> GSM1022334 2 0.000 0.905 0.000 1.000
#> GSM1022335 2 0.000 0.905 0.000 1.000
#> GSM1022336 2 0.000 0.905 0.000 1.000
#> GSM1022340 1 0.000 1.000 1.000 0.000
#> GSM1022341 1 0.000 1.000 1.000 0.000
#> GSM1022342 1 0.000 1.000 1.000 0.000
#> GSM1022343 1 0.000 1.000 1.000 0.000
#> GSM1022347 1 0.000 1.000 1.000 0.000
#> GSM1022348 1 0.000 1.000 1.000 0.000
#> GSM1022349 1 0.000 1.000 1.000 0.000
#> GSM1022350 1 0.000 1.000 1.000 0.000
#> GSM1022344 1 0.000 1.000 1.000 0.000
#> GSM1022345 1 0.000 1.000 1.000 0.000
#> GSM1022346 1 0.000 1.000 1.000 0.000
#> GSM1022355 1 0.000 1.000 1.000 0.000
#> GSM1022356 1 0.000 1.000 1.000 0.000
#> GSM1022357 1 0.000 1.000 1.000 0.000
#> GSM1022358 1 0.000 1.000 1.000 0.000
#> GSM1022351 1 0.000 1.000 1.000 0.000
#> GSM1022352 1 0.000 1.000 1.000 0.000
#> GSM1022353 1 0.000 1.000 1.000 0.000
#> GSM1022354 1 0.000 1.000 1.000 0.000
#> GSM1022359 2 0.000 0.905 0.000 1.000
#> GSM1022360 2 0.000 0.905 0.000 1.000
#> GSM1022361 2 0.000 0.905 0.000 1.000
#> GSM1022362 2 0.000 0.905 0.000 1.000
#> GSM1022367 2 0.722 0.729 0.200 0.800
#> GSM1022368 2 0.971 0.386 0.400 0.600
#> GSM1022369 2 0.971 0.386 0.400 0.600
#> GSM1022370 2 0.722 0.729 0.200 0.800
#> GSM1022363 2 0.000 0.905 0.000 1.000
#> GSM1022364 2 0.000 0.905 0.000 1.000
#> GSM1022365 2 0.000 0.905 0.000 1.000
#> GSM1022366 2 0.000 0.905 0.000 1.000
#> GSM1022374 2 0.971 0.429 0.400 0.600
#> GSM1022375 2 0.971 0.429 0.400 0.600
#> GSM1022376 2 0.971 0.429 0.400 0.600
#> GSM1022371 2 0.000 0.905 0.000 1.000
#> GSM1022372 2 0.000 0.905 0.000 1.000
#> GSM1022373 2 0.000 0.905 0.000 1.000
#> GSM1022377 2 0.000 0.905 0.000 1.000
#> GSM1022378 2 0.000 0.905 0.000 1.000
#> GSM1022379 2 0.000 0.905 0.000 1.000
#> GSM1022380 2 0.000 0.905 0.000 1.000
#> GSM1022385 1 0.000 1.000 1.000 0.000
#> GSM1022386 1 0.000 1.000 1.000 0.000
#> GSM1022387 1 0.000 1.000 1.000 0.000
#> GSM1022388 1 0.000 1.000 1.000 0.000
#> GSM1022381 2 0.000 0.905 0.000 1.000
#> GSM1022382 2 0.000 0.905 0.000 1.000
#> GSM1022383 2 0.000 0.905 0.000 1.000
#> GSM1022384 2 0.000 0.905 0.000 1.000
#> GSM1022393 1 0.000 1.000 1.000 0.000
#> GSM1022394 1 0.000 1.000 1.000 0.000
#> GSM1022395 1 0.000 1.000 1.000 0.000
#> GSM1022396 1 0.000 1.000 1.000 0.000
#> GSM1022389 2 0.000 0.905 0.000 1.000
#> GSM1022390 2 0.000 0.905 0.000 1.000
#> GSM1022391 2 0.000 0.905 0.000 1.000
#> GSM1022392 2 0.443 0.839 0.092 0.908
#> GSM1022397 1 0.000 1.000 1.000 0.000
#> GSM1022398 1 0.000 1.000 1.000 0.000
#> GSM1022399 1 0.000 1.000 1.000 0.000
#> GSM1022400 1 0.000 1.000 1.000 0.000
#> GSM1022401 1 0.000 1.000 1.000 0.000
#> GSM1022402 1 0.000 1.000 1.000 0.000
#> GSM1022403 1 0.000 1.000 1.000 0.000
#> GSM1022404 1 0.000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1022325 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022326 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022327 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022331 3 0.000 0.981 0.000 0.000 1.000
#> GSM1022332 3 0.000 0.981 0.000 0.000 1.000
#> GSM1022333 3 0.000 0.981 0.000 0.000 1.000
#> GSM1022328 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022329 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022330 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022337 1 0.000 0.956 1.000 0.000 0.000
#> GSM1022338 1 0.000 0.956 1.000 0.000 0.000
#> GSM1022339 1 0.000 0.956 1.000 0.000 0.000
#> GSM1022334 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022335 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022336 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022340 1 0.000 0.956 1.000 0.000 0.000
#> GSM1022341 1 0.000 0.956 1.000 0.000 0.000
#> GSM1022342 1 0.000 0.956 1.000 0.000 0.000
#> GSM1022343 1 0.000 0.956 1.000 0.000 0.000
#> GSM1022347 3 0.000 0.981 0.000 0.000 1.000
#> GSM1022348 3 0.000 0.981 0.000 0.000 1.000
#> GSM1022349 3 0.000 0.981 0.000 0.000 1.000
#> GSM1022350 3 0.000 0.981 0.000 0.000 1.000
#> GSM1022344 3 0.000 0.981 0.000 0.000 1.000
#> GSM1022345 3 0.000 0.981 0.000 0.000 1.000
#> GSM1022346 3 0.000 0.981 0.000 0.000 1.000
#> GSM1022355 1 0.000 0.956 1.000 0.000 0.000
#> GSM1022356 1 0.000 0.956 1.000 0.000 0.000
#> GSM1022357 1 0.000 0.956 1.000 0.000 0.000
#> GSM1022358 1 0.000 0.956 1.000 0.000 0.000
#> GSM1022351 1 0.000 0.956 1.000 0.000 0.000
#> GSM1022352 1 0.000 0.956 1.000 0.000 0.000
#> GSM1022353 1 0.000 0.956 1.000 0.000 0.000
#> GSM1022354 1 0.000 0.956 1.000 0.000 0.000
#> GSM1022359 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022360 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022361 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022362 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022367 3 0.435 0.782 0.000 0.184 0.816
#> GSM1022368 3 0.000 0.981 0.000 0.000 1.000
#> GSM1022369 3 0.000 0.981 0.000 0.000 1.000
#> GSM1022370 3 0.450 0.765 0.000 0.196 0.804
#> GSM1022363 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022364 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022365 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022366 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022374 1 0.418 0.788 0.828 0.172 0.000
#> GSM1022375 1 0.424 0.783 0.824 0.176 0.000
#> GSM1022376 1 0.000 0.956 1.000 0.000 0.000
#> GSM1022371 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022372 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022373 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022377 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022378 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022379 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022380 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022385 3 0.000 0.981 0.000 0.000 1.000
#> GSM1022386 3 0.000 0.981 0.000 0.000 1.000
#> GSM1022387 3 0.000 0.981 0.000 0.000 1.000
#> GSM1022388 3 0.000 0.981 0.000 0.000 1.000
#> GSM1022381 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022382 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022383 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022384 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022393 1 0.000 0.956 1.000 0.000 0.000
#> GSM1022394 1 0.000 0.956 1.000 0.000 0.000
#> GSM1022395 1 0.000 0.956 1.000 0.000 0.000
#> GSM1022396 1 0.000 0.956 1.000 0.000 0.000
#> GSM1022389 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022390 1 0.615 0.343 0.592 0.408 0.000
#> GSM1022391 2 0.000 1.000 0.000 1.000 0.000
#> GSM1022392 1 0.562 0.573 0.692 0.308 0.000
#> GSM1022397 3 0.000 0.981 0.000 0.000 1.000
#> GSM1022398 3 0.000 0.981 0.000 0.000 1.000
#> GSM1022399 3 0.000 0.981 0.000 0.000 1.000
#> GSM1022400 3 0.000 0.981 0.000 0.000 1.000
#> GSM1022401 1 0.000 0.956 1.000 0.000 0.000
#> GSM1022402 1 0.000 0.956 1.000 0.000 0.000
#> GSM1022403 1 0.000 0.956 1.000 0.000 0.000
#> GSM1022404 1 0.000 0.956 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1022325 2 0.380 0.981 0.000 0.780 0.000 0.220
#> GSM1022326 2 0.380 0.981 0.000 0.780 0.000 0.220
#> GSM1022327 2 0.380 0.981 0.000 0.780 0.000 0.220
#> GSM1022331 3 0.000 0.973 0.000 0.000 1.000 0.000
#> GSM1022332 3 0.000 0.973 0.000 0.000 1.000 0.000
#> GSM1022333 3 0.000 0.973 0.000 0.000 1.000 0.000
#> GSM1022328 2 0.380 0.981 0.000 0.780 0.000 0.220
#> GSM1022329 2 0.380 0.981 0.000 0.780 0.000 0.220
#> GSM1022330 2 0.380 0.981 0.000 0.780 0.000 0.220
#> GSM1022337 1 0.000 0.888 1.000 0.000 0.000 0.000
#> GSM1022338 1 0.000 0.888 1.000 0.000 0.000 0.000
#> GSM1022339 1 0.000 0.888 1.000 0.000 0.000 0.000
#> GSM1022334 2 0.380 0.981 0.000 0.780 0.000 0.220
#> GSM1022335 2 0.380 0.981 0.000 0.780 0.000 0.220
#> GSM1022336 2 0.380 0.981 0.000 0.780 0.000 0.220
#> GSM1022340 1 0.380 0.881 0.780 0.220 0.000 0.000
#> GSM1022341 1 0.380 0.881 0.780 0.220 0.000 0.000
#> GSM1022342 1 0.380 0.881 0.780 0.220 0.000 0.000
#> GSM1022343 1 0.380 0.881 0.780 0.220 0.000 0.000
#> GSM1022347 3 0.000 0.973 0.000 0.000 1.000 0.000
#> GSM1022348 3 0.000 0.973 0.000 0.000 1.000 0.000
#> GSM1022349 3 0.000 0.973 0.000 0.000 1.000 0.000
#> GSM1022350 3 0.000 0.973 0.000 0.000 1.000 0.000
#> GSM1022344 3 0.000 0.973 0.000 0.000 1.000 0.000
#> GSM1022345 3 0.000 0.973 0.000 0.000 1.000 0.000
#> GSM1022346 3 0.000 0.973 0.000 0.000 1.000 0.000
#> GSM1022355 1 0.380 0.881 0.780 0.220 0.000 0.000
#> GSM1022356 1 0.380 0.881 0.780 0.220 0.000 0.000
#> GSM1022357 1 0.380 0.881 0.780 0.220 0.000 0.000
#> GSM1022358 1 0.380 0.881 0.780 0.220 0.000 0.000
#> GSM1022351 1 0.380 0.881 0.780 0.220 0.000 0.000
#> GSM1022352 1 0.380 0.881 0.780 0.220 0.000 0.000
#> GSM1022353 1 0.380 0.881 0.780 0.220 0.000 0.000
#> GSM1022354 1 0.380 0.881 0.780 0.220 0.000 0.000
#> GSM1022359 2 0.380 0.981 0.000 0.780 0.000 0.220
#> GSM1022360 2 0.380 0.981 0.000 0.780 0.000 0.220
#> GSM1022361 2 0.380 0.981 0.000 0.780 0.000 0.220
#> GSM1022362 2 0.380 0.981 0.000 0.780 0.000 0.220
#> GSM1022367 3 0.471 0.766 0.000 0.152 0.784 0.064
#> GSM1022368 3 0.172 0.927 0.000 0.000 0.936 0.064
#> GSM1022369 3 0.172 0.927 0.000 0.000 0.936 0.064
#> GSM1022370 3 0.485 0.750 0.000 0.164 0.772 0.064
#> GSM1022363 2 0.430 0.920 0.000 0.716 0.000 0.284
#> GSM1022364 2 0.430 0.920 0.000 0.716 0.000 0.284
#> GSM1022365 2 0.430 0.920 0.000 0.716 0.000 0.284
#> GSM1022366 2 0.430 0.920 0.000 0.716 0.000 0.284
#> GSM1022374 1 0.401 0.730 0.820 0.148 0.000 0.032
#> GSM1022375 1 0.406 0.725 0.816 0.152 0.000 0.032
#> GSM1022376 1 0.102 0.870 0.968 0.000 0.000 0.032
#> GSM1022371 2 0.380 0.981 0.000 0.780 0.000 0.220
#> GSM1022372 2 0.380 0.981 0.000 0.780 0.000 0.220
#> GSM1022373 2 0.380 0.981 0.000 0.780 0.000 0.220
#> GSM1022377 4 0.172 0.954 0.000 0.064 0.000 0.936
#> GSM1022378 4 0.172 0.954 0.000 0.064 0.000 0.936
#> GSM1022379 4 0.172 0.954 0.000 0.064 0.000 0.936
#> GSM1022380 4 0.172 0.954 0.000 0.064 0.000 0.936
#> GSM1022385 3 0.000 0.973 0.000 0.000 1.000 0.000
#> GSM1022386 3 0.000 0.973 0.000 0.000 1.000 0.000
#> GSM1022387 3 0.000 0.973 0.000 0.000 1.000 0.000
#> GSM1022388 3 0.000 0.973 0.000 0.000 1.000 0.000
#> GSM1022381 4 0.000 0.935 0.000 0.000 0.000 1.000
#> GSM1022382 4 0.000 0.935 0.000 0.000 0.000 1.000
#> GSM1022383 4 0.000 0.935 0.000 0.000 0.000 1.000
#> GSM1022384 4 0.000 0.935 0.000 0.000 0.000 1.000
#> GSM1022393 1 0.000 0.888 1.000 0.000 0.000 0.000
#> GSM1022394 1 0.000 0.888 1.000 0.000 0.000 0.000
#> GSM1022395 1 0.000 0.888 1.000 0.000 0.000 0.000
#> GSM1022396 1 0.000 0.888 1.000 0.000 0.000 0.000
#> GSM1022389 4 0.194 0.943 0.000 0.076 0.000 0.924
#> GSM1022390 4 0.204 0.941 0.032 0.032 0.000 0.936
#> GSM1022391 4 0.172 0.954 0.000 0.064 0.000 0.936
#> GSM1022392 4 0.203 0.937 0.036 0.028 0.000 0.936
#> GSM1022397 3 0.000 0.973 0.000 0.000 1.000 0.000
#> GSM1022398 3 0.000 0.973 0.000 0.000 1.000 0.000
#> GSM1022399 3 0.000 0.973 0.000 0.000 1.000 0.000
#> GSM1022400 3 0.000 0.973 0.000 0.000 1.000 0.000
#> GSM1022401 1 0.000 0.888 1.000 0.000 0.000 0.000
#> GSM1022402 1 0.000 0.888 1.000 0.000 0.000 0.000
#> GSM1022403 1 0.000 0.888 1.000 0.000 0.000 0.000
#> GSM1022404 1 0.000 0.888 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
#> GSM1022325 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000
#> GSM1022326 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000
#> GSM1022327 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000
#> GSM1022331 3 0.4249 0.647 0.000 0.000 0.568 0.000 0.432
#> GSM1022332 3 0.4249 0.647 0.000 0.000 0.568 0.000 0.432
#> GSM1022333 3 0.4249 0.647 0.000 0.000 0.568 0.000 0.432
#> GSM1022328 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000
#> GSM1022329 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000
#> GSM1022330 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000
#> GSM1022337 5 0.4256 0.811 0.436 0.000 0.000 0.000 0.564
#> GSM1022338 5 0.4256 0.811 0.436 0.000 0.000 0.000 0.564
#> GSM1022339 5 0.4256 0.811 0.436 0.000 0.000 0.000 0.564
#> GSM1022334 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000
#> GSM1022335 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000
#> GSM1022336 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000
#> GSM1022340 1 0.0000 0.807 1.000 0.000 0.000 0.000 0.000
#> GSM1022341 1 0.0000 0.807 1.000 0.000 0.000 0.000 0.000
#> GSM1022342 1 0.0000 0.807 1.000 0.000 0.000 0.000 0.000
#> GSM1022343 1 0.0000 0.807 1.000 0.000 0.000 0.000 0.000
#> GSM1022347 3 0.0000 0.846 0.000 0.000 1.000 0.000 0.000
#> GSM1022348 3 0.0000 0.846 0.000 0.000 1.000 0.000 0.000
#> GSM1022349 3 0.0000 0.846 0.000 0.000 1.000 0.000 0.000
#> GSM1022350 3 0.0000 0.846 0.000 0.000 1.000 0.000 0.000
#> GSM1022344 3 0.0404 0.841 0.012 0.000 0.988 0.000 0.000
#> GSM1022345 3 0.0510 0.839 0.016 0.000 0.984 0.000 0.000
#> GSM1022346 3 0.0510 0.839 0.016 0.000 0.984 0.000 0.000
#> GSM1022355 1 0.0000 0.807 1.000 0.000 0.000 0.000 0.000
#> GSM1022356 1 0.0404 0.801 0.988 0.000 0.000 0.000 0.012
#> GSM1022357 1 0.0000 0.807 1.000 0.000 0.000 0.000 0.000
#> GSM1022358 1 0.0000 0.807 1.000 0.000 0.000 0.000 0.000
#> GSM1022351 1 0.0000 0.807 1.000 0.000 0.000 0.000 0.000
#> GSM1022352 1 0.0000 0.807 1.000 0.000 0.000 0.000 0.000
#> GSM1022353 1 0.0000 0.807 1.000 0.000 0.000 0.000 0.000
#> GSM1022354 1 0.0000 0.807 1.000 0.000 0.000 0.000 0.000
#> GSM1022359 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000
#> GSM1022360 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000
#> GSM1022361 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000
#> GSM1022362 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000
#> GSM1022367 3 0.5293 0.595 0.000 0.000 0.492 0.048 0.460
#> GSM1022368 3 0.5291 0.598 0.000 0.000 0.496 0.048 0.456
#> GSM1022369 3 0.5291 0.598 0.000 0.000 0.496 0.048 0.456
#> GSM1022370 3 0.5293 0.595 0.000 0.000 0.492 0.048 0.460
#> GSM1022363 2 0.5276 0.473 0.000 0.516 0.000 0.048 0.436
#> GSM1022364 2 0.5276 0.473 0.000 0.516 0.000 0.048 0.436
#> GSM1022365 2 0.5276 0.473 0.000 0.516 0.000 0.048 0.436
#> GSM1022366 2 0.5271 0.476 0.000 0.520 0.000 0.048 0.432
#> GSM1022374 5 0.5974 0.711 0.284 0.148 0.000 0.000 0.568
#> GSM1022375 5 0.5939 0.705 0.276 0.148 0.000 0.000 0.576
#> GSM1022376 5 0.4249 0.811 0.432 0.000 0.000 0.000 0.568
#> GSM1022371 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000
#> GSM1022372 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000
#> GSM1022373 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000
#> GSM1022377 4 0.1197 0.890 0.000 0.048 0.000 0.952 0.000
#> GSM1022378 4 0.1197 0.890 0.000 0.048 0.000 0.952 0.000
#> GSM1022379 4 0.1197 0.890 0.000 0.048 0.000 0.952 0.000
#> GSM1022380 4 0.1197 0.890 0.000 0.048 0.000 0.952 0.000
#> GSM1022385 3 0.0000 0.846 0.000 0.000 1.000 0.000 0.000
#> GSM1022386 3 0.0000 0.846 0.000 0.000 1.000 0.000 0.000
#> GSM1022387 3 0.0000 0.846 0.000 0.000 1.000 0.000 0.000
#> GSM1022388 3 0.0000 0.846 0.000 0.000 1.000 0.000 0.000
#> GSM1022381 4 0.0000 0.877 0.000 0.000 0.000 1.000 0.000
#> GSM1022382 4 0.0000 0.877 0.000 0.000 0.000 1.000 0.000
#> GSM1022383 4 0.0000 0.877 0.000 0.000 0.000 1.000 0.000
#> GSM1022384 4 0.0000 0.877 0.000 0.000 0.000 1.000 0.000
#> GSM1022393 1 0.3366 0.615 0.768 0.000 0.000 0.000 0.232
#> GSM1022394 1 0.3366 0.615 0.768 0.000 0.000 0.000 0.232
#> GSM1022395 1 0.3366 0.615 0.768 0.000 0.000 0.000 0.232
#> GSM1022396 1 0.3366 0.615 0.768 0.000 0.000 0.000 0.232
#> GSM1022389 4 0.3480 0.773 0.000 0.248 0.000 0.752 0.000
#> GSM1022390 4 0.3395 0.789 0.000 0.236 0.000 0.764 0.000
#> GSM1022391 4 0.3395 0.789 0.000 0.236 0.000 0.764 0.000
#> GSM1022392 4 0.3521 0.791 0.004 0.232 0.000 0.764 0.000
#> GSM1022397 3 0.0000 0.846 0.000 0.000 1.000 0.000 0.000
#> GSM1022398 3 0.0000 0.846 0.000 0.000 1.000 0.000 0.000
#> GSM1022399 3 0.0000 0.846 0.000 0.000 1.000 0.000 0.000
#> GSM1022400 3 0.0000 0.846 0.000 0.000 1.000 0.000 0.000
#> GSM1022401 1 0.3366 0.615 0.768 0.000 0.000 0.000 0.232
#> GSM1022402 1 0.3366 0.615 0.768 0.000 0.000 0.000 0.232
#> GSM1022403 1 0.3366 0.615 0.768 0.000 0.000 0.000 0.232
#> GSM1022404 1 0.3366 0.615 0.768 0.000 0.000 0.000 0.232
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1022325 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022326 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022327 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022331 6 0.3371 0.684 0.000 0.000 0.292 0.000 0.000 0.708
#> GSM1022332 6 0.3371 0.684 0.000 0.000 0.292 0.000 0.000 0.708
#> GSM1022333 6 0.3371 0.684 0.000 0.000 0.292 0.000 0.000 0.708
#> GSM1022328 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022329 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022330 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022337 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1022338 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1022339 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1022334 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022335 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022336 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022340 1 0.0000 0.878 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022341 1 0.0000 0.878 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022342 1 0.0000 0.878 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022343 1 0.0000 0.878 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022347 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022348 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022349 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022350 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022344 3 0.2416 0.815 0.156 0.000 0.844 0.000 0.000 0.000
#> GSM1022345 3 0.2996 0.742 0.228 0.000 0.772 0.000 0.000 0.000
#> GSM1022346 3 0.2996 0.742 0.228 0.000 0.772 0.000 0.000 0.000
#> GSM1022355 1 0.0000 0.878 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022356 1 0.0632 0.872 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM1022357 1 0.0000 0.878 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022358 1 0.0000 0.878 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022351 1 0.0000 0.878 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022352 1 0.0000 0.878 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022353 1 0.0000 0.878 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022354 1 0.0000 0.878 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM1022359 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022360 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022361 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022362 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022367 6 0.0000 0.890 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1022368 6 0.0000 0.890 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1022369 6 0.0000 0.890 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1022370 6 0.0000 0.890 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1022363 6 0.0000 0.890 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1022364 6 0.0000 0.890 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1022365 6 0.0000 0.890 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1022366 6 0.0713 0.867 0.000 0.028 0.000 0.000 0.000 0.972
#> GSM1022374 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1022375 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1022376 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM1022371 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022372 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022373 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022377 4 0.0000 0.905 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022378 4 0.0000 0.905 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022379 4 0.0000 0.905 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022380 4 0.0000 0.905 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022385 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022386 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022387 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022388 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022381 4 0.0000 0.905 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022382 4 0.0000 0.905 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022383 4 0.0000 0.905 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022384 4 0.0000 0.905 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022393 1 0.3101 0.791 0.756 0.000 0.000 0.000 0.244 0.000
#> GSM1022394 1 0.3101 0.791 0.756 0.000 0.000 0.000 0.244 0.000
#> GSM1022395 1 0.3101 0.791 0.756 0.000 0.000 0.000 0.244 0.000
#> GSM1022396 1 0.3101 0.791 0.756 0.000 0.000 0.000 0.244 0.000
#> GSM1022389 4 0.2912 0.790 0.000 0.216 0.000 0.784 0.000 0.000
#> GSM1022390 4 0.2793 0.807 0.000 0.200 0.000 0.800 0.000 0.000
#> GSM1022391 4 0.2793 0.807 0.000 0.200 0.000 0.800 0.000 0.000
#> GSM1022392 4 0.2793 0.807 0.000 0.200 0.000 0.800 0.000 0.000
#> GSM1022397 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022398 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022399 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022400 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022401 1 0.3101 0.791 0.756 0.000 0.000 0.000 0.244 0.000
#> GSM1022402 1 0.3101 0.791 0.756 0.000 0.000 0.000 0.244 0.000
#> GSM1022403 1 0.3101 0.791 0.756 0.000 0.000 0.000 0.244 0.000
#> GSM1022404 1 0.3101 0.791 0.756 0.000 0.000 0.000 0.244 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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
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 protocol(p) cell.type(p) k
#> CV:pam 72 3.06e-06 7.12e-08 2
#> CV:pam 79 1.78e-10 2.17e-10 3
#> CV:pam 80 2.97e-15 3.00e-10 4
#> CV:pam 76 3.70e-19 2.02e-09 5
#> CV:pam 80 1.08e-28 1.03e-07 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 31589 rows and 80 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.379 0.891 0.893 0.4414 0.556 0.556
#> 3 3 0.522 0.738 0.873 0.4516 0.714 0.512
#> 4 4 0.791 0.799 0.875 0.1451 0.797 0.485
#> 5 5 0.803 0.863 0.902 0.0680 0.973 0.895
#> 6 6 0.876 0.874 0.923 0.0506 0.920 0.666
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM1022325 2 0.4690 0.815 0.100 0.900
#> GSM1022326 2 0.4562 0.817 0.096 0.904
#> GSM1022327 2 0.5178 0.804 0.116 0.884
#> GSM1022331 1 0.0000 0.998 1.000 0.000
#> GSM1022332 1 0.0000 0.998 1.000 0.000
#> GSM1022333 1 0.0000 0.998 1.000 0.000
#> GSM1022328 2 0.3431 0.826 0.064 0.936
#> GSM1022329 2 0.4690 0.811 0.100 0.900
#> GSM1022330 2 0.5519 0.792 0.128 0.872
#> GSM1022337 2 0.5408 0.903 0.124 0.876
#> GSM1022338 2 0.5408 0.903 0.124 0.876
#> GSM1022339 2 0.5408 0.903 0.124 0.876
#> GSM1022334 2 0.4815 0.807 0.104 0.896
#> GSM1022335 2 0.4815 0.807 0.104 0.896
#> GSM1022336 2 0.4939 0.805 0.108 0.892
#> GSM1022340 2 0.5408 0.903 0.124 0.876
#> GSM1022341 2 0.5408 0.903 0.124 0.876
#> GSM1022342 2 0.5408 0.903 0.124 0.876
#> GSM1022343 2 0.5408 0.903 0.124 0.876
#> GSM1022347 1 0.0000 0.998 1.000 0.000
#> GSM1022348 1 0.0000 0.998 1.000 0.000
#> GSM1022349 1 0.0000 0.998 1.000 0.000
#> GSM1022350 1 0.0000 0.998 1.000 0.000
#> GSM1022344 1 0.0000 0.998 1.000 0.000
#> GSM1022345 1 0.0376 0.994 0.996 0.004
#> GSM1022346 1 0.0376 0.994 0.996 0.004
#> GSM1022355 2 0.5408 0.903 0.124 0.876
#> GSM1022356 2 0.5408 0.903 0.124 0.876
#> GSM1022357 2 0.5408 0.903 0.124 0.876
#> GSM1022358 2 0.5408 0.903 0.124 0.876
#> GSM1022351 2 0.5408 0.903 0.124 0.876
#> GSM1022352 2 0.5408 0.903 0.124 0.876
#> GSM1022353 2 0.5408 0.903 0.124 0.876
#> GSM1022354 2 0.5408 0.903 0.124 0.876
#> GSM1022359 2 0.8267 0.642 0.260 0.740
#> GSM1022360 2 0.8144 0.654 0.252 0.748
#> GSM1022361 2 0.8207 0.648 0.256 0.744
#> GSM1022362 2 0.8207 0.648 0.256 0.744
#> GSM1022367 1 0.0000 0.998 1.000 0.000
#> GSM1022368 1 0.0000 0.998 1.000 0.000
#> GSM1022369 1 0.0000 0.998 1.000 0.000
#> GSM1022370 1 0.0000 0.998 1.000 0.000
#> GSM1022363 1 0.0672 0.990 0.992 0.008
#> GSM1022364 1 0.0672 0.990 0.992 0.008
#> GSM1022365 1 0.0672 0.990 0.992 0.008
#> GSM1022366 1 0.0672 0.990 0.992 0.008
#> GSM1022374 2 0.5408 0.903 0.124 0.876
#> GSM1022375 2 0.5408 0.903 0.124 0.876
#> GSM1022376 2 0.5408 0.903 0.124 0.876
#> GSM1022371 2 0.6148 0.893 0.152 0.848
#> GSM1022372 2 0.6148 0.893 0.152 0.848
#> GSM1022373 2 0.6148 0.893 0.152 0.848
#> GSM1022377 2 0.6343 0.892 0.160 0.840
#> GSM1022378 2 0.6343 0.892 0.160 0.840
#> GSM1022379 2 0.6343 0.892 0.160 0.840
#> GSM1022380 2 0.6343 0.892 0.160 0.840
#> GSM1022385 1 0.0000 0.998 1.000 0.000
#> GSM1022386 1 0.0000 0.998 1.000 0.000
#> GSM1022387 1 0.0000 0.998 1.000 0.000
#> GSM1022388 1 0.0000 0.998 1.000 0.000
#> GSM1022381 2 0.9850 0.547 0.428 0.572
#> GSM1022382 2 0.9850 0.547 0.428 0.572
#> GSM1022383 2 0.9850 0.547 0.428 0.572
#> GSM1022384 2 0.9850 0.547 0.428 0.572
#> GSM1022393 2 0.5408 0.903 0.124 0.876
#> GSM1022394 2 0.5408 0.903 0.124 0.876
#> GSM1022395 2 0.5408 0.903 0.124 0.876
#> GSM1022396 2 0.5408 0.903 0.124 0.876
#> GSM1022389 2 0.6247 0.893 0.156 0.844
#> GSM1022390 2 0.6247 0.893 0.156 0.844
#> GSM1022391 2 0.6247 0.893 0.156 0.844
#> GSM1022392 2 0.6247 0.893 0.156 0.844
#> GSM1022397 1 0.0000 0.998 1.000 0.000
#> GSM1022398 1 0.0000 0.998 1.000 0.000
#> GSM1022399 1 0.0000 0.998 1.000 0.000
#> GSM1022400 1 0.0000 0.998 1.000 0.000
#> GSM1022401 2 0.5408 0.903 0.124 0.876
#> GSM1022402 2 0.5408 0.903 0.124 0.876
#> GSM1022403 2 0.5408 0.903 0.124 0.876
#> GSM1022404 2 0.5408 0.903 0.124 0.876
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1022325 2 0.000 0.791 0.000 1.000 0.000
#> GSM1022326 2 0.000 0.791 0.000 1.000 0.000
#> GSM1022327 2 0.000 0.791 0.000 1.000 0.000
#> GSM1022331 3 0.576 0.809 0.124 0.076 0.800
#> GSM1022332 3 0.576 0.809 0.124 0.076 0.800
#> GSM1022333 3 0.576 0.809 0.124 0.076 0.800
#> GSM1022328 2 0.000 0.791 0.000 1.000 0.000
#> GSM1022329 2 0.000 0.791 0.000 1.000 0.000
#> GSM1022330 2 0.000 0.791 0.000 1.000 0.000
#> GSM1022337 1 0.000 0.876 1.000 0.000 0.000
#> GSM1022338 1 0.000 0.876 1.000 0.000 0.000
#> GSM1022339 1 0.000 0.876 1.000 0.000 0.000
#> GSM1022334 2 0.000 0.791 0.000 1.000 0.000
#> GSM1022335 2 0.000 0.791 0.000 1.000 0.000
#> GSM1022336 2 0.000 0.791 0.000 1.000 0.000
#> GSM1022340 1 0.529 0.587 0.732 0.000 0.268
#> GSM1022341 1 0.529 0.587 0.732 0.000 0.268
#> GSM1022342 1 0.529 0.587 0.732 0.000 0.268
#> GSM1022343 1 0.529 0.587 0.732 0.000 0.268
#> GSM1022347 3 0.000 0.864 0.000 0.000 1.000
#> GSM1022348 3 0.000 0.864 0.000 0.000 1.000
#> GSM1022349 3 0.000 0.864 0.000 0.000 1.000
#> GSM1022350 3 0.000 0.864 0.000 0.000 1.000
#> GSM1022344 3 0.576 0.517 0.328 0.000 0.672
#> GSM1022345 3 0.576 0.517 0.328 0.000 0.672
#> GSM1022346 3 0.576 0.517 0.328 0.000 0.672
#> GSM1022355 1 0.116 0.872 0.972 0.000 0.028
#> GSM1022356 1 0.116 0.872 0.972 0.000 0.028
#> GSM1022357 1 0.116 0.872 0.972 0.000 0.028
#> GSM1022358 1 0.116 0.872 0.972 0.000 0.028
#> GSM1022351 1 0.116 0.872 0.972 0.000 0.028
#> GSM1022352 1 0.116 0.872 0.972 0.000 0.028
#> GSM1022353 1 0.116 0.872 0.972 0.000 0.028
#> GSM1022354 1 0.116 0.872 0.972 0.000 0.028
#> GSM1022359 2 0.000 0.791 0.000 1.000 0.000
#> GSM1022360 2 0.000 0.791 0.000 1.000 0.000
#> GSM1022361 2 0.000 0.791 0.000 1.000 0.000
#> GSM1022362 2 0.000 0.791 0.000 1.000 0.000
#> GSM1022367 3 0.660 0.784 0.124 0.120 0.756
#> GSM1022368 3 0.660 0.784 0.124 0.120 0.756
#> GSM1022369 3 0.660 0.784 0.124 0.120 0.756
#> GSM1022370 3 0.660 0.784 0.124 0.120 0.756
#> GSM1022363 2 0.369 0.767 0.052 0.896 0.052
#> GSM1022364 2 0.369 0.767 0.052 0.896 0.052
#> GSM1022365 2 0.369 0.767 0.052 0.896 0.052
#> GSM1022366 2 0.369 0.767 0.052 0.896 0.052
#> GSM1022374 1 0.000 0.876 1.000 0.000 0.000
#> GSM1022375 1 0.000 0.876 1.000 0.000 0.000
#> GSM1022376 1 0.000 0.876 1.000 0.000 0.000
#> GSM1022371 2 0.606 0.578 0.276 0.708 0.016
#> GSM1022372 2 0.606 0.578 0.276 0.708 0.016
#> GSM1022373 2 0.606 0.578 0.276 0.708 0.016
#> GSM1022377 2 0.846 0.478 0.328 0.564 0.108
#> GSM1022378 2 0.846 0.478 0.328 0.564 0.108
#> GSM1022379 2 0.846 0.478 0.328 0.564 0.108
#> GSM1022380 2 0.846 0.478 0.328 0.564 0.108
#> GSM1022385 3 0.000 0.864 0.000 0.000 1.000
#> GSM1022386 3 0.000 0.864 0.000 0.000 1.000
#> GSM1022387 3 0.000 0.864 0.000 0.000 1.000
#> GSM1022388 3 0.000 0.864 0.000 0.000 1.000
#> GSM1022381 2 0.846 0.478 0.328 0.564 0.108
#> GSM1022382 2 0.846 0.478 0.328 0.564 0.108
#> GSM1022383 2 0.846 0.478 0.328 0.564 0.108
#> GSM1022384 2 0.849 0.461 0.336 0.556 0.108
#> GSM1022393 1 0.000 0.876 1.000 0.000 0.000
#> GSM1022394 1 0.000 0.876 1.000 0.000 0.000
#> GSM1022395 1 0.000 0.876 1.000 0.000 0.000
#> GSM1022396 1 0.000 0.876 1.000 0.000 0.000
#> GSM1022389 1 0.733 0.278 0.612 0.344 0.044
#> GSM1022390 1 0.733 0.278 0.612 0.344 0.044
#> GSM1022391 1 0.733 0.278 0.612 0.344 0.044
#> GSM1022392 1 0.733 0.278 0.612 0.344 0.044
#> GSM1022397 3 0.000 0.864 0.000 0.000 1.000
#> GSM1022398 3 0.000 0.864 0.000 0.000 1.000
#> GSM1022399 3 0.000 0.864 0.000 0.000 1.000
#> GSM1022400 3 0.000 0.864 0.000 0.000 1.000
#> GSM1022401 1 0.000 0.876 1.000 0.000 0.000
#> GSM1022402 1 0.000 0.876 1.000 0.000 0.000
#> GSM1022403 1 0.000 0.876 1.000 0.000 0.000
#> GSM1022404 1 0.000 0.876 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1022325 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> GSM1022326 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> GSM1022327 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> GSM1022331 3 0.8195 0.313 0.244 0.032 0.500 0.224
#> GSM1022332 3 0.8195 0.313 0.244 0.032 0.500 0.224
#> GSM1022333 3 0.8195 0.313 0.244 0.032 0.500 0.224
#> GSM1022328 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> GSM1022329 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> GSM1022330 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> GSM1022337 1 0.5090 0.941 0.660 0.016 0.000 0.324
#> GSM1022338 1 0.5090 0.941 0.660 0.016 0.000 0.324
#> GSM1022339 1 0.5090 0.941 0.660 0.016 0.000 0.324
#> GSM1022334 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> GSM1022335 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> GSM1022336 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> GSM1022340 4 0.0336 0.747 0.000 0.000 0.008 0.992
#> GSM1022341 4 0.0336 0.747 0.000 0.000 0.008 0.992
#> GSM1022342 4 0.0336 0.747 0.000 0.000 0.008 0.992
#> GSM1022343 4 0.0336 0.747 0.000 0.000 0.008 0.992
#> GSM1022347 3 0.0000 0.771 0.000 0.000 1.000 0.000
#> GSM1022348 3 0.0000 0.771 0.000 0.000 1.000 0.000
#> GSM1022349 3 0.0000 0.771 0.000 0.000 1.000 0.000
#> GSM1022350 3 0.0000 0.771 0.000 0.000 1.000 0.000
#> GSM1022344 4 0.3166 0.734 0.000 0.016 0.116 0.868
#> GSM1022345 4 0.3166 0.734 0.000 0.016 0.116 0.868
#> GSM1022346 4 0.3166 0.734 0.000 0.016 0.116 0.868
#> GSM1022355 4 0.1940 0.721 0.076 0.000 0.000 0.924
#> GSM1022356 4 0.1940 0.721 0.076 0.000 0.000 0.924
#> GSM1022357 4 0.1940 0.721 0.076 0.000 0.000 0.924
#> GSM1022358 4 0.1940 0.721 0.076 0.000 0.000 0.924
#> GSM1022351 4 0.1474 0.735 0.052 0.000 0.000 0.948
#> GSM1022352 4 0.1867 0.723 0.072 0.000 0.000 0.928
#> GSM1022353 4 0.1867 0.723 0.072 0.000 0.000 0.928
#> GSM1022354 4 0.1867 0.723 0.072 0.000 0.000 0.928
#> GSM1022359 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> GSM1022360 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> GSM1022361 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> GSM1022362 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> GSM1022367 3 0.9472 0.231 0.244 0.132 0.400 0.224
#> GSM1022368 3 0.9472 0.231 0.244 0.132 0.400 0.224
#> GSM1022369 3 0.9472 0.231 0.244 0.132 0.400 0.224
#> GSM1022370 3 0.9472 0.231 0.244 0.132 0.400 0.224
#> GSM1022363 2 0.2635 0.905 0.000 0.904 0.076 0.020
#> GSM1022364 2 0.2635 0.905 0.000 0.904 0.076 0.020
#> GSM1022365 2 0.2635 0.905 0.000 0.904 0.076 0.020
#> GSM1022366 2 0.2635 0.905 0.000 0.904 0.076 0.020
#> GSM1022374 1 0.5090 0.941 0.660 0.016 0.000 0.324
#> GSM1022375 1 0.5090 0.941 0.660 0.016 0.000 0.324
#> GSM1022376 1 0.5090 0.941 0.660 0.016 0.000 0.324
#> GSM1022371 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> GSM1022372 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> GSM1022373 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> GSM1022377 4 0.5188 0.775 0.276 0.024 0.004 0.696
#> GSM1022378 4 0.5188 0.775 0.276 0.024 0.004 0.696
#> GSM1022379 4 0.5226 0.775 0.276 0.020 0.008 0.696
#> GSM1022380 4 0.5325 0.774 0.276 0.024 0.008 0.692
#> GSM1022385 3 0.0000 0.771 0.000 0.000 1.000 0.000
#> GSM1022386 3 0.0000 0.771 0.000 0.000 1.000 0.000
#> GSM1022387 3 0.0000 0.771 0.000 0.000 1.000 0.000
#> GSM1022388 3 0.0000 0.771 0.000 0.000 1.000 0.000
#> GSM1022381 4 0.5764 0.770 0.276 0.024 0.024 0.676
#> GSM1022382 4 0.5764 0.770 0.276 0.024 0.024 0.676
#> GSM1022383 4 0.5764 0.770 0.276 0.024 0.024 0.676
#> GSM1022384 4 0.5764 0.770 0.276 0.024 0.024 0.676
#> GSM1022393 1 0.4250 0.956 0.724 0.000 0.000 0.276
#> GSM1022394 1 0.4250 0.956 0.724 0.000 0.000 0.276
#> GSM1022395 1 0.4250 0.956 0.724 0.000 0.000 0.276
#> GSM1022396 1 0.4250 0.956 0.724 0.000 0.000 0.276
#> GSM1022389 4 0.4927 0.780 0.264 0.024 0.000 0.712
#> GSM1022390 4 0.4927 0.780 0.264 0.024 0.000 0.712
#> GSM1022391 4 0.4927 0.780 0.264 0.024 0.000 0.712
#> GSM1022392 4 0.4927 0.780 0.264 0.024 0.000 0.712
#> GSM1022397 3 0.0000 0.771 0.000 0.000 1.000 0.000
#> GSM1022398 3 0.0000 0.771 0.000 0.000 1.000 0.000
#> GSM1022399 3 0.0000 0.771 0.000 0.000 1.000 0.000
#> GSM1022400 3 0.0000 0.771 0.000 0.000 1.000 0.000
#> GSM1022401 1 0.4250 0.956 0.724 0.000 0.000 0.276
#> GSM1022402 1 0.4250 0.956 0.724 0.000 0.000 0.276
#> GSM1022403 1 0.4250 0.956 0.724 0.000 0.000 0.276
#> GSM1022404 1 0.4250 0.956 0.724 0.000 0.000 0.276
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1022325 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM1022326 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM1022327 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM1022331 5 0.0162 1.000 0.000 0.000 0.004 0.000 0.996
#> GSM1022332 5 0.0162 1.000 0.000 0.000 0.004 0.000 0.996
#> GSM1022333 5 0.0162 1.000 0.000 0.000 0.004 0.000 0.996
#> GSM1022328 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM1022329 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM1022330 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM1022337 1 0.3857 0.670 0.688 0.000 0.000 0.000 0.312
#> GSM1022338 1 0.3857 0.670 0.688 0.000 0.000 0.000 0.312
#> GSM1022339 1 0.3857 0.670 0.688 0.000 0.000 0.000 0.312
#> GSM1022334 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM1022335 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM1022336 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM1022340 4 0.3039 0.805 0.192 0.000 0.000 0.808 0.000
#> GSM1022341 4 0.3039 0.805 0.192 0.000 0.000 0.808 0.000
#> GSM1022342 4 0.3039 0.805 0.192 0.000 0.000 0.808 0.000
#> GSM1022343 4 0.3039 0.805 0.192 0.000 0.000 0.808 0.000
#> GSM1022347 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022348 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022349 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022350 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022344 4 0.5159 0.766 0.188 0.000 0.124 0.688 0.000
#> GSM1022345 4 0.5159 0.766 0.188 0.000 0.124 0.688 0.000
#> GSM1022346 4 0.5159 0.766 0.188 0.000 0.124 0.688 0.000
#> GSM1022355 4 0.4045 0.715 0.356 0.000 0.000 0.644 0.000
#> GSM1022356 4 0.4045 0.715 0.356 0.000 0.000 0.644 0.000
#> GSM1022357 4 0.4045 0.715 0.356 0.000 0.000 0.644 0.000
#> GSM1022358 4 0.4045 0.715 0.356 0.000 0.000 0.644 0.000
#> GSM1022351 4 0.3039 0.805 0.192 0.000 0.000 0.808 0.000
#> GSM1022352 4 0.4045 0.715 0.356 0.000 0.000 0.644 0.000
#> GSM1022353 4 0.4045 0.715 0.356 0.000 0.000 0.644 0.000
#> GSM1022354 4 0.4045 0.715 0.356 0.000 0.000 0.644 0.000
#> GSM1022359 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM1022360 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM1022361 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM1022362 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM1022367 5 0.0162 1.000 0.000 0.000 0.004 0.000 0.996
#> GSM1022368 5 0.0162 1.000 0.000 0.000 0.004 0.000 0.996
#> GSM1022369 5 0.0162 1.000 0.000 0.000 0.004 0.000 0.996
#> GSM1022370 5 0.0162 1.000 0.000 0.000 0.004 0.000 0.996
#> GSM1022363 2 0.2852 0.827 0.000 0.828 0.000 0.000 0.172
#> GSM1022364 2 0.2852 0.827 0.000 0.828 0.000 0.000 0.172
#> GSM1022365 2 0.2852 0.827 0.000 0.828 0.000 0.000 0.172
#> GSM1022366 2 0.2852 0.827 0.000 0.828 0.000 0.000 0.172
#> GSM1022374 1 0.3857 0.670 0.688 0.000 0.000 0.000 0.312
#> GSM1022375 1 0.3857 0.670 0.688 0.000 0.000 0.000 0.312
#> GSM1022376 1 0.3857 0.670 0.688 0.000 0.000 0.000 0.312
#> GSM1022371 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM1022372 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM1022373 2 0.0000 0.962 0.000 1.000 0.000 0.000 0.000
#> GSM1022377 4 0.1444 0.795 0.000 0.040 0.000 0.948 0.012
#> GSM1022378 4 0.1444 0.795 0.000 0.040 0.000 0.948 0.012
#> GSM1022379 4 0.1444 0.795 0.000 0.040 0.000 0.948 0.012
#> GSM1022380 4 0.1444 0.795 0.000 0.040 0.000 0.948 0.012
#> GSM1022385 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022386 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022387 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022388 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022381 4 0.2278 0.772 0.000 0.060 0.000 0.908 0.032
#> GSM1022382 4 0.2278 0.772 0.000 0.060 0.000 0.908 0.032
#> GSM1022383 4 0.2278 0.772 0.000 0.060 0.000 0.908 0.032
#> GSM1022384 4 0.2278 0.772 0.000 0.060 0.000 0.908 0.032
#> GSM1022393 1 0.0000 0.810 1.000 0.000 0.000 0.000 0.000
#> GSM1022394 1 0.0000 0.810 1.000 0.000 0.000 0.000 0.000
#> GSM1022395 1 0.0000 0.810 1.000 0.000 0.000 0.000 0.000
#> GSM1022396 1 0.0000 0.810 1.000 0.000 0.000 0.000 0.000
#> GSM1022389 4 0.1800 0.804 0.020 0.048 0.000 0.932 0.000
#> GSM1022390 4 0.1800 0.804 0.020 0.048 0.000 0.932 0.000
#> GSM1022391 4 0.1800 0.804 0.020 0.048 0.000 0.932 0.000
#> GSM1022392 4 0.1800 0.804 0.020 0.048 0.000 0.932 0.000
#> GSM1022397 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022398 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022399 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022400 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM1022401 1 0.0000 0.810 1.000 0.000 0.000 0.000 0.000
#> GSM1022402 1 0.0000 0.810 1.000 0.000 0.000 0.000 0.000
#> GSM1022403 1 0.0000 0.810 1.000 0.000 0.000 0.000 0.000
#> GSM1022404 1 0.0000 0.810 1.000 0.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1022325 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.00 0.000
#> GSM1022326 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.00 0.000
#> GSM1022327 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.00 0.000
#> GSM1022331 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.00 1.000
#> GSM1022332 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.00 1.000
#> GSM1022333 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.00 1.000
#> GSM1022328 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.00 0.000
#> GSM1022329 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.00 0.000
#> GSM1022330 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.00 0.000
#> GSM1022337 5 0.0000 0.736 0.000 0.000 0.000 0.000 1.00 0.000
#> GSM1022338 5 0.0000 0.736 0.000 0.000 0.000 0.000 1.00 0.000
#> GSM1022339 5 0.0000 0.736 0.000 0.000 0.000 0.000 1.00 0.000
#> GSM1022334 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.00 0.000
#> GSM1022335 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.00 0.000
#> GSM1022336 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.00 0.000
#> GSM1022340 1 0.2527 0.838 0.832 0.000 0.000 0.168 0.00 0.000
#> GSM1022341 1 0.2527 0.838 0.832 0.000 0.000 0.168 0.00 0.000
#> GSM1022342 1 0.2527 0.838 0.832 0.000 0.000 0.168 0.00 0.000
#> GSM1022343 1 0.2527 0.838 0.832 0.000 0.000 0.168 0.00 0.000
#> GSM1022347 3 0.0000 0.895 0.000 0.000 1.000 0.000 0.00 0.000
#> GSM1022348 3 0.0000 0.895 0.000 0.000 1.000 0.000 0.00 0.000
#> GSM1022349 3 0.0000 0.895 0.000 0.000 1.000 0.000 0.00 0.000
#> GSM1022350 3 0.0000 0.895 0.000 0.000 1.000 0.000 0.00 0.000
#> GSM1022344 3 0.5591 0.416 0.248 0.000 0.576 0.168 0.00 0.008
#> GSM1022345 3 0.5765 0.408 0.248 0.000 0.568 0.168 0.00 0.016
#> GSM1022346 3 0.5765 0.408 0.248 0.000 0.568 0.168 0.00 0.016
#> GSM1022355 1 0.0146 0.887 0.996 0.000 0.000 0.004 0.00 0.000
#> GSM1022356 1 0.0146 0.887 0.996 0.000 0.000 0.004 0.00 0.000
#> GSM1022357 1 0.0146 0.887 0.996 0.000 0.000 0.004 0.00 0.000
#> GSM1022358 1 0.0146 0.887 0.996 0.000 0.000 0.004 0.00 0.000
#> GSM1022351 1 0.2135 0.856 0.872 0.000 0.000 0.128 0.00 0.000
#> GSM1022352 1 0.0146 0.887 0.996 0.000 0.000 0.004 0.00 0.000
#> GSM1022353 1 0.0146 0.887 0.996 0.000 0.000 0.004 0.00 0.000
#> GSM1022354 1 0.0146 0.887 0.996 0.000 0.000 0.004 0.00 0.000
#> GSM1022359 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.00 0.000
#> GSM1022360 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.00 0.000
#> GSM1022361 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.00 0.000
#> GSM1022362 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.00 0.000
#> GSM1022367 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.00 1.000
#> GSM1022368 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.00 1.000
#> GSM1022369 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.00 1.000
#> GSM1022370 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.00 1.000
#> GSM1022363 2 0.2527 0.829 0.000 0.832 0.000 0.000 0.00 0.168
#> GSM1022364 2 0.2527 0.829 0.000 0.832 0.000 0.000 0.00 0.168
#> GSM1022365 2 0.2527 0.829 0.000 0.832 0.000 0.000 0.00 0.168
#> GSM1022366 2 0.2527 0.829 0.000 0.832 0.000 0.000 0.00 0.168
#> GSM1022374 5 0.0000 0.736 0.000 0.000 0.000 0.000 1.00 0.000
#> GSM1022375 5 0.0000 0.736 0.000 0.000 0.000 0.000 1.00 0.000
#> GSM1022376 5 0.0000 0.736 0.000 0.000 0.000 0.000 1.00 0.000
#> GSM1022371 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.00 0.000
#> GSM1022372 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.00 0.000
#> GSM1022373 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.00 0.000
#> GSM1022377 4 0.0000 0.954 0.000 0.000 0.000 1.000 0.00 0.000
#> GSM1022378 4 0.0000 0.954 0.000 0.000 0.000 1.000 0.00 0.000
#> GSM1022379 4 0.0000 0.954 0.000 0.000 0.000 1.000 0.00 0.000
#> GSM1022380 4 0.0000 0.954 0.000 0.000 0.000 1.000 0.00 0.000
#> GSM1022385 3 0.0000 0.895 0.000 0.000 1.000 0.000 0.00 0.000
#> GSM1022386 3 0.0000 0.895 0.000 0.000 1.000 0.000 0.00 0.000
#> GSM1022387 3 0.0000 0.895 0.000 0.000 1.000 0.000 0.00 0.000
#> GSM1022388 3 0.0000 0.895 0.000 0.000 1.000 0.000 0.00 0.000
#> GSM1022381 4 0.0000 0.954 0.000 0.000 0.000 1.000 0.00 0.000
#> GSM1022382 4 0.0000 0.954 0.000 0.000 0.000 1.000 0.00 0.000
#> GSM1022383 4 0.0000 0.954 0.000 0.000 0.000 1.000 0.00 0.000
#> GSM1022384 4 0.0000 0.954 0.000 0.000 0.000 1.000 0.00 0.000
#> GSM1022393 5 0.3647 0.765 0.360 0.000 0.000 0.000 0.64 0.000
#> GSM1022394 5 0.3647 0.765 0.360 0.000 0.000 0.000 0.64 0.000
#> GSM1022395 5 0.3647 0.765 0.360 0.000 0.000 0.000 0.64 0.000
#> GSM1022396 5 0.3647 0.765 0.360 0.000 0.000 0.000 0.64 0.000
#> GSM1022389 4 0.2499 0.903 0.072 0.048 0.000 0.880 0.00 0.000
#> GSM1022390 4 0.2499 0.903 0.072 0.048 0.000 0.880 0.00 0.000
#> GSM1022391 4 0.2499 0.903 0.072 0.048 0.000 0.880 0.00 0.000
#> GSM1022392 4 0.2499 0.903 0.072 0.048 0.000 0.880 0.00 0.000
#> GSM1022397 3 0.0000 0.895 0.000 0.000 1.000 0.000 0.00 0.000
#> GSM1022398 3 0.0000 0.895 0.000 0.000 1.000 0.000 0.00 0.000
#> GSM1022399 3 0.0000 0.895 0.000 0.000 1.000 0.000 0.00 0.000
#> GSM1022400 3 0.0000 0.895 0.000 0.000 1.000 0.000 0.00 0.000
#> GSM1022401 5 0.3647 0.765 0.360 0.000 0.000 0.000 0.64 0.000
#> GSM1022402 5 0.3647 0.765 0.360 0.000 0.000 0.000 0.64 0.000
#> GSM1022403 5 0.3647 0.765 0.360 0.000 0.000 0.000 0.64 0.000
#> GSM1022404 5 0.3647 0.765 0.360 0.000 0.000 0.000 0.64 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 protocol(p) cell.type(p) k
#> CV:mclust 80 9.82e-09 1.94e-03 2
#> CV:mclust 68 1.93e-10 2.24e-08 3
#> CV:mclust 73 6.10e-14 9.98e-13 4
#> CV:mclust 80 1.34e-16 1.37e-13 5
#> CV:mclust 77 2.13e-24 5.97e-13 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
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 31589 rows and 80 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.866 0.928 0.961 0.4960 0.499 0.499
#> 3 3 1.000 0.966 0.986 0.3479 0.748 0.534
#> 4 4 1.000 0.985 0.991 0.0835 0.893 0.701
#> 5 5 0.916 0.867 0.916 0.0586 0.934 0.763
#> 6 6 0.836 0.770 0.870 0.0493 0.981 0.916
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 4
There is also optional best \(k\) = 3 4 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM1022325 2 0.000 0.976 0.000 1.000
#> GSM1022326 2 0.000 0.976 0.000 1.000
#> GSM1022327 2 0.000 0.976 0.000 1.000
#> GSM1022331 1 0.000 0.942 1.000 0.000
#> GSM1022332 1 0.000 0.942 1.000 0.000
#> GSM1022333 1 0.000 0.942 1.000 0.000
#> GSM1022328 2 0.000 0.976 0.000 1.000
#> GSM1022329 2 0.000 0.976 0.000 1.000
#> GSM1022330 2 0.000 0.976 0.000 1.000
#> GSM1022337 1 0.909 0.594 0.676 0.324
#> GSM1022338 1 0.895 0.619 0.688 0.312
#> GSM1022339 2 0.958 0.322 0.380 0.620
#> GSM1022334 2 0.000 0.976 0.000 1.000
#> GSM1022335 2 0.000 0.976 0.000 1.000
#> GSM1022336 2 0.000 0.976 0.000 1.000
#> GSM1022340 1 0.327 0.940 0.940 0.060
#> GSM1022341 1 0.295 0.944 0.948 0.052
#> GSM1022342 1 0.295 0.944 0.948 0.052
#> GSM1022343 1 0.295 0.944 0.948 0.052
#> GSM1022347 1 0.000 0.942 1.000 0.000
#> GSM1022348 1 0.000 0.942 1.000 0.000
#> GSM1022349 1 0.000 0.942 1.000 0.000
#> GSM1022350 1 0.000 0.942 1.000 0.000
#> GSM1022344 1 0.000 0.942 1.000 0.000
#> GSM1022345 1 0.000 0.942 1.000 0.000
#> GSM1022346 1 0.000 0.942 1.000 0.000
#> GSM1022355 1 0.311 0.942 0.944 0.056
#> GSM1022356 1 0.327 0.940 0.940 0.060
#> GSM1022357 1 0.260 0.945 0.956 0.044
#> GSM1022358 1 0.327 0.940 0.940 0.060
#> GSM1022351 1 0.327 0.940 0.940 0.060
#> GSM1022352 1 0.278 0.944 0.952 0.048
#> GSM1022353 1 0.278 0.944 0.952 0.048
#> GSM1022354 1 0.295 0.944 0.948 0.052
#> GSM1022359 2 0.000 0.976 0.000 1.000
#> GSM1022360 2 0.000 0.976 0.000 1.000
#> GSM1022361 2 0.000 0.976 0.000 1.000
#> GSM1022362 2 0.000 0.976 0.000 1.000
#> GSM1022367 1 0.795 0.698 0.760 0.240
#> GSM1022368 1 0.518 0.863 0.884 0.116
#> GSM1022369 1 0.358 0.909 0.932 0.068
#> GSM1022370 1 0.827 0.664 0.740 0.260
#> GSM1022363 2 0.000 0.976 0.000 1.000
#> GSM1022364 2 0.000 0.976 0.000 1.000
#> GSM1022365 2 0.000 0.976 0.000 1.000
#> GSM1022366 2 0.000 0.976 0.000 1.000
#> GSM1022374 2 0.552 0.840 0.128 0.872
#> GSM1022375 2 0.541 0.845 0.124 0.876
#> GSM1022376 2 0.574 0.829 0.136 0.864
#> GSM1022371 2 0.000 0.976 0.000 1.000
#> GSM1022372 2 0.000 0.976 0.000 1.000
#> GSM1022373 2 0.000 0.976 0.000 1.000
#> GSM1022377 2 0.000 0.976 0.000 1.000
#> GSM1022378 2 0.000 0.976 0.000 1.000
#> GSM1022379 2 0.000 0.976 0.000 1.000
#> GSM1022380 2 0.000 0.976 0.000 1.000
#> GSM1022385 1 0.000 0.942 1.000 0.000
#> GSM1022386 1 0.000 0.942 1.000 0.000
#> GSM1022387 1 0.000 0.942 1.000 0.000
#> GSM1022388 1 0.000 0.942 1.000 0.000
#> GSM1022381 2 0.000 0.976 0.000 1.000
#> GSM1022382 2 0.000 0.976 0.000 1.000
#> GSM1022383 2 0.000 0.976 0.000 1.000
#> GSM1022384 2 0.000 0.976 0.000 1.000
#> GSM1022393 1 0.343 0.937 0.936 0.064
#> GSM1022394 1 0.242 0.945 0.960 0.040
#> GSM1022395 1 0.327 0.940 0.940 0.060
#> GSM1022396 1 0.295 0.944 0.948 0.052
#> GSM1022389 2 0.000 0.976 0.000 1.000
#> GSM1022390 2 0.000 0.976 0.000 1.000
#> GSM1022391 2 0.000 0.976 0.000 1.000
#> GSM1022392 2 0.000 0.976 0.000 1.000
#> GSM1022397 1 0.000 0.942 1.000 0.000
#> GSM1022398 1 0.000 0.942 1.000 0.000
#> GSM1022399 1 0.000 0.942 1.000 0.000
#> GSM1022400 1 0.000 0.942 1.000 0.000
#> GSM1022401 1 0.260 0.945 0.956 0.044
#> GSM1022402 1 0.311 0.942 0.944 0.056
#> GSM1022403 1 0.311 0.942 0.944 0.056
#> GSM1022404 1 0.278 0.944 0.952 0.048
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1022325 2 0.0000 0.993 0.000 1.000 0.000
#> GSM1022326 2 0.0000 0.993 0.000 1.000 0.000
#> GSM1022327 2 0.0000 0.993 0.000 1.000 0.000
#> GSM1022331 3 0.0000 0.990 0.000 0.000 1.000
#> GSM1022332 3 0.0000 0.990 0.000 0.000 1.000
#> GSM1022333 3 0.0000 0.990 0.000 0.000 1.000
#> GSM1022328 2 0.0000 0.993 0.000 1.000 0.000
#> GSM1022329 2 0.0000 0.993 0.000 1.000 0.000
#> GSM1022330 2 0.0000 0.993 0.000 1.000 0.000
#> GSM1022337 1 0.0000 0.971 1.000 0.000 0.000
#> GSM1022338 1 0.0000 0.971 1.000 0.000 0.000
#> GSM1022339 1 0.0000 0.971 1.000 0.000 0.000
#> GSM1022334 2 0.0000 0.993 0.000 1.000 0.000
#> GSM1022335 2 0.0000 0.993 0.000 1.000 0.000
#> GSM1022336 2 0.0000 0.993 0.000 1.000 0.000
#> GSM1022340 1 0.0000 0.971 1.000 0.000 0.000
#> GSM1022341 1 0.0000 0.971 1.000 0.000 0.000
#> GSM1022342 1 0.0000 0.971 1.000 0.000 0.000
#> GSM1022343 1 0.0000 0.971 1.000 0.000 0.000
#> GSM1022347 3 0.0000 0.990 0.000 0.000 1.000
#> GSM1022348 3 0.0000 0.990 0.000 0.000 1.000
#> GSM1022349 3 0.0000 0.990 0.000 0.000 1.000
#> GSM1022350 3 0.0000 0.990 0.000 0.000 1.000
#> GSM1022344 3 0.0000 0.990 0.000 0.000 1.000
#> GSM1022345 3 0.4504 0.752 0.196 0.000 0.804
#> GSM1022346 3 0.0592 0.979 0.012 0.000 0.988
#> GSM1022355 1 0.0000 0.971 1.000 0.000 0.000
#> GSM1022356 1 0.0000 0.971 1.000 0.000 0.000
#> GSM1022357 1 0.0000 0.971 1.000 0.000 0.000
#> GSM1022358 1 0.0000 0.971 1.000 0.000 0.000
#> GSM1022351 1 0.0000 0.971 1.000 0.000 0.000
#> GSM1022352 1 0.0000 0.971 1.000 0.000 0.000
#> GSM1022353 1 0.0000 0.971 1.000 0.000 0.000
#> GSM1022354 1 0.0000 0.971 1.000 0.000 0.000
#> GSM1022359 2 0.0000 0.993 0.000 1.000 0.000
#> GSM1022360 2 0.0000 0.993 0.000 1.000 0.000
#> GSM1022361 2 0.0000 0.993 0.000 1.000 0.000
#> GSM1022362 2 0.0000 0.993 0.000 1.000 0.000
#> GSM1022367 3 0.0000 0.990 0.000 0.000 1.000
#> GSM1022368 3 0.0000 0.990 0.000 0.000 1.000
#> GSM1022369 3 0.0000 0.990 0.000 0.000 1.000
#> GSM1022370 3 0.0000 0.990 0.000 0.000 1.000
#> GSM1022363 2 0.0000 0.993 0.000 1.000 0.000
#> GSM1022364 2 0.0000 0.993 0.000 1.000 0.000
#> GSM1022365 2 0.0000 0.993 0.000 1.000 0.000
#> GSM1022366 2 0.0000 0.993 0.000 1.000 0.000
#> GSM1022374 1 0.0000 0.971 1.000 0.000 0.000
#> GSM1022375 1 0.0424 0.964 0.992 0.008 0.000
#> GSM1022376 1 0.0000 0.971 1.000 0.000 0.000
#> GSM1022371 2 0.0000 0.993 0.000 1.000 0.000
#> GSM1022372 2 0.0000 0.993 0.000 1.000 0.000
#> GSM1022373 2 0.0000 0.993 0.000 1.000 0.000
#> GSM1022377 2 0.0000 0.993 0.000 1.000 0.000
#> GSM1022378 2 0.0000 0.993 0.000 1.000 0.000
#> GSM1022379 2 0.0000 0.993 0.000 1.000 0.000
#> GSM1022380 2 0.0000 0.993 0.000 1.000 0.000
#> GSM1022385 3 0.0000 0.990 0.000 0.000 1.000
#> GSM1022386 3 0.0000 0.990 0.000 0.000 1.000
#> GSM1022387 3 0.0000 0.990 0.000 0.000 1.000
#> GSM1022388 3 0.0000 0.990 0.000 0.000 1.000
#> GSM1022381 2 0.0000 0.993 0.000 1.000 0.000
#> GSM1022382 2 0.0000 0.993 0.000 1.000 0.000
#> GSM1022383 2 0.0000 0.993 0.000 1.000 0.000
#> GSM1022384 2 0.0000 0.993 0.000 1.000 0.000
#> GSM1022393 1 0.0000 0.971 1.000 0.000 0.000
#> GSM1022394 1 0.0000 0.971 1.000 0.000 0.000
#> GSM1022395 1 0.0000 0.971 1.000 0.000 0.000
#> GSM1022396 1 0.0000 0.971 1.000 0.000 0.000
#> GSM1022389 2 0.3267 0.867 0.116 0.884 0.000
#> GSM1022390 1 0.6079 0.376 0.612 0.388 0.000
#> GSM1022391 2 0.2711 0.901 0.088 0.912 0.000
#> GSM1022392 1 0.5591 0.566 0.696 0.304 0.000
#> GSM1022397 3 0.0000 0.990 0.000 0.000 1.000
#> GSM1022398 3 0.0000 0.990 0.000 0.000 1.000
#> GSM1022399 3 0.0000 0.990 0.000 0.000 1.000
#> GSM1022400 3 0.0000 0.990 0.000 0.000 1.000
#> GSM1022401 1 0.0000 0.971 1.000 0.000 0.000
#> GSM1022402 1 0.0000 0.971 1.000 0.000 0.000
#> GSM1022403 1 0.0000 0.971 1.000 0.000 0.000
#> GSM1022404 1 0.0000 0.971 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1022325 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM1022326 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM1022327 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM1022331 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022332 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022333 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022328 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM1022329 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM1022330 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM1022337 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM1022338 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM1022339 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM1022334 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM1022335 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM1022336 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM1022340 4 0.0000 0.999 0.000 0.000 0.000 1.000
#> GSM1022341 4 0.0000 0.999 0.000 0.000 0.000 1.000
#> GSM1022342 4 0.0000 0.999 0.000 0.000 0.000 1.000
#> GSM1022343 4 0.0000 0.999 0.000 0.000 0.000 1.000
#> GSM1022347 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022348 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022349 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022350 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022344 4 0.0188 0.995 0.000 0.000 0.004 0.996
#> GSM1022345 4 0.0000 0.999 0.000 0.000 0.000 1.000
#> GSM1022346 4 0.0000 0.999 0.000 0.000 0.000 1.000
#> GSM1022355 1 0.3123 0.850 0.844 0.000 0.000 0.156
#> GSM1022356 1 0.2345 0.904 0.900 0.000 0.000 0.100
#> GSM1022357 1 0.3219 0.841 0.836 0.000 0.000 0.164
#> GSM1022358 1 0.2469 0.898 0.892 0.000 0.000 0.108
#> GSM1022351 4 0.0000 0.999 0.000 0.000 0.000 1.000
#> GSM1022352 4 0.0000 0.999 0.000 0.000 0.000 1.000
#> GSM1022353 4 0.0000 0.999 0.000 0.000 0.000 1.000
#> GSM1022354 4 0.0188 0.995 0.004 0.000 0.000 0.996
#> GSM1022359 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM1022360 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM1022361 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM1022362 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM1022367 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022368 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022369 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022370 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022363 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM1022364 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM1022365 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM1022366 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM1022374 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM1022375 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM1022376 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM1022371 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM1022372 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM1022373 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM1022377 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM1022378 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM1022379 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM1022380 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM1022385 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022386 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022387 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022388 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022381 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM1022382 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM1022383 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM1022384 2 0.0188 0.993 0.000 0.996 0.000 0.004
#> GSM1022393 1 0.0188 0.967 0.996 0.000 0.000 0.004
#> GSM1022394 1 0.0336 0.967 0.992 0.000 0.000 0.008
#> GSM1022395 1 0.0188 0.967 0.996 0.000 0.000 0.004
#> GSM1022396 1 0.0336 0.967 0.992 0.000 0.000 0.008
#> GSM1022389 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM1022390 2 0.0921 0.971 0.000 0.972 0.000 0.028
#> GSM1022391 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM1022392 2 0.2011 0.915 0.000 0.920 0.000 0.080
#> GSM1022397 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022398 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022399 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022400 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022401 1 0.0336 0.967 0.992 0.000 0.000 0.008
#> GSM1022402 1 0.0188 0.967 0.996 0.000 0.000 0.004
#> GSM1022403 1 0.0336 0.967 0.992 0.000 0.000 0.008
#> GSM1022404 1 0.0336 0.967 0.992 0.000 0.000 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1022325 2 0.0000 0.878 0.000 1.000 0.000 0.000 0.000
#> GSM1022326 2 0.0000 0.878 0.000 1.000 0.000 0.000 0.000
#> GSM1022327 2 0.0000 0.878 0.000 1.000 0.000 0.000 0.000
#> GSM1022331 3 0.0510 0.985 0.000 0.000 0.984 0.016 0.000
#> GSM1022332 3 0.0510 0.985 0.000 0.000 0.984 0.016 0.000
#> GSM1022333 3 0.0510 0.985 0.000 0.000 0.984 0.016 0.000
#> GSM1022328 2 0.0000 0.878 0.000 1.000 0.000 0.000 0.000
#> GSM1022329 2 0.0000 0.878 0.000 1.000 0.000 0.000 0.000
#> GSM1022330 2 0.0000 0.878 0.000 1.000 0.000 0.000 0.000
#> GSM1022337 5 0.0000 0.952 0.000 0.000 0.000 0.000 1.000
#> GSM1022338 5 0.0000 0.952 0.000 0.000 0.000 0.000 1.000
#> GSM1022339 5 0.0000 0.952 0.000 0.000 0.000 0.000 1.000
#> GSM1022334 2 0.0000 0.878 0.000 1.000 0.000 0.000 0.000
#> GSM1022335 2 0.0000 0.878 0.000 1.000 0.000 0.000 0.000
#> GSM1022336 2 0.0000 0.878 0.000 1.000 0.000 0.000 0.000
#> GSM1022340 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000
#> GSM1022341 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000
#> GSM1022342 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000
#> GSM1022343 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000
#> GSM1022347 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000
#> GSM1022348 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000
#> GSM1022349 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000
#> GSM1022350 3 0.0000 0.988 0.000 0.000 1.000 0.000 0.000
#> GSM1022344 1 0.0290 0.992 0.992 0.000 0.008 0.000 0.000
#> GSM1022345 1 0.0162 0.996 0.996 0.000 0.004 0.000 0.000
#> GSM1022346 1 0.0162 0.996 0.996 0.000 0.004 0.000 0.000
#> GSM1022355 5 0.2773 0.812 0.164 0.000 0.000 0.000 0.836
#> GSM1022356 5 0.1270 0.916 0.052 0.000 0.000 0.000 0.948
#> GSM1022357 5 0.3999 0.536 0.344 0.000 0.000 0.000 0.656
#> GSM1022358 5 0.3452 0.711 0.244 0.000 0.000 0.000 0.756
#> GSM1022351 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000
#> GSM1022352 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000
#> GSM1022353 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000
#> GSM1022354 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000
#> GSM1022359 2 0.0000 0.878 0.000 1.000 0.000 0.000 0.000
#> GSM1022360 2 0.0000 0.878 0.000 1.000 0.000 0.000 0.000
#> GSM1022361 2 0.0000 0.878 0.000 1.000 0.000 0.000 0.000
#> GSM1022362 2 0.0000 0.878 0.000 1.000 0.000 0.000 0.000
#> GSM1022367 3 0.1124 0.973 0.000 0.004 0.960 0.036 0.000
#> GSM1022368 3 0.1124 0.973 0.000 0.004 0.960 0.036 0.000
#> GSM1022369 3 0.1124 0.973 0.000 0.004 0.960 0.036 0.000
#> GSM1022370 3 0.1469 0.963 0.000 0.016 0.948 0.036 0.000
#> GSM1022363 2 0.0880 0.841 0.000 0.968 0.000 0.032 0.000
#> GSM1022364 2 0.0880 0.841 0.000 0.968 0.000 0.032 0.000
#> GSM1022365 2 0.0880 0.841 0.000 0.968 0.000 0.032 0.000
#> GSM1022366 2 0.0880 0.841 0.000 0.968 0.000 0.032 0.000
#> GSM1022374 5 0.0000 0.952 0.000 0.000 0.000 0.000 1.000
#> GSM1022375 5 0.0000 0.952 0.000 0.000 0.000 0.000 1.000
#> GSM1022376 5 0.0000 0.952 0.000 0.000 0.000 0.000 1.000
#> GSM1022371 2 0.0000 0.878 0.000 1.000 0.000 0.000 0.000
#> GSM1022372 2 0.0000 0.878 0.000 1.000 0.000 0.000 0.000
#> GSM1022373 2 0.0000 0.878 0.000 1.000 0.000 0.000 0.000
#> GSM1022377 4 0.4304 0.905 0.000 0.484 0.000 0.516 0.000
#> GSM1022378 4 0.4304 0.905 0.000 0.484 0.000 0.516 0.000
#> GSM1022379 4 0.4304 0.905 0.000 0.484 0.000 0.516 0.000
#> GSM1022380 4 0.4304 0.905 0.000 0.484 0.000 0.516 0.000
#> GSM1022385 3 0.0162 0.989 0.000 0.000 0.996 0.004 0.000
#> GSM1022386 3 0.0162 0.989 0.000 0.000 0.996 0.004 0.000
#> GSM1022387 3 0.0162 0.989 0.000 0.000 0.996 0.004 0.000
#> GSM1022388 3 0.0162 0.989 0.000 0.000 0.996 0.004 0.000
#> GSM1022381 4 0.4590 0.894 0.012 0.420 0.000 0.568 0.000
#> GSM1022382 4 0.4627 0.909 0.012 0.444 0.000 0.544 0.000
#> GSM1022383 4 0.4610 0.904 0.012 0.432 0.000 0.556 0.000
#> GSM1022384 4 0.4547 0.869 0.012 0.400 0.000 0.588 0.000
#> GSM1022393 5 0.0000 0.952 0.000 0.000 0.000 0.000 1.000
#> GSM1022394 5 0.0000 0.952 0.000 0.000 0.000 0.000 1.000
#> GSM1022395 5 0.0000 0.952 0.000 0.000 0.000 0.000 1.000
#> GSM1022396 5 0.0000 0.952 0.000 0.000 0.000 0.000 1.000
#> GSM1022389 2 0.4310 -0.619 0.004 0.604 0.000 0.392 0.000
#> GSM1022390 2 0.4641 -0.745 0.012 0.532 0.000 0.456 0.000
#> GSM1022391 2 0.4310 -0.619 0.004 0.604 0.000 0.392 0.000
#> GSM1022392 4 0.4747 0.732 0.016 0.488 0.000 0.496 0.000
#> GSM1022397 3 0.0162 0.989 0.000 0.000 0.996 0.004 0.000
#> GSM1022398 3 0.0162 0.989 0.000 0.000 0.996 0.004 0.000
#> GSM1022399 3 0.0162 0.989 0.000 0.000 0.996 0.004 0.000
#> GSM1022400 3 0.0162 0.989 0.000 0.000 0.996 0.004 0.000
#> GSM1022401 5 0.0000 0.952 0.000 0.000 0.000 0.000 1.000
#> GSM1022402 5 0.0000 0.952 0.000 0.000 0.000 0.000 1.000
#> GSM1022403 5 0.0000 0.952 0.000 0.000 0.000 0.000 1.000
#> GSM1022404 5 0.0000 0.952 0.000 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1022325 2 0.1219 0.693 0.000 0.948 0.000 0.048 0.000 NA
#> GSM1022326 2 0.0692 0.709 0.000 0.976 0.000 0.020 0.000 NA
#> GSM1022327 2 0.0692 0.707 0.000 0.976 0.000 0.020 0.000 NA
#> GSM1022331 3 0.2003 0.860 0.000 0.000 0.884 0.000 0.000 NA
#> GSM1022332 3 0.1714 0.870 0.000 0.000 0.908 0.000 0.000 NA
#> GSM1022333 3 0.2260 0.849 0.000 0.000 0.860 0.000 0.000 NA
#> GSM1022328 2 0.0260 0.714 0.000 0.992 0.000 0.008 0.000 NA
#> GSM1022329 2 0.0146 0.714 0.000 0.996 0.000 0.004 0.000 NA
#> GSM1022330 2 0.0260 0.714 0.000 0.992 0.000 0.008 0.000 NA
#> GSM1022337 5 0.0508 0.931 0.000 0.000 0.000 0.004 0.984 NA
#> GSM1022338 5 0.0508 0.931 0.000 0.000 0.000 0.004 0.984 NA
#> GSM1022339 5 0.0508 0.931 0.000 0.000 0.000 0.004 0.984 NA
#> GSM1022334 2 0.0260 0.715 0.000 0.992 0.000 0.000 0.000 NA
#> GSM1022335 2 0.0260 0.715 0.000 0.992 0.000 0.000 0.000 NA
#> GSM1022336 2 0.0260 0.715 0.000 0.992 0.000 0.000 0.000 NA
#> GSM1022340 1 0.0146 0.946 0.996 0.000 0.000 0.000 0.000 NA
#> GSM1022341 1 0.0146 0.946 0.996 0.000 0.000 0.000 0.000 NA
#> GSM1022342 1 0.0146 0.946 0.996 0.000 0.000 0.000 0.000 NA
#> GSM1022343 1 0.0146 0.946 0.996 0.000 0.000 0.000 0.000 NA
#> GSM1022347 3 0.0000 0.892 0.000 0.000 1.000 0.000 0.000 NA
#> GSM1022348 3 0.0000 0.892 0.000 0.000 1.000 0.000 0.000 NA
#> GSM1022349 3 0.0000 0.892 0.000 0.000 1.000 0.000 0.000 NA
#> GSM1022350 3 0.0000 0.892 0.000 0.000 1.000 0.000 0.000 NA
#> GSM1022344 1 0.0146 0.946 0.996 0.000 0.000 0.000 0.000 NA
#> GSM1022345 1 0.0000 0.946 1.000 0.000 0.000 0.000 0.000 NA
#> GSM1022346 1 0.0000 0.946 1.000 0.000 0.000 0.000 0.000 NA
#> GSM1022355 5 0.4058 0.512 0.320 0.000 0.000 0.016 0.660 NA
#> GSM1022356 5 0.2636 0.818 0.120 0.000 0.000 0.016 0.860 NA
#> GSM1022357 1 0.4394 -0.121 0.496 0.000 0.000 0.016 0.484 NA
#> GSM1022358 5 0.4332 0.273 0.416 0.000 0.000 0.016 0.564 NA
#> GSM1022351 1 0.0146 0.946 0.996 0.000 0.000 0.000 0.000 NA
#> GSM1022352 1 0.0000 0.946 1.000 0.000 0.000 0.000 0.000 NA
#> GSM1022353 1 0.0000 0.946 1.000 0.000 0.000 0.000 0.000 NA
#> GSM1022354 1 0.0000 0.946 1.000 0.000 0.000 0.000 0.000 NA
#> GSM1022359 2 0.3109 0.481 0.000 0.772 0.000 0.224 0.000 NA
#> GSM1022360 2 0.3189 0.460 0.000 0.760 0.000 0.236 0.000 NA
#> GSM1022361 2 0.3189 0.460 0.000 0.760 0.000 0.236 0.000 NA
#> GSM1022362 2 0.3265 0.441 0.000 0.748 0.000 0.248 0.000 NA
#> GSM1022367 3 0.3838 0.641 0.000 0.000 0.552 0.000 0.000 NA
#> GSM1022368 3 0.3833 0.645 0.000 0.000 0.556 0.000 0.000 NA
#> GSM1022369 3 0.3833 0.645 0.000 0.000 0.556 0.000 0.000 NA
#> GSM1022370 3 0.3828 0.648 0.000 0.000 0.560 0.000 0.000 NA
#> GSM1022363 2 0.4293 0.457 0.000 0.536 0.004 0.012 0.000 NA
#> GSM1022364 2 0.4314 0.460 0.000 0.536 0.000 0.020 0.000 NA
#> GSM1022365 2 0.4314 0.460 0.000 0.536 0.000 0.020 0.000 NA
#> GSM1022366 2 0.4314 0.460 0.000 0.536 0.000 0.020 0.000 NA
#> GSM1022374 5 0.0405 0.932 0.000 0.000 0.000 0.004 0.988 NA
#> GSM1022375 5 0.0405 0.932 0.000 0.000 0.000 0.004 0.988 NA
#> GSM1022376 5 0.0405 0.932 0.000 0.000 0.000 0.004 0.988 NA
#> GSM1022371 2 0.2094 0.698 0.000 0.900 0.000 0.020 0.000 NA
#> GSM1022372 2 0.2199 0.695 0.000 0.892 0.000 0.020 0.000 NA
#> GSM1022373 2 0.2094 0.698 0.000 0.900 0.000 0.020 0.000 NA
#> GSM1022377 4 0.3076 0.953 0.000 0.240 0.000 0.760 0.000 NA
#> GSM1022378 4 0.3076 0.953 0.000 0.240 0.000 0.760 0.000 NA
#> GSM1022379 4 0.3076 0.953 0.000 0.240 0.000 0.760 0.000 NA
#> GSM1022380 4 0.3076 0.953 0.000 0.240 0.000 0.760 0.000 NA
#> GSM1022385 3 0.0547 0.891 0.000 0.000 0.980 0.000 0.000 NA
#> GSM1022386 3 0.0547 0.891 0.000 0.000 0.980 0.000 0.000 NA
#> GSM1022387 3 0.0547 0.891 0.000 0.000 0.980 0.000 0.000 NA
#> GSM1022388 3 0.0547 0.891 0.000 0.000 0.980 0.000 0.000 NA
#> GSM1022381 4 0.2697 0.955 0.000 0.188 0.000 0.812 0.000 NA
#> GSM1022382 4 0.2697 0.955 0.000 0.188 0.000 0.812 0.000 NA
#> GSM1022383 4 0.2664 0.952 0.000 0.184 0.000 0.816 0.000 NA
#> GSM1022384 4 0.2664 0.952 0.000 0.184 0.000 0.816 0.000 NA
#> GSM1022393 5 0.0291 0.930 0.000 0.000 0.000 0.004 0.992 NA
#> GSM1022394 5 0.0508 0.927 0.000 0.000 0.000 0.012 0.984 NA
#> GSM1022395 5 0.0000 0.932 0.000 0.000 0.000 0.000 1.000 NA
#> GSM1022396 5 0.0508 0.927 0.000 0.000 0.000 0.012 0.984 NA
#> GSM1022389 2 0.4416 0.188 0.000 0.600 0.000 0.372 0.008 NA
#> GSM1022390 2 0.4499 0.305 0.000 0.620 0.000 0.344 0.012 NA
#> GSM1022391 2 0.4432 0.256 0.000 0.616 0.000 0.352 0.008 NA
#> GSM1022392 2 0.4770 0.246 0.000 0.584 0.000 0.368 0.012 NA
#> GSM1022397 3 0.0146 0.891 0.000 0.000 0.996 0.000 0.000 NA
#> GSM1022398 3 0.0146 0.891 0.000 0.000 0.996 0.000 0.000 NA
#> GSM1022399 3 0.0146 0.891 0.000 0.000 0.996 0.000 0.000 NA
#> GSM1022400 3 0.0260 0.889 0.000 0.000 0.992 0.000 0.000 NA
#> GSM1022401 5 0.0146 0.933 0.000 0.000 0.000 0.000 0.996 NA
#> GSM1022402 5 0.0146 0.933 0.000 0.000 0.000 0.000 0.996 NA
#> GSM1022403 5 0.0000 0.932 0.000 0.000 0.000 0.000 1.000 NA
#> GSM1022404 5 0.0146 0.932 0.000 0.000 0.000 0.004 0.996 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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 3)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 4)
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 protocol(p) cell.type(p) k
#> CV:NMF 79 3.39e-05 1.50e-08 2
#> CV:NMF 79 1.78e-10 2.17e-10 3
#> CV:NMF 80 5.59e-11 3.07e-17 4
#> CV:NMF 77 7.58e-16 7.52e-16 5
#> CV:NMF 66 2.67e-15 1.58e-13 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
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 31589 rows and 80 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.838 0.914 0.959 0.4997 0.502 0.502
#> 3 3 0.926 0.927 0.968 0.2051 0.916 0.832
#> 4 4 0.785 0.825 0.849 0.1558 0.901 0.763
#> 5 5 0.886 0.925 0.910 0.0831 0.913 0.726
#> 6 6 1.000 0.999 1.000 0.0704 0.962 0.836
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] 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
#> GSM1022325 2 0.000 0.923 0.000 1.000
#> GSM1022326 2 0.000 0.923 0.000 1.000
#> GSM1022327 2 0.000 0.923 0.000 1.000
#> GSM1022331 2 0.963 0.487 0.388 0.612
#> GSM1022332 2 0.963 0.487 0.388 0.612
#> GSM1022333 2 0.963 0.487 0.388 0.612
#> GSM1022328 2 0.000 0.923 0.000 1.000
#> GSM1022329 2 0.000 0.923 0.000 1.000
#> GSM1022330 2 0.000 0.923 0.000 1.000
#> GSM1022337 2 0.456 0.866 0.096 0.904
#> GSM1022338 2 0.456 0.866 0.096 0.904
#> GSM1022339 2 0.456 0.866 0.096 0.904
#> GSM1022334 2 0.000 0.923 0.000 1.000
#> GSM1022335 2 0.000 0.923 0.000 1.000
#> GSM1022336 2 0.000 0.923 0.000 1.000
#> GSM1022340 1 0.000 1.000 1.000 0.000
#> GSM1022341 1 0.000 1.000 1.000 0.000
#> GSM1022342 1 0.000 1.000 1.000 0.000
#> GSM1022343 1 0.000 1.000 1.000 0.000
#> GSM1022347 1 0.000 1.000 1.000 0.000
#> GSM1022348 1 0.000 1.000 1.000 0.000
#> GSM1022349 1 0.000 1.000 1.000 0.000
#> GSM1022350 1 0.000 1.000 1.000 0.000
#> GSM1022344 1 0.000 1.000 1.000 0.000
#> GSM1022345 1 0.000 1.000 1.000 0.000
#> GSM1022346 1 0.000 1.000 1.000 0.000
#> GSM1022355 1 0.000 1.000 1.000 0.000
#> GSM1022356 1 0.000 1.000 1.000 0.000
#> GSM1022357 1 0.000 1.000 1.000 0.000
#> GSM1022358 1 0.000 1.000 1.000 0.000
#> GSM1022351 1 0.000 1.000 1.000 0.000
#> GSM1022352 1 0.000 1.000 1.000 0.000
#> GSM1022353 1 0.000 1.000 1.000 0.000
#> GSM1022354 1 0.000 1.000 1.000 0.000
#> GSM1022359 2 0.000 0.923 0.000 1.000
#> GSM1022360 2 0.000 0.923 0.000 1.000
#> GSM1022361 2 0.000 0.923 0.000 1.000
#> GSM1022362 2 0.000 0.923 0.000 1.000
#> GSM1022367 2 0.963 0.487 0.388 0.612
#> GSM1022368 2 0.963 0.487 0.388 0.612
#> GSM1022369 2 0.963 0.487 0.388 0.612
#> GSM1022370 2 0.963 0.487 0.388 0.612
#> GSM1022363 2 0.000 0.923 0.000 1.000
#> GSM1022364 2 0.000 0.923 0.000 1.000
#> GSM1022365 2 0.000 0.923 0.000 1.000
#> GSM1022366 2 0.000 0.923 0.000 1.000
#> GSM1022374 2 0.456 0.866 0.096 0.904
#> GSM1022375 2 0.456 0.866 0.096 0.904
#> GSM1022376 2 0.456 0.866 0.096 0.904
#> GSM1022371 2 0.000 0.923 0.000 1.000
#> GSM1022372 2 0.000 0.923 0.000 1.000
#> GSM1022373 2 0.000 0.923 0.000 1.000
#> GSM1022377 2 0.000 0.923 0.000 1.000
#> GSM1022378 2 0.000 0.923 0.000 1.000
#> GSM1022379 2 0.000 0.923 0.000 1.000
#> GSM1022380 2 0.000 0.923 0.000 1.000
#> GSM1022385 1 0.000 1.000 1.000 0.000
#> GSM1022386 1 0.000 1.000 1.000 0.000
#> GSM1022387 1 0.000 1.000 1.000 0.000
#> GSM1022388 1 0.000 1.000 1.000 0.000
#> GSM1022381 2 0.000 0.923 0.000 1.000
#> GSM1022382 2 0.000 0.923 0.000 1.000
#> GSM1022383 2 0.000 0.923 0.000 1.000
#> GSM1022384 2 0.000 0.923 0.000 1.000
#> GSM1022393 1 0.000 1.000 1.000 0.000
#> GSM1022394 1 0.000 1.000 1.000 0.000
#> GSM1022395 1 0.000 1.000 1.000 0.000
#> GSM1022396 1 0.000 1.000 1.000 0.000
#> GSM1022389 2 0.000 0.923 0.000 1.000
#> GSM1022390 2 0.000 0.923 0.000 1.000
#> GSM1022391 2 0.000 0.923 0.000 1.000
#> GSM1022392 2 0.000 0.923 0.000 1.000
#> GSM1022397 1 0.000 1.000 1.000 0.000
#> GSM1022398 1 0.000 1.000 1.000 0.000
#> GSM1022399 1 0.000 1.000 1.000 0.000
#> GSM1022400 1 0.000 1.000 1.000 0.000
#> GSM1022401 1 0.000 1.000 1.000 0.000
#> GSM1022402 1 0.000 1.000 1.000 0.000
#> GSM1022403 1 0.000 1.000 1.000 0.000
#> GSM1022404 1 0.000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1022325 2 0.0000 0.929 0.000 1.000 0.000
#> GSM1022326 2 0.0000 0.929 0.000 1.000 0.000
#> GSM1022327 2 0.0000 0.929 0.000 1.000 0.000
#> GSM1022331 3 0.0475 1.000 0.004 0.004 0.992
#> GSM1022332 3 0.0475 1.000 0.004 0.004 0.992
#> GSM1022333 3 0.0475 1.000 0.004 0.004 0.992
#> GSM1022328 2 0.0000 0.929 0.000 1.000 0.000
#> GSM1022329 2 0.0000 0.929 0.000 1.000 0.000
#> GSM1022330 2 0.0000 0.929 0.000 1.000 0.000
#> GSM1022337 2 0.6126 0.421 0.000 0.600 0.400
#> GSM1022338 2 0.6126 0.421 0.000 0.600 0.400
#> GSM1022339 2 0.6126 0.421 0.000 0.600 0.400
#> GSM1022334 2 0.0000 0.929 0.000 1.000 0.000
#> GSM1022335 2 0.0000 0.929 0.000 1.000 0.000
#> GSM1022336 2 0.0000 0.929 0.000 1.000 0.000
#> GSM1022340 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022341 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022342 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022343 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022347 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022348 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022349 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022350 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022344 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022345 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022346 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022355 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022356 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022357 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022358 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022351 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022352 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022353 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022354 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022359 2 0.0000 0.929 0.000 1.000 0.000
#> GSM1022360 2 0.0000 0.929 0.000 1.000 0.000
#> GSM1022361 2 0.0000 0.929 0.000 1.000 0.000
#> GSM1022362 2 0.0000 0.929 0.000 1.000 0.000
#> GSM1022367 3 0.0475 1.000 0.004 0.004 0.992
#> GSM1022368 3 0.0475 1.000 0.004 0.004 0.992
#> GSM1022369 3 0.0475 1.000 0.004 0.004 0.992
#> GSM1022370 3 0.0475 1.000 0.004 0.004 0.992
#> GSM1022363 2 0.0000 0.929 0.000 1.000 0.000
#> GSM1022364 2 0.0000 0.929 0.000 1.000 0.000
#> GSM1022365 2 0.0000 0.929 0.000 1.000 0.000
#> GSM1022366 2 0.0000 0.929 0.000 1.000 0.000
#> GSM1022374 2 0.6126 0.421 0.000 0.600 0.400
#> GSM1022375 2 0.6126 0.421 0.000 0.600 0.400
#> GSM1022376 2 0.6126 0.421 0.000 0.600 0.400
#> GSM1022371 2 0.0000 0.929 0.000 1.000 0.000
#> GSM1022372 2 0.0000 0.929 0.000 1.000 0.000
#> GSM1022373 2 0.0000 0.929 0.000 1.000 0.000
#> GSM1022377 2 0.0237 0.928 0.000 0.996 0.004
#> GSM1022378 2 0.0237 0.928 0.000 0.996 0.004
#> GSM1022379 2 0.0237 0.928 0.000 0.996 0.004
#> GSM1022380 2 0.0237 0.928 0.000 0.996 0.004
#> GSM1022385 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022386 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022387 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022388 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022381 2 0.0237 0.928 0.000 0.996 0.004
#> GSM1022382 2 0.0237 0.928 0.000 0.996 0.004
#> GSM1022383 2 0.0237 0.928 0.000 0.996 0.004
#> GSM1022384 2 0.0237 0.928 0.000 0.996 0.004
#> GSM1022393 1 0.0237 0.997 0.996 0.000 0.004
#> GSM1022394 1 0.0237 0.997 0.996 0.000 0.004
#> GSM1022395 1 0.0237 0.997 0.996 0.000 0.004
#> GSM1022396 1 0.0237 0.997 0.996 0.000 0.004
#> GSM1022389 2 0.0237 0.928 0.000 0.996 0.004
#> GSM1022390 2 0.0237 0.928 0.000 0.996 0.004
#> GSM1022391 2 0.0237 0.928 0.000 0.996 0.004
#> GSM1022392 2 0.0237 0.928 0.000 0.996 0.004
#> GSM1022397 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022398 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022399 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022400 1 0.0000 0.999 1.000 0.000 0.000
#> GSM1022401 1 0.0237 0.997 0.996 0.000 0.004
#> GSM1022402 1 0.0237 0.997 0.996 0.000 0.004
#> GSM1022403 1 0.0237 0.997 0.996 0.000 0.004
#> GSM1022404 1 0.0237 0.997 0.996 0.000 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1022325 2 0.000 0.826 0.000 1.0 0.000 0.000
#> GSM1022326 2 0.000 0.826 0.000 1.0 0.000 0.000
#> GSM1022327 2 0.000 0.826 0.000 1.0 0.000 0.000
#> GSM1022331 3 0.484 1.000 0.000 0.0 0.604 0.396
#> GSM1022332 3 0.484 1.000 0.000 0.0 0.604 0.396
#> GSM1022333 3 0.484 1.000 0.000 0.0 0.604 0.396
#> GSM1022328 2 0.000 0.826 0.000 1.0 0.000 0.000
#> GSM1022329 2 0.000 0.826 0.000 1.0 0.000 0.000
#> GSM1022330 2 0.000 0.826 0.000 1.0 0.000 0.000
#> GSM1022337 2 0.485 0.380 0.000 0.6 0.000 0.400
#> GSM1022338 2 0.485 0.380 0.000 0.6 0.000 0.400
#> GSM1022339 2 0.485 0.380 0.000 0.6 0.000 0.400
#> GSM1022334 2 0.000 0.826 0.000 1.0 0.000 0.000
#> GSM1022335 2 0.000 0.826 0.000 1.0 0.000 0.000
#> GSM1022336 2 0.000 0.826 0.000 1.0 0.000 0.000
#> GSM1022340 1 0.484 0.860 0.604 0.0 0.396 0.000
#> GSM1022341 1 0.484 0.860 0.604 0.0 0.396 0.000
#> GSM1022342 1 0.484 0.860 0.604 0.0 0.396 0.000
#> GSM1022343 1 0.484 0.860 0.604 0.0 0.396 0.000
#> GSM1022347 1 0.000 0.702 1.000 0.0 0.000 0.000
#> GSM1022348 1 0.000 0.702 1.000 0.0 0.000 0.000
#> GSM1022349 1 0.000 0.702 1.000 0.0 0.000 0.000
#> GSM1022350 1 0.000 0.702 1.000 0.0 0.000 0.000
#> GSM1022344 1 0.484 0.860 0.604 0.0 0.396 0.000
#> GSM1022345 1 0.484 0.860 0.604 0.0 0.396 0.000
#> GSM1022346 1 0.484 0.860 0.604 0.0 0.396 0.000
#> GSM1022355 1 0.484 0.860 0.604 0.0 0.396 0.000
#> GSM1022356 1 0.484 0.860 0.604 0.0 0.396 0.000
#> GSM1022357 1 0.484 0.860 0.604 0.0 0.396 0.000
#> GSM1022358 1 0.484 0.860 0.604 0.0 0.396 0.000
#> GSM1022351 1 0.484 0.860 0.604 0.0 0.396 0.000
#> GSM1022352 1 0.484 0.860 0.604 0.0 0.396 0.000
#> GSM1022353 1 0.484 0.860 0.604 0.0 0.396 0.000
#> GSM1022354 1 0.484 0.860 0.604 0.0 0.396 0.000
#> GSM1022359 2 0.000 0.826 0.000 1.0 0.000 0.000
#> GSM1022360 2 0.000 0.826 0.000 1.0 0.000 0.000
#> GSM1022361 2 0.000 0.826 0.000 1.0 0.000 0.000
#> GSM1022362 2 0.000 0.826 0.000 1.0 0.000 0.000
#> GSM1022367 3 0.484 1.000 0.000 0.0 0.604 0.396
#> GSM1022368 3 0.484 1.000 0.000 0.0 0.604 0.396
#> GSM1022369 3 0.484 1.000 0.000 0.0 0.604 0.396
#> GSM1022370 3 0.484 1.000 0.000 0.0 0.604 0.396
#> GSM1022363 2 0.000 0.826 0.000 1.0 0.000 0.000
#> GSM1022364 2 0.000 0.826 0.000 1.0 0.000 0.000
#> GSM1022365 2 0.000 0.826 0.000 1.0 0.000 0.000
#> GSM1022366 2 0.000 0.826 0.000 1.0 0.000 0.000
#> GSM1022374 2 0.485 0.380 0.000 0.6 0.000 0.400
#> GSM1022375 2 0.485 0.380 0.000 0.6 0.000 0.400
#> GSM1022376 2 0.485 0.380 0.000 0.6 0.000 0.400
#> GSM1022371 2 0.000 0.826 0.000 1.0 0.000 0.000
#> GSM1022372 2 0.000 0.826 0.000 1.0 0.000 0.000
#> GSM1022373 2 0.000 0.826 0.000 1.0 0.000 0.000
#> GSM1022377 4 0.485 1.000 0.000 0.4 0.000 0.600
#> GSM1022378 4 0.485 1.000 0.000 0.4 0.000 0.600
#> GSM1022379 4 0.485 1.000 0.000 0.4 0.000 0.600
#> GSM1022380 4 0.485 1.000 0.000 0.4 0.000 0.600
#> GSM1022385 1 0.000 0.702 1.000 0.0 0.000 0.000
#> GSM1022386 1 0.000 0.702 1.000 0.0 0.000 0.000
#> GSM1022387 1 0.000 0.702 1.000 0.0 0.000 0.000
#> GSM1022388 1 0.000 0.702 1.000 0.0 0.000 0.000
#> GSM1022381 4 0.485 1.000 0.000 0.4 0.000 0.600
#> GSM1022382 4 0.485 1.000 0.000 0.4 0.000 0.600
#> GSM1022383 4 0.485 1.000 0.000 0.4 0.000 0.600
#> GSM1022384 4 0.485 1.000 0.000 0.4 0.000 0.600
#> GSM1022393 1 0.502 0.858 0.600 0.0 0.396 0.004
#> GSM1022394 1 0.502 0.858 0.600 0.0 0.396 0.004
#> GSM1022395 1 0.502 0.858 0.600 0.0 0.396 0.004
#> GSM1022396 1 0.502 0.858 0.600 0.0 0.396 0.004
#> GSM1022389 4 0.485 1.000 0.000 0.4 0.000 0.600
#> GSM1022390 4 0.485 1.000 0.000 0.4 0.000 0.600
#> GSM1022391 4 0.485 1.000 0.000 0.4 0.000 0.600
#> GSM1022392 4 0.485 1.000 0.000 0.4 0.000 0.600
#> GSM1022397 1 0.000 0.702 1.000 0.0 0.000 0.000
#> GSM1022398 1 0.000 0.702 1.000 0.0 0.000 0.000
#> GSM1022399 1 0.000 0.702 1.000 0.0 0.000 0.000
#> GSM1022400 1 0.000 0.702 1.000 0.0 0.000 0.000
#> GSM1022401 1 0.502 0.858 0.600 0.0 0.396 0.004
#> GSM1022402 1 0.502 0.858 0.600 0.0 0.396 0.004
#> GSM1022403 1 0.502 0.858 0.600 0.0 0.396 0.004
#> GSM1022404 1 0.502 0.858 0.600 0.0 0.396 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1022325 2 0.4182 0.840 0.000 0.600 0 0.4 0
#> GSM1022326 2 0.4182 0.840 0.000 0.600 0 0.4 0
#> GSM1022327 2 0.4182 0.840 0.000 0.600 0 0.4 0
#> GSM1022331 5 0.0000 1.000 0.000 0.000 0 0.0 1
#> GSM1022332 5 0.0000 1.000 0.000 0.000 0 0.0 1
#> GSM1022333 5 0.0000 1.000 0.000 0.000 0 0.0 1
#> GSM1022328 2 0.4182 0.840 0.000 0.600 0 0.4 0
#> GSM1022329 2 0.4182 0.840 0.000 0.600 0 0.4 0
#> GSM1022330 2 0.4182 0.840 0.000 0.600 0 0.4 0
#> GSM1022337 2 0.0000 0.545 0.000 1.000 0 0.0 0
#> GSM1022338 2 0.0000 0.545 0.000 1.000 0 0.0 0
#> GSM1022339 2 0.0000 0.545 0.000 1.000 0 0.0 0
#> GSM1022334 2 0.4182 0.840 0.000 0.600 0 0.4 0
#> GSM1022335 2 0.4182 0.840 0.000 0.600 0 0.4 0
#> GSM1022336 2 0.4182 0.840 0.000 0.600 0 0.4 0
#> GSM1022340 1 0.0000 0.999 1.000 0.000 0 0.0 0
#> GSM1022341 1 0.0000 0.999 1.000 0.000 0 0.0 0
#> GSM1022342 1 0.0000 0.999 1.000 0.000 0 0.0 0
#> GSM1022343 1 0.0000 0.999 1.000 0.000 0 0.0 0
#> GSM1022347 3 0.0000 1.000 0.000 0.000 1 0.0 0
#> GSM1022348 3 0.0000 1.000 0.000 0.000 1 0.0 0
#> GSM1022349 3 0.0000 1.000 0.000 0.000 1 0.0 0
#> GSM1022350 3 0.0000 1.000 0.000 0.000 1 0.0 0
#> GSM1022344 1 0.0000 0.999 1.000 0.000 0 0.0 0
#> GSM1022345 1 0.0000 0.999 1.000 0.000 0 0.0 0
#> GSM1022346 1 0.0000 0.999 1.000 0.000 0 0.0 0
#> GSM1022355 1 0.0000 0.999 1.000 0.000 0 0.0 0
#> GSM1022356 1 0.0000 0.999 1.000 0.000 0 0.0 0
#> GSM1022357 1 0.0000 0.999 1.000 0.000 0 0.0 0
#> GSM1022358 1 0.0000 0.999 1.000 0.000 0 0.0 0
#> GSM1022351 1 0.0000 0.999 1.000 0.000 0 0.0 0
#> GSM1022352 1 0.0000 0.999 1.000 0.000 0 0.0 0
#> GSM1022353 1 0.0000 0.999 1.000 0.000 0 0.0 0
#> GSM1022354 1 0.0000 0.999 1.000 0.000 0 0.0 0
#> GSM1022359 2 0.4182 0.840 0.000 0.600 0 0.4 0
#> GSM1022360 2 0.4182 0.840 0.000 0.600 0 0.4 0
#> GSM1022361 2 0.4182 0.840 0.000 0.600 0 0.4 0
#> GSM1022362 2 0.4182 0.840 0.000 0.600 0 0.4 0
#> GSM1022367 5 0.0000 1.000 0.000 0.000 0 0.0 1
#> GSM1022368 5 0.0000 1.000 0.000 0.000 0 0.0 1
#> GSM1022369 5 0.0000 1.000 0.000 0.000 0 0.0 1
#> GSM1022370 5 0.0000 1.000 0.000 0.000 0 0.0 1
#> GSM1022363 2 0.4182 0.840 0.000 0.600 0 0.4 0
#> GSM1022364 2 0.4182 0.840 0.000 0.600 0 0.4 0
#> GSM1022365 2 0.4182 0.840 0.000 0.600 0 0.4 0
#> GSM1022366 2 0.4182 0.840 0.000 0.600 0 0.4 0
#> GSM1022374 2 0.0000 0.545 0.000 1.000 0 0.0 0
#> GSM1022375 2 0.0000 0.545 0.000 1.000 0 0.0 0
#> GSM1022376 2 0.0000 0.545 0.000 1.000 0 0.0 0
#> GSM1022371 2 0.4182 0.840 0.000 0.600 0 0.4 0
#> GSM1022372 2 0.4182 0.840 0.000 0.600 0 0.4 0
#> GSM1022373 2 0.4182 0.840 0.000 0.600 0 0.4 0
#> GSM1022377 4 0.0000 1.000 0.000 0.000 0 1.0 0
#> GSM1022378 4 0.0000 1.000 0.000 0.000 0 1.0 0
#> GSM1022379 4 0.0000 1.000 0.000 0.000 0 1.0 0
#> GSM1022380 4 0.0000 1.000 0.000 0.000 0 1.0 0
#> GSM1022385 3 0.0000 1.000 0.000 0.000 1 0.0 0
#> GSM1022386 3 0.0000 1.000 0.000 0.000 1 0.0 0
#> GSM1022387 3 0.0000 1.000 0.000 0.000 1 0.0 0
#> GSM1022388 3 0.0000 1.000 0.000 0.000 1 0.0 0
#> GSM1022381 4 0.0000 1.000 0.000 0.000 0 1.0 0
#> GSM1022382 4 0.0000 1.000 0.000 0.000 0 1.0 0
#> GSM1022383 4 0.0000 1.000 0.000 0.000 0 1.0 0
#> GSM1022384 4 0.0000 1.000 0.000 0.000 0 1.0 0
#> GSM1022393 1 0.0162 0.997 0.996 0.004 0 0.0 0
#> GSM1022394 1 0.0162 0.997 0.996 0.004 0 0.0 0
#> GSM1022395 1 0.0162 0.997 0.996 0.004 0 0.0 0
#> GSM1022396 1 0.0162 0.997 0.996 0.004 0 0.0 0
#> GSM1022389 4 0.0000 1.000 0.000 0.000 0 1.0 0
#> GSM1022390 4 0.0000 1.000 0.000 0.000 0 1.0 0
#> GSM1022391 4 0.0000 1.000 0.000 0.000 0 1.0 0
#> GSM1022392 4 0.0000 1.000 0.000 0.000 0 1.0 0
#> GSM1022397 3 0.0000 1.000 0.000 0.000 1 0.0 0
#> GSM1022398 3 0.0000 1.000 0.000 0.000 1 0.0 0
#> GSM1022399 3 0.0000 1.000 0.000 0.000 1 0.0 0
#> GSM1022400 3 0.0000 1.000 0.000 0.000 1 0.0 0
#> GSM1022401 1 0.0162 0.997 0.996 0.004 0 0.0 0
#> GSM1022402 1 0.0162 0.997 0.996 0.004 0 0.0 0
#> GSM1022403 1 0.0162 0.997 0.996 0.004 0 0.0 0
#> GSM1022404 1 0.0162 0.997 0.996 0.004 0 0.0 0
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1022325 2 0.0000 1.000 0.000 1 0 0 0.000 0
#> GSM1022326 2 0.0000 1.000 0.000 1 0 0 0.000 0
#> GSM1022327 2 0.0000 1.000 0.000 1 0 0 0.000 0
#> GSM1022331 6 0.0000 1.000 0.000 0 0 0 0.000 1
#> GSM1022332 6 0.0000 1.000 0.000 0 0 0 0.000 1
#> GSM1022333 6 0.0000 1.000 0.000 0 0 0 0.000 1
#> GSM1022328 2 0.0000 1.000 0.000 1 0 0 0.000 0
#> GSM1022329 2 0.0000 1.000 0.000 1 0 0 0.000 0
#> GSM1022330 2 0.0000 1.000 0.000 1 0 0 0.000 0
#> GSM1022337 5 0.0000 1.000 0.000 0 0 0 1.000 0
#> GSM1022338 5 0.0000 1.000 0.000 0 0 0 1.000 0
#> GSM1022339 5 0.0000 1.000 0.000 0 0 0 1.000 0
#> GSM1022334 2 0.0000 1.000 0.000 1 0 0 0.000 0
#> GSM1022335 2 0.0000 1.000 0.000 1 0 0 0.000 0
#> GSM1022336 2 0.0000 1.000 0.000 1 0 0 0.000 0
#> GSM1022340 1 0.0000 0.999 1.000 0 0 0 0.000 0
#> GSM1022341 1 0.0000 0.999 1.000 0 0 0 0.000 0
#> GSM1022342 1 0.0000 0.999 1.000 0 0 0 0.000 0
#> GSM1022343 1 0.0000 0.999 1.000 0 0 0 0.000 0
#> GSM1022347 3 0.0000 1.000 0.000 0 1 0 0.000 0
#> GSM1022348 3 0.0000 1.000 0.000 0 1 0 0.000 0
#> GSM1022349 3 0.0000 1.000 0.000 0 1 0 0.000 0
#> GSM1022350 3 0.0000 1.000 0.000 0 1 0 0.000 0
#> GSM1022344 1 0.0000 0.999 1.000 0 0 0 0.000 0
#> GSM1022345 1 0.0000 0.999 1.000 0 0 0 0.000 0
#> GSM1022346 1 0.0000 0.999 1.000 0 0 0 0.000 0
#> GSM1022355 1 0.0000 0.999 1.000 0 0 0 0.000 0
#> GSM1022356 1 0.0000 0.999 1.000 0 0 0 0.000 0
#> GSM1022357 1 0.0000 0.999 1.000 0 0 0 0.000 0
#> GSM1022358 1 0.0000 0.999 1.000 0 0 0 0.000 0
#> GSM1022351 1 0.0000 0.999 1.000 0 0 0 0.000 0
#> GSM1022352 1 0.0000 0.999 1.000 0 0 0 0.000 0
#> GSM1022353 1 0.0000 0.999 1.000 0 0 0 0.000 0
#> GSM1022354 1 0.0000 0.999 1.000 0 0 0 0.000 0
#> GSM1022359 2 0.0000 1.000 0.000 1 0 0 0.000 0
#> GSM1022360 2 0.0000 1.000 0.000 1 0 0 0.000 0
#> GSM1022361 2 0.0000 1.000 0.000 1 0 0 0.000 0
#> GSM1022362 2 0.0000 1.000 0.000 1 0 0 0.000 0
#> GSM1022367 6 0.0000 1.000 0.000 0 0 0 0.000 1
#> GSM1022368 6 0.0000 1.000 0.000 0 0 0 0.000 1
#> GSM1022369 6 0.0000 1.000 0.000 0 0 0 0.000 1
#> GSM1022370 6 0.0000 1.000 0.000 0 0 0 0.000 1
#> GSM1022363 2 0.0000 1.000 0.000 1 0 0 0.000 0
#> GSM1022364 2 0.0000 1.000 0.000 1 0 0 0.000 0
#> GSM1022365 2 0.0000 1.000 0.000 1 0 0 0.000 0
#> GSM1022366 2 0.0000 1.000 0.000 1 0 0 0.000 0
#> GSM1022374 5 0.0000 1.000 0.000 0 0 0 1.000 0
#> GSM1022375 5 0.0000 1.000 0.000 0 0 0 1.000 0
#> GSM1022376 5 0.0000 1.000 0.000 0 0 0 1.000 0
#> GSM1022371 2 0.0000 1.000 0.000 1 0 0 0.000 0
#> GSM1022372 2 0.0000 1.000 0.000 1 0 0 0.000 0
#> GSM1022373 2 0.0000 1.000 0.000 1 0 0 0.000 0
#> GSM1022377 4 0.0000 1.000 0.000 0 0 1 0.000 0
#> GSM1022378 4 0.0000 1.000 0.000 0 0 1 0.000 0
#> GSM1022379 4 0.0000 1.000 0.000 0 0 1 0.000 0
#> GSM1022380 4 0.0000 1.000 0.000 0 0 1 0.000 0
#> GSM1022385 3 0.0000 1.000 0.000 0 1 0 0.000 0
#> GSM1022386 3 0.0000 1.000 0.000 0 1 0 0.000 0
#> GSM1022387 3 0.0000 1.000 0.000 0 1 0 0.000 0
#> GSM1022388 3 0.0000 1.000 0.000 0 1 0 0.000 0
#> GSM1022381 4 0.0000 1.000 0.000 0 0 1 0.000 0
#> GSM1022382 4 0.0000 1.000 0.000 0 0 1 0.000 0
#> GSM1022383 4 0.0000 1.000 0.000 0 0 1 0.000 0
#> GSM1022384 4 0.0000 1.000 0.000 0 0 1 0.000 0
#> GSM1022393 1 0.0146 0.997 0.996 0 0 0 0.004 0
#> GSM1022394 1 0.0146 0.997 0.996 0 0 0 0.004 0
#> GSM1022395 1 0.0146 0.997 0.996 0 0 0 0.004 0
#> GSM1022396 1 0.0146 0.997 0.996 0 0 0 0.004 0
#> GSM1022389 4 0.0000 1.000 0.000 0 0 1 0.000 0
#> GSM1022390 4 0.0000 1.000 0.000 0 0 1 0.000 0
#> GSM1022391 4 0.0000 1.000 0.000 0 0 1 0.000 0
#> GSM1022392 4 0.0000 1.000 0.000 0 0 1 0.000 0
#> GSM1022397 3 0.0000 1.000 0.000 0 1 0 0.000 0
#> GSM1022398 3 0.0000 1.000 0.000 0 1 0 0.000 0
#> GSM1022399 3 0.0000 1.000 0.000 0 1 0 0.000 0
#> GSM1022400 3 0.0000 1.000 0.000 0 1 0 0.000 0
#> GSM1022401 1 0.0146 0.997 0.996 0 0 0 0.004 0
#> GSM1022402 1 0.0146 0.997 0.996 0 0 0 0.004 0
#> GSM1022403 1 0.0146 0.997 0.996 0 0 0 0.004 0
#> GSM1022404 1 0.0146 0.997 0.996 0 0 0 0.004 0
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n protocol(p) cell.type(p) k
#> MAD:hclust 73 1.81e-07 1.42e-05 2
#> MAD:hclust 74 3.24e-08 4.57e-10 3
#> MAD:hclust 74 3.92e-13 2.44e-09 4
#> MAD:hclust 80 5.03e-20 9.50e-08 5
#> MAD:hclust 80 3.12e-20 5.27e-11 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 31589 rows and 80 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.902 0.947 0.966 0.5001 0.495 0.495
#> 3 3 0.566 0.657 0.739 0.2742 0.836 0.679
#> 4 4 0.617 0.695 0.723 0.1256 0.851 0.613
#> 5 5 0.693 0.782 0.787 0.0723 0.930 0.738
#> 6 6 0.701 0.749 0.758 0.0466 0.992 0.963
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
#> GSM1022325 2 0.000 0.948 0.000 1.000
#> GSM1022326 2 0.000 0.948 0.000 1.000
#> GSM1022327 2 0.000 0.948 0.000 1.000
#> GSM1022331 1 0.224 0.954 0.964 0.036
#> GSM1022332 1 0.224 0.954 0.964 0.036
#> GSM1022333 1 0.224 0.954 0.964 0.036
#> GSM1022328 2 0.000 0.948 0.000 1.000
#> GSM1022329 2 0.000 0.948 0.000 1.000
#> GSM1022330 2 0.000 0.948 0.000 1.000
#> GSM1022337 2 0.795 0.694 0.240 0.760
#> GSM1022338 2 0.795 0.694 0.240 0.760
#> GSM1022339 2 0.795 0.694 0.240 0.760
#> GSM1022334 2 0.000 0.948 0.000 1.000
#> GSM1022335 2 0.000 0.948 0.000 1.000
#> GSM1022336 2 0.000 0.948 0.000 1.000
#> GSM1022340 1 0.204 0.981 0.968 0.032
#> GSM1022341 1 0.204 0.981 0.968 0.032
#> GSM1022342 1 0.204 0.981 0.968 0.032
#> GSM1022343 1 0.204 0.981 0.968 0.032
#> GSM1022347 1 0.000 0.978 1.000 0.000
#> GSM1022348 1 0.000 0.978 1.000 0.000
#> GSM1022349 1 0.000 0.978 1.000 0.000
#> GSM1022350 1 0.000 0.978 1.000 0.000
#> GSM1022344 1 0.000 0.978 1.000 0.000
#> GSM1022345 1 0.000 0.978 1.000 0.000
#> GSM1022346 1 0.000 0.978 1.000 0.000
#> GSM1022355 1 0.204 0.981 0.968 0.032
#> GSM1022356 1 0.204 0.981 0.968 0.032
#> GSM1022357 1 0.204 0.981 0.968 0.032
#> GSM1022358 1 0.204 0.981 0.968 0.032
#> GSM1022351 1 0.204 0.981 0.968 0.032
#> GSM1022352 1 0.204 0.981 0.968 0.032
#> GSM1022353 1 0.204 0.981 0.968 0.032
#> GSM1022354 1 0.204 0.981 0.968 0.032
#> GSM1022359 2 0.000 0.948 0.000 1.000
#> GSM1022360 2 0.000 0.948 0.000 1.000
#> GSM1022361 2 0.000 0.948 0.000 1.000
#> GSM1022362 2 0.000 0.948 0.000 1.000
#> GSM1022367 2 0.184 0.934 0.028 0.972
#> GSM1022368 2 0.184 0.934 0.028 0.972
#> GSM1022369 2 0.184 0.934 0.028 0.972
#> GSM1022370 2 0.184 0.934 0.028 0.972
#> GSM1022363 2 0.000 0.948 0.000 1.000
#> GSM1022364 2 0.000 0.948 0.000 1.000
#> GSM1022365 2 0.000 0.948 0.000 1.000
#> GSM1022366 2 0.000 0.948 0.000 1.000
#> GSM1022374 2 0.000 0.948 0.000 1.000
#> GSM1022375 2 0.000 0.948 0.000 1.000
#> GSM1022376 2 0.000 0.948 0.000 1.000
#> GSM1022371 2 0.000 0.948 0.000 1.000
#> GSM1022372 2 0.000 0.948 0.000 1.000
#> GSM1022373 2 0.000 0.948 0.000 1.000
#> GSM1022377 2 0.456 0.911 0.096 0.904
#> GSM1022378 2 0.456 0.911 0.096 0.904
#> GSM1022379 2 0.456 0.911 0.096 0.904
#> GSM1022380 2 0.456 0.911 0.096 0.904
#> GSM1022385 1 0.000 0.978 1.000 0.000
#> GSM1022386 1 0.000 0.978 1.000 0.000
#> GSM1022387 1 0.000 0.978 1.000 0.000
#> GSM1022388 1 0.000 0.978 1.000 0.000
#> GSM1022381 2 0.456 0.911 0.096 0.904
#> GSM1022382 2 0.456 0.911 0.096 0.904
#> GSM1022383 2 0.456 0.911 0.096 0.904
#> GSM1022384 2 0.456 0.911 0.096 0.904
#> GSM1022393 1 0.204 0.981 0.968 0.032
#> GSM1022394 1 0.204 0.981 0.968 0.032
#> GSM1022395 1 0.204 0.981 0.968 0.032
#> GSM1022396 1 0.204 0.981 0.968 0.032
#> GSM1022389 2 0.456 0.911 0.096 0.904
#> GSM1022390 2 0.456 0.911 0.096 0.904
#> GSM1022391 2 0.456 0.911 0.096 0.904
#> GSM1022392 2 0.456 0.911 0.096 0.904
#> GSM1022397 1 0.000 0.978 1.000 0.000
#> GSM1022398 1 0.000 0.978 1.000 0.000
#> GSM1022399 1 0.000 0.978 1.000 0.000
#> GSM1022400 1 0.000 0.978 1.000 0.000
#> GSM1022401 1 0.204 0.981 0.968 0.032
#> GSM1022402 1 0.204 0.981 0.968 0.032
#> GSM1022403 1 0.204 0.981 0.968 0.032
#> GSM1022404 1 0.204 0.981 0.968 0.032
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1022325 2 0.0000 0.826 0.000 1.000 0.000
#> GSM1022326 2 0.0000 0.826 0.000 1.000 0.000
#> GSM1022327 2 0.0000 0.826 0.000 1.000 0.000
#> GSM1022331 3 0.5138 0.508 0.252 0.000 0.748
#> GSM1022332 3 0.5138 0.508 0.252 0.000 0.748
#> GSM1022333 3 0.5138 0.508 0.252 0.000 0.748
#> GSM1022328 2 0.0000 0.826 0.000 1.000 0.000
#> GSM1022329 2 0.0000 0.826 0.000 1.000 0.000
#> GSM1022330 2 0.0000 0.826 0.000 1.000 0.000
#> GSM1022337 1 0.6967 0.205 0.668 0.288 0.044
#> GSM1022338 1 0.6967 0.205 0.668 0.288 0.044
#> GSM1022339 1 0.6967 0.205 0.668 0.288 0.044
#> GSM1022334 2 0.0000 0.826 0.000 1.000 0.000
#> GSM1022335 2 0.0000 0.826 0.000 1.000 0.000
#> GSM1022336 2 0.0000 0.826 0.000 1.000 0.000
#> GSM1022340 3 0.6267 -0.527 0.452 0.000 0.548
#> GSM1022341 3 0.6267 -0.527 0.452 0.000 0.548
#> GSM1022342 3 0.6267 -0.527 0.452 0.000 0.548
#> GSM1022343 3 0.6267 -0.527 0.452 0.000 0.548
#> GSM1022347 3 0.0000 0.767 0.000 0.000 1.000
#> GSM1022348 3 0.0000 0.767 0.000 0.000 1.000
#> GSM1022349 3 0.0000 0.767 0.000 0.000 1.000
#> GSM1022350 3 0.0000 0.767 0.000 0.000 1.000
#> GSM1022344 3 0.1964 0.714 0.056 0.000 0.944
#> GSM1022345 3 0.1964 0.714 0.056 0.000 0.944
#> GSM1022346 3 0.1964 0.714 0.056 0.000 0.944
#> GSM1022355 1 0.6260 0.767 0.552 0.000 0.448
#> GSM1022356 1 0.6260 0.767 0.552 0.000 0.448
#> GSM1022357 1 0.6260 0.767 0.552 0.000 0.448
#> GSM1022358 1 0.6260 0.767 0.552 0.000 0.448
#> GSM1022351 1 0.6260 0.767 0.552 0.000 0.448
#> GSM1022352 1 0.6260 0.767 0.552 0.000 0.448
#> GSM1022353 1 0.6260 0.767 0.552 0.000 0.448
#> GSM1022354 1 0.6260 0.767 0.552 0.000 0.448
#> GSM1022359 2 0.1031 0.824 0.024 0.976 0.000
#> GSM1022360 2 0.1031 0.824 0.024 0.976 0.000
#> GSM1022361 2 0.1031 0.824 0.024 0.976 0.000
#> GSM1022362 2 0.1031 0.824 0.024 0.976 0.000
#> GSM1022367 2 0.7159 0.659 0.288 0.660 0.052
#> GSM1022368 2 0.7159 0.659 0.288 0.660 0.052
#> GSM1022369 2 0.7159 0.659 0.288 0.660 0.052
#> GSM1022370 2 0.7159 0.659 0.288 0.660 0.052
#> GSM1022363 2 0.2625 0.807 0.084 0.916 0.000
#> GSM1022364 2 0.2625 0.807 0.084 0.916 0.000
#> GSM1022365 2 0.2625 0.807 0.084 0.916 0.000
#> GSM1022366 2 0.2625 0.807 0.084 0.916 0.000
#> GSM1022374 2 0.6468 0.471 0.444 0.552 0.004
#> GSM1022375 2 0.6468 0.471 0.444 0.552 0.004
#> GSM1022376 2 0.6468 0.471 0.444 0.552 0.004
#> GSM1022371 2 0.0237 0.826 0.004 0.996 0.000
#> GSM1022372 2 0.0237 0.826 0.004 0.996 0.000
#> GSM1022373 2 0.0237 0.826 0.004 0.996 0.000
#> GSM1022377 2 0.6872 0.717 0.276 0.680 0.044
#> GSM1022378 2 0.6872 0.717 0.276 0.680 0.044
#> GSM1022379 2 0.6872 0.717 0.276 0.680 0.044
#> GSM1022380 2 0.6872 0.717 0.276 0.680 0.044
#> GSM1022385 3 0.0000 0.767 0.000 0.000 1.000
#> GSM1022386 3 0.0000 0.767 0.000 0.000 1.000
#> GSM1022387 3 0.0000 0.767 0.000 0.000 1.000
#> GSM1022388 3 0.0000 0.767 0.000 0.000 1.000
#> GSM1022381 2 0.6905 0.716 0.280 0.676 0.044
#> GSM1022382 2 0.6905 0.716 0.280 0.676 0.044
#> GSM1022383 2 0.6905 0.716 0.280 0.676 0.044
#> GSM1022384 2 0.6905 0.716 0.280 0.676 0.044
#> GSM1022393 1 0.6235 0.773 0.564 0.000 0.436
#> GSM1022394 1 0.6235 0.773 0.564 0.000 0.436
#> GSM1022395 1 0.6235 0.773 0.564 0.000 0.436
#> GSM1022396 1 0.6235 0.773 0.564 0.000 0.436
#> GSM1022389 2 0.6665 0.709 0.276 0.688 0.036
#> GSM1022390 2 0.7150 0.628 0.348 0.616 0.036
#> GSM1022391 2 0.6665 0.709 0.276 0.688 0.036
#> GSM1022392 2 0.7150 0.628 0.348 0.616 0.036
#> GSM1022397 3 0.0000 0.767 0.000 0.000 1.000
#> GSM1022398 3 0.0000 0.767 0.000 0.000 1.000
#> GSM1022399 3 0.0000 0.767 0.000 0.000 1.000
#> GSM1022400 3 0.0000 0.767 0.000 0.000 1.000
#> GSM1022401 1 0.6235 0.773 0.564 0.000 0.436
#> GSM1022402 1 0.6235 0.773 0.564 0.000 0.436
#> GSM1022403 1 0.6235 0.773 0.564 0.000 0.436
#> GSM1022404 1 0.6235 0.773 0.564 0.000 0.436
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1022325 2 0.0336 0.677 0.000 0.992 0.000 0.008
#> GSM1022326 2 0.0336 0.677 0.000 0.992 0.000 0.008
#> GSM1022327 2 0.0336 0.677 0.000 0.992 0.000 0.008
#> GSM1022331 3 0.4562 0.556 0.028 0.000 0.764 0.208
#> GSM1022332 3 0.4562 0.556 0.028 0.000 0.764 0.208
#> GSM1022333 3 0.4562 0.556 0.028 0.000 0.764 0.208
#> GSM1022328 2 0.0336 0.677 0.000 0.992 0.000 0.008
#> GSM1022329 2 0.0336 0.677 0.000 0.992 0.000 0.008
#> GSM1022330 2 0.0336 0.677 0.000 0.992 0.000 0.008
#> GSM1022337 1 0.9380 0.159 0.428 0.168 0.160 0.244
#> GSM1022338 1 0.9380 0.159 0.428 0.168 0.160 0.244
#> GSM1022339 1 0.9380 0.159 0.428 0.168 0.160 0.244
#> GSM1022334 2 0.0336 0.677 0.000 0.992 0.000 0.008
#> GSM1022335 2 0.0336 0.677 0.000 0.992 0.000 0.008
#> GSM1022336 2 0.0336 0.677 0.000 0.992 0.000 0.008
#> GSM1022340 1 0.6078 0.604 0.684 0.000 0.152 0.164
#> GSM1022341 1 0.6078 0.604 0.684 0.000 0.152 0.164
#> GSM1022342 1 0.6078 0.604 0.684 0.000 0.152 0.164
#> GSM1022343 1 0.6078 0.604 0.684 0.000 0.152 0.164
#> GSM1022347 3 0.4059 0.859 0.200 0.000 0.788 0.012
#> GSM1022348 3 0.4059 0.859 0.200 0.000 0.788 0.012
#> GSM1022349 3 0.4059 0.859 0.200 0.000 0.788 0.012
#> GSM1022350 3 0.4059 0.859 0.200 0.000 0.788 0.012
#> GSM1022344 3 0.6855 0.639 0.276 0.000 0.580 0.144
#> GSM1022345 3 0.6855 0.639 0.276 0.000 0.580 0.144
#> GSM1022346 3 0.6855 0.639 0.276 0.000 0.580 0.144
#> GSM1022355 1 0.2999 0.776 0.864 0.000 0.004 0.132
#> GSM1022356 1 0.2999 0.776 0.864 0.000 0.004 0.132
#> GSM1022357 1 0.2999 0.776 0.864 0.000 0.004 0.132
#> GSM1022358 1 0.2999 0.776 0.864 0.000 0.004 0.132
#> GSM1022351 1 0.3105 0.774 0.856 0.000 0.004 0.140
#> GSM1022352 1 0.3105 0.774 0.856 0.000 0.004 0.140
#> GSM1022353 1 0.3105 0.774 0.856 0.000 0.004 0.140
#> GSM1022354 1 0.3105 0.774 0.856 0.000 0.004 0.140
#> GSM1022359 2 0.0707 0.676 0.000 0.980 0.000 0.020
#> GSM1022360 2 0.0707 0.676 0.000 0.980 0.000 0.020
#> GSM1022361 2 0.0707 0.676 0.000 0.980 0.000 0.020
#> GSM1022362 2 0.0707 0.676 0.000 0.980 0.000 0.020
#> GSM1022367 2 0.7815 0.318 0.004 0.444 0.224 0.328
#> GSM1022368 2 0.7815 0.318 0.004 0.444 0.224 0.328
#> GSM1022369 2 0.7815 0.318 0.004 0.444 0.224 0.328
#> GSM1022370 2 0.7815 0.318 0.004 0.444 0.224 0.328
#> GSM1022363 2 0.2466 0.652 0.000 0.900 0.004 0.096
#> GSM1022364 2 0.2466 0.652 0.000 0.900 0.004 0.096
#> GSM1022365 2 0.2466 0.652 0.000 0.900 0.004 0.096
#> GSM1022366 2 0.2466 0.652 0.000 0.900 0.004 0.096
#> GSM1022374 2 0.9820 0.156 0.288 0.292 0.160 0.260
#> GSM1022375 2 0.9820 0.156 0.288 0.292 0.160 0.260
#> GSM1022376 2 0.9820 0.156 0.288 0.292 0.160 0.260
#> GSM1022371 2 0.0592 0.679 0.000 0.984 0.000 0.016
#> GSM1022372 2 0.0592 0.679 0.000 0.984 0.000 0.016
#> GSM1022373 2 0.0592 0.679 0.000 0.984 0.000 0.016
#> GSM1022377 4 0.6951 0.952 0.068 0.440 0.016 0.476
#> GSM1022378 4 0.6951 0.952 0.068 0.440 0.016 0.476
#> GSM1022379 4 0.6951 0.952 0.068 0.440 0.016 0.476
#> GSM1022380 4 0.6951 0.952 0.068 0.440 0.016 0.476
#> GSM1022385 3 0.3933 0.860 0.200 0.000 0.792 0.008
#> GSM1022386 3 0.3933 0.860 0.200 0.000 0.792 0.008
#> GSM1022387 3 0.3933 0.860 0.200 0.000 0.792 0.008
#> GSM1022388 3 0.3933 0.860 0.200 0.000 0.792 0.008
#> GSM1022381 4 0.6834 0.951 0.068 0.424 0.012 0.496
#> GSM1022382 4 0.6834 0.951 0.068 0.424 0.012 0.496
#> GSM1022383 4 0.6834 0.951 0.068 0.424 0.012 0.496
#> GSM1022384 4 0.6834 0.951 0.068 0.424 0.012 0.496
#> GSM1022393 1 0.0000 0.772 1.000 0.000 0.000 0.000
#> GSM1022394 1 0.0000 0.772 1.000 0.000 0.000 0.000
#> GSM1022395 1 0.0000 0.772 1.000 0.000 0.000 0.000
#> GSM1022396 1 0.0000 0.772 1.000 0.000 0.000 0.000
#> GSM1022389 4 0.6959 0.932 0.076 0.444 0.012 0.468
#> GSM1022390 4 0.7353 0.896 0.112 0.408 0.012 0.468
#> GSM1022391 4 0.6959 0.932 0.076 0.444 0.012 0.468
#> GSM1022392 4 0.7353 0.896 0.112 0.408 0.012 0.468
#> GSM1022397 3 0.3610 0.861 0.200 0.000 0.800 0.000
#> GSM1022398 3 0.3610 0.861 0.200 0.000 0.800 0.000
#> GSM1022399 3 0.3610 0.861 0.200 0.000 0.800 0.000
#> GSM1022400 3 0.3610 0.861 0.200 0.000 0.800 0.000
#> GSM1022401 1 0.0000 0.772 1.000 0.000 0.000 0.000
#> GSM1022402 1 0.0000 0.772 1.000 0.000 0.000 0.000
#> GSM1022403 1 0.0000 0.772 1.000 0.000 0.000 0.000
#> GSM1022404 1 0.0000 0.772 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
#> GSM1022325 2 0.0162 0.934 0.000 0.996 0.000 0.004 0.000
#> GSM1022326 2 0.0162 0.934 0.000 0.996 0.000 0.004 0.000
#> GSM1022327 2 0.0162 0.934 0.000 0.996 0.000 0.004 0.000
#> GSM1022331 3 0.5708 0.332 0.000 0.000 0.588 0.112 0.300
#> GSM1022332 3 0.5708 0.332 0.000 0.000 0.588 0.112 0.300
#> GSM1022333 3 0.5708 0.332 0.000 0.000 0.588 0.112 0.300
#> GSM1022328 2 0.0162 0.934 0.000 0.996 0.000 0.004 0.000
#> GSM1022329 2 0.0162 0.934 0.000 0.996 0.000 0.004 0.000
#> GSM1022330 2 0.0162 0.934 0.000 0.996 0.000 0.004 0.000
#> GSM1022337 5 0.4428 0.650 0.160 0.084 0.000 0.000 0.756
#> GSM1022338 5 0.4428 0.650 0.160 0.084 0.000 0.000 0.756
#> GSM1022339 5 0.4428 0.650 0.160 0.084 0.000 0.000 0.756
#> GSM1022334 2 0.0290 0.932 0.000 0.992 0.000 0.008 0.000
#> GSM1022335 2 0.0290 0.932 0.000 0.992 0.000 0.008 0.000
#> GSM1022336 2 0.0290 0.932 0.000 0.992 0.000 0.008 0.000
#> GSM1022340 1 0.5661 0.572 0.696 0.000 0.164 0.096 0.044
#> GSM1022341 1 0.5661 0.572 0.696 0.000 0.164 0.096 0.044
#> GSM1022342 1 0.5661 0.572 0.696 0.000 0.164 0.096 0.044
#> GSM1022343 1 0.5661 0.572 0.696 0.000 0.164 0.096 0.044
#> GSM1022347 3 0.2956 0.813 0.096 0.000 0.872 0.020 0.012
#> GSM1022348 3 0.2956 0.813 0.096 0.000 0.872 0.020 0.012
#> GSM1022349 3 0.2956 0.813 0.096 0.000 0.872 0.020 0.012
#> GSM1022350 3 0.2956 0.813 0.096 0.000 0.872 0.020 0.012
#> GSM1022344 3 0.7076 0.346 0.356 0.000 0.468 0.120 0.056
#> GSM1022345 3 0.7076 0.346 0.356 0.000 0.468 0.120 0.056
#> GSM1022346 3 0.7076 0.346 0.356 0.000 0.468 0.120 0.056
#> GSM1022355 1 0.0162 0.812 0.996 0.000 0.000 0.000 0.004
#> GSM1022356 1 0.0162 0.812 0.996 0.000 0.000 0.000 0.004
#> GSM1022357 1 0.0162 0.812 0.996 0.000 0.000 0.000 0.004
#> GSM1022358 1 0.0162 0.812 0.996 0.000 0.000 0.000 0.004
#> GSM1022351 1 0.1124 0.805 0.960 0.000 0.004 0.036 0.000
#> GSM1022352 1 0.1124 0.805 0.960 0.000 0.004 0.036 0.000
#> GSM1022353 1 0.1124 0.805 0.960 0.000 0.004 0.036 0.000
#> GSM1022354 1 0.1124 0.805 0.960 0.000 0.004 0.036 0.000
#> GSM1022359 2 0.1041 0.923 0.000 0.964 0.004 0.032 0.000
#> GSM1022360 2 0.1041 0.923 0.000 0.964 0.004 0.032 0.000
#> GSM1022361 2 0.1041 0.923 0.000 0.964 0.004 0.032 0.000
#> GSM1022362 2 0.1041 0.923 0.000 0.964 0.004 0.032 0.000
#> GSM1022367 5 0.7635 0.594 0.000 0.248 0.096 0.176 0.480
#> GSM1022368 5 0.7635 0.594 0.000 0.248 0.096 0.176 0.480
#> GSM1022369 5 0.7635 0.594 0.000 0.248 0.096 0.176 0.480
#> GSM1022370 5 0.7635 0.594 0.000 0.248 0.096 0.176 0.480
#> GSM1022363 2 0.3804 0.829 0.000 0.832 0.020 0.092 0.056
#> GSM1022364 2 0.3804 0.829 0.000 0.832 0.020 0.092 0.056
#> GSM1022365 2 0.3804 0.829 0.000 0.832 0.020 0.092 0.056
#> GSM1022366 2 0.3804 0.829 0.000 0.832 0.020 0.092 0.056
#> GSM1022374 5 0.4836 0.725 0.072 0.164 0.004 0.012 0.748
#> GSM1022375 5 0.4836 0.725 0.072 0.164 0.004 0.012 0.748
#> GSM1022376 5 0.4836 0.725 0.072 0.164 0.004 0.012 0.748
#> GSM1022371 2 0.1243 0.921 0.000 0.960 0.008 0.028 0.004
#> GSM1022372 2 0.1243 0.921 0.000 0.960 0.008 0.028 0.004
#> GSM1022373 2 0.1243 0.921 0.000 0.960 0.008 0.028 0.004
#> GSM1022377 4 0.5277 0.943 0.016 0.316 0.012 0.636 0.020
#> GSM1022378 4 0.5277 0.943 0.016 0.316 0.012 0.636 0.020
#> GSM1022379 4 0.5277 0.943 0.016 0.316 0.012 0.636 0.020
#> GSM1022380 4 0.5277 0.943 0.016 0.316 0.012 0.636 0.020
#> GSM1022385 3 0.2859 0.812 0.096 0.000 0.876 0.016 0.012
#> GSM1022386 3 0.2859 0.812 0.096 0.000 0.876 0.016 0.012
#> GSM1022387 3 0.2859 0.812 0.096 0.000 0.876 0.016 0.012
#> GSM1022388 3 0.2859 0.812 0.096 0.000 0.876 0.016 0.012
#> GSM1022381 4 0.4769 0.946 0.016 0.316 0.004 0.656 0.008
#> GSM1022382 4 0.4769 0.946 0.016 0.316 0.004 0.656 0.008
#> GSM1022383 4 0.4769 0.946 0.016 0.316 0.004 0.656 0.008
#> GSM1022384 4 0.4769 0.946 0.016 0.316 0.004 0.656 0.008
#> GSM1022393 1 0.3639 0.769 0.792 0.000 0.000 0.024 0.184
#> GSM1022394 1 0.3639 0.769 0.792 0.000 0.000 0.024 0.184
#> GSM1022395 1 0.3639 0.769 0.792 0.000 0.000 0.024 0.184
#> GSM1022396 1 0.3639 0.769 0.792 0.000 0.000 0.024 0.184
#> GSM1022389 4 0.5592 0.913 0.024 0.308 0.016 0.628 0.024
#> GSM1022390 4 0.5952 0.892 0.052 0.280 0.016 0.628 0.024
#> GSM1022391 4 0.5592 0.913 0.024 0.308 0.016 0.628 0.024
#> GSM1022392 4 0.5952 0.892 0.052 0.280 0.016 0.628 0.024
#> GSM1022397 3 0.1965 0.817 0.096 0.000 0.904 0.000 0.000
#> GSM1022398 3 0.1965 0.817 0.096 0.000 0.904 0.000 0.000
#> GSM1022399 3 0.1965 0.817 0.096 0.000 0.904 0.000 0.000
#> GSM1022400 3 0.1965 0.817 0.096 0.000 0.904 0.000 0.000
#> GSM1022401 1 0.3639 0.769 0.792 0.000 0.000 0.024 0.184
#> GSM1022402 1 0.3639 0.769 0.792 0.000 0.000 0.024 0.184
#> GSM1022403 1 0.3639 0.769 0.792 0.000 0.000 0.024 0.184
#> GSM1022404 1 0.3639 0.769 0.792 0.000 0.000 0.024 0.184
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1022325 2 0.0146 0.8691 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM1022326 2 0.0146 0.8691 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM1022327 2 0.0146 0.8691 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM1022331 3 0.6299 0.0907 0.000 0.000 0.460 0.024 0.192 0.324
#> GSM1022332 3 0.6299 0.0907 0.000 0.000 0.460 0.024 0.192 0.324
#> GSM1022333 3 0.6299 0.0907 0.000 0.000 0.460 0.024 0.192 0.324
#> GSM1022328 2 0.0146 0.8691 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM1022329 2 0.0146 0.8691 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM1022330 2 0.0146 0.8691 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM1022337 5 0.2579 0.9006 0.088 0.040 0.000 0.000 0.872 0.000
#> GSM1022338 5 0.2579 0.9006 0.088 0.040 0.000 0.000 0.872 0.000
#> GSM1022339 5 0.2579 0.9006 0.088 0.040 0.000 0.000 0.872 0.000
#> GSM1022334 2 0.0291 0.8687 0.000 0.992 0.000 0.004 0.004 0.000
#> GSM1022335 2 0.0291 0.8687 0.000 0.992 0.000 0.004 0.004 0.000
#> GSM1022336 2 0.0291 0.8687 0.000 0.992 0.000 0.004 0.004 0.000
#> GSM1022340 1 0.5582 0.5371 0.660 0.000 0.140 0.048 0.004 0.148
#> GSM1022341 1 0.5582 0.5371 0.660 0.000 0.140 0.048 0.004 0.148
#> GSM1022342 1 0.5582 0.5371 0.660 0.000 0.140 0.048 0.004 0.148
#> GSM1022343 1 0.5582 0.5371 0.660 0.000 0.140 0.048 0.004 0.148
#> GSM1022347 3 0.1914 0.7722 0.056 0.000 0.920 0.008 0.000 0.016
#> GSM1022348 3 0.1914 0.7722 0.056 0.000 0.920 0.008 0.000 0.016
#> GSM1022349 3 0.1914 0.7722 0.056 0.000 0.920 0.008 0.000 0.016
#> GSM1022350 3 0.1914 0.7722 0.056 0.000 0.920 0.008 0.000 0.016
#> GSM1022344 3 0.7031 0.2807 0.316 0.000 0.444 0.076 0.012 0.152
#> GSM1022345 3 0.7031 0.2807 0.316 0.000 0.444 0.076 0.012 0.152
#> GSM1022346 3 0.7031 0.2807 0.316 0.000 0.444 0.076 0.012 0.152
#> GSM1022355 1 0.0622 0.7281 0.980 0.000 0.000 0.008 0.012 0.000
#> GSM1022356 1 0.0622 0.7281 0.980 0.000 0.000 0.008 0.012 0.000
#> GSM1022357 1 0.0622 0.7281 0.980 0.000 0.000 0.008 0.012 0.000
#> GSM1022358 1 0.0622 0.7281 0.980 0.000 0.000 0.008 0.012 0.000
#> GSM1022351 1 0.1700 0.7154 0.928 0.000 0.000 0.024 0.000 0.048
#> GSM1022352 1 0.1700 0.7154 0.928 0.000 0.000 0.024 0.000 0.048
#> GSM1022353 1 0.1700 0.7154 0.928 0.000 0.000 0.024 0.000 0.048
#> GSM1022354 1 0.1700 0.7154 0.928 0.000 0.000 0.024 0.000 0.048
#> GSM1022359 2 0.2556 0.8405 0.000 0.864 0.008 0.008 0.000 0.120
#> GSM1022360 2 0.2556 0.8405 0.000 0.864 0.008 0.008 0.000 0.120
#> GSM1022361 2 0.2556 0.8405 0.000 0.864 0.008 0.008 0.000 0.120
#> GSM1022362 2 0.2556 0.8405 0.000 0.864 0.008 0.008 0.000 0.120
#> GSM1022367 6 0.6688 1.0000 0.000 0.172 0.028 0.016 0.348 0.436
#> GSM1022368 6 0.6688 1.0000 0.000 0.172 0.028 0.016 0.348 0.436
#> GSM1022369 6 0.6688 1.0000 0.000 0.172 0.028 0.016 0.348 0.436
#> GSM1022370 6 0.6688 1.0000 0.000 0.172 0.028 0.016 0.348 0.436
#> GSM1022363 2 0.4639 0.6319 0.000 0.644 0.000 0.016 0.036 0.304
#> GSM1022364 2 0.4639 0.6319 0.000 0.644 0.000 0.016 0.036 0.304
#> GSM1022365 2 0.4639 0.6319 0.000 0.644 0.000 0.016 0.036 0.304
#> GSM1022366 2 0.4639 0.6319 0.000 0.644 0.000 0.016 0.036 0.304
#> GSM1022374 5 0.3525 0.8908 0.052 0.076 0.000 0.004 0.836 0.032
#> GSM1022375 5 0.3525 0.8908 0.052 0.076 0.000 0.004 0.836 0.032
#> GSM1022376 5 0.3525 0.8908 0.052 0.076 0.000 0.004 0.836 0.032
#> GSM1022371 2 0.2149 0.8502 0.000 0.900 0.000 0.004 0.016 0.080
#> GSM1022372 2 0.2149 0.8502 0.000 0.900 0.000 0.004 0.016 0.080
#> GSM1022373 2 0.2149 0.8502 0.000 0.900 0.000 0.004 0.016 0.080
#> GSM1022377 4 0.4319 0.9209 0.000 0.188 0.016 0.748 0.016 0.032
#> GSM1022378 4 0.4319 0.9209 0.000 0.188 0.016 0.748 0.016 0.032
#> GSM1022379 4 0.4299 0.9209 0.000 0.188 0.012 0.748 0.016 0.036
#> GSM1022380 4 0.4299 0.9209 0.000 0.188 0.012 0.748 0.016 0.036
#> GSM1022385 3 0.3510 0.7527 0.052 0.000 0.848 0.028 0.024 0.048
#> GSM1022386 3 0.3510 0.7527 0.052 0.000 0.848 0.028 0.024 0.048
#> GSM1022387 3 0.3510 0.7527 0.052 0.000 0.848 0.028 0.024 0.048
#> GSM1022388 3 0.3510 0.7527 0.052 0.000 0.848 0.028 0.024 0.048
#> GSM1022381 4 0.3262 0.9255 0.000 0.180 0.004 0.800 0.004 0.012
#> GSM1022382 4 0.3262 0.9255 0.000 0.180 0.004 0.800 0.004 0.012
#> GSM1022383 4 0.3262 0.9255 0.000 0.180 0.004 0.800 0.004 0.012
#> GSM1022384 4 0.3262 0.9255 0.000 0.180 0.004 0.800 0.004 0.012
#> GSM1022393 1 0.4973 0.6327 0.664 0.000 0.000 0.052 0.248 0.036
#> GSM1022394 1 0.4973 0.6327 0.664 0.000 0.000 0.052 0.248 0.036
#> GSM1022395 1 0.4973 0.6327 0.664 0.000 0.000 0.052 0.248 0.036
#> GSM1022396 1 0.4973 0.6327 0.664 0.000 0.000 0.052 0.248 0.036
#> GSM1022389 4 0.4929 0.8942 0.000 0.188 0.012 0.696 0.008 0.096
#> GSM1022390 4 0.5007 0.8901 0.004 0.180 0.012 0.700 0.008 0.096
#> GSM1022391 4 0.4929 0.8942 0.000 0.188 0.012 0.696 0.008 0.096
#> GSM1022392 4 0.5007 0.8901 0.004 0.180 0.012 0.700 0.008 0.096
#> GSM1022397 3 0.1204 0.7742 0.056 0.000 0.944 0.000 0.000 0.000
#> GSM1022398 3 0.1204 0.7742 0.056 0.000 0.944 0.000 0.000 0.000
#> GSM1022399 3 0.1204 0.7742 0.056 0.000 0.944 0.000 0.000 0.000
#> GSM1022400 3 0.1204 0.7742 0.056 0.000 0.944 0.000 0.000 0.000
#> GSM1022401 1 0.4973 0.6327 0.664 0.000 0.000 0.052 0.248 0.036
#> GSM1022402 1 0.4973 0.6327 0.664 0.000 0.000 0.052 0.248 0.036
#> GSM1022403 1 0.4973 0.6327 0.664 0.000 0.000 0.052 0.248 0.036
#> GSM1022404 1 0.4973 0.6327 0.664 0.000 0.000 0.052 0.248 0.036
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n protocol(p) cell.type(p) k
#> MAD:kmeans 80 1.22e-07 6.13e-05 2
#> MAD:kmeans 70 1.92e-12 5.88e-08 3
#> MAD:kmeans 70 9.95e-17 1.58e-08 4
#> MAD:kmeans 74 1.38e-18 3.80e-11 5
#> MAD:kmeans 74 8.86e-21 1.52e-10 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 31589 rows and 80 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.962 0.985 0.5059 0.495 0.495
#> 3 3 0.641 0.734 0.792 0.2831 0.830 0.669
#> 4 4 0.777 0.877 0.892 0.1293 0.853 0.621
#> 5 5 0.874 0.866 0.911 0.0805 0.937 0.763
#> 6 6 0.881 0.858 0.907 0.0358 0.974 0.877
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
#> GSM1022325 2 0.000 0.970 0.0 1.0
#> GSM1022326 2 0.000 0.970 0.0 1.0
#> GSM1022327 2 0.000 0.970 0.0 1.0
#> GSM1022331 1 0.000 1.000 1.0 0.0
#> GSM1022332 1 0.000 1.000 1.0 0.0
#> GSM1022333 1 0.000 1.000 1.0 0.0
#> GSM1022328 2 0.000 0.970 0.0 1.0
#> GSM1022329 2 0.000 0.970 0.0 1.0
#> GSM1022330 2 0.000 0.970 0.0 1.0
#> GSM1022337 2 0.971 0.366 0.4 0.6
#> GSM1022338 2 0.971 0.366 0.4 0.6
#> GSM1022339 2 0.971 0.366 0.4 0.6
#> GSM1022334 2 0.000 0.970 0.0 1.0
#> GSM1022335 2 0.000 0.970 0.0 1.0
#> GSM1022336 2 0.000 0.970 0.0 1.0
#> GSM1022340 1 0.000 1.000 1.0 0.0
#> GSM1022341 1 0.000 1.000 1.0 0.0
#> GSM1022342 1 0.000 1.000 1.0 0.0
#> GSM1022343 1 0.000 1.000 1.0 0.0
#> GSM1022347 1 0.000 1.000 1.0 0.0
#> GSM1022348 1 0.000 1.000 1.0 0.0
#> GSM1022349 1 0.000 1.000 1.0 0.0
#> GSM1022350 1 0.000 1.000 1.0 0.0
#> GSM1022344 1 0.000 1.000 1.0 0.0
#> GSM1022345 1 0.000 1.000 1.0 0.0
#> GSM1022346 1 0.000 1.000 1.0 0.0
#> GSM1022355 1 0.000 1.000 1.0 0.0
#> GSM1022356 1 0.000 1.000 1.0 0.0
#> GSM1022357 1 0.000 1.000 1.0 0.0
#> GSM1022358 1 0.000 1.000 1.0 0.0
#> GSM1022351 1 0.000 1.000 1.0 0.0
#> GSM1022352 1 0.000 1.000 1.0 0.0
#> GSM1022353 1 0.000 1.000 1.0 0.0
#> GSM1022354 1 0.000 1.000 1.0 0.0
#> GSM1022359 2 0.000 0.970 0.0 1.0
#> GSM1022360 2 0.000 0.970 0.0 1.0
#> GSM1022361 2 0.000 0.970 0.0 1.0
#> GSM1022362 2 0.000 0.970 0.0 1.0
#> GSM1022367 2 0.000 0.970 0.0 1.0
#> GSM1022368 2 0.000 0.970 0.0 1.0
#> GSM1022369 2 0.000 0.970 0.0 1.0
#> GSM1022370 2 0.000 0.970 0.0 1.0
#> GSM1022363 2 0.000 0.970 0.0 1.0
#> GSM1022364 2 0.000 0.970 0.0 1.0
#> GSM1022365 2 0.000 0.970 0.0 1.0
#> GSM1022366 2 0.000 0.970 0.0 1.0
#> GSM1022374 2 0.000 0.970 0.0 1.0
#> GSM1022375 2 0.000 0.970 0.0 1.0
#> GSM1022376 2 0.000 0.970 0.0 1.0
#> GSM1022371 2 0.000 0.970 0.0 1.0
#> GSM1022372 2 0.000 0.970 0.0 1.0
#> GSM1022373 2 0.000 0.970 0.0 1.0
#> GSM1022377 2 0.000 0.970 0.0 1.0
#> GSM1022378 2 0.000 0.970 0.0 1.0
#> GSM1022379 2 0.000 0.970 0.0 1.0
#> GSM1022380 2 0.000 0.970 0.0 1.0
#> GSM1022385 1 0.000 1.000 1.0 0.0
#> GSM1022386 1 0.000 1.000 1.0 0.0
#> GSM1022387 1 0.000 1.000 1.0 0.0
#> GSM1022388 1 0.000 1.000 1.0 0.0
#> GSM1022381 2 0.000 0.970 0.0 1.0
#> GSM1022382 2 0.000 0.970 0.0 1.0
#> GSM1022383 2 0.000 0.970 0.0 1.0
#> GSM1022384 2 0.000 0.970 0.0 1.0
#> GSM1022393 1 0.000 1.000 1.0 0.0
#> GSM1022394 1 0.000 1.000 1.0 0.0
#> GSM1022395 1 0.000 1.000 1.0 0.0
#> GSM1022396 1 0.000 1.000 1.0 0.0
#> GSM1022389 2 0.000 0.970 0.0 1.0
#> GSM1022390 2 0.000 0.970 0.0 1.0
#> GSM1022391 2 0.000 0.970 0.0 1.0
#> GSM1022392 2 0.000 0.970 0.0 1.0
#> GSM1022397 1 0.000 1.000 1.0 0.0
#> GSM1022398 1 0.000 1.000 1.0 0.0
#> GSM1022399 1 0.000 1.000 1.0 0.0
#> GSM1022400 1 0.000 1.000 1.0 0.0
#> GSM1022401 1 0.000 1.000 1.0 0.0
#> GSM1022402 1 0.000 1.000 1.0 0.0
#> GSM1022403 1 0.000 1.000 1.0 0.0
#> GSM1022404 1 0.000 1.000 1.0 0.0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1022325 2 0.0000 0.7917 0.000 1.000 0.000
#> GSM1022326 2 0.0000 0.7917 0.000 1.000 0.000
#> GSM1022327 2 0.0000 0.7917 0.000 1.000 0.000
#> GSM1022331 3 0.5881 0.5894 0.016 0.256 0.728
#> GSM1022332 3 0.5881 0.5894 0.016 0.256 0.728
#> GSM1022333 3 0.5881 0.5894 0.016 0.256 0.728
#> GSM1022328 2 0.0000 0.7917 0.000 1.000 0.000
#> GSM1022329 2 0.0000 0.7917 0.000 1.000 0.000
#> GSM1022330 2 0.0000 0.7917 0.000 1.000 0.000
#> GSM1022337 1 0.5859 0.4307 0.656 0.344 0.000
#> GSM1022338 1 0.5859 0.4307 0.656 0.344 0.000
#> GSM1022339 1 0.5859 0.4307 0.656 0.344 0.000
#> GSM1022334 2 0.0000 0.7917 0.000 1.000 0.000
#> GSM1022335 2 0.0000 0.7917 0.000 1.000 0.000
#> GSM1022336 2 0.0000 0.7917 0.000 1.000 0.000
#> GSM1022340 1 0.6244 0.7418 0.560 0.000 0.440
#> GSM1022341 1 0.6244 0.7418 0.560 0.000 0.440
#> GSM1022342 1 0.6244 0.7418 0.560 0.000 0.440
#> GSM1022343 1 0.6244 0.7418 0.560 0.000 0.440
#> GSM1022347 3 0.0000 0.9106 0.000 0.000 1.000
#> GSM1022348 3 0.0000 0.9106 0.000 0.000 1.000
#> GSM1022349 3 0.0000 0.9106 0.000 0.000 1.000
#> GSM1022350 3 0.0000 0.9106 0.000 0.000 1.000
#> GSM1022344 3 0.0000 0.9106 0.000 0.000 1.000
#> GSM1022345 3 0.0000 0.9106 0.000 0.000 1.000
#> GSM1022346 3 0.0000 0.9106 0.000 0.000 1.000
#> GSM1022355 1 0.5650 0.8825 0.688 0.000 0.312
#> GSM1022356 1 0.5650 0.8825 0.688 0.000 0.312
#> GSM1022357 1 0.5650 0.8825 0.688 0.000 0.312
#> GSM1022358 1 0.5650 0.8825 0.688 0.000 0.312
#> GSM1022351 1 0.5650 0.8825 0.688 0.000 0.312
#> GSM1022352 1 0.5650 0.8825 0.688 0.000 0.312
#> GSM1022353 1 0.5650 0.8825 0.688 0.000 0.312
#> GSM1022354 1 0.5650 0.8825 0.688 0.000 0.312
#> GSM1022359 2 0.0000 0.7917 0.000 1.000 0.000
#> GSM1022360 2 0.0000 0.7917 0.000 1.000 0.000
#> GSM1022361 2 0.0000 0.7917 0.000 1.000 0.000
#> GSM1022362 2 0.0000 0.7917 0.000 1.000 0.000
#> GSM1022367 2 0.6931 0.0672 0.016 0.528 0.456
#> GSM1022368 2 0.6931 0.0672 0.016 0.528 0.456
#> GSM1022369 2 0.6931 0.0672 0.016 0.528 0.456
#> GSM1022370 2 0.6931 0.0672 0.016 0.528 0.456
#> GSM1022363 2 0.0424 0.7885 0.008 0.992 0.000
#> GSM1022364 2 0.0424 0.7885 0.008 0.992 0.000
#> GSM1022365 2 0.0424 0.7885 0.008 0.992 0.000
#> GSM1022366 2 0.0424 0.7885 0.008 0.992 0.000
#> GSM1022374 2 0.6154 0.2316 0.408 0.592 0.000
#> GSM1022375 2 0.6154 0.2316 0.408 0.592 0.000
#> GSM1022376 2 0.6154 0.2316 0.408 0.592 0.000
#> GSM1022371 2 0.0000 0.7917 0.000 1.000 0.000
#> GSM1022372 2 0.0000 0.7917 0.000 1.000 0.000
#> GSM1022373 2 0.0000 0.7917 0.000 1.000 0.000
#> GSM1022377 2 0.5859 0.6832 0.344 0.656 0.000
#> GSM1022378 2 0.5859 0.6832 0.344 0.656 0.000
#> GSM1022379 2 0.5859 0.6832 0.344 0.656 0.000
#> GSM1022380 2 0.5859 0.6832 0.344 0.656 0.000
#> GSM1022385 3 0.0000 0.9106 0.000 0.000 1.000
#> GSM1022386 3 0.0000 0.9106 0.000 0.000 1.000
#> GSM1022387 3 0.0000 0.9106 0.000 0.000 1.000
#> GSM1022388 3 0.0000 0.9106 0.000 0.000 1.000
#> GSM1022381 2 0.5859 0.6832 0.344 0.656 0.000
#> GSM1022382 2 0.5859 0.6832 0.344 0.656 0.000
#> GSM1022383 2 0.5859 0.6832 0.344 0.656 0.000
#> GSM1022384 2 0.5859 0.6832 0.344 0.656 0.000
#> GSM1022393 1 0.5650 0.8825 0.688 0.000 0.312
#> GSM1022394 1 0.5650 0.8825 0.688 0.000 0.312
#> GSM1022395 1 0.5650 0.8825 0.688 0.000 0.312
#> GSM1022396 1 0.5650 0.8825 0.688 0.000 0.312
#> GSM1022389 2 0.5859 0.6832 0.344 0.656 0.000
#> GSM1022390 2 0.6095 0.6428 0.392 0.608 0.000
#> GSM1022391 2 0.5859 0.6832 0.344 0.656 0.000
#> GSM1022392 2 0.6095 0.6428 0.392 0.608 0.000
#> GSM1022397 3 0.0000 0.9106 0.000 0.000 1.000
#> GSM1022398 3 0.0000 0.9106 0.000 0.000 1.000
#> GSM1022399 3 0.0000 0.9106 0.000 0.000 1.000
#> GSM1022400 3 0.0000 0.9106 0.000 0.000 1.000
#> GSM1022401 1 0.5650 0.8825 0.688 0.000 0.312
#> GSM1022402 1 0.5650 0.8825 0.688 0.000 0.312
#> GSM1022403 1 0.5650 0.8825 0.688 0.000 0.312
#> GSM1022404 1 0.5650 0.8825 0.688 0.000 0.312
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1022325 2 0.4222 0.839 0.000 0.728 0.000 0.272
#> GSM1022326 2 0.4222 0.839 0.000 0.728 0.000 0.272
#> GSM1022327 2 0.4222 0.839 0.000 0.728 0.000 0.272
#> GSM1022331 3 0.0592 0.955 0.000 0.016 0.984 0.000
#> GSM1022332 3 0.0592 0.955 0.000 0.016 0.984 0.000
#> GSM1022333 3 0.0592 0.955 0.000 0.016 0.984 0.000
#> GSM1022328 2 0.4222 0.839 0.000 0.728 0.000 0.272
#> GSM1022329 2 0.4222 0.839 0.000 0.728 0.000 0.272
#> GSM1022330 2 0.4222 0.839 0.000 0.728 0.000 0.272
#> GSM1022337 2 0.3945 0.462 0.216 0.780 0.004 0.000
#> GSM1022338 2 0.3945 0.462 0.216 0.780 0.004 0.000
#> GSM1022339 2 0.3945 0.462 0.216 0.780 0.004 0.000
#> GSM1022334 2 0.4222 0.839 0.000 0.728 0.000 0.272
#> GSM1022335 2 0.4222 0.839 0.000 0.728 0.000 0.272
#> GSM1022336 2 0.4222 0.839 0.000 0.728 0.000 0.272
#> GSM1022340 1 0.1557 0.895 0.944 0.000 0.056 0.000
#> GSM1022341 1 0.1557 0.895 0.944 0.000 0.056 0.000
#> GSM1022342 1 0.1557 0.895 0.944 0.000 0.056 0.000
#> GSM1022343 1 0.1557 0.895 0.944 0.000 0.056 0.000
#> GSM1022347 3 0.0188 0.967 0.004 0.000 0.996 0.000
#> GSM1022348 3 0.0188 0.967 0.004 0.000 0.996 0.000
#> GSM1022349 3 0.0188 0.967 0.004 0.000 0.996 0.000
#> GSM1022350 3 0.0188 0.967 0.004 0.000 0.996 0.000
#> GSM1022344 3 0.3219 0.837 0.164 0.000 0.836 0.000
#> GSM1022345 3 0.3219 0.837 0.164 0.000 0.836 0.000
#> GSM1022346 3 0.3219 0.837 0.164 0.000 0.836 0.000
#> GSM1022355 1 0.0000 0.923 1.000 0.000 0.000 0.000
#> GSM1022356 1 0.0000 0.923 1.000 0.000 0.000 0.000
#> GSM1022357 1 0.0000 0.923 1.000 0.000 0.000 0.000
#> GSM1022358 1 0.0000 0.923 1.000 0.000 0.000 0.000
#> GSM1022351 1 0.0000 0.923 1.000 0.000 0.000 0.000
#> GSM1022352 1 0.0000 0.923 1.000 0.000 0.000 0.000
#> GSM1022353 1 0.0000 0.923 1.000 0.000 0.000 0.000
#> GSM1022354 1 0.0000 0.923 1.000 0.000 0.000 0.000
#> GSM1022359 2 0.4222 0.839 0.000 0.728 0.000 0.272
#> GSM1022360 2 0.4222 0.839 0.000 0.728 0.000 0.272
#> GSM1022361 2 0.4222 0.839 0.000 0.728 0.000 0.272
#> GSM1022362 2 0.4222 0.839 0.000 0.728 0.000 0.272
#> GSM1022367 2 0.3219 0.698 0.000 0.836 0.164 0.000
#> GSM1022368 2 0.3219 0.698 0.000 0.836 0.164 0.000
#> GSM1022369 2 0.3219 0.698 0.000 0.836 0.164 0.000
#> GSM1022370 2 0.3219 0.698 0.000 0.836 0.164 0.000
#> GSM1022363 2 0.3907 0.832 0.000 0.768 0.000 0.232
#> GSM1022364 2 0.3907 0.832 0.000 0.768 0.000 0.232
#> GSM1022365 2 0.3907 0.832 0.000 0.768 0.000 0.232
#> GSM1022366 2 0.3907 0.832 0.000 0.768 0.000 0.232
#> GSM1022374 2 0.0524 0.704 0.008 0.988 0.004 0.000
#> GSM1022375 2 0.0524 0.704 0.008 0.988 0.004 0.000
#> GSM1022376 2 0.0524 0.704 0.008 0.988 0.004 0.000
#> GSM1022371 2 0.4222 0.839 0.000 0.728 0.000 0.272
#> GSM1022372 2 0.4222 0.839 0.000 0.728 0.000 0.272
#> GSM1022373 2 0.4222 0.839 0.000 0.728 0.000 0.272
#> GSM1022377 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM1022378 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM1022379 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM1022380 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM1022385 3 0.0188 0.967 0.004 0.000 0.996 0.000
#> GSM1022386 3 0.0188 0.967 0.004 0.000 0.996 0.000
#> GSM1022387 3 0.0188 0.967 0.004 0.000 0.996 0.000
#> GSM1022388 3 0.0188 0.967 0.004 0.000 0.996 0.000
#> GSM1022381 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM1022382 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM1022383 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM1022384 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM1022393 1 0.3123 0.897 0.844 0.156 0.000 0.000
#> GSM1022394 1 0.3123 0.897 0.844 0.156 0.000 0.000
#> GSM1022395 1 0.3123 0.897 0.844 0.156 0.000 0.000
#> GSM1022396 1 0.3123 0.897 0.844 0.156 0.000 0.000
#> GSM1022389 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM1022390 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM1022391 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM1022392 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM1022397 3 0.0188 0.967 0.004 0.000 0.996 0.000
#> GSM1022398 3 0.0188 0.967 0.004 0.000 0.996 0.000
#> GSM1022399 3 0.0188 0.967 0.004 0.000 0.996 0.000
#> GSM1022400 3 0.0188 0.967 0.004 0.000 0.996 0.000
#> GSM1022401 1 0.3123 0.897 0.844 0.156 0.000 0.000
#> GSM1022402 1 0.3123 0.897 0.844 0.156 0.000 0.000
#> GSM1022403 1 0.3123 0.897 0.844 0.156 0.000 0.000
#> GSM1022404 1 0.3123 0.897 0.844 0.156 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1022325 2 0.1197 0.986 0.000 0.952 0.000 0.048 0.000
#> GSM1022326 2 0.1197 0.986 0.000 0.952 0.000 0.048 0.000
#> GSM1022327 2 0.1197 0.986 0.000 0.952 0.000 0.048 0.000
#> GSM1022331 3 0.3934 0.642 0.000 0.000 0.740 0.016 0.244
#> GSM1022332 3 0.3934 0.642 0.000 0.000 0.740 0.016 0.244
#> GSM1022333 3 0.3934 0.642 0.000 0.000 0.740 0.016 0.244
#> GSM1022328 2 0.1197 0.986 0.000 0.952 0.000 0.048 0.000
#> GSM1022329 2 0.1197 0.986 0.000 0.952 0.000 0.048 0.000
#> GSM1022330 2 0.1197 0.986 0.000 0.952 0.000 0.048 0.000
#> GSM1022337 5 0.0566 0.757 0.004 0.012 0.000 0.000 0.984
#> GSM1022338 5 0.0566 0.757 0.004 0.012 0.000 0.000 0.984
#> GSM1022339 5 0.0566 0.757 0.004 0.012 0.000 0.000 0.984
#> GSM1022334 2 0.1197 0.986 0.000 0.952 0.000 0.048 0.000
#> GSM1022335 2 0.1197 0.986 0.000 0.952 0.000 0.048 0.000
#> GSM1022336 2 0.1197 0.986 0.000 0.952 0.000 0.048 0.000
#> GSM1022340 1 0.2763 0.752 0.848 0.000 0.148 0.004 0.000
#> GSM1022341 1 0.2763 0.752 0.848 0.000 0.148 0.004 0.000
#> GSM1022342 1 0.2763 0.752 0.848 0.000 0.148 0.004 0.000
#> GSM1022343 1 0.2763 0.752 0.848 0.000 0.148 0.004 0.000
#> GSM1022347 3 0.0000 0.898 0.000 0.000 1.000 0.000 0.000
#> GSM1022348 3 0.0000 0.898 0.000 0.000 1.000 0.000 0.000
#> GSM1022349 3 0.0000 0.898 0.000 0.000 1.000 0.000 0.000
#> GSM1022350 3 0.0000 0.898 0.000 0.000 1.000 0.000 0.000
#> GSM1022344 3 0.3550 0.711 0.236 0.000 0.760 0.004 0.000
#> GSM1022345 3 0.3550 0.711 0.236 0.000 0.760 0.004 0.000
#> GSM1022346 3 0.3550 0.711 0.236 0.000 0.760 0.004 0.000
#> GSM1022355 1 0.0290 0.842 0.992 0.000 0.000 0.000 0.008
#> GSM1022356 1 0.0290 0.842 0.992 0.000 0.000 0.000 0.008
#> GSM1022357 1 0.0290 0.842 0.992 0.000 0.000 0.000 0.008
#> GSM1022358 1 0.0290 0.842 0.992 0.000 0.000 0.000 0.008
#> GSM1022351 1 0.0162 0.840 0.996 0.000 0.000 0.004 0.000
#> GSM1022352 1 0.0162 0.840 0.996 0.000 0.000 0.004 0.000
#> GSM1022353 1 0.0162 0.840 0.996 0.000 0.000 0.004 0.000
#> GSM1022354 1 0.0162 0.840 0.996 0.000 0.000 0.004 0.000
#> GSM1022359 2 0.1197 0.986 0.000 0.952 0.000 0.048 0.000
#> GSM1022360 2 0.1197 0.986 0.000 0.952 0.000 0.048 0.000
#> GSM1022361 2 0.1197 0.986 0.000 0.952 0.000 0.048 0.000
#> GSM1022362 2 0.1197 0.986 0.000 0.952 0.000 0.048 0.000
#> GSM1022367 5 0.5764 0.575 0.000 0.388 0.056 0.016 0.540
#> GSM1022368 5 0.5764 0.575 0.000 0.388 0.056 0.016 0.540
#> GSM1022369 5 0.5764 0.575 0.000 0.388 0.056 0.016 0.540
#> GSM1022370 5 0.5764 0.575 0.000 0.388 0.056 0.016 0.540
#> GSM1022363 2 0.0000 0.943 0.000 1.000 0.000 0.000 0.000
#> GSM1022364 2 0.0000 0.943 0.000 1.000 0.000 0.000 0.000
#> GSM1022365 2 0.0000 0.943 0.000 1.000 0.000 0.000 0.000
#> GSM1022366 2 0.0000 0.943 0.000 1.000 0.000 0.000 0.000
#> GSM1022374 5 0.0794 0.767 0.000 0.028 0.000 0.000 0.972
#> GSM1022375 5 0.0794 0.767 0.000 0.028 0.000 0.000 0.972
#> GSM1022376 5 0.0794 0.767 0.000 0.028 0.000 0.000 0.972
#> GSM1022371 2 0.1197 0.986 0.000 0.952 0.000 0.048 0.000
#> GSM1022372 2 0.1197 0.986 0.000 0.952 0.000 0.048 0.000
#> GSM1022373 2 0.1197 0.986 0.000 0.952 0.000 0.048 0.000
#> GSM1022377 4 0.0609 0.999 0.000 0.020 0.000 0.980 0.000
#> GSM1022378 4 0.0609 0.999 0.000 0.020 0.000 0.980 0.000
#> GSM1022379 4 0.0609 0.999 0.000 0.020 0.000 0.980 0.000
#> GSM1022380 4 0.0609 0.999 0.000 0.020 0.000 0.980 0.000
#> GSM1022385 3 0.0000 0.898 0.000 0.000 1.000 0.000 0.000
#> GSM1022386 3 0.0000 0.898 0.000 0.000 1.000 0.000 0.000
#> GSM1022387 3 0.0000 0.898 0.000 0.000 1.000 0.000 0.000
#> GSM1022388 3 0.0000 0.898 0.000 0.000 1.000 0.000 0.000
#> GSM1022381 4 0.0609 0.999 0.000 0.020 0.000 0.980 0.000
#> GSM1022382 4 0.0609 0.999 0.000 0.020 0.000 0.980 0.000
#> GSM1022383 4 0.0609 0.999 0.000 0.020 0.000 0.980 0.000
#> GSM1022384 4 0.0609 0.999 0.000 0.020 0.000 0.980 0.000
#> GSM1022393 1 0.3452 0.785 0.756 0.000 0.000 0.000 0.244
#> GSM1022394 1 0.3452 0.785 0.756 0.000 0.000 0.000 0.244
#> GSM1022395 1 0.3452 0.785 0.756 0.000 0.000 0.000 0.244
#> GSM1022396 1 0.3452 0.785 0.756 0.000 0.000 0.000 0.244
#> GSM1022389 4 0.0771 0.998 0.000 0.020 0.000 0.976 0.004
#> GSM1022390 4 0.0771 0.998 0.000 0.020 0.000 0.976 0.004
#> GSM1022391 4 0.0771 0.998 0.000 0.020 0.000 0.976 0.004
#> GSM1022392 4 0.0771 0.998 0.000 0.020 0.000 0.976 0.004
#> GSM1022397 3 0.0000 0.898 0.000 0.000 1.000 0.000 0.000
#> GSM1022398 3 0.0000 0.898 0.000 0.000 1.000 0.000 0.000
#> GSM1022399 3 0.0000 0.898 0.000 0.000 1.000 0.000 0.000
#> GSM1022400 3 0.0000 0.898 0.000 0.000 1.000 0.000 0.000
#> GSM1022401 1 0.3452 0.785 0.756 0.000 0.000 0.000 0.244
#> GSM1022402 1 0.3452 0.785 0.756 0.000 0.000 0.000 0.244
#> GSM1022403 1 0.3452 0.785 0.756 0.000 0.000 0.000 0.244
#> GSM1022404 1 0.3452 0.785 0.756 0.000 0.000 0.000 0.244
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1022325 2 0.0000 0.973 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022326 2 0.0000 0.973 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022327 2 0.0000 0.973 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022331 6 0.3446 0.712 0.000 0.000 0.308 0.000 0.000 0.692
#> GSM1022332 6 0.3446 0.712 0.000 0.000 0.308 0.000 0.000 0.692
#> GSM1022333 6 0.3446 0.712 0.000 0.000 0.308 0.000 0.000 0.692
#> GSM1022328 2 0.0000 0.973 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022329 2 0.0000 0.973 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022330 2 0.0000 0.973 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022337 5 0.0260 0.989 0.000 0.000 0.000 0.000 0.992 0.008
#> GSM1022338 5 0.0260 0.989 0.000 0.000 0.000 0.000 0.992 0.008
#> GSM1022339 5 0.0260 0.989 0.000 0.000 0.000 0.000 0.992 0.008
#> GSM1022334 2 0.0000 0.973 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022335 2 0.0000 0.973 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022336 2 0.0000 0.973 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022340 1 0.5100 0.554 0.644 0.000 0.200 0.004 0.000 0.152
#> GSM1022341 1 0.5100 0.554 0.644 0.000 0.200 0.004 0.000 0.152
#> GSM1022342 1 0.5100 0.554 0.644 0.000 0.200 0.004 0.000 0.152
#> GSM1022343 1 0.5100 0.554 0.644 0.000 0.200 0.004 0.000 0.152
#> GSM1022347 3 0.0000 0.921 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022348 3 0.0000 0.921 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022349 3 0.0000 0.921 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022350 3 0.0000 0.921 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022344 3 0.4446 0.674 0.120 0.000 0.724 0.004 0.000 0.152
#> GSM1022345 3 0.4486 0.670 0.124 0.000 0.720 0.004 0.000 0.152
#> GSM1022346 3 0.4486 0.670 0.124 0.000 0.720 0.004 0.000 0.152
#> GSM1022355 1 0.0363 0.745 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM1022356 1 0.0363 0.745 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM1022357 1 0.0363 0.745 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM1022358 1 0.0363 0.745 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM1022351 1 0.2278 0.720 0.868 0.000 0.000 0.004 0.000 0.128
#> GSM1022352 1 0.2278 0.720 0.868 0.000 0.000 0.004 0.000 0.128
#> GSM1022353 1 0.2278 0.720 0.868 0.000 0.000 0.004 0.000 0.128
#> GSM1022354 1 0.2278 0.720 0.868 0.000 0.000 0.004 0.000 0.128
#> GSM1022359 2 0.0000 0.973 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022360 2 0.0000 0.973 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022361 2 0.0000 0.973 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022362 2 0.0000 0.973 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022367 6 0.3556 0.777 0.000 0.068 0.012 0.000 0.104 0.816
#> GSM1022368 6 0.3556 0.777 0.000 0.068 0.012 0.000 0.104 0.816
#> GSM1022369 6 0.3556 0.777 0.000 0.068 0.012 0.000 0.104 0.816
#> GSM1022370 6 0.3556 0.777 0.000 0.068 0.012 0.000 0.104 0.816
#> GSM1022363 2 0.2092 0.882 0.000 0.876 0.000 0.000 0.000 0.124
#> GSM1022364 2 0.2092 0.882 0.000 0.876 0.000 0.000 0.000 0.124
#> GSM1022365 2 0.2092 0.882 0.000 0.876 0.000 0.000 0.000 0.124
#> GSM1022366 2 0.2092 0.882 0.000 0.876 0.000 0.000 0.000 0.124
#> GSM1022374 5 0.0603 0.989 0.000 0.004 0.000 0.000 0.980 0.016
#> GSM1022375 5 0.0603 0.989 0.000 0.004 0.000 0.000 0.980 0.016
#> GSM1022376 5 0.0603 0.989 0.000 0.004 0.000 0.000 0.980 0.016
#> GSM1022371 2 0.0000 0.973 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022372 2 0.0000 0.973 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022373 2 0.0000 0.973 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022377 4 0.0260 0.989 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM1022378 4 0.0260 0.989 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM1022379 4 0.0260 0.989 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM1022380 4 0.0260 0.989 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM1022385 3 0.0000 0.921 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022386 3 0.0000 0.921 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022387 3 0.0000 0.921 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022388 3 0.0000 0.921 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022381 4 0.0260 0.989 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM1022382 4 0.0260 0.989 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM1022383 4 0.0260 0.989 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM1022384 4 0.0260 0.989 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM1022393 1 0.3290 0.675 0.744 0.000 0.000 0.000 0.252 0.004
#> GSM1022394 1 0.3290 0.675 0.744 0.000 0.000 0.000 0.252 0.004
#> GSM1022395 1 0.3290 0.675 0.744 0.000 0.000 0.000 0.252 0.004
#> GSM1022396 1 0.3290 0.675 0.744 0.000 0.000 0.000 0.252 0.004
#> GSM1022389 4 0.0972 0.978 0.000 0.008 0.000 0.964 0.000 0.028
#> GSM1022390 4 0.0972 0.978 0.000 0.008 0.000 0.964 0.000 0.028
#> GSM1022391 4 0.0972 0.978 0.000 0.008 0.000 0.964 0.000 0.028
#> GSM1022392 4 0.0972 0.978 0.000 0.008 0.000 0.964 0.000 0.028
#> GSM1022397 3 0.0000 0.921 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022398 3 0.0000 0.921 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022399 3 0.0000 0.921 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022400 3 0.0000 0.921 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022401 1 0.3290 0.675 0.744 0.000 0.000 0.000 0.252 0.004
#> GSM1022402 1 0.3290 0.675 0.744 0.000 0.000 0.000 0.252 0.004
#> GSM1022403 1 0.3290 0.675 0.744 0.000 0.000 0.000 0.252 0.004
#> GSM1022404 1 0.3290 0.675 0.744 0.000 0.000 0.000 0.252 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 protocol(p) cell.type(p) k
#> MAD:skmeans 77 4.05e-07 8.12e-06 2
#> MAD:skmeans 70 7.45e-12 3.09e-09 3
#> MAD:skmeans 77 1.00e-19 7.99e-06 4
#> MAD:skmeans 80 7.64e-20 2.66e-10 5
#> MAD:skmeans 80 2.76e-23 8.50e-10 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 31589 rows and 80 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.898 0.964 0.981 0.5044 0.495 0.495
#> 3 3 0.906 0.941 0.975 0.2784 0.796 0.612
#> 4 4 0.955 0.945 0.977 0.1449 0.894 0.705
#> 5 5 1.000 1.000 1.000 0.0786 0.930 0.738
#> 6 6 1.000 0.961 0.980 0.0347 0.952 0.774
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] 3 4 5
There is also optional best \(k\) = 3 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
#> GSM1022325 2 0.000 0.962 0.000 1.000
#> GSM1022326 2 0.000 0.962 0.000 1.000
#> GSM1022327 2 0.000 0.962 0.000 1.000
#> GSM1022331 1 0.000 1.000 1.000 0.000
#> GSM1022332 1 0.000 1.000 1.000 0.000
#> GSM1022333 1 0.000 1.000 1.000 0.000
#> GSM1022328 2 0.000 0.962 0.000 1.000
#> GSM1022329 2 0.000 0.962 0.000 1.000
#> GSM1022330 2 0.000 0.962 0.000 1.000
#> GSM1022337 2 0.730 0.784 0.204 0.796
#> GSM1022338 2 0.730 0.784 0.204 0.796
#> GSM1022339 2 0.730 0.784 0.204 0.796
#> GSM1022334 2 0.000 0.962 0.000 1.000
#> GSM1022335 2 0.000 0.962 0.000 1.000
#> GSM1022336 2 0.000 0.962 0.000 1.000
#> GSM1022340 1 0.000 1.000 1.000 0.000
#> GSM1022341 1 0.000 1.000 1.000 0.000
#> GSM1022342 1 0.000 1.000 1.000 0.000
#> GSM1022343 1 0.000 1.000 1.000 0.000
#> GSM1022347 1 0.000 1.000 1.000 0.000
#> GSM1022348 1 0.000 1.000 1.000 0.000
#> GSM1022349 1 0.000 1.000 1.000 0.000
#> GSM1022350 1 0.000 1.000 1.000 0.000
#> GSM1022344 1 0.000 1.000 1.000 0.000
#> GSM1022345 1 0.000 1.000 1.000 0.000
#> GSM1022346 1 0.000 1.000 1.000 0.000
#> GSM1022355 1 0.000 1.000 1.000 0.000
#> GSM1022356 1 0.000 1.000 1.000 0.000
#> GSM1022357 1 0.000 1.000 1.000 0.000
#> GSM1022358 1 0.000 1.000 1.000 0.000
#> GSM1022351 1 0.000 1.000 1.000 0.000
#> GSM1022352 1 0.000 1.000 1.000 0.000
#> GSM1022353 1 0.000 1.000 1.000 0.000
#> GSM1022354 1 0.000 1.000 1.000 0.000
#> GSM1022359 2 0.000 0.962 0.000 1.000
#> GSM1022360 2 0.000 0.962 0.000 1.000
#> GSM1022361 2 0.000 0.962 0.000 1.000
#> GSM1022362 2 0.000 0.962 0.000 1.000
#> GSM1022367 2 0.000 0.962 0.000 1.000
#> GSM1022368 2 0.000 0.962 0.000 1.000
#> GSM1022369 2 0.000 0.962 0.000 1.000
#> GSM1022370 2 0.000 0.962 0.000 1.000
#> GSM1022363 2 0.000 0.962 0.000 1.000
#> GSM1022364 2 0.000 0.962 0.000 1.000
#> GSM1022365 2 0.000 0.962 0.000 1.000
#> GSM1022366 2 0.000 0.962 0.000 1.000
#> GSM1022374 2 0.714 0.793 0.196 0.804
#> GSM1022375 2 0.706 0.798 0.192 0.808
#> GSM1022376 2 0.722 0.788 0.200 0.800
#> GSM1022371 2 0.000 0.962 0.000 1.000
#> GSM1022372 2 0.000 0.962 0.000 1.000
#> GSM1022373 2 0.000 0.962 0.000 1.000
#> GSM1022377 2 0.000 0.962 0.000 1.000
#> GSM1022378 2 0.000 0.962 0.000 1.000
#> GSM1022379 2 0.000 0.962 0.000 1.000
#> GSM1022380 2 0.000 0.962 0.000 1.000
#> GSM1022385 1 0.000 1.000 1.000 0.000
#> GSM1022386 1 0.000 1.000 1.000 0.000
#> GSM1022387 1 0.000 1.000 1.000 0.000
#> GSM1022388 1 0.000 1.000 1.000 0.000
#> GSM1022381 2 0.000 0.962 0.000 1.000
#> GSM1022382 2 0.000 0.962 0.000 1.000
#> GSM1022383 2 0.000 0.962 0.000 1.000
#> GSM1022384 2 0.584 0.837 0.140 0.860
#> GSM1022393 1 0.000 1.000 1.000 0.000
#> GSM1022394 1 0.000 1.000 1.000 0.000
#> GSM1022395 1 0.000 1.000 1.000 0.000
#> GSM1022396 1 0.000 1.000 1.000 0.000
#> GSM1022389 2 0.000 0.962 0.000 1.000
#> GSM1022390 2 0.141 0.949 0.020 0.980
#> GSM1022391 2 0.000 0.962 0.000 1.000
#> GSM1022392 2 0.644 0.828 0.164 0.836
#> GSM1022397 1 0.000 1.000 1.000 0.000
#> GSM1022398 1 0.000 1.000 1.000 0.000
#> GSM1022399 1 0.000 1.000 1.000 0.000
#> GSM1022400 1 0.000 1.000 1.000 0.000
#> GSM1022401 1 0.000 1.000 1.000 0.000
#> GSM1022402 1 0.000 1.000 1.000 0.000
#> GSM1022403 1 0.000 1.000 1.000 0.000
#> GSM1022404 1 0.000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1022325 2 0.0000 0.973 0.000 1.000 0.000
#> GSM1022326 2 0.0000 0.973 0.000 1.000 0.000
#> GSM1022327 2 0.0000 0.973 0.000 1.000 0.000
#> GSM1022331 3 0.0000 1.000 0.000 0.000 1.000
#> GSM1022332 3 0.0000 1.000 0.000 0.000 1.000
#> GSM1022333 3 0.0000 1.000 0.000 0.000 1.000
#> GSM1022328 2 0.0000 0.973 0.000 1.000 0.000
#> GSM1022329 2 0.0000 0.973 0.000 1.000 0.000
#> GSM1022330 2 0.0000 0.973 0.000 1.000 0.000
#> GSM1022337 1 0.4974 0.694 0.764 0.236 0.000
#> GSM1022338 1 0.4974 0.694 0.764 0.236 0.000
#> GSM1022339 1 0.6126 0.346 0.600 0.400 0.000
#> GSM1022334 2 0.0000 0.973 0.000 1.000 0.000
#> GSM1022335 2 0.0000 0.973 0.000 1.000 0.000
#> GSM1022336 2 0.0000 0.973 0.000 1.000 0.000
#> GSM1022340 1 0.0000 0.945 1.000 0.000 0.000
#> GSM1022341 1 0.0000 0.945 1.000 0.000 0.000
#> GSM1022342 1 0.0000 0.945 1.000 0.000 0.000
#> GSM1022343 1 0.0000 0.945 1.000 0.000 0.000
#> GSM1022347 3 0.0000 1.000 0.000 0.000 1.000
#> GSM1022348 3 0.0000 1.000 0.000 0.000 1.000
#> GSM1022349 3 0.0000 1.000 0.000 0.000 1.000
#> GSM1022350 3 0.0000 1.000 0.000 0.000 1.000
#> GSM1022344 3 0.0000 1.000 0.000 0.000 1.000
#> GSM1022345 3 0.0000 1.000 0.000 0.000 1.000
#> GSM1022346 3 0.0000 1.000 0.000 0.000 1.000
#> GSM1022355 1 0.0000 0.945 1.000 0.000 0.000
#> GSM1022356 1 0.0000 0.945 1.000 0.000 0.000
#> GSM1022357 1 0.0000 0.945 1.000 0.000 0.000
#> GSM1022358 1 0.0000 0.945 1.000 0.000 0.000
#> GSM1022351 1 0.0000 0.945 1.000 0.000 0.000
#> GSM1022352 1 0.0000 0.945 1.000 0.000 0.000
#> GSM1022353 1 0.0000 0.945 1.000 0.000 0.000
#> GSM1022354 1 0.0000 0.945 1.000 0.000 0.000
#> GSM1022359 2 0.0000 0.973 0.000 1.000 0.000
#> GSM1022360 2 0.0000 0.973 0.000 1.000 0.000
#> GSM1022361 2 0.0000 0.973 0.000 1.000 0.000
#> GSM1022362 2 0.0000 0.973 0.000 1.000 0.000
#> GSM1022367 2 0.0000 0.973 0.000 1.000 0.000
#> GSM1022368 2 0.0237 0.970 0.000 0.996 0.004
#> GSM1022369 2 0.4452 0.770 0.000 0.808 0.192
#> GSM1022370 2 0.0237 0.970 0.000 0.996 0.004
#> GSM1022363 2 0.0000 0.973 0.000 1.000 0.000
#> GSM1022364 2 0.0000 0.973 0.000 1.000 0.000
#> GSM1022365 2 0.0000 0.973 0.000 1.000 0.000
#> GSM1022366 2 0.0000 0.973 0.000 1.000 0.000
#> GSM1022374 2 0.4504 0.759 0.196 0.804 0.000
#> GSM1022375 2 0.4452 0.764 0.192 0.808 0.000
#> GSM1022376 2 0.4555 0.753 0.200 0.800 0.000
#> GSM1022371 2 0.0000 0.973 0.000 1.000 0.000
#> GSM1022372 2 0.0000 0.973 0.000 1.000 0.000
#> GSM1022373 2 0.0000 0.973 0.000 1.000 0.000
#> GSM1022377 2 0.0000 0.973 0.000 1.000 0.000
#> GSM1022378 2 0.0000 0.973 0.000 1.000 0.000
#> GSM1022379 2 0.0000 0.973 0.000 1.000 0.000
#> GSM1022380 2 0.0000 0.973 0.000 1.000 0.000
#> GSM1022385 3 0.0000 1.000 0.000 0.000 1.000
#> GSM1022386 3 0.0000 1.000 0.000 0.000 1.000
#> GSM1022387 3 0.0000 1.000 0.000 0.000 1.000
#> GSM1022388 3 0.0000 1.000 0.000 0.000 1.000
#> GSM1022381 2 0.0000 0.973 0.000 1.000 0.000
#> GSM1022382 2 0.0000 0.973 0.000 1.000 0.000
#> GSM1022383 2 0.0000 0.973 0.000 1.000 0.000
#> GSM1022384 2 0.0000 0.973 0.000 1.000 0.000
#> GSM1022393 1 0.0000 0.945 1.000 0.000 0.000
#> GSM1022394 1 0.0000 0.945 1.000 0.000 0.000
#> GSM1022395 1 0.0000 0.945 1.000 0.000 0.000
#> GSM1022396 1 0.0000 0.945 1.000 0.000 0.000
#> GSM1022389 2 0.0237 0.970 0.004 0.996 0.000
#> GSM1022390 1 0.4346 0.760 0.816 0.184 0.000
#> GSM1022391 2 0.3482 0.839 0.128 0.872 0.000
#> GSM1022392 1 0.1529 0.911 0.960 0.040 0.000
#> GSM1022397 3 0.0000 1.000 0.000 0.000 1.000
#> GSM1022398 3 0.0000 1.000 0.000 0.000 1.000
#> GSM1022399 3 0.0000 1.000 0.000 0.000 1.000
#> GSM1022400 3 0.0000 1.000 0.000 0.000 1.000
#> GSM1022401 1 0.0000 0.945 1.000 0.000 0.000
#> GSM1022402 1 0.0000 0.945 1.000 0.000 0.000
#> GSM1022403 1 0.0000 0.945 1.000 0.000 0.000
#> GSM1022404 1 0.0000 0.945 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1022325 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> GSM1022326 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> GSM1022327 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> GSM1022331 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022332 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022333 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022328 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> GSM1022329 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> GSM1022330 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> GSM1022337 1 0.4624 0.489 0.660 0.340 0.000 0.000
#> GSM1022338 1 0.4134 0.642 0.740 0.260 0.000 0.000
#> GSM1022339 1 0.4866 0.329 0.596 0.404 0.000 0.000
#> GSM1022334 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> GSM1022335 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> GSM1022336 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> GSM1022340 1 0.0000 0.945 1.000 0.000 0.000 0.000
#> GSM1022341 1 0.0000 0.945 1.000 0.000 0.000 0.000
#> GSM1022342 1 0.0000 0.945 1.000 0.000 0.000 0.000
#> GSM1022343 1 0.0000 0.945 1.000 0.000 0.000 0.000
#> GSM1022347 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022348 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022349 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022350 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022344 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022345 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022346 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022355 1 0.0000 0.945 1.000 0.000 0.000 0.000
#> GSM1022356 1 0.0000 0.945 1.000 0.000 0.000 0.000
#> GSM1022357 1 0.0000 0.945 1.000 0.000 0.000 0.000
#> GSM1022358 1 0.0000 0.945 1.000 0.000 0.000 0.000
#> GSM1022351 1 0.0000 0.945 1.000 0.000 0.000 0.000
#> GSM1022352 1 0.0000 0.945 1.000 0.000 0.000 0.000
#> GSM1022353 1 0.0000 0.945 1.000 0.000 0.000 0.000
#> GSM1022354 1 0.0000 0.945 1.000 0.000 0.000 0.000
#> GSM1022359 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> GSM1022360 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> GSM1022361 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> GSM1022362 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> GSM1022367 2 0.0336 0.960 0.000 0.992 0.000 0.008
#> GSM1022368 2 0.1209 0.940 0.000 0.964 0.004 0.032
#> GSM1022369 2 0.4152 0.789 0.000 0.808 0.160 0.032
#> GSM1022370 2 0.0188 0.963 0.000 0.996 0.004 0.000
#> GSM1022363 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> GSM1022364 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> GSM1022365 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> GSM1022366 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> GSM1022374 2 0.3569 0.761 0.196 0.804 0.000 0.000
#> GSM1022375 2 0.3528 0.766 0.192 0.808 0.000 0.000
#> GSM1022376 2 0.3610 0.755 0.200 0.800 0.000 0.000
#> GSM1022371 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> GSM1022372 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> GSM1022373 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> GSM1022377 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM1022378 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM1022379 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM1022380 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM1022385 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022386 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022387 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022388 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022381 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM1022382 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM1022383 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM1022384 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM1022393 1 0.0000 0.945 1.000 0.000 0.000 0.000
#> GSM1022394 1 0.0000 0.945 1.000 0.000 0.000 0.000
#> GSM1022395 1 0.0000 0.945 1.000 0.000 0.000 0.000
#> GSM1022396 1 0.0000 0.945 1.000 0.000 0.000 0.000
#> GSM1022389 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM1022390 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM1022391 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM1022392 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM1022397 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022398 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022399 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022400 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022401 1 0.0000 0.945 1.000 0.000 0.000 0.000
#> GSM1022402 1 0.0000 0.945 1.000 0.000 0.000 0.000
#> GSM1022403 1 0.0000 0.945 1.000 0.000 0.000 0.000
#> GSM1022404 1 0.0000 0.945 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
#> GSM1022325 2 0 1 0 1 0 0 0
#> GSM1022326 2 0 1 0 1 0 0 0
#> GSM1022327 2 0 1 0 1 0 0 0
#> GSM1022331 3 0 1 0 0 1 0 0
#> GSM1022332 3 0 1 0 0 1 0 0
#> GSM1022333 3 0 1 0 0 1 0 0
#> GSM1022328 2 0 1 0 1 0 0 0
#> GSM1022329 2 0 1 0 1 0 0 0
#> GSM1022330 2 0 1 0 1 0 0 0
#> GSM1022337 5 0 1 0 0 0 0 1
#> GSM1022338 5 0 1 0 0 0 0 1
#> GSM1022339 5 0 1 0 0 0 0 1
#> GSM1022334 2 0 1 0 1 0 0 0
#> GSM1022335 2 0 1 0 1 0 0 0
#> GSM1022336 2 0 1 0 1 0 0 0
#> GSM1022340 1 0 1 1 0 0 0 0
#> GSM1022341 1 0 1 1 0 0 0 0
#> GSM1022342 1 0 1 1 0 0 0 0
#> GSM1022343 1 0 1 1 0 0 0 0
#> GSM1022347 3 0 1 0 0 1 0 0
#> GSM1022348 3 0 1 0 0 1 0 0
#> GSM1022349 3 0 1 0 0 1 0 0
#> GSM1022350 3 0 1 0 0 1 0 0
#> GSM1022344 3 0 1 0 0 1 0 0
#> GSM1022345 3 0 1 0 0 1 0 0
#> GSM1022346 3 0 1 0 0 1 0 0
#> GSM1022355 1 0 1 1 0 0 0 0
#> GSM1022356 1 0 1 1 0 0 0 0
#> GSM1022357 1 0 1 1 0 0 0 0
#> GSM1022358 1 0 1 1 0 0 0 0
#> GSM1022351 1 0 1 1 0 0 0 0
#> GSM1022352 1 0 1 1 0 0 0 0
#> GSM1022353 1 0 1 1 0 0 0 0
#> GSM1022354 1 0 1 1 0 0 0 0
#> GSM1022359 2 0 1 0 1 0 0 0
#> GSM1022360 2 0 1 0 1 0 0 0
#> GSM1022361 2 0 1 0 1 0 0 0
#> GSM1022362 2 0 1 0 1 0 0 0
#> GSM1022367 5 0 1 0 0 0 0 1
#> GSM1022368 5 0 1 0 0 0 0 1
#> GSM1022369 5 0 1 0 0 0 0 1
#> GSM1022370 5 0 1 0 0 0 0 1
#> GSM1022363 2 0 1 0 1 0 0 0
#> GSM1022364 2 0 1 0 1 0 0 0
#> GSM1022365 2 0 1 0 1 0 0 0
#> GSM1022366 2 0 1 0 1 0 0 0
#> GSM1022374 5 0 1 0 0 0 0 1
#> GSM1022375 5 0 1 0 0 0 0 1
#> GSM1022376 5 0 1 0 0 0 0 1
#> GSM1022371 2 0 1 0 1 0 0 0
#> GSM1022372 2 0 1 0 1 0 0 0
#> GSM1022373 2 0 1 0 1 0 0 0
#> GSM1022377 4 0 1 0 0 0 1 0
#> GSM1022378 4 0 1 0 0 0 1 0
#> GSM1022379 4 0 1 0 0 0 1 0
#> GSM1022380 4 0 1 0 0 0 1 0
#> GSM1022385 3 0 1 0 0 1 0 0
#> GSM1022386 3 0 1 0 0 1 0 0
#> GSM1022387 3 0 1 0 0 1 0 0
#> GSM1022388 3 0 1 0 0 1 0 0
#> GSM1022381 4 0 1 0 0 0 1 0
#> GSM1022382 4 0 1 0 0 0 1 0
#> GSM1022383 4 0 1 0 0 0 1 0
#> GSM1022384 4 0 1 0 0 0 1 0
#> GSM1022393 1 0 1 1 0 0 0 0
#> GSM1022394 1 0 1 1 0 0 0 0
#> GSM1022395 1 0 1 1 0 0 0 0
#> GSM1022396 1 0 1 1 0 0 0 0
#> GSM1022389 4 0 1 0 0 0 1 0
#> GSM1022390 4 0 1 0 0 0 1 0
#> GSM1022391 4 0 1 0 0 0 1 0
#> GSM1022392 4 0 1 0 0 0 1 0
#> GSM1022397 3 0 1 0 0 1 0 0
#> GSM1022398 3 0 1 0 0 1 0 0
#> GSM1022399 3 0 1 0 0 1 0 0
#> GSM1022400 3 0 1 0 0 1 0 0
#> GSM1022401 1 0 1 1 0 0 0 0
#> GSM1022402 1 0 1 1 0 0 0 0
#> GSM1022403 1 0 1 1 0 0 0 0
#> GSM1022404 1 0 1 1 0 0 0 0
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1022325 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022326 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022327 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022331 6 0.000 0.920 0.000 0.000 0.000 0 0.000 1.000
#> GSM1022332 6 0.000 0.920 0.000 0.000 0.000 0 0.000 1.000
#> GSM1022333 6 0.000 0.920 0.000 0.000 0.000 0 0.000 1.000
#> GSM1022328 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022329 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022330 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022337 5 0.000 0.932 0.000 0.000 0.000 0 1.000 0.000
#> GSM1022338 5 0.000 0.932 0.000 0.000 0.000 0 1.000 0.000
#> GSM1022339 5 0.000 0.932 0.000 0.000 0.000 0 1.000 0.000
#> GSM1022334 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022335 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022336 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022340 1 0.000 0.963 1.000 0.000 0.000 0 0.000 0.000
#> GSM1022341 1 0.000 0.963 1.000 0.000 0.000 0 0.000 0.000
#> GSM1022342 1 0.000 0.963 1.000 0.000 0.000 0 0.000 0.000
#> GSM1022343 1 0.000 0.963 1.000 0.000 0.000 0 0.000 0.000
#> GSM1022347 3 0.000 0.993 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022348 3 0.000 0.993 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022349 3 0.000 0.993 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022350 3 0.000 0.993 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022344 3 0.000 0.993 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022345 3 0.156 0.905 0.080 0.000 0.920 0 0.000 0.000
#> GSM1022346 3 0.026 0.985 0.008 0.000 0.992 0 0.000 0.000
#> GSM1022355 1 0.000 0.963 1.000 0.000 0.000 0 0.000 0.000
#> GSM1022356 1 0.000 0.963 1.000 0.000 0.000 0 0.000 0.000
#> GSM1022357 1 0.000 0.963 1.000 0.000 0.000 0 0.000 0.000
#> GSM1022358 1 0.000 0.963 1.000 0.000 0.000 0 0.000 0.000
#> GSM1022351 1 0.000 0.963 1.000 0.000 0.000 0 0.000 0.000
#> GSM1022352 1 0.000 0.963 1.000 0.000 0.000 0 0.000 0.000
#> GSM1022353 1 0.000 0.963 1.000 0.000 0.000 0 0.000 0.000
#> GSM1022354 1 0.000 0.963 1.000 0.000 0.000 0 0.000 0.000
#> GSM1022359 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022360 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022361 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022362 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022367 6 0.000 0.920 0.000 0.000 0.000 0 0.000 1.000
#> GSM1022368 6 0.000 0.920 0.000 0.000 0.000 0 0.000 1.000
#> GSM1022369 6 0.000 0.920 0.000 0.000 0.000 0 0.000 1.000
#> GSM1022370 6 0.000 0.920 0.000 0.000 0.000 0 0.000 1.000
#> GSM1022363 6 0.150 0.843 0.000 0.076 0.000 0 0.000 0.924
#> GSM1022364 6 0.382 0.250 0.000 0.436 0.000 0 0.000 0.564
#> GSM1022365 6 0.000 0.920 0.000 0.000 0.000 0 0.000 1.000
#> GSM1022366 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022374 5 0.181 0.925 0.000 0.008 0.000 0 0.912 0.080
#> GSM1022375 5 0.166 0.924 0.000 0.000 0.000 0 0.912 0.088
#> GSM1022376 5 0.166 0.924 0.000 0.000 0.000 0 0.912 0.088
#> GSM1022371 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022372 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022373 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022377 4 0.000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM1022378 4 0.000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM1022379 4 0.000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM1022380 4 0.000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM1022385 3 0.000 0.993 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022386 3 0.000 0.993 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022387 3 0.000 0.993 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022388 3 0.000 0.993 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022381 4 0.000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM1022382 4 0.000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM1022383 4 0.000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM1022384 4 0.000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM1022393 1 0.166 0.943 0.912 0.000 0.000 0 0.088 0.000
#> GSM1022394 1 0.166 0.943 0.912 0.000 0.000 0 0.088 0.000
#> GSM1022395 1 0.166 0.943 0.912 0.000 0.000 0 0.088 0.000
#> GSM1022396 1 0.166 0.943 0.912 0.000 0.000 0 0.088 0.000
#> GSM1022389 4 0.000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM1022390 4 0.000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM1022391 4 0.000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM1022392 4 0.000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM1022397 3 0.000 0.993 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022398 3 0.000 0.993 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022399 3 0.000 0.993 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022400 3 0.000 0.993 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022401 1 0.166 0.943 0.912 0.000 0.000 0 0.088 0.000
#> GSM1022402 1 0.166 0.943 0.912 0.000 0.000 0 0.088 0.000
#> GSM1022403 1 0.166 0.943 0.912 0.000 0.000 0 0.088 0.000
#> GSM1022404 1 0.166 0.943 0.912 0.000 0.000 0 0.088 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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n protocol(p) cell.type(p) k
#> MAD:pam 80 1.22e-07 6.13e-05 2
#> MAD:pam 79 4.03e-14 1.29e-05 3
#> MAD:pam 78 2.47e-19 6.14e-06 4
#> MAD:pam 80 7.64e-20 2.66e-10 5
#> MAD:pam 79 5.39e-26 2.50e-08 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 31589 rows and 80 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.357 0.817 0.871 0.4562 0.509 0.509
#> 3 3 0.574 0.754 0.858 0.3991 0.740 0.525
#> 4 4 0.656 0.694 0.832 0.1443 0.733 0.373
#> 5 5 0.876 0.908 0.942 0.0846 0.891 0.616
#> 6 6 0.885 0.905 0.919 0.0274 0.987 0.933
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM1022325 2 0.5946 0.790 0.144 0.856
#> GSM1022326 2 0.6048 0.789 0.148 0.852
#> GSM1022327 2 0.5842 0.791 0.140 0.860
#> GSM1022331 2 0.8861 0.613 0.304 0.696
#> GSM1022332 2 0.8861 0.613 0.304 0.696
#> GSM1022333 2 0.8861 0.613 0.304 0.696
#> GSM1022328 2 0.6048 0.789 0.148 0.852
#> GSM1022329 2 0.5946 0.790 0.144 0.856
#> GSM1022330 2 0.5946 0.790 0.144 0.856
#> GSM1022337 2 0.9933 0.607 0.452 0.548
#> GSM1022338 2 0.9933 0.607 0.452 0.548
#> GSM1022339 2 0.9933 0.607 0.452 0.548
#> GSM1022334 2 0.6048 0.789 0.148 0.852
#> GSM1022335 2 0.6048 0.789 0.148 0.852
#> GSM1022336 2 0.5946 0.790 0.144 0.856
#> GSM1022340 1 0.0000 0.898 1.000 0.000
#> GSM1022341 1 0.0000 0.898 1.000 0.000
#> GSM1022342 1 0.0000 0.898 1.000 0.000
#> GSM1022343 1 0.0000 0.898 1.000 0.000
#> GSM1022347 1 0.6343 0.877 0.840 0.160
#> GSM1022348 1 0.6343 0.877 0.840 0.160
#> GSM1022349 1 0.6343 0.877 0.840 0.160
#> GSM1022350 1 0.6343 0.877 0.840 0.160
#> GSM1022344 1 0.6148 0.878 0.848 0.152
#> GSM1022345 1 0.6148 0.878 0.848 0.152
#> GSM1022346 1 0.6148 0.878 0.848 0.152
#> GSM1022355 1 0.0376 0.897 0.996 0.004
#> GSM1022356 1 0.0376 0.897 0.996 0.004
#> GSM1022357 1 0.0376 0.897 0.996 0.004
#> GSM1022358 1 0.0376 0.897 0.996 0.004
#> GSM1022351 1 0.0376 0.897 0.996 0.004
#> GSM1022352 1 0.0376 0.897 0.996 0.004
#> GSM1022353 1 0.0376 0.897 0.996 0.004
#> GSM1022354 1 0.0376 0.897 0.996 0.004
#> GSM1022359 2 0.0672 0.769 0.008 0.992
#> GSM1022360 2 0.0938 0.771 0.012 0.988
#> GSM1022361 2 0.0938 0.771 0.012 0.988
#> GSM1022362 2 0.0938 0.771 0.012 0.988
#> GSM1022367 2 0.8861 0.613 0.304 0.696
#> GSM1022368 2 0.8861 0.613 0.304 0.696
#> GSM1022369 2 0.8861 0.613 0.304 0.696
#> GSM1022370 2 0.8861 0.613 0.304 0.696
#> GSM1022363 2 0.2778 0.773 0.048 0.952
#> GSM1022364 2 0.2778 0.773 0.048 0.952
#> GSM1022365 2 0.2778 0.773 0.048 0.952
#> GSM1022366 2 0.2778 0.773 0.048 0.952
#> GSM1022374 2 0.9933 0.607 0.452 0.548
#> GSM1022375 2 0.9933 0.607 0.452 0.548
#> GSM1022376 2 0.9933 0.607 0.452 0.548
#> GSM1022371 2 0.6712 0.786 0.176 0.824
#> GSM1022372 2 0.6712 0.786 0.176 0.824
#> GSM1022373 2 0.6712 0.786 0.176 0.824
#> GSM1022377 1 0.5294 0.891 0.880 0.120
#> GSM1022378 1 0.5059 0.893 0.888 0.112
#> GSM1022379 1 0.5178 0.892 0.884 0.116
#> GSM1022380 1 0.5059 0.893 0.888 0.112
#> GSM1022385 1 0.6343 0.877 0.840 0.160
#> GSM1022386 1 0.6343 0.877 0.840 0.160
#> GSM1022387 1 0.6343 0.877 0.840 0.160
#> GSM1022388 1 0.6343 0.877 0.840 0.160
#> GSM1022381 1 0.5842 0.885 0.860 0.140
#> GSM1022382 1 0.5842 0.885 0.860 0.140
#> GSM1022383 1 0.5842 0.885 0.860 0.140
#> GSM1022384 1 0.5842 0.885 0.860 0.140
#> GSM1022393 1 0.0376 0.897 0.996 0.004
#> GSM1022394 1 0.0376 0.897 0.996 0.004
#> GSM1022395 1 0.0376 0.897 0.996 0.004
#> GSM1022396 1 0.0376 0.897 0.996 0.004
#> GSM1022389 1 0.0000 0.898 1.000 0.000
#> GSM1022390 1 0.0000 0.898 1.000 0.000
#> GSM1022391 1 0.0000 0.898 1.000 0.000
#> GSM1022392 1 0.0000 0.898 1.000 0.000
#> GSM1022397 1 0.6343 0.877 0.840 0.160
#> GSM1022398 1 0.6343 0.877 0.840 0.160
#> GSM1022399 1 0.6343 0.877 0.840 0.160
#> GSM1022400 1 0.6343 0.877 0.840 0.160
#> GSM1022401 1 0.0376 0.897 0.996 0.004
#> GSM1022402 1 0.0376 0.897 0.996 0.004
#> GSM1022403 1 0.0376 0.897 0.996 0.004
#> GSM1022404 1 0.0376 0.897 0.996 0.004
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1022325 2 0.0000 0.850 0.000 1.000 0.000
#> GSM1022326 2 0.0000 0.850 0.000 1.000 0.000
#> GSM1022327 2 0.0000 0.850 0.000 1.000 0.000
#> GSM1022331 2 0.9730 0.248 0.256 0.448 0.296
#> GSM1022332 2 0.9730 0.248 0.256 0.448 0.296
#> GSM1022333 2 0.9730 0.248 0.256 0.448 0.296
#> GSM1022328 2 0.0000 0.850 0.000 1.000 0.000
#> GSM1022329 2 0.0000 0.850 0.000 1.000 0.000
#> GSM1022330 2 0.0000 0.850 0.000 1.000 0.000
#> GSM1022337 1 0.0592 0.961 0.988 0.012 0.000
#> GSM1022338 1 0.0592 0.961 0.988 0.012 0.000
#> GSM1022339 1 0.0592 0.961 0.988 0.012 0.000
#> GSM1022334 2 0.0000 0.850 0.000 1.000 0.000
#> GSM1022335 2 0.0000 0.850 0.000 1.000 0.000
#> GSM1022336 2 0.0000 0.850 0.000 1.000 0.000
#> GSM1022340 3 0.6647 0.572 0.396 0.012 0.592
#> GSM1022341 3 0.6647 0.572 0.396 0.012 0.592
#> GSM1022342 3 0.6647 0.572 0.396 0.012 0.592
#> GSM1022343 3 0.6647 0.572 0.396 0.012 0.592
#> GSM1022347 3 0.0000 0.675 0.000 0.000 1.000
#> GSM1022348 3 0.0000 0.675 0.000 0.000 1.000
#> GSM1022349 3 0.0000 0.675 0.000 0.000 1.000
#> GSM1022350 3 0.0000 0.675 0.000 0.000 1.000
#> GSM1022344 3 0.6470 0.605 0.356 0.012 0.632
#> GSM1022345 3 0.6470 0.605 0.356 0.012 0.632
#> GSM1022346 3 0.6470 0.605 0.356 0.012 0.632
#> GSM1022355 1 0.0000 0.967 1.000 0.000 0.000
#> GSM1022356 1 0.0000 0.967 1.000 0.000 0.000
#> GSM1022357 1 0.0000 0.967 1.000 0.000 0.000
#> GSM1022358 1 0.0000 0.967 1.000 0.000 0.000
#> GSM1022351 1 0.0000 0.967 1.000 0.000 0.000
#> GSM1022352 1 0.0000 0.967 1.000 0.000 0.000
#> GSM1022353 1 0.0000 0.967 1.000 0.000 0.000
#> GSM1022354 1 0.0000 0.967 1.000 0.000 0.000
#> GSM1022359 2 0.0000 0.850 0.000 1.000 0.000
#> GSM1022360 2 0.0000 0.850 0.000 1.000 0.000
#> GSM1022361 2 0.0000 0.850 0.000 1.000 0.000
#> GSM1022362 2 0.0000 0.850 0.000 1.000 0.000
#> GSM1022367 2 0.9120 0.407 0.256 0.544 0.200
#> GSM1022368 2 0.9120 0.407 0.256 0.544 0.200
#> GSM1022369 2 0.9120 0.407 0.256 0.544 0.200
#> GSM1022370 2 0.9120 0.407 0.256 0.544 0.200
#> GSM1022363 2 0.0000 0.850 0.000 1.000 0.000
#> GSM1022364 2 0.0000 0.850 0.000 1.000 0.000
#> GSM1022365 2 0.0000 0.850 0.000 1.000 0.000
#> GSM1022366 2 0.0000 0.850 0.000 1.000 0.000
#> GSM1022374 1 0.0592 0.961 0.988 0.012 0.000
#> GSM1022375 1 0.0592 0.961 0.988 0.012 0.000
#> GSM1022376 1 0.0592 0.961 0.988 0.012 0.000
#> GSM1022371 2 0.1163 0.833 0.028 0.972 0.000
#> GSM1022372 2 0.1163 0.833 0.028 0.972 0.000
#> GSM1022373 2 0.1163 0.833 0.028 0.972 0.000
#> GSM1022377 3 0.9594 0.528 0.360 0.204 0.436
#> GSM1022378 3 0.9594 0.528 0.360 0.204 0.436
#> GSM1022379 3 0.9594 0.528 0.360 0.204 0.436
#> GSM1022380 3 0.9594 0.528 0.360 0.204 0.436
#> GSM1022385 3 0.0000 0.675 0.000 0.000 1.000
#> GSM1022386 3 0.0000 0.675 0.000 0.000 1.000
#> GSM1022387 3 0.0000 0.675 0.000 0.000 1.000
#> GSM1022388 3 0.0000 0.675 0.000 0.000 1.000
#> GSM1022381 3 0.9594 0.528 0.360 0.204 0.436
#> GSM1022382 3 0.9594 0.528 0.360 0.204 0.436
#> GSM1022383 3 0.9594 0.528 0.360 0.204 0.436
#> GSM1022384 3 0.9594 0.528 0.360 0.204 0.436
#> GSM1022393 1 0.0000 0.967 1.000 0.000 0.000
#> GSM1022394 1 0.0000 0.967 1.000 0.000 0.000
#> GSM1022395 1 0.0000 0.967 1.000 0.000 0.000
#> GSM1022396 1 0.0000 0.967 1.000 0.000 0.000
#> GSM1022389 1 0.3412 0.837 0.876 0.124 0.000
#> GSM1022390 1 0.3412 0.837 0.876 0.124 0.000
#> GSM1022391 1 0.3412 0.837 0.876 0.124 0.000
#> GSM1022392 1 0.3412 0.837 0.876 0.124 0.000
#> GSM1022397 3 0.0000 0.675 0.000 0.000 1.000
#> GSM1022398 3 0.0000 0.675 0.000 0.000 1.000
#> GSM1022399 3 0.0000 0.675 0.000 0.000 1.000
#> GSM1022400 3 0.0000 0.675 0.000 0.000 1.000
#> GSM1022401 1 0.0000 0.967 1.000 0.000 0.000
#> GSM1022402 1 0.0000 0.967 1.000 0.000 0.000
#> GSM1022403 1 0.0000 0.967 1.000 0.000 0.000
#> GSM1022404 1 0.0000 0.967 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1022325 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022326 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022327 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022331 4 0.7735 0.511 0.104 0.136 0.136 0.624
#> GSM1022332 4 0.7735 0.511 0.104 0.136 0.136 0.624
#> GSM1022333 4 0.7735 0.511 0.104 0.136 0.136 0.624
#> GSM1022328 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022329 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022330 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022337 4 0.2647 0.518 0.120 0.000 0.000 0.880
#> GSM1022338 4 0.2647 0.518 0.120 0.000 0.000 0.880
#> GSM1022339 4 0.2647 0.518 0.120 0.000 0.000 0.880
#> GSM1022334 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022335 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022336 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022340 1 0.6447 -0.471 0.484 0.000 0.068 0.448
#> GSM1022341 1 0.6447 -0.471 0.484 0.000 0.068 0.448
#> GSM1022342 1 0.6447 -0.471 0.484 0.000 0.068 0.448
#> GSM1022343 1 0.6447 -0.471 0.484 0.000 0.068 0.448
#> GSM1022347 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022348 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022349 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022350 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022344 4 0.7184 0.520 0.416 0.000 0.136 0.448
#> GSM1022345 4 0.7184 0.520 0.416 0.000 0.136 0.448
#> GSM1022346 4 0.7184 0.520 0.416 0.000 0.136 0.448
#> GSM1022355 1 0.0000 0.620 1.000 0.000 0.000 0.000
#> GSM1022356 1 0.0000 0.620 1.000 0.000 0.000 0.000
#> GSM1022357 1 0.0000 0.620 1.000 0.000 0.000 0.000
#> GSM1022358 1 0.0000 0.620 1.000 0.000 0.000 0.000
#> GSM1022351 1 0.0469 0.613 0.988 0.000 0.000 0.012
#> GSM1022352 1 0.0469 0.613 0.988 0.000 0.000 0.012
#> GSM1022353 1 0.0469 0.613 0.988 0.000 0.000 0.012
#> GSM1022354 1 0.0469 0.613 0.988 0.000 0.000 0.012
#> GSM1022359 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022360 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022361 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022362 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022367 4 0.7680 0.508 0.104 0.168 0.104 0.624
#> GSM1022368 4 0.7680 0.508 0.104 0.168 0.104 0.624
#> GSM1022369 4 0.7680 0.508 0.104 0.168 0.104 0.624
#> GSM1022370 4 0.7680 0.508 0.104 0.168 0.104 0.624
#> GSM1022363 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022364 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022365 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022366 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022374 4 0.2647 0.518 0.120 0.000 0.000 0.880
#> GSM1022375 4 0.2647 0.518 0.120 0.000 0.000 0.880
#> GSM1022376 4 0.2647 0.518 0.120 0.000 0.000 0.880
#> GSM1022371 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022372 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022373 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM1022377 4 0.5901 0.621 0.280 0.000 0.068 0.652
#> GSM1022378 4 0.5901 0.621 0.280 0.000 0.068 0.652
#> GSM1022379 4 0.5901 0.621 0.280 0.000 0.068 0.652
#> GSM1022380 4 0.5901 0.621 0.280 0.000 0.068 0.652
#> GSM1022385 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022386 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022387 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022388 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022381 4 0.5901 0.621 0.280 0.000 0.068 0.652
#> GSM1022382 4 0.5901 0.621 0.280 0.000 0.068 0.652
#> GSM1022383 4 0.5901 0.621 0.280 0.000 0.068 0.652
#> GSM1022384 4 0.5901 0.621 0.280 0.000 0.068 0.652
#> GSM1022393 1 0.4277 0.610 0.720 0.000 0.000 0.280
#> GSM1022394 1 0.4277 0.610 0.720 0.000 0.000 0.280
#> GSM1022395 1 0.4277 0.610 0.720 0.000 0.000 0.280
#> GSM1022396 1 0.4277 0.610 0.720 0.000 0.000 0.280
#> GSM1022389 4 0.5835 0.606 0.280 0.000 0.064 0.656
#> GSM1022390 4 0.5835 0.606 0.280 0.000 0.064 0.656
#> GSM1022391 4 0.5835 0.606 0.280 0.000 0.064 0.656
#> GSM1022392 4 0.5835 0.606 0.280 0.000 0.064 0.656
#> GSM1022397 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022398 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022399 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022400 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM1022401 1 0.4277 0.610 0.720 0.000 0.000 0.280
#> GSM1022402 1 0.4277 0.610 0.720 0.000 0.000 0.280
#> GSM1022403 1 0.4277 0.610 0.720 0.000 0.000 0.280
#> GSM1022404 1 0.4277 0.610 0.720 0.000 0.000 0.280
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1022325 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> GSM1022326 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> GSM1022327 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> GSM1022331 5 0.0000 0.855 0.000 0 0 0.000 1.000
#> GSM1022332 5 0.0000 0.855 0.000 0 0 0.000 1.000
#> GSM1022333 5 0.0000 0.855 0.000 0 0 0.000 1.000
#> GSM1022328 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> GSM1022329 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> GSM1022330 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> GSM1022337 5 0.3752 0.809 0.292 0 0 0.000 0.708
#> GSM1022338 5 0.3752 0.809 0.292 0 0 0.000 0.708
#> GSM1022339 5 0.3752 0.809 0.292 0 0 0.000 0.708
#> GSM1022334 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> GSM1022335 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> GSM1022336 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> GSM1022340 4 0.2127 0.906 0.108 0 0 0.892 0.000
#> GSM1022341 4 0.2127 0.906 0.108 0 0 0.892 0.000
#> GSM1022342 4 0.2127 0.906 0.108 0 0 0.892 0.000
#> GSM1022343 4 0.2127 0.906 0.108 0 0 0.892 0.000
#> GSM1022347 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> GSM1022348 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> GSM1022349 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> GSM1022350 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> GSM1022344 4 0.2127 0.906 0.108 0 0 0.892 0.000
#> GSM1022345 4 0.2127 0.906 0.108 0 0 0.892 0.000
#> GSM1022346 4 0.2127 0.906 0.108 0 0 0.892 0.000
#> GSM1022355 1 0.3684 0.728 0.720 0 0 0.280 0.000
#> GSM1022356 1 0.3684 0.728 0.720 0 0 0.280 0.000
#> GSM1022357 1 0.3684 0.728 0.720 0 0 0.280 0.000
#> GSM1022358 1 0.3684 0.728 0.720 0 0 0.280 0.000
#> GSM1022351 4 0.2230 0.897 0.116 0 0 0.884 0.000
#> GSM1022352 1 0.3752 0.713 0.708 0 0 0.292 0.000
#> GSM1022353 1 0.3752 0.713 0.708 0 0 0.292 0.000
#> GSM1022354 1 0.3752 0.713 0.708 0 0 0.292 0.000
#> GSM1022359 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> GSM1022360 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> GSM1022361 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> GSM1022362 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> GSM1022367 5 0.0000 0.855 0.000 0 0 0.000 1.000
#> GSM1022368 5 0.0000 0.855 0.000 0 0 0.000 1.000
#> GSM1022369 5 0.0000 0.855 0.000 0 0 0.000 1.000
#> GSM1022370 5 0.0000 0.855 0.000 0 0 0.000 1.000
#> GSM1022363 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> GSM1022364 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> GSM1022365 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> GSM1022366 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> GSM1022374 5 0.3752 0.809 0.292 0 0 0.000 0.708
#> GSM1022375 5 0.3752 0.809 0.292 0 0 0.000 0.708
#> GSM1022376 5 0.3752 0.809 0.292 0 0 0.000 0.708
#> GSM1022371 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> GSM1022372 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> GSM1022373 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> GSM1022377 4 0.0000 0.941 0.000 0 0 1.000 0.000
#> GSM1022378 4 0.0000 0.941 0.000 0 0 1.000 0.000
#> GSM1022379 4 0.0000 0.941 0.000 0 0 1.000 0.000
#> GSM1022380 4 0.0000 0.941 0.000 0 0 1.000 0.000
#> GSM1022385 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> GSM1022386 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> GSM1022387 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> GSM1022388 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> GSM1022381 4 0.0000 0.941 0.000 0 0 1.000 0.000
#> GSM1022382 4 0.0000 0.941 0.000 0 0 1.000 0.000
#> GSM1022383 4 0.0000 0.941 0.000 0 0 1.000 0.000
#> GSM1022384 4 0.0000 0.941 0.000 0 0 1.000 0.000
#> GSM1022393 1 0.0000 0.779 1.000 0 0 0.000 0.000
#> GSM1022394 1 0.0000 0.779 1.000 0 0 0.000 0.000
#> GSM1022395 1 0.0000 0.779 1.000 0 0 0.000 0.000
#> GSM1022396 1 0.0000 0.779 1.000 0 0 0.000 0.000
#> GSM1022389 4 0.0162 0.941 0.004 0 0 0.996 0.000
#> GSM1022390 4 0.0162 0.941 0.004 0 0 0.996 0.000
#> GSM1022391 4 0.0162 0.941 0.004 0 0 0.996 0.000
#> GSM1022392 4 0.0162 0.941 0.004 0 0 0.996 0.000
#> GSM1022397 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> GSM1022398 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> GSM1022399 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> GSM1022400 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> GSM1022401 1 0.0000 0.779 1.000 0 0 0.000 0.000
#> GSM1022402 1 0.0000 0.779 1.000 0 0 0.000 0.000
#> GSM1022403 1 0.0000 0.779 1.000 0 0 0.000 0.000
#> GSM1022404 1 0.0000 0.779 1.000 0 0 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1022325 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0
#> GSM1022326 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0
#> GSM1022327 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0
#> GSM1022331 6 0.000 1.000 0.000 0 0.000 0.000 0.000 1
#> GSM1022332 6 0.000 1.000 0.000 0 0.000 0.000 0.000 1
#> GSM1022333 6 0.000 1.000 0.000 0 0.000 0.000 0.000 1
#> GSM1022328 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0
#> GSM1022329 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0
#> GSM1022330 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0
#> GSM1022337 5 0.000 1.000 0.000 0 0.000 0.000 1.000 0
#> GSM1022338 5 0.000 1.000 0.000 0 0.000 0.000 1.000 0
#> GSM1022339 5 0.000 1.000 0.000 0 0.000 0.000 1.000 0
#> GSM1022334 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0
#> GSM1022335 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0
#> GSM1022336 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0
#> GSM1022340 4 0.355 0.759 0.332 0 0.000 0.668 0.000 0
#> GSM1022341 4 0.355 0.759 0.332 0 0.000 0.668 0.000 0
#> GSM1022342 4 0.355 0.759 0.332 0 0.000 0.668 0.000 0
#> GSM1022343 4 0.355 0.759 0.332 0 0.000 0.668 0.000 0
#> GSM1022347 3 0.000 1.000 0.000 0 1.000 0.000 0.000 0
#> GSM1022348 3 0.000 1.000 0.000 0 1.000 0.000 0.000 0
#> GSM1022349 3 0.000 1.000 0.000 0 1.000 0.000 0.000 0
#> GSM1022350 3 0.000 1.000 0.000 0 1.000 0.000 0.000 0
#> GSM1022344 4 0.435 0.769 0.280 0 0.052 0.668 0.000 0
#> GSM1022345 4 0.435 0.769 0.280 0 0.052 0.668 0.000 0
#> GSM1022346 4 0.435 0.769 0.280 0 0.052 0.668 0.000 0
#> GSM1022355 1 0.139 0.782 0.932 0 0.000 0.068 0.000 0
#> GSM1022356 1 0.139 0.782 0.932 0 0.000 0.068 0.000 0
#> GSM1022357 1 0.139 0.782 0.932 0 0.000 0.068 0.000 0
#> GSM1022358 1 0.139 0.782 0.932 0 0.000 0.068 0.000 0
#> GSM1022351 4 0.387 0.492 0.484 0 0.000 0.516 0.000 0
#> GSM1022352 1 0.139 0.782 0.932 0 0.000 0.068 0.000 0
#> GSM1022353 1 0.139 0.782 0.932 0 0.000 0.068 0.000 0
#> GSM1022354 1 0.139 0.782 0.932 0 0.000 0.068 0.000 0
#> GSM1022359 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0
#> GSM1022360 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0
#> GSM1022361 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0
#> GSM1022362 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0
#> GSM1022367 6 0.000 1.000 0.000 0 0.000 0.000 0.000 1
#> GSM1022368 6 0.000 1.000 0.000 0 0.000 0.000 0.000 1
#> GSM1022369 6 0.000 1.000 0.000 0 0.000 0.000 0.000 1
#> GSM1022370 6 0.000 1.000 0.000 0 0.000 0.000 0.000 1
#> GSM1022363 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0
#> GSM1022364 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0
#> GSM1022365 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0
#> GSM1022366 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0
#> GSM1022374 5 0.000 1.000 0.000 0 0.000 0.000 1.000 0
#> GSM1022375 5 0.000 1.000 0.000 0 0.000 0.000 1.000 0
#> GSM1022376 5 0.000 1.000 0.000 0 0.000 0.000 1.000 0
#> GSM1022371 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0
#> GSM1022372 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0
#> GSM1022373 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0
#> GSM1022377 4 0.000 0.809 0.000 0 0.000 1.000 0.000 0
#> GSM1022378 4 0.000 0.809 0.000 0 0.000 1.000 0.000 0
#> GSM1022379 4 0.000 0.809 0.000 0 0.000 1.000 0.000 0
#> GSM1022380 4 0.000 0.809 0.000 0 0.000 1.000 0.000 0
#> GSM1022385 3 0.000 1.000 0.000 0 1.000 0.000 0.000 0
#> GSM1022386 3 0.000 1.000 0.000 0 1.000 0.000 0.000 0
#> GSM1022387 3 0.000 1.000 0.000 0 1.000 0.000 0.000 0
#> GSM1022388 3 0.000 1.000 0.000 0 1.000 0.000 0.000 0
#> GSM1022381 4 0.000 0.809 0.000 0 0.000 1.000 0.000 0
#> GSM1022382 4 0.000 0.809 0.000 0 0.000 1.000 0.000 0
#> GSM1022383 4 0.000 0.809 0.000 0 0.000 1.000 0.000 0
#> GSM1022384 4 0.000 0.809 0.000 0 0.000 1.000 0.000 0
#> GSM1022393 1 0.288 0.788 0.788 0 0.000 0.000 0.212 0
#> GSM1022394 1 0.288 0.788 0.788 0 0.000 0.000 0.212 0
#> GSM1022395 1 0.288 0.788 0.788 0 0.000 0.000 0.212 0
#> GSM1022396 1 0.288 0.788 0.788 0 0.000 0.000 0.212 0
#> GSM1022389 4 0.249 0.828 0.164 0 0.000 0.836 0.000 0
#> GSM1022390 4 0.249 0.828 0.164 0 0.000 0.836 0.000 0
#> GSM1022391 4 0.249 0.828 0.164 0 0.000 0.836 0.000 0
#> GSM1022392 4 0.249 0.828 0.164 0 0.000 0.836 0.000 0
#> GSM1022397 3 0.000 1.000 0.000 0 1.000 0.000 0.000 0
#> GSM1022398 3 0.000 1.000 0.000 0 1.000 0.000 0.000 0
#> GSM1022399 3 0.000 1.000 0.000 0 1.000 0.000 0.000 0
#> GSM1022400 3 0.000 1.000 0.000 0 1.000 0.000 0.000 0
#> GSM1022401 1 0.288 0.788 0.788 0 0.000 0.000 0.212 0
#> GSM1022402 1 0.288 0.788 0.788 0 0.000 0.000 0.212 0
#> GSM1022403 1 0.288 0.788 0.788 0 0.000 0.000 0.212 0
#> GSM1022404 1 0.288 0.788 0.788 0 0.000 0.000 0.212 0
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n protocol(p) cell.type(p) k
#> MAD:mclust 80 1.10e-11 4.22e-01 2
#> MAD:mclust 73 3.39e-15 1.25e-05 3
#> MAD:mclust 76 1.02e-13 7.08e-08 4
#> MAD:mclust 80 3.30e-17 1.92e-14 5
#> MAD:mclust 79 1.54e-20 1.39e-13 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
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 31589 rows and 80 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.974 0.975 0.988 0.5059 0.495 0.495
#> 3 3 0.747 0.822 0.923 0.3088 0.717 0.491
#> 4 4 0.744 0.829 0.895 0.1158 0.836 0.570
#> 5 5 0.801 0.732 0.858 0.0450 0.935 0.760
#> 6 6 0.789 0.740 0.822 0.0417 0.929 0.704
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
#> GSM1022325 2 0.0000 0.976 0.000 1.000
#> GSM1022326 2 0.0000 0.976 0.000 1.000
#> GSM1022327 2 0.0000 0.976 0.000 1.000
#> GSM1022331 1 0.0000 1.000 1.000 0.000
#> GSM1022332 1 0.0000 1.000 1.000 0.000
#> GSM1022333 1 0.0000 1.000 1.000 0.000
#> GSM1022328 2 0.0000 0.976 0.000 1.000
#> GSM1022329 2 0.0000 0.976 0.000 1.000
#> GSM1022330 2 0.0000 0.976 0.000 1.000
#> GSM1022337 2 0.7745 0.724 0.228 0.772
#> GSM1022338 2 0.7883 0.711 0.236 0.764
#> GSM1022339 2 0.6623 0.803 0.172 0.828
#> GSM1022334 2 0.0000 0.976 0.000 1.000
#> GSM1022335 2 0.0000 0.976 0.000 1.000
#> GSM1022336 2 0.0000 0.976 0.000 1.000
#> GSM1022340 1 0.0000 1.000 1.000 0.000
#> GSM1022341 1 0.0000 1.000 1.000 0.000
#> GSM1022342 1 0.0000 1.000 1.000 0.000
#> GSM1022343 1 0.0000 1.000 1.000 0.000
#> GSM1022347 1 0.0000 1.000 1.000 0.000
#> GSM1022348 1 0.0000 1.000 1.000 0.000
#> GSM1022349 1 0.0000 1.000 1.000 0.000
#> GSM1022350 1 0.0000 1.000 1.000 0.000
#> GSM1022344 1 0.0000 1.000 1.000 0.000
#> GSM1022345 1 0.0000 1.000 1.000 0.000
#> GSM1022346 1 0.0000 1.000 1.000 0.000
#> GSM1022355 1 0.0000 1.000 1.000 0.000
#> GSM1022356 1 0.0000 1.000 1.000 0.000
#> GSM1022357 1 0.0000 1.000 1.000 0.000
#> GSM1022358 1 0.0000 1.000 1.000 0.000
#> GSM1022351 1 0.0000 1.000 1.000 0.000
#> GSM1022352 1 0.0000 1.000 1.000 0.000
#> GSM1022353 1 0.0000 1.000 1.000 0.000
#> GSM1022354 1 0.0000 1.000 1.000 0.000
#> GSM1022359 2 0.0000 0.976 0.000 1.000
#> GSM1022360 2 0.0000 0.976 0.000 1.000
#> GSM1022361 2 0.0000 0.976 0.000 1.000
#> GSM1022362 2 0.0000 0.976 0.000 1.000
#> GSM1022367 2 0.0000 0.976 0.000 1.000
#> GSM1022368 2 0.0000 0.976 0.000 1.000
#> GSM1022369 2 0.0000 0.976 0.000 1.000
#> GSM1022370 2 0.0000 0.976 0.000 1.000
#> GSM1022363 2 0.0000 0.976 0.000 1.000
#> GSM1022364 2 0.0000 0.976 0.000 1.000
#> GSM1022365 2 0.0000 0.976 0.000 1.000
#> GSM1022366 2 0.0000 0.976 0.000 1.000
#> GSM1022374 2 0.0000 0.976 0.000 1.000
#> GSM1022375 2 0.0000 0.976 0.000 1.000
#> GSM1022376 2 0.0000 0.976 0.000 1.000
#> GSM1022371 2 0.0000 0.976 0.000 1.000
#> GSM1022372 2 0.0000 0.976 0.000 1.000
#> GSM1022373 2 0.0000 0.976 0.000 1.000
#> GSM1022377 2 0.0000 0.976 0.000 1.000
#> GSM1022378 2 0.0000 0.976 0.000 1.000
#> GSM1022379 2 0.0000 0.976 0.000 1.000
#> GSM1022380 2 0.0000 0.976 0.000 1.000
#> GSM1022385 1 0.0000 1.000 1.000 0.000
#> GSM1022386 1 0.0000 1.000 1.000 0.000
#> GSM1022387 1 0.0000 1.000 1.000 0.000
#> GSM1022388 1 0.0000 1.000 1.000 0.000
#> GSM1022381 2 0.0672 0.970 0.008 0.992
#> GSM1022382 2 0.0376 0.973 0.004 0.996
#> GSM1022383 2 0.1843 0.955 0.028 0.972
#> GSM1022384 2 0.5294 0.868 0.120 0.880
#> GSM1022393 1 0.0000 1.000 1.000 0.000
#> GSM1022394 1 0.0000 1.000 1.000 0.000
#> GSM1022395 1 0.0000 1.000 1.000 0.000
#> GSM1022396 1 0.0000 1.000 1.000 0.000
#> GSM1022389 2 0.0000 0.976 0.000 1.000
#> GSM1022390 2 0.2423 0.945 0.040 0.960
#> GSM1022391 2 0.0000 0.976 0.000 1.000
#> GSM1022392 2 0.6048 0.835 0.148 0.852
#> GSM1022397 1 0.0000 1.000 1.000 0.000
#> GSM1022398 1 0.0000 1.000 1.000 0.000
#> GSM1022399 1 0.0000 1.000 1.000 0.000
#> GSM1022400 1 0.0000 1.000 1.000 0.000
#> GSM1022401 1 0.0000 1.000 1.000 0.000
#> GSM1022402 1 0.0000 1.000 1.000 0.000
#> GSM1022403 1 0.0000 1.000 1.000 0.000
#> GSM1022404 1 0.0000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1022325 2 0.0000 0.8491 0.000 1.000 0.000
#> GSM1022326 2 0.0000 0.8491 0.000 1.000 0.000
#> GSM1022327 2 0.0000 0.8491 0.000 1.000 0.000
#> GSM1022331 3 0.0000 0.9200 0.000 0.000 1.000
#> GSM1022332 3 0.0000 0.9200 0.000 0.000 1.000
#> GSM1022333 3 0.0000 0.9200 0.000 0.000 1.000
#> GSM1022328 2 0.0000 0.8491 0.000 1.000 0.000
#> GSM1022329 2 0.0000 0.8491 0.000 1.000 0.000
#> GSM1022330 2 0.0000 0.8491 0.000 1.000 0.000
#> GSM1022337 1 0.2878 0.8758 0.904 0.096 0.000
#> GSM1022338 1 0.2878 0.8758 0.904 0.096 0.000
#> GSM1022339 1 0.4842 0.6773 0.776 0.224 0.000
#> GSM1022334 2 0.0000 0.8491 0.000 1.000 0.000
#> GSM1022335 2 0.0000 0.8491 0.000 1.000 0.000
#> GSM1022336 2 0.0000 0.8491 0.000 1.000 0.000
#> GSM1022340 1 0.0000 0.9680 1.000 0.000 0.000
#> GSM1022341 1 0.0000 0.9680 1.000 0.000 0.000
#> GSM1022342 1 0.0000 0.9680 1.000 0.000 0.000
#> GSM1022343 1 0.0000 0.9680 1.000 0.000 0.000
#> GSM1022347 3 0.0000 0.9200 0.000 0.000 1.000
#> GSM1022348 3 0.0000 0.9200 0.000 0.000 1.000
#> GSM1022349 3 0.0000 0.9200 0.000 0.000 1.000
#> GSM1022350 3 0.0000 0.9200 0.000 0.000 1.000
#> GSM1022344 3 0.1289 0.8982 0.032 0.000 0.968
#> GSM1022345 3 0.6280 0.1564 0.460 0.000 0.540
#> GSM1022346 3 0.3879 0.7855 0.152 0.000 0.848
#> GSM1022355 1 0.0000 0.9680 1.000 0.000 0.000
#> GSM1022356 1 0.0000 0.9680 1.000 0.000 0.000
#> GSM1022357 1 0.0000 0.9680 1.000 0.000 0.000
#> GSM1022358 1 0.0000 0.9680 1.000 0.000 0.000
#> GSM1022351 1 0.0000 0.9680 1.000 0.000 0.000
#> GSM1022352 1 0.0000 0.9680 1.000 0.000 0.000
#> GSM1022353 1 0.0000 0.9680 1.000 0.000 0.000
#> GSM1022354 1 0.0000 0.9680 1.000 0.000 0.000
#> GSM1022359 2 0.0000 0.8491 0.000 1.000 0.000
#> GSM1022360 2 0.0000 0.8491 0.000 1.000 0.000
#> GSM1022361 2 0.0000 0.8491 0.000 1.000 0.000
#> GSM1022362 2 0.0000 0.8491 0.000 1.000 0.000
#> GSM1022367 2 0.6244 0.0926 0.000 0.560 0.440
#> GSM1022368 3 0.5327 0.6155 0.000 0.272 0.728
#> GSM1022369 3 0.2959 0.8376 0.000 0.100 0.900
#> GSM1022370 3 0.6305 0.1105 0.000 0.484 0.516
#> GSM1022363 2 0.0000 0.8491 0.000 1.000 0.000
#> GSM1022364 2 0.0000 0.8491 0.000 1.000 0.000
#> GSM1022365 2 0.0000 0.8491 0.000 1.000 0.000
#> GSM1022366 2 0.0000 0.8491 0.000 1.000 0.000
#> GSM1022374 2 0.5363 0.5996 0.276 0.724 0.000
#> GSM1022375 2 0.4931 0.6614 0.232 0.768 0.000
#> GSM1022376 2 0.5948 0.4432 0.360 0.640 0.000
#> GSM1022371 2 0.0000 0.8491 0.000 1.000 0.000
#> GSM1022372 2 0.0000 0.8491 0.000 1.000 0.000
#> GSM1022373 2 0.0000 0.8491 0.000 1.000 0.000
#> GSM1022377 2 0.5058 0.6849 0.244 0.756 0.000
#> GSM1022378 2 0.5138 0.6766 0.252 0.748 0.000
#> GSM1022379 2 0.6154 0.4240 0.408 0.592 0.000
#> GSM1022380 2 0.6244 0.3441 0.440 0.560 0.000
#> GSM1022385 3 0.0000 0.9200 0.000 0.000 1.000
#> GSM1022386 3 0.0000 0.9200 0.000 0.000 1.000
#> GSM1022387 3 0.0000 0.9200 0.000 0.000 1.000
#> GSM1022388 3 0.0000 0.9200 0.000 0.000 1.000
#> GSM1022381 2 0.5785 0.5712 0.332 0.668 0.000
#> GSM1022382 2 0.5785 0.5712 0.332 0.668 0.000
#> GSM1022383 2 0.5327 0.6549 0.272 0.728 0.000
#> GSM1022384 2 0.6079 0.4706 0.388 0.612 0.000
#> GSM1022393 1 0.0000 0.9680 1.000 0.000 0.000
#> GSM1022394 1 0.0000 0.9680 1.000 0.000 0.000
#> GSM1022395 1 0.0000 0.9680 1.000 0.000 0.000
#> GSM1022396 1 0.0000 0.9680 1.000 0.000 0.000
#> GSM1022389 1 0.2796 0.8750 0.908 0.092 0.000
#> GSM1022390 1 0.0747 0.9550 0.984 0.016 0.000
#> GSM1022391 1 0.4062 0.7695 0.836 0.164 0.000
#> GSM1022392 1 0.0237 0.9651 0.996 0.004 0.000
#> GSM1022397 3 0.0000 0.9200 0.000 0.000 1.000
#> GSM1022398 3 0.0000 0.9200 0.000 0.000 1.000
#> GSM1022399 3 0.0000 0.9200 0.000 0.000 1.000
#> GSM1022400 3 0.0000 0.9200 0.000 0.000 1.000
#> GSM1022401 1 0.0000 0.9680 1.000 0.000 0.000
#> GSM1022402 1 0.0000 0.9680 1.000 0.000 0.000
#> GSM1022403 1 0.0000 0.9680 1.000 0.000 0.000
#> GSM1022404 1 0.0000 0.9680 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1022325 2 0.2530 0.8736 0.000 0.888 0.000 0.112
#> GSM1022326 2 0.2530 0.8736 0.000 0.888 0.000 0.112
#> GSM1022327 2 0.2011 0.8784 0.000 0.920 0.000 0.080
#> GSM1022331 3 0.0000 0.9515 0.000 0.000 1.000 0.000
#> GSM1022332 3 0.0000 0.9515 0.000 0.000 1.000 0.000
#> GSM1022333 3 0.0000 0.9515 0.000 0.000 1.000 0.000
#> GSM1022328 2 0.0188 0.8785 0.000 0.996 0.000 0.004
#> GSM1022329 2 0.0469 0.8796 0.000 0.988 0.000 0.012
#> GSM1022330 2 0.0707 0.8802 0.000 0.980 0.000 0.020
#> GSM1022337 1 0.1022 0.8606 0.968 0.032 0.000 0.000
#> GSM1022338 1 0.1022 0.8606 0.968 0.032 0.000 0.000
#> GSM1022339 1 0.2011 0.8287 0.920 0.080 0.000 0.000
#> GSM1022334 2 0.2530 0.8736 0.000 0.888 0.000 0.112
#> GSM1022335 2 0.2469 0.8745 0.000 0.892 0.000 0.108
#> GSM1022336 2 0.2408 0.8753 0.000 0.896 0.000 0.104
#> GSM1022340 4 0.3123 0.8114 0.156 0.000 0.000 0.844
#> GSM1022341 4 0.3123 0.8114 0.156 0.000 0.000 0.844
#> GSM1022342 4 0.3123 0.8114 0.156 0.000 0.000 0.844
#> GSM1022343 4 0.3123 0.8114 0.156 0.000 0.000 0.844
#> GSM1022347 3 0.0000 0.9515 0.000 0.000 1.000 0.000
#> GSM1022348 3 0.0000 0.9515 0.000 0.000 1.000 0.000
#> GSM1022349 3 0.0000 0.9515 0.000 0.000 1.000 0.000
#> GSM1022350 3 0.0000 0.9515 0.000 0.000 1.000 0.000
#> GSM1022344 4 0.3444 0.7232 0.000 0.000 0.184 0.816
#> GSM1022345 4 0.3400 0.7266 0.000 0.000 0.180 0.820
#> GSM1022346 4 0.3400 0.7266 0.000 0.000 0.180 0.820
#> GSM1022355 1 0.3726 0.7336 0.788 0.000 0.000 0.212
#> GSM1022356 1 0.3172 0.7925 0.840 0.000 0.000 0.160
#> GSM1022357 1 0.4356 0.6020 0.708 0.000 0.000 0.292
#> GSM1022358 1 0.3528 0.7589 0.808 0.000 0.000 0.192
#> GSM1022351 4 0.3172 0.8096 0.160 0.000 0.000 0.840
#> GSM1022352 4 0.3172 0.8096 0.160 0.000 0.000 0.840
#> GSM1022353 4 0.3172 0.8096 0.160 0.000 0.000 0.840
#> GSM1022354 4 0.3219 0.8050 0.164 0.000 0.000 0.836
#> GSM1022359 2 0.0188 0.8770 0.004 0.996 0.000 0.000
#> GSM1022360 2 0.0188 0.8770 0.004 0.996 0.000 0.000
#> GSM1022361 2 0.0188 0.8770 0.004 0.996 0.000 0.000
#> GSM1022362 2 0.0188 0.8770 0.004 0.996 0.000 0.000
#> GSM1022367 3 0.4010 0.8092 0.028 0.156 0.816 0.000
#> GSM1022368 3 0.4010 0.8092 0.028 0.156 0.816 0.000
#> GSM1022369 3 0.4010 0.8092 0.028 0.156 0.816 0.000
#> GSM1022370 3 0.4010 0.8092 0.028 0.156 0.816 0.000
#> GSM1022363 2 0.0921 0.8662 0.028 0.972 0.000 0.000
#> GSM1022364 2 0.0921 0.8662 0.028 0.972 0.000 0.000
#> GSM1022365 2 0.0921 0.8662 0.028 0.972 0.000 0.000
#> GSM1022366 2 0.0817 0.8684 0.024 0.976 0.000 0.000
#> GSM1022374 1 0.3123 0.7614 0.844 0.156 0.000 0.000
#> GSM1022375 1 0.3123 0.7614 0.844 0.156 0.000 0.000
#> GSM1022376 1 0.3123 0.7614 0.844 0.156 0.000 0.000
#> GSM1022371 2 0.0592 0.8725 0.016 0.984 0.000 0.000
#> GSM1022372 2 0.0469 0.8741 0.012 0.988 0.000 0.000
#> GSM1022373 2 0.0707 0.8705 0.020 0.980 0.000 0.000
#> GSM1022377 2 0.3356 0.8488 0.000 0.824 0.000 0.176
#> GSM1022378 2 0.3400 0.8472 0.000 0.820 0.000 0.180
#> GSM1022379 2 0.4040 0.8069 0.000 0.752 0.000 0.248
#> GSM1022380 2 0.4406 0.7596 0.000 0.700 0.000 0.300
#> GSM1022385 3 0.0000 0.9515 0.000 0.000 1.000 0.000
#> GSM1022386 3 0.0000 0.9515 0.000 0.000 1.000 0.000
#> GSM1022387 3 0.0000 0.9515 0.000 0.000 1.000 0.000
#> GSM1022388 3 0.0000 0.9515 0.000 0.000 1.000 0.000
#> GSM1022381 2 0.4431 0.7523 0.000 0.696 0.000 0.304
#> GSM1022382 2 0.4406 0.7567 0.000 0.700 0.000 0.300
#> GSM1022383 2 0.4500 0.7375 0.000 0.684 0.000 0.316
#> GSM1022384 2 0.4933 0.5385 0.000 0.568 0.000 0.432
#> GSM1022393 1 0.1118 0.8817 0.964 0.000 0.000 0.036
#> GSM1022394 1 0.1211 0.8801 0.960 0.000 0.000 0.040
#> GSM1022395 1 0.1118 0.8817 0.964 0.000 0.000 0.036
#> GSM1022396 1 0.1118 0.8817 0.964 0.000 0.000 0.036
#> GSM1022389 2 0.3688 0.8338 0.000 0.792 0.000 0.208
#> GSM1022390 4 0.4790 -0.0454 0.000 0.380 0.000 0.620
#> GSM1022391 2 0.3942 0.8147 0.000 0.764 0.000 0.236
#> GSM1022392 4 0.4304 0.2835 0.000 0.284 0.000 0.716
#> GSM1022397 3 0.0000 0.9515 0.000 0.000 1.000 0.000
#> GSM1022398 3 0.0000 0.9515 0.000 0.000 1.000 0.000
#> GSM1022399 3 0.0000 0.9515 0.000 0.000 1.000 0.000
#> GSM1022400 3 0.0000 0.9515 0.000 0.000 1.000 0.000
#> GSM1022401 1 0.1118 0.8817 0.964 0.000 0.000 0.036
#> GSM1022402 1 0.1022 0.8808 0.968 0.000 0.000 0.032
#> GSM1022403 1 0.1118 0.8817 0.964 0.000 0.000 0.036
#> GSM1022404 1 0.1118 0.8817 0.964 0.000 0.000 0.036
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1022325 2 0.0880 0.7570 0.000 0.968 0.000 0.032 0.000
#> GSM1022326 2 0.0794 0.7605 0.000 0.972 0.000 0.028 0.000
#> GSM1022327 2 0.0703 0.7630 0.000 0.976 0.000 0.024 0.000
#> GSM1022331 3 0.1731 0.9027 0.012 0.000 0.940 0.040 0.008
#> GSM1022332 3 0.1569 0.9057 0.012 0.000 0.948 0.032 0.008
#> GSM1022333 3 0.1913 0.8991 0.016 0.000 0.932 0.044 0.008
#> GSM1022328 2 0.0510 0.7683 0.000 0.984 0.000 0.016 0.000
#> GSM1022329 2 0.0609 0.7669 0.000 0.980 0.000 0.020 0.000
#> GSM1022330 2 0.0609 0.7650 0.000 0.980 0.000 0.020 0.000
#> GSM1022337 5 0.0290 0.8755 0.000 0.000 0.000 0.008 0.992
#> GSM1022338 5 0.0290 0.8755 0.000 0.000 0.000 0.008 0.992
#> GSM1022339 5 0.0290 0.8755 0.000 0.000 0.000 0.008 0.992
#> GSM1022334 2 0.0963 0.7539 0.000 0.964 0.000 0.036 0.000
#> GSM1022335 2 0.1043 0.7558 0.000 0.960 0.000 0.040 0.000
#> GSM1022336 2 0.0963 0.7539 0.000 0.964 0.000 0.036 0.000
#> GSM1022340 1 0.1278 0.9163 0.960 0.000 0.004 0.016 0.020
#> GSM1022341 1 0.1278 0.9163 0.960 0.000 0.004 0.016 0.020
#> GSM1022342 1 0.1179 0.9155 0.964 0.000 0.004 0.016 0.016
#> GSM1022343 1 0.1179 0.9155 0.964 0.000 0.004 0.016 0.016
#> GSM1022347 3 0.1043 0.9007 0.040 0.000 0.960 0.000 0.000
#> GSM1022348 3 0.0404 0.9167 0.012 0.000 0.988 0.000 0.000
#> GSM1022349 3 0.0703 0.9117 0.024 0.000 0.976 0.000 0.000
#> GSM1022350 3 0.0510 0.9155 0.016 0.000 0.984 0.000 0.000
#> GSM1022344 1 0.2124 0.8606 0.900 0.000 0.096 0.004 0.000
#> GSM1022345 1 0.1502 0.8865 0.940 0.000 0.056 0.004 0.000
#> GSM1022346 1 0.1830 0.8797 0.924 0.000 0.068 0.008 0.000
#> GSM1022355 5 0.4171 0.3900 0.396 0.000 0.000 0.000 0.604
#> GSM1022356 5 0.3336 0.7136 0.228 0.000 0.000 0.000 0.772
#> GSM1022357 1 0.4283 0.0238 0.544 0.000 0.000 0.000 0.456
#> GSM1022358 5 0.4015 0.5068 0.348 0.000 0.000 0.000 0.652
#> GSM1022351 1 0.1364 0.9128 0.952 0.000 0.000 0.012 0.036
#> GSM1022352 1 0.1124 0.9132 0.960 0.000 0.000 0.004 0.036
#> GSM1022353 1 0.1205 0.9113 0.956 0.000 0.000 0.004 0.040
#> GSM1022354 1 0.1205 0.9113 0.956 0.000 0.000 0.004 0.040
#> GSM1022359 2 0.0404 0.7684 0.000 0.988 0.000 0.012 0.000
#> GSM1022360 2 0.0510 0.7677 0.000 0.984 0.000 0.016 0.000
#> GSM1022361 2 0.0510 0.7677 0.000 0.984 0.000 0.016 0.000
#> GSM1022362 2 0.0404 0.7682 0.000 0.988 0.000 0.012 0.000
#> GSM1022367 3 0.5947 0.7215 0.016 0.164 0.684 0.112 0.024
#> GSM1022368 3 0.5633 0.7537 0.016 0.136 0.716 0.108 0.024
#> GSM1022369 3 0.5543 0.7601 0.016 0.132 0.724 0.104 0.024
#> GSM1022370 3 0.5782 0.7376 0.016 0.156 0.700 0.104 0.024
#> GSM1022363 2 0.3409 0.6502 0.016 0.844 0.000 0.116 0.024
#> GSM1022364 2 0.3319 0.6546 0.016 0.848 0.000 0.116 0.020
#> GSM1022365 2 0.3319 0.6546 0.016 0.848 0.000 0.116 0.020
#> GSM1022366 2 0.3070 0.6671 0.016 0.860 0.000 0.112 0.012
#> GSM1022374 5 0.3241 0.7769 0.012 0.104 0.000 0.028 0.856
#> GSM1022375 5 0.3405 0.7704 0.012 0.104 0.000 0.036 0.848
#> GSM1022376 5 0.2452 0.8243 0.012 0.052 0.000 0.028 0.908
#> GSM1022371 2 0.0771 0.7612 0.000 0.976 0.000 0.020 0.004
#> GSM1022372 2 0.1041 0.7631 0.000 0.964 0.000 0.032 0.004
#> GSM1022373 2 0.0865 0.7590 0.000 0.972 0.000 0.024 0.004
#> GSM1022377 2 0.4905 -0.7976 0.024 0.500 0.000 0.476 0.000
#> GSM1022378 2 0.4978 -0.8047 0.028 0.496 0.000 0.476 0.000
#> GSM1022379 2 0.4978 -0.8047 0.028 0.496 0.000 0.476 0.000
#> GSM1022380 4 0.4980 0.7991 0.028 0.484 0.000 0.488 0.000
#> GSM1022385 3 0.0000 0.9181 0.000 0.000 1.000 0.000 0.000
#> GSM1022386 3 0.0000 0.9181 0.000 0.000 1.000 0.000 0.000
#> GSM1022387 3 0.0000 0.9181 0.000 0.000 1.000 0.000 0.000
#> GSM1022388 3 0.0000 0.9181 0.000 0.000 1.000 0.000 0.000
#> GSM1022381 4 0.5170 0.8695 0.032 0.440 0.000 0.524 0.004
#> GSM1022382 4 0.5170 0.8695 0.032 0.440 0.000 0.524 0.004
#> GSM1022383 4 0.5166 0.8704 0.032 0.436 0.000 0.528 0.004
#> GSM1022384 4 0.5106 0.8553 0.032 0.400 0.000 0.564 0.004
#> GSM1022393 5 0.1282 0.8889 0.044 0.000 0.000 0.004 0.952
#> GSM1022394 5 0.1357 0.8874 0.048 0.000 0.000 0.004 0.948
#> GSM1022395 5 0.1282 0.8889 0.044 0.000 0.000 0.004 0.952
#> GSM1022396 5 0.1282 0.8889 0.044 0.000 0.000 0.004 0.952
#> GSM1022389 2 0.4972 -0.8155 0.020 0.500 0.000 0.476 0.004
#> GSM1022390 4 0.5933 0.7775 0.084 0.348 0.000 0.556 0.012
#> GSM1022391 4 0.5382 0.8195 0.044 0.476 0.000 0.476 0.004
#> GSM1022392 4 0.5919 0.7398 0.092 0.316 0.000 0.580 0.012
#> GSM1022397 3 0.0579 0.9170 0.008 0.000 0.984 0.008 0.000
#> GSM1022398 3 0.0579 0.9170 0.008 0.000 0.984 0.008 0.000
#> GSM1022399 3 0.0693 0.9160 0.012 0.000 0.980 0.008 0.000
#> GSM1022400 3 0.0798 0.9148 0.016 0.000 0.976 0.008 0.000
#> GSM1022401 5 0.1282 0.8889 0.044 0.000 0.000 0.004 0.952
#> GSM1022402 5 0.1043 0.8878 0.040 0.000 0.000 0.000 0.960
#> GSM1022403 5 0.1357 0.8874 0.048 0.000 0.000 0.004 0.948
#> GSM1022404 5 0.1282 0.8889 0.044 0.000 0.000 0.004 0.952
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1022325 2 0.0777 0.671 0.000 0.972 0.000 0.024 0.000 0.004
#> GSM1022326 2 0.0603 0.672 0.000 0.980 0.000 0.016 0.000 0.004
#> GSM1022327 2 0.0692 0.672 0.000 0.976 0.000 0.020 0.000 0.004
#> GSM1022331 3 0.2527 0.648 0.000 0.000 0.832 0.000 0.000 0.168
#> GSM1022332 3 0.2135 0.747 0.000 0.000 0.872 0.000 0.000 0.128
#> GSM1022333 3 0.2854 0.509 0.000 0.000 0.792 0.000 0.000 0.208
#> GSM1022328 2 0.0717 0.674 0.000 0.976 0.000 0.016 0.000 0.008
#> GSM1022329 2 0.0622 0.675 0.000 0.980 0.000 0.012 0.000 0.008
#> GSM1022330 2 0.0622 0.675 0.000 0.980 0.000 0.012 0.000 0.008
#> GSM1022337 5 0.2425 0.839 0.000 0.004 0.000 0.024 0.884 0.088
#> GSM1022338 5 0.2373 0.840 0.000 0.004 0.000 0.024 0.888 0.084
#> GSM1022339 5 0.2526 0.837 0.000 0.004 0.000 0.024 0.876 0.096
#> GSM1022334 2 0.0260 0.673 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM1022335 2 0.0260 0.673 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM1022336 2 0.0260 0.673 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM1022340 1 0.0748 0.982 0.976 0.000 0.000 0.016 0.004 0.004
#> GSM1022341 1 0.0748 0.982 0.976 0.000 0.000 0.016 0.004 0.004
#> GSM1022342 1 0.0748 0.982 0.976 0.000 0.000 0.016 0.004 0.004
#> GSM1022343 1 0.0748 0.982 0.976 0.000 0.000 0.016 0.004 0.004
#> GSM1022347 3 0.0748 0.899 0.016 0.000 0.976 0.004 0.000 0.004
#> GSM1022348 3 0.0653 0.900 0.012 0.000 0.980 0.004 0.000 0.004
#> GSM1022349 3 0.0603 0.899 0.016 0.000 0.980 0.004 0.000 0.000
#> GSM1022350 3 0.0692 0.898 0.020 0.000 0.976 0.004 0.000 0.000
#> GSM1022344 1 0.0777 0.968 0.972 0.000 0.004 0.000 0.000 0.024
#> GSM1022345 1 0.1082 0.963 0.956 0.000 0.000 0.004 0.000 0.040
#> GSM1022346 1 0.1152 0.960 0.952 0.000 0.004 0.000 0.000 0.044
#> GSM1022355 5 0.3835 0.552 0.320 0.000 0.000 0.012 0.668 0.000
#> GSM1022356 5 0.3201 0.709 0.208 0.000 0.000 0.012 0.780 0.000
#> GSM1022357 5 0.4478 0.246 0.444 0.000 0.000 0.012 0.532 0.012
#> GSM1022358 5 0.3629 0.622 0.276 0.000 0.000 0.012 0.712 0.000
#> GSM1022351 1 0.0622 0.983 0.980 0.000 0.000 0.012 0.008 0.000
#> GSM1022352 1 0.0622 0.983 0.980 0.000 0.000 0.012 0.008 0.000
#> GSM1022353 1 0.0881 0.982 0.972 0.000 0.000 0.012 0.008 0.008
#> GSM1022354 1 0.0622 0.983 0.980 0.000 0.000 0.012 0.008 0.000
#> GSM1022359 2 0.3241 0.618 0.000 0.824 0.000 0.112 0.000 0.064
#> GSM1022360 2 0.3426 0.610 0.000 0.808 0.000 0.124 0.000 0.068
#> GSM1022361 2 0.3066 0.602 0.000 0.832 0.000 0.124 0.000 0.044
#> GSM1022362 2 0.3313 0.607 0.000 0.816 0.000 0.124 0.000 0.060
#> GSM1022367 6 0.3847 0.979 0.000 0.000 0.456 0.000 0.000 0.544
#> GSM1022368 6 0.3851 0.979 0.000 0.000 0.460 0.000 0.000 0.540
#> GSM1022369 6 0.3857 0.969 0.000 0.000 0.468 0.000 0.000 0.532
#> GSM1022370 6 0.3966 0.963 0.000 0.000 0.444 0.004 0.000 0.552
#> GSM1022363 2 0.4184 0.362 0.000 0.504 0.000 0.012 0.000 0.484
#> GSM1022364 2 0.4389 0.410 0.000 0.528 0.000 0.024 0.000 0.448
#> GSM1022365 2 0.4403 0.377 0.000 0.508 0.000 0.024 0.000 0.468
#> GSM1022366 2 0.4381 0.423 0.000 0.536 0.000 0.024 0.000 0.440
#> GSM1022374 5 0.3441 0.775 0.000 0.004 0.000 0.024 0.784 0.188
#> GSM1022375 5 0.3534 0.768 0.000 0.004 0.000 0.024 0.772 0.200
#> GSM1022376 5 0.3274 0.790 0.000 0.004 0.000 0.024 0.804 0.168
#> GSM1022371 2 0.2531 0.654 0.000 0.856 0.000 0.012 0.000 0.132
#> GSM1022372 2 0.2664 0.653 0.000 0.848 0.000 0.016 0.000 0.136
#> GSM1022373 2 0.2531 0.654 0.000 0.856 0.000 0.012 0.000 0.132
#> GSM1022377 4 0.4015 0.891 0.012 0.372 0.000 0.616 0.000 0.000
#> GSM1022378 4 0.4015 0.891 0.012 0.372 0.000 0.616 0.000 0.000
#> GSM1022379 4 0.4174 0.909 0.016 0.352 0.004 0.628 0.000 0.000
#> GSM1022380 4 0.4174 0.909 0.016 0.352 0.004 0.628 0.000 0.000
#> GSM1022385 3 0.0713 0.888 0.000 0.000 0.972 0.000 0.000 0.028
#> GSM1022386 3 0.0865 0.884 0.000 0.000 0.964 0.000 0.000 0.036
#> GSM1022387 3 0.1007 0.877 0.000 0.000 0.956 0.000 0.000 0.044
#> GSM1022388 3 0.0865 0.884 0.000 0.000 0.964 0.000 0.000 0.036
#> GSM1022381 4 0.4170 0.910 0.020 0.328 0.004 0.648 0.000 0.000
#> GSM1022382 4 0.4170 0.910 0.020 0.328 0.004 0.648 0.000 0.000
#> GSM1022383 4 0.4211 0.900 0.020 0.312 0.008 0.660 0.000 0.000
#> GSM1022384 4 0.4313 0.892 0.020 0.304 0.008 0.664 0.000 0.004
#> GSM1022393 5 0.0405 0.861 0.000 0.000 0.000 0.008 0.988 0.004
#> GSM1022394 5 0.0508 0.860 0.000 0.000 0.000 0.012 0.984 0.004
#> GSM1022395 5 0.0260 0.862 0.000 0.000 0.000 0.000 0.992 0.008
#> GSM1022396 5 0.0405 0.861 0.000 0.000 0.000 0.008 0.988 0.004
#> GSM1022389 2 0.5758 -0.549 0.016 0.484 0.000 0.412 0.076 0.012
#> GSM1022390 2 0.6482 -0.535 0.020 0.432 0.000 0.416 0.080 0.052
#> GSM1022391 2 0.5474 -0.578 0.020 0.488 0.000 0.436 0.044 0.012
#> GSM1022392 4 0.6427 0.482 0.020 0.400 0.000 0.452 0.080 0.048
#> GSM1022397 3 0.0748 0.898 0.016 0.000 0.976 0.004 0.000 0.004
#> GSM1022398 3 0.0748 0.898 0.016 0.000 0.976 0.004 0.000 0.004
#> GSM1022399 3 0.0748 0.898 0.016 0.000 0.976 0.004 0.000 0.004
#> GSM1022400 3 0.0862 0.895 0.016 0.000 0.972 0.004 0.000 0.008
#> GSM1022401 5 0.0260 0.862 0.000 0.000 0.000 0.000 0.992 0.008
#> GSM1022402 5 0.0520 0.862 0.000 0.000 0.000 0.008 0.984 0.008
#> GSM1022403 5 0.0146 0.862 0.000 0.000 0.000 0.004 0.996 0.000
#> GSM1022404 5 0.0146 0.862 0.000 0.000 0.000 0.004 0.996 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 protocol(p) cell.type(p) k
#> MAD:NMF 80 1.22e-07 6.13e-05 2
#> MAD:NMF 73 5.52e-12 1.39e-07 3
#> MAD:NMF 78 6.04e-11 8.24e-17 4
#> MAD:NMF 74 4.45e-13 3.24e-15 5
#> MAD:NMF 71 1.25e-23 6.35e-14 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "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 31589 rows and 80 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.624 0.914 0.957 0.4835 0.509 0.509
#> 3 3 0.926 0.929 0.969 0.3148 0.867 0.739
#> 4 4 0.973 0.902 0.965 0.0869 0.932 0.818
#> 5 5 0.864 0.893 0.870 0.0991 0.905 0.692
#> 6 6 0.912 0.873 0.915 0.0616 0.965 0.839
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] 3 4
There is also optional best \(k\) = 3 4 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM1022325 2 0.000 0.950 0.000 1.000
#> GSM1022326 2 0.000 0.950 0.000 1.000
#> GSM1022327 2 0.000 0.950 0.000 1.000
#> GSM1022331 2 0.795 0.705 0.240 0.760
#> GSM1022332 2 0.795 0.705 0.240 0.760
#> GSM1022333 2 0.795 0.705 0.240 0.760
#> GSM1022328 2 0.000 0.950 0.000 1.000
#> GSM1022329 2 0.000 0.950 0.000 1.000
#> GSM1022330 2 0.000 0.950 0.000 1.000
#> GSM1022337 2 0.795 0.705 0.240 0.760
#> GSM1022338 2 0.795 0.705 0.240 0.760
#> GSM1022339 2 0.795 0.705 0.240 0.760
#> GSM1022334 2 0.000 0.950 0.000 1.000
#> GSM1022335 2 0.000 0.950 0.000 1.000
#> GSM1022336 2 0.000 0.950 0.000 1.000
#> GSM1022340 1 0.000 0.951 1.000 0.000
#> GSM1022341 1 0.000 0.951 1.000 0.000
#> GSM1022342 1 0.000 0.951 1.000 0.000
#> GSM1022343 1 0.000 0.951 1.000 0.000
#> GSM1022347 1 0.000 0.951 1.000 0.000
#> GSM1022348 1 0.000 0.951 1.000 0.000
#> GSM1022349 1 0.000 0.951 1.000 0.000
#> GSM1022350 1 0.000 0.951 1.000 0.000
#> GSM1022344 1 0.000 0.951 1.000 0.000
#> GSM1022345 1 0.000 0.951 1.000 0.000
#> GSM1022346 1 0.000 0.951 1.000 0.000
#> GSM1022355 1 0.000 0.951 1.000 0.000
#> GSM1022356 1 0.000 0.951 1.000 0.000
#> GSM1022357 1 0.000 0.951 1.000 0.000
#> GSM1022358 1 0.000 0.951 1.000 0.000
#> GSM1022351 1 0.000 0.951 1.000 0.000
#> GSM1022352 1 0.000 0.951 1.000 0.000
#> GSM1022353 1 0.000 0.951 1.000 0.000
#> GSM1022354 1 0.000 0.951 1.000 0.000
#> GSM1022359 2 0.000 0.950 0.000 1.000
#> GSM1022360 2 0.000 0.950 0.000 1.000
#> GSM1022361 2 0.000 0.950 0.000 1.000
#> GSM1022362 2 0.000 0.950 0.000 1.000
#> GSM1022367 2 0.000 0.950 0.000 1.000
#> GSM1022368 2 0.000 0.950 0.000 1.000
#> GSM1022369 2 0.000 0.950 0.000 1.000
#> GSM1022370 2 0.000 0.950 0.000 1.000
#> GSM1022363 2 0.000 0.950 0.000 1.000
#> GSM1022364 2 0.000 0.950 0.000 1.000
#> GSM1022365 2 0.000 0.950 0.000 1.000
#> GSM1022366 2 0.000 0.950 0.000 1.000
#> GSM1022374 2 0.000 0.950 0.000 1.000
#> GSM1022375 2 0.000 0.950 0.000 1.000
#> GSM1022376 2 0.000 0.950 0.000 1.000
#> GSM1022371 2 0.000 0.950 0.000 1.000
#> GSM1022372 2 0.000 0.950 0.000 1.000
#> GSM1022373 2 0.000 0.950 0.000 1.000
#> GSM1022377 1 0.653 0.833 0.832 0.168
#> GSM1022378 1 0.653 0.833 0.832 0.168
#> GSM1022379 1 0.653 0.833 0.832 0.168
#> GSM1022380 1 0.653 0.833 0.832 0.168
#> GSM1022385 1 0.000 0.951 1.000 0.000
#> GSM1022386 1 0.000 0.951 1.000 0.000
#> GSM1022387 1 0.000 0.951 1.000 0.000
#> GSM1022388 1 0.000 0.951 1.000 0.000
#> GSM1022381 1 0.653 0.833 0.832 0.168
#> GSM1022382 1 0.653 0.833 0.832 0.168
#> GSM1022383 1 0.653 0.833 0.832 0.168
#> GSM1022384 1 0.653 0.833 0.832 0.168
#> GSM1022393 1 0.000 0.951 1.000 0.000
#> GSM1022394 1 0.000 0.951 1.000 0.000
#> GSM1022395 1 0.000 0.951 1.000 0.000
#> GSM1022396 1 0.000 0.951 1.000 0.000
#> GSM1022389 1 0.653 0.833 0.832 0.168
#> GSM1022390 1 0.653 0.833 0.832 0.168
#> GSM1022391 1 0.653 0.833 0.832 0.168
#> GSM1022392 1 0.653 0.833 0.832 0.168
#> GSM1022397 1 0.000 0.951 1.000 0.000
#> GSM1022398 1 0.000 0.951 1.000 0.000
#> GSM1022399 1 0.000 0.951 1.000 0.000
#> GSM1022400 1 0.000 0.951 1.000 0.000
#> GSM1022401 1 0.000 0.951 1.000 0.000
#> GSM1022402 1 0.000 0.951 1.000 0.000
#> GSM1022403 1 0.000 0.951 1.000 0.000
#> GSM1022404 1 0.000 0.951 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1022325 2 0.000 0.918 0 1.000 0.000
#> GSM1022326 2 0.000 0.918 0 1.000 0.000
#> GSM1022327 2 0.000 0.918 0 1.000 0.000
#> GSM1022331 2 0.615 0.418 0 0.592 0.408
#> GSM1022332 2 0.615 0.418 0 0.592 0.408
#> GSM1022333 2 0.615 0.418 0 0.592 0.408
#> GSM1022328 2 0.000 0.918 0 1.000 0.000
#> GSM1022329 2 0.000 0.918 0 1.000 0.000
#> GSM1022330 2 0.000 0.918 0 1.000 0.000
#> GSM1022337 2 0.615 0.418 0 0.592 0.408
#> GSM1022338 2 0.615 0.418 0 0.592 0.408
#> GSM1022339 2 0.615 0.418 0 0.592 0.408
#> GSM1022334 2 0.000 0.918 0 1.000 0.000
#> GSM1022335 2 0.000 0.918 0 1.000 0.000
#> GSM1022336 2 0.000 0.918 0 1.000 0.000
#> GSM1022340 1 0.000 1.000 1 0.000 0.000
#> GSM1022341 1 0.000 1.000 1 0.000 0.000
#> GSM1022342 1 0.000 1.000 1 0.000 0.000
#> GSM1022343 1 0.000 1.000 1 0.000 0.000
#> GSM1022347 1 0.000 1.000 1 0.000 0.000
#> GSM1022348 1 0.000 1.000 1 0.000 0.000
#> GSM1022349 1 0.000 1.000 1 0.000 0.000
#> GSM1022350 1 0.000 1.000 1 0.000 0.000
#> GSM1022344 1 0.000 1.000 1 0.000 0.000
#> GSM1022345 1 0.000 1.000 1 0.000 0.000
#> GSM1022346 1 0.000 1.000 1 0.000 0.000
#> GSM1022355 1 0.000 1.000 1 0.000 0.000
#> GSM1022356 1 0.000 1.000 1 0.000 0.000
#> GSM1022357 1 0.000 1.000 1 0.000 0.000
#> GSM1022358 1 0.000 1.000 1 0.000 0.000
#> GSM1022351 1 0.000 1.000 1 0.000 0.000
#> GSM1022352 1 0.000 1.000 1 0.000 0.000
#> GSM1022353 1 0.000 1.000 1 0.000 0.000
#> GSM1022354 1 0.000 1.000 1 0.000 0.000
#> GSM1022359 2 0.000 0.918 0 1.000 0.000
#> GSM1022360 2 0.000 0.918 0 1.000 0.000
#> GSM1022361 2 0.000 0.918 0 1.000 0.000
#> GSM1022362 2 0.000 0.918 0 1.000 0.000
#> GSM1022367 2 0.000 0.918 0 1.000 0.000
#> GSM1022368 2 0.000 0.918 0 1.000 0.000
#> GSM1022369 2 0.000 0.918 0 1.000 0.000
#> GSM1022370 2 0.000 0.918 0 1.000 0.000
#> GSM1022363 2 0.000 0.918 0 1.000 0.000
#> GSM1022364 2 0.000 0.918 0 1.000 0.000
#> GSM1022365 2 0.000 0.918 0 1.000 0.000
#> GSM1022366 2 0.000 0.918 0 1.000 0.000
#> GSM1022374 2 0.000 0.918 0 1.000 0.000
#> GSM1022375 2 0.000 0.918 0 1.000 0.000
#> GSM1022376 2 0.000 0.918 0 1.000 0.000
#> GSM1022371 2 0.000 0.918 0 1.000 0.000
#> GSM1022372 2 0.000 0.918 0 1.000 0.000
#> GSM1022373 2 0.000 0.918 0 1.000 0.000
#> GSM1022377 3 0.000 1.000 0 0.000 1.000
#> GSM1022378 3 0.000 1.000 0 0.000 1.000
#> GSM1022379 3 0.000 1.000 0 0.000 1.000
#> GSM1022380 3 0.000 1.000 0 0.000 1.000
#> GSM1022385 1 0.000 1.000 1 0.000 0.000
#> GSM1022386 1 0.000 1.000 1 0.000 0.000
#> GSM1022387 1 0.000 1.000 1 0.000 0.000
#> GSM1022388 1 0.000 1.000 1 0.000 0.000
#> GSM1022381 3 0.000 1.000 0 0.000 1.000
#> GSM1022382 3 0.000 1.000 0 0.000 1.000
#> GSM1022383 3 0.000 1.000 0 0.000 1.000
#> GSM1022384 3 0.000 1.000 0 0.000 1.000
#> GSM1022393 1 0.000 1.000 1 0.000 0.000
#> GSM1022394 1 0.000 1.000 1 0.000 0.000
#> GSM1022395 1 0.000 1.000 1 0.000 0.000
#> GSM1022396 1 0.000 1.000 1 0.000 0.000
#> GSM1022389 3 0.000 1.000 0 0.000 1.000
#> GSM1022390 3 0.000 1.000 0 0.000 1.000
#> GSM1022391 3 0.000 1.000 0 0.000 1.000
#> GSM1022392 3 0.000 1.000 0 0.000 1.000
#> GSM1022397 1 0.000 1.000 1 0.000 0.000
#> GSM1022398 1 0.000 1.000 1 0.000 0.000
#> GSM1022399 1 0.000 1.000 1 0.000 0.000
#> GSM1022400 1 0.000 1.000 1 0.000 0.000
#> GSM1022401 1 0.000 1.000 1 0.000 0.000
#> GSM1022402 1 0.000 1.000 1 0.000 0.000
#> GSM1022403 1 0.000 1.000 1 0.000 0.000
#> GSM1022404 1 0.000 1.000 1 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1022325 2 0.000 0.912 0 1.000 0.000 0
#> GSM1022326 2 0.000 0.912 0 1.000 0.000 0
#> GSM1022327 2 0.000 0.912 0 1.000 0.000 0
#> GSM1022331 3 0.000 0.802 0 0.000 1.000 0
#> GSM1022332 3 0.000 0.802 0 0.000 1.000 0
#> GSM1022333 3 0.000 0.802 0 0.000 1.000 0
#> GSM1022328 2 0.000 0.912 0 1.000 0.000 0
#> GSM1022329 2 0.000 0.912 0 1.000 0.000 0
#> GSM1022330 2 0.000 0.912 0 1.000 0.000 0
#> GSM1022337 3 0.000 0.802 0 0.000 1.000 0
#> GSM1022338 3 0.000 0.802 0 0.000 1.000 0
#> GSM1022339 3 0.000 0.802 0 0.000 1.000 0
#> GSM1022334 2 0.000 0.912 0 1.000 0.000 0
#> GSM1022335 2 0.000 0.912 0 1.000 0.000 0
#> GSM1022336 2 0.000 0.912 0 1.000 0.000 0
#> GSM1022340 1 0.000 1.000 1 0.000 0.000 0
#> GSM1022341 1 0.000 1.000 1 0.000 0.000 0
#> GSM1022342 1 0.000 1.000 1 0.000 0.000 0
#> GSM1022343 1 0.000 1.000 1 0.000 0.000 0
#> GSM1022347 1 0.000 1.000 1 0.000 0.000 0
#> GSM1022348 1 0.000 1.000 1 0.000 0.000 0
#> GSM1022349 1 0.000 1.000 1 0.000 0.000 0
#> GSM1022350 1 0.000 1.000 1 0.000 0.000 0
#> GSM1022344 1 0.000 1.000 1 0.000 0.000 0
#> GSM1022345 1 0.000 1.000 1 0.000 0.000 0
#> GSM1022346 1 0.000 1.000 1 0.000 0.000 0
#> GSM1022355 1 0.000 1.000 1 0.000 0.000 0
#> GSM1022356 1 0.000 1.000 1 0.000 0.000 0
#> GSM1022357 1 0.000 1.000 1 0.000 0.000 0
#> GSM1022358 1 0.000 1.000 1 0.000 0.000 0
#> GSM1022351 1 0.000 1.000 1 0.000 0.000 0
#> GSM1022352 1 0.000 1.000 1 0.000 0.000 0
#> GSM1022353 1 0.000 1.000 1 0.000 0.000 0
#> GSM1022354 1 0.000 1.000 1 0.000 0.000 0
#> GSM1022359 2 0.000 0.912 0 1.000 0.000 0
#> GSM1022360 2 0.000 0.912 0 1.000 0.000 0
#> GSM1022361 2 0.000 0.912 0 1.000 0.000 0
#> GSM1022362 2 0.000 0.912 0 1.000 0.000 0
#> GSM1022367 2 0.484 0.238 0 0.604 0.396 0
#> GSM1022368 2 0.484 0.238 0 0.604 0.396 0
#> GSM1022369 2 0.484 0.238 0 0.604 0.396 0
#> GSM1022370 2 0.484 0.238 0 0.604 0.396 0
#> GSM1022363 2 0.000 0.912 0 1.000 0.000 0
#> GSM1022364 2 0.000 0.912 0 1.000 0.000 0
#> GSM1022365 2 0.000 0.912 0 1.000 0.000 0
#> GSM1022366 2 0.000 0.912 0 1.000 0.000 0
#> GSM1022374 3 0.488 0.386 0 0.408 0.592 0
#> GSM1022375 3 0.488 0.386 0 0.408 0.592 0
#> GSM1022376 3 0.488 0.386 0 0.408 0.592 0
#> GSM1022371 2 0.000 0.912 0 1.000 0.000 0
#> GSM1022372 2 0.000 0.912 0 1.000 0.000 0
#> GSM1022373 2 0.000 0.912 0 1.000 0.000 0
#> GSM1022377 4 0.000 1.000 0 0.000 0.000 1
#> GSM1022378 4 0.000 1.000 0 0.000 0.000 1
#> GSM1022379 4 0.000 1.000 0 0.000 0.000 1
#> GSM1022380 4 0.000 1.000 0 0.000 0.000 1
#> GSM1022385 1 0.000 1.000 1 0.000 0.000 0
#> GSM1022386 1 0.000 1.000 1 0.000 0.000 0
#> GSM1022387 1 0.000 1.000 1 0.000 0.000 0
#> GSM1022388 1 0.000 1.000 1 0.000 0.000 0
#> GSM1022381 4 0.000 1.000 0 0.000 0.000 1
#> GSM1022382 4 0.000 1.000 0 0.000 0.000 1
#> GSM1022383 4 0.000 1.000 0 0.000 0.000 1
#> GSM1022384 4 0.000 1.000 0 0.000 0.000 1
#> GSM1022393 1 0.000 1.000 1 0.000 0.000 0
#> GSM1022394 1 0.000 1.000 1 0.000 0.000 0
#> GSM1022395 1 0.000 1.000 1 0.000 0.000 0
#> GSM1022396 1 0.000 1.000 1 0.000 0.000 0
#> GSM1022389 4 0.000 1.000 0 0.000 0.000 1
#> GSM1022390 4 0.000 1.000 0 0.000 0.000 1
#> GSM1022391 4 0.000 1.000 0 0.000 0.000 1
#> GSM1022392 4 0.000 1.000 0 0.000 0.000 1
#> GSM1022397 1 0.000 1.000 1 0.000 0.000 0
#> GSM1022398 1 0.000 1.000 1 0.000 0.000 0
#> GSM1022399 1 0.000 1.000 1 0.000 0.000 0
#> GSM1022400 1 0.000 1.000 1 0.000 0.000 0
#> GSM1022401 1 0.000 1.000 1 0.000 0.000 0
#> GSM1022402 1 0.000 1.000 1 0.000 0.000 0
#> GSM1022403 1 0.000 1.000 1 0.000 0.000 0
#> GSM1022404 1 0.000 1.000 1 0.000 0.000 0
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1022325 2 0.000 0.913 0.000 1.000 0.000 0 0.000
#> GSM1022326 2 0.000 0.913 0.000 1.000 0.000 0 0.000
#> GSM1022327 2 0.000 0.913 0.000 1.000 0.000 0 0.000
#> GSM1022331 5 0.382 0.678 0.000 0.000 0.304 0 0.696
#> GSM1022332 5 0.382 0.678 0.000 0.000 0.304 0 0.696
#> GSM1022333 5 0.382 0.678 0.000 0.000 0.304 0 0.696
#> GSM1022328 2 0.000 0.913 0.000 1.000 0.000 0 0.000
#> GSM1022329 2 0.000 0.913 0.000 1.000 0.000 0 0.000
#> GSM1022330 2 0.000 0.913 0.000 1.000 0.000 0 0.000
#> GSM1022337 5 0.000 0.711 0.000 0.000 0.000 0 1.000
#> GSM1022338 5 0.000 0.711 0.000 0.000 0.000 0 1.000
#> GSM1022339 5 0.000 0.711 0.000 0.000 0.000 0 1.000
#> GSM1022334 2 0.000 0.913 0.000 1.000 0.000 0 0.000
#> GSM1022335 2 0.000 0.913 0.000 1.000 0.000 0 0.000
#> GSM1022336 2 0.000 0.913 0.000 1.000 0.000 0 0.000
#> GSM1022340 1 0.029 0.990 0.992 0.000 0.008 0 0.000
#> GSM1022341 1 0.029 0.990 0.992 0.000 0.008 0 0.000
#> GSM1022342 1 0.029 0.990 0.992 0.000 0.008 0 0.000
#> GSM1022343 1 0.029 0.990 0.992 0.000 0.008 0 0.000
#> GSM1022347 3 0.382 1.000 0.304 0.000 0.696 0 0.000
#> GSM1022348 3 0.382 1.000 0.304 0.000 0.696 0 0.000
#> GSM1022349 3 0.382 1.000 0.304 0.000 0.696 0 0.000
#> GSM1022350 3 0.382 1.000 0.304 0.000 0.696 0 0.000
#> GSM1022344 3 0.382 1.000 0.304 0.000 0.696 0 0.000
#> GSM1022345 3 0.382 1.000 0.304 0.000 0.696 0 0.000
#> GSM1022346 3 0.382 1.000 0.304 0.000 0.696 0 0.000
#> GSM1022355 1 0.000 0.998 1.000 0.000 0.000 0 0.000
#> GSM1022356 1 0.000 0.998 1.000 0.000 0.000 0 0.000
#> GSM1022357 1 0.000 0.998 1.000 0.000 0.000 0 0.000
#> GSM1022358 1 0.000 0.998 1.000 0.000 0.000 0 0.000
#> GSM1022351 1 0.000 0.998 1.000 0.000 0.000 0 0.000
#> GSM1022352 1 0.000 0.998 1.000 0.000 0.000 0 0.000
#> GSM1022353 1 0.000 0.998 1.000 0.000 0.000 0 0.000
#> GSM1022354 1 0.000 0.998 1.000 0.000 0.000 0 0.000
#> GSM1022359 2 0.000 0.913 0.000 1.000 0.000 0 0.000
#> GSM1022360 2 0.000 0.913 0.000 1.000 0.000 0 0.000
#> GSM1022361 2 0.000 0.913 0.000 1.000 0.000 0 0.000
#> GSM1022362 2 0.000 0.913 0.000 1.000 0.000 0 0.000
#> GSM1022367 2 0.534 0.277 0.000 0.604 0.072 0 0.324
#> GSM1022368 2 0.534 0.277 0.000 0.604 0.072 0 0.324
#> GSM1022369 2 0.534 0.277 0.000 0.604 0.072 0 0.324
#> GSM1022370 2 0.534 0.277 0.000 0.604 0.072 0 0.324
#> GSM1022363 2 0.000 0.913 0.000 1.000 0.000 0 0.000
#> GSM1022364 2 0.000 0.913 0.000 1.000 0.000 0 0.000
#> GSM1022365 2 0.000 0.913 0.000 1.000 0.000 0 0.000
#> GSM1022366 2 0.000 0.913 0.000 1.000 0.000 0 0.000
#> GSM1022374 5 0.420 0.323 0.000 0.408 0.000 0 0.592
#> GSM1022375 5 0.420 0.323 0.000 0.408 0.000 0 0.592
#> GSM1022376 5 0.420 0.323 0.000 0.408 0.000 0 0.592
#> GSM1022371 2 0.000 0.913 0.000 1.000 0.000 0 0.000
#> GSM1022372 2 0.000 0.913 0.000 1.000 0.000 0 0.000
#> GSM1022373 2 0.000 0.913 0.000 1.000 0.000 0 0.000
#> GSM1022377 4 0.000 1.000 0.000 0.000 0.000 1 0.000
#> GSM1022378 4 0.000 1.000 0.000 0.000 0.000 1 0.000
#> GSM1022379 4 0.000 1.000 0.000 0.000 0.000 1 0.000
#> GSM1022380 4 0.000 1.000 0.000 0.000 0.000 1 0.000
#> GSM1022385 3 0.382 1.000 0.304 0.000 0.696 0 0.000
#> GSM1022386 3 0.382 1.000 0.304 0.000 0.696 0 0.000
#> GSM1022387 3 0.382 1.000 0.304 0.000 0.696 0 0.000
#> GSM1022388 3 0.382 1.000 0.304 0.000 0.696 0 0.000
#> GSM1022381 4 0.000 1.000 0.000 0.000 0.000 1 0.000
#> GSM1022382 4 0.000 1.000 0.000 0.000 0.000 1 0.000
#> GSM1022383 4 0.000 1.000 0.000 0.000 0.000 1 0.000
#> GSM1022384 4 0.000 1.000 0.000 0.000 0.000 1 0.000
#> GSM1022393 1 0.000 0.998 1.000 0.000 0.000 0 0.000
#> GSM1022394 1 0.000 0.998 1.000 0.000 0.000 0 0.000
#> GSM1022395 1 0.000 0.998 1.000 0.000 0.000 0 0.000
#> GSM1022396 1 0.000 0.998 1.000 0.000 0.000 0 0.000
#> GSM1022389 4 0.000 1.000 0.000 0.000 0.000 1 0.000
#> GSM1022390 4 0.000 1.000 0.000 0.000 0.000 1 0.000
#> GSM1022391 4 0.000 1.000 0.000 0.000 0.000 1 0.000
#> GSM1022392 4 0.000 1.000 0.000 0.000 0.000 1 0.000
#> GSM1022397 3 0.382 1.000 0.304 0.000 0.696 0 0.000
#> GSM1022398 3 0.382 1.000 0.304 0.000 0.696 0 0.000
#> GSM1022399 3 0.382 1.000 0.304 0.000 0.696 0 0.000
#> GSM1022400 3 0.382 1.000 0.304 0.000 0.696 0 0.000
#> GSM1022401 1 0.000 0.998 1.000 0.000 0.000 0 0.000
#> GSM1022402 1 0.000 0.998 1.000 0.000 0.000 0 0.000
#> GSM1022403 1 0.000 0.998 1.000 0.000 0.000 0 0.000
#> GSM1022404 1 0.000 0.998 1.000 0.000 0.000 0 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1022325 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022326 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022327 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022331 6 0.377 0.157 0.000 0.000 0.000 0 0.408 0.592
#> GSM1022332 6 0.377 0.157 0.000 0.000 0.000 0 0.408 0.592
#> GSM1022333 6 0.377 0.157 0.000 0.000 0.000 0 0.408 0.592
#> GSM1022328 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022329 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022330 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022337 5 0.000 0.569 0.000 0.000 0.000 0 1.000 0.000
#> GSM1022338 5 0.000 0.569 0.000 0.000 0.000 0 1.000 0.000
#> GSM1022339 5 0.000 0.569 0.000 0.000 0.000 0 1.000 0.000
#> GSM1022334 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022335 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022336 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022340 1 0.026 0.892 0.992 0.000 0.008 0 0.000 0.000
#> GSM1022341 1 0.026 0.892 0.992 0.000 0.008 0 0.000 0.000
#> GSM1022342 1 0.026 0.892 0.992 0.000 0.008 0 0.000 0.000
#> GSM1022343 1 0.026 0.892 0.992 0.000 0.008 0 0.000 0.000
#> GSM1022347 3 0.000 0.998 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022348 3 0.000 0.998 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022349 3 0.000 0.998 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022350 3 0.000 0.998 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022344 3 0.000 0.998 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022345 3 0.000 0.998 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022346 3 0.000 0.998 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022355 1 0.000 0.895 1.000 0.000 0.000 0 0.000 0.000
#> GSM1022356 1 0.000 0.895 1.000 0.000 0.000 0 0.000 0.000
#> GSM1022357 1 0.000 0.895 1.000 0.000 0.000 0 0.000 0.000
#> GSM1022358 1 0.000 0.895 1.000 0.000 0.000 0 0.000 0.000
#> GSM1022351 1 0.000 0.895 1.000 0.000 0.000 0 0.000 0.000
#> GSM1022352 1 0.000 0.895 1.000 0.000 0.000 0 0.000 0.000
#> GSM1022353 1 0.000 0.895 1.000 0.000 0.000 0 0.000 0.000
#> GSM1022354 1 0.000 0.895 1.000 0.000 0.000 0 0.000 0.000
#> GSM1022359 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022360 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022361 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022362 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022367 6 0.503 0.436 0.000 0.460 0.000 0 0.072 0.468
#> GSM1022368 6 0.503 0.436 0.000 0.460 0.000 0 0.072 0.468
#> GSM1022369 6 0.503 0.436 0.000 0.460 0.000 0 0.072 0.468
#> GSM1022370 6 0.503 0.436 0.000 0.460 0.000 0 0.072 0.468
#> GSM1022363 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022364 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022365 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022366 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022374 5 0.525 0.506 0.000 0.264 0.000 0 0.592 0.144
#> GSM1022375 5 0.525 0.506 0.000 0.264 0.000 0 0.592 0.144
#> GSM1022376 5 0.525 0.506 0.000 0.264 0.000 0 0.592 0.144
#> GSM1022371 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022372 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022373 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022377 4 0.000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM1022378 4 0.000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM1022379 4 0.000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM1022380 4 0.000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM1022385 3 0.026 0.994 0.000 0.000 0.992 0 0.000 0.008
#> GSM1022386 3 0.026 0.994 0.000 0.000 0.992 0 0.000 0.008
#> GSM1022387 3 0.026 0.994 0.000 0.000 0.992 0 0.000 0.008
#> GSM1022388 3 0.026 0.994 0.000 0.000 0.992 0 0.000 0.008
#> GSM1022381 4 0.000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM1022382 4 0.000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM1022383 4 0.000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM1022384 4 0.000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM1022393 1 0.317 0.838 0.744 0.000 0.000 0 0.000 0.256
#> GSM1022394 1 0.317 0.838 0.744 0.000 0.000 0 0.000 0.256
#> GSM1022395 1 0.317 0.838 0.744 0.000 0.000 0 0.000 0.256
#> GSM1022396 1 0.317 0.838 0.744 0.000 0.000 0 0.000 0.256
#> GSM1022389 4 0.000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM1022390 4 0.000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM1022391 4 0.000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM1022392 4 0.000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM1022397 3 0.000 0.998 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022398 3 0.000 0.998 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022399 3 0.000 0.998 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022400 3 0.000 0.998 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022401 1 0.317 0.838 0.744 0.000 0.000 0 0.000 0.256
#> GSM1022402 1 0.317 0.838 0.744 0.000 0.000 0 0.000 0.256
#> GSM1022403 1 0.317 0.838 0.744 0.000 0.000 0 0.000 0.256
#> GSM1022404 1 0.317 0.838 0.744 0.000 0.000 0 0.000 0.256
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 protocol(p) cell.type(p) k
#> ATC:hclust 80 1.10e-11 4.22e-01 2
#> ATC:hclust 74 3.84e-13 1.93e-05 3
#> ATC:hclust 73 4.00e-13 4.34e-09 4
#> ATC:hclust 73 9.57e-20 9.15e-09 5
#> ATC:hclust 73 9.57e-20 9.15e-09 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 31589 rows and 80 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4913 0.509 0.509
#> 3 3 0.788 0.943 0.912 0.2475 0.867 0.739
#> 4 4 0.803 0.720 0.819 0.1369 0.949 0.864
#> 5 5 0.768 0.673 0.745 0.0720 0.905 0.708
#> 6 6 0.723 0.811 0.796 0.0604 0.903 0.631
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
#> GSM1022325 2 0 1 0 1
#> GSM1022326 2 0 1 0 1
#> GSM1022327 2 0 1 0 1
#> GSM1022331 2 0 1 0 1
#> GSM1022332 2 0 1 0 1
#> GSM1022333 2 0 1 0 1
#> GSM1022328 2 0 1 0 1
#> GSM1022329 2 0 1 0 1
#> GSM1022330 2 0 1 0 1
#> GSM1022337 2 0 1 0 1
#> GSM1022338 2 0 1 0 1
#> GSM1022339 2 0 1 0 1
#> GSM1022334 2 0 1 0 1
#> GSM1022335 2 0 1 0 1
#> GSM1022336 2 0 1 0 1
#> GSM1022340 1 0 1 1 0
#> GSM1022341 1 0 1 1 0
#> GSM1022342 1 0 1 1 0
#> GSM1022343 1 0 1 1 0
#> GSM1022347 1 0 1 1 0
#> GSM1022348 1 0 1 1 0
#> GSM1022349 1 0 1 1 0
#> GSM1022350 1 0 1 1 0
#> GSM1022344 1 0 1 1 0
#> GSM1022345 1 0 1 1 0
#> GSM1022346 1 0 1 1 0
#> GSM1022355 1 0 1 1 0
#> GSM1022356 1 0 1 1 0
#> GSM1022357 1 0 1 1 0
#> GSM1022358 1 0 1 1 0
#> GSM1022351 1 0 1 1 0
#> GSM1022352 1 0 1 1 0
#> GSM1022353 1 0 1 1 0
#> GSM1022354 1 0 1 1 0
#> GSM1022359 2 0 1 0 1
#> GSM1022360 2 0 1 0 1
#> GSM1022361 2 0 1 0 1
#> GSM1022362 2 0 1 0 1
#> GSM1022367 2 0 1 0 1
#> GSM1022368 2 0 1 0 1
#> GSM1022369 2 0 1 0 1
#> GSM1022370 2 0 1 0 1
#> GSM1022363 2 0 1 0 1
#> GSM1022364 2 0 1 0 1
#> GSM1022365 2 0 1 0 1
#> GSM1022366 2 0 1 0 1
#> GSM1022374 2 0 1 0 1
#> GSM1022375 2 0 1 0 1
#> GSM1022376 2 0 1 0 1
#> GSM1022371 2 0 1 0 1
#> GSM1022372 2 0 1 0 1
#> GSM1022373 2 0 1 0 1
#> GSM1022377 1 0 1 1 0
#> GSM1022378 1 0 1 1 0
#> GSM1022379 1 0 1 1 0
#> GSM1022380 1 0 1 1 0
#> GSM1022385 1 0 1 1 0
#> GSM1022386 1 0 1 1 0
#> GSM1022387 1 0 1 1 0
#> GSM1022388 1 0 1 1 0
#> GSM1022381 1 0 1 1 0
#> GSM1022382 1 0 1 1 0
#> GSM1022383 1 0 1 1 0
#> GSM1022384 1 0 1 1 0
#> GSM1022393 1 0 1 1 0
#> GSM1022394 1 0 1 1 0
#> GSM1022395 1 0 1 1 0
#> GSM1022396 1 0 1 1 0
#> GSM1022389 1 0 1 1 0
#> GSM1022390 1 0 1 1 0
#> GSM1022391 1 0 1 1 0
#> GSM1022392 1 0 1 1 0
#> GSM1022397 1 0 1 1 0
#> GSM1022398 1 0 1 1 0
#> GSM1022399 1 0 1 1 0
#> GSM1022400 1 0 1 1 0
#> GSM1022401 1 0 1 1 0
#> GSM1022402 1 0 1 1 0
#> GSM1022403 1 0 1 1 0
#> GSM1022404 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1022325 2 0.1289 0.901 0.000 0.968 0.032
#> GSM1022326 2 0.1289 0.901 0.000 0.968 0.032
#> GSM1022327 2 0.1289 0.901 0.000 0.968 0.032
#> GSM1022331 2 0.6204 0.681 0.000 0.576 0.424
#> GSM1022332 2 0.6204 0.681 0.000 0.576 0.424
#> GSM1022333 2 0.6204 0.681 0.000 0.576 0.424
#> GSM1022328 2 0.1289 0.901 0.000 0.968 0.032
#> GSM1022329 2 0.1289 0.901 0.000 0.968 0.032
#> GSM1022330 2 0.1289 0.901 0.000 0.968 0.032
#> GSM1022337 2 0.5431 0.825 0.000 0.716 0.284
#> GSM1022338 2 0.5431 0.825 0.000 0.716 0.284
#> GSM1022339 2 0.5254 0.837 0.000 0.736 0.264
#> GSM1022334 2 0.1289 0.901 0.000 0.968 0.032
#> GSM1022335 2 0.1289 0.901 0.000 0.968 0.032
#> GSM1022336 2 0.1289 0.901 0.000 0.968 0.032
#> GSM1022340 1 0.0000 0.997 1.000 0.000 0.000
#> GSM1022341 1 0.0000 0.997 1.000 0.000 0.000
#> GSM1022342 1 0.0000 0.997 1.000 0.000 0.000
#> GSM1022343 1 0.0000 0.997 1.000 0.000 0.000
#> GSM1022347 1 0.0000 0.997 1.000 0.000 0.000
#> GSM1022348 1 0.0000 0.997 1.000 0.000 0.000
#> GSM1022349 1 0.0000 0.997 1.000 0.000 0.000
#> GSM1022350 1 0.0000 0.997 1.000 0.000 0.000
#> GSM1022344 1 0.0000 0.997 1.000 0.000 0.000
#> GSM1022345 1 0.0000 0.997 1.000 0.000 0.000
#> GSM1022346 1 0.0000 0.997 1.000 0.000 0.000
#> GSM1022355 1 0.0237 0.997 0.996 0.000 0.004
#> GSM1022356 1 0.0237 0.997 0.996 0.000 0.004
#> GSM1022357 1 0.0237 0.997 0.996 0.000 0.004
#> GSM1022358 1 0.0237 0.997 0.996 0.000 0.004
#> GSM1022351 1 0.0237 0.997 0.996 0.000 0.004
#> GSM1022352 1 0.0237 0.997 0.996 0.000 0.004
#> GSM1022353 1 0.0237 0.997 0.996 0.000 0.004
#> GSM1022354 1 0.0237 0.997 0.996 0.000 0.004
#> GSM1022359 2 0.0000 0.902 0.000 1.000 0.000
#> GSM1022360 2 0.0000 0.902 0.000 1.000 0.000
#> GSM1022361 2 0.0000 0.902 0.000 1.000 0.000
#> GSM1022362 2 0.0000 0.902 0.000 1.000 0.000
#> GSM1022367 2 0.4605 0.855 0.000 0.796 0.204
#> GSM1022368 2 0.4605 0.855 0.000 0.796 0.204
#> GSM1022369 2 0.4605 0.855 0.000 0.796 0.204
#> GSM1022370 2 0.4555 0.856 0.000 0.800 0.200
#> GSM1022363 2 0.0000 0.902 0.000 1.000 0.000
#> GSM1022364 2 0.0000 0.902 0.000 1.000 0.000
#> GSM1022365 2 0.0000 0.902 0.000 1.000 0.000
#> GSM1022366 2 0.0000 0.902 0.000 1.000 0.000
#> GSM1022374 2 0.4555 0.856 0.000 0.800 0.200
#> GSM1022375 2 0.4555 0.856 0.000 0.800 0.200
#> GSM1022376 2 0.4555 0.856 0.000 0.800 0.200
#> GSM1022371 2 0.0000 0.902 0.000 1.000 0.000
#> GSM1022372 2 0.0000 0.902 0.000 1.000 0.000
#> GSM1022373 2 0.0000 0.902 0.000 1.000 0.000
#> GSM1022377 3 0.5291 0.998 0.268 0.000 0.732
#> GSM1022378 3 0.5291 0.998 0.268 0.000 0.732
#> GSM1022379 3 0.5291 0.998 0.268 0.000 0.732
#> GSM1022380 3 0.5291 0.998 0.268 0.000 0.732
#> GSM1022385 1 0.0000 0.997 1.000 0.000 0.000
#> GSM1022386 1 0.0000 0.997 1.000 0.000 0.000
#> GSM1022387 1 0.0000 0.997 1.000 0.000 0.000
#> GSM1022388 1 0.0000 0.997 1.000 0.000 0.000
#> GSM1022381 3 0.5291 0.998 0.268 0.000 0.732
#> GSM1022382 3 0.5291 0.998 0.268 0.000 0.732
#> GSM1022383 3 0.5291 0.998 0.268 0.000 0.732
#> GSM1022384 3 0.5291 0.998 0.268 0.000 0.732
#> GSM1022393 1 0.0237 0.997 0.996 0.000 0.004
#> GSM1022394 1 0.0237 0.997 0.996 0.000 0.004
#> GSM1022395 1 0.0237 0.997 0.996 0.000 0.004
#> GSM1022396 1 0.0237 0.997 0.996 0.000 0.004
#> GSM1022389 3 0.5254 0.996 0.264 0.000 0.736
#> GSM1022390 3 0.5254 0.996 0.264 0.000 0.736
#> GSM1022391 3 0.5254 0.996 0.264 0.000 0.736
#> GSM1022392 3 0.5254 0.996 0.264 0.000 0.736
#> GSM1022397 1 0.0000 0.997 1.000 0.000 0.000
#> GSM1022398 1 0.0000 0.997 1.000 0.000 0.000
#> GSM1022399 1 0.0000 0.997 1.000 0.000 0.000
#> GSM1022400 1 0.0000 0.997 1.000 0.000 0.000
#> GSM1022401 1 0.0237 0.997 0.996 0.000 0.004
#> GSM1022402 1 0.0237 0.997 0.996 0.000 0.004
#> GSM1022403 1 0.0237 0.997 0.996 0.000 0.004
#> GSM1022404 1 0.0237 0.997 0.996 0.000 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1022325 2 0.1975 0.758 0.000 0.936 0.016 0.048
#> GSM1022326 2 0.1975 0.758 0.000 0.936 0.016 0.048
#> GSM1022327 2 0.1975 0.758 0.000 0.936 0.016 0.048
#> GSM1022331 3 0.6644 0.871 0.000 0.392 0.520 0.088
#> GSM1022332 3 0.6644 0.871 0.000 0.392 0.520 0.088
#> GSM1022333 3 0.6644 0.871 0.000 0.392 0.520 0.088
#> GSM1022328 2 0.1975 0.758 0.000 0.936 0.016 0.048
#> GSM1022329 2 0.1975 0.758 0.000 0.936 0.016 0.048
#> GSM1022330 2 0.1975 0.758 0.000 0.936 0.016 0.048
#> GSM1022337 3 0.5503 0.851 0.000 0.468 0.516 0.016
#> GSM1022338 3 0.5503 0.851 0.000 0.468 0.516 0.016
#> GSM1022339 3 0.5163 0.821 0.000 0.480 0.516 0.004
#> GSM1022334 2 0.1975 0.758 0.000 0.936 0.016 0.048
#> GSM1022335 2 0.1975 0.758 0.000 0.936 0.016 0.048
#> GSM1022336 2 0.1975 0.758 0.000 0.936 0.016 0.048
#> GSM1022340 1 0.3074 0.778 0.848 0.000 0.152 0.000
#> GSM1022341 1 0.3074 0.778 0.848 0.000 0.152 0.000
#> GSM1022342 1 0.3074 0.778 0.848 0.000 0.152 0.000
#> GSM1022343 1 0.2973 0.777 0.856 0.000 0.144 0.000
#> GSM1022347 1 0.0000 0.766 1.000 0.000 0.000 0.000
#> GSM1022348 1 0.0000 0.766 1.000 0.000 0.000 0.000
#> GSM1022349 1 0.0000 0.766 1.000 0.000 0.000 0.000
#> GSM1022350 1 0.0000 0.766 1.000 0.000 0.000 0.000
#> GSM1022344 1 0.0000 0.766 1.000 0.000 0.000 0.000
#> GSM1022345 1 0.0000 0.766 1.000 0.000 0.000 0.000
#> GSM1022346 1 0.0000 0.766 1.000 0.000 0.000 0.000
#> GSM1022355 1 0.4933 0.761 0.568 0.000 0.432 0.000
#> GSM1022356 1 0.4933 0.761 0.568 0.000 0.432 0.000
#> GSM1022357 1 0.4933 0.761 0.568 0.000 0.432 0.000
#> GSM1022358 1 0.4933 0.761 0.568 0.000 0.432 0.000
#> GSM1022351 1 0.4933 0.761 0.568 0.000 0.432 0.000
#> GSM1022352 1 0.4933 0.761 0.568 0.000 0.432 0.000
#> GSM1022353 1 0.4933 0.761 0.568 0.000 0.432 0.000
#> GSM1022354 1 0.4933 0.761 0.568 0.000 0.432 0.000
#> GSM1022359 2 0.0000 0.767 0.000 1.000 0.000 0.000
#> GSM1022360 2 0.0000 0.767 0.000 1.000 0.000 0.000
#> GSM1022361 2 0.0000 0.767 0.000 1.000 0.000 0.000
#> GSM1022362 2 0.0000 0.767 0.000 1.000 0.000 0.000
#> GSM1022367 2 0.5530 -0.229 0.000 0.632 0.336 0.032
#> GSM1022368 2 0.5530 -0.229 0.000 0.632 0.336 0.032
#> GSM1022369 2 0.5530 -0.229 0.000 0.632 0.336 0.032
#> GSM1022370 2 0.5473 -0.172 0.000 0.644 0.324 0.032
#> GSM1022363 2 0.0592 0.761 0.000 0.984 0.000 0.016
#> GSM1022364 2 0.0592 0.761 0.000 0.984 0.000 0.016
#> GSM1022365 2 0.0592 0.761 0.000 0.984 0.000 0.016
#> GSM1022366 2 0.0592 0.761 0.000 0.984 0.000 0.016
#> GSM1022374 2 0.5538 -0.171 0.000 0.644 0.320 0.036
#> GSM1022375 2 0.5538 -0.171 0.000 0.644 0.320 0.036
#> GSM1022376 2 0.5538 -0.171 0.000 0.644 0.320 0.036
#> GSM1022371 2 0.0188 0.766 0.000 0.996 0.000 0.004
#> GSM1022372 2 0.0188 0.766 0.000 0.996 0.000 0.004
#> GSM1022373 2 0.0188 0.766 0.000 0.996 0.000 0.004
#> GSM1022377 4 0.2412 0.986 0.084 0.000 0.008 0.908
#> GSM1022378 4 0.2412 0.986 0.084 0.000 0.008 0.908
#> GSM1022379 4 0.2480 0.987 0.088 0.000 0.008 0.904
#> GSM1022380 4 0.2480 0.987 0.088 0.000 0.008 0.904
#> GSM1022385 1 0.0000 0.766 1.000 0.000 0.000 0.000
#> GSM1022386 1 0.0000 0.766 1.000 0.000 0.000 0.000
#> GSM1022387 1 0.0000 0.766 1.000 0.000 0.000 0.000
#> GSM1022388 1 0.0000 0.766 1.000 0.000 0.000 0.000
#> GSM1022381 4 0.2334 0.988 0.088 0.000 0.004 0.908
#> GSM1022382 4 0.2334 0.988 0.088 0.000 0.004 0.908
#> GSM1022383 4 0.2334 0.988 0.088 0.000 0.004 0.908
#> GSM1022384 4 0.2334 0.988 0.088 0.000 0.004 0.908
#> GSM1022393 1 0.4933 0.761 0.568 0.000 0.432 0.000
#> GSM1022394 1 0.4933 0.761 0.568 0.000 0.432 0.000
#> GSM1022395 1 0.4933 0.761 0.568 0.000 0.432 0.000
#> GSM1022396 1 0.4933 0.761 0.568 0.000 0.432 0.000
#> GSM1022389 4 0.3082 0.980 0.084 0.000 0.032 0.884
#> GSM1022390 4 0.3149 0.981 0.088 0.000 0.032 0.880
#> GSM1022391 4 0.3082 0.980 0.084 0.000 0.032 0.884
#> GSM1022392 4 0.3149 0.981 0.088 0.000 0.032 0.880
#> GSM1022397 1 0.0000 0.766 1.000 0.000 0.000 0.000
#> GSM1022398 1 0.0000 0.766 1.000 0.000 0.000 0.000
#> GSM1022399 1 0.0000 0.766 1.000 0.000 0.000 0.000
#> GSM1022400 1 0.0000 0.766 1.000 0.000 0.000 0.000
#> GSM1022401 1 0.4933 0.761 0.568 0.000 0.432 0.000
#> GSM1022402 1 0.4933 0.761 0.568 0.000 0.432 0.000
#> GSM1022403 1 0.4933 0.761 0.568 0.000 0.432 0.000
#> GSM1022404 1 0.4933 0.761 0.568 0.000 0.432 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1022325 2 0.3565 0.654 0.000 0.800 0.176 0.000 0.024
#> GSM1022326 2 0.3565 0.654 0.000 0.800 0.176 0.000 0.024
#> GSM1022327 2 0.3565 0.654 0.000 0.800 0.176 0.000 0.024
#> GSM1022331 5 0.5561 0.917 0.000 0.204 0.044 0.064 0.688
#> GSM1022332 5 0.5561 0.917 0.000 0.204 0.044 0.064 0.688
#> GSM1022333 5 0.5561 0.917 0.000 0.204 0.044 0.064 0.688
#> GSM1022328 2 0.3565 0.654 0.000 0.800 0.176 0.000 0.024
#> GSM1022329 2 0.3565 0.654 0.000 0.800 0.176 0.000 0.024
#> GSM1022330 2 0.3565 0.654 0.000 0.800 0.176 0.000 0.024
#> GSM1022337 5 0.3756 0.911 0.000 0.248 0.000 0.008 0.744
#> GSM1022338 5 0.3756 0.911 0.000 0.248 0.000 0.008 0.744
#> GSM1022339 5 0.3534 0.897 0.000 0.256 0.000 0.000 0.744
#> GSM1022334 2 0.3565 0.654 0.000 0.800 0.176 0.000 0.024
#> GSM1022335 2 0.3565 0.654 0.000 0.800 0.176 0.000 0.024
#> GSM1022336 2 0.3565 0.654 0.000 0.800 0.176 0.000 0.024
#> GSM1022340 1 0.5616 -0.457 0.552 0.000 0.364 0.000 0.084
#> GSM1022341 1 0.5616 -0.457 0.552 0.000 0.364 0.000 0.084
#> GSM1022342 1 0.5616 -0.457 0.552 0.000 0.364 0.000 0.084
#> GSM1022343 1 0.5616 -0.457 0.552 0.000 0.364 0.000 0.084
#> GSM1022347 3 0.4161 0.951 0.392 0.000 0.608 0.000 0.000
#> GSM1022348 3 0.4161 0.951 0.392 0.000 0.608 0.000 0.000
#> GSM1022349 3 0.4161 0.951 0.392 0.000 0.608 0.000 0.000
#> GSM1022350 3 0.4161 0.951 0.392 0.000 0.608 0.000 0.000
#> GSM1022344 3 0.5151 0.914 0.396 0.000 0.560 0.000 0.044
#> GSM1022345 3 0.5151 0.914 0.396 0.000 0.560 0.000 0.044
#> GSM1022346 3 0.5151 0.914 0.396 0.000 0.560 0.000 0.044
#> GSM1022355 1 0.1121 0.798 0.956 0.000 0.000 0.000 0.044
#> GSM1022356 1 0.1121 0.798 0.956 0.000 0.000 0.000 0.044
#> GSM1022357 1 0.1121 0.798 0.956 0.000 0.000 0.000 0.044
#> GSM1022358 1 0.1121 0.798 0.956 0.000 0.000 0.000 0.044
#> GSM1022351 1 0.1197 0.796 0.952 0.000 0.000 0.000 0.048
#> GSM1022352 1 0.1197 0.796 0.952 0.000 0.000 0.000 0.048
#> GSM1022353 1 0.1197 0.796 0.952 0.000 0.000 0.000 0.048
#> GSM1022354 1 0.1197 0.796 0.952 0.000 0.000 0.000 0.048
#> GSM1022359 2 0.0404 0.682 0.000 0.988 0.000 0.012 0.000
#> GSM1022360 2 0.0404 0.682 0.000 0.988 0.000 0.012 0.000
#> GSM1022361 2 0.0404 0.682 0.000 0.988 0.000 0.012 0.000
#> GSM1022362 2 0.0404 0.682 0.000 0.988 0.000 0.012 0.000
#> GSM1022367 2 0.6976 -0.215 0.000 0.464 0.144 0.036 0.356
#> GSM1022368 2 0.6976 -0.215 0.000 0.464 0.144 0.036 0.356
#> GSM1022369 2 0.6976 -0.215 0.000 0.464 0.144 0.036 0.356
#> GSM1022370 2 0.6976 -0.215 0.000 0.464 0.144 0.036 0.356
#> GSM1022363 2 0.1830 0.661 0.000 0.924 0.068 0.008 0.000
#> GSM1022364 2 0.1830 0.661 0.000 0.924 0.068 0.008 0.000
#> GSM1022365 2 0.1830 0.661 0.000 0.924 0.068 0.008 0.000
#> GSM1022366 2 0.1830 0.661 0.000 0.924 0.068 0.008 0.000
#> GSM1022374 2 0.6681 -0.254 0.000 0.452 0.108 0.032 0.408
#> GSM1022375 2 0.6681 -0.254 0.000 0.452 0.108 0.032 0.408
#> GSM1022376 2 0.6681 -0.254 0.000 0.452 0.108 0.032 0.408
#> GSM1022371 2 0.1082 0.675 0.000 0.964 0.028 0.008 0.000
#> GSM1022372 2 0.1082 0.675 0.000 0.964 0.028 0.008 0.000
#> GSM1022373 2 0.1082 0.675 0.000 0.964 0.028 0.008 0.000
#> GSM1022377 4 0.1990 0.983 0.068 0.000 0.008 0.920 0.004
#> GSM1022378 4 0.1990 0.983 0.068 0.000 0.008 0.920 0.004
#> GSM1022379 4 0.1990 0.983 0.068 0.000 0.008 0.920 0.004
#> GSM1022380 4 0.1990 0.983 0.068 0.000 0.008 0.920 0.004
#> GSM1022385 3 0.5476 0.920 0.388 0.000 0.544 0.000 0.068
#> GSM1022386 3 0.5476 0.920 0.388 0.000 0.544 0.000 0.068
#> GSM1022387 3 0.5476 0.920 0.388 0.000 0.544 0.000 0.068
#> GSM1022388 3 0.5476 0.920 0.388 0.000 0.544 0.000 0.068
#> GSM1022381 4 0.1704 0.984 0.068 0.000 0.000 0.928 0.004
#> GSM1022382 4 0.1704 0.984 0.068 0.000 0.000 0.928 0.004
#> GSM1022383 4 0.1704 0.984 0.068 0.000 0.000 0.928 0.004
#> GSM1022384 4 0.1704 0.984 0.068 0.000 0.000 0.928 0.004
#> GSM1022393 1 0.0963 0.797 0.964 0.000 0.000 0.000 0.036
#> GSM1022394 1 0.0963 0.797 0.964 0.000 0.000 0.000 0.036
#> GSM1022395 1 0.0963 0.797 0.964 0.000 0.000 0.000 0.036
#> GSM1022396 1 0.0963 0.797 0.964 0.000 0.000 0.000 0.036
#> GSM1022389 4 0.2824 0.974 0.068 0.000 0.016 0.888 0.028
#> GSM1022390 4 0.2824 0.974 0.068 0.000 0.016 0.888 0.028
#> GSM1022391 4 0.2824 0.974 0.068 0.000 0.016 0.888 0.028
#> GSM1022392 4 0.2824 0.974 0.068 0.000 0.016 0.888 0.028
#> GSM1022397 3 0.4527 0.952 0.392 0.000 0.596 0.000 0.012
#> GSM1022398 3 0.4527 0.952 0.392 0.000 0.596 0.000 0.012
#> GSM1022399 3 0.4527 0.952 0.392 0.000 0.596 0.000 0.012
#> GSM1022400 3 0.4527 0.952 0.392 0.000 0.596 0.000 0.012
#> GSM1022401 1 0.0963 0.797 0.964 0.000 0.000 0.000 0.036
#> GSM1022402 1 0.0963 0.797 0.964 0.000 0.000 0.000 0.036
#> GSM1022403 1 0.0963 0.797 0.964 0.000 0.000 0.000 0.036
#> GSM1022404 1 0.0963 0.797 0.964 0.000 0.000 0.000 0.036
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1022325 2 0.3596 0.787 0.004 0.748 0.000 0.000 NA 0.016
#> GSM1022326 2 0.3596 0.787 0.004 0.748 0.000 0.000 NA 0.016
#> GSM1022327 2 0.3483 0.787 0.000 0.748 0.000 0.000 NA 0.016
#> GSM1022331 6 0.6076 0.655 0.052 0.088 0.000 0.028 NA 0.624
#> GSM1022332 6 0.6076 0.655 0.052 0.088 0.000 0.028 NA 0.624
#> GSM1022333 6 0.6076 0.655 0.052 0.088 0.000 0.028 NA 0.624
#> GSM1022328 2 0.3596 0.787 0.004 0.748 0.000 0.000 NA 0.016
#> GSM1022329 2 0.3483 0.787 0.000 0.748 0.000 0.000 NA 0.016
#> GSM1022330 2 0.3596 0.787 0.000 0.748 0.000 0.004 NA 0.016
#> GSM1022337 6 0.5802 0.668 0.068 0.108 0.000 0.004 NA 0.640
#> GSM1022338 6 0.5802 0.668 0.068 0.108 0.000 0.004 NA 0.640
#> GSM1022339 6 0.5705 0.668 0.068 0.112 0.000 0.000 NA 0.640
#> GSM1022334 2 0.3596 0.787 0.000 0.748 0.000 0.004 NA 0.016
#> GSM1022335 2 0.3596 0.787 0.000 0.748 0.000 0.004 NA 0.016
#> GSM1022336 2 0.3596 0.787 0.000 0.748 0.000 0.004 NA 0.016
#> GSM1022340 3 0.5305 0.637 0.120 0.000 0.656 0.000 NA 0.028
#> GSM1022341 3 0.5305 0.637 0.120 0.000 0.656 0.000 NA 0.028
#> GSM1022342 3 0.5305 0.637 0.120 0.000 0.656 0.000 NA 0.028
#> GSM1022343 3 0.5267 0.643 0.116 0.000 0.660 0.000 NA 0.028
#> GSM1022347 3 0.0000 0.881 0.000 0.000 1.000 0.000 NA 0.000
#> GSM1022348 3 0.0000 0.881 0.000 0.000 1.000 0.000 NA 0.000
#> GSM1022349 3 0.0000 0.881 0.000 0.000 1.000 0.000 NA 0.000
#> GSM1022350 3 0.0000 0.881 0.000 0.000 1.000 0.000 NA 0.000
#> GSM1022344 3 0.1967 0.858 0.000 0.000 0.904 0.000 NA 0.012
#> GSM1022345 3 0.1967 0.858 0.000 0.000 0.904 0.000 NA 0.012
#> GSM1022346 3 0.1967 0.858 0.000 0.000 0.904 0.000 NA 0.012
#> GSM1022355 1 0.4946 0.903 0.652 0.000 0.188 0.000 NA 0.000
#> GSM1022356 1 0.4946 0.903 0.652 0.000 0.188 0.000 NA 0.000
#> GSM1022357 1 0.4946 0.903 0.652 0.000 0.188 0.000 NA 0.000
#> GSM1022358 1 0.4946 0.903 0.652 0.000 0.188 0.000 NA 0.000
#> GSM1022351 1 0.5037 0.898 0.640 0.000 0.188 0.000 NA 0.000
#> GSM1022352 1 0.5095 0.894 0.632 0.000 0.188 0.000 NA 0.000
#> GSM1022353 1 0.5095 0.894 0.632 0.000 0.188 0.000 NA 0.000
#> GSM1022354 1 0.5095 0.894 0.632 0.000 0.188 0.000 NA 0.000
#> GSM1022359 2 0.0547 0.800 0.020 0.980 0.000 0.000 NA 0.000
#> GSM1022360 2 0.0547 0.800 0.020 0.980 0.000 0.000 NA 0.000
#> GSM1022361 2 0.0547 0.800 0.020 0.980 0.000 0.000 NA 0.000
#> GSM1022362 2 0.0547 0.800 0.020 0.980 0.000 0.000 NA 0.000
#> GSM1022367 6 0.4782 0.584 0.048 0.380 0.000 0.000 NA 0.568
#> GSM1022368 6 0.4782 0.584 0.048 0.380 0.000 0.000 NA 0.568
#> GSM1022369 6 0.4782 0.584 0.048 0.380 0.000 0.000 NA 0.568
#> GSM1022370 6 0.4799 0.572 0.048 0.388 0.000 0.000 NA 0.560
#> GSM1022363 2 0.2622 0.730 0.016 0.888 0.000 0.004 NA 0.064
#> GSM1022364 2 0.2622 0.730 0.016 0.888 0.000 0.004 NA 0.064
#> GSM1022365 2 0.2622 0.730 0.016 0.888 0.000 0.004 NA 0.064
#> GSM1022366 2 0.2622 0.730 0.016 0.888 0.000 0.004 NA 0.064
#> GSM1022374 6 0.5083 0.611 0.012 0.352 0.000 0.008 NA 0.584
#> GSM1022375 6 0.5083 0.611 0.012 0.352 0.000 0.008 NA 0.584
#> GSM1022376 6 0.5083 0.611 0.012 0.352 0.000 0.008 NA 0.584
#> GSM1022371 2 0.1194 0.791 0.004 0.956 0.000 0.008 NA 0.000
#> GSM1022372 2 0.1194 0.791 0.004 0.956 0.000 0.008 NA 0.000
#> GSM1022373 2 0.1194 0.791 0.004 0.956 0.000 0.008 NA 0.000
#> GSM1022377 4 0.1774 0.942 0.020 0.000 0.024 0.936 NA 0.004
#> GSM1022378 4 0.1774 0.942 0.020 0.000 0.024 0.936 NA 0.004
#> GSM1022379 4 0.1774 0.942 0.020 0.000 0.024 0.936 NA 0.004
#> GSM1022380 4 0.1774 0.942 0.020 0.000 0.024 0.936 NA 0.004
#> GSM1022385 3 0.2433 0.859 0.000 0.000 0.884 0.000 NA 0.044
#> GSM1022386 3 0.2433 0.859 0.000 0.000 0.884 0.000 NA 0.044
#> GSM1022387 3 0.2433 0.859 0.000 0.000 0.884 0.000 NA 0.044
#> GSM1022388 3 0.2433 0.859 0.000 0.000 0.884 0.000 NA 0.044
#> GSM1022381 4 0.1138 0.944 0.004 0.000 0.024 0.960 NA 0.000
#> GSM1022382 4 0.1138 0.944 0.004 0.000 0.024 0.960 NA 0.000
#> GSM1022383 4 0.1138 0.944 0.004 0.000 0.024 0.960 NA 0.000
#> GSM1022384 4 0.1138 0.944 0.004 0.000 0.024 0.960 NA 0.000
#> GSM1022393 1 0.2948 0.905 0.804 0.000 0.188 0.000 NA 0.000
#> GSM1022394 1 0.2948 0.905 0.804 0.000 0.188 0.000 NA 0.000
#> GSM1022395 1 0.2948 0.905 0.804 0.000 0.188 0.000 NA 0.000
#> GSM1022396 1 0.2948 0.905 0.804 0.000 0.188 0.000 NA 0.000
#> GSM1022389 4 0.3455 0.911 0.016 0.000 0.024 0.836 NA 0.020
#> GSM1022390 4 0.3501 0.909 0.016 0.000 0.024 0.832 NA 0.020
#> GSM1022391 4 0.3455 0.911 0.016 0.000 0.024 0.836 NA 0.020
#> GSM1022392 4 0.3501 0.909 0.016 0.000 0.024 0.832 NA 0.020
#> GSM1022397 3 0.0622 0.879 0.000 0.000 0.980 0.000 NA 0.008
#> GSM1022398 3 0.0622 0.879 0.000 0.000 0.980 0.000 NA 0.008
#> GSM1022399 3 0.0622 0.879 0.000 0.000 0.980 0.000 NA 0.008
#> GSM1022400 3 0.0622 0.879 0.000 0.000 0.980 0.000 NA 0.008
#> GSM1022401 1 0.2948 0.905 0.804 0.000 0.188 0.000 NA 0.008
#> GSM1022402 1 0.2948 0.905 0.804 0.000 0.188 0.000 NA 0.008
#> GSM1022403 1 0.2948 0.905 0.804 0.000 0.188 0.000 NA 0.008
#> GSM1022404 1 0.2948 0.905 0.804 0.000 0.188 0.000 NA 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n protocol(p) cell.type(p) k
#> ATC:kmeans 80 1.10e-11 4.22e-01 2
#> ATC:kmeans 80 9.12e-15 1.26e-04 3
#> ATC:kmeans 73 4.00e-13 4.34e-09 4
#> ATC:kmeans 69 7.62e-19 1.51e-09 5
#> ATC:kmeans 80 1.08e-20 3.36e-10 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 31589 rows and 80 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4913 0.509 0.509
#> 3 3 1.000 0.999 0.999 0.2705 0.867 0.739
#> 4 4 0.968 0.974 0.972 0.0855 0.949 0.864
#> 5 5 0.829 0.963 0.938 0.1166 0.904 0.704
#> 6 6 0.940 0.897 0.896 0.0422 0.990 0.956
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
#> GSM1022325 2 0 1 0 1
#> GSM1022326 2 0 1 0 1
#> GSM1022327 2 0 1 0 1
#> GSM1022331 2 0 1 0 1
#> GSM1022332 2 0 1 0 1
#> GSM1022333 2 0 1 0 1
#> GSM1022328 2 0 1 0 1
#> GSM1022329 2 0 1 0 1
#> GSM1022330 2 0 1 0 1
#> GSM1022337 2 0 1 0 1
#> GSM1022338 2 0 1 0 1
#> GSM1022339 2 0 1 0 1
#> GSM1022334 2 0 1 0 1
#> GSM1022335 2 0 1 0 1
#> GSM1022336 2 0 1 0 1
#> GSM1022340 1 0 1 1 0
#> GSM1022341 1 0 1 1 0
#> GSM1022342 1 0 1 1 0
#> GSM1022343 1 0 1 1 0
#> GSM1022347 1 0 1 1 0
#> GSM1022348 1 0 1 1 0
#> GSM1022349 1 0 1 1 0
#> GSM1022350 1 0 1 1 0
#> GSM1022344 1 0 1 1 0
#> GSM1022345 1 0 1 1 0
#> GSM1022346 1 0 1 1 0
#> GSM1022355 1 0 1 1 0
#> GSM1022356 1 0 1 1 0
#> GSM1022357 1 0 1 1 0
#> GSM1022358 1 0 1 1 0
#> GSM1022351 1 0 1 1 0
#> GSM1022352 1 0 1 1 0
#> GSM1022353 1 0 1 1 0
#> GSM1022354 1 0 1 1 0
#> GSM1022359 2 0 1 0 1
#> GSM1022360 2 0 1 0 1
#> GSM1022361 2 0 1 0 1
#> GSM1022362 2 0 1 0 1
#> GSM1022367 2 0 1 0 1
#> GSM1022368 2 0 1 0 1
#> GSM1022369 2 0 1 0 1
#> GSM1022370 2 0 1 0 1
#> GSM1022363 2 0 1 0 1
#> GSM1022364 2 0 1 0 1
#> GSM1022365 2 0 1 0 1
#> GSM1022366 2 0 1 0 1
#> GSM1022374 2 0 1 0 1
#> GSM1022375 2 0 1 0 1
#> GSM1022376 2 0 1 0 1
#> GSM1022371 2 0 1 0 1
#> GSM1022372 2 0 1 0 1
#> GSM1022373 2 0 1 0 1
#> GSM1022377 1 0 1 1 0
#> GSM1022378 1 0 1 1 0
#> GSM1022379 1 0 1 1 0
#> GSM1022380 1 0 1 1 0
#> GSM1022385 1 0 1 1 0
#> GSM1022386 1 0 1 1 0
#> GSM1022387 1 0 1 1 0
#> GSM1022388 1 0 1 1 0
#> GSM1022381 1 0 1 1 0
#> GSM1022382 1 0 1 1 0
#> GSM1022383 1 0 1 1 0
#> GSM1022384 1 0 1 1 0
#> GSM1022393 1 0 1 1 0
#> GSM1022394 1 0 1 1 0
#> GSM1022395 1 0 1 1 0
#> GSM1022396 1 0 1 1 0
#> GSM1022389 1 0 1 1 0
#> GSM1022390 1 0 1 1 0
#> GSM1022391 1 0 1 1 0
#> GSM1022392 1 0 1 1 0
#> GSM1022397 1 0 1 1 0
#> GSM1022398 1 0 1 1 0
#> GSM1022399 1 0 1 1 0
#> GSM1022400 1 0 1 1 0
#> GSM1022401 1 0 1 1 0
#> GSM1022402 1 0 1 1 0
#> GSM1022403 1 0 1 1 0
#> GSM1022404 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1022325 2 0.0000 1.000 0.000 1 0.000
#> GSM1022326 2 0.0000 1.000 0.000 1 0.000
#> GSM1022327 2 0.0000 1.000 0.000 1 0.000
#> GSM1022331 2 0.0000 1.000 0.000 1 0.000
#> GSM1022332 2 0.0000 1.000 0.000 1 0.000
#> GSM1022333 2 0.0000 1.000 0.000 1 0.000
#> GSM1022328 2 0.0000 1.000 0.000 1 0.000
#> GSM1022329 2 0.0000 1.000 0.000 1 0.000
#> GSM1022330 2 0.0000 1.000 0.000 1 0.000
#> GSM1022337 2 0.0000 1.000 0.000 1 0.000
#> GSM1022338 2 0.0000 1.000 0.000 1 0.000
#> GSM1022339 2 0.0000 1.000 0.000 1 0.000
#> GSM1022334 2 0.0000 1.000 0.000 1 0.000
#> GSM1022335 2 0.0000 1.000 0.000 1 0.000
#> GSM1022336 2 0.0000 1.000 0.000 1 0.000
#> GSM1022340 1 0.0237 0.998 0.996 0 0.004
#> GSM1022341 1 0.0237 0.998 0.996 0 0.004
#> GSM1022342 1 0.0237 0.998 0.996 0 0.004
#> GSM1022343 1 0.0237 0.998 0.996 0 0.004
#> GSM1022347 1 0.0237 0.998 0.996 0 0.004
#> GSM1022348 1 0.0237 0.998 0.996 0 0.004
#> GSM1022349 1 0.0237 0.998 0.996 0 0.004
#> GSM1022350 1 0.0237 0.998 0.996 0 0.004
#> GSM1022344 1 0.0237 0.998 0.996 0 0.004
#> GSM1022345 1 0.0237 0.998 0.996 0 0.004
#> GSM1022346 1 0.0237 0.998 0.996 0 0.004
#> GSM1022355 1 0.0000 0.998 1.000 0 0.000
#> GSM1022356 1 0.0000 0.998 1.000 0 0.000
#> GSM1022357 1 0.0000 0.998 1.000 0 0.000
#> GSM1022358 1 0.0000 0.998 1.000 0 0.000
#> GSM1022351 1 0.0000 0.998 1.000 0 0.000
#> GSM1022352 1 0.0000 0.998 1.000 0 0.000
#> GSM1022353 1 0.0000 0.998 1.000 0 0.000
#> GSM1022354 1 0.0000 0.998 1.000 0 0.000
#> GSM1022359 2 0.0000 1.000 0.000 1 0.000
#> GSM1022360 2 0.0000 1.000 0.000 1 0.000
#> GSM1022361 2 0.0000 1.000 0.000 1 0.000
#> GSM1022362 2 0.0000 1.000 0.000 1 0.000
#> GSM1022367 2 0.0000 1.000 0.000 1 0.000
#> GSM1022368 2 0.0000 1.000 0.000 1 0.000
#> GSM1022369 2 0.0000 1.000 0.000 1 0.000
#> GSM1022370 2 0.0000 1.000 0.000 1 0.000
#> GSM1022363 2 0.0000 1.000 0.000 1 0.000
#> GSM1022364 2 0.0000 1.000 0.000 1 0.000
#> GSM1022365 2 0.0000 1.000 0.000 1 0.000
#> GSM1022366 2 0.0000 1.000 0.000 1 0.000
#> GSM1022374 2 0.0000 1.000 0.000 1 0.000
#> GSM1022375 2 0.0000 1.000 0.000 1 0.000
#> GSM1022376 2 0.0000 1.000 0.000 1 0.000
#> GSM1022371 2 0.0000 1.000 0.000 1 0.000
#> GSM1022372 2 0.0000 1.000 0.000 1 0.000
#> GSM1022373 2 0.0000 1.000 0.000 1 0.000
#> GSM1022377 3 0.0000 0.999 0.000 0 1.000
#> GSM1022378 3 0.0000 0.999 0.000 0 1.000
#> GSM1022379 3 0.0000 0.999 0.000 0 1.000
#> GSM1022380 3 0.0000 0.999 0.000 0 1.000
#> GSM1022385 1 0.0237 0.998 0.996 0 0.004
#> GSM1022386 1 0.0237 0.998 0.996 0 0.004
#> GSM1022387 1 0.0237 0.998 0.996 0 0.004
#> GSM1022388 1 0.0237 0.998 0.996 0 0.004
#> GSM1022381 3 0.0000 0.999 0.000 0 1.000
#> GSM1022382 3 0.0000 0.999 0.000 0 1.000
#> GSM1022383 3 0.0000 0.999 0.000 0 1.000
#> GSM1022384 3 0.0000 0.999 0.000 0 1.000
#> GSM1022393 1 0.0000 0.998 1.000 0 0.000
#> GSM1022394 1 0.0000 0.998 1.000 0 0.000
#> GSM1022395 1 0.0000 0.998 1.000 0 0.000
#> GSM1022396 1 0.0000 0.998 1.000 0 0.000
#> GSM1022389 3 0.0237 0.997 0.004 0 0.996
#> GSM1022390 3 0.0237 0.997 0.004 0 0.996
#> GSM1022391 3 0.0237 0.997 0.004 0 0.996
#> GSM1022392 3 0.0237 0.997 0.004 0 0.996
#> GSM1022397 1 0.0237 0.998 0.996 0 0.004
#> GSM1022398 1 0.0237 0.998 0.996 0 0.004
#> GSM1022399 1 0.0237 0.998 0.996 0 0.004
#> GSM1022400 1 0.0237 0.998 0.996 0 0.004
#> GSM1022401 1 0.0000 0.998 1.000 0 0.000
#> GSM1022402 1 0.0000 0.998 1.000 0 0.000
#> GSM1022403 1 0.0000 0.998 1.000 0 0.000
#> GSM1022404 1 0.0000 0.998 1.000 0 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1022325 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM1022326 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM1022327 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM1022331 3 0.2281 0.964 0.000 0.096 0.904 0.000
#> GSM1022332 3 0.2281 0.964 0.000 0.096 0.904 0.000
#> GSM1022333 3 0.2281 0.964 0.000 0.096 0.904 0.000
#> GSM1022328 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM1022329 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM1022330 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM1022337 3 0.2921 0.964 0.000 0.140 0.860 0.000
#> GSM1022338 3 0.2921 0.964 0.000 0.140 0.860 0.000
#> GSM1022339 3 0.2921 0.964 0.000 0.140 0.860 0.000
#> GSM1022334 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM1022335 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM1022336 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM1022340 1 0.0000 0.970 1.000 0.000 0.000 0.000
#> GSM1022341 1 0.0000 0.970 1.000 0.000 0.000 0.000
#> GSM1022342 1 0.0000 0.970 1.000 0.000 0.000 0.000
#> GSM1022343 1 0.0000 0.970 1.000 0.000 0.000 0.000
#> GSM1022347 1 0.0000 0.970 1.000 0.000 0.000 0.000
#> GSM1022348 1 0.0000 0.970 1.000 0.000 0.000 0.000
#> GSM1022349 1 0.0000 0.970 1.000 0.000 0.000 0.000
#> GSM1022350 1 0.0000 0.970 1.000 0.000 0.000 0.000
#> GSM1022344 1 0.0000 0.970 1.000 0.000 0.000 0.000
#> GSM1022345 1 0.0000 0.970 1.000 0.000 0.000 0.000
#> GSM1022346 1 0.0000 0.970 1.000 0.000 0.000 0.000
#> GSM1022355 1 0.1792 0.964 0.932 0.000 0.068 0.000
#> GSM1022356 1 0.1792 0.964 0.932 0.000 0.068 0.000
#> GSM1022357 1 0.1792 0.964 0.932 0.000 0.068 0.000
#> GSM1022358 1 0.1792 0.964 0.932 0.000 0.068 0.000
#> GSM1022351 1 0.1792 0.964 0.932 0.000 0.068 0.000
#> GSM1022352 1 0.1792 0.964 0.932 0.000 0.068 0.000
#> GSM1022353 1 0.1792 0.964 0.932 0.000 0.068 0.000
#> GSM1022354 1 0.1792 0.964 0.932 0.000 0.068 0.000
#> GSM1022359 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM1022360 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM1022361 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM1022362 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM1022367 2 0.1389 0.956 0.000 0.952 0.048 0.000
#> GSM1022368 2 0.1389 0.956 0.000 0.952 0.048 0.000
#> GSM1022369 2 0.1389 0.956 0.000 0.952 0.048 0.000
#> GSM1022370 2 0.1389 0.956 0.000 0.952 0.048 0.000
#> GSM1022363 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM1022364 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM1022365 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM1022366 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM1022374 2 0.1389 0.956 0.000 0.952 0.048 0.000
#> GSM1022375 2 0.1389 0.956 0.000 0.952 0.048 0.000
#> GSM1022376 2 0.1389 0.956 0.000 0.952 0.048 0.000
#> GSM1022371 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM1022372 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM1022373 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> GSM1022377 4 0.0000 0.992 0.000 0.000 0.000 1.000
#> GSM1022378 4 0.0000 0.992 0.000 0.000 0.000 1.000
#> GSM1022379 4 0.0000 0.992 0.000 0.000 0.000 1.000
#> GSM1022380 4 0.0000 0.992 0.000 0.000 0.000 1.000
#> GSM1022385 1 0.0000 0.970 1.000 0.000 0.000 0.000
#> GSM1022386 1 0.0000 0.970 1.000 0.000 0.000 0.000
#> GSM1022387 1 0.0000 0.970 1.000 0.000 0.000 0.000
#> GSM1022388 1 0.0000 0.970 1.000 0.000 0.000 0.000
#> GSM1022381 4 0.0000 0.992 0.000 0.000 0.000 1.000
#> GSM1022382 4 0.0000 0.992 0.000 0.000 0.000 1.000
#> GSM1022383 4 0.0000 0.992 0.000 0.000 0.000 1.000
#> GSM1022384 4 0.0000 0.992 0.000 0.000 0.000 1.000
#> GSM1022393 1 0.1792 0.964 0.932 0.000 0.068 0.000
#> GSM1022394 1 0.1792 0.964 0.932 0.000 0.068 0.000
#> GSM1022395 1 0.1792 0.964 0.932 0.000 0.068 0.000
#> GSM1022396 1 0.1792 0.964 0.932 0.000 0.068 0.000
#> GSM1022389 4 0.0921 0.983 0.000 0.000 0.028 0.972
#> GSM1022390 4 0.0921 0.983 0.000 0.000 0.028 0.972
#> GSM1022391 4 0.0921 0.983 0.000 0.000 0.028 0.972
#> GSM1022392 4 0.0921 0.983 0.000 0.000 0.028 0.972
#> GSM1022397 1 0.0000 0.970 1.000 0.000 0.000 0.000
#> GSM1022398 1 0.0000 0.970 1.000 0.000 0.000 0.000
#> GSM1022399 1 0.0000 0.970 1.000 0.000 0.000 0.000
#> GSM1022400 1 0.0000 0.970 1.000 0.000 0.000 0.000
#> GSM1022401 1 0.1792 0.964 0.932 0.000 0.068 0.000
#> GSM1022402 1 0.1792 0.964 0.932 0.000 0.068 0.000
#> GSM1022403 1 0.1792 0.964 0.932 0.000 0.068 0.000
#> GSM1022404 1 0.1792 0.964 0.932 0.000 0.068 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1022325 2 0.0000 0.969 0.000 1.000 0.00 0.000 0.000
#> GSM1022326 2 0.0000 0.969 0.000 1.000 0.00 0.000 0.000
#> GSM1022327 2 0.0000 0.969 0.000 1.000 0.00 0.000 0.000
#> GSM1022331 5 0.0898 0.937 0.008 0.020 0.00 0.000 0.972
#> GSM1022332 5 0.0898 0.937 0.008 0.020 0.00 0.000 0.972
#> GSM1022333 5 0.0898 0.937 0.008 0.020 0.00 0.000 0.972
#> GSM1022328 2 0.0000 0.969 0.000 1.000 0.00 0.000 0.000
#> GSM1022329 2 0.0000 0.969 0.000 1.000 0.00 0.000 0.000
#> GSM1022330 2 0.0000 0.969 0.000 1.000 0.00 0.000 0.000
#> GSM1022337 5 0.2136 0.937 0.008 0.088 0.00 0.000 0.904
#> GSM1022338 5 0.2136 0.937 0.008 0.088 0.00 0.000 0.904
#> GSM1022339 5 0.2136 0.937 0.008 0.088 0.00 0.000 0.904
#> GSM1022334 2 0.0000 0.969 0.000 1.000 0.00 0.000 0.000
#> GSM1022335 2 0.0000 0.969 0.000 1.000 0.00 0.000 0.000
#> GSM1022336 2 0.0000 0.969 0.000 1.000 0.00 0.000 0.000
#> GSM1022340 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM1022341 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM1022342 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM1022343 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM1022347 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM1022348 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM1022349 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM1022350 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM1022344 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM1022345 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM1022346 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM1022355 1 0.2929 1.000 0.820 0.000 0.18 0.000 0.000
#> GSM1022356 1 0.2929 1.000 0.820 0.000 0.18 0.000 0.000
#> GSM1022357 1 0.2929 1.000 0.820 0.000 0.18 0.000 0.000
#> GSM1022358 1 0.2929 1.000 0.820 0.000 0.18 0.000 0.000
#> GSM1022351 1 0.2929 1.000 0.820 0.000 0.18 0.000 0.000
#> GSM1022352 1 0.2929 1.000 0.820 0.000 0.18 0.000 0.000
#> GSM1022353 1 0.2929 1.000 0.820 0.000 0.18 0.000 0.000
#> GSM1022354 1 0.2929 1.000 0.820 0.000 0.18 0.000 0.000
#> GSM1022359 2 0.0000 0.969 0.000 1.000 0.00 0.000 0.000
#> GSM1022360 2 0.0000 0.969 0.000 1.000 0.00 0.000 0.000
#> GSM1022361 2 0.0000 0.969 0.000 1.000 0.00 0.000 0.000
#> GSM1022362 2 0.0000 0.969 0.000 1.000 0.00 0.000 0.000
#> GSM1022367 2 0.2074 0.904 0.000 0.896 0.00 0.000 0.104
#> GSM1022368 2 0.2074 0.904 0.000 0.896 0.00 0.000 0.104
#> GSM1022369 2 0.2074 0.904 0.000 0.896 0.00 0.000 0.104
#> GSM1022370 2 0.2074 0.904 0.000 0.896 0.00 0.000 0.104
#> GSM1022363 2 0.0000 0.969 0.000 1.000 0.00 0.000 0.000
#> GSM1022364 2 0.0000 0.969 0.000 1.000 0.00 0.000 0.000
#> GSM1022365 2 0.0000 0.969 0.000 1.000 0.00 0.000 0.000
#> GSM1022366 2 0.0000 0.969 0.000 1.000 0.00 0.000 0.000
#> GSM1022374 2 0.2358 0.898 0.008 0.888 0.00 0.000 0.104
#> GSM1022375 2 0.2358 0.898 0.008 0.888 0.00 0.000 0.104
#> GSM1022376 2 0.2358 0.898 0.008 0.888 0.00 0.000 0.104
#> GSM1022371 2 0.0000 0.969 0.000 1.000 0.00 0.000 0.000
#> GSM1022372 2 0.0000 0.969 0.000 1.000 0.00 0.000 0.000
#> GSM1022373 2 0.0000 0.969 0.000 1.000 0.00 0.000 0.000
#> GSM1022377 4 0.0000 0.928 0.000 0.000 0.00 1.000 0.000
#> GSM1022378 4 0.0000 0.928 0.000 0.000 0.00 1.000 0.000
#> GSM1022379 4 0.0000 0.928 0.000 0.000 0.00 1.000 0.000
#> GSM1022380 4 0.0000 0.928 0.000 0.000 0.00 1.000 0.000
#> GSM1022385 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM1022386 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM1022387 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM1022388 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM1022381 4 0.0000 0.928 0.000 0.000 0.00 1.000 0.000
#> GSM1022382 4 0.0000 0.928 0.000 0.000 0.00 1.000 0.000
#> GSM1022383 4 0.0000 0.928 0.000 0.000 0.00 1.000 0.000
#> GSM1022384 4 0.0000 0.928 0.000 0.000 0.00 1.000 0.000
#> GSM1022393 1 0.2929 1.000 0.820 0.000 0.18 0.000 0.000
#> GSM1022394 1 0.2929 1.000 0.820 0.000 0.18 0.000 0.000
#> GSM1022395 1 0.2929 1.000 0.820 0.000 0.18 0.000 0.000
#> GSM1022396 1 0.2929 1.000 0.820 0.000 0.18 0.000 0.000
#> GSM1022389 4 0.3359 0.856 0.164 0.000 0.00 0.816 0.020
#> GSM1022390 4 0.4106 0.788 0.256 0.000 0.00 0.724 0.020
#> GSM1022391 4 0.3359 0.856 0.164 0.000 0.00 0.816 0.020
#> GSM1022392 4 0.4132 0.784 0.260 0.000 0.00 0.720 0.020
#> GSM1022397 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM1022398 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM1022399 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM1022400 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM1022401 1 0.2929 1.000 0.820 0.000 0.18 0.000 0.000
#> GSM1022402 1 0.2929 1.000 0.820 0.000 0.18 0.000 0.000
#> GSM1022403 1 0.2929 1.000 0.820 0.000 0.18 0.000 0.000
#> GSM1022404 1 0.2929 1.000 0.820 0.000 0.18 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1022325 2 0.1644 0.857 0.000 0.932 0.000 0.040 0.028 0.000
#> GSM1022326 2 0.1644 0.857 0.000 0.932 0.000 0.040 0.028 0.000
#> GSM1022327 2 0.1644 0.857 0.000 0.932 0.000 0.040 0.028 0.000
#> GSM1022331 5 0.4645 0.780 0.060 0.008 0.000 0.268 0.664 0.000
#> GSM1022332 5 0.4645 0.780 0.060 0.008 0.000 0.268 0.664 0.000
#> GSM1022333 5 0.4645 0.780 0.060 0.008 0.000 0.268 0.664 0.000
#> GSM1022328 2 0.1644 0.857 0.000 0.932 0.000 0.040 0.028 0.000
#> GSM1022329 2 0.1644 0.857 0.000 0.932 0.000 0.040 0.028 0.000
#> GSM1022330 2 0.1644 0.857 0.000 0.932 0.000 0.040 0.028 0.000
#> GSM1022337 5 0.1327 0.786 0.000 0.064 0.000 0.000 0.936 0.000
#> GSM1022338 5 0.1327 0.786 0.000 0.064 0.000 0.000 0.936 0.000
#> GSM1022339 5 0.1327 0.786 0.000 0.064 0.000 0.000 0.936 0.000
#> GSM1022334 2 0.1644 0.857 0.000 0.932 0.000 0.040 0.028 0.000
#> GSM1022335 2 0.1644 0.857 0.000 0.932 0.000 0.040 0.028 0.000
#> GSM1022336 2 0.1644 0.857 0.000 0.932 0.000 0.040 0.028 0.000
#> GSM1022340 3 0.0777 0.977 0.000 0.000 0.972 0.024 0.004 0.000
#> GSM1022341 3 0.0777 0.977 0.000 0.000 0.972 0.024 0.004 0.000
#> GSM1022342 3 0.0777 0.977 0.000 0.000 0.972 0.024 0.004 0.000
#> GSM1022343 3 0.0777 0.977 0.000 0.000 0.972 0.024 0.004 0.000
#> GSM1022347 3 0.0000 0.991 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022348 3 0.0000 0.991 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022349 3 0.0000 0.991 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022350 3 0.0000 0.991 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022344 3 0.0146 0.990 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM1022345 3 0.0146 0.990 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM1022346 3 0.0146 0.990 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM1022355 1 0.3109 0.963 0.848 0.000 0.076 0.068 0.008 0.000
#> GSM1022356 1 0.3109 0.963 0.848 0.000 0.076 0.068 0.008 0.000
#> GSM1022357 1 0.3109 0.963 0.848 0.000 0.076 0.068 0.008 0.000
#> GSM1022358 1 0.3109 0.963 0.848 0.000 0.076 0.068 0.008 0.000
#> GSM1022351 1 0.3109 0.963 0.848 0.000 0.076 0.068 0.008 0.000
#> GSM1022352 1 0.3109 0.963 0.848 0.000 0.076 0.068 0.008 0.000
#> GSM1022353 1 0.3109 0.963 0.848 0.000 0.076 0.068 0.008 0.000
#> GSM1022354 1 0.3109 0.963 0.848 0.000 0.076 0.068 0.008 0.000
#> GSM1022359 2 0.0000 0.868 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022360 2 0.0000 0.868 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022361 2 0.0000 0.868 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022362 2 0.0000 0.868 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022367 2 0.4558 0.648 0.000 0.700 0.000 0.168 0.132 0.000
#> GSM1022368 2 0.4558 0.648 0.000 0.700 0.000 0.168 0.132 0.000
#> GSM1022369 2 0.4558 0.648 0.000 0.700 0.000 0.168 0.132 0.000
#> GSM1022370 2 0.4558 0.648 0.000 0.700 0.000 0.168 0.132 0.000
#> GSM1022363 2 0.0713 0.862 0.000 0.972 0.000 0.028 0.000 0.000
#> GSM1022364 2 0.0713 0.862 0.000 0.972 0.000 0.028 0.000 0.000
#> GSM1022365 2 0.0713 0.862 0.000 0.972 0.000 0.028 0.000 0.000
#> GSM1022366 2 0.0713 0.862 0.000 0.972 0.000 0.028 0.000 0.000
#> GSM1022374 2 0.4630 0.453 0.000 0.580 0.000 0.048 0.372 0.000
#> GSM1022375 2 0.4630 0.453 0.000 0.580 0.000 0.048 0.372 0.000
#> GSM1022376 2 0.4630 0.453 0.000 0.580 0.000 0.048 0.372 0.000
#> GSM1022371 2 0.0000 0.868 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022372 2 0.0000 0.868 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022373 2 0.0000 0.868 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM1022377 4 0.4234 0.987 0.016 0.000 0.000 0.544 0.000 0.440
#> GSM1022378 4 0.4234 0.987 0.016 0.000 0.000 0.544 0.000 0.440
#> GSM1022379 4 0.4234 0.987 0.016 0.000 0.000 0.544 0.000 0.440
#> GSM1022380 4 0.4234 0.987 0.016 0.000 0.000 0.544 0.000 0.440
#> GSM1022385 3 0.0363 0.987 0.000 0.000 0.988 0.012 0.000 0.000
#> GSM1022386 3 0.0363 0.987 0.000 0.000 0.988 0.012 0.000 0.000
#> GSM1022387 3 0.0363 0.987 0.000 0.000 0.988 0.012 0.000 0.000
#> GSM1022388 3 0.0363 0.987 0.000 0.000 0.988 0.012 0.000 0.000
#> GSM1022381 4 0.3828 0.987 0.000 0.000 0.000 0.560 0.000 0.440
#> GSM1022382 4 0.3828 0.987 0.000 0.000 0.000 0.560 0.000 0.440
#> GSM1022383 4 0.3828 0.987 0.000 0.000 0.000 0.560 0.000 0.440
#> GSM1022384 4 0.3828 0.987 0.000 0.000 0.000 0.560 0.000 0.440
#> GSM1022393 1 0.1501 0.963 0.924 0.000 0.076 0.000 0.000 0.000
#> GSM1022394 1 0.1501 0.963 0.924 0.000 0.076 0.000 0.000 0.000
#> GSM1022395 1 0.1501 0.963 0.924 0.000 0.076 0.000 0.000 0.000
#> GSM1022396 1 0.1501 0.963 0.924 0.000 0.076 0.000 0.000 0.000
#> GSM1022389 6 0.0000 0.948 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1022390 6 0.0790 0.950 0.032 0.000 0.000 0.000 0.000 0.968
#> GSM1022391 6 0.0000 0.948 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM1022392 6 0.0790 0.950 0.032 0.000 0.000 0.000 0.000 0.968
#> GSM1022397 3 0.0000 0.991 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022398 3 0.0000 0.991 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022399 3 0.0000 0.991 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022400 3 0.0000 0.991 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022401 1 0.1501 0.963 0.924 0.000 0.076 0.000 0.000 0.000
#> GSM1022402 1 0.1501 0.963 0.924 0.000 0.076 0.000 0.000 0.000
#> GSM1022403 1 0.1501 0.963 0.924 0.000 0.076 0.000 0.000 0.000
#> GSM1022404 1 0.1501 0.963 0.924 0.000 0.076 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n protocol(p) cell.type(p) k
#> ATC:skmeans 80 1.10e-11 4.22e-01 2
#> ATC:skmeans 80 9.12e-15 1.26e-04 3
#> ATC:skmeans 80 8.27e-16 2.47e-06 4
#> ATC:skmeans 80 1.46e-23 6.83e-06 5
#> ATC:skmeans 77 2.26e-25 3.15e-06 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "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 31589 rows and 80 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.00 1.000 1.000 0.4913 0.509 0.509
#> 3 3 0.83 0.910 0.940 0.2967 0.853 0.714
#> 4 4 1.00 0.957 0.961 0.1330 0.903 0.738
#> 5 5 1.00 0.963 0.985 0.0861 0.933 0.757
#> 6 6 1.00 0.964 0.985 0.0577 0.957 0.798
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 4 5
There is also optional best \(k\) = 2 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
#> GSM1022325 2 0 1 0 1
#> GSM1022326 2 0 1 0 1
#> GSM1022327 2 0 1 0 1
#> GSM1022331 2 0 1 0 1
#> GSM1022332 2 0 1 0 1
#> GSM1022333 2 0 1 0 1
#> GSM1022328 2 0 1 0 1
#> GSM1022329 2 0 1 0 1
#> GSM1022330 2 0 1 0 1
#> GSM1022337 2 0 1 0 1
#> GSM1022338 2 0 1 0 1
#> GSM1022339 2 0 1 0 1
#> GSM1022334 2 0 1 0 1
#> GSM1022335 2 0 1 0 1
#> GSM1022336 2 0 1 0 1
#> GSM1022340 1 0 1 1 0
#> GSM1022341 1 0 1 1 0
#> GSM1022342 1 0 1 1 0
#> GSM1022343 1 0 1 1 0
#> GSM1022347 1 0 1 1 0
#> GSM1022348 1 0 1 1 0
#> GSM1022349 1 0 1 1 0
#> GSM1022350 1 0 1 1 0
#> GSM1022344 1 0 1 1 0
#> GSM1022345 1 0 1 1 0
#> GSM1022346 1 0 1 1 0
#> GSM1022355 1 0 1 1 0
#> GSM1022356 1 0 1 1 0
#> GSM1022357 1 0 1 1 0
#> GSM1022358 1 0 1 1 0
#> GSM1022351 1 0 1 1 0
#> GSM1022352 1 0 1 1 0
#> GSM1022353 1 0 1 1 0
#> GSM1022354 1 0 1 1 0
#> GSM1022359 2 0 1 0 1
#> GSM1022360 2 0 1 0 1
#> GSM1022361 2 0 1 0 1
#> GSM1022362 2 0 1 0 1
#> GSM1022367 2 0 1 0 1
#> GSM1022368 2 0 1 0 1
#> GSM1022369 2 0 1 0 1
#> GSM1022370 2 0 1 0 1
#> GSM1022363 2 0 1 0 1
#> GSM1022364 2 0 1 0 1
#> GSM1022365 2 0 1 0 1
#> GSM1022366 2 0 1 0 1
#> GSM1022374 2 0 1 0 1
#> GSM1022375 2 0 1 0 1
#> GSM1022376 2 0 1 0 1
#> GSM1022371 2 0 1 0 1
#> GSM1022372 2 0 1 0 1
#> GSM1022373 2 0 1 0 1
#> GSM1022377 1 0 1 1 0
#> GSM1022378 1 0 1 1 0
#> GSM1022379 1 0 1 1 0
#> GSM1022380 1 0 1 1 0
#> GSM1022385 1 0 1 1 0
#> GSM1022386 1 0 1 1 0
#> GSM1022387 1 0 1 1 0
#> GSM1022388 1 0 1 1 0
#> GSM1022381 1 0 1 1 0
#> GSM1022382 1 0 1 1 0
#> GSM1022383 1 0 1 1 0
#> GSM1022384 1 0 1 1 0
#> GSM1022393 1 0 1 1 0
#> GSM1022394 1 0 1 1 0
#> GSM1022395 1 0 1 1 0
#> GSM1022396 1 0 1 1 0
#> GSM1022389 1 0 1 1 0
#> GSM1022390 1 0 1 1 0
#> GSM1022391 1 0 1 1 0
#> GSM1022392 1 0 1 1 0
#> GSM1022397 1 0 1 1 0
#> GSM1022398 1 0 1 1 0
#> GSM1022399 1 0 1 1 0
#> GSM1022400 1 0 1 1 0
#> GSM1022401 1 0 1 1 0
#> GSM1022402 1 0 1 1 0
#> GSM1022403 1 0 1 1 0
#> GSM1022404 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1022325 2 0.000 0.991 0.00 1.000 0.000
#> GSM1022326 2 0.000 0.991 0.00 1.000 0.000
#> GSM1022327 2 0.000 0.991 0.00 1.000 0.000
#> GSM1022331 2 0.455 0.747 0.00 0.800 0.200
#> GSM1022332 3 0.617 0.233 0.00 0.412 0.588
#> GSM1022333 2 0.263 0.904 0.00 0.916 0.084
#> GSM1022328 2 0.000 0.991 0.00 1.000 0.000
#> GSM1022329 2 0.000 0.991 0.00 1.000 0.000
#> GSM1022330 2 0.000 0.991 0.00 1.000 0.000
#> GSM1022337 2 0.000 0.991 0.00 1.000 0.000
#> GSM1022338 2 0.000 0.991 0.00 1.000 0.000
#> GSM1022339 2 0.000 0.991 0.00 1.000 0.000
#> GSM1022334 2 0.000 0.991 0.00 1.000 0.000
#> GSM1022335 2 0.000 0.991 0.00 1.000 0.000
#> GSM1022336 2 0.000 0.991 0.00 1.000 0.000
#> GSM1022340 1 0.502 0.836 0.76 0.000 0.240
#> GSM1022341 1 0.000 0.861 1.00 0.000 0.000
#> GSM1022342 1 0.000 0.861 1.00 0.000 0.000
#> GSM1022343 1 0.000 0.861 1.00 0.000 0.000
#> GSM1022347 1 0.000 0.861 1.00 0.000 0.000
#> GSM1022348 1 0.000 0.861 1.00 0.000 0.000
#> GSM1022349 1 0.000 0.861 1.00 0.000 0.000
#> GSM1022350 1 0.000 0.861 1.00 0.000 0.000
#> GSM1022344 1 0.000 0.861 1.00 0.000 0.000
#> GSM1022345 1 0.000 0.861 1.00 0.000 0.000
#> GSM1022346 1 0.000 0.861 1.00 0.000 0.000
#> GSM1022355 1 0.502 0.836 0.76 0.000 0.240
#> GSM1022356 1 0.502 0.836 0.76 0.000 0.240
#> GSM1022357 1 0.502 0.836 0.76 0.000 0.240
#> GSM1022358 1 0.502 0.836 0.76 0.000 0.240
#> GSM1022351 1 0.502 0.836 0.76 0.000 0.240
#> GSM1022352 1 0.502 0.836 0.76 0.000 0.240
#> GSM1022353 1 0.502 0.836 0.76 0.000 0.240
#> GSM1022354 1 0.502 0.836 0.76 0.000 0.240
#> GSM1022359 2 0.000 0.991 0.00 1.000 0.000
#> GSM1022360 2 0.000 0.991 0.00 1.000 0.000
#> GSM1022361 2 0.000 0.991 0.00 1.000 0.000
#> GSM1022362 2 0.000 0.991 0.00 1.000 0.000
#> GSM1022367 2 0.000 0.991 0.00 1.000 0.000
#> GSM1022368 2 0.000 0.991 0.00 1.000 0.000
#> GSM1022369 2 0.000 0.991 0.00 1.000 0.000
#> GSM1022370 2 0.000 0.991 0.00 1.000 0.000
#> GSM1022363 2 0.000 0.991 0.00 1.000 0.000
#> GSM1022364 2 0.000 0.991 0.00 1.000 0.000
#> GSM1022365 2 0.000 0.991 0.00 1.000 0.000
#> GSM1022366 2 0.000 0.991 0.00 1.000 0.000
#> GSM1022374 2 0.000 0.991 0.00 1.000 0.000
#> GSM1022375 2 0.000 0.991 0.00 1.000 0.000
#> GSM1022376 2 0.000 0.991 0.00 1.000 0.000
#> GSM1022371 2 0.000 0.991 0.00 1.000 0.000
#> GSM1022372 2 0.000 0.991 0.00 1.000 0.000
#> GSM1022373 2 0.000 0.991 0.00 1.000 0.000
#> GSM1022377 3 0.000 0.956 0.00 0.000 1.000
#> GSM1022378 3 0.000 0.956 0.00 0.000 1.000
#> GSM1022379 3 0.000 0.956 0.00 0.000 1.000
#> GSM1022380 3 0.000 0.956 0.00 0.000 1.000
#> GSM1022385 1 0.000 0.861 1.00 0.000 0.000
#> GSM1022386 1 0.000 0.861 1.00 0.000 0.000
#> GSM1022387 1 0.000 0.861 1.00 0.000 0.000
#> GSM1022388 1 0.000 0.861 1.00 0.000 0.000
#> GSM1022381 3 0.000 0.956 0.00 0.000 1.000
#> GSM1022382 3 0.000 0.956 0.00 0.000 1.000
#> GSM1022383 3 0.000 0.956 0.00 0.000 1.000
#> GSM1022384 3 0.000 0.956 0.00 0.000 1.000
#> GSM1022393 1 0.502 0.836 0.76 0.000 0.240
#> GSM1022394 1 0.502 0.836 0.76 0.000 0.240
#> GSM1022395 1 0.502 0.836 0.76 0.000 0.240
#> GSM1022396 1 0.502 0.836 0.76 0.000 0.240
#> GSM1022389 3 0.000 0.956 0.00 0.000 1.000
#> GSM1022390 3 0.000 0.956 0.00 0.000 1.000
#> GSM1022391 3 0.000 0.956 0.00 0.000 1.000
#> GSM1022392 3 0.000 0.956 0.00 0.000 1.000
#> GSM1022397 1 0.000 0.861 1.00 0.000 0.000
#> GSM1022398 1 0.000 0.861 1.00 0.000 0.000
#> GSM1022399 1 0.000 0.861 1.00 0.000 0.000
#> GSM1022400 1 0.000 0.861 1.00 0.000 0.000
#> GSM1022401 1 0.502 0.836 0.76 0.000 0.240
#> GSM1022402 1 0.502 0.836 0.76 0.000 0.240
#> GSM1022403 1 0.502 0.836 0.76 0.000 0.240
#> GSM1022404 1 0.502 0.836 0.76 0.000 0.240
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1022325 2 0.000 0.976 0.000 1.000 0.000 0.000
#> GSM1022326 2 0.000 0.976 0.000 1.000 0.000 0.000
#> GSM1022327 2 0.000 0.976 0.000 1.000 0.000 0.000
#> GSM1022331 2 0.517 0.743 0.092 0.756 0.000 0.152
#> GSM1022332 4 0.670 0.181 0.092 0.396 0.000 0.512
#> GSM1022333 2 0.389 0.862 0.092 0.844 0.000 0.064
#> GSM1022328 2 0.000 0.976 0.000 1.000 0.000 0.000
#> GSM1022329 2 0.000 0.976 0.000 1.000 0.000 0.000
#> GSM1022330 2 0.000 0.976 0.000 1.000 0.000 0.000
#> GSM1022337 2 0.222 0.923 0.092 0.908 0.000 0.000
#> GSM1022338 2 0.222 0.923 0.092 0.908 0.000 0.000
#> GSM1022339 2 0.222 0.923 0.092 0.908 0.000 0.000
#> GSM1022334 2 0.000 0.976 0.000 1.000 0.000 0.000
#> GSM1022335 2 0.000 0.976 0.000 1.000 0.000 0.000
#> GSM1022336 2 0.000 0.976 0.000 1.000 0.000 0.000
#> GSM1022340 1 0.471 0.581 0.640 0.000 0.360 0.000
#> GSM1022341 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM1022342 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM1022343 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM1022347 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM1022348 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM1022349 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM1022350 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM1022344 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM1022345 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM1022346 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM1022355 1 0.222 0.981 0.908 0.000 0.092 0.000
#> GSM1022356 1 0.222 0.981 0.908 0.000 0.092 0.000
#> GSM1022357 1 0.222 0.981 0.908 0.000 0.092 0.000
#> GSM1022358 1 0.222 0.981 0.908 0.000 0.092 0.000
#> GSM1022351 1 0.222 0.981 0.908 0.000 0.092 0.000
#> GSM1022352 1 0.222 0.981 0.908 0.000 0.092 0.000
#> GSM1022353 1 0.222 0.981 0.908 0.000 0.092 0.000
#> GSM1022354 1 0.222 0.981 0.908 0.000 0.092 0.000
#> GSM1022359 2 0.000 0.976 0.000 1.000 0.000 0.000
#> GSM1022360 2 0.000 0.976 0.000 1.000 0.000 0.000
#> GSM1022361 2 0.000 0.976 0.000 1.000 0.000 0.000
#> GSM1022362 2 0.000 0.976 0.000 1.000 0.000 0.000
#> GSM1022367 2 0.000 0.976 0.000 1.000 0.000 0.000
#> GSM1022368 2 0.000 0.976 0.000 1.000 0.000 0.000
#> GSM1022369 2 0.000 0.976 0.000 1.000 0.000 0.000
#> GSM1022370 2 0.000 0.976 0.000 1.000 0.000 0.000
#> GSM1022363 2 0.000 0.976 0.000 1.000 0.000 0.000
#> GSM1022364 2 0.000 0.976 0.000 1.000 0.000 0.000
#> GSM1022365 2 0.000 0.976 0.000 1.000 0.000 0.000
#> GSM1022366 2 0.000 0.976 0.000 1.000 0.000 0.000
#> GSM1022374 2 0.130 0.954 0.044 0.956 0.000 0.000
#> GSM1022375 2 0.130 0.954 0.044 0.956 0.000 0.000
#> GSM1022376 2 0.172 0.942 0.064 0.936 0.000 0.000
#> GSM1022371 2 0.000 0.976 0.000 1.000 0.000 0.000
#> GSM1022372 2 0.000 0.976 0.000 1.000 0.000 0.000
#> GSM1022373 2 0.000 0.976 0.000 1.000 0.000 0.000
#> GSM1022377 4 0.000 0.954 0.000 0.000 0.000 1.000
#> GSM1022378 4 0.000 0.954 0.000 0.000 0.000 1.000
#> GSM1022379 4 0.000 0.954 0.000 0.000 0.000 1.000
#> GSM1022380 4 0.000 0.954 0.000 0.000 0.000 1.000
#> GSM1022385 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM1022386 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM1022387 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM1022388 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM1022381 4 0.000 0.954 0.000 0.000 0.000 1.000
#> GSM1022382 4 0.000 0.954 0.000 0.000 0.000 1.000
#> GSM1022383 4 0.000 0.954 0.000 0.000 0.000 1.000
#> GSM1022384 4 0.000 0.954 0.000 0.000 0.000 1.000
#> GSM1022393 1 0.222 0.981 0.908 0.000 0.092 0.000
#> GSM1022394 1 0.222 0.981 0.908 0.000 0.092 0.000
#> GSM1022395 1 0.222 0.981 0.908 0.000 0.092 0.000
#> GSM1022396 1 0.222 0.981 0.908 0.000 0.092 0.000
#> GSM1022389 4 0.000 0.954 0.000 0.000 0.000 1.000
#> GSM1022390 4 0.000 0.954 0.000 0.000 0.000 1.000
#> GSM1022391 4 0.000 0.954 0.000 0.000 0.000 1.000
#> GSM1022392 4 0.000 0.954 0.000 0.000 0.000 1.000
#> GSM1022397 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM1022398 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM1022399 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM1022400 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM1022401 1 0.222 0.981 0.908 0.000 0.092 0.000
#> GSM1022402 1 0.222 0.981 0.908 0.000 0.092 0.000
#> GSM1022403 1 0.222 0.981 0.908 0.000 0.092 0.000
#> GSM1022404 1 0.222 0.981 0.908 0.000 0.092 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1022325 2 0.000 1.000 0.000 1.000 0.000 0 0.000
#> GSM1022326 2 0.000 1.000 0.000 1.000 0.000 0 0.000
#> GSM1022327 2 0.000 1.000 0.000 1.000 0.000 0 0.000
#> GSM1022331 5 0.000 0.855 0.000 0.000 0.000 0 1.000
#> GSM1022332 5 0.000 0.855 0.000 0.000 0.000 0 1.000
#> GSM1022333 5 0.000 0.855 0.000 0.000 0.000 0 1.000
#> GSM1022328 2 0.000 1.000 0.000 1.000 0.000 0 0.000
#> GSM1022329 2 0.000 1.000 0.000 1.000 0.000 0 0.000
#> GSM1022330 2 0.000 1.000 0.000 1.000 0.000 0 0.000
#> GSM1022337 5 0.000 0.855 0.000 0.000 0.000 0 1.000
#> GSM1022338 5 0.000 0.855 0.000 0.000 0.000 0 1.000
#> GSM1022339 5 0.000 0.855 0.000 0.000 0.000 0 1.000
#> GSM1022334 2 0.000 1.000 0.000 1.000 0.000 0 0.000
#> GSM1022335 2 0.000 1.000 0.000 1.000 0.000 0 0.000
#> GSM1022336 2 0.000 1.000 0.000 1.000 0.000 0 0.000
#> GSM1022340 1 0.382 0.563 0.696 0.000 0.304 0 0.000
#> GSM1022341 3 0.000 1.000 0.000 0.000 1.000 0 0.000
#> GSM1022342 3 0.000 1.000 0.000 0.000 1.000 0 0.000
#> GSM1022343 3 0.000 1.000 0.000 0.000 1.000 0 0.000
#> GSM1022347 3 0.000 1.000 0.000 0.000 1.000 0 0.000
#> GSM1022348 3 0.000 1.000 0.000 0.000 1.000 0 0.000
#> GSM1022349 3 0.000 1.000 0.000 0.000 1.000 0 0.000
#> GSM1022350 3 0.000 1.000 0.000 0.000 1.000 0 0.000
#> GSM1022344 3 0.000 1.000 0.000 0.000 1.000 0 0.000
#> GSM1022345 3 0.000 1.000 0.000 0.000 1.000 0 0.000
#> GSM1022346 3 0.000 1.000 0.000 0.000 1.000 0 0.000
#> GSM1022355 1 0.000 0.977 1.000 0.000 0.000 0 0.000
#> GSM1022356 1 0.000 0.977 1.000 0.000 0.000 0 0.000
#> GSM1022357 1 0.000 0.977 1.000 0.000 0.000 0 0.000
#> GSM1022358 1 0.000 0.977 1.000 0.000 0.000 0 0.000
#> GSM1022351 1 0.000 0.977 1.000 0.000 0.000 0 0.000
#> GSM1022352 1 0.000 0.977 1.000 0.000 0.000 0 0.000
#> GSM1022353 1 0.000 0.977 1.000 0.000 0.000 0 0.000
#> GSM1022354 1 0.000 0.977 1.000 0.000 0.000 0 0.000
#> GSM1022359 2 0.000 1.000 0.000 1.000 0.000 0 0.000
#> GSM1022360 2 0.000 1.000 0.000 1.000 0.000 0 0.000
#> GSM1022361 2 0.000 1.000 0.000 1.000 0.000 0 0.000
#> GSM1022362 2 0.000 1.000 0.000 1.000 0.000 0 0.000
#> GSM1022367 2 0.000 1.000 0.000 1.000 0.000 0 0.000
#> GSM1022368 2 0.000 1.000 0.000 1.000 0.000 0 0.000
#> GSM1022369 2 0.000 1.000 0.000 1.000 0.000 0 0.000
#> GSM1022370 2 0.000 1.000 0.000 1.000 0.000 0 0.000
#> GSM1022363 2 0.000 1.000 0.000 1.000 0.000 0 0.000
#> GSM1022364 2 0.000 1.000 0.000 1.000 0.000 0 0.000
#> GSM1022365 2 0.000 1.000 0.000 1.000 0.000 0 0.000
#> GSM1022366 2 0.000 1.000 0.000 1.000 0.000 0 0.000
#> GSM1022374 5 0.417 0.456 0.000 0.396 0.000 0 0.604
#> GSM1022375 5 0.417 0.456 0.000 0.396 0.000 0 0.604
#> GSM1022376 5 0.218 0.796 0.000 0.112 0.000 0 0.888
#> GSM1022371 2 0.000 1.000 0.000 1.000 0.000 0 0.000
#> GSM1022372 2 0.000 1.000 0.000 1.000 0.000 0 0.000
#> GSM1022373 2 0.000 1.000 0.000 1.000 0.000 0 0.000
#> GSM1022377 4 0.000 1.000 0.000 0.000 0.000 1 0.000
#> GSM1022378 4 0.000 1.000 0.000 0.000 0.000 1 0.000
#> GSM1022379 4 0.000 1.000 0.000 0.000 0.000 1 0.000
#> GSM1022380 4 0.000 1.000 0.000 0.000 0.000 1 0.000
#> GSM1022385 3 0.000 1.000 0.000 0.000 1.000 0 0.000
#> GSM1022386 3 0.000 1.000 0.000 0.000 1.000 0 0.000
#> GSM1022387 3 0.000 1.000 0.000 0.000 1.000 0 0.000
#> GSM1022388 3 0.000 1.000 0.000 0.000 1.000 0 0.000
#> GSM1022381 4 0.000 1.000 0.000 0.000 0.000 1 0.000
#> GSM1022382 4 0.000 1.000 0.000 0.000 0.000 1 0.000
#> GSM1022383 4 0.000 1.000 0.000 0.000 0.000 1 0.000
#> GSM1022384 4 0.000 1.000 0.000 0.000 0.000 1 0.000
#> GSM1022393 1 0.000 0.977 1.000 0.000 0.000 0 0.000
#> GSM1022394 1 0.000 0.977 1.000 0.000 0.000 0 0.000
#> GSM1022395 1 0.000 0.977 1.000 0.000 0.000 0 0.000
#> GSM1022396 1 0.000 0.977 1.000 0.000 0.000 0 0.000
#> GSM1022389 4 0.000 1.000 0.000 0.000 0.000 1 0.000
#> GSM1022390 4 0.000 1.000 0.000 0.000 0.000 1 0.000
#> GSM1022391 4 0.000 1.000 0.000 0.000 0.000 1 0.000
#> GSM1022392 4 0.000 1.000 0.000 0.000 0.000 1 0.000
#> GSM1022397 3 0.000 1.000 0.000 0.000 1.000 0 0.000
#> GSM1022398 3 0.000 1.000 0.000 0.000 1.000 0 0.000
#> GSM1022399 3 0.000 1.000 0.000 0.000 1.000 0 0.000
#> GSM1022400 3 0.000 1.000 0.000 0.000 1.000 0 0.000
#> GSM1022401 1 0.000 0.977 1.000 0.000 0.000 0 0.000
#> GSM1022402 1 0.000 0.977 1.000 0.000 0.000 0 0.000
#> GSM1022403 1 0.000 0.977 1.000 0.000 0.000 0 0.000
#> GSM1022404 1 0.000 0.977 1.000 0.000 0.000 0 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1022325 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022326 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022327 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022331 5 0.000 0.866 0.000 0.000 0.000 0 1.000 0.000
#> GSM1022332 5 0.000 0.866 0.000 0.000 0.000 0 1.000 0.000
#> GSM1022333 5 0.000 0.866 0.000 0.000 0.000 0 1.000 0.000
#> GSM1022328 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022329 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022330 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022337 5 0.000 0.866 0.000 0.000 0.000 0 1.000 0.000
#> GSM1022338 5 0.000 0.866 0.000 0.000 0.000 0 1.000 0.000
#> GSM1022339 5 0.000 0.866 0.000 0.000 0.000 0 1.000 0.000
#> GSM1022334 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022335 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022336 2 0.000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM1022340 1 0.343 0.563 0.696 0.000 0.304 0 0.000 0.000
#> GSM1022341 3 0.000 1.000 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022342 3 0.000 1.000 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022343 3 0.000 1.000 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022347 3 0.000 1.000 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022348 3 0.000 1.000 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022349 3 0.000 1.000 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022350 3 0.000 1.000 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022344 3 0.000 1.000 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022345 3 0.000 1.000 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022346 3 0.000 1.000 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022355 1 0.000 0.977 1.000 0.000 0.000 0 0.000 0.000
#> GSM1022356 1 0.000 0.977 1.000 0.000 0.000 0 0.000 0.000
#> GSM1022357 1 0.000 0.977 1.000 0.000 0.000 0 0.000 0.000
#> GSM1022358 1 0.000 0.977 1.000 0.000 0.000 0 0.000 0.000
#> GSM1022351 1 0.000 0.977 1.000 0.000 0.000 0 0.000 0.000
#> GSM1022352 1 0.000 0.977 1.000 0.000 0.000 0 0.000 0.000
#> GSM1022353 1 0.000 0.977 1.000 0.000 0.000 0 0.000 0.000
#> GSM1022354 1 0.000 0.977 1.000 0.000 0.000 0 0.000 0.000
#> GSM1022359 6 0.000 1.000 0.000 0.000 0.000 0 0.000 1.000
#> GSM1022360 6 0.000 1.000 0.000 0.000 0.000 0 0.000 1.000
#> GSM1022361 6 0.000 1.000 0.000 0.000 0.000 0 0.000 1.000
#> GSM1022362 6 0.000 1.000 0.000 0.000 0.000 0 0.000 1.000
#> GSM1022367 6 0.000 1.000 0.000 0.000 0.000 0 0.000 1.000
#> GSM1022368 6 0.000 1.000 0.000 0.000 0.000 0 0.000 1.000
#> GSM1022369 6 0.000 1.000 0.000 0.000 0.000 0 0.000 1.000
#> GSM1022370 6 0.000 1.000 0.000 0.000 0.000 0 0.000 1.000
#> GSM1022363 6 0.000 1.000 0.000 0.000 0.000 0 0.000 1.000
#> GSM1022364 6 0.000 1.000 0.000 0.000 0.000 0 0.000 1.000
#> GSM1022365 6 0.000 1.000 0.000 0.000 0.000 0 0.000 1.000
#> GSM1022366 6 0.000 1.000 0.000 0.000 0.000 0 0.000 1.000
#> GSM1022374 5 0.398 0.459 0.000 0.008 0.000 0 0.600 0.392
#> GSM1022375 5 0.376 0.446 0.000 0.000 0.000 0 0.600 0.400
#> GSM1022376 5 0.222 0.810 0.000 0.012 0.000 0 0.884 0.104
#> GSM1022371 6 0.000 1.000 0.000 0.000 0.000 0 0.000 1.000
#> GSM1022372 6 0.000 1.000 0.000 0.000 0.000 0 0.000 1.000
#> GSM1022373 6 0.000 1.000 0.000 0.000 0.000 0 0.000 1.000
#> GSM1022377 4 0.000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM1022378 4 0.000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM1022379 4 0.000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM1022380 4 0.000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM1022385 3 0.000 1.000 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022386 3 0.000 1.000 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022387 3 0.000 1.000 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022388 3 0.000 1.000 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022381 4 0.000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM1022382 4 0.000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM1022383 4 0.000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM1022384 4 0.000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM1022393 1 0.000 0.977 1.000 0.000 0.000 0 0.000 0.000
#> GSM1022394 1 0.000 0.977 1.000 0.000 0.000 0 0.000 0.000
#> GSM1022395 1 0.000 0.977 1.000 0.000 0.000 0 0.000 0.000
#> GSM1022396 1 0.000 0.977 1.000 0.000 0.000 0 0.000 0.000
#> GSM1022389 4 0.000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM1022390 4 0.000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM1022391 4 0.000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM1022392 4 0.000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM1022397 3 0.000 1.000 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022398 3 0.000 1.000 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022399 3 0.000 1.000 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022400 3 0.000 1.000 0.000 0.000 1.000 0 0.000 0.000
#> GSM1022401 1 0.000 0.977 1.000 0.000 0.000 0 0.000 0.000
#> GSM1022402 1 0.000 0.977 1.000 0.000 0.000 0 0.000 0.000
#> GSM1022403 1 0.000 0.977 1.000 0.000 0.000 0 0.000 0.000
#> GSM1022404 1 0.000 0.977 1.000 0.000 0.000 0 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 4)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n protocol(p) cell.type(p) k
#> ATC:pam 80 1.10e-11 4.22e-01 2
#> ATC:pam 79 1.71e-14 1.03e-04 3
#> ATC:pam 79 5.15e-21 3.63e-04 4
#> ATC:pam 78 1.86e-20 7.15e-07 5
#> ATC:pam 78 1.97e-26 1.09e-06 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "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 31589 rows and 80 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.519 0.874 0.868 0.4347 0.509 0.509
#> 3 3 0.789 0.834 0.887 0.4804 0.835 0.685
#> 4 4 0.881 0.905 0.951 0.0936 0.902 0.749
#> 5 5 0.938 0.955 0.974 0.1363 0.867 0.584
#> 6 6 0.958 0.956 0.945 0.0236 0.987 0.933
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 5
There is also optional best \(k\) = 5 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM1022325 2 0.000 1.000 0.00 1.00
#> GSM1022326 2 0.000 1.000 0.00 1.00
#> GSM1022327 2 0.000 1.000 0.00 1.00
#> GSM1022331 2 0.000 1.000 0.00 1.00
#> GSM1022332 2 0.000 1.000 0.00 1.00
#> GSM1022333 2 0.000 1.000 0.00 1.00
#> GSM1022328 2 0.000 1.000 0.00 1.00
#> GSM1022329 2 0.000 1.000 0.00 1.00
#> GSM1022330 2 0.000 1.000 0.00 1.00
#> GSM1022337 2 0.000 1.000 0.00 1.00
#> GSM1022338 2 0.000 1.000 0.00 1.00
#> GSM1022339 2 0.000 1.000 0.00 1.00
#> GSM1022334 2 0.000 1.000 0.00 1.00
#> GSM1022335 2 0.000 1.000 0.00 1.00
#> GSM1022336 2 0.000 1.000 0.00 1.00
#> GSM1022340 1 0.925 0.821 0.66 0.34
#> GSM1022341 1 0.925 0.821 0.66 0.34
#> GSM1022342 1 0.925 0.821 0.66 0.34
#> GSM1022343 1 0.925 0.821 0.66 0.34
#> GSM1022347 1 0.925 0.821 0.66 0.34
#> GSM1022348 1 0.925 0.821 0.66 0.34
#> GSM1022349 1 0.925 0.821 0.66 0.34
#> GSM1022350 1 0.925 0.821 0.66 0.34
#> GSM1022344 1 0.925 0.821 0.66 0.34
#> GSM1022345 1 0.925 0.821 0.66 0.34
#> GSM1022346 1 0.925 0.821 0.66 0.34
#> GSM1022355 1 0.000 0.716 1.00 0.00
#> GSM1022356 1 0.000 0.716 1.00 0.00
#> GSM1022357 1 0.000 0.716 1.00 0.00
#> GSM1022358 1 0.000 0.716 1.00 0.00
#> GSM1022351 1 0.000 0.716 1.00 0.00
#> GSM1022352 1 0.000 0.716 1.00 0.00
#> GSM1022353 1 0.000 0.716 1.00 0.00
#> GSM1022354 1 0.000 0.716 1.00 0.00
#> GSM1022359 2 0.000 1.000 0.00 1.00
#> GSM1022360 2 0.000 1.000 0.00 1.00
#> GSM1022361 2 0.000 1.000 0.00 1.00
#> GSM1022362 2 0.000 1.000 0.00 1.00
#> GSM1022367 2 0.000 1.000 0.00 1.00
#> GSM1022368 2 0.000 1.000 0.00 1.00
#> GSM1022369 2 0.000 1.000 0.00 1.00
#> GSM1022370 2 0.000 1.000 0.00 1.00
#> GSM1022363 2 0.000 1.000 0.00 1.00
#> GSM1022364 2 0.000 1.000 0.00 1.00
#> GSM1022365 2 0.000 1.000 0.00 1.00
#> GSM1022366 2 0.000 1.000 0.00 1.00
#> GSM1022374 2 0.000 1.000 0.00 1.00
#> GSM1022375 2 0.000 1.000 0.00 1.00
#> GSM1022376 2 0.000 1.000 0.00 1.00
#> GSM1022371 2 0.000 1.000 0.00 1.00
#> GSM1022372 2 0.000 1.000 0.00 1.00
#> GSM1022373 2 0.000 1.000 0.00 1.00
#> GSM1022377 1 0.925 0.821 0.66 0.34
#> GSM1022378 1 0.925 0.821 0.66 0.34
#> GSM1022379 1 0.925 0.821 0.66 0.34
#> GSM1022380 1 0.925 0.821 0.66 0.34
#> GSM1022385 1 0.925 0.821 0.66 0.34
#> GSM1022386 1 0.925 0.821 0.66 0.34
#> GSM1022387 1 0.925 0.821 0.66 0.34
#> GSM1022388 1 0.925 0.821 0.66 0.34
#> GSM1022381 1 0.925 0.821 0.66 0.34
#> GSM1022382 1 0.925 0.821 0.66 0.34
#> GSM1022383 1 0.925 0.821 0.66 0.34
#> GSM1022384 1 0.925 0.821 0.66 0.34
#> GSM1022393 1 0.000 0.716 1.00 0.00
#> GSM1022394 1 0.000 0.716 1.00 0.00
#> GSM1022395 1 0.000 0.716 1.00 0.00
#> GSM1022396 1 0.000 0.716 1.00 0.00
#> GSM1022389 1 0.925 0.821 0.66 0.34
#> GSM1022390 1 0.925 0.821 0.66 0.34
#> GSM1022391 1 0.925 0.821 0.66 0.34
#> GSM1022392 1 0.925 0.821 0.66 0.34
#> GSM1022397 1 0.925 0.821 0.66 0.34
#> GSM1022398 1 0.925 0.821 0.66 0.34
#> GSM1022399 1 0.925 0.821 0.66 0.34
#> GSM1022400 1 0.925 0.821 0.66 0.34
#> GSM1022401 1 0.000 0.716 1.00 0.00
#> GSM1022402 1 0.000 0.716 1.00 0.00
#> GSM1022403 1 0.000 0.716 1.00 0.00
#> GSM1022404 1 0.000 0.716 1.00 0.00
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1022325 2 0.0000 0.997 0.000 1.000 0.000
#> GSM1022326 2 0.0000 0.997 0.000 1.000 0.000
#> GSM1022327 2 0.0000 0.997 0.000 1.000 0.000
#> GSM1022331 2 0.0424 0.993 0.000 0.992 0.008
#> GSM1022332 2 0.0424 0.993 0.000 0.992 0.008
#> GSM1022333 2 0.0424 0.993 0.000 0.992 0.008
#> GSM1022328 2 0.0000 0.997 0.000 1.000 0.000
#> GSM1022329 2 0.0000 0.997 0.000 1.000 0.000
#> GSM1022330 2 0.0000 0.997 0.000 1.000 0.000
#> GSM1022337 3 0.2537 0.762 0.000 0.080 0.920
#> GSM1022338 3 0.2537 0.762 0.000 0.080 0.920
#> GSM1022339 3 0.2537 0.762 0.000 0.080 0.920
#> GSM1022334 2 0.0000 0.997 0.000 1.000 0.000
#> GSM1022335 2 0.0000 0.997 0.000 1.000 0.000
#> GSM1022336 2 0.0000 0.997 0.000 1.000 0.000
#> GSM1022340 1 0.0000 0.806 1.000 0.000 0.000
#> GSM1022341 1 0.0000 0.806 1.000 0.000 0.000
#> GSM1022342 1 0.0000 0.806 1.000 0.000 0.000
#> GSM1022343 1 0.0000 0.806 1.000 0.000 0.000
#> GSM1022347 1 0.0747 0.808 0.984 0.000 0.016
#> GSM1022348 1 0.0747 0.808 0.984 0.000 0.016
#> GSM1022349 1 0.0747 0.808 0.984 0.000 0.016
#> GSM1022350 1 0.0747 0.808 0.984 0.000 0.016
#> GSM1022344 1 0.0000 0.806 1.000 0.000 0.000
#> GSM1022345 1 0.0892 0.809 0.980 0.000 0.020
#> GSM1022346 1 0.0892 0.809 0.980 0.000 0.020
#> GSM1022355 1 0.5016 0.776 0.760 0.000 0.240
#> GSM1022356 1 0.5016 0.776 0.760 0.000 0.240
#> GSM1022357 1 0.5016 0.776 0.760 0.000 0.240
#> GSM1022358 1 0.5016 0.776 0.760 0.000 0.240
#> GSM1022351 1 0.5016 0.776 0.760 0.000 0.240
#> GSM1022352 1 0.5016 0.776 0.760 0.000 0.240
#> GSM1022353 1 0.5016 0.776 0.760 0.000 0.240
#> GSM1022354 1 0.5016 0.776 0.760 0.000 0.240
#> GSM1022359 2 0.0000 0.997 0.000 1.000 0.000
#> GSM1022360 2 0.0000 0.997 0.000 1.000 0.000
#> GSM1022361 2 0.0000 0.997 0.000 1.000 0.000
#> GSM1022362 2 0.0000 0.997 0.000 1.000 0.000
#> GSM1022367 2 0.0424 0.993 0.000 0.992 0.008
#> GSM1022368 2 0.0424 0.993 0.000 0.992 0.008
#> GSM1022369 2 0.0424 0.993 0.000 0.992 0.008
#> GSM1022370 2 0.0424 0.993 0.000 0.992 0.008
#> GSM1022363 2 0.0000 0.997 0.000 1.000 0.000
#> GSM1022364 2 0.0000 0.997 0.000 1.000 0.000
#> GSM1022365 2 0.0000 0.997 0.000 1.000 0.000
#> GSM1022366 2 0.0000 0.997 0.000 1.000 0.000
#> GSM1022374 3 0.2537 0.762 0.000 0.080 0.920
#> GSM1022375 3 0.2537 0.762 0.000 0.080 0.920
#> GSM1022376 3 0.2537 0.762 0.000 0.080 0.920
#> GSM1022371 2 0.0000 0.997 0.000 1.000 0.000
#> GSM1022372 2 0.0000 0.997 0.000 1.000 0.000
#> GSM1022373 2 0.0000 0.997 0.000 1.000 0.000
#> GSM1022377 3 0.5178 0.815 0.256 0.000 0.744
#> GSM1022378 3 0.5178 0.815 0.256 0.000 0.744
#> GSM1022379 3 0.5178 0.815 0.256 0.000 0.744
#> GSM1022380 3 0.5178 0.815 0.256 0.000 0.744
#> GSM1022385 1 0.1031 0.804 0.976 0.000 0.024
#> GSM1022386 1 0.1031 0.804 0.976 0.000 0.024
#> GSM1022387 1 0.1031 0.804 0.976 0.000 0.024
#> GSM1022388 1 0.1031 0.804 0.976 0.000 0.024
#> GSM1022381 3 0.5178 0.815 0.256 0.000 0.744
#> GSM1022382 3 0.5178 0.815 0.256 0.000 0.744
#> GSM1022383 3 0.5178 0.815 0.256 0.000 0.744
#> GSM1022384 3 0.5178 0.815 0.256 0.000 0.744
#> GSM1022393 1 0.5016 0.776 0.760 0.000 0.240
#> GSM1022394 1 0.5016 0.776 0.760 0.000 0.240
#> GSM1022395 1 0.5016 0.776 0.760 0.000 0.240
#> GSM1022396 1 0.5016 0.776 0.760 0.000 0.240
#> GSM1022389 1 0.5835 0.237 0.660 0.000 0.340
#> GSM1022390 1 0.5760 0.273 0.672 0.000 0.328
#> GSM1022391 1 0.5835 0.237 0.660 0.000 0.340
#> GSM1022392 1 0.5760 0.273 0.672 0.000 0.328
#> GSM1022397 1 0.0747 0.808 0.984 0.000 0.016
#> GSM1022398 1 0.0747 0.808 0.984 0.000 0.016
#> GSM1022399 1 0.0747 0.808 0.984 0.000 0.016
#> GSM1022400 1 0.0747 0.808 0.984 0.000 0.016
#> GSM1022401 1 0.5016 0.776 0.760 0.000 0.240
#> GSM1022402 1 0.5016 0.776 0.760 0.000 0.240
#> GSM1022403 1 0.5016 0.776 0.760 0.000 0.240
#> GSM1022404 1 0.5016 0.776 0.760 0.000 0.240
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1022325 2 0.000 0.916 0.000 1.000 0.000 0
#> GSM1022326 2 0.000 0.916 0.000 1.000 0.000 0
#> GSM1022327 2 0.000 0.916 0.000 1.000 0.000 0
#> GSM1022331 3 0.247 0.881 0.000 0.108 0.892 0
#> GSM1022332 3 0.247 0.881 0.000 0.108 0.892 0
#> GSM1022333 3 0.247 0.881 0.000 0.108 0.892 0
#> GSM1022328 2 0.000 0.916 0.000 1.000 0.000 0
#> GSM1022329 2 0.000 0.916 0.000 1.000 0.000 0
#> GSM1022330 2 0.000 0.916 0.000 1.000 0.000 0
#> GSM1022337 3 0.000 0.943 0.000 0.000 1.000 0
#> GSM1022338 3 0.000 0.943 0.000 0.000 1.000 0
#> GSM1022339 3 0.000 0.943 0.000 0.000 1.000 0
#> GSM1022334 2 0.000 0.916 0.000 1.000 0.000 0
#> GSM1022335 2 0.000 0.916 0.000 1.000 0.000 0
#> GSM1022336 2 0.000 0.916 0.000 1.000 0.000 0
#> GSM1022340 1 0.121 0.945 0.960 0.000 0.040 0
#> GSM1022341 1 0.121 0.945 0.960 0.000 0.040 0
#> GSM1022342 1 0.121 0.945 0.960 0.000 0.040 0
#> GSM1022343 1 0.121 0.945 0.960 0.000 0.040 0
#> GSM1022347 1 0.302 0.902 0.852 0.000 0.148 0
#> GSM1022348 1 0.302 0.902 0.852 0.000 0.148 0
#> GSM1022349 1 0.302 0.902 0.852 0.000 0.148 0
#> GSM1022350 1 0.302 0.902 0.852 0.000 0.148 0
#> GSM1022344 1 0.121 0.945 0.960 0.000 0.040 0
#> GSM1022345 1 0.121 0.945 0.960 0.000 0.040 0
#> GSM1022346 1 0.121 0.945 0.960 0.000 0.040 0
#> GSM1022355 1 0.000 0.946 1.000 0.000 0.000 0
#> GSM1022356 1 0.000 0.946 1.000 0.000 0.000 0
#> GSM1022357 1 0.000 0.946 1.000 0.000 0.000 0
#> GSM1022358 1 0.000 0.946 1.000 0.000 0.000 0
#> GSM1022351 1 0.000 0.946 1.000 0.000 0.000 0
#> GSM1022352 1 0.000 0.946 1.000 0.000 0.000 0
#> GSM1022353 1 0.000 0.946 1.000 0.000 0.000 0
#> GSM1022354 1 0.000 0.946 1.000 0.000 0.000 0
#> GSM1022359 2 0.000 0.916 0.000 1.000 0.000 0
#> GSM1022360 2 0.000 0.916 0.000 1.000 0.000 0
#> GSM1022361 2 0.000 0.916 0.000 1.000 0.000 0
#> GSM1022362 2 0.000 0.916 0.000 1.000 0.000 0
#> GSM1022367 2 0.493 0.280 0.000 0.568 0.432 0
#> GSM1022368 2 0.493 0.280 0.000 0.568 0.432 0
#> GSM1022369 2 0.493 0.280 0.000 0.568 0.432 0
#> GSM1022370 2 0.493 0.280 0.000 0.568 0.432 0
#> GSM1022363 2 0.000 0.916 0.000 1.000 0.000 0
#> GSM1022364 2 0.000 0.916 0.000 1.000 0.000 0
#> GSM1022365 2 0.000 0.916 0.000 1.000 0.000 0
#> GSM1022366 2 0.000 0.916 0.000 1.000 0.000 0
#> GSM1022374 3 0.000 0.943 0.000 0.000 1.000 0
#> GSM1022375 3 0.000 0.943 0.000 0.000 1.000 0
#> GSM1022376 3 0.000 0.943 0.000 0.000 1.000 0
#> GSM1022371 2 0.000 0.916 0.000 1.000 0.000 0
#> GSM1022372 2 0.000 0.916 0.000 1.000 0.000 0
#> GSM1022373 2 0.000 0.916 0.000 1.000 0.000 0
#> GSM1022377 4 0.000 1.000 0.000 0.000 0.000 1
#> GSM1022378 4 0.000 1.000 0.000 0.000 0.000 1
#> GSM1022379 4 0.000 1.000 0.000 0.000 0.000 1
#> GSM1022380 4 0.000 1.000 0.000 0.000 0.000 1
#> GSM1022385 1 0.297 0.904 0.856 0.000 0.144 0
#> GSM1022386 1 0.228 0.928 0.904 0.000 0.096 0
#> GSM1022387 1 0.228 0.928 0.904 0.000 0.096 0
#> GSM1022388 1 0.228 0.928 0.904 0.000 0.096 0
#> GSM1022381 4 0.000 1.000 0.000 0.000 0.000 1
#> GSM1022382 4 0.000 1.000 0.000 0.000 0.000 1
#> GSM1022383 4 0.000 1.000 0.000 0.000 0.000 1
#> GSM1022384 4 0.000 1.000 0.000 0.000 0.000 1
#> GSM1022393 1 0.000 0.946 1.000 0.000 0.000 0
#> GSM1022394 1 0.000 0.946 1.000 0.000 0.000 0
#> GSM1022395 1 0.000 0.946 1.000 0.000 0.000 0
#> GSM1022396 1 0.000 0.946 1.000 0.000 0.000 0
#> GSM1022389 4 0.000 1.000 0.000 0.000 0.000 1
#> GSM1022390 4 0.000 1.000 0.000 0.000 0.000 1
#> GSM1022391 4 0.000 1.000 0.000 0.000 0.000 1
#> GSM1022392 4 0.000 1.000 0.000 0.000 0.000 1
#> GSM1022397 1 0.302 0.902 0.852 0.000 0.148 0
#> GSM1022398 1 0.302 0.902 0.852 0.000 0.148 0
#> GSM1022399 1 0.302 0.902 0.852 0.000 0.148 0
#> GSM1022400 1 0.302 0.902 0.852 0.000 0.148 0
#> GSM1022401 1 0.000 0.946 1.000 0.000 0.000 0
#> GSM1022402 1 0.000 0.946 1.000 0.000 0.000 0
#> GSM1022403 1 0.000 0.946 1.000 0.000 0.000 0
#> GSM1022404 1 0.000 0.946 1.000 0.000 0.000 0
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1022325 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM1022326 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM1022327 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM1022331 5 0.0000 1.000 0.000 0 0.000 0 1
#> GSM1022332 5 0.0000 1.000 0.000 0 0.000 0 1
#> GSM1022333 5 0.0000 1.000 0.000 0 0.000 0 1
#> GSM1022328 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM1022329 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM1022330 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM1022337 5 0.0000 1.000 0.000 0 0.000 0 1
#> GSM1022338 5 0.0000 1.000 0.000 0 0.000 0 1
#> GSM1022339 5 0.0000 1.000 0.000 0 0.000 0 1
#> GSM1022334 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM1022335 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM1022336 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM1022340 3 0.3752 0.723 0.292 0 0.708 0 0
#> GSM1022341 3 0.3752 0.723 0.292 0 0.708 0 0
#> GSM1022342 3 0.3752 0.723 0.292 0 0.708 0 0
#> GSM1022343 3 0.3752 0.723 0.292 0 0.708 0 0
#> GSM1022347 3 0.0000 0.872 0.000 0 1.000 0 0
#> GSM1022348 3 0.0000 0.872 0.000 0 1.000 0 0
#> GSM1022349 3 0.0000 0.872 0.000 0 1.000 0 0
#> GSM1022350 3 0.0000 0.872 0.000 0 1.000 0 0
#> GSM1022344 3 0.3752 0.723 0.292 0 0.708 0 0
#> GSM1022345 3 0.3752 0.723 0.292 0 0.708 0 0
#> GSM1022346 3 0.3752 0.723 0.292 0 0.708 0 0
#> GSM1022355 1 0.0000 0.996 1.000 0 0.000 0 0
#> GSM1022356 1 0.0000 0.996 1.000 0 0.000 0 0
#> GSM1022357 1 0.0000 0.996 1.000 0 0.000 0 0
#> GSM1022358 1 0.0000 0.996 1.000 0 0.000 0 0
#> GSM1022351 1 0.0000 0.996 1.000 0 0.000 0 0
#> GSM1022352 1 0.0703 0.972 0.976 0 0.024 0 0
#> GSM1022353 1 0.0794 0.968 0.972 0 0.028 0 0
#> GSM1022354 1 0.0000 0.996 1.000 0 0.000 0 0
#> GSM1022359 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM1022360 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM1022361 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM1022362 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM1022367 5 0.0000 1.000 0.000 0 0.000 0 1
#> GSM1022368 5 0.0000 1.000 0.000 0 0.000 0 1
#> GSM1022369 5 0.0000 1.000 0.000 0 0.000 0 1
#> GSM1022370 5 0.0000 1.000 0.000 0 0.000 0 1
#> GSM1022363 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM1022364 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM1022365 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM1022366 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM1022374 5 0.0000 1.000 0.000 0 0.000 0 1
#> GSM1022375 5 0.0000 1.000 0.000 0 0.000 0 1
#> GSM1022376 5 0.0000 1.000 0.000 0 0.000 0 1
#> GSM1022371 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM1022372 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM1022373 2 0.0000 1.000 0.000 1 0.000 0 0
#> GSM1022377 4 0.0000 1.000 0.000 0 0.000 1 0
#> GSM1022378 4 0.0000 1.000 0.000 0 0.000 1 0
#> GSM1022379 4 0.0000 1.000 0.000 0 0.000 1 0
#> GSM1022380 4 0.0000 1.000 0.000 0 0.000 1 0
#> GSM1022385 3 0.0000 0.872 0.000 0 1.000 0 0
#> GSM1022386 3 0.0000 0.872 0.000 0 1.000 0 0
#> GSM1022387 3 0.0000 0.872 0.000 0 1.000 0 0
#> GSM1022388 3 0.0000 0.872 0.000 0 1.000 0 0
#> GSM1022381 4 0.0000 1.000 0.000 0 0.000 1 0
#> GSM1022382 4 0.0000 1.000 0.000 0 0.000 1 0
#> GSM1022383 4 0.0000 1.000 0.000 0 0.000 1 0
#> GSM1022384 4 0.0000 1.000 0.000 0 0.000 1 0
#> GSM1022393 1 0.0000 0.996 1.000 0 0.000 0 0
#> GSM1022394 1 0.0000 0.996 1.000 0 0.000 0 0
#> GSM1022395 1 0.0000 0.996 1.000 0 0.000 0 0
#> GSM1022396 1 0.0000 0.996 1.000 0 0.000 0 0
#> GSM1022389 4 0.0000 1.000 0.000 0 0.000 1 0
#> GSM1022390 4 0.0000 1.000 0.000 0 0.000 1 0
#> GSM1022391 4 0.0000 1.000 0.000 0 0.000 1 0
#> GSM1022392 4 0.0000 1.000 0.000 0 0.000 1 0
#> GSM1022397 3 0.0000 0.872 0.000 0 1.000 0 0
#> GSM1022398 3 0.0000 0.872 0.000 0 1.000 0 0
#> GSM1022399 3 0.0000 0.872 0.000 0 1.000 0 0
#> GSM1022400 3 0.0000 0.872 0.000 0 1.000 0 0
#> GSM1022401 1 0.0000 0.996 1.000 0 0.000 0 0
#> GSM1022402 1 0.0000 0.996 1.000 0 0.000 0 0
#> GSM1022403 1 0.0000 0.996 1.000 0 0.000 0 0
#> GSM1022404 1 0.0000 0.996 1.000 0 0.000 0 0
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1022325 2 0.0000 1.000 0.000 1 0.000 0.00 0.000 0.000
#> GSM1022326 2 0.0000 1.000 0.000 1 0.000 0.00 0.000 0.000
#> GSM1022327 2 0.0000 1.000 0.000 1 0.000 0.00 0.000 0.000
#> GSM1022331 6 0.0000 1.000 0.000 0 0.000 0.00 0.000 1.000
#> GSM1022332 6 0.0000 1.000 0.000 0 0.000 0.00 0.000 1.000
#> GSM1022333 6 0.0000 1.000 0.000 0 0.000 0.00 0.000 1.000
#> GSM1022328 2 0.0000 1.000 0.000 1 0.000 0.00 0.000 0.000
#> GSM1022329 2 0.0000 1.000 0.000 1 0.000 0.00 0.000 0.000
#> GSM1022330 2 0.0000 1.000 0.000 1 0.000 0.00 0.000 0.000
#> GSM1022337 5 0.3390 1.000 0.000 0 0.000 0.00 0.704 0.296
#> GSM1022338 5 0.3390 1.000 0.000 0 0.000 0.00 0.704 0.296
#> GSM1022339 5 0.3390 1.000 0.000 0 0.000 0.00 0.704 0.296
#> GSM1022334 2 0.0000 1.000 0.000 1 0.000 0.00 0.000 0.000
#> GSM1022335 2 0.0000 1.000 0.000 1 0.000 0.00 0.000 0.000
#> GSM1022336 2 0.0000 1.000 0.000 1 0.000 0.00 0.000 0.000
#> GSM1022340 3 0.4738 0.752 0.084 0 0.640 0.00 0.276 0.000
#> GSM1022341 3 0.4738 0.752 0.084 0 0.640 0.00 0.276 0.000
#> GSM1022342 3 0.4738 0.752 0.084 0 0.640 0.00 0.276 0.000
#> GSM1022343 3 0.4738 0.752 0.084 0 0.640 0.00 0.276 0.000
#> GSM1022347 3 0.0000 0.865 0.000 0 1.000 0.00 0.000 0.000
#> GSM1022348 3 0.0000 0.865 0.000 0 1.000 0.00 0.000 0.000
#> GSM1022349 3 0.0000 0.865 0.000 0 1.000 0.00 0.000 0.000
#> GSM1022350 3 0.0000 0.865 0.000 0 1.000 0.00 0.000 0.000
#> GSM1022344 3 0.4738 0.752 0.084 0 0.640 0.00 0.276 0.000
#> GSM1022345 3 0.4738 0.752 0.084 0 0.640 0.00 0.276 0.000
#> GSM1022346 3 0.4738 0.752 0.084 0 0.640 0.00 0.276 0.000
#> GSM1022355 1 0.0000 0.998 1.000 0 0.000 0.00 0.000 0.000
#> GSM1022356 1 0.0000 0.998 1.000 0 0.000 0.00 0.000 0.000
#> GSM1022357 1 0.0000 0.998 1.000 0 0.000 0.00 0.000 0.000
#> GSM1022358 1 0.0000 0.998 1.000 0 0.000 0.00 0.000 0.000
#> GSM1022351 1 0.0000 0.998 1.000 0 0.000 0.00 0.000 0.000
#> GSM1022352 1 0.0000 0.998 1.000 0 0.000 0.00 0.000 0.000
#> GSM1022353 1 0.0000 0.998 1.000 0 0.000 0.00 0.000 0.000
#> GSM1022354 1 0.0000 0.998 1.000 0 0.000 0.00 0.000 0.000
#> GSM1022359 2 0.0000 1.000 0.000 1 0.000 0.00 0.000 0.000
#> GSM1022360 2 0.0000 1.000 0.000 1 0.000 0.00 0.000 0.000
#> GSM1022361 2 0.0000 1.000 0.000 1 0.000 0.00 0.000 0.000
#> GSM1022362 2 0.0000 1.000 0.000 1 0.000 0.00 0.000 0.000
#> GSM1022367 6 0.0000 1.000 0.000 0 0.000 0.00 0.000 1.000
#> GSM1022368 6 0.0000 1.000 0.000 0 0.000 0.00 0.000 1.000
#> GSM1022369 6 0.0000 1.000 0.000 0 0.000 0.00 0.000 1.000
#> GSM1022370 6 0.0000 1.000 0.000 0 0.000 0.00 0.000 1.000
#> GSM1022363 2 0.0000 1.000 0.000 1 0.000 0.00 0.000 0.000
#> GSM1022364 2 0.0000 1.000 0.000 1 0.000 0.00 0.000 0.000
#> GSM1022365 2 0.0000 1.000 0.000 1 0.000 0.00 0.000 0.000
#> GSM1022366 2 0.0000 1.000 0.000 1 0.000 0.00 0.000 0.000
#> GSM1022374 5 0.3390 1.000 0.000 0 0.000 0.00 0.704 0.296
#> GSM1022375 5 0.3390 1.000 0.000 0 0.000 0.00 0.704 0.296
#> GSM1022376 5 0.3390 1.000 0.000 0 0.000 0.00 0.704 0.296
#> GSM1022371 2 0.0000 1.000 0.000 1 0.000 0.00 0.000 0.000
#> GSM1022372 2 0.0000 1.000 0.000 1 0.000 0.00 0.000 0.000
#> GSM1022373 2 0.0000 1.000 0.000 1 0.000 0.00 0.000 0.000
#> GSM1022377 4 0.0000 0.994 0.000 0 0.000 1.00 0.000 0.000
#> GSM1022378 4 0.0000 0.994 0.000 0 0.000 1.00 0.000 0.000
#> GSM1022379 4 0.0000 0.994 0.000 0 0.000 1.00 0.000 0.000
#> GSM1022380 4 0.0000 0.994 0.000 0 0.000 1.00 0.000 0.000
#> GSM1022385 3 0.0000 0.865 0.000 0 1.000 0.00 0.000 0.000
#> GSM1022386 3 0.0000 0.865 0.000 0 1.000 0.00 0.000 0.000
#> GSM1022387 3 0.0000 0.865 0.000 0 1.000 0.00 0.000 0.000
#> GSM1022388 3 0.0000 0.865 0.000 0 1.000 0.00 0.000 0.000
#> GSM1022381 4 0.0000 0.994 0.000 0 0.000 1.00 0.000 0.000
#> GSM1022382 4 0.0000 0.994 0.000 0 0.000 1.00 0.000 0.000
#> GSM1022383 4 0.0000 0.994 0.000 0 0.000 1.00 0.000 0.000
#> GSM1022384 4 0.0000 0.994 0.000 0 0.000 1.00 0.000 0.000
#> GSM1022393 1 0.0000 0.998 1.000 0 0.000 0.00 0.000 0.000
#> GSM1022394 1 0.0000 0.998 1.000 0 0.000 0.00 0.000 0.000
#> GSM1022395 1 0.0000 0.998 1.000 0 0.000 0.00 0.000 0.000
#> GSM1022396 1 0.0000 0.998 1.000 0 0.000 0.00 0.000 0.000
#> GSM1022389 4 0.0547 0.988 0.000 0 0.000 0.98 0.020 0.000
#> GSM1022390 4 0.0547 0.988 0.000 0 0.000 0.98 0.020 0.000
#> GSM1022391 4 0.0547 0.988 0.000 0 0.000 0.98 0.020 0.000
#> GSM1022392 4 0.0547 0.988 0.000 0 0.000 0.98 0.020 0.000
#> GSM1022397 3 0.0000 0.865 0.000 0 1.000 0.00 0.000 0.000
#> GSM1022398 3 0.0000 0.865 0.000 0 1.000 0.00 0.000 0.000
#> GSM1022399 3 0.0000 0.865 0.000 0 1.000 0.00 0.000 0.000
#> GSM1022400 3 0.0000 0.865 0.000 0 1.000 0.00 0.000 0.000
#> GSM1022401 1 0.0777 0.971 0.972 0 0.004 0.00 0.024 0.000
#> GSM1022402 1 0.0000 0.998 1.000 0 0.000 0.00 0.000 0.000
#> GSM1022403 1 0.0000 0.998 1.000 0 0.000 0.00 0.000 0.000
#> GSM1022404 1 0.0000 0.998 1.000 0 0.000 0.00 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n protocol(p) cell.type(p) k
#> ATC:mclust 80 1.10e-11 4.22e-01 2
#> ATC:mclust 76 1.17e-12 3.47e-03 3
#> ATC:mclust 76 3.99e-13 8.00e-10 4
#> ATC:mclust 80 1.08e-20 3.36e-10 5
#> ATC:mclust 80 2.52e-23 1.29e-09 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 31589 rows and 80 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.994 0.997 0.4921 0.509 0.509
#> 3 3 0.736 0.888 0.875 0.2478 0.867 0.739
#> 4 4 0.793 0.833 0.884 0.1693 0.862 0.647
#> 5 5 0.660 0.615 0.767 0.0671 0.916 0.724
#> 6 6 0.655 0.558 0.664 0.0362 0.896 0.618
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM1022325 2 0.0000 1.000 0.000 1.000
#> GSM1022326 2 0.0000 1.000 0.000 1.000
#> GSM1022327 2 0.0000 1.000 0.000 1.000
#> GSM1022331 2 0.0000 1.000 0.000 1.000
#> GSM1022332 2 0.0672 0.992 0.008 0.992
#> GSM1022333 2 0.0000 1.000 0.000 1.000
#> GSM1022328 2 0.0000 1.000 0.000 1.000
#> GSM1022329 2 0.0000 1.000 0.000 1.000
#> GSM1022330 2 0.0000 1.000 0.000 1.000
#> GSM1022337 2 0.0000 1.000 0.000 1.000
#> GSM1022338 2 0.0000 1.000 0.000 1.000
#> GSM1022339 2 0.0000 1.000 0.000 1.000
#> GSM1022334 2 0.0000 1.000 0.000 1.000
#> GSM1022335 2 0.0000 1.000 0.000 1.000
#> GSM1022336 2 0.0000 1.000 0.000 1.000
#> GSM1022340 1 0.0000 0.995 1.000 0.000
#> GSM1022341 1 0.0000 0.995 1.000 0.000
#> GSM1022342 1 0.0000 0.995 1.000 0.000
#> GSM1022343 1 0.0000 0.995 1.000 0.000
#> GSM1022347 1 0.0000 0.995 1.000 0.000
#> GSM1022348 1 0.0000 0.995 1.000 0.000
#> GSM1022349 1 0.0000 0.995 1.000 0.000
#> GSM1022350 1 0.0000 0.995 1.000 0.000
#> GSM1022344 1 0.0000 0.995 1.000 0.000
#> GSM1022345 1 0.0000 0.995 1.000 0.000
#> GSM1022346 1 0.0000 0.995 1.000 0.000
#> GSM1022355 1 0.0000 0.995 1.000 0.000
#> GSM1022356 1 0.0000 0.995 1.000 0.000
#> GSM1022357 1 0.0000 0.995 1.000 0.000
#> GSM1022358 1 0.0000 0.995 1.000 0.000
#> GSM1022351 1 0.0000 0.995 1.000 0.000
#> GSM1022352 1 0.0000 0.995 1.000 0.000
#> GSM1022353 1 0.0000 0.995 1.000 0.000
#> GSM1022354 1 0.0000 0.995 1.000 0.000
#> GSM1022359 2 0.0000 1.000 0.000 1.000
#> GSM1022360 2 0.0000 1.000 0.000 1.000
#> GSM1022361 2 0.0000 1.000 0.000 1.000
#> GSM1022362 2 0.0000 1.000 0.000 1.000
#> GSM1022367 2 0.0000 1.000 0.000 1.000
#> GSM1022368 2 0.0000 1.000 0.000 1.000
#> GSM1022369 2 0.0000 1.000 0.000 1.000
#> GSM1022370 2 0.0000 1.000 0.000 1.000
#> GSM1022363 2 0.0000 1.000 0.000 1.000
#> GSM1022364 2 0.0000 1.000 0.000 1.000
#> GSM1022365 2 0.0000 1.000 0.000 1.000
#> GSM1022366 2 0.0000 1.000 0.000 1.000
#> GSM1022374 2 0.0000 1.000 0.000 1.000
#> GSM1022375 2 0.0000 1.000 0.000 1.000
#> GSM1022376 2 0.0000 1.000 0.000 1.000
#> GSM1022371 2 0.0000 1.000 0.000 1.000
#> GSM1022372 2 0.0000 1.000 0.000 1.000
#> GSM1022373 2 0.0000 1.000 0.000 1.000
#> GSM1022377 1 0.5178 0.872 0.884 0.116
#> GSM1022378 1 0.4431 0.900 0.908 0.092
#> GSM1022379 1 0.0000 0.995 1.000 0.000
#> GSM1022380 1 0.0000 0.995 1.000 0.000
#> GSM1022385 1 0.0000 0.995 1.000 0.000
#> GSM1022386 1 0.0000 0.995 1.000 0.000
#> GSM1022387 1 0.0000 0.995 1.000 0.000
#> GSM1022388 1 0.0000 0.995 1.000 0.000
#> GSM1022381 1 0.0000 0.995 1.000 0.000
#> GSM1022382 1 0.0000 0.995 1.000 0.000
#> GSM1022383 1 0.0000 0.995 1.000 0.000
#> GSM1022384 1 0.0000 0.995 1.000 0.000
#> GSM1022393 1 0.0000 0.995 1.000 0.000
#> GSM1022394 1 0.0000 0.995 1.000 0.000
#> GSM1022395 1 0.0000 0.995 1.000 0.000
#> GSM1022396 1 0.0000 0.995 1.000 0.000
#> GSM1022389 1 0.0376 0.992 0.996 0.004
#> GSM1022390 1 0.0000 0.995 1.000 0.000
#> GSM1022391 1 0.0000 0.995 1.000 0.000
#> GSM1022392 1 0.0000 0.995 1.000 0.000
#> GSM1022397 1 0.0000 0.995 1.000 0.000
#> GSM1022398 1 0.0000 0.995 1.000 0.000
#> GSM1022399 1 0.0000 0.995 1.000 0.000
#> GSM1022400 1 0.0000 0.995 1.000 0.000
#> GSM1022401 1 0.0000 0.995 1.000 0.000
#> GSM1022402 1 0.0000 0.995 1.000 0.000
#> GSM1022403 1 0.0000 0.995 1.000 0.000
#> GSM1022404 1 0.0000 0.995 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM1022325 2 0.0592 0.940 0.000 0.988 0.012
#> GSM1022326 2 0.0592 0.940 0.000 0.988 0.012
#> GSM1022327 2 0.0424 0.942 0.000 0.992 0.008
#> GSM1022331 2 0.8278 0.654 0.132 0.620 0.248
#> GSM1022332 2 0.9383 0.487 0.236 0.512 0.252
#> GSM1022333 2 0.7782 0.694 0.100 0.652 0.248
#> GSM1022328 2 0.0000 0.944 0.000 1.000 0.000
#> GSM1022329 2 0.0000 0.944 0.000 1.000 0.000
#> GSM1022330 2 0.0237 0.943 0.000 0.996 0.004
#> GSM1022337 2 0.1529 0.930 0.000 0.960 0.040
#> GSM1022338 2 0.1529 0.930 0.000 0.960 0.040
#> GSM1022339 2 0.0592 0.941 0.000 0.988 0.012
#> GSM1022334 2 0.0892 0.935 0.000 0.980 0.020
#> GSM1022335 2 0.0592 0.940 0.000 0.988 0.012
#> GSM1022336 2 0.0592 0.940 0.000 0.988 0.012
#> GSM1022340 1 0.1753 0.887 0.952 0.000 0.048
#> GSM1022341 1 0.1411 0.888 0.964 0.000 0.036
#> GSM1022342 1 0.1529 0.888 0.960 0.000 0.040
#> GSM1022343 1 0.1411 0.888 0.964 0.000 0.036
#> GSM1022347 1 0.0424 0.875 0.992 0.000 0.008
#> GSM1022348 1 0.0892 0.864 0.980 0.000 0.020
#> GSM1022349 1 0.0424 0.875 0.992 0.000 0.008
#> GSM1022350 1 0.0592 0.872 0.988 0.000 0.012
#> GSM1022344 1 0.1031 0.887 0.976 0.000 0.024
#> GSM1022345 1 0.1289 0.888 0.968 0.000 0.032
#> GSM1022346 1 0.1031 0.887 0.976 0.000 0.024
#> GSM1022355 1 0.4062 0.834 0.836 0.000 0.164
#> GSM1022356 1 0.4702 0.775 0.788 0.000 0.212
#> GSM1022357 1 0.3192 0.870 0.888 0.000 0.112
#> GSM1022358 1 0.4399 0.810 0.812 0.000 0.188
#> GSM1022351 1 0.4062 0.834 0.836 0.000 0.164
#> GSM1022352 1 0.3116 0.872 0.892 0.000 0.108
#> GSM1022353 1 0.3116 0.872 0.892 0.000 0.108
#> GSM1022354 1 0.3116 0.872 0.892 0.000 0.108
#> GSM1022359 2 0.0000 0.944 0.000 1.000 0.000
#> GSM1022360 2 0.0000 0.944 0.000 1.000 0.000
#> GSM1022361 2 0.0000 0.944 0.000 1.000 0.000
#> GSM1022362 2 0.0000 0.944 0.000 1.000 0.000
#> GSM1022367 2 0.4002 0.860 0.000 0.840 0.160
#> GSM1022368 2 0.4796 0.816 0.000 0.780 0.220
#> GSM1022369 2 0.5058 0.798 0.000 0.756 0.244
#> GSM1022370 2 0.2711 0.904 0.000 0.912 0.088
#> GSM1022363 2 0.0000 0.944 0.000 1.000 0.000
#> GSM1022364 2 0.0000 0.944 0.000 1.000 0.000
#> GSM1022365 2 0.0000 0.944 0.000 1.000 0.000
#> GSM1022366 2 0.0000 0.944 0.000 1.000 0.000
#> GSM1022374 2 0.0592 0.942 0.000 0.988 0.012
#> GSM1022375 2 0.0592 0.942 0.000 0.988 0.012
#> GSM1022376 2 0.0424 0.942 0.000 0.992 0.008
#> GSM1022371 2 0.0000 0.944 0.000 1.000 0.000
#> GSM1022372 2 0.0000 0.944 0.000 1.000 0.000
#> GSM1022373 2 0.0000 0.944 0.000 1.000 0.000
#> GSM1022377 3 0.6511 0.882 0.180 0.072 0.748
#> GSM1022378 3 0.6398 0.901 0.192 0.060 0.748
#> GSM1022379 3 0.5138 0.970 0.252 0.000 0.748
#> GSM1022380 3 0.5138 0.970 0.252 0.000 0.748
#> GSM1022385 1 0.0000 0.880 1.000 0.000 0.000
#> GSM1022386 1 0.0237 0.878 0.996 0.000 0.004
#> GSM1022387 1 0.0237 0.878 0.996 0.000 0.004
#> GSM1022388 1 0.0237 0.878 0.996 0.000 0.004
#> GSM1022381 3 0.5138 0.970 0.252 0.000 0.748
#> GSM1022382 3 0.5138 0.970 0.252 0.000 0.748
#> GSM1022383 3 0.5138 0.970 0.252 0.000 0.748
#> GSM1022384 3 0.5138 0.970 0.252 0.000 0.748
#> GSM1022393 1 0.5138 0.700 0.748 0.000 0.252
#> GSM1022394 1 0.4399 0.809 0.812 0.000 0.188
#> GSM1022395 1 0.4062 0.835 0.836 0.000 0.164
#> GSM1022396 1 0.4452 0.804 0.808 0.000 0.192
#> GSM1022389 3 0.5774 0.954 0.232 0.020 0.748
#> GSM1022390 3 0.5138 0.970 0.252 0.000 0.748
#> GSM1022391 3 0.5578 0.962 0.240 0.012 0.748
#> GSM1022392 3 0.5138 0.970 0.252 0.000 0.748
#> GSM1022397 1 0.0237 0.878 0.996 0.000 0.004
#> GSM1022398 1 0.0237 0.878 0.996 0.000 0.004
#> GSM1022399 1 0.0237 0.878 0.996 0.000 0.004
#> GSM1022400 1 0.0237 0.878 0.996 0.000 0.004
#> GSM1022401 1 0.3116 0.873 0.892 0.000 0.108
#> GSM1022402 1 0.4750 0.769 0.784 0.000 0.216
#> GSM1022403 1 0.4399 0.810 0.812 0.000 0.188
#> GSM1022404 1 0.3816 0.847 0.852 0.000 0.148
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM1022325 2 0.3123 0.8462 0.000 0.844 0.000 0.156
#> GSM1022326 2 0.3074 0.8501 0.000 0.848 0.000 0.152
#> GSM1022327 2 0.1716 0.9240 0.000 0.936 0.000 0.064
#> GSM1022331 3 0.5394 0.5189 0.000 0.228 0.712 0.060
#> GSM1022332 3 0.4696 0.6209 0.004 0.136 0.796 0.064
#> GSM1022333 3 0.6265 -0.0369 0.000 0.444 0.500 0.056
#> GSM1022328 2 0.0469 0.9492 0.000 0.988 0.000 0.012
#> GSM1022329 2 0.1022 0.9421 0.000 0.968 0.000 0.032
#> GSM1022330 2 0.1022 0.9421 0.000 0.968 0.000 0.032
#> GSM1022337 2 0.2757 0.9253 0.020 0.912 0.016 0.052
#> GSM1022338 2 0.2757 0.9253 0.020 0.912 0.016 0.052
#> GSM1022339 2 0.2586 0.9293 0.020 0.920 0.016 0.044
#> GSM1022334 2 0.3486 0.8073 0.000 0.812 0.000 0.188
#> GSM1022335 2 0.2814 0.8700 0.000 0.868 0.000 0.132
#> GSM1022336 2 0.2149 0.9070 0.000 0.912 0.000 0.088
#> GSM1022340 1 0.5253 0.3599 0.624 0.000 0.360 0.016
#> GSM1022341 1 0.5130 0.4259 0.652 0.000 0.332 0.016
#> GSM1022342 1 0.5408 0.2171 0.576 0.000 0.408 0.016
#> GSM1022343 1 0.5444 0.1604 0.560 0.000 0.424 0.016
#> GSM1022347 3 0.2647 0.8258 0.120 0.000 0.880 0.000
#> GSM1022348 3 0.2589 0.8255 0.116 0.000 0.884 0.000
#> GSM1022349 3 0.2647 0.8258 0.120 0.000 0.880 0.000
#> GSM1022350 3 0.2589 0.8255 0.116 0.000 0.884 0.000
#> GSM1022344 3 0.4546 0.6695 0.256 0.000 0.732 0.012
#> GSM1022345 3 0.5383 0.2012 0.452 0.000 0.536 0.012
#> GSM1022346 3 0.5279 0.3671 0.400 0.000 0.588 0.012
#> GSM1022355 1 0.0336 0.8827 0.992 0.000 0.008 0.000
#> GSM1022356 1 0.0804 0.8671 0.980 0.000 0.008 0.012
#> GSM1022357 1 0.0592 0.8806 0.984 0.000 0.016 0.000
#> GSM1022358 1 0.0336 0.8827 0.992 0.000 0.008 0.000
#> GSM1022351 1 0.0524 0.8822 0.988 0.000 0.008 0.004
#> GSM1022352 1 0.1256 0.8704 0.964 0.000 0.028 0.008
#> GSM1022353 1 0.1388 0.8676 0.960 0.000 0.028 0.012
#> GSM1022354 1 0.0779 0.8792 0.980 0.000 0.016 0.004
#> GSM1022359 2 0.0336 0.9499 0.000 0.992 0.000 0.008
#> GSM1022360 2 0.0336 0.9499 0.000 0.992 0.000 0.008
#> GSM1022361 2 0.0336 0.9499 0.000 0.992 0.000 0.008
#> GSM1022362 2 0.0336 0.9499 0.000 0.992 0.000 0.008
#> GSM1022367 2 0.1929 0.9368 0.000 0.940 0.024 0.036
#> GSM1022368 2 0.2411 0.9278 0.000 0.920 0.040 0.040
#> GSM1022369 2 0.2500 0.9256 0.000 0.916 0.044 0.040
#> GSM1022370 2 0.1706 0.9398 0.000 0.948 0.016 0.036
#> GSM1022363 2 0.0188 0.9498 0.000 0.996 0.000 0.004
#> GSM1022364 2 0.0188 0.9498 0.000 0.996 0.000 0.004
#> GSM1022365 2 0.0188 0.9498 0.000 0.996 0.000 0.004
#> GSM1022366 2 0.0188 0.9498 0.000 0.996 0.000 0.004
#> GSM1022374 2 0.1590 0.9428 0.008 0.956 0.008 0.028
#> GSM1022375 2 0.1690 0.9419 0.008 0.952 0.008 0.032
#> GSM1022376 2 0.1721 0.9419 0.012 0.952 0.008 0.028
#> GSM1022371 2 0.0188 0.9500 0.000 0.996 0.000 0.004
#> GSM1022372 2 0.0336 0.9499 0.000 0.992 0.000 0.008
#> GSM1022373 2 0.0188 0.9500 0.000 0.996 0.000 0.004
#> GSM1022377 4 0.3257 0.9618 0.068 0.012 0.032 0.888
#> GSM1022378 4 0.3201 0.9658 0.072 0.008 0.032 0.888
#> GSM1022379 4 0.3150 0.9681 0.072 0.004 0.036 0.888
#> GSM1022380 4 0.3056 0.9692 0.072 0.000 0.040 0.888
#> GSM1022385 3 0.3443 0.8118 0.136 0.000 0.848 0.016
#> GSM1022386 3 0.2737 0.8209 0.104 0.000 0.888 0.008
#> GSM1022387 3 0.2048 0.7992 0.064 0.000 0.928 0.008
#> GSM1022388 3 0.2342 0.8089 0.080 0.000 0.912 0.008
#> GSM1022381 4 0.3056 0.9692 0.072 0.000 0.040 0.888
#> GSM1022382 4 0.3056 0.9692 0.072 0.000 0.040 0.888
#> GSM1022383 4 0.3056 0.9692 0.072 0.000 0.040 0.888
#> GSM1022384 4 0.3128 0.9670 0.076 0.000 0.040 0.884
#> GSM1022393 1 0.0779 0.8685 0.980 0.000 0.004 0.016
#> GSM1022394 1 0.0524 0.8822 0.988 0.000 0.008 0.004
#> GSM1022395 1 0.0336 0.8772 0.992 0.000 0.000 0.008
#> GSM1022396 1 0.0376 0.8816 0.992 0.000 0.004 0.004
#> GSM1022389 4 0.2998 0.9570 0.080 0.004 0.024 0.892
#> GSM1022390 4 0.4267 0.8658 0.188 0.000 0.024 0.788
#> GSM1022391 4 0.2998 0.9632 0.080 0.004 0.024 0.892
#> GSM1022392 4 0.4104 0.8935 0.164 0.000 0.028 0.808
#> GSM1022397 3 0.2704 0.8246 0.124 0.000 0.876 0.000
#> GSM1022398 3 0.2973 0.8123 0.144 0.000 0.856 0.000
#> GSM1022399 3 0.2760 0.8227 0.128 0.000 0.872 0.000
#> GSM1022400 3 0.2647 0.8258 0.120 0.000 0.880 0.000
#> GSM1022401 1 0.0657 0.8827 0.984 0.000 0.012 0.004
#> GSM1022402 1 0.0592 0.8714 0.984 0.000 0.000 0.016
#> GSM1022403 1 0.0376 0.8812 0.992 0.000 0.004 0.004
#> GSM1022404 1 0.0376 0.8816 0.992 0.000 0.004 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM1022325 2 0.4521 0.6492 0.000 0.748 0.000 0.088 0.164
#> GSM1022326 2 0.4277 0.6620 0.000 0.768 0.000 0.076 0.156
#> GSM1022327 2 0.4096 0.6724 0.000 0.784 0.000 0.072 0.144
#> GSM1022331 5 0.5605 0.6656 0.000 0.192 0.168 0.000 0.640
#> GSM1022332 5 0.5336 0.6467 0.000 0.100 0.252 0.000 0.648
#> GSM1022333 5 0.5452 0.5043 0.000 0.292 0.092 0.000 0.616
#> GSM1022328 2 0.3339 0.6986 0.000 0.840 0.000 0.048 0.112
#> GSM1022329 2 0.3803 0.6829 0.000 0.804 0.000 0.056 0.140
#> GSM1022330 2 0.3911 0.6786 0.000 0.796 0.000 0.060 0.144
#> GSM1022337 2 0.6576 0.2491 0.340 0.468 0.004 0.000 0.188
#> GSM1022338 2 0.6604 0.2480 0.332 0.468 0.004 0.000 0.196
#> GSM1022339 2 0.6418 0.2564 0.344 0.472 0.000 0.000 0.184
#> GSM1022334 2 0.4521 0.6483 0.000 0.748 0.000 0.088 0.164
#> GSM1022335 2 0.4412 0.6547 0.000 0.756 0.000 0.080 0.164
#> GSM1022336 2 0.4317 0.6607 0.000 0.764 0.000 0.076 0.160
#> GSM1022340 3 0.2362 0.6562 0.084 0.000 0.900 0.008 0.008
#> GSM1022341 3 0.2548 0.6305 0.116 0.000 0.876 0.004 0.004
#> GSM1022342 3 0.2408 0.6531 0.096 0.000 0.892 0.008 0.004
#> GSM1022343 3 0.2408 0.6562 0.096 0.000 0.892 0.008 0.004
#> GSM1022347 3 0.2707 0.6465 0.000 0.000 0.860 0.008 0.132
#> GSM1022348 3 0.2818 0.6472 0.004 0.000 0.860 0.008 0.128
#> GSM1022349 3 0.2233 0.6670 0.000 0.000 0.892 0.004 0.104
#> GSM1022350 3 0.3022 0.6380 0.004 0.000 0.848 0.012 0.136
#> GSM1022344 3 0.2069 0.6822 0.052 0.000 0.924 0.012 0.012
#> GSM1022345 3 0.2166 0.6694 0.072 0.000 0.912 0.012 0.004
#> GSM1022346 3 0.1901 0.6782 0.056 0.000 0.928 0.012 0.004
#> GSM1022355 1 0.4341 0.6702 0.592 0.000 0.404 0.004 0.000
#> GSM1022356 1 0.4101 0.7735 0.664 0.000 0.332 0.004 0.000
#> GSM1022357 1 0.4450 0.4559 0.508 0.000 0.488 0.004 0.000
#> GSM1022358 1 0.4151 0.7609 0.652 0.000 0.344 0.004 0.000
#> GSM1022351 3 0.4434 -0.3715 0.460 0.000 0.536 0.004 0.000
#> GSM1022352 3 0.4192 -0.1381 0.404 0.000 0.596 0.000 0.000
#> GSM1022353 3 0.4201 -0.1534 0.408 0.000 0.592 0.000 0.000
#> GSM1022354 3 0.4219 -0.1857 0.416 0.000 0.584 0.000 0.000
#> GSM1022359 2 0.0000 0.7428 0.000 1.000 0.000 0.000 0.000
#> GSM1022360 2 0.0000 0.7428 0.000 1.000 0.000 0.000 0.000
#> GSM1022361 2 0.0000 0.7428 0.000 1.000 0.000 0.000 0.000
#> GSM1022362 2 0.0000 0.7428 0.000 1.000 0.000 0.000 0.000
#> GSM1022367 2 0.3534 0.5853 0.000 0.744 0.000 0.000 0.256
#> GSM1022368 2 0.3966 0.4717 0.000 0.664 0.000 0.000 0.336
#> GSM1022369 2 0.4060 0.4274 0.000 0.640 0.000 0.000 0.360
#> GSM1022370 2 0.3039 0.6486 0.000 0.808 0.000 0.000 0.192
#> GSM1022363 2 0.1410 0.7290 0.000 0.940 0.000 0.000 0.060
#> GSM1022364 2 0.1638 0.7310 0.000 0.932 0.000 0.004 0.064
#> GSM1022365 2 0.1478 0.7298 0.000 0.936 0.000 0.000 0.064
#> GSM1022366 2 0.1430 0.7348 0.000 0.944 0.000 0.004 0.052
#> GSM1022374 2 0.5295 0.5287 0.200 0.672 0.000 0.000 0.128
#> GSM1022375 2 0.5210 0.5448 0.184 0.684 0.000 0.000 0.132
#> GSM1022376 2 0.5854 0.4386 0.252 0.596 0.000 0.000 0.152
#> GSM1022371 2 0.0451 0.7419 0.000 0.988 0.000 0.004 0.008
#> GSM1022372 2 0.0451 0.7419 0.000 0.988 0.000 0.004 0.008
#> GSM1022373 2 0.0324 0.7424 0.000 0.992 0.000 0.004 0.004
#> GSM1022377 4 0.1571 0.8918 0.000 0.000 0.004 0.936 0.060
#> GSM1022378 4 0.1041 0.9024 0.000 0.000 0.004 0.964 0.032
#> GSM1022379 4 0.0324 0.9074 0.000 0.000 0.004 0.992 0.004
#> GSM1022380 4 0.0451 0.9073 0.000 0.000 0.004 0.988 0.008
#> GSM1022385 3 0.4535 0.5894 0.008 0.000 0.760 0.072 0.160
#> GSM1022386 3 0.5756 0.2245 0.000 0.000 0.576 0.112 0.312
#> GSM1022387 5 0.6207 0.0557 0.000 0.000 0.400 0.140 0.460
#> GSM1022388 3 0.6150 -0.1564 0.000 0.000 0.464 0.132 0.404
#> GSM1022381 4 0.1267 0.9055 0.012 0.000 0.004 0.960 0.024
#> GSM1022382 4 0.1153 0.9049 0.008 0.000 0.004 0.964 0.024
#> GSM1022383 4 0.1243 0.9032 0.008 0.000 0.004 0.960 0.028
#> GSM1022384 4 0.1243 0.9032 0.008 0.000 0.004 0.960 0.028
#> GSM1022393 1 0.2052 0.7040 0.912 0.000 0.080 0.004 0.004
#> GSM1022394 1 0.3969 0.7926 0.692 0.000 0.304 0.004 0.000
#> GSM1022395 1 0.3280 0.7793 0.808 0.000 0.184 0.004 0.004
#> GSM1022396 1 0.3766 0.8014 0.728 0.000 0.268 0.004 0.000
#> GSM1022389 4 0.4166 0.8142 0.056 0.000 0.008 0.788 0.148
#> GSM1022390 4 0.4609 0.7790 0.172 0.000 0.016 0.756 0.056
#> GSM1022391 4 0.3595 0.8443 0.048 0.000 0.004 0.828 0.120
#> GSM1022392 4 0.3959 0.8116 0.140 0.000 0.028 0.808 0.024
#> GSM1022397 3 0.2612 0.6549 0.000 0.000 0.868 0.008 0.124
#> GSM1022398 3 0.2331 0.6890 0.016 0.000 0.908 0.008 0.068
#> GSM1022399 3 0.2439 0.6594 0.000 0.000 0.876 0.004 0.120
#> GSM1022400 3 0.2886 0.6280 0.000 0.000 0.844 0.008 0.148
#> GSM1022401 1 0.4260 0.7821 0.680 0.000 0.308 0.004 0.008
#> GSM1022402 1 0.2047 0.6381 0.928 0.000 0.040 0.012 0.020
#> GSM1022403 1 0.3107 0.7314 0.852 0.000 0.124 0.016 0.008
#> GSM1022404 1 0.3700 0.7984 0.752 0.000 0.240 0.008 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM1022325 2 0.2794 0.647 0.016 0.888 0.000 0.028 0.040 0.028
#> GSM1022326 2 0.2688 0.650 0.012 0.892 0.000 0.020 0.036 0.040
#> GSM1022327 2 0.1514 0.688 0.004 0.944 0.000 0.012 0.036 0.004
#> GSM1022331 6 0.7162 0.357 0.012 0.072 0.268 0.000 0.208 0.440
#> GSM1022332 6 0.6699 0.347 0.004 0.036 0.356 0.000 0.204 0.400
#> GSM1022333 6 0.7464 0.330 0.020 0.088 0.248 0.000 0.224 0.420
#> GSM1022328 2 0.1562 0.706 0.000 0.940 0.000 0.004 0.032 0.024
#> GSM1022329 2 0.1218 0.693 0.004 0.956 0.000 0.012 0.028 0.000
#> GSM1022330 2 0.1553 0.689 0.004 0.944 0.000 0.012 0.032 0.008
#> GSM1022337 5 0.3141 0.549 0.020 0.140 0.000 0.000 0.828 0.012
#> GSM1022338 5 0.3056 0.550 0.016 0.140 0.000 0.000 0.832 0.012
#> GSM1022339 5 0.3002 0.544 0.020 0.136 0.000 0.000 0.836 0.008
#> GSM1022334 2 0.3063 0.629 0.012 0.872 0.000 0.032 0.044 0.040
#> GSM1022335 2 0.2722 0.647 0.008 0.888 0.000 0.020 0.036 0.048
#> GSM1022336 2 0.2515 0.656 0.008 0.900 0.000 0.020 0.032 0.040
#> GSM1022340 3 0.4352 0.438 0.324 0.000 0.644 0.000 0.012 0.020
#> GSM1022341 3 0.4015 0.431 0.328 0.000 0.656 0.000 0.008 0.008
#> GSM1022342 3 0.4187 0.434 0.324 0.000 0.652 0.000 0.012 0.012
#> GSM1022343 3 0.4000 0.439 0.324 0.000 0.660 0.000 0.008 0.008
#> GSM1022347 3 0.0260 0.670 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM1022348 3 0.0551 0.663 0.008 0.000 0.984 0.000 0.004 0.004
#> GSM1022349 3 0.0260 0.670 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM1022350 3 0.1067 0.652 0.024 0.000 0.964 0.004 0.004 0.004
#> GSM1022344 3 0.3883 0.520 0.256 0.000 0.720 0.004 0.016 0.004
#> GSM1022345 3 0.4258 0.443 0.316 0.000 0.656 0.004 0.020 0.004
#> GSM1022346 3 0.4058 0.462 0.308 0.000 0.672 0.004 0.012 0.004
#> GSM1022355 1 0.3695 0.640 0.712 0.000 0.272 0.000 0.016 0.000
#> GSM1022356 1 0.3539 0.662 0.756 0.000 0.220 0.000 0.024 0.000
#> GSM1022357 1 0.3894 0.587 0.664 0.000 0.324 0.000 0.008 0.004
#> GSM1022358 1 0.3483 0.657 0.748 0.000 0.236 0.000 0.016 0.000
#> GSM1022351 1 0.3925 0.575 0.656 0.000 0.332 0.000 0.008 0.004
#> GSM1022352 1 0.4502 0.427 0.568 0.000 0.404 0.000 0.016 0.012
#> GSM1022353 1 0.4510 0.419 0.564 0.000 0.408 0.000 0.016 0.012
#> GSM1022354 1 0.4264 0.490 0.604 0.000 0.376 0.000 0.012 0.008
#> GSM1022359 2 0.3620 0.738 0.000 0.772 0.000 0.000 0.044 0.184
#> GSM1022360 2 0.3620 0.738 0.000 0.772 0.000 0.000 0.044 0.184
#> GSM1022361 2 0.3555 0.739 0.000 0.776 0.000 0.000 0.040 0.184
#> GSM1022362 2 0.3555 0.739 0.000 0.776 0.000 0.000 0.040 0.184
#> GSM1022367 2 0.5445 0.246 0.000 0.464 0.000 0.000 0.120 0.416
#> GSM1022368 6 0.5507 -0.290 0.000 0.424 0.000 0.000 0.128 0.448
#> GSM1022369 6 0.5555 -0.187 0.000 0.380 0.000 0.000 0.140 0.480
#> GSM1022370 2 0.5409 0.413 0.000 0.524 0.000 0.000 0.128 0.348
#> GSM1022363 2 0.4291 0.679 0.000 0.680 0.000 0.000 0.052 0.268
#> GSM1022364 2 0.4274 0.680 0.000 0.676 0.000 0.000 0.048 0.276
#> GSM1022365 2 0.4294 0.670 0.000 0.672 0.000 0.000 0.048 0.280
#> GSM1022366 2 0.4254 0.688 0.000 0.680 0.000 0.000 0.048 0.272
#> GSM1022374 5 0.6091 0.349 0.012 0.340 0.000 0.000 0.460 0.188
#> GSM1022375 5 0.6260 0.223 0.012 0.356 0.000 0.000 0.408 0.224
#> GSM1022376 5 0.5300 0.476 0.012 0.300 0.000 0.000 0.592 0.096
#> GSM1022371 2 0.3806 0.735 0.000 0.752 0.000 0.000 0.048 0.200
#> GSM1022372 2 0.4033 0.724 0.000 0.724 0.000 0.000 0.052 0.224
#> GSM1022373 2 0.3618 0.738 0.000 0.768 0.000 0.000 0.040 0.192
#> GSM1022377 4 0.2107 0.844 0.016 0.052 0.000 0.916 0.008 0.008
#> GSM1022378 4 0.1692 0.852 0.020 0.024 0.000 0.940 0.008 0.008
#> GSM1022379 4 0.0551 0.857 0.008 0.004 0.000 0.984 0.004 0.000
#> GSM1022380 4 0.0551 0.857 0.008 0.004 0.000 0.984 0.004 0.000
#> GSM1022385 3 0.5895 0.454 0.036 0.000 0.640 0.184 0.024 0.116
#> GSM1022386 3 0.6366 0.194 0.020 0.000 0.504 0.216 0.008 0.252
#> GSM1022387 6 0.6715 -0.040 0.020 0.000 0.328 0.268 0.008 0.376
#> GSM1022388 3 0.6674 -0.055 0.020 0.000 0.392 0.248 0.008 0.332
#> GSM1022381 4 0.0622 0.857 0.000 0.000 0.000 0.980 0.008 0.012
#> GSM1022382 4 0.0508 0.857 0.000 0.000 0.000 0.984 0.004 0.012
#> GSM1022383 4 0.0508 0.857 0.000 0.000 0.000 0.984 0.004 0.012
#> GSM1022384 4 0.0363 0.857 0.000 0.000 0.000 0.988 0.000 0.012
#> GSM1022393 1 0.5595 0.334 0.504 0.000 0.080 0.004 0.396 0.016
#> GSM1022394 1 0.5225 0.666 0.628 0.000 0.248 0.012 0.112 0.000
#> GSM1022395 1 0.5882 0.576 0.520 0.000 0.168 0.012 0.300 0.000
#> GSM1022396 1 0.5852 0.648 0.548 0.000 0.212 0.012 0.228 0.000
#> GSM1022389 4 0.5512 0.715 0.052 0.188 0.000 0.680 0.040 0.040
#> GSM1022390 4 0.6221 0.612 0.252 0.116 0.000 0.576 0.032 0.024
#> GSM1022391 4 0.4603 0.749 0.016 0.168 0.000 0.744 0.032 0.040
#> GSM1022392 4 0.5971 0.656 0.220 0.108 0.000 0.616 0.036 0.020
#> GSM1022397 3 0.0363 0.670 0.012 0.000 0.988 0.000 0.000 0.000
#> GSM1022398 3 0.1010 0.665 0.036 0.000 0.960 0.000 0.000 0.004
#> GSM1022399 3 0.0458 0.670 0.016 0.000 0.984 0.000 0.000 0.000
#> GSM1022400 3 0.0000 0.668 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM1022401 1 0.6082 0.646 0.512 0.000 0.248 0.016 0.224 0.000
#> GSM1022402 5 0.5042 -0.195 0.456 0.000 0.016 0.020 0.496 0.012
#> GSM1022403 1 0.6104 0.453 0.488 0.000 0.124 0.020 0.360 0.008
#> GSM1022404 1 0.5948 0.642 0.540 0.000 0.204 0.016 0.240 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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n protocol(p) cell.type(p) k
#> ATC:NMF 80 1.10e-11 4.22e-01 2
#> ATC:NMF 79 1.71e-14 1.03e-04 3
#> ATC:NMF 73 8.77e-19 1.04e-06 4
#> ATC:NMF 66 1.34e-18 3.00e-07 5
#> ATC:NMF 54 3.20e-15 2.10e-09 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