Date: 2019-12-25 22:16:32 CET, cola version: 1.3.2
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All available functions which can be applied to this res_list object:
res_list
#> A 'ConsensusPartitionList' object with 24 methods.
#> On a matrix with 11993 rows and 62 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] 11993 62
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:mclust | 2 | 1.000 | 1.000 | 1.000 | ** | |
| CV:skmeans | 4 | 1.000 | 0.971 | 0.976 | ** | 2,3 |
| CV:NMF | 2 | 1.000 | 1.000 | 1.000 | ** | |
| MAD:pam | 6 | 1.000 | 0.976 | 0.988 | ** | 2,3 |
| MAD:NMF | 2 | 1.000 | 0.977 | 0.992 | ** | |
| ATC:pam | 4 | 1.000 | 0.945 | 0.963 | ** | 2,3 |
| SD:pam | 6 | 0.969 | 0.929 | 0.971 | ** | 2,3,4 |
| SD:skmeans | 6 | 0.966 | 0.945 | 0.961 | ** | 2,3 |
| MAD:skmeans | 6 | 0.962 | 0.958 | 0.969 | ** | 2,3,5 |
| CV:pam | 5 | 0.948 | 0.900 | 0.944 | * | 2,3,4 |
| MAD:mclust | 6 | 0.930 | 0.915 | 0.947 | * | 2 |
| MAD:hclust | 4 | 0.918 | 0.984 | 0.973 | * | |
| ATC:skmeans | 5 | 0.918 | 0.909 | 0.949 | * | 2,3,4 |
| ATC:NMF | 4 | 0.910 | 0.916 | 0.948 | * | 2 |
| SD:NMF | 3 | 0.902 | 0.886 | 0.951 | * | 2 |
| ATC:hclust | 4 | 0.877 | 0.959 | 0.955 | ||
| CV:hclust | 5 | 0.867 | 0.829 | 0.928 | ||
| SD:hclust | 4 | 0.859 | 0.935 | 0.907 | ||
| CV:mclust | 5 | 0.840 | 0.826 | 0.885 | ||
| ATC:mclust | 3 | 0.807 | 0.928 | 0.958 | ||
| CV:kmeans | 2 | 0.648 | 0.946 | 0.947 | ||
| ATC:kmeans | 2 | 0.591 | 0.885 | 0.907 | ||
| SD:kmeans | 2 | 0.500 | 0.930 | 0.939 | ||
| MAD:kmeans | 2 | 0.500 | 0.894 | 0.915 |
**: 1-PAC > 0.95, *: 1-PAC > 0.9
Cumulative distribution function curves of consensus matrix for all methods.
collect_plots(res_list, fun = plot_ecdf)
Consensus heatmaps for all methods. (What is a consensus heatmap?)
collect_plots(res_list, k = 2, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = consensus_heatmap, mc.cores = 4)
Membership heatmaps for all methods. (What is a membership heatmap?)
collect_plots(res_list, k = 2, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = membership_heatmap, mc.cores = 4)
Signature heatmaps for all methods. (What is a signature heatmap?)
Note in following heatmaps, rows are scaled.
collect_plots(res_list, k = 2, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 3, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 4, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 5, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 6, fun = get_signatures, mc.cores = 4)
The statistics used for measuring the stability of consensus partitioning. (How are they defined?)
get_stats(res_list, k = 2)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 2 1.000 0.993 0.997 0.509 0.492 0.492
#> CV:NMF 2 1.000 1.000 1.000 0.509 0.492 0.492
#> MAD:NMF 2 1.000 0.977 0.992 0.508 0.492 0.492
#> ATC:NMF 2 1.000 1.000 1.000 0.507 0.494 0.494
#> SD:skmeans 2 1.000 1.000 1.000 0.509 0.492 0.492
#> CV:skmeans 2 1.000 1.000 1.000 0.509 0.492 0.492
#> MAD:skmeans 2 1.000 1.000 1.000 0.509 0.492 0.492
#> ATC:skmeans 2 1.000 0.999 1.000 0.507 0.494 0.494
#> SD:mclust 2 1.000 1.000 1.000 0.509 0.492 0.492
#> CV:mclust 2 0.390 0.232 0.655 0.464 0.772 0.772
#> MAD:mclust 2 1.000 1.000 1.000 0.509 0.492 0.492
#> ATC:mclust 2 0.715 0.850 0.919 0.444 0.535 0.535
#> SD:kmeans 2 0.500 0.930 0.939 0.497 0.492 0.492
#> CV:kmeans 2 0.648 0.946 0.947 0.491 0.492 0.492
#> MAD:kmeans 2 0.500 0.894 0.915 0.497 0.492 0.492
#> ATC:kmeans 2 0.591 0.885 0.907 0.456 0.494 0.494
#> SD:pam 2 1.000 0.986 0.993 0.506 0.494 0.494
#> CV:pam 2 1.000 0.946 0.980 0.505 0.494 0.494
#> MAD:pam 2 1.000 0.993 0.997 0.506 0.494 0.494
#> ATC:pam 2 1.000 0.986 0.994 0.508 0.492 0.492
#> SD:hclust 2 0.316 0.447 0.668 0.448 0.492 0.492
#> CV:hclust 2 0.367 0.799 0.836 0.485 0.492 0.492
#> MAD:hclust 2 0.526 0.915 0.912 0.459 0.511 0.511
#> ATC:hclust 2 0.732 0.887 0.922 0.394 0.535 0.535
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.902 0.886 0.951 0.238 0.862 0.723
#> CV:NMF 3 0.754 0.940 0.924 0.247 0.873 0.742
#> MAD:NMF 3 0.867 0.874 0.949 0.251 0.841 0.685
#> ATC:NMF 3 0.772 0.827 0.926 0.269 0.792 0.603
#> SD:skmeans 3 0.970 0.940 0.973 0.245 0.874 0.744
#> CV:skmeans 3 1.000 0.979 0.987 0.239 0.879 0.755
#> MAD:skmeans 3 1.000 0.976 0.985 0.248 0.874 0.744
#> ATC:skmeans 3 0.993 0.964 0.982 0.238 0.841 0.690
#> SD:mclust 3 0.892 0.865 0.900 0.218 0.876 0.748
#> CV:mclust 3 0.676 0.764 0.880 0.347 0.405 0.315
#> MAD:mclust 3 0.868 0.866 0.912 0.225 0.874 0.744
#> ATC:mclust 3 0.807 0.928 0.958 0.401 0.611 0.402
#> SD:kmeans 3 0.735 0.875 0.854 0.259 0.879 0.755
#> CV:kmeans 3 0.762 0.842 0.850 0.263 0.884 0.763
#> MAD:kmeans 3 0.766 0.871 0.836 0.263 0.879 0.755
#> ATC:kmeans 3 0.773 0.852 0.883 0.366 0.843 0.695
#> SD:pam 3 0.984 0.978 0.986 0.240 0.841 0.690
#> CV:pam 3 1.000 0.974 0.990 0.238 0.841 0.690
#> MAD:pam 3 1.000 0.998 0.999 0.243 0.841 0.690
#> ATC:pam 3 1.000 0.966 0.987 0.229 0.879 0.755
#> SD:hclust 3 0.714 0.813 0.912 0.438 0.874 0.744
#> CV:hclust 3 0.608 0.901 0.910 0.237 0.857 0.716
#> MAD:hclust 3 0.825 0.935 0.965 0.415 0.835 0.677
#> ATC:hclust 3 0.658 0.895 0.887 0.380 0.936 0.880
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.757 0.869 0.897 0.1763 0.824 0.551
#> CV:NMF 4 0.822 0.922 0.908 0.1534 0.889 0.696
#> MAD:NMF 4 0.840 0.808 0.911 0.1828 0.859 0.619
#> ATC:NMF 4 0.910 0.916 0.948 0.1702 0.789 0.469
#> SD:skmeans 4 0.846 0.882 0.928 0.1786 0.884 0.682
#> CV:skmeans 4 1.000 0.971 0.976 0.1623 0.895 0.718
#> MAD:skmeans 4 0.872 0.879 0.940 0.1878 0.884 0.682
#> ATC:skmeans 4 0.921 0.914 0.959 0.1689 0.895 0.718
#> SD:mclust 4 0.770 0.797 0.868 0.1734 0.835 0.584
#> CV:mclust 4 0.768 0.808 0.832 0.1292 0.911 0.761
#> MAD:mclust 4 0.825 0.870 0.912 0.1747 0.822 0.558
#> ATC:mclust 4 0.844 0.807 0.914 0.1792 0.820 0.558
#> SD:kmeans 4 0.659 0.874 0.853 0.1294 0.903 0.738
#> CV:kmeans 4 0.673 0.883 0.856 0.1325 0.887 0.703
#> MAD:kmeans 4 0.661 0.869 0.856 0.1335 0.903 0.738
#> ATC:kmeans 4 0.746 0.909 0.902 0.1348 0.887 0.703
#> SD:pam 4 0.929 0.957 0.972 0.1787 0.889 0.701
#> CV:pam 4 0.984 0.926 0.973 0.1624 0.895 0.718
#> MAD:pam 4 0.773 0.881 0.915 0.1795 0.889 0.701
#> ATC:pam 4 1.000 0.945 0.963 0.1546 0.874 0.671
#> SD:hclust 4 0.859 0.935 0.907 0.0873 0.903 0.734
#> CV:hclust 4 0.750 0.884 0.924 0.1807 0.885 0.698
#> MAD:hclust 4 0.918 0.984 0.973 0.1055 0.928 0.792
#> ATC:hclust 4 0.877 0.959 0.955 0.3192 0.789 0.552
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.777 0.721 0.811 0.0790 0.897 0.617
#> CV:NMF 5 0.857 0.782 0.891 0.0735 0.967 0.869
#> MAD:NMF 5 0.786 0.751 0.833 0.0661 0.886 0.587
#> ATC:NMF 5 0.761 0.722 0.862 0.0366 0.884 0.608
#> SD:skmeans 5 0.868 0.867 0.900 0.0672 0.929 0.726
#> CV:skmeans 5 0.898 0.898 0.900 0.0685 0.959 0.845
#> MAD:skmeans 5 0.930 0.937 0.952 0.0600 0.921 0.700
#> ATC:skmeans 5 0.918 0.909 0.949 0.0522 0.963 0.861
#> SD:mclust 5 0.726 0.642 0.794 0.0758 0.958 0.837
#> CV:mclust 5 0.840 0.826 0.885 0.0916 0.952 0.831
#> MAD:mclust 5 0.712 0.623 0.742 0.0698 0.884 0.647
#> ATC:mclust 5 0.747 0.770 0.874 0.0372 0.836 0.501
#> SD:kmeans 5 0.713 0.781 0.772 0.0805 0.950 0.819
#> CV:kmeans 5 0.745 0.739 0.845 0.0863 0.967 0.881
#> MAD:kmeans 5 0.733 0.875 0.795 0.0821 0.931 0.749
#> ATC:kmeans 5 0.750 0.825 0.843 0.0745 0.950 0.819
#> SD:pam 5 0.852 0.909 0.911 0.0735 0.928 0.732
#> CV:pam 5 0.948 0.900 0.944 0.0660 0.936 0.770
#> MAD:pam 5 0.866 0.893 0.897 0.0724 0.928 0.732
#> ATC:pam 5 0.873 0.838 0.879 0.0736 0.946 0.809
#> SD:hclust 5 0.858 0.903 0.934 0.0434 0.993 0.974
#> CV:hclust 5 0.867 0.829 0.928 0.0494 0.978 0.920
#> MAD:hclust 5 0.977 0.957 0.983 0.0272 0.994 0.977
#> ATC:hclust 5 0.879 0.932 0.952 0.0175 0.989 0.959
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.806 0.752 0.822 0.0440 0.880 0.493
#> CV:NMF 6 0.836 0.732 0.847 0.0467 0.907 0.616
#> MAD:NMF 6 0.813 0.731 0.835 0.0383 0.910 0.596
#> ATC:NMF 6 0.781 0.696 0.813 0.0489 0.893 0.582
#> SD:skmeans 6 0.966 0.945 0.961 0.0479 0.947 0.744
#> CV:skmeans 6 0.890 0.871 0.860 0.0607 0.938 0.725
#> MAD:skmeans 6 0.962 0.958 0.969 0.0446 0.956 0.783
#> ATC:skmeans 6 0.839 0.724 0.839 0.0502 0.956 0.808
#> SD:mclust 6 0.793 0.768 0.863 0.0557 0.925 0.667
#> CV:mclust 6 0.781 0.650 0.783 0.0493 0.909 0.653
#> MAD:mclust 6 0.930 0.915 0.947 0.0739 0.873 0.552
#> ATC:mclust 6 0.861 0.830 0.891 0.0381 0.934 0.741
#> SD:kmeans 6 0.838 0.886 0.856 0.0605 0.931 0.701
#> CV:kmeans 6 0.793 0.562 0.744 0.0508 0.897 0.621
#> MAD:kmeans 6 0.788 0.837 0.822 0.0521 0.942 0.724
#> ATC:kmeans 6 0.817 0.766 0.826 0.0505 0.978 0.910
#> SD:pam 6 0.969 0.929 0.971 0.0593 0.941 0.721
#> CV:pam 6 0.892 0.865 0.872 0.0591 0.905 0.604
#> MAD:pam 6 1.000 0.976 0.988 0.0577 0.942 0.724
#> ATC:pam 6 0.869 0.812 0.875 0.0681 0.915 0.654
#> SD:hclust 6 0.927 0.873 0.948 0.0391 0.988 0.956
#> CV:hclust 6 0.845 0.790 0.918 0.0210 0.969 0.880
#> MAD:hclust 6 0.921 0.901 0.960 0.0304 0.988 0.955
#> ATC:hclust 6 0.835 0.925 0.916 0.0441 0.959 0.834
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 tissue(p) individual(p) k
#> SD:NMF 62 1.14e-12 0.83009 2
#> CV:NMF 62 1.14e-12 0.83009 2
#> MAD:NMF 61 1.90e-12 0.85244 2
#> ATC:NMF 62 3.65e-11 0.89063 2
#> SD:skmeans 62 1.14e-12 0.83009 2
#> CV:skmeans 62 1.14e-12 0.83009 2
#> MAD:skmeans 62 1.14e-12 0.83009 2
#> ATC:skmeans 62 3.65e-11 0.89063 2
#> SD:mclust 62 1.14e-12 0.83009 2
#> CV:mclust 39 1.03e-07 0.07010 2
#> MAD:mclust 62 1.14e-12 0.83009 2
#> ATC:mclust 58 5.61e-07 0.00348 2
#> SD:kmeans 62 1.14e-12 0.83009 2
#> CV:kmeans 62 1.14e-12 0.83009 2
#> MAD:kmeans 62 1.14e-12 0.83009 2
#> ATC:kmeans 62 3.65e-11 0.89063 2
#> SD:pam 62 3.65e-11 0.89063 2
#> CV:pam 60 1.89e-11 0.84582 2
#> MAD:pam 62 3.65e-11 0.89063 2
#> ATC:pam 62 1.14e-12 0.83009 2
#> SD:hclust 22 NA NA 2
#> CV:hclust 61 1.90e-12 0.78776 2
#> MAD:hclust 62 1.20e-01 0.02271 2
#> ATC:hclust 62 7.91e-01 0.07592 2
test_to_known_factors(res_list, k = 3)
#> n tissue(p) individual(p) k
#> SD:NMF 58 7.11e-11 2.44e-03 3
#> CV:NMF 62 1.54e-12 9.76e-04 3
#> MAD:NMF 59 4.31e-11 5.75e-03 3
#> ATC:NMF 57 5.80e-10 6.38e-04 3
#> SD:skmeans 60 4.17e-12 1.27e-04 3
#> CV:skmeans 62 1.49e-12 1.94e-04 3
#> MAD:skmeans 61 2.52e-12 2.33e-04 3
#> ATC:skmeans 62 1.49e-12 1.94e-04 3
#> SD:mclust 61 3.93e-13 2.21e-04 3
#> CV:mclust 52 3.63e-11 6.74e-06 3
#> MAD:mclust 60 6.48e-13 3.53e-04 3
#> ATC:mclust 62 9.16e-12 1.83e-04 3
#> SD:kmeans 61 2.46e-12 2.21e-04 3
#> CV:kmeans 60 4.01e-12 1.05e-04 3
#> MAD:kmeans 61 2.46e-12 2.21e-04 3
#> ATC:kmeans 59 6.65e-12 1.69e-04 3
#> SD:pam 62 1.49e-12 1.94e-04 3
#> CV:pam 62 1.49e-12 1.94e-04 3
#> MAD:pam 62 1.49e-12 1.94e-04 3
#> ATC:pam 61 2.42e-12 8.63e-05 3
#> SD:hclust 54 9.11e-11 1.20e-05 3
#> CV:hclust 61 2.42e-12 6.35e-05 3
#> MAD:hclust 62 1.36e-07 1.72e-04 3
#> ATC:hclust 62 9.79e-05 4.21e-05 3
test_to_known_factors(res_list, k = 4)
#> n tissue(p) individual(p) k
#> SD:NMF 59 3.68e-11 3.90e-05 4
#> CV:NMF 61 1.32e-11 3.88e-05 4
#> MAD:NMF 56 9.86e-10 1.28e-05 4
#> ATC:NMF 60 1.42e-10 9.34e-05 4
#> SD:skmeans 59 3.50e-11 6.30e-06 4
#> CV:skmeans 62 7.66e-12 2.40e-06 4
#> MAD:skmeans 60 2.18e-11 4.00e-06 4
#> ATC:skmeans 60 2.34e-11 3.12e-06 4
#> SD:mclust 59 6.22e-12 6.34e-09 4
#> CV:mclust 58 1.57e-12 3.36e-07 4
#> MAD:mclust 61 1.51e-11 6.46e-09 4
#> ATC:mclust 54 7.45e-11 9.18e-08 4
#> SD:kmeans 62 8.75e-12 2.79e-06 4
#> CV:kmeans 62 8.75e-12 2.79e-06 4
#> MAD:kmeans 62 8.75e-12 2.79e-06 4
#> ATC:kmeans 60 2.31e-11 1.88e-06 4
#> SD:pam 62 7.83e-12 1.05e-05 4
#> CV:pam 60 1.99e-11 3.56e-06 4
#> MAD:pam 61 1.28e-11 1.67e-05 4
#> ATC:pam 60 1.32e-10 4.12e-06 4
#> SD:hclust 60 2.44e-11 4.43e-07 4
#> CV:hclust 60 3.51e-12 3.82e-07 4
#> MAD:hclust 62 5.13e-11 1.26e-06 4
#> ATC:hclust 61 7.52e-11 6.47e-06 4
test_to_known_factors(res_list, k = 5)
#> n tissue(p) individual(p) k
#> SD:NMF 47 5.45e-08 4.67e-04 5
#> CV:NMF 58 2.62e-10 1.35e-04 5
#> MAD:NMF 52 4.69e-09 1.75e-05 5
#> ATC:NMF 52 1.84e-10 7.21e-06 5
#> SD:skmeans 59 2.84e-11 7.18e-09 5
#> CV:skmeans 62 3.62e-11 4.35e-09 5
#> MAD:skmeans 61 6.13e-11 1.62e-08 5
#> ATC:skmeans 61 6.65e-11 1.89e-08 5
#> SD:mclust 51 1.42e-09 2.99e-08 5
#> CV:mclust 57 7.84e-11 1.39e-06 5
#> MAD:mclust 37 9.24e-09 1.68e-07 5
#> ATC:mclust 55 2.06e-10 1.02e-06 5
#> SD:kmeans 60 1.07e-10 8.81e-09 5
#> CV:kmeans 58 2.84e-10 2.75e-07 5
#> MAD:kmeans 61 5.90e-11 6.14e-09 5
#> ATC:kmeans 59 1.74e-10 1.67e-08 5
#> SD:pam 62 3.70e-11 1.07e-08 5
#> CV:pam 60 9.23e-11 1.88e-05 5
#> MAD:pam 62 3.70e-11 1.07e-08 5
#> ATC:pam 59 1.74e-10 3.95e-07 5
#> SD:hclust 60 2.46e-11 2.10e-06 5
#> CV:hclust 53 1.13e-10 1.55e-06 5
#> MAD:hclust 61 8.39e-11 2.10e-06 5
#> ATC:hclust 60 2.28e-11 3.79e-06 5
test_to_known_factors(res_list, k = 6)
#> n tissue(p) individual(p) k
#> SD:NMF 55 3.89e-09 2.55e-10 6
#> CV:NMF 49 1.85e-08 4.08e-05 6
#> MAD:NMF 53 1.02e-08 4.46e-09 6
#> ATC:NMF 53 1.88e-09 5.49e-08 6
#> SD:skmeans 61 4.26e-11 1.04e-11 6
#> CV:skmeans 60 3.70e-10 2.02e-11 6
#> MAD:skmeans 62 1.46e-10 2.39e-11 6
#> ATC:skmeans 50 8.13e-09 3.48e-09 6
#> SD:mclust 53 3.36e-10 1.12e-11 6
#> CV:mclust 50 1.39e-09 3.03e-07 6
#> MAD:mclust 62 1.43e-10 8.15e-13 6
#> ATC:mclust 57 3.10e-10 1.28e-06 6
#> SD:kmeans 61 2.35e-10 5.61e-13 6
#> CV:kmeans 46 2.48e-07 1.00e-09 6
#> MAD:kmeans 55 4.08e-09 2.17e-11 6
#> ATC:kmeans 59 2.99e-11 7.29e-10 6
#> SD:pam 61 2.35e-10 4.50e-10 6
#> CV:pam 60 6.95e-11 7.63e-08 6
#> MAD:pam 62 1.46e-10 7.27e-10 6
#> ATC:pam 58 1.00e-09 2.43e-11 6
#> SD:hclust 59 6.15e-12 1.83e-06 6
#> CV:hclust 52 1.86e-10 7.42e-07 6
#> MAD:hclust 59 6.15e-12 1.83e-06 6
#> ATC:hclust 60 1.06e-10 7.14e-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 11993 rows and 62 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 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 0.316 0.447 0.668 0.4478 0.492 0.492
#> 3 3 0.714 0.813 0.912 0.4379 0.874 0.744
#> 4 4 0.859 0.935 0.907 0.0873 0.903 0.734
#> 5 5 0.858 0.903 0.934 0.0434 0.993 0.974
#> 6 6 0.927 0.873 0.948 0.0391 0.988 0.956
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM26805 2 0.0000 0.746 0.000 1.000
#> GSM26806 2 0.9922 0.170 0.448 0.552
#> GSM26807 2 0.9922 0.170 0.448 0.552
#> GSM26808 2 0.9922 0.170 0.448 0.552
#> GSM26809 2 0.8267 0.232 0.260 0.740
#> GSM26810 2 0.9922 0.170 0.448 0.552
#> GSM26811 2 0.9922 0.170 0.448 0.552
#> GSM26812 2 0.9922 0.170 0.448 0.552
#> GSM26813 2 0.0000 0.746 0.000 1.000
#> GSM26814 2 0.0000 0.746 0.000 1.000
#> GSM26815 2 0.9922 0.170 0.448 0.552
#> GSM26816 2 0.0000 0.746 0.000 1.000
#> GSM26817 2 0.9922 0.170 0.448 0.552
#> GSM26818 1 0.9491 0.324 0.632 0.368
#> GSM26819 2 0.0000 0.746 0.000 1.000
#> GSM26820 2 0.0000 0.746 0.000 1.000
#> GSM26821 2 0.0000 0.746 0.000 1.000
#> GSM26822 2 0.0000 0.746 0.000 1.000
#> GSM26823 2 0.0000 0.746 0.000 1.000
#> GSM26824 2 0.0000 0.746 0.000 1.000
#> GSM26825 2 0.0000 0.746 0.000 1.000
#> GSM26826 2 0.0000 0.746 0.000 1.000
#> GSM26827 2 0.0000 0.746 0.000 1.000
#> GSM26828 2 0.0000 0.746 0.000 1.000
#> GSM26829 2 0.0000 0.746 0.000 1.000
#> GSM26830 2 0.0000 0.746 0.000 1.000
#> GSM26831 2 0.0000 0.746 0.000 1.000
#> GSM26832 2 0.0672 0.739 0.008 0.992
#> GSM26833 2 0.0672 0.739 0.008 0.992
#> GSM26834 2 0.0000 0.746 0.000 1.000
#> GSM26835 2 0.0000 0.746 0.000 1.000
#> GSM26836 1 0.9922 0.304 0.552 0.448
#> GSM26837 1 0.9922 0.304 0.552 0.448
#> GSM26838 1 0.9922 0.304 0.552 0.448
#> GSM26839 1 0.9922 0.304 0.552 0.448
#> GSM26840 1 0.9922 0.304 0.552 0.448
#> GSM26841 1 0.9922 0.304 0.552 0.448
#> GSM26842 1 0.9922 0.304 0.552 0.448
#> GSM26843 1 0.9922 0.304 0.552 0.448
#> GSM26844 1 0.9922 0.304 0.552 0.448
#> GSM26845 1 0.9922 0.304 0.552 0.448
#> GSM26846 1 0.9552 0.320 0.624 0.376
#> GSM26847 1 0.9552 0.320 0.624 0.376
#> GSM26848 1 0.9552 0.320 0.624 0.376
#> GSM26849 1 0.9552 0.320 0.624 0.376
#> GSM26850 1 0.9552 0.320 0.624 0.376
#> GSM26851 2 0.0672 0.739 0.008 0.992
#> GSM26852 1 0.9491 0.324 0.632 0.368
#> GSM26853 1 0.9491 0.324 0.632 0.368
#> GSM26854 1 0.9491 0.324 0.632 0.368
#> GSM26855 1 0.9491 0.324 0.632 0.368
#> GSM26856 1 0.9491 0.324 0.632 0.368
#> GSM26857 1 0.9491 0.324 0.632 0.368
#> GSM26858 1 0.9491 0.324 0.632 0.368
#> GSM26859 1 0.9491 0.324 0.632 0.368
#> GSM26860 1 0.9491 0.324 0.632 0.368
#> GSM26861 1 0.9491 0.324 0.632 0.368
#> GSM26862 1 0.9922 0.304 0.552 0.448
#> GSM26863 1 0.9922 0.304 0.552 0.448
#> GSM26864 1 0.9922 0.304 0.552 0.448
#> GSM26865 1 0.9552 0.320 0.624 0.376
#> GSM26866 1 0.9922 0.304 0.552 0.448
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM26805 2 0.0237 0.853 0.004 0.996 0.000
#> GSM26806 2 0.6252 0.355 0.000 0.556 0.444
#> GSM26807 2 0.6252 0.355 0.000 0.556 0.444
#> GSM26808 2 0.6252 0.355 0.000 0.556 0.444
#> GSM26809 2 0.5327 0.505 0.272 0.728 0.000
#> GSM26810 2 0.6252 0.355 0.000 0.556 0.444
#> GSM26811 2 0.6252 0.355 0.000 0.556 0.444
#> GSM26812 2 0.6252 0.355 0.000 0.556 0.444
#> GSM26813 2 0.0237 0.853 0.004 0.996 0.000
#> GSM26814 2 0.0237 0.853 0.004 0.996 0.000
#> GSM26815 2 0.6252 0.355 0.000 0.556 0.444
#> GSM26816 2 0.0237 0.853 0.004 0.996 0.000
#> GSM26817 2 0.6252 0.355 0.000 0.556 0.444
#> GSM26818 3 0.0237 0.924 0.000 0.004 0.996
#> GSM26819 2 0.0237 0.853 0.004 0.996 0.000
#> GSM26820 2 0.0237 0.853 0.004 0.996 0.000
#> GSM26821 2 0.0237 0.853 0.004 0.996 0.000
#> GSM26822 2 0.0237 0.853 0.004 0.996 0.000
#> GSM26823 2 0.0237 0.853 0.004 0.996 0.000
#> GSM26824 2 0.0237 0.853 0.004 0.996 0.000
#> GSM26825 2 0.0237 0.853 0.004 0.996 0.000
#> GSM26826 2 0.0237 0.853 0.004 0.996 0.000
#> GSM26827 2 0.0237 0.853 0.004 0.996 0.000
#> GSM26828 2 0.0237 0.853 0.004 0.996 0.000
#> GSM26829 2 0.0237 0.853 0.004 0.996 0.000
#> GSM26830 2 0.0237 0.853 0.004 0.996 0.000
#> GSM26831 2 0.0237 0.853 0.004 0.996 0.000
#> GSM26832 2 0.0237 0.849 0.000 0.996 0.004
#> GSM26833 2 0.0237 0.849 0.000 0.996 0.004
#> GSM26834 2 0.0237 0.853 0.004 0.996 0.000
#> GSM26835 2 0.0237 0.853 0.004 0.996 0.000
#> GSM26836 1 0.0000 0.969 1.000 0.000 0.000
#> GSM26837 1 0.0000 0.969 1.000 0.000 0.000
#> GSM26838 1 0.0000 0.969 1.000 0.000 0.000
#> GSM26839 1 0.0000 0.969 1.000 0.000 0.000
#> GSM26840 1 0.0000 0.969 1.000 0.000 0.000
#> GSM26841 1 0.0000 0.969 1.000 0.000 0.000
#> GSM26842 1 0.0000 0.969 1.000 0.000 0.000
#> GSM26843 1 0.0000 0.969 1.000 0.000 0.000
#> GSM26844 1 0.0000 0.969 1.000 0.000 0.000
#> GSM26845 1 0.5785 0.524 0.668 0.332 0.000
#> GSM26846 3 0.4968 0.840 0.188 0.012 0.800
#> GSM26847 3 0.4968 0.840 0.188 0.012 0.800
#> GSM26848 3 0.4968 0.840 0.188 0.012 0.800
#> GSM26849 3 0.4968 0.840 0.188 0.012 0.800
#> GSM26850 3 0.4968 0.840 0.188 0.012 0.800
#> GSM26851 2 0.0237 0.849 0.000 0.996 0.004
#> GSM26852 3 0.0237 0.924 0.000 0.004 0.996
#> GSM26853 3 0.0237 0.924 0.000 0.004 0.996
#> GSM26854 3 0.0237 0.924 0.000 0.004 0.996
#> GSM26855 3 0.0237 0.924 0.000 0.004 0.996
#> GSM26856 3 0.0237 0.924 0.000 0.004 0.996
#> GSM26857 3 0.0237 0.924 0.000 0.004 0.996
#> GSM26858 3 0.0237 0.924 0.000 0.004 0.996
#> GSM26859 3 0.0237 0.924 0.000 0.004 0.996
#> GSM26860 3 0.0237 0.924 0.000 0.004 0.996
#> GSM26861 3 0.0237 0.924 0.000 0.004 0.996
#> GSM26862 1 0.0000 0.969 1.000 0.000 0.000
#> GSM26863 1 0.0000 0.969 1.000 0.000 0.000
#> GSM26864 1 0.0000 0.969 1.000 0.000 0.000
#> GSM26865 3 0.4968 0.840 0.188 0.012 0.800
#> GSM26866 1 0.0000 0.969 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM26805 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM26806 4 0.5435 1.000 0.000 0.420 0.016 0.564
#> GSM26807 4 0.5435 1.000 0.000 0.420 0.016 0.564
#> GSM26808 4 0.5435 1.000 0.000 0.420 0.016 0.564
#> GSM26809 2 0.5395 0.486 0.084 0.732 0.000 0.184
#> GSM26810 4 0.5435 1.000 0.000 0.420 0.016 0.564
#> GSM26811 4 0.5435 1.000 0.000 0.420 0.016 0.564
#> GSM26812 4 0.5435 1.000 0.000 0.420 0.016 0.564
#> GSM26813 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM26814 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM26815 4 0.5435 1.000 0.000 0.420 0.016 0.564
#> GSM26816 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM26817 4 0.5435 1.000 0.000 0.420 0.016 0.564
#> GSM26818 3 0.0000 0.938 0.000 0.000 1.000 0.000
#> GSM26819 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM26820 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM26821 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM26822 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM26823 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM26824 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM26825 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM26826 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM26827 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM26828 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM26829 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM26830 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM26831 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM26832 2 0.0336 0.965 0.000 0.992 0.000 0.008
#> GSM26833 2 0.0336 0.965 0.000 0.992 0.000 0.008
#> GSM26834 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM26835 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM26836 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM26837 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM26838 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM26839 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM26840 1 0.4008 0.772 0.756 0.000 0.000 0.244
#> GSM26841 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM26842 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM26843 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM26844 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM26845 1 0.7393 0.288 0.488 0.332 0.000 0.180
#> GSM26846 3 0.4151 0.882 0.004 0.016 0.800 0.180
#> GSM26847 3 0.4151 0.882 0.004 0.016 0.800 0.180
#> GSM26848 3 0.4151 0.882 0.004 0.016 0.800 0.180
#> GSM26849 3 0.4151 0.882 0.004 0.016 0.800 0.180
#> GSM26850 3 0.4151 0.882 0.004 0.016 0.800 0.180
#> GSM26851 2 0.0707 0.952 0.000 0.980 0.000 0.020
#> GSM26852 3 0.0000 0.938 0.000 0.000 1.000 0.000
#> GSM26853 3 0.0000 0.938 0.000 0.000 1.000 0.000
#> GSM26854 3 0.0000 0.938 0.000 0.000 1.000 0.000
#> GSM26855 3 0.0000 0.938 0.000 0.000 1.000 0.000
#> GSM26856 3 0.0000 0.938 0.000 0.000 1.000 0.000
#> GSM26857 3 0.0000 0.938 0.000 0.000 1.000 0.000
#> GSM26858 3 0.0000 0.938 0.000 0.000 1.000 0.000
#> GSM26859 3 0.0000 0.938 0.000 0.000 1.000 0.000
#> GSM26860 3 0.0000 0.938 0.000 0.000 1.000 0.000
#> GSM26861 3 0.0000 0.938 0.000 0.000 1.000 0.000
#> GSM26862 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM26863 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM26864 1 0.0000 0.947 1.000 0.000 0.000 0.000
#> GSM26865 3 0.4151 0.882 0.004 0.016 0.800 0.180
#> GSM26866 1 0.0000 0.947 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
#> GSM26805 2 0.0000 0.9715 0.000 1.000 0.0 0.000 0.000
#> GSM26806 4 0.2966 1.0000 0.000 0.184 0.0 0.816 0.000
#> GSM26807 4 0.2966 1.0000 0.000 0.184 0.0 0.816 0.000
#> GSM26808 4 0.2966 1.0000 0.000 0.184 0.0 0.816 0.000
#> GSM26809 2 0.4647 0.6344 0.084 0.732 0.0 0.000 0.184
#> GSM26810 4 0.2966 1.0000 0.000 0.184 0.0 0.816 0.000
#> GSM26811 4 0.2966 1.0000 0.000 0.184 0.0 0.816 0.000
#> GSM26812 4 0.2966 1.0000 0.000 0.184 0.0 0.816 0.000
#> GSM26813 2 0.0000 0.9715 0.000 1.000 0.0 0.000 0.000
#> GSM26814 2 0.0000 0.9715 0.000 1.000 0.0 0.000 0.000
#> GSM26815 4 0.2966 1.0000 0.000 0.184 0.0 0.816 0.000
#> GSM26816 2 0.0000 0.9715 0.000 1.000 0.0 0.000 0.000
#> GSM26817 4 0.2966 1.0000 0.000 0.184 0.0 0.816 0.000
#> GSM26818 3 0.0000 0.9216 0.000 0.000 1.0 0.000 0.000
#> GSM26819 2 0.0000 0.9715 0.000 1.000 0.0 0.000 0.000
#> GSM26820 2 0.0000 0.9715 0.000 1.000 0.0 0.000 0.000
#> GSM26821 2 0.0000 0.9715 0.000 1.000 0.0 0.000 0.000
#> GSM26822 2 0.0000 0.9715 0.000 1.000 0.0 0.000 0.000
#> GSM26823 2 0.0000 0.9715 0.000 1.000 0.0 0.000 0.000
#> GSM26824 2 0.0000 0.9715 0.000 1.000 0.0 0.000 0.000
#> GSM26825 2 0.0000 0.9715 0.000 1.000 0.0 0.000 0.000
#> GSM26826 2 0.0000 0.9715 0.000 1.000 0.0 0.000 0.000
#> GSM26827 2 0.0000 0.9715 0.000 1.000 0.0 0.000 0.000
#> GSM26828 2 0.0000 0.9715 0.000 1.000 0.0 0.000 0.000
#> GSM26829 2 0.0000 0.9715 0.000 1.000 0.0 0.000 0.000
#> GSM26830 2 0.0000 0.9715 0.000 1.000 0.0 0.000 0.000
#> GSM26831 2 0.0000 0.9715 0.000 1.000 0.0 0.000 0.000
#> GSM26832 2 0.0963 0.9431 0.000 0.964 0.0 0.036 0.000
#> GSM26833 2 0.0963 0.9431 0.000 0.964 0.0 0.036 0.000
#> GSM26834 2 0.0000 0.9715 0.000 1.000 0.0 0.000 0.000
#> GSM26835 2 0.0000 0.9715 0.000 1.000 0.0 0.000 0.000
#> GSM26836 1 0.0000 0.9275 1.000 0.000 0.0 0.000 0.000
#> GSM26837 1 0.0000 0.9275 1.000 0.000 0.0 0.000 0.000
#> GSM26838 1 0.0000 0.9275 1.000 0.000 0.0 0.000 0.000
#> GSM26839 1 0.0000 0.9275 1.000 0.000 0.0 0.000 0.000
#> GSM26840 5 0.3242 0.0000 0.216 0.000 0.0 0.000 0.784
#> GSM26841 1 0.0000 0.9275 1.000 0.000 0.0 0.000 0.000
#> GSM26842 1 0.0000 0.9275 1.000 0.000 0.0 0.000 0.000
#> GSM26843 1 0.0000 0.9275 1.000 0.000 0.0 0.000 0.000
#> GSM26844 1 0.0000 0.9275 1.000 0.000 0.0 0.000 0.000
#> GSM26845 1 0.6392 -0.0629 0.484 0.332 0.0 0.000 0.184
#> GSM26846 3 0.3456 0.8478 0.000 0.016 0.8 0.000 0.184
#> GSM26847 3 0.3456 0.8478 0.000 0.016 0.8 0.000 0.184
#> GSM26848 3 0.3456 0.8478 0.000 0.016 0.8 0.000 0.184
#> GSM26849 3 0.3456 0.8478 0.000 0.016 0.8 0.000 0.184
#> GSM26850 3 0.3456 0.8478 0.000 0.016 0.8 0.000 0.184
#> GSM26851 2 0.3805 0.7172 0.000 0.784 0.0 0.184 0.032
#> GSM26852 3 0.0000 0.9216 0.000 0.000 1.0 0.000 0.000
#> GSM26853 3 0.0000 0.9216 0.000 0.000 1.0 0.000 0.000
#> GSM26854 3 0.0000 0.9216 0.000 0.000 1.0 0.000 0.000
#> GSM26855 3 0.0000 0.9216 0.000 0.000 1.0 0.000 0.000
#> GSM26856 3 0.0000 0.9216 0.000 0.000 1.0 0.000 0.000
#> GSM26857 3 0.0000 0.9216 0.000 0.000 1.0 0.000 0.000
#> GSM26858 3 0.0000 0.9216 0.000 0.000 1.0 0.000 0.000
#> GSM26859 3 0.0000 0.9216 0.000 0.000 1.0 0.000 0.000
#> GSM26860 3 0.0000 0.9216 0.000 0.000 1.0 0.000 0.000
#> GSM26861 3 0.0000 0.9216 0.000 0.000 1.0 0.000 0.000
#> GSM26862 1 0.0000 0.9275 1.000 0.000 0.0 0.000 0.000
#> GSM26863 1 0.0000 0.9275 1.000 0.000 0.0 0.000 0.000
#> GSM26864 1 0.0000 0.9275 1.000 0.000 0.0 0.000 0.000
#> GSM26865 3 0.3456 0.8478 0.000 0.016 0.8 0.000 0.184
#> GSM26866 1 0.0000 0.9275 1.000 0.000 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
#> GSM26805 2 0.0713 0.942 0.000 0.972 0.0 0.000 0.028 0.000
#> GSM26806 4 0.0547 1.000 0.000 0.020 0.0 0.980 0.000 0.000
#> GSM26807 4 0.0547 1.000 0.000 0.020 0.0 0.980 0.000 0.000
#> GSM26808 4 0.0547 1.000 0.000 0.020 0.0 0.980 0.000 0.000
#> GSM26809 2 0.4605 0.563 0.000 0.692 0.0 0.000 0.124 0.184
#> GSM26810 4 0.0547 1.000 0.000 0.020 0.0 0.980 0.000 0.000
#> GSM26811 4 0.0547 1.000 0.000 0.020 0.0 0.980 0.000 0.000
#> GSM26812 4 0.0547 1.000 0.000 0.020 0.0 0.980 0.000 0.000
#> GSM26813 2 0.0000 0.949 0.000 1.000 0.0 0.000 0.000 0.000
#> GSM26814 2 0.0000 0.949 0.000 1.000 0.0 0.000 0.000 0.000
#> GSM26815 4 0.0547 1.000 0.000 0.020 0.0 0.980 0.000 0.000
#> GSM26816 2 0.0713 0.942 0.000 0.972 0.0 0.000 0.028 0.000
#> GSM26817 4 0.0547 1.000 0.000 0.020 0.0 0.980 0.000 0.000
#> GSM26818 3 0.0000 0.921 0.000 0.000 1.0 0.000 0.000 0.000
#> GSM26819 2 0.0000 0.949 0.000 1.000 0.0 0.000 0.000 0.000
#> GSM26820 2 0.0000 0.949 0.000 1.000 0.0 0.000 0.000 0.000
#> GSM26821 2 0.0000 0.949 0.000 1.000 0.0 0.000 0.000 0.000
#> GSM26822 2 0.0000 0.949 0.000 1.000 0.0 0.000 0.000 0.000
#> GSM26823 2 0.0000 0.949 0.000 1.000 0.0 0.000 0.000 0.000
#> GSM26824 2 0.0000 0.949 0.000 1.000 0.0 0.000 0.000 0.000
#> GSM26825 2 0.0000 0.949 0.000 1.000 0.0 0.000 0.000 0.000
#> GSM26826 2 0.0000 0.949 0.000 1.000 0.0 0.000 0.000 0.000
#> GSM26827 2 0.0000 0.949 0.000 1.000 0.0 0.000 0.000 0.000
#> GSM26828 2 0.0858 0.941 0.000 0.968 0.0 0.004 0.028 0.000
#> GSM26829 2 0.0858 0.941 0.000 0.968 0.0 0.004 0.028 0.000
#> GSM26830 2 0.0000 0.949 0.000 1.000 0.0 0.000 0.000 0.000
#> GSM26831 2 0.0858 0.941 0.000 0.968 0.0 0.004 0.028 0.000
#> GSM26832 2 0.3481 0.732 0.000 0.792 0.0 0.160 0.048 0.000
#> GSM26833 2 0.3481 0.732 0.000 0.792 0.0 0.160 0.048 0.000
#> GSM26834 2 0.0858 0.941 0.000 0.968 0.0 0.004 0.028 0.000
#> GSM26835 2 0.0858 0.941 0.000 0.968 0.0 0.004 0.028 0.000
#> GSM26836 1 0.0000 0.926 1.000 0.000 0.0 0.000 0.000 0.000
#> GSM26837 1 0.0000 0.926 1.000 0.000 0.0 0.000 0.000 0.000
#> GSM26838 1 0.0000 0.926 1.000 0.000 0.0 0.000 0.000 0.000
#> GSM26839 1 0.0000 0.926 1.000 0.000 0.0 0.000 0.000 0.000
#> GSM26840 6 0.3017 0.000 0.164 0.000 0.0 0.020 0.000 0.816
#> GSM26841 1 0.0000 0.926 1.000 0.000 0.0 0.000 0.000 0.000
#> GSM26842 1 0.0000 0.926 1.000 0.000 0.0 0.000 0.000 0.000
#> GSM26843 1 0.0000 0.926 1.000 0.000 0.0 0.000 0.000 0.000
#> GSM26844 1 0.0000 0.926 1.000 0.000 0.0 0.000 0.000 0.000
#> GSM26845 1 0.7138 -0.193 0.384 0.320 0.0 0.000 0.096 0.200
#> GSM26846 3 0.3104 0.846 0.000 0.016 0.8 0.000 0.000 0.184
#> GSM26847 3 0.3104 0.846 0.000 0.016 0.8 0.000 0.000 0.184
#> GSM26848 3 0.3104 0.846 0.000 0.016 0.8 0.000 0.000 0.184
#> GSM26849 3 0.3104 0.846 0.000 0.016 0.8 0.000 0.000 0.184
#> GSM26850 3 0.3104 0.846 0.000 0.016 0.8 0.000 0.000 0.184
#> GSM26851 5 0.1765 0.000 0.000 0.096 0.0 0.000 0.904 0.000
#> GSM26852 3 0.0000 0.921 0.000 0.000 1.0 0.000 0.000 0.000
#> GSM26853 3 0.0000 0.921 0.000 0.000 1.0 0.000 0.000 0.000
#> GSM26854 3 0.0000 0.921 0.000 0.000 1.0 0.000 0.000 0.000
#> GSM26855 3 0.0000 0.921 0.000 0.000 1.0 0.000 0.000 0.000
#> GSM26856 3 0.0000 0.921 0.000 0.000 1.0 0.000 0.000 0.000
#> GSM26857 3 0.0000 0.921 0.000 0.000 1.0 0.000 0.000 0.000
#> GSM26858 3 0.0000 0.921 0.000 0.000 1.0 0.000 0.000 0.000
#> GSM26859 3 0.0000 0.921 0.000 0.000 1.0 0.000 0.000 0.000
#> GSM26860 3 0.0000 0.921 0.000 0.000 1.0 0.000 0.000 0.000
#> GSM26861 3 0.0000 0.921 0.000 0.000 1.0 0.000 0.000 0.000
#> GSM26862 1 0.0000 0.926 1.000 0.000 0.0 0.000 0.000 0.000
#> GSM26863 1 0.0000 0.926 1.000 0.000 0.0 0.000 0.000 0.000
#> GSM26864 1 0.0000 0.926 1.000 0.000 0.0 0.000 0.000 0.000
#> GSM26865 3 0.3104 0.846 0.000 0.016 0.8 0.000 0.000 0.184
#> GSM26866 1 0.0000 0.926 1.000 0.000 0.0 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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 6, scale_rows = FALSE)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> SD:hclust 22 NA NA 2
#> SD:hclust 54 9.11e-11 1.20e-05 3
#> SD:hclust 60 2.44e-11 4.43e-07 4
#> SD:hclust 60 2.46e-11 2.10e-06 5
#> SD:hclust 59 6.15e-12 1.83e-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["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 11993 rows and 62 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 0.500 0.930 0.939 0.4975 0.492 0.492
#> 3 3 0.735 0.875 0.854 0.2588 0.879 0.755
#> 4 4 0.659 0.874 0.853 0.1294 0.903 0.738
#> 5 5 0.713 0.781 0.772 0.0805 0.950 0.819
#> 6 6 0.838 0.886 0.856 0.0605 0.931 0.701
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
#> GSM26805 2 0.0376 0.959 0.004 0.996
#> GSM26806 2 0.5519 0.884 0.128 0.872
#> GSM26807 2 0.5519 0.884 0.128 0.872
#> GSM26808 2 0.5294 0.890 0.120 0.880
#> GSM26809 2 0.0376 0.959 0.004 0.996
#> GSM26810 2 0.5519 0.884 0.128 0.872
#> GSM26811 2 0.5294 0.890 0.120 0.880
#> GSM26812 2 0.5519 0.884 0.128 0.872
#> GSM26813 2 0.0000 0.960 0.000 1.000
#> GSM26814 2 0.0000 0.960 0.000 1.000
#> GSM26815 2 0.5519 0.884 0.128 0.872
#> GSM26816 2 0.0376 0.959 0.004 0.996
#> GSM26817 2 0.5294 0.890 0.120 0.880
#> GSM26818 1 0.0376 0.899 0.996 0.004
#> GSM26819 2 0.0000 0.960 0.000 1.000
#> GSM26820 2 0.0000 0.960 0.000 1.000
#> GSM26821 2 0.0000 0.960 0.000 1.000
#> GSM26822 2 0.0000 0.960 0.000 1.000
#> GSM26823 2 0.0000 0.960 0.000 1.000
#> GSM26824 2 0.0000 0.960 0.000 1.000
#> GSM26825 2 0.0000 0.960 0.000 1.000
#> GSM26826 2 0.0000 0.960 0.000 1.000
#> GSM26827 2 0.0000 0.960 0.000 1.000
#> GSM26828 2 0.0376 0.959 0.004 0.996
#> GSM26829 2 0.0376 0.959 0.004 0.996
#> GSM26830 2 0.0000 0.960 0.000 1.000
#> GSM26831 2 0.0376 0.959 0.004 0.996
#> GSM26832 2 0.0376 0.959 0.004 0.996
#> GSM26833 2 0.0000 0.960 0.000 1.000
#> GSM26834 2 0.0376 0.959 0.004 0.996
#> GSM26835 2 0.0376 0.959 0.004 0.996
#> GSM26836 1 0.5946 0.933 0.856 0.144
#> GSM26837 1 0.5629 0.930 0.868 0.132
#> GSM26838 1 0.5946 0.933 0.856 0.144
#> GSM26839 1 0.5946 0.933 0.856 0.144
#> GSM26840 1 0.5946 0.933 0.856 0.144
#> GSM26841 1 0.5946 0.933 0.856 0.144
#> GSM26842 1 0.5946 0.933 0.856 0.144
#> GSM26843 1 0.5946 0.933 0.856 0.144
#> GSM26844 1 0.5946 0.933 0.856 0.144
#> GSM26845 1 0.5946 0.933 0.856 0.144
#> GSM26846 1 0.6048 0.931 0.852 0.148
#> GSM26847 1 0.5946 0.933 0.856 0.144
#> GSM26848 1 0.5946 0.933 0.856 0.144
#> GSM26849 1 0.0376 0.899 0.996 0.004
#> GSM26850 1 0.5946 0.933 0.856 0.144
#> GSM26851 2 0.0000 0.960 0.000 1.000
#> GSM26852 1 0.0376 0.899 0.996 0.004
#> GSM26853 1 0.0376 0.899 0.996 0.004
#> GSM26854 1 0.0376 0.899 0.996 0.004
#> GSM26855 1 0.0376 0.899 0.996 0.004
#> GSM26856 1 0.0376 0.899 0.996 0.004
#> GSM26857 1 0.0376 0.899 0.996 0.004
#> GSM26858 1 0.0376 0.899 0.996 0.004
#> GSM26859 1 0.0376 0.899 0.996 0.004
#> GSM26860 1 0.0376 0.899 0.996 0.004
#> GSM26861 1 0.0376 0.899 0.996 0.004
#> GSM26862 1 0.5946 0.933 0.856 0.144
#> GSM26863 1 0.5946 0.933 0.856 0.144
#> GSM26864 1 0.5946 0.933 0.856 0.144
#> GSM26865 1 0.5946 0.933 0.856 0.144
#> GSM26866 1 0.5946 0.933 0.856 0.144
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM26805 2 0.1643 0.901 0.044 0.956 0.000
#> GSM26806 2 0.5873 0.764 0.312 0.684 0.004
#> GSM26807 2 0.5873 0.764 0.312 0.684 0.004
#> GSM26808 2 0.5873 0.764 0.312 0.684 0.004
#> GSM26809 2 0.1643 0.901 0.044 0.956 0.000
#> GSM26810 2 0.5873 0.764 0.312 0.684 0.004
#> GSM26811 2 0.5873 0.764 0.312 0.684 0.004
#> GSM26812 2 0.5873 0.764 0.312 0.684 0.004
#> GSM26813 2 0.0000 0.909 0.000 1.000 0.000
#> GSM26814 2 0.0000 0.909 0.000 1.000 0.000
#> GSM26815 2 0.5873 0.764 0.312 0.684 0.004
#> GSM26816 2 0.1643 0.901 0.044 0.956 0.000
#> GSM26817 2 0.5873 0.764 0.312 0.684 0.004
#> GSM26818 3 0.3349 0.814 0.108 0.004 0.888
#> GSM26819 2 0.0000 0.909 0.000 1.000 0.000
#> GSM26820 2 0.0000 0.909 0.000 1.000 0.000
#> GSM26821 2 0.0000 0.909 0.000 1.000 0.000
#> GSM26822 2 0.0000 0.909 0.000 1.000 0.000
#> GSM26823 2 0.0000 0.909 0.000 1.000 0.000
#> GSM26824 2 0.0000 0.909 0.000 1.000 0.000
#> GSM26825 2 0.0000 0.909 0.000 1.000 0.000
#> GSM26826 2 0.0000 0.909 0.000 1.000 0.000
#> GSM26827 2 0.0000 0.909 0.000 1.000 0.000
#> GSM26828 2 0.1643 0.901 0.044 0.956 0.000
#> GSM26829 2 0.1643 0.901 0.044 0.956 0.000
#> GSM26830 2 0.0000 0.909 0.000 1.000 0.000
#> GSM26831 2 0.1643 0.901 0.044 0.956 0.000
#> GSM26832 2 0.2711 0.896 0.088 0.912 0.000
#> GSM26833 2 0.2711 0.896 0.088 0.912 0.000
#> GSM26834 2 0.1643 0.901 0.044 0.956 0.000
#> GSM26835 2 0.1643 0.901 0.044 0.956 0.000
#> GSM26836 1 0.5948 0.893 0.640 0.000 0.360
#> GSM26837 1 0.6045 0.883 0.620 0.000 0.380
#> GSM26838 1 0.5948 0.893 0.640 0.000 0.360
#> GSM26839 1 0.5948 0.893 0.640 0.000 0.360
#> GSM26840 1 0.7635 0.680 0.676 0.112 0.212
#> GSM26841 1 0.5948 0.893 0.640 0.000 0.360
#> GSM26842 1 0.5948 0.893 0.640 0.000 0.360
#> GSM26843 1 0.5948 0.893 0.640 0.000 0.360
#> GSM26844 1 0.5948 0.893 0.640 0.000 0.360
#> GSM26845 1 0.6420 0.412 0.688 0.288 0.024
#> GSM26846 1 0.6495 0.799 0.536 0.004 0.460
#> GSM26847 1 0.6280 0.804 0.540 0.000 0.460
#> GSM26848 1 0.6495 0.799 0.536 0.004 0.460
#> GSM26849 3 0.0983 0.962 0.016 0.004 0.980
#> GSM26850 1 0.6495 0.799 0.536 0.004 0.460
#> GSM26851 2 0.3500 0.886 0.116 0.880 0.004
#> GSM26852 3 0.0237 0.980 0.000 0.004 0.996
#> GSM26853 3 0.0237 0.980 0.000 0.004 0.996
#> GSM26854 3 0.0237 0.980 0.000 0.004 0.996
#> GSM26855 3 0.0237 0.980 0.000 0.004 0.996
#> GSM26856 3 0.0237 0.980 0.000 0.004 0.996
#> GSM26857 3 0.0237 0.980 0.000 0.004 0.996
#> GSM26858 3 0.0237 0.980 0.000 0.004 0.996
#> GSM26859 3 0.0475 0.975 0.004 0.004 0.992
#> GSM26860 3 0.0237 0.980 0.000 0.004 0.996
#> GSM26861 3 0.0237 0.980 0.000 0.004 0.996
#> GSM26862 1 0.6045 0.883 0.620 0.000 0.380
#> GSM26863 1 0.5948 0.893 0.640 0.000 0.360
#> GSM26864 1 0.5948 0.893 0.640 0.000 0.360
#> GSM26865 1 0.6280 0.804 0.540 0.000 0.460
#> GSM26866 1 0.5948 0.893 0.640 0.000 0.360
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM26805 2 0.4060 0.848 0.004 0.836 0.112 0.048
#> GSM26806 4 0.4661 0.998 0.000 0.348 0.000 0.652
#> GSM26807 4 0.4661 0.998 0.000 0.348 0.000 0.652
#> GSM26808 4 0.4661 0.998 0.000 0.348 0.000 0.652
#> GSM26809 2 0.4386 0.815 0.004 0.820 0.068 0.108
#> GSM26810 4 0.4661 0.998 0.000 0.348 0.000 0.652
#> GSM26811 4 0.4661 0.998 0.000 0.348 0.000 0.652
#> GSM26812 4 0.4661 0.998 0.000 0.348 0.000 0.652
#> GSM26813 2 0.0188 0.872 0.000 0.996 0.004 0.000
#> GSM26814 2 0.0188 0.872 0.000 0.996 0.004 0.000
#> GSM26815 4 0.4973 0.994 0.000 0.348 0.008 0.644
#> GSM26816 2 0.4001 0.850 0.004 0.840 0.108 0.048
#> GSM26817 4 0.4973 0.994 0.000 0.348 0.008 0.644
#> GSM26818 3 0.3687 0.903 0.080 0.000 0.856 0.064
#> GSM26819 2 0.0000 0.874 0.000 1.000 0.000 0.000
#> GSM26820 2 0.0000 0.874 0.000 1.000 0.000 0.000
#> GSM26821 2 0.0000 0.874 0.000 1.000 0.000 0.000
#> GSM26822 2 0.0000 0.874 0.000 1.000 0.000 0.000
#> GSM26823 2 0.0000 0.874 0.000 1.000 0.000 0.000
#> GSM26824 2 0.0000 0.874 0.000 1.000 0.000 0.000
#> GSM26825 2 0.0000 0.874 0.000 1.000 0.000 0.000
#> GSM26826 2 0.0000 0.874 0.000 1.000 0.000 0.000
#> GSM26827 2 0.0000 0.874 0.000 1.000 0.000 0.000
#> GSM26828 2 0.4060 0.848 0.004 0.836 0.112 0.048
#> GSM26829 2 0.3941 0.852 0.004 0.844 0.104 0.048
#> GSM26830 2 0.0188 0.872 0.000 0.996 0.004 0.000
#> GSM26831 2 0.4060 0.848 0.004 0.836 0.112 0.048
#> GSM26832 2 0.5247 0.787 0.004 0.764 0.112 0.120
#> GSM26833 2 0.5082 0.796 0.004 0.776 0.112 0.108
#> GSM26834 2 0.4296 0.842 0.004 0.824 0.112 0.060
#> GSM26835 2 0.4296 0.842 0.004 0.824 0.112 0.060
#> GSM26836 1 0.2773 0.855 0.880 0.000 0.004 0.116
#> GSM26837 1 0.3384 0.851 0.860 0.000 0.024 0.116
#> GSM26838 1 0.0188 0.853 0.996 0.000 0.004 0.000
#> GSM26839 1 0.2401 0.857 0.904 0.000 0.004 0.092
#> GSM26840 1 0.3874 0.752 0.856 0.008 0.072 0.064
#> GSM26841 1 0.0188 0.853 0.996 0.000 0.004 0.000
#> GSM26842 1 0.0188 0.853 0.996 0.000 0.004 0.000
#> GSM26843 1 0.0000 0.852 1.000 0.000 0.000 0.000
#> GSM26844 1 0.0000 0.852 1.000 0.000 0.000 0.000
#> GSM26845 1 0.6888 0.712 0.628 0.020 0.108 0.244
#> GSM26846 1 0.6248 0.742 0.660 0.000 0.128 0.212
#> GSM26847 1 0.6201 0.743 0.664 0.000 0.124 0.212
#> GSM26848 1 0.6201 0.743 0.664 0.000 0.124 0.212
#> GSM26849 3 0.6634 0.661 0.164 0.000 0.624 0.212
#> GSM26850 1 0.6201 0.743 0.664 0.000 0.124 0.212
#> GSM26851 2 0.5686 0.736 0.004 0.728 0.112 0.156
#> GSM26852 3 0.2760 0.968 0.128 0.000 0.872 0.000
#> GSM26853 3 0.2760 0.968 0.128 0.000 0.872 0.000
#> GSM26854 3 0.2760 0.968 0.128 0.000 0.872 0.000
#> GSM26855 3 0.2760 0.968 0.128 0.000 0.872 0.000
#> GSM26856 3 0.2760 0.968 0.128 0.000 0.872 0.000
#> GSM26857 3 0.2760 0.968 0.128 0.000 0.872 0.000
#> GSM26858 3 0.2760 0.968 0.128 0.000 0.872 0.000
#> GSM26859 3 0.2704 0.964 0.124 0.000 0.876 0.000
#> GSM26860 3 0.2760 0.968 0.128 0.000 0.872 0.000
#> GSM26861 3 0.2760 0.968 0.128 0.000 0.872 0.000
#> GSM26862 1 0.3384 0.851 0.860 0.000 0.024 0.116
#> GSM26863 1 0.2773 0.855 0.880 0.000 0.004 0.116
#> GSM26864 1 0.0188 0.853 0.996 0.000 0.004 0.000
#> GSM26865 1 0.6201 0.743 0.664 0.000 0.124 0.212
#> GSM26866 1 0.0000 0.852 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
#> GSM26805 2 0.0162 0.708 0.000 0.996 0.000 0.000 0.004
#> GSM26806 4 0.2329 0.986 0.000 0.124 0.000 0.876 0.000
#> GSM26807 4 0.2329 0.986 0.000 0.124 0.000 0.876 0.000
#> GSM26808 4 0.2329 0.986 0.000 0.124 0.000 0.876 0.000
#> GSM26809 2 0.5353 0.657 0.000 0.576 0.000 0.064 0.360
#> GSM26810 4 0.2329 0.986 0.000 0.124 0.000 0.876 0.000
#> GSM26811 4 0.2329 0.986 0.000 0.124 0.000 0.876 0.000
#> GSM26812 4 0.2329 0.986 0.000 0.124 0.000 0.876 0.000
#> GSM26813 2 0.5681 0.757 0.000 0.588 0.024 0.048 0.340
#> GSM26814 2 0.5681 0.757 0.000 0.588 0.024 0.048 0.340
#> GSM26815 4 0.3939 0.960 0.000 0.124 0.024 0.816 0.036
#> GSM26816 2 0.0162 0.708 0.000 0.996 0.000 0.000 0.004
#> GSM26817 4 0.4256 0.951 0.000 0.124 0.032 0.800 0.044
#> GSM26818 3 0.2457 0.837 0.008 0.000 0.900 0.016 0.076
#> GSM26819 2 0.5107 0.763 0.000 0.596 0.000 0.048 0.356
#> GSM26820 2 0.5107 0.763 0.000 0.596 0.000 0.048 0.356
#> GSM26821 2 0.5131 0.760 0.000 0.588 0.000 0.048 0.364
#> GSM26822 2 0.5107 0.763 0.000 0.596 0.000 0.048 0.356
#> GSM26823 2 0.5107 0.763 0.000 0.596 0.000 0.048 0.356
#> GSM26824 2 0.5131 0.760 0.000 0.588 0.000 0.048 0.364
#> GSM26825 2 0.5107 0.763 0.000 0.596 0.000 0.048 0.356
#> GSM26826 2 0.5107 0.763 0.000 0.596 0.000 0.048 0.356
#> GSM26827 2 0.5107 0.763 0.000 0.596 0.000 0.048 0.356
#> GSM26828 2 0.0000 0.707 0.000 1.000 0.000 0.000 0.000
#> GSM26829 2 0.0162 0.708 0.000 0.996 0.000 0.000 0.004
#> GSM26830 2 0.5681 0.757 0.000 0.588 0.024 0.048 0.340
#> GSM26831 2 0.0000 0.707 0.000 1.000 0.000 0.000 0.000
#> GSM26832 2 0.1197 0.668 0.000 0.952 0.000 0.048 0.000
#> GSM26833 2 0.1408 0.668 0.000 0.948 0.000 0.044 0.008
#> GSM26834 2 0.0290 0.702 0.000 0.992 0.000 0.008 0.000
#> GSM26835 2 0.0290 0.702 0.000 0.992 0.000 0.008 0.000
#> GSM26836 1 0.4431 0.549 0.732 0.000 0.000 0.052 0.216
#> GSM26837 1 0.4909 0.513 0.716 0.000 0.016 0.052 0.216
#> GSM26838 1 0.0794 0.769 0.972 0.000 0.000 0.028 0.000
#> GSM26839 1 0.3944 0.626 0.788 0.000 0.000 0.052 0.160
#> GSM26840 1 0.4765 0.522 0.776 0.052 0.000 0.064 0.108
#> GSM26841 1 0.0000 0.775 1.000 0.000 0.000 0.000 0.000
#> GSM26842 1 0.0000 0.775 1.000 0.000 0.000 0.000 0.000
#> GSM26843 1 0.0404 0.775 0.988 0.000 0.000 0.012 0.000
#> GSM26844 1 0.0404 0.775 0.988 0.000 0.000 0.012 0.000
#> GSM26845 5 0.6545 0.469 0.412 0.036 0.040 0.024 0.488
#> GSM26846 5 0.6142 0.770 0.396 0.000 0.132 0.000 0.472
#> GSM26847 5 0.6024 0.787 0.412 0.000 0.116 0.000 0.472
#> GSM26848 5 0.6024 0.787 0.412 0.000 0.116 0.000 0.472
#> GSM26849 5 0.5889 0.221 0.100 0.000 0.428 0.000 0.472
#> GSM26850 5 0.6024 0.787 0.412 0.000 0.116 0.000 0.472
#> GSM26851 2 0.2388 0.626 0.000 0.900 0.000 0.072 0.028
#> GSM26852 3 0.1671 0.982 0.076 0.000 0.924 0.000 0.000
#> GSM26853 3 0.1671 0.982 0.076 0.000 0.924 0.000 0.000
#> GSM26854 3 0.1671 0.982 0.076 0.000 0.924 0.000 0.000
#> GSM26855 3 0.1671 0.982 0.076 0.000 0.924 0.000 0.000
#> GSM26856 3 0.1671 0.982 0.076 0.000 0.924 0.000 0.000
#> GSM26857 3 0.1671 0.982 0.076 0.000 0.924 0.000 0.000
#> GSM26858 3 0.1671 0.982 0.076 0.000 0.924 0.000 0.000
#> GSM26859 3 0.1341 0.959 0.056 0.000 0.944 0.000 0.000
#> GSM26860 3 0.1671 0.982 0.076 0.000 0.924 0.000 0.000
#> GSM26861 3 0.1671 0.982 0.076 0.000 0.924 0.000 0.000
#> GSM26862 1 0.4909 0.513 0.716 0.000 0.016 0.052 0.216
#> GSM26863 1 0.4431 0.549 0.732 0.000 0.000 0.052 0.216
#> GSM26864 1 0.0000 0.775 1.000 0.000 0.000 0.000 0.000
#> GSM26865 5 0.6024 0.787 0.412 0.000 0.116 0.000 0.472
#> GSM26866 1 0.0404 0.775 0.988 0.000 0.000 0.012 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM26805 5 0.3714 0.959 0.000 0.340 0.000 0.000 0.656 0.004
#> GSM26806 4 0.1663 0.979 0.000 0.088 0.000 0.912 0.000 0.000
#> GSM26807 4 0.1663 0.979 0.000 0.088 0.000 0.912 0.000 0.000
#> GSM26808 4 0.1663 0.979 0.000 0.088 0.000 0.912 0.000 0.000
#> GSM26809 2 0.5347 0.500 0.096 0.660 0.000 0.032 0.208 0.004
#> GSM26810 4 0.1663 0.979 0.000 0.088 0.000 0.912 0.000 0.000
#> GSM26811 4 0.1663 0.979 0.000 0.088 0.000 0.912 0.000 0.000
#> GSM26812 4 0.1663 0.979 0.000 0.088 0.000 0.912 0.000 0.000
#> GSM26813 2 0.0951 0.931 0.020 0.968 0.000 0.000 0.008 0.004
#> GSM26814 2 0.0951 0.931 0.020 0.968 0.000 0.000 0.008 0.004
#> GSM26815 4 0.3341 0.945 0.060 0.088 0.000 0.836 0.016 0.000
#> GSM26816 5 0.3714 0.959 0.000 0.340 0.000 0.000 0.656 0.004
#> GSM26817 4 0.4176 0.916 0.080 0.100 0.000 0.788 0.024 0.008
#> GSM26818 3 0.3728 0.784 0.004 0.000 0.800 0.008 0.056 0.132
#> GSM26819 2 0.0508 0.947 0.004 0.984 0.000 0.000 0.012 0.000
#> GSM26820 2 0.0508 0.947 0.004 0.984 0.000 0.000 0.012 0.000
#> GSM26821 2 0.0260 0.942 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM26822 2 0.0508 0.947 0.004 0.984 0.000 0.000 0.012 0.000
#> GSM26823 2 0.0363 0.947 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM26824 2 0.0260 0.942 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM26825 2 0.0508 0.947 0.004 0.984 0.000 0.000 0.012 0.000
#> GSM26826 2 0.0363 0.947 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM26827 2 0.0363 0.947 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM26828 5 0.3563 0.962 0.000 0.336 0.000 0.000 0.664 0.000
#> GSM26829 5 0.3578 0.960 0.000 0.340 0.000 0.000 0.660 0.000
#> GSM26830 2 0.0951 0.931 0.020 0.968 0.000 0.000 0.008 0.004
#> GSM26831 5 0.3563 0.962 0.000 0.336 0.000 0.000 0.664 0.000
#> GSM26832 5 0.4072 0.915 0.004 0.288 0.000 0.012 0.688 0.008
#> GSM26833 5 0.4197 0.944 0.004 0.316 0.000 0.012 0.660 0.008
#> GSM26834 5 0.3699 0.962 0.004 0.336 0.000 0.000 0.660 0.000
#> GSM26835 5 0.3699 0.962 0.004 0.336 0.000 0.000 0.660 0.000
#> GSM26836 1 0.6269 0.636 0.448 0.000 0.012 0.036 0.096 0.408
#> GSM26837 1 0.6418 0.624 0.440 0.000 0.020 0.036 0.096 0.408
#> GSM26838 1 0.5140 0.774 0.684 0.000 0.012 0.020 0.084 0.200
#> GSM26839 1 0.6206 0.682 0.500 0.000 0.012 0.036 0.096 0.356
#> GSM26840 1 0.4789 0.603 0.744 0.000 0.008 0.040 0.100 0.108
#> GSM26841 1 0.3110 0.794 0.792 0.000 0.012 0.000 0.000 0.196
#> GSM26842 1 0.3359 0.791 0.784 0.000 0.012 0.000 0.008 0.196
#> GSM26843 1 0.3110 0.794 0.792 0.000 0.012 0.000 0.000 0.196
#> GSM26844 1 0.3110 0.794 0.792 0.000 0.012 0.000 0.000 0.196
#> GSM26845 6 0.2999 0.779 0.024 0.000 0.000 0.032 0.084 0.860
#> GSM26846 6 0.0865 0.913 0.000 0.000 0.036 0.000 0.000 0.964
#> GSM26847 6 0.0937 0.914 0.000 0.000 0.040 0.000 0.000 0.960
#> GSM26848 6 0.1082 0.916 0.004 0.000 0.040 0.000 0.000 0.956
#> GSM26849 6 0.2793 0.712 0.000 0.000 0.200 0.000 0.000 0.800
#> GSM26850 6 0.1082 0.916 0.004 0.000 0.040 0.000 0.000 0.956
#> GSM26851 5 0.4989 0.832 0.032 0.240 0.000 0.024 0.680 0.024
#> GSM26852 3 0.0000 0.978 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26853 3 0.0000 0.978 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26854 3 0.0000 0.978 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26855 3 0.0000 0.978 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26856 3 0.0260 0.976 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM26857 3 0.0260 0.976 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM26858 3 0.0000 0.978 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26859 3 0.0520 0.970 0.000 0.000 0.984 0.008 0.000 0.008
#> GSM26860 3 0.0260 0.976 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM26861 3 0.0000 0.978 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26862 1 0.6418 0.624 0.440 0.000 0.020 0.036 0.096 0.408
#> GSM26863 1 0.6269 0.636 0.448 0.000 0.012 0.036 0.096 0.408
#> GSM26864 1 0.3359 0.791 0.784 0.000 0.012 0.000 0.008 0.196
#> GSM26865 6 0.1082 0.916 0.004 0.000 0.040 0.000 0.000 0.956
#> GSM26866 1 0.3110 0.794 0.792 0.000 0.012 0.000 0.000 0.196
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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 5, scale_rows = FALSE)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> SD:kmeans 62 1.14e-12 8.30e-01 2
#> SD:kmeans 61 2.46e-12 2.21e-04 3
#> SD:kmeans 62 8.75e-12 2.79e-06 4
#> SD:kmeans 60 1.07e-10 8.81e-09 5
#> SD:kmeans 61 2.35e-10 5.61e-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["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 11993 rows and 62 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 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5087 0.492 0.492
#> 3 3 0.970 0.940 0.973 0.2453 0.874 0.744
#> 4 4 0.846 0.882 0.928 0.1786 0.884 0.682
#> 5 5 0.868 0.867 0.900 0.0672 0.929 0.726
#> 6 6 0.966 0.945 0.961 0.0479 0.947 0.744
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM26805 2 0 1 0 1
#> GSM26806 2 0 1 0 1
#> GSM26807 2 0 1 0 1
#> GSM26808 2 0 1 0 1
#> GSM26809 2 0 1 0 1
#> GSM26810 2 0 1 0 1
#> GSM26811 2 0 1 0 1
#> GSM26812 2 0 1 0 1
#> GSM26813 2 0 1 0 1
#> GSM26814 2 0 1 0 1
#> GSM26815 2 0 1 0 1
#> GSM26816 2 0 1 0 1
#> GSM26817 2 0 1 0 1
#> GSM26818 1 0 1 1 0
#> GSM26819 2 0 1 0 1
#> GSM26820 2 0 1 0 1
#> GSM26821 2 0 1 0 1
#> GSM26822 2 0 1 0 1
#> GSM26823 2 0 1 0 1
#> GSM26824 2 0 1 0 1
#> GSM26825 2 0 1 0 1
#> GSM26826 2 0 1 0 1
#> GSM26827 2 0 1 0 1
#> GSM26828 2 0 1 0 1
#> GSM26829 2 0 1 0 1
#> GSM26830 2 0 1 0 1
#> GSM26831 2 0 1 0 1
#> GSM26832 2 0 1 0 1
#> GSM26833 2 0 1 0 1
#> GSM26834 2 0 1 0 1
#> GSM26835 2 0 1 0 1
#> GSM26836 1 0 1 1 0
#> GSM26837 1 0 1 1 0
#> GSM26838 1 0 1 1 0
#> GSM26839 1 0 1 1 0
#> GSM26840 1 0 1 1 0
#> GSM26841 1 0 1 1 0
#> GSM26842 1 0 1 1 0
#> GSM26843 1 0 1 1 0
#> GSM26844 1 0 1 1 0
#> GSM26845 1 0 1 1 0
#> GSM26846 1 0 1 1 0
#> GSM26847 1 0 1 1 0
#> GSM26848 1 0 1 1 0
#> GSM26849 1 0 1 1 0
#> GSM26850 1 0 1 1 0
#> GSM26851 2 0 1 0 1
#> GSM26852 1 0 1 1 0
#> GSM26853 1 0 1 1 0
#> GSM26854 1 0 1 1 0
#> GSM26855 1 0 1 1 0
#> GSM26856 1 0 1 1 0
#> GSM26857 1 0 1 1 0
#> GSM26858 1 0 1 1 0
#> GSM26859 1 0 1 1 0
#> GSM26860 1 0 1 1 0
#> GSM26861 1 0 1 1 0
#> GSM26862 1 0 1 1 0
#> GSM26863 1 0 1 1 0
#> GSM26864 1 0 1 1 0
#> GSM26865 1 0 1 1 0
#> GSM26866 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM26805 2 0.0000 0.998 0.000 1.000 0.000
#> GSM26806 2 0.0424 0.996 0.000 0.992 0.008
#> GSM26807 2 0.0424 0.996 0.000 0.992 0.008
#> GSM26808 2 0.0424 0.996 0.000 0.992 0.008
#> GSM26809 2 0.0000 0.998 0.000 1.000 0.000
#> GSM26810 2 0.0424 0.996 0.000 0.992 0.008
#> GSM26811 2 0.0424 0.996 0.000 0.992 0.008
#> GSM26812 2 0.0424 0.996 0.000 0.992 0.008
#> GSM26813 2 0.0000 0.998 0.000 1.000 0.000
#> GSM26814 2 0.0000 0.998 0.000 1.000 0.000
#> GSM26815 2 0.0424 0.996 0.000 0.992 0.008
#> GSM26816 2 0.0000 0.998 0.000 1.000 0.000
#> GSM26817 2 0.0424 0.996 0.000 0.992 0.008
#> GSM26818 3 0.0237 0.961 0.004 0.000 0.996
#> GSM26819 2 0.0000 0.998 0.000 1.000 0.000
#> GSM26820 2 0.0000 0.998 0.000 1.000 0.000
#> GSM26821 2 0.0000 0.998 0.000 1.000 0.000
#> GSM26822 2 0.0000 0.998 0.000 1.000 0.000
#> GSM26823 2 0.0000 0.998 0.000 1.000 0.000
#> GSM26824 2 0.0000 0.998 0.000 1.000 0.000
#> GSM26825 2 0.0000 0.998 0.000 1.000 0.000
#> GSM26826 2 0.0000 0.998 0.000 1.000 0.000
#> GSM26827 2 0.0000 0.998 0.000 1.000 0.000
#> GSM26828 2 0.0000 0.998 0.000 1.000 0.000
#> GSM26829 2 0.0000 0.998 0.000 1.000 0.000
#> GSM26830 2 0.0000 0.998 0.000 1.000 0.000
#> GSM26831 2 0.0000 0.998 0.000 1.000 0.000
#> GSM26832 2 0.0237 0.997 0.000 0.996 0.004
#> GSM26833 2 0.0424 0.996 0.000 0.992 0.008
#> GSM26834 2 0.0237 0.997 0.000 0.996 0.004
#> GSM26835 2 0.0237 0.997 0.000 0.996 0.004
#> GSM26836 1 0.0000 0.925 1.000 0.000 0.000
#> GSM26837 1 0.0000 0.925 1.000 0.000 0.000
#> GSM26838 1 0.0000 0.925 1.000 0.000 0.000
#> GSM26839 1 0.0000 0.925 1.000 0.000 0.000
#> GSM26840 1 0.0000 0.925 1.000 0.000 0.000
#> GSM26841 1 0.0000 0.925 1.000 0.000 0.000
#> GSM26842 1 0.0000 0.925 1.000 0.000 0.000
#> GSM26843 1 0.0000 0.925 1.000 0.000 0.000
#> GSM26844 1 0.0000 0.925 1.000 0.000 0.000
#> GSM26845 1 0.0237 0.921 0.996 0.004 0.000
#> GSM26846 3 0.4555 0.748 0.200 0.000 0.800
#> GSM26847 1 0.6095 0.382 0.608 0.000 0.392
#> GSM26848 1 0.6095 0.382 0.608 0.000 0.392
#> GSM26849 3 0.0424 0.966 0.008 0.000 0.992
#> GSM26850 3 0.4555 0.748 0.200 0.000 0.800
#> GSM26851 2 0.0424 0.996 0.000 0.992 0.008
#> GSM26852 3 0.0424 0.966 0.008 0.000 0.992
#> GSM26853 3 0.0424 0.966 0.008 0.000 0.992
#> GSM26854 3 0.0424 0.966 0.008 0.000 0.992
#> GSM26855 3 0.0424 0.966 0.008 0.000 0.992
#> GSM26856 3 0.0424 0.966 0.008 0.000 0.992
#> GSM26857 3 0.0424 0.966 0.008 0.000 0.992
#> GSM26858 3 0.0424 0.966 0.008 0.000 0.992
#> GSM26859 3 0.0424 0.966 0.008 0.000 0.992
#> GSM26860 3 0.0424 0.966 0.008 0.000 0.992
#> GSM26861 3 0.0424 0.966 0.008 0.000 0.992
#> GSM26862 1 0.0000 0.925 1.000 0.000 0.000
#> GSM26863 1 0.0000 0.925 1.000 0.000 0.000
#> GSM26864 1 0.0000 0.925 1.000 0.000 0.000
#> GSM26865 1 0.5529 0.578 0.704 0.000 0.296
#> GSM26866 1 0.0000 0.925 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM26805 2 0.2530 0.863 0.000 0.888 0.000 0.112
#> GSM26806 4 0.1557 0.949 0.000 0.056 0.000 0.944
#> GSM26807 4 0.1557 0.949 0.000 0.056 0.000 0.944
#> GSM26808 4 0.1557 0.949 0.000 0.056 0.000 0.944
#> GSM26809 2 0.0188 0.897 0.000 0.996 0.000 0.004
#> GSM26810 4 0.1557 0.949 0.000 0.056 0.000 0.944
#> GSM26811 4 0.1557 0.949 0.000 0.056 0.000 0.944
#> GSM26812 4 0.1557 0.949 0.000 0.056 0.000 0.944
#> GSM26813 4 0.4855 0.429 0.000 0.400 0.000 0.600
#> GSM26814 2 0.2530 0.857 0.000 0.888 0.000 0.112
#> GSM26815 4 0.1557 0.949 0.000 0.056 0.000 0.944
#> GSM26816 2 0.2530 0.863 0.000 0.888 0.000 0.112
#> GSM26817 4 0.1557 0.949 0.000 0.056 0.000 0.944
#> GSM26818 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM26819 2 0.1211 0.909 0.000 0.960 0.000 0.040
#> GSM26820 2 0.1211 0.909 0.000 0.960 0.000 0.040
#> GSM26821 2 0.1211 0.909 0.000 0.960 0.000 0.040
#> GSM26822 2 0.1211 0.909 0.000 0.960 0.000 0.040
#> GSM26823 2 0.1211 0.909 0.000 0.960 0.000 0.040
#> GSM26824 2 0.1211 0.909 0.000 0.960 0.000 0.040
#> GSM26825 2 0.1211 0.909 0.000 0.960 0.000 0.040
#> GSM26826 2 0.1211 0.909 0.000 0.960 0.000 0.040
#> GSM26827 2 0.1211 0.909 0.000 0.960 0.000 0.040
#> GSM26828 2 0.2589 0.860 0.000 0.884 0.000 0.116
#> GSM26829 2 0.1637 0.886 0.000 0.940 0.000 0.060
#> GSM26830 2 0.1637 0.899 0.000 0.940 0.000 0.060
#> GSM26831 2 0.2530 0.863 0.000 0.888 0.000 0.112
#> GSM26832 2 0.3801 0.748 0.000 0.780 0.000 0.220
#> GSM26833 4 0.2814 0.893 0.000 0.132 0.000 0.868
#> GSM26834 2 0.3688 0.765 0.000 0.792 0.000 0.208
#> GSM26835 2 0.3688 0.765 0.000 0.792 0.000 0.208
#> GSM26836 1 0.0000 0.926 1.000 0.000 0.000 0.000
#> GSM26837 1 0.0000 0.926 1.000 0.000 0.000 0.000
#> GSM26838 1 0.0000 0.926 1.000 0.000 0.000 0.000
#> GSM26839 1 0.0000 0.926 1.000 0.000 0.000 0.000
#> GSM26840 1 0.0000 0.926 1.000 0.000 0.000 0.000
#> GSM26841 1 0.0000 0.926 1.000 0.000 0.000 0.000
#> GSM26842 1 0.0000 0.926 1.000 0.000 0.000 0.000
#> GSM26843 1 0.0000 0.926 1.000 0.000 0.000 0.000
#> GSM26844 1 0.0000 0.926 1.000 0.000 0.000 0.000
#> GSM26845 1 0.0469 0.919 0.988 0.000 0.000 0.012
#> GSM26846 3 0.4562 0.772 0.152 0.000 0.792 0.056
#> GSM26847 1 0.6083 0.387 0.584 0.000 0.360 0.056
#> GSM26848 1 0.6069 0.397 0.588 0.000 0.356 0.056
#> GSM26849 3 0.1557 0.932 0.000 0.000 0.944 0.056
#> GSM26850 3 0.4562 0.772 0.152 0.000 0.792 0.056
#> GSM26851 4 0.2281 0.915 0.000 0.096 0.000 0.904
#> GSM26852 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM26853 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM26854 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM26855 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM26856 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM26857 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM26858 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM26859 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM26860 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM26861 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM26862 1 0.0000 0.926 1.000 0.000 0.000 0.000
#> GSM26863 1 0.0000 0.926 1.000 0.000 0.000 0.000
#> GSM26864 1 0.0000 0.926 1.000 0.000 0.000 0.000
#> GSM26865 1 0.5537 0.593 0.688 0.000 0.256 0.056
#> GSM26866 1 0.0000 0.926 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
#> GSM26805 5 0.4800 0.858 0.000 0.272 0.000 0.052 0.676
#> GSM26806 4 0.0000 0.943 0.000 0.000 0.000 1.000 0.000
#> GSM26807 4 0.0000 0.943 0.000 0.000 0.000 1.000 0.000
#> GSM26808 4 0.0000 0.943 0.000 0.000 0.000 1.000 0.000
#> GSM26809 2 0.1197 0.926 0.000 0.952 0.000 0.000 0.048
#> GSM26810 4 0.0000 0.943 0.000 0.000 0.000 1.000 0.000
#> GSM26811 4 0.0000 0.943 0.000 0.000 0.000 1.000 0.000
#> GSM26812 4 0.0000 0.943 0.000 0.000 0.000 1.000 0.000
#> GSM26813 2 0.1671 0.885 0.000 0.924 0.000 0.076 0.000
#> GSM26814 2 0.0404 0.972 0.000 0.988 0.000 0.012 0.000
#> GSM26815 4 0.0000 0.943 0.000 0.000 0.000 1.000 0.000
#> GSM26816 5 0.4800 0.858 0.000 0.272 0.000 0.052 0.676
#> GSM26817 4 0.0000 0.943 0.000 0.000 0.000 1.000 0.000
#> GSM26818 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000
#> GSM26819 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM26820 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM26821 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM26822 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM26823 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM26824 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM26825 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM26826 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM26827 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM26828 5 0.4840 0.861 0.000 0.268 0.000 0.056 0.676
#> GSM26829 5 0.4232 0.797 0.000 0.312 0.000 0.012 0.676
#> GSM26830 2 0.0404 0.972 0.000 0.988 0.000 0.012 0.000
#> GSM26831 5 0.4840 0.861 0.000 0.268 0.000 0.056 0.676
#> GSM26832 5 0.5283 0.817 0.000 0.136 0.000 0.188 0.676
#> GSM26833 5 0.4147 0.570 0.000 0.008 0.000 0.316 0.676
#> GSM26834 5 0.5290 0.821 0.000 0.140 0.000 0.184 0.676
#> GSM26835 5 0.5290 0.821 0.000 0.140 0.000 0.184 0.676
#> GSM26836 1 0.0510 0.911 0.984 0.000 0.000 0.000 0.016
#> GSM26837 1 0.0510 0.911 0.984 0.000 0.000 0.000 0.016
#> GSM26838 1 0.0162 0.912 0.996 0.000 0.000 0.000 0.004
#> GSM26839 1 0.0510 0.911 0.984 0.000 0.000 0.000 0.016
#> GSM26840 1 0.0000 0.913 1.000 0.000 0.000 0.000 0.000
#> GSM26841 1 0.0000 0.913 1.000 0.000 0.000 0.000 0.000
#> GSM26842 1 0.0000 0.913 1.000 0.000 0.000 0.000 0.000
#> GSM26843 1 0.0000 0.913 1.000 0.000 0.000 0.000 0.000
#> GSM26844 1 0.0000 0.913 1.000 0.000 0.000 0.000 0.000
#> GSM26845 1 0.2127 0.860 0.892 0.000 0.000 0.000 0.108
#> GSM26846 3 0.5987 0.537 0.132 0.000 0.544 0.000 0.324
#> GSM26847 1 0.6152 0.478 0.524 0.000 0.152 0.000 0.324
#> GSM26848 1 0.6082 0.489 0.540 0.000 0.148 0.000 0.312
#> GSM26849 3 0.3837 0.707 0.000 0.000 0.692 0.000 0.308
#> GSM26850 3 0.5974 0.544 0.132 0.000 0.548 0.000 0.320
#> GSM26851 4 0.4126 0.229 0.000 0.000 0.000 0.620 0.380
#> GSM26852 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000
#> GSM26853 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000
#> GSM26854 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000
#> GSM26855 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000
#> GSM26856 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000
#> GSM26857 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000
#> GSM26858 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000
#> GSM26859 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000
#> GSM26860 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000
#> GSM26861 3 0.0000 0.914 0.000 0.000 1.000 0.000 0.000
#> GSM26862 1 0.0510 0.911 0.984 0.000 0.000 0.000 0.016
#> GSM26863 1 0.0510 0.911 0.984 0.000 0.000 0.000 0.016
#> GSM26864 1 0.0000 0.913 1.000 0.000 0.000 0.000 0.000
#> GSM26865 1 0.5538 0.579 0.596 0.000 0.092 0.000 0.312
#> GSM26866 1 0.0000 0.913 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
#> GSM26805 5 0.1075 0.931 0.000 0.048 0.000 0.000 0.952 0.000
#> GSM26806 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26807 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26808 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26809 2 0.1644 0.911 0.004 0.920 0.000 0.000 0.076 0.000
#> GSM26810 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26811 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26812 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26813 2 0.1572 0.940 0.000 0.936 0.000 0.036 0.000 0.028
#> GSM26814 2 0.0713 0.971 0.000 0.972 0.000 0.000 0.000 0.028
#> GSM26815 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26816 5 0.1219 0.933 0.000 0.048 0.000 0.004 0.948 0.000
#> GSM26817 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26818 3 0.0146 0.996 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM26819 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26820 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26821 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26822 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26823 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26824 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26825 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26826 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26827 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26828 5 0.1152 0.935 0.000 0.044 0.000 0.004 0.952 0.000
#> GSM26829 5 0.1219 0.933 0.000 0.048 0.000 0.004 0.948 0.000
#> GSM26830 2 0.0713 0.971 0.000 0.972 0.000 0.000 0.000 0.028
#> GSM26831 5 0.1152 0.935 0.000 0.044 0.000 0.004 0.952 0.000
#> GSM26832 5 0.1401 0.933 0.000 0.028 0.000 0.020 0.948 0.004
#> GSM26833 5 0.1296 0.910 0.000 0.004 0.000 0.044 0.948 0.004
#> GSM26834 5 0.1401 0.933 0.000 0.028 0.000 0.020 0.948 0.004
#> GSM26835 5 0.1401 0.933 0.000 0.028 0.000 0.020 0.948 0.004
#> GSM26836 1 0.2795 0.902 0.856 0.000 0.000 0.000 0.044 0.100
#> GSM26837 1 0.2795 0.902 0.856 0.000 0.000 0.000 0.044 0.100
#> GSM26838 1 0.0725 0.930 0.976 0.000 0.000 0.000 0.012 0.012
#> GSM26839 1 0.2542 0.909 0.876 0.000 0.000 0.000 0.044 0.080
#> GSM26840 1 0.0000 0.933 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26841 1 0.0000 0.933 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26842 1 0.0000 0.933 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26843 1 0.0000 0.933 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26844 1 0.0000 0.933 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26845 1 0.3348 0.784 0.768 0.000 0.000 0.000 0.016 0.216
#> GSM26846 6 0.0632 0.929 0.000 0.000 0.024 0.000 0.000 0.976
#> GSM26847 6 0.1049 0.922 0.032 0.000 0.000 0.000 0.008 0.960
#> GSM26848 6 0.1444 0.924 0.072 0.000 0.000 0.000 0.000 0.928
#> GSM26849 6 0.2260 0.840 0.000 0.000 0.140 0.000 0.000 0.860
#> GSM26850 6 0.0935 0.930 0.004 0.000 0.032 0.000 0.000 0.964
#> GSM26851 5 0.3899 0.351 0.000 0.000 0.000 0.404 0.592 0.004
#> GSM26852 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26853 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26854 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26855 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26856 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26857 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26858 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26859 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26860 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26861 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26862 1 0.2795 0.902 0.856 0.000 0.000 0.000 0.044 0.100
#> GSM26863 1 0.2747 0.904 0.860 0.000 0.000 0.000 0.044 0.096
#> GSM26864 1 0.0000 0.933 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26865 6 0.1765 0.911 0.096 0.000 0.000 0.000 0.000 0.904
#> GSM26866 1 0.0000 0.933 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 tissue(p) individual(p) k
#> SD:skmeans 62 1.14e-12 8.30e-01 2
#> SD:skmeans 60 4.17e-12 1.27e-04 3
#> SD:skmeans 59 3.50e-11 6.30e-06 4
#> SD:skmeans 59 2.84e-11 7.18e-09 5
#> SD:skmeans 61 4.26e-11 1.04e-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", "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 11993 rows and 62 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.986 0.993 0.5064 0.494 0.494
#> 3 3 0.984 0.978 0.986 0.2396 0.841 0.690
#> 4 4 0.929 0.957 0.972 0.1787 0.889 0.701
#> 5 5 0.852 0.909 0.911 0.0735 0.928 0.732
#> 6 6 0.969 0.929 0.971 0.0593 0.941 0.721
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 3 4
There is also optional best \(k\) = 2 3 4 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM26805 2 0.000 0.991 0.000 1.000
#> GSM26806 2 0.000 0.991 0.000 1.000
#> GSM26807 2 0.000 0.991 0.000 1.000
#> GSM26808 2 0.000 0.991 0.000 1.000
#> GSM26809 2 0.000 0.991 0.000 1.000
#> GSM26810 2 0.000 0.991 0.000 1.000
#> GSM26811 2 0.000 0.991 0.000 1.000
#> GSM26812 2 0.000 0.991 0.000 1.000
#> GSM26813 2 0.000 0.991 0.000 1.000
#> GSM26814 2 0.000 0.991 0.000 1.000
#> GSM26815 2 0.000 0.991 0.000 1.000
#> GSM26816 2 0.000 0.991 0.000 1.000
#> GSM26817 2 0.000 0.991 0.000 1.000
#> GSM26818 1 0.000 0.995 1.000 0.000
#> GSM26819 2 0.000 0.991 0.000 1.000
#> GSM26820 2 0.000 0.991 0.000 1.000
#> GSM26821 2 0.000 0.991 0.000 1.000
#> GSM26822 2 0.000 0.991 0.000 1.000
#> GSM26823 2 0.000 0.991 0.000 1.000
#> GSM26824 2 0.000 0.991 0.000 1.000
#> GSM26825 2 0.000 0.991 0.000 1.000
#> GSM26826 2 0.000 0.991 0.000 1.000
#> GSM26827 2 0.000 0.991 0.000 1.000
#> GSM26828 2 0.000 0.991 0.000 1.000
#> GSM26829 2 0.000 0.991 0.000 1.000
#> GSM26830 2 0.000 0.991 0.000 1.000
#> GSM26831 2 0.000 0.991 0.000 1.000
#> GSM26832 2 0.000 0.991 0.000 1.000
#> GSM26833 2 0.000 0.991 0.000 1.000
#> GSM26834 2 0.000 0.991 0.000 1.000
#> GSM26835 2 0.000 0.991 0.000 1.000
#> GSM26836 1 0.000 0.995 1.000 0.000
#> GSM26837 1 0.000 0.995 1.000 0.000
#> GSM26838 1 0.000 0.995 1.000 0.000
#> GSM26839 1 0.000 0.995 1.000 0.000
#> GSM26840 2 0.595 0.835 0.144 0.856
#> GSM26841 1 0.000 0.995 1.000 0.000
#> GSM26842 1 0.000 0.995 1.000 0.000
#> GSM26843 1 0.000 0.995 1.000 0.000
#> GSM26844 1 0.000 0.995 1.000 0.000
#> GSM26845 2 0.563 0.851 0.132 0.868
#> GSM26846 1 0.373 0.924 0.928 0.072
#> GSM26847 1 0.000 0.995 1.000 0.000
#> GSM26848 1 0.000 0.995 1.000 0.000
#> GSM26849 1 0.000 0.995 1.000 0.000
#> GSM26850 1 0.373 0.924 0.928 0.072
#> GSM26851 2 0.000 0.991 0.000 1.000
#> GSM26852 1 0.000 0.995 1.000 0.000
#> GSM26853 1 0.000 0.995 1.000 0.000
#> GSM26854 1 0.000 0.995 1.000 0.000
#> GSM26855 1 0.000 0.995 1.000 0.000
#> GSM26856 1 0.000 0.995 1.000 0.000
#> GSM26857 1 0.000 0.995 1.000 0.000
#> GSM26858 1 0.000 0.995 1.000 0.000
#> GSM26859 1 0.000 0.995 1.000 0.000
#> GSM26860 1 0.000 0.995 1.000 0.000
#> GSM26861 1 0.000 0.995 1.000 0.000
#> GSM26862 1 0.000 0.995 1.000 0.000
#> GSM26863 1 0.000 0.995 1.000 0.000
#> GSM26864 1 0.000 0.995 1.000 0.000
#> GSM26865 1 0.000 0.995 1.000 0.000
#> GSM26866 1 0.000 0.995 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM26805 2 0.000 1.000 0.000 1.000 0.000
#> GSM26806 2 0.000 1.000 0.000 1.000 0.000
#> GSM26807 2 0.000 1.000 0.000 1.000 0.000
#> GSM26808 2 0.000 1.000 0.000 1.000 0.000
#> GSM26809 2 0.000 1.000 0.000 1.000 0.000
#> GSM26810 2 0.000 1.000 0.000 1.000 0.000
#> GSM26811 2 0.000 1.000 0.000 1.000 0.000
#> GSM26812 2 0.000 1.000 0.000 1.000 0.000
#> GSM26813 2 0.000 1.000 0.000 1.000 0.000
#> GSM26814 2 0.000 1.000 0.000 1.000 0.000
#> GSM26815 2 0.000 1.000 0.000 1.000 0.000
#> GSM26816 2 0.000 1.000 0.000 1.000 0.000
#> GSM26817 2 0.000 1.000 0.000 1.000 0.000
#> GSM26818 3 0.000 0.993 0.000 0.000 1.000
#> GSM26819 2 0.000 1.000 0.000 1.000 0.000
#> GSM26820 2 0.000 1.000 0.000 1.000 0.000
#> GSM26821 2 0.000 1.000 0.000 1.000 0.000
#> GSM26822 2 0.000 1.000 0.000 1.000 0.000
#> GSM26823 2 0.000 1.000 0.000 1.000 0.000
#> GSM26824 2 0.000 1.000 0.000 1.000 0.000
#> GSM26825 2 0.000 1.000 0.000 1.000 0.000
#> GSM26826 2 0.000 1.000 0.000 1.000 0.000
#> GSM26827 2 0.000 1.000 0.000 1.000 0.000
#> GSM26828 2 0.000 1.000 0.000 1.000 0.000
#> GSM26829 2 0.000 1.000 0.000 1.000 0.000
#> GSM26830 2 0.000 1.000 0.000 1.000 0.000
#> GSM26831 2 0.000 1.000 0.000 1.000 0.000
#> GSM26832 2 0.000 1.000 0.000 1.000 0.000
#> GSM26833 2 0.000 1.000 0.000 1.000 0.000
#> GSM26834 2 0.000 1.000 0.000 1.000 0.000
#> GSM26835 2 0.000 1.000 0.000 1.000 0.000
#> GSM26836 1 0.000 0.955 1.000 0.000 0.000
#> GSM26837 1 0.245 0.930 0.924 0.000 0.076
#> GSM26838 1 0.000 0.955 1.000 0.000 0.000
#> GSM26839 1 0.000 0.955 1.000 0.000 0.000
#> GSM26840 1 0.000 0.955 1.000 0.000 0.000
#> GSM26841 1 0.000 0.955 1.000 0.000 0.000
#> GSM26842 1 0.000 0.955 1.000 0.000 0.000
#> GSM26843 1 0.000 0.955 1.000 0.000 0.000
#> GSM26844 1 0.000 0.955 1.000 0.000 0.000
#> GSM26845 1 0.304 0.865 0.896 0.104 0.000
#> GSM26846 1 0.406 0.905 0.880 0.044 0.076
#> GSM26847 1 0.327 0.905 0.884 0.000 0.116
#> GSM26848 1 0.245 0.931 0.924 0.000 0.076
#> GSM26849 3 0.245 0.912 0.076 0.000 0.924
#> GSM26850 1 0.343 0.907 0.884 0.004 0.112
#> GSM26851 2 0.000 1.000 0.000 1.000 0.000
#> GSM26852 3 0.000 0.993 0.000 0.000 1.000
#> GSM26853 3 0.000 0.993 0.000 0.000 1.000
#> GSM26854 3 0.000 0.993 0.000 0.000 1.000
#> GSM26855 3 0.000 0.993 0.000 0.000 1.000
#> GSM26856 3 0.000 0.993 0.000 0.000 1.000
#> GSM26857 3 0.000 0.993 0.000 0.000 1.000
#> GSM26858 3 0.000 0.993 0.000 0.000 1.000
#> GSM26859 3 0.000 0.993 0.000 0.000 1.000
#> GSM26860 3 0.000 0.993 0.000 0.000 1.000
#> GSM26861 3 0.000 0.993 0.000 0.000 1.000
#> GSM26862 1 0.319 0.908 0.888 0.000 0.112
#> GSM26863 1 0.000 0.955 1.000 0.000 0.000
#> GSM26864 1 0.000 0.955 1.000 0.000 0.000
#> GSM26865 1 0.245 0.931 0.924 0.000 0.076
#> GSM26866 1 0.000 0.955 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM26805 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM26806 4 0.0336 0.992 0.000 0.008 0.000 0.992
#> GSM26807 4 0.0336 0.992 0.000 0.008 0.000 0.992
#> GSM26808 4 0.0336 0.992 0.000 0.008 0.000 0.992
#> GSM26809 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM26810 4 0.0336 0.992 0.000 0.008 0.000 0.992
#> GSM26811 4 0.0336 0.992 0.000 0.008 0.000 0.992
#> GSM26812 4 0.0336 0.992 0.000 0.008 0.000 0.992
#> GSM26813 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM26814 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM26815 4 0.0336 0.992 0.000 0.008 0.000 0.992
#> GSM26816 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM26817 4 0.0592 0.985 0.000 0.016 0.000 0.984
#> GSM26818 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM26819 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM26820 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM26821 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM26822 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM26823 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM26824 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM26825 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM26826 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM26827 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM26828 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM26829 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM26830 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM26831 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM26832 2 0.3649 0.737 0.000 0.796 0.000 0.204
#> GSM26833 4 0.1716 0.933 0.000 0.064 0.000 0.936
#> GSM26834 2 0.0000 0.989 0.000 1.000 0.000 0.000
#> GSM26835 2 0.0336 0.982 0.000 0.992 0.000 0.008
#> GSM26836 1 0.0188 0.925 0.996 0.000 0.000 0.004
#> GSM26837 1 0.2714 0.890 0.884 0.000 0.112 0.004
#> GSM26838 1 0.0188 0.926 0.996 0.000 0.000 0.004
#> GSM26839 1 0.0000 0.926 1.000 0.000 0.000 0.000
#> GSM26840 1 0.0188 0.926 0.996 0.000 0.000 0.004
#> GSM26841 1 0.0188 0.926 0.996 0.000 0.000 0.004
#> GSM26842 1 0.0188 0.926 0.996 0.000 0.000 0.004
#> GSM26843 1 0.0188 0.926 0.996 0.000 0.000 0.004
#> GSM26844 1 0.0188 0.926 0.996 0.000 0.000 0.004
#> GSM26845 1 0.3257 0.817 0.844 0.152 0.000 0.004
#> GSM26846 1 0.4271 0.856 0.816 0.040 0.140 0.004
#> GSM26847 1 0.3583 0.846 0.816 0.000 0.180 0.004
#> GSM26848 1 0.3105 0.876 0.856 0.000 0.140 0.004
#> GSM26849 3 0.1004 0.969 0.024 0.000 0.972 0.004
#> GSM26850 1 0.3721 0.848 0.816 0.004 0.176 0.004
#> GSM26851 4 0.0336 0.992 0.000 0.008 0.000 0.992
#> GSM26852 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM26853 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM26854 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM26855 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM26856 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM26857 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM26858 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM26859 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM26860 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM26861 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM26862 1 0.3539 0.850 0.820 0.000 0.176 0.004
#> GSM26863 1 0.0188 0.925 0.996 0.000 0.000 0.004
#> GSM26864 1 0.0188 0.926 0.996 0.000 0.000 0.004
#> GSM26865 1 0.3105 0.876 0.856 0.000 0.140 0.004
#> GSM26866 1 0.0188 0.926 0.996 0.000 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM26805 5 0.3586 0.868 0.000 0.264 0.000 0.000 0.736
#> GSM26806 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000
#> GSM26807 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000
#> GSM26808 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000
#> GSM26809 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM26810 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000
#> GSM26811 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000
#> GSM26812 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000
#> GSM26813 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM26814 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM26815 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000
#> GSM26816 5 0.3586 0.868 0.000 0.264 0.000 0.000 0.736
#> GSM26817 4 0.0290 0.988 0.000 0.008 0.000 0.992 0.000
#> GSM26818 3 0.2929 0.816 0.000 0.000 0.820 0.000 0.180
#> GSM26819 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM26820 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM26821 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM26822 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM26823 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM26824 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM26825 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM26826 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM26827 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM26828 5 0.3586 0.868 0.000 0.264 0.000 0.000 0.736
#> GSM26829 5 0.3857 0.811 0.000 0.312 0.000 0.000 0.688
#> GSM26830 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM26831 5 0.3586 0.868 0.000 0.264 0.000 0.000 0.736
#> GSM26832 5 0.4593 0.736 0.000 0.080 0.000 0.184 0.736
#> GSM26833 5 0.3715 0.628 0.000 0.004 0.000 0.260 0.736
#> GSM26834 5 0.3586 0.868 0.000 0.264 0.000 0.000 0.736
#> GSM26835 5 0.3809 0.867 0.000 0.256 0.000 0.008 0.736
#> GSM26836 1 0.1544 0.881 0.932 0.000 0.000 0.000 0.068
#> GSM26837 1 0.4421 0.788 0.748 0.000 0.184 0.000 0.068
#> GSM26838 1 0.0000 0.882 1.000 0.000 0.000 0.000 0.000
#> GSM26839 1 0.0162 0.882 0.996 0.000 0.000 0.000 0.004
#> GSM26840 1 0.2280 0.785 0.880 0.000 0.000 0.000 0.120
#> GSM26841 1 0.0000 0.882 1.000 0.000 0.000 0.000 0.000
#> GSM26842 1 0.0000 0.882 1.000 0.000 0.000 0.000 0.000
#> GSM26843 1 0.0000 0.882 1.000 0.000 0.000 0.000 0.000
#> GSM26844 1 0.0000 0.882 1.000 0.000 0.000 0.000 0.000
#> GSM26845 1 0.3684 0.832 0.720 0.000 0.000 0.000 0.280
#> GSM26846 1 0.3967 0.835 0.724 0.000 0.012 0.000 0.264
#> GSM26847 1 0.3967 0.835 0.724 0.000 0.012 0.000 0.264
#> GSM26848 1 0.3967 0.835 0.724 0.000 0.012 0.000 0.264
#> GSM26849 3 0.3861 0.731 0.008 0.000 0.728 0.000 0.264
#> GSM26850 1 0.3967 0.835 0.724 0.000 0.012 0.000 0.264
#> GSM26851 5 0.3586 0.620 0.000 0.000 0.000 0.264 0.736
#> GSM26852 3 0.0000 0.960 0.000 0.000 1.000 0.000 0.000
#> GSM26853 3 0.0000 0.960 0.000 0.000 1.000 0.000 0.000
#> GSM26854 3 0.0000 0.960 0.000 0.000 1.000 0.000 0.000
#> GSM26855 3 0.0000 0.960 0.000 0.000 1.000 0.000 0.000
#> GSM26856 3 0.0000 0.960 0.000 0.000 1.000 0.000 0.000
#> GSM26857 3 0.0000 0.960 0.000 0.000 1.000 0.000 0.000
#> GSM26858 3 0.0000 0.960 0.000 0.000 1.000 0.000 0.000
#> GSM26859 3 0.0000 0.960 0.000 0.000 1.000 0.000 0.000
#> GSM26860 3 0.0000 0.960 0.000 0.000 1.000 0.000 0.000
#> GSM26861 3 0.0000 0.960 0.000 0.000 1.000 0.000 0.000
#> GSM26862 1 0.4609 0.806 0.744 0.000 0.152 0.000 0.104
#> GSM26863 1 0.1544 0.881 0.932 0.000 0.000 0.000 0.068
#> GSM26864 1 0.0000 0.882 1.000 0.000 0.000 0.000 0.000
#> GSM26865 1 0.3967 0.835 0.724 0.000 0.012 0.000 0.264
#> GSM26866 1 0.0000 0.882 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
#> GSM26805 5 0.0000 0.971 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM26806 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26807 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26808 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26809 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26810 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26811 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26812 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26813 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26814 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26815 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26816 5 0.0000 0.971 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM26817 4 0.0405 0.988 0.000 0.008 0.000 0.988 0.004 0.000
#> GSM26818 3 0.2793 0.760 0.000 0.000 0.800 0.000 0.000 0.200
#> GSM26819 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26820 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26821 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26822 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26823 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26824 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26825 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26826 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26827 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26828 5 0.0000 0.971 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM26829 5 0.2996 0.705 0.000 0.228 0.000 0.000 0.772 0.000
#> GSM26830 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26831 5 0.0000 0.971 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM26832 5 0.0000 0.971 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM26833 5 0.0000 0.971 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM26834 5 0.0000 0.971 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM26835 5 0.0000 0.971 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM26836 6 0.3050 0.712 0.236 0.000 0.000 0.000 0.000 0.764
#> GSM26837 6 0.3612 0.753 0.036 0.000 0.200 0.000 0.000 0.764
#> GSM26838 1 0.0000 0.931 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26839 1 0.3866 -0.119 0.516 0.000 0.000 0.000 0.000 0.484
#> GSM26840 1 0.0000 0.931 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26841 1 0.0000 0.931 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26842 1 0.0000 0.931 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26843 1 0.0000 0.931 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26844 1 0.0000 0.931 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26845 6 0.0000 0.902 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM26846 6 0.0000 0.902 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM26847 6 0.0000 0.902 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM26848 6 0.0000 0.902 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM26849 6 0.0000 0.902 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM26850 6 0.0000 0.902 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM26851 5 0.0000 0.971 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM26852 3 0.0000 0.980 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26853 3 0.0000 0.980 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26854 3 0.0000 0.980 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26855 3 0.0000 0.980 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26856 3 0.0000 0.980 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26857 3 0.0000 0.980 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26858 3 0.0000 0.980 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26859 3 0.0000 0.980 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26860 3 0.0000 0.980 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26861 3 0.0000 0.980 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26862 6 0.3278 0.796 0.040 0.000 0.152 0.000 0.000 0.808
#> GSM26863 6 0.3050 0.712 0.236 0.000 0.000 0.000 0.000 0.764
#> GSM26864 1 0.0000 0.931 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26865 6 0.0000 0.902 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM26866 1 0.0000 0.931 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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> SD:pam 62 3.65e-11 8.91e-01 2
#> SD:pam 62 1.49e-12 1.94e-04 3
#> SD:pam 62 7.83e-12 1.05e-05 4
#> SD:pam 62 3.70e-11 1.07e-08 5
#> SD:pam 61 2.35e-10 4.50e-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["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 11993 rows and 62 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 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 0.5087 0.492 0.492
#> 3 3 0.892 0.865 0.900 0.2184 0.876 0.748
#> 4 4 0.770 0.797 0.868 0.1734 0.835 0.584
#> 5 5 0.726 0.642 0.794 0.0758 0.958 0.837
#> 6 6 0.793 0.768 0.863 0.0557 0.925 0.667
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM26805 2 0 1 0 1
#> GSM26806 2 0 1 0 1
#> GSM26807 2 0 1 0 1
#> GSM26808 2 0 1 0 1
#> GSM26809 2 0 1 0 1
#> GSM26810 2 0 1 0 1
#> GSM26811 2 0 1 0 1
#> GSM26812 2 0 1 0 1
#> GSM26813 2 0 1 0 1
#> GSM26814 2 0 1 0 1
#> GSM26815 2 0 1 0 1
#> GSM26816 2 0 1 0 1
#> GSM26817 2 0 1 0 1
#> GSM26818 1 0 1 1 0
#> GSM26819 2 0 1 0 1
#> GSM26820 2 0 1 0 1
#> GSM26821 2 0 1 0 1
#> GSM26822 2 0 1 0 1
#> GSM26823 2 0 1 0 1
#> GSM26824 2 0 1 0 1
#> GSM26825 2 0 1 0 1
#> GSM26826 2 0 1 0 1
#> GSM26827 2 0 1 0 1
#> GSM26828 2 0 1 0 1
#> GSM26829 2 0 1 0 1
#> GSM26830 2 0 1 0 1
#> GSM26831 2 0 1 0 1
#> GSM26832 2 0 1 0 1
#> GSM26833 2 0 1 0 1
#> GSM26834 2 0 1 0 1
#> GSM26835 2 0 1 0 1
#> GSM26836 1 0 1 1 0
#> GSM26837 1 0 1 1 0
#> GSM26838 1 0 1 1 0
#> GSM26839 1 0 1 1 0
#> GSM26840 1 0 1 1 0
#> GSM26841 1 0 1 1 0
#> GSM26842 1 0 1 1 0
#> GSM26843 1 0 1 1 0
#> GSM26844 1 0 1 1 0
#> GSM26845 1 0 1 1 0
#> GSM26846 1 0 1 1 0
#> GSM26847 1 0 1 1 0
#> GSM26848 1 0 1 1 0
#> GSM26849 1 0 1 1 0
#> GSM26850 1 0 1 1 0
#> GSM26851 2 0 1 0 1
#> GSM26852 1 0 1 1 0
#> GSM26853 1 0 1 1 0
#> GSM26854 1 0 1 1 0
#> GSM26855 1 0 1 1 0
#> GSM26856 1 0 1 1 0
#> GSM26857 1 0 1 1 0
#> GSM26858 1 0 1 1 0
#> GSM26859 1 0 1 1 0
#> GSM26860 1 0 1 1 0
#> GSM26861 1 0 1 1 0
#> GSM26862 1 0 1 1 0
#> GSM26863 1 0 1 1 0
#> GSM26864 1 0 1 1 0
#> GSM26865 1 0 1 1 0
#> GSM26866 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM26805 2 0.0237 0.992 0.004 0.996 0.000
#> GSM26806 2 0.1337 0.984 0.012 0.972 0.016
#> GSM26807 2 0.1337 0.984 0.012 0.972 0.016
#> GSM26808 2 0.1337 0.984 0.012 0.972 0.016
#> GSM26809 2 0.0237 0.992 0.004 0.996 0.000
#> GSM26810 2 0.1337 0.984 0.012 0.972 0.016
#> GSM26811 2 0.1337 0.984 0.012 0.972 0.016
#> GSM26812 2 0.1337 0.984 0.012 0.972 0.016
#> GSM26813 2 0.0237 0.992 0.004 0.996 0.000
#> GSM26814 2 0.0000 0.991 0.000 1.000 0.000
#> GSM26815 2 0.1751 0.977 0.012 0.960 0.028
#> GSM26816 2 0.0237 0.992 0.004 0.996 0.000
#> GSM26817 2 0.1482 0.982 0.012 0.968 0.020
#> GSM26818 3 0.0747 0.330 0.016 0.000 0.984
#> GSM26819 2 0.0000 0.991 0.000 1.000 0.000
#> GSM26820 2 0.0000 0.991 0.000 1.000 0.000
#> GSM26821 2 0.0000 0.991 0.000 1.000 0.000
#> GSM26822 2 0.0000 0.991 0.000 1.000 0.000
#> GSM26823 2 0.0000 0.991 0.000 1.000 0.000
#> GSM26824 2 0.0000 0.991 0.000 1.000 0.000
#> GSM26825 2 0.0000 0.991 0.000 1.000 0.000
#> GSM26826 2 0.0000 0.991 0.000 1.000 0.000
#> GSM26827 2 0.0000 0.991 0.000 1.000 0.000
#> GSM26828 2 0.0475 0.991 0.004 0.992 0.004
#> GSM26829 2 0.0237 0.992 0.004 0.996 0.000
#> GSM26830 2 0.0237 0.992 0.004 0.996 0.000
#> GSM26831 2 0.0475 0.991 0.004 0.992 0.004
#> GSM26832 2 0.0661 0.990 0.008 0.988 0.004
#> GSM26833 2 0.0661 0.990 0.008 0.988 0.004
#> GSM26834 2 0.0475 0.991 0.004 0.992 0.004
#> GSM26835 2 0.0475 0.991 0.004 0.992 0.004
#> GSM26836 1 0.0000 0.699 1.000 0.000 0.000
#> GSM26837 1 0.2711 0.534 0.912 0.000 0.088
#> GSM26838 1 0.1163 0.703 0.972 0.000 0.028
#> GSM26839 1 0.3116 0.700 0.892 0.000 0.108
#> GSM26840 1 0.6398 0.637 0.580 0.004 0.416
#> GSM26841 1 0.6008 0.669 0.628 0.000 0.372
#> GSM26842 1 0.6008 0.669 0.628 0.000 0.372
#> GSM26843 1 0.6111 0.657 0.604 0.000 0.396
#> GSM26844 1 0.6111 0.657 0.604 0.000 0.396
#> GSM26845 3 0.8546 0.525 0.276 0.136 0.588
#> GSM26846 1 0.0000 0.699 1.000 0.000 0.000
#> GSM26847 1 0.0000 0.699 1.000 0.000 0.000
#> GSM26848 1 0.0000 0.699 1.000 0.000 0.000
#> GSM26849 3 0.6260 0.887 0.448 0.000 0.552
#> GSM26850 1 0.0892 0.671 0.980 0.000 0.020
#> GSM26851 2 0.0829 0.988 0.012 0.984 0.004
#> GSM26852 3 0.6225 0.909 0.432 0.000 0.568
#> GSM26853 3 0.6225 0.909 0.432 0.000 0.568
#> GSM26854 3 0.6225 0.909 0.432 0.000 0.568
#> GSM26855 3 0.6225 0.909 0.432 0.000 0.568
#> GSM26856 3 0.6225 0.909 0.432 0.000 0.568
#> GSM26857 3 0.6225 0.909 0.432 0.000 0.568
#> GSM26858 3 0.6225 0.909 0.432 0.000 0.568
#> GSM26859 3 0.6225 0.909 0.432 0.000 0.568
#> GSM26860 3 0.6225 0.909 0.432 0.000 0.568
#> GSM26861 3 0.6225 0.909 0.432 0.000 0.568
#> GSM26862 1 0.0000 0.699 1.000 0.000 0.000
#> GSM26863 1 0.0000 0.699 1.000 0.000 0.000
#> GSM26864 1 0.6026 0.668 0.624 0.000 0.376
#> GSM26865 1 0.0000 0.699 1.000 0.000 0.000
#> GSM26866 1 0.6079 0.662 0.612 0.000 0.388
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM26805 4 0.4972 0.6444 0.000 0.456 0.000 0.544
#> GSM26806 4 0.0817 0.6113 0.000 0.024 0.000 0.976
#> GSM26807 4 0.1022 0.6175 0.000 0.032 0.000 0.968
#> GSM26808 4 0.1474 0.6262 0.000 0.052 0.000 0.948
#> GSM26809 4 0.4955 0.6508 0.000 0.444 0.000 0.556
#> GSM26810 4 0.1022 0.6175 0.000 0.032 0.000 0.968
#> GSM26811 4 0.2921 0.6470 0.000 0.140 0.000 0.860
#> GSM26812 4 0.0921 0.6146 0.000 0.028 0.000 0.972
#> GSM26813 2 0.4331 0.2699 0.000 0.712 0.000 0.288
#> GSM26814 2 0.0707 0.8826 0.000 0.980 0.000 0.020
#> GSM26815 4 0.1557 0.6258 0.000 0.056 0.000 0.944
#> GSM26816 4 0.4972 0.6444 0.000 0.456 0.000 0.544
#> GSM26817 4 0.3610 0.6531 0.000 0.200 0.000 0.800
#> GSM26818 1 0.7552 0.4505 0.536 0.008 0.232 0.224
#> GSM26819 2 0.0000 0.9029 0.000 1.000 0.000 0.000
#> GSM26820 2 0.0000 0.9029 0.000 1.000 0.000 0.000
#> GSM26821 2 0.0000 0.9029 0.000 1.000 0.000 0.000
#> GSM26822 2 0.0000 0.9029 0.000 1.000 0.000 0.000
#> GSM26823 2 0.0000 0.9029 0.000 1.000 0.000 0.000
#> GSM26824 2 0.0188 0.8998 0.000 0.996 0.000 0.004
#> GSM26825 2 0.0000 0.9029 0.000 1.000 0.000 0.000
#> GSM26826 2 0.0000 0.9029 0.000 1.000 0.000 0.000
#> GSM26827 2 0.0000 0.9029 0.000 1.000 0.000 0.000
#> GSM26828 4 0.4967 0.6503 0.000 0.452 0.000 0.548
#> GSM26829 4 0.4972 0.6444 0.000 0.456 0.000 0.544
#> GSM26830 2 0.4605 0.0541 0.000 0.664 0.000 0.336
#> GSM26831 4 0.4967 0.6503 0.000 0.452 0.000 0.548
#> GSM26832 4 0.4941 0.6579 0.000 0.436 0.000 0.564
#> GSM26833 4 0.4955 0.6552 0.000 0.444 0.000 0.556
#> GSM26834 4 0.4967 0.6503 0.000 0.452 0.000 0.548
#> GSM26835 4 0.4967 0.6503 0.000 0.452 0.000 0.548
#> GSM26836 1 0.1211 0.9079 0.960 0.000 0.040 0.000
#> GSM26837 1 0.2647 0.8820 0.880 0.000 0.120 0.000
#> GSM26838 1 0.1792 0.8977 0.932 0.000 0.068 0.000
#> GSM26839 1 0.1867 0.8976 0.928 0.000 0.072 0.000
#> GSM26840 1 0.0469 0.9059 0.988 0.000 0.000 0.012
#> GSM26841 1 0.0188 0.9072 0.996 0.000 0.004 0.000
#> GSM26842 1 0.0188 0.9065 0.996 0.000 0.000 0.004
#> GSM26843 1 0.0000 0.9065 1.000 0.000 0.000 0.000
#> GSM26844 1 0.0000 0.9065 1.000 0.000 0.000 0.000
#> GSM26845 1 0.2892 0.8840 0.896 0.000 0.036 0.068
#> GSM26846 1 0.3052 0.8671 0.860 0.000 0.136 0.004
#> GSM26847 1 0.2773 0.8793 0.880 0.000 0.116 0.004
#> GSM26848 1 0.2944 0.8726 0.868 0.000 0.128 0.004
#> GSM26849 1 0.4746 0.5741 0.632 0.000 0.368 0.000
#> GSM26850 1 0.3355 0.8480 0.836 0.000 0.160 0.004
#> GSM26851 4 0.4916 0.6593 0.000 0.424 0.000 0.576
#> GSM26852 3 0.0000 0.9936 0.000 0.000 1.000 0.000
#> GSM26853 3 0.0000 0.9936 0.000 0.000 1.000 0.000
#> GSM26854 3 0.0000 0.9936 0.000 0.000 1.000 0.000
#> GSM26855 3 0.0000 0.9936 0.000 0.000 1.000 0.000
#> GSM26856 3 0.1389 0.9396 0.048 0.000 0.952 0.000
#> GSM26857 3 0.0000 0.9936 0.000 0.000 1.000 0.000
#> GSM26858 3 0.0000 0.9936 0.000 0.000 1.000 0.000
#> GSM26859 3 0.0000 0.9936 0.000 0.000 1.000 0.000
#> GSM26860 3 0.0000 0.9936 0.000 0.000 1.000 0.000
#> GSM26861 3 0.0000 0.9936 0.000 0.000 1.000 0.000
#> GSM26862 1 0.1022 0.9091 0.968 0.000 0.032 0.000
#> GSM26863 1 0.1302 0.9078 0.956 0.000 0.044 0.000
#> GSM26864 1 0.0000 0.9065 1.000 0.000 0.000 0.000
#> GSM26865 1 0.2714 0.8822 0.884 0.000 0.112 0.004
#> GSM26866 1 0.0000 0.9065 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
#> GSM26805 4 0.3242 0.67738 0.000 0.216 0.000 0.784 0.000
#> GSM26806 4 0.4192 0.60270 0.000 0.000 0.000 0.596 0.404
#> GSM26807 4 0.4321 0.60519 0.000 0.004 0.000 0.600 0.396
#> GSM26808 4 0.4331 0.60334 0.000 0.004 0.000 0.596 0.400
#> GSM26809 4 0.3917 0.67934 0.024 0.184 0.000 0.784 0.008
#> GSM26810 4 0.4331 0.60334 0.000 0.004 0.000 0.596 0.400
#> GSM26811 4 0.5123 0.61636 0.000 0.044 0.000 0.572 0.384
#> GSM26812 4 0.4321 0.60519 0.000 0.004 0.000 0.600 0.396
#> GSM26813 2 0.3177 0.63726 0.000 0.792 0.000 0.208 0.000
#> GSM26814 2 0.0000 0.94232 0.000 1.000 0.000 0.000 0.000
#> GSM26815 4 0.4761 0.63011 0.000 0.104 0.000 0.728 0.168
#> GSM26816 4 0.3274 0.67604 0.000 0.220 0.000 0.780 0.000
#> GSM26817 4 0.5086 0.64230 0.000 0.144 0.000 0.700 0.156
#> GSM26818 1 0.6237 0.30889 0.656 0.000 0.168 0.092 0.084
#> GSM26819 2 0.0000 0.94232 0.000 1.000 0.000 0.000 0.000
#> GSM26820 2 0.0000 0.94232 0.000 1.000 0.000 0.000 0.000
#> GSM26821 2 0.0000 0.94232 0.000 1.000 0.000 0.000 0.000
#> GSM26822 2 0.0000 0.94232 0.000 1.000 0.000 0.000 0.000
#> GSM26823 2 0.0000 0.94232 0.000 1.000 0.000 0.000 0.000
#> GSM26824 2 0.0000 0.94232 0.000 1.000 0.000 0.000 0.000
#> GSM26825 2 0.0000 0.94232 0.000 1.000 0.000 0.000 0.000
#> GSM26826 2 0.0000 0.94232 0.000 1.000 0.000 0.000 0.000
#> GSM26827 2 0.0000 0.94232 0.000 1.000 0.000 0.000 0.000
#> GSM26828 4 0.3210 0.68079 0.000 0.212 0.000 0.788 0.000
#> GSM26829 4 0.4074 0.44937 0.000 0.364 0.000 0.636 0.000
#> GSM26830 2 0.3395 0.57860 0.000 0.764 0.000 0.236 0.000
#> GSM26831 4 0.3210 0.68079 0.000 0.212 0.000 0.788 0.000
#> GSM26832 4 0.2471 0.70066 0.000 0.136 0.000 0.864 0.000
#> GSM26833 4 0.2732 0.69848 0.000 0.160 0.000 0.840 0.000
#> GSM26834 4 0.3210 0.68079 0.000 0.212 0.000 0.788 0.000
#> GSM26835 4 0.3210 0.68079 0.000 0.212 0.000 0.788 0.000
#> GSM26836 1 0.3967 0.07738 0.724 0.000 0.012 0.000 0.264
#> GSM26837 1 0.4109 -0.00627 0.700 0.000 0.012 0.000 0.288
#> GSM26838 1 0.4537 -0.57965 0.592 0.000 0.012 0.000 0.396
#> GSM26839 1 0.4356 -0.26422 0.648 0.000 0.012 0.000 0.340
#> GSM26840 1 0.4318 -0.10992 0.688 0.000 0.000 0.020 0.292
#> GSM26841 1 0.4306 -0.91120 0.508 0.000 0.000 0.000 0.492
#> GSM26842 5 0.4448 0.98739 0.480 0.000 0.000 0.004 0.516
#> GSM26843 5 0.4302 0.99686 0.480 0.000 0.000 0.000 0.520
#> GSM26844 5 0.4302 0.99686 0.480 0.000 0.000 0.000 0.520
#> GSM26845 1 0.4493 0.40672 0.796 0.000 0.044 0.080 0.080
#> GSM26846 1 0.1668 0.52826 0.940 0.000 0.032 0.000 0.028
#> GSM26847 1 0.1485 0.53142 0.948 0.000 0.032 0.000 0.020
#> GSM26848 1 0.1043 0.52968 0.960 0.000 0.040 0.000 0.000
#> GSM26849 1 0.2992 0.52215 0.868 0.000 0.064 0.000 0.068
#> GSM26850 1 0.1668 0.52826 0.940 0.000 0.032 0.000 0.028
#> GSM26851 4 0.4361 0.69297 0.000 0.108 0.000 0.768 0.124
#> GSM26852 3 0.0000 0.98123 0.000 0.000 1.000 0.000 0.000
#> GSM26853 3 0.0000 0.98123 0.000 0.000 1.000 0.000 0.000
#> GSM26854 3 0.0000 0.98123 0.000 0.000 1.000 0.000 0.000
#> GSM26855 3 0.0000 0.98123 0.000 0.000 1.000 0.000 0.000
#> GSM26856 3 0.2280 0.82394 0.120 0.000 0.880 0.000 0.000
#> GSM26857 3 0.0000 0.98123 0.000 0.000 1.000 0.000 0.000
#> GSM26858 3 0.0000 0.98123 0.000 0.000 1.000 0.000 0.000
#> GSM26859 3 0.0404 0.97288 0.012 0.000 0.988 0.000 0.000
#> GSM26860 3 0.0000 0.98123 0.000 0.000 1.000 0.000 0.000
#> GSM26861 3 0.0162 0.97845 0.000 0.000 0.996 0.000 0.004
#> GSM26862 1 0.3807 0.15024 0.748 0.000 0.012 0.000 0.240
#> GSM26863 1 0.3942 0.09181 0.728 0.000 0.012 0.000 0.260
#> GSM26864 5 0.4302 0.99686 0.480 0.000 0.000 0.000 0.520
#> GSM26865 1 0.1918 0.51674 0.928 0.000 0.036 0.000 0.036
#> GSM26866 5 0.4302 0.99686 0.480 0.000 0.000 0.000 0.520
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM26805 5 0.1863 0.861 0.000 0.104 0.000 0.000 0.896 0.000
#> GSM26806 4 0.2445 0.730 0.000 0.020 0.000 0.872 0.108 0.000
#> GSM26807 4 0.3670 0.795 0.000 0.012 0.000 0.704 0.284 0.000
#> GSM26808 4 0.3898 0.789 0.000 0.020 0.000 0.684 0.296 0.000
#> GSM26809 5 0.1411 0.839 0.004 0.060 0.000 0.000 0.936 0.000
#> GSM26810 4 0.3650 0.797 0.000 0.012 0.000 0.708 0.280 0.000
#> GSM26811 4 0.4436 0.750 0.000 0.048 0.000 0.640 0.312 0.000
#> GSM26812 4 0.3490 0.796 0.000 0.008 0.000 0.724 0.268 0.000
#> GSM26813 2 0.1075 0.937 0.000 0.952 0.000 0.000 0.048 0.000
#> GSM26814 2 0.0458 0.968 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM26815 4 0.3122 0.657 0.000 0.176 0.000 0.804 0.020 0.000
#> GSM26816 5 0.2730 0.803 0.000 0.192 0.000 0.000 0.808 0.000
#> GSM26817 4 0.4363 0.540 0.000 0.324 0.000 0.636 0.040 0.000
#> GSM26818 6 0.5444 0.488 0.000 0.000 0.044 0.372 0.044 0.540
#> GSM26819 2 0.0000 0.973 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26820 2 0.0000 0.973 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26821 2 0.0363 0.968 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM26822 2 0.0000 0.973 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26823 2 0.0000 0.973 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26824 2 0.0458 0.968 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM26825 2 0.0000 0.973 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26826 2 0.0000 0.973 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26827 2 0.0000 0.973 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26828 5 0.1714 0.873 0.000 0.092 0.000 0.000 0.908 0.000
#> GSM26829 5 0.3695 0.537 0.000 0.376 0.000 0.000 0.624 0.000
#> GSM26830 2 0.2527 0.773 0.000 0.832 0.000 0.000 0.168 0.000
#> GSM26831 5 0.1714 0.873 0.000 0.092 0.000 0.000 0.908 0.000
#> GSM26832 5 0.1757 0.864 0.000 0.076 0.000 0.008 0.916 0.000
#> GSM26833 5 0.2662 0.828 0.000 0.120 0.000 0.024 0.856 0.000
#> GSM26834 5 0.1663 0.872 0.000 0.088 0.000 0.000 0.912 0.000
#> GSM26835 5 0.1714 0.873 0.000 0.092 0.000 0.000 0.908 0.000
#> GSM26836 6 0.3534 0.422 0.276 0.000 0.000 0.008 0.000 0.716
#> GSM26837 6 0.4076 0.148 0.452 0.000 0.000 0.008 0.000 0.540
#> GSM26838 1 0.3833 0.126 0.556 0.000 0.000 0.000 0.000 0.444
#> GSM26839 1 0.3955 0.139 0.608 0.000 0.000 0.008 0.000 0.384
#> GSM26840 6 0.4729 0.230 0.412 0.000 0.000 0.004 0.040 0.544
#> GSM26841 1 0.0458 0.827 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM26842 1 0.0000 0.838 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26843 1 0.0000 0.838 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26844 1 0.0000 0.838 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26845 6 0.5474 0.583 0.016 0.000 0.184 0.004 0.160 0.636
#> GSM26846 6 0.0146 0.639 0.000 0.000 0.000 0.004 0.000 0.996
#> GSM26847 6 0.0000 0.639 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM26848 6 0.3383 0.623 0.000 0.000 0.268 0.004 0.000 0.728
#> GSM26849 6 0.3383 0.625 0.004 0.000 0.268 0.000 0.000 0.728
#> GSM26850 6 0.2595 0.657 0.000 0.000 0.160 0.004 0.000 0.836
#> GSM26851 5 0.3999 0.342 0.000 0.032 0.000 0.272 0.696 0.000
#> GSM26852 3 0.0000 0.996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26853 3 0.0000 0.996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26854 3 0.0000 0.996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26855 3 0.0000 0.996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26856 3 0.0000 0.996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26857 3 0.0000 0.996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26858 3 0.0000 0.996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26859 3 0.0632 0.967 0.000 0.000 0.976 0.000 0.000 0.024
#> GSM26860 3 0.0000 0.996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26861 3 0.0000 0.996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26862 6 0.3349 0.459 0.244 0.000 0.000 0.008 0.000 0.748
#> GSM26863 6 0.3512 0.427 0.272 0.000 0.000 0.008 0.000 0.720
#> GSM26864 1 0.0000 0.838 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26865 6 0.4039 0.634 0.060 0.000 0.208 0.000 0.000 0.732
#> GSM26866 1 0.0000 0.838 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 tissue(p) individual(p) k
#> SD:mclust 62 1.14e-12 8.30e-01 2
#> SD:mclust 61 3.93e-13 2.21e-04 3
#> SD:mclust 59 6.22e-12 6.34e-09 4
#> SD:mclust 51 1.42e-09 2.99e-08 5
#> SD:mclust 53 3.36e-10 1.12e-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 11993 rows and 62 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 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.993 0.997 0.509 0.492 0.492
#> 3 3 0.902 0.886 0.951 0.238 0.862 0.723
#> 4 4 0.757 0.869 0.897 0.176 0.824 0.551
#> 5 5 0.777 0.721 0.811 0.079 0.897 0.617
#> 6 6 0.806 0.752 0.822 0.044 0.880 0.493
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
#> GSM26805 2 0.000 1.000 0.000 1.000
#> GSM26806 2 0.000 1.000 0.000 1.000
#> GSM26807 2 0.000 1.000 0.000 1.000
#> GSM26808 2 0.000 1.000 0.000 1.000
#> GSM26809 2 0.000 1.000 0.000 1.000
#> GSM26810 2 0.000 1.000 0.000 1.000
#> GSM26811 2 0.000 1.000 0.000 1.000
#> GSM26812 2 0.000 1.000 0.000 1.000
#> GSM26813 2 0.000 1.000 0.000 1.000
#> GSM26814 2 0.000 1.000 0.000 1.000
#> GSM26815 2 0.000 1.000 0.000 1.000
#> GSM26816 2 0.000 1.000 0.000 1.000
#> GSM26817 2 0.000 1.000 0.000 1.000
#> GSM26818 1 0.000 0.994 1.000 0.000
#> GSM26819 2 0.000 1.000 0.000 1.000
#> GSM26820 2 0.000 1.000 0.000 1.000
#> GSM26821 2 0.000 1.000 0.000 1.000
#> GSM26822 2 0.000 1.000 0.000 1.000
#> GSM26823 2 0.000 1.000 0.000 1.000
#> GSM26824 2 0.000 1.000 0.000 1.000
#> GSM26825 2 0.000 1.000 0.000 1.000
#> GSM26826 2 0.000 1.000 0.000 1.000
#> GSM26827 2 0.000 1.000 0.000 1.000
#> GSM26828 2 0.000 1.000 0.000 1.000
#> GSM26829 2 0.000 1.000 0.000 1.000
#> GSM26830 2 0.000 1.000 0.000 1.000
#> GSM26831 2 0.000 1.000 0.000 1.000
#> GSM26832 2 0.000 1.000 0.000 1.000
#> GSM26833 2 0.000 1.000 0.000 1.000
#> GSM26834 2 0.000 1.000 0.000 1.000
#> GSM26835 2 0.000 1.000 0.000 1.000
#> GSM26836 1 0.000 0.994 1.000 0.000
#> GSM26837 1 0.000 0.994 1.000 0.000
#> GSM26838 1 0.000 0.994 1.000 0.000
#> GSM26839 1 0.000 0.994 1.000 0.000
#> GSM26840 1 0.000 0.994 1.000 0.000
#> GSM26841 1 0.000 0.994 1.000 0.000
#> GSM26842 1 0.000 0.994 1.000 0.000
#> GSM26843 1 0.000 0.994 1.000 0.000
#> GSM26844 1 0.000 0.994 1.000 0.000
#> GSM26845 1 0.697 0.768 0.812 0.188
#> GSM26846 1 0.000 0.994 1.000 0.000
#> GSM26847 1 0.000 0.994 1.000 0.000
#> GSM26848 1 0.000 0.994 1.000 0.000
#> GSM26849 1 0.000 0.994 1.000 0.000
#> GSM26850 1 0.000 0.994 1.000 0.000
#> GSM26851 2 0.000 1.000 0.000 1.000
#> GSM26852 1 0.000 0.994 1.000 0.000
#> GSM26853 1 0.000 0.994 1.000 0.000
#> GSM26854 1 0.000 0.994 1.000 0.000
#> GSM26855 1 0.000 0.994 1.000 0.000
#> GSM26856 1 0.000 0.994 1.000 0.000
#> GSM26857 1 0.000 0.994 1.000 0.000
#> GSM26858 1 0.000 0.994 1.000 0.000
#> GSM26859 1 0.000 0.994 1.000 0.000
#> GSM26860 1 0.000 0.994 1.000 0.000
#> GSM26861 1 0.000 0.994 1.000 0.000
#> GSM26862 1 0.000 0.994 1.000 0.000
#> GSM26863 1 0.000 0.994 1.000 0.000
#> GSM26864 1 0.000 0.994 1.000 0.000
#> GSM26865 1 0.000 0.994 1.000 0.000
#> GSM26866 1 0.000 0.994 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM26805 2 0.6045 0.355 0.380 0.620 0.000
#> GSM26806 2 0.0237 0.981 0.004 0.996 0.000
#> GSM26807 2 0.0237 0.981 0.004 0.996 0.000
#> GSM26808 2 0.0237 0.981 0.004 0.996 0.000
#> GSM26809 1 0.4504 0.685 0.804 0.196 0.000
#> GSM26810 2 0.0237 0.981 0.004 0.996 0.000
#> GSM26811 2 0.0237 0.981 0.004 0.996 0.000
#> GSM26812 2 0.0237 0.981 0.004 0.996 0.000
#> GSM26813 2 0.0000 0.982 0.000 1.000 0.000
#> GSM26814 2 0.0000 0.982 0.000 1.000 0.000
#> GSM26815 2 0.0237 0.981 0.004 0.996 0.000
#> GSM26816 2 0.0000 0.982 0.000 1.000 0.000
#> GSM26817 2 0.0237 0.981 0.004 0.996 0.000
#> GSM26818 3 0.0237 0.938 0.004 0.000 0.996
#> GSM26819 2 0.0000 0.982 0.000 1.000 0.000
#> GSM26820 2 0.0000 0.982 0.000 1.000 0.000
#> GSM26821 2 0.0000 0.982 0.000 1.000 0.000
#> GSM26822 2 0.0000 0.982 0.000 1.000 0.000
#> GSM26823 2 0.0000 0.982 0.000 1.000 0.000
#> GSM26824 2 0.0000 0.982 0.000 1.000 0.000
#> GSM26825 2 0.0000 0.982 0.000 1.000 0.000
#> GSM26826 2 0.0000 0.982 0.000 1.000 0.000
#> GSM26827 2 0.0000 0.982 0.000 1.000 0.000
#> GSM26828 2 0.1860 0.931 0.052 0.948 0.000
#> GSM26829 2 0.0000 0.982 0.000 1.000 0.000
#> GSM26830 2 0.0000 0.982 0.000 1.000 0.000
#> GSM26831 2 0.1163 0.957 0.028 0.972 0.000
#> GSM26832 2 0.0000 0.982 0.000 1.000 0.000
#> GSM26833 2 0.0237 0.981 0.004 0.996 0.000
#> GSM26834 2 0.0000 0.982 0.000 1.000 0.000
#> GSM26835 2 0.0000 0.982 0.000 1.000 0.000
#> GSM26836 1 0.6244 0.320 0.560 0.000 0.440
#> GSM26837 3 0.0000 0.942 0.000 0.000 1.000
#> GSM26838 1 0.1163 0.835 0.972 0.000 0.028
#> GSM26839 3 0.5650 0.486 0.312 0.000 0.688
#> GSM26840 1 0.0237 0.833 0.996 0.000 0.004
#> GSM26841 1 0.1289 0.835 0.968 0.000 0.032
#> GSM26842 1 0.3267 0.792 0.884 0.000 0.116
#> GSM26843 1 0.0237 0.833 0.996 0.000 0.004
#> GSM26844 1 0.0237 0.833 0.996 0.000 0.004
#> GSM26845 1 0.0237 0.830 0.996 0.004 0.000
#> GSM26846 3 0.0000 0.942 0.000 0.000 1.000
#> GSM26847 3 0.0592 0.934 0.012 0.000 0.988
#> GSM26848 3 0.3482 0.818 0.128 0.000 0.872
#> GSM26849 3 0.0000 0.942 0.000 0.000 1.000
#> GSM26850 3 0.0000 0.942 0.000 0.000 1.000
#> GSM26851 2 0.0237 0.981 0.004 0.996 0.000
#> GSM26852 3 0.0000 0.942 0.000 0.000 1.000
#> GSM26853 3 0.0000 0.942 0.000 0.000 1.000
#> GSM26854 3 0.0000 0.942 0.000 0.000 1.000
#> GSM26855 3 0.0000 0.942 0.000 0.000 1.000
#> GSM26856 3 0.0000 0.942 0.000 0.000 1.000
#> GSM26857 3 0.0000 0.942 0.000 0.000 1.000
#> GSM26858 3 0.0000 0.942 0.000 0.000 1.000
#> GSM26859 3 0.0000 0.942 0.000 0.000 1.000
#> GSM26860 3 0.0000 0.942 0.000 0.000 1.000
#> GSM26861 3 0.0000 0.942 0.000 0.000 1.000
#> GSM26862 3 0.5363 0.571 0.276 0.000 0.724
#> GSM26863 1 0.6225 0.343 0.568 0.000 0.432
#> GSM26864 1 0.5926 0.508 0.644 0.000 0.356
#> GSM26865 3 0.3879 0.787 0.152 0.000 0.848
#> GSM26866 1 0.1643 0.832 0.956 0.000 0.044
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM26805 2 0.1118 0.936 0.036 0.964 0.000 0.000
#> GSM26806 4 0.2530 0.920 0.000 0.112 0.000 0.888
#> GSM26807 4 0.2530 0.920 0.000 0.112 0.000 0.888
#> GSM26808 4 0.2530 0.920 0.000 0.112 0.000 0.888
#> GSM26809 2 0.2124 0.897 0.040 0.932 0.000 0.028
#> GSM26810 4 0.2530 0.920 0.000 0.112 0.000 0.888
#> GSM26811 4 0.2530 0.920 0.000 0.112 0.000 0.888
#> GSM26812 4 0.2530 0.920 0.000 0.112 0.000 0.888
#> GSM26813 2 0.1474 0.954 0.000 0.948 0.000 0.052
#> GSM26814 2 0.1211 0.963 0.000 0.960 0.000 0.040
#> GSM26815 4 0.2530 0.920 0.000 0.112 0.000 0.888
#> GSM26816 2 0.1940 0.925 0.000 0.924 0.000 0.076
#> GSM26817 4 0.2530 0.920 0.000 0.112 0.000 0.888
#> GSM26818 3 0.1302 0.871 0.000 0.000 0.956 0.044
#> GSM26819 2 0.0921 0.966 0.000 0.972 0.000 0.028
#> GSM26820 2 0.0188 0.963 0.000 0.996 0.000 0.004
#> GSM26821 2 0.1118 0.965 0.000 0.964 0.000 0.036
#> GSM26822 2 0.1022 0.966 0.000 0.968 0.000 0.032
#> GSM26823 2 0.1022 0.966 0.000 0.968 0.000 0.032
#> GSM26824 2 0.1211 0.963 0.000 0.960 0.000 0.040
#> GSM26825 2 0.0188 0.963 0.000 0.996 0.000 0.004
#> GSM26826 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM26827 2 0.0817 0.966 0.000 0.976 0.000 0.024
#> GSM26828 2 0.0921 0.950 0.000 0.972 0.000 0.028
#> GSM26829 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM26830 2 0.1211 0.963 0.000 0.960 0.000 0.040
#> GSM26831 2 0.0524 0.959 0.004 0.988 0.000 0.008
#> GSM26832 4 0.4222 0.774 0.000 0.272 0.000 0.728
#> GSM26833 4 0.2530 0.920 0.000 0.112 0.000 0.888
#> GSM26834 4 0.4843 0.557 0.000 0.396 0.000 0.604
#> GSM26835 4 0.4999 0.362 0.000 0.492 0.000 0.508
#> GSM26836 1 0.2546 0.843 0.900 0.000 0.092 0.008
#> GSM26837 1 0.5057 0.444 0.648 0.000 0.340 0.012
#> GSM26838 1 0.1022 0.876 0.968 0.000 0.000 0.032
#> GSM26839 1 0.3428 0.795 0.844 0.000 0.144 0.012
#> GSM26840 1 0.3149 0.843 0.880 0.032 0.000 0.088
#> GSM26841 1 0.0188 0.879 0.996 0.004 0.000 0.000
#> GSM26842 1 0.0524 0.878 0.988 0.004 0.008 0.000
#> GSM26843 1 0.2623 0.858 0.908 0.028 0.000 0.064
#> GSM26844 1 0.2214 0.866 0.928 0.028 0.000 0.044
#> GSM26845 1 0.4640 0.805 0.828 0.076 0.044 0.052
#> GSM26846 3 0.3178 0.838 0.032 0.052 0.896 0.020
#> GSM26847 3 0.3757 0.768 0.152 0.000 0.828 0.020
#> GSM26848 3 0.2275 0.863 0.048 0.004 0.928 0.020
#> GSM26849 3 0.0469 0.881 0.000 0.000 0.988 0.012
#> GSM26850 3 0.1174 0.878 0.000 0.012 0.968 0.020
#> GSM26851 4 0.2530 0.920 0.000 0.112 0.000 0.888
#> GSM26852 3 0.2334 0.907 0.088 0.000 0.908 0.004
#> GSM26853 3 0.2334 0.907 0.088 0.000 0.908 0.004
#> GSM26854 3 0.2149 0.907 0.088 0.000 0.912 0.000
#> GSM26855 3 0.2334 0.907 0.088 0.000 0.908 0.004
#> GSM26856 3 0.2334 0.907 0.088 0.000 0.908 0.004
#> GSM26857 3 0.2149 0.907 0.088 0.000 0.912 0.000
#> GSM26858 3 0.2334 0.907 0.088 0.000 0.908 0.004
#> GSM26859 3 0.0469 0.881 0.000 0.000 0.988 0.012
#> GSM26860 3 0.2081 0.907 0.084 0.000 0.916 0.000
#> GSM26861 3 0.2334 0.907 0.088 0.000 0.908 0.004
#> GSM26862 1 0.4262 0.674 0.756 0.000 0.236 0.008
#> GSM26863 1 0.2675 0.838 0.892 0.000 0.100 0.008
#> GSM26864 1 0.1174 0.878 0.968 0.020 0.012 0.000
#> GSM26865 3 0.5632 0.289 0.352 0.008 0.620 0.020
#> GSM26866 1 0.0921 0.877 0.972 0.028 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM26805 5 0.3819 0.548 0.000 0.228 0.000 0.016 0.756
#> GSM26806 4 0.0162 0.888 0.000 0.004 0.000 0.996 0.000
#> GSM26807 4 0.0162 0.888 0.000 0.004 0.000 0.996 0.000
#> GSM26808 4 0.0162 0.888 0.000 0.004 0.000 0.996 0.000
#> GSM26809 5 0.3816 0.480 0.000 0.304 0.000 0.000 0.696
#> GSM26810 4 0.0162 0.888 0.000 0.004 0.000 0.996 0.000
#> GSM26811 4 0.0162 0.888 0.000 0.004 0.000 0.996 0.000
#> GSM26812 4 0.0162 0.888 0.000 0.004 0.000 0.996 0.000
#> GSM26813 2 0.0000 0.986 0.000 1.000 0.000 0.000 0.000
#> GSM26814 2 0.0000 0.986 0.000 1.000 0.000 0.000 0.000
#> GSM26815 4 0.0162 0.888 0.000 0.004 0.000 0.996 0.000
#> GSM26816 4 0.6399 0.268 0.000 0.308 0.000 0.496 0.196
#> GSM26817 4 0.0162 0.888 0.000 0.004 0.000 0.996 0.000
#> GSM26818 3 0.3890 0.733 0.252 0.000 0.736 0.012 0.000
#> GSM26819 2 0.0000 0.986 0.000 1.000 0.000 0.000 0.000
#> GSM26820 2 0.0000 0.986 0.000 1.000 0.000 0.000 0.000
#> GSM26821 2 0.0000 0.986 0.000 1.000 0.000 0.000 0.000
#> GSM26822 2 0.0000 0.986 0.000 1.000 0.000 0.000 0.000
#> GSM26823 2 0.0000 0.986 0.000 1.000 0.000 0.000 0.000
#> GSM26824 2 0.0000 0.986 0.000 1.000 0.000 0.000 0.000
#> GSM26825 2 0.0000 0.986 0.000 1.000 0.000 0.000 0.000
#> GSM26826 2 0.0000 0.986 0.000 1.000 0.000 0.000 0.000
#> GSM26827 2 0.0000 0.986 0.000 1.000 0.000 0.000 0.000
#> GSM26828 5 0.5577 0.448 0.000 0.256 0.000 0.120 0.624
#> GSM26829 2 0.2471 0.815 0.000 0.864 0.000 0.000 0.136
#> GSM26830 2 0.0000 0.986 0.000 1.000 0.000 0.000 0.000
#> GSM26831 5 0.4219 0.255 0.000 0.416 0.000 0.000 0.584
#> GSM26832 4 0.3196 0.768 0.000 0.004 0.000 0.804 0.192
#> GSM26833 4 0.1430 0.869 0.000 0.004 0.000 0.944 0.052
#> GSM26834 4 0.3010 0.788 0.000 0.004 0.000 0.824 0.172
#> GSM26835 4 0.4297 0.304 0.000 0.000 0.000 0.528 0.472
#> GSM26836 1 0.4181 0.712 0.712 0.000 0.268 0.000 0.020
#> GSM26837 1 0.3774 0.704 0.704 0.000 0.296 0.000 0.000
#> GSM26838 1 0.4948 0.627 0.708 0.000 0.108 0.000 0.184
#> GSM26839 1 0.3861 0.710 0.712 0.000 0.284 0.000 0.004
#> GSM26840 5 0.2966 0.478 0.184 0.000 0.000 0.000 0.816
#> GSM26841 1 0.5956 0.487 0.564 0.000 0.140 0.000 0.296
#> GSM26842 1 0.5905 0.498 0.572 0.000 0.136 0.000 0.292
#> GSM26843 5 0.3305 0.457 0.224 0.000 0.000 0.000 0.776
#> GSM26844 5 0.4138 0.387 0.276 0.000 0.016 0.000 0.708
#> GSM26845 1 0.4227 0.466 0.692 0.016 0.000 0.000 0.292
#> GSM26846 1 0.4629 0.369 0.772 0.044 0.144 0.000 0.040
#> GSM26847 1 0.2773 0.423 0.836 0.000 0.164 0.000 0.000
#> GSM26848 3 0.5370 0.633 0.348 0.000 0.584 0.000 0.068
#> GSM26849 3 0.3816 0.712 0.304 0.000 0.696 0.000 0.000
#> GSM26850 3 0.4166 0.681 0.348 0.000 0.648 0.000 0.004
#> GSM26851 4 0.1041 0.877 0.000 0.004 0.000 0.964 0.032
#> GSM26852 3 0.0162 0.822 0.000 0.000 0.996 0.004 0.000
#> GSM26853 3 0.0162 0.822 0.000 0.000 0.996 0.004 0.000
#> GSM26854 3 0.0000 0.823 0.000 0.000 1.000 0.000 0.000
#> GSM26855 3 0.0162 0.822 0.000 0.000 0.996 0.004 0.000
#> GSM26856 3 0.0000 0.823 0.000 0.000 1.000 0.000 0.000
#> GSM26857 3 0.0000 0.823 0.000 0.000 1.000 0.000 0.000
#> GSM26858 3 0.0162 0.822 0.000 0.000 0.996 0.004 0.000
#> GSM26859 3 0.3424 0.744 0.240 0.000 0.760 0.000 0.000
#> GSM26860 3 0.0000 0.823 0.000 0.000 1.000 0.000 0.000
#> GSM26861 3 0.0162 0.822 0.000 0.000 0.996 0.004 0.000
#> GSM26862 1 0.4206 0.710 0.696 0.000 0.288 0.000 0.016
#> GSM26863 1 0.4451 0.708 0.712 0.000 0.248 0.000 0.040
#> GSM26864 5 0.6589 -0.144 0.364 0.000 0.212 0.000 0.424
#> GSM26865 3 0.5664 0.600 0.348 0.000 0.560 0.000 0.092
#> GSM26866 5 0.5811 0.255 0.264 0.000 0.140 0.000 0.596
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM26805 5 0.2873 0.607 0.004 0.044 0.000 0.068 0.872 0.012
#> GSM26806 4 0.0146 0.951 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM26807 4 0.0260 0.950 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM26808 4 0.0405 0.950 0.000 0.000 0.000 0.988 0.008 0.004
#> GSM26809 5 0.5613 0.171 0.088 0.392 0.000 0.000 0.500 0.020
#> GSM26810 4 0.0260 0.951 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM26811 4 0.0260 0.951 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM26812 4 0.0000 0.950 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26813 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26814 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26815 4 0.0260 0.947 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM26816 5 0.4748 0.566 0.000 0.052 0.000 0.316 0.624 0.008
#> GSM26817 4 0.1787 0.887 0.000 0.008 0.000 0.920 0.068 0.004
#> GSM26818 3 0.3514 0.694 0.000 0.000 0.768 0.020 0.004 0.208
#> GSM26819 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26820 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26821 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26822 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26823 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26824 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26825 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26826 2 0.0146 0.996 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM26827 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26828 5 0.2201 0.635 0.000 0.056 0.000 0.036 0.904 0.004
#> GSM26829 5 0.4096 0.184 0.000 0.484 0.000 0.000 0.508 0.008
#> GSM26830 2 0.0146 0.996 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM26831 5 0.2692 0.613 0.000 0.148 0.000 0.012 0.840 0.000
#> GSM26832 5 0.3565 0.553 0.000 0.000 0.000 0.304 0.692 0.004
#> GSM26833 5 0.3971 0.274 0.000 0.000 0.000 0.448 0.548 0.004
#> GSM26834 5 0.3636 0.532 0.000 0.000 0.000 0.320 0.676 0.004
#> GSM26835 5 0.2597 0.634 0.000 0.000 0.000 0.176 0.824 0.000
#> GSM26836 1 0.5320 0.556 0.576 0.000 0.144 0.000 0.000 0.280
#> GSM26837 1 0.5667 0.502 0.520 0.000 0.192 0.000 0.000 0.288
#> GSM26838 1 0.3229 0.658 0.816 0.000 0.044 0.000 0.000 0.140
#> GSM26839 1 0.4890 0.621 0.660 0.000 0.160 0.000 0.000 0.180
#> GSM26840 1 0.3955 0.391 0.608 0.000 0.000 0.000 0.384 0.008
#> GSM26841 1 0.3338 0.693 0.844 0.000 0.064 0.000 0.060 0.032
#> GSM26842 1 0.3216 0.693 0.852 0.000 0.064 0.000 0.052 0.032
#> GSM26843 1 0.2915 0.621 0.808 0.000 0.000 0.000 0.184 0.008
#> GSM26844 1 0.2982 0.639 0.820 0.000 0.012 0.000 0.164 0.004
#> GSM26845 6 0.3670 0.391 0.284 0.000 0.000 0.000 0.012 0.704
#> GSM26846 6 0.1442 0.681 0.040 0.000 0.004 0.000 0.012 0.944
#> GSM26847 6 0.2450 0.632 0.116 0.000 0.016 0.000 0.000 0.868
#> GSM26848 6 0.3455 0.690 0.000 0.000 0.056 0.000 0.144 0.800
#> GSM26849 6 0.3695 0.341 0.000 0.000 0.376 0.000 0.000 0.624
#> GSM26850 6 0.3293 0.693 0.000 0.000 0.048 0.000 0.140 0.812
#> GSM26851 4 0.3103 0.695 0.000 0.000 0.000 0.784 0.208 0.008
#> GSM26852 3 0.0508 0.925 0.012 0.000 0.984 0.000 0.000 0.004
#> GSM26853 3 0.0146 0.928 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM26854 3 0.0790 0.928 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM26855 3 0.0260 0.927 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM26856 3 0.0790 0.928 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM26857 3 0.0790 0.928 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM26858 3 0.0508 0.925 0.012 0.000 0.984 0.000 0.000 0.004
#> GSM26859 3 0.2631 0.761 0.000 0.000 0.820 0.000 0.000 0.180
#> GSM26860 3 0.0865 0.926 0.000 0.000 0.964 0.000 0.000 0.036
#> GSM26861 3 0.0508 0.925 0.012 0.000 0.984 0.000 0.000 0.004
#> GSM26862 1 0.5771 0.438 0.484 0.000 0.160 0.000 0.004 0.352
#> GSM26863 1 0.5135 0.593 0.616 0.000 0.144 0.000 0.000 0.240
#> GSM26864 1 0.4380 0.673 0.744 0.000 0.108 0.000 0.136 0.012
#> GSM26865 6 0.4423 0.659 0.052 0.000 0.176 0.000 0.032 0.740
#> GSM26866 1 0.3785 0.660 0.780 0.000 0.064 0.000 0.152 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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> SD:NMF 62 1.14e-12 8.30e-01 2
#> SD:NMF 58 7.11e-11 2.44e-03 3
#> SD:NMF 59 3.68e-11 3.90e-05 4
#> SD:NMF 47 5.45e-08 4.67e-04 5
#> SD:NMF 55 3.89e-09 2.55e-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["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 11993 rows and 62 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.367 0.799 0.836 0.4851 0.492 0.492
#> 3 3 0.608 0.901 0.910 0.2372 0.857 0.716
#> 4 4 0.750 0.884 0.924 0.1807 0.885 0.698
#> 5 5 0.867 0.829 0.928 0.0494 0.978 0.920
#> 6 6 0.845 0.790 0.918 0.0210 0.969 0.880
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
#> GSM26805 2 0.000 0.889 0.000 1.000
#> GSM26806 2 0.760 0.761 0.220 0.780
#> GSM26807 2 0.760 0.761 0.220 0.780
#> GSM26808 2 0.760 0.761 0.220 0.780
#> GSM26809 2 0.952 0.130 0.372 0.628
#> GSM26810 2 0.760 0.761 0.220 0.780
#> GSM26811 2 0.760 0.761 0.220 0.780
#> GSM26812 2 0.760 0.761 0.220 0.780
#> GSM26813 2 0.000 0.889 0.000 1.000
#> GSM26814 2 0.000 0.889 0.000 1.000
#> GSM26815 2 0.760 0.761 0.220 0.780
#> GSM26816 2 0.000 0.889 0.000 1.000
#> GSM26817 2 0.760 0.761 0.220 0.780
#> GSM26818 1 0.680 0.652 0.820 0.180
#> GSM26819 2 0.000 0.889 0.000 1.000
#> GSM26820 2 0.000 0.889 0.000 1.000
#> GSM26821 2 0.000 0.889 0.000 1.000
#> GSM26822 2 0.000 0.889 0.000 1.000
#> GSM26823 2 0.000 0.889 0.000 1.000
#> GSM26824 2 0.000 0.889 0.000 1.000
#> GSM26825 2 0.000 0.889 0.000 1.000
#> GSM26826 2 0.000 0.889 0.000 1.000
#> GSM26827 2 0.000 0.889 0.000 1.000
#> GSM26828 2 0.000 0.889 0.000 1.000
#> GSM26829 2 0.000 0.889 0.000 1.000
#> GSM26830 2 0.000 0.889 0.000 1.000
#> GSM26831 2 0.000 0.889 0.000 1.000
#> GSM26832 2 0.000 0.889 0.000 1.000
#> GSM26833 2 0.000 0.889 0.000 1.000
#> GSM26834 2 0.000 0.889 0.000 1.000
#> GSM26835 2 0.000 0.889 0.000 1.000
#> GSM26836 1 0.760 0.835 0.780 0.220
#> GSM26837 1 0.760 0.835 0.780 0.220
#> GSM26838 1 0.760 0.835 0.780 0.220
#> GSM26839 1 0.760 0.835 0.780 0.220
#> GSM26840 1 0.760 0.835 0.780 0.220
#> GSM26841 1 0.760 0.835 0.780 0.220
#> GSM26842 1 0.760 0.835 0.780 0.220
#> GSM26843 1 0.760 0.835 0.780 0.220
#> GSM26844 1 0.760 0.835 0.780 0.220
#> GSM26845 1 0.760 0.835 0.780 0.220
#> GSM26846 1 0.760 0.835 0.780 0.220
#> GSM26847 1 0.760 0.835 0.780 0.220
#> GSM26848 1 0.760 0.835 0.780 0.220
#> GSM26849 1 0.760 0.835 0.780 0.220
#> GSM26850 1 0.760 0.835 0.780 0.220
#> GSM26851 2 0.760 0.761 0.220 0.780
#> GSM26852 1 0.680 0.652 0.820 0.180
#> GSM26853 1 0.680 0.652 0.820 0.180
#> GSM26854 1 0.680 0.652 0.820 0.180
#> GSM26855 1 0.680 0.652 0.820 0.180
#> GSM26856 1 0.680 0.652 0.820 0.180
#> GSM26857 1 0.680 0.652 0.820 0.180
#> GSM26858 1 0.680 0.652 0.820 0.180
#> GSM26859 1 0.680 0.652 0.820 0.180
#> GSM26860 1 0.680 0.652 0.820 0.180
#> GSM26861 1 0.680 0.652 0.820 0.180
#> GSM26862 1 0.760 0.835 0.780 0.220
#> GSM26863 1 0.760 0.835 0.780 0.220
#> GSM26864 1 0.760 0.835 0.780 0.220
#> GSM26865 1 0.760 0.835 0.780 0.220
#> GSM26866 1 0.760 0.835 0.780 0.220
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM26805 2 0.480 0.9076 0.220 0.780 0.000
#> GSM26806 2 0.000 0.8010 0.000 1.000 0.000
#> GSM26807 2 0.000 0.8010 0.000 1.000 0.000
#> GSM26808 2 0.000 0.8010 0.000 1.000 0.000
#> GSM26809 1 0.615 0.0125 0.592 0.408 0.000
#> GSM26810 2 0.000 0.8010 0.000 1.000 0.000
#> GSM26811 2 0.000 0.8010 0.000 1.000 0.000
#> GSM26812 2 0.000 0.8010 0.000 1.000 0.000
#> GSM26813 2 0.480 0.9076 0.220 0.780 0.000
#> GSM26814 2 0.480 0.9076 0.220 0.780 0.000
#> GSM26815 2 0.000 0.8010 0.000 1.000 0.000
#> GSM26816 2 0.480 0.9076 0.220 0.780 0.000
#> GSM26817 2 0.000 0.8010 0.000 1.000 0.000
#> GSM26818 3 0.000 1.0000 0.000 0.000 1.000
#> GSM26819 2 0.480 0.9076 0.220 0.780 0.000
#> GSM26820 2 0.480 0.9076 0.220 0.780 0.000
#> GSM26821 2 0.480 0.9076 0.220 0.780 0.000
#> GSM26822 2 0.480 0.9076 0.220 0.780 0.000
#> GSM26823 2 0.480 0.9076 0.220 0.780 0.000
#> GSM26824 2 0.480 0.9076 0.220 0.780 0.000
#> GSM26825 2 0.480 0.9076 0.220 0.780 0.000
#> GSM26826 2 0.480 0.9076 0.220 0.780 0.000
#> GSM26827 2 0.480 0.9076 0.220 0.780 0.000
#> GSM26828 2 0.480 0.9076 0.220 0.780 0.000
#> GSM26829 2 0.480 0.9076 0.220 0.780 0.000
#> GSM26830 2 0.480 0.9076 0.220 0.780 0.000
#> GSM26831 2 0.480 0.9076 0.220 0.780 0.000
#> GSM26832 2 0.480 0.9076 0.220 0.780 0.000
#> GSM26833 2 0.480 0.9076 0.220 0.780 0.000
#> GSM26834 2 0.480 0.9076 0.220 0.780 0.000
#> GSM26835 2 0.480 0.9076 0.220 0.780 0.000
#> GSM26836 1 0.000 0.9476 1.000 0.000 0.000
#> GSM26837 1 0.000 0.9476 1.000 0.000 0.000
#> GSM26838 1 0.000 0.9476 1.000 0.000 0.000
#> GSM26839 1 0.000 0.9476 1.000 0.000 0.000
#> GSM26840 1 0.000 0.9476 1.000 0.000 0.000
#> GSM26841 1 0.000 0.9476 1.000 0.000 0.000
#> GSM26842 1 0.000 0.9476 1.000 0.000 0.000
#> GSM26843 1 0.000 0.9476 1.000 0.000 0.000
#> GSM26844 1 0.000 0.9476 1.000 0.000 0.000
#> GSM26845 1 0.000 0.9476 1.000 0.000 0.000
#> GSM26846 1 0.000 0.9476 1.000 0.000 0.000
#> GSM26847 1 0.000 0.9476 1.000 0.000 0.000
#> GSM26848 1 0.355 0.8547 0.868 0.000 0.132
#> GSM26849 1 0.355 0.8547 0.868 0.000 0.132
#> GSM26850 1 0.355 0.8547 0.868 0.000 0.132
#> GSM26851 2 0.000 0.8010 0.000 1.000 0.000
#> GSM26852 3 0.000 1.0000 0.000 0.000 1.000
#> GSM26853 3 0.000 1.0000 0.000 0.000 1.000
#> GSM26854 3 0.000 1.0000 0.000 0.000 1.000
#> GSM26855 3 0.000 1.0000 0.000 0.000 1.000
#> GSM26856 3 0.000 1.0000 0.000 0.000 1.000
#> GSM26857 3 0.000 1.0000 0.000 0.000 1.000
#> GSM26858 3 0.000 1.0000 0.000 0.000 1.000
#> GSM26859 3 0.000 1.0000 0.000 0.000 1.000
#> GSM26860 3 0.000 1.0000 0.000 0.000 1.000
#> GSM26861 3 0.000 1.0000 0.000 0.000 1.000
#> GSM26862 1 0.000 0.9476 1.000 0.000 0.000
#> GSM26863 1 0.000 0.9476 1.000 0.000 0.000
#> GSM26864 1 0.000 0.9476 1.000 0.000 0.000
#> GSM26865 1 0.355 0.8547 0.868 0.000 0.132
#> GSM26866 1 0.000 0.9476 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM26805 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM26806 4 0.3569 0.995 0.000 0.196 0.000 0.804
#> GSM26807 4 0.3569 0.995 0.000 0.196 0.000 0.804
#> GSM26808 4 0.3569 0.995 0.000 0.196 0.000 0.804
#> GSM26809 2 0.7589 -0.079 0.396 0.408 0.000 0.196
#> GSM26810 4 0.3569 0.995 0.000 0.196 0.000 0.804
#> GSM26811 4 0.3569 0.995 0.000 0.196 0.000 0.804
#> GSM26812 4 0.3569 0.995 0.000 0.196 0.000 0.804
#> GSM26813 2 0.0336 0.933 0.000 0.992 0.000 0.008
#> GSM26814 2 0.0336 0.933 0.000 0.992 0.000 0.008
#> GSM26815 4 0.3569 0.995 0.000 0.196 0.000 0.804
#> GSM26816 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM26817 4 0.3837 0.962 0.000 0.224 0.000 0.776
#> GSM26818 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26819 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM26820 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM26821 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM26822 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM26823 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM26824 2 0.0336 0.933 0.000 0.992 0.000 0.008
#> GSM26825 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM26826 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM26827 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM26828 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM26829 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM26830 2 0.0336 0.933 0.000 0.992 0.000 0.008
#> GSM26831 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM26832 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM26833 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM26834 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM26835 2 0.0000 0.939 0.000 1.000 0.000 0.000
#> GSM26836 1 0.0000 0.884 1.000 0.000 0.000 0.000
#> GSM26837 1 0.0000 0.884 1.000 0.000 0.000 0.000
#> GSM26838 1 0.0000 0.884 1.000 0.000 0.000 0.000
#> GSM26839 1 0.0000 0.884 1.000 0.000 0.000 0.000
#> GSM26840 1 0.3569 0.742 0.804 0.000 0.000 0.196
#> GSM26841 1 0.0000 0.884 1.000 0.000 0.000 0.000
#> GSM26842 1 0.0000 0.884 1.000 0.000 0.000 0.000
#> GSM26843 1 0.0000 0.884 1.000 0.000 0.000 0.000
#> GSM26844 1 0.0000 0.884 1.000 0.000 0.000 0.000
#> GSM26845 1 0.0000 0.884 1.000 0.000 0.000 0.000
#> GSM26846 1 0.3801 0.739 0.780 0.220 0.000 0.000
#> GSM26847 1 0.3801 0.739 0.780 0.220 0.000 0.000
#> GSM26848 1 0.6359 0.671 0.648 0.220 0.132 0.000
#> GSM26849 1 0.6359 0.671 0.648 0.220 0.132 0.000
#> GSM26850 1 0.6359 0.671 0.648 0.220 0.132 0.000
#> GSM26851 2 0.4907 -0.122 0.000 0.580 0.000 0.420
#> GSM26852 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26853 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26854 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26855 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26856 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26857 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26858 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26859 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26860 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26861 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26862 1 0.0000 0.884 1.000 0.000 0.000 0.000
#> GSM26863 1 0.0000 0.884 1.000 0.000 0.000 0.000
#> GSM26864 1 0.0000 0.884 1.000 0.000 0.000 0.000
#> GSM26865 1 0.6359 0.671 0.648 0.220 0.132 0.000
#> GSM26866 1 0.0000 0.884 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
#> GSM26805 2 0.0000 0.9702 0.000 1.000 0.000 0.000 0.000
#> GSM26806 4 0.0000 0.9938 0.000 0.000 0.000 1.000 0.000
#> GSM26807 4 0.0000 0.9938 0.000 0.000 0.000 1.000 0.000
#> GSM26808 4 0.0000 0.9938 0.000 0.000 0.000 1.000 0.000
#> GSM26809 5 0.5747 0.1490 0.088 0.408 0.000 0.000 0.504
#> GSM26810 4 0.0000 0.9938 0.000 0.000 0.000 1.000 0.000
#> GSM26811 4 0.0000 0.9938 0.000 0.000 0.000 1.000 0.000
#> GSM26812 4 0.0000 0.9938 0.000 0.000 0.000 1.000 0.000
#> GSM26813 2 0.0290 0.9634 0.000 0.992 0.000 0.008 0.000
#> GSM26814 2 0.0290 0.9634 0.000 0.992 0.000 0.008 0.000
#> GSM26815 4 0.0000 0.9938 0.000 0.000 0.000 1.000 0.000
#> GSM26816 2 0.0000 0.9702 0.000 1.000 0.000 0.000 0.000
#> GSM26817 4 0.0794 0.9556 0.000 0.028 0.000 0.972 0.000
#> GSM26818 3 0.1908 0.9045 0.000 0.000 0.908 0.000 0.092
#> GSM26819 2 0.0000 0.9702 0.000 1.000 0.000 0.000 0.000
#> GSM26820 2 0.0000 0.9702 0.000 1.000 0.000 0.000 0.000
#> GSM26821 2 0.0000 0.9702 0.000 1.000 0.000 0.000 0.000
#> GSM26822 2 0.0000 0.9702 0.000 1.000 0.000 0.000 0.000
#> GSM26823 2 0.0000 0.9702 0.000 1.000 0.000 0.000 0.000
#> GSM26824 2 0.0290 0.9634 0.000 0.992 0.000 0.008 0.000
#> GSM26825 2 0.0000 0.9702 0.000 1.000 0.000 0.000 0.000
#> GSM26826 2 0.0000 0.9702 0.000 1.000 0.000 0.000 0.000
#> GSM26827 2 0.0000 0.9702 0.000 1.000 0.000 0.000 0.000
#> GSM26828 2 0.0000 0.9702 0.000 1.000 0.000 0.000 0.000
#> GSM26829 2 0.0000 0.9702 0.000 1.000 0.000 0.000 0.000
#> GSM26830 2 0.0290 0.9634 0.000 0.992 0.000 0.008 0.000
#> GSM26831 2 0.0000 0.9702 0.000 1.000 0.000 0.000 0.000
#> GSM26832 2 0.0000 0.9702 0.000 1.000 0.000 0.000 0.000
#> GSM26833 2 0.0000 0.9702 0.000 1.000 0.000 0.000 0.000
#> GSM26834 2 0.0000 0.9702 0.000 1.000 0.000 0.000 0.000
#> GSM26835 2 0.0000 0.9702 0.000 1.000 0.000 0.000 0.000
#> GSM26836 1 0.0000 0.7618 1.000 0.000 0.000 0.000 0.000
#> GSM26837 1 0.0000 0.7618 1.000 0.000 0.000 0.000 0.000
#> GSM26838 1 0.0000 0.7618 1.000 0.000 0.000 0.000 0.000
#> GSM26839 1 0.0000 0.7618 1.000 0.000 0.000 0.000 0.000
#> GSM26840 5 0.4302 -0.0993 0.480 0.000 0.000 0.000 0.520
#> GSM26841 1 0.0404 0.7593 0.988 0.000 0.000 0.000 0.012
#> GSM26842 1 0.0404 0.7593 0.988 0.000 0.000 0.000 0.012
#> GSM26843 1 0.0404 0.7593 0.988 0.000 0.000 0.000 0.012
#> GSM26844 1 0.0404 0.7593 0.988 0.000 0.000 0.000 0.012
#> GSM26845 1 0.2773 0.6117 0.836 0.000 0.000 0.000 0.164
#> GSM26846 1 0.6265 0.3713 0.540 0.220 0.000 0.000 0.240
#> GSM26847 1 0.6265 0.3713 0.540 0.220 0.000 0.000 0.240
#> GSM26848 1 0.6717 0.4255 0.572 0.220 0.040 0.000 0.168
#> GSM26849 1 0.6717 0.4255 0.572 0.220 0.040 0.000 0.168
#> GSM26850 1 0.6717 0.4255 0.572 0.220 0.040 0.000 0.168
#> GSM26851 2 0.6024 0.1178 0.000 0.556 0.000 0.296 0.148
#> GSM26852 3 0.0000 0.9910 0.000 0.000 1.000 0.000 0.000
#> GSM26853 3 0.0000 0.9910 0.000 0.000 1.000 0.000 0.000
#> GSM26854 3 0.0000 0.9910 0.000 0.000 1.000 0.000 0.000
#> GSM26855 3 0.0000 0.9910 0.000 0.000 1.000 0.000 0.000
#> GSM26856 3 0.0000 0.9910 0.000 0.000 1.000 0.000 0.000
#> GSM26857 3 0.0000 0.9910 0.000 0.000 1.000 0.000 0.000
#> GSM26858 3 0.0000 0.9910 0.000 0.000 1.000 0.000 0.000
#> GSM26859 3 0.0000 0.9910 0.000 0.000 1.000 0.000 0.000
#> GSM26860 3 0.0000 0.9910 0.000 0.000 1.000 0.000 0.000
#> GSM26861 3 0.0000 0.9910 0.000 0.000 1.000 0.000 0.000
#> GSM26862 1 0.0000 0.7618 1.000 0.000 0.000 0.000 0.000
#> GSM26863 1 0.0000 0.7618 1.000 0.000 0.000 0.000 0.000
#> GSM26864 1 0.0404 0.7593 0.988 0.000 0.000 0.000 0.012
#> GSM26865 1 0.6717 0.4255 0.572 0.220 0.040 0.000 0.168
#> GSM26866 1 0.0404 0.7593 0.988 0.000 0.000 0.000 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM26805 2 0.0000 0.9978 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26806 4 0.0000 0.9920 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26807 4 0.0000 0.9920 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26808 4 0.0000 0.9920 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26809 6 0.3774 -0.2100 0.000 0.408 0.000 0.000 0.000 0.592
#> GSM26810 4 0.0000 0.9920 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26811 4 0.0000 0.9920 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26812 4 0.0000 0.9920 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26813 2 0.0260 0.9906 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM26814 2 0.0260 0.9906 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM26815 4 0.0000 0.9920 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26816 2 0.0000 0.9978 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26817 4 0.0713 0.9424 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM26818 3 0.2510 0.8432 0.000 0.000 0.872 0.000 0.100 0.028
#> GSM26819 2 0.0000 0.9978 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26820 2 0.0000 0.9978 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26821 2 0.0000 0.9978 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26822 2 0.0000 0.9978 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26823 2 0.0000 0.9978 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26824 2 0.0260 0.9906 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM26825 2 0.0000 0.9978 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26826 2 0.0000 0.9978 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26827 2 0.0000 0.9978 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26828 2 0.0000 0.9978 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26829 2 0.0000 0.9978 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26830 2 0.0260 0.9906 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM26831 2 0.0000 0.9978 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26832 2 0.0000 0.9978 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26833 2 0.0000 0.9978 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26834 2 0.0000 0.9978 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26835 2 0.0000 0.9978 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26836 1 0.0000 0.7644 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26837 1 0.0000 0.7644 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26838 1 0.0000 0.7644 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26839 1 0.0000 0.7644 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26840 6 0.3737 -0.0928 0.392 0.000 0.000 0.000 0.000 0.608
#> GSM26841 1 0.0363 0.7632 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM26842 1 0.0363 0.7632 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM26843 1 0.0363 0.7632 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM26844 1 0.0363 0.7632 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM26845 1 0.3266 0.4280 0.728 0.000 0.000 0.000 0.000 0.272
#> GSM26846 6 0.7278 0.2797 0.308 0.220 0.000 0.000 0.108 0.364
#> GSM26847 6 0.7278 0.2797 0.308 0.220 0.000 0.000 0.108 0.364
#> GSM26848 1 0.7233 -0.1005 0.448 0.220 0.004 0.000 0.208 0.120
#> GSM26849 1 0.7233 -0.1005 0.448 0.220 0.004 0.000 0.208 0.120
#> GSM26850 1 0.7233 -0.1005 0.448 0.220 0.004 0.000 0.208 0.120
#> GSM26851 5 0.3657 0.0000 0.000 0.108 0.000 0.100 0.792 0.000
#> GSM26852 3 0.0000 0.9857 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26853 3 0.0000 0.9857 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26854 3 0.0000 0.9857 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26855 3 0.0000 0.9857 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26856 3 0.0000 0.9857 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26857 3 0.0000 0.9857 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26858 3 0.0000 0.9857 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26859 3 0.0000 0.9857 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26860 3 0.0000 0.9857 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26861 3 0.0000 0.9857 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26862 1 0.0000 0.7644 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26863 1 0.0000 0.7644 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26864 1 0.0363 0.7632 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM26865 1 0.7233 -0.1005 0.448 0.220 0.004 0.000 0.208 0.120
#> GSM26866 1 0.0363 0.7632 0.988 0.000 0.000 0.000 0.000 0.012
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> CV:hclust 61 1.90e-12 7.88e-01 2
#> CV:hclust 61 2.42e-12 6.35e-05 3
#> CV:hclust 60 3.51e-12 3.82e-07 4
#> CV:hclust 53 1.13e-10 1.55e-06 5
#> CV:hclust 52 1.86e-10 7.42e-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", "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 11993 rows and 62 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.648 0.946 0.947 0.4906 0.492 0.492
#> 3 3 0.762 0.842 0.850 0.2630 0.884 0.763
#> 4 4 0.673 0.883 0.856 0.1325 0.887 0.703
#> 5 5 0.745 0.739 0.845 0.0863 0.967 0.881
#> 6 6 0.793 0.562 0.744 0.0508 0.897 0.621
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
#> GSM26805 2 0.000 0.978 0.000 1.000
#> GSM26806 2 0.388 0.932 0.076 0.924
#> GSM26807 2 0.388 0.932 0.076 0.924
#> GSM26808 2 0.373 0.935 0.072 0.928
#> GSM26809 2 0.000 0.978 0.000 1.000
#> GSM26810 2 0.388 0.932 0.076 0.924
#> GSM26811 2 0.373 0.935 0.072 0.928
#> GSM26812 2 0.388 0.932 0.076 0.924
#> GSM26813 2 0.000 0.978 0.000 1.000
#> GSM26814 2 0.000 0.978 0.000 1.000
#> GSM26815 2 0.388 0.932 0.076 0.924
#> GSM26816 2 0.000 0.978 0.000 1.000
#> GSM26817 2 0.295 0.948 0.052 0.948
#> GSM26818 1 0.000 0.905 1.000 0.000
#> GSM26819 2 0.000 0.978 0.000 1.000
#> GSM26820 2 0.000 0.978 0.000 1.000
#> GSM26821 2 0.000 0.978 0.000 1.000
#> GSM26822 2 0.000 0.978 0.000 1.000
#> GSM26823 2 0.000 0.978 0.000 1.000
#> GSM26824 2 0.000 0.978 0.000 1.000
#> GSM26825 2 0.000 0.978 0.000 1.000
#> GSM26826 2 0.000 0.978 0.000 1.000
#> GSM26827 2 0.000 0.978 0.000 1.000
#> GSM26828 2 0.000 0.978 0.000 1.000
#> GSM26829 2 0.000 0.978 0.000 1.000
#> GSM26830 2 0.000 0.978 0.000 1.000
#> GSM26831 2 0.000 0.978 0.000 1.000
#> GSM26832 2 0.000 0.978 0.000 1.000
#> GSM26833 2 0.000 0.978 0.000 1.000
#> GSM26834 2 0.000 0.978 0.000 1.000
#> GSM26835 2 0.000 0.978 0.000 1.000
#> GSM26836 1 0.595 0.937 0.856 0.144
#> GSM26837 1 0.595 0.937 0.856 0.144
#> GSM26838 1 0.595 0.937 0.856 0.144
#> GSM26839 1 0.595 0.937 0.856 0.144
#> GSM26840 1 0.595 0.937 0.856 0.144
#> GSM26841 1 0.595 0.937 0.856 0.144
#> GSM26842 1 0.595 0.937 0.856 0.144
#> GSM26843 1 0.595 0.937 0.856 0.144
#> GSM26844 1 0.595 0.937 0.856 0.144
#> GSM26845 1 0.595 0.937 0.856 0.144
#> GSM26846 1 0.595 0.937 0.856 0.144
#> GSM26847 1 0.595 0.937 0.856 0.144
#> GSM26848 1 0.595 0.937 0.856 0.144
#> GSM26849 1 0.000 0.905 1.000 0.000
#> GSM26850 1 0.595 0.937 0.856 0.144
#> GSM26851 2 0.000 0.978 0.000 1.000
#> GSM26852 1 0.000 0.905 1.000 0.000
#> GSM26853 1 0.000 0.905 1.000 0.000
#> GSM26854 1 0.000 0.905 1.000 0.000
#> GSM26855 1 0.000 0.905 1.000 0.000
#> GSM26856 1 0.000 0.905 1.000 0.000
#> GSM26857 1 0.000 0.905 1.000 0.000
#> GSM26858 1 0.000 0.905 1.000 0.000
#> GSM26859 1 0.000 0.905 1.000 0.000
#> GSM26860 1 0.000 0.905 1.000 0.000
#> GSM26861 1 0.000 0.905 1.000 0.000
#> GSM26862 1 0.595 0.937 0.856 0.144
#> GSM26863 1 0.595 0.937 0.856 0.144
#> GSM26864 1 0.595 0.937 0.856 0.144
#> GSM26865 1 0.595 0.937 0.856 0.144
#> GSM26866 1 0.595 0.937 0.856 0.144
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM26805 2 0.0000 0.898 0.000 1.000 0.000
#> GSM26806 2 0.6225 0.666 0.000 0.568 0.432
#> GSM26807 2 0.6225 0.666 0.000 0.568 0.432
#> GSM26808 2 0.6225 0.666 0.000 0.568 0.432
#> GSM26809 2 0.0000 0.898 0.000 1.000 0.000
#> GSM26810 2 0.6225 0.666 0.000 0.568 0.432
#> GSM26811 2 0.6225 0.666 0.000 0.568 0.432
#> GSM26812 2 0.6225 0.666 0.000 0.568 0.432
#> GSM26813 2 0.0237 0.896 0.000 0.996 0.004
#> GSM26814 2 0.0237 0.896 0.000 0.996 0.004
#> GSM26815 2 0.6225 0.666 0.000 0.568 0.432
#> GSM26816 2 0.0000 0.898 0.000 1.000 0.000
#> GSM26817 2 0.5397 0.756 0.000 0.720 0.280
#> GSM26818 3 0.6057 0.820 0.340 0.004 0.656
#> GSM26819 2 0.0000 0.898 0.000 1.000 0.000
#> GSM26820 2 0.0000 0.898 0.000 1.000 0.000
#> GSM26821 2 0.0000 0.898 0.000 1.000 0.000
#> GSM26822 2 0.0000 0.898 0.000 1.000 0.000
#> GSM26823 2 0.0000 0.898 0.000 1.000 0.000
#> GSM26824 2 0.0000 0.898 0.000 1.000 0.000
#> GSM26825 2 0.0000 0.898 0.000 1.000 0.000
#> GSM26826 2 0.0000 0.898 0.000 1.000 0.000
#> GSM26827 2 0.0000 0.898 0.000 1.000 0.000
#> GSM26828 2 0.0000 0.898 0.000 1.000 0.000
#> GSM26829 2 0.0000 0.898 0.000 1.000 0.000
#> GSM26830 2 0.0237 0.896 0.000 0.996 0.004
#> GSM26831 2 0.0000 0.898 0.000 1.000 0.000
#> GSM26832 2 0.0000 0.898 0.000 1.000 0.000
#> GSM26833 2 0.0000 0.898 0.000 1.000 0.000
#> GSM26834 2 0.0000 0.898 0.000 1.000 0.000
#> GSM26835 2 0.0000 0.898 0.000 1.000 0.000
#> GSM26836 1 0.0747 0.899 0.984 0.016 0.000
#> GSM26837 1 0.0747 0.899 0.984 0.016 0.000
#> GSM26838 1 0.0747 0.899 0.984 0.016 0.000
#> GSM26839 1 0.0747 0.899 0.984 0.016 0.000
#> GSM26840 1 0.2280 0.835 0.940 0.052 0.008
#> GSM26841 1 0.0747 0.899 0.984 0.016 0.000
#> GSM26842 1 0.0747 0.899 0.984 0.016 0.000
#> GSM26843 1 0.0747 0.899 0.984 0.016 0.000
#> GSM26844 1 0.0747 0.899 0.984 0.016 0.000
#> GSM26845 1 0.6745 0.235 0.560 0.428 0.012
#> GSM26846 1 0.1482 0.889 0.968 0.020 0.012
#> GSM26847 1 0.1170 0.894 0.976 0.016 0.008
#> GSM26848 1 0.1315 0.892 0.972 0.020 0.008
#> GSM26849 1 0.6460 -0.717 0.556 0.004 0.440
#> GSM26850 1 0.1315 0.892 0.972 0.020 0.008
#> GSM26851 2 0.4399 0.809 0.000 0.812 0.188
#> GSM26852 3 0.6460 0.981 0.440 0.004 0.556
#> GSM26853 3 0.6460 0.981 0.440 0.004 0.556
#> GSM26854 3 0.6460 0.981 0.440 0.004 0.556
#> GSM26855 3 0.6460 0.981 0.440 0.004 0.556
#> GSM26856 3 0.6460 0.981 0.440 0.004 0.556
#> GSM26857 3 0.6460 0.981 0.440 0.004 0.556
#> GSM26858 3 0.6460 0.981 0.440 0.004 0.556
#> GSM26859 3 0.6460 0.981 0.440 0.004 0.556
#> GSM26860 3 0.6460 0.981 0.440 0.004 0.556
#> GSM26861 3 0.6460 0.981 0.440 0.004 0.556
#> GSM26862 1 0.0747 0.899 0.984 0.016 0.000
#> GSM26863 1 0.0747 0.899 0.984 0.016 0.000
#> GSM26864 1 0.0747 0.899 0.984 0.016 0.000
#> GSM26865 1 0.1170 0.894 0.976 0.016 0.008
#> GSM26866 1 0.0747 0.899 0.984 0.016 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM26805 2 0.2814 0.875 0.132 0.868 0.000 0.000
#> GSM26806 4 0.4008 0.954 0.000 0.244 0.000 0.756
#> GSM26807 4 0.4008 0.954 0.000 0.244 0.000 0.756
#> GSM26808 4 0.4008 0.954 0.000 0.244 0.000 0.756
#> GSM26809 2 0.2521 0.883 0.064 0.912 0.000 0.024
#> GSM26810 4 0.4008 0.954 0.000 0.244 0.000 0.756
#> GSM26811 4 0.4008 0.954 0.000 0.244 0.000 0.756
#> GSM26812 4 0.4008 0.954 0.000 0.244 0.000 0.756
#> GSM26813 2 0.0469 0.896 0.012 0.988 0.000 0.000
#> GSM26814 2 0.0469 0.896 0.012 0.988 0.000 0.000
#> GSM26815 4 0.4328 0.950 0.008 0.244 0.000 0.748
#> GSM26816 2 0.2921 0.873 0.140 0.860 0.000 0.000
#> GSM26817 4 0.6727 0.561 0.092 0.412 0.000 0.496
#> GSM26818 3 0.2198 0.900 0.008 0.000 0.920 0.072
#> GSM26819 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM26820 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM26821 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM26822 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM26823 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM26824 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM26825 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM26826 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM26827 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM26828 2 0.2921 0.873 0.140 0.860 0.000 0.000
#> GSM26829 2 0.2647 0.879 0.120 0.880 0.000 0.000
#> GSM26830 2 0.0469 0.896 0.012 0.988 0.000 0.000
#> GSM26831 2 0.3400 0.850 0.180 0.820 0.000 0.000
#> GSM26832 2 0.3400 0.850 0.180 0.820 0.000 0.000
#> GSM26833 2 0.3400 0.850 0.180 0.820 0.000 0.000
#> GSM26834 2 0.3400 0.850 0.180 0.820 0.000 0.000
#> GSM26835 2 0.3400 0.850 0.180 0.820 0.000 0.000
#> GSM26836 1 0.3764 0.890 0.784 0.000 0.216 0.000
#> GSM26837 1 0.3764 0.890 0.784 0.000 0.216 0.000
#> GSM26838 1 0.4086 0.889 0.776 0.000 0.216 0.008
#> GSM26839 1 0.4086 0.889 0.776 0.000 0.216 0.008
#> GSM26840 1 0.5649 0.828 0.732 0.004 0.148 0.116
#> GSM26841 1 0.5809 0.891 0.692 0.000 0.216 0.092
#> GSM26842 1 0.5809 0.891 0.692 0.000 0.216 0.092
#> GSM26843 1 0.5809 0.891 0.692 0.000 0.216 0.092
#> GSM26844 1 0.5809 0.891 0.692 0.000 0.216 0.092
#> GSM26845 1 0.5891 0.594 0.700 0.168 0.000 0.132
#> GSM26846 1 0.6215 0.832 0.664 0.000 0.208 0.128
#> GSM26847 1 0.6281 0.836 0.656 0.000 0.216 0.128
#> GSM26848 1 0.7036 0.845 0.576 0.000 0.216 0.208
#> GSM26849 3 0.5604 0.583 0.116 0.000 0.724 0.160
#> GSM26850 1 0.7036 0.845 0.576 0.000 0.216 0.208
#> GSM26851 2 0.6058 0.629 0.180 0.684 0.000 0.136
#> GSM26852 3 0.0000 0.965 0.000 0.000 1.000 0.000
#> GSM26853 3 0.0000 0.965 0.000 0.000 1.000 0.000
#> GSM26854 3 0.0000 0.965 0.000 0.000 1.000 0.000
#> GSM26855 3 0.0000 0.965 0.000 0.000 1.000 0.000
#> GSM26856 3 0.0000 0.965 0.000 0.000 1.000 0.000
#> GSM26857 3 0.0000 0.965 0.000 0.000 1.000 0.000
#> GSM26858 3 0.0000 0.965 0.000 0.000 1.000 0.000
#> GSM26859 3 0.0000 0.965 0.000 0.000 1.000 0.000
#> GSM26860 3 0.0000 0.965 0.000 0.000 1.000 0.000
#> GSM26861 3 0.0000 0.965 0.000 0.000 1.000 0.000
#> GSM26862 1 0.3764 0.890 0.784 0.000 0.216 0.000
#> GSM26863 1 0.3764 0.890 0.784 0.000 0.216 0.000
#> GSM26864 1 0.5809 0.891 0.692 0.000 0.216 0.092
#> GSM26865 1 0.7065 0.844 0.572 0.000 0.216 0.212
#> GSM26866 1 0.5809 0.891 0.692 0.000 0.216 0.092
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM26805 2 0.3143 0.828 0.000 0.796 0.000 0.000 0.204
#> GSM26806 4 0.2280 0.949 0.000 0.120 0.000 0.880 0.000
#> GSM26807 4 0.2280 0.949 0.000 0.120 0.000 0.880 0.000
#> GSM26808 4 0.2280 0.949 0.000 0.120 0.000 0.880 0.000
#> GSM26809 2 0.1469 0.839 0.000 0.948 0.000 0.016 0.036
#> GSM26810 4 0.2280 0.949 0.000 0.120 0.000 0.880 0.000
#> GSM26811 4 0.2280 0.949 0.000 0.120 0.000 0.880 0.000
#> GSM26812 4 0.2280 0.949 0.000 0.120 0.000 0.880 0.000
#> GSM26813 2 0.1357 0.859 0.000 0.948 0.004 0.000 0.048
#> GSM26814 2 0.1357 0.859 0.000 0.948 0.004 0.000 0.048
#> GSM26815 4 0.3059 0.938 0.000 0.120 0.008 0.856 0.016
#> GSM26816 2 0.3210 0.826 0.000 0.788 0.000 0.000 0.212
#> GSM26817 4 0.6440 0.564 0.000 0.272 0.012 0.548 0.168
#> GSM26818 3 0.2270 0.910 0.020 0.000 0.904 0.000 0.076
#> GSM26819 2 0.0000 0.865 0.000 1.000 0.000 0.000 0.000
#> GSM26820 2 0.0000 0.865 0.000 1.000 0.000 0.000 0.000
#> GSM26821 2 0.0671 0.861 0.000 0.980 0.004 0.000 0.016
#> GSM26822 2 0.0000 0.865 0.000 1.000 0.000 0.000 0.000
#> GSM26823 2 0.0000 0.865 0.000 1.000 0.000 0.000 0.000
#> GSM26824 2 0.0771 0.859 0.000 0.976 0.004 0.000 0.020
#> GSM26825 2 0.0000 0.865 0.000 1.000 0.000 0.000 0.000
#> GSM26826 2 0.0290 0.863 0.000 0.992 0.000 0.000 0.008
#> GSM26827 2 0.0000 0.865 0.000 1.000 0.000 0.000 0.000
#> GSM26828 2 0.3143 0.827 0.000 0.796 0.000 0.000 0.204
#> GSM26829 2 0.2929 0.834 0.000 0.820 0.000 0.000 0.180
#> GSM26830 2 0.1357 0.859 0.000 0.948 0.004 0.000 0.048
#> GSM26831 2 0.3707 0.786 0.000 0.716 0.000 0.000 0.284
#> GSM26832 2 0.3707 0.786 0.000 0.716 0.000 0.000 0.284
#> GSM26833 2 0.3796 0.781 0.000 0.700 0.000 0.000 0.300
#> GSM26834 2 0.3707 0.786 0.000 0.716 0.000 0.000 0.284
#> GSM26835 2 0.3707 0.786 0.000 0.716 0.000 0.000 0.284
#> GSM26836 1 0.1041 0.610 0.964 0.000 0.004 0.000 0.032
#> GSM26837 1 0.1041 0.610 0.964 0.000 0.004 0.000 0.032
#> GSM26838 1 0.0162 0.624 0.996 0.000 0.004 0.000 0.000
#> GSM26839 1 0.0162 0.624 0.996 0.000 0.004 0.000 0.000
#> GSM26840 1 0.4734 0.589 0.728 0.000 0.000 0.096 0.176
#> GSM26841 1 0.4450 0.631 0.764 0.000 0.004 0.080 0.152
#> GSM26842 1 0.4450 0.631 0.764 0.000 0.004 0.080 0.152
#> GSM26843 1 0.4450 0.631 0.764 0.000 0.004 0.080 0.152
#> GSM26844 1 0.4450 0.631 0.764 0.000 0.004 0.080 0.152
#> GSM26845 1 0.5195 -0.315 0.608 0.016 0.000 0.028 0.348
#> GSM26846 1 0.4848 -0.452 0.556 0.000 0.000 0.024 0.420
#> GSM26847 1 0.4639 -0.308 0.632 0.000 0.000 0.024 0.344
#> GSM26848 5 0.4283 0.570 0.456 0.000 0.000 0.000 0.544
#> GSM26849 5 0.6294 0.153 0.152 0.000 0.404 0.000 0.444
#> GSM26850 5 0.4283 0.570 0.456 0.000 0.000 0.000 0.544
#> GSM26851 2 0.6149 0.550 0.000 0.548 0.004 0.140 0.308
#> GSM26852 3 0.0510 0.992 0.016 0.000 0.984 0.000 0.000
#> GSM26853 3 0.0510 0.992 0.016 0.000 0.984 0.000 0.000
#> GSM26854 3 0.0510 0.992 0.016 0.000 0.984 0.000 0.000
#> GSM26855 3 0.0510 0.992 0.016 0.000 0.984 0.000 0.000
#> GSM26856 3 0.0510 0.992 0.016 0.000 0.984 0.000 0.000
#> GSM26857 3 0.0510 0.992 0.016 0.000 0.984 0.000 0.000
#> GSM26858 3 0.0510 0.992 0.016 0.000 0.984 0.000 0.000
#> GSM26859 3 0.0510 0.992 0.016 0.000 0.984 0.000 0.000
#> GSM26860 3 0.0510 0.992 0.016 0.000 0.984 0.000 0.000
#> GSM26861 3 0.0510 0.992 0.016 0.000 0.984 0.000 0.000
#> GSM26862 1 0.1041 0.610 0.964 0.000 0.004 0.000 0.032
#> GSM26863 1 0.1041 0.610 0.964 0.000 0.004 0.000 0.032
#> GSM26864 1 0.4450 0.631 0.764 0.000 0.004 0.080 0.152
#> GSM26865 5 0.4278 0.567 0.452 0.000 0.000 0.000 0.548
#> GSM26866 1 0.4450 0.631 0.764 0.000 0.004 0.080 0.152
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM26805 2 0.4468 -0.576 0.000 0.560 0.000 0.000 0.408 0.032
#> GSM26806 4 0.0713 0.918 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM26807 4 0.0713 0.918 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM26808 4 0.0713 0.918 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM26809 2 0.2669 0.631 0.000 0.880 0.000 0.016 0.032 0.072
#> GSM26810 4 0.0713 0.918 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM26811 4 0.0713 0.918 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM26812 4 0.0713 0.918 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM26813 2 0.2728 0.653 0.000 0.860 0.000 0.000 0.040 0.100
#> GSM26814 2 0.2728 0.653 0.000 0.860 0.000 0.000 0.040 0.100
#> GSM26815 4 0.3730 0.835 0.000 0.028 0.000 0.812 0.060 0.100
#> GSM26816 2 0.4475 -0.584 0.000 0.556 0.000 0.000 0.412 0.032
#> GSM26817 4 0.7278 0.356 0.000 0.152 0.000 0.428 0.224 0.196
#> GSM26818 3 0.3042 0.807 0.004 0.000 0.836 0.000 0.128 0.032
#> GSM26819 2 0.0146 0.733 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM26820 2 0.0000 0.733 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26821 2 0.0717 0.726 0.000 0.976 0.000 0.000 0.016 0.008
#> GSM26822 2 0.0146 0.733 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM26823 2 0.0000 0.733 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26824 2 0.0891 0.719 0.000 0.968 0.000 0.000 0.024 0.008
#> GSM26825 2 0.0146 0.733 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM26826 2 0.0146 0.732 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM26827 2 0.0000 0.733 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26828 2 0.4475 -0.584 0.000 0.556 0.000 0.000 0.412 0.032
#> GSM26829 2 0.4409 -0.504 0.000 0.588 0.000 0.000 0.380 0.032
#> GSM26830 2 0.2775 0.651 0.000 0.856 0.000 0.000 0.040 0.104
#> GSM26831 5 0.3857 0.871 0.000 0.468 0.000 0.000 0.532 0.000
#> GSM26832 5 0.4089 0.868 0.000 0.468 0.000 0.000 0.524 0.008
#> GSM26833 5 0.4161 0.846 0.000 0.448 0.000 0.000 0.540 0.012
#> GSM26834 5 0.3857 0.871 0.000 0.468 0.000 0.000 0.532 0.000
#> GSM26835 5 0.3857 0.871 0.000 0.468 0.000 0.000 0.532 0.000
#> GSM26836 1 0.3672 0.346 0.632 0.000 0.000 0.000 0.000 0.368
#> GSM26837 1 0.3672 0.346 0.632 0.000 0.000 0.000 0.000 0.368
#> GSM26838 1 0.3620 0.364 0.648 0.000 0.000 0.000 0.000 0.352
#> GSM26839 1 0.3634 0.360 0.644 0.000 0.000 0.000 0.000 0.356
#> GSM26840 1 0.2095 0.486 0.916 0.000 0.000 0.016 0.028 0.040
#> GSM26841 1 0.0000 0.548 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26842 1 0.0000 0.548 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26843 1 0.0000 0.548 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26844 1 0.0000 0.548 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26845 6 0.5029 0.809 0.308 0.004 0.000 0.016 0.052 0.620
#> GSM26846 6 0.6063 0.693 0.316 0.000 0.000 0.012 0.192 0.480
#> GSM26847 6 0.4663 0.807 0.324 0.000 0.000 0.008 0.044 0.624
#> GSM26848 1 0.5937 -0.531 0.436 0.000 0.000 0.000 0.224 0.340
#> GSM26849 3 0.7470 -0.296 0.140 0.000 0.332 0.000 0.224 0.304
#> GSM26850 1 0.5937 -0.531 0.436 0.000 0.000 0.000 0.224 0.340
#> GSM26851 5 0.6314 0.537 0.000 0.292 0.004 0.112 0.532 0.060
#> GSM26852 3 0.0146 0.928 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM26853 3 0.0146 0.928 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM26854 3 0.0146 0.928 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM26855 3 0.0146 0.928 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM26856 3 0.0146 0.928 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM26857 3 0.0146 0.928 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM26858 3 0.0146 0.928 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM26859 3 0.0146 0.928 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM26860 3 0.0146 0.928 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM26861 3 0.0146 0.928 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM26862 1 0.3672 0.346 0.632 0.000 0.000 0.000 0.000 0.368
#> GSM26863 1 0.3672 0.346 0.632 0.000 0.000 0.000 0.000 0.368
#> GSM26864 1 0.0000 0.548 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26865 1 0.5932 -0.524 0.440 0.000 0.000 0.000 0.224 0.336
#> GSM26866 1 0.0000 0.548 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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> CV:kmeans 62 1.14e-12 8.30e-01 2
#> CV:kmeans 60 4.01e-12 1.05e-04 3
#> CV:kmeans 62 8.75e-12 2.79e-06 4
#> CV:kmeans 58 2.84e-10 2.75e-07 5
#> CV:kmeans 46 2.48e-07 1.00e-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 11993 rows and 62 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 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 0.5087 0.492 0.492
#> 3 3 1.000 0.979 0.987 0.2389 0.879 0.755
#> 4 4 1.000 0.971 0.976 0.1623 0.895 0.718
#> 5 5 0.898 0.898 0.900 0.0685 0.959 0.845
#> 6 6 0.890 0.871 0.860 0.0607 0.938 0.725
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
#> GSM26805 2 0 1 0 1
#> GSM26806 2 0 1 0 1
#> GSM26807 2 0 1 0 1
#> GSM26808 2 0 1 0 1
#> GSM26809 2 0 1 0 1
#> GSM26810 2 0 1 0 1
#> GSM26811 2 0 1 0 1
#> GSM26812 2 0 1 0 1
#> GSM26813 2 0 1 0 1
#> GSM26814 2 0 1 0 1
#> GSM26815 2 0 1 0 1
#> GSM26816 2 0 1 0 1
#> GSM26817 2 0 1 0 1
#> GSM26818 1 0 1 1 0
#> GSM26819 2 0 1 0 1
#> GSM26820 2 0 1 0 1
#> GSM26821 2 0 1 0 1
#> GSM26822 2 0 1 0 1
#> GSM26823 2 0 1 0 1
#> GSM26824 2 0 1 0 1
#> GSM26825 2 0 1 0 1
#> GSM26826 2 0 1 0 1
#> GSM26827 2 0 1 0 1
#> GSM26828 2 0 1 0 1
#> GSM26829 2 0 1 0 1
#> GSM26830 2 0 1 0 1
#> GSM26831 2 0 1 0 1
#> GSM26832 2 0 1 0 1
#> GSM26833 2 0 1 0 1
#> GSM26834 2 0 1 0 1
#> GSM26835 2 0 1 0 1
#> GSM26836 1 0 1 1 0
#> GSM26837 1 0 1 1 0
#> GSM26838 1 0 1 1 0
#> GSM26839 1 0 1 1 0
#> GSM26840 1 0 1 1 0
#> GSM26841 1 0 1 1 0
#> GSM26842 1 0 1 1 0
#> GSM26843 1 0 1 1 0
#> GSM26844 1 0 1 1 0
#> GSM26845 1 0 1 1 0
#> GSM26846 1 0 1 1 0
#> GSM26847 1 0 1 1 0
#> GSM26848 1 0 1 1 0
#> GSM26849 1 0 1 1 0
#> GSM26850 1 0 1 1 0
#> GSM26851 2 0 1 0 1
#> GSM26852 1 0 1 1 0
#> GSM26853 1 0 1 1 0
#> GSM26854 1 0 1 1 0
#> GSM26855 1 0 1 1 0
#> GSM26856 1 0 1 1 0
#> GSM26857 1 0 1 1 0
#> GSM26858 1 0 1 1 0
#> GSM26859 1 0 1 1 0
#> GSM26860 1 0 1 1 0
#> GSM26861 1 0 1 1 0
#> GSM26862 1 0 1 1 0
#> GSM26863 1 0 1 1 0
#> GSM26864 1 0 1 1 0
#> GSM26865 1 0 1 1 0
#> GSM26866 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM26805 2 0.0000 0.997 0.000 1.000 0.000
#> GSM26806 2 0.0592 0.992 0.000 0.988 0.012
#> GSM26807 2 0.0592 0.992 0.000 0.988 0.012
#> GSM26808 2 0.0592 0.992 0.000 0.988 0.012
#> GSM26809 2 0.0000 0.997 0.000 1.000 0.000
#> GSM26810 2 0.0592 0.992 0.000 0.988 0.012
#> GSM26811 2 0.0592 0.992 0.000 0.988 0.012
#> GSM26812 2 0.0592 0.992 0.000 0.988 0.012
#> GSM26813 2 0.0000 0.997 0.000 1.000 0.000
#> GSM26814 2 0.0000 0.997 0.000 1.000 0.000
#> GSM26815 2 0.0592 0.992 0.000 0.988 0.012
#> GSM26816 2 0.0000 0.997 0.000 1.000 0.000
#> GSM26817 2 0.0592 0.992 0.000 0.988 0.012
#> GSM26818 3 0.0237 0.990 0.004 0.000 0.996
#> GSM26819 2 0.0000 0.997 0.000 1.000 0.000
#> GSM26820 2 0.0000 0.997 0.000 1.000 0.000
#> GSM26821 2 0.0000 0.997 0.000 1.000 0.000
#> GSM26822 2 0.0000 0.997 0.000 1.000 0.000
#> GSM26823 2 0.0000 0.997 0.000 1.000 0.000
#> GSM26824 2 0.0000 0.997 0.000 1.000 0.000
#> GSM26825 2 0.0000 0.997 0.000 1.000 0.000
#> GSM26826 2 0.0000 0.997 0.000 1.000 0.000
#> GSM26827 2 0.0000 0.997 0.000 1.000 0.000
#> GSM26828 2 0.0000 0.997 0.000 1.000 0.000
#> GSM26829 2 0.0000 0.997 0.000 1.000 0.000
#> GSM26830 2 0.0000 0.997 0.000 1.000 0.000
#> GSM26831 2 0.0000 0.997 0.000 1.000 0.000
#> GSM26832 2 0.0000 0.997 0.000 1.000 0.000
#> GSM26833 2 0.0000 0.997 0.000 1.000 0.000
#> GSM26834 2 0.0000 0.997 0.000 1.000 0.000
#> GSM26835 2 0.0000 0.997 0.000 1.000 0.000
#> GSM26836 1 0.0000 0.967 1.000 0.000 0.000
#> GSM26837 1 0.0000 0.967 1.000 0.000 0.000
#> GSM26838 1 0.0000 0.967 1.000 0.000 0.000
#> GSM26839 1 0.0000 0.967 1.000 0.000 0.000
#> GSM26840 1 0.0000 0.967 1.000 0.000 0.000
#> GSM26841 1 0.0000 0.967 1.000 0.000 0.000
#> GSM26842 1 0.0000 0.967 1.000 0.000 0.000
#> GSM26843 1 0.0000 0.967 1.000 0.000 0.000
#> GSM26844 1 0.0000 0.967 1.000 0.000 0.000
#> GSM26845 1 0.0000 0.967 1.000 0.000 0.000
#> GSM26846 1 0.1529 0.939 0.960 0.000 0.040
#> GSM26847 1 0.0000 0.967 1.000 0.000 0.000
#> GSM26848 1 0.4002 0.828 0.840 0.000 0.160
#> GSM26849 3 0.0592 0.999 0.012 0.000 0.988
#> GSM26850 1 0.4842 0.742 0.776 0.000 0.224
#> GSM26851 2 0.0592 0.992 0.000 0.988 0.012
#> GSM26852 3 0.0592 0.999 0.012 0.000 0.988
#> GSM26853 3 0.0592 0.999 0.012 0.000 0.988
#> GSM26854 3 0.0592 0.999 0.012 0.000 0.988
#> GSM26855 3 0.0592 0.999 0.012 0.000 0.988
#> GSM26856 3 0.0592 0.999 0.012 0.000 0.988
#> GSM26857 3 0.0592 0.999 0.012 0.000 0.988
#> GSM26858 3 0.0592 0.999 0.012 0.000 0.988
#> GSM26859 3 0.0592 0.999 0.012 0.000 0.988
#> GSM26860 3 0.0592 0.999 0.012 0.000 0.988
#> GSM26861 3 0.0592 0.999 0.012 0.000 0.988
#> GSM26862 1 0.0000 0.967 1.000 0.000 0.000
#> GSM26863 1 0.0000 0.967 1.000 0.000 0.000
#> GSM26864 1 0.0000 0.967 1.000 0.000 0.000
#> GSM26865 1 0.4002 0.828 0.840 0.000 0.160
#> GSM26866 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
#> GSM26805 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM26806 4 0.1302 0.998 0.000 0.044 0.000 0.956
#> GSM26807 4 0.1302 0.998 0.000 0.044 0.000 0.956
#> GSM26808 4 0.1302 0.998 0.000 0.044 0.000 0.956
#> GSM26809 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM26810 4 0.1302 0.998 0.000 0.044 0.000 0.956
#> GSM26811 4 0.1302 0.998 0.000 0.044 0.000 0.956
#> GSM26812 4 0.1302 0.998 0.000 0.044 0.000 0.956
#> GSM26813 2 0.0188 0.995 0.000 0.996 0.000 0.004
#> GSM26814 2 0.0188 0.995 0.000 0.996 0.000 0.004
#> GSM26815 4 0.1302 0.998 0.000 0.044 0.000 0.956
#> GSM26816 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM26817 4 0.1637 0.981 0.000 0.060 0.000 0.940
#> GSM26818 3 0.0000 0.995 0.000 0.000 1.000 0.000
#> GSM26819 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM26820 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM26821 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM26822 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM26823 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM26824 2 0.0188 0.995 0.000 0.996 0.000 0.004
#> GSM26825 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM26826 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM26827 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM26828 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM26829 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM26830 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM26831 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM26832 2 0.0469 0.988 0.000 0.988 0.000 0.012
#> GSM26833 2 0.1022 0.968 0.000 0.968 0.000 0.032
#> GSM26834 2 0.0188 0.995 0.000 0.996 0.000 0.004
#> GSM26835 2 0.0188 0.995 0.000 0.996 0.000 0.004
#> GSM26836 1 0.0188 0.951 0.996 0.000 0.000 0.004
#> GSM26837 1 0.0188 0.951 0.996 0.000 0.000 0.004
#> GSM26838 1 0.0188 0.951 0.996 0.000 0.000 0.004
#> GSM26839 1 0.0188 0.951 0.996 0.000 0.000 0.004
#> GSM26840 1 0.0188 0.951 0.996 0.000 0.000 0.004
#> GSM26841 1 0.0188 0.951 0.996 0.000 0.000 0.004
#> GSM26842 1 0.0188 0.951 0.996 0.000 0.000 0.004
#> GSM26843 1 0.0188 0.951 0.996 0.000 0.000 0.004
#> GSM26844 1 0.0188 0.951 0.996 0.000 0.000 0.004
#> GSM26845 1 0.1109 0.941 0.968 0.000 0.004 0.028
#> GSM26846 1 0.2670 0.907 0.908 0.000 0.052 0.040
#> GSM26847 1 0.1398 0.936 0.956 0.000 0.004 0.040
#> GSM26848 1 0.4423 0.790 0.788 0.000 0.176 0.036
#> GSM26849 3 0.0469 0.986 0.000 0.000 0.988 0.012
#> GSM26850 1 0.5172 0.669 0.704 0.000 0.260 0.036
#> GSM26851 4 0.1302 0.998 0.000 0.044 0.000 0.956
#> GSM26852 3 0.0188 0.998 0.004 0.000 0.996 0.000
#> GSM26853 3 0.0188 0.998 0.004 0.000 0.996 0.000
#> GSM26854 3 0.0188 0.998 0.004 0.000 0.996 0.000
#> GSM26855 3 0.0188 0.998 0.004 0.000 0.996 0.000
#> GSM26856 3 0.0188 0.998 0.004 0.000 0.996 0.000
#> GSM26857 3 0.0188 0.998 0.004 0.000 0.996 0.000
#> GSM26858 3 0.0188 0.998 0.004 0.000 0.996 0.000
#> GSM26859 3 0.0188 0.998 0.004 0.000 0.996 0.000
#> GSM26860 3 0.0188 0.998 0.004 0.000 0.996 0.000
#> GSM26861 3 0.0188 0.998 0.004 0.000 0.996 0.000
#> GSM26862 1 0.0188 0.951 0.996 0.000 0.000 0.004
#> GSM26863 1 0.0188 0.951 0.996 0.000 0.000 0.004
#> GSM26864 1 0.0188 0.951 0.996 0.000 0.000 0.004
#> GSM26865 1 0.4511 0.790 0.784 0.000 0.176 0.040
#> GSM26866 1 0.0188 0.951 0.996 0.000 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM26805 2 0.3966 0.786 0.000 0.664 0.000 0.000 0.336
#> GSM26806 4 0.0000 0.997 0.000 0.000 0.000 1.000 0.000
#> GSM26807 4 0.0000 0.997 0.000 0.000 0.000 1.000 0.000
#> GSM26808 4 0.0000 0.997 0.000 0.000 0.000 1.000 0.000
#> GSM26809 2 0.0000 0.860 0.000 1.000 0.000 0.000 0.000
#> GSM26810 4 0.0000 0.997 0.000 0.000 0.000 1.000 0.000
#> GSM26811 4 0.0000 0.997 0.000 0.000 0.000 1.000 0.000
#> GSM26812 4 0.0000 0.997 0.000 0.000 0.000 1.000 0.000
#> GSM26813 2 0.0290 0.855 0.000 0.992 0.000 0.008 0.000
#> GSM26814 2 0.0000 0.860 0.000 1.000 0.000 0.000 0.000
#> GSM26815 4 0.0000 0.997 0.000 0.000 0.000 1.000 0.000
#> GSM26816 2 0.3983 0.785 0.000 0.660 0.000 0.000 0.340
#> GSM26817 4 0.0693 0.977 0.000 0.012 0.000 0.980 0.008
#> GSM26818 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000
#> GSM26819 2 0.0000 0.860 0.000 1.000 0.000 0.000 0.000
#> GSM26820 2 0.0000 0.860 0.000 1.000 0.000 0.000 0.000
#> GSM26821 2 0.0000 0.860 0.000 1.000 0.000 0.000 0.000
#> GSM26822 2 0.0000 0.860 0.000 1.000 0.000 0.000 0.000
#> GSM26823 2 0.0000 0.860 0.000 1.000 0.000 0.000 0.000
#> GSM26824 2 0.0000 0.860 0.000 1.000 0.000 0.000 0.000
#> GSM26825 2 0.0000 0.860 0.000 1.000 0.000 0.000 0.000
#> GSM26826 2 0.0000 0.860 0.000 1.000 0.000 0.000 0.000
#> GSM26827 2 0.0000 0.860 0.000 1.000 0.000 0.000 0.000
#> GSM26828 2 0.3983 0.785 0.000 0.660 0.000 0.000 0.340
#> GSM26829 2 0.3966 0.786 0.000 0.664 0.000 0.000 0.336
#> GSM26830 2 0.0000 0.860 0.000 1.000 0.000 0.000 0.000
#> GSM26831 2 0.3983 0.785 0.000 0.660 0.000 0.000 0.340
#> GSM26832 2 0.4252 0.780 0.000 0.652 0.000 0.008 0.340
#> GSM26833 2 0.5052 0.748 0.000 0.612 0.000 0.048 0.340
#> GSM26834 2 0.3983 0.785 0.000 0.660 0.000 0.000 0.340
#> GSM26835 2 0.3983 0.785 0.000 0.660 0.000 0.000 0.340
#> GSM26836 1 0.1792 0.915 0.916 0.000 0.000 0.000 0.084
#> GSM26837 1 0.1792 0.915 0.916 0.000 0.000 0.000 0.084
#> GSM26838 1 0.1732 0.916 0.920 0.000 0.000 0.000 0.080
#> GSM26839 1 0.1732 0.916 0.920 0.000 0.000 0.000 0.080
#> GSM26840 1 0.0000 0.930 1.000 0.000 0.000 0.000 0.000
#> GSM26841 1 0.0000 0.930 1.000 0.000 0.000 0.000 0.000
#> GSM26842 1 0.0000 0.930 1.000 0.000 0.000 0.000 0.000
#> GSM26843 1 0.0000 0.930 1.000 0.000 0.000 0.000 0.000
#> GSM26844 1 0.0000 0.930 1.000 0.000 0.000 0.000 0.000
#> GSM26845 5 0.4307 0.576 0.496 0.000 0.000 0.000 0.504
#> GSM26846 5 0.4118 0.861 0.336 0.000 0.004 0.000 0.660
#> GSM26847 5 0.3983 0.859 0.340 0.000 0.000 0.000 0.660
#> GSM26848 5 0.4537 0.870 0.396 0.000 0.012 0.000 0.592
#> GSM26849 3 0.2690 0.828 0.000 0.000 0.844 0.000 0.156
#> GSM26850 5 0.5068 0.843 0.364 0.000 0.044 0.000 0.592
#> GSM26851 4 0.0162 0.994 0.000 0.000 0.000 0.996 0.004
#> GSM26852 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000
#> GSM26853 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000
#> GSM26854 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000
#> GSM26855 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000
#> GSM26856 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000
#> GSM26857 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000
#> GSM26858 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000
#> GSM26859 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000
#> GSM26860 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000
#> GSM26861 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000
#> GSM26862 1 0.1792 0.915 0.916 0.000 0.000 0.000 0.084
#> GSM26863 1 0.1792 0.915 0.916 0.000 0.000 0.000 0.084
#> GSM26864 1 0.0000 0.930 1.000 0.000 0.000 0.000 0.000
#> GSM26865 5 0.4547 0.868 0.400 0.000 0.012 0.000 0.588
#> GSM26866 1 0.0000 0.930 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
#> GSM26805 5 0.0713 0.9739 0.000 0.028 0.000 0.000 0.972 0.000
#> GSM26806 4 0.0000 0.9923 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26807 4 0.0000 0.9923 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26808 4 0.0000 0.9923 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26809 2 0.2793 0.9794 0.000 0.800 0.000 0.000 0.200 0.000
#> GSM26810 4 0.0000 0.9923 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26811 4 0.0000 0.9923 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26812 4 0.0000 0.9923 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26813 2 0.2772 0.9785 0.000 0.816 0.000 0.000 0.180 0.004
#> GSM26814 2 0.2772 0.9785 0.000 0.816 0.000 0.000 0.180 0.004
#> GSM26815 4 0.0000 0.9923 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26816 5 0.0632 0.9761 0.000 0.024 0.000 0.000 0.976 0.000
#> GSM26817 4 0.1367 0.9420 0.000 0.012 0.000 0.944 0.044 0.000
#> GSM26818 3 0.0000 0.9575 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26819 2 0.2697 0.9899 0.000 0.812 0.000 0.000 0.188 0.000
#> GSM26820 2 0.2697 0.9899 0.000 0.812 0.000 0.000 0.188 0.000
#> GSM26821 2 0.2631 0.9871 0.000 0.820 0.000 0.000 0.180 0.000
#> GSM26822 2 0.2697 0.9899 0.000 0.812 0.000 0.000 0.188 0.000
#> GSM26823 2 0.2697 0.9899 0.000 0.812 0.000 0.000 0.188 0.000
#> GSM26824 2 0.2597 0.9849 0.000 0.824 0.000 0.000 0.176 0.000
#> GSM26825 2 0.2697 0.9899 0.000 0.812 0.000 0.000 0.188 0.000
#> GSM26826 2 0.2697 0.9899 0.000 0.812 0.000 0.000 0.188 0.000
#> GSM26827 2 0.2697 0.9899 0.000 0.812 0.000 0.000 0.188 0.000
#> GSM26828 5 0.0458 0.9796 0.000 0.016 0.000 0.000 0.984 0.000
#> GSM26829 5 0.1267 0.9392 0.000 0.060 0.000 0.000 0.940 0.000
#> GSM26830 2 0.2772 0.9785 0.000 0.816 0.000 0.000 0.180 0.004
#> GSM26831 5 0.0363 0.9801 0.000 0.012 0.000 0.000 0.988 0.000
#> GSM26832 5 0.0363 0.9710 0.000 0.000 0.000 0.012 0.988 0.000
#> GSM26833 5 0.0858 0.9492 0.000 0.004 0.000 0.028 0.968 0.000
#> GSM26834 5 0.0363 0.9801 0.000 0.012 0.000 0.000 0.988 0.000
#> GSM26835 5 0.0363 0.9801 0.000 0.012 0.000 0.000 0.988 0.000
#> GSM26836 1 0.5440 0.6816 0.616 0.164 0.000 0.000 0.012 0.208
#> GSM26837 1 0.5440 0.6816 0.616 0.164 0.000 0.000 0.012 0.208
#> GSM26838 1 0.5390 0.6854 0.624 0.164 0.000 0.000 0.012 0.200
#> GSM26839 1 0.5360 0.6867 0.628 0.160 0.000 0.000 0.012 0.200
#> GSM26840 1 0.0000 0.7502 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26841 1 0.0000 0.7502 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26842 1 0.0000 0.7502 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26843 1 0.0000 0.7502 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26844 1 0.0000 0.7502 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26845 6 0.5740 0.0167 0.284 0.168 0.000 0.000 0.008 0.540
#> GSM26846 6 0.0508 0.6957 0.004 0.012 0.000 0.000 0.000 0.984
#> GSM26847 6 0.3053 0.5976 0.004 0.172 0.000 0.000 0.012 0.812
#> GSM26848 6 0.2730 0.7297 0.192 0.000 0.000 0.000 0.000 0.808
#> GSM26849 3 0.3847 0.2284 0.000 0.000 0.544 0.000 0.000 0.456
#> GSM26850 6 0.2915 0.7300 0.184 0.000 0.008 0.000 0.000 0.808
#> GSM26851 4 0.0146 0.9889 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM26852 3 0.0000 0.9575 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26853 3 0.0000 0.9575 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26854 3 0.0000 0.9575 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26855 3 0.0000 0.9575 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26856 3 0.0000 0.9575 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26857 3 0.0000 0.9575 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26858 3 0.0000 0.9575 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26859 3 0.0000 0.9575 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26860 3 0.0000 0.9575 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26861 3 0.0000 0.9575 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26862 1 0.5440 0.6816 0.616 0.164 0.000 0.000 0.012 0.208
#> GSM26863 1 0.5440 0.6816 0.616 0.164 0.000 0.000 0.012 0.208
#> GSM26864 1 0.0000 0.7502 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26865 6 0.2762 0.7270 0.196 0.000 0.000 0.000 0.000 0.804
#> GSM26866 1 0.0000 0.7502 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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> CV:skmeans 62 1.14e-12 8.30e-01 2
#> CV:skmeans 62 1.49e-12 1.94e-04 3
#> CV:skmeans 62 7.66e-12 2.40e-06 4
#> CV:skmeans 62 3.62e-11 4.35e-09 5
#> CV:skmeans 60 3.70e-10 2.02e-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 11993 rows and 62 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 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.946 0.980 0.5052 0.494 0.494
#> 3 3 1.000 0.974 0.990 0.2378 0.841 0.690
#> 4 4 0.984 0.926 0.973 0.1624 0.895 0.718
#> 5 5 0.948 0.900 0.944 0.0660 0.936 0.770
#> 6 6 0.892 0.865 0.872 0.0591 0.905 0.604
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
#> attr(,"optional")
#> [1] 2 3 4
There is also optional best \(k\) = 2 3 4 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM26805 2 0.000 0.983 0.000 1.000
#> GSM26806 2 0.000 0.983 0.000 1.000
#> GSM26807 2 0.000 0.983 0.000 1.000
#> GSM26808 2 0.000 0.983 0.000 1.000
#> GSM26809 2 0.000 0.983 0.000 1.000
#> GSM26810 2 0.000 0.983 0.000 1.000
#> GSM26811 2 0.000 0.983 0.000 1.000
#> GSM26812 2 0.000 0.983 0.000 1.000
#> GSM26813 2 0.000 0.983 0.000 1.000
#> GSM26814 2 0.000 0.983 0.000 1.000
#> GSM26815 2 0.000 0.983 0.000 1.000
#> GSM26816 2 0.000 0.983 0.000 1.000
#> GSM26817 2 0.000 0.983 0.000 1.000
#> GSM26818 1 0.000 0.973 1.000 0.000
#> GSM26819 2 0.000 0.983 0.000 1.000
#> GSM26820 2 0.000 0.983 0.000 1.000
#> GSM26821 2 0.000 0.983 0.000 1.000
#> GSM26822 2 0.000 0.983 0.000 1.000
#> GSM26823 2 0.000 0.983 0.000 1.000
#> GSM26824 2 0.000 0.983 0.000 1.000
#> GSM26825 2 0.000 0.983 0.000 1.000
#> GSM26826 2 0.000 0.983 0.000 1.000
#> GSM26827 2 0.000 0.983 0.000 1.000
#> GSM26828 2 0.000 0.983 0.000 1.000
#> GSM26829 2 0.000 0.983 0.000 1.000
#> GSM26830 2 0.000 0.983 0.000 1.000
#> GSM26831 2 0.000 0.983 0.000 1.000
#> GSM26832 2 0.000 0.983 0.000 1.000
#> GSM26833 2 0.000 0.983 0.000 1.000
#> GSM26834 2 0.000 0.983 0.000 1.000
#> GSM26835 2 0.000 0.983 0.000 1.000
#> GSM26836 1 0.000 0.973 1.000 0.000
#> GSM26837 1 0.000 0.973 1.000 0.000
#> GSM26838 1 0.000 0.973 1.000 0.000
#> GSM26839 1 0.000 0.973 1.000 0.000
#> GSM26840 2 0.980 0.262 0.416 0.584
#> GSM26841 1 0.000 0.973 1.000 0.000
#> GSM26842 1 0.000 0.973 1.000 0.000
#> GSM26843 1 0.000 0.973 1.000 0.000
#> GSM26844 1 0.000 0.973 1.000 0.000
#> GSM26845 2 0.506 0.860 0.112 0.888
#> GSM26846 1 0.993 0.172 0.548 0.452
#> GSM26847 1 0.000 0.973 1.000 0.000
#> GSM26848 1 0.000 0.973 1.000 0.000
#> GSM26849 1 0.000 0.973 1.000 0.000
#> GSM26850 1 0.855 0.601 0.720 0.280
#> GSM26851 2 0.000 0.983 0.000 1.000
#> GSM26852 1 0.000 0.973 1.000 0.000
#> GSM26853 1 0.000 0.973 1.000 0.000
#> GSM26854 1 0.000 0.973 1.000 0.000
#> GSM26855 1 0.000 0.973 1.000 0.000
#> GSM26856 1 0.000 0.973 1.000 0.000
#> GSM26857 1 0.000 0.973 1.000 0.000
#> GSM26858 1 0.000 0.973 1.000 0.000
#> GSM26859 1 0.000 0.973 1.000 0.000
#> GSM26860 1 0.000 0.973 1.000 0.000
#> GSM26861 1 0.000 0.973 1.000 0.000
#> GSM26862 1 0.000 0.973 1.000 0.000
#> GSM26863 1 0.000 0.973 1.000 0.000
#> GSM26864 1 0.000 0.973 1.000 0.000
#> GSM26865 1 0.000 0.973 1.000 0.000
#> GSM26866 1 0.000 0.973 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM26805 2 0.000 1.000 0.000 1.000 0.000
#> GSM26806 2 0.000 1.000 0.000 1.000 0.000
#> GSM26807 2 0.000 1.000 0.000 1.000 0.000
#> GSM26808 2 0.000 1.000 0.000 1.000 0.000
#> GSM26809 2 0.000 1.000 0.000 1.000 0.000
#> GSM26810 2 0.000 1.000 0.000 1.000 0.000
#> GSM26811 2 0.000 1.000 0.000 1.000 0.000
#> GSM26812 2 0.000 1.000 0.000 1.000 0.000
#> GSM26813 2 0.000 1.000 0.000 1.000 0.000
#> GSM26814 2 0.000 1.000 0.000 1.000 0.000
#> GSM26815 2 0.000 1.000 0.000 1.000 0.000
#> GSM26816 2 0.000 1.000 0.000 1.000 0.000
#> GSM26817 2 0.000 1.000 0.000 1.000 0.000
#> GSM26818 3 0.000 0.979 0.000 0.000 1.000
#> GSM26819 2 0.000 1.000 0.000 1.000 0.000
#> GSM26820 2 0.000 1.000 0.000 1.000 0.000
#> GSM26821 2 0.000 1.000 0.000 1.000 0.000
#> GSM26822 2 0.000 1.000 0.000 1.000 0.000
#> GSM26823 2 0.000 1.000 0.000 1.000 0.000
#> GSM26824 2 0.000 1.000 0.000 1.000 0.000
#> GSM26825 2 0.000 1.000 0.000 1.000 0.000
#> GSM26826 2 0.000 1.000 0.000 1.000 0.000
#> GSM26827 2 0.000 1.000 0.000 1.000 0.000
#> GSM26828 2 0.000 1.000 0.000 1.000 0.000
#> GSM26829 2 0.000 1.000 0.000 1.000 0.000
#> GSM26830 2 0.000 1.000 0.000 1.000 0.000
#> GSM26831 2 0.000 1.000 0.000 1.000 0.000
#> GSM26832 2 0.000 1.000 0.000 1.000 0.000
#> GSM26833 2 0.000 1.000 0.000 1.000 0.000
#> GSM26834 2 0.000 1.000 0.000 1.000 0.000
#> GSM26835 2 0.000 1.000 0.000 1.000 0.000
#> GSM26836 1 0.000 0.970 1.000 0.000 0.000
#> GSM26837 1 0.000 0.970 1.000 0.000 0.000
#> GSM26838 1 0.000 0.970 1.000 0.000 0.000
#> GSM26839 1 0.000 0.970 1.000 0.000 0.000
#> GSM26840 1 0.000 0.970 1.000 0.000 0.000
#> GSM26841 1 0.000 0.970 1.000 0.000 0.000
#> GSM26842 1 0.000 0.970 1.000 0.000 0.000
#> GSM26843 1 0.000 0.970 1.000 0.000 0.000
#> GSM26844 1 0.000 0.970 1.000 0.000 0.000
#> GSM26845 1 0.522 0.636 0.740 0.260 0.000
#> GSM26846 1 0.375 0.799 0.856 0.144 0.000
#> GSM26847 1 0.000 0.970 1.000 0.000 0.000
#> GSM26848 1 0.000 0.970 1.000 0.000 0.000
#> GSM26849 3 0.493 0.702 0.232 0.000 0.768
#> GSM26850 1 0.000 0.970 1.000 0.000 0.000
#> GSM26851 2 0.000 1.000 0.000 1.000 0.000
#> GSM26852 3 0.000 0.979 0.000 0.000 1.000
#> GSM26853 3 0.000 0.979 0.000 0.000 1.000
#> GSM26854 3 0.000 0.979 0.000 0.000 1.000
#> GSM26855 3 0.000 0.979 0.000 0.000 1.000
#> GSM26856 3 0.000 0.979 0.000 0.000 1.000
#> GSM26857 3 0.000 0.979 0.000 0.000 1.000
#> GSM26858 3 0.000 0.979 0.000 0.000 1.000
#> GSM26859 3 0.000 0.979 0.000 0.000 1.000
#> GSM26860 3 0.000 0.979 0.000 0.000 1.000
#> GSM26861 3 0.000 0.979 0.000 0.000 1.000
#> GSM26862 1 0.000 0.970 1.000 0.000 0.000
#> GSM26863 1 0.000 0.970 1.000 0.000 0.000
#> GSM26864 1 0.000 0.970 1.000 0.000 0.000
#> GSM26865 1 0.000 0.970 1.000 0.000 0.000
#> GSM26866 1 0.000 0.970 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM26805 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM26806 4 0.0000 0.929 0.000 0.000 0.000 1.000
#> GSM26807 4 0.0000 0.929 0.000 0.000 0.000 1.000
#> GSM26808 4 0.0000 0.929 0.000 0.000 0.000 1.000
#> GSM26809 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM26810 4 0.0000 0.929 0.000 0.000 0.000 1.000
#> GSM26811 4 0.0000 0.929 0.000 0.000 0.000 1.000
#> GSM26812 4 0.0000 0.929 0.000 0.000 0.000 1.000
#> GSM26813 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM26814 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM26815 4 0.0000 0.929 0.000 0.000 0.000 1.000
#> GSM26816 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM26817 4 0.4941 0.226 0.000 0.436 0.000 0.564
#> GSM26818 3 0.0000 0.973 0.000 0.000 1.000 0.000
#> GSM26819 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM26820 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM26821 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM26822 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM26823 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM26824 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM26825 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM26826 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM26827 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM26828 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM26829 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM26830 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM26831 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM26832 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM26833 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM26834 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM26835 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM26836 1 0.0000 0.929 1.000 0.000 0.000 0.000
#> GSM26837 1 0.0000 0.929 1.000 0.000 0.000 0.000
#> GSM26838 1 0.0000 0.929 1.000 0.000 0.000 0.000
#> GSM26839 1 0.0000 0.929 1.000 0.000 0.000 0.000
#> GSM26840 1 0.0000 0.929 1.000 0.000 0.000 0.000
#> GSM26841 1 0.0000 0.929 1.000 0.000 0.000 0.000
#> GSM26842 1 0.0000 0.929 1.000 0.000 0.000 0.000
#> GSM26843 1 0.0000 0.929 1.000 0.000 0.000 0.000
#> GSM26844 1 0.0000 0.929 1.000 0.000 0.000 0.000
#> GSM26845 1 0.4585 0.524 0.668 0.332 0.000 0.000
#> GSM26846 1 0.4103 0.642 0.744 0.256 0.000 0.000
#> GSM26847 1 0.0000 0.929 1.000 0.000 0.000 0.000
#> GSM26848 1 0.0000 0.929 1.000 0.000 0.000 0.000
#> GSM26849 3 0.4040 0.666 0.248 0.000 0.752 0.000
#> GSM26850 1 0.4888 0.327 0.588 0.412 0.000 0.000
#> GSM26851 4 0.0336 0.923 0.000 0.008 0.000 0.992
#> GSM26852 3 0.0000 0.973 0.000 0.000 1.000 0.000
#> GSM26853 3 0.0000 0.973 0.000 0.000 1.000 0.000
#> GSM26854 3 0.0000 0.973 0.000 0.000 1.000 0.000
#> GSM26855 3 0.0000 0.973 0.000 0.000 1.000 0.000
#> GSM26856 3 0.0000 0.973 0.000 0.000 1.000 0.000
#> GSM26857 3 0.0000 0.973 0.000 0.000 1.000 0.000
#> GSM26858 3 0.0000 0.973 0.000 0.000 1.000 0.000
#> GSM26859 3 0.0000 0.973 0.000 0.000 1.000 0.000
#> GSM26860 3 0.0000 0.973 0.000 0.000 1.000 0.000
#> GSM26861 3 0.0000 0.973 0.000 0.000 1.000 0.000
#> GSM26862 1 0.0000 0.929 1.000 0.000 0.000 0.000
#> GSM26863 1 0.0000 0.929 1.000 0.000 0.000 0.000
#> GSM26864 1 0.0000 0.929 1.000 0.000 0.000 0.000
#> GSM26865 1 0.0000 0.929 1.000 0.000 0.000 0.000
#> GSM26866 1 0.0000 0.929 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
#> GSM26805 2 0.000 0.972 0.000 1.000 0.000 0.000 0.000
#> GSM26806 4 0.000 0.923 0.000 0.000 0.000 1.000 0.000
#> GSM26807 4 0.000 0.923 0.000 0.000 0.000 1.000 0.000
#> GSM26808 4 0.000 0.923 0.000 0.000 0.000 1.000 0.000
#> GSM26809 2 0.000 0.972 0.000 1.000 0.000 0.000 0.000
#> GSM26810 4 0.000 0.923 0.000 0.000 0.000 1.000 0.000
#> GSM26811 4 0.000 0.923 0.000 0.000 0.000 1.000 0.000
#> GSM26812 4 0.000 0.923 0.000 0.000 0.000 1.000 0.000
#> GSM26813 2 0.000 0.972 0.000 1.000 0.000 0.000 0.000
#> GSM26814 2 0.000 0.972 0.000 1.000 0.000 0.000 0.000
#> GSM26815 4 0.000 0.923 0.000 0.000 0.000 1.000 0.000
#> GSM26816 2 0.000 0.972 0.000 1.000 0.000 0.000 0.000
#> GSM26817 4 0.426 0.228 0.000 0.436 0.000 0.564 0.000
#> GSM26818 3 0.293 0.818 0.180 0.000 0.820 0.000 0.000
#> GSM26819 2 0.000 0.972 0.000 1.000 0.000 0.000 0.000
#> GSM26820 2 0.000 0.972 0.000 1.000 0.000 0.000 0.000
#> GSM26821 2 0.000 0.972 0.000 1.000 0.000 0.000 0.000
#> GSM26822 2 0.000 0.972 0.000 1.000 0.000 0.000 0.000
#> GSM26823 2 0.000 0.972 0.000 1.000 0.000 0.000 0.000
#> GSM26824 2 0.000 0.972 0.000 1.000 0.000 0.000 0.000
#> GSM26825 2 0.000 0.972 0.000 1.000 0.000 0.000 0.000
#> GSM26826 2 0.000 0.972 0.000 1.000 0.000 0.000 0.000
#> GSM26827 2 0.000 0.972 0.000 1.000 0.000 0.000 0.000
#> GSM26828 2 0.000 0.972 0.000 1.000 0.000 0.000 0.000
#> GSM26829 2 0.000 0.972 0.000 1.000 0.000 0.000 0.000
#> GSM26830 2 0.000 0.972 0.000 1.000 0.000 0.000 0.000
#> GSM26831 2 0.000 0.972 0.000 1.000 0.000 0.000 0.000
#> GSM26832 2 0.000 0.972 0.000 1.000 0.000 0.000 0.000
#> GSM26833 2 0.000 0.972 0.000 1.000 0.000 0.000 0.000
#> GSM26834 2 0.000 0.972 0.000 1.000 0.000 0.000 0.000
#> GSM26835 2 0.000 0.972 0.000 1.000 0.000 0.000 0.000
#> GSM26836 1 0.318 0.895 0.792 0.000 0.000 0.000 0.208
#> GSM26837 1 0.318 0.895 0.792 0.000 0.000 0.000 0.208
#> GSM26838 1 0.318 0.895 0.792 0.000 0.000 0.000 0.208
#> GSM26839 1 0.318 0.895 0.792 0.000 0.000 0.000 0.208
#> GSM26840 5 0.000 0.931 0.000 0.000 0.000 0.000 1.000
#> GSM26841 5 0.000 0.931 0.000 0.000 0.000 0.000 1.000
#> GSM26842 5 0.000 0.931 0.000 0.000 0.000 0.000 1.000
#> GSM26843 5 0.000 0.931 0.000 0.000 0.000 0.000 1.000
#> GSM26844 5 0.000 0.931 0.000 0.000 0.000 0.000 1.000
#> GSM26845 1 0.000 0.799 1.000 0.000 0.000 0.000 0.000
#> GSM26846 1 0.000 0.799 1.000 0.000 0.000 0.000 0.000
#> GSM26847 1 0.000 0.799 1.000 0.000 0.000 0.000 0.000
#> GSM26848 5 0.318 0.756 0.208 0.000 0.000 0.000 0.792
#> GSM26849 3 0.376 0.771 0.208 0.000 0.772 0.000 0.020
#> GSM26850 2 0.679 -0.184 0.296 0.384 0.000 0.000 0.320
#> GSM26851 4 0.029 0.916 0.000 0.008 0.000 0.992 0.000
#> GSM26852 3 0.000 0.964 0.000 0.000 1.000 0.000 0.000
#> GSM26853 3 0.000 0.964 0.000 0.000 1.000 0.000 0.000
#> GSM26854 3 0.000 0.964 0.000 0.000 1.000 0.000 0.000
#> GSM26855 3 0.000 0.964 0.000 0.000 1.000 0.000 0.000
#> GSM26856 3 0.000 0.964 0.000 0.000 1.000 0.000 0.000
#> GSM26857 3 0.000 0.964 0.000 0.000 1.000 0.000 0.000
#> GSM26858 3 0.000 0.964 0.000 0.000 1.000 0.000 0.000
#> GSM26859 3 0.000 0.964 0.000 0.000 1.000 0.000 0.000
#> GSM26860 3 0.000 0.964 0.000 0.000 1.000 0.000 0.000
#> GSM26861 3 0.000 0.964 0.000 0.000 1.000 0.000 0.000
#> GSM26862 1 0.318 0.895 0.792 0.000 0.000 0.000 0.208
#> GSM26863 1 0.318 0.895 0.792 0.000 0.000 0.000 0.208
#> GSM26864 5 0.000 0.931 0.000 0.000 0.000 0.000 1.000
#> GSM26865 5 0.318 0.756 0.208 0.000 0.000 0.000 0.792
#> GSM26866 5 0.000 0.931 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
#> GSM26805 5 0.0146 0.8493 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM26806 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26807 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26808 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26809 2 0.3789 1.0000 0.000 0.584 0.000 0.000 0.416 0.000
#> GSM26810 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26811 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26812 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26813 2 0.3789 1.0000 0.000 0.584 0.000 0.000 0.416 0.000
#> GSM26814 2 0.3789 1.0000 0.000 0.584 0.000 0.000 0.416 0.000
#> GSM26815 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26816 5 0.0146 0.8493 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM26817 5 0.3126 0.5719 0.000 0.000 0.000 0.248 0.752 0.000
#> GSM26818 3 0.2996 0.7502 0.228 0.000 0.772 0.000 0.000 0.000
#> GSM26819 2 0.3789 1.0000 0.000 0.584 0.000 0.000 0.416 0.000
#> GSM26820 2 0.3789 1.0000 0.000 0.584 0.000 0.000 0.416 0.000
#> GSM26821 2 0.3789 1.0000 0.000 0.584 0.000 0.000 0.416 0.000
#> GSM26822 2 0.3789 1.0000 0.000 0.584 0.000 0.000 0.416 0.000
#> GSM26823 2 0.3789 1.0000 0.000 0.584 0.000 0.000 0.416 0.000
#> GSM26824 2 0.3789 1.0000 0.000 0.584 0.000 0.000 0.416 0.000
#> GSM26825 2 0.3789 1.0000 0.000 0.584 0.000 0.000 0.416 0.000
#> GSM26826 2 0.3789 1.0000 0.000 0.584 0.000 0.000 0.416 0.000
#> GSM26827 2 0.3789 1.0000 0.000 0.584 0.000 0.000 0.416 0.000
#> GSM26828 5 0.0000 0.8525 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM26829 5 0.2416 0.5315 0.000 0.156 0.000 0.000 0.844 0.000
#> GSM26830 2 0.3789 1.0000 0.000 0.584 0.000 0.000 0.416 0.000
#> GSM26831 5 0.0000 0.8525 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM26832 5 0.0000 0.8525 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM26833 5 0.0000 0.8525 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM26834 5 0.0000 0.8525 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM26835 5 0.0000 0.8525 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM26836 6 0.0000 0.9301 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM26837 6 0.0000 0.9301 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM26838 6 0.0000 0.9301 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM26839 6 0.0000 0.9301 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM26840 1 0.3923 0.8357 0.580 0.416 0.000 0.000 0.000 0.004
#> GSM26841 1 0.3923 0.8357 0.580 0.416 0.000 0.000 0.000 0.004
#> GSM26842 1 0.3923 0.8357 0.580 0.416 0.000 0.000 0.000 0.004
#> GSM26843 1 0.3923 0.8357 0.580 0.416 0.000 0.000 0.000 0.004
#> GSM26844 1 0.3923 0.8357 0.580 0.416 0.000 0.000 0.000 0.004
#> GSM26845 6 0.2454 0.8157 0.160 0.000 0.000 0.000 0.000 0.840
#> GSM26846 6 0.3797 0.5337 0.420 0.000 0.000 0.000 0.000 0.580
#> GSM26847 6 0.0146 0.9279 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM26848 1 0.0000 0.5967 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26849 3 0.3797 0.5182 0.420 0.000 0.580 0.000 0.000 0.000
#> GSM26850 1 0.5561 0.0201 0.568 0.252 0.000 0.000 0.004 0.176
#> GSM26851 5 0.3774 0.0724 0.000 0.000 0.000 0.408 0.592 0.000
#> GSM26852 3 0.0000 0.9442 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26853 3 0.0000 0.9442 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26854 3 0.0000 0.9442 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26855 3 0.0000 0.9442 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26856 3 0.0000 0.9442 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26857 3 0.0000 0.9442 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26858 3 0.0000 0.9442 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26859 3 0.0000 0.9442 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26860 3 0.0000 0.9442 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26861 3 0.0000 0.9442 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26862 6 0.0000 0.9301 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM26863 6 0.0000 0.9301 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM26864 1 0.3923 0.8357 0.580 0.416 0.000 0.000 0.000 0.004
#> GSM26865 1 0.0000 0.5967 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26866 1 0.3923 0.8357 0.580 0.416 0.000 0.000 0.000 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> CV:pam 60 1.89e-11 8.46e-01 2
#> CV:pam 62 1.49e-12 1.94e-04 3
#> CV:pam 60 1.99e-11 3.56e-06 4
#> CV:pam 60 9.23e-11 1.88e-05 5
#> CV:pam 60 6.95e-11 7.63e-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["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 11993 rows and 62 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 0.390 0.232 0.655 0.4637 0.772 0.772
#> 3 3 0.676 0.764 0.880 0.3468 0.405 0.315
#> 4 4 0.768 0.808 0.832 0.1292 0.911 0.761
#> 5 5 0.840 0.826 0.885 0.0916 0.952 0.831
#> 6 6 0.781 0.650 0.783 0.0493 0.909 0.653
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
#> GSM26805 1 1.000 -1.000 0.500 0.500
#> GSM26806 1 0.000 0.225 1.000 0.000
#> GSM26807 1 0.000 0.225 1.000 0.000
#> GSM26808 1 0.000 0.225 1.000 0.000
#> GSM26809 1 0.987 -0.860 0.568 0.432
#> GSM26810 1 0.000 0.225 1.000 0.000
#> GSM26811 1 0.000 0.225 1.000 0.000
#> GSM26812 1 0.000 0.225 1.000 0.000
#> GSM26813 1 0.988 -0.867 0.564 0.436
#> GSM26814 1 0.988 -0.867 0.564 0.436
#> GSM26815 1 0.204 0.278 0.968 0.032
#> GSM26816 1 1.000 -1.000 0.500 0.500
#> GSM26817 1 0.358 0.060 0.932 0.068
#> GSM26818 1 0.963 0.617 0.612 0.388
#> GSM26819 2 1.000 1.000 0.500 0.500
#> GSM26820 2 1.000 1.000 0.500 0.500
#> GSM26821 1 1.000 -1.000 0.500 0.500
#> GSM26822 2 1.000 1.000 0.500 0.500
#> GSM26823 1 1.000 -1.000 0.500 0.500
#> GSM26824 1 0.995 -0.926 0.540 0.460
#> GSM26825 2 1.000 1.000 0.500 0.500
#> GSM26826 2 1.000 1.000 0.500 0.500
#> GSM26827 1 1.000 -1.000 0.500 0.500
#> GSM26828 2 1.000 1.000 0.500 0.500
#> GSM26829 2 1.000 1.000 0.500 0.500
#> GSM26830 1 1.000 -0.965 0.512 0.488
#> GSM26831 2 1.000 1.000 0.500 0.500
#> GSM26832 1 1.000 -1.000 0.500 0.500
#> GSM26833 1 1.000 -0.978 0.512 0.488
#> GSM26834 1 1.000 -1.000 0.500 0.500
#> GSM26835 1 1.000 -1.000 0.500 0.500
#> GSM26836 1 0.981 0.622 0.580 0.420
#> GSM26837 1 0.981 0.622 0.580 0.420
#> GSM26838 1 0.981 0.622 0.580 0.420
#> GSM26839 1 0.981 0.622 0.580 0.420
#> GSM26840 1 0.981 0.622 0.580 0.420
#> GSM26841 1 0.981 0.622 0.580 0.420
#> GSM26842 1 0.981 0.622 0.580 0.420
#> GSM26843 1 0.981 0.622 0.580 0.420
#> GSM26844 1 0.981 0.622 0.580 0.420
#> GSM26845 1 0.981 0.622 0.580 0.420
#> GSM26846 1 0.980 0.621 0.584 0.416
#> GSM26847 1 0.981 0.622 0.580 0.420
#> GSM26848 1 0.980 0.621 0.584 0.416
#> GSM26849 1 0.969 0.618 0.604 0.396
#> GSM26850 1 0.980 0.621 0.584 0.416
#> GSM26851 1 0.963 -0.791 0.612 0.388
#> GSM26852 1 1.000 0.591 0.504 0.496
#> GSM26853 1 1.000 0.591 0.504 0.496
#> GSM26854 1 1.000 0.591 0.504 0.496
#> GSM26855 1 1.000 0.591 0.504 0.496
#> GSM26856 1 1.000 0.591 0.504 0.496
#> GSM26857 1 1.000 0.591 0.504 0.496
#> GSM26858 1 1.000 0.591 0.504 0.496
#> GSM26859 1 1.000 0.591 0.504 0.496
#> GSM26860 1 1.000 0.591 0.504 0.496
#> GSM26861 1 1.000 0.591 0.504 0.496
#> GSM26862 1 0.981 0.622 0.580 0.420
#> GSM26863 1 0.981 0.622 0.580 0.420
#> GSM26864 1 0.981 0.622 0.580 0.420
#> GSM26865 1 0.980 0.621 0.584 0.416
#> GSM26866 1 0.981 0.622 0.580 0.420
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM26805 2 0.0000 0.8553 0.000 1.000 0.000
#> GSM26806 2 0.7015 0.4512 0.392 0.584 0.024
#> GSM26807 2 0.7015 0.4512 0.392 0.584 0.024
#> GSM26808 2 0.7015 0.4512 0.392 0.584 0.024
#> GSM26809 2 0.0892 0.8482 0.020 0.980 0.000
#> GSM26810 2 0.7015 0.4512 0.392 0.584 0.024
#> GSM26811 2 0.7015 0.4512 0.392 0.584 0.024
#> GSM26812 2 0.7015 0.4512 0.392 0.584 0.024
#> GSM26813 2 0.1031 0.8467 0.024 0.976 0.000
#> GSM26814 2 0.1031 0.8467 0.024 0.976 0.000
#> GSM26815 2 0.7841 0.3701 0.408 0.536 0.056
#> GSM26816 2 0.0000 0.8553 0.000 1.000 0.000
#> GSM26817 2 0.6247 0.4941 0.376 0.620 0.004
#> GSM26818 3 0.6244 -0.0265 0.440 0.000 0.560
#> GSM26819 2 0.0000 0.8553 0.000 1.000 0.000
#> GSM26820 2 0.0000 0.8553 0.000 1.000 0.000
#> GSM26821 2 0.0000 0.8553 0.000 1.000 0.000
#> GSM26822 2 0.0000 0.8553 0.000 1.000 0.000
#> GSM26823 2 0.0000 0.8553 0.000 1.000 0.000
#> GSM26824 2 0.0000 0.8553 0.000 1.000 0.000
#> GSM26825 2 0.0000 0.8553 0.000 1.000 0.000
#> GSM26826 2 0.0000 0.8553 0.000 1.000 0.000
#> GSM26827 2 0.0000 0.8553 0.000 1.000 0.000
#> GSM26828 2 0.0000 0.8553 0.000 1.000 0.000
#> GSM26829 2 0.0000 0.8553 0.000 1.000 0.000
#> GSM26830 2 0.0592 0.8514 0.012 0.988 0.000
#> GSM26831 2 0.0000 0.8553 0.000 1.000 0.000
#> GSM26832 2 0.0000 0.8553 0.000 1.000 0.000
#> GSM26833 2 0.0000 0.8553 0.000 1.000 0.000
#> GSM26834 2 0.0000 0.8553 0.000 1.000 0.000
#> GSM26835 2 0.0000 0.8553 0.000 1.000 0.000
#> GSM26836 1 0.0000 0.8506 1.000 0.000 0.000
#> GSM26837 1 0.0424 0.8507 0.992 0.000 0.008
#> GSM26838 1 0.0000 0.8506 1.000 0.000 0.000
#> GSM26839 1 0.0000 0.8506 1.000 0.000 0.000
#> GSM26840 1 0.5791 0.8170 0.792 0.060 0.148
#> GSM26841 1 0.4121 0.8512 0.832 0.000 0.168
#> GSM26842 1 0.4121 0.8512 0.832 0.000 0.168
#> GSM26843 1 0.4178 0.8493 0.828 0.000 0.172
#> GSM26844 1 0.4178 0.8493 0.828 0.000 0.172
#> GSM26845 1 0.5357 0.7538 0.820 0.064 0.116
#> GSM26846 1 0.1860 0.8470 0.948 0.000 0.052
#> GSM26847 1 0.1031 0.8499 0.976 0.000 0.024
#> GSM26848 1 0.5431 0.7388 0.716 0.000 0.284
#> GSM26849 3 0.6244 -0.0740 0.440 0.000 0.560
#> GSM26850 1 0.5591 0.7083 0.696 0.000 0.304
#> GSM26851 2 0.6501 0.5650 0.316 0.664 0.020
#> GSM26852 3 0.1031 0.8872 0.024 0.000 0.976
#> GSM26853 3 0.1031 0.8872 0.024 0.000 0.976
#> GSM26854 3 0.1031 0.8872 0.024 0.000 0.976
#> GSM26855 3 0.1031 0.8872 0.024 0.000 0.976
#> GSM26856 3 0.1643 0.8815 0.044 0.000 0.956
#> GSM26857 3 0.1031 0.8872 0.024 0.000 0.976
#> GSM26858 3 0.1411 0.8847 0.036 0.000 0.964
#> GSM26859 3 0.1643 0.8815 0.044 0.000 0.956
#> GSM26860 3 0.1031 0.8872 0.024 0.000 0.976
#> GSM26861 3 0.1643 0.8815 0.044 0.000 0.956
#> GSM26862 1 0.0000 0.8506 1.000 0.000 0.000
#> GSM26863 1 0.0000 0.8506 1.000 0.000 0.000
#> GSM26864 1 0.4121 0.8512 0.832 0.000 0.168
#> GSM26865 1 0.5098 0.7844 0.752 0.000 0.248
#> GSM26866 1 0.4235 0.8470 0.824 0.000 0.176
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM26805 2 0.0000 0.946 0.000 1.000 0.000 0.000
#> GSM26806 4 0.6748 0.938 0.112 0.328 0.000 0.560
#> GSM26807 4 0.6819 0.944 0.112 0.348 0.000 0.540
#> GSM26808 4 0.6819 0.944 0.112 0.348 0.000 0.540
#> GSM26809 2 0.0657 0.933 0.000 0.984 0.004 0.012
#> GSM26810 4 0.6733 0.935 0.112 0.324 0.000 0.564
#> GSM26811 4 0.6831 0.939 0.112 0.352 0.000 0.536
#> GSM26812 4 0.6819 0.944 0.112 0.348 0.000 0.540
#> GSM26813 2 0.0592 0.933 0.000 0.984 0.000 0.016
#> GSM26814 2 0.0592 0.933 0.000 0.984 0.000 0.016
#> GSM26815 4 0.7894 0.772 0.232 0.228 0.020 0.520
#> GSM26816 2 0.0000 0.946 0.000 1.000 0.000 0.000
#> GSM26817 2 0.6552 -0.186 0.112 0.628 0.004 0.256
#> GSM26818 3 0.7156 0.311 0.328 0.000 0.520 0.152
#> GSM26819 2 0.0000 0.946 0.000 1.000 0.000 0.000
#> GSM26820 2 0.0000 0.946 0.000 1.000 0.000 0.000
#> GSM26821 2 0.0000 0.946 0.000 1.000 0.000 0.000
#> GSM26822 2 0.0000 0.946 0.000 1.000 0.000 0.000
#> GSM26823 2 0.0000 0.946 0.000 1.000 0.000 0.000
#> GSM26824 2 0.0336 0.940 0.000 0.992 0.000 0.008
#> GSM26825 2 0.0000 0.946 0.000 1.000 0.000 0.000
#> GSM26826 2 0.0000 0.946 0.000 1.000 0.000 0.000
#> GSM26827 2 0.0000 0.946 0.000 1.000 0.000 0.000
#> GSM26828 2 0.0000 0.946 0.000 1.000 0.000 0.000
#> GSM26829 2 0.0000 0.946 0.000 1.000 0.000 0.000
#> GSM26830 2 0.0336 0.941 0.000 0.992 0.000 0.008
#> GSM26831 2 0.0000 0.946 0.000 1.000 0.000 0.000
#> GSM26832 2 0.0000 0.946 0.000 1.000 0.000 0.000
#> GSM26833 2 0.0336 0.941 0.000 0.992 0.000 0.008
#> GSM26834 2 0.0000 0.946 0.000 1.000 0.000 0.000
#> GSM26835 2 0.0000 0.946 0.000 1.000 0.000 0.000
#> GSM26836 1 0.5161 0.742 0.592 0.000 0.008 0.400
#> GSM26837 1 0.5150 0.743 0.596 0.000 0.008 0.396
#> GSM26838 1 0.5236 0.733 0.560 0.000 0.008 0.432
#> GSM26839 1 0.5150 0.743 0.596 0.000 0.008 0.396
#> GSM26840 1 0.1411 0.728 0.960 0.000 0.020 0.020
#> GSM26841 1 0.0707 0.730 0.980 0.000 0.020 0.000
#> GSM26842 1 0.0707 0.730 0.980 0.000 0.020 0.000
#> GSM26843 1 0.0817 0.729 0.976 0.000 0.024 0.000
#> GSM26844 1 0.0817 0.729 0.976 0.000 0.024 0.000
#> GSM26845 1 0.6376 0.708 0.504 0.000 0.064 0.432
#> GSM26846 1 0.6393 0.697 0.480 0.000 0.064 0.456
#> GSM26847 1 0.6327 0.705 0.496 0.000 0.060 0.444
#> GSM26848 1 0.5123 0.597 0.724 0.000 0.232 0.044
#> GSM26849 3 0.5865 0.334 0.340 0.000 0.612 0.048
#> GSM26850 1 0.5123 0.597 0.724 0.000 0.232 0.044
#> GSM26851 2 0.6350 -0.138 0.112 0.636 0.000 0.252
#> GSM26852 3 0.0000 0.914 0.000 0.000 1.000 0.000
#> GSM26853 3 0.0000 0.914 0.000 0.000 1.000 0.000
#> GSM26854 3 0.0000 0.914 0.000 0.000 1.000 0.000
#> GSM26855 3 0.0000 0.914 0.000 0.000 1.000 0.000
#> GSM26856 3 0.0336 0.912 0.000 0.000 0.992 0.008
#> GSM26857 3 0.0000 0.914 0.000 0.000 1.000 0.000
#> GSM26858 3 0.0376 0.912 0.004 0.000 0.992 0.004
#> GSM26859 3 0.0336 0.912 0.000 0.000 0.992 0.008
#> GSM26860 3 0.0000 0.914 0.000 0.000 1.000 0.000
#> GSM26861 3 0.0336 0.912 0.000 0.000 0.992 0.008
#> GSM26862 1 0.5279 0.741 0.588 0.000 0.012 0.400
#> GSM26863 1 0.5161 0.742 0.592 0.000 0.008 0.400
#> GSM26864 1 0.0707 0.730 0.980 0.000 0.020 0.000
#> GSM26865 1 0.4716 0.633 0.764 0.000 0.196 0.040
#> GSM26866 1 0.0817 0.729 0.976 0.000 0.024 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM26805 2 0.0451 0.9112 0.008 0.988 0.000 0.004 0.000
#> GSM26806 4 0.0404 0.9689 0.000 0.012 0.000 0.988 0.000
#> GSM26807 4 0.0703 0.9734 0.000 0.024 0.000 0.976 0.000
#> GSM26808 4 0.0963 0.9666 0.000 0.036 0.000 0.964 0.000
#> GSM26809 2 0.3323 0.8342 0.036 0.844 0.000 0.116 0.004
#> GSM26810 4 0.0510 0.9722 0.000 0.016 0.000 0.984 0.000
#> GSM26811 4 0.1121 0.9583 0.000 0.044 0.000 0.956 0.000
#> GSM26812 4 0.0609 0.9737 0.000 0.020 0.000 0.980 0.000
#> GSM26813 2 0.2723 0.8390 0.012 0.864 0.000 0.124 0.000
#> GSM26814 2 0.2825 0.8399 0.016 0.860 0.000 0.124 0.000
#> GSM26815 4 0.2026 0.9182 0.032 0.008 0.004 0.932 0.024
#> GSM26816 2 0.0324 0.9121 0.004 0.992 0.000 0.004 0.000
#> GSM26817 2 0.5155 0.3347 0.028 0.560 0.000 0.404 0.008
#> GSM26818 3 0.8363 0.0243 0.144 0.000 0.312 0.308 0.236
#> GSM26819 2 0.1544 0.9098 0.068 0.932 0.000 0.000 0.000
#> GSM26820 2 0.1544 0.9098 0.068 0.932 0.000 0.000 0.000
#> GSM26821 2 0.1270 0.9114 0.052 0.948 0.000 0.000 0.000
#> GSM26822 2 0.1544 0.9098 0.068 0.932 0.000 0.000 0.000
#> GSM26823 2 0.1544 0.9098 0.068 0.932 0.000 0.000 0.000
#> GSM26824 2 0.3409 0.8576 0.052 0.836 0.000 0.112 0.000
#> GSM26825 2 0.1544 0.9098 0.068 0.932 0.000 0.000 0.000
#> GSM26826 2 0.1544 0.9098 0.068 0.932 0.000 0.000 0.000
#> GSM26827 2 0.1544 0.9098 0.068 0.932 0.000 0.000 0.000
#> GSM26828 2 0.0324 0.9121 0.004 0.992 0.000 0.004 0.000
#> GSM26829 2 0.1478 0.9104 0.064 0.936 0.000 0.000 0.000
#> GSM26830 2 0.1628 0.8915 0.008 0.936 0.000 0.056 0.000
#> GSM26831 2 0.0566 0.9120 0.012 0.984 0.000 0.004 0.000
#> GSM26832 2 0.0324 0.9121 0.004 0.992 0.000 0.004 0.000
#> GSM26833 2 0.0865 0.9076 0.004 0.972 0.000 0.024 0.000
#> GSM26834 2 0.0324 0.9121 0.004 0.992 0.000 0.004 0.000
#> GSM26835 2 0.0324 0.9121 0.004 0.992 0.000 0.004 0.000
#> GSM26836 5 0.0000 0.9238 0.000 0.000 0.000 0.000 1.000
#> GSM26837 5 0.0000 0.9238 0.000 0.000 0.000 0.000 1.000
#> GSM26838 5 0.0000 0.9238 0.000 0.000 0.000 0.000 1.000
#> GSM26839 5 0.0000 0.9238 0.000 0.000 0.000 0.000 1.000
#> GSM26840 1 0.4150 0.6287 0.612 0.000 0.000 0.000 0.388
#> GSM26841 1 0.3452 0.7852 0.756 0.000 0.000 0.000 0.244
#> GSM26842 1 0.3452 0.7852 0.756 0.000 0.000 0.000 0.244
#> GSM26843 1 0.3452 0.7852 0.756 0.000 0.000 0.000 0.244
#> GSM26844 1 0.3452 0.7852 0.756 0.000 0.000 0.000 0.244
#> GSM26845 5 0.2304 0.8611 0.100 0.000 0.008 0.000 0.892
#> GSM26846 5 0.3607 0.7836 0.144 0.000 0.028 0.008 0.820
#> GSM26847 5 0.2653 0.8449 0.096 0.000 0.024 0.000 0.880
#> GSM26848 1 0.6622 0.4089 0.504 0.000 0.204 0.008 0.284
#> GSM26849 3 0.6741 0.1867 0.236 0.000 0.504 0.012 0.248
#> GSM26850 1 0.6627 0.4137 0.500 0.000 0.200 0.008 0.292
#> GSM26851 2 0.4030 0.5619 0.000 0.648 0.000 0.352 0.000
#> GSM26852 3 0.0000 0.8892 0.000 0.000 1.000 0.000 0.000
#> GSM26853 3 0.0000 0.8892 0.000 0.000 1.000 0.000 0.000
#> GSM26854 3 0.0000 0.8892 0.000 0.000 1.000 0.000 0.000
#> GSM26855 3 0.0000 0.8892 0.000 0.000 1.000 0.000 0.000
#> GSM26856 3 0.0290 0.8875 0.008 0.000 0.992 0.000 0.000
#> GSM26857 3 0.0162 0.8875 0.004 0.000 0.996 0.000 0.000
#> GSM26858 3 0.0162 0.8887 0.004 0.000 0.996 0.000 0.000
#> GSM26859 3 0.0290 0.8875 0.008 0.000 0.992 0.000 0.000
#> GSM26860 3 0.0162 0.8875 0.004 0.000 0.996 0.000 0.000
#> GSM26861 3 0.0290 0.8875 0.008 0.000 0.992 0.000 0.000
#> GSM26862 5 0.0000 0.9238 0.000 0.000 0.000 0.000 1.000
#> GSM26863 5 0.0000 0.9238 0.000 0.000 0.000 0.000 1.000
#> GSM26864 1 0.3480 0.7835 0.752 0.000 0.000 0.000 0.248
#> GSM26865 1 0.5509 0.5303 0.612 0.000 0.080 0.004 0.304
#> GSM26866 1 0.3452 0.7852 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
#> GSM26805 5 0.3565 0.506 0.000 0.304 0.000 0.004 0.692 0.000
#> GSM26806 4 0.0146 0.915 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM26807 4 0.0806 0.911 0.000 0.020 0.000 0.972 0.008 0.000
#> GSM26808 4 0.0260 0.914 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM26809 2 0.4951 0.503 0.004 0.480 0.000 0.008 0.472 0.036
#> GSM26810 4 0.0146 0.915 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM26811 4 0.0520 0.912 0.000 0.008 0.000 0.984 0.008 0.000
#> GSM26812 4 0.0806 0.911 0.000 0.020 0.000 0.972 0.008 0.000
#> GSM26813 2 0.4312 0.582 0.000 0.508 0.000 0.012 0.476 0.004
#> GSM26814 2 0.4412 0.583 0.000 0.500 0.000 0.012 0.480 0.008
#> GSM26815 4 0.5295 0.420 0.000 0.440 0.000 0.460 0.000 0.100
#> GSM26816 5 0.3426 0.540 0.000 0.276 0.000 0.004 0.720 0.000
#> GSM26817 2 0.6917 0.375 0.000 0.436 0.000 0.268 0.224 0.072
#> GSM26818 6 0.7333 0.290 0.076 0.372 0.128 0.036 0.000 0.388
#> GSM26819 5 0.0603 0.615 0.000 0.004 0.000 0.016 0.980 0.000
#> GSM26820 5 0.0458 0.617 0.000 0.000 0.000 0.016 0.984 0.000
#> GSM26821 5 0.2877 0.577 0.000 0.124 0.000 0.020 0.848 0.008
#> GSM26822 5 0.1074 0.615 0.000 0.028 0.000 0.012 0.960 0.000
#> GSM26823 5 0.0000 0.629 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM26824 5 0.3502 0.482 0.000 0.192 0.000 0.020 0.780 0.008
#> GSM26825 5 0.0146 0.627 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM26826 5 0.0000 0.629 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM26827 5 0.0146 0.627 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM26828 5 0.3405 0.546 0.000 0.272 0.000 0.004 0.724 0.000
#> GSM26829 5 0.1387 0.633 0.000 0.068 0.000 0.000 0.932 0.000
#> GSM26830 5 0.3619 0.392 0.000 0.316 0.000 0.004 0.680 0.000
#> GSM26831 5 0.2933 0.597 0.000 0.200 0.000 0.004 0.796 0.000
#> GSM26832 5 0.3448 0.539 0.000 0.280 0.000 0.004 0.716 0.000
#> GSM26833 5 0.3699 0.418 0.000 0.336 0.000 0.004 0.660 0.000
#> GSM26834 5 0.3383 0.552 0.000 0.268 0.000 0.004 0.728 0.000
#> GSM26835 5 0.3405 0.548 0.000 0.272 0.000 0.004 0.724 0.000
#> GSM26836 6 0.2793 0.613 0.200 0.000 0.000 0.000 0.000 0.800
#> GSM26837 6 0.2762 0.615 0.196 0.000 0.000 0.000 0.000 0.804
#> GSM26838 6 0.2793 0.615 0.200 0.000 0.000 0.000 0.000 0.800
#> GSM26839 6 0.2762 0.615 0.196 0.000 0.000 0.000 0.000 0.804
#> GSM26840 1 0.5658 0.161 0.520 0.292 0.000 0.000 0.000 0.188
#> GSM26841 1 0.0000 0.901 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26842 1 0.0260 0.896 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM26843 1 0.0000 0.901 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26844 1 0.0000 0.901 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26845 6 0.4868 0.508 0.112 0.220 0.004 0.000 0.000 0.664
#> GSM26846 6 0.2649 0.592 0.068 0.052 0.004 0.000 0.000 0.876
#> GSM26847 6 0.2838 0.604 0.116 0.028 0.004 0.000 0.000 0.852
#> GSM26848 6 0.6514 0.248 0.284 0.276 0.024 0.000 0.000 0.416
#> GSM26849 6 0.7521 0.263 0.184 0.192 0.216 0.004 0.000 0.404
#> GSM26850 6 0.6514 0.248 0.284 0.276 0.024 0.000 0.000 0.416
#> GSM26851 5 0.7098 -0.478 0.000 0.312 0.000 0.296 0.324 0.068
#> GSM26852 3 0.0146 0.994 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM26853 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26854 3 0.0146 0.995 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM26855 3 0.0146 0.994 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM26856 3 0.0508 0.984 0.012 0.004 0.984 0.000 0.000 0.000
#> GSM26857 3 0.0146 0.995 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM26858 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26859 3 0.0260 0.994 0.000 0.008 0.992 0.000 0.000 0.000
#> GSM26860 3 0.0291 0.994 0.000 0.004 0.992 0.000 0.000 0.004
#> GSM26861 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26862 6 0.2793 0.613 0.200 0.000 0.000 0.000 0.000 0.800
#> GSM26863 6 0.2823 0.612 0.204 0.000 0.000 0.000 0.000 0.796
#> GSM26864 1 0.0146 0.899 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM26865 6 0.6785 0.241 0.300 0.260 0.044 0.000 0.000 0.396
#> GSM26866 1 0.0000 0.901 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 tissue(p) individual(p) k
#> CV:mclust 39 1.03e-07 7.01e-02 2
#> CV:mclust 52 3.63e-11 6.74e-06 3
#> CV:mclust 58 1.57e-12 3.36e-07 4
#> CV:mclust 57 7.84e-11 1.39e-06 5
#> CV:mclust 50 1.39e-09 3.03e-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", "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 11993 rows and 62 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5087 0.492 0.492
#> 3 3 0.754 0.940 0.924 0.2467 0.873 0.742
#> 4 4 0.822 0.922 0.908 0.1534 0.889 0.696
#> 5 5 0.857 0.782 0.891 0.0735 0.967 0.869
#> 6 6 0.836 0.732 0.847 0.0467 0.907 0.616
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
#> GSM26805 2 0 1 0 1
#> GSM26806 2 0 1 0 1
#> GSM26807 2 0 1 0 1
#> GSM26808 2 0 1 0 1
#> GSM26809 2 0 1 0 1
#> GSM26810 2 0 1 0 1
#> GSM26811 2 0 1 0 1
#> GSM26812 2 0 1 0 1
#> GSM26813 2 0 1 0 1
#> GSM26814 2 0 1 0 1
#> GSM26815 2 0 1 0 1
#> GSM26816 2 0 1 0 1
#> GSM26817 2 0 1 0 1
#> GSM26818 1 0 1 1 0
#> GSM26819 2 0 1 0 1
#> GSM26820 2 0 1 0 1
#> GSM26821 2 0 1 0 1
#> GSM26822 2 0 1 0 1
#> GSM26823 2 0 1 0 1
#> GSM26824 2 0 1 0 1
#> GSM26825 2 0 1 0 1
#> GSM26826 2 0 1 0 1
#> GSM26827 2 0 1 0 1
#> GSM26828 2 0 1 0 1
#> GSM26829 2 0 1 0 1
#> GSM26830 2 0 1 0 1
#> GSM26831 2 0 1 0 1
#> GSM26832 2 0 1 0 1
#> GSM26833 2 0 1 0 1
#> GSM26834 2 0 1 0 1
#> GSM26835 2 0 1 0 1
#> GSM26836 1 0 1 1 0
#> GSM26837 1 0 1 1 0
#> GSM26838 1 0 1 1 0
#> GSM26839 1 0 1 1 0
#> GSM26840 1 0 1 1 0
#> GSM26841 1 0 1 1 0
#> GSM26842 1 0 1 1 0
#> GSM26843 1 0 1 1 0
#> GSM26844 1 0 1 1 0
#> GSM26845 1 0 1 1 0
#> GSM26846 1 0 1 1 0
#> GSM26847 1 0 1 1 0
#> GSM26848 1 0 1 1 0
#> GSM26849 1 0 1 1 0
#> GSM26850 1 0 1 1 0
#> GSM26851 2 0 1 0 1
#> GSM26852 1 0 1 1 0
#> GSM26853 1 0 1 1 0
#> GSM26854 1 0 1 1 0
#> GSM26855 1 0 1 1 0
#> GSM26856 1 0 1 1 0
#> GSM26857 1 0 1 1 0
#> GSM26858 1 0 1 1 0
#> GSM26859 1 0 1 1 0
#> GSM26860 1 0 1 1 0
#> GSM26861 1 0 1 1 0
#> GSM26862 1 0 1 1 0
#> GSM26863 1 0 1 1 0
#> GSM26864 1 0 1 1 0
#> GSM26865 1 0 1 1 0
#> GSM26866 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM26805 2 0.0000 0.951 0.000 1.000 0.000
#> GSM26806 2 0.3752 0.919 0.000 0.856 0.144
#> GSM26807 2 0.3752 0.919 0.000 0.856 0.144
#> GSM26808 2 0.3752 0.919 0.000 0.856 0.144
#> GSM26809 2 0.1643 0.920 0.044 0.956 0.000
#> GSM26810 2 0.3752 0.919 0.000 0.856 0.144
#> GSM26811 2 0.3752 0.919 0.000 0.856 0.144
#> GSM26812 2 0.3752 0.919 0.000 0.856 0.144
#> GSM26813 2 0.0000 0.951 0.000 1.000 0.000
#> GSM26814 2 0.0000 0.951 0.000 1.000 0.000
#> GSM26815 2 0.3752 0.919 0.000 0.856 0.144
#> GSM26816 2 0.3686 0.920 0.000 0.860 0.140
#> GSM26817 2 0.3619 0.921 0.000 0.864 0.136
#> GSM26818 3 0.3551 0.979 0.132 0.000 0.868
#> GSM26819 2 0.0000 0.951 0.000 1.000 0.000
#> GSM26820 2 0.0000 0.951 0.000 1.000 0.000
#> GSM26821 2 0.0000 0.951 0.000 1.000 0.000
#> GSM26822 2 0.0000 0.951 0.000 1.000 0.000
#> GSM26823 2 0.0000 0.951 0.000 1.000 0.000
#> GSM26824 2 0.0000 0.951 0.000 1.000 0.000
#> GSM26825 2 0.0000 0.951 0.000 1.000 0.000
#> GSM26826 2 0.0000 0.951 0.000 1.000 0.000
#> GSM26827 2 0.0000 0.951 0.000 1.000 0.000
#> GSM26828 2 0.0000 0.951 0.000 1.000 0.000
#> GSM26829 2 0.0000 0.951 0.000 1.000 0.000
#> GSM26830 2 0.0000 0.951 0.000 1.000 0.000
#> GSM26831 2 0.0000 0.951 0.000 1.000 0.000
#> GSM26832 2 0.2261 0.939 0.000 0.932 0.068
#> GSM26833 2 0.3752 0.919 0.000 0.856 0.144
#> GSM26834 2 0.1031 0.948 0.000 0.976 0.024
#> GSM26835 2 0.0237 0.951 0.000 0.996 0.004
#> GSM26836 1 0.0000 0.930 1.000 0.000 0.000
#> GSM26837 1 0.0592 0.927 0.988 0.000 0.012
#> GSM26838 1 0.0000 0.930 1.000 0.000 0.000
#> GSM26839 1 0.0000 0.930 1.000 0.000 0.000
#> GSM26840 1 0.0000 0.930 1.000 0.000 0.000
#> GSM26841 1 0.2165 0.911 0.936 0.000 0.064
#> GSM26842 1 0.1529 0.921 0.960 0.000 0.040
#> GSM26843 1 0.3116 0.882 0.892 0.000 0.108
#> GSM26844 1 0.3192 0.878 0.888 0.000 0.112
#> GSM26845 1 0.3752 0.759 0.856 0.144 0.000
#> GSM26846 1 0.3192 0.844 0.888 0.000 0.112
#> GSM26847 1 0.0000 0.930 1.000 0.000 0.000
#> GSM26848 3 0.4121 0.970 0.168 0.000 0.832
#> GSM26849 3 0.3752 0.994 0.144 0.000 0.856
#> GSM26850 3 0.3752 0.994 0.144 0.000 0.856
#> GSM26851 2 0.3752 0.919 0.000 0.856 0.144
#> GSM26852 3 0.3752 0.994 0.144 0.000 0.856
#> GSM26853 3 0.3752 0.994 0.144 0.000 0.856
#> GSM26854 3 0.3752 0.994 0.144 0.000 0.856
#> GSM26855 3 0.3752 0.994 0.144 0.000 0.856
#> GSM26856 3 0.3752 0.994 0.144 0.000 0.856
#> GSM26857 3 0.3752 0.994 0.144 0.000 0.856
#> GSM26858 3 0.3752 0.994 0.144 0.000 0.856
#> GSM26859 3 0.3752 0.994 0.144 0.000 0.856
#> GSM26860 3 0.3752 0.994 0.144 0.000 0.856
#> GSM26861 3 0.3752 0.994 0.144 0.000 0.856
#> GSM26862 1 0.0000 0.930 1.000 0.000 0.000
#> GSM26863 1 0.0000 0.930 1.000 0.000 0.000
#> GSM26864 1 0.3116 0.882 0.892 0.000 0.108
#> GSM26865 3 0.4121 0.970 0.168 0.000 0.832
#> GSM26866 1 0.3551 0.855 0.868 0.000 0.132
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM26805 2 0.1118 0.923 0.000 0.964 0.000 0.036
#> GSM26806 4 0.4008 0.981 0.000 0.244 0.000 0.756
#> GSM26807 4 0.4008 0.981 0.000 0.244 0.000 0.756
#> GSM26808 4 0.4008 0.981 0.000 0.244 0.000 0.756
#> GSM26809 2 0.2216 0.853 0.000 0.908 0.000 0.092
#> GSM26810 4 0.4008 0.981 0.000 0.244 0.000 0.756
#> GSM26811 4 0.4008 0.981 0.000 0.244 0.000 0.756
#> GSM26812 4 0.4008 0.981 0.000 0.244 0.000 0.756
#> GSM26813 2 0.0921 0.925 0.000 0.972 0.000 0.028
#> GSM26814 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM26815 4 0.3975 0.977 0.000 0.240 0.000 0.760
#> GSM26816 2 0.4134 0.494 0.000 0.740 0.000 0.260
#> GSM26817 4 0.4585 0.866 0.000 0.332 0.000 0.668
#> GSM26818 3 0.1389 0.940 0.000 0.000 0.952 0.048
#> GSM26819 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM26820 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM26821 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM26822 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM26823 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM26824 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM26825 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM26826 2 0.0336 0.946 0.000 0.992 0.000 0.008
#> GSM26827 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM26828 2 0.1302 0.915 0.000 0.956 0.000 0.044
#> GSM26829 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM26830 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM26831 2 0.1211 0.919 0.000 0.960 0.000 0.040
#> GSM26832 2 0.3400 0.688 0.000 0.820 0.000 0.180
#> GSM26833 4 0.4222 0.952 0.000 0.272 0.000 0.728
#> GSM26834 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM26835 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM26836 1 0.1474 0.910 0.948 0.000 0.000 0.052
#> GSM26837 1 0.0469 0.916 0.988 0.000 0.012 0.000
#> GSM26838 1 0.1474 0.910 0.948 0.000 0.000 0.052
#> GSM26839 1 0.0376 0.916 0.992 0.000 0.004 0.004
#> GSM26840 1 0.3157 0.909 0.852 0.000 0.004 0.144
#> GSM26841 1 0.3550 0.902 0.860 0.000 0.044 0.096
#> GSM26842 1 0.3399 0.904 0.868 0.000 0.040 0.092
#> GSM26843 1 0.3634 0.901 0.856 0.000 0.048 0.096
#> GSM26844 1 0.3634 0.901 0.856 0.000 0.048 0.096
#> GSM26845 1 0.2149 0.900 0.912 0.000 0.000 0.088
#> GSM26846 1 0.4724 0.807 0.792 0.000 0.112 0.096
#> GSM26847 1 0.2760 0.891 0.872 0.000 0.000 0.128
#> GSM26848 3 0.2401 0.922 0.004 0.000 0.904 0.092
#> GSM26849 3 0.1716 0.935 0.000 0.000 0.936 0.064
#> GSM26850 3 0.2216 0.924 0.000 0.000 0.908 0.092
#> GSM26851 4 0.4008 0.981 0.000 0.244 0.000 0.756
#> GSM26852 3 0.1661 0.943 0.052 0.000 0.944 0.004
#> GSM26853 3 0.1489 0.946 0.044 0.000 0.952 0.004
#> GSM26854 3 0.0000 0.952 0.000 0.000 1.000 0.000
#> GSM26855 3 0.1661 0.943 0.052 0.000 0.944 0.004
#> GSM26856 3 0.1305 0.948 0.036 0.000 0.960 0.004
#> GSM26857 3 0.0000 0.952 0.000 0.000 1.000 0.000
#> GSM26858 3 0.1661 0.943 0.052 0.000 0.944 0.004
#> GSM26859 3 0.0469 0.951 0.000 0.000 0.988 0.012
#> GSM26860 3 0.0188 0.952 0.000 0.000 0.996 0.004
#> GSM26861 3 0.1661 0.943 0.052 0.000 0.944 0.004
#> GSM26862 1 0.1474 0.910 0.948 0.000 0.000 0.052
#> GSM26863 1 0.1389 0.911 0.952 0.000 0.000 0.048
#> GSM26864 1 0.3550 0.902 0.860 0.000 0.044 0.096
#> GSM26865 3 0.3533 0.892 0.056 0.000 0.864 0.080
#> GSM26866 1 0.4235 0.877 0.824 0.000 0.084 0.092
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM26805 2 0.2233 0.855 0.080 0.904 0.000 0.000 0.016
#> GSM26806 4 0.0510 0.967 0.000 0.016 0.000 0.984 0.000
#> GSM26807 4 0.0510 0.967 0.000 0.016 0.000 0.984 0.000
#> GSM26808 4 0.0510 0.967 0.000 0.016 0.000 0.984 0.000
#> GSM26809 2 0.3336 0.713 0.228 0.772 0.000 0.000 0.000
#> GSM26810 4 0.0510 0.967 0.000 0.016 0.000 0.984 0.000
#> GSM26811 4 0.0510 0.967 0.000 0.016 0.000 0.984 0.000
#> GSM26812 4 0.0510 0.967 0.000 0.016 0.000 0.984 0.000
#> GSM26813 2 0.0162 0.906 0.000 0.996 0.000 0.004 0.000
#> GSM26814 2 0.0162 0.906 0.000 0.996 0.000 0.004 0.000
#> GSM26815 4 0.0510 0.967 0.000 0.016 0.000 0.984 0.000
#> GSM26816 2 0.4740 0.178 0.000 0.516 0.000 0.468 0.016
#> GSM26817 4 0.3266 0.734 0.000 0.200 0.000 0.796 0.004
#> GSM26818 3 0.1357 0.892 0.000 0.000 0.948 0.004 0.048
#> GSM26819 2 0.0324 0.906 0.000 0.992 0.000 0.004 0.004
#> GSM26820 2 0.0162 0.906 0.000 0.996 0.000 0.004 0.000
#> GSM26821 2 0.0324 0.906 0.000 0.992 0.000 0.004 0.004
#> GSM26822 2 0.0162 0.906 0.000 0.996 0.000 0.004 0.000
#> GSM26823 2 0.0162 0.906 0.000 0.996 0.000 0.004 0.000
#> GSM26824 2 0.0162 0.906 0.000 0.996 0.000 0.004 0.000
#> GSM26825 2 0.0162 0.906 0.000 0.996 0.000 0.004 0.000
#> GSM26826 2 0.0000 0.905 0.000 1.000 0.000 0.000 0.000
#> GSM26827 2 0.0162 0.906 0.000 0.996 0.000 0.004 0.000
#> GSM26828 2 0.0794 0.898 0.000 0.972 0.000 0.000 0.028
#> GSM26829 2 0.0609 0.900 0.000 0.980 0.000 0.000 0.020
#> GSM26830 2 0.0162 0.906 0.000 0.996 0.000 0.004 0.000
#> GSM26831 2 0.0794 0.898 0.000 0.972 0.000 0.000 0.028
#> GSM26832 2 0.4787 0.460 0.000 0.608 0.000 0.364 0.028
#> GSM26833 4 0.1399 0.949 0.000 0.020 0.000 0.952 0.028
#> GSM26834 2 0.4397 0.625 0.000 0.696 0.000 0.276 0.028
#> GSM26835 2 0.4141 0.682 0.000 0.736 0.000 0.236 0.028
#> GSM26836 5 0.4276 0.675 0.380 0.000 0.000 0.004 0.616
#> GSM26837 5 0.4182 0.706 0.352 0.000 0.000 0.004 0.644
#> GSM26838 1 0.4297 -0.425 0.528 0.000 0.000 0.000 0.472
#> GSM26839 1 0.4305 -0.465 0.512 0.000 0.000 0.000 0.488
#> GSM26840 1 0.0162 0.719 0.996 0.004 0.000 0.000 0.000
#> GSM26841 1 0.1041 0.745 0.964 0.004 0.032 0.000 0.000
#> GSM26842 1 0.0671 0.736 0.980 0.004 0.016 0.000 0.000
#> GSM26843 1 0.1851 0.754 0.912 0.000 0.088 0.000 0.000
#> GSM26844 1 0.1908 0.753 0.908 0.000 0.092 0.000 0.000
#> GSM26845 5 0.2763 0.725 0.148 0.000 0.000 0.004 0.848
#> GSM26846 5 0.1200 0.639 0.016 0.008 0.000 0.012 0.964
#> GSM26847 5 0.1410 0.683 0.060 0.000 0.000 0.000 0.940
#> GSM26848 3 0.4356 0.671 0.000 0.000 0.648 0.012 0.340
#> GSM26849 3 0.3242 0.816 0.000 0.000 0.816 0.012 0.172
#> GSM26850 3 0.4152 0.717 0.000 0.000 0.692 0.012 0.296
#> GSM26851 4 0.1117 0.957 0.000 0.016 0.000 0.964 0.020
#> GSM26852 3 0.0000 0.915 0.000 0.000 1.000 0.000 0.000
#> GSM26853 3 0.0000 0.915 0.000 0.000 1.000 0.000 0.000
#> GSM26854 3 0.0000 0.915 0.000 0.000 1.000 0.000 0.000
#> GSM26855 3 0.0000 0.915 0.000 0.000 1.000 0.000 0.000
#> GSM26856 3 0.0000 0.915 0.000 0.000 1.000 0.000 0.000
#> GSM26857 3 0.0000 0.915 0.000 0.000 1.000 0.000 0.000
#> GSM26858 3 0.0162 0.913 0.004 0.000 0.996 0.000 0.000
#> GSM26859 3 0.0000 0.915 0.000 0.000 1.000 0.000 0.000
#> GSM26860 3 0.0000 0.915 0.000 0.000 1.000 0.000 0.000
#> GSM26861 3 0.0000 0.915 0.000 0.000 1.000 0.000 0.000
#> GSM26862 5 0.3928 0.732 0.296 0.000 0.000 0.004 0.700
#> GSM26863 5 0.4161 0.656 0.392 0.000 0.000 0.000 0.608
#> GSM26864 1 0.2124 0.751 0.900 0.004 0.096 0.000 0.000
#> GSM26865 3 0.6047 0.621 0.120 0.000 0.592 0.012 0.276
#> GSM26866 1 0.2230 0.732 0.884 0.000 0.116 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM26805 2 0.5453 0.4503 0.096 0.568 0.000 0.016 0.000 0.320
#> GSM26806 4 0.0000 0.8356 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26807 4 0.0000 0.8356 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26808 4 0.0000 0.8356 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26809 2 0.3835 0.6184 0.204 0.748 0.000 0.000 0.000 0.048
#> GSM26810 4 0.0000 0.8356 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26811 4 0.0000 0.8356 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26812 4 0.0000 0.8356 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26813 2 0.0000 0.8655 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26814 2 0.0000 0.8655 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26815 4 0.0000 0.8356 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26816 4 0.5851 0.1769 0.000 0.236 0.000 0.484 0.000 0.280
#> GSM26817 4 0.3163 0.6623 0.012 0.172 0.000 0.808 0.000 0.008
#> GSM26818 3 0.1908 0.8862 0.000 0.000 0.900 0.004 0.000 0.096
#> GSM26819 2 0.0000 0.8655 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26820 2 0.0000 0.8655 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26821 2 0.0000 0.8655 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26822 2 0.0000 0.8655 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26823 2 0.0000 0.8655 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26824 2 0.0000 0.8655 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26825 2 0.0000 0.8655 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26826 2 0.0146 0.8631 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM26827 2 0.0000 0.8655 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26828 2 0.4932 0.4089 0.072 0.556 0.000 0.000 0.000 0.372
#> GSM26829 2 0.3615 0.5934 0.008 0.700 0.000 0.000 0.000 0.292
#> GSM26830 2 0.0000 0.8655 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26831 2 0.4737 0.4293 0.056 0.572 0.000 0.000 0.000 0.372
#> GSM26832 6 0.6841 -0.0176 0.048 0.284 0.000 0.276 0.000 0.392
#> GSM26833 4 0.5038 0.4320 0.048 0.016 0.000 0.564 0.000 0.372
#> GSM26834 6 0.6813 -0.0127 0.048 0.336 0.000 0.236 0.000 0.380
#> GSM26835 6 0.6842 -0.0406 0.052 0.348 0.000 0.228 0.000 0.372
#> GSM26836 5 0.2378 0.8383 0.152 0.000 0.000 0.000 0.848 0.000
#> GSM26837 5 0.2340 0.8390 0.148 0.000 0.000 0.000 0.852 0.000
#> GSM26838 5 0.3547 0.7213 0.332 0.000 0.000 0.000 0.668 0.000
#> GSM26839 5 0.3592 0.7046 0.344 0.000 0.000 0.000 0.656 0.000
#> GSM26840 1 0.1700 0.9207 0.928 0.000 0.000 0.000 0.048 0.024
#> GSM26841 1 0.1257 0.9587 0.952 0.000 0.028 0.000 0.020 0.000
#> GSM26842 1 0.1225 0.9444 0.952 0.000 0.012 0.000 0.036 0.000
#> GSM26843 1 0.1285 0.9623 0.944 0.000 0.052 0.000 0.000 0.004
#> GSM26844 1 0.1285 0.9623 0.944 0.000 0.052 0.000 0.000 0.004
#> GSM26845 5 0.0000 0.7654 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM26846 6 0.3823 -0.0308 0.000 0.000 0.000 0.000 0.436 0.564
#> GSM26847 5 0.1556 0.7191 0.000 0.000 0.000 0.000 0.920 0.080
#> GSM26848 6 0.4955 0.3856 0.000 0.000 0.220 0.000 0.136 0.644
#> GSM26849 6 0.4543 0.1362 0.000 0.000 0.384 0.000 0.040 0.576
#> GSM26850 6 0.4888 0.3719 0.000 0.000 0.240 0.000 0.116 0.644
#> GSM26851 4 0.3746 0.6853 0.048 0.000 0.000 0.760 0.000 0.192
#> GSM26852 3 0.0146 0.9794 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM26853 3 0.0000 0.9816 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26854 3 0.0260 0.9811 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM26855 3 0.0000 0.9816 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26856 3 0.0146 0.9816 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM26857 3 0.0260 0.9811 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM26858 3 0.0146 0.9794 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM26859 3 0.0790 0.9631 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM26860 3 0.0260 0.9811 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM26861 3 0.0000 0.9816 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26862 5 0.1765 0.8285 0.096 0.000 0.000 0.000 0.904 0.000
#> GSM26863 5 0.3175 0.7947 0.256 0.000 0.000 0.000 0.744 0.000
#> GSM26864 1 0.1152 0.9635 0.952 0.000 0.044 0.000 0.004 0.000
#> GSM26865 6 0.6001 0.3272 0.076 0.000 0.248 0.000 0.092 0.584
#> GSM26866 1 0.1471 0.9490 0.932 0.000 0.064 0.000 0.000 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> CV:NMF 62 1.14e-12 8.30e-01 2
#> CV:NMF 62 1.54e-12 9.76e-04 3
#> CV:NMF 61 1.32e-11 3.88e-05 4
#> CV:NMF 58 2.62e-10 1.35e-04 5
#> CV:NMF 49 1.85e-08 4.08e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "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 11993 rows and 62 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 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 0.526 0.915 0.912 0.4595 0.511 0.511
#> 3 3 0.825 0.935 0.965 0.4150 0.835 0.677
#> 4 4 0.918 0.984 0.973 0.1055 0.928 0.792
#> 5 5 0.977 0.957 0.983 0.0272 0.994 0.977
#> 6 6 0.921 0.901 0.960 0.0304 0.988 0.955
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM26805 2 0.7815 0.880 0.232 0.768
#> GSM26806 1 0.0376 0.996 0.996 0.004
#> GSM26807 1 0.0376 0.996 0.996 0.004
#> GSM26808 1 0.0376 0.996 0.996 0.004
#> GSM26809 2 0.7139 0.872 0.196 0.804
#> GSM26810 1 0.0376 0.996 0.996 0.004
#> GSM26811 1 0.0376 0.996 0.996 0.004
#> GSM26812 1 0.0376 0.996 0.996 0.004
#> GSM26813 2 0.7815 0.880 0.232 0.768
#> GSM26814 2 0.7815 0.880 0.232 0.768
#> GSM26815 1 0.0376 0.996 0.996 0.004
#> GSM26816 2 0.7815 0.880 0.232 0.768
#> GSM26817 1 0.0376 0.996 0.996 0.004
#> GSM26818 1 0.0000 0.998 1.000 0.000
#> GSM26819 2 0.7815 0.880 0.232 0.768
#> GSM26820 2 0.7815 0.880 0.232 0.768
#> GSM26821 2 0.7815 0.880 0.232 0.768
#> GSM26822 2 0.7815 0.880 0.232 0.768
#> GSM26823 2 0.7815 0.880 0.232 0.768
#> GSM26824 2 0.7815 0.880 0.232 0.768
#> GSM26825 2 0.7815 0.880 0.232 0.768
#> GSM26826 2 0.7815 0.880 0.232 0.768
#> GSM26827 2 0.7815 0.880 0.232 0.768
#> GSM26828 2 0.7815 0.880 0.232 0.768
#> GSM26829 2 0.7815 0.880 0.232 0.768
#> GSM26830 2 0.7815 0.880 0.232 0.768
#> GSM26831 2 0.7815 0.880 0.232 0.768
#> GSM26832 2 0.7815 0.880 0.232 0.768
#> GSM26833 2 0.7815 0.880 0.232 0.768
#> GSM26834 2 0.7815 0.880 0.232 0.768
#> GSM26835 2 0.7815 0.880 0.232 0.768
#> GSM26836 2 0.0376 0.827 0.004 0.996
#> GSM26837 2 0.0376 0.827 0.004 0.996
#> GSM26838 2 0.0376 0.827 0.004 0.996
#> GSM26839 2 0.0376 0.827 0.004 0.996
#> GSM26840 2 0.0376 0.827 0.004 0.996
#> GSM26841 2 0.0376 0.827 0.004 0.996
#> GSM26842 2 0.0376 0.827 0.004 0.996
#> GSM26843 2 0.0376 0.827 0.004 0.996
#> GSM26844 2 0.0376 0.827 0.004 0.996
#> GSM26845 2 0.0376 0.827 0.004 0.996
#> GSM26846 1 0.0000 0.998 1.000 0.000
#> GSM26847 1 0.0000 0.998 1.000 0.000
#> GSM26848 1 0.0000 0.998 1.000 0.000
#> GSM26849 1 0.0000 0.998 1.000 0.000
#> GSM26850 1 0.0000 0.998 1.000 0.000
#> GSM26851 2 0.7815 0.880 0.232 0.768
#> GSM26852 1 0.0000 0.998 1.000 0.000
#> GSM26853 1 0.0000 0.998 1.000 0.000
#> GSM26854 1 0.0000 0.998 1.000 0.000
#> GSM26855 1 0.0000 0.998 1.000 0.000
#> GSM26856 1 0.0000 0.998 1.000 0.000
#> GSM26857 1 0.0000 0.998 1.000 0.000
#> GSM26858 1 0.0000 0.998 1.000 0.000
#> GSM26859 1 0.0000 0.998 1.000 0.000
#> GSM26860 1 0.0000 0.998 1.000 0.000
#> GSM26861 1 0.0000 0.998 1.000 0.000
#> GSM26862 2 0.0376 0.827 0.004 0.996
#> GSM26863 2 0.0376 0.827 0.004 0.996
#> GSM26864 2 0.0376 0.827 0.004 0.996
#> GSM26865 1 0.0000 0.998 1.000 0.000
#> GSM26866 2 0.0376 0.827 0.004 0.996
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM26805 2 0.000 0.986 0.000 1.000 0.000
#> GSM26806 3 0.497 0.783 0.000 0.236 0.764
#> GSM26807 3 0.497 0.783 0.000 0.236 0.764
#> GSM26808 3 0.497 0.783 0.000 0.236 0.764
#> GSM26809 2 0.153 0.946 0.040 0.960 0.000
#> GSM26810 3 0.497 0.783 0.000 0.236 0.764
#> GSM26811 3 0.497 0.783 0.000 0.236 0.764
#> GSM26812 3 0.497 0.783 0.000 0.236 0.764
#> GSM26813 2 0.000 0.986 0.000 1.000 0.000
#> GSM26814 2 0.000 0.986 0.000 1.000 0.000
#> GSM26815 3 0.497 0.783 0.000 0.236 0.764
#> GSM26816 2 0.000 0.986 0.000 1.000 0.000
#> GSM26817 3 0.497 0.783 0.000 0.236 0.764
#> GSM26818 3 0.000 0.908 0.000 0.000 1.000
#> GSM26819 2 0.000 0.986 0.000 1.000 0.000
#> GSM26820 2 0.000 0.986 0.000 1.000 0.000
#> GSM26821 2 0.000 0.986 0.000 1.000 0.000
#> GSM26822 2 0.000 0.986 0.000 1.000 0.000
#> GSM26823 2 0.000 0.986 0.000 1.000 0.000
#> GSM26824 2 0.000 0.986 0.000 1.000 0.000
#> GSM26825 2 0.000 0.986 0.000 1.000 0.000
#> GSM26826 2 0.000 0.986 0.000 1.000 0.000
#> GSM26827 2 0.000 0.986 0.000 1.000 0.000
#> GSM26828 2 0.000 0.986 0.000 1.000 0.000
#> GSM26829 2 0.000 0.986 0.000 1.000 0.000
#> GSM26830 2 0.000 0.986 0.000 1.000 0.000
#> GSM26831 2 0.000 0.986 0.000 1.000 0.000
#> GSM26832 2 0.000 0.986 0.000 1.000 0.000
#> GSM26833 2 0.000 0.986 0.000 1.000 0.000
#> GSM26834 2 0.000 0.986 0.000 1.000 0.000
#> GSM26835 2 0.000 0.986 0.000 1.000 0.000
#> GSM26836 1 0.000 1.000 1.000 0.000 0.000
#> GSM26837 1 0.000 1.000 1.000 0.000 0.000
#> GSM26838 1 0.000 1.000 1.000 0.000 0.000
#> GSM26839 1 0.000 1.000 1.000 0.000 0.000
#> GSM26840 1 0.000 1.000 1.000 0.000 0.000
#> GSM26841 1 0.000 1.000 1.000 0.000 0.000
#> GSM26842 1 0.000 1.000 1.000 0.000 0.000
#> GSM26843 1 0.000 1.000 1.000 0.000 0.000
#> GSM26844 1 0.000 1.000 1.000 0.000 0.000
#> GSM26845 2 0.514 0.637 0.252 0.748 0.000
#> GSM26846 3 0.000 0.908 0.000 0.000 1.000
#> GSM26847 3 0.000 0.908 0.000 0.000 1.000
#> GSM26848 3 0.000 0.908 0.000 0.000 1.000
#> GSM26849 3 0.000 0.908 0.000 0.000 1.000
#> GSM26850 3 0.000 0.908 0.000 0.000 1.000
#> GSM26851 2 0.000 0.986 0.000 1.000 0.000
#> GSM26852 3 0.000 0.908 0.000 0.000 1.000
#> GSM26853 3 0.000 0.908 0.000 0.000 1.000
#> GSM26854 3 0.000 0.908 0.000 0.000 1.000
#> GSM26855 3 0.000 0.908 0.000 0.000 1.000
#> GSM26856 3 0.000 0.908 0.000 0.000 1.000
#> GSM26857 3 0.000 0.908 0.000 0.000 1.000
#> GSM26858 3 0.000 0.908 0.000 0.000 1.000
#> GSM26859 3 0.000 0.908 0.000 0.000 1.000
#> GSM26860 3 0.000 0.908 0.000 0.000 1.000
#> GSM26861 3 0.000 0.908 0.000 0.000 1.000
#> GSM26862 1 0.000 1.000 1.000 0.000 0.000
#> GSM26863 1 0.000 1.000 1.000 0.000 0.000
#> GSM26864 1 0.000 1.000 1.000 0.000 0.000
#> GSM26865 3 0.000 0.908 0.000 0.000 1.000
#> GSM26866 1 0.000 1.000 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM26805 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM26806 4 0.3427 1.000 0.000 0.028 0.112 0.860
#> GSM26807 4 0.3427 1.000 0.000 0.028 0.112 0.860
#> GSM26808 4 0.3427 1.000 0.000 0.028 0.112 0.860
#> GSM26809 2 0.1406 0.950 0.024 0.960 0.000 0.016
#> GSM26810 4 0.3427 1.000 0.000 0.028 0.112 0.860
#> GSM26811 4 0.3427 1.000 0.000 0.028 0.112 0.860
#> GSM26812 4 0.3427 1.000 0.000 0.028 0.112 0.860
#> GSM26813 2 0.0188 0.983 0.000 0.996 0.000 0.004
#> GSM26814 2 0.0188 0.983 0.000 0.996 0.000 0.004
#> GSM26815 4 0.3427 1.000 0.000 0.028 0.112 0.860
#> GSM26816 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM26817 4 0.3427 1.000 0.000 0.028 0.112 0.860
#> GSM26818 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26819 2 0.0188 0.983 0.000 0.996 0.000 0.004
#> GSM26820 2 0.0188 0.983 0.000 0.996 0.000 0.004
#> GSM26821 2 0.0188 0.983 0.000 0.996 0.000 0.004
#> GSM26822 2 0.0188 0.983 0.000 0.996 0.000 0.004
#> GSM26823 2 0.0188 0.983 0.000 0.996 0.000 0.004
#> GSM26824 2 0.0188 0.983 0.000 0.996 0.000 0.004
#> GSM26825 2 0.0188 0.983 0.000 0.996 0.000 0.004
#> GSM26826 2 0.0188 0.983 0.000 0.996 0.000 0.004
#> GSM26827 2 0.0188 0.983 0.000 0.996 0.000 0.004
#> GSM26828 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM26829 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM26830 2 0.0188 0.983 0.000 0.996 0.000 0.004
#> GSM26831 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM26832 2 0.0707 0.974 0.000 0.980 0.000 0.020
#> GSM26833 2 0.0707 0.974 0.000 0.980 0.000 0.020
#> GSM26834 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM26835 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM26836 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM26837 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM26838 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM26839 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM26840 1 0.2760 0.892 0.872 0.000 0.000 0.128
#> GSM26841 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM26842 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM26843 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM26844 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM26845 2 0.4072 0.670 0.252 0.748 0.000 0.000
#> GSM26846 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26847 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26848 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26849 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26850 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26851 2 0.0817 0.969 0.000 0.976 0.000 0.024
#> GSM26852 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26853 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26854 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26855 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26856 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26857 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26858 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26859 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26860 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26861 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26862 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM26863 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM26864 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM26865 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26866 1 0.0000 0.992 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
#> GSM26805 2 0.0000 0.963 0.000 1.000 0 0.000 0.000
#> GSM26806 4 0.0000 1.000 0.000 0.000 0 1.000 0.000
#> GSM26807 4 0.0000 1.000 0.000 0.000 0 1.000 0.000
#> GSM26808 4 0.0000 1.000 0.000 0.000 0 1.000 0.000
#> GSM26809 2 0.1168 0.935 0.008 0.960 0 0.000 0.032
#> GSM26810 4 0.0000 1.000 0.000 0.000 0 1.000 0.000
#> GSM26811 4 0.0000 1.000 0.000 0.000 0 1.000 0.000
#> GSM26812 4 0.0000 1.000 0.000 0.000 0 1.000 0.000
#> GSM26813 2 0.0162 0.964 0.000 0.996 0 0.004 0.000
#> GSM26814 2 0.0162 0.964 0.000 0.996 0 0.004 0.000
#> GSM26815 4 0.0000 1.000 0.000 0.000 0 1.000 0.000
#> GSM26816 2 0.0000 0.963 0.000 1.000 0 0.000 0.000
#> GSM26817 4 0.0000 1.000 0.000 0.000 0 1.000 0.000
#> GSM26818 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM26819 2 0.0162 0.964 0.000 0.996 0 0.004 0.000
#> GSM26820 2 0.0162 0.964 0.000 0.996 0 0.004 0.000
#> GSM26821 2 0.0162 0.964 0.000 0.996 0 0.004 0.000
#> GSM26822 2 0.0162 0.964 0.000 0.996 0 0.004 0.000
#> GSM26823 2 0.0162 0.964 0.000 0.996 0 0.004 0.000
#> GSM26824 2 0.0162 0.964 0.000 0.996 0 0.004 0.000
#> GSM26825 2 0.0162 0.964 0.000 0.996 0 0.004 0.000
#> GSM26826 2 0.0162 0.964 0.000 0.996 0 0.004 0.000
#> GSM26827 2 0.0162 0.964 0.000 0.996 0 0.004 0.000
#> GSM26828 2 0.0000 0.963 0.000 1.000 0 0.000 0.000
#> GSM26829 2 0.0000 0.963 0.000 1.000 0 0.000 0.000
#> GSM26830 2 0.0162 0.964 0.000 0.996 0 0.004 0.000
#> GSM26831 2 0.0000 0.963 0.000 1.000 0 0.000 0.000
#> GSM26832 2 0.2536 0.865 0.000 0.868 0 0.004 0.128
#> GSM26833 2 0.2536 0.865 0.000 0.868 0 0.004 0.128
#> GSM26834 2 0.0000 0.963 0.000 1.000 0 0.000 0.000
#> GSM26835 2 0.0000 0.963 0.000 1.000 0 0.000 0.000
#> GSM26836 1 0.0000 1.000 1.000 0.000 0 0.000 0.000
#> GSM26837 1 0.0000 1.000 1.000 0.000 0 0.000 0.000
#> GSM26838 1 0.0000 1.000 1.000 0.000 0 0.000 0.000
#> GSM26839 1 0.0000 1.000 1.000 0.000 0 0.000 0.000
#> GSM26840 5 0.3395 0.000 0.236 0.000 0 0.000 0.764
#> GSM26841 1 0.0000 1.000 1.000 0.000 0 0.000 0.000
#> GSM26842 1 0.0000 1.000 1.000 0.000 0 0.000 0.000
#> GSM26843 1 0.0000 1.000 1.000 0.000 0 0.000 0.000
#> GSM26844 1 0.0000 1.000 1.000 0.000 0 0.000 0.000
#> GSM26845 2 0.3878 0.633 0.236 0.748 0 0.000 0.016
#> GSM26846 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM26847 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM26848 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM26849 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM26850 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM26851 2 0.3395 0.747 0.000 0.764 0 0.000 0.236
#> GSM26852 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM26853 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM26854 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM26855 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM26856 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM26857 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM26858 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM26859 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM26860 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM26861 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM26862 1 0.0000 1.000 1.000 0.000 0 0.000 0.000
#> GSM26863 1 0.0000 1.000 1.000 0.000 0 0.000 0.000
#> GSM26864 1 0.0000 1.000 1.000 0.000 0 0.000 0.000
#> GSM26865 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM26866 1 0.0000 1.000 1.000 0.000 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
#> GSM26805 2 0.2562 0.829 0.000 0.828 0 0.000 0.172 0.000
#> GSM26806 4 0.0000 1.000 0.000 0.000 0 1.000 0.000 0.000
#> GSM26807 4 0.0000 1.000 0.000 0.000 0 1.000 0.000 0.000
#> GSM26808 4 0.0000 1.000 0.000 0.000 0 1.000 0.000 0.000
#> GSM26809 2 0.3848 0.758 0.000 0.736 0 0.000 0.224 0.040
#> GSM26810 4 0.0000 1.000 0.000 0.000 0 1.000 0.000 0.000
#> GSM26811 4 0.0000 1.000 0.000 0.000 0 1.000 0.000 0.000
#> GSM26812 4 0.0000 1.000 0.000 0.000 0 1.000 0.000 0.000
#> GSM26813 2 0.0146 0.872 0.000 0.996 0 0.004 0.000 0.000
#> GSM26814 2 0.0146 0.872 0.000 0.996 0 0.004 0.000 0.000
#> GSM26815 4 0.0000 1.000 0.000 0.000 0 1.000 0.000 0.000
#> GSM26816 2 0.2562 0.829 0.000 0.828 0 0.000 0.172 0.000
#> GSM26817 4 0.0000 1.000 0.000 0.000 0 1.000 0.000 0.000
#> GSM26818 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM26819 2 0.0146 0.872 0.000 0.996 0 0.004 0.000 0.000
#> GSM26820 2 0.0146 0.872 0.000 0.996 0 0.004 0.000 0.000
#> GSM26821 2 0.0146 0.872 0.000 0.996 0 0.004 0.000 0.000
#> GSM26822 2 0.0146 0.872 0.000 0.996 0 0.004 0.000 0.000
#> GSM26823 2 0.0146 0.872 0.000 0.996 0 0.004 0.000 0.000
#> GSM26824 2 0.0146 0.872 0.000 0.996 0 0.004 0.000 0.000
#> GSM26825 2 0.0146 0.872 0.000 0.996 0 0.004 0.000 0.000
#> GSM26826 2 0.0146 0.872 0.000 0.996 0 0.004 0.000 0.000
#> GSM26827 2 0.0146 0.872 0.000 0.996 0 0.004 0.000 0.000
#> GSM26828 2 0.2562 0.829 0.000 0.828 0 0.000 0.172 0.000
#> GSM26829 2 0.2562 0.829 0.000 0.828 0 0.000 0.172 0.000
#> GSM26830 2 0.0146 0.872 0.000 0.996 0 0.004 0.000 0.000
#> GSM26831 2 0.2562 0.829 0.000 0.828 0 0.000 0.172 0.000
#> GSM26832 2 0.3547 0.704 0.000 0.696 0 0.004 0.300 0.000
#> GSM26833 2 0.3547 0.704 0.000 0.696 0 0.004 0.300 0.000
#> GSM26834 2 0.2562 0.829 0.000 0.828 0 0.000 0.172 0.000
#> GSM26835 2 0.2562 0.829 0.000 0.828 0 0.000 0.172 0.000
#> GSM26836 1 0.0000 1.000 1.000 0.000 0 0.000 0.000 0.000
#> GSM26837 1 0.0000 1.000 1.000 0.000 0 0.000 0.000 0.000
#> GSM26838 1 0.0000 1.000 1.000 0.000 0 0.000 0.000 0.000
#> GSM26839 1 0.0000 1.000 1.000 0.000 0 0.000 0.000 0.000
#> GSM26840 6 0.0000 0.000 0.000 0.000 0 0.000 0.000 1.000
#> GSM26841 1 0.0000 1.000 1.000 0.000 0 0.000 0.000 0.000
#> GSM26842 1 0.0000 1.000 1.000 0.000 0 0.000 0.000 0.000
#> GSM26843 1 0.0000 1.000 1.000 0.000 0 0.000 0.000 0.000
#> GSM26844 1 0.0000 1.000 1.000 0.000 0 0.000 0.000 0.000
#> GSM26845 2 0.4647 0.442 0.228 0.696 0 0.000 0.052 0.024
#> GSM26846 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM26847 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM26848 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM26849 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM26850 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM26851 5 0.1141 0.000 0.000 0.052 0 0.000 0.948 0.000
#> GSM26852 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM26853 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM26854 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM26855 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM26856 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM26857 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM26858 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM26859 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM26860 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM26861 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM26862 1 0.0000 1.000 1.000 0.000 0 0.000 0.000 0.000
#> GSM26863 1 0.0000 1.000 1.000 0.000 0 0.000 0.000 0.000
#> GSM26864 1 0.0000 1.000 1.000 0.000 0 0.000 0.000 0.000
#> GSM26865 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM26866 1 0.0000 1.000 1.000 0.000 0 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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> MAD:hclust 62 1.20e-01 2.27e-02 2
#> MAD:hclust 62 1.36e-07 1.72e-04 3
#> MAD:hclust 62 5.13e-11 1.26e-06 4
#> MAD:hclust 61 8.39e-11 2.10e-06 5
#> MAD:hclust 59 6.15e-12 1.83e-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["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 11993 rows and 62 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 0.500 0.894 0.915 0.4973 0.492 0.492
#> 3 3 0.766 0.871 0.836 0.2630 0.879 0.755
#> 4 4 0.661 0.869 0.856 0.1335 0.903 0.738
#> 5 5 0.733 0.875 0.795 0.0821 0.931 0.749
#> 6 6 0.788 0.837 0.822 0.0521 0.942 0.724
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
#> GSM26805 2 0.7219 0.925 0.200 0.800
#> GSM26806 2 0.0000 0.827 0.000 1.000
#> GSM26807 2 0.0000 0.827 0.000 1.000
#> GSM26808 2 0.0000 0.827 0.000 1.000
#> GSM26809 2 0.7219 0.925 0.200 0.800
#> GSM26810 2 0.0000 0.827 0.000 1.000
#> GSM26811 2 0.0000 0.827 0.000 1.000
#> GSM26812 2 0.0000 0.827 0.000 1.000
#> GSM26813 2 0.6712 0.934 0.176 0.824
#> GSM26814 2 0.6712 0.934 0.176 0.824
#> GSM26815 2 0.0000 0.827 0.000 1.000
#> GSM26816 2 0.7219 0.925 0.200 0.800
#> GSM26817 2 0.0000 0.827 0.000 1.000
#> GSM26818 1 0.7219 0.856 0.800 0.200
#> GSM26819 2 0.6712 0.934 0.176 0.824
#> GSM26820 2 0.6712 0.934 0.176 0.824
#> GSM26821 2 0.6712 0.934 0.176 0.824
#> GSM26822 2 0.6712 0.934 0.176 0.824
#> GSM26823 2 0.6712 0.934 0.176 0.824
#> GSM26824 2 0.6712 0.934 0.176 0.824
#> GSM26825 2 0.6712 0.934 0.176 0.824
#> GSM26826 2 0.6887 0.931 0.184 0.816
#> GSM26827 2 0.6712 0.934 0.176 0.824
#> GSM26828 2 0.7219 0.925 0.200 0.800
#> GSM26829 2 0.7219 0.925 0.200 0.800
#> GSM26830 2 0.6712 0.934 0.176 0.824
#> GSM26831 2 0.7219 0.925 0.200 0.800
#> GSM26832 2 0.7219 0.925 0.200 0.800
#> GSM26833 2 0.6712 0.934 0.176 0.824
#> GSM26834 2 0.7219 0.925 0.200 0.800
#> GSM26835 2 0.7219 0.925 0.200 0.800
#> GSM26836 1 0.0000 0.905 1.000 0.000
#> GSM26837 1 0.0000 0.905 1.000 0.000
#> GSM26838 1 0.0000 0.905 1.000 0.000
#> GSM26839 1 0.0000 0.905 1.000 0.000
#> GSM26840 1 0.0000 0.905 1.000 0.000
#> GSM26841 1 0.0000 0.905 1.000 0.000
#> GSM26842 1 0.0000 0.905 1.000 0.000
#> GSM26843 1 0.0000 0.905 1.000 0.000
#> GSM26844 1 0.0000 0.905 1.000 0.000
#> GSM26845 1 0.0376 0.901 0.996 0.004
#> GSM26846 1 0.1633 0.894 0.976 0.024
#> GSM26847 1 0.0000 0.905 1.000 0.000
#> GSM26848 1 0.0000 0.905 1.000 0.000
#> GSM26849 1 0.7219 0.856 0.800 0.200
#> GSM26850 1 0.0000 0.905 1.000 0.000
#> GSM26851 2 0.6712 0.934 0.176 0.824
#> GSM26852 1 0.7219 0.856 0.800 0.200
#> GSM26853 1 0.7219 0.856 0.800 0.200
#> GSM26854 1 0.7219 0.856 0.800 0.200
#> GSM26855 1 0.7219 0.856 0.800 0.200
#> GSM26856 1 0.7219 0.856 0.800 0.200
#> GSM26857 1 0.7219 0.856 0.800 0.200
#> GSM26858 1 0.7219 0.856 0.800 0.200
#> GSM26859 1 0.7219 0.856 0.800 0.200
#> GSM26860 1 0.7219 0.856 0.800 0.200
#> GSM26861 1 0.7219 0.856 0.800 0.200
#> GSM26862 1 0.0000 0.905 1.000 0.000
#> GSM26863 1 0.0000 0.905 1.000 0.000
#> GSM26864 1 0.0000 0.905 1.000 0.000
#> GSM26865 1 0.0000 0.905 1.000 0.000
#> GSM26866 1 0.0000 0.905 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM26805 2 0.2448 0.893 0.076 0.924 0.000
#> GSM26806 2 0.5797 0.774 0.280 0.712 0.008
#> GSM26807 2 0.5797 0.774 0.280 0.712 0.008
#> GSM26808 2 0.5797 0.774 0.280 0.712 0.008
#> GSM26809 2 0.2537 0.893 0.080 0.920 0.000
#> GSM26810 2 0.5797 0.774 0.280 0.712 0.008
#> GSM26811 2 0.5797 0.774 0.280 0.712 0.008
#> GSM26812 2 0.5797 0.774 0.280 0.712 0.008
#> GSM26813 2 0.0000 0.904 0.000 1.000 0.000
#> GSM26814 2 0.0000 0.904 0.000 1.000 0.000
#> GSM26815 2 0.5797 0.774 0.280 0.712 0.008
#> GSM26816 2 0.2448 0.893 0.076 0.924 0.000
#> GSM26817 2 0.5797 0.774 0.280 0.712 0.008
#> GSM26818 3 0.4702 0.656 0.212 0.000 0.788
#> GSM26819 2 0.0592 0.904 0.012 0.988 0.000
#> GSM26820 2 0.0592 0.904 0.012 0.988 0.000
#> GSM26821 2 0.0000 0.904 0.000 1.000 0.000
#> GSM26822 2 0.0592 0.904 0.012 0.988 0.000
#> GSM26823 2 0.0592 0.904 0.012 0.988 0.000
#> GSM26824 2 0.0000 0.904 0.000 1.000 0.000
#> GSM26825 2 0.0592 0.904 0.012 0.988 0.000
#> GSM26826 2 0.0592 0.904 0.012 0.988 0.000
#> GSM26827 2 0.0592 0.904 0.012 0.988 0.000
#> GSM26828 2 0.2448 0.893 0.076 0.924 0.000
#> GSM26829 2 0.2448 0.893 0.076 0.924 0.000
#> GSM26830 2 0.0000 0.904 0.000 1.000 0.000
#> GSM26831 2 0.2448 0.893 0.076 0.924 0.000
#> GSM26832 2 0.3038 0.893 0.104 0.896 0.000
#> GSM26833 2 0.3116 0.891 0.108 0.892 0.000
#> GSM26834 2 0.2878 0.893 0.096 0.904 0.000
#> GSM26835 2 0.2878 0.893 0.096 0.904 0.000
#> GSM26836 1 0.6126 0.890 0.644 0.004 0.352
#> GSM26837 1 0.6359 0.867 0.592 0.004 0.404
#> GSM26838 1 0.6081 0.891 0.652 0.004 0.344
#> GSM26839 1 0.6148 0.888 0.640 0.004 0.356
#> GSM26840 1 0.7155 0.590 0.720 0.152 0.128
#> GSM26841 1 0.6081 0.891 0.652 0.004 0.344
#> GSM26842 1 0.6081 0.891 0.652 0.004 0.344
#> GSM26843 1 0.6081 0.891 0.652 0.004 0.344
#> GSM26844 1 0.6081 0.891 0.652 0.004 0.344
#> GSM26845 1 0.6414 0.465 0.716 0.248 0.036
#> GSM26846 1 0.6617 0.835 0.556 0.008 0.436
#> GSM26847 1 0.6617 0.835 0.556 0.008 0.436
#> GSM26848 1 0.6598 0.844 0.564 0.008 0.428
#> GSM26849 3 0.0237 0.965 0.000 0.004 0.996
#> GSM26850 1 0.6608 0.840 0.560 0.008 0.432
#> GSM26851 2 0.3425 0.889 0.112 0.884 0.004
#> GSM26852 3 0.0237 0.965 0.000 0.004 0.996
#> GSM26853 3 0.0237 0.965 0.000 0.004 0.996
#> GSM26854 3 0.0237 0.965 0.000 0.004 0.996
#> GSM26855 3 0.0237 0.965 0.000 0.004 0.996
#> GSM26856 3 0.0237 0.965 0.000 0.004 0.996
#> GSM26857 3 0.0237 0.965 0.000 0.004 0.996
#> GSM26858 3 0.0237 0.965 0.000 0.004 0.996
#> GSM26859 3 0.0237 0.965 0.000 0.004 0.996
#> GSM26860 3 0.0237 0.965 0.000 0.004 0.996
#> GSM26861 3 0.0237 0.965 0.000 0.004 0.996
#> GSM26862 1 0.6359 0.867 0.592 0.004 0.404
#> GSM26863 1 0.6126 0.890 0.644 0.004 0.352
#> GSM26864 1 0.6081 0.891 0.652 0.004 0.344
#> GSM26865 1 0.6432 0.848 0.568 0.004 0.428
#> GSM26866 1 0.6081 0.891 0.652 0.004 0.344
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM26805 2 0.0336 0.813 0.000 0.992 0.000 0.008
#> GSM26806 4 0.4134 1.000 0.000 0.260 0.000 0.740
#> GSM26807 4 0.4134 1.000 0.000 0.260 0.000 0.740
#> GSM26808 4 0.4134 1.000 0.000 0.260 0.000 0.740
#> GSM26809 2 0.1661 0.769 0.000 0.944 0.004 0.052
#> GSM26810 4 0.4134 1.000 0.000 0.260 0.000 0.740
#> GSM26811 4 0.4134 1.000 0.000 0.260 0.000 0.740
#> GSM26812 4 0.4134 1.000 0.000 0.260 0.000 0.740
#> GSM26813 2 0.4840 0.828 0.000 0.784 0.116 0.100
#> GSM26814 2 0.4840 0.828 0.000 0.784 0.116 0.100
#> GSM26815 4 0.4134 1.000 0.000 0.260 0.000 0.740
#> GSM26816 2 0.0336 0.813 0.000 0.992 0.000 0.008
#> GSM26817 4 0.4134 1.000 0.000 0.260 0.000 0.740
#> GSM26818 3 0.3156 0.892 0.048 0.000 0.884 0.068
#> GSM26819 2 0.4840 0.828 0.000 0.784 0.116 0.100
#> GSM26820 2 0.4840 0.828 0.000 0.784 0.116 0.100
#> GSM26821 2 0.4840 0.828 0.000 0.784 0.116 0.100
#> GSM26822 2 0.4840 0.828 0.000 0.784 0.116 0.100
#> GSM26823 2 0.4840 0.828 0.000 0.784 0.116 0.100
#> GSM26824 2 0.4840 0.828 0.000 0.784 0.116 0.100
#> GSM26825 2 0.4840 0.828 0.000 0.784 0.116 0.100
#> GSM26826 2 0.4840 0.828 0.000 0.784 0.116 0.100
#> GSM26827 2 0.4840 0.828 0.000 0.784 0.116 0.100
#> GSM26828 2 0.0336 0.813 0.000 0.992 0.000 0.008
#> GSM26829 2 0.0188 0.813 0.000 0.996 0.000 0.004
#> GSM26830 2 0.4840 0.828 0.000 0.784 0.116 0.100
#> GSM26831 2 0.0336 0.813 0.000 0.992 0.000 0.008
#> GSM26832 2 0.1302 0.790 0.000 0.956 0.000 0.044
#> GSM26833 2 0.1118 0.794 0.000 0.964 0.000 0.036
#> GSM26834 2 0.0707 0.807 0.000 0.980 0.000 0.020
#> GSM26835 2 0.0707 0.807 0.000 0.980 0.000 0.020
#> GSM26836 1 0.0000 0.867 1.000 0.000 0.000 0.000
#> GSM26837 1 0.1661 0.852 0.944 0.000 0.052 0.004
#> GSM26838 1 0.2530 0.862 0.888 0.000 0.000 0.112
#> GSM26839 1 0.0707 0.868 0.980 0.000 0.000 0.020
#> GSM26840 1 0.5594 0.739 0.724 0.112 0.000 0.164
#> GSM26841 1 0.2530 0.862 0.888 0.000 0.000 0.112
#> GSM26842 1 0.2530 0.862 0.888 0.000 0.000 0.112
#> GSM26843 1 0.2714 0.861 0.884 0.004 0.000 0.112
#> GSM26844 1 0.2714 0.861 0.884 0.004 0.000 0.112
#> GSM26845 1 0.5400 0.756 0.772 0.100 0.020 0.108
#> GSM26846 1 0.4424 0.792 0.812 0.000 0.100 0.088
#> GSM26847 1 0.4424 0.792 0.812 0.000 0.100 0.088
#> GSM26848 1 0.4362 0.796 0.816 0.000 0.096 0.088
#> GSM26849 3 0.5940 0.733 0.240 0.000 0.672 0.088
#> GSM26850 1 0.4424 0.792 0.812 0.000 0.100 0.088
#> GSM26851 2 0.1302 0.790 0.000 0.956 0.000 0.044
#> GSM26852 3 0.2589 0.971 0.116 0.000 0.884 0.000
#> GSM26853 3 0.2589 0.971 0.116 0.000 0.884 0.000
#> GSM26854 3 0.2589 0.971 0.116 0.000 0.884 0.000
#> GSM26855 3 0.2589 0.971 0.116 0.000 0.884 0.000
#> GSM26856 3 0.2589 0.971 0.116 0.000 0.884 0.000
#> GSM26857 3 0.2589 0.971 0.116 0.000 0.884 0.000
#> GSM26858 3 0.2589 0.971 0.116 0.000 0.884 0.000
#> GSM26859 3 0.2589 0.971 0.116 0.000 0.884 0.000
#> GSM26860 3 0.2589 0.971 0.116 0.000 0.884 0.000
#> GSM26861 3 0.2589 0.971 0.116 0.000 0.884 0.000
#> GSM26862 1 0.2282 0.848 0.924 0.000 0.052 0.024
#> GSM26863 1 0.0000 0.867 1.000 0.000 0.000 0.000
#> GSM26864 1 0.2530 0.862 0.888 0.000 0.000 0.112
#> GSM26865 1 0.4362 0.796 0.816 0.000 0.096 0.088
#> GSM26866 1 0.2714 0.861 0.884 0.004 0.000 0.112
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM26805 5 0.4450 0.961 0.000 0.488 0.000 0.004 0.508
#> GSM26806 4 0.2929 0.991 0.000 0.180 0.000 0.820 0.000
#> GSM26807 4 0.2929 0.991 0.000 0.180 0.000 0.820 0.000
#> GSM26808 4 0.2929 0.991 0.000 0.180 0.000 0.820 0.000
#> GSM26809 2 0.3991 0.564 0.000 0.780 0.000 0.048 0.172
#> GSM26810 4 0.2929 0.991 0.000 0.180 0.000 0.820 0.000
#> GSM26811 4 0.2929 0.991 0.000 0.180 0.000 0.820 0.000
#> GSM26812 4 0.2929 0.991 0.000 0.180 0.000 0.820 0.000
#> GSM26813 2 0.0693 0.949 0.012 0.980 0.008 0.000 0.000
#> GSM26814 2 0.0693 0.949 0.012 0.980 0.008 0.000 0.000
#> GSM26815 4 0.4003 0.974 0.000 0.180 0.004 0.780 0.036
#> GSM26816 5 0.4450 0.961 0.000 0.488 0.000 0.004 0.508
#> GSM26817 4 0.4124 0.972 0.000 0.180 0.008 0.776 0.036
#> GSM26818 3 0.0955 0.921 0.004 0.000 0.968 0.028 0.000
#> GSM26819 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000
#> GSM26820 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000
#> GSM26821 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000
#> GSM26822 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000
#> GSM26823 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000
#> GSM26824 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000
#> GSM26825 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000
#> GSM26826 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000
#> GSM26827 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000
#> GSM26828 5 0.4450 0.961 0.000 0.488 0.000 0.004 0.508
#> GSM26829 5 0.4306 0.954 0.000 0.492 0.000 0.000 0.508
#> GSM26830 2 0.0693 0.949 0.012 0.980 0.008 0.000 0.000
#> GSM26831 5 0.4450 0.961 0.000 0.488 0.000 0.004 0.508
#> GSM26832 5 0.5042 0.953 0.000 0.460 0.000 0.032 0.508
#> GSM26833 5 0.5106 0.947 0.000 0.456 0.000 0.036 0.508
#> GSM26834 5 0.4902 0.960 0.000 0.468 0.000 0.024 0.508
#> GSM26835 5 0.4902 0.960 0.000 0.468 0.000 0.024 0.508
#> GSM26836 1 0.3826 0.776 0.832 0.000 0.024 0.052 0.092
#> GSM26837 1 0.4689 0.757 0.784 0.000 0.084 0.052 0.080
#> GSM26838 1 0.5759 0.759 0.592 0.000 0.024 0.056 0.328
#> GSM26839 1 0.4233 0.778 0.804 0.000 0.024 0.064 0.108
#> GSM26840 1 0.5689 0.679 0.480 0.000 0.000 0.080 0.440
#> GSM26841 1 0.5548 0.758 0.580 0.000 0.024 0.036 0.360
#> GSM26842 1 0.5548 0.758 0.580 0.000 0.024 0.036 0.360
#> GSM26843 1 0.5489 0.758 0.580 0.000 0.024 0.032 0.364
#> GSM26844 1 0.5489 0.758 0.580 0.000 0.024 0.032 0.364
#> GSM26845 1 0.1914 0.728 0.932 0.004 0.000 0.032 0.032
#> GSM26846 1 0.3170 0.679 0.856 0.000 0.104 0.036 0.004
#> GSM26847 1 0.3323 0.682 0.844 0.000 0.116 0.036 0.004
#> GSM26848 1 0.3273 0.685 0.848 0.000 0.112 0.036 0.004
#> GSM26849 3 0.5212 0.336 0.420 0.000 0.540 0.036 0.004
#> GSM26850 1 0.3323 0.682 0.844 0.000 0.116 0.036 0.004
#> GSM26851 5 0.5216 0.911 0.000 0.436 0.000 0.044 0.520
#> GSM26852 3 0.0404 0.955 0.012 0.000 0.988 0.000 0.000
#> GSM26853 3 0.0404 0.955 0.012 0.000 0.988 0.000 0.000
#> GSM26854 3 0.0404 0.955 0.012 0.000 0.988 0.000 0.000
#> GSM26855 3 0.0404 0.955 0.012 0.000 0.988 0.000 0.000
#> GSM26856 3 0.0404 0.955 0.012 0.000 0.988 0.000 0.000
#> GSM26857 3 0.0404 0.955 0.012 0.000 0.988 0.000 0.000
#> GSM26858 3 0.0404 0.955 0.012 0.000 0.988 0.000 0.000
#> GSM26859 3 0.0404 0.955 0.012 0.000 0.988 0.000 0.000
#> GSM26860 3 0.0404 0.955 0.012 0.000 0.988 0.000 0.000
#> GSM26861 3 0.0404 0.955 0.012 0.000 0.988 0.000 0.000
#> GSM26862 1 0.4646 0.751 0.788 0.000 0.084 0.064 0.064
#> GSM26863 1 0.3826 0.776 0.832 0.000 0.024 0.052 0.092
#> GSM26864 1 0.5548 0.758 0.580 0.000 0.024 0.036 0.360
#> GSM26865 1 0.3170 0.692 0.856 0.000 0.104 0.036 0.004
#> GSM26866 1 0.5489 0.758 0.580 0.000 0.024 0.032 0.364
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM26805 5 0.4258 0.9651 0.008 0.268 0.000 0.016 0.696 0.012
#> GSM26806 4 0.1957 0.9757 0.000 0.112 0.000 0.888 0.000 0.000
#> GSM26807 4 0.1957 0.9757 0.000 0.112 0.000 0.888 0.000 0.000
#> GSM26808 4 0.1957 0.9757 0.000 0.112 0.000 0.888 0.000 0.000
#> GSM26809 2 0.6361 0.4071 0.164 0.576 0.000 0.044 0.200 0.016
#> GSM26810 4 0.1957 0.9757 0.000 0.112 0.000 0.888 0.000 0.000
#> GSM26811 4 0.1957 0.9757 0.000 0.112 0.000 0.888 0.000 0.000
#> GSM26812 4 0.1957 0.9757 0.000 0.112 0.000 0.888 0.000 0.000
#> GSM26813 2 0.0622 0.9424 0.012 0.980 0.000 0.000 0.000 0.008
#> GSM26814 2 0.0622 0.9424 0.012 0.980 0.000 0.000 0.000 0.008
#> GSM26815 4 0.4254 0.9274 0.068 0.112 0.000 0.776 0.044 0.000
#> GSM26816 5 0.4258 0.9651 0.008 0.268 0.000 0.016 0.696 0.012
#> GSM26817 4 0.4453 0.9187 0.080 0.116 0.000 0.760 0.044 0.000
#> GSM26818 3 0.0922 0.9723 0.004 0.000 0.968 0.000 0.024 0.004
#> GSM26819 2 0.0405 0.9504 0.008 0.988 0.000 0.000 0.004 0.000
#> GSM26820 2 0.0405 0.9504 0.008 0.988 0.000 0.000 0.004 0.000
#> GSM26821 2 0.0000 0.9508 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26822 2 0.0405 0.9504 0.008 0.988 0.000 0.000 0.004 0.000
#> GSM26823 2 0.0146 0.9514 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM26824 2 0.0000 0.9508 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26825 2 0.0405 0.9504 0.008 0.988 0.000 0.000 0.004 0.000
#> GSM26826 2 0.0146 0.9514 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM26827 2 0.0146 0.9514 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM26828 5 0.3919 0.9677 0.000 0.268 0.000 0.016 0.708 0.008
#> GSM26829 5 0.3919 0.9677 0.000 0.268 0.000 0.016 0.708 0.008
#> GSM26830 2 0.0622 0.9424 0.012 0.980 0.000 0.000 0.000 0.008
#> GSM26831 5 0.4258 0.9651 0.008 0.268 0.000 0.016 0.696 0.012
#> GSM26832 5 0.4406 0.9590 0.016 0.256 0.000 0.028 0.696 0.004
#> GSM26833 5 0.4428 0.9609 0.016 0.260 0.000 0.028 0.692 0.004
#> GSM26834 5 0.4239 0.9654 0.016 0.268 0.000 0.016 0.696 0.004
#> GSM26835 5 0.4239 0.9654 0.016 0.268 0.000 0.016 0.696 0.004
#> GSM26836 6 0.5904 0.2128 0.320 0.000 0.004 0.052 0.072 0.552
#> GSM26837 6 0.6233 0.2814 0.292 0.000 0.024 0.052 0.072 0.560
#> GSM26838 1 0.4667 0.8540 0.664 0.000 0.004 0.016 0.036 0.280
#> GSM26839 6 0.6049 -0.0735 0.388 0.000 0.004 0.052 0.072 0.484
#> GSM26840 1 0.4866 0.5323 0.716 0.000 0.000 0.036 0.100 0.148
#> GSM26841 1 0.3586 0.9114 0.712 0.000 0.004 0.004 0.000 0.280
#> GSM26842 1 0.3724 0.9109 0.708 0.000 0.004 0.004 0.004 0.280
#> GSM26843 1 0.3693 0.9119 0.708 0.000 0.004 0.000 0.008 0.280
#> GSM26844 1 0.3693 0.9119 0.708 0.000 0.004 0.000 0.008 0.280
#> GSM26845 6 0.3436 0.5456 0.052 0.000 0.000 0.032 0.080 0.836
#> GSM26846 6 0.1141 0.6381 0.000 0.000 0.052 0.000 0.000 0.948
#> GSM26847 6 0.1204 0.6400 0.000 0.000 0.056 0.000 0.000 0.944
#> GSM26848 6 0.1204 0.6400 0.000 0.000 0.056 0.000 0.000 0.944
#> GSM26849 6 0.3499 0.3272 0.000 0.000 0.320 0.000 0.000 0.680
#> GSM26850 6 0.1204 0.6400 0.000 0.000 0.056 0.000 0.000 0.944
#> GSM26851 5 0.5046 0.8881 0.044 0.220 0.000 0.032 0.688 0.016
#> GSM26852 3 0.0260 0.9940 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM26853 3 0.0260 0.9940 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM26854 3 0.0000 0.9941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26855 3 0.0260 0.9940 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM26856 3 0.0000 0.9941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26857 3 0.0000 0.9941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26858 3 0.0260 0.9940 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM26859 3 0.0000 0.9941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26860 3 0.0000 0.9941 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26861 3 0.0260 0.9940 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM26862 6 0.6120 0.3344 0.264 0.000 0.024 0.052 0.072 0.588
#> GSM26863 6 0.5904 0.2128 0.320 0.000 0.004 0.052 0.072 0.552
#> GSM26864 1 0.3724 0.9109 0.708 0.000 0.004 0.004 0.004 0.280
#> GSM26865 6 0.1285 0.6389 0.004 0.000 0.052 0.000 0.000 0.944
#> GSM26866 1 0.3693 0.9119 0.708 0.000 0.004 0.000 0.008 0.280
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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> MAD:kmeans 62 1.14e-12 8.30e-01 2
#> MAD:kmeans 61 2.46e-12 2.21e-04 3
#> MAD:kmeans 62 8.75e-12 2.79e-06 4
#> MAD:kmeans 61 5.90e-11 6.14e-09 5
#> MAD:kmeans 55 4.08e-09 2.17e-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", "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 11993 rows and 62 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 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5087 0.492 0.492
#> 3 3 1.000 0.976 0.985 0.2478 0.874 0.744
#> 4 4 0.872 0.879 0.940 0.1878 0.884 0.682
#> 5 5 0.930 0.937 0.952 0.0600 0.921 0.700
#> 6 6 0.962 0.958 0.969 0.0446 0.956 0.783
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 3 5
There is also optional best \(k\) = 2 3 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
#> GSM26805 2 0.0000 1.000 0.000 1.000
#> GSM26806 2 0.0000 1.000 0.000 1.000
#> GSM26807 2 0.0000 1.000 0.000 1.000
#> GSM26808 2 0.0000 1.000 0.000 1.000
#> GSM26809 2 0.0000 1.000 0.000 1.000
#> GSM26810 2 0.0000 1.000 0.000 1.000
#> GSM26811 2 0.0000 1.000 0.000 1.000
#> GSM26812 2 0.0000 1.000 0.000 1.000
#> GSM26813 2 0.0000 1.000 0.000 1.000
#> GSM26814 2 0.0000 1.000 0.000 1.000
#> GSM26815 2 0.0000 1.000 0.000 1.000
#> GSM26816 2 0.0000 1.000 0.000 1.000
#> GSM26817 2 0.0000 1.000 0.000 1.000
#> GSM26818 1 0.0000 1.000 1.000 0.000
#> GSM26819 2 0.0000 1.000 0.000 1.000
#> GSM26820 2 0.0000 1.000 0.000 1.000
#> GSM26821 2 0.0000 1.000 0.000 1.000
#> GSM26822 2 0.0000 1.000 0.000 1.000
#> GSM26823 2 0.0000 1.000 0.000 1.000
#> GSM26824 2 0.0000 1.000 0.000 1.000
#> GSM26825 2 0.0000 1.000 0.000 1.000
#> GSM26826 2 0.0000 1.000 0.000 1.000
#> GSM26827 2 0.0000 1.000 0.000 1.000
#> GSM26828 2 0.0000 1.000 0.000 1.000
#> GSM26829 2 0.0000 1.000 0.000 1.000
#> GSM26830 2 0.0000 1.000 0.000 1.000
#> GSM26831 2 0.0000 1.000 0.000 1.000
#> GSM26832 2 0.0000 1.000 0.000 1.000
#> GSM26833 2 0.0000 1.000 0.000 1.000
#> GSM26834 2 0.0000 1.000 0.000 1.000
#> GSM26835 2 0.0000 1.000 0.000 1.000
#> GSM26836 1 0.0000 1.000 1.000 0.000
#> GSM26837 1 0.0000 1.000 1.000 0.000
#> GSM26838 1 0.0000 1.000 1.000 0.000
#> GSM26839 1 0.0000 1.000 1.000 0.000
#> GSM26840 1 0.0000 1.000 1.000 0.000
#> GSM26841 1 0.0000 1.000 1.000 0.000
#> GSM26842 1 0.0000 1.000 1.000 0.000
#> GSM26843 1 0.0000 1.000 1.000 0.000
#> GSM26844 1 0.0000 1.000 1.000 0.000
#> GSM26845 1 0.0376 0.996 0.996 0.004
#> GSM26846 1 0.0000 1.000 1.000 0.000
#> GSM26847 1 0.0000 1.000 1.000 0.000
#> GSM26848 1 0.0000 1.000 1.000 0.000
#> GSM26849 1 0.0000 1.000 1.000 0.000
#> GSM26850 1 0.0000 1.000 1.000 0.000
#> GSM26851 2 0.0000 1.000 0.000 1.000
#> GSM26852 1 0.0000 1.000 1.000 0.000
#> GSM26853 1 0.0000 1.000 1.000 0.000
#> GSM26854 1 0.0000 1.000 1.000 0.000
#> GSM26855 1 0.0000 1.000 1.000 0.000
#> GSM26856 1 0.0000 1.000 1.000 0.000
#> GSM26857 1 0.0000 1.000 1.000 0.000
#> GSM26858 1 0.0000 1.000 1.000 0.000
#> GSM26859 1 0.0000 1.000 1.000 0.000
#> GSM26860 1 0.0000 1.000 1.000 0.000
#> GSM26861 1 0.0000 1.000 1.000 0.000
#> GSM26862 1 0.0000 1.000 1.000 0.000
#> GSM26863 1 0.0000 1.000 1.000 0.000
#> GSM26864 1 0.0000 1.000 1.000 0.000
#> GSM26865 1 0.0000 1.000 1.000 0.000
#> GSM26866 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
#> GSM26805 2 0.0000 0.995 0.000 1.000 0.000
#> GSM26806 2 0.0747 0.992 0.000 0.984 0.016
#> GSM26807 2 0.0747 0.992 0.000 0.984 0.016
#> GSM26808 2 0.0747 0.992 0.000 0.984 0.016
#> GSM26809 2 0.0000 0.995 0.000 1.000 0.000
#> GSM26810 2 0.0747 0.992 0.000 0.984 0.016
#> GSM26811 2 0.0747 0.992 0.000 0.984 0.016
#> GSM26812 2 0.0747 0.992 0.000 0.984 0.016
#> GSM26813 2 0.0592 0.992 0.000 0.988 0.012
#> GSM26814 2 0.0237 0.995 0.000 0.996 0.004
#> GSM26815 2 0.0747 0.992 0.000 0.984 0.016
#> GSM26816 2 0.0000 0.995 0.000 1.000 0.000
#> GSM26817 2 0.0747 0.992 0.000 0.984 0.016
#> GSM26818 3 0.0237 0.985 0.004 0.000 0.996
#> GSM26819 2 0.0000 0.995 0.000 1.000 0.000
#> GSM26820 2 0.0000 0.995 0.000 1.000 0.000
#> GSM26821 2 0.0000 0.995 0.000 1.000 0.000
#> GSM26822 2 0.0000 0.995 0.000 1.000 0.000
#> GSM26823 2 0.0000 0.995 0.000 1.000 0.000
#> GSM26824 2 0.0000 0.995 0.000 1.000 0.000
#> GSM26825 2 0.0000 0.995 0.000 1.000 0.000
#> GSM26826 2 0.0000 0.995 0.000 1.000 0.000
#> GSM26827 2 0.0000 0.995 0.000 1.000 0.000
#> GSM26828 2 0.0000 0.995 0.000 1.000 0.000
#> GSM26829 2 0.0000 0.995 0.000 1.000 0.000
#> GSM26830 2 0.0237 0.995 0.000 0.996 0.004
#> GSM26831 2 0.0000 0.995 0.000 1.000 0.000
#> GSM26832 2 0.0237 0.995 0.000 0.996 0.004
#> GSM26833 2 0.0237 0.995 0.000 0.996 0.004
#> GSM26834 2 0.0237 0.995 0.000 0.996 0.004
#> GSM26835 2 0.0237 0.995 0.000 0.996 0.004
#> GSM26836 1 0.0000 0.968 1.000 0.000 0.000
#> GSM26837 1 0.0000 0.968 1.000 0.000 0.000
#> GSM26838 1 0.0000 0.968 1.000 0.000 0.000
#> GSM26839 1 0.0000 0.968 1.000 0.000 0.000
#> GSM26840 1 0.0592 0.957 0.988 0.012 0.000
#> GSM26841 1 0.0000 0.968 1.000 0.000 0.000
#> GSM26842 1 0.0000 0.968 1.000 0.000 0.000
#> GSM26843 1 0.0000 0.968 1.000 0.000 0.000
#> GSM26844 1 0.0000 0.968 1.000 0.000 0.000
#> GSM26845 1 0.0747 0.953 0.984 0.016 0.000
#> GSM26846 3 0.1031 0.991 0.024 0.000 0.976
#> GSM26847 1 0.6008 0.407 0.628 0.000 0.372
#> GSM26848 1 0.2066 0.919 0.940 0.000 0.060
#> GSM26849 3 0.0747 0.997 0.016 0.000 0.984
#> GSM26850 3 0.1163 0.987 0.028 0.000 0.972
#> GSM26851 2 0.0592 0.993 0.000 0.988 0.012
#> GSM26852 3 0.0747 0.997 0.016 0.000 0.984
#> GSM26853 3 0.0747 0.997 0.016 0.000 0.984
#> GSM26854 3 0.0747 0.997 0.016 0.000 0.984
#> GSM26855 3 0.0747 0.997 0.016 0.000 0.984
#> GSM26856 3 0.0747 0.997 0.016 0.000 0.984
#> GSM26857 3 0.0747 0.997 0.016 0.000 0.984
#> GSM26858 3 0.0747 0.997 0.016 0.000 0.984
#> GSM26859 3 0.0747 0.997 0.016 0.000 0.984
#> GSM26860 3 0.0747 0.997 0.016 0.000 0.984
#> GSM26861 3 0.0747 0.997 0.016 0.000 0.984
#> GSM26862 1 0.0000 0.968 1.000 0.000 0.000
#> GSM26863 1 0.0000 0.968 1.000 0.000 0.000
#> GSM26864 1 0.0000 0.968 1.000 0.000 0.000
#> GSM26865 1 0.1411 0.941 0.964 0.000 0.036
#> GSM26866 1 0.0000 0.968 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM26805 2 0.2469 0.829 0.000 0.892 0.000 0.108
#> GSM26806 4 0.0188 0.917 0.000 0.004 0.000 0.996
#> GSM26807 4 0.0188 0.917 0.000 0.004 0.000 0.996
#> GSM26808 4 0.0188 0.917 0.000 0.004 0.000 0.996
#> GSM26809 2 0.0000 0.846 0.000 1.000 0.000 0.000
#> GSM26810 4 0.0188 0.917 0.000 0.004 0.000 0.996
#> GSM26811 4 0.0188 0.917 0.000 0.004 0.000 0.996
#> GSM26812 4 0.0188 0.917 0.000 0.004 0.000 0.996
#> GSM26813 4 0.4222 0.589 0.000 0.272 0.000 0.728
#> GSM26814 2 0.4961 0.168 0.000 0.552 0.000 0.448
#> GSM26815 4 0.0188 0.917 0.000 0.004 0.000 0.996
#> GSM26816 2 0.2469 0.829 0.000 0.892 0.000 0.108
#> GSM26817 4 0.0188 0.917 0.000 0.004 0.000 0.996
#> GSM26818 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM26819 2 0.1118 0.857 0.000 0.964 0.000 0.036
#> GSM26820 2 0.1118 0.857 0.000 0.964 0.000 0.036
#> GSM26821 2 0.1118 0.857 0.000 0.964 0.000 0.036
#> GSM26822 2 0.1118 0.857 0.000 0.964 0.000 0.036
#> GSM26823 2 0.1118 0.857 0.000 0.964 0.000 0.036
#> GSM26824 2 0.2081 0.829 0.000 0.916 0.000 0.084
#> GSM26825 2 0.1118 0.857 0.000 0.964 0.000 0.036
#> GSM26826 2 0.1118 0.857 0.000 0.964 0.000 0.036
#> GSM26827 2 0.1118 0.857 0.000 0.964 0.000 0.036
#> GSM26828 2 0.2469 0.829 0.000 0.892 0.000 0.108
#> GSM26829 2 0.2469 0.829 0.000 0.892 0.000 0.108
#> GSM26830 2 0.4454 0.534 0.000 0.692 0.000 0.308
#> GSM26831 2 0.2469 0.829 0.000 0.892 0.000 0.108
#> GSM26832 2 0.4164 0.668 0.000 0.736 0.000 0.264
#> GSM26833 4 0.4164 0.614 0.000 0.264 0.000 0.736
#> GSM26834 2 0.4103 0.680 0.000 0.744 0.000 0.256
#> GSM26835 2 0.4103 0.680 0.000 0.744 0.000 0.256
#> GSM26836 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM26837 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM26838 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM26839 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM26840 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM26841 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM26842 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM26843 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM26844 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM26845 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM26846 3 0.0524 0.989 0.008 0.000 0.988 0.004
#> GSM26847 1 0.4905 0.437 0.632 0.000 0.364 0.004
#> GSM26848 1 0.1902 0.912 0.932 0.000 0.064 0.004
#> GSM26849 3 0.0188 0.995 0.000 0.000 0.996 0.004
#> GSM26850 3 0.0779 0.981 0.016 0.000 0.980 0.004
#> GSM26851 4 0.3311 0.764 0.000 0.172 0.000 0.828
#> GSM26852 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM26853 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM26854 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM26855 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM26856 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM26857 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM26858 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM26859 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM26860 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM26861 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM26862 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM26863 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM26864 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> GSM26865 1 0.1305 0.938 0.960 0.000 0.036 0.004
#> GSM26866 1 0.0000 0.968 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM26805 5 0.2574 0.946 0.000 0.112 0.000 0.012 0.876
#> GSM26806 4 0.0290 1.000 0.000 0.008 0.000 0.992 0.000
#> GSM26807 4 0.0290 1.000 0.000 0.008 0.000 0.992 0.000
#> GSM26808 4 0.0290 1.000 0.000 0.008 0.000 0.992 0.000
#> GSM26809 2 0.1732 0.892 0.000 0.920 0.000 0.000 0.080
#> GSM26810 4 0.0290 1.000 0.000 0.008 0.000 0.992 0.000
#> GSM26811 4 0.0290 1.000 0.000 0.008 0.000 0.992 0.000
#> GSM26812 4 0.0290 1.000 0.000 0.008 0.000 0.992 0.000
#> GSM26813 2 0.2179 0.863 0.000 0.888 0.000 0.112 0.000
#> GSM26814 2 0.1121 0.943 0.000 0.956 0.000 0.044 0.000
#> GSM26815 4 0.0290 1.000 0.000 0.008 0.000 0.992 0.000
#> GSM26816 5 0.2574 0.946 0.000 0.112 0.000 0.012 0.876
#> GSM26817 4 0.0290 1.000 0.000 0.008 0.000 0.992 0.000
#> GSM26818 3 0.0000 0.970 0.000 0.000 1.000 0.000 0.000
#> GSM26819 2 0.0000 0.974 0.000 1.000 0.000 0.000 0.000
#> GSM26820 2 0.0000 0.974 0.000 1.000 0.000 0.000 0.000
#> GSM26821 2 0.0000 0.974 0.000 1.000 0.000 0.000 0.000
#> GSM26822 2 0.0000 0.974 0.000 1.000 0.000 0.000 0.000
#> GSM26823 2 0.0000 0.974 0.000 1.000 0.000 0.000 0.000
#> GSM26824 2 0.0290 0.970 0.000 0.992 0.000 0.008 0.000
#> GSM26825 2 0.0000 0.974 0.000 1.000 0.000 0.000 0.000
#> GSM26826 2 0.0000 0.974 0.000 1.000 0.000 0.000 0.000
#> GSM26827 2 0.0000 0.974 0.000 1.000 0.000 0.000 0.000
#> GSM26828 5 0.2574 0.946 0.000 0.112 0.000 0.012 0.876
#> GSM26829 5 0.2574 0.946 0.000 0.112 0.000 0.012 0.876
#> GSM26830 2 0.0609 0.963 0.000 0.980 0.000 0.020 0.000
#> GSM26831 5 0.2574 0.946 0.000 0.112 0.000 0.012 0.876
#> GSM26832 5 0.2740 0.944 0.000 0.096 0.000 0.028 0.876
#> GSM26833 5 0.2707 0.870 0.000 0.024 0.000 0.100 0.876
#> GSM26834 5 0.2740 0.944 0.000 0.096 0.000 0.028 0.876
#> GSM26835 5 0.2740 0.944 0.000 0.096 0.000 0.028 0.876
#> GSM26836 1 0.0162 0.950 0.996 0.000 0.000 0.000 0.004
#> GSM26837 1 0.0162 0.950 0.996 0.000 0.000 0.000 0.004
#> GSM26838 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000
#> GSM26839 1 0.0162 0.950 0.996 0.000 0.000 0.000 0.004
#> GSM26840 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000
#> GSM26841 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000
#> GSM26842 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000
#> GSM26843 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000
#> GSM26844 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000
#> GSM26845 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000
#> GSM26846 3 0.3107 0.880 0.016 0.000 0.852 0.008 0.124
#> GSM26847 1 0.6175 0.341 0.544 0.000 0.324 0.008 0.124
#> GSM26848 1 0.3765 0.821 0.820 0.000 0.048 0.008 0.124
#> GSM26849 3 0.2612 0.891 0.000 0.000 0.868 0.008 0.124
#> GSM26850 3 0.3463 0.866 0.032 0.000 0.836 0.008 0.124
#> GSM26851 5 0.4088 0.601 0.000 0.008 0.000 0.304 0.688
#> GSM26852 3 0.0000 0.970 0.000 0.000 1.000 0.000 0.000
#> GSM26853 3 0.0000 0.970 0.000 0.000 1.000 0.000 0.000
#> GSM26854 3 0.0000 0.970 0.000 0.000 1.000 0.000 0.000
#> GSM26855 3 0.0000 0.970 0.000 0.000 1.000 0.000 0.000
#> GSM26856 3 0.0000 0.970 0.000 0.000 1.000 0.000 0.000
#> GSM26857 3 0.0000 0.970 0.000 0.000 1.000 0.000 0.000
#> GSM26858 3 0.0000 0.970 0.000 0.000 1.000 0.000 0.000
#> GSM26859 3 0.0000 0.970 0.000 0.000 1.000 0.000 0.000
#> GSM26860 3 0.0000 0.970 0.000 0.000 1.000 0.000 0.000
#> GSM26861 3 0.0000 0.970 0.000 0.000 1.000 0.000 0.000
#> GSM26862 1 0.0162 0.950 0.996 0.000 0.000 0.000 0.004
#> GSM26863 1 0.0162 0.950 0.996 0.000 0.000 0.000 0.004
#> GSM26864 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000
#> GSM26865 1 0.3380 0.839 0.840 0.000 0.028 0.008 0.124
#> GSM26866 1 0.0000 0.951 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
#> GSM26805 5 0.0458 0.962 0.000 0.016 0.000 0.000 0.984 0.000
#> GSM26806 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26807 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26808 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26809 2 0.2169 0.892 0.008 0.900 0.000 0.000 0.080 0.012
#> GSM26810 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26811 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26812 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26813 2 0.1549 0.948 0.000 0.936 0.000 0.020 0.000 0.044
#> GSM26814 2 0.1007 0.962 0.000 0.956 0.000 0.000 0.000 0.044
#> GSM26815 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26816 5 0.0458 0.962 0.000 0.016 0.000 0.000 0.984 0.000
#> GSM26817 4 0.0146 0.996 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM26818 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26819 2 0.0000 0.980 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26820 2 0.0000 0.980 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26821 2 0.0146 0.980 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM26822 2 0.0000 0.980 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26823 2 0.0000 0.980 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26824 2 0.0146 0.980 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM26825 2 0.0000 0.980 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26826 2 0.0000 0.980 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26827 2 0.0000 0.980 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26828 5 0.0458 0.962 0.000 0.016 0.000 0.000 0.984 0.000
#> GSM26829 5 0.0458 0.962 0.000 0.016 0.000 0.000 0.984 0.000
#> GSM26830 2 0.1007 0.962 0.000 0.956 0.000 0.000 0.000 0.044
#> GSM26831 5 0.0458 0.962 0.000 0.016 0.000 0.000 0.984 0.000
#> GSM26832 5 0.0767 0.961 0.000 0.004 0.000 0.012 0.976 0.008
#> GSM26833 5 0.0717 0.957 0.000 0.000 0.000 0.016 0.976 0.008
#> GSM26834 5 0.0767 0.961 0.000 0.004 0.000 0.012 0.976 0.008
#> GSM26835 5 0.0767 0.961 0.000 0.004 0.000 0.012 0.976 0.008
#> GSM26836 1 0.2263 0.922 0.884 0.000 0.000 0.000 0.016 0.100
#> GSM26837 1 0.2358 0.917 0.876 0.000 0.000 0.000 0.016 0.108
#> GSM26838 1 0.0260 0.946 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM26839 1 0.2214 0.924 0.888 0.000 0.000 0.000 0.016 0.096
#> GSM26840 1 0.0363 0.941 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM26841 1 0.0000 0.947 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26842 1 0.0000 0.947 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26843 1 0.0000 0.947 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26844 1 0.0000 0.947 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26845 1 0.1765 0.929 0.904 0.000 0.000 0.000 0.000 0.096
#> GSM26846 6 0.1285 0.914 0.004 0.000 0.052 0.000 0.000 0.944
#> GSM26847 6 0.1528 0.916 0.048 0.000 0.016 0.000 0.000 0.936
#> GSM26848 6 0.1663 0.906 0.088 0.000 0.000 0.000 0.000 0.912
#> GSM26849 6 0.2491 0.815 0.000 0.000 0.164 0.000 0.000 0.836
#> GSM26850 6 0.1528 0.919 0.016 0.000 0.048 0.000 0.000 0.936
#> GSM26851 5 0.3245 0.714 0.000 0.000 0.000 0.228 0.764 0.008
#> GSM26852 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26853 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26854 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26855 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26856 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26857 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26858 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26859 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26860 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26861 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26862 1 0.2404 0.914 0.872 0.000 0.000 0.000 0.016 0.112
#> GSM26863 1 0.2263 0.922 0.884 0.000 0.000 0.000 0.016 0.100
#> GSM26864 1 0.0000 0.947 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26865 6 0.2135 0.886 0.128 0.000 0.000 0.000 0.000 0.872
#> GSM26866 1 0.0000 0.947 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 tissue(p) individual(p) k
#> MAD:skmeans 62 1.14e-12 8.30e-01 2
#> MAD:skmeans 61 2.52e-12 2.33e-04 3
#> MAD:skmeans 60 2.18e-11 4.00e-06 4
#> MAD:skmeans 61 6.13e-11 1.62e-08 5
#> MAD:skmeans 62 1.46e-10 2.39e-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", "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 11993 rows and 62 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.993 0.997 0.5059 0.494 0.494
#> 3 3 1.000 0.998 0.999 0.2435 0.841 0.690
#> 4 4 0.773 0.881 0.915 0.1795 0.889 0.701
#> 5 5 0.866 0.893 0.897 0.0724 0.928 0.732
#> 6 6 1.000 0.976 0.988 0.0577 0.942 0.724
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM26805 2 0.000 1.000 0.000 1.000
#> GSM26806 2 0.000 1.000 0.000 1.000
#> GSM26807 2 0.000 1.000 0.000 1.000
#> GSM26808 2 0.000 1.000 0.000 1.000
#> GSM26809 2 0.000 1.000 0.000 1.000
#> GSM26810 2 0.000 1.000 0.000 1.000
#> GSM26811 2 0.000 1.000 0.000 1.000
#> GSM26812 2 0.000 1.000 0.000 1.000
#> GSM26813 2 0.000 1.000 0.000 1.000
#> GSM26814 2 0.000 1.000 0.000 1.000
#> GSM26815 2 0.000 1.000 0.000 1.000
#> GSM26816 2 0.000 1.000 0.000 1.000
#> GSM26817 2 0.000 1.000 0.000 1.000
#> GSM26818 1 0.000 0.992 1.000 0.000
#> GSM26819 2 0.000 1.000 0.000 1.000
#> GSM26820 2 0.000 1.000 0.000 1.000
#> GSM26821 2 0.000 1.000 0.000 1.000
#> GSM26822 2 0.000 1.000 0.000 1.000
#> GSM26823 2 0.000 1.000 0.000 1.000
#> GSM26824 2 0.000 1.000 0.000 1.000
#> GSM26825 2 0.000 1.000 0.000 1.000
#> GSM26826 2 0.000 1.000 0.000 1.000
#> GSM26827 2 0.000 1.000 0.000 1.000
#> GSM26828 2 0.000 1.000 0.000 1.000
#> GSM26829 2 0.000 1.000 0.000 1.000
#> GSM26830 2 0.000 1.000 0.000 1.000
#> GSM26831 2 0.000 1.000 0.000 1.000
#> GSM26832 2 0.000 1.000 0.000 1.000
#> GSM26833 2 0.000 1.000 0.000 1.000
#> GSM26834 2 0.000 1.000 0.000 1.000
#> GSM26835 2 0.000 1.000 0.000 1.000
#> GSM26836 1 0.000 0.992 1.000 0.000
#> GSM26837 1 0.000 0.992 1.000 0.000
#> GSM26838 1 0.000 0.992 1.000 0.000
#> GSM26839 1 0.000 0.992 1.000 0.000
#> GSM26840 2 0.000 1.000 0.000 1.000
#> GSM26841 1 0.000 0.992 1.000 0.000
#> GSM26842 1 0.000 0.992 1.000 0.000
#> GSM26843 1 0.000 0.992 1.000 0.000
#> GSM26844 1 0.000 0.992 1.000 0.000
#> GSM26845 2 0.000 1.000 0.000 1.000
#> GSM26846 1 0.358 0.927 0.932 0.068
#> GSM26847 1 0.000 0.992 1.000 0.000
#> GSM26848 1 0.000 0.992 1.000 0.000
#> GSM26849 1 0.000 0.992 1.000 0.000
#> GSM26850 1 0.605 0.830 0.852 0.148
#> GSM26851 2 0.000 1.000 0.000 1.000
#> GSM26852 1 0.000 0.992 1.000 0.000
#> GSM26853 1 0.000 0.992 1.000 0.000
#> GSM26854 1 0.000 0.992 1.000 0.000
#> GSM26855 1 0.000 0.992 1.000 0.000
#> GSM26856 1 0.000 0.992 1.000 0.000
#> GSM26857 1 0.000 0.992 1.000 0.000
#> GSM26858 1 0.000 0.992 1.000 0.000
#> GSM26859 1 0.000 0.992 1.000 0.000
#> GSM26860 1 0.000 0.992 1.000 0.000
#> GSM26861 1 0.000 0.992 1.000 0.000
#> GSM26862 1 0.000 0.992 1.000 0.000
#> GSM26863 1 0.000 0.992 1.000 0.000
#> GSM26864 1 0.000 0.992 1.000 0.000
#> GSM26865 1 0.000 0.992 1.000 0.000
#> GSM26866 1 0.000 0.992 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM26805 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26806 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26807 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26808 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26809 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26810 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26811 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26812 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26813 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26814 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26815 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26816 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26817 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26818 3 0.0000 1.000 0.000 0.000 1.000
#> GSM26819 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26820 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26821 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26822 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26823 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26824 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26825 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26826 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26827 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26828 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26829 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26830 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26831 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26832 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26833 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26834 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26835 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26836 1 0.0000 0.995 1.000 0.000 0.000
#> GSM26837 1 0.0424 0.993 0.992 0.000 0.008
#> GSM26838 1 0.0000 0.995 1.000 0.000 0.000
#> GSM26839 1 0.0000 0.995 1.000 0.000 0.000
#> GSM26840 1 0.0000 0.995 1.000 0.000 0.000
#> GSM26841 1 0.0000 0.995 1.000 0.000 0.000
#> GSM26842 1 0.0000 0.995 1.000 0.000 0.000
#> GSM26843 1 0.0000 0.995 1.000 0.000 0.000
#> GSM26844 1 0.0000 0.995 1.000 0.000 0.000
#> GSM26845 1 0.0424 0.989 0.992 0.008 0.000
#> GSM26846 1 0.1163 0.976 0.972 0.000 0.028
#> GSM26847 1 0.0424 0.993 0.992 0.000 0.008
#> GSM26848 1 0.0424 0.993 0.992 0.000 0.008
#> GSM26849 3 0.0000 1.000 0.000 0.000 1.000
#> GSM26850 1 0.0424 0.993 0.992 0.000 0.008
#> GSM26851 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26852 3 0.0000 1.000 0.000 0.000 1.000
#> GSM26853 3 0.0000 1.000 0.000 0.000 1.000
#> GSM26854 3 0.0000 1.000 0.000 0.000 1.000
#> GSM26855 3 0.0000 1.000 0.000 0.000 1.000
#> GSM26856 3 0.0000 1.000 0.000 0.000 1.000
#> GSM26857 3 0.0000 1.000 0.000 0.000 1.000
#> GSM26858 3 0.0000 1.000 0.000 0.000 1.000
#> GSM26859 3 0.0000 1.000 0.000 0.000 1.000
#> GSM26860 3 0.0000 1.000 0.000 0.000 1.000
#> GSM26861 3 0.0000 1.000 0.000 0.000 1.000
#> GSM26862 1 0.0424 0.993 0.992 0.000 0.008
#> GSM26863 1 0.0000 0.995 1.000 0.000 0.000
#> GSM26864 1 0.0000 0.995 1.000 0.000 0.000
#> GSM26865 1 0.0424 0.993 0.992 0.000 0.008
#> GSM26866 1 0.0000 0.995 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM26805 2 0.0000 0.821 0.000 1.000 0.000 0.000
#> GSM26806 4 0.3444 0.839 0.000 0.184 0.000 0.816
#> GSM26807 4 0.0921 0.927 0.000 0.028 0.000 0.972
#> GSM26808 4 0.1022 0.926 0.000 0.032 0.000 0.968
#> GSM26809 2 0.2973 0.881 0.000 0.856 0.000 0.144
#> GSM26810 4 0.0921 0.927 0.000 0.028 0.000 0.972
#> GSM26811 4 0.0921 0.927 0.000 0.028 0.000 0.972
#> GSM26812 4 0.0921 0.927 0.000 0.028 0.000 0.972
#> GSM26813 2 0.3266 0.888 0.000 0.832 0.000 0.168
#> GSM26814 2 0.3266 0.888 0.000 0.832 0.000 0.168
#> GSM26815 4 0.0921 0.927 0.000 0.028 0.000 0.972
#> GSM26816 2 0.0000 0.821 0.000 1.000 0.000 0.000
#> GSM26817 4 0.0921 0.927 0.000 0.028 0.000 0.972
#> GSM26818 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM26819 2 0.3266 0.888 0.000 0.832 0.000 0.168
#> GSM26820 2 0.3266 0.888 0.000 0.832 0.000 0.168
#> GSM26821 2 0.3266 0.888 0.000 0.832 0.000 0.168
#> GSM26822 2 0.3266 0.888 0.000 0.832 0.000 0.168
#> GSM26823 2 0.3266 0.888 0.000 0.832 0.000 0.168
#> GSM26824 2 0.3266 0.888 0.000 0.832 0.000 0.168
#> GSM26825 2 0.3266 0.888 0.000 0.832 0.000 0.168
#> GSM26826 2 0.3266 0.888 0.000 0.832 0.000 0.168
#> GSM26827 2 0.3266 0.888 0.000 0.832 0.000 0.168
#> GSM26828 2 0.0000 0.821 0.000 1.000 0.000 0.000
#> GSM26829 2 0.0000 0.821 0.000 1.000 0.000 0.000
#> GSM26830 2 0.3266 0.888 0.000 0.832 0.000 0.168
#> GSM26831 2 0.0000 0.821 0.000 1.000 0.000 0.000
#> GSM26832 2 0.4661 0.239 0.000 0.652 0.000 0.348
#> GSM26833 4 0.3569 0.830 0.000 0.196 0.000 0.804
#> GSM26834 2 0.2814 0.706 0.000 0.868 0.000 0.132
#> GSM26835 2 0.3528 0.615 0.000 0.808 0.000 0.192
#> GSM26836 1 0.0000 0.896 1.000 0.000 0.000 0.000
#> GSM26837 1 0.3569 0.830 0.804 0.000 0.196 0.000
#> GSM26838 1 0.0921 0.898 0.972 0.000 0.000 0.028
#> GSM26839 1 0.0592 0.898 0.984 0.000 0.000 0.016
#> GSM26840 1 0.2032 0.877 0.936 0.036 0.000 0.028
#> GSM26841 1 0.0921 0.898 0.972 0.000 0.000 0.028
#> GSM26842 1 0.0921 0.898 0.972 0.000 0.000 0.028
#> GSM26843 1 0.0921 0.898 0.972 0.000 0.000 0.028
#> GSM26844 1 0.0921 0.898 0.972 0.000 0.000 0.028
#> GSM26845 1 0.2589 0.829 0.884 0.116 0.000 0.000
#> GSM26846 1 0.3569 0.830 0.804 0.000 0.196 0.000
#> GSM26847 1 0.3569 0.830 0.804 0.000 0.196 0.000
#> GSM26848 1 0.3569 0.830 0.804 0.000 0.196 0.000
#> GSM26849 3 0.0921 0.971 0.028 0.000 0.972 0.000
#> GSM26850 1 0.3569 0.830 0.804 0.000 0.196 0.000
#> GSM26851 4 0.3569 0.830 0.000 0.196 0.000 0.804
#> GSM26852 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM26853 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM26854 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM26855 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM26856 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM26857 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM26858 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM26859 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM26860 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM26861 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM26862 1 0.3569 0.830 0.804 0.000 0.196 0.000
#> GSM26863 1 0.0000 0.896 1.000 0.000 0.000 0.000
#> GSM26864 1 0.0921 0.898 0.972 0.000 0.000 0.028
#> GSM26865 1 0.3569 0.830 0.804 0.000 0.196 0.000
#> GSM26866 1 0.0921 0.898 0.972 0.000 0.000 0.028
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM26805 5 0.051 0.829 0.000 0.016 0.000 0.000 0.984
#> GSM26806 4 0.000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM26807 4 0.000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM26808 4 0.000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM26809 2 0.351 1.000 0.000 0.748 0.000 0.000 0.252
#> GSM26810 4 0.000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM26811 4 0.000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM26812 4 0.000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM26813 2 0.351 1.000 0.000 0.748 0.000 0.000 0.252
#> GSM26814 2 0.351 1.000 0.000 0.748 0.000 0.000 0.252
#> GSM26815 4 0.000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM26816 5 0.051 0.829 0.000 0.016 0.000 0.000 0.984
#> GSM26817 4 0.000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM26818 3 0.000 0.975 0.000 0.000 1.000 0.000 0.000
#> GSM26819 2 0.351 1.000 0.000 0.748 0.000 0.000 0.252
#> GSM26820 2 0.351 1.000 0.000 0.748 0.000 0.000 0.252
#> GSM26821 2 0.351 1.000 0.000 0.748 0.000 0.000 0.252
#> GSM26822 2 0.351 1.000 0.000 0.748 0.000 0.000 0.252
#> GSM26823 2 0.351 1.000 0.000 0.748 0.000 0.000 0.252
#> GSM26824 2 0.351 1.000 0.000 0.748 0.000 0.000 0.252
#> GSM26825 2 0.351 1.000 0.000 0.748 0.000 0.000 0.252
#> GSM26826 2 0.351 1.000 0.000 0.748 0.000 0.000 0.252
#> GSM26827 2 0.351 1.000 0.000 0.748 0.000 0.000 0.252
#> GSM26828 5 0.051 0.829 0.000 0.016 0.000 0.000 0.984
#> GSM26829 5 0.161 0.760 0.000 0.072 0.000 0.000 0.928
#> GSM26830 2 0.351 1.000 0.000 0.748 0.000 0.000 0.252
#> GSM26831 5 0.051 0.829 0.000 0.016 0.000 0.000 0.984
#> GSM26832 5 0.342 0.699 0.000 0.000 0.000 0.240 0.760
#> GSM26833 5 0.361 0.659 0.000 0.000 0.000 0.268 0.732
#> GSM26834 5 0.207 0.838 0.000 0.012 0.000 0.076 0.912
#> GSM26835 5 0.191 0.832 0.000 0.000 0.000 0.092 0.908
#> GSM26836 1 0.029 0.824 0.992 0.008 0.000 0.000 0.000
#> GSM26837 1 0.207 0.803 0.896 0.000 0.104 0.000 0.000
#> GSM26838 1 0.351 0.813 0.748 0.252 0.000 0.000 0.000
#> GSM26839 1 0.318 0.819 0.792 0.208 0.000 0.000 0.000
#> GSM26840 1 0.604 0.625 0.572 0.252 0.000 0.000 0.176
#> GSM26841 1 0.351 0.813 0.748 0.252 0.000 0.000 0.000
#> GSM26842 1 0.351 0.813 0.748 0.252 0.000 0.000 0.000
#> GSM26843 1 0.351 0.813 0.748 0.252 0.000 0.000 0.000
#> GSM26844 1 0.351 0.813 0.748 0.252 0.000 0.000 0.000
#> GSM26845 1 0.246 0.780 0.880 0.008 0.000 0.000 0.112
#> GSM26846 1 0.246 0.803 0.888 0.000 0.096 0.000 0.016
#> GSM26847 1 0.246 0.803 0.888 0.000 0.096 0.000 0.016
#> GSM26848 1 0.246 0.803 0.888 0.000 0.096 0.000 0.016
#> GSM26849 3 0.399 0.673 0.252 0.000 0.732 0.000 0.016
#> GSM26850 1 0.246 0.803 0.888 0.000 0.096 0.000 0.016
#> GSM26851 5 0.361 0.659 0.000 0.000 0.000 0.268 0.732
#> GSM26852 3 0.000 0.975 0.000 0.000 1.000 0.000 0.000
#> GSM26853 3 0.000 0.975 0.000 0.000 1.000 0.000 0.000
#> GSM26854 3 0.000 0.975 0.000 0.000 1.000 0.000 0.000
#> GSM26855 3 0.000 0.975 0.000 0.000 1.000 0.000 0.000
#> GSM26856 3 0.000 0.975 0.000 0.000 1.000 0.000 0.000
#> GSM26857 3 0.000 0.975 0.000 0.000 1.000 0.000 0.000
#> GSM26858 3 0.000 0.975 0.000 0.000 1.000 0.000 0.000
#> GSM26859 3 0.000 0.975 0.000 0.000 1.000 0.000 0.000
#> GSM26860 3 0.000 0.975 0.000 0.000 1.000 0.000 0.000
#> GSM26861 3 0.000 0.975 0.000 0.000 1.000 0.000 0.000
#> GSM26862 1 0.246 0.803 0.888 0.000 0.096 0.000 0.016
#> GSM26863 1 0.000 0.823 1.000 0.000 0.000 0.000 0.000
#> GSM26864 1 0.351 0.813 0.748 0.252 0.000 0.000 0.000
#> GSM26865 1 0.246 0.803 0.888 0.000 0.096 0.000 0.016
#> GSM26866 1 0.351 0.813 0.748 0.252 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
#> GSM26805 5 0.0000 0.985 0.000 0.00 0.000 0 1.000 0.000
#> GSM26806 4 0.0000 1.000 0.000 0.00 0.000 1 0.000 0.000
#> GSM26807 4 0.0000 1.000 0.000 0.00 0.000 1 0.000 0.000
#> GSM26808 4 0.0000 1.000 0.000 0.00 0.000 1 0.000 0.000
#> GSM26809 2 0.0000 1.000 0.000 1.00 0.000 0 0.000 0.000
#> GSM26810 4 0.0000 1.000 0.000 0.00 0.000 1 0.000 0.000
#> GSM26811 4 0.0000 1.000 0.000 0.00 0.000 1 0.000 0.000
#> GSM26812 4 0.0000 1.000 0.000 0.00 0.000 1 0.000 0.000
#> GSM26813 2 0.0000 1.000 0.000 1.00 0.000 0 0.000 0.000
#> GSM26814 2 0.0000 1.000 0.000 1.00 0.000 0 0.000 0.000
#> GSM26815 4 0.0000 1.000 0.000 0.00 0.000 1 0.000 0.000
#> GSM26816 5 0.0000 0.985 0.000 0.00 0.000 0 1.000 0.000
#> GSM26817 4 0.0000 1.000 0.000 0.00 0.000 1 0.000 0.000
#> GSM26818 3 0.0000 1.000 0.000 0.00 1.000 0 0.000 0.000
#> GSM26819 2 0.0000 1.000 0.000 1.00 0.000 0 0.000 0.000
#> GSM26820 2 0.0000 1.000 0.000 1.00 0.000 0 0.000 0.000
#> GSM26821 2 0.0000 1.000 0.000 1.00 0.000 0 0.000 0.000
#> GSM26822 2 0.0000 1.000 0.000 1.00 0.000 0 0.000 0.000
#> GSM26823 2 0.0000 1.000 0.000 1.00 0.000 0 0.000 0.000
#> GSM26824 2 0.0000 1.000 0.000 1.00 0.000 0 0.000 0.000
#> GSM26825 2 0.0000 1.000 0.000 1.00 0.000 0 0.000 0.000
#> GSM26826 2 0.0000 1.000 0.000 1.00 0.000 0 0.000 0.000
#> GSM26827 2 0.0000 1.000 0.000 1.00 0.000 0 0.000 0.000
#> GSM26828 5 0.0000 0.985 0.000 0.00 0.000 0 1.000 0.000
#> GSM26829 5 0.2048 0.857 0.000 0.12 0.000 0 0.880 0.000
#> GSM26830 2 0.0000 1.000 0.000 1.00 0.000 0 0.000 0.000
#> GSM26831 5 0.0000 0.985 0.000 0.00 0.000 0 1.000 0.000
#> GSM26832 5 0.0000 0.985 0.000 0.00 0.000 0 1.000 0.000
#> GSM26833 5 0.0000 0.985 0.000 0.00 0.000 0 1.000 0.000
#> GSM26834 5 0.0000 0.985 0.000 0.00 0.000 0 1.000 0.000
#> GSM26835 5 0.0000 0.985 0.000 0.00 0.000 0 1.000 0.000
#> GSM26836 6 0.1610 0.906 0.084 0.00 0.000 0 0.000 0.916
#> GSM26837 6 0.1367 0.930 0.044 0.00 0.012 0 0.000 0.944
#> GSM26838 1 0.0000 1.000 1.000 0.00 0.000 0 0.000 0.000
#> GSM26839 6 0.3620 0.513 0.352 0.00 0.000 0 0.000 0.648
#> GSM26840 1 0.0000 1.000 1.000 0.00 0.000 0 0.000 0.000
#> GSM26841 1 0.0000 1.000 1.000 0.00 0.000 0 0.000 0.000
#> GSM26842 1 0.0000 1.000 1.000 0.00 0.000 0 0.000 0.000
#> GSM26843 1 0.0000 1.000 1.000 0.00 0.000 0 0.000 0.000
#> GSM26844 1 0.0000 1.000 1.000 0.00 0.000 0 0.000 0.000
#> GSM26845 6 0.1320 0.926 0.016 0.00 0.000 0 0.036 0.948
#> GSM26846 6 0.0000 0.946 0.000 0.00 0.000 0 0.000 1.000
#> GSM26847 6 0.0000 0.946 0.000 0.00 0.000 0 0.000 1.000
#> GSM26848 6 0.0000 0.946 0.000 0.00 0.000 0 0.000 1.000
#> GSM26849 6 0.0000 0.946 0.000 0.00 0.000 0 0.000 1.000
#> GSM26850 6 0.0000 0.946 0.000 0.00 0.000 0 0.000 1.000
#> GSM26851 5 0.0000 0.985 0.000 0.00 0.000 0 1.000 0.000
#> GSM26852 3 0.0000 1.000 0.000 0.00 1.000 0 0.000 0.000
#> GSM26853 3 0.0000 1.000 0.000 0.00 1.000 0 0.000 0.000
#> GSM26854 3 0.0000 1.000 0.000 0.00 1.000 0 0.000 0.000
#> GSM26855 3 0.0000 1.000 0.000 0.00 1.000 0 0.000 0.000
#> GSM26856 3 0.0000 1.000 0.000 0.00 1.000 0 0.000 0.000
#> GSM26857 3 0.0000 1.000 0.000 0.00 1.000 0 0.000 0.000
#> GSM26858 3 0.0000 1.000 0.000 0.00 1.000 0 0.000 0.000
#> GSM26859 3 0.0000 1.000 0.000 0.00 1.000 0 0.000 0.000
#> GSM26860 3 0.0000 1.000 0.000 0.00 1.000 0 0.000 0.000
#> GSM26861 3 0.0000 1.000 0.000 0.00 1.000 0 0.000 0.000
#> GSM26862 6 0.0458 0.943 0.016 0.00 0.000 0 0.000 0.984
#> GSM26863 6 0.1204 0.927 0.056 0.00 0.000 0 0.000 0.944
#> GSM26864 1 0.0000 1.000 1.000 0.00 0.000 0 0.000 0.000
#> GSM26865 6 0.0000 0.946 0.000 0.00 0.000 0 0.000 1.000
#> GSM26866 1 0.0000 1.000 1.000 0.00 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)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> MAD:pam 62 3.65e-11 8.91e-01 2
#> MAD:pam 62 1.49e-12 1.94e-04 3
#> MAD:pam 61 1.28e-11 1.67e-05 4
#> MAD:pam 62 3.70e-11 1.07e-08 5
#> MAD:pam 62 1.46e-10 7.27e-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", "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 11993 rows and 62 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 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5087 0.492 0.492
#> 3 3 0.868 0.866 0.912 0.2250 0.874 0.744
#> 4 4 0.825 0.870 0.912 0.1747 0.822 0.558
#> 5 5 0.712 0.623 0.742 0.0698 0.884 0.647
#> 6 6 0.930 0.915 0.947 0.0739 0.873 0.552
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM26805 2 0 1 0 1
#> GSM26806 2 0 1 0 1
#> GSM26807 2 0 1 0 1
#> GSM26808 2 0 1 0 1
#> GSM26809 2 0 1 0 1
#> GSM26810 2 0 1 0 1
#> GSM26811 2 0 1 0 1
#> GSM26812 2 0 1 0 1
#> GSM26813 2 0 1 0 1
#> GSM26814 2 0 1 0 1
#> GSM26815 2 0 1 0 1
#> GSM26816 2 0 1 0 1
#> GSM26817 2 0 1 0 1
#> GSM26818 1 0 1 1 0
#> GSM26819 2 0 1 0 1
#> GSM26820 2 0 1 0 1
#> GSM26821 2 0 1 0 1
#> GSM26822 2 0 1 0 1
#> GSM26823 2 0 1 0 1
#> GSM26824 2 0 1 0 1
#> GSM26825 2 0 1 0 1
#> GSM26826 2 0 1 0 1
#> GSM26827 2 0 1 0 1
#> GSM26828 2 0 1 0 1
#> GSM26829 2 0 1 0 1
#> GSM26830 2 0 1 0 1
#> GSM26831 2 0 1 0 1
#> GSM26832 2 0 1 0 1
#> GSM26833 2 0 1 0 1
#> GSM26834 2 0 1 0 1
#> GSM26835 2 0 1 0 1
#> GSM26836 1 0 1 1 0
#> GSM26837 1 0 1 1 0
#> GSM26838 1 0 1 1 0
#> GSM26839 1 0 1 1 0
#> GSM26840 1 0 1 1 0
#> GSM26841 1 0 1 1 0
#> GSM26842 1 0 1 1 0
#> GSM26843 1 0 1 1 0
#> GSM26844 1 0 1 1 0
#> GSM26845 1 0 1 1 0
#> GSM26846 1 0 1 1 0
#> GSM26847 1 0 1 1 0
#> GSM26848 1 0 1 1 0
#> GSM26849 1 0 1 1 0
#> GSM26850 1 0 1 1 0
#> GSM26851 2 0 1 0 1
#> GSM26852 1 0 1 1 0
#> GSM26853 1 0 1 1 0
#> GSM26854 1 0 1 1 0
#> GSM26855 1 0 1 1 0
#> GSM26856 1 0 1 1 0
#> GSM26857 1 0 1 1 0
#> GSM26858 1 0 1 1 0
#> GSM26859 1 0 1 1 0
#> GSM26860 1 0 1 1 0
#> GSM26861 1 0 1 1 0
#> GSM26862 1 0 1 1 0
#> GSM26863 1 0 1 1 0
#> GSM26864 1 0 1 1 0
#> GSM26865 1 0 1 1 0
#> GSM26866 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM26805 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26806 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26807 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26808 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26809 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26810 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26811 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26812 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26813 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26814 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26815 2 0.0237 0.996 0.004 0.996 0.000
#> GSM26816 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26817 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26818 3 0.6045 0.439 0.380 0.000 0.620
#> GSM26819 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26820 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26821 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26822 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26823 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26824 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26825 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26826 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26827 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26828 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26829 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26830 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26831 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26832 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26833 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26834 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26835 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26836 1 0.6045 0.728 0.620 0.000 0.380
#> GSM26837 3 0.6302 -0.483 0.480 0.000 0.520
#> GSM26838 1 0.4399 0.763 0.812 0.000 0.188
#> GSM26839 1 0.4974 0.761 0.764 0.000 0.236
#> GSM26840 1 0.0000 0.695 1.000 0.000 0.000
#> GSM26841 1 0.3267 0.757 0.884 0.000 0.116
#> GSM26842 1 0.3267 0.757 0.884 0.000 0.116
#> GSM26843 1 0.0000 0.695 1.000 0.000 0.000
#> GSM26844 1 0.0000 0.695 1.000 0.000 0.000
#> GSM26845 3 0.4555 0.690 0.200 0.000 0.800
#> GSM26846 1 0.6045 0.728 0.620 0.000 0.380
#> GSM26847 1 0.6045 0.728 0.620 0.000 0.380
#> GSM26848 1 0.6045 0.728 0.620 0.000 0.380
#> GSM26849 3 0.0892 0.863 0.020 0.000 0.980
#> GSM26850 1 0.6192 0.663 0.580 0.000 0.420
#> GSM26851 2 0.0000 1.000 0.000 1.000 0.000
#> GSM26852 3 0.0000 0.884 0.000 0.000 1.000
#> GSM26853 3 0.0000 0.884 0.000 0.000 1.000
#> GSM26854 3 0.0000 0.884 0.000 0.000 1.000
#> GSM26855 3 0.0000 0.884 0.000 0.000 1.000
#> GSM26856 3 0.0000 0.884 0.000 0.000 1.000
#> GSM26857 3 0.0000 0.884 0.000 0.000 1.000
#> GSM26858 3 0.0000 0.884 0.000 0.000 1.000
#> GSM26859 3 0.0000 0.884 0.000 0.000 1.000
#> GSM26860 3 0.0000 0.884 0.000 0.000 1.000
#> GSM26861 3 0.0000 0.884 0.000 0.000 1.000
#> GSM26862 1 0.6045 0.728 0.620 0.000 0.380
#> GSM26863 1 0.6045 0.728 0.620 0.000 0.380
#> GSM26864 1 0.3267 0.757 0.884 0.000 0.116
#> GSM26865 1 0.6045 0.728 0.620 0.000 0.380
#> GSM26866 1 0.0424 0.701 0.992 0.000 0.008
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM26805 4 0.4382 0.8146 0.000 0.296 0.000 0.704
#> GSM26806 4 0.0000 0.7535 0.000 0.000 0.000 1.000
#> GSM26807 4 0.0000 0.7535 0.000 0.000 0.000 1.000
#> GSM26808 4 0.0000 0.7535 0.000 0.000 0.000 1.000
#> GSM26809 4 0.4535 0.8159 0.004 0.292 0.000 0.704
#> GSM26810 4 0.0000 0.7535 0.000 0.000 0.000 1.000
#> GSM26811 4 0.3219 0.8181 0.000 0.164 0.000 0.836
#> GSM26812 4 0.0000 0.7535 0.000 0.000 0.000 1.000
#> GSM26813 2 0.3764 0.6015 0.000 0.784 0.000 0.216
#> GSM26814 2 0.0592 0.9081 0.000 0.984 0.000 0.016
#> GSM26815 4 0.1211 0.7352 0.000 0.040 0.000 0.960
#> GSM26816 4 0.4382 0.8146 0.000 0.296 0.000 0.704
#> GSM26817 4 0.3356 0.8138 0.000 0.176 0.000 0.824
#> GSM26818 1 0.6104 0.6448 0.664 0.000 0.104 0.232
#> GSM26819 2 0.0000 0.9222 0.000 1.000 0.000 0.000
#> GSM26820 2 0.0000 0.9222 0.000 1.000 0.000 0.000
#> GSM26821 2 0.0000 0.9222 0.000 1.000 0.000 0.000
#> GSM26822 2 0.0000 0.9222 0.000 1.000 0.000 0.000
#> GSM26823 2 0.0000 0.9222 0.000 1.000 0.000 0.000
#> GSM26824 2 0.0000 0.9222 0.000 1.000 0.000 0.000
#> GSM26825 2 0.0000 0.9222 0.000 1.000 0.000 0.000
#> GSM26826 2 0.0000 0.9222 0.000 1.000 0.000 0.000
#> GSM26827 2 0.0000 0.9222 0.000 1.000 0.000 0.000
#> GSM26828 4 0.4382 0.8146 0.000 0.296 0.000 0.704
#> GSM26829 4 0.4431 0.8062 0.000 0.304 0.000 0.696
#> GSM26830 2 0.4830 0.0116 0.000 0.608 0.000 0.392
#> GSM26831 4 0.4382 0.8146 0.000 0.296 0.000 0.704
#> GSM26832 4 0.4040 0.8323 0.000 0.248 0.000 0.752
#> GSM26833 4 0.4040 0.8323 0.000 0.248 0.000 0.752
#> GSM26834 4 0.4277 0.8238 0.000 0.280 0.000 0.720
#> GSM26835 4 0.4250 0.8254 0.000 0.276 0.000 0.724
#> GSM26836 1 0.1022 0.9414 0.968 0.000 0.032 0.000
#> GSM26837 1 0.2149 0.9180 0.912 0.000 0.088 0.000
#> GSM26838 1 0.1118 0.9406 0.964 0.000 0.036 0.000
#> GSM26839 1 0.2011 0.9223 0.920 0.000 0.080 0.000
#> GSM26840 1 0.0000 0.9420 1.000 0.000 0.000 0.000
#> GSM26841 1 0.0188 0.9427 0.996 0.000 0.004 0.000
#> GSM26842 1 0.0000 0.9420 1.000 0.000 0.000 0.000
#> GSM26843 1 0.0000 0.9420 1.000 0.000 0.000 0.000
#> GSM26844 1 0.0000 0.9420 1.000 0.000 0.000 0.000
#> GSM26845 1 0.1716 0.9296 0.936 0.000 0.064 0.000
#> GSM26846 1 0.1637 0.9295 0.940 0.000 0.060 0.000
#> GSM26847 1 0.2149 0.9187 0.912 0.000 0.088 0.000
#> GSM26848 1 0.1474 0.9325 0.948 0.000 0.052 0.000
#> GSM26849 1 0.3266 0.8592 0.832 0.000 0.168 0.000
#> GSM26850 1 0.2149 0.9187 0.912 0.000 0.088 0.000
#> GSM26851 4 0.4040 0.8323 0.000 0.248 0.000 0.752
#> GSM26852 3 0.0000 0.9841 0.000 0.000 1.000 0.000
#> GSM26853 3 0.0000 0.9841 0.000 0.000 1.000 0.000
#> GSM26854 3 0.0000 0.9841 0.000 0.000 1.000 0.000
#> GSM26855 3 0.0000 0.9841 0.000 0.000 1.000 0.000
#> GSM26856 3 0.2647 0.8462 0.120 0.000 0.880 0.000
#> GSM26857 3 0.0000 0.9841 0.000 0.000 1.000 0.000
#> GSM26858 3 0.0000 0.9841 0.000 0.000 1.000 0.000
#> GSM26859 3 0.0000 0.9841 0.000 0.000 1.000 0.000
#> GSM26860 3 0.0000 0.9841 0.000 0.000 1.000 0.000
#> GSM26861 3 0.0000 0.9841 0.000 0.000 1.000 0.000
#> GSM26862 1 0.1940 0.9245 0.924 0.000 0.076 0.000
#> GSM26863 1 0.1211 0.9400 0.960 0.000 0.040 0.000
#> GSM26864 1 0.0188 0.9428 0.996 0.000 0.004 0.000
#> GSM26865 1 0.0336 0.9432 0.992 0.000 0.008 0.000
#> GSM26866 1 0.0000 0.9420 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
#> GSM26805 2 0.3966 0.167646 0.000 0.664 0.000 0.336 NA
#> GSM26806 4 0.0510 0.848501 0.000 0.000 0.000 0.984 NA
#> GSM26807 4 0.0000 0.855985 0.000 0.000 0.000 1.000 NA
#> GSM26808 4 0.0000 0.855985 0.000 0.000 0.000 1.000 NA
#> GSM26809 2 0.3932 0.166844 0.000 0.672 0.000 0.328 NA
#> GSM26810 4 0.0000 0.855985 0.000 0.000 0.000 1.000 NA
#> GSM26811 4 0.2230 0.736297 0.000 0.116 0.000 0.884 NA
#> GSM26812 4 0.0000 0.855985 0.000 0.000 0.000 1.000 NA
#> GSM26813 2 0.4930 0.444989 0.000 0.548 0.000 0.028 NA
#> GSM26814 2 0.4450 0.478696 0.000 0.508 0.000 0.004 NA
#> GSM26815 4 0.5304 0.497618 0.000 0.384 0.000 0.560 NA
#> GSM26816 2 0.3966 0.167646 0.000 0.664 0.000 0.336 NA
#> GSM26817 4 0.3999 0.609636 0.000 0.344 0.000 0.656 NA
#> GSM26818 1 0.8524 0.415326 0.436 0.032 0.248 0.136 NA
#> GSM26819 2 0.4450 0.478696 0.000 0.508 0.000 0.004 NA
#> GSM26820 2 0.4450 0.478696 0.000 0.508 0.000 0.004 NA
#> GSM26821 2 0.4450 0.478696 0.000 0.508 0.000 0.004 NA
#> GSM26822 2 0.4450 0.478696 0.000 0.508 0.000 0.004 NA
#> GSM26823 2 0.4450 0.478696 0.000 0.508 0.000 0.004 NA
#> GSM26824 2 0.4449 0.477977 0.000 0.512 0.000 0.004 NA
#> GSM26825 2 0.4450 0.478696 0.000 0.508 0.000 0.004 NA
#> GSM26826 2 0.4450 0.478696 0.000 0.508 0.000 0.004 NA
#> GSM26827 2 0.4450 0.478696 0.000 0.508 0.000 0.004 NA
#> GSM26828 2 0.3966 0.167646 0.000 0.664 0.000 0.336 NA
#> GSM26829 2 0.3684 0.177254 0.000 0.720 0.000 0.280 NA
#> GSM26830 2 0.4885 0.435326 0.000 0.572 0.000 0.028 NA
#> GSM26831 2 0.3966 0.167646 0.000 0.664 0.000 0.336 NA
#> GSM26832 2 0.4161 0.070780 0.000 0.608 0.000 0.392 NA
#> GSM26833 2 0.4161 0.070780 0.000 0.608 0.000 0.392 NA
#> GSM26834 2 0.4074 0.127439 0.000 0.636 0.000 0.364 NA
#> GSM26835 2 0.4074 0.127439 0.000 0.636 0.000 0.364 NA
#> GSM26836 1 0.1608 0.798153 0.928 0.000 0.072 0.000 NA
#> GSM26837 1 0.4609 0.778202 0.744 0.000 0.104 0.000 NA
#> GSM26838 1 0.1818 0.803771 0.932 0.000 0.044 0.000 NA
#> GSM26839 1 0.4571 0.780345 0.736 0.000 0.076 0.000 NA
#> GSM26840 1 0.5156 0.719478 0.620 0.060 0.000 0.000 NA
#> GSM26841 1 0.1341 0.800417 0.944 0.000 0.000 0.000 NA
#> GSM26842 1 0.3480 0.765558 0.752 0.000 0.000 0.000 NA
#> GSM26843 1 0.3508 0.762261 0.748 0.000 0.000 0.000 NA
#> GSM26844 1 0.3508 0.762261 0.748 0.000 0.000 0.000 NA
#> GSM26845 1 0.6323 0.693900 0.652 0.060 0.112 0.004 NA
#> GSM26846 1 0.4624 0.726531 0.744 0.000 0.112 0.000 NA
#> GSM26847 1 0.4591 0.728976 0.748 0.000 0.120 0.000 NA
#> GSM26848 1 0.4541 0.730287 0.752 0.000 0.112 0.000 NA
#> GSM26849 1 0.4073 0.714688 0.752 0.000 0.216 0.000 NA
#> GSM26850 1 0.4679 0.724249 0.740 0.000 0.124 0.000 NA
#> GSM26851 2 0.4249 0.000148 0.000 0.568 0.000 0.432 NA
#> GSM26852 3 0.0000 0.989709 0.000 0.000 1.000 0.000 NA
#> GSM26853 3 0.0000 0.989709 0.000 0.000 1.000 0.000 NA
#> GSM26854 3 0.0000 0.989709 0.000 0.000 1.000 0.000 NA
#> GSM26855 3 0.0000 0.989709 0.000 0.000 1.000 0.000 NA
#> GSM26856 3 0.1410 0.920290 0.060 0.000 0.940 0.000 NA
#> GSM26857 3 0.0000 0.989709 0.000 0.000 1.000 0.000 NA
#> GSM26858 3 0.0000 0.989709 0.000 0.000 1.000 0.000 NA
#> GSM26859 3 0.0579 0.978536 0.008 0.000 0.984 0.000 NA
#> GSM26860 3 0.0000 0.989709 0.000 0.000 1.000 0.000 NA
#> GSM26861 3 0.0000 0.989709 0.000 0.000 1.000 0.000 NA
#> GSM26862 1 0.1965 0.792265 0.904 0.000 0.096 0.000 NA
#> GSM26863 1 0.1671 0.797203 0.924 0.000 0.076 0.000 NA
#> GSM26864 1 0.3508 0.763033 0.748 0.000 0.000 0.000 NA
#> GSM26865 1 0.2726 0.793606 0.884 0.000 0.052 0.000 NA
#> GSM26866 1 0.3508 0.762261 0.748 0.000 0.000 0.000 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM26805 5 0.0146 0.942 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM26806 4 0.0146 0.984 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM26807 4 0.0146 0.985 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM26808 4 0.0146 0.985 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM26809 5 0.0000 0.942 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM26810 4 0.0146 0.985 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM26811 4 0.1082 0.959 0.000 0.040 0.000 0.956 0.004 0.000
#> GSM26812 4 0.0291 0.985 0.000 0.004 0.000 0.992 0.004 0.000
#> GSM26813 2 0.1531 0.912 0.000 0.928 0.000 0.004 0.068 0.000
#> GSM26814 2 0.0000 0.965 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26815 4 0.0146 0.984 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM26816 5 0.1327 0.913 0.000 0.064 0.000 0.000 0.936 0.000
#> GSM26817 4 0.0865 0.964 0.000 0.036 0.000 0.964 0.000 0.000
#> GSM26818 6 0.2446 0.847 0.000 0.000 0.012 0.124 0.000 0.864
#> GSM26819 2 0.0000 0.965 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26820 2 0.0000 0.965 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26821 2 0.0000 0.965 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26822 2 0.0000 0.965 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26823 2 0.0000 0.965 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26824 2 0.0000 0.965 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26825 2 0.0000 0.965 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26826 2 0.0000 0.965 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26827 2 0.0146 0.962 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM26828 5 0.0146 0.943 0.000 0.000 0.000 0.004 0.996 0.000
#> GSM26829 5 0.1327 0.913 0.000 0.064 0.000 0.000 0.936 0.000
#> GSM26830 2 0.3547 0.585 0.000 0.696 0.000 0.004 0.300 0.000
#> GSM26831 5 0.0000 0.942 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM26832 5 0.1267 0.939 0.000 0.000 0.000 0.060 0.940 0.000
#> GSM26833 5 0.3213 0.851 0.000 0.048 0.000 0.132 0.820 0.000
#> GSM26834 5 0.1267 0.939 0.000 0.000 0.000 0.060 0.940 0.000
#> GSM26835 5 0.1267 0.939 0.000 0.000 0.000 0.060 0.940 0.000
#> GSM26836 1 0.3446 0.759 0.692 0.000 0.000 0.000 0.000 0.308
#> GSM26837 1 0.3547 0.761 0.696 0.000 0.004 0.000 0.000 0.300
#> GSM26838 1 0.2762 0.795 0.804 0.000 0.000 0.000 0.000 0.196
#> GSM26839 1 0.3330 0.770 0.716 0.000 0.000 0.000 0.000 0.284
#> GSM26840 6 0.2178 0.842 0.132 0.000 0.000 0.000 0.000 0.868
#> GSM26841 1 0.0363 0.827 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM26842 1 0.0000 0.828 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26843 1 0.0000 0.828 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26844 1 0.0000 0.828 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26845 6 0.2278 0.841 0.000 0.000 0.004 0.000 0.128 0.868
#> GSM26846 6 0.0000 0.937 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM26847 6 0.0000 0.937 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM26848 6 0.0146 0.936 0.000 0.000 0.004 0.000 0.000 0.996
#> GSM26849 6 0.0405 0.935 0.004 0.000 0.008 0.000 0.000 0.988
#> GSM26850 6 0.0000 0.937 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM26851 5 0.1267 0.939 0.000 0.000 0.000 0.060 0.940 0.000
#> GSM26852 3 0.0000 0.991 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26853 3 0.0000 0.991 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26854 3 0.0000 0.991 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26855 3 0.0000 0.991 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26856 3 0.0000 0.991 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26857 3 0.0000 0.991 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26858 3 0.0000 0.991 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26859 3 0.1501 0.916 0.000 0.000 0.924 0.000 0.000 0.076
#> GSM26860 3 0.0000 0.991 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26861 3 0.0000 0.991 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26862 1 0.3584 0.756 0.688 0.000 0.004 0.000 0.000 0.308
#> GSM26863 1 0.3446 0.759 0.692 0.000 0.000 0.000 0.000 0.308
#> GSM26864 1 0.0000 0.828 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26865 6 0.0777 0.922 0.024 0.000 0.004 0.000 0.000 0.972
#> GSM26866 1 0.0000 0.828 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 tissue(p) individual(p) k
#> MAD:mclust 62 1.14e-12 8.30e-01 2
#> MAD:mclust 60 6.48e-13 3.53e-04 3
#> MAD:mclust 61 1.51e-11 6.46e-09 4
#> MAD:mclust 37 9.24e-09 1.68e-07 5
#> MAD:mclust 62 1.43e-10 8.15e-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 11993 rows and 62 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.977 0.992 0.5084 0.492 0.492
#> 3 3 0.867 0.874 0.949 0.2514 0.841 0.685
#> 4 4 0.840 0.808 0.911 0.1828 0.859 0.619
#> 5 5 0.786 0.751 0.833 0.0661 0.886 0.587
#> 6 6 0.813 0.731 0.835 0.0383 0.910 0.596
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM26805 2 0.000 1.000 0.000 1.000
#> GSM26806 2 0.000 1.000 0.000 1.000
#> GSM26807 2 0.000 1.000 0.000 1.000
#> GSM26808 2 0.000 1.000 0.000 1.000
#> GSM26809 2 0.000 1.000 0.000 1.000
#> GSM26810 2 0.000 1.000 0.000 1.000
#> GSM26811 2 0.000 1.000 0.000 1.000
#> GSM26812 2 0.000 1.000 0.000 1.000
#> GSM26813 2 0.000 1.000 0.000 1.000
#> GSM26814 2 0.000 1.000 0.000 1.000
#> GSM26815 2 0.000 1.000 0.000 1.000
#> GSM26816 2 0.000 1.000 0.000 1.000
#> GSM26817 2 0.000 1.000 0.000 1.000
#> GSM26818 1 0.000 0.984 1.000 0.000
#> GSM26819 2 0.000 1.000 0.000 1.000
#> GSM26820 2 0.000 1.000 0.000 1.000
#> GSM26821 2 0.000 1.000 0.000 1.000
#> GSM26822 2 0.000 1.000 0.000 1.000
#> GSM26823 2 0.000 1.000 0.000 1.000
#> GSM26824 2 0.000 1.000 0.000 1.000
#> GSM26825 2 0.000 1.000 0.000 1.000
#> GSM26826 2 0.000 1.000 0.000 1.000
#> GSM26827 2 0.000 1.000 0.000 1.000
#> GSM26828 2 0.000 1.000 0.000 1.000
#> GSM26829 2 0.000 1.000 0.000 1.000
#> GSM26830 2 0.000 1.000 0.000 1.000
#> GSM26831 2 0.000 1.000 0.000 1.000
#> GSM26832 2 0.000 1.000 0.000 1.000
#> GSM26833 2 0.000 1.000 0.000 1.000
#> GSM26834 2 0.000 1.000 0.000 1.000
#> GSM26835 2 0.000 1.000 0.000 1.000
#> GSM26836 1 0.000 0.984 1.000 0.000
#> GSM26837 1 0.000 0.984 1.000 0.000
#> GSM26838 1 0.000 0.984 1.000 0.000
#> GSM26839 1 0.000 0.984 1.000 0.000
#> GSM26840 1 0.000 0.984 1.000 0.000
#> GSM26841 1 0.000 0.984 1.000 0.000
#> GSM26842 1 0.000 0.984 1.000 0.000
#> GSM26843 1 0.000 0.984 1.000 0.000
#> GSM26844 1 0.000 0.984 1.000 0.000
#> GSM26845 1 0.999 0.062 0.516 0.484
#> GSM26846 1 0.000 0.984 1.000 0.000
#> GSM26847 1 0.000 0.984 1.000 0.000
#> GSM26848 1 0.000 0.984 1.000 0.000
#> GSM26849 1 0.000 0.984 1.000 0.000
#> GSM26850 1 0.000 0.984 1.000 0.000
#> GSM26851 2 0.000 1.000 0.000 1.000
#> GSM26852 1 0.000 0.984 1.000 0.000
#> GSM26853 1 0.000 0.984 1.000 0.000
#> GSM26854 1 0.000 0.984 1.000 0.000
#> GSM26855 1 0.000 0.984 1.000 0.000
#> GSM26856 1 0.000 0.984 1.000 0.000
#> GSM26857 1 0.000 0.984 1.000 0.000
#> GSM26858 1 0.000 0.984 1.000 0.000
#> GSM26859 1 0.000 0.984 1.000 0.000
#> GSM26860 1 0.000 0.984 1.000 0.000
#> GSM26861 1 0.000 0.984 1.000 0.000
#> GSM26862 1 0.000 0.984 1.000 0.000
#> GSM26863 1 0.000 0.984 1.000 0.000
#> GSM26864 1 0.000 0.984 1.000 0.000
#> GSM26865 1 0.000 0.984 1.000 0.000
#> GSM26866 1 0.000 0.984 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM26805 1 0.6244 0.220 0.560 0.440 0.000
#> GSM26806 2 0.0000 0.985 0.000 1.000 0.000
#> GSM26807 2 0.0000 0.985 0.000 1.000 0.000
#> GSM26808 2 0.0000 0.985 0.000 1.000 0.000
#> GSM26809 1 0.3752 0.738 0.856 0.144 0.000
#> GSM26810 2 0.0000 0.985 0.000 1.000 0.000
#> GSM26811 2 0.0000 0.985 0.000 1.000 0.000
#> GSM26812 2 0.0000 0.985 0.000 1.000 0.000
#> GSM26813 2 0.0000 0.985 0.000 1.000 0.000
#> GSM26814 2 0.0000 0.985 0.000 1.000 0.000
#> GSM26815 2 0.0000 0.985 0.000 1.000 0.000
#> GSM26816 2 0.0000 0.985 0.000 1.000 0.000
#> GSM26817 2 0.0000 0.985 0.000 1.000 0.000
#> GSM26818 3 0.0000 0.931 0.000 0.000 1.000
#> GSM26819 2 0.0000 0.985 0.000 1.000 0.000
#> GSM26820 2 0.0000 0.985 0.000 1.000 0.000
#> GSM26821 2 0.0000 0.985 0.000 1.000 0.000
#> GSM26822 2 0.0000 0.985 0.000 1.000 0.000
#> GSM26823 2 0.0000 0.985 0.000 1.000 0.000
#> GSM26824 2 0.0000 0.985 0.000 1.000 0.000
#> GSM26825 2 0.0000 0.985 0.000 1.000 0.000
#> GSM26826 2 0.0000 0.985 0.000 1.000 0.000
#> GSM26827 2 0.0000 0.985 0.000 1.000 0.000
#> GSM26828 2 0.4002 0.788 0.160 0.840 0.000
#> GSM26829 2 0.0000 0.985 0.000 1.000 0.000
#> GSM26830 2 0.0000 0.985 0.000 1.000 0.000
#> GSM26831 2 0.4654 0.712 0.208 0.792 0.000
#> GSM26832 2 0.0000 0.985 0.000 1.000 0.000
#> GSM26833 2 0.0000 0.985 0.000 1.000 0.000
#> GSM26834 2 0.0000 0.985 0.000 1.000 0.000
#> GSM26835 2 0.0000 0.985 0.000 1.000 0.000
#> GSM26836 1 0.6244 0.204 0.560 0.000 0.440
#> GSM26837 3 0.0000 0.931 0.000 0.000 1.000
#> GSM26838 1 0.0000 0.835 1.000 0.000 0.000
#> GSM26839 3 0.5560 0.560 0.300 0.000 0.700
#> GSM26840 1 0.0000 0.835 1.000 0.000 0.000
#> GSM26841 1 0.0000 0.835 1.000 0.000 0.000
#> GSM26842 1 0.0892 0.826 0.980 0.000 0.020
#> GSM26843 1 0.0000 0.835 1.000 0.000 0.000
#> GSM26844 1 0.0000 0.835 1.000 0.000 0.000
#> GSM26845 1 0.0000 0.835 1.000 0.000 0.000
#> GSM26846 3 0.0000 0.931 0.000 0.000 1.000
#> GSM26847 3 0.0237 0.929 0.004 0.000 0.996
#> GSM26848 3 0.5650 0.534 0.312 0.000 0.688
#> GSM26849 3 0.0000 0.931 0.000 0.000 1.000
#> GSM26850 3 0.0424 0.926 0.008 0.000 0.992
#> GSM26851 2 0.0000 0.985 0.000 1.000 0.000
#> GSM26852 3 0.0000 0.931 0.000 0.000 1.000
#> GSM26853 3 0.0000 0.931 0.000 0.000 1.000
#> GSM26854 3 0.0000 0.931 0.000 0.000 1.000
#> GSM26855 3 0.0000 0.931 0.000 0.000 1.000
#> GSM26856 3 0.0000 0.931 0.000 0.000 1.000
#> GSM26857 3 0.0000 0.931 0.000 0.000 1.000
#> GSM26858 3 0.0000 0.931 0.000 0.000 1.000
#> GSM26859 3 0.0000 0.931 0.000 0.000 1.000
#> GSM26860 3 0.0000 0.931 0.000 0.000 1.000
#> GSM26861 3 0.0000 0.931 0.000 0.000 1.000
#> GSM26862 3 0.4235 0.753 0.176 0.000 0.824
#> GSM26863 1 0.6140 0.310 0.596 0.000 0.404
#> GSM26864 1 0.4887 0.640 0.772 0.000 0.228
#> GSM26865 3 0.5497 0.575 0.292 0.000 0.708
#> GSM26866 1 0.0000 0.835 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM26805 1 0.5994 0.5338 0.636 0.296 0.000 0.068
#> GSM26806 4 0.0000 0.9315 0.000 0.000 0.000 1.000
#> GSM26807 4 0.0000 0.9315 0.000 0.000 0.000 1.000
#> GSM26808 4 0.0000 0.9315 0.000 0.000 0.000 1.000
#> GSM26809 2 0.2281 0.8174 0.096 0.904 0.000 0.000
#> GSM26810 4 0.0000 0.9315 0.000 0.000 0.000 1.000
#> GSM26811 4 0.0000 0.9315 0.000 0.000 0.000 1.000
#> GSM26812 4 0.0000 0.9315 0.000 0.000 0.000 1.000
#> GSM26813 2 0.1940 0.9118 0.000 0.924 0.000 0.076
#> GSM26814 2 0.1867 0.9149 0.000 0.928 0.000 0.072
#> GSM26815 4 0.0000 0.9315 0.000 0.000 0.000 1.000
#> GSM26816 4 0.3356 0.7820 0.000 0.176 0.000 0.824
#> GSM26817 4 0.0000 0.9315 0.000 0.000 0.000 1.000
#> GSM26818 3 0.3837 0.6872 0.000 0.000 0.776 0.224
#> GSM26819 2 0.0921 0.9276 0.000 0.972 0.000 0.028
#> GSM26820 2 0.0592 0.9244 0.000 0.984 0.000 0.016
#> GSM26821 2 0.1637 0.9215 0.000 0.940 0.000 0.060
#> GSM26822 2 0.1118 0.9281 0.000 0.964 0.000 0.036
#> GSM26823 2 0.1118 0.9281 0.000 0.964 0.000 0.036
#> GSM26824 2 0.1792 0.9177 0.000 0.932 0.000 0.068
#> GSM26825 2 0.0592 0.9244 0.000 0.984 0.000 0.016
#> GSM26826 2 0.0336 0.9198 0.000 0.992 0.000 0.008
#> GSM26827 2 0.0817 0.9269 0.000 0.976 0.000 0.024
#> GSM26828 2 0.7512 0.1990 0.236 0.496 0.000 0.268
#> GSM26829 2 0.0336 0.9198 0.000 0.992 0.000 0.008
#> GSM26830 2 0.1716 0.9199 0.000 0.936 0.000 0.064
#> GSM26831 4 0.7835 -0.0374 0.336 0.268 0.000 0.396
#> GSM26832 4 0.1557 0.9035 0.000 0.056 0.000 0.944
#> GSM26833 4 0.0188 0.9297 0.000 0.004 0.000 0.996
#> GSM26834 4 0.1557 0.9035 0.000 0.056 0.000 0.944
#> GSM26835 4 0.1792 0.8956 0.000 0.068 0.000 0.932
#> GSM26836 1 0.4222 0.5877 0.728 0.000 0.272 0.000
#> GSM26837 3 0.3219 0.7820 0.164 0.000 0.836 0.000
#> GSM26838 1 0.0000 0.8315 1.000 0.000 0.000 0.000
#> GSM26839 1 0.4843 0.3061 0.604 0.000 0.396 0.000
#> GSM26840 1 0.1637 0.8156 0.940 0.060 0.000 0.000
#> GSM26841 1 0.0000 0.8315 1.000 0.000 0.000 0.000
#> GSM26842 1 0.0000 0.8315 1.000 0.000 0.000 0.000
#> GSM26843 1 0.1211 0.8257 0.960 0.040 0.000 0.000
#> GSM26844 1 0.0469 0.8313 0.988 0.012 0.000 0.000
#> GSM26845 1 0.4888 0.2293 0.588 0.412 0.000 0.000
#> GSM26846 3 0.4920 0.6720 0.052 0.192 0.756 0.000
#> GSM26847 3 0.1474 0.8730 0.052 0.000 0.948 0.000
#> GSM26848 3 0.2124 0.8563 0.068 0.008 0.924 0.000
#> GSM26849 3 0.0000 0.8988 0.000 0.000 1.000 0.000
#> GSM26850 3 0.1867 0.8511 0.000 0.072 0.928 0.000
#> GSM26851 4 0.0000 0.9315 0.000 0.000 0.000 1.000
#> GSM26852 3 0.0188 0.8993 0.004 0.000 0.996 0.000
#> GSM26853 3 0.0188 0.8993 0.004 0.000 0.996 0.000
#> GSM26854 3 0.0000 0.8988 0.000 0.000 1.000 0.000
#> GSM26855 3 0.0188 0.8993 0.004 0.000 0.996 0.000
#> GSM26856 3 0.0188 0.8993 0.004 0.000 0.996 0.000
#> GSM26857 3 0.0000 0.8988 0.000 0.000 1.000 0.000
#> GSM26858 3 0.0336 0.8981 0.008 0.000 0.992 0.000
#> GSM26859 3 0.0000 0.8988 0.000 0.000 1.000 0.000
#> GSM26860 3 0.0000 0.8988 0.000 0.000 1.000 0.000
#> GSM26861 3 0.0188 0.8993 0.004 0.000 0.996 0.000
#> GSM26862 3 0.4866 0.3216 0.404 0.000 0.596 0.000
#> GSM26863 1 0.3873 0.6518 0.772 0.000 0.228 0.000
#> GSM26864 1 0.1118 0.8198 0.964 0.000 0.036 0.000
#> GSM26865 3 0.4500 0.4990 0.316 0.000 0.684 0.000
#> GSM26866 1 0.1211 0.8252 0.960 0.040 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM26805 5 0.3414 0.639 0.024 0.060 0.000 0.056 0.860
#> GSM26806 4 0.0000 0.966 0.000 0.000 0.000 1.000 0.000
#> GSM26807 4 0.0000 0.966 0.000 0.000 0.000 1.000 0.000
#> GSM26808 4 0.0000 0.966 0.000 0.000 0.000 1.000 0.000
#> GSM26809 5 0.4015 0.347 0.000 0.348 0.000 0.000 0.652
#> GSM26810 4 0.0290 0.964 0.000 0.000 0.000 0.992 0.008
#> GSM26811 4 0.0290 0.964 0.000 0.000 0.000 0.992 0.008
#> GSM26812 4 0.0000 0.966 0.000 0.000 0.000 1.000 0.000
#> GSM26813 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000
#> GSM26814 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000
#> GSM26815 4 0.0510 0.958 0.000 0.000 0.000 0.984 0.016
#> GSM26816 5 0.4985 0.614 0.000 0.076 0.000 0.244 0.680
#> GSM26817 4 0.0579 0.958 0.000 0.008 0.000 0.984 0.008
#> GSM26818 3 0.1764 0.818 0.012 0.000 0.940 0.036 0.012
#> GSM26819 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000
#> GSM26820 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000
#> GSM26821 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000
#> GSM26822 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000
#> GSM26823 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000
#> GSM26824 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000
#> GSM26825 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000
#> GSM26826 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000
#> GSM26827 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000
#> GSM26828 5 0.3456 0.655 0.004 0.004 0.000 0.204 0.788
#> GSM26829 2 0.3932 0.491 0.000 0.672 0.000 0.000 0.328
#> GSM26830 2 0.0000 0.970 0.000 1.000 0.000 0.000 0.000
#> GSM26831 5 0.3509 0.656 0.008 0.004 0.000 0.196 0.792
#> GSM26832 5 0.4219 0.434 0.000 0.000 0.000 0.416 0.584
#> GSM26833 4 0.2424 0.820 0.000 0.000 0.000 0.868 0.132
#> GSM26834 5 0.4219 0.429 0.000 0.000 0.000 0.416 0.584
#> GSM26835 5 0.3586 0.619 0.000 0.000 0.000 0.264 0.736
#> GSM26836 1 0.0794 0.791 0.972 0.000 0.028 0.000 0.000
#> GSM26837 1 0.1121 0.784 0.956 0.000 0.044 0.000 0.000
#> GSM26838 1 0.2179 0.760 0.888 0.000 0.000 0.000 0.112
#> GSM26839 1 0.0880 0.789 0.968 0.000 0.032 0.000 0.000
#> GSM26840 5 0.3895 0.103 0.320 0.000 0.000 0.000 0.680
#> GSM26841 1 0.2648 0.738 0.848 0.000 0.000 0.000 0.152
#> GSM26842 1 0.1341 0.784 0.944 0.000 0.000 0.000 0.056
#> GSM26843 5 0.4306 -0.338 0.492 0.000 0.000 0.000 0.508
#> GSM26844 1 0.4138 0.487 0.616 0.000 0.000 0.000 0.384
#> GSM26845 1 0.5982 0.519 0.588 0.120 0.008 0.000 0.284
#> GSM26846 3 0.6224 0.164 0.328 0.108 0.548 0.000 0.016
#> GSM26847 1 0.4562 0.144 0.500 0.000 0.492 0.000 0.008
#> GSM26848 3 0.3241 0.722 0.024 0.000 0.832 0.000 0.144
#> GSM26849 3 0.0404 0.815 0.000 0.000 0.988 0.000 0.012
#> GSM26850 3 0.1983 0.795 0.008 0.008 0.924 0.000 0.060
#> GSM26851 4 0.1544 0.908 0.000 0.000 0.000 0.932 0.068
#> GSM26852 3 0.3177 0.826 0.208 0.000 0.792 0.000 0.000
#> GSM26853 3 0.2929 0.840 0.180 0.000 0.820 0.000 0.000
#> GSM26854 3 0.2471 0.852 0.136 0.000 0.864 0.000 0.000
#> GSM26855 3 0.3039 0.834 0.192 0.000 0.808 0.000 0.000
#> GSM26856 3 0.2516 0.851 0.140 0.000 0.860 0.000 0.000
#> GSM26857 3 0.2424 0.852 0.132 0.000 0.868 0.000 0.000
#> GSM26858 3 0.3177 0.826 0.208 0.000 0.792 0.000 0.000
#> GSM26859 3 0.0451 0.822 0.008 0.000 0.988 0.000 0.004
#> GSM26860 3 0.2074 0.850 0.104 0.000 0.896 0.000 0.000
#> GSM26861 3 0.3143 0.828 0.204 0.000 0.796 0.000 0.000
#> GSM26862 1 0.1608 0.763 0.928 0.000 0.072 0.000 0.000
#> GSM26863 1 0.0609 0.792 0.980 0.000 0.020 0.000 0.000
#> GSM26864 1 0.1168 0.790 0.960 0.000 0.008 0.000 0.032
#> GSM26865 3 0.3734 0.704 0.060 0.000 0.812 0.000 0.128
#> GSM26866 1 0.4294 0.293 0.532 0.000 0.000 0.000 0.468
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM26805 5 0.3121 0.7667 0.040 0.008 0.000 0.064 0.864 0.024
#> GSM26806 4 0.0000 0.9477 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26807 4 0.0000 0.9477 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26808 4 0.0260 0.9450 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM26809 2 0.7270 -0.1352 0.276 0.324 0.000 0.000 0.308 0.092
#> GSM26810 4 0.0000 0.9477 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26811 4 0.0146 0.9462 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM26812 4 0.0000 0.9477 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26813 2 0.0000 0.9433 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26814 2 0.0146 0.9430 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM26815 4 0.0260 0.9430 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM26816 5 0.3702 0.7883 0.000 0.024 0.000 0.164 0.788 0.024
#> GSM26817 4 0.1760 0.8945 0.000 0.004 0.000 0.928 0.048 0.020
#> GSM26818 3 0.3308 0.7796 0.000 0.000 0.844 0.080 0.032 0.044
#> GSM26819 2 0.0146 0.9430 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM26820 2 0.0291 0.9413 0.000 0.992 0.000 0.000 0.004 0.004
#> GSM26821 2 0.0000 0.9433 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26822 2 0.0000 0.9433 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26823 2 0.0000 0.9433 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26824 2 0.0000 0.9433 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26825 2 0.0146 0.9430 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM26826 2 0.0291 0.9413 0.000 0.992 0.000 0.000 0.004 0.004
#> GSM26827 2 0.0000 0.9433 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26828 5 0.1929 0.7899 0.016 0.004 0.000 0.048 0.924 0.008
#> GSM26829 5 0.3834 0.5442 0.000 0.268 0.000 0.000 0.708 0.024
#> GSM26830 2 0.0146 0.9430 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM26831 5 0.2872 0.7926 0.024 0.004 0.000 0.088 0.868 0.016
#> GSM26832 5 0.3555 0.7614 0.000 0.000 0.000 0.184 0.776 0.040
#> GSM26833 5 0.4569 0.3984 0.000 0.000 0.000 0.396 0.564 0.040
#> GSM26834 5 0.2830 0.7951 0.000 0.000 0.000 0.144 0.836 0.020
#> GSM26835 5 0.2446 0.8095 0.000 0.000 0.000 0.124 0.864 0.012
#> GSM26836 1 0.5548 0.6489 0.504 0.000 0.124 0.000 0.004 0.368
#> GSM26837 1 0.5968 0.5733 0.432 0.000 0.192 0.000 0.004 0.372
#> GSM26838 1 0.4088 0.6960 0.668 0.000 0.020 0.000 0.004 0.308
#> GSM26839 1 0.5510 0.6738 0.540 0.000 0.132 0.000 0.004 0.324
#> GSM26840 1 0.4228 0.2998 0.708 0.000 0.000 0.000 0.228 0.064
#> GSM26841 1 0.3431 0.6981 0.756 0.000 0.016 0.000 0.000 0.228
#> GSM26842 1 0.4280 0.7101 0.708 0.000 0.056 0.000 0.004 0.232
#> GSM26843 1 0.2221 0.5172 0.896 0.000 0.000 0.000 0.072 0.032
#> GSM26844 1 0.2190 0.6049 0.900 0.000 0.000 0.000 0.040 0.060
#> GSM26845 6 0.5092 -0.1862 0.316 0.048 0.000 0.000 0.028 0.608
#> GSM26846 6 0.4753 0.6041 0.012 0.008 0.124 0.000 0.132 0.724
#> GSM26847 6 0.3469 0.3836 0.092 0.000 0.072 0.000 0.012 0.824
#> GSM26848 6 0.5389 0.4396 0.004 0.000 0.116 0.000 0.328 0.552
#> GSM26849 3 0.3838 0.0701 0.000 0.000 0.552 0.000 0.000 0.448
#> GSM26850 6 0.5425 0.4714 0.000 0.000 0.148 0.000 0.300 0.552
#> GSM26851 4 0.4336 0.5872 0.000 0.004 0.000 0.704 0.232 0.060
#> GSM26852 3 0.0909 0.8925 0.012 0.000 0.968 0.000 0.020 0.000
#> GSM26853 3 0.0363 0.8986 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM26854 3 0.0363 0.8998 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM26855 3 0.0603 0.8968 0.004 0.000 0.980 0.000 0.016 0.000
#> GSM26856 3 0.0363 0.8998 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM26857 3 0.0508 0.8990 0.000 0.000 0.984 0.000 0.004 0.012
#> GSM26858 3 0.0909 0.8925 0.012 0.000 0.968 0.000 0.020 0.000
#> GSM26859 3 0.2112 0.8226 0.000 0.000 0.896 0.000 0.016 0.088
#> GSM26860 3 0.0806 0.8931 0.000 0.000 0.972 0.000 0.008 0.020
#> GSM26861 3 0.0806 0.8945 0.008 0.000 0.972 0.000 0.020 0.000
#> GSM26862 1 0.5800 0.5855 0.444 0.000 0.156 0.000 0.004 0.396
#> GSM26863 1 0.5288 0.6773 0.552 0.000 0.100 0.000 0.004 0.344
#> GSM26864 1 0.4757 0.7084 0.688 0.000 0.076 0.000 0.016 0.220
#> GSM26865 6 0.4778 0.2198 0.032 0.000 0.400 0.000 0.012 0.556
#> GSM26866 1 0.1411 0.5561 0.936 0.000 0.004 0.000 0.060 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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> MAD:NMF 61 1.90e-12 8.52e-01 2
#> MAD:NMF 59 4.31e-11 5.75e-03 3
#> MAD:NMF 56 9.86e-10 1.28e-05 4
#> MAD:NMF 52 4.69e-09 1.75e-05 5
#> MAD:NMF 53 1.02e-08 4.46e-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", "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 11993 rows and 62 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.732 0.887 0.922 0.3940 0.535 0.535
#> 3 3 0.658 0.895 0.887 0.3796 0.936 0.880
#> 4 4 0.877 0.959 0.955 0.3192 0.789 0.552
#> 5 5 0.879 0.932 0.952 0.0175 0.989 0.959
#> 6 6 0.835 0.925 0.916 0.0441 0.959 0.834
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM26805 1 0.978 0.994 0.588 0.412
#> GSM26806 2 0.000 0.643 0.000 1.000
#> GSM26807 2 0.000 0.643 0.000 1.000
#> GSM26808 2 0.000 0.643 0.000 1.000
#> GSM26809 1 0.973 0.995 0.596 0.404
#> GSM26810 2 0.000 0.643 0.000 1.000
#> GSM26811 2 0.000 0.643 0.000 1.000
#> GSM26812 2 0.000 0.643 0.000 1.000
#> GSM26813 2 0.204 0.589 0.032 0.968
#> GSM26814 2 0.204 0.589 0.032 0.968
#> GSM26815 2 0.000 0.643 0.000 1.000
#> GSM26816 1 0.978 0.994 0.588 0.412
#> GSM26817 2 0.000 0.643 0.000 1.000
#> GSM26818 2 0.861 0.739 0.284 0.716
#> GSM26819 1 0.978 0.994 0.588 0.412
#> GSM26820 1 0.978 0.994 0.588 0.412
#> GSM26821 1 0.978 0.994 0.588 0.412
#> GSM26822 1 0.978 0.994 0.588 0.412
#> GSM26823 1 0.978 0.994 0.588 0.412
#> GSM26824 1 0.978 0.994 0.588 0.412
#> GSM26825 1 0.978 0.994 0.588 0.412
#> GSM26826 1 0.978 0.994 0.588 0.412
#> GSM26827 1 0.978 0.994 0.588 0.412
#> GSM26828 1 0.978 0.994 0.588 0.412
#> GSM26829 1 0.978 0.994 0.588 0.412
#> GSM26830 2 0.204 0.589 0.032 0.968
#> GSM26831 1 0.978 0.994 0.588 0.412
#> GSM26832 1 0.978 0.994 0.588 0.412
#> GSM26833 1 0.978 0.994 0.588 0.412
#> GSM26834 1 0.978 0.994 0.588 0.412
#> GSM26835 1 0.978 0.994 0.588 0.412
#> GSM26836 1 0.973 0.995 0.596 0.404
#> GSM26837 1 0.973 0.995 0.596 0.404
#> GSM26838 1 0.973 0.995 0.596 0.404
#> GSM26839 1 0.973 0.995 0.596 0.404
#> GSM26840 1 0.973 0.995 0.596 0.404
#> GSM26841 1 0.973 0.995 0.596 0.404
#> GSM26842 1 0.973 0.995 0.596 0.404
#> GSM26843 1 0.973 0.995 0.596 0.404
#> GSM26844 1 0.973 0.995 0.596 0.404
#> GSM26845 1 0.973 0.995 0.596 0.404
#> GSM26846 1 0.973 0.995 0.596 0.404
#> GSM26847 1 0.973 0.995 0.596 0.404
#> GSM26848 1 0.973 0.995 0.596 0.404
#> GSM26849 1 0.973 0.995 0.596 0.404
#> GSM26850 1 0.973 0.995 0.596 0.404
#> GSM26851 1 0.978 0.994 0.588 0.412
#> GSM26852 2 0.973 0.756 0.404 0.596
#> GSM26853 2 0.973 0.756 0.404 0.596
#> GSM26854 2 0.973 0.756 0.404 0.596
#> GSM26855 2 0.973 0.756 0.404 0.596
#> GSM26856 2 0.973 0.756 0.404 0.596
#> GSM26857 2 0.973 0.756 0.404 0.596
#> GSM26858 2 0.973 0.756 0.404 0.596
#> GSM26859 2 0.973 0.756 0.404 0.596
#> GSM26860 2 0.973 0.756 0.404 0.596
#> GSM26861 2 0.973 0.756 0.404 0.596
#> GSM26862 1 0.973 0.995 0.596 0.404
#> GSM26863 1 0.973 0.995 0.596 0.404
#> GSM26864 1 0.973 0.995 0.596 0.404
#> GSM26865 1 0.973 0.995 0.596 0.404
#> GSM26866 1 0.973 0.995 0.596 0.404
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM26805 1 0.489 0.867 0.772 0.228 0.000
#> GSM26806 2 0.303 0.963 0.032 0.920 0.048
#> GSM26807 2 0.303 0.963 0.032 0.920 0.048
#> GSM26808 2 0.303 0.963 0.032 0.920 0.048
#> GSM26809 1 0.480 0.867 0.780 0.220 0.000
#> GSM26810 2 0.303 0.963 0.032 0.920 0.048
#> GSM26811 2 0.303 0.963 0.032 0.920 0.048
#> GSM26812 2 0.303 0.963 0.032 0.920 0.048
#> GSM26813 2 0.397 0.933 0.072 0.884 0.044
#> GSM26814 2 0.397 0.933 0.072 0.884 0.044
#> GSM26815 2 0.442 0.813 0.088 0.864 0.048
#> GSM26816 1 0.489 0.867 0.772 0.228 0.000
#> GSM26817 2 0.303 0.963 0.032 0.920 0.048
#> GSM26818 3 0.397 0.868 0.088 0.032 0.880
#> GSM26819 1 0.489 0.867 0.772 0.228 0.000
#> GSM26820 1 0.489 0.867 0.772 0.228 0.000
#> GSM26821 1 0.489 0.867 0.772 0.228 0.000
#> GSM26822 1 0.489 0.867 0.772 0.228 0.000
#> GSM26823 1 0.489 0.867 0.772 0.228 0.000
#> GSM26824 1 0.489 0.867 0.772 0.228 0.000
#> GSM26825 1 0.489 0.867 0.772 0.228 0.000
#> GSM26826 1 0.489 0.867 0.772 0.228 0.000
#> GSM26827 1 0.489 0.867 0.772 0.228 0.000
#> GSM26828 1 0.489 0.867 0.772 0.228 0.000
#> GSM26829 1 0.489 0.867 0.772 0.228 0.000
#> GSM26830 2 0.397 0.933 0.072 0.884 0.044
#> GSM26831 1 0.489 0.867 0.772 0.228 0.000
#> GSM26832 1 0.489 0.867 0.772 0.228 0.000
#> GSM26833 1 0.489 0.867 0.772 0.228 0.000
#> GSM26834 1 0.489 0.867 0.772 0.228 0.000
#> GSM26835 1 0.489 0.867 0.772 0.228 0.000
#> GSM26836 1 0.000 0.850 1.000 0.000 0.000
#> GSM26837 1 0.000 0.850 1.000 0.000 0.000
#> GSM26838 1 0.000 0.850 1.000 0.000 0.000
#> GSM26839 1 0.000 0.850 1.000 0.000 0.000
#> GSM26840 1 0.475 0.867 0.784 0.216 0.000
#> GSM26841 1 0.000 0.850 1.000 0.000 0.000
#> GSM26842 1 0.000 0.850 1.000 0.000 0.000
#> GSM26843 1 0.000 0.850 1.000 0.000 0.000
#> GSM26844 1 0.000 0.850 1.000 0.000 0.000
#> GSM26845 1 0.412 0.862 0.832 0.168 0.000
#> GSM26846 1 0.000 0.850 1.000 0.000 0.000
#> GSM26847 1 0.000 0.850 1.000 0.000 0.000
#> GSM26848 1 0.000 0.850 1.000 0.000 0.000
#> GSM26849 1 0.000 0.850 1.000 0.000 0.000
#> GSM26850 1 0.000 0.850 1.000 0.000 0.000
#> GSM26851 1 0.489 0.867 0.772 0.228 0.000
#> GSM26852 3 0.000 0.988 0.000 0.000 1.000
#> GSM26853 3 0.000 0.988 0.000 0.000 1.000
#> GSM26854 3 0.000 0.988 0.000 0.000 1.000
#> GSM26855 3 0.000 0.988 0.000 0.000 1.000
#> GSM26856 3 0.000 0.988 0.000 0.000 1.000
#> GSM26857 3 0.000 0.988 0.000 0.000 1.000
#> GSM26858 3 0.000 0.988 0.000 0.000 1.000
#> GSM26859 3 0.000 0.988 0.000 0.000 1.000
#> GSM26860 3 0.000 0.988 0.000 0.000 1.000
#> GSM26861 3 0.000 0.988 0.000 0.000 1.000
#> GSM26862 1 0.000 0.850 1.000 0.000 0.000
#> GSM26863 1 0.000 0.850 1.000 0.000 0.000
#> GSM26864 1 0.000 0.850 1.000 0.000 0.000
#> GSM26865 1 0.000 0.850 1.000 0.000 0.000
#> GSM26866 1 0.000 0.850 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM26805 2 0.0000 0.999 0.000 1.000 0.00 0.000
#> GSM26806 4 0.3610 0.952 0.000 0.200 0.00 0.800
#> GSM26807 4 0.3610 0.952 0.000 0.200 0.00 0.800
#> GSM26808 4 0.3610 0.952 0.000 0.200 0.00 0.800
#> GSM26809 2 0.0336 0.988 0.008 0.992 0.00 0.000
#> GSM26810 4 0.3610 0.952 0.000 0.200 0.00 0.800
#> GSM26811 4 0.3610 0.952 0.000 0.200 0.00 0.800
#> GSM26812 4 0.3610 0.952 0.000 0.200 0.00 0.800
#> GSM26813 4 0.4103 0.918 0.000 0.256 0.00 0.744
#> GSM26814 4 0.4103 0.918 0.000 0.256 0.00 0.744
#> GSM26815 4 0.0000 0.708 0.000 0.000 0.00 1.000
#> GSM26816 2 0.0000 0.999 0.000 1.000 0.00 0.000
#> GSM26817 4 0.3726 0.947 0.000 0.212 0.00 0.788
#> GSM26818 3 0.2647 0.905 0.000 0.000 0.88 0.120
#> GSM26819 2 0.0000 0.999 0.000 1.000 0.00 0.000
#> GSM26820 2 0.0000 0.999 0.000 1.000 0.00 0.000
#> GSM26821 2 0.0000 0.999 0.000 1.000 0.00 0.000
#> GSM26822 2 0.0000 0.999 0.000 1.000 0.00 0.000
#> GSM26823 2 0.0000 0.999 0.000 1.000 0.00 0.000
#> GSM26824 2 0.0000 0.999 0.000 1.000 0.00 0.000
#> GSM26825 2 0.0000 0.999 0.000 1.000 0.00 0.000
#> GSM26826 2 0.0000 0.999 0.000 1.000 0.00 0.000
#> GSM26827 2 0.0000 0.999 0.000 1.000 0.00 0.000
#> GSM26828 2 0.0000 0.999 0.000 1.000 0.00 0.000
#> GSM26829 2 0.0000 0.999 0.000 1.000 0.00 0.000
#> GSM26830 4 0.4103 0.918 0.000 0.256 0.00 0.744
#> GSM26831 2 0.0000 0.999 0.000 1.000 0.00 0.000
#> GSM26832 2 0.0000 0.999 0.000 1.000 0.00 0.000
#> GSM26833 2 0.0000 0.999 0.000 1.000 0.00 0.000
#> GSM26834 2 0.0000 0.999 0.000 1.000 0.00 0.000
#> GSM26835 2 0.0000 0.999 0.000 1.000 0.00 0.000
#> GSM26836 1 0.0000 0.969 1.000 0.000 0.00 0.000
#> GSM26837 1 0.0000 0.969 1.000 0.000 0.00 0.000
#> GSM26838 1 0.0000 0.969 1.000 0.000 0.00 0.000
#> GSM26839 1 0.0000 0.969 1.000 0.000 0.00 0.000
#> GSM26840 2 0.0469 0.983 0.012 0.988 0.00 0.000
#> GSM26841 1 0.0000 0.969 1.000 0.000 0.00 0.000
#> GSM26842 1 0.0000 0.969 1.000 0.000 0.00 0.000
#> GSM26843 1 0.0000 0.969 1.000 0.000 0.00 0.000
#> GSM26844 1 0.0000 0.969 1.000 0.000 0.00 0.000
#> GSM26845 1 0.4972 0.138 0.544 0.456 0.00 0.000
#> GSM26846 1 0.0000 0.969 1.000 0.000 0.00 0.000
#> GSM26847 1 0.0000 0.969 1.000 0.000 0.00 0.000
#> GSM26848 1 0.0000 0.969 1.000 0.000 0.00 0.000
#> GSM26849 1 0.0000 0.969 1.000 0.000 0.00 0.000
#> GSM26850 1 0.0000 0.969 1.000 0.000 0.00 0.000
#> GSM26851 2 0.0000 0.999 0.000 1.000 0.00 0.000
#> GSM26852 3 0.0000 0.991 0.000 0.000 1.00 0.000
#> GSM26853 3 0.0000 0.991 0.000 0.000 1.00 0.000
#> GSM26854 3 0.0000 0.991 0.000 0.000 1.00 0.000
#> GSM26855 3 0.0000 0.991 0.000 0.000 1.00 0.000
#> GSM26856 3 0.0000 0.991 0.000 0.000 1.00 0.000
#> GSM26857 3 0.0000 0.991 0.000 0.000 1.00 0.000
#> GSM26858 3 0.0000 0.991 0.000 0.000 1.00 0.000
#> GSM26859 3 0.0000 0.991 0.000 0.000 1.00 0.000
#> GSM26860 3 0.0000 0.991 0.000 0.000 1.00 0.000
#> GSM26861 3 0.0000 0.991 0.000 0.000 1.00 0.000
#> GSM26862 1 0.0000 0.969 1.000 0.000 0.00 0.000
#> GSM26863 1 0.0000 0.969 1.000 0.000 0.00 0.000
#> GSM26864 1 0.0000 0.969 1.000 0.000 0.00 0.000
#> GSM26865 1 0.0000 0.969 1.000 0.000 0.00 0.000
#> GSM26866 1 0.0000 0.969 1.000 0.000 0.00 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM26805 2 0.000 0.9994 0.000 1.000 0.000 0.000 0.000
#> GSM26806 4 0.311 0.9251 0.000 0.200 0.000 0.800 0.000
#> GSM26807 4 0.311 0.9251 0.000 0.200 0.000 0.800 0.000
#> GSM26808 4 0.311 0.9251 0.000 0.200 0.000 0.800 0.000
#> GSM26809 2 0.029 0.9894 0.000 0.992 0.000 0.000 0.008
#> GSM26810 4 0.311 0.9251 0.000 0.200 0.000 0.800 0.000
#> GSM26811 4 0.311 0.9251 0.000 0.200 0.000 0.800 0.000
#> GSM26812 4 0.311 0.9251 0.000 0.200 0.000 0.800 0.000
#> GSM26813 4 0.353 0.8772 0.000 0.256 0.000 0.744 0.000
#> GSM26814 4 0.353 0.8772 0.000 0.256 0.000 0.744 0.000
#> GSM26815 4 0.000 0.5313 0.000 0.000 0.000 1.000 0.000
#> GSM26816 2 0.000 0.9994 0.000 1.000 0.000 0.000 0.000
#> GSM26817 4 0.321 0.9184 0.000 0.212 0.000 0.788 0.000
#> GSM26818 3 0.324 0.8044 0.000 0.000 0.816 0.012 0.172
#> GSM26819 2 0.000 0.9994 0.000 1.000 0.000 0.000 0.000
#> GSM26820 2 0.000 0.9994 0.000 1.000 0.000 0.000 0.000
#> GSM26821 2 0.000 0.9994 0.000 1.000 0.000 0.000 0.000
#> GSM26822 2 0.000 0.9994 0.000 1.000 0.000 0.000 0.000
#> GSM26823 2 0.000 0.9994 0.000 1.000 0.000 0.000 0.000
#> GSM26824 2 0.000 0.9994 0.000 1.000 0.000 0.000 0.000
#> GSM26825 2 0.000 0.9994 0.000 1.000 0.000 0.000 0.000
#> GSM26826 2 0.000 0.9994 0.000 1.000 0.000 0.000 0.000
#> GSM26827 2 0.000 0.9994 0.000 1.000 0.000 0.000 0.000
#> GSM26828 2 0.000 0.9994 0.000 1.000 0.000 0.000 0.000
#> GSM26829 2 0.000 0.9994 0.000 1.000 0.000 0.000 0.000
#> GSM26830 4 0.353 0.8772 0.000 0.256 0.000 0.744 0.000
#> GSM26831 2 0.000 0.9994 0.000 1.000 0.000 0.000 0.000
#> GSM26832 2 0.000 0.9994 0.000 1.000 0.000 0.000 0.000
#> GSM26833 2 0.000 0.9994 0.000 1.000 0.000 0.000 0.000
#> GSM26834 2 0.000 0.9994 0.000 1.000 0.000 0.000 0.000
#> GSM26835 2 0.000 0.9994 0.000 1.000 0.000 0.000 0.000
#> GSM26836 1 0.000 0.9719 1.000 0.000 0.000 0.000 0.000
#> GSM26837 1 0.000 0.9719 1.000 0.000 0.000 0.000 0.000
#> GSM26838 1 0.000 0.9719 1.000 0.000 0.000 0.000 0.000
#> GSM26839 1 0.000 0.9719 1.000 0.000 0.000 0.000 0.000
#> GSM26840 5 0.285 0.0000 0.000 0.172 0.000 0.000 0.828
#> GSM26841 1 0.000 0.9719 1.000 0.000 0.000 0.000 0.000
#> GSM26842 1 0.000 0.9719 1.000 0.000 0.000 0.000 0.000
#> GSM26843 1 0.000 0.9719 1.000 0.000 0.000 0.000 0.000
#> GSM26844 1 0.000 0.9719 1.000 0.000 0.000 0.000 0.000
#> GSM26845 1 0.618 0.0741 0.544 0.180 0.000 0.000 0.276
#> GSM26846 1 0.000 0.9719 1.000 0.000 0.000 0.000 0.000
#> GSM26847 1 0.000 0.9719 1.000 0.000 0.000 0.000 0.000
#> GSM26848 1 0.000 0.9719 1.000 0.000 0.000 0.000 0.000
#> GSM26849 1 0.000 0.9719 1.000 0.000 0.000 0.000 0.000
#> GSM26850 1 0.000 0.9719 1.000 0.000 0.000 0.000 0.000
#> GSM26851 2 0.000 0.9994 0.000 1.000 0.000 0.000 0.000
#> GSM26852 3 0.000 0.9829 0.000 0.000 1.000 0.000 0.000
#> GSM26853 3 0.000 0.9829 0.000 0.000 1.000 0.000 0.000
#> GSM26854 3 0.000 0.9829 0.000 0.000 1.000 0.000 0.000
#> GSM26855 3 0.000 0.9829 0.000 0.000 1.000 0.000 0.000
#> GSM26856 3 0.000 0.9829 0.000 0.000 1.000 0.000 0.000
#> GSM26857 3 0.000 0.9829 0.000 0.000 1.000 0.000 0.000
#> GSM26858 3 0.000 0.9829 0.000 0.000 1.000 0.000 0.000
#> GSM26859 3 0.000 0.9829 0.000 0.000 1.000 0.000 0.000
#> GSM26860 3 0.000 0.9829 0.000 0.000 1.000 0.000 0.000
#> GSM26861 3 0.000 0.9829 0.000 0.000 1.000 0.000 0.000
#> GSM26862 1 0.000 0.9719 1.000 0.000 0.000 0.000 0.000
#> GSM26863 1 0.000 0.9719 1.000 0.000 0.000 0.000 0.000
#> GSM26864 1 0.000 0.9719 1.000 0.000 0.000 0.000 0.000
#> GSM26865 1 0.000 0.9719 1.000 0.000 0.000 0.000 0.000
#> GSM26866 1 0.000 0.9719 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
#> GSM26805 2 0.000 0.9995 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26806 4 0.279 0.9401 0.000 0.200 0.000 0.800 0.000 0.000
#> GSM26807 4 0.279 0.9401 0.000 0.200 0.000 0.800 0.000 0.000
#> GSM26808 4 0.279 0.9401 0.000 0.200 0.000 0.800 0.000 0.000
#> GSM26809 2 0.026 0.9908 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM26810 4 0.279 0.9401 0.000 0.200 0.000 0.800 0.000 0.000
#> GSM26811 4 0.279 0.9401 0.000 0.200 0.000 0.800 0.000 0.000
#> GSM26812 4 0.279 0.9401 0.000 0.200 0.000 0.800 0.000 0.000
#> GSM26813 4 0.317 0.9031 0.000 0.256 0.000 0.744 0.000 0.000
#> GSM26814 4 0.317 0.9031 0.000 0.256 0.000 0.744 0.000 0.000
#> GSM26815 4 0.000 0.5919 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26816 2 0.000 0.9995 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26817 4 0.288 0.9349 0.000 0.212 0.000 0.788 0.000 0.000
#> GSM26818 3 0.367 0.5096 0.000 0.000 0.632 0.000 0.000 0.368
#> GSM26819 2 0.000 0.9995 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26820 2 0.000 0.9995 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26821 2 0.000 0.9995 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26822 2 0.000 0.9995 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26823 2 0.000 0.9995 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26824 2 0.000 0.9995 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26825 2 0.000 0.9995 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26826 2 0.000 0.9995 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26827 2 0.000 0.9995 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26828 2 0.000 0.9995 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26829 2 0.000 0.9995 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26830 4 0.317 0.9031 0.000 0.256 0.000 0.744 0.000 0.000
#> GSM26831 2 0.000 0.9995 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26832 2 0.000 0.9995 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26833 2 0.000 0.9995 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26834 2 0.000 0.9995 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26835 2 0.000 0.9995 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26836 1 0.000 0.9413 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26837 1 0.000 0.9413 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26838 1 0.000 0.9413 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26839 1 0.000 0.9413 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26840 5 0.000 0.0000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM26841 1 0.000 0.9413 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26842 1 0.000 0.9413 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26843 1 0.000 0.9413 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26844 1 0.000 0.9413 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26845 1 0.407 0.0549 0.544 0.008 0.000 0.000 0.448 0.000
#> GSM26846 6 0.367 1.0000 0.368 0.000 0.000 0.000 0.000 0.632
#> GSM26847 6 0.367 1.0000 0.368 0.000 0.000 0.000 0.000 0.632
#> GSM26848 6 0.367 1.0000 0.368 0.000 0.000 0.000 0.000 0.632
#> GSM26849 6 0.367 1.0000 0.368 0.000 0.000 0.000 0.000 0.632
#> GSM26850 6 0.367 1.0000 0.368 0.000 0.000 0.000 0.000 0.632
#> GSM26851 2 0.000 0.9995 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26852 3 0.000 0.9642 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26853 3 0.000 0.9642 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26854 3 0.000 0.9642 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26855 3 0.000 0.9642 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26856 3 0.000 0.9642 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26857 3 0.000 0.9642 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26858 3 0.000 0.9642 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26859 3 0.000 0.9642 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26860 3 0.000 0.9642 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26861 3 0.000 0.9642 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26862 1 0.000 0.9413 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26863 1 0.000 0.9413 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26864 1 0.000 0.9413 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26865 6 0.367 1.0000 0.368 0.000 0.000 0.000 0.000 0.632
#> GSM26866 1 0.000 0.9413 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 tissue(p) individual(p) k
#> ATC:hclust 62 7.91e-01 7.59e-02 2
#> ATC:hclust 62 9.79e-05 4.21e-05 3
#> ATC:hclust 61 7.52e-11 6.47e-06 4
#> ATC:hclust 60 2.28e-11 3.79e-06 5
#> ATC:hclust 60 1.06e-10 7.14e-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 11993 rows and 62 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 0.591 0.885 0.907 0.4560 0.494 0.494
#> 3 3 0.773 0.852 0.883 0.3661 0.843 0.695
#> 4 4 0.746 0.909 0.902 0.1348 0.887 0.703
#> 5 5 0.750 0.825 0.843 0.0745 0.950 0.819
#> 6 6 0.817 0.766 0.826 0.0505 0.978 0.910
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
#> GSM26805 2 0.000 0.983 0.000 1.000
#> GSM26806 2 0.295 0.945 0.052 0.948
#> GSM26807 2 0.295 0.945 0.052 0.948
#> GSM26808 2 0.295 0.945 0.052 0.948
#> GSM26809 2 0.000 0.983 0.000 1.000
#> GSM26810 2 0.295 0.945 0.052 0.948
#> GSM26811 2 0.295 0.945 0.052 0.948
#> GSM26812 2 0.295 0.945 0.052 0.948
#> GSM26813 2 0.000 0.983 0.000 1.000
#> GSM26814 2 0.000 0.983 0.000 1.000
#> GSM26815 2 0.295 0.945 0.052 0.948
#> GSM26816 2 0.000 0.983 0.000 1.000
#> GSM26817 2 0.295 0.945 0.052 0.948
#> GSM26818 1 0.000 0.787 1.000 0.000
#> GSM26819 2 0.000 0.983 0.000 1.000
#> GSM26820 2 0.000 0.983 0.000 1.000
#> GSM26821 2 0.000 0.983 0.000 1.000
#> GSM26822 2 0.000 0.983 0.000 1.000
#> GSM26823 2 0.000 0.983 0.000 1.000
#> GSM26824 2 0.000 0.983 0.000 1.000
#> GSM26825 2 0.000 0.983 0.000 1.000
#> GSM26826 2 0.000 0.983 0.000 1.000
#> GSM26827 2 0.000 0.983 0.000 1.000
#> GSM26828 2 0.000 0.983 0.000 1.000
#> GSM26829 2 0.000 0.983 0.000 1.000
#> GSM26830 2 0.000 0.983 0.000 1.000
#> GSM26831 2 0.000 0.983 0.000 1.000
#> GSM26832 2 0.000 0.983 0.000 1.000
#> GSM26833 2 0.000 0.983 0.000 1.000
#> GSM26834 2 0.000 0.983 0.000 1.000
#> GSM26835 2 0.000 0.983 0.000 1.000
#> GSM26836 1 0.917 0.782 0.668 0.332
#> GSM26837 1 0.529 0.790 0.880 0.120
#> GSM26838 1 0.917 0.782 0.668 0.332
#> GSM26839 1 0.833 0.788 0.736 0.264
#> GSM26840 2 0.000 0.983 0.000 1.000
#> GSM26841 1 0.917 0.782 0.668 0.332
#> GSM26842 1 0.917 0.782 0.668 0.332
#> GSM26843 1 0.917 0.782 0.668 0.332
#> GSM26844 1 0.917 0.782 0.668 0.332
#> GSM26845 2 0.000 0.983 0.000 1.000
#> GSM26846 1 0.917 0.782 0.668 0.332
#> GSM26847 1 0.917 0.782 0.668 0.332
#> GSM26848 1 0.917 0.782 0.668 0.332
#> GSM26849 1 0.000 0.787 1.000 0.000
#> GSM26850 1 0.917 0.782 0.668 0.332
#> GSM26851 2 0.000 0.983 0.000 1.000
#> GSM26852 1 0.000 0.787 1.000 0.000
#> GSM26853 1 0.000 0.787 1.000 0.000
#> GSM26854 1 0.000 0.787 1.000 0.000
#> GSM26855 1 0.000 0.787 1.000 0.000
#> GSM26856 1 0.000 0.787 1.000 0.000
#> GSM26857 1 0.000 0.787 1.000 0.000
#> GSM26858 1 0.000 0.787 1.000 0.000
#> GSM26859 1 0.000 0.787 1.000 0.000
#> GSM26860 1 0.000 0.787 1.000 0.000
#> GSM26861 1 0.000 0.787 1.000 0.000
#> GSM26862 1 0.917 0.782 0.668 0.332
#> GSM26863 1 0.917 0.782 0.668 0.332
#> GSM26864 1 0.917 0.782 0.668 0.332
#> GSM26865 1 0.917 0.782 0.668 0.332
#> GSM26866 1 0.917 0.782 0.668 0.332
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM26805 2 0.0000 0.921 0.000 1.000 0.000
#> GSM26806 2 0.5706 0.748 0.000 0.680 0.320
#> GSM26807 2 0.5706 0.748 0.000 0.680 0.320
#> GSM26808 2 0.5706 0.748 0.000 0.680 0.320
#> GSM26809 2 0.0000 0.921 0.000 1.000 0.000
#> GSM26810 2 0.5706 0.748 0.000 0.680 0.320
#> GSM26811 2 0.5706 0.748 0.000 0.680 0.320
#> GSM26812 2 0.5706 0.748 0.000 0.680 0.320
#> GSM26813 2 0.0237 0.921 0.000 0.996 0.004
#> GSM26814 2 0.0237 0.921 0.000 0.996 0.004
#> GSM26815 2 0.5706 0.748 0.000 0.680 0.320
#> GSM26816 2 0.0000 0.921 0.000 1.000 0.000
#> GSM26817 2 0.5706 0.748 0.000 0.680 0.320
#> GSM26818 3 0.4504 0.804 0.196 0.000 0.804
#> GSM26819 2 0.0000 0.921 0.000 1.000 0.000
#> GSM26820 2 0.0000 0.921 0.000 1.000 0.000
#> GSM26821 2 0.0237 0.921 0.000 0.996 0.004
#> GSM26822 2 0.0000 0.921 0.000 1.000 0.000
#> GSM26823 2 0.0000 0.921 0.000 1.000 0.000
#> GSM26824 2 0.0237 0.921 0.000 0.996 0.004
#> GSM26825 2 0.0000 0.921 0.000 1.000 0.000
#> GSM26826 2 0.0000 0.921 0.000 1.000 0.000
#> GSM26827 2 0.0000 0.921 0.000 1.000 0.000
#> GSM26828 2 0.0000 0.921 0.000 1.000 0.000
#> GSM26829 2 0.0000 0.921 0.000 1.000 0.000
#> GSM26830 2 0.0237 0.921 0.000 0.996 0.004
#> GSM26831 2 0.0000 0.921 0.000 1.000 0.000
#> GSM26832 2 0.0000 0.921 0.000 1.000 0.000
#> GSM26833 2 0.0237 0.921 0.000 0.996 0.004
#> GSM26834 2 0.0000 0.921 0.000 1.000 0.000
#> GSM26835 2 0.0000 0.921 0.000 1.000 0.000
#> GSM26836 1 0.0000 0.880 1.000 0.000 0.000
#> GSM26837 1 0.0000 0.880 1.000 0.000 0.000
#> GSM26838 1 0.0237 0.879 0.996 0.004 0.000
#> GSM26839 1 0.0000 0.880 1.000 0.000 0.000
#> GSM26840 1 0.6026 0.385 0.624 0.376 0.000
#> GSM26841 1 0.0237 0.879 0.996 0.004 0.000
#> GSM26842 1 0.0237 0.879 0.996 0.004 0.000
#> GSM26843 1 0.0237 0.879 0.996 0.004 0.000
#> GSM26844 1 0.0237 0.879 0.996 0.004 0.000
#> GSM26845 1 0.6280 0.191 0.540 0.460 0.000
#> GSM26846 1 0.0000 0.880 1.000 0.000 0.000
#> GSM26847 1 0.0000 0.880 1.000 0.000 0.000
#> GSM26848 1 0.0000 0.880 1.000 0.000 0.000
#> GSM26849 1 0.6244 -0.477 0.560 0.000 0.440
#> GSM26850 1 0.0000 0.880 1.000 0.000 0.000
#> GSM26851 2 0.0237 0.921 0.000 0.996 0.004
#> GSM26852 3 0.5706 0.979 0.320 0.000 0.680
#> GSM26853 3 0.5706 0.979 0.320 0.000 0.680
#> GSM26854 3 0.5706 0.979 0.320 0.000 0.680
#> GSM26855 3 0.5706 0.979 0.320 0.000 0.680
#> GSM26856 3 0.5706 0.979 0.320 0.000 0.680
#> GSM26857 3 0.5706 0.979 0.320 0.000 0.680
#> GSM26858 3 0.5706 0.979 0.320 0.000 0.680
#> GSM26859 3 0.5706 0.979 0.320 0.000 0.680
#> GSM26860 3 0.5706 0.979 0.320 0.000 0.680
#> GSM26861 3 0.5706 0.979 0.320 0.000 0.680
#> GSM26862 1 0.0000 0.880 1.000 0.000 0.000
#> GSM26863 1 0.0000 0.880 1.000 0.000 0.000
#> GSM26864 1 0.0237 0.879 0.996 0.004 0.000
#> GSM26865 1 0.0000 0.880 1.000 0.000 0.000
#> GSM26866 1 0.0237 0.879 0.996 0.004 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM26805 2 0.2081 0.929 0.000 0.916 0.084 0.000
#> GSM26806 4 0.3837 0.999 0.000 0.224 0.000 0.776
#> GSM26807 4 0.3837 0.999 0.000 0.224 0.000 0.776
#> GSM26808 4 0.3837 0.999 0.000 0.224 0.000 0.776
#> GSM26809 2 0.3550 0.890 0.000 0.860 0.096 0.044
#> GSM26810 4 0.3837 0.999 0.000 0.224 0.000 0.776
#> GSM26811 4 0.3837 0.999 0.000 0.224 0.000 0.776
#> GSM26812 4 0.3837 0.999 0.000 0.224 0.000 0.776
#> GSM26813 2 0.0188 0.951 0.000 0.996 0.004 0.000
#> GSM26814 2 0.0188 0.951 0.000 0.996 0.004 0.000
#> GSM26815 4 0.3837 0.999 0.000 0.224 0.000 0.776
#> GSM26816 2 0.2081 0.929 0.000 0.916 0.084 0.000
#> GSM26817 4 0.4018 0.996 0.000 0.224 0.004 0.772
#> GSM26818 3 0.4010 0.878 0.064 0.000 0.836 0.100
#> GSM26819 2 0.0469 0.951 0.000 0.988 0.012 0.000
#> GSM26820 2 0.0469 0.951 0.000 0.988 0.012 0.000
#> GSM26821 2 0.0469 0.950 0.000 0.988 0.012 0.000
#> GSM26822 2 0.0469 0.951 0.000 0.988 0.012 0.000
#> GSM26823 2 0.0469 0.951 0.000 0.988 0.012 0.000
#> GSM26824 2 0.0469 0.950 0.000 0.988 0.012 0.000
#> GSM26825 2 0.0469 0.951 0.000 0.988 0.012 0.000
#> GSM26826 2 0.0469 0.951 0.000 0.988 0.012 0.000
#> GSM26827 2 0.0469 0.951 0.000 0.988 0.012 0.000
#> GSM26828 2 0.2081 0.929 0.000 0.916 0.084 0.000
#> GSM26829 2 0.2081 0.929 0.000 0.916 0.084 0.000
#> GSM26830 2 0.0188 0.951 0.000 0.996 0.004 0.000
#> GSM26831 2 0.2081 0.929 0.000 0.916 0.084 0.000
#> GSM26832 2 0.2081 0.929 0.000 0.916 0.084 0.000
#> GSM26833 2 0.0336 0.951 0.000 0.992 0.008 0.000
#> GSM26834 2 0.2081 0.929 0.000 0.916 0.084 0.000
#> GSM26835 2 0.2081 0.929 0.000 0.916 0.084 0.000
#> GSM26836 1 0.0592 0.906 0.984 0.000 0.000 0.016
#> GSM26837 1 0.0592 0.906 0.984 0.000 0.000 0.016
#> GSM26838 1 0.1302 0.904 0.956 0.000 0.000 0.044
#> GSM26839 1 0.0592 0.906 0.984 0.000 0.000 0.016
#> GSM26840 1 0.7049 0.612 0.676 0.144 0.092 0.088
#> GSM26841 1 0.1118 0.904 0.964 0.000 0.000 0.036
#> GSM26842 1 0.1118 0.904 0.964 0.000 0.000 0.036
#> GSM26843 1 0.0921 0.905 0.972 0.000 0.000 0.028
#> GSM26844 1 0.0921 0.905 0.972 0.000 0.000 0.028
#> GSM26845 1 0.7777 0.314 0.528 0.328 0.088 0.056
#> GSM26846 1 0.2530 0.867 0.888 0.000 0.000 0.112
#> GSM26847 1 0.2469 0.869 0.892 0.000 0.000 0.108
#> GSM26848 1 0.2408 0.868 0.896 0.000 0.000 0.104
#> GSM26849 3 0.7046 0.220 0.432 0.000 0.448 0.120
#> GSM26850 1 0.2408 0.868 0.896 0.000 0.000 0.104
#> GSM26851 2 0.0469 0.952 0.000 0.988 0.012 0.000
#> GSM26852 3 0.2345 0.950 0.100 0.000 0.900 0.000
#> GSM26853 3 0.2345 0.950 0.100 0.000 0.900 0.000
#> GSM26854 3 0.2345 0.950 0.100 0.000 0.900 0.000
#> GSM26855 3 0.2345 0.950 0.100 0.000 0.900 0.000
#> GSM26856 3 0.2345 0.950 0.100 0.000 0.900 0.000
#> GSM26857 3 0.2345 0.950 0.100 0.000 0.900 0.000
#> GSM26858 3 0.2345 0.950 0.100 0.000 0.900 0.000
#> GSM26859 3 0.2345 0.950 0.100 0.000 0.900 0.000
#> GSM26860 3 0.2345 0.950 0.100 0.000 0.900 0.000
#> GSM26861 3 0.2345 0.950 0.100 0.000 0.900 0.000
#> GSM26862 1 0.0592 0.906 0.984 0.000 0.000 0.016
#> GSM26863 1 0.0592 0.906 0.984 0.000 0.000 0.016
#> GSM26864 1 0.0921 0.905 0.972 0.000 0.000 0.028
#> GSM26865 1 0.2408 0.868 0.896 0.000 0.000 0.104
#> GSM26866 1 0.0921 0.905 0.972 0.000 0.000 0.028
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM26805 2 0.3336 0.84423 0.000 0.772 0.000 0.000 0.228
#> GSM26806 4 0.2329 0.99523 0.000 0.124 0.000 0.876 0.000
#> GSM26807 4 0.2329 0.99523 0.000 0.124 0.000 0.876 0.000
#> GSM26808 4 0.2329 0.99523 0.000 0.124 0.000 0.876 0.000
#> GSM26809 2 0.3912 0.82272 0.000 0.752 0.000 0.020 0.228
#> GSM26810 4 0.2329 0.99523 0.000 0.124 0.000 0.876 0.000
#> GSM26811 4 0.2329 0.99523 0.000 0.124 0.000 0.876 0.000
#> GSM26812 4 0.2329 0.99523 0.000 0.124 0.000 0.876 0.000
#> GSM26813 2 0.1626 0.87801 0.000 0.940 0.016 0.000 0.044
#> GSM26814 2 0.1626 0.87801 0.000 0.940 0.016 0.000 0.044
#> GSM26815 4 0.2074 0.97006 0.000 0.104 0.000 0.896 0.000
#> GSM26816 2 0.3336 0.84423 0.000 0.772 0.000 0.000 0.228
#> GSM26817 4 0.2488 0.99239 0.000 0.124 0.000 0.872 0.004
#> GSM26818 3 0.4382 0.74588 0.004 0.000 0.760 0.060 0.176
#> GSM26819 2 0.0162 0.88688 0.000 0.996 0.000 0.000 0.004
#> GSM26820 2 0.0162 0.88688 0.000 0.996 0.000 0.000 0.004
#> GSM26821 2 0.1041 0.87631 0.000 0.964 0.004 0.000 0.032
#> GSM26822 2 0.0290 0.88577 0.000 0.992 0.000 0.000 0.008
#> GSM26823 2 0.0162 0.88688 0.000 0.996 0.000 0.000 0.004
#> GSM26824 2 0.1041 0.87631 0.000 0.964 0.004 0.000 0.032
#> GSM26825 2 0.0162 0.88688 0.000 0.996 0.000 0.000 0.004
#> GSM26826 2 0.0162 0.88688 0.000 0.996 0.000 0.000 0.004
#> GSM26827 2 0.0162 0.88688 0.000 0.996 0.000 0.000 0.004
#> GSM26828 2 0.3336 0.84423 0.000 0.772 0.000 0.000 0.228
#> GSM26829 2 0.3336 0.84423 0.000 0.772 0.000 0.000 0.228
#> GSM26830 2 0.1626 0.87801 0.000 0.940 0.016 0.000 0.044
#> GSM26831 2 0.3336 0.84423 0.000 0.772 0.000 0.000 0.228
#> GSM26832 2 0.3336 0.84423 0.000 0.772 0.000 0.000 0.228
#> GSM26833 2 0.2124 0.88088 0.000 0.900 0.004 0.000 0.096
#> GSM26834 2 0.3336 0.84423 0.000 0.772 0.000 0.000 0.228
#> GSM26835 2 0.3336 0.84423 0.000 0.772 0.000 0.000 0.228
#> GSM26836 1 0.3355 0.72619 0.832 0.000 0.000 0.036 0.132
#> GSM26837 1 0.3355 0.72619 0.832 0.000 0.000 0.036 0.132
#> GSM26838 1 0.1830 0.76808 0.932 0.000 0.000 0.040 0.028
#> GSM26839 1 0.3355 0.72619 0.832 0.000 0.000 0.036 0.132
#> GSM26840 1 0.6568 0.03387 0.492 0.100 0.000 0.032 0.376
#> GSM26841 1 0.0162 0.77884 0.996 0.000 0.000 0.004 0.000
#> GSM26842 1 0.0162 0.77884 0.996 0.000 0.000 0.004 0.000
#> GSM26843 1 0.0898 0.76962 0.972 0.000 0.000 0.008 0.020
#> GSM26844 1 0.0898 0.76962 0.972 0.000 0.000 0.008 0.020
#> GSM26845 5 0.7519 -0.00443 0.340 0.252 0.008 0.024 0.376
#> GSM26846 5 0.4227 0.65354 0.420 0.000 0.000 0.000 0.580
#> GSM26847 5 0.4604 0.62187 0.428 0.000 0.000 0.012 0.560
#> GSM26848 5 0.4273 0.66473 0.448 0.000 0.000 0.000 0.552
#> GSM26849 5 0.6697 0.43415 0.188 0.000 0.228 0.028 0.556
#> GSM26850 5 0.4273 0.66473 0.448 0.000 0.000 0.000 0.552
#> GSM26851 2 0.1544 0.88549 0.000 0.932 0.000 0.000 0.068
#> GSM26852 3 0.0510 0.97728 0.016 0.000 0.984 0.000 0.000
#> GSM26853 3 0.0510 0.97728 0.016 0.000 0.984 0.000 0.000
#> GSM26854 3 0.0510 0.97728 0.016 0.000 0.984 0.000 0.000
#> GSM26855 3 0.0510 0.97728 0.016 0.000 0.984 0.000 0.000
#> GSM26856 3 0.0671 0.97669 0.016 0.000 0.980 0.004 0.000
#> GSM26857 3 0.0510 0.97728 0.016 0.000 0.984 0.000 0.000
#> GSM26858 3 0.0671 0.97669 0.016 0.000 0.980 0.004 0.000
#> GSM26859 3 0.0671 0.97669 0.016 0.000 0.980 0.004 0.000
#> GSM26860 3 0.0510 0.97728 0.016 0.000 0.984 0.000 0.000
#> GSM26861 3 0.0671 0.97669 0.016 0.000 0.980 0.004 0.000
#> GSM26862 1 0.3355 0.72619 0.832 0.000 0.000 0.036 0.132
#> GSM26863 1 0.3355 0.72619 0.832 0.000 0.000 0.036 0.132
#> GSM26864 1 0.0404 0.77550 0.988 0.000 0.000 0.000 0.012
#> GSM26865 5 0.4273 0.66473 0.448 0.000 0.000 0.000 0.552
#> GSM26866 1 0.0898 0.76962 0.972 0.000 0.000 0.008 0.020
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM26805 2 0.0000 0.679 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26806 4 0.0937 0.988 0.000 0.040 0.000 0.960 0.000 0.000
#> GSM26807 4 0.0937 0.988 0.000 0.040 0.000 0.960 0.000 0.000
#> GSM26808 4 0.0937 0.988 0.000 0.040 0.000 0.960 0.000 0.000
#> GSM26809 2 0.3481 0.634 0.000 0.776 0.000 0.000 0.192 0.032
#> GSM26810 4 0.0937 0.988 0.000 0.040 0.000 0.960 0.000 0.000
#> GSM26811 4 0.0937 0.988 0.000 0.040 0.000 0.960 0.000 0.000
#> GSM26812 4 0.0937 0.988 0.000 0.040 0.000 0.960 0.000 0.000
#> GSM26813 2 0.4938 0.679 0.000 0.568 0.000 0.000 0.356 0.076
#> GSM26814 2 0.4938 0.679 0.000 0.568 0.000 0.000 0.356 0.076
#> GSM26815 4 0.0790 0.978 0.000 0.032 0.000 0.968 0.000 0.000
#> GSM26816 2 0.0000 0.679 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26817 4 0.2471 0.929 0.000 0.040 0.000 0.896 0.044 0.020
#> GSM26818 3 0.5796 0.452 0.004 0.000 0.568 0.012 0.160 0.256
#> GSM26819 2 0.3795 0.736 0.000 0.632 0.000 0.000 0.364 0.004
#> GSM26820 2 0.3795 0.736 0.000 0.632 0.000 0.000 0.364 0.004
#> GSM26821 2 0.4726 0.693 0.000 0.536 0.008 0.000 0.424 0.032
#> GSM26822 2 0.3795 0.736 0.000 0.632 0.000 0.000 0.364 0.004
#> GSM26823 2 0.3672 0.736 0.000 0.632 0.000 0.000 0.368 0.000
#> GSM26824 2 0.4731 0.691 0.000 0.532 0.008 0.000 0.428 0.032
#> GSM26825 2 0.3795 0.736 0.000 0.632 0.000 0.000 0.364 0.004
#> GSM26826 2 0.3659 0.736 0.000 0.636 0.000 0.000 0.364 0.000
#> GSM26827 2 0.3672 0.736 0.000 0.632 0.000 0.000 0.368 0.000
#> GSM26828 2 0.0000 0.679 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26829 2 0.0000 0.679 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26830 2 0.4938 0.679 0.000 0.568 0.000 0.000 0.356 0.076
#> GSM26831 2 0.0000 0.679 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26832 2 0.0000 0.679 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26833 2 0.4094 0.687 0.000 0.728 0.008 0.000 0.224 0.040
#> GSM26834 2 0.0000 0.679 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26835 2 0.0000 0.679 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26836 1 0.1700 0.791 0.916 0.000 0.000 0.000 0.004 0.080
#> GSM26837 1 0.1700 0.791 0.916 0.000 0.000 0.000 0.004 0.080
#> GSM26838 1 0.0622 0.790 0.980 0.000 0.000 0.012 0.008 0.000
#> GSM26839 1 0.1700 0.791 0.916 0.000 0.000 0.000 0.004 0.080
#> GSM26840 5 0.7568 0.000 0.296 0.224 0.000 0.008 0.352 0.120
#> GSM26841 1 0.2956 0.783 0.856 0.000 0.000 0.016 0.100 0.028
#> GSM26842 1 0.2956 0.783 0.856 0.000 0.000 0.016 0.100 0.028
#> GSM26843 1 0.3585 0.738 0.792 0.000 0.000 0.004 0.156 0.048
#> GSM26844 1 0.3585 0.738 0.792 0.000 0.000 0.004 0.156 0.048
#> GSM26845 2 0.7860 -0.700 0.188 0.336 0.000 0.012 0.260 0.204
#> GSM26846 6 0.3360 0.875 0.264 0.000 0.000 0.004 0.000 0.732
#> GSM26847 6 0.3741 0.822 0.320 0.000 0.000 0.008 0.000 0.672
#> GSM26848 6 0.3050 0.889 0.236 0.000 0.000 0.000 0.000 0.764
#> GSM26849 6 0.4342 0.613 0.072 0.000 0.128 0.000 0.036 0.764
#> GSM26850 6 0.2996 0.887 0.228 0.000 0.000 0.000 0.000 0.772
#> GSM26851 2 0.4375 0.727 0.000 0.648 0.008 0.000 0.316 0.028
#> GSM26852 3 0.0260 0.957 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM26853 3 0.0260 0.957 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM26854 3 0.0260 0.957 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM26855 3 0.0260 0.957 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM26856 3 0.0520 0.956 0.008 0.000 0.984 0.000 0.008 0.000
#> GSM26857 3 0.0260 0.957 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM26858 3 0.0520 0.956 0.008 0.000 0.984 0.000 0.008 0.000
#> GSM26859 3 0.0520 0.956 0.008 0.000 0.984 0.000 0.008 0.000
#> GSM26860 3 0.0260 0.957 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM26861 3 0.0520 0.956 0.008 0.000 0.984 0.000 0.008 0.000
#> GSM26862 1 0.1700 0.790 0.916 0.000 0.000 0.004 0.000 0.080
#> GSM26863 1 0.1700 0.790 0.916 0.000 0.000 0.004 0.000 0.080
#> GSM26864 1 0.3147 0.779 0.844 0.000 0.000 0.012 0.100 0.044
#> GSM26865 6 0.3050 0.889 0.236 0.000 0.000 0.000 0.000 0.764
#> GSM26866 1 0.3585 0.738 0.792 0.000 0.000 0.004 0.156 0.048
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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> ATC:kmeans 62 3.65e-11 8.91e-01 2
#> ATC:kmeans 59 6.65e-12 1.69e-04 3
#> ATC:kmeans 60 2.31e-11 1.88e-06 4
#> ATC:kmeans 59 1.74e-10 1.67e-08 5
#> ATC:kmeans 59 2.99e-11 7.29e-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 11993 rows and 62 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.999 1.000 0.5066 0.494 0.494
#> 3 3 0.993 0.964 0.982 0.2383 0.841 0.690
#> 4 4 0.921 0.914 0.959 0.1689 0.895 0.718
#> 5 5 0.918 0.909 0.949 0.0522 0.963 0.861
#> 6 6 0.839 0.724 0.839 0.0502 0.956 0.808
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
#> attr(,"optional")
#> [1] 2 3 4
There is also optional best \(k\) = 2 3 4 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM26805 2 0.0000 0.999 0.000 1.000
#> GSM26806 2 0.0000 0.999 0.000 1.000
#> GSM26807 2 0.0000 0.999 0.000 1.000
#> GSM26808 2 0.0000 0.999 0.000 1.000
#> GSM26809 2 0.0000 0.999 0.000 1.000
#> GSM26810 2 0.0000 0.999 0.000 1.000
#> GSM26811 2 0.0000 0.999 0.000 1.000
#> GSM26812 2 0.0000 0.999 0.000 1.000
#> GSM26813 2 0.0000 0.999 0.000 1.000
#> GSM26814 2 0.0000 0.999 0.000 1.000
#> GSM26815 2 0.0000 0.999 0.000 1.000
#> GSM26816 2 0.0000 0.999 0.000 1.000
#> GSM26817 2 0.0000 0.999 0.000 1.000
#> GSM26818 1 0.0000 1.000 1.000 0.000
#> GSM26819 2 0.0000 0.999 0.000 1.000
#> GSM26820 2 0.0000 0.999 0.000 1.000
#> GSM26821 2 0.0000 0.999 0.000 1.000
#> GSM26822 2 0.0000 0.999 0.000 1.000
#> GSM26823 2 0.0000 0.999 0.000 1.000
#> GSM26824 2 0.0000 0.999 0.000 1.000
#> GSM26825 2 0.0000 0.999 0.000 1.000
#> GSM26826 2 0.0000 0.999 0.000 1.000
#> GSM26827 2 0.0000 0.999 0.000 1.000
#> GSM26828 2 0.0000 0.999 0.000 1.000
#> GSM26829 2 0.0000 0.999 0.000 1.000
#> GSM26830 2 0.0000 0.999 0.000 1.000
#> GSM26831 2 0.0000 0.999 0.000 1.000
#> GSM26832 2 0.0000 0.999 0.000 1.000
#> GSM26833 2 0.0000 0.999 0.000 1.000
#> GSM26834 2 0.0000 0.999 0.000 1.000
#> GSM26835 2 0.0000 0.999 0.000 1.000
#> GSM26836 1 0.0000 1.000 1.000 0.000
#> GSM26837 1 0.0000 1.000 1.000 0.000
#> GSM26838 1 0.0000 1.000 1.000 0.000
#> GSM26839 1 0.0000 1.000 1.000 0.000
#> GSM26840 2 0.0376 0.996 0.004 0.996
#> GSM26841 1 0.0000 1.000 1.000 0.000
#> GSM26842 1 0.0000 1.000 1.000 0.000
#> GSM26843 1 0.0000 1.000 1.000 0.000
#> GSM26844 1 0.0000 1.000 1.000 0.000
#> GSM26845 2 0.1414 0.980 0.020 0.980
#> GSM26846 1 0.0000 1.000 1.000 0.000
#> GSM26847 1 0.0000 1.000 1.000 0.000
#> GSM26848 1 0.0000 1.000 1.000 0.000
#> GSM26849 1 0.0000 1.000 1.000 0.000
#> GSM26850 1 0.0000 1.000 1.000 0.000
#> GSM26851 2 0.0000 0.999 0.000 1.000
#> GSM26852 1 0.0000 1.000 1.000 0.000
#> GSM26853 1 0.0000 1.000 1.000 0.000
#> GSM26854 1 0.0000 1.000 1.000 0.000
#> GSM26855 1 0.0000 1.000 1.000 0.000
#> GSM26856 1 0.0000 1.000 1.000 0.000
#> GSM26857 1 0.0000 1.000 1.000 0.000
#> GSM26858 1 0.0000 1.000 1.000 0.000
#> GSM26859 1 0.0000 1.000 1.000 0.000
#> GSM26860 1 0.0000 1.000 1.000 0.000
#> GSM26861 1 0.0000 1.000 1.000 0.000
#> GSM26862 1 0.0000 1.000 1.000 0.000
#> GSM26863 1 0.0000 1.000 1.000 0.000
#> GSM26864 1 0.0000 1.000 1.000 0.000
#> GSM26865 1 0.0000 1.000 1.000 0.000
#> GSM26866 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
#> GSM26805 2 0.0000 0.999 0.000 1.000 0.000
#> GSM26806 2 0.0237 0.997 0.000 0.996 0.004
#> GSM26807 2 0.0237 0.997 0.000 0.996 0.004
#> GSM26808 2 0.0237 0.997 0.000 0.996 0.004
#> GSM26809 2 0.0000 0.999 0.000 1.000 0.000
#> GSM26810 2 0.0237 0.997 0.000 0.996 0.004
#> GSM26811 2 0.0237 0.997 0.000 0.996 0.004
#> GSM26812 2 0.0237 0.997 0.000 0.996 0.004
#> GSM26813 2 0.0237 0.997 0.000 0.996 0.004
#> GSM26814 2 0.0000 0.999 0.000 1.000 0.000
#> GSM26815 2 0.0424 0.994 0.000 0.992 0.008
#> GSM26816 2 0.0000 0.999 0.000 1.000 0.000
#> GSM26817 2 0.0237 0.997 0.000 0.996 0.004
#> GSM26818 3 0.0000 0.995 0.000 0.000 1.000
#> GSM26819 2 0.0000 0.999 0.000 1.000 0.000
#> GSM26820 2 0.0000 0.999 0.000 1.000 0.000
#> GSM26821 2 0.0000 0.999 0.000 1.000 0.000
#> GSM26822 2 0.0000 0.999 0.000 1.000 0.000
#> GSM26823 2 0.0000 0.999 0.000 1.000 0.000
#> GSM26824 2 0.0000 0.999 0.000 1.000 0.000
#> GSM26825 2 0.0000 0.999 0.000 1.000 0.000
#> GSM26826 2 0.0000 0.999 0.000 1.000 0.000
#> GSM26827 2 0.0000 0.999 0.000 1.000 0.000
#> GSM26828 2 0.0000 0.999 0.000 1.000 0.000
#> GSM26829 2 0.0000 0.999 0.000 1.000 0.000
#> GSM26830 2 0.0000 0.999 0.000 1.000 0.000
#> GSM26831 2 0.0000 0.999 0.000 1.000 0.000
#> GSM26832 2 0.0000 0.999 0.000 1.000 0.000
#> GSM26833 2 0.0000 0.999 0.000 1.000 0.000
#> GSM26834 2 0.0000 0.999 0.000 1.000 0.000
#> GSM26835 2 0.0000 0.999 0.000 1.000 0.000
#> GSM26836 1 0.0000 0.938 1.000 0.000 0.000
#> GSM26837 1 0.0000 0.938 1.000 0.000 0.000
#> GSM26838 1 0.0000 0.938 1.000 0.000 0.000
#> GSM26839 1 0.0000 0.938 1.000 0.000 0.000
#> GSM26840 1 0.4452 0.746 0.808 0.192 0.000
#> GSM26841 1 0.0000 0.938 1.000 0.000 0.000
#> GSM26842 1 0.0000 0.938 1.000 0.000 0.000
#> GSM26843 1 0.0000 0.938 1.000 0.000 0.000
#> GSM26844 1 0.0000 0.938 1.000 0.000 0.000
#> GSM26845 1 0.4605 0.732 0.796 0.204 0.000
#> GSM26846 1 0.5785 0.542 0.668 0.000 0.332
#> GSM26847 1 0.0000 0.938 1.000 0.000 0.000
#> GSM26848 1 0.2066 0.903 0.940 0.000 0.060
#> GSM26849 3 0.0237 1.000 0.004 0.000 0.996
#> GSM26850 1 0.3482 0.848 0.872 0.000 0.128
#> GSM26851 2 0.0000 0.999 0.000 1.000 0.000
#> GSM26852 3 0.0237 1.000 0.004 0.000 0.996
#> GSM26853 3 0.0237 1.000 0.004 0.000 0.996
#> GSM26854 3 0.0237 1.000 0.004 0.000 0.996
#> GSM26855 3 0.0237 1.000 0.004 0.000 0.996
#> GSM26856 3 0.0237 1.000 0.004 0.000 0.996
#> GSM26857 3 0.0237 1.000 0.004 0.000 0.996
#> GSM26858 3 0.0237 1.000 0.004 0.000 0.996
#> GSM26859 3 0.0237 1.000 0.004 0.000 0.996
#> GSM26860 3 0.0237 1.000 0.004 0.000 0.996
#> GSM26861 3 0.0237 1.000 0.004 0.000 0.996
#> GSM26862 1 0.0000 0.938 1.000 0.000 0.000
#> GSM26863 1 0.0000 0.938 1.000 0.000 0.000
#> GSM26864 1 0.0000 0.938 1.000 0.000 0.000
#> GSM26865 1 0.2878 0.877 0.904 0.000 0.096
#> GSM26866 1 0.0000 0.938 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM26805 2 0.0000 0.964 0.000 1.000 0.000 0.000
#> GSM26806 4 0.0707 0.959 0.000 0.020 0.000 0.980
#> GSM26807 4 0.0707 0.959 0.000 0.020 0.000 0.980
#> GSM26808 4 0.0707 0.959 0.000 0.020 0.000 0.980
#> GSM26809 2 0.0000 0.964 0.000 1.000 0.000 0.000
#> GSM26810 4 0.0707 0.959 0.000 0.020 0.000 0.980
#> GSM26811 4 0.0707 0.959 0.000 0.020 0.000 0.980
#> GSM26812 4 0.0707 0.959 0.000 0.020 0.000 0.980
#> GSM26813 4 0.4277 0.598 0.000 0.280 0.000 0.720
#> GSM26814 2 0.3873 0.712 0.000 0.772 0.000 0.228
#> GSM26815 4 0.0707 0.959 0.000 0.020 0.000 0.980
#> GSM26816 2 0.0000 0.964 0.000 1.000 0.000 0.000
#> GSM26817 4 0.0707 0.959 0.000 0.020 0.000 0.980
#> GSM26818 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26819 2 0.0000 0.964 0.000 1.000 0.000 0.000
#> GSM26820 2 0.0000 0.964 0.000 1.000 0.000 0.000
#> GSM26821 2 0.0000 0.964 0.000 1.000 0.000 0.000
#> GSM26822 2 0.0000 0.964 0.000 1.000 0.000 0.000
#> GSM26823 2 0.0000 0.964 0.000 1.000 0.000 0.000
#> GSM26824 2 0.3837 0.718 0.000 0.776 0.000 0.224
#> GSM26825 2 0.0000 0.964 0.000 1.000 0.000 0.000
#> GSM26826 2 0.0000 0.964 0.000 1.000 0.000 0.000
#> GSM26827 2 0.0000 0.964 0.000 1.000 0.000 0.000
#> GSM26828 2 0.0000 0.964 0.000 1.000 0.000 0.000
#> GSM26829 2 0.0000 0.964 0.000 1.000 0.000 0.000
#> GSM26830 2 0.3873 0.712 0.000 0.772 0.000 0.228
#> GSM26831 2 0.0000 0.964 0.000 1.000 0.000 0.000
#> GSM26832 2 0.0000 0.964 0.000 1.000 0.000 0.000
#> GSM26833 2 0.0000 0.964 0.000 1.000 0.000 0.000
#> GSM26834 2 0.0000 0.964 0.000 1.000 0.000 0.000
#> GSM26835 2 0.0000 0.964 0.000 1.000 0.000 0.000
#> GSM26836 1 0.0000 0.914 1.000 0.000 0.000 0.000
#> GSM26837 1 0.0188 0.913 0.996 0.000 0.000 0.004
#> GSM26838 1 0.0000 0.914 1.000 0.000 0.000 0.000
#> GSM26839 1 0.0000 0.914 1.000 0.000 0.000 0.000
#> GSM26840 1 0.4053 0.683 0.768 0.228 0.000 0.004
#> GSM26841 1 0.0188 0.914 0.996 0.000 0.000 0.004
#> GSM26842 1 0.0188 0.914 0.996 0.000 0.000 0.004
#> GSM26843 1 0.0188 0.914 0.996 0.000 0.000 0.004
#> GSM26844 1 0.0188 0.914 0.996 0.000 0.000 0.004
#> GSM26845 1 0.4843 0.362 0.604 0.396 0.000 0.000
#> GSM26846 1 0.5203 0.493 0.636 0.000 0.348 0.016
#> GSM26847 1 0.0592 0.909 0.984 0.000 0.000 0.016
#> GSM26848 1 0.2300 0.876 0.920 0.000 0.064 0.016
#> GSM26849 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26850 1 0.3547 0.812 0.840 0.000 0.144 0.016
#> GSM26851 2 0.0000 0.964 0.000 1.000 0.000 0.000
#> GSM26852 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26853 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26854 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26855 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26856 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26857 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26858 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26859 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26860 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26861 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM26862 1 0.0188 0.913 0.996 0.000 0.000 0.004
#> GSM26863 1 0.0000 0.914 1.000 0.000 0.000 0.000
#> GSM26864 1 0.0188 0.914 0.996 0.000 0.000 0.004
#> GSM26865 1 0.3108 0.842 0.872 0.000 0.112 0.016
#> GSM26866 1 0.0188 0.914 0.996 0.000 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM26805 2 0.1270 0.944 0.000 0.948 0.000 0.000 0.052
#> GSM26806 4 0.0000 0.943 0.000 0.000 0.000 1.000 0.000
#> GSM26807 4 0.0000 0.943 0.000 0.000 0.000 1.000 0.000
#> GSM26808 4 0.0000 0.943 0.000 0.000 0.000 1.000 0.000
#> GSM26809 2 0.1043 0.945 0.000 0.960 0.000 0.000 0.040
#> GSM26810 4 0.0000 0.943 0.000 0.000 0.000 1.000 0.000
#> GSM26811 4 0.0000 0.943 0.000 0.000 0.000 1.000 0.000
#> GSM26812 4 0.0000 0.943 0.000 0.000 0.000 1.000 0.000
#> GSM26813 4 0.4193 0.521 0.000 0.304 0.000 0.684 0.012
#> GSM26814 2 0.3563 0.724 0.000 0.780 0.000 0.208 0.012
#> GSM26815 4 0.0000 0.943 0.000 0.000 0.000 1.000 0.000
#> GSM26816 2 0.1270 0.944 0.000 0.948 0.000 0.000 0.052
#> GSM26817 4 0.0000 0.943 0.000 0.000 0.000 1.000 0.000
#> GSM26818 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM26819 2 0.0000 0.942 0.000 1.000 0.000 0.000 0.000
#> GSM26820 2 0.0000 0.942 0.000 1.000 0.000 0.000 0.000
#> GSM26821 2 0.0404 0.938 0.000 0.988 0.000 0.000 0.012
#> GSM26822 2 0.0000 0.942 0.000 1.000 0.000 0.000 0.000
#> GSM26823 2 0.0000 0.942 0.000 1.000 0.000 0.000 0.000
#> GSM26824 2 0.3496 0.736 0.000 0.788 0.000 0.200 0.012
#> GSM26825 2 0.0000 0.942 0.000 1.000 0.000 0.000 0.000
#> GSM26826 2 0.0000 0.942 0.000 1.000 0.000 0.000 0.000
#> GSM26827 2 0.0000 0.942 0.000 1.000 0.000 0.000 0.000
#> GSM26828 2 0.1270 0.944 0.000 0.948 0.000 0.000 0.052
#> GSM26829 2 0.1270 0.944 0.000 0.948 0.000 0.000 0.052
#> GSM26830 2 0.3563 0.724 0.000 0.780 0.000 0.208 0.012
#> GSM26831 2 0.1270 0.944 0.000 0.948 0.000 0.000 0.052
#> GSM26832 2 0.1270 0.944 0.000 0.948 0.000 0.000 0.052
#> GSM26833 2 0.1341 0.943 0.000 0.944 0.000 0.000 0.056
#> GSM26834 2 0.1270 0.944 0.000 0.948 0.000 0.000 0.052
#> GSM26835 2 0.1270 0.944 0.000 0.948 0.000 0.000 0.052
#> GSM26836 1 0.2280 0.841 0.880 0.000 0.000 0.000 0.120
#> GSM26837 1 0.2424 0.832 0.868 0.000 0.000 0.000 0.132
#> GSM26838 1 0.0510 0.872 0.984 0.000 0.000 0.000 0.016
#> GSM26839 1 0.2230 0.843 0.884 0.000 0.000 0.000 0.116
#> GSM26840 1 0.3596 0.623 0.784 0.200 0.000 0.000 0.016
#> GSM26841 1 0.0162 0.873 0.996 0.000 0.000 0.000 0.004
#> GSM26842 1 0.0162 0.873 0.996 0.000 0.000 0.000 0.004
#> GSM26843 1 0.0000 0.871 1.000 0.000 0.000 0.000 0.000
#> GSM26844 1 0.0000 0.871 1.000 0.000 0.000 0.000 0.000
#> GSM26845 1 0.4675 0.354 0.600 0.380 0.000 0.000 0.020
#> GSM26846 5 0.1836 0.956 0.036 0.000 0.032 0.000 0.932
#> GSM26847 5 0.1544 0.983 0.068 0.000 0.000 0.000 0.932
#> GSM26848 5 0.1638 0.988 0.064 0.000 0.004 0.000 0.932
#> GSM26849 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM26850 5 0.1638 0.988 0.064 0.000 0.004 0.000 0.932
#> GSM26851 2 0.1121 0.944 0.000 0.956 0.000 0.000 0.044
#> GSM26852 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM26853 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM26854 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM26855 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM26856 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM26857 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM26858 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM26859 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM26860 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM26861 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM26862 1 0.2377 0.836 0.872 0.000 0.000 0.000 0.128
#> GSM26863 1 0.2230 0.843 0.884 0.000 0.000 0.000 0.116
#> GSM26864 1 0.0404 0.873 0.988 0.000 0.000 0.000 0.012
#> GSM26865 5 0.1638 0.988 0.064 0.000 0.004 0.000 0.932
#> GSM26866 1 0.0000 0.871 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
#> GSM26805 5 0.0000 0.5968 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM26806 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26807 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26808 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26809 5 0.2738 0.4717 0.000 0.176 0.000 0.000 0.820 0.004
#> GSM26810 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26811 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26812 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26813 2 0.6289 0.4520 0.000 0.456 0.000 0.276 0.252 0.016
#> GSM26814 2 0.5126 0.7544 0.000 0.544 0.000 0.052 0.388 0.016
#> GSM26815 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26816 5 0.0000 0.5968 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM26817 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26818 3 0.0000 0.9986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26819 5 0.3804 0.0129 0.000 0.424 0.000 0.000 0.576 0.000
#> GSM26820 5 0.3804 0.0129 0.000 0.424 0.000 0.000 0.576 0.000
#> GSM26821 2 0.3774 0.6642 0.000 0.592 0.000 0.000 0.408 0.000
#> GSM26822 5 0.3804 0.0129 0.000 0.424 0.000 0.000 0.576 0.000
#> GSM26823 5 0.3804 0.0129 0.000 0.424 0.000 0.000 0.576 0.000
#> GSM26824 2 0.4219 0.7204 0.000 0.592 0.000 0.020 0.388 0.000
#> GSM26825 5 0.3804 0.0129 0.000 0.424 0.000 0.000 0.576 0.000
#> GSM26826 5 0.3797 0.0221 0.000 0.420 0.000 0.000 0.580 0.000
#> GSM26827 5 0.3804 0.0129 0.000 0.424 0.000 0.000 0.576 0.000
#> GSM26828 5 0.0000 0.5968 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM26829 5 0.0000 0.5968 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM26830 2 0.5126 0.7544 0.000 0.544 0.000 0.052 0.388 0.016
#> GSM26831 5 0.0000 0.5968 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM26832 5 0.0000 0.5968 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM26833 5 0.2632 0.4025 0.000 0.164 0.000 0.000 0.832 0.004
#> GSM26834 5 0.0000 0.5968 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM26835 5 0.0000 0.5968 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM26836 1 0.3534 0.7943 0.800 0.076 0.000 0.000 0.000 0.124
#> GSM26837 1 0.3575 0.7912 0.796 0.076 0.000 0.000 0.000 0.128
#> GSM26838 1 0.2277 0.8203 0.892 0.076 0.000 0.000 0.000 0.032
#> GSM26839 1 0.3534 0.7943 0.800 0.076 0.000 0.000 0.000 0.124
#> GSM26840 1 0.4756 0.5447 0.608 0.332 0.000 0.000 0.056 0.004
#> GSM26841 1 0.0547 0.8268 0.980 0.020 0.000 0.000 0.000 0.000
#> GSM26842 1 0.0363 0.8279 0.988 0.012 0.000 0.000 0.000 0.000
#> GSM26843 1 0.1444 0.8150 0.928 0.072 0.000 0.000 0.000 0.000
#> GSM26844 1 0.1444 0.8150 0.928 0.072 0.000 0.000 0.000 0.000
#> GSM26845 1 0.6214 0.4626 0.504 0.316 0.000 0.000 0.140 0.040
#> GSM26846 6 0.0603 0.9709 0.016 0.000 0.004 0.000 0.000 0.980
#> GSM26847 6 0.2420 0.8997 0.040 0.076 0.000 0.000 0.000 0.884
#> GSM26848 6 0.0547 0.9737 0.020 0.000 0.000 0.000 0.000 0.980
#> GSM26849 3 0.0458 0.9842 0.000 0.000 0.984 0.000 0.000 0.016
#> GSM26850 6 0.0547 0.9737 0.020 0.000 0.000 0.000 0.000 0.980
#> GSM26851 5 0.3351 0.3135 0.000 0.288 0.000 0.000 0.712 0.000
#> GSM26852 3 0.0000 0.9986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26853 3 0.0000 0.9986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26854 3 0.0000 0.9986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26855 3 0.0000 0.9986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26856 3 0.0000 0.9986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26857 3 0.0000 0.9986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26858 3 0.0000 0.9986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26859 3 0.0000 0.9986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26860 3 0.0000 0.9986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26861 3 0.0000 0.9986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26862 1 0.3534 0.7943 0.800 0.076 0.000 0.000 0.000 0.124
#> GSM26863 1 0.3534 0.7943 0.800 0.076 0.000 0.000 0.000 0.124
#> GSM26864 1 0.0000 0.8288 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26865 6 0.0632 0.9716 0.024 0.000 0.000 0.000 0.000 0.976
#> GSM26866 1 0.1444 0.8150 0.928 0.072 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 tissue(p) individual(p) k
#> ATC:skmeans 62 3.65e-11 8.91e-01 2
#> ATC:skmeans 62 1.49e-12 1.94e-04 3
#> ATC:skmeans 60 2.34e-11 3.12e-06 4
#> ATC:skmeans 61 6.65e-11 1.89e-08 5
#> ATC:skmeans 50 8.13e-09 3.48e-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", "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 11993 rows and 62 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.986 0.994 0.5083 0.492 0.492
#> 3 3 1.000 0.966 0.987 0.2291 0.879 0.755
#> 4 4 1.000 0.945 0.963 0.1546 0.874 0.671
#> 5 5 0.873 0.838 0.879 0.0736 0.946 0.809
#> 6 6 0.869 0.812 0.875 0.0681 0.915 0.654
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 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
#> GSM26805 2 0.000 1.000 0.0 1.0
#> GSM26806 2 0.000 1.000 0.0 1.0
#> GSM26807 2 0.000 1.000 0.0 1.0
#> GSM26808 2 0.000 1.000 0.0 1.0
#> GSM26809 2 0.000 1.000 0.0 1.0
#> GSM26810 2 0.000 1.000 0.0 1.0
#> GSM26811 2 0.000 1.000 0.0 1.0
#> GSM26812 2 0.000 1.000 0.0 1.0
#> GSM26813 2 0.000 1.000 0.0 1.0
#> GSM26814 2 0.000 1.000 0.0 1.0
#> GSM26815 2 0.000 1.000 0.0 1.0
#> GSM26816 2 0.000 1.000 0.0 1.0
#> GSM26817 2 0.000 1.000 0.0 1.0
#> GSM26818 1 0.000 0.987 1.0 0.0
#> GSM26819 2 0.000 1.000 0.0 1.0
#> GSM26820 2 0.000 1.000 0.0 1.0
#> GSM26821 2 0.000 1.000 0.0 1.0
#> GSM26822 2 0.000 1.000 0.0 1.0
#> GSM26823 2 0.000 1.000 0.0 1.0
#> GSM26824 2 0.000 1.000 0.0 1.0
#> GSM26825 2 0.000 1.000 0.0 1.0
#> GSM26826 2 0.000 1.000 0.0 1.0
#> GSM26827 2 0.000 1.000 0.0 1.0
#> GSM26828 2 0.000 1.000 0.0 1.0
#> GSM26829 2 0.000 1.000 0.0 1.0
#> GSM26830 2 0.000 1.000 0.0 1.0
#> GSM26831 2 0.000 1.000 0.0 1.0
#> GSM26832 2 0.000 1.000 0.0 1.0
#> GSM26833 2 0.000 1.000 0.0 1.0
#> GSM26834 2 0.000 1.000 0.0 1.0
#> GSM26835 2 0.000 1.000 0.0 1.0
#> GSM26836 1 0.000 0.987 1.0 0.0
#> GSM26837 1 0.000 0.987 1.0 0.0
#> GSM26838 1 0.000 0.987 1.0 0.0
#> GSM26839 1 0.000 0.987 1.0 0.0
#> GSM26840 1 0.722 0.758 0.8 0.2
#> GSM26841 1 0.000 0.987 1.0 0.0
#> GSM26842 1 0.000 0.987 1.0 0.0
#> GSM26843 1 0.000 0.987 1.0 0.0
#> GSM26844 1 0.000 0.987 1.0 0.0
#> GSM26845 1 0.722 0.758 0.8 0.2
#> GSM26846 1 0.000 0.987 1.0 0.0
#> GSM26847 1 0.000 0.987 1.0 0.0
#> GSM26848 1 0.000 0.987 1.0 0.0
#> GSM26849 1 0.000 0.987 1.0 0.0
#> GSM26850 1 0.000 0.987 1.0 0.0
#> GSM26851 2 0.000 1.000 0.0 1.0
#> GSM26852 1 0.000 0.987 1.0 0.0
#> GSM26853 1 0.000 0.987 1.0 0.0
#> GSM26854 1 0.000 0.987 1.0 0.0
#> GSM26855 1 0.000 0.987 1.0 0.0
#> GSM26856 1 0.000 0.987 1.0 0.0
#> GSM26857 1 0.000 0.987 1.0 0.0
#> GSM26858 1 0.000 0.987 1.0 0.0
#> GSM26859 1 0.000 0.987 1.0 0.0
#> GSM26860 1 0.000 0.987 1.0 0.0
#> GSM26861 1 0.000 0.987 1.0 0.0
#> GSM26862 1 0.000 0.987 1.0 0.0
#> GSM26863 1 0.000 0.987 1.0 0.0
#> GSM26864 1 0.000 0.987 1.0 0.0
#> GSM26865 1 0.000 0.987 1.0 0.0
#> GSM26866 1 0.000 0.987 1.0 0.0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM26805 2 0.000 1.000 0.0 1.0 0.0
#> GSM26806 2 0.000 1.000 0.0 1.0 0.0
#> GSM26807 2 0.000 1.000 0.0 1.0 0.0
#> GSM26808 2 0.000 1.000 0.0 1.0 0.0
#> GSM26809 2 0.000 1.000 0.0 1.0 0.0
#> GSM26810 2 0.000 1.000 0.0 1.0 0.0
#> GSM26811 2 0.000 1.000 0.0 1.0 0.0
#> GSM26812 2 0.000 1.000 0.0 1.0 0.0
#> GSM26813 2 0.000 1.000 0.0 1.0 0.0
#> GSM26814 2 0.000 1.000 0.0 1.0 0.0
#> GSM26815 2 0.000 1.000 0.0 1.0 0.0
#> GSM26816 2 0.000 1.000 0.0 1.0 0.0
#> GSM26817 2 0.000 1.000 0.0 1.0 0.0
#> GSM26818 3 0.000 0.963 0.0 0.0 1.0
#> GSM26819 2 0.000 1.000 0.0 1.0 0.0
#> GSM26820 2 0.000 1.000 0.0 1.0 0.0
#> GSM26821 2 0.000 1.000 0.0 1.0 0.0
#> GSM26822 2 0.000 1.000 0.0 1.0 0.0
#> GSM26823 2 0.000 1.000 0.0 1.0 0.0
#> GSM26824 2 0.000 1.000 0.0 1.0 0.0
#> GSM26825 2 0.000 1.000 0.0 1.0 0.0
#> GSM26826 2 0.000 1.000 0.0 1.0 0.0
#> GSM26827 2 0.000 1.000 0.0 1.0 0.0
#> GSM26828 2 0.000 1.000 0.0 1.0 0.0
#> GSM26829 2 0.000 1.000 0.0 1.0 0.0
#> GSM26830 2 0.000 1.000 0.0 1.0 0.0
#> GSM26831 2 0.000 1.000 0.0 1.0 0.0
#> GSM26832 2 0.000 1.000 0.0 1.0 0.0
#> GSM26833 2 0.000 1.000 0.0 1.0 0.0
#> GSM26834 2 0.000 1.000 0.0 1.0 0.0
#> GSM26835 2 0.000 1.000 0.0 1.0 0.0
#> GSM26836 1 0.000 0.970 1.0 0.0 0.0
#> GSM26837 1 0.000 0.970 1.0 0.0 0.0
#> GSM26838 1 0.000 0.970 1.0 0.0 0.0
#> GSM26839 1 0.000 0.970 1.0 0.0 0.0
#> GSM26840 1 0.455 0.723 0.8 0.2 0.0
#> GSM26841 1 0.000 0.970 1.0 0.0 0.0
#> GSM26842 1 0.000 0.970 1.0 0.0 0.0
#> GSM26843 1 0.000 0.970 1.0 0.0 0.0
#> GSM26844 1 0.000 0.970 1.0 0.0 0.0
#> GSM26845 1 0.455 0.723 0.8 0.2 0.0
#> GSM26846 1 0.000 0.970 1.0 0.0 0.0
#> GSM26847 1 0.000 0.970 1.0 0.0 0.0
#> GSM26848 1 0.000 0.970 1.0 0.0 0.0
#> GSM26849 3 0.613 0.345 0.4 0.0 0.6
#> GSM26850 1 0.000 0.970 1.0 0.0 0.0
#> GSM26851 2 0.000 1.000 0.0 1.0 0.0
#> GSM26852 3 0.000 0.963 0.0 0.0 1.0
#> GSM26853 3 0.000 0.963 0.0 0.0 1.0
#> GSM26854 3 0.000 0.963 0.0 0.0 1.0
#> GSM26855 3 0.000 0.963 0.0 0.0 1.0
#> GSM26856 3 0.000 0.963 0.0 0.0 1.0
#> GSM26857 3 0.000 0.963 0.0 0.0 1.0
#> GSM26858 3 0.000 0.963 0.0 0.0 1.0
#> GSM26859 3 0.000 0.963 0.0 0.0 1.0
#> GSM26860 3 0.000 0.963 0.0 0.0 1.0
#> GSM26861 3 0.000 0.963 0.0 0.0 1.0
#> GSM26862 1 0.000 0.970 1.0 0.0 0.0
#> GSM26863 1 0.000 0.970 1.0 0.0 0.0
#> GSM26864 1 0.000 0.970 1.0 0.0 0.0
#> GSM26865 1 0.000 0.970 1.0 0.0 0.0
#> GSM26866 1 0.000 0.970 1.0 0.0 0.0
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM26805 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM26806 4 0.2149 0.967 0.000 0.088 0.000 0.912
#> GSM26807 4 0.2149 0.967 0.000 0.088 0.000 0.912
#> GSM26808 4 0.2149 0.967 0.000 0.088 0.000 0.912
#> GSM26809 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM26810 4 0.2149 0.967 0.000 0.088 0.000 0.912
#> GSM26811 4 0.2149 0.967 0.000 0.088 0.000 0.912
#> GSM26812 4 0.2149 0.967 0.000 0.088 0.000 0.912
#> GSM26813 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM26814 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM26815 4 0.2149 0.967 0.000 0.088 0.000 0.912
#> GSM26816 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM26817 4 0.2149 0.967 0.000 0.088 0.000 0.912
#> GSM26818 3 0.2342 0.890 0.008 0.000 0.912 0.080
#> GSM26819 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM26820 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM26821 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM26822 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM26823 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM26824 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM26825 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM26826 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM26827 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM26828 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM26829 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM26830 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM26831 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM26832 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM26833 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM26834 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM26835 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM26836 1 0.0000 0.951 1.000 0.000 0.000 0.000
#> GSM26837 1 0.0000 0.951 1.000 0.000 0.000 0.000
#> GSM26838 1 0.0336 0.951 0.992 0.000 0.000 0.008
#> GSM26839 1 0.0188 0.951 0.996 0.000 0.000 0.004
#> GSM26840 2 0.1302 0.945 0.000 0.956 0.000 0.044
#> GSM26841 1 0.0336 0.951 0.992 0.000 0.000 0.008
#> GSM26842 1 0.0336 0.951 0.992 0.000 0.000 0.008
#> GSM26843 1 0.0336 0.951 0.992 0.000 0.000 0.008
#> GSM26844 1 0.0336 0.951 0.992 0.000 0.000 0.008
#> GSM26845 1 0.4855 0.343 0.600 0.400 0.000 0.000
#> GSM26846 1 0.2011 0.915 0.920 0.000 0.000 0.080
#> GSM26847 1 0.0000 0.951 1.000 0.000 0.000 0.000
#> GSM26848 1 0.2011 0.915 0.920 0.000 0.000 0.080
#> GSM26849 3 0.6299 0.440 0.320 0.000 0.600 0.080
#> GSM26850 1 0.2011 0.915 0.920 0.000 0.000 0.080
#> GSM26851 4 0.4356 0.709 0.000 0.292 0.000 0.708
#> GSM26852 3 0.0000 0.953 0.000 0.000 1.000 0.000
#> GSM26853 3 0.0000 0.953 0.000 0.000 1.000 0.000
#> GSM26854 3 0.0000 0.953 0.000 0.000 1.000 0.000
#> GSM26855 3 0.0000 0.953 0.000 0.000 1.000 0.000
#> GSM26856 3 0.0000 0.953 0.000 0.000 1.000 0.000
#> GSM26857 3 0.0000 0.953 0.000 0.000 1.000 0.000
#> GSM26858 3 0.0000 0.953 0.000 0.000 1.000 0.000
#> GSM26859 3 0.0000 0.953 0.000 0.000 1.000 0.000
#> GSM26860 3 0.0000 0.953 0.000 0.000 1.000 0.000
#> GSM26861 3 0.0000 0.953 0.000 0.000 1.000 0.000
#> GSM26862 1 0.0000 0.951 1.000 0.000 0.000 0.000
#> GSM26863 1 0.0000 0.951 1.000 0.000 0.000 0.000
#> GSM26864 1 0.0336 0.951 0.992 0.000 0.000 0.008
#> GSM26865 1 0.2011 0.915 0.920 0.000 0.000 0.080
#> GSM26866 1 0.0336 0.951 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
#> GSM26805 2 0.0000 0.812 0.000 1.000 0.000 0.000 0.000
#> GSM26806 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM26807 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM26808 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM26809 2 0.3913 0.819 0.000 0.676 0.000 0.000 0.324
#> GSM26810 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM26811 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM26812 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM26813 2 0.0162 0.813 0.000 0.996 0.000 0.000 0.004
#> GSM26814 2 0.1965 0.820 0.000 0.904 0.000 0.000 0.096
#> GSM26815 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM26816 2 0.0000 0.812 0.000 1.000 0.000 0.000 0.000
#> GSM26817 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM26818 3 0.3109 0.742 0.000 0.000 0.800 0.000 0.200
#> GSM26819 2 0.3913 0.819 0.000 0.676 0.000 0.000 0.324
#> GSM26820 2 0.3913 0.819 0.000 0.676 0.000 0.000 0.324
#> GSM26821 2 0.3913 0.819 0.000 0.676 0.000 0.000 0.324
#> GSM26822 2 0.3913 0.819 0.000 0.676 0.000 0.000 0.324
#> GSM26823 2 0.3913 0.819 0.000 0.676 0.000 0.000 0.324
#> GSM26824 2 0.3913 0.819 0.000 0.676 0.000 0.000 0.324
#> GSM26825 2 0.3913 0.819 0.000 0.676 0.000 0.000 0.324
#> GSM26826 2 0.3913 0.819 0.000 0.676 0.000 0.000 0.324
#> GSM26827 2 0.3913 0.819 0.000 0.676 0.000 0.000 0.324
#> GSM26828 2 0.0000 0.812 0.000 1.000 0.000 0.000 0.000
#> GSM26829 2 0.0000 0.812 0.000 1.000 0.000 0.000 0.000
#> GSM26830 2 0.3707 0.822 0.000 0.716 0.000 0.000 0.284
#> GSM26831 2 0.0000 0.812 0.000 1.000 0.000 0.000 0.000
#> GSM26832 2 0.0000 0.812 0.000 1.000 0.000 0.000 0.000
#> GSM26833 2 0.0000 0.812 0.000 1.000 0.000 0.000 0.000
#> GSM26834 2 0.0000 0.812 0.000 1.000 0.000 0.000 0.000
#> GSM26835 2 0.0000 0.812 0.000 1.000 0.000 0.000 0.000
#> GSM26836 1 0.1792 0.841 0.916 0.000 0.000 0.000 0.084
#> GSM26837 1 0.1908 0.834 0.908 0.000 0.000 0.000 0.092
#> GSM26838 1 0.0000 0.858 1.000 0.000 0.000 0.000 0.000
#> GSM26839 1 0.0880 0.857 0.968 0.000 0.000 0.000 0.032
#> GSM26840 2 0.5287 0.759 0.092 0.648 0.000 0.000 0.260
#> GSM26841 1 0.0000 0.858 1.000 0.000 0.000 0.000 0.000
#> GSM26842 1 0.0000 0.858 1.000 0.000 0.000 0.000 0.000
#> GSM26843 1 0.0000 0.858 1.000 0.000 0.000 0.000 0.000
#> GSM26844 1 0.0000 0.858 1.000 0.000 0.000 0.000 0.000
#> GSM26845 1 0.5221 0.117 0.552 0.400 0.000 0.000 0.048
#> GSM26846 5 0.3913 0.822 0.324 0.000 0.000 0.000 0.676
#> GSM26847 1 0.1965 0.831 0.904 0.000 0.000 0.000 0.096
#> GSM26848 5 0.3913 0.822 0.324 0.000 0.000 0.000 0.676
#> GSM26849 5 0.3913 0.312 0.000 0.000 0.324 0.000 0.676
#> GSM26850 5 0.3913 0.822 0.324 0.000 0.000 0.000 0.676
#> GSM26851 2 0.4161 0.146 0.000 0.608 0.000 0.392 0.000
#> GSM26852 3 0.0000 0.979 0.000 0.000 1.000 0.000 0.000
#> GSM26853 3 0.0000 0.979 0.000 0.000 1.000 0.000 0.000
#> GSM26854 3 0.0000 0.979 0.000 0.000 1.000 0.000 0.000
#> GSM26855 3 0.0000 0.979 0.000 0.000 1.000 0.000 0.000
#> GSM26856 3 0.0000 0.979 0.000 0.000 1.000 0.000 0.000
#> GSM26857 3 0.0000 0.979 0.000 0.000 1.000 0.000 0.000
#> GSM26858 3 0.0000 0.979 0.000 0.000 1.000 0.000 0.000
#> GSM26859 3 0.0000 0.979 0.000 0.000 1.000 0.000 0.000
#> GSM26860 3 0.0000 0.979 0.000 0.000 1.000 0.000 0.000
#> GSM26861 3 0.0000 0.979 0.000 0.000 1.000 0.000 0.000
#> GSM26862 1 0.1792 0.841 0.916 0.000 0.000 0.000 0.084
#> GSM26863 1 0.1792 0.841 0.916 0.000 0.000 0.000 0.084
#> GSM26864 1 0.2690 0.652 0.844 0.000 0.000 0.000 0.156
#> GSM26865 5 0.3913 0.822 0.324 0.000 0.000 0.000 0.676
#> GSM26866 1 0.0794 0.842 0.972 0.000 0.000 0.000 0.028
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM26805 5 0.2762 0.9152 0.000 0.196 0.000 0.000 0.804 0.000
#> GSM26806 4 0.0000 0.9993 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26807 4 0.0000 0.9993 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26808 4 0.0000 0.9993 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26809 2 0.0363 0.9383 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM26810 4 0.0000 0.9993 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26811 4 0.0000 0.9993 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26812 4 0.0000 0.9993 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26813 5 0.2854 0.9076 0.000 0.208 0.000 0.000 0.792 0.000
#> GSM26814 5 0.3547 0.7400 0.000 0.332 0.000 0.000 0.668 0.000
#> GSM26815 4 0.0000 0.9993 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM26816 5 0.2762 0.9152 0.000 0.196 0.000 0.000 0.804 0.000
#> GSM26817 4 0.0146 0.9950 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM26818 3 0.2793 0.7581 0.000 0.000 0.800 0.000 0.000 0.200
#> GSM26819 2 0.0000 0.9482 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26820 2 0.0000 0.9482 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26821 2 0.0000 0.9482 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26822 2 0.0000 0.9482 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26823 2 0.0000 0.9482 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26824 2 0.0000 0.9482 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26825 2 0.0000 0.9482 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26826 2 0.0363 0.9383 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM26827 2 0.0000 0.9482 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26828 5 0.2762 0.9152 0.000 0.196 0.000 0.000 0.804 0.000
#> GSM26829 5 0.2762 0.9152 0.000 0.196 0.000 0.000 0.804 0.000
#> GSM26830 2 0.3647 0.1444 0.000 0.640 0.000 0.000 0.360 0.000
#> GSM26831 5 0.2762 0.9152 0.000 0.196 0.000 0.000 0.804 0.000
#> GSM26832 5 0.2762 0.9152 0.000 0.196 0.000 0.000 0.804 0.000
#> GSM26833 5 0.2854 0.9076 0.000 0.208 0.000 0.000 0.792 0.000
#> GSM26834 5 0.2762 0.9152 0.000 0.196 0.000 0.000 0.804 0.000
#> GSM26835 5 0.2762 0.9152 0.000 0.196 0.000 0.000 0.804 0.000
#> GSM26836 1 0.0790 0.6305 0.968 0.000 0.000 0.000 0.000 0.032
#> GSM26837 1 0.0865 0.6268 0.964 0.000 0.000 0.000 0.000 0.036
#> GSM26838 1 0.2969 0.6432 0.776 0.000 0.000 0.000 0.000 0.224
#> GSM26839 1 0.0000 0.6391 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26840 5 0.6418 -0.0303 0.036 0.244 0.000 0.000 0.492 0.228
#> GSM26841 1 0.5437 0.6203 0.576 0.000 0.000 0.000 0.196 0.228
#> GSM26842 1 0.5437 0.6203 0.576 0.000 0.000 0.000 0.196 0.228
#> GSM26843 1 0.5437 0.6203 0.576 0.000 0.000 0.000 0.196 0.228
#> GSM26844 1 0.5437 0.6203 0.576 0.000 0.000 0.000 0.196 0.228
#> GSM26845 1 0.5866 0.1678 0.576 0.196 0.000 0.000 0.204 0.024
#> GSM26846 6 0.2996 0.8340 0.228 0.000 0.000 0.000 0.000 0.772
#> GSM26847 1 0.0937 0.6224 0.960 0.000 0.000 0.000 0.000 0.040
#> GSM26848 6 0.2969 0.8345 0.224 0.000 0.000 0.000 0.000 0.776
#> GSM26849 6 0.3109 0.8329 0.224 0.000 0.004 0.000 0.000 0.772
#> GSM26850 6 0.2996 0.8340 0.228 0.000 0.000 0.000 0.000 0.772
#> GSM26851 5 0.3110 0.9006 0.000 0.196 0.000 0.012 0.792 0.000
#> GSM26852 3 0.0000 0.9799 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26853 3 0.0000 0.9799 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26854 3 0.0000 0.9799 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26855 3 0.0000 0.9799 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26856 3 0.0000 0.9799 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26857 3 0.0000 0.9799 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26858 3 0.0000 0.9799 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26859 3 0.0000 0.9799 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26860 3 0.0000 0.9799 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26861 3 0.0000 0.9799 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26862 1 0.0790 0.6305 0.968 0.000 0.000 0.000 0.000 0.032
#> GSM26863 1 0.0790 0.6305 0.968 0.000 0.000 0.000 0.000 0.032
#> GSM26864 6 0.5634 -0.3419 0.336 0.000 0.000 0.000 0.164 0.500
#> GSM26865 6 0.2969 0.8345 0.224 0.000 0.000 0.000 0.000 0.776
#> GSM26866 1 0.5662 0.5708 0.524 0.000 0.000 0.000 0.196 0.280
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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> ATC:pam 62 1.14e-12 8.30e-01 2
#> ATC:pam 61 2.42e-12 8.63e-05 3
#> ATC:pam 60 1.32e-10 4.12e-06 4
#> ATC:pam 59 1.74e-10 3.95e-07 5
#> ATC:pam 58 1.00e-09 2.43e-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["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 11993 rows and 62 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 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 0.715 0.850 0.919 0.4442 0.535 0.535
#> 3 3 0.807 0.928 0.958 0.4010 0.611 0.402
#> 4 4 0.844 0.807 0.914 0.1792 0.820 0.558
#> 5 5 0.747 0.770 0.874 0.0372 0.836 0.501
#> 6 6 0.861 0.830 0.891 0.0381 0.934 0.741
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
#> GSM26805 2 0.000 0.899 0.000 1.000
#> GSM26806 1 0.833 0.710 0.736 0.264
#> GSM26807 1 0.833 0.710 0.736 0.264
#> GSM26808 1 0.833 0.710 0.736 0.264
#> GSM26809 2 0.978 0.288 0.412 0.588
#> GSM26810 1 0.833 0.710 0.736 0.264
#> GSM26811 1 0.833 0.710 0.736 0.264
#> GSM26812 1 0.833 0.710 0.736 0.264
#> GSM26813 1 0.850 0.690 0.724 0.276
#> GSM26814 2 0.929 0.480 0.344 0.656
#> GSM26815 1 0.278 0.929 0.952 0.048
#> GSM26816 2 0.000 0.899 0.000 1.000
#> GSM26817 1 0.839 0.704 0.732 0.268
#> GSM26818 1 0.278 0.929 0.952 0.048
#> GSM26819 2 0.000 0.899 0.000 1.000
#> GSM26820 2 0.000 0.899 0.000 1.000
#> GSM26821 2 0.000 0.899 0.000 1.000
#> GSM26822 2 0.871 0.580 0.292 0.708
#> GSM26823 2 0.000 0.899 0.000 1.000
#> GSM26824 2 0.000 0.899 0.000 1.000
#> GSM26825 2 0.000 0.899 0.000 1.000
#> GSM26826 2 0.000 0.899 0.000 1.000
#> GSM26827 2 0.000 0.899 0.000 1.000
#> GSM26828 2 0.000 0.899 0.000 1.000
#> GSM26829 2 0.000 0.899 0.000 1.000
#> GSM26830 2 0.921 0.499 0.336 0.664
#> GSM26831 2 0.000 0.899 0.000 1.000
#> GSM26832 2 0.000 0.899 0.000 1.000
#> GSM26833 2 0.402 0.839 0.080 0.920
#> GSM26834 2 0.000 0.899 0.000 1.000
#> GSM26835 2 0.000 0.899 0.000 1.000
#> GSM26836 1 0.278 0.929 0.952 0.048
#> GSM26837 1 0.278 0.929 0.952 0.048
#> GSM26838 1 0.278 0.929 0.952 0.048
#> GSM26839 1 0.278 0.929 0.952 0.048
#> GSM26840 1 0.278 0.929 0.952 0.048
#> GSM26841 1 0.278 0.929 0.952 0.048
#> GSM26842 1 0.278 0.929 0.952 0.048
#> GSM26843 1 0.278 0.929 0.952 0.048
#> GSM26844 1 0.278 0.929 0.952 0.048
#> GSM26845 1 0.278 0.929 0.952 0.048
#> GSM26846 1 0.278 0.929 0.952 0.048
#> GSM26847 1 0.278 0.929 0.952 0.048
#> GSM26848 1 0.278 0.929 0.952 0.048
#> GSM26849 1 0.278 0.929 0.952 0.048
#> GSM26850 1 0.278 0.929 0.952 0.048
#> GSM26851 2 0.921 0.499 0.336 0.664
#> GSM26852 1 0.000 0.906 1.000 0.000
#> GSM26853 1 0.000 0.906 1.000 0.000
#> GSM26854 1 0.000 0.906 1.000 0.000
#> GSM26855 1 0.000 0.906 1.000 0.000
#> GSM26856 1 0.000 0.906 1.000 0.000
#> GSM26857 1 0.000 0.906 1.000 0.000
#> GSM26858 1 0.000 0.906 1.000 0.000
#> GSM26859 1 0.000 0.906 1.000 0.000
#> GSM26860 1 0.000 0.906 1.000 0.000
#> GSM26861 1 0.000 0.906 1.000 0.000
#> GSM26862 1 0.278 0.929 0.952 0.048
#> GSM26863 1 0.278 0.929 0.952 0.048
#> GSM26864 1 0.278 0.929 0.952 0.048
#> GSM26865 1 0.278 0.929 0.952 0.048
#> GSM26866 1 0.278 0.929 0.952 0.048
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM26805 2 0.0000 0.919 0.000 1.000 0.000
#> GSM26806 2 0.4654 0.822 0.208 0.792 0.000
#> GSM26807 2 0.4654 0.822 0.208 0.792 0.000
#> GSM26808 2 0.4654 0.822 0.208 0.792 0.000
#> GSM26809 2 0.2448 0.896 0.076 0.924 0.000
#> GSM26810 2 0.4654 0.822 0.208 0.792 0.000
#> GSM26811 2 0.4654 0.822 0.208 0.792 0.000
#> GSM26812 2 0.4654 0.822 0.208 0.792 0.000
#> GSM26813 2 0.4121 0.849 0.168 0.832 0.000
#> GSM26814 2 0.2066 0.903 0.060 0.940 0.000
#> GSM26815 2 0.4750 0.813 0.216 0.784 0.000
#> GSM26816 2 0.0000 0.919 0.000 1.000 0.000
#> GSM26817 2 0.4654 0.822 0.208 0.792 0.000
#> GSM26818 3 0.3879 0.806 0.152 0.000 0.848
#> GSM26819 2 0.0000 0.919 0.000 1.000 0.000
#> GSM26820 2 0.0000 0.919 0.000 1.000 0.000
#> GSM26821 2 0.0424 0.918 0.008 0.992 0.000
#> GSM26822 2 0.0000 0.919 0.000 1.000 0.000
#> GSM26823 2 0.0000 0.919 0.000 1.000 0.000
#> GSM26824 2 0.0747 0.917 0.016 0.984 0.000
#> GSM26825 2 0.0000 0.919 0.000 1.000 0.000
#> GSM26826 2 0.0000 0.919 0.000 1.000 0.000
#> GSM26827 2 0.0000 0.919 0.000 1.000 0.000
#> GSM26828 2 0.0000 0.919 0.000 1.000 0.000
#> GSM26829 2 0.0000 0.919 0.000 1.000 0.000
#> GSM26830 2 0.0747 0.917 0.016 0.984 0.000
#> GSM26831 2 0.0000 0.919 0.000 1.000 0.000
#> GSM26832 2 0.0000 0.919 0.000 1.000 0.000
#> GSM26833 2 0.0747 0.917 0.016 0.984 0.000
#> GSM26834 2 0.0000 0.919 0.000 1.000 0.000
#> GSM26835 2 0.0000 0.919 0.000 1.000 0.000
#> GSM26836 1 0.0000 1.000 1.000 0.000 0.000
#> GSM26837 1 0.0000 1.000 1.000 0.000 0.000
#> GSM26838 1 0.0000 1.000 1.000 0.000 0.000
#> GSM26839 1 0.0000 1.000 1.000 0.000 0.000
#> GSM26840 1 0.0000 1.000 1.000 0.000 0.000
#> GSM26841 1 0.0000 1.000 1.000 0.000 0.000
#> GSM26842 1 0.0000 1.000 1.000 0.000 0.000
#> GSM26843 1 0.0000 1.000 1.000 0.000 0.000
#> GSM26844 1 0.0000 1.000 1.000 0.000 0.000
#> GSM26845 2 0.4750 0.813 0.216 0.784 0.000
#> GSM26846 1 0.0000 1.000 1.000 0.000 0.000
#> GSM26847 1 0.0000 1.000 1.000 0.000 0.000
#> GSM26848 1 0.0000 1.000 1.000 0.000 0.000
#> GSM26849 3 0.4702 0.715 0.212 0.000 0.788
#> GSM26850 1 0.0000 1.000 1.000 0.000 0.000
#> GSM26851 2 0.0000 0.919 0.000 1.000 0.000
#> GSM26852 3 0.0000 0.962 0.000 0.000 1.000
#> GSM26853 3 0.0000 0.962 0.000 0.000 1.000
#> GSM26854 3 0.0000 0.962 0.000 0.000 1.000
#> GSM26855 3 0.0000 0.962 0.000 0.000 1.000
#> GSM26856 3 0.0000 0.962 0.000 0.000 1.000
#> GSM26857 3 0.0000 0.962 0.000 0.000 1.000
#> GSM26858 3 0.0000 0.962 0.000 0.000 1.000
#> GSM26859 3 0.0000 0.962 0.000 0.000 1.000
#> GSM26860 3 0.0000 0.962 0.000 0.000 1.000
#> GSM26861 3 0.0000 0.962 0.000 0.000 1.000
#> GSM26862 1 0.0000 1.000 1.000 0.000 0.000
#> GSM26863 1 0.0000 1.000 1.000 0.000 0.000
#> GSM26864 1 0.0000 1.000 1.000 0.000 0.000
#> GSM26865 1 0.0000 1.000 1.000 0.000 0.000
#> GSM26866 1 0.0000 1.000 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM26805 2 0.0000 0.869 0.000 1.000 0.000 0.000
#> GSM26806 4 0.0592 0.776 0.000 0.016 0.000 0.984
#> GSM26807 4 0.0921 0.784 0.000 0.028 0.000 0.972
#> GSM26808 4 0.1022 0.786 0.000 0.032 0.000 0.968
#> GSM26809 4 0.7355 0.383 0.172 0.340 0.000 0.488
#> GSM26810 4 0.1022 0.786 0.000 0.032 0.000 0.968
#> GSM26811 4 0.1022 0.786 0.000 0.032 0.000 0.968
#> GSM26812 4 0.1022 0.786 0.000 0.032 0.000 0.968
#> GSM26813 4 0.4522 0.572 0.000 0.320 0.000 0.680
#> GSM26814 4 0.4804 0.471 0.000 0.384 0.000 0.616
#> GSM26815 4 0.3105 0.701 0.120 0.012 0.000 0.868
#> GSM26816 2 0.0000 0.869 0.000 1.000 0.000 0.000
#> GSM26817 4 0.1716 0.776 0.000 0.064 0.000 0.936
#> GSM26818 1 0.6049 0.656 0.680 0.000 0.200 0.120
#> GSM26819 2 0.1022 0.841 0.000 0.968 0.000 0.032
#> GSM26820 2 0.0000 0.869 0.000 1.000 0.000 0.000
#> GSM26821 2 0.4790 0.217 0.000 0.620 0.000 0.380
#> GSM26822 2 0.4500 0.394 0.000 0.684 0.000 0.316
#> GSM26823 2 0.0000 0.869 0.000 1.000 0.000 0.000
#> GSM26824 4 0.4967 0.305 0.000 0.452 0.000 0.548
#> GSM26825 2 0.0000 0.869 0.000 1.000 0.000 0.000
#> GSM26826 2 0.0000 0.869 0.000 1.000 0.000 0.000
#> GSM26827 2 0.0000 0.869 0.000 1.000 0.000 0.000
#> GSM26828 2 0.0000 0.869 0.000 1.000 0.000 0.000
#> GSM26829 2 0.0000 0.869 0.000 1.000 0.000 0.000
#> GSM26830 4 0.4888 0.411 0.000 0.412 0.000 0.588
#> GSM26831 2 0.0000 0.869 0.000 1.000 0.000 0.000
#> GSM26832 2 0.0000 0.869 0.000 1.000 0.000 0.000
#> GSM26833 2 0.4981 -0.106 0.000 0.536 0.000 0.464
#> GSM26834 2 0.0000 0.869 0.000 1.000 0.000 0.000
#> GSM26835 2 0.0000 0.869 0.000 1.000 0.000 0.000
#> GSM26836 1 0.1022 0.959 0.968 0.000 0.000 0.032
#> GSM26837 1 0.0336 0.960 0.992 0.000 0.000 0.008
#> GSM26838 1 0.1118 0.958 0.964 0.000 0.000 0.036
#> GSM26839 1 0.0000 0.959 1.000 0.000 0.000 0.000
#> GSM26840 1 0.0188 0.959 0.996 0.000 0.000 0.004
#> GSM26841 1 0.0000 0.959 1.000 0.000 0.000 0.000
#> GSM26842 1 0.0000 0.959 1.000 0.000 0.000 0.000
#> GSM26843 1 0.0188 0.959 0.996 0.000 0.000 0.004
#> GSM26844 1 0.0188 0.959 0.996 0.000 0.000 0.004
#> GSM26845 1 0.2485 0.938 0.916 0.004 0.016 0.064
#> GSM26846 1 0.1022 0.958 0.968 0.000 0.000 0.032
#> GSM26847 1 0.1022 0.958 0.968 0.000 0.000 0.032
#> GSM26848 1 0.1489 0.954 0.952 0.000 0.004 0.044
#> GSM26849 1 0.4072 0.847 0.828 0.000 0.120 0.052
#> GSM26850 1 0.1975 0.947 0.936 0.000 0.016 0.048
#> GSM26851 2 0.4999 -0.188 0.000 0.508 0.000 0.492
#> GSM26852 3 0.0000 0.978 0.000 0.000 1.000 0.000
#> GSM26853 3 0.0000 0.978 0.000 0.000 1.000 0.000
#> GSM26854 3 0.0000 0.978 0.000 0.000 1.000 0.000
#> GSM26855 3 0.0000 0.978 0.000 0.000 1.000 0.000
#> GSM26856 3 0.3219 0.787 0.164 0.000 0.836 0.000
#> GSM26857 3 0.0000 0.978 0.000 0.000 1.000 0.000
#> GSM26858 3 0.0000 0.978 0.000 0.000 1.000 0.000
#> GSM26859 3 0.0000 0.978 0.000 0.000 1.000 0.000
#> GSM26860 3 0.0000 0.978 0.000 0.000 1.000 0.000
#> GSM26861 3 0.0000 0.978 0.000 0.000 1.000 0.000
#> GSM26862 1 0.1474 0.952 0.948 0.000 0.000 0.052
#> GSM26863 1 0.1022 0.959 0.968 0.000 0.000 0.032
#> GSM26864 1 0.0188 0.959 0.996 0.000 0.000 0.004
#> GSM26865 1 0.1576 0.952 0.948 0.000 0.004 0.048
#> GSM26866 1 0.0188 0.959 0.996 0.000 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM26805 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000
#> GSM26806 4 0.2179 0.839 0.000 0.112 0.000 0.888 0.000
#> GSM26807 4 0.2329 0.846 0.000 0.124 0.000 0.876 0.000
#> GSM26808 4 0.2329 0.846 0.000 0.124 0.000 0.876 0.000
#> GSM26809 2 0.3980 0.809 0.056 0.824 0.000 0.028 0.092
#> GSM26810 4 0.2929 0.796 0.000 0.180 0.000 0.820 0.000
#> GSM26811 4 0.2471 0.844 0.000 0.136 0.000 0.864 0.000
#> GSM26812 4 0.2471 0.844 0.000 0.136 0.000 0.864 0.000
#> GSM26813 2 0.4169 0.690 0.000 0.732 0.000 0.240 0.028
#> GSM26814 2 0.3123 0.793 0.000 0.812 0.000 0.184 0.004
#> GSM26815 4 0.3039 0.559 0.000 0.000 0.000 0.808 0.192
#> GSM26816 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000
#> GSM26817 2 0.4278 0.205 0.000 0.548 0.000 0.452 0.000
#> GSM26818 4 0.7437 0.152 0.072 0.000 0.264 0.488 0.176
#> GSM26819 2 0.0162 0.918 0.000 0.996 0.000 0.004 0.000
#> GSM26820 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000
#> GSM26821 2 0.1410 0.892 0.000 0.940 0.000 0.060 0.000
#> GSM26822 2 0.0609 0.912 0.000 0.980 0.000 0.020 0.000
#> GSM26823 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000
#> GSM26824 2 0.2690 0.823 0.000 0.844 0.000 0.156 0.000
#> GSM26825 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000
#> GSM26826 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000
#> GSM26827 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000
#> GSM26828 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000
#> GSM26829 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000
#> GSM26830 2 0.2852 0.807 0.000 0.828 0.000 0.172 0.000
#> GSM26831 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000
#> GSM26832 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000
#> GSM26833 2 0.2773 0.814 0.000 0.836 0.000 0.164 0.000
#> GSM26834 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000
#> GSM26835 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000
#> GSM26836 5 0.2813 0.795 0.168 0.000 0.000 0.000 0.832
#> GSM26837 1 0.3563 0.681 0.780 0.000 0.000 0.012 0.208
#> GSM26838 5 0.3642 0.741 0.232 0.000 0.000 0.008 0.760
#> GSM26839 1 0.2179 0.754 0.888 0.000 0.000 0.000 0.112
#> GSM26840 1 0.2020 0.699 0.900 0.000 0.000 0.000 0.100
#> GSM26841 1 0.2690 0.720 0.844 0.000 0.000 0.000 0.156
#> GSM26842 1 0.2377 0.752 0.872 0.000 0.000 0.000 0.128
#> GSM26843 1 0.0000 0.779 1.000 0.000 0.000 0.000 0.000
#> GSM26844 1 0.0162 0.781 0.996 0.000 0.000 0.000 0.004
#> GSM26845 5 0.7103 0.445 0.052 0.036 0.216 0.100 0.596
#> GSM26846 5 0.2446 0.727 0.044 0.000 0.000 0.056 0.900
#> GSM26847 5 0.3276 0.782 0.132 0.000 0.000 0.032 0.836
#> GSM26848 1 0.6988 0.204 0.464 0.000 0.128 0.044 0.364
#> GSM26849 3 0.5995 0.494 0.116 0.000 0.668 0.048 0.168
#> GSM26850 3 0.7568 -0.191 0.324 0.000 0.356 0.040 0.280
#> GSM26851 2 0.0794 0.909 0.000 0.972 0.000 0.028 0.000
#> GSM26852 3 0.0000 0.899 0.000 0.000 1.000 0.000 0.000
#> GSM26853 3 0.0000 0.899 0.000 0.000 1.000 0.000 0.000
#> GSM26854 3 0.0000 0.899 0.000 0.000 1.000 0.000 0.000
#> GSM26855 3 0.0162 0.896 0.000 0.000 0.996 0.004 0.000
#> GSM26856 3 0.0912 0.881 0.016 0.000 0.972 0.000 0.012
#> GSM26857 3 0.0000 0.899 0.000 0.000 1.000 0.000 0.000
#> GSM26858 3 0.0000 0.899 0.000 0.000 1.000 0.000 0.000
#> GSM26859 3 0.0609 0.887 0.000 0.000 0.980 0.020 0.000
#> GSM26860 3 0.0000 0.899 0.000 0.000 1.000 0.000 0.000
#> GSM26861 3 0.0000 0.899 0.000 0.000 1.000 0.000 0.000
#> GSM26862 5 0.2909 0.799 0.140 0.000 0.000 0.012 0.848
#> GSM26863 5 0.3388 0.776 0.200 0.000 0.000 0.008 0.792
#> GSM26864 1 0.1121 0.782 0.956 0.000 0.000 0.000 0.044
#> GSM26865 1 0.7007 0.218 0.468 0.000 0.132 0.044 0.356
#> GSM26866 1 0.0290 0.782 0.992 0.000 0.000 0.000 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM26805 2 0.0146 0.9488 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM26806 4 0.0692 0.8745 0.000 0.020 0.000 0.976 0.000 0.004
#> GSM26807 4 0.0547 0.8758 0.000 0.020 0.000 0.980 0.000 0.000
#> GSM26808 4 0.0632 0.8748 0.000 0.024 0.000 0.976 0.000 0.000
#> GSM26809 2 0.4225 0.6538 0.020 0.688 0.000 0.016 0.000 0.276
#> GSM26810 4 0.0547 0.8758 0.000 0.020 0.000 0.980 0.000 0.000
#> GSM26811 4 0.0632 0.8748 0.000 0.024 0.000 0.976 0.000 0.000
#> GSM26812 4 0.0547 0.8758 0.000 0.020 0.000 0.980 0.000 0.000
#> GSM26813 2 0.3852 0.7483 0.000 0.764 0.000 0.180 0.004 0.052
#> GSM26814 2 0.2618 0.8616 0.000 0.860 0.000 0.116 0.000 0.024
#> GSM26815 4 0.3664 0.6514 0.012 0.004 0.000 0.792 0.028 0.164
#> GSM26816 2 0.0000 0.9482 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26817 4 0.3737 0.2957 0.000 0.392 0.000 0.608 0.000 0.000
#> GSM26818 3 0.7126 -0.0047 0.044 0.000 0.376 0.368 0.024 0.188
#> GSM26819 2 0.0146 0.9472 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM26820 2 0.0000 0.9482 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26821 2 0.1152 0.9266 0.000 0.952 0.000 0.044 0.000 0.004
#> GSM26822 2 0.0692 0.9411 0.000 0.976 0.000 0.004 0.000 0.020
#> GSM26823 2 0.0146 0.9488 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM26824 2 0.1806 0.8975 0.000 0.908 0.000 0.088 0.000 0.004
#> GSM26825 2 0.0000 0.9482 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM26826 2 0.0146 0.9488 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM26827 2 0.0146 0.9488 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM26828 2 0.0146 0.9488 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM26829 2 0.0146 0.9488 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM26830 2 0.2165 0.8798 0.000 0.884 0.000 0.108 0.000 0.008
#> GSM26831 2 0.0146 0.9488 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM26832 2 0.0146 0.9488 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM26833 2 0.2053 0.8822 0.000 0.888 0.000 0.108 0.000 0.004
#> GSM26834 2 0.0146 0.9488 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM26835 2 0.0146 0.9488 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM26836 5 0.1082 0.8396 0.040 0.000 0.000 0.000 0.956 0.004
#> GSM26837 5 0.2122 0.8084 0.076 0.000 0.000 0.000 0.900 0.024
#> GSM26838 5 0.2308 0.8263 0.068 0.000 0.000 0.000 0.892 0.040
#> GSM26839 5 0.4552 0.4109 0.364 0.000 0.000 0.000 0.592 0.044
#> GSM26840 1 0.3198 0.6397 0.740 0.000 0.000 0.000 0.000 0.260
#> GSM26841 1 0.2384 0.8370 0.888 0.000 0.000 0.000 0.064 0.048
#> GSM26842 1 0.2658 0.8278 0.864 0.000 0.000 0.000 0.100 0.036
#> GSM26843 1 0.0000 0.8718 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26844 1 0.0000 0.8718 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM26845 6 0.5231 0.4775 0.048 0.012 0.008 0.008 0.308 0.616
#> GSM26846 5 0.3380 0.7523 0.024 0.000 0.004 0.004 0.804 0.164
#> GSM26847 5 0.2237 0.8016 0.020 0.000 0.000 0.004 0.896 0.080
#> GSM26848 6 0.5877 0.7407 0.248 0.000 0.008 0.004 0.192 0.548
#> GSM26849 6 0.5669 0.4772 0.044 0.000 0.296 0.000 0.080 0.580
#> GSM26850 6 0.5877 0.7407 0.248 0.000 0.008 0.004 0.192 0.548
#> GSM26851 2 0.0806 0.9396 0.000 0.972 0.000 0.008 0.000 0.020
#> GSM26852 3 0.0000 0.9277 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26853 3 0.0000 0.9277 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26854 3 0.0000 0.9277 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26855 3 0.0000 0.9277 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26856 3 0.1088 0.8969 0.024 0.000 0.960 0.000 0.000 0.016
#> GSM26857 3 0.0146 0.9263 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM26858 3 0.0146 0.9272 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM26859 3 0.0146 0.9272 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM26860 3 0.0146 0.9263 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM26861 3 0.0146 0.9272 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM26862 5 0.1605 0.8424 0.044 0.000 0.000 0.004 0.936 0.016
#> GSM26863 5 0.1461 0.8423 0.044 0.000 0.000 0.000 0.940 0.016
#> GSM26864 1 0.2537 0.8301 0.872 0.000 0.000 0.000 0.096 0.032
#> GSM26865 6 0.5812 0.7314 0.248 0.000 0.008 0.000 0.204 0.540
#> GSM26866 1 0.0146 0.8724 0.996 0.000 0.000 0.000 0.004 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> ATC:mclust 58 5.61e-07 3.48e-03 2
#> ATC:mclust 62 9.16e-12 1.83e-04 3
#> ATC:mclust 54 7.45e-11 9.18e-08 4
#> ATC:mclust 55 2.06e-10 1.02e-06 5
#> ATC:mclust 57 3.10e-10 1.28e-06 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "NMF"]
# you can also extract it by
# res = res_list["ATC:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 11993 rows and 62 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 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 0.5066 0.494 0.494
#> 3 3 0.772 0.827 0.926 0.2686 0.792 0.603
#> 4 4 0.910 0.916 0.948 0.1702 0.789 0.469
#> 5 5 0.761 0.722 0.862 0.0366 0.884 0.608
#> 6 6 0.781 0.696 0.813 0.0489 0.893 0.582
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM26805 2 0 1 0 1
#> GSM26806 2 0 1 0 1
#> GSM26807 2 0 1 0 1
#> GSM26808 2 0 1 0 1
#> GSM26809 2 0 1 0 1
#> GSM26810 2 0 1 0 1
#> GSM26811 2 0 1 0 1
#> GSM26812 2 0 1 0 1
#> GSM26813 2 0 1 0 1
#> GSM26814 2 0 1 0 1
#> GSM26815 2 0 1 0 1
#> GSM26816 2 0 1 0 1
#> GSM26817 2 0 1 0 1
#> GSM26818 1 0 1 1 0
#> GSM26819 2 0 1 0 1
#> GSM26820 2 0 1 0 1
#> GSM26821 2 0 1 0 1
#> GSM26822 2 0 1 0 1
#> GSM26823 2 0 1 0 1
#> GSM26824 2 0 1 0 1
#> GSM26825 2 0 1 0 1
#> GSM26826 2 0 1 0 1
#> GSM26827 2 0 1 0 1
#> GSM26828 2 0 1 0 1
#> GSM26829 2 0 1 0 1
#> GSM26830 2 0 1 0 1
#> GSM26831 2 0 1 0 1
#> GSM26832 2 0 1 0 1
#> GSM26833 2 0 1 0 1
#> GSM26834 2 0 1 0 1
#> GSM26835 2 0 1 0 1
#> GSM26836 1 0 1 1 0
#> GSM26837 1 0 1 1 0
#> GSM26838 1 0 1 1 0
#> GSM26839 1 0 1 1 0
#> GSM26840 2 0 1 0 1
#> GSM26841 1 0 1 1 0
#> GSM26842 1 0 1 1 0
#> GSM26843 1 0 1 1 0
#> GSM26844 1 0 1 1 0
#> GSM26845 2 0 1 0 1
#> GSM26846 1 0 1 1 0
#> GSM26847 1 0 1 1 0
#> GSM26848 1 0 1 1 0
#> GSM26849 1 0 1 1 0
#> GSM26850 1 0 1 1 0
#> GSM26851 2 0 1 0 1
#> GSM26852 1 0 1 1 0
#> GSM26853 1 0 1 1 0
#> GSM26854 1 0 1 1 0
#> GSM26855 1 0 1 1 0
#> GSM26856 1 0 1 1 0
#> GSM26857 1 0 1 1 0
#> GSM26858 1 0 1 1 0
#> GSM26859 1 0 1 1 0
#> GSM26860 1 0 1 1 0
#> GSM26861 1 0 1 1 0
#> GSM26862 1 0 1 1 0
#> GSM26863 1 0 1 1 0
#> GSM26864 1 0 1 1 0
#> GSM26865 1 0 1 1 0
#> GSM26866 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM26805 2 0.3192 0.8448 0.112 0.888 0.000
#> GSM26806 2 0.0000 0.9673 0.000 1.000 0.000
#> GSM26807 2 0.0000 0.9673 0.000 1.000 0.000
#> GSM26808 2 0.0000 0.9673 0.000 1.000 0.000
#> GSM26809 1 0.4346 0.7152 0.816 0.184 0.000
#> GSM26810 2 0.0000 0.9673 0.000 1.000 0.000
#> GSM26811 2 0.0000 0.9673 0.000 1.000 0.000
#> GSM26812 2 0.0000 0.9673 0.000 1.000 0.000
#> GSM26813 2 0.0000 0.9673 0.000 1.000 0.000
#> GSM26814 2 0.0000 0.9673 0.000 1.000 0.000
#> GSM26815 2 0.0000 0.9673 0.000 1.000 0.000
#> GSM26816 2 0.0000 0.9673 0.000 1.000 0.000
#> GSM26817 2 0.0000 0.9673 0.000 1.000 0.000
#> GSM26818 3 0.0000 0.8923 0.000 0.000 1.000
#> GSM26819 2 0.0000 0.9673 0.000 1.000 0.000
#> GSM26820 2 0.0237 0.9643 0.004 0.996 0.000
#> GSM26821 2 0.0000 0.9673 0.000 1.000 0.000
#> GSM26822 2 0.0000 0.9673 0.000 1.000 0.000
#> GSM26823 2 0.0000 0.9673 0.000 1.000 0.000
#> GSM26824 2 0.0000 0.9673 0.000 1.000 0.000
#> GSM26825 2 0.0000 0.9673 0.000 1.000 0.000
#> GSM26826 1 0.6280 0.1976 0.540 0.460 0.000
#> GSM26827 2 0.0892 0.9495 0.020 0.980 0.000
#> GSM26828 1 0.5016 0.6672 0.760 0.240 0.000
#> GSM26829 2 0.4002 0.7777 0.160 0.840 0.000
#> GSM26830 2 0.0000 0.9673 0.000 1.000 0.000
#> GSM26831 2 0.6302 -0.0486 0.480 0.520 0.000
#> GSM26832 2 0.0237 0.9643 0.004 0.996 0.000
#> GSM26833 2 0.0000 0.9673 0.000 1.000 0.000
#> GSM26834 2 0.0000 0.9673 0.000 1.000 0.000
#> GSM26835 2 0.0000 0.9673 0.000 1.000 0.000
#> GSM26836 1 0.4121 0.7884 0.832 0.000 0.168
#> GSM26837 3 0.3482 0.7852 0.128 0.000 0.872
#> GSM26838 1 0.0237 0.8115 0.996 0.000 0.004
#> GSM26839 1 0.6079 0.3944 0.612 0.000 0.388
#> GSM26840 1 0.0000 0.8096 1.000 0.000 0.000
#> GSM26841 1 0.1031 0.8167 0.976 0.000 0.024
#> GSM26842 1 0.2625 0.8189 0.916 0.000 0.084
#> GSM26843 1 0.0592 0.8142 0.988 0.000 0.012
#> GSM26844 1 0.2959 0.8167 0.900 0.000 0.100
#> GSM26845 1 0.0000 0.8096 1.000 0.000 0.000
#> GSM26846 3 0.0000 0.8923 0.000 0.000 1.000
#> GSM26847 3 0.5363 0.5823 0.276 0.000 0.724
#> GSM26848 3 0.6291 0.0364 0.468 0.000 0.532
#> GSM26849 3 0.0000 0.8923 0.000 0.000 1.000
#> GSM26850 3 0.4887 0.6606 0.228 0.000 0.772
#> GSM26851 2 0.0000 0.9673 0.000 1.000 0.000
#> GSM26852 3 0.0000 0.8923 0.000 0.000 1.000
#> GSM26853 3 0.0000 0.8923 0.000 0.000 1.000
#> GSM26854 3 0.0000 0.8923 0.000 0.000 1.000
#> GSM26855 3 0.0000 0.8923 0.000 0.000 1.000
#> GSM26856 3 0.0000 0.8923 0.000 0.000 1.000
#> GSM26857 3 0.0000 0.8923 0.000 0.000 1.000
#> GSM26858 3 0.0000 0.8923 0.000 0.000 1.000
#> GSM26859 3 0.0000 0.8923 0.000 0.000 1.000
#> GSM26860 3 0.0000 0.8923 0.000 0.000 1.000
#> GSM26861 3 0.0000 0.8923 0.000 0.000 1.000
#> GSM26862 1 0.4605 0.7515 0.796 0.000 0.204
#> GSM26863 1 0.4121 0.7884 0.832 0.000 0.168
#> GSM26864 1 0.4235 0.7818 0.824 0.000 0.176
#> GSM26865 3 0.6079 0.3185 0.388 0.000 0.612
#> GSM26866 1 0.3551 0.8068 0.868 0.000 0.132
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM26805 2 0.0000 0.984 0.000 1.000 0.000 0.000
#> GSM26806 4 0.1022 0.923 0.000 0.032 0.000 0.968
#> GSM26807 4 0.1022 0.923 0.000 0.032 0.000 0.968
#> GSM26808 4 0.1118 0.923 0.000 0.036 0.000 0.964
#> GSM26809 2 0.0000 0.984 0.000 1.000 0.000 0.000
#> GSM26810 4 0.1022 0.923 0.000 0.032 0.000 0.968
#> GSM26811 4 0.1118 0.923 0.000 0.036 0.000 0.964
#> GSM26812 4 0.1022 0.923 0.000 0.032 0.000 0.968
#> GSM26813 4 0.1022 0.923 0.000 0.032 0.000 0.968
#> GSM26814 4 0.1940 0.910 0.000 0.076 0.000 0.924
#> GSM26815 4 0.0592 0.893 0.000 0.000 0.016 0.984
#> GSM26816 2 0.0817 0.981 0.000 0.976 0.000 0.024
#> GSM26817 4 0.1022 0.923 0.000 0.032 0.000 0.968
#> GSM26818 3 0.0592 0.937 0.000 0.000 0.984 0.016
#> GSM26819 2 0.0707 0.984 0.000 0.980 0.000 0.020
#> GSM26820 2 0.0469 0.987 0.000 0.988 0.000 0.012
#> GSM26821 4 0.4877 0.454 0.000 0.408 0.000 0.592
#> GSM26822 2 0.0817 0.981 0.000 0.976 0.000 0.024
#> GSM26823 2 0.0469 0.987 0.000 0.988 0.000 0.012
#> GSM26824 4 0.2011 0.909 0.000 0.080 0.000 0.920
#> GSM26825 2 0.0592 0.986 0.000 0.984 0.000 0.016
#> GSM26826 2 0.0000 0.984 0.000 1.000 0.000 0.000
#> GSM26827 2 0.0336 0.986 0.000 0.992 0.000 0.008
#> GSM26828 2 0.0000 0.984 0.000 1.000 0.000 0.000
#> GSM26829 2 0.0336 0.986 0.000 0.992 0.000 0.008
#> GSM26830 4 0.3311 0.843 0.000 0.172 0.000 0.828
#> GSM26831 2 0.0000 0.984 0.000 1.000 0.000 0.000
#> GSM26832 2 0.0707 0.984 0.000 0.980 0.000 0.020
#> GSM26833 4 0.3356 0.840 0.000 0.176 0.000 0.824
#> GSM26834 2 0.0817 0.981 0.000 0.976 0.000 0.024
#> GSM26835 2 0.0469 0.987 0.000 0.988 0.000 0.012
#> GSM26836 1 0.0469 0.948 0.988 0.000 0.012 0.000
#> GSM26837 1 0.0707 0.946 0.980 0.000 0.020 0.000
#> GSM26838 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM26839 1 0.0592 0.948 0.984 0.000 0.016 0.000
#> GSM26840 2 0.1771 0.934 0.036 0.948 0.004 0.012
#> GSM26841 1 0.0376 0.946 0.992 0.004 0.004 0.000
#> GSM26842 1 0.0188 0.946 0.996 0.000 0.004 0.000
#> GSM26843 1 0.0672 0.946 0.984 0.008 0.008 0.000
#> GSM26844 1 0.0524 0.947 0.988 0.004 0.008 0.000
#> GSM26845 1 0.3455 0.833 0.852 0.132 0.004 0.012
#> GSM26846 1 0.3757 0.821 0.828 0.000 0.152 0.020
#> GSM26847 1 0.0592 0.948 0.984 0.000 0.016 0.000
#> GSM26848 1 0.3668 0.775 0.808 0.004 0.188 0.000
#> GSM26849 3 0.0469 0.956 0.012 0.000 0.988 0.000
#> GSM26850 3 0.0779 0.954 0.016 0.000 0.980 0.004
#> GSM26851 4 0.4134 0.739 0.000 0.260 0.000 0.740
#> GSM26852 3 0.0592 0.959 0.016 0.000 0.984 0.000
#> GSM26853 3 0.0592 0.959 0.016 0.000 0.984 0.000
#> GSM26854 3 0.0592 0.959 0.016 0.000 0.984 0.000
#> GSM26855 3 0.0592 0.959 0.016 0.000 0.984 0.000
#> GSM26856 3 0.0592 0.959 0.016 0.000 0.984 0.000
#> GSM26857 3 0.0592 0.959 0.016 0.000 0.984 0.000
#> GSM26858 3 0.0817 0.954 0.024 0.000 0.976 0.000
#> GSM26859 3 0.0592 0.959 0.016 0.000 0.984 0.000
#> GSM26860 3 0.0592 0.959 0.016 0.000 0.984 0.000
#> GSM26861 3 0.0707 0.957 0.020 0.000 0.980 0.000
#> GSM26862 1 0.0592 0.948 0.984 0.000 0.016 0.000
#> GSM26863 1 0.0592 0.948 0.984 0.000 0.016 0.000
#> GSM26864 1 0.0469 0.948 0.988 0.000 0.012 0.000
#> GSM26865 3 0.5132 0.111 0.448 0.004 0.548 0.000
#> GSM26866 1 0.3881 0.791 0.812 0.172 0.016 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM26805 2 0.3452 0.536 0.000 0.756 0.000 0.000 0.244
#> GSM26806 4 0.0404 0.910 0.000 0.000 0.000 0.988 0.012
#> GSM26807 4 0.0609 0.924 0.000 0.020 0.000 0.980 0.000
#> GSM26808 4 0.0963 0.920 0.000 0.036 0.000 0.964 0.000
#> GSM26809 5 0.4278 0.233 0.000 0.452 0.000 0.000 0.548
#> GSM26810 4 0.0162 0.919 0.000 0.004 0.000 0.996 0.000
#> GSM26811 4 0.0880 0.922 0.000 0.032 0.000 0.968 0.000
#> GSM26812 4 0.0510 0.924 0.000 0.016 0.000 0.984 0.000
#> GSM26813 2 0.4420 0.275 0.000 0.548 0.000 0.448 0.004
#> GSM26814 2 0.3579 0.628 0.000 0.756 0.000 0.240 0.004
#> GSM26815 4 0.0880 0.892 0.000 0.000 0.000 0.968 0.032
#> GSM26816 2 0.2233 0.737 0.000 0.904 0.000 0.016 0.080
#> GSM26817 4 0.1410 0.902 0.000 0.060 0.000 0.940 0.000
#> GSM26818 3 0.2068 0.900 0.000 0.000 0.904 0.004 0.092
#> GSM26819 2 0.1444 0.756 0.000 0.948 0.000 0.040 0.012
#> GSM26820 2 0.0794 0.758 0.000 0.972 0.000 0.028 0.000
#> GSM26821 2 0.3010 0.685 0.000 0.824 0.000 0.172 0.004
#> GSM26822 2 0.3090 0.699 0.000 0.856 0.000 0.040 0.104
#> GSM26823 2 0.0955 0.758 0.000 0.968 0.000 0.028 0.004
#> GSM26824 2 0.4367 0.343 0.000 0.580 0.000 0.416 0.004
#> GSM26825 2 0.1485 0.754 0.000 0.948 0.000 0.032 0.020
#> GSM26826 2 0.0162 0.754 0.000 0.996 0.000 0.000 0.004
#> GSM26827 2 0.0771 0.758 0.000 0.976 0.000 0.020 0.004
#> GSM26828 2 0.2280 0.698 0.000 0.880 0.000 0.000 0.120
#> GSM26829 2 0.1478 0.733 0.000 0.936 0.000 0.000 0.064
#> GSM26830 2 0.3461 0.643 0.000 0.772 0.000 0.224 0.004
#> GSM26831 2 0.1671 0.728 0.000 0.924 0.000 0.000 0.076
#> GSM26832 2 0.2286 0.711 0.000 0.888 0.000 0.004 0.108
#> GSM26833 2 0.4321 0.452 0.000 0.600 0.000 0.396 0.004
#> GSM26834 2 0.3282 0.622 0.000 0.804 0.000 0.008 0.188
#> GSM26835 2 0.3424 0.538 0.000 0.760 0.000 0.000 0.240
#> GSM26836 1 0.1043 0.798 0.960 0.000 0.000 0.000 0.040
#> GSM26837 1 0.1270 0.797 0.948 0.000 0.000 0.000 0.052
#> GSM26838 1 0.0290 0.800 0.992 0.000 0.000 0.000 0.008
#> GSM26839 1 0.0963 0.795 0.964 0.000 0.000 0.000 0.036
#> GSM26840 5 0.5304 0.495 0.080 0.292 0.000 0.000 0.628
#> GSM26841 1 0.1410 0.786 0.940 0.000 0.000 0.000 0.060
#> GSM26842 1 0.1197 0.790 0.952 0.000 0.000 0.000 0.048
#> GSM26843 1 0.4954 0.322 0.616 0.020 0.012 0.000 0.352
#> GSM26844 1 0.4296 0.555 0.720 0.012 0.012 0.000 0.256
#> GSM26845 1 0.4558 0.552 0.740 0.180 0.000 0.000 0.080
#> GSM26846 1 0.6606 0.495 0.596 0.044 0.120 0.004 0.236
#> GSM26847 1 0.1732 0.784 0.920 0.000 0.000 0.000 0.080
#> GSM26848 1 0.5082 0.618 0.684 0.000 0.096 0.000 0.220
#> GSM26849 3 0.2813 0.845 0.000 0.000 0.832 0.000 0.168
#> GSM26850 3 0.4377 0.773 0.048 0.008 0.760 0.000 0.184
#> GSM26851 4 0.5265 0.470 0.000 0.284 0.000 0.636 0.080
#> GSM26852 3 0.0404 0.951 0.000 0.000 0.988 0.000 0.012
#> GSM26853 3 0.0404 0.951 0.000 0.000 0.988 0.000 0.012
#> GSM26854 3 0.0000 0.951 0.000 0.000 1.000 0.000 0.000
#> GSM26855 3 0.0404 0.951 0.000 0.000 0.988 0.000 0.012
#> GSM26856 3 0.0404 0.951 0.000 0.000 0.988 0.000 0.012
#> GSM26857 3 0.0000 0.951 0.000 0.000 1.000 0.000 0.000
#> GSM26858 3 0.1608 0.914 0.000 0.000 0.928 0.000 0.072
#> GSM26859 3 0.0162 0.950 0.000 0.000 0.996 0.000 0.004
#> GSM26860 3 0.0000 0.951 0.000 0.000 1.000 0.000 0.000
#> GSM26861 3 0.0510 0.950 0.000 0.000 0.984 0.000 0.016
#> GSM26862 1 0.1197 0.796 0.952 0.000 0.000 0.000 0.048
#> GSM26863 1 0.0290 0.799 0.992 0.000 0.000 0.000 0.008
#> GSM26864 1 0.1608 0.780 0.928 0.000 0.000 0.000 0.072
#> GSM26865 1 0.6465 0.402 0.524 0.004 0.216 0.000 0.256
#> GSM26866 5 0.5559 -0.197 0.448 0.020 0.032 0.000 0.500
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM26805 5 0.3808 0.6957 0.000 0.228 0.000 0.000 0.736 0.036
#> GSM26806 4 0.0260 0.8385 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM26807 4 0.0547 0.8458 0.000 0.020 0.000 0.980 0.000 0.000
#> GSM26808 4 0.1080 0.8437 0.000 0.032 0.000 0.960 0.004 0.004
#> GSM26809 5 0.5947 0.2793 0.000 0.312 0.000 0.000 0.448 0.240
#> GSM26810 4 0.0547 0.8458 0.000 0.020 0.000 0.980 0.000 0.000
#> GSM26811 4 0.1116 0.8438 0.000 0.028 0.000 0.960 0.004 0.008
#> GSM26812 4 0.0547 0.8458 0.000 0.020 0.000 0.980 0.000 0.000
#> GSM26813 2 0.5177 0.5406 0.000 0.688 0.000 0.148 0.124 0.040
#> GSM26814 2 0.2982 0.7654 0.000 0.856 0.000 0.016 0.096 0.032
#> GSM26815 4 0.0458 0.8259 0.000 0.000 0.000 0.984 0.000 0.016
#> GSM26816 5 0.5172 0.6241 0.000 0.352 0.000 0.056 0.572 0.020
#> GSM26817 4 0.1285 0.8314 0.000 0.052 0.000 0.944 0.004 0.000
#> GSM26818 3 0.3737 0.6891 0.000 0.000 0.780 0.044 0.008 0.168
#> GSM26819 2 0.1003 0.8491 0.000 0.964 0.000 0.000 0.016 0.020
#> GSM26820 2 0.0806 0.8511 0.000 0.972 0.000 0.000 0.008 0.020
#> GSM26821 2 0.1148 0.8489 0.000 0.960 0.000 0.016 0.004 0.020
#> GSM26822 2 0.1633 0.8283 0.000 0.932 0.000 0.000 0.024 0.044
#> GSM26823 2 0.0972 0.8489 0.000 0.964 0.000 0.000 0.028 0.008
#> GSM26824 2 0.1713 0.8234 0.000 0.928 0.000 0.044 0.000 0.028
#> GSM26825 2 0.0806 0.8511 0.000 0.972 0.000 0.000 0.008 0.020
#> GSM26826 2 0.1265 0.8404 0.000 0.948 0.000 0.000 0.044 0.008
#> GSM26827 2 0.0858 0.8508 0.000 0.968 0.000 0.000 0.028 0.004
#> GSM26828 5 0.4684 0.6358 0.000 0.352 0.000 0.000 0.592 0.056
#> GSM26829 2 0.4530 0.0125 0.000 0.600 0.000 0.000 0.356 0.044
#> GSM26830 2 0.1555 0.8431 0.000 0.940 0.000 0.012 0.040 0.008
#> GSM26831 5 0.4212 0.5480 0.000 0.424 0.000 0.000 0.560 0.016
#> GSM26832 5 0.4131 0.6512 0.000 0.356 0.000 0.000 0.624 0.020
#> GSM26833 4 0.6416 -0.2122 0.000 0.304 0.000 0.404 0.276 0.016
#> GSM26834 5 0.4250 0.6953 0.000 0.244 0.000 0.036 0.708 0.012
#> GSM26835 5 0.3558 0.6922 0.000 0.212 0.000 0.000 0.760 0.028
#> GSM26836 1 0.0692 0.8026 0.976 0.000 0.000 0.000 0.004 0.020
#> GSM26837 1 0.0717 0.8032 0.976 0.000 0.000 0.000 0.008 0.016
#> GSM26838 1 0.0547 0.8038 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM26839 1 0.0405 0.8038 0.988 0.000 0.000 0.000 0.004 0.008
#> GSM26840 5 0.4693 0.2604 0.028 0.032 0.000 0.000 0.660 0.280
#> GSM26841 1 0.1196 0.7938 0.952 0.000 0.000 0.000 0.008 0.040
#> GSM26842 1 0.0363 0.8033 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM26843 1 0.5296 0.4113 0.572 0.004 0.004 0.000 0.328 0.092
#> GSM26844 1 0.4229 0.5974 0.728 0.000 0.008 0.000 0.208 0.056
#> GSM26845 1 0.4732 0.5333 0.728 0.072 0.000 0.000 0.044 0.156
#> GSM26846 6 0.6277 0.5338 0.240 0.008 0.020 0.000 0.208 0.524
#> GSM26847 1 0.3398 0.5257 0.740 0.000 0.000 0.000 0.008 0.252
#> GSM26848 6 0.6818 0.5883 0.288 0.000 0.116 0.000 0.124 0.472
#> GSM26849 3 0.3852 0.2517 0.000 0.000 0.612 0.000 0.004 0.384
#> GSM26850 6 0.6006 0.4359 0.008 0.008 0.344 0.000 0.148 0.492
#> GSM26851 4 0.6459 0.2727 0.000 0.348 0.000 0.468 0.072 0.112
#> GSM26852 3 0.0260 0.9056 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM26853 3 0.0146 0.9089 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM26854 3 0.0713 0.9055 0.000 0.000 0.972 0.000 0.000 0.028
#> GSM26855 3 0.0000 0.9085 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26856 3 0.0000 0.9085 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM26857 3 0.0547 0.9072 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM26858 3 0.1349 0.8653 0.000 0.000 0.940 0.000 0.004 0.056
#> GSM26859 3 0.1141 0.8895 0.000 0.000 0.948 0.000 0.000 0.052
#> GSM26860 3 0.0790 0.9033 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM26861 3 0.0260 0.9056 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM26862 1 0.0777 0.8010 0.972 0.000 0.000 0.000 0.004 0.024
#> GSM26863 1 0.0363 0.8046 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM26864 1 0.1261 0.7928 0.952 0.000 0.000 0.000 0.024 0.024
#> GSM26865 6 0.6626 0.5517 0.156 0.000 0.300 0.000 0.068 0.476
#> GSM26866 1 0.6402 0.1702 0.396 0.004 0.016 0.000 0.380 0.204
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) individual(p) k
#> ATC:NMF 62 3.65e-11 8.91e-01 2
#> ATC:NMF 57 5.80e-10 6.38e-04 3
#> ATC:NMF 60 1.42e-10 9.34e-05 4
#> ATC:NMF 52 1.84e-10 7.21e-06 5
#> ATC:NMF 53 1.88e-09 5.49e-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.
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