Date: 2019-12-25 21:10:42 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 79 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 79
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 | ||
|---|---|---|---|---|---|---|
| ATC:skmeans | 3 | 1.000 | 0.947 | 0.979 | ** | 2 |
| ATC:NMF | 2 | 0.999 | 0.957 | 0.982 | ** | |
| CV:kmeans | 2 | 0.998 | 0.955 | 0.981 | ** | |
| CV:NMF | 2 | 0.948 | 0.954 | 0.979 | * | |
| SD:skmeans | 2 | 0.947 | 0.953 | 0.980 | * | |
| ATC:pam | 2 | 0.947 | 0.926 | 0.970 | * | |
| CV:skmeans | 2 | 0.943 | 0.939 | 0.974 | * | |
| ATC:kmeans | 4 | 0.921 | 0.905 | 0.939 | * | 2 |
| MAD:kmeans | 2 | 0.919 | 0.923 | 0.953 | * | |
| ATC:mclust | 4 | 0.898 | 0.924 | 0.968 | ||
| SD:kmeans | 2 | 0.893 | 0.939 | 0.956 | ||
| MAD:skmeans | 2 | 0.870 | 0.933 | 0.970 | ||
| SD:NMF | 2 | 0.845 | 0.931 | 0.968 | ||
| MAD:NMF | 2 | 0.841 | 0.916 | 0.962 | ||
| CV:mclust | 4 | 0.758 | 0.850 | 0.914 | ||
| SD:mclust | 4 | 0.682 | 0.785 | 0.879 | ||
| MAD:mclust | 4 | 0.620 | 0.776 | 0.853 | ||
| SD:pam | 3 | 0.599 | 0.755 | 0.881 | ||
| MAD:pam | 3 | 0.524 | 0.699 | 0.860 | ||
| ATC:hclust | 3 | 0.524 | 0.714 | 0.833 | ||
| CV:pam | 2 | 0.368 | 0.725 | 0.872 | ||
| CV:hclust | 4 | 0.320 | 0.630 | 0.821 | ||
| MAD:hclust | 5 | 0.302 | 0.513 | 0.685 | ||
| SD:hclust | 3 | 0.256 | 0.645 | 0.825 |
**: 1-PAC > 0.95, *: 1-PAC > 0.9
Cumulative distribution function curves of consensus matrix for all methods.
collect_plots(res_list, fun = plot_ecdf)
Consensus heatmaps for all methods. (What is a consensus heatmap?)
collect_plots(res_list, k = 2, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = consensus_heatmap, mc.cores = 4)
Membership heatmaps for all methods. (What is a membership heatmap?)
collect_plots(res_list, k = 2, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = membership_heatmap, mc.cores = 4)
Signature heatmaps for all methods. (What is a signature heatmap?)
Note in following heatmaps, rows are scaled.
collect_plots(res_list, k = 2, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 3, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 4, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 5, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 6, fun = get_signatures, mc.cores = 4)
The statistics used for measuring the stability of consensus partitioning. (How are they defined?)
get_stats(res_list, k = 2)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 2 0.845 0.931 0.968 0.498 0.503 0.503
#> CV:NMF 2 0.948 0.954 0.979 0.501 0.498 0.498
#> MAD:NMF 2 0.841 0.916 0.962 0.500 0.503 0.503
#> ATC:NMF 2 0.999 0.957 0.982 0.462 0.529 0.529
#> SD:skmeans 2 0.947 0.953 0.980 0.503 0.496 0.496
#> CV:skmeans 2 0.943 0.939 0.974 0.503 0.498 0.498
#> MAD:skmeans 2 0.870 0.933 0.970 0.503 0.496 0.496
#> ATC:skmeans 2 1.000 0.993 0.997 0.500 0.500 0.500
#> SD:mclust 2 0.842 0.927 0.952 0.233 0.796 0.796
#> CV:mclust 2 0.733 0.870 0.944 0.345 0.658 0.658
#> MAD:mclust 2 0.526 0.748 0.879 0.282 0.705 0.705
#> ATC:mclust 2 0.150 0.000 0.656 0.369 1.000 1.000
#> SD:kmeans 2 0.893 0.939 0.956 0.486 0.512 0.512
#> CV:kmeans 2 0.998 0.955 0.981 0.490 0.512 0.512
#> MAD:kmeans 2 0.919 0.923 0.953 0.489 0.517 0.517
#> ATC:kmeans 2 1.000 0.979 0.991 0.494 0.503 0.503
#> SD:pam 2 0.271 0.639 0.830 0.493 0.494 0.494
#> CV:pam 2 0.368 0.725 0.872 0.499 0.496 0.496
#> MAD:pam 2 0.270 0.654 0.813 0.489 0.507 0.507
#> ATC:pam 2 0.947 0.926 0.970 0.499 0.500 0.500
#> SD:hclust 2 0.173 0.600 0.829 0.273 0.903 0.903
#> CV:hclust 2 0.233 0.703 0.832 0.226 0.926 0.926
#> MAD:hclust 2 0.172 0.644 0.823 0.330 0.705 0.705
#> ATC:hclust 2 0.436 0.731 0.884 0.324 0.739 0.739
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.497 0.674 0.835 0.347 0.755 0.545
#> CV:NMF 3 0.531 0.750 0.859 0.333 0.749 0.534
#> MAD:NMF 3 0.491 0.656 0.830 0.338 0.748 0.535
#> ATC:NMF 3 0.645 0.723 0.887 0.390 0.759 0.569
#> SD:skmeans 3 0.609 0.780 0.891 0.335 0.738 0.518
#> CV:skmeans 3 0.470 0.691 0.839 0.331 0.751 0.538
#> MAD:skmeans 3 0.561 0.775 0.886 0.336 0.744 0.527
#> ATC:skmeans 3 1.000 0.947 0.979 0.307 0.803 0.621
#> SD:mclust 3 0.342 0.519 0.739 1.123 0.753 0.691
#> CV:mclust 3 0.382 0.597 0.761 0.678 0.611 0.455
#> MAD:mclust 3 0.289 0.573 0.737 1.044 0.529 0.394
#> ATC:mclust 3 0.559 0.838 0.868 0.638 0.361 0.361
#> SD:kmeans 3 0.561 0.788 0.813 0.308 0.799 0.617
#> CV:kmeans 3 0.538 0.539 0.773 0.281 0.829 0.679
#> MAD:kmeans 3 0.619 0.859 0.873 0.334 0.790 0.603
#> ATC:kmeans 3 0.523 0.703 0.794 0.261 0.883 0.775
#> SD:pam 3 0.599 0.755 0.881 0.322 0.757 0.555
#> CV:pam 3 0.530 0.662 0.844 0.311 0.799 0.614
#> MAD:pam 3 0.524 0.699 0.860 0.327 0.784 0.597
#> ATC:pam 3 0.613 0.744 0.857 0.307 0.813 0.640
#> SD:hclust 3 0.256 0.645 0.825 0.585 0.772 0.747
#> CV:hclust 3 0.193 0.642 0.807 0.709 0.786 0.769
#> MAD:hclust 3 0.231 0.499 0.773 0.664 0.747 0.650
#> ATC:hclust 3 0.524 0.714 0.833 0.794 0.631 0.520
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.423 0.539 0.712 0.1151 0.835 0.554
#> CV:NMF 4 0.465 0.564 0.742 0.1231 0.850 0.586
#> MAD:NMF 4 0.404 0.456 0.673 0.1185 0.850 0.587
#> ATC:NMF 4 0.515 0.570 0.781 0.1448 0.798 0.500
#> SD:skmeans 4 0.459 0.516 0.733 0.1160 0.924 0.779
#> CV:skmeans 4 0.398 0.490 0.700 0.1157 0.934 0.808
#> MAD:skmeans 4 0.439 0.516 0.730 0.1157 0.922 0.770
#> ATC:skmeans 4 0.881 0.827 0.929 0.1135 0.875 0.660
#> SD:mclust 4 0.682 0.785 0.879 0.4442 0.624 0.380
#> CV:mclust 4 0.758 0.850 0.914 0.2637 0.789 0.506
#> MAD:mclust 4 0.620 0.776 0.853 0.2631 0.819 0.566
#> ATC:mclust 4 0.898 0.924 0.968 0.1803 0.853 0.630
#> SD:kmeans 4 0.695 0.834 0.876 0.1484 0.910 0.742
#> CV:kmeans 4 0.609 0.793 0.857 0.1606 0.766 0.465
#> MAD:kmeans 4 0.698 0.774 0.837 0.1257 0.932 0.797
#> ATC:kmeans 4 0.921 0.905 0.939 0.1541 0.817 0.581
#> SD:pam 4 0.591 0.690 0.855 0.0508 0.954 0.875
#> CV:pam 4 0.507 0.608 0.819 0.0393 0.975 0.929
#> MAD:pam 4 0.549 0.674 0.855 0.0401 0.973 0.922
#> ATC:pam 4 0.665 0.776 0.877 0.0823 0.934 0.818
#> SD:hclust 4 0.266 0.522 0.766 0.2338 0.922 0.884
#> CV:hclust 4 0.320 0.630 0.821 0.2472 0.895 0.853
#> MAD:hclust 4 0.273 0.383 0.698 0.1320 0.923 0.843
#> ATC:hclust 4 0.498 0.528 0.745 0.1802 0.823 0.608
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.499 0.431 0.674 0.0633 0.869 0.559
#> CV:NMF 5 0.515 0.466 0.684 0.0663 0.908 0.665
#> MAD:NMF 5 0.498 0.465 0.689 0.0652 0.890 0.607
#> ATC:NMF 5 0.554 0.565 0.739 0.0703 0.779 0.354
#> SD:skmeans 5 0.463 0.400 0.651 0.0648 0.875 0.586
#> CV:skmeans 5 0.407 0.351 0.613 0.0630 0.932 0.773
#> MAD:skmeans 5 0.436 0.391 0.650 0.0648 0.884 0.606
#> ATC:skmeans 5 0.717 0.589 0.791 0.0635 0.958 0.852
#> SD:mclust 5 0.584 0.556 0.771 0.0635 0.966 0.880
#> CV:mclust 5 0.661 0.766 0.834 0.0462 1.000 1.000
#> MAD:mclust 5 0.599 0.541 0.768 0.0765 0.946 0.804
#> ATC:mclust 5 0.661 0.724 0.812 0.0595 1.000 1.000
#> SD:kmeans 5 0.713 0.682 0.804 0.0647 0.985 0.945
#> CV:kmeans 5 0.668 0.644 0.803 0.0628 0.969 0.886
#> MAD:kmeans 5 0.726 0.637 0.811 0.0667 0.920 0.715
#> ATC:kmeans 5 0.745 0.655 0.802 0.0828 0.918 0.732
#> SD:pam 5 0.602 0.668 0.838 0.0262 0.970 0.912
#> CV:pam 5 0.509 0.553 0.795 0.0212 0.981 0.944
#> MAD:pam 5 0.570 0.560 0.827 0.0380 0.976 0.928
#> ATC:pam 5 0.768 0.845 0.910 0.0915 0.886 0.650
#> SD:hclust 5 0.302 0.380 0.717 0.1105 0.956 0.927
#> CV:hclust 5 0.291 0.506 0.754 0.1545 0.841 0.749
#> MAD:hclust 5 0.302 0.513 0.685 0.0944 0.785 0.526
#> ATC:hclust 5 0.562 0.524 0.741 0.0986 0.822 0.487
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.577 0.472 0.695 0.0374 0.933 0.713
#> CV:NMF 6 0.556 0.412 0.658 0.0379 0.932 0.706
#> MAD:NMF 6 0.590 0.456 0.690 0.0402 0.926 0.675
#> ATC:NMF 6 0.545 0.478 0.679 0.0334 0.969 0.854
#> SD:skmeans 6 0.506 0.317 0.595 0.0392 0.944 0.756
#> CV:skmeans 6 0.459 0.277 0.540 0.0425 0.924 0.706
#> MAD:skmeans 6 0.481 0.342 0.585 0.0400 0.934 0.706
#> ATC:skmeans 6 0.691 0.603 0.753 0.0430 0.896 0.624
#> SD:mclust 6 0.613 0.492 0.721 0.0446 0.945 0.802
#> CV:mclust 6 0.624 0.571 0.744 0.0378 0.925 0.728
#> MAD:mclust 6 0.610 0.444 0.687 0.0320 0.937 0.737
#> ATC:mclust 6 0.709 0.672 0.803 0.0619 0.852 0.520
#> SD:kmeans 6 0.716 0.495 0.763 0.0450 0.923 0.712
#> CV:kmeans 6 0.679 0.544 0.743 0.0433 0.941 0.779
#> MAD:kmeans 6 0.709 0.553 0.765 0.0411 0.978 0.898
#> ATC:kmeans 6 0.728 0.618 0.760 0.0496 0.883 0.565
#> SD:pam 6 0.626 0.601 0.832 0.0152 0.986 0.955
#> CV:pam 6 0.512 0.528 0.789 0.0150 0.968 0.902
#> MAD:pam 6 0.568 0.581 0.822 0.0132 0.969 0.906
#> ATC:pam 6 0.749 0.561 0.756 0.0636 0.856 0.489
#> SD:hclust 6 0.304 0.465 0.710 0.0871 0.793 0.634
#> CV:hclust 6 0.295 0.612 0.768 0.1206 0.847 0.706
#> MAD:hclust 6 0.370 0.487 0.678 0.0685 0.953 0.833
#> ATC:hclust 6 0.580 0.497 0.739 0.0282 0.982 0.919
Following heatmap plots the partition for each combination of methods and the lightness correspond to the silhouette scores for samples in each method. On top the consensus subgroup is inferred from all methods by taking the mean silhouette scores as weight.
collect_stats(res_list, k = 2)
collect_stats(res_list, k = 3)
collect_stats(res_list, k = 4)
collect_stats(res_list, k = 5)
collect_stats(res_list, k = 6)
Collect partitions from all methods:
collect_classes(res_list, k = 2)
collect_classes(res_list, k = 3)
collect_classes(res_list, k = 4)
collect_classes(res_list, k = 5)
collect_classes(res_list, k = 6)
Overlap of top rows from different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "euler")
top_rows_overlap(res_list, top_n = 2000, method = "euler")
top_rows_overlap(res_list, top_n = 3000, method = "euler")
top_rows_overlap(res_list, top_n = 4000, method = "euler")
top_rows_overlap(res_list, top_n = 5000, method = "euler")
Also visualize the correspondance of rankings between different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "correspondance")
top_rows_overlap(res_list, top_n = 2000, method = "correspondance")
top_rows_overlap(res_list, top_n = 3000, method = "correspondance")
top_rows_overlap(res_list, top_n = 4000, method = "correspondance")
top_rows_overlap(res_list, top_n = 5000, method = "correspondance")
Heatmaps of the top rows:
top_rows_heatmap(res_list, top_n = 1000)
top_rows_heatmap(res_list, top_n = 2000)
top_rows_heatmap(res_list, top_n = 3000)
top_rows_heatmap(res_list, top_n = 4000)
top_rows_heatmap(res_list, top_n = 5000)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res_list, k = 2)
#> n disease.state(p) k
#> SD:NMF 77 0.01538 2
#> CV:NMF 78 0.03818 2
#> MAD:NMF 77 0.01538 2
#> ATC:NMF 78 0.31199 2
#> SD:skmeans 78 0.04094 2
#> CV:skmeans 77 0.08416 2
#> MAD:skmeans 77 0.02890 2
#> ATC:skmeans 79 0.08695 2
#> SD:mclust 78 0.70899 2
#> CV:mclust 75 0.52534 2
#> MAD:mclust 72 0.13652 2
#> ATC:mclust 0 NA 2
#> SD:kmeans 79 0.13064 2
#> CV:kmeans 77 0.12783 2
#> MAD:kmeans 77 0.07747 2
#> ATC:kmeans 78 0.06673 2
#> SD:pam 71 0.00565 2
#> CV:pam 73 0.00713 2
#> MAD:pam 73 0.77542 2
#> ATC:pam 77 0.20434 2
#> SD:hclust 57 0.09550 2
#> CV:hclust 77 0.43959 2
#> MAD:hclust 69 0.01221 2
#> ATC:hclust 68 1.00000 2
test_to_known_factors(res_list, k = 3)
#> n disease.state(p) k
#> SD:NMF 67 0.004348 3
#> CV:NMF 71 0.000930 3
#> MAD:NMF 63 0.003669 3
#> ATC:NMF 66 0.604365 3
#> SD:skmeans 72 0.004020 3
#> CV:skmeans 67 0.013503 3
#> MAD:skmeans 72 0.004214 3
#> ATC:skmeans 75 0.198140 3
#> SD:mclust 57 0.217554 3
#> CV:mclust 64 0.004142 3
#> MAD:mclust 65 0.012202 3
#> ATC:mclust 78 0.191695 3
#> SD:kmeans 76 0.003389 3
#> CV:kmeans 54 0.827712 3
#> MAD:kmeans 77 0.003737 3
#> ATC:kmeans 65 0.164039 3
#> SD:pam 70 0.001008 3
#> CV:pam 65 0.000231 3
#> MAD:pam 67 0.000665 3
#> ATC:pam 75 0.215821 3
#> SD:hclust 63 0.078236 3
#> CV:hclust 64 0.221035 3
#> MAD:hclust 54 0.004346 3
#> ATC:hclust 64 0.079102 3
test_to_known_factors(res_list, k = 4)
#> n disease.state(p) k
#> SD:NMF 55 0.003728 4
#> CV:NMF 58 0.010181 4
#> MAD:NMF 37 0.073093 4
#> ATC:NMF 54 0.891771 4
#> SD:skmeans 54 0.012158 4
#> CV:skmeans 48 0.052392 4
#> MAD:skmeans 54 0.006391 4
#> ATC:skmeans 72 0.282472 4
#> SD:mclust 74 0.016786 4
#> CV:mclust 77 0.031371 4
#> MAD:mclust 74 0.005580 4
#> ATC:mclust 78 0.323696 4
#> SD:kmeans 76 0.009565 4
#> CV:kmeans 73 0.005367 4
#> MAD:kmeans 73 0.010510 4
#> ATC:kmeans 76 0.320126 4
#> SD:pam 67 0.000946 4
#> CV:pam 64 0.000175 4
#> MAD:pam 68 0.002427 4
#> ATC:pam 74 0.400867 4
#> SD:hclust 50 0.317075 4
#> CV:hclust 59 0.775445 4
#> MAD:hclust 49 0.012861 4
#> ATC:hclust 55 0.234594 4
test_to_known_factors(res_list, k = 5)
#> n disease.state(p) k
#> SD:NMF 39 0.024769 5
#> CV:NMF 38 0.005763 5
#> MAD:NMF 41 0.072088 5
#> ATC:NMF 56 0.213102 5
#> SD:skmeans 35 0.058151 5
#> CV:skmeans 29 0.035361 5
#> MAD:skmeans 35 0.104015 5
#> ATC:skmeans 55 0.198855 5
#> SD:mclust 59 0.105064 5
#> CV:mclust 75 0.018065 5
#> MAD:mclust 51 0.012708 5
#> ATC:mclust 70 0.313767 5
#> SD:kmeans 62 0.047107 5
#> CV:kmeans 63 0.013902 5
#> MAD:kmeans 57 0.015478 5
#> ATC:kmeans 71 0.351009 5
#> SD:pam 66 0.001101 5
#> CV:pam 56 0.000526 5
#> MAD:pam 56 0.023961 5
#> ATC:pam 76 0.245526 5
#> SD:hclust 40 0.540890 5
#> CV:hclust 60 0.107880 5
#> MAD:hclust 52 0.144130 5
#> ATC:hclust 58 0.042991 5
test_to_known_factors(res_list, k = 6)
#> n disease.state(p) k
#> SD:NMF 45 0.02113 6
#> CV:NMF 35 0.00437 6
#> MAD:NMF 43 0.02427 6
#> ATC:NMF 40 0.04979 6
#> SD:skmeans 28 0.20788 6
#> CV:skmeans 11 0.24030 6
#> MAD:skmeans 27 0.09979 6
#> ATC:skmeans 62 0.33922 6
#> SD:mclust 52 0.02316 6
#> CV:mclust 56 0.18827 6
#> MAD:mclust 42 0.15494 6
#> ATC:mclust 66 0.18297 6
#> SD:kmeans 43 0.09348 6
#> CV:kmeans 50 0.22323 6
#> MAD:kmeans 53 0.15886 6
#> ATC:kmeans 59 0.16496 6
#> SD:pam 61 0.00122 6
#> CV:pam 54 0.00278 6
#> MAD:pam 58 0.01847 6
#> ATC:pam 50 0.25029 6
#> SD:hclust 48 0.51590 6
#> CV:hclust 62 0.41699 6
#> MAD:hclust 50 0.52577 6
#> ATC:hclust 47 0.01878 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 79 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 0.173 0.600 0.829 0.2732 0.903 0.903
#> 3 3 0.256 0.645 0.825 0.5848 0.772 0.747
#> 4 4 0.266 0.522 0.766 0.2338 0.922 0.884
#> 5 5 0.302 0.380 0.717 0.1105 0.956 0.927
#> 6 6 0.304 0.465 0.710 0.0871 0.793 0.634
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
#> GSM617581 1 0.3584 0.7409 0.932 0.068
#> GSM617582 1 0.5629 0.6658 0.868 0.132
#> GSM617588 1 0.9933 0.1752 0.548 0.452
#> GSM617590 1 0.9732 0.2704 0.596 0.404
#> GSM617592 1 0.9686 0.2855 0.604 0.396
#> GSM617607 1 0.1633 0.7428 0.976 0.024
#> GSM617608 1 0.3431 0.7284 0.936 0.064
#> GSM617609 1 0.8207 0.4624 0.744 0.256
#> GSM617612 1 0.1414 0.7440 0.980 0.020
#> GSM617615 1 0.8661 0.4990 0.712 0.288
#> GSM617616 1 0.3431 0.7286 0.936 0.064
#> GSM617617 1 0.4690 0.7171 0.900 0.100
#> GSM617618 1 0.3733 0.7252 0.928 0.072
#> GSM617619 1 0.8081 0.5122 0.752 0.248
#> GSM617620 1 0.9661 0.2943 0.608 0.392
#> GSM617622 1 0.6531 0.6718 0.832 0.168
#> GSM617623 1 0.2236 0.7442 0.964 0.036
#> GSM617624 1 0.4690 0.7279 0.900 0.100
#> GSM617625 1 0.8081 0.4864 0.752 0.248
#> GSM617626 1 0.1633 0.7425 0.976 0.024
#> GSM617627 1 0.4431 0.7302 0.908 0.092
#> GSM617628 1 0.8081 0.4864 0.752 0.248
#> GSM617632 1 0.2043 0.7388 0.968 0.032
#> GSM617634 1 0.6048 0.6707 0.852 0.148
#> GSM617635 1 0.1184 0.7424 0.984 0.016
#> GSM617636 1 0.2778 0.7339 0.952 0.048
#> GSM617637 1 0.0938 0.7414 0.988 0.012
#> GSM617638 1 0.4161 0.7314 0.916 0.084
#> GSM617639 1 0.0938 0.7409 0.988 0.012
#> GSM617640 1 0.4939 0.7112 0.892 0.108
#> GSM617641 1 0.9754 0.2613 0.592 0.408
#> GSM617643 1 0.5294 0.7030 0.880 0.120
#> GSM617644 1 0.9850 0.2205 0.572 0.428
#> GSM617647 1 0.4690 0.7166 0.900 0.100
#> GSM617648 1 0.5842 0.6891 0.860 0.140
#> GSM617649 1 0.4939 0.7159 0.892 0.108
#> GSM617650 1 0.1184 0.7415 0.984 0.016
#> GSM617651 1 0.1184 0.7422 0.984 0.016
#> GSM617653 1 0.1633 0.7438 0.976 0.024
#> GSM617654 1 0.4690 0.7163 0.900 0.100
#> GSM617583 1 0.7219 0.5798 0.800 0.200
#> GSM617584 1 0.7528 0.6054 0.784 0.216
#> GSM617585 2 0.9754 0.6949 0.408 0.592
#> GSM617586 1 0.7950 0.4971 0.760 0.240
#> GSM617587 1 0.7219 0.5639 0.800 0.200
#> GSM617589 1 0.9977 0.1068 0.528 0.472
#> GSM617591 1 0.8608 0.4615 0.716 0.284
#> GSM617593 1 0.1414 0.7406 0.980 0.020
#> GSM617594 1 0.4690 0.7159 0.900 0.100
#> GSM617595 1 0.1184 0.7421 0.984 0.016
#> GSM617596 1 0.2043 0.7408 0.968 0.032
#> GSM617597 1 0.6531 0.6096 0.832 0.168
#> GSM617598 1 0.1184 0.7427 0.984 0.016
#> GSM617599 1 0.4690 0.7199 0.900 0.100
#> GSM617600 1 0.8909 0.2782 0.692 0.308
#> GSM617601 1 0.5737 0.6909 0.864 0.136
#> GSM617602 1 0.8763 0.2494 0.704 0.296
#> GSM617603 1 0.9996 0.0703 0.512 0.488
#> GSM617604 1 0.2778 0.7390 0.952 0.048
#> GSM617605 1 0.9732 0.2704 0.596 0.404
#> GSM617606 1 0.8661 0.4700 0.712 0.288
#> GSM617610 1 0.0938 0.7409 0.988 0.012
#> GSM617611 1 0.2236 0.7441 0.964 0.036
#> GSM617613 2 0.9795 0.7569 0.416 0.584
#> GSM617614 1 0.5737 0.6579 0.864 0.136
#> GSM617621 1 0.1414 0.7417 0.980 0.020
#> GSM617629 2 1.0000 0.6435 0.496 0.504
#> GSM617630 1 0.5408 0.7113 0.876 0.124
#> GSM617631 1 0.8763 0.2570 0.704 0.296
#> GSM617633 1 0.4815 0.6988 0.896 0.104
#> GSM617642 1 0.6887 0.6092 0.816 0.184
#> GSM617645 1 0.4690 0.7163 0.900 0.100
#> GSM617646 1 0.0938 0.7436 0.988 0.012
#> GSM617652 1 0.2236 0.7412 0.964 0.036
#> GSM617655 1 0.8144 0.4668 0.748 0.252
#> GSM617656 1 0.9209 0.1961 0.664 0.336
#> GSM617657 2 0.8499 0.7082 0.276 0.724
#> GSM617658 1 0.8763 0.2570 0.704 0.296
#> GSM617659 1 0.1633 0.7413 0.976 0.024
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM617581 1 0.3499 0.7655 0.900 0.072 0.028
#> GSM617582 1 0.4873 0.7057 0.824 0.024 0.152
#> GSM617588 2 0.3148 0.7722 0.048 0.916 0.036
#> GSM617590 2 0.2066 0.7927 0.060 0.940 0.000
#> GSM617592 2 0.2356 0.7895 0.072 0.928 0.000
#> GSM617607 1 0.1399 0.7760 0.968 0.004 0.028
#> GSM617608 1 0.2261 0.7691 0.932 0.000 0.068
#> GSM617609 1 0.5835 0.4519 0.660 0.000 0.340
#> GSM617612 1 0.1182 0.7753 0.976 0.012 0.012
#> GSM617615 2 0.7251 0.2734 0.348 0.612 0.040
#> GSM617616 1 0.3234 0.7605 0.908 0.020 0.072
#> GSM617617 1 0.5357 0.6949 0.820 0.116 0.064
#> GSM617618 1 0.3637 0.7523 0.892 0.024 0.084
#> GSM617619 1 0.6852 0.4913 0.664 0.036 0.300
#> GSM617620 2 0.3375 0.7685 0.100 0.892 0.008
#> GSM617622 1 0.6834 0.5302 0.692 0.260 0.048
#> GSM617623 1 0.2050 0.7756 0.952 0.028 0.020
#> GSM617624 1 0.5831 0.6902 0.796 0.128 0.076
#> GSM617625 1 0.7032 0.4938 0.676 0.052 0.272
#> GSM617626 1 0.1315 0.7753 0.972 0.008 0.020
#> GSM617627 1 0.5631 0.6933 0.804 0.132 0.064
#> GSM617628 1 0.7032 0.4938 0.676 0.052 0.272
#> GSM617632 1 0.1289 0.7745 0.968 0.000 0.032
#> GSM617634 1 0.6034 0.6741 0.780 0.068 0.152
#> GSM617635 1 0.0747 0.7724 0.984 0.000 0.016
#> GSM617636 1 0.1964 0.7722 0.944 0.000 0.056
#> GSM617637 1 0.0424 0.7705 0.992 0.000 0.008
#> GSM617638 1 0.3933 0.7430 0.880 0.028 0.092
#> GSM617639 1 0.0592 0.7720 0.988 0.000 0.012
#> GSM617640 1 0.5253 0.6938 0.828 0.096 0.076
#> GSM617641 2 0.2301 0.7925 0.060 0.936 0.004
#> GSM617643 1 0.6000 0.6169 0.760 0.200 0.040
#> GSM617644 2 0.6964 0.4492 0.264 0.684 0.052
#> GSM617647 1 0.5330 0.6846 0.812 0.144 0.044
#> GSM617648 1 0.6348 0.5997 0.740 0.212 0.048
#> GSM617649 1 0.5734 0.6648 0.788 0.164 0.048
#> GSM617650 1 0.0747 0.7737 0.984 0.000 0.016
#> GSM617651 1 0.0848 0.7729 0.984 0.008 0.008
#> GSM617653 1 0.1170 0.7742 0.976 0.016 0.008
#> GSM617654 1 0.4921 0.6978 0.844 0.072 0.084
#> GSM617583 1 0.6481 0.5834 0.728 0.048 0.224
#> GSM617584 2 0.6510 0.3347 0.364 0.624 0.012
#> GSM617585 3 0.9472 0.5934 0.288 0.220 0.492
#> GSM617586 1 0.5706 0.4892 0.680 0.000 0.320
#> GSM617587 1 0.5291 0.5804 0.732 0.000 0.268
#> GSM617589 2 0.2743 0.7389 0.020 0.928 0.052
#> GSM617591 1 0.8321 0.3910 0.620 0.140 0.240
#> GSM617593 1 0.1031 0.7741 0.976 0.000 0.024
#> GSM617594 1 0.5454 0.6760 0.804 0.152 0.044
#> GSM617595 1 0.0661 0.7711 0.988 0.004 0.008
#> GSM617596 1 0.1647 0.7731 0.960 0.004 0.036
#> GSM617597 1 0.5158 0.6234 0.764 0.004 0.232
#> GSM617598 1 0.0747 0.7735 0.984 0.000 0.016
#> GSM617599 1 0.5307 0.6971 0.816 0.136 0.048
#> GSM617600 1 0.6386 0.1965 0.584 0.004 0.412
#> GSM617601 1 0.6201 0.6085 0.748 0.208 0.044
#> GSM617602 1 0.6111 0.2379 0.604 0.000 0.396
#> GSM617603 2 0.2486 0.7292 0.008 0.932 0.060
#> GSM617604 1 0.2749 0.7715 0.924 0.012 0.064
#> GSM617605 2 0.2066 0.7927 0.060 0.940 0.000
#> GSM617606 1 0.8689 0.3102 0.596 0.200 0.204
#> GSM617610 1 0.0829 0.7735 0.984 0.004 0.012
#> GSM617611 1 0.1774 0.7754 0.960 0.016 0.024
#> GSM617613 3 0.5785 0.7132 0.300 0.004 0.696
#> GSM617614 1 0.4629 0.6831 0.808 0.004 0.188
#> GSM617621 1 0.0983 0.7729 0.980 0.004 0.016
#> GSM617629 3 0.6483 0.5954 0.392 0.008 0.600
#> GSM617630 1 0.4731 0.7199 0.840 0.032 0.128
#> GSM617631 1 0.6111 0.2328 0.604 0.000 0.396
#> GSM617633 1 0.4291 0.7167 0.840 0.008 0.152
#> GSM617642 1 0.5138 0.6131 0.748 0.000 0.252
#> GSM617645 1 0.4921 0.6978 0.844 0.072 0.084
#> GSM617646 1 0.1620 0.7734 0.964 0.024 0.012
#> GSM617652 1 0.1647 0.7762 0.960 0.004 0.036
#> GSM617655 1 0.5810 0.4589 0.664 0.000 0.336
#> GSM617656 1 0.6260 0.0783 0.552 0.000 0.448
#> GSM617657 3 0.3349 0.5256 0.108 0.004 0.888
#> GSM617658 1 0.6111 0.2328 0.604 0.000 0.396
#> GSM617659 1 0.1289 0.7749 0.968 0.000 0.032
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM617581 1 0.4414 0.6438 0.824 0.120 0.020 0.036
#> GSM617582 1 0.4530 0.6437 0.804 0.028 0.152 0.016
#> GSM617588 4 0.2799 0.7578 0.008 0.108 0.000 0.884
#> GSM617590 4 0.2530 0.7831 0.000 0.112 0.000 0.888
#> GSM617592 4 0.2589 0.7797 0.000 0.116 0.000 0.884
#> GSM617607 1 0.1936 0.7054 0.940 0.028 0.032 0.000
#> GSM617608 1 0.2124 0.7038 0.924 0.008 0.068 0.000
#> GSM617609 1 0.5110 0.4349 0.636 0.012 0.352 0.000
#> GSM617612 1 0.1139 0.7005 0.972 0.008 0.008 0.012
#> GSM617615 4 0.7109 0.1884 0.272 0.104 0.024 0.600
#> GSM617616 1 0.3330 0.6908 0.884 0.032 0.072 0.012
#> GSM617617 1 0.6161 -0.2028 0.512 0.444 0.004 0.040
#> GSM617618 1 0.3659 0.6847 0.868 0.032 0.084 0.016
#> GSM617619 1 0.7302 0.3566 0.564 0.116 0.300 0.020
#> GSM617620 4 0.3257 0.7613 0.004 0.152 0.000 0.844
#> GSM617622 1 0.7703 0.0964 0.524 0.300 0.020 0.156
#> GSM617623 1 0.2803 0.6876 0.900 0.080 0.012 0.008
#> GSM617624 1 0.7144 0.3102 0.596 0.292 0.060 0.052
#> GSM617625 1 0.6103 0.4683 0.648 0.008 0.284 0.060
#> GSM617626 1 0.1584 0.6997 0.952 0.036 0.012 0.000
#> GSM617627 1 0.6907 0.2778 0.592 0.316 0.044 0.048
#> GSM617628 1 0.6103 0.4683 0.648 0.008 0.284 0.060
#> GSM617632 1 0.1151 0.7024 0.968 0.008 0.024 0.000
#> GSM617634 1 0.6378 0.5731 0.708 0.100 0.156 0.036
#> GSM617635 1 0.0927 0.6981 0.976 0.016 0.008 0.000
#> GSM617636 1 0.1975 0.7048 0.936 0.016 0.048 0.000
#> GSM617637 1 0.0469 0.6957 0.988 0.012 0.000 0.000
#> GSM617638 1 0.6452 -0.4290 0.472 0.460 0.068 0.000
#> GSM617639 1 0.0672 0.6978 0.984 0.008 0.008 0.000
#> GSM617640 2 0.5630 0.6463 0.360 0.608 0.000 0.032
#> GSM617641 4 0.2345 0.7819 0.000 0.100 0.000 0.900
#> GSM617643 1 0.6760 0.0884 0.552 0.352 0.004 0.092
#> GSM617644 4 0.6875 0.2848 0.220 0.184 0.000 0.596
#> GSM617647 1 0.6313 0.3213 0.628 0.300 0.012 0.060
#> GSM617648 1 0.7001 0.1917 0.580 0.300 0.012 0.108
#> GSM617649 1 0.6932 0.2332 0.588 0.312 0.024 0.076
#> GSM617650 1 0.0804 0.7005 0.980 0.012 0.008 0.000
#> GSM617651 1 0.0804 0.6975 0.980 0.012 0.000 0.008
#> GSM617653 1 0.1174 0.6962 0.968 0.020 0.000 0.012
#> GSM617654 2 0.4499 0.7732 0.228 0.756 0.004 0.012
#> GSM617583 1 0.5702 0.5420 0.700 0.008 0.236 0.056
#> GSM617584 4 0.7093 0.2937 0.216 0.216 0.000 0.568
#> GSM617585 3 0.7996 0.5093 0.252 0.024 0.512 0.212
#> GSM617586 1 0.5018 0.4670 0.656 0.012 0.332 0.000
#> GSM617587 1 0.5131 0.5343 0.692 0.028 0.280 0.000
#> GSM617589 4 0.1256 0.7465 0.008 0.028 0.000 0.964
#> GSM617591 1 0.8252 0.3029 0.552 0.088 0.232 0.128
#> GSM617593 1 0.0779 0.7017 0.980 0.004 0.016 0.000
#> GSM617594 1 0.6367 0.2851 0.616 0.308 0.008 0.068
#> GSM617595 1 0.0817 0.6975 0.976 0.024 0.000 0.000
#> GSM617596 1 0.1724 0.7046 0.948 0.020 0.032 0.000
#> GSM617597 1 0.4252 0.5751 0.744 0.004 0.252 0.000
#> GSM617598 1 0.0937 0.6994 0.976 0.012 0.012 0.000
#> GSM617599 1 0.6300 0.3982 0.664 0.252 0.020 0.064
#> GSM617600 1 0.5901 0.2065 0.532 0.036 0.432 0.000
#> GSM617601 1 0.7473 0.0888 0.536 0.320 0.020 0.124
#> GSM617602 1 0.5060 0.2672 0.584 0.004 0.412 0.000
#> GSM617603 4 0.2216 0.7328 0.000 0.092 0.000 0.908
#> GSM617604 1 0.3088 0.7022 0.888 0.052 0.060 0.000
#> GSM617605 4 0.2530 0.7831 0.000 0.112 0.000 0.888
#> GSM617606 1 0.8409 0.2311 0.540 0.080 0.196 0.184
#> GSM617610 1 0.1114 0.7000 0.972 0.016 0.008 0.004
#> GSM617611 1 0.1762 0.7022 0.952 0.012 0.020 0.016
#> GSM617613 3 0.4222 0.6021 0.272 0.000 0.728 0.000
#> GSM617614 1 0.4335 0.6326 0.792 0.016 0.184 0.008
#> GSM617621 1 0.1256 0.6981 0.964 0.028 0.008 0.000
#> GSM617629 3 0.5237 0.5417 0.356 0.016 0.628 0.000
#> GSM617630 2 0.6425 0.6323 0.300 0.604 0.096 0.000
#> GSM617631 1 0.4898 0.2636 0.584 0.000 0.416 0.000
#> GSM617633 1 0.3813 0.6617 0.828 0.024 0.148 0.000
#> GSM617642 1 0.4482 0.5773 0.728 0.008 0.264 0.000
#> GSM617645 2 0.4600 0.7847 0.240 0.744 0.004 0.012
#> GSM617646 1 0.2480 0.6725 0.904 0.088 0.008 0.000
#> GSM617652 1 0.1584 0.7067 0.952 0.012 0.036 0.000
#> GSM617655 1 0.5093 0.4434 0.640 0.012 0.348 0.000
#> GSM617656 1 0.5285 0.1477 0.524 0.008 0.468 0.000
#> GSM617657 3 0.1902 0.3339 0.004 0.064 0.932 0.000
#> GSM617658 1 0.4898 0.2636 0.584 0.000 0.416 0.000
#> GSM617659 1 0.1256 0.7042 0.964 0.008 0.028 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM617581 1 0.5103 0.5673 0.772 0.028 0.036 0.108 0.056
#> GSM617582 1 0.5014 0.5362 0.748 0.020 0.168 0.016 0.048
#> GSM617588 4 0.3809 0.4313 0.008 0.000 0.000 0.736 0.256
#> GSM617590 4 0.0865 0.6327 0.000 0.004 0.000 0.972 0.024
#> GSM617592 4 0.0794 0.6276 0.000 0.000 0.000 0.972 0.028
#> GSM617607 1 0.2138 0.6361 0.924 0.024 0.044 0.004 0.004
#> GSM617608 1 0.1830 0.6270 0.924 0.008 0.068 0.000 0.000
#> GSM617609 1 0.4705 0.2341 0.580 0.004 0.404 0.000 0.012
#> GSM617612 1 0.1016 0.6333 0.972 0.012 0.008 0.004 0.004
#> GSM617615 4 0.8268 -0.3646 0.180 0.052 0.068 0.480 0.220
#> GSM617616 1 0.3834 0.6019 0.840 0.016 0.088 0.012 0.044
#> GSM617617 1 0.8147 -0.3244 0.384 0.328 0.012 0.084 0.192
#> GSM617618 1 0.4098 0.5919 0.824 0.016 0.100 0.016 0.044
#> GSM617619 1 0.7339 0.1012 0.472 0.064 0.344 0.008 0.112
#> GSM617620 4 0.1809 0.5926 0.000 0.012 0.000 0.928 0.060
#> GSM617622 1 0.8437 -0.1468 0.380 0.076 0.044 0.156 0.344
#> GSM617623 1 0.3838 0.6106 0.852 0.028 0.028 0.036 0.056
#> GSM617624 1 0.8287 0.1595 0.456 0.160 0.080 0.040 0.264
#> GSM617625 1 0.5494 0.2898 0.604 0.008 0.324 0.000 0.064
#> GSM617626 1 0.2194 0.6347 0.928 0.016 0.024 0.008 0.024
#> GSM617627 1 0.8262 0.1329 0.452 0.168 0.072 0.040 0.268
#> GSM617628 1 0.5478 0.2935 0.608 0.008 0.320 0.000 0.064
#> GSM617632 1 0.1372 0.6317 0.956 0.004 0.024 0.000 0.016
#> GSM617634 1 0.7004 0.3755 0.596 0.052 0.176 0.016 0.160
#> GSM617635 1 0.1405 0.6344 0.956 0.016 0.008 0.000 0.020
#> GSM617636 1 0.2452 0.6306 0.908 0.012 0.052 0.000 0.028
#> GSM617637 1 0.0579 0.6311 0.984 0.008 0.000 0.000 0.008
#> GSM617638 2 0.7827 0.3787 0.320 0.464 0.104 0.024 0.088
#> GSM617639 1 0.0740 0.6327 0.980 0.008 0.008 0.000 0.004
#> GSM617640 2 0.6772 0.4645 0.228 0.600 0.008 0.068 0.096
#> GSM617641 4 0.0290 0.6299 0.000 0.000 0.000 0.992 0.008
#> GSM617643 1 0.7781 -0.0802 0.408 0.148 0.012 0.068 0.364
#> GSM617644 5 0.6649 0.0000 0.132 0.020 0.000 0.388 0.460
#> GSM617647 1 0.7934 0.1569 0.480 0.168 0.036 0.052 0.264
#> GSM617648 1 0.7677 -0.0120 0.436 0.092 0.020 0.084 0.368
#> GSM617649 1 0.8023 0.0357 0.428 0.144 0.040 0.052 0.336
#> GSM617650 1 0.0613 0.6307 0.984 0.004 0.008 0.000 0.004
#> GSM617651 1 0.0566 0.6296 0.984 0.012 0.000 0.000 0.004
#> GSM617653 1 0.1173 0.6288 0.964 0.012 0.004 0.000 0.020
#> GSM617654 2 0.2952 0.5547 0.088 0.872 0.000 0.036 0.004
#> GSM617583 1 0.5284 0.3934 0.660 0.008 0.272 0.004 0.056
#> GSM617584 4 0.6485 -0.0986 0.156 0.048 0.016 0.652 0.128
#> GSM617585 3 0.7124 0.3773 0.204 0.004 0.548 0.192 0.052
#> GSM617586 1 0.4655 0.2786 0.600 0.004 0.384 0.000 0.012
#> GSM617587 1 0.5024 0.3694 0.636 0.024 0.324 0.000 0.016
#> GSM617589 4 0.3597 0.5176 0.008 0.012 0.000 0.800 0.180
#> GSM617591 1 0.8215 0.0233 0.444 0.052 0.280 0.048 0.176
#> GSM617593 1 0.0960 0.6330 0.972 0.004 0.016 0.000 0.008
#> GSM617594 1 0.7810 0.1310 0.472 0.164 0.032 0.044 0.288
#> GSM617595 1 0.0693 0.6317 0.980 0.012 0.000 0.000 0.008
#> GSM617596 1 0.2251 0.6293 0.916 0.008 0.052 0.000 0.024
#> GSM617597 1 0.4059 0.4432 0.700 0.000 0.292 0.004 0.004
#> GSM617598 1 0.0727 0.6314 0.980 0.004 0.012 0.000 0.004
#> GSM617599 1 0.7586 0.2300 0.508 0.104 0.056 0.036 0.296
#> GSM617600 1 0.5418 -0.0467 0.480 0.028 0.476 0.000 0.016
#> GSM617601 1 0.8594 -0.0154 0.408 0.164 0.044 0.096 0.288
#> GSM617602 1 0.4792 0.0765 0.536 0.008 0.448 0.000 0.008
#> GSM617603 4 0.5173 0.1555 0.000 0.040 0.000 0.500 0.460
#> GSM617604 1 0.3849 0.6161 0.840 0.016 0.084 0.012 0.048
#> GSM617605 4 0.0865 0.6327 0.000 0.004 0.000 0.972 0.024
#> GSM617606 1 0.8707 -0.0465 0.428 0.072 0.244 0.076 0.180
#> GSM617610 1 0.0867 0.6308 0.976 0.008 0.008 0.000 0.008
#> GSM617611 1 0.1393 0.6318 0.956 0.008 0.024 0.000 0.012
#> GSM617613 3 0.3707 0.5346 0.220 0.004 0.768 0.000 0.008
#> GSM617614 1 0.3907 0.5309 0.768 0.004 0.212 0.004 0.012
#> GSM617621 1 0.1898 0.6331 0.940 0.012 0.016 0.008 0.024
#> GSM617629 3 0.5735 0.4827 0.312 0.016 0.608 0.004 0.060
#> GSM617630 2 0.5573 0.5534 0.156 0.696 0.128 0.012 0.008
#> GSM617631 1 0.4688 0.0674 0.532 0.004 0.456 0.000 0.008
#> GSM617633 1 0.3925 0.5750 0.804 0.016 0.156 0.004 0.020
#> GSM617642 1 0.4127 0.4365 0.680 0.000 0.312 0.000 0.008
#> GSM617645 2 0.3273 0.5901 0.112 0.848 0.000 0.036 0.004
#> GSM617646 1 0.3053 0.6201 0.880 0.076 0.020 0.016 0.008
#> GSM617652 1 0.1730 0.6344 0.940 0.008 0.044 0.004 0.004
#> GSM617655 1 0.4696 0.2459 0.584 0.004 0.400 0.000 0.012
#> GSM617656 3 0.4555 -0.0925 0.472 0.000 0.520 0.000 0.008
#> GSM617657 3 0.3759 0.0598 0.000 0.056 0.808 0.000 0.136
#> GSM617658 1 0.4688 0.0674 0.532 0.004 0.456 0.000 0.008
#> GSM617659 1 0.0880 0.6328 0.968 0.000 0.032 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM617581 1 0.4603 0.5867 0.748 0.136 0.020 0.088 0.004 0.004
#> GSM617582 1 0.5304 0.5346 0.688 0.084 0.180 0.000 0.016 0.032
#> GSM617588 4 0.4807 0.2290 0.008 0.076 0.000 0.656 0.000 0.260
#> GSM617590 4 0.1720 0.6552 0.000 0.040 0.000 0.928 0.000 0.032
#> GSM617592 4 0.1204 0.6580 0.000 0.056 0.000 0.944 0.000 0.000
#> GSM617607 1 0.2308 0.6979 0.892 0.068 0.040 0.000 0.000 0.000
#> GSM617608 1 0.1728 0.6965 0.924 0.008 0.064 0.000 0.000 0.004
#> GSM617609 1 0.4517 0.1429 0.524 0.032 0.444 0.000 0.000 0.000
#> GSM617612 1 0.0881 0.7004 0.972 0.012 0.008 0.008 0.000 0.000
#> GSM617615 4 0.8054 0.0871 0.108 0.224 0.080 0.476 0.032 0.080
#> GSM617616 1 0.4324 0.6353 0.780 0.084 0.100 0.000 0.012 0.024
#> GSM617617 2 0.6845 0.3110 0.268 0.424 0.004 0.044 0.260 0.000
#> GSM617618 1 0.4532 0.6216 0.764 0.084 0.112 0.000 0.012 0.028
#> GSM617619 3 0.6802 0.1738 0.340 0.268 0.360 0.000 0.020 0.012
#> GSM617620 4 0.2320 0.6412 0.000 0.080 0.000 0.892 0.004 0.024
#> GSM617622 2 0.6984 0.5335 0.240 0.536 0.032 0.108 0.004 0.080
#> GSM617623 1 0.3502 0.6499 0.820 0.132 0.012 0.028 0.004 0.004
#> GSM617624 2 0.5736 0.6682 0.320 0.572 0.068 0.008 0.028 0.004
#> GSM617625 1 0.5548 0.2406 0.556 0.032 0.356 0.004 0.004 0.048
#> GSM617626 1 0.2213 0.6972 0.912 0.048 0.024 0.008 0.000 0.008
#> GSM617627 2 0.5529 0.6793 0.308 0.592 0.060 0.008 0.032 0.000
#> GSM617628 1 0.5538 0.2505 0.560 0.032 0.352 0.004 0.004 0.048
#> GSM617632 1 0.1852 0.6994 0.928 0.040 0.024 0.000 0.004 0.004
#> GSM617634 1 0.6785 0.0824 0.484 0.252 0.212 0.000 0.020 0.032
#> GSM617635 1 0.1410 0.6987 0.944 0.044 0.008 0.000 0.000 0.004
#> GSM617636 1 0.2945 0.6936 0.868 0.064 0.052 0.000 0.004 0.012
#> GSM617637 1 0.0547 0.6954 0.980 0.020 0.000 0.000 0.000 0.000
#> GSM617638 5 0.7448 0.1584 0.236 0.232 0.112 0.004 0.412 0.004
#> GSM617639 1 0.0508 0.6994 0.984 0.012 0.004 0.000 0.000 0.000
#> GSM617640 5 0.6086 0.4221 0.148 0.276 0.000 0.036 0.540 0.000
#> GSM617641 4 0.0692 0.6491 0.000 0.020 0.000 0.976 0.000 0.004
#> GSM617643 2 0.4643 0.6381 0.248 0.692 0.000 0.028 0.020 0.012
#> GSM617644 2 0.7117 -0.4397 0.060 0.360 0.000 0.276 0.004 0.300
#> GSM617647 2 0.5271 0.6812 0.348 0.580 0.016 0.016 0.040 0.000
#> GSM617648 2 0.5343 0.6545 0.276 0.640 0.012 0.032 0.012 0.028
#> GSM617649 2 0.4600 0.6811 0.244 0.700 0.028 0.008 0.012 0.008
#> GSM617650 1 0.0622 0.6985 0.980 0.012 0.008 0.000 0.000 0.000
#> GSM617651 1 0.0653 0.6955 0.980 0.012 0.000 0.004 0.004 0.000
#> GSM617653 1 0.1180 0.6965 0.960 0.024 0.000 0.004 0.008 0.004
#> GSM617654 5 0.2722 0.5323 0.032 0.088 0.000 0.004 0.872 0.004
#> GSM617583 1 0.5370 0.3657 0.612 0.032 0.304 0.008 0.004 0.040
#> GSM617584 4 0.5512 0.3294 0.116 0.244 0.004 0.620 0.012 0.004
#> GSM617585 3 0.7040 0.3535 0.160 0.044 0.564 0.160 0.008 0.064
#> GSM617586 1 0.4488 0.2157 0.548 0.032 0.420 0.000 0.000 0.000
#> GSM617587 1 0.4931 0.3201 0.576 0.064 0.356 0.000 0.004 0.000
#> GSM617589 4 0.3494 0.4040 0.004 0.016 0.000 0.788 0.008 0.184
#> GSM617591 1 0.8049 -0.3420 0.316 0.252 0.316 0.036 0.020 0.060
#> GSM617593 1 0.0767 0.7011 0.976 0.008 0.012 0.000 0.000 0.004
#> GSM617594 2 0.4984 0.7020 0.320 0.620 0.024 0.012 0.024 0.000
#> GSM617595 1 0.0632 0.6959 0.976 0.024 0.000 0.000 0.000 0.000
#> GSM617596 1 0.2965 0.6912 0.864 0.068 0.056 0.000 0.004 0.008
#> GSM617597 1 0.4182 0.4549 0.660 0.024 0.312 0.000 0.000 0.004
#> GSM617598 1 0.0912 0.7017 0.972 0.008 0.012 0.000 0.004 0.004
#> GSM617599 2 0.5692 0.6742 0.348 0.552 0.060 0.016 0.024 0.000
#> GSM617600 3 0.5483 0.1864 0.388 0.112 0.496 0.000 0.000 0.004
#> GSM617601 2 0.5969 0.6769 0.244 0.628 0.036 0.048 0.024 0.020
#> GSM617602 1 0.5233 0.0622 0.496 0.032 0.444 0.000 0.012 0.016
#> GSM617603 6 0.3641 0.0000 0.000 0.020 0.000 0.248 0.000 0.732
#> GSM617604 1 0.3917 0.6613 0.804 0.096 0.080 0.008 0.004 0.008
#> GSM617605 4 0.1720 0.6552 0.000 0.040 0.000 0.928 0.000 0.032
#> GSM617606 1 0.8595 -0.3332 0.328 0.208 0.280 0.048 0.032 0.104
#> GSM617610 1 0.0603 0.6975 0.980 0.016 0.004 0.000 0.000 0.000
#> GSM617611 1 0.1294 0.7001 0.956 0.008 0.024 0.004 0.000 0.008
#> GSM617613 3 0.3972 0.4834 0.184 0.020 0.768 0.000 0.012 0.016
#> GSM617614 1 0.4357 0.5660 0.716 0.036 0.232 0.004 0.004 0.008
#> GSM617621 1 0.2077 0.6932 0.916 0.056 0.012 0.008 0.000 0.008
#> GSM617629 3 0.6827 0.3839 0.244 0.076 0.540 0.000 0.032 0.108
#> GSM617630 5 0.5491 0.5447 0.088 0.072 0.144 0.004 0.688 0.004
#> GSM617631 1 0.5150 0.0500 0.492 0.032 0.452 0.000 0.008 0.016
#> GSM617633 1 0.4119 0.6348 0.776 0.052 0.148 0.000 0.016 0.008
#> GSM617642 1 0.4167 0.4221 0.632 0.024 0.344 0.000 0.000 0.000
#> GSM617645 5 0.3148 0.5899 0.064 0.092 0.000 0.004 0.840 0.000
#> GSM617646 1 0.2996 0.6532 0.832 0.144 0.016 0.000 0.008 0.000
#> GSM617652 1 0.1788 0.7038 0.928 0.028 0.040 0.000 0.000 0.004
#> GSM617655 1 0.4509 0.1734 0.532 0.032 0.436 0.000 0.000 0.000
#> GSM617656 3 0.4348 0.1116 0.416 0.024 0.560 0.000 0.000 0.000
#> GSM617657 3 0.5906 -0.2980 0.000 0.148 0.628 0.000 0.084 0.140
#> GSM617658 1 0.5150 0.0500 0.492 0.032 0.452 0.000 0.008 0.016
#> GSM617659 1 0.0858 0.7038 0.968 0.000 0.028 0.000 0.000 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:hclust 57 0.0955 2
#> SD:hclust 63 0.0782 3
#> SD:hclust 50 0.3171 4
#> SD:hclust 40 0.5409 5
#> SD:hclust 48 0.5159 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 79 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.893 0.939 0.956 0.4863 0.512 0.512
#> 3 3 0.561 0.788 0.813 0.3082 0.799 0.617
#> 4 4 0.695 0.834 0.876 0.1484 0.910 0.742
#> 5 5 0.713 0.682 0.804 0.0647 0.985 0.945
#> 6 6 0.716 0.495 0.763 0.0450 0.923 0.712
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
#> GSM617581 1 0.7453 0.778 0.788 0.212
#> GSM617582 1 0.5519 0.889 0.872 0.128
#> GSM617588 2 0.1184 0.960 0.016 0.984
#> GSM617590 2 0.1184 0.951 0.016 0.984
#> GSM617592 2 0.1184 0.960 0.016 0.984
#> GSM617607 1 0.1184 0.964 0.984 0.016
#> GSM617608 1 0.1184 0.964 0.984 0.016
#> GSM617609 1 0.1633 0.958 0.976 0.024
#> GSM617612 1 0.1184 0.964 0.984 0.016
#> GSM617615 2 0.1414 0.959 0.020 0.980
#> GSM617616 1 0.1633 0.962 0.976 0.024
#> GSM617617 2 0.1843 0.959 0.028 0.972
#> GSM617618 1 0.2236 0.958 0.964 0.036
#> GSM617619 2 0.6247 0.837 0.156 0.844
#> GSM617620 2 0.1184 0.960 0.016 0.984
#> GSM617622 2 0.1184 0.958 0.016 0.984
#> GSM617623 1 0.7745 0.754 0.772 0.228
#> GSM617624 2 0.4022 0.933 0.080 0.920
#> GSM617625 1 0.1633 0.959 0.976 0.024
#> GSM617626 1 0.6887 0.807 0.816 0.184
#> GSM617627 2 0.1843 0.960 0.028 0.972
#> GSM617628 1 0.1633 0.959 0.976 0.024
#> GSM617632 1 0.1633 0.962 0.976 0.024
#> GSM617634 2 0.3879 0.924 0.076 0.924
#> GSM617635 1 0.1184 0.964 0.984 0.016
#> GSM617636 1 0.1414 0.963 0.980 0.020
#> GSM617637 1 0.1184 0.964 0.984 0.016
#> GSM617638 2 0.6531 0.830 0.168 0.832
#> GSM617639 1 0.1184 0.964 0.984 0.016
#> GSM617640 2 0.2043 0.958 0.032 0.968
#> GSM617641 2 0.0376 0.959 0.004 0.996
#> GSM617643 2 0.1843 0.960 0.028 0.972
#> GSM617644 2 0.1184 0.960 0.016 0.984
#> GSM617647 2 0.2043 0.958 0.032 0.968
#> GSM617648 2 0.1414 0.960 0.020 0.980
#> GSM617649 2 0.1843 0.959 0.028 0.972
#> GSM617650 1 0.1184 0.964 0.984 0.016
#> GSM617651 1 0.1184 0.964 0.984 0.016
#> GSM617653 1 0.1184 0.964 0.984 0.016
#> GSM617654 2 0.2043 0.958 0.032 0.968
#> GSM617583 1 0.1633 0.959 0.976 0.024
#> GSM617584 2 0.1414 0.960 0.020 0.980
#> GSM617585 2 0.1184 0.951 0.016 0.984
#> GSM617586 1 0.1414 0.958 0.980 0.020
#> GSM617587 1 0.1414 0.959 0.980 0.020
#> GSM617589 2 0.0672 0.960 0.008 0.992
#> GSM617591 2 0.2778 0.948 0.048 0.952
#> GSM617593 1 0.1184 0.964 0.984 0.016
#> GSM617594 2 0.3274 0.946 0.060 0.940
#> GSM617595 1 0.1184 0.964 0.984 0.016
#> GSM617596 1 0.1633 0.962 0.976 0.024
#> GSM617597 1 0.0672 0.960 0.992 0.008
#> GSM617598 1 0.1184 0.964 0.984 0.016
#> GSM617599 2 0.2603 0.955 0.044 0.956
#> GSM617600 1 0.2236 0.954 0.964 0.036
#> GSM617601 2 0.1414 0.961 0.020 0.980
#> GSM617602 1 0.2778 0.950 0.952 0.048
#> GSM617603 2 0.0938 0.952 0.012 0.988
#> GSM617604 1 0.2423 0.956 0.960 0.040
#> GSM617605 2 0.1184 0.951 0.016 0.984
#> GSM617606 2 0.2423 0.950 0.040 0.960
#> GSM617610 1 0.1184 0.964 0.984 0.016
#> GSM617611 1 0.1184 0.964 0.984 0.016
#> GSM617613 1 0.2423 0.953 0.960 0.040
#> GSM617614 1 0.1633 0.956 0.976 0.024
#> GSM617621 1 0.1633 0.962 0.976 0.024
#> GSM617629 1 0.3431 0.941 0.936 0.064
#> GSM617630 1 0.7299 0.775 0.796 0.204
#> GSM617631 1 0.2778 0.950 0.952 0.048
#> GSM617633 1 0.1184 0.964 0.984 0.016
#> GSM617642 1 0.1184 0.959 0.984 0.016
#> GSM617645 2 0.2043 0.958 0.032 0.968
#> GSM617646 1 0.1184 0.964 0.984 0.016
#> GSM617652 1 0.0672 0.963 0.992 0.008
#> GSM617655 1 0.1843 0.956 0.972 0.028
#> GSM617656 1 0.1843 0.956 0.972 0.028
#> GSM617657 2 0.9286 0.501 0.344 0.656
#> GSM617658 1 0.2603 0.952 0.956 0.044
#> GSM617659 1 0.1184 0.964 0.984 0.016
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM617581 1 0.6000 0.658 0.760 0.200 0.040
#> GSM617582 1 0.7297 0.535 0.708 0.120 0.172
#> GSM617588 2 0.5810 0.750 0.000 0.664 0.336
#> GSM617590 2 0.5760 0.752 0.000 0.672 0.328
#> GSM617592 2 0.5760 0.752 0.000 0.672 0.328
#> GSM617607 1 0.0829 0.906 0.984 0.012 0.004
#> GSM617608 1 0.0424 0.902 0.992 0.000 0.008
#> GSM617609 3 0.6988 0.833 0.320 0.036 0.644
#> GSM617612 1 0.0000 0.906 1.000 0.000 0.000
#> GSM617615 2 0.2269 0.824 0.016 0.944 0.040
#> GSM617616 1 0.1774 0.894 0.960 0.016 0.024
#> GSM617617 2 0.2384 0.819 0.056 0.936 0.008
#> GSM617618 1 0.1919 0.891 0.956 0.020 0.024
#> GSM617619 3 0.6235 0.216 0.000 0.436 0.564
#> GSM617620 2 0.5760 0.752 0.000 0.672 0.328
#> GSM617622 2 0.3377 0.819 0.012 0.896 0.092
#> GSM617623 1 0.6096 0.647 0.752 0.208 0.040
#> GSM617624 2 0.6348 0.667 0.060 0.752 0.188
#> GSM617625 3 0.6111 0.792 0.396 0.000 0.604
#> GSM617626 1 0.2773 0.862 0.928 0.048 0.024
#> GSM617627 2 0.2773 0.818 0.048 0.928 0.024
#> GSM617628 3 0.6095 0.797 0.392 0.000 0.608
#> GSM617632 1 0.1337 0.900 0.972 0.012 0.016
#> GSM617634 2 0.6595 0.673 0.076 0.744 0.180
#> GSM617635 1 0.0237 0.907 0.996 0.004 0.000
#> GSM617636 1 0.1751 0.897 0.960 0.012 0.028
#> GSM617637 1 0.0424 0.907 0.992 0.008 0.000
#> GSM617638 2 0.6578 0.627 0.052 0.724 0.224
#> GSM617639 1 0.0237 0.907 0.996 0.004 0.000
#> GSM617640 2 0.1950 0.823 0.040 0.952 0.008
#> GSM617641 2 0.5760 0.752 0.000 0.672 0.328
#> GSM617643 2 0.1525 0.824 0.032 0.964 0.004
#> GSM617644 2 0.4346 0.800 0.000 0.816 0.184
#> GSM617647 2 0.2680 0.814 0.068 0.924 0.008
#> GSM617648 2 0.2116 0.824 0.040 0.948 0.012
#> GSM617649 2 0.2806 0.815 0.032 0.928 0.040
#> GSM617650 1 0.0747 0.895 0.984 0.000 0.016
#> GSM617651 1 0.0000 0.906 1.000 0.000 0.000
#> GSM617653 1 0.0475 0.907 0.992 0.004 0.004
#> GSM617654 2 0.2550 0.819 0.056 0.932 0.012
#> GSM617583 3 0.6079 0.801 0.388 0.000 0.612
#> GSM617584 2 0.5619 0.782 0.012 0.744 0.244
#> GSM617585 2 0.6008 0.678 0.000 0.628 0.372
#> GSM617586 3 0.6843 0.834 0.332 0.028 0.640
#> GSM617587 3 0.7013 0.834 0.324 0.036 0.640
#> GSM617589 2 0.5810 0.750 0.000 0.664 0.336
#> GSM617591 2 0.4755 0.726 0.008 0.808 0.184
#> GSM617593 1 0.0000 0.906 1.000 0.000 0.000
#> GSM617594 2 0.4045 0.789 0.104 0.872 0.024
#> GSM617595 1 0.0424 0.907 0.992 0.008 0.000
#> GSM617596 1 0.1015 0.904 0.980 0.008 0.012
#> GSM617597 3 0.6260 0.701 0.448 0.000 0.552
#> GSM617598 1 0.0000 0.906 1.000 0.000 0.000
#> GSM617599 2 0.3805 0.799 0.092 0.884 0.024
#> GSM617600 3 0.7189 0.824 0.292 0.052 0.656
#> GSM617601 2 0.3083 0.826 0.024 0.916 0.060
#> GSM617602 3 0.6422 0.827 0.324 0.016 0.660
#> GSM617603 2 0.5810 0.750 0.000 0.664 0.336
#> GSM617604 1 0.4912 0.645 0.796 0.008 0.196
#> GSM617605 2 0.5760 0.752 0.000 0.672 0.328
#> GSM617606 2 0.4033 0.771 0.008 0.856 0.136
#> GSM617610 1 0.0424 0.907 0.992 0.008 0.000
#> GSM617611 1 0.0237 0.904 0.996 0.000 0.004
#> GSM617613 3 0.7308 0.818 0.284 0.060 0.656
#> GSM617614 3 0.6111 0.789 0.396 0.000 0.604
#> GSM617621 1 0.1337 0.902 0.972 0.012 0.016
#> GSM617629 3 0.7821 0.758 0.224 0.116 0.660
#> GSM617630 3 0.5905 0.404 0.000 0.352 0.648
#> GSM617631 3 0.6553 0.830 0.324 0.020 0.656
#> GSM617633 1 0.5580 0.443 0.736 0.008 0.256
#> GSM617642 3 0.6095 0.796 0.392 0.000 0.608
#> GSM617645 2 0.2173 0.822 0.048 0.944 0.008
#> GSM617646 1 0.1647 0.889 0.960 0.036 0.004
#> GSM617652 1 0.4465 0.640 0.820 0.004 0.176
#> GSM617655 3 0.6819 0.835 0.328 0.028 0.644
#> GSM617656 3 0.6627 0.833 0.336 0.020 0.644
#> GSM617657 3 0.6984 0.502 0.040 0.304 0.656
#> GSM617658 3 0.6470 0.805 0.356 0.012 0.632
#> GSM617659 1 0.1643 0.863 0.956 0.000 0.044
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM617581 1 0.5419 0.765 0.764 0.084 0.016 0.136
#> GSM617582 1 0.7532 0.618 0.632 0.084 0.176 0.108
#> GSM617588 4 0.2831 0.916 0.000 0.120 0.004 0.876
#> GSM617590 4 0.3032 0.916 0.000 0.124 0.008 0.868
#> GSM617592 4 0.2704 0.917 0.000 0.124 0.000 0.876
#> GSM617607 1 0.2019 0.904 0.940 0.032 0.024 0.004
#> GSM617608 1 0.1209 0.906 0.964 0.004 0.032 0.000
#> GSM617609 3 0.2002 0.927 0.044 0.020 0.936 0.000
#> GSM617612 1 0.1398 0.905 0.956 0.004 0.040 0.000
#> GSM617615 2 0.2907 0.818 0.004 0.900 0.032 0.064
#> GSM617616 1 0.3240 0.878 0.892 0.036 0.016 0.056
#> GSM617617 2 0.1745 0.834 0.008 0.952 0.020 0.020
#> GSM617618 1 0.3904 0.862 0.860 0.044 0.020 0.076
#> GSM617619 2 0.5999 0.316 0.000 0.552 0.404 0.044
#> GSM617620 4 0.2704 0.917 0.000 0.124 0.000 0.876
#> GSM617622 2 0.5663 0.522 0.024 0.700 0.028 0.248
#> GSM617623 1 0.5354 0.768 0.768 0.080 0.016 0.136
#> GSM617624 2 0.2825 0.816 0.008 0.908 0.036 0.048
#> GSM617625 3 0.2520 0.916 0.088 0.004 0.904 0.004
#> GSM617626 1 0.2291 0.891 0.932 0.036 0.016 0.016
#> GSM617627 2 0.2165 0.838 0.008 0.936 0.024 0.032
#> GSM617628 3 0.2452 0.919 0.084 0.004 0.908 0.004
#> GSM617632 1 0.2422 0.890 0.928 0.028 0.016 0.028
#> GSM617634 2 0.4109 0.772 0.028 0.848 0.032 0.092
#> GSM617635 1 0.1697 0.907 0.952 0.016 0.028 0.004
#> GSM617636 1 0.3818 0.867 0.868 0.044 0.028 0.060
#> GSM617637 1 0.1284 0.908 0.964 0.012 0.024 0.000
#> GSM617638 2 0.3016 0.810 0.004 0.896 0.040 0.060
#> GSM617639 1 0.1406 0.907 0.960 0.016 0.024 0.000
#> GSM617640 2 0.1878 0.832 0.008 0.944 0.008 0.040
#> GSM617641 4 0.2704 0.917 0.000 0.124 0.000 0.876
#> GSM617643 2 0.1786 0.832 0.008 0.948 0.008 0.036
#> GSM617644 2 0.5038 0.416 0.000 0.652 0.012 0.336
#> GSM617647 2 0.1509 0.835 0.008 0.960 0.012 0.020
#> GSM617648 2 0.2499 0.821 0.012 0.924 0.032 0.032
#> GSM617649 2 0.1733 0.838 0.000 0.948 0.024 0.028
#> GSM617650 1 0.1743 0.900 0.940 0.004 0.056 0.000
#> GSM617651 1 0.1004 0.907 0.972 0.004 0.024 0.000
#> GSM617653 1 0.0895 0.903 0.976 0.000 0.004 0.020
#> GSM617654 2 0.1721 0.837 0.008 0.952 0.012 0.028
#> GSM617583 3 0.2053 0.925 0.072 0.004 0.924 0.000
#> GSM617584 4 0.5928 0.671 0.052 0.260 0.012 0.676
#> GSM617585 4 0.5935 0.531 0.000 0.080 0.256 0.664
#> GSM617586 3 0.1807 0.928 0.052 0.008 0.940 0.000
#> GSM617587 3 0.2089 0.927 0.048 0.020 0.932 0.000
#> GSM617589 4 0.2530 0.905 0.000 0.112 0.000 0.888
#> GSM617591 2 0.4817 0.716 0.004 0.768 0.188 0.040
#> GSM617593 1 0.1151 0.907 0.968 0.008 0.024 0.000
#> GSM617594 2 0.2291 0.834 0.036 0.932 0.016 0.016
#> GSM617595 1 0.1284 0.908 0.964 0.012 0.024 0.000
#> GSM617596 1 0.2733 0.887 0.916 0.032 0.020 0.032
#> GSM617597 3 0.3024 0.858 0.148 0.000 0.852 0.000
#> GSM617598 1 0.1004 0.908 0.972 0.004 0.024 0.000
#> GSM617599 2 0.2329 0.823 0.024 0.932 0.024 0.020
#> GSM617600 3 0.3015 0.912 0.020 0.036 0.904 0.040
#> GSM617601 2 0.2164 0.820 0.004 0.924 0.004 0.068
#> GSM617602 3 0.4157 0.876 0.060 0.020 0.848 0.072
#> GSM617603 4 0.3219 0.900 0.000 0.112 0.020 0.868
#> GSM617604 1 0.5319 0.771 0.764 0.024 0.164 0.048
#> GSM617605 4 0.3032 0.916 0.000 0.124 0.008 0.868
#> GSM617606 2 0.5117 0.720 0.004 0.760 0.172 0.064
#> GSM617610 1 0.1284 0.908 0.964 0.012 0.024 0.000
#> GSM617611 1 0.1661 0.901 0.944 0.004 0.052 0.000
#> GSM617613 3 0.2465 0.911 0.012 0.020 0.924 0.044
#> GSM617614 3 0.2125 0.924 0.076 0.000 0.920 0.004
#> GSM617621 1 0.2197 0.893 0.936 0.024 0.012 0.028
#> GSM617629 3 0.5401 0.822 0.052 0.060 0.784 0.104
#> GSM617630 2 0.6161 0.240 0.004 0.512 0.444 0.040
#> GSM617631 3 0.2825 0.911 0.036 0.008 0.908 0.048
#> GSM617633 1 0.6381 0.623 0.664 0.036 0.252 0.048
#> GSM617642 3 0.1940 0.924 0.076 0.000 0.924 0.000
#> GSM617645 2 0.1917 0.833 0.008 0.944 0.012 0.036
#> GSM617646 1 0.2909 0.875 0.888 0.092 0.020 0.000
#> GSM617652 1 0.4004 0.807 0.812 0.024 0.164 0.000
#> GSM617655 3 0.1677 0.928 0.040 0.012 0.948 0.000
#> GSM617656 3 0.2049 0.927 0.036 0.012 0.940 0.012
#> GSM617657 3 0.3170 0.882 0.008 0.056 0.892 0.044
#> GSM617658 3 0.4582 0.862 0.072 0.020 0.824 0.084
#> GSM617659 1 0.1867 0.893 0.928 0.000 0.072 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM617581 1 0.6204 0.471 0.600 0.028 0.000 0.108 0.264
#> GSM617582 5 0.6038 0.193 0.308 0.032 0.052 0.008 0.600
#> GSM617588 4 0.1399 0.860 0.000 0.020 0.000 0.952 0.028
#> GSM617590 4 0.1493 0.862 0.000 0.028 0.000 0.948 0.024
#> GSM617592 4 0.0865 0.864 0.000 0.024 0.000 0.972 0.004
#> GSM617607 1 0.2165 0.772 0.924 0.036 0.024 0.000 0.016
#> GSM617608 1 0.1124 0.773 0.960 0.000 0.036 0.000 0.004
#> GSM617609 3 0.1059 0.848 0.020 0.008 0.968 0.000 0.004
#> GSM617612 1 0.1365 0.773 0.952 0.004 0.040 0.000 0.004
#> GSM617615 2 0.3862 0.754 0.004 0.840 0.044 0.036 0.076
#> GSM617616 1 0.4691 0.493 0.636 0.020 0.004 0.000 0.340
#> GSM617617 2 0.2166 0.772 0.004 0.912 0.000 0.012 0.072
#> GSM617618 1 0.5109 0.372 0.580 0.020 0.008 0.004 0.388
#> GSM617619 2 0.6307 0.428 0.000 0.540 0.284 0.004 0.172
#> GSM617620 4 0.0771 0.864 0.000 0.020 0.000 0.976 0.004
#> GSM617622 2 0.5725 0.537 0.000 0.624 0.000 0.172 0.204
#> GSM617623 1 0.6225 0.475 0.604 0.028 0.000 0.116 0.252
#> GSM617624 2 0.2780 0.768 0.004 0.872 0.008 0.004 0.112
#> GSM617625 3 0.2270 0.831 0.072 0.004 0.908 0.000 0.016
#> GSM617626 1 0.3993 0.669 0.756 0.028 0.000 0.000 0.216
#> GSM617627 2 0.2636 0.771 0.004 0.888 0.008 0.008 0.092
#> GSM617628 3 0.2206 0.835 0.068 0.004 0.912 0.000 0.016
#> GSM617632 1 0.4309 0.569 0.676 0.016 0.000 0.000 0.308
#> GSM617634 2 0.5254 0.362 0.008 0.512 0.012 0.012 0.456
#> GSM617635 1 0.1588 0.778 0.948 0.008 0.028 0.000 0.016
#> GSM617636 1 0.4696 0.489 0.616 0.024 0.000 0.000 0.360
#> GSM617637 1 0.0867 0.782 0.976 0.008 0.008 0.000 0.008
#> GSM617638 2 0.4324 0.701 0.004 0.708 0.012 0.004 0.272
#> GSM617639 1 0.0867 0.782 0.976 0.008 0.008 0.000 0.008
#> GSM617640 2 0.4123 0.735 0.004 0.764 0.004 0.024 0.204
#> GSM617641 4 0.0865 0.864 0.000 0.024 0.000 0.972 0.004
#> GSM617643 2 0.1828 0.772 0.004 0.936 0.000 0.028 0.032
#> GSM617644 2 0.6120 0.418 0.000 0.560 0.000 0.256 0.184
#> GSM617647 2 0.1200 0.773 0.008 0.964 0.000 0.016 0.012
#> GSM617648 2 0.3516 0.714 0.000 0.812 0.004 0.020 0.164
#> GSM617649 2 0.1812 0.772 0.004 0.940 0.012 0.008 0.036
#> GSM617650 1 0.1502 0.762 0.940 0.000 0.056 0.000 0.004
#> GSM617651 1 0.0290 0.781 0.992 0.000 0.008 0.000 0.000
#> GSM617653 1 0.2674 0.730 0.856 0.000 0.000 0.004 0.140
#> GSM617654 2 0.4308 0.721 0.004 0.732 0.004 0.020 0.240
#> GSM617583 3 0.2005 0.841 0.056 0.004 0.924 0.000 0.016
#> GSM617584 4 0.6695 0.431 0.056 0.144 0.000 0.592 0.208
#> GSM617585 4 0.6867 0.313 0.000 0.048 0.108 0.484 0.360
#> GSM617586 3 0.1329 0.849 0.032 0.008 0.956 0.000 0.004
#> GSM617587 3 0.1329 0.849 0.032 0.008 0.956 0.000 0.004
#> GSM617589 4 0.2270 0.837 0.000 0.016 0.004 0.908 0.072
#> GSM617591 2 0.5620 0.650 0.004 0.684 0.196 0.020 0.096
#> GSM617593 1 0.0613 0.782 0.984 0.004 0.008 0.000 0.004
#> GSM617594 2 0.1659 0.771 0.024 0.948 0.004 0.008 0.016
#> GSM617595 1 0.0451 0.782 0.988 0.004 0.008 0.000 0.000
#> GSM617596 1 0.4244 0.627 0.712 0.016 0.000 0.004 0.268
#> GSM617597 3 0.2488 0.780 0.124 0.004 0.872 0.000 0.000
#> GSM617598 1 0.0613 0.782 0.984 0.004 0.004 0.000 0.008
#> GSM617599 2 0.3168 0.739 0.008 0.856 0.004 0.016 0.116
#> GSM617600 3 0.2851 0.805 0.004 0.016 0.880 0.008 0.092
#> GSM617601 2 0.2103 0.773 0.004 0.920 0.000 0.056 0.020
#> GSM617602 3 0.4453 0.399 0.004 0.004 0.644 0.004 0.344
#> GSM617603 4 0.3351 0.799 0.000 0.020 0.004 0.828 0.148
#> GSM617604 1 0.5688 0.469 0.608 0.000 0.088 0.008 0.296
#> GSM617605 4 0.1403 0.863 0.000 0.024 0.000 0.952 0.024
#> GSM617606 2 0.7111 0.523 0.004 0.484 0.152 0.036 0.324
#> GSM617610 1 0.0613 0.782 0.984 0.004 0.008 0.000 0.004
#> GSM617611 1 0.1043 0.772 0.960 0.000 0.040 0.000 0.000
#> GSM617613 3 0.2968 0.786 0.000 0.012 0.864 0.012 0.112
#> GSM617614 3 0.2238 0.842 0.064 0.000 0.912 0.004 0.020
#> GSM617621 1 0.4067 0.660 0.748 0.020 0.000 0.004 0.228
#> GSM617629 5 0.5079 0.155 0.004 0.032 0.340 0.004 0.620
#> GSM617630 2 0.6769 0.430 0.004 0.448 0.252 0.000 0.296
#> GSM617631 3 0.3134 0.779 0.004 0.004 0.848 0.012 0.132
#> GSM617633 1 0.6409 0.291 0.592 0.024 0.172 0.000 0.212
#> GSM617642 3 0.1628 0.844 0.056 0.008 0.936 0.000 0.000
#> GSM617645 2 0.4156 0.734 0.004 0.764 0.008 0.020 0.204
#> GSM617646 1 0.3043 0.727 0.864 0.104 0.024 0.000 0.008
#> GSM617652 1 0.4001 0.570 0.764 0.024 0.208 0.000 0.004
#> GSM617655 3 0.0693 0.848 0.012 0.008 0.980 0.000 0.000
#> GSM617656 3 0.1770 0.840 0.012 0.008 0.944 0.008 0.028
#> GSM617657 3 0.3667 0.747 0.000 0.020 0.812 0.012 0.156
#> GSM617658 3 0.4836 0.154 0.012 0.000 0.568 0.008 0.412
#> GSM617659 1 0.1768 0.752 0.924 0.000 0.072 0.000 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM617581 5 0.6902 0.1700 0.376 0.004 0.000 0.112 0.404 0.104
#> GSM617582 5 0.4635 0.4975 0.136 0.000 0.020 0.000 0.728 0.116
#> GSM617588 4 0.2001 0.7862 0.000 0.004 0.000 0.900 0.004 0.092
#> GSM617590 4 0.1176 0.8035 0.000 0.000 0.000 0.956 0.024 0.020
#> GSM617592 4 0.0260 0.8043 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM617607 1 0.1729 0.7444 0.940 0.012 0.016 0.000 0.016 0.016
#> GSM617608 1 0.1151 0.7501 0.956 0.000 0.032 0.000 0.012 0.000
#> GSM617609 3 0.1346 0.8391 0.016 0.008 0.952 0.000 0.000 0.024
#> GSM617612 1 0.1049 0.7489 0.960 0.000 0.032 0.000 0.000 0.008
#> GSM617615 2 0.5052 0.2639 0.000 0.712 0.076 0.020 0.024 0.168
#> GSM617616 5 0.4627 0.4107 0.396 0.000 0.000 0.000 0.560 0.044
#> GSM617617 2 0.2930 0.4945 0.000 0.840 0.000 0.000 0.036 0.124
#> GSM617618 5 0.4902 0.4436 0.364 0.000 0.004 0.000 0.572 0.060
#> GSM617619 2 0.6781 -0.4204 0.000 0.476 0.228 0.000 0.072 0.224
#> GSM617620 4 0.0520 0.8046 0.000 0.000 0.000 0.984 0.008 0.008
#> GSM617622 2 0.6461 0.2089 0.000 0.568 0.000 0.148 0.132 0.152
#> GSM617623 1 0.6987 -0.2587 0.384 0.004 0.000 0.120 0.384 0.108
#> GSM617624 2 0.3459 0.3923 0.000 0.792 0.004 0.000 0.032 0.172
#> GSM617625 3 0.2673 0.8222 0.064 0.000 0.880 0.000 0.012 0.044
#> GSM617626 1 0.4769 0.0397 0.576 0.000 0.000 0.000 0.364 0.060
#> GSM617627 2 0.3194 0.4077 0.000 0.808 0.004 0.004 0.012 0.172
#> GSM617628 3 0.2673 0.8222 0.064 0.000 0.880 0.000 0.012 0.044
#> GSM617632 5 0.4224 0.3263 0.432 0.000 0.000 0.000 0.552 0.016
#> GSM617634 5 0.6072 -0.1700 0.004 0.328 0.004 0.000 0.464 0.200
#> GSM617635 1 0.1257 0.7481 0.952 0.000 0.020 0.000 0.028 0.000
#> GSM617636 5 0.3996 0.4459 0.352 0.000 0.004 0.000 0.636 0.008
#> GSM617637 1 0.0405 0.7559 0.988 0.000 0.000 0.000 0.008 0.004
#> GSM617638 2 0.5144 -0.1280 0.000 0.548 0.004 0.000 0.080 0.368
#> GSM617639 1 0.0146 0.7562 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM617640 2 0.3878 0.1757 0.000 0.644 0.000 0.004 0.004 0.348
#> GSM617641 4 0.0260 0.8043 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM617643 2 0.1657 0.5277 0.000 0.928 0.000 0.000 0.016 0.056
#> GSM617644 2 0.6339 0.1803 0.000 0.532 0.000 0.156 0.056 0.256
#> GSM617647 2 0.0862 0.5312 0.004 0.972 0.000 0.000 0.008 0.016
#> GSM617648 2 0.4387 0.3953 0.000 0.720 0.000 0.000 0.128 0.152
#> GSM617649 2 0.1657 0.5273 0.000 0.928 0.000 0.000 0.016 0.056
#> GSM617650 1 0.1152 0.7438 0.952 0.000 0.044 0.000 0.004 0.000
#> GSM617651 1 0.0405 0.7558 0.988 0.000 0.000 0.000 0.004 0.008
#> GSM617653 1 0.4738 0.2871 0.640 0.000 0.000 0.000 0.276 0.084
#> GSM617654 2 0.3942 0.1133 0.000 0.624 0.000 0.004 0.004 0.368
#> GSM617583 3 0.2422 0.8300 0.052 0.000 0.896 0.000 0.012 0.040
#> GSM617584 4 0.7066 0.1446 0.052 0.048 0.000 0.464 0.324 0.112
#> GSM617585 4 0.7285 0.2383 0.000 0.024 0.044 0.380 0.276 0.276
#> GSM617586 3 0.1334 0.8409 0.020 0.000 0.948 0.000 0.000 0.032
#> GSM617587 3 0.1346 0.8391 0.016 0.008 0.952 0.000 0.000 0.024
#> GSM617589 4 0.2572 0.7645 0.000 0.000 0.000 0.852 0.012 0.136
#> GSM617591 2 0.6343 -0.2960 0.000 0.524 0.232 0.004 0.032 0.208
#> GSM617593 1 0.0000 0.7563 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617594 2 0.1010 0.5281 0.000 0.960 0.000 0.000 0.004 0.036
#> GSM617595 1 0.0291 0.7562 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM617596 1 0.5324 -0.1575 0.468 0.000 0.000 0.000 0.428 0.104
#> GSM617597 3 0.2257 0.7960 0.116 0.000 0.876 0.000 0.000 0.008
#> GSM617598 1 0.0291 0.7562 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM617599 2 0.3479 0.4651 0.008 0.820 0.000 0.000 0.088 0.084
#> GSM617600 3 0.2856 0.7926 0.000 0.000 0.856 0.000 0.068 0.076
#> GSM617601 2 0.2114 0.4987 0.000 0.904 0.000 0.008 0.012 0.076
#> GSM617602 3 0.4984 0.2650 0.000 0.000 0.492 0.000 0.440 0.068
#> GSM617603 4 0.4746 0.6666 0.000 0.008 0.000 0.676 0.084 0.232
#> GSM617604 5 0.6444 0.2066 0.384 0.000 0.056 0.000 0.432 0.128
#> GSM617605 4 0.1176 0.8035 0.000 0.000 0.000 0.956 0.024 0.020
#> GSM617606 6 0.7666 0.4898 0.000 0.312 0.136 0.028 0.136 0.388
#> GSM617610 1 0.0291 0.7562 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM617611 1 0.1007 0.7456 0.956 0.000 0.044 0.000 0.000 0.000
#> GSM617613 3 0.3520 0.7734 0.000 0.000 0.804 0.000 0.100 0.096
#> GSM617614 3 0.2933 0.8310 0.068 0.000 0.868 0.000 0.028 0.036
#> GSM617621 1 0.5198 -0.0252 0.524 0.000 0.000 0.000 0.380 0.096
#> GSM617629 5 0.4304 0.2823 0.000 0.004 0.128 0.000 0.740 0.128
#> GSM617630 6 0.6970 0.4582 0.004 0.356 0.148 0.004 0.072 0.416
#> GSM617631 3 0.3481 0.7643 0.000 0.000 0.804 0.000 0.124 0.072
#> GSM617633 1 0.5609 -0.1506 0.488 0.004 0.088 0.000 0.408 0.012
#> GSM617642 3 0.1434 0.8391 0.048 0.000 0.940 0.000 0.000 0.012
#> GSM617645 2 0.3864 0.1700 0.000 0.648 0.000 0.004 0.004 0.344
#> GSM617646 1 0.2570 0.6926 0.888 0.076 0.012 0.000 0.012 0.012
#> GSM617652 1 0.3728 0.5400 0.768 0.008 0.200 0.000 0.008 0.016
#> GSM617655 3 0.0603 0.8403 0.004 0.000 0.980 0.000 0.000 0.016
#> GSM617656 3 0.1826 0.8298 0.004 0.000 0.924 0.000 0.020 0.052
#> GSM617657 3 0.4946 0.6171 0.000 0.000 0.652 0.000 0.188 0.160
#> GSM617658 5 0.4786 0.0340 0.000 0.000 0.352 0.000 0.584 0.064
#> GSM617659 1 0.1411 0.7319 0.936 0.000 0.060 0.000 0.004 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:kmeans 79 0.13064 2
#> SD:kmeans 76 0.00339 3
#> SD:kmeans 76 0.00957 4
#> SD:kmeans 62 0.04711 5
#> SD:kmeans 43 0.09348 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 79 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 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 0.947 0.953 0.980 0.5029 0.496 0.496
#> 3 3 0.609 0.780 0.891 0.3348 0.738 0.518
#> 4 4 0.459 0.516 0.733 0.1160 0.924 0.779
#> 5 5 0.463 0.400 0.651 0.0648 0.875 0.586
#> 6 6 0.506 0.317 0.595 0.0392 0.944 0.756
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM617581 2 0.7453 0.743 0.212 0.788
#> GSM617582 2 0.9954 0.168 0.460 0.540
#> GSM617588 2 0.0000 0.966 0.000 1.000
#> GSM617590 2 0.0000 0.966 0.000 1.000
#> GSM617592 2 0.0000 0.966 0.000 1.000
#> GSM617607 1 0.0000 0.989 1.000 0.000
#> GSM617608 1 0.0000 0.989 1.000 0.000
#> GSM617609 1 0.0000 0.989 1.000 0.000
#> GSM617612 1 0.0000 0.989 1.000 0.000
#> GSM617615 2 0.0000 0.966 0.000 1.000
#> GSM617616 1 0.1843 0.965 0.972 0.028
#> GSM617617 2 0.0000 0.966 0.000 1.000
#> GSM617618 1 0.2778 0.945 0.952 0.048
#> GSM617619 2 0.0000 0.966 0.000 1.000
#> GSM617620 2 0.0000 0.966 0.000 1.000
#> GSM617622 2 0.0000 0.966 0.000 1.000
#> GSM617623 2 0.2948 0.927 0.052 0.948
#> GSM617624 2 0.0000 0.966 0.000 1.000
#> GSM617625 1 0.0000 0.989 1.000 0.000
#> GSM617626 2 0.7139 0.767 0.196 0.804
#> GSM617627 2 0.0000 0.966 0.000 1.000
#> GSM617628 1 0.0000 0.989 1.000 0.000
#> GSM617632 1 0.0000 0.989 1.000 0.000
#> GSM617634 2 0.0000 0.966 0.000 1.000
#> GSM617635 1 0.0000 0.989 1.000 0.000
#> GSM617636 1 0.0000 0.989 1.000 0.000
#> GSM617637 1 0.0000 0.989 1.000 0.000
#> GSM617638 2 0.0000 0.966 0.000 1.000
#> GSM617639 1 0.0000 0.989 1.000 0.000
#> GSM617640 2 0.0000 0.966 0.000 1.000
#> GSM617641 2 0.0000 0.966 0.000 1.000
#> GSM617643 2 0.0000 0.966 0.000 1.000
#> GSM617644 2 0.0000 0.966 0.000 1.000
#> GSM617647 2 0.0000 0.966 0.000 1.000
#> GSM617648 2 0.0000 0.966 0.000 1.000
#> GSM617649 2 0.0000 0.966 0.000 1.000
#> GSM617650 1 0.0000 0.989 1.000 0.000
#> GSM617651 1 0.0000 0.989 1.000 0.000
#> GSM617653 1 0.0000 0.989 1.000 0.000
#> GSM617654 2 0.0000 0.966 0.000 1.000
#> GSM617583 1 0.0000 0.989 1.000 0.000
#> GSM617584 2 0.0000 0.966 0.000 1.000
#> GSM617585 2 0.0000 0.966 0.000 1.000
#> GSM617586 1 0.0000 0.989 1.000 0.000
#> GSM617587 1 0.2423 0.953 0.960 0.040
#> GSM617589 2 0.0000 0.966 0.000 1.000
#> GSM617591 2 0.1184 0.955 0.016 0.984
#> GSM617593 1 0.0000 0.989 1.000 0.000
#> GSM617594 2 0.0672 0.961 0.008 0.992
#> GSM617595 1 0.0000 0.989 1.000 0.000
#> GSM617596 1 0.0376 0.986 0.996 0.004
#> GSM617597 1 0.0000 0.989 1.000 0.000
#> GSM617598 1 0.0000 0.989 1.000 0.000
#> GSM617599 2 0.0000 0.966 0.000 1.000
#> GSM617600 1 0.0672 0.984 0.992 0.008
#> GSM617601 2 0.0000 0.966 0.000 1.000
#> GSM617602 1 0.0376 0.987 0.996 0.004
#> GSM617603 2 0.0000 0.966 0.000 1.000
#> GSM617604 1 0.0000 0.989 1.000 0.000
#> GSM617605 2 0.0000 0.966 0.000 1.000
#> GSM617606 2 0.0000 0.966 0.000 1.000
#> GSM617610 1 0.0000 0.989 1.000 0.000
#> GSM617611 1 0.0000 0.989 1.000 0.000
#> GSM617613 1 0.0938 0.980 0.988 0.012
#> GSM617614 1 0.0000 0.989 1.000 0.000
#> GSM617621 1 0.0000 0.989 1.000 0.000
#> GSM617629 1 0.8499 0.610 0.724 0.276
#> GSM617630 2 0.5519 0.853 0.128 0.872
#> GSM617631 1 0.0000 0.989 1.000 0.000
#> GSM617633 1 0.0000 0.989 1.000 0.000
#> GSM617642 1 0.0000 0.989 1.000 0.000
#> GSM617645 2 0.0000 0.966 0.000 1.000
#> GSM617646 1 0.0000 0.989 1.000 0.000
#> GSM617652 1 0.0000 0.989 1.000 0.000
#> GSM617655 1 0.0000 0.989 1.000 0.000
#> GSM617656 1 0.0000 0.989 1.000 0.000
#> GSM617657 2 0.5178 0.865 0.116 0.884
#> GSM617658 1 0.0000 0.989 1.000 0.000
#> GSM617659 1 0.0000 0.989 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM617581 1 0.7905 0.334955 0.560 0.376 0.064
#> GSM617582 1 0.9811 -0.051487 0.380 0.240 0.380
#> GSM617588 2 0.0000 0.910215 0.000 1.000 0.000
#> GSM617590 2 0.0000 0.910215 0.000 1.000 0.000
#> GSM617592 2 0.0000 0.910215 0.000 1.000 0.000
#> GSM617607 1 0.3482 0.810171 0.872 0.000 0.128
#> GSM617608 1 0.4178 0.760151 0.828 0.000 0.172
#> GSM617609 3 0.0424 0.861258 0.008 0.000 0.992
#> GSM617612 1 0.2537 0.837076 0.920 0.000 0.080
#> GSM617615 2 0.0892 0.904807 0.000 0.980 0.020
#> GSM617616 1 0.2096 0.849314 0.944 0.004 0.052
#> GSM617617 2 0.1163 0.901006 0.028 0.972 0.000
#> GSM617618 1 0.3618 0.818372 0.884 0.012 0.104
#> GSM617619 3 0.5443 0.580672 0.004 0.260 0.736
#> GSM617620 2 0.0000 0.910215 0.000 1.000 0.000
#> GSM617622 2 0.0475 0.909060 0.004 0.992 0.004
#> GSM617623 1 0.6497 0.479938 0.648 0.336 0.016
#> GSM617624 2 0.5414 0.748957 0.016 0.772 0.212
#> GSM617625 3 0.3192 0.835079 0.112 0.000 0.888
#> GSM617626 1 0.3192 0.788664 0.888 0.112 0.000
#> GSM617627 2 0.1765 0.896767 0.004 0.956 0.040
#> GSM617628 3 0.2711 0.848446 0.088 0.000 0.912
#> GSM617632 1 0.1643 0.850215 0.956 0.000 0.044
#> GSM617634 2 0.7564 0.622555 0.096 0.672 0.232
#> GSM617635 1 0.2711 0.836107 0.912 0.000 0.088
#> GSM617636 1 0.4654 0.725310 0.792 0.000 0.208
#> GSM617637 1 0.0424 0.854838 0.992 0.000 0.008
#> GSM617638 2 0.6487 0.648298 0.032 0.700 0.268
#> GSM617639 1 0.0424 0.854838 0.992 0.000 0.008
#> GSM617640 2 0.0237 0.909574 0.004 0.996 0.000
#> GSM617641 2 0.0000 0.910215 0.000 1.000 0.000
#> GSM617643 2 0.0000 0.910215 0.000 1.000 0.000
#> GSM617644 2 0.0000 0.910215 0.000 1.000 0.000
#> GSM617647 2 0.3192 0.843644 0.112 0.888 0.000
#> GSM617648 2 0.0237 0.909689 0.000 0.996 0.004
#> GSM617649 2 0.2066 0.884344 0.000 0.940 0.060
#> GSM617650 1 0.3619 0.796914 0.864 0.000 0.136
#> GSM617651 1 0.0424 0.854838 0.992 0.000 0.008
#> GSM617653 1 0.0237 0.853389 0.996 0.004 0.000
#> GSM617654 2 0.0592 0.908295 0.012 0.988 0.000
#> GSM617583 3 0.2711 0.848534 0.088 0.000 0.912
#> GSM617584 2 0.2625 0.863738 0.084 0.916 0.000
#> GSM617585 2 0.5178 0.693636 0.000 0.744 0.256
#> GSM617586 3 0.1411 0.860218 0.036 0.000 0.964
#> GSM617587 3 0.3583 0.844675 0.056 0.044 0.900
#> GSM617589 2 0.0000 0.910215 0.000 1.000 0.000
#> GSM617591 2 0.6297 0.480212 0.008 0.640 0.352
#> GSM617593 1 0.0424 0.854838 0.992 0.000 0.008
#> GSM617594 2 0.5741 0.734194 0.188 0.776 0.036
#> GSM617595 1 0.0424 0.854838 0.992 0.000 0.008
#> GSM617596 1 0.1620 0.852215 0.964 0.012 0.024
#> GSM617597 3 0.4654 0.727675 0.208 0.000 0.792
#> GSM617598 1 0.0424 0.854838 0.992 0.000 0.008
#> GSM617599 2 0.4473 0.785278 0.164 0.828 0.008
#> GSM617600 3 0.0000 0.860321 0.000 0.000 1.000
#> GSM617601 2 0.0475 0.909342 0.004 0.992 0.004
#> GSM617602 3 0.1411 0.858370 0.036 0.000 0.964
#> GSM617603 2 0.0000 0.910215 0.000 1.000 0.000
#> GSM617604 3 0.6309 -0.000793 0.500 0.000 0.500
#> GSM617605 2 0.0000 0.910215 0.000 1.000 0.000
#> GSM617606 2 0.5216 0.681300 0.000 0.740 0.260
#> GSM617610 1 0.0424 0.854838 0.992 0.000 0.008
#> GSM617611 1 0.2165 0.845262 0.936 0.000 0.064
#> GSM617613 3 0.0237 0.859855 0.004 0.000 0.996
#> GSM617614 3 0.3116 0.838342 0.108 0.000 0.892
#> GSM617621 1 0.0747 0.854067 0.984 0.000 0.016
#> GSM617629 3 0.5519 0.767623 0.120 0.068 0.812
#> GSM617630 3 0.5412 0.729737 0.032 0.172 0.796
#> GSM617631 3 0.0424 0.858829 0.008 0.000 0.992
#> GSM617633 3 0.6295 0.040410 0.472 0.000 0.528
#> GSM617642 3 0.3412 0.825847 0.124 0.000 0.876
#> GSM617645 2 0.0237 0.909574 0.004 0.996 0.000
#> GSM617646 1 0.1163 0.855994 0.972 0.000 0.028
#> GSM617652 1 0.6274 0.142256 0.544 0.000 0.456
#> GSM617655 3 0.0424 0.861258 0.008 0.000 0.992
#> GSM617656 3 0.0592 0.861320 0.012 0.000 0.988
#> GSM617657 3 0.0424 0.858829 0.008 0.000 0.992
#> GSM617658 3 0.2356 0.848497 0.072 0.000 0.928
#> GSM617659 1 0.4887 0.684224 0.772 0.000 0.228
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM617581 4 0.8962 0.20558 0.280 0.324 0.052 0.344
#> GSM617582 4 0.8813 0.41402 0.132 0.200 0.156 0.512
#> GSM617588 2 0.0921 0.69469 0.000 0.972 0.000 0.028
#> GSM617590 2 0.0707 0.69681 0.000 0.980 0.000 0.020
#> GSM617592 2 0.0921 0.69312 0.000 0.972 0.000 0.028
#> GSM617607 1 0.5964 0.58829 0.684 0.000 0.108 0.208
#> GSM617608 1 0.4994 0.61592 0.744 0.000 0.208 0.048
#> GSM617609 3 0.2402 0.72624 0.012 0.000 0.912 0.076
#> GSM617612 1 0.3928 0.69976 0.852 0.008 0.084 0.056
#> GSM617615 2 0.4506 0.67597 0.008 0.812 0.052 0.128
#> GSM617616 1 0.6758 0.48539 0.612 0.028 0.064 0.296
#> GSM617617 2 0.5582 0.51221 0.024 0.576 0.000 0.400
#> GSM617618 1 0.7338 0.21739 0.476 0.032 0.072 0.420
#> GSM617619 3 0.7341 -0.00898 0.000 0.164 0.476 0.360
#> GSM617620 2 0.0707 0.69416 0.000 0.980 0.000 0.020
#> GSM617622 2 0.3881 0.64843 0.000 0.812 0.016 0.172
#> GSM617623 1 0.7965 -0.08841 0.416 0.304 0.004 0.276
#> GSM617624 4 0.7265 -0.05392 0.008 0.340 0.128 0.524
#> GSM617625 3 0.4224 0.69828 0.144 0.000 0.812 0.044
#> GSM617626 1 0.6756 0.40110 0.600 0.148 0.000 0.252
#> GSM617627 2 0.6384 0.43297 0.000 0.532 0.068 0.400
#> GSM617628 3 0.3818 0.71812 0.108 0.000 0.844 0.048
#> GSM617632 1 0.5206 0.56531 0.668 0.000 0.024 0.308
#> GSM617634 4 0.7795 0.17921 0.048 0.344 0.096 0.512
#> GSM617635 1 0.5119 0.65733 0.768 0.004 0.080 0.148
#> GSM617636 4 0.7568 -0.22869 0.404 0.000 0.192 0.404
#> GSM617637 1 0.1716 0.71064 0.936 0.000 0.000 0.064
#> GSM617638 4 0.7172 0.11119 0.012 0.288 0.128 0.572
#> GSM617639 1 0.1792 0.71051 0.932 0.000 0.000 0.068
#> GSM617640 2 0.4277 0.63791 0.000 0.720 0.000 0.280
#> GSM617641 2 0.0592 0.69321 0.000 0.984 0.000 0.016
#> GSM617643 2 0.4008 0.66264 0.000 0.756 0.000 0.244
#> GSM617644 2 0.2814 0.69506 0.000 0.868 0.000 0.132
#> GSM617647 2 0.6578 0.49012 0.108 0.592 0.000 0.300
#> GSM617648 2 0.4535 0.63390 0.000 0.704 0.004 0.292
#> GSM617649 2 0.6568 0.53131 0.008 0.600 0.080 0.312
#> GSM617650 1 0.3948 0.67163 0.828 0.000 0.136 0.036
#> GSM617651 1 0.0921 0.71225 0.972 0.000 0.000 0.028
#> GSM617653 1 0.2999 0.69249 0.864 0.000 0.004 0.132
#> GSM617654 2 0.5805 0.49048 0.036 0.576 0.000 0.388
#> GSM617583 3 0.3606 0.71031 0.140 0.000 0.840 0.020
#> GSM617584 2 0.5962 0.43646 0.100 0.696 0.004 0.200
#> GSM617585 2 0.6560 0.30105 0.000 0.620 0.132 0.248
#> GSM617586 3 0.1733 0.73260 0.028 0.000 0.948 0.024
#> GSM617587 3 0.5629 0.64315 0.084 0.024 0.756 0.136
#> GSM617589 2 0.1576 0.69060 0.000 0.948 0.004 0.048
#> GSM617591 2 0.6790 0.27831 0.000 0.576 0.296 0.128
#> GSM617593 1 0.0895 0.71147 0.976 0.000 0.004 0.020
#> GSM617594 2 0.8891 0.23721 0.124 0.456 0.120 0.300
#> GSM617595 1 0.0921 0.71148 0.972 0.000 0.000 0.028
#> GSM617596 1 0.5356 0.62496 0.728 0.016 0.032 0.224
#> GSM617597 3 0.5404 0.56290 0.248 0.000 0.700 0.052
#> GSM617598 1 0.1109 0.71282 0.968 0.000 0.004 0.028
#> GSM617599 2 0.8245 0.12719 0.148 0.420 0.040 0.392
#> GSM617600 3 0.1867 0.72509 0.000 0.000 0.928 0.072
#> GSM617601 2 0.3569 0.67833 0.000 0.804 0.000 0.196
#> GSM617602 3 0.4910 0.56893 0.020 0.000 0.704 0.276
#> GSM617603 2 0.1940 0.69143 0.000 0.924 0.000 0.076
#> GSM617604 3 0.8487 0.01593 0.300 0.024 0.388 0.288
#> GSM617605 2 0.1118 0.69417 0.000 0.964 0.000 0.036
#> GSM617606 2 0.6327 0.50153 0.008 0.676 0.120 0.196
#> GSM617610 1 0.1302 0.70812 0.956 0.000 0.000 0.044
#> GSM617611 1 0.3497 0.68553 0.852 0.000 0.124 0.024
#> GSM617613 3 0.2011 0.72220 0.000 0.000 0.920 0.080
#> GSM617614 3 0.5077 0.66698 0.160 0.000 0.760 0.080
#> GSM617621 1 0.4391 0.62312 0.740 0.000 0.008 0.252
#> GSM617629 4 0.8010 0.03365 0.060 0.092 0.376 0.472
#> GSM617630 3 0.8540 -0.05169 0.056 0.160 0.436 0.348
#> GSM617631 3 0.2408 0.71605 0.000 0.000 0.896 0.104
#> GSM617633 1 0.7921 -0.06225 0.348 0.000 0.324 0.328
#> GSM617642 3 0.3706 0.71448 0.112 0.000 0.848 0.040
#> GSM617645 2 0.4761 0.59950 0.000 0.664 0.004 0.332
#> GSM617646 1 0.5325 0.62628 0.748 0.012 0.052 0.188
#> GSM617652 1 0.7417 -0.01468 0.428 0.004 0.424 0.144
#> GSM617655 3 0.0707 0.73090 0.000 0.000 0.980 0.020
#> GSM617656 3 0.0524 0.73114 0.004 0.000 0.988 0.008
#> GSM617657 3 0.3384 0.69340 0.000 0.024 0.860 0.116
#> GSM617658 3 0.6522 0.45754 0.112 0.000 0.608 0.280
#> GSM617659 1 0.5143 0.56465 0.708 0.000 0.256 0.036
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM617581 5 0.839 0.3046 0.228 0.120 0.016 0.212 0.424
#> GSM617582 5 0.774 0.3364 0.080 0.116 0.068 0.160 0.576
#> GSM617588 4 0.104 0.6148 0.000 0.032 0.000 0.964 0.004
#> GSM617590 4 0.204 0.6112 0.000 0.056 0.000 0.920 0.024
#> GSM617592 4 0.139 0.6079 0.000 0.032 0.000 0.952 0.016
#> GSM617607 1 0.742 0.3374 0.524 0.148 0.108 0.000 0.220
#> GSM617608 1 0.662 0.4460 0.588 0.040 0.196 0.000 0.176
#> GSM617609 3 0.306 0.6912 0.004 0.108 0.860 0.000 0.028
#> GSM617612 1 0.412 0.6212 0.828 0.048 0.080 0.008 0.036
#> GSM617615 4 0.499 0.4894 0.004 0.140 0.080 0.752 0.024
#> GSM617616 5 0.740 0.0612 0.404 0.088 0.032 0.044 0.432
#> GSM617617 2 0.647 0.2699 0.024 0.460 0.000 0.416 0.100
#> GSM617618 5 0.696 0.3087 0.268 0.120 0.020 0.032 0.560
#> GSM617619 3 0.798 -0.0482 0.000 0.332 0.388 0.136 0.144
#> GSM617620 4 0.157 0.6115 0.000 0.060 0.000 0.936 0.004
#> GSM617622 4 0.590 0.3399 0.004 0.220 0.008 0.636 0.132
#> GSM617623 5 0.842 0.2090 0.300 0.160 0.000 0.228 0.312
#> GSM617624 2 0.738 0.4611 0.008 0.564 0.112 0.176 0.140
#> GSM617625 3 0.539 0.6227 0.156 0.028 0.720 0.004 0.092
#> GSM617626 1 0.753 0.0399 0.488 0.100 0.000 0.144 0.268
#> GSM617627 2 0.641 0.4280 0.004 0.572 0.072 0.308 0.044
#> GSM617628 3 0.521 0.6402 0.160 0.040 0.736 0.004 0.060
#> GSM617632 1 0.643 0.0395 0.460 0.088 0.020 0.004 0.428
#> GSM617634 5 0.826 -0.2376 0.040 0.284 0.036 0.276 0.364
#> GSM617635 1 0.564 0.5696 0.708 0.124 0.052 0.000 0.116
#> GSM617636 5 0.662 0.3611 0.220 0.076 0.088 0.004 0.612
#> GSM617637 1 0.259 0.6403 0.892 0.060 0.000 0.000 0.048
#> GSM617638 2 0.724 0.3859 0.016 0.576 0.096 0.096 0.216
#> GSM617639 1 0.273 0.6436 0.884 0.052 0.000 0.000 0.064
#> GSM617640 4 0.504 -0.1080 0.000 0.456 0.000 0.512 0.032
#> GSM617641 4 0.104 0.6141 0.000 0.032 0.000 0.964 0.004
#> GSM617643 4 0.504 -0.0271 0.000 0.456 0.000 0.512 0.032
#> GSM617644 4 0.439 0.5216 0.000 0.156 0.000 0.760 0.084
#> GSM617647 2 0.754 0.3817 0.092 0.468 0.012 0.336 0.092
#> GSM617648 4 0.672 -0.0124 0.004 0.336 0.008 0.480 0.172
#> GSM617649 2 0.722 0.3935 0.008 0.504 0.112 0.316 0.060
#> GSM617650 1 0.494 0.5909 0.756 0.032 0.124 0.000 0.088
#> GSM617651 1 0.191 0.6512 0.928 0.008 0.008 0.000 0.056
#> GSM617653 1 0.435 0.5199 0.744 0.032 0.000 0.008 0.216
#> GSM617654 2 0.637 0.3540 0.052 0.532 0.000 0.356 0.060
#> GSM617583 3 0.485 0.6585 0.140 0.020 0.760 0.004 0.076
#> GSM617584 4 0.746 0.1095 0.104 0.132 0.004 0.528 0.232
#> GSM617585 4 0.705 0.2477 0.000 0.108 0.140 0.580 0.172
#> GSM617586 3 0.275 0.6989 0.048 0.036 0.896 0.000 0.020
#> GSM617587 3 0.673 0.5587 0.080 0.168 0.648 0.032 0.072
#> GSM617589 4 0.175 0.6112 0.000 0.028 0.000 0.936 0.036
#> GSM617591 4 0.715 0.0744 0.008 0.152 0.300 0.504 0.036
#> GSM617593 1 0.230 0.6467 0.900 0.004 0.008 0.000 0.088
#> GSM617594 2 0.839 0.3911 0.128 0.440 0.068 0.296 0.068
#> GSM617595 1 0.203 0.6502 0.924 0.020 0.004 0.000 0.052
#> GSM617596 5 0.734 0.0399 0.400 0.088 0.036 0.036 0.440
#> GSM617597 3 0.604 0.4569 0.248 0.036 0.628 0.000 0.088
#> GSM617598 1 0.177 0.6461 0.936 0.008 0.008 0.000 0.048
#> GSM617599 2 0.864 0.2818 0.120 0.360 0.020 0.276 0.224
#> GSM617600 3 0.370 0.6830 0.000 0.064 0.816 0.000 0.120
#> GSM617601 4 0.462 0.3387 0.000 0.288 0.000 0.676 0.036
#> GSM617602 3 0.576 0.1753 0.020 0.044 0.476 0.000 0.460
#> GSM617603 4 0.275 0.6075 0.000 0.080 0.000 0.880 0.040
#> GSM617604 5 0.847 0.2865 0.240 0.072 0.248 0.036 0.404
#> GSM617605 4 0.152 0.6159 0.000 0.044 0.000 0.944 0.012
#> GSM617606 4 0.761 0.2164 0.008 0.168 0.140 0.540 0.144
#> GSM617610 1 0.186 0.6447 0.932 0.016 0.000 0.004 0.048
#> GSM617611 1 0.360 0.6255 0.840 0.020 0.104 0.000 0.036
#> GSM617613 3 0.275 0.6959 0.000 0.040 0.880 0.000 0.080
#> GSM617614 3 0.628 0.5322 0.156 0.036 0.628 0.000 0.180
#> GSM617621 1 0.619 0.1247 0.500 0.076 0.016 0.004 0.404
#> GSM617629 5 0.728 0.2501 0.028 0.160 0.232 0.032 0.548
#> GSM617630 2 0.871 0.0326 0.044 0.348 0.336 0.096 0.176
#> GSM617631 3 0.382 0.6307 0.004 0.016 0.772 0.000 0.208
#> GSM617633 5 0.801 0.2520 0.268 0.120 0.192 0.000 0.420
#> GSM617642 3 0.491 0.6327 0.148 0.032 0.752 0.000 0.068
#> GSM617645 2 0.512 0.3154 0.008 0.588 0.008 0.380 0.016
#> GSM617646 1 0.720 0.3175 0.532 0.264 0.052 0.008 0.144
#> GSM617652 1 0.836 -0.0628 0.328 0.212 0.328 0.004 0.128
#> GSM617655 3 0.191 0.7052 0.000 0.044 0.928 0.000 0.028
#> GSM617656 3 0.160 0.7054 0.008 0.024 0.948 0.000 0.020
#> GSM617657 3 0.578 0.5728 0.000 0.140 0.680 0.032 0.148
#> GSM617658 5 0.632 -0.0938 0.052 0.040 0.404 0.004 0.500
#> GSM617659 1 0.582 0.4722 0.644 0.016 0.220 0.000 0.120
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM617581 4 0.880 -0.40376 0.160 0.044 0.028 0.276 0.244 0.248
#> GSM617582 5 0.659 0.19392 0.048 0.036 0.068 0.084 0.652 0.112
#> GSM617588 4 0.218 0.52497 0.000 0.052 0.000 0.908 0.008 0.032
#> GSM617590 4 0.301 0.51826 0.000 0.080 0.008 0.864 0.012 0.036
#> GSM617592 4 0.191 0.52788 0.000 0.020 0.000 0.924 0.012 0.044
#> GSM617607 1 0.796 0.22021 0.452 0.108 0.100 0.000 0.140 0.200
#> GSM617608 1 0.655 0.42632 0.596 0.032 0.128 0.000 0.072 0.172
#> GSM617609 3 0.499 0.55686 0.012 0.100 0.732 0.000 0.044 0.112
#> GSM617612 1 0.505 0.50296 0.724 0.020 0.080 0.008 0.016 0.152
#> GSM617615 4 0.695 0.30413 0.020 0.148 0.068 0.588 0.032 0.144
#> GSM617616 5 0.766 0.07607 0.316 0.080 0.028 0.016 0.420 0.140
#> GSM617617 2 0.731 0.41737 0.040 0.492 0.000 0.244 0.128 0.096
#> GSM617618 5 0.653 0.19183 0.200 0.060 0.032 0.012 0.608 0.088
#> GSM617619 3 0.823 -0.01288 0.000 0.300 0.340 0.076 0.120 0.164
#> GSM617620 4 0.153 0.52264 0.000 0.048 0.000 0.936 0.000 0.016
#> GSM617622 4 0.613 0.30281 0.000 0.160 0.004 0.616 0.124 0.096
#> GSM617623 4 0.847 -0.36033 0.204 0.056 0.004 0.292 0.160 0.284
#> GSM617624 2 0.784 0.39649 0.008 0.492 0.068 0.120 0.160 0.152
#> GSM617625 3 0.560 0.51211 0.156 0.008 0.656 0.000 0.036 0.144
#> GSM617626 1 0.784 0.00794 0.456 0.088 0.000 0.104 0.224 0.128
#> GSM617627 2 0.644 0.49111 0.008 0.608 0.044 0.208 0.040 0.092
#> GSM617628 3 0.624 0.51445 0.120 0.016 0.620 0.000 0.084 0.160
#> GSM617632 1 0.709 -0.02983 0.400 0.028 0.020 0.008 0.348 0.196
#> GSM617634 5 0.786 0.03503 0.032 0.216 0.028 0.160 0.472 0.092
#> GSM617635 1 0.738 0.37800 0.520 0.080 0.052 0.004 0.160 0.184
#> GSM617636 5 0.693 -0.08659 0.200 0.032 0.056 0.000 0.528 0.184
#> GSM617637 1 0.372 0.54066 0.820 0.068 0.000 0.000 0.044 0.068
#> GSM617638 2 0.747 0.42314 0.012 0.548 0.072 0.136 0.140 0.092
#> GSM617639 1 0.447 0.53003 0.760 0.072 0.012 0.000 0.020 0.136
#> GSM617640 2 0.477 0.41844 0.000 0.612 0.000 0.336 0.020 0.032
#> GSM617641 4 0.193 0.53040 0.000 0.044 0.000 0.920 0.004 0.032
#> GSM617643 2 0.607 0.20761 0.004 0.448 0.004 0.432 0.044 0.068
#> GSM617644 4 0.573 0.30682 0.000 0.208 0.000 0.628 0.068 0.096
#> GSM617647 2 0.751 0.36165 0.096 0.456 0.004 0.292 0.048 0.104
#> GSM617648 4 0.725 -0.13369 0.008 0.320 0.000 0.412 0.136 0.124
#> GSM617649 2 0.833 0.36389 0.020 0.408 0.092 0.264 0.088 0.128
#> GSM617650 1 0.494 0.49056 0.696 0.000 0.148 0.000 0.020 0.136
#> GSM617651 1 0.362 0.55855 0.820 0.012 0.024 0.000 0.024 0.120
#> GSM617653 1 0.565 0.34556 0.652 0.020 0.000 0.036 0.084 0.208
#> GSM617654 2 0.635 0.50106 0.036 0.612 0.004 0.200 0.044 0.104
#> GSM617583 3 0.512 0.57677 0.088 0.004 0.712 0.000 0.060 0.136
#> GSM617584 4 0.672 0.28139 0.076 0.044 0.004 0.588 0.088 0.200
#> GSM617585 4 0.703 0.22552 0.000 0.068 0.072 0.528 0.252 0.080
#> GSM617586 3 0.245 0.62216 0.016 0.004 0.884 0.000 0.004 0.092
#> GSM617587 3 0.634 0.50250 0.084 0.080 0.656 0.012 0.044 0.124
#> GSM617589 4 0.304 0.52203 0.000 0.040 0.004 0.868 0.032 0.056
#> GSM617591 4 0.723 0.10711 0.000 0.132 0.244 0.484 0.020 0.120
#> GSM617593 1 0.231 0.55606 0.904 0.020 0.004 0.000 0.012 0.060
#> GSM617594 2 0.891 0.34237 0.112 0.376 0.072 0.232 0.064 0.144
#> GSM617595 1 0.294 0.56091 0.860 0.020 0.004 0.000 0.016 0.100
#> GSM617596 1 0.843 -0.44173 0.344 0.056 0.068 0.032 0.216 0.284
#> GSM617597 3 0.605 0.34008 0.200 0.012 0.580 0.000 0.020 0.188
#> GSM617598 1 0.250 0.55041 0.880 0.004 0.000 0.000 0.028 0.088
#> GSM617599 2 0.928 0.24364 0.084 0.268 0.044 0.216 0.172 0.216
#> GSM617600 3 0.551 0.51745 0.000 0.088 0.664 0.000 0.168 0.080
#> GSM617601 4 0.502 0.26346 0.000 0.280 0.004 0.640 0.016 0.060
#> GSM617602 5 0.570 0.02427 0.016 0.012 0.396 0.000 0.504 0.072
#> GSM617603 4 0.426 0.48525 0.000 0.112 0.000 0.776 0.048 0.064
#> GSM617604 6 0.884 0.00000 0.216 0.028 0.156 0.052 0.264 0.284
#> GSM617605 4 0.232 0.52967 0.000 0.052 0.000 0.900 0.008 0.040
#> GSM617606 4 0.855 0.05464 0.016 0.176 0.136 0.404 0.088 0.180
#> GSM617610 1 0.197 0.55441 0.916 0.004 0.000 0.000 0.024 0.056
#> GSM617611 1 0.457 0.51426 0.736 0.012 0.124 0.000 0.004 0.124
#> GSM617613 3 0.434 0.55230 0.000 0.020 0.744 0.000 0.172 0.064
#> GSM617614 3 0.683 0.37377 0.136 0.008 0.540 0.000 0.144 0.172
#> GSM617621 1 0.717 -0.06056 0.476 0.048 0.016 0.012 0.192 0.256
#> GSM617629 5 0.637 0.25474 0.008 0.092 0.172 0.020 0.624 0.084
#> GSM617630 2 0.846 0.18136 0.032 0.424 0.212 0.072 0.100 0.160
#> GSM617631 3 0.490 0.44894 0.000 0.012 0.652 0.000 0.260 0.076
#> GSM617633 5 0.804 0.05140 0.216 0.040 0.196 0.000 0.388 0.160
#> GSM617642 3 0.481 0.54565 0.104 0.000 0.732 0.000 0.052 0.112
#> GSM617645 2 0.514 0.48062 0.012 0.644 0.004 0.276 0.012 0.052
#> GSM617646 1 0.771 0.22280 0.456 0.240 0.048 0.004 0.092 0.160
#> GSM617652 1 0.810 -0.01097 0.392 0.096 0.248 0.000 0.080 0.184
#> GSM617655 3 0.296 0.62653 0.000 0.028 0.868 0.000 0.056 0.048
#> GSM617656 3 0.184 0.62353 0.000 0.016 0.928 0.000 0.040 0.016
#> GSM617657 3 0.672 0.39560 0.000 0.068 0.584 0.060 0.196 0.092
#> GSM617658 5 0.694 -0.08283 0.068 0.008 0.292 0.004 0.476 0.152
#> GSM617659 1 0.602 0.30125 0.552 0.004 0.252 0.000 0.020 0.172
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:skmeans 78 0.04094 2
#> SD:skmeans 72 0.00402 3
#> SD:skmeans 54 0.01216 4
#> SD:skmeans 35 0.05815 5
#> SD:skmeans 28 0.20788 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 79 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.271 0.639 0.830 0.4931 0.494 0.494
#> 3 3 0.599 0.755 0.881 0.3222 0.757 0.555
#> 4 4 0.591 0.690 0.855 0.0508 0.954 0.875
#> 5 5 0.602 0.668 0.838 0.0262 0.970 0.912
#> 6 6 0.626 0.601 0.832 0.0152 0.986 0.955
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
#> GSM617581 2 0.0376 0.6473 0.004 0.996
#> GSM617582 2 0.4815 0.5587 0.104 0.896
#> GSM617588 2 0.8144 0.7554 0.252 0.748
#> GSM617590 2 0.8813 0.7317 0.300 0.700
#> GSM617592 2 0.8144 0.7554 0.252 0.748
#> GSM617607 1 0.8861 0.7634 0.696 0.304
#> GSM617608 1 0.9866 0.7126 0.568 0.432
#> GSM617609 1 0.8144 0.7621 0.748 0.252
#> GSM617612 1 0.9460 0.7476 0.636 0.364
#> GSM617615 2 0.9129 0.7137 0.328 0.672
#> GSM617616 2 0.7376 0.2874 0.208 0.792
#> GSM617617 2 0.0000 0.6503 0.000 1.000
#> GSM617618 2 0.0938 0.6405 0.012 0.988
#> GSM617619 2 0.8813 0.7397 0.300 0.700
#> GSM617620 2 0.8144 0.7554 0.252 0.748
#> GSM617622 2 0.8144 0.7554 0.252 0.748
#> GSM617623 2 0.7815 0.2115 0.232 0.768
#> GSM617624 2 0.8555 0.7193 0.280 0.720
#> GSM617625 1 0.0376 0.6002 0.996 0.004
#> GSM617626 2 0.0000 0.6503 0.000 1.000
#> GSM617627 2 0.8499 0.7488 0.276 0.724
#> GSM617628 1 0.0000 0.6012 1.000 0.000
#> GSM617632 2 0.8267 0.1122 0.260 0.740
#> GSM617634 2 0.8144 0.7554 0.252 0.748
#> GSM617635 1 0.9833 0.7186 0.576 0.424
#> GSM617636 1 0.9970 0.6805 0.532 0.468
#> GSM617637 1 0.9977 0.6755 0.528 0.472
#> GSM617638 1 0.8443 0.7631 0.728 0.272
#> GSM617639 1 0.9970 0.6780 0.532 0.468
#> GSM617640 2 0.0000 0.6503 0.000 1.000
#> GSM617641 2 0.8144 0.7554 0.252 0.748
#> GSM617643 2 0.8144 0.7554 0.252 0.748
#> GSM617644 2 0.8144 0.7554 0.252 0.748
#> GSM617647 2 0.5737 0.4710 0.136 0.864
#> GSM617648 2 0.8144 0.7554 0.252 0.748
#> GSM617649 2 0.5519 0.5748 0.128 0.872
#> GSM617650 1 0.9795 0.7241 0.584 0.416
#> GSM617651 1 0.9909 0.7025 0.556 0.444
#> GSM617653 1 0.9795 0.7250 0.584 0.416
#> GSM617654 2 0.0000 0.6503 0.000 1.000
#> GSM617583 1 0.0376 0.6002 0.996 0.004
#> GSM617584 2 0.4431 0.7059 0.092 0.908
#> GSM617585 2 0.8555 0.7453 0.280 0.720
#> GSM617586 1 0.0000 0.6012 1.000 0.000
#> GSM617587 1 0.1633 0.5945 0.976 0.024
#> GSM617589 2 0.8144 0.7554 0.252 0.748
#> GSM617591 2 0.9963 0.5659 0.464 0.536
#> GSM617593 1 0.9970 0.6805 0.532 0.468
#> GSM617594 2 0.9896 0.1685 0.440 0.560
#> GSM617595 1 0.9977 0.6755 0.528 0.472
#> GSM617596 1 0.8608 0.7650 0.716 0.284
#> GSM617597 1 0.8144 0.7621 0.748 0.252
#> GSM617598 1 0.9970 0.6780 0.532 0.468
#> GSM617599 2 0.0376 0.6496 0.004 0.996
#> GSM617600 1 0.0000 0.6012 1.000 0.000
#> GSM617601 2 0.8207 0.7544 0.256 0.744
#> GSM617602 1 0.7745 0.7593 0.772 0.228
#> GSM617603 2 0.9522 0.6705 0.372 0.628
#> GSM617604 1 0.8144 0.7621 0.748 0.252
#> GSM617605 2 0.8207 0.7544 0.256 0.744
#> GSM617606 2 0.9977 0.5560 0.472 0.528
#> GSM617610 1 0.9977 0.6755 0.528 0.472
#> GSM617611 1 0.9710 0.7336 0.600 0.400
#> GSM617613 1 0.0938 0.5880 0.988 0.012
#> GSM617614 1 0.7745 0.7589 0.772 0.228
#> GSM617621 1 0.9977 0.6755 0.528 0.472
#> GSM617629 2 0.9996 -0.1285 0.488 0.512
#> GSM617630 1 0.8144 0.7621 0.748 0.252
#> GSM617631 1 0.0000 0.6012 1.000 0.000
#> GSM617633 1 0.8909 0.7633 0.692 0.308
#> GSM617642 1 0.7815 0.7602 0.768 0.232
#> GSM617645 2 0.8499 0.0563 0.276 0.724
#> GSM617646 1 0.9944 0.6913 0.544 0.456
#> GSM617652 1 0.8207 0.7631 0.744 0.256
#> GSM617655 1 0.9000 -0.1898 0.684 0.316
#> GSM617656 1 0.0000 0.6012 1.000 0.000
#> GSM617657 1 0.0000 0.6012 1.000 0.000
#> GSM617658 1 0.8207 0.7622 0.744 0.256
#> GSM617659 1 0.8144 0.7621 0.748 0.252
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM617581 2 0.0424 0.85206 0.008 0.992 0.000
#> GSM617582 2 0.3941 0.75334 0.156 0.844 0.000
#> GSM617588 2 0.0000 0.85402 0.000 1.000 0.000
#> GSM617590 2 0.4842 0.70398 0.000 0.776 0.224
#> GSM617592 2 0.0000 0.85402 0.000 1.000 0.000
#> GSM617607 1 0.0000 0.84404 1.000 0.000 0.000
#> GSM617608 1 0.0000 0.84404 1.000 0.000 0.000
#> GSM617609 1 0.5138 0.72071 0.748 0.000 0.252
#> GSM617612 1 0.3481 0.82401 0.904 0.044 0.052
#> GSM617615 3 0.4228 0.78154 0.008 0.148 0.844
#> GSM617616 2 0.6192 0.23735 0.420 0.580 0.000
#> GSM617617 2 0.0000 0.85402 0.000 1.000 0.000
#> GSM617618 2 0.3619 0.77411 0.136 0.864 0.000
#> GSM617619 2 0.6905 0.29076 0.016 0.544 0.440
#> GSM617620 2 0.0000 0.85402 0.000 1.000 0.000
#> GSM617622 2 0.0000 0.85402 0.000 1.000 0.000
#> GSM617623 2 0.6299 0.04468 0.476 0.524 0.000
#> GSM617624 2 0.7979 0.58614 0.112 0.640 0.248
#> GSM617625 3 0.0237 0.95943 0.004 0.000 0.996
#> GSM617626 2 0.0000 0.85402 0.000 1.000 0.000
#> GSM617627 2 0.2584 0.83216 0.008 0.928 0.064
#> GSM617628 3 0.0000 0.95971 0.000 0.000 1.000
#> GSM617632 1 0.6309 -0.00561 0.500 0.500 0.000
#> GSM617634 2 0.2261 0.82974 0.000 0.932 0.068
#> GSM617635 1 0.0000 0.84404 1.000 0.000 0.000
#> GSM617636 1 0.0747 0.84284 0.984 0.016 0.000
#> GSM617637 1 0.0424 0.84401 0.992 0.008 0.000
#> GSM617638 1 0.4663 0.78760 0.828 0.016 0.156
#> GSM617639 1 0.0000 0.84404 1.000 0.000 0.000
#> GSM617640 2 0.0000 0.85402 0.000 1.000 0.000
#> GSM617641 2 0.0000 0.85402 0.000 1.000 0.000
#> GSM617643 2 0.0000 0.85402 0.000 1.000 0.000
#> GSM617644 2 0.0000 0.85402 0.000 1.000 0.000
#> GSM617647 2 0.5810 0.46871 0.336 0.664 0.000
#> GSM617648 2 0.0000 0.85402 0.000 1.000 0.000
#> GSM617649 2 0.3826 0.76738 0.008 0.868 0.124
#> GSM617650 1 0.0000 0.84404 1.000 0.000 0.000
#> GSM617651 1 0.0000 0.84404 1.000 0.000 0.000
#> GSM617653 1 0.4609 0.77555 0.844 0.128 0.028
#> GSM617654 2 0.0237 0.85331 0.004 0.996 0.000
#> GSM617583 3 0.0237 0.95943 0.004 0.000 0.996
#> GSM617584 2 0.0000 0.85402 0.000 1.000 0.000
#> GSM617585 3 0.4654 0.68224 0.000 0.208 0.792
#> GSM617586 3 0.0237 0.95943 0.004 0.000 0.996
#> GSM617587 3 0.2269 0.92747 0.040 0.016 0.944
#> GSM617589 2 0.3116 0.80719 0.000 0.892 0.108
#> GSM617591 3 0.0661 0.95529 0.004 0.008 0.988
#> GSM617593 1 0.0424 0.84401 0.992 0.008 0.000
#> GSM617594 1 0.9995 -0.07979 0.348 0.332 0.320
#> GSM617595 1 0.0747 0.84298 0.984 0.016 0.000
#> GSM617596 1 0.4749 0.77959 0.816 0.012 0.172
#> GSM617597 1 0.3340 0.80761 0.880 0.000 0.120
#> GSM617598 1 0.0237 0.84430 0.996 0.004 0.000
#> GSM617599 2 0.0237 0.85274 0.004 0.996 0.000
#> GSM617600 3 0.0747 0.95242 0.016 0.000 0.984
#> GSM617601 2 0.6148 0.50499 0.004 0.640 0.356
#> GSM617602 1 0.6608 0.43616 0.560 0.008 0.432
#> GSM617603 2 0.3752 0.75786 0.000 0.856 0.144
#> GSM617604 1 0.4842 0.74690 0.776 0.000 0.224
#> GSM617605 2 0.6008 0.54402 0.004 0.664 0.332
#> GSM617606 3 0.0000 0.95971 0.000 0.000 1.000
#> GSM617610 1 0.1860 0.82959 0.948 0.052 0.000
#> GSM617611 1 0.0237 0.84391 0.996 0.004 0.000
#> GSM617613 3 0.0000 0.95971 0.000 0.000 1.000
#> GSM617614 1 0.5650 0.65573 0.688 0.000 0.312
#> GSM617621 1 0.0424 0.84401 0.992 0.008 0.000
#> GSM617629 1 0.9931 0.17065 0.388 0.324 0.288
#> GSM617630 1 0.4931 0.74030 0.768 0.000 0.232
#> GSM617631 3 0.0000 0.95971 0.000 0.000 1.000
#> GSM617633 1 0.0424 0.84364 0.992 0.000 0.008
#> GSM617642 1 0.5678 0.65103 0.684 0.000 0.316
#> GSM617645 1 0.6295 0.08641 0.528 0.472 0.000
#> GSM617646 1 0.0237 0.84430 0.996 0.004 0.000
#> GSM617652 1 0.0237 0.84403 0.996 0.000 0.004
#> GSM617655 3 0.0424 0.95783 0.008 0.000 0.992
#> GSM617656 3 0.0000 0.95971 0.000 0.000 1.000
#> GSM617657 3 0.0000 0.95971 0.000 0.000 1.000
#> GSM617658 1 0.5158 0.73919 0.764 0.004 0.232
#> GSM617659 1 0.0237 0.84386 0.996 0.000 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM617581 2 0.0336 0.72437 0.008 0.992 0.000 0.000
#> GSM617582 2 0.3123 0.60991 0.156 0.844 0.000 0.000
#> GSM617588 2 0.2530 0.65354 0.000 0.888 0.000 0.112
#> GSM617590 4 0.5334 0.86004 0.000 0.172 0.088 0.740
#> GSM617592 2 0.2921 0.62367 0.000 0.860 0.000 0.140
#> GSM617607 1 0.0188 0.84075 0.996 0.000 0.000 0.004
#> GSM617608 1 0.0188 0.84090 0.996 0.000 0.000 0.004
#> GSM617609 1 0.5483 0.72563 0.736 0.000 0.128 0.136
#> GSM617612 1 0.3280 0.81492 0.892 0.048 0.040 0.020
#> GSM617615 3 0.4583 0.74700 0.004 0.112 0.808 0.076
#> GSM617616 2 0.4907 0.24917 0.420 0.580 0.000 0.000
#> GSM617617 2 0.0000 0.72457 0.000 1.000 0.000 0.000
#> GSM617618 2 0.2868 0.63385 0.136 0.864 0.000 0.000
#> GSM617619 2 0.7200 -0.00642 0.012 0.452 0.440 0.096
#> GSM617620 2 0.2081 0.67788 0.000 0.916 0.000 0.084
#> GSM617622 2 0.0000 0.72457 0.000 1.000 0.000 0.000
#> GSM617623 2 0.4992 0.06389 0.476 0.524 0.000 0.000
#> GSM617624 2 0.8363 0.21074 0.096 0.532 0.256 0.116
#> GSM617625 3 0.0376 0.90275 0.004 0.000 0.992 0.004
#> GSM617626 2 0.0000 0.72457 0.000 1.000 0.000 0.000
#> GSM617627 2 0.3851 0.64708 0.004 0.852 0.056 0.088
#> GSM617628 3 0.0000 0.90105 0.000 0.000 1.000 0.000
#> GSM617632 2 0.5000 -0.03202 0.500 0.500 0.000 0.000
#> GSM617634 2 0.1792 0.69688 0.000 0.932 0.068 0.000
#> GSM617635 1 0.0000 0.84066 1.000 0.000 0.000 0.000
#> GSM617636 1 0.0469 0.83938 0.988 0.012 0.000 0.000
#> GSM617637 1 0.0188 0.84082 0.996 0.004 0.000 0.000
#> GSM617638 1 0.5282 0.75945 0.772 0.012 0.096 0.120
#> GSM617639 1 0.0000 0.84066 1.000 0.000 0.000 0.000
#> GSM617640 2 0.0000 0.72457 0.000 1.000 0.000 0.000
#> GSM617641 2 0.4040 0.44328 0.000 0.752 0.000 0.248
#> GSM617643 2 0.0000 0.72457 0.000 1.000 0.000 0.000
#> GSM617644 2 0.0000 0.72457 0.000 1.000 0.000 0.000
#> GSM617647 2 0.5233 0.37391 0.332 0.648 0.000 0.020
#> GSM617648 2 0.0000 0.72457 0.000 1.000 0.000 0.000
#> GSM617649 2 0.4287 0.59206 0.004 0.828 0.088 0.080
#> GSM617650 1 0.0000 0.84066 1.000 0.000 0.000 0.000
#> GSM617651 1 0.0000 0.84066 1.000 0.000 0.000 0.000
#> GSM617653 1 0.3749 0.76297 0.840 0.128 0.032 0.000
#> GSM617654 2 0.0524 0.72445 0.004 0.988 0.000 0.008
#> GSM617583 3 0.0524 0.90035 0.004 0.000 0.988 0.008
#> GSM617584 2 0.1118 0.71121 0.000 0.964 0.000 0.036
#> GSM617585 3 0.4136 0.63852 0.000 0.196 0.788 0.016
#> GSM617586 3 0.2999 0.85465 0.004 0.000 0.864 0.132
#> GSM617587 3 0.3943 0.83145 0.028 0.004 0.832 0.136
#> GSM617589 2 0.2799 0.66244 0.000 0.884 0.108 0.008
#> GSM617591 3 0.1909 0.89912 0.004 0.008 0.940 0.048
#> GSM617593 1 0.0188 0.84082 0.996 0.004 0.000 0.000
#> GSM617594 1 0.9037 -0.19563 0.320 0.308 0.316 0.056
#> GSM617595 1 0.0469 0.83955 0.988 0.012 0.000 0.000
#> GSM617596 1 0.3881 0.77609 0.812 0.016 0.172 0.000
#> GSM617597 1 0.3667 0.80426 0.856 0.000 0.088 0.056
#> GSM617598 1 0.0188 0.84082 0.996 0.004 0.000 0.000
#> GSM617599 2 0.1118 0.71420 0.000 0.964 0.000 0.036
#> GSM617600 3 0.2542 0.88637 0.012 0.000 0.904 0.084
#> GSM617601 2 0.5929 0.24212 0.000 0.596 0.356 0.048
#> GSM617602 1 0.5714 0.45045 0.552 0.004 0.424 0.020
#> GSM617603 4 0.5517 0.80691 0.000 0.184 0.092 0.724
#> GSM617604 1 0.4086 0.75130 0.776 0.008 0.216 0.000
#> GSM617605 4 0.5143 0.84835 0.000 0.172 0.076 0.752
#> GSM617606 3 0.0336 0.90069 0.000 0.008 0.992 0.000
#> GSM617610 1 0.1389 0.82457 0.952 0.048 0.000 0.000
#> GSM617611 1 0.0000 0.84066 1.000 0.000 0.000 0.000
#> GSM617613 3 0.0592 0.89770 0.000 0.000 0.984 0.016
#> GSM617614 1 0.4792 0.65765 0.680 0.000 0.312 0.008
#> GSM617621 1 0.0188 0.84082 0.996 0.004 0.000 0.000
#> GSM617629 1 0.8413 0.07181 0.384 0.316 0.280 0.020
#> GSM617630 1 0.4655 0.74330 0.760 0.000 0.208 0.032
#> GSM617631 3 0.0592 0.89770 0.000 0.000 0.984 0.016
#> GSM617633 1 0.0188 0.84052 0.996 0.000 0.004 0.000
#> GSM617642 1 0.5297 0.65900 0.676 0.000 0.292 0.032
#> GSM617645 1 0.6347 0.15783 0.524 0.412 0.000 0.064
#> GSM617646 1 0.0188 0.84082 0.996 0.004 0.000 0.000
#> GSM617652 1 0.1824 0.82650 0.936 0.000 0.004 0.060
#> GSM617655 3 0.2466 0.88213 0.004 0.000 0.900 0.096
#> GSM617656 3 0.1792 0.89482 0.000 0.000 0.932 0.068
#> GSM617657 3 0.0592 0.89770 0.000 0.000 0.984 0.016
#> GSM617658 1 0.4579 0.73584 0.756 0.004 0.224 0.016
#> GSM617659 1 0.0000 0.84066 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM617581 2 0.0290 0.7562 0.008 0.992 0.000 0.000 0.000
#> GSM617582 2 0.2690 0.6629 0.156 0.844 0.000 0.000 0.000
#> GSM617588 2 0.2891 0.6546 0.000 0.824 0.000 0.176 0.000
#> GSM617590 4 0.0671 0.9300 0.000 0.016 0.004 0.980 0.000
#> GSM617592 2 0.3210 0.6142 0.000 0.788 0.000 0.212 0.000
#> GSM617607 1 0.0000 0.8529 1.000 0.000 0.000 0.000 0.000
#> GSM617608 1 0.0162 0.8524 0.996 0.000 0.000 0.000 0.004
#> GSM617609 1 0.4927 0.6373 0.652 0.000 0.052 0.000 0.296
#> GSM617612 1 0.2827 0.8262 0.892 0.044 0.044 0.000 0.020
#> GSM617615 3 0.3918 0.7056 0.000 0.096 0.804 0.000 0.100
#> GSM617616 2 0.4227 0.2495 0.420 0.580 0.000 0.000 0.000
#> GSM617617 2 0.0000 0.7564 0.000 1.000 0.000 0.000 0.000
#> GSM617618 2 0.2471 0.6811 0.136 0.864 0.000 0.000 0.000
#> GSM617619 3 0.7074 0.2461 0.012 0.352 0.416 0.004 0.216
#> GSM617620 2 0.1965 0.7151 0.000 0.904 0.000 0.096 0.000
#> GSM617622 2 0.0000 0.7564 0.000 1.000 0.000 0.000 0.000
#> GSM617623 2 0.4300 0.0622 0.476 0.524 0.000 0.000 0.000
#> GSM617624 2 0.7968 0.1347 0.092 0.436 0.248 0.004 0.220
#> GSM617625 3 0.0290 0.7704 0.000 0.000 0.992 0.000 0.008
#> GSM617626 2 0.0000 0.7564 0.000 1.000 0.000 0.000 0.000
#> GSM617627 2 0.3804 0.6613 0.000 0.812 0.052 0.004 0.132
#> GSM617628 3 0.0000 0.7688 0.000 0.000 1.000 0.000 0.000
#> GSM617632 2 0.4307 -0.0355 0.500 0.500 0.000 0.000 0.000
#> GSM617634 2 0.1544 0.7328 0.000 0.932 0.068 0.000 0.000
#> GSM617635 1 0.0000 0.8529 1.000 0.000 0.000 0.000 0.000
#> GSM617636 1 0.0404 0.8503 0.988 0.012 0.000 0.000 0.000
#> GSM617637 1 0.0000 0.8529 1.000 0.000 0.000 0.000 0.000
#> GSM617638 1 0.4729 0.6993 0.708 0.008 0.032 0.004 0.248
#> GSM617639 1 0.0000 0.8529 1.000 0.000 0.000 0.000 0.000
#> GSM617640 2 0.0000 0.7564 0.000 1.000 0.000 0.000 0.000
#> GSM617641 2 0.4294 0.1107 0.000 0.532 0.000 0.468 0.000
#> GSM617643 2 0.0000 0.7564 0.000 1.000 0.000 0.000 0.000
#> GSM617644 2 0.0000 0.7564 0.000 1.000 0.000 0.000 0.000
#> GSM617647 2 0.4592 0.4495 0.332 0.644 0.000 0.000 0.024
#> GSM617648 2 0.0000 0.7564 0.000 1.000 0.000 0.000 0.000
#> GSM617649 2 0.4421 0.5676 0.000 0.748 0.068 0.000 0.184
#> GSM617650 1 0.0000 0.8529 1.000 0.000 0.000 0.000 0.000
#> GSM617651 1 0.0000 0.8529 1.000 0.000 0.000 0.000 0.000
#> GSM617653 1 0.3229 0.7753 0.840 0.128 0.032 0.000 0.000
#> GSM617654 2 0.0324 0.7567 0.004 0.992 0.000 0.000 0.004
#> GSM617583 3 0.0000 0.7688 0.000 0.000 1.000 0.000 0.000
#> GSM617584 2 0.1043 0.7455 0.000 0.960 0.000 0.040 0.000
#> GSM617585 3 0.3948 0.6210 0.000 0.196 0.776 0.016 0.012
#> GSM617586 3 0.3561 0.7070 0.000 0.000 0.740 0.000 0.260
#> GSM617587 3 0.3766 0.6981 0.004 0.000 0.728 0.000 0.268
#> GSM617589 2 0.2411 0.7060 0.000 0.884 0.108 0.008 0.000
#> GSM617591 3 0.2011 0.7677 0.000 0.004 0.908 0.000 0.088
#> GSM617593 1 0.0000 0.8529 1.000 0.000 0.000 0.000 0.000
#> GSM617594 3 0.7866 0.0227 0.316 0.304 0.316 0.000 0.064
#> GSM617595 1 0.0510 0.8491 0.984 0.016 0.000 0.000 0.000
#> GSM617596 1 0.3559 0.7786 0.804 0.012 0.176 0.000 0.008
#> GSM617597 1 0.3593 0.8005 0.828 0.000 0.084 0.000 0.088
#> GSM617598 1 0.0000 0.8529 1.000 0.000 0.000 0.000 0.000
#> GSM617599 2 0.0963 0.7477 0.000 0.964 0.000 0.000 0.036
#> GSM617600 3 0.3684 0.7380 0.004 0.000 0.788 0.016 0.192
#> GSM617601 2 0.5376 0.2786 0.000 0.584 0.356 0.004 0.056
#> GSM617602 1 0.5558 0.4583 0.548 0.004 0.400 0.016 0.032
#> GSM617603 5 0.5841 0.0000 0.000 0.044 0.032 0.364 0.560
#> GSM617604 1 0.3582 0.7505 0.768 0.000 0.224 0.000 0.008
#> GSM617605 4 0.1299 0.9298 0.000 0.020 0.008 0.960 0.012
#> GSM617606 3 0.0000 0.7688 0.000 0.000 1.000 0.000 0.000
#> GSM617610 1 0.1197 0.8357 0.952 0.048 0.000 0.000 0.000
#> GSM617611 1 0.0000 0.8529 1.000 0.000 0.000 0.000 0.000
#> GSM617613 3 0.0566 0.7686 0.000 0.000 0.984 0.012 0.004
#> GSM617614 1 0.4127 0.6673 0.680 0.000 0.312 0.000 0.008
#> GSM617621 1 0.0000 0.8529 1.000 0.000 0.000 0.000 0.000
#> GSM617629 1 0.8143 0.1012 0.360 0.288 0.276 0.012 0.064
#> GSM617630 1 0.4886 0.7196 0.712 0.000 0.188 0.000 0.100
#> GSM617631 3 0.1018 0.7614 0.000 0.000 0.968 0.016 0.016
#> GSM617633 1 0.0000 0.8529 1.000 0.000 0.000 0.000 0.000
#> GSM617642 1 0.4948 0.6722 0.676 0.000 0.256 0.000 0.068
#> GSM617645 1 0.5820 0.2110 0.524 0.376 0.000 0.000 0.100
#> GSM617646 1 0.0000 0.8529 1.000 0.000 0.000 0.000 0.000
#> GSM617652 1 0.1544 0.8338 0.932 0.000 0.000 0.000 0.068
#> GSM617655 3 0.2966 0.7451 0.000 0.000 0.816 0.000 0.184
#> GSM617656 3 0.3010 0.7528 0.000 0.000 0.824 0.004 0.172
#> GSM617657 3 0.3847 0.6461 0.000 0.000 0.784 0.036 0.180
#> GSM617658 1 0.4271 0.7348 0.744 0.000 0.224 0.016 0.016
#> GSM617659 1 0.0000 0.8529 1.000 0.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM617581 2 0.0260 0.71798 0.008 0.992 0.000 0.000 0.000 0.000
#> GSM617582 2 0.2416 0.61865 0.156 0.844 0.000 0.000 0.000 0.000
#> GSM617588 2 0.2941 0.50731 0.000 0.780 0.000 0.220 0.000 0.000
#> GSM617590 4 0.0000 0.36496 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM617592 2 0.3309 0.39184 0.000 0.720 0.000 0.280 0.000 0.000
#> GSM617607 1 0.0000 0.84653 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617608 1 0.0146 0.84643 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM617609 1 0.4399 0.56559 0.616 0.000 0.028 0.000 0.004 0.352
#> GSM617612 1 0.2453 0.82039 0.896 0.044 0.044 0.000 0.000 0.016
#> GSM617615 3 0.3325 0.64222 0.000 0.084 0.820 0.000 0.000 0.096
#> GSM617616 2 0.3797 0.24009 0.420 0.580 0.000 0.000 0.000 0.000
#> GSM617617 2 0.0000 0.71818 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM617618 2 0.2219 0.63872 0.136 0.864 0.000 0.000 0.000 0.000
#> GSM617619 3 0.6797 0.18545 0.012 0.312 0.404 0.000 0.024 0.248
#> GSM617620 2 0.2135 0.62729 0.000 0.872 0.000 0.128 0.000 0.000
#> GSM617622 2 0.0000 0.71818 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM617623 2 0.3862 0.04724 0.476 0.524 0.000 0.000 0.000 0.000
#> GSM617624 2 0.8140 -0.02976 0.092 0.368 0.244 0.008 0.048 0.240
#> GSM617625 3 0.0260 0.68210 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM617626 2 0.0000 0.71818 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM617627 2 0.4376 0.56961 0.000 0.772 0.052 0.008 0.040 0.128
#> GSM617628 3 0.0000 0.67918 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM617632 2 0.3869 -0.05173 0.500 0.500 0.000 0.000 0.000 0.000
#> GSM617634 2 0.1387 0.69216 0.000 0.932 0.068 0.000 0.000 0.000
#> GSM617635 1 0.0260 0.84640 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM617636 1 0.0363 0.84486 0.988 0.012 0.000 0.000 0.000 0.000
#> GSM617637 1 0.0000 0.84653 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617638 1 0.4827 0.64817 0.676 0.008 0.012 0.008 0.036 0.260
#> GSM617639 1 0.0000 0.84653 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617640 2 0.0000 0.71818 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM617641 4 0.3966 0.17309 0.000 0.444 0.000 0.552 0.000 0.004
#> GSM617643 2 0.0000 0.71818 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM617644 2 0.0000 0.71818 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM617647 2 0.4196 0.40963 0.332 0.640 0.000 0.000 0.000 0.028
#> GSM617648 2 0.0000 0.71818 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM617649 2 0.4233 0.47218 0.000 0.724 0.064 0.000 0.004 0.208
#> GSM617650 1 0.0000 0.84653 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617651 1 0.0260 0.84640 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM617653 1 0.2972 0.76693 0.836 0.128 0.036 0.000 0.000 0.000
#> GSM617654 2 0.0405 0.71829 0.004 0.988 0.000 0.000 0.000 0.008
#> GSM617583 3 0.0000 0.67918 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM617584 2 0.1219 0.69458 0.000 0.948 0.000 0.048 0.000 0.004
#> GSM617585 3 0.4361 0.52366 0.000 0.184 0.748 0.012 0.024 0.032
#> GSM617586 3 0.3508 0.62002 0.000 0.000 0.704 0.000 0.004 0.292
#> GSM617587 3 0.3684 0.61044 0.004 0.000 0.692 0.000 0.004 0.300
#> GSM617589 2 0.2165 0.66107 0.000 0.884 0.108 0.008 0.000 0.000
#> GSM617591 3 0.1674 0.68842 0.000 0.004 0.924 0.000 0.004 0.068
#> GSM617593 1 0.0000 0.84653 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617594 3 0.7100 -0.00952 0.308 0.304 0.320 0.000 0.000 0.068
#> GSM617595 1 0.0508 0.84485 0.984 0.012 0.004 0.000 0.000 0.000
#> GSM617596 1 0.3246 0.76816 0.812 0.016 0.160 0.000 0.000 0.012
#> GSM617597 1 0.3448 0.78245 0.816 0.000 0.072 0.000 0.004 0.108
#> GSM617598 1 0.0000 0.84653 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617599 2 0.0937 0.70680 0.000 0.960 0.000 0.000 0.000 0.040
#> GSM617600 3 0.4199 0.60196 0.000 0.000 0.704 0.004 0.044 0.248
#> GSM617601 2 0.5639 0.20435 0.000 0.548 0.356 0.008 0.040 0.048
#> GSM617602 1 0.5941 0.39663 0.540 0.004 0.344 0.012 0.028 0.072
#> GSM617603 5 0.1610 0.00000 0.000 0.000 0.000 0.084 0.916 0.000
#> GSM617604 1 0.3539 0.73360 0.768 0.008 0.208 0.000 0.000 0.016
#> GSM617605 4 0.0603 0.39091 0.000 0.016 0.000 0.980 0.000 0.004
#> GSM617606 3 0.0000 0.67918 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM617610 1 0.1219 0.83007 0.948 0.048 0.004 0.000 0.000 0.000
#> GSM617611 1 0.0260 0.84640 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM617613 3 0.1230 0.67385 0.000 0.000 0.956 0.008 0.028 0.008
#> GSM617614 1 0.4183 0.62861 0.668 0.000 0.296 0.000 0.000 0.036
#> GSM617621 1 0.0000 0.84653 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617629 1 0.7882 -0.06035 0.348 0.268 0.260 0.008 0.020 0.096
#> GSM617630 1 0.4432 0.69650 0.708 0.000 0.188 0.000 0.000 0.104
#> GSM617631 3 0.2058 0.63375 0.000 0.000 0.916 0.012 0.024 0.048
#> GSM617633 1 0.0000 0.84653 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617642 1 0.4836 0.63602 0.664 0.000 0.228 0.000 0.004 0.104
#> GSM617645 1 0.5414 0.22408 0.524 0.372 0.000 0.000 0.008 0.096
#> GSM617646 1 0.0000 0.84653 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617652 1 0.1387 0.82726 0.932 0.000 0.000 0.000 0.000 0.068
#> GSM617655 3 0.3052 0.65862 0.000 0.000 0.780 0.000 0.004 0.216
#> GSM617656 3 0.3348 0.64612 0.000 0.000 0.768 0.000 0.016 0.216
#> GSM617657 6 0.4338 0.00000 0.000 0.000 0.248 0.012 0.040 0.700
#> GSM617658 1 0.4672 0.68669 0.716 0.000 0.208 0.012 0.024 0.040
#> GSM617659 1 0.0260 0.84640 0.992 0.000 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) k
#> SD:pam 71 0.005653 2
#> SD:pam 70 0.001008 3
#> SD:pam 67 0.000946 4
#> SD:pam 66 0.001101 5
#> SD:pam 61 0.001218 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 79 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 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 0.842 0.927 0.952 0.2330 0.796 0.796
#> 3 3 0.342 0.519 0.739 1.1228 0.753 0.691
#> 4 4 0.682 0.785 0.879 0.4442 0.624 0.380
#> 5 5 0.584 0.556 0.771 0.0635 0.966 0.880
#> 6 6 0.613 0.492 0.721 0.0446 0.945 0.802
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
#> GSM617581 1 0.1843 0.953 0.972 0.028
#> GSM617582 1 0.1843 0.953 0.972 0.028
#> GSM617588 2 0.3733 0.956 0.072 0.928
#> GSM617590 2 0.3584 0.952 0.068 0.932
#> GSM617592 2 0.3733 0.956 0.072 0.928
#> GSM617607 1 0.0376 0.956 0.996 0.004
#> GSM617608 1 0.1633 0.951 0.976 0.024
#> GSM617609 1 0.0000 0.956 1.000 0.000
#> GSM617612 1 0.0672 0.956 0.992 0.008
#> GSM617615 1 0.5294 0.866 0.880 0.120
#> GSM617616 1 0.0938 0.956 0.988 0.012
#> GSM617617 1 0.4815 0.891 0.896 0.104
#> GSM617618 1 0.1184 0.955 0.984 0.016
#> GSM617619 1 0.0672 0.956 0.992 0.008
#> GSM617620 2 0.3733 0.956 0.072 0.928
#> GSM617622 1 0.6801 0.801 0.820 0.180
#> GSM617623 1 0.1843 0.953 0.972 0.028
#> GSM617624 1 0.1184 0.955 0.984 0.016
#> GSM617625 1 0.0672 0.956 0.992 0.008
#> GSM617626 1 0.1633 0.954 0.976 0.024
#> GSM617627 1 0.1633 0.952 0.976 0.024
#> GSM617628 1 0.0672 0.956 0.992 0.008
#> GSM617632 1 0.1414 0.956 0.980 0.020
#> GSM617634 1 0.1843 0.953 0.972 0.028
#> GSM617635 1 0.1184 0.954 0.984 0.016
#> GSM617636 1 0.1184 0.955 0.984 0.016
#> GSM617637 1 0.1843 0.949 0.972 0.028
#> GSM617638 1 0.1184 0.955 0.984 0.016
#> GSM617639 1 0.1843 0.949 0.972 0.028
#> GSM617640 1 0.6623 0.801 0.828 0.172
#> GSM617641 2 0.3733 0.956 0.072 0.928
#> GSM617643 1 0.6623 0.800 0.828 0.172
#> GSM617644 2 0.9460 0.488 0.364 0.636
#> GSM617647 1 0.1184 0.955 0.984 0.016
#> GSM617648 1 0.6623 0.812 0.828 0.172
#> GSM617649 1 0.1414 0.953 0.980 0.020
#> GSM617650 1 0.1414 0.952 0.980 0.020
#> GSM617651 1 0.2236 0.943 0.964 0.036
#> GSM617653 1 0.1414 0.956 0.980 0.020
#> GSM617654 1 0.3114 0.930 0.944 0.056
#> GSM617583 1 0.0672 0.956 0.992 0.008
#> GSM617584 1 0.3584 0.927 0.932 0.068
#> GSM617585 1 0.8608 0.619 0.716 0.284
#> GSM617586 1 0.0672 0.956 0.992 0.008
#> GSM617587 1 0.0000 0.956 1.000 0.000
#> GSM617589 2 0.3879 0.953 0.076 0.924
#> GSM617591 1 0.1184 0.955 0.984 0.016
#> GSM617593 1 0.1184 0.954 0.984 0.016
#> GSM617594 1 0.1184 0.955 0.984 0.016
#> GSM617595 1 0.2236 0.943 0.964 0.036
#> GSM617596 1 0.1414 0.955 0.980 0.020
#> GSM617597 1 0.0938 0.956 0.988 0.012
#> GSM617598 1 0.1843 0.954 0.972 0.028
#> GSM617599 1 0.1414 0.954 0.980 0.020
#> GSM617600 1 0.2423 0.940 0.960 0.040
#> GSM617601 1 0.8555 0.611 0.720 0.280
#> GSM617602 1 0.1843 0.954 0.972 0.028
#> GSM617603 2 0.3733 0.956 0.072 0.928
#> GSM617604 1 0.1184 0.955 0.984 0.016
#> GSM617605 2 0.3733 0.956 0.072 0.928
#> GSM617606 1 0.1184 0.955 0.984 0.016
#> GSM617610 1 0.2043 0.946 0.968 0.032
#> GSM617611 1 0.1633 0.951 0.976 0.024
#> GSM617613 1 0.2423 0.940 0.960 0.040
#> GSM617614 1 0.0376 0.956 0.996 0.004
#> GSM617621 1 0.1633 0.955 0.976 0.024
#> GSM617629 1 0.1414 0.955 0.980 0.020
#> GSM617630 1 0.0000 0.956 1.000 0.000
#> GSM617631 1 0.2948 0.939 0.948 0.052
#> GSM617633 1 0.0000 0.956 1.000 0.000
#> GSM617642 1 0.0376 0.956 0.996 0.004
#> GSM617645 1 0.5737 0.847 0.864 0.136
#> GSM617646 1 0.0000 0.956 1.000 0.000
#> GSM617652 1 0.0376 0.956 0.996 0.004
#> GSM617655 1 0.1414 0.953 0.980 0.020
#> GSM617656 1 0.2236 0.942 0.964 0.036
#> GSM617657 1 0.2603 0.941 0.956 0.044
#> GSM617658 1 0.1633 0.955 0.976 0.024
#> GSM617659 1 0.1184 0.955 0.984 0.016
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM617581 1 0.3375 0.6579 0.892 0.100 0.008
#> GSM617582 1 0.3009 0.6936 0.920 0.052 0.028
#> GSM617588 3 0.5690 0.9973 0.004 0.288 0.708
#> GSM617590 3 0.5690 0.9973 0.004 0.288 0.708
#> GSM617592 3 0.5690 0.9973 0.004 0.288 0.708
#> GSM617607 1 0.1267 0.7091 0.972 0.024 0.004
#> GSM617608 1 0.0237 0.7163 0.996 0.000 0.004
#> GSM617609 1 0.5115 0.5660 0.768 0.004 0.228
#> GSM617612 1 0.0237 0.7163 0.996 0.000 0.004
#> GSM617615 2 0.8701 0.6091 0.400 0.492 0.108
#> GSM617616 1 0.0592 0.7157 0.988 0.012 0.000
#> GSM617617 2 0.5873 0.7085 0.312 0.684 0.004
#> GSM617618 1 0.1289 0.7110 0.968 0.032 0.000
#> GSM617619 1 0.9367 -0.1455 0.504 0.292 0.204
#> GSM617620 3 0.5690 0.9973 0.004 0.288 0.708
#> GSM617622 2 0.7922 0.6071 0.408 0.532 0.060
#> GSM617623 1 0.4164 0.6008 0.848 0.144 0.008
#> GSM617624 1 0.7295 -0.4789 0.488 0.484 0.028
#> GSM617625 1 0.3589 0.6782 0.900 0.048 0.052
#> GSM617626 1 0.2280 0.6934 0.940 0.052 0.008
#> GSM617627 2 0.7004 0.5907 0.428 0.552 0.020
#> GSM617628 1 0.7398 0.5004 0.700 0.120 0.180
#> GSM617632 1 0.1129 0.7144 0.976 0.020 0.004
#> GSM617634 1 0.6758 0.0231 0.620 0.360 0.020
#> GSM617635 1 0.1163 0.7061 0.972 0.028 0.000
#> GSM617636 1 0.1765 0.7082 0.956 0.040 0.004
#> GSM617637 1 0.0475 0.7165 0.992 0.004 0.004
#> GSM617638 1 0.7735 -0.3816 0.512 0.440 0.048
#> GSM617639 1 0.0475 0.7165 0.992 0.004 0.004
#> GSM617640 2 0.5754 0.7014 0.296 0.700 0.004
#> GSM617641 3 0.5690 0.9973 0.004 0.288 0.708
#> GSM617643 2 0.5754 0.7014 0.296 0.700 0.004
#> GSM617644 2 0.8488 -0.3007 0.096 0.520 0.384
#> GSM617647 1 0.7054 -0.3804 0.524 0.456 0.020
#> GSM617648 2 0.6113 0.7047 0.300 0.688 0.012
#> GSM617649 2 0.7013 0.5840 0.432 0.548 0.020
#> GSM617650 1 0.0000 0.7161 1.000 0.000 0.000
#> GSM617651 1 0.0475 0.7165 0.992 0.004 0.004
#> GSM617653 1 0.1129 0.7134 0.976 0.020 0.004
#> GSM617654 2 0.5706 0.7079 0.320 0.680 0.000
#> GSM617583 1 0.4357 0.6605 0.868 0.052 0.080
#> GSM617584 1 0.8618 -0.3895 0.508 0.388 0.104
#> GSM617585 2 0.9372 0.0934 0.200 0.500 0.300
#> GSM617586 1 0.8517 0.3579 0.584 0.128 0.288
#> GSM617587 1 0.2682 0.6909 0.920 0.004 0.076
#> GSM617589 3 0.6051 0.9806 0.012 0.292 0.696
#> GSM617591 1 0.7883 -0.4144 0.516 0.428 0.056
#> GSM617593 1 0.0475 0.7165 0.992 0.004 0.004
#> GSM617594 1 0.6924 -0.1929 0.580 0.400 0.020
#> GSM617595 1 0.0661 0.7158 0.988 0.008 0.004
#> GSM617596 1 0.0983 0.7140 0.980 0.016 0.004
#> GSM617597 1 0.0592 0.7163 0.988 0.000 0.012
#> GSM617598 1 0.0592 0.7157 0.988 0.012 0.000
#> GSM617599 1 0.6195 0.2715 0.704 0.276 0.020
#> GSM617600 1 0.9871 0.1459 0.412 0.280 0.308
#> GSM617601 2 0.9351 0.5062 0.256 0.516 0.228
#> GSM617602 1 0.9401 0.2727 0.504 0.216 0.280
#> GSM617603 3 0.5690 0.9973 0.004 0.288 0.708
#> GSM617604 1 0.1636 0.7142 0.964 0.016 0.020
#> GSM617605 3 0.5690 0.9973 0.004 0.288 0.708
#> GSM617606 1 0.7555 -0.4002 0.520 0.440 0.040
#> GSM617610 1 0.0475 0.7167 0.992 0.004 0.004
#> GSM617611 1 0.0000 0.7161 1.000 0.000 0.000
#> GSM617613 1 0.9871 0.1459 0.412 0.280 0.308
#> GSM617614 1 0.4887 0.6384 0.844 0.096 0.060
#> GSM617621 1 0.0983 0.7140 0.980 0.016 0.004
#> GSM617629 1 0.6728 0.5496 0.736 0.080 0.184
#> GSM617630 1 0.6865 0.4743 0.736 0.160 0.104
#> GSM617631 1 0.9907 0.1422 0.400 0.288 0.312
#> GSM617633 1 0.1411 0.7026 0.964 0.036 0.000
#> GSM617642 1 0.2297 0.7047 0.944 0.020 0.036
#> GSM617645 2 0.5560 0.7051 0.300 0.700 0.000
#> GSM617646 1 0.1411 0.7014 0.964 0.036 0.000
#> GSM617652 1 0.0000 0.7161 1.000 0.000 0.000
#> GSM617655 1 0.9092 0.2915 0.528 0.168 0.304
#> GSM617656 1 0.9857 0.1473 0.416 0.276 0.308
#> GSM617657 2 0.9947 -0.0251 0.316 0.384 0.300
#> GSM617658 1 0.7572 0.4911 0.688 0.184 0.128
#> GSM617659 1 0.0000 0.7161 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM617581 1 0.6609 0.658 0.668 0.224 0.068 0.040
#> GSM617582 1 0.7312 0.558 0.608 0.200 0.168 0.024
#> GSM617588 4 0.1022 0.872 0.000 0.032 0.000 0.968
#> GSM617590 4 0.1022 0.872 0.000 0.032 0.000 0.968
#> GSM617592 4 0.1022 0.872 0.000 0.032 0.000 0.968
#> GSM617607 1 0.1411 0.888 0.960 0.020 0.020 0.000
#> GSM617608 1 0.0592 0.888 0.984 0.000 0.016 0.000
#> GSM617609 3 0.3009 0.798 0.056 0.052 0.892 0.000
#> GSM617612 1 0.0188 0.891 0.996 0.004 0.000 0.000
#> GSM617615 2 0.3982 0.712 0.000 0.776 0.004 0.220
#> GSM617616 1 0.2207 0.879 0.928 0.004 0.056 0.012
#> GSM617617 2 0.0657 0.875 0.000 0.984 0.004 0.012
#> GSM617618 1 0.3144 0.874 0.892 0.020 0.072 0.016
#> GSM617619 2 0.4522 0.519 0.000 0.680 0.320 0.000
#> GSM617620 4 0.1022 0.872 0.000 0.032 0.000 0.968
#> GSM617622 2 0.3842 0.792 0.004 0.836 0.024 0.136
#> GSM617623 1 0.6674 0.656 0.668 0.220 0.060 0.052
#> GSM617624 2 0.0779 0.877 0.004 0.980 0.016 0.000
#> GSM617625 3 0.4898 0.487 0.416 0.000 0.584 0.000
#> GSM617626 1 0.5430 0.709 0.732 0.204 0.056 0.008
#> GSM617627 2 0.0779 0.877 0.000 0.980 0.016 0.004
#> GSM617628 3 0.4844 0.683 0.300 0.012 0.688 0.000
#> GSM617632 1 0.3130 0.873 0.892 0.012 0.072 0.024
#> GSM617634 2 0.4198 0.759 0.116 0.828 0.052 0.004
#> GSM617635 1 0.0672 0.891 0.984 0.008 0.008 0.000
#> GSM617636 1 0.3877 0.866 0.860 0.032 0.084 0.024
#> GSM617637 1 0.0188 0.891 0.996 0.004 0.000 0.000
#> GSM617638 2 0.1492 0.868 0.004 0.956 0.036 0.004
#> GSM617639 1 0.0779 0.891 0.980 0.016 0.004 0.000
#> GSM617640 2 0.0469 0.875 0.000 0.988 0.000 0.012
#> GSM617641 4 0.1022 0.872 0.000 0.032 0.000 0.968
#> GSM617643 2 0.0469 0.875 0.000 0.988 0.000 0.012
#> GSM617644 2 0.4898 0.295 0.000 0.584 0.000 0.416
#> GSM617647 2 0.1182 0.876 0.016 0.968 0.016 0.000
#> GSM617648 2 0.2300 0.850 0.000 0.920 0.016 0.064
#> GSM617649 2 0.0524 0.877 0.000 0.988 0.008 0.004
#> GSM617650 1 0.0000 0.890 1.000 0.000 0.000 0.000
#> GSM617651 1 0.0000 0.890 1.000 0.000 0.000 0.000
#> GSM617653 1 0.2222 0.877 0.924 0.000 0.060 0.016
#> GSM617654 2 0.0188 0.875 0.000 0.996 0.000 0.004
#> GSM617583 3 0.4855 0.598 0.352 0.004 0.644 0.000
#> GSM617584 4 0.8691 0.127 0.280 0.300 0.036 0.384
#> GSM617585 4 0.6851 0.177 0.000 0.104 0.400 0.496
#> GSM617586 3 0.2443 0.805 0.060 0.024 0.916 0.000
#> GSM617587 3 0.7033 0.399 0.364 0.128 0.508 0.000
#> GSM617589 4 0.1716 0.848 0.000 0.064 0.000 0.936
#> GSM617591 2 0.4688 0.768 0.000 0.792 0.080 0.128
#> GSM617593 1 0.0188 0.890 0.996 0.000 0.004 0.000
#> GSM617594 2 0.0779 0.877 0.004 0.980 0.016 0.000
#> GSM617595 1 0.0188 0.890 0.996 0.000 0.004 0.000
#> GSM617596 1 0.4387 0.839 0.840 0.068 0.060 0.032
#> GSM617597 1 0.2469 0.820 0.892 0.000 0.108 0.000
#> GSM617598 1 0.1474 0.883 0.948 0.000 0.052 0.000
#> GSM617599 2 0.3037 0.814 0.100 0.880 0.020 0.000
#> GSM617600 3 0.1929 0.804 0.036 0.024 0.940 0.000
#> GSM617601 2 0.3123 0.789 0.000 0.844 0.000 0.156
#> GSM617602 3 0.0376 0.783 0.004 0.000 0.992 0.004
#> GSM617603 4 0.1022 0.872 0.000 0.032 0.000 0.968
#> GSM617604 1 0.5622 0.693 0.696 0.020 0.256 0.028
#> GSM617605 4 0.1022 0.872 0.000 0.032 0.000 0.968
#> GSM617606 2 0.2708 0.863 0.028 0.916 0.040 0.016
#> GSM617610 1 0.0000 0.890 1.000 0.000 0.000 0.000
#> GSM617611 1 0.0188 0.890 0.996 0.000 0.004 0.000
#> GSM617613 3 0.1936 0.802 0.032 0.028 0.940 0.000
#> GSM617614 3 0.4072 0.701 0.252 0.000 0.748 0.000
#> GSM617621 1 0.3448 0.869 0.884 0.028 0.060 0.028
#> GSM617629 3 0.4809 0.590 0.012 0.220 0.752 0.016
#> GSM617630 2 0.3937 0.738 0.012 0.800 0.188 0.000
#> GSM617631 3 0.0000 0.783 0.000 0.000 1.000 0.000
#> GSM617633 1 0.1771 0.881 0.948 0.012 0.036 0.004
#> GSM617642 1 0.4560 0.546 0.700 0.004 0.296 0.000
#> GSM617645 2 0.0469 0.875 0.000 0.988 0.000 0.012
#> GSM617646 1 0.1474 0.880 0.948 0.052 0.000 0.000
#> GSM617652 1 0.1837 0.883 0.944 0.028 0.028 0.000
#> GSM617655 3 0.1929 0.804 0.036 0.024 0.940 0.000
#> GSM617656 3 0.1929 0.804 0.036 0.024 0.940 0.000
#> GSM617657 3 0.1833 0.799 0.024 0.032 0.944 0.000
#> GSM617658 3 0.2629 0.769 0.060 0.004 0.912 0.024
#> GSM617659 1 0.0817 0.891 0.976 0.000 0.024 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM617581 1 0.7621 -0.19676 0.456 0.212 0.048 0.008 0.276
#> GSM617582 5 0.8512 0.00000 0.228 0.188 0.284 0.000 0.300
#> GSM617588 4 0.0162 0.83752 0.000 0.004 0.000 0.996 0.000
#> GSM617590 4 0.0162 0.83752 0.000 0.004 0.000 0.996 0.000
#> GSM617592 4 0.0162 0.83752 0.000 0.004 0.000 0.996 0.000
#> GSM617607 1 0.3634 0.66182 0.844 0.020 0.080 0.000 0.056
#> GSM617608 1 0.1907 0.68996 0.928 0.000 0.028 0.000 0.044
#> GSM617609 3 0.3100 0.57351 0.040 0.064 0.876 0.000 0.020
#> GSM617612 1 0.2775 0.67865 0.876 0.004 0.100 0.000 0.020
#> GSM617615 2 0.5369 0.63096 0.004 0.672 0.016 0.252 0.056
#> GSM617616 1 0.4943 0.56596 0.716 0.008 0.076 0.000 0.200
#> GSM617617 2 0.2452 0.77505 0.000 0.896 0.004 0.016 0.084
#> GSM617618 1 0.6277 0.40524 0.604 0.028 0.128 0.000 0.240
#> GSM617619 2 0.4762 0.69563 0.008 0.748 0.140 0.000 0.104
#> GSM617620 4 0.0162 0.83752 0.000 0.004 0.000 0.996 0.000
#> GSM617622 2 0.4986 0.63948 0.008 0.704 0.008 0.236 0.044
#> GSM617623 1 0.7531 -0.15006 0.468 0.208 0.044 0.008 0.272
#> GSM617624 2 0.3161 0.77949 0.008 0.860 0.032 0.000 0.100
#> GSM617625 3 0.4884 0.38442 0.232 0.008 0.704 0.000 0.056
#> GSM617626 1 0.6901 0.05459 0.532 0.160 0.040 0.000 0.268
#> GSM617627 2 0.3070 0.78521 0.008 0.872 0.028 0.004 0.088
#> GSM617628 3 0.4332 0.52015 0.132 0.016 0.788 0.000 0.064
#> GSM617632 1 0.4928 0.57986 0.724 0.012 0.072 0.000 0.192
#> GSM617634 2 0.5212 0.63458 0.016 0.692 0.068 0.000 0.224
#> GSM617635 1 0.2464 0.68670 0.904 0.004 0.048 0.000 0.044
#> GSM617636 1 0.5993 0.47338 0.628 0.016 0.140 0.000 0.216
#> GSM617637 1 0.0404 0.69639 0.988 0.000 0.000 0.000 0.012
#> GSM617638 2 0.3376 0.77905 0.012 0.848 0.032 0.000 0.108
#> GSM617639 1 0.0566 0.69685 0.984 0.004 0.000 0.000 0.012
#> GSM617640 2 0.2069 0.77902 0.000 0.912 0.000 0.012 0.076
#> GSM617641 4 0.0162 0.83752 0.000 0.004 0.000 0.996 0.000
#> GSM617643 2 0.2069 0.77902 0.000 0.912 0.000 0.012 0.076
#> GSM617644 4 0.5891 -0.00136 0.000 0.432 0.000 0.468 0.100
#> GSM617647 2 0.4018 0.74885 0.092 0.824 0.012 0.008 0.064
#> GSM617648 2 0.3906 0.73615 0.000 0.812 0.004 0.080 0.104
#> GSM617649 2 0.2237 0.79461 0.008 0.904 0.004 0.000 0.084
#> GSM617650 1 0.1502 0.68350 0.940 0.000 0.004 0.000 0.056
#> GSM617651 1 0.0510 0.69448 0.984 0.000 0.000 0.000 0.016
#> GSM617653 1 0.4354 0.52750 0.712 0.000 0.032 0.000 0.256
#> GSM617654 2 0.1956 0.77938 0.000 0.916 0.000 0.008 0.076
#> GSM617583 3 0.4686 0.44643 0.192 0.012 0.740 0.000 0.056
#> GSM617584 4 0.8241 -0.00849 0.100 0.264 0.008 0.396 0.232
#> GSM617585 4 0.6650 0.52912 0.004 0.124 0.136 0.636 0.100
#> GSM617586 3 0.1815 0.60319 0.016 0.020 0.940 0.000 0.024
#> GSM617587 3 0.6311 0.01787 0.204 0.148 0.616 0.000 0.032
#> GSM617589 4 0.1907 0.80523 0.000 0.044 0.000 0.928 0.028
#> GSM617591 2 0.5934 0.67494 0.004 0.692 0.092 0.148 0.064
#> GSM617593 1 0.1430 0.68390 0.944 0.000 0.004 0.000 0.052
#> GSM617594 2 0.2813 0.74790 0.084 0.880 0.032 0.000 0.004
#> GSM617595 1 0.0510 0.69578 0.984 0.000 0.000 0.000 0.016
#> GSM617596 1 0.5886 0.45651 0.636 0.032 0.080 0.000 0.252
#> GSM617597 1 0.5235 -0.08211 0.524 0.012 0.440 0.000 0.024
#> GSM617598 1 0.2179 0.66316 0.888 0.000 0.000 0.000 0.112
#> GSM617599 2 0.3809 0.72163 0.100 0.832 0.032 0.000 0.036
#> GSM617600 3 0.4199 0.55059 0.004 0.008 0.692 0.000 0.296
#> GSM617601 2 0.4254 0.69011 0.000 0.740 0.000 0.220 0.040
#> GSM617602 3 0.3209 0.54780 0.000 0.008 0.812 0.000 0.180
#> GSM617603 4 0.0290 0.83272 0.000 0.000 0.000 0.992 0.008
#> GSM617604 1 0.6922 -0.31082 0.408 0.008 0.344 0.000 0.240
#> GSM617605 4 0.0162 0.83752 0.000 0.004 0.000 0.996 0.000
#> GSM617606 2 0.5808 0.70032 0.008 0.716 0.104 0.092 0.080
#> GSM617610 1 0.0671 0.69664 0.980 0.000 0.004 0.000 0.016
#> GSM617611 1 0.0451 0.69531 0.988 0.000 0.004 0.000 0.008
#> GSM617613 3 0.4046 0.54875 0.000 0.008 0.696 0.000 0.296
#> GSM617614 3 0.4686 0.46894 0.112 0.008 0.756 0.000 0.124
#> GSM617621 1 0.4930 0.60265 0.740 0.020 0.076 0.000 0.164
#> GSM617629 3 0.6834 -0.06723 0.008 0.256 0.460 0.000 0.276
#> GSM617630 2 0.5232 0.65406 0.020 0.716 0.168 0.000 0.096
#> GSM617631 3 0.4225 0.51964 0.000 0.004 0.632 0.000 0.364
#> GSM617633 1 0.5521 0.44835 0.692 0.028 0.188 0.000 0.092
#> GSM617642 3 0.5555 0.05608 0.328 0.012 0.600 0.000 0.060
#> GSM617645 2 0.2069 0.77902 0.000 0.912 0.000 0.012 0.076
#> GSM617646 1 0.3393 0.67160 0.860 0.044 0.072 0.000 0.024
#> GSM617652 1 0.5309 0.42915 0.684 0.028 0.236 0.000 0.052
#> GSM617655 3 0.2103 0.60602 0.004 0.020 0.920 0.000 0.056
#> GSM617656 3 0.4064 0.56024 0.004 0.008 0.716 0.000 0.272
#> GSM617657 3 0.4401 0.52372 0.000 0.016 0.656 0.000 0.328
#> GSM617658 3 0.4033 0.49806 0.024 0.004 0.760 0.000 0.212
#> GSM617659 1 0.1670 0.68536 0.936 0.000 0.012 0.000 0.052
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM617581 1 0.6980 -0.3344 0.376 0.208 0.016 0.004 0.368 0.028
#> GSM617582 5 0.8304 0.0000 0.208 0.228 0.196 0.008 0.332 0.028
#> GSM617588 4 0.0146 0.8371 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM617590 4 0.0508 0.8376 0.000 0.004 0.000 0.984 0.000 0.012
#> GSM617592 4 0.0146 0.8389 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM617607 1 0.3925 0.6474 0.812 0.012 0.072 0.000 0.080 0.024
#> GSM617608 1 0.1370 0.6946 0.948 0.004 0.012 0.000 0.036 0.000
#> GSM617609 3 0.7084 0.0664 0.040 0.216 0.496 0.000 0.044 0.204
#> GSM617612 1 0.2663 0.6884 0.884 0.004 0.068 0.000 0.032 0.012
#> GSM617615 2 0.5381 0.5095 0.000 0.616 0.004 0.260 0.108 0.012
#> GSM617616 1 0.4723 0.5053 0.684 0.012 0.060 0.004 0.240 0.000
#> GSM617617 2 0.4009 0.6048 0.000 0.632 0.000 0.008 0.356 0.004
#> GSM617618 1 0.5994 0.3256 0.576 0.072 0.072 0.004 0.276 0.000
#> GSM617619 2 0.3835 0.5291 0.000 0.812 0.072 0.000 0.048 0.068
#> GSM617620 4 0.0146 0.8389 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM617622 2 0.5540 0.4906 0.000 0.588 0.000 0.232 0.172 0.008
#> GSM617623 1 0.6934 -0.2784 0.396 0.196 0.016 0.004 0.360 0.028
#> GSM617624 2 0.1464 0.6161 0.004 0.944 0.000 0.000 0.016 0.036
#> GSM617625 3 0.2584 0.5079 0.144 0.000 0.848 0.004 0.004 0.000
#> GSM617626 1 0.6512 -0.1170 0.464 0.140 0.020 0.000 0.352 0.024
#> GSM617627 2 0.1321 0.6348 0.004 0.952 0.000 0.000 0.024 0.020
#> GSM617628 3 0.2568 0.4921 0.088 0.000 0.880 0.004 0.004 0.024
#> GSM617632 1 0.4634 0.5572 0.704 0.008 0.076 0.000 0.208 0.004
#> GSM617634 2 0.4754 0.4147 0.004 0.708 0.020 0.008 0.216 0.044
#> GSM617635 1 0.2726 0.6785 0.880 0.008 0.052 0.000 0.056 0.004
#> GSM617636 1 0.7233 0.2601 0.520 0.056 0.156 0.000 0.200 0.068
#> GSM617637 1 0.1129 0.6994 0.964 0.004 0.012 0.000 0.008 0.012
#> GSM617638 2 0.2256 0.6023 0.004 0.908 0.008 0.000 0.032 0.048
#> GSM617639 1 0.0976 0.6991 0.968 0.000 0.016 0.000 0.008 0.008
#> GSM617640 2 0.3756 0.6081 0.000 0.644 0.000 0.000 0.352 0.004
#> GSM617641 4 0.0146 0.8389 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM617643 2 0.3892 0.6087 0.004 0.640 0.000 0.000 0.352 0.004
#> GSM617644 4 0.5856 0.2364 0.000 0.264 0.000 0.528 0.200 0.008
#> GSM617647 2 0.4137 0.5745 0.108 0.756 0.000 0.000 0.132 0.004
#> GSM617648 2 0.5171 0.5490 0.000 0.524 0.000 0.068 0.400 0.008
#> GSM617649 2 0.2051 0.6485 0.000 0.896 0.000 0.004 0.096 0.004
#> GSM617650 1 0.2535 0.6731 0.892 0.004 0.004 0.004 0.064 0.032
#> GSM617651 1 0.1605 0.6897 0.936 0.000 0.004 0.000 0.044 0.016
#> GSM617653 1 0.5053 0.3875 0.628 0.000 0.052 0.000 0.292 0.028
#> GSM617654 2 0.3769 0.6074 0.000 0.640 0.000 0.000 0.356 0.004
#> GSM617583 3 0.2308 0.5136 0.108 0.000 0.880 0.004 0.000 0.008
#> GSM617584 4 0.7428 -0.1020 0.040 0.224 0.004 0.356 0.344 0.032
#> GSM617585 4 0.5526 0.6037 0.000 0.152 0.024 0.688 0.092 0.044
#> GSM617586 3 0.3902 0.1551 0.008 0.004 0.720 0.000 0.012 0.256
#> GSM617587 3 0.7440 -0.0532 0.164 0.268 0.448 0.000 0.032 0.088
#> GSM617589 4 0.2146 0.8013 0.000 0.044 0.000 0.908 0.044 0.004
#> GSM617591 2 0.5928 0.4913 0.000 0.620 0.028 0.216 0.112 0.024
#> GSM617593 1 0.2007 0.6811 0.916 0.004 0.000 0.000 0.044 0.036
#> GSM617594 2 0.3174 0.5763 0.104 0.836 0.004 0.000 0.056 0.000
#> GSM617595 1 0.1464 0.6930 0.944 0.000 0.004 0.000 0.036 0.016
#> GSM617596 1 0.5665 0.4274 0.620 0.032 0.084 0.000 0.252 0.012
#> GSM617597 3 0.4519 0.0791 0.468 0.004 0.508 0.000 0.016 0.004
#> GSM617598 1 0.2969 0.6663 0.860 0.000 0.032 0.000 0.088 0.020
#> GSM617599 2 0.4154 0.4964 0.112 0.744 0.000 0.000 0.144 0.000
#> GSM617600 6 0.3428 0.7949 0.000 0.000 0.304 0.000 0.000 0.696
#> GSM617601 2 0.4905 0.5374 0.004 0.648 0.000 0.272 0.068 0.008
#> GSM617602 3 0.3695 0.2756 0.000 0.004 0.776 0.000 0.044 0.176
#> GSM617603 4 0.0806 0.8326 0.000 0.000 0.000 0.972 0.020 0.008
#> GSM617604 3 0.6654 -0.3030 0.400 0.008 0.404 0.000 0.140 0.048
#> GSM617605 4 0.0508 0.8376 0.000 0.004 0.000 0.984 0.000 0.012
#> GSM617606 2 0.6060 0.4830 0.000 0.632 0.044 0.156 0.144 0.024
#> GSM617610 1 0.1577 0.6933 0.940 0.000 0.008 0.000 0.036 0.016
#> GSM617611 1 0.0291 0.6971 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM617613 6 0.3175 0.8005 0.000 0.000 0.256 0.000 0.000 0.744
#> GSM617614 3 0.2463 0.5013 0.068 0.000 0.892 0.000 0.020 0.020
#> GSM617621 1 0.4706 0.5936 0.732 0.008 0.084 0.000 0.156 0.020
#> GSM617629 2 0.7355 -0.2891 0.004 0.388 0.312 0.000 0.140 0.156
#> GSM617630 2 0.4388 0.4571 0.000 0.760 0.136 0.000 0.044 0.060
#> GSM617631 6 0.4456 0.5297 0.000 0.000 0.448 0.000 0.028 0.524
#> GSM617633 1 0.6993 0.2052 0.564 0.108 0.180 0.000 0.092 0.056
#> GSM617642 3 0.3159 0.5016 0.168 0.004 0.812 0.000 0.012 0.004
#> GSM617645 2 0.3892 0.6087 0.004 0.640 0.000 0.000 0.352 0.004
#> GSM617646 1 0.3714 0.6573 0.828 0.036 0.072 0.000 0.056 0.008
#> GSM617652 1 0.4420 0.5597 0.744 0.016 0.176 0.000 0.056 0.008
#> GSM617655 3 0.4033 0.0849 0.004 0.004 0.692 0.000 0.016 0.284
#> GSM617656 6 0.3717 0.7264 0.000 0.000 0.384 0.000 0.000 0.616
#> GSM617657 6 0.3203 0.7317 0.000 0.024 0.160 0.000 0.004 0.812
#> GSM617658 3 0.3419 0.3525 0.008 0.000 0.820 0.000 0.056 0.116
#> GSM617659 1 0.2842 0.6715 0.884 0.004 0.028 0.004 0.048 0.032
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:mclust 78 0.7090 2
#> SD:mclust 57 0.2176 3
#> SD:mclust 74 0.0168 4
#> SD:mclust 59 0.1051 5
#> SD:mclust 52 0.0232 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 79 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 0.845 0.931 0.968 0.4975 0.503 0.503
#> 3 3 0.497 0.674 0.835 0.3474 0.755 0.545
#> 4 4 0.423 0.539 0.712 0.1151 0.835 0.554
#> 5 5 0.499 0.431 0.674 0.0633 0.869 0.559
#> 6 6 0.577 0.472 0.695 0.0374 0.933 0.713
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
#> GSM617581 2 0.6712 0.792 0.176 0.824
#> GSM617582 1 0.9881 0.261 0.564 0.436
#> GSM617588 2 0.0000 0.973 0.000 1.000
#> GSM617590 2 0.0000 0.973 0.000 1.000
#> GSM617592 2 0.0000 0.973 0.000 1.000
#> GSM617607 1 0.0000 0.962 1.000 0.000
#> GSM617608 1 0.0000 0.962 1.000 0.000
#> GSM617609 1 0.0000 0.962 1.000 0.000
#> GSM617612 1 0.0000 0.962 1.000 0.000
#> GSM617615 2 0.0000 0.973 0.000 1.000
#> GSM617616 1 0.7745 0.721 0.772 0.228
#> GSM617617 2 0.0000 0.973 0.000 1.000
#> GSM617618 1 0.6801 0.788 0.820 0.180
#> GSM617619 2 0.7745 0.724 0.228 0.772
#> GSM617620 2 0.0000 0.973 0.000 1.000
#> GSM617622 2 0.0000 0.973 0.000 1.000
#> GSM617623 2 0.2423 0.945 0.040 0.960
#> GSM617624 2 0.5842 0.847 0.140 0.860
#> GSM617625 1 0.0000 0.962 1.000 0.000
#> GSM617626 2 0.1414 0.961 0.020 0.980
#> GSM617627 2 0.0000 0.973 0.000 1.000
#> GSM617628 1 0.0000 0.962 1.000 0.000
#> GSM617632 1 0.2043 0.941 0.968 0.032
#> GSM617634 2 0.0672 0.969 0.008 0.992
#> GSM617635 1 0.0000 0.962 1.000 0.000
#> GSM617636 1 0.0000 0.962 1.000 0.000
#> GSM617637 1 0.0672 0.957 0.992 0.008
#> GSM617638 2 0.5737 0.850 0.136 0.864
#> GSM617639 1 0.0000 0.962 1.000 0.000
#> GSM617640 2 0.0000 0.973 0.000 1.000
#> GSM617641 2 0.0000 0.973 0.000 1.000
#> GSM617643 2 0.0000 0.973 0.000 1.000
#> GSM617644 2 0.0000 0.973 0.000 1.000
#> GSM617647 2 0.0000 0.973 0.000 1.000
#> GSM617648 2 0.0000 0.973 0.000 1.000
#> GSM617649 2 0.0000 0.973 0.000 1.000
#> GSM617650 1 0.0000 0.962 1.000 0.000
#> GSM617651 1 0.0000 0.962 1.000 0.000
#> GSM617653 1 0.0938 0.955 0.988 0.012
#> GSM617654 2 0.0000 0.973 0.000 1.000
#> GSM617583 1 0.0000 0.962 1.000 0.000
#> GSM617584 2 0.0000 0.973 0.000 1.000
#> GSM617585 2 0.0000 0.973 0.000 1.000
#> GSM617586 1 0.0000 0.962 1.000 0.000
#> GSM617587 1 0.0672 0.957 0.992 0.008
#> GSM617589 2 0.0000 0.973 0.000 1.000
#> GSM617591 2 0.3879 0.914 0.076 0.924
#> GSM617593 1 0.0000 0.962 1.000 0.000
#> GSM617594 2 0.1184 0.964 0.016 0.984
#> GSM617595 1 0.0000 0.962 1.000 0.000
#> GSM617596 1 0.3274 0.917 0.940 0.060
#> GSM617597 1 0.0000 0.962 1.000 0.000
#> GSM617598 1 0.0000 0.962 1.000 0.000
#> GSM617599 2 0.0938 0.967 0.012 0.988
#> GSM617600 1 0.0000 0.962 1.000 0.000
#> GSM617601 2 0.0000 0.973 0.000 1.000
#> GSM617602 1 0.0376 0.959 0.996 0.004
#> GSM617603 2 0.0000 0.973 0.000 1.000
#> GSM617604 1 0.0376 0.959 0.996 0.004
#> GSM617605 2 0.0000 0.973 0.000 1.000
#> GSM617606 2 0.0938 0.967 0.012 0.988
#> GSM617610 1 0.2603 0.931 0.956 0.044
#> GSM617611 1 0.0000 0.962 1.000 0.000
#> GSM617613 1 0.0000 0.962 1.000 0.000
#> GSM617614 1 0.0000 0.962 1.000 0.000
#> GSM617621 1 0.0000 0.962 1.000 0.000
#> GSM617629 1 0.5294 0.860 0.880 0.120
#> GSM617630 1 0.5294 0.854 0.880 0.120
#> GSM617631 1 0.0000 0.962 1.000 0.000
#> GSM617633 1 0.0000 0.962 1.000 0.000
#> GSM617642 1 0.0000 0.962 1.000 0.000
#> GSM617645 2 0.0000 0.973 0.000 1.000
#> GSM617646 1 0.0000 0.962 1.000 0.000
#> GSM617652 1 0.0000 0.962 1.000 0.000
#> GSM617655 1 0.0000 0.962 1.000 0.000
#> GSM617656 1 0.0000 0.962 1.000 0.000
#> GSM617657 1 0.9608 0.371 0.616 0.384
#> GSM617658 1 0.0000 0.962 1.000 0.000
#> GSM617659 1 0.0000 0.962 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM617581 1 0.5760 0.3680 0.672 0.328 0.000
#> GSM617582 1 0.9190 0.4054 0.524 0.184 0.292
#> GSM617588 2 0.2537 0.7859 0.080 0.920 0.000
#> GSM617590 2 0.2625 0.7706 0.000 0.916 0.084
#> GSM617592 2 0.2165 0.7910 0.064 0.936 0.000
#> GSM617607 1 0.6026 0.3704 0.624 0.000 0.376
#> GSM617608 1 0.6308 -0.0226 0.508 0.000 0.492
#> GSM617609 3 0.0661 0.8352 0.004 0.008 0.988
#> GSM617612 1 0.2165 0.7867 0.936 0.000 0.064
#> GSM617615 2 0.1170 0.7924 0.008 0.976 0.016
#> GSM617616 1 0.1636 0.7820 0.964 0.016 0.020
#> GSM617617 2 0.6008 0.5142 0.372 0.628 0.000
#> GSM617618 1 0.4413 0.7615 0.852 0.024 0.124
#> GSM617619 3 0.5988 0.3729 0.000 0.368 0.632
#> GSM617620 2 0.1529 0.7952 0.040 0.960 0.000
#> GSM617622 2 0.1950 0.7963 0.040 0.952 0.008
#> GSM617623 1 0.5733 0.3616 0.676 0.324 0.000
#> GSM617624 2 0.8362 0.4629 0.112 0.588 0.300
#> GSM617625 3 0.3038 0.8105 0.104 0.000 0.896
#> GSM617626 1 0.4504 0.5762 0.804 0.196 0.000
#> GSM617627 2 0.4139 0.7541 0.016 0.860 0.124
#> GSM617628 3 0.1411 0.8370 0.036 0.000 0.964
#> GSM617632 1 0.2356 0.7839 0.928 0.000 0.072
#> GSM617634 2 0.4370 0.7872 0.076 0.868 0.056
#> GSM617635 1 0.3619 0.7503 0.864 0.000 0.136
#> GSM617636 3 0.5706 0.5245 0.320 0.000 0.680
#> GSM617637 1 0.1529 0.7555 0.960 0.040 0.000
#> GSM617638 2 0.7102 0.2391 0.024 0.556 0.420
#> GSM617639 1 0.0747 0.7843 0.984 0.000 0.016
#> GSM617640 2 0.5529 0.6327 0.296 0.704 0.000
#> GSM617641 2 0.1289 0.7953 0.032 0.968 0.000
#> GSM617643 2 0.4605 0.7211 0.204 0.796 0.000
#> GSM617644 2 0.2165 0.7910 0.064 0.936 0.000
#> GSM617647 1 0.6307 -0.2423 0.512 0.488 0.000
#> GSM617648 2 0.4062 0.7460 0.164 0.836 0.000
#> GSM617649 2 0.2564 0.7971 0.036 0.936 0.028
#> GSM617650 3 0.6274 0.1547 0.456 0.000 0.544
#> GSM617651 1 0.0592 0.7831 0.988 0.000 0.012
#> GSM617653 1 0.0892 0.7689 0.980 0.020 0.000
#> GSM617654 2 0.6280 0.3407 0.460 0.540 0.000
#> GSM617583 3 0.2066 0.8309 0.060 0.000 0.940
#> GSM617584 2 0.5882 0.5510 0.348 0.652 0.000
#> GSM617585 2 0.4887 0.6444 0.000 0.772 0.228
#> GSM617586 3 0.0829 0.8344 0.004 0.012 0.984
#> GSM617587 3 0.0892 0.8381 0.020 0.000 0.980
#> GSM617589 2 0.2066 0.7942 0.060 0.940 0.000
#> GSM617591 2 0.5254 0.6075 0.000 0.736 0.264
#> GSM617593 1 0.5397 0.5661 0.720 0.000 0.280
#> GSM617594 2 0.5948 0.5509 0.360 0.640 0.000
#> GSM617595 1 0.0747 0.7709 0.984 0.016 0.000
#> GSM617596 1 0.3425 0.7684 0.884 0.004 0.112
#> GSM617597 3 0.3340 0.8005 0.120 0.000 0.880
#> GSM617598 1 0.2878 0.7742 0.904 0.000 0.096
#> GSM617599 2 0.6235 0.3945 0.436 0.564 0.000
#> GSM617600 3 0.0424 0.8337 0.000 0.008 0.992
#> GSM617601 2 0.1765 0.7866 0.004 0.956 0.040
#> GSM617602 3 0.0661 0.8368 0.008 0.004 0.988
#> GSM617603 2 0.1753 0.7835 0.000 0.952 0.048
#> GSM617604 3 0.4883 0.7047 0.208 0.004 0.788
#> GSM617605 2 0.2537 0.7725 0.000 0.920 0.080
#> GSM617606 2 0.3846 0.7635 0.016 0.876 0.108
#> GSM617610 1 0.1529 0.7555 0.960 0.040 0.000
#> GSM617611 1 0.5327 0.5826 0.728 0.000 0.272
#> GSM617613 3 0.3116 0.7856 0.000 0.108 0.892
#> GSM617614 3 0.2356 0.8255 0.072 0.000 0.928
#> GSM617621 1 0.3192 0.7666 0.888 0.000 0.112
#> GSM617629 3 0.3816 0.7594 0.000 0.148 0.852
#> GSM617630 3 0.3116 0.7870 0.000 0.108 0.892
#> GSM617631 3 0.2537 0.8037 0.000 0.080 0.920
#> GSM617633 3 0.4399 0.7326 0.188 0.000 0.812
#> GSM617642 3 0.2448 0.8237 0.076 0.000 0.924
#> GSM617645 2 0.5529 0.6381 0.296 0.704 0.000
#> GSM617646 1 0.2261 0.7865 0.932 0.000 0.068
#> GSM617652 3 0.3816 0.7780 0.148 0.000 0.852
#> GSM617655 3 0.2625 0.8006 0.000 0.084 0.916
#> GSM617656 3 0.0424 0.8368 0.008 0.000 0.992
#> GSM617657 3 0.5178 0.6014 0.000 0.256 0.744
#> GSM617658 3 0.1989 0.8342 0.048 0.004 0.948
#> GSM617659 3 0.5785 0.5001 0.332 0.000 0.668
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM617581 1 0.6701 0.4230 0.592 0.104 0.004 0.300
#> GSM617582 1 0.9497 0.3135 0.404 0.248 0.200 0.148
#> GSM617588 4 0.2635 0.7088 0.020 0.076 0.000 0.904
#> GSM617590 4 0.2376 0.7130 0.000 0.068 0.016 0.916
#> GSM617592 4 0.2586 0.7078 0.048 0.040 0.000 0.912
#> GSM617607 2 0.7540 -0.0915 0.364 0.444 0.192 0.000
#> GSM617608 3 0.7139 0.1148 0.360 0.140 0.500 0.000
#> GSM617609 3 0.2593 0.7456 0.000 0.080 0.904 0.016
#> GSM617612 1 0.7028 0.5870 0.652 0.192 0.116 0.040
#> GSM617615 4 0.6166 0.5305 0.048 0.292 0.016 0.644
#> GSM617616 1 0.5125 0.6138 0.720 0.248 0.024 0.008
#> GSM617617 2 0.6238 0.5887 0.112 0.652 0.000 0.236
#> GSM617618 1 0.7120 0.5423 0.552 0.328 0.108 0.012
#> GSM617619 3 0.6508 0.4725 0.000 0.192 0.640 0.168
#> GSM617620 4 0.2909 0.7016 0.020 0.092 0.000 0.888
#> GSM617622 4 0.5170 0.5735 0.048 0.228 0.000 0.724
#> GSM617623 1 0.6352 0.4493 0.632 0.108 0.000 0.260
#> GSM617624 2 0.7759 0.5170 0.056 0.596 0.152 0.196
#> GSM617625 3 0.5271 0.6506 0.180 0.068 0.748 0.004
#> GSM617626 1 0.5226 0.5815 0.756 0.128 0.000 0.116
#> GSM617627 2 0.6949 0.4343 0.000 0.528 0.124 0.348
#> GSM617628 3 0.5464 0.6980 0.112 0.076 0.776 0.036
#> GSM617632 1 0.5210 0.6417 0.748 0.188 0.060 0.004
#> GSM617634 2 0.6558 0.2309 0.024 0.564 0.040 0.372
#> GSM617635 2 0.6473 0.2803 0.280 0.612 0.108 0.000
#> GSM617636 1 0.8001 0.2320 0.408 0.228 0.356 0.008
#> GSM617637 1 0.5105 0.2474 0.564 0.432 0.000 0.004
#> GSM617638 2 0.6816 0.5179 0.020 0.648 0.124 0.208
#> GSM617639 1 0.5442 0.4317 0.636 0.336 0.028 0.000
#> GSM617640 2 0.5407 0.5854 0.036 0.668 0.000 0.296
#> GSM617641 4 0.2089 0.7190 0.020 0.048 0.000 0.932
#> GSM617643 2 0.4999 0.5425 0.012 0.660 0.000 0.328
#> GSM617644 4 0.5349 0.3820 0.024 0.336 0.000 0.640
#> GSM617647 2 0.6475 0.5884 0.184 0.644 0.000 0.172
#> GSM617648 2 0.5388 0.2138 0.012 0.532 0.000 0.456
#> GSM617649 2 0.6263 0.5210 0.004 0.604 0.064 0.328
#> GSM617650 1 0.6214 0.0527 0.476 0.052 0.472 0.000
#> GSM617651 1 0.3577 0.6357 0.832 0.156 0.012 0.000
#> GSM617653 1 0.2287 0.6576 0.924 0.060 0.004 0.012
#> GSM617654 2 0.5416 0.6214 0.112 0.740 0.000 0.148
#> GSM617583 3 0.4627 0.7250 0.104 0.024 0.820 0.052
#> GSM617584 4 0.6052 0.4069 0.284 0.076 0.000 0.640
#> GSM617585 4 0.4998 0.6024 0.004 0.088 0.128 0.780
#> GSM617586 3 0.1878 0.7588 0.008 0.008 0.944 0.040
#> GSM617587 3 0.2483 0.7533 0.012 0.056 0.920 0.012
#> GSM617589 4 0.5672 0.6018 0.100 0.188 0.000 0.712
#> GSM617591 4 0.7017 0.4113 0.020 0.112 0.256 0.612
#> GSM617593 1 0.5096 0.6481 0.760 0.084 0.156 0.000
#> GSM617594 2 0.6619 0.5787 0.068 0.652 0.032 0.248
#> GSM617595 1 0.4053 0.5810 0.768 0.228 0.004 0.000
#> GSM617596 1 0.4866 0.6493 0.784 0.160 0.044 0.012
#> GSM617597 3 0.2714 0.7271 0.112 0.004 0.884 0.000
#> GSM617598 1 0.3870 0.6664 0.852 0.064 0.080 0.004
#> GSM617599 2 0.6568 0.4223 0.096 0.572 0.000 0.332
#> GSM617600 3 0.1284 0.7562 0.000 0.024 0.964 0.012
#> GSM617601 4 0.4720 0.4729 0.000 0.264 0.016 0.720
#> GSM617602 3 0.4626 0.7169 0.064 0.072 0.828 0.036
#> GSM617603 4 0.2593 0.7141 0.004 0.104 0.000 0.892
#> GSM617604 1 0.7713 0.0372 0.444 0.084 0.428 0.044
#> GSM617605 4 0.2353 0.7189 0.012 0.056 0.008 0.924
#> GSM617606 4 0.6054 0.6377 0.048 0.192 0.044 0.716
#> GSM617610 1 0.4012 0.6112 0.800 0.184 0.000 0.016
#> GSM617611 1 0.7351 0.4249 0.544 0.156 0.292 0.008
#> GSM617613 3 0.2589 0.7507 0.000 0.044 0.912 0.044
#> GSM617614 3 0.2924 0.7311 0.100 0.016 0.884 0.000
#> GSM617621 1 0.4342 0.6564 0.820 0.128 0.044 0.008
#> GSM617629 3 0.7511 0.5344 0.040 0.212 0.604 0.144
#> GSM617630 3 0.6564 0.1924 0.000 0.380 0.536 0.084
#> GSM617631 3 0.3744 0.7426 0.028 0.048 0.872 0.052
#> GSM617633 3 0.6346 0.5327 0.116 0.244 0.640 0.000
#> GSM617642 3 0.3694 0.7195 0.124 0.000 0.844 0.032
#> GSM617645 2 0.5393 0.6047 0.044 0.688 0.000 0.268
#> GSM617646 2 0.5920 0.2679 0.336 0.612 0.052 0.000
#> GSM617652 3 0.4332 0.6903 0.112 0.072 0.816 0.000
#> GSM617655 3 0.1854 0.7557 0.000 0.012 0.940 0.048
#> GSM617656 3 0.0564 0.7549 0.004 0.004 0.988 0.004
#> GSM617657 3 0.6100 0.5825 0.004 0.100 0.680 0.216
#> GSM617658 3 0.6120 0.6218 0.168 0.080 0.720 0.032
#> GSM617659 3 0.5126 0.1319 0.444 0.004 0.552 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM617581 1 0.5689 0.18893 0.556 0.008 0.000 0.368 0.068
#> GSM617582 5 0.7246 0.18948 0.300 0.008 0.040 0.156 0.496
#> GSM617588 4 0.3830 0.62100 0.016 0.124 0.000 0.820 0.040
#> GSM617590 4 0.2900 0.61291 0.000 0.040 0.012 0.884 0.064
#> GSM617592 4 0.3914 0.59968 0.076 0.056 0.000 0.832 0.036
#> GSM617607 2 0.6755 0.37577 0.272 0.564 0.080 0.000 0.084
#> GSM617608 3 0.7473 0.31833 0.220 0.052 0.484 0.004 0.240
#> GSM617609 3 0.3166 0.67018 0.000 0.112 0.856 0.012 0.020
#> GSM617612 1 0.8652 0.26771 0.456 0.136 0.176 0.048 0.184
#> GSM617615 4 0.8293 0.18137 0.008 0.256 0.092 0.348 0.296
#> GSM617616 1 0.5828 0.25655 0.552 0.064 0.000 0.016 0.368
#> GSM617617 2 0.4750 0.66639 0.060 0.776 0.000 0.112 0.052
#> GSM617618 5 0.5820 0.04470 0.312 0.036 0.012 0.028 0.612
#> GSM617619 3 0.5979 0.52124 0.000 0.168 0.676 0.080 0.076
#> GSM617620 4 0.3257 0.62922 0.024 0.112 0.000 0.852 0.012
#> GSM617622 4 0.5917 0.46409 0.056 0.104 0.000 0.680 0.160
#> GSM617623 1 0.5848 0.20549 0.560 0.012 0.000 0.352 0.076
#> GSM617624 2 0.5199 0.65440 0.004 0.748 0.060 0.056 0.132
#> GSM617625 3 0.5135 0.55003 0.064 0.000 0.660 0.004 0.272
#> GSM617626 1 0.4522 0.48049 0.788 0.056 0.000 0.116 0.040
#> GSM617627 2 0.5060 0.62004 0.000 0.744 0.104 0.124 0.028
#> GSM617628 3 0.4565 0.60699 0.016 0.000 0.720 0.024 0.240
#> GSM617632 1 0.5473 0.27543 0.620 0.016 0.012 0.028 0.324
#> GSM617634 5 0.7554 0.01211 0.024 0.240 0.016 0.280 0.440
#> GSM617635 2 0.4915 0.63811 0.132 0.756 0.080 0.000 0.032
#> GSM617636 1 0.6781 -0.00879 0.472 0.020 0.068 0.032 0.408
#> GSM617637 2 0.5299 0.14196 0.436 0.520 0.004 0.000 0.040
#> GSM617638 2 0.5502 0.63616 0.016 0.716 0.032 0.056 0.180
#> GSM617639 1 0.5098 0.15942 0.564 0.404 0.020 0.000 0.012
#> GSM617640 2 0.2859 0.69329 0.016 0.876 0.000 0.096 0.012
#> GSM617641 4 0.2784 0.62916 0.028 0.072 0.000 0.888 0.012
#> GSM617643 2 0.3464 0.67447 0.008 0.848 0.008 0.108 0.028
#> GSM617644 4 0.6901 0.30227 0.008 0.320 0.000 0.428 0.244
#> GSM617647 2 0.3130 0.69491 0.096 0.856 0.000 0.048 0.000
#> GSM617648 4 0.7362 0.08202 0.032 0.364 0.000 0.372 0.232
#> GSM617649 2 0.3623 0.68861 0.000 0.848 0.052 0.072 0.028
#> GSM617650 3 0.5899 0.15847 0.404 0.052 0.520 0.000 0.024
#> GSM617651 1 0.5362 0.45556 0.672 0.080 0.012 0.000 0.236
#> GSM617653 1 0.2388 0.52245 0.904 0.004 0.004 0.012 0.076
#> GSM617654 2 0.2438 0.70996 0.040 0.908 0.000 0.008 0.044
#> GSM617583 3 0.4465 0.64770 0.052 0.004 0.780 0.016 0.148
#> GSM617584 4 0.5816 0.32739 0.304 0.056 0.000 0.608 0.032
#> GSM617585 4 0.5502 0.44532 0.008 0.024 0.104 0.716 0.148
#> GSM617586 3 0.1893 0.69019 0.000 0.028 0.936 0.012 0.024
#> GSM617587 3 0.2532 0.68038 0.000 0.088 0.892 0.012 0.008
#> GSM617589 5 0.5914 -0.35483 0.036 0.036 0.000 0.456 0.472
#> GSM617591 3 0.7434 0.27471 0.000 0.128 0.496 0.276 0.100
#> GSM617593 1 0.4180 0.51089 0.804 0.076 0.104 0.000 0.016
#> GSM617594 2 0.4031 0.68808 0.008 0.836 0.048 0.060 0.048
#> GSM617595 1 0.6382 0.41929 0.608 0.228 0.040 0.000 0.124
#> GSM617596 1 0.5323 0.36137 0.688 0.012 0.008 0.060 0.232
#> GSM617597 3 0.2568 0.67563 0.092 0.016 0.888 0.000 0.004
#> GSM617598 1 0.4019 0.50812 0.820 0.004 0.072 0.012 0.092
#> GSM617599 2 0.6862 0.49893 0.116 0.604 0.000 0.148 0.132
#> GSM617600 3 0.1934 0.68156 0.000 0.020 0.932 0.008 0.040
#> GSM617601 2 0.6890 -0.00799 0.000 0.456 0.064 0.396 0.084
#> GSM617602 3 0.6785 0.06413 0.056 0.000 0.508 0.092 0.344
#> GSM617603 4 0.3798 0.58503 0.000 0.064 0.000 0.808 0.128
#> GSM617604 1 0.6846 0.22212 0.576 0.000 0.060 0.152 0.212
#> GSM617605 4 0.2404 0.61180 0.016 0.024 0.004 0.916 0.040
#> GSM617606 4 0.6850 0.34481 0.008 0.064 0.068 0.524 0.336
#> GSM617610 1 0.5486 0.47372 0.696 0.104 0.024 0.000 0.176
#> GSM617611 3 0.8447 -0.02354 0.304 0.168 0.344 0.004 0.180
#> GSM617613 3 0.2492 0.67535 0.000 0.020 0.908 0.024 0.048
#> GSM617614 3 0.3413 0.64929 0.100 0.000 0.844 0.004 0.052
#> GSM617621 1 0.4448 0.49168 0.808 0.044 0.008 0.052 0.088
#> GSM617629 5 0.8119 0.32540 0.048 0.040 0.224 0.232 0.456
#> GSM617630 2 0.6880 0.26636 0.004 0.512 0.336 0.048 0.100
#> GSM617631 3 0.4286 0.57997 0.024 0.000 0.784 0.036 0.156
#> GSM617633 3 0.8131 -0.14080 0.164 0.144 0.368 0.000 0.324
#> GSM617642 3 0.2907 0.67000 0.096 0.004 0.876 0.008 0.016
#> GSM617645 2 0.2187 0.70671 0.004 0.920 0.008 0.056 0.012
#> GSM617646 2 0.4293 0.64046 0.156 0.784 0.032 0.000 0.028
#> GSM617652 3 0.3496 0.65888 0.040 0.124 0.832 0.000 0.004
#> GSM617655 3 0.2006 0.68599 0.000 0.020 0.932 0.024 0.024
#> GSM617656 3 0.0609 0.68522 0.000 0.000 0.980 0.000 0.020
#> GSM617657 3 0.6217 0.40409 0.000 0.028 0.620 0.140 0.212
#> GSM617658 5 0.8133 0.17078 0.272 0.000 0.284 0.100 0.344
#> GSM617659 1 0.5096 0.04996 0.520 0.000 0.444 0.000 0.036
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM617581 1 0.4961 0.2043 0.560 0.008 0.000 0.388 0.036 0.008
#> GSM617582 5 0.3573 0.5993 0.036 0.000 0.004 0.044 0.832 0.084
#> GSM617588 4 0.4046 0.5260 0.012 0.048 0.000 0.808 0.048 0.084
#> GSM617590 4 0.3410 0.5389 0.000 0.024 0.012 0.848 0.068 0.048
#> GSM617592 4 0.2044 0.5757 0.068 0.008 0.000 0.912 0.008 0.004
#> GSM617607 2 0.5827 0.5146 0.216 0.632 0.092 0.000 0.044 0.016
#> GSM617608 3 0.6379 0.3534 0.156 0.004 0.472 0.000 0.032 0.336
#> GSM617609 3 0.2266 0.6855 0.000 0.108 0.880 0.012 0.000 0.000
#> GSM617612 1 0.6692 0.1902 0.496 0.048 0.324 0.032 0.000 0.100
#> GSM617615 6 0.7188 0.3497 0.000 0.140 0.164 0.268 0.000 0.428
#> GSM617616 5 0.6650 0.3937 0.152 0.060 0.000 0.004 0.480 0.304
#> GSM617617 2 0.3650 0.6356 0.020 0.820 0.000 0.012 0.116 0.032
#> GSM617618 5 0.4248 0.6097 0.048 0.044 0.000 0.000 0.768 0.140
#> GSM617619 3 0.6445 0.3804 0.000 0.204 0.596 0.084 0.088 0.028
#> GSM617620 4 0.3005 0.5682 0.036 0.088 0.000 0.860 0.004 0.012
#> GSM617622 4 0.5979 0.4381 0.036 0.068 0.000 0.624 0.228 0.044
#> GSM617623 1 0.4900 0.2952 0.604 0.012 0.000 0.344 0.028 0.012
#> GSM617624 2 0.4642 0.6327 0.008 0.756 0.048 0.028 0.148 0.012
#> GSM617625 3 0.4428 0.6067 0.052 0.000 0.676 0.000 0.004 0.268
#> GSM617626 1 0.5844 0.5020 0.684 0.100 0.000 0.104 0.064 0.048
#> GSM617627 2 0.5155 0.5337 0.000 0.680 0.184 0.112 0.008 0.016
#> GSM617628 3 0.4520 0.5729 0.020 0.000 0.664 0.020 0.004 0.292
#> GSM617632 5 0.4963 0.3829 0.352 0.036 0.000 0.008 0.592 0.012
#> GSM617634 5 0.4650 0.5148 0.004 0.112 0.000 0.016 0.732 0.136
#> GSM617635 2 0.4432 0.6562 0.072 0.780 0.096 0.000 0.016 0.036
#> GSM617636 5 0.4318 0.6043 0.180 0.028 0.020 0.004 0.756 0.012
#> GSM617637 2 0.5853 0.2447 0.364 0.504 0.000 0.000 0.028 0.104
#> GSM617638 2 0.5204 0.5806 0.016 0.696 0.020 0.036 0.208 0.024
#> GSM617639 1 0.4747 0.1063 0.564 0.400 0.020 0.004 0.004 0.008
#> GSM617640 2 0.1750 0.6815 0.000 0.928 0.004 0.056 0.008 0.004
#> GSM617641 4 0.2082 0.5836 0.040 0.036 0.000 0.916 0.004 0.004
#> GSM617643 2 0.3648 0.6524 0.000 0.832 0.008 0.040 0.044 0.076
#> GSM617644 6 0.7255 0.2043 0.004 0.220 0.000 0.128 0.200 0.448
#> GSM617647 2 0.4085 0.6612 0.112 0.792 0.000 0.068 0.012 0.016
#> GSM617648 5 0.6717 0.1154 0.004 0.324 0.000 0.044 0.436 0.192
#> GSM617649 2 0.4467 0.6451 0.000 0.788 0.064 0.068 0.028 0.052
#> GSM617650 3 0.5548 0.4264 0.296 0.020 0.604 0.000 0.024 0.056
#> GSM617651 1 0.5122 0.3640 0.516 0.044 0.012 0.000 0.004 0.424
#> GSM617653 1 0.2521 0.5731 0.896 0.000 0.012 0.056 0.008 0.028
#> GSM617654 2 0.2195 0.6883 0.024 0.920 0.008 0.016 0.028 0.004
#> GSM617583 3 0.3641 0.6936 0.052 0.000 0.812 0.012 0.004 0.120
#> GSM617584 4 0.4105 0.3110 0.348 0.020 0.000 0.632 0.000 0.000
#> GSM617585 4 0.6004 0.1523 0.000 0.016 0.024 0.484 0.396 0.080
#> GSM617586 3 0.1699 0.7102 0.000 0.032 0.936 0.016 0.000 0.016
#> GSM617587 3 0.2597 0.6922 0.004 0.088 0.880 0.020 0.000 0.008
#> GSM617589 6 0.4000 0.3750 0.028 0.000 0.004 0.220 0.008 0.740
#> GSM617591 3 0.6013 0.2502 0.000 0.080 0.556 0.292 0.000 0.072
#> GSM617593 1 0.3832 0.5583 0.824 0.056 0.072 0.000 0.032 0.016
#> GSM617594 2 0.5227 0.6228 0.004 0.728 0.108 0.060 0.016 0.084
#> GSM617595 1 0.6745 0.2497 0.420 0.244 0.028 0.000 0.008 0.300
#> GSM617596 1 0.5124 0.4035 0.660 0.004 0.008 0.080 0.240 0.008
#> GSM617597 3 0.2609 0.7093 0.112 0.008 0.868 0.000 0.008 0.004
#> GSM617598 1 0.5159 0.4905 0.624 0.000 0.032 0.000 0.056 0.288
#> GSM617599 2 0.6942 0.0405 0.020 0.420 0.000 0.028 0.236 0.296
#> GSM617600 3 0.2429 0.7029 0.000 0.008 0.888 0.008 0.088 0.008
#> GSM617601 4 0.6845 -0.1318 0.000 0.352 0.088 0.440 0.008 0.112
#> GSM617602 5 0.4009 0.5046 0.032 0.000 0.196 0.008 0.756 0.008
#> GSM617603 4 0.6549 0.1141 0.004 0.048 0.000 0.480 0.312 0.156
#> GSM617604 1 0.5867 0.4259 0.584 0.000 0.020 0.216 0.176 0.004
#> GSM617605 4 0.2025 0.5805 0.004 0.004 0.004 0.920 0.052 0.016
#> GSM617606 6 0.7698 0.2757 0.004 0.048 0.080 0.340 0.140 0.388
#> GSM617610 1 0.4866 0.4872 0.664 0.064 0.012 0.000 0.004 0.256
#> GSM617611 3 0.6471 0.4255 0.224 0.068 0.548 0.004 0.000 0.156
#> GSM617613 3 0.3019 0.6752 0.000 0.012 0.840 0.020 0.128 0.000
#> GSM617614 3 0.4090 0.6743 0.120 0.000 0.784 0.008 0.076 0.012
#> GSM617621 1 0.3310 0.5531 0.824 0.016 0.000 0.132 0.028 0.000
#> GSM617629 5 0.1854 0.6140 0.004 0.020 0.020 0.008 0.936 0.012
#> GSM617630 2 0.6935 0.1691 0.008 0.444 0.380 0.068 0.068 0.032
#> GSM617631 3 0.4667 0.3567 0.016 0.000 0.584 0.016 0.380 0.004
#> GSM617633 5 0.5168 0.5936 0.040 0.132 0.044 0.000 0.728 0.056
#> GSM617642 3 0.2891 0.7082 0.096 0.000 0.864 0.024 0.008 0.008
#> GSM617645 2 0.3832 0.6361 0.020 0.808 0.044 0.120 0.004 0.004
#> GSM617646 2 0.4300 0.6715 0.104 0.788 0.036 0.000 0.016 0.056
#> GSM617652 3 0.2393 0.7006 0.020 0.092 0.884 0.004 0.000 0.000
#> GSM617655 3 0.1629 0.7131 0.000 0.012 0.944 0.020 0.012 0.012
#> GSM617656 3 0.0858 0.7149 0.000 0.004 0.968 0.000 0.028 0.000
#> GSM617657 3 0.6121 0.1053 0.000 0.012 0.448 0.108 0.412 0.020
#> GSM617658 5 0.5721 0.4971 0.140 0.000 0.148 0.044 0.656 0.012
#> GSM617659 1 0.5422 -0.0920 0.464 0.000 0.456 0.000 0.044 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) k
#> SD:NMF 77 0.01538 2
#> SD:NMF 67 0.00435 3
#> SD:NMF 55 0.00373 4
#> SD:NMF 39 0.02477 5
#> SD:NMF 45 0.02113 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 79 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 0.233 0.703 0.832 0.226 0.926 0.926
#> 3 3 0.193 0.642 0.807 0.709 0.786 0.769
#> 4 4 0.320 0.630 0.821 0.247 0.895 0.853
#> 5 5 0.291 0.506 0.754 0.155 0.841 0.749
#> 6 6 0.295 0.612 0.768 0.121 0.847 0.706
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
#> GSM617581 1 0.2603 0.799 0.956 0.044
#> GSM617582 1 0.2603 0.790 0.956 0.044
#> GSM617588 1 0.8267 0.621 0.740 0.260
#> GSM617590 1 0.8267 0.621 0.740 0.260
#> GSM617592 1 0.8207 0.628 0.744 0.256
#> GSM617607 1 0.0938 0.797 0.988 0.012
#> GSM617608 1 0.2236 0.789 0.964 0.036
#> GSM617609 1 0.7056 0.598 0.808 0.192
#> GSM617612 1 0.1184 0.794 0.984 0.016
#> GSM617615 1 0.6531 0.739 0.832 0.168
#> GSM617616 1 0.1184 0.796 0.984 0.016
#> GSM617617 1 0.6623 0.736 0.828 0.172
#> GSM617618 1 0.1184 0.796 0.984 0.016
#> GSM617619 1 0.7299 0.652 0.796 0.204
#> GSM617620 1 0.8016 0.650 0.756 0.244
#> GSM617622 1 0.6247 0.743 0.844 0.156
#> GSM617623 1 0.1414 0.795 0.980 0.020
#> GSM617624 1 0.5946 0.765 0.856 0.144
#> GSM617625 1 0.5737 0.704 0.864 0.136
#> GSM617626 1 0.2236 0.799 0.964 0.036
#> GSM617627 1 0.6438 0.744 0.836 0.164
#> GSM617628 1 0.5842 0.700 0.860 0.140
#> GSM617632 1 0.0672 0.795 0.992 0.008
#> GSM617634 1 0.7376 0.645 0.792 0.208
#> GSM617635 1 0.1843 0.797 0.972 0.028
#> GSM617636 1 0.0672 0.794 0.992 0.008
#> GSM617637 1 0.1414 0.798 0.980 0.020
#> GSM617638 1 0.7376 0.675 0.792 0.208
#> GSM617639 1 0.1414 0.793 0.980 0.020
#> GSM617640 1 0.7056 0.710 0.808 0.192
#> GSM617641 1 0.8327 0.618 0.736 0.264
#> GSM617643 1 0.6623 0.726 0.828 0.172
#> GSM617644 1 0.8144 0.634 0.748 0.252
#> GSM617647 1 0.5629 0.762 0.868 0.132
#> GSM617648 1 0.6438 0.740 0.836 0.164
#> GSM617649 1 0.6438 0.741 0.836 0.164
#> GSM617650 1 0.1843 0.794 0.972 0.028
#> GSM617651 1 0.0672 0.796 0.992 0.008
#> GSM617653 1 0.0672 0.796 0.992 0.008
#> GSM617654 1 0.8861 0.517 0.696 0.304
#> GSM617583 1 0.3274 0.780 0.940 0.060
#> GSM617584 1 0.6973 0.710 0.812 0.188
#> GSM617585 2 0.9993 0.496 0.484 0.516
#> GSM617586 1 0.7376 0.557 0.792 0.208
#> GSM617587 1 0.7219 0.577 0.800 0.200
#> GSM617589 1 0.8267 0.621 0.740 0.260
#> GSM617591 1 0.7453 0.656 0.788 0.212
#> GSM617593 1 0.2236 0.789 0.964 0.036
#> GSM617594 1 0.5629 0.762 0.868 0.132
#> GSM617595 1 0.0938 0.797 0.988 0.012
#> GSM617596 1 0.0672 0.796 0.992 0.008
#> GSM617597 1 0.4815 0.737 0.896 0.104
#> GSM617598 1 0.0938 0.794 0.988 0.012
#> GSM617599 1 0.5408 0.768 0.876 0.124
#> GSM617600 1 0.7056 0.605 0.808 0.192
#> GSM617601 1 0.7299 0.704 0.796 0.204
#> GSM617602 1 0.5178 0.730 0.884 0.116
#> GSM617603 1 0.8267 0.622 0.740 0.260
#> GSM617604 1 0.2948 0.795 0.948 0.052
#> GSM617605 1 0.8327 0.615 0.736 0.264
#> GSM617606 1 0.6623 0.748 0.828 0.172
#> GSM617610 1 0.1184 0.794 0.984 0.016
#> GSM617611 1 0.2603 0.788 0.956 0.044
#> GSM617613 1 0.9963 -0.558 0.536 0.464
#> GSM617614 1 0.4161 0.766 0.916 0.084
#> GSM617621 1 0.2043 0.799 0.968 0.032
#> GSM617629 2 0.9393 0.808 0.356 0.644
#> GSM617630 1 0.8443 0.573 0.728 0.272
#> GSM617631 1 0.5519 0.719 0.872 0.128
#> GSM617633 1 0.3274 0.785 0.940 0.060
#> GSM617642 1 0.6148 0.679 0.848 0.152
#> GSM617645 1 0.8861 0.512 0.696 0.304
#> GSM617646 1 0.1633 0.798 0.976 0.024
#> GSM617652 1 0.1843 0.792 0.972 0.028
#> GSM617655 1 0.7453 0.549 0.788 0.212
#> GSM617656 1 0.7139 0.597 0.804 0.196
#> GSM617657 2 0.9248 0.805 0.340 0.660
#> GSM617658 1 0.4939 0.738 0.892 0.108
#> GSM617659 1 0.3274 0.776 0.940 0.060
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM617581 1 0.2599 0.779 0.932 0.052 0.016
#> GSM617582 1 0.1999 0.781 0.952 0.012 0.036
#> GSM617588 2 0.4121 0.807 0.168 0.832 0.000
#> GSM617590 2 0.4409 0.809 0.172 0.824 0.004
#> GSM617592 2 0.4629 0.803 0.188 0.808 0.004
#> GSM617607 1 0.1182 0.781 0.976 0.012 0.012
#> GSM617608 1 0.1832 0.781 0.956 0.008 0.036
#> GSM617609 1 0.5253 0.663 0.792 0.020 0.188
#> GSM617612 1 0.1170 0.780 0.976 0.008 0.016
#> GSM617615 1 0.7074 -0.216 0.500 0.480 0.020
#> GSM617616 1 0.1636 0.782 0.964 0.020 0.016
#> GSM617617 1 0.7031 0.580 0.716 0.196 0.088
#> GSM617618 1 0.1636 0.782 0.964 0.020 0.016
#> GSM617619 1 0.6920 0.622 0.732 0.104 0.164
#> GSM617620 2 0.6587 0.568 0.352 0.632 0.016
#> GSM617622 1 0.6908 0.424 0.656 0.308 0.036
#> GSM617623 1 0.2301 0.775 0.936 0.060 0.004
#> GSM617624 1 0.6481 0.600 0.728 0.224 0.048
#> GSM617625 1 0.4059 0.739 0.860 0.012 0.128
#> GSM617626 1 0.2031 0.784 0.952 0.032 0.016
#> GSM617627 1 0.6872 0.487 0.680 0.276 0.044
#> GSM617628 1 0.3784 0.733 0.864 0.004 0.132
#> GSM617632 1 0.1315 0.780 0.972 0.020 0.008
#> GSM617634 1 0.6875 0.621 0.724 0.080 0.196
#> GSM617635 1 0.1129 0.783 0.976 0.004 0.020
#> GSM617636 1 0.0475 0.780 0.992 0.004 0.004
#> GSM617637 1 0.1905 0.783 0.956 0.028 0.016
#> GSM617638 1 0.6886 0.609 0.728 0.088 0.184
#> GSM617639 1 0.0983 0.780 0.980 0.004 0.016
#> GSM617640 1 0.7844 0.438 0.652 0.240 0.108
#> GSM617641 2 0.4645 0.806 0.176 0.816 0.008
#> GSM617643 1 0.6702 0.381 0.648 0.328 0.024
#> GSM617644 2 0.6404 0.595 0.344 0.644 0.012
#> GSM617647 1 0.6099 0.595 0.740 0.228 0.032
#> GSM617648 1 0.6387 0.456 0.680 0.300 0.020
#> GSM617649 1 0.6420 0.479 0.688 0.288 0.024
#> GSM617650 1 0.0892 0.782 0.980 0.000 0.020
#> GSM617651 1 0.1315 0.780 0.972 0.020 0.008
#> GSM617653 1 0.1453 0.780 0.968 0.024 0.008
#> GSM617654 1 0.8868 0.123 0.576 0.196 0.228
#> GSM617583 1 0.2280 0.780 0.940 0.008 0.052
#> GSM617584 2 0.6521 0.276 0.492 0.504 0.004
#> GSM617585 3 0.9738 0.306 0.344 0.232 0.424
#> GSM617586 1 0.5171 0.641 0.784 0.012 0.204
#> GSM617587 1 0.5253 0.657 0.792 0.020 0.188
#> GSM617589 2 0.4121 0.806 0.168 0.832 0.000
#> GSM617591 1 0.7670 0.561 0.684 0.152 0.164
#> GSM617593 1 0.1525 0.779 0.964 0.004 0.032
#> GSM617594 1 0.5982 0.588 0.744 0.228 0.028
#> GSM617595 1 0.1129 0.782 0.976 0.020 0.004
#> GSM617596 1 0.1170 0.781 0.976 0.016 0.008
#> GSM617597 1 0.3532 0.754 0.884 0.008 0.108
#> GSM617598 1 0.1182 0.781 0.976 0.012 0.012
#> GSM617599 1 0.6067 0.594 0.736 0.236 0.028
#> GSM617600 1 0.4808 0.673 0.804 0.008 0.188
#> GSM617601 1 0.7310 0.254 0.600 0.360 0.040
#> GSM617602 1 0.3573 0.743 0.876 0.004 0.120
#> GSM617603 2 0.4589 0.805 0.172 0.820 0.008
#> GSM617604 1 0.2550 0.783 0.936 0.024 0.040
#> GSM617605 2 0.4531 0.804 0.168 0.824 0.008
#> GSM617606 1 0.8286 0.313 0.588 0.308 0.104
#> GSM617610 1 0.1170 0.780 0.976 0.008 0.016
#> GSM617611 1 0.1832 0.783 0.956 0.008 0.036
#> GSM617613 1 0.6816 -0.247 0.516 0.012 0.472
#> GSM617614 1 0.2682 0.768 0.920 0.004 0.076
#> GSM617621 1 0.1877 0.783 0.956 0.032 0.012
#> GSM617629 3 0.5098 0.730 0.248 0.000 0.752
#> GSM617630 1 0.8557 0.207 0.608 0.180 0.212
#> GSM617631 1 0.3965 0.734 0.860 0.008 0.132
#> GSM617633 1 0.2301 0.775 0.936 0.004 0.060
#> GSM617642 1 0.4411 0.716 0.844 0.016 0.140
#> GSM617645 1 0.8940 0.113 0.568 0.200 0.232
#> GSM617646 1 0.1774 0.784 0.960 0.024 0.016
#> GSM617652 1 0.1751 0.782 0.960 0.012 0.028
#> GSM617655 1 0.5503 0.633 0.772 0.020 0.208
#> GSM617656 1 0.4861 0.668 0.800 0.008 0.192
#> GSM617657 3 0.5986 0.734 0.240 0.024 0.736
#> GSM617658 1 0.3607 0.751 0.880 0.008 0.112
#> GSM617659 1 0.1860 0.775 0.948 0.000 0.052
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM617581 1 0.3303 0.7859 0.892 0.028 0.048 0.032
#> GSM617582 1 0.2140 0.7950 0.932 0.008 0.052 0.008
#> GSM617588 4 0.0469 0.6934 0.012 0.000 0.000 0.988
#> GSM617590 4 0.0524 0.6876 0.004 0.000 0.008 0.988
#> GSM617592 4 0.1042 0.6909 0.020 0.000 0.008 0.972
#> GSM617607 1 0.1182 0.7912 0.968 0.016 0.016 0.000
#> GSM617608 1 0.1356 0.7923 0.960 0.008 0.032 0.000
#> GSM617609 1 0.4612 0.6645 0.764 0.008 0.212 0.016
#> GSM617612 1 0.0804 0.7907 0.980 0.008 0.012 0.000
#> GSM617615 4 0.7289 0.0373 0.432 0.080 0.024 0.464
#> GSM617616 1 0.1871 0.7932 0.948 0.016 0.024 0.012
#> GSM617617 1 0.7072 0.3947 0.596 0.284 0.024 0.096
#> GSM617618 1 0.1993 0.7935 0.944 0.016 0.024 0.016
#> GSM617619 1 0.7323 0.4961 0.640 0.080 0.196 0.084
#> GSM617620 4 0.5628 0.4311 0.236 0.052 0.008 0.704
#> GSM617622 1 0.7296 0.4267 0.600 0.072 0.056 0.272
#> GSM617623 1 0.3027 0.7809 0.904 0.024 0.032 0.040
#> GSM617624 1 0.6764 0.5831 0.688 0.108 0.052 0.152
#> GSM617625 1 0.3196 0.7517 0.856 0.000 0.136 0.008
#> GSM617626 1 0.2495 0.7937 0.924 0.028 0.036 0.012
#> GSM617627 1 0.7196 0.4566 0.612 0.120 0.028 0.240
#> GSM617628 1 0.3052 0.7490 0.860 0.000 0.136 0.004
#> GSM617632 1 0.1593 0.7903 0.956 0.016 0.024 0.004
#> GSM617634 1 0.6494 0.5688 0.680 0.072 0.212 0.036
#> GSM617635 1 0.1724 0.7960 0.948 0.020 0.032 0.000
#> GSM617636 1 0.1388 0.7931 0.960 0.012 0.028 0.000
#> GSM617637 1 0.1911 0.7935 0.944 0.032 0.020 0.004
#> GSM617638 1 0.6964 0.4998 0.656 0.144 0.168 0.032
#> GSM617639 1 0.1284 0.7915 0.964 0.012 0.024 0.000
#> GSM617640 1 0.8235 -0.2111 0.416 0.364 0.024 0.196
#> GSM617641 4 0.1007 0.6888 0.008 0.008 0.008 0.976
#> GSM617643 1 0.7008 0.3847 0.580 0.080 0.024 0.316
#> GSM617644 4 0.5843 0.4616 0.200 0.068 0.016 0.716
#> GSM617647 1 0.6474 0.5858 0.696 0.104 0.032 0.168
#> GSM617648 1 0.6680 0.4857 0.640 0.080 0.024 0.256
#> GSM617649 1 0.6831 0.4894 0.640 0.076 0.036 0.248
#> GSM617650 1 0.1109 0.7930 0.968 0.004 0.028 0.000
#> GSM617651 1 0.1707 0.7881 0.952 0.020 0.024 0.004
#> GSM617653 1 0.1920 0.7876 0.944 0.028 0.024 0.004
#> GSM617654 2 0.2466 0.7495 0.096 0.900 0.000 0.004
#> GSM617583 1 0.1930 0.7920 0.936 0.004 0.056 0.004
#> GSM617584 4 0.6580 0.1066 0.424 0.040 0.020 0.516
#> GSM617585 3 0.7843 0.3056 0.220 0.008 0.472 0.300
#> GSM617586 1 0.4479 0.6481 0.760 0.008 0.224 0.008
#> GSM617587 1 0.4574 0.6640 0.768 0.008 0.208 0.016
#> GSM617589 4 0.1114 0.6866 0.016 0.004 0.008 0.972
#> GSM617591 1 0.8233 0.3362 0.568 0.092 0.188 0.152
#> GSM617593 1 0.1545 0.7922 0.952 0.008 0.040 0.000
#> GSM617594 1 0.6511 0.5714 0.692 0.092 0.036 0.180
#> GSM617595 1 0.1271 0.7931 0.968 0.012 0.008 0.012
#> GSM617596 1 0.1509 0.7920 0.960 0.020 0.012 0.008
#> GSM617597 1 0.2805 0.7697 0.888 0.012 0.100 0.000
#> GSM617598 1 0.0937 0.7906 0.976 0.012 0.012 0.000
#> GSM617599 1 0.6432 0.5802 0.700 0.092 0.036 0.172
#> GSM617600 1 0.4230 0.6795 0.776 0.004 0.212 0.008
#> GSM617601 1 0.7486 0.2764 0.532 0.104 0.028 0.336
#> GSM617602 1 0.2814 0.7576 0.868 0.000 0.132 0.000
#> GSM617603 4 0.0844 0.6827 0.004 0.004 0.012 0.980
#> GSM617604 1 0.2957 0.7913 0.900 0.016 0.068 0.016
#> GSM617605 4 0.0804 0.6902 0.008 0.000 0.012 0.980
#> GSM617606 1 0.8651 -0.0490 0.464 0.124 0.092 0.320
#> GSM617610 1 0.0804 0.7907 0.980 0.008 0.012 0.000
#> GSM617611 1 0.1585 0.7939 0.952 0.004 0.040 0.004
#> GSM617613 3 0.5562 0.0530 0.460 0.004 0.524 0.012
#> GSM617614 1 0.2011 0.7829 0.920 0.000 0.080 0.000
#> GSM617621 1 0.2499 0.7919 0.924 0.032 0.032 0.012
#> GSM617629 3 0.3335 0.3163 0.120 0.020 0.860 0.000
#> GSM617630 2 0.4034 0.8203 0.180 0.804 0.012 0.004
#> GSM617631 1 0.3157 0.7487 0.852 0.000 0.144 0.004
#> GSM617633 1 0.2053 0.7896 0.924 0.004 0.072 0.000
#> GSM617642 1 0.3712 0.7312 0.832 0.004 0.152 0.012
#> GSM617645 2 0.4662 0.7736 0.204 0.768 0.016 0.012
#> GSM617646 1 0.2096 0.7950 0.940 0.028 0.016 0.016
#> GSM617652 1 0.1471 0.7951 0.960 0.012 0.024 0.004
#> GSM617655 1 0.4707 0.6377 0.744 0.008 0.236 0.012
#> GSM617656 1 0.4163 0.6772 0.772 0.004 0.220 0.004
#> GSM617657 3 0.2363 0.2748 0.056 0.000 0.920 0.024
#> GSM617658 1 0.2760 0.7640 0.872 0.000 0.128 0.000
#> GSM617659 1 0.1557 0.7872 0.944 0.000 0.056 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM617581 1 0.3374 0.6893 0.852 0.100 0.032 0.016 0.000
#> GSM617582 1 0.2054 0.7422 0.920 0.052 0.028 0.000 0.000
#> GSM617588 4 0.0510 0.6929 0.000 0.016 0.000 0.984 0.000
#> GSM617590 4 0.0771 0.6950 0.000 0.020 0.000 0.976 0.004
#> GSM617592 4 0.1365 0.6920 0.000 0.040 0.004 0.952 0.004
#> GSM617607 1 0.1618 0.7312 0.944 0.040 0.008 0.000 0.008
#> GSM617608 1 0.1630 0.7428 0.944 0.036 0.016 0.000 0.004
#> GSM617609 1 0.4960 0.5780 0.728 0.160 0.104 0.008 0.000
#> GSM617612 1 0.1124 0.7363 0.960 0.036 0.000 0.000 0.004
#> GSM617615 4 0.7314 -0.4084 0.256 0.308 0.004 0.412 0.020
#> GSM617616 1 0.1990 0.7339 0.928 0.052 0.004 0.012 0.004
#> GSM617617 2 0.7363 0.5831 0.352 0.396 0.000 0.036 0.216
#> GSM617618 1 0.2197 0.7301 0.916 0.064 0.004 0.012 0.004
#> GSM617619 1 0.7336 0.0901 0.568 0.236 0.104 0.044 0.048
#> GSM617620 4 0.6077 0.3868 0.124 0.216 0.004 0.636 0.020
#> GSM617622 2 0.7267 0.7692 0.372 0.416 0.024 0.180 0.008
#> GSM617623 1 0.3940 0.6449 0.812 0.140 0.020 0.024 0.004
#> GSM617624 1 0.6327 -0.5327 0.492 0.412 0.008 0.064 0.024
#> GSM617625 1 0.3384 0.6989 0.848 0.088 0.060 0.004 0.000
#> GSM617626 1 0.2452 0.7226 0.896 0.084 0.016 0.000 0.004
#> GSM617627 2 0.7094 0.7840 0.376 0.436 0.004 0.156 0.028
#> GSM617628 1 0.3169 0.6992 0.856 0.084 0.060 0.000 0.000
#> GSM617632 1 0.1990 0.7256 0.920 0.068 0.008 0.000 0.004
#> GSM617634 1 0.6837 -0.1298 0.524 0.328 0.108 0.016 0.024
#> GSM617635 1 0.1717 0.7415 0.936 0.052 0.004 0.000 0.008
#> GSM617636 1 0.1862 0.7357 0.932 0.048 0.016 0.000 0.004
#> GSM617637 1 0.2166 0.7308 0.912 0.072 0.004 0.000 0.012
#> GSM617638 1 0.7646 -0.3242 0.472 0.316 0.088 0.012 0.112
#> GSM617639 1 0.1412 0.7369 0.952 0.036 0.008 0.000 0.004
#> GSM617640 5 0.8422 -0.2437 0.272 0.224 0.000 0.168 0.336
#> GSM617641 4 0.0880 0.6931 0.000 0.032 0.000 0.968 0.000
#> GSM617643 2 0.6819 0.7690 0.316 0.476 0.004 0.196 0.008
#> GSM617644 4 0.5650 0.4318 0.076 0.288 0.004 0.624 0.008
#> GSM617647 1 0.6472 -0.4461 0.536 0.344 0.004 0.084 0.032
#> GSM617648 2 0.6582 0.8063 0.380 0.476 0.004 0.128 0.012
#> GSM617649 2 0.6796 0.7957 0.388 0.460 0.012 0.128 0.012
#> GSM617650 1 0.0992 0.7407 0.968 0.024 0.008 0.000 0.000
#> GSM617651 1 0.2102 0.7189 0.916 0.068 0.012 0.000 0.004
#> GSM617653 1 0.2332 0.7143 0.904 0.076 0.016 0.000 0.004
#> GSM617654 5 0.1173 0.3531 0.012 0.020 0.004 0.000 0.964
#> GSM617583 1 0.2005 0.7389 0.924 0.056 0.016 0.004 0.000
#> GSM617584 4 0.7168 -0.3003 0.292 0.220 0.016 0.464 0.008
#> GSM617585 3 0.8417 0.2965 0.148 0.272 0.296 0.284 0.000
#> GSM617586 1 0.4911 0.5746 0.728 0.148 0.120 0.004 0.000
#> GSM617587 1 0.4970 0.5785 0.728 0.156 0.108 0.008 0.000
#> GSM617589 4 0.0981 0.6826 0.012 0.008 0.000 0.972 0.008
#> GSM617591 1 0.8369 -0.3171 0.460 0.276 0.100 0.104 0.060
#> GSM617593 1 0.1605 0.7411 0.944 0.040 0.012 0.000 0.004
#> GSM617594 1 0.6146 -0.6175 0.484 0.412 0.000 0.092 0.012
#> GSM617595 1 0.1730 0.7338 0.940 0.044 0.004 0.008 0.004
#> GSM617596 1 0.1996 0.7301 0.932 0.040 0.016 0.008 0.004
#> GSM617597 1 0.2928 0.7199 0.872 0.092 0.032 0.000 0.004
#> GSM617598 1 0.1124 0.7333 0.960 0.036 0.000 0.000 0.004
#> GSM617599 1 0.6312 -0.5673 0.500 0.392 0.004 0.088 0.016
#> GSM617600 1 0.4565 0.6115 0.760 0.124 0.112 0.004 0.000
#> GSM617601 2 0.7023 0.7373 0.300 0.444 0.000 0.240 0.016
#> GSM617602 1 0.3051 0.7045 0.864 0.060 0.076 0.000 0.000
#> GSM617603 4 0.1285 0.6821 0.000 0.036 0.004 0.956 0.004
#> GSM617604 1 0.3340 0.7186 0.860 0.076 0.048 0.016 0.000
#> GSM617605 4 0.0865 0.6929 0.000 0.024 0.000 0.972 0.004
#> GSM617606 1 0.8538 -0.4451 0.388 0.192 0.032 0.296 0.092
#> GSM617610 1 0.1124 0.7363 0.960 0.036 0.000 0.000 0.004
#> GSM617611 1 0.1443 0.7409 0.948 0.044 0.004 0.004 0.000
#> GSM617613 1 0.6930 -0.2094 0.376 0.324 0.296 0.004 0.000
#> GSM617614 1 0.2236 0.7334 0.908 0.068 0.024 0.000 0.000
#> GSM617621 1 0.2664 0.7134 0.884 0.092 0.020 0.000 0.004
#> GSM617629 3 0.3117 0.4090 0.100 0.036 0.860 0.000 0.004
#> GSM617630 5 0.3608 0.5021 0.148 0.040 0.000 0.000 0.812
#> GSM617631 1 0.3239 0.6975 0.852 0.068 0.080 0.000 0.000
#> GSM617633 1 0.2110 0.7375 0.912 0.072 0.016 0.000 0.000
#> GSM617642 1 0.3937 0.6643 0.804 0.132 0.060 0.004 0.000
#> GSM617645 5 0.4787 0.5236 0.152 0.088 0.000 0.012 0.748
#> GSM617646 1 0.2630 0.7173 0.892 0.080 0.000 0.012 0.016
#> GSM617652 1 0.1766 0.7412 0.940 0.040 0.012 0.004 0.004
#> GSM617655 1 0.5135 0.5421 0.704 0.172 0.120 0.004 0.000
#> GSM617656 1 0.4503 0.6125 0.756 0.120 0.124 0.000 0.000
#> GSM617657 3 0.5374 0.4681 0.024 0.376 0.580 0.012 0.008
#> GSM617658 1 0.2922 0.7120 0.872 0.056 0.072 0.000 0.000
#> GSM617659 1 0.1364 0.7384 0.952 0.036 0.012 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM617581 1 0.3564 0.7544 0.812 0.140 0.024 0.008 0.000 0.016
#> GSM617582 1 0.2307 0.8348 0.904 0.048 0.032 0.000 0.000 0.016
#> GSM617588 4 0.0777 0.7714 0.000 0.024 0.000 0.972 0.000 0.004
#> GSM617590 4 0.0858 0.7754 0.000 0.028 0.004 0.968 0.000 0.000
#> GSM617592 4 0.1440 0.7719 0.000 0.044 0.004 0.944 0.004 0.004
#> GSM617607 1 0.1995 0.8228 0.924 0.036 0.012 0.000 0.004 0.024
#> GSM617608 1 0.1719 0.8361 0.932 0.032 0.032 0.000 0.000 0.004
#> GSM617609 1 0.4676 0.6250 0.684 0.096 0.216 0.004 0.000 0.000
#> GSM617612 1 0.1483 0.8292 0.944 0.036 0.012 0.000 0.000 0.008
#> GSM617615 2 0.6931 0.1464 0.140 0.412 0.016 0.388 0.020 0.024
#> GSM617616 1 0.2299 0.8225 0.904 0.064 0.008 0.012 0.000 0.012
#> GSM617617 2 0.6393 0.4305 0.172 0.568 0.004 0.012 0.208 0.036
#> GSM617618 1 0.2392 0.8185 0.900 0.064 0.008 0.012 0.000 0.016
#> GSM617619 1 0.7038 -0.0565 0.484 0.252 0.184 0.024 0.056 0.000
#> GSM617620 4 0.4864 0.4260 0.016 0.352 0.000 0.600 0.020 0.012
#> GSM617622 2 0.6132 0.5303 0.192 0.620 0.028 0.128 0.004 0.028
#> GSM617623 1 0.4013 0.6964 0.764 0.184 0.008 0.012 0.000 0.032
#> GSM617624 2 0.5215 0.5219 0.328 0.600 0.036 0.012 0.024 0.000
#> GSM617625 1 0.3406 0.7796 0.816 0.040 0.136 0.004 0.000 0.004
#> GSM617626 1 0.2415 0.8171 0.888 0.084 0.012 0.000 0.000 0.016
#> GSM617627 2 0.5289 0.5627 0.180 0.688 0.020 0.088 0.024 0.000
#> GSM617628 1 0.3149 0.7811 0.824 0.044 0.132 0.000 0.000 0.000
#> GSM617632 1 0.2322 0.8080 0.896 0.064 0.004 0.000 0.000 0.036
#> GSM617634 2 0.7536 0.2443 0.344 0.400 0.148 0.020 0.016 0.072
#> GSM617635 1 0.1906 0.8356 0.928 0.040 0.016 0.000 0.008 0.008
#> GSM617636 1 0.1716 0.8295 0.932 0.036 0.004 0.000 0.000 0.028
#> GSM617637 1 0.2414 0.8248 0.896 0.072 0.012 0.000 0.008 0.012
#> GSM617638 2 0.8103 0.2671 0.312 0.388 0.116 0.012 0.104 0.068
#> GSM617639 1 0.1750 0.8290 0.932 0.040 0.012 0.000 0.000 0.016
#> GSM617640 2 0.7167 -0.0105 0.116 0.408 0.000 0.128 0.340 0.008
#> GSM617641 4 0.0937 0.7746 0.000 0.040 0.000 0.960 0.000 0.000
#> GSM617643 2 0.5061 0.4697 0.096 0.736 0.012 0.104 0.004 0.048
#> GSM617644 4 0.5295 0.4189 0.008 0.348 0.008 0.568 0.000 0.068
#> GSM617647 2 0.5392 0.5199 0.348 0.576 0.008 0.032 0.032 0.004
#> GSM617648 2 0.4847 0.5281 0.144 0.744 0.016 0.036 0.004 0.056
#> GSM617649 2 0.4864 0.5351 0.148 0.744 0.024 0.036 0.004 0.044
#> GSM617650 1 0.1552 0.8334 0.940 0.020 0.036 0.000 0.000 0.004
#> GSM617651 1 0.2704 0.7930 0.876 0.076 0.012 0.000 0.000 0.036
#> GSM617653 1 0.2833 0.7829 0.864 0.088 0.008 0.000 0.000 0.040
#> GSM617654 5 0.2536 0.5060 0.000 0.020 0.000 0.000 0.864 0.116
#> GSM617583 1 0.2352 0.8288 0.900 0.040 0.052 0.004 0.000 0.004
#> GSM617584 4 0.6712 -0.1372 0.192 0.344 0.008 0.428 0.008 0.020
#> GSM617585 3 0.7398 0.1808 0.100 0.128 0.460 0.276 0.000 0.036
#> GSM617586 1 0.4663 0.6139 0.672 0.080 0.244 0.000 0.000 0.004
#> GSM617587 1 0.4853 0.6069 0.664 0.108 0.224 0.000 0.000 0.004
#> GSM617589 4 0.0982 0.7596 0.004 0.020 0.004 0.968 0.004 0.000
#> GSM617591 2 0.7878 0.1759 0.324 0.352 0.188 0.076 0.060 0.000
#> GSM617593 1 0.1794 0.8341 0.932 0.024 0.028 0.000 0.000 0.016
#> GSM617594 2 0.4842 0.5702 0.284 0.656 0.012 0.036 0.008 0.004
#> GSM617595 1 0.1698 0.8305 0.936 0.044 0.008 0.004 0.004 0.004
#> GSM617596 1 0.1965 0.8250 0.924 0.040 0.008 0.004 0.000 0.024
#> GSM617597 1 0.3124 0.8096 0.844 0.032 0.108 0.000 0.000 0.016
#> GSM617598 1 0.1555 0.8261 0.940 0.040 0.012 0.000 0.000 0.008
#> GSM617599 2 0.5350 0.5440 0.332 0.592 0.020 0.040 0.012 0.004
#> GSM617600 1 0.4223 0.6747 0.720 0.076 0.204 0.000 0.000 0.000
#> GSM617601 2 0.4851 0.4830 0.100 0.708 0.008 0.172 0.012 0.000
#> GSM617602 1 0.2784 0.7954 0.848 0.028 0.124 0.000 0.000 0.000
#> GSM617603 4 0.1806 0.7543 0.000 0.044 0.008 0.928 0.000 0.020
#> GSM617604 1 0.3469 0.7880 0.828 0.112 0.036 0.004 0.000 0.020
#> GSM617605 4 0.0972 0.7722 0.000 0.028 0.008 0.964 0.000 0.000
#> GSM617606 1 0.8769 -0.5384 0.284 0.240 0.088 0.272 0.096 0.020
#> GSM617610 1 0.1483 0.8292 0.944 0.036 0.012 0.000 0.000 0.008
#> GSM617611 1 0.1860 0.8322 0.928 0.028 0.036 0.004 0.000 0.004
#> GSM617613 3 0.6427 0.1118 0.284 0.176 0.500 0.004 0.000 0.036
#> GSM617614 1 0.2294 0.8237 0.892 0.036 0.072 0.000 0.000 0.000
#> GSM617621 1 0.2615 0.8081 0.876 0.088 0.008 0.000 0.000 0.028
#> GSM617629 6 0.4062 0.0000 0.060 0.004 0.192 0.000 0.000 0.744
#> GSM617630 5 0.3281 0.6573 0.120 0.036 0.008 0.000 0.832 0.004
#> GSM617631 1 0.3054 0.7846 0.828 0.036 0.136 0.000 0.000 0.000
#> GSM617633 1 0.2138 0.8300 0.908 0.036 0.052 0.000 0.000 0.004
#> GSM617642 1 0.3991 0.7190 0.756 0.088 0.156 0.000 0.000 0.000
#> GSM617645 5 0.4341 0.6437 0.104 0.132 0.004 0.008 0.752 0.000
#> GSM617646 1 0.2850 0.8007 0.864 0.104 0.008 0.004 0.016 0.004
#> GSM617652 1 0.1852 0.8349 0.928 0.040 0.024 0.004 0.000 0.004
#> GSM617655 1 0.4791 0.5733 0.652 0.104 0.244 0.000 0.000 0.000
#> GSM617656 1 0.4340 0.6803 0.720 0.064 0.208 0.000 0.000 0.008
#> GSM617657 3 0.1680 -0.3056 0.016 0.004 0.936 0.004 0.000 0.040
#> GSM617658 1 0.2696 0.8077 0.856 0.028 0.116 0.000 0.000 0.000
#> GSM617659 1 0.1707 0.8294 0.928 0.012 0.056 0.000 0.000 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:hclust 77 0.440 2
#> CV:hclust 64 0.221 3
#> CV:hclust 59 0.775 4
#> CV:hclust 60 0.108 5
#> CV:hclust 62 0.417 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 79 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.998 0.955 0.981 0.4898 0.512 0.512
#> 3 3 0.538 0.539 0.773 0.2811 0.829 0.679
#> 4 4 0.609 0.793 0.857 0.1606 0.766 0.465
#> 5 5 0.668 0.644 0.803 0.0628 0.969 0.886
#> 6 6 0.679 0.544 0.743 0.0433 0.941 0.779
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
#> GSM617581 1 0.4815 0.875 0.896 0.104
#> GSM617582 1 0.0000 0.979 1.000 0.000
#> GSM617588 2 0.0000 0.983 0.000 1.000
#> GSM617590 2 0.0000 0.983 0.000 1.000
#> GSM617592 2 0.0000 0.983 0.000 1.000
#> GSM617607 1 0.0000 0.979 1.000 0.000
#> GSM617608 1 0.0000 0.979 1.000 0.000
#> GSM617609 1 0.0000 0.979 1.000 0.000
#> GSM617612 1 0.0000 0.979 1.000 0.000
#> GSM617615 2 0.0000 0.983 0.000 1.000
#> GSM617616 1 0.0000 0.979 1.000 0.000
#> GSM617617 2 0.0000 0.983 0.000 1.000
#> GSM617618 1 0.0000 0.979 1.000 0.000
#> GSM617619 2 0.2948 0.941 0.052 0.948
#> GSM617620 2 0.0000 0.983 0.000 1.000
#> GSM617622 2 0.0000 0.983 0.000 1.000
#> GSM617623 1 0.9608 0.383 0.616 0.384
#> GSM617624 2 0.0000 0.983 0.000 1.000
#> GSM617625 1 0.0000 0.979 1.000 0.000
#> GSM617626 1 0.4298 0.893 0.912 0.088
#> GSM617627 2 0.0000 0.983 0.000 1.000
#> GSM617628 1 0.0000 0.979 1.000 0.000
#> GSM617632 1 0.0000 0.979 1.000 0.000
#> GSM617634 2 0.2778 0.944 0.048 0.952
#> GSM617635 1 0.0000 0.979 1.000 0.000
#> GSM617636 1 0.0000 0.979 1.000 0.000
#> GSM617637 1 0.0000 0.979 1.000 0.000
#> GSM617638 2 0.3114 0.936 0.056 0.944
#> GSM617639 1 0.0000 0.979 1.000 0.000
#> GSM617640 2 0.0000 0.983 0.000 1.000
#> GSM617641 2 0.0000 0.983 0.000 1.000
#> GSM617643 2 0.0000 0.983 0.000 1.000
#> GSM617644 2 0.0000 0.983 0.000 1.000
#> GSM617647 2 0.0000 0.983 0.000 1.000
#> GSM617648 2 0.0000 0.983 0.000 1.000
#> GSM617649 2 0.0000 0.983 0.000 1.000
#> GSM617650 1 0.0000 0.979 1.000 0.000
#> GSM617651 1 0.0000 0.979 1.000 0.000
#> GSM617653 1 0.0000 0.979 1.000 0.000
#> GSM617654 2 0.0000 0.983 0.000 1.000
#> GSM617583 1 0.0000 0.979 1.000 0.000
#> GSM617584 2 0.1633 0.965 0.024 0.976
#> GSM617585 2 0.0000 0.983 0.000 1.000
#> GSM617586 1 0.0000 0.979 1.000 0.000
#> GSM617587 1 0.0000 0.979 1.000 0.000
#> GSM617589 2 0.0000 0.983 0.000 1.000
#> GSM617591 2 0.0000 0.983 0.000 1.000
#> GSM617593 1 0.0000 0.979 1.000 0.000
#> GSM617594 2 0.0672 0.977 0.008 0.992
#> GSM617595 1 0.0000 0.979 1.000 0.000
#> GSM617596 1 0.0000 0.979 1.000 0.000
#> GSM617597 1 0.0000 0.979 1.000 0.000
#> GSM617598 1 0.0000 0.979 1.000 0.000
#> GSM617599 2 0.1414 0.969 0.020 0.980
#> GSM617600 1 0.0000 0.979 1.000 0.000
#> GSM617601 2 0.0000 0.983 0.000 1.000
#> GSM617602 1 0.0000 0.979 1.000 0.000
#> GSM617603 2 0.0000 0.983 0.000 1.000
#> GSM617604 1 0.0000 0.979 1.000 0.000
#> GSM617605 2 0.0000 0.983 0.000 1.000
#> GSM617606 2 0.0000 0.983 0.000 1.000
#> GSM617610 1 0.0000 0.979 1.000 0.000
#> GSM617611 1 0.0000 0.979 1.000 0.000
#> GSM617613 1 0.0000 0.979 1.000 0.000
#> GSM617614 1 0.0000 0.979 1.000 0.000
#> GSM617621 1 0.0000 0.979 1.000 0.000
#> GSM617629 1 0.0672 0.972 0.992 0.008
#> GSM617630 1 0.9552 0.402 0.624 0.376
#> GSM617631 1 0.0000 0.979 1.000 0.000
#> GSM617633 1 0.0000 0.979 1.000 0.000
#> GSM617642 1 0.0000 0.979 1.000 0.000
#> GSM617645 2 0.0000 0.983 0.000 1.000
#> GSM617646 1 0.0000 0.979 1.000 0.000
#> GSM617652 1 0.0000 0.979 1.000 0.000
#> GSM617655 1 0.0000 0.979 1.000 0.000
#> GSM617656 1 0.0000 0.979 1.000 0.000
#> GSM617657 2 0.9044 0.527 0.320 0.680
#> GSM617658 1 0.0000 0.979 1.000 0.000
#> GSM617659 1 0.0000 0.979 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM617581 1 0.4449 0.7750 0.860 0.040 0.100
#> GSM617582 1 0.4002 0.7805 0.840 0.000 0.160
#> GSM617588 2 0.0000 0.7139 0.000 1.000 0.000
#> GSM617590 2 0.0000 0.7139 0.000 1.000 0.000
#> GSM617592 2 0.0000 0.7139 0.000 1.000 0.000
#> GSM617607 1 0.1643 0.8220 0.956 0.000 0.044
#> GSM617608 1 0.1163 0.8215 0.972 0.000 0.028
#> GSM617609 3 0.6252 -0.3143 0.444 0.000 0.556
#> GSM617612 1 0.0000 0.8196 1.000 0.000 0.000
#> GSM617615 2 0.4974 0.6672 0.000 0.764 0.236
#> GSM617616 1 0.0892 0.8165 0.980 0.000 0.020
#> GSM617617 2 0.6521 0.4144 0.004 0.504 0.492
#> GSM617618 1 0.1163 0.8159 0.972 0.000 0.028
#> GSM617619 3 0.3183 0.3771 0.016 0.076 0.908
#> GSM617620 2 0.0237 0.7148 0.000 0.996 0.004
#> GSM617622 2 0.5905 0.5638 0.000 0.648 0.352
#> GSM617623 1 0.7133 0.5574 0.712 0.096 0.192
#> GSM617624 3 0.6275 -0.0521 0.008 0.348 0.644
#> GSM617625 1 0.5363 0.6886 0.724 0.000 0.276
#> GSM617626 1 0.2414 0.7972 0.940 0.020 0.040
#> GSM617627 3 0.6398 -0.2228 0.004 0.416 0.580
#> GSM617628 1 0.5760 0.6339 0.672 0.000 0.328
#> GSM617632 1 0.1289 0.8134 0.968 0.000 0.032
#> GSM617634 3 0.5848 0.1441 0.012 0.268 0.720
#> GSM617635 1 0.0892 0.8197 0.980 0.000 0.020
#> GSM617636 1 0.3192 0.8030 0.888 0.000 0.112
#> GSM617637 1 0.0747 0.8169 0.984 0.000 0.016
#> GSM617638 3 0.5156 0.1990 0.008 0.216 0.776
#> GSM617639 1 0.0237 0.8193 0.996 0.000 0.004
#> GSM617640 2 0.6180 0.5355 0.000 0.584 0.416
#> GSM617641 2 0.0000 0.7139 0.000 1.000 0.000
#> GSM617643 2 0.5905 0.5857 0.000 0.648 0.352
#> GSM617644 2 0.2165 0.7176 0.000 0.936 0.064
#> GSM617647 2 0.6468 0.4570 0.004 0.552 0.444
#> GSM617648 2 0.6460 0.4788 0.004 0.556 0.440
#> GSM617649 3 0.6516 -0.3717 0.004 0.480 0.516
#> GSM617650 1 0.1411 0.8199 0.964 0.000 0.036
#> GSM617651 1 0.0424 0.8185 0.992 0.000 0.008
#> GSM617653 1 0.0747 0.8165 0.984 0.000 0.016
#> GSM617654 3 0.6813 -0.4149 0.012 0.468 0.520
#> GSM617583 1 0.5497 0.6766 0.708 0.000 0.292
#> GSM617584 2 0.5659 0.6258 0.052 0.796 0.152
#> GSM617585 2 0.5216 0.5895 0.000 0.740 0.260
#> GSM617586 1 0.6308 0.4099 0.508 0.000 0.492
#> GSM617587 3 0.6274 -0.3472 0.456 0.000 0.544
#> GSM617589 2 0.0424 0.7078 0.008 0.992 0.000
#> GSM617591 2 0.5810 0.6007 0.000 0.664 0.336
#> GSM617593 1 0.0000 0.8196 1.000 0.000 0.000
#> GSM617594 3 0.7395 -0.3874 0.032 0.476 0.492
#> GSM617595 1 0.0237 0.8193 0.996 0.000 0.004
#> GSM617596 1 0.2448 0.8121 0.924 0.000 0.076
#> GSM617597 1 0.5529 0.6915 0.704 0.000 0.296
#> GSM617598 1 0.0592 0.8180 0.988 0.000 0.012
#> GSM617599 3 0.7581 -0.2356 0.044 0.408 0.548
#> GSM617600 3 0.6295 -0.3953 0.472 0.000 0.528
#> GSM617601 2 0.3340 0.7097 0.000 0.880 0.120
#> GSM617602 1 0.6260 0.5151 0.552 0.000 0.448
#> GSM617603 2 0.0424 0.7132 0.000 0.992 0.008
#> GSM617604 1 0.3619 0.7994 0.864 0.000 0.136
#> GSM617605 2 0.0237 0.7141 0.000 0.996 0.004
#> GSM617606 2 0.6299 0.3969 0.000 0.524 0.476
#> GSM617610 1 0.0424 0.8185 0.992 0.000 0.008
#> GSM617611 1 0.0592 0.8204 0.988 0.000 0.012
#> GSM617613 3 0.5905 -0.0622 0.352 0.000 0.648
#> GSM617614 1 0.5760 0.6642 0.672 0.000 0.328
#> GSM617621 1 0.2448 0.8124 0.924 0.000 0.076
#> GSM617629 3 0.3340 0.4107 0.120 0.000 0.880
#> GSM617630 3 0.1453 0.3861 0.008 0.024 0.968
#> GSM617631 1 0.6291 0.4750 0.532 0.000 0.468
#> GSM617633 1 0.5621 0.6688 0.692 0.000 0.308
#> GSM617642 1 0.5760 0.6648 0.672 0.000 0.328
#> GSM617645 2 0.6308 0.4174 0.000 0.508 0.492
#> GSM617646 1 0.3412 0.7945 0.876 0.000 0.124
#> GSM617652 1 0.4452 0.7636 0.808 0.000 0.192
#> GSM617655 1 0.6309 0.4033 0.504 0.000 0.496
#> GSM617656 1 0.6286 0.4735 0.536 0.000 0.464
#> GSM617657 3 0.3234 0.3855 0.020 0.072 0.908
#> GSM617658 1 0.5968 0.6368 0.636 0.000 0.364
#> GSM617659 1 0.1411 0.8199 0.964 0.000 0.036
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM617581 1 0.4628 0.8314 0.828 0.080 0.048 0.044
#> GSM617582 1 0.5800 0.7686 0.748 0.092 0.132 0.028
#> GSM617588 4 0.1211 0.8626 0.000 0.040 0.000 0.960
#> GSM617590 4 0.1302 0.8632 0.000 0.044 0.000 0.956
#> GSM617592 4 0.1302 0.8632 0.000 0.044 0.000 0.956
#> GSM617607 1 0.2984 0.8861 0.888 0.028 0.084 0.000
#> GSM617608 1 0.1940 0.8835 0.924 0.000 0.076 0.000
#> GSM617609 3 0.3215 0.8872 0.092 0.032 0.876 0.000
#> GSM617612 1 0.0921 0.8984 0.972 0.000 0.028 0.000
#> GSM617615 2 0.5345 0.2802 0.000 0.560 0.012 0.428
#> GSM617616 1 0.2089 0.8932 0.940 0.028 0.020 0.012
#> GSM617617 2 0.2441 0.8317 0.004 0.916 0.012 0.068
#> GSM617618 1 0.2996 0.8844 0.904 0.048 0.028 0.020
#> GSM617619 2 0.4360 0.6773 0.000 0.744 0.248 0.008
#> GSM617620 4 0.1302 0.8632 0.000 0.044 0.000 0.956
#> GSM617622 2 0.6801 0.3785 0.020 0.568 0.064 0.348
#> GSM617623 1 0.4778 0.8186 0.816 0.100 0.040 0.044
#> GSM617624 2 0.2565 0.8299 0.000 0.912 0.056 0.032
#> GSM617625 3 0.4252 0.7965 0.252 0.000 0.744 0.004
#> GSM617626 1 0.2099 0.8832 0.936 0.040 0.004 0.020
#> GSM617627 2 0.2830 0.8331 0.000 0.900 0.040 0.060
#> GSM617628 3 0.4188 0.8048 0.244 0.000 0.752 0.004
#> GSM617632 1 0.2170 0.8882 0.936 0.036 0.012 0.016
#> GSM617634 2 0.3790 0.7996 0.008 0.856 0.096 0.040
#> GSM617635 1 0.1798 0.8978 0.944 0.016 0.040 0.000
#> GSM617636 1 0.4488 0.8363 0.820 0.076 0.096 0.008
#> GSM617637 1 0.1004 0.8993 0.972 0.004 0.024 0.000
#> GSM617638 2 0.2654 0.7923 0.000 0.888 0.108 0.004
#> GSM617639 1 0.0817 0.8986 0.976 0.000 0.024 0.000
#> GSM617640 2 0.3158 0.8236 0.004 0.880 0.020 0.096
#> GSM617641 4 0.1211 0.8630 0.000 0.040 0.000 0.960
#> GSM617643 2 0.3443 0.8083 0.000 0.848 0.016 0.136
#> GSM617644 4 0.4635 0.5737 0.000 0.268 0.012 0.720
#> GSM617647 2 0.3190 0.8289 0.016 0.880 0.008 0.096
#> GSM617648 2 0.4036 0.8214 0.012 0.840 0.032 0.116
#> GSM617649 2 0.3421 0.8295 0.000 0.868 0.044 0.088
#> GSM617650 1 0.2530 0.8551 0.888 0.000 0.112 0.000
#> GSM617651 1 0.1022 0.8980 0.968 0.000 0.032 0.000
#> GSM617653 1 0.0779 0.8951 0.980 0.004 0.000 0.016
#> GSM617654 2 0.3001 0.8208 0.004 0.896 0.064 0.036
#> GSM617583 3 0.3908 0.8355 0.212 0.000 0.784 0.004
#> GSM617584 4 0.7065 0.5359 0.120 0.200 0.036 0.644
#> GSM617585 4 0.4203 0.7601 0.000 0.108 0.068 0.824
#> GSM617586 3 0.2737 0.8903 0.104 0.008 0.888 0.000
#> GSM617587 3 0.3015 0.8884 0.092 0.024 0.884 0.000
#> GSM617589 4 0.0921 0.8551 0.000 0.028 0.000 0.972
#> GSM617591 2 0.5565 0.4811 0.000 0.624 0.032 0.344
#> GSM617593 1 0.0921 0.8984 0.972 0.000 0.028 0.000
#> GSM617594 2 0.3902 0.8144 0.060 0.864 0.028 0.048
#> GSM617595 1 0.1022 0.8979 0.968 0.000 0.032 0.000
#> GSM617596 1 0.3487 0.8667 0.880 0.040 0.064 0.016
#> GSM617597 3 0.3528 0.8468 0.192 0.000 0.808 0.000
#> GSM617598 1 0.0817 0.8990 0.976 0.000 0.024 0.000
#> GSM617599 2 0.3370 0.8254 0.028 0.888 0.028 0.056
#> GSM617600 3 0.2489 0.8764 0.068 0.020 0.912 0.000
#> GSM617601 4 0.5168 -0.0795 0.000 0.492 0.004 0.504
#> GSM617602 3 0.3109 0.8875 0.100 0.016 0.880 0.004
#> GSM617603 4 0.1109 0.8555 0.000 0.028 0.004 0.968
#> GSM617604 1 0.5025 0.7499 0.752 0.024 0.208 0.016
#> GSM617605 4 0.1211 0.8630 0.000 0.040 0.000 0.960
#> GSM617606 2 0.5061 0.7601 0.004 0.752 0.048 0.196
#> GSM617610 1 0.0817 0.8986 0.976 0.000 0.024 0.000
#> GSM617611 1 0.1716 0.8887 0.936 0.000 0.064 0.000
#> GSM617613 3 0.1920 0.8388 0.028 0.024 0.944 0.004
#> GSM617614 3 0.3052 0.8795 0.136 0.004 0.860 0.000
#> GSM617621 1 0.3225 0.8688 0.892 0.032 0.060 0.016
#> GSM617629 3 0.6229 0.1781 0.032 0.380 0.572 0.016
#> GSM617630 2 0.3208 0.7626 0.004 0.848 0.148 0.000
#> GSM617631 3 0.2530 0.8890 0.100 0.004 0.896 0.000
#> GSM617633 3 0.5110 0.6240 0.328 0.016 0.656 0.000
#> GSM617642 3 0.3157 0.8767 0.144 0.004 0.852 0.000
#> GSM617645 2 0.3027 0.8265 0.004 0.888 0.020 0.088
#> GSM617646 1 0.4022 0.8418 0.836 0.096 0.068 0.000
#> GSM617652 1 0.5548 0.2638 0.588 0.024 0.388 0.000
#> GSM617655 3 0.2805 0.8902 0.100 0.012 0.888 0.000
#> GSM617656 3 0.2805 0.8902 0.100 0.012 0.888 0.000
#> GSM617657 3 0.2408 0.7809 0.016 0.060 0.920 0.004
#> GSM617658 3 0.4264 0.8611 0.140 0.028 0.820 0.012
#> GSM617659 1 0.2589 0.8516 0.884 0.000 0.116 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM617581 1 0.5856 0.6848 0.660 0.028 0.020 0.048 0.244
#> GSM617582 1 0.6064 0.5340 0.520 0.020 0.060 0.004 0.396
#> GSM617588 4 0.1012 0.8841 0.000 0.012 0.000 0.968 0.020
#> GSM617590 4 0.0740 0.8867 0.000 0.008 0.008 0.980 0.004
#> GSM617592 4 0.0451 0.8863 0.000 0.008 0.000 0.988 0.004
#> GSM617607 1 0.2512 0.8225 0.904 0.004 0.060 0.004 0.028
#> GSM617608 1 0.1697 0.8200 0.932 0.000 0.060 0.000 0.008
#> GSM617609 3 0.1106 0.8557 0.024 0.012 0.964 0.000 0.000
#> GSM617612 1 0.1300 0.8296 0.956 0.000 0.028 0.000 0.016
#> GSM617615 2 0.3759 0.5316 0.000 0.764 0.000 0.220 0.016
#> GSM617616 1 0.3777 0.7840 0.784 0.004 0.020 0.000 0.192
#> GSM617617 2 0.3496 0.4891 0.000 0.788 0.000 0.012 0.200
#> GSM617618 1 0.4382 0.7592 0.736 0.012 0.024 0.000 0.228
#> GSM617619 2 0.6115 -0.0463 0.000 0.520 0.356 0.004 0.120
#> GSM617620 4 0.0794 0.8839 0.000 0.028 0.000 0.972 0.000
#> GSM617622 2 0.6639 0.3206 0.004 0.568 0.024 0.248 0.156
#> GSM617623 1 0.6012 0.6677 0.644 0.036 0.020 0.044 0.256
#> GSM617624 2 0.2802 0.5650 0.000 0.876 0.016 0.008 0.100
#> GSM617625 3 0.3652 0.7382 0.200 0.004 0.784 0.000 0.012
#> GSM617626 1 0.3732 0.7802 0.796 0.016 0.004 0.004 0.180
#> GSM617627 2 0.2733 0.5730 0.000 0.888 0.016 0.016 0.080
#> GSM617628 3 0.3575 0.7617 0.180 0.004 0.800 0.000 0.016
#> GSM617632 1 0.3908 0.7766 0.776 0.016 0.004 0.004 0.200
#> GSM617634 2 0.4989 0.2278 0.000 0.572 0.020 0.008 0.400
#> GSM617635 1 0.2913 0.8129 0.876 0.000 0.040 0.004 0.080
#> GSM617636 1 0.5356 0.7029 0.652 0.016 0.044 0.004 0.284
#> GSM617637 1 0.1334 0.8288 0.960 0.004 0.020 0.004 0.012
#> GSM617638 2 0.4680 0.0194 0.000 0.540 0.008 0.004 0.448
#> GSM617639 1 0.1356 0.8292 0.956 0.000 0.028 0.004 0.012
#> GSM617640 2 0.4747 0.2768 0.000 0.620 0.000 0.028 0.352
#> GSM617641 4 0.0451 0.8863 0.000 0.008 0.000 0.988 0.004
#> GSM617643 2 0.3336 0.5817 0.000 0.844 0.000 0.060 0.096
#> GSM617644 2 0.5932 0.0406 0.000 0.456 0.000 0.440 0.104
#> GSM617647 2 0.2256 0.5898 0.016 0.920 0.000 0.032 0.032
#> GSM617648 2 0.3370 0.5543 0.000 0.824 0.000 0.028 0.148
#> GSM617649 2 0.2956 0.5740 0.000 0.872 0.012 0.020 0.096
#> GSM617650 1 0.2249 0.8034 0.896 0.000 0.096 0.000 0.008
#> GSM617651 1 0.0703 0.8282 0.976 0.000 0.024 0.000 0.000
#> GSM617653 1 0.3013 0.7932 0.832 0.000 0.000 0.008 0.160
#> GSM617654 2 0.4560 -0.0761 0.000 0.508 0.000 0.008 0.484
#> GSM617583 3 0.2783 0.8189 0.116 0.004 0.868 0.000 0.012
#> GSM617584 4 0.8091 0.2107 0.084 0.240 0.016 0.452 0.208
#> GSM617585 4 0.5440 0.6755 0.000 0.100 0.044 0.720 0.136
#> GSM617586 3 0.0992 0.8569 0.024 0.008 0.968 0.000 0.000
#> GSM617587 3 0.0992 0.8569 0.024 0.008 0.968 0.000 0.000
#> GSM617589 4 0.1493 0.8768 0.000 0.028 0.000 0.948 0.024
#> GSM617591 2 0.4518 0.5508 0.000 0.772 0.044 0.156 0.028
#> GSM617593 1 0.0703 0.8282 0.976 0.000 0.024 0.000 0.000
#> GSM617594 2 0.2756 0.5769 0.036 0.900 0.008 0.012 0.044
#> GSM617595 1 0.0880 0.8268 0.968 0.000 0.032 0.000 0.000
#> GSM617596 1 0.4603 0.7501 0.732 0.008 0.028 0.008 0.224
#> GSM617597 3 0.3368 0.7733 0.164 0.004 0.820 0.004 0.008
#> GSM617598 1 0.0703 0.8282 0.976 0.000 0.024 0.000 0.000
#> GSM617599 2 0.2589 0.5750 0.020 0.896 0.004 0.004 0.076
#> GSM617600 3 0.1560 0.8488 0.020 0.004 0.948 0.000 0.028
#> GSM617601 2 0.3949 0.4849 0.000 0.696 0.000 0.300 0.004
#> GSM617602 3 0.2951 0.8013 0.028 0.000 0.860 0.000 0.112
#> GSM617603 4 0.2819 0.8467 0.000 0.076 0.008 0.884 0.032
#> GSM617604 1 0.5890 0.6438 0.612 0.000 0.152 0.004 0.232
#> GSM617605 4 0.0740 0.8867 0.000 0.008 0.008 0.980 0.004
#> GSM617606 2 0.6649 0.2570 0.000 0.508 0.016 0.164 0.312
#> GSM617610 1 0.0992 0.8288 0.968 0.000 0.024 0.000 0.008
#> GSM617611 1 0.1704 0.8166 0.928 0.000 0.068 0.000 0.004
#> GSM617613 3 0.1808 0.8212 0.008 0.012 0.936 0.000 0.044
#> GSM617614 3 0.2362 0.8453 0.076 0.000 0.900 0.000 0.024
#> GSM617621 1 0.4491 0.7450 0.732 0.008 0.020 0.008 0.232
#> GSM617629 5 0.6156 0.1253 0.008 0.128 0.308 0.000 0.556
#> GSM617630 5 0.4961 -0.3349 0.000 0.448 0.028 0.000 0.524
#> GSM617631 3 0.1568 0.8484 0.020 0.000 0.944 0.000 0.036
#> GSM617633 3 0.6169 0.3513 0.364 0.004 0.508 0.000 0.124
#> GSM617642 3 0.1443 0.8553 0.044 0.004 0.948 0.000 0.004
#> GSM617645 2 0.4651 0.2359 0.000 0.608 0.000 0.020 0.372
#> GSM617646 1 0.4493 0.7691 0.800 0.096 0.060 0.004 0.040
#> GSM617652 1 0.5291 0.2756 0.572 0.024 0.388 0.004 0.012
#> GSM617655 3 0.0992 0.8569 0.024 0.008 0.968 0.000 0.000
#> GSM617656 3 0.0703 0.8572 0.024 0.000 0.976 0.000 0.000
#> GSM617657 3 0.2464 0.7588 0.000 0.016 0.888 0.000 0.096
#> GSM617658 3 0.5030 0.6051 0.072 0.000 0.688 0.004 0.236
#> GSM617659 1 0.2513 0.7888 0.876 0.000 0.116 0.000 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM617581 1 0.6183 0.1178 0.476 0.052 0.012 0.040 0.012 0.408
#> GSM617582 6 0.6733 0.2284 0.296 0.032 0.044 0.000 0.120 0.508
#> GSM617588 4 0.1334 0.8967 0.000 0.000 0.000 0.948 0.032 0.020
#> GSM617590 4 0.0508 0.9057 0.000 0.004 0.000 0.984 0.000 0.012
#> GSM617592 4 0.0405 0.9033 0.000 0.004 0.000 0.988 0.008 0.000
#> GSM617607 1 0.3699 0.5948 0.824 0.024 0.020 0.000 0.028 0.104
#> GSM617608 1 0.2586 0.6130 0.880 0.000 0.080 0.000 0.008 0.032
#> GSM617609 3 0.1579 0.8527 0.024 0.020 0.944 0.000 0.008 0.004
#> GSM617612 1 0.0622 0.6488 0.980 0.000 0.012 0.000 0.000 0.008
#> GSM617615 2 0.4254 0.5277 0.000 0.768 0.004 0.144 0.060 0.024
#> GSM617616 1 0.4742 0.3054 0.612 0.004 0.000 0.000 0.056 0.328
#> GSM617617 2 0.4229 0.0628 0.000 0.668 0.000 0.000 0.292 0.040
#> GSM617618 1 0.5419 0.1794 0.556 0.004 0.012 0.000 0.080 0.348
#> GSM617619 2 0.5928 0.1612 0.000 0.512 0.360 0.000 0.068 0.060
#> GSM617620 4 0.1860 0.8905 0.000 0.036 0.004 0.928 0.028 0.004
#> GSM617622 2 0.6100 0.4234 0.000 0.592 0.016 0.096 0.048 0.248
#> GSM617623 1 0.6204 0.0954 0.468 0.048 0.008 0.040 0.020 0.416
#> GSM617624 2 0.2703 0.4925 0.000 0.876 0.016 0.000 0.080 0.028
#> GSM617625 3 0.3865 0.7368 0.216 0.000 0.748 0.000 0.016 0.020
#> GSM617626 1 0.4602 0.3677 0.636 0.036 0.000 0.000 0.012 0.316
#> GSM617627 2 0.2560 0.4830 0.000 0.880 0.016 0.000 0.088 0.016
#> GSM617628 3 0.3720 0.7584 0.196 0.000 0.768 0.000 0.016 0.020
#> GSM617632 1 0.4836 0.1762 0.536 0.008 0.000 0.000 0.040 0.416
#> GSM617634 2 0.6718 0.0546 0.000 0.380 0.028 0.004 0.252 0.336
#> GSM617635 1 0.3622 0.5388 0.792 0.012 0.004 0.000 0.024 0.168
#> GSM617636 6 0.5783 -0.1454 0.428 0.012 0.024 0.000 0.064 0.472
#> GSM617637 1 0.1003 0.6462 0.964 0.004 0.004 0.000 0.000 0.028
#> GSM617638 5 0.5137 0.6498 0.000 0.328 0.008 0.000 0.584 0.080
#> GSM617639 1 0.0922 0.6466 0.968 0.000 0.004 0.000 0.004 0.024
#> GSM617640 5 0.4487 0.6893 0.000 0.420 0.000 0.004 0.552 0.024
#> GSM617641 4 0.0291 0.9043 0.000 0.004 0.000 0.992 0.004 0.000
#> GSM617643 2 0.5123 0.4649 0.000 0.688 0.000 0.032 0.140 0.140
#> GSM617644 2 0.7016 0.2999 0.000 0.428 0.004 0.316 0.084 0.168
#> GSM617647 2 0.2044 0.5341 0.008 0.924 0.000 0.016 0.032 0.020
#> GSM617648 2 0.4997 0.4756 0.000 0.688 0.004 0.012 0.128 0.168
#> GSM617649 2 0.4450 0.4932 0.000 0.752 0.004 0.016 0.108 0.120
#> GSM617650 1 0.2290 0.6153 0.892 0.000 0.084 0.000 0.004 0.020
#> GSM617651 1 0.0951 0.6464 0.968 0.000 0.004 0.000 0.008 0.020
#> GSM617653 1 0.3912 0.3864 0.648 0.000 0.000 0.000 0.012 0.340
#> GSM617654 5 0.3489 0.7756 0.000 0.288 0.000 0.000 0.708 0.004
#> GSM617583 3 0.3016 0.8168 0.136 0.000 0.836 0.000 0.012 0.016
#> GSM617584 6 0.7286 0.0158 0.052 0.208 0.008 0.332 0.012 0.388
#> GSM617585 4 0.6645 0.5771 0.000 0.104 0.040 0.604 0.128 0.124
#> GSM617586 3 0.1225 0.8565 0.032 0.004 0.956 0.000 0.004 0.004
#> GSM617587 3 0.1457 0.8556 0.028 0.016 0.948 0.000 0.004 0.004
#> GSM617589 4 0.1824 0.8931 0.004 0.004 0.004 0.932 0.040 0.016
#> GSM617591 2 0.5094 0.4860 0.000 0.736 0.108 0.076 0.056 0.024
#> GSM617593 1 0.0405 0.6478 0.988 0.000 0.000 0.000 0.004 0.008
#> GSM617594 2 0.2649 0.5454 0.028 0.896 0.008 0.008 0.012 0.048
#> GSM617595 1 0.0653 0.6481 0.980 0.000 0.012 0.000 0.004 0.004
#> GSM617596 1 0.4481 0.2909 0.568 0.008 0.008 0.000 0.008 0.408
#> GSM617597 3 0.3905 0.7309 0.200 0.000 0.756 0.000 0.016 0.028
#> GSM617598 1 0.0291 0.6481 0.992 0.000 0.004 0.000 0.000 0.004
#> GSM617599 2 0.3140 0.5500 0.012 0.864 0.008 0.004 0.060 0.052
#> GSM617600 3 0.1957 0.8393 0.012 0.008 0.928 0.000 0.028 0.024
#> GSM617601 2 0.3770 0.5123 0.000 0.776 0.004 0.176 0.040 0.004
#> GSM617602 3 0.3889 0.7358 0.012 0.000 0.776 0.000 0.052 0.160
#> GSM617603 4 0.4358 0.8048 0.000 0.036 0.004 0.772 0.072 0.116
#> GSM617604 1 0.5946 0.0898 0.456 0.008 0.116 0.000 0.012 0.408
#> GSM617605 4 0.0622 0.9058 0.000 0.008 0.000 0.980 0.000 0.012
#> GSM617606 2 0.7198 -0.0787 0.000 0.396 0.004 0.168 0.328 0.104
#> GSM617610 1 0.0291 0.6481 0.992 0.000 0.004 0.000 0.000 0.004
#> GSM617611 1 0.1732 0.6254 0.920 0.000 0.072 0.000 0.004 0.004
#> GSM617613 3 0.2221 0.8301 0.004 0.004 0.908 0.000 0.040 0.044
#> GSM617614 3 0.2747 0.8392 0.096 0.000 0.868 0.000 0.020 0.016
#> GSM617621 1 0.4702 0.2801 0.568 0.016 0.016 0.000 0.004 0.396
#> GSM617629 6 0.6311 0.0600 0.000 0.060 0.120 0.000 0.312 0.508
#> GSM617630 5 0.3536 0.7627 0.000 0.252 0.008 0.000 0.736 0.004
#> GSM617631 3 0.2100 0.8393 0.016 0.000 0.916 0.000 0.032 0.036
#> GSM617633 1 0.7050 -0.0608 0.380 0.004 0.336 0.000 0.064 0.216
#> GSM617642 3 0.1615 0.8519 0.064 0.000 0.928 0.000 0.004 0.004
#> GSM617645 5 0.4276 0.7140 0.000 0.416 0.000 0.000 0.564 0.020
#> GSM617646 1 0.4703 0.5418 0.764 0.088 0.024 0.000 0.036 0.088
#> GSM617652 1 0.5450 0.2059 0.544 0.040 0.376 0.000 0.008 0.032
#> GSM617655 3 0.1003 0.8566 0.028 0.004 0.964 0.000 0.000 0.004
#> GSM617656 3 0.0858 0.8568 0.028 0.000 0.968 0.000 0.004 0.000
#> GSM617657 3 0.3820 0.7082 0.000 0.008 0.784 0.000 0.064 0.144
#> GSM617658 3 0.5391 0.3405 0.036 0.000 0.540 0.000 0.048 0.376
#> GSM617659 1 0.2871 0.5835 0.852 0.000 0.116 0.000 0.008 0.024
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:kmeans 77 0.12783 2
#> CV:kmeans 54 0.82771 3
#> CV:kmeans 73 0.00537 4
#> CV:kmeans 63 0.01390 5
#> CV:kmeans 50 0.22323 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 79 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 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 0.943 0.939 0.974 0.5027 0.498 0.498
#> 3 3 0.470 0.691 0.839 0.3312 0.751 0.538
#> 4 4 0.398 0.490 0.700 0.1157 0.934 0.808
#> 5 5 0.407 0.351 0.613 0.0630 0.932 0.773
#> 6 6 0.459 0.277 0.540 0.0425 0.924 0.706
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
#> GSM617581 2 0.9000 0.545 0.316 0.684
#> GSM617582 1 0.9000 0.536 0.684 0.316
#> GSM617588 2 0.0000 0.971 0.000 1.000
#> GSM617590 2 0.0000 0.971 0.000 1.000
#> GSM617592 2 0.0000 0.971 0.000 1.000
#> GSM617607 1 0.0000 0.973 1.000 0.000
#> GSM617608 1 0.0000 0.973 1.000 0.000
#> GSM617609 1 0.2603 0.940 0.956 0.044
#> GSM617612 1 0.0000 0.973 1.000 0.000
#> GSM617615 2 0.0000 0.971 0.000 1.000
#> GSM617616 1 0.0672 0.969 0.992 0.008
#> GSM617617 2 0.0000 0.971 0.000 1.000
#> GSM617618 1 0.1633 0.957 0.976 0.024
#> GSM617619 2 0.0000 0.971 0.000 1.000
#> GSM617620 2 0.0000 0.971 0.000 1.000
#> GSM617622 2 0.0000 0.971 0.000 1.000
#> GSM617623 2 0.5294 0.857 0.120 0.880
#> GSM617624 2 0.0000 0.971 0.000 1.000
#> GSM617625 1 0.0000 0.973 1.000 0.000
#> GSM617626 2 0.9552 0.402 0.376 0.624
#> GSM617627 2 0.0000 0.971 0.000 1.000
#> GSM617628 1 0.0000 0.973 1.000 0.000
#> GSM617632 1 0.0672 0.969 0.992 0.008
#> GSM617634 2 0.0376 0.969 0.004 0.996
#> GSM617635 1 0.0376 0.971 0.996 0.004
#> GSM617636 1 0.0000 0.973 1.000 0.000
#> GSM617637 1 0.1184 0.963 0.984 0.016
#> GSM617638 2 0.0376 0.969 0.004 0.996
#> GSM617639 1 0.0000 0.973 1.000 0.000
#> GSM617640 2 0.0000 0.971 0.000 1.000
#> GSM617641 2 0.0000 0.971 0.000 1.000
#> GSM617643 2 0.0000 0.971 0.000 1.000
#> GSM617644 2 0.0000 0.971 0.000 1.000
#> GSM617647 2 0.0000 0.971 0.000 1.000
#> GSM617648 2 0.0000 0.971 0.000 1.000
#> GSM617649 2 0.0000 0.971 0.000 1.000
#> GSM617650 1 0.0000 0.973 1.000 0.000
#> GSM617651 1 0.0000 0.973 1.000 0.000
#> GSM617653 1 0.0000 0.973 1.000 0.000
#> GSM617654 2 0.0000 0.971 0.000 1.000
#> GSM617583 1 0.0000 0.973 1.000 0.000
#> GSM617584 2 0.0938 0.963 0.012 0.988
#> GSM617585 2 0.0000 0.971 0.000 1.000
#> GSM617586 1 0.0376 0.971 0.996 0.004
#> GSM617587 1 0.6887 0.774 0.816 0.184
#> GSM617589 2 0.0000 0.971 0.000 1.000
#> GSM617591 2 0.0000 0.971 0.000 1.000
#> GSM617593 1 0.0000 0.973 1.000 0.000
#> GSM617594 2 0.0000 0.971 0.000 1.000
#> GSM617595 1 0.0000 0.973 1.000 0.000
#> GSM617596 1 0.0000 0.973 1.000 0.000
#> GSM617597 1 0.0000 0.973 1.000 0.000
#> GSM617598 1 0.0000 0.973 1.000 0.000
#> GSM617599 2 0.0376 0.969 0.004 0.996
#> GSM617600 1 0.0000 0.973 1.000 0.000
#> GSM617601 2 0.0000 0.971 0.000 1.000
#> GSM617602 1 0.0000 0.973 1.000 0.000
#> GSM617603 2 0.0000 0.971 0.000 1.000
#> GSM617604 1 0.0376 0.971 0.996 0.004
#> GSM617605 2 0.0000 0.971 0.000 1.000
#> GSM617606 2 0.0000 0.971 0.000 1.000
#> GSM617610 1 0.0000 0.973 1.000 0.000
#> GSM617611 1 0.0000 0.973 1.000 0.000
#> GSM617613 1 0.2043 0.951 0.968 0.032
#> GSM617614 1 0.0000 0.973 1.000 0.000
#> GSM617621 1 0.0000 0.973 1.000 0.000
#> GSM617629 1 0.9393 0.449 0.644 0.356
#> GSM617630 2 0.3431 0.917 0.064 0.936
#> GSM617631 1 0.0000 0.973 1.000 0.000
#> GSM617633 1 0.0000 0.973 1.000 0.000
#> GSM617642 1 0.0000 0.973 1.000 0.000
#> GSM617645 2 0.0000 0.971 0.000 1.000
#> GSM617646 1 0.3879 0.908 0.924 0.076
#> GSM617652 1 0.0376 0.971 0.996 0.004
#> GSM617655 1 0.1633 0.958 0.976 0.024
#> GSM617656 1 0.0000 0.973 1.000 0.000
#> GSM617657 2 0.4022 0.900 0.080 0.920
#> GSM617658 1 0.0000 0.973 1.000 0.000
#> GSM617659 1 0.0000 0.973 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM617581 1 0.9070 0.366 0.536 0.292 0.172
#> GSM617582 1 0.9434 -0.020 0.416 0.176 0.408
#> GSM617588 2 0.0000 0.898 0.000 1.000 0.000
#> GSM617590 2 0.0000 0.898 0.000 1.000 0.000
#> GSM617592 2 0.0000 0.898 0.000 1.000 0.000
#> GSM617607 1 0.4887 0.692 0.772 0.000 0.228
#> GSM617608 1 0.5760 0.519 0.672 0.000 0.328
#> GSM617609 3 0.2063 0.756 0.044 0.008 0.948
#> GSM617612 1 0.3879 0.732 0.848 0.000 0.152
#> GSM617615 2 0.0237 0.898 0.000 0.996 0.004
#> GSM617616 1 0.4349 0.738 0.852 0.020 0.128
#> GSM617617 2 0.1647 0.889 0.036 0.960 0.004
#> GSM617618 1 0.5435 0.698 0.784 0.024 0.192
#> GSM617619 3 0.6410 0.159 0.004 0.420 0.576
#> GSM617620 2 0.0000 0.898 0.000 1.000 0.000
#> GSM617622 2 0.2955 0.873 0.008 0.912 0.080
#> GSM617623 1 0.7507 0.474 0.644 0.288 0.068
#> GSM617624 2 0.5826 0.740 0.032 0.764 0.204
#> GSM617625 3 0.5363 0.592 0.276 0.000 0.724
#> GSM617626 1 0.4861 0.643 0.808 0.180 0.012
#> GSM617627 2 0.3686 0.829 0.000 0.860 0.140
#> GSM617628 3 0.4504 0.686 0.196 0.000 0.804
#> GSM617632 1 0.2486 0.755 0.932 0.008 0.060
#> GSM617634 2 0.8771 0.326 0.132 0.544 0.324
#> GSM617635 1 0.4834 0.712 0.792 0.004 0.204
#> GSM617636 1 0.5363 0.631 0.724 0.000 0.276
#> GSM617637 1 0.1015 0.758 0.980 0.008 0.012
#> GSM617638 2 0.8238 0.458 0.104 0.596 0.300
#> GSM617639 1 0.0892 0.759 0.980 0.000 0.020
#> GSM617640 2 0.0000 0.898 0.000 1.000 0.000
#> GSM617641 2 0.0000 0.898 0.000 1.000 0.000
#> GSM617643 2 0.0475 0.898 0.004 0.992 0.004
#> GSM617644 2 0.0475 0.898 0.004 0.992 0.004
#> GSM617647 2 0.3193 0.848 0.100 0.896 0.004
#> GSM617648 2 0.1170 0.897 0.016 0.976 0.008
#> GSM617649 2 0.3091 0.873 0.016 0.912 0.072
#> GSM617650 1 0.5254 0.619 0.736 0.000 0.264
#> GSM617651 1 0.1031 0.760 0.976 0.000 0.024
#> GSM617653 1 0.0892 0.760 0.980 0.000 0.020
#> GSM617654 2 0.1525 0.892 0.032 0.964 0.004
#> GSM617583 3 0.4654 0.681 0.208 0.000 0.792
#> GSM617584 2 0.5138 0.802 0.120 0.828 0.052
#> GSM617585 2 0.4351 0.798 0.004 0.828 0.168
#> GSM617586 3 0.2165 0.752 0.064 0.000 0.936
#> GSM617587 3 0.5426 0.708 0.092 0.088 0.820
#> GSM617589 2 0.0829 0.897 0.012 0.984 0.004
#> GSM617591 2 0.4291 0.782 0.000 0.820 0.180
#> GSM617593 1 0.1031 0.759 0.976 0.000 0.024
#> GSM617594 2 0.7447 0.655 0.184 0.696 0.120
#> GSM617595 1 0.1529 0.761 0.960 0.000 0.040
#> GSM617596 1 0.3116 0.755 0.892 0.000 0.108
#> GSM617597 3 0.5926 0.422 0.356 0.000 0.644
#> GSM617598 1 0.1031 0.759 0.976 0.000 0.024
#> GSM617599 2 0.7944 0.559 0.244 0.644 0.112
#> GSM617600 3 0.0592 0.750 0.012 0.000 0.988
#> GSM617601 2 0.0237 0.898 0.000 0.996 0.004
#> GSM617602 3 0.2165 0.747 0.064 0.000 0.936
#> GSM617603 2 0.0237 0.898 0.000 0.996 0.004
#> GSM617604 1 0.6295 0.189 0.528 0.000 0.472
#> GSM617605 2 0.0000 0.898 0.000 1.000 0.000
#> GSM617606 2 0.2173 0.886 0.008 0.944 0.048
#> GSM617610 1 0.0983 0.759 0.980 0.004 0.016
#> GSM617611 1 0.4750 0.676 0.784 0.000 0.216
#> GSM617613 3 0.1129 0.751 0.020 0.004 0.976
#> GSM617614 3 0.5016 0.639 0.240 0.000 0.760
#> GSM617621 1 0.2711 0.757 0.912 0.000 0.088
#> GSM617629 3 0.8641 0.426 0.248 0.160 0.592
#> GSM617630 3 0.9030 0.199 0.136 0.388 0.476
#> GSM617631 3 0.0747 0.752 0.016 0.000 0.984
#> GSM617633 3 0.6244 0.175 0.440 0.000 0.560
#> GSM617642 3 0.4555 0.680 0.200 0.000 0.800
#> GSM617645 2 0.0237 0.898 0.000 0.996 0.004
#> GSM617646 1 0.6758 0.662 0.728 0.072 0.200
#> GSM617652 1 0.6682 0.042 0.504 0.008 0.488
#> GSM617655 3 0.1129 0.754 0.020 0.004 0.976
#> GSM617656 3 0.0892 0.753 0.020 0.000 0.980
#> GSM617657 3 0.3459 0.702 0.012 0.096 0.892
#> GSM617658 3 0.5254 0.588 0.264 0.000 0.736
#> GSM617659 1 0.5760 0.509 0.672 0.000 0.328
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM617581 1 0.9554 -0.05478 0.340 0.260 0.116 0.284
#> GSM617582 4 0.9728 0.25233 0.228 0.164 0.252 0.356
#> GSM617588 2 0.0817 0.70592 0.000 0.976 0.000 0.024
#> GSM617590 2 0.1474 0.70940 0.000 0.948 0.000 0.052
#> GSM617592 2 0.1022 0.70531 0.000 0.968 0.000 0.032
#> GSM617607 1 0.7062 0.51144 0.564 0.000 0.176 0.260
#> GSM617608 1 0.6323 0.46697 0.628 0.000 0.272 0.100
#> GSM617609 3 0.5130 0.52497 0.044 0.004 0.740 0.212
#> GSM617612 1 0.4844 0.65759 0.784 0.000 0.108 0.108
#> GSM617615 2 0.3789 0.69540 0.004 0.836 0.020 0.140
#> GSM617616 1 0.8038 0.47948 0.560 0.072 0.120 0.248
#> GSM617617 2 0.5712 0.54351 0.048 0.644 0.000 0.308
#> GSM617618 1 0.8234 0.34834 0.476 0.032 0.192 0.300
#> GSM617619 3 0.7947 -0.34062 0.008 0.224 0.436 0.332
#> GSM617620 2 0.1211 0.70860 0.000 0.960 0.000 0.040
#> GSM617622 2 0.5915 0.57500 0.016 0.708 0.068 0.208
#> GSM617623 1 0.8269 0.06268 0.436 0.248 0.020 0.296
#> GSM617624 4 0.7699 0.27209 0.024 0.336 0.132 0.508
#> GSM617625 3 0.5810 0.53204 0.276 0.000 0.660 0.064
#> GSM617626 1 0.7407 0.36228 0.548 0.176 0.008 0.268
#> GSM617627 2 0.7102 0.26058 0.000 0.540 0.156 0.304
#> GSM617628 3 0.5142 0.59887 0.192 0.000 0.744 0.064
#> GSM617632 1 0.5707 0.60785 0.680 0.008 0.044 0.268
#> GSM617634 4 0.8445 0.44675 0.056 0.308 0.160 0.476
#> GSM617635 1 0.6854 0.55941 0.600 0.004 0.136 0.260
#> GSM617636 1 0.7366 0.41388 0.484 0.000 0.172 0.344
#> GSM617637 1 0.3988 0.66239 0.820 0.004 0.020 0.156
#> GSM617638 4 0.7870 0.47662 0.044 0.236 0.156 0.564
#> GSM617639 1 0.3243 0.68700 0.876 0.000 0.036 0.088
#> GSM617640 2 0.3569 0.67851 0.000 0.804 0.000 0.196
#> GSM617641 2 0.0921 0.70708 0.000 0.972 0.000 0.028
#> GSM617643 2 0.3074 0.69217 0.000 0.848 0.000 0.152
#> GSM617644 2 0.2081 0.70872 0.000 0.916 0.000 0.084
#> GSM617647 2 0.6483 0.42193 0.092 0.584 0.000 0.324
#> GSM617648 2 0.5093 0.59337 0.008 0.704 0.016 0.272
#> GSM617649 2 0.6626 0.38733 0.012 0.580 0.068 0.340
#> GSM617650 1 0.5404 0.55978 0.700 0.000 0.248 0.052
#> GSM617651 1 0.2399 0.68168 0.920 0.000 0.032 0.048
#> GSM617653 1 0.3048 0.68066 0.876 0.000 0.016 0.108
#> GSM617654 2 0.6563 0.19408 0.056 0.488 0.008 0.448
#> GSM617583 3 0.5203 0.59273 0.232 0.000 0.720 0.048
#> GSM617584 2 0.6334 0.47443 0.120 0.692 0.016 0.172
#> GSM617585 2 0.6080 0.47315 0.000 0.684 0.156 0.160
#> GSM617586 3 0.3241 0.61944 0.040 0.004 0.884 0.072
#> GSM617587 3 0.7802 0.36566 0.108 0.084 0.600 0.208
#> GSM617589 2 0.1771 0.70423 0.012 0.948 0.004 0.036
#> GSM617591 2 0.6206 0.49840 0.008 0.692 0.168 0.132
#> GSM617593 1 0.2002 0.68001 0.936 0.000 0.044 0.020
#> GSM617594 2 0.8825 0.11720 0.156 0.492 0.108 0.244
#> GSM617595 1 0.2996 0.68124 0.892 0.000 0.044 0.064
#> GSM617596 1 0.6011 0.62049 0.688 0.000 0.132 0.180
#> GSM617597 3 0.6941 0.26329 0.360 0.000 0.520 0.120
#> GSM617598 1 0.2256 0.68115 0.924 0.000 0.020 0.056
#> GSM617599 2 0.8799 -0.22372 0.112 0.400 0.108 0.380
#> GSM617600 3 0.2676 0.60760 0.012 0.000 0.896 0.092
#> GSM617601 2 0.2530 0.70684 0.000 0.896 0.004 0.100
#> GSM617602 3 0.4841 0.58170 0.080 0.000 0.780 0.140
#> GSM617603 2 0.1792 0.70757 0.000 0.932 0.000 0.068
#> GSM617604 3 0.7760 -0.01644 0.400 0.008 0.416 0.176
#> GSM617605 2 0.1211 0.70662 0.000 0.960 0.000 0.040
#> GSM617606 2 0.6843 0.37496 0.016 0.604 0.092 0.288
#> GSM617610 1 0.2587 0.68156 0.908 0.004 0.012 0.076
#> GSM617611 1 0.4370 0.63970 0.800 0.000 0.156 0.044
#> GSM617613 3 0.2408 0.59456 0.000 0.000 0.896 0.104
#> GSM617614 3 0.6055 0.54322 0.240 0.000 0.664 0.096
#> GSM617621 1 0.5556 0.64627 0.720 0.000 0.092 0.188
#> GSM617629 4 0.8279 0.27812 0.080 0.096 0.348 0.476
#> GSM617630 4 0.8842 0.50092 0.092 0.188 0.236 0.484
#> GSM617631 3 0.1798 0.61368 0.016 0.000 0.944 0.040
#> GSM617633 3 0.7581 -0.00897 0.380 0.000 0.424 0.196
#> GSM617642 3 0.5292 0.59522 0.208 0.000 0.728 0.064
#> GSM617645 2 0.4720 0.56629 0.000 0.672 0.004 0.324
#> GSM617646 1 0.8527 0.40318 0.500 0.072 0.160 0.268
#> GSM617652 1 0.7481 0.11111 0.476 0.012 0.384 0.128
#> GSM617655 3 0.3255 0.59762 0.016 0.012 0.880 0.092
#> GSM617656 3 0.1724 0.61883 0.020 0.000 0.948 0.032
#> GSM617657 3 0.5850 0.37566 0.004 0.100 0.708 0.188
#> GSM617658 3 0.6834 0.46918 0.240 0.000 0.596 0.164
#> GSM617659 1 0.5420 0.50814 0.684 0.000 0.272 0.044
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM617581 5 0.921 0.30957 0.236 0.088 0.108 0.196 0.372
#> GSM617582 5 0.926 0.26917 0.140 0.148 0.192 0.116 0.404
#> GSM617588 4 0.117 0.62059 0.000 0.032 0.000 0.960 0.008
#> GSM617590 4 0.111 0.61785 0.000 0.024 0.000 0.964 0.012
#> GSM617592 4 0.128 0.61803 0.004 0.020 0.000 0.960 0.016
#> GSM617607 1 0.758 0.32161 0.516 0.152 0.140 0.000 0.192
#> GSM617608 1 0.720 0.38971 0.544 0.084 0.220 0.000 0.152
#> GSM617609 3 0.701 0.44060 0.060 0.188 0.604 0.020 0.128
#> GSM617612 1 0.571 0.50110 0.716 0.040 0.104 0.012 0.128
#> GSM617615 4 0.518 0.53930 0.004 0.156 0.044 0.740 0.056
#> GSM617616 1 0.850 0.08621 0.416 0.188 0.076 0.044 0.276
#> GSM617617 4 0.645 0.19307 0.012 0.336 0.000 0.512 0.140
#> GSM617618 1 0.855 -0.00908 0.368 0.172 0.108 0.028 0.324
#> GSM617619 3 0.806 -0.19257 0.000 0.324 0.380 0.164 0.132
#> GSM617620 4 0.248 0.62246 0.000 0.084 0.000 0.892 0.024
#> GSM617622 4 0.644 0.44426 0.012 0.216 0.064 0.636 0.072
#> GSM617623 5 0.900 0.25155 0.264 0.180 0.032 0.184 0.340
#> GSM617624 2 0.780 0.40427 0.016 0.512 0.104 0.232 0.136
#> GSM617625 3 0.687 0.38071 0.284 0.036 0.524 0.000 0.156
#> GSM617626 1 0.799 -0.01063 0.464 0.140 0.008 0.132 0.256
#> GSM617627 2 0.752 0.21491 0.012 0.424 0.136 0.376 0.052
#> GSM617628 3 0.636 0.50935 0.188 0.048 0.628 0.000 0.136
#> GSM617632 1 0.718 0.17430 0.476 0.100 0.044 0.016 0.364
#> GSM617634 2 0.885 0.19697 0.060 0.412 0.100 0.208 0.220
#> GSM617635 1 0.712 0.37830 0.576 0.188 0.068 0.008 0.160
#> GSM617636 5 0.808 0.08807 0.292 0.168 0.120 0.004 0.416
#> GSM617637 1 0.535 0.47028 0.708 0.164 0.012 0.004 0.112
#> GSM617638 2 0.848 0.33026 0.060 0.488 0.108 0.168 0.176
#> GSM617639 1 0.380 0.52830 0.820 0.044 0.012 0.000 0.124
#> GSM617640 4 0.458 0.50816 0.000 0.268 0.000 0.692 0.040
#> GSM617641 4 0.214 0.62267 0.000 0.088 0.000 0.904 0.008
#> GSM617643 4 0.456 0.52931 0.004 0.252 0.004 0.712 0.028
#> GSM617644 4 0.373 0.59633 0.000 0.160 0.000 0.800 0.040
#> GSM617647 4 0.796 0.02046 0.100 0.328 0.024 0.444 0.104
#> GSM617648 4 0.651 0.25874 0.032 0.340 0.004 0.536 0.088
#> GSM617649 2 0.779 0.16055 0.016 0.408 0.092 0.380 0.104
#> GSM617650 1 0.605 0.47013 0.644 0.028 0.188 0.000 0.140
#> GSM617651 1 0.360 0.53850 0.832 0.024 0.020 0.000 0.124
#> GSM617653 1 0.451 0.46289 0.728 0.016 0.024 0.000 0.232
#> GSM617654 4 0.778 -0.17606 0.072 0.376 0.012 0.400 0.140
#> GSM617583 3 0.594 0.52884 0.176 0.040 0.676 0.004 0.104
#> GSM617584 4 0.778 0.20552 0.080 0.160 0.032 0.540 0.188
#> GSM617585 4 0.691 0.25061 0.000 0.128 0.144 0.600 0.128
#> GSM617586 3 0.502 0.57477 0.108 0.064 0.760 0.000 0.068
#> GSM617587 3 0.845 0.35735 0.120 0.164 0.500 0.064 0.152
#> GSM617589 4 0.171 0.61770 0.012 0.024 0.000 0.944 0.020
#> GSM617591 4 0.674 0.31233 0.000 0.160 0.152 0.608 0.080
#> GSM617593 1 0.325 0.53829 0.864 0.016 0.040 0.000 0.080
#> GSM617594 4 0.886 -0.23097 0.112 0.332 0.060 0.352 0.144
#> GSM617595 1 0.328 0.53939 0.856 0.044 0.008 0.000 0.092
#> GSM617596 1 0.751 0.14090 0.444 0.084 0.092 0.012 0.368
#> GSM617597 3 0.762 0.07975 0.348 0.064 0.396 0.000 0.192
#> GSM617598 1 0.360 0.54299 0.848 0.028 0.044 0.000 0.080
#> GSM617599 2 0.926 0.23689 0.164 0.332 0.060 0.268 0.176
#> GSM617600 3 0.360 0.57026 0.004 0.060 0.832 0.000 0.104
#> GSM617601 4 0.417 0.58622 0.008 0.156 0.008 0.792 0.036
#> GSM617602 3 0.587 0.48165 0.064 0.068 0.672 0.000 0.196
#> GSM617603 4 0.297 0.61249 0.000 0.128 0.000 0.852 0.020
#> GSM617604 3 0.822 -0.06509 0.192 0.056 0.384 0.032 0.336
#> GSM617605 4 0.198 0.61986 0.000 0.044 0.004 0.928 0.024
#> GSM617606 4 0.752 0.25254 0.028 0.240 0.068 0.544 0.120
#> GSM617610 1 0.282 0.53430 0.888 0.040 0.004 0.004 0.064
#> GSM617611 1 0.498 0.50917 0.748 0.032 0.144 0.000 0.076
#> GSM617613 3 0.379 0.56058 0.000 0.072 0.820 0.004 0.104
#> GSM617614 3 0.604 0.45324 0.216 0.012 0.616 0.000 0.156
#> GSM617621 1 0.679 0.22614 0.512 0.056 0.068 0.008 0.356
#> GSM617629 5 0.897 0.02685 0.080 0.316 0.200 0.072 0.332
#> GSM617630 2 0.872 0.14935 0.068 0.456 0.192 0.108 0.176
#> GSM617631 3 0.322 0.57366 0.012 0.016 0.848 0.000 0.124
#> GSM617633 1 0.848 -0.06314 0.292 0.164 0.268 0.000 0.276
#> GSM617642 3 0.648 0.49838 0.180 0.048 0.616 0.000 0.156
#> GSM617645 4 0.644 0.27124 0.032 0.320 0.004 0.556 0.088
#> GSM617646 1 0.844 0.17579 0.468 0.216 0.104 0.044 0.168
#> GSM617652 1 0.815 0.18015 0.416 0.120 0.268 0.004 0.192
#> GSM617655 3 0.461 0.57287 0.028 0.072 0.800 0.016 0.084
#> GSM617656 3 0.128 0.58513 0.004 0.020 0.960 0.000 0.016
#> GSM617657 3 0.716 0.36188 0.008 0.172 0.588 0.108 0.124
#> GSM617658 3 0.698 0.27087 0.156 0.040 0.508 0.000 0.296
#> GSM617659 1 0.620 0.42215 0.580 0.008 0.244 0.000 0.168
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM617581 6 0.829 0.1384 0.124 0.072 0.056 0.248 0.060 0.440
#> GSM617582 5 0.943 0.1415 0.112 0.112 0.112 0.112 0.300 0.252
#> GSM617588 4 0.271 0.5612 0.000 0.080 0.000 0.876 0.020 0.024
#> GSM617590 4 0.246 0.5637 0.000 0.064 0.000 0.888 0.044 0.004
#> GSM617592 4 0.154 0.5617 0.000 0.016 0.000 0.944 0.016 0.024
#> GSM617607 1 0.837 0.1125 0.392 0.116 0.128 0.000 0.172 0.192
#> GSM617608 1 0.764 0.2776 0.484 0.056 0.180 0.000 0.120 0.160
#> GSM617609 3 0.750 0.3747 0.076 0.160 0.524 0.004 0.152 0.084
#> GSM617612 1 0.620 0.3873 0.668 0.052 0.104 0.020 0.036 0.120
#> GSM617615 4 0.651 0.4183 0.012 0.196 0.044 0.616 0.076 0.056
#> GSM617616 1 0.901 -0.0641 0.344 0.112 0.072 0.056 0.232 0.184
#> GSM617617 2 0.669 0.1389 0.028 0.456 0.000 0.368 0.104 0.044
#> GSM617618 5 0.854 0.1359 0.300 0.060 0.060 0.044 0.324 0.212
#> GSM617619 3 0.889 -0.0881 0.008 0.204 0.292 0.144 0.236 0.116
#> GSM617620 4 0.306 0.5595 0.000 0.072 0.000 0.860 0.032 0.036
#> GSM617622 4 0.735 0.2945 0.008 0.192 0.060 0.540 0.088 0.112
#> GSM617623 6 0.836 0.1497 0.188 0.084 0.020 0.204 0.084 0.420
#> GSM617624 2 0.840 0.2402 0.016 0.356 0.096 0.156 0.300 0.076
#> GSM617625 3 0.706 0.3277 0.276 0.028 0.492 0.000 0.080 0.124
#> GSM617626 1 0.889 -0.1099 0.312 0.132 0.016 0.164 0.116 0.260
#> GSM617627 2 0.825 0.2833 0.016 0.384 0.100 0.272 0.176 0.052
#> GSM617628 3 0.691 0.4235 0.212 0.040 0.552 0.000 0.112 0.084
#> GSM617632 1 0.795 0.0314 0.384 0.052 0.048 0.016 0.268 0.232
#> GSM617634 5 0.840 -0.0566 0.052 0.224 0.056 0.156 0.432 0.080
#> GSM617635 1 0.785 0.1332 0.408 0.156 0.056 0.004 0.292 0.084
#> GSM617636 5 0.802 0.1389 0.188 0.064 0.096 0.000 0.380 0.272
#> GSM617637 1 0.599 0.3975 0.664 0.100 0.012 0.008 0.116 0.100
#> GSM617638 2 0.816 0.1517 0.040 0.404 0.060 0.112 0.312 0.072
#> GSM617639 1 0.588 0.3724 0.632 0.112 0.000 0.000 0.096 0.160
#> GSM617640 4 0.471 0.2392 0.004 0.368 0.000 0.588 0.036 0.004
#> GSM617641 4 0.168 0.5633 0.000 0.036 0.000 0.936 0.012 0.016
#> GSM617643 4 0.593 0.2898 0.004 0.340 0.004 0.540 0.072 0.040
#> GSM617644 4 0.500 0.4792 0.000 0.240 0.004 0.672 0.052 0.032
#> GSM617647 4 0.795 -0.0506 0.056 0.316 0.012 0.396 0.136 0.084
#> GSM617648 4 0.740 0.0271 0.008 0.368 0.016 0.380 0.148 0.080
#> GSM617649 2 0.817 0.2405 0.028 0.404 0.064 0.288 0.152 0.064
#> GSM617650 1 0.625 0.3746 0.600 0.012 0.204 0.000 0.076 0.108
#> GSM617651 1 0.407 0.4444 0.800 0.016 0.020 0.000 0.064 0.100
#> GSM617653 1 0.616 0.2095 0.560 0.032 0.024 0.012 0.056 0.316
#> GSM617654 2 0.701 0.2708 0.036 0.484 0.008 0.316 0.112 0.044
#> GSM617583 3 0.610 0.4351 0.248 0.008 0.600 0.008 0.056 0.080
#> GSM617584 4 0.684 0.1863 0.060 0.108 0.004 0.508 0.024 0.296
#> GSM617585 4 0.677 0.3826 0.004 0.116 0.084 0.612 0.116 0.068
#> GSM617586 3 0.585 0.5242 0.072 0.024 0.680 0.004 0.116 0.104
#> GSM617587 3 0.858 0.3303 0.092 0.124 0.456 0.056 0.156 0.116
#> GSM617589 4 0.425 0.5475 0.028 0.068 0.000 0.800 0.072 0.032
#> GSM617591 4 0.777 0.2021 0.004 0.180 0.156 0.488 0.088 0.084
#> GSM617593 1 0.379 0.4209 0.800 0.008 0.044 0.000 0.012 0.136
#> GSM617594 4 0.911 -0.2074 0.128 0.288 0.044 0.292 0.148 0.100
#> GSM617595 1 0.547 0.4405 0.716 0.064 0.048 0.000 0.072 0.100
#> GSM617596 6 0.763 0.1178 0.340 0.044 0.096 0.012 0.092 0.416
#> GSM617597 3 0.753 0.1313 0.280 0.028 0.412 0.000 0.084 0.196
#> GSM617598 1 0.435 0.4439 0.784 0.028 0.036 0.000 0.036 0.116
#> GSM617599 2 0.926 0.2191 0.124 0.332 0.056 0.216 0.148 0.124
#> GSM617600 3 0.544 0.4899 0.020 0.048 0.692 0.000 0.160 0.080
#> GSM617601 4 0.561 0.4631 0.008 0.204 0.012 0.664 0.072 0.040
#> GSM617602 3 0.691 0.1775 0.044 0.028 0.504 0.000 0.232 0.192
#> GSM617603 4 0.447 0.5401 0.000 0.132 0.004 0.760 0.068 0.036
#> GSM617604 6 0.769 0.2096 0.156 0.020 0.300 0.032 0.064 0.428
#> GSM617605 4 0.276 0.5617 0.000 0.052 0.004 0.884 0.032 0.028
#> GSM617606 4 0.793 0.1188 0.032 0.240 0.020 0.444 0.160 0.104
#> GSM617610 1 0.391 0.4399 0.816 0.036 0.008 0.004 0.040 0.096
#> GSM617611 1 0.499 0.4320 0.736 0.020 0.128 0.000 0.044 0.072
#> GSM617613 3 0.497 0.4779 0.004 0.044 0.724 0.008 0.164 0.056
#> GSM617614 3 0.617 0.3425 0.156 0.012 0.576 0.000 0.032 0.224
#> GSM617621 6 0.706 0.0687 0.384 0.032 0.068 0.016 0.064 0.436
#> GSM617629 5 0.775 0.2934 0.048 0.124 0.168 0.032 0.524 0.104
#> GSM617630 2 0.878 0.1072 0.060 0.416 0.152 0.080 0.184 0.108
#> GSM617631 3 0.422 0.4958 0.016 0.004 0.772 0.000 0.088 0.120
#> GSM617633 5 0.823 0.1590 0.224 0.056 0.232 0.000 0.352 0.136
#> GSM617642 3 0.576 0.4557 0.144 0.012 0.652 0.000 0.044 0.148
#> GSM617645 2 0.626 0.1613 0.028 0.492 0.004 0.384 0.052 0.040
#> GSM617646 1 0.900 -0.0027 0.296 0.200 0.096 0.016 0.188 0.204
#> GSM617652 1 0.869 0.0534 0.336 0.088 0.284 0.020 0.120 0.152
#> GSM617655 3 0.471 0.5256 0.012 0.040 0.780 0.024 0.064 0.080
#> GSM617656 3 0.248 0.5461 0.008 0.012 0.900 0.000 0.040 0.040
#> GSM617657 3 0.715 0.3011 0.000 0.092 0.540 0.092 0.208 0.068
#> GSM617658 6 0.750 0.0116 0.132 0.028 0.352 0.000 0.108 0.380
#> GSM617659 1 0.657 0.2076 0.500 0.004 0.236 0.000 0.044 0.216
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:skmeans 77 0.0842 2
#> CV:skmeans 67 0.0135 3
#> CV:skmeans 48 0.0524 4
#> CV:skmeans 29 0.0354 5
#> CV:skmeans 11 0.2403 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 79 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 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 0.368 0.725 0.872 0.4987 0.496 0.496
#> 3 3 0.530 0.662 0.844 0.3111 0.799 0.614
#> 4 4 0.507 0.608 0.819 0.0393 0.975 0.929
#> 5 5 0.509 0.553 0.795 0.0212 0.981 0.944
#> 6 6 0.512 0.528 0.789 0.0150 0.968 0.902
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
#> GSM617581 2 0.4022 0.8125 0.080 0.920
#> GSM617582 2 0.7674 0.7135 0.224 0.776
#> GSM617588 2 0.0000 0.8405 0.000 1.000
#> GSM617590 2 0.0376 0.8408 0.004 0.996
#> GSM617592 2 0.0000 0.8405 0.000 1.000
#> GSM617607 1 0.0672 0.8410 0.992 0.008
#> GSM617608 1 0.1184 0.8409 0.984 0.016
#> GSM617609 1 0.0672 0.8410 0.992 0.008
#> GSM617612 1 0.6048 0.7842 0.852 0.148
#> GSM617615 2 0.0672 0.8404 0.008 0.992
#> GSM617616 2 0.9993 -0.0354 0.484 0.516
#> GSM617617 2 0.3274 0.8233 0.060 0.940
#> GSM617618 2 0.9000 0.5270 0.316 0.684
#> GSM617619 2 0.1633 0.8399 0.024 0.976
#> GSM617620 2 0.0000 0.8405 0.000 1.000
#> GSM617622 2 0.0376 0.8410 0.004 0.996
#> GSM617623 1 0.9970 0.1863 0.532 0.468
#> GSM617624 2 0.8386 0.6218 0.268 0.732
#> GSM617625 1 0.4298 0.8149 0.912 0.088
#> GSM617626 2 0.4022 0.8125 0.080 0.920
#> GSM617627 2 0.6801 0.7207 0.180 0.820
#> GSM617628 1 0.4815 0.8059 0.896 0.104
#> GSM617632 2 0.9970 0.0359 0.468 0.532
#> GSM617634 2 0.1633 0.8380 0.024 0.976
#> GSM617635 1 0.2603 0.8345 0.956 0.044
#> GSM617636 1 0.9358 0.5208 0.648 0.352
#> GSM617637 1 0.8555 0.6414 0.720 0.280
#> GSM617638 1 0.9000 0.4299 0.684 0.316
#> GSM617639 1 0.7299 0.7301 0.796 0.204
#> GSM617640 2 0.2778 0.8288 0.048 0.952
#> GSM617641 2 0.0938 0.8400 0.012 0.988
#> GSM617643 2 0.0000 0.8405 0.000 1.000
#> GSM617644 2 0.0000 0.8405 0.000 1.000
#> GSM617647 2 0.8499 0.6200 0.276 0.724
#> GSM617648 2 0.0000 0.8405 0.000 1.000
#> GSM617649 2 0.5842 0.8006 0.140 0.860
#> GSM617650 1 0.0000 0.8397 1.000 0.000
#> GSM617651 1 0.5946 0.7838 0.856 0.144
#> GSM617653 1 0.1633 0.8396 0.976 0.024
#> GSM617654 2 0.4161 0.8113 0.084 0.916
#> GSM617583 1 0.4815 0.8062 0.896 0.104
#> GSM617584 2 0.0672 0.8413 0.008 0.992
#> GSM617585 2 0.7453 0.6862 0.212 0.788
#> GSM617586 1 0.4690 0.8063 0.900 0.100
#> GSM617587 1 0.9358 0.5105 0.648 0.352
#> GSM617589 2 0.0000 0.8405 0.000 1.000
#> GSM617591 2 0.5294 0.7776 0.120 0.880
#> GSM617593 1 0.7453 0.7230 0.788 0.212
#> GSM617594 2 0.9896 0.1366 0.440 0.560
#> GSM617595 1 0.7528 0.7174 0.784 0.216
#> GSM617596 1 0.0672 0.8405 0.992 0.008
#> GSM617597 1 0.0376 0.8398 0.996 0.004
#> GSM617598 1 0.7674 0.7087 0.776 0.224
#> GSM617599 2 0.4431 0.8146 0.092 0.908
#> GSM617600 1 0.3733 0.8160 0.928 0.072
#> GSM617601 2 0.0376 0.8399 0.004 0.996
#> GSM617602 1 0.0000 0.8397 1.000 0.000
#> GSM617603 2 0.7299 0.6944 0.204 0.796
#> GSM617604 1 0.0672 0.8406 0.992 0.008
#> GSM617605 2 0.0672 0.8408 0.008 0.992
#> GSM617606 2 0.7745 0.6670 0.228 0.772
#> GSM617610 1 0.8081 0.6826 0.752 0.248
#> GSM617611 1 0.1184 0.8409 0.984 0.016
#> GSM617613 1 0.7528 0.6981 0.784 0.216
#> GSM617614 1 0.0376 0.8398 0.996 0.004
#> GSM617621 1 0.7299 0.7299 0.796 0.204
#> GSM617629 1 0.9998 -0.2066 0.508 0.492
#> GSM617630 1 0.6712 0.7326 0.824 0.176
#> GSM617631 1 0.4022 0.8120 0.920 0.080
#> GSM617633 1 0.0000 0.8397 1.000 0.000
#> GSM617642 1 0.0672 0.8397 0.992 0.008
#> GSM617645 2 0.9129 0.5098 0.328 0.672
#> GSM617646 1 0.7299 0.7393 0.796 0.204
#> GSM617652 1 0.0000 0.8397 1.000 0.000
#> GSM617655 2 0.9044 0.5513 0.320 0.680
#> GSM617656 1 0.4022 0.8120 0.920 0.080
#> GSM617657 1 0.4562 0.8090 0.904 0.096
#> GSM617658 1 0.0376 0.8398 0.996 0.004
#> GSM617659 1 0.0000 0.8397 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM617581 2 0.0237 0.8185 0.000 0.996 0.004
#> GSM617582 2 0.5551 0.6656 0.212 0.768 0.020
#> GSM617588 2 0.0000 0.8188 0.000 1.000 0.000
#> GSM617590 2 0.0237 0.8186 0.000 0.996 0.004
#> GSM617592 2 0.0000 0.8188 0.000 1.000 0.000
#> GSM617607 1 0.0000 0.8136 1.000 0.000 0.000
#> GSM617608 1 0.0000 0.8136 1.000 0.000 0.000
#> GSM617609 1 0.5785 0.6316 0.696 0.004 0.300
#> GSM617612 1 0.1267 0.8089 0.972 0.024 0.004
#> GSM617615 2 0.6204 0.2587 0.000 0.576 0.424
#> GSM617616 2 0.7178 0.0545 0.464 0.512 0.024
#> GSM617617 2 0.0000 0.8188 0.000 1.000 0.000
#> GSM617618 2 0.5678 0.5086 0.316 0.684 0.000
#> GSM617619 2 0.4634 0.7107 0.012 0.824 0.164
#> GSM617620 2 0.0000 0.8188 0.000 1.000 0.000
#> GSM617622 2 0.0424 0.8182 0.000 0.992 0.008
#> GSM617623 1 0.7647 0.1438 0.516 0.440 0.044
#> GSM617624 3 0.8604 0.3510 0.124 0.312 0.564
#> GSM617625 3 0.1950 0.7718 0.040 0.008 0.952
#> GSM617626 2 0.0000 0.8188 0.000 1.000 0.000
#> GSM617627 2 0.6095 0.2757 0.000 0.608 0.392
#> GSM617628 3 0.0237 0.7826 0.004 0.000 0.996
#> GSM617632 2 0.6286 0.0918 0.464 0.536 0.000
#> GSM617634 2 0.1860 0.8015 0.000 0.948 0.052
#> GSM617635 1 0.2866 0.7963 0.916 0.008 0.076
#> GSM617636 1 0.5529 0.5545 0.704 0.296 0.000
#> GSM617637 1 0.3686 0.7357 0.860 0.140 0.000
#> GSM617638 3 0.9811 -0.1018 0.376 0.240 0.384
#> GSM617639 1 0.0000 0.8136 1.000 0.000 0.000
#> GSM617640 2 0.0000 0.8188 0.000 1.000 0.000
#> GSM617641 2 0.0892 0.8152 0.000 0.980 0.020
#> GSM617643 2 0.0000 0.8188 0.000 1.000 0.000
#> GSM617644 2 0.0000 0.8188 0.000 1.000 0.000
#> GSM617647 2 0.6482 0.5669 0.296 0.680 0.024
#> GSM617648 2 0.0000 0.8188 0.000 1.000 0.000
#> GSM617649 2 0.3340 0.7419 0.000 0.880 0.120
#> GSM617650 1 0.0000 0.8136 1.000 0.000 0.000
#> GSM617651 1 0.0000 0.8136 1.000 0.000 0.000
#> GSM617653 1 0.1860 0.8059 0.948 0.000 0.052
#> GSM617654 2 0.0424 0.8178 0.008 0.992 0.000
#> GSM617583 3 0.0000 0.7838 0.000 0.000 1.000
#> GSM617584 2 0.0747 0.8161 0.000 0.984 0.016
#> GSM617585 3 0.4555 0.6544 0.000 0.200 0.800
#> GSM617586 3 0.0000 0.7838 0.000 0.000 1.000
#> GSM617587 3 0.4371 0.7286 0.032 0.108 0.860
#> GSM617589 2 0.4796 0.6531 0.000 0.780 0.220
#> GSM617591 3 0.4796 0.6016 0.000 0.220 0.780
#> GSM617593 1 0.0000 0.8136 1.000 0.000 0.000
#> GSM617594 3 0.9925 0.2225 0.336 0.280 0.384
#> GSM617595 1 0.0000 0.8136 1.000 0.000 0.000
#> GSM617596 1 0.5948 0.5692 0.640 0.000 0.360
#> GSM617597 1 0.3192 0.7775 0.888 0.000 0.112
#> GSM617598 1 0.0000 0.8136 1.000 0.000 0.000
#> GSM617599 2 0.1529 0.8042 0.040 0.960 0.000
#> GSM617600 3 0.5706 0.5069 0.320 0.000 0.680
#> GSM617601 2 0.4796 0.6537 0.000 0.780 0.220
#> GSM617602 1 0.6008 0.5569 0.628 0.000 0.372
#> GSM617603 2 0.6026 0.2849 0.000 0.624 0.376
#> GSM617604 1 0.6008 0.5537 0.628 0.000 0.372
#> GSM617605 2 0.2261 0.7945 0.000 0.932 0.068
#> GSM617606 3 0.0592 0.7830 0.000 0.012 0.988
#> GSM617610 1 0.2066 0.7910 0.940 0.060 0.000
#> GSM617611 1 0.1163 0.8116 0.972 0.000 0.028
#> GSM617613 3 0.0000 0.7838 0.000 0.000 1.000
#> GSM617614 1 0.6235 0.4559 0.564 0.000 0.436
#> GSM617621 1 0.0000 0.8136 1.000 0.000 0.000
#> GSM617629 3 0.9734 0.1056 0.224 0.376 0.400
#> GSM617630 1 0.7143 0.4913 0.576 0.028 0.396
#> GSM617631 3 0.0000 0.7838 0.000 0.000 1.000
#> GSM617633 1 0.0000 0.8136 1.000 0.000 0.000
#> GSM617642 1 0.6302 0.3557 0.520 0.000 0.480
#> GSM617645 2 0.6148 0.4581 0.356 0.640 0.004
#> GSM617646 1 0.4865 0.7209 0.832 0.136 0.032
#> GSM617652 1 0.1860 0.8056 0.948 0.000 0.052
#> GSM617655 3 0.0000 0.7838 0.000 0.000 1.000
#> GSM617656 3 0.3412 0.7172 0.124 0.000 0.876
#> GSM617657 3 0.0000 0.7838 0.000 0.000 1.000
#> GSM617658 1 0.6026 0.5485 0.624 0.000 0.376
#> GSM617659 1 0.0000 0.8136 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM617581 2 0.0188 0.7619 0.000 0.996 0.000 0.004
#> GSM617582 2 0.4399 0.6273 0.212 0.768 0.020 0.000
#> GSM617588 2 0.0469 0.7604 0.000 0.988 0.000 0.012
#> GSM617590 2 0.4509 0.5129 0.000 0.708 0.004 0.288
#> GSM617592 2 0.2868 0.6950 0.000 0.864 0.000 0.136
#> GSM617607 1 0.0000 0.7919 1.000 0.000 0.000 0.000
#> GSM617608 1 0.0000 0.7919 1.000 0.000 0.000 0.000
#> GSM617609 1 0.6313 0.6187 0.652 0.000 0.220 0.128
#> GSM617612 1 0.1004 0.7882 0.972 0.024 0.004 0.000
#> GSM617615 2 0.6871 0.0274 0.000 0.480 0.416 0.104
#> GSM617616 2 0.5688 0.0156 0.464 0.512 0.024 0.000
#> GSM617617 2 0.0000 0.7615 0.000 1.000 0.000 0.000
#> GSM617618 2 0.4500 0.4841 0.316 0.684 0.000 0.000
#> GSM617619 2 0.4781 0.6561 0.012 0.788 0.160 0.040
#> GSM617620 2 0.0000 0.7615 0.000 1.000 0.000 0.000
#> GSM617622 2 0.0336 0.7621 0.000 0.992 0.008 0.000
#> GSM617623 1 0.7276 0.2630 0.516 0.380 0.032 0.072
#> GSM617624 3 0.7862 0.2969 0.096 0.292 0.548 0.064
#> GSM617625 3 0.2597 0.6832 0.040 0.004 0.916 0.040
#> GSM617626 2 0.0000 0.7615 0.000 1.000 0.000 0.000
#> GSM617627 2 0.5957 0.2968 0.000 0.588 0.364 0.048
#> GSM617628 3 0.0524 0.6807 0.004 0.000 0.988 0.008
#> GSM617632 2 0.4981 0.0504 0.464 0.536 0.000 0.000
#> GSM617634 2 0.1661 0.7512 0.000 0.944 0.052 0.004
#> GSM617635 1 0.2271 0.7791 0.916 0.008 0.076 0.000
#> GSM617636 1 0.4382 0.5672 0.704 0.296 0.000 0.000
#> GSM617637 1 0.2921 0.7214 0.860 0.140 0.000 0.000
#> GSM617638 1 0.9104 0.1398 0.376 0.236 0.316 0.072
#> GSM617639 1 0.0000 0.7919 1.000 0.000 0.000 0.000
#> GSM617640 2 0.0188 0.7619 0.000 0.996 0.000 0.004
#> GSM617641 2 0.4228 0.6086 0.000 0.760 0.008 0.232
#> GSM617643 2 0.0000 0.7615 0.000 1.000 0.000 0.000
#> GSM617644 2 0.0707 0.7602 0.000 0.980 0.000 0.020
#> GSM617647 2 0.5963 0.5150 0.284 0.660 0.016 0.040
#> GSM617648 2 0.0000 0.7615 0.000 1.000 0.000 0.000
#> GSM617649 2 0.4549 0.6540 0.000 0.804 0.096 0.100
#> GSM617650 1 0.0000 0.7919 1.000 0.000 0.000 0.000
#> GSM617651 1 0.0000 0.7919 1.000 0.000 0.000 0.000
#> GSM617653 1 0.1474 0.7868 0.948 0.000 0.052 0.000
#> GSM617654 2 0.0524 0.7619 0.008 0.988 0.000 0.004
#> GSM617583 3 0.0376 0.6855 0.004 0.000 0.992 0.004
#> GSM617584 2 0.1890 0.7462 0.000 0.936 0.008 0.056
#> GSM617585 3 0.3569 0.5240 0.000 0.196 0.804 0.000
#> GSM617586 3 0.2345 0.6743 0.000 0.000 0.900 0.100
#> GSM617587 3 0.5477 0.6113 0.020 0.084 0.764 0.132
#> GSM617589 2 0.3945 0.6258 0.000 0.780 0.216 0.004
#> GSM617591 3 0.5325 0.5567 0.000 0.160 0.744 0.096
#> GSM617593 1 0.0000 0.7919 1.000 0.000 0.000 0.000
#> GSM617594 3 0.8698 0.1271 0.304 0.280 0.380 0.036
#> GSM617595 1 0.0000 0.7919 1.000 0.000 0.000 0.000
#> GSM617596 1 0.4905 0.5914 0.632 0.000 0.364 0.004
#> GSM617597 1 0.3691 0.7482 0.856 0.000 0.076 0.068
#> GSM617598 1 0.0000 0.7919 1.000 0.000 0.000 0.000
#> GSM617599 2 0.2319 0.7423 0.040 0.924 0.000 0.036
#> GSM617600 3 0.4980 0.4181 0.304 0.000 0.680 0.016
#> GSM617601 2 0.4364 0.6136 0.000 0.764 0.220 0.016
#> GSM617602 1 0.5253 0.5873 0.624 0.000 0.360 0.016
#> GSM617603 4 0.4244 0.0000 0.000 0.032 0.168 0.800
#> GSM617604 1 0.4950 0.5784 0.620 0.000 0.376 0.004
#> GSM617605 2 0.5827 0.4386 0.000 0.632 0.052 0.316
#> GSM617606 3 0.1452 0.6907 0.000 0.008 0.956 0.036
#> GSM617610 1 0.1637 0.7722 0.940 0.060 0.000 0.000
#> GSM617611 1 0.1022 0.7905 0.968 0.000 0.032 0.000
#> GSM617613 3 0.0188 0.6823 0.000 0.000 0.996 0.004
#> GSM617614 1 0.5105 0.5022 0.564 0.000 0.432 0.004
#> GSM617621 1 0.0000 0.7919 1.000 0.000 0.000 0.000
#> GSM617629 3 0.8285 -0.0446 0.224 0.368 0.388 0.020
#> GSM617630 1 0.6016 0.5381 0.576 0.032 0.384 0.008
#> GSM617631 3 0.0188 0.6823 0.000 0.000 0.996 0.004
#> GSM617633 1 0.0000 0.7919 1.000 0.000 0.000 0.000
#> GSM617642 1 0.6686 0.4139 0.520 0.000 0.388 0.092
#> GSM617645 2 0.5478 0.4445 0.344 0.628 0.000 0.028
#> GSM617646 1 0.4441 0.7009 0.816 0.136 0.028 0.020
#> GSM617652 1 0.2227 0.7823 0.928 0.000 0.036 0.036
#> GSM617655 3 0.2589 0.6712 0.000 0.000 0.884 0.116
#> GSM617656 3 0.4827 0.5856 0.124 0.000 0.784 0.092
#> GSM617657 3 0.0921 0.6824 0.000 0.000 0.972 0.028
#> GSM617658 1 0.4964 0.5736 0.616 0.000 0.380 0.004
#> GSM617659 1 0.0000 0.7919 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM617581 2 0.0162 0.6277 0.000 0.996 0.000 0.000 NA
#> GSM617582 2 0.3789 0.4782 0.212 0.768 0.020 0.000 NA
#> GSM617588 2 0.1908 0.5706 0.000 0.908 0.000 0.092 NA
#> GSM617590 4 0.4307 0.3535 0.000 0.496 0.000 0.504 NA
#> GSM617592 2 0.3876 0.1049 0.000 0.684 0.000 0.316 NA
#> GSM617607 1 0.0000 0.8073 1.000 0.000 0.000 0.000 NA
#> GSM617608 1 0.0000 0.8073 1.000 0.000 0.000 0.000 NA
#> GSM617609 1 0.5602 0.6143 0.640 0.000 0.196 0.000 NA
#> GSM617612 1 0.0865 0.8045 0.972 0.024 0.004 0.000 NA
#> GSM617615 2 0.6188 -0.0434 0.000 0.448 0.416 0.000 NA
#> GSM617616 2 0.4900 0.0178 0.464 0.512 0.024 0.000 NA
#> GSM617617 2 0.0000 0.6273 0.000 1.000 0.000 0.000 NA
#> GSM617618 2 0.3876 0.3729 0.316 0.684 0.000 0.000 NA
#> GSM617619 2 0.4351 0.5040 0.012 0.784 0.160 0.012 NA
#> GSM617620 2 0.0290 0.6257 0.000 0.992 0.000 0.008 NA
#> GSM617622 2 0.0290 0.6276 0.000 0.992 0.008 0.000 NA
#> GSM617623 1 0.6292 0.2594 0.516 0.372 0.024 0.000 NA
#> GSM617624 3 0.7178 0.3229 0.092 0.292 0.536 0.016 NA
#> GSM617625 3 0.2308 0.7327 0.036 0.004 0.912 0.000 NA
#> GSM617626 2 0.0000 0.6273 0.000 1.000 0.000 0.000 NA
#> GSM617627 2 0.5478 0.0968 0.000 0.584 0.352 0.008 NA
#> GSM617628 3 0.0290 0.7260 0.000 0.000 0.992 0.000 NA
#> GSM617632 2 0.4291 0.0515 0.464 0.536 0.000 0.000 NA
#> GSM617634 2 0.1644 0.6125 0.000 0.940 0.048 0.008 NA
#> GSM617635 1 0.1956 0.7927 0.916 0.008 0.076 0.000 NA
#> GSM617636 1 0.3774 0.5702 0.704 0.296 0.000 0.000 NA
#> GSM617637 1 0.2516 0.7453 0.860 0.140 0.000 0.000 NA
#> GSM617638 1 0.8087 0.1373 0.368 0.236 0.308 0.004 NA
#> GSM617639 1 0.0000 0.8073 1.000 0.000 0.000 0.000 NA
#> GSM617640 2 0.0162 0.6275 0.000 0.996 0.000 0.000 NA
#> GSM617641 2 0.4621 -0.3207 0.000 0.576 0.004 0.412 NA
#> GSM617643 2 0.0000 0.6273 0.000 1.000 0.000 0.000 NA
#> GSM617644 2 0.0912 0.6199 0.000 0.972 0.000 0.016 NA
#> GSM617647 2 0.5162 0.3914 0.276 0.664 0.016 0.000 NA
#> GSM617648 2 0.0000 0.6273 0.000 1.000 0.000 0.000 NA
#> GSM617649 2 0.4342 0.4496 0.000 0.788 0.084 0.012 NA
#> GSM617650 1 0.0000 0.8073 1.000 0.000 0.000 0.000 NA
#> GSM617651 1 0.0000 0.8073 1.000 0.000 0.000 0.000 NA
#> GSM617653 1 0.1341 0.8007 0.944 0.000 0.056 0.000 NA
#> GSM617654 2 0.4196 0.2076 0.000 0.640 0.000 0.004 NA
#> GSM617583 3 0.0162 0.7285 0.000 0.000 0.996 0.000 NA
#> GSM617584 2 0.1764 0.5996 0.000 0.928 0.008 0.000 NA
#> GSM617585 3 0.3352 0.5897 0.000 0.192 0.800 0.004 NA
#> GSM617586 3 0.2516 0.7179 0.000 0.000 0.860 0.000 NA
#> GSM617587 3 0.5023 0.6581 0.020 0.080 0.732 0.000 NA
#> GSM617589 2 0.3821 0.4663 0.000 0.764 0.216 0.020 NA
#> GSM617591 3 0.4723 0.6308 0.000 0.136 0.736 0.000 NA
#> GSM617593 1 0.0000 0.8073 1.000 0.000 0.000 0.000 NA
#> GSM617594 3 0.7492 0.1694 0.304 0.280 0.380 0.000 NA
#> GSM617595 1 0.0000 0.8073 1.000 0.000 0.000 0.000 NA
#> GSM617596 1 0.4444 0.5883 0.624 0.000 0.364 0.000 NA
#> GSM617597 1 0.3234 0.7618 0.852 0.000 0.064 0.000 NA
#> GSM617598 1 0.0000 0.8073 1.000 0.000 0.000 0.000 NA
#> GSM617599 2 0.2077 0.5968 0.040 0.920 0.000 0.000 NA
#> GSM617600 3 0.4604 0.5450 0.292 0.000 0.680 0.012 NA
#> GSM617601 2 0.3707 0.4713 0.000 0.768 0.220 0.004 NA
#> GSM617602 1 0.4804 0.5920 0.624 0.000 0.348 0.004 NA
#> GSM617603 4 0.5830 0.1232 0.000 0.016 0.144 0.652 NA
#> GSM617604 1 0.4482 0.5743 0.612 0.000 0.376 0.000 NA
#> GSM617605 4 0.4883 0.3912 0.000 0.464 0.016 0.516 NA
#> GSM617606 3 0.1329 0.7340 0.000 0.008 0.956 0.004 NA
#> GSM617610 1 0.1410 0.7894 0.940 0.060 0.000 0.000 NA
#> GSM617611 1 0.0880 0.8055 0.968 0.000 0.032 0.000 NA
#> GSM617613 3 0.0162 0.7263 0.000 0.000 0.996 0.000 NA
#> GSM617614 1 0.4597 0.5076 0.564 0.000 0.424 0.000 NA
#> GSM617621 1 0.0000 0.8073 1.000 0.000 0.000 0.000 NA
#> GSM617629 3 0.8422 -0.0856 0.204 0.336 0.336 0.012 NA
#> GSM617630 1 0.5225 0.5406 0.576 0.024 0.384 0.000 NA
#> GSM617631 3 0.0404 0.7240 0.000 0.000 0.988 0.000 NA
#> GSM617633 1 0.0000 0.8073 1.000 0.000 0.000 0.000 NA
#> GSM617642 1 0.6031 0.4192 0.520 0.000 0.352 0.000 NA
#> GSM617645 2 0.4929 0.3470 0.340 0.624 0.000 0.004 NA
#> GSM617646 1 0.3825 0.7209 0.816 0.136 0.028 0.000 NA
#> GSM617652 1 0.2077 0.7965 0.920 0.000 0.040 0.000 NA
#> GSM617655 3 0.2719 0.7143 0.000 0.000 0.852 0.004 NA
#> GSM617656 3 0.4458 0.6611 0.120 0.000 0.760 0.000 NA
#> GSM617657 3 0.3333 0.6267 0.000 0.000 0.788 0.004 NA
#> GSM617658 1 0.4494 0.5695 0.608 0.000 0.380 0.000 NA
#> GSM617659 1 0.0000 0.8073 1.000 0.000 0.000 0.000 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM617581 2 0.0146 0.54579 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM617582 2 0.3403 0.38580 0.212 0.768 0.020 0.000 0.000 0.000
#> GSM617588 2 0.2135 0.40260 0.000 0.872 0.000 0.128 0.000 0.000
#> GSM617590 4 0.3756 0.86028 0.000 0.400 0.000 0.600 0.000 0.000
#> GSM617592 2 0.3706 -0.47033 0.000 0.620 0.000 0.380 0.000 0.000
#> GSM617607 1 0.0000 0.79717 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617608 1 0.0000 0.79717 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617609 1 0.5817 0.62553 0.640 0.000 0.184 0.008 0.056 0.112
#> GSM617612 1 0.0777 0.79420 0.972 0.024 0.004 0.000 0.000 0.000
#> GSM617615 2 0.6155 -0.06739 0.000 0.440 0.424 0.004 0.052 0.080
#> GSM617616 2 0.4401 0.02551 0.464 0.512 0.024 0.000 0.000 0.000
#> GSM617617 2 0.0000 0.54554 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM617618 2 0.3482 0.30924 0.316 0.684 0.000 0.000 0.000 0.000
#> GSM617619 2 0.4085 0.40605 0.012 0.780 0.160 0.008 0.012 0.028
#> GSM617620 2 0.0260 0.54221 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM617622 2 0.0260 0.54555 0.000 0.992 0.008 0.000 0.000 0.000
#> GSM617623 1 0.5974 0.25044 0.516 0.372 0.024 0.000 0.032 0.056
#> GSM617624 3 0.6702 0.27074 0.084 0.288 0.540 0.012 0.040 0.036
#> GSM617625 3 0.2194 0.72139 0.036 0.004 0.912 0.000 0.008 0.040
#> GSM617626 2 0.0000 0.54554 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM617627 2 0.5393 -0.00704 0.000 0.584 0.332 0.008 0.032 0.044
#> GSM617628 3 0.0291 0.71137 0.000 0.000 0.992 0.000 0.004 0.004
#> GSM617632 2 0.3854 0.05717 0.464 0.536 0.000 0.000 0.000 0.000
#> GSM617634 2 0.1621 0.52478 0.000 0.936 0.048 0.004 0.004 0.008
#> GSM617635 1 0.1931 0.78627 0.916 0.008 0.068 0.004 0.000 0.004
#> GSM617636 1 0.3390 0.55441 0.704 0.296 0.000 0.000 0.000 0.000
#> GSM617637 1 0.2260 0.72882 0.860 0.140 0.000 0.000 0.000 0.000
#> GSM617638 1 0.7814 0.15385 0.368 0.236 0.292 0.012 0.032 0.060
#> GSM617639 1 0.0000 0.79717 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617640 2 0.0260 0.54400 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM617641 4 0.3996 0.76797 0.000 0.484 0.000 0.512 0.000 0.004
#> GSM617643 2 0.0000 0.54554 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM617644 2 0.0976 0.53157 0.000 0.968 0.000 0.016 0.008 0.008
#> GSM617647 2 0.5018 0.31006 0.276 0.656 0.016 0.004 0.024 0.024
#> GSM617648 2 0.0000 0.54554 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM617649 2 0.4382 0.31617 0.000 0.784 0.084 0.012 0.044 0.076
#> GSM617650 1 0.0000 0.79717 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617651 1 0.0000 0.79717 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617653 1 0.1204 0.79194 0.944 0.000 0.056 0.000 0.000 0.000
#> GSM617654 5 0.3531 0.00000 0.000 0.328 0.000 0.000 0.672 0.000
#> GSM617583 3 0.0146 0.71504 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM617584 2 0.1820 0.50474 0.000 0.924 0.008 0.000 0.012 0.056
#> GSM617585 3 0.3230 0.57446 0.000 0.192 0.792 0.008 0.000 0.008
#> GSM617586 3 0.3002 0.70688 0.000 0.000 0.848 0.004 0.048 0.100
#> GSM617587 3 0.5103 0.65727 0.020 0.072 0.740 0.004 0.056 0.108
#> GSM617589 2 0.3511 0.36591 0.000 0.760 0.216 0.024 0.000 0.000
#> GSM617591 3 0.4655 0.63975 0.000 0.120 0.744 0.000 0.048 0.088
#> GSM617593 1 0.0000 0.79717 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617594 3 0.7038 0.05713 0.296 0.276 0.384 0.004 0.024 0.016
#> GSM617595 1 0.0000 0.79717 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617596 1 0.4064 0.59978 0.624 0.000 0.360 0.000 0.000 0.016
#> GSM617597 1 0.3263 0.75175 0.848 0.000 0.064 0.000 0.028 0.060
#> GSM617598 1 0.0000 0.79717 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617599 2 0.2247 0.49828 0.040 0.912 0.000 0.004 0.024 0.020
#> GSM617600 3 0.4381 0.49499 0.276 0.000 0.684 0.008 0.012 0.020
#> GSM617601 2 0.3469 0.37863 0.000 0.764 0.220 0.004 0.008 0.004
#> GSM617602 1 0.4528 0.60407 0.624 0.000 0.340 0.008 0.004 0.024
#> GSM617603 6 0.4270 0.00000 0.000 0.004 0.100 0.156 0.000 0.740
#> GSM617604 1 0.4223 0.58727 0.612 0.000 0.368 0.004 0.000 0.016
#> GSM617605 4 0.4026 0.83918 0.000 0.376 0.012 0.612 0.000 0.000
#> GSM617606 3 0.1396 0.72412 0.000 0.008 0.952 0.004 0.012 0.024
#> GSM617610 1 0.1267 0.77939 0.940 0.060 0.000 0.000 0.000 0.000
#> GSM617611 1 0.0790 0.79612 0.968 0.000 0.032 0.000 0.000 0.000
#> GSM617613 3 0.0146 0.71185 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM617614 1 0.4332 0.52171 0.564 0.000 0.416 0.004 0.000 0.016
#> GSM617621 1 0.0000 0.79717 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617629 2 0.9619 -0.32039 0.152 0.252 0.208 0.096 0.204 0.088
#> GSM617630 1 0.4886 0.55479 0.576 0.024 0.376 0.004 0.000 0.020
#> GSM617631 3 0.0603 0.70455 0.000 0.000 0.980 0.004 0.000 0.016
#> GSM617633 1 0.0000 0.79717 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617642 1 0.6042 0.43342 0.520 0.000 0.340 0.004 0.040 0.096
#> GSM617645 2 0.5123 0.28329 0.320 0.612 0.000 0.024 0.032 0.012
#> GSM617646 1 0.3602 0.70413 0.812 0.136 0.028 0.000 0.016 0.008
#> GSM617652 1 0.2176 0.78518 0.916 0.000 0.036 0.004 0.024 0.020
#> GSM617655 3 0.3128 0.70203 0.000 0.000 0.844 0.008 0.052 0.096
#> GSM617656 3 0.4360 0.64214 0.112 0.000 0.768 0.000 0.044 0.076
#> GSM617657 3 0.5418 0.28193 0.000 0.000 0.616 0.272 0.040 0.072
#> GSM617658 1 0.4234 0.58245 0.608 0.000 0.372 0.004 0.000 0.016
#> GSM617659 1 0.0000 0.79717 1.000 0.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:pam 73 0.007135 2
#> CV:pam 65 0.000231 3
#> CV:pam 64 0.000175 4
#> CV:pam 56 0.000526 5
#> CV:pam 54 0.002776 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 79 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 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 0.733 0.870 0.944 0.3447 0.658 0.658
#> 3 3 0.382 0.597 0.761 0.6781 0.611 0.455
#> 4 4 0.758 0.850 0.914 0.2637 0.789 0.506
#> 5 5 0.661 0.766 0.834 0.0462 1.000 1.000
#> 6 6 0.624 0.571 0.744 0.0378 0.925 0.728
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
#> GSM617581 1 0.0000 0.9522 1.000 0.000
#> GSM617582 1 0.0000 0.9522 1.000 0.000
#> GSM617588 2 0.0938 0.8846 0.012 0.988
#> GSM617590 2 0.0938 0.8846 0.012 0.988
#> GSM617592 2 0.0938 0.8846 0.012 0.988
#> GSM617607 1 0.0000 0.9522 1.000 0.000
#> GSM617608 1 0.0000 0.9522 1.000 0.000
#> GSM617609 1 0.0376 0.9503 0.996 0.004
#> GSM617612 1 0.0000 0.9522 1.000 0.000
#> GSM617615 2 0.4939 0.8566 0.108 0.892
#> GSM617616 1 0.0000 0.9522 1.000 0.000
#> GSM617617 1 0.9944 0.0305 0.544 0.456
#> GSM617618 1 0.0000 0.9522 1.000 0.000
#> GSM617619 1 0.0000 0.9522 1.000 0.000
#> GSM617620 2 0.0938 0.8846 0.012 0.988
#> GSM617622 2 0.9815 0.3796 0.420 0.580
#> GSM617623 1 0.0376 0.9501 0.996 0.004
#> GSM617624 1 0.3733 0.8886 0.928 0.072
#> GSM617625 1 0.0000 0.9522 1.000 0.000
#> GSM617626 1 0.0000 0.9522 1.000 0.000
#> GSM617627 1 0.7299 0.7147 0.796 0.204
#> GSM617628 1 0.0000 0.9522 1.000 0.000
#> GSM617632 1 0.0000 0.9522 1.000 0.000
#> GSM617634 1 0.1633 0.9353 0.976 0.024
#> GSM617635 1 0.0000 0.9522 1.000 0.000
#> GSM617636 1 0.0000 0.9522 1.000 0.000
#> GSM617637 1 0.0000 0.9522 1.000 0.000
#> GSM617638 1 0.1843 0.9319 0.972 0.028
#> GSM617639 1 0.0000 0.9522 1.000 0.000
#> GSM617640 2 0.5178 0.8516 0.116 0.884
#> GSM617641 2 0.0938 0.8846 0.012 0.988
#> GSM617643 2 0.5059 0.8543 0.112 0.888
#> GSM617644 2 0.2236 0.8830 0.036 0.964
#> GSM617647 1 0.7950 0.6529 0.760 0.240
#> GSM617648 2 0.9552 0.4977 0.376 0.624
#> GSM617649 1 0.8555 0.5741 0.720 0.280
#> GSM617650 1 0.0000 0.9522 1.000 0.000
#> GSM617651 1 0.0000 0.9522 1.000 0.000
#> GSM617653 1 0.0672 0.9470 0.992 0.008
#> GSM617654 1 0.8861 0.5195 0.696 0.304
#> GSM617583 1 0.0000 0.9522 1.000 0.000
#> GSM617584 1 1.0000 -0.1634 0.504 0.496
#> GSM617585 2 0.9044 0.6123 0.320 0.680
#> GSM617586 1 0.0376 0.9503 0.996 0.004
#> GSM617587 1 0.0000 0.9522 1.000 0.000
#> GSM617589 2 0.0938 0.8846 0.012 0.988
#> GSM617591 1 0.5519 0.8248 0.872 0.128
#> GSM617593 1 0.0000 0.9522 1.000 0.000
#> GSM617594 1 0.2043 0.9280 0.968 0.032
#> GSM617595 1 0.0672 0.9470 0.992 0.008
#> GSM617596 1 0.0000 0.9522 1.000 0.000
#> GSM617597 1 0.0000 0.9522 1.000 0.000
#> GSM617598 1 0.0000 0.9522 1.000 0.000
#> GSM617599 1 0.0000 0.9522 1.000 0.000
#> GSM617600 1 0.0376 0.9503 0.996 0.004
#> GSM617601 2 0.2236 0.8830 0.036 0.964
#> GSM617602 1 0.0376 0.9503 0.996 0.004
#> GSM617603 2 0.0938 0.8846 0.012 0.988
#> GSM617604 1 0.0000 0.9522 1.000 0.000
#> GSM617605 2 0.1184 0.8844 0.016 0.984
#> GSM617606 1 0.6531 0.7709 0.832 0.168
#> GSM617610 1 0.0672 0.9470 0.992 0.008
#> GSM617611 1 0.0000 0.9522 1.000 0.000
#> GSM617613 1 0.0000 0.9522 1.000 0.000
#> GSM617614 1 0.0376 0.9503 0.996 0.004
#> GSM617621 1 0.0000 0.9522 1.000 0.000
#> GSM617629 1 0.1184 0.9441 0.984 0.016
#> GSM617630 1 0.0938 0.9444 0.988 0.012
#> GSM617631 1 0.0376 0.9503 0.996 0.004
#> GSM617633 1 0.0000 0.9522 1.000 0.000
#> GSM617642 1 0.0376 0.9503 0.996 0.004
#> GSM617645 2 0.8267 0.7040 0.260 0.740
#> GSM617646 1 0.0000 0.9522 1.000 0.000
#> GSM617652 1 0.0000 0.9522 1.000 0.000
#> GSM617655 1 0.0376 0.9503 0.996 0.004
#> GSM617656 1 0.0000 0.9522 1.000 0.000
#> GSM617657 1 0.0376 0.9501 0.996 0.004
#> GSM617658 1 0.0376 0.9503 0.996 0.004
#> GSM617659 1 0.0000 0.9522 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM617581 1 0.5235 0.5990 0.812 0.152 0.036
#> GSM617582 1 0.4249 0.6774 0.864 0.108 0.028
#> GSM617588 2 0.0000 0.7028 0.000 1.000 0.000
#> GSM617590 2 0.0237 0.7012 0.000 0.996 0.004
#> GSM617592 2 0.0424 0.6997 0.000 0.992 0.008
#> GSM617607 1 0.0892 0.8144 0.980 0.000 0.020
#> GSM617608 1 0.0000 0.8186 1.000 0.000 0.000
#> GSM617609 3 0.7757 0.4280 0.464 0.048 0.488
#> GSM617612 1 0.0237 0.8185 0.996 0.000 0.004
#> GSM617615 2 0.3764 0.7174 0.040 0.892 0.068
#> GSM617616 1 0.0237 0.8172 0.996 0.000 0.004
#> GSM617617 2 0.7519 0.6940 0.044 0.568 0.388
#> GSM617618 1 0.0424 0.8169 0.992 0.000 0.008
#> GSM617619 3 0.9063 0.1820 0.200 0.248 0.552
#> GSM617620 2 0.0000 0.7028 0.000 1.000 0.000
#> GSM617622 2 0.8233 0.6721 0.120 0.616 0.264
#> GSM617623 1 0.4931 0.6238 0.828 0.140 0.032
#> GSM617624 2 0.8957 0.5471 0.128 0.472 0.400
#> GSM617625 1 0.4452 0.6153 0.808 0.000 0.192
#> GSM617626 1 0.0237 0.8183 0.996 0.004 0.000
#> GSM617627 2 0.8720 0.6309 0.124 0.540 0.336
#> GSM617628 1 0.6079 0.0267 0.612 0.000 0.388
#> GSM617632 1 0.0424 0.8159 0.992 0.000 0.008
#> GSM617634 2 0.9651 0.3670 0.208 0.400 0.392
#> GSM617635 1 0.0592 0.8173 0.988 0.000 0.012
#> GSM617636 1 0.2200 0.7923 0.940 0.004 0.056
#> GSM617637 1 0.0000 0.8186 1.000 0.000 0.000
#> GSM617638 3 0.9332 -0.4666 0.164 0.404 0.432
#> GSM617639 1 0.0237 0.8185 0.996 0.000 0.004
#> GSM617640 2 0.6617 0.7001 0.012 0.600 0.388
#> GSM617641 2 0.0000 0.7028 0.000 1.000 0.000
#> GSM617643 2 0.6952 0.7041 0.024 0.600 0.376
#> GSM617644 2 0.4452 0.7235 0.000 0.808 0.192
#> GSM617647 2 0.9386 0.5550 0.204 0.500 0.296
#> GSM617648 2 0.7442 0.7014 0.044 0.588 0.368
#> GSM617649 2 0.8703 0.6393 0.124 0.544 0.332
#> GSM617650 1 0.0000 0.8186 1.000 0.000 0.000
#> GSM617651 1 0.0000 0.8186 1.000 0.000 0.000
#> GSM617653 1 0.0237 0.8170 0.996 0.000 0.004
#> GSM617654 2 0.8097 0.6757 0.072 0.540 0.388
#> GSM617583 1 0.5016 0.5322 0.760 0.000 0.240
#> GSM617584 2 0.6441 0.4165 0.276 0.696 0.028
#> GSM617585 2 0.7365 0.6899 0.112 0.700 0.188
#> GSM617586 3 0.6192 0.5155 0.420 0.000 0.580
#> GSM617587 1 0.6676 -0.3220 0.516 0.008 0.476
#> GSM617589 2 0.0475 0.7024 0.004 0.992 0.004
#> GSM617591 2 0.7065 0.3787 0.288 0.664 0.048
#> GSM617593 1 0.0000 0.8186 1.000 0.000 0.000
#> GSM617594 1 0.8577 -0.2111 0.468 0.436 0.096
#> GSM617595 1 0.0000 0.8186 1.000 0.000 0.000
#> GSM617596 1 0.1031 0.8134 0.976 0.000 0.024
#> GSM617597 1 0.2711 0.7690 0.912 0.000 0.088
#> GSM617598 1 0.0000 0.8186 1.000 0.000 0.000
#> GSM617599 1 0.7493 0.2666 0.676 0.232 0.092
#> GSM617600 3 0.6330 0.5487 0.396 0.004 0.600
#> GSM617601 2 0.1525 0.7100 0.004 0.964 0.032
#> GSM617602 3 0.6168 0.5316 0.412 0.000 0.588
#> GSM617603 2 0.1163 0.7088 0.000 0.972 0.028
#> GSM617604 1 0.4796 0.5851 0.780 0.000 0.220
#> GSM617605 2 0.0424 0.6997 0.000 0.992 0.008
#> GSM617606 2 0.8911 0.5950 0.176 0.564 0.260
#> GSM617610 1 0.0000 0.8186 1.000 0.000 0.000
#> GSM617611 1 0.0000 0.8186 1.000 0.000 0.000
#> GSM617613 3 0.7969 0.5405 0.396 0.064 0.540
#> GSM617614 1 0.5948 0.2197 0.640 0.000 0.360
#> GSM617621 1 0.1163 0.8112 0.972 0.000 0.028
#> GSM617629 3 0.7944 0.3082 0.196 0.144 0.660
#> GSM617630 3 0.9330 0.0471 0.244 0.236 0.520
#> GSM617631 3 0.6111 0.5473 0.396 0.000 0.604
#> GSM617633 1 0.3669 0.7494 0.896 0.040 0.064
#> GSM617642 1 0.5254 0.5055 0.736 0.000 0.264
#> GSM617645 2 0.6798 0.6977 0.016 0.584 0.400
#> GSM617646 1 0.1411 0.8081 0.964 0.000 0.036
#> GSM617652 1 0.1753 0.8003 0.952 0.000 0.048
#> GSM617655 3 0.6386 0.5326 0.412 0.004 0.584
#> GSM617656 3 0.6140 0.5392 0.404 0.000 0.596
#> GSM617657 3 0.8001 0.4544 0.212 0.136 0.652
#> GSM617658 1 0.6267 -0.1832 0.548 0.000 0.452
#> GSM617659 1 0.0000 0.8186 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM617581 1 0.3985 0.865 0.832 0.136 0.008 0.024
#> GSM617582 1 0.3769 0.858 0.864 0.072 0.052 0.012
#> GSM617588 4 0.0817 0.866 0.000 0.024 0.000 0.976
#> GSM617590 4 0.0817 0.866 0.000 0.024 0.000 0.976
#> GSM617592 4 0.0817 0.866 0.000 0.024 0.000 0.976
#> GSM617607 1 0.1743 0.929 0.940 0.056 0.004 0.000
#> GSM617608 1 0.0188 0.938 0.996 0.000 0.004 0.000
#> GSM617609 3 0.2125 0.873 0.004 0.076 0.920 0.000
#> GSM617612 1 0.0188 0.938 0.996 0.000 0.004 0.000
#> GSM617615 4 0.3873 0.740 0.000 0.228 0.000 0.772
#> GSM617616 1 0.0188 0.938 0.996 0.000 0.004 0.000
#> GSM617617 2 0.0707 0.872 0.000 0.980 0.000 0.020
#> GSM617618 1 0.0188 0.938 0.996 0.000 0.004 0.000
#> GSM617619 2 0.4941 0.294 0.000 0.564 0.436 0.000
#> GSM617620 4 0.0817 0.866 0.000 0.024 0.000 0.976
#> GSM617622 2 0.4690 0.630 0.000 0.724 0.016 0.260
#> GSM617623 1 0.4085 0.863 0.828 0.136 0.008 0.028
#> GSM617624 2 0.0657 0.874 0.000 0.984 0.004 0.012
#> GSM617625 3 0.4193 0.704 0.268 0.000 0.732 0.000
#> GSM617626 1 0.2156 0.927 0.928 0.060 0.004 0.008
#> GSM617627 2 0.0804 0.874 0.000 0.980 0.008 0.012
#> GSM617628 3 0.3610 0.784 0.200 0.000 0.800 0.000
#> GSM617632 1 0.0967 0.937 0.976 0.004 0.004 0.016
#> GSM617634 2 0.2074 0.868 0.016 0.940 0.012 0.032
#> GSM617635 1 0.1489 0.932 0.952 0.044 0.004 0.000
#> GSM617636 1 0.3723 0.886 0.856 0.108 0.024 0.012
#> GSM617637 1 0.1022 0.936 0.968 0.032 0.000 0.000
#> GSM617638 2 0.0817 0.865 0.000 0.976 0.024 0.000
#> GSM617639 1 0.1474 0.931 0.948 0.052 0.000 0.000
#> GSM617640 2 0.1022 0.868 0.000 0.968 0.000 0.032
#> GSM617641 4 0.0817 0.866 0.000 0.024 0.000 0.976
#> GSM617643 2 0.2216 0.828 0.000 0.908 0.000 0.092
#> GSM617644 4 0.4855 0.320 0.000 0.400 0.000 0.600
#> GSM617647 2 0.0376 0.872 0.000 0.992 0.004 0.004
#> GSM617648 2 0.2704 0.809 0.000 0.876 0.000 0.124
#> GSM617649 2 0.1109 0.871 0.000 0.968 0.004 0.028
#> GSM617650 1 0.0188 0.938 0.996 0.000 0.004 0.000
#> GSM617651 1 0.0000 0.937 1.000 0.000 0.000 0.000
#> GSM617653 1 0.0592 0.936 0.984 0.000 0.000 0.016
#> GSM617654 2 0.0336 0.873 0.000 0.992 0.000 0.008
#> GSM617583 3 0.3649 0.781 0.204 0.000 0.796 0.000
#> GSM617584 4 0.5869 0.642 0.112 0.160 0.008 0.720
#> GSM617585 4 0.4780 0.754 0.000 0.096 0.116 0.788
#> GSM617586 3 0.0000 0.922 0.000 0.000 1.000 0.000
#> GSM617587 3 0.1004 0.912 0.004 0.024 0.972 0.000
#> GSM617589 4 0.0817 0.866 0.000 0.024 0.000 0.976
#> GSM617591 4 0.4883 0.662 0.000 0.288 0.016 0.696
#> GSM617593 1 0.0188 0.938 0.996 0.000 0.004 0.000
#> GSM617594 2 0.2197 0.812 0.080 0.916 0.004 0.000
#> GSM617595 1 0.0000 0.937 1.000 0.000 0.000 0.000
#> GSM617596 1 0.2605 0.926 0.920 0.040 0.016 0.024
#> GSM617597 1 0.1902 0.918 0.932 0.004 0.064 0.000
#> GSM617598 1 0.0188 0.938 0.996 0.000 0.004 0.000
#> GSM617599 2 0.4318 0.662 0.208 0.776 0.004 0.012
#> GSM617600 3 0.0000 0.922 0.000 0.000 1.000 0.000
#> GSM617601 4 0.3873 0.747 0.000 0.228 0.000 0.772
#> GSM617602 3 0.0000 0.922 0.000 0.000 1.000 0.000
#> GSM617603 4 0.1637 0.852 0.000 0.060 0.000 0.940
#> GSM617604 1 0.5248 0.693 0.716 0.012 0.248 0.024
#> GSM617605 4 0.0817 0.866 0.000 0.024 0.000 0.976
#> GSM617606 2 0.4381 0.720 0.008 0.780 0.012 0.200
#> GSM617610 1 0.0000 0.937 1.000 0.000 0.000 0.000
#> GSM617611 1 0.0188 0.938 0.996 0.000 0.004 0.000
#> GSM617613 3 0.0000 0.922 0.000 0.000 1.000 0.000
#> GSM617614 3 0.0921 0.914 0.028 0.000 0.972 0.000
#> GSM617621 1 0.3264 0.898 0.876 0.096 0.004 0.024
#> GSM617629 2 0.4250 0.656 0.000 0.724 0.276 0.000
#> GSM617630 2 0.1118 0.860 0.000 0.964 0.036 0.000
#> GSM617631 3 0.0000 0.922 0.000 0.000 1.000 0.000
#> GSM617633 1 0.1716 0.906 0.936 0.000 0.064 0.000
#> GSM617642 3 0.2814 0.829 0.132 0.000 0.868 0.000
#> GSM617645 2 0.0469 0.873 0.000 0.988 0.000 0.012
#> GSM617646 1 0.4049 0.790 0.780 0.212 0.008 0.000
#> GSM617652 1 0.3047 0.890 0.872 0.116 0.012 0.000
#> GSM617655 3 0.0000 0.922 0.000 0.000 1.000 0.000
#> GSM617656 3 0.0000 0.922 0.000 0.000 1.000 0.000
#> GSM617657 3 0.0000 0.922 0.000 0.000 1.000 0.000
#> GSM617658 3 0.1182 0.914 0.016 0.000 0.968 0.016
#> GSM617659 1 0.0188 0.938 0.996 0.000 0.004 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM617581 1 0.4901 0.7987 0.752 0.124 0.012 0.004 NA
#> GSM617582 1 0.6579 0.6282 0.632 0.144 0.120 0.000 NA
#> GSM617588 4 0.1117 0.8327 0.000 0.016 0.000 0.964 NA
#> GSM617590 4 0.0510 0.8311 0.000 0.016 0.000 0.984 NA
#> GSM617592 4 0.1117 0.8327 0.000 0.016 0.000 0.964 NA
#> GSM617607 1 0.4593 0.8184 0.756 0.076 0.008 0.000 NA
#> GSM617608 1 0.2077 0.8534 0.908 0.000 0.008 0.000 NA
#> GSM617609 3 0.3692 0.7860 0.008 0.152 0.812 0.000 NA
#> GSM617612 1 0.0898 0.8628 0.972 0.000 0.008 0.000 NA
#> GSM617615 4 0.3905 0.6959 0.000 0.232 0.004 0.752 NA
#> GSM617616 1 0.1608 0.8628 0.928 0.000 0.000 0.000 NA
#> GSM617617 2 0.2505 0.8052 0.000 0.888 0.000 0.020 NA
#> GSM617618 1 0.2818 0.8453 0.860 0.004 0.008 0.000 NA
#> GSM617619 2 0.5044 0.2242 0.000 0.556 0.408 0.000 NA
#> GSM617620 4 0.1117 0.8327 0.000 0.016 0.000 0.964 NA
#> GSM617622 2 0.4449 0.5554 0.000 0.688 0.004 0.288 NA
#> GSM617623 1 0.4967 0.7969 0.752 0.128 0.012 0.008 NA
#> GSM617624 2 0.0960 0.8106 0.000 0.972 0.008 0.004 NA
#> GSM617625 3 0.4547 0.7544 0.192 0.000 0.736 0.000 NA
#> GSM617626 1 0.3466 0.8477 0.844 0.048 0.008 0.000 NA
#> GSM617627 2 0.1565 0.8107 0.004 0.952 0.008 0.020 NA
#> GSM617628 3 0.4349 0.7698 0.176 0.000 0.756 0.000 NA
#> GSM617632 1 0.1892 0.8626 0.916 0.004 0.000 0.000 NA
#> GSM617634 2 0.2791 0.8058 0.000 0.892 0.016 0.036 NA
#> GSM617635 1 0.3570 0.8465 0.828 0.044 0.004 0.000 NA
#> GSM617636 1 0.6569 0.5749 0.496 0.092 0.028 0.004 NA
#> GSM617637 1 0.1954 0.8629 0.932 0.028 0.008 0.000 NA
#> GSM617638 2 0.3852 0.7045 0.000 0.760 0.020 0.000 NA
#> GSM617639 1 0.2464 0.8560 0.904 0.048 0.004 0.000 NA
#> GSM617640 2 0.2984 0.7966 0.000 0.860 0.000 0.032 NA
#> GSM617641 4 0.1117 0.8327 0.000 0.016 0.000 0.964 NA
#> GSM617643 2 0.3569 0.7695 0.000 0.828 0.000 0.104 NA
#> GSM617644 4 0.4821 0.0145 0.000 0.464 0.000 0.516 NA
#> GSM617647 2 0.2556 0.8119 0.024 0.900 0.004 0.004 NA
#> GSM617648 2 0.2921 0.7702 0.000 0.856 0.000 0.124 NA
#> GSM617649 2 0.1560 0.8111 0.000 0.948 0.004 0.028 NA
#> GSM617650 1 0.1502 0.8602 0.940 0.000 0.004 0.000 NA
#> GSM617651 1 0.0404 0.8613 0.988 0.000 0.000 0.000 NA
#> GSM617653 1 0.1851 0.8496 0.912 0.000 0.000 0.000 NA
#> GSM617654 2 0.2179 0.8050 0.000 0.896 0.000 0.004 NA
#> GSM617583 3 0.4395 0.7635 0.188 0.000 0.748 0.000 NA
#> GSM617584 4 0.6709 0.6003 0.100 0.148 0.008 0.636 NA
#> GSM617585 4 0.4898 0.7048 0.000 0.144 0.088 0.748 NA
#> GSM617586 3 0.1106 0.8674 0.000 0.012 0.964 0.000 NA
#> GSM617587 3 0.2756 0.8319 0.012 0.096 0.880 0.000 NA
#> GSM617589 4 0.1893 0.8233 0.000 0.024 0.000 0.928 NA
#> GSM617591 4 0.4800 0.6090 0.000 0.296 0.012 0.668 NA
#> GSM617593 1 0.1205 0.8640 0.956 0.000 0.004 0.000 NA
#> GSM617594 2 0.2869 0.7810 0.052 0.892 0.008 0.008 NA
#> GSM617595 1 0.0404 0.8615 0.988 0.000 0.000 0.000 NA
#> GSM617596 1 0.3714 0.8539 0.836 0.044 0.012 0.004 NA
#> GSM617597 1 0.5590 0.5676 0.620 0.016 0.300 0.000 NA
#> GSM617598 1 0.0510 0.8611 0.984 0.000 0.000 0.000 NA
#> GSM617599 2 0.3864 0.7385 0.112 0.828 0.012 0.008 NA
#> GSM617600 3 0.3010 0.8210 0.000 0.004 0.824 0.000 NA
#> GSM617601 4 0.3863 0.7328 0.000 0.200 0.000 0.772 NA
#> GSM617602 3 0.0794 0.8655 0.000 0.000 0.972 0.000 NA
#> GSM617603 4 0.2519 0.7899 0.000 0.100 0.000 0.884 NA
#> GSM617604 1 0.6155 0.2669 0.484 0.008 0.416 0.004 NA
#> GSM617605 4 0.0510 0.8311 0.000 0.016 0.000 0.984 NA
#> GSM617606 2 0.4084 0.7088 0.004 0.784 0.008 0.176 NA
#> GSM617610 1 0.0609 0.8609 0.980 0.000 0.000 0.000 NA
#> GSM617611 1 0.0771 0.8617 0.976 0.000 0.004 0.000 NA
#> GSM617613 3 0.3715 0.7705 0.000 0.004 0.736 0.000 NA
#> GSM617614 3 0.1862 0.8627 0.016 0.004 0.932 0.000 NA
#> GSM617621 1 0.3681 0.8411 0.840 0.072 0.008 0.004 NA
#> GSM617629 2 0.6517 0.4273 0.000 0.480 0.228 0.000 NA
#> GSM617630 2 0.4054 0.7113 0.000 0.760 0.036 0.000 NA
#> GSM617631 3 0.1478 0.8640 0.000 0.000 0.936 0.000 NA
#> GSM617633 1 0.5609 0.5700 0.564 0.016 0.048 0.000 NA
#> GSM617642 3 0.3175 0.8505 0.044 0.020 0.872 0.000 NA
#> GSM617645 2 0.2625 0.8017 0.000 0.876 0.000 0.016 NA
#> GSM617646 1 0.5311 0.7555 0.692 0.184 0.008 0.000 NA
#> GSM617652 1 0.5079 0.8135 0.756 0.092 0.056 0.000 NA
#> GSM617655 3 0.1997 0.8633 0.000 0.036 0.924 0.000 NA
#> GSM617656 3 0.1671 0.8574 0.000 0.000 0.924 0.000 NA
#> GSM617657 3 0.3741 0.7679 0.000 0.004 0.732 0.000 NA
#> GSM617658 3 0.2006 0.8588 0.012 0.000 0.916 0.000 NA
#> GSM617659 1 0.1124 0.8616 0.960 0.000 0.004 0.000 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM617581 1 0.5268 0.68705 0.688 0.052 0.004 0.000 0.172 0.084
#> GSM617582 1 0.8164 0.07668 0.416 0.128 0.224 0.000 0.120 0.112
#> GSM617588 4 0.1793 0.77779 0.000 0.012 0.000 0.928 0.012 0.048
#> GSM617590 4 0.1296 0.77722 0.000 0.012 0.000 0.952 0.032 0.004
#> GSM617592 4 0.1952 0.77815 0.000 0.016 0.000 0.920 0.012 0.052
#> GSM617607 1 0.5330 0.62046 0.628 0.016 0.012 0.000 0.272 0.072
#> GSM617608 1 0.2812 0.79646 0.860 0.000 0.008 0.000 0.104 0.028
#> GSM617609 3 0.4799 0.32778 0.012 0.020 0.688 0.000 0.240 0.040
#> GSM617612 1 0.1599 0.82510 0.940 0.000 0.008 0.000 0.028 0.024
#> GSM617615 4 0.5575 0.57407 0.000 0.140 0.000 0.644 0.172 0.044
#> GSM617616 1 0.2345 0.82232 0.900 0.004 0.004 0.000 0.056 0.036
#> GSM617617 2 0.1176 0.64373 0.000 0.956 0.000 0.024 0.020 0.000
#> GSM617618 1 0.3907 0.74125 0.756 0.000 0.000 0.000 0.176 0.068
#> GSM617619 5 0.7302 -0.12365 0.000 0.332 0.184 0.000 0.356 0.128
#> GSM617620 4 0.1820 0.78008 0.000 0.016 0.000 0.928 0.012 0.044
#> GSM617622 2 0.6839 0.39166 0.000 0.444 0.004 0.316 0.172 0.064
#> GSM617623 1 0.5393 0.68600 0.692 0.056 0.004 0.004 0.152 0.092
#> GSM617624 2 0.4467 0.53490 0.000 0.624 0.008 0.004 0.344 0.020
#> GSM617625 3 0.4976 0.50252 0.156 0.000 0.680 0.000 0.012 0.152
#> GSM617626 1 0.3844 0.78917 0.812 0.028 0.004 0.000 0.084 0.072
#> GSM617627 2 0.5715 0.57133 0.000 0.588 0.004 0.056 0.292 0.060
#> GSM617628 3 0.4874 0.50535 0.148 0.000 0.692 0.000 0.012 0.148
#> GSM617632 1 0.2879 0.81731 0.864 0.008 0.000 0.000 0.072 0.056
#> GSM617634 2 0.5283 0.43844 0.008 0.532 0.008 0.020 0.408 0.024
#> GSM617635 1 0.4197 0.75040 0.752 0.016 0.000 0.000 0.172 0.060
#> GSM617636 5 0.5522 0.08862 0.316 0.020 0.016 0.000 0.588 0.060
#> GSM617637 1 0.2171 0.82367 0.912 0.016 0.000 0.000 0.040 0.032
#> GSM617638 5 0.4039 0.09796 0.000 0.352 0.016 0.000 0.632 0.000
#> GSM617639 1 0.2719 0.81071 0.876 0.012 0.000 0.000 0.072 0.040
#> GSM617640 2 0.0790 0.63050 0.000 0.968 0.000 0.032 0.000 0.000
#> GSM617641 4 0.1820 0.78008 0.000 0.016 0.000 0.928 0.012 0.044
#> GSM617643 2 0.2560 0.64475 0.000 0.872 0.000 0.092 0.036 0.000
#> GSM617644 4 0.5072 -0.06783 0.000 0.464 0.000 0.480 0.028 0.028
#> GSM617647 2 0.4312 0.60783 0.084 0.772 0.004 0.004 0.120 0.016
#> GSM617648 2 0.4097 0.64491 0.000 0.760 0.000 0.128 0.108 0.004
#> GSM617649 2 0.4392 0.60598 0.000 0.676 0.004 0.024 0.284 0.012
#> GSM617650 1 0.2884 0.80195 0.864 0.000 0.008 0.000 0.064 0.064
#> GSM617651 1 0.0508 0.82279 0.984 0.000 0.000 0.000 0.004 0.012
#> GSM617653 1 0.2649 0.80018 0.876 0.004 0.000 0.000 0.052 0.068
#> GSM617654 2 0.0717 0.63497 0.000 0.976 0.000 0.008 0.016 0.000
#> GSM617583 3 0.4927 0.51483 0.144 0.000 0.692 0.000 0.016 0.148
#> GSM617584 4 0.7024 0.53019 0.064 0.076 0.000 0.564 0.164 0.132
#> GSM617585 4 0.5228 0.64662 0.000 0.132 0.008 0.708 0.096 0.056
#> GSM617586 3 0.1934 0.46742 0.000 0.000 0.916 0.000 0.040 0.044
#> GSM617587 3 0.4063 0.45518 0.036 0.004 0.760 0.000 0.184 0.016
#> GSM617589 4 0.2964 0.76323 0.000 0.024 0.000 0.856 0.020 0.100
#> GSM617591 4 0.6367 0.47660 0.000 0.136 0.008 0.564 0.232 0.060
#> GSM617593 1 0.2796 0.81589 0.872 0.004 0.004 0.000 0.056 0.064
#> GSM617594 2 0.6775 0.50405 0.084 0.548 0.008 0.032 0.264 0.064
#> GSM617595 1 0.0717 0.82253 0.976 0.000 0.000 0.000 0.016 0.008
#> GSM617596 1 0.3731 0.80749 0.808 0.012 0.004 0.000 0.112 0.064
#> GSM617597 3 0.5839 0.10331 0.408 0.004 0.484 0.000 0.048 0.056
#> GSM617598 1 0.1405 0.82134 0.948 0.004 0.000 0.000 0.024 0.024
#> GSM617599 2 0.6594 0.44547 0.132 0.548 0.016 0.000 0.240 0.064
#> GSM617600 3 0.3668 -0.52091 0.000 0.000 0.668 0.000 0.004 0.328
#> GSM617601 4 0.4750 0.67503 0.000 0.132 0.000 0.724 0.116 0.028
#> GSM617602 3 0.1075 0.44851 0.000 0.000 0.952 0.000 0.000 0.048
#> GSM617603 4 0.3436 0.74225 0.000 0.080 0.000 0.836 0.032 0.052
#> GSM617604 3 0.5570 0.30488 0.244 0.004 0.608 0.000 0.016 0.128
#> GSM617605 4 0.1296 0.77722 0.000 0.012 0.000 0.952 0.032 0.004
#> GSM617606 2 0.6550 0.53845 0.000 0.520 0.000 0.212 0.200 0.068
#> GSM617610 1 0.1092 0.82059 0.960 0.000 0.000 0.000 0.020 0.020
#> GSM617611 1 0.1257 0.82118 0.952 0.000 0.000 0.000 0.020 0.028
#> GSM617613 6 0.4097 0.96128 0.000 0.000 0.488 0.000 0.008 0.504
#> GSM617614 3 0.3178 0.56018 0.028 0.000 0.832 0.000 0.012 0.128
#> GSM617621 1 0.3876 0.78444 0.796 0.020 0.000 0.000 0.112 0.072
#> GSM617629 5 0.5729 0.31403 0.000 0.156 0.184 0.000 0.620 0.040
#> GSM617630 5 0.4269 0.15451 0.000 0.316 0.036 0.000 0.648 0.000
#> GSM617631 3 0.2048 0.33663 0.000 0.000 0.880 0.000 0.000 0.120
#> GSM617633 5 0.5410 0.00994 0.404 0.004 0.020 0.000 0.516 0.056
#> GSM617642 3 0.3538 0.56221 0.024 0.000 0.816 0.000 0.036 0.124
#> GSM617645 2 0.0458 0.63186 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM617646 1 0.5460 0.63393 0.632 0.044 0.020 0.000 0.268 0.036
#> GSM617652 1 0.6374 0.47847 0.560 0.016 0.224 0.000 0.164 0.036
#> GSM617655 3 0.2488 0.46287 0.000 0.000 0.880 0.000 0.076 0.044
#> GSM617656 3 0.2234 0.31891 0.000 0.000 0.872 0.000 0.004 0.124
#> GSM617657 6 0.4405 0.96204 0.000 0.000 0.472 0.000 0.024 0.504
#> GSM617658 3 0.2600 0.54505 0.008 0.000 0.860 0.000 0.008 0.124
#> GSM617659 1 0.2614 0.80581 0.888 0.000 0.036 0.000 0.024 0.052
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:mclust 75 0.52534 2
#> CV:mclust 64 0.00414 3
#> CV:mclust 77 0.03137 4
#> CV:mclust 75 0.01806 5
#> CV:mclust 56 0.18827 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 79 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.948 0.954 0.979 0.5011 0.498 0.498
#> 3 3 0.531 0.750 0.859 0.3330 0.749 0.534
#> 4 4 0.465 0.564 0.742 0.1231 0.850 0.586
#> 5 5 0.515 0.466 0.684 0.0663 0.908 0.665
#> 6 6 0.556 0.412 0.658 0.0379 0.932 0.706
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
#> GSM617581 2 0.7453 0.736 0.212 0.788
#> GSM617582 1 0.8386 0.635 0.732 0.268
#> GSM617588 2 0.0000 0.974 0.000 1.000
#> GSM617590 2 0.0000 0.974 0.000 1.000
#> GSM617592 2 0.0000 0.974 0.000 1.000
#> GSM617607 1 0.0000 0.981 1.000 0.000
#> GSM617608 1 0.0000 0.981 1.000 0.000
#> GSM617609 1 0.0938 0.974 0.988 0.012
#> GSM617612 1 0.0000 0.981 1.000 0.000
#> GSM617615 2 0.0000 0.974 0.000 1.000
#> GSM617616 1 0.1414 0.968 0.980 0.020
#> GSM617617 2 0.0000 0.974 0.000 1.000
#> GSM617618 1 0.0672 0.976 0.992 0.008
#> GSM617619 2 0.1633 0.958 0.024 0.976
#> GSM617620 2 0.0000 0.974 0.000 1.000
#> GSM617622 2 0.0000 0.974 0.000 1.000
#> GSM617623 2 0.3114 0.931 0.056 0.944
#> GSM617624 2 0.0000 0.974 0.000 1.000
#> GSM617625 1 0.0000 0.981 1.000 0.000
#> GSM617626 2 0.5059 0.872 0.112 0.888
#> GSM617627 2 0.0000 0.974 0.000 1.000
#> GSM617628 1 0.0000 0.981 1.000 0.000
#> GSM617632 1 0.1414 0.968 0.980 0.020
#> GSM617634 2 0.0000 0.974 0.000 1.000
#> GSM617635 1 0.0000 0.981 1.000 0.000
#> GSM617636 1 0.0000 0.981 1.000 0.000
#> GSM617637 1 0.1414 0.968 0.980 0.020
#> GSM617638 2 0.0938 0.966 0.012 0.988
#> GSM617639 1 0.0000 0.981 1.000 0.000
#> GSM617640 2 0.0000 0.974 0.000 1.000
#> GSM617641 2 0.0000 0.974 0.000 1.000
#> GSM617643 2 0.0000 0.974 0.000 1.000
#> GSM617644 2 0.0000 0.974 0.000 1.000
#> GSM617647 2 0.0000 0.974 0.000 1.000
#> GSM617648 2 0.0000 0.974 0.000 1.000
#> GSM617649 2 0.0000 0.974 0.000 1.000
#> GSM617650 1 0.0000 0.981 1.000 0.000
#> GSM617651 1 0.0000 0.981 1.000 0.000
#> GSM617653 1 0.0000 0.981 1.000 0.000
#> GSM617654 2 0.0000 0.974 0.000 1.000
#> GSM617583 1 0.0000 0.981 1.000 0.000
#> GSM617584 2 0.0000 0.974 0.000 1.000
#> GSM617585 2 0.0000 0.974 0.000 1.000
#> GSM617586 1 0.0000 0.981 1.000 0.000
#> GSM617587 1 0.4690 0.888 0.900 0.100
#> GSM617589 2 0.0000 0.974 0.000 1.000
#> GSM617591 2 0.0000 0.974 0.000 1.000
#> GSM617593 1 0.0000 0.981 1.000 0.000
#> GSM617594 2 0.0672 0.969 0.008 0.992
#> GSM617595 1 0.0000 0.981 1.000 0.000
#> GSM617596 1 0.0000 0.981 1.000 0.000
#> GSM617597 1 0.0000 0.981 1.000 0.000
#> GSM617598 1 0.0000 0.981 1.000 0.000
#> GSM617599 2 0.1633 0.958 0.024 0.976
#> GSM617600 1 0.0000 0.981 1.000 0.000
#> GSM617601 2 0.0000 0.974 0.000 1.000
#> GSM617602 1 0.0000 0.981 1.000 0.000
#> GSM617603 2 0.0000 0.974 0.000 1.000
#> GSM617604 1 0.0000 0.981 1.000 0.000
#> GSM617605 2 0.0000 0.974 0.000 1.000
#> GSM617606 2 0.0000 0.974 0.000 1.000
#> GSM617610 1 0.0000 0.981 1.000 0.000
#> GSM617611 1 0.0000 0.981 1.000 0.000
#> GSM617613 1 0.1184 0.971 0.984 0.016
#> GSM617614 1 0.0000 0.981 1.000 0.000
#> GSM617621 1 0.0000 0.981 1.000 0.000
#> GSM617629 1 0.7745 0.709 0.772 0.228
#> GSM617630 2 0.9522 0.413 0.372 0.628
#> GSM617631 1 0.0000 0.981 1.000 0.000
#> GSM617633 1 0.0000 0.981 1.000 0.000
#> GSM617642 1 0.0000 0.981 1.000 0.000
#> GSM617645 2 0.0000 0.974 0.000 1.000
#> GSM617646 1 0.0672 0.976 0.992 0.008
#> GSM617652 1 0.0000 0.981 1.000 0.000
#> GSM617655 1 0.3879 0.914 0.924 0.076
#> GSM617656 1 0.0000 0.981 1.000 0.000
#> GSM617657 2 0.3733 0.916 0.072 0.928
#> GSM617658 1 0.0000 0.981 1.000 0.000
#> GSM617659 1 0.0000 0.981 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM617581 1 0.5882 0.4203 0.652 0.348 0.000
#> GSM617582 1 0.9387 0.3851 0.508 0.220 0.272
#> GSM617588 2 0.1529 0.8837 0.040 0.960 0.000
#> GSM617590 2 0.2486 0.8795 0.008 0.932 0.060
#> GSM617592 2 0.1399 0.8852 0.028 0.968 0.004
#> GSM617607 1 0.5098 0.6581 0.752 0.000 0.248
#> GSM617608 3 0.6126 0.3744 0.400 0.000 0.600
#> GSM617609 3 0.1711 0.8081 0.008 0.032 0.960
#> GSM617612 1 0.2448 0.8125 0.924 0.000 0.076
#> GSM617615 2 0.1919 0.8870 0.020 0.956 0.024
#> GSM617616 1 0.2414 0.8185 0.940 0.040 0.020
#> GSM617617 2 0.4861 0.7761 0.192 0.800 0.008
#> GSM617618 1 0.4575 0.7592 0.828 0.012 0.160
#> GSM617619 3 0.6451 0.1259 0.004 0.436 0.560
#> GSM617620 2 0.1163 0.8852 0.028 0.972 0.000
#> GSM617622 2 0.1964 0.8811 0.000 0.944 0.056
#> GSM617623 1 0.5926 0.4070 0.644 0.356 0.000
#> GSM617624 2 0.4645 0.7971 0.008 0.816 0.176
#> GSM617625 3 0.3941 0.7621 0.156 0.000 0.844
#> GSM617626 1 0.5178 0.5963 0.744 0.256 0.000
#> GSM617627 2 0.4555 0.7762 0.000 0.800 0.200
#> GSM617628 3 0.1964 0.8118 0.056 0.000 0.944
#> GSM617632 1 0.2443 0.8225 0.940 0.032 0.028
#> GSM617634 2 0.3610 0.8634 0.016 0.888 0.096
#> GSM617635 1 0.4164 0.7747 0.848 0.008 0.144
#> GSM617636 3 0.6305 0.0849 0.484 0.000 0.516
#> GSM617637 1 0.2651 0.8061 0.928 0.060 0.012
#> GSM617638 2 0.5881 0.6840 0.016 0.728 0.256
#> GSM617639 1 0.1399 0.8216 0.968 0.004 0.028
#> GSM617640 2 0.3031 0.8725 0.076 0.912 0.012
#> GSM617641 2 0.1031 0.8853 0.024 0.976 0.000
#> GSM617643 2 0.2063 0.8828 0.044 0.948 0.008
#> GSM617644 2 0.1289 0.8845 0.032 0.968 0.000
#> GSM617647 2 0.5848 0.6714 0.268 0.720 0.012
#> GSM617648 2 0.2866 0.8759 0.076 0.916 0.008
#> GSM617649 2 0.3377 0.8663 0.012 0.896 0.092
#> GSM617650 3 0.6215 0.2667 0.428 0.000 0.572
#> GSM617651 1 0.0892 0.8201 0.980 0.000 0.020
#> GSM617653 1 0.2152 0.8174 0.948 0.036 0.016
#> GSM617654 2 0.5072 0.7722 0.196 0.792 0.012
#> GSM617583 3 0.3349 0.8002 0.108 0.004 0.888
#> GSM617584 2 0.5178 0.6964 0.256 0.744 0.000
#> GSM617585 2 0.4883 0.7609 0.004 0.788 0.208
#> GSM617586 3 0.1525 0.8067 0.004 0.032 0.964
#> GSM617587 3 0.2066 0.7940 0.000 0.060 0.940
#> GSM617589 2 0.3213 0.8659 0.092 0.900 0.008
#> GSM617591 2 0.3532 0.8592 0.008 0.884 0.108
#> GSM617593 1 0.5138 0.6349 0.748 0.000 0.252
#> GSM617594 2 0.2774 0.8755 0.072 0.920 0.008
#> GSM617595 1 0.1491 0.8206 0.968 0.016 0.016
#> GSM617596 1 0.2711 0.8039 0.912 0.000 0.088
#> GSM617597 3 0.3879 0.7615 0.152 0.000 0.848
#> GSM617598 1 0.2537 0.8069 0.920 0.000 0.080
#> GSM617599 2 0.5450 0.7397 0.228 0.760 0.012
#> GSM617600 3 0.0983 0.8103 0.004 0.016 0.980
#> GSM617601 2 0.1711 0.8851 0.008 0.960 0.032
#> GSM617602 3 0.1170 0.8126 0.016 0.008 0.976
#> GSM617603 2 0.1529 0.8833 0.000 0.960 0.040
#> GSM617604 3 0.3816 0.7650 0.148 0.000 0.852
#> GSM617605 2 0.2384 0.8807 0.008 0.936 0.056
#> GSM617606 2 0.2173 0.8835 0.008 0.944 0.048
#> GSM617610 1 0.2063 0.8118 0.948 0.044 0.008
#> GSM617611 1 0.5178 0.6327 0.744 0.000 0.256
#> GSM617613 3 0.2356 0.7873 0.000 0.072 0.928
#> GSM617614 3 0.2261 0.8083 0.068 0.000 0.932
#> GSM617621 1 0.2356 0.8123 0.928 0.000 0.072
#> GSM617629 3 0.3695 0.7600 0.012 0.108 0.880
#> GSM617630 3 0.6407 0.5530 0.028 0.272 0.700
#> GSM617631 3 0.1170 0.8110 0.008 0.016 0.976
#> GSM617633 3 0.3267 0.7932 0.116 0.000 0.884
#> GSM617642 3 0.2356 0.8076 0.072 0.000 0.928
#> GSM617645 2 0.3293 0.8662 0.088 0.900 0.012
#> GSM617646 1 0.6066 0.6600 0.728 0.024 0.248
#> GSM617652 3 0.3267 0.7892 0.116 0.000 0.884
#> GSM617655 3 0.2356 0.7874 0.000 0.072 0.928
#> GSM617656 3 0.1129 0.8128 0.020 0.004 0.976
#> GSM617657 3 0.5115 0.6350 0.004 0.228 0.768
#> GSM617658 3 0.2356 0.8085 0.072 0.000 0.928
#> GSM617659 3 0.5859 0.4812 0.344 0.000 0.656
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM617581 4 0.6294 -0.03160 0.436 0.048 0.004 0.512
#> GSM617582 1 0.9825 0.27001 0.348 0.208 0.216 0.228
#> GSM617588 4 0.1890 0.75451 0.008 0.056 0.000 0.936
#> GSM617590 4 0.3149 0.75199 0.000 0.088 0.032 0.880
#> GSM617592 4 0.1520 0.73105 0.020 0.024 0.000 0.956
#> GSM617607 2 0.6242 -0.05650 0.424 0.520 0.056 0.000
#> GSM617608 3 0.6780 0.16914 0.416 0.096 0.488 0.000
#> GSM617609 3 0.3257 0.70319 0.004 0.152 0.844 0.000
#> GSM617612 1 0.5791 0.65086 0.752 0.032 0.124 0.092
#> GSM617615 4 0.3711 0.72816 0.000 0.140 0.024 0.836
#> GSM617616 1 0.4846 0.70526 0.776 0.180 0.016 0.028
#> GSM617617 2 0.5180 0.59644 0.064 0.740 0.000 0.196
#> GSM617618 1 0.7418 0.53297 0.564 0.308 0.088 0.040
#> GSM617619 3 0.7026 0.27834 0.000 0.248 0.572 0.180
#> GSM617620 4 0.2480 0.75448 0.008 0.088 0.000 0.904
#> GSM617622 4 0.4244 0.72837 0.000 0.168 0.032 0.800
#> GSM617623 1 0.6584 0.38065 0.568 0.096 0.000 0.336
#> GSM617624 2 0.5351 0.58313 0.000 0.744 0.104 0.152
#> GSM617625 3 0.5509 0.67931 0.180 0.060 0.744 0.016
#> GSM617626 1 0.5614 0.42788 0.628 0.036 0.000 0.336
#> GSM617627 2 0.7524 -0.00522 0.000 0.408 0.184 0.408
#> GSM617628 3 0.3992 0.74823 0.080 0.040 0.856 0.024
#> GSM617632 1 0.5337 0.60785 0.704 0.260 0.012 0.024
#> GSM617634 2 0.5013 0.56365 0.004 0.764 0.056 0.176
#> GSM617635 2 0.5698 0.19726 0.356 0.608 0.036 0.000
#> GSM617636 2 0.7174 0.20998 0.272 0.580 0.136 0.012
#> GSM617637 1 0.4957 0.50310 0.668 0.320 0.000 0.012
#> GSM617638 2 0.3875 0.62850 0.004 0.852 0.068 0.076
#> GSM617639 1 0.4600 0.63449 0.744 0.240 0.012 0.004
#> GSM617640 2 0.5113 0.51404 0.024 0.684 0.000 0.292
#> GSM617641 4 0.2530 0.75309 0.000 0.100 0.004 0.896
#> GSM617643 2 0.4857 0.46871 0.008 0.668 0.000 0.324
#> GSM617644 4 0.4422 0.66265 0.008 0.256 0.000 0.736
#> GSM617647 2 0.6422 0.46760 0.104 0.616 0.000 0.280
#> GSM617648 2 0.4857 0.49896 0.016 0.700 0.000 0.284
#> GSM617649 2 0.5165 0.59270 0.000 0.752 0.080 0.168
#> GSM617650 3 0.6277 0.03877 0.468 0.056 0.476 0.000
#> GSM617651 1 0.2647 0.72967 0.880 0.120 0.000 0.000
#> GSM617653 1 0.2546 0.72914 0.912 0.060 0.000 0.028
#> GSM617654 2 0.4015 0.62586 0.052 0.832 0.000 0.116
#> GSM617583 3 0.6430 0.65370 0.148 0.028 0.700 0.124
#> GSM617584 4 0.4669 0.61338 0.168 0.052 0.000 0.780
#> GSM617585 4 0.6420 0.49573 0.000 0.132 0.228 0.640
#> GSM617586 3 0.2261 0.75867 0.008 0.024 0.932 0.036
#> GSM617587 3 0.2830 0.75024 0.004 0.060 0.904 0.032
#> GSM617589 4 0.4318 0.65185 0.116 0.068 0.000 0.816
#> GSM617591 4 0.4599 0.68254 0.000 0.088 0.112 0.800
#> GSM617593 1 0.4904 0.60616 0.744 0.040 0.216 0.000
#> GSM617594 4 0.5271 0.47632 0.020 0.340 0.000 0.640
#> GSM617595 1 0.2413 0.73413 0.916 0.064 0.020 0.000
#> GSM617596 1 0.5530 0.71118 0.760 0.144 0.072 0.024
#> GSM617597 3 0.4008 0.71669 0.148 0.032 0.820 0.000
#> GSM617598 1 0.3533 0.70912 0.872 0.020 0.088 0.020
#> GSM617599 4 0.7282 -0.02125 0.148 0.416 0.000 0.436
#> GSM617600 3 0.1661 0.75531 0.004 0.052 0.944 0.000
#> GSM617601 4 0.3351 0.73069 0.000 0.148 0.008 0.844
#> GSM617602 3 0.1388 0.75946 0.012 0.028 0.960 0.000
#> GSM617603 4 0.4303 0.71856 0.004 0.184 0.020 0.792
#> GSM617604 3 0.7085 0.50802 0.284 0.044 0.604 0.068
#> GSM617605 4 0.2101 0.75537 0.000 0.060 0.012 0.928
#> GSM617606 4 0.4988 0.65920 0.000 0.236 0.036 0.728
#> GSM617610 1 0.3069 0.73008 0.896 0.060 0.008 0.036
#> GSM617611 1 0.5812 0.57487 0.712 0.060 0.212 0.016
#> GSM617613 3 0.2949 0.72387 0.000 0.088 0.888 0.024
#> GSM617614 3 0.2981 0.74575 0.092 0.016 0.888 0.004
#> GSM617621 1 0.4542 0.73072 0.824 0.076 0.084 0.016
#> GSM617629 2 0.5318 0.32590 0.004 0.624 0.360 0.012
#> GSM617630 2 0.5072 0.56973 0.000 0.740 0.208 0.052
#> GSM617631 3 0.1811 0.75901 0.004 0.028 0.948 0.020
#> GSM617633 3 0.6407 0.29837 0.072 0.384 0.544 0.000
#> GSM617642 3 0.4360 0.71790 0.140 0.012 0.816 0.032
#> GSM617645 2 0.4290 0.59259 0.016 0.772 0.000 0.212
#> GSM617646 2 0.6276 0.09996 0.380 0.556 0.064 0.000
#> GSM617652 3 0.5229 0.66512 0.168 0.084 0.748 0.000
#> GSM617655 3 0.2670 0.74586 0.000 0.040 0.908 0.052
#> GSM617656 3 0.0657 0.75960 0.004 0.012 0.984 0.000
#> GSM617657 3 0.5883 0.54682 0.000 0.172 0.700 0.128
#> GSM617658 3 0.3556 0.74757 0.096 0.036 0.864 0.004
#> GSM617659 3 0.5244 0.28067 0.436 0.008 0.556 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM617581 1 0.6768 0.1440 0.444 0.012 0.004 0.388 0.152
#> GSM617582 5 0.6459 0.3379 0.136 0.032 0.048 0.112 0.672
#> GSM617588 4 0.2535 0.7073 0.000 0.076 0.000 0.892 0.032
#> GSM617590 4 0.2393 0.7072 0.000 0.080 0.004 0.900 0.016
#> GSM617592 4 0.2607 0.6831 0.032 0.032 0.004 0.908 0.024
#> GSM617607 2 0.6603 0.2547 0.296 0.556 0.048 0.000 0.100
#> GSM617608 3 0.7081 0.2116 0.304 0.032 0.476 0.000 0.188
#> GSM617609 3 0.2866 0.6873 0.000 0.100 0.872 0.004 0.024
#> GSM617612 1 0.6399 0.4687 0.660 0.020 0.156 0.040 0.124
#> GSM617615 4 0.6807 0.4070 0.000 0.268 0.040 0.544 0.148
#> GSM617616 1 0.6290 0.3002 0.480 0.092 0.004 0.012 0.412
#> GSM617617 2 0.3673 0.6597 0.052 0.848 0.000 0.060 0.040
#> GSM617618 5 0.5182 0.3345 0.148 0.092 0.012 0.012 0.736
#> GSM617619 3 0.6672 0.3885 0.000 0.140 0.624 0.116 0.120
#> GSM617620 4 0.2824 0.6982 0.000 0.116 0.000 0.864 0.020
#> GSM617622 4 0.6049 0.5816 0.020 0.108 0.016 0.664 0.192
#> GSM617623 1 0.7016 0.1825 0.464 0.020 0.000 0.292 0.224
#> GSM617624 2 0.4550 0.6124 0.000 0.792 0.084 0.044 0.080
#> GSM617625 3 0.5670 0.5643 0.100 0.008 0.664 0.008 0.220
#> GSM617626 1 0.5186 0.4438 0.704 0.020 0.000 0.208 0.068
#> GSM617627 2 0.6472 0.3760 0.000 0.548 0.180 0.260 0.012
#> GSM617628 3 0.5082 0.6603 0.060 0.004 0.752 0.044 0.140
#> GSM617632 1 0.5427 0.3077 0.636 0.072 0.000 0.008 0.284
#> GSM617634 5 0.6204 -0.0679 0.000 0.436 0.020 0.080 0.464
#> GSM617635 2 0.4959 0.5322 0.144 0.752 0.040 0.000 0.064
#> GSM617636 5 0.7481 0.3276 0.260 0.200 0.040 0.012 0.488
#> GSM617637 1 0.5719 0.2561 0.564 0.348 0.004 0.000 0.084
#> GSM617638 2 0.4680 0.5750 0.004 0.760 0.028 0.036 0.172
#> GSM617639 1 0.4673 0.3954 0.680 0.288 0.012 0.000 0.020
#> GSM617640 2 0.3423 0.6661 0.012 0.840 0.004 0.128 0.016
#> GSM617641 4 0.2972 0.7004 0.004 0.108 0.000 0.864 0.024
#> GSM617643 2 0.4077 0.6319 0.000 0.780 0.004 0.172 0.044
#> GSM617644 4 0.6545 0.3605 0.000 0.284 0.000 0.476 0.240
#> GSM617647 2 0.4071 0.6478 0.072 0.808 0.000 0.108 0.012
#> GSM617648 2 0.6173 0.3426 0.012 0.568 0.000 0.124 0.296
#> GSM617649 2 0.4236 0.6466 0.000 0.812 0.056 0.088 0.044
#> GSM617650 3 0.5837 0.0810 0.444 0.028 0.488 0.000 0.040
#> GSM617651 1 0.5097 0.4896 0.712 0.076 0.004 0.008 0.200
#> GSM617653 1 0.2887 0.5105 0.884 0.016 0.000 0.028 0.072
#> GSM617654 2 0.3245 0.6496 0.020 0.872 0.004 0.036 0.068
#> GSM617583 3 0.6061 0.6278 0.092 0.012 0.700 0.084 0.112
#> GSM617584 4 0.5656 0.4274 0.244 0.028 0.000 0.656 0.072
#> GSM617585 4 0.5598 0.5510 0.000 0.048 0.060 0.684 0.208
#> GSM617586 3 0.2459 0.7124 0.012 0.024 0.916 0.036 0.012
#> GSM617587 3 0.2333 0.7123 0.008 0.040 0.920 0.020 0.012
#> GSM617589 4 0.5278 0.4832 0.024 0.024 0.004 0.640 0.308
#> GSM617591 4 0.6644 0.5094 0.000 0.108 0.204 0.608 0.080
#> GSM617593 1 0.3646 0.5162 0.844 0.036 0.088 0.000 0.032
#> GSM617594 2 0.7845 0.2148 0.080 0.480 0.056 0.316 0.068
#> GSM617595 1 0.6335 0.4737 0.640 0.100 0.072 0.000 0.188
#> GSM617596 1 0.5255 0.1458 0.556 0.012 0.000 0.028 0.404
#> GSM617597 3 0.3553 0.6884 0.128 0.024 0.832 0.000 0.016
#> GSM617598 1 0.4166 0.5176 0.788 0.008 0.040 0.004 0.160
#> GSM617599 2 0.7625 0.3727 0.068 0.512 0.012 0.208 0.200
#> GSM617600 3 0.1740 0.6991 0.000 0.012 0.932 0.000 0.056
#> GSM617601 4 0.5667 0.4346 0.000 0.296 0.040 0.624 0.040
#> GSM617602 3 0.4672 0.4596 0.016 0.004 0.676 0.008 0.296
#> GSM617603 4 0.5149 0.5962 0.000 0.104 0.000 0.680 0.216
#> GSM617604 1 0.7902 0.0610 0.412 0.000 0.116 0.160 0.312
#> GSM617605 4 0.3087 0.6889 0.004 0.044 0.004 0.872 0.076
#> GSM617606 4 0.6621 0.4233 0.000 0.120 0.028 0.508 0.344
#> GSM617610 1 0.5867 0.4685 0.640 0.056 0.016 0.020 0.268
#> GSM617611 1 0.7242 0.2063 0.436 0.032 0.320 0.000 0.212
#> GSM617613 3 0.2838 0.6795 0.000 0.036 0.884 0.008 0.072
#> GSM617614 3 0.4558 0.6618 0.100 0.000 0.776 0.016 0.108
#> GSM617621 1 0.3872 0.4945 0.828 0.024 0.004 0.032 0.112
#> GSM617629 5 0.6877 0.3737 0.004 0.264 0.204 0.016 0.512
#> GSM617630 2 0.6374 0.4105 0.004 0.624 0.128 0.036 0.208
#> GSM617631 3 0.4275 0.6541 0.024 0.000 0.796 0.052 0.128
#> GSM617633 3 0.7399 0.0433 0.052 0.280 0.464 0.000 0.204
#> GSM617642 3 0.4334 0.6863 0.116 0.004 0.800 0.060 0.020
#> GSM617645 2 0.2889 0.6714 0.016 0.880 0.000 0.084 0.020
#> GSM617646 2 0.5377 0.4791 0.204 0.700 0.048 0.000 0.048
#> GSM617652 3 0.4732 0.6556 0.096 0.112 0.772 0.008 0.012
#> GSM617655 3 0.1442 0.7115 0.000 0.012 0.952 0.032 0.004
#> GSM617656 3 0.0865 0.7089 0.000 0.000 0.972 0.004 0.024
#> GSM617657 3 0.6693 0.2245 0.000 0.052 0.544 0.100 0.304
#> GSM617658 5 0.7420 -0.0179 0.180 0.004 0.384 0.040 0.392
#> GSM617659 1 0.5381 -0.1055 0.484 0.004 0.468 0.000 0.044
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM617581 1 0.518 0.1530 0.544 0.004 0.004 0.396 0.036 0.016
#> GSM617582 5 0.571 0.1409 0.044 0.000 0.008 0.048 0.536 0.364
#> GSM617588 4 0.338 0.5736 0.008 0.060 0.000 0.844 0.016 0.072
#> GSM617590 4 0.277 0.5822 0.000 0.044 0.024 0.888 0.012 0.032
#> GSM617592 4 0.226 0.5813 0.048 0.012 0.004 0.912 0.004 0.020
#> GSM617607 2 0.592 0.4661 0.204 0.640 0.040 0.000 0.080 0.036
#> GSM617608 3 0.679 0.3008 0.180 0.032 0.424 0.000 0.016 0.348
#> GSM617609 3 0.390 0.5824 0.000 0.200 0.756 0.000 0.028 0.016
#> GSM617612 1 0.674 0.3339 0.524 0.064 0.224 0.012 0.000 0.176
#> GSM617615 4 0.734 -0.0152 0.000 0.204 0.072 0.364 0.016 0.344
#> GSM617616 6 0.551 0.1218 0.112 0.024 0.000 0.004 0.232 0.628
#> GSM617617 2 0.468 0.6501 0.016 0.748 0.000 0.064 0.144 0.028
#> GSM617618 5 0.535 -0.0178 0.052 0.000 0.008 0.012 0.472 0.456
#> GSM617619 3 0.709 0.2804 0.000 0.112 0.528 0.180 0.156 0.024
#> GSM617620 4 0.258 0.5899 0.012 0.064 0.000 0.892 0.012 0.020
#> GSM617622 4 0.613 0.4458 0.080 0.032 0.008 0.648 0.176 0.056
#> GSM617623 1 0.562 0.2992 0.596 0.016 0.000 0.296 0.068 0.024
#> GSM617624 2 0.500 0.6475 0.000 0.724 0.048 0.032 0.164 0.032
#> GSM617625 3 0.462 0.5477 0.048 0.004 0.624 0.000 0.000 0.324
#> GSM617626 1 0.417 0.4964 0.768 0.004 0.000 0.156 0.020 0.052
#> GSM617627 2 0.654 0.4374 0.000 0.564 0.156 0.212 0.036 0.032
#> GSM617628 3 0.484 0.4740 0.024 0.000 0.568 0.016 0.004 0.388
#> GSM617632 1 0.547 0.1296 0.492 0.012 0.000 0.008 0.424 0.064
#> GSM617634 5 0.486 0.2544 0.000 0.108 0.004 0.008 0.692 0.188
#> GSM617635 2 0.475 0.6092 0.064 0.772 0.052 0.000 0.060 0.052
#> GSM617636 5 0.426 0.3926 0.116 0.048 0.016 0.008 0.792 0.020
#> GSM617637 1 0.621 0.1398 0.448 0.396 0.008 0.000 0.024 0.124
#> GSM617638 2 0.485 0.6111 0.000 0.688 0.024 0.024 0.240 0.024
#> GSM617639 1 0.483 0.1823 0.532 0.424 0.016 0.000 0.000 0.028
#> GSM617640 2 0.327 0.6842 0.000 0.844 0.004 0.100 0.028 0.024
#> GSM617641 4 0.247 0.5931 0.024 0.056 0.004 0.900 0.012 0.004
#> GSM617643 2 0.524 0.5996 0.000 0.708 0.004 0.080 0.108 0.100
#> GSM617644 6 0.722 0.3059 0.000 0.148 0.000 0.188 0.224 0.440
#> GSM617647 2 0.369 0.6679 0.032 0.820 0.000 0.108 0.008 0.032
#> GSM617648 5 0.598 0.0253 0.004 0.228 0.000 0.024 0.572 0.172
#> GSM617649 2 0.557 0.6299 0.000 0.700 0.040 0.064 0.132 0.064
#> GSM617650 3 0.627 0.3353 0.320 0.036 0.532 0.000 0.024 0.088
#> GSM617651 1 0.551 0.3452 0.500 0.068 0.012 0.000 0.008 0.412
#> GSM617653 1 0.240 0.5428 0.908 0.020 0.000 0.032 0.012 0.028
#> GSM617654 2 0.363 0.6806 0.000 0.824 0.000 0.052 0.084 0.040
#> GSM617583 3 0.465 0.6363 0.044 0.000 0.740 0.036 0.012 0.168
#> GSM617584 4 0.491 0.3331 0.324 0.020 0.004 0.624 0.016 0.012
#> GSM617585 4 0.666 0.2919 0.004 0.012 0.068 0.520 0.292 0.104
#> GSM617586 3 0.222 0.6675 0.004 0.036 0.912 0.012 0.000 0.036
#> GSM617587 3 0.326 0.6488 0.000 0.072 0.852 0.048 0.004 0.024
#> GSM617589 6 0.432 0.1482 0.008 0.004 0.000 0.324 0.016 0.648
#> GSM617591 4 0.684 0.2569 0.000 0.132 0.232 0.512 0.004 0.120
#> GSM617593 1 0.410 0.5271 0.800 0.044 0.092 0.000 0.008 0.056
#> GSM617594 2 0.851 0.1440 0.088 0.400 0.096 0.260 0.032 0.124
#> GSM617595 1 0.676 0.3705 0.484 0.124 0.092 0.000 0.004 0.296
#> GSM617596 1 0.485 0.3702 0.664 0.000 0.008 0.052 0.264 0.012
#> GSM617597 3 0.365 0.6669 0.100 0.028 0.828 0.000 0.024 0.020
#> GSM617598 1 0.502 0.4377 0.592 0.008 0.056 0.000 0.004 0.340
#> GSM617599 6 0.767 0.0615 0.020 0.352 0.008 0.096 0.164 0.360
#> GSM617600 3 0.235 0.6358 0.000 0.008 0.876 0.000 0.112 0.004
#> GSM617601 4 0.622 0.2954 0.000 0.280 0.092 0.544 0.000 0.084
#> GSM617602 3 0.486 0.2204 0.028 0.000 0.548 0.012 0.408 0.004
#> GSM617603 4 0.642 0.2331 0.004 0.032 0.004 0.504 0.300 0.156
#> GSM617604 1 0.647 0.3727 0.580 0.000 0.064 0.188 0.152 0.016
#> GSM617605 4 0.211 0.5849 0.024 0.004 0.000 0.920 0.024 0.028
#> GSM617606 4 0.732 -0.0561 0.004 0.052 0.012 0.344 0.260 0.328
#> GSM617610 1 0.540 0.4037 0.544 0.072 0.020 0.000 0.000 0.364
#> GSM617611 3 0.729 0.0782 0.288 0.116 0.380 0.000 0.000 0.216
#> GSM617613 3 0.382 0.5890 0.000 0.016 0.780 0.012 0.176 0.016
#> GSM617614 3 0.413 0.6370 0.072 0.000 0.792 0.020 0.104 0.012
#> GSM617621 1 0.327 0.5346 0.864 0.028 0.016 0.064 0.020 0.008
#> GSM617629 5 0.264 0.4171 0.000 0.044 0.040 0.008 0.892 0.016
#> GSM617630 2 0.589 0.5241 0.004 0.640 0.088 0.020 0.208 0.040
#> GSM617631 3 0.377 0.5726 0.004 0.000 0.772 0.036 0.184 0.004
#> GSM617633 5 0.683 0.3043 0.016 0.164 0.232 0.000 0.520 0.068
#> GSM617642 3 0.348 0.6646 0.096 0.000 0.836 0.032 0.008 0.028
#> GSM617645 2 0.279 0.6874 0.000 0.876 0.012 0.080 0.008 0.024
#> GSM617646 2 0.482 0.5941 0.092 0.768 0.044 0.004 0.036 0.056
#> GSM617652 3 0.423 0.6208 0.068 0.144 0.764 0.000 0.000 0.024
#> GSM617655 3 0.207 0.6617 0.000 0.020 0.924 0.028 0.012 0.016
#> GSM617656 3 0.154 0.6588 0.008 0.004 0.936 0.000 0.052 0.000
#> GSM617657 5 0.594 0.0549 0.000 0.012 0.408 0.068 0.480 0.032
#> GSM617658 5 0.707 0.1021 0.184 0.000 0.324 0.044 0.424 0.024
#> GSM617659 3 0.564 0.1581 0.440 0.000 0.460 0.000 0.032 0.068
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:NMF 78 0.03818 2
#> CV:NMF 71 0.00093 3
#> CV:NMF 58 0.01018 4
#> CV:NMF 38 0.00576 5
#> CV:NMF 35 0.00437 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 79 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.172 0.644 0.823 0.3296 0.705 0.705
#> 3 3 0.231 0.499 0.773 0.6640 0.747 0.650
#> 4 4 0.273 0.383 0.698 0.1320 0.923 0.843
#> 5 5 0.302 0.513 0.685 0.0944 0.785 0.526
#> 6 6 0.370 0.487 0.678 0.0685 0.953 0.833
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM617581 2 0.5294 0.7982 0.120 0.880
#> GSM617582 2 0.7139 0.6535 0.196 0.804
#> GSM617588 2 0.6887 0.7367 0.184 0.816
#> GSM617590 2 0.7139 0.7324 0.196 0.804
#> GSM617592 2 0.6531 0.7524 0.168 0.832
#> GSM617607 2 0.3733 0.7985 0.072 0.928
#> GSM617608 2 0.9393 0.0311 0.356 0.644
#> GSM617609 1 0.9988 0.5230 0.520 0.480
#> GSM617612 2 0.2043 0.8040 0.032 0.968
#> GSM617615 2 0.5946 0.7743 0.144 0.856
#> GSM617616 2 0.6531 0.6956 0.168 0.832
#> GSM617617 2 0.3274 0.7998 0.060 0.940
#> GSM617618 2 0.6148 0.7192 0.152 0.848
#> GSM617619 2 0.9754 0.0386 0.408 0.592
#> GSM617620 2 0.6438 0.7553 0.164 0.836
#> GSM617622 2 0.5178 0.7889 0.116 0.884
#> GSM617623 2 0.3584 0.8071 0.068 0.932
#> GSM617624 2 0.5294 0.7947 0.120 0.880
#> GSM617625 1 0.9998 0.5067 0.508 0.492
#> GSM617626 2 0.3114 0.7959 0.056 0.944
#> GSM617627 2 0.4690 0.7981 0.100 0.900
#> GSM617628 1 1.0000 0.4912 0.500 0.500
#> GSM617632 2 0.3274 0.7905 0.060 0.940
#> GSM617634 2 0.7376 0.6761 0.208 0.792
#> GSM617635 2 0.1414 0.8013 0.020 0.980
#> GSM617636 2 0.4298 0.7851 0.088 0.912
#> GSM617637 2 0.0672 0.7984 0.008 0.992
#> GSM617638 2 0.5946 0.7728 0.144 0.856
#> GSM617639 2 0.1843 0.7993 0.028 0.972
#> GSM617640 2 0.2948 0.8002 0.052 0.948
#> GSM617641 2 0.6973 0.7352 0.188 0.812
#> GSM617643 2 0.4161 0.7968 0.084 0.916
#> GSM617644 2 0.6531 0.7530 0.168 0.832
#> GSM617647 2 0.3114 0.7997 0.056 0.944
#> GSM617648 2 0.4022 0.7991 0.080 0.920
#> GSM617649 2 0.4161 0.7969 0.084 0.916
#> GSM617650 2 0.3114 0.7951 0.056 0.944
#> GSM617651 2 0.1843 0.8016 0.028 0.972
#> GSM617653 2 0.2043 0.8033 0.032 0.968
#> GSM617654 2 0.1843 0.7963 0.028 0.972
#> GSM617583 2 0.9795 -0.2097 0.416 0.584
#> GSM617584 2 0.4939 0.7906 0.108 0.892
#> GSM617585 1 0.9881 0.4829 0.564 0.436
#> GSM617586 1 0.9963 0.5431 0.536 0.464
#> GSM617587 2 0.9977 -0.3732 0.472 0.528
#> GSM617589 2 0.6887 0.7354 0.184 0.816
#> GSM617591 2 0.9460 0.2125 0.364 0.636
#> GSM617593 2 0.4815 0.7631 0.104 0.896
#> GSM617594 2 0.4022 0.7988 0.080 0.920
#> GSM617595 2 0.0376 0.7976 0.004 0.996
#> GSM617596 2 0.3879 0.7931 0.076 0.924
#> GSM617597 2 0.9933 -0.3910 0.452 0.548
#> GSM617598 2 0.1184 0.8001 0.016 0.984
#> GSM617599 2 0.3584 0.8038 0.068 0.932
#> GSM617600 1 0.9248 0.6975 0.660 0.340
#> GSM617601 2 0.4562 0.7966 0.096 0.904
#> GSM617602 1 0.9209 0.6901 0.664 0.336
#> GSM617603 2 0.7056 0.7298 0.192 0.808
#> GSM617604 2 0.6801 0.7280 0.180 0.820
#> GSM617605 2 0.7139 0.7324 0.196 0.804
#> GSM617606 2 0.7299 0.6952 0.204 0.796
#> GSM617610 2 0.0938 0.7987 0.012 0.988
#> GSM617611 2 0.2778 0.8010 0.048 0.952
#> GSM617613 1 0.3879 0.6153 0.924 0.076
#> GSM617614 2 0.9850 -0.2565 0.428 0.572
#> GSM617621 2 0.2948 0.8009 0.052 0.948
#> GSM617629 1 0.6247 0.6464 0.844 0.156
#> GSM617630 2 0.7528 0.6409 0.216 0.784
#> GSM617631 1 0.8207 0.7114 0.744 0.256
#> GSM617633 2 0.6048 0.7331 0.148 0.852
#> GSM617642 2 0.9998 -0.4537 0.492 0.508
#> GSM617645 2 0.2236 0.7956 0.036 0.964
#> GSM617646 2 0.0672 0.7991 0.008 0.992
#> GSM617652 2 0.7528 0.6007 0.216 0.784
#> GSM617655 1 0.9933 0.5691 0.548 0.452
#> GSM617656 1 0.9087 0.7056 0.676 0.324
#> GSM617657 1 0.1843 0.5823 0.972 0.028
#> GSM617658 1 0.8207 0.7114 0.744 0.256
#> GSM617659 2 0.5408 0.7403 0.124 0.876
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM617581 1 0.6388 0.5963 0.752 0.184 0.064
#> GSM617582 1 0.5956 0.5721 0.768 0.044 0.188
#> GSM617588 2 0.1751 0.7999 0.028 0.960 0.012
#> GSM617590 2 0.1015 0.7964 0.008 0.980 0.012
#> GSM617592 2 0.2651 0.8025 0.060 0.928 0.012
#> GSM617607 1 0.2400 0.6794 0.932 0.004 0.064
#> GSM617608 1 0.6427 0.1341 0.640 0.012 0.348
#> GSM617609 3 0.6941 0.4500 0.464 0.016 0.520
#> GSM617612 1 0.1585 0.6864 0.964 0.008 0.028
#> GSM617615 2 0.4563 0.7785 0.112 0.852 0.036
#> GSM617616 1 0.5119 0.6150 0.812 0.028 0.160
#> GSM617617 1 0.4645 0.6233 0.816 0.176 0.008
#> GSM617618 1 0.4810 0.6320 0.832 0.028 0.140
#> GSM617619 1 0.9409 -0.0342 0.460 0.180 0.360
#> GSM617620 2 0.4045 0.7917 0.104 0.872 0.024
#> GSM617622 2 0.6859 0.4183 0.356 0.620 0.024
#> GSM617623 1 0.3649 0.6804 0.896 0.068 0.036
#> GSM617624 1 0.7749 0.4563 0.624 0.300 0.076
#> GSM617625 3 0.7585 0.3804 0.476 0.040 0.484
#> GSM617626 1 0.3369 0.6834 0.908 0.040 0.052
#> GSM617627 1 0.7624 0.3070 0.580 0.368 0.052
#> GSM617628 1 0.7674 -0.4176 0.480 0.044 0.476
#> GSM617632 1 0.2066 0.6789 0.940 0.000 0.060
#> GSM617634 1 0.8263 0.4477 0.636 0.188 0.176
#> GSM617635 1 0.1031 0.6856 0.976 0.000 0.024
#> GSM617636 1 0.2625 0.6712 0.916 0.000 0.084
#> GSM617637 1 0.1170 0.6866 0.976 0.008 0.016
#> GSM617638 1 0.5656 0.6385 0.804 0.068 0.128
#> GSM617639 1 0.1163 0.6839 0.972 0.000 0.028
#> GSM617640 1 0.4099 0.6448 0.852 0.140 0.008
#> GSM617641 2 0.1491 0.7976 0.016 0.968 0.016
#> GSM617643 1 0.6669 0.0412 0.524 0.468 0.008
#> GSM617644 2 0.4475 0.7596 0.144 0.840 0.016
#> GSM617647 1 0.6262 0.4983 0.696 0.284 0.020
#> GSM617648 2 0.6520 0.0184 0.488 0.508 0.004
#> GSM617649 1 0.6509 0.0360 0.524 0.472 0.004
#> GSM617650 1 0.1860 0.6793 0.948 0.000 0.052
#> GSM617651 1 0.1315 0.6850 0.972 0.008 0.020
#> GSM617653 1 0.1482 0.6860 0.968 0.012 0.020
#> GSM617654 1 0.3325 0.6645 0.904 0.076 0.020
#> GSM617583 1 0.7339 -0.1070 0.572 0.036 0.392
#> GSM617584 2 0.5486 0.7188 0.196 0.780 0.024
#> GSM617585 3 0.8337 0.1372 0.088 0.376 0.536
#> GSM617586 3 0.6793 0.4759 0.452 0.012 0.536
#> GSM617587 1 0.7069 -0.3485 0.508 0.020 0.472
#> GSM617589 2 0.1919 0.7922 0.020 0.956 0.024
#> GSM617591 1 0.9805 -0.1856 0.424 0.256 0.320
#> GSM617593 1 0.2959 0.6537 0.900 0.000 0.100
#> GSM617594 1 0.6950 0.2314 0.572 0.408 0.020
#> GSM617595 1 0.0424 0.6826 0.992 0.000 0.008
#> GSM617596 1 0.2590 0.6750 0.924 0.004 0.072
#> GSM617597 1 0.6483 -0.2862 0.544 0.004 0.452
#> GSM617598 1 0.0747 0.6844 0.984 0.000 0.016
#> GSM617599 1 0.6608 0.3845 0.628 0.356 0.016
#> GSM617600 3 0.6497 0.6487 0.336 0.016 0.648
#> GSM617601 1 0.7169 0.0804 0.520 0.456 0.024
#> GSM617602 3 0.5760 0.6445 0.328 0.000 0.672
#> GSM617603 2 0.1919 0.7950 0.020 0.956 0.024
#> GSM617604 1 0.5696 0.6068 0.796 0.056 0.148
#> GSM617605 2 0.1015 0.7964 0.008 0.980 0.012
#> GSM617606 2 0.8520 0.3845 0.280 0.588 0.132
#> GSM617610 1 0.0829 0.6849 0.984 0.004 0.012
#> GSM617611 1 0.2229 0.6856 0.944 0.012 0.044
#> GSM617613 3 0.2651 0.5953 0.060 0.012 0.928
#> GSM617614 1 0.6859 -0.1411 0.564 0.016 0.420
#> GSM617621 1 0.2200 0.6846 0.940 0.004 0.056
#> GSM617629 3 0.4291 0.6501 0.152 0.008 0.840
#> GSM617630 1 0.6585 0.5512 0.736 0.064 0.200
#> GSM617631 3 0.5325 0.6915 0.248 0.004 0.748
#> GSM617633 1 0.3983 0.6340 0.852 0.004 0.144
#> GSM617642 1 0.6683 -0.3993 0.500 0.008 0.492
#> GSM617645 1 0.3765 0.6587 0.888 0.084 0.028
#> GSM617646 1 0.0848 0.6854 0.984 0.008 0.008
#> GSM617652 1 0.6354 0.5140 0.744 0.052 0.204
#> GSM617655 3 0.6771 0.5066 0.440 0.012 0.548
#> GSM617656 3 0.5929 0.6636 0.320 0.004 0.676
#> GSM617657 3 0.1182 0.5304 0.012 0.012 0.976
#> GSM617658 3 0.5325 0.6915 0.248 0.004 0.748
#> GSM617659 1 0.3340 0.6375 0.880 0.000 0.120
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM617581 1 0.6616 0.3862 0.700 0.132 0.048 0.120
#> GSM617582 1 0.5430 0.5012 0.752 0.036 0.180 0.032
#> GSM617588 4 0.3052 0.7572 0.004 0.136 0.000 0.860
#> GSM617590 4 0.2654 0.7695 0.000 0.108 0.004 0.888
#> GSM617592 4 0.3105 0.7510 0.004 0.140 0.000 0.856
#> GSM617607 1 0.2797 0.6149 0.900 0.032 0.068 0.000
#> GSM617608 1 0.5847 0.0279 0.612 0.024 0.352 0.012
#> GSM617609 3 0.6194 0.4758 0.428 0.036 0.528 0.008
#> GSM617612 1 0.1707 0.6164 0.952 0.024 0.020 0.004
#> GSM617615 4 0.4774 0.7017 0.072 0.096 0.020 0.812
#> GSM617616 1 0.4687 0.5469 0.796 0.040 0.152 0.012
#> GSM617617 1 0.6256 -0.0950 0.580 0.360 0.004 0.056
#> GSM617618 1 0.4400 0.5615 0.816 0.036 0.136 0.012
#> GSM617619 1 0.8964 -0.1436 0.372 0.204 0.356 0.068
#> GSM617620 4 0.3999 0.7325 0.036 0.140 0.000 0.824
#> GSM617622 2 0.7955 0.5099 0.240 0.448 0.008 0.304
#> GSM617623 1 0.3460 0.5755 0.884 0.056 0.024 0.036
#> GSM617624 1 0.7991 -0.4912 0.464 0.384 0.052 0.100
#> GSM617625 3 0.6443 0.4215 0.460 0.016 0.488 0.036
#> GSM617626 1 0.3030 0.6101 0.904 0.036 0.036 0.024
#> GSM617627 1 0.7873 -0.6767 0.424 0.420 0.028 0.128
#> GSM617628 3 0.6517 0.4094 0.464 0.016 0.480 0.040
#> GSM617632 1 0.1888 0.6184 0.940 0.016 0.044 0.000
#> GSM617634 1 0.8075 0.1117 0.568 0.196 0.172 0.064
#> GSM617635 1 0.1297 0.6100 0.964 0.020 0.016 0.000
#> GSM617636 1 0.2473 0.6183 0.908 0.012 0.080 0.000
#> GSM617637 1 0.1639 0.6037 0.952 0.036 0.008 0.004
#> GSM617638 1 0.6759 0.1052 0.548 0.344 0.108 0.000
#> GSM617639 1 0.1520 0.6116 0.956 0.024 0.020 0.000
#> GSM617640 1 0.6095 -0.0385 0.552 0.404 0.004 0.040
#> GSM617641 4 0.1389 0.7604 0.000 0.048 0.000 0.952
#> GSM617643 2 0.7349 0.8287 0.384 0.456 0.000 0.160
#> GSM617644 4 0.6532 0.3481 0.092 0.336 0.000 0.572
#> GSM617647 1 0.6532 -0.3895 0.548 0.368 0.000 0.084
#> GSM617648 2 0.7489 0.8278 0.364 0.452 0.000 0.184
#> GSM617649 2 0.7292 0.8288 0.388 0.460 0.000 0.152
#> GSM617650 1 0.1576 0.6194 0.948 0.004 0.048 0.000
#> GSM617651 1 0.1151 0.6124 0.968 0.024 0.008 0.000
#> GSM617653 1 0.1229 0.6134 0.968 0.020 0.008 0.004
#> GSM617654 1 0.5168 -0.0248 0.504 0.492 0.004 0.000
#> GSM617583 1 0.6252 -0.1870 0.564 0.016 0.388 0.032
#> GSM617584 4 0.5954 0.5714 0.112 0.168 0.008 0.712
#> GSM617585 3 0.8027 0.1079 0.080 0.092 0.540 0.288
#> GSM617586 3 0.5552 0.4795 0.440 0.008 0.544 0.008
#> GSM617587 1 0.6305 -0.3888 0.480 0.040 0.472 0.008
#> GSM617589 4 0.1022 0.7503 0.000 0.032 0.000 0.968
#> GSM617591 1 0.9474 -0.2428 0.376 0.152 0.308 0.164
#> GSM617593 1 0.2334 0.6074 0.908 0.004 0.088 0.000
#> GSM617594 1 0.7352 -0.7358 0.436 0.424 0.004 0.136
#> GSM617595 1 0.0779 0.6043 0.980 0.016 0.004 0.000
#> GSM617596 1 0.2198 0.6197 0.920 0.008 0.072 0.000
#> GSM617597 1 0.4981 -0.3181 0.536 0.000 0.464 0.000
#> GSM617598 1 0.1042 0.6092 0.972 0.020 0.008 0.000
#> GSM617599 1 0.7382 -0.5231 0.520 0.348 0.016 0.116
#> GSM617600 3 0.5173 0.6277 0.320 0.020 0.660 0.000
#> GSM617601 2 0.7747 0.7835 0.380 0.436 0.008 0.176
#> GSM617602 3 0.4978 0.6156 0.324 0.012 0.664 0.000
#> GSM617603 4 0.4088 0.6789 0.000 0.232 0.004 0.764
#> GSM617604 1 0.4968 0.5566 0.788 0.040 0.148 0.024
#> GSM617605 4 0.2654 0.7695 0.000 0.108 0.004 0.888
#> GSM617606 4 0.9432 -0.0422 0.232 0.252 0.120 0.396
#> GSM617610 1 0.1082 0.6076 0.972 0.020 0.004 0.004
#> GSM617611 1 0.2039 0.6180 0.940 0.016 0.036 0.008
#> GSM617613 3 0.3168 0.5296 0.056 0.060 0.884 0.000
#> GSM617614 1 0.5838 -0.1779 0.560 0.012 0.412 0.016
#> GSM617621 1 0.2313 0.6162 0.924 0.032 0.044 0.000
#> GSM617629 3 0.4387 0.6003 0.144 0.052 0.804 0.000
#> GSM617630 1 0.7476 0.0940 0.412 0.412 0.176 0.000
#> GSM617631 3 0.4420 0.6556 0.240 0.012 0.748 0.000
#> GSM617633 1 0.3495 0.5746 0.844 0.016 0.140 0.000
#> GSM617642 1 0.5336 -0.4024 0.496 0.004 0.496 0.004
#> GSM617645 1 0.5167 -0.0222 0.508 0.488 0.004 0.000
#> GSM617646 1 0.1722 0.5997 0.944 0.048 0.008 0.000
#> GSM617652 1 0.6425 0.4348 0.688 0.088 0.196 0.028
#> GSM617655 3 0.5532 0.5058 0.428 0.008 0.556 0.008
#> GSM617656 3 0.4655 0.6372 0.312 0.004 0.684 0.000
#> GSM617657 3 0.2589 0.3911 0.000 0.116 0.884 0.000
#> GSM617658 3 0.4420 0.6556 0.240 0.012 0.748 0.000
#> GSM617659 1 0.2714 0.5890 0.884 0.004 0.112 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM617581 1 0.6475 0.46205 0.664 0.172 0.048 0.080 0.036
#> GSM617582 1 0.5700 0.56516 0.712 0.060 0.168 0.020 0.040
#> GSM617588 4 0.3988 0.72961 0.000 0.252 0.000 0.732 0.016
#> GSM617590 4 0.3993 0.75957 0.000 0.216 0.000 0.756 0.028
#> GSM617592 4 0.3565 0.75981 0.000 0.176 0.000 0.800 0.024
#> GSM617607 1 0.3343 0.72368 0.860 0.028 0.084 0.000 0.028
#> GSM617608 1 0.5766 -0.00512 0.568 0.028 0.368 0.008 0.028
#> GSM617609 3 0.5602 0.51894 0.380 0.036 0.560 0.000 0.024
#> GSM617612 1 0.1498 0.74616 0.952 0.016 0.024 0.000 0.008
#> GSM617615 4 0.5094 0.70893 0.056 0.108 0.024 0.772 0.040
#> GSM617616 1 0.5018 0.62044 0.756 0.056 0.140 0.004 0.044
#> GSM617617 1 0.7588 -0.59674 0.344 0.328 0.008 0.024 0.296
#> GSM617618 1 0.4838 0.63588 0.768 0.052 0.136 0.004 0.040
#> GSM617619 3 0.8283 0.17462 0.272 0.268 0.376 0.024 0.060
#> GSM617620 4 0.4226 0.74168 0.012 0.188 0.000 0.768 0.032
#> GSM617622 2 0.6536 0.44514 0.160 0.616 0.008 0.184 0.032
#> GSM617623 1 0.3581 0.70254 0.848 0.100 0.028 0.012 0.012
#> GSM617624 2 0.7389 0.39488 0.316 0.496 0.056 0.016 0.116
#> GSM617625 3 0.5997 0.43932 0.428 0.028 0.504 0.020 0.020
#> GSM617626 1 0.2963 0.73939 0.888 0.048 0.044 0.016 0.004
#> GSM617627 2 0.6892 0.50686 0.260 0.572 0.024 0.028 0.116
#> GSM617628 3 0.6078 0.42639 0.432 0.028 0.496 0.024 0.020
#> GSM617632 1 0.1978 0.74333 0.928 0.024 0.044 0.000 0.004
#> GSM617634 1 0.7688 -0.04825 0.456 0.304 0.172 0.012 0.056
#> GSM617635 1 0.1560 0.74743 0.948 0.028 0.020 0.000 0.004
#> GSM617636 1 0.2712 0.73209 0.880 0.032 0.088 0.000 0.000
#> GSM617637 1 0.1618 0.74115 0.944 0.040 0.008 0.000 0.008
#> GSM617638 5 0.8123 0.39432 0.312 0.216 0.112 0.000 0.360
#> GSM617639 1 0.1377 0.74565 0.956 0.020 0.020 0.000 0.004
#> GSM617640 5 0.7116 0.50247 0.288 0.252 0.000 0.020 0.440
#> GSM617641 4 0.2172 0.77483 0.000 0.076 0.000 0.908 0.016
#> GSM617643 2 0.5185 0.59345 0.236 0.692 0.000 0.032 0.040
#> GSM617644 2 0.5724 -0.21759 0.044 0.552 0.004 0.384 0.016
#> GSM617647 2 0.6501 0.34154 0.396 0.472 0.004 0.012 0.116
#> GSM617648 2 0.5041 0.59345 0.236 0.700 0.004 0.048 0.012
#> GSM617649 2 0.4703 0.60156 0.240 0.716 0.004 0.028 0.012
#> GSM617650 1 0.1270 0.74299 0.948 0.000 0.052 0.000 0.000
#> GSM617651 1 0.1087 0.74578 0.968 0.016 0.008 0.000 0.008
#> GSM617653 1 0.1362 0.74687 0.960 0.016 0.012 0.004 0.008
#> GSM617654 5 0.5357 0.64352 0.224 0.104 0.000 0.004 0.668
#> GSM617583 1 0.5733 -0.21721 0.536 0.020 0.408 0.020 0.016
#> GSM617584 4 0.5900 0.60561 0.076 0.220 0.008 0.664 0.032
#> GSM617585 3 0.7723 0.13794 0.052 0.168 0.540 0.196 0.044
#> GSM617586 3 0.4980 0.51010 0.396 0.020 0.576 0.000 0.008
#> GSM617587 3 0.5633 0.41023 0.440 0.048 0.500 0.000 0.012
#> GSM617589 4 0.1822 0.74887 0.004 0.036 0.000 0.936 0.024
#> GSM617591 3 0.9118 0.30141 0.304 0.184 0.332 0.112 0.068
#> GSM617593 1 0.2629 0.71197 0.880 0.004 0.104 0.000 0.012
#> GSM617594 2 0.5468 0.56945 0.312 0.628 0.008 0.016 0.036
#> GSM617595 1 0.1059 0.74175 0.968 0.020 0.008 0.000 0.004
#> GSM617596 1 0.2707 0.73378 0.888 0.024 0.080 0.000 0.008
#> GSM617597 1 0.4560 -0.33416 0.508 0.000 0.484 0.000 0.008
#> GSM617598 1 0.0854 0.74382 0.976 0.012 0.008 0.000 0.004
#> GSM617599 2 0.6404 0.48397 0.372 0.532 0.028 0.024 0.044
#> GSM617600 3 0.4605 0.61475 0.272 0.032 0.692 0.000 0.004
#> GSM617601 2 0.5898 0.59179 0.240 0.656 0.008 0.048 0.048
#> GSM617602 3 0.4769 0.58275 0.288 0.020 0.676 0.000 0.016
#> GSM617603 4 0.5322 0.48819 0.000 0.408 0.004 0.544 0.044
#> GSM617604 1 0.4759 0.62801 0.756 0.072 0.156 0.004 0.012
#> GSM617605 4 0.3993 0.75957 0.000 0.216 0.000 0.756 0.028
#> GSM617606 2 0.9401 0.00821 0.168 0.348 0.140 0.248 0.096
#> GSM617610 1 0.0960 0.74433 0.972 0.016 0.008 0.000 0.004
#> GSM617611 1 0.1843 0.74477 0.936 0.012 0.044 0.004 0.004
#> GSM617613 3 0.3756 0.36357 0.032 0.036 0.836 0.000 0.096
#> GSM617614 1 0.5671 -0.22808 0.516 0.016 0.432 0.012 0.024
#> GSM617621 1 0.2627 0.74431 0.900 0.044 0.044 0.000 0.012
#> GSM617629 3 0.4918 0.44792 0.108 0.044 0.764 0.000 0.084
#> GSM617630 5 0.7141 0.48809 0.192 0.076 0.180 0.000 0.552
#> GSM617631 3 0.4301 0.60330 0.204 0.020 0.756 0.000 0.020
#> GSM617633 1 0.3824 0.67505 0.820 0.024 0.128 0.000 0.028
#> GSM617642 3 0.4895 0.40516 0.452 0.012 0.528 0.000 0.008
#> GSM617645 5 0.5847 0.65564 0.236 0.132 0.000 0.008 0.624
#> GSM617646 1 0.2825 0.70885 0.888 0.076 0.012 0.004 0.020
#> GSM617652 1 0.6203 0.40335 0.644 0.084 0.216 0.004 0.052
#> GSM617655 3 0.4950 0.52936 0.384 0.020 0.588 0.000 0.008
#> GSM617656 3 0.3838 0.61021 0.280 0.004 0.716 0.000 0.000
#> GSM617657 3 0.4701 0.15941 0.000 0.076 0.720 0.000 0.204
#> GSM617658 3 0.4301 0.60330 0.204 0.020 0.756 0.000 0.020
#> GSM617659 1 0.2929 0.68853 0.856 0.004 0.128 0.000 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM617581 1 0.6622 0.5042 0.632 0.148 0.064 0.092 0.024 0.040
#> GSM617582 1 0.6169 0.5166 0.624 0.072 0.196 0.016 0.004 0.088
#> GSM617588 4 0.4794 0.5573 0.000 0.228 0.004 0.668 0.000 0.100
#> GSM617590 4 0.4602 0.6050 0.000 0.148 0.004 0.708 0.000 0.140
#> GSM617592 4 0.3897 0.6575 0.000 0.164 0.004 0.780 0.016 0.036
#> GSM617607 1 0.3432 0.7509 0.840 0.032 0.092 0.000 0.028 0.008
#> GSM617608 1 0.5513 -0.0126 0.536 0.036 0.388 0.004 0.020 0.016
#> GSM617609 3 0.5185 0.5453 0.324 0.048 0.600 0.000 0.024 0.004
#> GSM617612 1 0.1642 0.7774 0.936 0.028 0.032 0.000 0.000 0.004
#> GSM617615 4 0.5212 0.5598 0.032 0.112 0.024 0.744 0.028 0.060
#> GSM617616 1 0.5639 0.5900 0.676 0.076 0.160 0.004 0.008 0.076
#> GSM617617 2 0.6515 -0.1788 0.132 0.420 0.008 0.012 0.408 0.020
#> GSM617618 1 0.5734 0.5833 0.668 0.084 0.160 0.004 0.008 0.076
#> GSM617619 3 0.7963 -0.0301 0.200 0.292 0.384 0.020 0.072 0.032
#> GSM617620 4 0.4680 0.6378 0.008 0.180 0.008 0.736 0.024 0.044
#> GSM617622 2 0.6294 0.3842 0.088 0.652 0.016 0.136 0.024 0.084
#> GSM617623 1 0.3752 0.7359 0.832 0.080 0.040 0.016 0.004 0.028
#> GSM617624 2 0.6961 0.4891 0.176 0.560 0.064 0.016 0.164 0.020
#> GSM617625 3 0.5448 0.4567 0.392 0.024 0.536 0.012 0.004 0.032
#> GSM617626 1 0.3464 0.7642 0.848 0.048 0.060 0.016 0.000 0.028
#> GSM617627 2 0.5979 0.5498 0.120 0.652 0.032 0.020 0.164 0.012
#> GSM617628 3 0.5577 0.4413 0.392 0.028 0.528 0.012 0.004 0.036
#> GSM617632 1 0.2842 0.7709 0.880 0.040 0.048 0.004 0.000 0.028
#> GSM617634 2 0.7716 0.0211 0.304 0.388 0.184 0.004 0.028 0.092
#> GSM617635 1 0.1780 0.7798 0.932 0.028 0.028 0.000 0.012 0.000
#> GSM617636 1 0.3532 0.7547 0.828 0.044 0.092 0.000 0.000 0.036
#> GSM617637 1 0.1882 0.7678 0.920 0.060 0.008 0.000 0.012 0.000
#> GSM617638 5 0.7392 0.3120 0.112 0.268 0.116 0.004 0.472 0.028
#> GSM617639 1 0.1749 0.7770 0.932 0.036 0.024 0.000 0.008 0.000
#> GSM617640 5 0.5144 0.4833 0.100 0.268 0.000 0.004 0.624 0.004
#> GSM617641 4 0.2213 0.6647 0.000 0.068 0.004 0.904 0.004 0.020
#> GSM617643 2 0.3955 0.6011 0.124 0.800 0.000 0.012 0.040 0.024
#> GSM617644 2 0.5720 -0.0725 0.012 0.552 0.000 0.284 0.000 0.152
#> GSM617647 2 0.6146 0.4711 0.264 0.548 0.004 0.008 0.160 0.016
#> GSM617648 2 0.3923 0.5735 0.124 0.800 0.000 0.024 0.008 0.044
#> GSM617649 2 0.3409 0.6039 0.136 0.824 0.004 0.008 0.012 0.016
#> GSM617650 1 0.1204 0.7720 0.944 0.000 0.056 0.000 0.000 0.000
#> GSM617651 1 0.1476 0.7745 0.948 0.008 0.012 0.004 0.000 0.028
#> GSM617653 1 0.1684 0.7759 0.940 0.008 0.016 0.008 0.000 0.028
#> GSM617654 5 0.2122 0.5950 0.040 0.040 0.000 0.000 0.912 0.008
#> GSM617583 1 0.5399 -0.2225 0.504 0.024 0.432 0.012 0.008 0.020
#> GSM617584 4 0.5929 0.5059 0.064 0.212 0.016 0.648 0.028 0.032
#> GSM617585 3 0.6876 -0.3292 0.016 0.084 0.520 0.140 0.000 0.240
#> GSM617586 3 0.4506 0.5396 0.344 0.036 0.616 0.000 0.004 0.000
#> GSM617587 3 0.5146 0.4670 0.388 0.060 0.540 0.000 0.012 0.000
#> GSM617589 4 0.2520 0.6088 0.004 0.024 0.000 0.888 0.008 0.076
#> GSM617591 3 0.8860 -0.1121 0.244 0.192 0.352 0.084 0.056 0.072
#> GSM617593 1 0.2451 0.7431 0.876 0.004 0.108 0.000 0.008 0.004
#> GSM617594 2 0.4427 0.6082 0.196 0.732 0.012 0.008 0.052 0.000
#> GSM617595 1 0.0951 0.7717 0.968 0.020 0.008 0.000 0.004 0.000
#> GSM617596 1 0.2948 0.7622 0.860 0.024 0.092 0.000 0.000 0.024
#> GSM617597 3 0.4222 0.3108 0.472 0.008 0.516 0.000 0.004 0.000
#> GSM617598 1 0.0912 0.7731 0.972 0.012 0.008 0.000 0.004 0.004
#> GSM617599 2 0.5516 0.5641 0.228 0.656 0.028 0.012 0.068 0.008
#> GSM617600 3 0.4314 0.5638 0.232 0.036 0.716 0.000 0.004 0.012
#> GSM617601 2 0.4928 0.6053 0.124 0.752 0.016 0.024 0.064 0.020
#> GSM617602 3 0.4703 0.4952 0.236 0.016 0.684 0.000 0.000 0.064
#> GSM617603 4 0.6105 0.0258 0.000 0.228 0.000 0.396 0.004 0.372
#> GSM617604 1 0.5063 0.6305 0.712 0.056 0.176 0.008 0.004 0.044
#> GSM617605 4 0.4602 0.6050 0.000 0.148 0.004 0.708 0.000 0.140
#> GSM617606 6 0.9541 0.0000 0.128 0.216 0.156 0.152 0.068 0.280
#> GSM617610 1 0.1053 0.7752 0.964 0.020 0.012 0.000 0.004 0.000
#> GSM617611 1 0.1621 0.7757 0.936 0.008 0.048 0.000 0.004 0.004
#> GSM617613 3 0.3769 0.1517 0.012 0.000 0.776 0.000 0.036 0.176
#> GSM617614 1 0.5230 -0.2528 0.476 0.024 0.468 0.004 0.008 0.020
#> GSM617621 1 0.3376 0.7720 0.856 0.048 0.056 0.004 0.012 0.024
#> GSM617629 3 0.4593 0.1662 0.032 0.024 0.716 0.000 0.012 0.216
#> GSM617630 5 0.5366 0.3007 0.080 0.036 0.192 0.004 0.680 0.008
#> GSM617631 3 0.3948 0.4921 0.160 0.012 0.772 0.000 0.000 0.056
#> GSM617633 1 0.4256 0.6865 0.776 0.048 0.136 0.000 0.008 0.032
#> GSM617642 3 0.4256 0.4219 0.420 0.012 0.564 0.000 0.004 0.000
#> GSM617645 5 0.3079 0.6298 0.052 0.092 0.000 0.008 0.848 0.000
#> GSM617646 1 0.2753 0.7440 0.872 0.092 0.016 0.004 0.016 0.000
#> GSM617652 1 0.6054 0.4012 0.612 0.092 0.224 0.008 0.060 0.004
#> GSM617655 3 0.4465 0.5538 0.332 0.036 0.628 0.000 0.004 0.000
#> GSM617656 3 0.3488 0.5755 0.244 0.004 0.744 0.000 0.000 0.008
#> GSM617657 3 0.4690 -0.1409 0.000 0.000 0.552 0.000 0.048 0.400
#> GSM617658 3 0.3948 0.4921 0.160 0.012 0.772 0.000 0.000 0.056
#> GSM617659 1 0.2716 0.7196 0.852 0.004 0.132 0.000 0.008 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) k
#> MAD:hclust 69 0.01221 2
#> MAD:hclust 54 0.00435 3
#> MAD:hclust 49 0.01286 4
#> MAD:hclust 52 0.14413 5
#> MAD:hclust 50 0.52577 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 79 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.919 0.923 0.953 0.4895 0.517 0.517
#> 3 3 0.619 0.859 0.873 0.3341 0.790 0.603
#> 4 4 0.698 0.774 0.837 0.1257 0.932 0.797
#> 5 5 0.726 0.637 0.811 0.0667 0.920 0.715
#> 6 6 0.709 0.553 0.765 0.0411 0.978 0.898
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
#> GSM617581 1 0.7528 0.746 0.784 0.216
#> GSM617582 1 0.3733 0.914 0.928 0.072
#> GSM617588 2 0.1843 0.970 0.028 0.972
#> GSM617590 2 0.1633 0.959 0.024 0.976
#> GSM617592 2 0.1843 0.970 0.028 0.972
#> GSM617607 1 0.1184 0.945 0.984 0.016
#> GSM617608 1 0.0672 0.945 0.992 0.008
#> GSM617609 1 0.1843 0.940 0.972 0.028
#> GSM617612 1 0.1633 0.944 0.976 0.024
#> GSM617615 2 0.1184 0.965 0.016 0.984
#> GSM617616 1 0.1633 0.944 0.976 0.024
#> GSM617617 2 0.1843 0.970 0.028 0.972
#> GSM617618 1 0.2236 0.939 0.964 0.036
#> GSM617619 2 0.5294 0.878 0.120 0.880
#> GSM617620 2 0.1633 0.971 0.024 0.976
#> GSM617622 2 0.1843 0.970 0.028 0.972
#> GSM617623 1 0.8207 0.685 0.744 0.256
#> GSM617624 2 0.2043 0.960 0.032 0.968
#> GSM617625 1 0.1843 0.941 0.972 0.028
#> GSM617626 1 0.9850 0.290 0.572 0.428
#> GSM617627 2 0.2043 0.963 0.032 0.968
#> GSM617628 1 0.1843 0.941 0.972 0.028
#> GSM617632 1 0.1414 0.945 0.980 0.020
#> GSM617634 2 0.4690 0.920 0.100 0.900
#> GSM617635 1 0.1633 0.944 0.976 0.024
#> GSM617636 1 0.0938 0.945 0.988 0.012
#> GSM617637 1 0.1633 0.944 0.976 0.024
#> GSM617638 2 0.5629 0.863 0.132 0.868
#> GSM617639 1 0.1633 0.944 0.976 0.024
#> GSM617640 2 0.1843 0.970 0.028 0.972
#> GSM617641 2 0.1633 0.970 0.024 0.976
#> GSM617643 2 0.1843 0.970 0.028 0.972
#> GSM617644 2 0.1843 0.970 0.028 0.972
#> GSM617647 2 0.1843 0.970 0.028 0.972
#> GSM617648 2 0.1843 0.970 0.028 0.972
#> GSM617649 2 0.1843 0.970 0.028 0.972
#> GSM617650 1 0.1633 0.944 0.976 0.024
#> GSM617651 1 0.1633 0.944 0.976 0.024
#> GSM617653 1 0.1633 0.944 0.976 0.024
#> GSM617654 2 0.1843 0.970 0.028 0.972
#> GSM617583 1 0.1843 0.941 0.972 0.028
#> GSM617584 2 0.1843 0.970 0.028 0.972
#> GSM617585 2 0.1633 0.959 0.024 0.976
#> GSM617586 1 0.1843 0.940 0.972 0.028
#> GSM617587 1 0.1633 0.941 0.976 0.024
#> GSM617589 2 0.1184 0.967 0.016 0.984
#> GSM617591 2 0.1633 0.962 0.024 0.976
#> GSM617593 1 0.1633 0.944 0.976 0.024
#> GSM617594 2 0.1843 0.970 0.028 0.972
#> GSM617595 1 0.1633 0.944 0.976 0.024
#> GSM617596 1 0.1633 0.944 0.976 0.024
#> GSM617597 1 0.1843 0.940 0.972 0.028
#> GSM617598 1 0.1633 0.944 0.976 0.024
#> GSM617599 2 0.1843 0.970 0.028 0.972
#> GSM617600 1 0.1843 0.940 0.972 0.028
#> GSM617601 2 0.1633 0.962 0.024 0.976
#> GSM617602 1 0.1843 0.940 0.972 0.028
#> GSM617603 2 0.1414 0.961 0.020 0.980
#> GSM617604 1 0.1633 0.944 0.976 0.024
#> GSM617605 2 0.1633 0.959 0.024 0.976
#> GSM617606 2 0.1633 0.962 0.024 0.976
#> GSM617610 1 0.1633 0.944 0.976 0.024
#> GSM617611 1 0.1633 0.944 0.976 0.024
#> GSM617613 1 0.1843 0.940 0.972 0.028
#> GSM617614 1 0.1843 0.940 0.972 0.028
#> GSM617621 1 0.1414 0.944 0.980 0.020
#> GSM617629 1 0.2043 0.939 0.968 0.032
#> GSM617630 1 0.8144 0.699 0.748 0.252
#> GSM617631 1 0.1843 0.940 0.972 0.028
#> GSM617633 1 0.1184 0.945 0.984 0.016
#> GSM617642 1 0.1843 0.940 0.972 0.028
#> GSM617645 2 0.2043 0.970 0.032 0.968
#> GSM617646 1 0.1633 0.944 0.976 0.024
#> GSM617652 1 0.1184 0.943 0.984 0.016
#> GSM617655 1 0.1843 0.940 0.972 0.028
#> GSM617656 1 0.1843 0.940 0.972 0.028
#> GSM617657 1 0.9833 0.290 0.576 0.424
#> GSM617658 1 0.1843 0.940 0.972 0.028
#> GSM617659 1 0.0376 0.945 0.996 0.004
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM617581 1 0.5357 0.795 0.820 0.064 0.116
#> GSM617582 1 0.5551 0.632 0.760 0.016 0.224
#> GSM617588 2 0.4291 0.874 0.000 0.820 0.180
#> GSM617590 2 0.4346 0.873 0.000 0.816 0.184
#> GSM617592 2 0.4291 0.874 0.000 0.820 0.180
#> GSM617607 1 0.0424 0.916 0.992 0.000 0.008
#> GSM617608 1 0.0424 0.916 0.992 0.000 0.008
#> GSM617609 3 0.5269 0.904 0.200 0.016 0.784
#> GSM617612 1 0.0829 0.917 0.984 0.012 0.004
#> GSM617615 2 0.3340 0.893 0.000 0.880 0.120
#> GSM617616 1 0.2031 0.909 0.952 0.032 0.016
#> GSM617617 2 0.1620 0.892 0.012 0.964 0.024
#> GSM617618 1 0.1315 0.915 0.972 0.008 0.020
#> GSM617619 3 0.5678 0.728 0.032 0.192 0.776
#> GSM617620 2 0.4291 0.874 0.000 0.820 0.180
#> GSM617622 2 0.2496 0.895 0.004 0.928 0.068
#> GSM617623 1 0.4469 0.834 0.864 0.076 0.060
#> GSM617624 2 0.5315 0.705 0.012 0.772 0.216
#> GSM617625 3 0.5621 0.825 0.308 0.000 0.692
#> GSM617626 1 0.3500 0.837 0.880 0.116 0.004
#> GSM617627 2 0.1267 0.894 0.004 0.972 0.024
#> GSM617628 3 0.5678 0.814 0.316 0.000 0.684
#> GSM617632 1 0.0829 0.916 0.984 0.004 0.012
#> GSM617634 2 0.5295 0.770 0.036 0.808 0.156
#> GSM617635 1 0.2063 0.905 0.948 0.044 0.008
#> GSM617636 1 0.1765 0.907 0.956 0.004 0.040
#> GSM617637 1 0.2200 0.897 0.940 0.056 0.004
#> GSM617638 2 0.6161 0.590 0.016 0.696 0.288
#> GSM617639 1 0.1647 0.909 0.960 0.036 0.004
#> GSM617640 2 0.1267 0.895 0.004 0.972 0.024
#> GSM617641 2 0.4291 0.874 0.000 0.820 0.180
#> GSM617643 2 0.0829 0.896 0.004 0.984 0.012
#> GSM617644 2 0.2066 0.897 0.000 0.940 0.060
#> GSM617647 2 0.1620 0.892 0.012 0.964 0.024
#> GSM617648 2 0.0983 0.896 0.004 0.980 0.016
#> GSM617649 2 0.1129 0.895 0.004 0.976 0.020
#> GSM617650 1 0.0424 0.916 0.992 0.000 0.008
#> GSM617651 1 0.0237 0.917 0.996 0.000 0.004
#> GSM617653 1 0.0237 0.917 0.996 0.000 0.004
#> GSM617654 2 0.1751 0.892 0.012 0.960 0.028
#> GSM617583 3 0.5178 0.885 0.256 0.000 0.744
#> GSM617584 2 0.4465 0.876 0.004 0.820 0.176
#> GSM617585 3 0.5327 0.282 0.000 0.272 0.728
#> GSM617586 3 0.4750 0.905 0.216 0.000 0.784
#> GSM617587 3 0.5269 0.904 0.200 0.016 0.784
#> GSM617589 2 0.4346 0.873 0.000 0.816 0.184
#> GSM617591 2 0.3941 0.884 0.000 0.844 0.156
#> GSM617593 1 0.0237 0.917 0.996 0.000 0.004
#> GSM617594 2 0.2636 0.875 0.048 0.932 0.020
#> GSM617595 1 0.1878 0.905 0.952 0.044 0.004
#> GSM617596 1 0.1163 0.912 0.972 0.000 0.028
#> GSM617597 3 0.5016 0.895 0.240 0.000 0.760
#> GSM617598 1 0.0000 0.917 1.000 0.000 0.000
#> GSM617599 2 0.1636 0.892 0.016 0.964 0.020
#> GSM617600 3 0.4808 0.904 0.188 0.008 0.804
#> GSM617601 2 0.2261 0.898 0.000 0.932 0.068
#> GSM617602 3 0.4750 0.900 0.216 0.000 0.784
#> GSM617603 2 0.4291 0.875 0.000 0.820 0.180
#> GSM617604 1 0.4062 0.772 0.836 0.000 0.164
#> GSM617605 2 0.4346 0.873 0.000 0.816 0.184
#> GSM617606 2 0.5553 0.784 0.004 0.724 0.272
#> GSM617610 1 0.1878 0.905 0.952 0.044 0.004
#> GSM617611 1 0.0237 0.917 0.996 0.000 0.004
#> GSM617613 3 0.5036 0.897 0.172 0.020 0.808
#> GSM617614 3 0.5138 0.886 0.252 0.000 0.748
#> GSM617621 1 0.1031 0.914 0.976 0.000 0.024
#> GSM617629 3 0.5092 0.897 0.176 0.020 0.804
#> GSM617630 3 0.6309 0.811 0.100 0.128 0.772
#> GSM617631 3 0.4654 0.903 0.208 0.000 0.792
#> GSM617633 1 0.4834 0.667 0.792 0.004 0.204
#> GSM617642 3 0.4974 0.897 0.236 0.000 0.764
#> GSM617645 2 0.1399 0.894 0.004 0.968 0.028
#> GSM617646 1 0.2486 0.892 0.932 0.060 0.008
#> GSM617652 1 0.5363 0.493 0.724 0.000 0.276
#> GSM617655 3 0.4912 0.906 0.196 0.008 0.796
#> GSM617656 3 0.4702 0.906 0.212 0.000 0.788
#> GSM617657 3 0.4994 0.852 0.112 0.052 0.836
#> GSM617658 3 0.4750 0.900 0.216 0.000 0.784
#> GSM617659 1 0.0747 0.912 0.984 0.000 0.016
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM617581 1 0.6358 0.73988 0.684 0.060 0.036 0.220
#> GSM617582 1 0.7989 0.58466 0.556 0.048 0.164 0.232
#> GSM617588 4 0.4462 0.88238 0.004 0.256 0.004 0.736
#> GSM617590 4 0.4122 0.88079 0.000 0.236 0.004 0.760
#> GSM617592 4 0.4283 0.88191 0.004 0.256 0.000 0.740
#> GSM617607 1 0.2301 0.87495 0.932 0.012 0.028 0.028
#> GSM617608 1 0.1296 0.87786 0.964 0.004 0.028 0.004
#> GSM617609 3 0.1724 0.89072 0.032 0.020 0.948 0.000
#> GSM617612 1 0.1151 0.87747 0.968 0.008 0.024 0.000
#> GSM617615 2 0.4690 0.44106 0.000 0.712 0.012 0.276
#> GSM617616 1 0.5429 0.81087 0.748 0.048 0.020 0.184
#> GSM617617 2 0.1082 0.77977 0.004 0.972 0.004 0.020
#> GSM617618 1 0.5665 0.79866 0.732 0.044 0.028 0.196
#> GSM617619 3 0.5574 0.67263 0.008 0.204 0.724 0.064
#> GSM617620 4 0.4313 0.88212 0.004 0.260 0.000 0.736
#> GSM617622 2 0.4875 0.36409 0.004 0.692 0.008 0.296
#> GSM617623 1 0.5745 0.77582 0.728 0.048 0.028 0.196
#> GSM617624 2 0.3509 0.70399 0.004 0.860 0.024 0.112
#> GSM617625 3 0.3128 0.84672 0.128 0.004 0.864 0.004
#> GSM617626 1 0.4208 0.84793 0.840 0.048 0.016 0.096
#> GSM617627 2 0.1229 0.78219 0.004 0.968 0.008 0.020
#> GSM617628 3 0.3391 0.82905 0.148 0.004 0.844 0.004
#> GSM617632 1 0.4789 0.82442 0.776 0.024 0.016 0.184
#> GSM617634 2 0.5497 0.57849 0.020 0.720 0.032 0.228
#> GSM617635 1 0.2107 0.87719 0.940 0.020 0.016 0.024
#> GSM617636 1 0.6040 0.78818 0.712 0.028 0.064 0.196
#> GSM617637 1 0.1042 0.87748 0.972 0.020 0.008 0.000
#> GSM617638 2 0.4557 0.63482 0.004 0.784 0.032 0.180
#> GSM617639 1 0.1059 0.87917 0.972 0.012 0.016 0.000
#> GSM617640 2 0.1585 0.77574 0.004 0.952 0.004 0.040
#> GSM617641 4 0.4313 0.88215 0.004 0.260 0.000 0.736
#> GSM617643 2 0.1824 0.76754 0.004 0.936 0.000 0.060
#> GSM617644 2 0.4353 0.55769 0.000 0.756 0.012 0.232
#> GSM617647 2 0.0927 0.78205 0.008 0.976 0.000 0.016
#> GSM617648 2 0.2099 0.77761 0.004 0.936 0.020 0.040
#> GSM617649 2 0.1639 0.77728 0.004 0.952 0.008 0.036
#> GSM617650 1 0.1022 0.87711 0.968 0.000 0.032 0.000
#> GSM617651 1 0.0592 0.87935 0.984 0.000 0.016 0.000
#> GSM617653 1 0.1762 0.87496 0.944 0.004 0.004 0.048
#> GSM617654 2 0.1492 0.77147 0.004 0.956 0.004 0.036
#> GSM617583 3 0.2334 0.87552 0.088 0.000 0.908 0.004
#> GSM617584 4 0.4969 0.79399 0.008 0.312 0.004 0.676
#> GSM617585 4 0.6421 0.21340 0.000 0.076 0.368 0.556
#> GSM617586 3 0.1576 0.89023 0.048 0.004 0.948 0.000
#> GSM617587 3 0.1584 0.89012 0.036 0.012 0.952 0.000
#> GSM617589 4 0.4453 0.87441 0.000 0.244 0.012 0.744
#> GSM617591 2 0.7869 0.00551 0.004 0.408 0.364 0.224
#> GSM617593 1 0.0817 0.87831 0.976 0.000 0.024 0.000
#> GSM617594 2 0.2066 0.77971 0.024 0.940 0.008 0.028
#> GSM617595 1 0.1059 0.87830 0.972 0.012 0.016 0.000
#> GSM617596 1 0.4529 0.84223 0.820 0.016 0.052 0.112
#> GSM617597 3 0.1824 0.88767 0.060 0.004 0.936 0.000
#> GSM617598 1 0.0707 0.87895 0.980 0.000 0.020 0.000
#> GSM617599 2 0.1721 0.77897 0.008 0.952 0.012 0.028
#> GSM617600 3 0.1707 0.88791 0.024 0.004 0.952 0.020
#> GSM617601 2 0.3351 0.70039 0.000 0.844 0.008 0.148
#> GSM617602 3 0.4745 0.77270 0.036 0.000 0.756 0.208
#> GSM617603 4 0.4567 0.86286 0.000 0.244 0.016 0.740
#> GSM617604 1 0.5954 0.75228 0.712 0.008 0.168 0.112
#> GSM617605 4 0.4122 0.88079 0.000 0.236 0.004 0.760
#> GSM617606 2 0.7899 0.00432 0.008 0.448 0.216 0.328
#> GSM617610 1 0.1059 0.87816 0.972 0.016 0.012 0.000
#> GSM617611 1 0.1209 0.87610 0.964 0.004 0.032 0.000
#> GSM617613 3 0.1911 0.88406 0.020 0.004 0.944 0.032
#> GSM617614 3 0.1867 0.88487 0.072 0.000 0.928 0.000
#> GSM617621 1 0.4274 0.84652 0.832 0.028 0.024 0.116
#> GSM617629 3 0.5935 0.71522 0.032 0.036 0.696 0.236
#> GSM617630 3 0.6272 0.46837 0.004 0.316 0.612 0.068
#> GSM617631 3 0.1833 0.88498 0.024 0.000 0.944 0.032
#> GSM617633 1 0.5977 0.79455 0.732 0.024 0.104 0.140
#> GSM617642 3 0.1474 0.88971 0.052 0.000 0.948 0.000
#> GSM617645 2 0.1396 0.77909 0.004 0.960 0.004 0.032
#> GSM617646 1 0.2142 0.86685 0.928 0.056 0.016 0.000
#> GSM617652 1 0.5262 0.54961 0.672 0.020 0.304 0.004
#> GSM617655 3 0.1256 0.89115 0.028 0.008 0.964 0.000
#> GSM617656 3 0.1109 0.89130 0.028 0.004 0.968 0.000
#> GSM617657 3 0.1985 0.86962 0.004 0.016 0.940 0.040
#> GSM617658 3 0.4781 0.76930 0.036 0.000 0.752 0.212
#> GSM617659 1 0.1398 0.87488 0.956 0.004 0.040 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM617581 1 0.5973 0.24008 0.528 0.008 0.004 0.076 0.384
#> GSM617582 5 0.5075 0.43938 0.212 0.004 0.068 0.008 0.708
#> GSM617588 4 0.1285 0.89444 0.000 0.036 0.004 0.956 0.004
#> GSM617590 4 0.1469 0.89454 0.000 0.036 0.000 0.948 0.016
#> GSM617592 4 0.1469 0.89332 0.000 0.036 0.000 0.948 0.016
#> GSM617607 1 0.1626 0.75504 0.940 0.000 0.016 0.000 0.044
#> GSM617608 1 0.1216 0.75850 0.960 0.000 0.020 0.000 0.020
#> GSM617609 3 0.1644 0.82690 0.048 0.004 0.940 0.000 0.008
#> GSM617612 1 0.0324 0.76993 0.992 0.004 0.004 0.000 0.000
#> GSM617615 2 0.4946 0.55711 0.000 0.680 0.004 0.260 0.056
#> GSM617616 5 0.5018 0.18262 0.424 0.008 0.008 0.008 0.552
#> GSM617617 2 0.1270 0.84101 0.000 0.948 0.000 0.000 0.052
#> GSM617618 5 0.4908 0.27497 0.380 0.004 0.012 0.008 0.596
#> GSM617619 3 0.5923 0.46264 0.000 0.216 0.612 0.004 0.168
#> GSM617620 4 0.1469 0.89332 0.000 0.036 0.000 0.948 0.016
#> GSM617622 2 0.4840 0.58089 0.000 0.688 0.000 0.248 0.064
#> GSM617623 1 0.5570 0.31111 0.564 0.004 0.004 0.056 0.372
#> GSM617624 2 0.2462 0.82221 0.000 0.880 0.008 0.000 0.112
#> GSM617625 3 0.2674 0.79150 0.120 0.000 0.868 0.000 0.012
#> GSM617626 1 0.4954 0.37397 0.616 0.012 0.000 0.020 0.352
#> GSM617627 2 0.1704 0.83180 0.000 0.928 0.004 0.000 0.068
#> GSM617628 3 0.3039 0.75930 0.152 0.000 0.836 0.000 0.012
#> GSM617632 5 0.4735 0.00982 0.472 0.004 0.004 0.004 0.516
#> GSM617634 2 0.4967 0.40570 0.000 0.540 0.008 0.016 0.436
#> GSM617635 1 0.1588 0.75658 0.948 0.008 0.016 0.000 0.028
#> GSM617636 5 0.4854 0.19959 0.404 0.004 0.012 0.004 0.576
#> GSM617637 1 0.0992 0.76695 0.968 0.008 0.000 0.000 0.024
#> GSM617638 2 0.4507 0.66256 0.000 0.644 0.012 0.004 0.340
#> GSM617639 1 0.0451 0.77139 0.988 0.004 0.000 0.000 0.008
#> GSM617640 2 0.3360 0.79476 0.000 0.816 0.012 0.004 0.168
#> GSM617641 4 0.1469 0.89332 0.000 0.036 0.000 0.948 0.016
#> GSM617643 2 0.0566 0.83967 0.000 0.984 0.000 0.012 0.004
#> GSM617644 2 0.4872 0.67000 0.000 0.724 0.004 0.180 0.092
#> GSM617647 2 0.0566 0.83998 0.000 0.984 0.000 0.004 0.012
#> GSM617648 2 0.2331 0.82061 0.000 0.900 0.000 0.020 0.080
#> GSM617649 2 0.0807 0.83893 0.000 0.976 0.000 0.012 0.012
#> GSM617650 1 0.0609 0.76480 0.980 0.000 0.020 0.000 0.000
#> GSM617651 1 0.0510 0.77003 0.984 0.000 0.000 0.000 0.016
#> GSM617653 1 0.4040 0.54026 0.724 0.000 0.000 0.016 0.260
#> GSM617654 2 0.3381 0.78899 0.000 0.808 0.016 0.000 0.176
#> GSM617583 3 0.2361 0.80945 0.096 0.000 0.892 0.000 0.012
#> GSM617584 4 0.4112 0.76101 0.016 0.056 0.000 0.804 0.124
#> GSM617585 4 0.6988 0.33951 0.000 0.020 0.232 0.476 0.272
#> GSM617586 3 0.1502 0.82609 0.056 0.000 0.940 0.000 0.004
#> GSM617587 3 0.1717 0.82634 0.052 0.008 0.936 0.000 0.004
#> GSM617589 4 0.2075 0.87954 0.000 0.032 0.004 0.924 0.040
#> GSM617591 3 0.7423 0.18149 0.000 0.336 0.452 0.132 0.080
#> GSM617593 1 0.0290 0.77152 0.992 0.000 0.000 0.000 0.008
#> GSM617594 2 0.1299 0.83881 0.008 0.960 0.000 0.012 0.020
#> GSM617595 1 0.0451 0.77018 0.988 0.008 0.004 0.000 0.000
#> GSM617596 1 0.4675 0.38386 0.620 0.000 0.004 0.016 0.360
#> GSM617597 3 0.1697 0.82506 0.060 0.000 0.932 0.000 0.008
#> GSM617598 1 0.0609 0.76866 0.980 0.000 0.000 0.000 0.020
#> GSM617599 2 0.1981 0.82699 0.000 0.920 0.000 0.016 0.064
#> GSM617600 3 0.1830 0.79853 0.012 0.000 0.932 0.004 0.052
#> GSM617601 2 0.1670 0.83087 0.000 0.936 0.000 0.052 0.012
#> GSM617602 5 0.4804 0.11164 0.008 0.000 0.460 0.008 0.524
#> GSM617603 4 0.4017 0.80696 0.000 0.068 0.004 0.800 0.128
#> GSM617604 1 0.5976 0.29303 0.568 0.000 0.076 0.020 0.336
#> GSM617605 4 0.1469 0.89454 0.000 0.036 0.000 0.948 0.016
#> GSM617606 5 0.8381 -0.27406 0.000 0.276 0.152 0.236 0.336
#> GSM617610 1 0.0898 0.76749 0.972 0.008 0.000 0.000 0.020
#> GSM617611 1 0.0671 0.76599 0.980 0.004 0.016 0.000 0.000
#> GSM617613 3 0.2645 0.77888 0.012 0.000 0.884 0.008 0.096
#> GSM617614 3 0.2681 0.80043 0.108 0.000 0.876 0.004 0.012
#> GSM617621 1 0.4633 0.40779 0.632 0.000 0.004 0.016 0.348
#> GSM617629 5 0.4654 0.30914 0.008 0.004 0.312 0.012 0.664
#> GSM617630 3 0.6775 -0.01604 0.000 0.336 0.384 0.000 0.280
#> GSM617631 3 0.2295 0.77542 0.004 0.000 0.900 0.008 0.088
#> GSM617633 1 0.5263 0.22410 0.616 0.004 0.056 0.000 0.324
#> GSM617642 3 0.1557 0.82604 0.052 0.000 0.940 0.000 0.008
#> GSM617645 2 0.3461 0.79329 0.000 0.812 0.016 0.004 0.168
#> GSM617646 1 0.0740 0.77009 0.980 0.008 0.008 0.000 0.004
#> GSM617652 1 0.4365 0.33201 0.676 0.004 0.308 0.000 0.012
#> GSM617655 3 0.1082 0.82234 0.028 0.000 0.964 0.000 0.008
#> GSM617656 3 0.1116 0.82167 0.028 0.000 0.964 0.004 0.004
#> GSM617657 3 0.2920 0.74326 0.000 0.000 0.852 0.016 0.132
#> GSM617658 5 0.4792 0.14118 0.008 0.000 0.448 0.008 0.536
#> GSM617659 1 0.1557 0.73836 0.940 0.000 0.052 0.000 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM617581 1 0.7139 0.0488 0.388 0.004 0.000 0.128 0.124 0.356
#> GSM617582 6 0.4397 0.6230 0.124 0.008 0.032 0.004 0.056 0.776
#> GSM617588 4 0.2084 0.7986 0.000 0.016 0.000 0.916 0.044 0.024
#> GSM617590 4 0.2220 0.8039 0.000 0.020 0.000 0.908 0.052 0.020
#> GSM617592 4 0.0692 0.8025 0.000 0.020 0.000 0.976 0.004 0.000
#> GSM617607 1 0.2287 0.6980 0.904 0.000 0.036 0.000 0.012 0.048
#> GSM617608 1 0.1700 0.7099 0.928 0.000 0.048 0.000 0.000 0.024
#> GSM617609 3 0.1515 0.8277 0.020 0.000 0.944 0.000 0.028 0.008
#> GSM617612 1 0.1149 0.7257 0.960 0.000 0.024 0.000 0.008 0.008
#> GSM617615 2 0.5643 0.3875 0.000 0.660 0.004 0.104 0.164 0.068
#> GSM617616 6 0.4440 0.5206 0.292 0.016 0.004 0.000 0.020 0.668
#> GSM617617 2 0.1528 0.6532 0.000 0.936 0.000 0.000 0.048 0.016
#> GSM617618 6 0.4478 0.5557 0.260 0.012 0.004 0.004 0.028 0.692
#> GSM617619 3 0.6696 0.2357 0.000 0.128 0.508 0.000 0.252 0.112
#> GSM617620 4 0.0806 0.8037 0.000 0.020 0.000 0.972 0.008 0.000
#> GSM617622 2 0.5436 0.3855 0.000 0.648 0.000 0.216 0.084 0.052
#> GSM617623 1 0.6992 0.1168 0.420 0.004 0.000 0.108 0.124 0.344
#> GSM617624 2 0.4002 0.4058 0.000 0.704 0.000 0.000 0.260 0.036
#> GSM617625 3 0.2537 0.8067 0.068 0.000 0.888 0.000 0.028 0.016
#> GSM617626 1 0.5349 0.2853 0.560 0.012 0.000 0.000 0.088 0.340
#> GSM617627 2 0.3483 0.4723 0.000 0.748 0.000 0.000 0.236 0.016
#> GSM617628 3 0.3140 0.7649 0.116 0.000 0.840 0.000 0.028 0.016
#> GSM617632 6 0.4371 0.3926 0.344 0.000 0.000 0.000 0.036 0.620
#> GSM617634 6 0.5414 -0.1345 0.000 0.440 0.000 0.008 0.088 0.464
#> GSM617635 1 0.2240 0.6966 0.904 0.000 0.032 0.000 0.008 0.056
#> GSM617636 6 0.4087 0.5161 0.276 0.000 0.004 0.000 0.028 0.692
#> GSM617637 1 0.0837 0.7249 0.972 0.004 0.000 0.000 0.004 0.020
#> GSM617638 5 0.5261 0.0762 0.000 0.444 0.000 0.000 0.460 0.096
#> GSM617639 1 0.0291 0.7295 0.992 0.000 0.004 0.000 0.000 0.004
#> GSM617640 2 0.3915 0.0620 0.000 0.584 0.000 0.004 0.412 0.000
#> GSM617641 4 0.0806 0.8038 0.000 0.020 0.000 0.972 0.000 0.008
#> GSM617643 2 0.1649 0.6645 0.000 0.936 0.000 0.016 0.040 0.008
#> GSM617644 2 0.5250 0.4496 0.000 0.688 0.000 0.120 0.140 0.052
#> GSM617647 2 0.1219 0.6522 0.004 0.948 0.000 0.000 0.048 0.000
#> GSM617648 2 0.2865 0.6273 0.000 0.868 0.000 0.012 0.056 0.064
#> GSM617649 2 0.1409 0.6623 0.000 0.948 0.000 0.008 0.032 0.012
#> GSM617650 1 0.1007 0.7207 0.956 0.000 0.044 0.000 0.000 0.000
#> GSM617651 1 0.0717 0.7265 0.976 0.000 0.000 0.000 0.008 0.016
#> GSM617653 1 0.4989 0.4397 0.640 0.000 0.000 0.004 0.108 0.248
#> GSM617654 2 0.4103 -0.0675 0.000 0.544 0.000 0.004 0.448 0.004
#> GSM617583 3 0.1930 0.8241 0.036 0.000 0.924 0.000 0.028 0.012
#> GSM617584 4 0.4991 0.5668 0.016 0.020 0.000 0.720 0.120 0.124
#> GSM617585 4 0.7649 0.1353 0.000 0.012 0.112 0.320 0.312 0.244
#> GSM617586 3 0.0922 0.8308 0.024 0.000 0.968 0.000 0.004 0.004
#> GSM617587 3 0.2006 0.8186 0.024 0.008 0.924 0.000 0.036 0.008
#> GSM617589 4 0.3865 0.7368 0.000 0.016 0.000 0.792 0.124 0.068
#> GSM617591 3 0.7274 0.0868 0.000 0.204 0.488 0.040 0.204 0.064
#> GSM617593 1 0.0146 0.7292 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM617594 2 0.1801 0.6596 0.012 0.932 0.000 0.012 0.040 0.004
#> GSM617595 1 0.0551 0.7292 0.984 0.004 0.008 0.000 0.000 0.004
#> GSM617596 1 0.5455 0.1912 0.496 0.000 0.000 0.004 0.108 0.392
#> GSM617597 3 0.0713 0.8308 0.028 0.000 0.972 0.000 0.000 0.000
#> GSM617598 1 0.0692 0.7261 0.976 0.000 0.000 0.000 0.004 0.020
#> GSM617599 2 0.1991 0.6587 0.000 0.920 0.000 0.012 0.044 0.024
#> GSM617600 3 0.2740 0.7873 0.000 0.000 0.864 0.000 0.076 0.060
#> GSM617601 2 0.2790 0.6285 0.000 0.872 0.000 0.028 0.080 0.020
#> GSM617602 6 0.4592 0.4912 0.004 0.000 0.240 0.000 0.076 0.680
#> GSM617603 4 0.5818 0.5802 0.000 0.052 0.000 0.604 0.232 0.112
#> GSM617604 1 0.6596 0.0684 0.428 0.000 0.052 0.008 0.124 0.388
#> GSM617605 4 0.2156 0.8042 0.000 0.020 0.000 0.912 0.048 0.020
#> GSM617606 5 0.7321 0.3325 0.000 0.144 0.068 0.116 0.540 0.132
#> GSM617610 1 0.0837 0.7249 0.972 0.004 0.000 0.000 0.004 0.020
#> GSM617611 1 0.1219 0.7184 0.948 0.000 0.048 0.000 0.004 0.000
#> GSM617613 3 0.3930 0.7395 0.000 0.000 0.776 0.004 0.104 0.116
#> GSM617614 3 0.2478 0.8075 0.076 0.000 0.888 0.000 0.024 0.012
#> GSM617621 1 0.5601 0.2484 0.512 0.000 0.000 0.008 0.120 0.360
#> GSM617629 6 0.4340 0.5028 0.004 0.004 0.176 0.000 0.080 0.736
#> GSM617630 5 0.6048 0.4315 0.000 0.236 0.212 0.000 0.532 0.020
#> GSM617631 3 0.3552 0.7531 0.000 0.000 0.800 0.000 0.084 0.116
#> GSM617633 1 0.4850 -0.0813 0.512 0.004 0.020 0.000 0.016 0.448
#> GSM617642 3 0.0632 0.8312 0.024 0.000 0.976 0.000 0.000 0.000
#> GSM617645 2 0.3961 -0.0112 0.000 0.556 0.000 0.004 0.440 0.000
#> GSM617646 1 0.0912 0.7286 0.972 0.012 0.008 0.000 0.004 0.004
#> GSM617652 1 0.4602 0.3696 0.644 0.016 0.312 0.000 0.024 0.004
#> GSM617655 3 0.1148 0.8247 0.004 0.000 0.960 0.000 0.016 0.020
#> GSM617656 3 0.1257 0.8202 0.000 0.000 0.952 0.000 0.028 0.020
#> GSM617657 3 0.4763 0.6539 0.000 0.000 0.688 0.004 0.172 0.136
#> GSM617658 6 0.4676 0.5065 0.004 0.000 0.216 0.000 0.096 0.684
#> GSM617659 1 0.1610 0.6980 0.916 0.000 0.084 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) k
#> MAD:kmeans 77 0.07747 2
#> MAD:kmeans 77 0.00374 3
#> MAD:kmeans 73 0.01051 4
#> MAD:kmeans 57 0.01548 5
#> MAD:kmeans 53 0.15886 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 79 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.870 0.933 0.970 0.5029 0.496 0.496
#> 3 3 0.561 0.775 0.886 0.3356 0.744 0.527
#> 4 4 0.439 0.516 0.730 0.1157 0.922 0.770
#> 5 5 0.436 0.391 0.650 0.0648 0.884 0.606
#> 6 6 0.481 0.342 0.585 0.0400 0.934 0.706
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
#> GSM617581 2 0.7139 0.762 0.196 0.804
#> GSM617582 2 0.9795 0.322 0.416 0.584
#> GSM617588 2 0.0000 0.955 0.000 1.000
#> GSM617590 2 0.0000 0.955 0.000 1.000
#> GSM617592 2 0.0000 0.955 0.000 1.000
#> GSM617607 1 0.0000 0.979 1.000 0.000
#> GSM617608 1 0.0000 0.979 1.000 0.000
#> GSM617609 1 0.0938 0.972 0.988 0.012
#> GSM617612 1 0.0672 0.976 0.992 0.008
#> GSM617615 2 0.0000 0.955 0.000 1.000
#> GSM617616 1 0.3733 0.916 0.928 0.072
#> GSM617617 2 0.0000 0.955 0.000 1.000
#> GSM617618 1 0.5946 0.830 0.856 0.144
#> GSM617619 2 0.0672 0.952 0.008 0.992
#> GSM617620 2 0.0000 0.955 0.000 1.000
#> GSM617622 2 0.0000 0.955 0.000 1.000
#> GSM617623 2 0.5059 0.863 0.112 0.888
#> GSM617624 2 0.0376 0.953 0.004 0.996
#> GSM617625 1 0.0000 0.979 1.000 0.000
#> GSM617626 2 0.4815 0.870 0.104 0.896
#> GSM617627 2 0.0000 0.955 0.000 1.000
#> GSM617628 1 0.0000 0.979 1.000 0.000
#> GSM617632 1 0.0376 0.978 0.996 0.004
#> GSM617634 2 0.0672 0.952 0.008 0.992
#> GSM617635 1 0.0000 0.979 1.000 0.000
#> GSM617636 1 0.0000 0.979 1.000 0.000
#> GSM617637 1 0.0672 0.976 0.992 0.008
#> GSM617638 2 0.1843 0.938 0.028 0.972
#> GSM617639 1 0.0376 0.978 0.996 0.004
#> GSM617640 2 0.0000 0.955 0.000 1.000
#> GSM617641 2 0.0000 0.955 0.000 1.000
#> GSM617643 2 0.0000 0.955 0.000 1.000
#> GSM617644 2 0.0000 0.955 0.000 1.000
#> GSM617647 2 0.0000 0.955 0.000 1.000
#> GSM617648 2 0.0000 0.955 0.000 1.000
#> GSM617649 2 0.0000 0.955 0.000 1.000
#> GSM617650 1 0.0000 0.979 1.000 0.000
#> GSM617651 1 0.0000 0.979 1.000 0.000
#> GSM617653 1 0.0376 0.978 0.996 0.004
#> GSM617654 2 0.0000 0.955 0.000 1.000
#> GSM617583 1 0.0000 0.979 1.000 0.000
#> GSM617584 2 0.0000 0.955 0.000 1.000
#> GSM617585 2 0.0376 0.953 0.004 0.996
#> GSM617586 1 0.0000 0.979 1.000 0.000
#> GSM617587 1 0.7139 0.753 0.804 0.196
#> GSM617589 2 0.0000 0.955 0.000 1.000
#> GSM617591 2 0.0000 0.955 0.000 1.000
#> GSM617593 1 0.0000 0.979 1.000 0.000
#> GSM617594 2 0.1843 0.937 0.028 0.972
#> GSM617595 1 0.0672 0.976 0.992 0.008
#> GSM617596 1 0.0376 0.978 0.996 0.004
#> GSM617597 1 0.0000 0.979 1.000 0.000
#> GSM617598 1 0.0000 0.979 1.000 0.000
#> GSM617599 2 0.0000 0.955 0.000 1.000
#> GSM617600 1 0.0000 0.979 1.000 0.000
#> GSM617601 2 0.0000 0.955 0.000 1.000
#> GSM617602 1 0.0000 0.979 1.000 0.000
#> GSM617603 2 0.0000 0.955 0.000 1.000
#> GSM617604 1 0.0000 0.979 1.000 0.000
#> GSM617605 2 0.0000 0.955 0.000 1.000
#> GSM617606 2 0.0376 0.953 0.004 0.996
#> GSM617610 1 0.1843 0.961 0.972 0.028
#> GSM617611 1 0.0000 0.979 1.000 0.000
#> GSM617613 1 0.1184 0.969 0.984 0.016
#> GSM617614 1 0.0000 0.979 1.000 0.000
#> GSM617621 1 0.0376 0.978 0.996 0.004
#> GSM617629 1 0.8327 0.635 0.736 0.264
#> GSM617630 2 0.9522 0.437 0.372 0.628
#> GSM617631 1 0.0000 0.979 1.000 0.000
#> GSM617633 1 0.0000 0.979 1.000 0.000
#> GSM617642 1 0.0000 0.979 1.000 0.000
#> GSM617645 2 0.0000 0.955 0.000 1.000
#> GSM617646 1 0.1843 0.961 0.972 0.028
#> GSM617652 1 0.0000 0.979 1.000 0.000
#> GSM617655 1 0.0376 0.978 0.996 0.004
#> GSM617656 1 0.0000 0.979 1.000 0.000
#> GSM617657 2 0.8661 0.619 0.288 0.712
#> GSM617658 1 0.0000 0.979 1.000 0.000
#> GSM617659 1 0.0000 0.979 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM617581 1 0.8926 0.4738 0.568 0.240 0.192
#> GSM617582 3 0.9434 -0.0546 0.412 0.176 0.412
#> GSM617588 2 0.0000 0.8986 0.000 1.000 0.000
#> GSM617590 2 0.0000 0.8986 0.000 1.000 0.000
#> GSM617592 2 0.0000 0.8986 0.000 1.000 0.000
#> GSM617607 1 0.4178 0.7730 0.828 0.000 0.172
#> GSM617608 1 0.4702 0.7324 0.788 0.000 0.212
#> GSM617609 3 0.1031 0.8719 0.024 0.000 0.976
#> GSM617612 1 0.2496 0.8397 0.928 0.004 0.068
#> GSM617615 2 0.0747 0.8951 0.000 0.984 0.016
#> GSM617616 1 0.5815 0.7630 0.800 0.096 0.104
#> GSM617617 2 0.1163 0.8919 0.028 0.972 0.000
#> GSM617618 1 0.4930 0.8003 0.836 0.044 0.120
#> GSM617619 3 0.5443 0.6090 0.004 0.260 0.736
#> GSM617620 2 0.0000 0.8986 0.000 1.000 0.000
#> GSM617622 2 0.0237 0.8982 0.000 0.996 0.004
#> GSM617623 1 0.5987 0.6867 0.756 0.208 0.036
#> GSM617624 2 0.4963 0.7419 0.008 0.792 0.200
#> GSM617625 3 0.3879 0.8111 0.152 0.000 0.848
#> GSM617626 1 0.4233 0.7506 0.836 0.160 0.004
#> GSM617627 2 0.2096 0.8788 0.004 0.944 0.052
#> GSM617628 3 0.3482 0.8275 0.128 0.000 0.872
#> GSM617632 1 0.1411 0.8474 0.964 0.000 0.036
#> GSM617634 2 0.8016 0.5827 0.188 0.656 0.156
#> GSM617635 1 0.2200 0.8433 0.940 0.004 0.056
#> GSM617636 1 0.5098 0.7063 0.752 0.000 0.248
#> GSM617637 1 0.0000 0.8457 1.000 0.000 0.000
#> GSM617638 2 0.7578 0.0991 0.040 0.500 0.460
#> GSM617639 1 0.0237 0.8464 0.996 0.000 0.004
#> GSM617640 2 0.0237 0.8983 0.004 0.996 0.000
#> GSM617641 2 0.0000 0.8986 0.000 1.000 0.000
#> GSM617643 2 0.0237 0.8983 0.004 0.996 0.000
#> GSM617644 2 0.0237 0.8983 0.004 0.996 0.000
#> GSM617647 2 0.3116 0.8433 0.108 0.892 0.000
#> GSM617648 2 0.0237 0.8983 0.004 0.996 0.000
#> GSM617649 2 0.1989 0.8815 0.004 0.948 0.048
#> GSM617650 1 0.1753 0.8458 0.952 0.000 0.048
#> GSM617651 1 0.0237 0.8460 0.996 0.000 0.004
#> GSM617653 1 0.0424 0.8459 0.992 0.000 0.008
#> GSM617654 2 0.2711 0.8591 0.088 0.912 0.000
#> GSM617583 3 0.3116 0.8444 0.108 0.000 0.892
#> GSM617584 2 0.3272 0.8403 0.104 0.892 0.004
#> GSM617585 2 0.6307 0.0928 0.000 0.512 0.488
#> GSM617586 3 0.0747 0.8725 0.016 0.000 0.984
#> GSM617587 3 0.6157 0.7485 0.092 0.128 0.780
#> GSM617589 2 0.0000 0.8986 0.000 1.000 0.000
#> GSM617591 2 0.5098 0.6749 0.000 0.752 0.248
#> GSM617593 1 0.0237 0.8460 0.996 0.000 0.004
#> GSM617594 2 0.3921 0.8323 0.112 0.872 0.016
#> GSM617595 1 0.0000 0.8457 1.000 0.000 0.000
#> GSM617596 1 0.3192 0.8233 0.888 0.000 0.112
#> GSM617597 3 0.3686 0.8180 0.140 0.000 0.860
#> GSM617598 1 0.0424 0.8459 0.992 0.000 0.008
#> GSM617599 2 0.3573 0.8322 0.120 0.876 0.004
#> GSM617600 3 0.0237 0.8731 0.004 0.000 0.996
#> GSM617601 2 0.0237 0.8981 0.000 0.996 0.004
#> GSM617602 3 0.0237 0.8736 0.004 0.000 0.996
#> GSM617603 2 0.0000 0.8986 0.000 1.000 0.000
#> GSM617604 1 0.6168 0.3956 0.588 0.000 0.412
#> GSM617605 2 0.0000 0.8986 0.000 1.000 0.000
#> GSM617606 2 0.5848 0.6294 0.012 0.720 0.268
#> GSM617610 1 0.0000 0.8457 1.000 0.000 0.000
#> GSM617611 1 0.1289 0.8473 0.968 0.000 0.032
#> GSM617613 3 0.0000 0.8729 0.000 0.000 1.000
#> GSM617614 3 0.3941 0.7993 0.156 0.000 0.844
#> GSM617621 1 0.1643 0.8455 0.956 0.000 0.044
#> GSM617629 3 0.3461 0.8439 0.076 0.024 0.900
#> GSM617630 3 0.6049 0.7044 0.040 0.204 0.756
#> GSM617631 3 0.0000 0.8729 0.000 0.000 1.000
#> GSM617633 1 0.6291 0.1983 0.532 0.000 0.468
#> GSM617642 3 0.2711 0.8513 0.088 0.000 0.912
#> GSM617645 2 0.0237 0.8983 0.004 0.996 0.000
#> GSM617646 1 0.2446 0.8438 0.936 0.012 0.052
#> GSM617652 1 0.6302 0.1260 0.520 0.000 0.480
#> GSM617655 3 0.0000 0.8729 0.000 0.000 1.000
#> GSM617656 3 0.0237 0.8731 0.004 0.000 0.996
#> GSM617657 3 0.0237 0.8725 0.000 0.004 0.996
#> GSM617658 3 0.2448 0.8541 0.076 0.000 0.924
#> GSM617659 1 0.4605 0.7379 0.796 0.000 0.204
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM617581 4 0.9439 0.2268 0.292 0.292 0.096 0.320
#> GSM617582 4 0.9093 0.4484 0.156 0.200 0.164 0.480
#> GSM617588 2 0.1211 0.7162 0.000 0.960 0.000 0.040
#> GSM617590 2 0.1584 0.7121 0.000 0.952 0.012 0.036
#> GSM617592 2 0.1474 0.7136 0.000 0.948 0.000 0.052
#> GSM617607 1 0.6578 0.4770 0.620 0.000 0.136 0.244
#> GSM617608 1 0.6011 0.5084 0.688 0.000 0.180 0.132
#> GSM617609 3 0.3215 0.7380 0.032 0.000 0.876 0.092
#> GSM617612 1 0.2924 0.6834 0.900 0.004 0.060 0.036
#> GSM617615 2 0.5506 0.6395 0.004 0.744 0.116 0.136
#> GSM617616 4 0.7840 0.0536 0.404 0.056 0.080 0.460
#> GSM617617 2 0.6042 0.5381 0.048 0.560 0.000 0.392
#> GSM617618 4 0.7434 0.0753 0.400 0.052 0.056 0.492
#> GSM617619 3 0.6946 0.2949 0.000 0.200 0.588 0.212
#> GSM617620 2 0.1118 0.7161 0.000 0.964 0.000 0.036
#> GSM617622 2 0.3727 0.7092 0.004 0.824 0.008 0.164
#> GSM617623 1 0.7962 0.0215 0.476 0.248 0.012 0.264
#> GSM617624 4 0.7463 -0.1726 0.008 0.400 0.136 0.456
#> GSM617625 3 0.4713 0.6809 0.172 0.000 0.776 0.052
#> GSM617626 1 0.7439 0.1207 0.516 0.176 0.004 0.304
#> GSM617627 2 0.6483 0.5445 0.000 0.584 0.092 0.324
#> GSM617628 3 0.4893 0.6739 0.168 0.000 0.768 0.064
#> GSM617632 1 0.5713 0.4230 0.620 0.000 0.040 0.340
#> GSM617634 4 0.7493 0.2651 0.056 0.240 0.100 0.604
#> GSM617635 1 0.5363 0.5770 0.728 0.004 0.056 0.212
#> GSM617636 4 0.7120 0.0469 0.368 0.000 0.136 0.496
#> GSM617637 1 0.2053 0.6823 0.924 0.000 0.004 0.072
#> GSM617638 4 0.7593 0.2679 0.012 0.196 0.252 0.540
#> GSM617639 1 0.1792 0.6871 0.932 0.000 0.000 0.068
#> GSM617640 2 0.4103 0.6830 0.000 0.744 0.000 0.256
#> GSM617641 2 0.0921 0.7143 0.000 0.972 0.000 0.028
#> GSM617643 2 0.4040 0.6912 0.000 0.752 0.000 0.248
#> GSM617644 2 0.3123 0.7159 0.000 0.844 0.000 0.156
#> GSM617647 2 0.6897 0.5108 0.144 0.572 0.000 0.284
#> GSM617648 2 0.4792 0.6450 0.008 0.680 0.000 0.312
#> GSM617649 2 0.7502 0.5439 0.028 0.552 0.116 0.304
#> GSM617650 1 0.2996 0.6808 0.892 0.000 0.044 0.064
#> GSM617651 1 0.1356 0.6899 0.960 0.000 0.008 0.032
#> GSM617653 1 0.3171 0.6701 0.876 0.004 0.016 0.104
#> GSM617654 2 0.6495 0.4421 0.072 0.492 0.000 0.436
#> GSM617583 3 0.4017 0.7236 0.128 0.000 0.828 0.044
#> GSM617584 2 0.5815 0.5496 0.112 0.716 0.004 0.168
#> GSM617585 2 0.7529 0.0116 0.000 0.472 0.324 0.204
#> GSM617586 3 0.1833 0.7549 0.024 0.000 0.944 0.032
#> GSM617587 3 0.7451 0.4905 0.096 0.092 0.640 0.172
#> GSM617589 2 0.2010 0.7094 0.012 0.940 0.008 0.040
#> GSM617591 2 0.6646 0.3692 0.000 0.584 0.304 0.112
#> GSM617593 1 0.1042 0.6895 0.972 0.000 0.008 0.020
#> GSM617594 2 0.8306 0.4193 0.140 0.512 0.064 0.284
#> GSM617595 1 0.1109 0.6913 0.968 0.000 0.004 0.028
#> GSM617596 1 0.5664 0.5613 0.696 0.000 0.076 0.228
#> GSM617597 3 0.4959 0.6387 0.196 0.000 0.752 0.052
#> GSM617598 1 0.0779 0.6903 0.980 0.000 0.004 0.016
#> GSM617599 2 0.7579 0.4203 0.120 0.540 0.028 0.312
#> GSM617600 3 0.1661 0.7526 0.004 0.000 0.944 0.052
#> GSM617601 2 0.2408 0.7187 0.000 0.896 0.000 0.104
#> GSM617602 3 0.4883 0.5500 0.016 0.000 0.696 0.288
#> GSM617603 2 0.2469 0.7143 0.000 0.892 0.000 0.108
#> GSM617604 1 0.8299 0.0638 0.440 0.024 0.308 0.228
#> GSM617605 2 0.2048 0.7135 0.000 0.928 0.008 0.064
#> GSM617606 2 0.8111 0.2390 0.036 0.524 0.216 0.224
#> GSM617610 1 0.0469 0.6881 0.988 0.000 0.000 0.012
#> GSM617611 1 0.2131 0.6904 0.932 0.000 0.036 0.032
#> GSM617613 3 0.1661 0.7504 0.000 0.004 0.944 0.052
#> GSM617614 3 0.5522 0.5998 0.204 0.000 0.716 0.080
#> GSM617621 1 0.5401 0.5426 0.700 0.008 0.032 0.260
#> GSM617629 4 0.6608 -0.1242 0.020 0.040 0.452 0.488
#> GSM617630 3 0.8352 0.1183 0.048 0.168 0.484 0.300
#> GSM617631 3 0.2011 0.7423 0.000 0.000 0.920 0.080
#> GSM617633 1 0.8022 -0.1347 0.384 0.004 0.280 0.332
#> GSM617642 3 0.3239 0.7492 0.068 0.000 0.880 0.052
#> GSM617645 2 0.5227 0.6473 0.012 0.668 0.008 0.312
#> GSM617646 1 0.5238 0.5935 0.752 0.016 0.040 0.192
#> GSM617652 1 0.7727 0.0918 0.452 0.008 0.364 0.176
#> GSM617655 3 0.0859 0.7565 0.008 0.004 0.980 0.008
#> GSM617656 3 0.0524 0.7561 0.008 0.000 0.988 0.004
#> GSM617657 3 0.2882 0.7328 0.000 0.024 0.892 0.084
#> GSM617658 3 0.5941 0.5107 0.072 0.000 0.652 0.276
#> GSM617659 1 0.5343 0.5048 0.708 0.000 0.240 0.052
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM617581 5 0.860 0.160368 0.176 0.100 0.040 0.272 0.412
#> GSM617582 5 0.809 0.251941 0.068 0.160 0.068 0.176 0.528
#> GSM617588 4 0.163 0.558685 0.000 0.044 0.000 0.940 0.016
#> GSM617590 4 0.269 0.554399 0.000 0.044 0.028 0.900 0.028
#> GSM617592 4 0.191 0.557400 0.000 0.028 0.000 0.928 0.044
#> GSM617607 1 0.735 0.403376 0.540 0.132 0.124 0.000 0.204
#> GSM617608 1 0.603 0.532423 0.676 0.064 0.140 0.000 0.120
#> GSM617609 3 0.443 0.682368 0.020 0.104 0.796 0.004 0.076
#> GSM617612 1 0.412 0.653624 0.832 0.068 0.048 0.012 0.040
#> GSM617615 4 0.606 0.381259 0.012 0.204 0.068 0.668 0.048
#> GSM617616 5 0.837 0.230007 0.316 0.180 0.052 0.052 0.400
#> GSM617617 2 0.687 0.333527 0.024 0.476 0.000 0.336 0.164
#> GSM617618 5 0.784 0.347607 0.244 0.156 0.044 0.048 0.508
#> GSM617619 3 0.774 0.249467 0.004 0.240 0.492 0.116 0.148
#> GSM617620 4 0.207 0.554225 0.000 0.092 0.000 0.904 0.004
#> GSM617622 4 0.529 0.428762 0.012 0.204 0.004 0.700 0.080
#> GSM617623 5 0.829 0.077350 0.336 0.100 0.008 0.220 0.336
#> GSM617624 2 0.807 0.358122 0.008 0.452 0.108 0.200 0.232
#> GSM617625 3 0.571 0.549904 0.240 0.040 0.664 0.004 0.052
#> GSM617626 1 0.781 0.092995 0.460 0.132 0.000 0.148 0.260
#> GSM617627 2 0.715 0.219457 0.004 0.436 0.064 0.400 0.096
#> GSM617628 3 0.556 0.616890 0.176 0.056 0.708 0.004 0.056
#> GSM617632 5 0.677 -0.000866 0.384 0.108 0.024 0.008 0.476
#> GSM617634 5 0.842 -0.063137 0.048 0.316 0.068 0.164 0.404
#> GSM617635 1 0.693 0.451156 0.580 0.212 0.060 0.004 0.144
#> GSM617636 5 0.648 0.338218 0.208 0.072 0.100 0.000 0.620
#> GSM617637 1 0.370 0.650120 0.820 0.088 0.000 0.000 0.092
#> GSM617638 2 0.814 0.281878 0.016 0.452 0.132 0.128 0.272
#> GSM617639 1 0.370 0.657449 0.832 0.084 0.008 0.000 0.076
#> GSM617640 4 0.517 -0.098563 0.004 0.444 0.000 0.520 0.032
#> GSM617641 4 0.149 0.558786 0.000 0.024 0.000 0.948 0.028
#> GSM617643 4 0.527 0.173308 0.008 0.364 0.000 0.588 0.040
#> GSM617644 4 0.447 0.435529 0.000 0.240 0.000 0.716 0.044
#> GSM617647 2 0.726 0.329146 0.128 0.476 0.008 0.340 0.048
#> GSM617648 4 0.693 -0.099193 0.036 0.392 0.000 0.440 0.132
#> GSM617649 2 0.729 0.249122 0.016 0.476 0.072 0.360 0.076
#> GSM617650 1 0.420 0.638910 0.812 0.032 0.084 0.000 0.072
#> GSM617651 1 0.228 0.671027 0.908 0.032 0.000 0.000 0.060
#> GSM617653 1 0.537 0.547115 0.688 0.068 0.004 0.016 0.224
#> GSM617654 2 0.692 0.323753 0.080 0.496 0.000 0.348 0.076
#> GSM617583 3 0.504 0.670881 0.144 0.036 0.760 0.016 0.044
#> GSM617584 4 0.684 0.235690 0.080 0.160 0.000 0.596 0.164
#> GSM617585 4 0.767 0.053355 0.000 0.096 0.240 0.476 0.188
#> GSM617586 3 0.259 0.726645 0.020 0.032 0.904 0.000 0.044
#> GSM617587 3 0.755 0.448233 0.056 0.140 0.596 0.116 0.092
#> GSM617589 4 0.270 0.552549 0.012 0.052 0.004 0.900 0.032
#> GSM617591 4 0.752 0.097328 0.008 0.156 0.256 0.508 0.072
#> GSM617593 1 0.216 0.670186 0.916 0.012 0.008 0.000 0.064
#> GSM617594 2 0.834 0.308108 0.140 0.448 0.044 0.280 0.088
#> GSM617595 1 0.223 0.671300 0.920 0.040 0.012 0.000 0.028
#> GSM617596 1 0.695 0.232166 0.488 0.084 0.052 0.008 0.368
#> GSM617597 3 0.552 0.557242 0.176 0.028 0.696 0.000 0.100
#> GSM617598 1 0.230 0.665212 0.904 0.024 0.000 0.000 0.072
#> GSM617599 4 0.830 -0.235179 0.124 0.360 0.016 0.360 0.140
#> GSM617600 3 0.267 0.713375 0.000 0.020 0.876 0.000 0.104
#> GSM617601 4 0.444 0.409387 0.000 0.240 0.008 0.724 0.028
#> GSM617602 5 0.564 -0.129027 0.012 0.048 0.464 0.000 0.476
#> GSM617603 4 0.353 0.532379 0.000 0.116 0.000 0.828 0.056
#> GSM617604 5 0.815 0.232208 0.272 0.072 0.228 0.016 0.412
#> GSM617605 4 0.247 0.558398 0.000 0.036 0.012 0.908 0.044
#> GSM617606 4 0.832 0.005671 0.036 0.244 0.096 0.464 0.160
#> GSM617610 1 0.198 0.671319 0.928 0.024 0.004 0.000 0.044
#> GSM617611 1 0.261 0.666750 0.900 0.020 0.060 0.000 0.020
#> GSM617613 3 0.313 0.694224 0.000 0.032 0.848 0.000 0.120
#> GSM617614 3 0.585 0.585818 0.164 0.044 0.680 0.000 0.112
#> GSM617621 1 0.648 0.213097 0.488 0.088 0.024 0.004 0.396
#> GSM617629 5 0.709 0.257765 0.012 0.124 0.300 0.040 0.524
#> GSM617630 2 0.882 0.080492 0.048 0.376 0.300 0.124 0.152
#> GSM617631 3 0.297 0.691593 0.000 0.016 0.848 0.000 0.136
#> GSM617633 5 0.837 0.272602 0.272 0.180 0.192 0.000 0.356
#> GSM617642 3 0.389 0.701861 0.076 0.020 0.828 0.000 0.076
#> GSM617645 2 0.609 0.303873 0.036 0.536 0.008 0.384 0.036
#> GSM617646 1 0.680 0.470253 0.608 0.224 0.044 0.024 0.100
#> GSM617652 1 0.841 -0.007137 0.360 0.192 0.308 0.008 0.132
#> GSM617655 3 0.118 0.727882 0.000 0.016 0.964 0.004 0.016
#> GSM617656 3 0.051 0.725853 0.000 0.000 0.984 0.000 0.016
#> GSM617657 3 0.479 0.618748 0.000 0.056 0.748 0.024 0.172
#> GSM617658 5 0.619 -0.096810 0.072 0.024 0.440 0.000 0.464
#> GSM617659 1 0.591 0.516758 0.672 0.044 0.176 0.000 0.108
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM617581 6 0.792 0.3294 0.096 0.048 0.032 0.244 0.108 0.472
#> GSM617582 5 0.850 0.2432 0.072 0.096 0.076 0.116 0.464 0.176
#> GSM617588 4 0.300 0.5435 0.000 0.104 0.000 0.852 0.028 0.016
#> GSM617590 4 0.249 0.5646 0.000 0.048 0.008 0.900 0.020 0.024
#> GSM617592 4 0.233 0.5436 0.000 0.056 0.000 0.892 0.000 0.052
#> GSM617607 1 0.749 0.2777 0.500 0.072 0.060 0.004 0.152 0.212
#> GSM617608 1 0.724 0.3165 0.528 0.036 0.136 0.000 0.140 0.160
#> GSM617609 3 0.566 0.5579 0.032 0.088 0.696 0.000 0.084 0.100
#> GSM617612 1 0.513 0.5156 0.740 0.044 0.064 0.004 0.032 0.116
#> GSM617615 4 0.719 0.2744 0.012 0.240 0.068 0.536 0.056 0.088
#> GSM617616 5 0.837 0.2013 0.232 0.152 0.028 0.044 0.408 0.136
#> GSM617617 2 0.725 0.3631 0.032 0.492 0.000 0.248 0.128 0.100
#> GSM617618 5 0.722 0.3190 0.192 0.072 0.032 0.036 0.564 0.104
#> GSM617619 3 0.831 0.0366 0.000 0.224 0.376 0.144 0.176 0.080
#> GSM617620 4 0.280 0.5484 0.000 0.108 0.000 0.860 0.012 0.020
#> GSM617622 4 0.624 0.3752 0.008 0.208 0.012 0.612 0.060 0.100
#> GSM617623 6 0.765 0.4056 0.184 0.068 0.004 0.216 0.060 0.468
#> GSM617624 2 0.846 0.2819 0.008 0.396 0.104 0.172 0.208 0.112
#> GSM617625 3 0.624 0.5132 0.180 0.032 0.624 0.000 0.060 0.104
#> GSM617626 1 0.872 -0.2394 0.320 0.128 0.000 0.180 0.176 0.196
#> GSM617627 2 0.814 0.3266 0.008 0.416 0.076 0.260 0.124 0.116
#> GSM617628 3 0.672 0.4648 0.188 0.028 0.588 0.008 0.116 0.072
#> GSM617632 1 0.771 -0.2245 0.360 0.032 0.040 0.016 0.300 0.252
#> GSM617634 5 0.809 0.0465 0.044 0.276 0.052 0.108 0.440 0.080
#> GSM617635 1 0.662 0.4274 0.596 0.096 0.036 0.000 0.172 0.100
#> GSM617636 5 0.704 0.0689 0.156 0.028 0.044 0.008 0.504 0.260
#> GSM617637 1 0.468 0.5193 0.756 0.092 0.000 0.004 0.072 0.076
#> GSM617638 2 0.863 0.1995 0.016 0.384 0.140 0.100 0.224 0.136
#> GSM617639 1 0.420 0.5295 0.776 0.076 0.004 0.000 0.020 0.124
#> GSM617640 2 0.564 0.2145 0.008 0.520 0.000 0.388 0.052 0.032
#> GSM617641 4 0.251 0.5580 0.000 0.060 0.000 0.888 0.008 0.044
#> GSM617643 2 0.535 -0.0673 0.000 0.480 0.000 0.444 0.048 0.028
#> GSM617644 4 0.573 0.3073 0.000 0.328 0.000 0.544 0.100 0.028
#> GSM617647 2 0.727 0.3723 0.080 0.508 0.008 0.260 0.044 0.100
#> GSM617648 4 0.705 -0.0897 0.012 0.372 0.004 0.392 0.168 0.052
#> GSM617649 2 0.765 0.3182 0.024 0.512 0.068 0.224 0.096 0.076
#> GSM617650 1 0.386 0.5501 0.816 0.004 0.044 0.000 0.064 0.072
#> GSM617651 1 0.247 0.5580 0.880 0.000 0.000 0.000 0.040 0.080
#> GSM617653 1 0.595 0.1198 0.556 0.012 0.004 0.032 0.072 0.324
#> GSM617654 2 0.755 0.4052 0.052 0.504 0.004 0.196 0.132 0.112
#> GSM617583 3 0.601 0.5563 0.116 0.028 0.680 0.016 0.060 0.100
#> GSM617584 4 0.677 0.1460 0.064 0.092 0.008 0.536 0.024 0.276
#> GSM617585 4 0.781 0.1185 0.000 0.084 0.200 0.448 0.196 0.072
#> GSM617586 3 0.348 0.6139 0.024 0.024 0.844 0.000 0.028 0.080
#> GSM617587 3 0.809 0.3427 0.124 0.100 0.512 0.048 0.076 0.140
#> GSM617589 4 0.372 0.5491 0.008 0.072 0.000 0.828 0.040 0.052
#> GSM617591 4 0.804 0.0747 0.012 0.164 0.256 0.420 0.052 0.096
#> GSM617593 1 0.262 0.5567 0.876 0.000 0.008 0.000 0.028 0.088
#> GSM617594 2 0.850 0.3141 0.120 0.432 0.032 0.204 0.084 0.128
#> GSM617595 1 0.298 0.5689 0.876 0.024 0.012 0.000 0.048 0.040
#> GSM617596 6 0.775 0.2605 0.336 0.028 0.052 0.020 0.200 0.364
#> GSM617597 3 0.647 0.4271 0.192 0.032 0.592 0.000 0.052 0.132
#> GSM617598 1 0.302 0.5320 0.840 0.012 0.000 0.000 0.020 0.128
#> GSM617599 2 0.875 0.2640 0.152 0.344 0.008 0.224 0.156 0.116
#> GSM617600 3 0.427 0.5793 0.004 0.028 0.772 0.000 0.132 0.064
#> GSM617601 4 0.502 0.4143 0.000 0.244 0.004 0.668 0.032 0.052
#> GSM617602 5 0.653 -0.0469 0.016 0.012 0.380 0.008 0.436 0.148
#> GSM617603 4 0.486 0.4977 0.000 0.168 0.008 0.720 0.076 0.028
#> GSM617604 6 0.861 0.2144 0.196 0.044 0.188 0.044 0.132 0.396
#> GSM617605 4 0.234 0.5585 0.000 0.028 0.004 0.908 0.028 0.032
#> GSM617606 4 0.887 0.0594 0.048 0.220 0.084 0.380 0.156 0.112
#> GSM617610 1 0.298 0.5510 0.868 0.028 0.000 0.004 0.028 0.072
#> GSM617611 1 0.311 0.5664 0.868 0.012 0.056 0.000 0.028 0.036
#> GSM617613 3 0.441 0.5647 0.004 0.012 0.752 0.016 0.176 0.040
#> GSM617614 3 0.709 0.3759 0.172 0.020 0.520 0.000 0.108 0.180
#> GSM617621 6 0.670 0.2101 0.392 0.040 0.012 0.020 0.088 0.448
#> GSM617629 5 0.675 0.3837 0.012 0.076 0.184 0.032 0.596 0.100
#> GSM617630 2 0.894 0.0190 0.032 0.316 0.248 0.068 0.160 0.176
#> GSM617631 3 0.426 0.5485 0.000 0.004 0.756 0.008 0.148 0.084
#> GSM617633 5 0.776 0.2715 0.252 0.080 0.148 0.008 0.456 0.056
#> GSM617642 3 0.496 0.5822 0.076 0.024 0.736 0.000 0.032 0.132
#> GSM617645 2 0.669 0.3771 0.024 0.548 0.012 0.276 0.060 0.080
#> GSM617646 1 0.779 0.2684 0.496 0.196 0.044 0.020 0.120 0.124
#> GSM617652 1 0.851 0.0589 0.344 0.088 0.248 0.008 0.100 0.212
#> GSM617655 3 0.226 0.6193 0.004 0.008 0.912 0.004 0.032 0.040
#> GSM617656 3 0.146 0.6167 0.000 0.000 0.940 0.000 0.044 0.016
#> GSM617657 3 0.588 0.4983 0.000 0.048 0.668 0.056 0.160 0.068
#> GSM617658 3 0.716 -0.0153 0.040 0.004 0.384 0.012 0.304 0.256
#> GSM617659 1 0.603 0.3253 0.592 0.008 0.220 0.000 0.036 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) k
#> MAD:skmeans 77 0.02890 2
#> MAD:skmeans 72 0.00421 3
#> MAD:skmeans 54 0.00639 4
#> MAD:skmeans 35 0.10401 5
#> MAD:skmeans 27 0.09979 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 79 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 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 0.270 0.654 0.813 0.4888 0.507 0.507
#> 3 3 0.524 0.699 0.860 0.3267 0.784 0.597
#> 4 4 0.549 0.674 0.855 0.0401 0.973 0.922
#> 5 5 0.570 0.560 0.827 0.0380 0.976 0.928
#> 6 6 0.568 0.581 0.822 0.0132 0.969 0.906
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
#> GSM617581 1 0.0000 0.615 1.000 0.000
#> GSM617582 1 0.4022 0.695 0.920 0.080
#> GSM617588 2 0.9686 0.700 0.396 0.604
#> GSM617590 2 0.9170 0.717 0.332 0.668
#> GSM617592 2 0.9686 0.700 0.396 0.604
#> GSM617607 1 0.9686 0.754 0.604 0.396
#> GSM617608 1 0.9686 0.754 0.604 0.396
#> GSM617609 1 0.9686 0.754 0.604 0.396
#> GSM617612 1 0.9686 0.754 0.604 0.396
#> GSM617615 2 0.8499 0.714 0.276 0.724
#> GSM617616 1 0.6801 0.761 0.820 0.180
#> GSM617617 1 0.0376 0.611 0.996 0.004
#> GSM617618 1 0.0000 0.615 1.000 0.000
#> GSM617619 2 0.9954 0.638 0.460 0.540
#> GSM617620 2 0.9686 0.700 0.396 0.604
#> GSM617622 1 0.8713 -0.162 0.708 0.292
#> GSM617623 1 0.5408 0.717 0.876 0.124
#> GSM617624 2 0.9963 0.374 0.464 0.536
#> GSM617625 2 0.0000 0.642 0.000 1.000
#> GSM617626 1 0.0000 0.615 1.000 0.000
#> GSM617627 2 0.9881 0.540 0.436 0.564
#> GSM617628 2 0.0000 0.642 0.000 1.000
#> GSM617632 1 0.3879 0.697 0.924 0.076
#> GSM617634 2 0.9732 0.699 0.404 0.596
#> GSM617635 1 0.8144 0.786 0.748 0.252
#> GSM617636 1 0.7815 0.783 0.768 0.232
#> GSM617637 1 0.7815 0.783 0.768 0.232
#> GSM617638 1 0.9686 0.754 0.604 0.396
#> GSM617639 1 0.7815 0.783 0.768 0.232
#> GSM617640 1 0.0000 0.615 1.000 0.000
#> GSM617641 2 0.9686 0.700 0.396 0.604
#> GSM617643 2 0.9896 0.675 0.440 0.560
#> GSM617644 2 0.9686 0.700 0.396 0.604
#> GSM617647 1 0.5737 0.743 0.864 0.136
#> GSM617648 2 0.9909 0.672 0.444 0.556
#> GSM617649 1 0.3431 0.643 0.936 0.064
#> GSM617650 1 0.9686 0.754 0.604 0.396
#> GSM617651 1 0.8016 0.786 0.756 0.244
#> GSM617653 1 0.9686 0.754 0.604 0.396
#> GSM617654 1 0.4815 0.720 0.896 0.104
#> GSM617583 2 0.0000 0.642 0.000 1.000
#> GSM617584 1 0.6048 0.344 0.852 0.148
#> GSM617585 2 0.9286 0.715 0.344 0.656
#> GSM617586 2 0.0000 0.642 0.000 1.000
#> GSM617587 2 0.4939 0.495 0.108 0.892
#> GSM617589 2 0.9686 0.700 0.396 0.604
#> GSM617591 2 0.9000 0.718 0.316 0.684
#> GSM617593 1 0.8144 0.786 0.748 0.252
#> GSM617594 1 0.7745 0.669 0.772 0.228
#> GSM617595 1 0.8327 0.785 0.736 0.264
#> GSM617596 1 0.9686 0.754 0.604 0.396
#> GSM617597 1 0.9686 0.754 0.604 0.396
#> GSM617598 1 0.7815 0.783 0.768 0.232
#> GSM617599 1 0.0672 0.624 0.992 0.008
#> GSM617600 2 0.0000 0.642 0.000 1.000
#> GSM617601 2 0.9686 0.700 0.396 0.604
#> GSM617602 2 0.9881 -0.525 0.436 0.564
#> GSM617603 2 0.7815 0.702 0.232 0.768
#> GSM617604 1 0.9661 0.754 0.608 0.392
#> GSM617605 2 0.8763 0.717 0.296 0.704
#> GSM617606 2 0.2423 0.662 0.040 0.960
#> GSM617610 1 0.7602 0.781 0.780 0.220
#> GSM617611 1 0.9686 0.754 0.604 0.396
#> GSM617613 2 0.0376 0.644 0.004 0.996
#> GSM617614 1 0.9954 0.688 0.540 0.460
#> GSM617621 1 0.7883 0.784 0.764 0.236
#> GSM617629 1 0.9209 0.644 0.664 0.336
#> GSM617630 1 0.9686 0.754 0.604 0.396
#> GSM617631 2 0.0000 0.642 0.000 1.000
#> GSM617633 1 0.9686 0.754 0.604 0.396
#> GSM617642 2 0.9866 -0.515 0.432 0.568
#> GSM617645 1 0.6887 0.768 0.816 0.184
#> GSM617646 1 0.8207 0.786 0.744 0.256
#> GSM617652 1 0.9686 0.754 0.604 0.396
#> GSM617655 2 0.2043 0.659 0.032 0.968
#> GSM617656 2 0.0000 0.642 0.000 1.000
#> GSM617657 2 0.0000 0.642 0.000 1.000
#> GSM617658 1 0.9661 0.754 0.608 0.392
#> GSM617659 1 0.9686 0.754 0.604 0.396
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM617581 2 0.1163 0.87881 0.028 0.972 0.000
#> GSM617582 2 0.6495 0.00496 0.460 0.536 0.004
#> GSM617588 2 0.0000 0.87905 0.000 1.000 0.000
#> GSM617590 3 0.4291 0.69859 0.000 0.180 0.820
#> GSM617592 2 0.0000 0.87905 0.000 1.000 0.000
#> GSM617607 1 0.0000 0.85209 1.000 0.000 0.000
#> GSM617608 1 0.0000 0.85209 1.000 0.000 0.000
#> GSM617609 1 0.4555 0.74725 0.800 0.000 0.200
#> GSM617612 1 0.1031 0.84783 0.976 0.000 0.024
#> GSM617615 3 0.4605 0.66873 0.000 0.204 0.796
#> GSM617616 1 0.6033 0.52984 0.660 0.336 0.004
#> GSM617617 2 0.0892 0.88321 0.020 0.980 0.000
#> GSM617618 2 0.4399 0.70770 0.188 0.812 0.000
#> GSM617619 3 0.8487 0.35390 0.100 0.364 0.536
#> GSM617620 2 0.0000 0.87905 0.000 1.000 0.000
#> GSM617622 2 0.1015 0.88309 0.012 0.980 0.008
#> GSM617623 1 0.7164 0.63813 0.680 0.256 0.064
#> GSM617624 3 0.9702 0.25100 0.364 0.220 0.416
#> GSM617625 3 0.0237 0.77273 0.004 0.000 0.996
#> GSM617626 2 0.0892 0.88321 0.020 0.980 0.000
#> GSM617627 2 0.8592 0.18868 0.108 0.532 0.360
#> GSM617628 3 0.0000 0.77216 0.000 0.000 1.000
#> GSM617632 1 0.5835 0.54289 0.660 0.340 0.000
#> GSM617634 2 0.3267 0.78733 0.000 0.884 0.116
#> GSM617635 1 0.0000 0.85209 1.000 0.000 0.000
#> GSM617636 1 0.0000 0.85209 1.000 0.000 0.000
#> GSM617637 1 0.0000 0.85209 1.000 0.000 0.000
#> GSM617638 1 0.5138 0.70188 0.748 0.000 0.252
#> GSM617639 1 0.0000 0.85209 1.000 0.000 0.000
#> GSM617640 2 0.0892 0.88321 0.020 0.980 0.000
#> GSM617641 2 0.0000 0.87905 0.000 1.000 0.000
#> GSM617643 2 0.0892 0.87631 0.000 0.980 0.020
#> GSM617644 2 0.0892 0.87631 0.000 0.980 0.020
#> GSM617647 1 0.5465 0.62839 0.712 0.288 0.000
#> GSM617648 2 0.1015 0.88179 0.008 0.980 0.012
#> GSM617649 2 0.6562 0.63854 0.072 0.744 0.184
#> GSM617650 1 0.0000 0.85209 1.000 0.000 0.000
#> GSM617651 1 0.0000 0.85209 1.000 0.000 0.000
#> GSM617653 1 0.4654 0.74672 0.792 0.000 0.208
#> GSM617654 1 0.6302 0.05822 0.520 0.480 0.000
#> GSM617583 3 0.1031 0.76994 0.024 0.000 0.976
#> GSM617584 2 0.0892 0.88321 0.020 0.980 0.000
#> GSM617585 3 0.5327 0.60087 0.000 0.272 0.728
#> GSM617586 3 0.0237 0.77273 0.004 0.000 0.996
#> GSM617587 3 0.4293 0.67793 0.164 0.004 0.832
#> GSM617589 3 0.5988 0.44055 0.000 0.368 0.632
#> GSM617591 3 0.3116 0.73303 0.000 0.108 0.892
#> GSM617593 1 0.0000 0.85209 1.000 0.000 0.000
#> GSM617594 1 0.6546 0.70006 0.756 0.148 0.096
#> GSM617595 1 0.0000 0.85209 1.000 0.000 0.000
#> GSM617596 1 0.4121 0.77703 0.832 0.000 0.168
#> GSM617597 1 0.0000 0.85209 1.000 0.000 0.000
#> GSM617598 1 0.0000 0.85209 1.000 0.000 0.000
#> GSM617599 2 0.2448 0.84549 0.076 0.924 0.000
#> GSM617600 3 0.1163 0.76756 0.028 0.000 0.972
#> GSM617601 3 0.6045 0.42085 0.000 0.380 0.620
#> GSM617602 3 0.6299 -0.16261 0.476 0.000 0.524
#> GSM617603 3 0.6215 0.23753 0.000 0.428 0.572
#> GSM617604 1 0.5016 0.71580 0.760 0.000 0.240
#> GSM617605 3 0.5291 0.61739 0.000 0.268 0.732
#> GSM617606 3 0.0237 0.77273 0.004 0.000 0.996
#> GSM617610 1 0.1643 0.83997 0.956 0.044 0.000
#> GSM617611 1 0.1529 0.84275 0.960 0.000 0.040
#> GSM617613 3 0.0000 0.77216 0.000 0.000 1.000
#> GSM617614 1 0.6111 0.47964 0.604 0.000 0.396
#> GSM617621 1 0.0000 0.85209 1.000 0.000 0.000
#> GSM617629 1 0.8533 0.40138 0.536 0.104 0.360
#> GSM617630 1 0.4504 0.75743 0.804 0.000 0.196
#> GSM617631 3 0.0592 0.77171 0.012 0.000 0.988
#> GSM617633 1 0.0237 0.85163 0.996 0.000 0.004
#> GSM617642 3 0.6309 -0.22539 0.496 0.000 0.504
#> GSM617645 1 0.4452 0.74299 0.808 0.192 0.000
#> GSM617646 1 0.1647 0.84357 0.960 0.036 0.004
#> GSM617652 1 0.0592 0.85056 0.988 0.000 0.012
#> GSM617655 3 0.0000 0.77216 0.000 0.000 1.000
#> GSM617656 3 0.0424 0.77292 0.008 0.000 0.992
#> GSM617657 3 0.0000 0.77216 0.000 0.000 1.000
#> GSM617658 1 0.5785 0.59766 0.668 0.000 0.332
#> GSM617659 1 0.0000 0.85209 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM617581 2 0.0817 0.83931 0.024 0.976 0.000 0.000
#> GSM617582 2 0.5147 -0.00644 0.460 0.536 0.004 0.000
#> GSM617588 2 0.0921 0.82086 0.000 0.972 0.000 0.028
#> GSM617590 4 0.3711 0.80581 0.000 0.024 0.140 0.836
#> GSM617592 2 0.3444 0.63747 0.000 0.816 0.000 0.184
#> GSM617607 1 0.0000 0.84726 1.000 0.000 0.000 0.000
#> GSM617608 1 0.0000 0.84726 1.000 0.000 0.000 0.000
#> GSM617609 1 0.4880 0.71863 0.760 0.000 0.188 0.052
#> GSM617612 1 0.0817 0.84396 0.976 0.000 0.024 0.000
#> GSM617615 3 0.3893 0.57472 0.000 0.196 0.796 0.008
#> GSM617616 1 0.4781 0.52914 0.660 0.336 0.004 0.000
#> GSM617617 2 0.0592 0.84315 0.016 0.984 0.000 0.000
#> GSM617618 2 0.3486 0.65050 0.188 0.812 0.000 0.000
#> GSM617619 3 0.7773 0.32564 0.100 0.344 0.512 0.044
#> GSM617620 2 0.0000 0.83393 0.000 1.000 0.000 0.000
#> GSM617622 2 0.0657 0.84260 0.012 0.984 0.004 0.000
#> GSM617623 1 0.5677 0.64111 0.680 0.256 0.064 0.000
#> GSM617624 3 0.8728 0.17194 0.352 0.200 0.396 0.052
#> GSM617625 3 0.0000 0.70124 0.000 0.000 1.000 0.000
#> GSM617626 2 0.0592 0.84315 0.016 0.984 0.000 0.000
#> GSM617627 2 0.7097 0.20998 0.108 0.528 0.356 0.008
#> GSM617628 3 0.0000 0.70124 0.000 0.000 1.000 0.000
#> GSM617632 1 0.4624 0.54805 0.660 0.340 0.000 0.000
#> GSM617634 2 0.2530 0.75074 0.000 0.888 0.112 0.000
#> GSM617635 1 0.0000 0.84726 1.000 0.000 0.000 0.000
#> GSM617636 1 0.0000 0.84726 1.000 0.000 0.000 0.000
#> GSM617637 1 0.0000 0.84726 1.000 0.000 0.000 0.000
#> GSM617638 1 0.4420 0.70371 0.748 0.000 0.240 0.012
#> GSM617639 1 0.0000 0.84726 1.000 0.000 0.000 0.000
#> GSM617640 2 0.0592 0.84315 0.016 0.984 0.000 0.000
#> GSM617641 4 0.3975 0.63729 0.000 0.240 0.000 0.760
#> GSM617643 2 0.0592 0.83482 0.000 0.984 0.016 0.000
#> GSM617644 2 0.0592 0.83482 0.000 0.984 0.016 0.000
#> GSM617647 1 0.4331 0.63128 0.712 0.288 0.000 0.000
#> GSM617648 2 0.0672 0.84088 0.008 0.984 0.008 0.000
#> GSM617649 2 0.5964 0.57346 0.068 0.728 0.172 0.032
#> GSM617650 1 0.0000 0.84726 1.000 0.000 0.000 0.000
#> GSM617651 1 0.0000 0.84726 1.000 0.000 0.000 0.000
#> GSM617653 1 0.3688 0.74338 0.792 0.000 0.208 0.000
#> GSM617654 1 0.4994 0.05156 0.520 0.480 0.000 0.000
#> GSM617583 3 0.0707 0.69837 0.020 0.000 0.980 0.000
#> GSM617584 2 0.0592 0.84315 0.016 0.984 0.000 0.000
#> GSM617585 3 0.4222 0.51111 0.000 0.272 0.728 0.000
#> GSM617586 3 0.0000 0.70124 0.000 0.000 1.000 0.000
#> GSM617587 3 0.3855 0.57071 0.164 0.004 0.820 0.012
#> GSM617589 3 0.4889 0.39053 0.000 0.360 0.636 0.004
#> GSM617591 3 0.2469 0.64934 0.000 0.108 0.892 0.000
#> GSM617593 1 0.0000 0.84726 1.000 0.000 0.000 0.000
#> GSM617594 1 0.5508 0.69560 0.748 0.148 0.096 0.008
#> GSM617595 1 0.0000 0.84726 1.000 0.000 0.000 0.000
#> GSM617596 1 0.3266 0.77405 0.832 0.000 0.168 0.000
#> GSM617597 1 0.0000 0.84726 1.000 0.000 0.000 0.000
#> GSM617598 1 0.0000 0.84726 1.000 0.000 0.000 0.000
#> GSM617599 2 0.1978 0.80546 0.068 0.928 0.000 0.004
#> GSM617600 3 0.2111 0.68613 0.024 0.000 0.932 0.044
#> GSM617601 3 0.5174 0.38384 0.000 0.368 0.620 0.012
#> GSM617602 3 0.5600 -0.14314 0.468 0.000 0.512 0.020
#> GSM617603 4 0.4464 0.68188 0.000 0.024 0.208 0.768
#> GSM617604 1 0.3975 0.71241 0.760 0.000 0.240 0.000
#> GSM617605 4 0.3300 0.80133 0.000 0.008 0.144 0.848
#> GSM617606 3 0.0000 0.70124 0.000 0.000 1.000 0.000
#> GSM617610 1 0.1302 0.83563 0.956 0.044 0.000 0.000
#> GSM617611 1 0.1211 0.83975 0.960 0.000 0.040 0.000
#> GSM617613 3 0.1211 0.69472 0.000 0.000 0.960 0.040
#> GSM617614 1 0.4843 0.47401 0.604 0.000 0.396 0.000
#> GSM617621 1 0.0000 0.84726 1.000 0.000 0.000 0.000
#> GSM617629 1 0.7627 0.38938 0.528 0.096 0.336 0.040
#> GSM617630 1 0.4182 0.75546 0.796 0.000 0.180 0.024
#> GSM617631 3 0.0657 0.70067 0.012 0.000 0.984 0.004
#> GSM617633 1 0.0188 0.84690 0.996 0.000 0.004 0.000
#> GSM617642 3 0.5000 -0.21914 0.496 0.000 0.504 0.000
#> GSM617645 1 0.3768 0.74891 0.808 0.184 0.000 0.008
#> GSM617646 1 0.1305 0.83928 0.960 0.036 0.004 0.000
#> GSM617652 1 0.0804 0.84539 0.980 0.000 0.012 0.008
#> GSM617655 3 0.0188 0.70098 0.000 0.000 0.996 0.004
#> GSM617656 3 0.1635 0.69479 0.008 0.000 0.948 0.044
#> GSM617657 3 0.1940 0.67298 0.000 0.000 0.924 0.076
#> GSM617658 1 0.4585 0.59256 0.668 0.000 0.332 0.000
#> GSM617659 1 0.0000 0.84726 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM617581 2 0.0703 0.8422 0.024 0.976 0.000 0.000 0.000
#> GSM617582 2 0.4434 -0.0248 0.460 0.536 0.004 0.000 0.000
#> GSM617588 2 0.0794 0.8269 0.000 0.972 0.000 0.028 0.000
#> GSM617590 4 0.1012 0.8293 0.000 0.012 0.020 0.968 0.000
#> GSM617592 2 0.3003 0.6620 0.000 0.812 0.000 0.188 0.000
#> GSM617607 1 0.0000 0.8012 1.000 0.000 0.000 0.000 0.000
#> GSM617608 1 0.0000 0.8012 1.000 0.000 0.000 0.000 0.000
#> GSM617609 1 0.5289 0.0579 0.500 0.000 0.048 0.000 0.452
#> GSM617612 1 0.0703 0.7976 0.976 0.000 0.024 0.000 0.000
#> GSM617615 3 0.4502 0.3528 0.000 0.180 0.744 0.000 0.076
#> GSM617616 1 0.4118 0.4857 0.660 0.336 0.004 0.000 0.000
#> GSM617617 2 0.0510 0.8458 0.016 0.984 0.000 0.000 0.000
#> GSM617618 2 0.3003 0.6343 0.188 0.812 0.000 0.000 0.000
#> GSM617619 3 0.7290 -0.4534 0.056 0.144 0.408 0.000 0.392
#> GSM617620 2 0.0162 0.8374 0.000 0.996 0.000 0.000 0.004
#> GSM617622 2 0.0566 0.8454 0.012 0.984 0.004 0.000 0.000
#> GSM617623 1 0.5076 0.5741 0.680 0.252 0.060 0.000 0.008
#> GSM617624 5 0.7371 0.0000 0.184 0.048 0.336 0.000 0.432
#> GSM617625 3 0.0000 0.5325 0.000 0.000 1.000 0.000 0.000
#> GSM617626 2 0.0510 0.8458 0.016 0.984 0.000 0.000 0.000
#> GSM617627 2 0.7657 -0.0594 0.108 0.460 0.292 0.000 0.140
#> GSM617628 3 0.0000 0.5325 0.000 0.000 1.000 0.000 0.000
#> GSM617632 1 0.3983 0.5067 0.660 0.340 0.000 0.000 0.000
#> GSM617634 2 0.2179 0.7527 0.000 0.888 0.112 0.000 0.000
#> GSM617635 1 0.0000 0.8012 1.000 0.000 0.000 0.000 0.000
#> GSM617636 1 0.0000 0.8012 1.000 0.000 0.000 0.000 0.000
#> GSM617637 1 0.0000 0.8012 1.000 0.000 0.000 0.000 0.000
#> GSM617638 1 0.4696 0.6590 0.736 0.000 0.156 0.000 0.108
#> GSM617639 1 0.0000 0.8012 1.000 0.000 0.000 0.000 0.000
#> GSM617640 2 0.0510 0.8458 0.016 0.984 0.000 0.000 0.000
#> GSM617641 4 0.1544 0.8011 0.000 0.068 0.000 0.932 0.000
#> GSM617643 2 0.0671 0.8376 0.000 0.980 0.016 0.000 0.004
#> GSM617644 2 0.0798 0.8374 0.000 0.976 0.016 0.000 0.008
#> GSM617647 1 0.4404 0.5858 0.704 0.264 0.000 0.000 0.032
#> GSM617648 2 0.0579 0.8437 0.008 0.984 0.008 0.000 0.000
#> GSM617649 2 0.6400 0.4571 0.068 0.640 0.140 0.000 0.152
#> GSM617650 1 0.0000 0.8012 1.000 0.000 0.000 0.000 0.000
#> GSM617651 1 0.0000 0.8012 1.000 0.000 0.000 0.000 0.000
#> GSM617653 1 0.3109 0.6956 0.800 0.000 0.200 0.000 0.000
#> GSM617654 1 0.4555 0.0597 0.520 0.472 0.000 0.000 0.008
#> GSM617583 3 0.0609 0.5222 0.020 0.000 0.980 0.000 0.000
#> GSM617584 2 0.0510 0.8458 0.016 0.984 0.000 0.000 0.000
#> GSM617585 3 0.3790 0.3106 0.000 0.272 0.724 0.000 0.004
#> GSM617586 3 0.1270 0.5241 0.000 0.000 0.948 0.000 0.052
#> GSM617587 3 0.4779 0.1470 0.144 0.004 0.740 0.000 0.112
#> GSM617589 3 0.4182 0.1927 0.000 0.352 0.644 0.004 0.000
#> GSM617591 3 0.2358 0.4771 0.000 0.104 0.888 0.000 0.008
#> GSM617593 1 0.0000 0.8012 1.000 0.000 0.000 0.000 0.000
#> GSM617594 1 0.5827 0.5675 0.700 0.116 0.100 0.000 0.084
#> GSM617595 1 0.0000 0.8012 1.000 0.000 0.000 0.000 0.000
#> GSM617596 1 0.2813 0.7228 0.832 0.000 0.168 0.000 0.000
#> GSM617597 1 0.0510 0.7991 0.984 0.000 0.000 0.000 0.016
#> GSM617598 1 0.0000 0.8012 1.000 0.000 0.000 0.000 0.000
#> GSM617599 2 0.2036 0.8108 0.056 0.920 0.000 0.000 0.024
#> GSM617600 3 0.4649 -0.0580 0.016 0.000 0.580 0.000 0.404
#> GSM617601 3 0.5200 0.1909 0.000 0.304 0.628 0.000 0.068
#> GSM617602 3 0.6000 -0.2744 0.428 0.000 0.460 0.000 0.112
#> GSM617603 4 0.6455 0.4800 0.000 0.000 0.200 0.480 0.320
#> GSM617604 1 0.3424 0.6587 0.760 0.000 0.240 0.000 0.000
#> GSM617605 4 0.0992 0.8287 0.000 0.008 0.024 0.968 0.000
#> GSM617606 3 0.0162 0.5327 0.000 0.000 0.996 0.000 0.004
#> GSM617610 1 0.1121 0.7895 0.956 0.044 0.000 0.000 0.000
#> GSM617611 1 0.1043 0.7931 0.960 0.000 0.040 0.000 0.000
#> GSM617613 3 0.4030 0.0938 0.000 0.000 0.648 0.000 0.352
#> GSM617614 1 0.4126 0.4461 0.620 0.000 0.380 0.000 0.000
#> GSM617621 1 0.0000 0.8012 1.000 0.000 0.000 0.000 0.000
#> GSM617629 1 0.7427 0.0279 0.464 0.052 0.260 0.000 0.224
#> GSM617630 1 0.4637 0.6673 0.740 0.000 0.100 0.000 0.160
#> GSM617631 3 0.0579 0.5275 0.008 0.000 0.984 0.000 0.008
#> GSM617633 1 0.0162 0.8008 0.996 0.000 0.004 0.000 0.000
#> GSM617642 1 0.4827 0.1175 0.504 0.000 0.476 0.000 0.020
#> GSM617645 1 0.3868 0.7062 0.800 0.140 0.000 0.000 0.060
#> GSM617646 1 0.1124 0.7929 0.960 0.036 0.004 0.000 0.000
#> GSM617652 1 0.1697 0.7823 0.932 0.000 0.008 0.000 0.060
#> GSM617655 3 0.1410 0.5207 0.000 0.000 0.940 0.000 0.060
#> GSM617656 3 0.4210 -0.0151 0.000 0.000 0.588 0.000 0.412
#> GSM617657 3 0.4088 0.1020 0.000 0.000 0.632 0.000 0.368
#> GSM617658 1 0.4029 0.5570 0.680 0.000 0.316 0.000 0.004
#> GSM617659 1 0.0000 0.8012 1.000 0.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM617581 2 0.0632 0.83675 0.024 0.976 0.000 0.000 0.000 0.000
#> GSM617582 2 0.3982 -0.02384 0.460 0.536 0.004 0.000 0.000 0.000
#> GSM617588 2 0.1007 0.81942 0.000 0.956 0.000 0.044 0.000 0.000
#> GSM617590 4 0.0291 0.96229 0.000 0.004 0.004 0.992 0.000 0.000
#> GSM617592 2 0.2793 0.66543 0.000 0.800 0.000 0.200 0.000 0.000
#> GSM617607 1 0.0000 0.81723 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617608 1 0.0000 0.81723 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617609 6 0.5249 -0.17487 0.464 0.000 0.040 0.000 0.028 0.468
#> GSM617612 1 0.0632 0.81371 0.976 0.000 0.024 0.000 0.000 0.000
#> GSM617615 3 0.4401 0.47182 0.000 0.164 0.748 0.000 0.044 0.044
#> GSM617616 1 0.3699 0.51754 0.660 0.336 0.004 0.000 0.000 0.000
#> GSM617617 2 0.0458 0.83997 0.016 0.984 0.000 0.000 0.000 0.000
#> GSM617618 2 0.2697 0.64691 0.188 0.812 0.000 0.000 0.000 0.000
#> GSM617619 6 0.6287 0.14635 0.052 0.096 0.396 0.000 0.004 0.452
#> GSM617620 2 0.0622 0.83107 0.000 0.980 0.000 0.012 0.008 0.000
#> GSM617622 2 0.0508 0.83976 0.012 0.984 0.004 0.000 0.000 0.000
#> GSM617623 1 0.4632 0.59981 0.680 0.248 0.060 0.000 0.000 0.012
#> GSM617624 6 0.7582 0.24580 0.148 0.040 0.332 0.000 0.088 0.392
#> GSM617625 3 0.0146 0.59263 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM617626 2 0.0458 0.83997 0.016 0.984 0.000 0.000 0.000 0.000
#> GSM617627 2 0.7771 0.08644 0.108 0.448 0.256 0.000 0.084 0.104
#> GSM617628 3 0.0000 0.59155 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM617632 1 0.3578 0.53714 0.660 0.340 0.000 0.000 0.000 0.000
#> GSM617634 2 0.1957 0.75295 0.000 0.888 0.112 0.000 0.000 0.000
#> GSM617635 1 0.0000 0.81723 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617636 1 0.0000 0.81723 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617637 1 0.0000 0.81723 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617638 1 0.4842 0.67553 0.732 0.000 0.120 0.000 0.080 0.068
#> GSM617639 1 0.0000 0.81723 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617640 2 0.0748 0.83951 0.016 0.976 0.000 0.000 0.004 0.004
#> GSM617641 4 0.0935 0.93457 0.000 0.032 0.000 0.964 0.004 0.000
#> GSM617643 2 0.0405 0.83339 0.000 0.988 0.008 0.000 0.004 0.000
#> GSM617644 2 0.0964 0.83058 0.000 0.968 0.016 0.000 0.012 0.004
#> GSM617647 1 0.3926 0.61113 0.708 0.268 0.000 0.000 0.012 0.012
#> GSM617648 2 0.0520 0.83813 0.008 0.984 0.008 0.000 0.000 0.000
#> GSM617649 2 0.6123 0.43222 0.064 0.620 0.140 0.000 0.012 0.164
#> GSM617650 1 0.0000 0.81723 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617651 1 0.0000 0.81723 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617653 1 0.2762 0.71672 0.804 0.000 0.196 0.000 0.000 0.000
#> GSM617654 1 0.5161 -0.00209 0.472 0.452 0.000 0.000 0.072 0.004
#> GSM617583 3 0.0547 0.58672 0.020 0.000 0.980 0.000 0.000 0.000
#> GSM617584 2 0.0458 0.83997 0.016 0.984 0.000 0.000 0.000 0.000
#> GSM617585 3 0.3521 0.41694 0.000 0.268 0.724 0.000 0.004 0.004
#> GSM617586 3 0.1802 0.57517 0.000 0.000 0.916 0.000 0.012 0.072
#> GSM617587 3 0.4886 0.33453 0.144 0.004 0.728 0.000 0.052 0.072
#> GSM617589 3 0.3864 0.31666 0.000 0.344 0.648 0.004 0.004 0.000
#> GSM617591 3 0.2213 0.55997 0.000 0.100 0.888 0.000 0.004 0.008
#> GSM617593 1 0.0000 0.81723 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617594 1 0.5494 0.60067 0.704 0.116 0.100 0.000 0.036 0.044
#> GSM617595 1 0.0000 0.81723 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617596 1 0.2527 0.73988 0.832 0.000 0.168 0.000 0.000 0.000
#> GSM617597 1 0.0717 0.81354 0.976 0.000 0.000 0.000 0.008 0.016
#> GSM617598 1 0.0000 0.81723 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617599 2 0.1921 0.80642 0.056 0.920 0.000 0.000 0.012 0.012
#> GSM617600 3 0.4097 -0.21250 0.008 0.000 0.500 0.000 0.000 0.492
#> GSM617601 3 0.5193 0.33149 0.000 0.276 0.628 0.000 0.068 0.028
#> GSM617602 3 0.5519 -0.19685 0.432 0.000 0.452 0.000 0.004 0.112
#> GSM617603 5 0.4552 0.00000 0.000 0.000 0.172 0.128 0.700 0.000
#> GSM617604 1 0.3076 0.67807 0.760 0.000 0.240 0.000 0.000 0.000
#> GSM617605 4 0.0260 0.96108 0.000 0.000 0.008 0.992 0.000 0.000
#> GSM617606 3 0.0146 0.59257 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM617610 1 0.1007 0.80599 0.956 0.044 0.000 0.000 0.000 0.000
#> GSM617611 1 0.0937 0.80930 0.960 0.000 0.040 0.000 0.000 0.000
#> GSM617613 3 0.3782 -0.07288 0.000 0.000 0.588 0.000 0.000 0.412
#> GSM617614 1 0.3695 0.48467 0.624 0.000 0.376 0.000 0.000 0.000
#> GSM617621 1 0.0000 0.81723 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617629 1 0.8265 -0.13247 0.376 0.048 0.232 0.008 0.128 0.208
#> GSM617630 1 0.4821 0.68411 0.736 0.000 0.076 0.000 0.080 0.108
#> GSM617631 3 0.0665 0.58644 0.008 0.000 0.980 0.000 0.004 0.008
#> GSM617633 1 0.0146 0.81687 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM617642 1 0.4719 0.18728 0.500 0.000 0.464 0.000 0.012 0.024
#> GSM617645 1 0.4040 0.72943 0.784 0.092 0.000 0.000 0.104 0.020
#> GSM617646 1 0.1010 0.80875 0.960 0.036 0.000 0.000 0.000 0.004
#> GSM617652 1 0.1666 0.80058 0.936 0.000 0.008 0.000 0.036 0.020
#> GSM617655 3 0.2019 0.56949 0.000 0.000 0.900 0.000 0.012 0.088
#> GSM617656 6 0.3869 -0.04728 0.000 0.000 0.500 0.000 0.000 0.500
#> GSM617657 6 0.4218 -0.25538 0.000 0.000 0.360 0.000 0.024 0.616
#> GSM617658 1 0.3738 0.57955 0.680 0.000 0.312 0.000 0.004 0.004
#> GSM617659 1 0.0000 0.81723 1.000 0.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:pam 73 0.775415 2
#> MAD:pam 67 0.000665 3
#> MAD:pam 68 0.002427 4
#> MAD:pam 56 0.023961 5
#> MAD:pam 58 0.018469 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 79 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.526 0.748 0.879 0.2819 0.705 0.705
#> 3 3 0.289 0.573 0.737 1.0438 0.529 0.394
#> 4 4 0.620 0.776 0.853 0.2631 0.819 0.566
#> 5 5 0.599 0.541 0.768 0.0765 0.946 0.804
#> 6 6 0.610 0.444 0.687 0.0320 0.937 0.737
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
#> GSM617581 1 0.1414 0.883 0.980 0.020
#> GSM617582 1 0.1184 0.884 0.984 0.016
#> GSM617588 2 0.9491 0.803 0.368 0.632
#> GSM617590 2 0.9460 0.800 0.364 0.636
#> GSM617592 2 0.9460 0.803 0.364 0.636
#> GSM617607 1 0.1843 0.875 0.972 0.028
#> GSM617608 1 0.0000 0.886 1.000 0.000
#> GSM617609 1 0.0000 0.886 1.000 0.000
#> GSM617612 1 0.0000 0.886 1.000 0.000
#> GSM617615 1 0.9635 -0.237 0.612 0.388
#> GSM617616 1 0.1414 0.885 0.980 0.020
#> GSM617617 2 0.9358 0.650 0.352 0.648
#> GSM617618 1 0.2948 0.867 0.948 0.052
#> GSM617619 1 0.2236 0.871 0.964 0.036
#> GSM617620 2 0.9460 0.803 0.364 0.636
#> GSM617622 1 1.0000 -0.521 0.504 0.496
#> GSM617623 1 0.1414 0.883 0.980 0.020
#> GSM617624 1 0.4562 0.809 0.904 0.096
#> GSM617625 1 0.0000 0.886 1.000 0.000
#> GSM617626 1 0.1184 0.884 0.984 0.016
#> GSM617627 1 0.7376 0.598 0.792 0.208
#> GSM617628 1 0.0000 0.886 1.000 0.000
#> GSM617632 1 0.0938 0.884 0.988 0.012
#> GSM617634 1 0.3274 0.852 0.940 0.060
#> GSM617635 1 0.2043 0.872 0.968 0.032
#> GSM617636 1 0.2043 0.880 0.968 0.032
#> GSM617637 1 0.0000 0.886 1.000 0.000
#> GSM617638 1 0.3114 0.856 0.944 0.056
#> GSM617639 1 0.0000 0.886 1.000 0.000
#> GSM617640 2 0.8327 0.714 0.264 0.736
#> GSM617641 2 0.9460 0.803 0.364 0.636
#> GSM617643 2 0.8207 0.715 0.256 0.744
#> GSM617644 2 0.8608 0.763 0.284 0.716
#> GSM617647 1 0.5408 0.774 0.876 0.124
#> GSM617648 2 0.8861 0.696 0.304 0.696
#> GSM617649 1 0.9286 0.226 0.656 0.344
#> GSM617650 1 0.0000 0.886 1.000 0.000
#> GSM617651 1 0.0376 0.886 0.996 0.004
#> GSM617653 1 0.0938 0.884 0.988 0.012
#> GSM617654 1 0.9954 -0.214 0.540 0.460
#> GSM617583 1 0.0000 0.886 1.000 0.000
#> GSM617584 1 0.9732 -0.285 0.596 0.404
#> GSM617585 1 0.9087 0.127 0.676 0.324
#> GSM617586 1 0.2948 0.851 0.948 0.052
#> GSM617587 1 0.0000 0.886 1.000 0.000
#> GSM617589 2 0.9491 0.803 0.368 0.632
#> GSM617591 1 0.1414 0.878 0.980 0.020
#> GSM617593 1 0.0000 0.886 1.000 0.000
#> GSM617594 1 0.6148 0.719 0.848 0.152
#> GSM617595 1 0.0376 0.886 0.996 0.004
#> GSM617596 1 0.0938 0.884 0.988 0.012
#> GSM617597 1 0.0000 0.886 1.000 0.000
#> GSM617598 1 0.0672 0.886 0.992 0.008
#> GSM617599 1 0.3114 0.856 0.944 0.056
#> GSM617600 1 0.3274 0.843 0.940 0.060
#> GSM617601 1 1.0000 -0.595 0.500 0.500
#> GSM617602 1 0.3431 0.845 0.936 0.064
#> GSM617603 2 0.9522 0.801 0.372 0.628
#> GSM617604 1 0.1414 0.882 0.980 0.020
#> GSM617605 2 0.9460 0.800 0.364 0.636
#> GSM617606 1 0.1414 0.877 0.980 0.020
#> GSM617610 1 0.0376 0.886 0.996 0.004
#> GSM617611 1 0.0000 0.886 1.000 0.000
#> GSM617613 1 0.3274 0.843 0.940 0.060
#> GSM617614 1 0.0376 0.886 0.996 0.004
#> GSM617621 1 0.0938 0.884 0.988 0.012
#> GSM617629 1 0.2778 0.873 0.952 0.048
#> GSM617630 1 0.0938 0.885 0.988 0.012
#> GSM617631 1 0.3584 0.839 0.932 0.068
#> GSM617633 1 0.2043 0.872 0.968 0.032
#> GSM617642 1 0.1184 0.881 0.984 0.016
#> GSM617645 2 0.9754 0.554 0.408 0.592
#> GSM617646 1 0.2043 0.872 0.968 0.032
#> GSM617652 1 0.0000 0.886 1.000 0.000
#> GSM617655 1 0.3274 0.843 0.940 0.060
#> GSM617656 1 0.3274 0.843 0.940 0.060
#> GSM617657 1 0.3114 0.847 0.944 0.056
#> GSM617658 1 0.3584 0.840 0.932 0.068
#> GSM617659 1 0.0000 0.886 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM617581 1 0.6587 0.3225 0.632 0.352 0.016
#> GSM617582 1 0.6108 0.5042 0.732 0.240 0.028
#> GSM617588 2 0.0424 0.6783 0.008 0.992 0.000
#> GSM617590 2 0.0424 0.6783 0.008 0.992 0.000
#> GSM617592 2 0.0424 0.6783 0.008 0.992 0.000
#> GSM617607 1 0.3434 0.7181 0.904 0.064 0.032
#> GSM617608 1 0.2301 0.7283 0.936 0.060 0.004
#> GSM617609 3 0.9715 0.6648 0.380 0.220 0.400
#> GSM617612 1 0.1267 0.7359 0.972 0.024 0.004
#> GSM617615 2 0.5815 0.6624 0.104 0.800 0.096
#> GSM617616 1 0.3213 0.7278 0.912 0.060 0.028
#> GSM617617 2 0.7974 0.6445 0.060 0.504 0.436
#> GSM617618 1 0.4865 0.6644 0.832 0.136 0.032
#> GSM617619 3 0.9612 0.5326 0.204 0.372 0.424
#> GSM617620 2 0.0424 0.6783 0.008 0.992 0.000
#> GSM617622 2 0.7400 0.7060 0.072 0.664 0.264
#> GSM617623 1 0.5268 0.5896 0.776 0.212 0.012
#> GSM617624 2 0.7828 0.6303 0.160 0.672 0.168
#> GSM617625 1 0.9283 -0.2451 0.524 0.216 0.260
#> GSM617626 1 0.1999 0.7267 0.952 0.036 0.012
#> GSM617627 2 0.7064 0.6937 0.076 0.704 0.220
#> GSM617628 1 0.9678 -0.6055 0.420 0.216 0.364
#> GSM617632 1 0.1585 0.7347 0.964 0.028 0.008
#> GSM617634 2 0.8887 0.2239 0.388 0.488 0.124
#> GSM617635 1 0.3369 0.7218 0.908 0.052 0.040
#> GSM617636 1 0.4995 0.6539 0.824 0.144 0.032
#> GSM617637 1 0.0661 0.7339 0.988 0.004 0.008
#> GSM617638 2 0.9174 0.3285 0.276 0.532 0.192
#> GSM617639 1 0.0424 0.7304 0.992 0.000 0.008
#> GSM617640 2 0.7021 0.6452 0.020 0.544 0.436
#> GSM617641 2 0.0424 0.6783 0.008 0.992 0.000
#> GSM617643 2 0.7021 0.6470 0.020 0.544 0.436
#> GSM617644 2 0.6228 0.6907 0.012 0.672 0.316
#> GSM617647 2 0.8918 0.6509 0.160 0.552 0.288
#> GSM617648 2 0.7627 0.6511 0.044 0.528 0.428
#> GSM617649 2 0.8037 0.6833 0.076 0.572 0.352
#> GSM617650 1 0.0747 0.7365 0.984 0.016 0.000
#> GSM617651 1 0.0661 0.7295 0.988 0.004 0.008
#> GSM617653 1 0.1015 0.7309 0.980 0.012 0.008
#> GSM617654 2 0.8326 0.6404 0.080 0.488 0.432
#> GSM617583 1 0.8876 -0.0179 0.576 0.220 0.204
#> GSM617584 2 0.4068 0.6357 0.120 0.864 0.016
#> GSM617585 2 0.6880 0.3971 0.156 0.736 0.108
#> GSM617586 3 0.9178 0.9014 0.240 0.220 0.540
#> GSM617587 1 0.9439 -0.3273 0.500 0.224 0.276
#> GSM617589 2 0.0829 0.6798 0.012 0.984 0.004
#> GSM617591 2 0.5728 0.5375 0.196 0.772 0.032
#> GSM617593 1 0.0424 0.7345 0.992 0.008 0.000
#> GSM617594 2 0.9405 0.5985 0.204 0.496 0.300
#> GSM617595 1 0.0424 0.7304 0.992 0.000 0.008
#> GSM617596 1 0.1015 0.7266 0.980 0.008 0.012
#> GSM617597 1 0.8977 -0.0777 0.564 0.204 0.232
#> GSM617598 1 0.0848 0.7323 0.984 0.008 0.008
#> GSM617599 2 0.8625 0.4057 0.316 0.560 0.124
#> GSM617600 3 0.9086 0.8965 0.228 0.220 0.552
#> GSM617601 2 0.6044 0.6924 0.056 0.772 0.172
#> GSM617602 3 0.9298 0.8839 0.248 0.228 0.524
#> GSM617603 2 0.0661 0.6797 0.008 0.988 0.004
#> GSM617604 1 0.4569 0.6858 0.860 0.068 0.072
#> GSM617605 2 0.0424 0.6783 0.008 0.992 0.000
#> GSM617606 2 0.5986 0.4921 0.240 0.736 0.024
#> GSM617610 1 0.0475 0.7324 0.992 0.004 0.004
#> GSM617611 1 0.0475 0.7322 0.992 0.004 0.004
#> GSM617613 3 0.9148 0.9023 0.236 0.220 0.544
#> GSM617614 1 0.9587 -0.4312 0.468 0.224 0.308
#> GSM617621 1 0.1015 0.7266 0.980 0.008 0.012
#> GSM617629 3 0.9379 0.7987 0.288 0.208 0.504
#> GSM617630 1 0.9963 -0.6037 0.360 0.292 0.348
#> GSM617631 3 0.9151 0.8975 0.228 0.228 0.544
#> GSM617633 1 0.5891 0.5536 0.764 0.200 0.036
#> GSM617642 1 0.9717 -0.6653 0.392 0.220 0.388
#> GSM617645 2 0.7729 0.6502 0.048 0.516 0.436
#> GSM617646 1 0.2116 0.7277 0.948 0.012 0.040
#> GSM617652 1 0.4682 0.5909 0.804 0.192 0.004
#> GSM617655 3 0.9148 0.9023 0.236 0.220 0.544
#> GSM617656 3 0.9148 0.9023 0.236 0.220 0.544
#> GSM617657 3 0.9118 0.9000 0.232 0.220 0.548
#> GSM617658 3 0.9528 0.8349 0.288 0.228 0.484
#> GSM617659 1 0.2356 0.7264 0.928 0.072 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM617581 1 0.6907 0.721 0.632 0.180 0.012 0.176
#> GSM617582 1 0.9210 0.243 0.420 0.124 0.296 0.160
#> GSM617588 4 0.3266 0.941 0.000 0.168 0.000 0.832
#> GSM617590 4 0.3266 0.941 0.000 0.168 0.000 0.832
#> GSM617592 4 0.3266 0.941 0.000 0.168 0.000 0.832
#> GSM617607 1 0.1733 0.858 0.948 0.024 0.028 0.000
#> GSM617608 1 0.0921 0.856 0.972 0.000 0.028 0.000
#> GSM617609 3 0.1909 0.837 0.008 0.048 0.940 0.004
#> GSM617612 1 0.0336 0.861 0.992 0.000 0.008 0.000
#> GSM617615 2 0.4781 0.340 0.000 0.660 0.004 0.336
#> GSM617616 1 0.3775 0.848 0.864 0.040 0.016 0.080
#> GSM617617 2 0.0336 0.831 0.000 0.992 0.000 0.008
#> GSM617618 1 0.5745 0.807 0.756 0.096 0.032 0.116
#> GSM617619 3 0.4500 0.559 0.000 0.316 0.684 0.000
#> GSM617620 4 0.3266 0.941 0.000 0.168 0.000 0.832
#> GSM617622 2 0.3355 0.696 0.000 0.836 0.004 0.160
#> GSM617623 1 0.6635 0.738 0.652 0.176 0.008 0.164
#> GSM617624 2 0.1732 0.814 0.004 0.948 0.040 0.008
#> GSM617625 3 0.3942 0.728 0.236 0.000 0.764 0.000
#> GSM617626 1 0.5577 0.798 0.744 0.144 0.008 0.104
#> GSM617627 2 0.0707 0.829 0.000 0.980 0.020 0.000
#> GSM617628 3 0.3610 0.766 0.200 0.000 0.800 0.000
#> GSM617632 1 0.5309 0.810 0.756 0.072 0.008 0.164
#> GSM617634 2 0.3225 0.768 0.060 0.892 0.032 0.016
#> GSM617635 1 0.1174 0.862 0.968 0.020 0.012 0.000
#> GSM617636 1 0.7177 0.742 0.640 0.160 0.036 0.164
#> GSM617637 1 0.0188 0.861 0.996 0.000 0.004 0.000
#> GSM617638 2 0.4071 0.721 0.016 0.844 0.104 0.036
#> GSM617639 1 0.1356 0.860 0.960 0.032 0.008 0.000
#> GSM617640 2 0.0188 0.832 0.000 0.996 0.000 0.004
#> GSM617641 4 0.3266 0.941 0.000 0.168 0.000 0.832
#> GSM617643 2 0.1716 0.798 0.000 0.936 0.000 0.064
#> GSM617644 2 0.4103 0.536 0.000 0.744 0.000 0.256
#> GSM617647 2 0.0188 0.832 0.000 0.996 0.004 0.000
#> GSM617648 2 0.1637 0.808 0.000 0.940 0.000 0.060
#> GSM617649 2 0.0376 0.833 0.000 0.992 0.004 0.004
#> GSM617650 1 0.0336 0.861 0.992 0.000 0.008 0.000
#> GSM617651 1 0.0188 0.861 0.996 0.000 0.004 0.000
#> GSM617653 1 0.2859 0.843 0.880 0.000 0.008 0.112
#> GSM617654 2 0.0000 0.832 0.000 1.000 0.000 0.000
#> GSM617583 3 0.3837 0.737 0.224 0.000 0.776 0.000
#> GSM617584 4 0.5186 0.610 0.016 0.344 0.000 0.640
#> GSM617585 3 0.7096 0.157 0.000 0.140 0.516 0.344
#> GSM617586 3 0.0712 0.844 0.004 0.008 0.984 0.004
#> GSM617587 3 0.5201 0.716 0.180 0.064 0.752 0.004
#> GSM617589 4 0.3610 0.915 0.000 0.200 0.000 0.800
#> GSM617591 2 0.7497 0.269 0.012 0.528 0.308 0.152
#> GSM617593 1 0.0188 0.861 0.996 0.000 0.004 0.000
#> GSM617594 2 0.0844 0.833 0.004 0.980 0.012 0.004
#> GSM617595 1 0.0188 0.861 0.996 0.000 0.004 0.000
#> GSM617596 1 0.5170 0.813 0.764 0.064 0.008 0.164
#> GSM617597 3 0.3074 0.803 0.152 0.000 0.848 0.000
#> GSM617598 1 0.0188 0.862 0.996 0.000 0.004 0.000
#> GSM617599 2 0.1007 0.831 0.008 0.976 0.008 0.008
#> GSM617600 3 0.0564 0.845 0.004 0.004 0.988 0.004
#> GSM617601 2 0.3208 0.716 0.000 0.848 0.004 0.148
#> GSM617602 3 0.2561 0.825 0.016 0.004 0.912 0.068
#> GSM617603 4 0.4008 0.862 0.000 0.244 0.000 0.756
#> GSM617604 1 0.7332 0.710 0.636 0.048 0.152 0.164
#> GSM617605 4 0.3266 0.941 0.000 0.168 0.000 0.832
#> GSM617606 2 0.7718 0.268 0.036 0.512 0.344 0.108
#> GSM617610 1 0.0188 0.861 0.996 0.000 0.004 0.000
#> GSM617611 1 0.0336 0.861 0.992 0.000 0.008 0.000
#> GSM617613 3 0.0564 0.845 0.004 0.004 0.988 0.004
#> GSM617614 3 0.1743 0.843 0.056 0.000 0.940 0.004
#> GSM617621 1 0.6436 0.756 0.672 0.160 0.008 0.160
#> GSM617629 3 0.4362 0.782 0.008 0.088 0.828 0.076
#> GSM617630 3 0.5496 0.504 0.008 0.344 0.632 0.016
#> GSM617631 3 0.0188 0.843 0.004 0.000 0.996 0.000
#> GSM617633 1 0.5189 0.766 0.784 0.120 0.076 0.020
#> GSM617642 3 0.1302 0.845 0.044 0.000 0.956 0.000
#> GSM617645 2 0.0188 0.832 0.000 0.996 0.000 0.004
#> GSM617646 1 0.2918 0.835 0.876 0.116 0.008 0.000
#> GSM617652 1 0.4998 0.795 0.780 0.128 0.088 0.004
#> GSM617655 3 0.0564 0.845 0.004 0.004 0.988 0.004
#> GSM617656 3 0.0564 0.845 0.004 0.004 0.988 0.004
#> GSM617657 3 0.0524 0.844 0.000 0.008 0.988 0.004
#> GSM617658 3 0.4378 0.762 0.036 0.004 0.804 0.156
#> GSM617659 1 0.0707 0.859 0.980 0.000 0.020 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM617581 5 0.6550 0.4389 0.388 0.172 0.004 0.000 0.436
#> GSM617582 5 0.6388 0.4599 0.200 0.060 0.112 0.000 0.628
#> GSM617588 4 0.0703 0.8663 0.000 0.024 0.000 0.976 0.000
#> GSM617590 4 0.0451 0.8636 0.000 0.008 0.000 0.988 0.004
#> GSM617592 4 0.0703 0.8666 0.000 0.024 0.000 0.976 0.000
#> GSM617607 1 0.4335 0.3619 0.664 0.004 0.008 0.000 0.324
#> GSM617608 1 0.3123 0.4944 0.828 0.000 0.012 0.000 0.160
#> GSM617609 3 0.4048 0.6306 0.016 0.012 0.764 0.000 0.208
#> GSM617612 1 0.1043 0.6049 0.960 0.000 0.000 0.000 0.040
#> GSM617615 2 0.5128 0.4031 0.000 0.580 0.004 0.380 0.036
#> GSM617616 1 0.4481 -0.0599 0.576 0.008 0.000 0.000 0.416
#> GSM617617 2 0.0404 0.7827 0.000 0.988 0.000 0.012 0.000
#> GSM617618 5 0.5128 0.2895 0.420 0.012 0.020 0.000 0.548
#> GSM617619 3 0.6789 0.2432 0.004 0.252 0.440 0.000 0.304
#> GSM617620 4 0.0609 0.8671 0.000 0.020 0.000 0.980 0.000
#> GSM617622 2 0.4220 0.4857 0.000 0.688 0.004 0.300 0.008
#> GSM617623 5 0.6620 0.4169 0.404 0.184 0.004 0.000 0.408
#> GSM617624 2 0.4465 0.6426 0.000 0.672 0.024 0.000 0.304
#> GSM617625 3 0.5191 0.5860 0.252 0.000 0.660 0.000 0.088
#> GSM617626 1 0.6309 -0.4038 0.492 0.168 0.000 0.000 0.340
#> GSM617627 2 0.3061 0.7590 0.000 0.844 0.020 0.000 0.136
#> GSM617628 3 0.4901 0.6422 0.184 0.000 0.712 0.000 0.104
#> GSM617632 1 0.4825 -0.1896 0.568 0.024 0.000 0.000 0.408
#> GSM617634 2 0.4905 0.6358 0.008 0.656 0.024 0.004 0.308
#> GSM617635 1 0.3534 0.4406 0.744 0.000 0.000 0.000 0.256
#> GSM617636 5 0.5180 0.3663 0.304 0.020 0.032 0.000 0.644
#> GSM617637 1 0.0963 0.6169 0.964 0.000 0.000 0.000 0.036
#> GSM617638 2 0.5595 0.5203 0.000 0.560 0.084 0.000 0.356
#> GSM617639 1 0.2074 0.5874 0.896 0.000 0.000 0.000 0.104
#> GSM617640 2 0.0162 0.7834 0.000 0.996 0.000 0.004 0.000
#> GSM617641 4 0.0771 0.8672 0.000 0.020 0.000 0.976 0.004
#> GSM617643 2 0.1197 0.7706 0.000 0.952 0.000 0.048 0.000
#> GSM617644 2 0.3684 0.5672 0.000 0.720 0.000 0.280 0.000
#> GSM617647 2 0.0451 0.7851 0.004 0.988 0.000 0.000 0.008
#> GSM617648 2 0.1043 0.7762 0.000 0.960 0.000 0.040 0.000
#> GSM617649 2 0.1662 0.7835 0.000 0.936 0.004 0.004 0.056
#> GSM617650 1 0.1197 0.6148 0.952 0.000 0.000 0.000 0.048
#> GSM617651 1 0.0404 0.6183 0.988 0.000 0.000 0.000 0.012
#> GSM617653 1 0.4088 -0.0575 0.632 0.000 0.000 0.000 0.368
#> GSM617654 2 0.0290 0.7845 0.000 0.992 0.000 0.000 0.008
#> GSM617583 3 0.4789 0.6704 0.156 0.000 0.728 0.000 0.116
#> GSM617584 4 0.6087 0.4107 0.000 0.244 0.000 0.568 0.188
#> GSM617585 4 0.5657 0.3144 0.000 0.044 0.352 0.580 0.024
#> GSM617586 3 0.0703 0.7334 0.000 0.000 0.976 0.000 0.024
#> GSM617587 3 0.6100 0.4711 0.092 0.032 0.612 0.000 0.264
#> GSM617589 4 0.3081 0.7243 0.000 0.156 0.000 0.832 0.012
#> GSM617591 2 0.7792 0.3378 0.000 0.456 0.160 0.268 0.116
#> GSM617593 1 0.2074 0.5985 0.896 0.000 0.000 0.000 0.104
#> GSM617594 2 0.1179 0.7844 0.016 0.964 0.004 0.000 0.016
#> GSM617595 1 0.0404 0.6181 0.988 0.000 0.000 0.000 0.012
#> GSM617596 1 0.4855 -0.1910 0.544 0.016 0.004 0.000 0.436
#> GSM617597 3 0.5211 0.5738 0.232 0.000 0.668 0.000 0.100
#> GSM617598 1 0.2561 0.4784 0.856 0.000 0.000 0.000 0.144
#> GSM617599 2 0.3149 0.7380 0.080 0.872 0.004 0.012 0.032
#> GSM617600 3 0.0609 0.7316 0.000 0.000 0.980 0.000 0.020
#> GSM617601 2 0.4003 0.6414 0.000 0.740 0.008 0.244 0.008
#> GSM617602 3 0.3838 0.6180 0.004 0.000 0.716 0.000 0.280
#> GSM617603 4 0.1408 0.8475 0.000 0.044 0.000 0.948 0.008
#> GSM617604 5 0.6560 0.3447 0.416 0.012 0.140 0.000 0.432
#> GSM617605 4 0.0451 0.8636 0.000 0.008 0.000 0.988 0.004
#> GSM617606 2 0.8282 0.3737 0.008 0.436 0.164 0.172 0.220
#> GSM617610 1 0.0609 0.6154 0.980 0.000 0.000 0.000 0.020
#> GSM617611 1 0.0162 0.6191 0.996 0.000 0.000 0.000 0.004
#> GSM617613 3 0.0898 0.7307 0.000 0.000 0.972 0.008 0.020
#> GSM617614 3 0.4548 0.6878 0.096 0.000 0.748 0.000 0.156
#> GSM617621 1 0.4957 -0.2027 0.528 0.028 0.000 0.000 0.444
#> GSM617629 3 0.4651 0.4274 0.008 0.004 0.560 0.000 0.428
#> GSM617630 3 0.6810 0.2297 0.004 0.264 0.436 0.000 0.296
#> GSM617631 3 0.3282 0.6765 0.000 0.000 0.804 0.008 0.188
#> GSM617633 1 0.5099 0.2223 0.608 0.004 0.040 0.000 0.348
#> GSM617642 3 0.4035 0.7064 0.060 0.000 0.784 0.000 0.156
#> GSM617645 2 0.0324 0.7838 0.000 0.992 0.000 0.004 0.004
#> GSM617646 1 0.3016 0.5679 0.848 0.020 0.000 0.000 0.132
#> GSM617652 1 0.6256 0.1797 0.552 0.020 0.104 0.000 0.324
#> GSM617655 3 0.0510 0.7332 0.000 0.000 0.984 0.000 0.016
#> GSM617656 3 0.0671 0.7314 0.000 0.000 0.980 0.004 0.016
#> GSM617657 3 0.1106 0.7306 0.000 0.000 0.964 0.012 0.024
#> GSM617658 3 0.4367 0.5090 0.008 0.000 0.620 0.000 0.372
#> GSM617659 1 0.1282 0.6153 0.952 0.000 0.004 0.000 0.044
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM617581 5 0.6664 -0.03265 0.348 0.148 0.004 0.000 0.444 0.056
#> GSM617582 5 0.6354 0.33504 0.132 0.036 0.068 0.004 0.636 0.124
#> GSM617588 4 0.0692 0.81969 0.000 0.020 0.000 0.976 0.004 0.000
#> GSM617590 4 0.1265 0.81709 0.000 0.000 0.000 0.948 0.008 0.044
#> GSM617592 4 0.1116 0.81800 0.000 0.028 0.000 0.960 0.008 0.004
#> GSM617607 1 0.4315 0.36440 0.596 0.004 0.004 0.000 0.384 0.012
#> GSM617608 1 0.3492 0.51886 0.788 0.000 0.004 0.000 0.176 0.032
#> GSM617609 3 0.6023 0.11709 0.016 0.008 0.516 0.000 0.328 0.132
#> GSM617612 1 0.1434 0.64844 0.940 0.000 0.000 0.000 0.048 0.012
#> GSM617615 2 0.5988 0.09891 0.008 0.452 0.000 0.428 0.032 0.080
#> GSM617616 1 0.4566 0.24337 0.520 0.012 0.000 0.000 0.452 0.016
#> GSM617617 2 0.0820 0.69764 0.000 0.972 0.000 0.012 0.000 0.016
#> GSM617618 5 0.4744 0.03964 0.344 0.008 0.004 0.000 0.608 0.036
#> GSM617619 5 0.7636 -0.04079 0.004 0.172 0.316 0.004 0.348 0.156
#> GSM617620 4 0.0837 0.82003 0.000 0.020 0.000 0.972 0.004 0.004
#> GSM617622 2 0.4452 0.40848 0.000 0.644 0.000 0.312 0.040 0.004
#> GSM617623 5 0.6400 -0.05994 0.356 0.148 0.000 0.000 0.452 0.044
#> GSM617624 2 0.5569 0.46571 0.000 0.560 0.020 0.000 0.320 0.100
#> GSM617625 6 0.5361 0.59401 0.156 0.000 0.268 0.000 0.000 0.576
#> GSM617626 1 0.6079 0.09765 0.452 0.128 0.000 0.004 0.396 0.020
#> GSM617627 2 0.4710 0.57421 0.000 0.660 0.008 0.004 0.276 0.052
#> GSM617628 6 0.5240 0.59871 0.132 0.000 0.284 0.000 0.000 0.584
#> GSM617632 1 0.4901 0.27027 0.528 0.024 0.004 0.000 0.428 0.016
#> GSM617634 2 0.6176 0.40979 0.016 0.496 0.012 0.004 0.356 0.116
#> GSM617635 1 0.3620 0.37616 0.648 0.000 0.000 0.000 0.352 0.000
#> GSM617636 5 0.5393 0.22468 0.196 0.004 0.016 0.000 0.644 0.140
#> GSM617637 1 0.1444 0.64832 0.928 0.000 0.000 0.000 0.072 0.000
#> GSM617638 2 0.6171 0.34625 0.000 0.484 0.032 0.004 0.360 0.120
#> GSM617639 1 0.2146 0.62837 0.880 0.000 0.000 0.000 0.116 0.004
#> GSM617640 2 0.0777 0.69806 0.000 0.972 0.000 0.004 0.000 0.024
#> GSM617641 4 0.0976 0.82043 0.000 0.016 0.000 0.968 0.008 0.008
#> GSM617643 2 0.1951 0.68541 0.000 0.916 0.000 0.060 0.004 0.020
#> GSM617644 2 0.4106 0.43811 0.004 0.664 0.000 0.312 0.000 0.020
#> GSM617647 2 0.1592 0.69684 0.024 0.944 0.000 0.004 0.016 0.012
#> GSM617648 2 0.1974 0.69248 0.000 0.920 0.000 0.048 0.012 0.020
#> GSM617649 2 0.2933 0.69170 0.000 0.856 0.000 0.008 0.096 0.040
#> GSM617650 1 0.1092 0.64791 0.960 0.000 0.000 0.000 0.020 0.020
#> GSM617651 1 0.0937 0.64662 0.960 0.000 0.000 0.000 0.040 0.000
#> GSM617653 1 0.4184 0.31287 0.576 0.000 0.000 0.000 0.408 0.016
#> GSM617654 2 0.0653 0.69876 0.000 0.980 0.000 0.004 0.004 0.012
#> GSM617583 6 0.5052 0.62811 0.084 0.000 0.320 0.000 0.004 0.592
#> GSM617584 4 0.6538 0.25301 0.004 0.232 0.000 0.444 0.296 0.024
#> GSM617585 4 0.3799 0.72872 0.004 0.004 0.072 0.812 0.012 0.096
#> GSM617586 3 0.4290 -0.07661 0.004 0.000 0.612 0.000 0.020 0.364
#> GSM617587 3 0.7598 -0.01996 0.048 0.052 0.364 0.000 0.324 0.212
#> GSM617589 4 0.3584 0.70096 0.000 0.128 0.000 0.808 0.012 0.052
#> GSM617591 4 0.7629 -0.17433 0.004 0.340 0.028 0.340 0.064 0.224
#> GSM617593 1 0.2199 0.63456 0.892 0.000 0.000 0.000 0.088 0.020
#> GSM617594 2 0.3432 0.67673 0.016 0.832 0.004 0.012 0.120 0.016
#> GSM617595 1 0.0865 0.64711 0.964 0.000 0.000 0.000 0.036 0.000
#> GSM617596 1 0.4978 0.27145 0.496 0.008 0.000 0.000 0.448 0.048
#> GSM617597 6 0.7342 0.40813 0.204 0.000 0.280 0.000 0.132 0.384
#> GSM617598 1 0.2442 0.59804 0.852 0.000 0.000 0.000 0.144 0.004
#> GSM617599 2 0.5232 0.57716 0.052 0.676 0.000 0.016 0.220 0.036
#> GSM617600 3 0.0692 0.54274 0.000 0.000 0.976 0.000 0.004 0.020
#> GSM617601 2 0.5320 0.31095 0.000 0.552 0.004 0.372 0.024 0.048
#> GSM617602 6 0.5578 0.37538 0.000 0.000 0.360 0.000 0.148 0.492
#> GSM617603 4 0.1265 0.81543 0.000 0.000 0.000 0.948 0.008 0.044
#> GSM617604 1 0.7215 0.00528 0.380 0.004 0.096 0.000 0.336 0.184
#> GSM617605 4 0.1265 0.81709 0.000 0.000 0.000 0.948 0.008 0.044
#> GSM617606 2 0.8410 0.26803 0.004 0.336 0.048 0.196 0.208 0.208
#> GSM617610 1 0.1141 0.64429 0.948 0.000 0.000 0.000 0.052 0.000
#> GSM617611 1 0.0291 0.64895 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM617613 3 0.0146 0.54848 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM617614 6 0.5100 0.63455 0.068 0.000 0.288 0.000 0.020 0.624
#> GSM617621 1 0.4444 0.29993 0.496 0.012 0.004 0.000 0.484 0.004
#> GSM617629 5 0.6374 -0.20312 0.004 0.008 0.332 0.000 0.400 0.256
#> GSM617630 5 0.7453 0.04132 0.000 0.236 0.264 0.000 0.360 0.140
#> GSM617631 3 0.3744 0.28304 0.000 0.000 0.756 0.000 0.044 0.200
#> GSM617633 1 0.5661 0.08287 0.488 0.000 0.020 0.000 0.400 0.092
#> GSM617642 6 0.4784 0.61808 0.048 0.000 0.316 0.000 0.012 0.624
#> GSM617645 2 0.0458 0.69778 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM617646 1 0.3373 0.60054 0.808 0.020 0.004 0.000 0.160 0.008
#> GSM617652 1 0.6711 0.00129 0.420 0.004 0.084 0.000 0.384 0.108
#> GSM617655 3 0.3489 0.16291 0.000 0.000 0.708 0.000 0.004 0.288
#> GSM617656 3 0.0146 0.54919 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM617657 3 0.0837 0.53831 0.000 0.000 0.972 0.004 0.004 0.020
#> GSM617658 6 0.5514 0.45313 0.000 0.000 0.272 0.000 0.176 0.552
#> GSM617659 1 0.1434 0.64694 0.940 0.000 0.000 0.000 0.012 0.048
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:mclust 72 0.13652 2
#> MAD:mclust 65 0.01220 3
#> MAD:mclust 74 0.00558 4
#> MAD:mclust 51 0.01271 5
#> MAD:mclust 42 0.15494 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 79 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.841 0.916 0.962 0.5000 0.503 0.503
#> 3 3 0.491 0.656 0.830 0.3382 0.748 0.535
#> 4 4 0.404 0.456 0.673 0.1185 0.850 0.587
#> 5 5 0.498 0.465 0.689 0.0652 0.890 0.607
#> 6 6 0.590 0.456 0.690 0.0402 0.926 0.675
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
#> GSM617581 2 0.4022 0.9033 0.080 0.920
#> GSM617582 1 0.9996 0.0813 0.512 0.488
#> GSM617588 2 0.0000 0.9796 0.000 1.000
#> GSM617590 2 0.0000 0.9796 0.000 1.000
#> GSM617592 2 0.0000 0.9796 0.000 1.000
#> GSM617607 1 0.0000 0.9452 1.000 0.000
#> GSM617608 1 0.0000 0.9452 1.000 0.000
#> GSM617609 1 0.0000 0.9452 1.000 0.000
#> GSM617612 1 0.2043 0.9298 0.968 0.032
#> GSM617615 2 0.0000 0.9796 0.000 1.000
#> GSM617616 1 0.5842 0.8453 0.860 0.140
#> GSM617617 2 0.0000 0.9796 0.000 1.000
#> GSM617618 1 0.6048 0.8296 0.852 0.148
#> GSM617619 2 0.8555 0.6056 0.280 0.720
#> GSM617620 2 0.0000 0.9796 0.000 1.000
#> GSM617622 2 0.0000 0.9796 0.000 1.000
#> GSM617623 2 0.1414 0.9648 0.020 0.980
#> GSM617624 2 0.2423 0.9468 0.040 0.960
#> GSM617625 1 0.0000 0.9452 1.000 0.000
#> GSM617626 2 0.0376 0.9773 0.004 0.996
#> GSM617627 2 0.0000 0.9796 0.000 1.000
#> GSM617628 1 0.0000 0.9452 1.000 0.000
#> GSM617632 1 0.2043 0.9296 0.968 0.032
#> GSM617634 2 0.1414 0.9651 0.020 0.980
#> GSM617635 1 0.0000 0.9452 1.000 0.000
#> GSM617636 1 0.0000 0.9452 1.000 0.000
#> GSM617637 1 0.6438 0.8154 0.836 0.164
#> GSM617638 2 0.6712 0.7826 0.176 0.824
#> GSM617639 1 0.1184 0.9384 0.984 0.016
#> GSM617640 2 0.0000 0.9796 0.000 1.000
#> GSM617641 2 0.0000 0.9796 0.000 1.000
#> GSM617643 2 0.0000 0.9796 0.000 1.000
#> GSM617644 2 0.0000 0.9796 0.000 1.000
#> GSM617647 2 0.0000 0.9796 0.000 1.000
#> GSM617648 2 0.0000 0.9796 0.000 1.000
#> GSM617649 2 0.0000 0.9796 0.000 1.000
#> GSM617650 1 0.0000 0.9452 1.000 0.000
#> GSM617651 1 0.0000 0.9452 1.000 0.000
#> GSM617653 1 0.4161 0.8933 0.916 0.084
#> GSM617654 2 0.0000 0.9796 0.000 1.000
#> GSM617583 1 0.0000 0.9452 1.000 0.000
#> GSM617584 2 0.0000 0.9796 0.000 1.000
#> GSM617585 2 0.0376 0.9773 0.004 0.996
#> GSM617586 1 0.0000 0.9452 1.000 0.000
#> GSM617587 1 0.2948 0.9181 0.948 0.052
#> GSM617589 2 0.0000 0.9796 0.000 1.000
#> GSM617591 2 0.0000 0.9796 0.000 1.000
#> GSM617593 1 0.0000 0.9452 1.000 0.000
#> GSM617594 2 0.0000 0.9796 0.000 1.000
#> GSM617595 1 0.4298 0.8900 0.912 0.088
#> GSM617596 1 0.0376 0.9438 0.996 0.004
#> GSM617597 1 0.0000 0.9452 1.000 0.000
#> GSM617598 1 0.0000 0.9452 1.000 0.000
#> GSM617599 2 0.0376 0.9773 0.004 0.996
#> GSM617600 1 0.0000 0.9452 1.000 0.000
#> GSM617601 2 0.0000 0.9796 0.000 1.000
#> GSM617602 1 0.0000 0.9452 1.000 0.000
#> GSM617603 2 0.0000 0.9796 0.000 1.000
#> GSM617604 1 0.0000 0.9452 1.000 0.000
#> GSM617605 2 0.0000 0.9796 0.000 1.000
#> GSM617606 2 0.0376 0.9772 0.004 0.996
#> GSM617610 1 0.7602 0.7427 0.780 0.220
#> GSM617611 1 0.0000 0.9452 1.000 0.000
#> GSM617613 1 0.0376 0.9437 0.996 0.004
#> GSM617614 1 0.0000 0.9452 1.000 0.000
#> GSM617621 1 0.0376 0.9438 0.996 0.004
#> GSM617629 1 0.5629 0.8446 0.868 0.132
#> GSM617630 1 0.6973 0.7750 0.812 0.188
#> GSM617631 1 0.0000 0.9452 1.000 0.000
#> GSM617633 1 0.0000 0.9452 1.000 0.000
#> GSM617642 1 0.0000 0.9452 1.000 0.000
#> GSM617645 2 0.0000 0.9796 0.000 1.000
#> GSM617646 1 0.3114 0.9150 0.944 0.056
#> GSM617652 1 0.0000 0.9452 1.000 0.000
#> GSM617655 1 0.0376 0.9438 0.996 0.004
#> GSM617656 1 0.0000 0.9452 1.000 0.000
#> GSM617657 1 0.9996 0.0588 0.512 0.488
#> GSM617658 1 0.0000 0.9452 1.000 0.000
#> GSM617659 1 0.0000 0.9452 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM617581 1 0.6252 0.0138 0.556 0.444 0.000
#> GSM617582 1 0.9956 0.1318 0.380 0.312 0.308
#> GSM617588 2 0.3412 0.7833 0.124 0.876 0.000
#> GSM617590 2 0.1964 0.7730 0.000 0.944 0.056
#> GSM617592 2 0.3192 0.7884 0.112 0.888 0.000
#> GSM617607 3 0.6180 0.3036 0.416 0.000 0.584
#> GSM617608 3 0.5621 0.5499 0.308 0.000 0.692
#> GSM617609 3 0.1289 0.8180 0.000 0.032 0.968
#> GSM617612 1 0.1751 0.7561 0.960 0.012 0.028
#> GSM617615 2 0.0829 0.7921 0.012 0.984 0.004
#> GSM617616 1 0.1877 0.7482 0.956 0.032 0.012
#> GSM617617 2 0.6079 0.4675 0.388 0.612 0.000
#> GSM617618 1 0.5486 0.6553 0.780 0.024 0.196
#> GSM617619 3 0.6295 0.1851 0.000 0.472 0.528
#> GSM617620 2 0.2796 0.7948 0.092 0.908 0.000
#> GSM617622 2 0.2537 0.7979 0.080 0.920 0.000
#> GSM617623 1 0.5216 0.4761 0.740 0.260 0.000
#> GSM617624 2 0.5115 0.6695 0.016 0.796 0.188
#> GSM617625 3 0.2448 0.8009 0.076 0.000 0.924
#> GSM617626 1 0.4346 0.5954 0.816 0.184 0.000
#> GSM617627 2 0.1860 0.7752 0.000 0.948 0.052
#> GSM617628 3 0.1832 0.8184 0.036 0.008 0.956
#> GSM617632 1 0.3896 0.7119 0.864 0.008 0.128
#> GSM617634 2 0.4821 0.7691 0.120 0.840 0.040
#> GSM617635 1 0.4291 0.6621 0.820 0.000 0.180
#> GSM617636 3 0.4291 0.7234 0.180 0.000 0.820
#> GSM617637 1 0.1529 0.7370 0.960 0.040 0.000
#> GSM617638 2 0.6008 0.2964 0.000 0.628 0.372
#> GSM617639 1 0.1315 0.7547 0.972 0.008 0.020
#> GSM617640 2 0.5465 0.6459 0.288 0.712 0.000
#> GSM617641 2 0.1643 0.7973 0.044 0.956 0.000
#> GSM617643 2 0.4605 0.7330 0.204 0.796 0.000
#> GSM617644 2 0.2625 0.7969 0.084 0.916 0.000
#> GSM617647 1 0.6267 -0.0519 0.548 0.452 0.000
#> GSM617648 2 0.4887 0.7130 0.228 0.772 0.000
#> GSM617649 2 0.4540 0.7849 0.124 0.848 0.028
#> GSM617650 3 0.6062 0.3808 0.384 0.000 0.616
#> GSM617651 1 0.0747 0.7540 0.984 0.000 0.016
#> GSM617653 1 0.0747 0.7489 0.984 0.016 0.000
#> GSM617654 1 0.6295 -0.1276 0.528 0.472 0.000
#> GSM617583 3 0.1163 0.8169 0.028 0.000 0.972
#> GSM617584 2 0.5529 0.6340 0.296 0.704 0.000
#> GSM617585 2 0.5216 0.5551 0.000 0.740 0.260
#> GSM617586 3 0.1411 0.8175 0.000 0.036 0.964
#> GSM617587 3 0.1643 0.8167 0.000 0.044 0.956
#> GSM617589 2 0.2711 0.7944 0.088 0.912 0.000
#> GSM617591 2 0.3619 0.7180 0.000 0.864 0.136
#> GSM617593 1 0.6062 0.2935 0.616 0.000 0.384
#> GSM617594 2 0.6045 0.4938 0.380 0.620 0.000
#> GSM617595 1 0.0747 0.7488 0.984 0.016 0.000
#> GSM617596 1 0.5650 0.4708 0.688 0.000 0.312
#> GSM617597 3 0.2066 0.8065 0.060 0.000 0.940
#> GSM617598 1 0.3752 0.6920 0.856 0.000 0.144
#> GSM617599 2 0.6215 0.3836 0.428 0.572 0.000
#> GSM617600 3 0.2066 0.8094 0.000 0.060 0.940
#> GSM617601 2 0.1015 0.7896 0.008 0.980 0.012
#> GSM617602 3 0.1289 0.8184 0.000 0.032 0.968
#> GSM617603 2 0.1163 0.7827 0.000 0.972 0.028
#> GSM617604 3 0.4062 0.7306 0.164 0.000 0.836
#> GSM617605 2 0.1964 0.7730 0.000 0.944 0.056
#> GSM617606 2 0.3532 0.7451 0.008 0.884 0.108
#> GSM617610 1 0.1643 0.7344 0.956 0.044 0.000
#> GSM617611 1 0.5529 0.4965 0.704 0.000 0.296
#> GSM617613 3 0.4121 0.7498 0.000 0.168 0.832
#> GSM617614 3 0.1643 0.8115 0.044 0.000 0.956
#> GSM617621 1 0.2796 0.7342 0.908 0.000 0.092
#> GSM617629 3 0.4796 0.7035 0.000 0.220 0.780
#> GSM617630 3 0.4654 0.7156 0.000 0.208 0.792
#> GSM617631 3 0.2959 0.7912 0.000 0.100 0.900
#> GSM617633 3 0.4346 0.7177 0.184 0.000 0.816
#> GSM617642 3 0.0592 0.8189 0.012 0.000 0.988
#> GSM617645 2 0.5254 0.6746 0.264 0.736 0.000
#> GSM617646 1 0.3091 0.7498 0.912 0.016 0.072
#> GSM617652 3 0.2448 0.8005 0.076 0.000 0.924
#> GSM617655 3 0.3941 0.7583 0.000 0.156 0.844
#> GSM617656 3 0.0892 0.8191 0.000 0.020 0.980
#> GSM617657 3 0.5926 0.4855 0.000 0.356 0.644
#> GSM617658 3 0.0424 0.8189 0.008 0.000 0.992
#> GSM617659 3 0.5098 0.6348 0.248 0.000 0.752
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM617581 1 0.631 0.3151 0.604 0.068 0.004 0.324
#> GSM617582 1 0.963 0.1942 0.372 0.216 0.152 0.260
#> GSM617588 4 0.349 0.6302 0.044 0.092 0.000 0.864
#> GSM617590 4 0.194 0.6494 0.000 0.032 0.028 0.940
#> GSM617592 4 0.371 0.6148 0.112 0.040 0.000 0.848
#> GSM617607 2 0.790 -0.2502 0.300 0.372 0.328 0.000
#> GSM617608 3 0.678 0.4321 0.232 0.164 0.604 0.000
#> GSM617609 3 0.291 0.7114 0.000 0.092 0.888 0.020
#> GSM617612 1 0.788 0.4488 0.512 0.308 0.152 0.028
#> GSM617615 4 0.704 0.4018 0.028 0.348 0.068 0.556
#> GSM617616 1 0.540 0.4642 0.632 0.348 0.012 0.008
#> GSM617617 2 0.648 0.4616 0.088 0.576 0.000 0.336
#> GSM617618 1 0.763 0.3827 0.500 0.372 0.088 0.040
#> GSM617619 3 0.726 0.3231 0.000 0.204 0.540 0.256
#> GSM617620 4 0.308 0.6337 0.024 0.096 0.000 0.880
#> GSM617622 4 0.594 0.3882 0.044 0.268 0.016 0.672
#> GSM617623 1 0.596 0.4335 0.676 0.096 0.000 0.228
#> GSM617624 2 0.783 0.0868 0.024 0.424 0.132 0.420
#> GSM617625 3 0.557 0.6568 0.120 0.108 0.756 0.016
#> GSM617626 1 0.595 0.4806 0.692 0.184 0.000 0.124
#> GSM617627 4 0.703 -0.0954 0.000 0.404 0.120 0.476
#> GSM617628 3 0.536 0.6901 0.092 0.072 0.788 0.048
#> GSM617632 1 0.566 0.5530 0.732 0.188 0.064 0.016
#> GSM617634 2 0.731 0.2053 0.064 0.516 0.040 0.380
#> GSM617635 2 0.655 0.0784 0.276 0.608 0.116 0.000
#> GSM617636 1 0.787 0.1223 0.448 0.208 0.336 0.008
#> GSM617637 2 0.528 -0.1939 0.464 0.528 0.000 0.008
#> GSM617638 2 0.870 0.1213 0.056 0.428 0.192 0.324
#> GSM617639 1 0.522 0.3455 0.568 0.424 0.008 0.000
#> GSM617640 2 0.533 0.4084 0.016 0.604 0.000 0.380
#> GSM617641 4 0.200 0.6507 0.044 0.020 0.000 0.936
#> GSM617643 2 0.506 0.3944 0.008 0.624 0.000 0.368
#> GSM617644 4 0.478 0.2774 0.004 0.336 0.000 0.660
#> GSM617647 2 0.642 0.5096 0.152 0.648 0.000 0.200
#> GSM617648 2 0.551 0.2183 0.016 0.508 0.000 0.476
#> GSM617649 2 0.682 0.2763 0.004 0.512 0.088 0.396
#> GSM617650 3 0.661 0.2125 0.376 0.088 0.536 0.000
#> GSM617651 1 0.433 0.5430 0.712 0.288 0.000 0.000
#> GSM617653 1 0.310 0.5980 0.868 0.120 0.000 0.012
#> GSM617654 2 0.623 0.5209 0.124 0.660 0.000 0.216
#> GSM617583 3 0.579 0.6636 0.116 0.068 0.760 0.056
#> GSM617584 4 0.601 0.3924 0.268 0.080 0.000 0.652
#> GSM617585 4 0.519 0.5129 0.004 0.068 0.172 0.756
#> GSM617586 3 0.294 0.7246 0.024 0.032 0.908 0.036
#> GSM617587 3 0.388 0.7148 0.028 0.084 0.860 0.028
#> GSM617589 4 0.615 0.5171 0.088 0.244 0.004 0.664
#> GSM617591 4 0.745 0.4254 0.016 0.204 0.204 0.576
#> GSM617593 1 0.544 0.5588 0.732 0.092 0.176 0.000
#> GSM617594 2 0.645 0.4305 0.056 0.608 0.016 0.320
#> GSM617595 1 0.530 0.4757 0.612 0.372 0.016 0.000
#> GSM617596 1 0.430 0.5971 0.832 0.076 0.084 0.008
#> GSM617597 3 0.234 0.7128 0.080 0.008 0.912 0.000
#> GSM617598 1 0.417 0.6035 0.828 0.092 0.080 0.000
#> GSM617599 2 0.673 0.4536 0.112 0.564 0.000 0.324
#> GSM617600 3 0.235 0.7223 0.008 0.040 0.928 0.024
#> GSM617601 4 0.528 0.4704 0.000 0.252 0.044 0.704
#> GSM617602 3 0.657 0.6041 0.140 0.104 0.704 0.052
#> GSM617603 4 0.253 0.6438 0.008 0.072 0.008 0.912
#> GSM617604 1 0.744 0.1438 0.536 0.052 0.348 0.064
#> GSM617605 4 0.199 0.6528 0.020 0.024 0.012 0.944
#> GSM617606 4 0.507 0.5931 0.000 0.148 0.088 0.764
#> GSM617610 1 0.502 0.5074 0.656 0.332 0.000 0.012
#> GSM617611 1 0.792 0.3405 0.432 0.296 0.268 0.004
#> GSM617613 3 0.371 0.7101 0.008 0.052 0.864 0.076
#> GSM617614 3 0.294 0.7018 0.128 0.000 0.868 0.004
#> GSM617621 1 0.341 0.5967 0.876 0.088 0.024 0.012
#> GSM617629 3 0.882 0.3883 0.108 0.172 0.500 0.220
#> GSM617630 3 0.665 0.4919 0.004 0.236 0.628 0.132
#> GSM617631 3 0.395 0.7104 0.044 0.044 0.864 0.048
#> GSM617633 3 0.736 0.2807 0.176 0.332 0.492 0.000
#> GSM617642 3 0.417 0.6948 0.132 0.004 0.824 0.040
#> GSM617645 2 0.601 0.4589 0.028 0.632 0.020 0.320
#> GSM617646 2 0.588 0.0967 0.312 0.632 0.056 0.000
#> GSM617652 3 0.345 0.7073 0.080 0.052 0.868 0.000
#> GSM617655 3 0.337 0.7155 0.008 0.020 0.872 0.100
#> GSM617656 3 0.111 0.7247 0.016 0.008 0.972 0.004
#> GSM617657 3 0.727 0.4437 0.024 0.112 0.580 0.284
#> GSM617658 3 0.717 0.5145 0.252 0.092 0.616 0.040
#> GSM617659 3 0.527 0.4311 0.340 0.020 0.640 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM617581 5 0.7397 0.1123 0.260 0.040 0.000 0.260 0.440
#> GSM617582 5 0.4322 0.5010 0.044 0.012 0.036 0.092 0.816
#> GSM617588 4 0.4117 0.6491 0.020 0.164 0.000 0.788 0.028
#> GSM617590 4 0.2728 0.6700 0.000 0.040 0.004 0.888 0.068
#> GSM617592 4 0.4758 0.6357 0.048 0.068 0.000 0.776 0.108
#> GSM617607 2 0.7627 0.1985 0.176 0.476 0.256 0.000 0.092
#> GSM617608 3 0.5837 0.4460 0.316 0.028 0.608 0.012 0.036
#> GSM617609 3 0.3007 0.6918 0.000 0.104 0.864 0.004 0.028
#> GSM617612 1 0.5885 0.4795 0.704 0.040 0.168 0.056 0.032
#> GSM617615 4 0.7950 0.3846 0.160 0.208 0.124 0.496 0.012
#> GSM617616 5 0.6389 0.1806 0.348 0.124 0.004 0.008 0.516
#> GSM617617 2 0.3103 0.6903 0.012 0.872 0.000 0.072 0.044
#> GSM617618 5 0.5725 0.4314 0.196 0.080 0.012 0.024 0.688
#> GSM617619 3 0.7338 0.3600 0.000 0.160 0.544 0.112 0.184
#> GSM617620 4 0.4221 0.6540 0.008 0.160 0.000 0.780 0.052
#> GSM617622 4 0.6667 0.4034 0.004 0.248 0.000 0.480 0.268
#> GSM617623 5 0.7398 -0.0253 0.356 0.044 0.000 0.196 0.404
#> GSM617624 2 0.5852 0.5895 0.000 0.688 0.056 0.108 0.148
#> GSM617625 3 0.5370 0.5642 0.256 0.000 0.668 0.048 0.028
#> GSM617626 1 0.7252 0.2576 0.480 0.088 0.000 0.104 0.328
#> GSM617627 2 0.5082 0.5959 0.000 0.732 0.096 0.152 0.020
#> GSM617628 3 0.5913 0.5677 0.208 0.000 0.648 0.120 0.024
#> GSM617632 5 0.4844 0.3440 0.236 0.036 0.008 0.008 0.712
#> GSM617634 5 0.6997 0.0162 0.020 0.340 0.004 0.172 0.464
#> GSM617635 2 0.4326 0.6139 0.080 0.776 0.140 0.000 0.004
#> GSM617636 5 0.3597 0.4984 0.052 0.024 0.076 0.000 0.848
#> GSM617637 2 0.5338 0.3484 0.308 0.632 0.004 0.008 0.048
#> GSM617638 2 0.6570 0.3060 0.000 0.504 0.056 0.068 0.372
#> GSM617639 2 0.6169 -0.0813 0.420 0.484 0.012 0.004 0.080
#> GSM617640 2 0.2102 0.6956 0.000 0.916 0.004 0.068 0.012
#> GSM617641 4 0.3879 0.6729 0.020 0.088 0.000 0.828 0.064
#> GSM617643 2 0.3334 0.6691 0.008 0.844 0.008 0.128 0.012
#> GSM617644 2 0.5960 -0.0322 0.028 0.468 0.000 0.456 0.048
#> GSM617647 2 0.1787 0.6982 0.032 0.940 0.000 0.016 0.012
#> GSM617648 2 0.6331 0.4045 0.016 0.584 0.000 0.232 0.168
#> GSM617649 2 0.4017 0.6634 0.000 0.812 0.056 0.116 0.016
#> GSM617650 3 0.6401 0.1843 0.352 0.044 0.532 0.000 0.072
#> GSM617651 1 0.3966 0.5867 0.836 0.076 0.020 0.012 0.056
#> GSM617653 1 0.5347 0.4809 0.680 0.020 0.004 0.052 0.244
#> GSM617654 2 0.1862 0.7017 0.016 0.940 0.004 0.012 0.028
#> GSM617583 3 0.5608 0.5859 0.200 0.004 0.680 0.100 0.016
#> GSM617584 4 0.6742 0.4033 0.140 0.060 0.000 0.588 0.212
#> GSM617585 4 0.5212 0.5339 0.000 0.020 0.060 0.692 0.228
#> GSM617586 3 0.1498 0.7218 0.024 0.008 0.952 0.016 0.000
#> GSM617587 3 0.3206 0.7087 0.024 0.060 0.876 0.036 0.004
#> GSM617589 4 0.5245 0.4571 0.296 0.016 0.008 0.652 0.028
#> GSM617591 4 0.7551 0.1910 0.108 0.088 0.332 0.464 0.008
#> GSM617593 1 0.7164 0.4816 0.564 0.096 0.116 0.004 0.220
#> GSM617594 2 0.3716 0.6821 0.036 0.844 0.048 0.072 0.000
#> GSM617595 1 0.4886 0.4885 0.736 0.200 0.036 0.016 0.012
#> GSM617596 5 0.5393 0.1175 0.356 0.008 0.012 0.028 0.596
#> GSM617597 3 0.1300 0.7189 0.028 0.000 0.956 0.000 0.016
#> GSM617598 1 0.4190 0.5610 0.768 0.000 0.060 0.000 0.172
#> GSM617599 2 0.4519 0.6548 0.052 0.784 0.000 0.128 0.036
#> GSM617600 3 0.1591 0.7127 0.000 0.004 0.940 0.004 0.052
#> GSM617601 4 0.6205 0.1481 0.004 0.412 0.084 0.488 0.012
#> GSM617602 5 0.4734 0.2772 0.008 0.000 0.344 0.016 0.632
#> GSM617603 4 0.4635 0.6181 0.004 0.064 0.004 0.748 0.180
#> GSM617604 5 0.6772 0.2013 0.284 0.008 0.048 0.096 0.564
#> GSM617605 4 0.3339 0.6549 0.000 0.040 0.000 0.836 0.124
#> GSM617606 4 0.5925 0.5864 0.136 0.040 0.024 0.708 0.092
#> GSM617610 1 0.3469 0.5779 0.856 0.088 0.012 0.008 0.036
#> GSM617611 1 0.5961 -0.0403 0.520 0.056 0.404 0.008 0.012
#> GSM617613 3 0.3646 0.6716 0.000 0.008 0.828 0.044 0.120
#> GSM617614 3 0.3622 0.6875 0.068 0.000 0.832 0.004 0.096
#> GSM617621 1 0.5788 0.1692 0.472 0.052 0.000 0.016 0.460
#> GSM617629 5 0.5601 0.4450 0.000 0.024 0.196 0.100 0.680
#> GSM617630 3 0.6770 0.2785 0.000 0.304 0.532 0.044 0.120
#> GSM617631 3 0.4229 0.5307 0.000 0.000 0.704 0.020 0.276
#> GSM617633 5 0.7601 0.1936 0.052 0.236 0.308 0.000 0.404
#> GSM617642 3 0.3738 0.7025 0.064 0.000 0.844 0.040 0.052
#> GSM617645 2 0.2061 0.7011 0.004 0.928 0.024 0.040 0.004
#> GSM617646 2 0.4023 0.6312 0.144 0.800 0.048 0.004 0.004
#> GSM617652 3 0.2787 0.7050 0.028 0.088 0.880 0.000 0.004
#> GSM617655 3 0.1857 0.7218 0.000 0.004 0.928 0.060 0.008
#> GSM617656 3 0.0963 0.7181 0.000 0.000 0.964 0.000 0.036
#> GSM617657 3 0.6394 0.1330 0.000 0.008 0.464 0.132 0.396
#> GSM617658 5 0.5073 0.4601 0.040 0.000 0.220 0.032 0.708
#> GSM617659 3 0.5951 0.1534 0.364 0.000 0.520 0.000 0.116
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM617581 1 0.467 0.36207 0.624 0.004 0.004 0.332 0.032 0.004
#> GSM617582 5 0.322 0.63808 0.060 0.000 0.000 0.020 0.848 0.072
#> GSM617588 4 0.378 0.49274 0.000 0.080 0.000 0.812 0.032 0.076
#> GSM617590 4 0.329 0.50610 0.000 0.024 0.020 0.860 0.052 0.044
#> GSM617592 4 0.317 0.50804 0.128 0.020 0.000 0.836 0.008 0.008
#> GSM617607 2 0.697 0.38217 0.120 0.556 0.188 0.000 0.096 0.040
#> GSM617608 3 0.691 0.31987 0.096 0.040 0.432 0.000 0.052 0.380
#> GSM617609 3 0.288 0.66694 0.000 0.152 0.832 0.000 0.008 0.008
#> GSM617612 1 0.702 0.32315 0.508 0.032 0.192 0.040 0.004 0.224
#> GSM617615 6 0.659 0.16181 0.000 0.080 0.084 0.340 0.012 0.484
#> GSM617616 5 0.558 0.51517 0.076 0.036 0.004 0.004 0.628 0.252
#> GSM617617 2 0.459 0.62028 0.012 0.764 0.000 0.060 0.116 0.048
#> GSM617618 5 0.340 0.63463 0.036 0.016 0.000 0.008 0.836 0.104
#> GSM617619 3 0.697 0.35851 0.000 0.148 0.536 0.128 0.172 0.016
#> GSM617620 4 0.225 0.54108 0.032 0.064 0.000 0.900 0.004 0.000
#> GSM617622 4 0.712 0.30723 0.068 0.156 0.000 0.536 0.188 0.052
#> GSM617623 1 0.439 0.47307 0.696 0.012 0.000 0.256 0.032 0.004
#> GSM617624 2 0.516 0.58334 0.000 0.704 0.040 0.076 0.168 0.012
#> GSM617625 3 0.429 0.60327 0.028 0.000 0.692 0.008 0.004 0.268
#> GSM617626 1 0.459 0.60033 0.780 0.040 0.000 0.084 0.048 0.048
#> GSM617627 2 0.492 0.55324 0.000 0.704 0.116 0.160 0.012 0.008
#> GSM617628 3 0.506 0.32797 0.016 0.000 0.480 0.032 0.004 0.468
#> GSM617632 5 0.457 0.42420 0.304 0.016 0.004 0.024 0.652 0.000
#> GSM617634 5 0.534 0.47164 0.004 0.108 0.000 0.032 0.668 0.188
#> GSM617635 2 0.414 0.62432 0.040 0.804 0.092 0.000 0.024 0.040
#> GSM617636 5 0.297 0.64393 0.116 0.012 0.024 0.000 0.848 0.000
#> GSM617637 2 0.557 0.44333 0.244 0.620 0.008 0.000 0.020 0.108
#> GSM617638 2 0.581 0.32810 0.008 0.552 0.028 0.052 0.348 0.012
#> GSM617639 2 0.533 0.16306 0.436 0.504 0.024 0.012 0.008 0.016
#> GSM617640 2 0.256 0.66225 0.008 0.880 0.004 0.096 0.004 0.008
#> GSM617641 4 0.162 0.54241 0.040 0.020 0.000 0.936 0.004 0.000
#> GSM617643 2 0.467 0.59825 0.000 0.744 0.000 0.104 0.048 0.104
#> GSM617644 6 0.763 -0.07087 0.000 0.292 0.000 0.180 0.228 0.300
#> GSM617647 2 0.349 0.66412 0.056 0.840 0.000 0.064 0.004 0.036
#> GSM617648 5 0.709 -0.10983 0.004 0.364 0.000 0.076 0.364 0.192
#> GSM617649 2 0.567 0.57680 0.000 0.684 0.084 0.148 0.044 0.040
#> GSM617650 3 0.606 0.40507 0.296 0.024 0.568 0.000 0.036 0.076
#> GSM617651 1 0.541 0.32784 0.496 0.032 0.008 0.000 0.032 0.432
#> GSM617653 1 0.281 0.62070 0.876 0.000 0.000 0.040 0.024 0.060
#> GSM617654 2 0.273 0.66866 0.028 0.892 0.000 0.036 0.024 0.020
#> GSM617583 3 0.457 0.63483 0.036 0.000 0.732 0.044 0.004 0.184
#> GSM617584 4 0.432 0.19038 0.380 0.008 0.000 0.600 0.008 0.004
#> GSM617585 4 0.631 0.12863 0.000 0.020 0.040 0.476 0.384 0.080
#> GSM617586 3 0.146 0.70887 0.000 0.020 0.948 0.016 0.000 0.016
#> GSM617587 3 0.237 0.69322 0.000 0.084 0.892 0.012 0.004 0.008
#> GSM617589 6 0.414 0.25869 0.004 0.000 0.016 0.284 0.008 0.688
#> GSM617591 4 0.637 -0.03059 0.000 0.040 0.376 0.452 0.004 0.128
#> GSM617593 1 0.473 0.54870 0.768 0.072 0.084 0.000 0.044 0.032
#> GSM617594 2 0.631 0.54599 0.008 0.636 0.056 0.136 0.028 0.136
#> GSM617595 6 0.657 -0.26174 0.372 0.164 0.032 0.000 0.008 0.424
#> GSM617596 1 0.422 0.42151 0.660 0.000 0.000 0.036 0.304 0.000
#> GSM617597 3 0.151 0.71433 0.016 0.012 0.948 0.000 0.020 0.004
#> GSM617598 1 0.518 0.48962 0.624 0.000 0.040 0.000 0.048 0.288
#> GSM617599 2 0.690 0.25704 0.004 0.476 0.004 0.064 0.180 0.272
#> GSM617600 3 0.220 0.70511 0.000 0.016 0.896 0.004 0.084 0.000
#> GSM617601 4 0.678 0.16867 0.000 0.252 0.084 0.532 0.020 0.112
#> GSM617602 5 0.309 0.60549 0.024 0.000 0.148 0.004 0.824 0.000
#> GSM617603 4 0.633 0.13113 0.000 0.032 0.000 0.492 0.280 0.196
#> GSM617604 1 0.485 0.56788 0.712 0.000 0.016 0.136 0.132 0.004
#> GSM617605 4 0.263 0.54058 0.028 0.016 0.008 0.896 0.048 0.004
#> GSM617606 6 0.662 0.13742 0.000 0.036 0.032 0.352 0.104 0.476
#> GSM617610 1 0.535 0.34564 0.536 0.044 0.016 0.000 0.012 0.392
#> GSM617611 3 0.695 0.28268 0.204 0.064 0.432 0.000 0.004 0.296
#> GSM617613 3 0.359 0.64945 0.000 0.012 0.796 0.024 0.164 0.004
#> GSM617614 3 0.377 0.69512 0.072 0.000 0.816 0.004 0.084 0.024
#> GSM617621 1 0.300 0.61409 0.860 0.016 0.004 0.092 0.028 0.000
#> GSM617629 5 0.176 0.64552 0.004 0.012 0.028 0.020 0.936 0.000
#> GSM617630 3 0.658 -0.00636 0.000 0.416 0.428 0.072 0.056 0.028
#> GSM617631 3 0.437 0.48890 0.004 0.000 0.664 0.024 0.300 0.008
#> GSM617633 5 0.473 0.58102 0.016 0.152 0.040 0.000 0.744 0.048
#> GSM617642 3 0.245 0.70993 0.044 0.000 0.904 0.020 0.016 0.016
#> GSM617645 2 0.344 0.65633 0.020 0.840 0.028 0.100 0.004 0.008
#> GSM617646 2 0.414 0.63350 0.072 0.796 0.048 0.000 0.004 0.080
#> GSM617652 3 0.294 0.68106 0.012 0.124 0.848 0.000 0.012 0.004
#> GSM617655 3 0.167 0.70810 0.000 0.000 0.936 0.036 0.020 0.008
#> GSM617656 3 0.115 0.71068 0.000 0.000 0.952 0.004 0.044 0.000
#> GSM617657 5 0.630 0.06569 0.000 0.036 0.396 0.084 0.464 0.020
#> GSM617658 5 0.501 0.54374 0.176 0.000 0.112 0.012 0.692 0.008
#> GSM617659 3 0.538 0.39800 0.328 0.000 0.580 0.000 0.048 0.044
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:NMF 77 0.01538 2
#> MAD:NMF 63 0.00367 3
#> MAD:NMF 37 0.07309 4
#> MAD:NMF 41 0.07209 5
#> MAD:NMF 43 0.02427 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 79 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 0.436 0.731 0.884 0.3241 0.739 0.739
#> 3 3 0.524 0.714 0.833 0.7938 0.631 0.520
#> 4 4 0.498 0.528 0.745 0.1802 0.823 0.608
#> 5 5 0.562 0.524 0.741 0.0986 0.822 0.487
#> 6 6 0.580 0.497 0.739 0.0282 0.982 0.919
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
#> GSM617581 1 0.833 0.6426 0.736 0.264
#> GSM617582 1 0.760 0.6980 0.780 0.220
#> GSM617588 2 0.000 0.8319 0.000 1.000
#> GSM617590 2 0.311 0.8189 0.056 0.944
#> GSM617592 2 0.000 0.8319 0.000 1.000
#> GSM617607 1 0.000 0.8542 1.000 0.000
#> GSM617608 1 0.000 0.8542 1.000 0.000
#> GSM617609 1 0.000 0.8542 1.000 0.000
#> GSM617612 1 0.000 0.8542 1.000 0.000
#> GSM617615 1 0.978 0.3794 0.588 0.412
#> GSM617616 1 0.000 0.8542 1.000 0.000
#> GSM617617 1 0.895 0.5773 0.688 0.312
#> GSM617618 1 0.506 0.7895 0.888 0.112
#> GSM617619 1 0.745 0.7060 0.788 0.212
#> GSM617620 2 0.000 0.8319 0.000 1.000
#> GSM617622 1 0.987 0.3296 0.568 0.432
#> GSM617623 1 0.833 0.6426 0.736 0.264
#> GSM617624 1 0.634 0.7560 0.840 0.160
#> GSM617625 1 0.000 0.8542 1.000 0.000
#> GSM617626 1 0.000 0.8542 1.000 0.000
#> GSM617627 1 0.662 0.7449 0.828 0.172
#> GSM617628 1 0.000 0.8542 1.000 0.000
#> GSM617632 1 0.000 0.8542 1.000 0.000
#> GSM617634 1 0.518 0.7885 0.884 0.116
#> GSM617635 1 0.000 0.8542 1.000 0.000
#> GSM617636 1 0.000 0.8542 1.000 0.000
#> GSM617637 1 0.000 0.8542 1.000 0.000
#> GSM617638 1 0.584 0.7706 0.860 0.140
#> GSM617639 1 0.000 0.8542 1.000 0.000
#> GSM617640 1 0.917 0.5441 0.668 0.332
#> GSM617641 2 0.000 0.8319 0.000 1.000
#> GSM617643 1 0.990 0.3076 0.560 0.440
#> GSM617644 1 0.990 0.3076 0.560 0.440
#> GSM617647 1 0.990 0.3076 0.560 0.440
#> GSM617648 1 0.990 0.3076 0.560 0.440
#> GSM617649 1 0.990 0.3076 0.560 0.440
#> GSM617650 1 0.000 0.8542 1.000 0.000
#> GSM617651 1 0.000 0.8542 1.000 0.000
#> GSM617653 1 0.000 0.8542 1.000 0.000
#> GSM617654 1 0.917 0.5441 0.668 0.332
#> GSM617583 1 0.000 0.8542 1.000 0.000
#> GSM617584 2 0.844 0.6017 0.272 0.728
#> GSM617585 2 0.895 0.5398 0.312 0.688
#> GSM617586 1 0.000 0.8542 1.000 0.000
#> GSM617587 1 0.625 0.7596 0.844 0.156
#> GSM617589 2 0.000 0.8319 0.000 1.000
#> GSM617591 2 0.994 0.0897 0.456 0.544
#> GSM617593 1 0.000 0.8542 1.000 0.000
#> GSM617594 1 0.981 0.3601 0.580 0.420
#> GSM617595 1 0.000 0.8542 1.000 0.000
#> GSM617596 1 0.000 0.8542 1.000 0.000
#> GSM617597 1 0.000 0.8542 1.000 0.000
#> GSM617598 1 0.000 0.8542 1.000 0.000
#> GSM617599 1 0.981 0.3601 0.580 0.420
#> GSM617600 1 0.000 0.8542 1.000 0.000
#> GSM617601 1 0.969 0.4155 0.604 0.396
#> GSM617602 1 0.000 0.8542 1.000 0.000
#> GSM617603 2 0.000 0.8319 0.000 1.000
#> GSM617604 1 0.000 0.8542 1.000 0.000
#> GSM617605 2 0.311 0.8189 0.056 0.944
#> GSM617606 2 0.895 0.5398 0.312 0.688
#> GSM617610 1 0.000 0.8542 1.000 0.000
#> GSM617611 1 0.000 0.8542 1.000 0.000
#> GSM617613 1 0.000 0.8542 1.000 0.000
#> GSM617614 1 0.000 0.8542 1.000 0.000
#> GSM617621 1 0.000 0.8542 1.000 0.000
#> GSM617629 1 0.000 0.8542 1.000 0.000
#> GSM617630 1 0.871 0.6046 0.708 0.292
#> GSM617631 1 0.000 0.8542 1.000 0.000
#> GSM617633 1 0.000 0.8542 1.000 0.000
#> GSM617642 1 0.000 0.8542 1.000 0.000
#> GSM617645 1 0.917 0.5441 0.668 0.332
#> GSM617646 1 0.000 0.8542 1.000 0.000
#> GSM617652 1 0.000 0.8542 1.000 0.000
#> GSM617655 1 0.000 0.8542 1.000 0.000
#> GSM617656 1 0.000 0.8542 1.000 0.000
#> GSM617657 1 0.000 0.8542 1.000 0.000
#> GSM617658 1 0.000 0.8542 1.000 0.000
#> GSM617659 1 0.000 0.8542 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM617581 2 0.2165 0.6727 0.064 0.936 0.000
#> GSM617582 2 0.8054 0.4813 0.356 0.568 0.076
#> GSM617588 3 0.0424 0.9801 0.000 0.008 0.992
#> GSM617590 3 0.2165 0.9370 0.000 0.064 0.936
#> GSM617592 3 0.0424 0.9801 0.000 0.008 0.992
#> GSM617607 1 0.0747 0.8511 0.984 0.016 0.000
#> GSM617608 1 0.0424 0.8503 0.992 0.008 0.000
#> GSM617609 1 0.0747 0.8511 0.984 0.016 0.000
#> GSM617612 1 0.5138 0.7304 0.748 0.252 0.000
#> GSM617615 2 0.5791 0.7312 0.060 0.792 0.148
#> GSM617616 1 0.0747 0.8511 0.984 0.016 0.000
#> GSM617617 2 0.5371 0.6986 0.140 0.812 0.048
#> GSM617618 1 0.6451 0.0587 0.560 0.436 0.004
#> GSM617619 2 0.7953 0.4623 0.368 0.564 0.068
#> GSM617620 3 0.0424 0.9801 0.000 0.008 0.992
#> GSM617622 2 0.5524 0.7259 0.040 0.796 0.164
#> GSM617623 2 0.2165 0.6727 0.064 0.936 0.000
#> GSM617624 2 0.6819 0.2100 0.476 0.512 0.012
#> GSM617625 1 0.1453 0.8416 0.968 0.024 0.008
#> GSM617626 1 0.5138 0.7304 0.748 0.252 0.000
#> GSM617627 2 0.6804 0.2659 0.460 0.528 0.012
#> GSM617628 1 0.1453 0.8416 0.968 0.024 0.008
#> GSM617632 1 0.1753 0.8479 0.952 0.048 0.000
#> GSM617634 1 0.6509 -0.0551 0.524 0.472 0.004
#> GSM617635 1 0.1860 0.8470 0.948 0.052 0.000
#> GSM617636 1 0.1753 0.8479 0.952 0.048 0.000
#> GSM617637 1 0.2066 0.8450 0.940 0.060 0.000
#> GSM617638 2 0.6314 0.3767 0.392 0.604 0.004
#> GSM617639 1 0.5138 0.7304 0.748 0.252 0.000
#> GSM617640 2 0.2749 0.7019 0.012 0.924 0.064
#> GSM617641 3 0.0424 0.9801 0.000 0.008 0.992
#> GSM617643 2 0.5412 0.7217 0.032 0.796 0.172
#> GSM617644 2 0.5412 0.7217 0.032 0.796 0.172
#> GSM617647 2 0.5412 0.7217 0.032 0.796 0.172
#> GSM617648 2 0.5412 0.7217 0.032 0.796 0.172
#> GSM617649 2 0.5412 0.7217 0.032 0.796 0.172
#> GSM617650 1 0.1411 0.8508 0.964 0.036 0.000
#> GSM617651 1 0.6244 0.4605 0.560 0.440 0.000
#> GSM617653 1 0.6244 0.4605 0.560 0.440 0.000
#> GSM617654 2 0.2749 0.7019 0.012 0.924 0.064
#> GSM617583 1 0.1453 0.8416 0.968 0.024 0.008
#> GSM617584 2 0.6664 0.3041 0.008 0.528 0.464
#> GSM617585 2 0.6771 0.3260 0.012 0.548 0.440
#> GSM617586 1 0.1878 0.8373 0.952 0.044 0.004
#> GSM617587 2 0.7021 0.3184 0.436 0.544 0.020
#> GSM617589 3 0.0424 0.9801 0.000 0.008 0.992
#> GSM617591 2 0.8028 0.5551 0.096 0.616 0.288
#> GSM617593 1 0.1411 0.8508 0.964 0.036 0.000
#> GSM617594 2 0.5852 0.7302 0.060 0.788 0.152
#> GSM617595 1 0.5138 0.7304 0.748 0.252 0.000
#> GSM617596 1 0.6244 0.4605 0.560 0.440 0.000
#> GSM617597 1 0.0983 0.8508 0.980 0.016 0.004
#> GSM617598 1 0.4974 0.7421 0.764 0.236 0.000
#> GSM617599 2 0.5852 0.7302 0.060 0.788 0.152
#> GSM617600 1 0.1453 0.8416 0.968 0.024 0.008
#> GSM617601 2 0.6286 0.7274 0.092 0.772 0.136
#> GSM617602 1 0.1453 0.8416 0.968 0.024 0.008
#> GSM617603 3 0.0424 0.9801 0.000 0.008 0.992
#> GSM617604 1 0.6244 0.4605 0.560 0.440 0.000
#> GSM617605 3 0.2165 0.9370 0.000 0.064 0.936
#> GSM617606 2 0.6771 0.3260 0.012 0.548 0.440
#> GSM617610 1 0.5138 0.7304 0.748 0.252 0.000
#> GSM617611 1 0.1411 0.8508 0.964 0.036 0.000
#> GSM617613 1 0.1453 0.8416 0.968 0.024 0.008
#> GSM617614 1 0.1031 0.8516 0.976 0.024 0.000
#> GSM617621 1 0.5138 0.7304 0.748 0.252 0.000
#> GSM617629 1 0.3965 0.7697 0.860 0.132 0.008
#> GSM617630 2 0.2903 0.7089 0.048 0.924 0.028
#> GSM617631 1 0.1453 0.8416 0.968 0.024 0.008
#> GSM617633 1 0.1163 0.8518 0.972 0.028 0.000
#> GSM617642 1 0.1411 0.8508 0.964 0.036 0.000
#> GSM617645 2 0.2749 0.7019 0.012 0.924 0.064
#> GSM617646 1 0.5138 0.7304 0.748 0.252 0.000
#> GSM617652 1 0.0747 0.8511 0.984 0.016 0.000
#> GSM617655 1 0.1453 0.8416 0.968 0.024 0.008
#> GSM617656 1 0.1453 0.8416 0.968 0.024 0.008
#> GSM617657 1 0.4531 0.7363 0.824 0.168 0.008
#> GSM617658 1 0.1453 0.8416 0.968 0.024 0.008
#> GSM617659 1 0.1411 0.8508 0.964 0.036 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM617581 1 0.4866 -0.3542 0.596 0.404 0.000 0.000
#> GSM617582 2 0.6505 0.4609 0.064 0.572 0.356 0.008
#> GSM617588 4 0.0592 0.8644 0.000 0.016 0.000 0.984
#> GSM617590 4 0.3311 0.7757 0.000 0.172 0.000 0.828
#> GSM617592 4 0.0592 0.8644 0.000 0.016 0.000 0.984
#> GSM617607 3 0.3498 0.6511 0.160 0.008 0.832 0.000
#> GSM617608 3 0.3172 0.6494 0.160 0.000 0.840 0.000
#> GSM617609 3 0.3498 0.6511 0.160 0.008 0.832 0.000
#> GSM617612 1 0.4406 0.6378 0.700 0.000 0.300 0.000
#> GSM617615 2 0.1762 0.7024 0.012 0.952 0.020 0.016
#> GSM617616 3 0.3498 0.6511 0.160 0.008 0.832 0.000
#> GSM617617 2 0.6198 0.6243 0.224 0.660 0.116 0.000
#> GSM617618 3 0.5805 0.0802 0.036 0.388 0.576 0.000
#> GSM617619 2 0.6290 0.4453 0.068 0.568 0.364 0.000
#> GSM617620 4 0.0592 0.8644 0.000 0.016 0.000 0.984
#> GSM617622 2 0.0844 0.6997 0.004 0.980 0.004 0.012
#> GSM617623 1 0.4866 -0.3542 0.596 0.404 0.000 0.000
#> GSM617624 3 0.5861 -0.2077 0.032 0.480 0.488 0.000
#> GSM617625 3 0.2530 0.6520 0.112 0.000 0.888 0.000
#> GSM617626 1 0.4406 0.6378 0.700 0.000 0.300 0.000
#> GSM617627 2 0.6149 0.1926 0.048 0.480 0.472 0.000
#> GSM617628 3 0.1940 0.6639 0.076 0.000 0.924 0.000
#> GSM617632 3 0.4981 0.2424 0.464 0.000 0.536 0.000
#> GSM617634 3 0.5738 -0.0654 0.028 0.432 0.540 0.000
#> GSM617635 3 0.4985 0.2261 0.468 0.000 0.532 0.000
#> GSM617636 3 0.4955 0.2811 0.444 0.000 0.556 0.000
#> GSM617637 3 0.4994 0.1853 0.480 0.000 0.520 0.000
#> GSM617638 2 0.7502 0.3501 0.188 0.456 0.356 0.000
#> GSM617639 1 0.4406 0.6378 0.700 0.000 0.300 0.000
#> GSM617640 2 0.4605 0.5862 0.336 0.664 0.000 0.000
#> GSM617641 4 0.0592 0.8644 0.000 0.016 0.000 0.984
#> GSM617643 2 0.0469 0.6965 0.000 0.988 0.000 0.012
#> GSM617644 2 0.0469 0.6965 0.000 0.988 0.000 0.012
#> GSM617647 2 0.0469 0.6965 0.000 0.988 0.000 0.012
#> GSM617648 2 0.0469 0.6965 0.000 0.988 0.000 0.012
#> GSM617649 2 0.0469 0.6965 0.000 0.988 0.000 0.012
#> GSM617650 3 0.4972 0.2609 0.456 0.000 0.544 0.000
#> GSM617651 1 0.2773 0.6341 0.880 0.004 0.116 0.000
#> GSM617653 1 0.2773 0.6341 0.880 0.004 0.116 0.000
#> GSM617654 2 0.4605 0.5862 0.336 0.664 0.000 0.000
#> GSM617583 3 0.2408 0.6524 0.104 0.000 0.896 0.000
#> GSM617584 4 0.7182 -0.1318 0.136 0.412 0.000 0.452
#> GSM617585 2 0.6937 0.2939 0.100 0.556 0.008 0.336
#> GSM617586 3 0.3080 0.6626 0.096 0.024 0.880 0.000
#> GSM617587 2 0.6285 0.2836 0.060 0.528 0.412 0.000
#> GSM617589 4 0.0707 0.8638 0.000 0.020 0.000 0.980
#> GSM617591 2 0.7704 0.5210 0.096 0.608 0.088 0.208
#> GSM617593 3 0.4972 0.2609 0.456 0.000 0.544 0.000
#> GSM617594 2 0.1471 0.7024 0.004 0.960 0.024 0.012
#> GSM617595 1 0.4406 0.6378 0.700 0.000 0.300 0.000
#> GSM617596 1 0.2773 0.6341 0.880 0.004 0.116 0.000
#> GSM617597 3 0.2973 0.6565 0.144 0.000 0.856 0.000
#> GSM617598 1 0.4500 0.5996 0.684 0.000 0.316 0.000
#> GSM617599 2 0.1471 0.7024 0.004 0.960 0.024 0.012
#> GSM617600 3 0.0336 0.6445 0.008 0.000 0.992 0.000
#> GSM617601 2 0.2522 0.6947 0.012 0.920 0.052 0.016
#> GSM617602 3 0.0000 0.6488 0.000 0.000 1.000 0.000
#> GSM617603 4 0.1940 0.8381 0.000 0.076 0.000 0.924
#> GSM617604 1 0.2773 0.6341 0.880 0.004 0.116 0.000
#> GSM617605 4 0.3311 0.7757 0.000 0.172 0.000 0.828
#> GSM617606 2 0.6937 0.2939 0.100 0.556 0.008 0.336
#> GSM617610 1 0.4406 0.6378 0.700 0.000 0.300 0.000
#> GSM617611 3 0.4972 0.2609 0.456 0.000 0.544 0.000
#> GSM617613 3 0.0469 0.6421 0.012 0.000 0.988 0.000
#> GSM617614 3 0.4624 0.4749 0.340 0.000 0.660 0.000
#> GSM617621 1 0.4406 0.6378 0.700 0.000 0.300 0.000
#> GSM617629 3 0.3099 0.5645 0.020 0.104 0.876 0.000
#> GSM617630 2 0.5495 0.5922 0.348 0.624 0.028 0.000
#> GSM617631 3 0.0592 0.6520 0.016 0.000 0.984 0.000
#> GSM617633 3 0.4304 0.5322 0.284 0.000 0.716 0.000
#> GSM617642 3 0.4605 0.4586 0.336 0.000 0.664 0.000
#> GSM617645 2 0.4605 0.5862 0.336 0.664 0.000 0.000
#> GSM617646 1 0.4406 0.6378 0.700 0.000 0.300 0.000
#> GSM617652 3 0.3591 0.6469 0.168 0.008 0.824 0.000
#> GSM617655 3 0.0188 0.6504 0.004 0.000 0.996 0.000
#> GSM617656 3 0.0336 0.6488 0.008 0.000 0.992 0.000
#> GSM617657 3 0.3925 0.4979 0.016 0.176 0.808 0.000
#> GSM617658 3 0.2149 0.6637 0.088 0.000 0.912 0.000
#> GSM617659 3 0.4972 0.2609 0.456 0.000 0.544 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM617581 5 0.5117 0.5108 0.276 0.072 0.000 0.000 0.652
#> GSM617582 2 0.7787 0.1154 0.076 0.416 0.284 0.000 0.224
#> GSM617588 4 0.0162 0.8100 0.000 0.004 0.000 0.996 0.000
#> GSM617590 4 0.5067 0.6918 0.000 0.172 0.000 0.700 0.128
#> GSM617592 4 0.0162 0.8100 0.000 0.004 0.000 0.996 0.000
#> GSM617607 3 0.4088 0.4732 0.304 0.008 0.688 0.000 0.000
#> GSM617608 3 0.3816 0.4680 0.304 0.000 0.696 0.000 0.000
#> GSM617609 3 0.4088 0.4732 0.304 0.008 0.688 0.000 0.000
#> GSM617612 1 0.0000 0.7028 1.000 0.000 0.000 0.000 0.000
#> GSM617615 2 0.1405 0.7161 0.008 0.956 0.020 0.000 0.016
#> GSM617616 3 0.4088 0.4732 0.304 0.008 0.688 0.000 0.000
#> GSM617617 5 0.6794 0.2744 0.096 0.388 0.048 0.000 0.468
#> GSM617618 3 0.7292 0.1652 0.092 0.300 0.496 0.000 0.112
#> GSM617619 2 0.7816 0.1132 0.080 0.412 0.292 0.000 0.216
#> GSM617620 4 0.0162 0.8100 0.000 0.004 0.000 0.996 0.000
#> GSM617622 2 0.0486 0.7224 0.004 0.988 0.004 0.000 0.004
#> GSM617623 5 0.5117 0.5108 0.276 0.072 0.000 0.000 0.652
#> GSM617624 3 0.7336 -0.1163 0.084 0.400 0.408 0.000 0.108
#> GSM617625 3 0.2674 0.6535 0.120 0.000 0.868 0.000 0.012
#> GSM617626 1 0.0000 0.7028 1.000 0.000 0.000 0.000 0.000
#> GSM617627 3 0.7592 -0.1406 0.084 0.380 0.392 0.000 0.144
#> GSM617628 3 0.1965 0.6745 0.096 0.000 0.904 0.000 0.000
#> GSM617632 1 0.3752 0.5741 0.708 0.000 0.292 0.000 0.000
#> GSM617634 3 0.6898 0.0744 0.060 0.352 0.492 0.000 0.096
#> GSM617635 1 0.3730 0.5788 0.712 0.000 0.288 0.000 0.000
#> GSM617636 1 0.3999 0.5187 0.656 0.000 0.344 0.000 0.000
#> GSM617637 1 0.3534 0.6007 0.744 0.000 0.256 0.000 0.000
#> GSM617638 5 0.8219 0.0605 0.116 0.260 0.276 0.000 0.348
#> GSM617639 1 0.0000 0.7028 1.000 0.000 0.000 0.000 0.000
#> GSM617640 5 0.3582 0.6044 0.008 0.224 0.000 0.000 0.768
#> GSM617641 4 0.0162 0.8100 0.000 0.004 0.000 0.996 0.000
#> GSM617643 2 0.0000 0.7222 0.000 1.000 0.000 0.000 0.000
#> GSM617644 2 0.0000 0.7222 0.000 1.000 0.000 0.000 0.000
#> GSM617647 2 0.0000 0.7222 0.000 1.000 0.000 0.000 0.000
#> GSM617648 2 0.0000 0.7222 0.000 1.000 0.000 0.000 0.000
#> GSM617649 2 0.0000 0.7222 0.000 1.000 0.000 0.000 0.000
#> GSM617650 1 0.4015 0.5149 0.652 0.000 0.348 0.000 0.000
#> GSM617651 1 0.3177 0.5166 0.792 0.000 0.000 0.000 0.208
#> GSM617653 1 0.3177 0.5166 0.792 0.000 0.000 0.000 0.208
#> GSM617654 5 0.3612 0.6026 0.008 0.228 0.000 0.000 0.764
#> GSM617583 3 0.2574 0.6576 0.112 0.000 0.876 0.000 0.012
#> GSM617584 4 0.6161 -0.1371 0.020 0.076 0.000 0.464 0.440
#> GSM617585 5 0.6892 0.2387 0.004 0.312 0.008 0.212 0.464
#> GSM617586 3 0.3264 0.6653 0.132 0.024 0.840 0.000 0.004
#> GSM617587 2 0.7458 0.1375 0.100 0.436 0.356 0.000 0.108
#> GSM617589 4 0.1952 0.8000 0.000 0.004 0.000 0.912 0.084
#> GSM617591 2 0.8081 -0.2101 0.040 0.388 0.056 0.140 0.376
#> GSM617593 1 0.4015 0.5149 0.652 0.000 0.348 0.000 0.000
#> GSM617594 2 0.1200 0.7194 0.012 0.964 0.016 0.000 0.008
#> GSM617595 1 0.0000 0.7028 1.000 0.000 0.000 0.000 0.000
#> GSM617596 1 0.3177 0.5166 0.792 0.000 0.000 0.000 0.208
#> GSM617597 3 0.3336 0.5684 0.228 0.000 0.772 0.000 0.000
#> GSM617598 1 0.1792 0.6882 0.916 0.000 0.084 0.000 0.000
#> GSM617599 2 0.1314 0.7185 0.012 0.960 0.016 0.000 0.012
#> GSM617600 3 0.1043 0.6829 0.000 0.000 0.960 0.000 0.040
#> GSM617601 2 0.2213 0.6928 0.016 0.924 0.040 0.004 0.016
#> GSM617602 3 0.1251 0.6863 0.008 0.000 0.956 0.000 0.036
#> GSM617603 4 0.4038 0.7614 0.000 0.080 0.000 0.792 0.128
#> GSM617604 1 0.3177 0.5166 0.792 0.000 0.000 0.000 0.208
#> GSM617605 4 0.5067 0.6918 0.000 0.172 0.000 0.700 0.128
#> GSM617606 5 0.6892 0.2387 0.004 0.312 0.008 0.212 0.464
#> GSM617610 1 0.0000 0.7028 1.000 0.000 0.000 0.000 0.000
#> GSM617611 1 0.3949 0.5355 0.668 0.000 0.332 0.000 0.000
#> GSM617613 3 0.1121 0.6819 0.000 0.000 0.956 0.000 0.044
#> GSM617614 1 0.4304 0.1533 0.516 0.000 0.484 0.000 0.000
#> GSM617621 1 0.0000 0.7028 1.000 0.000 0.000 0.000 0.000
#> GSM617629 3 0.3154 0.6323 0.012 0.104 0.860 0.000 0.024
#> GSM617630 5 0.4210 0.6003 0.016 0.184 0.028 0.000 0.772
#> GSM617631 3 0.0703 0.6892 0.024 0.000 0.976 0.000 0.000
#> GSM617633 3 0.4294 -0.0863 0.468 0.000 0.532 0.000 0.000
#> GSM617642 1 0.4297 0.2258 0.528 0.000 0.472 0.000 0.000
#> GSM617645 5 0.3582 0.6044 0.008 0.224 0.000 0.000 0.768
#> GSM617646 1 0.0290 0.7047 0.992 0.000 0.008 0.000 0.000
#> GSM617652 3 0.4127 0.4581 0.312 0.008 0.680 0.000 0.000
#> GSM617655 3 0.1364 0.6867 0.012 0.000 0.952 0.000 0.036
#> GSM617656 3 0.1251 0.6861 0.008 0.000 0.956 0.000 0.036
#> GSM617657 3 0.4162 0.5126 0.000 0.176 0.768 0.000 0.056
#> GSM617658 3 0.2074 0.6698 0.104 0.000 0.896 0.000 0.000
#> GSM617659 1 0.4015 0.5149 0.652 0.000 0.348 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM617581 5 0.4339 0.4851 0.256 0.000 0.000 0.016 0.696 0.032
#> GSM617582 2 0.8698 0.0858 0.076 0.328 0.252 0.020 0.216 0.108
#> GSM617588 6 0.3288 1.0000 0.000 0.000 0.000 0.276 0.000 0.724
#> GSM617590 4 0.3134 0.4627 0.000 0.144 0.000 0.820 0.000 0.036
#> GSM617592 6 0.3288 1.0000 0.000 0.000 0.000 0.276 0.000 0.724
#> GSM617607 3 0.3885 0.4299 0.300 0.000 0.684 0.000 0.004 0.012
#> GSM617608 3 0.3684 0.4272 0.300 0.000 0.692 0.000 0.004 0.004
#> GSM617609 3 0.3885 0.4299 0.300 0.000 0.684 0.000 0.004 0.012
#> GSM617612 1 0.0000 0.6960 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617615 2 0.1425 0.7121 0.008 0.952 0.020 0.008 0.012 0.000
#> GSM617616 3 0.3885 0.4299 0.300 0.000 0.684 0.000 0.004 0.012
#> GSM617617 5 0.6364 0.2143 0.092 0.332 0.048 0.000 0.512 0.016
#> GSM617618 3 0.8150 0.1975 0.092 0.216 0.456 0.016 0.108 0.112
#> GSM617619 2 0.8606 0.0843 0.080 0.324 0.260 0.012 0.216 0.108
#> GSM617620 6 0.3288 1.0000 0.000 0.000 0.000 0.276 0.000 0.724
#> GSM617622 2 0.0436 0.7197 0.004 0.988 0.004 0.000 0.004 0.000
#> GSM617623 5 0.4339 0.4851 0.256 0.000 0.000 0.016 0.696 0.032
#> GSM617624 3 0.8348 -0.0523 0.084 0.320 0.368 0.024 0.104 0.100
#> GSM617625 3 0.3392 0.6298 0.116 0.000 0.832 0.008 0.028 0.016
#> GSM617626 1 0.0000 0.6960 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617627 3 0.8435 -0.0780 0.084 0.312 0.360 0.024 0.128 0.092
#> GSM617628 3 0.2001 0.6472 0.092 0.000 0.900 0.004 0.004 0.000
#> GSM617632 1 0.3626 0.5890 0.704 0.000 0.288 0.000 0.004 0.004
#> GSM617634 3 0.7846 0.1160 0.060 0.272 0.448 0.012 0.096 0.112
#> GSM617635 1 0.3606 0.5931 0.708 0.000 0.284 0.000 0.004 0.004
#> GSM617636 1 0.3850 0.5378 0.652 0.000 0.340 0.000 0.004 0.004
#> GSM617637 1 0.3429 0.6120 0.740 0.000 0.252 0.000 0.004 0.004
#> GSM617638 5 0.8519 0.1189 0.112 0.176 0.236 0.012 0.376 0.088
#> GSM617639 1 0.0000 0.6960 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617640 5 0.1663 0.5872 0.000 0.088 0.000 0.000 0.912 0.000
#> GSM617641 6 0.3288 1.0000 0.000 0.000 0.000 0.276 0.000 0.724
#> GSM617643 2 0.0000 0.7186 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM617644 2 0.0000 0.7186 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM617647 2 0.0000 0.7186 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM617648 2 0.0000 0.7186 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM617649 2 0.0000 0.7186 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM617650 1 0.3864 0.5323 0.648 0.000 0.344 0.000 0.004 0.004
#> GSM617651 1 0.3716 0.4782 0.780 0.000 0.000 0.016 0.176 0.028
#> GSM617653 1 0.3716 0.4782 0.780 0.000 0.000 0.016 0.176 0.028
#> GSM617654 5 0.3424 0.5613 0.000 0.096 0.000 0.000 0.812 0.092
#> GSM617583 3 0.3303 0.6337 0.108 0.000 0.840 0.008 0.028 0.016
#> GSM617584 5 0.5183 -0.0103 0.012 0.000 0.000 0.060 0.516 0.412
#> GSM617585 4 0.7420 0.2419 0.004 0.256 0.000 0.360 0.276 0.104
#> GSM617586 3 0.3242 0.6361 0.128 0.004 0.832 0.012 0.000 0.024
#> GSM617587 2 0.8273 0.0562 0.100 0.356 0.328 0.012 0.104 0.100
#> GSM617589 4 0.3789 -0.5096 0.000 0.000 0.000 0.584 0.000 0.416
#> GSM617591 2 0.8629 -0.1656 0.040 0.340 0.044 0.228 0.248 0.100
#> GSM617593 1 0.3864 0.5323 0.648 0.000 0.344 0.000 0.004 0.004
#> GSM617594 2 0.1078 0.7170 0.012 0.964 0.016 0.000 0.008 0.000
#> GSM617595 1 0.0000 0.6960 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617596 1 0.3716 0.4782 0.780 0.000 0.000 0.016 0.176 0.028
#> GSM617597 3 0.2969 0.5351 0.224 0.000 0.776 0.000 0.000 0.000
#> GSM617598 1 0.1753 0.6863 0.912 0.000 0.084 0.000 0.000 0.004
#> GSM617599 2 0.1275 0.7156 0.012 0.956 0.016 0.000 0.016 0.000
#> GSM617600 3 0.2541 0.6456 0.000 0.000 0.892 0.024 0.052 0.032
#> GSM617601 2 0.2101 0.6902 0.016 0.920 0.040 0.016 0.000 0.008
#> GSM617602 3 0.2721 0.6527 0.008 0.000 0.888 0.024 0.052 0.028
#> GSM617603 4 0.1723 0.3426 0.000 0.036 0.000 0.928 0.000 0.036
#> GSM617604 1 0.3716 0.4782 0.780 0.000 0.000 0.016 0.176 0.028
#> GSM617605 4 0.3134 0.4627 0.000 0.144 0.000 0.820 0.000 0.036
#> GSM617606 4 0.7420 0.2419 0.004 0.256 0.000 0.360 0.276 0.104
#> GSM617610 1 0.0000 0.6960 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617611 1 0.3805 0.5519 0.664 0.000 0.328 0.000 0.004 0.004
#> GSM617613 3 0.2614 0.6438 0.000 0.000 0.888 0.024 0.052 0.036
#> GSM617614 1 0.4126 0.1962 0.512 0.000 0.480 0.000 0.004 0.004
#> GSM617621 1 0.0000 0.6960 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617629 3 0.4327 0.5977 0.012 0.044 0.796 0.020 0.024 0.104
#> GSM617630 5 0.3577 0.5575 0.004 0.048 0.020 0.000 0.824 0.104
#> GSM617631 3 0.0837 0.6642 0.020 0.000 0.972 0.004 0.004 0.000
#> GSM617633 3 0.4117 -0.1296 0.464 0.000 0.528 0.004 0.004 0.000
#> GSM617642 1 0.4120 0.2661 0.524 0.000 0.468 0.000 0.004 0.004
#> GSM617645 5 0.1663 0.5872 0.000 0.088 0.000 0.000 0.912 0.000
#> GSM617646 1 0.0260 0.6979 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM617652 3 0.3921 0.4144 0.308 0.000 0.676 0.000 0.004 0.012
#> GSM617655 3 0.2674 0.6574 0.012 0.000 0.892 0.020 0.048 0.028
#> GSM617656 3 0.2574 0.6554 0.008 0.000 0.896 0.020 0.048 0.028
#> GSM617657 3 0.6258 0.4136 0.000 0.108 0.644 0.056 0.060 0.132
#> GSM617658 3 0.2101 0.6427 0.100 0.000 0.892 0.004 0.004 0.000
#> GSM617659 1 0.3864 0.5323 0.648 0.000 0.344 0.000 0.004 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) k
#> ATC:hclust 68 1.0000 2
#> ATC:hclust 64 0.0791 3
#> ATC:hclust 55 0.2346 4
#> ATC:hclust 58 0.0430 5
#> ATC:hclust 47 0.0188 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 79 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 0.979 0.991 0.4939 0.503 0.503
#> 3 3 0.523 0.703 0.794 0.2608 0.883 0.775
#> 4 4 0.921 0.905 0.939 0.1541 0.817 0.581
#> 5 5 0.745 0.655 0.802 0.0828 0.918 0.732
#> 6 6 0.728 0.618 0.760 0.0496 0.883 0.565
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
#> GSM617581 2 0.000 0.978 0.000 1.000
#> GSM617582 2 0.402 0.911 0.080 0.920
#> GSM617588 2 0.000 0.978 0.000 1.000
#> GSM617590 2 0.000 0.978 0.000 1.000
#> GSM617592 2 0.000 0.978 0.000 1.000
#> GSM617607 1 0.000 1.000 1.000 0.000
#> GSM617608 1 0.000 1.000 1.000 0.000
#> GSM617609 1 0.000 1.000 1.000 0.000
#> GSM617612 1 0.000 1.000 1.000 0.000
#> GSM617615 2 0.000 0.978 0.000 1.000
#> GSM617616 1 0.000 1.000 1.000 0.000
#> GSM617617 2 0.000 0.978 0.000 1.000
#> GSM617618 1 0.000 1.000 1.000 0.000
#> GSM617619 2 0.402 0.911 0.080 0.920
#> GSM617620 2 0.000 0.978 0.000 1.000
#> GSM617622 2 0.000 0.978 0.000 1.000
#> GSM617623 2 0.000 0.978 0.000 1.000
#> GSM617624 2 0.402 0.911 0.080 0.920
#> GSM617625 1 0.000 1.000 1.000 0.000
#> GSM617626 1 0.000 1.000 1.000 0.000
#> GSM617627 2 0.242 0.947 0.040 0.960
#> GSM617628 1 0.000 1.000 1.000 0.000
#> GSM617632 1 0.000 1.000 1.000 0.000
#> GSM617634 2 0.987 0.264 0.432 0.568
#> GSM617635 1 0.000 1.000 1.000 0.000
#> GSM617636 1 0.000 1.000 1.000 0.000
#> GSM617637 1 0.000 1.000 1.000 0.000
#> GSM617638 1 0.000 1.000 1.000 0.000
#> GSM617639 1 0.000 1.000 1.000 0.000
#> GSM617640 2 0.000 0.978 0.000 1.000
#> GSM617641 2 0.000 0.978 0.000 1.000
#> GSM617643 2 0.000 0.978 0.000 1.000
#> GSM617644 2 0.000 0.978 0.000 1.000
#> GSM617647 2 0.000 0.978 0.000 1.000
#> GSM617648 2 0.000 0.978 0.000 1.000
#> GSM617649 2 0.000 0.978 0.000 1.000
#> GSM617650 1 0.000 1.000 1.000 0.000
#> GSM617651 1 0.000 1.000 1.000 0.000
#> GSM617653 1 0.000 1.000 1.000 0.000
#> GSM617654 2 0.000 0.978 0.000 1.000
#> GSM617583 1 0.000 1.000 1.000 0.000
#> GSM617584 2 0.000 0.978 0.000 1.000
#> GSM617585 2 0.000 0.978 0.000 1.000
#> GSM617586 1 0.000 1.000 1.000 0.000
#> GSM617587 1 0.000 1.000 1.000 0.000
#> GSM617589 2 0.000 0.978 0.000 1.000
#> GSM617591 2 0.000 0.978 0.000 1.000
#> GSM617593 1 0.000 1.000 1.000 0.000
#> GSM617594 2 0.000 0.978 0.000 1.000
#> GSM617595 1 0.000 1.000 1.000 0.000
#> GSM617596 1 0.000 1.000 1.000 0.000
#> GSM617597 1 0.000 1.000 1.000 0.000
#> GSM617598 1 0.000 1.000 1.000 0.000
#> GSM617599 2 0.000 0.978 0.000 1.000
#> GSM617600 1 0.000 1.000 1.000 0.000
#> GSM617601 2 0.000 0.978 0.000 1.000
#> GSM617602 1 0.000 1.000 1.000 0.000
#> GSM617603 2 0.000 0.978 0.000 1.000
#> GSM617604 1 0.000 1.000 1.000 0.000
#> GSM617605 2 0.000 0.978 0.000 1.000
#> GSM617606 2 0.000 0.978 0.000 1.000
#> GSM617610 1 0.000 1.000 1.000 0.000
#> GSM617611 1 0.000 1.000 1.000 0.000
#> GSM617613 1 0.000 1.000 1.000 0.000
#> GSM617614 1 0.000 1.000 1.000 0.000
#> GSM617621 1 0.000 1.000 1.000 0.000
#> GSM617629 1 0.000 1.000 1.000 0.000
#> GSM617630 2 0.000 0.978 0.000 1.000
#> GSM617631 1 0.000 1.000 1.000 0.000
#> GSM617633 1 0.000 1.000 1.000 0.000
#> GSM617642 1 0.000 1.000 1.000 0.000
#> GSM617645 2 0.000 0.978 0.000 1.000
#> GSM617646 1 0.000 1.000 1.000 0.000
#> GSM617652 1 0.000 1.000 1.000 0.000
#> GSM617655 1 0.000 1.000 1.000 0.000
#> GSM617656 1 0.000 1.000 1.000 0.000
#> GSM617657 1 0.000 1.000 1.000 0.000
#> GSM617658 1 0.000 1.000 1.000 0.000
#> GSM617659 1 0.000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM617581 2 0.5621 0.521 0.000 0.692 0.308
#> GSM617582 2 0.4555 0.651 0.200 0.800 0.000
#> GSM617588 3 0.5621 0.997 0.000 0.308 0.692
#> GSM617590 3 0.5621 0.997 0.000 0.308 0.692
#> GSM617592 3 0.5621 0.997 0.000 0.308 0.692
#> GSM617607 1 0.0000 0.799 1.000 0.000 0.000
#> GSM617608 1 0.0000 0.799 1.000 0.000 0.000
#> GSM617609 1 0.0424 0.796 0.992 0.008 0.000
#> GSM617612 1 0.9940 0.408 0.388 0.304 0.308
#> GSM617615 2 0.2356 0.711 0.000 0.928 0.072
#> GSM617616 1 0.0424 0.799 0.992 0.000 0.008
#> GSM617617 2 0.0747 0.745 0.000 0.984 0.016
#> GSM617618 1 0.6917 0.377 0.608 0.368 0.024
#> GSM617619 2 0.4605 0.647 0.204 0.796 0.000
#> GSM617620 3 0.5621 0.997 0.000 0.308 0.692
#> GSM617622 2 0.0592 0.745 0.000 0.988 0.012
#> GSM617623 2 0.5431 0.542 0.000 0.716 0.284
#> GSM617624 2 0.4555 0.651 0.200 0.800 0.000
#> GSM617625 1 0.0000 0.799 1.000 0.000 0.000
#> GSM617626 1 0.9898 0.436 0.404 0.288 0.308
#> GSM617627 2 0.4002 0.679 0.160 0.840 0.000
#> GSM617628 1 0.0000 0.799 1.000 0.000 0.000
#> GSM617632 1 0.5588 0.718 0.720 0.004 0.276
#> GSM617634 2 0.4931 0.637 0.212 0.784 0.004
#> GSM617635 1 0.0892 0.798 0.980 0.000 0.020
#> GSM617636 1 0.0000 0.799 1.000 0.000 0.000
#> GSM617637 1 0.7644 0.668 0.624 0.068 0.308
#> GSM617638 1 0.5597 0.641 0.764 0.216 0.020
#> GSM617639 1 0.7391 0.675 0.636 0.056 0.308
#> GSM617640 2 0.4974 0.413 0.000 0.764 0.236
#> GSM617641 3 0.5621 0.997 0.000 0.308 0.692
#> GSM617643 2 0.5138 0.368 0.000 0.748 0.252
#> GSM617644 2 0.5138 0.368 0.000 0.748 0.252
#> GSM617647 2 0.0592 0.745 0.000 0.988 0.012
#> GSM617648 2 0.2711 0.695 0.000 0.912 0.088
#> GSM617649 2 0.0237 0.746 0.000 0.996 0.004
#> GSM617650 1 0.3816 0.763 0.852 0.000 0.148
#> GSM617651 1 0.9963 0.383 0.376 0.316 0.308
#> GSM617653 1 0.9751 0.488 0.440 0.252 0.308
#> GSM617654 2 0.1163 0.738 0.000 0.972 0.028
#> GSM617583 1 0.0000 0.799 1.000 0.000 0.000
#> GSM617584 3 0.5733 0.974 0.000 0.324 0.676
#> GSM617585 2 0.2711 0.694 0.000 0.912 0.088
#> GSM617586 1 0.0424 0.796 0.992 0.008 0.000
#> GSM617587 2 0.7330 0.559 0.092 0.692 0.216
#> GSM617589 3 0.5621 0.997 0.000 0.308 0.692
#> GSM617591 2 0.2261 0.713 0.000 0.932 0.068
#> GSM617593 1 0.5763 0.716 0.716 0.008 0.276
#> GSM617594 2 0.0000 0.747 0.000 1.000 0.000
#> GSM617595 1 0.9771 0.483 0.436 0.256 0.308
#> GSM617596 1 0.9940 0.408 0.388 0.304 0.308
#> GSM617597 1 0.0000 0.799 1.000 0.000 0.000
#> GSM617598 1 0.5763 0.716 0.716 0.008 0.276
#> GSM617599 2 0.0000 0.747 0.000 1.000 0.000
#> GSM617600 1 0.0424 0.796 0.992 0.008 0.000
#> GSM617601 2 0.1267 0.747 0.024 0.972 0.004
#> GSM617602 1 0.0000 0.799 1.000 0.000 0.000
#> GSM617603 3 0.5621 0.997 0.000 0.308 0.692
#> GSM617604 1 0.9931 0.416 0.392 0.300 0.308
#> GSM617605 3 0.5621 0.997 0.000 0.308 0.692
#> GSM617606 2 0.2711 0.694 0.000 0.912 0.088
#> GSM617610 1 0.9940 0.408 0.388 0.304 0.308
#> GSM617611 1 0.5831 0.712 0.708 0.008 0.284
#> GSM617613 1 0.0424 0.796 0.992 0.008 0.000
#> GSM617614 1 0.1031 0.797 0.976 0.000 0.024
#> GSM617621 1 0.7876 0.660 0.612 0.080 0.308
#> GSM617629 1 0.0424 0.796 0.992 0.008 0.000
#> GSM617630 2 0.1315 0.748 0.020 0.972 0.008
#> GSM617631 1 0.0000 0.799 1.000 0.000 0.000
#> GSM617633 1 0.0000 0.799 1.000 0.000 0.000
#> GSM617642 1 0.0592 0.798 0.988 0.000 0.012
#> GSM617645 2 0.5327 0.301 0.000 0.728 0.272
#> GSM617646 1 0.9638 0.513 0.460 0.232 0.308
#> GSM617652 1 0.0592 0.798 0.988 0.000 0.012
#> GSM617655 1 0.0000 0.799 1.000 0.000 0.000
#> GSM617656 1 0.0000 0.799 1.000 0.000 0.000
#> GSM617657 2 0.6235 0.333 0.436 0.564 0.000
#> GSM617658 1 0.0000 0.799 1.000 0.000 0.000
#> GSM617659 1 0.3816 0.763 0.852 0.000 0.148
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM617581 1 0.1867 0.767 0.928 0.072 0.000 0.000
#> GSM617582 2 0.0657 0.938 0.012 0.984 0.004 0.000
#> GSM617588 4 0.0937 0.985 0.012 0.012 0.000 0.976
#> GSM617590 4 0.0657 0.985 0.004 0.012 0.000 0.984
#> GSM617592 4 0.0937 0.985 0.012 0.012 0.000 0.976
#> GSM617607 3 0.0188 0.978 0.000 0.004 0.996 0.000
#> GSM617608 3 0.0188 0.978 0.000 0.004 0.996 0.000
#> GSM617609 3 0.0336 0.977 0.000 0.008 0.992 0.000
#> GSM617612 1 0.1824 0.877 0.936 0.004 0.060 0.000
#> GSM617615 2 0.1256 0.942 0.028 0.964 0.000 0.008
#> GSM617616 3 0.1209 0.953 0.032 0.004 0.964 0.000
#> GSM617617 2 0.1389 0.939 0.048 0.952 0.000 0.000
#> GSM617618 2 0.6295 0.553 0.144 0.660 0.196 0.000
#> GSM617619 2 0.0657 0.938 0.012 0.984 0.004 0.000
#> GSM617620 4 0.0937 0.985 0.012 0.012 0.000 0.976
#> GSM617622 2 0.1118 0.942 0.036 0.964 0.000 0.000
#> GSM617623 1 0.1792 0.768 0.932 0.068 0.000 0.000
#> GSM617624 2 0.0524 0.938 0.008 0.988 0.004 0.000
#> GSM617625 3 0.0524 0.977 0.004 0.000 0.988 0.008
#> GSM617626 1 0.1716 0.878 0.936 0.000 0.064 0.000
#> GSM617627 2 0.0657 0.938 0.012 0.984 0.004 0.000
#> GSM617628 3 0.0524 0.978 0.000 0.004 0.988 0.008
#> GSM617632 1 0.4905 0.571 0.632 0.004 0.364 0.000
#> GSM617634 2 0.0524 0.938 0.008 0.988 0.004 0.000
#> GSM617635 3 0.1489 0.943 0.044 0.004 0.952 0.000
#> GSM617636 3 0.0376 0.977 0.004 0.004 0.992 0.000
#> GSM617637 1 0.1978 0.875 0.928 0.004 0.068 0.000
#> GSM617638 3 0.4234 0.794 0.132 0.052 0.816 0.000
#> GSM617639 1 0.1978 0.875 0.928 0.004 0.068 0.000
#> GSM617640 2 0.1545 0.940 0.040 0.952 0.000 0.008
#> GSM617641 4 0.0937 0.985 0.012 0.012 0.000 0.976
#> GSM617643 2 0.1256 0.942 0.028 0.964 0.000 0.008
#> GSM617644 2 0.1256 0.942 0.028 0.964 0.000 0.008
#> GSM617647 2 0.1118 0.941 0.036 0.964 0.000 0.000
#> GSM617648 2 0.1256 0.942 0.028 0.964 0.000 0.008
#> GSM617649 2 0.1022 0.942 0.032 0.968 0.000 0.000
#> GSM617650 3 0.0376 0.977 0.004 0.004 0.992 0.000
#> GSM617651 1 0.1743 0.873 0.940 0.004 0.056 0.000
#> GSM617653 1 0.1716 0.878 0.936 0.000 0.064 0.000
#> GSM617654 2 0.1302 0.940 0.044 0.956 0.000 0.000
#> GSM617583 3 0.0469 0.977 0.000 0.000 0.988 0.012
#> GSM617584 4 0.2699 0.919 0.028 0.068 0.000 0.904
#> GSM617585 2 0.0672 0.941 0.008 0.984 0.000 0.008
#> GSM617586 3 0.0657 0.975 0.000 0.004 0.984 0.012
#> GSM617587 2 0.3157 0.814 0.144 0.852 0.004 0.000
#> GSM617589 4 0.0657 0.985 0.004 0.012 0.000 0.984
#> GSM617591 2 0.0672 0.941 0.008 0.984 0.000 0.008
#> GSM617593 1 0.5112 0.420 0.560 0.004 0.436 0.000
#> GSM617594 2 0.1022 0.943 0.032 0.968 0.000 0.000
#> GSM617595 1 0.1902 0.878 0.932 0.004 0.064 0.000
#> GSM617596 1 0.1824 0.877 0.936 0.004 0.060 0.000
#> GSM617597 3 0.0188 0.978 0.000 0.004 0.996 0.000
#> GSM617598 1 0.5060 0.479 0.584 0.004 0.412 0.000
#> GSM617599 2 0.0921 0.942 0.028 0.972 0.000 0.000
#> GSM617600 3 0.0657 0.975 0.000 0.004 0.984 0.012
#> GSM617601 2 0.0524 0.938 0.008 0.988 0.004 0.000
#> GSM617602 3 0.0469 0.977 0.000 0.000 0.988 0.012
#> GSM617603 4 0.0657 0.985 0.004 0.012 0.000 0.984
#> GSM617604 1 0.1902 0.878 0.932 0.004 0.064 0.000
#> GSM617605 4 0.0657 0.985 0.004 0.012 0.000 0.984
#> GSM617606 2 0.0927 0.940 0.016 0.976 0.000 0.008
#> GSM617610 1 0.1824 0.877 0.936 0.004 0.060 0.000
#> GSM617611 1 0.4741 0.631 0.668 0.004 0.328 0.000
#> GSM617613 3 0.0657 0.975 0.000 0.004 0.984 0.012
#> GSM617614 3 0.0376 0.977 0.004 0.004 0.992 0.000
#> GSM617621 1 0.1716 0.878 0.936 0.000 0.064 0.000
#> GSM617629 3 0.1509 0.952 0.008 0.020 0.960 0.012
#> GSM617630 2 0.0707 0.941 0.020 0.980 0.000 0.000
#> GSM617631 3 0.0469 0.977 0.000 0.000 0.988 0.012
#> GSM617633 3 0.0188 0.978 0.000 0.000 0.996 0.004
#> GSM617642 3 0.0188 0.977 0.004 0.000 0.996 0.000
#> GSM617645 2 0.2224 0.926 0.040 0.928 0.000 0.032
#> GSM617646 1 0.1902 0.878 0.932 0.004 0.064 0.000
#> GSM617652 3 0.1398 0.945 0.040 0.004 0.956 0.000
#> GSM617655 3 0.0469 0.977 0.000 0.000 0.988 0.012
#> GSM617656 3 0.0469 0.977 0.000 0.000 0.988 0.012
#> GSM617657 2 0.5349 0.482 0.008 0.644 0.336 0.012
#> GSM617658 3 0.0188 0.978 0.000 0.004 0.996 0.000
#> GSM617659 3 0.0376 0.977 0.004 0.004 0.992 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM617581 1 0.2520 0.84233 0.896 0.048 0.000 0.000 0.056
#> GSM617582 2 0.4235 0.61445 0.000 0.576 0.000 0.000 0.424
#> GSM617588 4 0.0000 0.96269 0.000 0.000 0.000 1.000 0.000
#> GSM617590 4 0.1410 0.95727 0.000 0.000 0.000 0.940 0.060
#> GSM617592 4 0.0000 0.96269 0.000 0.000 0.000 1.000 0.000
#> GSM617607 3 0.2179 0.60762 0.000 0.000 0.888 0.000 0.112
#> GSM617608 3 0.1410 0.62515 0.000 0.000 0.940 0.000 0.060
#> GSM617609 3 0.3684 0.57438 0.000 0.000 0.720 0.000 0.280
#> GSM617612 1 0.0324 0.91968 0.992 0.000 0.004 0.000 0.004
#> GSM617615 2 0.0000 0.76244 0.000 1.000 0.000 0.000 0.000
#> GSM617616 3 0.2864 0.59488 0.024 0.000 0.864 0.000 0.112
#> GSM617617 2 0.3196 0.71179 0.004 0.804 0.000 0.000 0.192
#> GSM617618 5 0.7301 0.14440 0.052 0.284 0.184 0.000 0.480
#> GSM617619 2 0.4235 0.61445 0.000 0.576 0.000 0.000 0.424
#> GSM617620 4 0.0290 0.96229 0.000 0.000 0.000 0.992 0.008
#> GSM617622 2 0.0703 0.75978 0.000 0.976 0.000 0.000 0.024
#> GSM617623 1 0.2729 0.83123 0.884 0.060 0.000 0.000 0.056
#> GSM617624 2 0.3876 0.63748 0.000 0.684 0.000 0.000 0.316
#> GSM617625 3 0.3534 0.59016 0.000 0.000 0.744 0.000 0.256
#> GSM617626 1 0.0324 0.91968 0.992 0.000 0.004 0.000 0.004
#> GSM617627 2 0.4126 0.63100 0.000 0.620 0.000 0.000 0.380
#> GSM617628 3 0.3661 0.58249 0.000 0.000 0.724 0.000 0.276
#> GSM617632 3 0.5230 -0.11938 0.452 0.000 0.504 0.000 0.044
#> GSM617634 2 0.3983 0.61082 0.000 0.660 0.000 0.000 0.340
#> GSM617635 3 0.2719 0.53435 0.068 0.000 0.884 0.000 0.048
#> GSM617636 3 0.0510 0.60871 0.000 0.000 0.984 0.000 0.016
#> GSM617637 1 0.3635 0.71001 0.748 0.000 0.248 0.000 0.004
#> GSM617638 5 0.5681 0.39789 0.044 0.024 0.360 0.000 0.572
#> GSM617639 1 0.3550 0.72518 0.760 0.000 0.236 0.000 0.004
#> GSM617640 2 0.3489 0.70080 0.004 0.784 0.000 0.004 0.208
#> GSM617641 4 0.0290 0.96229 0.000 0.000 0.000 0.992 0.008
#> GSM617643 2 0.0162 0.76185 0.000 0.996 0.000 0.000 0.004
#> GSM617644 2 0.0162 0.76185 0.000 0.996 0.000 0.000 0.004
#> GSM617647 2 0.0290 0.76091 0.000 0.992 0.000 0.000 0.008
#> GSM617648 2 0.0000 0.76244 0.000 1.000 0.000 0.000 0.000
#> GSM617649 2 0.0000 0.76244 0.000 1.000 0.000 0.000 0.000
#> GSM617650 3 0.0566 0.60676 0.012 0.000 0.984 0.000 0.004
#> GSM617651 1 0.0451 0.91881 0.988 0.000 0.004 0.000 0.008
#> GSM617653 1 0.0162 0.91897 0.996 0.000 0.004 0.000 0.000
#> GSM617654 2 0.3333 0.70295 0.004 0.788 0.000 0.000 0.208
#> GSM617583 3 0.3895 0.55675 0.000 0.000 0.680 0.000 0.320
#> GSM617584 4 0.2669 0.84853 0.000 0.104 0.000 0.876 0.020
#> GSM617585 2 0.4138 0.66681 0.000 0.616 0.000 0.000 0.384
#> GSM617586 3 0.3999 0.54506 0.000 0.000 0.656 0.000 0.344
#> GSM617587 2 0.5056 0.55502 0.044 0.596 0.000 0.000 0.360
#> GSM617589 4 0.0963 0.96166 0.000 0.000 0.000 0.964 0.036
#> GSM617591 2 0.3837 0.71155 0.000 0.692 0.000 0.000 0.308
#> GSM617593 3 0.4383 0.01520 0.424 0.000 0.572 0.000 0.004
#> GSM617594 2 0.0794 0.76007 0.000 0.972 0.000 0.000 0.028
#> GSM617595 1 0.0324 0.91771 0.992 0.000 0.004 0.000 0.004
#> GSM617596 1 0.0451 0.91881 0.988 0.000 0.004 0.000 0.008
#> GSM617597 3 0.2471 0.62341 0.000 0.000 0.864 0.000 0.136
#> GSM617598 3 0.4390 0.00316 0.428 0.000 0.568 0.000 0.004
#> GSM617599 2 0.0703 0.76112 0.000 0.976 0.000 0.000 0.024
#> GSM617600 3 0.4015 0.53427 0.000 0.000 0.652 0.000 0.348
#> GSM617601 2 0.3395 0.69433 0.000 0.764 0.000 0.000 0.236
#> GSM617602 3 0.3999 0.53879 0.000 0.000 0.656 0.000 0.344
#> GSM617603 4 0.1410 0.95903 0.000 0.000 0.000 0.940 0.060
#> GSM617604 1 0.0451 0.91881 0.988 0.000 0.004 0.000 0.008
#> GSM617605 4 0.1410 0.95727 0.000 0.000 0.000 0.940 0.060
#> GSM617606 2 0.4367 0.65047 0.004 0.580 0.000 0.000 0.416
#> GSM617610 1 0.0324 0.91968 0.992 0.000 0.004 0.000 0.004
#> GSM617611 3 0.4452 -0.21227 0.496 0.000 0.500 0.000 0.004
#> GSM617613 3 0.4015 0.53427 0.000 0.000 0.652 0.000 0.348
#> GSM617614 3 0.0000 0.61377 0.000 0.000 1.000 0.000 0.000
#> GSM617621 1 0.0162 0.91897 0.996 0.000 0.004 0.000 0.000
#> GSM617629 5 0.4219 -0.16318 0.000 0.000 0.416 0.000 0.584
#> GSM617630 2 0.4425 0.62420 0.004 0.544 0.000 0.000 0.452
#> GSM617631 3 0.3999 0.53688 0.000 0.000 0.656 0.000 0.344
#> GSM617633 3 0.2020 0.61103 0.000 0.000 0.900 0.000 0.100
#> GSM617642 3 0.0510 0.61914 0.000 0.000 0.984 0.000 0.016
#> GSM617645 2 0.3489 0.70080 0.004 0.784 0.000 0.004 0.208
#> GSM617646 1 0.2890 0.80065 0.836 0.000 0.160 0.000 0.004
#> GSM617652 3 0.2729 0.54981 0.056 0.000 0.884 0.000 0.060
#> GSM617655 3 0.3895 0.55675 0.000 0.000 0.680 0.000 0.320
#> GSM617656 3 0.3966 0.54488 0.000 0.000 0.664 0.000 0.336
#> GSM617657 5 0.4525 0.42692 0.000 0.220 0.056 0.000 0.724
#> GSM617658 3 0.3424 0.59254 0.000 0.000 0.760 0.000 0.240
#> GSM617659 3 0.0290 0.61114 0.008 0.000 0.992 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM617581 1 0.1863 0.8423 0.920 0.000 0.044 0.000 0.036 0.000
#> GSM617582 5 0.3536 0.5579 0.000 0.252 0.008 0.000 0.736 0.004
#> GSM617588 4 0.0000 0.9025 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM617590 4 0.3494 0.8846 0.000 0.004 0.168 0.792 0.036 0.000
#> GSM617592 4 0.0000 0.9025 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM617607 6 0.2680 0.5842 0.000 0.000 0.056 0.000 0.076 0.868
#> GSM617608 6 0.2527 0.5596 0.000 0.000 0.084 0.000 0.040 0.876
#> GSM617609 6 0.5250 -0.4103 0.000 0.000 0.352 0.000 0.108 0.540
#> GSM617612 1 0.0000 0.8831 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617615 2 0.0146 0.7649 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM617616 6 0.2649 0.5956 0.004 0.000 0.052 0.000 0.068 0.876
#> GSM617617 2 0.4931 0.5023 0.000 0.636 0.116 0.000 0.248 0.000
#> GSM617618 5 0.5869 0.5250 0.020 0.100 0.056 0.000 0.652 0.172
#> GSM617619 5 0.3512 0.5602 0.000 0.248 0.008 0.000 0.740 0.004
#> GSM617620 4 0.0363 0.9018 0.000 0.000 0.012 0.988 0.000 0.000
#> GSM617622 2 0.1196 0.7380 0.000 0.952 0.008 0.000 0.040 0.000
#> GSM617623 1 0.2119 0.8364 0.912 0.008 0.044 0.000 0.036 0.000
#> GSM617624 5 0.4025 0.4564 0.000 0.416 0.008 0.000 0.576 0.000
#> GSM617625 3 0.3868 0.7926 0.000 0.000 0.508 0.000 0.000 0.492
#> GSM617626 1 0.0000 0.8831 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617627 5 0.3563 0.5244 0.000 0.336 0.000 0.000 0.664 0.000
#> GSM617628 3 0.4256 0.8101 0.000 0.000 0.520 0.000 0.016 0.464
#> GSM617632 6 0.4810 0.4524 0.260 0.000 0.020 0.000 0.056 0.664
#> GSM617634 5 0.4237 0.4778 0.000 0.396 0.020 0.000 0.584 0.000
#> GSM617635 6 0.2463 0.6203 0.020 0.000 0.020 0.000 0.068 0.892
#> GSM617636 6 0.0790 0.6202 0.000 0.000 0.000 0.000 0.032 0.968
#> GSM617637 1 0.4378 0.4129 0.588 0.000 0.008 0.000 0.016 0.388
#> GSM617638 5 0.4975 0.4796 0.016 0.008 0.076 0.000 0.684 0.216
#> GSM617639 1 0.4099 0.4552 0.612 0.000 0.000 0.000 0.016 0.372
#> GSM617640 2 0.5080 0.4673 0.000 0.600 0.112 0.000 0.288 0.000
#> GSM617641 4 0.0363 0.9018 0.000 0.000 0.012 0.988 0.000 0.000
#> GSM617643 2 0.0146 0.7650 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM617644 2 0.0146 0.7650 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM617647 2 0.0717 0.7608 0.000 0.976 0.016 0.000 0.008 0.000
#> GSM617648 2 0.0000 0.7655 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM617649 2 0.0291 0.7648 0.000 0.992 0.004 0.000 0.004 0.000
#> GSM617650 6 0.1801 0.6018 0.004 0.000 0.056 0.000 0.016 0.924
#> GSM617651 1 0.0603 0.8809 0.980 0.000 0.016 0.000 0.004 0.000
#> GSM617653 1 0.0146 0.8830 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM617654 2 0.5046 0.4776 0.000 0.608 0.112 0.000 0.280 0.000
#> GSM617583 3 0.3789 0.8887 0.000 0.000 0.584 0.000 0.000 0.416
#> GSM617584 4 0.3272 0.7598 0.000 0.144 0.020 0.820 0.016 0.000
#> GSM617585 5 0.5184 0.2903 0.000 0.316 0.112 0.000 0.572 0.000
#> GSM617586 3 0.4808 0.7600 0.000 0.000 0.536 0.000 0.056 0.408
#> GSM617587 5 0.5706 0.5067 0.028 0.324 0.036 0.000 0.576 0.036
#> GSM617589 4 0.2783 0.8943 0.000 0.000 0.148 0.836 0.016 0.000
#> GSM617591 5 0.5350 0.0447 0.000 0.416 0.108 0.000 0.476 0.000
#> GSM617593 6 0.3828 0.5121 0.252 0.000 0.008 0.000 0.016 0.724
#> GSM617594 2 0.1204 0.7305 0.000 0.944 0.000 0.000 0.056 0.000
#> GSM617595 1 0.0603 0.8783 0.980 0.000 0.004 0.000 0.016 0.000
#> GSM617596 1 0.0508 0.8810 0.984 0.000 0.012 0.000 0.004 0.000
#> GSM617597 6 0.3923 -0.4493 0.000 0.000 0.372 0.000 0.008 0.620
#> GSM617598 6 0.3875 0.5085 0.260 0.000 0.008 0.000 0.016 0.716
#> GSM617599 2 0.1141 0.7350 0.000 0.948 0.000 0.000 0.052 0.000
#> GSM617600 3 0.4110 0.8878 0.000 0.000 0.608 0.000 0.016 0.376
#> GSM617601 2 0.3547 0.1059 0.000 0.668 0.000 0.000 0.332 0.000
#> GSM617602 3 0.4076 0.8989 0.000 0.000 0.592 0.000 0.012 0.396
#> GSM617603 4 0.3376 0.8880 0.000 0.004 0.180 0.792 0.024 0.000
#> GSM617604 1 0.0508 0.8810 0.984 0.000 0.012 0.000 0.004 0.000
#> GSM617605 4 0.3494 0.8846 0.000 0.004 0.168 0.792 0.036 0.000
#> GSM617606 5 0.5276 0.1919 0.000 0.312 0.124 0.000 0.564 0.000
#> GSM617610 1 0.0000 0.8831 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617611 6 0.4078 0.4267 0.300 0.000 0.008 0.000 0.016 0.676
#> GSM617613 3 0.4110 0.8878 0.000 0.000 0.608 0.000 0.016 0.376
#> GSM617614 6 0.1204 0.5998 0.000 0.000 0.056 0.000 0.000 0.944
#> GSM617621 1 0.0632 0.8756 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM617629 5 0.5683 0.1349 0.000 0.000 0.308 0.000 0.508 0.184
#> GSM617630 5 0.4888 0.3237 0.000 0.240 0.116 0.000 0.644 0.000
#> GSM617631 3 0.4150 0.8955 0.000 0.000 0.592 0.000 0.016 0.392
#> GSM617633 6 0.3102 0.4533 0.000 0.000 0.156 0.000 0.028 0.816
#> GSM617642 6 0.2135 0.5141 0.000 0.000 0.128 0.000 0.000 0.872
#> GSM617645 2 0.5080 0.4673 0.000 0.600 0.112 0.000 0.288 0.000
#> GSM617646 1 0.4014 0.6092 0.704 0.000 0.012 0.000 0.016 0.268
#> GSM617652 6 0.2507 0.6118 0.016 0.000 0.036 0.000 0.056 0.892
#> GSM617655 3 0.3789 0.8887 0.000 0.000 0.584 0.000 0.000 0.416
#> GSM617656 3 0.3737 0.8960 0.000 0.000 0.608 0.000 0.000 0.392
#> GSM617657 5 0.5508 0.5020 0.000 0.096 0.276 0.000 0.600 0.028
#> GSM617658 6 0.4823 -0.5708 0.000 0.000 0.388 0.000 0.060 0.552
#> GSM617659 6 0.1349 0.6020 0.004 0.000 0.056 0.000 0.000 0.940
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:kmeans 78 0.0667 2
#> ATC:kmeans 65 0.1640 3
#> ATC:kmeans 76 0.3201 4
#> ATC:kmeans 71 0.3510 5
#> ATC:kmeans 59 0.1650 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 79 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.993 0.997 0.5004 0.500 0.500
#> 3 3 1.000 0.947 0.979 0.3066 0.803 0.621
#> 4 4 0.881 0.827 0.929 0.1135 0.875 0.660
#> 5 5 0.717 0.589 0.791 0.0635 0.958 0.852
#> 6 6 0.691 0.603 0.753 0.0430 0.896 0.624
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
#> GSM617581 2 0.000 0.997 0.000 1.000
#> GSM617582 2 0.000 0.997 0.000 1.000
#> GSM617588 2 0.000 0.997 0.000 1.000
#> GSM617590 2 0.000 0.997 0.000 1.000
#> GSM617592 2 0.000 0.997 0.000 1.000
#> GSM617607 1 0.000 0.997 1.000 0.000
#> GSM617608 1 0.000 0.997 1.000 0.000
#> GSM617609 1 0.000 0.997 1.000 0.000
#> GSM617612 1 0.000 0.997 1.000 0.000
#> GSM617615 2 0.000 0.997 0.000 1.000
#> GSM617616 1 0.000 0.997 1.000 0.000
#> GSM617617 2 0.000 0.997 0.000 1.000
#> GSM617618 1 0.000 0.997 1.000 0.000
#> GSM617619 2 0.000 0.997 0.000 1.000
#> GSM617620 2 0.000 0.997 0.000 1.000
#> GSM617622 2 0.000 0.997 0.000 1.000
#> GSM617623 2 0.000 0.997 0.000 1.000
#> GSM617624 2 0.000 0.997 0.000 1.000
#> GSM617625 1 0.000 0.997 1.000 0.000
#> GSM617626 1 0.000 0.997 1.000 0.000
#> GSM617627 2 0.000 0.997 0.000 1.000
#> GSM617628 1 0.000 0.997 1.000 0.000
#> GSM617632 1 0.000 0.997 1.000 0.000
#> GSM617634 2 0.000 0.997 0.000 1.000
#> GSM617635 1 0.000 0.997 1.000 0.000
#> GSM617636 1 0.000 0.997 1.000 0.000
#> GSM617637 1 0.000 0.997 1.000 0.000
#> GSM617638 1 0.000 0.997 1.000 0.000
#> GSM617639 1 0.000 0.997 1.000 0.000
#> GSM617640 2 0.000 0.997 0.000 1.000
#> GSM617641 2 0.000 0.997 0.000 1.000
#> GSM617643 2 0.000 0.997 0.000 1.000
#> GSM617644 2 0.000 0.997 0.000 1.000
#> GSM617647 2 0.000 0.997 0.000 1.000
#> GSM617648 2 0.000 0.997 0.000 1.000
#> GSM617649 2 0.000 0.997 0.000 1.000
#> GSM617650 1 0.000 0.997 1.000 0.000
#> GSM617651 1 0.000 0.997 1.000 0.000
#> GSM617653 1 0.000 0.997 1.000 0.000
#> GSM617654 2 0.000 0.997 0.000 1.000
#> GSM617583 1 0.000 0.997 1.000 0.000
#> GSM617584 2 0.000 0.997 0.000 1.000
#> GSM617585 2 0.000 0.997 0.000 1.000
#> GSM617586 1 0.000 0.997 1.000 0.000
#> GSM617587 1 0.595 0.832 0.856 0.144
#> GSM617589 2 0.000 0.997 0.000 1.000
#> GSM617591 2 0.000 0.997 0.000 1.000
#> GSM617593 1 0.000 0.997 1.000 0.000
#> GSM617594 2 0.000 0.997 0.000 1.000
#> GSM617595 1 0.000 0.997 1.000 0.000
#> GSM617596 1 0.000 0.997 1.000 0.000
#> GSM617597 1 0.000 0.997 1.000 0.000
#> GSM617598 1 0.000 0.997 1.000 0.000
#> GSM617599 2 0.000 0.997 0.000 1.000
#> GSM617600 1 0.000 0.997 1.000 0.000
#> GSM617601 2 0.000 0.997 0.000 1.000
#> GSM617602 1 0.000 0.997 1.000 0.000
#> GSM617603 2 0.000 0.997 0.000 1.000
#> GSM617604 1 0.000 0.997 1.000 0.000
#> GSM617605 2 0.000 0.997 0.000 1.000
#> GSM617606 2 0.000 0.997 0.000 1.000
#> GSM617610 1 0.000 0.997 1.000 0.000
#> GSM617611 1 0.000 0.997 1.000 0.000
#> GSM617613 1 0.000 0.997 1.000 0.000
#> GSM617614 1 0.000 0.997 1.000 0.000
#> GSM617621 1 0.000 0.997 1.000 0.000
#> GSM617629 1 0.000 0.997 1.000 0.000
#> GSM617630 2 0.000 0.997 0.000 1.000
#> GSM617631 1 0.000 0.997 1.000 0.000
#> GSM617633 1 0.000 0.997 1.000 0.000
#> GSM617642 1 0.000 0.997 1.000 0.000
#> GSM617645 2 0.000 0.997 0.000 1.000
#> GSM617646 1 0.000 0.997 1.000 0.000
#> GSM617652 1 0.000 0.997 1.000 0.000
#> GSM617655 1 0.000 0.997 1.000 0.000
#> GSM617656 1 0.000 0.997 1.000 0.000
#> GSM617657 2 0.518 0.869 0.116 0.884
#> GSM617658 1 0.000 0.997 1.000 0.000
#> GSM617659 1 0.000 0.997 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM617581 1 0.0237 0.922 0.996 0.004 0.000
#> GSM617582 2 0.0237 0.996 0.000 0.996 0.004
#> GSM617588 2 0.0000 0.999 0.000 1.000 0.000
#> GSM617590 2 0.0000 0.999 0.000 1.000 0.000
#> GSM617592 2 0.0000 0.999 0.000 1.000 0.000
#> GSM617607 3 0.0000 0.983 0.000 0.000 1.000
#> GSM617608 3 0.0000 0.983 0.000 0.000 1.000
#> GSM617609 3 0.0000 0.983 0.000 0.000 1.000
#> GSM617612 1 0.0000 0.924 1.000 0.000 0.000
#> GSM617615 2 0.0000 0.999 0.000 1.000 0.000
#> GSM617616 3 0.0000 0.983 0.000 0.000 1.000
#> GSM617617 2 0.0000 0.999 0.000 1.000 0.000
#> GSM617618 3 0.0000 0.983 0.000 0.000 1.000
#> GSM617619 2 0.0424 0.992 0.000 0.992 0.008
#> GSM617620 2 0.0000 0.999 0.000 1.000 0.000
#> GSM617622 2 0.0000 0.999 0.000 1.000 0.000
#> GSM617623 1 0.0747 0.913 0.984 0.016 0.000
#> GSM617624 2 0.0237 0.996 0.000 0.996 0.004
#> GSM617625 3 0.0000 0.983 0.000 0.000 1.000
#> GSM617626 1 0.0000 0.924 1.000 0.000 0.000
#> GSM617627 2 0.0000 0.999 0.000 1.000 0.000
#> GSM617628 3 0.0000 0.983 0.000 0.000 1.000
#> GSM617632 3 0.6126 0.233 0.400 0.000 0.600
#> GSM617634 2 0.0424 0.992 0.000 0.992 0.008
#> GSM617635 3 0.0237 0.979 0.004 0.000 0.996
#> GSM617636 3 0.0000 0.983 0.000 0.000 1.000
#> GSM617637 1 0.0000 0.924 1.000 0.000 0.000
#> GSM617638 3 0.0000 0.983 0.000 0.000 1.000
#> GSM617639 1 0.0000 0.924 1.000 0.000 0.000
#> GSM617640 2 0.0000 0.999 0.000 1.000 0.000
#> GSM617641 2 0.0000 0.999 0.000 1.000 0.000
#> GSM617643 2 0.0000 0.999 0.000 1.000 0.000
#> GSM617644 2 0.0000 0.999 0.000 1.000 0.000
#> GSM617647 2 0.0000 0.999 0.000 1.000 0.000
#> GSM617648 2 0.0000 0.999 0.000 1.000 0.000
#> GSM617649 2 0.0000 0.999 0.000 1.000 0.000
#> GSM617650 3 0.0592 0.972 0.012 0.000 0.988
#> GSM617651 1 0.0000 0.924 1.000 0.000 0.000
#> GSM617653 1 0.0000 0.924 1.000 0.000 0.000
#> GSM617654 2 0.0000 0.999 0.000 1.000 0.000
#> GSM617583 3 0.0000 0.983 0.000 0.000 1.000
#> GSM617584 2 0.0000 0.999 0.000 1.000 0.000
#> GSM617585 2 0.0000 0.999 0.000 1.000 0.000
#> GSM617586 3 0.0000 0.983 0.000 0.000 1.000
#> GSM617587 1 0.2845 0.871 0.920 0.012 0.068
#> GSM617589 2 0.0000 0.999 0.000 1.000 0.000
#> GSM617591 2 0.0000 0.999 0.000 1.000 0.000
#> GSM617593 1 0.6026 0.455 0.624 0.000 0.376
#> GSM617594 2 0.0000 0.999 0.000 1.000 0.000
#> GSM617595 1 0.0000 0.924 1.000 0.000 0.000
#> GSM617596 1 0.0000 0.924 1.000 0.000 0.000
#> GSM617597 3 0.0000 0.983 0.000 0.000 1.000
#> GSM617598 1 0.6026 0.455 0.624 0.000 0.376
#> GSM617599 2 0.0000 0.999 0.000 1.000 0.000
#> GSM617600 3 0.0000 0.983 0.000 0.000 1.000
#> GSM617601 2 0.0000 0.999 0.000 1.000 0.000
#> GSM617602 3 0.0000 0.983 0.000 0.000 1.000
#> GSM617603 2 0.0000 0.999 0.000 1.000 0.000
#> GSM617604 1 0.0000 0.924 1.000 0.000 0.000
#> GSM617605 2 0.0000 0.999 0.000 1.000 0.000
#> GSM617606 2 0.0000 0.999 0.000 1.000 0.000
#> GSM617610 1 0.0000 0.924 1.000 0.000 0.000
#> GSM617611 1 0.6008 0.463 0.628 0.000 0.372
#> GSM617613 3 0.0000 0.983 0.000 0.000 1.000
#> GSM617614 3 0.0000 0.983 0.000 0.000 1.000
#> GSM617621 1 0.0000 0.924 1.000 0.000 0.000
#> GSM617629 3 0.0000 0.983 0.000 0.000 1.000
#> GSM617630 2 0.0000 0.999 0.000 1.000 0.000
#> GSM617631 3 0.0000 0.983 0.000 0.000 1.000
#> GSM617633 3 0.0000 0.983 0.000 0.000 1.000
#> GSM617642 3 0.0000 0.983 0.000 0.000 1.000
#> GSM617645 2 0.0000 0.999 0.000 1.000 0.000
#> GSM617646 1 0.0000 0.924 1.000 0.000 0.000
#> GSM617652 3 0.0000 0.983 0.000 0.000 1.000
#> GSM617655 3 0.0000 0.983 0.000 0.000 1.000
#> GSM617656 3 0.0000 0.983 0.000 0.000 1.000
#> GSM617657 3 0.0237 0.979 0.000 0.004 0.996
#> GSM617658 3 0.0000 0.983 0.000 0.000 1.000
#> GSM617659 3 0.0592 0.972 0.012 0.000 0.988
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM617581 1 0.2281 0.8130 0.904 0.096 0.000 0.000
#> GSM617582 4 0.0707 0.7704 0.000 0.020 0.000 0.980
#> GSM617588 2 0.0000 0.9504 0.000 1.000 0.000 0.000
#> GSM617590 2 0.0592 0.9493 0.000 0.984 0.000 0.016
#> GSM617592 2 0.0000 0.9504 0.000 1.000 0.000 0.000
#> GSM617607 3 0.0000 0.9379 0.000 0.000 1.000 0.000
#> GSM617608 3 0.0000 0.9379 0.000 0.000 1.000 0.000
#> GSM617609 3 0.0000 0.9379 0.000 0.000 1.000 0.000
#> GSM617612 1 0.0000 0.9012 1.000 0.000 0.000 0.000
#> GSM617615 2 0.0707 0.9486 0.000 0.980 0.000 0.020
#> GSM617616 3 0.0000 0.9379 0.000 0.000 1.000 0.000
#> GSM617617 2 0.0592 0.9460 0.000 0.984 0.000 0.016
#> GSM617618 4 0.4331 0.5887 0.000 0.000 0.288 0.712
#> GSM617619 4 0.0000 0.7733 0.000 0.000 0.000 1.000
#> GSM617620 2 0.0000 0.9504 0.000 1.000 0.000 0.000
#> GSM617622 2 0.2530 0.8964 0.000 0.888 0.000 0.112
#> GSM617623 1 0.2345 0.8085 0.900 0.100 0.000 0.000
#> GSM617624 4 0.0188 0.7736 0.000 0.004 0.000 0.996
#> GSM617625 3 0.0000 0.9379 0.000 0.000 1.000 0.000
#> GSM617626 1 0.0000 0.9012 1.000 0.000 0.000 0.000
#> GSM617627 4 0.0469 0.7723 0.000 0.012 0.000 0.988
#> GSM617628 3 0.0000 0.9379 0.000 0.000 1.000 0.000
#> GSM617632 3 0.4406 0.5460 0.300 0.000 0.700 0.000
#> GSM617634 4 0.0000 0.7733 0.000 0.000 0.000 1.000
#> GSM617635 3 0.0000 0.9379 0.000 0.000 1.000 0.000
#> GSM617636 3 0.0000 0.9379 0.000 0.000 1.000 0.000
#> GSM617637 1 0.0000 0.9012 1.000 0.000 0.000 0.000
#> GSM617638 4 0.4713 0.4858 0.000 0.000 0.360 0.640
#> GSM617639 1 0.0000 0.9012 1.000 0.000 0.000 0.000
#> GSM617640 2 0.0188 0.9496 0.000 0.996 0.000 0.004
#> GSM617641 2 0.0000 0.9504 0.000 1.000 0.000 0.000
#> GSM617643 2 0.0817 0.9480 0.000 0.976 0.000 0.024
#> GSM617644 2 0.1940 0.9245 0.000 0.924 0.000 0.076
#> GSM617647 2 0.0188 0.9504 0.000 0.996 0.000 0.004
#> GSM617648 2 0.1867 0.9271 0.000 0.928 0.000 0.072
#> GSM617649 2 0.2081 0.9192 0.000 0.916 0.000 0.084
#> GSM617650 3 0.0188 0.9343 0.004 0.000 0.996 0.000
#> GSM617651 1 0.0000 0.9012 1.000 0.000 0.000 0.000
#> GSM617653 1 0.0000 0.9012 1.000 0.000 0.000 0.000
#> GSM617654 2 0.0469 0.9473 0.000 0.988 0.000 0.012
#> GSM617583 3 0.0000 0.9379 0.000 0.000 1.000 0.000
#> GSM617584 2 0.0000 0.9504 0.000 1.000 0.000 0.000
#> GSM617585 4 0.4776 0.3580 0.000 0.376 0.000 0.624
#> GSM617586 3 0.0000 0.9379 0.000 0.000 1.000 0.000
#> GSM617587 1 0.8674 0.0397 0.424 0.060 0.172 0.344
#> GSM617589 2 0.0000 0.9504 0.000 1.000 0.000 0.000
#> GSM617591 2 0.1792 0.9226 0.000 0.932 0.000 0.068
#> GSM617593 3 0.4999 0.0326 0.492 0.000 0.508 0.000
#> GSM617594 2 0.3266 0.8378 0.000 0.832 0.000 0.168
#> GSM617595 1 0.0000 0.9012 1.000 0.000 0.000 0.000
#> GSM617596 1 0.0000 0.9012 1.000 0.000 0.000 0.000
#> GSM617597 3 0.0000 0.9379 0.000 0.000 1.000 0.000
#> GSM617598 3 0.5000 0.0182 0.496 0.000 0.504 0.000
#> GSM617599 2 0.1792 0.9306 0.000 0.932 0.000 0.068
#> GSM617600 3 0.0000 0.9379 0.000 0.000 1.000 0.000
#> GSM617601 2 0.4164 0.7106 0.000 0.736 0.000 0.264
#> GSM617602 3 0.0000 0.9379 0.000 0.000 1.000 0.000
#> GSM617603 2 0.0817 0.9475 0.000 0.976 0.000 0.024
#> GSM617604 1 0.0000 0.9012 1.000 0.000 0.000 0.000
#> GSM617605 2 0.0000 0.9504 0.000 1.000 0.000 0.000
#> GSM617606 2 0.2921 0.8336 0.000 0.860 0.000 0.140
#> GSM617610 1 0.0000 0.9012 1.000 0.000 0.000 0.000
#> GSM617611 1 0.5000 -0.0842 0.504 0.000 0.496 0.000
#> GSM617613 3 0.0000 0.9379 0.000 0.000 1.000 0.000
#> GSM617614 3 0.0000 0.9379 0.000 0.000 1.000 0.000
#> GSM617621 1 0.0000 0.9012 1.000 0.000 0.000 0.000
#> GSM617629 4 0.5000 0.1177 0.000 0.000 0.496 0.504
#> GSM617630 4 0.4356 0.5638 0.000 0.292 0.000 0.708
#> GSM617631 3 0.0000 0.9379 0.000 0.000 1.000 0.000
#> GSM617633 3 0.0000 0.9379 0.000 0.000 1.000 0.000
#> GSM617642 3 0.0000 0.9379 0.000 0.000 1.000 0.000
#> GSM617645 2 0.0000 0.9504 0.000 1.000 0.000 0.000
#> GSM617646 1 0.0000 0.9012 1.000 0.000 0.000 0.000
#> GSM617652 3 0.0000 0.9379 0.000 0.000 1.000 0.000
#> GSM617655 3 0.0000 0.9379 0.000 0.000 1.000 0.000
#> GSM617656 3 0.0000 0.9379 0.000 0.000 1.000 0.000
#> GSM617657 4 0.0188 0.7732 0.000 0.000 0.004 0.996
#> GSM617658 3 0.0000 0.9379 0.000 0.000 1.000 0.000
#> GSM617659 3 0.0188 0.9343 0.004 0.000 0.996 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM617581 1 0.4599 0.2584 0.744 0.156 0.000 0.100 0.000
#> GSM617582 5 0.1403 0.4759 0.000 0.024 0.000 0.024 0.952
#> GSM617588 2 0.0162 0.7381 0.000 0.996 0.000 0.004 0.000
#> GSM617590 2 0.1281 0.7366 0.000 0.956 0.000 0.012 0.032
#> GSM617592 2 0.0290 0.7377 0.000 0.992 0.000 0.008 0.000
#> GSM617607 3 0.1557 0.8600 0.000 0.000 0.940 0.052 0.008
#> GSM617608 3 0.0963 0.8606 0.000 0.000 0.964 0.036 0.000
#> GSM617609 3 0.1041 0.8520 0.000 0.000 0.964 0.004 0.032
#> GSM617612 1 0.0703 0.6184 0.976 0.000 0.000 0.024 0.000
#> GSM617615 2 0.2953 0.7127 0.000 0.844 0.000 0.144 0.012
#> GSM617616 3 0.1952 0.8476 0.000 0.000 0.912 0.084 0.004
#> GSM617617 2 0.4418 0.6307 0.004 0.756 0.000 0.180 0.060
#> GSM617618 5 0.4933 0.3202 0.000 0.000 0.236 0.076 0.688
#> GSM617619 5 0.0451 0.4821 0.000 0.008 0.004 0.000 0.988
#> GSM617620 2 0.0162 0.7378 0.000 0.996 0.000 0.004 0.000
#> GSM617622 2 0.5276 0.4805 0.000 0.516 0.000 0.436 0.048
#> GSM617623 1 0.4675 0.2405 0.736 0.164 0.000 0.100 0.000
#> GSM617624 5 0.3300 0.3818 0.000 0.004 0.000 0.204 0.792
#> GSM617625 3 0.0162 0.8629 0.000 0.000 0.996 0.004 0.000
#> GSM617626 1 0.0794 0.6196 0.972 0.000 0.000 0.028 0.000
#> GSM617627 5 0.3723 0.3881 0.000 0.044 0.000 0.152 0.804
#> GSM617628 3 0.0510 0.8607 0.000 0.000 0.984 0.000 0.016
#> GSM617632 3 0.6800 -0.0978 0.292 0.000 0.364 0.344 0.000
#> GSM617634 5 0.3521 0.3532 0.000 0.004 0.000 0.232 0.764
#> GSM617635 3 0.3949 0.6196 0.000 0.000 0.668 0.332 0.000
#> GSM617636 3 0.2891 0.7967 0.000 0.000 0.824 0.176 0.000
#> GSM617637 1 0.4251 0.4681 0.672 0.000 0.012 0.316 0.000
#> GSM617638 5 0.5458 0.1282 0.000 0.000 0.464 0.060 0.476
#> GSM617639 1 0.4329 0.4677 0.672 0.000 0.016 0.312 0.000
#> GSM617640 2 0.3291 0.6747 0.000 0.840 0.000 0.120 0.040
#> GSM617641 2 0.0290 0.7377 0.000 0.992 0.000 0.008 0.000
#> GSM617643 2 0.4315 0.6437 0.000 0.700 0.000 0.276 0.024
#> GSM617644 2 0.4761 0.5864 0.000 0.616 0.000 0.356 0.028
#> GSM617647 2 0.4696 0.5803 0.000 0.616 0.000 0.360 0.024
#> GSM617648 2 0.4709 0.5824 0.000 0.612 0.000 0.364 0.024
#> GSM617649 2 0.4982 0.5287 0.000 0.556 0.000 0.412 0.032
#> GSM617650 3 0.4491 0.5902 0.020 0.000 0.652 0.328 0.000
#> GSM617651 1 0.0963 0.6110 0.964 0.000 0.000 0.036 0.000
#> GSM617653 1 0.0162 0.6174 0.996 0.000 0.000 0.004 0.000
#> GSM617654 2 0.3565 0.6670 0.000 0.816 0.000 0.144 0.040
#> GSM617583 3 0.0162 0.8629 0.000 0.000 0.996 0.004 0.000
#> GSM617584 2 0.0404 0.7371 0.000 0.988 0.000 0.012 0.000
#> GSM617585 2 0.5694 0.0687 0.000 0.460 0.000 0.080 0.460
#> GSM617586 3 0.1106 0.8564 0.000 0.000 0.964 0.012 0.024
#> GSM617587 4 0.8767 0.0000 0.276 0.048 0.108 0.396 0.172
#> GSM617589 2 0.0912 0.7383 0.000 0.972 0.000 0.016 0.012
#> GSM617591 2 0.3861 0.6657 0.000 0.804 0.000 0.068 0.128
#> GSM617593 1 0.6771 0.1009 0.392 0.000 0.284 0.324 0.000
#> GSM617594 2 0.5591 0.4442 0.000 0.496 0.000 0.432 0.072
#> GSM617595 1 0.2074 0.6008 0.896 0.000 0.000 0.104 0.000
#> GSM617596 1 0.0880 0.6002 0.968 0.000 0.000 0.032 0.000
#> GSM617597 3 0.0794 0.8618 0.000 0.000 0.972 0.028 0.000
#> GSM617598 1 0.6771 0.1015 0.392 0.000 0.284 0.324 0.000
#> GSM617599 2 0.4777 0.6256 0.000 0.664 0.000 0.292 0.044
#> GSM617600 3 0.0794 0.8565 0.000 0.000 0.972 0.000 0.028
#> GSM617601 2 0.6410 0.3736 0.000 0.476 0.000 0.340 0.184
#> GSM617602 3 0.0703 0.8579 0.000 0.000 0.976 0.000 0.024
#> GSM617603 2 0.1872 0.7364 0.000 0.928 0.000 0.052 0.020
#> GSM617604 1 0.1121 0.5963 0.956 0.000 0.000 0.044 0.000
#> GSM617605 2 0.0898 0.7373 0.000 0.972 0.000 0.008 0.020
#> GSM617606 2 0.5277 0.5124 0.000 0.664 0.000 0.108 0.228
#> GSM617610 1 0.0162 0.6143 0.996 0.000 0.000 0.004 0.000
#> GSM617611 1 0.6700 0.1358 0.420 0.000 0.256 0.324 0.000
#> GSM617613 3 0.0794 0.8565 0.000 0.000 0.972 0.000 0.028
#> GSM617614 3 0.3086 0.7852 0.004 0.000 0.816 0.180 0.000
#> GSM617621 1 0.2020 0.6050 0.900 0.000 0.000 0.100 0.000
#> GSM617629 5 0.5353 0.1361 0.000 0.000 0.472 0.052 0.476
#> GSM617630 5 0.6614 -0.0115 0.008 0.396 0.000 0.164 0.432
#> GSM617631 3 0.0703 0.8579 0.000 0.000 0.976 0.000 0.024
#> GSM617633 3 0.2230 0.8320 0.000 0.000 0.884 0.116 0.000
#> GSM617642 3 0.2970 0.7948 0.004 0.000 0.828 0.168 0.000
#> GSM617645 2 0.3214 0.6762 0.000 0.844 0.000 0.120 0.036
#> GSM617646 1 0.4130 0.4863 0.696 0.000 0.012 0.292 0.000
#> GSM617652 3 0.2970 0.7947 0.004 0.000 0.828 0.168 0.000
#> GSM617655 3 0.0324 0.8626 0.000 0.000 0.992 0.004 0.004
#> GSM617656 3 0.0510 0.8602 0.000 0.000 0.984 0.000 0.016
#> GSM617657 5 0.3297 0.4596 0.000 0.000 0.084 0.068 0.848
#> GSM617658 3 0.0955 0.8548 0.000 0.000 0.968 0.004 0.028
#> GSM617659 3 0.3961 0.7038 0.016 0.000 0.736 0.248 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM617581 1 0.3755 0.7000 0.808 0.020 0.000 0.120 0.004 0.048
#> GSM617582 5 0.1863 0.5948 0.000 0.032 0.004 0.004 0.928 0.032
#> GSM617588 4 0.0000 0.7226 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM617590 4 0.2484 0.7110 0.000 0.036 0.000 0.896 0.044 0.024
#> GSM617592 4 0.0000 0.7226 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM617607 3 0.3081 0.7710 0.000 0.012 0.824 0.000 0.012 0.152
#> GSM617608 3 0.2473 0.7746 0.000 0.008 0.856 0.000 0.000 0.136
#> GSM617609 3 0.1737 0.7960 0.000 0.008 0.932 0.000 0.020 0.040
#> GSM617612 1 0.1858 0.8373 0.904 0.004 0.000 0.000 0.000 0.092
#> GSM617615 4 0.3232 0.5748 0.000 0.140 0.000 0.824 0.016 0.020
#> GSM617616 3 0.3454 0.7154 0.000 0.012 0.760 0.000 0.004 0.224
#> GSM617617 4 0.5856 0.5147 0.004 0.172 0.000 0.640 0.088 0.096
#> GSM617618 5 0.6519 0.5100 0.004 0.088 0.188 0.000 0.560 0.160
#> GSM617619 5 0.0862 0.6009 0.000 0.008 0.000 0.004 0.972 0.016
#> GSM617620 4 0.0000 0.7226 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM617622 2 0.3360 0.6578 0.000 0.732 0.000 0.264 0.004 0.000
#> GSM617623 1 0.3879 0.6863 0.796 0.020 0.000 0.132 0.004 0.048
#> GSM617624 5 0.4863 0.4315 0.000 0.412 0.000 0.000 0.528 0.060
#> GSM617625 3 0.0937 0.8117 0.000 0.000 0.960 0.000 0.000 0.040
#> GSM617626 1 0.2362 0.8074 0.860 0.004 0.000 0.000 0.000 0.136
#> GSM617627 5 0.4983 0.4956 0.000 0.224 0.000 0.032 0.676 0.068
#> GSM617628 3 0.0508 0.8138 0.000 0.000 0.984 0.000 0.004 0.012
#> GSM617632 6 0.4631 0.7069 0.168 0.000 0.140 0.000 0.000 0.692
#> GSM617634 5 0.4802 0.4299 0.000 0.404 0.000 0.000 0.540 0.056
#> GSM617635 6 0.4303 0.3449 0.016 0.012 0.332 0.000 0.000 0.640
#> GSM617636 3 0.3874 0.5453 0.000 0.008 0.636 0.000 0.000 0.356
#> GSM617637 6 0.3756 0.5631 0.352 0.000 0.004 0.000 0.000 0.644
#> GSM617638 5 0.6136 0.1536 0.000 0.052 0.416 0.000 0.440 0.092
#> GSM617639 6 0.3789 0.4503 0.416 0.000 0.000 0.000 0.000 0.584
#> GSM617640 4 0.4288 0.6555 0.004 0.088 0.000 0.784 0.048 0.076
#> GSM617641 4 0.0000 0.7226 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM617643 4 0.3659 -0.1199 0.000 0.364 0.000 0.636 0.000 0.000
#> GSM617644 2 0.3999 0.4871 0.000 0.500 0.000 0.496 0.004 0.000
#> GSM617647 2 0.4107 0.5520 0.004 0.540 0.000 0.452 0.000 0.004
#> GSM617648 2 0.3993 0.5312 0.000 0.520 0.000 0.476 0.004 0.000
#> GSM617649 2 0.3728 0.6535 0.000 0.652 0.000 0.344 0.004 0.000
#> GSM617650 6 0.4004 0.2826 0.012 0.000 0.368 0.000 0.000 0.620
#> GSM617651 1 0.1268 0.8373 0.952 0.008 0.000 0.000 0.004 0.036
#> GSM617653 1 0.1444 0.8423 0.928 0.000 0.000 0.000 0.000 0.072
#> GSM617654 4 0.4619 0.6354 0.004 0.116 0.000 0.756 0.056 0.068
#> GSM617583 3 0.0458 0.8136 0.000 0.000 0.984 0.000 0.000 0.016
#> GSM617584 4 0.0000 0.7226 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM617585 4 0.5997 0.2324 0.000 0.068 0.000 0.456 0.416 0.060
#> GSM617586 3 0.1080 0.8069 0.000 0.004 0.960 0.000 0.004 0.032
#> GSM617587 2 0.8905 -0.1501 0.228 0.352 0.076 0.052 0.092 0.200
#> GSM617589 4 0.1458 0.7194 0.000 0.016 0.000 0.948 0.016 0.020
#> GSM617591 4 0.4913 0.6283 0.000 0.076 0.000 0.720 0.144 0.060
#> GSM617593 6 0.4614 0.7260 0.228 0.000 0.096 0.000 0.000 0.676
#> GSM617594 2 0.3628 0.6585 0.000 0.720 0.000 0.268 0.004 0.008
#> GSM617595 1 0.3190 0.7079 0.772 0.008 0.000 0.000 0.000 0.220
#> GSM617596 1 0.0862 0.8330 0.972 0.008 0.000 0.000 0.004 0.016
#> GSM617597 3 0.1753 0.8025 0.000 0.004 0.912 0.000 0.000 0.084
#> GSM617598 6 0.4699 0.7262 0.228 0.000 0.104 0.000 0.000 0.668
#> GSM617599 4 0.4467 -0.1662 0.000 0.376 0.000 0.592 0.004 0.028
#> GSM617600 3 0.0951 0.8059 0.000 0.004 0.968 0.000 0.020 0.008
#> GSM617601 2 0.6287 0.4932 0.000 0.524 0.004 0.300 0.124 0.048
#> GSM617602 3 0.0909 0.8093 0.000 0.000 0.968 0.000 0.020 0.012
#> GSM617603 4 0.2401 0.7067 0.000 0.048 0.000 0.900 0.024 0.028
#> GSM617604 1 0.1155 0.8355 0.956 0.004 0.000 0.000 0.004 0.036
#> GSM617605 4 0.2266 0.7162 0.000 0.028 0.000 0.908 0.040 0.024
#> GSM617606 4 0.5636 0.5573 0.000 0.092 0.000 0.640 0.200 0.068
#> GSM617610 1 0.1471 0.8436 0.932 0.004 0.000 0.000 0.000 0.064
#> GSM617611 6 0.4662 0.7228 0.236 0.000 0.096 0.000 0.000 0.668
#> GSM617613 3 0.0891 0.8054 0.000 0.000 0.968 0.000 0.024 0.008
#> GSM617614 3 0.3684 0.5498 0.000 0.004 0.664 0.000 0.000 0.332
#> GSM617621 1 0.2996 0.6751 0.772 0.000 0.000 0.000 0.000 0.228
#> GSM617629 3 0.6352 -0.2202 0.000 0.084 0.440 0.000 0.396 0.080
#> GSM617630 5 0.7209 0.0105 0.012 0.124 0.000 0.296 0.444 0.124
#> GSM617631 3 0.1003 0.8077 0.000 0.000 0.964 0.000 0.020 0.016
#> GSM617633 3 0.3445 0.6940 0.000 0.012 0.744 0.000 0.000 0.244
#> GSM617642 3 0.3741 0.5846 0.000 0.008 0.672 0.000 0.000 0.320
#> GSM617645 4 0.3848 0.6703 0.000 0.084 0.000 0.808 0.036 0.072
#> GSM617646 6 0.4230 0.4526 0.400 0.008 0.008 0.000 0.000 0.584
#> GSM617652 3 0.4060 0.5269 0.008 0.008 0.644 0.000 0.000 0.340
#> GSM617655 3 0.0603 0.8135 0.000 0.004 0.980 0.000 0.000 0.016
#> GSM617656 3 0.0291 0.8127 0.000 0.004 0.992 0.000 0.000 0.004
#> GSM617657 5 0.5122 0.5797 0.000 0.112 0.112 0.000 0.708 0.068
#> GSM617658 3 0.2113 0.8049 0.000 0.008 0.912 0.000 0.032 0.048
#> GSM617659 3 0.4279 0.2759 0.012 0.004 0.548 0.000 0.000 0.436
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:skmeans 79 0.0869 2
#> ATC:skmeans 75 0.1981 3
#> ATC:skmeans 72 0.2825 4
#> ATC:skmeans 55 0.1989 5
#> ATC:skmeans 62 0.3392 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 79 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 0.947 0.926 0.970 0.4993 0.500 0.500
#> 3 3 0.613 0.744 0.857 0.3066 0.813 0.640
#> 4 4 0.665 0.776 0.877 0.0823 0.934 0.818
#> 5 5 0.768 0.845 0.910 0.0915 0.886 0.650
#> 6 6 0.749 0.561 0.756 0.0636 0.856 0.489
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
#> GSM617581 1 1.0000 -0.0317 0.500 0.500
#> GSM617582 2 0.3431 0.9150 0.064 0.936
#> GSM617588 2 0.0000 0.9634 0.000 1.000
#> GSM617590 2 0.0000 0.9634 0.000 1.000
#> GSM617592 2 0.0000 0.9634 0.000 1.000
#> GSM617607 1 0.0000 0.9717 1.000 0.000
#> GSM617608 1 0.0000 0.9717 1.000 0.000
#> GSM617609 1 0.0000 0.9717 1.000 0.000
#> GSM617612 1 0.0000 0.9717 1.000 0.000
#> GSM617615 2 0.0000 0.9634 0.000 1.000
#> GSM617616 1 0.0000 0.9717 1.000 0.000
#> GSM617617 2 0.0000 0.9634 0.000 1.000
#> GSM617618 1 0.0000 0.9717 1.000 0.000
#> GSM617619 2 0.3274 0.9183 0.060 0.940
#> GSM617620 2 0.0000 0.9634 0.000 1.000
#> GSM617622 2 0.0000 0.9634 0.000 1.000
#> GSM617623 2 0.8763 0.5813 0.296 0.704
#> GSM617624 2 0.0000 0.9634 0.000 1.000
#> GSM617625 1 0.0000 0.9717 1.000 0.000
#> GSM617626 1 0.0000 0.9717 1.000 0.000
#> GSM617627 2 0.0000 0.9634 0.000 1.000
#> GSM617628 1 0.0000 0.9717 1.000 0.000
#> GSM617632 1 0.0000 0.9717 1.000 0.000
#> GSM617634 2 0.4562 0.8837 0.096 0.904
#> GSM617635 1 0.0000 0.9717 1.000 0.000
#> GSM617636 1 0.0000 0.9717 1.000 0.000
#> GSM617637 1 0.0000 0.9717 1.000 0.000
#> GSM617638 1 0.0938 0.9603 0.988 0.012
#> GSM617639 1 0.0000 0.9717 1.000 0.000
#> GSM617640 2 0.0000 0.9634 0.000 1.000
#> GSM617641 2 0.0000 0.9634 0.000 1.000
#> GSM617643 2 0.0000 0.9634 0.000 1.000
#> GSM617644 2 0.0000 0.9634 0.000 1.000
#> GSM617647 2 0.0000 0.9634 0.000 1.000
#> GSM617648 2 0.0000 0.9634 0.000 1.000
#> GSM617649 2 0.0000 0.9634 0.000 1.000
#> GSM617650 1 0.0000 0.9717 1.000 0.000
#> GSM617651 1 0.0000 0.9717 1.000 0.000
#> GSM617653 1 0.0000 0.9717 1.000 0.000
#> GSM617654 2 0.0000 0.9634 0.000 1.000
#> GSM617583 1 0.0000 0.9717 1.000 0.000
#> GSM617584 2 0.0000 0.9634 0.000 1.000
#> GSM617585 2 0.0000 0.9634 0.000 1.000
#> GSM617586 1 0.9522 0.3836 0.628 0.372
#> GSM617587 2 0.8661 0.6102 0.288 0.712
#> GSM617589 2 0.0000 0.9634 0.000 1.000
#> GSM617591 2 0.0000 0.9634 0.000 1.000
#> GSM617593 1 0.0000 0.9717 1.000 0.000
#> GSM617594 2 0.0000 0.9634 0.000 1.000
#> GSM617595 1 0.0000 0.9717 1.000 0.000
#> GSM617596 1 0.0000 0.9717 1.000 0.000
#> GSM617597 1 0.0000 0.9717 1.000 0.000
#> GSM617598 1 0.0000 0.9717 1.000 0.000
#> GSM617599 2 0.0000 0.9634 0.000 1.000
#> GSM617600 1 0.0000 0.9717 1.000 0.000
#> GSM617601 2 0.0000 0.9634 0.000 1.000
#> GSM617602 1 0.0000 0.9717 1.000 0.000
#> GSM617603 2 0.0000 0.9634 0.000 1.000
#> GSM617604 1 0.0000 0.9717 1.000 0.000
#> GSM617605 2 0.0000 0.9634 0.000 1.000
#> GSM617606 2 0.0000 0.9634 0.000 1.000
#> GSM617610 1 0.0000 0.9717 1.000 0.000
#> GSM617611 1 0.0000 0.9717 1.000 0.000
#> GSM617613 1 0.0000 0.9717 1.000 0.000
#> GSM617614 1 0.0000 0.9717 1.000 0.000
#> GSM617621 1 0.0000 0.9717 1.000 0.000
#> GSM617629 1 0.8386 0.6132 0.732 0.268
#> GSM617630 2 0.3431 0.9150 0.064 0.936
#> GSM617631 1 0.0000 0.9717 1.000 0.000
#> GSM617633 1 0.0000 0.9717 1.000 0.000
#> GSM617642 1 0.0000 0.9717 1.000 0.000
#> GSM617645 2 0.0000 0.9634 0.000 1.000
#> GSM617646 1 0.0000 0.9717 1.000 0.000
#> GSM617652 1 0.0000 0.9717 1.000 0.000
#> GSM617655 1 0.0000 0.9717 1.000 0.000
#> GSM617656 1 0.0000 0.9717 1.000 0.000
#> GSM617657 2 0.9044 0.5392 0.320 0.680
#> GSM617658 1 0.0000 0.9717 1.000 0.000
#> GSM617659 1 0.0000 0.9717 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM617581 1 0.4960 0.722 0.832 0.128 0.040
#> GSM617582 2 0.4399 0.761 0.000 0.812 0.188
#> GSM617588 2 0.1411 0.881 0.036 0.964 0.000
#> GSM617590 2 0.0000 0.890 0.000 1.000 0.000
#> GSM617592 2 0.1964 0.872 0.056 0.944 0.000
#> GSM617607 3 0.2878 0.790 0.096 0.000 0.904
#> GSM617608 3 0.4291 0.773 0.180 0.000 0.820
#> GSM617609 3 0.0000 0.789 0.000 0.000 1.000
#> GSM617612 1 0.2711 0.802 0.912 0.000 0.088
#> GSM617615 2 0.0000 0.890 0.000 1.000 0.000
#> GSM617616 3 0.0592 0.791 0.012 0.000 0.988
#> GSM617617 2 0.6180 0.310 0.416 0.584 0.000
#> GSM617618 3 0.2878 0.790 0.096 0.000 0.904
#> GSM617619 2 0.5397 0.674 0.000 0.720 0.280
#> GSM617620 2 0.1411 0.881 0.036 0.964 0.000
#> GSM617622 1 0.8705 0.212 0.524 0.360 0.116
#> GSM617623 1 0.5254 0.556 0.736 0.264 0.000
#> GSM617624 2 0.4796 0.741 0.000 0.780 0.220
#> GSM617625 3 0.4452 0.751 0.192 0.000 0.808
#> GSM617626 1 0.1411 0.825 0.964 0.000 0.036
#> GSM617627 2 0.4842 0.737 0.000 0.776 0.224
#> GSM617628 3 0.0747 0.792 0.016 0.000 0.984
#> GSM617632 3 0.6062 0.624 0.384 0.000 0.616
#> GSM617634 2 0.5760 0.589 0.000 0.672 0.328
#> GSM617635 3 0.5431 0.709 0.284 0.000 0.716
#> GSM617636 3 0.6045 0.629 0.380 0.000 0.620
#> GSM617637 1 0.1964 0.812 0.944 0.000 0.056
#> GSM617638 3 0.3030 0.790 0.092 0.004 0.904
#> GSM617639 1 0.1411 0.825 0.964 0.000 0.036
#> GSM617640 2 0.0000 0.890 0.000 1.000 0.000
#> GSM617641 2 0.1411 0.881 0.036 0.964 0.000
#> GSM617643 2 0.0000 0.890 0.000 1.000 0.000
#> GSM617644 2 0.0000 0.890 0.000 1.000 0.000
#> GSM617647 2 0.5706 0.516 0.320 0.680 0.000
#> GSM617648 2 0.0000 0.890 0.000 1.000 0.000
#> GSM617649 2 0.0000 0.890 0.000 1.000 0.000
#> GSM617650 3 0.6062 0.624 0.384 0.000 0.616
#> GSM617651 1 0.2711 0.802 0.912 0.000 0.088
#> GSM617653 1 0.1411 0.825 0.964 0.000 0.036
#> GSM617654 2 0.0000 0.890 0.000 1.000 0.000
#> GSM617583 3 0.4346 0.754 0.184 0.000 0.816
#> GSM617584 2 0.5621 0.574 0.308 0.692 0.000
#> GSM617585 2 0.0000 0.890 0.000 1.000 0.000
#> GSM617586 3 0.0000 0.789 0.000 0.000 1.000
#> GSM617587 2 0.8094 0.557 0.100 0.612 0.288
#> GSM617589 2 0.1411 0.881 0.036 0.964 0.000
#> GSM617591 2 0.0000 0.890 0.000 1.000 0.000
#> GSM617593 3 0.6062 0.624 0.384 0.000 0.616
#> GSM617594 2 0.0000 0.890 0.000 1.000 0.000
#> GSM617595 1 0.1411 0.825 0.964 0.000 0.036
#> GSM617596 1 0.3192 0.785 0.888 0.000 0.112
#> GSM617597 3 0.1753 0.794 0.048 0.000 0.952
#> GSM617598 1 0.6260 -0.216 0.552 0.000 0.448
#> GSM617599 2 0.0000 0.890 0.000 1.000 0.000
#> GSM617600 3 0.0000 0.789 0.000 0.000 1.000
#> GSM617601 2 0.0000 0.890 0.000 1.000 0.000
#> GSM617602 3 0.0000 0.789 0.000 0.000 1.000
#> GSM617603 2 0.1411 0.881 0.036 0.964 0.000
#> GSM617604 1 0.1643 0.823 0.956 0.000 0.044
#> GSM617605 2 0.1411 0.881 0.036 0.964 0.000
#> GSM617606 2 0.0000 0.890 0.000 1.000 0.000
#> GSM617610 1 0.1411 0.825 0.964 0.000 0.036
#> GSM617611 1 0.5988 0.125 0.632 0.000 0.368
#> GSM617613 3 0.0000 0.789 0.000 0.000 1.000
#> GSM617614 3 0.6062 0.624 0.384 0.000 0.616
#> GSM617621 1 0.1411 0.825 0.964 0.000 0.036
#> GSM617629 3 0.0000 0.789 0.000 0.000 1.000
#> GSM617630 2 0.5285 0.774 0.040 0.812 0.148
#> GSM617631 3 0.0592 0.790 0.012 0.000 0.988
#> GSM617633 3 0.5529 0.701 0.296 0.000 0.704
#> GSM617642 3 0.6062 0.624 0.384 0.000 0.616
#> GSM617645 2 0.0000 0.890 0.000 1.000 0.000
#> GSM617646 3 0.6140 0.585 0.404 0.000 0.596
#> GSM617652 3 0.5178 0.730 0.256 0.000 0.744
#> GSM617655 3 0.0000 0.789 0.000 0.000 1.000
#> GSM617656 3 0.0000 0.789 0.000 0.000 1.000
#> GSM617657 3 0.3551 0.663 0.000 0.132 0.868
#> GSM617658 3 0.4235 0.776 0.176 0.000 0.824
#> GSM617659 3 0.6062 0.624 0.384 0.000 0.616
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM617581 1 0.3876 0.705 0.836 0.124 0.000 0.040
#> GSM617582 2 0.1637 0.868 0.000 0.940 0.060 0.000
#> GSM617588 4 0.0817 0.983 0.000 0.024 0.000 0.976
#> GSM617590 2 0.1557 0.868 0.000 0.944 0.000 0.056
#> GSM617592 4 0.0817 0.983 0.000 0.024 0.000 0.976
#> GSM617607 3 0.2408 0.801 0.104 0.000 0.896 0.000
#> GSM617608 3 0.3444 0.787 0.184 0.000 0.816 0.000
#> GSM617609 3 0.0336 0.797 0.008 0.000 0.992 0.000
#> GSM617612 1 0.0937 0.844 0.976 0.012 0.012 0.000
#> GSM617615 2 0.0000 0.894 0.000 1.000 0.000 0.000
#> GSM617616 3 0.0707 0.800 0.020 0.000 0.980 0.000
#> GSM617617 2 0.4866 0.343 0.404 0.596 0.000 0.000
#> GSM617618 3 0.2408 0.801 0.104 0.000 0.896 0.000
#> GSM617619 2 0.3172 0.797 0.000 0.840 0.160 0.000
#> GSM617620 4 0.0817 0.983 0.000 0.024 0.000 0.976
#> GSM617622 1 0.6770 0.406 0.604 0.236 0.160 0.000
#> GSM617623 1 0.5994 0.346 0.636 0.068 0.000 0.296
#> GSM617624 2 0.3123 0.800 0.000 0.844 0.156 0.000
#> GSM617625 3 0.3497 0.785 0.124 0.000 0.852 0.024
#> GSM617626 1 0.0000 0.851 1.000 0.000 0.000 0.000
#> GSM617627 2 0.3172 0.797 0.000 0.840 0.160 0.000
#> GSM617628 3 0.0000 0.796 0.000 0.000 1.000 0.000
#> GSM617632 3 0.5467 0.661 0.364 0.000 0.612 0.024
#> GSM617634 2 0.3764 0.722 0.000 0.784 0.216 0.000
#> GSM617635 3 0.4621 0.731 0.284 0.000 0.708 0.008
#> GSM617636 3 0.5467 0.661 0.364 0.000 0.612 0.024
#> GSM617637 1 0.2111 0.808 0.932 0.000 0.044 0.024
#> GSM617638 3 0.2530 0.801 0.100 0.004 0.896 0.000
#> GSM617639 1 0.0817 0.842 0.976 0.000 0.000 0.024
#> GSM617640 2 0.0000 0.894 0.000 1.000 0.000 0.000
#> GSM617641 4 0.0817 0.983 0.000 0.024 0.000 0.976
#> GSM617643 2 0.0000 0.894 0.000 1.000 0.000 0.000
#> GSM617644 2 0.0000 0.894 0.000 1.000 0.000 0.000
#> GSM617647 2 0.4477 0.539 0.312 0.688 0.000 0.000
#> GSM617648 2 0.0000 0.894 0.000 1.000 0.000 0.000
#> GSM617649 2 0.0000 0.894 0.000 1.000 0.000 0.000
#> GSM617650 3 0.5467 0.661 0.364 0.000 0.612 0.024
#> GSM617651 1 0.0817 0.841 0.976 0.024 0.000 0.000
#> GSM617653 1 0.0000 0.851 1.000 0.000 0.000 0.000
#> GSM617654 2 0.0000 0.894 0.000 1.000 0.000 0.000
#> GSM617583 3 0.3166 0.791 0.116 0.000 0.868 0.016
#> GSM617584 4 0.1716 0.952 0.000 0.064 0.000 0.936
#> GSM617585 2 0.0000 0.894 0.000 1.000 0.000 0.000
#> GSM617586 3 0.0000 0.796 0.000 0.000 1.000 0.000
#> GSM617587 2 0.5511 0.696 0.084 0.720 0.196 0.000
#> GSM617589 4 0.1474 0.964 0.000 0.052 0.000 0.948
#> GSM617591 2 0.0000 0.894 0.000 1.000 0.000 0.000
#> GSM617593 3 0.5467 0.661 0.364 0.000 0.612 0.024
#> GSM617594 2 0.0000 0.894 0.000 1.000 0.000 0.000
#> GSM617595 1 0.0000 0.851 1.000 0.000 0.000 0.000
#> GSM617596 1 0.1824 0.815 0.936 0.004 0.060 0.000
#> GSM617597 3 0.1474 0.803 0.052 0.000 0.948 0.000
#> GSM617598 3 0.5695 0.440 0.476 0.000 0.500 0.024
#> GSM617599 2 0.0000 0.894 0.000 1.000 0.000 0.000
#> GSM617600 3 0.0000 0.796 0.000 0.000 1.000 0.000
#> GSM617601 2 0.0188 0.893 0.000 0.996 0.004 0.000
#> GSM617602 3 0.0000 0.796 0.000 0.000 1.000 0.000
#> GSM617603 2 0.3726 0.724 0.000 0.788 0.000 0.212
#> GSM617604 1 0.0188 0.850 0.996 0.000 0.004 0.000
#> GSM617605 2 0.3528 0.745 0.000 0.808 0.000 0.192
#> GSM617606 2 0.0000 0.894 0.000 1.000 0.000 0.000
#> GSM617610 1 0.0000 0.851 1.000 0.000 0.000 0.000
#> GSM617611 1 0.5602 -0.213 0.568 0.000 0.408 0.024
#> GSM617613 3 0.0000 0.796 0.000 0.000 1.000 0.000
#> GSM617614 3 0.5467 0.661 0.364 0.000 0.612 0.024
#> GSM617621 1 0.0817 0.842 0.976 0.000 0.000 0.024
#> GSM617629 3 0.0000 0.796 0.000 0.000 1.000 0.000
#> GSM617630 2 0.1637 0.868 0.000 0.940 0.060 0.000
#> GSM617631 3 0.0469 0.797 0.012 0.000 0.988 0.000
#> GSM617633 3 0.4464 0.766 0.208 0.000 0.768 0.024
#> GSM617642 3 0.5436 0.665 0.356 0.000 0.620 0.024
#> GSM617645 2 0.0000 0.894 0.000 1.000 0.000 0.000
#> GSM617646 3 0.4925 0.574 0.428 0.000 0.572 0.000
#> GSM617652 3 0.4331 0.732 0.288 0.000 0.712 0.000
#> GSM617655 3 0.0000 0.796 0.000 0.000 1.000 0.000
#> GSM617656 3 0.0000 0.796 0.000 0.000 1.000 0.000
#> GSM617657 3 0.2868 0.694 0.000 0.136 0.864 0.000
#> GSM617658 3 0.3768 0.787 0.184 0.000 0.808 0.008
#> GSM617659 3 0.5467 0.661 0.364 0.000 0.612 0.024
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM617581 5 0.0000 0.901 0.000 0.000 0.000 0.000 1.000
#> GSM617582 2 0.2726 0.870 0.052 0.884 0.064 0.000 0.000
#> GSM617588 4 0.0000 0.964 0.000 0.000 0.000 1.000 0.000
#> GSM617590 2 0.2329 0.851 0.000 0.876 0.000 0.124 0.000
#> GSM617592 4 0.0000 0.964 0.000 0.000 0.000 1.000 0.000
#> GSM617607 3 0.2179 0.841 0.112 0.000 0.888 0.000 0.000
#> GSM617608 3 0.3039 0.790 0.192 0.000 0.808 0.000 0.000
#> GSM617609 3 0.0000 0.870 0.000 0.000 1.000 0.000 0.000
#> GSM617612 5 0.0000 0.901 0.000 0.000 0.000 0.000 1.000
#> GSM617615 2 0.0162 0.900 0.004 0.996 0.000 0.000 0.000
#> GSM617616 3 0.0404 0.870 0.012 0.000 0.988 0.000 0.000
#> GSM617617 5 0.3635 0.635 0.004 0.248 0.000 0.000 0.748
#> GSM617618 3 0.2179 0.841 0.112 0.000 0.888 0.000 0.000
#> GSM617619 2 0.4096 0.787 0.052 0.772 0.176 0.000 0.000
#> GSM617620 4 0.0000 0.964 0.000 0.000 0.000 1.000 0.000
#> GSM617622 5 0.2894 0.784 0.008 0.124 0.008 0.000 0.860
#> GSM617623 5 0.0000 0.901 0.000 0.000 0.000 0.000 1.000
#> GSM617624 2 0.4059 0.791 0.052 0.776 0.172 0.000 0.000
#> GSM617625 3 0.2852 0.775 0.172 0.000 0.828 0.000 0.000
#> GSM617626 5 0.0000 0.901 0.000 0.000 0.000 0.000 1.000
#> GSM617627 2 0.4096 0.787 0.052 0.772 0.176 0.000 0.000
#> GSM617628 3 0.0000 0.870 0.000 0.000 1.000 0.000 0.000
#> GSM617632 1 0.1851 0.920 0.912 0.000 0.088 0.000 0.000
#> GSM617634 2 0.4519 0.716 0.052 0.720 0.228 0.000 0.000
#> GSM617635 3 0.4210 0.393 0.412 0.000 0.588 0.000 0.000
#> GSM617636 1 0.1608 0.937 0.928 0.000 0.072 0.000 0.000
#> GSM617637 1 0.1648 0.918 0.940 0.000 0.020 0.000 0.040
#> GSM617638 3 0.2233 0.844 0.104 0.004 0.892 0.000 0.000
#> GSM617639 1 0.1410 0.899 0.940 0.000 0.000 0.000 0.060
#> GSM617640 2 0.0000 0.901 0.000 1.000 0.000 0.000 0.000
#> GSM617641 4 0.0000 0.964 0.000 0.000 0.000 1.000 0.000
#> GSM617643 2 0.0290 0.899 0.008 0.992 0.000 0.000 0.000
#> GSM617644 2 0.0162 0.900 0.004 0.996 0.000 0.000 0.000
#> GSM617647 5 0.4510 0.320 0.008 0.432 0.000 0.000 0.560
#> GSM617648 2 0.0290 0.899 0.008 0.992 0.000 0.000 0.000
#> GSM617649 2 0.0290 0.899 0.008 0.992 0.000 0.000 0.000
#> GSM617650 1 0.1410 0.946 0.940 0.000 0.060 0.000 0.000
#> GSM617651 5 0.0000 0.901 0.000 0.000 0.000 0.000 1.000
#> GSM617653 5 0.0000 0.901 0.000 0.000 0.000 0.000 1.000
#> GSM617654 2 0.0162 0.900 0.004 0.996 0.000 0.000 0.000
#> GSM617583 3 0.2471 0.810 0.136 0.000 0.864 0.000 0.000
#> GSM617584 4 0.2513 0.855 0.008 0.116 0.000 0.876 0.000
#> GSM617585 2 0.1270 0.895 0.052 0.948 0.000 0.000 0.000
#> GSM617586 3 0.0000 0.870 0.000 0.000 1.000 0.000 0.000
#> GSM617587 2 0.5258 0.651 0.000 0.664 0.232 0.000 0.104
#> GSM617589 4 0.0794 0.945 0.000 0.028 0.000 0.972 0.000
#> GSM617591 2 0.1270 0.895 0.052 0.948 0.000 0.000 0.000
#> GSM617593 1 0.1410 0.946 0.940 0.000 0.060 0.000 0.000
#> GSM617594 2 0.0290 0.899 0.008 0.992 0.000 0.000 0.000
#> GSM617595 5 0.0000 0.901 0.000 0.000 0.000 0.000 1.000
#> GSM617596 5 0.0000 0.901 0.000 0.000 0.000 0.000 1.000
#> GSM617597 3 0.1197 0.864 0.048 0.000 0.952 0.000 0.000
#> GSM617598 1 0.1410 0.946 0.940 0.000 0.060 0.000 0.000
#> GSM617599 2 0.0290 0.901 0.008 0.992 0.000 0.000 0.000
#> GSM617600 3 0.0000 0.870 0.000 0.000 1.000 0.000 0.000
#> GSM617601 2 0.1197 0.896 0.048 0.952 0.000 0.000 0.000
#> GSM617602 3 0.0000 0.870 0.000 0.000 1.000 0.000 0.000
#> GSM617603 2 0.2439 0.829 0.004 0.876 0.000 0.120 0.000
#> GSM617604 1 0.3876 0.577 0.684 0.000 0.000 0.000 0.316
#> GSM617605 2 0.3109 0.779 0.000 0.800 0.000 0.200 0.000
#> GSM617606 2 0.1270 0.895 0.052 0.948 0.000 0.000 0.000
#> GSM617610 5 0.0000 0.901 0.000 0.000 0.000 0.000 1.000
#> GSM617611 1 0.1410 0.946 0.940 0.000 0.060 0.000 0.000
#> GSM617613 3 0.0000 0.870 0.000 0.000 1.000 0.000 0.000
#> GSM617614 1 0.1410 0.946 0.940 0.000 0.060 0.000 0.000
#> GSM617621 1 0.1410 0.899 0.940 0.000 0.000 0.000 0.060
#> GSM617629 3 0.0000 0.870 0.000 0.000 1.000 0.000 0.000
#> GSM617630 2 0.2726 0.870 0.052 0.884 0.064 0.000 0.000
#> GSM617631 3 0.0510 0.868 0.016 0.000 0.984 0.000 0.000
#> GSM617633 3 0.3586 0.704 0.264 0.000 0.736 0.000 0.000
#> GSM617642 1 0.1410 0.946 0.940 0.000 0.060 0.000 0.000
#> GSM617645 2 0.0162 0.900 0.004 0.996 0.000 0.000 0.000
#> GSM617646 3 0.6287 0.420 0.276 0.000 0.528 0.000 0.196
#> GSM617652 3 0.3913 0.616 0.324 0.000 0.676 0.000 0.000
#> GSM617655 3 0.0000 0.870 0.000 0.000 1.000 0.000 0.000
#> GSM617656 3 0.0000 0.870 0.000 0.000 1.000 0.000 0.000
#> GSM617657 3 0.3692 0.688 0.052 0.136 0.812 0.000 0.000
#> GSM617658 3 0.3039 0.791 0.192 0.000 0.808 0.000 0.000
#> GSM617659 1 0.1410 0.946 0.940 0.000 0.060 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM617581 5 0.0000 0.9673 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM617582 2 0.0713 0.7859 0.000 0.972 0.028 0.000 0.000 0.000
#> GSM617588 4 0.0000 0.9510 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM617590 2 0.2841 0.7341 0.000 0.824 0.000 0.164 0.000 0.012
#> GSM617592 4 0.0000 0.9510 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM617607 3 0.2092 0.5377 0.124 0.000 0.876 0.000 0.000 0.000
#> GSM617608 3 0.3828 0.0645 0.440 0.000 0.560 0.000 0.000 0.000
#> GSM617609 3 0.0547 0.5833 0.000 0.020 0.980 0.000 0.000 0.000
#> GSM617612 5 0.0000 0.9673 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM617615 2 0.2416 0.7810 0.000 0.844 0.000 0.000 0.000 0.156
#> GSM617616 3 0.0363 0.5851 0.012 0.000 0.988 0.000 0.000 0.000
#> GSM617617 5 0.3273 0.6492 0.000 0.212 0.004 0.000 0.776 0.008
#> GSM617618 3 0.2625 0.5636 0.072 0.056 0.872 0.000 0.000 0.000
#> GSM617619 3 0.3857 0.1839 0.000 0.468 0.532 0.000 0.000 0.000
#> GSM617620 4 0.0000 0.9510 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM617622 6 0.4998 -0.1343 0.000 0.028 0.024 0.000 0.444 0.504
#> GSM617623 5 0.0000 0.9673 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM617624 3 0.4179 0.1616 0.000 0.472 0.516 0.000 0.000 0.012
#> GSM617625 6 0.5061 -0.4315 0.076 0.000 0.428 0.000 0.000 0.496
#> GSM617626 5 0.0000 0.9673 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM617627 3 0.3868 0.1215 0.000 0.496 0.504 0.000 0.000 0.000
#> GSM617628 3 0.3868 0.4139 0.000 0.000 0.504 0.000 0.000 0.496
#> GSM617632 1 0.1714 0.7847 0.908 0.000 0.092 0.000 0.000 0.000
#> GSM617634 3 0.6131 -0.1032 0.000 0.332 0.340 0.000 0.000 0.328
#> GSM617635 1 0.5015 0.1767 0.504 0.000 0.424 0.000 0.000 0.072
#> GSM617636 1 0.0937 0.8216 0.960 0.000 0.040 0.000 0.000 0.000
#> GSM617637 1 0.0000 0.8410 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617638 3 0.2685 0.5629 0.072 0.060 0.868 0.000 0.000 0.000
#> GSM617639 1 0.0000 0.8410 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617640 2 0.2340 0.7861 0.000 0.852 0.000 0.000 0.000 0.148
#> GSM617641 4 0.0000 0.9510 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM617643 6 0.3868 0.0799 0.000 0.496 0.000 0.000 0.000 0.504
#> GSM617644 6 0.3868 0.0799 0.000 0.496 0.000 0.000 0.000 0.504
#> GSM617647 6 0.5787 0.2120 0.000 0.252 0.000 0.000 0.244 0.504
#> GSM617648 6 0.3868 0.0799 0.000 0.496 0.000 0.000 0.000 0.504
#> GSM617649 6 0.3868 0.0799 0.000 0.496 0.000 0.000 0.000 0.504
#> GSM617650 1 0.0000 0.8410 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617651 5 0.0000 0.9673 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM617653 5 0.0000 0.9673 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM617654 2 0.3737 0.2318 0.000 0.608 0.000 0.000 0.000 0.392
#> GSM617583 6 0.5061 -0.4315 0.076 0.000 0.428 0.000 0.000 0.496
#> GSM617584 4 0.2981 0.7681 0.000 0.020 0.000 0.820 0.000 0.160
#> GSM617585 2 0.0000 0.8089 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM617586 3 0.0937 0.5801 0.000 0.000 0.960 0.000 0.000 0.040
#> GSM617587 3 0.5184 0.2801 0.000 0.316 0.572 0.000 0.112 0.000
#> GSM617589 4 0.0790 0.9292 0.000 0.032 0.000 0.968 0.000 0.000
#> GSM617591 2 0.0000 0.8089 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM617593 1 0.0000 0.8410 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617594 2 0.2454 0.7776 0.000 0.840 0.000 0.000 0.000 0.160
#> GSM617595 5 0.0000 0.9673 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM617596 5 0.0000 0.9673 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM617597 3 0.1633 0.5864 0.044 0.000 0.932 0.000 0.000 0.024
#> GSM617598 1 0.0000 0.8410 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617599 2 0.2703 0.7643 0.000 0.824 0.004 0.000 0.000 0.172
#> GSM617600 3 0.3868 0.4139 0.000 0.000 0.504 0.000 0.000 0.496
#> GSM617601 2 0.0632 0.8131 0.000 0.976 0.000 0.000 0.000 0.024
#> GSM617602 3 0.3868 0.4139 0.000 0.000 0.504 0.000 0.000 0.496
#> GSM617603 6 0.5029 0.0845 0.000 0.444 0.000 0.072 0.000 0.484
#> GSM617604 1 0.3482 0.5290 0.684 0.000 0.000 0.000 0.316 0.000
#> GSM617605 2 0.2883 0.6823 0.000 0.788 0.000 0.212 0.000 0.000
#> GSM617606 2 0.0000 0.8089 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM617610 5 0.0000 0.9673 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM617611 1 0.0000 0.8410 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617613 3 0.3868 0.4139 0.000 0.000 0.504 0.000 0.000 0.496
#> GSM617614 1 0.0000 0.8410 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617621 1 0.0000 0.8410 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM617629 3 0.0547 0.5831 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM617630 2 0.0547 0.7918 0.000 0.980 0.020 0.000 0.000 0.000
#> GSM617631 3 0.3868 0.4139 0.000 0.000 0.504 0.000 0.000 0.496
#> GSM617633 1 0.5697 0.0774 0.476 0.000 0.356 0.000 0.000 0.168
#> GSM617642 1 0.2956 0.7314 0.840 0.000 0.040 0.000 0.000 0.120
#> GSM617645 2 0.2416 0.7810 0.000 0.844 0.000 0.000 0.000 0.156
#> GSM617646 1 0.5855 0.1625 0.408 0.000 0.192 0.000 0.400 0.000
#> GSM617652 3 0.3867 -0.1097 0.488 0.000 0.512 0.000 0.000 0.000
#> GSM617655 3 0.3868 0.4139 0.000 0.000 0.504 0.000 0.000 0.496
#> GSM617656 3 0.3868 0.4139 0.000 0.000 0.504 0.000 0.000 0.496
#> GSM617657 3 0.4061 0.4797 0.000 0.248 0.708 0.000 0.000 0.044
#> GSM617658 3 0.3823 0.0555 0.436 0.000 0.564 0.000 0.000 0.000
#> GSM617659 1 0.0000 0.8410 1.000 0.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:pam 77 0.204 2
#> ATC:pam 75 0.216 3
#> ATC:pam 74 0.401 4
#> ATC:pam 76 0.246 5
#> ATC:pam 50 0.250 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 79 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 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 0.150 0.000 0.656 0.3687 1.000 1.000
#> 3 3 0.559 0.838 0.868 0.6381 0.361 0.361
#> 4 4 0.898 0.924 0.968 0.1803 0.853 0.630
#> 5 5 0.661 0.724 0.812 0.0595 1.000 1.000
#> 6 6 0.709 0.672 0.803 0.0619 0.852 0.520
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
#> GSM617581 1 0.886 0 0.696 0.304
#> GSM617582 1 0.689 0 0.816 0.184
#> GSM617588 1 0.952 0 0.628 0.372
#> GSM617590 1 0.952 0 0.628 0.372
#> GSM617592 1 0.952 0 0.628 0.372
#> GSM617607 1 1.000 0 0.512 0.488
#> GSM617608 1 1.000 0 0.512 0.488
#> GSM617609 1 0.998 0 0.528 0.472
#> GSM617612 1 0.574 0 0.864 0.136
#> GSM617615 1 0.802 0 0.756 0.244
#> GSM617616 1 0.946 0 0.636 0.364
#> GSM617617 1 0.788 0 0.764 0.236
#> GSM617618 1 0.224 0 0.964 0.036
#> GSM617619 1 0.781 0 0.768 0.232
#> GSM617620 1 0.952 0 0.628 0.372
#> GSM617622 1 0.788 0 0.764 0.236
#> GSM617623 1 0.958 0 0.620 0.380
#> GSM617624 1 0.644 0 0.836 0.164
#> GSM617625 1 1.000 0 0.512 0.488
#> GSM617626 1 0.900 0 0.684 0.316
#> GSM617627 1 0.260 0 0.956 0.044
#> GSM617628 1 1.000 0 0.512 0.488
#> GSM617632 1 0.722 0 0.800 0.200
#> GSM617634 1 0.184 0 0.972 0.028
#> GSM617635 1 0.671 0 0.824 0.176
#> GSM617636 1 0.999 0 0.516 0.484
#> GSM617637 1 0.689 0 0.816 0.184
#> GSM617638 1 0.000 0 1.000 0.000
#> GSM617639 1 0.917 0 0.668 0.332
#> GSM617640 1 0.946 0 0.636 0.364
#> GSM617641 1 0.952 0 0.628 0.372
#> GSM617643 1 0.939 0 0.644 0.356
#> GSM617644 1 0.936 0 0.648 0.352
#> GSM617647 1 0.788 0 0.764 0.236
#> GSM617648 1 0.929 0 0.656 0.344
#> GSM617649 1 0.788 0 0.764 0.236
#> GSM617650 1 0.738 0 0.792 0.208
#> GSM617651 1 0.653 0 0.832 0.168
#> GSM617653 1 0.900 0 0.684 0.316
#> GSM617654 1 0.814 0 0.748 0.252
#> GSM617583 1 0.993 0 0.548 0.452
#> GSM617584 1 0.952 0 0.628 0.372
#> GSM617585 1 0.909 0 0.676 0.324
#> GSM617586 1 1.000 0 0.512 0.488
#> GSM617587 1 0.224 0 0.964 0.036
#> GSM617589 1 0.952 0 0.628 0.372
#> GSM617591 1 0.814 0 0.748 0.252
#> GSM617593 1 0.913 0 0.672 0.328
#> GSM617594 1 0.788 0 0.764 0.236
#> GSM617595 1 0.494 0 0.892 0.108
#> GSM617596 1 0.844 0 0.728 0.272
#> GSM617597 1 1.000 0 0.512 0.488
#> GSM617598 1 0.706 0 0.808 0.192
#> GSM617599 1 0.788 0 0.764 0.236
#> GSM617600 1 0.760 0 0.780 0.220
#> GSM617601 1 0.788 0 0.764 0.236
#> GSM617602 1 0.999 0 0.516 0.484
#> GSM617603 1 0.952 0 0.628 0.372
#> GSM617604 1 0.000 0 1.000 0.000
#> GSM617605 1 0.952 0 0.628 0.372
#> GSM617606 1 0.921 0 0.664 0.336
#> GSM617610 1 0.900 0 0.684 0.316
#> GSM617611 1 0.760 0 0.780 0.220
#> GSM617613 1 0.722 0 0.800 0.200
#> GSM617614 1 0.722 0 0.800 0.200
#> GSM617621 1 0.900 0 0.684 0.316
#> GSM617629 1 0.738 0 0.792 0.208
#> GSM617630 1 0.814 0 0.748 0.252
#> GSM617631 1 0.788 0 0.764 0.236
#> GSM617633 1 0.753 0 0.784 0.216
#> GSM617642 1 0.936 0 0.648 0.352
#> GSM617645 1 0.952 0 0.628 0.372
#> GSM617646 1 0.680 0 0.820 0.180
#> GSM617652 1 1.000 0 0.512 0.488
#> GSM617655 1 0.827 0 0.740 0.260
#> GSM617656 1 0.775 0 0.772 0.228
#> GSM617657 1 0.855 0 0.720 0.280
#> GSM617658 1 0.000 0 1.000 0.000
#> GSM617659 1 0.714 0 0.804 0.196
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM617581 2 0.3742 0.8632 0.036 0.892 0.072
#> GSM617582 2 0.5734 0.7903 0.048 0.788 0.164
#> GSM617588 2 0.0747 0.8806 0.016 0.984 0.000
#> GSM617590 2 0.0592 0.8804 0.012 0.988 0.000
#> GSM617592 2 0.0592 0.8804 0.012 0.988 0.000
#> GSM617607 3 0.0592 0.9219 0.012 0.000 0.988
#> GSM617608 3 0.0592 0.9219 0.012 0.000 0.988
#> GSM617609 3 0.0237 0.9223 0.004 0.000 0.996
#> GSM617612 1 0.4842 0.8508 0.776 0.000 0.224
#> GSM617615 2 0.4413 0.8571 0.160 0.832 0.008
#> GSM617616 3 0.0592 0.9219 0.012 0.000 0.988
#> GSM617617 2 0.5631 0.7914 0.044 0.792 0.164
#> GSM617618 3 0.2096 0.9046 0.004 0.052 0.944
#> GSM617619 2 0.5734 0.7903 0.048 0.788 0.164
#> GSM617620 2 0.0592 0.8804 0.012 0.988 0.000
#> GSM617622 2 0.5734 0.8472 0.164 0.788 0.048
#> GSM617623 2 0.1753 0.8789 0.048 0.952 0.000
#> GSM617624 2 0.6100 0.8299 0.120 0.784 0.096
#> GSM617625 3 0.0000 0.9218 0.000 0.000 1.000
#> GSM617626 1 0.5406 0.8505 0.764 0.012 0.224
#> GSM617627 2 0.4750 0.7403 0.000 0.784 0.216
#> GSM617628 3 0.0000 0.9218 0.000 0.000 1.000
#> GSM617632 3 0.6955 0.0752 0.332 0.032 0.636
#> GSM617634 2 0.5974 0.8416 0.148 0.784 0.068
#> GSM617635 3 0.4609 0.8160 0.092 0.052 0.856
#> GSM617636 3 0.0592 0.9219 0.012 0.000 0.988
#> GSM617637 1 0.7116 0.7719 0.636 0.040 0.324
#> GSM617638 3 0.5905 0.6236 0.044 0.184 0.772
#> GSM617639 1 0.4974 0.8507 0.764 0.000 0.236
#> GSM617640 2 0.1753 0.8789 0.048 0.952 0.000
#> GSM617641 2 0.0592 0.8804 0.012 0.988 0.000
#> GSM617643 2 0.4121 0.8544 0.168 0.832 0.000
#> GSM617644 2 0.4121 0.8544 0.168 0.832 0.000
#> GSM617647 2 0.4634 0.8553 0.164 0.824 0.012
#> GSM617648 2 0.4121 0.8544 0.168 0.832 0.000
#> GSM617649 2 0.4782 0.8551 0.164 0.820 0.016
#> GSM617650 3 0.2918 0.8953 0.044 0.032 0.924
#> GSM617651 1 0.5024 0.8488 0.776 0.004 0.220
#> GSM617653 1 0.5292 0.8522 0.764 0.008 0.228
#> GSM617654 2 0.2339 0.8790 0.048 0.940 0.012
#> GSM617583 3 0.0000 0.9218 0.000 0.000 1.000
#> GSM617584 2 0.0237 0.8814 0.004 0.996 0.000
#> GSM617585 2 0.1753 0.8789 0.048 0.952 0.000
#> GSM617586 3 0.0000 0.9218 0.000 0.000 1.000
#> GSM617587 2 0.6357 0.5071 0.012 0.652 0.336
#> GSM617589 2 0.0592 0.8804 0.012 0.988 0.000
#> GSM617591 2 0.1753 0.8789 0.048 0.952 0.000
#> GSM617593 1 0.6309 0.5239 0.504 0.000 0.496
#> GSM617594 2 0.5524 0.8500 0.164 0.796 0.040
#> GSM617595 1 0.7447 0.6831 0.700 0.160 0.140
#> GSM617596 1 0.4842 0.8508 0.776 0.000 0.224
#> GSM617597 3 0.0000 0.9218 0.000 0.000 1.000
#> GSM617598 1 0.7484 0.5713 0.504 0.036 0.460
#> GSM617599 2 0.5269 0.7566 0.016 0.784 0.200
#> GSM617600 3 0.1289 0.9226 0.000 0.032 0.968
#> GSM617601 2 0.4663 0.8584 0.156 0.828 0.016
#> GSM617602 3 0.0000 0.9218 0.000 0.000 1.000
#> GSM617603 2 0.0592 0.8804 0.012 0.988 0.000
#> GSM617604 1 0.8902 0.6729 0.536 0.144 0.320
#> GSM617605 2 0.1411 0.8794 0.036 0.964 0.000
#> GSM617606 2 0.1753 0.8789 0.048 0.952 0.000
#> GSM617610 1 0.4842 0.8508 0.776 0.000 0.224
#> GSM617611 1 0.6126 0.7198 0.600 0.000 0.400
#> GSM617613 3 0.1289 0.9226 0.000 0.032 0.968
#> GSM617614 3 0.1877 0.9193 0.012 0.032 0.956
#> GSM617621 1 0.4974 0.8507 0.764 0.000 0.236
#> GSM617629 3 0.1950 0.9128 0.008 0.040 0.952
#> GSM617630 2 0.1753 0.8789 0.048 0.952 0.000
#> GSM617631 3 0.1289 0.9226 0.000 0.032 0.968
#> GSM617633 3 0.2550 0.9030 0.024 0.040 0.936
#> GSM617642 3 0.1337 0.9249 0.012 0.016 0.972
#> GSM617645 2 0.1753 0.8789 0.048 0.952 0.000
#> GSM617646 1 0.6905 0.7689 0.676 0.044 0.280
#> GSM617652 3 0.0592 0.9219 0.012 0.000 0.988
#> GSM617655 3 0.1163 0.9241 0.000 0.028 0.972
#> GSM617656 3 0.1289 0.9226 0.000 0.032 0.968
#> GSM617657 2 0.4796 0.7349 0.000 0.780 0.220
#> GSM617658 3 0.3112 0.8818 0.028 0.056 0.916
#> GSM617659 3 0.2806 0.8996 0.040 0.032 0.928
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM617581 1 0.3649 0.708 0.796 0.204 0.000 0.000
#> GSM617582 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM617588 4 0.0188 0.870 0.000 0.004 0.000 0.996
#> GSM617590 4 0.4972 0.213 0.000 0.456 0.000 0.544
#> GSM617592 4 0.0000 0.869 0.000 0.000 0.000 1.000
#> GSM617607 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM617608 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM617609 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM617612 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> GSM617615 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM617616 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM617617 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM617618 3 0.3636 0.755 0.008 0.172 0.820 0.000
#> GSM617619 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM617620 4 0.0000 0.869 0.000 0.000 0.000 1.000
#> GSM617622 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM617623 1 0.3649 0.708 0.796 0.204 0.000 0.000
#> GSM617624 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM617625 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM617626 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> GSM617627 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM617628 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM617632 3 0.2408 0.871 0.104 0.000 0.896 0.000
#> GSM617634 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM617635 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM617636 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM617637 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> GSM617638 3 0.3356 0.754 0.000 0.176 0.824 0.000
#> GSM617639 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> GSM617640 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM617641 4 0.0000 0.869 0.000 0.000 0.000 1.000
#> GSM617643 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM617644 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM617647 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM617648 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM617649 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM617650 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM617651 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> GSM617653 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> GSM617654 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM617583 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM617584 4 0.3688 0.741 0.000 0.208 0.000 0.792
#> GSM617585 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM617586 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM617587 2 0.0188 0.994 0.004 0.996 0.000 0.000
#> GSM617589 4 0.0188 0.870 0.000 0.004 0.000 0.996
#> GSM617591 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM617593 3 0.3024 0.821 0.148 0.000 0.852 0.000
#> GSM617594 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM617595 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> GSM617596 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> GSM617597 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM617598 3 0.3801 0.726 0.220 0.000 0.780 0.000
#> GSM617599 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM617600 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM617601 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM617602 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM617603 4 0.0336 0.870 0.000 0.008 0.000 0.992
#> GSM617604 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> GSM617605 4 0.1118 0.860 0.000 0.036 0.000 0.964
#> GSM617606 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM617610 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> GSM617611 3 0.4500 0.563 0.316 0.000 0.684 0.000
#> GSM617613 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM617614 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM617621 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> GSM617629 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM617630 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM617631 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM617633 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM617642 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM617645 4 0.3726 0.738 0.000 0.212 0.000 0.788
#> GSM617646 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> GSM617652 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM617655 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM617656 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM617657 2 0.0592 0.976 0.000 0.984 0.016 0.000
#> GSM617658 3 0.0000 0.957 0.000 0.000 1.000 0.000
#> GSM617659 3 0.0000 0.957 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM617581 1 0.6598 0.416 0.620 0.160 0.004 0.164 NA
#> GSM617582 2 0.4444 0.770 0.000 0.800 0.056 0.088 NA
#> GSM617588 4 0.0000 0.796 0.000 0.000 0.000 1.000 NA
#> GSM617590 4 0.5899 0.648 0.000 0.160 0.000 0.592 NA
#> GSM617592 4 0.0000 0.796 0.000 0.000 0.000 1.000 NA
#> GSM617607 3 0.0404 0.811 0.000 0.000 0.988 0.000 NA
#> GSM617608 3 0.0510 0.811 0.000 0.000 0.984 0.000 NA
#> GSM617609 3 0.1121 0.810 0.000 0.000 0.956 0.000 NA
#> GSM617612 1 0.0000 0.831 1.000 0.000 0.000 0.000 NA
#> GSM617615 2 0.0162 0.815 0.000 0.996 0.000 0.004 NA
#> GSM617616 3 0.1043 0.809 0.000 0.000 0.960 0.000 NA
#> GSM617617 2 0.4700 0.734 0.012 0.760 0.004 0.156 NA
#> GSM617618 3 0.4668 0.542 0.028 0.276 0.688 0.000 NA
#> GSM617619 2 0.4444 0.770 0.000 0.800 0.056 0.088 NA
#> GSM617620 4 0.0609 0.787 0.000 0.000 0.000 0.980 NA
#> GSM617622 2 0.0000 0.814 0.000 1.000 0.000 0.000 NA
#> GSM617623 1 0.6598 0.416 0.620 0.160 0.004 0.164 NA
#> GSM617624 2 0.0000 0.814 0.000 1.000 0.000 0.000 NA
#> GSM617625 3 0.0566 0.812 0.004 0.000 0.984 0.000 NA
#> GSM617626 1 0.0000 0.831 1.000 0.000 0.000 0.000 NA
#> GSM617627 2 0.3834 0.733 0.000 0.812 0.140 0.012 NA
#> GSM617628 3 0.1671 0.806 0.000 0.000 0.924 0.000 NA
#> GSM617632 3 0.5112 0.649 0.080 0.000 0.664 0.000 NA
#> GSM617634 2 0.0290 0.814 0.000 0.992 0.008 0.000 NA
#> GSM617635 3 0.3990 0.680 0.004 0.000 0.688 0.000 NA
#> GSM617636 3 0.1831 0.801 0.004 0.000 0.920 0.000 NA
#> GSM617637 1 0.5708 0.546 0.528 0.000 0.088 0.000 NA
#> GSM617638 3 0.3224 0.704 0.000 0.160 0.824 0.000 NA
#> GSM617639 1 0.2971 0.755 0.836 0.000 0.008 0.000 NA
#> GSM617640 2 0.6257 0.431 0.000 0.512 0.000 0.168 NA
#> GSM617641 4 0.0609 0.787 0.000 0.000 0.000 0.980 NA
#> GSM617643 2 0.0609 0.815 0.000 0.980 0.000 0.020 NA
#> GSM617644 2 0.0609 0.815 0.000 0.980 0.000 0.020 NA
#> GSM617647 2 0.0609 0.815 0.000 0.980 0.000 0.020 NA
#> GSM617648 2 0.0609 0.815 0.000 0.980 0.000 0.020 NA
#> GSM617649 2 0.0000 0.814 0.000 1.000 0.000 0.000 NA
#> GSM617650 3 0.3766 0.708 0.004 0.000 0.728 0.000 NA
#> GSM617651 1 0.0000 0.831 1.000 0.000 0.000 0.000 NA
#> GSM617653 1 0.0000 0.831 1.000 0.000 0.000 0.000 NA
#> GSM617654 2 0.4412 0.731 0.000 0.756 0.000 0.164 NA
#> GSM617583 3 0.2179 0.801 0.004 0.000 0.896 0.000 NA
#> GSM617584 4 0.3847 0.651 0.000 0.180 0.000 0.784 NA
#> GSM617585 2 0.6118 0.485 0.000 0.548 0.000 0.164 NA
#> GSM617586 3 0.2127 0.798 0.000 0.000 0.892 0.000 NA
#> GSM617587 2 0.3764 0.709 0.044 0.800 0.156 0.000 NA
#> GSM617589 4 0.3491 0.797 0.000 0.004 0.000 0.768 NA
#> GSM617591 2 0.5123 0.672 0.000 0.696 0.000 0.144 NA
#> GSM617593 3 0.6049 0.493 0.164 0.000 0.564 0.000 NA
#> GSM617594 2 0.0000 0.814 0.000 1.000 0.000 0.000 NA
#> GSM617595 1 0.2561 0.787 0.856 0.000 0.000 0.000 NA
#> GSM617596 1 0.0162 0.828 0.996 0.000 0.004 0.000 NA
#> GSM617597 3 0.0451 0.812 0.004 0.000 0.988 0.000 NA
#> GSM617598 3 0.6376 0.380 0.192 0.000 0.500 0.000 NA
#> GSM617599 2 0.2020 0.794 0.000 0.900 0.000 0.100 NA
#> GSM617600 3 0.3395 0.742 0.000 0.000 0.764 0.000 NA
#> GSM617601 2 0.0162 0.815 0.000 0.996 0.004 0.000 NA
#> GSM617602 3 0.3366 0.744 0.000 0.000 0.768 0.000 NA
#> GSM617603 4 0.3612 0.797 0.000 0.008 0.000 0.764 NA
#> GSM617604 1 0.2605 0.720 0.852 0.000 0.148 0.000 NA
#> GSM617605 4 0.4206 0.783 0.000 0.020 0.000 0.708 NA
#> GSM617606 2 0.6118 0.485 0.000 0.548 0.000 0.164 NA
#> GSM617610 1 0.0000 0.831 1.000 0.000 0.000 0.000 NA
#> GSM617611 3 0.6650 0.225 0.280 0.000 0.448 0.000 NA
#> GSM617613 3 0.3395 0.742 0.000 0.000 0.764 0.000 NA
#> GSM617614 3 0.3123 0.758 0.004 0.000 0.812 0.000 NA
#> GSM617621 1 0.0000 0.831 1.000 0.000 0.000 0.000 NA
#> GSM617629 3 0.2329 0.792 0.000 0.000 0.876 0.000 NA
#> GSM617630 2 0.6241 0.435 0.000 0.512 0.000 0.164 NA
#> GSM617631 3 0.3366 0.744 0.000 0.000 0.768 0.000 NA
#> GSM617633 3 0.0451 0.812 0.004 0.000 0.988 0.000 NA
#> GSM617642 3 0.3550 0.729 0.004 0.000 0.760 0.000 NA
#> GSM617645 4 0.6158 0.600 0.000 0.156 0.000 0.528 NA
#> GSM617646 1 0.4482 0.656 0.636 0.000 0.016 0.000 NA
#> GSM617652 3 0.2179 0.791 0.000 0.000 0.888 0.000 NA
#> GSM617655 3 0.3521 0.745 0.004 0.000 0.764 0.000 NA
#> GSM617656 3 0.3521 0.745 0.004 0.000 0.764 0.000 NA
#> GSM617657 2 0.3696 0.656 0.000 0.772 0.212 0.000 NA
#> GSM617658 3 0.1732 0.805 0.000 0.000 0.920 0.000 NA
#> GSM617659 3 0.3766 0.708 0.004 0.000 0.728 0.000 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM617581 1 0.4127 0.5593 0.716 0.044 0.000 0.000 0.236 0.004
#> GSM617582 2 0.4178 0.4607 0.000 0.608 0.000 0.000 0.372 0.020
#> GSM617588 4 0.2118 0.7925 0.000 0.008 0.000 0.888 0.104 0.000
#> GSM617590 5 0.4343 0.5610 0.000 0.048 0.000 0.244 0.700 0.008
#> GSM617592 4 0.1204 0.8334 0.000 0.000 0.000 0.944 0.056 0.000
#> GSM617607 3 0.2442 0.7622 0.000 0.000 0.852 0.000 0.004 0.144
#> GSM617608 3 0.2632 0.7530 0.000 0.000 0.832 0.000 0.004 0.164
#> GSM617609 3 0.1806 0.7922 0.000 0.000 0.908 0.000 0.004 0.088
#> GSM617612 1 0.2135 0.8292 0.872 0.000 0.000 0.000 0.000 0.128
#> GSM617615 2 0.0000 0.8285 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM617616 3 0.3337 0.6054 0.000 0.000 0.736 0.000 0.004 0.260
#> GSM617617 2 0.5296 0.4438 0.128 0.564 0.000 0.000 0.308 0.000
#> GSM617618 3 0.4820 0.6436 0.056 0.140 0.728 0.000 0.000 0.076
#> GSM617619 2 0.5106 0.4037 0.000 0.564 0.048 0.000 0.368 0.020
#> GSM617620 4 0.0000 0.8341 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM617622 2 0.0000 0.8285 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM617623 1 0.4127 0.5593 0.716 0.044 0.000 0.000 0.236 0.004
#> GSM617624 2 0.0725 0.8286 0.000 0.976 0.000 0.000 0.012 0.012
#> GSM617625 3 0.2793 0.7246 0.000 0.000 0.800 0.000 0.000 0.200
#> GSM617626 1 0.1663 0.8606 0.912 0.000 0.000 0.000 0.000 0.088
#> GSM617627 2 0.4603 0.6417 0.000 0.712 0.068 0.000 0.200 0.020
#> GSM617628 3 0.1471 0.7973 0.000 0.000 0.932 0.000 0.004 0.064
#> GSM617632 6 0.3991 0.7444 0.088 0.000 0.156 0.000 0.000 0.756
#> GSM617634 2 0.1167 0.8225 0.000 0.960 0.012 0.000 0.008 0.020
#> GSM617635 6 0.2454 0.7550 0.000 0.000 0.160 0.000 0.000 0.840
#> GSM617636 6 0.3866 0.1037 0.000 0.000 0.484 0.000 0.000 0.516
#> GSM617637 6 0.3221 0.4142 0.264 0.000 0.000 0.000 0.000 0.736
#> GSM617638 3 0.3781 0.7600 0.016 0.040 0.820 0.000 0.024 0.100
#> GSM617639 6 0.3989 0.0380 0.468 0.000 0.004 0.000 0.000 0.528
#> GSM617640 5 0.1285 0.6810 0.004 0.052 0.000 0.000 0.944 0.000
#> GSM617641 4 0.0000 0.8341 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM617643 2 0.0790 0.8252 0.000 0.968 0.000 0.000 0.032 0.000
#> GSM617644 2 0.0790 0.8252 0.000 0.968 0.000 0.000 0.032 0.000
#> GSM617647 2 0.0713 0.8255 0.000 0.972 0.000 0.000 0.028 0.000
#> GSM617648 2 0.0458 0.8282 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM617649 2 0.0000 0.8285 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM617650 6 0.2562 0.7549 0.000 0.000 0.172 0.000 0.000 0.828
#> GSM617651 1 0.0937 0.8574 0.960 0.000 0.000 0.000 0.000 0.040
#> GSM617653 1 0.1531 0.8683 0.928 0.000 0.004 0.000 0.000 0.068
#> GSM617654 2 0.3989 0.3294 0.004 0.528 0.000 0.000 0.468 0.000
#> GSM617583 3 0.2618 0.7640 0.000 0.000 0.860 0.000 0.024 0.116
#> GSM617584 4 0.4965 0.5194 0.000 0.140 0.000 0.644 0.216 0.000
#> GSM617585 5 0.2841 0.6743 0.000 0.164 0.000 0.000 0.824 0.012
#> GSM617586 3 0.1349 0.7973 0.000 0.000 0.940 0.000 0.004 0.056
#> GSM617587 2 0.5559 0.5423 0.044 0.664 0.188 0.000 0.012 0.092
#> GSM617589 5 0.5197 0.2434 0.000 0.068 0.000 0.420 0.504 0.008
#> GSM617591 5 0.3874 0.3160 0.000 0.356 0.000 0.000 0.636 0.008
#> GSM617593 6 0.3348 0.7429 0.016 0.000 0.216 0.000 0.000 0.768
#> GSM617594 2 0.0000 0.8285 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM617595 1 0.3330 0.7051 0.716 0.000 0.000 0.000 0.000 0.284
#> GSM617596 1 0.1204 0.8653 0.944 0.000 0.000 0.000 0.000 0.056
#> GSM617597 3 0.2730 0.7371 0.000 0.000 0.808 0.000 0.000 0.192
#> GSM617598 6 0.2613 0.7533 0.012 0.000 0.140 0.000 0.000 0.848
#> GSM617599 2 0.1204 0.8069 0.000 0.944 0.000 0.000 0.056 0.000
#> GSM617600 3 0.2088 0.7554 0.000 0.000 0.904 0.000 0.028 0.068
#> GSM617601 2 0.0363 0.8298 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM617602 3 0.1492 0.7757 0.000 0.000 0.940 0.000 0.024 0.036
#> GSM617603 5 0.5279 0.2404 0.000 0.076 0.000 0.416 0.500 0.008
#> GSM617604 1 0.2039 0.8016 0.904 0.000 0.076 0.000 0.020 0.000
#> GSM617605 5 0.3510 0.6147 0.000 0.016 0.000 0.204 0.772 0.008
#> GSM617606 5 0.2632 0.6767 0.000 0.164 0.000 0.000 0.832 0.004
#> GSM617610 1 0.1387 0.8677 0.932 0.000 0.000 0.000 0.000 0.068
#> GSM617611 6 0.3683 0.7545 0.044 0.000 0.192 0.000 0.000 0.764
#> GSM617613 3 0.2088 0.7554 0.000 0.000 0.904 0.000 0.028 0.068
#> GSM617614 6 0.3499 0.6133 0.000 0.000 0.320 0.000 0.000 0.680
#> GSM617621 1 0.1531 0.8683 0.928 0.000 0.004 0.000 0.000 0.068
#> GSM617629 3 0.0935 0.7933 0.000 0.004 0.964 0.000 0.000 0.032
#> GSM617630 5 0.1204 0.6826 0.000 0.056 0.000 0.000 0.944 0.000
#> GSM617631 3 0.2009 0.7595 0.000 0.000 0.908 0.000 0.024 0.068
#> GSM617633 3 0.3330 0.6480 0.000 0.000 0.716 0.000 0.000 0.284
#> GSM617642 6 0.3244 0.7020 0.000 0.000 0.268 0.000 0.000 0.732
#> GSM617645 5 0.2705 0.6569 0.004 0.040 0.000 0.076 0.876 0.004
#> GSM617646 6 0.3368 0.4836 0.232 0.000 0.012 0.000 0.000 0.756
#> GSM617652 3 0.3923 0.1272 0.000 0.000 0.580 0.000 0.004 0.416
#> GSM617655 3 0.2573 0.7532 0.000 0.000 0.864 0.000 0.024 0.112
#> GSM617656 3 0.2122 0.7600 0.000 0.000 0.900 0.000 0.024 0.076
#> GSM617657 3 0.5183 -0.0264 0.000 0.456 0.480 0.000 0.040 0.024
#> GSM617658 3 0.1812 0.7940 0.000 0.000 0.912 0.000 0.008 0.080
#> GSM617659 6 0.3266 0.6936 0.000 0.000 0.272 0.000 0.000 0.728
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:mclust 0 NA 2
#> ATC:mclust 78 0.192 3
#> ATC:mclust 78 0.324 4
#> ATC:mclust 70 0.314 5
#> ATC:mclust 66 0.183 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 79 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 0.999 0.957 0.982 0.4617 0.529 0.529
#> 3 3 0.645 0.723 0.887 0.3897 0.759 0.569
#> 4 4 0.515 0.570 0.781 0.1448 0.798 0.500
#> 5 5 0.554 0.565 0.739 0.0703 0.779 0.354
#> 6 6 0.545 0.478 0.679 0.0334 0.969 0.854
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
#> GSM617581 2 0.0672 0.948 0.008 0.992
#> GSM617582 1 0.0938 0.986 0.988 0.012
#> GSM617588 2 0.0000 0.953 0.000 1.000
#> GSM617590 2 0.0000 0.953 0.000 1.000
#> GSM617592 2 0.0000 0.953 0.000 1.000
#> GSM617607 1 0.0000 0.997 1.000 0.000
#> GSM617608 1 0.0000 0.997 1.000 0.000
#> GSM617609 1 0.0000 0.997 1.000 0.000
#> GSM617612 1 0.0000 0.997 1.000 0.000
#> GSM617615 2 0.0000 0.953 0.000 1.000
#> GSM617616 1 0.0000 0.997 1.000 0.000
#> GSM617617 2 0.1843 0.933 0.028 0.972
#> GSM617618 1 0.0000 0.997 1.000 0.000
#> GSM617619 1 0.0376 0.994 0.996 0.004
#> GSM617620 2 0.0000 0.953 0.000 1.000
#> GSM617622 2 0.9248 0.521 0.340 0.660
#> GSM617623 2 0.0000 0.953 0.000 1.000
#> GSM617624 1 0.0938 0.986 0.988 0.012
#> GSM617625 1 0.0000 0.997 1.000 0.000
#> GSM617626 1 0.0000 0.997 1.000 0.000
#> GSM617627 1 0.4431 0.892 0.908 0.092
#> GSM617628 1 0.0000 0.997 1.000 0.000
#> GSM617632 1 0.0000 0.997 1.000 0.000
#> GSM617634 1 0.0000 0.997 1.000 0.000
#> GSM617635 1 0.0000 0.997 1.000 0.000
#> GSM617636 1 0.0000 0.997 1.000 0.000
#> GSM617637 1 0.0000 0.997 1.000 0.000
#> GSM617638 1 0.0000 0.997 1.000 0.000
#> GSM617639 1 0.0000 0.997 1.000 0.000
#> GSM617640 2 0.0000 0.953 0.000 1.000
#> GSM617641 2 0.0000 0.953 0.000 1.000
#> GSM617643 2 0.0000 0.953 0.000 1.000
#> GSM617644 2 0.0000 0.953 0.000 1.000
#> GSM617647 2 0.0000 0.953 0.000 1.000
#> GSM617648 2 0.0000 0.953 0.000 1.000
#> GSM617649 2 0.0000 0.953 0.000 1.000
#> GSM617650 1 0.0000 0.997 1.000 0.000
#> GSM617651 1 0.0000 0.997 1.000 0.000
#> GSM617653 1 0.0000 0.997 1.000 0.000
#> GSM617654 2 0.0000 0.953 0.000 1.000
#> GSM617583 1 0.0000 0.997 1.000 0.000
#> GSM617584 2 0.0000 0.953 0.000 1.000
#> GSM617585 2 0.0000 0.953 0.000 1.000
#> GSM617586 1 0.0000 0.997 1.000 0.000
#> GSM617587 1 0.0000 0.997 1.000 0.000
#> GSM617589 2 0.0000 0.953 0.000 1.000
#> GSM617591 2 0.0000 0.953 0.000 1.000
#> GSM617593 1 0.0000 0.997 1.000 0.000
#> GSM617594 2 0.5408 0.842 0.124 0.876
#> GSM617595 1 0.0000 0.997 1.000 0.000
#> GSM617596 1 0.0000 0.997 1.000 0.000
#> GSM617597 1 0.0000 0.997 1.000 0.000
#> GSM617598 1 0.0000 0.997 1.000 0.000
#> GSM617599 2 0.0938 0.945 0.012 0.988
#> GSM617600 1 0.0000 0.997 1.000 0.000
#> GSM617601 2 0.9996 0.107 0.488 0.512
#> GSM617602 1 0.0000 0.997 1.000 0.000
#> GSM617603 2 0.0000 0.953 0.000 1.000
#> GSM617604 1 0.0000 0.997 1.000 0.000
#> GSM617605 2 0.0000 0.953 0.000 1.000
#> GSM617606 2 0.0000 0.953 0.000 1.000
#> GSM617610 1 0.0000 0.997 1.000 0.000
#> GSM617611 1 0.0000 0.997 1.000 0.000
#> GSM617613 1 0.0000 0.997 1.000 0.000
#> GSM617614 1 0.0000 0.997 1.000 0.000
#> GSM617621 1 0.0000 0.997 1.000 0.000
#> GSM617629 1 0.0000 0.997 1.000 0.000
#> GSM617630 2 0.8955 0.576 0.312 0.688
#> GSM617631 1 0.0000 0.997 1.000 0.000
#> GSM617633 1 0.0000 0.997 1.000 0.000
#> GSM617642 1 0.0000 0.997 1.000 0.000
#> GSM617645 2 0.0000 0.953 0.000 1.000
#> GSM617646 1 0.0000 0.997 1.000 0.000
#> GSM617652 1 0.0000 0.997 1.000 0.000
#> GSM617655 1 0.0000 0.997 1.000 0.000
#> GSM617656 1 0.0000 0.997 1.000 0.000
#> GSM617657 1 0.0000 0.997 1.000 0.000
#> GSM617658 1 0.0000 0.997 1.000 0.000
#> GSM617659 1 0.0000 0.997 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM617581 1 0.0000 0.7613 1.000 0.000 0.000
#> GSM617582 3 0.4062 0.7597 0.000 0.164 0.836
#> GSM617588 2 0.2711 0.8290 0.088 0.912 0.000
#> GSM617590 2 0.0000 0.8670 0.000 1.000 0.000
#> GSM617592 2 0.5859 0.5264 0.344 0.656 0.000
#> GSM617607 3 0.0000 0.8935 0.000 0.000 1.000
#> GSM617608 3 0.0000 0.8935 0.000 0.000 1.000
#> GSM617609 3 0.0000 0.8935 0.000 0.000 1.000
#> GSM617612 1 0.1289 0.7674 0.968 0.000 0.032
#> GSM617615 2 0.0000 0.8670 0.000 1.000 0.000
#> GSM617616 3 0.0237 0.8915 0.004 0.000 0.996
#> GSM617617 1 0.6566 0.2030 0.636 0.348 0.016
#> GSM617618 3 0.0000 0.8935 0.000 0.000 1.000
#> GSM617619 3 0.4931 0.6768 0.000 0.232 0.768
#> GSM617620 2 0.1643 0.8544 0.044 0.956 0.000
#> GSM617622 2 0.8280 0.3635 0.092 0.564 0.344
#> GSM617623 1 0.0000 0.7613 1.000 0.000 0.000
#> GSM617624 3 0.4062 0.7610 0.000 0.164 0.836
#> GSM617625 3 0.0000 0.8935 0.000 0.000 1.000
#> GSM617626 1 0.1964 0.7642 0.944 0.000 0.056
#> GSM617627 3 0.3879 0.7722 0.000 0.152 0.848
#> GSM617628 3 0.0000 0.8935 0.000 0.000 1.000
#> GSM617632 3 0.6244 0.0395 0.440 0.000 0.560
#> GSM617634 3 0.2356 0.8449 0.000 0.072 0.928
#> GSM617635 3 0.2165 0.8478 0.064 0.000 0.936
#> GSM617636 3 0.0424 0.8893 0.008 0.000 0.992
#> GSM617637 1 0.5178 0.6291 0.744 0.000 0.256
#> GSM617638 3 0.0000 0.8935 0.000 0.000 1.000
#> GSM617639 1 0.3686 0.7411 0.860 0.000 0.140
#> GSM617640 2 0.1163 0.8608 0.028 0.972 0.000
#> GSM617641 2 0.3619 0.7946 0.136 0.864 0.000
#> GSM617643 2 0.0000 0.8670 0.000 1.000 0.000
#> GSM617644 2 0.0000 0.8670 0.000 1.000 0.000
#> GSM617647 1 0.6252 -0.0966 0.556 0.444 0.000
#> GSM617648 2 0.0000 0.8670 0.000 1.000 0.000
#> GSM617649 2 0.1711 0.8589 0.032 0.960 0.008
#> GSM617650 3 0.6126 0.1856 0.400 0.000 0.600
#> GSM617651 1 0.0000 0.7613 1.000 0.000 0.000
#> GSM617653 1 0.0000 0.7613 1.000 0.000 0.000
#> GSM617654 2 0.3686 0.7902 0.140 0.860 0.000
#> GSM617583 3 0.0000 0.8935 0.000 0.000 1.000
#> GSM617584 2 0.6305 0.2432 0.484 0.516 0.000
#> GSM617585 2 0.3941 0.7390 0.000 0.844 0.156
#> GSM617586 3 0.0000 0.8935 0.000 0.000 1.000
#> GSM617587 3 0.2066 0.8513 0.060 0.000 0.940
#> GSM617589 2 0.0000 0.8670 0.000 1.000 0.000
#> GSM617591 2 0.1411 0.8483 0.000 0.964 0.036
#> GSM617593 1 0.6286 0.2511 0.536 0.000 0.464
#> GSM617594 2 0.4796 0.6665 0.000 0.780 0.220
#> GSM617595 1 0.0424 0.7644 0.992 0.000 0.008
#> GSM617596 1 0.0892 0.7672 0.980 0.000 0.020
#> GSM617597 3 0.0000 0.8935 0.000 0.000 1.000
#> GSM617598 1 0.6305 0.1879 0.516 0.000 0.484
#> GSM617599 2 0.0829 0.8641 0.004 0.984 0.012
#> GSM617600 3 0.0000 0.8935 0.000 0.000 1.000
#> GSM617601 3 0.6168 0.2798 0.000 0.412 0.588
#> GSM617602 3 0.0000 0.8935 0.000 0.000 1.000
#> GSM617603 2 0.0000 0.8670 0.000 1.000 0.000
#> GSM617604 1 0.3686 0.7408 0.860 0.000 0.140
#> GSM617605 2 0.0000 0.8670 0.000 1.000 0.000
#> GSM617606 2 0.0000 0.8670 0.000 1.000 0.000
#> GSM617610 1 0.0000 0.7613 1.000 0.000 0.000
#> GSM617611 1 0.6286 0.2508 0.536 0.000 0.464
#> GSM617613 3 0.0000 0.8935 0.000 0.000 1.000
#> GSM617614 3 0.3686 0.7596 0.140 0.000 0.860
#> GSM617621 1 0.0892 0.7671 0.980 0.000 0.020
#> GSM617629 3 0.0000 0.8935 0.000 0.000 1.000
#> GSM617630 2 0.6252 0.2101 0.000 0.556 0.444
#> GSM617631 3 0.0000 0.8935 0.000 0.000 1.000
#> GSM617633 3 0.0000 0.8935 0.000 0.000 1.000
#> GSM617642 3 0.2711 0.8222 0.088 0.000 0.912
#> GSM617645 2 0.1860 0.8539 0.052 0.948 0.000
#> GSM617646 1 0.6225 0.3288 0.568 0.000 0.432
#> GSM617652 3 0.0424 0.8893 0.008 0.000 0.992
#> GSM617655 3 0.0000 0.8935 0.000 0.000 1.000
#> GSM617656 3 0.0000 0.8935 0.000 0.000 1.000
#> GSM617657 3 0.3038 0.8183 0.000 0.104 0.896
#> GSM617658 3 0.0000 0.8935 0.000 0.000 1.000
#> GSM617659 3 0.6215 0.0871 0.428 0.000 0.572
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM617581 1 0.3687 0.74221 0.856 0.064 0.000 0.080
#> GSM617582 2 0.3372 0.60555 0.000 0.868 0.036 0.096
#> GSM617588 4 0.1356 0.81397 0.032 0.008 0.000 0.960
#> GSM617590 4 0.1545 0.81363 0.000 0.040 0.008 0.952
#> GSM617592 4 0.3400 0.72769 0.180 0.000 0.000 0.820
#> GSM617607 2 0.2149 0.63169 0.000 0.912 0.088 0.000
#> GSM617608 2 0.4996 0.02515 0.000 0.516 0.484 0.000
#> GSM617609 2 0.2530 0.62386 0.000 0.888 0.112 0.000
#> GSM617612 1 0.1807 0.81226 0.940 0.000 0.052 0.008
#> GSM617615 4 0.2048 0.80593 0.000 0.008 0.064 0.928
#> GSM617616 3 0.3554 0.64954 0.020 0.136 0.844 0.000
#> GSM617617 4 0.7467 0.48025 0.264 0.204 0.004 0.528
#> GSM617618 3 0.4103 0.55289 0.000 0.256 0.744 0.000
#> GSM617619 2 0.4206 0.57989 0.000 0.816 0.048 0.136
#> GSM617620 4 0.0469 0.81432 0.012 0.000 0.000 0.988
#> GSM617622 3 0.4238 0.57110 0.060 0.004 0.828 0.108
#> GSM617623 1 0.1724 0.79717 0.948 0.020 0.000 0.032
#> GSM617624 3 0.1854 0.61927 0.000 0.012 0.940 0.048
#> GSM617625 2 0.5132 0.14615 0.004 0.548 0.448 0.000
#> GSM617626 1 0.2261 0.81000 0.932 0.024 0.036 0.008
#> GSM617627 2 0.6207 -0.05677 0.000 0.496 0.052 0.452
#> GSM617628 2 0.4608 0.45832 0.004 0.692 0.304 0.000
#> GSM617632 3 0.5920 0.41675 0.336 0.052 0.612 0.000
#> GSM617634 3 0.1059 0.63437 0.000 0.012 0.972 0.016
#> GSM617635 3 0.1637 0.64708 0.060 0.000 0.940 0.000
#> GSM617636 3 0.3925 0.63173 0.016 0.176 0.808 0.000
#> GSM617637 1 0.4907 0.30785 0.580 0.000 0.420 0.000
#> GSM617638 2 0.0336 0.62692 0.000 0.992 0.008 0.000
#> GSM617639 1 0.2799 0.77456 0.884 0.008 0.108 0.000
#> GSM617640 4 0.4188 0.72308 0.004 0.244 0.000 0.752
#> GSM617641 4 0.1637 0.80796 0.060 0.000 0.000 0.940
#> GSM617643 4 0.3105 0.77359 0.000 0.004 0.140 0.856
#> GSM617644 4 0.4509 0.63917 0.000 0.004 0.288 0.708
#> GSM617647 1 0.6292 0.32801 0.592 0.000 0.076 0.332
#> GSM617648 4 0.4401 0.66316 0.000 0.004 0.272 0.724
#> GSM617649 3 0.5920 0.22313 0.040 0.004 0.608 0.348
#> GSM617650 3 0.5650 0.57111 0.180 0.104 0.716 0.000
#> GSM617651 1 0.0712 0.81345 0.984 0.008 0.004 0.004
#> GSM617653 1 0.0188 0.81437 0.996 0.000 0.004 0.000
#> GSM617654 4 0.4282 0.77443 0.024 0.160 0.008 0.808
#> GSM617583 3 0.3356 0.63071 0.000 0.176 0.824 0.000
#> GSM617584 4 0.4697 0.47754 0.356 0.000 0.000 0.644
#> GSM617585 4 0.4855 0.57401 0.000 0.352 0.004 0.644
#> GSM617586 3 0.4981 0.12796 0.000 0.464 0.536 0.000
#> GSM617587 3 0.4359 0.64200 0.100 0.084 0.816 0.000
#> GSM617589 4 0.0336 0.81314 0.000 0.008 0.000 0.992
#> GSM617591 4 0.3975 0.69366 0.000 0.240 0.000 0.760
#> GSM617593 1 0.7200 0.33927 0.552 0.228 0.220 0.000
#> GSM617594 3 0.4372 0.42718 0.000 0.004 0.728 0.268
#> GSM617595 1 0.2868 0.77544 0.864 0.000 0.136 0.000
#> GSM617596 1 0.0188 0.81350 0.996 0.004 0.000 0.000
#> GSM617597 2 0.5080 0.22812 0.004 0.576 0.420 0.000
#> GSM617598 3 0.5511 0.37572 0.352 0.028 0.620 0.000
#> GSM617599 4 0.2384 0.80393 0.004 0.008 0.072 0.916
#> GSM617600 3 0.4992 0.09384 0.000 0.476 0.524 0.000
#> GSM617601 3 0.5143 0.30624 0.000 0.012 0.628 0.360
#> GSM617602 3 0.4164 0.55404 0.000 0.264 0.736 0.000
#> GSM617603 4 0.2402 0.80219 0.000 0.012 0.076 0.912
#> GSM617604 2 0.5689 0.00262 0.412 0.564 0.004 0.020
#> GSM617605 4 0.1867 0.80633 0.000 0.072 0.000 0.928
#> GSM617606 4 0.4624 0.59614 0.000 0.340 0.000 0.660
#> GSM617610 1 0.0188 0.81305 0.996 0.000 0.000 0.004
#> GSM617611 1 0.6461 0.43869 0.632 0.128 0.240 0.000
#> GSM617613 2 0.4543 0.41507 0.000 0.676 0.324 0.000
#> GSM617614 2 0.4212 0.55318 0.012 0.772 0.216 0.000
#> GSM617621 1 0.1443 0.81231 0.960 0.028 0.008 0.004
#> GSM617629 3 0.1302 0.64755 0.000 0.044 0.956 0.000
#> GSM617630 2 0.2589 0.54554 0.000 0.884 0.000 0.116
#> GSM617631 3 0.4585 0.46797 0.000 0.332 0.668 0.000
#> GSM617633 3 0.2216 0.65559 0.000 0.092 0.908 0.000
#> GSM617642 3 0.4877 0.60348 0.044 0.204 0.752 0.000
#> GSM617645 4 0.3547 0.78069 0.016 0.144 0.000 0.840
#> GSM617646 3 0.4991 0.24417 0.388 0.000 0.608 0.004
#> GSM617652 3 0.5004 0.30625 0.004 0.392 0.604 0.000
#> GSM617655 3 0.3172 0.63991 0.000 0.160 0.840 0.000
#> GSM617656 3 0.4679 0.41819 0.000 0.352 0.648 0.000
#> GSM617657 3 0.4290 0.56510 0.000 0.164 0.800 0.036
#> GSM617658 2 0.0592 0.62875 0.000 0.984 0.016 0.000
#> GSM617659 2 0.6683 0.43152 0.176 0.620 0.204 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM617581 1 0.1911 0.7330 0.932 0.004 0.000 0.036 0.028
#> GSM617582 5 0.4550 0.6313 0.000 0.044 0.080 0.084 0.792
#> GSM617588 4 0.1741 0.8220 0.040 0.024 0.000 0.936 0.000
#> GSM617590 4 0.0324 0.8189 0.000 0.004 0.004 0.992 0.000
#> GSM617592 4 0.3826 0.7443 0.172 0.020 0.000 0.796 0.012
#> GSM617607 5 0.3087 0.5857 0.004 0.008 0.152 0.000 0.836
#> GSM617608 3 0.3513 0.7165 0.000 0.020 0.800 0.000 0.180
#> GSM617609 5 0.3160 0.5560 0.000 0.004 0.188 0.000 0.808
#> GSM617612 1 0.5785 0.4224 0.596 0.012 0.320 0.068 0.004
#> GSM617615 4 0.1285 0.8238 0.004 0.036 0.004 0.956 0.000
#> GSM617616 3 0.3362 0.6343 0.012 0.156 0.824 0.000 0.008
#> GSM617617 5 0.6137 0.5011 0.076 0.316 0.000 0.032 0.576
#> GSM617618 2 0.5959 -0.0817 0.000 0.472 0.108 0.000 0.420
#> GSM617619 5 0.3812 0.6286 0.000 0.136 0.016 0.032 0.816
#> GSM617620 4 0.3340 0.7642 0.004 0.156 0.000 0.824 0.016
#> GSM617622 2 0.4441 0.5976 0.024 0.716 0.252 0.008 0.000
#> GSM617623 1 0.2228 0.7318 0.920 0.040 0.000 0.012 0.028
#> GSM617624 2 0.5261 0.6027 0.000 0.696 0.200 0.012 0.092
#> GSM617625 3 0.3953 0.7090 0.012 0.040 0.804 0.000 0.144
#> GSM617626 1 0.5472 0.3396 0.580 0.036 0.368 0.008 0.008
#> GSM617627 5 0.6321 0.5635 0.000 0.216 0.020 0.168 0.596
#> GSM617628 3 0.6036 0.6360 0.012 0.052 0.684 0.080 0.172
#> GSM617632 3 0.5283 0.5305 0.188 0.136 0.676 0.000 0.000
#> GSM617634 2 0.4506 0.5716 0.000 0.676 0.296 0.000 0.028
#> GSM617635 2 0.5289 0.3165 0.040 0.528 0.428 0.000 0.004
#> GSM617636 3 0.3403 0.6298 0.012 0.160 0.820 0.000 0.008
#> GSM617637 1 0.6535 0.1086 0.476 0.232 0.292 0.000 0.000
#> GSM617638 5 0.1928 0.6235 0.004 0.004 0.072 0.000 0.920
#> GSM617639 1 0.3796 0.5026 0.700 0.000 0.300 0.000 0.000
#> GSM617640 5 0.6028 0.5178 0.004 0.304 0.000 0.128 0.564
#> GSM617641 4 0.3818 0.7699 0.028 0.144 0.000 0.812 0.016
#> GSM617643 2 0.4743 0.3672 0.004 0.700 0.000 0.248 0.048
#> GSM617644 2 0.4347 0.4117 0.000 0.712 0.012 0.264 0.012
#> GSM617647 2 0.5492 0.4157 0.236 0.672 0.000 0.064 0.028
#> GSM617648 2 0.4002 0.4873 0.000 0.780 0.008 0.184 0.028
#> GSM617649 2 0.3288 0.5637 0.008 0.876 0.028 0.048 0.040
#> GSM617650 3 0.4258 0.6068 0.072 0.160 0.768 0.000 0.000
#> GSM617651 1 0.3201 0.6925 0.852 0.096 0.000 0.000 0.052
#> GSM617653 1 0.0404 0.7547 0.988 0.000 0.012 0.000 0.000
#> GSM617654 5 0.6257 0.4705 0.024 0.340 0.000 0.092 0.544
#> GSM617583 3 0.2260 0.7087 0.012 0.048 0.920 0.016 0.004
#> GSM617584 4 0.4402 0.4979 0.352 0.012 0.000 0.636 0.000
#> GSM617585 5 0.5620 0.5003 0.000 0.092 0.004 0.296 0.608
#> GSM617586 3 0.2915 0.7266 0.000 0.024 0.860 0.000 0.116
#> GSM617587 3 0.5314 0.3463 0.068 0.296 0.632 0.000 0.004
#> GSM617589 4 0.1460 0.8112 0.012 0.020 0.008 0.956 0.004
#> GSM617591 4 0.4883 0.4814 0.000 0.052 0.004 0.684 0.260
#> GSM617593 3 0.5177 0.2164 0.416 0.008 0.548 0.000 0.028
#> GSM617594 2 0.4075 0.6309 0.000 0.780 0.160 0.060 0.000
#> GSM617595 1 0.3694 0.6255 0.796 0.172 0.032 0.000 0.000
#> GSM617596 1 0.1205 0.7480 0.956 0.040 0.000 0.000 0.004
#> GSM617597 3 0.3320 0.7171 0.012 0.008 0.828 0.000 0.152
#> GSM617598 3 0.4679 0.5727 0.216 0.068 0.716 0.000 0.000
#> GSM617599 4 0.2497 0.7985 0.000 0.112 0.004 0.880 0.004
#> GSM617600 3 0.5206 0.5914 0.000 0.048 0.664 0.016 0.272
#> GSM617601 4 0.4128 0.6879 0.004 0.068 0.124 0.800 0.004
#> GSM617602 3 0.1774 0.7264 0.000 0.016 0.932 0.000 0.052
#> GSM617603 4 0.3732 0.7122 0.000 0.176 0.000 0.792 0.032
#> GSM617604 5 0.5382 -0.0557 0.472 0.000 0.044 0.004 0.480
#> GSM617605 4 0.0727 0.8204 0.000 0.012 0.004 0.980 0.004
#> GSM617606 5 0.5096 0.5320 0.000 0.072 0.000 0.272 0.656
#> GSM617610 1 0.0324 0.7541 0.992 0.004 0.004 0.000 0.000
#> GSM617611 3 0.4517 0.1878 0.436 0.008 0.556 0.000 0.000
#> GSM617613 3 0.5430 0.4373 0.000 0.032 0.576 0.020 0.372
#> GSM617614 3 0.5740 0.5955 0.064 0.040 0.656 0.000 0.240
#> GSM617621 1 0.2054 0.7486 0.920 0.000 0.052 0.000 0.028
#> GSM617629 2 0.4736 0.4202 0.000 0.576 0.404 0.000 0.020
#> GSM617630 5 0.2143 0.6402 0.008 0.060 0.008 0.004 0.920
#> GSM617631 3 0.2813 0.7258 0.000 0.040 0.876 0.000 0.084
#> GSM617633 3 0.4242 -0.0224 0.000 0.428 0.572 0.000 0.000
#> GSM617642 3 0.2679 0.7114 0.056 0.048 0.892 0.000 0.004
#> GSM617645 5 0.6719 0.4282 0.008 0.316 0.000 0.204 0.472
#> GSM617646 2 0.6781 0.3783 0.228 0.468 0.296 0.000 0.008
#> GSM617652 3 0.2533 0.7320 0.008 0.008 0.888 0.000 0.096
#> GSM617655 3 0.1908 0.6763 0.000 0.092 0.908 0.000 0.000
#> GSM617656 3 0.2351 0.7294 0.000 0.016 0.896 0.000 0.088
#> GSM617657 2 0.8235 0.3057 0.000 0.388 0.268 0.164 0.180
#> GSM617658 5 0.4181 0.3846 0.000 0.020 0.268 0.000 0.712
#> GSM617659 3 0.6227 0.5524 0.144 0.024 0.612 0.000 0.220
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM617581 1 0.289 0.73115 0.872 0.000 0.000 0.040 0.028 0.060
#> GSM617582 5 0.571 0.40653 0.000 0.052 0.040 0.096 0.688 0.124
#> GSM617588 4 0.250 0.68670 0.020 0.012 0.000 0.884 0.000 0.084
#> GSM617590 4 0.242 0.68542 0.000 0.020 0.008 0.900 0.012 0.060
#> GSM617592 4 0.381 0.65259 0.096 0.016 0.000 0.800 0.000 0.088
#> GSM617607 5 0.374 0.43531 0.012 0.004 0.192 0.000 0.772 0.020
#> GSM617608 3 0.377 0.71979 0.028 0.032 0.804 0.000 0.132 0.004
#> GSM617609 5 0.458 0.35661 0.000 0.000 0.320 0.000 0.624 0.056
#> GSM617612 1 0.504 0.64452 0.708 0.004 0.164 0.044 0.000 0.080
#> GSM617615 4 0.472 0.64520 0.004 0.084 0.040 0.752 0.004 0.116
#> GSM617616 3 0.547 0.46333 0.056 0.300 0.604 0.000 0.012 0.028
#> GSM617617 6 0.739 0.72634 0.020 0.172 0.000 0.084 0.348 0.376
#> GSM617618 2 0.721 0.12855 0.004 0.404 0.104 0.004 0.340 0.144
#> GSM617619 5 0.363 0.36093 0.000 0.080 0.008 0.008 0.820 0.084
#> GSM617620 4 0.340 0.64888 0.016 0.040 0.000 0.824 0.000 0.120
#> GSM617622 2 0.375 0.50554 0.012 0.816 0.072 0.004 0.004 0.092
#> GSM617623 1 0.277 0.73446 0.880 0.004 0.000 0.016 0.036 0.064
#> GSM617624 2 0.517 0.48769 0.000 0.708 0.092 0.004 0.060 0.136
#> GSM617625 3 0.325 0.70635 0.020 0.000 0.848 0.004 0.040 0.088
#> GSM617626 1 0.641 0.51912 0.580 0.016 0.200 0.020 0.016 0.168
#> GSM617627 5 0.843 -0.47408 0.000 0.172 0.056 0.232 0.276 0.264
#> GSM617628 3 0.493 0.64852 0.028 0.000 0.736 0.032 0.060 0.144
#> GSM617632 3 0.650 0.20791 0.364 0.172 0.432 0.000 0.016 0.016
#> GSM617634 2 0.451 0.52522 0.000 0.744 0.152 0.000 0.036 0.068
#> GSM617635 2 0.443 0.28973 0.000 0.580 0.388 0.000 0.000 0.032
#> GSM617636 3 0.506 0.48508 0.040 0.292 0.636 0.000 0.020 0.012
#> GSM617637 1 0.697 0.20376 0.428 0.268 0.228 0.000 0.000 0.076
#> GSM617638 5 0.410 0.41004 0.004 0.012 0.108 0.000 0.780 0.096
#> GSM617639 1 0.490 0.34786 0.612 0.004 0.328 0.000 0.012 0.044
#> GSM617640 5 0.725 -0.76973 0.004 0.112 0.000 0.164 0.368 0.352
#> GSM617641 4 0.355 0.64559 0.028 0.028 0.000 0.812 0.000 0.132
#> GSM617643 2 0.634 -0.22971 0.000 0.408 0.000 0.276 0.012 0.304
#> GSM617644 2 0.394 0.38256 0.000 0.752 0.000 0.180 0.000 0.068
#> GSM617647 2 0.687 -0.00501 0.168 0.480 0.000 0.060 0.012 0.280
#> GSM617648 2 0.399 0.40661 0.000 0.768 0.004 0.136 0.000 0.092
#> GSM617649 2 0.424 0.42917 0.004 0.772 0.032 0.036 0.004 0.152
#> GSM617650 3 0.494 0.62124 0.116 0.164 0.700 0.000 0.004 0.016
#> GSM617651 1 0.422 0.71728 0.800 0.048 0.016 0.000 0.064 0.072
#> GSM617653 1 0.087 0.75628 0.972 0.000 0.012 0.004 0.000 0.012
#> GSM617654 6 0.757 0.72300 0.004 0.200 0.000 0.148 0.316 0.332
#> GSM617583 3 0.283 0.70341 0.000 0.044 0.872 0.008 0.004 0.072
#> GSM617584 4 0.484 0.39294 0.360 0.004 0.000 0.580 0.000 0.056
#> GSM617585 5 0.625 0.25028 0.000 0.060 0.000 0.244 0.552 0.144
#> GSM617586 3 0.287 0.71710 0.000 0.040 0.868 0.000 0.076 0.016
#> GSM617587 3 0.567 0.40341 0.020 0.268 0.620 0.024 0.004 0.064
#> GSM617589 4 0.307 0.66966 0.004 0.004 0.020 0.832 0.000 0.140
#> GSM617591 4 0.637 0.29246 0.000 0.060 0.012 0.576 0.216 0.136
#> GSM617593 3 0.525 0.16209 0.452 0.012 0.488 0.000 0.024 0.024
#> GSM617594 2 0.589 0.34381 0.000 0.612 0.064 0.092 0.004 0.228
#> GSM617595 1 0.412 0.65765 0.768 0.156 0.028 0.000 0.000 0.048
#> GSM617596 1 0.310 0.75450 0.872 0.024 0.028 0.000 0.028 0.048
#> GSM617597 3 0.322 0.71657 0.020 0.008 0.852 0.000 0.088 0.032
#> GSM617598 3 0.544 0.42624 0.332 0.028 0.576 0.000 0.004 0.060
#> GSM617599 4 0.583 0.49446 0.004 0.208 0.008 0.592 0.008 0.180
#> GSM617600 3 0.532 0.54435 0.000 0.032 0.652 0.000 0.212 0.104
#> GSM617601 4 0.717 0.31807 0.004 0.076 0.300 0.436 0.008 0.176
#> GSM617602 3 0.250 0.71301 0.000 0.060 0.892 0.000 0.032 0.016
#> GSM617603 4 0.562 0.48923 0.000 0.132 0.000 0.636 0.044 0.188
#> GSM617604 1 0.547 0.48232 0.588 0.004 0.068 0.000 0.312 0.028
#> GSM617605 4 0.144 0.69109 0.000 0.004 0.000 0.944 0.012 0.040
#> GSM617606 5 0.568 0.21711 0.000 0.028 0.004 0.276 0.592 0.100
#> GSM617610 1 0.100 0.75211 0.964 0.004 0.000 0.004 0.000 0.028
#> GSM617611 3 0.485 0.39077 0.380 0.012 0.576 0.000 0.012 0.020
#> GSM617613 3 0.481 0.54200 0.000 0.008 0.660 0.000 0.252 0.080
#> GSM617614 3 0.585 0.59295 0.168 0.000 0.620 0.000 0.156 0.056
#> GSM617621 1 0.256 0.75790 0.896 0.008 0.048 0.000 0.016 0.032
#> GSM617629 2 0.563 0.39793 0.000 0.564 0.320 0.000 0.036 0.080
#> GSM617630 5 0.262 0.37621 0.012 0.008 0.016 0.000 0.884 0.080
#> GSM617631 3 0.390 0.68852 0.000 0.072 0.800 0.000 0.100 0.028
#> GSM617633 2 0.422 0.05964 0.000 0.516 0.472 0.000 0.004 0.008
#> GSM617642 3 0.285 0.72047 0.044 0.032 0.880 0.000 0.004 0.040
#> GSM617645 6 0.733 0.69655 0.004 0.112 0.000 0.200 0.284 0.400
#> GSM617646 2 0.660 0.41923 0.104 0.536 0.208 0.000 0.000 0.152
#> GSM617652 3 0.289 0.73100 0.048 0.020 0.880 0.000 0.040 0.012
#> GSM617655 3 0.231 0.68618 0.000 0.092 0.888 0.000 0.004 0.016
#> GSM617656 3 0.216 0.71633 0.000 0.028 0.912 0.000 0.044 0.016
#> GSM617657 2 0.819 0.27651 0.000 0.412 0.148 0.092 0.136 0.212
#> GSM617658 5 0.450 0.42820 0.008 0.000 0.232 0.000 0.696 0.064
#> GSM617659 3 0.572 0.54037 0.236 0.000 0.612 0.000 0.100 0.052
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:NMF 78 0.3120 2
#> ATC:NMF 66 0.6044 3
#> ATC:NMF 54 0.8918 4
#> ATC:NMF 56 0.2131 5
#> ATC:NMF 40 0.0498 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
sessionInfo()
#> R version 3.6.0 (2019-04-26)
#> Platform: x86_64-pc-linux-gnu (64-bit)
#> Running under: CentOS Linux 7 (Core)
#>
#> Matrix products: default
#> BLAS: /usr/lib64/libblas.so.3.4.2
#> LAPACK: /usr/lib64/liblapack.so.3.4.2
#>
#> locale:
#> [1] LC_CTYPE=en_GB.UTF-8 LC_NUMERIC=C LC_TIME=en_GB.UTF-8
#> [4] LC_COLLATE=en_GB.UTF-8 LC_MONETARY=en_GB.UTF-8 LC_MESSAGES=en_GB.UTF-8
#> [7] LC_PAPER=en_GB.UTF-8 LC_NAME=C LC_ADDRESS=C
#> [10] LC_TELEPHONE=C LC_MEASUREMENT=en_GB.UTF-8 LC_IDENTIFICATION=C
#>
#> attached base packages:
#> [1] grid stats graphics grDevices utils datasets methods base
#>
#> other attached packages:
#> [1] genefilter_1.66.0 ComplexHeatmap_2.3.1 markdown_1.1 knitr_1.26
#> [5] GetoptLong_0.1.7 cola_1.3.2
#>
#> loaded via a namespace (and not attached):
#> [1] circlize_0.4.8 shape_1.4.4 xfun_0.11 slam_0.1-46
#> [5] lattice_0.20-38 splines_3.6.0 colorspace_1.4-1 vctrs_0.2.0
#> [9] stats4_3.6.0 blob_1.2.0 XML_3.98-1.20 survival_2.44-1.1
#> [13] rlang_0.4.2 pillar_1.4.2 DBI_1.0.0 BiocGenerics_0.30.0
#> [17] bit64_0.9-7 RColorBrewer_1.1-2 matrixStats_0.55.0 stringr_1.4.0
#> [21] GlobalOptions_0.1.1 evaluate_0.14 memoise_1.1.0 Biobase_2.44.0
#> [25] IRanges_2.18.3 parallel_3.6.0 AnnotationDbi_1.46.1 highr_0.8
#> [29] Rcpp_1.0.3 xtable_1.8-4 backports_1.1.5 S4Vectors_0.22.1
#> [33] annotate_1.62.0 skmeans_0.2-11 bit_1.1-14 microbenchmark_1.4-7
#> [37] brew_1.0-6 impute_1.58.0 rjson_0.2.20 png_0.1-7
#> [41] digest_0.6.23 stringi_1.4.3 polyclip_1.10-0 clue_0.3-57
#> [45] tools_3.6.0 bitops_1.0-6 magrittr_1.5 eulerr_6.0.0
#> [49] RCurl_1.95-4.12 RSQLite_2.1.4 tibble_2.1.3 cluster_2.1.0
#> [53] crayon_1.3.4 pkgconfig_2.0.3 zeallot_0.1.0 Matrix_1.2-17
#> [57] xml2_1.2.2 httr_1.4.1 R6_2.4.1 mclust_5.4.5
#> [61] compiler_3.6.0