Date: 2019-12-25 20:17:12 CET, cola version: 1.3.2
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All available functions which can be applied to this res_list object:
res_list
#> A 'ConsensusPartitionList' object with 24 methods.
#> On a matrix with 21168 rows and 75 columns.
#> Top rows are extracted by 'SD, CV, MAD, ATC' methods.
#> Subgroups are detected by 'hclust, kmeans, skmeans, pam, mclust, NMF' method.
#> Number of partitions are tried for k = 2, 3, 4, 5, 6.
#> Performed in total 30000 partitions by row resampling.
#>
#> Following methods can be applied to this 'ConsensusPartitionList' object:
#> [1] "cola_report" "collect_classes" "collect_plots" "collect_stats"
#> [5] "colnames" "functional_enrichment" "get_anno_col" "get_anno"
#> [9] "get_classes" "get_matrix" "get_membership" "get_stats"
#> [13] "is_best_k" "is_stable_k" "ncol" "nrow"
#> [17] "rownames" "show" "suggest_best_k" "test_to_known_factors"
#> [21] "top_rows_heatmap" "top_rows_overlap"
#>
#> You can get result for a single method by, e.g. object["SD", "hclust"] or object["SD:hclust"]
#> or a subset of methods by object[c("SD", "CV")], c("hclust", "kmeans")]
The call of run_all_consensus_partition_methods() was:
#> run_all_consensus_partition_methods(data = mat, mc.cores = 4, anno = anno)
Dimension of the input matrix:
mat = get_matrix(res_list)
dim(mat)
#> [1] 21168 75
The density distribution for each sample is visualized as in one column in the following heatmap. The clustering is based on the distance which is the Kolmogorov-Smirnov statistic between two distributions.
library(ComplexHeatmap)
densityHeatmap(mat, top_annotation = HeatmapAnnotation(df = get_anno(res_list),
col = get_anno_col(res_list)), ylab = "value", cluster_columns = TRUE, show_column_names = FALSE,
mc.cores = 4)
Folowing table shows the best k (number of partitions) for each combination
of top-value methods and partition methods. Clicking on the method name in
the table goes to the section for a single combination of methods.
The cola vignette explains the definition of the metrics used for determining the best number of partitions.
suggest_best_k(res_list)
| The best k | 1-PAC | Mean silhouette | Concordance | Optional k | ||
|---|---|---|---|---|---|---|
| SD:kmeans | 2 | 1.000 | 0.980 | 0.992 | ** | |
| SD:skmeans | 3 | 1.000 | 0.966 | 0.978 | ** | 2 |
| SD:mclust | 2 | 1.000 | 0.973 | 0.987 | ** | |
| SD:NMF | 2 | 1.000 | 0.953 | 0.982 | ** | |
| CV:kmeans | 2 | 1.000 | 0.990 | 0.996 | ** | |
| CV:skmeans | 3 | 1.000 | 0.952 | 0.977 | ** | 2 |
| CV:mclust | 2 | 1.000 | 0.949 | 0.981 | ** | |
| MAD:kmeans | 2 | 1.000 | 0.970 | 0.989 | ** | |
| MAD:skmeans | 3 | 1.000 | 0.942 | 0.969 | ** | 2 |
| MAD:mclust | 2 | 1.000 | 0.993 | 0.997 | ** | |
| MAD:NMF | 2 | 1.000 | 0.974 | 0.990 | ** | |
| ATC:pam | 2 | 1.000 | 0.987 | 0.995 | ** | |
| ATC:NMF | 2 | 1.000 | 0.989 | 0.995 | ** | |
| MAD:pam | 4 | 0.943 | 0.923 | 0.969 | * | 2 |
| SD:pam | 6 | 0.940 | 0.847 | 0.941 | * | 2,4,5 |
| ATC:skmeans | 5 | 0.938 | 0.858 | 0.953 | * | 2,3,4 |
| ATC:hclust | 3 | 0.931 | 0.826 | 0.918 | * | |
| CV:pam | 5 | 0.930 | 0.902 | 0.944 | * | 2,4 |
| CV:NMF | 3 | 0.925 | 0.889 | 0.955 | * | 2 |
| ATC:kmeans | 4 | 0.910 | 0.948 | 0.965 | * | 2 |
| CV:hclust | 4 | 0.750 | 0.751 | 0.845 | ||
| SD:hclust | 3 | 0.732 | 0.822 | 0.902 | ||
| MAD:hclust | 3 | 0.725 | 0.786 | 0.897 | ||
| ATC:mclust | 2 | 0.674 | 0.950 | 0.954 |
**: 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 0.953 0.982 0.428 0.580 0.580
#> CV:NMF 2 0.972 0.963 0.984 0.438 0.559 0.559
#> MAD:NMF 2 1.000 0.974 0.990 0.457 0.550 0.550
#> ATC:NMF 2 1.000 0.989 0.995 0.444 0.559 0.559
#> SD:skmeans 2 1.000 0.994 0.997 0.476 0.526 0.526
#> CV:skmeans 2 1.000 0.987 0.994 0.477 0.526 0.526
#> MAD:skmeans 2 1.000 0.980 0.992 0.487 0.514 0.514
#> ATC:skmeans 2 1.000 0.998 0.999 0.467 0.533 0.533
#> SD:mclust 2 1.000 0.973 0.987 0.474 0.526 0.526
#> CV:mclust 2 1.000 0.949 0.981 0.472 0.519 0.519
#> MAD:mclust 2 1.000 0.993 0.997 0.466 0.533 0.533
#> ATC:mclust 2 0.674 0.950 0.954 0.455 0.550 0.550
#> SD:kmeans 2 1.000 0.980 0.992 0.449 0.550 0.550
#> CV:kmeans 2 1.000 0.990 0.996 0.454 0.550 0.550
#> MAD:kmeans 2 1.000 0.970 0.989 0.459 0.541 0.541
#> ATC:kmeans 2 1.000 1.000 1.000 0.421 0.580 0.580
#> SD:pam 2 1.000 0.946 0.979 0.454 0.559 0.559
#> CV:pam 2 1.000 0.954 0.979 0.482 0.508 0.508
#> MAD:pam 2 1.000 0.969 0.987 0.488 0.508 0.508
#> ATC:pam 2 1.000 0.987 0.995 0.425 0.580 0.580
#> SD:hclust 2 0.839 0.907 0.961 0.381 0.630 0.630
#> CV:hclust 2 0.567 0.888 0.942 0.364 0.630 0.630
#> MAD:hclust 2 0.614 0.889 0.941 0.356 0.630 0.630
#> ATC:hclust 2 0.792 0.911 0.940 0.344 0.591 0.591
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.862 0.828 0.930 0.306 0.823 0.706
#> CV:NMF 3 0.925 0.889 0.955 0.286 0.835 0.714
#> MAD:NMF 3 0.748 0.763 0.897 0.290 0.847 0.730
#> ATC:NMF 3 0.807 0.898 0.939 0.191 0.921 0.861
#> SD:skmeans 3 1.000 0.966 0.978 0.394 0.788 0.605
#> CV:skmeans 3 1.000 0.952 0.977 0.390 0.792 0.612
#> MAD:skmeans 3 1.000 0.942 0.969 0.360 0.783 0.592
#> ATC:skmeans 3 1.000 0.950 0.982 0.256 0.838 0.707
#> SD:mclust 3 0.597 0.733 0.830 0.192 0.934 0.878
#> CV:mclust 3 0.728 0.837 0.856 0.183 0.870 0.772
#> MAD:mclust 3 0.542 0.658 0.767 0.268 0.930 0.871
#> ATC:mclust 3 0.629 0.854 0.866 0.223 0.944 0.898
#> SD:kmeans 3 0.671 0.798 0.839 0.282 0.904 0.829
#> CV:kmeans 3 0.663 0.772 0.822 0.288 0.882 0.792
#> MAD:kmeans 3 0.552 0.549 0.707 0.329 0.890 0.799
#> ATC:kmeans 3 0.686 0.812 0.911 0.341 0.717 0.553
#> SD:pam 3 0.728 0.886 0.926 0.258 0.803 0.669
#> CV:pam 3 0.715 0.745 0.782 0.288 0.745 0.536
#> MAD:pam 3 0.647 0.224 0.654 0.260 0.699 0.484
#> ATC:pam 3 0.632 0.799 0.886 0.424 0.717 0.540
#> SD:hclust 3 0.732 0.822 0.902 0.431 0.818 0.711
#> CV:hclust 3 0.651 0.722 0.864 0.500 0.790 0.672
#> MAD:hclust 3 0.725 0.786 0.897 0.615 0.751 0.611
#> ATC:hclust 3 0.931 0.826 0.918 0.374 0.950 0.916
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.839 0.854 0.925 0.1431 0.846 0.683
#> CV:NMF 4 0.818 0.826 0.921 0.1353 0.901 0.781
#> MAD:NMF 4 0.666 0.717 0.865 0.1501 0.829 0.634
#> ATC:NMF 4 0.692 0.777 0.886 0.2421 0.790 0.593
#> SD:skmeans 4 0.831 0.820 0.883 0.0924 0.938 0.819
#> CV:skmeans 4 0.831 0.849 0.923 0.0969 0.922 0.776
#> MAD:skmeans 4 0.870 0.857 0.931 0.1026 0.907 0.737
#> ATC:skmeans 4 0.967 0.898 0.965 0.1019 0.928 0.826
#> SD:mclust 4 0.604 0.826 0.767 0.2098 0.660 0.384
#> CV:mclust 4 0.514 0.527 0.674 0.1545 0.761 0.579
#> MAD:mclust 4 0.682 0.829 0.895 0.1163 0.792 0.589
#> ATC:mclust 4 0.573 0.663 0.746 0.2278 0.795 0.595
#> SD:kmeans 4 0.653 0.859 0.854 0.1889 0.801 0.586
#> CV:kmeans 4 0.643 0.872 0.873 0.1843 0.789 0.562
#> MAD:kmeans 4 0.583 0.707 0.785 0.1549 0.731 0.457
#> ATC:kmeans 4 0.910 0.948 0.965 0.2452 0.735 0.445
#> SD:pam 4 0.967 0.913 0.963 0.2582 0.764 0.505
#> CV:pam 4 0.999 0.949 0.981 0.1631 0.879 0.670
#> MAD:pam 4 0.943 0.923 0.969 0.1787 0.704 0.364
#> ATC:pam 4 0.835 0.838 0.935 0.1636 0.797 0.527
#> SD:hclust 4 0.829 0.780 0.894 0.0692 0.954 0.900
#> CV:hclust 4 0.750 0.751 0.845 0.0813 0.953 0.898
#> MAD:hclust 4 0.771 0.736 0.855 0.0622 0.981 0.953
#> ATC:hclust 4 0.743 0.816 0.915 0.1508 0.941 0.893
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.648 0.662 0.812 0.1815 0.758 0.439
#> CV:NMF 5 0.651 0.581 0.805 0.1779 0.776 0.469
#> MAD:NMF 5 0.681 0.524 0.769 0.1111 0.801 0.495
#> ATC:NMF 5 0.612 0.649 0.812 0.0921 0.856 0.625
#> SD:skmeans 5 0.866 0.814 0.911 0.0707 0.924 0.745
#> CV:skmeans 5 0.828 0.799 0.903 0.0661 0.943 0.802
#> MAD:skmeans 5 0.828 0.753 0.886 0.0705 0.936 0.772
#> ATC:skmeans 5 0.938 0.858 0.953 0.0398 0.966 0.904
#> SD:mclust 5 0.628 0.717 0.765 0.0879 0.908 0.675
#> CV:mclust 5 0.557 0.650 0.736 0.1457 0.730 0.396
#> MAD:mclust 5 0.709 0.793 0.815 0.1354 0.827 0.517
#> ATC:mclust 5 0.630 0.774 0.799 0.0663 0.809 0.492
#> SD:kmeans 5 0.612 0.507 0.693 0.1130 0.889 0.631
#> CV:kmeans 5 0.696 0.718 0.801 0.1095 0.919 0.720
#> MAD:kmeans 5 0.625 0.760 0.801 0.0965 0.906 0.673
#> ATC:kmeans 5 0.780 0.648 0.786 0.0931 0.929 0.759
#> SD:pam 5 0.916 0.858 0.935 0.0409 0.969 0.889
#> CV:pam 5 0.930 0.902 0.944 0.0357 0.968 0.884
#> MAD:pam 5 0.900 0.831 0.914 0.0364 0.977 0.918
#> ATC:pam 5 0.796 0.828 0.892 0.0786 0.878 0.620
#> SD:hclust 5 0.861 0.864 0.940 0.0388 0.967 0.925
#> CV:hclust 5 0.842 0.737 0.871 0.0552 0.966 0.920
#> MAD:hclust 5 0.640 0.707 0.820 0.0821 0.964 0.909
#> ATC:hclust 5 0.656 0.724 0.847 0.3076 0.746 0.505
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.739 0.721 0.853 0.0646 0.834 0.451
#> CV:NMF 6 0.784 0.758 0.884 0.0788 0.836 0.446
#> MAD:NMF 6 0.751 0.737 0.880 0.0761 0.814 0.405
#> ATC:NMF 6 0.593 0.587 0.778 0.0402 0.994 0.980
#> SD:skmeans 6 0.822 0.718 0.852 0.0363 0.963 0.843
#> CV:skmeans 6 0.818 0.678 0.844 0.0364 0.979 0.912
#> MAD:skmeans 6 0.795 0.606 0.800 0.0316 0.957 0.825
#> ATC:skmeans 6 0.748 0.766 0.878 0.0663 0.962 0.882
#> SD:mclust 6 0.693 0.781 0.855 0.0652 0.991 0.955
#> CV:mclust 6 0.580 0.734 0.788 0.0513 0.936 0.721
#> MAD:mclust 6 0.715 0.803 0.856 0.0667 0.947 0.763
#> ATC:mclust 6 0.825 0.867 0.885 0.0997 0.926 0.710
#> SD:kmeans 6 0.775 0.727 0.839 0.0669 0.885 0.542
#> CV:kmeans 6 0.795 0.656 0.827 0.0634 0.942 0.745
#> MAD:kmeans 6 0.768 0.708 0.822 0.0617 0.957 0.801
#> ATC:kmeans 6 0.788 0.775 0.824 0.0499 0.881 0.559
#> SD:pam 6 0.940 0.847 0.941 0.0305 0.952 0.818
#> CV:pam 6 0.832 0.733 0.831 0.0555 0.947 0.796
#> MAD:pam 6 0.851 0.842 0.917 0.0460 0.933 0.753
#> ATC:pam 6 0.784 0.551 0.807 0.0325 0.921 0.709
#> SD:hclust 6 0.680 0.760 0.874 0.0575 0.989 0.974
#> CV:hclust 6 0.652 0.662 0.793 0.0704 0.968 0.924
#> MAD:hclust 6 0.619 0.691 0.765 0.0843 0.942 0.844
#> ATC:hclust 6 0.716 0.776 0.876 0.0226 0.978 0.921
Following heatmap plots the partition for each combination of methods and the lightness correspond to the silhouette scores for samples in each method. On top the consensus subgroup is inferred from all methods by taking the mean silhouette scores as weight.
collect_stats(res_list, k = 2)
collect_stats(res_list, k = 3)
collect_stats(res_list, k = 4)
collect_stats(res_list, k = 5)
collect_stats(res_list, k = 6)
Collect partitions from all methods:
collect_classes(res_list, k = 2)
collect_classes(res_list, k = 3)
collect_classes(res_list, k = 4)
collect_classes(res_list, k = 5)
collect_classes(res_list, k = 6)
Overlap of top rows from different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "euler")
top_rows_overlap(res_list, top_n = 2000, method = "euler")
top_rows_overlap(res_list, top_n = 3000, method = "euler")
top_rows_overlap(res_list, top_n = 4000, method = "euler")
top_rows_overlap(res_list, top_n = 5000, method = "euler")
Also visualize the correspondance of rankings between different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "correspondance")
top_rows_overlap(res_list, top_n = 2000, method = "correspondance")
top_rows_overlap(res_list, top_n = 3000, method = "correspondance")
top_rows_overlap(res_list, top_n = 4000, method = "correspondance")
top_rows_overlap(res_list, top_n = 5000, method = "correspondance")
Heatmaps of the top rows:
top_rows_heatmap(res_list, top_n = 1000)
top_rows_heatmap(res_list, top_n = 2000)
top_rows_heatmap(res_list, top_n = 3000)
top_rows_heatmap(res_list, top_n = 4000)
top_rows_heatmap(res_list, top_n = 5000)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res_list, k = 2)
#> n disease.state(p) other(p) genotype/variation(p) k
#> SD:NMF 73 0.345 1.000 0.453 2
#> CV:NMF 74 0.309 0.876 0.447 2
#> MAD:NMF 74 0.565 1.000 0.744 2
#> ATC:NMF 75 0.666 1.000 0.753 2
#> SD:skmeans 75 0.824 1.000 0.806 2
#> CV:skmeans 75 0.824 1.000 0.806 2
#> MAD:skmeans 74 0.815 1.000 0.749 2
#> ATC:skmeans 75 0.453 0.570 0.713 2
#> SD:mclust 75 0.824 0.881 0.806 2
#> CV:mclust 72 0.747 1.000 0.811 2
#> MAD:mclust 75 0.909 1.000 0.811 2
#> ATC:mclust 75 0.590 0.935 0.748 2
#> SD:kmeans 74 0.640 1.000 0.752 2
#> CV:kmeans 75 0.590 0.935 0.748 2
#> MAD:kmeans 73 0.685 1.000 0.791 2
#> ATC:kmeans 75 0.379 1.000 0.456 2
#> SD:pam 72 0.737 1.000 0.794 2
#> CV:pam 74 1.000 0.964 0.661 2
#> MAD:pam 74 1.000 0.964 0.661 2
#> ATC:pam 74 0.362 1.000 0.455 2
#> SD:hclust 75 0.247 0.737 0.442 2
#> CV:hclust 75 0.247 0.737 0.442 2
#> MAD:hclust 73 0.318 0.730 0.358 2
#> ATC:hclust 75 0.439 0.943 0.454 2
test_to_known_factors(res_list, k = 3)
#> n disease.state(p) other(p) genotype/variation(p) k
#> SD:NMF 66 0.052527 0.183 0.1640 3
#> CV:NMF 71 0.010333 0.139 0.1968 3
#> MAD:NMF 67 0.178000 0.578 0.3090 3
#> ATC:NMF 74 0.007855 0.232 0.5561 3
#> SD:skmeans 74 0.001421 0.752 0.0372 3
#> CV:skmeans 73 0.001689 0.823 0.0378 3
#> MAD:skmeans 73 0.001807 0.763 0.0348 3
#> ATC:skmeans 73 0.511869 0.411 0.0361 3
#> SD:mclust 66 0.566264 0.946 0.9663 3
#> CV:mclust 73 0.361725 0.761 0.7414 3
#> MAD:mclust 65 0.259024 0.758 0.5528 3
#> ATC:mclust 69 0.199585 0.843 0.6419 3
#> SD:kmeans 72 0.402469 0.748 0.7928 3
#> CV:kmeans 70 0.391695 0.745 0.8200 3
#> MAD:kmeans 58 0.568772 0.874 0.5252 3
#> ATC:kmeans 67 0.272784 0.548 0.9529 3
#> SD:pam 74 0.287294 0.924 0.6716 3
#> CV:pam 66 0.000535 0.487 0.0379 3
#> MAD:pam 32 0.042258 0.653 0.3681 3
#> ATC:pam 69 0.373818 0.816 0.2377 3
#> SD:hclust 73 0.253041 0.421 0.4818 3
#> CV:hclust 65 0.193270 0.297 0.2281 3
#> MAD:hclust 69 0.307899 0.652 0.3201 3
#> ATC:hclust 67 0.551176 0.636 0.8204 3
test_to_known_factors(res_list, k = 4)
#> n disease.state(p) other(p) genotype/variation(p) k
#> SD:NMF 71 0.224177 0.1944 0.66012 4
#> CV:NMF 69 0.037263 0.1331 0.48807 4
#> MAD:NMF 64 0.001506 0.1321 0.18030 4
#> ATC:NMF 68 0.049888 0.3067 0.83114 4
#> SD:skmeans 71 0.001238 0.9066 0.10041 4
#> CV:skmeans 70 0.005868 0.8457 0.16870 4
#> MAD:skmeans 70 0.004230 0.9111 0.12371 4
#> ATC:skmeans 70 0.357776 0.5988 0.00548 4
#> SD:mclust 73 0.002448 0.8741 0.35441 4
#> CV:mclust 52 0.002713 0.5864 0.14274 4
#> MAD:mclust 71 0.352475 0.5029 0.21180 4
#> ATC:mclust 56 0.287596 0.1722 0.37478 4
#> SD:kmeans 72 0.001048 0.6508 0.05855 4
#> CV:kmeans 75 0.000715 0.7674 0.07887 4
#> MAD:kmeans 66 0.005810 0.7387 0.11970 4
#> ATC:kmeans 75 0.541677 0.7662 0.24119 4
#> SD:pam 71 0.000538 0.4611 0.07001 4
#> CV:pam 73 0.000841 0.5838 0.07081 4
#> MAD:pam 73 0.000105 0.5240 0.06918 4
#> ATC:pam 67 0.587473 0.9234 0.43299 4
#> SD:hclust 70 0.487927 0.5728 0.77561 4
#> CV:hclust 64 0.505398 0.2806 0.74874 4
#> MAD:hclust 59 0.321006 0.0961 0.85564 4
#> ATC:hclust 70 0.657129 0.7659 0.83760 4
test_to_known_factors(res_list, k = 5)
#> n disease.state(p) other(p) genotype/variation(p) k
#> SD:NMF 63 0.000176 0.587 0.18127 5
#> CV:NMF 45 0.004589 0.229 0.15688 5
#> MAD:NMF 47 0.007345 0.147 0.09751 5
#> ATC:NMF 60 0.062578 0.340 0.93590 5
#> SD:skmeans 67 0.003010 0.933 0.27830 5
#> CV:skmeans 68 0.005865 0.913 0.39047 5
#> MAD:skmeans 67 0.007780 0.892 0.05352 5
#> ATC:skmeans 69 0.718979 0.703 0.03915 5
#> SD:mclust 60 0.005094 0.824 0.37698 5
#> CV:mclust 54 0.011620 0.853 0.48081 5
#> MAD:mclust 71 0.017914 0.847 0.39516 5
#> ATC:mclust 71 0.707488 0.773 0.38854 5
#> SD:kmeans 41 0.031084 0.201 0.00686 5
#> CV:kmeans 65 0.006004 0.598 0.05930 5
#> MAD:kmeans 70 0.005756 0.767 0.06749 5
#> ATC:kmeans 58 0.646907 0.771 0.19308 5
#> SD:pam 70 0.000227 0.580 0.12319 5
#> CV:pam 72 0.000419 0.692 0.14116 5
#> MAD:pam 68 0.000189 0.864 0.10618 5
#> ATC:pam 72 0.617977 0.116 0.03196 5
#> SD:hclust 73 0.121102 0.370 0.68014 5
#> CV:hclust 58 0.493728 0.236 0.98000 5
#> MAD:hclust 59 0.149134 0.313 0.96129 5
#> ATC:hclust 70 0.730214 0.937 0.52496 5
test_to_known_factors(res_list, k = 6)
#> n disease.state(p) other(p) genotype/variation(p) k
#> SD:NMF 66 5.62e-04 0.483 0.1753 6
#> CV:NMF 67 2.34e-04 0.189 0.0681 6
#> MAD:NMF 64 1.02e-03 0.541 0.1707 6
#> ATC:NMF 50 1.87e-02 0.459 0.2911 6
#> SD:skmeans 63 3.44e-04 0.471 0.3397 6
#> CV:skmeans 60 1.02e-03 0.575 0.2353 6
#> MAD:skmeans 53 8.95e-04 0.891 0.2355 6
#> ATC:skmeans 67 6.04e-01 0.536 0.0669 6
#> SD:mclust 72 1.10e-02 0.771 0.6890 6
#> CV:mclust 68 3.12e-03 0.768 0.4616 6
#> MAD:mclust 69 1.29e-02 0.929 0.5392 6
#> ATC:mclust 73 3.26e-01 0.450 0.1041 6
#> SD:kmeans 68 5.47e-03 0.636 0.1350 6
#> CV:kmeans 60 8.14e-03 0.203 0.3440 6
#> MAD:kmeans 64 4.26e-03 0.792 0.2004 6
#> ATC:kmeans 68 4.57e-01 0.794 0.1252 6
#> SD:pam 66 5.16e-05 0.358 0.2058 6
#> CV:pam 59 5.34e-05 0.578 0.1340 6
#> MAD:pam 69 1.72e-05 0.318 0.2467 6
#> ATC:pam 39 6.40e-01 0.682 0.3520 6
#> SD:hclust 68 1.77e-01 0.351 0.7957 6
#> CV:hclust 59 4.74e-02 0.346 0.3712 6
#> MAD:hclust 68 6.86e-02 0.486 0.6597 6
#> ATC:hclust 72 6.77e-01 0.719 0.7626 6
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "hclust"]
# you can also extract it by
# res = res_list["SD:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 75 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 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 0.839 0.907 0.961 0.3810 0.630 0.630
#> 3 3 0.732 0.822 0.902 0.4308 0.818 0.711
#> 4 4 0.829 0.780 0.894 0.0692 0.954 0.900
#> 5 5 0.861 0.864 0.940 0.0388 0.967 0.925
#> 6 6 0.680 0.760 0.874 0.0575 0.989 0.974
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
#> GSM62248 2 0.0000 0.961 0.000 1.000
#> GSM62256 2 0.0000 0.961 0.000 1.000
#> GSM62259 2 0.0000 0.961 0.000 1.000
#> GSM62267 1 0.7299 0.757 0.796 0.204
#> GSM62280 2 0.0672 0.953 0.008 0.992
#> GSM62284 1 0.0000 0.941 1.000 0.000
#> GSM62289 2 0.0000 0.961 0.000 1.000
#> GSM62307 2 0.0000 0.961 0.000 1.000
#> GSM62316 2 0.0000 0.961 0.000 1.000
#> GSM62254 2 0.0000 0.961 0.000 1.000
#> GSM62292 2 0.0000 0.961 0.000 1.000
#> GSM62253 1 0.0000 0.941 1.000 0.000
#> GSM62270 1 0.0000 0.941 1.000 0.000
#> GSM62278 1 0.0000 0.941 1.000 0.000
#> GSM62297 2 0.0000 0.961 0.000 1.000
#> GSM62298 2 0.0000 0.961 0.000 1.000
#> GSM62299 2 0.0000 0.961 0.000 1.000
#> GSM62258 1 0.7299 0.756 0.796 0.204
#> GSM62281 2 0.0000 0.961 0.000 1.000
#> GSM62294 2 0.0000 0.961 0.000 1.000
#> GSM62305 2 0.0000 0.961 0.000 1.000
#> GSM62306 2 0.0000 0.961 0.000 1.000
#> GSM62310 2 0.0000 0.961 0.000 1.000
#> GSM62311 2 0.0000 0.961 0.000 1.000
#> GSM62317 2 0.0000 0.961 0.000 1.000
#> GSM62318 2 0.0000 0.961 0.000 1.000
#> GSM62321 2 0.0000 0.961 0.000 1.000
#> GSM62322 1 0.0000 0.941 1.000 0.000
#> GSM62250 2 0.0000 0.961 0.000 1.000
#> GSM62252 2 0.0000 0.961 0.000 1.000
#> GSM62255 2 0.0000 0.961 0.000 1.000
#> GSM62257 2 0.0000 0.961 0.000 1.000
#> GSM62260 2 0.9129 0.514 0.328 0.672
#> GSM62261 2 0.0000 0.961 0.000 1.000
#> GSM62262 2 0.0000 0.961 0.000 1.000
#> GSM62264 2 0.9129 0.514 0.328 0.672
#> GSM62268 1 0.0000 0.941 1.000 0.000
#> GSM62269 1 0.0000 0.941 1.000 0.000
#> GSM62271 1 0.0000 0.941 1.000 0.000
#> GSM62272 1 0.0000 0.941 1.000 0.000
#> GSM62273 2 0.0000 0.961 0.000 1.000
#> GSM62274 1 0.0000 0.941 1.000 0.000
#> GSM62275 1 0.0000 0.941 1.000 0.000
#> GSM62276 1 0.7299 0.757 0.796 0.204
#> GSM62277 1 0.0000 0.941 1.000 0.000
#> GSM62279 1 0.0672 0.936 0.992 0.008
#> GSM62282 1 0.8909 0.570 0.692 0.308
#> GSM62283 2 0.9170 0.505 0.332 0.668
#> GSM62286 2 0.0000 0.961 0.000 1.000
#> GSM62287 2 0.0000 0.961 0.000 1.000
#> GSM62288 2 0.0000 0.961 0.000 1.000
#> GSM62290 2 0.0000 0.961 0.000 1.000
#> GSM62293 2 0.0000 0.961 0.000 1.000
#> GSM62301 2 0.0000 0.961 0.000 1.000
#> GSM62302 2 0.0000 0.961 0.000 1.000
#> GSM62303 2 0.0000 0.961 0.000 1.000
#> GSM62304 2 0.0000 0.961 0.000 1.000
#> GSM62312 2 0.0000 0.961 0.000 1.000
#> GSM62313 2 0.0000 0.961 0.000 1.000
#> GSM62314 2 0.0000 0.961 0.000 1.000
#> GSM62319 2 0.0000 0.961 0.000 1.000
#> GSM62320 2 0.0000 0.961 0.000 1.000
#> GSM62249 2 0.9170 0.505 0.332 0.668
#> GSM62251 2 0.9170 0.505 0.332 0.668
#> GSM62263 2 0.0000 0.961 0.000 1.000
#> GSM62285 2 0.0000 0.961 0.000 1.000
#> GSM62315 2 0.0000 0.961 0.000 1.000
#> GSM62291 2 0.0000 0.961 0.000 1.000
#> GSM62265 2 0.9170 0.505 0.332 0.668
#> GSM62266 1 0.0000 0.941 1.000 0.000
#> GSM62296 2 0.0000 0.961 0.000 1.000
#> GSM62309 2 0.0000 0.961 0.000 1.000
#> GSM62295 2 0.0000 0.961 0.000 1.000
#> GSM62300 2 0.0000 0.961 0.000 1.000
#> GSM62308 2 0.0000 0.961 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM62248 2 0.1411 0.923 0.036 0.964 0.000
#> GSM62256 2 0.0000 0.946 0.000 1.000 0.000
#> GSM62259 2 0.0000 0.946 0.000 1.000 0.000
#> GSM62267 3 0.5020 0.616 0.192 0.012 0.796
#> GSM62280 1 0.5061 0.675 0.784 0.208 0.008
#> GSM62284 3 0.0000 0.851 0.000 0.000 1.000
#> GSM62289 2 0.5098 0.641 0.248 0.752 0.000
#> GSM62307 2 0.0000 0.946 0.000 1.000 0.000
#> GSM62316 2 0.1411 0.923 0.036 0.964 0.000
#> GSM62254 2 0.0000 0.946 0.000 1.000 0.000
#> GSM62292 2 0.0000 0.946 0.000 1.000 0.000
#> GSM62253 3 0.0000 0.851 0.000 0.000 1.000
#> GSM62270 3 0.4654 0.776 0.208 0.000 0.792
#> GSM62278 3 0.0000 0.851 0.000 0.000 1.000
#> GSM62297 2 0.1411 0.923 0.036 0.964 0.000
#> GSM62298 2 0.0000 0.946 0.000 1.000 0.000
#> GSM62299 2 0.0000 0.946 0.000 1.000 0.000
#> GSM62258 3 0.4784 0.617 0.200 0.004 0.796
#> GSM62281 2 0.0000 0.946 0.000 1.000 0.000
#> GSM62294 2 0.0000 0.946 0.000 1.000 0.000
#> GSM62305 2 0.5529 0.549 0.296 0.704 0.000
#> GSM62306 2 0.5529 0.549 0.296 0.704 0.000
#> GSM62310 2 0.0000 0.946 0.000 1.000 0.000
#> GSM62311 2 0.0000 0.946 0.000 1.000 0.000
#> GSM62317 1 0.4654 0.677 0.792 0.208 0.000
#> GSM62318 1 0.4654 0.677 0.792 0.208 0.000
#> GSM62321 1 0.4654 0.677 0.792 0.208 0.000
#> GSM62322 3 0.4654 0.776 0.208 0.000 0.792
#> GSM62250 2 0.5529 0.549 0.296 0.704 0.000
#> GSM62252 2 0.5529 0.549 0.296 0.704 0.000
#> GSM62255 2 0.0000 0.946 0.000 1.000 0.000
#> GSM62257 2 0.0000 0.946 0.000 1.000 0.000
#> GSM62260 1 0.6448 0.632 0.656 0.016 0.328
#> GSM62261 2 0.1411 0.923 0.036 0.964 0.000
#> GSM62262 2 0.0000 0.946 0.000 1.000 0.000
#> GSM62264 1 0.6448 0.632 0.656 0.016 0.328
#> GSM62268 3 0.0000 0.851 0.000 0.000 1.000
#> GSM62269 3 0.4654 0.776 0.208 0.000 0.792
#> GSM62271 3 0.0000 0.851 0.000 0.000 1.000
#> GSM62272 3 0.4654 0.776 0.208 0.000 0.792
#> GSM62273 2 0.0000 0.946 0.000 1.000 0.000
#> GSM62274 3 0.0000 0.851 0.000 0.000 1.000
#> GSM62275 3 0.4654 0.776 0.208 0.000 0.792
#> GSM62276 3 0.5020 0.616 0.192 0.012 0.796
#> GSM62277 3 0.0000 0.851 0.000 0.000 1.000
#> GSM62279 3 0.0424 0.845 0.000 0.008 0.992
#> GSM62282 3 0.7558 0.468 0.164 0.144 0.692
#> GSM62283 1 0.6726 0.637 0.644 0.024 0.332
#> GSM62286 2 0.5529 0.549 0.296 0.704 0.000
#> GSM62287 2 0.0000 0.946 0.000 1.000 0.000
#> GSM62288 2 0.1411 0.923 0.036 0.964 0.000
#> GSM62290 2 0.0000 0.946 0.000 1.000 0.000
#> GSM62293 2 0.0000 0.946 0.000 1.000 0.000
#> GSM62301 2 0.0000 0.946 0.000 1.000 0.000
#> GSM62302 2 0.0000 0.946 0.000 1.000 0.000
#> GSM62303 2 0.0000 0.946 0.000 1.000 0.000
#> GSM62304 2 0.0000 0.946 0.000 1.000 0.000
#> GSM62312 2 0.1411 0.923 0.036 0.964 0.000
#> GSM62313 2 0.0000 0.946 0.000 1.000 0.000
#> GSM62314 2 0.1411 0.923 0.036 0.964 0.000
#> GSM62319 2 0.0000 0.946 0.000 1.000 0.000
#> GSM62320 2 0.0000 0.946 0.000 1.000 0.000
#> GSM62249 1 0.6726 0.637 0.644 0.024 0.332
#> GSM62251 1 0.6603 0.635 0.648 0.020 0.332
#> GSM62263 1 0.6295 0.183 0.528 0.472 0.000
#> GSM62285 2 0.0000 0.946 0.000 1.000 0.000
#> GSM62315 2 0.0000 0.946 0.000 1.000 0.000
#> GSM62291 2 0.0000 0.946 0.000 1.000 0.000
#> GSM62265 1 0.6726 0.637 0.644 0.024 0.332
#> GSM62266 3 0.0000 0.851 0.000 0.000 1.000
#> GSM62296 2 0.0000 0.946 0.000 1.000 0.000
#> GSM62309 2 0.0000 0.946 0.000 1.000 0.000
#> GSM62295 2 0.0000 0.946 0.000 1.000 0.000
#> GSM62300 2 0.0000 0.946 0.000 1.000 0.000
#> GSM62308 2 0.0000 0.946 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM62248 2 0.1211 0.9265 0.040 0.960 0.000 0.000
#> GSM62256 2 0.0000 0.9497 0.000 1.000 0.000 0.000
#> GSM62259 2 0.0000 0.9497 0.000 1.000 0.000 0.000
#> GSM62267 1 0.5158 -0.5474 0.524 0.004 0.000 0.472
#> GSM62280 1 0.4661 0.5024 0.652 0.000 0.000 0.348
#> GSM62284 4 0.5090 0.9008 0.324 0.000 0.016 0.660
#> GSM62289 2 0.4103 0.6820 0.256 0.744 0.000 0.000
#> GSM62307 2 0.0000 0.9497 0.000 1.000 0.000 0.000
#> GSM62316 2 0.1211 0.9265 0.040 0.960 0.000 0.000
#> GSM62254 2 0.0000 0.9497 0.000 1.000 0.000 0.000
#> GSM62292 2 0.0000 0.9497 0.000 1.000 0.000 0.000
#> GSM62253 4 0.5090 0.9008 0.324 0.000 0.016 0.660
#> GSM62270 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM62278 4 0.7142 0.8076 0.324 0.000 0.152 0.524
#> GSM62297 2 0.1211 0.9265 0.040 0.960 0.000 0.000
#> GSM62298 2 0.0000 0.9497 0.000 1.000 0.000 0.000
#> GSM62299 2 0.0000 0.9497 0.000 1.000 0.000 0.000
#> GSM62258 1 0.5451 -0.5494 0.524 0.004 0.008 0.464
#> GSM62281 2 0.0000 0.9497 0.000 1.000 0.000 0.000
#> GSM62294 2 0.0000 0.9497 0.000 1.000 0.000 0.000
#> GSM62305 2 0.4454 0.6004 0.308 0.692 0.000 0.000
#> GSM62306 2 0.4454 0.6004 0.308 0.692 0.000 0.000
#> GSM62310 2 0.0000 0.9497 0.000 1.000 0.000 0.000
#> GSM62311 2 0.0000 0.9497 0.000 1.000 0.000 0.000
#> GSM62317 1 0.4624 0.5038 0.660 0.000 0.000 0.340
#> GSM62318 1 0.4624 0.5038 0.660 0.000 0.000 0.340
#> GSM62321 1 0.4624 0.5038 0.660 0.000 0.000 0.340
#> GSM62322 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM62250 2 0.4454 0.6004 0.308 0.692 0.000 0.000
#> GSM62252 2 0.4454 0.6004 0.308 0.692 0.000 0.000
#> GSM62255 2 0.0000 0.9497 0.000 1.000 0.000 0.000
#> GSM62257 2 0.0000 0.9497 0.000 1.000 0.000 0.000
#> GSM62260 1 0.0188 0.5538 0.996 0.000 0.000 0.004
#> GSM62261 2 0.1211 0.9265 0.040 0.960 0.000 0.000
#> GSM62262 2 0.0000 0.9497 0.000 1.000 0.000 0.000
#> GSM62264 1 0.0188 0.5538 0.996 0.000 0.000 0.004
#> GSM62268 4 0.5090 0.9008 0.324 0.000 0.016 0.660
#> GSM62269 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM62271 4 0.7142 0.8076 0.324 0.000 0.152 0.524
#> GSM62272 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM62273 2 0.0000 0.9497 0.000 1.000 0.000 0.000
#> GSM62274 4 0.5090 0.9008 0.324 0.000 0.016 0.660
#> GSM62275 3 0.0000 1.0000 0.000 0.000 1.000 0.000
#> GSM62276 1 0.5158 -0.5474 0.524 0.004 0.000 0.472
#> GSM62277 4 0.5090 0.9008 0.324 0.000 0.016 0.660
#> GSM62279 4 0.4897 0.8913 0.332 0.000 0.008 0.660
#> GSM62282 4 0.6851 0.3792 0.268 0.000 0.148 0.584
#> GSM62283 1 0.0927 0.5566 0.976 0.016 0.000 0.008
#> GSM62286 2 0.4454 0.6004 0.308 0.692 0.000 0.000
#> GSM62287 2 0.0000 0.9497 0.000 1.000 0.000 0.000
#> GSM62288 2 0.1211 0.9265 0.040 0.960 0.000 0.000
#> GSM62290 2 0.0000 0.9497 0.000 1.000 0.000 0.000
#> GSM62293 2 0.0000 0.9497 0.000 1.000 0.000 0.000
#> GSM62301 2 0.0000 0.9497 0.000 1.000 0.000 0.000
#> GSM62302 2 0.0000 0.9497 0.000 1.000 0.000 0.000
#> GSM62303 2 0.0000 0.9497 0.000 1.000 0.000 0.000
#> GSM62304 2 0.0000 0.9497 0.000 1.000 0.000 0.000
#> GSM62312 2 0.1211 0.9265 0.040 0.960 0.000 0.000
#> GSM62313 2 0.0000 0.9497 0.000 1.000 0.000 0.000
#> GSM62314 2 0.1211 0.9265 0.040 0.960 0.000 0.000
#> GSM62319 2 0.0000 0.9497 0.000 1.000 0.000 0.000
#> GSM62320 2 0.0000 0.9497 0.000 1.000 0.000 0.000
#> GSM62249 1 0.0927 0.5566 0.976 0.016 0.000 0.008
#> GSM62251 1 0.0804 0.5563 0.980 0.012 0.000 0.008
#> GSM62263 1 0.4981 -0.0392 0.536 0.464 0.000 0.000
#> GSM62285 2 0.0000 0.9497 0.000 1.000 0.000 0.000
#> GSM62315 2 0.0000 0.9497 0.000 1.000 0.000 0.000
#> GSM62291 2 0.0000 0.9497 0.000 1.000 0.000 0.000
#> GSM62265 1 0.0927 0.5566 0.976 0.016 0.000 0.008
#> GSM62266 4 0.5090 0.9008 0.324 0.000 0.016 0.660
#> GSM62296 2 0.0000 0.9497 0.000 1.000 0.000 0.000
#> GSM62309 2 0.0000 0.9497 0.000 1.000 0.000 0.000
#> GSM62295 2 0.0000 0.9497 0.000 1.000 0.000 0.000
#> GSM62300 2 0.0000 0.9497 0.000 1.000 0.000 0.000
#> GSM62308 2 0.0000 0.9497 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM62248 4 0.1121 0.9195 0.000 0.000 0.000 0.956 0.044
#> GSM62256 4 0.0162 0.9433 0.000 0.000 0.000 0.996 0.004
#> GSM62259 4 0.0000 0.9452 0.000 0.000 0.000 1.000 0.000
#> GSM62267 1 0.3861 0.6728 0.712 0.004 0.000 0.000 0.284
#> GSM62280 2 0.0451 0.9887 0.004 0.988 0.000 0.000 0.008
#> GSM62284 1 0.0000 0.8526 1.000 0.000 0.000 0.000 0.000
#> GSM62289 4 0.3636 0.6433 0.000 0.000 0.000 0.728 0.272
#> GSM62307 4 0.0000 0.9452 0.000 0.000 0.000 1.000 0.000
#> GSM62316 4 0.1121 0.9195 0.000 0.000 0.000 0.956 0.044
#> GSM62254 4 0.0000 0.9452 0.000 0.000 0.000 1.000 0.000
#> GSM62292 4 0.0000 0.9452 0.000 0.000 0.000 1.000 0.000
#> GSM62253 1 0.0000 0.8526 1.000 0.000 0.000 0.000 0.000
#> GSM62270 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM62278 1 0.2787 0.7941 0.856 0.004 0.136 0.000 0.004
#> GSM62297 4 0.1121 0.9195 0.000 0.000 0.000 0.956 0.044
#> GSM62298 4 0.0000 0.9452 0.000 0.000 0.000 1.000 0.000
#> GSM62299 4 0.0000 0.9452 0.000 0.000 0.000 1.000 0.000
#> GSM62258 1 0.3741 0.6915 0.732 0.004 0.000 0.000 0.264
#> GSM62281 4 0.0162 0.9433 0.000 0.000 0.000 0.996 0.004
#> GSM62294 4 0.0000 0.9452 0.000 0.000 0.000 1.000 0.000
#> GSM62305 4 0.3913 0.5518 0.000 0.000 0.000 0.676 0.324
#> GSM62306 4 0.3913 0.5518 0.000 0.000 0.000 0.676 0.324
#> GSM62310 4 0.0000 0.9452 0.000 0.000 0.000 1.000 0.000
#> GSM62311 4 0.0000 0.9452 0.000 0.000 0.000 1.000 0.000
#> GSM62317 2 0.0162 0.9929 0.000 0.996 0.000 0.000 0.004
#> GSM62318 2 0.0404 0.9912 0.000 0.988 0.000 0.000 0.012
#> GSM62321 2 0.0162 0.9929 0.000 0.996 0.000 0.000 0.004
#> GSM62322 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM62250 4 0.3913 0.5518 0.000 0.000 0.000 0.676 0.324
#> GSM62252 4 0.3913 0.5518 0.000 0.000 0.000 0.676 0.324
#> GSM62255 4 0.0000 0.9452 0.000 0.000 0.000 1.000 0.000
#> GSM62257 4 0.0000 0.9452 0.000 0.000 0.000 1.000 0.000
#> GSM62260 5 0.1041 0.8001 0.004 0.032 0.000 0.000 0.964
#> GSM62261 4 0.1121 0.9195 0.000 0.000 0.000 0.956 0.044
#> GSM62262 4 0.0000 0.9452 0.000 0.000 0.000 1.000 0.000
#> GSM62264 5 0.1041 0.8001 0.004 0.032 0.000 0.000 0.964
#> GSM62268 1 0.0000 0.8526 1.000 0.000 0.000 0.000 0.000
#> GSM62269 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM62271 1 0.2787 0.7941 0.856 0.004 0.136 0.000 0.004
#> GSM62272 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM62273 4 0.0000 0.9452 0.000 0.000 0.000 1.000 0.000
#> GSM62274 1 0.0000 0.8526 1.000 0.000 0.000 0.000 0.000
#> GSM62275 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM62276 1 0.3861 0.6728 0.712 0.004 0.000 0.000 0.284
#> GSM62277 1 0.0000 0.8526 1.000 0.000 0.000 0.000 0.000
#> GSM62279 1 0.1410 0.8313 0.940 0.000 0.000 0.000 0.060
#> GSM62282 1 0.6943 0.3455 0.520 0.296 0.136 0.000 0.048
#> GSM62283 5 0.0162 0.8184 0.004 0.000 0.000 0.000 0.996
#> GSM62286 4 0.3913 0.5518 0.000 0.000 0.000 0.676 0.324
#> GSM62287 4 0.0000 0.9452 0.000 0.000 0.000 1.000 0.000
#> GSM62288 4 0.1121 0.9195 0.000 0.000 0.000 0.956 0.044
#> GSM62290 4 0.0000 0.9452 0.000 0.000 0.000 1.000 0.000
#> GSM62293 4 0.0000 0.9452 0.000 0.000 0.000 1.000 0.000
#> GSM62301 4 0.0000 0.9452 0.000 0.000 0.000 1.000 0.000
#> GSM62302 4 0.0000 0.9452 0.000 0.000 0.000 1.000 0.000
#> GSM62303 4 0.0000 0.9452 0.000 0.000 0.000 1.000 0.000
#> GSM62304 4 0.0000 0.9452 0.000 0.000 0.000 1.000 0.000
#> GSM62312 4 0.1121 0.9195 0.000 0.000 0.000 0.956 0.044
#> GSM62313 4 0.0000 0.9452 0.000 0.000 0.000 1.000 0.000
#> GSM62314 4 0.1121 0.9195 0.000 0.000 0.000 0.956 0.044
#> GSM62319 4 0.0290 0.9408 0.000 0.000 0.000 0.992 0.008
#> GSM62320 4 0.0000 0.9452 0.000 0.000 0.000 1.000 0.000
#> GSM62249 5 0.0162 0.8184 0.004 0.000 0.000 0.000 0.996
#> GSM62251 5 0.0324 0.8175 0.004 0.004 0.000 0.000 0.992
#> GSM62263 5 0.4430 0.0288 0.000 0.004 0.000 0.456 0.540
#> GSM62285 4 0.0000 0.9452 0.000 0.000 0.000 1.000 0.000
#> GSM62315 4 0.0000 0.9452 0.000 0.000 0.000 1.000 0.000
#> GSM62291 4 0.0000 0.9452 0.000 0.000 0.000 1.000 0.000
#> GSM62265 5 0.0162 0.8184 0.004 0.000 0.000 0.000 0.996
#> GSM62266 1 0.0000 0.8526 1.000 0.000 0.000 0.000 0.000
#> GSM62296 4 0.0000 0.9452 0.000 0.000 0.000 1.000 0.000
#> GSM62309 4 0.0000 0.9452 0.000 0.000 0.000 1.000 0.000
#> GSM62295 4 0.0000 0.9452 0.000 0.000 0.000 1.000 0.000
#> GSM62300 4 0.0000 0.9452 0.000 0.000 0.000 1.000 0.000
#> GSM62308 4 0.0000 0.9452 0.000 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM62248 4 0.2445 0.866 0.000 0.020 0.00 0.872 0.108 0.000
#> GSM62256 4 0.0146 0.900 0.000 0.004 0.00 0.996 0.000 0.000
#> GSM62259 4 0.0000 0.901 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM62267 5 0.5392 0.486 0.436 0.112 0.00 0.000 0.452 0.000
#> GSM62280 6 0.3446 0.823 0.000 0.000 0.00 0.000 0.308 0.692
#> GSM62284 1 0.0000 0.720 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM62289 4 0.4583 0.618 0.000 0.176 0.00 0.696 0.128 0.000
#> GSM62307 4 0.0000 0.901 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM62316 4 0.2445 0.866 0.000 0.020 0.00 0.872 0.108 0.000
#> GSM62254 4 0.0000 0.901 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM62292 4 0.0000 0.901 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM62253 1 0.0000 0.720 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM62270 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM62278 1 0.5287 -0.048 0.588 0.004 0.12 0.000 0.288 0.000
#> GSM62297 4 0.3017 0.839 0.000 0.020 0.00 0.816 0.164 0.000
#> GSM62298 4 0.0547 0.899 0.000 0.000 0.00 0.980 0.020 0.000
#> GSM62299 4 0.0547 0.899 0.000 0.000 0.00 0.980 0.020 0.000
#> GSM62258 1 0.5560 -0.557 0.476 0.140 0.00 0.000 0.384 0.000
#> GSM62281 4 0.0146 0.900 0.000 0.004 0.00 0.996 0.000 0.000
#> GSM62294 4 0.0000 0.901 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM62305 4 0.5008 0.529 0.000 0.188 0.00 0.644 0.168 0.000
#> GSM62306 4 0.5008 0.529 0.000 0.188 0.00 0.644 0.168 0.000
#> GSM62310 4 0.0000 0.901 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM62311 4 0.0000 0.901 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM62317 6 0.0000 0.833 0.000 0.000 0.00 0.000 0.000 1.000
#> GSM62318 6 0.3409 0.827 0.000 0.000 0.00 0.000 0.300 0.700
#> GSM62321 6 0.0000 0.833 0.000 0.000 0.00 0.000 0.000 1.000
#> GSM62322 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM62250 4 0.5008 0.529 0.000 0.188 0.00 0.644 0.168 0.000
#> GSM62252 4 0.5008 0.529 0.000 0.188 0.00 0.644 0.168 0.000
#> GSM62255 4 0.0000 0.901 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM62257 4 0.0000 0.901 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM62260 2 0.1572 0.715 0.000 0.936 0.00 0.000 0.036 0.028
#> GSM62261 4 0.2981 0.841 0.000 0.020 0.00 0.820 0.160 0.000
#> GSM62262 4 0.0000 0.901 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM62264 2 0.1572 0.715 0.000 0.936 0.00 0.000 0.036 0.028
#> GSM62268 1 0.0000 0.720 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM62269 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM62271 1 0.5287 -0.048 0.588 0.004 0.12 0.000 0.288 0.000
#> GSM62272 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM62273 4 0.0146 0.900 0.000 0.000 0.00 0.996 0.004 0.000
#> GSM62274 1 0.0000 0.720 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM62275 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM62276 5 0.5392 0.486 0.436 0.112 0.00 0.000 0.452 0.000
#> GSM62277 1 0.0000 0.720 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM62279 1 0.1806 0.610 0.908 0.004 0.00 0.000 0.088 0.000
#> GSM62282 5 0.5675 0.199 0.248 0.032 0.12 0.000 0.600 0.000
#> GSM62283 2 0.2092 0.732 0.000 0.876 0.00 0.000 0.124 0.000
#> GSM62286 4 0.5008 0.529 0.000 0.188 0.00 0.644 0.168 0.000
#> GSM62287 4 0.0000 0.901 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM62288 4 0.2445 0.866 0.000 0.020 0.00 0.872 0.108 0.000
#> GSM62290 4 0.2178 0.863 0.000 0.000 0.00 0.868 0.132 0.000
#> GSM62293 4 0.0000 0.901 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM62301 4 0.2178 0.863 0.000 0.000 0.00 0.868 0.132 0.000
#> GSM62302 4 0.0000 0.901 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM62303 4 0.0000 0.901 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM62304 4 0.0000 0.901 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM62312 4 0.3017 0.839 0.000 0.020 0.00 0.816 0.164 0.000
#> GSM62313 4 0.0000 0.901 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM62314 4 0.2445 0.866 0.000 0.020 0.00 0.872 0.108 0.000
#> GSM62319 4 0.0858 0.894 0.000 0.004 0.00 0.968 0.028 0.000
#> GSM62320 4 0.0547 0.899 0.000 0.000 0.00 0.980 0.020 0.000
#> GSM62249 2 0.2092 0.732 0.000 0.876 0.00 0.000 0.124 0.000
#> GSM62251 2 0.0000 0.736 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM62263 2 0.5647 0.224 0.000 0.520 0.00 0.296 0.184 0.000
#> GSM62285 4 0.2178 0.863 0.000 0.000 0.00 0.868 0.132 0.000
#> GSM62315 4 0.2178 0.863 0.000 0.000 0.00 0.868 0.132 0.000
#> GSM62291 4 0.2178 0.863 0.000 0.000 0.00 0.868 0.132 0.000
#> GSM62265 2 0.2092 0.732 0.000 0.876 0.00 0.000 0.124 0.000
#> GSM62266 1 0.0000 0.720 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM62296 4 0.2178 0.863 0.000 0.000 0.00 0.868 0.132 0.000
#> GSM62309 4 0.2178 0.863 0.000 0.000 0.00 0.868 0.132 0.000
#> GSM62295 4 0.0000 0.901 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM62300 4 0.2178 0.863 0.000 0.000 0.00 0.868 0.132 0.000
#> GSM62308 4 0.2178 0.863 0.000 0.000 0.00 0.868 0.132 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) other(p) genotype/variation(p) k
#> SD:hclust 75 0.247 0.737 0.442 2
#> SD:hclust 73 0.253 0.421 0.482 3
#> SD:hclust 70 0.488 0.573 0.776 4
#> SD:hclust 73 0.121 0.370 0.680 5
#> SD:hclust 68 0.177 0.351 0.796 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "kmeans"]
# you can also extract it by
# res = res_list["SD:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 75 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.980 0.992 0.4491 0.550 0.550
#> 3 3 0.671 0.798 0.839 0.2823 0.904 0.829
#> 4 4 0.653 0.859 0.854 0.1889 0.801 0.586
#> 5 5 0.612 0.507 0.693 0.1130 0.889 0.631
#> 6 6 0.775 0.727 0.839 0.0669 0.885 0.542
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
#> GSM62248 2 0.000 0.996 0.000 1.000
#> GSM62256 2 0.000 0.996 0.000 1.000
#> GSM62259 2 0.000 0.996 0.000 1.000
#> GSM62267 1 0.000 0.983 1.000 0.000
#> GSM62280 1 0.000 0.983 1.000 0.000
#> GSM62284 1 0.000 0.983 1.000 0.000
#> GSM62289 2 0.000 0.996 0.000 1.000
#> GSM62307 2 0.000 0.996 0.000 1.000
#> GSM62316 2 0.000 0.996 0.000 1.000
#> GSM62254 2 0.000 0.996 0.000 1.000
#> GSM62292 2 0.000 0.996 0.000 1.000
#> GSM62253 1 0.000 0.983 1.000 0.000
#> GSM62270 1 0.000 0.983 1.000 0.000
#> GSM62278 1 0.000 0.983 1.000 0.000
#> GSM62297 2 0.000 0.996 0.000 1.000
#> GSM62298 2 0.000 0.996 0.000 1.000
#> GSM62299 2 0.000 0.996 0.000 1.000
#> GSM62258 1 0.000 0.983 1.000 0.000
#> GSM62281 2 0.000 0.996 0.000 1.000
#> GSM62294 2 0.000 0.996 0.000 1.000
#> GSM62305 2 0.000 0.996 0.000 1.000
#> GSM62306 2 0.000 0.996 0.000 1.000
#> GSM62310 2 0.000 0.996 0.000 1.000
#> GSM62311 2 0.000 0.996 0.000 1.000
#> GSM62317 2 0.000 0.996 0.000 1.000
#> GSM62318 1 0.000 0.983 1.000 0.000
#> GSM62321 2 0.738 0.730 0.208 0.792
#> GSM62322 1 0.000 0.983 1.000 0.000
#> GSM62250 2 0.000 0.996 0.000 1.000
#> GSM62252 2 0.000 0.996 0.000 1.000
#> GSM62255 2 0.000 0.996 0.000 1.000
#> GSM62257 2 0.000 0.996 0.000 1.000
#> GSM62260 1 0.966 0.347 0.608 0.392
#> GSM62261 2 0.000 0.996 0.000 1.000
#> GSM62262 2 0.000 0.996 0.000 1.000
#> GSM62264 1 0.000 0.983 1.000 0.000
#> GSM62268 1 0.000 0.983 1.000 0.000
#> GSM62269 1 0.000 0.983 1.000 0.000
#> GSM62271 1 0.000 0.983 1.000 0.000
#> GSM62272 1 0.000 0.983 1.000 0.000
#> GSM62273 2 0.000 0.996 0.000 1.000
#> GSM62274 1 0.000 0.983 1.000 0.000
#> GSM62275 1 0.000 0.983 1.000 0.000
#> GSM62276 1 0.000 0.983 1.000 0.000
#> GSM62277 1 0.000 0.983 1.000 0.000
#> GSM62279 1 0.000 0.983 1.000 0.000
#> GSM62282 1 0.000 0.983 1.000 0.000
#> GSM62283 1 0.000 0.983 1.000 0.000
#> GSM62286 2 0.000 0.996 0.000 1.000
#> GSM62287 2 0.000 0.996 0.000 1.000
#> GSM62288 2 0.000 0.996 0.000 1.000
#> GSM62290 2 0.000 0.996 0.000 1.000
#> GSM62293 2 0.000 0.996 0.000 1.000
#> GSM62301 2 0.000 0.996 0.000 1.000
#> GSM62302 2 0.000 0.996 0.000 1.000
#> GSM62303 2 0.000 0.996 0.000 1.000
#> GSM62304 2 0.000 0.996 0.000 1.000
#> GSM62312 2 0.000 0.996 0.000 1.000
#> GSM62313 2 0.000 0.996 0.000 1.000
#> GSM62314 2 0.000 0.996 0.000 1.000
#> GSM62319 2 0.000 0.996 0.000 1.000
#> GSM62320 2 0.000 0.996 0.000 1.000
#> GSM62249 2 0.000 0.996 0.000 1.000
#> GSM62251 1 0.000 0.983 1.000 0.000
#> GSM62263 2 0.000 0.996 0.000 1.000
#> GSM62285 2 0.000 0.996 0.000 1.000
#> GSM62315 2 0.000 0.996 0.000 1.000
#> GSM62291 2 0.000 0.996 0.000 1.000
#> GSM62265 1 0.000 0.983 1.000 0.000
#> GSM62266 1 0.000 0.983 1.000 0.000
#> GSM62296 2 0.000 0.996 0.000 1.000
#> GSM62309 2 0.000 0.996 0.000 1.000
#> GSM62295 2 0.000 0.996 0.000 1.000
#> GSM62300 2 0.000 0.996 0.000 1.000
#> GSM62308 2 0.000 0.996 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM62248 2 0.1411 0.869 0.000 0.964 0.036
#> GSM62256 2 0.2796 0.864 0.000 0.908 0.092
#> GSM62259 2 0.0000 0.868 0.000 1.000 0.000
#> GSM62267 1 0.0000 0.791 1.000 0.000 0.000
#> GSM62280 1 0.1163 0.787 0.972 0.000 0.028
#> GSM62284 1 0.6302 -0.690 0.520 0.000 0.480
#> GSM62289 2 0.1289 0.869 0.000 0.968 0.032
#> GSM62307 2 0.0000 0.868 0.000 1.000 0.000
#> GSM62316 2 0.0892 0.869 0.000 0.980 0.020
#> GSM62254 2 0.0000 0.868 0.000 1.000 0.000
#> GSM62292 2 0.0000 0.868 0.000 1.000 0.000
#> GSM62253 1 0.0592 0.780 0.988 0.000 0.012
#> GSM62270 3 0.5968 0.995 0.364 0.000 0.636
#> GSM62278 3 0.5968 0.995 0.364 0.000 0.636
#> GSM62297 2 0.5810 0.780 0.000 0.664 0.336
#> GSM62298 2 0.4504 0.825 0.000 0.804 0.196
#> GSM62299 2 0.5810 0.780 0.000 0.664 0.336
#> GSM62258 1 0.0000 0.791 1.000 0.000 0.000
#> GSM62281 2 0.2711 0.864 0.000 0.912 0.088
#> GSM62294 2 0.0000 0.868 0.000 1.000 0.000
#> GSM62305 2 0.3267 0.856 0.000 0.884 0.116
#> GSM62306 2 0.1289 0.869 0.000 0.968 0.032
#> GSM62310 2 0.0000 0.868 0.000 1.000 0.000
#> GSM62311 2 0.0000 0.868 0.000 1.000 0.000
#> GSM62317 2 0.6189 0.754 0.004 0.632 0.364
#> GSM62318 1 0.1163 0.787 0.972 0.000 0.028
#> GSM62321 1 0.5785 0.531 0.668 0.000 0.332
#> GSM62322 3 0.5968 0.995 0.364 0.000 0.636
#> GSM62250 2 0.2599 0.863 0.016 0.932 0.052
#> GSM62252 2 0.7552 0.324 0.352 0.596 0.052
#> GSM62255 2 0.0000 0.868 0.000 1.000 0.000
#> GSM62257 2 0.0000 0.868 0.000 1.000 0.000
#> GSM62260 1 0.5431 0.582 0.716 0.000 0.284
#> GSM62261 2 0.1289 0.869 0.000 0.968 0.032
#> GSM62262 2 0.0000 0.868 0.000 1.000 0.000
#> GSM62264 1 0.4178 0.693 0.828 0.000 0.172
#> GSM62268 1 0.3941 0.529 0.844 0.000 0.156
#> GSM62269 3 0.5968 0.995 0.364 0.000 0.636
#> GSM62271 1 0.0000 0.791 1.000 0.000 0.000
#> GSM62272 3 0.5968 0.995 0.364 0.000 0.636
#> GSM62273 2 0.3267 0.853 0.000 0.884 0.116
#> GSM62274 3 0.6062 0.966 0.384 0.000 0.616
#> GSM62275 3 0.5968 0.995 0.364 0.000 0.636
#> GSM62276 1 0.0000 0.791 1.000 0.000 0.000
#> GSM62277 3 0.5968 0.995 0.364 0.000 0.636
#> GSM62279 1 0.0000 0.791 1.000 0.000 0.000
#> GSM62282 1 0.1031 0.788 0.976 0.000 0.024
#> GSM62283 1 0.2711 0.749 0.912 0.000 0.088
#> GSM62286 2 0.1860 0.867 0.000 0.948 0.052
#> GSM62287 2 0.0000 0.868 0.000 1.000 0.000
#> GSM62288 2 0.1289 0.869 0.000 0.968 0.032
#> GSM62290 2 0.5810 0.780 0.000 0.664 0.336
#> GSM62293 2 0.0000 0.868 0.000 1.000 0.000
#> GSM62301 2 0.5810 0.780 0.000 0.664 0.336
#> GSM62302 2 0.0000 0.868 0.000 1.000 0.000
#> GSM62303 2 0.0000 0.868 0.000 1.000 0.000
#> GSM62304 2 0.0000 0.868 0.000 1.000 0.000
#> GSM62312 2 0.5678 0.787 0.000 0.684 0.316
#> GSM62313 2 0.0000 0.868 0.000 1.000 0.000
#> GSM62314 2 0.0747 0.869 0.000 0.984 0.016
#> GSM62319 2 0.5810 0.780 0.000 0.664 0.336
#> GSM62320 2 0.4504 0.825 0.000 0.804 0.196
#> GSM62249 1 0.6867 0.476 0.636 0.028 0.336
#> GSM62251 1 0.3267 0.729 0.884 0.000 0.116
#> GSM62263 2 0.5810 0.780 0.000 0.664 0.336
#> GSM62285 2 0.5810 0.780 0.000 0.664 0.336
#> GSM62315 2 0.5810 0.780 0.000 0.664 0.336
#> GSM62291 2 0.5810 0.780 0.000 0.664 0.336
#> GSM62265 1 0.0000 0.791 1.000 0.000 0.000
#> GSM62266 1 0.0000 0.791 1.000 0.000 0.000
#> GSM62296 2 0.5810 0.780 0.000 0.664 0.336
#> GSM62309 2 0.5810 0.780 0.000 0.664 0.336
#> GSM62295 2 0.0000 0.868 0.000 1.000 0.000
#> GSM62300 2 0.5810 0.780 0.000 0.664 0.336
#> GSM62308 2 0.5810 0.780 0.000 0.664 0.336
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM62248 4 0.3402 0.8561 0.000 0.164 0.004 0.832
#> GSM62256 4 0.2888 0.8660 0.000 0.124 0.004 0.872
#> GSM62259 4 0.1356 0.8891 0.000 0.032 0.008 0.960
#> GSM62267 1 0.1022 0.8895 0.968 0.000 0.032 0.000
#> GSM62280 1 0.3791 0.8025 0.796 0.200 0.004 0.000
#> GSM62284 3 0.5040 0.4592 0.364 0.008 0.628 0.000
#> GSM62289 4 0.3432 0.8547 0.008 0.140 0.004 0.848
#> GSM62307 4 0.1022 0.8906 0.000 0.032 0.000 0.968
#> GSM62316 4 0.3123 0.8610 0.000 0.156 0.000 0.844
#> GSM62254 4 0.0336 0.8922 0.000 0.000 0.008 0.992
#> GSM62292 4 0.0336 0.8922 0.000 0.000 0.008 0.992
#> GSM62253 1 0.1545 0.8853 0.952 0.008 0.040 0.000
#> GSM62270 3 0.0469 0.9213 0.012 0.000 0.988 0.000
#> GSM62278 3 0.1389 0.9119 0.048 0.000 0.952 0.000
#> GSM62297 2 0.3764 0.8916 0.000 0.784 0.000 0.216
#> GSM62298 2 0.4699 0.9052 0.000 0.676 0.004 0.320
#> GSM62299 2 0.4250 0.9533 0.000 0.724 0.000 0.276
#> GSM62258 1 0.1284 0.8899 0.964 0.012 0.024 0.000
#> GSM62281 4 0.2530 0.8717 0.000 0.100 0.004 0.896
#> GSM62294 4 0.0188 0.8921 0.000 0.000 0.004 0.996
#> GSM62305 4 0.3534 0.8504 0.008 0.148 0.004 0.840
#> GSM62306 4 0.3052 0.8609 0.000 0.136 0.004 0.860
#> GSM62310 4 0.0817 0.8912 0.000 0.024 0.000 0.976
#> GSM62311 4 0.0817 0.8912 0.000 0.024 0.000 0.976
#> GSM62317 2 0.2907 0.6447 0.032 0.900 0.004 0.064
#> GSM62318 1 0.3791 0.8025 0.796 0.200 0.004 0.000
#> GSM62321 1 0.4343 0.7562 0.732 0.264 0.004 0.000
#> GSM62322 3 0.0469 0.9213 0.012 0.000 0.988 0.000
#> GSM62250 4 0.5136 0.7698 0.084 0.144 0.004 0.768
#> GSM62252 4 0.5563 0.7191 0.128 0.128 0.004 0.740
#> GSM62255 4 0.0817 0.8912 0.000 0.024 0.000 0.976
#> GSM62257 4 0.1022 0.8906 0.000 0.032 0.000 0.968
#> GSM62260 1 0.2216 0.8616 0.908 0.092 0.000 0.000
#> GSM62261 4 0.3172 0.8585 0.000 0.160 0.000 0.840
#> GSM62262 4 0.0188 0.8921 0.000 0.000 0.004 0.996
#> GSM62264 1 0.2281 0.8638 0.904 0.096 0.000 0.000
#> GSM62268 1 0.4792 0.4926 0.680 0.008 0.312 0.000
#> GSM62269 3 0.0469 0.9213 0.012 0.000 0.988 0.000
#> GSM62271 1 0.1356 0.8899 0.960 0.008 0.032 0.000
#> GSM62272 3 0.0469 0.9213 0.012 0.000 0.988 0.000
#> GSM62273 4 0.4973 0.0412 0.000 0.348 0.008 0.644
#> GSM62274 3 0.3725 0.7947 0.180 0.008 0.812 0.000
#> GSM62275 3 0.0469 0.9213 0.012 0.000 0.988 0.000
#> GSM62276 1 0.1022 0.8895 0.968 0.000 0.032 0.000
#> GSM62277 3 0.1302 0.9136 0.044 0.000 0.956 0.000
#> GSM62279 1 0.1356 0.8881 0.960 0.008 0.032 0.000
#> GSM62282 1 0.3545 0.8220 0.828 0.164 0.008 0.000
#> GSM62283 1 0.1624 0.8881 0.952 0.020 0.028 0.000
#> GSM62286 4 0.3432 0.8547 0.008 0.140 0.004 0.848
#> GSM62287 4 0.0000 0.8931 0.000 0.000 0.000 1.000
#> GSM62288 4 0.3172 0.8585 0.000 0.160 0.000 0.840
#> GSM62290 2 0.4250 0.9533 0.000 0.724 0.000 0.276
#> GSM62293 4 0.0336 0.8922 0.000 0.000 0.008 0.992
#> GSM62301 2 0.4250 0.9533 0.000 0.724 0.000 0.276
#> GSM62302 4 0.0000 0.8931 0.000 0.000 0.000 1.000
#> GSM62303 4 0.0000 0.8931 0.000 0.000 0.000 1.000
#> GSM62304 4 0.0817 0.8912 0.000 0.024 0.000 0.976
#> GSM62312 2 0.4304 0.9471 0.000 0.716 0.000 0.284
#> GSM62313 4 0.0817 0.8912 0.000 0.024 0.000 0.976
#> GSM62314 4 0.2973 0.8660 0.000 0.144 0.000 0.856
#> GSM62319 2 0.4746 0.9228 0.000 0.688 0.008 0.304
#> GSM62320 2 0.4522 0.9103 0.000 0.680 0.000 0.320
#> GSM62249 1 0.4804 0.6953 0.776 0.160 0.000 0.064
#> GSM62251 1 0.1833 0.8883 0.944 0.024 0.032 0.000
#> GSM62263 2 0.3791 0.8756 0.004 0.796 0.000 0.200
#> GSM62285 2 0.4250 0.9533 0.000 0.724 0.000 0.276
#> GSM62315 2 0.4250 0.9533 0.000 0.724 0.000 0.276
#> GSM62291 2 0.4250 0.9533 0.000 0.724 0.000 0.276
#> GSM62265 1 0.1488 0.8889 0.956 0.012 0.032 0.000
#> GSM62266 1 0.1356 0.8881 0.960 0.008 0.032 0.000
#> GSM62296 2 0.4250 0.9533 0.000 0.724 0.000 0.276
#> GSM62309 2 0.4250 0.9533 0.000 0.724 0.000 0.276
#> GSM62295 4 0.0336 0.8922 0.000 0.000 0.008 0.992
#> GSM62300 2 0.4250 0.9533 0.000 0.724 0.000 0.276
#> GSM62308 2 0.4250 0.9533 0.000 0.724 0.000 0.276
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM62248 4 0.3012 0.524 0.000 0.104 0.000 0.860 0.036
#> GSM62256 4 0.3141 0.520 0.000 0.152 0.000 0.832 0.016
#> GSM62259 4 0.5925 0.188 0.000 0.128 0.000 0.556 0.316
#> GSM62267 1 0.2053 0.840 0.924 0.004 0.000 0.048 0.024
#> GSM62280 5 0.4591 -0.590 0.476 0.000 0.004 0.004 0.516
#> GSM62284 3 0.4889 0.259 0.476 0.004 0.504 0.000 0.016
#> GSM62289 4 0.1808 0.500 0.012 0.044 0.000 0.936 0.008
#> GSM62307 5 0.6130 0.153 0.000 0.128 0.000 0.424 0.448
#> GSM62316 4 0.4630 0.483 0.000 0.116 0.000 0.744 0.140
#> GSM62254 4 0.5799 0.146 0.000 0.112 0.000 0.564 0.324
#> GSM62292 4 0.5799 0.146 0.000 0.112 0.000 0.564 0.324
#> GSM62253 1 0.0703 0.821 0.976 0.000 0.000 0.000 0.024
#> GSM62270 3 0.0162 0.873 0.004 0.000 0.996 0.000 0.000
#> GSM62278 3 0.2295 0.848 0.088 0.004 0.900 0.000 0.008
#> GSM62297 2 0.1956 0.853 0.000 0.916 0.000 0.076 0.008
#> GSM62298 2 0.0912 0.893 0.000 0.972 0.000 0.016 0.012
#> GSM62299 2 0.0451 0.901 0.000 0.988 0.000 0.004 0.008
#> GSM62258 1 0.2885 0.838 0.880 0.004 0.000 0.052 0.064
#> GSM62281 4 0.4067 0.418 0.000 0.300 0.000 0.692 0.008
#> GSM62294 5 0.6003 0.119 0.000 0.112 0.000 0.440 0.448
#> GSM62305 4 0.3067 0.457 0.068 0.040 0.000 0.876 0.016
#> GSM62306 4 0.2522 0.526 0.000 0.108 0.000 0.880 0.012
#> GSM62310 5 0.6068 0.158 0.000 0.120 0.000 0.428 0.452
#> GSM62311 5 0.6068 0.158 0.000 0.120 0.000 0.428 0.452
#> GSM62317 2 0.4670 0.426 0.000 0.548 0.004 0.008 0.440
#> GSM62318 5 0.4591 -0.590 0.476 0.000 0.004 0.004 0.516
#> GSM62321 5 0.5890 -0.553 0.400 0.004 0.004 0.076 0.516
#> GSM62322 3 0.0162 0.873 0.004 0.000 0.996 0.000 0.000
#> GSM62250 4 0.4218 0.364 0.176 0.032 0.000 0.776 0.016
#> GSM62252 4 0.4174 0.362 0.180 0.028 0.000 0.776 0.016
#> GSM62255 5 0.6100 0.162 0.000 0.124 0.000 0.428 0.448
#> GSM62257 5 0.6102 0.157 0.000 0.124 0.000 0.436 0.440
#> GSM62260 1 0.4634 0.780 0.752 0.004 0.000 0.100 0.144
#> GSM62261 4 0.4676 0.486 0.000 0.120 0.000 0.740 0.140
#> GSM62262 4 0.6003 -0.222 0.000 0.112 0.000 0.448 0.440
#> GSM62264 1 0.3622 0.799 0.820 0.000 0.000 0.056 0.124
#> GSM62268 1 0.4086 0.480 0.736 0.000 0.240 0.000 0.024
#> GSM62269 3 0.0162 0.873 0.004 0.000 0.996 0.000 0.000
#> GSM62271 1 0.2304 0.834 0.908 0.004 0.000 0.020 0.068
#> GSM62272 3 0.0162 0.873 0.004 0.000 0.996 0.000 0.000
#> GSM62273 2 0.5719 0.088 0.000 0.552 0.000 0.352 0.096
#> GSM62274 3 0.4491 0.597 0.336 0.004 0.648 0.000 0.012
#> GSM62275 3 0.0162 0.873 0.004 0.000 0.996 0.000 0.000
#> GSM62276 1 0.1862 0.842 0.932 0.004 0.000 0.048 0.016
#> GSM62277 3 0.2408 0.845 0.096 0.004 0.892 0.000 0.008
#> GSM62279 1 0.1329 0.833 0.956 0.004 0.000 0.032 0.008
#> GSM62282 1 0.4714 0.511 0.540 0.004 0.004 0.004 0.448
#> GSM62283 1 0.3081 0.832 0.868 0.004 0.000 0.072 0.056
#> GSM62286 4 0.1731 0.499 0.012 0.040 0.000 0.940 0.008
#> GSM62287 4 0.5968 -0.229 0.000 0.108 0.000 0.448 0.444
#> GSM62288 4 0.4634 0.486 0.000 0.120 0.000 0.744 0.136
#> GSM62290 2 0.0579 0.901 0.000 0.984 0.000 0.008 0.008
#> GSM62293 4 0.5989 -0.149 0.000 0.112 0.000 0.476 0.412
#> GSM62301 2 0.0579 0.900 0.000 0.984 0.000 0.008 0.008
#> GSM62302 5 0.6037 0.145 0.000 0.116 0.000 0.440 0.444
#> GSM62303 4 0.5968 -0.229 0.000 0.108 0.000 0.448 0.444
#> GSM62304 5 0.6101 0.160 0.000 0.124 0.000 0.432 0.444
#> GSM62312 2 0.0693 0.899 0.000 0.980 0.000 0.008 0.012
#> GSM62313 5 0.6069 0.158 0.000 0.120 0.000 0.432 0.448
#> GSM62314 4 0.5459 0.384 0.000 0.120 0.000 0.644 0.236
#> GSM62319 2 0.2329 0.807 0.000 0.876 0.000 0.124 0.000
#> GSM62320 2 0.0912 0.893 0.000 0.972 0.000 0.016 0.012
#> GSM62249 1 0.6684 0.353 0.436 0.064 0.000 0.436 0.064
#> GSM62251 1 0.2491 0.831 0.896 0.000 0.000 0.068 0.036
#> GSM62263 2 0.4675 0.524 0.004 0.640 0.000 0.336 0.020
#> GSM62285 2 0.0579 0.900 0.000 0.984 0.000 0.008 0.008
#> GSM62315 2 0.0451 0.900 0.000 0.988 0.000 0.008 0.004
#> GSM62291 2 0.0290 0.901 0.000 0.992 0.000 0.008 0.000
#> GSM62265 1 0.1444 0.842 0.948 0.000 0.000 0.040 0.012
#> GSM62266 1 0.0703 0.821 0.976 0.000 0.000 0.000 0.024
#> GSM62296 2 0.0290 0.901 0.000 0.992 0.000 0.008 0.000
#> GSM62309 2 0.0290 0.901 0.000 0.992 0.000 0.008 0.000
#> GSM62295 4 0.5799 0.146 0.000 0.112 0.000 0.564 0.324
#> GSM62300 2 0.0290 0.901 0.000 0.992 0.000 0.008 0.000
#> GSM62308 2 0.0290 0.901 0.000 0.992 0.000 0.008 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM62248 5 0.4054 0.7436 0.000 0.024 0.000 0.180 0.760 0.036
#> GSM62256 5 0.4787 0.6988 0.000 0.020 0.000 0.212 0.692 0.076
#> GSM62259 4 0.5583 0.4663 0.000 0.020 0.000 0.600 0.244 0.136
#> GSM62267 1 0.2864 0.7482 0.860 0.012 0.000 0.000 0.100 0.028
#> GSM62280 6 0.2845 0.8058 0.172 0.004 0.000 0.000 0.004 0.820
#> GSM62284 1 0.5251 0.1136 0.532 0.012 0.404 0.000 0.036 0.016
#> GSM62289 5 0.2540 0.7584 0.000 0.004 0.000 0.104 0.872 0.020
#> GSM62307 4 0.1176 0.8489 0.000 0.024 0.000 0.956 0.000 0.020
#> GSM62316 5 0.4934 0.5727 0.000 0.028 0.000 0.364 0.580 0.028
#> GSM62254 4 0.4358 0.6753 0.000 0.012 0.000 0.744 0.148 0.096
#> GSM62292 4 0.4358 0.6753 0.000 0.012 0.000 0.744 0.148 0.096
#> GSM62253 1 0.1364 0.7279 0.952 0.016 0.000 0.000 0.020 0.012
#> GSM62270 3 0.0000 0.9420 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62278 3 0.3220 0.8453 0.104 0.016 0.844 0.000 0.032 0.004
#> GSM62297 2 0.2255 0.8686 0.000 0.908 0.000 0.024 0.044 0.024
#> GSM62298 2 0.1777 0.8875 0.000 0.928 0.000 0.044 0.004 0.024
#> GSM62299 2 0.1844 0.8871 0.000 0.924 0.000 0.048 0.004 0.024
#> GSM62258 1 0.3692 0.7290 0.808 0.016 0.000 0.000 0.108 0.068
#> GSM62281 5 0.5943 0.6210 0.000 0.080 0.000 0.200 0.612 0.108
#> GSM62294 4 0.0291 0.8569 0.000 0.004 0.000 0.992 0.000 0.004
#> GSM62305 5 0.2395 0.7195 0.020 0.004 0.000 0.044 0.904 0.028
#> GSM62306 5 0.3761 0.7373 0.000 0.008 0.000 0.196 0.764 0.032
#> GSM62310 4 0.0547 0.8574 0.000 0.020 0.000 0.980 0.000 0.000
#> GSM62311 4 0.0547 0.8574 0.000 0.020 0.000 0.980 0.000 0.000
#> GSM62317 6 0.3420 0.5939 0.000 0.240 0.000 0.000 0.012 0.748
#> GSM62318 6 0.2597 0.8054 0.176 0.000 0.000 0.000 0.000 0.824
#> GSM62321 6 0.3229 0.7864 0.120 0.004 0.000 0.000 0.048 0.828
#> GSM62322 3 0.0000 0.9420 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62250 5 0.2113 0.7046 0.048 0.000 0.000 0.032 0.912 0.008
#> GSM62252 5 0.2113 0.7046 0.048 0.000 0.000 0.032 0.912 0.008
#> GSM62255 4 0.0806 0.8558 0.000 0.020 0.000 0.972 0.000 0.008
#> GSM62257 4 0.1088 0.8499 0.000 0.024 0.000 0.960 0.000 0.016
#> GSM62260 1 0.5101 0.5223 0.648 0.008 0.000 0.000 0.128 0.216
#> GSM62261 5 0.4989 0.5769 0.000 0.032 0.000 0.360 0.580 0.028
#> GSM62262 4 0.1036 0.8487 0.000 0.008 0.000 0.964 0.004 0.024
#> GSM62264 1 0.4411 0.5742 0.720 0.008 0.000 0.000 0.076 0.196
#> GSM62268 1 0.3659 0.6031 0.804 0.016 0.148 0.000 0.020 0.012
#> GSM62269 3 0.0000 0.9420 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62271 1 0.3103 0.7377 0.856 0.020 0.000 0.000 0.060 0.064
#> GSM62272 3 0.0000 0.9420 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62273 2 0.7017 0.2837 0.000 0.464 0.000 0.240 0.180 0.116
#> GSM62274 1 0.5134 -0.0809 0.484 0.012 0.460 0.000 0.036 0.008
#> GSM62275 3 0.0000 0.9420 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62276 1 0.2912 0.7478 0.856 0.012 0.000 0.000 0.104 0.028
#> GSM62277 3 0.3447 0.8333 0.116 0.012 0.828 0.000 0.036 0.008
#> GSM62279 1 0.1606 0.7451 0.932 0.004 0.000 0.000 0.056 0.008
#> GSM62282 6 0.4454 0.5982 0.308 0.020 0.000 0.000 0.020 0.652
#> GSM62283 1 0.3413 0.7260 0.824 0.012 0.000 0.000 0.112 0.052
#> GSM62286 5 0.2051 0.7554 0.004 0.004 0.000 0.096 0.896 0.000
#> GSM62287 4 0.0260 0.8569 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM62288 5 0.4944 0.5964 0.000 0.032 0.000 0.344 0.596 0.028
#> GSM62290 2 0.1075 0.8915 0.000 0.952 0.000 0.048 0.000 0.000
#> GSM62293 4 0.2402 0.8132 0.000 0.012 0.000 0.896 0.032 0.060
#> GSM62301 2 0.1219 0.8910 0.000 0.948 0.000 0.048 0.000 0.004
#> GSM62302 4 0.0914 0.8586 0.000 0.016 0.000 0.968 0.000 0.016
#> GSM62303 4 0.0458 0.8563 0.000 0.000 0.000 0.984 0.000 0.016
#> GSM62304 4 0.0806 0.8558 0.000 0.020 0.000 0.972 0.000 0.008
#> GSM62312 2 0.2201 0.8777 0.000 0.904 0.000 0.056 0.004 0.036
#> GSM62313 4 0.0458 0.8579 0.000 0.016 0.000 0.984 0.000 0.000
#> GSM62314 4 0.5029 -0.0401 0.000 0.028 0.000 0.564 0.376 0.032
#> GSM62319 2 0.4763 0.6835 0.000 0.728 0.000 0.044 0.148 0.080
#> GSM62320 2 0.1844 0.8871 0.000 0.924 0.000 0.048 0.004 0.024
#> GSM62249 5 0.4302 0.1817 0.368 0.000 0.000 0.004 0.608 0.020
#> GSM62251 1 0.2540 0.7302 0.872 0.004 0.000 0.000 0.104 0.020
#> GSM62263 2 0.4908 0.1809 0.008 0.520 0.000 0.008 0.436 0.028
#> GSM62285 2 0.1219 0.8910 0.000 0.948 0.000 0.048 0.000 0.004
#> GSM62315 2 0.1296 0.8909 0.000 0.948 0.000 0.044 0.004 0.004
#> GSM62291 2 0.1226 0.8917 0.000 0.952 0.000 0.040 0.004 0.004
#> GSM62265 1 0.1668 0.7503 0.928 0.004 0.000 0.000 0.060 0.008
#> GSM62266 1 0.1364 0.7279 0.952 0.016 0.000 0.000 0.020 0.012
#> GSM62296 2 0.1624 0.8893 0.000 0.936 0.000 0.040 0.020 0.004
#> GSM62309 2 0.1666 0.8868 0.000 0.936 0.000 0.036 0.020 0.008
#> GSM62295 4 0.4614 0.6516 0.000 0.012 0.000 0.720 0.148 0.120
#> GSM62300 2 0.1624 0.8893 0.000 0.936 0.000 0.040 0.020 0.004
#> GSM62308 2 0.1624 0.8893 0.000 0.936 0.000 0.040 0.020 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) other(p) genotype/variation(p) k
#> SD:kmeans 74 0.64023 1.000 0.75225 2
#> SD:kmeans 72 0.40247 0.748 0.79276 3
#> SD:kmeans 72 0.00105 0.651 0.05855 4
#> SD:kmeans 41 0.03108 0.201 0.00686 5
#> SD:kmeans 68 0.00547 0.636 0.13500 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "skmeans"]
# you can also extract it by
# res = res_list["SD:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 75 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.994 0.997 0.4760 0.526 0.526
#> 3 3 1.000 0.966 0.978 0.3936 0.788 0.605
#> 4 4 0.831 0.820 0.883 0.0924 0.938 0.819
#> 5 5 0.866 0.814 0.911 0.0707 0.924 0.745
#> 6 6 0.822 0.718 0.852 0.0363 0.963 0.843
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
#> GSM62248 2 0.000 0.996 0.000 1.000
#> GSM62256 2 0.000 0.996 0.000 1.000
#> GSM62259 2 0.000 0.996 0.000 1.000
#> GSM62267 1 0.000 1.000 1.000 0.000
#> GSM62280 1 0.000 1.000 1.000 0.000
#> GSM62284 1 0.000 1.000 1.000 0.000
#> GSM62289 2 0.000 0.996 0.000 1.000
#> GSM62307 2 0.000 0.996 0.000 1.000
#> GSM62316 2 0.000 0.996 0.000 1.000
#> GSM62254 2 0.000 0.996 0.000 1.000
#> GSM62292 2 0.000 0.996 0.000 1.000
#> GSM62253 1 0.000 1.000 1.000 0.000
#> GSM62270 1 0.000 1.000 1.000 0.000
#> GSM62278 1 0.000 1.000 1.000 0.000
#> GSM62297 2 0.000 0.996 0.000 1.000
#> GSM62298 2 0.000 0.996 0.000 1.000
#> GSM62299 2 0.000 0.996 0.000 1.000
#> GSM62258 1 0.000 1.000 1.000 0.000
#> GSM62281 2 0.000 0.996 0.000 1.000
#> GSM62294 2 0.000 0.996 0.000 1.000
#> GSM62305 2 0.000 0.996 0.000 1.000
#> GSM62306 2 0.000 0.996 0.000 1.000
#> GSM62310 2 0.000 0.996 0.000 1.000
#> GSM62311 2 0.000 0.996 0.000 1.000
#> GSM62317 2 0.000 0.996 0.000 1.000
#> GSM62318 1 0.000 1.000 1.000 0.000
#> GSM62321 1 0.000 1.000 1.000 0.000
#> GSM62322 1 0.000 1.000 1.000 0.000
#> GSM62250 2 0.714 0.756 0.196 0.804
#> GSM62252 1 0.000 1.000 1.000 0.000
#> GSM62255 2 0.000 0.996 0.000 1.000
#> GSM62257 2 0.000 0.996 0.000 1.000
#> GSM62260 1 0.000 1.000 1.000 0.000
#> GSM62261 2 0.000 0.996 0.000 1.000
#> GSM62262 2 0.000 0.996 0.000 1.000
#> GSM62264 1 0.000 1.000 1.000 0.000
#> GSM62268 1 0.000 1.000 1.000 0.000
#> GSM62269 1 0.000 1.000 1.000 0.000
#> GSM62271 1 0.000 1.000 1.000 0.000
#> GSM62272 1 0.000 1.000 1.000 0.000
#> GSM62273 2 0.000 0.996 0.000 1.000
#> GSM62274 1 0.000 1.000 1.000 0.000
#> GSM62275 1 0.000 1.000 1.000 0.000
#> GSM62276 1 0.000 1.000 1.000 0.000
#> GSM62277 1 0.000 1.000 1.000 0.000
#> GSM62279 1 0.000 1.000 1.000 0.000
#> GSM62282 1 0.000 1.000 1.000 0.000
#> GSM62283 1 0.000 1.000 1.000 0.000
#> GSM62286 2 0.000 0.996 0.000 1.000
#> GSM62287 2 0.000 0.996 0.000 1.000
#> GSM62288 2 0.000 0.996 0.000 1.000
#> GSM62290 2 0.000 0.996 0.000 1.000
#> GSM62293 2 0.000 0.996 0.000 1.000
#> GSM62301 2 0.000 0.996 0.000 1.000
#> GSM62302 2 0.000 0.996 0.000 1.000
#> GSM62303 2 0.000 0.996 0.000 1.000
#> GSM62304 2 0.000 0.996 0.000 1.000
#> GSM62312 2 0.000 0.996 0.000 1.000
#> GSM62313 2 0.000 0.996 0.000 1.000
#> GSM62314 2 0.000 0.996 0.000 1.000
#> GSM62319 2 0.000 0.996 0.000 1.000
#> GSM62320 2 0.000 0.996 0.000 1.000
#> GSM62249 1 0.000 1.000 1.000 0.000
#> GSM62251 1 0.000 1.000 1.000 0.000
#> GSM62263 2 0.000 0.996 0.000 1.000
#> GSM62285 2 0.000 0.996 0.000 1.000
#> GSM62315 2 0.000 0.996 0.000 1.000
#> GSM62291 2 0.000 0.996 0.000 1.000
#> GSM62265 1 0.000 1.000 1.000 0.000
#> GSM62266 1 0.000 1.000 1.000 0.000
#> GSM62296 2 0.000 0.996 0.000 1.000
#> GSM62309 2 0.000 0.996 0.000 1.000
#> GSM62295 2 0.000 0.996 0.000 1.000
#> GSM62300 2 0.000 0.996 0.000 1.000
#> GSM62308 2 0.000 0.996 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM62248 2 0.0892 0.964 0.000 0.980 0.020
#> GSM62256 2 0.3482 0.900 0.000 0.872 0.128
#> GSM62259 2 0.1529 0.976 0.000 0.960 0.040
#> GSM62267 1 0.0000 0.995 1.000 0.000 0.000
#> GSM62280 1 0.0000 0.995 1.000 0.000 0.000
#> GSM62284 1 0.0000 0.995 1.000 0.000 0.000
#> GSM62289 2 0.0237 0.964 0.000 0.996 0.004
#> GSM62307 2 0.1964 0.971 0.000 0.944 0.056
#> GSM62316 2 0.0747 0.965 0.000 0.984 0.016
#> GSM62254 2 0.1529 0.976 0.000 0.960 0.040
#> GSM62292 2 0.1529 0.976 0.000 0.960 0.040
#> GSM62253 1 0.0000 0.995 1.000 0.000 0.000
#> GSM62270 1 0.0000 0.995 1.000 0.000 0.000
#> GSM62278 1 0.0000 0.995 1.000 0.000 0.000
#> GSM62297 3 0.0000 0.971 0.000 0.000 1.000
#> GSM62298 3 0.0237 0.968 0.000 0.004 0.996
#> GSM62299 3 0.0000 0.971 0.000 0.000 1.000
#> GSM62258 1 0.0000 0.995 1.000 0.000 0.000
#> GSM62281 3 0.6126 0.270 0.000 0.400 0.600
#> GSM62294 2 0.1529 0.976 0.000 0.960 0.040
#> GSM62305 2 0.0424 0.964 0.000 0.992 0.008
#> GSM62306 2 0.0237 0.964 0.000 0.996 0.004
#> GSM62310 2 0.1860 0.972 0.000 0.948 0.052
#> GSM62311 2 0.1860 0.972 0.000 0.948 0.052
#> GSM62317 3 0.0000 0.971 0.000 0.000 1.000
#> GSM62318 1 0.0000 0.995 1.000 0.000 0.000
#> GSM62321 1 0.2878 0.893 0.904 0.000 0.096
#> GSM62322 1 0.0000 0.995 1.000 0.000 0.000
#> GSM62250 2 0.0237 0.964 0.000 0.996 0.004
#> GSM62252 2 0.1163 0.948 0.028 0.972 0.000
#> GSM62255 2 0.1860 0.972 0.000 0.948 0.052
#> GSM62257 2 0.1860 0.973 0.000 0.948 0.052
#> GSM62260 1 0.0000 0.995 1.000 0.000 0.000
#> GSM62261 2 0.0892 0.964 0.000 0.980 0.020
#> GSM62262 2 0.1529 0.976 0.000 0.960 0.040
#> GSM62264 1 0.0000 0.995 1.000 0.000 0.000
#> GSM62268 1 0.0000 0.995 1.000 0.000 0.000
#> GSM62269 1 0.0000 0.995 1.000 0.000 0.000
#> GSM62271 1 0.0000 0.995 1.000 0.000 0.000
#> GSM62272 1 0.0000 0.995 1.000 0.000 0.000
#> GSM62273 3 0.1289 0.949 0.000 0.032 0.968
#> GSM62274 1 0.0000 0.995 1.000 0.000 0.000
#> GSM62275 1 0.0000 0.995 1.000 0.000 0.000
#> GSM62276 1 0.0000 0.995 1.000 0.000 0.000
#> GSM62277 1 0.0000 0.995 1.000 0.000 0.000
#> GSM62279 1 0.0000 0.995 1.000 0.000 0.000
#> GSM62282 1 0.0000 0.995 1.000 0.000 0.000
#> GSM62283 1 0.0000 0.995 1.000 0.000 0.000
#> GSM62286 2 0.0000 0.964 0.000 1.000 0.000
#> GSM62287 2 0.1529 0.976 0.000 0.960 0.040
#> GSM62288 2 0.0892 0.964 0.000 0.980 0.020
#> GSM62290 3 0.0000 0.971 0.000 0.000 1.000
#> GSM62293 2 0.1529 0.976 0.000 0.960 0.040
#> GSM62301 3 0.0000 0.971 0.000 0.000 1.000
#> GSM62302 2 0.1529 0.976 0.000 0.960 0.040
#> GSM62303 2 0.1529 0.976 0.000 0.960 0.040
#> GSM62304 2 0.1643 0.975 0.000 0.956 0.044
#> GSM62312 3 0.0000 0.971 0.000 0.000 1.000
#> GSM62313 2 0.1529 0.976 0.000 0.960 0.040
#> GSM62314 2 0.0892 0.964 0.000 0.980 0.020
#> GSM62319 3 0.0747 0.960 0.000 0.016 0.984
#> GSM62320 3 0.0000 0.971 0.000 0.000 1.000
#> GSM62249 1 0.1765 0.957 0.956 0.040 0.004
#> GSM62251 1 0.0000 0.995 1.000 0.000 0.000
#> GSM62263 3 0.1529 0.935 0.000 0.040 0.960
#> GSM62285 3 0.0000 0.971 0.000 0.000 1.000
#> GSM62315 3 0.0000 0.971 0.000 0.000 1.000
#> GSM62291 3 0.0000 0.971 0.000 0.000 1.000
#> GSM62265 1 0.0000 0.995 1.000 0.000 0.000
#> GSM62266 1 0.0000 0.995 1.000 0.000 0.000
#> GSM62296 3 0.0000 0.971 0.000 0.000 1.000
#> GSM62309 3 0.0000 0.971 0.000 0.000 1.000
#> GSM62295 2 0.1529 0.976 0.000 0.960 0.040
#> GSM62300 3 0.0000 0.971 0.000 0.000 1.000
#> GSM62308 3 0.0000 0.971 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM62248 4 0.4522 0.732 0.000 0.000 0.320 0.680
#> GSM62256 4 0.1743 0.826 0.000 0.056 0.004 0.940
#> GSM62259 4 0.0524 0.849 0.000 0.004 0.008 0.988
#> GSM62267 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM62280 3 0.5000 0.664 0.496 0.000 0.504 0.000
#> GSM62284 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM62289 4 0.4877 0.671 0.000 0.000 0.408 0.592
#> GSM62307 4 0.0000 0.853 0.000 0.000 0.000 1.000
#> GSM62316 4 0.4283 0.764 0.000 0.004 0.256 0.740
#> GSM62254 4 0.0336 0.851 0.000 0.000 0.008 0.992
#> GSM62292 4 0.0336 0.851 0.000 0.000 0.008 0.992
#> GSM62253 1 0.0817 0.934 0.976 0.000 0.024 0.000
#> GSM62270 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM62278 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM62297 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM62298 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM62299 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM62258 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM62281 4 0.4761 0.383 0.000 0.372 0.000 0.628
#> GSM62294 4 0.0188 0.852 0.000 0.000 0.004 0.996
#> GSM62305 4 0.5774 0.589 0.000 0.028 0.464 0.508
#> GSM62306 4 0.4790 0.693 0.000 0.000 0.380 0.620
#> GSM62310 4 0.0000 0.853 0.000 0.000 0.000 1.000
#> GSM62311 4 0.0000 0.853 0.000 0.000 0.000 1.000
#> GSM62317 2 0.5000 0.218 0.000 0.504 0.496 0.000
#> GSM62318 3 0.4981 0.703 0.464 0.000 0.536 0.000
#> GSM62321 3 0.6538 0.680 0.292 0.108 0.600 0.000
#> GSM62322 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM62250 4 0.4977 0.619 0.000 0.000 0.460 0.540
#> GSM62252 4 0.6008 0.563 0.040 0.000 0.464 0.496
#> GSM62255 4 0.0000 0.853 0.000 0.000 0.000 1.000
#> GSM62257 4 0.0000 0.853 0.000 0.000 0.000 1.000
#> GSM62260 3 0.4855 0.758 0.400 0.000 0.600 0.000
#> GSM62261 4 0.4283 0.764 0.000 0.004 0.256 0.740
#> GSM62262 4 0.0336 0.851 0.000 0.000 0.008 0.992
#> GSM62264 3 0.4866 0.757 0.404 0.000 0.596 0.000
#> GSM62268 1 0.0817 0.934 0.976 0.000 0.024 0.000
#> GSM62269 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM62271 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM62272 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM62273 2 0.4697 0.569 0.000 0.696 0.008 0.296
#> GSM62274 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM62275 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM62276 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM62277 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM62279 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM62282 1 0.4277 0.137 0.720 0.000 0.280 0.000
#> GSM62283 1 0.0921 0.930 0.972 0.000 0.028 0.000
#> GSM62286 4 0.4877 0.671 0.000 0.000 0.408 0.592
#> GSM62287 4 0.0000 0.853 0.000 0.000 0.000 1.000
#> GSM62288 4 0.4608 0.739 0.000 0.004 0.304 0.692
#> GSM62290 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM62293 4 0.0336 0.851 0.000 0.000 0.008 0.992
#> GSM62301 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM62302 4 0.0000 0.853 0.000 0.000 0.000 1.000
#> GSM62303 4 0.0000 0.853 0.000 0.000 0.000 1.000
#> GSM62304 4 0.0000 0.853 0.000 0.000 0.000 1.000
#> GSM62312 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM62313 4 0.0000 0.853 0.000 0.000 0.000 1.000
#> GSM62314 4 0.3791 0.788 0.000 0.004 0.200 0.796
#> GSM62319 2 0.0672 0.919 0.000 0.984 0.008 0.008
#> GSM62320 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM62249 3 0.4679 0.387 0.352 0.000 0.648 0.000
#> GSM62251 1 0.2704 0.751 0.876 0.000 0.124 0.000
#> GSM62263 2 0.4304 0.629 0.000 0.716 0.284 0.000
#> GSM62285 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM62315 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM62291 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM62265 1 0.0921 0.930 0.972 0.000 0.028 0.000
#> GSM62266 1 0.0921 0.930 0.972 0.000 0.028 0.000
#> GSM62296 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM62309 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM62295 4 0.0524 0.849 0.000 0.004 0.008 0.988
#> GSM62300 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM62308 2 0.0000 0.931 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM62248 5 0.4510 0.3502 0.000 0.008 0.000 0.432 0.560
#> GSM62256 4 0.1774 0.8455 0.000 0.052 0.000 0.932 0.016
#> GSM62259 4 0.1956 0.8504 0.000 0.000 0.008 0.916 0.076
#> GSM62267 1 0.0162 0.9446 0.996 0.000 0.004 0.000 0.000
#> GSM62280 3 0.2074 0.8572 0.104 0.000 0.896 0.000 0.000
#> GSM62284 1 0.0000 0.9459 1.000 0.000 0.000 0.000 0.000
#> GSM62289 5 0.2074 0.7539 0.000 0.000 0.000 0.104 0.896
#> GSM62307 4 0.0579 0.8762 0.000 0.008 0.000 0.984 0.008
#> GSM62316 4 0.4298 0.2919 0.000 0.008 0.000 0.640 0.352
#> GSM62254 4 0.2017 0.8480 0.000 0.000 0.008 0.912 0.080
#> GSM62292 4 0.2017 0.8480 0.000 0.000 0.008 0.912 0.080
#> GSM62253 1 0.1956 0.9048 0.916 0.000 0.076 0.000 0.008
#> GSM62270 1 0.0000 0.9459 1.000 0.000 0.000 0.000 0.000
#> GSM62278 1 0.0000 0.9459 1.000 0.000 0.000 0.000 0.000
#> GSM62297 2 0.0000 0.9337 0.000 1.000 0.000 0.000 0.000
#> GSM62298 2 0.0000 0.9337 0.000 1.000 0.000 0.000 0.000
#> GSM62299 2 0.0000 0.9337 0.000 1.000 0.000 0.000 0.000
#> GSM62258 1 0.0000 0.9459 1.000 0.000 0.000 0.000 0.000
#> GSM62281 4 0.3522 0.6650 0.000 0.212 0.004 0.780 0.004
#> GSM62294 4 0.1041 0.8680 0.000 0.000 0.004 0.964 0.032
#> GSM62305 5 0.1282 0.7092 0.000 0.004 0.000 0.044 0.952
#> GSM62306 5 0.3003 0.7241 0.000 0.000 0.000 0.188 0.812
#> GSM62310 4 0.0579 0.8762 0.000 0.008 0.000 0.984 0.008
#> GSM62311 4 0.0579 0.8762 0.000 0.008 0.000 0.984 0.008
#> GSM62317 3 0.2127 0.8394 0.000 0.108 0.892 0.000 0.000
#> GSM62318 3 0.0510 0.9331 0.016 0.000 0.984 0.000 0.000
#> GSM62321 3 0.0451 0.9327 0.008 0.004 0.988 0.000 0.000
#> GSM62322 1 0.0000 0.9459 1.000 0.000 0.000 0.000 0.000
#> GSM62250 5 0.2020 0.7528 0.000 0.000 0.000 0.100 0.900
#> GSM62252 5 0.2116 0.7393 0.008 0.000 0.004 0.076 0.912
#> GSM62255 4 0.0579 0.8762 0.000 0.008 0.000 0.984 0.008
#> GSM62257 4 0.0579 0.8762 0.000 0.008 0.000 0.984 0.008
#> GSM62260 3 0.0807 0.9325 0.012 0.000 0.976 0.000 0.012
#> GSM62261 4 0.4403 0.1819 0.000 0.008 0.000 0.608 0.384
#> GSM62262 4 0.2017 0.8480 0.000 0.000 0.008 0.912 0.080
#> GSM62264 3 0.1211 0.9240 0.016 0.000 0.960 0.000 0.024
#> GSM62268 1 0.1956 0.9048 0.916 0.000 0.076 0.000 0.008
#> GSM62269 1 0.0000 0.9459 1.000 0.000 0.000 0.000 0.000
#> GSM62271 1 0.0000 0.9459 1.000 0.000 0.000 0.000 0.000
#> GSM62272 1 0.0000 0.9459 1.000 0.000 0.000 0.000 0.000
#> GSM62273 2 0.5981 0.0707 0.000 0.476 0.008 0.432 0.084
#> GSM62274 1 0.0000 0.9459 1.000 0.000 0.000 0.000 0.000
#> GSM62275 1 0.0000 0.9459 1.000 0.000 0.000 0.000 0.000
#> GSM62276 1 0.0162 0.9446 0.996 0.000 0.004 0.000 0.000
#> GSM62277 1 0.0000 0.9459 1.000 0.000 0.000 0.000 0.000
#> GSM62279 1 0.0162 0.9446 0.996 0.000 0.004 0.000 0.000
#> GSM62282 1 0.4101 0.3601 0.628 0.000 0.372 0.000 0.000
#> GSM62283 1 0.2046 0.9083 0.916 0.000 0.068 0.000 0.016
#> GSM62286 5 0.2020 0.7539 0.000 0.000 0.000 0.100 0.900
#> GSM62287 4 0.0290 0.8761 0.000 0.000 0.000 0.992 0.008
#> GSM62288 5 0.4552 0.2473 0.000 0.008 0.000 0.468 0.524
#> GSM62290 2 0.0000 0.9337 0.000 1.000 0.000 0.000 0.000
#> GSM62293 4 0.2017 0.8480 0.000 0.000 0.008 0.912 0.080
#> GSM62301 2 0.0000 0.9337 0.000 1.000 0.000 0.000 0.000
#> GSM62302 4 0.0324 0.8764 0.000 0.000 0.004 0.992 0.004
#> GSM62303 4 0.0324 0.8764 0.000 0.000 0.004 0.992 0.004
#> GSM62304 4 0.0579 0.8762 0.000 0.008 0.000 0.984 0.008
#> GSM62312 2 0.0510 0.9195 0.000 0.984 0.000 0.016 0.000
#> GSM62313 4 0.0290 0.8761 0.000 0.000 0.000 0.992 0.008
#> GSM62314 4 0.3980 0.4738 0.000 0.008 0.000 0.708 0.284
#> GSM62319 2 0.2289 0.8518 0.000 0.904 0.004 0.012 0.080
#> GSM62320 2 0.0000 0.9337 0.000 1.000 0.000 0.000 0.000
#> GSM62249 5 0.6667 -0.0536 0.244 0.000 0.328 0.000 0.428
#> GSM62251 1 0.3821 0.7957 0.800 0.000 0.148 0.000 0.052
#> GSM62263 2 0.4762 0.5766 0.000 0.700 0.236 0.000 0.064
#> GSM62285 2 0.0000 0.9337 0.000 1.000 0.000 0.000 0.000
#> GSM62315 2 0.0000 0.9337 0.000 1.000 0.000 0.000 0.000
#> GSM62291 2 0.0000 0.9337 0.000 1.000 0.000 0.000 0.000
#> GSM62265 1 0.2351 0.8927 0.896 0.000 0.088 0.000 0.016
#> GSM62266 1 0.2136 0.8980 0.904 0.000 0.088 0.000 0.008
#> GSM62296 2 0.0000 0.9337 0.000 1.000 0.000 0.000 0.000
#> GSM62309 2 0.0000 0.9337 0.000 1.000 0.000 0.000 0.000
#> GSM62295 4 0.2302 0.8419 0.000 0.008 0.008 0.904 0.080
#> GSM62300 2 0.0000 0.9337 0.000 1.000 0.000 0.000 0.000
#> GSM62308 2 0.0000 0.9337 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM62248 5 0.5324 0.05426 0.104 0.000 0.000 0.428 0.468 0.000
#> GSM62256 4 0.3679 0.73019 0.124 0.024 0.000 0.812 0.036 0.004
#> GSM62259 4 0.3511 0.75702 0.216 0.000 0.000 0.760 0.024 0.000
#> GSM62267 3 0.0146 0.90188 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM62280 6 0.1444 0.75299 0.000 0.000 0.072 0.000 0.000 0.928
#> GSM62284 3 0.0363 0.89719 0.012 0.000 0.988 0.000 0.000 0.000
#> GSM62289 5 0.0993 0.79430 0.012 0.000 0.000 0.024 0.964 0.000
#> GSM62307 4 0.1967 0.77747 0.084 0.000 0.000 0.904 0.012 0.000
#> GSM62316 4 0.4914 0.42894 0.104 0.000 0.000 0.628 0.268 0.000
#> GSM62254 4 0.3301 0.73143 0.188 0.000 0.000 0.788 0.024 0.000
#> GSM62292 4 0.3301 0.73143 0.188 0.000 0.000 0.788 0.024 0.000
#> GSM62253 3 0.3394 0.65840 0.144 0.000 0.804 0.000 0.000 0.052
#> GSM62270 3 0.0000 0.90348 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62278 3 0.0000 0.90348 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62297 2 0.0458 0.89647 0.016 0.984 0.000 0.000 0.000 0.000
#> GSM62298 2 0.0363 0.89799 0.012 0.988 0.000 0.000 0.000 0.000
#> GSM62299 2 0.0363 0.89799 0.012 0.988 0.000 0.000 0.000 0.000
#> GSM62258 3 0.0000 0.90348 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62281 4 0.4560 0.61194 0.088 0.212 0.000 0.696 0.000 0.004
#> GSM62294 4 0.1895 0.78965 0.072 0.000 0.000 0.912 0.016 0.000
#> GSM62305 5 0.3010 0.74653 0.148 0.000 0.000 0.020 0.828 0.004
#> GSM62306 5 0.4634 0.67517 0.164 0.000 0.000 0.144 0.692 0.000
#> GSM62310 4 0.0405 0.80335 0.008 0.000 0.000 0.988 0.004 0.000
#> GSM62311 4 0.0291 0.80371 0.004 0.000 0.000 0.992 0.004 0.000
#> GSM62317 6 0.1327 0.76601 0.000 0.064 0.000 0.000 0.000 0.936
#> GSM62318 6 0.0146 0.80239 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM62321 6 0.0000 0.80346 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM62322 3 0.0000 0.90348 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62250 5 0.0777 0.79462 0.004 0.000 0.000 0.024 0.972 0.000
#> GSM62252 5 0.1152 0.76323 0.044 0.000 0.000 0.004 0.952 0.000
#> GSM62255 4 0.1010 0.79826 0.036 0.000 0.000 0.960 0.004 0.000
#> GSM62257 4 0.2006 0.77717 0.080 0.000 0.000 0.904 0.016 0.000
#> GSM62260 6 0.3930 0.11887 0.420 0.000 0.004 0.000 0.000 0.576
#> GSM62261 4 0.5025 0.38370 0.108 0.000 0.000 0.608 0.284 0.000
#> GSM62262 4 0.3062 0.74707 0.160 0.000 0.000 0.816 0.024 0.000
#> GSM62264 1 0.4152 -0.02767 0.548 0.000 0.012 0.000 0.000 0.440
#> GSM62268 3 0.3254 0.67976 0.136 0.000 0.816 0.000 0.000 0.048
#> GSM62269 3 0.0000 0.90348 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62271 3 0.0146 0.90108 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM62272 3 0.0000 0.90348 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62273 2 0.6565 0.02241 0.216 0.404 0.000 0.352 0.024 0.004
#> GSM62274 3 0.0146 0.90188 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM62275 3 0.0000 0.90348 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62276 3 0.0000 0.90348 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62277 3 0.0000 0.90348 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62279 3 0.0632 0.88786 0.024 0.000 0.976 0.000 0.000 0.000
#> GSM62282 3 0.3737 0.25292 0.000 0.000 0.608 0.000 0.000 0.392
#> GSM62283 1 0.4653 0.63097 0.588 0.000 0.360 0.000 0.000 0.052
#> GSM62286 5 0.0858 0.79364 0.004 0.000 0.000 0.028 0.968 0.000
#> GSM62287 4 0.0547 0.80405 0.020 0.000 0.000 0.980 0.000 0.000
#> GSM62288 4 0.5368 -0.00276 0.112 0.000 0.000 0.488 0.400 0.000
#> GSM62290 2 0.0000 0.90122 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62293 4 0.3236 0.73598 0.180 0.000 0.000 0.796 0.024 0.000
#> GSM62301 2 0.0000 0.90122 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62302 4 0.0790 0.80352 0.032 0.000 0.000 0.968 0.000 0.000
#> GSM62303 4 0.0865 0.80304 0.036 0.000 0.000 0.964 0.000 0.000
#> GSM62304 4 0.1333 0.79319 0.048 0.000 0.000 0.944 0.008 0.000
#> GSM62312 2 0.3565 0.72675 0.096 0.808 0.000 0.092 0.004 0.000
#> GSM62313 4 0.0260 0.80433 0.008 0.000 0.000 0.992 0.000 0.000
#> GSM62314 4 0.4704 0.49515 0.100 0.000 0.000 0.664 0.236 0.000
#> GSM62319 2 0.3452 0.72355 0.176 0.792 0.000 0.008 0.024 0.000
#> GSM62320 2 0.0363 0.89799 0.012 0.988 0.000 0.000 0.000 0.000
#> GSM62249 1 0.5771 0.42221 0.628 0.000 0.060 0.000 0.188 0.124
#> GSM62251 1 0.5679 0.65860 0.588 0.000 0.284 0.000 0.048 0.080
#> GSM62263 2 0.5257 0.37850 0.292 0.596 0.000 0.000 0.008 0.104
#> GSM62285 2 0.0000 0.90122 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62315 2 0.0000 0.90122 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62291 2 0.0000 0.90122 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62265 1 0.4899 0.53652 0.532 0.000 0.404 0.000 0.000 0.064
#> GSM62266 3 0.4604 0.18015 0.300 0.000 0.636 0.000 0.000 0.064
#> GSM62296 2 0.0000 0.90122 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62309 2 0.0000 0.90122 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62295 4 0.3394 0.72399 0.200 0.000 0.000 0.776 0.024 0.000
#> GSM62300 2 0.0000 0.90122 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62308 2 0.0000 0.90122 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) other(p) genotype/variation(p) k
#> SD:skmeans 75 0.823665 1.000 0.8057 2
#> SD:skmeans 74 0.001421 0.752 0.0372 3
#> SD:skmeans 71 0.001238 0.907 0.1004 4
#> SD:skmeans 67 0.003010 0.933 0.2783 5
#> SD:skmeans 63 0.000344 0.471 0.3397 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "pam"]
# you can also extract it by
# res = res_list["SD:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 75 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 0.946 0.979 0.4536 0.559 0.559
#> 3 3 0.728 0.886 0.926 0.2584 0.803 0.669
#> 4 4 0.967 0.913 0.963 0.2582 0.764 0.505
#> 5 5 0.916 0.858 0.935 0.0409 0.969 0.889
#> 6 6 0.940 0.847 0.941 0.0305 0.952 0.818
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 4 5
There is also optional best \(k\) = 2 4 5 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM62248 2 0.000 0.969 0.000 1.000
#> GSM62256 2 0.000 0.969 0.000 1.000
#> GSM62259 2 0.000 0.969 0.000 1.000
#> GSM62267 1 0.000 0.996 1.000 0.000
#> GSM62280 1 0.000 0.996 1.000 0.000
#> GSM62284 1 0.000 0.996 1.000 0.000
#> GSM62289 2 0.000 0.969 0.000 1.000
#> GSM62307 2 0.000 0.969 0.000 1.000
#> GSM62316 2 0.000 0.969 0.000 1.000
#> GSM62254 2 0.000 0.969 0.000 1.000
#> GSM62292 2 0.000 0.969 0.000 1.000
#> GSM62253 1 0.000 0.996 1.000 0.000
#> GSM62270 1 0.000 0.996 1.000 0.000
#> GSM62278 1 0.000 0.996 1.000 0.000
#> GSM62297 2 0.000 0.969 0.000 1.000
#> GSM62298 2 0.000 0.969 0.000 1.000
#> GSM62299 2 0.000 0.969 0.000 1.000
#> GSM62258 1 0.000 0.996 1.000 0.000
#> GSM62281 2 0.000 0.969 0.000 1.000
#> GSM62294 2 0.000 0.969 0.000 1.000
#> GSM62305 2 0.373 0.904 0.072 0.928
#> GSM62306 2 0.000 0.969 0.000 1.000
#> GSM62310 2 0.000 0.969 0.000 1.000
#> GSM62311 2 0.000 0.969 0.000 1.000
#> GSM62317 2 0.000 0.969 0.000 1.000
#> GSM62318 1 0.000 0.996 1.000 0.000
#> GSM62321 2 0.961 0.389 0.384 0.616
#> GSM62322 1 0.000 0.996 1.000 0.000
#> GSM62250 2 0.000 0.969 0.000 1.000
#> GSM62252 2 0.373 0.904 0.072 0.928
#> GSM62255 2 0.000 0.969 0.000 1.000
#> GSM62257 2 0.000 0.969 0.000 1.000
#> GSM62260 2 0.994 0.204 0.456 0.544
#> GSM62261 2 0.000 0.969 0.000 1.000
#> GSM62262 2 0.000 0.969 0.000 1.000
#> GSM62264 1 0.416 0.903 0.916 0.084
#> GSM62268 1 0.000 0.996 1.000 0.000
#> GSM62269 1 0.000 0.996 1.000 0.000
#> GSM62271 1 0.000 0.996 1.000 0.000
#> GSM62272 1 0.000 0.996 1.000 0.000
#> GSM62273 2 0.000 0.969 0.000 1.000
#> GSM62274 1 0.000 0.996 1.000 0.000
#> GSM62275 1 0.000 0.996 1.000 0.000
#> GSM62276 1 0.000 0.996 1.000 0.000
#> GSM62277 1 0.000 0.996 1.000 0.000
#> GSM62279 1 0.000 0.996 1.000 0.000
#> GSM62282 1 0.000 0.996 1.000 0.000
#> GSM62283 1 0.000 0.996 1.000 0.000
#> GSM62286 2 0.000 0.969 0.000 1.000
#> GSM62287 2 0.000 0.969 0.000 1.000
#> GSM62288 2 0.000 0.969 0.000 1.000
#> GSM62290 2 0.000 0.969 0.000 1.000
#> GSM62293 2 0.000 0.969 0.000 1.000
#> GSM62301 2 0.000 0.969 0.000 1.000
#> GSM62302 2 0.000 0.969 0.000 1.000
#> GSM62303 2 0.000 0.969 0.000 1.000
#> GSM62304 2 0.000 0.969 0.000 1.000
#> GSM62312 2 0.000 0.969 0.000 1.000
#> GSM62313 2 0.000 0.969 0.000 1.000
#> GSM62314 2 0.000 0.969 0.000 1.000
#> GSM62319 2 0.373 0.904 0.072 0.928
#> GSM62320 2 0.000 0.969 0.000 1.000
#> GSM62249 2 0.994 0.204 0.456 0.544
#> GSM62251 1 0.000 0.996 1.000 0.000
#> GSM62263 2 0.000 0.969 0.000 1.000
#> GSM62285 2 0.000 0.969 0.000 1.000
#> GSM62315 2 0.000 0.969 0.000 1.000
#> GSM62291 2 0.000 0.969 0.000 1.000
#> GSM62265 1 0.000 0.996 1.000 0.000
#> GSM62266 1 0.000 0.996 1.000 0.000
#> GSM62296 2 0.000 0.969 0.000 1.000
#> GSM62309 2 0.000 0.969 0.000 1.000
#> GSM62295 2 0.000 0.969 0.000 1.000
#> GSM62300 2 0.000 0.969 0.000 1.000
#> GSM62308 2 0.000 0.969 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM62248 2 0.0000 0.950 0.000 1.000 0.000
#> GSM62256 2 0.0000 0.950 0.000 1.000 0.000
#> GSM62259 2 0.0000 0.950 0.000 1.000 0.000
#> GSM62267 1 0.3686 0.874 0.860 0.000 0.140
#> GSM62280 1 0.3686 0.874 0.860 0.000 0.140
#> GSM62284 3 0.5591 0.507 0.304 0.000 0.696
#> GSM62289 2 0.0000 0.950 0.000 1.000 0.000
#> GSM62307 2 0.0000 0.950 0.000 1.000 0.000
#> GSM62316 2 0.0000 0.950 0.000 1.000 0.000
#> GSM62254 2 0.0000 0.950 0.000 1.000 0.000
#> GSM62292 2 0.0000 0.950 0.000 1.000 0.000
#> GSM62253 1 0.3941 0.861 0.844 0.000 0.156
#> GSM62270 3 0.0000 0.926 0.000 0.000 1.000
#> GSM62278 3 0.0424 0.922 0.008 0.000 0.992
#> GSM62297 2 0.3686 0.900 0.140 0.860 0.000
#> GSM62298 2 0.3686 0.900 0.140 0.860 0.000
#> GSM62299 2 0.3686 0.900 0.140 0.860 0.000
#> GSM62258 1 0.3686 0.874 0.860 0.000 0.140
#> GSM62281 2 0.0000 0.950 0.000 1.000 0.000
#> GSM62294 2 0.0000 0.950 0.000 1.000 0.000
#> GSM62305 1 0.5810 0.313 0.664 0.336 0.000
#> GSM62306 2 0.0000 0.950 0.000 1.000 0.000
#> GSM62310 2 0.0000 0.950 0.000 1.000 0.000
#> GSM62311 2 0.0000 0.950 0.000 1.000 0.000
#> GSM62317 2 0.3686 0.900 0.140 0.860 0.000
#> GSM62318 1 0.3686 0.874 0.860 0.000 0.140
#> GSM62321 1 0.0000 0.788 1.000 0.000 0.000
#> GSM62322 3 0.0000 0.926 0.000 0.000 1.000
#> GSM62250 2 0.0000 0.950 0.000 1.000 0.000
#> GSM62252 1 0.5254 0.571 0.736 0.264 0.000
#> GSM62255 2 0.0000 0.950 0.000 1.000 0.000
#> GSM62257 2 0.0000 0.950 0.000 1.000 0.000
#> GSM62260 1 0.2537 0.845 0.920 0.000 0.080
#> GSM62261 2 0.0000 0.950 0.000 1.000 0.000
#> GSM62262 2 0.0000 0.950 0.000 1.000 0.000
#> GSM62264 1 0.3686 0.874 0.860 0.000 0.140
#> GSM62268 1 0.4796 0.790 0.780 0.000 0.220
#> GSM62269 3 0.0000 0.926 0.000 0.000 1.000
#> GSM62271 1 0.3686 0.874 0.860 0.000 0.140
#> GSM62272 3 0.0000 0.926 0.000 0.000 1.000
#> GSM62273 2 0.3686 0.900 0.140 0.860 0.000
#> GSM62274 3 0.4291 0.743 0.180 0.000 0.820
#> GSM62275 3 0.0000 0.926 0.000 0.000 1.000
#> GSM62276 1 0.3686 0.874 0.860 0.000 0.140
#> GSM62277 3 0.0000 0.926 0.000 0.000 1.000
#> GSM62279 1 0.3686 0.874 0.860 0.000 0.140
#> GSM62282 1 0.3686 0.874 0.860 0.000 0.140
#> GSM62283 1 0.1163 0.812 0.972 0.000 0.028
#> GSM62286 2 0.0000 0.950 0.000 1.000 0.000
#> GSM62287 2 0.0000 0.950 0.000 1.000 0.000
#> GSM62288 2 0.0000 0.950 0.000 1.000 0.000
#> GSM62290 2 0.3686 0.900 0.140 0.860 0.000
#> GSM62293 2 0.0000 0.950 0.000 1.000 0.000
#> GSM62301 2 0.3686 0.900 0.140 0.860 0.000
#> GSM62302 2 0.0000 0.950 0.000 1.000 0.000
#> GSM62303 2 0.0000 0.950 0.000 1.000 0.000
#> GSM62304 2 0.0000 0.950 0.000 1.000 0.000
#> GSM62312 2 0.0000 0.950 0.000 1.000 0.000
#> GSM62313 2 0.0000 0.950 0.000 1.000 0.000
#> GSM62314 2 0.0000 0.950 0.000 1.000 0.000
#> GSM62319 1 0.3619 0.623 0.864 0.136 0.000
#> GSM62320 2 0.3340 0.908 0.120 0.880 0.000
#> GSM62249 1 0.0747 0.803 0.984 0.000 0.016
#> GSM62251 1 0.3686 0.874 0.860 0.000 0.140
#> GSM62263 1 0.0592 0.779 0.988 0.012 0.000
#> GSM62285 2 0.3686 0.900 0.140 0.860 0.000
#> GSM62315 2 0.3686 0.900 0.140 0.860 0.000
#> GSM62291 2 0.3686 0.900 0.140 0.860 0.000
#> GSM62265 1 0.3686 0.874 0.860 0.000 0.140
#> GSM62266 1 0.3686 0.874 0.860 0.000 0.140
#> GSM62296 2 0.3686 0.900 0.140 0.860 0.000
#> GSM62309 2 0.4121 0.876 0.168 0.832 0.000
#> GSM62295 2 0.0592 0.947 0.012 0.988 0.000
#> GSM62300 2 0.3686 0.900 0.140 0.860 0.000
#> GSM62308 2 0.3686 0.900 0.140 0.860 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM62248 4 0.0000 0.982 0.000 0.000 0.000 1.000
#> GSM62256 4 0.0000 0.982 0.000 0.000 0.000 1.000
#> GSM62259 4 0.0000 0.982 0.000 0.000 0.000 1.000
#> GSM62267 1 0.0817 0.961 0.976 0.000 0.024 0.000
#> GSM62280 1 0.0376 0.950 0.992 0.004 0.004 0.000
#> GSM62284 1 0.4843 0.331 0.604 0.000 0.396 0.000
#> GSM62289 4 0.0000 0.982 0.000 0.000 0.000 1.000
#> GSM62307 4 0.0000 0.982 0.000 0.000 0.000 1.000
#> GSM62316 4 0.0000 0.982 0.000 0.000 0.000 1.000
#> GSM62254 4 0.0000 0.982 0.000 0.000 0.000 1.000
#> GSM62292 4 0.0000 0.982 0.000 0.000 0.000 1.000
#> GSM62253 1 0.1022 0.956 0.968 0.000 0.032 0.000
#> GSM62270 3 0.0188 0.936 0.004 0.000 0.996 0.000
#> GSM62278 3 0.2408 0.852 0.104 0.000 0.896 0.000
#> GSM62297 2 0.0188 0.929 0.000 0.996 0.000 0.004
#> GSM62298 2 0.0188 0.929 0.000 0.996 0.000 0.004
#> GSM62299 2 0.0188 0.929 0.000 0.996 0.000 0.004
#> GSM62258 1 0.0817 0.961 0.976 0.000 0.024 0.000
#> GSM62281 4 0.0000 0.982 0.000 0.000 0.000 1.000
#> GSM62294 4 0.0000 0.982 0.000 0.000 0.000 1.000
#> GSM62305 2 0.0779 0.915 0.016 0.980 0.000 0.004
#> GSM62306 4 0.0000 0.982 0.000 0.000 0.000 1.000
#> GSM62310 4 0.0000 0.982 0.000 0.000 0.000 1.000
#> GSM62311 4 0.0000 0.982 0.000 0.000 0.000 1.000
#> GSM62317 2 0.1004 0.907 0.024 0.972 0.004 0.000
#> GSM62318 1 0.0376 0.950 0.992 0.004 0.004 0.000
#> GSM62321 2 0.3791 0.710 0.200 0.796 0.004 0.000
#> GSM62322 3 0.0188 0.936 0.004 0.000 0.996 0.000
#> GSM62250 4 0.0000 0.982 0.000 0.000 0.000 1.000
#> GSM62252 4 0.5784 0.220 0.412 0.032 0.000 0.556
#> GSM62255 4 0.0000 0.982 0.000 0.000 0.000 1.000
#> GSM62257 4 0.0000 0.982 0.000 0.000 0.000 1.000
#> GSM62260 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM62261 4 0.0000 0.982 0.000 0.000 0.000 1.000
#> GSM62262 4 0.0000 0.982 0.000 0.000 0.000 1.000
#> GSM62264 1 0.0000 0.954 1.000 0.000 0.000 0.000
#> GSM62268 1 0.1211 0.950 0.960 0.000 0.040 0.000
#> GSM62269 3 0.0188 0.936 0.004 0.000 0.996 0.000
#> GSM62271 1 0.0817 0.961 0.976 0.000 0.024 0.000
#> GSM62272 3 0.0188 0.936 0.004 0.000 0.996 0.000
#> GSM62273 2 0.0336 0.926 0.000 0.992 0.000 0.008
#> GSM62274 3 0.4454 0.524 0.308 0.000 0.692 0.000
#> GSM62275 3 0.0188 0.936 0.004 0.000 0.996 0.000
#> GSM62276 1 0.0817 0.961 0.976 0.000 0.024 0.000
#> GSM62277 3 0.0188 0.936 0.004 0.000 0.996 0.000
#> GSM62279 1 0.0817 0.961 0.976 0.000 0.024 0.000
#> GSM62282 1 0.0376 0.950 0.992 0.004 0.004 0.000
#> GSM62283 1 0.0921 0.943 0.972 0.028 0.000 0.000
#> GSM62286 4 0.0000 0.982 0.000 0.000 0.000 1.000
#> GSM62287 4 0.0000 0.982 0.000 0.000 0.000 1.000
#> GSM62288 4 0.0000 0.982 0.000 0.000 0.000 1.000
#> GSM62290 2 0.0188 0.929 0.000 0.996 0.000 0.004
#> GSM62293 4 0.0000 0.982 0.000 0.000 0.000 1.000
#> GSM62301 2 0.0188 0.929 0.000 0.996 0.000 0.004
#> GSM62302 4 0.0000 0.982 0.000 0.000 0.000 1.000
#> GSM62303 4 0.0000 0.982 0.000 0.000 0.000 1.000
#> GSM62304 4 0.0000 0.982 0.000 0.000 0.000 1.000
#> GSM62312 4 0.0188 0.978 0.000 0.004 0.000 0.996
#> GSM62313 4 0.0000 0.982 0.000 0.000 0.000 1.000
#> GSM62314 4 0.0000 0.982 0.000 0.000 0.000 1.000
#> GSM62319 2 0.0188 0.929 0.000 0.996 0.000 0.004
#> GSM62320 2 0.4948 0.247 0.000 0.560 0.000 0.440
#> GSM62249 1 0.0921 0.943 0.972 0.028 0.000 0.000
#> GSM62251 1 0.0817 0.961 0.976 0.000 0.024 0.000
#> GSM62263 2 0.0188 0.925 0.004 0.996 0.000 0.000
#> GSM62285 2 0.0188 0.929 0.000 0.996 0.000 0.004
#> GSM62315 2 0.0188 0.929 0.000 0.996 0.000 0.004
#> GSM62291 2 0.0188 0.929 0.000 0.996 0.000 0.004
#> GSM62265 1 0.0817 0.961 0.976 0.000 0.024 0.000
#> GSM62266 1 0.0817 0.961 0.976 0.000 0.024 0.000
#> GSM62296 2 0.0188 0.929 0.000 0.996 0.000 0.004
#> GSM62309 2 0.0188 0.929 0.000 0.996 0.000 0.004
#> GSM62295 2 0.4679 0.480 0.000 0.648 0.000 0.352
#> GSM62300 2 0.0188 0.929 0.000 0.996 0.000 0.004
#> GSM62308 2 0.0188 0.929 0.000 0.996 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM62248 4 0.0000 0.9793 0.000 0.000 0.000 1.000 0.000
#> GSM62256 4 0.0000 0.9793 0.000 0.000 0.000 1.000 0.000
#> GSM62259 4 0.0000 0.9793 0.000 0.000 0.000 1.000 0.000
#> GSM62267 1 0.0000 0.8155 1.000 0.000 0.000 0.000 0.000
#> GSM62280 5 0.3210 0.7775 0.212 0.000 0.000 0.000 0.788
#> GSM62284 1 0.6603 0.1715 0.400 0.000 0.388 0.000 0.212
#> GSM62289 4 0.0000 0.9793 0.000 0.000 0.000 1.000 0.000
#> GSM62307 4 0.0000 0.9793 0.000 0.000 0.000 1.000 0.000
#> GSM62316 4 0.0000 0.9793 0.000 0.000 0.000 1.000 0.000
#> GSM62254 4 0.0000 0.9793 0.000 0.000 0.000 1.000 0.000
#> GSM62292 4 0.0000 0.9793 0.000 0.000 0.000 1.000 0.000
#> GSM62253 1 0.3877 0.7921 0.764 0.000 0.024 0.000 0.212
#> GSM62270 3 0.0000 0.9393 0.000 0.000 1.000 0.000 0.000
#> GSM62278 3 0.0000 0.9393 0.000 0.000 1.000 0.000 0.000
#> GSM62297 2 0.0000 0.9105 0.000 1.000 0.000 0.000 0.000
#> GSM62298 2 0.0000 0.9105 0.000 1.000 0.000 0.000 0.000
#> GSM62299 2 0.0000 0.9105 0.000 1.000 0.000 0.000 0.000
#> GSM62258 1 0.0000 0.8155 1.000 0.000 0.000 0.000 0.000
#> GSM62281 4 0.0000 0.9793 0.000 0.000 0.000 1.000 0.000
#> GSM62294 4 0.0000 0.9793 0.000 0.000 0.000 1.000 0.000
#> GSM62305 2 0.2753 0.7477 0.136 0.856 0.000 0.008 0.000
#> GSM62306 4 0.0000 0.9793 0.000 0.000 0.000 1.000 0.000
#> GSM62310 4 0.0000 0.9793 0.000 0.000 0.000 1.000 0.000
#> GSM62311 4 0.0000 0.9793 0.000 0.000 0.000 1.000 0.000
#> GSM62317 5 0.3730 0.6089 0.000 0.288 0.000 0.000 0.712
#> GSM62318 5 0.0000 0.6904 0.000 0.000 0.000 0.000 1.000
#> GSM62321 5 0.4123 0.7799 0.104 0.108 0.000 0.000 0.788
#> GSM62322 3 0.0000 0.9393 0.000 0.000 1.000 0.000 0.000
#> GSM62250 4 0.0000 0.9793 0.000 0.000 0.000 1.000 0.000
#> GSM62252 4 0.4451 0.0734 0.492 0.004 0.000 0.504 0.000
#> GSM62255 4 0.0000 0.9793 0.000 0.000 0.000 1.000 0.000
#> GSM62257 4 0.0000 0.9793 0.000 0.000 0.000 1.000 0.000
#> GSM62260 1 0.2230 0.7137 0.884 0.000 0.000 0.000 0.116
#> GSM62261 4 0.0000 0.9793 0.000 0.000 0.000 1.000 0.000
#> GSM62262 4 0.0000 0.9793 0.000 0.000 0.000 1.000 0.000
#> GSM62264 1 0.3305 0.8001 0.776 0.000 0.000 0.000 0.224
#> GSM62268 1 0.4818 0.7476 0.708 0.000 0.080 0.000 0.212
#> GSM62269 3 0.0000 0.9393 0.000 0.000 1.000 0.000 0.000
#> GSM62271 1 0.0000 0.8155 1.000 0.000 0.000 0.000 0.000
#> GSM62272 3 0.0000 0.9393 0.000 0.000 1.000 0.000 0.000
#> GSM62273 2 0.0963 0.8710 0.000 0.964 0.000 0.036 0.000
#> GSM62274 3 0.5607 0.4915 0.228 0.000 0.632 0.000 0.140
#> GSM62275 3 0.0000 0.9393 0.000 0.000 1.000 0.000 0.000
#> GSM62276 1 0.0000 0.8155 1.000 0.000 0.000 0.000 0.000
#> GSM62277 3 0.0000 0.9393 0.000 0.000 1.000 0.000 0.000
#> GSM62279 1 0.2074 0.8175 0.896 0.000 0.000 0.000 0.104
#> GSM62282 5 0.3366 0.7679 0.232 0.000 0.000 0.000 0.768
#> GSM62283 1 0.0000 0.8155 1.000 0.000 0.000 0.000 0.000
#> GSM62286 4 0.0000 0.9793 0.000 0.000 0.000 1.000 0.000
#> GSM62287 4 0.0000 0.9793 0.000 0.000 0.000 1.000 0.000
#> GSM62288 4 0.0000 0.9793 0.000 0.000 0.000 1.000 0.000
#> GSM62290 2 0.0000 0.9105 0.000 1.000 0.000 0.000 0.000
#> GSM62293 4 0.0000 0.9793 0.000 0.000 0.000 1.000 0.000
#> GSM62301 2 0.0000 0.9105 0.000 1.000 0.000 0.000 0.000
#> GSM62302 4 0.0000 0.9793 0.000 0.000 0.000 1.000 0.000
#> GSM62303 4 0.0000 0.9793 0.000 0.000 0.000 1.000 0.000
#> GSM62304 4 0.0000 0.9793 0.000 0.000 0.000 1.000 0.000
#> GSM62312 4 0.0880 0.9438 0.000 0.032 0.000 0.968 0.000
#> GSM62313 4 0.0000 0.9793 0.000 0.000 0.000 1.000 0.000
#> GSM62314 4 0.0000 0.9793 0.000 0.000 0.000 1.000 0.000
#> GSM62319 2 0.0000 0.9105 0.000 1.000 0.000 0.000 0.000
#> GSM62320 2 0.4256 0.2493 0.000 0.564 0.000 0.436 0.000
#> GSM62249 1 0.2773 0.6741 0.836 0.164 0.000 0.000 0.000
#> GSM62251 1 0.3210 0.8026 0.788 0.000 0.000 0.000 0.212
#> GSM62263 2 0.0290 0.9035 0.008 0.992 0.000 0.000 0.000
#> GSM62285 2 0.0000 0.9105 0.000 1.000 0.000 0.000 0.000
#> GSM62315 2 0.0000 0.9105 0.000 1.000 0.000 0.000 0.000
#> GSM62291 2 0.0000 0.9105 0.000 1.000 0.000 0.000 0.000
#> GSM62265 1 0.2127 0.8179 0.892 0.000 0.000 0.000 0.108
#> GSM62266 1 0.3210 0.8026 0.788 0.000 0.000 0.000 0.212
#> GSM62296 2 0.0000 0.9105 0.000 1.000 0.000 0.000 0.000
#> GSM62309 2 0.0000 0.9105 0.000 1.000 0.000 0.000 0.000
#> GSM62295 2 0.4030 0.3797 0.000 0.648 0.000 0.352 0.000
#> GSM62300 2 0.0000 0.9105 0.000 1.000 0.000 0.000 0.000
#> GSM62308 2 0.0000 0.9105 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM62248 4 0.0000 0.9975 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62256 4 0.0000 0.9975 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62259 4 0.0000 0.9975 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62267 5 0.0260 0.7418 0.008 0.000 0.000 0.000 0.992 0.000
#> GSM62280 6 0.0000 0.8750 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM62284 1 0.0000 0.7735 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM62289 4 0.0000 0.9975 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62307 4 0.0000 0.9975 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62316 4 0.0000 0.9975 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62254 4 0.0000 0.9975 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62292 4 0.0000 0.9975 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62253 1 0.0000 0.7735 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM62270 3 0.0000 0.9593 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62278 3 0.2260 0.8458 0.140 0.000 0.860 0.000 0.000 0.000
#> GSM62297 2 0.0000 0.9213 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62298 2 0.0000 0.9213 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62299 2 0.0000 0.9213 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62258 5 0.0000 0.7465 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM62281 4 0.0000 0.9975 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62294 4 0.0000 0.9975 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62305 5 0.3782 0.3838 0.000 0.412 0.000 0.000 0.588 0.000
#> GSM62306 4 0.0000 0.9975 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62310 4 0.0000 0.9975 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62311 4 0.0000 0.9975 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62317 6 0.0000 0.8750 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM62318 6 0.0000 0.8750 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM62321 6 0.0000 0.8750 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM62322 3 0.0000 0.9593 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62250 4 0.0547 0.9780 0.000 0.000 0.000 0.980 0.020 0.000
#> GSM62252 5 0.0547 0.7280 0.000 0.000 0.000 0.020 0.980 0.000
#> GSM62255 4 0.0000 0.9975 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62257 4 0.0000 0.9975 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62260 5 0.3659 0.3860 0.000 0.000 0.000 0.000 0.636 0.364
#> GSM62261 4 0.0000 0.9975 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62262 4 0.0000 0.9975 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62264 1 0.3175 0.5716 0.744 0.000 0.000 0.000 0.256 0.000
#> GSM62268 1 0.0000 0.7735 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM62269 3 0.0000 0.9593 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62271 5 0.0000 0.7465 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM62272 3 0.0000 0.9593 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62273 2 0.1007 0.8727 0.000 0.956 0.000 0.044 0.000 0.000
#> GSM62274 1 0.2260 0.7100 0.860 0.000 0.000 0.000 0.140 0.000
#> GSM62275 3 0.0000 0.9593 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62276 5 0.0000 0.7465 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM62277 3 0.1663 0.9060 0.088 0.000 0.912 0.000 0.000 0.000
#> GSM62279 1 0.3789 0.3880 0.584 0.000 0.000 0.000 0.416 0.000
#> GSM62282 6 0.3838 0.3001 0.000 0.000 0.000 0.000 0.448 0.552
#> GSM62283 5 0.0000 0.7465 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM62286 4 0.0000 0.9975 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62287 4 0.0000 0.9975 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62288 4 0.0000 0.9975 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62290 2 0.0000 0.9213 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62293 4 0.0000 0.9975 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62301 2 0.0000 0.9213 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62302 4 0.0000 0.9975 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62303 4 0.0000 0.9975 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62304 4 0.0000 0.9975 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62312 4 0.0937 0.9520 0.000 0.040 0.000 0.960 0.000 0.000
#> GSM62313 4 0.0000 0.9975 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62314 4 0.0000 0.9975 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62319 2 0.0000 0.9213 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62320 2 0.3817 0.2613 0.000 0.568 0.000 0.432 0.000 0.000
#> GSM62249 5 0.3659 0.4656 0.000 0.364 0.000 0.000 0.636 0.000
#> GSM62251 1 0.3854 0.0973 0.536 0.000 0.000 0.000 0.464 0.000
#> GSM62263 2 0.0363 0.9107 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM62285 2 0.0000 0.9213 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62315 2 0.0000 0.9213 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62291 2 0.0000 0.9213 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62265 5 0.3672 0.2677 0.368 0.000 0.000 0.000 0.632 0.000
#> GSM62266 1 0.0000 0.7735 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM62296 2 0.0000 0.9213 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62309 2 0.0000 0.9213 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62295 2 0.3620 0.4380 0.000 0.648 0.000 0.352 0.000 0.000
#> GSM62300 2 0.0000 0.9213 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62308 2 0.0000 0.9213 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) other(p) genotype/variation(p) k
#> SD:pam 72 7.37e-01 1.000 0.794 2
#> SD:pam 74 2.87e-01 0.924 0.672 3
#> SD:pam 71 5.38e-04 0.461 0.070 4
#> SD:pam 70 2.27e-04 0.580 0.123 5
#> SD:pam 66 5.16e-05 0.358 0.206 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "mclust"]
# you can also extract it by
# res = res_list["SD:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 75 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 0.973 0.987 0.4738 0.526 0.526
#> 3 3 0.597 0.733 0.830 0.1916 0.934 0.878
#> 4 4 0.604 0.826 0.767 0.2098 0.660 0.384
#> 5 5 0.628 0.717 0.765 0.0879 0.908 0.675
#> 6 6 0.693 0.781 0.855 0.0652 0.991 0.955
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
#> GSM62248 2 0.0000 0.989 0.000 1.000
#> GSM62256 2 0.1633 0.970 0.024 0.976
#> GSM62259 2 0.0000 0.989 0.000 1.000
#> GSM62267 1 0.0000 0.983 1.000 0.000
#> GSM62280 1 0.0000 0.983 1.000 0.000
#> GSM62284 1 0.0000 0.983 1.000 0.000
#> GSM62289 2 0.2948 0.949 0.052 0.948
#> GSM62307 2 0.0000 0.989 0.000 1.000
#> GSM62316 2 0.0000 0.989 0.000 1.000
#> GSM62254 2 0.0000 0.989 0.000 1.000
#> GSM62292 2 0.0000 0.989 0.000 1.000
#> GSM62253 1 0.0000 0.983 1.000 0.000
#> GSM62270 1 0.0000 0.983 1.000 0.000
#> GSM62278 1 0.0000 0.983 1.000 0.000
#> GSM62297 2 0.0000 0.989 0.000 1.000
#> GSM62298 2 0.0000 0.989 0.000 1.000
#> GSM62299 2 0.0000 0.989 0.000 1.000
#> GSM62258 1 0.0000 0.983 1.000 0.000
#> GSM62281 2 0.0376 0.986 0.004 0.996
#> GSM62294 2 0.0000 0.989 0.000 1.000
#> GSM62305 2 0.2948 0.949 0.052 0.948
#> GSM62306 2 0.0000 0.989 0.000 1.000
#> GSM62310 2 0.0000 0.989 0.000 1.000
#> GSM62311 2 0.0000 0.989 0.000 1.000
#> GSM62317 1 0.6531 0.794 0.832 0.168
#> GSM62318 1 0.0000 0.983 1.000 0.000
#> GSM62321 1 0.0000 0.983 1.000 0.000
#> GSM62322 1 0.0000 0.983 1.000 0.000
#> GSM62250 2 0.2948 0.949 0.052 0.948
#> GSM62252 2 0.2948 0.949 0.052 0.948
#> GSM62255 2 0.0000 0.989 0.000 1.000
#> GSM62257 2 0.0000 0.989 0.000 1.000
#> GSM62260 1 0.0000 0.983 1.000 0.000
#> GSM62261 2 0.0000 0.989 0.000 1.000
#> GSM62262 2 0.0000 0.989 0.000 1.000
#> GSM62264 1 0.0000 0.983 1.000 0.000
#> GSM62268 1 0.0000 0.983 1.000 0.000
#> GSM62269 1 0.0000 0.983 1.000 0.000
#> GSM62271 1 0.0000 0.983 1.000 0.000
#> GSM62272 1 0.0000 0.983 1.000 0.000
#> GSM62273 2 0.0000 0.989 0.000 1.000
#> GSM62274 1 0.0000 0.983 1.000 0.000
#> GSM62275 1 0.0000 0.983 1.000 0.000
#> GSM62276 1 0.0000 0.983 1.000 0.000
#> GSM62277 1 0.0000 0.983 1.000 0.000
#> GSM62279 1 0.0000 0.983 1.000 0.000
#> GSM62282 1 0.0000 0.983 1.000 0.000
#> GSM62283 1 0.0000 0.983 1.000 0.000
#> GSM62286 2 0.2948 0.949 0.052 0.948
#> GSM62287 2 0.0000 0.989 0.000 1.000
#> GSM62288 2 0.0000 0.989 0.000 1.000
#> GSM62290 2 0.0000 0.989 0.000 1.000
#> GSM62293 2 0.0000 0.989 0.000 1.000
#> GSM62301 2 0.0000 0.989 0.000 1.000
#> GSM62302 2 0.0000 0.989 0.000 1.000
#> GSM62303 2 0.0000 0.989 0.000 1.000
#> GSM62304 2 0.0000 0.989 0.000 1.000
#> GSM62312 2 0.0000 0.989 0.000 1.000
#> GSM62313 2 0.0000 0.989 0.000 1.000
#> GSM62314 2 0.0000 0.989 0.000 1.000
#> GSM62319 2 0.2948 0.949 0.052 0.948
#> GSM62320 2 0.0000 0.989 0.000 1.000
#> GSM62249 1 0.8713 0.589 0.708 0.292
#> GSM62251 1 0.0000 0.983 1.000 0.000
#> GSM62263 2 0.6531 0.809 0.168 0.832
#> GSM62285 2 0.0000 0.989 0.000 1.000
#> GSM62315 2 0.0000 0.989 0.000 1.000
#> GSM62291 2 0.0000 0.989 0.000 1.000
#> GSM62265 1 0.0000 0.983 1.000 0.000
#> GSM62266 1 0.0000 0.983 1.000 0.000
#> GSM62296 2 0.0000 0.989 0.000 1.000
#> GSM62309 2 0.0000 0.989 0.000 1.000
#> GSM62295 2 0.0000 0.989 0.000 1.000
#> GSM62300 2 0.0000 0.989 0.000 1.000
#> GSM62308 2 0.0000 0.989 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM62248 2 0.5291 0.8552 0.000 0.732 0.268
#> GSM62256 2 0.6033 0.8409 0.004 0.660 0.336
#> GSM62259 2 0.4974 0.8564 0.000 0.764 0.236
#> GSM62267 1 0.0000 0.7527 1.000 0.000 0.000
#> GSM62280 1 0.4399 0.4599 0.812 0.000 0.188
#> GSM62284 1 0.1289 0.7322 0.968 0.000 0.032
#> GSM62289 2 0.7433 0.8298 0.072 0.660 0.268
#> GSM62307 2 0.2165 0.8200 0.000 0.936 0.064
#> GSM62316 2 0.5291 0.8552 0.000 0.732 0.268
#> GSM62254 2 0.0000 0.7971 0.000 1.000 0.000
#> GSM62292 2 0.0000 0.7971 0.000 1.000 0.000
#> GSM62253 1 0.1031 0.7423 0.976 0.000 0.024
#> GSM62270 3 0.6274 0.9903 0.456 0.000 0.544
#> GSM62278 1 0.6168 -0.6043 0.588 0.000 0.412
#> GSM62297 2 0.5785 0.8467 0.000 0.668 0.332
#> GSM62298 2 0.4452 0.8395 0.000 0.808 0.192
#> GSM62299 2 0.5835 0.8445 0.000 0.660 0.340
#> GSM62258 1 0.0000 0.7527 1.000 0.000 0.000
#> GSM62281 2 0.5327 0.8565 0.000 0.728 0.272
#> GSM62294 2 0.0000 0.7971 0.000 1.000 0.000
#> GSM62305 2 0.7433 0.8336 0.072 0.660 0.268
#> GSM62306 2 0.5291 0.8552 0.000 0.732 0.268
#> GSM62310 2 0.0000 0.7971 0.000 1.000 0.000
#> GSM62311 2 0.0000 0.7971 0.000 1.000 0.000
#> GSM62317 1 0.9507 -0.1258 0.432 0.380 0.188
#> GSM62318 1 0.4399 0.4599 0.812 0.000 0.188
#> GSM62321 1 0.7963 0.0534 0.660 0.152 0.188
#> GSM62322 3 0.6267 0.9976 0.452 0.000 0.548
#> GSM62250 2 0.8263 0.7934 0.120 0.612 0.268
#> GSM62252 2 0.7665 0.8227 0.084 0.648 0.268
#> GSM62255 2 0.0000 0.7971 0.000 1.000 0.000
#> GSM62257 2 0.2625 0.8262 0.000 0.916 0.084
#> GSM62260 1 0.0424 0.7513 0.992 0.000 0.008
#> GSM62261 2 0.5291 0.8552 0.000 0.732 0.268
#> GSM62262 2 0.0000 0.7971 0.000 1.000 0.000
#> GSM62264 1 0.0424 0.7513 0.992 0.000 0.008
#> GSM62268 1 0.1031 0.7423 0.976 0.000 0.024
#> GSM62269 3 0.6267 0.9976 0.452 0.000 0.548
#> GSM62271 1 0.0237 0.7530 0.996 0.000 0.004
#> GSM62272 3 0.6267 0.9976 0.452 0.000 0.548
#> GSM62273 2 0.4974 0.8564 0.000 0.764 0.236
#> GSM62274 1 0.1753 0.7055 0.952 0.000 0.048
#> GSM62275 3 0.6267 0.9976 0.452 0.000 0.548
#> GSM62276 1 0.0000 0.7527 1.000 0.000 0.000
#> GSM62277 1 0.6095 -0.5587 0.608 0.000 0.392
#> GSM62279 1 0.0000 0.7527 1.000 0.000 0.000
#> GSM62282 1 0.4399 0.4599 0.812 0.000 0.188
#> GSM62283 1 0.0237 0.7530 0.996 0.000 0.004
#> GSM62286 2 0.6126 0.8527 0.020 0.712 0.268
#> GSM62287 2 0.0000 0.7971 0.000 1.000 0.000
#> GSM62288 2 0.5291 0.8552 0.000 0.732 0.268
#> GSM62290 2 0.5810 0.8451 0.000 0.664 0.336
#> GSM62293 2 0.0000 0.7971 0.000 1.000 0.000
#> GSM62301 2 0.5785 0.8456 0.000 0.668 0.332
#> GSM62302 2 0.0000 0.7971 0.000 1.000 0.000
#> GSM62303 2 0.0000 0.7971 0.000 1.000 0.000
#> GSM62304 2 0.0000 0.7971 0.000 1.000 0.000
#> GSM62312 2 0.5733 0.8476 0.000 0.676 0.324
#> GSM62313 2 0.0000 0.7971 0.000 1.000 0.000
#> GSM62314 2 0.5254 0.8558 0.000 0.736 0.264
#> GSM62319 2 0.7644 0.8231 0.072 0.632 0.296
#> GSM62320 2 0.5465 0.8532 0.000 0.712 0.288
#> GSM62249 2 0.6500 0.2205 0.464 0.532 0.004
#> GSM62251 1 0.0237 0.7530 0.996 0.000 0.004
#> GSM62263 2 0.7885 0.4537 0.352 0.580 0.068
#> GSM62285 2 0.5785 0.8456 0.000 0.668 0.332
#> GSM62315 2 0.7378 0.8275 0.052 0.628 0.320
#> GSM62291 2 0.6154 0.8149 0.000 0.592 0.408
#> GSM62265 1 0.0237 0.7530 0.996 0.000 0.004
#> GSM62266 1 0.1031 0.7423 0.976 0.000 0.024
#> GSM62296 2 0.6140 0.8169 0.000 0.596 0.404
#> GSM62309 2 0.6819 0.8388 0.028 0.644 0.328
#> GSM62295 2 0.0000 0.7971 0.000 1.000 0.000
#> GSM62300 2 0.6180 0.8098 0.000 0.584 0.416
#> GSM62308 2 0.6180 0.8098 0.000 0.584 0.416
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM62248 3 0.3972 0.866 0.000 0.008 0.788 0.204
#> GSM62256 2 0.6979 0.780 0.004 0.600 0.220 0.176
#> GSM62259 4 0.6788 0.587 0.000 0.144 0.264 0.592
#> GSM62267 1 0.1022 0.884 0.968 0.000 0.032 0.000
#> GSM62280 1 0.4817 0.727 0.612 0.388 0.000 0.000
#> GSM62284 1 0.3674 0.871 0.848 0.000 0.036 0.116
#> GSM62289 3 0.3335 0.853 0.016 0.000 0.856 0.128
#> GSM62307 4 0.4391 0.792 0.000 0.008 0.252 0.740
#> GSM62316 3 0.4323 0.858 0.000 0.020 0.776 0.204
#> GSM62254 4 0.2760 0.828 0.000 0.000 0.128 0.872
#> GSM62292 4 0.2760 0.828 0.000 0.000 0.128 0.872
#> GSM62253 1 0.0469 0.882 0.988 0.000 0.012 0.000
#> GSM62270 1 0.5012 0.856 0.792 0.020 0.060 0.128
#> GSM62278 1 0.3791 0.870 0.844 0.012 0.016 0.128
#> GSM62297 3 0.2586 0.714 0.004 0.004 0.900 0.092
#> GSM62298 4 0.5271 0.692 0.000 0.020 0.340 0.640
#> GSM62299 2 0.6421 0.908 0.000 0.556 0.368 0.076
#> GSM62258 1 0.1792 0.883 0.932 0.000 0.068 0.000
#> GSM62281 2 0.7306 0.713 0.004 0.556 0.240 0.200
#> GSM62294 4 0.3400 0.869 0.000 0.000 0.180 0.820
#> GSM62305 3 0.3598 0.850 0.028 0.000 0.848 0.124
#> GSM62306 3 0.4098 0.864 0.000 0.012 0.784 0.204
#> GSM62310 4 0.3626 0.867 0.004 0.000 0.184 0.812
#> GSM62311 4 0.3444 0.870 0.000 0.000 0.184 0.816
#> GSM62317 1 0.4817 0.727 0.612 0.388 0.000 0.000
#> GSM62318 1 0.4817 0.727 0.612 0.388 0.000 0.000
#> GSM62321 1 0.4817 0.727 0.612 0.388 0.000 0.000
#> GSM62322 1 0.5086 0.856 0.788 0.020 0.064 0.128
#> GSM62250 3 0.3587 0.723 0.104 0.000 0.856 0.040
#> GSM62252 3 0.3978 0.807 0.056 0.000 0.836 0.108
#> GSM62255 4 0.3486 0.868 0.000 0.000 0.188 0.812
#> GSM62257 4 0.4720 0.765 0.000 0.016 0.264 0.720
#> GSM62260 1 0.1854 0.878 0.940 0.012 0.048 0.000
#> GSM62261 3 0.3831 0.867 0.000 0.004 0.792 0.204
#> GSM62262 4 0.3400 0.869 0.000 0.000 0.180 0.820
#> GSM62264 1 0.1576 0.878 0.948 0.004 0.048 0.000
#> GSM62268 1 0.0804 0.884 0.980 0.000 0.012 0.008
#> GSM62269 1 0.5012 0.856 0.792 0.020 0.060 0.128
#> GSM62271 1 0.1211 0.878 0.960 0.000 0.040 0.000
#> GSM62272 1 0.5012 0.856 0.792 0.020 0.060 0.128
#> GSM62273 4 0.7297 0.442 0.000 0.204 0.264 0.532
#> GSM62274 1 0.3674 0.871 0.848 0.000 0.036 0.116
#> GSM62275 1 0.5012 0.856 0.792 0.020 0.060 0.128
#> GSM62276 1 0.1022 0.884 0.968 0.000 0.032 0.000
#> GSM62277 1 0.3842 0.868 0.836 0.000 0.036 0.128
#> GSM62279 1 0.1022 0.884 0.968 0.000 0.032 0.000
#> GSM62282 1 0.4103 0.819 0.744 0.256 0.000 0.000
#> GSM62283 1 0.1211 0.878 0.960 0.000 0.040 0.000
#> GSM62286 3 0.3271 0.856 0.012 0.000 0.856 0.132
#> GSM62287 4 0.3444 0.870 0.000 0.000 0.184 0.816
#> GSM62288 3 0.3831 0.867 0.000 0.004 0.792 0.204
#> GSM62290 2 0.6421 0.908 0.000 0.556 0.368 0.076
#> GSM62293 4 0.2760 0.828 0.000 0.000 0.128 0.872
#> GSM62301 2 0.6421 0.908 0.000 0.556 0.368 0.076
#> GSM62302 4 0.3444 0.870 0.000 0.000 0.184 0.816
#> GSM62303 4 0.3444 0.870 0.000 0.000 0.184 0.816
#> GSM62304 4 0.3444 0.870 0.000 0.000 0.184 0.816
#> GSM62312 2 0.6549 0.896 0.000 0.556 0.356 0.088
#> GSM62313 4 0.3444 0.870 0.000 0.000 0.184 0.816
#> GSM62314 3 0.4323 0.858 0.000 0.020 0.776 0.204
#> GSM62319 2 0.8473 0.798 0.100 0.496 0.300 0.104
#> GSM62320 4 0.7581 0.133 0.000 0.200 0.360 0.440
#> GSM62249 1 0.1557 0.874 0.944 0.000 0.056 0.000
#> GSM62251 1 0.0817 0.881 0.976 0.000 0.024 0.000
#> GSM62263 1 0.5559 0.578 0.696 0.000 0.240 0.064
#> GSM62285 2 0.6421 0.908 0.000 0.556 0.368 0.076
#> GSM62315 2 0.7520 0.879 0.044 0.516 0.364 0.076
#> GSM62291 2 0.6280 0.894 0.000 0.604 0.316 0.080
#> GSM62265 1 0.1211 0.878 0.960 0.000 0.040 0.000
#> GSM62266 1 0.0469 0.882 0.988 0.000 0.012 0.000
#> GSM62296 2 0.6319 0.894 0.000 0.604 0.312 0.084
#> GSM62309 2 0.7520 0.879 0.044 0.516 0.364 0.076
#> GSM62295 4 0.2814 0.829 0.000 0.000 0.132 0.868
#> GSM62300 2 0.6240 0.892 0.000 0.604 0.320 0.076
#> GSM62308 2 0.6240 0.892 0.000 0.604 0.320 0.076
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM62248 5 0.5375 0.80371 0.000 0.320 0.000 0.076 0.604
#> GSM62256 2 0.4214 0.65561 0.004 0.788 0.000 0.088 0.120
#> GSM62259 4 0.5576 0.50967 0.000 0.388 0.000 0.536 0.076
#> GSM62267 1 0.1082 0.90275 0.964 0.000 0.000 0.008 0.028
#> GSM62280 3 0.4192 0.33934 0.404 0.000 0.596 0.000 0.000
#> GSM62284 1 0.2720 0.83043 0.880 0.000 0.004 0.020 0.096
#> GSM62289 5 0.4763 0.78257 0.000 0.212 0.000 0.076 0.712
#> GSM62307 4 0.5338 0.62571 0.000 0.324 0.000 0.604 0.072
#> GSM62316 5 0.5491 0.79735 0.000 0.312 0.000 0.088 0.600
#> GSM62254 4 0.0880 0.74445 0.000 0.032 0.000 0.968 0.000
#> GSM62292 4 0.0880 0.74445 0.000 0.032 0.000 0.968 0.000
#> GSM62253 1 0.0451 0.90508 0.988 0.000 0.004 0.008 0.000
#> GSM62270 3 0.7166 0.42775 0.336 0.000 0.404 0.020 0.240
#> GSM62278 1 0.2172 0.86094 0.908 0.000 0.000 0.016 0.076
#> GSM62297 5 0.4555 0.57565 0.008 0.472 0.000 0.000 0.520
#> GSM62298 4 0.5232 0.44082 0.000 0.456 0.000 0.500 0.044
#> GSM62299 2 0.0162 0.84155 0.000 0.996 0.000 0.000 0.004
#> GSM62258 1 0.1082 0.90275 0.964 0.000 0.000 0.008 0.028
#> GSM62281 2 0.4022 0.64427 0.004 0.804 0.000 0.092 0.100
#> GSM62294 4 0.3048 0.84988 0.000 0.176 0.000 0.820 0.004
#> GSM62305 5 0.4932 0.75529 0.028 0.232 0.000 0.032 0.708
#> GSM62306 5 0.5375 0.80371 0.000 0.320 0.000 0.076 0.604
#> GSM62310 4 0.3243 0.84799 0.004 0.180 0.000 0.812 0.004
#> GSM62311 4 0.3048 0.84988 0.000 0.176 0.000 0.820 0.004
#> GSM62317 3 0.4192 0.33934 0.404 0.000 0.596 0.000 0.000
#> GSM62318 3 0.4192 0.33934 0.404 0.000 0.596 0.000 0.000
#> GSM62321 3 0.4192 0.33934 0.404 0.000 0.596 0.000 0.000
#> GSM62322 3 0.7171 0.42615 0.340 0.000 0.400 0.020 0.240
#> GSM62250 5 0.6071 0.61074 0.180 0.120 0.000 0.044 0.656
#> GSM62252 5 0.6987 0.47251 0.264 0.136 0.000 0.060 0.540
#> GSM62255 4 0.4558 0.79910 0.000 0.180 0.000 0.740 0.080
#> GSM62257 4 0.5470 0.61167 0.000 0.296 0.000 0.612 0.092
#> GSM62260 1 0.1569 0.85283 0.944 0.000 0.044 0.004 0.008
#> GSM62261 5 0.5390 0.80147 0.000 0.324 0.000 0.076 0.600
#> GSM62262 4 0.2929 0.85089 0.000 0.180 0.000 0.820 0.000
#> GSM62264 1 0.0451 0.90217 0.988 0.000 0.000 0.004 0.008
#> GSM62268 1 0.1153 0.89632 0.964 0.000 0.004 0.008 0.024
#> GSM62269 3 0.7166 0.42775 0.336 0.000 0.404 0.020 0.240
#> GSM62271 1 0.0000 0.90357 1.000 0.000 0.000 0.000 0.000
#> GSM62272 3 0.7166 0.42775 0.336 0.000 0.404 0.020 0.240
#> GSM62273 2 0.5447 -0.00558 0.000 0.572 0.000 0.356 0.072
#> GSM62274 1 0.2172 0.87076 0.916 0.000 0.004 0.020 0.060
#> GSM62275 3 0.7166 0.42775 0.336 0.000 0.404 0.020 0.240
#> GSM62276 1 0.1082 0.90275 0.964 0.000 0.000 0.008 0.028
#> GSM62277 1 0.2932 0.80796 0.864 0.000 0.004 0.020 0.112
#> GSM62279 1 0.1243 0.90224 0.960 0.000 0.004 0.008 0.028
#> GSM62282 3 0.4307 0.18662 0.496 0.000 0.504 0.000 0.000
#> GSM62283 1 0.0451 0.90217 0.988 0.000 0.000 0.004 0.008
#> GSM62286 5 0.4763 0.78257 0.000 0.212 0.000 0.076 0.712
#> GSM62287 4 0.2929 0.85089 0.000 0.180 0.000 0.820 0.000
#> GSM62288 5 0.5390 0.80147 0.000 0.324 0.000 0.076 0.600
#> GSM62290 2 0.0000 0.84485 0.000 1.000 0.000 0.000 0.000
#> GSM62293 4 0.0880 0.74445 0.000 0.032 0.000 0.968 0.000
#> GSM62301 2 0.0000 0.84485 0.000 1.000 0.000 0.000 0.000
#> GSM62302 4 0.2929 0.85089 0.000 0.180 0.000 0.820 0.000
#> GSM62303 4 0.3003 0.84902 0.000 0.188 0.000 0.812 0.000
#> GSM62304 4 0.3003 0.84902 0.000 0.188 0.000 0.812 0.000
#> GSM62312 2 0.0000 0.84485 0.000 1.000 0.000 0.000 0.000
#> GSM62313 4 0.2929 0.85089 0.000 0.180 0.000 0.820 0.000
#> GSM62314 5 0.5697 0.77645 0.000 0.288 0.000 0.116 0.596
#> GSM62319 2 0.4480 0.16908 0.400 0.592 0.000 0.004 0.004
#> GSM62320 2 0.0451 0.83701 0.000 0.988 0.000 0.004 0.008
#> GSM62249 1 0.1012 0.89111 0.968 0.012 0.000 0.000 0.020
#> GSM62251 1 0.0771 0.89890 0.976 0.000 0.004 0.000 0.020
#> GSM62263 1 0.4419 0.27985 0.668 0.312 0.000 0.000 0.020
#> GSM62285 2 0.0000 0.84485 0.000 1.000 0.000 0.000 0.000
#> GSM62315 2 0.0000 0.84485 0.000 1.000 0.000 0.000 0.000
#> GSM62291 2 0.1197 0.82276 0.000 0.952 0.000 0.000 0.048
#> GSM62265 1 0.0613 0.90306 0.984 0.000 0.004 0.004 0.008
#> GSM62266 1 0.0451 0.90508 0.988 0.000 0.004 0.008 0.000
#> GSM62296 2 0.1197 0.82276 0.000 0.952 0.000 0.000 0.048
#> GSM62309 2 0.0000 0.84485 0.000 1.000 0.000 0.000 0.000
#> GSM62295 4 0.1753 0.74198 0.000 0.032 0.000 0.936 0.032
#> GSM62300 2 0.1197 0.82276 0.000 0.952 0.000 0.000 0.048
#> GSM62308 2 0.1197 0.82276 0.000 0.952 0.000 0.000 0.048
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM62248 5 0.445 0.762 0.000 0.100 0.000 0.196 0.704 0.000
#> GSM62256 2 0.453 0.764 0.000 0.704 0.000 0.164 0.132 0.000
#> GSM62259 4 0.453 0.528 0.000 0.164 0.000 0.704 0.132 0.000
#> GSM62267 1 0.249 0.810 0.880 0.000 0.076 0.000 0.044 0.000
#> GSM62280 6 0.000 0.907 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM62284 1 0.295 0.770 0.812 0.000 0.176 0.000 0.012 0.000
#> GSM62289 5 0.141 0.728 0.000 0.004 0.000 0.060 0.936 0.000
#> GSM62307 4 0.365 0.653 0.000 0.092 0.000 0.792 0.116 0.000
#> GSM62316 5 0.481 0.724 0.000 0.096 0.000 0.264 0.640 0.000
#> GSM62254 4 0.321 0.722 0.000 0.132 0.000 0.820 0.048 0.000
#> GSM62292 4 0.321 0.722 0.000 0.132 0.000 0.820 0.048 0.000
#> GSM62253 1 0.000 0.815 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM62270 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62278 1 0.415 0.301 0.548 0.000 0.440 0.000 0.012 0.000
#> GSM62297 5 0.577 0.509 0.008 0.272 0.000 0.180 0.540 0.000
#> GSM62298 4 0.446 0.420 0.000 0.268 0.000 0.668 0.064 0.000
#> GSM62299 2 0.263 0.897 0.000 0.820 0.000 0.180 0.000 0.000
#> GSM62258 1 0.246 0.810 0.880 0.000 0.084 0.000 0.036 0.000
#> GSM62281 2 0.468 0.759 0.000 0.684 0.000 0.184 0.132 0.000
#> GSM62294 4 0.000 0.855 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62305 5 0.143 0.724 0.000 0.012 0.000 0.048 0.940 0.000
#> GSM62306 5 0.440 0.764 0.000 0.096 0.000 0.196 0.708 0.000
#> GSM62310 4 0.000 0.855 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62311 4 0.000 0.855 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62317 6 0.000 0.907 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM62318 6 0.000 0.907 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM62321 6 0.000 0.907 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM62322 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62250 5 0.192 0.699 0.028 0.004 0.000 0.048 0.920 0.000
#> GSM62252 5 0.122 0.650 0.000 0.004 0.000 0.000 0.948 0.048
#> GSM62255 4 0.186 0.780 0.000 0.000 0.000 0.896 0.104 0.000
#> GSM62257 4 0.254 0.750 0.000 0.020 0.000 0.864 0.116 0.000
#> GSM62260 1 0.358 0.505 0.660 0.000 0.000 0.000 0.000 0.340
#> GSM62261 5 0.456 0.755 0.000 0.108 0.000 0.200 0.692 0.000
#> GSM62262 4 0.000 0.855 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62264 1 0.285 0.688 0.792 0.000 0.000 0.000 0.000 0.208
#> GSM62268 1 0.000 0.815 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM62269 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62271 1 0.159 0.811 0.940 0.000 0.008 0.000 0.020 0.032
#> GSM62272 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62273 2 0.515 0.679 0.000 0.604 0.000 0.264 0.132 0.000
#> GSM62274 1 0.291 0.787 0.832 0.000 0.144 0.000 0.024 0.000
#> GSM62275 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62276 1 0.249 0.810 0.880 0.000 0.076 0.000 0.044 0.000
#> GSM62277 1 0.305 0.773 0.812 0.000 0.168 0.000 0.020 0.000
#> GSM62279 1 0.243 0.811 0.884 0.000 0.072 0.000 0.044 0.000
#> GSM62282 6 0.324 0.594 0.268 0.000 0.000 0.000 0.000 0.732
#> GSM62283 1 0.144 0.791 0.928 0.000 0.000 0.000 0.000 0.072
#> GSM62286 5 0.147 0.730 0.000 0.004 0.000 0.064 0.932 0.000
#> GSM62287 4 0.000 0.855 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62288 5 0.454 0.759 0.000 0.096 0.000 0.216 0.688 0.000
#> GSM62290 2 0.263 0.897 0.000 0.820 0.000 0.180 0.000 0.000
#> GSM62293 4 0.321 0.722 0.000 0.132 0.000 0.820 0.048 0.000
#> GSM62301 2 0.263 0.897 0.000 0.820 0.000 0.180 0.000 0.000
#> GSM62302 4 0.000 0.855 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62303 4 0.000 0.855 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62304 4 0.000 0.855 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62312 2 0.263 0.897 0.000 0.820 0.000 0.180 0.000 0.000
#> GSM62313 4 0.000 0.855 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62314 5 0.483 0.718 0.000 0.092 0.000 0.276 0.632 0.000
#> GSM62319 2 0.422 0.600 0.000 0.712 0.000 0.004 0.052 0.232
#> GSM62320 2 0.362 0.871 0.000 0.772 0.000 0.184 0.044 0.000
#> GSM62249 1 0.279 0.695 0.800 0.000 0.000 0.000 0.000 0.200
#> GSM62251 1 0.263 0.713 0.820 0.000 0.000 0.000 0.000 0.180
#> GSM62263 1 0.606 0.342 0.516 0.252 0.000 0.000 0.016 0.216
#> GSM62285 2 0.263 0.897 0.000 0.820 0.000 0.180 0.000 0.000
#> GSM62315 2 0.353 0.886 0.000 0.784 0.000 0.180 0.004 0.032
#> GSM62291 2 0.218 0.880 0.000 0.868 0.000 0.132 0.000 0.000
#> GSM62265 1 0.000 0.815 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM62266 1 0.000 0.815 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM62296 2 0.253 0.881 0.000 0.856 0.000 0.132 0.012 0.000
#> GSM62309 2 0.353 0.886 0.000 0.784 0.000 0.180 0.004 0.032
#> GSM62295 4 0.382 0.722 0.000 0.132 0.000 0.776 0.092 0.000
#> GSM62300 2 0.218 0.880 0.000 0.868 0.000 0.132 0.000 0.000
#> GSM62308 2 0.218 0.880 0.000 0.868 0.000 0.132 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) other(p) genotype/variation(p) k
#> SD:mclust 75 0.82366 0.881 0.806 2
#> SD:mclust 66 0.56626 0.946 0.966 3
#> SD:mclust 73 0.00245 0.874 0.354 4
#> SD:mclust 60 0.00509 0.824 0.377 5
#> SD:mclust 72 0.01102 0.771 0.689 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "NMF"]
# you can also extract it by
# res = res_list["SD:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 75 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.953 0.982 0.4275 0.580 0.580
#> 3 3 0.862 0.828 0.930 0.3062 0.823 0.706
#> 4 4 0.839 0.854 0.925 0.1431 0.846 0.683
#> 5 5 0.648 0.662 0.812 0.1815 0.758 0.439
#> 6 6 0.739 0.721 0.853 0.0646 0.834 0.451
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
#> GSM62248 2 0.0000 0.980 0.000 1.000
#> GSM62256 2 0.0000 0.980 0.000 1.000
#> GSM62259 2 0.0000 0.980 0.000 1.000
#> GSM62267 1 0.1414 0.967 0.980 0.020
#> GSM62280 1 0.0000 0.982 1.000 0.000
#> GSM62284 1 0.0000 0.982 1.000 0.000
#> GSM62289 2 0.0000 0.980 0.000 1.000
#> GSM62307 2 0.0000 0.980 0.000 1.000
#> GSM62316 2 0.0000 0.980 0.000 1.000
#> GSM62254 2 0.0000 0.980 0.000 1.000
#> GSM62292 2 0.0000 0.980 0.000 1.000
#> GSM62253 1 0.0000 0.982 1.000 0.000
#> GSM62270 1 0.0000 0.982 1.000 0.000
#> GSM62278 1 0.0000 0.982 1.000 0.000
#> GSM62297 2 0.0000 0.980 0.000 1.000
#> GSM62298 2 0.0000 0.980 0.000 1.000
#> GSM62299 2 0.0000 0.980 0.000 1.000
#> GSM62258 1 0.0000 0.982 1.000 0.000
#> GSM62281 2 0.0000 0.980 0.000 1.000
#> GSM62294 2 0.0000 0.980 0.000 1.000
#> GSM62305 2 0.0000 0.980 0.000 1.000
#> GSM62306 2 0.0000 0.980 0.000 1.000
#> GSM62310 2 0.0000 0.980 0.000 1.000
#> GSM62311 2 0.0000 0.980 0.000 1.000
#> GSM62317 2 0.0000 0.980 0.000 1.000
#> GSM62318 1 0.0000 0.982 1.000 0.000
#> GSM62321 2 0.7056 0.752 0.192 0.808
#> GSM62322 1 0.0000 0.982 1.000 0.000
#> GSM62250 2 0.0000 0.980 0.000 1.000
#> GSM62252 2 0.0000 0.980 0.000 1.000
#> GSM62255 2 0.0000 0.980 0.000 1.000
#> GSM62257 2 0.0000 0.980 0.000 1.000
#> GSM62260 2 0.9954 0.140 0.460 0.540
#> GSM62261 2 0.0000 0.980 0.000 1.000
#> GSM62262 2 0.0000 0.980 0.000 1.000
#> GSM62264 1 0.8763 0.567 0.704 0.296
#> GSM62268 1 0.0000 0.982 1.000 0.000
#> GSM62269 1 0.0000 0.982 1.000 0.000
#> GSM62271 1 0.0000 0.982 1.000 0.000
#> GSM62272 1 0.0000 0.982 1.000 0.000
#> GSM62273 2 0.0000 0.980 0.000 1.000
#> GSM62274 1 0.0000 0.982 1.000 0.000
#> GSM62275 1 0.0000 0.982 1.000 0.000
#> GSM62276 1 0.0000 0.982 1.000 0.000
#> GSM62277 1 0.0000 0.982 1.000 0.000
#> GSM62279 1 0.2043 0.955 0.968 0.032
#> GSM62282 1 0.0000 0.982 1.000 0.000
#> GSM62283 2 0.9323 0.461 0.348 0.652
#> GSM62286 2 0.0000 0.980 0.000 1.000
#> GSM62287 2 0.0000 0.980 0.000 1.000
#> GSM62288 2 0.0000 0.980 0.000 1.000
#> GSM62290 2 0.0000 0.980 0.000 1.000
#> GSM62293 2 0.0000 0.980 0.000 1.000
#> GSM62301 2 0.0000 0.980 0.000 1.000
#> GSM62302 2 0.0000 0.980 0.000 1.000
#> GSM62303 2 0.0000 0.980 0.000 1.000
#> GSM62304 2 0.0000 0.980 0.000 1.000
#> GSM62312 2 0.0000 0.980 0.000 1.000
#> GSM62313 2 0.0000 0.980 0.000 1.000
#> GSM62314 2 0.0000 0.980 0.000 1.000
#> GSM62319 2 0.0000 0.980 0.000 1.000
#> GSM62320 2 0.0000 0.980 0.000 1.000
#> GSM62249 2 0.0000 0.980 0.000 1.000
#> GSM62251 2 0.0938 0.969 0.012 0.988
#> GSM62263 2 0.0000 0.980 0.000 1.000
#> GSM62285 2 0.0000 0.980 0.000 1.000
#> GSM62315 2 0.0000 0.980 0.000 1.000
#> GSM62291 2 0.0000 0.980 0.000 1.000
#> GSM62265 1 0.1184 0.970 0.984 0.016
#> GSM62266 1 0.0000 0.982 1.000 0.000
#> GSM62296 2 0.0000 0.980 0.000 1.000
#> GSM62309 2 0.0000 0.980 0.000 1.000
#> GSM62295 2 0.0000 0.980 0.000 1.000
#> GSM62300 2 0.0000 0.980 0.000 1.000
#> GSM62308 2 0.0000 0.980 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM62248 2 0.1031 0.963 0.024 0.976 0.000
#> GSM62256 2 0.0424 0.972 0.008 0.992 0.000
#> GSM62259 2 0.0000 0.975 0.000 1.000 0.000
#> GSM62267 3 0.2492 0.784 0.016 0.048 0.936
#> GSM62280 1 0.0829 0.743 0.984 0.004 0.012
#> GSM62284 3 0.5733 0.361 0.324 0.000 0.676
#> GSM62289 2 0.0747 0.969 0.016 0.984 0.000
#> GSM62307 2 0.0000 0.975 0.000 1.000 0.000
#> GSM62316 2 0.0424 0.974 0.008 0.992 0.000
#> GSM62254 2 0.0237 0.975 0.004 0.996 0.000
#> GSM62292 2 0.0424 0.974 0.008 0.992 0.000
#> GSM62253 1 0.6154 0.379 0.592 0.000 0.408
#> GSM62270 3 0.0000 0.849 0.000 0.000 1.000
#> GSM62278 3 0.0000 0.849 0.000 0.000 1.000
#> GSM62297 2 0.0000 0.975 0.000 1.000 0.000
#> GSM62298 2 0.0000 0.975 0.000 1.000 0.000
#> GSM62299 2 0.0000 0.975 0.000 1.000 0.000
#> GSM62258 1 0.6168 0.379 0.588 0.000 0.412
#> GSM62281 2 0.0000 0.975 0.000 1.000 0.000
#> GSM62294 2 0.0000 0.975 0.000 1.000 0.000
#> GSM62305 2 0.0892 0.967 0.020 0.980 0.000
#> GSM62306 2 0.0424 0.974 0.008 0.992 0.000
#> GSM62310 2 0.0000 0.975 0.000 1.000 0.000
#> GSM62311 2 0.0000 0.975 0.000 1.000 0.000
#> GSM62317 1 0.4887 0.512 0.772 0.228 0.000
#> GSM62318 1 0.0747 0.742 0.984 0.000 0.016
#> GSM62321 1 0.0829 0.741 0.984 0.012 0.004
#> GSM62322 3 0.0000 0.849 0.000 0.000 1.000
#> GSM62250 2 0.0747 0.969 0.016 0.984 0.000
#> GSM62252 2 0.0747 0.969 0.016 0.984 0.000
#> GSM62255 2 0.0000 0.975 0.000 1.000 0.000
#> GSM62257 2 0.0237 0.975 0.004 0.996 0.000
#> GSM62260 1 0.0592 0.743 0.988 0.000 0.012
#> GSM62261 2 0.0592 0.972 0.012 0.988 0.000
#> GSM62262 2 0.0237 0.975 0.004 0.996 0.000
#> GSM62264 1 0.0592 0.743 0.988 0.000 0.012
#> GSM62268 1 0.6168 0.375 0.588 0.000 0.412
#> GSM62269 3 0.0000 0.849 0.000 0.000 1.000
#> GSM62271 3 0.4062 0.693 0.164 0.000 0.836
#> GSM62272 3 0.0000 0.849 0.000 0.000 1.000
#> GSM62273 2 0.0000 0.975 0.000 1.000 0.000
#> GSM62274 3 0.0237 0.848 0.004 0.000 0.996
#> GSM62275 3 0.0000 0.849 0.000 0.000 1.000
#> GSM62276 3 0.0747 0.841 0.016 0.000 0.984
#> GSM62277 3 0.0237 0.848 0.004 0.000 0.996
#> GSM62279 3 0.6299 -0.108 0.476 0.000 0.524
#> GSM62282 3 0.6280 0.152 0.460 0.000 0.540
#> GSM62283 1 0.3993 0.722 0.884 0.064 0.052
#> GSM62286 2 0.0592 0.972 0.012 0.988 0.000
#> GSM62287 2 0.0424 0.974 0.008 0.992 0.000
#> GSM62288 2 0.0592 0.972 0.012 0.988 0.000
#> GSM62290 2 0.0000 0.975 0.000 1.000 0.000
#> GSM62293 2 0.0237 0.975 0.004 0.996 0.000
#> GSM62301 2 0.0424 0.971 0.008 0.992 0.000
#> GSM62302 2 0.0237 0.975 0.004 0.996 0.000
#> GSM62303 2 0.0237 0.975 0.004 0.996 0.000
#> GSM62304 2 0.0237 0.975 0.004 0.996 0.000
#> GSM62312 2 0.0000 0.975 0.000 1.000 0.000
#> GSM62313 2 0.0237 0.975 0.004 0.996 0.000
#> GSM62314 2 0.0592 0.972 0.012 0.988 0.000
#> GSM62319 2 0.0424 0.971 0.008 0.992 0.000
#> GSM62320 2 0.0000 0.975 0.000 1.000 0.000
#> GSM62249 1 0.3482 0.681 0.872 0.128 0.000
#> GSM62251 1 0.5467 0.624 0.792 0.176 0.032
#> GSM62263 1 0.0424 0.743 0.992 0.008 0.000
#> GSM62285 2 0.0237 0.974 0.004 0.996 0.000
#> GSM62315 2 0.6095 0.380 0.392 0.608 0.000
#> GSM62291 2 0.0237 0.974 0.004 0.996 0.000
#> GSM62265 1 0.4750 0.635 0.784 0.000 0.216
#> GSM62266 1 0.6095 0.409 0.608 0.000 0.392
#> GSM62296 2 0.0000 0.975 0.000 1.000 0.000
#> GSM62309 2 0.6260 0.224 0.448 0.552 0.000
#> GSM62295 2 0.0000 0.975 0.000 1.000 0.000
#> GSM62300 2 0.0424 0.971 0.008 0.992 0.000
#> GSM62308 2 0.0592 0.969 0.012 0.988 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM62248 2 0.2053 0.908 0.072 0.924 0.000 0.004
#> GSM62256 2 0.4790 0.447 0.000 0.620 0.000 0.380
#> GSM62259 2 0.0188 0.954 0.000 0.996 0.000 0.004
#> GSM62267 1 0.2383 0.787 0.924 0.024 0.048 0.004
#> GSM62280 4 0.0336 0.901 0.000 0.000 0.008 0.992
#> GSM62284 1 0.4193 0.631 0.732 0.000 0.268 0.000
#> GSM62289 1 0.5070 0.356 0.580 0.416 0.000 0.004
#> GSM62307 2 0.0188 0.954 0.000 0.996 0.000 0.004
#> GSM62316 2 0.0376 0.952 0.004 0.992 0.000 0.004
#> GSM62254 2 0.0188 0.953 0.000 0.996 0.000 0.004
#> GSM62292 2 0.0188 0.953 0.000 0.996 0.000 0.004
#> GSM62253 1 0.1302 0.791 0.956 0.000 0.044 0.000
#> GSM62270 3 0.0000 0.959 0.000 0.000 1.000 0.000
#> GSM62278 3 0.0000 0.959 0.000 0.000 1.000 0.000
#> GSM62297 2 0.3123 0.854 0.156 0.844 0.000 0.000
#> GSM62298 2 0.0927 0.950 0.016 0.976 0.000 0.008
#> GSM62299 2 0.1854 0.935 0.048 0.940 0.000 0.012
#> GSM62258 1 0.4933 0.572 0.688 0.000 0.296 0.016
#> GSM62281 2 0.0336 0.953 0.000 0.992 0.000 0.008
#> GSM62294 2 0.0188 0.954 0.000 0.996 0.000 0.004
#> GSM62305 2 0.4331 0.631 0.288 0.712 0.000 0.000
#> GSM62306 2 0.0657 0.949 0.012 0.984 0.000 0.004
#> GSM62310 2 0.0188 0.954 0.000 0.996 0.000 0.004
#> GSM62311 2 0.0188 0.954 0.000 0.996 0.000 0.004
#> GSM62317 4 0.0188 0.901 0.000 0.004 0.000 0.996
#> GSM62318 4 0.0524 0.900 0.004 0.000 0.008 0.988
#> GSM62321 4 0.0188 0.902 0.000 0.000 0.004 0.996
#> GSM62322 3 0.0000 0.959 0.000 0.000 1.000 0.000
#> GSM62250 1 0.4372 0.583 0.728 0.268 0.000 0.004
#> GSM62252 1 0.4741 0.513 0.668 0.328 0.000 0.004
#> GSM62255 2 0.0188 0.954 0.000 0.996 0.000 0.004
#> GSM62257 2 0.0188 0.953 0.000 0.996 0.000 0.004
#> GSM62260 4 0.2011 0.879 0.080 0.000 0.000 0.920
#> GSM62261 2 0.1209 0.937 0.032 0.964 0.000 0.004
#> GSM62262 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> GSM62264 1 0.3266 0.693 0.832 0.000 0.000 0.168
#> GSM62268 1 0.2345 0.773 0.900 0.000 0.100 0.000
#> GSM62269 3 0.0000 0.959 0.000 0.000 1.000 0.000
#> GSM62271 3 0.4319 0.697 0.228 0.000 0.760 0.012
#> GSM62272 3 0.0000 0.959 0.000 0.000 1.000 0.000
#> GSM62273 2 0.0336 0.953 0.000 0.992 0.000 0.008
#> GSM62274 1 0.3486 0.719 0.812 0.000 0.188 0.000
#> GSM62275 3 0.0000 0.959 0.000 0.000 1.000 0.000
#> GSM62276 1 0.5093 0.497 0.652 0.008 0.336 0.004
#> GSM62277 3 0.0469 0.948 0.012 0.000 0.988 0.000
#> GSM62279 1 0.1909 0.790 0.940 0.008 0.048 0.004
#> GSM62282 4 0.4713 0.402 0.000 0.000 0.360 0.640
#> GSM62283 1 0.0188 0.793 0.996 0.000 0.000 0.004
#> GSM62286 2 0.1661 0.924 0.052 0.944 0.000 0.004
#> GSM62287 2 0.0188 0.953 0.000 0.996 0.000 0.004
#> GSM62288 2 0.1489 0.929 0.044 0.952 0.000 0.004
#> GSM62290 2 0.1807 0.935 0.052 0.940 0.000 0.008
#> GSM62293 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> GSM62301 2 0.3464 0.882 0.056 0.868 0.000 0.076
#> GSM62302 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> GSM62303 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> GSM62304 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> GSM62312 2 0.1635 0.939 0.044 0.948 0.000 0.008
#> GSM62313 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> GSM62314 2 0.0376 0.952 0.004 0.992 0.000 0.004
#> GSM62319 2 0.2111 0.931 0.044 0.932 0.000 0.024
#> GSM62320 2 0.0927 0.950 0.016 0.976 0.000 0.008
#> GSM62249 1 0.0188 0.793 0.996 0.000 0.000 0.004
#> GSM62251 1 0.0000 0.793 1.000 0.000 0.000 0.000
#> GSM62263 1 0.3688 0.620 0.792 0.000 0.000 0.208
#> GSM62285 2 0.2174 0.929 0.052 0.928 0.000 0.020
#> GSM62315 4 0.2483 0.864 0.052 0.032 0.000 0.916
#> GSM62291 2 0.2089 0.932 0.048 0.932 0.000 0.020
#> GSM62265 1 0.0000 0.793 1.000 0.000 0.000 0.000
#> GSM62266 1 0.1022 0.793 0.968 0.000 0.032 0.000
#> GSM62296 2 0.2174 0.929 0.052 0.928 0.000 0.020
#> GSM62309 4 0.1970 0.883 0.060 0.008 0.000 0.932
#> GSM62295 2 0.0188 0.954 0.000 0.996 0.000 0.004
#> GSM62300 2 0.2282 0.927 0.052 0.924 0.000 0.024
#> GSM62308 2 0.2578 0.920 0.052 0.912 0.000 0.036
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM62248 4 0.0771 0.6643 0.020 0.000 0.000 0.976 0.004
#> GSM62256 5 0.0609 0.8989 0.000 0.000 0.000 0.020 0.980
#> GSM62259 4 0.4074 0.6236 0.000 0.364 0.000 0.636 0.000
#> GSM62267 4 0.4410 -0.1572 0.440 0.000 0.000 0.556 0.004
#> GSM62280 5 0.0162 0.9070 0.004 0.000 0.000 0.000 0.996
#> GSM62284 1 0.3895 0.4072 0.680 0.000 0.320 0.000 0.000
#> GSM62289 4 0.0771 0.6568 0.020 0.000 0.000 0.976 0.004
#> GSM62307 4 0.4278 0.5535 0.000 0.452 0.000 0.548 0.000
#> GSM62316 4 0.0609 0.6831 0.000 0.020 0.000 0.980 0.000
#> GSM62254 4 0.4060 0.6534 0.000 0.360 0.000 0.640 0.000
#> GSM62292 4 0.3480 0.6989 0.000 0.248 0.000 0.752 0.000
#> GSM62253 1 0.0000 0.7173 1.000 0.000 0.000 0.000 0.000
#> GSM62270 3 0.0000 0.9416 0.000 0.000 1.000 0.000 0.000
#> GSM62278 3 0.0000 0.9416 0.000 0.000 1.000 0.000 0.000
#> GSM62297 2 0.3752 0.5133 0.292 0.708 0.000 0.000 0.000
#> GSM62298 2 0.0703 0.8258 0.000 0.976 0.000 0.024 0.000
#> GSM62299 2 0.1331 0.8406 0.040 0.952 0.000 0.008 0.000
#> GSM62258 5 0.5000 0.6165 0.068 0.000 0.004 0.240 0.688
#> GSM62281 4 0.5103 0.5094 0.000 0.452 0.000 0.512 0.036
#> GSM62294 4 0.4171 0.6259 0.000 0.396 0.000 0.604 0.000
#> GSM62305 4 0.3807 0.4653 0.176 0.028 0.000 0.792 0.004
#> GSM62306 4 0.1041 0.6881 0.000 0.032 0.000 0.964 0.004
#> GSM62310 4 0.4182 0.6223 0.000 0.400 0.000 0.600 0.000
#> GSM62311 4 0.4219 0.6052 0.000 0.416 0.000 0.584 0.000
#> GSM62317 5 0.0162 0.9070 0.004 0.000 0.000 0.000 0.996
#> GSM62318 5 0.0162 0.9070 0.004 0.000 0.000 0.000 0.996
#> GSM62321 5 0.0162 0.9070 0.004 0.000 0.000 0.000 0.996
#> GSM62322 3 0.0000 0.9416 0.000 0.000 1.000 0.000 0.000
#> GSM62250 4 0.2286 0.5763 0.108 0.000 0.000 0.888 0.004
#> GSM62252 4 0.0865 0.6545 0.024 0.000 0.000 0.972 0.004
#> GSM62255 4 0.4305 0.4889 0.000 0.488 0.000 0.512 0.000
#> GSM62257 4 0.3074 0.7072 0.000 0.196 0.000 0.804 0.000
#> GSM62260 5 0.3085 0.7921 0.116 0.032 0.000 0.000 0.852
#> GSM62261 4 0.2124 0.6980 0.000 0.096 0.000 0.900 0.004
#> GSM62262 4 0.4291 0.5344 0.000 0.464 0.000 0.536 0.000
#> GSM62264 1 0.1041 0.7102 0.964 0.004 0.000 0.000 0.032
#> GSM62268 1 0.1851 0.6668 0.912 0.000 0.088 0.000 0.000
#> GSM62269 3 0.0000 0.9416 0.000 0.000 1.000 0.000 0.000
#> GSM62271 3 0.4546 0.4705 0.304 0.028 0.668 0.000 0.000
#> GSM62272 3 0.0000 0.9416 0.000 0.000 1.000 0.000 0.000
#> GSM62273 2 0.1608 0.7626 0.000 0.928 0.000 0.072 0.000
#> GSM62274 1 0.4210 0.2339 0.588 0.000 0.412 0.000 0.000
#> GSM62275 3 0.0000 0.9416 0.000 0.000 1.000 0.000 0.000
#> GSM62276 4 0.6135 -0.0351 0.248 0.000 0.192 0.560 0.000
#> GSM62277 3 0.0510 0.9275 0.016 0.000 0.984 0.000 0.000
#> GSM62279 1 0.4066 0.4511 0.672 0.000 0.000 0.324 0.004
#> GSM62282 5 0.2230 0.8249 0.000 0.000 0.116 0.000 0.884
#> GSM62283 1 0.6070 0.2134 0.504 0.424 0.020 0.028 0.024
#> GSM62286 4 0.0486 0.6689 0.004 0.004 0.000 0.988 0.004
#> GSM62287 4 0.3074 0.7086 0.000 0.196 0.000 0.804 0.000
#> GSM62288 4 0.1560 0.6841 0.020 0.028 0.000 0.948 0.004
#> GSM62290 2 0.2068 0.8164 0.092 0.904 0.000 0.004 0.000
#> GSM62293 4 0.4249 0.5848 0.000 0.432 0.000 0.568 0.000
#> GSM62301 2 0.3003 0.6970 0.188 0.812 0.000 0.000 0.000
#> GSM62302 4 0.4138 0.6365 0.000 0.384 0.000 0.616 0.000
#> GSM62303 4 0.3949 0.6699 0.000 0.332 0.000 0.668 0.000
#> GSM62304 4 0.3366 0.7033 0.000 0.232 0.000 0.768 0.000
#> GSM62312 2 0.0609 0.8295 0.000 0.980 0.000 0.020 0.000
#> GSM62313 4 0.4150 0.6339 0.000 0.388 0.000 0.612 0.000
#> GSM62314 4 0.3151 0.6933 0.020 0.144 0.000 0.836 0.000
#> GSM62319 2 0.0404 0.8346 0.000 0.988 0.000 0.012 0.000
#> GSM62320 2 0.0609 0.8292 0.000 0.980 0.000 0.020 0.000
#> GSM62249 1 0.3990 0.4906 0.688 0.308 0.000 0.004 0.000
#> GSM62251 1 0.0162 0.7183 0.996 0.004 0.000 0.000 0.000
#> GSM62263 1 0.4219 0.2835 0.584 0.416 0.000 0.000 0.000
#> GSM62285 2 0.2020 0.8058 0.100 0.900 0.000 0.000 0.000
#> GSM62315 2 0.2124 0.8198 0.056 0.916 0.000 0.000 0.028
#> GSM62291 2 0.0162 0.8418 0.004 0.996 0.000 0.000 0.000
#> GSM62265 1 0.0671 0.7162 0.980 0.016 0.000 0.004 0.000
#> GSM62266 1 0.0162 0.7183 0.996 0.004 0.000 0.000 0.000
#> GSM62296 2 0.0671 0.8435 0.016 0.980 0.000 0.004 0.000
#> GSM62309 2 0.4193 0.6075 0.212 0.748 0.000 0.000 0.040
#> GSM62295 2 0.4304 -0.4761 0.000 0.516 0.000 0.484 0.000
#> GSM62300 2 0.2462 0.8003 0.112 0.880 0.000 0.008 0.000
#> GSM62308 2 0.0671 0.8434 0.016 0.980 0.000 0.004 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM62248 5 0.2723 0.7814 0.016 0.004 0.000 0.128 0.852 0.000
#> GSM62256 6 0.0000 0.8901 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM62259 5 0.3964 0.7168 0.000 0.044 0.000 0.232 0.724 0.000
#> GSM62267 5 0.0291 0.7564 0.004 0.000 0.004 0.000 0.992 0.000
#> GSM62280 6 0.0000 0.8901 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM62284 1 0.2260 0.8080 0.860 0.000 0.140 0.000 0.000 0.000
#> GSM62289 5 0.1578 0.7785 0.012 0.004 0.000 0.048 0.936 0.000
#> GSM62307 4 0.3584 0.3877 0.004 0.000 0.000 0.688 0.308 0.000
#> GSM62316 5 0.2933 0.7724 0.000 0.004 0.000 0.200 0.796 0.000
#> GSM62254 5 0.3727 0.5702 0.000 0.000 0.000 0.388 0.612 0.000
#> GSM62292 5 0.3076 0.7579 0.000 0.000 0.000 0.240 0.760 0.000
#> GSM62253 1 0.0632 0.8791 0.976 0.024 0.000 0.000 0.000 0.000
#> GSM62270 3 0.0000 0.9960 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62278 3 0.0291 0.9912 0.004 0.004 0.992 0.000 0.000 0.000
#> GSM62297 2 0.1141 0.8159 0.052 0.948 0.000 0.000 0.000 0.000
#> GSM62298 4 0.2562 0.6192 0.000 0.172 0.000 0.828 0.000 0.000
#> GSM62299 2 0.1958 0.8200 0.004 0.896 0.000 0.100 0.000 0.000
#> GSM62258 5 0.3192 0.6143 0.000 0.000 0.004 0.004 0.776 0.216
#> GSM62281 6 0.4885 -0.1008 0.000 0.004 0.000 0.464 0.048 0.484
#> GSM62294 4 0.3817 -0.0813 0.000 0.000 0.000 0.568 0.432 0.000
#> GSM62305 5 0.2791 0.6760 0.016 0.124 0.000 0.008 0.852 0.000
#> GSM62306 5 0.1434 0.7640 0.008 0.020 0.000 0.024 0.948 0.000
#> GSM62310 4 0.0713 0.7513 0.000 0.000 0.000 0.972 0.028 0.000
#> GSM62311 4 0.0632 0.7510 0.000 0.000 0.000 0.976 0.024 0.000
#> GSM62317 6 0.0000 0.8901 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM62318 6 0.0000 0.8901 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM62321 6 0.0000 0.8901 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM62322 3 0.0000 0.9960 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62250 5 0.1313 0.7723 0.016 0.004 0.000 0.028 0.952 0.000
#> GSM62252 5 0.0725 0.7576 0.012 0.012 0.000 0.000 0.976 0.000
#> GSM62255 4 0.0837 0.7507 0.004 0.004 0.000 0.972 0.020 0.000
#> GSM62257 5 0.3076 0.7556 0.000 0.000 0.000 0.240 0.760 0.000
#> GSM62260 2 0.3364 0.6794 0.024 0.780 0.000 0.000 0.000 0.196
#> GSM62261 5 0.4471 0.6765 0.040 0.008 0.000 0.292 0.660 0.000
#> GSM62262 4 0.1910 0.7290 0.000 0.000 0.000 0.892 0.108 0.000
#> GSM62264 1 0.1483 0.8756 0.944 0.036 0.000 0.000 0.008 0.012
#> GSM62268 1 0.0717 0.8791 0.976 0.016 0.008 0.000 0.000 0.000
#> GSM62269 3 0.0000 0.9960 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62271 2 0.5597 0.2570 0.048 0.524 0.384 0.004 0.040 0.000
#> GSM62272 3 0.0146 0.9941 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM62273 4 0.3101 0.5346 0.000 0.244 0.000 0.756 0.000 0.000
#> GSM62274 1 0.3741 0.5752 0.672 0.000 0.320 0.000 0.008 0.000
#> GSM62275 3 0.0000 0.9960 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62276 5 0.0893 0.7526 0.004 0.016 0.004 0.004 0.972 0.000
#> GSM62277 3 0.0405 0.9880 0.004 0.000 0.988 0.000 0.008 0.000
#> GSM62279 1 0.3721 0.6822 0.728 0.016 0.000 0.004 0.252 0.000
#> GSM62282 6 0.0000 0.8901 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM62283 2 0.2009 0.7831 0.004 0.904 0.000 0.008 0.084 0.000
#> GSM62286 5 0.1225 0.7750 0.000 0.012 0.000 0.036 0.952 0.000
#> GSM62287 5 0.3151 0.7473 0.000 0.000 0.000 0.252 0.748 0.000
#> GSM62288 5 0.2845 0.7776 0.004 0.004 0.000 0.172 0.820 0.000
#> GSM62290 2 0.2595 0.7747 0.004 0.836 0.000 0.160 0.000 0.000
#> GSM62293 4 0.3221 0.5035 0.000 0.000 0.000 0.736 0.264 0.000
#> GSM62301 2 0.1082 0.8348 0.004 0.956 0.000 0.040 0.000 0.000
#> GSM62302 4 0.2178 0.7089 0.000 0.000 0.000 0.868 0.132 0.000
#> GSM62303 5 0.3782 0.5128 0.000 0.000 0.000 0.412 0.588 0.000
#> GSM62304 5 0.3428 0.6986 0.000 0.000 0.000 0.304 0.696 0.000
#> GSM62312 2 0.3851 0.2049 0.000 0.540 0.000 0.460 0.000 0.000
#> GSM62313 4 0.1957 0.7242 0.000 0.000 0.000 0.888 0.112 0.000
#> GSM62314 5 0.4459 0.2998 0.020 0.004 0.000 0.460 0.516 0.000
#> GSM62319 2 0.1584 0.8335 0.008 0.928 0.000 0.064 0.000 0.000
#> GSM62320 4 0.3464 0.4020 0.000 0.312 0.000 0.688 0.000 0.000
#> GSM62249 2 0.2407 0.7785 0.048 0.892 0.000 0.004 0.056 0.000
#> GSM62251 1 0.1636 0.8735 0.936 0.036 0.000 0.004 0.024 0.000
#> GSM62263 2 0.3950 0.2416 0.432 0.564 0.000 0.004 0.000 0.000
#> GSM62285 2 0.1610 0.8297 0.000 0.916 0.000 0.084 0.000 0.000
#> GSM62315 2 0.1387 0.8327 0.000 0.932 0.000 0.068 0.000 0.000
#> GSM62291 2 0.2969 0.7112 0.000 0.776 0.000 0.224 0.000 0.000
#> GSM62265 2 0.4405 0.4849 0.316 0.644 0.000 0.004 0.036 0.000
#> GSM62266 1 0.0972 0.8793 0.964 0.028 0.000 0.000 0.008 0.000
#> GSM62296 2 0.1141 0.8357 0.000 0.948 0.000 0.052 0.000 0.000
#> GSM62309 2 0.0820 0.8256 0.016 0.972 0.000 0.012 0.000 0.000
#> GSM62295 4 0.1462 0.7198 0.008 0.056 0.000 0.936 0.000 0.000
#> GSM62300 2 0.1196 0.8355 0.008 0.952 0.000 0.040 0.000 0.000
#> GSM62308 2 0.1327 0.8335 0.000 0.936 0.000 0.064 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) other(p) genotype/variation(p) k
#> SD:NMF 73 0.344519 1.000 0.453 2
#> SD:NMF 66 0.052527 0.183 0.164 3
#> SD:NMF 71 0.224177 0.194 0.660 4
#> SD:NMF 63 0.000176 0.587 0.181 5
#> SD:NMF 66 0.000562 0.483 0.175 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "hclust"]
# you can also extract it by
# res = res_list["CV:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 75 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 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 0.567 0.888 0.942 0.3643 0.630 0.630
#> 3 3 0.651 0.722 0.864 0.5005 0.790 0.672
#> 4 4 0.750 0.751 0.845 0.0813 0.953 0.898
#> 5 5 0.842 0.737 0.871 0.0552 0.966 0.920
#> 6 6 0.652 0.662 0.793 0.0704 0.968 0.924
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
#> GSM62248 2 0.0000 0.951 0.000 1.000
#> GSM62256 2 0.0000 0.951 0.000 1.000
#> GSM62259 2 0.0000 0.951 0.000 1.000
#> GSM62267 1 0.8608 0.709 0.716 0.284
#> GSM62280 2 0.6247 0.816 0.156 0.844
#> GSM62284 1 0.4161 0.871 0.916 0.084
#> GSM62289 2 0.0000 0.951 0.000 1.000
#> GSM62307 2 0.0000 0.951 0.000 1.000
#> GSM62316 2 0.0000 0.951 0.000 1.000
#> GSM62254 2 0.0000 0.951 0.000 1.000
#> GSM62292 2 0.0000 0.951 0.000 1.000
#> GSM62253 1 0.6531 0.834 0.832 0.168
#> GSM62270 1 0.0000 0.872 1.000 0.000
#> GSM62278 1 0.0376 0.873 0.996 0.004
#> GSM62297 2 0.0000 0.951 0.000 1.000
#> GSM62298 2 0.0000 0.951 0.000 1.000
#> GSM62299 2 0.0000 0.951 0.000 1.000
#> GSM62258 1 0.9000 0.650 0.684 0.316
#> GSM62281 2 0.0000 0.951 0.000 1.000
#> GSM62294 2 0.0000 0.951 0.000 1.000
#> GSM62305 2 0.6531 0.794 0.168 0.832
#> GSM62306 2 0.6531 0.794 0.168 0.832
#> GSM62310 2 0.0000 0.951 0.000 1.000
#> GSM62311 2 0.0000 0.951 0.000 1.000
#> GSM62317 2 0.0000 0.951 0.000 1.000
#> GSM62318 2 0.4939 0.867 0.108 0.892
#> GSM62321 2 0.0000 0.951 0.000 1.000
#> GSM62322 1 0.0000 0.872 1.000 0.000
#> GSM62250 2 0.4815 0.868 0.104 0.896
#> GSM62252 2 0.4815 0.868 0.104 0.896
#> GSM62255 2 0.0000 0.951 0.000 1.000
#> GSM62257 2 0.0000 0.951 0.000 1.000
#> GSM62260 2 0.7602 0.722 0.220 0.780
#> GSM62261 2 0.0000 0.951 0.000 1.000
#> GSM62262 2 0.0000 0.951 0.000 1.000
#> GSM62264 2 0.4939 0.857 0.108 0.892
#> GSM62268 1 0.4815 0.865 0.896 0.104
#> GSM62269 1 0.0000 0.872 1.000 0.000
#> GSM62271 1 0.0376 0.873 0.996 0.004
#> GSM62272 1 0.0000 0.872 1.000 0.000
#> GSM62273 2 0.0000 0.951 0.000 1.000
#> GSM62274 1 0.2236 0.877 0.964 0.036
#> GSM62275 1 0.0000 0.872 1.000 0.000
#> GSM62276 1 0.8608 0.709 0.716 0.284
#> GSM62277 1 0.2236 0.877 0.964 0.036
#> GSM62279 1 0.7219 0.809 0.800 0.200
#> GSM62282 1 0.8713 0.692 0.708 0.292
#> GSM62283 2 0.8144 0.665 0.252 0.748
#> GSM62286 2 0.4815 0.868 0.104 0.896
#> GSM62287 2 0.0000 0.951 0.000 1.000
#> GSM62288 2 0.0000 0.951 0.000 1.000
#> GSM62290 2 0.0000 0.951 0.000 1.000
#> GSM62293 2 0.0000 0.951 0.000 1.000
#> GSM62301 2 0.0000 0.951 0.000 1.000
#> GSM62302 2 0.0000 0.951 0.000 1.000
#> GSM62303 2 0.0000 0.951 0.000 1.000
#> GSM62304 2 0.0000 0.951 0.000 1.000
#> GSM62312 2 0.0000 0.951 0.000 1.000
#> GSM62313 2 0.0000 0.951 0.000 1.000
#> GSM62314 2 0.0000 0.951 0.000 1.000
#> GSM62319 2 0.6343 0.804 0.160 0.840
#> GSM62320 2 0.0000 0.951 0.000 1.000
#> GSM62249 2 0.8144 0.665 0.252 0.748
#> GSM62251 2 0.6887 0.759 0.184 0.816
#> GSM62263 2 0.0000 0.951 0.000 1.000
#> GSM62285 2 0.0000 0.951 0.000 1.000
#> GSM62315 2 0.0000 0.951 0.000 1.000
#> GSM62291 2 0.0000 0.951 0.000 1.000
#> GSM62265 2 0.8813 0.570 0.300 0.700
#> GSM62266 1 0.6531 0.834 0.832 0.168
#> GSM62296 2 0.0000 0.951 0.000 1.000
#> GSM62309 2 0.0000 0.951 0.000 1.000
#> GSM62295 2 0.0000 0.951 0.000 1.000
#> GSM62300 2 0.0000 0.951 0.000 1.000
#> GSM62308 2 0.0000 0.951 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM62248 2 0.1411 0.904 0.036 0.964 0.000
#> GSM62256 2 0.0000 0.931 0.000 1.000 0.000
#> GSM62259 2 0.0237 0.929 0.004 0.996 0.000
#> GSM62267 1 0.7181 -0.429 0.508 0.024 0.468
#> GSM62280 1 0.6151 0.615 0.772 0.160 0.068
#> GSM62284 3 0.5785 0.703 0.332 0.000 0.668
#> GSM62289 2 0.1964 0.885 0.056 0.944 0.000
#> GSM62307 2 0.0000 0.931 0.000 1.000 0.000
#> GSM62316 2 0.1411 0.904 0.036 0.964 0.000
#> GSM62254 2 0.0592 0.924 0.012 0.988 0.000
#> GSM62292 2 0.0592 0.924 0.012 0.988 0.000
#> GSM62253 3 0.6180 0.616 0.416 0.000 0.584
#> GSM62270 3 0.0000 0.719 0.000 0.000 1.000
#> GSM62278 3 0.3412 0.747 0.124 0.000 0.876
#> GSM62297 2 0.0000 0.931 0.000 1.000 0.000
#> GSM62298 2 0.0000 0.931 0.000 1.000 0.000
#> GSM62299 2 0.0000 0.931 0.000 1.000 0.000
#> GSM62258 1 0.7021 -0.383 0.544 0.020 0.436
#> GSM62281 2 0.0000 0.931 0.000 1.000 0.000
#> GSM62294 2 0.0000 0.931 0.000 1.000 0.000
#> GSM62305 2 0.6154 0.257 0.408 0.592 0.000
#> GSM62306 2 0.6154 0.257 0.408 0.592 0.000
#> GSM62310 2 0.0000 0.931 0.000 1.000 0.000
#> GSM62311 2 0.0000 0.931 0.000 1.000 0.000
#> GSM62317 1 0.5926 0.507 0.644 0.356 0.000
#> GSM62318 1 0.6402 0.619 0.744 0.200 0.056
#> GSM62321 1 0.5926 0.507 0.644 0.356 0.000
#> GSM62322 3 0.0000 0.719 0.000 0.000 1.000
#> GSM62250 2 0.6095 0.297 0.392 0.608 0.000
#> GSM62252 2 0.6095 0.297 0.392 0.608 0.000
#> GSM62255 2 0.0000 0.931 0.000 1.000 0.000
#> GSM62257 2 0.0000 0.931 0.000 1.000 0.000
#> GSM62260 1 0.3499 0.565 0.900 0.072 0.028
#> GSM62261 2 0.0000 0.931 0.000 1.000 0.000
#> GSM62262 2 0.0000 0.931 0.000 1.000 0.000
#> GSM62264 1 0.5348 0.614 0.796 0.176 0.028
#> GSM62268 3 0.5905 0.686 0.352 0.000 0.648
#> GSM62269 3 0.0000 0.719 0.000 0.000 1.000
#> GSM62271 3 0.3412 0.747 0.124 0.000 0.876
#> GSM62272 3 0.0000 0.719 0.000 0.000 1.000
#> GSM62273 2 0.0592 0.924 0.012 0.988 0.000
#> GSM62274 3 0.5431 0.730 0.284 0.000 0.716
#> GSM62275 3 0.0000 0.719 0.000 0.000 1.000
#> GSM62276 1 0.7181 -0.429 0.508 0.024 0.468
#> GSM62277 3 0.5431 0.730 0.284 0.000 0.716
#> GSM62279 3 0.6625 0.569 0.440 0.008 0.552
#> GSM62282 3 0.6274 0.474 0.456 0.000 0.544
#> GSM62283 1 0.3112 0.569 0.900 0.096 0.004
#> GSM62286 2 0.6095 0.297 0.392 0.608 0.000
#> GSM62287 2 0.0000 0.931 0.000 1.000 0.000
#> GSM62288 2 0.1411 0.904 0.036 0.964 0.000
#> GSM62290 2 0.0000 0.931 0.000 1.000 0.000
#> GSM62293 2 0.0000 0.931 0.000 1.000 0.000
#> GSM62301 2 0.0000 0.931 0.000 1.000 0.000
#> GSM62302 2 0.0000 0.931 0.000 1.000 0.000
#> GSM62303 2 0.0000 0.931 0.000 1.000 0.000
#> GSM62304 2 0.0000 0.931 0.000 1.000 0.000
#> GSM62312 2 0.0000 0.931 0.000 1.000 0.000
#> GSM62313 2 0.0000 0.931 0.000 1.000 0.000
#> GSM62314 2 0.1411 0.904 0.036 0.964 0.000
#> GSM62319 2 0.5706 0.468 0.320 0.680 0.000
#> GSM62320 2 0.0000 0.931 0.000 1.000 0.000
#> GSM62249 1 0.3112 0.569 0.900 0.096 0.004
#> GSM62251 1 0.7945 0.587 0.652 0.224 0.124
#> GSM62263 1 0.5733 0.575 0.676 0.324 0.000
#> GSM62285 2 0.0000 0.931 0.000 1.000 0.000
#> GSM62315 2 0.0000 0.931 0.000 1.000 0.000
#> GSM62291 2 0.0000 0.931 0.000 1.000 0.000
#> GSM62265 1 0.4087 0.524 0.880 0.068 0.052
#> GSM62266 3 0.6180 0.616 0.416 0.000 0.584
#> GSM62296 2 0.0000 0.931 0.000 1.000 0.000
#> GSM62309 2 0.0000 0.931 0.000 1.000 0.000
#> GSM62295 2 0.0424 0.926 0.008 0.992 0.000
#> GSM62300 2 0.0000 0.931 0.000 1.000 0.000
#> GSM62308 2 0.0000 0.931 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM62248 2 0.1706 0.903 0.000 0.948 0.016 0.036
#> GSM62256 2 0.0188 0.930 0.000 0.996 0.004 0.000
#> GSM62259 2 0.0336 0.929 0.000 0.992 0.008 0.000
#> GSM62267 1 0.3107 0.653 0.884 0.000 0.036 0.080
#> GSM62280 4 0.7474 0.500 0.280 0.000 0.220 0.500
#> GSM62284 1 0.2216 0.663 0.908 0.000 0.092 0.000
#> GSM62289 2 0.2328 0.884 0.004 0.924 0.016 0.056
#> GSM62307 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM62316 2 0.1706 0.903 0.000 0.948 0.016 0.036
#> GSM62254 2 0.0921 0.920 0.000 0.972 0.028 0.000
#> GSM62292 2 0.0921 0.920 0.000 0.972 0.028 0.000
#> GSM62253 1 0.0657 0.707 0.984 0.000 0.004 0.012
#> GSM62270 3 0.4624 1.000 0.340 0.000 0.660 0.000
#> GSM62278 1 0.4406 0.161 0.700 0.000 0.300 0.000
#> GSM62297 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM62298 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM62299 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM62258 1 0.4139 0.613 0.816 0.000 0.040 0.144
#> GSM62281 2 0.0188 0.930 0.000 0.996 0.004 0.000
#> GSM62294 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM62305 2 0.7581 0.343 0.268 0.572 0.036 0.124
#> GSM62306 2 0.7581 0.343 0.268 0.572 0.036 0.124
#> GSM62310 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM62311 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM62317 4 0.5691 0.520 0.000 0.048 0.304 0.648
#> GSM62318 4 0.6941 0.552 0.192 0.000 0.220 0.588
#> GSM62321 4 0.5691 0.520 0.000 0.048 0.304 0.648
#> GSM62322 3 0.4624 1.000 0.340 0.000 0.660 0.000
#> GSM62250 2 0.7678 0.375 0.200 0.584 0.036 0.180
#> GSM62252 2 0.7678 0.375 0.200 0.584 0.036 0.180
#> GSM62255 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM62257 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM62260 4 0.6024 0.449 0.376 0.012 0.028 0.584
#> GSM62261 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM62262 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM62264 4 0.4194 0.576 0.172 0.000 0.028 0.800
#> GSM62268 1 0.2198 0.676 0.920 0.000 0.072 0.008
#> GSM62269 3 0.4624 1.000 0.340 0.000 0.660 0.000
#> GSM62271 1 0.4406 0.161 0.700 0.000 0.300 0.000
#> GSM62272 3 0.4624 1.000 0.340 0.000 0.660 0.000
#> GSM62273 2 0.0921 0.920 0.000 0.972 0.028 0.000
#> GSM62274 1 0.2921 0.607 0.860 0.000 0.140 0.000
#> GSM62275 3 0.4624 1.000 0.340 0.000 0.660 0.000
#> GSM62276 1 0.3107 0.653 0.884 0.000 0.036 0.080
#> GSM62277 1 0.2921 0.607 0.860 0.000 0.140 0.000
#> GSM62279 1 0.1211 0.701 0.960 0.000 0.000 0.040
#> GSM62282 1 0.5332 0.551 0.748 0.000 0.124 0.128
#> GSM62283 4 0.7338 0.329 0.420 0.072 0.032 0.476
#> GSM62286 2 0.7678 0.375 0.200 0.584 0.036 0.180
#> GSM62287 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM62288 2 0.1706 0.903 0.000 0.948 0.016 0.036
#> GSM62290 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM62293 2 0.0592 0.925 0.000 0.984 0.016 0.000
#> GSM62301 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM62302 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM62303 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM62304 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM62312 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM62313 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM62314 2 0.1706 0.903 0.000 0.948 0.016 0.036
#> GSM62319 2 0.6428 0.526 0.248 0.664 0.036 0.052
#> GSM62320 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM62249 4 0.7338 0.329 0.420 0.072 0.032 0.476
#> GSM62251 4 0.5279 0.536 0.252 0.044 0.000 0.704
#> GSM62263 4 0.4686 0.547 0.068 0.144 0.000 0.788
#> GSM62285 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM62315 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM62291 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM62265 1 0.6933 -0.373 0.464 0.044 0.032 0.460
#> GSM62266 1 0.0657 0.707 0.984 0.000 0.004 0.012
#> GSM62296 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM62309 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM62295 2 0.0817 0.922 0.000 0.976 0.024 0.000
#> GSM62300 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM62308 2 0.0000 0.932 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM62248 4 0.1908 0.8637 0.000 0.000 0.000 0.908 0.092
#> GSM62256 4 0.0162 0.9248 0.000 0.000 0.000 0.996 0.004
#> GSM62259 4 0.0451 0.9218 0.000 0.000 0.004 0.988 0.008
#> GSM62267 1 0.4774 0.4341 0.540 0.004 0.012 0.000 0.444
#> GSM62280 2 0.5924 0.6152 0.156 0.608 0.004 0.000 0.232
#> GSM62284 1 0.2127 0.7228 0.892 0.000 0.108 0.000 0.000
#> GSM62289 4 0.2230 0.8411 0.000 0.000 0.000 0.884 0.116
#> GSM62307 4 0.0000 0.9259 0.000 0.000 0.000 1.000 0.000
#> GSM62316 4 0.1908 0.8637 0.000 0.000 0.000 0.908 0.092
#> GSM62254 4 0.0955 0.9113 0.000 0.000 0.004 0.968 0.028
#> GSM62292 4 0.0955 0.9113 0.000 0.000 0.004 0.968 0.028
#> GSM62253 1 0.1764 0.7191 0.928 0.000 0.008 0.000 0.064
#> GSM62270 3 0.0404 1.0000 0.012 0.000 0.988 0.000 0.000
#> GSM62278 1 0.4238 0.5394 0.628 0.004 0.368 0.000 0.000
#> GSM62297 4 0.0162 0.9256 0.000 0.004 0.000 0.996 0.000
#> GSM62298 4 0.0162 0.9256 0.000 0.004 0.000 0.996 0.000
#> GSM62299 4 0.0162 0.9256 0.000 0.004 0.000 0.996 0.000
#> GSM62258 1 0.4738 0.3975 0.564 0.012 0.004 0.000 0.420
#> GSM62281 4 0.0162 0.9248 0.000 0.000 0.000 0.996 0.004
#> GSM62294 4 0.0000 0.9259 0.000 0.000 0.000 1.000 0.000
#> GSM62305 4 0.4562 0.0504 0.000 0.000 0.008 0.496 0.496
#> GSM62306 5 0.4562 -0.1875 0.000 0.000 0.008 0.496 0.496
#> GSM62310 4 0.0000 0.9259 0.000 0.000 0.000 1.000 0.000
#> GSM62311 4 0.0000 0.9259 0.000 0.000 0.000 1.000 0.000
#> GSM62317 2 0.1331 0.7286 0.000 0.952 0.000 0.040 0.008
#> GSM62318 2 0.5229 0.6798 0.108 0.688 0.004 0.000 0.200
#> GSM62321 2 0.1331 0.7286 0.000 0.952 0.000 0.040 0.008
#> GSM62322 3 0.0404 1.0000 0.012 0.000 0.988 0.000 0.000
#> GSM62250 4 0.4538 0.2084 0.000 0.000 0.008 0.540 0.452
#> GSM62252 4 0.4538 0.2084 0.000 0.000 0.008 0.540 0.452
#> GSM62255 4 0.0000 0.9259 0.000 0.000 0.000 1.000 0.000
#> GSM62257 4 0.0000 0.9259 0.000 0.000 0.000 1.000 0.000
#> GSM62260 5 0.3961 0.3294 0.032 0.184 0.004 0.000 0.780
#> GSM62261 4 0.0162 0.9256 0.000 0.004 0.000 0.996 0.000
#> GSM62262 4 0.0000 0.9259 0.000 0.000 0.000 1.000 0.000
#> GSM62264 5 0.5218 0.0297 0.036 0.424 0.004 0.000 0.536
#> GSM62268 1 0.1732 0.7261 0.920 0.000 0.080 0.000 0.000
#> GSM62269 3 0.0404 1.0000 0.012 0.000 0.988 0.000 0.000
#> GSM62271 1 0.4238 0.5394 0.628 0.004 0.368 0.000 0.000
#> GSM62272 3 0.0404 1.0000 0.012 0.000 0.988 0.000 0.000
#> GSM62273 4 0.0955 0.9113 0.000 0.000 0.004 0.968 0.028
#> GSM62274 1 0.2690 0.7115 0.844 0.000 0.156 0.000 0.000
#> GSM62275 3 0.0404 1.0000 0.012 0.000 0.988 0.000 0.000
#> GSM62276 1 0.4774 0.4341 0.540 0.004 0.012 0.000 0.444
#> GSM62277 1 0.2690 0.7115 0.844 0.000 0.156 0.000 0.000
#> GSM62279 1 0.1965 0.7068 0.904 0.000 0.000 0.000 0.096
#> GSM62282 1 0.6839 0.4378 0.568 0.056 0.144 0.000 0.232
#> GSM62283 5 0.1564 0.4961 0.024 0.004 0.000 0.024 0.948
#> GSM62286 4 0.4538 0.2084 0.000 0.000 0.008 0.540 0.452
#> GSM62287 4 0.0000 0.9259 0.000 0.000 0.000 1.000 0.000
#> GSM62288 4 0.1908 0.8637 0.000 0.000 0.000 0.908 0.092
#> GSM62290 4 0.0162 0.9256 0.000 0.004 0.000 0.996 0.000
#> GSM62293 4 0.0510 0.9191 0.000 0.000 0.000 0.984 0.016
#> GSM62301 4 0.0162 0.9256 0.000 0.004 0.000 0.996 0.000
#> GSM62302 4 0.0000 0.9259 0.000 0.000 0.000 1.000 0.000
#> GSM62303 4 0.0000 0.9259 0.000 0.000 0.000 1.000 0.000
#> GSM62304 4 0.0000 0.9259 0.000 0.000 0.000 1.000 0.000
#> GSM62312 4 0.0162 0.9256 0.000 0.004 0.000 0.996 0.000
#> GSM62313 4 0.0000 0.9259 0.000 0.000 0.000 1.000 0.000
#> GSM62314 4 0.1908 0.8637 0.000 0.000 0.000 0.908 0.092
#> GSM62319 4 0.4425 0.3579 0.000 0.000 0.008 0.600 0.392
#> GSM62320 4 0.0000 0.9259 0.000 0.000 0.000 1.000 0.000
#> GSM62249 5 0.1564 0.4961 0.024 0.004 0.000 0.024 0.948
#> GSM62251 5 0.6035 0.1706 0.132 0.340 0.000 0.000 0.528
#> GSM62263 5 0.5787 0.2274 0.004 0.340 0.000 0.092 0.564
#> GSM62285 4 0.0162 0.9256 0.000 0.004 0.000 0.996 0.000
#> GSM62315 4 0.0162 0.9256 0.000 0.004 0.000 0.996 0.000
#> GSM62291 4 0.0162 0.9256 0.000 0.004 0.000 0.996 0.000
#> GSM62265 5 0.1768 0.4718 0.072 0.004 0.000 0.000 0.924
#> GSM62266 1 0.1764 0.7191 0.928 0.000 0.008 0.000 0.064
#> GSM62296 4 0.0162 0.9256 0.000 0.004 0.000 0.996 0.000
#> GSM62309 4 0.0162 0.9256 0.000 0.004 0.000 0.996 0.000
#> GSM62295 4 0.0865 0.9136 0.000 0.000 0.004 0.972 0.024
#> GSM62300 4 0.0162 0.9256 0.000 0.004 0.000 0.996 0.000
#> GSM62308 4 0.0162 0.9256 0.000 0.004 0.000 0.996 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM62248 4 0.3738 0.7799 0.020 0.132 0.000 0.800 0.048 0.000
#> GSM62256 4 0.1116 0.8591 0.004 0.028 0.000 0.960 0.000 0.008
#> GSM62259 4 0.1667 0.8524 0.004 0.044 0.000 0.936 0.008 0.008
#> GSM62267 1 0.2715 0.2853 0.860 0.024 0.004 0.000 0.112 0.000
#> GSM62280 6 0.3290 0.6413 0.252 0.000 0.000 0.000 0.004 0.744
#> GSM62284 1 0.5300 -0.4833 0.516 0.376 0.108 0.000 0.000 0.000
#> GSM62289 4 0.4128 0.7542 0.020 0.148 0.000 0.768 0.064 0.000
#> GSM62307 4 0.0520 0.8585 0.000 0.008 0.000 0.984 0.000 0.008
#> GSM62316 4 0.3738 0.7799 0.020 0.132 0.000 0.800 0.048 0.000
#> GSM62254 4 0.2265 0.8388 0.024 0.068 0.000 0.900 0.008 0.000
#> GSM62292 4 0.2265 0.8388 0.024 0.068 0.000 0.900 0.008 0.000
#> GSM62253 2 0.4783 0.9044 0.420 0.536 0.008 0.000 0.036 0.000
#> GSM62270 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62278 1 0.3911 0.2466 0.624 0.008 0.368 0.000 0.000 0.000
#> GSM62297 4 0.1124 0.8547 0.000 0.008 0.000 0.956 0.000 0.036
#> GSM62298 4 0.1176 0.8549 0.000 0.020 0.000 0.956 0.000 0.024
#> GSM62299 4 0.1088 0.8557 0.000 0.016 0.000 0.960 0.000 0.024
#> GSM62258 1 0.3447 0.3023 0.804 0.004 0.000 0.000 0.044 0.148
#> GSM62281 4 0.1116 0.8591 0.004 0.028 0.000 0.960 0.000 0.008
#> GSM62294 4 0.1327 0.8501 0.000 0.064 0.000 0.936 0.000 0.000
#> GSM62305 4 0.7471 -0.1560 0.296 0.164 0.000 0.352 0.188 0.000
#> GSM62306 4 0.7471 -0.1560 0.296 0.164 0.000 0.352 0.188 0.000
#> GSM62310 4 0.1327 0.8501 0.000 0.064 0.000 0.936 0.000 0.000
#> GSM62311 4 0.1327 0.8501 0.000 0.064 0.000 0.936 0.000 0.000
#> GSM62317 6 0.2805 0.7340 0.000 0.184 0.000 0.000 0.004 0.812
#> GSM62318 6 0.2632 0.6986 0.164 0.000 0.000 0.000 0.004 0.832
#> GSM62321 6 0.2805 0.7340 0.000 0.184 0.000 0.000 0.004 0.812
#> GSM62322 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62250 4 0.7343 0.0778 0.168 0.168 0.000 0.404 0.260 0.000
#> GSM62252 4 0.7343 0.0778 0.168 0.168 0.000 0.404 0.260 0.000
#> GSM62255 4 0.0363 0.8587 0.000 0.012 0.000 0.988 0.000 0.000
#> GSM62257 4 0.0520 0.8585 0.000 0.008 0.000 0.984 0.000 0.008
#> GSM62260 5 0.4681 0.6226 0.176 0.016 0.000 0.000 0.712 0.096
#> GSM62261 4 0.0865 0.8558 0.000 0.000 0.000 0.964 0.000 0.036
#> GSM62262 4 0.1327 0.8501 0.000 0.064 0.000 0.936 0.000 0.000
#> GSM62264 5 0.3313 0.4980 0.004 0.036 0.000 0.000 0.812 0.148
#> GSM62268 2 0.5077 0.7655 0.404 0.516 0.080 0.000 0.000 0.000
#> GSM62269 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62271 1 0.3911 0.2466 0.624 0.008 0.368 0.000 0.000 0.000
#> GSM62272 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62273 4 0.2878 0.8103 0.024 0.100 0.000 0.860 0.016 0.000
#> GSM62274 1 0.5564 -0.3482 0.516 0.328 0.156 0.000 0.000 0.000
#> GSM62275 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62276 1 0.2715 0.2853 0.860 0.024 0.004 0.000 0.112 0.000
#> GSM62277 1 0.5564 -0.3482 0.516 0.328 0.156 0.000 0.000 0.000
#> GSM62279 2 0.4763 0.8561 0.412 0.536 0.000 0.000 0.052 0.000
#> GSM62282 1 0.5082 0.2948 0.660 0.004 0.140 0.000 0.004 0.192
#> GSM62283 5 0.3710 0.6690 0.292 0.012 0.000 0.000 0.696 0.000
#> GSM62286 4 0.7343 0.0778 0.168 0.168 0.000 0.404 0.260 0.000
#> GSM62287 4 0.1327 0.8501 0.000 0.064 0.000 0.936 0.000 0.000
#> GSM62288 4 0.3738 0.7799 0.020 0.132 0.000 0.800 0.048 0.000
#> GSM62290 4 0.1408 0.8520 0.000 0.020 0.000 0.944 0.000 0.036
#> GSM62293 4 0.1779 0.8470 0.016 0.064 0.000 0.920 0.000 0.000
#> GSM62301 4 0.1408 0.8520 0.000 0.020 0.000 0.944 0.000 0.036
#> GSM62302 4 0.1327 0.8501 0.000 0.064 0.000 0.936 0.000 0.000
#> GSM62303 4 0.1327 0.8501 0.000 0.064 0.000 0.936 0.000 0.000
#> GSM62304 4 0.1327 0.8501 0.000 0.064 0.000 0.936 0.000 0.000
#> GSM62312 4 0.1010 0.8553 0.000 0.004 0.000 0.960 0.000 0.036
#> GSM62313 4 0.1327 0.8501 0.000 0.064 0.000 0.936 0.000 0.000
#> GSM62314 4 0.3738 0.7799 0.020 0.132 0.000 0.800 0.048 0.000
#> GSM62319 4 0.6832 0.2073 0.272 0.152 0.000 0.476 0.100 0.000
#> GSM62320 4 0.0820 0.8571 0.000 0.016 0.000 0.972 0.000 0.012
#> GSM62249 5 0.3710 0.6690 0.292 0.012 0.000 0.000 0.696 0.000
#> GSM62251 5 0.4658 0.5044 0.140 0.068 0.000 0.000 0.740 0.052
#> GSM62263 5 0.3649 0.5465 0.004 0.080 0.000 0.036 0.828 0.052
#> GSM62285 4 0.1408 0.8520 0.000 0.020 0.000 0.944 0.000 0.036
#> GSM62315 4 0.1408 0.8520 0.000 0.020 0.000 0.944 0.000 0.036
#> GSM62291 4 0.1408 0.8520 0.000 0.020 0.000 0.944 0.000 0.036
#> GSM62265 5 0.4092 0.6547 0.344 0.020 0.000 0.000 0.636 0.000
#> GSM62266 2 0.4783 0.9044 0.420 0.536 0.008 0.000 0.036 0.000
#> GSM62296 4 0.1408 0.8520 0.000 0.020 0.000 0.944 0.000 0.036
#> GSM62309 4 0.1408 0.8520 0.000 0.020 0.000 0.944 0.000 0.036
#> GSM62295 4 0.2747 0.8155 0.020 0.096 0.000 0.868 0.016 0.000
#> GSM62300 4 0.1408 0.8520 0.000 0.020 0.000 0.944 0.000 0.036
#> GSM62308 4 0.1408 0.8520 0.000 0.020 0.000 0.944 0.000 0.036
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) other(p) genotype/variation(p) k
#> CV:hclust 75 0.2472 0.737 0.442 2
#> CV:hclust 65 0.1933 0.297 0.228 3
#> CV:hclust 64 0.5054 0.281 0.749 4
#> CV:hclust 58 0.4937 0.236 0.980 5
#> CV:hclust 59 0.0474 0.346 0.371 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "kmeans"]
# you can also extract it by
# res = res_list["CV:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 75 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.990 0.996 0.4537 0.550 0.550
#> 3 3 0.663 0.772 0.822 0.2884 0.882 0.792
#> 4 4 0.643 0.872 0.873 0.1843 0.789 0.562
#> 5 5 0.696 0.718 0.801 0.1095 0.919 0.720
#> 6 6 0.795 0.656 0.827 0.0634 0.942 0.745
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
#> GSM62248 2 0.000 0.994 0.000 1.000
#> GSM62256 2 0.000 0.994 0.000 1.000
#> GSM62259 2 0.000 0.994 0.000 1.000
#> GSM62267 1 0.000 1.000 1.000 0.000
#> GSM62280 1 0.000 1.000 1.000 0.000
#> GSM62284 1 0.000 1.000 1.000 0.000
#> GSM62289 2 0.000 0.994 0.000 1.000
#> GSM62307 2 0.000 0.994 0.000 1.000
#> GSM62316 2 0.000 0.994 0.000 1.000
#> GSM62254 2 0.000 0.994 0.000 1.000
#> GSM62292 2 0.000 0.994 0.000 1.000
#> GSM62253 1 0.000 1.000 1.000 0.000
#> GSM62270 1 0.000 1.000 1.000 0.000
#> GSM62278 1 0.000 1.000 1.000 0.000
#> GSM62297 2 0.000 0.994 0.000 1.000
#> GSM62298 2 0.000 0.994 0.000 1.000
#> GSM62299 2 0.000 0.994 0.000 1.000
#> GSM62258 1 0.000 1.000 1.000 0.000
#> GSM62281 2 0.000 0.994 0.000 1.000
#> GSM62294 2 0.000 0.994 0.000 1.000
#> GSM62305 2 0.000 0.994 0.000 1.000
#> GSM62306 2 0.000 0.994 0.000 1.000
#> GSM62310 2 0.000 0.994 0.000 1.000
#> GSM62311 2 0.000 0.994 0.000 1.000
#> GSM62317 2 0.000 0.994 0.000 1.000
#> GSM62318 1 0.000 1.000 1.000 0.000
#> GSM62321 2 0.891 0.555 0.308 0.692
#> GSM62322 1 0.000 1.000 1.000 0.000
#> GSM62250 2 0.000 0.994 0.000 1.000
#> GSM62252 2 0.000 0.994 0.000 1.000
#> GSM62255 2 0.000 0.994 0.000 1.000
#> GSM62257 2 0.000 0.994 0.000 1.000
#> GSM62260 1 0.000 1.000 1.000 0.000
#> GSM62261 2 0.000 0.994 0.000 1.000
#> GSM62262 2 0.000 0.994 0.000 1.000
#> GSM62264 1 0.000 1.000 1.000 0.000
#> GSM62268 1 0.000 1.000 1.000 0.000
#> GSM62269 1 0.000 1.000 1.000 0.000
#> GSM62271 1 0.000 1.000 1.000 0.000
#> GSM62272 1 0.000 1.000 1.000 0.000
#> GSM62273 2 0.000 0.994 0.000 1.000
#> GSM62274 1 0.000 1.000 1.000 0.000
#> GSM62275 1 0.000 1.000 1.000 0.000
#> GSM62276 1 0.000 1.000 1.000 0.000
#> GSM62277 1 0.000 1.000 1.000 0.000
#> GSM62279 1 0.000 1.000 1.000 0.000
#> GSM62282 1 0.000 1.000 1.000 0.000
#> GSM62283 1 0.000 1.000 1.000 0.000
#> GSM62286 2 0.000 0.994 0.000 1.000
#> GSM62287 2 0.000 0.994 0.000 1.000
#> GSM62288 2 0.000 0.994 0.000 1.000
#> GSM62290 2 0.000 0.994 0.000 1.000
#> GSM62293 2 0.000 0.994 0.000 1.000
#> GSM62301 2 0.000 0.994 0.000 1.000
#> GSM62302 2 0.000 0.994 0.000 1.000
#> GSM62303 2 0.000 0.994 0.000 1.000
#> GSM62304 2 0.000 0.994 0.000 1.000
#> GSM62312 2 0.000 0.994 0.000 1.000
#> GSM62313 2 0.000 0.994 0.000 1.000
#> GSM62314 2 0.000 0.994 0.000 1.000
#> GSM62319 2 0.000 0.994 0.000 1.000
#> GSM62320 2 0.000 0.994 0.000 1.000
#> GSM62249 2 0.000 0.994 0.000 1.000
#> GSM62251 1 0.000 1.000 1.000 0.000
#> GSM62263 2 0.000 0.994 0.000 1.000
#> GSM62285 2 0.000 0.994 0.000 1.000
#> GSM62315 2 0.000 0.994 0.000 1.000
#> GSM62291 2 0.000 0.994 0.000 1.000
#> GSM62265 1 0.000 1.000 1.000 0.000
#> GSM62266 1 0.000 1.000 1.000 0.000
#> GSM62296 2 0.000 0.994 0.000 1.000
#> GSM62309 2 0.000 0.994 0.000 1.000
#> GSM62295 2 0.000 0.994 0.000 1.000
#> GSM62300 2 0.000 0.994 0.000 1.000
#> GSM62308 2 0.000 0.994 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM62248 2 0.5431 0.854 0.000 0.716 0.284
#> GSM62256 2 0.5254 0.853 0.000 0.736 0.264
#> GSM62259 2 0.5859 0.857 0.000 0.656 0.344
#> GSM62267 1 0.1031 0.718 0.976 0.000 0.024
#> GSM62280 1 0.1529 0.722 0.960 0.000 0.040
#> GSM62284 1 0.6235 -0.660 0.564 0.000 0.436
#> GSM62289 2 0.5678 0.856 0.000 0.684 0.316
#> GSM62307 2 0.5968 0.855 0.000 0.636 0.364
#> GSM62316 2 0.5760 0.857 0.000 0.672 0.328
#> GSM62254 2 0.5968 0.855 0.000 0.636 0.364
#> GSM62292 2 0.5968 0.855 0.000 0.636 0.364
#> GSM62253 1 0.1753 0.689 0.952 0.000 0.048
#> GSM62270 3 0.6168 1.000 0.412 0.000 0.588
#> GSM62278 3 0.6168 1.000 0.412 0.000 0.588
#> GSM62297 2 0.0000 0.768 0.000 1.000 0.000
#> GSM62298 2 0.2537 0.787 0.000 0.920 0.080
#> GSM62299 2 0.0000 0.768 0.000 1.000 0.000
#> GSM62258 1 0.0000 0.727 1.000 0.000 0.000
#> GSM62281 2 0.5254 0.853 0.000 0.736 0.264
#> GSM62294 2 0.5968 0.855 0.000 0.636 0.364
#> GSM62305 2 0.7394 0.816 0.064 0.652 0.284
#> GSM62306 2 0.5465 0.855 0.000 0.712 0.288
#> GSM62310 2 0.5968 0.855 0.000 0.636 0.364
#> GSM62311 2 0.5968 0.855 0.000 0.636 0.364
#> GSM62317 2 0.2773 0.705 0.024 0.928 0.048
#> GSM62318 1 0.1529 0.722 0.960 0.000 0.040
#> GSM62321 1 0.7442 0.412 0.604 0.348 0.048
#> GSM62322 3 0.6168 1.000 0.412 0.000 0.588
#> GSM62250 2 0.7637 0.810 0.076 0.640 0.284
#> GSM62252 1 0.8777 0.291 0.564 0.148 0.288
#> GSM62255 2 0.5968 0.855 0.000 0.636 0.364
#> GSM62257 2 0.5968 0.855 0.000 0.636 0.364
#> GSM62260 1 0.5847 0.584 0.780 0.172 0.048
#> GSM62261 2 0.5733 0.857 0.000 0.676 0.324
#> GSM62262 2 0.5968 0.855 0.000 0.636 0.364
#> GSM62264 1 0.4930 0.637 0.836 0.120 0.044
#> GSM62268 1 0.4399 0.365 0.812 0.000 0.188
#> GSM62269 3 0.6168 1.000 0.412 0.000 0.588
#> GSM62271 1 0.0892 0.720 0.980 0.000 0.020
#> GSM62272 3 0.6168 1.000 0.412 0.000 0.588
#> GSM62273 2 0.5254 0.851 0.000 0.736 0.264
#> GSM62274 3 0.6168 1.000 0.412 0.000 0.588
#> GSM62275 3 0.6168 1.000 0.412 0.000 0.588
#> GSM62276 1 0.1031 0.718 0.976 0.000 0.024
#> GSM62277 3 0.6168 1.000 0.412 0.000 0.588
#> GSM62279 1 0.1031 0.718 0.976 0.000 0.024
#> GSM62282 1 0.1643 0.725 0.956 0.000 0.044
#> GSM62283 1 0.1170 0.726 0.976 0.016 0.008
#> GSM62286 2 0.5431 0.854 0.000 0.716 0.284
#> GSM62287 2 0.5968 0.855 0.000 0.636 0.364
#> GSM62288 2 0.5733 0.857 0.000 0.676 0.324
#> GSM62290 2 0.0000 0.768 0.000 1.000 0.000
#> GSM62293 2 0.5968 0.855 0.000 0.636 0.364
#> GSM62301 2 0.0424 0.770 0.000 0.992 0.008
#> GSM62302 2 0.5968 0.855 0.000 0.636 0.364
#> GSM62303 2 0.5968 0.855 0.000 0.636 0.364
#> GSM62304 2 0.5968 0.855 0.000 0.636 0.364
#> GSM62312 2 0.0747 0.773 0.000 0.984 0.016
#> GSM62313 2 0.5968 0.855 0.000 0.636 0.364
#> GSM62314 2 0.5760 0.857 0.000 0.672 0.328
#> GSM62319 2 0.0424 0.763 0.000 0.992 0.008
#> GSM62320 2 0.2537 0.787 0.000 0.920 0.080
#> GSM62249 1 0.6527 0.378 0.588 0.404 0.008
#> GSM62251 1 0.2261 0.698 0.932 0.068 0.000
#> GSM62263 2 0.1315 0.747 0.020 0.972 0.008
#> GSM62285 2 0.0424 0.770 0.000 0.992 0.008
#> GSM62315 2 0.0424 0.763 0.000 0.992 0.008
#> GSM62291 2 0.0000 0.768 0.000 1.000 0.000
#> GSM62265 1 0.0237 0.726 0.996 0.000 0.004
#> GSM62266 1 0.1031 0.718 0.976 0.000 0.024
#> GSM62296 2 0.0424 0.763 0.000 0.992 0.008
#> GSM62309 2 0.0424 0.763 0.000 0.992 0.008
#> GSM62295 2 0.5968 0.855 0.000 0.636 0.364
#> GSM62300 2 0.0424 0.763 0.000 0.992 0.008
#> GSM62308 2 0.0424 0.763 0.000 0.992 0.008
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM62248 4 0.2814 0.865 0.000 0.132 0.000 0.868
#> GSM62256 4 0.2654 0.865 0.000 0.108 0.004 0.888
#> GSM62259 4 0.2125 0.880 0.000 0.076 0.004 0.920
#> GSM62267 1 0.2081 0.883 0.916 0.000 0.084 0.000
#> GSM62280 1 0.3074 0.812 0.848 0.152 0.000 0.000
#> GSM62284 3 0.4840 0.618 0.240 0.028 0.732 0.000
#> GSM62289 4 0.3427 0.851 0.028 0.112 0.000 0.860
#> GSM62307 4 0.1824 0.891 0.000 0.060 0.004 0.936
#> GSM62316 4 0.2530 0.879 0.000 0.112 0.000 0.888
#> GSM62254 4 0.0707 0.888 0.000 0.020 0.000 0.980
#> GSM62292 4 0.0707 0.888 0.000 0.020 0.000 0.980
#> GSM62253 1 0.3895 0.850 0.832 0.036 0.132 0.000
#> GSM62270 3 0.0188 0.957 0.004 0.000 0.996 0.000
#> GSM62278 3 0.0336 0.956 0.008 0.000 0.992 0.000
#> GSM62297 2 0.3791 0.930 0.000 0.796 0.004 0.200
#> GSM62298 2 0.4220 0.936 0.000 0.748 0.004 0.248
#> GSM62299 2 0.4088 0.946 0.000 0.764 0.004 0.232
#> GSM62258 1 0.2586 0.884 0.912 0.012 0.068 0.008
#> GSM62281 4 0.2593 0.867 0.000 0.104 0.004 0.892
#> GSM62294 4 0.0921 0.894 0.000 0.028 0.000 0.972
#> GSM62305 4 0.5707 0.720 0.144 0.124 0.004 0.728
#> GSM62306 4 0.2773 0.863 0.000 0.116 0.004 0.880
#> GSM62310 4 0.1474 0.889 0.000 0.052 0.000 0.948
#> GSM62311 4 0.1389 0.891 0.000 0.048 0.000 0.952
#> GSM62317 2 0.3900 0.709 0.084 0.844 0.000 0.072
#> GSM62318 1 0.3356 0.809 0.824 0.176 0.000 0.000
#> GSM62321 1 0.3400 0.801 0.820 0.180 0.000 0.000
#> GSM62322 3 0.0188 0.957 0.004 0.000 0.996 0.000
#> GSM62250 4 0.5528 0.720 0.144 0.124 0.000 0.732
#> GSM62252 4 0.6127 0.616 0.228 0.108 0.000 0.664
#> GSM62255 4 0.1576 0.891 0.000 0.048 0.004 0.948
#> GSM62257 4 0.1576 0.895 0.000 0.048 0.004 0.948
#> GSM62260 1 0.1474 0.858 0.948 0.052 0.000 0.000
#> GSM62261 4 0.2647 0.874 0.000 0.120 0.000 0.880
#> GSM62262 4 0.0921 0.894 0.000 0.028 0.000 0.972
#> GSM62264 1 0.1867 0.861 0.928 0.072 0.000 0.000
#> GSM62268 1 0.5577 0.563 0.636 0.036 0.328 0.000
#> GSM62269 3 0.0188 0.957 0.004 0.000 0.996 0.000
#> GSM62271 1 0.2480 0.882 0.904 0.008 0.088 0.000
#> GSM62272 3 0.0188 0.957 0.004 0.000 0.996 0.000
#> GSM62273 4 0.3908 0.708 0.000 0.212 0.004 0.784
#> GSM62274 3 0.1389 0.929 0.048 0.000 0.952 0.000
#> GSM62275 3 0.0188 0.957 0.004 0.000 0.996 0.000
#> GSM62276 1 0.2081 0.883 0.916 0.000 0.084 0.000
#> GSM62277 3 0.0469 0.954 0.012 0.000 0.988 0.000
#> GSM62279 1 0.2542 0.882 0.904 0.012 0.084 0.000
#> GSM62282 1 0.3787 0.835 0.840 0.124 0.036 0.000
#> GSM62283 1 0.2695 0.880 0.912 0.024 0.056 0.008
#> GSM62286 4 0.3991 0.829 0.048 0.120 0.000 0.832
#> GSM62287 4 0.0921 0.894 0.000 0.028 0.000 0.972
#> GSM62288 4 0.2647 0.874 0.000 0.120 0.000 0.880
#> GSM62290 2 0.3907 0.947 0.000 0.768 0.000 0.232
#> GSM62293 4 0.0336 0.892 0.000 0.008 0.000 0.992
#> GSM62301 2 0.3942 0.945 0.000 0.764 0.000 0.236
#> GSM62302 4 0.1389 0.891 0.000 0.048 0.000 0.952
#> GSM62303 4 0.0707 0.894 0.000 0.020 0.000 0.980
#> GSM62304 4 0.1389 0.891 0.000 0.048 0.000 0.952
#> GSM62312 2 0.4155 0.942 0.000 0.756 0.004 0.240
#> GSM62313 4 0.1389 0.891 0.000 0.048 0.000 0.952
#> GSM62314 4 0.2530 0.877 0.000 0.112 0.000 0.888
#> GSM62319 2 0.4610 0.875 0.020 0.744 0.000 0.236
#> GSM62320 2 0.4220 0.936 0.000 0.748 0.004 0.248
#> GSM62249 1 0.4508 0.727 0.780 0.184 0.000 0.036
#> GSM62251 1 0.3168 0.880 0.884 0.060 0.056 0.000
#> GSM62263 2 0.3899 0.831 0.052 0.840 0.000 0.108
#> GSM62285 2 0.3942 0.945 0.000 0.764 0.000 0.236
#> GSM62315 2 0.3907 0.947 0.000 0.768 0.000 0.232
#> GSM62291 2 0.3907 0.947 0.000 0.768 0.000 0.232
#> GSM62265 1 0.3082 0.878 0.884 0.032 0.084 0.000
#> GSM62266 1 0.3557 0.867 0.856 0.036 0.108 0.000
#> GSM62296 2 0.3726 0.943 0.000 0.788 0.000 0.212
#> GSM62309 2 0.3688 0.941 0.000 0.792 0.000 0.208
#> GSM62295 4 0.0895 0.889 0.000 0.020 0.004 0.976
#> GSM62300 2 0.3726 0.943 0.000 0.788 0.000 0.212
#> GSM62308 2 0.3726 0.943 0.000 0.788 0.000 0.212
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM62248 5 0.4855 0.5919 0.000 0.024 0.000 0.424 0.552
#> GSM62256 5 0.4964 0.5452 0.000 0.020 0.004 0.460 0.516
#> GSM62259 4 0.4449 0.2655 0.000 0.020 0.004 0.688 0.288
#> GSM62267 1 0.4995 0.8174 0.584 0.004 0.028 0.000 0.384
#> GSM62280 1 0.1697 0.6228 0.932 0.060 0.000 0.000 0.008
#> GSM62284 3 0.6381 0.3573 0.240 0.024 0.588 0.000 0.148
#> GSM62289 5 0.4630 0.6371 0.000 0.016 0.000 0.396 0.588
#> GSM62307 4 0.0609 0.7769 0.000 0.020 0.000 0.980 0.000
#> GSM62316 4 0.4338 0.3197 0.000 0.024 0.000 0.696 0.280
#> GSM62254 4 0.3544 0.5108 0.000 0.008 0.004 0.788 0.200
#> GSM62292 4 0.3544 0.5108 0.000 0.008 0.004 0.788 0.200
#> GSM62253 1 0.5620 0.8044 0.552 0.036 0.024 0.000 0.388
#> GSM62270 3 0.0162 0.9287 0.004 0.000 0.996 0.000 0.000
#> GSM62278 3 0.0162 0.9287 0.004 0.000 0.996 0.000 0.000
#> GSM62297 2 0.2863 0.8766 0.000 0.876 0.000 0.060 0.064
#> GSM62298 2 0.2179 0.9307 0.000 0.888 0.000 0.112 0.000
#> GSM62299 2 0.2179 0.9307 0.000 0.888 0.000 0.112 0.000
#> GSM62258 1 0.4613 0.8163 0.620 0.000 0.020 0.000 0.360
#> GSM62281 5 0.5050 0.4936 0.000 0.024 0.004 0.476 0.496
#> GSM62294 4 0.0162 0.7797 0.000 0.004 0.000 0.996 0.000
#> GSM62305 5 0.4237 0.6358 0.016 0.016 0.004 0.200 0.764
#> GSM62306 5 0.4860 0.5853 0.000 0.016 0.004 0.440 0.540
#> GSM62310 4 0.0510 0.7777 0.000 0.016 0.000 0.984 0.000
#> GSM62311 4 0.0404 0.7808 0.000 0.012 0.000 0.988 0.000
#> GSM62317 2 0.4854 0.5147 0.340 0.628 0.000 0.028 0.004
#> GSM62318 1 0.1410 0.6226 0.940 0.060 0.000 0.000 0.000
#> GSM62321 1 0.2569 0.6050 0.892 0.068 0.000 0.000 0.040
#> GSM62322 3 0.0162 0.9287 0.004 0.000 0.996 0.000 0.000
#> GSM62250 5 0.3628 0.6382 0.000 0.012 0.000 0.216 0.772
#> GSM62252 5 0.3697 0.6156 0.016 0.008 0.000 0.180 0.796
#> GSM62255 4 0.0404 0.7808 0.000 0.012 0.000 0.988 0.000
#> GSM62257 4 0.0510 0.7795 0.000 0.016 0.000 0.984 0.000
#> GSM62260 1 0.4497 0.7813 0.632 0.016 0.000 0.000 0.352
#> GSM62261 4 0.4397 0.3278 0.000 0.028 0.000 0.696 0.276
#> GSM62262 4 0.0162 0.7797 0.000 0.004 0.000 0.996 0.000
#> GSM62264 1 0.5155 0.8004 0.596 0.052 0.000 0.000 0.352
#> GSM62268 1 0.7265 0.4960 0.460 0.036 0.276 0.000 0.228
#> GSM62269 3 0.0162 0.9287 0.004 0.000 0.996 0.000 0.000
#> GSM62271 1 0.4718 0.8182 0.628 0.000 0.028 0.000 0.344
#> GSM62272 3 0.0162 0.9287 0.004 0.000 0.996 0.000 0.000
#> GSM62273 4 0.6658 -0.0444 0.000 0.304 0.004 0.472 0.220
#> GSM62274 3 0.2867 0.8434 0.044 0.004 0.880 0.000 0.072
#> GSM62275 3 0.0162 0.9287 0.004 0.000 0.996 0.000 0.000
#> GSM62276 1 0.4846 0.8169 0.588 0.000 0.028 0.000 0.384
#> GSM62277 3 0.0960 0.9175 0.008 0.004 0.972 0.000 0.016
#> GSM62279 1 0.5468 0.8087 0.528 0.024 0.024 0.000 0.424
#> GSM62282 1 0.3238 0.6545 0.872 0.048 0.032 0.000 0.048
#> GSM62283 1 0.4171 0.8135 0.604 0.000 0.000 0.000 0.396
#> GSM62286 5 0.4630 0.6371 0.000 0.016 0.000 0.396 0.588
#> GSM62287 4 0.0162 0.7797 0.000 0.004 0.000 0.996 0.000
#> GSM62288 4 0.4584 0.2104 0.000 0.028 0.000 0.660 0.312
#> GSM62290 2 0.2179 0.9307 0.000 0.888 0.000 0.112 0.000
#> GSM62293 4 0.0451 0.7673 0.000 0.004 0.000 0.988 0.008
#> GSM62301 2 0.2338 0.9304 0.000 0.884 0.000 0.112 0.004
#> GSM62302 4 0.0404 0.7808 0.000 0.012 0.000 0.988 0.000
#> GSM62303 4 0.0162 0.7797 0.000 0.004 0.000 0.996 0.000
#> GSM62304 4 0.0404 0.7808 0.000 0.012 0.000 0.988 0.000
#> GSM62312 2 0.2338 0.9304 0.000 0.884 0.000 0.112 0.004
#> GSM62313 4 0.0404 0.7808 0.000 0.012 0.000 0.988 0.000
#> GSM62314 4 0.4169 0.4200 0.000 0.028 0.000 0.732 0.240
#> GSM62319 2 0.5690 0.6418 0.020 0.672 0.004 0.092 0.212
#> GSM62320 2 0.2179 0.9307 0.000 0.888 0.000 0.112 0.000
#> GSM62249 5 0.3474 0.1743 0.116 0.044 0.000 0.004 0.836
#> GSM62251 1 0.5014 0.8026 0.536 0.032 0.000 0.000 0.432
#> GSM62263 2 0.4456 0.6492 0.004 0.716 0.000 0.032 0.248
#> GSM62285 2 0.2338 0.9304 0.000 0.884 0.000 0.112 0.004
#> GSM62315 2 0.2338 0.9304 0.000 0.884 0.000 0.112 0.004
#> GSM62291 2 0.2127 0.9302 0.000 0.892 0.000 0.108 0.000
#> GSM62265 1 0.5370 0.8076 0.544 0.020 0.024 0.000 0.412
#> GSM62266 1 0.5620 0.8044 0.552 0.036 0.024 0.000 0.388
#> GSM62296 2 0.2074 0.9291 0.000 0.896 0.000 0.104 0.000
#> GSM62309 2 0.2179 0.9267 0.000 0.896 0.000 0.100 0.004
#> GSM62295 4 0.3544 0.5108 0.000 0.008 0.004 0.788 0.200
#> GSM62300 2 0.2074 0.9291 0.000 0.896 0.000 0.104 0.000
#> GSM62308 2 0.2074 0.9291 0.000 0.896 0.000 0.104 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM62248 5 0.2920 0.7679 0.000 0.008 0.000 0.128 0.844 0.020
#> GSM62256 5 0.4585 0.7315 0.000 0.016 0.000 0.144 0.728 0.112
#> GSM62259 4 0.5979 -0.0668 0.000 0.004 0.000 0.412 0.392 0.192
#> GSM62267 1 0.3852 0.7113 0.796 0.016 0.000 0.000 0.080 0.108
#> GSM62280 6 0.2969 0.7030 0.224 0.000 0.000 0.000 0.000 0.776
#> GSM62284 1 0.4653 -0.2247 0.484 0.020 0.484 0.000 0.012 0.000
#> GSM62289 5 0.2261 0.7873 0.000 0.004 0.000 0.104 0.884 0.008
#> GSM62307 4 0.1332 0.7653 0.000 0.012 0.000 0.952 0.008 0.028
#> GSM62316 4 0.4565 -0.0977 0.000 0.008 0.000 0.496 0.476 0.020
#> GSM62254 4 0.5177 0.4019 0.000 0.000 0.000 0.612 0.236 0.152
#> GSM62292 4 0.5177 0.4019 0.000 0.000 0.000 0.612 0.236 0.152
#> GSM62253 1 0.1251 0.7063 0.956 0.024 0.000 0.000 0.012 0.008
#> GSM62270 3 0.0146 0.9368 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM62278 3 0.0458 0.9316 0.016 0.000 0.984 0.000 0.000 0.000
#> GSM62297 2 0.1838 0.8301 0.000 0.928 0.000 0.012 0.040 0.020
#> GSM62298 2 0.1549 0.8625 0.000 0.936 0.000 0.044 0.000 0.020
#> GSM62299 2 0.1549 0.8625 0.000 0.936 0.000 0.044 0.000 0.020
#> GSM62258 1 0.4191 0.6740 0.752 0.008 0.000 0.000 0.084 0.156
#> GSM62281 5 0.5029 0.6852 0.000 0.016 0.000 0.156 0.680 0.148
#> GSM62294 4 0.0260 0.7757 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM62305 5 0.3033 0.7424 0.032 0.004 0.000 0.012 0.856 0.096
#> GSM62306 5 0.4002 0.7545 0.000 0.004 0.000 0.132 0.768 0.096
#> GSM62310 4 0.0551 0.7751 0.000 0.008 0.000 0.984 0.004 0.004
#> GSM62311 4 0.0508 0.7758 0.000 0.012 0.000 0.984 0.004 0.000
#> GSM62317 6 0.4088 0.2618 0.000 0.368 0.000 0.000 0.016 0.616
#> GSM62318 6 0.2969 0.7030 0.224 0.000 0.000 0.000 0.000 0.776
#> GSM62321 6 0.3660 0.6773 0.160 0.000 0.000 0.000 0.060 0.780
#> GSM62322 3 0.0146 0.9368 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM62250 5 0.1413 0.7622 0.036 0.004 0.000 0.008 0.948 0.004
#> GSM62252 5 0.1413 0.7622 0.036 0.004 0.000 0.008 0.948 0.004
#> GSM62255 4 0.0508 0.7760 0.000 0.012 0.000 0.984 0.000 0.004
#> GSM62257 4 0.1364 0.7667 0.000 0.012 0.000 0.952 0.016 0.020
#> GSM62260 1 0.5584 0.4373 0.580 0.016 0.000 0.000 0.128 0.276
#> GSM62261 4 0.4933 -0.0913 0.000 0.020 0.004 0.492 0.464 0.020
#> GSM62262 4 0.1049 0.7646 0.000 0.008 0.000 0.960 0.000 0.032
#> GSM62264 1 0.3313 0.6037 0.820 0.016 0.000 0.000 0.024 0.140
#> GSM62268 1 0.3474 0.5681 0.816 0.024 0.140 0.000 0.012 0.008
#> GSM62269 3 0.0146 0.9368 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM62271 1 0.4124 0.6784 0.764 0.008 0.004 0.000 0.068 0.156
#> GSM62272 3 0.0146 0.9368 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM62273 2 0.7661 -0.1467 0.000 0.288 0.000 0.252 0.276 0.184
#> GSM62274 3 0.4096 0.5994 0.268 0.020 0.700 0.000 0.012 0.000
#> GSM62275 3 0.0146 0.9368 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM62276 1 0.3715 0.7100 0.800 0.008 0.000 0.000 0.084 0.108
#> GSM62277 3 0.2103 0.8848 0.056 0.020 0.912 0.000 0.012 0.000
#> GSM62279 1 0.1895 0.7333 0.912 0.016 0.000 0.000 0.072 0.000
#> GSM62282 6 0.4704 0.4402 0.352 0.008 0.004 0.000 0.032 0.604
#> GSM62283 1 0.4222 0.6976 0.764 0.016 0.000 0.000 0.100 0.120
#> GSM62286 5 0.1806 0.7926 0.000 0.004 0.000 0.088 0.908 0.000
#> GSM62287 4 0.0405 0.7760 0.000 0.008 0.000 0.988 0.004 0.000
#> GSM62288 5 0.4542 0.1597 0.000 0.008 0.000 0.440 0.532 0.020
#> GSM62290 2 0.1007 0.8666 0.000 0.956 0.000 0.044 0.000 0.000
#> GSM62293 4 0.1829 0.7414 0.000 0.004 0.000 0.920 0.012 0.064
#> GSM62301 2 0.1152 0.8664 0.000 0.952 0.004 0.044 0.000 0.000
#> GSM62302 4 0.0551 0.7760 0.000 0.008 0.000 0.984 0.004 0.004
#> GSM62303 4 0.0405 0.7754 0.000 0.008 0.000 0.988 0.000 0.004
#> GSM62304 4 0.0653 0.7755 0.000 0.012 0.000 0.980 0.004 0.004
#> GSM62312 2 0.1296 0.8658 0.000 0.948 0.004 0.044 0.000 0.004
#> GSM62313 4 0.0508 0.7758 0.000 0.012 0.000 0.984 0.004 0.000
#> GSM62314 4 0.4546 0.0055 0.000 0.008 0.000 0.528 0.444 0.020
#> GSM62319 2 0.6407 0.3197 0.000 0.500 0.000 0.044 0.276 0.180
#> GSM62320 2 0.1713 0.8591 0.000 0.928 0.000 0.044 0.000 0.028
#> GSM62249 5 0.3712 0.5098 0.232 0.012 0.000 0.000 0.744 0.012
#> GSM62251 1 0.1679 0.7127 0.936 0.016 0.000 0.000 0.036 0.012
#> GSM62263 2 0.4820 0.1804 0.012 0.532 0.000 0.004 0.428 0.024
#> GSM62285 2 0.1152 0.8664 0.000 0.952 0.004 0.044 0.000 0.000
#> GSM62315 2 0.1152 0.8664 0.000 0.952 0.004 0.044 0.000 0.000
#> GSM62291 2 0.1511 0.8658 0.000 0.940 0.000 0.044 0.012 0.004
#> GSM62265 1 0.1333 0.7347 0.944 0.008 0.000 0.000 0.048 0.000
#> GSM62266 1 0.1251 0.7063 0.956 0.024 0.000 0.000 0.012 0.008
#> GSM62296 2 0.1605 0.8650 0.000 0.936 0.000 0.044 0.016 0.004
#> GSM62309 2 0.1605 0.8650 0.000 0.936 0.000 0.044 0.016 0.004
#> GSM62295 4 0.5217 0.3967 0.000 0.000 0.000 0.608 0.232 0.160
#> GSM62300 2 0.1718 0.8649 0.000 0.932 0.000 0.044 0.016 0.008
#> GSM62308 2 0.1605 0.8650 0.000 0.936 0.000 0.044 0.016 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) other(p) genotype/variation(p) k
#> CV:kmeans 75 0.589716 0.935 0.7479 2
#> CV:kmeans 70 0.391695 0.745 0.8200 3
#> CV:kmeans 75 0.000715 0.767 0.0789 4
#> CV:kmeans 65 0.006004 0.598 0.0593 5
#> CV:kmeans 60 0.008136 0.203 0.3440 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "skmeans"]
# you can also extract it by
# res = res_list["CV:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 75 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.987 0.994 0.4775 0.526 0.526
#> 3 3 1.000 0.952 0.977 0.3896 0.792 0.612
#> 4 4 0.831 0.849 0.923 0.0969 0.922 0.776
#> 5 5 0.828 0.799 0.903 0.0661 0.943 0.802
#> 6 6 0.818 0.678 0.844 0.0364 0.979 0.912
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
#> GSM62248 2 0.000 0.990 0.000 1.000
#> GSM62256 2 0.000 0.990 0.000 1.000
#> GSM62259 2 0.000 0.990 0.000 1.000
#> GSM62267 1 0.000 1.000 1.000 0.000
#> GSM62280 1 0.000 1.000 1.000 0.000
#> GSM62284 1 0.000 1.000 1.000 0.000
#> GSM62289 2 0.000 0.990 0.000 1.000
#> GSM62307 2 0.000 0.990 0.000 1.000
#> GSM62316 2 0.000 0.990 0.000 1.000
#> GSM62254 2 0.000 0.990 0.000 1.000
#> GSM62292 2 0.000 0.990 0.000 1.000
#> GSM62253 1 0.000 1.000 1.000 0.000
#> GSM62270 1 0.000 1.000 1.000 0.000
#> GSM62278 1 0.000 1.000 1.000 0.000
#> GSM62297 2 0.000 0.990 0.000 1.000
#> GSM62298 2 0.000 0.990 0.000 1.000
#> GSM62299 2 0.000 0.990 0.000 1.000
#> GSM62258 1 0.000 1.000 1.000 0.000
#> GSM62281 2 0.000 0.990 0.000 1.000
#> GSM62294 2 0.000 0.990 0.000 1.000
#> GSM62305 2 0.605 0.826 0.148 0.852
#> GSM62306 2 0.000 0.990 0.000 1.000
#> GSM62310 2 0.000 0.990 0.000 1.000
#> GSM62311 2 0.000 0.990 0.000 1.000
#> GSM62317 2 0.000 0.990 0.000 1.000
#> GSM62318 1 0.000 1.000 1.000 0.000
#> GSM62321 1 0.000 1.000 1.000 0.000
#> GSM62322 1 0.000 1.000 1.000 0.000
#> GSM62250 2 0.866 0.602 0.288 0.712
#> GSM62252 1 0.000 1.000 1.000 0.000
#> GSM62255 2 0.000 0.990 0.000 1.000
#> GSM62257 2 0.000 0.990 0.000 1.000
#> GSM62260 1 0.000 1.000 1.000 0.000
#> GSM62261 2 0.000 0.990 0.000 1.000
#> GSM62262 2 0.000 0.990 0.000 1.000
#> GSM62264 1 0.000 1.000 1.000 0.000
#> GSM62268 1 0.000 1.000 1.000 0.000
#> GSM62269 1 0.000 1.000 1.000 0.000
#> GSM62271 1 0.000 1.000 1.000 0.000
#> GSM62272 1 0.000 1.000 1.000 0.000
#> GSM62273 2 0.000 0.990 0.000 1.000
#> GSM62274 1 0.000 1.000 1.000 0.000
#> GSM62275 1 0.000 1.000 1.000 0.000
#> GSM62276 1 0.000 1.000 1.000 0.000
#> GSM62277 1 0.000 1.000 1.000 0.000
#> GSM62279 1 0.000 1.000 1.000 0.000
#> GSM62282 1 0.000 1.000 1.000 0.000
#> GSM62283 1 0.000 1.000 1.000 0.000
#> GSM62286 2 0.000 0.990 0.000 1.000
#> GSM62287 2 0.000 0.990 0.000 1.000
#> GSM62288 2 0.000 0.990 0.000 1.000
#> GSM62290 2 0.000 0.990 0.000 1.000
#> GSM62293 2 0.000 0.990 0.000 1.000
#> GSM62301 2 0.000 0.990 0.000 1.000
#> GSM62302 2 0.000 0.990 0.000 1.000
#> GSM62303 2 0.000 0.990 0.000 1.000
#> GSM62304 2 0.000 0.990 0.000 1.000
#> GSM62312 2 0.000 0.990 0.000 1.000
#> GSM62313 2 0.000 0.990 0.000 1.000
#> GSM62314 2 0.000 0.990 0.000 1.000
#> GSM62319 2 0.000 0.990 0.000 1.000
#> GSM62320 2 0.000 0.990 0.000 1.000
#> GSM62249 1 0.000 1.000 1.000 0.000
#> GSM62251 1 0.000 1.000 1.000 0.000
#> GSM62263 2 0.000 0.990 0.000 1.000
#> GSM62285 2 0.000 0.990 0.000 1.000
#> GSM62315 2 0.000 0.990 0.000 1.000
#> GSM62291 2 0.000 0.990 0.000 1.000
#> GSM62265 1 0.000 1.000 1.000 0.000
#> GSM62266 1 0.000 1.000 1.000 0.000
#> GSM62296 2 0.000 0.990 0.000 1.000
#> GSM62309 2 0.000 0.990 0.000 1.000
#> GSM62295 2 0.000 0.990 0.000 1.000
#> GSM62300 2 0.000 0.990 0.000 1.000
#> GSM62308 2 0.000 0.990 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM62248 2 0.1031 0.944 0.000 0.976 0.024
#> GSM62256 2 0.1643 0.938 0.000 0.956 0.044
#> GSM62259 2 0.0747 0.955 0.000 0.984 0.016
#> GSM62267 1 0.0000 0.996 1.000 0.000 0.000
#> GSM62280 1 0.0000 0.996 1.000 0.000 0.000
#> GSM62284 1 0.0000 0.996 1.000 0.000 0.000
#> GSM62289 2 0.0237 0.949 0.000 0.996 0.004
#> GSM62307 2 0.0892 0.955 0.000 0.980 0.020
#> GSM62316 2 0.0424 0.950 0.000 0.992 0.008
#> GSM62254 2 0.0747 0.955 0.000 0.984 0.016
#> GSM62292 2 0.0747 0.955 0.000 0.984 0.016
#> GSM62253 1 0.0000 0.996 1.000 0.000 0.000
#> GSM62270 1 0.0000 0.996 1.000 0.000 0.000
#> GSM62278 1 0.0000 0.996 1.000 0.000 0.000
#> GSM62297 3 0.0000 0.988 0.000 0.000 1.000
#> GSM62298 3 0.0000 0.988 0.000 0.000 1.000
#> GSM62299 3 0.0000 0.988 0.000 0.000 1.000
#> GSM62258 1 0.0000 0.996 1.000 0.000 0.000
#> GSM62281 2 0.6291 0.137 0.000 0.532 0.468
#> GSM62294 2 0.0747 0.955 0.000 0.984 0.016
#> GSM62305 2 0.2680 0.887 0.068 0.924 0.008
#> GSM62306 2 0.0000 0.949 0.000 1.000 0.000
#> GSM62310 2 0.1411 0.947 0.000 0.964 0.036
#> GSM62311 2 0.0892 0.955 0.000 0.980 0.020
#> GSM62317 3 0.0000 0.988 0.000 0.000 1.000
#> GSM62318 1 0.0000 0.996 1.000 0.000 0.000
#> GSM62321 1 0.2066 0.938 0.940 0.000 0.060
#> GSM62322 1 0.0000 0.996 1.000 0.000 0.000
#> GSM62250 2 0.0237 0.949 0.000 0.996 0.004
#> GSM62252 2 0.6154 0.309 0.408 0.592 0.000
#> GSM62255 2 0.0892 0.955 0.000 0.980 0.020
#> GSM62257 2 0.0892 0.955 0.000 0.980 0.020
#> GSM62260 1 0.0000 0.996 1.000 0.000 0.000
#> GSM62261 2 0.1031 0.944 0.000 0.976 0.024
#> GSM62262 2 0.0747 0.955 0.000 0.984 0.016
#> GSM62264 1 0.0000 0.996 1.000 0.000 0.000
#> GSM62268 1 0.0000 0.996 1.000 0.000 0.000
#> GSM62269 1 0.0000 0.996 1.000 0.000 0.000
#> GSM62271 1 0.0000 0.996 1.000 0.000 0.000
#> GSM62272 1 0.0000 0.996 1.000 0.000 0.000
#> GSM62273 3 0.3941 0.815 0.000 0.156 0.844
#> GSM62274 1 0.0000 0.996 1.000 0.000 0.000
#> GSM62275 1 0.0000 0.996 1.000 0.000 0.000
#> GSM62276 1 0.0000 0.996 1.000 0.000 0.000
#> GSM62277 1 0.0000 0.996 1.000 0.000 0.000
#> GSM62279 1 0.0000 0.996 1.000 0.000 0.000
#> GSM62282 1 0.0000 0.996 1.000 0.000 0.000
#> GSM62283 1 0.0000 0.996 1.000 0.000 0.000
#> GSM62286 2 0.0000 0.949 0.000 1.000 0.000
#> GSM62287 2 0.0747 0.955 0.000 0.984 0.016
#> GSM62288 2 0.1031 0.944 0.000 0.976 0.024
#> GSM62290 3 0.0000 0.988 0.000 0.000 1.000
#> GSM62293 2 0.0747 0.955 0.000 0.984 0.016
#> GSM62301 3 0.0000 0.988 0.000 0.000 1.000
#> GSM62302 2 0.0892 0.955 0.000 0.980 0.020
#> GSM62303 2 0.0747 0.955 0.000 0.984 0.016
#> GSM62304 2 0.0892 0.955 0.000 0.980 0.020
#> GSM62312 3 0.0000 0.988 0.000 0.000 1.000
#> GSM62313 2 0.0892 0.955 0.000 0.980 0.020
#> GSM62314 2 0.1031 0.944 0.000 0.976 0.024
#> GSM62319 3 0.1031 0.969 0.000 0.024 0.976
#> GSM62320 3 0.0000 0.988 0.000 0.000 1.000
#> GSM62249 1 0.1999 0.955 0.952 0.012 0.036
#> GSM62251 1 0.0000 0.996 1.000 0.000 0.000
#> GSM62263 3 0.0747 0.974 0.000 0.016 0.984
#> GSM62285 3 0.0000 0.988 0.000 0.000 1.000
#> GSM62315 3 0.0000 0.988 0.000 0.000 1.000
#> GSM62291 3 0.0000 0.988 0.000 0.000 1.000
#> GSM62265 1 0.0000 0.996 1.000 0.000 0.000
#> GSM62266 1 0.0000 0.996 1.000 0.000 0.000
#> GSM62296 3 0.0000 0.988 0.000 0.000 1.000
#> GSM62309 3 0.0000 0.988 0.000 0.000 1.000
#> GSM62295 2 0.0892 0.954 0.000 0.980 0.020
#> GSM62300 3 0.0000 0.988 0.000 0.000 1.000
#> GSM62308 3 0.0000 0.988 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM62248 4 0.5273 -0.0647 0.000 0.008 0.456 0.536
#> GSM62256 4 0.2048 0.8129 0.000 0.064 0.008 0.928
#> GSM62259 4 0.0672 0.8544 0.000 0.008 0.008 0.984
#> GSM62267 1 0.0000 0.9476 1.000 0.000 0.000 0.000
#> GSM62280 1 0.3172 0.8499 0.840 0.000 0.160 0.000
#> GSM62284 1 0.0000 0.9476 1.000 0.000 0.000 0.000
#> GSM62289 3 0.4088 0.8332 0.000 0.004 0.764 0.232
#> GSM62307 4 0.0336 0.8617 0.000 0.008 0.000 0.992
#> GSM62316 4 0.4744 0.4992 0.000 0.012 0.284 0.704
#> GSM62254 4 0.0336 0.8578 0.000 0.000 0.008 0.992
#> GSM62292 4 0.0336 0.8578 0.000 0.000 0.008 0.992
#> GSM62253 1 0.1022 0.9376 0.968 0.000 0.032 0.000
#> GSM62270 1 0.0000 0.9476 1.000 0.000 0.000 0.000
#> GSM62278 1 0.0000 0.9476 1.000 0.000 0.000 0.000
#> GSM62297 2 0.0000 0.9768 0.000 1.000 0.000 0.000
#> GSM62298 2 0.0000 0.9768 0.000 1.000 0.000 0.000
#> GSM62299 2 0.0000 0.9768 0.000 1.000 0.000 0.000
#> GSM62258 1 0.0000 0.9476 1.000 0.000 0.000 0.000
#> GSM62281 4 0.3668 0.6639 0.000 0.188 0.004 0.808
#> GSM62294 4 0.0000 0.8605 0.000 0.000 0.000 1.000
#> GSM62305 3 0.3895 0.8281 0.000 0.012 0.804 0.184
#> GSM62306 3 0.4277 0.7848 0.000 0.000 0.720 0.280
#> GSM62310 4 0.0469 0.8597 0.000 0.012 0.000 0.988
#> GSM62311 4 0.0336 0.8617 0.000 0.008 0.000 0.992
#> GSM62317 2 0.3172 0.8295 0.000 0.840 0.160 0.000
#> GSM62318 1 0.3569 0.8333 0.804 0.000 0.196 0.000
#> GSM62321 1 0.5489 0.7276 0.700 0.060 0.240 0.000
#> GSM62322 1 0.0000 0.9476 1.000 0.000 0.000 0.000
#> GSM62250 3 0.3649 0.8443 0.000 0.000 0.796 0.204
#> GSM62252 3 0.4188 0.7710 0.112 0.000 0.824 0.064
#> GSM62255 4 0.0336 0.8617 0.000 0.008 0.000 0.992
#> GSM62257 4 0.0336 0.8617 0.000 0.008 0.000 0.992
#> GSM62260 1 0.3942 0.7994 0.764 0.000 0.236 0.000
#> GSM62261 4 0.4744 0.4992 0.000 0.012 0.284 0.704
#> GSM62262 4 0.0000 0.8605 0.000 0.000 0.000 1.000
#> GSM62264 1 0.4103 0.7796 0.744 0.000 0.256 0.000
#> GSM62268 1 0.1022 0.9376 0.968 0.000 0.032 0.000
#> GSM62269 1 0.0000 0.9476 1.000 0.000 0.000 0.000
#> GSM62271 1 0.0000 0.9476 1.000 0.000 0.000 0.000
#> GSM62272 1 0.0000 0.9476 1.000 0.000 0.000 0.000
#> GSM62273 4 0.5288 0.0570 0.000 0.472 0.008 0.520
#> GSM62274 1 0.0000 0.9476 1.000 0.000 0.000 0.000
#> GSM62275 1 0.0000 0.9476 1.000 0.000 0.000 0.000
#> GSM62276 1 0.0000 0.9476 1.000 0.000 0.000 0.000
#> GSM62277 1 0.0000 0.9476 1.000 0.000 0.000 0.000
#> GSM62279 1 0.0000 0.9476 1.000 0.000 0.000 0.000
#> GSM62282 1 0.1557 0.9210 0.944 0.000 0.056 0.000
#> GSM62283 1 0.0188 0.9466 0.996 0.000 0.004 0.000
#> GSM62286 3 0.3975 0.8332 0.000 0.000 0.760 0.240
#> GSM62287 4 0.0000 0.8605 0.000 0.000 0.000 1.000
#> GSM62288 4 0.5075 0.3494 0.000 0.012 0.344 0.644
#> GSM62290 2 0.0000 0.9768 0.000 1.000 0.000 0.000
#> GSM62293 4 0.0000 0.8605 0.000 0.000 0.000 1.000
#> GSM62301 2 0.0000 0.9768 0.000 1.000 0.000 0.000
#> GSM62302 4 0.0336 0.8617 0.000 0.008 0.000 0.992
#> GSM62303 4 0.0000 0.8605 0.000 0.000 0.000 1.000
#> GSM62304 4 0.0336 0.8617 0.000 0.008 0.000 0.992
#> GSM62312 2 0.0000 0.9768 0.000 1.000 0.000 0.000
#> GSM62313 4 0.0336 0.8617 0.000 0.008 0.000 0.992
#> GSM62314 4 0.4137 0.6350 0.000 0.012 0.208 0.780
#> GSM62319 2 0.1042 0.9533 0.000 0.972 0.008 0.020
#> GSM62320 2 0.0000 0.9768 0.000 1.000 0.000 0.000
#> GSM62249 3 0.2589 0.6996 0.116 0.000 0.884 0.000
#> GSM62251 1 0.2345 0.8960 0.900 0.000 0.100 0.000
#> GSM62263 2 0.3528 0.7930 0.000 0.808 0.192 0.000
#> GSM62285 2 0.0000 0.9768 0.000 1.000 0.000 0.000
#> GSM62315 2 0.0000 0.9768 0.000 1.000 0.000 0.000
#> GSM62291 2 0.0000 0.9768 0.000 1.000 0.000 0.000
#> GSM62265 1 0.1022 0.9376 0.968 0.000 0.032 0.000
#> GSM62266 1 0.1022 0.9376 0.968 0.000 0.032 0.000
#> GSM62296 2 0.0000 0.9768 0.000 1.000 0.000 0.000
#> GSM62309 2 0.0000 0.9768 0.000 1.000 0.000 0.000
#> GSM62295 4 0.0524 0.8566 0.000 0.004 0.008 0.988
#> GSM62300 2 0.0000 0.9768 0.000 1.000 0.000 0.000
#> GSM62308 2 0.0000 0.9768 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM62248 5 0.4675 0.1716 0.000 0.004 0.008 0.444 0.544
#> GSM62256 4 0.2783 0.8058 0.000 0.036 0.032 0.896 0.036
#> GSM62259 4 0.3058 0.7883 0.000 0.000 0.044 0.860 0.096
#> GSM62267 1 0.0000 0.9425 1.000 0.000 0.000 0.000 0.000
#> GSM62280 3 0.3366 0.6986 0.232 0.000 0.768 0.000 0.000
#> GSM62284 1 0.0000 0.9425 1.000 0.000 0.000 0.000 0.000
#> GSM62289 5 0.2127 0.7583 0.000 0.000 0.000 0.108 0.892
#> GSM62307 4 0.0451 0.8391 0.000 0.004 0.008 0.988 0.000
#> GSM62316 4 0.4478 0.3387 0.000 0.004 0.008 0.628 0.360
#> GSM62254 4 0.2561 0.7966 0.000 0.000 0.020 0.884 0.096
#> GSM62292 4 0.2561 0.7966 0.000 0.000 0.020 0.884 0.096
#> GSM62253 1 0.2707 0.8455 0.860 0.000 0.132 0.000 0.008
#> GSM62270 1 0.0000 0.9425 1.000 0.000 0.000 0.000 0.000
#> GSM62278 1 0.0000 0.9425 1.000 0.000 0.000 0.000 0.000
#> GSM62297 2 0.0000 0.9616 0.000 1.000 0.000 0.000 0.000
#> GSM62298 2 0.0000 0.9616 0.000 1.000 0.000 0.000 0.000
#> GSM62299 2 0.0000 0.9616 0.000 1.000 0.000 0.000 0.000
#> GSM62258 1 0.0000 0.9425 1.000 0.000 0.000 0.000 0.000
#> GSM62281 4 0.4037 0.6679 0.000 0.184 0.016 0.780 0.020
#> GSM62294 4 0.0404 0.8386 0.000 0.000 0.000 0.988 0.012
#> GSM62305 5 0.3209 0.6789 0.000 0.004 0.060 0.076 0.860
#> GSM62306 5 0.3732 0.7002 0.000 0.000 0.032 0.176 0.792
#> GSM62310 4 0.0324 0.8400 0.000 0.004 0.000 0.992 0.004
#> GSM62311 4 0.0324 0.8400 0.000 0.004 0.000 0.992 0.004
#> GSM62317 3 0.3424 0.6205 0.000 0.240 0.760 0.000 0.000
#> GSM62318 3 0.1671 0.8455 0.076 0.000 0.924 0.000 0.000
#> GSM62321 3 0.1205 0.8520 0.040 0.004 0.956 0.000 0.000
#> GSM62322 1 0.0000 0.9425 1.000 0.000 0.000 0.000 0.000
#> GSM62250 5 0.2248 0.7572 0.000 0.000 0.012 0.088 0.900
#> GSM62252 5 0.2673 0.7225 0.020 0.000 0.044 0.036 0.900
#> GSM62255 4 0.0162 0.8400 0.000 0.004 0.000 0.996 0.000
#> GSM62257 4 0.0613 0.8377 0.000 0.004 0.008 0.984 0.004
#> GSM62260 3 0.1270 0.8549 0.052 0.000 0.948 0.000 0.000
#> GSM62261 4 0.4464 0.3484 0.000 0.004 0.008 0.632 0.356
#> GSM62262 4 0.1522 0.8254 0.000 0.000 0.012 0.944 0.044
#> GSM62264 3 0.1549 0.8457 0.040 0.000 0.944 0.000 0.016
#> GSM62268 1 0.2074 0.8751 0.896 0.000 0.104 0.000 0.000
#> GSM62269 1 0.0000 0.9425 1.000 0.000 0.000 0.000 0.000
#> GSM62271 1 0.0000 0.9425 1.000 0.000 0.000 0.000 0.000
#> GSM62272 1 0.0000 0.9425 1.000 0.000 0.000 0.000 0.000
#> GSM62273 4 0.6581 0.1958 0.000 0.384 0.032 0.484 0.100
#> GSM62274 1 0.0000 0.9425 1.000 0.000 0.000 0.000 0.000
#> GSM62275 1 0.0000 0.9425 1.000 0.000 0.000 0.000 0.000
#> GSM62276 1 0.0000 0.9425 1.000 0.000 0.000 0.000 0.000
#> GSM62277 1 0.0000 0.9425 1.000 0.000 0.000 0.000 0.000
#> GSM62279 1 0.0000 0.9425 1.000 0.000 0.000 0.000 0.000
#> GSM62282 1 0.3561 0.5927 0.740 0.000 0.260 0.000 0.000
#> GSM62283 1 0.0609 0.9327 0.980 0.000 0.020 0.000 0.000
#> GSM62286 5 0.1965 0.7616 0.000 0.000 0.000 0.096 0.904
#> GSM62287 4 0.0000 0.8398 0.000 0.000 0.000 1.000 0.000
#> GSM62288 4 0.4651 0.1257 0.000 0.004 0.008 0.560 0.428
#> GSM62290 2 0.0000 0.9616 0.000 1.000 0.000 0.000 0.000
#> GSM62293 4 0.1914 0.8173 0.000 0.000 0.016 0.924 0.060
#> GSM62301 2 0.0000 0.9616 0.000 1.000 0.000 0.000 0.000
#> GSM62302 4 0.0324 0.8400 0.000 0.004 0.000 0.992 0.004
#> GSM62303 4 0.0162 0.8398 0.000 0.000 0.000 0.996 0.004
#> GSM62304 4 0.0324 0.8400 0.000 0.004 0.000 0.992 0.004
#> GSM62312 2 0.0510 0.9455 0.000 0.984 0.000 0.016 0.000
#> GSM62313 4 0.0324 0.8400 0.000 0.004 0.000 0.992 0.004
#> GSM62314 4 0.4088 0.5185 0.000 0.004 0.008 0.712 0.276
#> GSM62319 2 0.3182 0.8274 0.000 0.864 0.028 0.016 0.092
#> GSM62320 2 0.0000 0.9616 0.000 1.000 0.000 0.000 0.000
#> GSM62249 5 0.5876 0.0418 0.100 0.000 0.412 0.000 0.488
#> GSM62251 1 0.3909 0.7229 0.760 0.000 0.216 0.000 0.024
#> GSM62263 2 0.5203 0.3833 0.000 0.608 0.332 0.000 0.060
#> GSM62285 2 0.0000 0.9616 0.000 1.000 0.000 0.000 0.000
#> GSM62315 2 0.0000 0.9616 0.000 1.000 0.000 0.000 0.000
#> GSM62291 2 0.0000 0.9616 0.000 1.000 0.000 0.000 0.000
#> GSM62265 1 0.2338 0.8669 0.884 0.000 0.112 0.000 0.004
#> GSM62266 1 0.2707 0.8455 0.860 0.000 0.132 0.000 0.008
#> GSM62296 2 0.0000 0.9616 0.000 1.000 0.000 0.000 0.000
#> GSM62309 2 0.0000 0.9616 0.000 1.000 0.000 0.000 0.000
#> GSM62295 4 0.2616 0.7940 0.000 0.000 0.020 0.880 0.100
#> GSM62300 2 0.0000 0.9616 0.000 1.000 0.000 0.000 0.000
#> GSM62308 2 0.0000 0.9616 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM62248 5 0.5161 0.1797 0.000 0.004 0.080 0.376 0.540 0.000
#> GSM62256 4 0.4746 0.3578 0.000 0.036 0.332 0.616 0.016 0.000
#> GSM62259 4 0.3997 0.0823 0.000 0.000 0.488 0.508 0.004 0.000
#> GSM62267 1 0.0000 0.8882 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM62280 6 0.5147 0.5897 0.096 0.000 0.356 0.000 0.000 0.548
#> GSM62284 1 0.0000 0.8882 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM62289 5 0.1176 0.7083 0.000 0.000 0.020 0.024 0.956 0.000
#> GSM62307 4 0.2009 0.7100 0.000 0.008 0.084 0.904 0.004 0.000
#> GSM62316 4 0.4961 0.4092 0.000 0.004 0.084 0.616 0.296 0.000
#> GSM62254 4 0.3215 0.5348 0.000 0.000 0.240 0.756 0.004 0.000
#> GSM62292 4 0.3215 0.5348 0.000 0.000 0.240 0.756 0.004 0.000
#> GSM62253 1 0.3507 0.7247 0.752 0.000 0.004 0.000 0.012 0.232
#> GSM62270 1 0.0000 0.8882 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM62278 1 0.0000 0.8882 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM62297 2 0.0146 0.9488 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM62298 2 0.0146 0.9488 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM62299 2 0.0146 0.9488 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM62258 1 0.0146 0.8861 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM62281 4 0.5446 0.1857 0.000 0.156 0.236 0.600 0.008 0.000
#> GSM62294 4 0.1152 0.7237 0.000 0.000 0.044 0.952 0.004 0.000
#> GSM62305 5 0.4574 0.4386 0.000 0.000 0.440 0.000 0.524 0.036
#> GSM62306 5 0.5400 0.4053 0.000 0.000 0.400 0.116 0.484 0.000
#> GSM62310 4 0.0508 0.7374 0.000 0.004 0.012 0.984 0.000 0.000
#> GSM62311 4 0.0146 0.7385 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM62317 6 0.5195 0.5928 0.000 0.100 0.360 0.000 0.000 0.540
#> GSM62318 6 0.3769 0.6448 0.004 0.000 0.356 0.000 0.000 0.640
#> GSM62321 6 0.3634 0.6449 0.000 0.000 0.356 0.000 0.000 0.644
#> GSM62322 1 0.0000 0.8882 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM62250 5 0.0363 0.7076 0.000 0.000 0.000 0.012 0.988 0.000
#> GSM62252 5 0.0748 0.6876 0.004 0.000 0.004 0.000 0.976 0.016
#> GSM62255 4 0.0291 0.7387 0.000 0.004 0.000 0.992 0.004 0.000
#> GSM62257 4 0.1888 0.7159 0.000 0.004 0.068 0.916 0.012 0.000
#> GSM62260 6 0.2544 0.6189 0.004 0.000 0.140 0.000 0.004 0.852
#> GSM62261 4 0.4921 0.4594 0.000 0.008 0.084 0.644 0.264 0.000
#> GSM62262 4 0.2146 0.6726 0.000 0.000 0.116 0.880 0.004 0.000
#> GSM62264 6 0.0508 0.5598 0.004 0.000 0.000 0.000 0.012 0.984
#> GSM62268 1 0.3121 0.7671 0.804 0.000 0.004 0.000 0.012 0.180
#> GSM62269 1 0.0000 0.8882 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM62271 1 0.0000 0.8882 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM62272 1 0.0000 0.8882 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM62273 3 0.6202 0.0000 0.000 0.320 0.392 0.284 0.004 0.000
#> GSM62274 1 0.0000 0.8882 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM62275 1 0.0000 0.8882 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM62276 1 0.0000 0.8882 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM62277 1 0.0000 0.8882 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM62279 1 0.0405 0.8832 0.988 0.000 0.004 0.000 0.000 0.008
#> GSM62282 1 0.4361 0.5796 0.720 0.000 0.112 0.000 0.000 0.168
#> GSM62283 1 0.3817 0.6786 0.720 0.000 0.028 0.000 0.000 0.252
#> GSM62286 5 0.0547 0.7114 0.000 0.000 0.000 0.020 0.980 0.000
#> GSM62287 4 0.0146 0.7385 0.000 0.000 0.004 0.996 0.000 0.000
#> GSM62288 4 0.5065 0.3425 0.000 0.004 0.084 0.588 0.324 0.000
#> GSM62290 2 0.0000 0.9501 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62293 4 0.2668 0.6225 0.000 0.000 0.168 0.828 0.004 0.000
#> GSM62301 2 0.0000 0.9501 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62302 4 0.0363 0.7396 0.000 0.000 0.012 0.988 0.000 0.000
#> GSM62303 4 0.0865 0.7294 0.000 0.000 0.036 0.964 0.000 0.000
#> GSM62304 4 0.0291 0.7387 0.000 0.004 0.004 0.992 0.000 0.000
#> GSM62312 2 0.1845 0.8328 0.000 0.920 0.028 0.052 0.000 0.000
#> GSM62313 4 0.0000 0.7388 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62314 4 0.4486 0.5427 0.000 0.004 0.084 0.704 0.208 0.000
#> GSM62319 2 0.3979 0.0460 0.000 0.628 0.360 0.012 0.000 0.000
#> GSM62320 2 0.0458 0.9368 0.000 0.984 0.016 0.000 0.000 0.000
#> GSM62249 6 0.5693 0.0698 0.040 0.004 0.060 0.000 0.356 0.540
#> GSM62251 1 0.5058 0.3244 0.484 0.000 0.020 0.000 0.036 0.460
#> GSM62263 6 0.5603 -0.0204 0.000 0.448 0.064 0.000 0.032 0.456
#> GSM62285 2 0.0000 0.9501 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62315 2 0.0000 0.9501 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62291 2 0.0000 0.9501 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62265 1 0.4116 0.6604 0.684 0.000 0.016 0.000 0.012 0.288
#> GSM62266 1 0.3915 0.6709 0.696 0.000 0.008 0.000 0.012 0.284
#> GSM62296 2 0.0000 0.9501 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62309 2 0.0000 0.9501 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62295 4 0.3521 0.4817 0.000 0.004 0.268 0.724 0.004 0.000
#> GSM62300 2 0.0146 0.9488 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM62308 2 0.0000 0.9501 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) other(p) genotype/variation(p) k
#> CV:skmeans 75 0.82366 1.000 0.8057 2
#> CV:skmeans 73 0.00169 0.823 0.0378 3
#> CV:skmeans 70 0.00587 0.846 0.1687 4
#> CV:skmeans 68 0.00587 0.913 0.3905 5
#> CV:skmeans 60 0.00102 0.575 0.2353 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "pam"]
# you can also extract it by
# res = res_list["CV:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 75 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 0.954 0.979 0.4821 0.508 0.508
#> 3 3 0.715 0.745 0.782 0.2884 0.745 0.536
#> 4 4 0.999 0.949 0.981 0.1631 0.879 0.670
#> 5 5 0.930 0.902 0.944 0.0357 0.968 0.884
#> 6 6 0.832 0.733 0.831 0.0555 0.947 0.796
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
#> attr(,"optional")
#> [1] 2 4
There is also optional best \(k\) = 2 4 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM62248 2 0.000 1.000 0.000 1.000
#> GSM62256 2 0.000 1.000 0.000 1.000
#> GSM62259 2 0.000 1.000 0.000 1.000
#> GSM62267 1 0.000 0.947 1.000 0.000
#> GSM62280 1 0.000 0.947 1.000 0.000
#> GSM62284 1 0.000 0.947 1.000 0.000
#> GSM62289 2 0.000 1.000 0.000 1.000
#> GSM62307 2 0.000 1.000 0.000 1.000
#> GSM62316 2 0.000 1.000 0.000 1.000
#> GSM62254 2 0.000 1.000 0.000 1.000
#> GSM62292 2 0.000 1.000 0.000 1.000
#> GSM62253 1 0.000 0.947 1.000 0.000
#> GSM62270 1 0.000 0.947 1.000 0.000
#> GSM62278 1 0.000 0.947 1.000 0.000
#> GSM62297 2 0.000 1.000 0.000 1.000
#> GSM62298 2 0.000 1.000 0.000 1.000
#> GSM62299 2 0.000 1.000 0.000 1.000
#> GSM62258 1 0.000 0.947 1.000 0.000
#> GSM62281 2 0.000 1.000 0.000 1.000
#> GSM62294 2 0.000 1.000 0.000 1.000
#> GSM62305 1 0.895 0.599 0.688 0.312
#> GSM62306 2 0.000 1.000 0.000 1.000
#> GSM62310 2 0.000 1.000 0.000 1.000
#> GSM62311 2 0.000 1.000 0.000 1.000
#> GSM62317 2 0.000 1.000 0.000 1.000
#> GSM62318 1 0.000 0.947 1.000 0.000
#> GSM62321 1 0.430 0.882 0.912 0.088
#> GSM62322 1 0.000 0.947 1.000 0.000
#> GSM62250 2 0.000 1.000 0.000 1.000
#> GSM62252 1 0.904 0.584 0.680 0.320
#> GSM62255 2 0.000 1.000 0.000 1.000
#> GSM62257 2 0.000 1.000 0.000 1.000
#> GSM62260 1 0.224 0.923 0.964 0.036
#> GSM62261 2 0.000 1.000 0.000 1.000
#> GSM62262 2 0.000 1.000 0.000 1.000
#> GSM62264 1 0.000 0.947 1.000 0.000
#> GSM62268 1 0.000 0.947 1.000 0.000
#> GSM62269 1 0.000 0.947 1.000 0.000
#> GSM62271 1 0.000 0.947 1.000 0.000
#> GSM62272 1 0.000 0.947 1.000 0.000
#> GSM62273 2 0.000 1.000 0.000 1.000
#> GSM62274 1 0.000 0.947 1.000 0.000
#> GSM62275 1 0.000 0.947 1.000 0.000
#> GSM62276 1 0.000 0.947 1.000 0.000
#> GSM62277 1 0.000 0.947 1.000 0.000
#> GSM62279 1 0.000 0.947 1.000 0.000
#> GSM62282 1 0.000 0.947 1.000 0.000
#> GSM62283 1 0.000 0.947 1.000 0.000
#> GSM62286 2 0.000 1.000 0.000 1.000
#> GSM62287 2 0.000 1.000 0.000 1.000
#> GSM62288 2 0.000 1.000 0.000 1.000
#> GSM62290 2 0.000 1.000 0.000 1.000
#> GSM62293 2 0.000 1.000 0.000 1.000
#> GSM62301 2 0.000 1.000 0.000 1.000
#> GSM62302 2 0.000 1.000 0.000 1.000
#> GSM62303 2 0.000 1.000 0.000 1.000
#> GSM62304 2 0.000 1.000 0.000 1.000
#> GSM62312 2 0.000 1.000 0.000 1.000
#> GSM62313 2 0.000 1.000 0.000 1.000
#> GSM62314 2 0.000 1.000 0.000 1.000
#> GSM62319 1 0.990 0.301 0.560 0.440
#> GSM62320 2 0.000 1.000 0.000 1.000
#> GSM62249 1 0.430 0.882 0.912 0.088
#> GSM62251 1 0.000 0.947 1.000 0.000
#> GSM62263 1 0.876 0.626 0.704 0.296
#> GSM62285 2 0.000 1.000 0.000 1.000
#> GSM62315 2 0.000 1.000 0.000 1.000
#> GSM62291 2 0.000 1.000 0.000 1.000
#> GSM62265 1 0.000 0.947 1.000 0.000
#> GSM62266 1 0.000 0.947 1.000 0.000
#> GSM62296 2 0.000 1.000 0.000 1.000
#> GSM62309 2 0.000 1.000 0.000 1.000
#> GSM62295 2 0.000 1.000 0.000 1.000
#> GSM62300 2 0.000 1.000 0.000 1.000
#> GSM62308 2 0.000 1.000 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM62248 2 0.0000 0.940 0.000 1.000 0.000
#> GSM62256 2 0.0000 0.940 0.000 1.000 0.000
#> GSM62259 2 0.0000 0.940 0.000 1.000 0.000
#> GSM62267 1 0.0000 0.824 1.000 0.000 0.000
#> GSM62280 1 0.0000 0.824 1.000 0.000 0.000
#> GSM62284 1 0.1860 0.813 0.948 0.000 0.052
#> GSM62289 2 0.0000 0.940 0.000 1.000 0.000
#> GSM62307 2 0.0000 0.940 0.000 1.000 0.000
#> GSM62316 2 0.0000 0.940 0.000 1.000 0.000
#> GSM62254 2 0.0000 0.940 0.000 1.000 0.000
#> GSM62292 2 0.0000 0.940 0.000 1.000 0.000
#> GSM62253 1 0.0000 0.824 1.000 0.000 0.000
#> GSM62270 1 0.6215 0.692 0.572 0.000 0.428
#> GSM62278 1 0.6215 0.692 0.572 0.000 0.428
#> GSM62297 3 0.6215 0.718 0.000 0.428 0.572
#> GSM62298 3 0.6215 0.718 0.000 0.428 0.572
#> GSM62299 3 0.6215 0.718 0.000 0.428 0.572
#> GSM62258 1 0.0000 0.824 1.000 0.000 0.000
#> GSM62281 2 0.0000 0.940 0.000 1.000 0.000
#> GSM62294 2 0.0000 0.940 0.000 1.000 0.000
#> GSM62305 3 0.6836 0.344 0.412 0.016 0.572
#> GSM62306 2 0.0000 0.940 0.000 1.000 0.000
#> GSM62310 2 0.0000 0.940 0.000 1.000 0.000
#> GSM62311 2 0.0000 0.940 0.000 1.000 0.000
#> GSM62317 3 0.6215 0.718 0.000 0.428 0.572
#> GSM62318 1 0.0000 0.824 1.000 0.000 0.000
#> GSM62321 3 0.6299 0.220 0.476 0.000 0.524
#> GSM62322 1 0.6215 0.692 0.572 0.000 0.428
#> GSM62250 2 0.0000 0.940 0.000 1.000 0.000
#> GSM62252 2 0.7591 0.129 0.412 0.544 0.044
#> GSM62255 2 0.0000 0.940 0.000 1.000 0.000
#> GSM62257 2 0.0000 0.940 0.000 1.000 0.000
#> GSM62260 3 0.6309 0.160 0.500 0.000 0.500
#> GSM62261 2 0.0000 0.940 0.000 1.000 0.000
#> GSM62262 2 0.0000 0.940 0.000 1.000 0.000
#> GSM62264 1 0.0424 0.818 0.992 0.000 0.008
#> GSM62268 1 0.0000 0.824 1.000 0.000 0.000
#> GSM62269 1 0.6215 0.692 0.572 0.000 0.428
#> GSM62271 1 0.0000 0.824 1.000 0.000 0.000
#> GSM62272 1 0.6215 0.692 0.572 0.000 0.428
#> GSM62273 3 0.6215 0.718 0.000 0.428 0.572
#> GSM62274 1 0.5882 0.719 0.652 0.000 0.348
#> GSM62275 1 0.6215 0.692 0.572 0.000 0.428
#> GSM62276 1 0.0000 0.824 1.000 0.000 0.000
#> GSM62277 1 0.6215 0.692 0.572 0.000 0.428
#> GSM62279 1 0.0000 0.824 1.000 0.000 0.000
#> GSM62282 1 0.1860 0.813 0.948 0.000 0.052
#> GSM62283 1 0.6308 -0.214 0.508 0.000 0.492
#> GSM62286 2 0.0000 0.940 0.000 1.000 0.000
#> GSM62287 2 0.0000 0.940 0.000 1.000 0.000
#> GSM62288 2 0.0000 0.940 0.000 1.000 0.000
#> GSM62290 3 0.6215 0.718 0.000 0.428 0.572
#> GSM62293 2 0.0000 0.940 0.000 1.000 0.000
#> GSM62301 3 0.6215 0.718 0.000 0.428 0.572
#> GSM62302 2 0.0000 0.940 0.000 1.000 0.000
#> GSM62303 2 0.0000 0.940 0.000 1.000 0.000
#> GSM62304 2 0.0000 0.940 0.000 1.000 0.000
#> GSM62312 2 0.0000 0.940 0.000 1.000 0.000
#> GSM62313 2 0.0000 0.940 0.000 1.000 0.000
#> GSM62314 2 0.0000 0.940 0.000 1.000 0.000
#> GSM62319 3 0.7726 0.408 0.372 0.056 0.572
#> GSM62320 2 0.6309 -0.575 0.000 0.504 0.496
#> GSM62249 3 0.6244 0.293 0.440 0.000 0.560
#> GSM62251 1 0.0000 0.824 1.000 0.000 0.000
#> GSM62263 3 0.6215 0.313 0.428 0.000 0.572
#> GSM62285 3 0.6215 0.718 0.000 0.428 0.572
#> GSM62315 3 0.6215 0.718 0.000 0.428 0.572
#> GSM62291 3 0.6215 0.718 0.000 0.428 0.572
#> GSM62265 1 0.0000 0.824 1.000 0.000 0.000
#> GSM62266 1 0.0000 0.824 1.000 0.000 0.000
#> GSM62296 3 0.6215 0.718 0.000 0.428 0.572
#> GSM62309 3 0.6215 0.718 0.000 0.428 0.572
#> GSM62295 2 0.4605 0.542 0.000 0.796 0.204
#> GSM62300 3 0.6215 0.718 0.000 0.428 0.572
#> GSM62308 3 0.6215 0.718 0.000 0.428 0.572
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM62248 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM62256 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM62259 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM62267 1 0.000 0.971 1.000 0.000 0.000 0.000
#> GSM62280 1 0.000 0.971 1.000 0.000 0.000 0.000
#> GSM62284 1 0.460 0.485 0.664 0.000 0.336 0.000
#> GSM62289 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM62307 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM62316 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM62254 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM62292 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM62253 1 0.000 0.971 1.000 0.000 0.000 0.000
#> GSM62270 3 0.000 0.988 0.000 0.000 1.000 0.000
#> GSM62278 3 0.000 0.988 0.000 0.000 1.000 0.000
#> GSM62297 2 0.000 0.941 0.000 1.000 0.000 0.000
#> GSM62298 2 0.000 0.941 0.000 1.000 0.000 0.000
#> GSM62299 2 0.000 0.941 0.000 1.000 0.000 0.000
#> GSM62258 1 0.000 0.971 1.000 0.000 0.000 0.000
#> GSM62281 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM62294 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM62305 2 0.000 0.941 0.000 1.000 0.000 0.000
#> GSM62306 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM62310 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM62311 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM62317 2 0.000 0.941 0.000 1.000 0.000 0.000
#> GSM62318 1 0.000 0.971 1.000 0.000 0.000 0.000
#> GSM62321 2 0.384 0.685 0.224 0.776 0.000 0.000
#> GSM62322 3 0.000 0.988 0.000 0.000 1.000 0.000
#> GSM62250 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM62252 1 0.215 0.862 0.912 0.000 0.000 0.088
#> GSM62255 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM62257 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM62260 1 0.000 0.971 1.000 0.000 0.000 0.000
#> GSM62261 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM62262 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM62264 1 0.000 0.971 1.000 0.000 0.000 0.000
#> GSM62268 1 0.000 0.971 1.000 0.000 0.000 0.000
#> GSM62269 3 0.000 0.988 0.000 0.000 1.000 0.000
#> GSM62271 1 0.000 0.971 1.000 0.000 0.000 0.000
#> GSM62272 3 0.000 0.988 0.000 0.000 1.000 0.000
#> GSM62273 2 0.000 0.941 0.000 1.000 0.000 0.000
#> GSM62274 3 0.201 0.910 0.080 0.000 0.920 0.000
#> GSM62275 3 0.000 0.988 0.000 0.000 1.000 0.000
#> GSM62276 1 0.000 0.971 1.000 0.000 0.000 0.000
#> GSM62277 3 0.000 0.988 0.000 0.000 1.000 0.000
#> GSM62279 1 0.000 0.971 1.000 0.000 0.000 0.000
#> GSM62282 1 0.147 0.926 0.948 0.000 0.052 0.000
#> GSM62283 1 0.000 0.971 1.000 0.000 0.000 0.000
#> GSM62286 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM62287 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM62288 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM62290 2 0.000 0.941 0.000 1.000 0.000 0.000
#> GSM62293 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM62301 2 0.000 0.941 0.000 1.000 0.000 0.000
#> GSM62302 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM62303 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM62304 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM62312 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM62313 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM62314 4 0.000 1.000 0.000 0.000 0.000 1.000
#> GSM62319 2 0.000 0.941 0.000 1.000 0.000 0.000
#> GSM62320 2 0.340 0.727 0.000 0.820 0.000 0.180
#> GSM62249 1 0.000 0.971 1.000 0.000 0.000 0.000
#> GSM62251 1 0.000 0.971 1.000 0.000 0.000 0.000
#> GSM62263 2 0.000 0.941 0.000 1.000 0.000 0.000
#> GSM62285 2 0.000 0.941 0.000 1.000 0.000 0.000
#> GSM62315 2 0.000 0.941 0.000 1.000 0.000 0.000
#> GSM62291 2 0.000 0.941 0.000 1.000 0.000 0.000
#> GSM62265 1 0.000 0.971 1.000 0.000 0.000 0.000
#> GSM62266 1 0.000 0.971 1.000 0.000 0.000 0.000
#> GSM62296 2 0.000 0.941 0.000 1.000 0.000 0.000
#> GSM62309 2 0.000 0.941 0.000 1.000 0.000 0.000
#> GSM62295 2 0.498 0.158 0.000 0.536 0.000 0.464
#> GSM62300 2 0.000 0.941 0.000 1.000 0.000 0.000
#> GSM62308 2 0.000 0.941 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM62248 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM62256 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM62259 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM62267 1 0.0794 0.869 0.972 0.000 0.000 0.000 0.028
#> GSM62280 5 0.2471 0.738 0.136 0.000 0.000 0.000 0.864
#> GSM62284 1 0.6058 0.393 0.528 0.000 0.336 0.000 0.136
#> GSM62289 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM62307 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM62316 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM62254 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM62292 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM62253 1 0.2471 0.861 0.864 0.000 0.000 0.000 0.136
#> GSM62270 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> GSM62278 3 0.0794 0.943 0.000 0.000 0.972 0.000 0.028
#> GSM62297 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000
#> GSM62298 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000
#> GSM62299 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000
#> GSM62258 1 0.0794 0.869 0.972 0.000 0.000 0.000 0.028
#> GSM62281 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM62294 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM62305 2 0.0404 0.922 0.012 0.988 0.000 0.000 0.000
#> GSM62306 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM62310 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM62311 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM62317 5 0.4182 0.394 0.000 0.400 0.000 0.000 0.600
#> GSM62318 5 0.0794 0.688 0.028 0.000 0.000 0.000 0.972
#> GSM62321 5 0.2773 0.721 0.000 0.164 0.000 0.000 0.836
#> GSM62322 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> GSM62250 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM62252 1 0.2519 0.763 0.884 0.016 0.000 0.100 0.000
#> GSM62255 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM62257 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM62260 1 0.0794 0.869 0.972 0.000 0.000 0.000 0.028
#> GSM62261 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM62262 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM62264 1 0.2471 0.861 0.864 0.000 0.000 0.000 0.136
#> GSM62268 1 0.2471 0.861 0.864 0.000 0.000 0.000 0.136
#> GSM62269 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> GSM62271 1 0.0794 0.869 0.972 0.000 0.000 0.000 0.028
#> GSM62272 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> GSM62273 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000
#> GSM62274 3 0.3231 0.746 0.196 0.000 0.800 0.000 0.004
#> GSM62275 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> GSM62276 1 0.0794 0.869 0.972 0.000 0.000 0.000 0.028
#> GSM62277 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> GSM62279 1 0.0000 0.870 1.000 0.000 0.000 0.000 0.000
#> GSM62282 5 0.2471 0.738 0.136 0.000 0.000 0.000 0.864
#> GSM62283 1 0.0794 0.869 0.972 0.000 0.000 0.000 0.028
#> GSM62286 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM62287 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM62288 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM62290 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000
#> GSM62293 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM62301 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000
#> GSM62302 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM62303 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM62304 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM62312 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM62313 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM62314 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM62319 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000
#> GSM62320 2 0.2929 0.651 0.000 0.820 0.000 0.180 0.000
#> GSM62249 1 0.2773 0.740 0.836 0.164 0.000 0.000 0.000
#> GSM62251 1 0.2471 0.861 0.864 0.000 0.000 0.000 0.136
#> GSM62263 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000
#> GSM62285 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000
#> GSM62315 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000
#> GSM62291 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000
#> GSM62265 1 0.2471 0.861 0.864 0.000 0.000 0.000 0.136
#> GSM62266 1 0.2471 0.861 0.864 0.000 0.000 0.000 0.136
#> GSM62296 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000
#> GSM62309 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000
#> GSM62295 2 0.4291 0.154 0.000 0.536 0.000 0.464 0.000
#> GSM62300 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000
#> GSM62308 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM62248 4 0.387 0.5038 0.000 0.000 0.000 0.508 0.492 0.000
#> GSM62256 4 0.266 0.8096 0.000 0.000 0.000 0.816 0.184 0.000
#> GSM62259 4 0.101 0.8732 0.000 0.000 0.000 0.956 0.044 0.000
#> GSM62267 1 0.000 0.7967 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM62280 6 0.000 0.8871 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM62284 5 0.577 0.2289 0.220 0.000 0.276 0.000 0.504 0.000
#> GSM62289 4 0.387 0.4983 0.000 0.000 0.000 0.504 0.496 0.000
#> GSM62307 4 0.000 0.8867 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62316 4 0.276 0.7987 0.000 0.000 0.000 0.804 0.196 0.000
#> GSM62254 4 0.000 0.8867 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62292 4 0.000 0.8867 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62253 5 0.387 0.4488 0.496 0.000 0.000 0.000 0.504 0.000
#> GSM62270 3 0.000 0.9351 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62278 3 0.000 0.9351 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62297 2 0.000 0.9046 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62298 2 0.000 0.9046 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62299 2 0.000 0.9046 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62258 1 0.000 0.7967 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM62281 4 0.366 0.6586 0.000 0.000 0.000 0.636 0.364 0.000
#> GSM62294 4 0.000 0.8867 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62305 5 0.583 -0.1355 0.196 0.348 0.000 0.000 0.456 0.000
#> GSM62306 4 0.234 0.8308 0.000 0.000 0.000 0.852 0.148 0.000
#> GSM62310 4 0.000 0.8867 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62311 4 0.000 0.8867 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62317 6 0.254 0.8115 0.000 0.032 0.000 0.000 0.096 0.872
#> GSM62318 6 0.000 0.8871 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM62321 6 0.000 0.8871 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM62322 3 0.000 0.9351 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62250 5 0.506 -0.4489 0.076 0.000 0.000 0.428 0.496 0.000
#> GSM62252 1 0.387 0.1451 0.504 0.000 0.000 0.000 0.496 0.000
#> GSM62255 4 0.000 0.8867 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62257 4 0.000 0.8867 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62260 1 0.333 0.4053 0.716 0.000 0.000 0.000 0.000 0.284
#> GSM62261 4 0.196 0.8471 0.000 0.000 0.000 0.888 0.112 0.000
#> GSM62262 4 0.000 0.8867 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62264 5 0.387 0.4488 0.496 0.000 0.000 0.000 0.504 0.000
#> GSM62268 5 0.387 0.4488 0.496 0.000 0.000 0.000 0.504 0.000
#> GSM62269 3 0.000 0.9351 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62271 1 0.000 0.7967 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM62272 3 0.000 0.9351 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62273 2 0.000 0.9046 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62274 3 0.533 0.4181 0.300 0.000 0.564 0.000 0.136 0.000
#> GSM62275 3 0.000 0.9351 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62276 1 0.000 0.7967 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM62277 3 0.000 0.9351 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62279 1 0.000 0.7967 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM62282 6 0.333 0.6007 0.284 0.000 0.000 0.000 0.000 0.716
#> GSM62283 1 0.000 0.7967 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM62286 4 0.387 0.4983 0.000 0.000 0.000 0.504 0.496 0.000
#> GSM62287 4 0.000 0.8867 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62288 4 0.327 0.7476 0.000 0.000 0.000 0.728 0.272 0.000
#> GSM62290 2 0.000 0.9046 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62293 4 0.000 0.8867 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62301 2 0.000 0.9046 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62302 4 0.000 0.8867 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62303 4 0.000 0.8867 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62304 4 0.000 0.8867 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62312 4 0.000 0.8867 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62313 4 0.000 0.8867 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62314 4 0.305 0.7745 0.000 0.000 0.000 0.764 0.236 0.000
#> GSM62319 2 0.000 0.9046 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62320 2 0.263 0.6940 0.000 0.820 0.000 0.180 0.000 0.000
#> GSM62249 2 0.387 -0.0464 0.496 0.504 0.000 0.000 0.000 0.000
#> GSM62251 5 0.387 0.4488 0.496 0.000 0.000 0.000 0.504 0.000
#> GSM62263 2 0.196 0.7992 0.000 0.888 0.000 0.000 0.112 0.000
#> GSM62285 2 0.000 0.9046 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62315 2 0.000 0.9046 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62291 2 0.000 0.9046 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62265 5 0.387 0.4488 0.496 0.000 0.000 0.000 0.504 0.000
#> GSM62266 5 0.387 0.4488 0.496 0.000 0.000 0.000 0.504 0.000
#> GSM62296 2 0.000 0.9046 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62309 2 0.000 0.9046 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62295 2 0.385 0.1569 0.000 0.536 0.000 0.464 0.000 0.000
#> GSM62300 2 0.000 0.9046 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62308 2 0.000 0.9046 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) other(p) genotype/variation(p) k
#> CV:pam 74 1.00e+00 0.964 0.6606 2
#> CV:pam 66 5.35e-04 0.487 0.0379 3
#> CV:pam 73 8.41e-04 0.584 0.0708 4
#> CV:pam 72 4.19e-04 0.692 0.1412 5
#> CV:pam 59 5.34e-05 0.578 0.1340 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "mclust"]
# you can also extract it by
# res = res_list["CV:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 75 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 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 0.949 0.981 0.4720 0.519 0.519
#> 3 3 0.728 0.837 0.856 0.1832 0.870 0.772
#> 4 4 0.514 0.527 0.674 0.1545 0.761 0.579
#> 5 5 0.557 0.650 0.736 0.1457 0.730 0.396
#> 6 6 0.580 0.734 0.788 0.0513 0.936 0.721
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
#> GSM62248 2 0.0000 0.999 0.000 1.000
#> GSM62256 2 0.1633 0.974 0.024 0.976
#> GSM62259 2 0.0000 0.999 0.000 1.000
#> GSM62267 1 0.0000 0.950 1.000 0.000
#> GSM62280 1 0.0000 0.950 1.000 0.000
#> GSM62284 1 0.0000 0.950 1.000 0.000
#> GSM62289 2 0.0000 0.999 0.000 1.000
#> GSM62307 2 0.0000 0.999 0.000 1.000
#> GSM62316 2 0.0000 0.999 0.000 1.000
#> GSM62254 2 0.0000 0.999 0.000 1.000
#> GSM62292 2 0.0000 0.999 0.000 1.000
#> GSM62253 1 0.0000 0.950 1.000 0.000
#> GSM62270 1 0.0000 0.950 1.000 0.000
#> GSM62278 1 0.0000 0.950 1.000 0.000
#> GSM62297 2 0.0000 0.999 0.000 1.000
#> GSM62298 2 0.0000 0.999 0.000 1.000
#> GSM62299 2 0.0000 0.999 0.000 1.000
#> GSM62258 1 0.0000 0.950 1.000 0.000
#> GSM62281 2 0.0672 0.991 0.008 0.992
#> GSM62294 2 0.0000 0.999 0.000 1.000
#> GSM62305 2 0.0000 0.999 0.000 1.000
#> GSM62306 2 0.0000 0.999 0.000 1.000
#> GSM62310 2 0.0000 0.999 0.000 1.000
#> GSM62311 2 0.0000 0.999 0.000 1.000
#> GSM62317 1 0.9933 0.221 0.548 0.452
#> GSM62318 1 0.0000 0.950 1.000 0.000
#> GSM62321 1 0.0000 0.950 1.000 0.000
#> GSM62322 1 0.0000 0.950 1.000 0.000
#> GSM62250 2 0.0000 0.999 0.000 1.000
#> GSM62252 2 0.0376 0.995 0.004 0.996
#> GSM62255 2 0.0000 0.999 0.000 1.000
#> GSM62257 2 0.0000 0.999 0.000 1.000
#> GSM62260 1 0.0000 0.950 1.000 0.000
#> GSM62261 2 0.0000 0.999 0.000 1.000
#> GSM62262 2 0.0000 0.999 0.000 1.000
#> GSM62264 1 0.0000 0.950 1.000 0.000
#> GSM62268 1 0.0000 0.950 1.000 0.000
#> GSM62269 1 0.0000 0.950 1.000 0.000
#> GSM62271 1 0.0000 0.950 1.000 0.000
#> GSM62272 1 0.0000 0.950 1.000 0.000
#> GSM62273 2 0.0000 0.999 0.000 1.000
#> GSM62274 1 0.0000 0.950 1.000 0.000
#> GSM62275 1 0.0000 0.950 1.000 0.000
#> GSM62276 1 0.0000 0.950 1.000 0.000
#> GSM62277 1 0.0000 0.950 1.000 0.000
#> GSM62279 1 0.0000 0.950 1.000 0.000
#> GSM62282 1 0.0000 0.950 1.000 0.000
#> GSM62283 1 0.0000 0.950 1.000 0.000
#> GSM62286 2 0.0000 0.999 0.000 1.000
#> GSM62287 2 0.0000 0.999 0.000 1.000
#> GSM62288 2 0.0000 0.999 0.000 1.000
#> GSM62290 2 0.0000 0.999 0.000 1.000
#> GSM62293 2 0.0000 0.999 0.000 1.000
#> GSM62301 2 0.0000 0.999 0.000 1.000
#> GSM62302 2 0.0000 0.999 0.000 1.000
#> GSM62303 2 0.0000 0.999 0.000 1.000
#> GSM62304 2 0.0000 0.999 0.000 1.000
#> GSM62312 2 0.0000 0.999 0.000 1.000
#> GSM62313 2 0.0000 0.999 0.000 1.000
#> GSM62314 2 0.0000 0.999 0.000 1.000
#> GSM62319 2 0.0000 0.999 0.000 1.000
#> GSM62320 2 0.0000 0.999 0.000 1.000
#> GSM62249 1 0.9944 0.209 0.544 0.456
#> GSM62251 1 0.0000 0.950 1.000 0.000
#> GSM62263 1 0.9993 0.107 0.516 0.484
#> GSM62285 2 0.0000 0.999 0.000 1.000
#> GSM62315 2 0.0000 0.999 0.000 1.000
#> GSM62291 2 0.0000 0.999 0.000 1.000
#> GSM62265 1 0.0000 0.950 1.000 0.000
#> GSM62266 1 0.0000 0.950 1.000 0.000
#> GSM62296 2 0.0000 0.999 0.000 1.000
#> GSM62309 2 0.0000 0.999 0.000 1.000
#> GSM62295 2 0.0000 0.999 0.000 1.000
#> GSM62300 2 0.0000 0.999 0.000 1.000
#> GSM62308 2 0.0000 0.999 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM62248 2 0.0237 0.871 0.000 0.996 0.004
#> GSM62256 2 0.1170 0.867 0.016 0.976 0.008
#> GSM62259 2 0.0424 0.871 0.000 0.992 0.008
#> GSM62267 1 0.0475 0.917 0.992 0.004 0.004
#> GSM62280 1 0.3619 0.776 0.864 0.000 0.136
#> GSM62284 1 0.3412 0.779 0.876 0.000 0.124
#> GSM62289 2 0.0237 0.871 0.000 0.996 0.004
#> GSM62307 2 0.5497 0.775 0.000 0.708 0.292
#> GSM62316 2 0.0237 0.871 0.000 0.996 0.004
#> GSM62254 2 0.5591 0.769 0.000 0.696 0.304
#> GSM62292 2 0.5591 0.769 0.000 0.696 0.304
#> GSM62253 1 0.0237 0.919 0.996 0.004 0.000
#> GSM62270 3 0.5835 0.966 0.340 0.000 0.660
#> GSM62278 3 0.5835 0.966 0.340 0.000 0.660
#> GSM62297 2 0.0892 0.869 0.000 0.980 0.020
#> GSM62298 2 0.1163 0.871 0.000 0.972 0.028
#> GSM62299 2 0.1031 0.868 0.000 0.976 0.024
#> GSM62258 1 0.0237 0.915 0.996 0.000 0.004
#> GSM62281 2 0.0424 0.871 0.000 0.992 0.008
#> GSM62294 2 0.5621 0.768 0.000 0.692 0.308
#> GSM62305 2 0.0892 0.865 0.020 0.980 0.000
#> GSM62306 2 0.0237 0.871 0.000 0.996 0.004
#> GSM62310 2 0.5016 0.798 0.000 0.760 0.240
#> GSM62311 2 0.5621 0.768 0.000 0.692 0.308
#> GSM62317 2 0.8858 0.234 0.332 0.532 0.136
#> GSM62318 1 0.3619 0.776 0.864 0.000 0.136
#> GSM62321 1 0.6788 0.479 0.744 0.120 0.136
#> GSM62322 3 0.5835 0.966 0.340 0.000 0.660
#> GSM62250 2 0.1031 0.863 0.024 0.976 0.000
#> GSM62252 2 0.1031 0.863 0.024 0.976 0.000
#> GSM62255 2 0.5591 0.769 0.000 0.696 0.304
#> GSM62257 2 0.4796 0.805 0.000 0.780 0.220
#> GSM62260 1 0.0661 0.916 0.988 0.004 0.008
#> GSM62261 2 0.0000 0.871 0.000 1.000 0.000
#> GSM62262 2 0.5621 0.768 0.000 0.692 0.308
#> GSM62264 1 0.0237 0.919 0.996 0.004 0.000
#> GSM62268 1 0.0237 0.919 0.996 0.004 0.000
#> GSM62269 3 0.5835 0.966 0.340 0.000 0.660
#> GSM62271 1 0.0475 0.918 0.992 0.004 0.004
#> GSM62272 3 0.5835 0.966 0.340 0.000 0.660
#> GSM62273 2 0.0424 0.871 0.000 0.992 0.008
#> GSM62274 3 0.6299 0.727 0.476 0.000 0.524
#> GSM62275 3 0.5835 0.966 0.340 0.000 0.660
#> GSM62276 1 0.0475 0.917 0.992 0.004 0.004
#> GSM62277 3 0.5905 0.952 0.352 0.000 0.648
#> GSM62279 1 0.0237 0.919 0.996 0.004 0.000
#> GSM62282 1 0.3619 0.776 0.864 0.000 0.136
#> GSM62283 1 0.0237 0.919 0.996 0.004 0.000
#> GSM62286 2 0.0000 0.871 0.000 1.000 0.000
#> GSM62287 2 0.5621 0.768 0.000 0.692 0.308
#> GSM62288 2 0.0000 0.871 0.000 1.000 0.000
#> GSM62290 2 0.1031 0.868 0.000 0.976 0.024
#> GSM62293 2 0.5591 0.769 0.000 0.696 0.304
#> GSM62301 2 0.0892 0.869 0.000 0.980 0.020
#> GSM62302 2 0.5621 0.768 0.000 0.692 0.308
#> GSM62303 2 0.5621 0.768 0.000 0.692 0.308
#> GSM62304 2 0.5621 0.768 0.000 0.692 0.308
#> GSM62312 2 0.0892 0.869 0.000 0.980 0.020
#> GSM62313 2 0.5621 0.768 0.000 0.692 0.308
#> GSM62314 2 0.0237 0.871 0.000 0.996 0.004
#> GSM62319 2 0.0892 0.869 0.000 0.980 0.020
#> GSM62320 2 0.1031 0.870 0.000 0.976 0.024
#> GSM62249 2 0.5859 0.517 0.344 0.656 0.000
#> GSM62251 1 0.0237 0.919 0.996 0.004 0.000
#> GSM62263 2 0.5733 0.553 0.324 0.676 0.000
#> GSM62285 2 0.0892 0.869 0.000 0.980 0.020
#> GSM62315 2 0.0892 0.869 0.000 0.980 0.020
#> GSM62291 2 0.1031 0.868 0.000 0.976 0.024
#> GSM62265 1 0.0237 0.919 0.996 0.004 0.000
#> GSM62266 1 0.0237 0.919 0.996 0.004 0.000
#> GSM62296 2 0.0892 0.869 0.000 0.980 0.020
#> GSM62309 2 0.0892 0.869 0.000 0.980 0.020
#> GSM62295 2 0.5621 0.768 0.000 0.692 0.308
#> GSM62300 2 0.1031 0.868 0.000 0.976 0.024
#> GSM62308 2 0.1031 0.868 0.000 0.976 0.024
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM62248 2 0.0188 0.3832 0.004 0.996 NA 0.000
#> GSM62256 2 0.5250 -0.8224 0.008 0.552 NA 0.440
#> GSM62259 2 0.5929 0.3729 0.000 0.688 NA 0.108
#> GSM62267 1 0.0188 0.8095 0.996 0.000 NA 0.004
#> GSM62280 1 0.6039 0.7092 0.596 0.000 NA 0.056
#> GSM62284 1 0.4158 0.7854 0.768 0.000 NA 0.224
#> GSM62289 2 0.1576 0.3595 0.048 0.948 NA 0.004
#> GSM62307 2 0.5070 0.5396 0.000 0.620 NA 0.008
#> GSM62316 2 0.0188 0.3854 0.000 0.996 NA 0.004
#> GSM62254 2 0.4948 0.5209 0.000 0.560 NA 0.000
#> GSM62292 2 0.4948 0.5209 0.000 0.560 NA 0.000
#> GSM62253 1 0.0336 0.8077 0.992 0.000 NA 0.008
#> GSM62270 1 0.7221 0.6460 0.436 0.000 NA 0.424
#> GSM62278 1 0.5055 0.7453 0.624 0.000 NA 0.368
#> GSM62297 2 0.1722 0.2977 0.008 0.944 NA 0.048
#> GSM62298 2 0.5675 0.4545 0.004 0.676 NA 0.048
#> GSM62299 4 0.5168 0.9984 0.004 0.492 NA 0.504
#> GSM62258 1 0.2281 0.8074 0.904 0.000 NA 0.096
#> GSM62281 2 0.4836 -0.3334 0.008 0.672 NA 0.320
#> GSM62294 2 0.4855 0.5418 0.000 0.600 NA 0.000
#> GSM62305 2 0.2805 0.2993 0.100 0.888 NA 0.012
#> GSM62306 2 0.0000 0.3871 0.000 1.000 NA 0.000
#> GSM62310 2 0.4018 0.5075 0.004 0.772 NA 0.000
#> GSM62311 2 0.4830 0.5454 0.000 0.608 NA 0.000
#> GSM62317 1 0.8464 0.5754 0.492 0.132 NA 0.076
#> GSM62318 1 0.6039 0.7092 0.596 0.000 NA 0.056
#> GSM62321 1 0.6570 0.7002 0.580 0.016 NA 0.056
#> GSM62322 1 0.7221 0.6460 0.436 0.000 NA 0.424
#> GSM62250 2 0.3052 0.2750 0.136 0.860 NA 0.004
#> GSM62252 2 0.4401 0.1027 0.272 0.724 NA 0.004
#> GSM62255 2 0.4830 0.5454 0.000 0.608 NA 0.000
#> GSM62257 2 0.4605 0.5275 0.000 0.664 NA 0.000
#> GSM62260 1 0.2773 0.8008 0.900 0.000 NA 0.028
#> GSM62261 2 0.0188 0.3832 0.004 0.996 NA 0.000
#> GSM62262 2 0.4855 0.5418 0.000 0.600 NA 0.000
#> GSM62264 1 0.2111 0.8019 0.932 0.000 NA 0.024
#> GSM62268 1 0.0592 0.8094 0.984 0.000 NA 0.016
#> GSM62269 1 0.7221 0.6460 0.436 0.000 NA 0.424
#> GSM62271 1 0.1716 0.8101 0.936 0.000 NA 0.064
#> GSM62272 1 0.7221 0.6460 0.436 0.000 NA 0.424
#> GSM62273 2 0.6258 0.3537 0.012 0.688 NA 0.108
#> GSM62274 1 0.4328 0.7809 0.748 0.000 NA 0.244
#> GSM62275 1 0.7221 0.6460 0.436 0.000 NA 0.424
#> GSM62276 1 0.0188 0.8095 0.996 0.000 NA 0.004
#> GSM62277 1 0.4857 0.7581 0.668 0.000 NA 0.324
#> GSM62279 1 0.0000 0.8090 1.000 0.000 NA 0.000
#> GSM62282 1 0.5916 0.7364 0.656 0.000 NA 0.072
#> GSM62283 1 0.0707 0.8050 0.980 0.000 NA 0.020
#> GSM62286 2 0.1661 0.3555 0.052 0.944 NA 0.004
#> GSM62287 2 0.4830 0.5454 0.000 0.608 NA 0.000
#> GSM62288 2 0.0188 0.3832 0.004 0.996 NA 0.000
#> GSM62290 4 0.5168 0.9984 0.004 0.492 NA 0.504
#> GSM62293 2 0.4948 0.5209 0.000 0.560 NA 0.000
#> GSM62301 4 0.5168 0.9984 0.004 0.492 NA 0.504
#> GSM62302 2 0.4830 0.5454 0.000 0.608 NA 0.000
#> GSM62303 2 0.4830 0.5454 0.000 0.608 NA 0.000
#> GSM62304 2 0.4830 0.5454 0.000 0.608 NA 0.000
#> GSM62312 2 0.5167 -0.9644 0.004 0.508 NA 0.488
#> GSM62313 2 0.4830 0.5454 0.000 0.608 NA 0.000
#> GSM62314 2 0.0188 0.3854 0.000 0.996 NA 0.004
#> GSM62319 2 0.6719 -0.0753 0.240 0.608 NA 0.152
#> GSM62320 2 0.7289 -0.3325 0.004 0.544 NA 0.284
#> GSM62249 1 0.3757 0.6719 0.828 0.152 NA 0.020
#> GSM62251 1 0.0469 0.8068 0.988 0.000 NA 0.012
#> GSM62263 1 0.5512 0.3769 0.660 0.300 NA 0.040
#> GSM62285 4 0.5168 0.9984 0.004 0.492 NA 0.504
#> GSM62315 2 0.7468 -0.4748 0.196 0.484 NA 0.320
#> GSM62291 4 0.5168 0.9984 0.004 0.492 NA 0.504
#> GSM62265 1 0.0336 0.8077 0.992 0.000 NA 0.008
#> GSM62266 1 0.0336 0.8077 0.992 0.000 NA 0.008
#> GSM62296 4 0.5168 0.9886 0.004 0.496 NA 0.500
#> GSM62309 2 0.7443 -0.4789 0.196 0.492 NA 0.312
#> GSM62295 2 0.4948 0.5209 0.000 0.560 NA 0.000
#> GSM62300 4 0.5168 0.9984 0.004 0.492 NA 0.504
#> GSM62308 4 0.5168 0.9984 0.004 0.492 NA 0.504
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM62248 5 0.6245 0.4795 0.000 0.144 0.000 0.416 0.440
#> GSM62256 2 0.3883 0.7155 0.004 0.744 0.000 0.244 0.008
#> GSM62259 4 0.2248 0.7669 0.000 0.088 0.000 0.900 0.012
#> GSM62267 1 0.1544 0.7979 0.932 0.000 0.068 0.000 0.000
#> GSM62280 5 0.6739 -0.3464 0.348 0.000 0.260 0.000 0.392
#> GSM62284 1 0.2648 0.7347 0.848 0.000 0.152 0.000 0.000
#> GSM62289 5 0.6177 0.4832 0.000 0.136 0.000 0.400 0.464
#> GSM62307 4 0.2361 0.7741 0.000 0.096 0.000 0.892 0.012
#> GSM62316 5 0.6191 0.4653 0.000 0.136 0.000 0.428 0.436
#> GSM62254 4 0.3321 0.7200 0.000 0.032 0.000 0.832 0.136
#> GSM62292 4 0.3321 0.7200 0.000 0.032 0.000 0.832 0.136
#> GSM62253 1 0.0404 0.8076 0.988 0.000 0.012 0.000 0.000
#> GSM62270 3 0.3636 1.0000 0.272 0.000 0.728 0.000 0.000
#> GSM62278 1 0.3210 0.6694 0.788 0.000 0.212 0.000 0.000
#> GSM62297 5 0.6783 0.4287 0.004 0.232 0.000 0.340 0.424
#> GSM62298 4 0.3980 0.4523 0.000 0.284 0.000 0.708 0.008
#> GSM62299 2 0.2179 0.8138 0.000 0.888 0.000 0.112 0.000
#> GSM62258 1 0.2710 0.8003 0.892 0.008 0.064 0.000 0.036
#> GSM62281 2 0.4670 0.3303 0.004 0.548 0.000 0.440 0.008
#> GSM62294 4 0.0000 0.8506 0.000 0.000 0.000 1.000 0.000
#> GSM62305 5 0.6846 0.4880 0.024 0.152 0.000 0.368 0.456
#> GSM62306 5 0.6219 0.4692 0.000 0.140 0.000 0.424 0.436
#> GSM62310 4 0.3031 0.6939 0.004 0.016 0.000 0.852 0.128
#> GSM62311 4 0.0162 0.8480 0.000 0.004 0.000 0.996 0.000
#> GSM62317 5 0.7974 -0.2865 0.296 0.068 0.260 0.004 0.372
#> GSM62318 5 0.6726 -0.3616 0.360 0.000 0.252 0.000 0.388
#> GSM62321 5 0.6872 -0.3365 0.340 0.004 0.260 0.000 0.396
#> GSM62322 3 0.3636 1.0000 0.272 0.000 0.728 0.000 0.000
#> GSM62250 5 0.6911 0.4717 0.044 0.116 0.000 0.380 0.460
#> GSM62252 5 0.8202 0.3283 0.296 0.116 0.000 0.240 0.348
#> GSM62255 4 0.0162 0.8490 0.000 0.000 0.000 0.996 0.004
#> GSM62257 4 0.1942 0.7828 0.000 0.068 0.000 0.920 0.012
#> GSM62260 1 0.4867 0.6159 0.716 0.000 0.104 0.000 0.180
#> GSM62261 5 0.6247 0.4736 0.000 0.144 0.000 0.420 0.436
#> GSM62262 4 0.0000 0.8506 0.000 0.000 0.000 1.000 0.000
#> GSM62264 1 0.3239 0.7267 0.828 0.004 0.012 0.000 0.156
#> GSM62268 1 0.0963 0.8075 0.964 0.000 0.036 0.000 0.000
#> GSM62269 3 0.3636 1.0000 0.272 0.000 0.728 0.000 0.000
#> GSM62271 1 0.2227 0.8078 0.916 0.004 0.032 0.000 0.048
#> GSM62272 3 0.3636 1.0000 0.272 0.000 0.728 0.000 0.000
#> GSM62273 4 0.4206 0.4908 0.000 0.272 0.000 0.708 0.020
#> GSM62274 1 0.2605 0.7388 0.852 0.000 0.148 0.000 0.000
#> GSM62275 3 0.3636 1.0000 0.272 0.000 0.728 0.000 0.000
#> GSM62276 1 0.1544 0.7979 0.932 0.000 0.068 0.000 0.000
#> GSM62277 1 0.2648 0.7347 0.848 0.000 0.152 0.000 0.000
#> GSM62279 1 0.0162 0.8114 0.996 0.000 0.004 0.000 0.000
#> GSM62282 1 0.6612 0.2991 0.456 0.000 0.248 0.000 0.296
#> GSM62283 1 0.1041 0.8098 0.964 0.004 0.000 0.000 0.032
#> GSM62286 5 0.6177 0.4832 0.000 0.136 0.000 0.400 0.464
#> GSM62287 4 0.0000 0.8506 0.000 0.000 0.000 1.000 0.000
#> GSM62288 5 0.6245 0.4795 0.000 0.144 0.000 0.416 0.440
#> GSM62290 2 0.3003 0.7878 0.000 0.812 0.000 0.188 0.000
#> GSM62293 4 0.3321 0.7200 0.000 0.032 0.000 0.832 0.136
#> GSM62301 2 0.1792 0.8053 0.000 0.916 0.000 0.084 0.000
#> GSM62302 4 0.0000 0.8506 0.000 0.000 0.000 1.000 0.000
#> GSM62303 4 0.0000 0.8506 0.000 0.000 0.000 1.000 0.000
#> GSM62304 4 0.0000 0.8506 0.000 0.000 0.000 1.000 0.000
#> GSM62312 2 0.2852 0.8006 0.000 0.828 0.000 0.172 0.000
#> GSM62313 4 0.0000 0.8506 0.000 0.000 0.000 1.000 0.000
#> GSM62314 5 0.6102 0.4528 0.000 0.124 0.000 0.436 0.440
#> GSM62319 2 0.8617 0.0765 0.324 0.376 0.104 0.156 0.040
#> GSM62320 2 0.3969 0.6729 0.000 0.692 0.000 0.304 0.004
#> GSM62249 1 0.4170 0.7023 0.804 0.016 0.008 0.036 0.136
#> GSM62251 1 0.1851 0.7803 0.912 0.000 0.000 0.000 0.088
#> GSM62263 1 0.6079 0.5627 0.676 0.136 0.012 0.032 0.144
#> GSM62285 2 0.1792 0.8053 0.000 0.916 0.000 0.084 0.000
#> GSM62315 2 0.4061 0.6940 0.004 0.816 0.116 0.044 0.020
#> GSM62291 2 0.2813 0.8035 0.000 0.832 0.000 0.168 0.000
#> GSM62265 1 0.0000 0.8108 1.000 0.000 0.000 0.000 0.000
#> GSM62266 1 0.0404 0.8076 0.988 0.000 0.012 0.000 0.000
#> GSM62296 2 0.2605 0.8107 0.000 0.852 0.000 0.148 0.000
#> GSM62309 2 0.4111 0.7509 0.004 0.796 0.116 0.084 0.000
#> GSM62295 4 0.3366 0.7201 0.000 0.032 0.000 0.828 0.140
#> GSM62300 2 0.2127 0.8142 0.000 0.892 0.000 0.108 0.000
#> GSM62308 2 0.1908 0.8094 0.000 0.908 0.000 0.092 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM62248 5 0.4314 0.9087 0.000 0.184 0.000 0.096 0.720 0.000
#> GSM62256 2 0.3522 0.7166 0.000 0.800 0.000 0.128 0.072 0.000
#> GSM62259 4 0.5269 0.6939 0.000 0.248 0.000 0.596 0.156 0.000
#> GSM62267 1 0.1957 0.7448 0.888 0.000 0.112 0.000 0.000 0.000
#> GSM62280 6 0.1168 0.8040 0.016 0.000 0.000 0.000 0.028 0.956
#> GSM62284 1 0.2631 0.7061 0.820 0.000 0.180 0.000 0.000 0.000
#> GSM62289 5 0.3961 0.9124 0.000 0.124 0.000 0.112 0.764 0.000
#> GSM62307 4 0.5257 0.6822 0.000 0.280 0.000 0.584 0.136 0.000
#> GSM62316 5 0.4603 0.8864 0.000 0.156 0.000 0.148 0.696 0.000
#> GSM62254 4 0.1765 0.7944 0.000 0.096 0.000 0.904 0.000 0.000
#> GSM62292 4 0.1765 0.7944 0.000 0.096 0.000 0.904 0.000 0.000
#> GSM62253 1 0.0603 0.7561 0.980 0.000 0.000 0.000 0.004 0.016
#> GSM62270 3 0.0000 0.9458 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62278 3 0.2793 0.6996 0.200 0.000 0.800 0.000 0.000 0.000
#> GSM62297 5 0.4975 0.7443 0.000 0.312 0.000 0.092 0.596 0.000
#> GSM62298 2 0.5784 -0.2610 0.000 0.420 0.000 0.404 0.176 0.000
#> GSM62299 2 0.0790 0.7977 0.000 0.968 0.000 0.032 0.000 0.000
#> GSM62258 1 0.4681 0.6388 0.676 0.000 0.112 0.000 0.000 0.212
#> GSM62281 2 0.4148 0.6504 0.000 0.744 0.000 0.148 0.108 0.000
#> GSM62294 4 0.3088 0.8384 0.000 0.120 0.000 0.832 0.048 0.000
#> GSM62305 5 0.4003 0.9117 0.000 0.124 0.000 0.116 0.760 0.000
#> GSM62306 5 0.4267 0.9144 0.000 0.152 0.000 0.116 0.732 0.000
#> GSM62310 4 0.4762 0.7985 0.000 0.176 0.000 0.676 0.148 0.000
#> GSM62311 4 0.4148 0.8503 0.000 0.148 0.000 0.744 0.108 0.000
#> GSM62317 6 0.4764 0.6985 0.016 0.112 0.000 0.096 0.028 0.748
#> GSM62318 6 0.0458 0.8013 0.016 0.000 0.000 0.000 0.000 0.984
#> GSM62321 6 0.2807 0.7824 0.016 0.000 0.000 0.088 0.028 0.868
#> GSM62322 3 0.0000 0.9458 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62250 5 0.4702 0.8897 0.032 0.124 0.000 0.112 0.732 0.000
#> GSM62252 5 0.5282 0.8642 0.036 0.124 0.000 0.112 0.708 0.020
#> GSM62255 4 0.4039 0.8269 0.000 0.208 0.000 0.732 0.060 0.000
#> GSM62257 4 0.5348 0.6023 0.000 0.152 0.000 0.576 0.272 0.000
#> GSM62260 6 0.3923 0.0962 0.416 0.000 0.000 0.000 0.004 0.580
#> GSM62261 5 0.4299 0.9059 0.000 0.188 0.000 0.092 0.720 0.000
#> GSM62262 4 0.3088 0.8384 0.000 0.120 0.000 0.832 0.048 0.000
#> GSM62264 1 0.5465 0.3986 0.572 0.000 0.000 0.000 0.208 0.220
#> GSM62268 1 0.0603 0.7561 0.980 0.000 0.000 0.000 0.004 0.016
#> GSM62269 3 0.0000 0.9458 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62271 1 0.3952 0.5161 0.672 0.000 0.020 0.000 0.000 0.308
#> GSM62272 3 0.0000 0.9458 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62273 2 0.6081 0.1053 0.000 0.492 0.000 0.348 0.128 0.032
#> GSM62274 1 0.2664 0.7047 0.816 0.000 0.184 0.000 0.000 0.000
#> GSM62275 3 0.0000 0.9458 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62276 1 0.1957 0.7448 0.888 0.000 0.112 0.000 0.000 0.000
#> GSM62277 1 0.2664 0.7047 0.816 0.000 0.184 0.000 0.000 0.000
#> GSM62279 1 0.0146 0.7574 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM62282 6 0.1753 0.7646 0.084 0.000 0.004 0.000 0.000 0.912
#> GSM62283 1 0.3023 0.6454 0.784 0.000 0.004 0.000 0.000 0.212
#> GSM62286 5 0.3961 0.9124 0.000 0.124 0.000 0.112 0.764 0.000
#> GSM62287 4 0.4148 0.8503 0.000 0.148 0.000 0.744 0.108 0.000
#> GSM62288 5 0.4314 0.9087 0.000 0.184 0.000 0.096 0.720 0.000
#> GSM62290 2 0.1682 0.7800 0.000 0.928 0.000 0.052 0.020 0.000
#> GSM62293 4 0.1765 0.7944 0.000 0.096 0.000 0.904 0.000 0.000
#> GSM62301 2 0.0000 0.7889 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62302 4 0.4427 0.8274 0.000 0.148 0.000 0.716 0.136 0.000
#> GSM62303 4 0.4148 0.8503 0.000 0.148 0.000 0.744 0.108 0.000
#> GSM62304 4 0.4148 0.8503 0.000 0.148 0.000 0.744 0.108 0.000
#> GSM62312 2 0.1265 0.7914 0.000 0.948 0.000 0.044 0.008 0.000
#> GSM62313 4 0.4148 0.8503 0.000 0.148 0.000 0.744 0.108 0.000
#> GSM62314 5 0.4603 0.8864 0.000 0.156 0.000 0.148 0.696 0.000
#> GSM62319 2 0.6988 0.2925 0.016 0.440 0.000 0.064 0.148 0.332
#> GSM62320 2 0.3176 0.7400 0.000 0.832 0.000 0.084 0.084 0.000
#> GSM62249 1 0.6953 0.2813 0.560 0.140 0.004 0.080 0.032 0.184
#> GSM62251 1 0.4024 0.6278 0.744 0.000 0.000 0.000 0.184 0.072
#> GSM62263 1 0.7723 0.2395 0.424 0.136 0.000 0.028 0.228 0.184
#> GSM62285 2 0.0146 0.7917 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM62315 2 0.2882 0.6669 0.000 0.812 0.000 0.008 0.000 0.180
#> GSM62291 2 0.0820 0.7986 0.000 0.972 0.000 0.016 0.012 0.000
#> GSM62265 1 0.0146 0.7574 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM62266 1 0.0603 0.7561 0.980 0.000 0.000 0.000 0.004 0.016
#> GSM62296 2 0.1686 0.7841 0.000 0.924 0.000 0.012 0.064 0.000
#> GSM62309 2 0.2744 0.7173 0.000 0.840 0.000 0.000 0.016 0.144
#> GSM62295 4 0.1814 0.7925 0.000 0.100 0.000 0.900 0.000 0.000
#> GSM62300 2 0.0363 0.7957 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM62308 2 0.0458 0.7971 0.000 0.984 0.000 0.016 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) other(p) genotype/variation(p) k
#> CV:mclust 72 0.74742 1.000 0.811 2
#> CV:mclust 73 0.36173 0.761 0.741 3
#> CV:mclust 52 0.00271 0.586 0.143 4
#> CV:mclust 54 0.01162 0.853 0.481 5
#> CV:mclust 68 0.00312 0.768 0.462 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "NMF"]
# you can also extract it by
# res = res_list["CV:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 75 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 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 0.972 0.963 0.984 0.4381 0.559 0.559
#> 3 3 0.925 0.889 0.955 0.2862 0.835 0.714
#> 4 4 0.818 0.826 0.921 0.1353 0.901 0.781
#> 5 5 0.651 0.581 0.805 0.1779 0.776 0.469
#> 6 6 0.784 0.758 0.884 0.0788 0.836 0.446
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
#> GSM62248 2 0.000 0.991 0.000 1.000
#> GSM62256 2 0.000 0.991 0.000 1.000
#> GSM62259 2 0.000 0.991 0.000 1.000
#> GSM62267 1 0.000 0.967 1.000 0.000
#> GSM62280 1 0.000 0.967 1.000 0.000
#> GSM62284 1 0.000 0.967 1.000 0.000
#> GSM62289 2 0.000 0.991 0.000 1.000
#> GSM62307 2 0.000 0.991 0.000 1.000
#> GSM62316 2 0.000 0.991 0.000 1.000
#> GSM62254 2 0.000 0.991 0.000 1.000
#> GSM62292 2 0.000 0.991 0.000 1.000
#> GSM62253 1 0.000 0.967 1.000 0.000
#> GSM62270 1 0.000 0.967 1.000 0.000
#> GSM62278 1 0.000 0.967 1.000 0.000
#> GSM62297 2 0.000 0.991 0.000 1.000
#> GSM62298 2 0.000 0.991 0.000 1.000
#> GSM62299 2 0.000 0.991 0.000 1.000
#> GSM62258 1 0.000 0.967 1.000 0.000
#> GSM62281 2 0.000 0.991 0.000 1.000
#> GSM62294 2 0.000 0.991 0.000 1.000
#> GSM62305 2 0.000 0.991 0.000 1.000
#> GSM62306 2 0.000 0.991 0.000 1.000
#> GSM62310 2 0.000 0.991 0.000 1.000
#> GSM62311 2 0.000 0.991 0.000 1.000
#> GSM62317 2 0.000 0.991 0.000 1.000
#> GSM62318 1 0.000 0.967 1.000 0.000
#> GSM62321 2 0.781 0.687 0.232 0.768
#> GSM62322 1 0.000 0.967 1.000 0.000
#> GSM62250 2 0.000 0.991 0.000 1.000
#> GSM62252 2 0.000 0.991 0.000 1.000
#> GSM62255 2 0.000 0.991 0.000 1.000
#> GSM62257 2 0.000 0.991 0.000 1.000
#> GSM62260 1 0.850 0.629 0.724 0.276
#> GSM62261 2 0.000 0.991 0.000 1.000
#> GSM62262 2 0.000 0.991 0.000 1.000
#> GSM62264 1 0.552 0.843 0.872 0.128
#> GSM62268 1 0.000 0.967 1.000 0.000
#> GSM62269 1 0.000 0.967 1.000 0.000
#> GSM62271 1 0.000 0.967 1.000 0.000
#> GSM62272 1 0.000 0.967 1.000 0.000
#> GSM62273 2 0.000 0.991 0.000 1.000
#> GSM62274 1 0.000 0.967 1.000 0.000
#> GSM62275 1 0.000 0.967 1.000 0.000
#> GSM62276 1 0.000 0.967 1.000 0.000
#> GSM62277 1 0.000 0.967 1.000 0.000
#> GSM62279 1 0.000 0.967 1.000 0.000
#> GSM62282 1 0.000 0.967 1.000 0.000
#> GSM62283 1 0.929 0.487 0.656 0.344
#> GSM62286 2 0.000 0.991 0.000 1.000
#> GSM62287 2 0.000 0.991 0.000 1.000
#> GSM62288 2 0.000 0.991 0.000 1.000
#> GSM62290 2 0.000 0.991 0.000 1.000
#> GSM62293 2 0.000 0.991 0.000 1.000
#> GSM62301 2 0.000 0.991 0.000 1.000
#> GSM62302 2 0.000 0.991 0.000 1.000
#> GSM62303 2 0.000 0.991 0.000 1.000
#> GSM62304 2 0.000 0.991 0.000 1.000
#> GSM62312 2 0.000 0.991 0.000 1.000
#> GSM62313 2 0.000 0.991 0.000 1.000
#> GSM62314 2 0.000 0.991 0.000 1.000
#> GSM62319 2 0.000 0.991 0.000 1.000
#> GSM62320 2 0.000 0.991 0.000 1.000
#> GSM62249 2 0.000 0.991 0.000 1.000
#> GSM62251 2 0.722 0.741 0.200 0.800
#> GSM62263 2 0.000 0.991 0.000 1.000
#> GSM62285 2 0.000 0.991 0.000 1.000
#> GSM62315 2 0.000 0.991 0.000 1.000
#> GSM62291 2 0.000 0.991 0.000 1.000
#> GSM62265 1 0.000 0.967 1.000 0.000
#> GSM62266 1 0.000 0.967 1.000 0.000
#> GSM62296 2 0.000 0.991 0.000 1.000
#> GSM62309 2 0.000 0.991 0.000 1.000
#> GSM62295 2 0.000 0.991 0.000 1.000
#> GSM62300 2 0.000 0.991 0.000 1.000
#> GSM62308 2 0.000 0.991 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM62248 2 0.1163 0.96014 0.028 0.972 0.000
#> GSM62256 2 0.1031 0.96826 0.024 0.976 0.000
#> GSM62259 2 0.0000 0.98776 0.000 1.000 0.000
#> GSM62267 3 0.0237 0.93331 0.000 0.004 0.996
#> GSM62280 1 0.1964 0.77460 0.944 0.000 0.056
#> GSM62284 3 0.4842 0.69062 0.224 0.000 0.776
#> GSM62289 2 0.0000 0.98776 0.000 1.000 0.000
#> GSM62307 2 0.0000 0.98776 0.000 1.000 0.000
#> GSM62316 2 0.0000 0.98776 0.000 1.000 0.000
#> GSM62254 2 0.0000 0.98776 0.000 1.000 0.000
#> GSM62292 2 0.0000 0.98776 0.000 1.000 0.000
#> GSM62253 1 0.6062 0.36838 0.616 0.000 0.384
#> GSM62270 3 0.0000 0.93722 0.000 0.000 1.000
#> GSM62278 3 0.0000 0.93722 0.000 0.000 1.000
#> GSM62297 2 0.0237 0.98606 0.004 0.996 0.000
#> GSM62298 2 0.0000 0.98776 0.000 1.000 0.000
#> GSM62299 2 0.0237 0.98606 0.004 0.996 0.000
#> GSM62258 3 0.1529 0.90798 0.040 0.000 0.960
#> GSM62281 2 0.0000 0.98776 0.000 1.000 0.000
#> GSM62294 2 0.0000 0.98776 0.000 1.000 0.000
#> GSM62305 2 0.0000 0.98776 0.000 1.000 0.000
#> GSM62306 2 0.0000 0.98776 0.000 1.000 0.000
#> GSM62310 2 0.0000 0.98776 0.000 1.000 0.000
#> GSM62311 2 0.0000 0.98776 0.000 1.000 0.000
#> GSM62317 1 0.4887 0.56950 0.772 0.228 0.000
#> GSM62318 1 0.0000 0.79765 1.000 0.000 0.000
#> GSM62321 1 0.0000 0.79765 1.000 0.000 0.000
#> GSM62322 3 0.0000 0.93722 0.000 0.000 1.000
#> GSM62250 2 0.0000 0.98776 0.000 1.000 0.000
#> GSM62252 2 0.0000 0.98776 0.000 1.000 0.000
#> GSM62255 2 0.0000 0.98776 0.000 1.000 0.000
#> GSM62257 2 0.0000 0.98776 0.000 1.000 0.000
#> GSM62260 1 0.0237 0.79786 0.996 0.000 0.004
#> GSM62261 2 0.0000 0.98776 0.000 1.000 0.000
#> GSM62262 2 0.0000 0.98776 0.000 1.000 0.000
#> GSM62264 1 0.0237 0.79786 0.996 0.000 0.004
#> GSM62268 1 0.6126 0.32971 0.600 0.000 0.400
#> GSM62269 3 0.0000 0.93722 0.000 0.000 1.000
#> GSM62271 3 0.0237 0.93498 0.004 0.000 0.996
#> GSM62272 3 0.0000 0.93722 0.000 0.000 1.000
#> GSM62273 2 0.0000 0.98776 0.000 1.000 0.000
#> GSM62274 3 0.0000 0.93722 0.000 0.000 1.000
#> GSM62275 3 0.0000 0.93722 0.000 0.000 1.000
#> GSM62276 3 0.0000 0.93722 0.000 0.000 1.000
#> GSM62277 3 0.0000 0.93722 0.000 0.000 1.000
#> GSM62279 3 0.5016 0.66278 0.240 0.000 0.760
#> GSM62282 3 0.4887 0.66283 0.228 0.000 0.772
#> GSM62283 1 0.1163 0.79340 0.972 0.000 0.028
#> GSM62286 2 0.0000 0.98776 0.000 1.000 0.000
#> GSM62287 2 0.0000 0.98776 0.000 1.000 0.000
#> GSM62288 2 0.0000 0.98776 0.000 1.000 0.000
#> GSM62290 2 0.0237 0.98606 0.004 0.996 0.000
#> GSM62293 2 0.0000 0.98776 0.000 1.000 0.000
#> GSM62301 2 0.0424 0.98365 0.008 0.992 0.000
#> GSM62302 2 0.0000 0.98776 0.000 1.000 0.000
#> GSM62303 2 0.0000 0.98776 0.000 1.000 0.000
#> GSM62304 2 0.0000 0.98776 0.000 1.000 0.000
#> GSM62312 2 0.0237 0.98606 0.004 0.996 0.000
#> GSM62313 2 0.0000 0.98776 0.000 1.000 0.000
#> GSM62314 2 0.0000 0.98776 0.000 1.000 0.000
#> GSM62319 2 0.0237 0.98606 0.004 0.996 0.000
#> GSM62320 2 0.0237 0.98606 0.004 0.996 0.000
#> GSM62249 1 0.0592 0.79521 0.988 0.012 0.000
#> GSM62251 1 0.3690 0.75753 0.884 0.016 0.100
#> GSM62263 1 0.0000 0.79765 1.000 0.000 0.000
#> GSM62285 2 0.0424 0.98365 0.008 0.992 0.000
#> GSM62315 2 0.6095 0.32793 0.392 0.608 0.000
#> GSM62291 2 0.0424 0.98365 0.008 0.992 0.000
#> GSM62265 1 0.4178 0.70390 0.828 0.000 0.172
#> GSM62266 1 0.5016 0.62694 0.760 0.000 0.240
#> GSM62296 2 0.0237 0.98606 0.004 0.996 0.000
#> GSM62309 1 0.6307 0.00733 0.512 0.488 0.000
#> GSM62295 2 0.0000 0.98776 0.000 1.000 0.000
#> GSM62300 2 0.0424 0.98365 0.008 0.992 0.000
#> GSM62308 2 0.0424 0.98365 0.008 0.992 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM62248 2 0.2469 0.86969 0.108 0.892 0.000 0.000
#> GSM62256 2 0.4981 0.21062 0.000 0.536 0.000 0.464
#> GSM62259 2 0.0000 0.94150 0.000 1.000 0.000 0.000
#> GSM62267 1 0.4720 0.53458 0.720 0.016 0.264 0.000
#> GSM62280 4 0.0000 0.95434 0.000 0.000 0.000 1.000
#> GSM62284 1 0.4431 0.49318 0.696 0.000 0.304 0.000
#> GSM62289 2 0.4713 0.41476 0.360 0.640 0.000 0.000
#> GSM62307 2 0.0000 0.94150 0.000 1.000 0.000 0.000
#> GSM62316 2 0.0592 0.93561 0.016 0.984 0.000 0.000
#> GSM62254 2 0.0000 0.94150 0.000 1.000 0.000 0.000
#> GSM62292 2 0.0000 0.94150 0.000 1.000 0.000 0.000
#> GSM62253 1 0.0524 0.77953 0.988 0.000 0.008 0.004
#> GSM62270 3 0.0000 0.87509 0.000 0.000 1.000 0.000
#> GSM62278 3 0.0000 0.87509 0.000 0.000 1.000 0.000
#> GSM62297 2 0.3142 0.83796 0.132 0.860 0.000 0.008
#> GSM62298 2 0.0657 0.93840 0.004 0.984 0.000 0.012
#> GSM62299 2 0.1151 0.93300 0.008 0.968 0.000 0.024
#> GSM62258 3 0.3448 0.75057 0.168 0.000 0.828 0.004
#> GSM62281 2 0.0592 0.93830 0.000 0.984 0.000 0.016
#> GSM62294 2 0.0000 0.94150 0.000 1.000 0.000 0.000
#> GSM62305 2 0.3528 0.76918 0.192 0.808 0.000 0.000
#> GSM62306 2 0.0188 0.94027 0.004 0.996 0.000 0.000
#> GSM62310 2 0.0000 0.94150 0.000 1.000 0.000 0.000
#> GSM62311 2 0.0000 0.94150 0.000 1.000 0.000 0.000
#> GSM62317 4 0.0000 0.95434 0.000 0.000 0.000 1.000
#> GSM62318 4 0.0592 0.94586 0.016 0.000 0.000 0.984
#> GSM62321 4 0.0000 0.95434 0.000 0.000 0.000 1.000
#> GSM62322 3 0.0000 0.87509 0.000 0.000 1.000 0.000
#> GSM62250 1 0.4925 0.24468 0.572 0.428 0.000 0.000
#> GSM62252 1 0.4776 0.39741 0.624 0.376 0.000 0.000
#> GSM62255 2 0.0000 0.94150 0.000 1.000 0.000 0.000
#> GSM62257 2 0.0000 0.94150 0.000 1.000 0.000 0.000
#> GSM62260 4 0.1557 0.92991 0.056 0.000 0.000 0.944
#> GSM62261 2 0.0921 0.92969 0.028 0.972 0.000 0.000
#> GSM62262 2 0.0000 0.94150 0.000 1.000 0.000 0.000
#> GSM62264 1 0.3266 0.69326 0.832 0.000 0.000 0.168
#> GSM62268 1 0.3105 0.70923 0.856 0.000 0.140 0.004
#> GSM62269 3 0.0000 0.87509 0.000 0.000 1.000 0.000
#> GSM62271 3 0.1557 0.84607 0.056 0.000 0.944 0.000
#> GSM62272 3 0.0000 0.87509 0.000 0.000 1.000 0.000
#> GSM62273 2 0.0779 0.93715 0.004 0.980 0.000 0.016
#> GSM62274 3 0.4992 0.00268 0.476 0.000 0.524 0.000
#> GSM62275 3 0.0000 0.87509 0.000 0.000 1.000 0.000
#> GSM62276 3 0.4277 0.60312 0.280 0.000 0.720 0.000
#> GSM62277 3 0.0336 0.87228 0.008 0.000 0.992 0.000
#> GSM62279 1 0.0469 0.77785 0.988 0.000 0.012 0.000
#> GSM62282 3 0.3907 0.66275 0.000 0.000 0.768 0.232
#> GSM62283 1 0.4188 0.68073 0.812 0.000 0.148 0.040
#> GSM62286 2 0.1867 0.89795 0.072 0.928 0.000 0.000
#> GSM62287 2 0.0000 0.94150 0.000 1.000 0.000 0.000
#> GSM62288 2 0.1389 0.91746 0.048 0.952 0.000 0.000
#> GSM62290 2 0.0927 0.93601 0.008 0.976 0.000 0.016
#> GSM62293 2 0.0000 0.94150 0.000 1.000 0.000 0.000
#> GSM62301 2 0.4248 0.72886 0.012 0.768 0.000 0.220
#> GSM62302 2 0.0000 0.94150 0.000 1.000 0.000 0.000
#> GSM62303 2 0.0000 0.94150 0.000 1.000 0.000 0.000
#> GSM62304 2 0.0000 0.94150 0.000 1.000 0.000 0.000
#> GSM62312 2 0.0927 0.93601 0.008 0.976 0.000 0.016
#> GSM62313 2 0.0000 0.94150 0.000 1.000 0.000 0.000
#> GSM62314 2 0.0707 0.93375 0.020 0.980 0.000 0.000
#> GSM62319 2 0.2342 0.89856 0.008 0.912 0.000 0.080
#> GSM62320 2 0.0927 0.93601 0.008 0.976 0.000 0.016
#> GSM62249 1 0.1118 0.77686 0.964 0.000 0.000 0.036
#> GSM62251 1 0.0336 0.78030 0.992 0.000 0.000 0.008
#> GSM62263 1 0.3219 0.69023 0.836 0.000 0.000 0.164
#> GSM62285 2 0.2271 0.90124 0.008 0.916 0.000 0.076
#> GSM62315 4 0.2342 0.86208 0.008 0.080 0.000 0.912
#> GSM62291 2 0.1452 0.92745 0.008 0.956 0.000 0.036
#> GSM62265 1 0.0469 0.78066 0.988 0.000 0.000 0.012
#> GSM62266 1 0.0895 0.78055 0.976 0.000 0.004 0.020
#> GSM62296 2 0.1970 0.91280 0.008 0.932 0.000 0.060
#> GSM62309 4 0.1888 0.93491 0.044 0.016 0.000 0.940
#> GSM62295 2 0.0000 0.94150 0.000 1.000 0.000 0.000
#> GSM62300 2 0.1970 0.91343 0.008 0.932 0.000 0.060
#> GSM62308 2 0.3351 0.83370 0.008 0.844 0.000 0.148
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM62248 4 0.1082 0.72508 0.028 0.008 0.000 0.964 0.000
#> GSM62256 5 0.1012 0.81554 0.000 0.012 0.000 0.020 0.968
#> GSM62259 4 0.4219 0.18105 0.000 0.416 0.000 0.584 0.000
#> GSM62267 4 0.3991 0.46763 0.172 0.000 0.048 0.780 0.000
#> GSM62280 5 0.0404 0.82472 0.012 0.000 0.000 0.000 0.988
#> GSM62284 1 0.4114 0.31381 0.624 0.000 0.376 0.000 0.000
#> GSM62289 4 0.0404 0.72229 0.012 0.000 0.000 0.988 0.000
#> GSM62307 2 0.4249 0.28807 0.000 0.568 0.000 0.432 0.000
#> GSM62316 4 0.0963 0.72171 0.000 0.036 0.000 0.964 0.000
#> GSM62254 2 0.4262 0.29089 0.000 0.560 0.000 0.440 0.000
#> GSM62292 4 0.4278 0.01471 0.000 0.452 0.000 0.548 0.000
#> GSM62253 1 0.0162 0.74665 0.996 0.000 0.004 0.000 0.000
#> GSM62270 3 0.0000 0.97676 0.000 0.000 1.000 0.000 0.000
#> GSM62278 3 0.0000 0.97676 0.000 0.000 1.000 0.000 0.000
#> GSM62297 2 0.4385 0.31812 0.312 0.672 0.000 0.004 0.012
#> GSM62298 2 0.0865 0.64447 0.000 0.972 0.000 0.024 0.004
#> GSM62299 2 0.1012 0.64330 0.020 0.968 0.000 0.000 0.012
#> GSM62258 5 0.5445 0.35615 0.016 0.000 0.032 0.420 0.532
#> GSM62281 2 0.5982 0.38328 0.000 0.552 0.000 0.312 0.136
#> GSM62294 2 0.4138 0.39953 0.000 0.616 0.000 0.384 0.000
#> GSM62305 4 0.2387 0.67632 0.040 0.048 0.000 0.908 0.004
#> GSM62306 4 0.0880 0.72259 0.000 0.032 0.000 0.968 0.000
#> GSM62310 2 0.4397 0.30451 0.000 0.564 0.000 0.432 0.004
#> GSM62311 2 0.4350 0.35508 0.000 0.588 0.000 0.408 0.004
#> GSM62317 5 0.0324 0.82301 0.004 0.004 0.000 0.000 0.992
#> GSM62318 5 0.0404 0.82472 0.012 0.000 0.000 0.000 0.988
#> GSM62321 5 0.0404 0.82472 0.012 0.000 0.000 0.000 0.988
#> GSM62322 3 0.0000 0.97676 0.000 0.000 1.000 0.000 0.000
#> GSM62250 4 0.1544 0.68404 0.068 0.000 0.000 0.932 0.000
#> GSM62252 4 0.0880 0.71468 0.032 0.000 0.000 0.968 0.000
#> GSM62255 2 0.3816 0.49027 0.000 0.696 0.000 0.304 0.000
#> GSM62257 4 0.2891 0.63257 0.000 0.176 0.000 0.824 0.000
#> GSM62260 5 0.4019 0.63465 0.152 0.052 0.000 0.004 0.792
#> GSM62261 4 0.3612 0.48337 0.000 0.268 0.000 0.732 0.000
#> GSM62262 2 0.4088 0.42339 0.000 0.632 0.000 0.368 0.000
#> GSM62264 1 0.1357 0.72693 0.948 0.004 0.000 0.000 0.048
#> GSM62268 1 0.2424 0.67733 0.868 0.000 0.132 0.000 0.000
#> GSM62269 3 0.0000 0.97676 0.000 0.000 1.000 0.000 0.000
#> GSM62271 3 0.1571 0.91585 0.060 0.004 0.936 0.000 0.000
#> GSM62272 3 0.0000 0.97676 0.000 0.000 1.000 0.000 0.000
#> GSM62273 2 0.1571 0.63476 0.000 0.936 0.000 0.060 0.004
#> GSM62274 3 0.1908 0.88525 0.092 0.000 0.908 0.000 0.000
#> GSM62275 3 0.0000 0.97676 0.000 0.000 1.000 0.000 0.000
#> GSM62276 4 0.4780 0.34249 0.060 0.000 0.248 0.692 0.000
#> GSM62277 3 0.0000 0.97676 0.000 0.000 1.000 0.000 0.000
#> GSM62279 1 0.4114 0.39189 0.624 0.000 0.000 0.376 0.000
#> GSM62282 5 0.3913 0.46562 0.000 0.000 0.324 0.000 0.676
#> GSM62283 1 0.8505 0.33881 0.428 0.256 0.088 0.188 0.040
#> GSM62286 4 0.0162 0.72413 0.000 0.004 0.000 0.996 0.000
#> GSM62287 4 0.3895 0.41993 0.000 0.320 0.000 0.680 0.000
#> GSM62288 4 0.2900 0.68174 0.028 0.108 0.000 0.864 0.000
#> GSM62290 2 0.1830 0.62714 0.068 0.924 0.000 0.000 0.008
#> GSM62293 2 0.4088 0.42353 0.000 0.632 0.000 0.368 0.000
#> GSM62301 2 0.3039 0.55069 0.152 0.836 0.000 0.000 0.012
#> GSM62302 2 0.4278 0.25842 0.000 0.548 0.000 0.452 0.000
#> GSM62303 2 0.4305 0.14691 0.000 0.512 0.000 0.488 0.000
#> GSM62304 4 0.4150 0.24103 0.000 0.388 0.000 0.612 0.000
#> GSM62312 2 0.1267 0.64714 0.012 0.960 0.000 0.024 0.004
#> GSM62313 2 0.4291 0.22489 0.000 0.536 0.000 0.464 0.000
#> GSM62314 4 0.4716 0.37766 0.036 0.308 0.000 0.656 0.000
#> GSM62319 2 0.1029 0.64584 0.008 0.972 0.004 0.008 0.008
#> GSM62320 2 0.0671 0.64644 0.000 0.980 0.000 0.016 0.004
#> GSM62249 1 0.7032 0.39064 0.492 0.216 0.000 0.264 0.028
#> GSM62251 1 0.0162 0.74752 0.996 0.000 0.000 0.004 0.000
#> GSM62263 1 0.1792 0.70839 0.916 0.084 0.000 0.000 0.000
#> GSM62285 2 0.2011 0.61623 0.088 0.908 0.000 0.000 0.004
#> GSM62315 2 0.4735 0.30014 0.048 0.680 0.000 0.000 0.272
#> GSM62291 2 0.0798 0.64533 0.016 0.976 0.000 0.000 0.008
#> GSM62265 1 0.1369 0.74199 0.956 0.008 0.000 0.028 0.008
#> GSM62266 1 0.0000 0.74708 1.000 0.000 0.000 0.000 0.000
#> GSM62296 2 0.1211 0.64212 0.016 0.960 0.000 0.000 0.024
#> GSM62309 2 0.6361 -0.00792 0.196 0.508 0.000 0.000 0.296
#> GSM62295 2 0.3774 0.49739 0.000 0.704 0.000 0.296 0.000
#> GSM62300 2 0.2136 0.61449 0.088 0.904 0.000 0.000 0.008
#> GSM62308 2 0.1168 0.64032 0.032 0.960 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
#> GSM62248 5 0.2389 0.7905 0.008 0.000 0.000 0.128 0.864 0.000
#> GSM62256 6 0.0000 0.9362 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM62259 5 0.3418 0.7452 0.004 0.092 0.000 0.084 0.820 0.000
#> GSM62267 5 0.0291 0.7846 0.004 0.000 0.000 0.004 0.992 0.000
#> GSM62280 6 0.0000 0.9362 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM62284 1 0.1610 0.8435 0.916 0.000 0.084 0.000 0.000 0.000
#> GSM62289 5 0.0717 0.7888 0.008 0.000 0.000 0.016 0.976 0.000
#> GSM62307 5 0.3819 0.6082 0.000 0.004 0.000 0.372 0.624 0.000
#> GSM62316 5 0.2378 0.7882 0.000 0.000 0.000 0.152 0.848 0.000
#> GSM62254 5 0.3756 0.5686 0.000 0.000 0.000 0.400 0.600 0.000
#> GSM62292 5 0.3405 0.7292 0.000 0.004 0.000 0.272 0.724 0.000
#> GSM62253 1 0.0146 0.8936 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM62270 3 0.0000 0.9762 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62278 3 0.0000 0.9762 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62297 2 0.0458 0.8932 0.016 0.984 0.000 0.000 0.000 0.000
#> GSM62298 4 0.2178 0.6994 0.000 0.132 0.000 0.868 0.000 0.000
#> GSM62299 2 0.0632 0.8955 0.000 0.976 0.000 0.024 0.000 0.000
#> GSM62258 5 0.3942 0.2857 0.004 0.004 0.000 0.000 0.624 0.368
#> GSM62281 6 0.3710 0.5288 0.000 0.000 0.000 0.292 0.012 0.696
#> GSM62294 4 0.3515 0.2236 0.000 0.000 0.000 0.676 0.324 0.000
#> GSM62305 5 0.2520 0.6847 0.004 0.152 0.000 0.000 0.844 0.000
#> GSM62306 5 0.0748 0.7816 0.004 0.016 0.000 0.004 0.976 0.000
#> GSM62310 4 0.0000 0.7852 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62311 4 0.0000 0.7852 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62317 6 0.0000 0.9362 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM62318 6 0.0000 0.9362 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM62321 6 0.0000 0.9362 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM62322 3 0.0000 0.9762 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62250 5 0.0405 0.7850 0.008 0.000 0.000 0.004 0.988 0.000
#> GSM62252 5 0.0767 0.7877 0.004 0.008 0.000 0.012 0.976 0.000
#> GSM62255 4 0.0291 0.7854 0.000 0.004 0.000 0.992 0.004 0.000
#> GSM62257 5 0.2562 0.7847 0.000 0.000 0.000 0.172 0.828 0.000
#> GSM62260 2 0.2765 0.7917 0.004 0.848 0.000 0.000 0.016 0.132
#> GSM62261 5 0.3575 0.7166 0.008 0.000 0.000 0.284 0.708 0.000
#> GSM62262 4 0.0547 0.7801 0.000 0.000 0.000 0.980 0.020 0.000
#> GSM62264 1 0.0520 0.8918 0.984 0.008 0.000 0.000 0.000 0.008
#> GSM62268 1 0.0363 0.8912 0.988 0.000 0.012 0.000 0.000 0.000
#> GSM62269 3 0.0000 0.9762 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62271 3 0.2592 0.8295 0.004 0.116 0.864 0.000 0.016 0.000
#> GSM62272 3 0.0000 0.9762 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62273 4 0.2912 0.6315 0.000 0.216 0.000 0.784 0.000 0.000
#> GSM62274 3 0.0632 0.9583 0.024 0.000 0.976 0.000 0.000 0.000
#> GSM62275 3 0.0000 0.9762 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62276 5 0.0291 0.7819 0.004 0.004 0.000 0.000 0.992 0.000
#> GSM62277 3 0.0146 0.9740 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM62279 1 0.4067 0.2687 0.548 0.008 0.000 0.000 0.444 0.000
#> GSM62282 6 0.0000 0.9362 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM62283 2 0.1806 0.8459 0.004 0.908 0.000 0.000 0.088 0.000
#> GSM62286 5 0.0862 0.7888 0.004 0.008 0.000 0.016 0.972 0.000
#> GSM62287 5 0.3371 0.7189 0.000 0.000 0.000 0.292 0.708 0.000
#> GSM62288 5 0.2805 0.7776 0.004 0.000 0.000 0.184 0.812 0.000
#> GSM62290 2 0.2664 0.7495 0.000 0.816 0.000 0.184 0.000 0.000
#> GSM62293 4 0.0713 0.7740 0.000 0.000 0.000 0.972 0.028 0.000
#> GSM62301 2 0.0622 0.8958 0.012 0.980 0.000 0.008 0.000 0.000
#> GSM62302 4 0.0000 0.7852 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62303 5 0.3843 0.4604 0.000 0.000 0.000 0.452 0.548 0.000
#> GSM62304 5 0.3499 0.6884 0.000 0.000 0.000 0.320 0.680 0.000
#> GSM62312 4 0.3774 0.2901 0.000 0.408 0.000 0.592 0.000 0.000
#> GSM62313 4 0.0547 0.7801 0.000 0.000 0.000 0.980 0.020 0.000
#> GSM62314 4 0.5713 -0.2823 0.140 0.004 0.000 0.436 0.420 0.000
#> GSM62319 2 0.0632 0.8955 0.000 0.976 0.000 0.024 0.000 0.000
#> GSM62320 4 0.3868 -0.0138 0.000 0.496 0.000 0.504 0.000 0.000
#> GSM62249 2 0.1802 0.8597 0.012 0.916 0.000 0.000 0.072 0.000
#> GSM62251 1 0.0405 0.8931 0.988 0.004 0.000 0.000 0.008 0.000
#> GSM62263 1 0.1204 0.8583 0.944 0.056 0.000 0.000 0.000 0.000
#> GSM62285 2 0.1663 0.8559 0.000 0.912 0.000 0.088 0.000 0.000
#> GSM62315 2 0.0547 0.8967 0.000 0.980 0.000 0.020 0.000 0.000
#> GSM62291 2 0.3266 0.6095 0.000 0.728 0.000 0.272 0.000 0.000
#> GSM62265 2 0.4300 0.2379 0.432 0.548 0.000 0.000 0.020 0.000
#> GSM62266 1 0.0146 0.8936 0.996 0.004 0.000 0.000 0.000 0.000
#> GSM62296 2 0.0458 0.8967 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM62309 2 0.0363 0.8936 0.012 0.988 0.000 0.000 0.000 0.000
#> GSM62295 4 0.0146 0.7841 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM62300 2 0.0260 0.8962 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM62308 2 0.0937 0.8889 0.000 0.960 0.000 0.040 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) other(p) genotype/variation(p) k
#> CV:NMF 74 0.309249 0.876 0.4468 2
#> CV:NMF 71 0.010333 0.139 0.1968 3
#> CV:NMF 69 0.037263 0.133 0.4881 4
#> CV:NMF 45 0.004589 0.229 0.1569 5
#> CV:NMF 67 0.000234 0.189 0.0681 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "hclust"]
# you can also extract it by
# res = res_list["MAD:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 75 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 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 0.614 0.889 0.941 0.3559 0.630 0.630
#> 3 3 0.725 0.786 0.897 0.6149 0.751 0.611
#> 4 4 0.771 0.736 0.855 0.0622 0.981 0.953
#> 5 5 0.640 0.707 0.820 0.0821 0.964 0.909
#> 6 6 0.619 0.691 0.765 0.0843 0.942 0.844
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
#> GSM62248 2 0.0000 0.955 0.000 1.000
#> GSM62256 2 0.0000 0.955 0.000 1.000
#> GSM62259 2 0.0000 0.955 0.000 1.000
#> GSM62267 1 0.9815 0.408 0.580 0.420
#> GSM62280 2 0.8327 0.648 0.264 0.736
#> GSM62284 1 0.6247 0.840 0.844 0.156
#> GSM62289 2 0.4161 0.897 0.084 0.916
#> GSM62307 2 0.0000 0.955 0.000 1.000
#> GSM62316 2 0.0000 0.955 0.000 1.000
#> GSM62254 2 0.0000 0.955 0.000 1.000
#> GSM62292 2 0.0000 0.955 0.000 1.000
#> GSM62253 1 0.6247 0.840 0.844 0.156
#> GSM62270 1 0.0000 0.854 1.000 0.000
#> GSM62278 1 0.0376 0.855 0.996 0.004
#> GSM62297 2 0.0000 0.955 0.000 1.000
#> GSM62298 2 0.0000 0.955 0.000 1.000
#> GSM62299 2 0.0000 0.955 0.000 1.000
#> GSM62258 1 0.9323 0.577 0.652 0.348
#> GSM62281 2 0.0000 0.955 0.000 1.000
#> GSM62294 2 0.0000 0.955 0.000 1.000
#> GSM62305 2 0.3733 0.907 0.072 0.928
#> GSM62306 2 0.3733 0.907 0.072 0.928
#> GSM62310 2 0.0000 0.955 0.000 1.000
#> GSM62311 2 0.0000 0.955 0.000 1.000
#> GSM62317 2 0.2603 0.927 0.044 0.956
#> GSM62318 2 0.7528 0.729 0.216 0.784
#> GSM62321 2 0.2778 0.924 0.048 0.952
#> GSM62322 1 0.0000 0.854 1.000 0.000
#> GSM62250 2 0.5178 0.867 0.116 0.884
#> GSM62252 2 0.5178 0.867 0.116 0.884
#> GSM62255 2 0.0000 0.955 0.000 1.000
#> GSM62257 2 0.0000 0.955 0.000 1.000
#> GSM62260 2 0.4815 0.877 0.104 0.896
#> GSM62261 2 0.0000 0.955 0.000 1.000
#> GSM62262 2 0.0000 0.955 0.000 1.000
#> GSM62264 2 0.4690 0.880 0.100 0.900
#> GSM62268 1 0.6247 0.840 0.844 0.156
#> GSM62269 1 0.0000 0.854 1.000 0.000
#> GSM62271 1 0.0376 0.855 0.996 0.004
#> GSM62272 1 0.0000 0.854 1.000 0.000
#> GSM62273 2 0.0000 0.955 0.000 1.000
#> GSM62274 1 0.2778 0.859 0.952 0.048
#> GSM62275 1 0.0000 0.854 1.000 0.000
#> GSM62276 1 0.9815 0.408 0.580 0.420
#> GSM62277 1 0.2778 0.859 0.952 0.048
#> GSM62279 1 0.6438 0.834 0.836 0.164
#> GSM62282 1 0.6973 0.808 0.812 0.188
#> GSM62283 2 0.6887 0.786 0.184 0.816
#> GSM62286 2 0.5178 0.867 0.116 0.884
#> GSM62287 2 0.0000 0.955 0.000 1.000
#> GSM62288 2 0.0000 0.955 0.000 1.000
#> GSM62290 2 0.0000 0.955 0.000 1.000
#> GSM62293 2 0.0000 0.955 0.000 1.000
#> GSM62301 2 0.0000 0.955 0.000 1.000
#> GSM62302 2 0.0000 0.955 0.000 1.000
#> GSM62303 2 0.0000 0.955 0.000 1.000
#> GSM62304 2 0.0000 0.955 0.000 1.000
#> GSM62312 2 0.0000 0.955 0.000 1.000
#> GSM62313 2 0.0000 0.955 0.000 1.000
#> GSM62314 2 0.0000 0.955 0.000 1.000
#> GSM62319 2 0.2778 0.926 0.048 0.952
#> GSM62320 2 0.0000 0.955 0.000 1.000
#> GSM62249 2 0.6887 0.786 0.184 0.816
#> GSM62251 2 0.5408 0.856 0.124 0.876
#> GSM62263 2 0.4161 0.895 0.084 0.916
#> GSM62285 2 0.0000 0.955 0.000 1.000
#> GSM62315 2 0.0000 0.955 0.000 1.000
#> GSM62291 2 0.0000 0.955 0.000 1.000
#> GSM62265 2 0.6973 0.780 0.188 0.812
#> GSM62266 1 0.6247 0.840 0.844 0.156
#> GSM62296 2 0.0000 0.955 0.000 1.000
#> GSM62309 2 0.0000 0.955 0.000 1.000
#> GSM62295 2 0.0000 0.955 0.000 1.000
#> GSM62300 2 0.0000 0.955 0.000 1.000
#> GSM62308 2 0.0000 0.955 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM62248 2 0.1529 0.930 0.040 0.960 0.000
#> GSM62256 2 0.1643 0.927 0.044 0.956 0.000
#> GSM62259 2 0.1643 0.927 0.044 0.956 0.000
#> GSM62267 1 0.6286 -0.289 0.536 0.000 0.464
#> GSM62280 1 0.4915 0.560 0.832 0.036 0.132
#> GSM62284 3 0.5138 0.788 0.252 0.000 0.748
#> GSM62289 1 0.6154 0.425 0.592 0.408 0.000
#> GSM62307 2 0.0000 0.959 0.000 1.000 0.000
#> GSM62316 2 0.1529 0.930 0.040 0.960 0.000
#> GSM62254 2 0.0237 0.958 0.004 0.996 0.000
#> GSM62292 2 0.0237 0.958 0.004 0.996 0.000
#> GSM62253 3 0.5178 0.787 0.256 0.000 0.744
#> GSM62270 3 0.0000 0.820 0.000 0.000 1.000
#> GSM62278 3 0.1031 0.826 0.024 0.000 0.976
#> GSM62297 2 0.0424 0.957 0.008 0.992 0.000
#> GSM62298 2 0.0000 0.959 0.000 1.000 0.000
#> GSM62299 2 0.0000 0.959 0.000 1.000 0.000
#> GSM62258 3 0.6286 0.416 0.464 0.000 0.536
#> GSM62281 2 0.1643 0.927 0.044 0.956 0.000
#> GSM62294 2 0.0000 0.959 0.000 1.000 0.000
#> GSM62305 2 0.6111 0.219 0.396 0.604 0.000
#> GSM62306 2 0.6111 0.219 0.396 0.604 0.000
#> GSM62310 2 0.0000 0.959 0.000 1.000 0.000
#> GSM62311 2 0.0000 0.959 0.000 1.000 0.000
#> GSM62317 1 0.5678 0.561 0.684 0.316 0.000
#> GSM62318 1 0.6157 0.604 0.780 0.128 0.092
#> GSM62321 1 0.5650 0.564 0.688 0.312 0.000
#> GSM62322 3 0.0000 0.820 0.000 0.000 1.000
#> GSM62250 1 0.6738 0.530 0.624 0.356 0.020
#> GSM62252 1 0.6738 0.530 0.624 0.356 0.020
#> GSM62255 2 0.0000 0.959 0.000 1.000 0.000
#> GSM62257 2 0.0000 0.959 0.000 1.000 0.000
#> GSM62260 1 0.2356 0.657 0.928 0.072 0.000
#> GSM62261 2 0.0424 0.957 0.008 0.992 0.000
#> GSM62262 2 0.0000 0.959 0.000 1.000 0.000
#> GSM62264 1 0.2448 0.658 0.924 0.076 0.000
#> GSM62268 3 0.5178 0.787 0.256 0.000 0.744
#> GSM62269 3 0.0000 0.820 0.000 0.000 1.000
#> GSM62271 3 0.1031 0.826 0.024 0.000 0.976
#> GSM62272 3 0.0000 0.820 0.000 0.000 1.000
#> GSM62273 2 0.1643 0.924 0.044 0.956 0.000
#> GSM62274 3 0.3752 0.826 0.144 0.000 0.856
#> GSM62275 3 0.0000 0.820 0.000 0.000 1.000
#> GSM62276 1 0.6286 -0.289 0.536 0.000 0.464
#> GSM62277 3 0.3752 0.826 0.144 0.000 0.856
#> GSM62279 3 0.5397 0.763 0.280 0.000 0.720
#> GSM62282 3 0.5497 0.718 0.292 0.000 0.708
#> GSM62283 1 0.1170 0.613 0.976 0.008 0.016
#> GSM62286 1 0.6738 0.530 0.624 0.356 0.020
#> GSM62287 2 0.0000 0.959 0.000 1.000 0.000
#> GSM62288 2 0.1529 0.930 0.040 0.960 0.000
#> GSM62290 2 0.0237 0.958 0.004 0.996 0.000
#> GSM62293 2 0.0000 0.959 0.000 1.000 0.000
#> GSM62301 2 0.0424 0.957 0.008 0.992 0.000
#> GSM62302 2 0.0000 0.959 0.000 1.000 0.000
#> GSM62303 2 0.0000 0.959 0.000 1.000 0.000
#> GSM62304 2 0.0000 0.959 0.000 1.000 0.000
#> GSM62312 2 0.0424 0.957 0.008 0.992 0.000
#> GSM62313 2 0.0000 0.959 0.000 1.000 0.000
#> GSM62314 2 0.1529 0.930 0.040 0.960 0.000
#> GSM62319 2 0.4663 0.751 0.156 0.828 0.016
#> GSM62320 2 0.0000 0.959 0.000 1.000 0.000
#> GSM62249 1 0.1170 0.613 0.976 0.008 0.016
#> GSM62251 1 0.3234 0.655 0.908 0.072 0.020
#> GSM62263 1 0.3267 0.662 0.884 0.116 0.000
#> GSM62285 2 0.0237 0.958 0.004 0.996 0.000
#> GSM62315 2 0.0237 0.958 0.004 0.996 0.000
#> GSM62291 2 0.0237 0.958 0.004 0.996 0.000
#> GSM62265 1 0.1315 0.611 0.972 0.008 0.020
#> GSM62266 3 0.5178 0.787 0.256 0.000 0.744
#> GSM62296 2 0.0237 0.958 0.004 0.996 0.000
#> GSM62309 2 0.0237 0.958 0.004 0.996 0.000
#> GSM62295 2 0.0237 0.958 0.004 0.996 0.000
#> GSM62300 2 0.0237 0.958 0.004 0.996 0.000
#> GSM62308 2 0.0237 0.958 0.004 0.996 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM62248 2 0.1545 0.931 0.008 0.952 0.000 0.040
#> GSM62256 2 0.1820 0.928 0.036 0.944 0.000 0.020
#> GSM62259 2 0.1820 0.928 0.036 0.944 0.000 0.020
#> GSM62267 1 0.5570 -0.254 0.540 0.000 0.440 0.020
#> GSM62280 4 0.6951 0.584 0.324 0.000 0.132 0.544
#> GSM62284 3 0.5170 0.749 0.228 0.000 0.724 0.048
#> GSM62289 1 0.6070 0.263 0.548 0.404 0.000 0.048
#> GSM62307 2 0.0188 0.953 0.004 0.996 0.000 0.000
#> GSM62316 2 0.1545 0.931 0.008 0.952 0.000 0.040
#> GSM62254 2 0.0336 0.952 0.008 0.992 0.000 0.000
#> GSM62292 2 0.0336 0.952 0.008 0.992 0.000 0.000
#> GSM62253 3 0.5203 0.747 0.232 0.000 0.720 0.048
#> GSM62270 3 0.2149 0.728 0.000 0.000 0.912 0.088
#> GSM62278 3 0.1042 0.759 0.020 0.000 0.972 0.008
#> GSM62297 2 0.1109 0.947 0.004 0.968 0.000 0.028
#> GSM62298 2 0.0188 0.952 0.000 0.996 0.000 0.004
#> GSM62299 2 0.0188 0.952 0.000 0.996 0.000 0.004
#> GSM62258 3 0.5600 0.361 0.468 0.000 0.512 0.020
#> GSM62281 2 0.1820 0.928 0.036 0.944 0.000 0.020
#> GSM62294 2 0.0188 0.953 0.004 0.996 0.000 0.000
#> GSM62305 2 0.5839 0.279 0.352 0.604 0.000 0.044
#> GSM62306 2 0.5839 0.279 0.352 0.604 0.000 0.044
#> GSM62310 2 0.0188 0.953 0.004 0.996 0.000 0.000
#> GSM62311 2 0.0188 0.953 0.004 0.996 0.000 0.000
#> GSM62317 4 0.4022 0.718 0.096 0.068 0.000 0.836
#> GSM62318 4 0.6214 0.678 0.272 0.000 0.092 0.636
#> GSM62321 4 0.3948 0.721 0.096 0.064 0.000 0.840
#> GSM62322 3 0.2149 0.728 0.000 0.000 0.912 0.088
#> GSM62250 1 0.5913 0.310 0.600 0.352 0.000 0.048
#> GSM62252 1 0.5913 0.310 0.600 0.352 0.000 0.048
#> GSM62255 2 0.0188 0.953 0.004 0.996 0.000 0.000
#> GSM62257 2 0.0188 0.953 0.004 0.996 0.000 0.000
#> GSM62260 1 0.3610 0.273 0.800 0.000 0.000 0.200
#> GSM62261 2 0.1109 0.947 0.004 0.968 0.000 0.028
#> GSM62262 2 0.0188 0.953 0.004 0.996 0.000 0.000
#> GSM62264 1 0.3649 0.268 0.796 0.000 0.000 0.204
#> GSM62268 3 0.5203 0.747 0.232 0.000 0.720 0.048
#> GSM62269 3 0.2149 0.728 0.000 0.000 0.912 0.088
#> GSM62271 3 0.1042 0.759 0.020 0.000 0.972 0.008
#> GSM62272 3 0.2149 0.728 0.000 0.000 0.912 0.088
#> GSM62273 2 0.1398 0.927 0.040 0.956 0.000 0.004
#> GSM62274 3 0.3647 0.774 0.152 0.000 0.832 0.016
#> GSM62275 3 0.2149 0.728 0.000 0.000 0.912 0.088
#> GSM62276 1 0.5570 -0.254 0.540 0.000 0.440 0.020
#> GSM62277 3 0.3647 0.774 0.152 0.000 0.832 0.016
#> GSM62279 3 0.5387 0.723 0.256 0.000 0.696 0.048
#> GSM62282 3 0.5256 0.656 0.260 0.000 0.700 0.040
#> GSM62283 1 0.1792 0.355 0.932 0.000 0.000 0.068
#> GSM62286 1 0.5913 0.310 0.600 0.352 0.000 0.048
#> GSM62287 2 0.0188 0.953 0.004 0.996 0.000 0.000
#> GSM62288 2 0.1545 0.931 0.008 0.952 0.000 0.040
#> GSM62290 2 0.0817 0.948 0.000 0.976 0.000 0.024
#> GSM62293 2 0.0188 0.953 0.004 0.996 0.000 0.000
#> GSM62301 2 0.1109 0.947 0.004 0.968 0.000 0.028
#> GSM62302 2 0.0188 0.953 0.004 0.996 0.000 0.000
#> GSM62303 2 0.0188 0.953 0.004 0.996 0.000 0.000
#> GSM62304 2 0.0188 0.953 0.004 0.996 0.000 0.000
#> GSM62312 2 0.1109 0.947 0.004 0.968 0.000 0.028
#> GSM62313 2 0.0188 0.953 0.004 0.996 0.000 0.000
#> GSM62314 2 0.1545 0.931 0.008 0.952 0.000 0.040
#> GSM62319 2 0.3923 0.767 0.148 0.828 0.008 0.016
#> GSM62320 2 0.0188 0.952 0.000 0.996 0.000 0.004
#> GSM62249 1 0.1792 0.355 0.932 0.000 0.000 0.068
#> GSM62251 1 0.3539 0.297 0.820 0.000 0.004 0.176
#> GSM62263 1 0.4595 0.268 0.776 0.040 0.000 0.184
#> GSM62285 2 0.0921 0.947 0.000 0.972 0.000 0.028
#> GSM62315 2 0.0921 0.947 0.000 0.972 0.000 0.028
#> GSM62291 2 0.0817 0.948 0.000 0.976 0.000 0.024
#> GSM62265 1 0.1902 0.355 0.932 0.000 0.004 0.064
#> GSM62266 3 0.5203 0.747 0.232 0.000 0.720 0.048
#> GSM62296 2 0.0921 0.947 0.000 0.972 0.000 0.028
#> GSM62309 2 0.0921 0.947 0.000 0.972 0.000 0.028
#> GSM62295 2 0.0188 0.952 0.004 0.996 0.000 0.000
#> GSM62300 2 0.0921 0.947 0.000 0.972 0.000 0.028
#> GSM62308 2 0.0921 0.947 0.000 0.972 0.000 0.028
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM62248 4 0.2971 0.8269 0.000 0.156 0.000 0.836 0.008
#> GSM62256 4 0.2208 0.8830 0.000 0.072 0.000 0.908 0.020
#> GSM62259 4 0.2208 0.8830 0.000 0.072 0.000 0.908 0.020
#> GSM62267 1 0.5799 0.3329 0.492 0.092 0.000 0.000 0.416
#> GSM62280 2 0.7989 0.6664 0.096 0.392 0.224 0.000 0.288
#> GSM62284 1 0.0671 0.6008 0.980 0.000 0.016 0.000 0.004
#> GSM62289 5 0.6941 0.3805 0.016 0.228 0.000 0.288 0.468
#> GSM62307 4 0.0609 0.8990 0.000 0.020 0.000 0.980 0.000
#> GSM62316 4 0.2971 0.8269 0.000 0.156 0.000 0.836 0.008
#> GSM62254 4 0.0794 0.8968 0.000 0.028 0.000 0.972 0.000
#> GSM62292 4 0.0794 0.8968 0.000 0.028 0.000 0.972 0.000
#> GSM62253 1 0.0290 0.6063 0.992 0.000 0.000 0.000 0.008
#> GSM62270 3 0.3612 1.0000 0.268 0.000 0.732 0.000 0.000
#> GSM62278 1 0.4787 -0.2093 0.548 0.020 0.432 0.000 0.000
#> GSM62297 4 0.2304 0.8839 0.000 0.100 0.000 0.892 0.008
#> GSM62298 4 0.1502 0.8957 0.000 0.056 0.000 0.940 0.004
#> GSM62299 4 0.1502 0.8959 0.000 0.056 0.000 0.940 0.004
#> GSM62258 1 0.5819 0.4298 0.552 0.080 0.008 0.000 0.360
#> GSM62281 4 0.2208 0.8830 0.000 0.072 0.000 0.908 0.020
#> GSM62294 4 0.0703 0.8977 0.000 0.024 0.000 0.976 0.000
#> GSM62305 4 0.6298 0.0625 0.000 0.188 0.000 0.520 0.292
#> GSM62306 4 0.6298 0.0625 0.000 0.188 0.000 0.520 0.292
#> GSM62310 4 0.0703 0.8977 0.000 0.024 0.000 0.976 0.000
#> GSM62311 4 0.0703 0.8977 0.000 0.024 0.000 0.976 0.000
#> GSM62317 2 0.5334 0.7742 0.000 0.656 0.268 0.012 0.064
#> GSM62318 2 0.7550 0.7436 0.080 0.484 0.196 0.000 0.240
#> GSM62321 2 0.5391 0.7753 0.000 0.652 0.268 0.012 0.068
#> GSM62322 3 0.3612 1.0000 0.268 0.000 0.732 0.000 0.000
#> GSM62250 5 0.7298 0.4220 0.048 0.212 0.000 0.256 0.484
#> GSM62252 5 0.7298 0.4220 0.048 0.212 0.000 0.256 0.484
#> GSM62255 4 0.0609 0.8990 0.000 0.020 0.000 0.980 0.000
#> GSM62257 4 0.0609 0.8990 0.000 0.020 0.000 0.980 0.000
#> GSM62260 5 0.3810 0.4263 0.088 0.100 0.000 0.000 0.812
#> GSM62261 4 0.2193 0.8857 0.000 0.092 0.000 0.900 0.008
#> GSM62262 4 0.0703 0.8977 0.000 0.024 0.000 0.976 0.000
#> GSM62264 5 0.4022 0.4125 0.100 0.104 0.000 0.000 0.796
#> GSM62268 1 0.0290 0.6063 0.992 0.000 0.000 0.000 0.008
#> GSM62269 3 0.3612 1.0000 0.268 0.000 0.732 0.000 0.000
#> GSM62271 1 0.4787 -0.2093 0.548 0.020 0.432 0.000 0.000
#> GSM62272 3 0.3612 1.0000 0.268 0.000 0.732 0.000 0.000
#> GSM62273 4 0.2079 0.8715 0.000 0.064 0.000 0.916 0.020
#> GSM62274 1 0.2329 0.5255 0.876 0.000 0.124 0.000 0.000
#> GSM62275 3 0.3612 1.0000 0.268 0.000 0.732 0.000 0.000
#> GSM62276 1 0.5799 0.3329 0.492 0.092 0.000 0.000 0.416
#> GSM62277 1 0.2648 0.5014 0.848 0.000 0.152 0.000 0.000
#> GSM62279 1 0.1106 0.6030 0.964 0.012 0.000 0.000 0.024
#> GSM62282 1 0.7108 0.1790 0.476 0.028 0.264 0.000 0.232
#> GSM62283 5 0.1043 0.5072 0.040 0.000 0.000 0.000 0.960
#> GSM62286 5 0.7298 0.4220 0.048 0.212 0.000 0.256 0.484
#> GSM62287 4 0.0703 0.8977 0.000 0.024 0.000 0.976 0.000
#> GSM62288 4 0.2971 0.8269 0.000 0.156 0.000 0.836 0.008
#> GSM62290 4 0.2338 0.8799 0.000 0.112 0.000 0.884 0.004
#> GSM62293 4 0.0703 0.8977 0.000 0.024 0.000 0.976 0.000
#> GSM62301 4 0.2563 0.8750 0.000 0.120 0.000 0.872 0.008
#> GSM62302 4 0.0703 0.8977 0.000 0.024 0.000 0.976 0.000
#> GSM62303 4 0.0703 0.8977 0.000 0.024 0.000 0.976 0.000
#> GSM62304 4 0.0703 0.8977 0.000 0.024 0.000 0.976 0.000
#> GSM62312 4 0.2193 0.8857 0.000 0.092 0.000 0.900 0.008
#> GSM62313 4 0.0703 0.8977 0.000 0.024 0.000 0.976 0.000
#> GSM62314 4 0.2971 0.8269 0.000 0.156 0.000 0.836 0.008
#> GSM62319 4 0.4203 0.7132 0.000 0.128 0.000 0.780 0.092
#> GSM62320 4 0.1502 0.8957 0.000 0.056 0.000 0.940 0.004
#> GSM62249 5 0.1043 0.5072 0.040 0.000 0.000 0.000 0.960
#> GSM62251 5 0.4149 0.4443 0.128 0.088 0.000 0.000 0.784
#> GSM62263 5 0.4441 0.4314 0.096 0.120 0.000 0.008 0.776
#> GSM62285 4 0.2439 0.8759 0.000 0.120 0.000 0.876 0.004
#> GSM62315 4 0.2439 0.8759 0.000 0.120 0.000 0.876 0.004
#> GSM62291 4 0.2338 0.8799 0.000 0.112 0.000 0.884 0.004
#> GSM62265 5 0.1121 0.5067 0.044 0.000 0.000 0.000 0.956
#> GSM62266 1 0.0290 0.6063 0.992 0.000 0.000 0.000 0.008
#> GSM62296 4 0.2439 0.8759 0.000 0.120 0.000 0.876 0.004
#> GSM62309 4 0.2439 0.8759 0.000 0.120 0.000 0.876 0.004
#> GSM62295 4 0.0963 0.8941 0.000 0.036 0.000 0.964 0.000
#> GSM62300 4 0.2439 0.8759 0.000 0.120 0.000 0.876 0.004
#> GSM62308 4 0.2439 0.8759 0.000 0.120 0.000 0.876 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM62248 4 0.2664 0.666 0.000 0.000 0.000 0.816 0.184 0.000
#> GSM62256 4 0.3210 0.736 0.000 0.000 0.028 0.804 0.168 0.000
#> GSM62259 4 0.3210 0.736 0.000 0.000 0.028 0.804 0.168 0.000
#> GSM62267 1 0.5821 0.299 0.412 0.184 0.000 0.000 0.404 0.000
#> GSM62280 6 0.6003 0.667 0.016 0.104 0.040 0.000 0.236 0.604
#> GSM62284 1 0.0972 0.690 0.964 0.008 0.028 0.000 0.000 0.000
#> GSM62289 5 0.5915 0.745 0.016 0.224 0.000 0.212 0.548 0.000
#> GSM62307 4 0.2631 0.757 0.000 0.000 0.008 0.840 0.152 0.000
#> GSM62316 4 0.2664 0.666 0.000 0.000 0.000 0.816 0.184 0.000
#> GSM62254 4 0.2948 0.737 0.000 0.000 0.008 0.804 0.188 0.000
#> GSM62292 4 0.2948 0.737 0.000 0.000 0.008 0.804 0.188 0.000
#> GSM62253 1 0.0725 0.696 0.976 0.012 0.012 0.000 0.000 0.000
#> GSM62270 3 0.1075 0.739 0.048 0.000 0.952 0.000 0.000 0.000
#> GSM62278 3 0.5749 0.341 0.376 0.000 0.480 0.000 0.136 0.008
#> GSM62297 4 0.2939 0.747 0.000 0.004 0.036 0.872 0.064 0.024
#> GSM62298 4 0.1701 0.768 0.000 0.000 0.008 0.920 0.072 0.000
#> GSM62299 4 0.1625 0.767 0.000 0.000 0.012 0.928 0.060 0.000
#> GSM62258 1 0.5772 0.372 0.472 0.156 0.004 0.000 0.368 0.000
#> GSM62281 4 0.3245 0.735 0.000 0.000 0.028 0.800 0.172 0.000
#> GSM62294 4 0.2848 0.746 0.000 0.000 0.008 0.816 0.176 0.000
#> GSM62305 5 0.5120 0.644 0.000 0.088 0.000 0.380 0.532 0.000
#> GSM62306 5 0.5120 0.644 0.000 0.088 0.000 0.380 0.532 0.000
#> GSM62310 4 0.2848 0.746 0.000 0.000 0.008 0.816 0.176 0.000
#> GSM62311 4 0.2848 0.746 0.000 0.000 0.008 0.816 0.176 0.000
#> GSM62317 6 0.0508 0.777 0.000 0.012 0.000 0.004 0.000 0.984
#> GSM62318 6 0.5352 0.743 0.016 0.112 0.032 0.000 0.148 0.692
#> GSM62321 6 0.0603 0.779 0.000 0.016 0.000 0.004 0.000 0.980
#> GSM62322 3 0.1075 0.739 0.048 0.000 0.952 0.000 0.000 0.000
#> GSM62250 5 0.5690 0.743 0.016 0.244 0.000 0.160 0.580 0.000
#> GSM62252 5 0.5690 0.743 0.016 0.244 0.000 0.160 0.580 0.000
#> GSM62255 4 0.2631 0.757 0.000 0.000 0.008 0.840 0.152 0.000
#> GSM62257 4 0.2631 0.757 0.000 0.000 0.008 0.840 0.152 0.000
#> GSM62260 2 0.1718 0.811 0.008 0.932 0.000 0.000 0.016 0.044
#> GSM62261 4 0.2649 0.752 0.000 0.004 0.028 0.888 0.060 0.020
#> GSM62262 4 0.2848 0.746 0.000 0.000 0.008 0.816 0.176 0.000
#> GSM62264 2 0.1265 0.799 0.008 0.948 0.000 0.000 0.000 0.044
#> GSM62268 1 0.0725 0.696 0.976 0.012 0.012 0.000 0.000 0.000
#> GSM62269 3 0.1075 0.739 0.048 0.000 0.952 0.000 0.000 0.000
#> GSM62271 3 0.5749 0.341 0.376 0.000 0.480 0.000 0.136 0.008
#> GSM62272 3 0.1075 0.739 0.048 0.000 0.952 0.000 0.000 0.000
#> GSM62273 4 0.3163 0.704 0.000 0.000 0.004 0.764 0.232 0.000
#> GSM62274 1 0.2219 0.614 0.864 0.000 0.136 0.000 0.000 0.000
#> GSM62275 3 0.1075 0.739 0.048 0.000 0.952 0.000 0.000 0.000
#> GSM62276 1 0.5821 0.299 0.412 0.184 0.000 0.000 0.404 0.000
#> GSM62277 1 0.2597 0.573 0.824 0.000 0.176 0.000 0.000 0.000
#> GSM62279 1 0.1124 0.686 0.956 0.008 0.000 0.000 0.036 0.000
#> GSM62282 3 0.7791 0.167 0.264 0.100 0.312 0.000 0.300 0.024
#> GSM62283 2 0.3014 0.788 0.012 0.804 0.000 0.000 0.184 0.000
#> GSM62286 5 0.5690 0.743 0.016 0.244 0.000 0.160 0.580 0.000
#> GSM62287 4 0.2848 0.746 0.000 0.000 0.008 0.816 0.176 0.000
#> GSM62288 4 0.2664 0.666 0.000 0.000 0.000 0.816 0.184 0.000
#> GSM62290 4 0.3838 0.717 0.000 0.004 0.036 0.800 0.132 0.028
#> GSM62293 4 0.2915 0.740 0.000 0.000 0.008 0.808 0.184 0.000
#> GSM62301 4 0.4023 0.708 0.000 0.004 0.040 0.784 0.144 0.028
#> GSM62302 4 0.2848 0.746 0.000 0.000 0.008 0.816 0.176 0.000
#> GSM62303 4 0.2848 0.746 0.000 0.000 0.008 0.816 0.176 0.000
#> GSM62304 4 0.2848 0.746 0.000 0.000 0.008 0.816 0.176 0.000
#> GSM62312 4 0.2732 0.750 0.000 0.004 0.028 0.884 0.060 0.024
#> GSM62313 4 0.2848 0.746 0.000 0.000 0.008 0.816 0.176 0.000
#> GSM62314 4 0.2664 0.666 0.000 0.000 0.000 0.816 0.184 0.000
#> GSM62319 4 0.4144 0.352 0.000 0.000 0.008 0.580 0.408 0.004
#> GSM62320 4 0.1701 0.768 0.000 0.000 0.008 0.920 0.072 0.000
#> GSM62249 2 0.3014 0.788 0.012 0.804 0.000 0.000 0.184 0.000
#> GSM62251 2 0.0603 0.822 0.016 0.980 0.000 0.000 0.004 0.000
#> GSM62263 2 0.1452 0.792 0.008 0.948 0.000 0.032 0.004 0.008
#> GSM62285 4 0.3985 0.710 0.000 0.004 0.040 0.788 0.140 0.028
#> GSM62315 4 0.3985 0.710 0.000 0.004 0.040 0.788 0.140 0.028
#> GSM62291 4 0.3838 0.717 0.000 0.004 0.036 0.800 0.132 0.028
#> GSM62265 2 0.3104 0.786 0.016 0.800 0.000 0.000 0.184 0.000
#> GSM62266 1 0.0725 0.696 0.976 0.012 0.012 0.000 0.000 0.000
#> GSM62296 4 0.3985 0.710 0.000 0.004 0.040 0.788 0.140 0.028
#> GSM62309 4 0.3985 0.710 0.000 0.004 0.040 0.788 0.140 0.028
#> GSM62295 4 0.2805 0.737 0.000 0.000 0.004 0.812 0.184 0.000
#> GSM62300 4 0.3985 0.710 0.000 0.004 0.040 0.788 0.140 0.028
#> GSM62308 4 0.3985 0.710 0.000 0.004 0.040 0.788 0.140 0.028
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) other(p) genotype/variation(p) k
#> MAD:hclust 73 0.3184 0.7301 0.358 2
#> MAD:hclust 69 0.3079 0.6515 0.320 3
#> MAD:hclust 59 0.3210 0.0961 0.856 4
#> MAD:hclust 59 0.1491 0.3128 0.961 5
#> MAD:hclust 68 0.0686 0.4857 0.660 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "kmeans"]
# you can also extract it by
# res = res_list["MAD:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 75 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.970 0.989 0.4593 0.541 0.541
#> 3 3 0.552 0.549 0.707 0.3294 0.890 0.799
#> 4 4 0.583 0.707 0.785 0.1549 0.731 0.457
#> 5 5 0.625 0.760 0.801 0.0965 0.906 0.673
#> 6 6 0.768 0.708 0.822 0.0617 0.957 0.801
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
#> GSM62248 2 0.000 0.991 0.000 1.000
#> GSM62256 2 0.000 0.991 0.000 1.000
#> GSM62259 2 0.000 0.991 0.000 1.000
#> GSM62267 1 0.000 0.983 1.000 0.000
#> GSM62280 1 0.000 0.983 1.000 0.000
#> GSM62284 1 0.000 0.983 1.000 0.000
#> GSM62289 2 0.000 0.991 0.000 1.000
#> GSM62307 2 0.000 0.991 0.000 1.000
#> GSM62316 2 0.000 0.991 0.000 1.000
#> GSM62254 2 0.000 0.991 0.000 1.000
#> GSM62292 2 0.000 0.991 0.000 1.000
#> GSM62253 1 0.000 0.983 1.000 0.000
#> GSM62270 1 0.000 0.983 1.000 0.000
#> GSM62278 1 0.000 0.983 1.000 0.000
#> GSM62297 2 0.000 0.991 0.000 1.000
#> GSM62298 2 0.000 0.991 0.000 1.000
#> GSM62299 2 0.000 0.991 0.000 1.000
#> GSM62258 1 0.000 0.983 1.000 0.000
#> GSM62281 2 0.000 0.991 0.000 1.000
#> GSM62294 2 0.000 0.991 0.000 1.000
#> GSM62305 2 0.000 0.991 0.000 1.000
#> GSM62306 2 0.000 0.991 0.000 1.000
#> GSM62310 2 0.000 0.991 0.000 1.000
#> GSM62311 2 0.000 0.991 0.000 1.000
#> GSM62317 2 0.000 0.991 0.000 1.000
#> GSM62318 1 0.000 0.983 1.000 0.000
#> GSM62321 1 0.975 0.297 0.592 0.408
#> GSM62322 1 0.000 0.983 1.000 0.000
#> GSM62250 2 0.000 0.991 0.000 1.000
#> GSM62252 2 0.000 0.991 0.000 1.000
#> GSM62255 2 0.000 0.991 0.000 1.000
#> GSM62257 2 0.000 0.991 0.000 1.000
#> GSM62260 1 0.000 0.983 1.000 0.000
#> GSM62261 2 0.000 0.991 0.000 1.000
#> GSM62262 2 0.000 0.991 0.000 1.000
#> GSM62264 1 0.000 0.983 1.000 0.000
#> GSM62268 1 0.000 0.983 1.000 0.000
#> GSM62269 1 0.000 0.983 1.000 0.000
#> GSM62271 1 0.000 0.983 1.000 0.000
#> GSM62272 1 0.000 0.983 1.000 0.000
#> GSM62273 2 0.000 0.991 0.000 1.000
#> GSM62274 1 0.000 0.983 1.000 0.000
#> GSM62275 1 0.000 0.983 1.000 0.000
#> GSM62276 1 0.000 0.983 1.000 0.000
#> GSM62277 1 0.000 0.983 1.000 0.000
#> GSM62279 1 0.000 0.983 1.000 0.000
#> GSM62282 1 0.000 0.983 1.000 0.000
#> GSM62283 1 0.000 0.983 1.000 0.000
#> GSM62286 2 0.000 0.991 0.000 1.000
#> GSM62287 2 0.000 0.991 0.000 1.000
#> GSM62288 2 0.000 0.991 0.000 1.000
#> GSM62290 2 0.000 0.991 0.000 1.000
#> GSM62293 2 0.000 0.991 0.000 1.000
#> GSM62301 2 0.000 0.991 0.000 1.000
#> GSM62302 2 0.000 0.991 0.000 1.000
#> GSM62303 2 0.000 0.991 0.000 1.000
#> GSM62304 2 0.000 0.991 0.000 1.000
#> GSM62312 2 0.000 0.991 0.000 1.000
#> GSM62313 2 0.000 0.991 0.000 1.000
#> GSM62314 2 0.000 0.991 0.000 1.000
#> GSM62319 2 0.000 0.991 0.000 1.000
#> GSM62320 2 0.000 0.991 0.000 1.000
#> GSM62249 2 0.973 0.300 0.404 0.596
#> GSM62251 1 0.000 0.983 1.000 0.000
#> GSM62263 2 0.000 0.991 0.000 1.000
#> GSM62285 2 0.000 0.991 0.000 1.000
#> GSM62315 2 0.000 0.991 0.000 1.000
#> GSM62291 2 0.000 0.991 0.000 1.000
#> GSM62265 1 0.000 0.983 1.000 0.000
#> GSM62266 1 0.000 0.983 1.000 0.000
#> GSM62296 2 0.000 0.991 0.000 1.000
#> GSM62309 2 0.000 0.991 0.000 1.000
#> GSM62295 2 0.000 0.991 0.000 1.000
#> GSM62300 2 0.000 0.991 0.000 1.000
#> GSM62308 2 0.000 0.991 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM62248 2 0.5785 0.7317 0.332 0.668 0.000
#> GSM62256 2 0.5733 0.7302 0.324 0.676 0.000
#> GSM62259 2 0.6244 0.7470 0.440 0.560 0.000
#> GSM62267 3 0.6309 0.4004 0.496 0.000 0.504
#> GSM62280 3 0.6291 0.4523 0.468 0.000 0.532
#> GSM62284 3 0.4002 0.5912 0.160 0.000 0.840
#> GSM62289 2 0.6215 0.6994 0.428 0.572 0.000
#> GSM62307 2 0.6286 0.7446 0.464 0.536 0.000
#> GSM62316 2 0.6095 0.7422 0.392 0.608 0.000
#> GSM62254 2 0.6302 0.7394 0.480 0.520 0.000
#> GSM62292 2 0.6302 0.7394 0.480 0.520 0.000
#> GSM62253 3 0.6168 0.5130 0.412 0.000 0.588
#> GSM62270 3 0.0000 0.5982 0.000 0.000 1.000
#> GSM62278 3 0.0000 0.5982 0.000 0.000 1.000
#> GSM62297 2 0.0747 0.6423 0.016 0.984 0.000
#> GSM62298 2 0.3116 0.6649 0.108 0.892 0.000
#> GSM62299 2 0.0000 0.6505 0.000 1.000 0.000
#> GSM62258 3 0.6309 0.4004 0.496 0.000 0.504
#> GSM62281 2 0.5650 0.7348 0.312 0.688 0.000
#> GSM62294 2 0.6295 0.7423 0.472 0.528 0.000
#> GSM62305 1 0.6008 -0.1620 0.628 0.372 0.000
#> GSM62306 2 0.5859 0.7305 0.344 0.656 0.000
#> GSM62310 2 0.6286 0.7446 0.464 0.536 0.000
#> GSM62311 2 0.6286 0.7446 0.464 0.536 0.000
#> GSM62317 2 0.0592 0.6413 0.012 0.988 0.000
#> GSM62318 3 0.6291 0.4523 0.468 0.000 0.532
#> GSM62321 1 0.9046 0.2642 0.516 0.332 0.152
#> GSM62322 3 0.0000 0.5982 0.000 0.000 1.000
#> GSM62250 1 0.5733 -0.0511 0.676 0.324 0.000
#> GSM62252 1 0.4002 0.3405 0.840 0.160 0.000
#> GSM62255 2 0.6286 0.7446 0.464 0.536 0.000
#> GSM62257 2 0.6286 0.7446 0.464 0.536 0.000
#> GSM62260 1 0.8549 -0.1569 0.516 0.100 0.384
#> GSM62261 2 0.5968 0.7418 0.364 0.636 0.000
#> GSM62262 2 0.6295 0.7423 0.472 0.528 0.000
#> GSM62264 1 0.8173 -0.2622 0.508 0.072 0.420
#> GSM62268 3 0.5926 0.5457 0.356 0.000 0.644
#> GSM62269 3 0.0000 0.5982 0.000 0.000 1.000
#> GSM62271 3 0.5926 0.5463 0.356 0.000 0.644
#> GSM62272 3 0.0000 0.5982 0.000 0.000 1.000
#> GSM62273 2 0.4750 0.7083 0.216 0.784 0.000
#> GSM62274 3 0.0000 0.5982 0.000 0.000 1.000
#> GSM62275 3 0.0000 0.5982 0.000 0.000 1.000
#> GSM62276 3 0.6309 0.4004 0.496 0.000 0.504
#> GSM62277 3 0.0000 0.5982 0.000 0.000 1.000
#> GSM62279 3 0.6309 0.4004 0.496 0.000 0.504
#> GSM62282 3 0.5948 0.5436 0.360 0.000 0.640
#> GSM62283 1 0.6309 -0.4780 0.504 0.000 0.496
#> GSM62286 2 0.6095 0.6943 0.392 0.608 0.000
#> GSM62287 2 0.6295 0.7423 0.472 0.528 0.000
#> GSM62288 2 0.5988 0.7424 0.368 0.632 0.000
#> GSM62290 2 0.0237 0.6486 0.004 0.996 0.000
#> GSM62293 2 0.6302 0.7394 0.480 0.520 0.000
#> GSM62301 2 0.0000 0.6505 0.000 1.000 0.000
#> GSM62302 2 0.6286 0.7446 0.464 0.536 0.000
#> GSM62303 2 0.6295 0.7423 0.472 0.528 0.000
#> GSM62304 2 0.6286 0.7446 0.464 0.536 0.000
#> GSM62312 2 0.0424 0.6530 0.008 0.992 0.000
#> GSM62313 2 0.6286 0.7446 0.464 0.536 0.000
#> GSM62314 2 0.6180 0.7444 0.416 0.584 0.000
#> GSM62319 2 0.1031 0.6469 0.024 0.976 0.000
#> GSM62320 2 0.3116 0.6649 0.108 0.892 0.000
#> GSM62249 1 0.8872 0.2734 0.536 0.324 0.140
#> GSM62251 1 0.6825 -0.4470 0.500 0.012 0.488
#> GSM62263 2 0.5948 -0.1724 0.360 0.640 0.000
#> GSM62285 2 0.0237 0.6519 0.004 0.996 0.000
#> GSM62315 2 0.0000 0.6505 0.000 1.000 0.000
#> GSM62291 2 0.0237 0.6486 0.004 0.996 0.000
#> GSM62265 3 0.6308 0.4078 0.492 0.000 0.508
#> GSM62266 3 0.6168 0.5130 0.412 0.000 0.588
#> GSM62296 2 0.0237 0.6486 0.004 0.996 0.000
#> GSM62309 2 0.0237 0.6486 0.004 0.996 0.000
#> GSM62295 2 0.6302 0.7394 0.480 0.520 0.000
#> GSM62300 2 0.0237 0.6486 0.004 0.996 0.000
#> GSM62308 2 0.0237 0.6486 0.004 0.996 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM62248 4 0.6603 0.61081 0.008 0.296 0.088 0.608
#> GSM62256 4 0.6929 0.65590 0.008 0.348 0.096 0.548
#> GSM62259 4 0.5713 0.71030 0.000 0.360 0.036 0.604
#> GSM62267 1 0.2546 0.75786 0.912 0.000 0.060 0.028
#> GSM62280 1 0.5624 0.62521 0.720 0.000 0.172 0.108
#> GSM62284 3 0.5781 0.00407 0.480 0.000 0.492 0.028
#> GSM62289 4 0.8534 0.38233 0.220 0.160 0.092 0.528
#> GSM62307 4 0.4624 0.74403 0.000 0.340 0.000 0.660
#> GSM62316 4 0.6486 0.63550 0.008 0.320 0.072 0.600
#> GSM62254 4 0.4963 0.75017 0.000 0.284 0.020 0.696
#> GSM62292 4 0.4963 0.75017 0.000 0.284 0.020 0.696
#> GSM62253 1 0.4964 0.59403 0.716 0.000 0.256 0.028
#> GSM62270 3 0.2530 0.91866 0.112 0.000 0.888 0.000
#> GSM62278 3 0.2530 0.91866 0.112 0.000 0.888 0.000
#> GSM62297 2 0.3108 0.75037 0.000 0.872 0.016 0.112
#> GSM62298 2 0.0895 0.87477 0.000 0.976 0.004 0.020
#> GSM62299 2 0.0188 0.89122 0.000 0.996 0.004 0.000
#> GSM62258 1 0.2214 0.76073 0.928 0.000 0.044 0.028
#> GSM62281 4 0.6709 0.63836 0.000 0.400 0.092 0.508
#> GSM62294 4 0.4535 0.75353 0.000 0.292 0.004 0.704
#> GSM62305 4 0.8872 0.19686 0.336 0.140 0.096 0.428
#> GSM62306 4 0.6554 0.62001 0.008 0.268 0.096 0.628
#> GSM62310 4 0.4585 0.74633 0.000 0.332 0.000 0.668
#> GSM62311 4 0.4585 0.74633 0.000 0.332 0.000 0.668
#> GSM62317 2 0.4102 0.73378 0.040 0.840 0.012 0.108
#> GSM62318 1 0.5834 0.61744 0.704 0.000 0.172 0.124
#> GSM62321 1 0.4989 0.66783 0.792 0.020 0.056 0.132
#> GSM62322 3 0.2530 0.91866 0.112 0.000 0.888 0.000
#> GSM62250 4 0.8784 0.24067 0.316 0.140 0.092 0.452
#> GSM62252 1 0.7185 0.25561 0.512 0.016 0.092 0.380
#> GSM62255 4 0.4585 0.74633 0.000 0.332 0.000 0.668
#> GSM62257 4 0.4585 0.74633 0.000 0.332 0.000 0.668
#> GSM62260 1 0.2856 0.72435 0.900 0.004 0.024 0.072
#> GSM62261 4 0.6564 0.62859 0.008 0.324 0.076 0.592
#> GSM62262 4 0.4535 0.75353 0.000 0.292 0.004 0.704
#> GSM62264 1 0.2342 0.74050 0.912 0.008 0.000 0.080
#> GSM62268 1 0.5322 0.48964 0.660 0.000 0.312 0.028
#> GSM62269 3 0.2530 0.91866 0.112 0.000 0.888 0.000
#> GSM62271 1 0.4155 0.63176 0.756 0.000 0.240 0.004
#> GSM62272 3 0.2530 0.91866 0.112 0.000 0.888 0.000
#> GSM62273 2 0.5228 0.10877 0.000 0.664 0.024 0.312
#> GSM62274 3 0.3881 0.84839 0.172 0.000 0.812 0.016
#> GSM62275 3 0.2530 0.91866 0.112 0.000 0.888 0.000
#> GSM62276 1 0.2546 0.75786 0.912 0.000 0.060 0.028
#> GSM62277 3 0.2714 0.91636 0.112 0.000 0.884 0.004
#> GSM62279 1 0.2739 0.75676 0.904 0.000 0.060 0.036
#> GSM62282 1 0.5327 0.61121 0.720 0.000 0.220 0.060
#> GSM62283 1 0.1510 0.75996 0.956 0.000 0.028 0.016
#> GSM62286 4 0.8564 0.39942 0.200 0.180 0.092 0.528
#> GSM62287 4 0.4356 0.75460 0.000 0.292 0.000 0.708
#> GSM62288 4 0.6564 0.62859 0.008 0.324 0.076 0.592
#> GSM62290 2 0.0000 0.89211 0.000 1.000 0.000 0.000
#> GSM62293 4 0.4647 0.75260 0.000 0.288 0.008 0.704
#> GSM62301 2 0.0000 0.89211 0.000 1.000 0.000 0.000
#> GSM62302 4 0.4543 0.74921 0.000 0.324 0.000 0.676
#> GSM62303 4 0.4356 0.75460 0.000 0.292 0.000 0.708
#> GSM62304 4 0.4585 0.74633 0.000 0.332 0.000 0.668
#> GSM62312 2 0.0376 0.88899 0.000 0.992 0.004 0.004
#> GSM62313 4 0.4585 0.74633 0.000 0.332 0.000 0.668
#> GSM62314 4 0.5381 0.66894 0.008 0.320 0.016 0.656
#> GSM62319 2 0.2587 0.81555 0.008 0.916 0.020 0.056
#> GSM62320 2 0.0779 0.87909 0.000 0.980 0.004 0.016
#> GSM62249 1 0.5304 0.59857 0.780 0.024 0.080 0.116
#> GSM62251 1 0.2578 0.75914 0.912 0.000 0.036 0.052
#> GSM62263 2 0.8521 0.30053 0.252 0.504 0.068 0.176
#> GSM62285 2 0.0000 0.89211 0.000 1.000 0.000 0.000
#> GSM62315 2 0.0000 0.89211 0.000 1.000 0.000 0.000
#> GSM62291 2 0.0000 0.89211 0.000 1.000 0.000 0.000
#> GSM62265 1 0.2399 0.75996 0.920 0.000 0.048 0.032
#> GSM62266 1 0.4964 0.59403 0.716 0.000 0.256 0.028
#> GSM62296 2 0.0188 0.89157 0.000 0.996 0.000 0.004
#> GSM62309 2 0.0188 0.89157 0.000 0.996 0.000 0.004
#> GSM62295 4 0.5062 0.74891 0.000 0.284 0.024 0.692
#> GSM62300 2 0.0188 0.89157 0.000 0.996 0.000 0.004
#> GSM62308 2 0.0188 0.89157 0.000 0.996 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM62248 5 0.5814 0.6991 0.000 0.128 0.000 0.288 0.584
#> GSM62256 5 0.6211 0.6739 0.000 0.144 0.012 0.264 0.580
#> GSM62259 4 0.6368 0.2958 0.000 0.148 0.012 0.548 0.292
#> GSM62267 1 0.5375 0.7471 0.684 0.000 0.116 0.008 0.192
#> GSM62280 1 0.5858 0.6436 0.636 0.000 0.016 0.116 0.232
#> GSM62284 1 0.4452 0.0380 0.500 0.000 0.496 0.000 0.004
#> GSM62289 5 0.4088 0.7067 0.008 0.036 0.000 0.176 0.780
#> GSM62307 4 0.3277 0.8881 0.000 0.148 0.012 0.832 0.008
#> GSM62316 5 0.6225 0.6312 0.000 0.148 0.000 0.368 0.484
#> GSM62254 4 0.4457 0.7858 0.000 0.116 0.000 0.760 0.124
#> GSM62292 4 0.4457 0.7858 0.000 0.116 0.000 0.760 0.124
#> GSM62253 1 0.2773 0.7218 0.836 0.000 0.164 0.000 0.000
#> GSM62270 3 0.0609 0.9725 0.020 0.000 0.980 0.000 0.000
#> GSM62278 3 0.0609 0.9725 0.020 0.000 0.980 0.000 0.000
#> GSM62297 2 0.2130 0.8210 0.000 0.908 0.012 0.000 0.080
#> GSM62298 2 0.0566 0.8842 0.000 0.984 0.012 0.004 0.000
#> GSM62299 2 0.0566 0.8856 0.000 0.984 0.012 0.004 0.000
#> GSM62258 1 0.5334 0.7556 0.672 0.000 0.076 0.012 0.240
#> GSM62281 5 0.6932 0.5246 0.000 0.268 0.012 0.264 0.456
#> GSM62294 4 0.2230 0.9025 0.000 0.116 0.000 0.884 0.000
#> GSM62305 5 0.4453 0.6554 0.076 0.036 0.000 0.092 0.796
#> GSM62306 5 0.5579 0.6992 0.000 0.116 0.000 0.264 0.620
#> GSM62310 4 0.2674 0.9026 0.000 0.140 0.000 0.856 0.004
#> GSM62311 4 0.2674 0.9026 0.000 0.140 0.000 0.856 0.004
#> GSM62317 2 0.6518 0.5743 0.100 0.656 0.008 0.108 0.128
#> GSM62318 1 0.5608 0.6392 0.672 0.000 0.016 0.116 0.196
#> GSM62321 1 0.6023 0.6361 0.620 0.008 0.008 0.116 0.248
#> GSM62322 3 0.0609 0.9725 0.020 0.000 0.980 0.000 0.000
#> GSM62250 5 0.4506 0.6578 0.076 0.036 0.000 0.096 0.792
#> GSM62252 5 0.4111 0.5953 0.116 0.004 0.000 0.084 0.796
#> GSM62255 4 0.2674 0.9026 0.000 0.140 0.000 0.856 0.004
#> GSM62257 4 0.3001 0.8967 0.000 0.144 0.004 0.844 0.008
#> GSM62260 1 0.3821 0.7292 0.764 0.000 0.000 0.020 0.216
#> GSM62261 5 0.6260 0.6251 0.000 0.152 0.000 0.372 0.476
#> GSM62262 4 0.2439 0.8992 0.000 0.120 0.000 0.876 0.004
#> GSM62264 1 0.2069 0.7378 0.912 0.000 0.000 0.012 0.076
#> GSM62268 1 0.3177 0.6881 0.792 0.000 0.208 0.000 0.000
#> GSM62269 3 0.0609 0.9725 0.020 0.000 0.980 0.000 0.000
#> GSM62271 1 0.5019 0.7584 0.732 0.000 0.128 0.012 0.128
#> GSM62272 3 0.0609 0.9725 0.020 0.000 0.980 0.000 0.000
#> GSM62273 2 0.6178 0.2397 0.000 0.572 0.012 0.288 0.128
#> GSM62274 3 0.3048 0.7882 0.176 0.000 0.820 0.000 0.004
#> GSM62275 3 0.0609 0.9725 0.020 0.000 0.980 0.000 0.000
#> GSM62276 1 0.5407 0.7461 0.680 0.000 0.116 0.008 0.196
#> GSM62277 3 0.0794 0.9670 0.028 0.000 0.972 0.000 0.000
#> GSM62279 1 0.4864 0.7412 0.720 0.000 0.116 0.000 0.164
#> GSM62282 1 0.6318 0.6875 0.644 0.000 0.084 0.088 0.184
#> GSM62283 1 0.4352 0.7671 0.772 0.000 0.060 0.008 0.160
#> GSM62286 5 0.3927 0.7053 0.004 0.040 0.000 0.164 0.792
#> GSM62287 4 0.2439 0.9041 0.000 0.120 0.000 0.876 0.004
#> GSM62288 5 0.6260 0.6251 0.000 0.152 0.000 0.372 0.476
#> GSM62290 2 0.0162 0.8883 0.000 0.996 0.000 0.000 0.004
#> GSM62293 4 0.3389 0.8678 0.000 0.116 0.000 0.836 0.048
#> GSM62301 2 0.0162 0.8873 0.000 0.996 0.000 0.004 0.000
#> GSM62302 4 0.2536 0.9050 0.000 0.128 0.000 0.868 0.004
#> GSM62303 4 0.2389 0.9033 0.000 0.116 0.000 0.880 0.004
#> GSM62304 4 0.2674 0.9026 0.000 0.140 0.000 0.856 0.004
#> GSM62312 2 0.0566 0.8856 0.000 0.984 0.012 0.004 0.000
#> GSM62313 4 0.2583 0.9042 0.000 0.132 0.000 0.864 0.004
#> GSM62314 5 0.6289 0.5832 0.000 0.152 0.000 0.396 0.452
#> GSM62319 2 0.3449 0.7149 0.000 0.812 0.000 0.024 0.164
#> GSM62320 2 0.0693 0.8835 0.000 0.980 0.012 0.008 0.000
#> GSM62249 1 0.4390 0.4900 0.568 0.004 0.000 0.000 0.428
#> GSM62251 1 0.2974 0.7601 0.868 0.000 0.052 0.000 0.080
#> GSM62263 2 0.5708 0.0362 0.060 0.480 0.000 0.008 0.452
#> GSM62285 2 0.0162 0.8873 0.000 0.996 0.000 0.004 0.000
#> GSM62315 2 0.0162 0.8873 0.000 0.996 0.000 0.004 0.000
#> GSM62291 2 0.0162 0.8883 0.000 0.996 0.000 0.000 0.004
#> GSM62265 1 0.2694 0.7592 0.884 0.000 0.076 0.000 0.040
#> GSM62266 1 0.2773 0.7218 0.836 0.000 0.164 0.000 0.000
#> GSM62296 2 0.0290 0.8877 0.000 0.992 0.000 0.000 0.008
#> GSM62309 2 0.0290 0.8877 0.000 0.992 0.000 0.000 0.008
#> GSM62295 4 0.4840 0.7762 0.000 0.116 0.012 0.748 0.124
#> GSM62300 2 0.0290 0.8877 0.000 0.992 0.000 0.000 0.008
#> GSM62308 2 0.0290 0.8877 0.000 0.992 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
#> GSM62248 5 0.3951 0.74731 0.000 0.036 0.004 0.136 0.792 0.032
#> GSM62256 5 0.5627 0.66447 0.000 0.028 0.004 0.132 0.628 0.208
#> GSM62259 4 0.6478 0.17269 0.000 0.008 0.008 0.404 0.276 0.304
#> GSM62267 1 0.5677 0.61606 0.660 0.004 0.084 0.000 0.160 0.092
#> GSM62280 6 0.3887 0.84713 0.360 0.000 0.000 0.000 0.008 0.632
#> GSM62284 1 0.4382 0.17574 0.564 0.004 0.416 0.000 0.012 0.004
#> GSM62289 5 0.1096 0.72289 0.008 0.004 0.004 0.020 0.964 0.000
#> GSM62307 4 0.1668 0.84478 0.000 0.008 0.004 0.928 0.000 0.060
#> GSM62316 5 0.4799 0.69386 0.000 0.036 0.004 0.248 0.680 0.032
#> GSM62254 4 0.4657 0.69319 0.000 0.004 0.004 0.688 0.076 0.228
#> GSM62292 4 0.4657 0.69319 0.000 0.004 0.004 0.688 0.076 0.228
#> GSM62253 1 0.2149 0.65000 0.888 0.004 0.104 0.000 0.004 0.000
#> GSM62270 3 0.0458 0.93614 0.016 0.000 0.984 0.000 0.000 0.000
#> GSM62278 3 0.0547 0.93426 0.020 0.000 0.980 0.000 0.000 0.000
#> GSM62297 2 0.1973 0.86501 0.000 0.924 0.008 0.004 0.028 0.036
#> GSM62298 2 0.1749 0.87387 0.000 0.932 0.008 0.024 0.000 0.036
#> GSM62299 2 0.1749 0.87336 0.000 0.932 0.008 0.024 0.000 0.036
#> GSM62258 1 0.5808 0.49373 0.624 0.004 0.040 0.000 0.156 0.176
#> GSM62281 5 0.7099 0.53663 0.000 0.160 0.008 0.116 0.484 0.232
#> GSM62294 4 0.0790 0.86458 0.000 0.000 0.000 0.968 0.000 0.032
#> GSM62305 5 0.1686 0.70850 0.000 0.000 0.000 0.012 0.924 0.064
#> GSM62306 5 0.4255 0.73738 0.000 0.024 0.000 0.112 0.768 0.096
#> GSM62310 4 0.0260 0.86739 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM62311 4 0.0260 0.86739 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM62317 2 0.4649 0.17634 0.040 0.492 0.000 0.000 0.000 0.468
#> GSM62318 6 0.3684 0.84451 0.372 0.000 0.000 0.000 0.000 0.628
#> GSM62321 6 0.4420 0.80986 0.320 0.004 0.000 0.000 0.036 0.640
#> GSM62322 3 0.0458 0.93614 0.016 0.000 0.984 0.000 0.000 0.000
#> GSM62250 5 0.1223 0.71632 0.012 0.004 0.000 0.016 0.960 0.008
#> GSM62252 5 0.1325 0.71107 0.012 0.004 0.000 0.012 0.956 0.016
#> GSM62255 4 0.0806 0.86436 0.000 0.008 0.000 0.972 0.000 0.020
#> GSM62257 4 0.1912 0.84332 0.000 0.008 0.008 0.924 0.008 0.052
#> GSM62260 1 0.5414 0.06945 0.600 0.012 0.000 0.000 0.124 0.264
#> GSM62261 5 0.4888 0.68983 0.000 0.036 0.004 0.252 0.672 0.036
#> GSM62262 4 0.1644 0.84874 0.000 0.004 0.000 0.920 0.000 0.076
#> GSM62264 1 0.2949 0.41894 0.848 0.008 0.000 0.000 0.028 0.116
#> GSM62268 1 0.2288 0.64464 0.876 0.004 0.116 0.000 0.004 0.000
#> GSM62269 3 0.0458 0.93614 0.016 0.000 0.984 0.000 0.000 0.000
#> GSM62271 1 0.5471 0.47664 0.672 0.004 0.092 0.000 0.060 0.172
#> GSM62272 3 0.0458 0.93614 0.016 0.000 0.984 0.000 0.000 0.000
#> GSM62273 2 0.7244 0.14602 0.000 0.380 0.004 0.232 0.084 0.300
#> GSM62274 3 0.4119 0.40600 0.348 0.004 0.636 0.000 0.008 0.004
#> GSM62275 3 0.0458 0.93614 0.016 0.000 0.984 0.000 0.000 0.000
#> GSM62276 1 0.5674 0.61295 0.660 0.004 0.080 0.000 0.160 0.096
#> GSM62277 3 0.1010 0.92110 0.036 0.000 0.960 0.000 0.004 0.000
#> GSM62279 1 0.4540 0.63327 0.732 0.000 0.076 0.000 0.168 0.024
#> GSM62282 6 0.5625 0.54009 0.432 0.004 0.088 0.000 0.012 0.464
#> GSM62283 1 0.4892 0.59110 0.732 0.008 0.036 0.000 0.120 0.104
#> GSM62286 5 0.0862 0.72042 0.008 0.004 0.000 0.016 0.972 0.000
#> GSM62287 4 0.0000 0.86852 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62288 5 0.4822 0.69082 0.000 0.036 0.004 0.252 0.676 0.032
#> GSM62290 2 0.0603 0.88136 0.000 0.980 0.000 0.016 0.004 0.000
#> GSM62293 4 0.2734 0.82376 0.000 0.004 0.004 0.860 0.016 0.116
#> GSM62301 2 0.0632 0.88066 0.000 0.976 0.000 0.024 0.000 0.000
#> GSM62302 4 0.0837 0.86800 0.000 0.004 0.004 0.972 0.000 0.020
#> GSM62303 4 0.0777 0.86776 0.000 0.000 0.004 0.972 0.000 0.024
#> GSM62304 4 0.0520 0.86632 0.000 0.008 0.000 0.984 0.000 0.008
#> GSM62312 2 0.2408 0.84492 0.000 0.892 0.004 0.052 0.000 0.052
#> GSM62313 4 0.0146 0.86806 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM62314 5 0.4991 0.67777 0.000 0.036 0.008 0.264 0.660 0.032
#> GSM62319 2 0.5252 0.57475 0.000 0.628 0.000 0.016 0.104 0.252
#> GSM62320 2 0.1844 0.87041 0.000 0.924 0.004 0.024 0.000 0.048
#> GSM62249 5 0.4853 -0.00092 0.396 0.016 0.000 0.000 0.556 0.032
#> GSM62251 1 0.2179 0.62858 0.916 0.012 0.024 0.000 0.040 0.008
#> GSM62263 5 0.4997 0.32032 0.020 0.396 0.004 0.000 0.552 0.028
#> GSM62285 2 0.0632 0.88066 0.000 0.976 0.000 0.024 0.000 0.000
#> GSM62315 2 0.0891 0.88117 0.000 0.968 0.000 0.024 0.000 0.008
#> GSM62291 2 0.0748 0.88143 0.000 0.976 0.000 0.016 0.004 0.004
#> GSM62265 1 0.1586 0.64731 0.940 0.004 0.040 0.000 0.012 0.004
#> GSM62266 1 0.2149 0.65000 0.888 0.004 0.104 0.000 0.004 0.000
#> GSM62296 2 0.1313 0.87940 0.000 0.952 0.000 0.016 0.004 0.028
#> GSM62309 2 0.1313 0.87940 0.000 0.952 0.000 0.016 0.004 0.028
#> GSM62295 4 0.5132 0.63731 0.000 0.004 0.008 0.624 0.084 0.280
#> GSM62300 2 0.1313 0.87940 0.000 0.952 0.000 0.016 0.004 0.028
#> GSM62308 2 0.1313 0.87940 0.000 0.952 0.000 0.016 0.004 0.028
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) other(p) genotype/variation(p) k
#> MAD:kmeans 73 0.68498 1.000 0.7909 2
#> MAD:kmeans 58 0.56877 0.874 0.5252 3
#> MAD:kmeans 66 0.00581 0.739 0.1197 4
#> MAD:kmeans 70 0.00576 0.767 0.0675 5
#> MAD:kmeans 64 0.00426 0.792 0.2004 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "skmeans"]
# you can also extract it by
# res = res_list["MAD:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 75 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 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 0.980 0.992 0.4871 0.514 0.514
#> 3 3 1.000 0.942 0.969 0.3596 0.783 0.592
#> 4 4 0.870 0.857 0.931 0.1026 0.907 0.737
#> 5 5 0.828 0.753 0.886 0.0705 0.936 0.772
#> 6 6 0.795 0.606 0.800 0.0316 0.957 0.825
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
#> GSM62248 2 0.000 0.992 0.000 1.000
#> GSM62256 2 0.000 0.992 0.000 1.000
#> GSM62259 2 0.000 0.992 0.000 1.000
#> GSM62267 1 0.000 0.990 1.000 0.000
#> GSM62280 1 0.000 0.990 1.000 0.000
#> GSM62284 1 0.000 0.990 1.000 0.000
#> GSM62289 2 0.000 0.992 0.000 1.000
#> GSM62307 2 0.000 0.992 0.000 1.000
#> GSM62316 2 0.000 0.992 0.000 1.000
#> GSM62254 2 0.000 0.992 0.000 1.000
#> GSM62292 2 0.000 0.992 0.000 1.000
#> GSM62253 1 0.000 0.990 1.000 0.000
#> GSM62270 1 0.000 0.990 1.000 0.000
#> GSM62278 1 0.000 0.990 1.000 0.000
#> GSM62297 2 0.000 0.992 0.000 1.000
#> GSM62298 2 0.000 0.992 0.000 1.000
#> GSM62299 2 0.000 0.992 0.000 1.000
#> GSM62258 1 0.000 0.990 1.000 0.000
#> GSM62281 2 0.000 0.992 0.000 1.000
#> GSM62294 2 0.000 0.992 0.000 1.000
#> GSM62305 1 0.781 0.696 0.768 0.232
#> GSM62306 2 0.000 0.992 0.000 1.000
#> GSM62310 2 0.000 0.992 0.000 1.000
#> GSM62311 2 0.000 0.992 0.000 1.000
#> GSM62317 2 0.000 0.992 0.000 1.000
#> GSM62318 1 0.000 0.990 1.000 0.000
#> GSM62321 1 0.000 0.990 1.000 0.000
#> GSM62322 1 0.000 0.990 1.000 0.000
#> GSM62250 1 0.260 0.948 0.956 0.044
#> GSM62252 1 0.000 0.990 1.000 0.000
#> GSM62255 2 0.000 0.992 0.000 1.000
#> GSM62257 2 0.000 0.992 0.000 1.000
#> GSM62260 1 0.000 0.990 1.000 0.000
#> GSM62261 2 0.000 0.992 0.000 1.000
#> GSM62262 2 0.000 0.992 0.000 1.000
#> GSM62264 1 0.000 0.990 1.000 0.000
#> GSM62268 1 0.000 0.990 1.000 0.000
#> GSM62269 1 0.000 0.990 1.000 0.000
#> GSM62271 1 0.000 0.990 1.000 0.000
#> GSM62272 1 0.000 0.990 1.000 0.000
#> GSM62273 2 0.000 0.992 0.000 1.000
#> GSM62274 1 0.000 0.990 1.000 0.000
#> GSM62275 1 0.000 0.990 1.000 0.000
#> GSM62276 1 0.000 0.990 1.000 0.000
#> GSM62277 1 0.000 0.990 1.000 0.000
#> GSM62279 1 0.000 0.990 1.000 0.000
#> GSM62282 1 0.000 0.990 1.000 0.000
#> GSM62283 1 0.000 0.990 1.000 0.000
#> GSM62286 2 0.000 0.992 0.000 1.000
#> GSM62287 2 0.000 0.992 0.000 1.000
#> GSM62288 2 0.000 0.992 0.000 1.000
#> GSM62290 2 0.000 0.992 0.000 1.000
#> GSM62293 2 0.000 0.992 0.000 1.000
#> GSM62301 2 0.000 0.992 0.000 1.000
#> GSM62302 2 0.000 0.992 0.000 1.000
#> GSM62303 2 0.000 0.992 0.000 1.000
#> GSM62304 2 0.000 0.992 0.000 1.000
#> GSM62312 2 0.000 0.992 0.000 1.000
#> GSM62313 2 0.000 0.992 0.000 1.000
#> GSM62314 2 0.000 0.992 0.000 1.000
#> GSM62319 2 0.000 0.992 0.000 1.000
#> GSM62320 2 0.000 0.992 0.000 1.000
#> GSM62249 1 0.000 0.990 1.000 0.000
#> GSM62251 1 0.000 0.990 1.000 0.000
#> GSM62263 2 0.925 0.474 0.340 0.660
#> GSM62285 2 0.000 0.992 0.000 1.000
#> GSM62315 2 0.000 0.992 0.000 1.000
#> GSM62291 2 0.000 0.992 0.000 1.000
#> GSM62265 1 0.000 0.990 1.000 0.000
#> GSM62266 1 0.000 0.990 1.000 0.000
#> GSM62296 2 0.000 0.992 0.000 1.000
#> GSM62309 2 0.000 0.992 0.000 1.000
#> GSM62295 2 0.000 0.992 0.000 1.000
#> GSM62300 2 0.000 0.992 0.000 1.000
#> GSM62308 2 0.000 0.992 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM62248 2 0.0747 0.9314 0.000 0.984 0.016
#> GSM62256 2 0.1964 0.9487 0.000 0.944 0.056
#> GSM62259 2 0.1753 0.9495 0.000 0.952 0.048
#> GSM62267 1 0.0000 0.9970 1.000 0.000 0.000
#> GSM62280 1 0.0000 0.9970 1.000 0.000 0.000
#> GSM62284 1 0.0000 0.9970 1.000 0.000 0.000
#> GSM62289 2 0.0000 0.9306 0.000 1.000 0.000
#> GSM62307 2 0.1964 0.9487 0.000 0.944 0.056
#> GSM62316 2 0.0592 0.9322 0.000 0.988 0.012
#> GSM62254 2 0.1753 0.9495 0.000 0.952 0.048
#> GSM62292 2 0.1753 0.9495 0.000 0.952 0.048
#> GSM62253 1 0.0000 0.9970 1.000 0.000 0.000
#> GSM62270 1 0.0000 0.9970 1.000 0.000 0.000
#> GSM62278 1 0.0000 0.9970 1.000 0.000 0.000
#> GSM62297 3 0.0000 0.9647 0.000 0.000 1.000
#> GSM62298 3 0.0000 0.9647 0.000 0.000 1.000
#> GSM62299 3 0.0000 0.9647 0.000 0.000 1.000
#> GSM62258 1 0.0000 0.9970 1.000 0.000 0.000
#> GSM62281 3 0.6274 0.0957 0.000 0.456 0.544
#> GSM62294 2 0.1753 0.9495 0.000 0.952 0.048
#> GSM62305 2 0.5948 0.4172 0.360 0.640 0.000
#> GSM62306 2 0.0000 0.9306 0.000 1.000 0.000
#> GSM62310 2 0.2066 0.9464 0.000 0.940 0.060
#> GSM62311 2 0.1964 0.9487 0.000 0.944 0.056
#> GSM62317 3 0.0000 0.9647 0.000 0.000 1.000
#> GSM62318 1 0.0000 0.9970 1.000 0.000 0.000
#> GSM62321 1 0.0000 0.9970 1.000 0.000 0.000
#> GSM62322 1 0.0000 0.9970 1.000 0.000 0.000
#> GSM62250 2 0.5529 0.5589 0.296 0.704 0.000
#> GSM62252 1 0.1964 0.9493 0.944 0.056 0.000
#> GSM62255 2 0.1964 0.9487 0.000 0.944 0.056
#> GSM62257 2 0.1964 0.9487 0.000 0.944 0.056
#> GSM62260 1 0.0000 0.9970 1.000 0.000 0.000
#> GSM62261 2 0.0747 0.9314 0.000 0.984 0.016
#> GSM62262 2 0.1753 0.9495 0.000 0.952 0.048
#> GSM62264 1 0.0000 0.9970 1.000 0.000 0.000
#> GSM62268 1 0.0000 0.9970 1.000 0.000 0.000
#> GSM62269 1 0.0000 0.9970 1.000 0.000 0.000
#> GSM62271 1 0.0000 0.9970 1.000 0.000 0.000
#> GSM62272 1 0.0000 0.9970 1.000 0.000 0.000
#> GSM62273 3 0.2537 0.8938 0.000 0.080 0.920
#> GSM62274 1 0.0000 0.9970 1.000 0.000 0.000
#> GSM62275 1 0.0000 0.9970 1.000 0.000 0.000
#> GSM62276 1 0.0000 0.9970 1.000 0.000 0.000
#> GSM62277 1 0.0000 0.9970 1.000 0.000 0.000
#> GSM62279 1 0.0000 0.9970 1.000 0.000 0.000
#> GSM62282 1 0.0000 0.9970 1.000 0.000 0.000
#> GSM62283 1 0.0000 0.9970 1.000 0.000 0.000
#> GSM62286 2 0.0000 0.9306 0.000 1.000 0.000
#> GSM62287 2 0.1753 0.9495 0.000 0.952 0.048
#> GSM62288 2 0.0747 0.9314 0.000 0.984 0.016
#> GSM62290 3 0.0000 0.9647 0.000 0.000 1.000
#> GSM62293 2 0.1753 0.9495 0.000 0.952 0.048
#> GSM62301 3 0.0000 0.9647 0.000 0.000 1.000
#> GSM62302 2 0.1964 0.9487 0.000 0.944 0.056
#> GSM62303 2 0.1753 0.9495 0.000 0.952 0.048
#> GSM62304 2 0.1964 0.9487 0.000 0.944 0.056
#> GSM62312 3 0.0000 0.9647 0.000 0.000 1.000
#> GSM62313 2 0.1964 0.9487 0.000 0.944 0.056
#> GSM62314 2 0.0747 0.9314 0.000 0.984 0.016
#> GSM62319 3 0.0747 0.9532 0.000 0.016 0.984
#> GSM62320 3 0.0000 0.9647 0.000 0.000 1.000
#> GSM62249 1 0.1289 0.9702 0.968 0.032 0.000
#> GSM62251 1 0.0000 0.9970 1.000 0.000 0.000
#> GSM62263 3 0.1753 0.9200 0.000 0.048 0.952
#> GSM62285 3 0.0000 0.9647 0.000 0.000 1.000
#> GSM62315 3 0.0000 0.9647 0.000 0.000 1.000
#> GSM62291 3 0.0000 0.9647 0.000 0.000 1.000
#> GSM62265 1 0.0000 0.9970 1.000 0.000 0.000
#> GSM62266 1 0.0000 0.9970 1.000 0.000 0.000
#> GSM62296 3 0.0000 0.9647 0.000 0.000 1.000
#> GSM62309 3 0.0000 0.9647 0.000 0.000 1.000
#> GSM62295 2 0.1753 0.9495 0.000 0.952 0.048
#> GSM62300 3 0.0000 0.9647 0.000 0.000 1.000
#> GSM62308 3 0.0000 0.9647 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM62248 3 0.3908 0.8247 0.000 0.004 0.784 0.212
#> GSM62256 4 0.0469 0.8644 0.000 0.012 0.000 0.988
#> GSM62259 4 0.0707 0.8656 0.000 0.000 0.020 0.980
#> GSM62267 1 0.0000 0.9574 1.000 0.000 0.000 0.000
#> GSM62280 1 0.1474 0.9368 0.948 0.000 0.052 0.000
#> GSM62284 1 0.0000 0.9574 1.000 0.000 0.000 0.000
#> GSM62289 3 0.3123 0.8540 0.000 0.000 0.844 0.156
#> GSM62307 4 0.0000 0.8713 0.000 0.000 0.000 1.000
#> GSM62316 4 0.5126 -0.1033 0.000 0.004 0.444 0.552
#> GSM62254 4 0.0707 0.8656 0.000 0.000 0.020 0.980
#> GSM62292 4 0.0707 0.8656 0.000 0.000 0.020 0.980
#> GSM62253 1 0.1557 0.9430 0.944 0.000 0.056 0.000
#> GSM62270 1 0.0000 0.9574 1.000 0.000 0.000 0.000
#> GSM62278 1 0.0000 0.9574 1.000 0.000 0.000 0.000
#> GSM62297 2 0.0000 0.9830 0.000 1.000 0.000 0.000
#> GSM62298 2 0.0000 0.9830 0.000 1.000 0.000 0.000
#> GSM62299 2 0.0000 0.9830 0.000 1.000 0.000 0.000
#> GSM62258 1 0.0000 0.9574 1.000 0.000 0.000 0.000
#> GSM62281 4 0.3726 0.6258 0.000 0.212 0.000 0.788
#> GSM62294 4 0.0188 0.8704 0.000 0.000 0.004 0.996
#> GSM62305 3 0.1807 0.8176 0.008 0.000 0.940 0.052
#> GSM62306 3 0.3837 0.8159 0.000 0.000 0.776 0.224
#> GSM62310 4 0.0000 0.8713 0.000 0.000 0.000 1.000
#> GSM62311 4 0.0000 0.8713 0.000 0.000 0.000 1.000
#> GSM62317 2 0.1474 0.9418 0.000 0.948 0.052 0.000
#> GSM62318 1 0.2469 0.9168 0.892 0.000 0.108 0.000
#> GSM62321 1 0.3024 0.8910 0.852 0.000 0.148 0.000
#> GSM62322 1 0.0000 0.9574 1.000 0.000 0.000 0.000
#> GSM62250 3 0.3037 0.8325 0.036 0.000 0.888 0.076
#> GSM62252 3 0.2760 0.7557 0.128 0.000 0.872 0.000
#> GSM62255 4 0.0000 0.8713 0.000 0.000 0.000 1.000
#> GSM62257 4 0.0000 0.8713 0.000 0.000 0.000 1.000
#> GSM62260 1 0.3074 0.8891 0.848 0.000 0.152 0.000
#> GSM62261 4 0.5250 -0.0989 0.000 0.008 0.440 0.552
#> GSM62262 4 0.0707 0.8656 0.000 0.000 0.020 0.980
#> GSM62264 1 0.3123 0.8859 0.844 0.000 0.156 0.000
#> GSM62268 1 0.1557 0.9430 0.944 0.000 0.056 0.000
#> GSM62269 1 0.0000 0.9574 1.000 0.000 0.000 0.000
#> GSM62271 1 0.0000 0.9574 1.000 0.000 0.000 0.000
#> GSM62272 1 0.0000 0.9574 1.000 0.000 0.000 0.000
#> GSM62273 4 0.5570 0.1608 0.000 0.440 0.020 0.540
#> GSM62274 1 0.0000 0.9574 1.000 0.000 0.000 0.000
#> GSM62275 1 0.0000 0.9574 1.000 0.000 0.000 0.000
#> GSM62276 1 0.0000 0.9574 1.000 0.000 0.000 0.000
#> GSM62277 1 0.0000 0.9574 1.000 0.000 0.000 0.000
#> GSM62279 1 0.0592 0.9523 0.984 0.000 0.016 0.000
#> GSM62282 1 0.0188 0.9565 0.996 0.000 0.004 0.000
#> GSM62283 1 0.0592 0.9549 0.984 0.000 0.016 0.000
#> GSM62286 3 0.3074 0.8542 0.000 0.000 0.848 0.152
#> GSM62287 4 0.0000 0.8713 0.000 0.000 0.000 1.000
#> GSM62288 3 0.5039 0.4866 0.000 0.004 0.592 0.404
#> GSM62290 2 0.0000 0.9830 0.000 1.000 0.000 0.000
#> GSM62293 4 0.0707 0.8656 0.000 0.000 0.020 0.980
#> GSM62301 2 0.0000 0.9830 0.000 1.000 0.000 0.000
#> GSM62302 4 0.0000 0.8713 0.000 0.000 0.000 1.000
#> GSM62303 4 0.0000 0.8713 0.000 0.000 0.000 1.000
#> GSM62304 4 0.0000 0.8713 0.000 0.000 0.000 1.000
#> GSM62312 2 0.0188 0.9797 0.000 0.996 0.000 0.004
#> GSM62313 4 0.0000 0.8713 0.000 0.000 0.000 1.000
#> GSM62314 4 0.4991 0.1165 0.000 0.004 0.388 0.608
#> GSM62319 2 0.1411 0.9489 0.000 0.960 0.020 0.020
#> GSM62320 2 0.0000 0.9830 0.000 1.000 0.000 0.000
#> GSM62249 1 0.4382 0.7137 0.704 0.000 0.296 0.000
#> GSM62251 1 0.2408 0.9180 0.896 0.000 0.104 0.000
#> GSM62263 2 0.3400 0.8073 0.000 0.820 0.180 0.000
#> GSM62285 2 0.0000 0.9830 0.000 1.000 0.000 0.000
#> GSM62315 2 0.0000 0.9830 0.000 1.000 0.000 0.000
#> GSM62291 2 0.0000 0.9830 0.000 1.000 0.000 0.000
#> GSM62265 1 0.1557 0.9430 0.944 0.000 0.056 0.000
#> GSM62266 1 0.1557 0.9430 0.944 0.000 0.056 0.000
#> GSM62296 2 0.0000 0.9830 0.000 1.000 0.000 0.000
#> GSM62309 2 0.0000 0.9830 0.000 1.000 0.000 0.000
#> GSM62295 4 0.0895 0.8630 0.000 0.004 0.020 0.976
#> GSM62300 2 0.0000 0.9830 0.000 1.000 0.000 0.000
#> GSM62308 2 0.0000 0.9830 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM62248 5 0.3810 0.7523 0.000 0.000 0.036 0.176 0.788
#> GSM62256 4 0.3318 0.7643 0.000 0.036 0.048 0.868 0.048
#> GSM62259 4 0.2863 0.8190 0.000 0.000 0.060 0.876 0.064
#> GSM62267 1 0.0000 0.8721 1.000 0.000 0.000 0.000 0.000
#> GSM62280 3 0.4450 0.2483 0.488 0.000 0.508 0.000 0.004
#> GSM62284 1 0.0000 0.8721 1.000 0.000 0.000 0.000 0.000
#> GSM62289 5 0.1638 0.7714 0.000 0.000 0.004 0.064 0.932
#> GSM62307 4 0.1116 0.8329 0.000 0.004 0.028 0.964 0.004
#> GSM62316 4 0.5259 -0.3105 0.000 0.004 0.036 0.484 0.476
#> GSM62254 4 0.2104 0.8249 0.000 0.000 0.024 0.916 0.060
#> GSM62292 4 0.2104 0.8249 0.000 0.000 0.024 0.916 0.060
#> GSM62253 1 0.3932 0.5292 0.672 0.000 0.328 0.000 0.000
#> GSM62270 1 0.0000 0.8721 1.000 0.000 0.000 0.000 0.000
#> GSM62278 1 0.0000 0.8721 1.000 0.000 0.000 0.000 0.000
#> GSM62297 2 0.0162 0.9497 0.000 0.996 0.004 0.000 0.000
#> GSM62298 2 0.0162 0.9497 0.000 0.996 0.004 0.000 0.000
#> GSM62299 2 0.0162 0.9497 0.000 0.996 0.004 0.000 0.000
#> GSM62258 1 0.0000 0.8721 1.000 0.000 0.000 0.000 0.000
#> GSM62281 4 0.4651 0.5801 0.000 0.248 0.036 0.708 0.008
#> GSM62294 4 0.1106 0.8402 0.000 0.000 0.012 0.964 0.024
#> GSM62305 5 0.2470 0.7021 0.000 0.000 0.104 0.012 0.884
#> GSM62306 5 0.4031 0.7533 0.000 0.000 0.044 0.184 0.772
#> GSM62310 4 0.0324 0.8434 0.000 0.004 0.004 0.992 0.000
#> GSM62311 4 0.0162 0.8440 0.000 0.004 0.000 0.996 0.000
#> GSM62317 2 0.4561 0.0744 0.000 0.504 0.488 0.000 0.008
#> GSM62318 3 0.3010 0.7952 0.172 0.000 0.824 0.000 0.004
#> GSM62321 3 0.2124 0.8253 0.096 0.000 0.900 0.000 0.004
#> GSM62322 1 0.0000 0.8721 1.000 0.000 0.000 0.000 0.000
#> GSM62250 5 0.1992 0.7620 0.000 0.000 0.032 0.044 0.924
#> GSM62252 5 0.2504 0.6979 0.064 0.000 0.040 0.000 0.896
#> GSM62255 4 0.0566 0.8419 0.000 0.004 0.012 0.984 0.000
#> GSM62257 4 0.1461 0.8254 0.000 0.004 0.028 0.952 0.016
#> GSM62260 3 0.2280 0.8330 0.120 0.000 0.880 0.000 0.000
#> GSM62261 5 0.5259 0.2025 0.000 0.004 0.036 0.480 0.480
#> GSM62262 4 0.2104 0.8249 0.000 0.000 0.024 0.916 0.060
#> GSM62264 3 0.2127 0.8324 0.108 0.000 0.892 0.000 0.000
#> GSM62268 1 0.3895 0.5423 0.680 0.000 0.320 0.000 0.000
#> GSM62269 1 0.0000 0.8721 1.000 0.000 0.000 0.000 0.000
#> GSM62271 1 0.0000 0.8721 1.000 0.000 0.000 0.000 0.000
#> GSM62272 1 0.0000 0.8721 1.000 0.000 0.000 0.000 0.000
#> GSM62273 4 0.6182 0.1059 0.000 0.432 0.032 0.476 0.060
#> GSM62274 1 0.0000 0.8721 1.000 0.000 0.000 0.000 0.000
#> GSM62275 1 0.0000 0.8721 1.000 0.000 0.000 0.000 0.000
#> GSM62276 1 0.0000 0.8721 1.000 0.000 0.000 0.000 0.000
#> GSM62277 1 0.0000 0.8721 1.000 0.000 0.000 0.000 0.000
#> GSM62279 1 0.0693 0.8571 0.980 0.000 0.008 0.000 0.012
#> GSM62282 1 0.1197 0.8298 0.952 0.000 0.048 0.000 0.000
#> GSM62283 1 0.3177 0.6954 0.792 0.000 0.208 0.000 0.000
#> GSM62286 5 0.1331 0.7672 0.000 0.000 0.008 0.040 0.952
#> GSM62287 4 0.0000 0.8444 0.000 0.000 0.000 1.000 0.000
#> GSM62288 5 0.5139 0.4634 0.000 0.004 0.036 0.384 0.576
#> GSM62290 2 0.0000 0.9508 0.000 1.000 0.000 0.000 0.000
#> GSM62293 4 0.2104 0.8249 0.000 0.000 0.024 0.916 0.060
#> GSM62301 2 0.0000 0.9508 0.000 1.000 0.000 0.000 0.000
#> GSM62302 4 0.0162 0.8446 0.000 0.000 0.004 0.996 0.000
#> GSM62303 4 0.0324 0.8448 0.000 0.000 0.004 0.992 0.004
#> GSM62304 4 0.0833 0.8387 0.000 0.004 0.016 0.976 0.004
#> GSM62312 2 0.2546 0.8633 0.000 0.904 0.036 0.048 0.012
#> GSM62313 4 0.0000 0.8444 0.000 0.000 0.000 1.000 0.000
#> GSM62314 4 0.5206 -0.1079 0.000 0.004 0.036 0.544 0.416
#> GSM62319 2 0.2409 0.8691 0.000 0.908 0.020 0.012 0.060
#> GSM62320 2 0.0162 0.9497 0.000 0.996 0.004 0.000 0.000
#> GSM62249 3 0.3667 0.7919 0.140 0.000 0.812 0.000 0.048
#> GSM62251 1 0.4171 0.3847 0.604 0.000 0.396 0.000 0.000
#> GSM62263 3 0.2852 0.6641 0.000 0.172 0.828 0.000 0.000
#> GSM62285 2 0.0000 0.9508 0.000 1.000 0.000 0.000 0.000
#> GSM62315 2 0.0000 0.9508 0.000 1.000 0.000 0.000 0.000
#> GSM62291 2 0.0000 0.9508 0.000 1.000 0.000 0.000 0.000
#> GSM62265 1 0.3837 0.5619 0.692 0.000 0.308 0.000 0.000
#> GSM62266 1 0.3949 0.5216 0.668 0.000 0.332 0.000 0.000
#> GSM62296 2 0.0000 0.9508 0.000 1.000 0.000 0.000 0.000
#> GSM62309 2 0.0000 0.9508 0.000 1.000 0.000 0.000 0.000
#> GSM62295 4 0.2104 0.8249 0.000 0.000 0.024 0.916 0.060
#> GSM62300 2 0.0000 0.9508 0.000 1.000 0.000 0.000 0.000
#> GSM62308 2 0.0000 0.9508 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM62248 5 0.5497 0.4483 0.000 0.000 0.176 0.268 0.556 0.000
#> GSM62256 4 0.4759 0.5992 0.000 0.024 0.224 0.696 0.052 0.004
#> GSM62259 4 0.4139 0.6306 0.000 0.000 0.336 0.640 0.024 0.000
#> GSM62267 1 0.0000 0.8290 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM62280 6 0.2912 0.2864 0.216 0.000 0.000 0.000 0.000 0.784
#> GSM62284 1 0.0291 0.8264 0.992 0.000 0.004 0.000 0.000 0.004
#> GSM62289 5 0.2066 0.7191 0.000 0.000 0.072 0.024 0.904 0.000
#> GSM62307 4 0.1524 0.7580 0.000 0.000 0.060 0.932 0.008 0.000
#> GSM62316 4 0.5544 0.2487 0.000 0.000 0.176 0.544 0.280 0.000
#> GSM62254 4 0.3230 0.7016 0.000 0.000 0.212 0.776 0.012 0.000
#> GSM62292 4 0.3230 0.7016 0.000 0.000 0.212 0.776 0.012 0.000
#> GSM62253 1 0.5556 0.3402 0.588 0.000 0.220 0.000 0.008 0.184
#> GSM62270 1 0.0146 0.8291 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM62278 1 0.0146 0.8291 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM62297 2 0.0547 0.9069 0.000 0.980 0.020 0.000 0.000 0.000
#> GSM62298 2 0.0508 0.9079 0.000 0.984 0.012 0.004 0.000 0.000
#> GSM62299 2 0.0458 0.9081 0.000 0.984 0.016 0.000 0.000 0.000
#> GSM62258 1 0.0146 0.8281 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM62281 4 0.5728 0.4841 0.000 0.220 0.164 0.596 0.016 0.004
#> GSM62294 4 0.2070 0.7556 0.000 0.000 0.092 0.896 0.012 0.000
#> GSM62305 5 0.4391 0.5520 0.000 0.000 0.320 0.028 0.644 0.008
#> GSM62306 5 0.5738 0.4924 0.000 0.000 0.240 0.244 0.516 0.000
#> GSM62310 4 0.0458 0.7755 0.000 0.000 0.016 0.984 0.000 0.000
#> GSM62311 4 0.0000 0.7770 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62317 6 0.3190 0.3146 0.000 0.220 0.008 0.000 0.000 0.772
#> GSM62318 6 0.0692 0.3865 0.020 0.000 0.004 0.000 0.000 0.976
#> GSM62321 6 0.0146 0.3815 0.000 0.000 0.004 0.000 0.000 0.996
#> GSM62322 1 0.0146 0.8291 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM62250 5 0.0717 0.7217 0.000 0.000 0.016 0.008 0.976 0.000
#> GSM62252 5 0.2074 0.6697 0.036 0.000 0.048 0.000 0.912 0.004
#> GSM62255 4 0.0363 0.7761 0.000 0.000 0.012 0.988 0.000 0.000
#> GSM62257 4 0.1657 0.7555 0.000 0.000 0.056 0.928 0.016 0.000
#> GSM62260 6 0.4076 -0.3872 0.016 0.000 0.364 0.000 0.000 0.620
#> GSM62261 4 0.5506 0.2734 0.000 0.000 0.180 0.556 0.264 0.000
#> GSM62262 4 0.3046 0.7137 0.000 0.000 0.188 0.800 0.012 0.000
#> GSM62264 6 0.4452 -0.5787 0.016 0.000 0.428 0.000 0.008 0.548
#> GSM62268 1 0.5437 0.3800 0.608 0.000 0.204 0.000 0.008 0.180
#> GSM62269 1 0.0146 0.8291 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM62271 1 0.0260 0.8284 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM62272 1 0.0146 0.8291 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM62273 2 0.6306 -0.0188 0.000 0.380 0.288 0.324 0.008 0.000
#> GSM62274 1 0.0000 0.8290 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM62275 1 0.0146 0.8291 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM62276 1 0.0000 0.8290 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM62277 1 0.0000 0.8290 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM62279 1 0.0820 0.8166 0.972 0.000 0.012 0.000 0.016 0.000
#> GSM62282 1 0.1327 0.7855 0.936 0.000 0.000 0.000 0.000 0.064
#> GSM62283 1 0.5127 0.1971 0.544 0.000 0.364 0.000 0.000 0.092
#> GSM62286 5 0.0551 0.7266 0.000 0.000 0.008 0.004 0.984 0.004
#> GSM62287 4 0.0291 0.7776 0.000 0.000 0.004 0.992 0.004 0.000
#> GSM62288 4 0.5728 0.0604 0.000 0.000 0.180 0.484 0.336 0.000
#> GSM62290 2 0.0146 0.9096 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM62293 4 0.3141 0.7078 0.000 0.000 0.200 0.788 0.012 0.000
#> GSM62301 2 0.0146 0.9096 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM62302 4 0.0363 0.7774 0.000 0.000 0.012 0.988 0.000 0.000
#> GSM62303 4 0.0935 0.7749 0.000 0.000 0.032 0.964 0.004 0.000
#> GSM62304 4 0.0806 0.7720 0.000 0.000 0.020 0.972 0.008 0.000
#> GSM62312 2 0.4178 0.6522 0.000 0.756 0.092 0.144 0.008 0.000
#> GSM62313 4 0.0146 0.7773 0.000 0.000 0.004 0.996 0.000 0.000
#> GSM62314 4 0.5287 0.3661 0.000 0.000 0.176 0.600 0.224 0.000
#> GSM62319 2 0.3290 0.6775 0.000 0.744 0.252 0.000 0.004 0.000
#> GSM62320 2 0.0363 0.9086 0.000 0.988 0.012 0.000 0.000 0.000
#> GSM62249 3 0.6387 0.0000 0.064 0.000 0.444 0.000 0.108 0.384
#> GSM62251 1 0.6120 -0.1323 0.436 0.000 0.344 0.000 0.008 0.212
#> GSM62263 6 0.5258 -0.5756 0.000 0.064 0.448 0.000 0.012 0.476
#> GSM62285 2 0.0000 0.9102 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62315 2 0.0000 0.9102 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62291 2 0.0000 0.9102 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62265 1 0.5806 0.1871 0.524 0.000 0.296 0.000 0.008 0.172
#> GSM62266 1 0.5866 0.1629 0.516 0.000 0.292 0.000 0.008 0.184
#> GSM62296 2 0.0363 0.9090 0.000 0.988 0.012 0.000 0.000 0.000
#> GSM62309 2 0.0260 0.9091 0.000 0.992 0.008 0.000 0.000 0.000
#> GSM62295 4 0.3394 0.6880 0.000 0.000 0.236 0.752 0.012 0.000
#> GSM62300 2 0.0363 0.9090 0.000 0.988 0.012 0.000 0.000 0.000
#> GSM62308 2 0.0260 0.9091 0.000 0.992 0.008 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) other(p) genotype/variation(p) k
#> MAD:skmeans 74 0.814696 1.000 0.7495 2
#> MAD:skmeans 73 0.001807 0.763 0.0348 3
#> MAD:skmeans 70 0.004230 0.911 0.1237 4
#> MAD:skmeans 67 0.007780 0.892 0.0535 5
#> MAD:skmeans 53 0.000895 0.891 0.2355 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "pam"]
# you can also extract it by
# res = res_list["MAD:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 75 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 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 0.969 0.987 0.4876 0.508 0.508
#> 3 3 0.647 0.224 0.654 0.2597 0.699 0.484
#> 4 4 0.943 0.923 0.969 0.1787 0.704 0.364
#> 5 5 0.900 0.831 0.914 0.0364 0.977 0.918
#> 6 6 0.851 0.842 0.917 0.0460 0.933 0.753
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
#> GSM62248 2 0.000 0.9989 0.000 1.000
#> GSM62256 2 0.000 0.9989 0.000 1.000
#> GSM62259 2 0.000 0.9989 0.000 1.000
#> GSM62267 1 0.000 0.9700 1.000 0.000
#> GSM62280 1 0.000 0.9700 1.000 0.000
#> GSM62284 1 0.000 0.9700 1.000 0.000
#> GSM62289 2 0.000 0.9989 0.000 1.000
#> GSM62307 2 0.000 0.9989 0.000 1.000
#> GSM62316 2 0.000 0.9989 0.000 1.000
#> GSM62254 2 0.000 0.9989 0.000 1.000
#> GSM62292 2 0.000 0.9989 0.000 1.000
#> GSM62253 1 0.000 0.9700 1.000 0.000
#> GSM62270 1 0.000 0.9700 1.000 0.000
#> GSM62278 1 0.000 0.9700 1.000 0.000
#> GSM62297 2 0.000 0.9989 0.000 1.000
#> GSM62298 2 0.000 0.9989 0.000 1.000
#> GSM62299 2 0.000 0.9989 0.000 1.000
#> GSM62258 1 0.000 0.9700 1.000 0.000
#> GSM62281 2 0.000 0.9989 0.000 1.000
#> GSM62294 2 0.000 0.9989 0.000 1.000
#> GSM62305 1 0.689 0.7762 0.816 0.184
#> GSM62306 2 0.000 0.9989 0.000 1.000
#> GSM62310 2 0.000 0.9989 0.000 1.000
#> GSM62311 2 0.000 0.9989 0.000 1.000
#> GSM62317 2 0.000 0.9989 0.000 1.000
#> GSM62318 1 0.000 0.9700 1.000 0.000
#> GSM62321 1 0.278 0.9322 0.952 0.048
#> GSM62322 1 0.000 0.9700 1.000 0.000
#> GSM62250 2 0.278 0.9481 0.048 0.952
#> GSM62252 1 0.482 0.8764 0.896 0.104
#> GSM62255 2 0.000 0.9989 0.000 1.000
#> GSM62257 2 0.000 0.9989 0.000 1.000
#> GSM62260 1 0.000 0.9700 1.000 0.000
#> GSM62261 2 0.000 0.9989 0.000 1.000
#> GSM62262 2 0.000 0.9989 0.000 1.000
#> GSM62264 1 0.000 0.9700 1.000 0.000
#> GSM62268 1 0.000 0.9700 1.000 0.000
#> GSM62269 1 0.000 0.9700 1.000 0.000
#> GSM62271 1 0.000 0.9700 1.000 0.000
#> GSM62272 1 0.000 0.9700 1.000 0.000
#> GSM62273 2 0.000 0.9989 0.000 1.000
#> GSM62274 1 0.000 0.9700 1.000 0.000
#> GSM62275 1 0.000 0.9700 1.000 0.000
#> GSM62276 1 0.000 0.9700 1.000 0.000
#> GSM62277 1 0.000 0.9700 1.000 0.000
#> GSM62279 1 0.000 0.9700 1.000 0.000
#> GSM62282 1 0.000 0.9700 1.000 0.000
#> GSM62283 1 0.000 0.9700 1.000 0.000
#> GSM62286 2 0.000 0.9989 0.000 1.000
#> GSM62287 2 0.000 0.9989 0.000 1.000
#> GSM62288 2 0.000 0.9989 0.000 1.000
#> GSM62290 2 0.000 0.9989 0.000 1.000
#> GSM62293 2 0.000 0.9989 0.000 1.000
#> GSM62301 2 0.000 0.9989 0.000 1.000
#> GSM62302 2 0.000 0.9989 0.000 1.000
#> GSM62303 2 0.000 0.9989 0.000 1.000
#> GSM62304 2 0.000 0.9989 0.000 1.000
#> GSM62312 2 0.000 0.9989 0.000 1.000
#> GSM62313 2 0.000 0.9989 0.000 1.000
#> GSM62314 2 0.000 0.9989 0.000 1.000
#> GSM62319 1 0.999 0.0844 0.516 0.484
#> GSM62320 2 0.000 0.9989 0.000 1.000
#> GSM62249 1 0.000 0.9700 1.000 0.000
#> GSM62251 1 0.000 0.9700 1.000 0.000
#> GSM62263 1 0.373 0.9111 0.928 0.072
#> GSM62285 2 0.000 0.9989 0.000 1.000
#> GSM62315 2 0.000 0.9989 0.000 1.000
#> GSM62291 2 0.000 0.9989 0.000 1.000
#> GSM62265 1 0.000 0.9700 1.000 0.000
#> GSM62266 1 0.000 0.9700 1.000 0.000
#> GSM62296 2 0.000 0.9989 0.000 1.000
#> GSM62309 2 0.000 0.9989 0.000 1.000
#> GSM62295 2 0.000 0.9989 0.000 1.000
#> GSM62300 2 0.000 0.9989 0.000 1.000
#> GSM62308 2 0.000 0.9989 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM62248 2 0.6309 0.3636 0.500 0.500 0.000
#> GSM62256 2 0.6309 0.3636 0.500 0.500 0.000
#> GSM62259 2 0.6309 0.3636 0.500 0.500 0.000
#> GSM62267 1 0.6309 -0.7144 0.500 0.000 0.500
#> GSM62280 3 0.6309 0.6825 0.500 0.000 0.500
#> GSM62284 3 0.5254 0.7102 0.264 0.000 0.736
#> GSM62289 2 0.6309 0.3636 0.500 0.500 0.000
#> GSM62307 2 0.6309 0.3636 0.500 0.500 0.000
#> GSM62316 2 0.6309 0.3636 0.500 0.500 0.000
#> GSM62254 2 0.6309 0.3636 0.500 0.500 0.000
#> GSM62292 2 0.6309 0.3636 0.500 0.500 0.000
#> GSM62253 1 0.6309 -0.7144 0.500 0.000 0.500
#> GSM62270 3 0.0000 0.6999 0.000 0.000 1.000
#> GSM62278 3 0.0000 0.6999 0.000 0.000 1.000
#> GSM62297 2 0.0000 0.5367 0.000 1.000 0.000
#> GSM62298 2 0.0000 0.5367 0.000 1.000 0.000
#> GSM62299 2 0.0000 0.5367 0.000 1.000 0.000
#> GSM62258 3 0.6309 0.6825 0.500 0.000 0.500
#> GSM62281 2 0.5678 0.4593 0.316 0.684 0.000
#> GSM62294 1 0.6309 -0.4108 0.500 0.500 0.000
#> GSM62305 2 0.6489 -0.1862 0.456 0.540 0.004
#> GSM62306 1 0.6309 -0.4108 0.500 0.500 0.000
#> GSM62310 2 0.6309 0.3636 0.500 0.500 0.000
#> GSM62311 2 0.6309 0.3636 0.500 0.500 0.000
#> GSM62317 2 0.0000 0.5367 0.000 1.000 0.000
#> GSM62318 3 0.6309 0.6825 0.500 0.000 0.500
#> GSM62321 1 0.8859 -0.3085 0.500 0.376 0.124
#> GSM62322 3 0.0000 0.6999 0.000 0.000 1.000
#> GSM62250 1 0.6669 -0.3880 0.524 0.468 0.008
#> GSM62252 1 0.2165 -0.0917 0.936 0.000 0.064
#> GSM62255 1 0.6309 -0.4108 0.500 0.500 0.000
#> GSM62257 2 0.6309 0.3636 0.500 0.500 0.000
#> GSM62260 1 0.9372 -0.3900 0.500 0.300 0.200
#> GSM62261 1 0.6309 -0.4108 0.500 0.500 0.000
#> GSM62262 1 0.6309 -0.4108 0.500 0.500 0.000
#> GSM62264 1 0.7979 -0.6560 0.500 0.060 0.440
#> GSM62268 3 0.6309 0.6825 0.500 0.000 0.500
#> GSM62269 3 0.0000 0.6999 0.000 0.000 1.000
#> GSM62271 3 0.6309 0.6825 0.500 0.000 0.500
#> GSM62272 3 0.0000 0.6999 0.000 0.000 1.000
#> GSM62273 2 0.0000 0.5367 0.000 1.000 0.000
#> GSM62274 3 0.2878 0.7074 0.096 0.000 0.904
#> GSM62275 3 0.0000 0.6999 0.000 0.000 1.000
#> GSM62276 3 0.6309 0.6825 0.500 0.000 0.500
#> GSM62277 3 0.0000 0.6999 0.000 0.000 1.000
#> GSM62279 1 0.6309 -0.7144 0.500 0.000 0.500
#> GSM62282 3 0.5882 0.6990 0.348 0.000 0.652
#> GSM62283 1 0.8310 -0.6363 0.500 0.080 0.420
#> GSM62286 2 0.6309 0.3636 0.500 0.500 0.000
#> GSM62287 1 0.6309 -0.4108 0.500 0.500 0.000
#> GSM62288 2 0.6309 0.3636 0.500 0.500 0.000
#> GSM62290 2 0.0000 0.5367 0.000 1.000 0.000
#> GSM62293 2 0.6309 0.3636 0.500 0.500 0.000
#> GSM62301 2 0.0000 0.5367 0.000 1.000 0.000
#> GSM62302 1 0.6309 -0.4108 0.500 0.500 0.000
#> GSM62303 1 0.6309 -0.4108 0.500 0.500 0.000
#> GSM62304 2 0.6309 0.3636 0.500 0.500 0.000
#> GSM62312 2 0.6309 0.3659 0.496 0.504 0.000
#> GSM62313 1 0.6309 -0.4108 0.500 0.500 0.000
#> GSM62314 1 0.6309 -0.4108 0.500 0.500 0.000
#> GSM62319 2 0.6309 -0.2579 0.500 0.500 0.000
#> GSM62320 2 0.4887 0.4908 0.228 0.772 0.000
#> GSM62249 1 0.8936 -0.3161 0.500 0.368 0.132
#> GSM62251 3 0.6309 0.6825 0.500 0.000 0.500
#> GSM62263 2 0.6309 -0.2579 0.500 0.500 0.000
#> GSM62285 2 0.0000 0.5367 0.000 1.000 0.000
#> GSM62315 2 0.0000 0.5367 0.000 1.000 0.000
#> GSM62291 2 0.0000 0.5367 0.000 1.000 0.000
#> GSM62265 1 0.6309 -0.7144 0.500 0.000 0.500
#> GSM62266 3 0.6309 0.6825 0.500 0.000 0.500
#> GSM62296 2 0.0000 0.5367 0.000 1.000 0.000
#> GSM62309 2 0.0424 0.5284 0.008 0.992 0.000
#> GSM62295 2 0.5363 0.4754 0.276 0.724 0.000
#> GSM62300 2 0.0000 0.5367 0.000 1.000 0.000
#> GSM62308 2 0.0000 0.5367 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM62248 4 0.0000 0.977 0.000 0.000 0.000 1.000
#> GSM62256 4 0.0000 0.977 0.000 0.000 0.000 1.000
#> GSM62259 4 0.0000 0.977 0.000 0.000 0.000 1.000
#> GSM62267 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM62280 1 0.0592 0.961 0.984 0.000 0.016 0.000
#> GSM62284 1 0.4431 0.534 0.696 0.000 0.304 0.000
#> GSM62289 4 0.0000 0.977 0.000 0.000 0.000 1.000
#> GSM62307 4 0.0000 0.977 0.000 0.000 0.000 1.000
#> GSM62316 4 0.0000 0.977 0.000 0.000 0.000 1.000
#> GSM62254 4 0.0000 0.977 0.000 0.000 0.000 1.000
#> GSM62292 4 0.0000 0.977 0.000 0.000 0.000 1.000
#> GSM62253 1 0.0592 0.961 0.984 0.000 0.016 0.000
#> GSM62270 3 0.0000 0.932 0.000 0.000 1.000 0.000
#> GSM62278 3 0.0000 0.932 0.000 0.000 1.000 0.000
#> GSM62297 2 0.0000 0.947 0.000 1.000 0.000 0.000
#> GSM62298 2 0.0000 0.947 0.000 1.000 0.000 0.000
#> GSM62299 2 0.0000 0.947 0.000 1.000 0.000 0.000
#> GSM62258 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM62281 4 0.2530 0.860 0.000 0.112 0.000 0.888
#> GSM62294 4 0.0000 0.977 0.000 0.000 0.000 1.000
#> GSM62305 2 0.2469 0.843 0.108 0.892 0.000 0.000
#> GSM62306 4 0.0000 0.977 0.000 0.000 0.000 1.000
#> GSM62310 4 0.0000 0.977 0.000 0.000 0.000 1.000
#> GSM62311 4 0.0000 0.977 0.000 0.000 0.000 1.000
#> GSM62317 2 0.0000 0.947 0.000 1.000 0.000 0.000
#> GSM62318 1 0.0592 0.961 0.984 0.000 0.016 0.000
#> GSM62321 2 0.4746 0.445 0.368 0.632 0.000 0.000
#> GSM62322 3 0.0000 0.932 0.000 0.000 1.000 0.000
#> GSM62250 4 0.2011 0.892 0.080 0.000 0.000 0.920
#> GSM62252 1 0.1940 0.872 0.924 0.000 0.000 0.076
#> GSM62255 4 0.0000 0.977 0.000 0.000 0.000 1.000
#> GSM62257 4 0.0000 0.977 0.000 0.000 0.000 1.000
#> GSM62260 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM62261 4 0.0000 0.977 0.000 0.000 0.000 1.000
#> GSM62262 4 0.0000 0.977 0.000 0.000 0.000 1.000
#> GSM62264 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM62268 1 0.0592 0.961 0.984 0.000 0.016 0.000
#> GSM62269 3 0.0000 0.932 0.000 0.000 1.000 0.000
#> GSM62271 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM62272 3 0.0000 0.932 0.000 0.000 1.000 0.000
#> GSM62273 2 0.0188 0.943 0.000 0.996 0.000 0.004
#> GSM62274 3 0.3610 0.734 0.200 0.000 0.800 0.000
#> GSM62275 3 0.0000 0.932 0.000 0.000 1.000 0.000
#> GSM62276 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM62277 3 0.0000 0.932 0.000 0.000 1.000 0.000
#> GSM62279 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM62282 3 0.4431 0.560 0.304 0.000 0.696 0.000
#> GSM62283 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM62286 4 0.0469 0.966 0.000 0.012 0.000 0.988
#> GSM62287 4 0.0000 0.977 0.000 0.000 0.000 1.000
#> GSM62288 4 0.0000 0.977 0.000 0.000 0.000 1.000
#> GSM62290 2 0.0000 0.947 0.000 1.000 0.000 0.000
#> GSM62293 4 0.0000 0.977 0.000 0.000 0.000 1.000
#> GSM62301 2 0.0000 0.947 0.000 1.000 0.000 0.000
#> GSM62302 4 0.0000 0.977 0.000 0.000 0.000 1.000
#> GSM62303 4 0.0000 0.977 0.000 0.000 0.000 1.000
#> GSM62304 4 0.0000 0.977 0.000 0.000 0.000 1.000
#> GSM62312 4 0.0336 0.970 0.000 0.008 0.000 0.992
#> GSM62313 4 0.0000 0.977 0.000 0.000 0.000 1.000
#> GSM62314 4 0.0000 0.977 0.000 0.000 0.000 1.000
#> GSM62319 2 0.0000 0.947 0.000 1.000 0.000 0.000
#> GSM62320 4 0.4761 0.409 0.000 0.372 0.000 0.628
#> GSM62249 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM62251 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM62263 2 0.0817 0.928 0.024 0.976 0.000 0.000
#> GSM62285 2 0.0000 0.947 0.000 1.000 0.000 0.000
#> GSM62315 2 0.0000 0.947 0.000 1.000 0.000 0.000
#> GSM62291 2 0.0000 0.947 0.000 1.000 0.000 0.000
#> GSM62265 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM62266 1 0.0000 0.969 1.000 0.000 0.000 0.000
#> GSM62296 2 0.0000 0.947 0.000 1.000 0.000 0.000
#> GSM62309 2 0.0000 0.947 0.000 1.000 0.000 0.000
#> GSM62295 2 0.4304 0.577 0.000 0.716 0.000 0.284
#> GSM62300 2 0.0000 0.947 0.000 1.000 0.000 0.000
#> GSM62308 2 0.0000 0.947 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM62248 4 0.0000 0.978 0.000 0.000 0.000 1.000 0.000
#> GSM62256 4 0.0000 0.978 0.000 0.000 0.000 1.000 0.000
#> GSM62259 4 0.0000 0.978 0.000 0.000 0.000 1.000 0.000
#> GSM62267 1 0.0000 0.707 1.000 0.000 0.000 0.000 0.000
#> GSM62280 5 0.4088 0.697 0.368 0.000 0.000 0.000 0.632
#> GSM62284 1 0.6728 0.346 0.380 0.000 0.252 0.000 0.368
#> GSM62289 4 0.0000 0.978 0.000 0.000 0.000 1.000 0.000
#> GSM62307 4 0.0000 0.978 0.000 0.000 0.000 1.000 0.000
#> GSM62316 4 0.0000 0.978 0.000 0.000 0.000 1.000 0.000
#> GSM62254 4 0.0000 0.978 0.000 0.000 0.000 1.000 0.000
#> GSM62292 4 0.0000 0.978 0.000 0.000 0.000 1.000 0.000
#> GSM62253 1 0.4088 0.673 0.632 0.000 0.000 0.000 0.368
#> GSM62270 3 0.0000 0.943 0.000 0.000 1.000 0.000 0.000
#> GSM62278 3 0.0000 0.943 0.000 0.000 1.000 0.000 0.000
#> GSM62297 2 0.0000 0.913 0.000 1.000 0.000 0.000 0.000
#> GSM62298 2 0.0000 0.913 0.000 1.000 0.000 0.000 0.000
#> GSM62299 2 0.0000 0.913 0.000 1.000 0.000 0.000 0.000
#> GSM62258 1 0.0000 0.707 1.000 0.000 0.000 0.000 0.000
#> GSM62281 4 0.1270 0.925 0.000 0.052 0.000 0.948 0.000
#> GSM62294 4 0.0000 0.978 0.000 0.000 0.000 1.000 0.000
#> GSM62305 2 0.4171 0.264 0.396 0.604 0.000 0.000 0.000
#> GSM62306 4 0.0000 0.978 0.000 0.000 0.000 1.000 0.000
#> GSM62310 4 0.0000 0.978 0.000 0.000 0.000 1.000 0.000
#> GSM62311 4 0.0000 0.978 0.000 0.000 0.000 1.000 0.000
#> GSM62317 2 0.4273 0.155 0.000 0.552 0.000 0.000 0.448
#> GSM62318 5 0.0000 0.483 0.000 0.000 0.000 0.000 1.000
#> GSM62321 5 0.5670 0.639 0.192 0.176 0.000 0.000 0.632
#> GSM62322 3 0.0000 0.943 0.000 0.000 1.000 0.000 0.000
#> GSM62250 4 0.2020 0.870 0.100 0.000 0.000 0.900 0.000
#> GSM62252 1 0.1671 0.618 0.924 0.000 0.000 0.076 0.000
#> GSM62255 4 0.0000 0.978 0.000 0.000 0.000 1.000 0.000
#> GSM62257 4 0.0000 0.978 0.000 0.000 0.000 1.000 0.000
#> GSM62260 1 0.0794 0.685 0.972 0.000 0.000 0.000 0.028
#> GSM62261 4 0.0000 0.978 0.000 0.000 0.000 1.000 0.000
#> GSM62262 4 0.0000 0.978 0.000 0.000 0.000 1.000 0.000
#> GSM62264 1 0.4088 0.673 0.632 0.000 0.000 0.000 0.368
#> GSM62268 1 0.4238 0.670 0.628 0.000 0.004 0.000 0.368
#> GSM62269 3 0.0000 0.943 0.000 0.000 1.000 0.000 0.000
#> GSM62271 1 0.0000 0.707 1.000 0.000 0.000 0.000 0.000
#> GSM62272 3 0.0000 0.943 0.000 0.000 1.000 0.000 0.000
#> GSM62273 2 0.0162 0.909 0.000 0.996 0.000 0.004 0.000
#> GSM62274 3 0.5670 0.472 0.176 0.000 0.632 0.000 0.192
#> GSM62275 3 0.0000 0.943 0.000 0.000 1.000 0.000 0.000
#> GSM62276 1 0.0000 0.707 1.000 0.000 0.000 0.000 0.000
#> GSM62277 3 0.0000 0.943 0.000 0.000 1.000 0.000 0.000
#> GSM62279 1 0.3039 0.694 0.808 0.000 0.000 0.000 0.192
#> GSM62282 5 0.4800 0.694 0.368 0.000 0.028 0.000 0.604
#> GSM62283 1 0.0000 0.707 1.000 0.000 0.000 0.000 0.000
#> GSM62286 4 0.0404 0.967 0.000 0.012 0.000 0.988 0.000
#> GSM62287 4 0.0000 0.978 0.000 0.000 0.000 1.000 0.000
#> GSM62288 4 0.0000 0.978 0.000 0.000 0.000 1.000 0.000
#> GSM62290 2 0.0000 0.913 0.000 1.000 0.000 0.000 0.000
#> GSM62293 4 0.0000 0.978 0.000 0.000 0.000 1.000 0.000
#> GSM62301 2 0.0000 0.913 0.000 1.000 0.000 0.000 0.000
#> GSM62302 4 0.0000 0.978 0.000 0.000 0.000 1.000 0.000
#> GSM62303 4 0.0000 0.978 0.000 0.000 0.000 1.000 0.000
#> GSM62304 4 0.0000 0.978 0.000 0.000 0.000 1.000 0.000
#> GSM62312 4 0.0290 0.971 0.000 0.008 0.000 0.992 0.000
#> GSM62313 4 0.0000 0.978 0.000 0.000 0.000 1.000 0.000
#> GSM62314 4 0.0000 0.978 0.000 0.000 0.000 1.000 0.000
#> GSM62319 2 0.0000 0.913 0.000 1.000 0.000 0.000 0.000
#> GSM62320 4 0.4045 0.437 0.000 0.356 0.000 0.644 0.000
#> GSM62249 1 0.2852 0.565 0.828 0.172 0.000 0.000 0.000
#> GSM62251 1 0.4088 0.673 0.632 0.000 0.000 0.000 0.368
#> GSM62263 2 0.0794 0.886 0.028 0.972 0.000 0.000 0.000
#> GSM62285 2 0.0000 0.913 0.000 1.000 0.000 0.000 0.000
#> GSM62315 2 0.0000 0.913 0.000 1.000 0.000 0.000 0.000
#> GSM62291 2 0.0000 0.913 0.000 1.000 0.000 0.000 0.000
#> GSM62265 1 0.2891 0.697 0.824 0.000 0.000 0.000 0.176
#> GSM62266 1 0.4088 0.673 0.632 0.000 0.000 0.000 0.368
#> GSM62296 2 0.0000 0.913 0.000 1.000 0.000 0.000 0.000
#> GSM62309 2 0.0000 0.913 0.000 1.000 0.000 0.000 0.000
#> GSM62295 2 0.3730 0.474 0.000 0.712 0.000 0.288 0.000
#> GSM62300 2 0.0000 0.913 0.000 1.000 0.000 0.000 0.000
#> GSM62308 2 0.0000 0.913 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM62248 4 0.2793 0.8404 0.000 0.000 0.000 0.800 0.200 0.000
#> GSM62256 4 0.2416 0.8692 0.000 0.000 0.000 0.844 0.156 0.000
#> GSM62259 4 0.0000 0.9221 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62267 5 0.2883 0.7167 0.212 0.000 0.000 0.000 0.788 0.000
#> GSM62280 6 0.0000 0.8441 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM62284 1 0.2697 0.6959 0.812 0.000 0.188 0.000 0.000 0.000
#> GSM62289 4 0.2883 0.8306 0.000 0.000 0.000 0.788 0.212 0.000
#> GSM62307 4 0.0000 0.9221 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62316 4 0.2416 0.8692 0.000 0.000 0.000 0.844 0.156 0.000
#> GSM62254 4 0.0000 0.9221 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62292 4 0.0000 0.9221 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62253 1 0.0000 0.9423 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM62270 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62278 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62297 2 0.0000 0.9721 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62298 2 0.0000 0.9721 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62299 2 0.0000 0.9721 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62258 5 0.2793 0.7175 0.200 0.000 0.000 0.000 0.800 0.000
#> GSM62281 4 0.3210 0.8517 0.000 0.036 0.000 0.812 0.152 0.000
#> GSM62294 4 0.0000 0.9221 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62305 5 0.0790 0.6143 0.000 0.032 0.000 0.000 0.968 0.000
#> GSM62306 4 0.2562 0.8607 0.000 0.000 0.000 0.828 0.172 0.000
#> GSM62310 4 0.0000 0.9221 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62311 4 0.0000 0.9221 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62317 6 0.1610 0.7845 0.000 0.084 0.000 0.000 0.000 0.916
#> GSM62318 6 0.0000 0.8441 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM62321 6 0.0000 0.8441 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM62322 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62250 5 0.2762 0.4063 0.000 0.000 0.000 0.196 0.804 0.000
#> GSM62252 5 0.0000 0.6225 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM62255 4 0.0000 0.9221 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62257 4 0.0000 0.9221 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62260 6 0.5488 0.2599 0.216 0.000 0.000 0.000 0.216 0.568
#> GSM62261 4 0.2219 0.8789 0.000 0.000 0.000 0.864 0.136 0.000
#> GSM62262 4 0.0000 0.9221 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62264 1 0.0000 0.9423 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM62268 1 0.0000 0.9423 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM62269 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62271 5 0.2912 0.7146 0.216 0.000 0.000 0.000 0.784 0.000
#> GSM62272 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62273 2 0.0000 0.9721 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62274 5 0.5419 0.0824 0.116 0.000 0.424 0.000 0.460 0.000
#> GSM62275 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62276 5 0.2883 0.7167 0.212 0.000 0.000 0.000 0.788 0.000
#> GSM62277 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62279 5 0.3101 0.6943 0.244 0.000 0.000 0.000 0.756 0.000
#> GSM62282 5 0.3817 0.2125 0.000 0.000 0.000 0.000 0.568 0.432
#> GSM62283 5 0.2883 0.7167 0.212 0.000 0.000 0.000 0.788 0.000
#> GSM62286 4 0.3133 0.8250 0.000 0.008 0.000 0.780 0.212 0.000
#> GSM62287 4 0.0000 0.9221 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62288 4 0.2416 0.8692 0.000 0.000 0.000 0.844 0.156 0.000
#> GSM62290 2 0.0000 0.9721 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62293 4 0.0000 0.9221 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62301 2 0.0000 0.9721 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62302 4 0.0000 0.9221 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62303 4 0.0000 0.9221 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62304 4 0.0000 0.9221 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62312 4 0.0146 0.9204 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM62313 4 0.0000 0.9221 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62314 4 0.2135 0.8822 0.000 0.000 0.000 0.872 0.128 0.000
#> GSM62319 2 0.0000 0.9721 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62320 4 0.3634 0.4575 0.000 0.356 0.000 0.644 0.000 0.000
#> GSM62249 5 0.6002 0.2744 0.236 0.368 0.000 0.000 0.396 0.000
#> GSM62251 1 0.0000 0.9423 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM62263 2 0.0632 0.9471 0.000 0.976 0.000 0.000 0.024 0.000
#> GSM62285 2 0.0000 0.9721 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62315 2 0.0000 0.9721 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62291 2 0.0000 0.9721 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62265 1 0.1075 0.8931 0.952 0.000 0.000 0.000 0.048 0.000
#> GSM62266 1 0.0000 0.9423 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM62296 2 0.0000 0.9721 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62309 2 0.0000 0.9721 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62295 2 0.3351 0.5471 0.000 0.712 0.000 0.288 0.000 0.000
#> GSM62300 2 0.0000 0.9721 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62308 2 0.0000 0.9721 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) other(p) genotype/variation(p) k
#> MAD:pam 74 1.00e+00 0.964 0.6606 2
#> MAD:pam 32 4.23e-02 0.653 0.3681 3
#> MAD:pam 73 1.05e-04 0.524 0.0692 4
#> MAD:pam 68 1.89e-04 0.864 0.1062 5
#> MAD:pam 69 1.72e-05 0.318 0.2467 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "mclust"]
# you can also extract it by
# res = res_list["MAD:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 75 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.993 0.997 0.4661 0.533 0.533
#> 3 3 0.542 0.658 0.767 0.2682 0.930 0.871
#> 4 4 0.682 0.829 0.895 0.1163 0.792 0.589
#> 5 5 0.709 0.793 0.815 0.1354 0.827 0.517
#> 6 6 0.715 0.803 0.856 0.0667 0.947 0.763
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
#> GSM62248 2 0.0376 0.997 0.004 0.996
#> GSM62256 2 0.0000 0.999 0.000 1.000
#> GSM62259 2 0.0000 0.999 0.000 1.000
#> GSM62267 1 0.0000 0.992 1.000 0.000
#> GSM62280 1 0.0000 0.992 1.000 0.000
#> GSM62284 1 0.0000 0.992 1.000 0.000
#> GSM62289 2 0.0376 0.997 0.004 0.996
#> GSM62307 2 0.0000 0.999 0.000 1.000
#> GSM62316 2 0.0000 0.999 0.000 1.000
#> GSM62254 2 0.0000 0.999 0.000 1.000
#> GSM62292 2 0.0000 0.999 0.000 1.000
#> GSM62253 1 0.0000 0.992 1.000 0.000
#> GSM62270 1 0.0000 0.992 1.000 0.000
#> GSM62278 1 0.0000 0.992 1.000 0.000
#> GSM62297 2 0.0000 0.999 0.000 1.000
#> GSM62298 2 0.0000 0.999 0.000 1.000
#> GSM62299 2 0.0000 0.999 0.000 1.000
#> GSM62258 1 0.0000 0.992 1.000 0.000
#> GSM62281 2 0.0000 0.999 0.000 1.000
#> GSM62294 2 0.0000 0.999 0.000 1.000
#> GSM62305 2 0.0376 0.997 0.004 0.996
#> GSM62306 2 0.0000 0.999 0.000 1.000
#> GSM62310 2 0.0000 0.999 0.000 1.000
#> GSM62311 2 0.0000 0.999 0.000 1.000
#> GSM62317 2 0.0000 0.999 0.000 1.000
#> GSM62318 1 0.0000 0.992 1.000 0.000
#> GSM62321 1 0.0000 0.992 1.000 0.000
#> GSM62322 1 0.0000 0.992 1.000 0.000
#> GSM62250 2 0.0376 0.997 0.004 0.996
#> GSM62252 2 0.0376 0.997 0.004 0.996
#> GSM62255 2 0.0000 0.999 0.000 1.000
#> GSM62257 2 0.0000 0.999 0.000 1.000
#> GSM62260 1 0.0000 0.992 1.000 0.000
#> GSM62261 2 0.0000 0.999 0.000 1.000
#> GSM62262 2 0.0000 0.999 0.000 1.000
#> GSM62264 1 0.0000 0.992 1.000 0.000
#> GSM62268 1 0.0000 0.992 1.000 0.000
#> GSM62269 1 0.0000 0.992 1.000 0.000
#> GSM62271 1 0.0000 0.992 1.000 0.000
#> GSM62272 1 0.0000 0.992 1.000 0.000
#> GSM62273 2 0.0000 0.999 0.000 1.000
#> GSM62274 1 0.0000 0.992 1.000 0.000
#> GSM62275 1 0.0000 0.992 1.000 0.000
#> GSM62276 1 0.0000 0.992 1.000 0.000
#> GSM62277 1 0.0000 0.992 1.000 0.000
#> GSM62279 1 0.0000 0.992 1.000 0.000
#> GSM62282 1 0.0000 0.992 1.000 0.000
#> GSM62283 1 0.0000 0.992 1.000 0.000
#> GSM62286 2 0.0376 0.997 0.004 0.996
#> GSM62287 2 0.0000 0.999 0.000 1.000
#> GSM62288 2 0.0000 0.999 0.000 1.000
#> GSM62290 2 0.0000 0.999 0.000 1.000
#> GSM62293 2 0.0000 0.999 0.000 1.000
#> GSM62301 2 0.0000 0.999 0.000 1.000
#> GSM62302 2 0.0000 0.999 0.000 1.000
#> GSM62303 2 0.0000 0.999 0.000 1.000
#> GSM62304 2 0.0000 0.999 0.000 1.000
#> GSM62312 2 0.0000 0.999 0.000 1.000
#> GSM62313 2 0.0000 0.999 0.000 1.000
#> GSM62314 2 0.0000 0.999 0.000 1.000
#> GSM62319 2 0.0376 0.997 0.004 0.996
#> GSM62320 2 0.0000 0.999 0.000 1.000
#> GSM62249 1 0.7299 0.743 0.796 0.204
#> GSM62251 1 0.0000 0.992 1.000 0.000
#> GSM62263 2 0.0376 0.997 0.004 0.996
#> GSM62285 2 0.0000 0.999 0.000 1.000
#> GSM62315 2 0.0000 0.999 0.000 1.000
#> GSM62291 2 0.0000 0.999 0.000 1.000
#> GSM62265 1 0.0000 0.992 1.000 0.000
#> GSM62266 1 0.0000 0.992 1.000 0.000
#> GSM62296 2 0.0000 0.999 0.000 1.000
#> GSM62309 2 0.0000 0.999 0.000 1.000
#> GSM62295 2 0.0000 0.999 0.000 1.000
#> GSM62300 2 0.0000 0.999 0.000 1.000
#> GSM62308 2 0.0000 0.999 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM62248 2 0.6228 0.610 0.316 0.672 0.012
#> GSM62256 2 0.3967 0.796 0.044 0.884 0.072
#> GSM62259 2 0.0000 0.813 0.000 1.000 0.000
#> GSM62267 1 0.0000 0.636 1.000 0.000 0.000
#> GSM62280 1 0.5678 0.188 0.684 0.000 0.316
#> GSM62284 1 0.3816 0.576 0.852 0.000 0.148
#> GSM62289 2 0.6228 0.610 0.316 0.672 0.012
#> GSM62307 2 0.1753 0.812 0.000 0.952 0.048
#> GSM62316 2 0.5884 0.655 0.272 0.716 0.012
#> GSM62254 2 0.4887 0.760 0.000 0.772 0.228
#> GSM62292 2 0.4750 0.766 0.000 0.784 0.216
#> GSM62253 1 0.2625 0.638 0.916 0.000 0.084
#> GSM62270 3 0.5905 0.996 0.352 0.000 0.648
#> GSM62278 3 0.5948 0.982 0.360 0.000 0.640
#> GSM62297 2 0.6228 0.610 0.316 0.672 0.012
#> GSM62298 2 0.0237 0.813 0.000 0.996 0.004
#> GSM62299 2 0.0848 0.813 0.008 0.984 0.008
#> GSM62258 1 0.0000 0.636 1.000 0.000 0.000
#> GSM62281 2 0.2261 0.805 0.000 0.932 0.068
#> GSM62294 2 0.5098 0.747 0.000 0.752 0.248
#> GSM62305 2 0.6228 0.610 0.316 0.672 0.012
#> GSM62306 2 0.6172 0.619 0.308 0.680 0.012
#> GSM62310 2 0.4750 0.764 0.000 0.784 0.216
#> GSM62311 2 0.5098 0.747 0.000 0.752 0.248
#> GSM62317 2 0.2356 0.792 0.072 0.928 0.000
#> GSM62318 1 0.5678 0.188 0.684 0.000 0.316
#> GSM62321 1 0.5678 0.188 0.684 0.000 0.316
#> GSM62322 3 0.5905 0.996 0.352 0.000 0.648
#> GSM62250 2 0.6282 0.602 0.324 0.664 0.012
#> GSM62252 2 0.6688 0.455 0.408 0.580 0.012
#> GSM62255 2 0.4452 0.775 0.000 0.808 0.192
#> GSM62257 2 0.5239 0.789 0.032 0.808 0.160
#> GSM62260 1 0.4702 0.468 0.788 0.000 0.212
#> GSM62261 2 0.6228 0.610 0.316 0.672 0.012
#> GSM62262 2 0.5098 0.747 0.000 0.752 0.248
#> GSM62264 1 0.3816 0.577 0.852 0.000 0.148
#> GSM62268 1 0.2625 0.638 0.916 0.000 0.084
#> GSM62269 3 0.5905 0.996 0.352 0.000 0.648
#> GSM62271 1 0.5621 0.216 0.692 0.000 0.308
#> GSM62272 3 0.5905 0.996 0.352 0.000 0.648
#> GSM62273 2 0.0424 0.813 0.008 0.992 0.000
#> GSM62274 1 0.5254 0.370 0.736 0.000 0.264
#> GSM62275 3 0.5905 0.996 0.352 0.000 0.648
#> GSM62276 1 0.0000 0.636 1.000 0.000 0.000
#> GSM62277 1 0.6308 -0.588 0.508 0.000 0.492
#> GSM62279 1 0.0000 0.636 1.000 0.000 0.000
#> GSM62282 1 0.6062 -0.120 0.616 0.000 0.384
#> GSM62283 1 0.0000 0.636 1.000 0.000 0.000
#> GSM62286 2 0.6228 0.610 0.316 0.672 0.012
#> GSM62287 2 0.5098 0.747 0.000 0.752 0.248
#> GSM62288 2 0.6228 0.610 0.316 0.672 0.012
#> GSM62290 2 0.0424 0.813 0.000 0.992 0.008
#> GSM62293 2 0.4887 0.760 0.000 0.772 0.228
#> GSM62301 2 0.0424 0.813 0.000 0.992 0.008
#> GSM62302 2 0.5098 0.747 0.000 0.752 0.248
#> GSM62303 2 0.5098 0.747 0.000 0.752 0.248
#> GSM62304 2 0.5016 0.752 0.000 0.760 0.240
#> GSM62312 2 0.0747 0.812 0.016 0.984 0.000
#> GSM62313 2 0.5098 0.747 0.000 0.752 0.248
#> GSM62314 2 0.5884 0.655 0.272 0.716 0.012
#> GSM62319 2 0.2356 0.792 0.072 0.928 0.000
#> GSM62320 2 0.0424 0.813 0.000 0.992 0.008
#> GSM62249 1 0.2448 0.531 0.924 0.076 0.000
#> GSM62251 1 0.0000 0.636 1.000 0.000 0.000
#> GSM62263 1 0.6308 -0.315 0.508 0.492 0.000
#> GSM62285 2 0.0424 0.813 0.000 0.992 0.008
#> GSM62315 2 0.2356 0.792 0.072 0.928 0.000
#> GSM62291 2 0.2356 0.803 0.000 0.928 0.072
#> GSM62265 1 0.2356 0.640 0.928 0.000 0.072
#> GSM62266 1 0.2625 0.638 0.916 0.000 0.084
#> GSM62296 2 0.2356 0.803 0.000 0.928 0.072
#> GSM62309 2 0.2496 0.794 0.068 0.928 0.004
#> GSM62295 2 0.3752 0.793 0.000 0.856 0.144
#> GSM62300 2 0.2356 0.803 0.000 0.928 0.072
#> GSM62308 2 0.2356 0.803 0.000 0.928 0.072
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM62248 2 0.2156 0.872 0.008 0.928 0.060 0.004
#> GSM62256 2 0.1398 0.876 0.000 0.956 0.040 0.004
#> GSM62259 2 0.0921 0.873 0.000 0.972 0.000 0.028
#> GSM62267 1 0.0000 0.942 1.000 0.000 0.000 0.000
#> GSM62280 1 0.1022 0.933 0.968 0.000 0.000 0.032
#> GSM62284 1 0.0336 0.940 0.992 0.000 0.008 0.000
#> GSM62289 2 0.2101 0.872 0.012 0.928 0.060 0.000
#> GSM62307 2 0.1716 0.849 0.000 0.936 0.000 0.064
#> GSM62316 2 0.1824 0.873 0.000 0.936 0.060 0.004
#> GSM62254 4 0.2149 0.689 0.000 0.088 0.000 0.912
#> GSM62292 4 0.2149 0.689 0.000 0.088 0.000 0.912
#> GSM62253 1 0.0000 0.942 1.000 0.000 0.000 0.000
#> GSM62270 3 0.2469 0.990 0.108 0.000 0.892 0.000
#> GSM62278 1 0.4955 0.109 0.556 0.000 0.444 0.000
#> GSM62297 2 0.1890 0.875 0.008 0.936 0.056 0.000
#> GSM62298 2 0.1022 0.872 0.000 0.968 0.000 0.032
#> GSM62299 2 0.1118 0.878 0.000 0.964 0.000 0.036
#> GSM62258 1 0.0336 0.940 0.992 0.000 0.008 0.000
#> GSM62281 2 0.1398 0.876 0.000 0.956 0.040 0.004
#> GSM62294 4 0.3486 0.788 0.000 0.188 0.000 0.812
#> GSM62305 2 0.2101 0.872 0.012 0.928 0.060 0.000
#> GSM62306 2 0.2010 0.873 0.004 0.932 0.060 0.004
#> GSM62310 4 0.4855 0.705 0.000 0.400 0.000 0.600
#> GSM62311 4 0.4817 0.724 0.000 0.388 0.000 0.612
#> GSM62317 2 0.3071 0.835 0.068 0.888 0.000 0.044
#> GSM62318 1 0.1022 0.933 0.968 0.000 0.000 0.032
#> GSM62321 1 0.1724 0.918 0.948 0.020 0.000 0.032
#> GSM62322 3 0.2345 0.997 0.100 0.000 0.900 0.000
#> GSM62250 2 0.5905 0.391 0.304 0.636 0.060 0.000
#> GSM62252 1 0.4776 0.639 0.776 0.164 0.060 0.000
#> GSM62255 2 0.4941 -0.281 0.000 0.564 0.000 0.436
#> GSM62257 2 0.4072 0.491 0.000 0.748 0.000 0.252
#> GSM62260 1 0.0817 0.936 0.976 0.000 0.000 0.024
#> GSM62261 2 0.2156 0.872 0.008 0.928 0.060 0.004
#> GSM62262 4 0.3444 0.785 0.000 0.184 0.000 0.816
#> GSM62264 1 0.0592 0.938 0.984 0.000 0.000 0.016
#> GSM62268 1 0.0000 0.942 1.000 0.000 0.000 0.000
#> GSM62269 3 0.2345 0.997 0.100 0.000 0.900 0.000
#> GSM62271 1 0.0672 0.939 0.984 0.000 0.008 0.008
#> GSM62272 3 0.2345 0.997 0.100 0.000 0.900 0.000
#> GSM62273 2 0.0000 0.880 0.000 1.000 0.000 0.000
#> GSM62274 1 0.0336 0.940 0.992 0.000 0.008 0.000
#> GSM62275 3 0.2345 0.997 0.100 0.000 0.900 0.000
#> GSM62276 1 0.0000 0.942 1.000 0.000 0.000 0.000
#> GSM62277 1 0.2704 0.842 0.876 0.000 0.124 0.000
#> GSM62279 1 0.0000 0.942 1.000 0.000 0.000 0.000
#> GSM62282 1 0.2546 0.873 0.900 0.000 0.092 0.008
#> GSM62283 1 0.0000 0.942 1.000 0.000 0.000 0.000
#> GSM62286 2 0.2156 0.872 0.008 0.928 0.060 0.004
#> GSM62287 4 0.4382 0.819 0.000 0.296 0.000 0.704
#> GSM62288 2 0.2156 0.872 0.008 0.928 0.060 0.004
#> GSM62290 2 0.1118 0.878 0.000 0.964 0.000 0.036
#> GSM62293 4 0.2149 0.689 0.000 0.088 0.000 0.912
#> GSM62301 2 0.1118 0.878 0.000 0.964 0.000 0.036
#> GSM62302 4 0.4431 0.817 0.000 0.304 0.000 0.696
#> GSM62303 4 0.4431 0.817 0.000 0.304 0.000 0.696
#> GSM62304 4 0.4855 0.705 0.000 0.400 0.000 0.600
#> GSM62312 2 0.0336 0.881 0.000 0.992 0.000 0.008
#> GSM62313 4 0.4431 0.817 0.000 0.304 0.000 0.696
#> GSM62314 2 0.1824 0.873 0.000 0.936 0.060 0.004
#> GSM62319 2 0.1389 0.865 0.048 0.952 0.000 0.000
#> GSM62320 2 0.0000 0.880 0.000 1.000 0.000 0.000
#> GSM62249 1 0.1109 0.915 0.968 0.028 0.000 0.004
#> GSM62251 1 0.0000 0.942 1.000 0.000 0.000 0.000
#> GSM62263 2 0.4040 0.611 0.248 0.752 0.000 0.000
#> GSM62285 2 0.1118 0.878 0.000 0.964 0.000 0.036
#> GSM62315 2 0.2319 0.856 0.040 0.924 0.000 0.036
#> GSM62291 2 0.2319 0.861 0.000 0.924 0.040 0.036
#> GSM62265 1 0.0000 0.942 1.000 0.000 0.000 0.000
#> GSM62266 1 0.0000 0.942 1.000 0.000 0.000 0.000
#> GSM62296 2 0.2319 0.861 0.000 0.924 0.040 0.036
#> GSM62309 2 0.2319 0.856 0.040 0.924 0.000 0.036
#> GSM62295 4 0.4585 0.587 0.000 0.332 0.000 0.668
#> GSM62300 2 0.2319 0.861 0.000 0.924 0.040 0.036
#> GSM62308 2 0.2319 0.861 0.000 0.924 0.040 0.036
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM62248 5 0.0510 0.8737 0.000 0.016 0.000 0.000 0.984
#> GSM62256 2 0.2074 0.8595 0.000 0.896 0.000 0.000 0.104
#> GSM62259 4 0.6219 0.7762 0.000 0.140 0.000 0.440 0.420
#> GSM62267 1 0.1121 0.8121 0.956 0.000 0.000 0.000 0.044
#> GSM62280 1 0.4746 0.6682 0.600 0.000 0.024 0.376 0.000
#> GSM62284 1 0.0290 0.8198 0.992 0.000 0.008 0.000 0.000
#> GSM62289 5 0.0510 0.8737 0.000 0.016 0.000 0.000 0.984
#> GSM62307 4 0.5483 0.9001 0.000 0.064 0.000 0.512 0.424
#> GSM62316 5 0.0671 0.8695 0.000 0.016 0.000 0.004 0.980
#> GSM62254 4 0.5139 0.8114 0.000 0.060 0.000 0.624 0.316
#> GSM62292 4 0.5139 0.8114 0.000 0.060 0.000 0.624 0.316
#> GSM62253 1 0.0290 0.8198 0.992 0.000 0.008 0.000 0.000
#> GSM62270 3 0.0963 0.8906 0.036 0.000 0.964 0.000 0.000
#> GSM62278 3 0.4268 0.0559 0.444 0.000 0.556 0.000 0.000
#> GSM62297 5 0.4227 0.1756 0.000 0.420 0.000 0.000 0.580
#> GSM62298 2 0.4158 0.7722 0.000 0.784 0.000 0.092 0.124
#> GSM62299 2 0.1908 0.8638 0.000 0.908 0.000 0.000 0.092
#> GSM62258 1 0.1195 0.8217 0.960 0.000 0.000 0.028 0.012
#> GSM62281 2 0.2329 0.8465 0.000 0.876 0.000 0.000 0.124
#> GSM62294 4 0.5220 0.9226 0.000 0.044 0.000 0.516 0.440
#> GSM62305 5 0.0510 0.8737 0.000 0.016 0.000 0.000 0.984
#> GSM62306 5 0.0510 0.8737 0.000 0.016 0.000 0.000 0.984
#> GSM62310 4 0.5220 0.9226 0.000 0.044 0.000 0.516 0.440
#> GSM62311 4 0.5220 0.9226 0.000 0.044 0.000 0.516 0.440
#> GSM62317 2 0.2540 0.8009 0.000 0.888 0.024 0.088 0.000
#> GSM62318 1 0.4380 0.6790 0.616 0.000 0.008 0.376 0.000
#> GSM62321 1 0.4746 0.6682 0.600 0.000 0.024 0.376 0.000
#> GSM62322 3 0.0794 0.8955 0.028 0.000 0.972 0.000 0.000
#> GSM62250 5 0.1117 0.8484 0.020 0.016 0.000 0.000 0.964
#> GSM62252 5 0.3663 0.5497 0.208 0.016 0.000 0.000 0.776
#> GSM62255 4 0.5329 0.9149 0.000 0.052 0.000 0.516 0.432
#> GSM62257 4 0.5334 0.9124 0.000 0.052 0.000 0.512 0.436
#> GSM62260 1 0.4380 0.6800 0.616 0.000 0.008 0.376 0.000
#> GSM62261 5 0.0510 0.8737 0.000 0.016 0.000 0.000 0.984
#> GSM62262 4 0.5220 0.9226 0.000 0.044 0.000 0.516 0.440
#> GSM62264 1 0.3039 0.7922 0.836 0.000 0.012 0.152 0.000
#> GSM62268 1 0.0290 0.8198 0.992 0.000 0.008 0.000 0.000
#> GSM62269 3 0.0794 0.8955 0.028 0.000 0.972 0.000 0.000
#> GSM62271 1 0.4925 0.6807 0.632 0.000 0.044 0.324 0.000
#> GSM62272 3 0.0794 0.8955 0.028 0.000 0.972 0.000 0.000
#> GSM62273 2 0.3992 0.7844 0.000 0.796 0.000 0.080 0.124
#> GSM62274 1 0.0000 0.8200 1.000 0.000 0.000 0.000 0.000
#> GSM62275 3 0.0794 0.8955 0.028 0.000 0.972 0.000 0.000
#> GSM62276 1 0.1121 0.8121 0.956 0.000 0.000 0.000 0.044
#> GSM62277 1 0.0510 0.8182 0.984 0.000 0.016 0.000 0.000
#> GSM62279 1 0.1121 0.8121 0.956 0.000 0.000 0.000 0.044
#> GSM62282 1 0.5172 0.6686 0.616 0.000 0.060 0.324 0.000
#> GSM62283 1 0.2020 0.8040 0.900 0.000 0.000 0.100 0.000
#> GSM62286 5 0.0510 0.8737 0.000 0.016 0.000 0.000 0.984
#> GSM62287 4 0.5220 0.9226 0.000 0.044 0.000 0.516 0.440
#> GSM62288 5 0.0510 0.8737 0.000 0.016 0.000 0.000 0.984
#> GSM62290 2 0.2074 0.8602 0.000 0.896 0.000 0.000 0.104
#> GSM62293 4 0.5139 0.8114 0.000 0.060 0.000 0.624 0.316
#> GSM62301 2 0.0880 0.8675 0.000 0.968 0.000 0.000 0.032
#> GSM62302 4 0.5220 0.9226 0.000 0.044 0.000 0.516 0.440
#> GSM62303 4 0.5220 0.9226 0.000 0.044 0.000 0.516 0.440
#> GSM62304 4 0.5220 0.9226 0.000 0.044 0.000 0.516 0.440
#> GSM62312 2 0.4278 0.1227 0.000 0.548 0.000 0.000 0.452
#> GSM62313 4 0.5220 0.9226 0.000 0.044 0.000 0.516 0.440
#> GSM62314 5 0.2293 0.7341 0.000 0.016 0.000 0.084 0.900
#> GSM62319 2 0.5211 0.6348 0.188 0.708 0.000 0.088 0.016
#> GSM62320 2 0.2612 0.8425 0.000 0.868 0.000 0.008 0.124
#> GSM62249 1 0.4268 0.5484 0.708 0.000 0.000 0.024 0.268
#> GSM62251 1 0.0579 0.8211 0.984 0.000 0.008 0.008 0.000
#> GSM62263 1 0.7116 0.4726 0.572 0.136 0.004 0.084 0.204
#> GSM62285 2 0.0404 0.8566 0.000 0.988 0.000 0.000 0.012
#> GSM62315 2 0.2011 0.8119 0.000 0.908 0.004 0.088 0.000
#> GSM62291 2 0.0703 0.8639 0.000 0.976 0.000 0.000 0.024
#> GSM62265 1 0.0000 0.8200 1.000 0.000 0.000 0.000 0.000
#> GSM62266 1 0.0290 0.8198 0.992 0.000 0.008 0.000 0.000
#> GSM62296 2 0.1121 0.8692 0.000 0.956 0.000 0.000 0.044
#> GSM62309 2 0.2407 0.8221 0.000 0.896 0.004 0.088 0.012
#> GSM62295 4 0.5642 0.7051 0.000 0.136 0.000 0.624 0.240
#> GSM62300 2 0.0880 0.8673 0.000 0.968 0.000 0.000 0.032
#> GSM62308 2 0.0510 0.8594 0.000 0.984 0.000 0.000 0.016
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM62248 5 0.3419 0.844 0.000 0.084 0.000 0.104 0.812 0.000
#> GSM62256 2 0.0146 0.896 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM62259 4 0.2980 0.835 0.000 0.180 0.000 0.808 0.012 0.000
#> GSM62267 1 0.0260 0.794 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM62280 6 0.0146 0.906 0.000 0.000 0.004 0.000 0.000 0.996
#> GSM62284 1 0.2278 0.769 0.868 0.000 0.128 0.000 0.000 0.004
#> GSM62289 5 0.3716 0.843 0.012 0.080 0.000 0.092 0.812 0.004
#> GSM62307 4 0.2553 0.874 0.000 0.144 0.000 0.848 0.008 0.000
#> GSM62316 5 0.3552 0.835 0.000 0.084 0.000 0.116 0.800 0.000
#> GSM62254 4 0.1007 0.799 0.000 0.000 0.000 0.956 0.044 0.000
#> GSM62292 4 0.1007 0.799 0.000 0.000 0.000 0.956 0.044 0.000
#> GSM62253 1 0.3586 0.781 0.796 0.000 0.000 0.000 0.080 0.124
#> GSM62270 3 0.0000 0.977 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62278 3 0.1908 0.880 0.096 0.000 0.900 0.000 0.000 0.004
#> GSM62297 5 0.5066 0.599 0.000 0.304 0.000 0.104 0.592 0.000
#> GSM62298 2 0.2048 0.839 0.000 0.880 0.000 0.120 0.000 0.000
#> GSM62299 2 0.1007 0.901 0.000 0.956 0.000 0.044 0.000 0.000
#> GSM62258 1 0.0260 0.794 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM62281 2 0.0790 0.901 0.000 0.968 0.000 0.032 0.000 0.000
#> GSM62294 4 0.1556 0.889 0.000 0.080 0.000 0.920 0.000 0.000
#> GSM62305 5 0.3419 0.844 0.000 0.084 0.000 0.104 0.812 0.000
#> GSM62306 5 0.3419 0.844 0.000 0.084 0.000 0.104 0.812 0.000
#> GSM62310 4 0.2962 0.904 0.000 0.084 0.000 0.848 0.068 0.000
#> GSM62311 4 0.2965 0.906 0.000 0.080 0.000 0.848 0.072 0.000
#> GSM62317 2 0.2883 0.713 0.000 0.788 0.000 0.000 0.000 0.212
#> GSM62318 6 0.0146 0.906 0.000 0.000 0.004 0.000 0.000 0.996
#> GSM62321 6 0.0000 0.905 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM62322 3 0.0000 0.977 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62250 5 0.3969 0.824 0.012 0.072 0.000 0.072 0.812 0.032
#> GSM62252 5 0.4131 0.673 0.044 0.000 0.000 0.048 0.780 0.128
#> GSM62255 4 0.2948 0.903 0.000 0.092 0.000 0.848 0.060 0.000
#> GSM62257 4 0.2962 0.904 0.000 0.084 0.000 0.848 0.068 0.000
#> GSM62260 6 0.1007 0.887 0.044 0.000 0.000 0.000 0.000 0.956
#> GSM62261 5 0.3277 0.844 0.000 0.084 0.000 0.092 0.824 0.000
#> GSM62262 4 0.1556 0.889 0.000 0.080 0.000 0.920 0.000 0.000
#> GSM62264 1 0.4704 0.268 0.488 0.000 0.000 0.000 0.044 0.468
#> GSM62268 1 0.3586 0.781 0.796 0.000 0.000 0.000 0.080 0.124
#> GSM62269 3 0.0000 0.977 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62271 6 0.3081 0.719 0.220 0.000 0.000 0.000 0.004 0.776
#> GSM62272 3 0.0000 0.977 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62273 2 0.1219 0.899 0.000 0.948 0.000 0.048 0.000 0.004
#> GSM62274 1 0.2668 0.743 0.828 0.000 0.168 0.000 0.000 0.004
#> GSM62275 3 0.0000 0.977 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62276 1 0.0260 0.794 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM62277 1 0.3699 0.518 0.660 0.000 0.336 0.000 0.000 0.004
#> GSM62279 1 0.0260 0.794 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM62282 6 0.2261 0.839 0.104 0.000 0.008 0.000 0.004 0.884
#> GSM62283 1 0.4301 0.462 0.584 0.000 0.000 0.000 0.024 0.392
#> GSM62286 5 0.3419 0.844 0.000 0.084 0.000 0.104 0.812 0.000
#> GSM62287 4 0.2965 0.906 0.000 0.080 0.000 0.848 0.072 0.000
#> GSM62288 5 0.3277 0.844 0.000 0.084 0.000 0.092 0.824 0.000
#> GSM62290 2 0.1007 0.901 0.000 0.956 0.000 0.044 0.000 0.000
#> GSM62293 4 0.1007 0.799 0.000 0.000 0.000 0.956 0.044 0.000
#> GSM62301 2 0.1007 0.901 0.000 0.956 0.000 0.044 0.000 0.000
#> GSM62302 4 0.2965 0.906 0.000 0.080 0.000 0.848 0.072 0.000
#> GSM62303 4 0.2965 0.906 0.000 0.080 0.000 0.848 0.072 0.000
#> GSM62304 4 0.2965 0.906 0.000 0.080 0.000 0.848 0.072 0.000
#> GSM62312 2 0.4660 0.104 0.000 0.540 0.000 0.416 0.044 0.000
#> GSM62313 4 0.2965 0.906 0.000 0.080 0.000 0.848 0.072 0.000
#> GSM62314 5 0.4982 0.472 0.000 0.084 0.000 0.340 0.576 0.000
#> GSM62319 2 0.3052 0.705 0.000 0.780 0.000 0.004 0.000 0.216
#> GSM62320 2 0.1007 0.901 0.000 0.956 0.000 0.044 0.000 0.000
#> GSM62249 5 0.4788 0.206 0.060 0.000 0.000 0.000 0.568 0.372
#> GSM62251 1 0.3175 0.706 0.744 0.000 0.000 0.000 0.000 0.256
#> GSM62263 5 0.5633 0.359 0.044 0.084 0.000 0.000 0.596 0.276
#> GSM62285 2 0.1007 0.901 0.000 0.956 0.000 0.044 0.000 0.000
#> GSM62315 2 0.2647 0.861 0.000 0.868 0.000 0.044 0.000 0.088
#> GSM62291 2 0.0000 0.896 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62265 1 0.2378 0.777 0.848 0.000 0.000 0.000 0.000 0.152
#> GSM62266 1 0.3586 0.781 0.796 0.000 0.000 0.000 0.080 0.124
#> GSM62296 2 0.0000 0.896 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62309 2 0.2647 0.861 0.000 0.868 0.000 0.044 0.000 0.088
#> GSM62295 4 0.1152 0.797 0.000 0.004 0.000 0.952 0.044 0.000
#> GSM62300 2 0.0000 0.896 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62308 2 0.0000 0.896 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) other(p) genotype/variation(p) k
#> MAD:mclust 75 0.9089 1.000 0.811 2
#> MAD:mclust 65 0.2590 0.758 0.553 3
#> MAD:mclust 71 0.3525 0.503 0.212 4
#> MAD:mclust 71 0.0179 0.847 0.395 5
#> MAD:mclust 69 0.0129 0.929 0.539 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "NMF"]
# you can also extract it by
# res = res_list["MAD:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 75 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 0.974 0.990 0.4567 0.550 0.550
#> 3 3 0.748 0.763 0.897 0.2900 0.847 0.730
#> 4 4 0.666 0.717 0.865 0.1501 0.829 0.634
#> 5 5 0.681 0.524 0.769 0.1111 0.801 0.495
#> 6 6 0.751 0.737 0.880 0.0761 0.814 0.405
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
#> GSM62248 2 0.0000 0.985 0.000 1.000
#> GSM62256 2 0.0000 0.985 0.000 1.000
#> GSM62259 2 0.0000 0.985 0.000 1.000
#> GSM62267 1 0.0000 0.998 1.000 0.000
#> GSM62280 1 0.0000 0.998 1.000 0.000
#> GSM62284 1 0.0000 0.998 1.000 0.000
#> GSM62289 2 0.0000 0.985 0.000 1.000
#> GSM62307 2 0.0000 0.985 0.000 1.000
#> GSM62316 2 0.0000 0.985 0.000 1.000
#> GSM62254 2 0.0000 0.985 0.000 1.000
#> GSM62292 2 0.0000 0.985 0.000 1.000
#> GSM62253 1 0.0000 0.998 1.000 0.000
#> GSM62270 1 0.0000 0.998 1.000 0.000
#> GSM62278 1 0.0000 0.998 1.000 0.000
#> GSM62297 2 0.0000 0.985 0.000 1.000
#> GSM62298 2 0.0000 0.985 0.000 1.000
#> GSM62299 2 0.0000 0.985 0.000 1.000
#> GSM62258 1 0.0000 0.998 1.000 0.000
#> GSM62281 2 0.0000 0.985 0.000 1.000
#> GSM62294 2 0.0000 0.985 0.000 1.000
#> GSM62305 2 0.0000 0.985 0.000 1.000
#> GSM62306 2 0.0000 0.985 0.000 1.000
#> GSM62310 2 0.0000 0.985 0.000 1.000
#> GSM62311 2 0.0000 0.985 0.000 1.000
#> GSM62317 2 0.0000 0.985 0.000 1.000
#> GSM62318 1 0.0000 0.998 1.000 0.000
#> GSM62321 2 0.9775 0.311 0.412 0.588
#> GSM62322 1 0.0000 0.998 1.000 0.000
#> GSM62250 2 0.0000 0.985 0.000 1.000
#> GSM62252 2 0.0000 0.985 0.000 1.000
#> GSM62255 2 0.0000 0.985 0.000 1.000
#> GSM62257 2 0.0000 0.985 0.000 1.000
#> GSM62260 1 0.2236 0.962 0.964 0.036
#> GSM62261 2 0.0000 0.985 0.000 1.000
#> GSM62262 2 0.0000 0.985 0.000 1.000
#> GSM62264 1 0.0000 0.998 1.000 0.000
#> GSM62268 1 0.0000 0.998 1.000 0.000
#> GSM62269 1 0.0000 0.998 1.000 0.000
#> GSM62271 1 0.0000 0.998 1.000 0.000
#> GSM62272 1 0.0000 0.998 1.000 0.000
#> GSM62273 2 0.0000 0.985 0.000 1.000
#> GSM62274 1 0.0000 0.998 1.000 0.000
#> GSM62275 1 0.0000 0.998 1.000 0.000
#> GSM62276 1 0.0000 0.998 1.000 0.000
#> GSM62277 1 0.0000 0.998 1.000 0.000
#> GSM62279 1 0.0000 0.998 1.000 0.000
#> GSM62282 1 0.0000 0.998 1.000 0.000
#> GSM62283 1 0.0000 0.998 1.000 0.000
#> GSM62286 2 0.0000 0.985 0.000 1.000
#> GSM62287 2 0.0000 0.985 0.000 1.000
#> GSM62288 2 0.0000 0.985 0.000 1.000
#> GSM62290 2 0.0000 0.985 0.000 1.000
#> GSM62293 2 0.0000 0.985 0.000 1.000
#> GSM62301 2 0.0000 0.985 0.000 1.000
#> GSM62302 2 0.0000 0.985 0.000 1.000
#> GSM62303 2 0.0000 0.985 0.000 1.000
#> GSM62304 2 0.0000 0.985 0.000 1.000
#> GSM62312 2 0.0000 0.985 0.000 1.000
#> GSM62313 2 0.0000 0.985 0.000 1.000
#> GSM62314 2 0.0000 0.985 0.000 1.000
#> GSM62319 2 0.0000 0.985 0.000 1.000
#> GSM62320 2 0.0000 0.985 0.000 1.000
#> GSM62249 2 0.9000 0.542 0.316 0.684
#> GSM62251 1 0.0000 0.998 1.000 0.000
#> GSM62263 2 0.0376 0.981 0.004 0.996
#> GSM62285 2 0.0000 0.985 0.000 1.000
#> GSM62315 2 0.0000 0.985 0.000 1.000
#> GSM62291 2 0.0000 0.985 0.000 1.000
#> GSM62265 1 0.0000 0.998 1.000 0.000
#> GSM62266 1 0.0000 0.998 1.000 0.000
#> GSM62296 2 0.0000 0.985 0.000 1.000
#> GSM62309 2 0.0000 0.985 0.000 1.000
#> GSM62295 2 0.0000 0.985 0.000 1.000
#> GSM62300 2 0.0000 0.985 0.000 1.000
#> GSM62308 2 0.0000 0.985 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM62248 2 0.2448 0.834 0.076 0.924 0.000
#> GSM62256 2 0.0424 0.900 0.008 0.992 0.000
#> GSM62259 2 0.0237 0.901 0.004 0.996 0.000
#> GSM62267 3 0.0237 0.940 0.000 0.004 0.996
#> GSM62280 1 0.4235 0.575 0.824 0.000 0.176
#> GSM62284 3 0.5621 0.500 0.308 0.000 0.692
#> GSM62289 2 0.0000 0.902 0.000 1.000 0.000
#> GSM62307 2 0.0237 0.901 0.004 0.996 0.000
#> GSM62316 2 0.0000 0.902 0.000 1.000 0.000
#> GSM62254 2 0.0000 0.902 0.000 1.000 0.000
#> GSM62292 2 0.0000 0.902 0.000 1.000 0.000
#> GSM62253 1 0.6154 0.288 0.592 0.000 0.408
#> GSM62270 3 0.0000 0.944 0.000 0.000 1.000
#> GSM62278 3 0.0000 0.944 0.000 0.000 1.000
#> GSM62297 2 0.5397 0.677 0.280 0.720 0.000
#> GSM62298 2 0.0237 0.901 0.004 0.996 0.000
#> GSM62299 2 0.4931 0.725 0.232 0.768 0.000
#> GSM62258 3 0.0747 0.931 0.016 0.000 0.984
#> GSM62281 2 0.0237 0.901 0.004 0.996 0.000
#> GSM62294 2 0.0237 0.901 0.004 0.996 0.000
#> GSM62305 2 0.0000 0.902 0.000 1.000 0.000
#> GSM62306 2 0.0000 0.902 0.000 1.000 0.000
#> GSM62310 2 0.0237 0.901 0.004 0.996 0.000
#> GSM62311 2 0.0237 0.901 0.004 0.996 0.000
#> GSM62317 1 0.5905 0.178 0.648 0.352 0.000
#> GSM62318 1 0.0237 0.684 0.996 0.000 0.004
#> GSM62321 1 0.0000 0.684 1.000 0.000 0.000
#> GSM62322 3 0.0000 0.944 0.000 0.000 1.000
#> GSM62250 2 0.0000 0.902 0.000 1.000 0.000
#> GSM62252 2 0.0000 0.902 0.000 1.000 0.000
#> GSM62255 2 0.0237 0.901 0.004 0.996 0.000
#> GSM62257 2 0.0000 0.902 0.000 1.000 0.000
#> GSM62260 1 0.0237 0.684 0.996 0.000 0.004
#> GSM62261 2 0.0237 0.901 0.004 0.996 0.000
#> GSM62262 2 0.0237 0.901 0.004 0.996 0.000
#> GSM62264 1 0.3879 0.615 0.848 0.000 0.152
#> GSM62268 1 0.6252 0.192 0.556 0.000 0.444
#> GSM62269 3 0.0000 0.944 0.000 0.000 1.000
#> GSM62271 3 0.0000 0.944 0.000 0.000 1.000
#> GSM62272 3 0.0000 0.944 0.000 0.000 1.000
#> GSM62273 2 0.0237 0.901 0.004 0.996 0.000
#> GSM62274 3 0.0000 0.944 0.000 0.000 1.000
#> GSM62275 3 0.0000 0.944 0.000 0.000 1.000
#> GSM62276 3 0.0237 0.940 0.000 0.004 0.996
#> GSM62277 3 0.0000 0.944 0.000 0.000 1.000
#> GSM62279 3 0.5722 0.533 0.292 0.004 0.704
#> GSM62282 3 0.0237 0.940 0.004 0.000 0.996
#> GSM62283 1 0.1529 0.677 0.960 0.000 0.040
#> GSM62286 2 0.0000 0.902 0.000 1.000 0.000
#> GSM62287 2 0.0000 0.902 0.000 1.000 0.000
#> GSM62288 2 0.0000 0.902 0.000 1.000 0.000
#> GSM62290 2 0.5706 0.630 0.320 0.680 0.000
#> GSM62293 2 0.0000 0.902 0.000 1.000 0.000
#> GSM62301 2 0.6111 0.509 0.396 0.604 0.000
#> GSM62302 2 0.0000 0.902 0.000 1.000 0.000
#> GSM62303 2 0.0000 0.902 0.000 1.000 0.000
#> GSM62304 2 0.0000 0.902 0.000 1.000 0.000
#> GSM62312 2 0.2165 0.865 0.064 0.936 0.000
#> GSM62313 2 0.0000 0.902 0.000 1.000 0.000
#> GSM62314 2 0.0000 0.902 0.000 1.000 0.000
#> GSM62319 2 0.5835 0.604 0.340 0.660 0.000
#> GSM62320 2 0.0424 0.900 0.008 0.992 0.000
#> GSM62249 1 0.0000 0.684 1.000 0.000 0.000
#> GSM62251 1 0.5882 0.403 0.652 0.000 0.348
#> GSM62263 1 0.0000 0.684 1.000 0.000 0.000
#> GSM62285 2 0.5760 0.620 0.328 0.672 0.000
#> GSM62315 2 0.6204 0.451 0.424 0.576 0.000
#> GSM62291 2 0.5835 0.604 0.340 0.660 0.000
#> GSM62265 1 0.5926 0.391 0.644 0.000 0.356
#> GSM62266 1 0.6140 0.297 0.596 0.000 0.404
#> GSM62296 2 0.5859 0.598 0.344 0.656 0.000
#> GSM62309 1 0.6295 -0.230 0.528 0.472 0.000
#> GSM62295 2 0.0237 0.901 0.004 0.996 0.000
#> GSM62300 2 0.5882 0.592 0.348 0.652 0.000
#> GSM62308 2 0.5926 0.579 0.356 0.644 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM62248 2 0.4522 0.5637 0.320 0.680 0.000 0.000
#> GSM62256 2 0.4511 0.5786 0.008 0.724 0.000 0.268
#> GSM62259 2 0.0469 0.8681 0.000 0.988 0.000 0.012
#> GSM62267 1 0.3581 0.6556 0.852 0.032 0.116 0.000
#> GSM62280 4 0.0592 0.7347 0.000 0.000 0.016 0.984
#> GSM62284 1 0.4008 0.6224 0.756 0.000 0.244 0.000
#> GSM62289 1 0.4477 0.4649 0.688 0.312 0.000 0.000
#> GSM62307 2 0.0469 0.8681 0.000 0.988 0.000 0.012
#> GSM62316 2 0.2530 0.8058 0.112 0.888 0.000 0.000
#> GSM62254 2 0.0188 0.8690 0.000 0.996 0.000 0.004
#> GSM62292 2 0.0000 0.8687 0.000 1.000 0.000 0.000
#> GSM62253 1 0.3370 0.7302 0.872 0.000 0.080 0.048
#> GSM62270 3 0.0000 0.9267 0.000 0.000 1.000 0.000
#> GSM62278 3 0.0000 0.9267 0.000 0.000 1.000 0.000
#> GSM62297 2 0.4907 0.6893 0.060 0.764 0.000 0.176
#> GSM62298 2 0.1629 0.8534 0.024 0.952 0.000 0.024
#> GSM62299 2 0.3812 0.7528 0.028 0.832 0.000 0.140
#> GSM62258 3 0.4585 0.5547 0.332 0.000 0.668 0.000
#> GSM62281 2 0.0707 0.8658 0.000 0.980 0.000 0.020
#> GSM62294 2 0.0336 0.8687 0.000 0.992 0.000 0.008
#> GSM62305 2 0.3649 0.7426 0.204 0.796 0.000 0.000
#> GSM62306 2 0.1118 0.8546 0.036 0.964 0.000 0.000
#> GSM62310 2 0.0336 0.8687 0.000 0.992 0.000 0.008
#> GSM62311 2 0.0188 0.8690 0.000 0.996 0.000 0.004
#> GSM62317 4 0.0188 0.7426 0.000 0.004 0.000 0.996
#> GSM62318 4 0.0895 0.7287 0.004 0.000 0.020 0.976
#> GSM62321 4 0.0376 0.7389 0.004 0.000 0.004 0.992
#> GSM62322 3 0.0000 0.9267 0.000 0.000 1.000 0.000
#> GSM62250 1 0.4730 0.3573 0.636 0.364 0.000 0.000
#> GSM62252 1 0.4866 0.2633 0.596 0.404 0.000 0.000
#> GSM62255 2 0.0469 0.8681 0.000 0.988 0.000 0.012
#> GSM62257 2 0.0592 0.8638 0.016 0.984 0.000 0.000
#> GSM62260 4 0.2179 0.6967 0.064 0.000 0.012 0.924
#> GSM62261 2 0.2868 0.7862 0.136 0.864 0.000 0.000
#> GSM62262 2 0.0336 0.8687 0.000 0.992 0.000 0.008
#> GSM62264 1 0.4182 0.7244 0.796 0.000 0.024 0.180
#> GSM62268 1 0.3668 0.6711 0.808 0.000 0.188 0.004
#> GSM62269 3 0.0000 0.9267 0.000 0.000 1.000 0.000
#> GSM62271 3 0.0804 0.9162 0.012 0.000 0.980 0.008
#> GSM62272 3 0.0000 0.9267 0.000 0.000 1.000 0.000
#> GSM62273 2 0.1302 0.8559 0.000 0.956 0.000 0.044
#> GSM62274 1 0.4790 0.4242 0.620 0.000 0.380 0.000
#> GSM62275 3 0.0000 0.9267 0.000 0.000 1.000 0.000
#> GSM62276 3 0.4718 0.6342 0.280 0.012 0.708 0.000
#> GSM62277 3 0.0336 0.9227 0.008 0.000 0.992 0.000
#> GSM62279 1 0.1510 0.7042 0.956 0.016 0.028 0.000
#> GSM62282 3 0.0921 0.9059 0.000 0.000 0.972 0.028
#> GSM62283 1 0.5727 0.6776 0.704 0.000 0.096 0.200
#> GSM62286 2 0.3074 0.7738 0.152 0.848 0.000 0.000
#> GSM62287 2 0.0188 0.8676 0.004 0.996 0.000 0.000
#> GSM62288 2 0.3074 0.7730 0.152 0.848 0.000 0.000
#> GSM62290 2 0.3581 0.7739 0.032 0.852 0.000 0.116
#> GSM62293 2 0.0188 0.8690 0.000 0.996 0.000 0.004
#> GSM62301 4 0.5530 0.4643 0.032 0.336 0.000 0.632
#> GSM62302 2 0.0000 0.8687 0.000 1.000 0.000 0.000
#> GSM62303 2 0.0000 0.8687 0.000 1.000 0.000 0.000
#> GSM62304 2 0.0000 0.8687 0.000 1.000 0.000 0.000
#> GSM62312 2 0.2021 0.8463 0.024 0.936 0.000 0.040
#> GSM62313 2 0.0000 0.8687 0.000 1.000 0.000 0.000
#> GSM62314 2 0.2281 0.8177 0.096 0.904 0.000 0.000
#> GSM62319 2 0.5693 -0.0819 0.024 0.504 0.000 0.472
#> GSM62320 2 0.1929 0.8466 0.024 0.940 0.000 0.036
#> GSM62249 1 0.3311 0.7183 0.828 0.000 0.000 0.172
#> GSM62251 1 0.1716 0.7384 0.936 0.000 0.000 0.064
#> GSM62263 1 0.4222 0.6230 0.728 0.000 0.000 0.272
#> GSM62285 2 0.5420 0.3549 0.024 0.624 0.000 0.352
#> GSM62315 4 0.1151 0.7416 0.024 0.008 0.000 0.968
#> GSM62291 2 0.5452 0.3329 0.024 0.616 0.000 0.360
#> GSM62265 1 0.2921 0.7327 0.860 0.000 0.000 0.140
#> GSM62266 1 0.3850 0.7385 0.840 0.000 0.044 0.116
#> GSM62296 2 0.5691 -0.0683 0.024 0.508 0.000 0.468
#> GSM62309 4 0.1256 0.7411 0.028 0.008 0.000 0.964
#> GSM62295 2 0.0592 0.8669 0.000 0.984 0.000 0.016
#> GSM62300 4 0.5695 0.0848 0.024 0.476 0.000 0.500
#> GSM62308 4 0.5643 0.2513 0.024 0.428 0.000 0.548
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM62248 5 0.4555 0.8263 0.020 0.000 0.000 0.344 0.636
#> GSM62256 2 0.5645 0.4227 0.000 0.540 0.000 0.084 0.376
#> GSM62259 4 0.3928 0.0311 0.000 0.004 0.000 0.700 0.296
#> GSM62267 5 0.5395 0.4607 0.272 0.000 0.044 0.028 0.656
#> GSM62280 2 0.4268 0.5145 0.008 0.648 0.000 0.000 0.344
#> GSM62284 1 0.3857 0.4682 0.688 0.000 0.312 0.000 0.000
#> GSM62289 5 0.4135 0.8280 0.004 0.000 0.000 0.340 0.656
#> GSM62307 4 0.2471 0.4739 0.000 0.000 0.000 0.864 0.136
#> GSM62316 5 0.4060 0.8179 0.000 0.000 0.000 0.360 0.640
#> GSM62254 4 0.0880 0.5942 0.000 0.000 0.000 0.968 0.032
#> GSM62292 4 0.2773 0.4444 0.000 0.000 0.000 0.836 0.164
#> GSM62253 1 0.0000 0.8114 1.000 0.000 0.000 0.000 0.000
#> GSM62270 3 0.0000 0.8865 0.000 0.000 1.000 0.000 0.000
#> GSM62278 3 0.0000 0.8865 0.000 0.000 1.000 0.000 0.000
#> GSM62297 2 0.7029 -0.1525 0.284 0.356 0.000 0.352 0.008
#> GSM62298 4 0.3966 0.5172 0.000 0.336 0.000 0.664 0.000
#> GSM62299 4 0.5181 0.4509 0.052 0.360 0.000 0.588 0.000
#> GSM62258 5 0.3561 0.4292 0.032 0.024 0.100 0.000 0.844
#> GSM62281 4 0.0404 0.6083 0.000 0.012 0.000 0.988 0.000
#> GSM62294 4 0.1478 0.5726 0.000 0.000 0.000 0.936 0.064
#> GSM62305 5 0.5592 0.7952 0.068 0.024 0.000 0.256 0.652
#> GSM62306 5 0.4060 0.8177 0.000 0.000 0.000 0.360 0.640
#> GSM62310 4 0.1952 0.5586 0.000 0.004 0.000 0.912 0.084
#> GSM62311 4 0.1851 0.5509 0.000 0.000 0.000 0.912 0.088
#> GSM62317 2 0.4419 0.5136 0.004 0.644 0.000 0.008 0.344
#> GSM62318 2 0.4467 0.5113 0.016 0.640 0.000 0.000 0.344
#> GSM62321 2 0.4268 0.5145 0.008 0.648 0.000 0.000 0.344
#> GSM62322 3 0.0000 0.8865 0.000 0.000 1.000 0.000 0.000
#> GSM62250 5 0.5062 0.8094 0.068 0.000 0.000 0.276 0.656
#> GSM62252 5 0.4401 0.8286 0.016 0.000 0.000 0.328 0.656
#> GSM62255 4 0.0162 0.6050 0.000 0.000 0.000 0.996 0.004
#> GSM62257 4 0.4307 -0.5763 0.000 0.000 0.000 0.504 0.496
#> GSM62260 2 0.6109 0.4339 0.148 0.532 0.000 0.000 0.320
#> GSM62261 5 0.4201 0.7535 0.000 0.000 0.000 0.408 0.592
#> GSM62262 4 0.0880 0.5946 0.000 0.000 0.000 0.968 0.032
#> GSM62264 1 0.0404 0.8070 0.988 0.000 0.000 0.000 0.012
#> GSM62268 1 0.1792 0.7691 0.916 0.000 0.084 0.000 0.000
#> GSM62269 3 0.0000 0.8865 0.000 0.000 1.000 0.000 0.000
#> GSM62271 3 0.0865 0.8651 0.024 0.004 0.972 0.000 0.000
#> GSM62272 3 0.0000 0.8865 0.000 0.000 1.000 0.000 0.000
#> GSM62273 4 0.3796 0.5359 0.000 0.300 0.000 0.700 0.000
#> GSM62274 3 0.3684 0.5252 0.280 0.000 0.720 0.000 0.000
#> GSM62275 3 0.0000 0.8865 0.000 0.000 1.000 0.000 0.000
#> GSM62276 5 0.4791 0.4073 0.020 0.000 0.336 0.008 0.636
#> GSM62277 3 0.0000 0.8865 0.000 0.000 1.000 0.000 0.000
#> GSM62279 1 0.3932 0.4431 0.672 0.000 0.000 0.000 0.328
#> GSM62282 3 0.6817 -0.1254 0.000 0.308 0.348 0.000 0.344
#> GSM62283 2 0.6851 -0.2030 0.408 0.412 0.160 0.000 0.020
#> GSM62286 5 0.3999 0.8267 0.000 0.000 0.000 0.344 0.656
#> GSM62287 4 0.4060 -0.1581 0.000 0.000 0.000 0.640 0.360
#> GSM62288 5 0.4482 0.7985 0.012 0.000 0.000 0.376 0.612
#> GSM62290 4 0.5080 0.4668 0.048 0.348 0.000 0.604 0.000
#> GSM62293 4 0.0880 0.5946 0.000 0.000 0.000 0.968 0.032
#> GSM62301 4 0.5520 0.4100 0.076 0.364 0.000 0.560 0.000
#> GSM62302 4 0.1792 0.5542 0.000 0.000 0.000 0.916 0.084
#> GSM62303 4 0.2516 0.4845 0.000 0.000 0.000 0.860 0.140
#> GSM62304 4 0.4262 -0.4263 0.000 0.000 0.000 0.560 0.440
#> GSM62312 4 0.4101 0.5201 0.004 0.332 0.000 0.664 0.000
#> GSM62313 4 0.2127 0.5269 0.000 0.000 0.000 0.892 0.108
#> GSM62314 4 0.4371 -0.1295 0.012 0.000 0.000 0.644 0.344
#> GSM62319 4 0.4238 0.4912 0.000 0.368 0.004 0.628 0.000
#> GSM62320 4 0.3966 0.5172 0.000 0.336 0.000 0.664 0.000
#> GSM62249 1 0.4863 0.4942 0.672 0.272 0.000 0.000 0.056
#> GSM62251 1 0.0000 0.8114 1.000 0.000 0.000 0.000 0.000
#> GSM62263 1 0.3333 0.6016 0.788 0.208 0.000 0.000 0.004
#> GSM62285 4 0.4402 0.4986 0.012 0.352 0.000 0.636 0.000
#> GSM62315 2 0.4613 -0.0564 0.020 0.620 0.000 0.360 0.000
#> GSM62291 4 0.4015 0.5085 0.000 0.348 0.000 0.652 0.000
#> GSM62265 1 0.0451 0.8085 0.988 0.004 0.000 0.000 0.008
#> GSM62266 1 0.0000 0.8114 1.000 0.000 0.000 0.000 0.000
#> GSM62296 4 0.4264 0.4844 0.004 0.376 0.000 0.620 0.000
#> GSM62309 2 0.5484 0.1953 0.120 0.640 0.000 0.240 0.000
#> GSM62295 4 0.0880 0.6135 0.000 0.032 0.000 0.968 0.000
#> GSM62300 4 0.4457 0.4859 0.012 0.368 0.000 0.620 0.000
#> GSM62308 4 0.4060 0.5006 0.000 0.360 0.000 0.640 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM62248 5 0.2400 0.8246 0.008 0.000 0.000 0.116 0.872 0.004
#> GSM62256 6 0.0777 0.9653 0.000 0.000 0.000 0.004 0.024 0.972
#> GSM62259 5 0.3671 0.7267 0.000 0.036 0.000 0.208 0.756 0.000
#> GSM62267 5 0.0000 0.8152 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM62280 6 0.0000 0.9908 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM62284 1 0.1327 0.7746 0.936 0.000 0.064 0.000 0.000 0.000
#> GSM62289 5 0.0405 0.8169 0.008 0.000 0.000 0.004 0.988 0.000
#> GSM62307 4 0.3843 -0.0821 0.000 0.000 0.000 0.548 0.452 0.000
#> GSM62316 5 0.2260 0.8196 0.000 0.000 0.000 0.140 0.860 0.000
#> GSM62254 4 0.2631 0.6650 0.000 0.000 0.000 0.820 0.180 0.000
#> GSM62292 5 0.3578 0.6307 0.000 0.000 0.000 0.340 0.660 0.000
#> GSM62253 1 0.0146 0.8001 0.996 0.004 0.000 0.000 0.000 0.000
#> GSM62270 3 0.0000 0.9708 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62278 3 0.0000 0.9708 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62297 2 0.0632 0.8234 0.024 0.976 0.000 0.000 0.000 0.000
#> GSM62298 4 0.2135 0.7457 0.000 0.128 0.000 0.872 0.000 0.000
#> GSM62299 2 0.1387 0.8193 0.000 0.932 0.000 0.068 0.000 0.000
#> GSM62258 5 0.2378 0.7116 0.000 0.000 0.000 0.000 0.848 0.152
#> GSM62281 4 0.2048 0.7639 0.000 0.000 0.000 0.880 0.000 0.120
#> GSM62294 4 0.2300 0.7116 0.000 0.000 0.000 0.856 0.144 0.000
#> GSM62305 5 0.2234 0.7427 0.004 0.124 0.000 0.000 0.872 0.000
#> GSM62306 5 0.0603 0.8128 0.004 0.016 0.000 0.000 0.980 0.000
#> GSM62310 4 0.0146 0.8209 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM62311 4 0.0000 0.8212 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62317 6 0.0000 0.9908 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM62318 6 0.0000 0.9908 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM62321 6 0.0000 0.9908 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM62322 3 0.0000 0.9708 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62250 5 0.0146 0.8171 0.000 0.000 0.000 0.004 0.996 0.000
#> GSM62252 5 0.0146 0.8148 0.004 0.000 0.000 0.000 0.996 0.000
#> GSM62255 4 0.0000 0.8212 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62257 5 0.2562 0.8081 0.000 0.000 0.000 0.172 0.828 0.000
#> GSM62260 2 0.3468 0.7047 0.028 0.808 0.000 0.000 0.016 0.148
#> GSM62261 5 0.2805 0.7989 0.004 0.000 0.000 0.184 0.812 0.000
#> GSM62262 4 0.0458 0.8168 0.000 0.000 0.000 0.984 0.016 0.000
#> GSM62264 1 0.0405 0.7989 0.988 0.008 0.000 0.000 0.000 0.004
#> GSM62268 1 0.0508 0.7986 0.984 0.004 0.012 0.000 0.000 0.000
#> GSM62269 3 0.0000 0.9708 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62271 3 0.2747 0.8232 0.028 0.108 0.860 0.000 0.004 0.000
#> GSM62272 3 0.0000 0.9708 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62273 4 0.2378 0.7315 0.000 0.152 0.000 0.848 0.000 0.000
#> GSM62274 1 0.3868 0.0320 0.508 0.000 0.492 0.000 0.000 0.000
#> GSM62275 3 0.0000 0.9708 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62276 5 0.0790 0.8068 0.000 0.000 0.032 0.000 0.968 0.000
#> GSM62277 3 0.0865 0.9420 0.036 0.000 0.964 0.000 0.000 0.000
#> GSM62279 1 0.3944 0.3076 0.568 0.004 0.000 0.000 0.428 0.000
#> GSM62282 6 0.0405 0.9848 0.000 0.000 0.008 0.000 0.004 0.988
#> GSM62283 2 0.2011 0.7853 0.020 0.912 0.004 0.000 0.064 0.000
#> GSM62286 5 0.0632 0.8231 0.000 0.000 0.000 0.024 0.976 0.000
#> GSM62287 5 0.3578 0.6298 0.000 0.000 0.000 0.340 0.660 0.000
#> GSM62288 5 0.2378 0.8153 0.000 0.000 0.000 0.152 0.848 0.000
#> GSM62290 2 0.3828 0.1554 0.000 0.560 0.000 0.440 0.000 0.000
#> GSM62293 4 0.0000 0.8212 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62301 2 0.0458 0.8327 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM62302 4 0.0000 0.8212 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62303 4 0.3499 0.3845 0.000 0.000 0.000 0.680 0.320 0.000
#> GSM62304 5 0.3547 0.6403 0.000 0.000 0.000 0.332 0.668 0.000
#> GSM62312 4 0.3515 0.4886 0.000 0.324 0.000 0.676 0.000 0.000
#> GSM62313 4 0.0363 0.8182 0.000 0.000 0.000 0.988 0.012 0.000
#> GSM62314 5 0.4453 0.3274 0.028 0.000 0.000 0.444 0.528 0.000
#> GSM62319 2 0.0937 0.8301 0.000 0.960 0.000 0.040 0.000 0.000
#> GSM62320 4 0.2527 0.7114 0.000 0.168 0.000 0.832 0.000 0.000
#> GSM62249 2 0.2263 0.7733 0.048 0.896 0.000 0.000 0.056 0.000
#> GSM62251 1 0.0508 0.7977 0.984 0.004 0.000 0.000 0.012 0.000
#> GSM62263 1 0.3807 0.3421 0.628 0.368 0.000 0.000 0.000 0.004
#> GSM62285 2 0.3747 0.2946 0.000 0.604 0.000 0.396 0.000 0.000
#> GSM62315 2 0.1327 0.8209 0.000 0.936 0.000 0.064 0.000 0.000
#> GSM62291 4 0.3765 0.2856 0.000 0.404 0.000 0.596 0.000 0.000
#> GSM62265 2 0.4465 0.0386 0.460 0.512 0.000 0.000 0.028 0.000
#> GSM62266 1 0.0146 0.8001 0.996 0.004 0.000 0.000 0.000 0.000
#> GSM62296 2 0.0363 0.8318 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM62309 2 0.0146 0.8266 0.004 0.996 0.000 0.000 0.000 0.000
#> GSM62295 4 0.1285 0.8046 0.004 0.052 0.000 0.944 0.000 0.000
#> GSM62300 2 0.0363 0.8319 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM62308 2 0.1444 0.8169 0.000 0.928 0.000 0.072 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) other(p) genotype/variation(p) k
#> MAD:NMF 74 0.56459 1.000 0.7441 2
#> MAD:NMF 67 0.17800 0.578 0.3090 3
#> MAD:NMF 64 0.00151 0.132 0.1803 4
#> MAD:NMF 47 0.00735 0.147 0.0975 5
#> MAD:NMF 64 0.00102 0.541 0.1707 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "hclust"]
# you can also extract it by
# res = res_list["ATC:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 75 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 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 0.792 0.911 0.940 0.3436 0.591 0.591
#> 3 3 0.931 0.826 0.918 0.3738 0.950 0.916
#> 4 4 0.743 0.816 0.915 0.1508 0.941 0.893
#> 5 5 0.656 0.724 0.847 0.3076 0.746 0.505
#> 6 6 0.716 0.776 0.876 0.0226 0.978 0.921
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
#> GSM62248 2 0.000 0.996 0.000 1.000
#> GSM62256 2 0.000 0.996 0.000 1.000
#> GSM62259 2 0.000 0.996 0.000 1.000
#> GSM62267 1 0.943 0.695 0.640 0.360
#> GSM62280 1 0.943 0.695 0.640 0.360
#> GSM62284 1 0.808 0.738 0.752 0.248
#> GSM62289 2 0.000 0.996 0.000 1.000
#> GSM62307 2 0.000 0.996 0.000 1.000
#> GSM62316 2 0.000 0.996 0.000 1.000
#> GSM62254 2 0.000 0.996 0.000 1.000
#> GSM62292 2 0.000 0.996 0.000 1.000
#> GSM62253 1 0.992 0.551 0.552 0.448
#> GSM62270 1 0.000 0.771 1.000 0.000
#> GSM62278 1 0.000 0.771 1.000 0.000
#> GSM62297 2 0.000 0.996 0.000 1.000
#> GSM62298 2 0.000 0.996 0.000 1.000
#> GSM62299 2 0.000 0.996 0.000 1.000
#> GSM62258 1 0.943 0.695 0.640 0.360
#> GSM62281 2 0.000 0.996 0.000 1.000
#> GSM62294 2 0.000 0.996 0.000 1.000
#> GSM62305 2 0.000 0.996 0.000 1.000
#> GSM62306 2 0.000 0.996 0.000 1.000
#> GSM62310 2 0.000 0.996 0.000 1.000
#> GSM62311 2 0.000 0.996 0.000 1.000
#> GSM62317 2 0.000 0.996 0.000 1.000
#> GSM62318 2 0.671 0.699 0.176 0.824
#> GSM62321 2 0.000 0.996 0.000 1.000
#> GSM62322 1 0.000 0.771 1.000 0.000
#> GSM62250 2 0.000 0.996 0.000 1.000
#> GSM62252 2 0.000 0.996 0.000 1.000
#> GSM62255 2 0.000 0.996 0.000 1.000
#> GSM62257 2 0.000 0.996 0.000 1.000
#> GSM62260 2 0.000 0.996 0.000 1.000
#> GSM62261 2 0.000 0.996 0.000 1.000
#> GSM62262 2 0.000 0.996 0.000 1.000
#> GSM62264 2 0.000 0.996 0.000 1.000
#> GSM62268 1 0.992 0.551 0.552 0.448
#> GSM62269 1 0.000 0.771 1.000 0.000
#> GSM62271 1 0.388 0.773 0.924 0.076
#> GSM62272 1 0.000 0.771 1.000 0.000
#> GSM62273 2 0.000 0.996 0.000 1.000
#> GSM62274 1 0.000 0.771 1.000 0.000
#> GSM62275 1 0.000 0.771 1.000 0.000
#> GSM62276 1 0.943 0.695 0.640 0.360
#> GSM62277 1 0.000 0.771 1.000 0.000
#> GSM62279 1 0.975 0.625 0.592 0.408
#> GSM62282 1 0.388 0.773 0.924 0.076
#> GSM62283 1 0.943 0.695 0.640 0.360
#> GSM62286 2 0.000 0.996 0.000 1.000
#> GSM62287 2 0.000 0.996 0.000 1.000
#> GSM62288 2 0.000 0.996 0.000 1.000
#> GSM62290 2 0.000 0.996 0.000 1.000
#> GSM62293 2 0.000 0.996 0.000 1.000
#> GSM62301 2 0.000 0.996 0.000 1.000
#> GSM62302 2 0.000 0.996 0.000 1.000
#> GSM62303 2 0.000 0.996 0.000 1.000
#> GSM62304 2 0.000 0.996 0.000 1.000
#> GSM62312 2 0.000 0.996 0.000 1.000
#> GSM62313 2 0.000 0.996 0.000 1.000
#> GSM62314 2 0.000 0.996 0.000 1.000
#> GSM62319 2 0.000 0.996 0.000 1.000
#> GSM62320 2 0.000 0.996 0.000 1.000
#> GSM62249 2 0.000 0.996 0.000 1.000
#> GSM62251 2 0.000 0.996 0.000 1.000
#> GSM62263 2 0.000 0.996 0.000 1.000
#> GSM62285 2 0.000 0.996 0.000 1.000
#> GSM62315 2 0.000 0.996 0.000 1.000
#> GSM62291 2 0.000 0.996 0.000 1.000
#> GSM62265 1 0.943 0.695 0.640 0.360
#> GSM62266 1 0.992 0.551 0.552 0.448
#> GSM62296 2 0.000 0.996 0.000 1.000
#> GSM62309 2 0.000 0.996 0.000 1.000
#> GSM62295 2 0.000 0.996 0.000 1.000
#> GSM62300 2 0.000 0.996 0.000 1.000
#> GSM62308 2 0.000 0.996 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM62248 2 0.000 0.9660 0.000 1.000 0.000
#> GSM62256 2 0.000 0.9660 0.000 1.000 0.000
#> GSM62259 2 0.000 0.9660 0.000 1.000 0.000
#> GSM62267 1 0.588 0.7542 0.652 0.000 0.348
#> GSM62280 1 0.588 0.7542 0.652 0.000 0.348
#> GSM62284 1 0.630 0.5703 0.528 0.000 0.472
#> GSM62289 2 0.199 0.9377 0.048 0.948 0.004
#> GSM62307 2 0.000 0.9660 0.000 1.000 0.000
#> GSM62316 2 0.000 0.9660 0.000 1.000 0.000
#> GSM62254 2 0.129 0.9495 0.032 0.968 0.000
#> GSM62292 2 0.175 0.9402 0.048 0.952 0.000
#> GSM62253 1 0.623 0.7141 0.564 0.000 0.436
#> GSM62270 3 0.623 0.7171 0.436 0.000 0.564
#> GSM62278 1 0.450 0.0899 0.804 0.000 0.196
#> GSM62297 2 0.000 0.9660 0.000 1.000 0.000
#> GSM62298 2 0.000 0.9660 0.000 1.000 0.000
#> GSM62299 2 0.000 0.9660 0.000 1.000 0.000
#> GSM62258 1 0.588 0.7542 0.652 0.000 0.348
#> GSM62281 2 0.000 0.9660 0.000 1.000 0.000
#> GSM62294 2 0.000 0.9660 0.000 1.000 0.000
#> GSM62305 2 0.206 0.9379 0.044 0.948 0.008
#> GSM62306 2 0.000 0.9660 0.000 1.000 0.000
#> GSM62310 2 0.000 0.9660 0.000 1.000 0.000
#> GSM62311 2 0.000 0.9660 0.000 1.000 0.000
#> GSM62317 2 0.000 0.9660 0.000 1.000 0.000
#> GSM62318 3 0.950 -0.2104 0.188 0.376 0.436
#> GSM62321 2 0.238 0.9283 0.056 0.936 0.008
#> GSM62322 3 0.623 0.7171 0.436 0.000 0.564
#> GSM62250 2 0.238 0.9283 0.056 0.936 0.008
#> GSM62252 2 0.238 0.9283 0.056 0.936 0.008
#> GSM62255 2 0.000 0.9660 0.000 1.000 0.000
#> GSM62257 2 0.000 0.9660 0.000 1.000 0.000
#> GSM62260 2 0.238 0.9283 0.056 0.936 0.008
#> GSM62261 2 0.000 0.9660 0.000 1.000 0.000
#> GSM62262 2 0.000 0.9660 0.000 1.000 0.000
#> GSM62264 2 0.812 0.2913 0.076 0.552 0.372
#> GSM62268 1 0.623 0.7141 0.564 0.000 0.436
#> GSM62269 3 0.623 0.7171 0.436 0.000 0.564
#> GSM62271 1 0.000 0.4548 1.000 0.000 0.000
#> GSM62272 3 0.623 0.7171 0.436 0.000 0.564
#> GSM62273 2 0.129 0.9495 0.032 0.968 0.000
#> GSM62274 1 0.450 0.0899 0.804 0.000 0.196
#> GSM62275 3 0.623 0.7171 0.436 0.000 0.564
#> GSM62276 1 0.588 0.7542 0.652 0.000 0.348
#> GSM62277 1 0.450 0.0899 0.804 0.000 0.196
#> GSM62279 1 0.611 0.7356 0.604 0.000 0.396
#> GSM62282 1 0.000 0.4548 1.000 0.000 0.000
#> GSM62283 1 0.588 0.7542 0.652 0.000 0.348
#> GSM62286 2 0.238 0.9283 0.056 0.936 0.008
#> GSM62287 2 0.000 0.9660 0.000 1.000 0.000
#> GSM62288 2 0.000 0.9660 0.000 1.000 0.000
#> GSM62290 2 0.000 0.9660 0.000 1.000 0.000
#> GSM62293 2 0.175 0.9402 0.048 0.952 0.000
#> GSM62301 2 0.000 0.9660 0.000 1.000 0.000
#> GSM62302 2 0.000 0.9660 0.000 1.000 0.000
#> GSM62303 2 0.000 0.9660 0.000 1.000 0.000
#> GSM62304 2 0.000 0.9660 0.000 1.000 0.000
#> GSM62312 2 0.000 0.9660 0.000 1.000 0.000
#> GSM62313 2 0.000 0.9660 0.000 1.000 0.000
#> GSM62314 2 0.000 0.9660 0.000 1.000 0.000
#> GSM62319 2 0.175 0.9402 0.048 0.952 0.000
#> GSM62320 2 0.000 0.9660 0.000 1.000 0.000
#> GSM62249 2 0.238 0.9283 0.056 0.936 0.008
#> GSM62251 2 0.812 0.2913 0.076 0.552 0.372
#> GSM62263 2 0.000 0.9660 0.000 1.000 0.000
#> GSM62285 2 0.000 0.9660 0.000 1.000 0.000
#> GSM62315 2 0.000 0.9660 0.000 1.000 0.000
#> GSM62291 2 0.000 0.9660 0.000 1.000 0.000
#> GSM62265 1 0.588 0.7542 0.652 0.000 0.348
#> GSM62266 1 0.623 0.7141 0.564 0.000 0.436
#> GSM62296 2 0.000 0.9660 0.000 1.000 0.000
#> GSM62309 2 0.000 0.9660 0.000 1.000 0.000
#> GSM62295 2 0.175 0.9402 0.048 0.952 0.000
#> GSM62300 2 0.000 0.9660 0.000 1.000 0.000
#> GSM62308 2 0.000 0.9660 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM62248 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> GSM62256 2 0.0188 0.927 0.000 0.996 0.000 0.004
#> GSM62259 2 0.0188 0.927 0.000 0.996 0.000 0.004
#> GSM62267 1 0.0000 0.852 1.000 0.000 0.000 0.000
#> GSM62280 1 0.0000 0.852 1.000 0.000 0.000 0.000
#> GSM62284 1 0.4353 0.556 0.756 0.000 0.232 0.012
#> GSM62289 2 0.3837 0.775 0.000 0.776 0.000 0.224
#> GSM62307 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> GSM62316 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> GSM62254 2 0.3123 0.830 0.000 0.844 0.000 0.156
#> GSM62292 2 0.3649 0.793 0.000 0.796 0.000 0.204
#> GSM62253 1 0.2589 0.809 0.884 0.000 0.000 0.116
#> GSM62270 3 0.0000 0.715 0.000 0.000 1.000 0.000
#> GSM62278 3 0.5388 0.272 0.456 0.000 0.532 0.012
#> GSM62297 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> GSM62298 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> GSM62299 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> GSM62258 1 0.0000 0.852 1.000 0.000 0.000 0.000
#> GSM62281 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> GSM62294 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> GSM62305 2 0.4103 0.739 0.000 0.744 0.000 0.256
#> GSM62306 2 0.0188 0.927 0.000 0.996 0.000 0.004
#> GSM62310 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> GSM62311 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> GSM62317 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> GSM62318 4 0.3444 0.718 0.184 0.000 0.000 0.816
#> GSM62321 2 0.4382 0.692 0.000 0.704 0.000 0.296
#> GSM62322 3 0.0000 0.715 0.000 0.000 1.000 0.000
#> GSM62250 2 0.4382 0.692 0.000 0.704 0.000 0.296
#> GSM62252 2 0.4382 0.692 0.000 0.704 0.000 0.296
#> GSM62255 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> GSM62257 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> GSM62260 2 0.4382 0.692 0.000 0.704 0.000 0.296
#> GSM62261 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> GSM62262 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> GSM62264 4 0.0469 0.870 0.000 0.012 0.000 0.988
#> GSM62268 1 0.2469 0.812 0.892 0.000 0.000 0.108
#> GSM62269 3 0.0000 0.715 0.000 0.000 1.000 0.000
#> GSM62271 1 0.5038 0.300 0.652 0.000 0.336 0.012
#> GSM62272 3 0.0000 0.715 0.000 0.000 1.000 0.000
#> GSM62273 2 0.3123 0.830 0.000 0.844 0.000 0.156
#> GSM62274 3 0.5388 0.272 0.456 0.000 0.532 0.012
#> GSM62275 3 0.0000 0.715 0.000 0.000 1.000 0.000
#> GSM62276 1 0.0000 0.852 1.000 0.000 0.000 0.000
#> GSM62277 3 0.5388 0.272 0.456 0.000 0.532 0.012
#> GSM62279 1 0.1792 0.832 0.932 0.000 0.000 0.068
#> GSM62282 1 0.5038 0.300 0.652 0.000 0.336 0.012
#> GSM62283 1 0.0000 0.852 1.000 0.000 0.000 0.000
#> GSM62286 2 0.4382 0.692 0.000 0.704 0.000 0.296
#> GSM62287 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> GSM62288 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> GSM62290 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> GSM62293 2 0.3649 0.793 0.000 0.796 0.000 0.204
#> GSM62301 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> GSM62302 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> GSM62303 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> GSM62304 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> GSM62312 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> GSM62313 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> GSM62314 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> GSM62319 2 0.3649 0.793 0.000 0.796 0.000 0.204
#> GSM62320 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> GSM62249 2 0.4382 0.692 0.000 0.704 0.000 0.296
#> GSM62251 4 0.0469 0.870 0.000 0.012 0.000 0.988
#> GSM62263 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> GSM62285 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> GSM62315 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> GSM62291 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> GSM62265 1 0.0000 0.852 1.000 0.000 0.000 0.000
#> GSM62266 1 0.2469 0.812 0.892 0.000 0.000 0.108
#> GSM62296 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> GSM62309 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> GSM62295 2 0.3649 0.793 0.000 0.796 0.000 0.204
#> GSM62300 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> GSM62308 2 0.0000 0.928 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM62248 4 0.4304 0.343 0.000 0.484 0.000 0.516 0.000
#> GSM62256 4 0.4060 0.624 0.000 0.360 0.000 0.640 0.000
#> GSM62259 4 0.4060 0.624 0.000 0.360 0.000 0.640 0.000
#> GSM62267 1 0.0000 0.753 1.000 0.000 0.000 0.000 0.000
#> GSM62280 1 0.0000 0.753 1.000 0.000 0.000 0.000 0.000
#> GSM62284 1 0.5115 0.635 0.720 0.000 0.108 0.012 0.160
#> GSM62289 4 0.3182 0.671 0.000 0.124 0.000 0.844 0.032
#> GSM62307 2 0.0000 0.916 0.000 1.000 0.000 0.000 0.000
#> GSM62316 4 0.4304 0.343 0.000 0.484 0.000 0.516 0.000
#> GSM62254 4 0.2813 0.687 0.000 0.168 0.000 0.832 0.000
#> GSM62292 4 0.0404 0.630 0.000 0.012 0.000 0.988 0.000
#> GSM62253 1 0.2624 0.691 0.872 0.000 0.000 0.012 0.116
#> GSM62270 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM62278 1 0.6347 0.251 0.432 0.000 0.408 0.000 0.160
#> GSM62297 2 0.3305 0.653 0.000 0.776 0.000 0.224 0.000
#> GSM62298 2 0.3305 0.653 0.000 0.776 0.000 0.224 0.000
#> GSM62299 2 0.3305 0.653 0.000 0.776 0.000 0.224 0.000
#> GSM62258 1 0.0000 0.753 1.000 0.000 0.000 0.000 0.000
#> GSM62281 4 0.4074 0.620 0.000 0.364 0.000 0.636 0.000
#> GSM62294 4 0.4074 0.620 0.000 0.364 0.000 0.636 0.000
#> GSM62305 4 0.3215 0.619 0.000 0.056 0.000 0.852 0.092
#> GSM62306 4 0.4060 0.624 0.000 0.360 0.000 0.640 0.000
#> GSM62310 2 0.0000 0.916 0.000 1.000 0.000 0.000 0.000
#> GSM62311 2 0.0000 0.916 0.000 1.000 0.000 0.000 0.000
#> GSM62317 2 0.0000 0.916 0.000 1.000 0.000 0.000 0.000
#> GSM62318 5 0.4325 0.737 0.180 0.000 0.000 0.064 0.756
#> GSM62321 4 0.2305 0.585 0.000 0.012 0.000 0.896 0.092
#> GSM62322 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM62250 4 0.2305 0.585 0.000 0.012 0.000 0.896 0.092
#> GSM62252 4 0.2305 0.585 0.000 0.012 0.000 0.896 0.092
#> GSM62255 2 0.0000 0.916 0.000 1.000 0.000 0.000 0.000
#> GSM62257 2 0.0000 0.916 0.000 1.000 0.000 0.000 0.000
#> GSM62260 4 0.2305 0.585 0.000 0.012 0.000 0.896 0.092
#> GSM62261 2 0.0000 0.916 0.000 1.000 0.000 0.000 0.000
#> GSM62262 4 0.4074 0.620 0.000 0.364 0.000 0.636 0.000
#> GSM62264 5 0.2732 0.873 0.000 0.000 0.000 0.160 0.840
#> GSM62268 1 0.2522 0.694 0.880 0.000 0.000 0.012 0.108
#> GSM62269 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM62271 1 0.4990 0.504 0.628 0.000 0.324 0.000 0.048
#> GSM62272 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM62273 4 0.2813 0.687 0.000 0.168 0.000 0.832 0.000
#> GSM62274 1 0.6347 0.251 0.432 0.000 0.408 0.000 0.160
#> GSM62275 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM62276 1 0.0000 0.753 1.000 0.000 0.000 0.000 0.000
#> GSM62277 1 0.6347 0.251 0.432 0.000 0.408 0.000 0.160
#> GSM62279 1 0.1942 0.721 0.920 0.000 0.000 0.012 0.068
#> GSM62282 1 0.4990 0.504 0.628 0.000 0.324 0.000 0.048
#> GSM62283 1 0.0000 0.753 1.000 0.000 0.000 0.000 0.000
#> GSM62286 4 0.2305 0.585 0.000 0.012 0.000 0.896 0.092
#> GSM62287 4 0.4074 0.620 0.000 0.364 0.000 0.636 0.000
#> GSM62288 2 0.0000 0.916 0.000 1.000 0.000 0.000 0.000
#> GSM62290 2 0.0963 0.891 0.000 0.964 0.000 0.036 0.000
#> GSM62293 4 0.0404 0.630 0.000 0.012 0.000 0.988 0.000
#> GSM62301 2 0.0000 0.916 0.000 1.000 0.000 0.000 0.000
#> GSM62302 2 0.0000 0.916 0.000 1.000 0.000 0.000 0.000
#> GSM62303 2 0.3424 0.627 0.000 0.760 0.000 0.240 0.000
#> GSM62304 2 0.0000 0.916 0.000 1.000 0.000 0.000 0.000
#> GSM62312 2 0.0000 0.916 0.000 1.000 0.000 0.000 0.000
#> GSM62313 2 0.0000 0.916 0.000 1.000 0.000 0.000 0.000
#> GSM62314 2 0.0000 0.916 0.000 1.000 0.000 0.000 0.000
#> GSM62319 4 0.0404 0.630 0.000 0.012 0.000 0.988 0.000
#> GSM62320 2 0.0000 0.916 0.000 1.000 0.000 0.000 0.000
#> GSM62249 4 0.2305 0.585 0.000 0.012 0.000 0.896 0.092
#> GSM62251 5 0.2732 0.873 0.000 0.000 0.000 0.160 0.840
#> GSM62263 2 0.0000 0.916 0.000 1.000 0.000 0.000 0.000
#> GSM62285 2 0.0000 0.916 0.000 1.000 0.000 0.000 0.000
#> GSM62315 2 0.0000 0.916 0.000 1.000 0.000 0.000 0.000
#> GSM62291 2 0.0963 0.891 0.000 0.964 0.000 0.036 0.000
#> GSM62265 1 0.0000 0.753 1.000 0.000 0.000 0.000 0.000
#> GSM62266 1 0.2522 0.694 0.880 0.000 0.000 0.012 0.108
#> GSM62296 2 0.3424 0.627 0.000 0.760 0.000 0.240 0.000
#> GSM62309 4 0.4074 0.620 0.000 0.364 0.000 0.636 0.000
#> GSM62295 4 0.0404 0.630 0.000 0.012 0.000 0.988 0.000
#> GSM62300 2 0.3424 0.627 0.000 0.760 0.000 0.240 0.000
#> GSM62308 4 0.4074 0.620 0.000 0.364 0.000 0.636 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM62248 4 0.3860 0.360 0.000 0.472 0.000 0.528 0.000 0.000
#> GSM62256 4 0.3607 0.634 0.000 0.348 0.000 0.652 0.000 0.000
#> GSM62259 4 0.3607 0.634 0.000 0.348 0.000 0.652 0.000 0.000
#> GSM62267 1 0.1556 0.920 0.920 0.000 0.000 0.000 0.000 0.080
#> GSM62280 1 0.1556 0.920 0.920 0.000 0.000 0.000 0.000 0.080
#> GSM62284 6 0.3737 0.330 0.392 0.000 0.000 0.000 0.000 0.608
#> GSM62289 4 0.2726 0.701 0.000 0.112 0.000 0.856 0.032 0.000
#> GSM62307 2 0.0000 0.914 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62316 4 0.3860 0.360 0.000 0.472 0.000 0.528 0.000 0.000
#> GSM62254 4 0.2416 0.712 0.000 0.156 0.000 0.844 0.000 0.000
#> GSM62292 4 0.0000 0.667 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62253 1 0.1858 0.865 0.912 0.000 0.000 0.000 0.076 0.012
#> GSM62270 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62278 6 0.0363 0.772 0.000 0.000 0.012 0.000 0.000 0.988
#> GSM62297 2 0.3023 0.642 0.000 0.768 0.000 0.232 0.000 0.000
#> GSM62298 2 0.3023 0.642 0.000 0.768 0.000 0.232 0.000 0.000
#> GSM62299 2 0.3023 0.642 0.000 0.768 0.000 0.232 0.000 0.000
#> GSM62258 1 0.1556 0.920 0.920 0.000 0.000 0.000 0.000 0.080
#> GSM62281 4 0.3620 0.629 0.000 0.352 0.000 0.648 0.000 0.000
#> GSM62294 4 0.3620 0.629 0.000 0.352 0.000 0.648 0.000 0.000
#> GSM62305 4 0.2697 0.657 0.000 0.044 0.000 0.864 0.092 0.000
#> GSM62306 4 0.3607 0.634 0.000 0.348 0.000 0.652 0.000 0.000
#> GSM62310 2 0.0000 0.914 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62311 2 0.0000 0.914 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62317 2 0.0000 0.914 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62318 5 0.2664 0.730 0.184 0.000 0.000 0.000 0.816 0.000
#> GSM62321 4 0.1714 0.631 0.000 0.000 0.000 0.908 0.092 0.000
#> GSM62322 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62250 4 0.1714 0.631 0.000 0.000 0.000 0.908 0.092 0.000
#> GSM62252 4 0.1714 0.631 0.000 0.000 0.000 0.908 0.092 0.000
#> GSM62255 2 0.0000 0.914 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62257 2 0.0000 0.914 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62260 4 0.1714 0.631 0.000 0.000 0.000 0.908 0.092 0.000
#> GSM62261 2 0.0000 0.914 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62262 4 0.3620 0.629 0.000 0.352 0.000 0.648 0.000 0.000
#> GSM62264 5 0.0000 0.874 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM62268 1 0.1745 0.870 0.920 0.000 0.000 0.000 0.068 0.012
#> GSM62269 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62271 6 0.2823 0.725 0.204 0.000 0.000 0.000 0.000 0.796
#> GSM62272 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62273 4 0.2416 0.712 0.000 0.156 0.000 0.844 0.000 0.000
#> GSM62274 6 0.0508 0.773 0.004 0.000 0.012 0.000 0.000 0.984
#> GSM62275 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62276 1 0.1556 0.920 0.920 0.000 0.000 0.000 0.000 0.080
#> GSM62277 6 0.0363 0.772 0.000 0.000 0.012 0.000 0.000 0.988
#> GSM62279 1 0.1074 0.884 0.960 0.000 0.000 0.000 0.028 0.012
#> GSM62282 6 0.2823 0.725 0.204 0.000 0.000 0.000 0.000 0.796
#> GSM62283 1 0.1556 0.920 0.920 0.000 0.000 0.000 0.000 0.080
#> GSM62286 4 0.1714 0.631 0.000 0.000 0.000 0.908 0.092 0.000
#> GSM62287 4 0.3620 0.629 0.000 0.352 0.000 0.648 0.000 0.000
#> GSM62288 2 0.0000 0.914 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62290 2 0.0865 0.889 0.000 0.964 0.000 0.036 0.000 0.000
#> GSM62293 4 0.0000 0.667 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62301 2 0.0000 0.914 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62302 2 0.0000 0.914 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62303 2 0.3126 0.616 0.000 0.752 0.000 0.248 0.000 0.000
#> GSM62304 2 0.0000 0.914 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62312 2 0.0000 0.914 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62313 2 0.0000 0.914 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62314 2 0.0000 0.914 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62319 4 0.0000 0.667 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62320 2 0.0000 0.914 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62249 4 0.1714 0.631 0.000 0.000 0.000 0.908 0.092 0.000
#> GSM62251 5 0.0000 0.874 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM62263 2 0.0000 0.914 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62285 2 0.0000 0.914 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62315 2 0.0000 0.914 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62291 2 0.0865 0.889 0.000 0.964 0.000 0.036 0.000 0.000
#> GSM62265 1 0.1556 0.920 0.920 0.000 0.000 0.000 0.000 0.080
#> GSM62266 1 0.1745 0.870 0.920 0.000 0.000 0.000 0.068 0.012
#> GSM62296 2 0.3126 0.616 0.000 0.752 0.000 0.248 0.000 0.000
#> GSM62309 4 0.3620 0.629 0.000 0.352 0.000 0.648 0.000 0.000
#> GSM62295 4 0.0000 0.667 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62300 2 0.3126 0.616 0.000 0.752 0.000 0.248 0.000 0.000
#> GSM62308 4 0.3620 0.629 0.000 0.352 0.000 0.648 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) other(p) genotype/variation(p) k
#> ATC:hclust 75 0.439 0.943 0.454 2
#> ATC:hclust 67 0.551 0.636 0.820 3
#> ATC:hclust 70 0.657 0.766 0.838 4
#> ATC:hclust 70 0.730 0.937 0.525 5
#> ATC:hclust 72 0.677 0.719 0.763 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "kmeans"]
# you can also extract it by
# res = res_list["ATC:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 75 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 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 0.4208 0.580 0.580
#> 3 3 0.686 0.812 0.911 0.3412 0.717 0.553
#> 4 4 0.910 0.948 0.965 0.2452 0.735 0.445
#> 5 5 0.780 0.648 0.786 0.0931 0.929 0.759
#> 6 6 0.788 0.775 0.824 0.0499 0.881 0.559
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
#> GSM62248 2 0 1 0 1
#> GSM62256 2 0 1 0 1
#> GSM62259 2 0 1 0 1
#> GSM62267 1 0 1 1 0
#> GSM62280 1 0 1 1 0
#> GSM62284 1 0 1 1 0
#> GSM62289 2 0 1 0 1
#> GSM62307 2 0 1 0 1
#> GSM62316 2 0 1 0 1
#> GSM62254 2 0 1 0 1
#> GSM62292 2 0 1 0 1
#> GSM62253 1 0 1 1 0
#> GSM62270 1 0 1 1 0
#> GSM62278 1 0 1 1 0
#> GSM62297 2 0 1 0 1
#> GSM62298 2 0 1 0 1
#> GSM62299 2 0 1 0 1
#> GSM62258 1 0 1 1 0
#> GSM62281 2 0 1 0 1
#> GSM62294 2 0 1 0 1
#> GSM62305 2 0 1 0 1
#> GSM62306 2 0 1 0 1
#> GSM62310 2 0 1 0 1
#> GSM62311 2 0 1 0 1
#> GSM62317 2 0 1 0 1
#> GSM62318 1 0 1 1 0
#> GSM62321 2 0 1 0 1
#> GSM62322 1 0 1 1 0
#> GSM62250 2 0 1 0 1
#> GSM62252 2 0 1 0 1
#> GSM62255 2 0 1 0 1
#> GSM62257 2 0 1 0 1
#> GSM62260 2 0 1 0 1
#> GSM62261 2 0 1 0 1
#> GSM62262 2 0 1 0 1
#> GSM62264 2 0 1 0 1
#> GSM62268 1 0 1 1 0
#> GSM62269 1 0 1 1 0
#> GSM62271 1 0 1 1 0
#> GSM62272 1 0 1 1 0
#> GSM62273 2 0 1 0 1
#> GSM62274 1 0 1 1 0
#> GSM62275 1 0 1 1 0
#> GSM62276 1 0 1 1 0
#> GSM62277 1 0 1 1 0
#> GSM62279 1 0 1 1 0
#> GSM62282 1 0 1 1 0
#> GSM62283 1 0 1 1 0
#> GSM62286 2 0 1 0 1
#> GSM62287 2 0 1 0 1
#> GSM62288 2 0 1 0 1
#> GSM62290 2 0 1 0 1
#> GSM62293 2 0 1 0 1
#> GSM62301 2 0 1 0 1
#> GSM62302 2 0 1 0 1
#> GSM62303 2 0 1 0 1
#> GSM62304 2 0 1 0 1
#> GSM62312 2 0 1 0 1
#> GSM62313 2 0 1 0 1
#> GSM62314 2 0 1 0 1
#> GSM62319 2 0 1 0 1
#> GSM62320 2 0 1 0 1
#> GSM62249 2 0 1 0 1
#> GSM62251 2 0 1 0 1
#> GSM62263 2 0 1 0 1
#> GSM62285 2 0 1 0 1
#> GSM62315 2 0 1 0 1
#> GSM62291 2 0 1 0 1
#> GSM62265 1 0 1 1 0
#> GSM62266 1 0 1 1 0
#> GSM62296 2 0 1 0 1
#> GSM62309 2 0 1 0 1
#> GSM62295 2 0 1 0 1
#> GSM62300 2 0 1 0 1
#> GSM62308 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM62248 2 0.0892 0.970 0.020 0.980 0.000
#> GSM62256 2 0.0892 0.970 0.020 0.980 0.000
#> GSM62259 2 0.0892 0.970 0.020 0.980 0.000
#> GSM62267 1 0.3412 0.536 0.876 0.000 0.124
#> GSM62280 1 0.0892 0.624 0.980 0.000 0.020
#> GSM62284 3 0.4842 0.792 0.224 0.000 0.776
#> GSM62289 2 0.4452 0.722 0.192 0.808 0.000
#> GSM62307 2 0.0000 0.980 0.000 1.000 0.000
#> GSM62316 2 0.0892 0.970 0.020 0.980 0.000
#> GSM62254 2 0.3412 0.841 0.124 0.876 0.000
#> GSM62292 1 0.6215 0.476 0.572 0.428 0.000
#> GSM62253 1 0.3412 0.536 0.876 0.000 0.124
#> GSM62270 3 0.0000 0.887 0.000 0.000 1.000
#> GSM62278 3 0.0000 0.887 0.000 0.000 1.000
#> GSM62297 2 0.0000 0.980 0.000 1.000 0.000
#> GSM62298 2 0.0000 0.980 0.000 1.000 0.000
#> GSM62299 2 0.0000 0.980 0.000 1.000 0.000
#> GSM62258 1 0.0892 0.624 0.980 0.000 0.020
#> GSM62281 2 0.0892 0.970 0.020 0.980 0.000
#> GSM62294 2 0.0892 0.970 0.020 0.980 0.000
#> GSM62305 1 0.6307 0.313 0.512 0.488 0.000
#> GSM62306 2 0.0892 0.970 0.020 0.980 0.000
#> GSM62310 2 0.0000 0.980 0.000 1.000 0.000
#> GSM62311 2 0.0000 0.980 0.000 1.000 0.000
#> GSM62317 2 0.0000 0.980 0.000 1.000 0.000
#> GSM62318 1 0.0000 0.632 1.000 0.000 0.000
#> GSM62321 1 0.6215 0.476 0.572 0.428 0.000
#> GSM62322 3 0.0000 0.887 0.000 0.000 1.000
#> GSM62250 1 0.6215 0.476 0.572 0.428 0.000
#> GSM62252 1 0.4887 0.634 0.772 0.228 0.000
#> GSM62255 2 0.0000 0.980 0.000 1.000 0.000
#> GSM62257 2 0.0000 0.980 0.000 1.000 0.000
#> GSM62260 1 0.0000 0.632 1.000 0.000 0.000
#> GSM62261 2 0.0000 0.980 0.000 1.000 0.000
#> GSM62262 2 0.0892 0.970 0.020 0.980 0.000
#> GSM62264 1 0.4750 0.636 0.784 0.216 0.000
#> GSM62268 1 0.3412 0.536 0.876 0.000 0.124
#> GSM62269 3 0.0000 0.887 0.000 0.000 1.000
#> GSM62271 3 0.6215 0.540 0.428 0.000 0.572
#> GSM62272 3 0.0000 0.887 0.000 0.000 1.000
#> GSM62273 2 0.3412 0.841 0.124 0.876 0.000
#> GSM62274 3 0.4842 0.792 0.224 0.000 0.776
#> GSM62275 3 0.0000 0.887 0.000 0.000 1.000
#> GSM62276 1 0.3412 0.536 0.876 0.000 0.124
#> GSM62277 3 0.0000 0.887 0.000 0.000 1.000
#> GSM62279 1 0.0892 0.624 0.980 0.000 0.020
#> GSM62282 3 0.5431 0.739 0.284 0.000 0.716
#> GSM62283 1 0.0000 0.632 1.000 0.000 0.000
#> GSM62286 1 0.6215 0.476 0.572 0.428 0.000
#> GSM62287 2 0.0000 0.980 0.000 1.000 0.000
#> GSM62288 2 0.0000 0.980 0.000 1.000 0.000
#> GSM62290 2 0.0000 0.980 0.000 1.000 0.000
#> GSM62293 1 0.6215 0.476 0.572 0.428 0.000
#> GSM62301 2 0.0000 0.980 0.000 1.000 0.000
#> GSM62302 2 0.0000 0.980 0.000 1.000 0.000
#> GSM62303 2 0.0000 0.980 0.000 1.000 0.000
#> GSM62304 2 0.0000 0.980 0.000 1.000 0.000
#> GSM62312 2 0.0000 0.980 0.000 1.000 0.000
#> GSM62313 2 0.0000 0.980 0.000 1.000 0.000
#> GSM62314 2 0.0000 0.980 0.000 1.000 0.000
#> GSM62319 1 0.4842 0.635 0.776 0.224 0.000
#> GSM62320 2 0.0000 0.980 0.000 1.000 0.000
#> GSM62249 1 0.6215 0.476 0.572 0.428 0.000
#> GSM62251 1 0.0000 0.632 1.000 0.000 0.000
#> GSM62263 2 0.0000 0.980 0.000 1.000 0.000
#> GSM62285 2 0.0000 0.980 0.000 1.000 0.000
#> GSM62315 2 0.0000 0.980 0.000 1.000 0.000
#> GSM62291 2 0.0000 0.980 0.000 1.000 0.000
#> GSM62265 1 0.0892 0.624 0.980 0.000 0.020
#> GSM62266 1 0.3412 0.536 0.876 0.000 0.124
#> GSM62296 2 0.0000 0.980 0.000 1.000 0.000
#> GSM62309 2 0.0892 0.970 0.020 0.980 0.000
#> GSM62295 1 0.6215 0.476 0.572 0.428 0.000
#> GSM62300 2 0.0000 0.980 0.000 1.000 0.000
#> GSM62308 2 0.0892 0.970 0.020 0.980 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM62248 4 0.1867 0.897 0.000 0.072 0.000 0.928
#> GSM62256 4 0.3873 0.788 0.000 0.228 0.000 0.772
#> GSM62259 4 0.2647 0.870 0.000 0.120 0.000 0.880
#> GSM62267 1 0.0336 0.985 0.992 0.000 0.000 0.008
#> GSM62280 1 0.0336 0.985 0.992 0.000 0.000 0.008
#> GSM62284 1 0.0469 0.985 0.988 0.000 0.000 0.012
#> GSM62289 4 0.0921 0.910 0.000 0.028 0.000 0.972
#> GSM62307 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM62316 4 0.4103 0.755 0.000 0.256 0.000 0.744
#> GSM62254 4 0.0921 0.910 0.000 0.028 0.000 0.972
#> GSM62292 4 0.0921 0.910 0.000 0.028 0.000 0.972
#> GSM62253 1 0.0817 0.983 0.976 0.000 0.000 0.024
#> GSM62270 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM62278 3 0.0376 0.994 0.004 0.000 0.992 0.004
#> GSM62297 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM62298 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM62299 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM62258 1 0.0336 0.985 0.992 0.000 0.000 0.008
#> GSM62281 4 0.1867 0.897 0.000 0.072 0.000 0.928
#> GSM62294 4 0.3873 0.788 0.000 0.228 0.000 0.772
#> GSM62305 4 0.0921 0.910 0.000 0.028 0.000 0.972
#> GSM62306 4 0.2081 0.891 0.000 0.084 0.000 0.916
#> GSM62310 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM62311 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM62317 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM62318 1 0.0817 0.983 0.976 0.000 0.000 0.024
#> GSM62321 4 0.0921 0.910 0.000 0.028 0.000 0.972
#> GSM62322 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM62250 4 0.0921 0.910 0.000 0.028 0.000 0.972
#> GSM62252 4 0.0927 0.902 0.008 0.016 0.000 0.976
#> GSM62255 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM62257 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM62260 4 0.0469 0.887 0.012 0.000 0.000 0.988
#> GSM62261 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM62262 4 0.3873 0.788 0.000 0.228 0.000 0.772
#> GSM62264 4 0.0469 0.885 0.012 0.000 0.000 0.988
#> GSM62268 1 0.0817 0.984 0.976 0.000 0.000 0.024
#> GSM62269 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM62271 1 0.0524 0.984 0.988 0.000 0.008 0.004
#> GSM62272 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM62273 4 0.0921 0.910 0.000 0.028 0.000 0.972
#> GSM62274 1 0.0804 0.982 0.980 0.000 0.012 0.008
#> GSM62275 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM62276 1 0.0336 0.985 0.992 0.000 0.000 0.008
#> GSM62277 3 0.0188 0.997 0.000 0.000 0.996 0.004
#> GSM62279 1 0.0817 0.983 0.976 0.000 0.000 0.024
#> GSM62282 1 0.0524 0.984 0.988 0.000 0.008 0.004
#> GSM62283 1 0.0469 0.985 0.988 0.000 0.000 0.012
#> GSM62286 4 0.0921 0.910 0.000 0.028 0.000 0.972
#> GSM62287 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM62288 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM62290 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM62293 4 0.0921 0.910 0.000 0.028 0.000 0.972
#> GSM62301 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM62302 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM62303 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM62304 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM62312 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM62313 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM62314 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM62319 4 0.0937 0.898 0.012 0.012 0.000 0.976
#> GSM62320 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM62249 4 0.0817 0.907 0.000 0.024 0.000 0.976
#> GSM62251 4 0.3266 0.730 0.168 0.000 0.000 0.832
#> GSM62263 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM62285 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM62315 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM62291 2 0.1940 0.901 0.000 0.924 0.000 0.076
#> GSM62265 1 0.0592 0.985 0.984 0.000 0.000 0.016
#> GSM62266 1 0.0817 0.983 0.976 0.000 0.000 0.024
#> GSM62296 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM62309 4 0.3873 0.788 0.000 0.228 0.000 0.772
#> GSM62295 4 0.0921 0.910 0.000 0.028 0.000 0.972
#> GSM62300 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM62308 4 0.4072 0.761 0.000 0.252 0.000 0.748
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM62248 5 0.4305 -0.4528 0.000 0.000 0.000 0.488 0.512
#> GSM62256 4 0.5458 0.5847 0.000 0.060 0.000 0.476 0.464
#> GSM62259 4 0.4848 0.5480 0.000 0.024 0.000 0.556 0.420
#> GSM62267 1 0.0000 0.8777 1.000 0.000 0.000 0.000 0.000
#> GSM62280 1 0.0000 0.8777 1.000 0.000 0.000 0.000 0.000
#> GSM62284 1 0.2605 0.8693 0.852 0.000 0.000 0.148 0.000
#> GSM62289 5 0.0794 0.6485 0.000 0.000 0.000 0.028 0.972
#> GSM62307 2 0.0000 0.8461 0.000 1.000 0.000 0.000 0.000
#> GSM62316 4 0.5529 0.6093 0.000 0.068 0.000 0.512 0.420
#> GSM62254 5 0.3999 0.4066 0.000 0.000 0.000 0.344 0.656
#> GSM62292 5 0.3796 0.4897 0.000 0.000 0.000 0.300 0.700
#> GSM62253 1 0.3661 0.8419 0.724 0.000 0.000 0.276 0.000
#> GSM62270 3 0.0000 0.9843 0.000 0.000 1.000 0.000 0.000
#> GSM62278 3 0.2193 0.9268 0.060 0.000 0.912 0.028 0.000
#> GSM62297 2 0.4273 0.1978 0.000 0.552 0.000 0.448 0.000
#> GSM62298 2 0.3752 0.5411 0.000 0.708 0.000 0.292 0.000
#> GSM62299 2 0.0000 0.8461 0.000 1.000 0.000 0.000 0.000
#> GSM62258 1 0.0000 0.8777 1.000 0.000 0.000 0.000 0.000
#> GSM62281 5 0.4307 -0.5091 0.000 0.000 0.000 0.496 0.504
#> GSM62294 4 0.4946 0.5544 0.000 0.036 0.000 0.596 0.368
#> GSM62305 5 0.0000 0.6545 0.000 0.000 0.000 0.000 1.000
#> GSM62306 5 0.4655 -0.5303 0.000 0.012 0.000 0.476 0.512
#> GSM62310 2 0.0000 0.8461 0.000 1.000 0.000 0.000 0.000
#> GSM62311 2 0.0000 0.8461 0.000 1.000 0.000 0.000 0.000
#> GSM62317 2 0.0000 0.8461 0.000 1.000 0.000 0.000 0.000
#> GSM62318 1 0.3837 0.8198 0.692 0.000 0.000 0.308 0.000
#> GSM62321 5 0.0794 0.6493 0.000 0.000 0.000 0.028 0.972
#> GSM62322 3 0.0000 0.9843 0.000 0.000 1.000 0.000 0.000
#> GSM62250 5 0.0000 0.6545 0.000 0.000 0.000 0.000 1.000
#> GSM62252 5 0.1121 0.6534 0.000 0.000 0.000 0.044 0.956
#> GSM62255 2 0.0000 0.8461 0.000 1.000 0.000 0.000 0.000
#> GSM62257 2 0.0000 0.8461 0.000 1.000 0.000 0.000 0.000
#> GSM62260 5 0.1608 0.6258 0.000 0.000 0.000 0.072 0.928
#> GSM62261 2 0.0000 0.8461 0.000 1.000 0.000 0.000 0.000
#> GSM62262 4 0.4946 0.5544 0.000 0.036 0.000 0.596 0.368
#> GSM62264 5 0.4030 0.4114 0.000 0.000 0.000 0.352 0.648
#> GSM62268 1 0.3636 0.8434 0.728 0.000 0.000 0.272 0.000
#> GSM62269 3 0.0000 0.9843 0.000 0.000 1.000 0.000 0.000
#> GSM62271 1 0.0794 0.8682 0.972 0.000 0.000 0.028 0.000
#> GSM62272 3 0.0000 0.9843 0.000 0.000 1.000 0.000 0.000
#> GSM62273 5 0.3999 0.4066 0.000 0.000 0.000 0.344 0.656
#> GSM62274 1 0.1270 0.8694 0.948 0.000 0.000 0.052 0.000
#> GSM62275 3 0.0000 0.9843 0.000 0.000 1.000 0.000 0.000
#> GSM62276 1 0.0000 0.8777 1.000 0.000 0.000 0.000 0.000
#> GSM62277 3 0.0794 0.9722 0.000 0.000 0.972 0.028 0.000
#> GSM62279 1 0.3612 0.8434 0.732 0.000 0.000 0.268 0.000
#> GSM62282 1 0.0794 0.8682 0.972 0.000 0.000 0.028 0.000
#> GSM62283 1 0.1270 0.8779 0.948 0.000 0.000 0.052 0.000
#> GSM62286 5 0.1043 0.6532 0.000 0.000 0.000 0.040 0.960
#> GSM62287 2 0.4549 0.1145 0.000 0.528 0.000 0.464 0.008
#> GSM62288 2 0.0000 0.8461 0.000 1.000 0.000 0.000 0.000
#> GSM62290 2 0.4302 0.1220 0.000 0.520 0.000 0.480 0.000
#> GSM62293 5 0.3796 0.4897 0.000 0.000 0.000 0.300 0.700
#> GSM62301 2 0.0000 0.8461 0.000 1.000 0.000 0.000 0.000
#> GSM62302 2 0.3561 0.5888 0.000 0.740 0.000 0.260 0.000
#> GSM62303 2 0.4268 0.2074 0.000 0.556 0.000 0.444 0.000
#> GSM62304 2 0.0000 0.8461 0.000 1.000 0.000 0.000 0.000
#> GSM62312 2 0.0000 0.8461 0.000 1.000 0.000 0.000 0.000
#> GSM62313 2 0.0000 0.8461 0.000 1.000 0.000 0.000 0.000
#> GSM62314 2 0.0703 0.8296 0.000 0.976 0.000 0.024 0.000
#> GSM62319 5 0.2329 0.6205 0.000 0.000 0.000 0.124 0.876
#> GSM62320 2 0.0000 0.8461 0.000 1.000 0.000 0.000 0.000
#> GSM62249 5 0.0404 0.6532 0.000 0.000 0.000 0.012 0.988
#> GSM62251 5 0.4402 0.4014 0.012 0.000 0.000 0.352 0.636
#> GSM62263 2 0.1270 0.8096 0.000 0.948 0.000 0.052 0.000
#> GSM62285 2 0.0000 0.8461 0.000 1.000 0.000 0.000 0.000
#> GSM62315 2 0.0000 0.8461 0.000 1.000 0.000 0.000 0.000
#> GSM62291 4 0.5393 0.0691 0.000 0.440 0.000 0.504 0.056
#> GSM62265 1 0.3480 0.8477 0.752 0.000 0.000 0.248 0.000
#> GSM62266 1 0.3661 0.8419 0.724 0.000 0.000 0.276 0.000
#> GSM62296 4 0.6051 0.2816 0.000 0.404 0.000 0.476 0.120
#> GSM62309 4 0.5435 0.6026 0.000 0.060 0.000 0.512 0.428
#> GSM62295 5 0.3796 0.4897 0.000 0.000 0.000 0.300 0.700
#> GSM62300 2 0.4300 0.1043 0.000 0.524 0.000 0.476 0.000
#> GSM62308 4 0.6122 0.6234 0.000 0.140 0.000 0.512 0.348
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM62248 2 0.1493 0.784 0.000 0.936 0.000 0.004 0.056 0.004
#> GSM62256 2 0.1261 0.810 0.000 0.952 0.000 0.024 0.024 0.000
#> GSM62259 2 0.0692 0.791 0.000 0.976 0.000 0.004 0.020 0.000
#> GSM62267 1 0.0000 0.727 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM62280 1 0.0000 0.727 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM62284 1 0.4294 0.622 0.672 0.000 0.000 0.000 0.048 0.280
#> GSM62289 5 0.2664 0.742 0.000 0.184 0.000 0.000 0.816 0.000
#> GSM62307 4 0.0146 0.981 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM62316 2 0.1138 0.814 0.000 0.960 0.000 0.024 0.012 0.004
#> GSM62254 5 0.5478 0.706 0.000 0.236 0.000 0.000 0.568 0.196
#> GSM62292 5 0.5416 0.713 0.000 0.224 0.000 0.000 0.580 0.196
#> GSM62253 1 0.3864 0.462 0.520 0.000 0.000 0.000 0.000 0.480
#> GSM62270 3 0.0000 0.962 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62278 3 0.3396 0.851 0.076 0.000 0.840 0.000 0.044 0.040
#> GSM62297 2 0.3509 0.767 0.000 0.744 0.000 0.240 0.000 0.016
#> GSM62298 2 0.3853 0.689 0.000 0.680 0.000 0.304 0.000 0.016
#> GSM62299 4 0.1168 0.948 0.000 0.028 0.000 0.956 0.000 0.016
#> GSM62258 1 0.0000 0.727 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM62281 2 0.0632 0.794 0.000 0.976 0.000 0.000 0.024 0.000
#> GSM62294 2 0.2585 0.746 0.000 0.880 0.000 0.004 0.068 0.048
#> GSM62305 5 0.2454 0.748 0.000 0.160 0.000 0.000 0.840 0.000
#> GSM62306 2 0.1285 0.789 0.000 0.944 0.000 0.004 0.052 0.000
#> GSM62310 4 0.0790 0.969 0.000 0.000 0.000 0.968 0.000 0.032
#> GSM62311 4 0.0000 0.982 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62317 4 0.1151 0.962 0.000 0.012 0.000 0.956 0.000 0.032
#> GSM62318 6 0.4741 -0.195 0.344 0.004 0.000 0.000 0.052 0.600
#> GSM62321 5 0.2730 0.736 0.000 0.152 0.000 0.000 0.836 0.012
#> GSM62322 3 0.0000 0.962 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62250 5 0.2416 0.746 0.000 0.156 0.000 0.000 0.844 0.000
#> GSM62252 5 0.2048 0.745 0.000 0.120 0.000 0.000 0.880 0.000
#> GSM62255 4 0.0146 0.981 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM62257 4 0.0146 0.981 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM62260 5 0.4269 0.356 0.000 0.092 0.000 0.000 0.724 0.184
#> GSM62261 4 0.0000 0.982 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62262 2 0.2585 0.746 0.000 0.880 0.000 0.004 0.068 0.048
#> GSM62264 6 0.4361 0.621 0.000 0.024 0.000 0.000 0.424 0.552
#> GSM62268 1 0.4177 0.468 0.520 0.000 0.000 0.000 0.012 0.468
#> GSM62269 3 0.0000 0.962 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62271 1 0.0937 0.712 0.960 0.000 0.000 0.000 0.000 0.040
#> GSM62272 3 0.0000 0.962 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62273 5 0.5478 0.706 0.000 0.236 0.000 0.000 0.568 0.196
#> GSM62274 1 0.3835 0.655 0.748 0.000 0.000 0.000 0.048 0.204
#> GSM62275 3 0.0000 0.962 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62276 1 0.0000 0.727 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM62277 3 0.1934 0.919 0.000 0.000 0.916 0.000 0.044 0.040
#> GSM62279 1 0.4083 0.470 0.532 0.000 0.000 0.000 0.008 0.460
#> GSM62282 1 0.0937 0.712 0.960 0.000 0.000 0.000 0.000 0.040
#> GSM62283 1 0.1588 0.706 0.924 0.000 0.000 0.000 0.004 0.072
#> GSM62286 5 0.2431 0.752 0.000 0.132 0.000 0.000 0.860 0.008
#> GSM62287 2 0.3200 0.799 0.000 0.788 0.000 0.196 0.000 0.016
#> GSM62288 4 0.0790 0.969 0.000 0.000 0.000 0.968 0.000 0.032
#> GSM62290 2 0.3261 0.787 0.000 0.780 0.000 0.204 0.000 0.016
#> GSM62293 5 0.5416 0.713 0.000 0.224 0.000 0.000 0.580 0.196
#> GSM62301 4 0.0000 0.982 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62302 2 0.4465 0.342 0.000 0.512 0.000 0.460 0.000 0.028
#> GSM62303 2 0.3606 0.754 0.000 0.728 0.000 0.256 0.000 0.016
#> GSM62304 4 0.0146 0.981 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM62312 4 0.0000 0.982 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62313 4 0.0146 0.981 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM62314 4 0.1334 0.956 0.000 0.020 0.000 0.948 0.000 0.032
#> GSM62319 5 0.4871 0.718 0.000 0.144 0.000 0.000 0.660 0.196
#> GSM62320 4 0.0146 0.981 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM62249 5 0.2378 0.743 0.000 0.152 0.000 0.000 0.848 0.000
#> GSM62251 6 0.4218 0.621 0.000 0.016 0.000 0.000 0.428 0.556
#> GSM62263 4 0.2250 0.905 0.000 0.020 0.000 0.888 0.000 0.092
#> GSM62285 4 0.0000 0.982 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62315 4 0.0000 0.982 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62291 2 0.2558 0.811 0.000 0.840 0.000 0.156 0.000 0.004
#> GSM62265 1 0.3684 0.531 0.664 0.000 0.000 0.000 0.004 0.332
#> GSM62266 1 0.3864 0.462 0.520 0.000 0.000 0.000 0.000 0.480
#> GSM62296 2 0.2446 0.822 0.000 0.864 0.000 0.124 0.000 0.012
#> GSM62309 2 0.0993 0.813 0.000 0.964 0.000 0.024 0.012 0.000
#> GSM62295 5 0.5416 0.713 0.000 0.224 0.000 0.000 0.580 0.196
#> GSM62300 2 0.2946 0.806 0.000 0.812 0.000 0.176 0.000 0.012
#> GSM62308 2 0.0865 0.818 0.000 0.964 0.000 0.036 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) other(p) genotype/variation(p) k
#> ATC:kmeans 75 0.379 1.000 0.456 2
#> ATC:kmeans 67 0.273 0.548 0.953 3
#> ATC:kmeans 75 0.542 0.766 0.241 4
#> ATC:kmeans 58 0.647 0.771 0.193 5
#> ATC:kmeans 68 0.457 0.794 0.125 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "skmeans"]
# you can also extract it by
# res = res_list["ATC:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 75 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 0.998 0.999 0.4669 0.533 0.533
#> 3 3 1.000 0.950 0.982 0.2564 0.838 0.707
#> 4 4 0.967 0.898 0.965 0.1019 0.928 0.826
#> 5 5 0.938 0.858 0.953 0.0398 0.966 0.904
#> 6 6 0.748 0.766 0.878 0.0663 0.962 0.882
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
#> GSM62248 2 0.000 1.000 0.00 1.00
#> GSM62256 2 0.000 1.000 0.00 1.00
#> GSM62259 2 0.000 1.000 0.00 1.00
#> GSM62267 1 0.000 0.997 1.00 0.00
#> GSM62280 1 0.000 0.997 1.00 0.00
#> GSM62284 1 0.000 0.997 1.00 0.00
#> GSM62289 2 0.000 1.000 0.00 1.00
#> GSM62307 2 0.000 1.000 0.00 1.00
#> GSM62316 2 0.000 1.000 0.00 1.00
#> GSM62254 2 0.000 1.000 0.00 1.00
#> GSM62292 2 0.000 1.000 0.00 1.00
#> GSM62253 1 0.000 0.997 1.00 0.00
#> GSM62270 1 0.000 0.997 1.00 0.00
#> GSM62278 1 0.000 0.997 1.00 0.00
#> GSM62297 2 0.000 1.000 0.00 1.00
#> GSM62298 2 0.000 1.000 0.00 1.00
#> GSM62299 2 0.000 1.000 0.00 1.00
#> GSM62258 1 0.000 0.997 1.00 0.00
#> GSM62281 2 0.000 1.000 0.00 1.00
#> GSM62294 2 0.000 1.000 0.00 1.00
#> GSM62305 2 0.000 1.000 0.00 1.00
#> GSM62306 2 0.000 1.000 0.00 1.00
#> GSM62310 2 0.000 1.000 0.00 1.00
#> GSM62311 2 0.000 1.000 0.00 1.00
#> GSM62317 2 0.000 1.000 0.00 1.00
#> GSM62318 1 0.000 0.997 1.00 0.00
#> GSM62321 2 0.000 1.000 0.00 1.00
#> GSM62322 1 0.000 0.997 1.00 0.00
#> GSM62250 2 0.000 1.000 0.00 1.00
#> GSM62252 1 0.000 0.997 1.00 0.00
#> GSM62255 2 0.000 1.000 0.00 1.00
#> GSM62257 2 0.000 1.000 0.00 1.00
#> GSM62260 1 0.000 0.997 1.00 0.00
#> GSM62261 2 0.000 1.000 0.00 1.00
#> GSM62262 2 0.000 1.000 0.00 1.00
#> GSM62264 1 0.402 0.913 0.92 0.08
#> GSM62268 1 0.000 0.997 1.00 0.00
#> GSM62269 1 0.000 0.997 1.00 0.00
#> GSM62271 1 0.000 0.997 1.00 0.00
#> GSM62272 1 0.000 0.997 1.00 0.00
#> GSM62273 2 0.000 1.000 0.00 1.00
#> GSM62274 1 0.000 0.997 1.00 0.00
#> GSM62275 1 0.000 0.997 1.00 0.00
#> GSM62276 1 0.000 0.997 1.00 0.00
#> GSM62277 1 0.000 0.997 1.00 0.00
#> GSM62279 1 0.000 0.997 1.00 0.00
#> GSM62282 1 0.000 0.997 1.00 0.00
#> GSM62283 1 0.000 0.997 1.00 0.00
#> GSM62286 2 0.000 1.000 0.00 1.00
#> GSM62287 2 0.000 1.000 0.00 1.00
#> GSM62288 2 0.000 1.000 0.00 1.00
#> GSM62290 2 0.000 1.000 0.00 1.00
#> GSM62293 2 0.000 1.000 0.00 1.00
#> GSM62301 2 0.000 1.000 0.00 1.00
#> GSM62302 2 0.000 1.000 0.00 1.00
#> GSM62303 2 0.000 1.000 0.00 1.00
#> GSM62304 2 0.000 1.000 0.00 1.00
#> GSM62312 2 0.000 1.000 0.00 1.00
#> GSM62313 2 0.000 1.000 0.00 1.00
#> GSM62314 2 0.000 1.000 0.00 1.00
#> GSM62319 1 0.000 0.997 1.00 0.00
#> GSM62320 2 0.000 1.000 0.00 1.00
#> GSM62249 2 0.000 1.000 0.00 1.00
#> GSM62251 1 0.000 0.997 1.00 0.00
#> GSM62263 2 0.000 1.000 0.00 1.00
#> GSM62285 2 0.000 1.000 0.00 1.00
#> GSM62315 2 0.000 1.000 0.00 1.00
#> GSM62291 2 0.000 1.000 0.00 1.00
#> GSM62265 1 0.000 0.997 1.00 0.00
#> GSM62266 1 0.000 0.997 1.00 0.00
#> GSM62296 2 0.000 1.000 0.00 1.00
#> GSM62309 2 0.000 1.000 0.00 1.00
#> GSM62295 2 0.000 1.000 0.00 1.00
#> GSM62300 2 0.000 1.000 0.00 1.00
#> GSM62308 2 0.000 1.000 0.00 1.00
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM62248 2 0.0000 0.9823 0.000 1.000 0.000
#> GSM62256 2 0.0000 0.9823 0.000 1.000 0.000
#> GSM62259 2 0.0000 0.9823 0.000 1.000 0.000
#> GSM62267 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM62280 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM62284 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM62289 2 0.0000 0.9823 0.000 1.000 0.000
#> GSM62307 2 0.0000 0.9823 0.000 1.000 0.000
#> GSM62316 2 0.0000 0.9823 0.000 1.000 0.000
#> GSM62254 3 0.0000 0.9020 0.000 0.000 1.000
#> GSM62292 3 0.0000 0.9020 0.000 0.000 1.000
#> GSM62253 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM62270 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM62278 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM62297 2 0.0000 0.9823 0.000 1.000 0.000
#> GSM62298 2 0.0000 0.9823 0.000 1.000 0.000
#> GSM62299 2 0.0000 0.9823 0.000 1.000 0.000
#> GSM62258 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM62281 2 0.0000 0.9823 0.000 1.000 0.000
#> GSM62294 3 0.5591 0.5809 0.000 0.304 0.696
#> GSM62305 2 0.0000 0.9823 0.000 1.000 0.000
#> GSM62306 2 0.0000 0.9823 0.000 1.000 0.000
#> GSM62310 2 0.0000 0.9823 0.000 1.000 0.000
#> GSM62311 2 0.0000 0.9823 0.000 1.000 0.000
#> GSM62317 2 0.0000 0.9823 0.000 1.000 0.000
#> GSM62318 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM62321 2 0.0000 0.9823 0.000 1.000 0.000
#> GSM62322 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM62250 2 0.6267 0.0431 0.000 0.548 0.452
#> GSM62252 3 0.0000 0.9020 0.000 0.000 1.000
#> GSM62255 2 0.0000 0.9823 0.000 1.000 0.000
#> GSM62257 2 0.0000 0.9823 0.000 1.000 0.000
#> GSM62260 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM62261 2 0.0000 0.9823 0.000 1.000 0.000
#> GSM62262 3 0.6154 0.3526 0.000 0.408 0.592
#> GSM62264 2 0.4062 0.7609 0.164 0.836 0.000
#> GSM62268 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM62269 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM62271 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM62272 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM62273 3 0.0000 0.9020 0.000 0.000 1.000
#> GSM62274 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM62275 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM62276 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM62277 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM62279 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM62282 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM62283 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM62286 3 0.0000 0.9020 0.000 0.000 1.000
#> GSM62287 2 0.0000 0.9823 0.000 1.000 0.000
#> GSM62288 2 0.0000 0.9823 0.000 1.000 0.000
#> GSM62290 2 0.0000 0.9823 0.000 1.000 0.000
#> GSM62293 3 0.0000 0.9020 0.000 0.000 1.000
#> GSM62301 2 0.0000 0.9823 0.000 1.000 0.000
#> GSM62302 2 0.0000 0.9823 0.000 1.000 0.000
#> GSM62303 2 0.0000 0.9823 0.000 1.000 0.000
#> GSM62304 2 0.0000 0.9823 0.000 1.000 0.000
#> GSM62312 2 0.0000 0.9823 0.000 1.000 0.000
#> GSM62313 2 0.0000 0.9823 0.000 1.000 0.000
#> GSM62314 2 0.0000 0.9823 0.000 1.000 0.000
#> GSM62319 3 0.0237 0.8989 0.004 0.000 0.996
#> GSM62320 2 0.0000 0.9823 0.000 1.000 0.000
#> GSM62249 2 0.0237 0.9783 0.000 0.996 0.004
#> GSM62251 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM62263 2 0.0000 0.9823 0.000 1.000 0.000
#> GSM62285 2 0.0000 0.9823 0.000 1.000 0.000
#> GSM62315 2 0.0000 0.9823 0.000 1.000 0.000
#> GSM62291 2 0.0000 0.9823 0.000 1.000 0.000
#> GSM62265 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM62266 1 0.0000 1.0000 1.000 0.000 0.000
#> GSM62296 2 0.0000 0.9823 0.000 1.000 0.000
#> GSM62309 2 0.0000 0.9823 0.000 1.000 0.000
#> GSM62295 3 0.0000 0.9020 0.000 0.000 1.000
#> GSM62300 2 0.0000 0.9823 0.000 1.000 0.000
#> GSM62308 2 0.0000 0.9823 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM62248 2 0.0000 0.9827 0.000 1.000 0.000 0.000
#> GSM62256 2 0.0000 0.9827 0.000 1.000 0.000 0.000
#> GSM62259 2 0.0000 0.9827 0.000 1.000 0.000 0.000
#> GSM62267 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM62280 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM62284 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM62289 2 0.4008 0.6446 0.000 0.756 0.244 0.000
#> GSM62307 2 0.0000 0.9827 0.000 1.000 0.000 0.000
#> GSM62316 2 0.0000 0.9827 0.000 1.000 0.000 0.000
#> GSM62254 4 0.0000 0.7622 0.000 0.000 0.000 1.000
#> GSM62292 4 0.0000 0.7622 0.000 0.000 0.000 1.000
#> GSM62253 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM62270 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM62278 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM62297 2 0.0000 0.9827 0.000 1.000 0.000 0.000
#> GSM62298 2 0.0000 0.9827 0.000 1.000 0.000 0.000
#> GSM62299 2 0.0000 0.9827 0.000 1.000 0.000 0.000
#> GSM62258 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM62281 2 0.0000 0.9827 0.000 1.000 0.000 0.000
#> GSM62294 4 0.4790 0.2959 0.000 0.380 0.000 0.620
#> GSM62305 2 0.4522 0.4816 0.000 0.680 0.320 0.000
#> GSM62306 2 0.0000 0.9827 0.000 1.000 0.000 0.000
#> GSM62310 2 0.0000 0.9827 0.000 1.000 0.000 0.000
#> GSM62311 2 0.0000 0.9827 0.000 1.000 0.000 0.000
#> GSM62317 2 0.0000 0.9827 0.000 1.000 0.000 0.000
#> GSM62318 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM62321 3 0.1716 0.7451 0.000 0.064 0.936 0.000
#> GSM62322 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM62250 3 0.7042 0.1671 0.000 0.388 0.488 0.124
#> GSM62252 4 0.4981 0.0633 0.000 0.000 0.464 0.536
#> GSM62255 2 0.0000 0.9827 0.000 1.000 0.000 0.000
#> GSM62257 2 0.0000 0.9827 0.000 1.000 0.000 0.000
#> GSM62260 3 0.1867 0.7560 0.072 0.000 0.928 0.000
#> GSM62261 2 0.0000 0.9827 0.000 1.000 0.000 0.000
#> GSM62262 4 0.4989 0.1578 0.000 0.472 0.000 0.528
#> GSM62264 3 0.0000 0.7773 0.000 0.000 1.000 0.000
#> GSM62268 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM62269 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM62271 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM62272 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM62273 4 0.0000 0.7622 0.000 0.000 0.000 1.000
#> GSM62274 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM62275 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM62276 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM62277 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM62279 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM62282 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM62283 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM62286 4 0.0336 0.7575 0.000 0.000 0.008 0.992
#> GSM62287 2 0.0000 0.9827 0.000 1.000 0.000 0.000
#> GSM62288 2 0.0000 0.9827 0.000 1.000 0.000 0.000
#> GSM62290 2 0.0000 0.9827 0.000 1.000 0.000 0.000
#> GSM62293 4 0.0000 0.7622 0.000 0.000 0.000 1.000
#> GSM62301 2 0.0000 0.9827 0.000 1.000 0.000 0.000
#> GSM62302 2 0.0000 0.9827 0.000 1.000 0.000 0.000
#> GSM62303 2 0.0000 0.9827 0.000 1.000 0.000 0.000
#> GSM62304 2 0.0000 0.9827 0.000 1.000 0.000 0.000
#> GSM62312 2 0.0000 0.9827 0.000 1.000 0.000 0.000
#> GSM62313 2 0.0000 0.9827 0.000 1.000 0.000 0.000
#> GSM62314 2 0.0000 0.9827 0.000 1.000 0.000 0.000
#> GSM62319 4 0.0336 0.7555 0.008 0.000 0.000 0.992
#> GSM62320 2 0.0000 0.9827 0.000 1.000 0.000 0.000
#> GSM62249 3 0.0000 0.7773 0.000 0.000 1.000 0.000
#> GSM62251 3 0.1557 0.7692 0.056 0.000 0.944 0.000
#> GSM62263 2 0.0000 0.9827 0.000 1.000 0.000 0.000
#> GSM62285 2 0.0000 0.9827 0.000 1.000 0.000 0.000
#> GSM62315 2 0.0000 0.9827 0.000 1.000 0.000 0.000
#> GSM62291 2 0.0000 0.9827 0.000 1.000 0.000 0.000
#> GSM62265 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM62266 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM62296 2 0.0000 0.9827 0.000 1.000 0.000 0.000
#> GSM62309 2 0.0000 0.9827 0.000 1.000 0.000 0.000
#> GSM62295 4 0.0000 0.7622 0.000 0.000 0.000 1.000
#> GSM62300 2 0.0000 0.9827 0.000 1.000 0.000 0.000
#> GSM62308 2 0.0000 0.9827 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM62248 2 0.0324 0.9803 0.000 0.992 0.004 0.000 0.004
#> GSM62256 2 0.0000 0.9839 0.000 1.000 0.000 0.000 0.000
#> GSM62259 2 0.0000 0.9839 0.000 1.000 0.000 0.000 0.000
#> GSM62267 1 0.0000 0.9531 1.000 0.000 0.000 0.000 0.000
#> GSM62280 1 0.0000 0.9531 1.000 0.000 0.000 0.000 0.000
#> GSM62284 1 0.0000 0.9531 1.000 0.000 0.000 0.000 0.000
#> GSM62289 5 0.3395 0.4797 0.000 0.236 0.000 0.000 0.764
#> GSM62307 2 0.0000 0.9839 0.000 1.000 0.000 0.000 0.000
#> GSM62316 2 0.0162 0.9826 0.000 0.996 0.000 0.000 0.004
#> GSM62254 4 0.0000 0.7653 0.000 0.000 0.000 1.000 0.000
#> GSM62292 4 0.0000 0.7653 0.000 0.000 0.000 1.000 0.000
#> GSM62253 1 0.3612 0.6413 0.732 0.000 0.268 0.000 0.000
#> GSM62270 1 0.0000 0.9531 1.000 0.000 0.000 0.000 0.000
#> GSM62278 1 0.0000 0.9531 1.000 0.000 0.000 0.000 0.000
#> GSM62297 2 0.0000 0.9839 0.000 1.000 0.000 0.000 0.000
#> GSM62298 2 0.0000 0.9839 0.000 1.000 0.000 0.000 0.000
#> GSM62299 2 0.0000 0.9839 0.000 1.000 0.000 0.000 0.000
#> GSM62258 1 0.0000 0.9531 1.000 0.000 0.000 0.000 0.000
#> GSM62281 2 0.0162 0.9826 0.000 0.996 0.000 0.000 0.004
#> GSM62294 4 0.4268 0.3680 0.000 0.344 0.000 0.648 0.008
#> GSM62305 2 0.5770 0.1042 0.000 0.540 0.028 0.040 0.392
#> GSM62306 2 0.0000 0.9839 0.000 1.000 0.000 0.000 0.000
#> GSM62310 2 0.0162 0.9826 0.000 0.996 0.000 0.000 0.004
#> GSM62311 2 0.0000 0.9839 0.000 1.000 0.000 0.000 0.000
#> GSM62317 2 0.0324 0.9803 0.000 0.992 0.004 0.000 0.004
#> GSM62318 3 0.4278 -0.0173 0.452 0.000 0.548 0.000 0.000
#> GSM62321 3 0.5296 0.1908 0.000 0.280 0.636 0.000 0.084
#> GSM62322 1 0.0000 0.9531 1.000 0.000 0.000 0.000 0.000
#> GSM62250 5 0.0162 0.7990 0.000 0.004 0.000 0.000 0.996
#> GSM62252 5 0.0880 0.8007 0.000 0.000 0.000 0.032 0.968
#> GSM62255 2 0.0000 0.9839 0.000 1.000 0.000 0.000 0.000
#> GSM62257 2 0.0000 0.9839 0.000 1.000 0.000 0.000 0.000
#> GSM62260 3 0.1818 0.5873 0.044 0.000 0.932 0.000 0.024
#> GSM62261 2 0.0000 0.9839 0.000 1.000 0.000 0.000 0.000
#> GSM62262 4 0.4262 0.2657 0.000 0.440 0.000 0.560 0.000
#> GSM62264 3 0.0000 0.5998 0.000 0.000 1.000 0.000 0.000
#> GSM62268 1 0.3508 0.6665 0.748 0.000 0.252 0.000 0.000
#> GSM62269 1 0.0000 0.9531 1.000 0.000 0.000 0.000 0.000
#> GSM62271 1 0.0000 0.9531 1.000 0.000 0.000 0.000 0.000
#> GSM62272 1 0.0000 0.9531 1.000 0.000 0.000 0.000 0.000
#> GSM62273 4 0.0290 0.7608 0.000 0.000 0.000 0.992 0.008
#> GSM62274 1 0.0000 0.9531 1.000 0.000 0.000 0.000 0.000
#> GSM62275 1 0.0000 0.9531 1.000 0.000 0.000 0.000 0.000
#> GSM62276 1 0.0000 0.9531 1.000 0.000 0.000 0.000 0.000
#> GSM62277 1 0.0000 0.9531 1.000 0.000 0.000 0.000 0.000
#> GSM62279 1 0.0880 0.9275 0.968 0.000 0.032 0.000 0.000
#> GSM62282 1 0.0000 0.9531 1.000 0.000 0.000 0.000 0.000
#> GSM62283 1 0.0000 0.9531 1.000 0.000 0.000 0.000 0.000
#> GSM62286 5 0.2690 0.7309 0.000 0.000 0.000 0.156 0.844
#> GSM62287 2 0.0000 0.9839 0.000 1.000 0.000 0.000 0.000
#> GSM62288 2 0.0162 0.9826 0.000 0.996 0.000 0.000 0.004
#> GSM62290 2 0.0162 0.9826 0.000 0.996 0.000 0.000 0.004
#> GSM62293 4 0.0000 0.7653 0.000 0.000 0.000 1.000 0.000
#> GSM62301 2 0.0000 0.9839 0.000 1.000 0.000 0.000 0.000
#> GSM62302 2 0.0162 0.9826 0.000 0.996 0.000 0.000 0.004
#> GSM62303 2 0.0000 0.9839 0.000 1.000 0.000 0.000 0.000
#> GSM62304 2 0.0000 0.9839 0.000 1.000 0.000 0.000 0.000
#> GSM62312 2 0.0000 0.9839 0.000 1.000 0.000 0.000 0.000
#> GSM62313 2 0.0000 0.9839 0.000 1.000 0.000 0.000 0.000
#> GSM62314 2 0.0324 0.9803 0.000 0.992 0.004 0.000 0.004
#> GSM62319 4 0.0162 0.7619 0.004 0.000 0.000 0.996 0.000
#> GSM62320 2 0.0000 0.9839 0.000 1.000 0.000 0.000 0.000
#> GSM62249 5 0.1732 0.7675 0.000 0.000 0.080 0.000 0.920
#> GSM62251 3 0.0162 0.6022 0.004 0.000 0.996 0.000 0.000
#> GSM62263 2 0.0324 0.9803 0.000 0.992 0.004 0.000 0.004
#> GSM62285 2 0.0000 0.9839 0.000 1.000 0.000 0.000 0.000
#> GSM62315 2 0.0000 0.9839 0.000 1.000 0.000 0.000 0.000
#> GSM62291 2 0.0324 0.9803 0.000 0.992 0.004 0.000 0.004
#> GSM62265 1 0.0162 0.9502 0.996 0.000 0.004 0.000 0.000
#> GSM62266 1 0.3586 0.6481 0.736 0.000 0.264 0.000 0.000
#> GSM62296 2 0.0000 0.9839 0.000 1.000 0.000 0.000 0.000
#> GSM62309 2 0.0162 0.9826 0.000 0.996 0.000 0.000 0.004
#> GSM62295 4 0.0000 0.7653 0.000 0.000 0.000 1.000 0.000
#> GSM62300 2 0.0000 0.9839 0.000 1.000 0.000 0.000 0.000
#> GSM62308 2 0.0162 0.9826 0.000 0.996 0.000 0.000 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM62248 4 0.3175 0.7194 0.000 0.000 0.000 0.744 0.000 0.256
#> GSM62256 4 0.2278 0.8024 0.000 0.000 0.000 0.868 0.004 0.128
#> GSM62259 4 0.2320 0.7978 0.000 0.000 0.000 0.864 0.004 0.132
#> GSM62267 3 0.0000 0.9627 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62280 3 0.0000 0.9627 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62284 3 0.2048 0.8275 0.120 0.000 0.880 0.000 0.000 0.000
#> GSM62289 5 0.4680 0.3434 0.000 0.000 0.000 0.132 0.684 0.184
#> GSM62307 4 0.0260 0.8910 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM62316 4 0.3244 0.7223 0.000 0.000 0.000 0.732 0.000 0.268
#> GSM62254 2 0.0508 0.7383 0.000 0.984 0.000 0.000 0.004 0.012
#> GSM62292 2 0.0000 0.7399 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62253 1 0.3756 0.5410 0.600 0.000 0.400 0.000 0.000 0.000
#> GSM62270 3 0.0000 0.9627 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62278 3 0.0000 0.9627 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62297 4 0.0260 0.8912 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM62298 4 0.0260 0.8912 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM62299 4 0.0146 0.8914 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM62258 3 0.0000 0.9627 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62281 4 0.2597 0.8212 0.000 0.000 0.000 0.824 0.000 0.176
#> GSM62294 2 0.5081 0.1373 0.000 0.592 0.000 0.316 0.004 0.088
#> GSM62305 6 0.5878 0.3367 0.000 0.004 0.000 0.308 0.196 0.492
#> GSM62306 4 0.2442 0.7814 0.000 0.000 0.000 0.852 0.004 0.144
#> GSM62310 4 0.1957 0.8470 0.000 0.000 0.000 0.888 0.000 0.112
#> GSM62311 4 0.0000 0.8917 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62317 4 0.2597 0.8001 0.000 0.000 0.000 0.824 0.000 0.176
#> GSM62318 1 0.3351 0.6034 0.712 0.000 0.288 0.000 0.000 0.000
#> GSM62321 6 0.6260 0.3082 0.256 0.000 0.000 0.152 0.052 0.540
#> GSM62322 3 0.0000 0.9627 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62250 5 0.0665 0.7735 0.000 0.004 0.000 0.008 0.980 0.008
#> GSM62252 5 0.1895 0.7676 0.000 0.016 0.000 0.000 0.912 0.072
#> GSM62255 4 0.0363 0.8899 0.000 0.000 0.000 0.988 0.000 0.012
#> GSM62257 4 0.0146 0.8914 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM62260 1 0.4938 -0.0102 0.560 0.000 0.052 0.000 0.008 0.380
#> GSM62261 4 0.0000 0.8917 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62262 2 0.5310 -0.0743 0.000 0.480 0.000 0.428 0.004 0.088
#> GSM62264 1 0.2738 0.2188 0.820 0.000 0.000 0.000 0.004 0.176
#> GSM62268 1 0.3782 0.5167 0.588 0.000 0.412 0.000 0.000 0.000
#> GSM62269 3 0.0000 0.9627 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62271 3 0.0000 0.9627 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62272 3 0.0000 0.9627 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62273 2 0.1152 0.7249 0.000 0.952 0.000 0.000 0.004 0.044
#> GSM62274 3 0.0260 0.9558 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM62275 3 0.0000 0.9627 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62276 3 0.0000 0.9627 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62277 3 0.0000 0.9627 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62279 3 0.2793 0.6916 0.200 0.000 0.800 0.000 0.000 0.000
#> GSM62282 3 0.0000 0.9627 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62283 3 0.0000 0.9627 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62286 5 0.2706 0.7199 0.000 0.124 0.000 0.000 0.852 0.024
#> GSM62287 4 0.1806 0.8413 0.000 0.000 0.000 0.908 0.004 0.088
#> GSM62288 4 0.2178 0.8346 0.000 0.000 0.000 0.868 0.000 0.132
#> GSM62290 4 0.2730 0.7904 0.000 0.000 0.000 0.808 0.000 0.192
#> GSM62293 2 0.0000 0.7399 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62301 4 0.0000 0.8917 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62302 4 0.0937 0.8859 0.000 0.000 0.000 0.960 0.000 0.040
#> GSM62303 4 0.0458 0.8888 0.000 0.000 0.000 0.984 0.000 0.016
#> GSM62304 4 0.0363 0.8899 0.000 0.000 0.000 0.988 0.000 0.012
#> GSM62312 4 0.0000 0.8917 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62313 4 0.0146 0.8910 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM62314 4 0.2854 0.7694 0.000 0.000 0.000 0.792 0.000 0.208
#> GSM62319 2 0.2051 0.6776 0.000 0.896 0.004 0.000 0.004 0.096
#> GSM62320 4 0.0000 0.8917 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62249 5 0.2826 0.7243 0.028 0.000 0.000 0.000 0.844 0.128
#> GSM62251 1 0.0508 0.3547 0.984 0.000 0.004 0.000 0.000 0.012
#> GSM62263 4 0.2912 0.7611 0.000 0.000 0.000 0.784 0.000 0.216
#> GSM62285 4 0.0000 0.8917 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62315 4 0.0000 0.8917 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62291 4 0.2969 0.7548 0.000 0.000 0.000 0.776 0.000 0.224
#> GSM62265 3 0.2340 0.7878 0.148 0.000 0.852 0.000 0.000 0.000
#> GSM62266 1 0.3756 0.5410 0.600 0.000 0.400 0.000 0.000 0.000
#> GSM62296 4 0.1588 0.8535 0.000 0.000 0.000 0.924 0.004 0.072
#> GSM62309 4 0.2793 0.7990 0.000 0.000 0.000 0.800 0.000 0.200
#> GSM62295 2 0.0000 0.7399 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62300 4 0.0790 0.8831 0.000 0.000 0.000 0.968 0.000 0.032
#> GSM62308 4 0.2300 0.8395 0.000 0.000 0.000 0.856 0.000 0.144
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) other(p) genotype/variation(p) k
#> ATC:skmeans 75 0.453 0.570 0.71263 2
#> ATC:skmeans 73 0.512 0.411 0.03614 3
#> ATC:skmeans 70 0.358 0.599 0.00548 4
#> ATC:skmeans 69 0.719 0.703 0.03915 5
#> ATC:skmeans 67 0.604 0.536 0.06692 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "pam"]
# you can also extract it by
# res = res_list["ATC:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 75 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.987 0.995 0.4247 0.580 0.580
#> 3 3 0.632 0.799 0.886 0.4235 0.717 0.540
#> 4 4 0.835 0.838 0.935 0.1636 0.797 0.527
#> 5 5 0.796 0.828 0.892 0.0786 0.878 0.620
#> 6 6 0.784 0.551 0.807 0.0325 0.921 0.709
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
#> GSM62248 2 0.000 0.993 0.000 1.000
#> GSM62256 2 0.000 0.993 0.000 1.000
#> GSM62259 2 0.000 0.993 0.000 1.000
#> GSM62267 1 0.000 1.000 1.000 0.000
#> GSM62280 1 0.000 1.000 1.000 0.000
#> GSM62284 1 0.000 1.000 1.000 0.000
#> GSM62289 2 0.000 0.993 0.000 1.000
#> GSM62307 2 0.000 0.993 0.000 1.000
#> GSM62316 2 0.000 0.993 0.000 1.000
#> GSM62254 2 0.000 0.993 0.000 1.000
#> GSM62292 2 0.000 0.993 0.000 1.000
#> GSM62253 1 0.000 1.000 1.000 0.000
#> GSM62270 1 0.000 1.000 1.000 0.000
#> GSM62278 1 0.000 1.000 1.000 0.000
#> GSM62297 2 0.000 0.993 0.000 1.000
#> GSM62298 2 0.000 0.993 0.000 1.000
#> GSM62299 2 0.000 0.993 0.000 1.000
#> GSM62258 1 0.000 1.000 1.000 0.000
#> GSM62281 2 0.000 0.993 0.000 1.000
#> GSM62294 2 0.000 0.993 0.000 1.000
#> GSM62305 2 0.000 0.993 0.000 1.000
#> GSM62306 2 0.000 0.993 0.000 1.000
#> GSM62310 2 0.000 0.993 0.000 1.000
#> GSM62311 2 0.000 0.993 0.000 1.000
#> GSM62317 2 0.000 0.993 0.000 1.000
#> GSM62318 1 0.000 1.000 1.000 0.000
#> GSM62321 2 0.000 0.993 0.000 1.000
#> GSM62322 1 0.000 1.000 1.000 0.000
#> GSM62250 2 0.000 0.993 0.000 1.000
#> GSM62252 2 0.000 0.993 0.000 1.000
#> GSM62255 2 0.000 0.993 0.000 1.000
#> GSM62257 2 0.000 0.993 0.000 1.000
#> GSM62260 2 0.949 0.418 0.368 0.632
#> GSM62261 2 0.000 0.993 0.000 1.000
#> GSM62262 2 0.000 0.993 0.000 1.000
#> GSM62264 2 0.000 0.993 0.000 1.000
#> GSM62268 1 0.000 1.000 1.000 0.000
#> GSM62269 1 0.000 1.000 1.000 0.000
#> GSM62271 1 0.000 1.000 1.000 0.000
#> GSM62272 1 0.000 1.000 1.000 0.000
#> GSM62273 2 0.000 0.993 0.000 1.000
#> GSM62274 1 0.000 1.000 1.000 0.000
#> GSM62275 1 0.000 1.000 1.000 0.000
#> GSM62276 1 0.000 1.000 1.000 0.000
#> GSM62277 1 0.000 1.000 1.000 0.000
#> GSM62279 1 0.000 1.000 1.000 0.000
#> GSM62282 1 0.000 1.000 1.000 0.000
#> GSM62283 1 0.000 1.000 1.000 0.000
#> GSM62286 2 0.000 0.993 0.000 1.000
#> GSM62287 2 0.000 0.993 0.000 1.000
#> GSM62288 2 0.000 0.993 0.000 1.000
#> GSM62290 2 0.000 0.993 0.000 1.000
#> GSM62293 2 0.000 0.993 0.000 1.000
#> GSM62301 2 0.000 0.993 0.000 1.000
#> GSM62302 2 0.000 0.993 0.000 1.000
#> GSM62303 2 0.000 0.993 0.000 1.000
#> GSM62304 2 0.000 0.993 0.000 1.000
#> GSM62312 2 0.000 0.993 0.000 1.000
#> GSM62313 2 0.000 0.993 0.000 1.000
#> GSM62314 2 0.000 0.993 0.000 1.000
#> GSM62319 2 0.000 0.993 0.000 1.000
#> GSM62320 2 0.000 0.993 0.000 1.000
#> GSM62249 2 0.000 0.993 0.000 1.000
#> GSM62251 2 0.000 0.993 0.000 1.000
#> GSM62263 2 0.000 0.993 0.000 1.000
#> GSM62285 2 0.000 0.993 0.000 1.000
#> GSM62315 2 0.000 0.993 0.000 1.000
#> GSM62291 2 0.000 0.993 0.000 1.000
#> GSM62265 1 0.000 1.000 1.000 0.000
#> GSM62266 1 0.000 1.000 1.000 0.000
#> GSM62296 2 0.000 0.993 0.000 1.000
#> GSM62309 2 0.000 0.993 0.000 1.000
#> GSM62295 2 0.000 0.993 0.000 1.000
#> GSM62300 2 0.000 0.993 0.000 1.000
#> GSM62308 2 0.000 0.993 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM62248 2 0.4504 0.744 0.196 0.804 0.000
#> GSM62256 2 0.0592 0.935 0.012 0.988 0.000
#> GSM62259 2 0.3267 0.841 0.116 0.884 0.000
#> GSM62267 3 0.0000 0.822 0.000 0.000 1.000
#> GSM62280 1 0.6308 0.384 0.508 0.000 0.492
#> GSM62284 3 0.0000 0.822 0.000 0.000 1.000
#> GSM62289 1 0.5591 0.706 0.696 0.304 0.000
#> GSM62307 2 0.0000 0.943 0.000 1.000 0.000
#> GSM62316 2 0.4178 0.779 0.172 0.828 0.000
#> GSM62254 1 0.5591 0.706 0.696 0.304 0.000
#> GSM62292 1 0.5591 0.706 0.696 0.304 0.000
#> GSM62253 3 0.0000 0.822 0.000 0.000 1.000
#> GSM62270 3 0.5591 0.836 0.304 0.000 0.696
#> GSM62278 3 0.5591 0.836 0.304 0.000 0.696
#> GSM62297 2 0.0000 0.943 0.000 1.000 0.000
#> GSM62298 2 0.0000 0.943 0.000 1.000 0.000
#> GSM62299 2 0.0000 0.943 0.000 1.000 0.000
#> GSM62258 1 0.6299 0.416 0.524 0.000 0.476
#> GSM62281 2 0.6026 0.301 0.376 0.624 0.000
#> GSM62294 2 0.0000 0.943 0.000 1.000 0.000
#> GSM62305 1 0.5591 0.706 0.696 0.304 0.000
#> GSM62306 2 0.4346 0.762 0.184 0.816 0.000
#> GSM62310 2 0.0000 0.943 0.000 1.000 0.000
#> GSM62311 2 0.0000 0.943 0.000 1.000 0.000
#> GSM62317 2 0.0000 0.943 0.000 1.000 0.000
#> GSM62318 1 0.5591 0.620 0.696 0.000 0.304
#> GSM62321 1 0.5591 0.706 0.696 0.304 0.000
#> GSM62322 3 0.5591 0.836 0.304 0.000 0.696
#> GSM62250 1 0.5591 0.706 0.696 0.304 0.000
#> GSM62252 1 0.6597 0.715 0.696 0.268 0.036
#> GSM62255 2 0.0000 0.943 0.000 1.000 0.000
#> GSM62257 2 0.0000 0.943 0.000 1.000 0.000
#> GSM62260 1 0.5591 0.620 0.696 0.000 0.304
#> GSM62261 2 0.0000 0.943 0.000 1.000 0.000
#> GSM62262 2 0.0892 0.929 0.020 0.980 0.000
#> GSM62264 1 0.5785 0.623 0.696 0.004 0.300
#> GSM62268 3 0.0000 0.822 0.000 0.000 1.000
#> GSM62269 3 0.5591 0.836 0.304 0.000 0.696
#> GSM62271 3 0.0000 0.822 0.000 0.000 1.000
#> GSM62272 3 0.5591 0.836 0.304 0.000 0.696
#> GSM62273 1 0.5591 0.706 0.696 0.304 0.000
#> GSM62274 3 0.5529 0.836 0.296 0.000 0.704
#> GSM62275 3 0.5591 0.836 0.304 0.000 0.696
#> GSM62276 3 0.0000 0.822 0.000 0.000 1.000
#> GSM62277 3 0.5591 0.836 0.304 0.000 0.696
#> GSM62279 1 0.6299 0.416 0.524 0.000 0.476
#> GSM62282 3 0.0000 0.822 0.000 0.000 1.000
#> GSM62283 1 0.6299 0.416 0.524 0.000 0.476
#> GSM62286 1 0.5591 0.706 0.696 0.304 0.000
#> GSM62287 2 0.0000 0.943 0.000 1.000 0.000
#> GSM62288 2 0.0000 0.943 0.000 1.000 0.000
#> GSM62290 2 0.0000 0.943 0.000 1.000 0.000
#> GSM62293 1 0.5591 0.706 0.696 0.304 0.000
#> GSM62301 2 0.0000 0.943 0.000 1.000 0.000
#> GSM62302 2 0.0000 0.943 0.000 1.000 0.000
#> GSM62303 2 0.0000 0.943 0.000 1.000 0.000
#> GSM62304 2 0.0000 0.943 0.000 1.000 0.000
#> GSM62312 2 0.0000 0.943 0.000 1.000 0.000
#> GSM62313 2 0.0000 0.943 0.000 1.000 0.000
#> GSM62314 2 0.0000 0.943 0.000 1.000 0.000
#> GSM62319 1 0.5591 0.620 0.696 0.000 0.304
#> GSM62320 2 0.0000 0.943 0.000 1.000 0.000
#> GSM62249 1 0.5591 0.706 0.696 0.304 0.000
#> GSM62251 1 0.5591 0.620 0.696 0.000 0.304
#> GSM62263 2 0.0000 0.943 0.000 1.000 0.000
#> GSM62285 2 0.0000 0.943 0.000 1.000 0.000
#> GSM62315 2 0.0000 0.943 0.000 1.000 0.000
#> GSM62291 2 0.4178 0.779 0.172 0.828 0.000
#> GSM62265 1 0.6299 0.416 0.524 0.000 0.476
#> GSM62266 3 0.0000 0.822 0.000 0.000 1.000
#> GSM62296 2 0.0000 0.943 0.000 1.000 0.000
#> GSM62309 2 0.4842 0.697 0.224 0.776 0.000
#> GSM62295 1 0.5591 0.706 0.696 0.304 0.000
#> GSM62300 2 0.0000 0.943 0.000 1.000 0.000
#> GSM62308 2 0.4178 0.779 0.172 0.828 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM62248 4 0.4985 0.171 0.000 0.468 0.000 0.532
#> GSM62256 2 0.1557 0.906 0.000 0.944 0.000 0.056
#> GSM62259 4 0.4543 0.580 0.000 0.324 0.000 0.676
#> GSM62267 1 0.0000 0.903 1.000 0.000 0.000 0.000
#> GSM62280 1 0.0000 0.903 1.000 0.000 0.000 0.000
#> GSM62284 1 0.0000 0.903 1.000 0.000 0.000 0.000
#> GSM62289 4 0.0000 0.820 0.000 0.000 0.000 1.000
#> GSM62307 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM62316 2 0.3123 0.773 0.000 0.844 0.000 0.156
#> GSM62254 4 0.0000 0.820 0.000 0.000 0.000 1.000
#> GSM62292 4 0.0000 0.820 0.000 0.000 0.000 1.000
#> GSM62253 1 0.0000 0.903 1.000 0.000 0.000 0.000
#> GSM62270 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM62278 3 0.0469 0.987 0.012 0.000 0.988 0.000
#> GSM62297 2 0.1022 0.931 0.000 0.968 0.000 0.032
#> GSM62298 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM62299 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM62258 1 0.0000 0.903 1.000 0.000 0.000 0.000
#> GSM62281 4 0.2408 0.761 0.000 0.104 0.000 0.896
#> GSM62294 4 0.4888 0.424 0.000 0.412 0.000 0.588
#> GSM62305 4 0.0000 0.820 0.000 0.000 0.000 1.000
#> GSM62306 2 0.4925 0.143 0.000 0.572 0.000 0.428
#> GSM62310 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM62311 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM62317 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM62318 1 0.0000 0.903 1.000 0.000 0.000 0.000
#> GSM62321 4 0.0000 0.820 0.000 0.000 0.000 1.000
#> GSM62322 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM62250 4 0.0000 0.820 0.000 0.000 0.000 1.000
#> GSM62252 4 0.0000 0.820 0.000 0.000 0.000 1.000
#> GSM62255 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM62257 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM62260 1 0.4992 0.252 0.524 0.000 0.000 0.476
#> GSM62261 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM62262 4 0.4855 0.451 0.000 0.400 0.000 0.600
#> GSM62264 1 0.4643 0.526 0.656 0.000 0.000 0.344
#> GSM62268 1 0.0000 0.903 1.000 0.000 0.000 0.000
#> GSM62269 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM62271 1 0.0000 0.903 1.000 0.000 0.000 0.000
#> GSM62272 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM62273 4 0.0000 0.820 0.000 0.000 0.000 1.000
#> GSM62274 1 0.4790 0.357 0.620 0.000 0.380 0.000
#> GSM62275 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM62276 1 0.0000 0.903 1.000 0.000 0.000 0.000
#> GSM62277 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM62279 1 0.0000 0.903 1.000 0.000 0.000 0.000
#> GSM62282 1 0.0000 0.903 1.000 0.000 0.000 0.000
#> GSM62283 1 0.0000 0.903 1.000 0.000 0.000 0.000
#> GSM62286 4 0.0000 0.820 0.000 0.000 0.000 1.000
#> GSM62287 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM62288 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM62290 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM62293 4 0.0000 0.820 0.000 0.000 0.000 1.000
#> GSM62301 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM62302 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM62303 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM62304 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM62312 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM62313 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM62314 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM62319 4 0.0000 0.820 0.000 0.000 0.000 1.000
#> GSM62320 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM62249 4 0.0000 0.820 0.000 0.000 0.000 1.000
#> GSM62251 1 0.3801 0.697 0.780 0.000 0.000 0.220
#> GSM62263 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM62285 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM62315 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM62291 2 0.4222 0.566 0.000 0.728 0.000 0.272
#> GSM62265 1 0.0000 0.903 1.000 0.000 0.000 0.000
#> GSM62266 1 0.0000 0.903 1.000 0.000 0.000 0.000
#> GSM62296 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM62309 4 0.4761 0.500 0.000 0.372 0.000 0.628
#> GSM62295 4 0.0000 0.820 0.000 0.000 0.000 1.000
#> GSM62300 2 0.0000 0.961 0.000 1.000 0.000 0.000
#> GSM62308 4 0.4804 0.477 0.000 0.384 0.000 0.616
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM62248 5 0.0510 0.7654 0.000 0.016 0.000 0.000 0.984
#> GSM62256 5 0.4210 0.3684 0.000 0.412 0.000 0.000 0.588
#> GSM62259 5 0.3561 0.5853 0.000 0.260 0.000 0.000 0.740
#> GSM62267 1 0.0000 0.9006 1.000 0.000 0.000 0.000 0.000
#> GSM62280 1 0.0000 0.9006 1.000 0.000 0.000 0.000 0.000
#> GSM62284 1 0.3508 0.7822 0.748 0.000 0.000 0.252 0.000
#> GSM62289 5 0.0290 0.7540 0.000 0.000 0.000 0.008 0.992
#> GSM62307 2 0.0000 0.9365 0.000 1.000 0.000 0.000 0.000
#> GSM62316 5 0.3274 0.6438 0.000 0.220 0.000 0.000 0.780
#> GSM62254 4 0.3508 0.9394 0.000 0.000 0.000 0.748 0.252
#> GSM62292 4 0.3508 0.9394 0.000 0.000 0.000 0.748 0.252
#> GSM62253 1 0.1341 0.8966 0.944 0.000 0.000 0.056 0.000
#> GSM62270 3 0.0000 0.9407 0.000 0.000 1.000 0.000 0.000
#> GSM62278 3 0.3988 0.8309 0.036 0.000 0.768 0.196 0.000
#> GSM62297 2 0.3534 0.6399 0.000 0.744 0.000 0.000 0.256
#> GSM62298 2 0.1121 0.9208 0.000 0.956 0.000 0.000 0.044
#> GSM62299 2 0.0963 0.9252 0.000 0.964 0.000 0.000 0.036
#> GSM62258 1 0.0000 0.9006 1.000 0.000 0.000 0.000 0.000
#> GSM62281 5 0.0510 0.7651 0.000 0.016 0.000 0.000 0.984
#> GSM62294 2 0.4491 0.4553 0.000 0.652 0.000 0.020 0.328
#> GSM62305 5 0.1965 0.6716 0.000 0.000 0.000 0.096 0.904
#> GSM62306 5 0.0794 0.7662 0.000 0.028 0.000 0.000 0.972
#> GSM62310 2 0.0000 0.9365 0.000 1.000 0.000 0.000 0.000
#> GSM62311 2 0.0000 0.9365 0.000 1.000 0.000 0.000 0.000
#> GSM62317 2 0.0000 0.9365 0.000 1.000 0.000 0.000 0.000
#> GSM62318 1 0.1341 0.8966 0.944 0.000 0.000 0.056 0.000
#> GSM62321 5 0.0290 0.7540 0.000 0.000 0.000 0.008 0.992
#> GSM62322 3 0.0000 0.9407 0.000 0.000 1.000 0.000 0.000
#> GSM62250 5 0.1121 0.7246 0.000 0.000 0.000 0.044 0.956
#> GSM62252 4 0.3508 0.9394 0.000 0.000 0.000 0.748 0.252
#> GSM62255 2 0.0000 0.9365 0.000 1.000 0.000 0.000 0.000
#> GSM62257 2 0.0000 0.9365 0.000 1.000 0.000 0.000 0.000
#> GSM62260 5 0.3388 0.6089 0.200 0.000 0.000 0.008 0.792
#> GSM62261 2 0.0000 0.9365 0.000 1.000 0.000 0.000 0.000
#> GSM62262 4 0.5727 0.5444 0.000 0.100 0.000 0.560 0.340
#> GSM62264 5 0.3318 0.6292 0.180 0.000 0.000 0.012 0.808
#> GSM62268 1 0.1341 0.8966 0.944 0.000 0.000 0.056 0.000
#> GSM62269 3 0.0000 0.9407 0.000 0.000 1.000 0.000 0.000
#> GSM62271 1 0.3074 0.7876 0.804 0.000 0.000 0.196 0.000
#> GSM62272 3 0.0000 0.9407 0.000 0.000 1.000 0.000 0.000
#> GSM62273 4 0.3612 0.9263 0.000 0.000 0.000 0.732 0.268
#> GSM62274 1 0.6715 0.0198 0.392 0.000 0.360 0.248 0.000
#> GSM62275 3 0.0000 0.9407 0.000 0.000 1.000 0.000 0.000
#> GSM62276 1 0.0000 0.9006 1.000 0.000 0.000 0.000 0.000
#> GSM62277 3 0.3074 0.8512 0.000 0.000 0.804 0.196 0.000
#> GSM62279 1 0.1197 0.8976 0.952 0.000 0.000 0.048 0.000
#> GSM62282 1 0.3074 0.7876 0.804 0.000 0.000 0.196 0.000
#> GSM62283 1 0.0000 0.9006 1.000 0.000 0.000 0.000 0.000
#> GSM62286 4 0.3932 0.8576 0.000 0.000 0.000 0.672 0.328
#> GSM62287 2 0.0963 0.9252 0.000 0.964 0.000 0.000 0.036
#> GSM62288 2 0.0000 0.9365 0.000 1.000 0.000 0.000 0.000
#> GSM62290 2 0.3177 0.7542 0.000 0.792 0.000 0.000 0.208
#> GSM62293 4 0.3508 0.9394 0.000 0.000 0.000 0.748 0.252
#> GSM62301 2 0.0000 0.9365 0.000 1.000 0.000 0.000 0.000
#> GSM62302 2 0.0963 0.9252 0.000 0.964 0.000 0.000 0.036
#> GSM62303 2 0.0963 0.9252 0.000 0.964 0.000 0.000 0.036
#> GSM62304 2 0.0000 0.9365 0.000 1.000 0.000 0.000 0.000
#> GSM62312 2 0.0000 0.9365 0.000 1.000 0.000 0.000 0.000
#> GSM62313 2 0.0000 0.9365 0.000 1.000 0.000 0.000 0.000
#> GSM62314 2 0.2773 0.7748 0.000 0.836 0.000 0.000 0.164
#> GSM62319 4 0.3508 0.9394 0.000 0.000 0.000 0.748 0.252
#> GSM62320 2 0.0000 0.9365 0.000 1.000 0.000 0.000 0.000
#> GSM62249 5 0.0880 0.7354 0.000 0.000 0.000 0.032 0.968
#> GSM62251 1 0.2068 0.8414 0.904 0.000 0.000 0.004 0.092
#> GSM62263 2 0.3177 0.7542 0.000 0.792 0.000 0.000 0.208
#> GSM62285 2 0.0000 0.9365 0.000 1.000 0.000 0.000 0.000
#> GSM62315 2 0.0000 0.9365 0.000 1.000 0.000 0.000 0.000
#> GSM62291 5 0.2329 0.7281 0.000 0.124 0.000 0.000 0.876
#> GSM62265 1 0.0000 0.9006 1.000 0.000 0.000 0.000 0.000
#> GSM62266 1 0.1341 0.8966 0.944 0.000 0.000 0.056 0.000
#> GSM62296 2 0.1410 0.9099 0.000 0.940 0.000 0.000 0.060
#> GSM62309 5 0.1908 0.7455 0.000 0.092 0.000 0.000 0.908
#> GSM62295 4 0.3508 0.9394 0.000 0.000 0.000 0.748 0.252
#> GSM62300 2 0.1121 0.9208 0.000 0.956 0.000 0.000 0.044
#> GSM62308 5 0.3796 0.5481 0.000 0.300 0.000 0.000 0.700
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM62248 5 0.3765 0.3854 0.404 0.000 0.000 0.000 0.596 0.000
#> GSM62256 5 0.3774 0.0323 0.000 0.000 0.000 0.408 0.592 0.000
#> GSM62259 5 0.3765 0.0429 0.000 0.000 0.000 0.404 0.596 0.000
#> GSM62267 5 0.5902 -0.3540 0.392 0.000 0.000 0.000 0.404 0.204
#> GSM62280 5 0.5917 -0.3577 0.388 0.000 0.000 0.000 0.404 0.208
#> GSM62284 6 0.2823 0.1016 0.204 0.000 0.000 0.000 0.000 0.796
#> GSM62289 5 0.4851 0.3642 0.404 0.060 0.000 0.000 0.536 0.000
#> GSM62307 4 0.0000 0.9242 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62316 5 0.3765 0.3854 0.404 0.000 0.000 0.000 0.596 0.000
#> GSM62254 2 0.0000 0.8660 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62292 2 0.0000 0.8660 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62253 1 0.3804 0.4706 0.576 0.000 0.000 0.000 0.000 0.424
#> GSM62270 3 0.0000 0.9150 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62278 6 0.5993 0.2903 0.004 0.000 0.296 0.000 0.228 0.472
#> GSM62297 4 0.3695 0.4913 0.000 0.000 0.000 0.624 0.376 0.000
#> GSM62298 4 0.1814 0.8902 0.000 0.000 0.000 0.900 0.100 0.000
#> GSM62299 4 0.1556 0.9004 0.000 0.000 0.000 0.920 0.080 0.000
#> GSM62258 5 0.5902 -0.3540 0.392 0.000 0.000 0.000 0.404 0.204
#> GSM62281 5 0.3765 0.3854 0.404 0.000 0.000 0.000 0.596 0.000
#> GSM62294 4 0.4534 0.4312 0.000 0.040 0.000 0.580 0.380 0.000
#> GSM62305 5 0.5659 0.3064 0.336 0.168 0.000 0.000 0.496 0.000
#> GSM62306 5 0.4141 0.3862 0.388 0.000 0.000 0.016 0.596 0.000
#> GSM62310 4 0.0000 0.9242 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62311 4 0.0000 0.9242 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62317 4 0.0000 0.9242 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62318 1 0.3804 0.4706 0.576 0.000 0.000 0.000 0.000 0.424
#> GSM62321 5 0.4851 0.3642 0.404 0.060 0.000 0.000 0.536 0.000
#> GSM62322 3 0.0000 0.9150 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62250 5 0.5270 0.3354 0.404 0.100 0.000 0.000 0.496 0.000
#> GSM62252 2 0.0000 0.8660 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62255 4 0.0000 0.9242 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62257 4 0.0000 0.9242 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62260 1 0.4838 -0.2683 0.564 0.064 0.000 0.000 0.372 0.000
#> GSM62261 4 0.0000 0.9242 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62262 2 0.4057 0.3992 0.000 0.600 0.000 0.012 0.388 0.000
#> GSM62264 1 0.4674 -0.2355 0.608 0.060 0.000 0.000 0.332 0.000
#> GSM62268 1 0.3810 0.4658 0.572 0.000 0.000 0.000 0.000 0.428
#> GSM62269 3 0.0000 0.9150 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62271 6 0.4254 0.5722 0.020 0.000 0.000 0.000 0.404 0.576
#> GSM62272 3 0.0000 0.9150 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62273 2 0.0363 0.8539 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM62274 6 0.0000 0.4014 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM62275 3 0.0000 0.9150 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM62276 5 0.5902 -0.3540 0.392 0.000 0.000 0.000 0.404 0.204
#> GSM62277 3 0.3684 0.4015 0.000 0.000 0.628 0.000 0.000 0.372
#> GSM62279 1 0.3923 0.4646 0.580 0.000 0.000 0.000 0.004 0.416
#> GSM62282 6 0.4254 0.5722 0.020 0.000 0.000 0.000 0.404 0.576
#> GSM62283 5 0.5902 -0.3540 0.392 0.000 0.000 0.000 0.404 0.204
#> GSM62286 2 0.4110 0.4062 0.376 0.608 0.000 0.000 0.016 0.000
#> GSM62287 4 0.1556 0.9004 0.000 0.000 0.000 0.920 0.080 0.000
#> GSM62288 4 0.0000 0.9242 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62290 4 0.2558 0.8725 0.028 0.000 0.000 0.868 0.104 0.000
#> GSM62293 2 0.0000 0.8660 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62301 4 0.0000 0.9242 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62302 4 0.1814 0.8902 0.000 0.000 0.000 0.900 0.100 0.000
#> GSM62303 4 0.1663 0.8967 0.000 0.000 0.000 0.912 0.088 0.000
#> GSM62304 4 0.0000 0.9242 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62312 4 0.0000 0.9242 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62313 4 0.0000 0.9242 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62314 4 0.0972 0.9083 0.028 0.000 0.000 0.964 0.008 0.000
#> GSM62319 2 0.0000 0.8660 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62320 4 0.0000 0.9242 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62249 5 0.5233 0.3390 0.404 0.096 0.000 0.000 0.500 0.000
#> GSM62251 1 0.0622 0.3027 0.980 0.008 0.000 0.000 0.012 0.000
#> GSM62263 4 0.2558 0.8725 0.028 0.000 0.000 0.868 0.104 0.000
#> GSM62285 4 0.0000 0.9242 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62315 4 0.0000 0.9242 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62291 5 0.5095 0.3632 0.368 0.000 0.000 0.088 0.544 0.000
#> GSM62265 5 0.5902 -0.3540 0.392 0.000 0.000 0.000 0.404 0.204
#> GSM62266 1 0.3804 0.4706 0.576 0.000 0.000 0.000 0.000 0.424
#> GSM62296 4 0.2823 0.7831 0.000 0.000 0.000 0.796 0.204 0.000
#> GSM62309 5 0.4756 0.3768 0.380 0.000 0.000 0.056 0.564 0.000
#> GSM62295 2 0.0000 0.8660 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM62300 4 0.1814 0.8902 0.000 0.000 0.000 0.900 0.100 0.000
#> GSM62308 5 0.3979 -0.1080 0.004 0.000 0.000 0.456 0.540 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) other(p) genotype/variation(p) k
#> ATC:pam 74 0.362 1.000 0.455 2
#> ATC:pam 69 0.374 0.816 0.238 3
#> ATC:pam 67 0.587 0.923 0.433 4
#> ATC:pam 72 0.618 0.116 0.032 5
#> ATC:pam 39 0.640 0.682 0.352 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "mclust"]
# you can also extract it by
# res = res_list["ATC:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 75 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.674 0.950 0.954 0.4548 0.550 0.550
#> 3 3 0.629 0.854 0.866 0.2233 0.944 0.898
#> 4 4 0.573 0.663 0.746 0.2278 0.795 0.595
#> 5 5 0.630 0.774 0.799 0.0663 0.809 0.492
#> 6 6 0.825 0.867 0.885 0.0997 0.926 0.710
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
#> GSM62248 2 0.4562 0.933 0.096 0.904
#> GSM62256 2 0.0000 0.934 0.000 1.000
#> GSM62259 2 0.4161 0.935 0.084 0.916
#> GSM62267 1 0.0000 0.999 1.000 0.000
#> GSM62280 1 0.0000 0.999 1.000 0.000
#> GSM62284 1 0.0000 0.999 1.000 0.000
#> GSM62289 2 0.4939 0.921 0.108 0.892
#> GSM62307 2 0.0000 0.934 0.000 1.000
#> GSM62316 2 0.0938 0.938 0.012 0.988
#> GSM62254 2 0.5408 0.922 0.124 0.876
#> GSM62292 2 0.5408 0.922 0.124 0.876
#> GSM62253 1 0.0000 0.999 1.000 0.000
#> GSM62270 1 0.0000 0.999 1.000 0.000
#> GSM62278 1 0.0000 0.999 1.000 0.000
#> GSM62297 2 0.5842 0.909 0.140 0.860
#> GSM62298 2 0.0000 0.934 0.000 1.000
#> GSM62299 2 0.2603 0.940 0.044 0.956
#> GSM62258 1 0.0000 0.999 1.000 0.000
#> GSM62281 2 0.0938 0.938 0.012 0.988
#> GSM62294 2 0.5408 0.922 0.124 0.876
#> GSM62305 2 0.6148 0.903 0.152 0.848
#> GSM62306 2 0.2236 0.934 0.036 0.964
#> GSM62310 2 0.0938 0.938 0.012 0.988
#> GSM62311 2 0.0000 0.934 0.000 1.000
#> GSM62317 2 0.4690 0.932 0.100 0.900
#> GSM62318 1 0.0000 0.999 1.000 0.000
#> GSM62321 2 0.6531 0.890 0.168 0.832
#> GSM62322 1 0.0000 0.999 1.000 0.000
#> GSM62250 2 0.6247 0.898 0.156 0.844
#> GSM62252 2 0.6623 0.884 0.172 0.828
#> GSM62255 2 0.0000 0.934 0.000 1.000
#> GSM62257 2 0.0376 0.936 0.004 0.996
#> GSM62260 1 0.1633 0.972 0.976 0.024
#> GSM62261 2 0.5519 0.917 0.128 0.872
#> GSM62262 2 0.4562 0.934 0.096 0.904
#> GSM62264 1 0.0000 0.999 1.000 0.000
#> GSM62268 1 0.0000 0.999 1.000 0.000
#> GSM62269 1 0.0000 0.999 1.000 0.000
#> GSM62271 1 0.0000 0.999 1.000 0.000
#> GSM62272 1 0.0000 0.999 1.000 0.000
#> GSM62273 2 0.5294 0.924 0.120 0.880
#> GSM62274 1 0.0000 0.999 1.000 0.000
#> GSM62275 1 0.0000 0.999 1.000 0.000
#> GSM62276 1 0.0000 0.999 1.000 0.000
#> GSM62277 1 0.0000 0.999 1.000 0.000
#> GSM62279 1 0.0000 0.999 1.000 0.000
#> GSM62282 1 0.0000 0.999 1.000 0.000
#> GSM62283 1 0.0000 0.999 1.000 0.000
#> GSM62286 2 0.6438 0.892 0.164 0.836
#> GSM62287 2 0.4690 0.932 0.100 0.900
#> GSM62288 2 0.2423 0.940 0.040 0.960
#> GSM62290 2 0.0938 0.938 0.012 0.988
#> GSM62293 2 0.5408 0.922 0.124 0.876
#> GSM62301 2 0.0000 0.934 0.000 1.000
#> GSM62302 2 0.0938 0.938 0.012 0.988
#> GSM62303 2 0.0000 0.934 0.000 1.000
#> GSM62304 2 0.0000 0.934 0.000 1.000
#> GSM62312 2 0.3584 0.938 0.068 0.932
#> GSM62313 2 0.0000 0.934 0.000 1.000
#> GSM62314 2 0.4690 0.932 0.100 0.900
#> GSM62319 2 0.5519 0.920 0.128 0.872
#> GSM62320 2 0.0000 0.934 0.000 1.000
#> GSM62249 2 0.6531 0.888 0.168 0.832
#> GSM62251 1 0.0000 0.999 1.000 0.000
#> GSM62263 2 0.6973 0.871 0.188 0.812
#> GSM62285 2 0.0000 0.934 0.000 1.000
#> GSM62315 2 0.0000 0.934 0.000 1.000
#> GSM62291 2 0.4690 0.932 0.100 0.900
#> GSM62265 1 0.0000 0.999 1.000 0.000
#> GSM62266 1 0.0000 0.999 1.000 0.000
#> GSM62296 2 0.2236 0.940 0.036 0.964
#> GSM62309 2 0.0938 0.938 0.012 0.988
#> GSM62295 2 0.5408 0.922 0.124 0.876
#> GSM62300 2 0.0000 0.934 0.000 1.000
#> GSM62308 2 0.0938 0.938 0.012 0.988
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM62248 2 0.3896 0.877 0.060 0.888 0.052
#> GSM62256 2 0.2356 0.891 0.072 0.928 0.000
#> GSM62259 2 0.2998 0.892 0.068 0.916 0.016
#> GSM62267 1 0.4605 0.968 0.796 0.000 0.204
#> GSM62280 1 0.4605 0.968 0.796 0.000 0.204
#> GSM62284 3 0.0892 0.937 0.020 0.000 0.980
#> GSM62289 2 0.7424 0.440 0.388 0.572 0.040
#> GSM62307 2 0.3116 0.876 0.108 0.892 0.000
#> GSM62316 2 0.1964 0.891 0.056 0.944 0.000
#> GSM62254 2 0.3045 0.891 0.064 0.916 0.020
#> GSM62292 2 0.3181 0.891 0.064 0.912 0.024
#> GSM62253 3 0.1411 0.932 0.036 0.000 0.964
#> GSM62270 3 0.0000 0.938 0.000 0.000 1.000
#> GSM62278 3 0.0424 0.937 0.008 0.000 0.992
#> GSM62297 2 0.3683 0.881 0.060 0.896 0.044
#> GSM62298 2 0.1964 0.892 0.056 0.944 0.000
#> GSM62299 2 0.1989 0.894 0.048 0.948 0.004
#> GSM62258 1 0.4605 0.968 0.796 0.000 0.204
#> GSM62281 2 0.1860 0.891 0.052 0.948 0.000
#> GSM62294 2 0.2998 0.892 0.068 0.916 0.016
#> GSM62305 2 0.4887 0.858 0.096 0.844 0.060
#> GSM62306 2 0.2866 0.885 0.076 0.916 0.008
#> GSM62310 2 0.2066 0.893 0.060 0.940 0.000
#> GSM62311 2 0.3116 0.871 0.108 0.892 0.000
#> GSM62317 2 0.3045 0.892 0.064 0.916 0.020
#> GSM62318 3 0.6274 -0.149 0.456 0.000 0.544
#> GSM62321 2 0.8465 0.355 0.376 0.528 0.096
#> GSM62322 3 0.0000 0.938 0.000 0.000 1.000
#> GSM62250 2 0.7490 0.455 0.380 0.576 0.044
#> GSM62252 2 0.7878 0.389 0.392 0.548 0.060
#> GSM62255 2 0.3038 0.872 0.104 0.896 0.000
#> GSM62257 2 0.2261 0.884 0.068 0.932 0.000
#> GSM62260 1 0.5239 0.917 0.808 0.032 0.160
#> GSM62261 2 0.3253 0.888 0.052 0.912 0.036
#> GSM62262 2 0.2998 0.892 0.068 0.916 0.016
#> GSM62264 1 0.4796 0.933 0.780 0.000 0.220
#> GSM62268 3 0.1289 0.933 0.032 0.000 0.968
#> GSM62269 3 0.0000 0.938 0.000 0.000 1.000
#> GSM62271 1 0.4605 0.968 0.796 0.000 0.204
#> GSM62272 3 0.0000 0.938 0.000 0.000 1.000
#> GSM62273 2 0.3045 0.891 0.064 0.916 0.020
#> GSM62274 3 0.1163 0.935 0.028 0.000 0.972
#> GSM62275 3 0.0000 0.938 0.000 0.000 1.000
#> GSM62276 1 0.4605 0.968 0.796 0.000 0.204
#> GSM62277 3 0.0892 0.936 0.020 0.000 0.980
#> GSM62279 3 0.1163 0.935 0.028 0.000 0.972
#> GSM62282 1 0.4605 0.968 0.796 0.000 0.204
#> GSM62283 1 0.4861 0.959 0.800 0.008 0.192
#> GSM62286 2 0.7138 0.587 0.312 0.644 0.044
#> GSM62287 2 0.2939 0.892 0.072 0.916 0.012
#> GSM62288 2 0.3134 0.893 0.052 0.916 0.032
#> GSM62290 2 0.1964 0.893 0.056 0.944 0.000
#> GSM62293 2 0.3181 0.891 0.064 0.912 0.024
#> GSM62301 2 0.3038 0.876 0.104 0.896 0.000
#> GSM62302 2 0.1031 0.894 0.024 0.976 0.000
#> GSM62303 2 0.1643 0.893 0.044 0.956 0.000
#> GSM62304 2 0.3116 0.876 0.108 0.892 0.000
#> GSM62312 2 0.2550 0.895 0.056 0.932 0.012
#> GSM62313 2 0.3116 0.871 0.108 0.892 0.000
#> GSM62314 2 0.3045 0.892 0.064 0.916 0.020
#> GSM62319 2 0.4087 0.879 0.068 0.880 0.052
#> GSM62320 2 0.2959 0.873 0.100 0.900 0.000
#> GSM62249 2 0.8046 0.348 0.396 0.536 0.068
#> GSM62251 1 0.4750 0.941 0.784 0.000 0.216
#> GSM62263 2 0.4802 0.818 0.020 0.824 0.156
#> GSM62285 2 0.3038 0.871 0.104 0.896 0.000
#> GSM62315 2 0.3412 0.875 0.124 0.876 0.000
#> GSM62291 2 0.3083 0.892 0.060 0.916 0.024
#> GSM62265 1 0.4654 0.953 0.792 0.000 0.208
#> GSM62266 1 0.4796 0.933 0.780 0.000 0.220
#> GSM62296 2 0.2400 0.894 0.064 0.932 0.004
#> GSM62309 2 0.2066 0.892 0.060 0.940 0.000
#> GSM62295 2 0.3310 0.891 0.064 0.908 0.028
#> GSM62300 2 0.1031 0.895 0.024 0.976 0.000
#> GSM62308 2 0.2066 0.892 0.060 0.940 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM62248 4 0.5609 0.82146 0.068 0.176 0.016 0.740
#> GSM62256 4 0.4072 0.77932 0.000 0.252 0.000 0.748
#> GSM62259 2 0.5376 0.39246 0.016 0.588 0.000 0.396
#> GSM62267 1 0.2255 0.91416 0.920 0.000 0.068 0.012
#> GSM62280 1 0.2255 0.91416 0.920 0.000 0.068 0.012
#> GSM62284 3 0.4039 0.76409 0.084 0.000 0.836 0.080
#> GSM62289 4 0.5275 0.81073 0.120 0.088 0.016 0.776
#> GSM62307 2 0.1042 0.74179 0.020 0.972 0.000 0.008
#> GSM62316 4 0.4535 0.78953 0.016 0.240 0.000 0.744
#> GSM62254 2 0.5843 0.38704 0.028 0.568 0.004 0.400
#> GSM62292 2 0.5837 0.37970 0.036 0.564 0.000 0.400
#> GSM62253 3 0.4150 0.74340 0.056 0.000 0.824 0.120
#> GSM62270 3 0.1792 0.75582 0.068 0.000 0.932 0.000
#> GSM62278 3 0.2888 0.75832 0.124 0.000 0.872 0.004
#> GSM62297 2 0.3289 0.72981 0.012 0.864 0.004 0.120
#> GSM62298 2 0.1305 0.75158 0.004 0.960 0.000 0.036
#> GSM62299 2 0.2466 0.74238 0.004 0.900 0.000 0.096
#> GSM62258 1 0.2255 0.91416 0.920 0.000 0.068 0.012
#> GSM62281 4 0.4328 0.77511 0.008 0.244 0.000 0.748
#> GSM62294 2 0.5837 0.37970 0.036 0.564 0.000 0.400
#> GSM62305 4 0.4755 0.81500 0.024 0.192 0.012 0.772
#> GSM62306 4 0.4098 0.80199 0.012 0.204 0.000 0.784
#> GSM62310 2 0.1256 0.74952 0.008 0.964 0.000 0.028
#> GSM62311 2 0.1297 0.74014 0.020 0.964 0.000 0.016
#> GSM62317 2 0.2256 0.74662 0.020 0.924 0.000 0.056
#> GSM62318 3 0.7393 0.25949 0.400 0.000 0.436 0.164
#> GSM62321 4 0.5845 0.79153 0.136 0.080 0.036 0.748
#> GSM62322 3 0.1792 0.75582 0.068 0.000 0.932 0.000
#> GSM62250 4 0.4914 0.82418 0.084 0.116 0.008 0.792
#> GSM62252 4 0.5127 0.80155 0.132 0.084 0.008 0.776
#> GSM62255 2 0.1297 0.74014 0.020 0.964 0.000 0.016
#> GSM62257 2 0.1398 0.74611 0.004 0.956 0.000 0.040
#> GSM62260 1 0.4967 0.78498 0.808 0.036 0.068 0.088
#> GSM62261 2 0.3113 0.73217 0.012 0.876 0.004 0.108
#> GSM62262 2 0.5746 0.38944 0.032 0.572 0.000 0.396
#> GSM62264 3 0.7349 0.25411 0.384 0.000 0.456 0.160
#> GSM62268 3 0.4758 0.72227 0.064 0.000 0.780 0.156
#> GSM62269 3 0.1792 0.75582 0.068 0.000 0.932 0.000
#> GSM62271 1 0.2300 0.91326 0.920 0.000 0.064 0.016
#> GSM62272 3 0.1474 0.75985 0.052 0.000 0.948 0.000
#> GSM62273 2 0.5937 0.37326 0.032 0.560 0.004 0.404
#> GSM62274 3 0.2489 0.76802 0.068 0.000 0.912 0.020
#> GSM62275 3 0.1792 0.75582 0.068 0.000 0.932 0.000
#> GSM62276 1 0.2300 0.91326 0.920 0.000 0.064 0.016
#> GSM62277 3 0.2611 0.76757 0.096 0.000 0.896 0.008
#> GSM62279 3 0.4292 0.75075 0.080 0.000 0.820 0.100
#> GSM62282 1 0.2255 0.91416 0.920 0.000 0.068 0.012
#> GSM62283 1 0.3465 0.87595 0.880 0.028 0.072 0.020
#> GSM62286 4 0.4666 0.82728 0.052 0.152 0.004 0.792
#> GSM62287 2 0.5638 0.39458 0.028 0.584 0.000 0.388
#> GSM62288 2 0.5614 -0.00444 0.008 0.568 0.012 0.412
#> GSM62290 2 0.1545 0.74936 0.008 0.952 0.000 0.040
#> GSM62293 2 0.5837 0.37970 0.036 0.564 0.000 0.400
#> GSM62301 2 0.1174 0.74242 0.020 0.968 0.000 0.012
#> GSM62302 2 0.1824 0.75005 0.004 0.936 0.000 0.060
#> GSM62303 2 0.1209 0.75143 0.004 0.964 0.000 0.032
#> GSM62304 2 0.1042 0.74179 0.020 0.972 0.000 0.008
#> GSM62312 2 0.2530 0.74079 0.004 0.896 0.000 0.100
#> GSM62313 2 0.1297 0.74014 0.020 0.964 0.000 0.016
#> GSM62314 2 0.2521 0.74480 0.020 0.916 0.004 0.060
#> GSM62319 2 0.6469 0.34261 0.036 0.540 0.020 0.404
#> GSM62320 2 0.1297 0.74014 0.020 0.964 0.000 0.016
#> GSM62249 4 0.5430 0.74949 0.160 0.056 0.024 0.760
#> GSM62251 3 0.7276 0.20798 0.404 0.000 0.448 0.148
#> GSM62263 4 0.8070 0.06880 0.048 0.112 0.400 0.440
#> GSM62285 2 0.1297 0.74014 0.020 0.964 0.000 0.016
#> GSM62315 2 0.0895 0.74061 0.020 0.976 0.000 0.004
#> GSM62291 2 0.2707 0.74289 0.016 0.908 0.008 0.068
#> GSM62265 1 0.6009 0.43739 0.632 0.020 0.320 0.028
#> GSM62266 3 0.7349 0.25411 0.384 0.000 0.456 0.160
#> GSM62296 2 0.5496 0.40797 0.024 0.604 0.000 0.372
#> GSM62309 4 0.4295 0.78510 0.008 0.240 0.000 0.752
#> GSM62295 2 0.5837 0.37970 0.036 0.564 0.000 0.400
#> GSM62300 2 0.2593 0.73072 0.004 0.892 0.000 0.104
#> GSM62308 2 0.5300 0.36233 0.012 0.580 0.000 0.408
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM62248 4 0.6234 0.681 0.056 0.320 0.044 0.576 0.004
#> GSM62256 4 0.5403 0.664 0.016 0.368 0.036 0.580 0.000
#> GSM62259 4 0.5445 0.666 0.028 0.352 0.020 0.596 0.004
#> GSM62267 1 0.2793 0.918 0.876 0.000 0.036 0.000 0.088
#> GSM62280 1 0.2793 0.918 0.876 0.000 0.036 0.000 0.088
#> GSM62284 5 0.1310 0.880 0.024 0.000 0.020 0.000 0.956
#> GSM62289 4 0.6305 0.527 0.344 0.076 0.028 0.548 0.004
#> GSM62307 2 0.2890 0.743 0.000 0.836 0.004 0.160 0.000
#> GSM62316 4 0.5734 0.666 0.028 0.352 0.044 0.576 0.000
#> GSM62254 4 0.5585 0.690 0.036 0.308 0.028 0.624 0.004
#> GSM62292 4 0.2433 0.598 0.024 0.024 0.032 0.916 0.004
#> GSM62253 5 0.0000 0.887 0.000 0.000 0.000 0.000 1.000
#> GSM62270 3 0.1892 0.895 0.004 0.000 0.916 0.000 0.080
#> GSM62278 3 0.3319 0.836 0.020 0.000 0.820 0.000 0.160
#> GSM62297 2 0.3336 0.877 0.044 0.864 0.008 0.076 0.008
#> GSM62298 2 0.1502 0.907 0.004 0.940 0.000 0.056 0.000
#> GSM62299 2 0.2284 0.900 0.028 0.912 0.004 0.056 0.000
#> GSM62258 1 0.2793 0.918 0.876 0.000 0.036 0.000 0.088
#> GSM62281 4 0.5643 0.674 0.028 0.344 0.040 0.588 0.000
#> GSM62294 4 0.2074 0.612 0.004 0.032 0.032 0.928 0.004
#> GSM62305 4 0.6253 0.689 0.068 0.316 0.036 0.576 0.004
#> GSM62306 4 0.5588 0.673 0.028 0.348 0.036 0.588 0.000
#> GSM62310 2 0.1772 0.906 0.020 0.940 0.008 0.032 0.000
#> GSM62311 2 0.0324 0.909 0.004 0.992 0.000 0.004 0.000
#> GSM62317 2 0.3005 0.889 0.052 0.884 0.012 0.048 0.004
#> GSM62318 5 0.1408 0.877 0.044 0.000 0.008 0.000 0.948
#> GSM62321 4 0.6344 0.540 0.332 0.060 0.032 0.564 0.012
#> GSM62322 3 0.1892 0.895 0.004 0.000 0.916 0.000 0.080
#> GSM62250 4 0.6454 0.569 0.304 0.076 0.032 0.576 0.012
#> GSM62252 4 0.6582 0.522 0.320 0.056 0.032 0.564 0.028
#> GSM62255 2 0.0324 0.909 0.004 0.992 0.000 0.004 0.000
#> GSM62257 2 0.0898 0.911 0.008 0.972 0.000 0.020 0.000
#> GSM62260 1 0.5650 0.583 0.688 0.024 0.012 0.208 0.068
#> GSM62261 2 0.2568 0.892 0.036 0.908 0.008 0.040 0.008
#> GSM62262 4 0.3210 0.645 0.008 0.092 0.032 0.864 0.004
#> GSM62264 5 0.0771 0.888 0.020 0.000 0.000 0.004 0.976
#> GSM62268 5 0.0162 0.888 0.004 0.000 0.000 0.000 0.996
#> GSM62269 3 0.1892 0.895 0.004 0.000 0.916 0.000 0.080
#> GSM62271 1 0.2793 0.918 0.876 0.000 0.036 0.000 0.088
#> GSM62272 3 0.2068 0.891 0.004 0.000 0.904 0.000 0.092
#> GSM62273 4 0.5183 0.705 0.036 0.224 0.032 0.704 0.004
#> GSM62274 3 0.4971 0.258 0.020 0.000 0.504 0.004 0.472
#> GSM62275 3 0.1892 0.895 0.004 0.000 0.916 0.000 0.080
#> GSM62276 1 0.2793 0.918 0.876 0.000 0.036 0.000 0.088
#> GSM62277 3 0.3304 0.842 0.016 0.000 0.816 0.000 0.168
#> GSM62279 5 0.2787 0.798 0.028 0.000 0.088 0.004 0.880
#> GSM62282 1 0.2959 0.907 0.864 0.000 0.036 0.000 0.100
#> GSM62283 1 0.3183 0.897 0.868 0.012 0.020 0.008 0.092
#> GSM62286 4 0.6516 0.597 0.280 0.096 0.028 0.584 0.012
#> GSM62287 4 0.4937 0.698 0.012 0.292 0.032 0.664 0.000
#> GSM62288 2 0.3530 0.844 0.024 0.844 0.028 0.104 0.000
#> GSM62290 2 0.2321 0.899 0.024 0.912 0.008 0.056 0.000
#> GSM62293 4 0.2522 0.596 0.028 0.024 0.032 0.912 0.004
#> GSM62301 2 0.0451 0.909 0.008 0.988 0.000 0.004 0.000
#> GSM62302 2 0.2050 0.904 0.008 0.920 0.008 0.064 0.000
#> GSM62303 2 0.1704 0.902 0.004 0.928 0.000 0.068 0.000
#> GSM62304 2 0.2848 0.750 0.000 0.840 0.004 0.156 0.000
#> GSM62312 2 0.1981 0.903 0.028 0.924 0.000 0.048 0.000
#> GSM62313 2 0.0324 0.909 0.004 0.992 0.000 0.004 0.000
#> GSM62314 2 0.3005 0.889 0.052 0.884 0.012 0.048 0.004
#> GSM62319 4 0.5765 0.699 0.036 0.296 0.016 0.628 0.024
#> GSM62320 2 0.0162 0.909 0.000 0.996 0.000 0.004 0.000
#> GSM62249 4 0.6689 0.424 0.372 0.044 0.032 0.516 0.036
#> GSM62251 5 0.1282 0.881 0.044 0.000 0.000 0.004 0.952
#> GSM62263 5 0.5880 0.413 0.048 0.296 0.004 0.036 0.616
#> GSM62285 2 0.0324 0.909 0.004 0.992 0.000 0.004 0.000
#> GSM62315 2 0.0451 0.909 0.008 0.988 0.000 0.004 0.000
#> GSM62291 2 0.3279 0.881 0.052 0.868 0.012 0.064 0.004
#> GSM62265 1 0.4134 0.723 0.720 0.008 0.008 0.000 0.264
#> GSM62266 5 0.0451 0.888 0.008 0.000 0.004 0.000 0.988
#> GSM62296 4 0.4871 0.655 0.004 0.368 0.024 0.604 0.000
#> GSM62309 4 0.5782 0.669 0.032 0.344 0.044 0.580 0.000
#> GSM62295 4 0.2522 0.596 0.028 0.024 0.032 0.912 0.004
#> GSM62300 2 0.4081 0.450 0.004 0.696 0.004 0.296 0.000
#> GSM62308 4 0.4994 0.655 0.020 0.364 0.012 0.604 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM62248 5 0.2781 0.825 0.004 0.008 0.052 0.020 0.888 0.028
#> GSM62256 5 0.2686 0.829 0.000 0.024 0.008 0.100 0.868 0.000
#> GSM62259 5 0.6900 0.176 0.004 0.292 0.028 0.232 0.432 0.012
#> GSM62267 6 0.1405 0.956 0.024 0.004 0.024 0.000 0.000 0.948
#> GSM62280 6 0.1401 0.954 0.028 0.004 0.020 0.000 0.000 0.948
#> GSM62284 1 0.1765 0.882 0.924 0.000 0.024 0.000 0.000 0.052
#> GSM62289 5 0.1767 0.849 0.000 0.036 0.000 0.020 0.932 0.012
#> GSM62307 4 0.0508 0.942 0.000 0.004 0.000 0.984 0.012 0.000
#> GSM62316 5 0.2695 0.832 0.000 0.012 0.020 0.072 0.884 0.012
#> GSM62254 2 0.2595 0.908 0.004 0.900 0.028 0.016 0.040 0.012
#> GSM62292 2 0.0767 0.912 0.000 0.976 0.000 0.004 0.012 0.008
#> GSM62253 1 0.0837 0.886 0.972 0.000 0.004 0.000 0.004 0.020
#> GSM62270 3 0.1572 0.957 0.028 0.000 0.936 0.000 0.000 0.036
#> GSM62278 3 0.2745 0.919 0.068 0.000 0.864 0.000 0.000 0.068
#> GSM62297 4 0.3472 0.891 0.004 0.032 0.008 0.832 0.112 0.012
#> GSM62298 4 0.1716 0.934 0.004 0.036 0.000 0.932 0.028 0.000
#> GSM62299 4 0.2545 0.915 0.004 0.020 0.008 0.884 0.084 0.000
#> GSM62258 6 0.1434 0.953 0.024 0.008 0.020 0.000 0.000 0.948
#> GSM62281 5 0.2880 0.832 0.000 0.016 0.020 0.072 0.876 0.016
#> GSM62294 2 0.1049 0.914 0.000 0.960 0.000 0.008 0.032 0.000
#> GSM62305 5 0.2471 0.846 0.008 0.032 0.008 0.024 0.908 0.020
#> GSM62306 5 0.2307 0.841 0.004 0.032 0.000 0.068 0.896 0.000
#> GSM62310 4 0.2107 0.930 0.000 0.008 0.024 0.920 0.036 0.012
#> GSM62311 4 0.0551 0.940 0.004 0.008 0.000 0.984 0.000 0.004
#> GSM62317 4 0.3440 0.904 0.008 0.012 0.048 0.856 0.048 0.028
#> GSM62318 1 0.2006 0.873 0.904 0.000 0.016 0.000 0.000 0.080
#> GSM62321 5 0.2714 0.844 0.008 0.040 0.004 0.016 0.892 0.040
#> GSM62322 3 0.1572 0.957 0.028 0.000 0.936 0.000 0.000 0.036
#> GSM62250 5 0.2274 0.840 0.004 0.028 0.008 0.016 0.916 0.028
#> GSM62252 5 0.2615 0.834 0.012 0.028 0.008 0.012 0.900 0.040
#> GSM62255 4 0.0291 0.941 0.004 0.000 0.000 0.992 0.000 0.004
#> GSM62257 4 0.0260 0.942 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM62260 5 0.6597 0.191 0.256 0.024 0.004 0.004 0.468 0.244
#> GSM62261 4 0.2951 0.901 0.004 0.020 0.008 0.868 0.088 0.012
#> GSM62262 2 0.1572 0.911 0.000 0.936 0.000 0.036 0.028 0.000
#> GSM62264 1 0.0870 0.879 0.972 0.000 0.004 0.000 0.012 0.012
#> GSM62268 1 0.0806 0.887 0.972 0.000 0.008 0.000 0.000 0.020
#> GSM62269 3 0.1649 0.957 0.032 0.000 0.932 0.000 0.000 0.036
#> GSM62271 6 0.1405 0.956 0.024 0.004 0.024 0.000 0.000 0.948
#> GSM62272 3 0.1895 0.942 0.072 0.000 0.912 0.000 0.000 0.016
#> GSM62273 2 0.2650 0.908 0.004 0.896 0.028 0.020 0.044 0.008
#> GSM62274 1 0.3373 0.785 0.816 0.000 0.140 0.000 0.012 0.032
#> GSM62275 3 0.1572 0.957 0.028 0.000 0.936 0.000 0.000 0.036
#> GSM62276 6 0.1405 0.956 0.024 0.004 0.024 0.000 0.000 0.948
#> GSM62277 3 0.2930 0.894 0.124 0.000 0.840 0.000 0.000 0.036
#> GSM62279 1 0.2045 0.881 0.916 0.000 0.016 0.000 0.016 0.052
#> GSM62282 6 0.1777 0.940 0.044 0.004 0.024 0.000 0.000 0.928
#> GSM62283 6 0.3776 0.737 0.188 0.008 0.004 0.008 0.016 0.776
#> GSM62286 5 0.2391 0.844 0.004 0.044 0.008 0.024 0.908 0.012
#> GSM62287 2 0.2442 0.890 0.000 0.884 0.000 0.068 0.048 0.000
#> GSM62288 4 0.2918 0.906 0.004 0.020 0.004 0.856 0.112 0.004
#> GSM62290 4 0.2635 0.920 0.000 0.016 0.024 0.892 0.056 0.012
#> GSM62293 2 0.0520 0.907 0.000 0.984 0.000 0.000 0.008 0.008
#> GSM62301 4 0.0291 0.941 0.000 0.004 0.000 0.992 0.000 0.004
#> GSM62302 4 0.2296 0.927 0.000 0.020 0.012 0.908 0.052 0.008
#> GSM62303 4 0.1498 0.933 0.000 0.032 0.000 0.940 0.028 0.000
#> GSM62304 4 0.0291 0.941 0.000 0.004 0.000 0.992 0.004 0.000
#> GSM62312 4 0.2508 0.911 0.004 0.012 0.008 0.888 0.084 0.004
#> GSM62313 4 0.0405 0.940 0.000 0.008 0.000 0.988 0.000 0.004
#> GSM62314 4 0.3603 0.901 0.012 0.012 0.048 0.848 0.052 0.028
#> GSM62319 2 0.4346 0.802 0.016 0.784 0.032 0.016 0.132 0.020
#> GSM62320 4 0.0000 0.940 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM62249 5 0.2777 0.830 0.024 0.028 0.008 0.008 0.892 0.040
#> GSM62251 1 0.1367 0.879 0.944 0.000 0.000 0.000 0.012 0.044
#> GSM62263 1 0.5553 0.597 0.684 0.016 0.008 0.180 0.064 0.048
#> GSM62285 4 0.0665 0.940 0.004 0.008 0.000 0.980 0.000 0.008
#> GSM62315 4 0.0767 0.940 0.004 0.012 0.000 0.976 0.000 0.008
#> GSM62291 4 0.4016 0.893 0.012 0.020 0.048 0.824 0.068 0.028
#> GSM62265 1 0.3772 0.569 0.672 0.000 0.004 0.000 0.004 0.320
#> GSM62266 1 0.0777 0.887 0.972 0.000 0.004 0.000 0.000 0.024
#> GSM62296 2 0.3139 0.808 0.000 0.812 0.000 0.160 0.028 0.000
#> GSM62309 5 0.2580 0.835 0.000 0.012 0.020 0.064 0.892 0.012
#> GSM62295 2 0.0520 0.907 0.000 0.984 0.000 0.000 0.008 0.008
#> GSM62300 4 0.1498 0.932 0.000 0.032 0.000 0.940 0.028 0.000
#> GSM62308 5 0.4592 0.699 0.000 0.060 0.020 0.180 0.732 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) other(p) genotype/variation(p) k
#> ATC:mclust 75 0.590 0.935 0.748 2
#> ATC:mclust 69 0.200 0.843 0.642 3
#> ATC:mclust 56 0.288 0.172 0.375 4
#> ATC:mclust 71 0.707 0.773 0.389 5
#> ATC:mclust 73 0.326 0.450 0.104 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "NMF"]
# you can also extract it by
# res = res_list["ATC:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21168 rows and 75 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.989 0.995 0.4439 0.559 0.559
#> 3 3 0.807 0.898 0.939 0.1915 0.921 0.861
#> 4 4 0.692 0.777 0.886 0.2421 0.790 0.593
#> 5 5 0.612 0.649 0.812 0.0921 0.856 0.625
#> 6 6 0.593 0.587 0.778 0.0402 0.994 0.980
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
#> GSM62248 2 0.0000 0.994 0.000 1.000
#> GSM62256 2 0.0000 0.994 0.000 1.000
#> GSM62259 2 0.0000 0.994 0.000 1.000
#> GSM62267 1 0.0000 0.997 1.000 0.000
#> GSM62280 1 0.0000 0.997 1.000 0.000
#> GSM62284 1 0.0000 0.997 1.000 0.000
#> GSM62289 2 0.0000 0.994 0.000 1.000
#> GSM62307 2 0.0000 0.994 0.000 1.000
#> GSM62316 2 0.0000 0.994 0.000 1.000
#> GSM62254 2 0.0000 0.994 0.000 1.000
#> GSM62292 2 0.0000 0.994 0.000 1.000
#> GSM62253 1 0.0000 0.997 1.000 0.000
#> GSM62270 1 0.0000 0.997 1.000 0.000
#> GSM62278 1 0.0000 0.997 1.000 0.000
#> GSM62297 2 0.0000 0.994 0.000 1.000
#> GSM62298 2 0.0000 0.994 0.000 1.000
#> GSM62299 2 0.0000 0.994 0.000 1.000
#> GSM62258 1 0.0000 0.997 1.000 0.000
#> GSM62281 2 0.0000 0.994 0.000 1.000
#> GSM62294 2 0.0000 0.994 0.000 1.000
#> GSM62305 2 0.0000 0.994 0.000 1.000
#> GSM62306 2 0.0000 0.994 0.000 1.000
#> GSM62310 2 0.0000 0.994 0.000 1.000
#> GSM62311 2 0.0000 0.994 0.000 1.000
#> GSM62317 2 0.0000 0.994 0.000 1.000
#> GSM62318 1 0.0000 0.997 1.000 0.000
#> GSM62321 2 0.0000 0.994 0.000 1.000
#> GSM62322 1 0.0000 0.997 1.000 0.000
#> GSM62250 2 0.0000 0.994 0.000 1.000
#> GSM62252 2 0.4939 0.878 0.108 0.892
#> GSM62255 2 0.0000 0.994 0.000 1.000
#> GSM62257 2 0.0000 0.994 0.000 1.000
#> GSM62260 1 0.3431 0.931 0.936 0.064
#> GSM62261 2 0.0000 0.994 0.000 1.000
#> GSM62262 2 0.0000 0.994 0.000 1.000
#> GSM62264 2 0.0376 0.990 0.004 0.996
#> GSM62268 1 0.0000 0.997 1.000 0.000
#> GSM62269 1 0.0000 0.997 1.000 0.000
#> GSM62271 1 0.0000 0.997 1.000 0.000
#> GSM62272 1 0.0000 0.997 1.000 0.000
#> GSM62273 2 0.0000 0.994 0.000 1.000
#> GSM62274 1 0.0000 0.997 1.000 0.000
#> GSM62275 1 0.0000 0.997 1.000 0.000
#> GSM62276 1 0.0000 0.997 1.000 0.000
#> GSM62277 1 0.0000 0.997 1.000 0.000
#> GSM62279 1 0.0000 0.997 1.000 0.000
#> GSM62282 1 0.0000 0.997 1.000 0.000
#> GSM62283 1 0.0000 0.997 1.000 0.000
#> GSM62286 2 0.0000 0.994 0.000 1.000
#> GSM62287 2 0.0000 0.994 0.000 1.000
#> GSM62288 2 0.0000 0.994 0.000 1.000
#> GSM62290 2 0.0000 0.994 0.000 1.000
#> GSM62293 2 0.0000 0.994 0.000 1.000
#> GSM62301 2 0.0000 0.994 0.000 1.000
#> GSM62302 2 0.0000 0.994 0.000 1.000
#> GSM62303 2 0.0000 0.994 0.000 1.000
#> GSM62304 2 0.0000 0.994 0.000 1.000
#> GSM62312 2 0.0000 0.994 0.000 1.000
#> GSM62313 2 0.0000 0.994 0.000 1.000
#> GSM62314 2 0.0000 0.994 0.000 1.000
#> GSM62319 2 0.7376 0.741 0.208 0.792
#> GSM62320 2 0.0000 0.994 0.000 1.000
#> GSM62249 2 0.0000 0.994 0.000 1.000
#> GSM62251 1 0.0376 0.993 0.996 0.004
#> GSM62263 2 0.0000 0.994 0.000 1.000
#> GSM62285 2 0.0000 0.994 0.000 1.000
#> GSM62315 2 0.0000 0.994 0.000 1.000
#> GSM62291 2 0.0000 0.994 0.000 1.000
#> GSM62265 1 0.0000 0.997 1.000 0.000
#> GSM62266 1 0.0000 0.997 1.000 0.000
#> GSM62296 2 0.0000 0.994 0.000 1.000
#> GSM62309 2 0.0000 0.994 0.000 1.000
#> GSM62295 2 0.0000 0.994 0.000 1.000
#> GSM62300 2 0.0000 0.994 0.000 1.000
#> GSM62308 2 0.0000 0.994 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM62248 2 0.3686 0.825 0.140 0.860 0.000
#> GSM62256 2 0.0000 0.955 0.000 1.000 0.000
#> GSM62259 2 0.0000 0.955 0.000 1.000 0.000
#> GSM62267 3 0.0000 0.908 0.000 0.000 1.000
#> GSM62280 3 0.1529 0.884 0.040 0.000 0.960
#> GSM62284 3 0.4178 0.819 0.172 0.000 0.828
#> GSM62289 2 0.0000 0.955 0.000 1.000 0.000
#> GSM62307 2 0.0000 0.955 0.000 1.000 0.000
#> GSM62316 2 0.0000 0.955 0.000 1.000 0.000
#> GSM62254 2 0.2165 0.920 0.064 0.936 0.000
#> GSM62292 2 0.3607 0.879 0.112 0.880 0.008
#> GSM62253 1 0.3412 0.894 0.876 0.000 0.124
#> GSM62270 3 0.0424 0.905 0.008 0.000 0.992
#> GSM62278 3 0.1964 0.915 0.056 0.000 0.944
#> GSM62297 2 0.0000 0.955 0.000 1.000 0.000
#> GSM62298 2 0.0000 0.955 0.000 1.000 0.000
#> GSM62299 2 0.0000 0.955 0.000 1.000 0.000
#> GSM62258 3 0.1753 0.916 0.048 0.000 0.952
#> GSM62281 2 0.0000 0.955 0.000 1.000 0.000
#> GSM62294 2 0.3116 0.888 0.108 0.892 0.000
#> GSM62305 2 0.0000 0.955 0.000 1.000 0.000
#> GSM62306 2 0.0000 0.955 0.000 1.000 0.000
#> GSM62310 2 0.0000 0.955 0.000 1.000 0.000
#> GSM62311 2 0.0000 0.955 0.000 1.000 0.000
#> GSM62317 2 0.0000 0.955 0.000 1.000 0.000
#> GSM62318 1 0.3412 0.894 0.876 0.000 0.124
#> GSM62321 2 0.0237 0.953 0.004 0.996 0.000
#> GSM62322 3 0.0424 0.905 0.008 0.000 0.992
#> GSM62250 2 0.1163 0.941 0.028 0.972 0.000
#> GSM62252 2 0.7412 0.643 0.112 0.696 0.192
#> GSM62255 2 0.0000 0.955 0.000 1.000 0.000
#> GSM62257 2 0.0000 0.955 0.000 1.000 0.000
#> GSM62260 3 0.5689 0.612 0.036 0.184 0.780
#> GSM62261 2 0.0000 0.955 0.000 1.000 0.000
#> GSM62262 2 0.2878 0.897 0.096 0.904 0.000
#> GSM62264 1 0.3966 0.798 0.876 0.100 0.024
#> GSM62268 1 0.3551 0.888 0.868 0.000 0.132
#> GSM62269 3 0.2066 0.914 0.060 0.000 0.940
#> GSM62271 3 0.3340 0.811 0.120 0.000 0.880
#> GSM62272 3 0.2066 0.914 0.060 0.000 0.940
#> GSM62273 2 0.2625 0.906 0.084 0.916 0.000
#> GSM62274 3 0.2796 0.896 0.092 0.000 0.908
#> GSM62275 3 0.0424 0.910 0.008 0.000 0.992
#> GSM62276 3 0.2711 0.844 0.088 0.000 0.912
#> GSM62277 3 0.2165 0.913 0.064 0.000 0.936
#> GSM62279 3 0.3879 0.843 0.152 0.000 0.848
#> GSM62282 3 0.1643 0.916 0.044 0.000 0.956
#> GSM62283 3 0.2165 0.913 0.064 0.000 0.936
#> GSM62286 2 0.2959 0.895 0.100 0.900 0.000
#> GSM62287 2 0.1529 0.935 0.040 0.960 0.000
#> GSM62288 2 0.0000 0.955 0.000 1.000 0.000
#> GSM62290 2 0.0000 0.955 0.000 1.000 0.000
#> GSM62293 2 0.5428 0.815 0.120 0.816 0.064
#> GSM62301 2 0.0000 0.955 0.000 1.000 0.000
#> GSM62302 2 0.0000 0.955 0.000 1.000 0.000
#> GSM62303 2 0.0000 0.955 0.000 1.000 0.000
#> GSM62304 2 0.0000 0.955 0.000 1.000 0.000
#> GSM62312 2 0.0000 0.955 0.000 1.000 0.000
#> GSM62313 2 0.0000 0.955 0.000 1.000 0.000
#> GSM62314 2 0.4291 0.772 0.180 0.820 0.000
#> GSM62319 2 0.7537 0.436 0.056 0.612 0.332
#> GSM62320 2 0.0000 0.955 0.000 1.000 0.000
#> GSM62249 2 0.0000 0.955 0.000 1.000 0.000
#> GSM62251 1 0.3412 0.894 0.876 0.000 0.124
#> GSM62263 1 0.5254 0.590 0.736 0.264 0.000
#> GSM62285 2 0.0000 0.955 0.000 1.000 0.000
#> GSM62315 2 0.0000 0.955 0.000 1.000 0.000
#> GSM62291 2 0.0237 0.953 0.004 0.996 0.000
#> GSM62265 1 0.4002 0.860 0.840 0.000 0.160
#> GSM62266 1 0.3412 0.894 0.876 0.000 0.124
#> GSM62296 2 0.1289 0.939 0.032 0.968 0.000
#> GSM62309 2 0.0000 0.955 0.000 1.000 0.000
#> GSM62295 2 0.6317 0.761 0.124 0.772 0.104
#> GSM62300 2 0.0000 0.955 0.000 1.000 0.000
#> GSM62308 2 0.0000 0.955 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM62248 1 0.6347 0.274 0.524 0.412 0.000 0.064
#> GSM62256 2 0.3610 0.741 0.000 0.800 0.000 0.200
#> GSM62259 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM62267 3 0.1022 0.872 0.000 0.000 0.968 0.032
#> GSM62280 4 0.4500 0.569 0.000 0.000 0.316 0.684
#> GSM62284 3 0.4049 0.727 0.212 0.000 0.780 0.008
#> GSM62289 4 0.1913 0.655 0.040 0.020 0.000 0.940
#> GSM62307 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM62316 2 0.3907 0.723 0.000 0.768 0.000 0.232
#> GSM62254 2 0.0188 0.930 0.000 0.996 0.000 0.004
#> GSM62292 2 0.4776 0.352 0.000 0.624 0.000 0.376
#> GSM62253 1 0.0469 0.750 0.988 0.000 0.012 0.000
#> GSM62270 3 0.0336 0.886 0.000 0.000 0.992 0.008
#> GSM62278 3 0.0188 0.887 0.000 0.000 0.996 0.004
#> GSM62297 2 0.0188 0.930 0.000 0.996 0.000 0.004
#> GSM62298 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM62299 2 0.0188 0.930 0.000 0.996 0.000 0.004
#> GSM62258 4 0.5000 0.192 0.000 0.000 0.496 0.504
#> GSM62281 4 0.4804 0.436 0.000 0.384 0.000 0.616
#> GSM62294 4 0.4193 0.623 0.000 0.268 0.000 0.732
#> GSM62305 2 0.3311 0.785 0.000 0.828 0.000 0.172
#> GSM62306 2 0.3219 0.802 0.000 0.836 0.000 0.164
#> GSM62310 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM62311 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM62317 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM62318 1 0.2730 0.775 0.896 0.000 0.016 0.088
#> GSM62321 2 0.7133 0.189 0.148 0.520 0.000 0.332
#> GSM62322 3 0.0188 0.887 0.000 0.000 0.996 0.004
#> GSM62250 4 0.3219 0.664 0.000 0.164 0.000 0.836
#> GSM62252 4 0.3015 0.694 0.000 0.024 0.092 0.884
#> GSM62255 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM62257 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM62260 4 0.4479 0.612 0.056 0.020 0.096 0.828
#> GSM62261 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM62262 2 0.1940 0.884 0.000 0.924 0.000 0.076
#> GSM62264 1 0.3610 0.783 0.800 0.000 0.000 0.200
#> GSM62268 1 0.2530 0.675 0.888 0.000 0.112 0.000
#> GSM62269 3 0.0804 0.883 0.012 0.000 0.980 0.008
#> GSM62271 4 0.4500 0.561 0.000 0.000 0.316 0.684
#> GSM62272 3 0.0804 0.883 0.012 0.000 0.980 0.008
#> GSM62273 2 0.2760 0.836 0.000 0.872 0.000 0.128
#> GSM62274 3 0.0188 0.887 0.000 0.000 0.996 0.004
#> GSM62275 3 0.0000 0.887 0.000 0.000 1.000 0.000
#> GSM62276 4 0.4817 0.476 0.000 0.000 0.388 0.612
#> GSM62277 3 0.0469 0.885 0.000 0.000 0.988 0.012
#> GSM62279 3 0.3695 0.777 0.156 0.000 0.828 0.016
#> GSM62282 3 0.2704 0.774 0.000 0.000 0.876 0.124
#> GSM62283 4 0.1510 0.651 0.028 0.000 0.016 0.956
#> GSM62286 4 0.4540 0.679 0.000 0.196 0.032 0.772
#> GSM62287 2 0.2216 0.872 0.000 0.908 0.000 0.092
#> GSM62288 2 0.0188 0.929 0.000 0.996 0.000 0.004
#> GSM62290 2 0.0707 0.922 0.000 0.980 0.000 0.020
#> GSM62293 4 0.4072 0.638 0.000 0.252 0.000 0.748
#> GSM62301 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM62302 2 0.0188 0.930 0.000 0.996 0.000 0.004
#> GSM62303 2 0.0469 0.926 0.000 0.988 0.000 0.012
#> GSM62304 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM62312 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM62313 2 0.0188 0.930 0.000 0.996 0.000 0.004
#> GSM62314 2 0.0188 0.929 0.004 0.996 0.000 0.000
#> GSM62319 3 0.5183 0.201 0.000 0.408 0.584 0.008
#> GSM62320 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM62249 4 0.1610 0.656 0.032 0.016 0.000 0.952
#> GSM62251 1 0.3569 0.784 0.804 0.000 0.000 0.196
#> GSM62263 1 0.4253 0.610 0.776 0.208 0.000 0.016
#> GSM62285 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM62315 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM62291 2 0.0336 0.928 0.000 0.992 0.000 0.008
#> GSM62265 1 0.4253 0.774 0.776 0.000 0.016 0.208
#> GSM62266 1 0.3311 0.787 0.828 0.000 0.000 0.172
#> GSM62296 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM62309 2 0.4134 0.646 0.000 0.740 0.000 0.260
#> GSM62295 4 0.5220 0.696 0.000 0.156 0.092 0.752
#> GSM62300 2 0.0000 0.931 0.000 1.000 0.000 0.000
#> GSM62308 2 0.2011 0.880 0.000 0.920 0.000 0.080
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM62248 2 0.6232 0.3121 0.288 0.584 0.000 0.028 0.100
#> GSM62256 5 0.4321 0.4899 0.000 0.396 0.000 0.004 0.600
#> GSM62259 2 0.4113 0.5849 0.000 0.740 0.000 0.028 0.232
#> GSM62267 3 0.1341 0.8004 0.000 0.000 0.944 0.056 0.000
#> GSM62280 3 0.6215 0.3899 0.000 0.000 0.508 0.156 0.336
#> GSM62284 3 0.4171 0.7323 0.108 0.000 0.804 0.072 0.016
#> GSM62289 5 0.6642 0.1558 0.148 0.016 0.000 0.356 0.480
#> GSM62307 2 0.2358 0.7826 0.000 0.888 0.000 0.008 0.104
#> GSM62316 2 0.6420 -0.0375 0.024 0.480 0.000 0.096 0.400
#> GSM62254 2 0.2011 0.7985 0.000 0.908 0.000 0.088 0.004
#> GSM62292 4 0.4738 0.3234 0.000 0.420 0.004 0.564 0.012
#> GSM62253 1 0.0579 0.8393 0.984 0.000 0.000 0.008 0.008
#> GSM62270 3 0.1197 0.8007 0.000 0.000 0.952 0.048 0.000
#> GSM62278 3 0.1638 0.7898 0.000 0.000 0.932 0.064 0.004
#> GSM62297 2 0.3307 0.7783 0.000 0.844 0.000 0.104 0.052
#> GSM62298 2 0.1270 0.8147 0.000 0.948 0.000 0.052 0.000
#> GSM62299 2 0.0671 0.8279 0.000 0.980 0.000 0.004 0.016
#> GSM62258 3 0.4708 0.3842 0.000 0.000 0.548 0.016 0.436
#> GSM62281 2 0.5334 -0.1023 0.000 0.512 0.000 0.436 0.052
#> GSM62294 4 0.4657 0.5790 0.000 0.296 0.000 0.668 0.036
#> GSM62305 5 0.5554 0.5097 0.004 0.264 0.000 0.100 0.632
#> GSM62306 5 0.4610 0.4860 0.000 0.388 0.000 0.016 0.596
#> GSM62310 2 0.0290 0.8266 0.000 0.992 0.000 0.008 0.000
#> GSM62311 2 0.0693 0.8284 0.000 0.980 0.000 0.008 0.012
#> GSM62317 2 0.0807 0.8274 0.000 0.976 0.000 0.012 0.012
#> GSM62318 1 0.6275 0.6340 0.652 0.000 0.112 0.072 0.164
#> GSM62321 5 0.4986 0.5020 0.008 0.368 0.000 0.024 0.600
#> GSM62322 3 0.1197 0.8007 0.000 0.000 0.952 0.048 0.000
#> GSM62250 5 0.6191 0.2006 0.000 0.164 0.000 0.308 0.528
#> GSM62252 4 0.4561 0.3931 0.004 0.016 0.044 0.764 0.172
#> GSM62255 2 0.1484 0.8191 0.000 0.944 0.000 0.008 0.048
#> GSM62257 2 0.1981 0.8128 0.000 0.920 0.000 0.016 0.064
#> GSM62260 5 0.1721 0.5006 0.016 0.020 0.000 0.020 0.944
#> GSM62261 2 0.1638 0.8126 0.000 0.932 0.000 0.004 0.064
#> GSM62262 2 0.4604 0.1209 0.000 0.560 0.000 0.428 0.012
#> GSM62264 1 0.2964 0.8354 0.856 0.000 0.000 0.024 0.120
#> GSM62268 1 0.1569 0.8248 0.944 0.000 0.044 0.008 0.004
#> GSM62269 3 0.2173 0.7873 0.016 0.000 0.920 0.052 0.012
#> GSM62271 3 0.5091 0.6229 0.000 0.000 0.672 0.244 0.084
#> GSM62272 3 0.2277 0.7860 0.016 0.000 0.916 0.052 0.016
#> GSM62273 2 0.3160 0.7109 0.000 0.808 0.000 0.188 0.004
#> GSM62274 3 0.1597 0.8014 0.012 0.000 0.940 0.048 0.000
#> GSM62275 3 0.0000 0.7992 0.000 0.000 1.000 0.000 0.000
#> GSM62276 3 0.5191 0.6299 0.000 0.000 0.684 0.124 0.192
#> GSM62277 3 0.2020 0.7919 0.000 0.000 0.900 0.100 0.000
#> GSM62279 3 0.6026 0.5566 0.192 0.000 0.652 0.120 0.036
#> GSM62282 3 0.3182 0.7549 0.000 0.000 0.844 0.124 0.032
#> GSM62283 5 0.4558 0.3785 0.040 0.000 0.008 0.224 0.728
#> GSM62286 4 0.5335 0.5965 0.000 0.128 0.028 0.720 0.124
#> GSM62287 2 0.3993 0.6771 0.000 0.756 0.000 0.216 0.028
#> GSM62288 2 0.1571 0.8142 0.000 0.936 0.000 0.004 0.060
#> GSM62290 2 0.3671 0.6478 0.000 0.756 0.000 0.236 0.008
#> GSM62293 4 0.3852 0.6636 0.000 0.168 0.028 0.796 0.008
#> GSM62301 2 0.0703 0.8261 0.000 0.976 0.000 0.000 0.024
#> GSM62302 2 0.1341 0.8142 0.000 0.944 0.000 0.056 0.000
#> GSM62303 2 0.2930 0.7329 0.000 0.832 0.000 0.164 0.004
#> GSM62304 2 0.1331 0.8217 0.000 0.952 0.000 0.008 0.040
#> GSM62312 2 0.1571 0.8133 0.000 0.936 0.000 0.004 0.060
#> GSM62313 2 0.0510 0.8287 0.000 0.984 0.000 0.016 0.000
#> GSM62314 2 0.0566 0.8256 0.004 0.984 0.000 0.012 0.000
#> GSM62319 3 0.7317 0.0693 0.000 0.244 0.496 0.204 0.056
#> GSM62320 2 0.0703 0.8261 0.000 0.976 0.000 0.000 0.024
#> GSM62249 5 0.4415 0.4604 0.048 0.020 0.000 0.156 0.776
#> GSM62251 1 0.2124 0.8427 0.900 0.000 0.000 0.004 0.096
#> GSM62263 1 0.3790 0.5063 0.744 0.248 0.000 0.004 0.004
#> GSM62285 2 0.0451 0.8272 0.000 0.988 0.000 0.008 0.004
#> GSM62315 2 0.0324 0.8273 0.000 0.992 0.000 0.004 0.004
#> GSM62291 2 0.4230 0.6644 0.036 0.764 0.000 0.192 0.008
#> GSM62265 1 0.2771 0.8274 0.860 0.000 0.000 0.012 0.128
#> GSM62266 1 0.0794 0.8452 0.972 0.000 0.000 0.000 0.028
#> GSM62296 2 0.0794 0.8254 0.000 0.972 0.000 0.000 0.028
#> GSM62309 2 0.4141 0.6090 0.000 0.736 0.000 0.236 0.028
#> GSM62295 4 0.3748 0.6312 0.000 0.100 0.052 0.832 0.016
#> GSM62300 2 0.0510 0.8268 0.000 0.984 0.000 0.016 0.000
#> GSM62308 2 0.3783 0.6091 0.000 0.740 0.000 0.252 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM62248 4 0.6361 0.2122 0.308 0.040 0.000 0.540 0.076 0.036
#> GSM62256 5 0.5133 0.3661 0.000 0.088 0.000 0.332 0.576 0.004
#> GSM62259 4 0.6084 0.3732 0.000 0.140 0.000 0.588 0.208 0.064
#> GSM62267 3 0.2058 0.7804 0.000 0.036 0.908 0.000 0.000 0.056
#> GSM62280 3 0.6746 0.3140 0.000 0.244 0.444 0.000 0.260 0.052
#> GSM62284 3 0.2905 0.7450 0.048 0.092 0.856 0.000 0.000 0.004
#> GSM62289 5 0.7157 0.2864 0.160 0.096 0.000 0.016 0.480 0.248
#> GSM62307 4 0.2346 0.7621 0.000 0.000 0.000 0.868 0.124 0.008
#> GSM62316 4 0.6287 0.3251 0.012 0.056 0.000 0.556 0.276 0.100
#> GSM62254 4 0.3253 0.6784 0.000 0.020 0.000 0.788 0.000 0.192
#> GSM62292 6 0.5435 0.0323 0.000 0.120 0.000 0.300 0.008 0.572
#> GSM62253 1 0.1049 0.8039 0.960 0.032 0.000 0.000 0.000 0.008
#> GSM62270 3 0.1856 0.7806 0.000 0.032 0.920 0.000 0.000 0.048
#> GSM62278 3 0.1471 0.7751 0.000 0.064 0.932 0.000 0.000 0.004
#> GSM62297 4 0.5795 0.5163 0.004 0.044 0.000 0.628 0.140 0.184
#> GSM62298 4 0.1434 0.7776 0.000 0.012 0.000 0.940 0.000 0.048
#> GSM62299 4 0.1477 0.7867 0.000 0.004 0.000 0.940 0.048 0.008
#> GSM62258 3 0.5023 0.4776 0.004 0.052 0.576 0.000 0.360 0.008
#> GSM62281 4 0.5697 0.3641 0.000 0.080 0.000 0.608 0.060 0.252
#> GSM62294 6 0.5464 0.1437 0.000 0.044 0.000 0.424 0.040 0.492
#> GSM62305 5 0.7309 0.0417 0.024 0.320 0.000 0.096 0.428 0.132
#> GSM62306 5 0.4734 0.4105 0.008 0.028 0.000 0.268 0.672 0.024
#> GSM62310 4 0.0260 0.7865 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM62311 4 0.1649 0.7893 0.000 0.008 0.000 0.936 0.040 0.016
#> GSM62317 4 0.2622 0.7249 0.000 0.104 0.000 0.868 0.024 0.004
#> GSM62318 1 0.6758 0.2442 0.404 0.380 0.128 0.000 0.088 0.000
#> GSM62321 5 0.6343 0.3289 0.004 0.232 0.004 0.288 0.464 0.008
#> GSM62322 3 0.1320 0.7835 0.000 0.016 0.948 0.000 0.000 0.036
#> GSM62250 5 0.5506 0.4073 0.016 0.028 0.000 0.080 0.648 0.228
#> GSM62252 6 0.4622 0.2247 0.020 0.092 0.000 0.000 0.164 0.724
#> GSM62255 4 0.2342 0.7773 0.000 0.004 0.000 0.888 0.088 0.020
#> GSM62257 4 0.2912 0.7671 0.000 0.012 0.000 0.856 0.104 0.028
#> GSM62260 5 0.2278 0.4641 0.004 0.128 0.000 0.000 0.868 0.000
#> GSM62261 4 0.3099 0.7114 0.000 0.008 0.000 0.808 0.176 0.008
#> GSM62262 4 0.5097 0.0193 0.000 0.068 0.000 0.508 0.004 0.420
#> GSM62264 1 0.2257 0.8059 0.904 0.020 0.000 0.000 0.060 0.016
#> GSM62268 1 0.1649 0.7910 0.932 0.032 0.036 0.000 0.000 0.000
#> GSM62269 3 0.1296 0.7780 0.004 0.044 0.948 0.000 0.000 0.004
#> GSM62271 3 0.5790 0.5679 0.000 0.108 0.612 0.000 0.056 0.224
#> GSM62272 3 0.1219 0.7786 0.000 0.048 0.948 0.000 0.000 0.004
#> GSM62273 4 0.2834 0.7300 0.000 0.020 0.000 0.852 0.008 0.120
#> GSM62274 3 0.1410 0.7858 0.004 0.044 0.944 0.000 0.000 0.008
#> GSM62275 3 0.0405 0.7837 0.000 0.008 0.988 0.000 0.000 0.004
#> GSM62276 3 0.5220 0.5957 0.000 0.024 0.668 0.000 0.156 0.152
#> GSM62277 3 0.3566 0.7366 0.000 0.104 0.800 0.000 0.000 0.096
#> GSM62279 3 0.7309 0.1159 0.084 0.276 0.472 0.000 0.040 0.128
#> GSM62282 3 0.3590 0.7440 0.000 0.092 0.820 0.000 0.020 0.068
#> GSM62283 5 0.5366 0.4102 0.016 0.192 0.004 0.000 0.648 0.140
#> GSM62286 6 0.5638 0.3038 0.000 0.128 0.016 0.060 0.116 0.680
#> GSM62287 4 0.4141 0.7265 0.000 0.008 0.000 0.756 0.080 0.156
#> GSM62288 4 0.2400 0.7638 0.004 0.000 0.000 0.872 0.116 0.008
#> GSM62290 4 0.3539 0.6435 0.000 0.024 0.000 0.756 0.000 0.220
#> GSM62293 6 0.3422 0.3594 0.000 0.036 0.000 0.176 0.000 0.788
#> GSM62301 4 0.1493 0.7837 0.000 0.004 0.000 0.936 0.056 0.004
#> GSM62302 4 0.0777 0.7855 0.000 0.004 0.000 0.972 0.000 0.024
#> GSM62303 4 0.3921 0.6565 0.000 0.020 0.000 0.748 0.020 0.212
#> GSM62304 4 0.1866 0.7779 0.000 0.000 0.000 0.908 0.084 0.008
#> GSM62312 4 0.2920 0.7215 0.000 0.004 0.000 0.820 0.168 0.008
#> GSM62313 4 0.1923 0.7836 0.000 0.004 0.000 0.916 0.016 0.064
#> GSM62314 4 0.1768 0.7874 0.012 0.012 0.000 0.936 0.008 0.032
#> GSM62319 2 0.7874 0.0000 0.000 0.372 0.148 0.200 0.024 0.256
#> GSM62320 4 0.0717 0.7879 0.000 0.008 0.000 0.976 0.016 0.000
#> GSM62249 5 0.4340 0.5021 0.060 0.028 0.000 0.032 0.792 0.088
#> GSM62251 1 0.1493 0.8074 0.936 0.004 0.000 0.000 0.056 0.004
#> GSM62263 1 0.3583 0.4252 0.728 0.008 0.000 0.260 0.004 0.000
#> GSM62285 4 0.0692 0.7843 0.000 0.020 0.000 0.976 0.000 0.004
#> GSM62315 4 0.1367 0.7785 0.000 0.044 0.000 0.944 0.012 0.000
#> GSM62291 4 0.4376 0.6201 0.020 0.060 0.000 0.736 0.000 0.184
#> GSM62265 1 0.3139 0.7831 0.852 0.048 0.000 0.000 0.080 0.020
#> GSM62266 1 0.0806 0.8097 0.972 0.020 0.000 0.000 0.008 0.000
#> GSM62296 4 0.1462 0.7838 0.000 0.008 0.000 0.936 0.056 0.000
#> GSM62309 4 0.4856 0.6221 0.012 0.056 0.000 0.732 0.044 0.156
#> GSM62295 6 0.2717 0.3442 0.000 0.020 0.020 0.068 0.008 0.884
#> GSM62300 4 0.0363 0.7858 0.000 0.000 0.000 0.988 0.000 0.012
#> GSM62308 4 0.3602 0.6691 0.000 0.032 0.000 0.784 0.008 0.176
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) other(p) genotype/variation(p) k
#> ATC:NMF 75 0.66603 1.000 0.753 2
#> ATC:NMF 74 0.00785 0.232 0.556 3
#> ATC:NMF 68 0.04989 0.307 0.831 4
#> ATC:NMF 60 0.06258 0.340 0.936 5
#> ATC:NMF 50 0.01870 0.459 0.291 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
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