Date: 2019-12-25 23:48:32 CET, cola version: 1.3.2
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All available functions which can be applied to this res_list object:
res_list
#> A 'ConsensusPartitionList' object with 24 methods.
#> On a matrix with 16816 rows and 54 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)
Dimension of the input matrix:
mat = get_matrix(res_list)
dim(mat)
#> [1] 16816 54
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, 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:kmeans | 2 | 1.000 | 0.955 | 0.981 | ** | |
| ATC:skmeans | 3 | 1.000 | 0.989 | 0.994 | ** | 2 |
| MAD:pam | 5 | 0.999 | 0.962 | 0.984 | ** | 2,4 |
| MAD:NMF | 2 | 0.994 | 0.944 | 0.977 | ** | |
| CV:pam | 4 | 0.954 | 0.933 | 0.977 | ** | |
| SD:skmeans | 4 | 0.948 | 0.869 | 0.947 | * | |
| CV:skmeans | 4 | 0.947 | 0.905 | 0.961 | * | 2 |
| ATC:NMF | 3 | 0.947 | 0.922 | 0.970 | * | 2 |
| CV:NMF | 4 | 0.926 | 0.894 | 0.956 | * | |
| ATC:mclust | 2 | 0.923 | 0.910 | 0.944 | * | |
| SD:pam | 5 | 0.904 | 0.816 | 0.931 | * | 4 |
| CV:mclust | 2 | 0.885 | 0.954 | 0.969 | ||
| SD:NMF | 4 | 0.870 | 0.840 | 0.930 | ||
| ATC:pam | 5 | 0.824 | 0.798 | 0.916 | ||
| SD:mclust | 4 | 0.820 | 0.756 | 0.902 | ||
| ATC:hclust | 4 | 0.774 | 0.914 | 0.947 | ||
| SD:hclust | 5 | 0.727 | 0.759 | 0.847 | ||
| SD:kmeans | 5 | 0.701 | 0.715 | 0.804 | ||
| MAD:skmeans | 2 | 0.698 | 0.871 | 0.941 | ||
| MAD:hclust | 5 | 0.606 | 0.615 | 0.758 | ||
| MAD:kmeans | 5 | 0.594 | 0.627 | 0.727 | ||
| CV:kmeans | 4 | 0.581 | 0.803 | 0.810 | ||
| CV:hclust | 3 | 0.560 | 0.775 | 0.814 | ||
| MAD:mclust | 2 | 0.354 | 0.766 | 0.860 |
**: 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 0.854 0.921 0.966 0.434 0.560 0.560
#> CV:NMF 2 0.812 0.869 0.948 0.481 0.516 0.516
#> MAD:NMF 2 0.994 0.944 0.977 0.427 0.575 0.575
#> ATC:NMF 2 1.000 0.969 0.988 0.371 0.628 0.628
#> SD:skmeans 2 0.726 0.833 0.935 0.484 0.502 0.502
#> CV:skmeans 2 1.000 0.987 0.994 0.506 0.493 0.493
#> MAD:skmeans 2 0.698 0.871 0.941 0.481 0.547 0.547
#> ATC:skmeans 2 1.000 0.963 0.986 0.497 0.508 0.508
#> SD:mclust 2 0.448 0.689 0.863 0.474 0.508 0.508
#> CV:mclust 2 0.885 0.954 0.969 0.507 0.493 0.493
#> MAD:mclust 2 0.354 0.766 0.860 0.434 0.547 0.547
#> ATC:mclust 2 0.923 0.910 0.944 0.298 0.693 0.693
#> SD:kmeans 2 0.693 0.896 0.940 0.401 0.609 0.609
#> CV:kmeans 2 0.341 0.685 0.811 0.394 0.591 0.591
#> MAD:kmeans 2 0.666 0.877 0.932 0.431 0.575 0.575
#> ATC:kmeans 2 1.000 0.955 0.981 0.466 0.535 0.535
#> SD:pam 2 0.885 0.885 0.921 0.389 0.575 0.575
#> CV:pam 2 0.456 0.912 0.852 0.432 0.547 0.547
#> MAD:pam 2 0.923 0.928 0.971 0.433 0.575 0.575
#> ATC:pam 2 0.779 0.826 0.937 0.363 0.628 0.628
#> SD:hclust 2 0.545 0.756 0.903 0.353 0.717 0.717
#> CV:hclust 2 0.858 0.954 0.980 0.262 0.743 0.743
#> MAD:hclust 2 0.592 0.781 0.909 0.355 0.628 0.628
#> ATC:hclust 2 0.621 0.877 0.942 0.428 0.547 0.547
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.587 0.670 0.847 0.521 0.739 0.547
#> CV:NMF 3 0.706 0.821 0.906 0.387 0.676 0.442
#> MAD:NMF 3 0.641 0.810 0.903 0.564 0.679 0.475
#> ATC:NMF 3 0.947 0.922 0.970 0.765 0.690 0.515
#> SD:skmeans 3 0.754 0.809 0.892 0.385 0.704 0.471
#> CV:skmeans 3 0.849 0.835 0.929 0.329 0.792 0.598
#> MAD:skmeans 3 0.710 0.693 0.885 0.398 0.751 0.554
#> ATC:skmeans 3 1.000 0.989 0.994 0.311 0.815 0.644
#> SD:mclust 3 0.430 0.682 0.827 0.320 0.765 0.570
#> CV:mclust 3 0.470 0.680 0.855 0.288 0.734 0.512
#> MAD:mclust 3 0.394 0.548 0.758 0.406 0.682 0.470
#> ATC:mclust 3 0.780 0.811 0.906 1.058 0.499 0.360
#> SD:kmeans 3 0.478 0.595 0.782 0.527 0.760 0.632
#> CV:kmeans 3 0.346 0.555 0.693 0.500 0.678 0.499
#> MAD:kmeans 3 0.459 0.547 0.773 0.461 0.735 0.568
#> ATC:kmeans 3 0.561 0.717 0.825 0.377 0.776 0.600
#> SD:pam 3 0.802 0.888 0.944 0.661 0.759 0.581
#> CV:pam 3 0.752 0.767 0.874 0.288 0.942 0.894
#> MAD:pam 3 0.827 0.902 0.951 0.533 0.732 0.544
#> ATC:pam 3 0.456 0.523 0.753 0.750 0.686 0.507
#> SD:hclust 3 0.387 0.516 0.762 0.491 0.697 0.604
#> CV:hclust 3 0.560 0.775 0.814 1.122 0.655 0.536
#> MAD:hclust 3 0.355 0.580 0.801 0.585 0.677 0.524
#> ATC:hclust 3 0.614 0.663 0.847 0.295 0.843 0.722
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.870 0.840 0.930 0.1335 0.770 0.438
#> CV:NMF 4 0.926 0.894 0.956 0.1349 0.853 0.587
#> MAD:NMF 4 0.712 0.749 0.885 0.1281 0.787 0.457
#> ATC:NMF 4 0.809 0.844 0.926 0.1294 0.846 0.590
#> SD:skmeans 4 0.948 0.869 0.947 0.1260 0.887 0.667
#> CV:skmeans 4 0.947 0.905 0.961 0.1232 0.882 0.661
#> MAD:skmeans 4 0.857 0.851 0.928 0.1206 0.880 0.649
#> ATC:skmeans 4 0.856 0.874 0.928 0.1185 0.912 0.751
#> SD:mclust 4 0.820 0.756 0.902 0.1282 0.820 0.571
#> CV:mclust 4 0.691 0.717 0.848 0.0884 0.923 0.787
#> MAD:mclust 4 0.580 0.679 0.825 0.1760 0.860 0.619
#> ATC:mclust 4 0.623 0.705 0.805 0.1325 0.895 0.731
#> SD:kmeans 4 0.500 0.658 0.766 0.1756 0.790 0.553
#> CV:kmeans 4 0.581 0.803 0.810 0.1881 0.826 0.559
#> MAD:kmeans 4 0.536 0.582 0.729 0.1585 0.834 0.585
#> ATC:kmeans 4 0.686 0.792 0.857 0.1260 0.899 0.729
#> SD:pam 4 0.938 0.912 0.964 0.1124 0.908 0.738
#> CV:pam 4 0.954 0.933 0.977 0.2273 0.816 0.626
#> MAD:pam 4 0.902 0.933 0.971 0.1008 0.870 0.644
#> ATC:pam 4 0.766 0.848 0.873 0.0755 0.695 0.385
#> SD:hclust 4 0.454 0.498 0.675 0.2817 0.700 0.458
#> CV:hclust 4 0.539 0.651 0.775 0.1090 0.980 0.951
#> MAD:hclust 4 0.397 0.443 0.664 0.2328 0.736 0.451
#> ATC:hclust 4 0.774 0.914 0.947 0.2397 0.841 0.643
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.770 0.601 0.821 0.0561 0.985 0.941
#> CV:NMF 5 0.847 0.767 0.870 0.0438 0.931 0.734
#> MAD:NMF 5 0.689 0.570 0.774 0.0550 0.984 0.935
#> ATC:NMF 5 0.715 0.584 0.804 0.0712 0.924 0.722
#> SD:skmeans 5 0.844 0.805 0.878 0.0481 0.973 0.892
#> CV:skmeans 5 0.842 0.782 0.867 0.0513 0.908 0.668
#> MAD:skmeans 5 0.785 0.710 0.826 0.0550 0.958 0.831
#> ATC:skmeans 5 0.843 0.889 0.883 0.0948 0.877 0.577
#> SD:mclust 5 0.761 0.715 0.820 0.1147 0.892 0.656
#> CV:mclust 5 0.820 0.844 0.921 0.0941 0.843 0.543
#> MAD:mclust 5 0.614 0.560 0.731 0.0833 0.867 0.571
#> ATC:mclust 5 0.744 0.667 0.840 0.1148 0.814 0.467
#> SD:kmeans 5 0.701 0.715 0.804 0.0861 0.911 0.686
#> CV:kmeans 5 0.801 0.748 0.808 0.0980 0.964 0.857
#> MAD:kmeans 5 0.594 0.627 0.727 0.0779 0.943 0.778
#> ATC:kmeans 5 0.729 0.746 0.798 0.0855 0.887 0.612
#> SD:pam 5 0.904 0.816 0.931 0.0844 0.900 0.664
#> CV:pam 5 0.762 0.763 0.759 0.1052 0.900 0.676
#> MAD:pam 5 0.999 0.962 0.984 0.0666 0.934 0.764
#> ATC:pam 5 0.824 0.798 0.916 0.1509 0.817 0.510
#> SD:hclust 5 0.727 0.759 0.847 0.1611 0.829 0.497
#> CV:hclust 5 0.590 0.820 0.786 0.1159 0.869 0.655
#> MAD:hclust 5 0.606 0.615 0.758 0.1041 0.836 0.509
#> ATC:hclust 5 0.897 0.898 0.929 0.0316 0.994 0.982
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.775 0.660 0.803 0.0414 0.899 0.608
#> CV:NMF 6 0.860 0.779 0.876 0.0365 0.932 0.703
#> MAD:NMF 6 0.737 0.602 0.750 0.0400 0.879 0.537
#> ATC:NMF 6 0.664 0.618 0.789 0.0485 0.843 0.411
#> SD:skmeans 6 0.823 0.743 0.856 0.0376 0.966 0.850
#> CV:skmeans 6 0.833 0.767 0.837 0.0393 0.954 0.788
#> MAD:skmeans 6 0.759 0.673 0.800 0.0369 0.996 0.980
#> ATC:skmeans 6 0.847 0.790 0.861 0.0363 0.977 0.881
#> SD:mclust 6 0.729 0.719 0.780 0.0403 0.941 0.735
#> CV:mclust 6 0.878 0.837 0.890 0.0393 0.975 0.882
#> MAD:mclust 6 0.593 0.533 0.677 0.0349 0.930 0.714
#> ATC:mclust 6 0.876 0.841 0.929 0.0532 0.939 0.731
#> SD:kmeans 6 0.737 0.646 0.751 0.0437 0.979 0.902
#> CV:kmeans 6 0.781 0.641 0.792 0.0440 0.981 0.914
#> MAD:kmeans 6 0.716 0.536 0.712 0.0435 0.983 0.919
#> ATC:kmeans 6 0.729 0.745 0.799 0.0457 0.970 0.847
#> SD:pam 6 0.859 0.782 0.895 0.0484 0.945 0.755
#> CV:pam 6 0.758 0.512 0.764 0.0564 0.864 0.492
#> MAD:pam 6 0.885 0.831 0.893 0.0451 0.956 0.801
#> ATC:pam 6 0.859 0.793 0.911 0.0214 0.958 0.814
#> SD:hclust 6 0.769 0.755 0.834 0.0316 0.987 0.941
#> CV:hclust 6 0.896 0.899 0.945 0.1317 0.964 0.854
#> MAD:hclust 6 0.682 0.605 0.762 0.0478 0.987 0.940
#> ATC:hclust 6 0.898 0.886 0.909 0.0338 0.978 0.925
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)
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 16816 rows and 54 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 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 0.545 0.756 0.903 0.3526 0.717 0.717
#> 3 3 0.387 0.516 0.762 0.4908 0.697 0.604
#> 4 4 0.454 0.498 0.675 0.2817 0.700 0.458
#> 5 5 0.727 0.759 0.847 0.1611 0.829 0.497
#> 6 6 0.769 0.755 0.834 0.0316 0.987 0.941
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
#> SRR949076 1 0.0000 0.8747 1.000 0.000
#> SRR949078 2 0.9286 0.4425 0.344 0.656
#> SRR949077 1 0.0000 0.8747 1.000 0.000
#> SRR949079 1 0.0000 0.8747 1.000 0.000
#> SRR949080 1 0.0000 0.8747 1.000 0.000
#> SRR949081 1 0.0938 0.8681 0.988 0.012
#> SRR949082 2 0.9286 0.4425 0.344 0.656
#> SRR949083 1 0.0000 0.8747 1.000 0.000
#> SRR949084 1 0.0000 0.8747 1.000 0.000
#> SRR949085 2 0.0000 0.8778 0.000 1.000
#> SRR949087 1 0.8555 0.5465 0.720 0.280
#> SRR949088 1 0.8555 0.5465 0.720 0.280
#> SRR949086 1 0.7602 0.6911 0.780 0.220
#> SRR949089 2 0.0000 0.8778 0.000 1.000
#> SRR949090 1 0.0938 0.8688 0.988 0.012
#> SRR949092 1 0.0000 0.8747 1.000 0.000
#> SRR949093 1 0.0000 0.8747 1.000 0.000
#> SRR949091 1 0.7674 0.6869 0.776 0.224
#> SRR949095 1 0.8955 0.4830 0.688 0.312
#> SRR949094 1 0.0000 0.8747 1.000 0.000
#> SRR949096 1 0.0000 0.8747 1.000 0.000
#> SRR949097 1 0.0000 0.8747 1.000 0.000
#> SRR949098 2 0.0000 0.8778 0.000 1.000
#> SRR949099 1 0.0000 0.8747 1.000 0.000
#> SRR949101 1 0.7674 0.6869 0.776 0.224
#> SRR949100 1 0.8861 0.4999 0.696 0.304
#> SRR949102 1 0.0938 0.8681 0.988 0.012
#> SRR949103 1 0.0000 0.8747 1.000 0.000
#> SRR949104 2 0.0000 0.8778 0.000 1.000
#> SRR949105 1 0.7674 0.6869 0.776 0.224
#> SRR949106 1 0.7674 0.6869 0.776 0.224
#> SRR949107 1 0.7674 0.6869 0.776 0.224
#> SRR949108 1 0.0000 0.8747 1.000 0.000
#> SRR949109 1 0.0000 0.8747 1.000 0.000
#> SRR949110 1 0.0000 0.8747 1.000 0.000
#> SRR949111 1 0.0000 0.8747 1.000 0.000
#> SRR949112 1 0.0000 0.8747 1.000 0.000
#> SRR949113 2 0.4431 0.8224 0.092 0.908
#> SRR949114 1 0.0672 0.8714 0.992 0.008
#> SRR949115 1 0.0672 0.8714 0.992 0.008
#> SRR949116 1 0.0672 0.8714 0.992 0.008
#> SRR949117 1 0.7602 0.6911 0.780 0.220
#> SRR949118 1 0.7674 0.6869 0.776 0.224
#> SRR949119 1 0.0000 0.8747 1.000 0.000
#> SRR949120 1 0.0000 0.8747 1.000 0.000
#> SRR949121 1 0.0000 0.8747 1.000 0.000
#> SRR949122 1 0.0000 0.8747 1.000 0.000
#> SRR949123 2 0.1184 0.8725 0.016 0.984
#> SRR949124 2 0.0000 0.8778 0.000 1.000
#> SRR949125 1 0.0000 0.8747 1.000 0.000
#> SRR949126 1 0.0000 0.8747 1.000 0.000
#> SRR949127 1 0.9977 0.0156 0.528 0.472
#> SRR949128 1 0.9977 0.0156 0.528 0.472
#> SRR949129 1 0.9977 0.0156 0.528 0.472
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR949076 1 0.6295 0.382 0.528 0.000 0.472
#> SRR949078 1 0.6079 -0.238 0.612 0.388 0.000
#> SRR949077 1 0.6295 0.382 0.528 0.000 0.472
#> SRR949079 1 0.6305 0.383 0.516 0.000 0.484
#> SRR949080 1 0.6305 0.383 0.516 0.000 0.484
#> SRR949081 1 0.6111 0.508 0.604 0.000 0.396
#> SRR949082 1 0.6244 -0.284 0.560 0.440 0.000
#> SRR949083 1 0.5529 0.586 0.704 0.000 0.296
#> SRR949084 1 0.5529 0.586 0.704 0.000 0.296
#> SRR949085 2 0.0000 0.954 0.000 1.000 0.000
#> SRR949087 1 0.4683 0.387 0.836 0.024 0.140
#> SRR949088 1 0.4683 0.387 0.836 0.024 0.140
#> SRR949086 3 0.0237 0.796 0.004 0.000 0.996
#> SRR949089 2 0.0000 0.954 0.000 1.000 0.000
#> SRR949090 3 0.6291 -0.358 0.468 0.000 0.532
#> SRR949092 1 0.5760 0.587 0.672 0.000 0.328
#> SRR949093 1 0.5760 0.587 0.672 0.000 0.328
#> SRR949091 3 0.2796 0.688 0.092 0.000 0.908
#> SRR949095 1 0.0892 0.409 0.980 0.020 0.000
#> SRR949094 1 0.6305 0.383 0.516 0.000 0.484
#> SRR949096 1 0.5529 0.586 0.704 0.000 0.296
#> SRR949097 1 0.6180 0.555 0.584 0.000 0.416
#> SRR949098 2 0.0000 0.954 0.000 1.000 0.000
#> SRR949099 3 0.6302 -0.491 0.480 0.000 0.520
#> SRR949101 3 0.0000 0.798 0.000 0.000 1.000
#> SRR949100 1 0.3832 0.388 0.880 0.020 0.100
#> SRR949102 1 0.6126 0.508 0.600 0.000 0.400
#> SRR949103 1 0.6180 0.555 0.584 0.000 0.416
#> SRR949104 2 0.0000 0.954 0.000 1.000 0.000
#> SRR949105 3 0.0000 0.798 0.000 0.000 1.000
#> SRR949106 3 0.0000 0.798 0.000 0.000 1.000
#> SRR949107 3 0.0000 0.798 0.000 0.000 1.000
#> SRR949108 1 0.6180 0.555 0.584 0.000 0.416
#> SRR949109 1 0.6305 0.383 0.516 0.000 0.484
#> SRR949110 1 0.6180 0.555 0.584 0.000 0.416
#> SRR949111 1 0.6305 0.383 0.516 0.000 0.484
#> SRR949112 1 0.6180 0.555 0.584 0.000 0.416
#> SRR949113 2 0.3038 0.871 0.104 0.896 0.000
#> SRR949114 1 0.6244 0.526 0.560 0.000 0.440
#> SRR949115 1 0.6244 0.526 0.560 0.000 0.440
#> SRR949116 1 0.6244 0.526 0.560 0.000 0.440
#> SRR949117 3 0.0237 0.796 0.004 0.000 0.996
#> SRR949118 3 0.0000 0.798 0.000 0.000 1.000
#> SRR949119 1 0.5926 0.582 0.644 0.000 0.356
#> SRR949120 1 0.5926 0.582 0.644 0.000 0.356
#> SRR949121 1 0.6180 0.555 0.584 0.000 0.416
#> SRR949122 1 0.6180 0.555 0.584 0.000 0.416
#> SRR949123 2 0.5219 0.839 0.196 0.788 0.016
#> SRR949124 2 0.0000 0.954 0.000 1.000 0.000
#> SRR949125 1 0.6305 0.383 0.516 0.000 0.484
#> SRR949126 1 0.6305 0.383 0.516 0.000 0.484
#> SRR949127 1 0.4605 0.303 0.796 0.204 0.000
#> SRR949128 1 0.4605 0.303 0.796 0.204 0.000
#> SRR949129 1 0.4605 0.303 0.796 0.204 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR949076 4 0.0707 0.5518 0.020 0.000 0.000 0.980
#> SRR949078 1 0.4746 -0.1026 0.632 0.368 0.000 0.000
#> SRR949077 4 0.0707 0.5518 0.020 0.000 0.000 0.980
#> SRR949079 4 0.3688 0.6701 0.208 0.000 0.000 0.792
#> SRR949080 4 0.3688 0.6701 0.208 0.000 0.000 0.792
#> SRR949081 3 0.7908 0.0658 0.336 0.000 0.360 0.304
#> SRR949082 1 0.4907 -0.1651 0.580 0.420 0.000 0.000
#> SRR949083 4 0.6621 -0.1844 0.408 0.000 0.084 0.508
#> SRR949084 4 0.6621 -0.1844 0.408 0.000 0.084 0.508
#> SRR949085 2 0.0000 0.9438 0.000 1.000 0.000 0.000
#> SRR949087 1 0.3060 0.3825 0.888 0.008 0.088 0.016
#> SRR949088 1 0.3060 0.3825 0.888 0.008 0.088 0.016
#> SRR949086 3 0.0707 0.8137 0.020 0.000 0.980 0.000
#> SRR949089 2 0.0000 0.9438 0.000 1.000 0.000 0.000
#> SRR949090 4 0.4881 0.6397 0.196 0.000 0.048 0.756
#> SRR949092 1 0.6500 0.3959 0.580 0.000 0.092 0.328
#> SRR949093 1 0.6500 0.3959 0.580 0.000 0.092 0.328
#> SRR949091 4 0.4948 0.1367 0.000 0.000 0.440 0.560
#> SRR949095 1 0.4040 0.2418 0.752 0.000 0.000 0.248
#> SRR949094 4 0.3688 0.6701 0.208 0.000 0.000 0.792
#> SRR949096 4 0.6621 -0.1844 0.408 0.000 0.084 0.508
#> SRR949097 1 0.6993 0.4680 0.556 0.000 0.148 0.296
#> SRR949098 2 0.0000 0.9438 0.000 1.000 0.000 0.000
#> SRR949099 1 0.7003 0.2783 0.460 0.000 0.424 0.116
#> SRR949101 3 0.0000 0.8191 0.000 0.000 1.000 0.000
#> SRR949100 1 0.1798 0.3888 0.944 0.000 0.040 0.016
#> SRR949102 3 0.7913 0.0611 0.324 0.000 0.360 0.316
#> SRR949103 1 0.6993 0.4680 0.556 0.000 0.148 0.296
#> SRR949104 2 0.0000 0.9438 0.000 1.000 0.000 0.000
#> SRR949105 3 0.0000 0.8191 0.000 0.000 1.000 0.000
#> SRR949106 3 0.0000 0.8191 0.000 0.000 1.000 0.000
#> SRR949107 3 0.0000 0.8191 0.000 0.000 1.000 0.000
#> SRR949108 1 0.7028 0.4664 0.548 0.000 0.148 0.304
#> SRR949109 4 0.3688 0.6701 0.208 0.000 0.000 0.792
#> SRR949110 1 0.6993 0.4680 0.556 0.000 0.148 0.296
#> SRR949111 4 0.3688 0.6701 0.208 0.000 0.000 0.792
#> SRR949112 1 0.7028 0.4664 0.548 0.000 0.148 0.304
#> SRR949113 2 0.2530 0.8565 0.112 0.888 0.000 0.000
#> SRR949114 1 0.7170 0.4587 0.540 0.000 0.172 0.288
#> SRR949115 1 0.7170 0.4587 0.540 0.000 0.172 0.288
#> SRR949116 1 0.7170 0.4587 0.540 0.000 0.172 0.288
#> SRR949117 3 0.0707 0.8137 0.020 0.000 0.980 0.000
#> SRR949118 3 0.0188 0.8186 0.004 0.000 0.996 0.000
#> SRR949119 1 0.6903 0.3907 0.508 0.000 0.112 0.380
#> SRR949120 1 0.6903 0.3907 0.508 0.000 0.112 0.380
#> SRR949121 1 0.7028 0.4664 0.548 0.000 0.148 0.304
#> SRR949122 1 0.7028 0.4664 0.548 0.000 0.148 0.304
#> SRR949123 2 0.4253 0.7894 0.208 0.776 0.000 0.016
#> SRR949124 2 0.0000 0.9438 0.000 1.000 0.000 0.000
#> SRR949125 4 0.3688 0.6701 0.208 0.000 0.000 0.792
#> SRR949126 4 0.3688 0.6701 0.208 0.000 0.000 0.792
#> SRR949127 1 0.3444 0.3450 0.816 0.184 0.000 0.000
#> SRR949128 1 0.3444 0.3450 0.816 0.184 0.000 0.000
#> SRR949129 1 0.3444 0.3450 0.816 0.184 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR949076 4 0.3203 0.769 0.012 0.000 0.000 0.820 0.168
#> SRR949078 5 0.4551 0.390 0.016 0.368 0.000 0.000 0.616
#> SRR949077 4 0.3203 0.769 0.012 0.000 0.000 0.820 0.168
#> SRR949079 4 0.0963 0.907 0.036 0.000 0.000 0.964 0.000
#> SRR949080 4 0.0963 0.907 0.036 0.000 0.000 0.964 0.000
#> SRR949081 5 0.6462 0.191 0.124 0.000 0.304 0.024 0.548
#> SRR949082 5 0.4682 0.306 0.016 0.420 0.000 0.000 0.564
#> SRR949083 1 0.4313 0.581 0.636 0.000 0.000 0.008 0.356
#> SRR949084 1 0.4313 0.581 0.636 0.000 0.000 0.008 0.356
#> SRR949085 2 0.0000 0.931 0.000 1.000 0.000 0.000 0.000
#> SRR949087 5 0.4916 0.653 0.268 0.008 0.044 0.000 0.680
#> SRR949088 5 0.4916 0.653 0.268 0.008 0.044 0.000 0.680
#> SRR949086 3 0.1862 0.949 0.016 0.000 0.932 0.004 0.048
#> SRR949089 2 0.0000 0.931 0.000 1.000 0.000 0.000 0.000
#> SRR949090 4 0.2149 0.878 0.036 0.000 0.048 0.916 0.000
#> SRR949092 1 0.3622 0.782 0.816 0.000 0.000 0.048 0.136
#> SRR949093 1 0.3622 0.782 0.816 0.000 0.000 0.048 0.136
#> SRR949091 4 0.4410 0.286 0.004 0.000 0.440 0.556 0.000
#> SRR949095 5 0.1956 0.563 0.076 0.000 0.000 0.008 0.916
#> SRR949094 4 0.0963 0.907 0.036 0.000 0.000 0.964 0.000
#> SRR949096 1 0.4313 0.581 0.636 0.000 0.000 0.008 0.356
#> SRR949097 1 0.0510 0.820 0.984 0.000 0.000 0.000 0.016
#> SRR949098 2 0.0000 0.931 0.000 1.000 0.000 0.000 0.000
#> SRR949099 1 0.5333 0.294 0.628 0.000 0.300 0.004 0.068
#> SRR949101 3 0.0000 0.968 0.000 0.000 1.000 0.000 0.000
#> SRR949100 5 0.3949 0.630 0.300 0.000 0.004 0.000 0.696
#> SRR949102 5 0.6744 0.176 0.124 0.000 0.304 0.040 0.532
#> SRR949103 1 0.0510 0.820 0.984 0.000 0.000 0.000 0.016
#> SRR949104 2 0.0000 0.931 0.000 1.000 0.000 0.000 0.000
#> SRR949105 3 0.0000 0.968 0.000 0.000 1.000 0.000 0.000
#> SRR949106 3 0.0000 0.968 0.000 0.000 1.000 0.000 0.000
#> SRR949107 3 0.0000 0.968 0.000 0.000 1.000 0.000 0.000
#> SRR949108 1 0.1197 0.840 0.952 0.000 0.000 0.048 0.000
#> SRR949109 4 0.0963 0.907 0.036 0.000 0.000 0.964 0.000
#> SRR949110 1 0.0324 0.827 0.992 0.000 0.000 0.004 0.004
#> SRR949111 4 0.0963 0.907 0.036 0.000 0.000 0.964 0.000
#> SRR949112 1 0.1197 0.840 0.952 0.000 0.000 0.048 0.000
#> SRR949113 2 0.2179 0.813 0.000 0.888 0.000 0.000 0.112
#> SRR949114 1 0.1893 0.835 0.928 0.000 0.024 0.048 0.000
#> SRR949115 1 0.1893 0.835 0.928 0.000 0.024 0.048 0.000
#> SRR949116 1 0.1893 0.835 0.928 0.000 0.024 0.048 0.000
#> SRR949117 3 0.1862 0.949 0.016 0.000 0.932 0.004 0.048
#> SRR949118 3 0.1430 0.954 0.000 0.000 0.944 0.004 0.052
#> SRR949119 1 0.3226 0.806 0.852 0.000 0.000 0.060 0.088
#> SRR949120 1 0.3226 0.806 0.852 0.000 0.000 0.060 0.088
#> SRR949121 1 0.1197 0.840 0.952 0.000 0.000 0.048 0.000
#> SRR949122 1 0.1197 0.840 0.952 0.000 0.000 0.048 0.000
#> SRR949123 2 0.3305 0.699 0.000 0.776 0.000 0.000 0.224
#> SRR949124 2 0.0000 0.931 0.000 1.000 0.000 0.000 0.000
#> SRR949125 4 0.0963 0.907 0.036 0.000 0.000 0.964 0.000
#> SRR949126 4 0.0963 0.907 0.036 0.000 0.000 0.964 0.000
#> SRR949127 5 0.5673 0.640 0.184 0.184 0.000 0.000 0.632
#> SRR949128 5 0.5673 0.640 0.184 0.184 0.000 0.000 0.632
#> SRR949129 5 0.5673 0.640 0.184 0.184 0.000 0.000 0.632
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR949076 4 0.304 0.744 0.008 0.000 0.000 0.792 0.000 0.200
#> SRR949078 5 0.365 0.495 0.000 0.360 0.000 0.000 0.640 0.000
#> SRR949077 4 0.304 0.744 0.008 0.000 0.000 0.792 0.000 0.200
#> SRR949079 4 0.026 0.899 0.008 0.000 0.000 0.992 0.000 0.000
#> SRR949080 4 0.026 0.899 0.008 0.000 0.000 0.992 0.000 0.000
#> SRR949081 6 0.301 0.974 0.028 0.000 0.044 0.000 0.064 0.864
#> SRR949082 5 0.378 0.408 0.000 0.412 0.000 0.000 0.588 0.000
#> SRR949083 1 0.495 0.589 0.656 0.000 0.000 0.008 0.236 0.100
#> SRR949084 1 0.495 0.589 0.656 0.000 0.000 0.008 0.236 0.100
#> SRR949085 2 0.026 0.928 0.000 0.992 0.000 0.000 0.008 0.000
#> SRR949087 5 0.485 0.623 0.188 0.000 0.000 0.000 0.664 0.148
#> SRR949088 5 0.485 0.623 0.188 0.000 0.000 0.000 0.664 0.148
#> SRR949086 3 0.385 0.648 0.012 0.000 0.664 0.000 0.000 0.324
#> SRR949089 2 0.000 0.932 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949090 4 0.133 0.865 0.008 0.000 0.048 0.944 0.000 0.000
#> SRR949092 1 0.400 0.787 0.800 0.000 0.000 0.048 0.076 0.076
#> SRR949093 1 0.400 0.787 0.800 0.000 0.000 0.048 0.076 0.076
#> SRR949091 4 0.383 0.234 0.000 0.000 0.440 0.560 0.000 0.000
#> SRR949095 5 0.346 0.360 0.048 0.000 0.000 0.008 0.812 0.132
#> SRR949094 4 0.026 0.899 0.008 0.000 0.000 0.992 0.000 0.000
#> SRR949096 1 0.495 0.589 0.656 0.000 0.000 0.008 0.236 0.100
#> SRR949097 1 0.141 0.816 0.936 0.000 0.000 0.000 0.060 0.004
#> SRR949098 2 0.000 0.932 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949099 1 0.564 0.186 0.564 0.000 0.052 0.000 0.060 0.324
#> SRR949101 3 0.000 0.795 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR949100 5 0.418 0.639 0.212 0.000 0.000 0.000 0.720 0.068
#> SRR949102 6 0.297 0.974 0.028 0.000 0.044 0.004 0.052 0.872
#> SRR949103 1 0.141 0.816 0.936 0.000 0.000 0.000 0.060 0.004
#> SRR949104 2 0.000 0.932 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949105 3 0.000 0.795 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR949106 3 0.000 0.795 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR949107 3 0.000 0.795 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR949108 1 0.133 0.836 0.944 0.000 0.000 0.048 0.000 0.008
#> SRR949109 4 0.026 0.899 0.008 0.000 0.000 0.992 0.000 0.000
#> SRR949110 1 0.122 0.824 0.948 0.000 0.000 0.004 0.048 0.000
#> SRR949111 4 0.026 0.899 0.008 0.000 0.000 0.992 0.000 0.000
#> SRR949112 1 0.107 0.836 0.952 0.000 0.000 0.048 0.000 0.000
#> SRR949113 2 0.196 0.828 0.000 0.888 0.000 0.000 0.112 0.000
#> SRR949114 1 0.176 0.832 0.928 0.000 0.020 0.048 0.000 0.004
#> SRR949115 1 0.176 0.832 0.928 0.000 0.020 0.048 0.000 0.004
#> SRR949116 1 0.176 0.832 0.928 0.000 0.020 0.048 0.000 0.004
#> SRR949117 3 0.385 0.648 0.012 0.000 0.664 0.000 0.000 0.324
#> SRR949118 3 0.355 0.646 0.000 0.000 0.668 0.000 0.000 0.332
#> SRR949119 1 0.352 0.734 0.776 0.000 0.000 0.036 0.000 0.188
#> SRR949120 1 0.352 0.734 0.776 0.000 0.000 0.036 0.000 0.188
#> SRR949121 1 0.107 0.836 0.952 0.000 0.000 0.048 0.000 0.000
#> SRR949122 1 0.107 0.836 0.952 0.000 0.000 0.048 0.000 0.000
#> SRR949123 2 0.359 0.693 0.000 0.776 0.000 0.000 0.180 0.044
#> SRR949124 2 0.000 0.932 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949125 4 0.026 0.899 0.008 0.000 0.000 0.992 0.000 0.000
#> SRR949126 4 0.026 0.899 0.008 0.000 0.000 0.992 0.000 0.000
#> SRR949127 5 0.454 0.739 0.124 0.176 0.000 0.000 0.700 0.000
#> SRR949128 5 0.454 0.739 0.124 0.176 0.000 0.000 0.700 0.000
#> SRR949129 5 0.454 0.739 0.124 0.176 0.000 0.000 0.700 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)
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 16816 rows and 54 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 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 0.693 0.896 0.940 0.4012 0.609 0.609
#> 3 3 0.478 0.595 0.782 0.5272 0.760 0.632
#> 4 4 0.500 0.658 0.766 0.1756 0.790 0.553
#> 5 5 0.701 0.715 0.804 0.0861 0.911 0.686
#> 6 6 0.737 0.646 0.751 0.0437 0.979 0.902
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
#> SRR949076 1 0.0376 0.943 0.996 0.004
#> SRR949078 2 0.2423 0.953 0.040 0.960
#> SRR949077 1 0.0376 0.943 0.996 0.004
#> SRR949079 1 0.0376 0.943 0.996 0.004
#> SRR949080 1 0.0376 0.943 0.996 0.004
#> SRR949081 1 0.9850 0.235 0.572 0.428
#> SRR949082 2 0.2423 0.953 0.040 0.960
#> SRR949083 1 0.0376 0.944 0.996 0.004
#> SRR949084 1 0.0376 0.944 0.996 0.004
#> SRR949085 2 0.2423 0.953 0.040 0.960
#> SRR949087 2 0.8861 0.603 0.304 0.696
#> SRR949088 2 0.8861 0.603 0.304 0.696
#> SRR949086 1 0.5946 0.858 0.856 0.144
#> SRR949089 2 0.2423 0.953 0.040 0.960
#> SRR949090 1 0.0376 0.943 0.996 0.004
#> SRR949092 1 0.0376 0.944 0.996 0.004
#> SRR949093 1 0.0376 0.944 0.996 0.004
#> SRR949091 1 0.2236 0.924 0.964 0.036
#> SRR949095 1 0.9286 0.440 0.656 0.344
#> SRR949094 1 0.0376 0.943 0.996 0.004
#> SRR949096 1 0.0376 0.944 0.996 0.004
#> SRR949097 1 0.0376 0.944 0.996 0.004
#> SRR949098 2 0.2423 0.953 0.040 0.960
#> SRR949099 1 0.2043 0.930 0.968 0.032
#> SRR949101 1 0.4690 0.892 0.900 0.100
#> SRR949100 1 0.5059 0.859 0.888 0.112
#> SRR949102 1 0.2603 0.922 0.956 0.044
#> SRR949103 1 0.0376 0.944 0.996 0.004
#> SRR949104 2 0.2423 0.953 0.040 0.960
#> SRR949105 1 0.6712 0.823 0.824 0.176
#> SRR949106 1 0.6712 0.823 0.824 0.176
#> SRR949107 1 0.6712 0.823 0.824 0.176
#> SRR949108 1 0.0376 0.944 0.996 0.004
#> SRR949109 1 0.0376 0.943 0.996 0.004
#> SRR949110 1 0.0376 0.944 0.996 0.004
#> SRR949111 1 0.0376 0.943 0.996 0.004
#> SRR949112 1 0.0376 0.944 0.996 0.004
#> SRR949113 2 0.2423 0.953 0.040 0.960
#> SRR949114 1 0.0938 0.942 0.988 0.012
#> SRR949115 1 0.0938 0.942 0.988 0.012
#> SRR949116 1 0.0938 0.942 0.988 0.012
#> SRR949117 1 0.5946 0.858 0.856 0.144
#> SRR949118 1 0.4815 0.893 0.896 0.104
#> SRR949119 1 0.0376 0.944 0.996 0.004
#> SRR949120 1 0.0376 0.944 0.996 0.004
#> SRR949121 1 0.0376 0.944 0.996 0.004
#> SRR949122 1 0.0376 0.944 0.996 0.004
#> SRR949123 2 0.2423 0.953 0.040 0.960
#> SRR949124 2 0.2423 0.953 0.040 0.960
#> SRR949125 1 0.0376 0.943 0.996 0.004
#> SRR949126 1 0.0376 0.943 0.996 0.004
#> SRR949127 2 0.2423 0.953 0.040 0.960
#> SRR949128 2 0.2423 0.953 0.040 0.960
#> SRR949129 2 0.2423 0.953 0.040 0.960
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR949076 1 0.5926 0.4806 0.644 0.000 0.356
#> SRR949078 2 0.1878 0.9722 0.004 0.952 0.044
#> SRR949077 1 0.5926 0.4806 0.644 0.000 0.356
#> SRR949079 1 0.5926 0.4802 0.644 0.000 0.356
#> SRR949080 1 0.5926 0.4802 0.644 0.000 0.356
#> SRR949081 1 0.9026 0.0832 0.556 0.196 0.248
#> SRR949082 2 0.1878 0.9722 0.004 0.952 0.044
#> SRR949083 1 0.0661 0.6111 0.988 0.004 0.008
#> SRR949084 1 0.0661 0.6121 0.988 0.004 0.008
#> SRR949085 2 0.0000 0.9802 0.000 1.000 0.000
#> SRR949087 1 0.9649 -0.0291 0.404 0.388 0.208
#> SRR949088 1 0.9649 -0.0291 0.404 0.388 0.208
#> SRR949086 3 0.6422 0.7746 0.324 0.016 0.660
#> SRR949089 2 0.0000 0.9802 0.000 1.000 0.000
#> SRR949090 1 0.6309 0.3874 0.504 0.000 0.496
#> SRR949092 1 0.1647 0.6122 0.960 0.004 0.036
#> SRR949093 1 0.1647 0.6122 0.960 0.004 0.036
#> SRR949091 3 0.4178 0.4214 0.172 0.000 0.828
#> SRR949095 1 0.6506 0.4049 0.720 0.236 0.044
#> SRR949094 1 0.5926 0.4802 0.644 0.000 0.356
#> SRR949096 1 0.0983 0.6131 0.980 0.004 0.016
#> SRR949097 1 0.3425 0.5720 0.884 0.004 0.112
#> SRR949098 2 0.0000 0.9802 0.000 1.000 0.000
#> SRR949099 1 0.6286 -0.2407 0.536 0.000 0.464
#> SRR949101 3 0.5414 0.8054 0.212 0.016 0.772
#> SRR949100 1 0.7777 0.4274 0.676 0.164 0.160
#> SRR949102 1 0.5775 0.3757 0.728 0.012 0.260
#> SRR949103 1 0.3482 0.5587 0.872 0.000 0.128
#> SRR949104 2 0.0000 0.9802 0.000 1.000 0.000
#> SRR949105 3 0.6495 0.8252 0.200 0.060 0.740
#> SRR949106 3 0.6495 0.8252 0.200 0.060 0.740
#> SRR949107 3 0.6495 0.8252 0.200 0.060 0.740
#> SRR949108 1 0.1525 0.6129 0.964 0.004 0.032
#> SRR949109 1 0.6308 0.3939 0.508 0.000 0.492
#> SRR949110 1 0.3425 0.5720 0.884 0.004 0.112
#> SRR949111 1 0.6252 0.4370 0.556 0.000 0.444
#> SRR949112 1 0.2496 0.5971 0.928 0.004 0.068
#> SRR949113 2 0.0000 0.9802 0.000 1.000 0.000
#> SRR949114 1 0.6282 0.1737 0.664 0.012 0.324
#> SRR949115 1 0.6282 0.1737 0.664 0.012 0.324
#> SRR949116 1 0.6282 0.1737 0.664 0.012 0.324
#> SRR949117 3 0.6473 0.7617 0.332 0.016 0.652
#> SRR949118 3 0.6422 0.7746 0.324 0.016 0.660
#> SRR949119 1 0.1525 0.6138 0.964 0.004 0.032
#> SRR949120 1 0.1525 0.6138 0.964 0.004 0.032
#> SRR949121 1 0.2400 0.5988 0.932 0.004 0.064
#> SRR949122 1 0.1647 0.6122 0.960 0.004 0.036
#> SRR949123 2 0.0000 0.9802 0.000 1.000 0.000
#> SRR949124 2 0.0000 0.9802 0.000 1.000 0.000
#> SRR949125 1 0.6280 0.4181 0.540 0.000 0.460
#> SRR949126 1 0.6280 0.4181 0.540 0.000 0.460
#> SRR949127 2 0.1878 0.9722 0.004 0.952 0.044
#> SRR949128 2 0.1878 0.9722 0.004 0.952 0.044
#> SRR949129 2 0.1878 0.9722 0.004 0.952 0.044
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR949076 4 0.3801 0.8572 0.220 0.000 0.000 0.780
#> SRR949078 2 0.4300 0.8835 0.000 0.820 0.092 0.088
#> SRR949077 4 0.3801 0.8572 0.220 0.000 0.000 0.780
#> SRR949079 4 0.3801 0.8896 0.220 0.000 0.000 0.780
#> SRR949080 4 0.3801 0.8896 0.220 0.000 0.000 0.780
#> SRR949081 3 0.9440 0.0485 0.260 0.108 0.372 0.260
#> SRR949082 2 0.4300 0.8835 0.000 0.820 0.092 0.088
#> SRR949083 1 0.3048 0.6663 0.876 0.000 0.016 0.108
#> SRR949084 1 0.2730 0.6693 0.896 0.000 0.016 0.088
#> SRR949085 2 0.0336 0.9220 0.000 0.992 0.000 0.008
#> SRR949087 1 0.9698 0.0329 0.352 0.232 0.264 0.152
#> SRR949088 1 0.9698 0.0329 0.352 0.232 0.264 0.152
#> SRR949086 3 0.4874 0.6657 0.180 0.000 0.764 0.056
#> SRR949089 2 0.0336 0.9220 0.000 0.992 0.000 0.008
#> SRR949090 4 0.5785 0.8762 0.272 0.000 0.064 0.664
#> SRR949092 1 0.0188 0.7081 0.996 0.000 0.000 0.004
#> SRR949093 1 0.0188 0.7081 0.996 0.000 0.000 0.004
#> SRR949091 3 0.6557 -0.0611 0.076 0.000 0.476 0.448
#> SRR949095 1 0.8623 0.3572 0.508 0.144 0.096 0.252
#> SRR949094 4 0.3801 0.8896 0.220 0.000 0.000 0.780
#> SRR949096 1 0.2805 0.6624 0.888 0.000 0.012 0.100
#> SRR949097 1 0.1209 0.6957 0.964 0.000 0.004 0.032
#> SRR949098 2 0.0336 0.9220 0.000 0.992 0.000 0.008
#> SRR949099 1 0.6727 -0.0911 0.496 0.000 0.412 0.092
#> SRR949101 3 0.3471 0.7096 0.072 0.000 0.868 0.060
#> SRR949100 1 0.8918 0.2346 0.484 0.108 0.232 0.176
#> SRR949102 3 0.7925 0.0533 0.332 0.000 0.336 0.332
#> SRR949103 1 0.1209 0.6957 0.964 0.000 0.004 0.032
#> SRR949104 2 0.0000 0.9220 0.000 1.000 0.000 0.000
#> SRR949105 3 0.4149 0.7115 0.072 0.004 0.836 0.088
#> SRR949106 3 0.4149 0.7115 0.072 0.004 0.836 0.088
#> SRR949107 3 0.4149 0.7115 0.072 0.004 0.836 0.088
#> SRR949108 1 0.0188 0.7081 0.996 0.000 0.000 0.004
#> SRR949109 4 0.5785 0.8762 0.272 0.000 0.064 0.664
#> SRR949110 1 0.1209 0.6957 0.964 0.000 0.004 0.032
#> SRR949111 4 0.5537 0.8895 0.256 0.000 0.056 0.688
#> SRR949112 1 0.0672 0.7090 0.984 0.000 0.008 0.008
#> SRR949113 2 0.0000 0.9220 0.000 1.000 0.000 0.000
#> SRR949114 1 0.5460 0.3111 0.632 0.000 0.340 0.028
#> SRR949115 1 0.5460 0.3111 0.632 0.000 0.340 0.028
#> SRR949116 1 0.5460 0.3111 0.632 0.000 0.340 0.028
#> SRR949117 3 0.4880 0.6584 0.188 0.000 0.760 0.052
#> SRR949118 3 0.4562 0.6827 0.152 0.000 0.792 0.056
#> SRR949119 1 0.3569 0.5617 0.804 0.000 0.000 0.196
#> SRR949120 1 0.3569 0.5617 0.804 0.000 0.000 0.196
#> SRR949121 1 0.0376 0.7084 0.992 0.000 0.004 0.004
#> SRR949122 1 0.0336 0.7091 0.992 0.000 0.000 0.008
#> SRR949123 2 0.0336 0.9193 0.000 0.992 0.000 0.008
#> SRR949124 2 0.0000 0.9220 0.000 1.000 0.000 0.000
#> SRR949125 4 0.5772 0.8848 0.260 0.000 0.068 0.672
#> SRR949126 4 0.5772 0.8848 0.260 0.000 0.068 0.672
#> SRR949127 2 0.4104 0.8906 0.000 0.832 0.088 0.080
#> SRR949128 2 0.4104 0.8906 0.000 0.832 0.088 0.080
#> SRR949129 2 0.4104 0.8906 0.000 0.832 0.088 0.080
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR949076 4 0.3269 0.8360 0.056 0.000 0.000 0.848 0.096
#> SRR949078 2 0.4773 0.6956 0.000 0.656 0.008 0.024 0.312
#> SRR949077 4 0.3269 0.8360 0.056 0.000 0.000 0.848 0.096
#> SRR949079 4 0.2914 0.8716 0.076 0.000 0.000 0.872 0.052
#> SRR949080 4 0.2914 0.8716 0.076 0.000 0.000 0.872 0.052
#> SRR949081 5 0.6256 0.5568 0.080 0.024 0.140 0.068 0.688
#> SRR949082 2 0.4773 0.6956 0.000 0.656 0.008 0.024 0.312
#> SRR949083 1 0.3322 0.7604 0.848 0.000 0.004 0.044 0.104
#> SRR949084 1 0.2694 0.7853 0.888 0.000 0.004 0.032 0.076
#> SRR949085 2 0.0898 0.8152 0.000 0.972 0.008 0.020 0.000
#> SRR949087 5 0.5922 0.6385 0.176 0.088 0.060 0.000 0.676
#> SRR949088 5 0.5922 0.6385 0.176 0.088 0.060 0.000 0.676
#> SRR949086 3 0.6109 0.5600 0.084 0.000 0.548 0.020 0.348
#> SRR949089 2 0.0693 0.8150 0.000 0.980 0.008 0.012 0.000
#> SRR949090 4 0.3539 0.8698 0.092 0.000 0.028 0.848 0.032
#> SRR949092 1 0.0290 0.8285 0.992 0.000 0.000 0.008 0.000
#> SRR949093 1 0.0290 0.8285 0.992 0.000 0.000 0.008 0.000
#> SRR949091 4 0.5802 0.3003 0.016 0.000 0.380 0.544 0.060
#> SRR949095 5 0.6163 0.5556 0.220 0.044 0.012 0.072 0.652
#> SRR949094 4 0.2770 0.8729 0.076 0.000 0.000 0.880 0.044
#> SRR949096 1 0.2775 0.7827 0.884 0.000 0.004 0.036 0.076
#> SRR949097 1 0.2124 0.8048 0.916 0.000 0.000 0.028 0.056
#> SRR949098 2 0.0693 0.8150 0.000 0.980 0.008 0.012 0.000
#> SRR949099 5 0.7578 -0.0414 0.252 0.000 0.296 0.048 0.404
#> SRR949101 3 0.3070 0.6993 0.012 0.000 0.860 0.016 0.112
#> SRR949100 5 0.4976 0.6130 0.128 0.040 0.024 0.036 0.772
#> SRR949102 5 0.7476 0.3746 0.116 0.004 0.196 0.144 0.540
#> SRR949103 1 0.2209 0.8031 0.912 0.000 0.000 0.032 0.056
#> SRR949104 2 0.0000 0.8155 0.000 1.000 0.000 0.000 0.000
#> SRR949105 3 0.1815 0.7107 0.016 0.000 0.940 0.024 0.020
#> SRR949106 3 0.1815 0.7107 0.016 0.000 0.940 0.024 0.020
#> SRR949107 3 0.1815 0.7107 0.016 0.000 0.940 0.024 0.020
#> SRR949108 1 0.0566 0.8273 0.984 0.000 0.000 0.012 0.004
#> SRR949109 4 0.3369 0.8718 0.092 0.000 0.028 0.856 0.024
#> SRR949110 1 0.2036 0.8067 0.920 0.000 0.000 0.024 0.056
#> SRR949111 4 0.2540 0.8783 0.088 0.000 0.024 0.888 0.000
#> SRR949112 1 0.0510 0.8260 0.984 0.000 0.000 0.000 0.016
#> SRR949113 2 0.0000 0.8155 0.000 1.000 0.000 0.000 0.000
#> SRR949114 1 0.5884 0.4987 0.640 0.000 0.168 0.012 0.180
#> SRR949115 1 0.5884 0.4987 0.640 0.000 0.168 0.012 0.180
#> SRR949116 1 0.5884 0.4987 0.640 0.000 0.168 0.012 0.180
#> SRR949117 3 0.6155 0.5548 0.088 0.000 0.544 0.020 0.348
#> SRR949118 3 0.5803 0.5842 0.060 0.000 0.572 0.020 0.348
#> SRR949119 1 0.4471 0.6903 0.768 0.000 0.004 0.108 0.120
#> SRR949120 1 0.4471 0.6903 0.768 0.000 0.004 0.108 0.120
#> SRR949121 1 0.0404 0.8261 0.988 0.000 0.000 0.000 0.012
#> SRR949122 1 0.0000 0.8278 1.000 0.000 0.000 0.000 0.000
#> SRR949123 2 0.0932 0.8055 0.000 0.972 0.004 0.004 0.020
#> SRR949124 2 0.0000 0.8155 0.000 1.000 0.000 0.000 0.000
#> SRR949125 4 0.3386 0.8752 0.088 0.000 0.036 0.856 0.020
#> SRR949126 4 0.3386 0.8752 0.088 0.000 0.036 0.856 0.020
#> SRR949127 2 0.4401 0.6981 0.000 0.656 0.000 0.016 0.328
#> SRR949128 2 0.4401 0.6981 0.000 0.656 0.000 0.016 0.328
#> SRR949129 2 0.4401 0.6981 0.000 0.656 0.000 0.016 0.328
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR949076 4 0.4378 0.7416 0.028 0.000 0.000 0.760 0.108 0.104
#> SRR949078 2 0.4261 0.5641 0.000 0.572 0.000 0.000 0.408 0.020
#> SRR949077 4 0.4450 0.7435 0.032 0.000 0.000 0.756 0.108 0.104
#> SRR949079 4 0.2271 0.8419 0.024 0.000 0.000 0.908 0.036 0.032
#> SRR949080 4 0.2271 0.8419 0.024 0.000 0.000 0.908 0.036 0.032
#> SRR949081 5 0.6837 0.3687 0.044 0.000 0.340 0.020 0.448 0.148
#> SRR949082 2 0.4261 0.5641 0.000 0.572 0.000 0.000 0.408 0.020
#> SRR949083 1 0.3956 0.6799 0.788 0.000 0.000 0.016 0.104 0.092
#> SRR949084 1 0.3014 0.7274 0.860 0.000 0.000 0.016 0.068 0.056
#> SRR949085 2 0.0632 0.7688 0.000 0.976 0.000 0.000 0.000 0.024
#> SRR949087 5 0.6134 0.6432 0.080 0.044 0.272 0.000 0.580 0.024
#> SRR949088 5 0.6134 0.6432 0.080 0.044 0.272 0.000 0.580 0.024
#> SRR949086 3 0.0862 0.5171 0.008 0.000 0.972 0.000 0.016 0.004
#> SRR949089 2 0.0632 0.7688 0.000 0.976 0.000 0.000 0.000 0.024
#> SRR949090 4 0.2494 0.8414 0.036 0.000 0.004 0.900 0.028 0.032
#> SRR949092 1 0.0291 0.7815 0.992 0.000 0.000 0.000 0.004 0.004
#> SRR949093 1 0.0291 0.7815 0.992 0.000 0.000 0.000 0.004 0.004
#> SRR949091 4 0.6345 0.1608 0.008 0.000 0.380 0.468 0.056 0.088
#> SRR949095 5 0.6087 0.5083 0.100 0.004 0.060 0.032 0.656 0.148
#> SRR949094 4 0.2201 0.8440 0.028 0.000 0.000 0.912 0.032 0.028
#> SRR949096 1 0.3130 0.7244 0.852 0.000 0.000 0.016 0.072 0.060
#> SRR949097 1 0.2998 0.7464 0.876 0.000 0.012 0.036 0.040 0.036
#> SRR949098 2 0.0632 0.7688 0.000 0.976 0.000 0.000 0.000 0.024
#> SRR949099 3 0.6148 0.2798 0.176 0.000 0.632 0.036 0.108 0.048
#> SRR949101 3 0.4229 -0.0414 0.000 0.000 0.732 0.008 0.060 0.200
#> SRR949100 5 0.6156 0.5592 0.044 0.008 0.208 0.028 0.628 0.084
#> SRR949102 3 0.7671 -0.2573 0.060 0.000 0.408 0.056 0.272 0.204
#> SRR949103 1 0.2998 0.7464 0.876 0.000 0.012 0.036 0.040 0.036
#> SRR949104 2 0.0000 0.7686 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949105 6 0.3828 1.0000 0.000 0.000 0.440 0.000 0.000 0.560
#> SRR949106 6 0.3828 1.0000 0.000 0.000 0.440 0.000 0.000 0.560
#> SRR949107 6 0.3828 1.0000 0.000 0.000 0.440 0.000 0.000 0.560
#> SRR949108 1 0.0520 0.7795 0.984 0.000 0.000 0.000 0.008 0.008
#> SRR949109 4 0.2176 0.8450 0.036 0.000 0.004 0.916 0.024 0.020
#> SRR949110 1 0.2884 0.7533 0.880 0.000 0.008 0.028 0.048 0.036
#> SRR949111 4 0.1010 0.8495 0.036 0.000 0.000 0.960 0.000 0.004
#> SRR949112 1 0.1340 0.7723 0.948 0.000 0.008 0.000 0.040 0.004
#> SRR949113 2 0.0146 0.7691 0.000 0.996 0.000 0.000 0.004 0.000
#> SRR949114 1 0.6578 0.2945 0.500 0.000 0.320 0.012 0.096 0.072
#> SRR949115 1 0.6578 0.2945 0.500 0.000 0.320 0.012 0.096 0.072
#> SRR949116 1 0.6578 0.2945 0.500 0.000 0.320 0.012 0.096 0.072
#> SRR949117 3 0.1059 0.5216 0.016 0.000 0.964 0.000 0.016 0.004
#> SRR949118 3 0.0717 0.5172 0.008 0.000 0.976 0.000 0.016 0.000
#> SRR949119 1 0.6291 0.5366 0.624 0.000 0.020 0.096 0.140 0.120
#> SRR949120 1 0.6291 0.5366 0.624 0.000 0.020 0.096 0.140 0.120
#> SRR949121 1 0.0260 0.7809 0.992 0.000 0.000 0.000 0.008 0.000
#> SRR949122 1 0.0260 0.7811 0.992 0.000 0.000 0.000 0.008 0.000
#> SRR949123 2 0.1503 0.7462 0.000 0.944 0.000 0.008 0.032 0.016
#> SRR949124 2 0.0000 0.7686 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949125 4 0.2494 0.8430 0.036 0.000 0.004 0.900 0.028 0.032
#> SRR949126 4 0.2494 0.8430 0.036 0.000 0.004 0.900 0.028 0.032
#> SRR949127 2 0.4379 0.5846 0.000 0.576 0.000 0.000 0.396 0.028
#> SRR949128 2 0.4379 0.5846 0.000 0.576 0.000 0.000 0.396 0.028
#> SRR949129 2 0.4379 0.5846 0.000 0.576 0.000 0.000 0.396 0.028
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 16816 rows and 54 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 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 0.726 0.833 0.935 0.4837 0.502 0.502
#> 3 3 0.754 0.809 0.892 0.3848 0.704 0.471
#> 4 4 0.948 0.869 0.947 0.1260 0.887 0.667
#> 5 5 0.844 0.805 0.878 0.0481 0.973 0.892
#> 6 6 0.823 0.743 0.856 0.0376 0.966 0.850
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
#> SRR949076 1 0.3114 0.9002 0.944 0.056
#> SRR949078 2 0.0000 0.8754 0.000 1.000
#> SRR949077 1 0.0000 0.9588 1.000 0.000
#> SRR949079 1 0.0000 0.9588 1.000 0.000
#> SRR949080 1 0.0000 0.9588 1.000 0.000
#> SRR949081 2 0.0000 0.8754 0.000 1.000
#> SRR949082 2 0.0000 0.8754 0.000 1.000
#> SRR949083 1 0.7219 0.6964 0.800 0.200
#> SRR949084 1 0.0000 0.9588 1.000 0.000
#> SRR949085 2 0.0000 0.8754 0.000 1.000
#> SRR949087 2 0.0000 0.8754 0.000 1.000
#> SRR949088 2 0.0000 0.8754 0.000 1.000
#> SRR949086 2 0.9896 0.3273 0.440 0.560
#> SRR949089 2 0.0000 0.8754 0.000 1.000
#> SRR949090 1 0.0000 0.9588 1.000 0.000
#> SRR949092 1 0.0000 0.9588 1.000 0.000
#> SRR949093 1 0.0000 0.9588 1.000 0.000
#> SRR949091 1 0.0000 0.9588 1.000 0.000
#> SRR949095 2 0.0000 0.8754 0.000 1.000
#> SRR949094 1 0.0000 0.9588 1.000 0.000
#> SRR949096 1 0.0000 0.9588 1.000 0.000
#> SRR949097 1 0.0000 0.9588 1.000 0.000
#> SRR949098 2 0.0000 0.8754 0.000 1.000
#> SRR949099 1 0.0000 0.9588 1.000 0.000
#> SRR949101 1 0.8763 0.4858 0.704 0.296
#> SRR949100 2 0.0000 0.8754 0.000 1.000
#> SRR949102 2 0.8499 0.5722 0.276 0.724
#> SRR949103 1 0.0000 0.9588 1.000 0.000
#> SRR949104 2 0.0000 0.8754 0.000 1.000
#> SRR949105 2 0.9896 0.3273 0.440 0.560
#> SRR949106 2 0.9896 0.3273 0.440 0.560
#> SRR949107 2 0.9896 0.3273 0.440 0.560
#> SRR949108 1 0.0000 0.9588 1.000 0.000
#> SRR949109 1 0.0000 0.9588 1.000 0.000
#> SRR949110 1 0.0000 0.9588 1.000 0.000
#> SRR949111 1 0.0000 0.9588 1.000 0.000
#> SRR949112 1 0.0672 0.9514 0.992 0.008
#> SRR949113 2 0.0000 0.8754 0.000 1.000
#> SRR949114 1 0.0000 0.9588 1.000 0.000
#> SRR949115 1 0.0000 0.9588 1.000 0.000
#> SRR949116 1 0.0000 0.9588 1.000 0.000
#> SRR949117 2 0.9896 0.3273 0.440 0.560
#> SRR949118 1 0.9977 -0.0962 0.528 0.472
#> SRR949119 1 0.0000 0.9588 1.000 0.000
#> SRR949120 1 0.0000 0.9588 1.000 0.000
#> SRR949121 1 0.0000 0.9588 1.000 0.000
#> SRR949122 1 0.0000 0.9588 1.000 0.000
#> SRR949123 2 0.0000 0.8754 0.000 1.000
#> SRR949124 2 0.0000 0.8754 0.000 1.000
#> SRR949125 1 0.0000 0.9588 1.000 0.000
#> SRR949126 1 0.0000 0.9588 1.000 0.000
#> SRR949127 2 0.0000 0.8754 0.000 1.000
#> SRR949128 2 0.0000 0.8754 0.000 1.000
#> SRR949129 2 0.0000 0.8754 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR949076 3 0.6111 0.635 0.396 0.000 0.604
#> SRR949078 2 0.0000 1.000 0.000 1.000 0.000
#> SRR949077 3 0.6111 0.635 0.396 0.000 0.604
#> SRR949079 3 0.6111 0.635 0.396 0.000 0.604
#> SRR949080 3 0.6111 0.635 0.396 0.000 0.604
#> SRR949081 2 0.0000 1.000 0.000 1.000 0.000
#> SRR949082 2 0.0000 1.000 0.000 1.000 0.000
#> SRR949083 1 0.0000 0.887 1.000 0.000 0.000
#> SRR949084 1 0.0000 0.887 1.000 0.000 0.000
#> SRR949085 2 0.0000 1.000 0.000 1.000 0.000
#> SRR949087 2 0.0000 1.000 0.000 1.000 0.000
#> SRR949088 2 0.0000 1.000 0.000 1.000 0.000
#> SRR949086 3 0.4555 0.566 0.000 0.200 0.800
#> SRR949089 2 0.0000 1.000 0.000 1.000 0.000
#> SRR949090 3 0.5835 0.667 0.340 0.000 0.660
#> SRR949092 1 0.0000 0.887 1.000 0.000 0.000
#> SRR949093 1 0.0000 0.887 1.000 0.000 0.000
#> SRR949091 3 0.0000 0.694 0.000 0.000 1.000
#> SRR949095 2 0.0000 1.000 0.000 1.000 0.000
#> SRR949094 3 0.6111 0.635 0.396 0.000 0.604
#> SRR949096 1 0.0000 0.887 1.000 0.000 0.000
#> SRR949097 1 0.1411 0.864 0.964 0.000 0.036
#> SRR949098 2 0.0000 1.000 0.000 1.000 0.000
#> SRR949099 3 0.0000 0.694 0.000 0.000 1.000
#> SRR949101 3 0.0000 0.694 0.000 0.000 1.000
#> SRR949100 2 0.0000 1.000 0.000 1.000 0.000
#> SRR949102 3 0.6984 0.511 0.040 0.304 0.656
#> SRR949103 1 0.1643 0.858 0.956 0.000 0.044
#> SRR949104 2 0.0000 1.000 0.000 1.000 0.000
#> SRR949105 3 0.1031 0.690 0.000 0.024 0.976
#> SRR949106 3 0.1031 0.690 0.000 0.024 0.976
#> SRR949107 3 0.1031 0.690 0.000 0.024 0.976
#> SRR949108 1 0.0000 0.887 1.000 0.000 0.000
#> SRR949109 3 0.5835 0.667 0.340 0.000 0.660
#> SRR949110 1 0.1411 0.864 0.964 0.000 0.036
#> SRR949111 3 0.5926 0.660 0.356 0.000 0.644
#> SRR949112 1 0.0000 0.887 1.000 0.000 0.000
#> SRR949113 2 0.0000 1.000 0.000 1.000 0.000
#> SRR949114 1 0.6111 0.455 0.604 0.000 0.396
#> SRR949115 1 0.6111 0.455 0.604 0.000 0.396
#> SRR949116 1 0.6111 0.455 0.604 0.000 0.396
#> SRR949117 3 0.4555 0.566 0.000 0.200 0.800
#> SRR949118 3 0.0000 0.694 0.000 0.000 1.000
#> SRR949119 1 0.0237 0.884 0.996 0.000 0.004
#> SRR949120 1 0.0237 0.884 0.996 0.000 0.004
#> SRR949121 1 0.0000 0.887 1.000 0.000 0.000
#> SRR949122 1 0.0000 0.887 1.000 0.000 0.000
#> SRR949123 2 0.0000 1.000 0.000 1.000 0.000
#> SRR949124 2 0.0000 1.000 0.000 1.000 0.000
#> SRR949125 3 0.5926 0.660 0.356 0.000 0.644
#> SRR949126 3 0.5926 0.660 0.356 0.000 0.644
#> SRR949127 2 0.0000 1.000 0.000 1.000 0.000
#> SRR949128 2 0.0000 1.000 0.000 1.000 0.000
#> SRR949129 2 0.0000 1.000 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR949076 4 0.0188 0.902 0.004 0.000 0.000 0.996
#> SRR949078 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR949077 4 0.0188 0.902 0.004 0.000 0.000 0.996
#> SRR949079 4 0.0000 0.903 0.000 0.000 0.000 1.000
#> SRR949080 4 0.0000 0.903 0.000 0.000 0.000 1.000
#> SRR949081 2 0.5138 0.389 0.000 0.600 0.392 0.008
#> SRR949082 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR949083 1 0.0188 0.986 0.996 0.000 0.000 0.004
#> SRR949084 1 0.0188 0.986 0.996 0.000 0.000 0.004
#> SRR949085 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR949087 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR949088 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR949086 3 0.0000 0.836 0.000 0.000 1.000 0.000
#> SRR949089 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR949090 4 0.0336 0.904 0.000 0.000 0.008 0.992
#> SRR949092 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> SRR949093 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> SRR949091 4 0.4948 0.211 0.000 0.000 0.440 0.560
#> SRR949095 2 0.0336 0.967 0.000 0.992 0.000 0.008
#> SRR949094 4 0.0000 0.903 0.000 0.000 0.000 1.000
#> SRR949096 1 0.0188 0.986 0.996 0.000 0.000 0.004
#> SRR949097 1 0.0336 0.984 0.992 0.000 0.000 0.008
#> SRR949098 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR949099 3 0.0469 0.827 0.000 0.000 0.988 0.012
#> SRR949101 3 0.0000 0.836 0.000 0.000 1.000 0.000
#> SRR949100 2 0.0188 0.971 0.000 0.996 0.000 0.004
#> SRR949102 4 0.7241 0.159 0.004 0.124 0.416 0.456
#> SRR949103 1 0.0336 0.984 0.992 0.000 0.000 0.008
#> SRR949104 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR949105 3 0.0000 0.836 0.000 0.000 1.000 0.000
#> SRR949106 3 0.0000 0.836 0.000 0.000 1.000 0.000
#> SRR949107 3 0.0000 0.836 0.000 0.000 1.000 0.000
#> SRR949108 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> SRR949109 4 0.0336 0.904 0.000 0.000 0.008 0.992
#> SRR949110 1 0.0188 0.986 0.996 0.000 0.000 0.004
#> SRR949111 4 0.0336 0.904 0.000 0.000 0.008 0.992
#> SRR949112 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> SRR949113 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR949114 3 0.4916 0.393 0.424 0.000 0.576 0.000
#> SRR949115 3 0.4916 0.393 0.424 0.000 0.576 0.000
#> SRR949116 3 0.4916 0.393 0.424 0.000 0.576 0.000
#> SRR949117 3 0.0000 0.836 0.000 0.000 1.000 0.000
#> SRR949118 3 0.0000 0.836 0.000 0.000 1.000 0.000
#> SRR949119 1 0.1557 0.941 0.944 0.000 0.000 0.056
#> SRR949120 1 0.1557 0.941 0.944 0.000 0.000 0.056
#> SRR949121 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> SRR949122 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> SRR949123 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR949124 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR949125 4 0.0336 0.904 0.000 0.000 0.008 0.992
#> SRR949126 4 0.0336 0.904 0.000 0.000 0.008 0.992
#> SRR949127 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR949128 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR949129 2 0.0000 0.974 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR949076 4 0.1043 0.8849 0.000 0.000 0.000 0.960 0.040
#> SRR949078 2 0.0290 0.9089 0.000 0.992 0.000 0.000 0.008
#> SRR949077 4 0.1410 0.8701 0.000 0.000 0.000 0.940 0.060
#> SRR949079 4 0.0162 0.9017 0.000 0.000 0.000 0.996 0.004
#> SRR949080 4 0.0162 0.9017 0.000 0.000 0.000 0.996 0.004
#> SRR949081 2 0.7490 0.0562 0.000 0.396 0.248 0.040 0.316
#> SRR949082 2 0.0000 0.9101 0.000 1.000 0.000 0.000 0.000
#> SRR949083 1 0.2074 0.8329 0.896 0.000 0.000 0.000 0.104
#> SRR949084 1 0.1792 0.8419 0.916 0.000 0.000 0.000 0.084
#> SRR949085 2 0.0000 0.9101 0.000 1.000 0.000 0.000 0.000
#> SRR949087 2 0.3109 0.8211 0.000 0.800 0.000 0.000 0.200
#> SRR949088 2 0.3109 0.8211 0.000 0.800 0.000 0.000 0.200
#> SRR949086 3 0.1544 0.9108 0.000 0.000 0.932 0.000 0.068
#> SRR949089 2 0.0000 0.9101 0.000 1.000 0.000 0.000 0.000
#> SRR949090 4 0.1671 0.8847 0.000 0.000 0.000 0.924 0.076
#> SRR949092 1 0.0162 0.8605 0.996 0.000 0.000 0.000 0.004
#> SRR949093 1 0.0162 0.8605 0.996 0.000 0.000 0.000 0.004
#> SRR949091 4 0.4283 0.1848 0.000 0.000 0.456 0.544 0.000
#> SRR949095 2 0.3478 0.7922 0.004 0.828 0.000 0.032 0.136
#> SRR949094 4 0.0162 0.9017 0.000 0.000 0.000 0.996 0.004
#> SRR949096 1 0.1851 0.8403 0.912 0.000 0.000 0.000 0.088
#> SRR949097 1 0.2020 0.8249 0.900 0.000 0.000 0.000 0.100
#> SRR949098 2 0.0000 0.9101 0.000 1.000 0.000 0.000 0.000
#> SRR949099 3 0.3880 0.7102 0.020 0.000 0.772 0.004 0.204
#> SRR949101 3 0.0000 0.9225 0.000 0.000 1.000 0.000 0.000
#> SRR949100 2 0.3074 0.8087 0.000 0.804 0.000 0.000 0.196
#> SRR949102 5 0.7513 -0.0378 0.000 0.048 0.304 0.228 0.420
#> SRR949103 1 0.2020 0.8249 0.900 0.000 0.000 0.000 0.100
#> SRR949104 2 0.0000 0.9101 0.000 1.000 0.000 0.000 0.000
#> SRR949105 3 0.0000 0.9225 0.000 0.000 1.000 0.000 0.000
#> SRR949106 3 0.0000 0.9225 0.000 0.000 1.000 0.000 0.000
#> SRR949107 3 0.0000 0.9225 0.000 0.000 1.000 0.000 0.000
#> SRR949108 1 0.0404 0.8606 0.988 0.000 0.000 0.000 0.012
#> SRR949109 4 0.1732 0.8819 0.000 0.000 0.000 0.920 0.080
#> SRR949110 1 0.1908 0.8282 0.908 0.000 0.000 0.000 0.092
#> SRR949111 4 0.1043 0.9030 0.000 0.000 0.000 0.960 0.040
#> SRR949112 1 0.4045 0.3306 0.644 0.000 0.000 0.000 0.356
#> SRR949113 2 0.0000 0.9101 0.000 1.000 0.000 0.000 0.000
#> SRR949114 5 0.6319 0.6984 0.196 0.000 0.284 0.000 0.520
#> SRR949115 5 0.6319 0.6984 0.196 0.000 0.284 0.000 0.520
#> SRR949116 5 0.6319 0.6984 0.196 0.000 0.284 0.000 0.520
#> SRR949117 3 0.1478 0.9115 0.000 0.000 0.936 0.000 0.064
#> SRR949118 3 0.1732 0.9020 0.000 0.000 0.920 0.000 0.080
#> SRR949119 1 0.4736 0.6781 0.712 0.000 0.000 0.072 0.216
#> SRR949120 1 0.4736 0.6781 0.712 0.000 0.000 0.072 0.216
#> SRR949121 1 0.0290 0.8597 0.992 0.000 0.000 0.000 0.008
#> SRR949122 1 0.0404 0.8598 0.988 0.000 0.000 0.000 0.012
#> SRR949123 2 0.0000 0.9101 0.000 1.000 0.000 0.000 0.000
#> SRR949124 2 0.0000 0.9101 0.000 1.000 0.000 0.000 0.000
#> SRR949125 4 0.1043 0.9030 0.000 0.000 0.000 0.960 0.040
#> SRR949126 4 0.1043 0.9030 0.000 0.000 0.000 0.960 0.040
#> SRR949127 2 0.1478 0.8935 0.000 0.936 0.000 0.000 0.064
#> SRR949128 2 0.1478 0.8935 0.000 0.936 0.000 0.000 0.064
#> SRR949129 2 0.1478 0.8935 0.000 0.936 0.000 0.000 0.064
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR949076 4 0.1806 0.87668 0.000 0.000 0.000 0.908 0.088 0.004
#> SRR949078 2 0.1563 0.79333 0.000 0.932 0.000 0.000 0.056 0.012
#> SRR949077 4 0.1908 0.87007 0.000 0.000 0.000 0.900 0.096 0.004
#> SRR949079 4 0.0405 0.91939 0.000 0.000 0.000 0.988 0.008 0.004
#> SRR949080 4 0.0405 0.91939 0.000 0.000 0.000 0.988 0.008 0.004
#> SRR949081 5 0.3700 0.43167 0.000 0.152 0.068 0.000 0.780 0.000
#> SRR949082 2 0.0146 0.82747 0.000 0.996 0.000 0.000 0.004 0.000
#> SRR949083 1 0.1812 0.81577 0.912 0.000 0.000 0.000 0.080 0.008
#> SRR949084 1 0.1524 0.82275 0.932 0.000 0.000 0.000 0.060 0.008
#> SRR949085 2 0.0000 0.83007 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949087 5 0.5051 0.25748 0.000 0.388 0.004 0.000 0.540 0.068
#> SRR949088 5 0.5051 0.25748 0.000 0.388 0.004 0.000 0.540 0.068
#> SRR949086 3 0.3493 0.82225 0.000 0.000 0.800 0.000 0.136 0.064
#> SRR949089 2 0.0000 0.83007 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949090 4 0.1088 0.90148 0.000 0.000 0.000 0.960 0.016 0.024
#> SRR949092 1 0.0146 0.83379 0.996 0.000 0.000 0.000 0.000 0.004
#> SRR949093 1 0.0146 0.83379 0.996 0.000 0.000 0.000 0.000 0.004
#> SRR949091 4 0.3950 0.23826 0.000 0.000 0.432 0.564 0.000 0.004
#> SRR949095 2 0.3420 0.47799 0.000 0.748 0.000 0.000 0.240 0.012
#> SRR949094 4 0.0405 0.91939 0.000 0.000 0.000 0.988 0.008 0.004
#> SRR949096 1 0.1524 0.82275 0.932 0.000 0.000 0.000 0.060 0.008
#> SRR949097 1 0.2917 0.78341 0.852 0.000 0.000 0.004 0.040 0.104
#> SRR949098 2 0.0000 0.83007 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949099 3 0.5702 0.62742 0.012 0.000 0.596 0.008 0.240 0.144
#> SRR949101 3 0.0405 0.84849 0.000 0.000 0.988 0.004 0.000 0.008
#> SRR949100 2 0.5451 0.30505 0.000 0.564 0.000 0.004 0.296 0.136
#> SRR949102 5 0.5957 0.31218 0.000 0.116 0.128 0.052 0.664 0.040
#> SRR949103 1 0.2917 0.78341 0.852 0.000 0.000 0.004 0.040 0.104
#> SRR949104 2 0.0000 0.83007 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949105 3 0.0291 0.85104 0.000 0.000 0.992 0.000 0.004 0.004
#> SRR949106 3 0.0291 0.85104 0.000 0.000 0.992 0.000 0.004 0.004
#> SRR949107 3 0.0291 0.85104 0.000 0.000 0.992 0.000 0.004 0.004
#> SRR949108 1 0.0000 0.83386 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949109 4 0.1176 0.89911 0.000 0.000 0.000 0.956 0.020 0.024
#> SRR949110 1 0.2870 0.78402 0.856 0.000 0.000 0.004 0.040 0.100
#> SRR949111 4 0.0000 0.91959 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949112 1 0.3860 -0.00422 0.528 0.000 0.000 0.000 0.000 0.472
#> SRR949113 2 0.0000 0.83007 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949114 6 0.3183 1.00000 0.060 0.000 0.112 0.000 0.000 0.828
#> SRR949115 6 0.3183 1.00000 0.060 0.000 0.112 0.000 0.000 0.828
#> SRR949116 6 0.3183 1.00000 0.060 0.000 0.112 0.000 0.000 0.828
#> SRR949117 3 0.3341 0.82795 0.000 0.000 0.816 0.000 0.116 0.068
#> SRR949118 3 0.3530 0.81575 0.000 0.000 0.792 0.000 0.152 0.056
#> SRR949119 1 0.5635 0.52442 0.584 0.000 0.000 0.048 0.296 0.072
#> SRR949120 1 0.5635 0.52442 0.584 0.000 0.000 0.048 0.296 0.072
#> SRR949121 1 0.0547 0.83141 0.980 0.000 0.000 0.000 0.000 0.020
#> SRR949122 1 0.0547 0.83110 0.980 0.000 0.000 0.000 0.000 0.020
#> SRR949123 2 0.0000 0.83007 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949124 2 0.0000 0.83007 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949125 4 0.0000 0.91959 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949126 4 0.0000 0.91959 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949127 2 0.4011 0.60953 0.000 0.732 0.000 0.000 0.212 0.056
#> SRR949128 2 0.4011 0.60953 0.000 0.732 0.000 0.000 0.212 0.056
#> SRR949129 2 0.4011 0.60953 0.000 0.732 0.000 0.000 0.212 0.056
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)
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 16816 rows and 54 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 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 0.885 0.885 0.921 0.3894 0.575 0.575
#> 3 3 0.802 0.888 0.944 0.6613 0.759 0.581
#> 4 4 0.938 0.912 0.964 0.1124 0.908 0.738
#> 5 5 0.904 0.816 0.931 0.0844 0.900 0.664
#> 6 6 0.859 0.782 0.895 0.0484 0.945 0.755
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
#> attr(,"optional")
#> [1] 4
There is also optional best \(k\) = 4 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR949076 1 0.000 0.915 1.000 0.000
#> SRR949078 2 0.000 0.870 0.000 1.000
#> SRR949077 1 0.000 0.915 1.000 0.000
#> SRR949079 1 0.000 0.915 1.000 0.000
#> SRR949080 1 0.000 0.915 1.000 0.000
#> SRR949081 2 0.963 0.404 0.388 0.612
#> SRR949082 2 0.000 0.870 0.000 1.000
#> SRR949083 1 0.443 0.959 0.908 0.092
#> SRR949084 1 0.443 0.959 0.908 0.092
#> SRR949085 2 0.000 0.870 0.000 1.000
#> SRR949087 2 0.936 0.493 0.352 0.648
#> SRR949088 2 0.900 0.563 0.316 0.684
#> SRR949086 1 0.443 0.959 0.908 0.092
#> SRR949089 2 0.000 0.870 0.000 1.000
#> SRR949090 1 0.000 0.915 1.000 0.000
#> SRR949092 1 0.443 0.959 0.908 0.092
#> SRR949093 1 0.443 0.959 0.908 0.092
#> SRR949091 1 0.000 0.915 1.000 0.000
#> SRR949095 1 0.714 0.826 0.804 0.196
#> SRR949094 1 0.000 0.915 1.000 0.000
#> SRR949096 1 0.443 0.959 0.908 0.092
#> SRR949097 1 0.443 0.959 0.908 0.092
#> SRR949098 2 0.000 0.870 0.000 1.000
#> SRR949099 1 0.443 0.959 0.908 0.092
#> SRR949101 1 0.443 0.959 0.908 0.092
#> SRR949100 2 0.833 0.629 0.264 0.736
#> SRR949102 1 0.443 0.959 0.908 0.092
#> SRR949103 1 0.443 0.959 0.908 0.092
#> SRR949104 2 0.000 0.870 0.000 1.000
#> SRR949105 1 0.443 0.959 0.908 0.092
#> SRR949106 1 0.443 0.959 0.908 0.092
#> SRR949107 1 0.443 0.959 0.908 0.092
#> SRR949108 1 0.443 0.959 0.908 0.092
#> SRR949109 1 0.000 0.915 1.000 0.000
#> SRR949110 1 0.443 0.959 0.908 0.092
#> SRR949111 1 0.000 0.915 1.000 0.000
#> SRR949112 1 0.443 0.959 0.908 0.092
#> SRR949113 2 0.000 0.870 0.000 1.000
#> SRR949114 1 0.443 0.959 0.908 0.092
#> SRR949115 1 0.443 0.959 0.908 0.092
#> SRR949116 1 0.443 0.959 0.908 0.092
#> SRR949117 1 0.443 0.959 0.908 0.092
#> SRR949118 1 0.443 0.959 0.908 0.092
#> SRR949119 1 0.311 0.944 0.944 0.056
#> SRR949120 1 0.311 0.944 0.944 0.056
#> SRR949121 1 0.443 0.959 0.908 0.092
#> SRR949122 1 0.443 0.959 0.908 0.092
#> SRR949123 2 0.973 0.356 0.404 0.596
#> SRR949124 2 0.000 0.870 0.000 1.000
#> SRR949125 1 0.000 0.915 1.000 0.000
#> SRR949126 1 0.000 0.915 1.000 0.000
#> SRR949127 2 0.000 0.870 0.000 1.000
#> SRR949128 2 0.000 0.870 0.000 1.000
#> SRR949129 2 0.000 0.870 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR949076 3 0.1529 0.877 0.040 0.000 0.960
#> SRR949078 2 0.0000 0.942 0.000 1.000 0.000
#> SRR949077 3 0.3340 0.829 0.120 0.000 0.880
#> SRR949079 3 0.1529 0.877 0.040 0.000 0.960
#> SRR949080 3 0.1529 0.877 0.040 0.000 0.960
#> SRR949081 2 0.5291 0.659 0.268 0.732 0.000
#> SRR949082 2 0.0000 0.942 0.000 1.000 0.000
#> SRR949083 1 0.0000 0.974 1.000 0.000 0.000
#> SRR949084 1 0.0000 0.974 1.000 0.000 0.000
#> SRR949085 2 0.0000 0.942 0.000 1.000 0.000
#> SRR949087 2 0.3412 0.863 0.124 0.876 0.000
#> SRR949088 2 0.3192 0.873 0.112 0.888 0.000
#> SRR949086 1 0.0000 0.974 1.000 0.000 0.000
#> SRR949089 2 0.0000 0.942 0.000 1.000 0.000
#> SRR949090 3 0.1529 0.877 0.040 0.000 0.960
#> SRR949092 1 0.0000 0.974 1.000 0.000 0.000
#> SRR949093 1 0.0000 0.974 1.000 0.000 0.000
#> SRR949091 3 0.0000 0.845 0.000 0.000 1.000
#> SRR949095 1 0.7279 0.271 0.588 0.376 0.036
#> SRR949094 3 0.1529 0.877 0.040 0.000 0.960
#> SRR949096 1 0.0424 0.968 0.992 0.000 0.008
#> SRR949097 1 0.0000 0.974 1.000 0.000 0.000
#> SRR949098 2 0.0000 0.942 0.000 1.000 0.000
#> SRR949099 1 0.0000 0.974 1.000 0.000 0.000
#> SRR949101 3 0.6204 0.371 0.424 0.000 0.576
#> SRR949100 2 0.2448 0.894 0.076 0.924 0.000
#> SRR949102 1 0.0237 0.971 0.996 0.000 0.004
#> SRR949103 1 0.0000 0.974 1.000 0.000 0.000
#> SRR949104 2 0.0000 0.942 0.000 1.000 0.000
#> SRR949105 3 0.5845 0.624 0.308 0.004 0.688
#> SRR949106 3 0.5845 0.624 0.308 0.004 0.688
#> SRR949107 3 0.5845 0.624 0.308 0.004 0.688
#> SRR949108 1 0.0000 0.974 1.000 0.000 0.000
#> SRR949109 3 0.1529 0.877 0.040 0.000 0.960
#> SRR949110 1 0.0000 0.974 1.000 0.000 0.000
#> SRR949111 3 0.1529 0.877 0.040 0.000 0.960
#> SRR949112 1 0.0000 0.974 1.000 0.000 0.000
#> SRR949113 2 0.0000 0.942 0.000 1.000 0.000
#> SRR949114 1 0.0000 0.974 1.000 0.000 0.000
#> SRR949115 1 0.0000 0.974 1.000 0.000 0.000
#> SRR949116 1 0.0000 0.974 1.000 0.000 0.000
#> SRR949117 1 0.0000 0.974 1.000 0.000 0.000
#> SRR949118 1 0.1529 0.932 0.960 0.000 0.040
#> SRR949119 1 0.0424 0.968 0.992 0.000 0.008
#> SRR949120 1 0.0237 0.971 0.996 0.000 0.004
#> SRR949121 1 0.0000 0.974 1.000 0.000 0.000
#> SRR949122 1 0.0000 0.974 1.000 0.000 0.000
#> SRR949123 2 0.3686 0.847 0.140 0.860 0.000
#> SRR949124 2 0.0000 0.942 0.000 1.000 0.000
#> SRR949125 3 0.1529 0.877 0.040 0.000 0.960
#> SRR949126 3 0.1529 0.877 0.040 0.000 0.960
#> SRR949127 2 0.0000 0.942 0.000 1.000 0.000
#> SRR949128 2 0.0000 0.942 0.000 1.000 0.000
#> SRR949129 2 0.0000 0.942 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR949076 4 0.0000 0.879 0.000 0.000 0.000 1.000
#> SRR949078 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> SRR949077 4 0.3569 0.695 0.196 0.000 0.000 0.804
#> SRR949079 4 0.0000 0.879 0.000 0.000 0.000 1.000
#> SRR949080 4 0.0000 0.879 0.000 0.000 0.000 1.000
#> SRR949081 2 0.0592 0.982 0.016 0.984 0.000 0.000
#> SRR949082 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> SRR949083 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> SRR949084 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> SRR949085 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> SRR949087 2 0.0336 0.991 0.008 0.992 0.000 0.000
#> SRR949088 2 0.0336 0.991 0.008 0.992 0.000 0.000
#> SRR949086 1 0.2760 0.832 0.872 0.000 0.128 0.000
#> SRR949089 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> SRR949090 4 0.0000 0.879 0.000 0.000 0.000 1.000
#> SRR949092 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> SRR949093 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> SRR949091 4 0.1716 0.825 0.000 0.000 0.064 0.936
#> SRR949095 4 0.7784 0.190 0.244 0.364 0.000 0.392
#> SRR949094 4 0.0000 0.879 0.000 0.000 0.000 1.000
#> SRR949096 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> SRR949097 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> SRR949098 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> SRR949099 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> SRR949101 3 0.0188 0.995 0.004 0.000 0.996 0.000
#> SRR949100 2 0.0188 0.993 0.004 0.996 0.000 0.000
#> SRR949102 4 0.4431 0.550 0.304 0.000 0.000 0.696
#> SRR949103 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> SRR949104 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> SRR949105 3 0.0000 0.996 0.000 0.000 1.000 0.000
#> SRR949106 3 0.0000 0.996 0.000 0.000 1.000 0.000
#> SRR949107 3 0.0000 0.996 0.000 0.000 1.000 0.000
#> SRR949108 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> SRR949109 4 0.0000 0.879 0.000 0.000 0.000 1.000
#> SRR949110 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> SRR949111 4 0.0000 0.879 0.000 0.000 0.000 1.000
#> SRR949112 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> SRR949113 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> SRR949114 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> SRR949115 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> SRR949116 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> SRR949117 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> SRR949118 3 0.0336 0.991 0.008 0.000 0.992 0.000
#> SRR949119 1 0.4564 0.485 0.672 0.000 0.000 0.328
#> SRR949120 1 0.4193 0.608 0.732 0.000 0.000 0.268
#> SRR949121 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> SRR949122 1 0.0000 0.957 1.000 0.000 0.000 0.000
#> SRR949123 2 0.0469 0.987 0.012 0.988 0.000 0.000
#> SRR949124 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> SRR949125 4 0.0000 0.879 0.000 0.000 0.000 1.000
#> SRR949126 4 0.0000 0.879 0.000 0.000 0.000 1.000
#> SRR949127 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> SRR949128 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> SRR949129 2 0.0000 0.996 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR949076 4 0.0000 0.8632 0.000 0.000 0.000 1.000 0.000
#> SRR949078 2 0.0000 0.9893 0.000 1.000 0.000 0.000 0.000
#> SRR949077 4 0.1792 0.7791 0.084 0.000 0.000 0.916 0.000
#> SRR949079 4 0.0000 0.8632 0.000 0.000 0.000 1.000 0.000
#> SRR949080 4 0.0000 0.8632 0.000 0.000 0.000 1.000 0.000
#> SRR949081 2 0.2471 0.8232 0.000 0.864 0.136 0.000 0.000
#> SRR949082 2 0.0000 0.9893 0.000 1.000 0.000 0.000 0.000
#> SRR949083 1 0.0000 0.8957 1.000 0.000 0.000 0.000 0.000
#> SRR949084 1 0.0000 0.8957 1.000 0.000 0.000 0.000 0.000
#> SRR949085 2 0.0000 0.9893 0.000 1.000 0.000 0.000 0.000
#> SRR949087 2 0.0000 0.9893 0.000 1.000 0.000 0.000 0.000
#> SRR949088 2 0.0000 0.9893 0.000 1.000 0.000 0.000 0.000
#> SRR949086 3 0.0000 0.8051 0.000 0.000 1.000 0.000 0.000
#> SRR949089 2 0.0000 0.9893 0.000 1.000 0.000 0.000 0.000
#> SRR949090 4 0.0000 0.8632 0.000 0.000 0.000 1.000 0.000
#> SRR949092 1 0.0000 0.8957 1.000 0.000 0.000 0.000 0.000
#> SRR949093 1 0.0000 0.8957 1.000 0.000 0.000 0.000 0.000
#> SRR949091 3 0.4304 0.0758 0.000 0.000 0.516 0.484 0.000
#> SRR949095 4 0.7797 0.1312 0.092 0.288 0.188 0.432 0.000
#> SRR949094 4 0.0000 0.8632 0.000 0.000 0.000 1.000 0.000
#> SRR949096 1 0.0000 0.8957 1.000 0.000 0.000 0.000 0.000
#> SRR949097 1 0.0000 0.8957 1.000 0.000 0.000 0.000 0.000
#> SRR949098 2 0.0000 0.9893 0.000 1.000 0.000 0.000 0.000
#> SRR949099 1 0.3837 0.5667 0.692 0.000 0.308 0.000 0.000
#> SRR949101 5 0.1851 0.8838 0.000 0.000 0.088 0.000 0.912
#> SRR949100 2 0.0000 0.9893 0.000 1.000 0.000 0.000 0.000
#> SRR949102 3 0.5731 0.0439 0.084 0.000 0.480 0.436 0.000
#> SRR949103 1 0.0000 0.8957 1.000 0.000 0.000 0.000 0.000
#> SRR949104 2 0.0000 0.9893 0.000 1.000 0.000 0.000 0.000
#> SRR949105 5 0.0000 0.9642 0.000 0.000 0.000 0.000 1.000
#> SRR949106 5 0.0000 0.9642 0.000 0.000 0.000 0.000 1.000
#> SRR949107 5 0.0000 0.9642 0.000 0.000 0.000 0.000 1.000
#> SRR949108 1 0.0000 0.8957 1.000 0.000 0.000 0.000 0.000
#> SRR949109 4 0.0000 0.8632 0.000 0.000 0.000 1.000 0.000
#> SRR949110 1 0.0000 0.8957 1.000 0.000 0.000 0.000 0.000
#> SRR949111 4 0.0000 0.8632 0.000 0.000 0.000 1.000 0.000
#> SRR949112 1 0.4060 0.4738 0.640 0.000 0.360 0.000 0.000
#> SRR949113 2 0.0000 0.9893 0.000 1.000 0.000 0.000 0.000
#> SRR949114 3 0.0000 0.8051 0.000 0.000 1.000 0.000 0.000
#> SRR949115 3 0.0000 0.8051 0.000 0.000 1.000 0.000 0.000
#> SRR949116 3 0.0000 0.8051 0.000 0.000 1.000 0.000 0.000
#> SRR949117 3 0.0609 0.7899 0.020 0.000 0.980 0.000 0.000
#> SRR949118 3 0.0162 0.8024 0.000 0.000 0.996 0.000 0.004
#> SRR949119 4 0.6756 -0.0131 0.344 0.000 0.268 0.388 0.000
#> SRR949120 1 0.6685 0.1109 0.436 0.000 0.284 0.280 0.000
#> SRR949121 1 0.0000 0.8957 1.000 0.000 0.000 0.000 0.000
#> SRR949122 1 0.0000 0.8957 1.000 0.000 0.000 0.000 0.000
#> SRR949123 2 0.0000 0.9893 0.000 1.000 0.000 0.000 0.000
#> SRR949124 2 0.0000 0.9893 0.000 1.000 0.000 0.000 0.000
#> SRR949125 4 0.0000 0.8632 0.000 0.000 0.000 1.000 0.000
#> SRR949126 4 0.0000 0.8632 0.000 0.000 0.000 1.000 0.000
#> SRR949127 2 0.0000 0.9893 0.000 1.000 0.000 0.000 0.000
#> SRR949128 2 0.0000 0.9893 0.000 1.000 0.000 0.000 0.000
#> SRR949129 2 0.0000 0.9893 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR949076 4 0.0000 0.8297 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949078 5 0.2491 0.9529 0.000 0.164 0.000 0.000 0.836 0.000
#> SRR949077 4 0.1610 0.7622 0.084 0.000 0.000 0.916 0.000 0.000
#> SRR949079 4 0.0000 0.8297 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949080 4 0.0000 0.8297 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949081 5 0.2219 0.5530 0.000 0.000 0.000 0.000 0.864 0.136
#> SRR949082 5 0.2491 0.9529 0.000 0.164 0.000 0.000 0.836 0.000
#> SRR949083 1 0.0000 0.8928 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949084 1 0.0000 0.8928 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949085 5 0.2491 0.9529 0.000 0.164 0.000 0.000 0.836 0.000
#> SRR949087 5 0.2491 0.9529 0.000 0.164 0.000 0.000 0.836 0.000
#> SRR949088 5 0.2491 0.9529 0.000 0.164 0.000 0.000 0.836 0.000
#> SRR949086 6 0.0000 0.8843 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR949089 2 0.0632 0.8906 0.000 0.976 0.000 0.000 0.024 0.000
#> SRR949090 4 0.0000 0.8297 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949092 1 0.0000 0.8928 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949093 1 0.0000 0.8928 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949091 6 0.3866 0.0470 0.000 0.000 0.000 0.484 0.000 0.516
#> SRR949095 4 0.7948 0.2493 0.096 0.092 0.000 0.448 0.176 0.188
#> SRR949094 4 0.0000 0.8297 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949096 1 0.0000 0.8928 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949097 1 0.0000 0.8928 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949098 2 0.0632 0.8906 0.000 0.976 0.000 0.000 0.024 0.000
#> SRR949099 1 0.3464 0.5684 0.688 0.000 0.000 0.000 0.000 0.312
#> SRR949101 3 0.1663 0.8857 0.000 0.000 0.912 0.000 0.000 0.088
#> SRR949100 5 0.2491 0.9529 0.000 0.164 0.000 0.000 0.836 0.000
#> SRR949102 4 0.7402 0.1000 0.084 0.024 0.000 0.400 0.164 0.328
#> SRR949103 1 0.0000 0.8928 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949104 2 0.0632 0.8906 0.000 0.976 0.000 0.000 0.024 0.000
#> SRR949105 3 0.0000 0.9638 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR949106 3 0.0000 0.9638 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR949107 3 0.0000 0.9638 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR949108 1 0.0000 0.8928 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949109 4 0.0000 0.8297 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949110 1 0.0146 0.8905 0.996 0.000 0.000 0.000 0.004 0.000
#> SRR949111 4 0.0000 0.8297 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949112 1 0.3672 0.4698 0.632 0.000 0.000 0.000 0.000 0.368
#> SRR949113 2 0.3833 -0.0758 0.000 0.556 0.000 0.000 0.444 0.000
#> SRR949114 6 0.0000 0.8843 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR949115 6 0.0000 0.8843 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR949116 6 0.0000 0.8843 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR949117 6 0.0547 0.8645 0.020 0.000 0.000 0.000 0.000 0.980
#> SRR949118 6 0.0146 0.8815 0.000 0.000 0.004 0.000 0.000 0.996
#> SRR949119 4 0.8031 0.0654 0.280 0.024 0.000 0.312 0.164 0.220
#> SRR949120 1 0.7898 0.1132 0.380 0.024 0.000 0.204 0.164 0.228
#> SRR949121 1 0.0000 0.8928 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949122 1 0.0000 0.8928 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949123 2 0.0632 0.8906 0.000 0.976 0.000 0.000 0.024 0.000
#> SRR949124 2 0.0632 0.8906 0.000 0.976 0.000 0.000 0.024 0.000
#> SRR949125 4 0.0000 0.8297 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949126 4 0.0000 0.8297 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949127 5 0.2491 0.9529 0.000 0.164 0.000 0.000 0.836 0.000
#> SRR949128 5 0.2491 0.9529 0.000 0.164 0.000 0.000 0.836 0.000
#> SRR949129 5 0.2491 0.9529 0.000 0.164 0.000 0.000 0.836 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)
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 16816 rows and 54 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 0.448 0.689 0.863 0.4737 0.508 0.508
#> 3 3 0.430 0.682 0.827 0.3203 0.765 0.570
#> 4 4 0.820 0.756 0.902 0.1282 0.820 0.571
#> 5 5 0.761 0.715 0.820 0.1147 0.892 0.656
#> 6 6 0.729 0.719 0.780 0.0403 0.941 0.735
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
#> SRR949076 2 0.9815 0.3259 0.420 0.580
#> SRR949078 2 0.0000 0.8503 0.000 1.000
#> SRR949077 2 0.9815 0.3259 0.420 0.580
#> SRR949079 2 0.9815 0.3259 0.420 0.580
#> SRR949080 2 0.9815 0.3259 0.420 0.580
#> SRR949081 2 0.6712 0.7513 0.176 0.824
#> SRR949082 2 0.0000 0.8503 0.000 1.000
#> SRR949083 1 0.2778 0.8318 0.952 0.048
#> SRR949084 1 0.4298 0.8180 0.912 0.088
#> SRR949085 2 0.0000 0.8503 0.000 1.000
#> SRR949087 2 0.6343 0.7685 0.160 0.840
#> SRR949088 2 0.6623 0.7562 0.172 0.828
#> SRR949086 1 0.0000 0.8221 1.000 0.000
#> SRR949089 2 0.0000 0.8503 0.000 1.000
#> SRR949090 1 0.9983 0.0234 0.524 0.476
#> SRR949092 1 0.2603 0.8327 0.956 0.044
#> SRR949093 1 0.2603 0.8327 0.956 0.044
#> SRR949091 1 0.9393 0.3691 0.644 0.356
#> SRR949095 2 0.4431 0.8111 0.092 0.908
#> SRR949094 1 0.9983 0.0234 0.524 0.476
#> SRR949096 1 0.4690 0.8112 0.900 0.100
#> SRR949097 1 0.2603 0.8327 0.956 0.044
#> SRR949098 2 0.0000 0.8503 0.000 1.000
#> SRR949099 1 0.0672 0.8252 0.992 0.008
#> SRR949101 1 0.3114 0.8056 0.944 0.056
#> SRR949100 2 0.4562 0.8089 0.096 0.904
#> SRR949102 2 0.7883 0.7228 0.236 0.764
#> SRR949103 1 0.2603 0.8327 0.956 0.044
#> SRR949104 2 0.0000 0.8503 0.000 1.000
#> SRR949105 1 0.0000 0.8221 1.000 0.000
#> SRR949106 1 0.0000 0.8221 1.000 0.000
#> SRR949107 1 0.0000 0.8221 1.000 0.000
#> SRR949108 1 0.2948 0.8323 0.948 0.052
#> SRR949109 1 0.9983 0.0234 0.524 0.476
#> SRR949110 1 0.2603 0.8327 0.956 0.044
#> SRR949111 1 0.9983 0.0234 0.524 0.476
#> SRR949112 1 0.6623 0.7371 0.828 0.172
#> SRR949113 2 0.0000 0.8503 0.000 1.000
#> SRR949114 1 0.2603 0.8327 0.956 0.044
#> SRR949115 1 0.2603 0.8327 0.956 0.044
#> SRR949116 1 0.2603 0.8327 0.956 0.044
#> SRR949117 1 0.0376 0.8238 0.996 0.004
#> SRR949118 1 0.0000 0.8221 1.000 0.000
#> SRR949119 1 0.4690 0.8112 0.900 0.100
#> SRR949120 1 0.4690 0.8112 0.900 0.100
#> SRR949121 1 0.2778 0.8328 0.952 0.048
#> SRR949122 1 0.2948 0.8323 0.948 0.052
#> SRR949123 2 0.0000 0.8503 0.000 1.000
#> SRR949124 2 0.0000 0.8503 0.000 1.000
#> SRR949125 1 0.9983 0.0234 0.524 0.476
#> SRR949126 1 0.9983 0.0234 0.524 0.476
#> SRR949127 2 0.0000 0.8503 0.000 1.000
#> SRR949128 2 0.0000 0.8503 0.000 1.000
#> SRR949129 2 0.0000 0.8503 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR949076 1 0.4915 0.9360 0.804 0.012 0.184
#> SRR949078 2 0.0237 0.8195 0.000 0.996 0.004
#> SRR949077 1 0.4915 0.9360 0.804 0.012 0.184
#> SRR949079 1 0.4915 0.9360 0.804 0.012 0.184
#> SRR949080 1 0.4915 0.9360 0.804 0.012 0.184
#> SRR949081 3 0.7295 -0.0831 0.028 0.484 0.488
#> SRR949082 2 0.0237 0.8195 0.000 0.996 0.004
#> SRR949083 3 0.4277 0.7460 0.016 0.132 0.852
#> SRR949084 3 0.3686 0.7429 0.000 0.140 0.860
#> SRR949085 2 0.0000 0.8204 0.000 1.000 0.000
#> SRR949087 2 0.8579 0.1625 0.096 0.464 0.440
#> SRR949088 2 0.8579 0.1625 0.096 0.464 0.440
#> SRR949086 3 0.1453 0.7823 0.024 0.008 0.968
#> SRR949089 2 0.0000 0.8204 0.000 1.000 0.000
#> SRR949090 1 0.4346 0.9398 0.816 0.000 0.184
#> SRR949092 3 0.0747 0.7840 0.016 0.000 0.984
#> SRR949093 3 0.0747 0.7840 0.016 0.000 0.984
#> SRR949091 1 0.2537 0.8158 0.920 0.000 0.080
#> SRR949095 2 0.6473 0.4726 0.020 0.668 0.312
#> SRR949094 1 0.4346 0.9398 0.816 0.000 0.184
#> SRR949096 3 0.4744 0.7401 0.028 0.136 0.836
#> SRR949097 3 0.0892 0.7837 0.020 0.000 0.980
#> SRR949098 2 0.0000 0.8204 0.000 1.000 0.000
#> SRR949099 3 0.0661 0.7847 0.004 0.008 0.988
#> SRR949101 1 0.6155 0.4721 0.664 0.008 0.328
#> SRR949100 2 0.8308 0.4092 0.096 0.568 0.336
#> SRR949102 2 0.9940 -0.0439 0.280 0.360 0.360
#> SRR949103 3 0.0747 0.7840 0.016 0.000 0.984
#> SRR949104 2 0.0000 0.8204 0.000 1.000 0.000
#> SRR949105 3 0.6683 0.0159 0.492 0.008 0.500
#> SRR949106 3 0.6682 0.0300 0.488 0.008 0.504
#> SRR949107 3 0.6683 0.0159 0.492 0.008 0.500
#> SRR949108 3 0.3713 0.7702 0.032 0.076 0.892
#> SRR949109 1 0.4346 0.9398 0.816 0.000 0.184
#> SRR949110 3 0.0747 0.7840 0.016 0.000 0.984
#> SRR949111 1 0.4346 0.9398 0.816 0.000 0.184
#> SRR949112 3 0.6192 0.6482 0.060 0.176 0.764
#> SRR949113 2 0.0000 0.8204 0.000 1.000 0.000
#> SRR949114 3 0.0747 0.7837 0.016 0.000 0.984
#> SRR949115 3 0.0747 0.7837 0.016 0.000 0.984
#> SRR949116 3 0.0747 0.7837 0.016 0.000 0.984
#> SRR949117 3 0.1453 0.7823 0.024 0.008 0.968
#> SRR949118 3 0.5156 0.6088 0.216 0.008 0.776
#> SRR949119 3 0.8716 0.4340 0.240 0.172 0.588
#> SRR949120 3 0.8716 0.4340 0.240 0.172 0.588
#> SRR949121 3 0.2796 0.7423 0.092 0.000 0.908
#> SRR949122 3 0.3551 0.7461 0.000 0.132 0.868
#> SRR949123 2 0.0000 0.8204 0.000 1.000 0.000
#> SRR949124 2 0.0000 0.8204 0.000 1.000 0.000
#> SRR949125 1 0.4346 0.9398 0.816 0.000 0.184
#> SRR949126 1 0.4346 0.9398 0.816 0.000 0.184
#> SRR949127 2 0.2537 0.7989 0.080 0.920 0.000
#> SRR949128 2 0.2537 0.7989 0.080 0.920 0.000
#> SRR949129 2 0.2537 0.7989 0.080 0.920 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR949076 4 0.0336 0.9136 0.008 0.000 0.000 0.992
#> SRR949078 2 0.0000 0.9989 0.000 1.000 0.000 0.000
#> SRR949077 4 0.0336 0.9136 0.008 0.000 0.000 0.992
#> SRR949079 4 0.0336 0.9136 0.008 0.000 0.000 0.992
#> SRR949080 4 0.0336 0.9136 0.008 0.000 0.000 0.992
#> SRR949081 1 0.9254 0.0128 0.388 0.100 0.200 0.312
#> SRR949082 2 0.0000 0.9989 0.000 1.000 0.000 0.000
#> SRR949083 1 0.0188 0.8162 0.996 0.000 0.000 0.004
#> SRR949084 1 0.0188 0.8162 0.996 0.000 0.000 0.004
#> SRR949085 2 0.0000 0.9989 0.000 1.000 0.000 0.000
#> SRR949087 1 0.4839 0.6318 0.756 0.044 0.200 0.000
#> SRR949088 1 0.4839 0.6318 0.756 0.044 0.200 0.000
#> SRR949086 1 0.5229 0.2252 0.564 0.000 0.428 0.008
#> SRR949089 2 0.0000 0.9989 0.000 1.000 0.000 0.000
#> SRR949090 4 0.1118 0.8907 0.036 0.000 0.000 0.964
#> SRR949092 1 0.0188 0.8162 0.996 0.000 0.000 0.004
#> SRR949093 1 0.0188 0.8162 0.996 0.000 0.000 0.004
#> SRR949091 4 0.1211 0.8803 0.000 0.000 0.040 0.960
#> SRR949095 1 0.9235 -0.0118 0.376 0.096 0.200 0.328
#> SRR949094 4 0.0336 0.9136 0.008 0.000 0.000 0.992
#> SRR949096 1 0.0188 0.8162 0.996 0.000 0.000 0.004
#> SRR949097 1 0.0188 0.8162 0.996 0.000 0.000 0.004
#> SRR949098 2 0.0000 0.9989 0.000 1.000 0.000 0.000
#> SRR949099 1 0.3402 0.7016 0.832 0.000 0.164 0.004
#> SRR949101 3 0.6277 0.2928 0.068 0.000 0.572 0.360
#> SRR949100 1 0.4839 0.6318 0.756 0.044 0.200 0.000
#> SRR949102 4 0.8615 -0.1551 0.364 0.044 0.200 0.392
#> SRR949103 1 0.0188 0.8162 0.996 0.000 0.000 0.004
#> SRR949104 2 0.0000 0.9989 0.000 1.000 0.000 0.000
#> SRR949105 3 0.0000 0.7454 0.000 0.000 1.000 0.000
#> SRR949106 3 0.0000 0.7454 0.000 0.000 1.000 0.000
#> SRR949107 3 0.0000 0.7454 0.000 0.000 1.000 0.000
#> SRR949108 1 0.0188 0.8162 0.996 0.000 0.000 0.004
#> SRR949109 4 0.1211 0.8867 0.040 0.000 0.000 0.960
#> SRR949110 1 0.0188 0.8162 0.996 0.000 0.000 0.004
#> SRR949111 4 0.0336 0.9136 0.008 0.000 0.000 0.992
#> SRR949112 1 0.0000 0.8146 1.000 0.000 0.000 0.000
#> SRR949113 2 0.0000 0.9989 0.000 1.000 0.000 0.000
#> SRR949114 1 0.0927 0.8050 0.976 0.000 0.016 0.008
#> SRR949115 1 0.0927 0.8050 0.976 0.000 0.016 0.008
#> SRR949116 1 0.0804 0.8071 0.980 0.000 0.012 0.008
#> SRR949117 1 0.5279 0.2952 0.588 0.000 0.400 0.012
#> SRR949118 3 0.4898 0.0862 0.416 0.000 0.584 0.000
#> SRR949119 1 0.4304 0.5177 0.716 0.000 0.000 0.284
#> SRR949120 1 0.3975 0.5811 0.760 0.000 0.000 0.240
#> SRR949121 1 0.0000 0.8146 1.000 0.000 0.000 0.000
#> SRR949122 1 0.0188 0.8162 0.996 0.000 0.000 0.004
#> SRR949123 2 0.0000 0.9989 0.000 1.000 0.000 0.000
#> SRR949124 2 0.0000 0.9989 0.000 1.000 0.000 0.000
#> SRR949125 4 0.0336 0.9136 0.008 0.000 0.000 0.992
#> SRR949126 4 0.0336 0.9136 0.008 0.000 0.000 0.992
#> SRR949127 2 0.0188 0.9965 0.004 0.996 0.000 0.000
#> SRR949128 2 0.0188 0.9965 0.004 0.996 0.000 0.000
#> SRR949129 2 0.0188 0.9965 0.004 0.996 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR949076 4 0.0703 0.9005 0.000 0.000 0.000 0.976 0.024
#> SRR949078 2 0.0703 0.9705 0.024 0.976 0.000 0.000 0.000
#> SRR949077 4 0.0703 0.9005 0.000 0.000 0.000 0.976 0.024
#> SRR949079 4 0.0703 0.9005 0.000 0.000 0.000 0.976 0.024
#> SRR949080 4 0.0703 0.9005 0.000 0.000 0.000 0.976 0.024
#> SRR949081 5 0.4811 0.5062 0.204 0.036 0.008 0.016 0.736
#> SRR949082 2 0.0771 0.9741 0.004 0.976 0.000 0.000 0.020
#> SRR949083 1 0.2798 0.6580 0.852 0.000 0.008 0.000 0.140
#> SRR949084 1 0.3203 0.6406 0.820 0.000 0.000 0.012 0.168
#> SRR949085 2 0.0290 0.9835 0.000 0.992 0.000 0.000 0.008
#> SRR949087 5 0.4416 0.6073 0.356 0.012 0.000 0.000 0.632
#> SRR949088 5 0.4416 0.6073 0.356 0.012 0.000 0.000 0.632
#> SRR949086 5 0.6232 0.2706 0.164 0.004 0.280 0.000 0.552
#> SRR949089 2 0.0000 0.9837 0.000 1.000 0.000 0.000 0.000
#> SRR949090 4 0.2864 0.7713 0.136 0.000 0.000 0.852 0.012
#> SRR949092 1 0.1410 0.6907 0.940 0.000 0.000 0.000 0.060
#> SRR949093 1 0.1792 0.6850 0.916 0.000 0.000 0.000 0.084
#> SRR949091 4 0.4658 0.3024 0.000 0.000 0.408 0.576 0.016
#> SRR949095 5 0.4956 0.5059 0.204 0.044 0.008 0.016 0.728
#> SRR949094 4 0.0000 0.9019 0.000 0.000 0.000 1.000 0.000
#> SRR949096 1 0.3527 0.6337 0.804 0.000 0.000 0.024 0.172
#> SRR949097 1 0.3242 0.6500 0.784 0.000 0.000 0.000 0.216
#> SRR949098 2 0.0290 0.9835 0.000 0.992 0.000 0.000 0.008
#> SRR949099 5 0.4807 -0.0101 0.448 0.000 0.020 0.000 0.532
#> SRR949101 3 0.4227 0.6081 0.000 0.000 0.692 0.016 0.292
#> SRR949100 5 0.4974 0.6054 0.364 0.024 0.008 0.000 0.604
#> SRR949102 5 0.6075 0.3186 0.056 0.020 0.016 0.312 0.596
#> SRR949103 1 0.3242 0.6500 0.784 0.000 0.000 0.000 0.216
#> SRR949104 2 0.0000 0.9837 0.000 1.000 0.000 0.000 0.000
#> SRR949105 3 0.0000 0.8036 0.000 0.000 1.000 0.000 0.000
#> SRR949106 3 0.0000 0.8036 0.000 0.000 1.000 0.000 0.000
#> SRR949107 3 0.0000 0.8036 0.000 0.000 1.000 0.000 0.000
#> SRR949108 1 0.0693 0.6906 0.980 0.000 0.000 0.008 0.012
#> SRR949109 4 0.3197 0.7504 0.140 0.000 0.000 0.836 0.024
#> SRR949110 1 0.3242 0.6500 0.784 0.000 0.000 0.000 0.216
#> SRR949111 4 0.0000 0.9019 0.000 0.000 0.000 1.000 0.000
#> SRR949112 1 0.3242 0.4745 0.784 0.000 0.000 0.000 0.216
#> SRR949113 2 0.0771 0.9741 0.004 0.976 0.000 0.000 0.020
#> SRR949114 1 0.4880 0.4913 0.616 0.000 0.036 0.000 0.348
#> SRR949115 1 0.4866 0.4984 0.620 0.000 0.036 0.000 0.344
#> SRR949116 1 0.4866 0.4984 0.620 0.000 0.036 0.000 0.344
#> SRR949117 5 0.6211 0.3172 0.204 0.000 0.248 0.000 0.548
#> SRR949118 3 0.4201 0.5671 0.008 0.000 0.664 0.000 0.328
#> SRR949119 1 0.3847 0.6232 0.784 0.000 0.000 0.036 0.180
#> SRR949120 1 0.3847 0.6232 0.784 0.000 0.000 0.036 0.180
#> SRR949121 1 0.3039 0.6591 0.808 0.000 0.000 0.000 0.192
#> SRR949122 1 0.1043 0.6802 0.960 0.000 0.000 0.000 0.040
#> SRR949123 2 0.0162 0.9832 0.000 0.996 0.000 0.000 0.004
#> SRR949124 2 0.0000 0.9837 0.000 1.000 0.000 0.000 0.000
#> SRR949125 4 0.0000 0.9019 0.000 0.000 0.000 1.000 0.000
#> SRR949126 4 0.0000 0.9019 0.000 0.000 0.000 1.000 0.000
#> SRR949127 2 0.0703 0.9774 0.000 0.976 0.000 0.000 0.024
#> SRR949128 2 0.0703 0.9774 0.000 0.976 0.000 0.000 0.024
#> SRR949129 2 0.0703 0.9774 0.000 0.976 0.000 0.000 0.024
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR949076 4 0.1578 0.9051 0.012 0.000 0.000 0.936 0.048 0.004
#> SRR949078 2 0.3507 0.7489 0.012 0.752 0.000 0.004 0.232 0.000
#> SRR949077 4 0.2110 0.8939 0.012 0.000 0.000 0.900 0.084 0.004
#> SRR949079 4 0.1888 0.9035 0.012 0.000 0.000 0.916 0.068 0.004
#> SRR949080 4 0.1888 0.9035 0.012 0.000 0.000 0.916 0.068 0.004
#> SRR949081 5 0.3945 0.7413 0.032 0.044 0.000 0.112 0.804 0.008
#> SRR949082 2 0.4173 0.7486 0.012 0.732 0.000 0.044 0.212 0.000
#> SRR949083 1 0.0964 0.7892 0.968 0.004 0.000 0.000 0.016 0.012
#> SRR949084 1 0.0893 0.7864 0.972 0.004 0.000 0.004 0.016 0.004
#> SRR949085 2 0.2597 0.7827 0.000 0.824 0.000 0.000 0.176 0.000
#> SRR949087 5 0.3112 0.7429 0.096 0.000 0.000 0.000 0.836 0.068
#> SRR949088 5 0.3112 0.7429 0.096 0.000 0.000 0.000 0.836 0.068
#> SRR949086 6 0.5304 0.5461 0.008 0.000 0.152 0.000 0.216 0.624
#> SRR949089 2 0.2631 0.7191 0.000 0.820 0.000 0.000 0.000 0.180
#> SRR949090 4 0.1204 0.9261 0.000 0.000 0.000 0.944 0.000 0.056
#> SRR949092 1 0.2006 0.8038 0.904 0.000 0.000 0.000 0.080 0.016
#> SRR949093 1 0.2006 0.8038 0.904 0.000 0.000 0.000 0.080 0.016
#> SRR949091 3 0.4057 0.1499 0.000 0.000 0.556 0.436 0.000 0.008
#> SRR949095 5 0.4381 0.7203 0.036 0.084 0.000 0.104 0.772 0.004
#> SRR949094 4 0.2364 0.8929 0.072 0.000 0.000 0.892 0.032 0.004
#> SRR949096 1 0.0972 0.7799 0.964 0.000 0.000 0.008 0.028 0.000
#> SRR949097 1 0.4281 0.6906 0.708 0.000 0.000 0.000 0.072 0.220
#> SRR949098 2 0.2913 0.7168 0.004 0.812 0.000 0.000 0.004 0.180
#> SRR949099 6 0.5748 0.5080 0.060 0.000 0.072 0.000 0.284 0.584
#> SRR949101 3 0.4633 0.5421 0.000 0.000 0.716 0.056 0.196 0.032
#> SRR949100 5 0.2863 0.7524 0.096 0.008 0.000 0.000 0.860 0.036
#> SRR949102 5 0.4970 0.4910 0.008 0.012 0.012 0.316 0.628 0.024
#> SRR949103 1 0.4809 0.4978 0.600 0.000 0.000 0.000 0.072 0.328
#> SRR949104 2 0.2631 0.7191 0.000 0.820 0.000 0.000 0.000 0.180
#> SRR949105 3 0.0000 0.6999 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR949106 3 0.0000 0.6999 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR949107 3 0.0000 0.6999 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR949108 1 0.2452 0.8051 0.884 0.000 0.000 0.004 0.084 0.028
#> SRR949109 4 0.1267 0.9238 0.000 0.000 0.000 0.940 0.000 0.060
#> SRR949110 1 0.4332 0.6832 0.700 0.000 0.000 0.000 0.072 0.228
#> SRR949111 4 0.1204 0.9261 0.000 0.000 0.000 0.944 0.000 0.056
#> SRR949112 1 0.4465 0.6658 0.704 0.000 0.004 0.000 0.212 0.080
#> SRR949113 2 0.4182 0.7671 0.008 0.756 0.000 0.044 0.180 0.012
#> SRR949114 6 0.4770 0.6193 0.284 0.000 0.040 0.000 0.024 0.652
#> SRR949115 6 0.4788 0.6152 0.288 0.000 0.040 0.000 0.024 0.648
#> SRR949116 6 0.4788 0.6152 0.288 0.000 0.040 0.000 0.024 0.648
#> SRR949117 6 0.5304 0.5461 0.008 0.000 0.152 0.000 0.216 0.624
#> SRR949118 3 0.5964 0.0557 0.004 0.000 0.468 0.000 0.208 0.320
#> SRR949119 1 0.3108 0.7106 0.860 0.000 0.000 0.052 0.036 0.052
#> SRR949120 1 0.3108 0.7106 0.860 0.000 0.000 0.052 0.036 0.052
#> SRR949121 1 0.4012 0.7185 0.748 0.000 0.000 0.000 0.076 0.176
#> SRR949122 1 0.3375 0.7802 0.816 0.000 0.000 0.000 0.096 0.088
#> SRR949123 2 0.1851 0.7586 0.000 0.928 0.000 0.012 0.036 0.024
#> SRR949124 2 0.2772 0.7177 0.000 0.816 0.000 0.000 0.004 0.180
#> SRR949125 4 0.1204 0.9261 0.000 0.000 0.000 0.944 0.000 0.056
#> SRR949126 4 0.1204 0.9261 0.000 0.000 0.000 0.944 0.000 0.056
#> SRR949127 2 0.3175 0.7653 0.000 0.744 0.000 0.000 0.256 0.000
#> SRR949128 2 0.3175 0.7653 0.000 0.744 0.000 0.000 0.256 0.000
#> SRR949129 2 0.3175 0.7653 0.000 0.744 0.000 0.000 0.256 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)
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 16816 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.854 0.921 0.966 0.4337 0.560 0.560
#> 3 3 0.587 0.670 0.847 0.5214 0.739 0.547
#> 4 4 0.870 0.840 0.930 0.1335 0.770 0.438
#> 5 5 0.770 0.601 0.821 0.0561 0.985 0.941
#> 6 6 0.775 0.660 0.803 0.0414 0.899 0.608
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
#> SRR949076 1 0.000 0.975 1.000 0.000
#> SRR949078 2 0.000 0.934 0.000 1.000
#> SRR949077 1 0.000 0.975 1.000 0.000
#> SRR949079 1 0.000 0.975 1.000 0.000
#> SRR949080 1 0.000 0.975 1.000 0.000
#> SRR949081 2 0.242 0.911 0.040 0.960
#> SRR949082 2 0.000 0.934 0.000 1.000
#> SRR949083 1 0.000 0.975 1.000 0.000
#> SRR949084 1 0.000 0.975 1.000 0.000
#> SRR949085 2 0.000 0.934 0.000 1.000
#> SRR949087 2 0.358 0.891 0.068 0.932
#> SRR949088 2 0.373 0.887 0.072 0.928
#> SRR949086 1 0.327 0.921 0.940 0.060
#> SRR949089 2 0.000 0.934 0.000 1.000
#> SRR949090 1 0.000 0.975 1.000 0.000
#> SRR949092 1 0.000 0.975 1.000 0.000
#> SRR949093 1 0.000 0.975 1.000 0.000
#> SRR949091 1 0.000 0.975 1.000 0.000
#> SRR949095 2 0.966 0.384 0.392 0.608
#> SRR949094 1 0.000 0.975 1.000 0.000
#> SRR949096 1 0.000 0.975 1.000 0.000
#> SRR949097 1 0.000 0.975 1.000 0.000
#> SRR949098 2 0.000 0.934 0.000 1.000
#> SRR949099 1 0.000 0.975 1.000 0.000
#> SRR949101 1 0.000 0.975 1.000 0.000
#> SRR949100 2 0.990 0.224 0.440 0.560
#> SRR949102 1 0.000 0.975 1.000 0.000
#> SRR949103 1 0.000 0.975 1.000 0.000
#> SRR949104 2 0.000 0.934 0.000 1.000
#> SRR949105 1 0.722 0.753 0.800 0.200
#> SRR949106 1 0.722 0.753 0.800 0.200
#> SRR949107 1 0.722 0.753 0.800 0.200
#> SRR949108 1 0.000 0.975 1.000 0.000
#> SRR949109 1 0.000 0.975 1.000 0.000
#> SRR949110 1 0.000 0.975 1.000 0.000
#> SRR949111 1 0.000 0.975 1.000 0.000
#> SRR949112 1 0.000 0.975 1.000 0.000
#> SRR949113 2 0.000 0.934 0.000 1.000
#> SRR949114 1 0.000 0.975 1.000 0.000
#> SRR949115 1 0.000 0.975 1.000 0.000
#> SRR949116 1 0.000 0.975 1.000 0.000
#> SRR949117 1 0.605 0.823 0.852 0.148
#> SRR949118 1 0.000 0.975 1.000 0.000
#> SRR949119 1 0.000 0.975 1.000 0.000
#> SRR949120 1 0.000 0.975 1.000 0.000
#> SRR949121 1 0.000 0.975 1.000 0.000
#> SRR949122 1 0.000 0.975 1.000 0.000
#> SRR949123 2 0.000 0.934 0.000 1.000
#> SRR949124 2 0.000 0.934 0.000 1.000
#> SRR949125 1 0.000 0.975 1.000 0.000
#> SRR949126 1 0.000 0.975 1.000 0.000
#> SRR949127 2 0.000 0.934 0.000 1.000
#> SRR949128 2 0.000 0.934 0.000 1.000
#> SRR949129 2 0.000 0.934 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR949076 1 0.5706 0.521 0.680 0.000 0.320
#> SRR949078 2 0.0000 0.927 0.000 1.000 0.000
#> SRR949077 1 0.5327 0.578 0.728 0.000 0.272
#> SRR949079 1 0.5760 0.510 0.672 0.000 0.328
#> SRR949080 1 0.5760 0.510 0.672 0.000 0.328
#> SRR949081 2 0.7141 0.369 0.368 0.600 0.032
#> SRR949082 2 0.0000 0.927 0.000 1.000 0.000
#> SRR949083 1 0.1753 0.763 0.952 0.000 0.048
#> SRR949084 1 0.0000 0.771 1.000 0.000 0.000
#> SRR949085 2 0.0000 0.927 0.000 1.000 0.000
#> SRR949087 2 0.2636 0.878 0.048 0.932 0.020
#> SRR949088 2 0.2636 0.878 0.048 0.932 0.020
#> SRR949086 3 0.5355 0.650 0.036 0.160 0.804
#> SRR949089 2 0.0000 0.927 0.000 1.000 0.000
#> SRR949090 3 0.4399 0.615 0.188 0.000 0.812
#> SRR949092 1 0.1753 0.763 0.952 0.000 0.048
#> SRR949093 1 0.1753 0.763 0.952 0.000 0.048
#> SRR949091 3 0.2066 0.671 0.060 0.000 0.940
#> SRR949095 1 0.6102 0.454 0.672 0.320 0.008
#> SRR949094 1 0.5591 0.543 0.696 0.000 0.304
#> SRR949096 1 0.0000 0.771 1.000 0.000 0.000
#> SRR949097 1 0.1860 0.761 0.948 0.000 0.052
#> SRR949098 2 0.0000 0.927 0.000 1.000 0.000
#> SRR949099 3 0.5621 0.518 0.308 0.000 0.692
#> SRR949101 3 0.0237 0.687 0.004 0.000 0.996
#> SRR949100 2 0.6062 0.369 0.384 0.616 0.000
#> SRR949102 1 0.5678 0.533 0.684 0.000 0.316
#> SRR949103 1 0.4931 0.497 0.768 0.000 0.232
#> SRR949104 2 0.0000 0.927 0.000 1.000 0.000
#> SRR949105 3 0.3276 0.699 0.024 0.068 0.908
#> SRR949106 3 0.3499 0.699 0.028 0.072 0.900
#> SRR949107 3 0.3550 0.697 0.024 0.080 0.896
#> SRR949108 1 0.0424 0.772 0.992 0.000 0.008
#> SRR949109 3 0.4887 0.578 0.228 0.000 0.772
#> SRR949110 1 0.2711 0.731 0.912 0.000 0.088
#> SRR949111 3 0.6079 0.266 0.388 0.000 0.612
#> SRR949112 1 0.1411 0.767 0.964 0.000 0.036
#> SRR949113 2 0.0000 0.927 0.000 1.000 0.000
#> SRR949114 3 0.6291 0.278 0.468 0.000 0.532
#> SRR949115 3 0.6308 0.223 0.492 0.000 0.508
#> SRR949116 1 0.6309 -0.279 0.504 0.000 0.496
#> SRR949117 3 0.7026 0.614 0.120 0.152 0.728
#> SRR949118 3 0.3941 0.662 0.156 0.000 0.844
#> SRR949119 1 0.0237 0.770 0.996 0.000 0.004
#> SRR949120 1 0.0237 0.770 0.996 0.000 0.004
#> SRR949121 1 0.1753 0.763 0.952 0.000 0.048
#> SRR949122 1 0.0424 0.772 0.992 0.000 0.008
#> SRR949123 2 0.0000 0.927 0.000 1.000 0.000
#> SRR949124 2 0.0000 0.927 0.000 1.000 0.000
#> SRR949125 3 0.5650 0.455 0.312 0.000 0.688
#> SRR949126 3 0.5650 0.455 0.312 0.000 0.688
#> SRR949127 2 0.0000 0.927 0.000 1.000 0.000
#> SRR949128 2 0.0000 0.927 0.000 1.000 0.000
#> SRR949129 2 0.0000 0.927 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR949076 4 0.0336 0.914 0.000 0.000 0.008 0.992
#> SRR949078 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> SRR949077 4 0.0000 0.918 0.000 0.000 0.000 1.000
#> SRR949079 4 0.0000 0.918 0.000 0.000 0.000 1.000
#> SRR949080 4 0.0000 0.918 0.000 0.000 0.000 1.000
#> SRR949081 2 0.5486 0.643 0.000 0.720 0.200 0.080
#> SRR949082 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> SRR949083 1 0.1302 0.874 0.956 0.000 0.000 0.044
#> SRR949084 1 0.1302 0.874 0.956 0.000 0.000 0.044
#> SRR949085 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> SRR949087 1 0.5594 0.137 0.520 0.460 0.020 0.000
#> SRR949088 1 0.5594 0.137 0.520 0.460 0.020 0.000
#> SRR949086 3 0.0524 0.941 0.004 0.008 0.988 0.000
#> SRR949089 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> SRR949090 4 0.1302 0.919 0.000 0.000 0.044 0.956
#> SRR949092 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> SRR949093 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> SRR949091 4 0.4843 0.375 0.000 0.000 0.396 0.604
#> SRR949095 2 0.5268 0.217 0.000 0.540 0.008 0.452
#> SRR949094 4 0.0000 0.918 0.000 0.000 0.000 1.000
#> SRR949096 1 0.1302 0.874 0.956 0.000 0.000 0.044
#> SRR949097 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> SRR949098 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> SRR949099 3 0.3837 0.714 0.224 0.000 0.776 0.000
#> SRR949101 3 0.0336 0.944 0.000 0.000 0.992 0.008
#> SRR949100 2 0.2965 0.848 0.072 0.892 0.000 0.036
#> SRR949102 4 0.3569 0.730 0.000 0.000 0.196 0.804
#> SRR949103 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> SRR949104 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> SRR949105 3 0.0336 0.944 0.000 0.000 0.992 0.008
#> SRR949106 3 0.0336 0.944 0.000 0.000 0.992 0.008
#> SRR949107 3 0.0336 0.944 0.000 0.000 0.992 0.008
#> SRR949108 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> SRR949109 4 0.1302 0.919 0.000 0.000 0.044 0.956
#> SRR949110 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> SRR949111 4 0.1302 0.919 0.000 0.000 0.044 0.956
#> SRR949112 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> SRR949113 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> SRR949114 1 0.3801 0.670 0.780 0.000 0.220 0.000
#> SRR949115 1 0.3074 0.762 0.848 0.000 0.152 0.000
#> SRR949116 1 0.3074 0.762 0.848 0.000 0.152 0.000
#> SRR949117 3 0.1722 0.919 0.048 0.008 0.944 0.000
#> SRR949118 3 0.1256 0.936 0.028 0.000 0.964 0.008
#> SRR949119 1 0.1637 0.867 0.940 0.000 0.000 0.060
#> SRR949120 1 0.1637 0.867 0.940 0.000 0.000 0.060
#> SRR949121 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> SRR949122 1 0.0000 0.887 1.000 0.000 0.000 0.000
#> SRR949123 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> SRR949124 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> SRR949125 4 0.1302 0.919 0.000 0.000 0.044 0.956
#> SRR949126 4 0.1302 0.919 0.000 0.000 0.044 0.956
#> SRR949127 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> SRR949128 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> SRR949129 2 0.0000 0.938 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR949076 4 0.1571 0.859 0.000 0.000 0.004 0.936 0.060
#> SRR949078 2 0.0609 0.903 0.000 0.980 0.000 0.000 0.020
#> SRR949077 4 0.2648 0.773 0.000 0.000 0.000 0.848 0.152
#> SRR949079 4 0.0000 0.895 0.000 0.000 0.000 1.000 0.000
#> SRR949080 4 0.0000 0.895 0.000 0.000 0.000 1.000 0.000
#> SRR949081 5 0.7759 0.135 0.280 0.080 0.128 0.020 0.492
#> SRR949082 2 0.0404 0.905 0.000 0.988 0.000 0.000 0.012
#> SRR949083 1 0.1851 0.638 0.912 0.000 0.000 0.000 0.088
#> SRR949084 1 0.2074 0.628 0.896 0.000 0.000 0.000 0.104
#> SRR949085 2 0.0000 0.907 0.000 1.000 0.000 0.000 0.000
#> SRR949087 1 0.8136 -0.261 0.348 0.328 0.116 0.000 0.208
#> SRR949088 1 0.8136 -0.259 0.348 0.328 0.116 0.000 0.208
#> SRR949086 3 0.3366 0.509 0.000 0.000 0.768 0.000 0.232
#> SRR949089 2 0.0000 0.907 0.000 1.000 0.000 0.000 0.000
#> SRR949090 4 0.0404 0.892 0.000 0.000 0.012 0.988 0.000
#> SRR949092 1 0.0000 0.671 1.000 0.000 0.000 0.000 0.000
#> SRR949093 1 0.0000 0.671 1.000 0.000 0.000 0.000 0.000
#> SRR949091 4 0.4980 0.539 0.000 0.000 0.072 0.676 0.252
#> SRR949095 2 0.7843 -0.025 0.060 0.400 0.004 0.252 0.284
#> SRR949094 4 0.0000 0.895 0.000 0.000 0.000 1.000 0.000
#> SRR949096 1 0.2230 0.619 0.884 0.000 0.000 0.000 0.116
#> SRR949097 1 0.0794 0.669 0.972 0.000 0.000 0.000 0.028
#> SRR949098 2 0.0000 0.907 0.000 1.000 0.000 0.000 0.000
#> SRR949099 3 0.6243 0.129 0.184 0.000 0.532 0.000 0.284
#> SRR949101 3 0.3590 0.555 0.000 0.000 0.828 0.092 0.080
#> SRR949100 2 0.6294 0.267 0.100 0.552 0.024 0.000 0.324
#> SRR949102 4 0.5880 0.176 0.000 0.000 0.100 0.484 0.416
#> SRR949103 1 0.2732 0.599 0.840 0.000 0.000 0.000 0.160
#> SRR949104 2 0.0000 0.907 0.000 1.000 0.000 0.000 0.000
#> SRR949105 3 0.0162 0.681 0.000 0.000 0.996 0.004 0.000
#> SRR949106 3 0.0162 0.681 0.000 0.000 0.996 0.004 0.000
#> SRR949107 3 0.0162 0.681 0.000 0.000 0.996 0.004 0.000
#> SRR949108 1 0.0510 0.672 0.984 0.000 0.000 0.000 0.016
#> SRR949109 4 0.0451 0.892 0.000 0.000 0.008 0.988 0.004
#> SRR949110 1 0.1043 0.672 0.960 0.000 0.000 0.000 0.040
#> SRR949111 4 0.0162 0.895 0.000 0.000 0.004 0.996 0.000
#> SRR949112 1 0.3586 0.539 0.736 0.000 0.000 0.000 0.264
#> SRR949113 2 0.0000 0.907 0.000 1.000 0.000 0.000 0.000
#> SRR949114 1 0.5059 0.357 0.548 0.000 0.036 0.000 0.416
#> SRR949115 1 0.5059 0.357 0.548 0.000 0.036 0.000 0.416
#> SRR949116 1 0.4989 0.362 0.552 0.000 0.032 0.000 0.416
#> SRR949117 3 0.5771 0.211 0.112 0.000 0.572 0.000 0.316
#> SRR949118 5 0.4304 -0.431 0.000 0.000 0.484 0.000 0.516
#> SRR949119 1 0.5226 0.224 0.572 0.000 0.000 0.052 0.376
#> SRR949120 1 0.5226 0.224 0.572 0.000 0.000 0.052 0.376
#> SRR949121 1 0.2471 0.631 0.864 0.000 0.000 0.000 0.136
#> SRR949122 1 0.1121 0.669 0.956 0.000 0.000 0.000 0.044
#> SRR949123 2 0.0162 0.904 0.000 0.996 0.000 0.000 0.004
#> SRR949124 2 0.0000 0.907 0.000 1.000 0.000 0.000 0.000
#> SRR949125 4 0.0162 0.895 0.000 0.000 0.004 0.996 0.000
#> SRR949126 4 0.0162 0.895 0.000 0.000 0.004 0.996 0.000
#> SRR949127 2 0.0609 0.903 0.000 0.980 0.000 0.000 0.020
#> SRR949128 2 0.0609 0.903 0.000 0.980 0.000 0.000 0.020
#> SRR949129 2 0.0609 0.903 0.000 0.980 0.000 0.000 0.020
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR949076 4 0.3482 0.5187 0.000 0.000 0.000 0.684 0.316 0.000
#> SRR949078 2 0.1528 0.9012 0.000 0.936 0.000 0.000 0.016 0.048
#> SRR949077 4 0.3672 0.4095 0.000 0.000 0.000 0.632 0.368 0.000
#> SRR949079 4 0.0146 0.8998 0.000 0.000 0.000 0.996 0.004 0.000
#> SRR949080 4 0.0146 0.8998 0.000 0.000 0.000 0.996 0.004 0.000
#> SRR949081 5 0.5964 0.4528 0.068 0.004 0.084 0.004 0.616 0.224
#> SRR949082 2 0.1124 0.9061 0.000 0.956 0.000 0.000 0.008 0.036
#> SRR949083 1 0.2331 0.7731 0.888 0.000 0.000 0.000 0.080 0.032
#> SRR949084 1 0.1753 0.7772 0.912 0.000 0.000 0.004 0.084 0.000
#> SRR949085 2 0.0000 0.9106 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949087 6 0.8678 0.1806 0.256 0.200 0.152 0.000 0.108 0.284
#> SRR949088 6 0.8678 0.1806 0.256 0.200 0.152 0.000 0.108 0.284
#> SRR949086 3 0.4947 0.5259 0.000 0.000 0.636 0.000 0.120 0.244
#> SRR949089 2 0.0000 0.9106 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949090 4 0.0520 0.8966 0.000 0.000 0.008 0.984 0.008 0.000
#> SRR949092 1 0.0260 0.8000 0.992 0.000 0.000 0.000 0.008 0.000
#> SRR949093 1 0.0260 0.8000 0.992 0.000 0.000 0.000 0.008 0.000
#> SRR949091 4 0.2269 0.8279 0.000 0.000 0.012 0.896 0.012 0.080
#> SRR949095 5 0.5637 0.4830 0.040 0.292 0.000 0.072 0.592 0.004
#> SRR949094 4 0.0000 0.9005 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949096 1 0.2362 0.7356 0.860 0.000 0.000 0.004 0.136 0.000
#> SRR949097 1 0.3103 0.7301 0.836 0.000 0.000 0.000 0.064 0.100
#> SRR949098 2 0.0000 0.9106 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949099 6 0.7327 0.1397 0.312 0.000 0.132 0.000 0.188 0.368
#> SRR949101 3 0.2833 0.6790 0.000 0.000 0.836 0.012 0.004 0.148
#> SRR949100 2 0.7169 0.0189 0.084 0.416 0.004 0.004 0.172 0.320
#> SRR949102 5 0.5683 0.5236 0.004 0.000 0.036 0.100 0.612 0.248
#> SRR949103 1 0.4148 0.6192 0.744 0.000 0.000 0.000 0.108 0.148
#> SRR949104 2 0.0000 0.9106 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949105 3 0.0000 0.7584 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR949106 3 0.0000 0.7584 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR949107 3 0.0000 0.7584 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR949108 1 0.2191 0.7465 0.876 0.000 0.000 0.000 0.004 0.120
#> SRR949109 4 0.1049 0.8833 0.000 0.000 0.008 0.960 0.032 0.000
#> SRR949110 1 0.2837 0.7553 0.856 0.000 0.000 0.000 0.056 0.088
#> SRR949111 4 0.0291 0.9003 0.000 0.000 0.004 0.992 0.000 0.004
#> SRR949112 1 0.3684 0.4462 0.664 0.000 0.000 0.000 0.004 0.332
#> SRR949113 2 0.0000 0.9106 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949114 6 0.3898 0.2253 0.336 0.000 0.012 0.000 0.000 0.652
#> SRR949115 6 0.3898 0.2253 0.336 0.000 0.012 0.000 0.000 0.652
#> SRR949116 6 0.3898 0.2253 0.336 0.000 0.012 0.000 0.000 0.652
#> SRR949117 3 0.6255 0.2391 0.036 0.000 0.428 0.000 0.136 0.400
#> SRR949118 6 0.5517 -0.3986 0.000 0.000 0.396 0.000 0.132 0.472
#> SRR949119 5 0.3089 0.6408 0.188 0.000 0.000 0.008 0.800 0.004
#> SRR949120 5 0.3089 0.6408 0.188 0.000 0.000 0.008 0.800 0.004
#> SRR949121 1 0.1814 0.7701 0.900 0.000 0.000 0.000 0.000 0.100
#> SRR949122 1 0.2527 0.7016 0.832 0.000 0.000 0.000 0.000 0.168
#> SRR949123 2 0.2199 0.8243 0.000 0.892 0.000 0.000 0.020 0.088
#> SRR949124 2 0.0363 0.9051 0.000 0.988 0.000 0.000 0.000 0.012
#> SRR949125 4 0.0146 0.9007 0.000 0.000 0.004 0.996 0.000 0.000
#> SRR949126 4 0.0146 0.9007 0.000 0.000 0.004 0.996 0.000 0.000
#> SRR949127 2 0.1682 0.8978 0.000 0.928 0.000 0.000 0.020 0.052
#> SRR949128 2 0.1682 0.8978 0.000 0.928 0.000 0.000 0.020 0.052
#> SRR949129 2 0.1594 0.8992 0.000 0.932 0.000 0.000 0.016 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)
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 16816 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.858 0.954 0.980 0.262 0.743 0.743
#> 3 3 0.560 0.775 0.814 1.122 0.655 0.536
#> 4 4 0.539 0.651 0.775 0.109 0.980 0.951
#> 5 5 0.590 0.820 0.786 0.116 0.869 0.655
#> 6 6 0.896 0.899 0.945 0.132 0.964 0.854
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
#> SRR949076 1 0.0000 0.984 1.000 0.000
#> SRR949078 1 0.5737 0.849 0.864 0.136
#> SRR949077 1 0.0000 0.984 1.000 0.000
#> SRR949079 1 0.0000 0.984 1.000 0.000
#> SRR949080 1 0.0000 0.984 1.000 0.000
#> SRR949081 1 0.0000 0.984 1.000 0.000
#> SRR949082 2 0.9732 0.286 0.404 0.596
#> SRR949083 1 0.0000 0.984 1.000 0.000
#> SRR949084 1 0.0000 0.984 1.000 0.000
#> SRR949085 2 0.0000 0.939 0.000 1.000
#> SRR949087 1 0.1843 0.962 0.972 0.028
#> SRR949088 1 0.1843 0.962 0.972 0.028
#> SRR949086 1 0.0000 0.984 1.000 0.000
#> SRR949089 2 0.0000 0.939 0.000 1.000
#> SRR949090 1 0.0000 0.984 1.000 0.000
#> SRR949092 1 0.0000 0.984 1.000 0.000
#> SRR949093 1 0.0000 0.984 1.000 0.000
#> SRR949091 1 0.0000 0.984 1.000 0.000
#> SRR949095 1 0.3274 0.933 0.940 0.060
#> SRR949094 1 0.0000 0.984 1.000 0.000
#> SRR949096 1 0.0000 0.984 1.000 0.000
#> SRR949097 1 0.0000 0.984 1.000 0.000
#> SRR949098 2 0.0000 0.939 0.000 1.000
#> SRR949099 1 0.0000 0.984 1.000 0.000
#> SRR949101 1 0.0000 0.984 1.000 0.000
#> SRR949100 1 0.0376 0.981 0.996 0.004
#> SRR949102 1 0.0000 0.984 1.000 0.000
#> SRR949103 1 0.0000 0.984 1.000 0.000
#> SRR949104 2 0.0000 0.939 0.000 1.000
#> SRR949105 1 0.0000 0.984 1.000 0.000
#> SRR949106 1 0.0000 0.984 1.000 0.000
#> SRR949107 1 0.0000 0.984 1.000 0.000
#> SRR949108 1 0.0000 0.984 1.000 0.000
#> SRR949109 1 0.0000 0.984 1.000 0.000
#> SRR949110 1 0.0000 0.984 1.000 0.000
#> SRR949111 1 0.0000 0.984 1.000 0.000
#> SRR949112 1 0.0000 0.984 1.000 0.000
#> SRR949113 2 0.0000 0.939 0.000 1.000
#> SRR949114 1 0.0000 0.984 1.000 0.000
#> SRR949115 1 0.0000 0.984 1.000 0.000
#> SRR949116 1 0.0000 0.984 1.000 0.000
#> SRR949117 1 0.0000 0.984 1.000 0.000
#> SRR949118 1 0.0000 0.984 1.000 0.000
#> SRR949119 1 0.0000 0.984 1.000 0.000
#> SRR949120 1 0.0000 0.984 1.000 0.000
#> SRR949121 1 0.0000 0.984 1.000 0.000
#> SRR949122 1 0.0000 0.984 1.000 0.000
#> SRR949123 2 0.0376 0.937 0.004 0.996
#> SRR949124 2 0.0000 0.939 0.000 1.000
#> SRR949125 1 0.0000 0.984 1.000 0.000
#> SRR949126 1 0.0000 0.984 1.000 0.000
#> SRR949127 1 0.5737 0.849 0.864 0.136
#> SRR949128 1 0.5737 0.849 0.864 0.136
#> SRR949129 1 0.5737 0.849 0.864 0.136
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR949076 1 0.1031 0.666 0.976 0.000 0.024
#> SRR949078 3 0.4277 0.858 0.016 0.132 0.852
#> SRR949077 1 0.1031 0.666 0.976 0.000 0.024
#> SRR949079 1 0.1031 0.666 0.976 0.000 0.024
#> SRR949080 1 0.1031 0.666 0.976 0.000 0.024
#> SRR949081 3 0.1860 0.938 0.052 0.000 0.948
#> SRR949082 2 0.6359 0.199 0.004 0.592 0.404
#> SRR949083 1 0.6180 0.689 0.584 0.000 0.416
#> SRR949084 1 0.6180 0.689 0.584 0.000 0.416
#> SRR949085 2 0.0000 0.934 0.000 1.000 0.000
#> SRR949087 3 0.2773 0.933 0.048 0.024 0.928
#> SRR949088 3 0.2773 0.933 0.048 0.024 0.928
#> SRR949086 3 0.1860 0.938 0.052 0.000 0.948
#> SRR949089 2 0.0000 0.934 0.000 1.000 0.000
#> SRR949090 1 0.1031 0.666 0.976 0.000 0.024
#> SRR949092 1 0.6180 0.689 0.584 0.000 0.416
#> SRR949093 1 0.6180 0.689 0.584 0.000 0.416
#> SRR949091 1 0.1031 0.666 0.976 0.000 0.024
#> SRR949095 1 0.2448 0.631 0.924 0.000 0.076
#> SRR949094 1 0.3038 0.671 0.896 0.000 0.104
#> SRR949096 1 0.6180 0.689 0.584 0.000 0.416
#> SRR949097 1 0.6180 0.689 0.584 0.000 0.416
#> SRR949098 2 0.0000 0.934 0.000 1.000 0.000
#> SRR949099 3 0.1860 0.938 0.052 0.000 0.948
#> SRR949101 3 0.1529 0.934 0.040 0.000 0.960
#> SRR949100 3 0.1753 0.939 0.048 0.000 0.952
#> SRR949102 3 0.2796 0.886 0.092 0.000 0.908
#> SRR949103 1 0.6180 0.689 0.584 0.000 0.416
#> SRR949104 2 0.0000 0.934 0.000 1.000 0.000
#> SRR949105 3 0.1411 0.936 0.036 0.000 0.964
#> SRR949106 3 0.1411 0.936 0.036 0.000 0.964
#> SRR949107 3 0.1411 0.936 0.036 0.000 0.964
#> SRR949108 1 0.6180 0.689 0.584 0.000 0.416
#> SRR949109 1 0.1031 0.666 0.976 0.000 0.024
#> SRR949110 1 0.6180 0.689 0.584 0.000 0.416
#> SRR949111 1 0.1031 0.666 0.976 0.000 0.024
#> SRR949112 1 0.6215 0.672 0.572 0.000 0.428
#> SRR949113 2 0.0237 0.932 0.000 0.996 0.004
#> SRR949114 1 0.6225 0.666 0.568 0.000 0.432
#> SRR949115 1 0.6225 0.666 0.568 0.000 0.432
#> SRR949116 1 0.6225 0.666 0.568 0.000 0.432
#> SRR949117 3 0.1860 0.938 0.052 0.000 0.948
#> SRR949118 3 0.1860 0.938 0.052 0.000 0.948
#> SRR949119 1 0.6180 0.689 0.584 0.000 0.416
#> SRR949120 1 0.6180 0.689 0.584 0.000 0.416
#> SRR949121 1 0.6180 0.689 0.584 0.000 0.416
#> SRR949122 1 0.6215 0.672 0.572 0.000 0.428
#> SRR949123 2 0.0237 0.931 0.000 0.996 0.004
#> SRR949124 2 0.0000 0.934 0.000 1.000 0.000
#> SRR949125 1 0.1031 0.666 0.976 0.000 0.024
#> SRR949126 1 0.1031 0.666 0.976 0.000 0.024
#> SRR949127 3 0.4277 0.858 0.016 0.132 0.852
#> SRR949128 3 0.4277 0.858 0.016 0.132 0.852
#> SRR949129 3 0.4277 0.858 0.016 0.132 0.852
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR949076 1 0.4999 0.364 0.508 0.000 0.000 0.492
#> SRR949078 3 0.7182 0.802 0.356 0.128 0.512 0.004
#> SRR949077 1 0.4999 0.364 0.508 0.000 0.000 0.492
#> SRR949079 1 0.4999 0.364 0.508 0.000 0.000 0.492
#> SRR949080 1 0.4999 0.364 0.508 0.000 0.000 0.492
#> SRR949081 3 0.4925 0.837 0.428 0.000 0.572 0.000
#> SRR949082 2 0.7088 0.159 0.196 0.588 0.212 0.004
#> SRR949083 1 0.0000 0.690 1.000 0.000 0.000 0.000
#> SRR949084 1 0.0000 0.690 1.000 0.000 0.000 0.000
#> SRR949085 2 0.0188 0.894 0.000 0.996 0.004 0.000
#> SRR949087 3 0.5706 0.837 0.420 0.020 0.556 0.004
#> SRR949088 3 0.5706 0.837 0.420 0.020 0.556 0.004
#> SRR949086 3 0.4916 0.839 0.424 0.000 0.576 0.000
#> SRR949089 2 0.0188 0.894 0.000 0.996 0.004 0.000
#> SRR949090 1 0.4999 0.364 0.508 0.000 0.000 0.492
#> SRR949092 1 0.0000 0.690 1.000 0.000 0.000 0.000
#> SRR949093 1 0.0000 0.690 1.000 0.000 0.000 0.000
#> SRR949091 1 0.4999 0.364 0.508 0.000 0.000 0.492
#> SRR949095 4 0.5119 0.000 0.112 0.000 0.124 0.764
#> SRR949094 1 0.4817 0.430 0.612 0.000 0.000 0.388
#> SRR949096 1 0.0000 0.690 1.000 0.000 0.000 0.000
#> SRR949097 1 0.0000 0.690 1.000 0.000 0.000 0.000
#> SRR949098 2 0.0188 0.894 0.000 0.996 0.004 0.000
#> SRR949099 3 0.4916 0.839 0.424 0.000 0.576 0.000
#> SRR949101 3 0.3392 0.580 0.124 0.000 0.856 0.020
#> SRR949100 3 0.5088 0.839 0.424 0.000 0.572 0.004
#> SRR949102 3 0.5158 0.776 0.472 0.000 0.524 0.004
#> SRR949103 1 0.0000 0.690 1.000 0.000 0.000 0.000
#> SRR949104 2 0.0336 0.891 0.000 0.992 0.000 0.008
#> SRR949105 3 0.3280 0.585 0.124 0.000 0.860 0.016
#> SRR949106 3 0.3280 0.585 0.124 0.000 0.860 0.016
#> SRR949107 3 0.3280 0.585 0.124 0.000 0.860 0.016
#> SRR949108 1 0.0000 0.690 1.000 0.000 0.000 0.000
#> SRR949109 1 0.4999 0.364 0.508 0.000 0.000 0.492
#> SRR949110 1 0.0000 0.690 1.000 0.000 0.000 0.000
#> SRR949111 1 0.4999 0.364 0.508 0.000 0.000 0.492
#> SRR949112 1 0.0592 0.677 0.984 0.000 0.016 0.000
#> SRR949113 2 0.0376 0.891 0.000 0.992 0.004 0.004
#> SRR949114 1 0.0707 0.672 0.980 0.000 0.020 0.000
#> SRR949115 1 0.0707 0.672 0.980 0.000 0.020 0.000
#> SRR949116 1 0.0707 0.672 0.980 0.000 0.020 0.000
#> SRR949117 3 0.4916 0.839 0.424 0.000 0.576 0.000
#> SRR949118 3 0.4916 0.839 0.424 0.000 0.576 0.000
#> SRR949119 1 0.0188 0.690 0.996 0.000 0.000 0.004
#> SRR949120 1 0.0188 0.690 0.996 0.000 0.000 0.004
#> SRR949121 1 0.0000 0.690 1.000 0.000 0.000 0.000
#> SRR949122 1 0.0592 0.677 0.984 0.000 0.016 0.000
#> SRR949123 2 0.0524 0.888 0.004 0.988 0.000 0.008
#> SRR949124 2 0.0336 0.891 0.000 0.992 0.000 0.008
#> SRR949125 1 0.4999 0.364 0.508 0.000 0.000 0.492
#> SRR949126 1 0.4999 0.364 0.508 0.000 0.000 0.492
#> SRR949127 3 0.7182 0.802 0.356 0.128 0.512 0.004
#> SRR949128 3 0.7182 0.802 0.356 0.128 0.512 0.004
#> SRR949129 3 0.7182 0.802 0.356 0.128 0.512 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR949076 4 0.3752 0.984 0.292 0.000 0.000 0.708 0.000
#> SRR949078 3 0.5731 0.733 0.236 0.132 0.628 0.000 0.004
#> SRR949077 4 0.3752 0.984 0.292 0.000 0.000 0.708 0.000
#> SRR949079 4 0.3752 0.984 0.292 0.000 0.000 0.708 0.000
#> SRR949080 4 0.3752 0.984 0.292 0.000 0.000 0.708 0.000
#> SRR949081 3 0.3876 0.771 0.316 0.000 0.684 0.000 0.000
#> SRR949082 2 0.5624 0.194 0.084 0.592 0.320 0.000 0.004
#> SRR949083 1 0.0000 0.980 1.000 0.000 0.000 0.000 0.000
#> SRR949084 1 0.0000 0.980 1.000 0.000 0.000 0.000 0.000
#> SRR949085 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000
#> SRR949087 3 0.4597 0.774 0.300 0.024 0.672 0.000 0.004
#> SRR949088 3 0.4597 0.774 0.300 0.024 0.672 0.000 0.004
#> SRR949086 3 0.3837 0.776 0.308 0.000 0.692 0.000 0.000
#> SRR949089 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000
#> SRR949090 4 0.3752 0.984 0.292 0.000 0.000 0.708 0.000
#> SRR949092 1 0.0000 0.980 1.000 0.000 0.000 0.000 0.000
#> SRR949093 1 0.0000 0.980 1.000 0.000 0.000 0.000 0.000
#> SRR949091 4 0.3752 0.984 0.292 0.000 0.000 0.708 0.000
#> SRR949095 5 0.0486 0.000 0.004 0.000 0.004 0.004 0.988
#> SRR949094 4 0.4331 0.825 0.400 0.000 0.004 0.596 0.000
#> SRR949096 1 0.0000 0.980 1.000 0.000 0.000 0.000 0.000
#> SRR949097 1 0.0000 0.980 1.000 0.000 0.000 0.000 0.000
#> SRR949098 2 0.0000 0.888 0.000 1.000 0.000 0.000 0.000
#> SRR949099 3 0.3837 0.776 0.308 0.000 0.692 0.000 0.000
#> SRR949101 3 0.4111 0.211 0.008 0.000 0.708 0.280 0.004
#> SRR949100 3 0.3990 0.776 0.308 0.000 0.688 0.000 0.004
#> SRR949102 3 0.4482 0.713 0.348 0.000 0.636 0.016 0.000
#> SRR949103 1 0.0000 0.980 1.000 0.000 0.000 0.000 0.000
#> SRR949104 2 0.0798 0.881 0.000 0.976 0.000 0.016 0.008
#> SRR949105 3 0.3968 0.217 0.004 0.000 0.716 0.276 0.004
#> SRR949106 3 0.3968 0.217 0.004 0.000 0.716 0.276 0.004
#> SRR949107 3 0.3968 0.217 0.004 0.000 0.716 0.276 0.004
#> SRR949108 1 0.0000 0.980 1.000 0.000 0.000 0.000 0.000
#> SRR949109 4 0.3752 0.984 0.292 0.000 0.000 0.708 0.000
#> SRR949110 1 0.0000 0.980 1.000 0.000 0.000 0.000 0.000
#> SRR949111 4 0.3752 0.984 0.292 0.000 0.000 0.708 0.000
#> SRR949112 1 0.0794 0.962 0.972 0.000 0.028 0.000 0.000
#> SRR949113 2 0.0162 0.885 0.000 0.996 0.000 0.000 0.004
#> SRR949114 1 0.0963 0.955 0.964 0.000 0.036 0.000 0.000
#> SRR949115 1 0.0963 0.955 0.964 0.000 0.036 0.000 0.000
#> SRR949116 1 0.0963 0.955 0.964 0.000 0.036 0.000 0.000
#> SRR949117 3 0.3837 0.776 0.308 0.000 0.692 0.000 0.000
#> SRR949118 3 0.3837 0.776 0.308 0.000 0.692 0.000 0.000
#> SRR949119 1 0.0671 0.958 0.980 0.000 0.004 0.016 0.000
#> SRR949120 1 0.0671 0.958 0.980 0.000 0.004 0.016 0.000
#> SRR949121 1 0.0000 0.980 1.000 0.000 0.000 0.000 0.000
#> SRR949122 1 0.0794 0.962 0.972 0.000 0.028 0.000 0.000
#> SRR949123 2 0.0912 0.879 0.000 0.972 0.000 0.016 0.012
#> SRR949124 2 0.0798 0.881 0.000 0.976 0.000 0.016 0.008
#> SRR949125 4 0.3752 0.984 0.292 0.000 0.000 0.708 0.000
#> SRR949126 4 0.3752 0.984 0.292 0.000 0.000 0.708 0.000
#> SRR949127 3 0.5731 0.733 0.236 0.132 0.628 0.000 0.004
#> SRR949128 3 0.5731 0.733 0.236 0.132 0.628 0.000 0.004
#> SRR949129 3 0.5731 0.733 0.236 0.132 0.628 0.000 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR949076 4 0.0000 0.982 0.000 0.000 0.000 1.00 0.000 0.000
#> SRR949078 5 0.4090 0.852 0.064 0.108 0.040 0.00 0.788 0.000
#> SRR949077 4 0.0000 0.982 0.000 0.000 0.000 1.00 0.000 0.000
#> SRR949079 4 0.0000 0.982 0.000 0.000 0.000 1.00 0.000 0.000
#> SRR949080 4 0.0000 0.982 0.000 0.000 0.000 1.00 0.000 0.000
#> SRR949081 5 0.2361 0.887 0.088 0.000 0.028 0.00 0.884 0.000
#> SRR949082 2 0.5282 0.231 0.040 0.568 0.040 0.00 0.352 0.000
#> SRR949083 1 0.0000 0.977 1.000 0.000 0.000 0.00 0.000 0.000
#> SRR949084 1 0.0000 0.977 1.000 0.000 0.000 0.00 0.000 0.000
#> SRR949085 2 0.0632 0.890 0.000 0.976 0.000 0.00 0.024 0.000
#> SRR949087 5 0.2250 0.893 0.064 0.000 0.040 0.00 0.896 0.000
#> SRR949088 5 0.2250 0.893 0.064 0.000 0.040 0.00 0.896 0.000
#> SRR949086 5 0.2088 0.898 0.068 0.000 0.028 0.00 0.904 0.000
#> SRR949089 2 0.0632 0.890 0.000 0.976 0.000 0.00 0.024 0.000
#> SRR949090 4 0.0000 0.982 0.000 0.000 0.000 1.00 0.000 0.000
#> SRR949092 1 0.0000 0.977 1.000 0.000 0.000 0.00 0.000 0.000
#> SRR949093 1 0.0000 0.977 1.000 0.000 0.000 0.00 0.000 0.000
#> SRR949091 4 0.0000 0.982 0.000 0.000 0.000 1.00 0.000 0.000
#> SRR949095 6 0.0000 0.000 0.000 0.000 0.000 0.00 0.000 1.000
#> SRR949094 4 0.2146 0.805 0.116 0.000 0.000 0.88 0.004 0.000
#> SRR949096 1 0.0000 0.977 1.000 0.000 0.000 0.00 0.000 0.000
#> SRR949097 1 0.0000 0.977 1.000 0.000 0.000 0.00 0.000 0.000
#> SRR949098 2 0.0632 0.890 0.000 0.976 0.000 0.00 0.024 0.000
#> SRR949099 5 0.2088 0.898 0.068 0.000 0.028 0.00 0.904 0.000
#> SRR949101 3 0.1327 0.912 0.000 0.000 0.936 0.00 0.064 0.000
#> SRR949100 5 0.1926 0.899 0.068 0.000 0.020 0.00 0.912 0.000
#> SRR949102 5 0.3293 0.710 0.140 0.000 0.048 0.00 0.812 0.000
#> SRR949103 1 0.0000 0.977 1.000 0.000 0.000 0.00 0.000 0.000
#> SRR949104 2 0.0547 0.880 0.000 0.980 0.020 0.00 0.000 0.000
#> SRR949105 3 0.0713 0.971 0.000 0.000 0.972 0.00 0.028 0.000
#> SRR949106 3 0.0713 0.971 0.000 0.000 0.972 0.00 0.028 0.000
#> SRR949107 3 0.0713 0.971 0.000 0.000 0.972 0.00 0.028 0.000
#> SRR949108 1 0.0000 0.977 1.000 0.000 0.000 0.00 0.000 0.000
#> SRR949109 4 0.0000 0.982 0.000 0.000 0.000 1.00 0.000 0.000
#> SRR949110 1 0.0000 0.977 1.000 0.000 0.000 0.00 0.000 0.000
#> SRR949111 4 0.0000 0.982 0.000 0.000 0.000 1.00 0.000 0.000
#> SRR949112 1 0.0713 0.962 0.972 0.000 0.000 0.00 0.028 0.000
#> SRR949113 2 0.0713 0.887 0.000 0.972 0.000 0.00 0.028 0.000
#> SRR949114 1 0.0865 0.957 0.964 0.000 0.000 0.00 0.036 0.000
#> SRR949115 1 0.0865 0.957 0.964 0.000 0.000 0.00 0.036 0.000
#> SRR949116 1 0.0865 0.957 0.964 0.000 0.000 0.00 0.036 0.000
#> SRR949117 5 0.2009 0.899 0.068 0.000 0.024 0.00 0.908 0.000
#> SRR949118 5 0.2088 0.898 0.068 0.000 0.028 0.00 0.904 0.000
#> SRR949119 1 0.1327 0.911 0.936 0.000 0.000 0.00 0.064 0.000
#> SRR949120 1 0.1327 0.911 0.936 0.000 0.000 0.00 0.064 0.000
#> SRR949121 1 0.0000 0.977 1.000 0.000 0.000 0.00 0.000 0.000
#> SRR949122 1 0.0713 0.962 0.972 0.000 0.000 0.00 0.028 0.000
#> SRR949123 2 0.0692 0.879 0.000 0.976 0.020 0.00 0.000 0.004
#> SRR949124 2 0.0547 0.880 0.000 0.980 0.020 0.00 0.000 0.000
#> SRR949125 4 0.0000 0.982 0.000 0.000 0.000 1.00 0.000 0.000
#> SRR949126 4 0.0000 0.982 0.000 0.000 0.000 1.00 0.000 0.000
#> SRR949127 5 0.4090 0.852 0.064 0.108 0.040 0.00 0.788 0.000
#> SRR949128 5 0.4090 0.852 0.064 0.108 0.040 0.00 0.788 0.000
#> SRR949129 5 0.4090 0.852 0.064 0.108 0.040 0.00 0.788 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)
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 16816 rows and 54 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 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 0.341 0.685 0.811 0.394 0.591 0.591
#> 3 3 0.346 0.555 0.693 0.500 0.678 0.499
#> 4 4 0.581 0.803 0.810 0.188 0.826 0.559
#> 5 5 0.801 0.748 0.808 0.098 0.964 0.857
#> 6 6 0.781 0.641 0.792 0.044 0.981 0.914
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
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
#> SRR949076 1 0.7674 0.705 0.776 0.224
#> SRR949078 2 0.8661 0.871 0.288 0.712
#> SRR949077 1 0.7602 0.704 0.780 0.220
#> SRR949079 1 0.7674 0.705 0.776 0.224
#> SRR949080 1 0.7674 0.705 0.776 0.224
#> SRR949081 1 0.7950 0.478 0.760 0.240
#> SRR949082 2 0.8661 0.871 0.288 0.712
#> SRR949083 1 0.0672 0.793 0.992 0.008
#> SRR949084 1 0.0672 0.793 0.992 0.008
#> SRR949085 2 0.8386 0.872 0.268 0.732
#> SRR949087 1 0.9993 -0.483 0.516 0.484
#> SRR949088 1 0.9993 -0.483 0.516 0.484
#> SRR949086 1 0.7674 0.510 0.776 0.224
#> SRR949089 2 0.8267 0.874 0.260 0.740
#> SRR949090 1 0.7674 0.705 0.776 0.224
#> SRR949092 1 0.0672 0.793 0.992 0.008
#> SRR949093 1 0.0672 0.793 0.992 0.008
#> SRR949091 1 0.7745 0.702 0.772 0.228
#> SRR949095 1 0.3879 0.759 0.924 0.076
#> SRR949094 1 0.7528 0.703 0.784 0.216
#> SRR949096 1 0.1184 0.792 0.984 0.016
#> SRR949097 1 0.0672 0.793 0.992 0.008
#> SRR949098 2 0.8267 0.874 0.260 0.740
#> SRR949099 1 0.2603 0.780 0.956 0.044
#> SRR949101 1 0.8955 0.487 0.688 0.312
#> SRR949100 1 0.3584 0.758 0.932 0.068
#> SRR949102 1 0.6148 0.667 0.848 0.152
#> SRR949103 1 0.0000 0.793 1.000 0.000
#> SRR949104 2 0.8267 0.874 0.260 0.740
#> SRR949105 2 0.9993 0.283 0.484 0.516
#> SRR949106 2 0.9993 0.283 0.484 0.516
#> SRR949107 2 0.9993 0.283 0.484 0.516
#> SRR949108 1 0.0672 0.793 0.992 0.008
#> SRR949109 1 0.7674 0.705 0.776 0.224
#> SRR949110 1 0.0672 0.793 0.992 0.008
#> SRR949111 1 0.7674 0.705 0.776 0.224
#> SRR949112 1 0.1633 0.785 0.976 0.024
#> SRR949113 2 0.8267 0.874 0.260 0.740
#> SRR949114 1 0.2236 0.781 0.964 0.036
#> SRR949115 1 0.2236 0.781 0.964 0.036
#> SRR949116 1 0.2236 0.781 0.964 0.036
#> SRR949117 1 0.7815 0.503 0.768 0.232
#> SRR949118 1 0.7674 0.510 0.776 0.224
#> SRR949119 1 0.1633 0.788 0.976 0.024
#> SRR949120 1 0.1633 0.788 0.976 0.024
#> SRR949121 1 0.0672 0.793 0.992 0.008
#> SRR949122 1 0.0672 0.793 0.992 0.008
#> SRR949123 2 0.8267 0.874 0.260 0.740
#> SRR949124 2 0.8267 0.874 0.260 0.740
#> SRR949125 1 0.7674 0.705 0.776 0.224
#> SRR949126 1 0.7674 0.705 0.776 0.224
#> SRR949127 2 0.8713 0.870 0.292 0.708
#> SRR949128 2 0.8713 0.870 0.292 0.708
#> SRR949129 2 0.8713 0.870 0.292 0.708
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR949076 1 0.0237 0.821 0.996 0.004 0.000
#> SRR949078 2 0.4261 0.922 0.012 0.848 0.140
#> SRR949077 1 0.0237 0.821 0.996 0.004 0.000
#> SRR949079 1 0.0237 0.821 0.996 0.004 0.000
#> SRR949080 1 0.0237 0.821 0.996 0.004 0.000
#> SRR949081 3 0.7256 0.455 0.164 0.124 0.712
#> SRR949082 2 0.4326 0.917 0.012 0.844 0.144
#> SRR949083 3 0.7665 0.392 0.456 0.044 0.500
#> SRR949084 3 0.7665 0.392 0.456 0.044 0.500
#> SRR949085 2 0.2261 0.940 0.000 0.932 0.068
#> SRR949087 3 0.8037 0.152 0.076 0.352 0.572
#> SRR949088 3 0.8037 0.152 0.076 0.352 0.572
#> SRR949086 3 0.6757 0.468 0.180 0.084 0.736
#> SRR949089 2 0.1647 0.943 0.004 0.960 0.036
#> SRR949090 1 0.0237 0.821 0.996 0.004 0.000
#> SRR949092 3 0.7665 0.392 0.456 0.044 0.500
#> SRR949093 3 0.7665 0.392 0.456 0.044 0.500
#> SRR949091 1 0.1267 0.787 0.972 0.004 0.024
#> SRR949095 1 0.8849 -0.217 0.556 0.152 0.292
#> SRR949094 1 0.0237 0.814 0.996 0.000 0.004
#> SRR949096 3 0.7665 0.392 0.456 0.044 0.500
#> SRR949097 3 0.7665 0.392 0.456 0.044 0.500
#> SRR949098 2 0.1647 0.943 0.004 0.960 0.036
#> SRR949099 3 0.4399 0.464 0.188 0.000 0.812
#> SRR949101 3 0.8668 0.310 0.304 0.132 0.564
#> SRR949100 3 0.8464 0.457 0.280 0.128 0.592
#> SRR949102 3 0.7180 0.448 0.196 0.096 0.708
#> SRR949103 3 0.7665 0.392 0.456 0.044 0.500
#> SRR949104 2 0.1647 0.943 0.004 0.960 0.036
#> SRR949105 3 0.8322 0.219 0.124 0.268 0.608
#> SRR949106 3 0.8322 0.219 0.124 0.268 0.608
#> SRR949107 3 0.8322 0.219 0.124 0.268 0.608
#> SRR949108 3 0.7665 0.392 0.456 0.044 0.500
#> SRR949109 1 0.0237 0.821 0.996 0.004 0.000
#> SRR949110 3 0.7665 0.392 0.456 0.044 0.500
#> SRR949111 1 0.0237 0.821 0.996 0.004 0.000
#> SRR949112 3 0.7634 0.405 0.432 0.044 0.524
#> SRR949113 2 0.1647 0.943 0.004 0.960 0.036
#> SRR949114 3 0.7395 0.434 0.380 0.040 0.580
#> SRR949115 3 0.7395 0.434 0.380 0.040 0.580
#> SRR949116 3 0.7395 0.434 0.380 0.040 0.580
#> SRR949117 3 0.6783 0.471 0.176 0.088 0.736
#> SRR949118 3 0.6728 0.469 0.184 0.080 0.736
#> SRR949119 1 0.7466 -0.260 0.520 0.036 0.444
#> SRR949120 1 0.7466 -0.260 0.520 0.036 0.444
#> SRR949121 3 0.7665 0.392 0.456 0.044 0.500
#> SRR949122 3 0.7665 0.392 0.456 0.044 0.500
#> SRR949123 2 0.1765 0.942 0.004 0.956 0.040
#> SRR949124 2 0.1647 0.943 0.004 0.960 0.036
#> SRR949125 1 0.0424 0.819 0.992 0.008 0.000
#> SRR949126 1 0.0424 0.819 0.992 0.008 0.000
#> SRR949127 2 0.4261 0.922 0.012 0.848 0.140
#> SRR949128 2 0.4261 0.922 0.012 0.848 0.140
#> SRR949129 2 0.4261 0.922 0.012 0.848 0.140
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR949076 4 0.0804 0.921 0.012 0.000 0.008 0.980
#> SRR949078 2 0.5186 0.841 0.084 0.752 0.164 0.000
#> SRR949077 4 0.0804 0.921 0.012 0.000 0.008 0.980
#> SRR949079 4 0.1174 0.920 0.012 0.000 0.020 0.968
#> SRR949080 4 0.1174 0.920 0.012 0.000 0.020 0.968
#> SRR949081 3 0.5926 0.734 0.304 0.020 0.648 0.028
#> SRR949082 2 0.5186 0.841 0.084 0.752 0.164 0.000
#> SRR949083 1 0.3356 0.918 0.824 0.000 0.000 0.176
#> SRR949084 1 0.3356 0.918 0.824 0.000 0.000 0.176
#> SRR949085 2 0.3009 0.874 0.056 0.892 0.052 0.000
#> SRR949087 3 0.7382 0.570 0.248 0.204 0.544 0.004
#> SRR949088 3 0.7382 0.570 0.248 0.204 0.544 0.004
#> SRR949086 3 0.5944 0.735 0.328 0.016 0.628 0.028
#> SRR949089 2 0.0469 0.881 0.012 0.988 0.000 0.000
#> SRR949090 4 0.1042 0.920 0.008 0.000 0.020 0.972
#> SRR949092 1 0.3356 0.918 0.824 0.000 0.000 0.176
#> SRR949093 1 0.3356 0.918 0.824 0.000 0.000 0.176
#> SRR949091 4 0.1174 0.910 0.012 0.000 0.020 0.968
#> SRR949095 4 0.8607 -0.344 0.308 0.028 0.308 0.356
#> SRR949094 4 0.0469 0.921 0.012 0.000 0.000 0.988
#> SRR949096 1 0.3356 0.918 0.824 0.000 0.000 0.176
#> SRR949097 1 0.3356 0.918 0.824 0.000 0.000 0.176
#> SRR949098 2 0.0469 0.881 0.012 0.988 0.000 0.000
#> SRR949099 3 0.5495 0.715 0.348 0.000 0.624 0.028
#> SRR949101 3 0.6777 0.628 0.140 0.024 0.664 0.172
#> SRR949100 3 0.6849 0.661 0.344 0.020 0.568 0.068
#> SRR949102 3 0.6017 0.734 0.308 0.016 0.640 0.036
#> SRR949103 1 0.3356 0.918 0.824 0.000 0.000 0.176
#> SRR949104 2 0.1124 0.878 0.012 0.972 0.012 0.004
#> SRR949105 3 0.7129 0.618 0.160 0.108 0.664 0.068
#> SRR949106 3 0.7129 0.618 0.160 0.108 0.664 0.068
#> SRR949107 3 0.7129 0.618 0.160 0.108 0.664 0.068
#> SRR949108 1 0.3356 0.918 0.824 0.000 0.000 0.176
#> SRR949109 4 0.0804 0.919 0.008 0.000 0.012 0.980
#> SRR949110 1 0.3356 0.918 0.824 0.000 0.000 0.176
#> SRR949111 4 0.0469 0.921 0.012 0.000 0.000 0.988
#> SRR949112 1 0.3208 0.894 0.848 0.000 0.004 0.148
#> SRR949113 2 0.0469 0.881 0.012 0.988 0.000 0.000
#> SRR949114 1 0.5897 0.678 0.700 0.000 0.164 0.136
#> SRR949115 1 0.5897 0.678 0.700 0.000 0.164 0.136
#> SRR949116 1 0.5897 0.678 0.700 0.000 0.164 0.136
#> SRR949117 3 0.5889 0.727 0.340 0.012 0.620 0.028
#> SRR949118 3 0.5944 0.735 0.328 0.016 0.628 0.028
#> SRR949119 1 0.5727 0.784 0.704 0.000 0.096 0.200
#> SRR949120 1 0.5727 0.784 0.704 0.000 0.096 0.200
#> SRR949121 1 0.3356 0.918 0.824 0.000 0.000 0.176
#> SRR949122 1 0.3356 0.918 0.824 0.000 0.000 0.176
#> SRR949123 2 0.1362 0.876 0.020 0.964 0.012 0.004
#> SRR949124 2 0.1124 0.878 0.012 0.972 0.012 0.004
#> SRR949125 4 0.1545 0.912 0.008 0.000 0.040 0.952
#> SRR949126 4 0.1545 0.912 0.008 0.000 0.040 0.952
#> SRR949127 2 0.5229 0.839 0.084 0.748 0.168 0.000
#> SRR949128 2 0.5229 0.839 0.084 0.748 0.168 0.000
#> SRR949129 2 0.5229 0.839 0.084 0.748 0.168 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR949076 4 0.1732 0.982 0.080 0.000 0.000 0.920 0.000
#> SRR949078 2 0.6240 0.700 0.024 0.580 0.288 0.000 0.108
#> SRR949077 4 0.1892 0.981 0.080 0.000 0.000 0.916 0.004
#> SRR949079 4 0.2490 0.975 0.080 0.000 0.020 0.896 0.004
#> SRR949080 4 0.2490 0.975 0.080 0.000 0.020 0.896 0.004
#> SRR949081 5 0.2400 0.596 0.020 0.000 0.048 0.020 0.912
#> SRR949082 2 0.6240 0.700 0.024 0.580 0.288 0.000 0.108
#> SRR949083 1 0.0955 0.860 0.968 0.000 0.028 0.000 0.004
#> SRR949084 1 0.0290 0.857 0.992 0.000 0.008 0.000 0.000
#> SRR949085 2 0.3742 0.751 0.004 0.788 0.188 0.000 0.020
#> SRR949087 5 0.6365 0.230 0.052 0.080 0.280 0.000 0.588
#> SRR949088 5 0.6365 0.230 0.052 0.080 0.280 0.000 0.588
#> SRR949086 5 0.1830 0.617 0.052 0.000 0.004 0.012 0.932
#> SRR949089 2 0.0162 0.765 0.004 0.996 0.000 0.000 0.000
#> SRR949090 4 0.2052 0.981 0.080 0.000 0.004 0.912 0.004
#> SRR949092 1 0.0955 0.860 0.968 0.000 0.028 0.000 0.004
#> SRR949093 1 0.0955 0.860 0.968 0.000 0.028 0.000 0.004
#> SRR949091 4 0.2166 0.976 0.072 0.000 0.012 0.912 0.004
#> SRR949095 5 0.7858 0.146 0.140 0.004 0.144 0.228 0.484
#> SRR949094 4 0.1732 0.982 0.080 0.000 0.000 0.920 0.000
#> SRR949096 1 0.0963 0.857 0.964 0.000 0.036 0.000 0.000
#> SRR949097 1 0.0955 0.860 0.968 0.000 0.028 0.000 0.004
#> SRR949098 2 0.0162 0.765 0.004 0.996 0.000 0.000 0.000
#> SRR949099 5 0.1809 0.619 0.060 0.000 0.000 0.012 0.928
#> SRR949101 5 0.4883 0.252 0.020 0.000 0.128 0.100 0.752
#> SRR949100 5 0.3920 0.544 0.052 0.008 0.108 0.008 0.824
#> SRR949102 5 0.2581 0.589 0.020 0.000 0.048 0.028 0.904
#> SRR949103 1 0.0955 0.860 0.968 0.000 0.028 0.000 0.004
#> SRR949104 2 0.1356 0.756 0.004 0.956 0.028 0.012 0.000
#> SRR949105 3 0.6990 1.000 0.036 0.020 0.440 0.080 0.424
#> SRR949106 3 0.6990 1.000 0.036 0.020 0.440 0.080 0.424
#> SRR949107 3 0.6990 1.000 0.036 0.020 0.440 0.080 0.424
#> SRR949108 1 0.0290 0.857 0.992 0.000 0.008 0.000 0.000
#> SRR949109 4 0.2130 0.980 0.080 0.000 0.012 0.908 0.000
#> SRR949110 1 0.0162 0.860 0.996 0.000 0.000 0.000 0.004
#> SRR949111 4 0.2017 0.980 0.080 0.000 0.008 0.912 0.000
#> SRR949112 1 0.0798 0.853 0.976 0.000 0.016 0.000 0.008
#> SRR949113 2 0.0162 0.765 0.004 0.996 0.000 0.000 0.000
#> SRR949114 1 0.5933 0.427 0.584 0.000 0.096 0.012 0.308
#> SRR949115 1 0.5933 0.427 0.584 0.000 0.096 0.012 0.308
#> SRR949116 1 0.5933 0.427 0.584 0.000 0.096 0.012 0.308
#> SRR949117 5 0.2115 0.611 0.068 0.000 0.008 0.008 0.916
#> SRR949118 5 0.1901 0.616 0.056 0.000 0.004 0.012 0.928
#> SRR949119 1 0.6216 0.618 0.672 0.004 0.132 0.072 0.120
#> SRR949120 1 0.6216 0.618 0.672 0.004 0.132 0.072 0.120
#> SRR949121 1 0.0162 0.860 0.996 0.000 0.000 0.000 0.004
#> SRR949122 1 0.0290 0.859 0.992 0.000 0.000 0.000 0.008
#> SRR949123 2 0.2061 0.747 0.004 0.928 0.040 0.024 0.004
#> SRR949124 2 0.1356 0.756 0.004 0.956 0.028 0.012 0.000
#> SRR949125 4 0.3268 0.953 0.080 0.000 0.060 0.856 0.004
#> SRR949126 4 0.3268 0.953 0.080 0.000 0.060 0.856 0.004
#> SRR949127 2 0.6274 0.695 0.024 0.572 0.296 0.000 0.108
#> SRR949128 2 0.6274 0.695 0.024 0.572 0.296 0.000 0.108
#> SRR949129 2 0.6274 0.695 0.024 0.572 0.296 0.000 0.108
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR949076 4 0.0806 0.957 0.020 0.000 0.000 0.972 0.000 0.008
#> SRR949078 2 0.1461 0.566 0.016 0.940 0.000 0.000 0.044 0.000
#> SRR949077 4 0.0806 0.957 0.020 0.000 0.000 0.972 0.000 0.008
#> SRR949079 4 0.2183 0.941 0.020 0.000 0.028 0.912 0.000 0.040
#> SRR949080 4 0.2183 0.941 0.020 0.000 0.028 0.912 0.000 0.040
#> SRR949081 5 0.2815 0.663 0.020 0.004 0.048 0.000 0.880 0.048
#> SRR949082 2 0.1461 0.566 0.016 0.940 0.000 0.000 0.044 0.000
#> SRR949083 1 0.1036 0.835 0.964 0.000 0.008 0.000 0.004 0.024
#> SRR949084 1 0.0260 0.834 0.992 0.000 0.000 0.000 0.000 0.008
#> SRR949085 2 0.2703 0.198 0.004 0.824 0.000 0.000 0.000 0.172
#> SRR949087 5 0.5387 0.254 0.032 0.444 0.020 0.000 0.488 0.016
#> SRR949088 5 0.5387 0.254 0.032 0.444 0.020 0.000 0.488 0.016
#> SRR949086 5 0.1520 0.682 0.020 0.016 0.008 0.000 0.948 0.008
#> SRR949089 2 0.3993 -0.813 0.004 0.520 0.000 0.000 0.000 0.476
#> SRR949090 4 0.1334 0.955 0.020 0.000 0.000 0.948 0.000 0.032
#> SRR949092 1 0.1138 0.835 0.960 0.000 0.012 0.000 0.004 0.024
#> SRR949093 1 0.1138 0.835 0.960 0.000 0.012 0.000 0.004 0.024
#> SRR949091 4 0.1515 0.954 0.020 0.000 0.008 0.944 0.000 0.028
#> SRR949095 5 0.8000 0.282 0.040 0.020 0.164 0.112 0.456 0.208
#> SRR949094 4 0.0806 0.957 0.020 0.000 0.000 0.972 0.000 0.008
#> SRR949096 1 0.0806 0.834 0.972 0.000 0.008 0.000 0.000 0.020
#> SRR949097 1 0.1232 0.835 0.956 0.000 0.016 0.000 0.004 0.024
#> SRR949098 2 0.3993 -0.813 0.004 0.520 0.000 0.000 0.000 0.476
#> SRR949099 5 0.1313 0.682 0.028 0.016 0.004 0.000 0.952 0.000
#> SRR949101 5 0.5692 0.385 0.016 0.000 0.156 0.068 0.672 0.088
#> SRR949100 5 0.3638 0.612 0.036 0.156 0.000 0.004 0.796 0.008
#> SRR949102 5 0.2706 0.661 0.016 0.000 0.040 0.008 0.888 0.048
#> SRR949103 1 0.1232 0.835 0.956 0.000 0.016 0.000 0.004 0.024
#> SRR949104 6 0.4672 0.911 0.004 0.480 0.008 0.012 0.004 0.492
#> SRR949105 3 0.5593 1.000 0.028 0.096 0.624 0.008 0.244 0.000
#> SRR949106 3 0.5593 1.000 0.028 0.096 0.624 0.008 0.244 0.000
#> SRR949107 3 0.5593 1.000 0.028 0.096 0.624 0.008 0.244 0.000
#> SRR949108 1 0.0260 0.834 0.992 0.000 0.000 0.000 0.000 0.008
#> SRR949109 4 0.1515 0.954 0.020 0.000 0.008 0.944 0.000 0.028
#> SRR949110 1 0.0436 0.836 0.988 0.000 0.004 0.000 0.004 0.004
#> SRR949111 4 0.1065 0.957 0.020 0.000 0.008 0.964 0.000 0.008
#> SRR949112 1 0.1026 0.831 0.968 0.008 0.008 0.000 0.012 0.004
#> SRR949113 2 0.3993 -0.813 0.004 0.520 0.000 0.000 0.000 0.476
#> SRR949114 1 0.7018 0.420 0.524 0.040 0.140 0.000 0.232 0.064
#> SRR949115 1 0.7018 0.420 0.524 0.040 0.140 0.000 0.232 0.064
#> SRR949116 1 0.7018 0.420 0.524 0.040 0.140 0.000 0.232 0.064
#> SRR949117 5 0.1168 0.683 0.028 0.016 0.000 0.000 0.956 0.000
#> SRR949118 5 0.1262 0.682 0.020 0.016 0.008 0.000 0.956 0.000
#> SRR949119 1 0.7179 0.428 0.528 0.000 0.128 0.040 0.104 0.200
#> SRR949120 1 0.7179 0.428 0.528 0.000 0.128 0.040 0.104 0.200
#> SRR949121 1 0.0436 0.836 0.988 0.000 0.004 0.000 0.004 0.004
#> SRR949122 1 0.0291 0.836 0.992 0.000 0.000 0.000 0.004 0.004
#> SRR949123 6 0.5451 0.826 0.004 0.456 0.044 0.008 0.016 0.472
#> SRR949124 6 0.4672 0.911 0.004 0.480 0.008 0.012 0.004 0.492
#> SRR949125 4 0.3264 0.911 0.020 0.000 0.056 0.844 0.000 0.080
#> SRR949126 4 0.3264 0.911 0.020 0.000 0.056 0.844 0.000 0.080
#> SRR949127 2 0.1844 0.569 0.016 0.928 0.016 0.000 0.040 0.000
#> SRR949128 2 0.1844 0.569 0.016 0.928 0.016 0.000 0.040 0.000
#> SRR949129 2 0.1844 0.569 0.016 0.928 0.016 0.000 0.040 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)
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 16816 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.987 0.994 0.5065 0.493 0.493
#> 3 3 0.849 0.835 0.929 0.3292 0.792 0.598
#> 4 4 0.947 0.905 0.961 0.1232 0.882 0.661
#> 5 5 0.842 0.782 0.867 0.0513 0.908 0.668
#> 6 6 0.833 0.767 0.837 0.0393 0.954 0.788
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
#> SRR949076 1 0.000 0.998 1.000 0.000
#> SRR949078 2 0.000 0.989 0.000 1.000
#> SRR949077 1 0.000 0.998 1.000 0.000
#> SRR949079 1 0.000 0.998 1.000 0.000
#> SRR949080 1 0.000 0.998 1.000 0.000
#> SRR949081 2 0.000 0.989 0.000 1.000
#> SRR949082 2 0.000 0.989 0.000 1.000
#> SRR949083 1 0.000 0.998 1.000 0.000
#> SRR949084 1 0.000 0.998 1.000 0.000
#> SRR949085 2 0.000 0.989 0.000 1.000
#> SRR949087 2 0.000 0.989 0.000 1.000
#> SRR949088 2 0.000 0.989 0.000 1.000
#> SRR949086 2 0.000 0.989 0.000 1.000
#> SRR949089 2 0.000 0.989 0.000 1.000
#> SRR949090 1 0.000 0.998 1.000 0.000
#> SRR949092 1 0.000 0.998 1.000 0.000
#> SRR949093 1 0.000 0.998 1.000 0.000
#> SRR949091 1 0.000 0.998 1.000 0.000
#> SRR949095 2 0.311 0.936 0.056 0.944
#> SRR949094 1 0.000 0.998 1.000 0.000
#> SRR949096 1 0.000 0.998 1.000 0.000
#> SRR949097 1 0.000 0.998 1.000 0.000
#> SRR949098 2 0.000 0.989 0.000 1.000
#> SRR949099 1 0.343 0.930 0.936 0.064
#> SRR949101 2 0.722 0.753 0.200 0.800
#> SRR949100 2 0.000 0.989 0.000 1.000
#> SRR949102 2 0.000 0.989 0.000 1.000
#> SRR949103 1 0.000 0.998 1.000 0.000
#> SRR949104 2 0.000 0.989 0.000 1.000
#> SRR949105 2 0.000 0.989 0.000 1.000
#> SRR949106 2 0.000 0.989 0.000 1.000
#> SRR949107 2 0.000 0.989 0.000 1.000
#> SRR949108 1 0.000 0.998 1.000 0.000
#> SRR949109 1 0.000 0.998 1.000 0.000
#> SRR949110 1 0.000 0.998 1.000 0.000
#> SRR949111 1 0.000 0.998 1.000 0.000
#> SRR949112 1 0.000 0.998 1.000 0.000
#> SRR949113 2 0.000 0.989 0.000 1.000
#> SRR949114 1 0.000 0.998 1.000 0.000
#> SRR949115 1 0.000 0.998 1.000 0.000
#> SRR949116 1 0.000 0.998 1.000 0.000
#> SRR949117 2 0.000 0.989 0.000 1.000
#> SRR949118 2 0.000 0.989 0.000 1.000
#> SRR949119 1 0.000 0.998 1.000 0.000
#> SRR949120 1 0.000 0.998 1.000 0.000
#> SRR949121 1 0.000 0.998 1.000 0.000
#> SRR949122 1 0.000 0.998 1.000 0.000
#> SRR949123 2 0.000 0.989 0.000 1.000
#> SRR949124 2 0.000 0.989 0.000 1.000
#> SRR949125 1 0.000 0.998 1.000 0.000
#> SRR949126 1 0.000 0.998 1.000 0.000
#> SRR949127 2 0.000 0.989 0.000 1.000
#> SRR949128 2 0.000 0.989 0.000 1.000
#> SRR949129 2 0.000 0.989 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR949076 1 0.0424 0.952 0.992 0.000 0.008
#> SRR949078 2 0.0000 0.857 0.000 1.000 0.000
#> SRR949077 1 0.0424 0.952 0.992 0.000 0.008
#> SRR949079 1 0.0424 0.952 0.992 0.000 0.008
#> SRR949080 1 0.0424 0.952 0.992 0.000 0.008
#> SRR949081 2 0.0424 0.853 0.008 0.992 0.000
#> SRR949082 2 0.0000 0.857 0.000 1.000 0.000
#> SRR949083 3 0.0000 0.970 0.000 0.000 1.000
#> SRR949084 3 0.0000 0.970 0.000 0.000 1.000
#> SRR949085 2 0.0000 0.857 0.000 1.000 0.000
#> SRR949087 2 0.0000 0.857 0.000 1.000 0.000
#> SRR949088 2 0.0000 0.857 0.000 1.000 0.000
#> SRR949086 2 0.6095 0.448 0.392 0.608 0.000
#> SRR949089 2 0.0000 0.857 0.000 1.000 0.000
#> SRR949090 1 0.0424 0.952 0.992 0.000 0.008
#> SRR949092 3 0.0000 0.970 0.000 0.000 1.000
#> SRR949093 3 0.0000 0.970 0.000 0.000 1.000
#> SRR949091 1 0.0000 0.946 1.000 0.000 0.000
#> SRR949095 1 0.6244 0.155 0.560 0.440 0.000
#> SRR949094 1 0.0424 0.952 0.992 0.000 0.008
#> SRR949096 3 0.0000 0.970 0.000 0.000 1.000
#> SRR949097 3 0.0000 0.970 0.000 0.000 1.000
#> SRR949098 2 0.0000 0.857 0.000 1.000 0.000
#> SRR949099 3 0.6180 0.259 0.416 0.000 0.584
#> SRR949101 1 0.0424 0.941 0.992 0.008 0.000
#> SRR949100 2 0.6243 0.675 0.124 0.776 0.100
#> SRR949102 1 0.2280 0.896 0.940 0.052 0.008
#> SRR949103 3 0.0000 0.970 0.000 0.000 1.000
#> SRR949104 2 0.0000 0.857 0.000 1.000 0.000
#> SRR949105 2 0.6215 0.385 0.428 0.572 0.000
#> SRR949106 2 0.6215 0.385 0.428 0.572 0.000
#> SRR949107 2 0.6215 0.385 0.428 0.572 0.000
#> SRR949108 3 0.0000 0.970 0.000 0.000 1.000
#> SRR949109 1 0.0424 0.952 0.992 0.000 0.008
#> SRR949110 3 0.0000 0.970 0.000 0.000 1.000
#> SRR949111 1 0.0424 0.952 0.992 0.000 0.008
#> SRR949112 3 0.0000 0.970 0.000 0.000 1.000
#> SRR949113 2 0.0000 0.857 0.000 1.000 0.000
#> SRR949114 3 0.0424 0.965 0.008 0.000 0.992
#> SRR949115 3 0.0424 0.965 0.008 0.000 0.992
#> SRR949116 3 0.0424 0.965 0.008 0.000 0.992
#> SRR949117 2 0.6968 0.647 0.204 0.716 0.080
#> SRR949118 2 0.9625 0.150 0.388 0.408 0.204
#> SRR949119 3 0.0892 0.955 0.020 0.000 0.980
#> SRR949120 3 0.0892 0.955 0.020 0.000 0.980
#> SRR949121 3 0.0000 0.970 0.000 0.000 1.000
#> SRR949122 3 0.0000 0.970 0.000 0.000 1.000
#> SRR949123 2 0.0000 0.857 0.000 1.000 0.000
#> SRR949124 2 0.0000 0.857 0.000 1.000 0.000
#> SRR949125 1 0.0424 0.952 0.992 0.000 0.008
#> SRR949126 1 0.0424 0.952 0.992 0.000 0.008
#> SRR949127 2 0.0000 0.857 0.000 1.000 0.000
#> SRR949128 2 0.0000 0.857 0.000 1.000 0.000
#> SRR949129 2 0.0000 0.857 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR949076 4 0.0000 0.9495 0.000 0.000 0.000 1.000
#> SRR949078 2 0.0000 0.9234 0.000 1.000 0.000 0.000
#> SRR949077 4 0.0000 0.9495 0.000 0.000 0.000 1.000
#> SRR949079 4 0.0000 0.9495 0.000 0.000 0.000 1.000
#> SRR949080 4 0.0000 0.9495 0.000 0.000 0.000 1.000
#> SRR949081 3 0.1302 0.9240 0.000 0.044 0.956 0.000
#> SRR949082 2 0.0000 0.9234 0.000 1.000 0.000 0.000
#> SRR949083 1 0.0000 0.9806 1.000 0.000 0.000 0.000
#> SRR949084 1 0.0000 0.9806 1.000 0.000 0.000 0.000
#> SRR949085 2 0.0000 0.9234 0.000 1.000 0.000 0.000
#> SRR949087 2 0.4382 0.6196 0.000 0.704 0.296 0.000
#> SRR949088 2 0.4382 0.6196 0.000 0.704 0.296 0.000
#> SRR949086 3 0.0000 0.9668 0.000 0.000 1.000 0.000
#> SRR949089 2 0.0000 0.9234 0.000 1.000 0.000 0.000
#> SRR949090 4 0.0000 0.9495 0.000 0.000 0.000 1.000
#> SRR949092 1 0.0000 0.9806 1.000 0.000 0.000 0.000
#> SRR949093 1 0.0000 0.9806 1.000 0.000 0.000 0.000
#> SRR949091 4 0.0000 0.9495 0.000 0.000 0.000 1.000
#> SRR949095 4 0.5000 0.0252 0.000 0.496 0.000 0.504
#> SRR949094 4 0.0000 0.9495 0.000 0.000 0.000 1.000
#> SRR949096 1 0.0000 0.9806 1.000 0.000 0.000 0.000
#> SRR949097 1 0.0000 0.9806 1.000 0.000 0.000 0.000
#> SRR949098 2 0.0000 0.9234 0.000 1.000 0.000 0.000
#> SRR949099 3 0.0000 0.9668 0.000 0.000 1.000 0.000
#> SRR949101 3 0.3801 0.7032 0.000 0.000 0.780 0.220
#> SRR949100 2 0.5459 0.2882 0.000 0.552 0.432 0.016
#> SRR949102 3 0.0188 0.9644 0.000 0.000 0.996 0.004
#> SRR949103 1 0.0000 0.9806 1.000 0.000 0.000 0.000
#> SRR949104 2 0.0000 0.9234 0.000 1.000 0.000 0.000
#> SRR949105 3 0.0000 0.9668 0.000 0.000 1.000 0.000
#> SRR949106 3 0.0000 0.9668 0.000 0.000 1.000 0.000
#> SRR949107 3 0.0000 0.9668 0.000 0.000 1.000 0.000
#> SRR949108 1 0.0000 0.9806 1.000 0.000 0.000 0.000
#> SRR949109 4 0.0000 0.9495 0.000 0.000 0.000 1.000
#> SRR949110 1 0.0000 0.9806 1.000 0.000 0.000 0.000
#> SRR949111 4 0.0000 0.9495 0.000 0.000 0.000 1.000
#> SRR949112 1 0.0000 0.9806 1.000 0.000 0.000 0.000
#> SRR949113 2 0.0000 0.9234 0.000 1.000 0.000 0.000
#> SRR949114 1 0.2281 0.9078 0.904 0.000 0.096 0.000
#> SRR949115 1 0.2281 0.9078 0.904 0.000 0.096 0.000
#> SRR949116 1 0.2281 0.9078 0.904 0.000 0.096 0.000
#> SRR949117 3 0.0000 0.9668 0.000 0.000 1.000 0.000
#> SRR949118 3 0.0000 0.9668 0.000 0.000 1.000 0.000
#> SRR949119 1 0.0336 0.9756 0.992 0.000 0.000 0.008
#> SRR949120 1 0.0336 0.9756 0.992 0.000 0.000 0.008
#> SRR949121 1 0.0000 0.9806 1.000 0.000 0.000 0.000
#> SRR949122 1 0.0000 0.9806 1.000 0.000 0.000 0.000
#> SRR949123 2 0.0000 0.9234 0.000 1.000 0.000 0.000
#> SRR949124 2 0.0000 0.9234 0.000 1.000 0.000 0.000
#> SRR949125 4 0.0000 0.9495 0.000 0.000 0.000 1.000
#> SRR949126 4 0.0000 0.9495 0.000 0.000 0.000 1.000
#> SRR949127 2 0.0000 0.9234 0.000 1.000 0.000 0.000
#> SRR949128 2 0.0000 0.9234 0.000 1.000 0.000 0.000
#> SRR949129 2 0.0000 0.9234 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR949076 4 0.0000 1.00000 0.000 0.000 0.000 1.000 0.000
#> SRR949078 2 0.2516 0.86295 0.000 0.860 0.000 0.000 0.140
#> SRR949077 4 0.0000 1.00000 0.000 0.000 0.000 1.000 0.000
#> SRR949079 4 0.0000 1.00000 0.000 0.000 0.000 1.000 0.000
#> SRR949080 4 0.0000 1.00000 0.000 0.000 0.000 1.000 0.000
#> SRR949081 3 0.3276 0.62935 0.000 0.032 0.836 0.000 0.132
#> SRR949082 2 0.2329 0.86842 0.000 0.876 0.000 0.000 0.124
#> SRR949083 1 0.0162 0.90147 0.996 0.000 0.000 0.000 0.004
#> SRR949084 1 0.0000 0.90086 1.000 0.000 0.000 0.000 0.000
#> SRR949085 2 0.0290 0.89366 0.000 0.992 0.000 0.000 0.008
#> SRR949087 3 0.6418 0.00305 0.000 0.412 0.416 0.000 0.172
#> SRR949088 3 0.6418 0.00305 0.000 0.412 0.416 0.000 0.172
#> SRR949086 3 0.0404 0.63363 0.000 0.000 0.988 0.000 0.012
#> SRR949089 2 0.0000 0.89431 0.000 1.000 0.000 0.000 0.000
#> SRR949090 4 0.0000 1.00000 0.000 0.000 0.000 1.000 0.000
#> SRR949092 1 0.0162 0.90147 0.996 0.000 0.000 0.000 0.004
#> SRR949093 1 0.0162 0.90147 0.996 0.000 0.000 0.000 0.004
#> SRR949091 4 0.0000 1.00000 0.000 0.000 0.000 1.000 0.000
#> SRR949095 2 0.5997 0.27274 0.004 0.556 0.016 0.356 0.068
#> SRR949094 4 0.0000 1.00000 0.000 0.000 0.000 1.000 0.000
#> SRR949096 1 0.0162 0.90147 0.996 0.000 0.000 0.000 0.004
#> SRR949097 1 0.0162 0.90147 0.996 0.000 0.000 0.000 0.004
#> SRR949098 2 0.0000 0.89431 0.000 1.000 0.000 0.000 0.000
#> SRR949099 3 0.1341 0.61735 0.000 0.000 0.944 0.000 0.056
#> SRR949101 3 0.6422 0.41585 0.000 0.000 0.460 0.180 0.360
#> SRR949100 3 0.7055 0.26148 0.000 0.160 0.488 0.040 0.312
#> SRR949102 3 0.2877 0.60091 0.000 0.004 0.848 0.004 0.144
#> SRR949103 1 0.0162 0.90147 0.996 0.000 0.000 0.000 0.004
#> SRR949104 2 0.0000 0.89431 0.000 1.000 0.000 0.000 0.000
#> SRR949105 3 0.4126 0.56209 0.000 0.000 0.620 0.000 0.380
#> SRR949106 3 0.4126 0.56209 0.000 0.000 0.620 0.000 0.380
#> SRR949107 3 0.4126 0.56209 0.000 0.000 0.620 0.000 0.380
#> SRR949108 1 0.0000 0.90086 1.000 0.000 0.000 0.000 0.000
#> SRR949109 4 0.0000 1.00000 0.000 0.000 0.000 1.000 0.000
#> SRR949110 1 0.0162 0.89858 0.996 0.000 0.000 0.000 0.004
#> SRR949111 4 0.0000 1.00000 0.000 0.000 0.000 1.000 0.000
#> SRR949112 1 0.3074 0.56588 0.804 0.000 0.000 0.000 0.196
#> SRR949113 2 0.0000 0.89431 0.000 1.000 0.000 0.000 0.000
#> SRR949114 5 0.6335 1.00000 0.352 0.000 0.168 0.000 0.480
#> SRR949115 5 0.6335 1.00000 0.352 0.000 0.168 0.000 0.480
#> SRR949116 5 0.6335 1.00000 0.352 0.000 0.168 0.000 0.480
#> SRR949117 3 0.1197 0.63450 0.000 0.000 0.952 0.000 0.048
#> SRR949118 3 0.1121 0.62257 0.000 0.000 0.956 0.000 0.044
#> SRR949119 1 0.5038 0.38404 0.692 0.000 0.032 0.028 0.248
#> SRR949120 1 0.5038 0.38404 0.692 0.000 0.032 0.028 0.248
#> SRR949121 1 0.0162 0.89858 0.996 0.000 0.000 0.000 0.004
#> SRR949122 1 0.0000 0.90086 1.000 0.000 0.000 0.000 0.000
#> SRR949123 2 0.0000 0.89431 0.000 1.000 0.000 0.000 0.000
#> SRR949124 2 0.0000 0.89431 0.000 1.000 0.000 0.000 0.000
#> SRR949125 4 0.0000 1.00000 0.000 0.000 0.000 1.000 0.000
#> SRR949126 4 0.0000 1.00000 0.000 0.000 0.000 1.000 0.000
#> SRR949127 2 0.2516 0.86295 0.000 0.860 0.000 0.000 0.140
#> SRR949128 2 0.2516 0.86295 0.000 0.860 0.000 0.000 0.140
#> SRR949129 2 0.2516 0.86295 0.000 0.860 0.000 0.000 0.140
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR949076 4 0.0146 0.996 0.000 0.000 0.000 0.996 0.004 0.000
#> SRR949078 2 0.3742 0.677 0.000 0.648 0.004 0.000 0.348 0.000
#> SRR949077 4 0.0146 0.996 0.000 0.000 0.000 0.996 0.004 0.000
#> SRR949079 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949080 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949081 5 0.5701 0.432 0.000 0.004 0.256 0.000 0.544 0.196
#> SRR949082 2 0.3547 0.700 0.000 0.696 0.004 0.000 0.300 0.000
#> SRR949083 1 0.0146 0.946 0.996 0.000 0.000 0.000 0.004 0.000
#> SRR949084 1 0.0725 0.940 0.976 0.000 0.000 0.000 0.012 0.012
#> SRR949085 2 0.0547 0.791 0.000 0.980 0.000 0.000 0.020 0.000
#> SRR949087 5 0.4111 0.378 0.000 0.144 0.108 0.000 0.748 0.000
#> SRR949088 5 0.4111 0.378 0.000 0.144 0.108 0.000 0.748 0.000
#> SRR949086 5 0.5887 0.488 0.000 0.000 0.392 0.000 0.408 0.200
#> SRR949089 2 0.0000 0.794 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949090 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949092 1 0.0146 0.946 0.996 0.000 0.000 0.000 0.004 0.000
#> SRR949093 1 0.0146 0.946 0.996 0.000 0.000 0.000 0.004 0.000
#> SRR949091 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949095 2 0.6887 0.295 0.012 0.568 0.048 0.228 0.084 0.060
#> SRR949094 4 0.0405 0.989 0.000 0.000 0.000 0.988 0.008 0.004
#> SRR949096 1 0.0520 0.941 0.984 0.000 0.000 0.000 0.008 0.008
#> SRR949097 1 0.0291 0.945 0.992 0.000 0.000 0.000 0.004 0.004
#> SRR949098 2 0.0000 0.794 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949099 5 0.5987 0.533 0.000 0.000 0.300 0.000 0.440 0.260
#> SRR949101 3 0.3906 0.713 0.000 0.000 0.796 0.120 0.052 0.032
#> SRR949100 5 0.5472 0.452 0.000 0.064 0.048 0.008 0.648 0.232
#> SRR949102 5 0.5999 0.369 0.000 0.008 0.212 0.000 0.492 0.288
#> SRR949103 1 0.0291 0.945 0.992 0.000 0.000 0.000 0.004 0.004
#> SRR949104 2 0.0000 0.794 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949105 3 0.0000 0.903 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR949106 3 0.0000 0.903 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR949107 3 0.0000 0.903 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR949108 1 0.0725 0.940 0.976 0.000 0.000 0.000 0.012 0.012
#> SRR949109 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949110 1 0.0622 0.942 0.980 0.000 0.000 0.000 0.008 0.012
#> SRR949111 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949112 1 0.3684 0.389 0.664 0.000 0.000 0.000 0.004 0.332
#> SRR949113 2 0.0000 0.794 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949114 6 0.3275 0.671 0.140 0.000 0.032 0.000 0.008 0.820
#> SRR949115 6 0.3275 0.671 0.140 0.000 0.032 0.000 0.008 0.820
#> SRR949116 6 0.3275 0.671 0.140 0.000 0.032 0.000 0.008 0.820
#> SRR949117 5 0.5809 0.507 0.000 0.000 0.360 0.000 0.452 0.188
#> SRR949118 5 0.6016 0.518 0.000 0.000 0.340 0.000 0.412 0.248
#> SRR949119 6 0.6663 0.499 0.312 0.000 0.008 0.032 0.200 0.448
#> SRR949120 6 0.6663 0.499 0.312 0.000 0.008 0.032 0.200 0.448
#> SRR949121 1 0.0622 0.942 0.980 0.000 0.000 0.000 0.008 0.012
#> SRR949122 1 0.1049 0.927 0.960 0.000 0.000 0.000 0.008 0.032
#> SRR949123 2 0.0000 0.794 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949124 2 0.0000 0.794 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949125 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949126 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949127 2 0.3830 0.660 0.000 0.620 0.004 0.000 0.376 0.000
#> SRR949128 2 0.3830 0.660 0.000 0.620 0.004 0.000 0.376 0.000
#> SRR949129 2 0.3830 0.660 0.000 0.620 0.004 0.000 0.376 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)
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 16816 rows and 54 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 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 0.456 0.912 0.852 0.4324 0.547 0.547
#> 3 3 0.752 0.767 0.874 0.2879 0.942 0.894
#> 4 4 0.954 0.933 0.977 0.2273 0.816 0.626
#> 5 5 0.762 0.763 0.759 0.1052 0.900 0.676
#> 6 6 0.758 0.512 0.764 0.0564 0.864 0.492
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
#> SRR949076 1 0.5842 0.874 0.860 0.140
#> SRR949078 2 0.5842 0.961 0.140 0.860
#> SRR949077 1 0.5842 0.874 0.860 0.140
#> SRR949079 1 0.5842 0.874 0.860 0.140
#> SRR949080 1 0.5842 0.874 0.860 0.140
#> SRR949081 2 0.6801 0.932 0.180 0.820
#> SRR949082 2 0.5842 0.961 0.140 0.860
#> SRR949083 1 0.0000 0.933 1.000 0.000
#> SRR949084 1 0.0000 0.933 1.000 0.000
#> SRR949085 2 0.5842 0.961 0.140 0.860
#> SRR949087 2 0.5842 0.961 0.140 0.860
#> SRR949088 2 0.5842 0.961 0.140 0.860
#> SRR949086 1 0.0376 0.931 0.996 0.004
#> SRR949089 2 0.5842 0.961 0.140 0.860
#> SRR949090 1 0.5842 0.874 0.860 0.140
#> SRR949092 1 0.0000 0.933 1.000 0.000
#> SRR949093 1 0.0000 0.933 1.000 0.000
#> SRR949091 1 0.5842 0.874 0.860 0.140
#> SRR949095 1 0.4815 0.827 0.896 0.104
#> SRR949094 1 0.5842 0.874 0.860 0.140
#> SRR949096 1 0.0000 0.933 1.000 0.000
#> SRR949097 1 0.0000 0.933 1.000 0.000
#> SRR949098 2 0.5842 0.961 0.140 0.860
#> SRR949099 1 0.0000 0.933 1.000 0.000
#> SRR949101 1 0.6712 0.763 0.824 0.176
#> SRR949100 1 0.3879 0.863 0.924 0.076
#> SRR949102 1 0.2423 0.900 0.960 0.040
#> SRR949103 1 0.0000 0.933 1.000 0.000
#> SRR949104 2 0.5842 0.961 0.140 0.860
#> SRR949105 2 0.9580 0.643 0.380 0.620
#> SRR949106 2 0.8327 0.843 0.264 0.736
#> SRR949107 2 0.8443 0.832 0.272 0.728
#> SRR949108 1 0.0000 0.933 1.000 0.000
#> SRR949109 1 0.5294 0.883 0.880 0.120
#> SRR949110 1 0.0000 0.933 1.000 0.000
#> SRR949111 1 0.5842 0.874 0.860 0.140
#> SRR949112 1 0.0000 0.933 1.000 0.000
#> SRR949113 2 0.5842 0.961 0.140 0.860
#> SRR949114 1 0.0000 0.933 1.000 0.000
#> SRR949115 1 0.0000 0.933 1.000 0.000
#> SRR949116 1 0.0000 0.933 1.000 0.000
#> SRR949117 1 0.0376 0.931 0.996 0.004
#> SRR949118 1 0.0376 0.931 0.996 0.004
#> SRR949119 1 0.0000 0.933 1.000 0.000
#> SRR949120 1 0.0000 0.933 1.000 0.000
#> SRR949121 1 0.0000 0.933 1.000 0.000
#> SRR949122 1 0.0000 0.933 1.000 0.000
#> SRR949123 2 0.6247 0.951 0.156 0.844
#> SRR949124 2 0.5842 0.961 0.140 0.860
#> SRR949125 1 0.5842 0.874 0.860 0.140
#> SRR949126 1 0.5842 0.874 0.860 0.140
#> SRR949127 2 0.5842 0.961 0.140 0.860
#> SRR949128 2 0.5842 0.961 0.140 0.860
#> SRR949129 2 0.5842 0.961 0.140 0.860
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR949076 1 0.0892 0.5772 0.980 0.000 0.020
#> SRR949078 2 0.6126 0.9537 0.000 0.600 0.400
#> SRR949077 1 0.0892 0.5772 0.980 0.000 0.020
#> SRR949079 1 0.0892 0.5772 0.980 0.000 0.020
#> SRR949080 1 0.0892 0.5772 0.980 0.000 0.020
#> SRR949081 2 0.6968 0.3211 0.080 0.716 0.204
#> SRR949082 2 0.5926 0.8887 0.000 0.644 0.356
#> SRR949083 1 0.6126 0.8215 0.600 0.400 0.000
#> SRR949084 1 0.6126 0.8215 0.600 0.400 0.000
#> SRR949085 2 0.6126 0.9537 0.000 0.600 0.400
#> SRR949087 2 0.6126 0.9537 0.000 0.600 0.400
#> SRR949088 2 0.6126 0.9537 0.000 0.600 0.400
#> SRR949086 1 0.6126 0.8215 0.600 0.400 0.000
#> SRR949089 2 0.6126 0.9537 0.000 0.600 0.400
#> SRR949090 1 0.0892 0.5772 0.980 0.000 0.020
#> SRR949092 1 0.6126 0.8215 0.600 0.400 0.000
#> SRR949093 1 0.6126 0.8215 0.600 0.400 0.000
#> SRR949091 1 0.0892 0.5772 0.980 0.000 0.020
#> SRR949095 1 0.5926 0.7939 0.644 0.356 0.000
#> SRR949094 1 0.0000 0.5889 1.000 0.000 0.000
#> SRR949096 1 0.6126 0.8215 0.600 0.400 0.000
#> SRR949097 1 0.6126 0.8215 0.600 0.400 0.000
#> SRR949098 2 0.6126 0.9537 0.000 0.600 0.400
#> SRR949099 1 0.6126 0.8215 0.600 0.400 0.000
#> SRR949101 3 0.9512 0.0186 0.188 0.384 0.428
#> SRR949100 1 0.6111 0.8197 0.604 0.396 0.000
#> SRR949102 1 0.6095 0.8178 0.608 0.392 0.000
#> SRR949103 1 0.6126 0.8215 0.600 0.400 0.000
#> SRR949104 2 0.6126 0.9537 0.000 0.600 0.400
#> SRR949105 3 0.4551 0.6185 0.020 0.140 0.840
#> SRR949106 3 0.2846 0.5789 0.020 0.056 0.924
#> SRR949107 3 0.2636 0.5625 0.020 0.048 0.932
#> SRR949108 1 0.6126 0.8215 0.600 0.400 0.000
#> SRR949109 1 0.0424 0.5933 0.992 0.008 0.000
#> SRR949110 1 0.6126 0.8215 0.600 0.400 0.000
#> SRR949111 1 0.0892 0.5772 0.980 0.000 0.020
#> SRR949112 1 0.6126 0.8215 0.600 0.400 0.000
#> SRR949113 2 0.6126 0.9537 0.000 0.600 0.400
#> SRR949114 1 0.6126 0.8215 0.600 0.400 0.000
#> SRR949115 1 0.6126 0.8215 0.600 0.400 0.000
#> SRR949116 1 0.6126 0.8215 0.600 0.400 0.000
#> SRR949117 1 0.6126 0.8215 0.600 0.400 0.000
#> SRR949118 1 0.6126 0.8215 0.600 0.400 0.000
#> SRR949119 1 0.6126 0.8215 0.600 0.400 0.000
#> SRR949120 1 0.6126 0.8215 0.600 0.400 0.000
#> SRR949121 1 0.6126 0.8215 0.600 0.400 0.000
#> SRR949122 1 0.6126 0.8215 0.600 0.400 0.000
#> SRR949123 2 0.6617 0.9209 0.012 0.600 0.388
#> SRR949124 2 0.6126 0.9537 0.000 0.600 0.400
#> SRR949125 1 0.0892 0.5772 0.980 0.000 0.020
#> SRR949126 1 0.0892 0.5772 0.980 0.000 0.020
#> SRR949127 2 0.6126 0.9537 0.000 0.600 0.400
#> SRR949128 2 0.6126 0.9537 0.000 0.600 0.400
#> SRR949129 2 0.6126 0.9537 0.000 0.600 0.400
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR949076 4 0.0188 0.919 0.004 0.000 0.0 0.996
#> SRR949078 2 0.0000 0.968 0.000 1.000 0.0 0.000
#> SRR949077 4 0.0000 0.922 0.000 0.000 0.0 1.000
#> SRR949079 4 0.0000 0.922 0.000 0.000 0.0 1.000
#> SRR949080 4 0.0000 0.922 0.000 0.000 0.0 1.000
#> SRR949081 2 0.4072 0.577 0.252 0.748 0.0 0.000
#> SRR949082 2 0.1022 0.934 0.032 0.968 0.0 0.000
#> SRR949083 1 0.0000 0.987 1.000 0.000 0.0 0.000
#> SRR949084 1 0.0000 0.987 1.000 0.000 0.0 0.000
#> SRR949085 2 0.0000 0.968 0.000 1.000 0.0 0.000
#> SRR949087 2 0.0000 0.968 0.000 1.000 0.0 0.000
#> SRR949088 2 0.0000 0.968 0.000 1.000 0.0 0.000
#> SRR949086 1 0.0000 0.987 1.000 0.000 0.0 0.000
#> SRR949089 2 0.0000 0.968 0.000 1.000 0.0 0.000
#> SRR949090 4 0.0000 0.922 0.000 0.000 0.0 1.000
#> SRR949092 1 0.0000 0.987 1.000 0.000 0.0 0.000
#> SRR949093 1 0.0000 0.987 1.000 0.000 0.0 0.000
#> SRR949091 4 0.0000 0.922 0.000 0.000 0.0 1.000
#> SRR949095 1 0.3764 0.699 0.784 0.000 0.0 0.216
#> SRR949094 4 0.2921 0.754 0.140 0.000 0.0 0.860
#> SRR949096 1 0.0000 0.987 1.000 0.000 0.0 0.000
#> SRR949097 1 0.0000 0.987 1.000 0.000 0.0 0.000
#> SRR949098 2 0.0000 0.968 0.000 1.000 0.0 0.000
#> SRR949099 1 0.0000 0.987 1.000 0.000 0.0 0.000
#> SRR949101 3 0.4290 0.722 0.164 0.000 0.8 0.036
#> SRR949100 1 0.0524 0.977 0.988 0.004 0.0 0.008
#> SRR949102 1 0.1004 0.960 0.972 0.004 0.0 0.024
#> SRR949103 1 0.0000 0.987 1.000 0.000 0.0 0.000
#> SRR949104 2 0.0000 0.968 0.000 1.000 0.0 0.000
#> SRR949105 3 0.0000 0.913 0.000 0.000 1.0 0.000
#> SRR949106 3 0.0000 0.913 0.000 0.000 1.0 0.000
#> SRR949107 3 0.0000 0.913 0.000 0.000 1.0 0.000
#> SRR949108 1 0.0000 0.987 1.000 0.000 0.0 0.000
#> SRR949109 4 0.4522 0.464 0.320 0.000 0.0 0.680
#> SRR949110 1 0.0000 0.987 1.000 0.000 0.0 0.000
#> SRR949111 4 0.0817 0.902 0.024 0.000 0.0 0.976
#> SRR949112 1 0.0000 0.987 1.000 0.000 0.0 0.000
#> SRR949113 2 0.0000 0.968 0.000 1.000 0.0 0.000
#> SRR949114 1 0.0000 0.987 1.000 0.000 0.0 0.000
#> SRR949115 1 0.0000 0.987 1.000 0.000 0.0 0.000
#> SRR949116 1 0.0000 0.987 1.000 0.000 0.0 0.000
#> SRR949117 1 0.0000 0.987 1.000 0.000 0.0 0.000
#> SRR949118 1 0.0188 0.983 0.996 0.004 0.0 0.000
#> SRR949119 1 0.0000 0.987 1.000 0.000 0.0 0.000
#> SRR949120 1 0.0000 0.987 1.000 0.000 0.0 0.000
#> SRR949121 1 0.0000 0.987 1.000 0.000 0.0 0.000
#> SRR949122 1 0.0000 0.987 1.000 0.000 0.0 0.000
#> SRR949123 2 0.0817 0.944 0.024 0.976 0.0 0.000
#> SRR949124 2 0.0000 0.968 0.000 1.000 0.0 0.000
#> SRR949125 4 0.0000 0.922 0.000 0.000 0.0 1.000
#> SRR949126 4 0.0000 0.922 0.000 0.000 0.0 1.000
#> SRR949127 2 0.0000 0.968 0.000 1.000 0.0 0.000
#> SRR949128 2 0.0000 0.968 0.000 1.000 0.0 0.000
#> SRR949129 2 0.0000 0.968 0.000 1.000 0.0 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR949076 4 0.0162 0.9329 0.000 0.000 0.004 0.996 0.000
#> SRR949078 2 0.0000 0.8348 0.000 1.000 0.000 0.000 0.000
#> SRR949077 4 0.0000 0.9354 0.000 0.000 0.000 1.000 0.000
#> SRR949079 4 0.0000 0.9354 0.000 0.000 0.000 1.000 0.000
#> SRR949080 4 0.0000 0.9354 0.000 0.000 0.000 1.000 0.000
#> SRR949081 2 0.4392 0.3310 0.008 0.612 0.380 0.000 0.000
#> SRR949082 2 0.1121 0.8118 0.000 0.956 0.044 0.000 0.000
#> SRR949083 1 0.4045 0.9821 0.644 0.000 0.356 0.000 0.000
#> SRR949084 1 0.4045 0.9821 0.644 0.000 0.356 0.000 0.000
#> SRR949085 2 0.0000 0.8348 0.000 1.000 0.000 0.000 0.000
#> SRR949087 2 0.0000 0.8348 0.000 1.000 0.000 0.000 0.000
#> SRR949088 2 0.0000 0.8348 0.000 1.000 0.000 0.000 0.000
#> SRR949086 3 0.2516 0.5942 0.140 0.000 0.860 0.000 0.000
#> SRR949089 2 0.3796 0.7895 0.300 0.700 0.000 0.000 0.000
#> SRR949090 4 0.0000 0.9354 0.000 0.000 0.000 1.000 0.000
#> SRR949092 1 0.4045 0.9821 0.644 0.000 0.356 0.000 0.000
#> SRR949093 1 0.4045 0.9821 0.644 0.000 0.356 0.000 0.000
#> SRR949091 4 0.0000 0.9354 0.000 0.000 0.000 1.000 0.000
#> SRR949095 3 0.6453 0.0864 0.180 0.000 0.432 0.388 0.000
#> SRR949094 4 0.3281 0.7683 0.060 0.000 0.092 0.848 0.000
#> SRR949096 1 0.4045 0.9821 0.644 0.000 0.356 0.000 0.000
#> SRR949097 1 0.4045 0.9821 0.644 0.000 0.356 0.000 0.000
#> SRR949098 2 0.3796 0.7895 0.300 0.700 0.000 0.000 0.000
#> SRR949099 3 0.0404 0.6867 0.012 0.000 0.988 0.000 0.000
#> SRR949101 5 0.4768 0.4291 0.000 0.000 0.384 0.024 0.592
#> SRR949100 3 0.6284 0.1368 0.136 0.372 0.488 0.004 0.000
#> SRR949102 3 0.0693 0.6806 0.008 0.000 0.980 0.012 0.000
#> SRR949103 1 0.4045 0.9821 0.644 0.000 0.356 0.000 0.000
#> SRR949104 2 0.3796 0.7895 0.300 0.700 0.000 0.000 0.000
#> SRR949105 5 0.0000 0.8669 0.000 0.000 0.000 0.000 1.000
#> SRR949106 5 0.0000 0.8669 0.000 0.000 0.000 0.000 1.000
#> SRR949107 5 0.0000 0.8669 0.000 0.000 0.000 0.000 1.000
#> SRR949108 1 0.4045 0.9821 0.644 0.000 0.356 0.000 0.000
#> SRR949109 4 0.4696 0.6072 0.156 0.000 0.108 0.736 0.000
#> SRR949110 1 0.4235 0.8297 0.576 0.000 0.424 0.000 0.000
#> SRR949111 4 0.0798 0.9168 0.008 0.000 0.016 0.976 0.000
#> SRR949112 3 0.2424 0.6027 0.132 0.000 0.868 0.000 0.000
#> SRR949113 2 0.3796 0.7895 0.300 0.700 0.000 0.000 0.000
#> SRR949114 3 0.0000 0.6891 0.000 0.000 1.000 0.000 0.000
#> SRR949115 3 0.0000 0.6891 0.000 0.000 1.000 0.000 0.000
#> SRR949116 3 0.0000 0.6891 0.000 0.000 1.000 0.000 0.000
#> SRR949117 3 0.4251 -0.1342 0.372 0.004 0.624 0.000 0.000
#> SRR949118 3 0.0000 0.6891 0.000 0.000 1.000 0.000 0.000
#> SRR949119 3 0.4030 0.3131 0.352 0.000 0.648 0.000 0.000
#> SRR949120 3 0.4045 0.3007 0.356 0.000 0.644 0.000 0.000
#> SRR949121 1 0.4074 0.9698 0.636 0.000 0.364 0.000 0.000
#> SRR949122 1 0.4060 0.9763 0.640 0.000 0.360 0.000 0.000
#> SRR949123 2 0.3796 0.7895 0.300 0.700 0.000 0.000 0.000
#> SRR949124 2 0.3796 0.7895 0.300 0.700 0.000 0.000 0.000
#> SRR949125 4 0.0000 0.9354 0.000 0.000 0.000 1.000 0.000
#> SRR949126 4 0.0000 0.9354 0.000 0.000 0.000 1.000 0.000
#> SRR949127 2 0.0000 0.8348 0.000 1.000 0.000 0.000 0.000
#> SRR949128 2 0.0000 0.8348 0.000 1.000 0.000 0.000 0.000
#> SRR949129 2 0.0000 0.8348 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR949076 4 0.0146 0.8798 0.004 0.000 0.00 0.996 0.000 0.000
#> SRR949078 6 0.3864 -0.0635 0.000 0.480 0.00 0.000 0.000 0.520
#> SRR949077 4 0.0000 0.8821 0.000 0.000 0.00 1.000 0.000 0.000
#> SRR949079 4 0.0000 0.8821 0.000 0.000 0.00 1.000 0.000 0.000
#> SRR949080 4 0.0000 0.8821 0.000 0.000 0.00 1.000 0.000 0.000
#> SRR949081 2 0.7009 0.2099 0.132 0.480 0.00 0.000 0.196 0.192
#> SRR949082 6 0.4535 -0.1045 0.032 0.480 0.00 0.000 0.000 0.488
#> SRR949083 1 0.0000 0.9327 1.000 0.000 0.00 0.000 0.000 0.000
#> SRR949084 1 0.0000 0.9327 1.000 0.000 0.00 0.000 0.000 0.000
#> SRR949085 6 0.3864 -0.0635 0.000 0.480 0.00 0.000 0.000 0.520
#> SRR949087 6 0.3864 -0.0635 0.000 0.480 0.00 0.000 0.000 0.520
#> SRR949088 6 0.3864 -0.0635 0.000 0.480 0.00 0.000 0.000 0.520
#> SRR949086 6 0.5655 -0.2971 0.360 0.000 0.00 0.000 0.160 0.480
#> SRR949089 2 0.0000 0.8003 0.000 1.000 0.00 0.000 0.000 0.000
#> SRR949090 4 0.0000 0.8821 0.000 0.000 0.00 1.000 0.000 0.000
#> SRR949092 1 0.0000 0.9327 1.000 0.000 0.00 0.000 0.000 0.000
#> SRR949093 1 0.0000 0.9327 1.000 0.000 0.00 0.000 0.000 0.000
#> SRR949091 4 0.0000 0.8821 0.000 0.000 0.00 1.000 0.000 0.000
#> SRR949095 4 0.6090 -0.0565 0.380 0.000 0.00 0.472 0.108 0.040
#> SRR949094 4 0.2454 0.7276 0.160 0.000 0.00 0.840 0.000 0.000
#> SRR949096 1 0.0000 0.9327 1.000 0.000 0.00 0.000 0.000 0.000
#> SRR949097 1 0.0000 0.9327 1.000 0.000 0.00 0.000 0.000 0.000
#> SRR949098 2 0.0000 0.8003 0.000 1.000 0.00 0.000 0.000 0.000
#> SRR949099 6 0.5655 -0.1234 0.160 0.000 0.00 0.000 0.360 0.480
#> SRR949101 3 0.4246 0.3286 0.000 0.000 0.58 0.000 0.400 0.020
#> SRR949100 2 0.6048 0.1237 0.340 0.476 0.00 0.004 0.172 0.008
#> SRR949102 5 0.1957 0.3810 0.112 0.000 0.00 0.000 0.888 0.000
#> SRR949103 1 0.0000 0.9327 1.000 0.000 0.00 0.000 0.000 0.000
#> SRR949104 2 0.0000 0.8003 0.000 1.000 0.00 0.000 0.000 0.000
#> SRR949105 3 0.0000 0.8271 0.000 0.000 1.00 0.000 0.000 0.000
#> SRR949106 3 0.0000 0.8271 0.000 0.000 1.00 0.000 0.000 0.000
#> SRR949107 3 0.0000 0.8271 0.000 0.000 1.00 0.000 0.000 0.000
#> SRR949108 1 0.0000 0.9327 1.000 0.000 0.00 0.000 0.000 0.000
#> SRR949109 4 0.3405 0.5463 0.272 0.000 0.00 0.724 0.000 0.004
#> SRR949110 1 0.1387 0.8318 0.932 0.000 0.00 0.000 0.068 0.000
#> SRR949111 4 0.0632 0.8671 0.024 0.000 0.00 0.976 0.000 0.000
#> SRR949112 6 0.5848 -0.2458 0.296 0.000 0.00 0.000 0.224 0.480
#> SRR949113 2 0.0000 0.8003 0.000 1.000 0.00 0.000 0.000 0.000
#> SRR949114 6 0.5404 -0.0880 0.116 0.000 0.00 0.000 0.404 0.480
#> SRR949115 6 0.5404 -0.0880 0.116 0.000 0.00 0.000 0.404 0.480
#> SRR949116 6 0.5404 -0.0880 0.116 0.000 0.00 0.000 0.404 0.480
#> SRR949117 1 0.4851 0.2146 0.632 0.000 0.00 0.000 0.096 0.272
#> SRR949118 6 0.5404 -0.0880 0.116 0.000 0.00 0.000 0.404 0.480
#> SRR949119 5 0.3464 0.7068 0.312 0.000 0.00 0.000 0.688 0.000
#> SRR949120 5 0.3464 0.7068 0.312 0.000 0.00 0.000 0.688 0.000
#> SRR949121 1 0.0146 0.9290 0.996 0.000 0.00 0.000 0.004 0.000
#> SRR949122 1 0.0458 0.9141 0.984 0.000 0.00 0.000 0.016 0.000
#> SRR949123 2 0.0000 0.8003 0.000 1.000 0.00 0.000 0.000 0.000
#> SRR949124 2 0.0000 0.8003 0.000 1.000 0.00 0.000 0.000 0.000
#> SRR949125 4 0.0000 0.8821 0.000 0.000 0.00 1.000 0.000 0.000
#> SRR949126 4 0.0000 0.8821 0.000 0.000 0.00 1.000 0.000 0.000
#> SRR949127 6 0.3864 -0.0635 0.000 0.480 0.00 0.000 0.000 0.520
#> SRR949128 6 0.3864 -0.0635 0.000 0.480 0.00 0.000 0.000 0.520
#> SRR949129 6 0.3864 -0.0635 0.000 0.480 0.00 0.000 0.000 0.520
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)
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 16816 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.885 0.954 0.969 0.5065 0.493 0.493
#> 3 3 0.470 0.680 0.855 0.2884 0.734 0.512
#> 4 4 0.691 0.717 0.848 0.0884 0.923 0.787
#> 5 5 0.820 0.844 0.921 0.0941 0.843 0.543
#> 6 6 0.878 0.837 0.890 0.0393 0.975 0.882
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
#> SRR949076 2 0.0938 0.959 0.012 0.988
#> SRR949078 2 0.1184 0.959 0.016 0.984
#> SRR949077 2 0.0938 0.959 0.012 0.988
#> SRR949079 2 0.0938 0.959 0.012 0.988
#> SRR949080 2 0.0938 0.959 0.012 0.988
#> SRR949081 2 0.7602 0.774 0.220 0.780
#> SRR949082 2 0.1843 0.956 0.028 0.972
#> SRR949083 1 0.0000 0.988 1.000 0.000
#> SRR949084 1 0.0000 0.988 1.000 0.000
#> SRR949085 2 0.1184 0.959 0.016 0.984
#> SRR949087 2 0.5629 0.874 0.132 0.868
#> SRR949088 2 0.5842 0.867 0.140 0.860
#> SRR949086 1 0.1633 0.979 0.976 0.024
#> SRR949089 2 0.1184 0.959 0.016 0.984
#> SRR949090 2 0.0938 0.959 0.012 0.988
#> SRR949092 1 0.0000 0.988 1.000 0.000
#> SRR949093 1 0.0000 0.988 1.000 0.000
#> SRR949091 2 0.0938 0.959 0.012 0.988
#> SRR949095 2 0.1843 0.958 0.028 0.972
#> SRR949094 2 0.0938 0.959 0.012 0.988
#> SRR949096 1 0.0000 0.988 1.000 0.000
#> SRR949097 1 0.0000 0.988 1.000 0.000
#> SRR949098 2 0.1184 0.959 0.016 0.984
#> SRR949099 1 0.0938 0.985 0.988 0.012
#> SRR949101 1 0.6623 0.806 0.828 0.172
#> SRR949100 2 0.8327 0.715 0.264 0.736
#> SRR949102 2 0.6247 0.843 0.156 0.844
#> SRR949103 1 0.0000 0.988 1.000 0.000
#> SRR949104 2 0.1184 0.959 0.016 0.984
#> SRR949105 1 0.1843 0.978 0.972 0.028
#> SRR949106 1 0.1843 0.978 0.972 0.028
#> SRR949107 1 0.1843 0.978 0.972 0.028
#> SRR949108 1 0.0000 0.988 1.000 0.000
#> SRR949109 2 0.0938 0.959 0.012 0.988
#> SRR949110 1 0.0000 0.988 1.000 0.000
#> SRR949111 2 0.0938 0.959 0.012 0.988
#> SRR949112 1 0.0000 0.988 1.000 0.000
#> SRR949113 2 0.1184 0.959 0.016 0.984
#> SRR949114 1 0.0000 0.988 1.000 0.000
#> SRR949115 1 0.0000 0.988 1.000 0.000
#> SRR949116 1 0.0000 0.988 1.000 0.000
#> SRR949117 1 0.1184 0.983 0.984 0.016
#> SRR949118 1 0.1414 0.982 0.980 0.020
#> SRR949119 1 0.0376 0.987 0.996 0.004
#> SRR949120 1 0.0376 0.987 0.996 0.004
#> SRR949121 1 0.0000 0.988 1.000 0.000
#> SRR949122 1 0.0000 0.988 1.000 0.000
#> SRR949123 2 0.1184 0.959 0.016 0.984
#> SRR949124 2 0.1184 0.959 0.016 0.984
#> SRR949125 2 0.0938 0.959 0.012 0.988
#> SRR949126 2 0.0938 0.959 0.012 0.988
#> SRR949127 2 0.1843 0.956 0.028 0.972
#> SRR949128 2 0.1843 0.956 0.028 0.972
#> SRR949129 2 0.1843 0.956 0.028 0.972
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR949076 1 0.0000 0.8034 1.000 0.000 0.000
#> SRR949078 2 0.3192 0.7740 0.000 0.888 0.112
#> SRR949077 1 0.0000 0.8034 1.000 0.000 0.000
#> SRR949079 1 0.0000 0.8034 1.000 0.000 0.000
#> SRR949080 1 0.0000 0.8034 1.000 0.000 0.000
#> SRR949081 1 0.8702 0.4263 0.568 0.140 0.292
#> SRR949082 2 0.3752 0.7404 0.000 0.856 0.144
#> SRR949083 3 0.0000 0.8417 0.000 0.000 1.000
#> SRR949084 3 0.0000 0.8417 0.000 0.000 1.000
#> SRR949085 2 0.0592 0.8288 0.000 0.988 0.012
#> SRR949087 1 0.9515 0.3297 0.480 0.216 0.304
#> SRR949088 1 0.9471 0.3310 0.484 0.208 0.308
#> SRR949086 3 0.8571 0.3617 0.272 0.140 0.588
#> SRR949089 2 0.0424 0.8290 0.000 0.992 0.008
#> SRR949090 1 0.0000 0.8034 1.000 0.000 0.000
#> SRR949092 3 0.0000 0.8417 0.000 0.000 1.000
#> SRR949093 3 0.0000 0.8417 0.000 0.000 1.000
#> SRR949091 1 0.0000 0.8034 1.000 0.000 0.000
#> SRR949095 3 0.9541 0.0540 0.348 0.200 0.452
#> SRR949094 1 0.0000 0.8034 1.000 0.000 0.000
#> SRR949096 3 0.0000 0.8417 0.000 0.000 1.000
#> SRR949097 3 0.0000 0.8417 0.000 0.000 1.000
#> SRR949098 2 0.0424 0.8290 0.000 0.992 0.008
#> SRR949099 3 0.7702 0.5383 0.180 0.140 0.680
#> SRR949101 1 0.8286 0.4575 0.624 0.140 0.236
#> SRR949100 1 0.8853 0.3686 0.540 0.140 0.320
#> SRR949102 1 0.8571 0.4590 0.588 0.140 0.272
#> SRR949103 3 0.0000 0.8417 0.000 0.000 1.000
#> SRR949104 2 0.0424 0.8290 0.000 0.992 0.008
#> SRR949105 2 0.9931 0.1698 0.288 0.388 0.324
#> SRR949106 2 0.9931 0.1698 0.288 0.388 0.324
#> SRR949107 2 0.9931 0.1698 0.288 0.388 0.324
#> SRR949108 3 0.0000 0.8417 0.000 0.000 1.000
#> SRR949109 1 0.0000 0.8034 1.000 0.000 0.000
#> SRR949110 3 0.0000 0.8417 0.000 0.000 1.000
#> SRR949111 1 0.0000 0.8034 1.000 0.000 0.000
#> SRR949112 3 0.5220 0.6267 0.012 0.208 0.780
#> SRR949113 2 0.0424 0.8290 0.000 0.992 0.008
#> SRR949114 3 0.0661 0.8386 0.008 0.004 0.988
#> SRR949115 3 0.0661 0.8386 0.008 0.004 0.988
#> SRR949116 3 0.0661 0.8386 0.008 0.004 0.988
#> SRR949117 3 0.9050 0.0574 0.376 0.140 0.484
#> SRR949118 3 0.8113 0.4794 0.212 0.144 0.644
#> SRR949119 3 0.4094 0.7670 0.100 0.028 0.872
#> SRR949120 3 0.4094 0.7670 0.100 0.028 0.872
#> SRR949121 3 0.0000 0.8417 0.000 0.000 1.000
#> SRR949122 3 0.4555 0.6433 0.000 0.200 0.800
#> SRR949123 2 0.3038 0.7794 0.000 0.896 0.104
#> SRR949124 2 0.0424 0.8290 0.000 0.992 0.008
#> SRR949125 1 0.0000 0.8034 1.000 0.000 0.000
#> SRR949126 1 0.0000 0.8034 1.000 0.000 0.000
#> SRR949127 2 0.0424 0.8277 0.000 0.992 0.008
#> SRR949128 2 0.0424 0.8277 0.000 0.992 0.008
#> SRR949129 2 0.0424 0.8277 0.000 0.992 0.008
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR949076 4 0.0000 0.815 0.000 0.000 0.000 1.000
#> SRR949078 2 0.0804 0.973 0.000 0.980 0.008 0.012
#> SRR949077 4 0.0188 0.813 0.004 0.000 0.000 0.996
#> SRR949079 4 0.0000 0.815 0.000 0.000 0.000 1.000
#> SRR949080 4 0.0000 0.815 0.000 0.000 0.000 1.000
#> SRR949081 4 0.8661 0.107 0.328 0.088 0.128 0.456
#> SRR949082 2 0.0804 0.970 0.008 0.980 0.000 0.012
#> SRR949083 1 0.0188 0.731 0.996 0.000 0.004 0.000
#> SRR949084 1 0.2125 0.729 0.920 0.004 0.076 0.000
#> SRR949085 2 0.0469 0.978 0.000 0.988 0.012 0.000
#> SRR949087 1 0.9474 0.200 0.376 0.308 0.152 0.164
#> SRR949088 1 0.9455 0.199 0.376 0.312 0.152 0.160
#> SRR949086 1 0.8806 0.365 0.452 0.064 0.256 0.228
#> SRR949089 2 0.0000 0.979 0.000 1.000 0.000 0.000
#> SRR949090 4 0.0000 0.815 0.000 0.000 0.000 1.000
#> SRR949092 1 0.0188 0.731 0.996 0.000 0.004 0.000
#> SRR949093 1 0.0188 0.731 0.996 0.000 0.004 0.000
#> SRR949091 4 0.0000 0.815 0.000 0.000 0.000 1.000
#> SRR949095 1 0.9269 0.148 0.412 0.120 0.176 0.292
#> SRR949094 4 0.0188 0.813 0.004 0.000 0.000 0.996
#> SRR949096 1 0.1082 0.721 0.972 0.004 0.020 0.004
#> SRR949097 1 0.1557 0.731 0.944 0.000 0.056 0.000
#> SRR949098 2 0.0000 0.979 0.000 1.000 0.000 0.000
#> SRR949099 1 0.7452 0.573 0.604 0.088 0.248 0.060
#> SRR949101 4 0.8638 0.212 0.180 0.060 0.304 0.456
#> SRR949100 4 0.8383 0.172 0.324 0.076 0.116 0.484
#> SRR949102 4 0.7847 0.283 0.300 0.064 0.092 0.544
#> SRR949103 1 0.1743 0.731 0.940 0.000 0.056 0.004
#> SRR949104 2 0.0000 0.979 0.000 1.000 0.000 0.000
#> SRR949105 3 0.0707 1.000 0.020 0.000 0.980 0.000
#> SRR949106 3 0.0707 1.000 0.020 0.000 0.980 0.000
#> SRR949107 3 0.0707 1.000 0.020 0.000 0.980 0.000
#> SRR949108 1 0.0779 0.727 0.980 0.004 0.016 0.000
#> SRR949109 4 0.0000 0.815 0.000 0.000 0.000 1.000
#> SRR949110 1 0.1022 0.732 0.968 0.000 0.032 0.000
#> SRR949111 4 0.0000 0.815 0.000 0.000 0.000 1.000
#> SRR949112 1 0.4871 0.693 0.768 0.008 0.188 0.036
#> SRR949113 2 0.0000 0.979 0.000 1.000 0.000 0.000
#> SRR949114 1 0.4313 0.658 0.736 0.004 0.260 0.000
#> SRR949115 1 0.4313 0.658 0.736 0.004 0.260 0.000
#> SRR949116 1 0.4313 0.658 0.736 0.004 0.260 0.000
#> SRR949117 1 0.7976 0.508 0.548 0.072 0.280 0.100
#> SRR949118 1 0.7545 0.453 0.516 0.084 0.360 0.040
#> SRR949119 1 0.5615 0.607 0.748 0.028 0.056 0.168
#> SRR949120 1 0.5615 0.607 0.748 0.028 0.056 0.168
#> SRR949121 1 0.0592 0.733 0.984 0.000 0.016 0.000
#> SRR949122 1 0.3831 0.689 0.792 0.004 0.204 0.000
#> SRR949123 2 0.0469 0.978 0.000 0.988 0.012 0.000
#> SRR949124 2 0.0000 0.979 0.000 1.000 0.000 0.000
#> SRR949125 4 0.0000 0.815 0.000 0.000 0.000 1.000
#> SRR949126 4 0.0000 0.815 0.000 0.000 0.000 1.000
#> SRR949127 2 0.1637 0.956 0.000 0.940 0.060 0.000
#> SRR949128 2 0.1637 0.956 0.000 0.940 0.060 0.000
#> SRR949129 2 0.1637 0.956 0.000 0.940 0.060 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR949076 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> SRR949078 2 0.3160 0.882 0.004 0.808 0.188 0.000 0
#> SRR949077 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> SRR949079 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> SRR949080 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> SRR949081 3 0.0609 0.764 0.000 0.000 0.980 0.020 0
#> SRR949082 2 0.3266 0.872 0.004 0.796 0.200 0.000 0
#> SRR949083 1 0.0000 0.942 1.000 0.000 0.000 0.000 0
#> SRR949084 1 0.0162 0.942 0.996 0.000 0.004 0.000 0
#> SRR949085 2 0.2930 0.885 0.004 0.832 0.164 0.000 0
#> SRR949087 3 0.0162 0.769 0.000 0.000 0.996 0.004 0
#> SRR949088 3 0.0162 0.769 0.000 0.000 0.996 0.004 0
#> SRR949086 3 0.0162 0.769 0.000 0.000 0.996 0.004 0
#> SRR949089 2 0.0000 0.846 0.000 1.000 0.000 0.000 0
#> SRR949090 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> SRR949092 1 0.0000 0.942 1.000 0.000 0.000 0.000 0
#> SRR949093 1 0.0000 0.942 1.000 0.000 0.000 0.000 0
#> SRR949091 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> SRR949095 3 0.6890 0.450 0.048 0.168 0.556 0.228 0
#> SRR949094 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> SRR949096 1 0.0000 0.942 1.000 0.000 0.000 0.000 0
#> SRR949097 1 0.0162 0.942 0.996 0.000 0.004 0.000 0
#> SRR949098 2 0.0000 0.846 0.000 1.000 0.000 0.000 0
#> SRR949099 3 0.0000 0.767 0.000 0.000 1.000 0.000 0
#> SRR949101 3 0.4030 0.464 0.000 0.000 0.648 0.352 0
#> SRR949100 3 0.0865 0.764 0.004 0.000 0.972 0.024 0
#> SRR949102 3 0.3305 0.620 0.000 0.000 0.776 0.224 0
#> SRR949103 1 0.0162 0.942 0.996 0.000 0.004 0.000 0
#> SRR949104 2 0.0000 0.846 0.000 1.000 0.000 0.000 0
#> SRR949105 5 0.0000 1.000 0.000 0.000 0.000 0.000 1
#> SRR949106 5 0.0000 1.000 0.000 0.000 0.000 0.000 1
#> SRR949107 5 0.0000 1.000 0.000 0.000 0.000 0.000 1
#> SRR949108 1 0.0000 0.942 1.000 0.000 0.000 0.000 0
#> SRR949109 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> SRR949110 1 0.0162 0.942 0.996 0.000 0.004 0.000 0
#> SRR949111 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> SRR949112 1 0.2011 0.866 0.908 0.000 0.088 0.004 0
#> SRR949113 2 0.0000 0.846 0.000 1.000 0.000 0.000 0
#> SRR949114 3 0.4101 0.405 0.372 0.000 0.628 0.000 0
#> SRR949115 3 0.4171 0.354 0.396 0.000 0.604 0.000 0
#> SRR949116 3 0.4287 0.178 0.460 0.000 0.540 0.000 0
#> SRR949117 3 0.0162 0.769 0.000 0.000 0.996 0.004 0
#> SRR949118 3 0.0000 0.767 0.000 0.000 1.000 0.000 0
#> SRR949119 1 0.4402 0.678 0.740 0.000 0.056 0.204 0
#> SRR949120 1 0.4402 0.678 0.740 0.000 0.056 0.204 0
#> SRR949121 1 0.0000 0.942 1.000 0.000 0.000 0.000 0
#> SRR949122 1 0.0162 0.942 0.996 0.000 0.004 0.000 0
#> SRR949123 2 0.2732 0.886 0.000 0.840 0.160 0.000 0
#> SRR949124 2 0.0000 0.846 0.000 1.000 0.000 0.000 0
#> SRR949125 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> SRR949126 4 0.0000 1.000 0.000 0.000 0.000 1.000 0
#> SRR949127 2 0.3074 0.880 0.000 0.804 0.196 0.000 0
#> SRR949128 2 0.3074 0.880 0.000 0.804 0.196 0.000 0
#> SRR949129 2 0.3074 0.880 0.000 0.804 0.196 0.000 0
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR949076 4 0.0260 0.982 0.000 0.008 0 0.992 0.000 0.000
#> SRR949078 2 0.4146 0.979 0.000 0.676 0 0.000 0.036 0.288
#> SRR949077 4 0.0260 0.983 0.000 0.008 0 0.992 0.000 0.000
#> SRR949079 4 0.0713 0.983 0.000 0.028 0 0.972 0.000 0.000
#> SRR949080 4 0.0713 0.983 0.000 0.028 0 0.972 0.000 0.000
#> SRR949081 5 0.1806 0.737 0.000 0.088 0 0.004 0.908 0.000
#> SRR949082 2 0.4210 0.974 0.000 0.672 0 0.000 0.040 0.288
#> SRR949083 1 0.0000 0.942 1.000 0.000 0 0.000 0.000 0.000
#> SRR949084 1 0.0146 0.940 0.996 0.000 0 0.000 0.004 0.000
#> SRR949085 2 0.3871 0.957 0.000 0.676 0 0.000 0.016 0.308
#> SRR949087 5 0.0000 0.766 0.000 0.000 0 0.000 1.000 0.000
#> SRR949088 5 0.0000 0.766 0.000 0.000 0 0.000 1.000 0.000
#> SRR949086 5 0.0146 0.765 0.000 0.000 0 0.004 0.996 0.000
#> SRR949089 6 0.0000 0.883 0.000 0.000 0 0.000 0.000 1.000
#> SRR949090 4 0.0547 0.985 0.000 0.020 0 0.980 0.000 0.000
#> SRR949092 1 0.0000 0.942 1.000 0.000 0 0.000 0.000 0.000
#> SRR949093 1 0.0000 0.942 1.000 0.000 0 0.000 0.000 0.000
#> SRR949091 4 0.0547 0.976 0.000 0.020 0 0.980 0.000 0.000
#> SRR949095 5 0.6086 0.459 0.020 0.256 0 0.180 0.540 0.004
#> SRR949094 4 0.0146 0.984 0.000 0.004 0 0.996 0.000 0.000
#> SRR949096 1 0.0000 0.942 1.000 0.000 0 0.000 0.000 0.000
#> SRR949097 1 0.0000 0.942 1.000 0.000 0 0.000 0.000 0.000
#> SRR949098 6 0.0000 0.883 0.000 0.000 0 0.000 0.000 1.000
#> SRR949099 5 0.0000 0.766 0.000 0.000 0 0.000 1.000 0.000
#> SRR949101 5 0.5234 0.442 0.000 0.124 0 0.300 0.576 0.000
#> SRR949100 5 0.1075 0.756 0.000 0.048 0 0.000 0.952 0.000
#> SRR949102 5 0.2726 0.709 0.000 0.112 0 0.032 0.856 0.000
#> SRR949103 1 0.0000 0.942 1.000 0.000 0 0.000 0.000 0.000
#> SRR949104 6 0.0000 0.883 0.000 0.000 0 0.000 0.000 1.000
#> SRR949105 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> SRR949106 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> SRR949107 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> SRR949108 1 0.0000 0.942 1.000 0.000 0 0.000 0.000 0.000
#> SRR949109 4 0.0000 0.985 0.000 0.000 0 1.000 0.000 0.000
#> SRR949110 1 0.0000 0.942 1.000 0.000 0 0.000 0.000 0.000
#> SRR949111 4 0.0000 0.985 0.000 0.000 0 1.000 0.000 0.000
#> SRR949112 1 0.2301 0.841 0.884 0.020 0 0.000 0.096 0.000
#> SRR949113 6 0.1387 0.824 0.000 0.068 0 0.000 0.000 0.932
#> SRR949114 5 0.3890 0.343 0.400 0.004 0 0.000 0.596 0.000
#> SRR949115 5 0.3923 0.304 0.416 0.004 0 0.000 0.580 0.000
#> SRR949116 5 0.3997 0.083 0.488 0.004 0 0.000 0.508 0.000
#> SRR949117 5 0.0000 0.766 0.000 0.000 0 0.000 1.000 0.000
#> SRR949118 5 0.0000 0.766 0.000 0.000 0 0.000 1.000 0.000
#> SRR949119 1 0.4551 0.670 0.676 0.268 0 0.036 0.020 0.000
#> SRR949120 1 0.4551 0.670 0.676 0.268 0 0.036 0.020 0.000
#> SRR949121 1 0.0000 0.942 1.000 0.000 0 0.000 0.000 0.000
#> SRR949122 1 0.0146 0.940 0.996 0.000 0 0.000 0.004 0.000
#> SRR949123 6 0.3871 0.193 0.000 0.308 0 0.000 0.016 0.676
#> SRR949124 6 0.0000 0.883 0.000 0.000 0 0.000 0.000 1.000
#> SRR949125 4 0.0713 0.983 0.000 0.028 0 0.972 0.000 0.000
#> SRR949126 4 0.0713 0.983 0.000 0.028 0 0.972 0.000 0.000
#> SRR949127 2 0.4009 0.984 0.000 0.684 0 0.000 0.028 0.288
#> SRR949128 2 0.4009 0.984 0.000 0.684 0 0.000 0.028 0.288
#> SRR949129 2 0.4009 0.984 0.000 0.684 0 0.000 0.028 0.288
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)
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 16816 rows and 54 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 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 0.812 0.869 0.948 0.4808 0.516 0.516
#> 3 3 0.706 0.821 0.906 0.3869 0.676 0.442
#> 4 4 0.926 0.894 0.956 0.1349 0.853 0.587
#> 5 5 0.847 0.767 0.870 0.0438 0.931 0.734
#> 6 6 0.860 0.779 0.876 0.0365 0.932 0.703
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
#> SRR949076 1 0.0000 0.950 1.000 0.000
#> SRR949078 2 0.0000 0.926 0.000 1.000
#> SRR949077 1 0.0000 0.950 1.000 0.000
#> SRR949079 1 0.0000 0.950 1.000 0.000
#> SRR949080 1 0.0000 0.950 1.000 0.000
#> SRR949081 2 0.0938 0.920 0.012 0.988
#> SRR949082 2 0.0000 0.926 0.000 1.000
#> SRR949083 1 0.0000 0.950 1.000 0.000
#> SRR949084 1 0.0000 0.950 1.000 0.000
#> SRR949085 2 0.0000 0.926 0.000 1.000
#> SRR949087 2 0.0000 0.926 0.000 1.000
#> SRR949088 2 0.0000 0.926 0.000 1.000
#> SRR949086 1 0.9608 0.338 0.616 0.384
#> SRR949089 2 0.0000 0.926 0.000 1.000
#> SRR949090 1 0.0000 0.950 1.000 0.000
#> SRR949092 1 0.0000 0.950 1.000 0.000
#> SRR949093 1 0.0000 0.950 1.000 0.000
#> SRR949091 1 0.0000 0.950 1.000 0.000
#> SRR949095 1 0.8207 0.641 0.744 0.256
#> SRR949094 1 0.0000 0.950 1.000 0.000
#> SRR949096 1 0.0000 0.950 1.000 0.000
#> SRR949097 1 0.0000 0.950 1.000 0.000
#> SRR949098 2 0.0000 0.926 0.000 1.000
#> SRR949099 1 0.0376 0.946 0.996 0.004
#> SRR949101 1 0.9580 0.362 0.620 0.380
#> SRR949100 2 0.8555 0.608 0.280 0.720
#> SRR949102 1 0.8081 0.655 0.752 0.248
#> SRR949103 1 0.0000 0.950 1.000 0.000
#> SRR949104 2 0.0000 0.926 0.000 1.000
#> SRR949105 2 0.3584 0.883 0.068 0.932
#> SRR949106 2 0.3733 0.879 0.072 0.928
#> SRR949107 2 0.2778 0.898 0.048 0.952
#> SRR949108 1 0.0000 0.950 1.000 0.000
#> SRR949109 1 0.0000 0.950 1.000 0.000
#> SRR949110 1 0.0000 0.950 1.000 0.000
#> SRR949111 1 0.0000 0.950 1.000 0.000
#> SRR949112 1 0.6712 0.761 0.824 0.176
#> SRR949113 2 0.0000 0.926 0.000 1.000
#> SRR949114 1 0.0000 0.950 1.000 0.000
#> SRR949115 1 0.0000 0.950 1.000 0.000
#> SRR949116 1 0.0000 0.950 1.000 0.000
#> SRR949117 2 0.9922 0.208 0.448 0.552
#> SRR949118 2 0.9896 0.233 0.440 0.560
#> SRR949119 1 0.0000 0.950 1.000 0.000
#> SRR949120 1 0.0000 0.950 1.000 0.000
#> SRR949121 1 0.0000 0.950 1.000 0.000
#> SRR949122 1 0.0000 0.950 1.000 0.000
#> SRR949123 2 0.0000 0.926 0.000 1.000
#> SRR949124 2 0.0000 0.926 0.000 1.000
#> SRR949125 1 0.0000 0.950 1.000 0.000
#> SRR949126 1 0.0000 0.950 1.000 0.000
#> SRR949127 2 0.0000 0.926 0.000 1.000
#> SRR949128 2 0.0000 0.926 0.000 1.000
#> SRR949129 2 0.0000 0.926 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR949076 1 0.2959 0.8531 0.900 0.000 0.100
#> SRR949078 2 0.0000 0.9398 0.000 1.000 0.000
#> SRR949077 1 0.2959 0.8531 0.900 0.000 0.100
#> SRR949079 1 0.2959 0.8531 0.900 0.000 0.100
#> SRR949080 1 0.2959 0.8531 0.900 0.000 0.100
#> SRR949081 2 0.3293 0.8762 0.088 0.900 0.012
#> SRR949082 2 0.0000 0.9398 0.000 1.000 0.000
#> SRR949083 3 0.0000 0.9277 0.000 0.000 1.000
#> SRR949084 3 0.0000 0.9277 0.000 0.000 1.000
#> SRR949085 2 0.0000 0.9398 0.000 1.000 0.000
#> SRR949087 2 0.3234 0.8861 0.072 0.908 0.020
#> SRR949088 2 0.3234 0.8861 0.072 0.908 0.020
#> SRR949086 2 0.8069 -0.0151 0.460 0.476 0.064
#> SRR949089 2 0.0000 0.9398 0.000 1.000 0.000
#> SRR949090 1 0.2959 0.8531 0.900 0.000 0.100
#> SRR949092 3 0.0000 0.9277 0.000 0.000 1.000
#> SRR949093 3 0.0000 0.9277 0.000 0.000 1.000
#> SRR949091 1 0.2625 0.8455 0.916 0.000 0.084
#> SRR949095 1 0.8338 0.3924 0.516 0.400 0.084
#> SRR949094 1 0.2959 0.8531 0.900 0.000 0.100
#> SRR949096 3 0.0000 0.9277 0.000 0.000 1.000
#> SRR949097 3 0.0000 0.9277 0.000 0.000 1.000
#> SRR949098 2 0.0000 0.9398 0.000 1.000 0.000
#> SRR949099 3 0.2959 0.8681 0.100 0.000 0.900
#> SRR949101 1 0.0000 0.7900 1.000 0.000 0.000
#> SRR949100 2 0.3550 0.8612 0.024 0.896 0.080
#> SRR949102 1 0.5956 0.6643 0.768 0.188 0.044
#> SRR949103 3 0.0000 0.9277 0.000 0.000 1.000
#> SRR949104 2 0.0000 0.9398 0.000 1.000 0.000
#> SRR949105 1 0.6686 0.3421 0.612 0.372 0.016
#> SRR949106 1 0.6667 0.3514 0.616 0.368 0.016
#> SRR949107 1 0.6686 0.3421 0.612 0.372 0.016
#> SRR949108 3 0.0000 0.9277 0.000 0.000 1.000
#> SRR949109 1 0.2959 0.8531 0.900 0.000 0.100
#> SRR949110 3 0.0000 0.9277 0.000 0.000 1.000
#> SRR949111 1 0.2959 0.8531 0.900 0.000 0.100
#> SRR949112 3 0.0000 0.9277 0.000 0.000 1.000
#> SRR949113 2 0.0000 0.9398 0.000 1.000 0.000
#> SRR949114 3 0.2959 0.8681 0.100 0.000 0.900
#> SRR949115 3 0.2711 0.8771 0.088 0.000 0.912
#> SRR949116 3 0.2711 0.8771 0.088 0.000 0.912
#> SRR949117 3 0.8390 0.3432 0.100 0.340 0.560
#> SRR949118 3 0.8285 0.4627 0.112 0.288 0.600
#> SRR949119 3 0.0237 0.9252 0.004 0.000 0.996
#> SRR949120 3 0.0424 0.9221 0.008 0.000 0.992
#> SRR949121 3 0.0000 0.9277 0.000 0.000 1.000
#> SRR949122 3 0.0000 0.9277 0.000 0.000 1.000
#> SRR949123 2 0.0000 0.9398 0.000 1.000 0.000
#> SRR949124 2 0.0000 0.9398 0.000 1.000 0.000
#> SRR949125 1 0.2959 0.8531 0.900 0.000 0.100
#> SRR949126 1 0.2959 0.8531 0.900 0.000 0.100
#> SRR949127 2 0.0000 0.9398 0.000 1.000 0.000
#> SRR949128 2 0.0000 0.9398 0.000 1.000 0.000
#> SRR949129 2 0.0000 0.9398 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR949076 4 0.0000 0.9569 0.000 0.000 0.000 1.000
#> SRR949078 2 0.0000 0.9545 0.000 1.000 0.000 0.000
#> SRR949077 4 0.0000 0.9569 0.000 0.000 0.000 1.000
#> SRR949079 4 0.0000 0.9569 0.000 0.000 0.000 1.000
#> SRR949080 4 0.0000 0.9569 0.000 0.000 0.000 1.000
#> SRR949081 3 0.1118 0.8974 0.000 0.036 0.964 0.000
#> SRR949082 2 0.0000 0.9545 0.000 1.000 0.000 0.000
#> SRR949083 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> SRR949084 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> SRR949085 2 0.0000 0.9545 0.000 1.000 0.000 0.000
#> SRR949087 3 0.4741 0.6957 0.028 0.228 0.744 0.000
#> SRR949088 3 0.4212 0.7234 0.012 0.216 0.772 0.000
#> SRR949086 3 0.0469 0.9142 0.000 0.000 0.988 0.012
#> SRR949089 2 0.0000 0.9545 0.000 1.000 0.000 0.000
#> SRR949090 4 0.0000 0.9569 0.000 0.000 0.000 1.000
#> SRR949092 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> SRR949093 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> SRR949091 4 0.0000 0.9569 0.000 0.000 0.000 1.000
#> SRR949095 4 0.5229 0.2590 0.000 0.428 0.008 0.564
#> SRR949094 4 0.0000 0.9569 0.000 0.000 0.000 1.000
#> SRR949096 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> SRR949097 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> SRR949098 2 0.0000 0.9545 0.000 1.000 0.000 0.000
#> SRR949099 3 0.0469 0.9124 0.012 0.000 0.988 0.000
#> SRR949101 3 0.0707 0.9122 0.000 0.000 0.980 0.020
#> SRR949100 2 0.6008 -0.0936 0.040 0.496 0.464 0.000
#> SRR949102 3 0.4543 0.5130 0.000 0.000 0.676 0.324
#> SRR949103 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> SRR949104 2 0.0000 0.9545 0.000 1.000 0.000 0.000
#> SRR949105 3 0.0657 0.9150 0.000 0.004 0.984 0.012
#> SRR949106 3 0.0657 0.9150 0.000 0.004 0.984 0.012
#> SRR949107 3 0.0657 0.9150 0.000 0.004 0.984 0.012
#> SRR949108 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> SRR949109 4 0.0000 0.9569 0.000 0.000 0.000 1.000
#> SRR949110 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> SRR949111 4 0.0000 0.9569 0.000 0.000 0.000 1.000
#> SRR949112 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> SRR949113 2 0.0000 0.9545 0.000 1.000 0.000 0.000
#> SRR949114 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> SRR949115 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> SRR949116 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> SRR949117 3 0.0469 0.9124 0.012 0.000 0.988 0.000
#> SRR949118 3 0.0469 0.9124 0.012 0.000 0.988 0.000
#> SRR949119 1 0.4472 0.7074 0.760 0.000 0.020 0.220
#> SRR949120 1 0.4399 0.7198 0.768 0.000 0.020 0.212
#> SRR949121 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> SRR949122 1 0.0000 0.9693 1.000 0.000 0.000 0.000
#> SRR949123 2 0.0000 0.9545 0.000 1.000 0.000 0.000
#> SRR949124 2 0.0000 0.9545 0.000 1.000 0.000 0.000
#> SRR949125 4 0.0000 0.9569 0.000 0.000 0.000 1.000
#> SRR949126 4 0.0000 0.9569 0.000 0.000 0.000 1.000
#> SRR949127 2 0.0000 0.9545 0.000 1.000 0.000 0.000
#> SRR949128 2 0.0000 0.9545 0.000 1.000 0.000 0.000
#> SRR949129 2 0.0000 0.9545 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR949076 4 0.0000 0.9996 0.000 0.000 0.000 1.000 0.000
#> SRR949078 2 0.3074 0.8018 0.000 0.804 0.000 0.000 0.196
#> SRR949077 4 0.0000 0.9996 0.000 0.000 0.000 1.000 0.000
#> SRR949079 4 0.0000 0.9996 0.000 0.000 0.000 1.000 0.000
#> SRR949080 4 0.0000 0.9996 0.000 0.000 0.000 1.000 0.000
#> SRR949081 5 0.4557 0.1750 0.000 0.008 0.476 0.000 0.516
#> SRR949082 2 0.3177 0.7965 0.000 0.792 0.000 0.000 0.208
#> SRR949083 1 0.0000 0.9601 1.000 0.000 0.000 0.000 0.000
#> SRR949084 1 0.0000 0.9601 1.000 0.000 0.000 0.000 0.000
#> SRR949085 2 0.1732 0.8317 0.000 0.920 0.000 0.000 0.080
#> SRR949087 3 0.6963 0.2440 0.016 0.284 0.464 0.000 0.236
#> SRR949088 3 0.6911 0.2192 0.012 0.296 0.456 0.000 0.236
#> SRR949086 3 0.1478 0.5482 0.000 0.000 0.936 0.000 0.064
#> SRR949089 2 0.0000 0.8395 0.000 1.000 0.000 0.000 0.000
#> SRR949090 4 0.0000 0.9996 0.000 0.000 0.000 1.000 0.000
#> SRR949092 1 0.0000 0.9601 1.000 0.000 0.000 0.000 0.000
#> SRR949093 1 0.0000 0.9601 1.000 0.000 0.000 0.000 0.000
#> SRR949091 4 0.0000 0.9996 0.000 0.000 0.000 1.000 0.000
#> SRR949095 2 0.4268 0.0971 0.000 0.556 0.000 0.444 0.000
#> SRR949094 4 0.0162 0.9959 0.000 0.000 0.000 0.996 0.004
#> SRR949096 1 0.0000 0.9601 1.000 0.000 0.000 0.000 0.000
#> SRR949097 1 0.0000 0.9601 1.000 0.000 0.000 0.000 0.000
#> SRR949098 2 0.0000 0.8395 0.000 1.000 0.000 0.000 0.000
#> SRR949099 3 0.1732 0.5462 0.000 0.000 0.920 0.000 0.080
#> SRR949101 3 0.4251 0.5422 0.000 0.004 0.756 0.040 0.200
#> SRR949100 3 0.7184 0.0568 0.000 0.340 0.368 0.016 0.276
#> SRR949102 5 0.6066 0.3806 0.000 0.020 0.320 0.088 0.572
#> SRR949103 1 0.0000 0.9601 1.000 0.000 0.000 0.000 0.000
#> SRR949104 2 0.0000 0.8395 0.000 1.000 0.000 0.000 0.000
#> SRR949105 3 0.3333 0.5632 0.000 0.004 0.788 0.000 0.208
#> SRR949106 3 0.3333 0.5632 0.000 0.004 0.788 0.000 0.208
#> SRR949107 3 0.3333 0.5632 0.000 0.004 0.788 0.000 0.208
#> SRR949108 1 0.0000 0.9601 1.000 0.000 0.000 0.000 0.000
#> SRR949109 4 0.0000 0.9996 0.000 0.000 0.000 1.000 0.000
#> SRR949110 1 0.0000 0.9601 1.000 0.000 0.000 0.000 0.000
#> SRR949111 4 0.0000 0.9996 0.000 0.000 0.000 1.000 0.000
#> SRR949112 1 0.0000 0.9601 1.000 0.000 0.000 0.000 0.000
#> SRR949113 2 0.0000 0.8395 0.000 1.000 0.000 0.000 0.000
#> SRR949114 1 0.2932 0.8215 0.864 0.000 0.104 0.000 0.032
#> SRR949115 1 0.2932 0.8215 0.864 0.000 0.104 0.000 0.032
#> SRR949116 1 0.2932 0.8215 0.864 0.000 0.104 0.000 0.032
#> SRR949117 3 0.2516 0.5352 0.000 0.000 0.860 0.000 0.140
#> SRR949118 3 0.1410 0.5483 0.000 0.000 0.940 0.000 0.060
#> SRR949119 5 0.5427 0.5317 0.368 0.000 0.024 0.028 0.580
#> SRR949120 5 0.5361 0.5270 0.372 0.000 0.024 0.024 0.580
#> SRR949121 1 0.0000 0.9601 1.000 0.000 0.000 0.000 0.000
#> SRR949122 1 0.0000 0.9601 1.000 0.000 0.000 0.000 0.000
#> SRR949123 2 0.0000 0.8395 0.000 1.000 0.000 0.000 0.000
#> SRR949124 2 0.0000 0.8395 0.000 1.000 0.000 0.000 0.000
#> SRR949125 4 0.0000 0.9996 0.000 0.000 0.000 1.000 0.000
#> SRR949126 4 0.0000 0.9996 0.000 0.000 0.000 1.000 0.000
#> SRR949127 2 0.3819 0.7751 0.000 0.756 0.016 0.000 0.228
#> SRR949128 2 0.3819 0.7751 0.000 0.756 0.016 0.000 0.228
#> SRR949129 2 0.3819 0.7751 0.000 0.756 0.016 0.000 0.228
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR949076 4 0.0000 0.9904 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949078 2 0.4809 0.6947 0.000 0.668 0.000 0.000 0.140 0.192
#> SRR949077 4 0.0000 0.9904 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949079 4 0.0000 0.9904 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949080 4 0.0000 0.9904 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949081 6 0.3828 0.0012 0.000 0.000 0.000 0.000 0.440 0.560
#> SRR949082 2 0.4273 0.7247 0.000 0.732 0.000 0.000 0.148 0.120
#> SRR949083 1 0.0000 0.9968 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949084 1 0.0000 0.9968 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949085 2 0.1745 0.7738 0.000 0.920 0.000 0.000 0.068 0.012
#> SRR949087 6 0.4256 0.4636 0.024 0.044 0.012 0.000 0.148 0.772
#> SRR949088 6 0.4345 0.4621 0.024 0.044 0.016 0.000 0.148 0.768
#> SRR949086 6 0.3748 0.5091 0.000 0.000 0.108 0.000 0.108 0.784
#> SRR949089 2 0.0000 0.7813 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949090 4 0.0000 0.9904 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949092 1 0.0000 0.9968 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949093 1 0.0000 0.9968 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949091 4 0.0508 0.9899 0.000 0.000 0.012 0.984 0.004 0.000
#> SRR949095 2 0.4209 0.1927 0.000 0.588 0.012 0.396 0.004 0.000
#> SRR949094 4 0.0547 0.9776 0.000 0.000 0.000 0.980 0.020 0.000
#> SRR949096 1 0.0000 0.9968 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949097 1 0.0000 0.9968 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949098 2 0.0000 0.7813 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949099 6 0.3703 0.5104 0.000 0.000 0.108 0.000 0.104 0.788
#> SRR949101 3 0.1938 0.8938 0.000 0.000 0.920 0.040 0.004 0.036
#> SRR949100 6 0.4100 0.4867 0.000 0.032 0.016 0.020 0.152 0.780
#> SRR949102 5 0.3441 0.5909 0.000 0.004 0.004 0.008 0.768 0.216
#> SRR949103 1 0.0000 0.9968 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949104 2 0.0000 0.7813 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949105 3 0.0458 0.9657 0.000 0.000 0.984 0.000 0.000 0.016
#> SRR949106 3 0.0458 0.9657 0.000 0.000 0.984 0.000 0.000 0.016
#> SRR949107 3 0.0458 0.9657 0.000 0.000 0.984 0.000 0.000 0.016
#> SRR949108 1 0.0000 0.9968 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949109 4 0.0508 0.9899 0.000 0.000 0.012 0.984 0.004 0.000
#> SRR949110 1 0.0000 0.9968 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949111 4 0.0508 0.9899 0.000 0.000 0.012 0.984 0.004 0.000
#> SRR949112 1 0.0891 0.9637 0.968 0.000 0.000 0.000 0.008 0.024
#> SRR949113 2 0.0000 0.7813 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949114 6 0.4770 0.2513 0.448 0.000 0.004 0.000 0.040 0.508
#> SRR949115 6 0.4770 0.2513 0.448 0.000 0.004 0.000 0.040 0.508
#> SRR949116 6 0.4770 0.2513 0.448 0.000 0.004 0.000 0.040 0.508
#> SRR949117 6 0.1411 0.5379 0.000 0.000 0.060 0.000 0.004 0.936
#> SRR949118 6 0.3834 0.4949 0.000 0.000 0.116 0.000 0.108 0.776
#> SRR949119 5 0.2872 0.8261 0.152 0.000 0.012 0.000 0.832 0.004
#> SRR949120 5 0.2872 0.8261 0.152 0.000 0.012 0.000 0.832 0.004
#> SRR949121 1 0.0000 0.9968 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949122 1 0.0000 0.9968 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949123 2 0.0363 0.7751 0.000 0.988 0.000 0.000 0.012 0.000
#> SRR949124 2 0.0000 0.7813 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949125 4 0.0508 0.9899 0.000 0.000 0.012 0.984 0.004 0.000
#> SRR949126 4 0.0508 0.9899 0.000 0.000 0.012 0.984 0.004 0.000
#> SRR949127 2 0.5265 0.6387 0.000 0.592 0.000 0.000 0.148 0.260
#> SRR949128 2 0.5265 0.6387 0.000 0.592 0.000 0.000 0.148 0.260
#> SRR949129 2 0.5283 0.6343 0.000 0.588 0.000 0.000 0.148 0.264
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)
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 16816 rows and 54 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 0.592 0.781 0.909 0.3550 0.628 0.628
#> 3 3 0.355 0.580 0.801 0.5854 0.677 0.524
#> 4 4 0.397 0.443 0.664 0.2328 0.736 0.451
#> 5 5 0.606 0.615 0.758 0.1041 0.836 0.509
#> 6 6 0.682 0.605 0.762 0.0478 0.987 0.940
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
#> SRR949076 1 0.634 0.7526 0.840 0.160
#> SRR949078 2 0.999 0.2666 0.484 0.516
#> SRR949077 1 0.634 0.7526 0.840 0.160
#> SRR949079 1 0.000 0.9190 1.000 0.000
#> SRR949080 1 0.000 0.9190 1.000 0.000
#> SRR949081 1 0.697 0.7093 0.812 0.188
#> SRR949082 2 0.999 0.2666 0.484 0.516
#> SRR949083 1 0.634 0.7526 0.840 0.160
#> SRR949084 1 0.000 0.9190 1.000 0.000
#> SRR949085 2 0.000 0.7663 0.000 1.000
#> SRR949087 1 0.969 0.1027 0.604 0.396
#> SRR949088 1 0.969 0.1027 0.604 0.396
#> SRR949086 1 0.224 0.9063 0.964 0.036
#> SRR949089 2 0.000 0.7663 0.000 1.000
#> SRR949090 1 0.000 0.9190 1.000 0.000
#> SRR949092 1 0.000 0.9190 1.000 0.000
#> SRR949093 1 0.000 0.9190 1.000 0.000
#> SRR949091 1 0.204 0.9071 0.968 0.032
#> SRR949095 1 0.990 -0.0647 0.560 0.440
#> SRR949094 1 0.000 0.9190 1.000 0.000
#> SRR949096 1 0.000 0.9190 1.000 0.000
#> SRR949097 1 0.000 0.9190 1.000 0.000
#> SRR949098 2 0.000 0.7663 0.000 1.000
#> SRR949099 1 0.000 0.9190 1.000 0.000
#> SRR949101 1 0.204 0.9071 0.968 0.032
#> SRR949100 2 0.999 0.2850 0.484 0.516
#> SRR949102 1 0.697 0.7093 0.812 0.188
#> SRR949103 1 0.000 0.9190 1.000 0.000
#> SRR949104 2 0.000 0.7663 0.000 1.000
#> SRR949105 1 0.204 0.9071 0.968 0.032
#> SRR949106 1 0.204 0.9071 0.968 0.032
#> SRR949107 1 0.204 0.9071 0.968 0.032
#> SRR949108 1 0.000 0.9190 1.000 0.000
#> SRR949109 1 0.000 0.9190 1.000 0.000
#> SRR949110 1 0.000 0.9190 1.000 0.000
#> SRR949111 1 0.000 0.9190 1.000 0.000
#> SRR949112 1 0.000 0.9190 1.000 0.000
#> SRR949113 2 0.000 0.7663 0.000 1.000
#> SRR949114 1 0.204 0.9071 0.968 0.032
#> SRR949115 1 0.204 0.9071 0.968 0.032
#> SRR949116 1 0.204 0.9071 0.968 0.032
#> SRR949117 1 0.224 0.9063 0.964 0.036
#> SRR949118 1 0.204 0.9071 0.968 0.032
#> SRR949119 1 0.000 0.9190 1.000 0.000
#> SRR949120 1 0.000 0.9190 1.000 0.000
#> SRR949121 1 0.000 0.9190 1.000 0.000
#> SRR949122 1 0.000 0.9190 1.000 0.000
#> SRR949123 2 0.574 0.7404 0.136 0.864
#> SRR949124 2 0.000 0.7663 0.000 1.000
#> SRR949125 1 0.000 0.9190 1.000 0.000
#> SRR949126 1 0.000 0.9190 1.000 0.000
#> SRR949127 2 0.861 0.6620 0.284 0.716
#> SRR949128 2 0.861 0.6620 0.284 0.716
#> SRR949129 2 0.861 0.6620 0.284 0.716
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR949076 1 0.6225 0.345 0.568 0.000 0.432
#> SRR949078 1 0.4504 0.365 0.804 0.196 0.000
#> SRR949077 1 0.6225 0.345 0.568 0.000 0.432
#> SRR949079 3 0.5926 0.192 0.356 0.000 0.644
#> SRR949080 3 0.5926 0.192 0.356 0.000 0.644
#> SRR949081 1 0.6339 0.428 0.632 0.008 0.360
#> SRR949082 1 0.4504 0.365 0.804 0.196 0.000
#> SRR949083 1 0.5497 0.432 0.708 0.000 0.292
#> SRR949084 1 0.6267 0.147 0.548 0.000 0.452
#> SRR949085 2 0.1964 0.901 0.056 0.944 0.000
#> SRR949087 1 0.4821 0.513 0.848 0.064 0.088
#> SRR949088 1 0.4821 0.513 0.848 0.064 0.088
#> SRR949086 3 0.1411 0.776 0.036 0.000 0.964
#> SRR949089 2 0.0000 0.934 0.000 1.000 0.000
#> SRR949090 3 0.3192 0.739 0.112 0.000 0.888
#> SRR949092 3 0.4178 0.776 0.172 0.000 0.828
#> SRR949093 3 0.4178 0.776 0.172 0.000 0.828
#> SRR949091 3 0.1289 0.778 0.032 0.000 0.968
#> SRR949095 1 0.1482 0.466 0.968 0.020 0.012
#> SRR949094 3 0.5926 0.192 0.356 0.000 0.644
#> SRR949096 1 0.6267 0.147 0.548 0.000 0.452
#> SRR949097 3 0.4062 0.782 0.164 0.000 0.836
#> SRR949098 2 0.0000 0.934 0.000 1.000 0.000
#> SRR949099 3 0.2261 0.794 0.068 0.000 0.932
#> SRR949101 3 0.1289 0.778 0.032 0.000 0.968
#> SRR949100 1 0.9441 0.261 0.484 0.316 0.200
#> SRR949102 1 0.6339 0.428 0.632 0.008 0.360
#> SRR949103 3 0.4062 0.782 0.164 0.000 0.836
#> SRR949104 2 0.0237 0.934 0.004 0.996 0.000
#> SRR949105 3 0.1289 0.778 0.032 0.000 0.968
#> SRR949106 3 0.1289 0.778 0.032 0.000 0.968
#> SRR949107 3 0.1289 0.778 0.032 0.000 0.968
#> SRR949108 3 0.4062 0.782 0.164 0.000 0.836
#> SRR949109 3 0.3192 0.739 0.112 0.000 0.888
#> SRR949110 3 0.4062 0.782 0.164 0.000 0.836
#> SRR949111 3 0.3192 0.739 0.112 0.000 0.888
#> SRR949112 3 0.4062 0.782 0.164 0.000 0.836
#> SRR949113 2 0.0237 0.934 0.004 0.996 0.000
#> SRR949114 3 0.3816 0.776 0.148 0.000 0.852
#> SRR949115 3 0.3816 0.776 0.148 0.000 0.852
#> SRR949116 3 0.3816 0.776 0.148 0.000 0.852
#> SRR949117 3 0.1411 0.776 0.036 0.000 0.964
#> SRR949118 3 0.1289 0.778 0.032 0.000 0.968
#> SRR949119 1 0.6280 0.127 0.540 0.000 0.460
#> SRR949120 1 0.6280 0.127 0.540 0.000 0.460
#> SRR949121 3 0.4062 0.782 0.164 0.000 0.836
#> SRR949122 3 0.4062 0.782 0.164 0.000 0.836
#> SRR949123 2 0.5591 0.583 0.304 0.696 0.000
#> SRR949124 2 0.0000 0.934 0.000 1.000 0.000
#> SRR949125 3 0.3192 0.739 0.112 0.000 0.888
#> SRR949126 3 0.3192 0.739 0.112 0.000 0.888
#> SRR949127 1 0.6295 -0.150 0.528 0.472 0.000
#> SRR949128 1 0.6295 -0.150 0.528 0.472 0.000
#> SRR949129 1 0.6295 -0.150 0.528 0.472 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR949076 1 0.490 -0.0046 0.584 0.000 0.000 0.416
#> SRR949078 4 0.327 0.5527 0.000 0.168 0.000 0.832
#> SRR949077 1 0.490 -0.0046 0.584 0.000 0.000 0.416
#> SRR949079 1 0.331 0.3692 0.828 0.000 0.000 0.172
#> SRR949080 1 0.331 0.3692 0.828 0.000 0.000 0.172
#> SRR949081 4 0.661 0.3354 0.168 0.000 0.204 0.628
#> SRR949082 4 0.327 0.5527 0.000 0.168 0.000 0.832
#> SRR949083 4 0.719 0.0227 0.244 0.000 0.204 0.552
#> SRR949084 1 0.760 0.2997 0.436 0.000 0.204 0.360
#> SRR949085 2 0.156 0.8450 0.000 0.944 0.000 0.056
#> SRR949087 4 0.385 0.6022 0.044 0.036 0.052 0.868
#> SRR949088 4 0.385 0.6022 0.044 0.036 0.052 0.868
#> SRR949086 3 0.475 0.7198 0.304 0.000 0.688 0.008
#> SRR949089 2 0.000 0.8753 0.000 1.000 0.000 0.000
#> SRR949090 1 0.201 0.3243 0.920 0.000 0.080 0.000
#> SRR949092 1 0.688 0.3803 0.520 0.000 0.368 0.112
#> SRR949093 1 0.688 0.3803 0.520 0.000 0.368 0.112
#> SRR949091 3 0.500 0.5130 0.484 0.000 0.516 0.000
#> SRR949095 4 0.287 0.5379 0.136 0.000 0.000 0.864
#> SRR949094 1 0.331 0.3692 0.828 0.000 0.000 0.172
#> SRR949096 1 0.760 0.2997 0.436 0.000 0.204 0.360
#> SRR949097 1 0.689 0.3750 0.512 0.000 0.376 0.112
#> SRR949098 2 0.000 0.8753 0.000 1.000 0.000 0.000
#> SRR949099 1 0.564 0.0908 0.636 0.000 0.324 0.040
#> SRR949101 3 0.419 0.7422 0.268 0.000 0.732 0.000
#> SRR949100 4 0.885 0.3806 0.180 0.164 0.144 0.512
#> SRR949102 4 0.661 0.3354 0.168 0.000 0.204 0.628
#> SRR949103 1 0.689 0.3750 0.512 0.000 0.376 0.112
#> SRR949104 2 0.298 0.8351 0.000 0.872 0.120 0.008
#> SRR949105 3 0.419 0.7422 0.268 0.000 0.732 0.000
#> SRR949106 3 0.419 0.7422 0.268 0.000 0.732 0.000
#> SRR949107 3 0.419 0.7422 0.268 0.000 0.732 0.000
#> SRR949108 1 0.689 0.3750 0.512 0.000 0.376 0.112
#> SRR949109 1 0.187 0.3370 0.928 0.000 0.072 0.000
#> SRR949110 1 0.689 0.3750 0.512 0.000 0.376 0.112
#> SRR949111 1 0.187 0.3370 0.928 0.000 0.072 0.000
#> SRR949112 1 0.689 0.3750 0.512 0.000 0.376 0.112
#> SRR949113 2 0.298 0.8351 0.000 0.872 0.120 0.008
#> SRR949114 3 0.668 0.1529 0.312 0.000 0.576 0.112
#> SRR949115 3 0.668 0.1529 0.312 0.000 0.576 0.112
#> SRR949116 3 0.668 0.1529 0.312 0.000 0.576 0.112
#> SRR949117 3 0.475 0.7198 0.304 0.000 0.688 0.008
#> SRR949118 3 0.422 0.7414 0.272 0.000 0.728 0.000
#> SRR949119 1 0.762 0.3202 0.444 0.000 0.212 0.344
#> SRR949120 1 0.762 0.3202 0.444 0.000 0.212 0.344
#> SRR949121 1 0.689 0.3750 0.512 0.000 0.376 0.112
#> SRR949122 1 0.689 0.3750 0.512 0.000 0.376 0.112
#> SRR949123 2 0.456 0.4678 0.000 0.672 0.000 0.328
#> SRR949124 2 0.000 0.8753 0.000 1.000 0.000 0.000
#> SRR949125 1 0.187 0.3370 0.928 0.000 0.072 0.000
#> SRR949126 1 0.187 0.3370 0.928 0.000 0.072 0.000
#> SRR949127 4 0.681 0.2685 0.000 0.320 0.120 0.560
#> SRR949128 4 0.681 0.2685 0.000 0.320 0.120 0.560
#> SRR949129 4 0.681 0.2685 0.000 0.320 0.120 0.560
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR949076 4 0.4374 0.407 0.028 0.000 0.000 0.700 0.272
#> SRR949078 5 0.2806 0.594 0.000 0.152 0.000 0.004 0.844
#> SRR949077 4 0.4374 0.407 0.028 0.000 0.000 0.700 0.272
#> SRR949079 4 0.5851 0.664 0.272 0.000 0.000 0.588 0.140
#> SRR949080 4 0.5851 0.664 0.272 0.000 0.000 0.588 0.140
#> SRR949081 5 0.7021 0.349 0.140 0.000 0.232 0.072 0.556
#> SRR949082 5 0.2806 0.594 0.000 0.152 0.000 0.004 0.844
#> SRR949083 1 0.7106 0.155 0.428 0.000 0.060 0.112 0.400
#> SRR949084 1 0.6325 0.386 0.620 0.000 0.060 0.088 0.232
#> SRR949085 2 0.4575 0.797 0.000 0.712 0.000 0.236 0.052
#> SRR949087 5 0.2653 0.624 0.052 0.020 0.028 0.000 0.900
#> SRR949088 5 0.2653 0.624 0.052 0.020 0.028 0.000 0.900
#> SRR949086 3 0.3043 0.880 0.104 0.000 0.864 0.008 0.024
#> SRR949089 2 0.3612 0.818 0.000 0.732 0.000 0.268 0.000
#> SRR949090 4 0.5178 0.642 0.476 0.000 0.040 0.484 0.000
#> SRR949092 1 0.0162 0.704 0.996 0.000 0.000 0.004 0.000
#> SRR949093 1 0.0162 0.704 0.996 0.000 0.000 0.004 0.000
#> SRR949091 3 0.5498 0.392 0.076 0.000 0.568 0.356 0.000
#> SRR949095 5 0.3701 0.530 0.004 0.000 0.060 0.112 0.824
#> SRR949094 4 0.5851 0.664 0.272 0.000 0.000 0.588 0.140
#> SRR949096 1 0.6325 0.386 0.620 0.000 0.060 0.088 0.232
#> SRR949097 1 0.0162 0.707 0.996 0.000 0.004 0.000 0.000
#> SRR949098 2 0.3612 0.818 0.000 0.732 0.000 0.268 0.000
#> SRR949099 1 0.4397 0.349 0.696 0.000 0.276 0.028 0.000
#> SRR949101 3 0.1544 0.909 0.068 0.000 0.932 0.000 0.000
#> SRR949100 5 0.7251 0.428 0.200 0.268 0.016 0.020 0.496
#> SRR949102 5 0.7946 0.331 0.140 0.000 0.232 0.176 0.452
#> SRR949103 1 0.0162 0.707 0.996 0.000 0.004 0.000 0.000
#> SRR949104 2 0.0290 0.692 0.000 0.992 0.000 0.000 0.008
#> SRR949105 3 0.1544 0.909 0.068 0.000 0.932 0.000 0.000
#> SRR949106 3 0.1544 0.909 0.068 0.000 0.932 0.000 0.000
#> SRR949107 3 0.1544 0.909 0.068 0.000 0.932 0.000 0.000
#> SRR949108 1 0.0162 0.707 0.996 0.000 0.004 0.000 0.000
#> SRR949109 4 0.5049 0.647 0.480 0.000 0.032 0.488 0.000
#> SRR949110 1 0.0162 0.707 0.996 0.000 0.004 0.000 0.000
#> SRR949111 4 0.5049 0.647 0.480 0.000 0.032 0.488 0.000
#> SRR949112 1 0.0162 0.707 0.996 0.000 0.004 0.000 0.000
#> SRR949113 2 0.0404 0.688 0.000 0.988 0.000 0.000 0.012
#> SRR949114 1 0.3492 0.580 0.796 0.000 0.188 0.000 0.016
#> SRR949115 1 0.3492 0.580 0.796 0.000 0.188 0.000 0.016
#> SRR949116 1 0.3492 0.580 0.796 0.000 0.188 0.000 0.016
#> SRR949117 3 0.3043 0.880 0.104 0.000 0.864 0.008 0.024
#> SRR949118 3 0.2331 0.902 0.068 0.000 0.908 0.008 0.016
#> SRR949119 1 0.5732 0.338 0.624 0.000 0.000 0.192 0.184
#> SRR949120 1 0.5732 0.338 0.624 0.000 0.000 0.192 0.184
#> SRR949121 1 0.0162 0.707 0.996 0.000 0.004 0.000 0.000
#> SRR949122 1 0.0162 0.707 0.996 0.000 0.004 0.000 0.000
#> SRR949123 2 0.6973 0.419 0.000 0.404 0.008 0.268 0.320
#> SRR949124 2 0.3612 0.818 0.000 0.732 0.000 0.268 0.000
#> SRR949125 4 0.5049 0.647 0.480 0.000 0.032 0.488 0.000
#> SRR949126 4 0.5049 0.647 0.480 0.000 0.032 0.488 0.000
#> SRR949127 5 0.4235 0.443 0.000 0.424 0.000 0.000 0.576
#> SRR949128 5 0.4235 0.443 0.000 0.424 0.000 0.000 0.576
#> SRR949129 5 0.4235 0.443 0.000 0.424 0.000 0.000 0.576
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR949076 4 0.0363 0.3691 0.000 0.000 0.000 0.988 0.000 0.012
#> SRR949078 5 0.2655 0.6360 0.000 0.140 0.000 0.004 0.848 0.008
#> SRR949077 4 0.0363 0.3691 0.000 0.000 0.000 0.988 0.000 0.012
#> SRR949079 4 0.3023 0.6943 0.232 0.000 0.000 0.768 0.000 0.000
#> SRR949080 4 0.3023 0.6943 0.232 0.000 0.000 0.768 0.000 0.000
#> SRR949081 6 0.5291 0.4322 0.000 0.000 0.016 0.060 0.448 0.476
#> SRR949082 5 0.2655 0.6360 0.000 0.140 0.000 0.004 0.848 0.008
#> SRR949083 1 0.6633 0.0552 0.404 0.000 0.000 0.064 0.388 0.144
#> SRR949084 1 0.5982 0.4333 0.596 0.000 0.000 0.064 0.220 0.120
#> SRR949085 2 0.1606 0.7873 0.000 0.932 0.000 0.004 0.056 0.008
#> SRR949087 5 0.2231 0.5622 0.028 0.016 0.000 0.000 0.908 0.048
#> SRR949088 5 0.2231 0.5622 0.028 0.016 0.000 0.000 0.908 0.048
#> SRR949086 3 0.4267 0.6715 0.012 0.000 0.688 0.000 0.028 0.272
#> SRR949089 2 0.0000 0.8059 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949090 4 0.4912 0.6922 0.432 0.000 0.008 0.516 0.000 0.044
#> SRR949092 1 0.0291 0.7143 0.992 0.000 0.000 0.004 0.000 0.004
#> SRR949093 1 0.0291 0.7143 0.992 0.000 0.000 0.004 0.000 0.004
#> SRR949091 3 0.4518 0.3670 0.000 0.000 0.604 0.352 0.000 0.044
#> SRR949095 5 0.3453 0.3216 0.000 0.000 0.000 0.064 0.804 0.132
#> SRR949094 4 0.3023 0.6943 0.232 0.000 0.000 0.768 0.000 0.000
#> SRR949096 1 0.5982 0.4333 0.596 0.000 0.000 0.064 0.220 0.120
#> SRR949097 1 0.0632 0.7157 0.976 0.000 0.000 0.000 0.000 0.024
#> SRR949098 2 0.0000 0.8059 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949099 1 0.4766 0.2830 0.612 0.000 0.072 0.000 0.000 0.316
#> SRR949101 3 0.0000 0.7821 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR949100 5 0.5372 0.3739 0.112 0.000 0.000 0.000 0.484 0.404
#> SRR949102 6 0.5768 0.5438 0.000 0.000 0.016 0.408 0.112 0.464
#> SRR949103 1 0.0632 0.7157 0.976 0.000 0.000 0.000 0.000 0.024
#> SRR949104 2 0.3330 0.6717 0.000 0.716 0.000 0.000 0.000 0.284
#> SRR949105 3 0.0000 0.7821 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR949106 3 0.0000 0.7821 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR949107 3 0.0000 0.7821 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR949108 1 0.0000 0.7157 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949109 4 0.4681 0.6990 0.432 0.000 0.000 0.524 0.000 0.044
#> SRR949110 1 0.0632 0.7157 0.976 0.000 0.000 0.000 0.000 0.024
#> SRR949111 4 0.4681 0.6990 0.432 0.000 0.000 0.524 0.000 0.044
#> SRR949112 1 0.0000 0.7157 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949113 2 0.3468 0.6675 0.000 0.712 0.000 0.000 0.004 0.284
#> SRR949114 1 0.3432 0.6145 0.800 0.000 0.148 0.000 0.000 0.052
#> SRR949115 1 0.3432 0.6145 0.800 0.000 0.148 0.000 0.000 0.052
#> SRR949116 1 0.3432 0.6145 0.800 0.000 0.148 0.000 0.000 0.052
#> SRR949117 3 0.4267 0.6715 0.012 0.000 0.688 0.000 0.028 0.272
#> SRR949118 3 0.3244 0.6937 0.000 0.000 0.732 0.000 0.000 0.268
#> SRR949119 1 0.5147 0.2351 0.548 0.000 0.000 0.356 0.000 0.096
#> SRR949120 1 0.5147 0.2351 0.548 0.000 0.000 0.356 0.000 0.096
#> SRR949121 1 0.0000 0.7157 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949122 1 0.0000 0.7157 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949123 2 0.4408 0.4064 0.000 0.664 0.000 0.000 0.280 0.056
#> SRR949124 2 0.0000 0.8059 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949125 4 0.4681 0.6990 0.432 0.000 0.000 0.524 0.000 0.044
#> SRR949126 4 0.4681 0.6990 0.432 0.000 0.000 0.524 0.000 0.044
#> SRR949127 5 0.5336 0.6164 0.000 0.144 0.000 0.000 0.572 0.284
#> SRR949128 5 0.5336 0.6164 0.000 0.144 0.000 0.000 0.572 0.284
#> SRR949129 5 0.5336 0.6164 0.000 0.144 0.000 0.000 0.572 0.284
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)
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 16816 rows and 54 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 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 0.666 0.877 0.932 0.4310 0.575 0.575
#> 3 3 0.459 0.547 0.773 0.4614 0.735 0.568
#> 4 4 0.536 0.582 0.729 0.1585 0.834 0.585
#> 5 5 0.594 0.627 0.727 0.0779 0.943 0.778
#> 6 6 0.716 0.536 0.712 0.0435 0.983 0.919
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
#> SRR949076 1 0.2778 0.918 0.952 0.048
#> SRR949078 2 0.1184 0.930 0.016 0.984
#> SRR949077 1 0.2778 0.918 0.952 0.048
#> SRR949079 1 0.2778 0.918 0.952 0.048
#> SRR949080 1 0.2778 0.918 0.952 0.048
#> SRR949081 2 0.8555 0.616 0.280 0.720
#> SRR949082 2 0.1184 0.930 0.016 0.984
#> SRR949083 1 0.2778 0.918 0.952 0.048
#> SRR949084 1 0.2778 0.918 0.952 0.048
#> SRR949085 2 0.0672 0.929 0.008 0.992
#> SRR949087 2 0.6343 0.811 0.160 0.840
#> SRR949088 2 0.6343 0.811 0.160 0.840
#> SRR949086 1 0.6801 0.810 0.820 0.180
#> SRR949089 2 0.0672 0.929 0.008 0.992
#> SRR949090 1 0.0000 0.922 1.000 0.000
#> SRR949092 1 0.2778 0.918 0.952 0.048
#> SRR949093 1 0.2778 0.918 0.952 0.048
#> SRR949091 1 0.1843 0.914 0.972 0.028
#> SRR949095 2 0.9129 0.540 0.328 0.672
#> SRR949094 1 0.0000 0.922 1.000 0.000
#> SRR949096 1 0.2778 0.918 0.952 0.048
#> SRR949097 1 0.0000 0.922 1.000 0.000
#> SRR949098 2 0.0672 0.929 0.008 0.992
#> SRR949099 1 0.0000 0.922 1.000 0.000
#> SRR949101 1 0.6712 0.814 0.824 0.176
#> SRR949100 1 0.9833 0.300 0.576 0.424
#> SRR949102 1 0.7139 0.806 0.804 0.196
#> SRR949103 1 0.0000 0.922 1.000 0.000
#> SRR949104 2 0.0672 0.929 0.008 0.992
#> SRR949105 1 0.6887 0.806 0.816 0.184
#> SRR949106 1 0.6887 0.806 0.816 0.184
#> SRR949107 1 0.6887 0.806 0.816 0.184
#> SRR949108 1 0.0000 0.922 1.000 0.000
#> SRR949109 1 0.0000 0.922 1.000 0.000
#> SRR949110 1 0.0000 0.922 1.000 0.000
#> SRR949111 1 0.0000 0.922 1.000 0.000
#> SRR949112 1 0.2778 0.918 0.952 0.048
#> SRR949113 2 0.1184 0.930 0.016 0.984
#> SRR949114 1 0.1843 0.914 0.972 0.028
#> SRR949115 1 0.1843 0.914 0.972 0.028
#> SRR949116 1 0.1843 0.914 0.972 0.028
#> SRR949117 1 0.6801 0.810 0.820 0.180
#> SRR949118 1 0.6712 0.814 0.824 0.176
#> SRR949119 1 0.2778 0.918 0.952 0.048
#> SRR949120 1 0.2778 0.918 0.952 0.048
#> SRR949121 1 0.0000 0.922 1.000 0.000
#> SRR949122 1 0.2778 0.918 0.952 0.048
#> SRR949123 2 0.0672 0.929 0.008 0.992
#> SRR949124 2 0.0672 0.929 0.008 0.992
#> SRR949125 1 0.0000 0.922 1.000 0.000
#> SRR949126 1 0.0000 0.922 1.000 0.000
#> SRR949127 2 0.1184 0.930 0.016 0.984
#> SRR949128 2 0.1184 0.930 0.016 0.984
#> SRR949129 2 0.1184 0.930 0.016 0.984
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR949076 1 0.5115 0.562 0.768 0.004 0.228
#> SRR949078 2 0.1453 0.895 0.024 0.968 0.008
#> SRR949077 1 0.5070 0.564 0.772 0.004 0.224
#> SRR949079 1 0.5244 0.565 0.756 0.004 0.240
#> SRR949080 1 0.5244 0.565 0.756 0.004 0.240
#> SRR949081 1 0.9144 -0.075 0.448 0.408 0.144
#> SRR949082 2 0.1453 0.895 0.024 0.968 0.008
#> SRR949083 1 0.1315 0.637 0.972 0.020 0.008
#> SRR949084 1 0.0848 0.642 0.984 0.008 0.008
#> SRR949085 2 0.1529 0.901 0.000 0.960 0.040
#> SRR949087 2 0.8085 0.401 0.332 0.584 0.084
#> SRR949088 2 0.8085 0.401 0.332 0.584 0.084
#> SRR949086 3 0.5791 0.728 0.148 0.060 0.792
#> SRR949089 2 0.1643 0.900 0.000 0.956 0.044
#> SRR949090 3 0.6302 -0.229 0.480 0.000 0.520
#> SRR949092 1 0.1878 0.648 0.952 0.004 0.044
#> SRR949093 1 0.1878 0.648 0.952 0.004 0.044
#> SRR949091 3 0.2400 0.659 0.064 0.004 0.932
#> SRR949095 1 0.7015 0.179 0.584 0.392 0.024
#> SRR949094 1 0.5016 0.565 0.760 0.000 0.240
#> SRR949096 1 0.0848 0.642 0.984 0.008 0.008
#> SRR949097 1 0.5480 0.427 0.732 0.004 0.264
#> SRR949098 2 0.1643 0.900 0.000 0.956 0.044
#> SRR949099 3 0.6264 0.364 0.380 0.004 0.616
#> SRR949101 3 0.3973 0.729 0.088 0.032 0.880
#> SRR949100 1 0.9374 0.194 0.464 0.360 0.176
#> SRR949102 1 0.6361 0.480 0.728 0.040 0.232
#> SRR949103 1 0.5656 0.390 0.712 0.004 0.284
#> SRR949104 2 0.1529 0.901 0.000 0.960 0.040
#> SRR949105 3 0.5165 0.743 0.096 0.072 0.832
#> SRR949106 3 0.5165 0.743 0.096 0.072 0.832
#> SRR949107 3 0.5165 0.743 0.096 0.072 0.832
#> SRR949108 1 0.1878 0.648 0.952 0.004 0.044
#> SRR949109 3 0.6305 -0.240 0.484 0.000 0.516
#> SRR949110 1 0.5480 0.427 0.732 0.004 0.264
#> SRR949111 1 0.6267 0.289 0.548 0.000 0.452
#> SRR949112 1 0.2400 0.640 0.932 0.004 0.064
#> SRR949113 2 0.1647 0.901 0.004 0.960 0.036
#> SRR949114 1 0.6678 -0.130 0.512 0.008 0.480
#> SRR949115 1 0.6678 -0.130 0.512 0.008 0.480
#> SRR949116 1 0.6678 -0.130 0.512 0.008 0.480
#> SRR949117 3 0.5791 0.728 0.148 0.060 0.792
#> SRR949118 3 0.5222 0.732 0.144 0.040 0.816
#> SRR949119 1 0.1950 0.649 0.952 0.008 0.040
#> SRR949120 1 0.1950 0.649 0.952 0.008 0.040
#> SRR949121 1 0.2772 0.631 0.916 0.004 0.080
#> SRR949122 1 0.1878 0.648 0.952 0.004 0.044
#> SRR949123 2 0.1643 0.900 0.000 0.956 0.044
#> SRR949124 2 0.1643 0.900 0.000 0.956 0.044
#> SRR949125 1 0.6307 0.208 0.512 0.000 0.488
#> SRR949126 1 0.6307 0.208 0.512 0.000 0.488
#> SRR949127 2 0.1031 0.898 0.024 0.976 0.000
#> SRR949128 2 0.1031 0.898 0.024 0.976 0.000
#> SRR949129 2 0.1031 0.898 0.024 0.976 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR949076 4 0.5284 0.5541 0.264 0.000 0.040 0.696
#> SRR949078 2 0.4781 0.8011 0.008 0.772 0.032 0.188
#> SRR949077 4 0.5078 0.5488 0.272 0.000 0.028 0.700
#> SRR949079 4 0.5417 0.5863 0.284 0.000 0.040 0.676
#> SRR949080 4 0.5417 0.5863 0.284 0.000 0.040 0.676
#> SRR949081 4 0.9443 -0.0852 0.168 0.204 0.200 0.428
#> SRR949082 2 0.4781 0.8011 0.008 0.772 0.032 0.188
#> SRR949083 1 0.3975 0.5089 0.760 0.000 0.000 0.240
#> SRR949084 1 0.3444 0.5536 0.816 0.000 0.000 0.184
#> SRR949085 2 0.0336 0.8301 0.000 0.992 0.008 0.000
#> SRR949087 2 0.9525 0.3427 0.236 0.360 0.120 0.284
#> SRR949088 2 0.9525 0.3427 0.236 0.360 0.120 0.284
#> SRR949086 3 0.2775 0.8156 0.084 0.000 0.896 0.020
#> SRR949089 2 0.0188 0.8304 0.000 0.996 0.004 0.000
#> SRR949090 4 0.7474 0.5493 0.292 0.000 0.212 0.496
#> SRR949092 1 0.1174 0.6767 0.968 0.000 0.012 0.020
#> SRR949093 1 0.1174 0.6767 0.968 0.000 0.012 0.020
#> SRR949091 3 0.4718 0.5048 0.012 0.000 0.708 0.280
#> SRR949095 4 0.8733 -0.1022 0.268 0.256 0.048 0.428
#> SRR949094 4 0.5417 0.5863 0.284 0.000 0.040 0.676
#> SRR949096 1 0.3444 0.5536 0.816 0.000 0.000 0.184
#> SRR949097 1 0.3013 0.6401 0.888 0.000 0.080 0.032
#> SRR949098 2 0.0336 0.8301 0.000 0.992 0.008 0.000
#> SRR949099 3 0.6285 0.2169 0.412 0.000 0.528 0.060
#> SRR949101 3 0.2670 0.8179 0.040 0.000 0.908 0.052
#> SRR949100 1 0.9501 -0.0660 0.388 0.244 0.128 0.240
#> SRR949102 4 0.8088 0.1905 0.300 0.012 0.248 0.440
#> SRR949103 1 0.3342 0.6246 0.868 0.000 0.100 0.032
#> SRR949104 2 0.0000 0.8306 0.000 1.000 0.000 0.000
#> SRR949105 3 0.3796 0.8247 0.056 0.000 0.848 0.096
#> SRR949106 3 0.3796 0.8247 0.056 0.000 0.848 0.096
#> SRR949107 3 0.3796 0.8247 0.056 0.000 0.848 0.096
#> SRR949108 1 0.0672 0.6769 0.984 0.000 0.008 0.008
#> SRR949109 4 0.7474 0.5493 0.292 0.000 0.212 0.496
#> SRR949110 1 0.2943 0.6411 0.892 0.000 0.076 0.032
#> SRR949111 4 0.7330 0.5669 0.304 0.000 0.184 0.512
#> SRR949112 1 0.1388 0.6787 0.960 0.000 0.028 0.012
#> SRR949113 2 0.0000 0.8306 0.000 1.000 0.000 0.000
#> SRR949114 1 0.5650 0.1543 0.544 0.000 0.432 0.024
#> SRR949115 1 0.5650 0.1543 0.544 0.000 0.432 0.024
#> SRR949116 1 0.5650 0.1543 0.544 0.000 0.432 0.024
#> SRR949117 3 0.3037 0.8033 0.100 0.000 0.880 0.020
#> SRR949118 3 0.2596 0.8216 0.068 0.000 0.908 0.024
#> SRR949119 1 0.4277 0.4048 0.720 0.000 0.000 0.280
#> SRR949120 1 0.4277 0.4048 0.720 0.000 0.000 0.280
#> SRR949121 1 0.1305 0.6785 0.960 0.000 0.036 0.004
#> SRR949122 1 0.0336 0.6785 0.992 0.000 0.008 0.000
#> SRR949123 2 0.0000 0.8306 0.000 1.000 0.000 0.000
#> SRR949124 2 0.0000 0.8306 0.000 1.000 0.000 0.000
#> SRR949125 4 0.7412 0.5652 0.296 0.000 0.200 0.504
#> SRR949126 4 0.7412 0.5652 0.296 0.000 0.200 0.504
#> SRR949127 2 0.4604 0.8089 0.004 0.784 0.036 0.176
#> SRR949128 2 0.4604 0.8089 0.004 0.784 0.036 0.176
#> SRR949129 2 0.4604 0.8089 0.004 0.784 0.036 0.176
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR949076 4 0.4991 0.627 0.092 0.000 0.008 0.720 0.180
#> SRR949078 2 0.4707 0.513 0.000 0.588 0.000 0.020 0.392
#> SRR949077 4 0.4914 0.628 0.108 0.000 0.000 0.712 0.180
#> SRR949079 4 0.4155 0.738 0.144 0.000 0.000 0.780 0.076
#> SRR949080 4 0.4155 0.738 0.144 0.000 0.000 0.780 0.076
#> SRR949081 5 0.7420 0.596 0.068 0.068 0.124 0.132 0.608
#> SRR949082 2 0.4707 0.513 0.000 0.588 0.000 0.020 0.392
#> SRR949083 1 0.4879 0.530 0.716 0.000 0.000 0.108 0.176
#> SRR949084 1 0.3862 0.623 0.808 0.000 0.000 0.104 0.088
#> SRR949085 2 0.0510 0.784 0.000 0.984 0.000 0.016 0.000
#> SRR949087 5 0.6696 0.533 0.144 0.212 0.032 0.012 0.600
#> SRR949088 5 0.6696 0.533 0.144 0.212 0.032 0.012 0.600
#> SRR949086 3 0.3673 0.711 0.028 0.000 0.820 0.012 0.140
#> SRR949089 2 0.0404 0.784 0.000 0.988 0.000 0.012 0.000
#> SRR949090 4 0.5195 0.738 0.136 0.000 0.092 0.736 0.036
#> SRR949092 1 0.0162 0.725 0.996 0.000 0.000 0.004 0.000
#> SRR949093 1 0.0162 0.725 0.996 0.000 0.000 0.004 0.000
#> SRR949091 3 0.5259 0.299 0.016 0.000 0.588 0.368 0.028
#> SRR949095 5 0.6295 0.623 0.108 0.088 0.004 0.132 0.668
#> SRR949094 4 0.3975 0.741 0.144 0.000 0.000 0.792 0.064
#> SRR949096 1 0.3967 0.617 0.800 0.000 0.000 0.108 0.092
#> SRR949097 1 0.4339 0.656 0.800 0.000 0.028 0.100 0.072
#> SRR949098 2 0.0404 0.784 0.000 0.988 0.000 0.012 0.000
#> SRR949099 3 0.8033 0.248 0.244 0.000 0.408 0.108 0.240
#> SRR949101 3 0.2267 0.731 0.008 0.000 0.916 0.028 0.048
#> SRR949100 5 0.7206 0.484 0.152 0.100 0.036 0.096 0.616
#> SRR949102 5 0.7854 0.286 0.092 0.008 0.148 0.308 0.444
#> SRR949103 1 0.4421 0.654 0.796 0.000 0.032 0.100 0.072
#> SRR949104 2 0.0162 0.785 0.000 0.996 0.000 0.000 0.004
#> SRR949105 3 0.3268 0.726 0.004 0.000 0.856 0.060 0.080
#> SRR949106 3 0.3268 0.726 0.004 0.000 0.856 0.060 0.080
#> SRR949107 3 0.3268 0.726 0.004 0.000 0.856 0.060 0.080
#> SRR949108 1 0.0451 0.723 0.988 0.000 0.000 0.004 0.008
#> SRR949109 4 0.5172 0.742 0.144 0.000 0.084 0.736 0.036
#> SRR949110 1 0.4404 0.658 0.796 0.000 0.028 0.096 0.080
#> SRR949111 4 0.4655 0.768 0.140 0.000 0.080 0.764 0.016
#> SRR949112 1 0.0833 0.721 0.976 0.000 0.004 0.004 0.016
#> SRR949113 2 0.0162 0.785 0.000 0.996 0.000 0.000 0.004
#> SRR949114 1 0.6330 0.252 0.512 0.000 0.376 0.028 0.084
#> SRR949115 1 0.6330 0.252 0.512 0.000 0.376 0.028 0.084
#> SRR949116 1 0.6330 0.252 0.512 0.000 0.376 0.028 0.084
#> SRR949117 3 0.3673 0.711 0.028 0.000 0.820 0.012 0.140
#> SRR949118 3 0.3667 0.707 0.020 0.000 0.812 0.012 0.156
#> SRR949119 1 0.5797 0.377 0.592 0.000 0.000 0.276 0.132
#> SRR949120 1 0.5797 0.377 0.592 0.000 0.000 0.276 0.132
#> SRR949121 1 0.0727 0.722 0.980 0.000 0.004 0.004 0.012
#> SRR949122 1 0.0162 0.725 0.996 0.000 0.000 0.004 0.000
#> SRR949123 2 0.0000 0.785 0.000 1.000 0.000 0.000 0.000
#> SRR949124 2 0.0000 0.785 0.000 1.000 0.000 0.000 0.000
#> SRR949125 4 0.4382 0.767 0.140 0.000 0.084 0.772 0.004
#> SRR949126 4 0.4382 0.767 0.140 0.000 0.084 0.772 0.004
#> SRR949127 2 0.4440 0.626 0.000 0.660 0.004 0.012 0.324
#> SRR949128 2 0.4440 0.626 0.000 0.660 0.004 0.012 0.324
#> SRR949129 2 0.4440 0.626 0.000 0.660 0.004 0.012 0.324
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR949076 4 0.5647 0.5247 0.020 0.000 0.000 0.592 0.144 0.244
#> SRR949078 2 0.4314 0.5136 0.000 0.536 0.000 0.000 0.444 0.020
#> SRR949077 4 0.5717 0.5024 0.020 0.000 0.000 0.580 0.148 0.252
#> SRR949079 4 0.4251 0.6912 0.056 0.000 0.000 0.772 0.044 0.128
#> SRR949080 4 0.4251 0.6912 0.056 0.000 0.000 0.772 0.044 0.128
#> SRR949081 5 0.5884 0.4213 0.032 0.000 0.044 0.040 0.580 0.304
#> SRR949082 2 0.4314 0.5136 0.000 0.536 0.000 0.000 0.444 0.020
#> SRR949083 1 0.5761 0.4464 0.600 0.000 0.000 0.028 0.184 0.188
#> SRR949084 1 0.5165 0.5496 0.700 0.000 0.000 0.068 0.088 0.144
#> SRR949085 2 0.1268 0.7550 0.000 0.952 0.000 0.004 0.008 0.036
#> SRR949087 5 0.5092 0.4833 0.104 0.084 0.024 0.000 0.736 0.052
#> SRR949088 5 0.5092 0.4833 0.104 0.084 0.024 0.000 0.736 0.052
#> SRR949086 3 0.5673 0.4483 0.004 0.000 0.512 0.008 0.112 0.364
#> SRR949089 2 0.0935 0.7545 0.000 0.964 0.000 0.004 0.000 0.032
#> SRR949090 4 0.3407 0.6719 0.064 0.000 0.036 0.852 0.020 0.028
#> SRR949092 1 0.0870 0.6617 0.972 0.000 0.000 0.012 0.012 0.004
#> SRR949093 1 0.0870 0.6617 0.972 0.000 0.000 0.012 0.012 0.004
#> SRR949091 4 0.5696 -0.0898 0.000 0.000 0.396 0.444 0.000 0.160
#> SRR949095 5 0.5056 0.4805 0.048 0.000 0.000 0.048 0.664 0.240
#> SRR949094 4 0.3924 0.6944 0.056 0.000 0.000 0.796 0.032 0.116
#> SRR949096 1 0.5251 0.5438 0.692 0.000 0.000 0.072 0.088 0.148
#> SRR949097 1 0.4175 0.5366 0.780 0.000 0.000 0.112 0.036 0.072
#> SRR949098 2 0.1080 0.7541 0.000 0.960 0.000 0.004 0.004 0.032
#> SRR949099 6 0.8776 0.0000 0.200 0.000 0.236 0.116 0.176 0.272
#> SRR949101 3 0.4034 0.5421 0.000 0.000 0.692 0.024 0.004 0.280
#> SRR949100 5 0.5748 0.2376 0.112 0.020 0.004 0.080 0.688 0.096
#> SRR949102 5 0.7195 0.2469 0.048 0.000 0.060 0.108 0.396 0.388
#> SRR949103 1 0.4218 0.5318 0.776 0.000 0.000 0.116 0.036 0.072
#> SRR949104 2 0.0405 0.7573 0.000 0.988 0.000 0.000 0.004 0.008
#> SRR949105 3 0.0508 0.5817 0.000 0.000 0.984 0.012 0.004 0.000
#> SRR949106 3 0.0508 0.5817 0.000 0.000 0.984 0.012 0.004 0.000
#> SRR949107 3 0.0508 0.5817 0.000 0.000 0.984 0.012 0.004 0.000
#> SRR949108 1 0.1332 0.6590 0.952 0.000 0.000 0.008 0.012 0.028
#> SRR949109 4 0.3304 0.6719 0.068 0.000 0.036 0.856 0.020 0.020
#> SRR949110 1 0.4213 0.5464 0.780 0.000 0.000 0.100 0.040 0.080
#> SRR949111 4 0.3229 0.6970 0.064 0.000 0.036 0.860 0.012 0.028
#> SRR949112 1 0.0622 0.6565 0.980 0.000 0.000 0.000 0.008 0.012
#> SRR949113 2 0.0622 0.7573 0.000 0.980 0.000 0.000 0.012 0.008
#> SRR949114 1 0.6454 0.1988 0.536 0.000 0.164 0.028 0.020 0.252
#> SRR949115 1 0.6454 0.1988 0.536 0.000 0.164 0.028 0.020 0.252
#> SRR949116 1 0.6454 0.1988 0.536 0.000 0.164 0.028 0.020 0.252
#> SRR949117 3 0.5739 0.4490 0.008 0.000 0.512 0.008 0.108 0.364
#> SRR949118 3 0.5444 0.4609 0.000 0.000 0.524 0.008 0.100 0.368
#> SRR949119 1 0.6763 0.3762 0.508 0.000 0.000 0.180 0.100 0.212
#> SRR949120 1 0.6763 0.3762 0.508 0.000 0.000 0.180 0.100 0.212
#> SRR949121 1 0.0260 0.6579 0.992 0.000 0.000 0.000 0.000 0.008
#> SRR949122 1 0.0000 0.6597 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949123 2 0.0260 0.7556 0.000 0.992 0.000 0.000 0.000 0.008
#> SRR949124 2 0.0146 0.7552 0.000 0.996 0.000 0.000 0.000 0.004
#> SRR949125 4 0.2461 0.6938 0.064 0.000 0.044 0.888 0.000 0.004
#> SRR949126 4 0.2461 0.6938 0.064 0.000 0.044 0.888 0.000 0.004
#> SRR949127 2 0.4649 0.5731 0.000 0.560 0.000 0.004 0.400 0.036
#> SRR949128 2 0.4649 0.5731 0.000 0.560 0.000 0.004 0.400 0.036
#> SRR949129 2 0.4649 0.5731 0.000 0.560 0.000 0.004 0.400 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)
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 16816 rows and 54 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 0.698 0.871 0.941 0.4805 0.547 0.547
#> 3 3 0.710 0.693 0.885 0.3983 0.751 0.554
#> 4 4 0.857 0.851 0.928 0.1206 0.880 0.649
#> 5 5 0.785 0.710 0.826 0.0550 0.958 0.831
#> 6 6 0.759 0.673 0.800 0.0369 0.996 0.980
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR949076 1 0.730 0.717 0.796 0.204
#> SRR949078 2 0.000 0.995 0.000 1.000
#> SRR949077 1 0.722 0.722 0.800 0.200
#> SRR949079 1 0.000 0.903 1.000 0.000
#> SRR949080 1 0.000 0.903 1.000 0.000
#> SRR949081 2 0.000 0.995 0.000 1.000
#> SRR949082 2 0.000 0.995 0.000 1.000
#> SRR949083 1 0.973 0.341 0.596 0.404
#> SRR949084 1 0.000 0.903 1.000 0.000
#> SRR949085 2 0.000 0.995 0.000 1.000
#> SRR949087 2 0.000 0.995 0.000 1.000
#> SRR949088 2 0.000 0.995 0.000 1.000
#> SRR949086 1 0.949 0.513 0.632 0.368
#> SRR949089 2 0.000 0.995 0.000 1.000
#> SRR949090 1 0.000 0.903 1.000 0.000
#> SRR949092 1 0.000 0.903 1.000 0.000
#> SRR949093 1 0.000 0.903 1.000 0.000
#> SRR949091 1 0.000 0.903 1.000 0.000
#> SRR949095 2 0.000 0.995 0.000 1.000
#> SRR949094 1 0.000 0.903 1.000 0.000
#> SRR949096 1 0.000 0.903 1.000 0.000
#> SRR949097 1 0.000 0.903 1.000 0.000
#> SRR949098 2 0.000 0.995 0.000 1.000
#> SRR949099 1 0.000 0.903 1.000 0.000
#> SRR949101 1 0.662 0.769 0.828 0.172
#> SRR949100 2 0.000 0.995 0.000 1.000
#> SRR949102 2 0.358 0.914 0.068 0.932
#> SRR949103 1 0.000 0.903 1.000 0.000
#> SRR949104 2 0.000 0.995 0.000 1.000
#> SRR949105 1 0.949 0.513 0.632 0.368
#> SRR949106 1 0.949 0.513 0.632 0.368
#> SRR949107 1 0.949 0.513 0.632 0.368
#> SRR949108 1 0.000 0.903 1.000 0.000
#> SRR949109 1 0.000 0.903 1.000 0.000
#> SRR949110 1 0.000 0.903 1.000 0.000
#> SRR949111 1 0.000 0.903 1.000 0.000
#> SRR949112 1 0.000 0.903 1.000 0.000
#> SRR949113 2 0.000 0.995 0.000 1.000
#> SRR949114 1 0.000 0.903 1.000 0.000
#> SRR949115 1 0.000 0.903 1.000 0.000
#> SRR949116 1 0.000 0.903 1.000 0.000
#> SRR949117 1 0.949 0.513 0.632 0.368
#> SRR949118 1 0.900 0.594 0.684 0.316
#> SRR949119 1 0.000 0.903 1.000 0.000
#> SRR949120 1 0.000 0.903 1.000 0.000
#> SRR949121 1 0.000 0.903 1.000 0.000
#> SRR949122 1 0.000 0.903 1.000 0.000
#> SRR949123 2 0.000 0.995 0.000 1.000
#> SRR949124 2 0.000 0.995 0.000 1.000
#> SRR949125 1 0.000 0.903 1.000 0.000
#> SRR949126 1 0.000 0.903 1.000 0.000
#> SRR949127 2 0.000 0.995 0.000 1.000
#> SRR949128 2 0.000 0.995 0.000 1.000
#> SRR949129 2 0.000 0.995 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR949076 1 0.6204 0.2619 0.576 0.000 0.424
#> SRR949078 2 0.0000 1.0000 0.000 1.000 0.000
#> SRR949077 1 0.6204 0.2619 0.576 0.000 0.424
#> SRR949079 1 0.6204 0.2619 0.576 0.000 0.424
#> SRR949080 1 0.6204 0.2619 0.576 0.000 0.424
#> SRR949081 2 0.0000 1.0000 0.000 1.000 0.000
#> SRR949082 2 0.0000 1.0000 0.000 1.000 0.000
#> SRR949083 1 0.0000 0.7454 1.000 0.000 0.000
#> SRR949084 1 0.0000 0.7454 1.000 0.000 0.000
#> SRR949085 2 0.0000 1.0000 0.000 1.000 0.000
#> SRR949087 2 0.0000 1.0000 0.000 1.000 0.000
#> SRR949088 2 0.0000 1.0000 0.000 1.000 0.000
#> SRR949086 3 0.0592 0.7297 0.000 0.012 0.988
#> SRR949089 2 0.0000 1.0000 0.000 1.000 0.000
#> SRR949090 3 0.5058 0.5565 0.244 0.000 0.756
#> SRR949092 1 0.0000 0.7454 1.000 0.000 0.000
#> SRR949093 1 0.0000 0.7454 1.000 0.000 0.000
#> SRR949091 3 0.0000 0.7355 0.000 0.000 1.000
#> SRR949095 2 0.0000 1.0000 0.000 1.000 0.000
#> SRR949094 1 0.6204 0.2619 0.576 0.000 0.424
#> SRR949096 1 0.0000 0.7454 1.000 0.000 0.000
#> SRR949097 1 0.5678 0.3280 0.684 0.000 0.316
#> SRR949098 2 0.0000 1.0000 0.000 1.000 0.000
#> SRR949099 3 0.0000 0.7355 0.000 0.000 1.000
#> SRR949101 3 0.0000 0.7355 0.000 0.000 1.000
#> SRR949100 2 0.0000 1.0000 0.000 1.000 0.000
#> SRR949102 3 0.9885 0.0287 0.308 0.284 0.408
#> SRR949103 1 0.5733 0.3099 0.676 0.000 0.324
#> SRR949104 2 0.0000 1.0000 0.000 1.000 0.000
#> SRR949105 3 0.0000 0.7355 0.000 0.000 1.000
#> SRR949106 3 0.0000 0.7355 0.000 0.000 1.000
#> SRR949107 3 0.0000 0.7355 0.000 0.000 1.000
#> SRR949108 1 0.0000 0.7454 1.000 0.000 0.000
#> SRR949109 3 0.5098 0.5519 0.248 0.000 0.752
#> SRR949110 1 0.5678 0.3280 0.684 0.000 0.316
#> SRR949111 3 0.5138 0.5466 0.252 0.000 0.748
#> SRR949112 1 0.0000 0.7454 1.000 0.000 0.000
#> SRR949113 2 0.0000 1.0000 0.000 1.000 0.000
#> SRR949114 3 0.6204 0.1951 0.424 0.000 0.576
#> SRR949115 3 0.6204 0.1951 0.424 0.000 0.576
#> SRR949116 3 0.6204 0.1951 0.424 0.000 0.576
#> SRR949117 3 0.0424 0.7320 0.000 0.008 0.992
#> SRR949118 3 0.0000 0.7355 0.000 0.000 1.000
#> SRR949119 1 0.0000 0.7454 1.000 0.000 0.000
#> SRR949120 1 0.0000 0.7454 1.000 0.000 0.000
#> SRR949121 1 0.0000 0.7454 1.000 0.000 0.000
#> SRR949122 1 0.0000 0.7454 1.000 0.000 0.000
#> SRR949123 2 0.0000 1.0000 0.000 1.000 0.000
#> SRR949124 2 0.0000 1.0000 0.000 1.000 0.000
#> SRR949125 3 0.5138 0.5466 0.252 0.000 0.748
#> SRR949126 3 0.5138 0.5466 0.252 0.000 0.748
#> SRR949127 2 0.0000 1.0000 0.000 1.000 0.000
#> SRR949128 2 0.0000 1.0000 0.000 1.000 0.000
#> SRR949129 2 0.0000 1.0000 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR949076 4 0.1978 0.850 0.068 0.004 0.000 0.928
#> SRR949078 2 0.0000 0.975 0.000 1.000 0.000 0.000
#> SRR949077 4 0.1867 0.850 0.072 0.000 0.000 0.928
#> SRR949079 4 0.0336 0.887 0.008 0.000 0.000 0.992
#> SRR949080 4 0.0336 0.887 0.008 0.000 0.000 0.992
#> SRR949081 2 0.4998 0.704 0.000 0.748 0.200 0.052
#> SRR949082 2 0.0000 0.975 0.000 1.000 0.000 0.000
#> SRR949083 1 0.1474 0.924 0.948 0.000 0.000 0.052
#> SRR949084 1 0.1474 0.924 0.948 0.000 0.000 0.052
#> SRR949085 2 0.0000 0.975 0.000 1.000 0.000 0.000
#> SRR949087 2 0.0188 0.974 0.000 0.996 0.000 0.004
#> SRR949088 2 0.0188 0.974 0.000 0.996 0.000 0.004
#> SRR949086 3 0.0000 0.814 0.000 0.000 1.000 0.000
#> SRR949089 2 0.0000 0.975 0.000 1.000 0.000 0.000
#> SRR949090 4 0.1798 0.890 0.040 0.000 0.016 0.944
#> SRR949092 1 0.0000 0.941 1.000 0.000 0.000 0.000
#> SRR949093 1 0.0000 0.941 1.000 0.000 0.000 0.000
#> SRR949091 3 0.4697 0.392 0.000 0.000 0.644 0.356
#> SRR949095 2 0.1474 0.930 0.000 0.948 0.000 0.052
#> SRR949094 4 0.0336 0.887 0.008 0.000 0.000 0.992
#> SRR949096 1 0.1474 0.924 0.948 0.000 0.000 0.052
#> SRR949097 1 0.1867 0.903 0.928 0.000 0.000 0.072
#> SRR949098 2 0.0000 0.975 0.000 1.000 0.000 0.000
#> SRR949099 3 0.3128 0.731 0.040 0.000 0.884 0.076
#> SRR949101 3 0.0000 0.814 0.000 0.000 1.000 0.000
#> SRR949100 2 0.1792 0.914 0.000 0.932 0.000 0.068
#> SRR949102 4 0.8437 0.118 0.020 0.316 0.292 0.372
#> SRR949103 1 0.1867 0.903 0.928 0.000 0.000 0.072
#> SRR949104 2 0.0000 0.975 0.000 1.000 0.000 0.000
#> SRR949105 3 0.0000 0.814 0.000 0.000 1.000 0.000
#> SRR949106 3 0.0000 0.814 0.000 0.000 1.000 0.000
#> SRR949107 3 0.0000 0.814 0.000 0.000 1.000 0.000
#> SRR949108 1 0.0000 0.941 1.000 0.000 0.000 0.000
#> SRR949109 4 0.1798 0.890 0.040 0.000 0.016 0.944
#> SRR949110 1 0.1792 0.906 0.932 0.000 0.000 0.068
#> SRR949111 4 0.1798 0.890 0.040 0.000 0.016 0.944
#> SRR949112 1 0.0000 0.941 1.000 0.000 0.000 0.000
#> SRR949113 2 0.0000 0.975 0.000 1.000 0.000 0.000
#> SRR949114 3 0.4907 0.394 0.420 0.000 0.580 0.000
#> SRR949115 3 0.4907 0.394 0.420 0.000 0.580 0.000
#> SRR949116 3 0.4907 0.394 0.420 0.000 0.580 0.000
#> SRR949117 3 0.0000 0.814 0.000 0.000 1.000 0.000
#> SRR949118 3 0.0000 0.814 0.000 0.000 1.000 0.000
#> SRR949119 1 0.3074 0.851 0.848 0.000 0.000 0.152
#> SRR949120 1 0.3074 0.851 0.848 0.000 0.000 0.152
#> SRR949121 1 0.0000 0.941 1.000 0.000 0.000 0.000
#> SRR949122 1 0.0000 0.941 1.000 0.000 0.000 0.000
#> SRR949123 2 0.0000 0.975 0.000 1.000 0.000 0.000
#> SRR949124 2 0.0000 0.975 0.000 1.000 0.000 0.000
#> SRR949125 4 0.1798 0.890 0.040 0.000 0.016 0.944
#> SRR949126 4 0.1798 0.890 0.040 0.000 0.016 0.944
#> SRR949127 2 0.0188 0.974 0.000 0.996 0.000 0.004
#> SRR949128 2 0.0188 0.974 0.000 0.996 0.000 0.004
#> SRR949129 2 0.0188 0.974 0.000 0.996 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR949076 4 0.3796 0.7313 0.000 0.000 0.000 0.700 0.300
#> SRR949078 2 0.0794 0.9058 0.000 0.972 0.000 0.000 0.028
#> SRR949077 4 0.3895 0.7101 0.000 0.000 0.000 0.680 0.320
#> SRR949079 4 0.2929 0.8215 0.000 0.000 0.000 0.820 0.180
#> SRR949080 4 0.2929 0.8215 0.000 0.000 0.000 0.820 0.180
#> SRR949081 5 0.6289 -0.1121 0.000 0.396 0.152 0.000 0.452
#> SRR949082 2 0.0794 0.9058 0.000 0.972 0.000 0.000 0.028
#> SRR949083 1 0.3612 0.6702 0.732 0.000 0.000 0.000 0.268
#> SRR949084 1 0.3074 0.7118 0.804 0.000 0.000 0.000 0.196
#> SRR949085 2 0.0000 0.9136 0.000 1.000 0.000 0.000 0.000
#> SRR949087 2 0.2813 0.8383 0.000 0.832 0.000 0.000 0.168
#> SRR949088 2 0.2813 0.8383 0.000 0.832 0.000 0.000 0.168
#> SRR949086 3 0.0794 0.8261 0.000 0.000 0.972 0.000 0.028
#> SRR949089 2 0.0000 0.9136 0.000 1.000 0.000 0.000 0.000
#> SRR949090 4 0.0963 0.8124 0.000 0.000 0.000 0.964 0.036
#> SRR949092 1 0.0290 0.7518 0.992 0.000 0.000 0.000 0.008
#> SRR949093 1 0.0290 0.7518 0.992 0.000 0.000 0.000 0.008
#> SRR949091 3 0.4161 0.2452 0.000 0.000 0.608 0.392 0.000
#> SRR949095 2 0.4138 0.4325 0.000 0.616 0.000 0.000 0.384
#> SRR949094 4 0.2929 0.8215 0.000 0.000 0.000 0.820 0.180
#> SRR949096 1 0.3143 0.7086 0.796 0.000 0.000 0.000 0.204
#> SRR949097 1 0.4766 0.6223 0.708 0.000 0.000 0.220 0.072
#> SRR949098 2 0.0000 0.9136 0.000 1.000 0.000 0.000 0.000
#> SRR949099 3 0.6055 0.3702 0.032 0.000 0.632 0.232 0.104
#> SRR949101 3 0.0000 0.8302 0.000 0.000 1.000 0.000 0.000
#> SRR949100 2 0.5233 0.5977 0.000 0.680 0.000 0.192 0.128
#> SRR949102 5 0.7379 0.0273 0.004 0.072 0.220 0.176 0.528
#> SRR949103 1 0.4766 0.6223 0.708 0.000 0.000 0.220 0.072
#> SRR949104 2 0.0000 0.9136 0.000 1.000 0.000 0.000 0.000
#> SRR949105 3 0.0162 0.8319 0.000 0.000 0.996 0.004 0.000
#> SRR949106 3 0.0162 0.8319 0.000 0.000 0.996 0.004 0.000
#> SRR949107 3 0.0162 0.8319 0.000 0.000 0.996 0.004 0.000
#> SRR949108 1 0.0290 0.7527 0.992 0.000 0.000 0.000 0.008
#> SRR949109 4 0.1043 0.8096 0.000 0.000 0.000 0.960 0.040
#> SRR949110 1 0.4514 0.6508 0.740 0.000 0.000 0.188 0.072
#> SRR949111 4 0.0162 0.8313 0.000 0.000 0.000 0.996 0.004
#> SRR949112 1 0.3816 0.4117 0.696 0.000 0.000 0.000 0.304
#> SRR949113 2 0.0000 0.9136 0.000 1.000 0.000 0.000 0.000
#> SRR949114 5 0.6632 0.3652 0.220 0.000 0.380 0.000 0.400
#> SRR949115 5 0.6632 0.3652 0.220 0.000 0.380 0.000 0.400
#> SRR949116 5 0.6632 0.3652 0.220 0.000 0.380 0.000 0.400
#> SRR949117 3 0.0703 0.8280 0.000 0.000 0.976 0.000 0.024
#> SRR949118 3 0.0703 0.8280 0.000 0.000 0.976 0.000 0.024
#> SRR949119 1 0.5315 0.5654 0.600 0.000 0.000 0.068 0.332
#> SRR949120 1 0.5315 0.5654 0.600 0.000 0.000 0.068 0.332
#> SRR949121 1 0.0404 0.7507 0.988 0.000 0.000 0.000 0.012
#> SRR949122 1 0.0290 0.7512 0.992 0.000 0.000 0.000 0.008
#> SRR949123 2 0.0000 0.9136 0.000 1.000 0.000 0.000 0.000
#> SRR949124 2 0.0000 0.9136 0.000 1.000 0.000 0.000 0.000
#> SRR949125 4 0.0000 0.8326 0.000 0.000 0.000 1.000 0.000
#> SRR949126 4 0.0000 0.8326 0.000 0.000 0.000 1.000 0.000
#> SRR949127 2 0.1341 0.8978 0.000 0.944 0.000 0.000 0.056
#> SRR949128 2 0.1341 0.8978 0.000 0.944 0.000 0.000 0.056
#> SRR949129 2 0.1341 0.8978 0.000 0.944 0.000 0.000 0.056
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR949076 4 0.3446 0.640 0.000 0.000 0.000 0.692 0.308 0.000
#> SRR949078 2 0.0717 0.788 0.000 0.976 0.000 0.000 0.016 0.008
#> SRR949077 4 0.3482 0.629 0.000 0.000 0.000 0.684 0.316 0.000
#> SRR949079 4 0.2165 0.833 0.000 0.000 0.000 0.884 0.108 0.008
#> SRR949080 4 0.2165 0.833 0.000 0.000 0.000 0.884 0.108 0.008
#> SRR949081 5 0.4441 0.709 0.000 0.204 0.028 0.000 0.724 0.044
#> SRR949082 2 0.0725 0.785 0.000 0.976 0.000 0.000 0.012 0.012
#> SRR949083 1 0.4204 0.587 0.696 0.000 0.000 0.000 0.252 0.052
#> SRR949084 1 0.3168 0.655 0.804 0.000 0.000 0.000 0.172 0.024
#> SRR949085 2 0.0000 0.792 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949087 2 0.5771 0.371 0.000 0.484 0.004 0.000 0.352 0.160
#> SRR949088 2 0.5771 0.371 0.000 0.484 0.004 0.000 0.352 0.160
#> SRR949086 3 0.2350 0.772 0.000 0.000 0.880 0.000 0.100 0.020
#> SRR949089 2 0.0000 0.792 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949090 4 0.1864 0.807 0.000 0.000 0.004 0.924 0.032 0.040
#> SRR949092 1 0.0632 0.703 0.976 0.000 0.000 0.000 0.000 0.024
#> SRR949093 1 0.0632 0.703 0.976 0.000 0.000 0.000 0.000 0.024
#> SRR949091 3 0.3782 0.246 0.000 0.000 0.588 0.412 0.000 0.000
#> SRR949095 2 0.4642 -0.163 0.000 0.508 0.000 0.000 0.452 0.040
#> SRR949094 4 0.2165 0.833 0.000 0.000 0.000 0.884 0.108 0.008
#> SRR949096 1 0.3269 0.649 0.792 0.000 0.000 0.000 0.184 0.024
#> SRR949097 1 0.5899 0.535 0.616 0.000 0.000 0.124 0.068 0.192
#> SRR949098 2 0.0000 0.792 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949099 3 0.7335 0.314 0.024 0.000 0.492 0.124 0.172 0.188
#> SRR949101 3 0.0291 0.788 0.000 0.000 0.992 0.000 0.004 0.004
#> SRR949100 2 0.6757 0.361 0.000 0.484 0.000 0.076 0.196 0.244
#> SRR949102 5 0.5229 0.697 0.000 0.072 0.072 0.092 0.732 0.032
#> SRR949103 1 0.5899 0.535 0.616 0.000 0.000 0.124 0.068 0.192
#> SRR949104 2 0.0000 0.792 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949105 3 0.0000 0.789 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR949106 3 0.0000 0.789 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR949107 3 0.0000 0.789 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR949108 1 0.0363 0.706 0.988 0.000 0.000 0.000 0.012 0.000
#> SRR949109 4 0.1864 0.807 0.000 0.000 0.004 0.924 0.032 0.040
#> SRR949110 1 0.5736 0.546 0.640 0.000 0.000 0.116 0.072 0.172
#> SRR949111 4 0.0405 0.844 0.000 0.000 0.004 0.988 0.000 0.008
#> SRR949112 1 0.3841 0.152 0.616 0.000 0.000 0.000 0.004 0.380
#> SRR949113 2 0.0000 0.792 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949114 6 0.4756 1.000 0.128 0.000 0.200 0.000 0.000 0.672
#> SRR949115 6 0.4756 1.000 0.128 0.000 0.200 0.000 0.000 0.672
#> SRR949116 6 0.4756 1.000 0.128 0.000 0.200 0.000 0.000 0.672
#> SRR949117 3 0.2214 0.774 0.000 0.000 0.888 0.000 0.096 0.016
#> SRR949118 3 0.2510 0.767 0.000 0.000 0.872 0.000 0.100 0.028
#> SRR949119 1 0.5511 0.317 0.516 0.000 0.000 0.060 0.392 0.032
#> SRR949120 1 0.5511 0.317 0.516 0.000 0.000 0.060 0.392 0.032
#> SRR949121 1 0.1219 0.692 0.948 0.000 0.000 0.000 0.004 0.048
#> SRR949122 1 0.0858 0.702 0.968 0.000 0.000 0.000 0.004 0.028
#> SRR949123 2 0.0000 0.792 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949124 2 0.0000 0.792 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949125 4 0.0146 0.847 0.000 0.000 0.004 0.996 0.000 0.000
#> SRR949126 4 0.0146 0.847 0.000 0.000 0.004 0.996 0.000 0.000
#> SRR949127 2 0.3962 0.703 0.000 0.764 0.000 0.000 0.120 0.116
#> SRR949128 2 0.3962 0.703 0.000 0.764 0.000 0.000 0.120 0.116
#> SRR949129 2 0.3962 0.703 0.000 0.764 0.000 0.000 0.120 0.116
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 16816 rows and 54 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 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 0.923 0.928 0.971 0.4334 0.575 0.575
#> 3 3 0.827 0.902 0.951 0.5333 0.732 0.544
#> 4 4 0.902 0.933 0.971 0.1008 0.870 0.644
#> 5 5 0.999 0.962 0.984 0.0666 0.934 0.764
#> 6 6 0.885 0.831 0.893 0.0451 0.956 0.801
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
#> attr(,"optional")
#> [1] 2 4
There is also optional best \(k\) = 2 4 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR949076 1 0.0000 0.968 1.000 0.000
#> SRR949078 2 0.0000 0.970 0.000 1.000
#> SRR949077 1 0.0000 0.968 1.000 0.000
#> SRR949079 1 0.0000 0.968 1.000 0.000
#> SRR949080 1 0.0000 0.968 1.000 0.000
#> SRR949081 2 0.0000 0.970 0.000 1.000
#> SRR949082 2 0.0000 0.970 0.000 1.000
#> SRR949083 1 0.0000 0.968 1.000 0.000
#> SRR949084 1 0.0000 0.968 1.000 0.000
#> SRR949085 2 0.0000 0.970 0.000 1.000
#> SRR949087 2 0.2423 0.939 0.040 0.960
#> SRR949088 2 0.2236 0.943 0.036 0.964
#> SRR949086 1 0.0000 0.968 1.000 0.000
#> SRR949089 2 0.0000 0.970 0.000 1.000
#> SRR949090 1 0.0000 0.968 1.000 0.000
#> SRR949092 1 0.0000 0.968 1.000 0.000
#> SRR949093 1 0.0000 0.968 1.000 0.000
#> SRR949091 1 0.0000 0.968 1.000 0.000
#> SRR949095 2 0.9358 0.429 0.352 0.648
#> SRR949094 1 0.0000 0.968 1.000 0.000
#> SRR949096 1 0.0000 0.968 1.000 0.000
#> SRR949097 1 0.0000 0.968 1.000 0.000
#> SRR949098 2 0.0000 0.970 0.000 1.000
#> SRR949099 1 0.0000 0.968 1.000 0.000
#> SRR949101 1 0.0000 0.968 1.000 0.000
#> SRR949100 2 0.0376 0.967 0.004 0.996
#> SRR949102 1 0.0000 0.968 1.000 0.000
#> SRR949103 1 0.0000 0.968 1.000 0.000
#> SRR949104 2 0.0000 0.970 0.000 1.000
#> SRR949105 1 0.8207 0.659 0.744 0.256
#> SRR949106 1 0.7453 0.728 0.788 0.212
#> SRR949107 1 0.7745 0.705 0.772 0.228
#> SRR949108 1 0.0000 0.968 1.000 0.000
#> SRR949109 1 0.0000 0.968 1.000 0.000
#> SRR949110 1 0.0000 0.968 1.000 0.000
#> SRR949111 1 0.0000 0.968 1.000 0.000
#> SRR949112 1 0.0000 0.968 1.000 0.000
#> SRR949113 2 0.0000 0.970 0.000 1.000
#> SRR949114 1 0.0000 0.968 1.000 0.000
#> SRR949115 1 0.0000 0.968 1.000 0.000
#> SRR949116 1 0.0000 0.968 1.000 0.000
#> SRR949117 1 0.0000 0.968 1.000 0.000
#> SRR949118 1 0.0000 0.968 1.000 0.000
#> SRR949119 1 0.0000 0.968 1.000 0.000
#> SRR949120 1 0.0000 0.968 1.000 0.000
#> SRR949121 1 0.0000 0.968 1.000 0.000
#> SRR949122 1 0.0000 0.968 1.000 0.000
#> SRR949123 1 0.9896 0.230 0.560 0.440
#> SRR949124 2 0.0000 0.970 0.000 1.000
#> SRR949125 1 0.0000 0.968 1.000 0.000
#> SRR949126 1 0.0000 0.968 1.000 0.000
#> SRR949127 2 0.0000 0.970 0.000 1.000
#> SRR949128 2 0.0000 0.970 0.000 1.000
#> SRR949129 2 0.0000 0.970 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR949076 3 0.1289 0.907 0.032 0.000 0.968
#> SRR949078 2 0.0000 0.956 0.000 1.000 0.000
#> SRR949077 3 0.4796 0.710 0.220 0.000 0.780
#> SRR949079 3 0.1163 0.909 0.028 0.000 0.972
#> SRR949080 3 0.1163 0.909 0.028 0.000 0.972
#> SRR949081 2 0.0000 0.956 0.000 1.000 0.000
#> SRR949082 2 0.0000 0.956 0.000 1.000 0.000
#> SRR949083 1 0.0000 0.966 1.000 0.000 0.000
#> SRR949084 1 0.0000 0.966 1.000 0.000 0.000
#> SRR949085 2 0.0000 0.956 0.000 1.000 0.000
#> SRR949087 2 0.0237 0.953 0.004 0.996 0.000
#> SRR949088 2 0.0424 0.950 0.008 0.992 0.000
#> SRR949086 1 0.0000 0.966 1.000 0.000 0.000
#> SRR949089 2 0.0000 0.956 0.000 1.000 0.000
#> SRR949090 3 0.1163 0.909 0.028 0.000 0.972
#> SRR949092 1 0.0000 0.966 1.000 0.000 0.000
#> SRR949093 1 0.0000 0.966 1.000 0.000 0.000
#> SRR949091 3 0.0000 0.891 0.000 0.000 1.000
#> SRR949095 2 0.8399 0.482 0.188 0.624 0.188
#> SRR949094 3 0.1163 0.909 0.028 0.000 0.972
#> SRR949096 1 0.0000 0.966 1.000 0.000 0.000
#> SRR949097 1 0.0000 0.966 1.000 0.000 0.000
#> SRR949098 2 0.0000 0.956 0.000 1.000 0.000
#> SRR949099 1 0.0000 0.966 1.000 0.000 0.000
#> SRR949101 3 0.5733 0.520 0.324 0.000 0.676
#> SRR949100 2 0.0000 0.956 0.000 1.000 0.000
#> SRR949102 1 0.4235 0.797 0.824 0.000 0.176
#> SRR949103 1 0.0000 0.966 1.000 0.000 0.000
#> SRR949104 2 0.0000 0.956 0.000 1.000 0.000
#> SRR949105 3 0.4897 0.761 0.016 0.172 0.812
#> SRR949106 3 0.4897 0.761 0.016 0.172 0.812
#> SRR949107 3 0.4897 0.761 0.016 0.172 0.812
#> SRR949108 1 0.0000 0.966 1.000 0.000 0.000
#> SRR949109 3 0.1163 0.909 0.028 0.000 0.972
#> SRR949110 1 0.0000 0.966 1.000 0.000 0.000
#> SRR949111 3 0.1163 0.909 0.028 0.000 0.972
#> SRR949112 1 0.0000 0.966 1.000 0.000 0.000
#> SRR949113 2 0.0000 0.956 0.000 1.000 0.000
#> SRR949114 1 0.0000 0.966 1.000 0.000 0.000
#> SRR949115 1 0.0000 0.966 1.000 0.000 0.000
#> SRR949116 1 0.0000 0.966 1.000 0.000 0.000
#> SRR949117 1 0.0000 0.966 1.000 0.000 0.000
#> SRR949118 1 0.3412 0.850 0.876 0.000 0.124
#> SRR949119 1 0.4291 0.792 0.820 0.000 0.180
#> SRR949120 1 0.4291 0.792 0.820 0.000 0.180
#> SRR949121 1 0.0000 0.966 1.000 0.000 0.000
#> SRR949122 1 0.0000 0.966 1.000 0.000 0.000
#> SRR949123 2 0.4974 0.676 0.236 0.764 0.000
#> SRR949124 2 0.0000 0.956 0.000 1.000 0.000
#> SRR949125 3 0.1163 0.909 0.028 0.000 0.972
#> SRR949126 3 0.1163 0.909 0.028 0.000 0.972
#> SRR949127 2 0.0000 0.956 0.000 1.000 0.000
#> SRR949128 2 0.0000 0.956 0.000 1.000 0.000
#> SRR949129 2 0.0000 0.956 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR949076 4 0.000 0.8991 0.000 0.000 0.000 1.000
#> SRR949078 2 0.000 1.0000 0.000 1.000 0.000 0.000
#> SRR949077 4 0.281 0.8408 0.132 0.000 0.000 0.868
#> SRR949079 4 0.000 0.8991 0.000 0.000 0.000 1.000
#> SRR949080 4 0.000 0.8991 0.000 0.000 0.000 1.000
#> SRR949081 2 0.000 1.0000 0.000 1.000 0.000 0.000
#> SRR949082 2 0.000 1.0000 0.000 1.000 0.000 0.000
#> SRR949083 1 0.000 0.9776 1.000 0.000 0.000 0.000
#> SRR949084 1 0.000 0.9776 1.000 0.000 0.000 0.000
#> SRR949085 2 0.000 1.0000 0.000 1.000 0.000 0.000
#> SRR949087 2 0.000 1.0000 0.000 1.000 0.000 0.000
#> SRR949088 2 0.000 1.0000 0.000 1.000 0.000 0.000
#> SRR949086 1 0.478 0.4056 0.624 0.000 0.376 0.000
#> SRR949089 2 0.000 1.0000 0.000 1.000 0.000 0.000
#> SRR949090 4 0.000 0.8991 0.000 0.000 0.000 1.000
#> SRR949092 1 0.000 0.9776 1.000 0.000 0.000 0.000
#> SRR949093 1 0.000 0.9776 1.000 0.000 0.000 0.000
#> SRR949091 4 0.499 0.0707 0.000 0.000 0.468 0.532
#> SRR949095 4 0.344 0.8378 0.120 0.024 0.000 0.856
#> SRR949094 4 0.000 0.8991 0.000 0.000 0.000 1.000
#> SRR949096 1 0.000 0.9776 1.000 0.000 0.000 0.000
#> SRR949097 1 0.000 0.9776 1.000 0.000 0.000 0.000
#> SRR949098 2 0.000 1.0000 0.000 1.000 0.000 0.000
#> SRR949099 1 0.000 0.9776 1.000 0.000 0.000 0.000
#> SRR949101 3 0.000 1.0000 0.000 0.000 1.000 0.000
#> SRR949100 2 0.000 1.0000 0.000 1.000 0.000 0.000
#> SRR949102 4 0.281 0.8408 0.132 0.000 0.000 0.868
#> SRR949103 1 0.000 0.9776 1.000 0.000 0.000 0.000
#> SRR949104 2 0.000 1.0000 0.000 1.000 0.000 0.000
#> SRR949105 3 0.000 1.0000 0.000 0.000 1.000 0.000
#> SRR949106 3 0.000 1.0000 0.000 0.000 1.000 0.000
#> SRR949107 3 0.000 1.0000 0.000 0.000 1.000 0.000
#> SRR949108 1 0.000 0.9776 1.000 0.000 0.000 0.000
#> SRR949109 4 0.000 0.8991 0.000 0.000 0.000 1.000
#> SRR949110 1 0.000 0.9776 1.000 0.000 0.000 0.000
#> SRR949111 4 0.000 0.8991 0.000 0.000 0.000 1.000
#> SRR949112 1 0.000 0.9776 1.000 0.000 0.000 0.000
#> SRR949113 2 0.000 1.0000 0.000 1.000 0.000 0.000
#> SRR949114 1 0.000 0.9776 1.000 0.000 0.000 0.000
#> SRR949115 1 0.000 0.9776 1.000 0.000 0.000 0.000
#> SRR949116 1 0.000 0.9776 1.000 0.000 0.000 0.000
#> SRR949117 1 0.000 0.9776 1.000 0.000 0.000 0.000
#> SRR949118 3 0.000 1.0000 0.000 0.000 1.000 0.000
#> SRR949119 4 0.297 0.8310 0.144 0.000 0.000 0.856
#> SRR949120 4 0.297 0.8310 0.144 0.000 0.000 0.856
#> SRR949121 1 0.000 0.9776 1.000 0.000 0.000 0.000
#> SRR949122 1 0.000 0.9776 1.000 0.000 0.000 0.000
#> SRR949123 2 0.000 1.0000 0.000 1.000 0.000 0.000
#> SRR949124 2 0.000 1.0000 0.000 1.000 0.000 0.000
#> SRR949125 4 0.000 0.8991 0.000 0.000 0.000 1.000
#> SRR949126 4 0.000 0.8991 0.000 0.000 0.000 1.000
#> SRR949127 2 0.000 1.0000 0.000 1.000 0.000 0.000
#> SRR949128 2 0.000 1.0000 0.000 1.000 0.000 0.000
#> SRR949129 2 0.000 1.0000 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR949076 4 0.0000 0.977 0.000 0.000 0.000 1.000 0.000
#> SRR949078 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> SRR949077 4 0.0290 0.973 0.008 0.000 0.000 0.992 0.000
#> SRR949079 4 0.0000 0.977 0.000 0.000 0.000 1.000 0.000
#> SRR949080 4 0.0000 0.977 0.000 0.000 0.000 1.000 0.000
#> SRR949081 2 0.0162 0.991 0.000 0.996 0.000 0.004 0.000
#> SRR949082 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> SRR949083 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000
#> SRR949084 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000
#> SRR949085 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> SRR949087 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> SRR949088 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> SRR949086 3 0.0290 0.923 0.008 0.000 0.992 0.000 0.000
#> SRR949089 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> SRR949090 4 0.0000 0.977 0.000 0.000 0.000 1.000 0.000
#> SRR949092 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000
#> SRR949093 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000
#> SRR949091 3 0.3143 0.696 0.000 0.000 0.796 0.204 0.000
#> SRR949095 4 0.0693 0.965 0.008 0.012 0.000 0.980 0.000
#> SRR949094 4 0.0000 0.977 0.000 0.000 0.000 1.000 0.000
#> SRR949096 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000
#> SRR949097 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000
#> SRR949098 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> SRR949099 1 0.0290 0.976 0.992 0.000 0.008 0.000 0.000
#> SRR949101 5 0.0162 0.996 0.000 0.000 0.004 0.000 0.996
#> SRR949100 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> SRR949102 4 0.3388 0.739 0.008 0.000 0.200 0.792 0.000
#> SRR949103 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000
#> SRR949104 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> SRR949105 5 0.0000 0.999 0.000 0.000 0.000 0.000 1.000
#> SRR949106 5 0.0000 0.999 0.000 0.000 0.000 0.000 1.000
#> SRR949107 5 0.0000 0.999 0.000 0.000 0.000 0.000 1.000
#> SRR949108 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000
#> SRR949109 4 0.0000 0.977 0.000 0.000 0.000 1.000 0.000
#> SRR949110 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000
#> SRR949111 4 0.0000 0.977 0.000 0.000 0.000 1.000 0.000
#> SRR949112 1 0.2966 0.775 0.816 0.000 0.184 0.000 0.000
#> SRR949113 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> SRR949114 3 0.0000 0.925 0.000 0.000 1.000 0.000 0.000
#> SRR949115 3 0.0000 0.925 0.000 0.000 1.000 0.000 0.000
#> SRR949116 3 0.0000 0.925 0.000 0.000 1.000 0.000 0.000
#> SRR949117 3 0.1197 0.890 0.048 0.000 0.952 0.000 0.000
#> SRR949118 3 0.1671 0.876 0.000 0.000 0.924 0.000 0.076
#> SRR949119 4 0.0609 0.965 0.020 0.000 0.000 0.980 0.000
#> SRR949120 4 0.0609 0.965 0.020 0.000 0.000 0.980 0.000
#> SRR949121 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000
#> SRR949122 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000
#> SRR949123 2 0.1544 0.924 0.000 0.932 0.068 0.000 0.000
#> SRR949124 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> SRR949125 4 0.0000 0.977 0.000 0.000 0.000 1.000 0.000
#> SRR949126 4 0.0000 0.977 0.000 0.000 0.000 1.000 0.000
#> SRR949127 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> SRR949128 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> SRR949129 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR949076 4 0.0000 0.900 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949078 5 0.3607 0.949 0.000 0.348 0.000 0.000 0.652 0.000
#> SRR949077 4 0.0363 0.897 0.012 0.000 0.000 0.988 0.000 0.000
#> SRR949079 4 0.0000 0.900 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949080 4 0.0000 0.900 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949081 5 0.2730 0.643 0.000 0.192 0.000 0.000 0.808 0.000
#> SRR949082 5 0.3607 0.949 0.000 0.348 0.000 0.000 0.652 0.000
#> SRR949083 1 0.0000 0.979 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949084 1 0.0000 0.979 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949085 2 0.3860 -0.526 0.000 0.528 0.000 0.000 0.472 0.000
#> SRR949087 5 0.3578 0.941 0.000 0.340 0.000 0.000 0.660 0.000
#> SRR949088 5 0.3578 0.941 0.000 0.340 0.000 0.000 0.660 0.000
#> SRR949086 6 0.0520 0.905 0.008 0.000 0.000 0.000 0.008 0.984
#> SRR949089 2 0.0000 0.695 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949090 4 0.1863 0.884 0.000 0.000 0.000 0.896 0.104 0.000
#> SRR949092 1 0.0000 0.979 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949093 1 0.0000 0.979 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949091 6 0.4599 0.589 0.000 0.000 0.000 0.212 0.104 0.684
#> SRR949095 4 0.0767 0.895 0.008 0.012 0.000 0.976 0.004 0.000
#> SRR949094 4 0.0000 0.900 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949096 1 0.0000 0.979 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949097 1 0.0000 0.979 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949098 2 0.0000 0.695 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949099 1 0.1398 0.933 0.940 0.000 0.000 0.000 0.052 0.008
#> SRR949101 3 0.0146 0.996 0.000 0.000 0.996 0.000 0.000 0.004
#> SRR949100 5 0.3607 0.949 0.000 0.348 0.000 0.000 0.652 0.000
#> SRR949102 4 0.4154 0.716 0.008 0.000 0.000 0.712 0.244 0.036
#> SRR949103 1 0.0000 0.979 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949104 2 0.2631 0.498 0.000 0.820 0.000 0.000 0.180 0.000
#> SRR949105 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR949106 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR949107 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR949108 1 0.0000 0.979 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949109 4 0.1863 0.884 0.000 0.000 0.000 0.896 0.104 0.000
#> SRR949110 1 0.0000 0.979 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949111 4 0.1863 0.884 0.000 0.000 0.000 0.896 0.104 0.000
#> SRR949112 1 0.2664 0.783 0.816 0.000 0.000 0.000 0.000 0.184
#> SRR949113 2 0.3868 -0.567 0.000 0.508 0.000 0.000 0.492 0.000
#> SRR949114 6 0.0000 0.909 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR949115 6 0.0000 0.909 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR949116 6 0.0000 0.909 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR949117 6 0.1333 0.873 0.048 0.000 0.000 0.000 0.008 0.944
#> SRR949118 6 0.1501 0.862 0.000 0.000 0.076 0.000 0.000 0.924
#> SRR949119 4 0.3394 0.755 0.012 0.000 0.000 0.752 0.236 0.000
#> SRR949120 4 0.3394 0.755 0.012 0.000 0.000 0.752 0.236 0.000
#> SRR949121 1 0.0000 0.979 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949122 1 0.0000 0.979 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949123 2 0.0000 0.695 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949124 2 0.0000 0.695 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949125 4 0.1863 0.884 0.000 0.000 0.000 0.896 0.104 0.000
#> SRR949126 4 0.1863 0.884 0.000 0.000 0.000 0.896 0.104 0.000
#> SRR949127 5 0.3607 0.949 0.000 0.348 0.000 0.000 0.652 0.000
#> SRR949128 5 0.3607 0.949 0.000 0.348 0.000 0.000 0.652 0.000
#> SRR949129 5 0.3607 0.949 0.000 0.348 0.000 0.000 0.652 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)
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 16816 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.354 0.766 0.860 0.4336 0.547 0.547
#> 3 3 0.394 0.548 0.758 0.4060 0.682 0.470
#> 4 4 0.580 0.679 0.825 0.1760 0.860 0.619
#> 5 5 0.614 0.560 0.731 0.0833 0.867 0.571
#> 6 6 0.593 0.533 0.677 0.0349 0.930 0.714
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
#> SRR949076 1 0.9522 0.387 0.628 0.372
#> SRR949078 2 0.3733 0.908 0.072 0.928
#> SRR949077 1 0.9522 0.387 0.628 0.372
#> SRR949079 1 0.9460 0.408 0.636 0.364
#> SRR949080 1 0.9460 0.408 0.636 0.364
#> SRR949081 2 0.7745 0.792 0.228 0.772
#> SRR949082 2 0.3733 0.908 0.072 0.928
#> SRR949083 1 0.3274 0.827 0.940 0.060
#> SRR949084 1 0.2423 0.839 0.960 0.040
#> SRR949085 2 0.3733 0.908 0.072 0.928
#> SRR949087 2 0.7815 0.787 0.232 0.768
#> SRR949088 2 0.7815 0.787 0.232 0.768
#> SRR949086 1 0.0672 0.830 0.992 0.008
#> SRR949089 2 0.3733 0.908 0.072 0.928
#> SRR949090 1 0.9087 0.494 0.676 0.324
#> SRR949092 1 0.2236 0.841 0.964 0.036
#> SRR949093 1 0.2236 0.841 0.964 0.036
#> SRR949091 1 0.1414 0.827 0.980 0.020
#> SRR949095 2 0.7815 0.787 0.232 0.768
#> SRR949094 1 0.9170 0.480 0.668 0.332
#> SRR949096 1 0.2236 0.841 0.964 0.036
#> SRR949097 1 0.2236 0.841 0.964 0.036
#> SRR949098 2 0.3733 0.908 0.072 0.928
#> SRR949099 1 0.0376 0.830 0.996 0.004
#> SRR949101 1 0.0672 0.830 0.992 0.008
#> SRR949100 2 0.9248 0.564 0.340 0.660
#> SRR949102 2 0.8909 0.694 0.308 0.692
#> SRR949103 1 0.2236 0.841 0.964 0.036
#> SRR949104 2 0.3733 0.908 0.072 0.928
#> SRR949105 1 0.4022 0.783 0.920 0.080
#> SRR949106 1 0.4022 0.783 0.920 0.080
#> SRR949107 1 0.4022 0.783 0.920 0.080
#> SRR949108 1 0.2236 0.841 0.964 0.036
#> SRR949109 1 0.9170 0.480 0.668 0.332
#> SRR949110 1 0.2236 0.841 0.964 0.036
#> SRR949111 1 0.9170 0.480 0.668 0.332
#> SRR949112 1 0.2236 0.841 0.964 0.036
#> SRR949113 2 0.3733 0.908 0.072 0.928
#> SRR949114 1 0.2236 0.841 0.964 0.036
#> SRR949115 1 0.2236 0.841 0.964 0.036
#> SRR949116 1 0.2236 0.841 0.964 0.036
#> SRR949117 1 0.0672 0.830 0.992 0.008
#> SRR949118 1 0.3879 0.786 0.924 0.076
#> SRR949119 1 0.2236 0.841 0.964 0.036
#> SRR949120 1 0.2236 0.841 0.964 0.036
#> SRR949121 1 0.2236 0.841 0.964 0.036
#> SRR949122 1 0.2236 0.841 0.964 0.036
#> SRR949123 2 0.3733 0.908 0.072 0.928
#> SRR949124 2 0.3733 0.908 0.072 0.928
#> SRR949125 1 0.9170 0.480 0.668 0.332
#> SRR949126 1 0.9170 0.480 0.668 0.332
#> SRR949127 2 0.3733 0.908 0.072 0.928
#> SRR949128 2 0.3733 0.908 0.072 0.928
#> SRR949129 2 0.3733 0.908 0.072 0.928
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR949076 3 0.7228 0.679 0.364 0.036 0.600
#> SRR949078 2 0.0592 0.865 0.012 0.988 0.000
#> SRR949077 3 0.7228 0.679 0.364 0.036 0.600
#> SRR949079 3 0.7141 0.679 0.368 0.032 0.600
#> SRR949080 3 0.7141 0.679 0.368 0.032 0.600
#> SRR949081 2 0.9263 -0.288 0.360 0.476 0.164
#> SRR949082 2 0.0592 0.865 0.012 0.988 0.000
#> SRR949083 1 0.4887 0.557 0.772 0.228 0.000
#> SRR949084 1 0.6081 0.519 0.652 0.344 0.004
#> SRR949085 2 0.0000 0.869 0.000 1.000 0.000
#> SRR949087 1 0.9566 0.357 0.440 0.360 0.200
#> SRR949088 1 0.9566 0.357 0.440 0.360 0.200
#> SRR949086 1 0.6824 0.164 0.576 0.016 0.408
#> SRR949089 2 0.0000 0.869 0.000 1.000 0.000
#> SRR949090 3 0.6510 0.691 0.364 0.012 0.624
#> SRR949092 1 0.2261 0.565 0.932 0.068 0.000
#> SRR949093 1 0.2261 0.565 0.932 0.068 0.000
#> SRR949091 3 0.2599 0.538 0.052 0.016 0.932
#> SRR949095 2 0.9263 -0.288 0.360 0.476 0.164
#> SRR949094 3 0.6529 0.691 0.368 0.012 0.620
#> SRR949096 1 0.6081 0.519 0.652 0.344 0.004
#> SRR949097 1 0.0237 0.537 0.996 0.000 0.004
#> SRR949098 2 0.0000 0.869 0.000 1.000 0.000
#> SRR949099 1 0.4575 0.354 0.828 0.012 0.160
#> SRR949101 3 0.3091 0.536 0.072 0.016 0.912
#> SRR949100 1 0.9633 0.347 0.436 0.352 0.212
#> SRR949102 3 0.9388 0.344 0.388 0.172 0.440
#> SRR949103 1 0.0237 0.537 0.996 0.000 0.004
#> SRR949104 2 0.0000 0.869 0.000 1.000 0.000
#> SRR949105 3 0.3573 0.513 0.120 0.004 0.876
#> SRR949106 3 0.3644 0.510 0.124 0.004 0.872
#> SRR949107 3 0.3644 0.510 0.124 0.004 0.872
#> SRR949108 1 0.4413 0.563 0.852 0.124 0.024
#> SRR949109 3 0.6510 0.691 0.364 0.012 0.624
#> SRR949110 1 0.0237 0.537 0.996 0.000 0.004
#> SRR949111 3 0.6529 0.691 0.368 0.012 0.620
#> SRR949112 1 0.7262 0.486 0.624 0.332 0.044
#> SRR949113 2 0.0592 0.865 0.012 0.988 0.000
#> SRR949114 1 0.5775 0.357 0.728 0.012 0.260
#> SRR949115 1 0.5406 0.394 0.764 0.012 0.224
#> SRR949116 1 0.5406 0.394 0.764 0.012 0.224
#> SRR949117 1 0.6888 0.136 0.552 0.016 0.432
#> SRR949118 3 0.6955 -0.135 0.488 0.016 0.496
#> SRR949119 1 0.8798 0.404 0.520 0.356 0.124
#> SRR949120 1 0.8836 0.404 0.520 0.352 0.128
#> SRR949121 1 0.1482 0.546 0.968 0.012 0.020
#> SRR949122 1 0.5760 0.526 0.672 0.328 0.000
#> SRR949123 2 0.0000 0.869 0.000 1.000 0.000
#> SRR949124 2 0.0000 0.869 0.000 1.000 0.000
#> SRR949125 3 0.6529 0.691 0.368 0.012 0.620
#> SRR949126 3 0.6529 0.691 0.368 0.012 0.620
#> SRR949127 2 0.1989 0.848 0.004 0.948 0.048
#> SRR949128 2 0.1989 0.848 0.004 0.948 0.048
#> SRR949129 2 0.1989 0.848 0.004 0.948 0.048
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR949076 4 0.1109 0.765 0.028 0.000 0.004 0.968
#> SRR949078 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> SRR949077 4 0.1109 0.765 0.028 0.004 0.000 0.968
#> SRR949079 4 0.0921 0.775 0.028 0.000 0.000 0.972
#> SRR949080 4 0.0921 0.775 0.028 0.000 0.000 0.972
#> SRR949081 2 0.7943 0.356 0.104 0.572 0.080 0.244
#> SRR949082 2 0.0188 0.952 0.000 0.996 0.004 0.000
#> SRR949083 1 0.3945 0.710 0.780 0.004 0.000 0.216
#> SRR949084 1 0.3801 0.709 0.780 0.000 0.000 0.220
#> SRR949085 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> SRR949087 1 0.6975 0.439 0.572 0.316 0.012 0.100
#> SRR949088 1 0.6992 0.434 0.568 0.320 0.012 0.100
#> SRR949086 3 0.5285 0.240 0.468 0.000 0.524 0.008
#> SRR949089 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> SRR949090 4 0.3852 0.735 0.192 0.000 0.008 0.800
#> SRR949092 1 0.2814 0.755 0.868 0.000 0.000 0.132
#> SRR949093 1 0.2921 0.755 0.860 0.000 0.000 0.140
#> SRR949091 4 0.4800 0.341 0.004 0.000 0.340 0.656
#> SRR949095 4 0.7996 0.133 0.224 0.372 0.008 0.396
#> SRR949094 4 0.1356 0.776 0.032 0.000 0.008 0.960
#> SRR949096 1 0.3837 0.713 0.776 0.000 0.000 0.224
#> SRR949097 1 0.1389 0.734 0.952 0.000 0.000 0.048
#> SRR949098 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> SRR949099 1 0.4839 0.531 0.764 0.000 0.184 0.052
#> SRR949101 3 0.4560 0.370 0.004 0.000 0.700 0.296
#> SRR949100 1 0.6840 0.442 0.580 0.312 0.008 0.100
#> SRR949102 4 0.6239 0.587 0.048 0.160 0.072 0.720
#> SRR949103 1 0.1389 0.734 0.952 0.000 0.000 0.048
#> SRR949104 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> SRR949105 3 0.0376 0.678 0.004 0.000 0.992 0.004
#> SRR949106 3 0.0376 0.678 0.004 0.000 0.992 0.004
#> SRR949107 3 0.0376 0.678 0.004 0.000 0.992 0.004
#> SRR949108 1 0.3032 0.752 0.868 0.000 0.008 0.124
#> SRR949109 4 0.3972 0.726 0.204 0.000 0.008 0.788
#> SRR949110 1 0.1389 0.734 0.952 0.000 0.000 0.048
#> SRR949111 4 0.2976 0.768 0.120 0.000 0.008 0.872
#> SRR949112 1 0.2466 0.750 0.900 0.000 0.004 0.096
#> SRR949113 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> SRR949114 1 0.4454 0.353 0.692 0.000 0.308 0.000
#> SRR949115 1 0.4608 0.362 0.692 0.000 0.304 0.004
#> SRR949116 1 0.4560 0.378 0.700 0.000 0.296 0.004
#> SRR949117 3 0.5285 0.240 0.468 0.000 0.524 0.008
#> SRR949118 3 0.4331 0.528 0.288 0.000 0.712 0.000
#> SRR949119 4 0.4762 0.515 0.300 0.004 0.004 0.692
#> SRR949120 4 0.4809 0.501 0.308 0.004 0.004 0.684
#> SRR949121 1 0.2469 0.756 0.892 0.000 0.000 0.108
#> SRR949122 1 0.2469 0.757 0.892 0.000 0.000 0.108
#> SRR949123 2 0.0188 0.951 0.000 0.996 0.000 0.004
#> SRR949124 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> SRR949125 4 0.2918 0.770 0.116 0.000 0.008 0.876
#> SRR949126 4 0.2976 0.768 0.120 0.000 0.008 0.872
#> SRR949127 2 0.1471 0.937 0.024 0.960 0.004 0.012
#> SRR949128 2 0.1471 0.937 0.024 0.960 0.004 0.012
#> SRR949129 2 0.1471 0.937 0.024 0.960 0.004 0.012
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR949076 4 0.1168 0.707 0.000 0.008 0.000 0.960 0.032
#> SRR949078 2 0.1690 0.922 0.008 0.944 0.000 0.024 0.024
#> SRR949077 4 0.1822 0.723 0.024 0.000 0.004 0.936 0.036
#> SRR949079 4 0.2331 0.774 0.080 0.000 0.000 0.900 0.020
#> SRR949080 4 0.2331 0.774 0.080 0.000 0.000 0.900 0.020
#> SRR949081 5 0.9760 0.840 0.168 0.236 0.128 0.180 0.288
#> SRR949082 2 0.1153 0.927 0.004 0.964 0.000 0.024 0.008
#> SRR949083 1 0.3966 0.462 0.788 0.004 0.000 0.168 0.040
#> SRR949084 1 0.3376 0.531 0.840 0.004 0.004 0.128 0.024
#> SRR949085 2 0.0000 0.939 0.000 1.000 0.000 0.000 0.000
#> SRR949087 1 0.9483 -0.355 0.292 0.112 0.240 0.100 0.256
#> SRR949088 1 0.9483 -0.355 0.292 0.112 0.240 0.100 0.256
#> SRR949086 3 0.1205 0.528 0.040 0.000 0.956 0.000 0.004
#> SRR949089 2 0.0162 0.939 0.000 0.996 0.000 0.000 0.004
#> SRR949090 4 0.4936 0.728 0.172 0.000 0.116 0.712 0.000
#> SRR949092 1 0.1831 0.563 0.920 0.000 0.000 0.076 0.004
#> SRR949093 1 0.2408 0.547 0.892 0.000 0.000 0.092 0.016
#> SRR949091 3 0.6216 0.439 0.000 0.000 0.548 0.208 0.244
#> SRR949095 5 0.9539 0.835 0.252 0.188 0.076 0.196 0.288
#> SRR949094 4 0.2983 0.787 0.076 0.000 0.056 0.868 0.000
#> SRR949096 1 0.3304 0.531 0.840 0.000 0.004 0.128 0.028
#> SRR949097 1 0.5838 0.422 0.620 0.000 0.248 0.008 0.124
#> SRR949098 2 0.0486 0.938 0.004 0.988 0.004 0.000 0.004
#> SRR949099 3 0.6232 -0.110 0.380 0.000 0.488 0.004 0.128
#> SRR949101 3 0.4522 0.543 0.000 0.000 0.708 0.044 0.248
#> SRR949100 1 0.8887 -0.292 0.372 0.112 0.216 0.044 0.256
#> SRR949102 4 0.7490 -0.292 0.028 0.040 0.152 0.520 0.260
#> SRR949103 1 0.5745 0.423 0.620 0.000 0.252 0.004 0.124
#> SRR949104 2 0.0162 0.939 0.000 0.996 0.000 0.000 0.004
#> SRR949105 3 0.3949 0.566 0.000 0.000 0.668 0.000 0.332
#> SRR949106 3 0.3949 0.566 0.000 0.000 0.668 0.000 0.332
#> SRR949107 3 0.3949 0.566 0.000 0.000 0.668 0.000 0.332
#> SRR949108 1 0.2819 0.584 0.884 0.004 0.052 0.060 0.000
#> SRR949109 4 0.4936 0.728 0.172 0.000 0.116 0.712 0.000
#> SRR949110 1 0.5838 0.422 0.620 0.000 0.248 0.008 0.124
#> SRR949111 4 0.3821 0.798 0.148 0.000 0.052 0.800 0.000
#> SRR949112 1 0.4452 0.559 0.772 0.004 0.168 0.040 0.016
#> SRR949113 2 0.0324 0.939 0.004 0.992 0.000 0.000 0.004
#> SRR949114 3 0.4709 0.100 0.400 0.000 0.584 0.008 0.008
#> SRR949115 3 0.4709 0.100 0.400 0.000 0.584 0.008 0.008
#> SRR949116 3 0.4718 0.092 0.404 0.000 0.580 0.008 0.008
#> SRR949117 3 0.2068 0.515 0.092 0.000 0.904 0.004 0.000
#> SRR949118 3 0.3395 0.563 0.000 0.000 0.764 0.000 0.236
#> SRR949119 1 0.5676 0.314 0.632 0.000 0.004 0.240 0.124
#> SRR949120 1 0.5676 0.314 0.632 0.000 0.004 0.240 0.124
#> SRR949121 1 0.4578 0.525 0.712 0.004 0.244 0.040 0.000
#> SRR949122 1 0.2597 0.585 0.896 0.004 0.060 0.040 0.000
#> SRR949123 2 0.1012 0.925 0.000 0.968 0.000 0.012 0.020
#> SRR949124 2 0.0162 0.939 0.000 0.996 0.000 0.000 0.004
#> SRR949125 4 0.3821 0.798 0.148 0.000 0.052 0.800 0.000
#> SRR949126 4 0.3821 0.798 0.148 0.000 0.052 0.800 0.000
#> SRR949127 2 0.2806 0.858 0.004 0.844 0.000 0.000 0.152
#> SRR949128 2 0.2806 0.858 0.004 0.844 0.000 0.000 0.152
#> SRR949129 2 0.2806 0.858 0.004 0.844 0.000 0.000 0.152
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR949076 4 0.4738 0.7672 0.112 0.008 0.000 0.752 0.072 NA
#> SRR949078 2 0.2873 0.7426 0.044 0.872 0.000 0.068 0.012 NA
#> SRR949077 4 0.5561 0.8150 0.176 0.032 0.000 0.680 0.072 NA
#> SRR949079 4 0.5195 0.8204 0.200 0.000 0.000 0.676 0.068 NA
#> SRR949080 4 0.5195 0.8204 0.200 0.000 0.000 0.676 0.068 NA
#> SRR949081 5 0.8656 0.0957 0.128 0.256 0.000 0.176 0.304 NA
#> SRR949082 2 0.3039 0.7416 0.028 0.868 0.000 0.068 0.028 NA
#> SRR949083 1 0.2914 0.6079 0.864 0.004 0.000 0.068 0.004 NA
#> SRR949084 1 0.1411 0.6467 0.936 0.004 0.000 0.000 0.000 NA
#> SRR949085 2 0.0865 0.7827 0.000 0.964 0.000 0.000 0.000 NA
#> SRR949087 5 0.8439 0.1548 0.292 0.156 0.000 0.076 0.300 NA
#> SRR949088 5 0.8439 0.1548 0.292 0.156 0.000 0.076 0.300 NA
#> SRR949086 3 0.5900 0.4208 0.032 0.000 0.524 0.080 0.356 NA
#> SRR949089 2 0.2260 0.7834 0.000 0.860 0.000 0.000 0.000 NA
#> SRR949090 4 0.3270 0.8399 0.152 0.024 0.004 0.816 0.004 NA
#> SRR949092 1 0.0508 0.6585 0.984 0.000 0.000 0.000 0.012 NA
#> SRR949093 1 0.0508 0.6585 0.984 0.000 0.000 0.000 0.012 NA
#> SRR949091 3 0.5279 0.3626 0.000 0.024 0.584 0.336 0.052 NA
#> SRR949095 5 0.8724 0.1000 0.140 0.252 0.000 0.176 0.292 NA
#> SRR949094 4 0.4096 0.8322 0.204 0.028 0.000 0.744 0.000 NA
#> SRR949096 1 0.2333 0.6210 0.872 0.004 0.000 0.004 0.000 NA
#> SRR949097 1 0.4227 0.1273 0.496 0.000 0.000 0.008 0.492 NA
#> SRR949098 2 0.2738 0.7777 0.004 0.820 0.000 0.000 0.000 NA
#> SRR949099 5 0.4548 0.1121 0.156 0.000 0.116 0.008 0.720 NA
#> SRR949101 3 0.3833 0.6304 0.000 0.016 0.804 0.108 0.068 NA
#> SRR949100 1 0.7930 -0.2276 0.344 0.188 0.000 0.028 0.296 NA
#> SRR949102 4 0.8451 0.1309 0.116 0.064 0.020 0.336 0.320 NA
#> SRR949103 1 0.4227 0.1273 0.496 0.000 0.000 0.008 0.492 NA
#> SRR949104 2 0.2178 0.7856 0.000 0.868 0.000 0.000 0.000 NA
#> SRR949105 3 0.0260 0.7050 0.000 0.000 0.992 0.008 0.000 NA
#> SRR949106 3 0.0260 0.7050 0.000 0.000 0.992 0.008 0.000 NA
#> SRR949107 3 0.0260 0.7050 0.000 0.000 0.992 0.008 0.000 NA
#> SRR949108 1 0.1616 0.6552 0.940 0.000 0.000 0.012 0.028 NA
#> SRR949109 4 0.3457 0.8383 0.152 0.028 0.004 0.808 0.008 NA
#> SRR949110 5 0.4227 -0.2756 0.492 0.000 0.000 0.008 0.496 NA
#> SRR949111 4 0.2662 0.8399 0.152 0.000 0.004 0.840 0.004 NA
#> SRR949112 1 0.3397 0.5862 0.836 0.000 0.000 0.024 0.084 NA
#> SRR949113 2 0.1257 0.7754 0.020 0.952 0.000 0.000 0.028 NA
#> SRR949114 5 0.7463 0.0658 0.272 0.000 0.296 0.072 0.344 NA
#> SRR949115 5 0.7463 0.0658 0.272 0.000 0.296 0.072 0.344 NA
#> SRR949116 5 0.7463 0.0658 0.272 0.000 0.296 0.072 0.344 NA
#> SRR949117 3 0.5933 0.4164 0.032 0.000 0.524 0.084 0.352 NA
#> SRR949118 3 0.3704 0.6665 0.012 0.000 0.804 0.048 0.132 NA
#> SRR949119 1 0.5648 0.4212 0.604 0.000 0.000 0.108 0.036 NA
#> SRR949120 1 0.5648 0.4212 0.604 0.000 0.000 0.108 0.036 NA
#> SRR949121 1 0.2841 0.5486 0.824 0.000 0.000 0.012 0.164 NA
#> SRR949122 1 0.2085 0.6350 0.912 0.000 0.000 0.008 0.024 NA
#> SRR949123 2 0.3346 0.7713 0.008 0.816 0.000 0.000 0.036 NA
#> SRR949124 2 0.2260 0.7834 0.000 0.860 0.000 0.000 0.000 NA
#> SRR949125 4 0.2624 0.8388 0.148 0.000 0.004 0.844 0.004 NA
#> SRR949126 4 0.2624 0.8388 0.148 0.000 0.004 0.844 0.004 NA
#> SRR949127 2 0.3899 0.5998 0.000 0.592 0.000 0.004 0.000 NA
#> SRR949128 2 0.3899 0.5998 0.000 0.592 0.000 0.004 0.000 NA
#> SRR949129 2 0.3899 0.5998 0.000 0.592 0.000 0.004 0.000 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 16816 rows and 54 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 0.994 0.944 0.977 0.427 0.575 0.575
#> 3 3 0.641 0.810 0.903 0.564 0.679 0.475
#> 4 4 0.712 0.749 0.885 0.128 0.787 0.457
#> 5 5 0.689 0.570 0.774 0.055 0.984 0.935
#> 6 6 0.737 0.602 0.750 0.040 0.879 0.537
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
#> SRR949076 1 0.0000 0.980 1.000 0.000
#> SRR949078 2 0.0000 0.966 0.000 1.000
#> SRR949077 1 0.0000 0.980 1.000 0.000
#> SRR949079 1 0.0000 0.980 1.000 0.000
#> SRR949080 1 0.0000 0.980 1.000 0.000
#> SRR949081 2 0.0000 0.966 0.000 1.000
#> SRR949082 2 0.0000 0.966 0.000 1.000
#> SRR949083 1 0.0000 0.980 1.000 0.000
#> SRR949084 1 0.0000 0.980 1.000 0.000
#> SRR949085 2 0.0000 0.966 0.000 1.000
#> SRR949087 2 0.4022 0.902 0.080 0.920
#> SRR949088 2 0.4022 0.902 0.080 0.920
#> SRR949086 1 0.1184 0.968 0.984 0.016
#> SRR949089 2 0.0000 0.966 0.000 1.000
#> SRR949090 1 0.0000 0.980 1.000 0.000
#> SRR949092 1 0.0000 0.980 1.000 0.000
#> SRR949093 1 0.0000 0.980 1.000 0.000
#> SRR949091 1 0.0000 0.980 1.000 0.000
#> SRR949095 2 0.9209 0.501 0.336 0.664
#> SRR949094 1 0.0000 0.980 1.000 0.000
#> SRR949096 1 0.0000 0.980 1.000 0.000
#> SRR949097 1 0.0000 0.980 1.000 0.000
#> SRR949098 2 0.0000 0.966 0.000 1.000
#> SRR949099 1 0.0000 0.980 1.000 0.000
#> SRR949101 1 0.0000 0.980 1.000 0.000
#> SRR949100 1 0.9963 0.108 0.536 0.464
#> SRR949102 1 0.0376 0.977 0.996 0.004
#> SRR949103 1 0.0000 0.980 1.000 0.000
#> SRR949104 2 0.0000 0.966 0.000 1.000
#> SRR949105 1 0.2778 0.939 0.952 0.048
#> SRR949106 1 0.4161 0.903 0.916 0.084
#> SRR949107 1 0.4161 0.903 0.916 0.084
#> SRR949108 1 0.0000 0.980 1.000 0.000
#> SRR949109 1 0.0000 0.980 1.000 0.000
#> SRR949110 1 0.0000 0.980 1.000 0.000
#> SRR949111 1 0.0000 0.980 1.000 0.000
#> SRR949112 1 0.0672 0.974 0.992 0.008
#> SRR949113 2 0.0000 0.966 0.000 1.000
#> SRR949114 1 0.0000 0.980 1.000 0.000
#> SRR949115 1 0.0000 0.980 1.000 0.000
#> SRR949116 1 0.0000 0.980 1.000 0.000
#> SRR949117 1 0.1633 0.961 0.976 0.024
#> SRR949118 1 0.0000 0.980 1.000 0.000
#> SRR949119 1 0.0000 0.980 1.000 0.000
#> SRR949120 1 0.0000 0.980 1.000 0.000
#> SRR949121 1 0.0000 0.980 1.000 0.000
#> SRR949122 1 0.0000 0.980 1.000 0.000
#> SRR949123 2 0.0000 0.966 0.000 1.000
#> SRR949124 2 0.0000 0.966 0.000 1.000
#> SRR949125 1 0.0000 0.980 1.000 0.000
#> SRR949126 1 0.0000 0.980 1.000 0.000
#> SRR949127 2 0.0000 0.966 0.000 1.000
#> SRR949128 2 0.0000 0.966 0.000 1.000
#> SRR949129 2 0.0000 0.966 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR949076 1 0.4346 0.777 0.816 0.000 0.184
#> SRR949078 2 0.0000 0.949 0.000 1.000 0.000
#> SRR949077 1 0.3879 0.795 0.848 0.000 0.152
#> SRR949079 1 0.4346 0.777 0.816 0.000 0.184
#> SRR949080 1 0.4346 0.777 0.816 0.000 0.184
#> SRR949081 1 0.6527 0.268 0.588 0.404 0.008
#> SRR949082 2 0.0000 0.949 0.000 1.000 0.000
#> SRR949083 1 0.0592 0.850 0.988 0.000 0.012
#> SRR949084 1 0.0592 0.850 0.988 0.000 0.012
#> SRR949085 2 0.0000 0.949 0.000 1.000 0.000
#> SRR949087 2 0.3619 0.828 0.136 0.864 0.000
#> SRR949088 2 0.3482 0.837 0.128 0.872 0.000
#> SRR949086 3 0.3207 0.837 0.012 0.084 0.904
#> SRR949089 2 0.0000 0.949 0.000 1.000 0.000
#> SRR949090 3 0.1529 0.864 0.040 0.000 0.960
#> SRR949092 1 0.0592 0.850 0.988 0.000 0.012
#> SRR949093 1 0.0592 0.850 0.988 0.000 0.012
#> SRR949091 3 0.0592 0.864 0.012 0.000 0.988
#> SRR949095 1 0.4999 0.746 0.820 0.152 0.028
#> SRR949094 1 0.4555 0.765 0.800 0.000 0.200
#> SRR949096 1 0.0592 0.850 0.988 0.000 0.012
#> SRR949097 1 0.5859 0.299 0.656 0.000 0.344
#> SRR949098 2 0.0000 0.949 0.000 1.000 0.000
#> SRR949099 3 0.4002 0.813 0.160 0.000 0.840
#> SRR949101 3 0.0000 0.869 0.000 0.000 1.000
#> SRR949100 2 0.6062 0.361 0.384 0.616 0.000
#> SRR949102 1 0.4452 0.773 0.808 0.000 0.192
#> SRR949103 3 0.5882 0.636 0.348 0.000 0.652
#> SRR949104 2 0.0000 0.949 0.000 1.000 0.000
#> SRR949105 3 0.0829 0.872 0.012 0.004 0.984
#> SRR949106 3 0.0829 0.872 0.012 0.004 0.984
#> SRR949107 3 0.0829 0.872 0.012 0.004 0.984
#> SRR949108 1 0.0592 0.850 0.988 0.000 0.012
#> SRR949109 3 0.2878 0.844 0.096 0.000 0.904
#> SRR949110 1 0.5968 0.231 0.636 0.000 0.364
#> SRR949111 3 0.4121 0.774 0.168 0.000 0.832
#> SRR949112 1 0.0592 0.850 0.988 0.000 0.012
#> SRR949113 2 0.0000 0.949 0.000 1.000 0.000
#> SRR949114 3 0.4654 0.787 0.208 0.000 0.792
#> SRR949115 3 0.5058 0.761 0.244 0.000 0.756
#> SRR949116 3 0.5058 0.761 0.244 0.000 0.756
#> SRR949117 3 0.4891 0.799 0.040 0.124 0.836
#> SRR949118 3 0.0747 0.872 0.016 0.000 0.984
#> SRR949119 1 0.0424 0.847 0.992 0.000 0.008
#> SRR949120 1 0.0424 0.847 0.992 0.000 0.008
#> SRR949121 1 0.0592 0.850 0.988 0.000 0.012
#> SRR949122 1 0.0592 0.850 0.988 0.000 0.012
#> SRR949123 2 0.0000 0.949 0.000 1.000 0.000
#> SRR949124 2 0.0000 0.949 0.000 1.000 0.000
#> SRR949125 3 0.2878 0.844 0.096 0.000 0.904
#> SRR949126 3 0.2878 0.844 0.096 0.000 0.904
#> SRR949127 2 0.0000 0.949 0.000 1.000 0.000
#> SRR949128 2 0.0000 0.949 0.000 1.000 0.000
#> SRR949129 2 0.0000 0.949 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR949076 4 0.0000 0.7128 0.000 0.000 0.000 1.000
#> SRR949078 2 0.0000 0.9320 0.000 1.000 0.000 0.000
#> SRR949077 4 0.0188 0.7138 0.000 0.000 0.004 0.996
#> SRR949079 4 0.0592 0.7153 0.000 0.000 0.016 0.984
#> SRR949080 4 0.0592 0.7153 0.000 0.000 0.016 0.984
#> SRR949081 4 0.7472 0.0625 0.008 0.412 0.136 0.444
#> SRR949082 2 0.0000 0.9320 0.000 1.000 0.000 0.000
#> SRR949083 1 0.3219 0.7844 0.836 0.000 0.000 0.164
#> SRR949084 1 0.2973 0.8014 0.856 0.000 0.000 0.144
#> SRR949085 2 0.0000 0.9320 0.000 1.000 0.000 0.000
#> SRR949087 2 0.4720 0.5720 0.324 0.672 0.000 0.004
#> SRR949088 2 0.4761 0.5567 0.332 0.664 0.000 0.004
#> SRR949086 3 0.0592 0.8600 0.016 0.000 0.984 0.000
#> SRR949089 2 0.0000 0.9320 0.000 1.000 0.000 0.000
#> SRR949090 4 0.4941 0.3255 0.000 0.000 0.436 0.564
#> SRR949092 1 0.0000 0.8989 1.000 0.000 0.000 0.000
#> SRR949093 1 0.0000 0.8989 1.000 0.000 0.000 0.000
#> SRR949091 3 0.3486 0.6428 0.000 0.000 0.812 0.188
#> SRR949095 4 0.3306 0.6277 0.004 0.156 0.000 0.840
#> SRR949094 4 0.1389 0.7118 0.000 0.000 0.048 0.952
#> SRR949096 1 0.3074 0.7946 0.848 0.000 0.000 0.152
#> SRR949097 1 0.0188 0.8974 0.996 0.000 0.000 0.004
#> SRR949098 2 0.0000 0.9320 0.000 1.000 0.000 0.000
#> SRR949099 3 0.4585 0.4674 0.332 0.000 0.668 0.000
#> SRR949101 3 0.0000 0.8623 0.000 0.000 1.000 0.000
#> SRR949100 2 0.4862 0.7696 0.108 0.800 0.012 0.080
#> SRR949102 4 0.2921 0.6647 0.000 0.000 0.140 0.860
#> SRR949103 1 0.0188 0.8969 0.996 0.000 0.004 0.000
#> SRR949104 2 0.0000 0.9320 0.000 1.000 0.000 0.000
#> SRR949105 3 0.0000 0.8623 0.000 0.000 1.000 0.000
#> SRR949106 3 0.0000 0.8623 0.000 0.000 1.000 0.000
#> SRR949107 3 0.0000 0.8623 0.000 0.000 1.000 0.000
#> SRR949108 1 0.0000 0.8989 1.000 0.000 0.000 0.000
#> SRR949109 4 0.4898 0.3674 0.000 0.000 0.416 0.584
#> SRR949110 1 0.0000 0.8989 1.000 0.000 0.000 0.000
#> SRR949111 4 0.3942 0.6181 0.000 0.000 0.236 0.764
#> SRR949112 1 0.0000 0.8989 1.000 0.000 0.000 0.000
#> SRR949113 2 0.0000 0.9320 0.000 1.000 0.000 0.000
#> SRR949114 1 0.4500 0.5230 0.684 0.000 0.316 0.000
#> SRR949115 1 0.3688 0.7123 0.792 0.000 0.208 0.000
#> SRR949116 1 0.3649 0.7174 0.796 0.000 0.204 0.000
#> SRR949117 3 0.3958 0.7504 0.160 0.024 0.816 0.000
#> SRR949118 3 0.2216 0.8200 0.092 0.000 0.908 0.000
#> SRR949119 4 0.4790 0.2707 0.380 0.000 0.000 0.620
#> SRR949120 4 0.4804 0.2615 0.384 0.000 0.000 0.616
#> SRR949121 1 0.0000 0.8989 1.000 0.000 0.000 0.000
#> SRR949122 1 0.0000 0.8989 1.000 0.000 0.000 0.000
#> SRR949123 2 0.0000 0.9320 0.000 1.000 0.000 0.000
#> SRR949124 2 0.0000 0.9320 0.000 1.000 0.000 0.000
#> SRR949125 4 0.4277 0.5829 0.000 0.000 0.280 0.720
#> SRR949126 4 0.4277 0.5829 0.000 0.000 0.280 0.720
#> SRR949127 2 0.0000 0.9320 0.000 1.000 0.000 0.000
#> SRR949128 2 0.0000 0.9320 0.000 1.000 0.000 0.000
#> SRR949129 2 0.0000 0.9320 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR949076 4 0.1908 0.649 0.000 0.000 0.000 0.908 0.092
#> SRR949078 2 0.0000 0.881 0.000 1.000 0.000 0.000 0.000
#> SRR949077 4 0.2074 0.645 0.000 0.000 0.000 0.896 0.104
#> SRR949079 4 0.0000 0.649 0.000 0.000 0.000 1.000 0.000
#> SRR949080 4 0.0000 0.649 0.000 0.000 0.000 1.000 0.000
#> SRR949081 4 0.8983 0.284 0.072 0.144 0.132 0.408 0.244
#> SRR949082 2 0.0000 0.881 0.000 1.000 0.000 0.000 0.000
#> SRR949083 1 0.2927 0.691 0.872 0.000 0.000 0.068 0.060
#> SRR949084 1 0.2719 0.693 0.884 0.000 0.000 0.068 0.048
#> SRR949085 2 0.0000 0.881 0.000 1.000 0.000 0.000 0.000
#> SRR949087 2 0.7437 0.253 0.344 0.448 0.096 0.000 0.112
#> SRR949088 2 0.7437 0.254 0.344 0.448 0.096 0.000 0.112
#> SRR949086 3 0.2389 0.687 0.004 0.000 0.880 0.000 0.116
#> SRR949089 2 0.0000 0.881 0.000 1.000 0.000 0.000 0.000
#> SRR949090 4 0.6200 0.186 0.000 0.000 0.320 0.520 0.160
#> SRR949092 1 0.0609 0.731 0.980 0.000 0.000 0.000 0.020
#> SRR949093 1 0.0609 0.731 0.980 0.000 0.000 0.000 0.020
#> SRR949091 5 0.6819 -0.159 0.000 0.000 0.312 0.340 0.348
#> SRR949095 4 0.4985 0.564 0.000 0.076 0.000 0.680 0.244
#> SRR949094 4 0.0955 0.643 0.000 0.000 0.004 0.968 0.028
#> SRR949096 1 0.3336 0.664 0.844 0.000 0.000 0.096 0.060
#> SRR949097 1 0.2583 0.690 0.864 0.000 0.004 0.000 0.132
#> SRR949098 2 0.0000 0.881 0.000 1.000 0.000 0.000 0.000
#> SRR949099 3 0.6628 0.162 0.372 0.000 0.408 0.000 0.220
#> SRR949101 3 0.4342 0.493 0.000 0.000 0.728 0.040 0.232
#> SRR949100 2 0.7565 0.415 0.156 0.536 0.060 0.024 0.224
#> SRR949102 4 0.5555 0.532 0.004 0.000 0.104 0.636 0.256
#> SRR949103 1 0.3123 0.657 0.812 0.000 0.004 0.000 0.184
#> SRR949104 2 0.0000 0.881 0.000 1.000 0.000 0.000 0.000
#> SRR949105 3 0.0324 0.697 0.000 0.000 0.992 0.004 0.004
#> SRR949106 3 0.0162 0.697 0.000 0.000 0.996 0.004 0.000
#> SRR949107 3 0.0162 0.697 0.000 0.000 0.996 0.004 0.000
#> SRR949108 1 0.2471 0.689 0.864 0.000 0.000 0.000 0.136
#> SRR949109 4 0.6147 0.254 0.000 0.000 0.256 0.556 0.188
#> SRR949110 1 0.2389 0.697 0.880 0.000 0.004 0.000 0.116
#> SRR949111 4 0.4350 0.530 0.000 0.000 0.152 0.764 0.084
#> SRR949112 1 0.3661 0.516 0.724 0.000 0.000 0.000 0.276
#> SRR949113 2 0.0000 0.881 0.000 1.000 0.000 0.000 0.000
#> SRR949114 5 0.5854 -0.351 0.436 0.000 0.096 0.000 0.468
#> SRR949115 1 0.5458 -0.147 0.476 0.000 0.060 0.000 0.464
#> SRR949116 1 0.5458 -0.147 0.476 0.000 0.060 0.000 0.464
#> SRR949117 3 0.5738 0.492 0.132 0.000 0.604 0.000 0.264
#> SRR949118 3 0.4691 0.584 0.044 0.000 0.680 0.000 0.276
#> SRR949119 4 0.6009 0.454 0.180 0.000 0.000 0.580 0.240
#> SRR949120 4 0.6009 0.454 0.180 0.000 0.000 0.580 0.240
#> SRR949121 1 0.2424 0.695 0.868 0.000 0.000 0.000 0.132
#> SRR949122 1 0.2471 0.689 0.864 0.000 0.000 0.000 0.136
#> SRR949123 2 0.1043 0.857 0.000 0.960 0.000 0.000 0.040
#> SRR949124 2 0.0404 0.875 0.000 0.988 0.000 0.000 0.012
#> SRR949125 4 0.4743 0.492 0.000 0.000 0.156 0.732 0.112
#> SRR949126 4 0.4781 0.488 0.000 0.000 0.160 0.728 0.112
#> SRR949127 2 0.0404 0.877 0.000 0.988 0.000 0.000 0.012
#> SRR949128 2 0.0510 0.875 0.000 0.984 0.000 0.000 0.016
#> SRR949129 2 0.0000 0.881 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR949076 4 0.3828 0.03128 0.000 0.000 0.000 0.560 0.440 0.000
#> SRR949078 2 0.0363 0.92680 0.000 0.988 0.000 0.000 0.012 0.000
#> SRR949077 4 0.3944 0.04093 0.004 0.000 0.000 0.568 0.428 0.000
#> SRR949079 4 0.2562 0.62231 0.000 0.000 0.000 0.828 0.172 0.000
#> SRR949080 4 0.2562 0.62231 0.000 0.000 0.000 0.828 0.172 0.000
#> SRR949081 5 0.6627 0.54813 0.280 0.028 0.100 0.048 0.540 0.004
#> SRR949082 2 0.0363 0.92538 0.000 0.988 0.000 0.000 0.012 0.000
#> SRR949083 1 0.3946 0.46600 0.768 0.000 0.000 0.004 0.076 0.152
#> SRR949084 1 0.4626 0.44903 0.704 0.000 0.000 0.004 0.128 0.164
#> SRR949085 2 0.0000 0.92937 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949087 1 0.6411 0.19217 0.528 0.252 0.176 0.000 0.036 0.008
#> SRR949088 1 0.6406 0.18092 0.520 0.260 0.180 0.000 0.032 0.008
#> SRR949086 3 0.3814 0.77635 0.096 0.000 0.816 0.008 0.052 0.028
#> SRR949089 2 0.0000 0.92937 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949090 4 0.3605 0.63772 0.000 0.000 0.084 0.804 0.108 0.004
#> SRR949092 1 0.3758 0.35452 0.700 0.000 0.000 0.000 0.016 0.284
#> SRR949093 1 0.3738 0.35936 0.704 0.000 0.000 0.000 0.016 0.280
#> SRR949091 4 0.4795 0.57249 0.000 0.000 0.112 0.696 0.012 0.180
#> SRR949095 5 0.5002 0.67159 0.024 0.068 0.000 0.228 0.676 0.004
#> SRR949094 4 0.2003 0.65916 0.000 0.000 0.000 0.884 0.116 0.000
#> SRR949096 1 0.5024 0.42831 0.672 0.000 0.000 0.012 0.180 0.136
#> SRR949097 1 0.5858 0.40021 0.636 0.000 0.004 0.064 0.164 0.132
#> SRR949098 2 0.0000 0.92937 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949099 1 0.6580 0.15870 0.540 0.000 0.192 0.060 0.200 0.008
#> SRR949101 3 0.3934 0.72635 0.000 0.000 0.764 0.044 0.012 0.180
#> SRR949100 2 0.7981 0.00907 0.284 0.364 0.040 0.096 0.212 0.004
#> SRR949102 5 0.6541 0.67347 0.068 0.000 0.064 0.180 0.608 0.080
#> SRR949103 1 0.5519 0.42561 0.676 0.000 0.004 0.064 0.132 0.124
#> SRR949104 2 0.0000 0.92937 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949105 3 0.1251 0.81733 0.000 0.000 0.956 0.024 0.008 0.012
#> SRR949106 3 0.1251 0.81733 0.000 0.000 0.956 0.024 0.008 0.012
#> SRR949107 3 0.1251 0.81733 0.000 0.000 0.956 0.024 0.008 0.012
#> SRR949108 6 0.4830 0.26477 0.412 0.000 0.000 0.008 0.040 0.540
#> SRR949109 4 0.3804 0.63021 0.004 0.000 0.032 0.792 0.152 0.020
#> SRR949110 1 0.6289 0.33221 0.568 0.000 0.004 0.056 0.160 0.212
#> SRR949111 4 0.3513 0.63215 0.020 0.000 0.024 0.804 0.152 0.000
#> SRR949112 6 0.3240 0.57529 0.244 0.000 0.000 0.004 0.000 0.752
#> SRR949113 2 0.0000 0.92937 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949114 6 0.0767 0.66531 0.004 0.000 0.008 0.012 0.000 0.976
#> SRR949115 6 0.0405 0.67196 0.004 0.000 0.008 0.000 0.000 0.988
#> SRR949116 6 0.0405 0.67196 0.004 0.000 0.008 0.000 0.000 0.988
#> SRR949117 3 0.5320 0.72412 0.148 0.000 0.680 0.000 0.052 0.120
#> SRR949118 3 0.5934 0.65429 0.116 0.000 0.600 0.004 0.048 0.232
#> SRR949119 5 0.4683 0.74666 0.052 0.000 0.000 0.176 0.724 0.048
#> SRR949120 5 0.4683 0.74666 0.052 0.000 0.000 0.176 0.724 0.048
#> SRR949121 1 0.3838 -0.08890 0.552 0.000 0.000 0.000 0.000 0.448
#> SRR949122 6 0.3899 0.36261 0.404 0.000 0.000 0.000 0.004 0.592
#> SRR949123 2 0.1584 0.88062 0.000 0.928 0.000 0.000 0.008 0.064
#> SRR949124 2 0.0790 0.91275 0.000 0.968 0.000 0.000 0.000 0.032
#> SRR949125 4 0.1682 0.69111 0.000 0.000 0.020 0.928 0.000 0.052
#> SRR949126 4 0.1921 0.69058 0.000 0.000 0.032 0.916 0.000 0.052
#> SRR949127 2 0.0777 0.92158 0.024 0.972 0.000 0.000 0.000 0.004
#> SRR949128 2 0.0922 0.91972 0.024 0.968 0.000 0.000 0.004 0.004
#> SRR949129 2 0.0777 0.92158 0.024 0.972 0.000 0.000 0.000 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 16816 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.621 0.877 0.942 0.4280 0.547 0.547
#> 3 3 0.614 0.663 0.847 0.2952 0.843 0.722
#> 4 4 0.774 0.914 0.947 0.2397 0.841 0.643
#> 5 5 0.897 0.898 0.929 0.0316 0.994 0.982
#> 6 6 0.898 0.886 0.909 0.0338 0.978 0.925
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
#> SRR949076 2 0.932 0.589 0.348 0.652
#> SRR949078 2 0.000 0.862 0.000 1.000
#> SRR949077 2 0.932 0.589 0.348 0.652
#> SRR949079 1 0.000 0.964 1.000 0.000
#> SRR949080 1 0.000 0.964 1.000 0.000
#> SRR949081 2 0.932 0.589 0.348 0.652
#> SRR949082 2 0.000 0.862 0.000 1.000
#> SRR949083 2 0.932 0.589 0.348 0.652
#> SRR949084 1 0.000 0.964 1.000 0.000
#> SRR949085 2 0.000 0.862 0.000 1.000
#> SRR949087 1 0.767 0.692 0.776 0.224
#> SRR949088 1 0.767 0.692 0.776 0.224
#> SRR949086 1 0.595 0.816 0.856 0.144
#> SRR949089 2 0.000 0.862 0.000 1.000
#> SRR949090 1 0.000 0.964 1.000 0.000
#> SRR949092 1 0.000 0.964 1.000 0.000
#> SRR949093 1 0.000 0.964 1.000 0.000
#> SRR949091 1 0.000 0.964 1.000 0.000
#> SRR949095 2 0.932 0.589 0.348 0.652
#> SRR949094 1 0.000 0.964 1.000 0.000
#> SRR949096 1 0.000 0.964 1.000 0.000
#> SRR949097 1 0.000 0.964 1.000 0.000
#> SRR949098 2 0.000 0.862 0.000 1.000
#> SRR949099 1 0.000 0.964 1.000 0.000
#> SRR949101 1 0.714 0.741 0.804 0.196
#> SRR949100 1 0.000 0.964 1.000 0.000
#> SRR949102 2 0.932 0.589 0.348 0.652
#> SRR949103 1 0.000 0.964 1.000 0.000
#> SRR949104 2 0.000 0.862 0.000 1.000
#> SRR949105 1 0.000 0.964 1.000 0.000
#> SRR949106 1 0.000 0.964 1.000 0.000
#> SRR949107 1 0.000 0.964 1.000 0.000
#> SRR949108 1 0.000 0.964 1.000 0.000
#> SRR949109 1 0.000 0.964 1.000 0.000
#> SRR949110 1 0.000 0.964 1.000 0.000
#> SRR949111 1 0.000 0.964 1.000 0.000
#> SRR949112 1 0.000 0.964 1.000 0.000
#> SRR949113 2 0.000 0.862 0.000 1.000
#> SRR949114 1 0.000 0.964 1.000 0.000
#> SRR949115 1 0.000 0.964 1.000 0.000
#> SRR949116 1 0.000 0.964 1.000 0.000
#> SRR949117 1 0.595 0.816 0.856 0.144
#> SRR949118 1 0.574 0.827 0.864 0.136
#> SRR949119 1 0.000 0.964 1.000 0.000
#> SRR949120 1 0.000 0.964 1.000 0.000
#> SRR949121 1 0.000 0.964 1.000 0.000
#> SRR949122 1 0.000 0.964 1.000 0.000
#> SRR949123 2 0.000 0.862 0.000 1.000
#> SRR949124 2 0.000 0.862 0.000 1.000
#> SRR949125 1 0.000 0.964 1.000 0.000
#> SRR949126 1 0.000 0.964 1.000 0.000
#> SRR949127 2 0.000 0.862 0.000 1.000
#> SRR949128 2 0.000 0.862 0.000 1.000
#> SRR949129 2 0.000 0.862 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR949076 3 0.657 0.6022 0.348 0.016 0.636
#> SRR949078 2 0.606 0.6355 0.000 0.616 0.384
#> SRR949077 3 0.657 0.6022 0.348 0.016 0.636
#> SRR949079 1 0.000 0.8235 1.000 0.000 0.000
#> SRR949080 1 0.000 0.8235 1.000 0.000 0.000
#> SRR949081 3 0.657 0.6022 0.348 0.016 0.636
#> SRR949082 2 0.606 0.6355 0.000 0.616 0.384
#> SRR949083 3 0.657 0.6022 0.348 0.016 0.636
#> SRR949084 1 0.000 0.8235 1.000 0.000 0.000
#> SRR949085 2 0.000 0.9017 0.000 1.000 0.000
#> SRR949087 1 0.484 0.3736 0.776 0.000 0.224
#> SRR949088 1 0.484 0.3736 0.776 0.000 0.224
#> SRR949086 3 0.631 -0.0410 0.492 0.000 0.508
#> SRR949089 2 0.000 0.9017 0.000 1.000 0.000
#> SRR949090 1 0.000 0.8235 1.000 0.000 0.000
#> SRR949092 1 0.000 0.8235 1.000 0.000 0.000
#> SRR949093 1 0.000 0.8235 1.000 0.000 0.000
#> SRR949091 1 0.597 0.3446 0.636 0.000 0.364
#> SRR949095 3 0.657 0.6022 0.348 0.016 0.636
#> SRR949094 1 0.000 0.8235 1.000 0.000 0.000
#> SRR949096 1 0.000 0.8235 1.000 0.000 0.000
#> SRR949097 1 0.000 0.8235 1.000 0.000 0.000
#> SRR949098 2 0.000 0.9017 0.000 1.000 0.000
#> SRR949099 1 0.000 0.8235 1.000 0.000 0.000
#> SRR949101 3 0.624 0.0716 0.440 0.000 0.560
#> SRR949100 1 0.000 0.8235 1.000 0.000 0.000
#> SRR949102 3 0.657 0.6022 0.348 0.016 0.636
#> SRR949103 1 0.000 0.8235 1.000 0.000 0.000
#> SRR949104 2 0.000 0.9017 0.000 1.000 0.000
#> SRR949105 1 0.597 0.3446 0.636 0.000 0.364
#> SRR949106 1 0.597 0.3446 0.636 0.000 0.364
#> SRR949107 1 0.597 0.3446 0.636 0.000 0.364
#> SRR949108 1 0.000 0.8235 1.000 0.000 0.000
#> SRR949109 1 0.000 0.8235 1.000 0.000 0.000
#> SRR949110 1 0.000 0.8235 1.000 0.000 0.000
#> SRR949111 1 0.000 0.8235 1.000 0.000 0.000
#> SRR949112 1 0.000 0.8235 1.000 0.000 0.000
#> SRR949113 2 0.000 0.9017 0.000 1.000 0.000
#> SRR949114 1 0.597 0.3446 0.636 0.000 0.364
#> SRR949115 1 0.597 0.3446 0.636 0.000 0.364
#> SRR949116 1 0.597 0.3446 0.636 0.000 0.364
#> SRR949117 3 0.631 -0.0410 0.492 0.000 0.508
#> SRR949118 3 0.631 -0.0682 0.500 0.000 0.500
#> SRR949119 1 0.000 0.8235 1.000 0.000 0.000
#> SRR949120 1 0.000 0.8235 1.000 0.000 0.000
#> SRR949121 1 0.000 0.8235 1.000 0.000 0.000
#> SRR949122 1 0.000 0.8235 1.000 0.000 0.000
#> SRR949123 2 0.000 0.9017 0.000 1.000 0.000
#> SRR949124 2 0.000 0.9017 0.000 1.000 0.000
#> SRR949125 1 0.000 0.8235 1.000 0.000 0.000
#> SRR949126 1 0.000 0.8235 1.000 0.000 0.000
#> SRR949127 2 0.348 0.8651 0.000 0.872 0.128
#> SRR949128 2 0.348 0.8651 0.000 0.872 0.128
#> SRR949129 2 0.348 0.8651 0.000 0.872 0.128
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR949076 4 0.000 1.000 0.000 0.000 0.000 1.000
#> SRR949078 2 0.480 0.504 0.000 0.616 0.000 0.384
#> SRR949077 4 0.000 1.000 0.000 0.000 0.000 1.000
#> SRR949079 1 0.000 0.978 1.000 0.000 0.000 0.000
#> SRR949080 1 0.000 0.978 1.000 0.000 0.000 0.000
#> SRR949081 4 0.000 1.000 0.000 0.000 0.000 1.000
#> SRR949082 2 0.480 0.504 0.000 0.616 0.000 0.384
#> SRR949083 4 0.000 1.000 0.000 0.000 0.000 1.000
#> SRR949084 1 0.000 0.978 1.000 0.000 0.000 0.000
#> SRR949085 2 0.000 0.887 0.000 1.000 0.000 0.000
#> SRR949087 1 0.428 0.689 0.764 0.000 0.012 0.224
#> SRR949088 1 0.428 0.689 0.764 0.000 0.012 0.224
#> SRR949086 3 0.308 0.835 0.024 0.000 0.880 0.096
#> SRR949089 2 0.000 0.887 0.000 1.000 0.000 0.000
#> SRR949090 1 0.000 0.978 1.000 0.000 0.000 0.000
#> SRR949092 1 0.000 0.978 1.000 0.000 0.000 0.000
#> SRR949093 1 0.000 0.978 1.000 0.000 0.000 0.000
#> SRR949091 3 0.287 0.922 0.136 0.000 0.864 0.000
#> SRR949095 4 0.000 1.000 0.000 0.000 0.000 1.000
#> SRR949094 1 0.000 0.978 1.000 0.000 0.000 0.000
#> SRR949096 1 0.000 0.978 1.000 0.000 0.000 0.000
#> SRR949097 1 0.000 0.978 1.000 0.000 0.000 0.000
#> SRR949098 2 0.000 0.887 0.000 1.000 0.000 0.000
#> SRR949099 1 0.000 0.978 1.000 0.000 0.000 0.000
#> SRR949101 3 0.164 0.806 0.000 0.000 0.940 0.060
#> SRR949100 1 0.000 0.978 1.000 0.000 0.000 0.000
#> SRR949102 4 0.000 1.000 0.000 0.000 0.000 1.000
#> SRR949103 1 0.000 0.978 1.000 0.000 0.000 0.000
#> SRR949104 2 0.000 0.887 0.000 1.000 0.000 0.000
#> SRR949105 3 0.287 0.922 0.136 0.000 0.864 0.000
#> SRR949106 3 0.287 0.922 0.136 0.000 0.864 0.000
#> SRR949107 3 0.287 0.922 0.136 0.000 0.864 0.000
#> SRR949108 1 0.000 0.978 1.000 0.000 0.000 0.000
#> SRR949109 1 0.000 0.978 1.000 0.000 0.000 0.000
#> SRR949110 1 0.000 0.978 1.000 0.000 0.000 0.000
#> SRR949111 1 0.000 0.978 1.000 0.000 0.000 0.000
#> SRR949112 1 0.000 0.978 1.000 0.000 0.000 0.000
#> SRR949113 2 0.000 0.887 0.000 1.000 0.000 0.000
#> SRR949114 3 0.287 0.922 0.136 0.000 0.864 0.000
#> SRR949115 3 0.287 0.922 0.136 0.000 0.864 0.000
#> SRR949116 3 0.287 0.922 0.136 0.000 0.864 0.000
#> SRR949117 3 0.308 0.835 0.024 0.000 0.880 0.096
#> SRR949118 3 0.000 0.831 0.000 0.000 1.000 0.000
#> SRR949119 1 0.000 0.978 1.000 0.000 0.000 0.000
#> SRR949120 1 0.000 0.978 1.000 0.000 0.000 0.000
#> SRR949121 1 0.000 0.978 1.000 0.000 0.000 0.000
#> SRR949122 1 0.000 0.978 1.000 0.000 0.000 0.000
#> SRR949123 2 0.000 0.887 0.000 1.000 0.000 0.000
#> SRR949124 2 0.000 0.887 0.000 1.000 0.000 0.000
#> SRR949125 1 0.000 0.978 1.000 0.000 0.000 0.000
#> SRR949126 1 0.000 0.978 1.000 0.000 0.000 0.000
#> SRR949127 2 0.276 0.840 0.000 0.872 0.000 0.128
#> SRR949128 2 0.276 0.840 0.000 0.872 0.000 0.128
#> SRR949129 2 0.276 0.840 0.000 0.872 0.000 0.128
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR949076 4 0.3452 1.000 0.00 0.000 0.000 0.756 0.244
#> SRR949078 2 0.5172 0.505 0.00 0.616 0.000 0.060 0.324
#> SRR949077 5 0.0609 0.946 0.00 0.000 0.000 0.020 0.980
#> SRR949079 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000
#> SRR949080 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000
#> SRR949081 5 0.1410 0.886 0.00 0.000 0.000 0.060 0.940
#> SRR949082 2 0.5172 0.505 0.00 0.616 0.000 0.060 0.324
#> SRR949083 5 0.0000 0.955 0.00 0.000 0.000 0.000 1.000
#> SRR949084 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000
#> SRR949085 2 0.0000 0.878 0.00 1.000 0.000 0.000 0.000
#> SRR949087 1 0.4501 0.662 0.74 0.000 0.036 0.012 0.212
#> SRR949088 1 0.4501 0.662 0.74 0.000 0.036 0.012 0.212
#> SRR949086 3 0.4417 0.767 0.00 0.000 0.760 0.148 0.092
#> SRR949089 2 0.0000 0.878 0.00 1.000 0.000 0.000 0.000
#> SRR949090 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000
#> SRR949092 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000
#> SRR949093 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000
#> SRR949091 3 0.1043 0.893 0.04 0.000 0.960 0.000 0.000
#> SRR949095 5 0.0000 0.955 0.00 0.000 0.000 0.000 1.000
#> SRR949094 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000
#> SRR949096 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000
#> SRR949097 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000
#> SRR949098 2 0.0000 0.878 0.00 1.000 0.000 0.000 0.000
#> SRR949099 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000
#> SRR949101 3 0.3707 0.731 0.00 0.000 0.716 0.284 0.000
#> SRR949100 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000
#> SRR949102 4 0.3452 1.000 0.00 0.000 0.000 0.756 0.244
#> SRR949103 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000
#> SRR949104 2 0.0404 0.877 0.00 0.988 0.000 0.012 0.000
#> SRR949105 3 0.1043 0.893 0.04 0.000 0.960 0.000 0.000
#> SRR949106 3 0.1043 0.893 0.04 0.000 0.960 0.000 0.000
#> SRR949107 3 0.1043 0.893 0.04 0.000 0.960 0.000 0.000
#> SRR949108 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000
#> SRR949109 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000
#> SRR949110 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000
#> SRR949111 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000
#> SRR949112 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000
#> SRR949113 2 0.0404 0.877 0.00 0.988 0.000 0.012 0.000
#> SRR949114 3 0.1043 0.893 0.04 0.000 0.960 0.000 0.000
#> SRR949115 3 0.1043 0.893 0.04 0.000 0.960 0.000 0.000
#> SRR949116 3 0.1043 0.893 0.04 0.000 0.960 0.000 0.000
#> SRR949117 3 0.4417 0.767 0.00 0.000 0.760 0.148 0.092
#> SRR949118 3 0.3305 0.778 0.00 0.000 0.776 0.224 0.000
#> SRR949119 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000
#> SRR949120 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000
#> SRR949121 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000
#> SRR949122 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000
#> SRR949123 2 0.0000 0.878 0.00 1.000 0.000 0.000 0.000
#> SRR949124 2 0.0000 0.878 0.00 1.000 0.000 0.000 0.000
#> SRR949125 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000
#> SRR949126 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000
#> SRR949127 2 0.2873 0.833 0.00 0.860 0.000 0.020 0.120
#> SRR949128 2 0.2873 0.833 0.00 0.860 0.000 0.020 0.120
#> SRR949129 2 0.2873 0.833 0.00 0.860 0.000 0.020 0.120
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR949076 4 0.2454 1.000 0.00 0.000 0.000 0.840 0.160 0.000
#> SRR949078 2 0.5176 0.575 0.00 0.616 0.000 0.092 0.280 0.012
#> SRR949077 5 0.0547 0.933 0.00 0.000 0.000 0.020 0.980 0.000
#> SRR949079 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000 0.000
#> SRR949080 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000 0.000
#> SRR949081 5 0.2070 0.834 0.00 0.012 0.000 0.092 0.896 0.000
#> SRR949082 2 0.5176 0.575 0.00 0.616 0.000 0.092 0.280 0.012
#> SRR949083 5 0.0000 0.941 0.00 0.000 0.000 0.000 1.000 0.000
#> SRR949084 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000 0.000
#> SRR949085 2 0.3747 0.534 0.00 0.604 0.000 0.000 0.000 0.396
#> SRR949087 1 0.4268 0.667 0.74 0.020 0.036 0.004 0.200 0.000
#> SRR949088 1 0.4268 0.667 0.74 0.020 0.036 0.004 0.200 0.000
#> SRR949086 3 0.5746 0.703 0.00 0.152 0.656 0.096 0.092 0.004
#> SRR949089 6 0.0146 1.000 0.00 0.004 0.000 0.000 0.000 0.996
#> SRR949090 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000 0.000
#> SRR949092 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000 0.000
#> SRR949093 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000 0.000
#> SRR949091 3 0.0000 0.863 0.00 0.000 1.000 0.000 0.000 0.000
#> SRR949095 5 0.0000 0.941 0.00 0.000 0.000 0.000 1.000 0.000
#> SRR949094 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000 0.000
#> SRR949096 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000 0.000
#> SRR949097 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000 0.000
#> SRR949098 6 0.0146 1.000 0.00 0.004 0.000 0.000 0.000 0.996
#> SRR949099 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000 0.000
#> SRR949101 3 0.5408 0.660 0.00 0.184 0.600 0.212 0.000 0.004
#> SRR949100 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000 0.000
#> SRR949102 4 0.2454 1.000 0.00 0.000 0.000 0.840 0.160 0.000
#> SRR949103 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000 0.000
#> SRR949104 2 0.2762 0.749 0.00 0.804 0.000 0.000 0.000 0.196
#> SRR949105 3 0.0000 0.863 0.00 0.000 1.000 0.000 0.000 0.000
#> SRR949106 3 0.0000 0.863 0.00 0.000 1.000 0.000 0.000 0.000
#> SRR949107 3 0.0000 0.863 0.00 0.000 1.000 0.000 0.000 0.000
#> SRR949108 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000 0.000
#> SRR949109 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000 0.000
#> SRR949110 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000 0.000
#> SRR949111 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000 0.000
#> SRR949112 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000 0.000
#> SRR949113 2 0.2762 0.749 0.00 0.804 0.000 0.000 0.000 0.196
#> SRR949114 3 0.0000 0.863 0.00 0.000 1.000 0.000 0.000 0.000
#> SRR949115 3 0.0000 0.863 0.00 0.000 1.000 0.000 0.000 0.000
#> SRR949116 3 0.0000 0.863 0.00 0.000 1.000 0.000 0.000 0.000
#> SRR949117 3 0.5746 0.703 0.00 0.152 0.656 0.096 0.092 0.004
#> SRR949118 3 0.4997 0.712 0.00 0.176 0.660 0.160 0.000 0.004
#> SRR949119 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000 0.000
#> SRR949120 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000 0.000
#> SRR949121 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000 0.000
#> SRR949122 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000 0.000
#> SRR949123 6 0.0146 1.000 0.00 0.004 0.000 0.000 0.000 0.996
#> SRR949124 6 0.0146 1.000 0.00 0.004 0.000 0.000 0.000 0.996
#> SRR949125 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000 0.000
#> SRR949126 1 0.0000 0.977 1.00 0.000 0.000 0.000 0.000 0.000
#> SRR949127 2 0.3252 0.795 0.00 0.824 0.000 0.000 0.108 0.068
#> SRR949128 2 0.3252 0.795 0.00 0.824 0.000 0.000 0.108 0.068
#> SRR949129 2 0.3252 0.795 0.00 0.824 0.000 0.000 0.108 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)
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 16816 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.955 0.981 0.4656 0.535 0.535
#> 3 3 0.561 0.717 0.825 0.3768 0.776 0.600
#> 4 4 0.686 0.792 0.857 0.1260 0.899 0.729
#> 5 5 0.729 0.746 0.798 0.0855 0.887 0.612
#> 6 6 0.729 0.745 0.799 0.0457 0.970 0.847
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
#> SRR949076 2 0.000 0.975 0.000 1.000
#> SRR949078 2 0.000 0.975 0.000 1.000
#> SRR949077 2 0.973 0.307 0.404 0.596
#> SRR949079 1 0.000 0.981 1.000 0.000
#> SRR949080 1 0.000 0.981 1.000 0.000
#> SRR949081 2 0.000 0.975 0.000 1.000
#> SRR949082 2 0.000 0.975 0.000 1.000
#> SRR949083 2 0.118 0.962 0.016 0.984
#> SRR949084 1 0.000 0.981 1.000 0.000
#> SRR949085 2 0.000 0.975 0.000 1.000
#> SRR949087 1 0.760 0.716 0.780 0.220
#> SRR949088 1 0.760 0.716 0.780 0.220
#> SRR949086 1 0.141 0.973 0.980 0.020
#> SRR949089 2 0.000 0.975 0.000 1.000
#> SRR949090 1 0.000 0.981 1.000 0.000
#> SRR949092 1 0.000 0.981 1.000 0.000
#> SRR949093 1 0.000 0.981 1.000 0.000
#> SRR949091 1 0.118 0.975 0.984 0.016
#> SRR949095 2 0.141 0.960 0.020 0.980
#> SRR949094 1 0.000 0.981 1.000 0.000
#> SRR949096 1 0.000 0.981 1.000 0.000
#> SRR949097 1 0.000 0.981 1.000 0.000
#> SRR949098 2 0.000 0.975 0.000 1.000
#> SRR949099 1 0.000 0.981 1.000 0.000
#> SRR949101 2 0.000 0.975 0.000 1.000
#> SRR949100 1 0.000 0.981 1.000 0.000
#> SRR949102 2 0.000 0.975 0.000 1.000
#> SRR949103 1 0.000 0.981 1.000 0.000
#> SRR949104 2 0.000 0.975 0.000 1.000
#> SRR949105 1 0.118 0.975 0.984 0.016
#> SRR949106 1 0.118 0.975 0.984 0.016
#> SRR949107 1 0.118 0.975 0.984 0.016
#> SRR949108 1 0.000 0.981 1.000 0.000
#> SRR949109 1 0.000 0.981 1.000 0.000
#> SRR949110 1 0.000 0.981 1.000 0.000
#> SRR949111 1 0.000 0.981 1.000 0.000
#> SRR949112 1 0.000 0.981 1.000 0.000
#> SRR949113 2 0.000 0.975 0.000 1.000
#> SRR949114 1 0.118 0.975 0.984 0.016
#> SRR949115 1 0.118 0.975 0.984 0.016
#> SRR949116 1 0.118 0.975 0.984 0.016
#> SRR949117 1 0.118 0.975 0.984 0.016
#> SRR949118 1 0.118 0.975 0.984 0.016
#> SRR949119 1 0.000 0.981 1.000 0.000
#> SRR949120 1 0.000 0.981 1.000 0.000
#> SRR949121 1 0.000 0.981 1.000 0.000
#> SRR949122 1 0.000 0.981 1.000 0.000
#> SRR949123 2 0.000 0.975 0.000 1.000
#> SRR949124 2 0.000 0.975 0.000 1.000
#> SRR949125 1 0.000 0.981 1.000 0.000
#> SRR949126 1 0.000 0.981 1.000 0.000
#> SRR949127 2 0.000 0.975 0.000 1.000
#> SRR949128 2 0.000 0.975 0.000 1.000
#> SRR949129 2 0.000 0.975 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR949076 2 0.701 0.739 0.064 0.696 0.240
#> SRR949078 2 0.186 0.866 0.000 0.948 0.052
#> SRR949077 1 0.891 0.309 0.556 0.164 0.280
#> SRR949079 1 0.000 0.739 1.000 0.000 0.000
#> SRR949080 1 0.000 0.739 1.000 0.000 0.000
#> SRR949081 2 0.537 0.802 0.016 0.776 0.208
#> SRR949082 2 0.186 0.866 0.000 0.948 0.052
#> SRR949083 2 0.924 0.562 0.224 0.532 0.244
#> SRR949084 1 0.585 0.562 0.776 0.044 0.180
#> SRR949085 2 0.164 0.857 0.000 0.956 0.044
#> SRR949087 1 0.930 0.224 0.496 0.180 0.324
#> SRR949088 1 0.930 0.224 0.496 0.180 0.324
#> SRR949086 3 0.343 0.666 0.112 0.004 0.884
#> SRR949089 2 0.164 0.857 0.000 0.956 0.044
#> SRR949090 1 0.484 0.646 0.776 0.000 0.224
#> SRR949092 1 0.103 0.732 0.976 0.000 0.024
#> SRR949093 1 0.103 0.732 0.976 0.000 0.024
#> SRR949091 3 0.522 0.847 0.260 0.000 0.740
#> SRR949095 2 0.962 0.471 0.280 0.472 0.248
#> SRR949094 1 0.141 0.734 0.964 0.000 0.036
#> SRR949096 1 0.337 0.683 0.904 0.024 0.072
#> SRR949097 1 0.484 0.646 0.776 0.000 0.224
#> SRR949098 2 0.164 0.857 0.000 0.956 0.044
#> SRR949099 1 0.484 0.646 0.776 0.000 0.224
#> SRR949101 3 0.440 0.387 0.000 0.188 0.812
#> SRR949100 1 0.445 0.667 0.808 0.000 0.192
#> SRR949102 2 0.465 0.810 0.000 0.792 0.208
#> SRR949103 1 0.484 0.646 0.776 0.000 0.224
#> SRR949104 2 0.164 0.857 0.000 0.956 0.044
#> SRR949105 3 0.525 0.846 0.264 0.000 0.736
#> SRR949106 3 0.525 0.846 0.264 0.000 0.736
#> SRR949107 3 0.525 0.846 0.264 0.000 0.736
#> SRR949108 1 0.186 0.730 0.948 0.000 0.052
#> SRR949109 1 0.484 0.646 0.776 0.000 0.224
#> SRR949110 1 0.484 0.646 0.776 0.000 0.224
#> SRR949111 1 0.484 0.646 0.776 0.000 0.224
#> SRR949112 1 0.355 0.653 0.868 0.000 0.132
#> SRR949113 2 0.000 0.863 0.000 1.000 0.000
#> SRR949114 3 0.525 0.846 0.264 0.000 0.736
#> SRR949115 3 0.522 0.847 0.260 0.000 0.740
#> SRR949116 3 0.522 0.847 0.260 0.000 0.740
#> SRR949117 3 0.429 0.761 0.180 0.000 0.820
#> SRR949118 3 0.400 0.796 0.160 0.000 0.840
#> SRR949119 1 0.000 0.739 1.000 0.000 0.000
#> SRR949120 1 0.000 0.739 1.000 0.000 0.000
#> SRR949121 1 0.164 0.725 0.956 0.000 0.044
#> SRR949122 1 0.175 0.723 0.952 0.000 0.048
#> SRR949123 2 0.164 0.857 0.000 0.956 0.044
#> SRR949124 2 0.164 0.857 0.000 0.956 0.044
#> SRR949125 1 0.484 0.646 0.776 0.000 0.224
#> SRR949126 1 0.484 0.646 0.776 0.000 0.224
#> SRR949127 2 0.280 0.860 0.000 0.908 0.092
#> SRR949128 2 0.280 0.860 0.000 0.908 0.092
#> SRR949129 2 0.280 0.860 0.000 0.908 0.092
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR949076 4 0.2081 0.859 0.000 0.084 0.000 0.916
#> SRR949078 2 0.5708 0.436 0.000 0.556 0.028 0.416
#> SRR949077 4 0.1724 0.864 0.032 0.020 0.000 0.948
#> SRR949079 1 0.2760 0.832 0.872 0.000 0.000 0.128
#> SRR949080 1 0.2760 0.832 0.872 0.000 0.000 0.128
#> SRR949081 4 0.3444 0.732 0.000 0.184 0.000 0.816
#> SRR949082 2 0.5731 0.414 0.000 0.544 0.028 0.428
#> SRR949083 4 0.1677 0.878 0.012 0.040 0.000 0.948
#> SRR949084 1 0.5112 0.502 0.560 0.000 0.004 0.436
#> SRR949085 2 0.0000 0.757 0.000 1.000 0.000 0.000
#> SRR949087 4 0.3363 0.856 0.020 0.024 0.072 0.884
#> SRR949088 4 0.3363 0.856 0.020 0.024 0.072 0.884
#> SRR949086 3 0.2466 0.902 0.028 0.000 0.916 0.056
#> SRR949089 2 0.0000 0.757 0.000 1.000 0.000 0.000
#> SRR949090 1 0.1022 0.845 0.968 0.000 0.032 0.000
#> SRR949092 1 0.4584 0.723 0.696 0.000 0.004 0.300
#> SRR949093 1 0.4584 0.723 0.696 0.000 0.004 0.300
#> SRR949091 3 0.2480 0.940 0.088 0.000 0.904 0.008
#> SRR949095 4 0.1863 0.878 0.012 0.040 0.004 0.944
#> SRR949094 1 0.2011 0.841 0.920 0.000 0.000 0.080
#> SRR949096 1 0.4741 0.689 0.668 0.000 0.004 0.328
#> SRR949097 1 0.1022 0.845 0.968 0.000 0.032 0.000
#> SRR949098 2 0.0000 0.757 0.000 1.000 0.000 0.000
#> SRR949099 1 0.1022 0.845 0.968 0.000 0.032 0.000
#> SRR949101 3 0.4057 0.787 0.000 0.032 0.816 0.152
#> SRR949100 1 0.0657 0.845 0.984 0.000 0.012 0.004
#> SRR949102 4 0.3688 0.679 0.000 0.208 0.000 0.792
#> SRR949103 1 0.1022 0.845 0.968 0.000 0.032 0.000
#> SRR949104 2 0.1635 0.751 0.000 0.948 0.044 0.008
#> SRR949105 3 0.2610 0.941 0.088 0.000 0.900 0.012
#> SRR949106 3 0.2610 0.941 0.088 0.000 0.900 0.012
#> SRR949107 3 0.2610 0.941 0.088 0.000 0.900 0.012
#> SRR949108 1 0.0188 0.845 0.996 0.000 0.000 0.004
#> SRR949109 1 0.1022 0.845 0.968 0.000 0.032 0.000
#> SRR949110 1 0.1022 0.845 0.968 0.000 0.032 0.000
#> SRR949111 1 0.1022 0.845 0.968 0.000 0.032 0.000
#> SRR949112 1 0.5475 0.685 0.656 0.000 0.036 0.308
#> SRR949113 2 0.4713 0.708 0.000 0.776 0.052 0.172
#> SRR949114 3 0.2843 0.940 0.088 0.000 0.892 0.020
#> SRR949115 3 0.2843 0.940 0.088 0.000 0.892 0.020
#> SRR949116 3 0.2843 0.940 0.088 0.000 0.892 0.020
#> SRR949117 3 0.2385 0.905 0.028 0.000 0.920 0.052
#> SRR949118 3 0.2227 0.917 0.036 0.000 0.928 0.036
#> SRR949119 1 0.2944 0.831 0.868 0.000 0.004 0.128
#> SRR949120 1 0.2944 0.831 0.868 0.000 0.004 0.128
#> SRR949121 1 0.4584 0.723 0.696 0.000 0.004 0.300
#> SRR949122 1 0.4560 0.727 0.700 0.000 0.004 0.296
#> SRR949123 2 0.0000 0.757 0.000 1.000 0.000 0.000
#> SRR949124 2 0.0000 0.757 0.000 1.000 0.000 0.000
#> SRR949125 1 0.1022 0.845 0.968 0.000 0.032 0.000
#> SRR949126 1 0.1022 0.845 0.968 0.000 0.032 0.000
#> SRR949127 2 0.6412 0.586 0.000 0.592 0.088 0.320
#> SRR949128 2 0.6412 0.586 0.000 0.592 0.088 0.320
#> SRR949129 2 0.6412 0.586 0.000 0.592 0.088 0.320
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR949076 5 0.203 0.779 0.056 0.012 0.000 0.008 0.924
#> SRR949078 5 0.506 0.259 0.000 0.360 0.000 0.044 0.596
#> SRR949077 5 0.208 0.778 0.084 0.000 0.000 0.008 0.908
#> SRR949079 1 0.297 0.632 0.816 0.000 0.000 0.184 0.000
#> SRR949080 1 0.297 0.632 0.816 0.000 0.000 0.184 0.000
#> SRR949081 5 0.175 0.770 0.028 0.036 0.000 0.000 0.936
#> SRR949082 5 0.497 0.311 0.000 0.336 0.000 0.044 0.620
#> SRR949083 5 0.199 0.780 0.076 0.004 0.000 0.004 0.916
#> SRR949084 1 0.219 0.731 0.900 0.000 0.000 0.008 0.092
#> SRR949085 2 0.029 0.766 0.000 0.992 0.000 0.000 0.008
#> SRR949087 5 0.617 0.603 0.252 0.000 0.016 0.136 0.596
#> SRR949088 5 0.617 0.603 0.252 0.000 0.016 0.136 0.596
#> SRR949086 3 0.245 0.904 0.000 0.000 0.896 0.076 0.028
#> SRR949089 2 0.029 0.766 0.000 0.992 0.000 0.000 0.008
#> SRR949090 4 0.445 0.992 0.340 0.000 0.016 0.644 0.000
#> SRR949092 1 0.127 0.768 0.948 0.000 0.000 0.000 0.052
#> SRR949093 1 0.127 0.768 0.948 0.000 0.000 0.000 0.052
#> SRR949091 3 0.163 0.918 0.000 0.000 0.936 0.056 0.008
#> SRR949095 5 0.312 0.771 0.100 0.004 0.000 0.036 0.860
#> SRR949094 1 0.340 0.526 0.764 0.000 0.000 0.236 0.000
#> SRR949096 1 0.147 0.767 0.948 0.000 0.000 0.016 0.036
#> SRR949097 4 0.448 0.991 0.348 0.000 0.016 0.636 0.000
#> SRR949098 2 0.029 0.766 0.000 0.992 0.000 0.000 0.008
#> SRR949099 4 0.448 0.991 0.348 0.000 0.016 0.636 0.000
#> SRR949101 3 0.417 0.772 0.000 0.000 0.764 0.052 0.184
#> SRR949100 1 0.431 -0.670 0.504 0.000 0.000 0.496 0.000
#> SRR949102 5 0.199 0.759 0.016 0.048 0.000 0.008 0.928
#> SRR949103 4 0.448 0.991 0.348 0.000 0.016 0.636 0.000
#> SRR949104 2 0.273 0.740 0.000 0.868 0.000 0.116 0.016
#> SRR949105 3 0.214 0.910 0.000 0.000 0.916 0.052 0.032
#> SRR949106 3 0.214 0.910 0.000 0.000 0.916 0.052 0.032
#> SRR949107 3 0.214 0.910 0.000 0.000 0.916 0.052 0.032
#> SRR949108 1 0.307 0.598 0.804 0.000 0.000 0.196 0.000
#> SRR949109 4 0.445 0.992 0.340 0.000 0.016 0.644 0.000
#> SRR949110 4 0.448 0.991 0.348 0.000 0.016 0.636 0.000
#> SRR949111 4 0.445 0.992 0.340 0.000 0.016 0.644 0.000
#> SRR949112 1 0.249 0.736 0.904 0.000 0.008 0.032 0.056
#> SRR949113 2 0.537 0.639 0.000 0.668 0.000 0.184 0.148
#> SRR949114 3 0.188 0.917 0.008 0.000 0.932 0.048 0.012
#> SRR949115 3 0.188 0.917 0.008 0.000 0.932 0.048 0.012
#> SRR949116 3 0.188 0.917 0.008 0.000 0.932 0.048 0.012
#> SRR949117 3 0.233 0.907 0.004 0.000 0.904 0.076 0.016
#> SRR949118 3 0.160 0.916 0.000 0.000 0.940 0.048 0.012
#> SRR949119 1 0.207 0.716 0.896 0.000 0.000 0.104 0.000
#> SRR949120 1 0.207 0.716 0.896 0.000 0.000 0.104 0.000
#> SRR949121 1 0.156 0.765 0.940 0.000 0.000 0.008 0.052
#> SRR949122 1 0.156 0.765 0.940 0.000 0.000 0.008 0.052
#> SRR949123 2 0.029 0.766 0.000 0.992 0.000 0.000 0.008
#> SRR949124 2 0.029 0.766 0.000 0.992 0.000 0.000 0.008
#> SRR949125 4 0.445 0.992 0.340 0.000 0.016 0.644 0.000
#> SRR949126 4 0.445 0.992 0.340 0.000 0.016 0.644 0.000
#> SRR949127 2 0.725 0.470 0.020 0.484 0.012 0.220 0.264
#> SRR949128 2 0.725 0.470 0.020 0.484 0.012 0.220 0.264
#> SRR949129 2 0.725 0.470 0.020 0.484 0.012 0.220 0.264
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR949076 5 0.2307 0.720 0.028 0.004 0.000 0.016 0.908 0.044
#> SRR949078 5 0.4602 0.406 0.000 0.260 0.000 0.004 0.668 0.068
#> SRR949077 5 0.1777 0.725 0.044 0.000 0.000 0.004 0.928 0.024
#> SRR949079 1 0.4641 0.668 0.684 0.000 0.000 0.200 0.000 0.116
#> SRR949080 1 0.4641 0.668 0.684 0.000 0.000 0.200 0.000 0.116
#> SRR949081 5 0.1180 0.722 0.016 0.012 0.000 0.000 0.960 0.012
#> SRR949082 5 0.4393 0.455 0.000 0.224 0.000 0.004 0.704 0.068
#> SRR949083 5 0.1265 0.726 0.044 0.000 0.000 0.000 0.948 0.008
#> SRR949084 1 0.1625 0.799 0.928 0.000 0.000 0.000 0.060 0.012
#> SRR949085 2 0.0260 0.781 0.000 0.992 0.000 0.000 0.008 0.000
#> SRR949087 5 0.6464 0.229 0.272 0.000 0.004 0.012 0.404 0.308
#> SRR949088 5 0.6464 0.229 0.272 0.000 0.004 0.012 0.404 0.308
#> SRR949086 3 0.1442 0.838 0.004 0.000 0.944 0.012 0.000 0.040
#> SRR949089 2 0.0260 0.781 0.000 0.992 0.000 0.000 0.008 0.000
#> SRR949090 4 0.2178 0.932 0.132 0.000 0.000 0.868 0.000 0.000
#> SRR949092 1 0.1364 0.833 0.952 0.000 0.000 0.016 0.020 0.012
#> SRR949093 1 0.1364 0.833 0.952 0.000 0.000 0.016 0.020 0.012
#> SRR949091 3 0.0146 0.851 0.000 0.004 0.996 0.000 0.000 0.000
#> SRR949095 5 0.3013 0.691 0.068 0.000 0.000 0.000 0.844 0.088
#> SRR949094 1 0.5011 0.555 0.620 0.000 0.000 0.264 0.000 0.116
#> SRR949096 1 0.1462 0.827 0.936 0.000 0.000 0.008 0.000 0.056
#> SRR949097 4 0.3062 0.933 0.144 0.000 0.000 0.824 0.000 0.032
#> SRR949098 2 0.0260 0.781 0.000 0.992 0.000 0.000 0.008 0.000
#> SRR949099 4 0.3062 0.933 0.144 0.000 0.000 0.824 0.000 0.032
#> SRR949101 3 0.3582 0.727 0.000 0.004 0.816 0.016 0.124 0.040
#> SRR949100 4 0.4315 0.686 0.328 0.000 0.000 0.636 0.000 0.036
#> SRR949102 5 0.2465 0.710 0.012 0.016 0.000 0.016 0.900 0.056
#> SRR949103 4 0.3062 0.933 0.144 0.000 0.000 0.824 0.000 0.032
#> SRR949104 2 0.3910 0.132 0.000 0.660 0.000 0.004 0.008 0.328
#> SRR949105 3 0.4499 0.833 0.000 0.004 0.712 0.076 0.004 0.204
#> SRR949106 3 0.4499 0.833 0.000 0.004 0.712 0.076 0.004 0.204
#> SRR949107 3 0.4499 0.833 0.000 0.004 0.712 0.076 0.004 0.204
#> SRR949108 1 0.3261 0.719 0.780 0.000 0.000 0.204 0.000 0.016
#> SRR949109 4 0.2178 0.932 0.132 0.000 0.000 0.868 0.000 0.000
#> SRR949110 4 0.3062 0.933 0.144 0.000 0.000 0.824 0.000 0.032
#> SRR949111 4 0.2431 0.930 0.132 0.000 0.000 0.860 0.000 0.008
#> SRR949112 1 0.2330 0.812 0.908 0.000 0.004 0.024 0.024 0.040
#> SRR949113 2 0.5197 -0.602 0.000 0.484 0.000 0.004 0.076 0.436
#> SRR949114 3 0.4304 0.855 0.004 0.000 0.772 0.092 0.024 0.108
#> SRR949115 3 0.4304 0.855 0.004 0.000 0.772 0.092 0.024 0.108
#> SRR949116 3 0.4304 0.855 0.004 0.000 0.772 0.092 0.024 0.108
#> SRR949117 3 0.1442 0.838 0.004 0.000 0.944 0.012 0.000 0.040
#> SRR949118 3 0.0260 0.849 0.000 0.000 0.992 0.000 0.000 0.008
#> SRR949119 1 0.2786 0.811 0.860 0.000 0.000 0.084 0.000 0.056
#> SRR949120 1 0.2786 0.811 0.860 0.000 0.000 0.084 0.000 0.056
#> SRR949121 1 0.1546 0.830 0.944 0.000 0.000 0.016 0.020 0.020
#> SRR949122 1 0.1787 0.826 0.932 0.000 0.000 0.016 0.020 0.032
#> SRR949123 2 0.0260 0.781 0.000 0.992 0.000 0.000 0.008 0.000
#> SRR949124 2 0.0260 0.781 0.000 0.992 0.000 0.000 0.008 0.000
#> SRR949125 4 0.3551 0.893 0.148 0.000 0.000 0.792 0.000 0.060
#> SRR949126 4 0.3551 0.893 0.148 0.000 0.000 0.792 0.000 0.060
#> SRR949127 6 0.5663 1.000 0.008 0.332 0.000 0.000 0.136 0.524
#> SRR949128 6 0.5663 1.000 0.008 0.332 0.000 0.000 0.136 0.524
#> SRR949129 6 0.5663 1.000 0.008 0.332 0.000 0.000 0.136 0.524
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)
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 16816 rows and 54 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 0.963 0.986 0.4968 0.508 0.508
#> 3 3 1.000 0.989 0.994 0.3105 0.815 0.644
#> 4 4 0.856 0.874 0.928 0.1185 0.912 0.751
#> 5 5 0.843 0.889 0.883 0.0948 0.877 0.577
#> 6 6 0.847 0.790 0.861 0.0363 0.977 0.881
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
#> SRR949076 2 0.000 1.0000 0.000 1.000
#> SRR949078 2 0.000 1.0000 0.000 1.000
#> SRR949077 2 0.000 1.0000 0.000 1.000
#> SRR949079 1 0.000 0.9756 1.000 0.000
#> SRR949080 1 0.000 0.9756 1.000 0.000
#> SRR949081 2 0.000 1.0000 0.000 1.000
#> SRR949082 2 0.000 1.0000 0.000 1.000
#> SRR949083 2 0.000 1.0000 0.000 1.000
#> SRR949084 1 0.000 0.9756 1.000 0.000
#> SRR949085 2 0.000 1.0000 0.000 1.000
#> SRR949087 2 0.000 1.0000 0.000 1.000
#> SRR949088 2 0.000 1.0000 0.000 1.000
#> SRR949086 2 0.000 1.0000 0.000 1.000
#> SRR949089 2 0.000 1.0000 0.000 1.000
#> SRR949090 1 0.000 0.9756 1.000 0.000
#> SRR949092 1 0.000 0.9756 1.000 0.000
#> SRR949093 1 0.000 0.9756 1.000 0.000
#> SRR949091 1 0.000 0.9756 1.000 0.000
#> SRR949095 2 0.000 1.0000 0.000 1.000
#> SRR949094 1 0.000 0.9756 1.000 0.000
#> SRR949096 1 0.000 0.9756 1.000 0.000
#> SRR949097 1 0.000 0.9756 1.000 0.000
#> SRR949098 2 0.000 1.0000 0.000 1.000
#> SRR949099 1 0.000 0.9756 1.000 0.000
#> SRR949101 2 0.000 1.0000 0.000 1.000
#> SRR949100 1 0.000 0.9756 1.000 0.000
#> SRR949102 2 0.000 1.0000 0.000 1.000
#> SRR949103 1 0.000 0.9756 1.000 0.000
#> SRR949104 2 0.000 1.0000 0.000 1.000
#> SRR949105 1 0.000 0.9756 1.000 0.000
#> SRR949106 1 0.000 0.9756 1.000 0.000
#> SRR949107 1 0.000 0.9756 1.000 0.000
#> SRR949108 1 0.000 0.9756 1.000 0.000
#> SRR949109 1 0.000 0.9756 1.000 0.000
#> SRR949110 1 0.000 0.9756 1.000 0.000
#> SRR949111 1 0.000 0.9756 1.000 0.000
#> SRR949112 1 0.000 0.9756 1.000 0.000
#> SRR949113 2 0.000 1.0000 0.000 1.000
#> SRR949114 1 0.000 0.9756 1.000 0.000
#> SRR949115 1 0.000 0.9756 1.000 0.000
#> SRR949116 1 0.000 0.9756 1.000 0.000
#> SRR949117 1 1.000 0.0718 0.512 0.488
#> SRR949118 1 0.827 0.6472 0.740 0.260
#> SRR949119 1 0.000 0.9756 1.000 0.000
#> SRR949120 1 0.000 0.9756 1.000 0.000
#> SRR949121 1 0.000 0.9756 1.000 0.000
#> SRR949122 1 0.000 0.9756 1.000 0.000
#> SRR949123 2 0.000 1.0000 0.000 1.000
#> SRR949124 2 0.000 1.0000 0.000 1.000
#> SRR949125 1 0.000 0.9756 1.000 0.000
#> SRR949126 1 0.000 0.9756 1.000 0.000
#> SRR949127 2 0.000 1.0000 0.000 1.000
#> SRR949128 2 0.000 1.0000 0.000 1.000
#> SRR949129 2 0.000 1.0000 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR949076 2 0.0000 1.000 0.000 1.000 0.000
#> SRR949078 2 0.0000 1.000 0.000 1.000 0.000
#> SRR949077 2 0.0424 0.991 0.008 0.992 0.000
#> SRR949079 1 0.0000 0.996 1.000 0.000 0.000
#> SRR949080 1 0.0000 0.996 1.000 0.000 0.000
#> SRR949081 2 0.0000 1.000 0.000 1.000 0.000
#> SRR949082 2 0.0000 1.000 0.000 1.000 0.000
#> SRR949083 2 0.0000 1.000 0.000 1.000 0.000
#> SRR949084 1 0.0000 0.996 1.000 0.000 0.000
#> SRR949085 2 0.0000 1.000 0.000 1.000 0.000
#> SRR949087 2 0.0000 1.000 0.000 1.000 0.000
#> SRR949088 2 0.0000 1.000 0.000 1.000 0.000
#> SRR949086 3 0.0424 0.971 0.000 0.008 0.992
#> SRR949089 2 0.0000 1.000 0.000 1.000 0.000
#> SRR949090 1 0.0424 0.995 0.992 0.000 0.008
#> SRR949092 1 0.0000 0.996 1.000 0.000 0.000
#> SRR949093 1 0.0000 0.996 1.000 0.000 0.000
#> SRR949091 3 0.0000 0.978 0.000 0.000 1.000
#> SRR949095 2 0.0000 1.000 0.000 1.000 0.000
#> SRR949094 1 0.0000 0.996 1.000 0.000 0.000
#> SRR949096 1 0.0000 0.996 1.000 0.000 0.000
#> SRR949097 1 0.0424 0.995 0.992 0.000 0.008
#> SRR949098 2 0.0000 1.000 0.000 1.000 0.000
#> SRR949099 1 0.0424 0.995 0.992 0.000 0.008
#> SRR949101 3 0.4654 0.739 0.000 0.208 0.792
#> SRR949100 1 0.0424 0.995 0.992 0.000 0.008
#> SRR949102 2 0.0000 1.000 0.000 1.000 0.000
#> SRR949103 1 0.0424 0.995 0.992 0.000 0.008
#> SRR949104 2 0.0000 1.000 0.000 1.000 0.000
#> SRR949105 3 0.0000 0.978 0.000 0.000 1.000
#> SRR949106 3 0.0000 0.978 0.000 0.000 1.000
#> SRR949107 3 0.0000 0.978 0.000 0.000 1.000
#> SRR949108 1 0.0000 0.996 1.000 0.000 0.000
#> SRR949109 1 0.0424 0.995 0.992 0.000 0.008
#> SRR949110 1 0.0424 0.995 0.992 0.000 0.008
#> SRR949111 1 0.0424 0.995 0.992 0.000 0.008
#> SRR949112 1 0.0000 0.996 1.000 0.000 0.000
#> SRR949113 2 0.0000 1.000 0.000 1.000 0.000
#> SRR949114 3 0.0000 0.978 0.000 0.000 1.000
#> SRR949115 3 0.0000 0.978 0.000 0.000 1.000
#> SRR949116 3 0.0000 0.978 0.000 0.000 1.000
#> SRR949117 3 0.0000 0.978 0.000 0.000 1.000
#> SRR949118 3 0.0000 0.978 0.000 0.000 1.000
#> SRR949119 1 0.0000 0.996 1.000 0.000 0.000
#> SRR949120 1 0.0000 0.996 1.000 0.000 0.000
#> SRR949121 1 0.0000 0.996 1.000 0.000 0.000
#> SRR949122 1 0.0000 0.996 1.000 0.000 0.000
#> SRR949123 2 0.0000 1.000 0.000 1.000 0.000
#> SRR949124 2 0.0000 1.000 0.000 1.000 0.000
#> SRR949125 1 0.0424 0.995 0.992 0.000 0.008
#> SRR949126 1 0.0424 0.995 0.992 0.000 0.008
#> SRR949127 2 0.0000 1.000 0.000 1.000 0.000
#> SRR949128 2 0.0000 1.000 0.000 1.000 0.000
#> SRR949129 2 0.0000 1.000 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR949076 4 0.2973 0.791 0.000 0.144 0.0 0.856
#> SRR949078 2 0.4679 0.335 0.000 0.648 0.0 0.352
#> SRR949077 4 0.0000 0.740 0.000 0.000 0.0 1.000
#> SRR949079 1 0.2814 0.923 0.868 0.000 0.0 0.132
#> SRR949080 1 0.2814 0.923 0.868 0.000 0.0 0.132
#> SRR949081 4 0.2973 0.791 0.000 0.144 0.0 0.856
#> SRR949082 2 0.4697 0.323 0.000 0.644 0.0 0.356
#> SRR949083 4 0.1940 0.794 0.000 0.076 0.0 0.924
#> SRR949084 4 0.4477 0.343 0.312 0.000 0.0 0.688
#> SRR949085 2 0.0336 0.912 0.000 0.992 0.0 0.008
#> SRR949087 4 0.4222 0.706 0.000 0.272 0.0 0.728
#> SRR949088 4 0.4222 0.706 0.000 0.272 0.0 0.728
#> SRR949086 3 0.0000 0.981 0.000 0.000 1.0 0.000
#> SRR949089 2 0.0336 0.912 0.000 0.992 0.0 0.008
#> SRR949090 1 0.0000 0.941 1.000 0.000 0.0 0.000
#> SRR949092 1 0.2921 0.920 0.860 0.000 0.0 0.140
#> SRR949093 1 0.2921 0.920 0.860 0.000 0.0 0.140
#> SRR949091 3 0.0000 0.981 0.000 0.000 1.0 0.000
#> SRR949095 4 0.1940 0.794 0.000 0.076 0.0 0.924
#> SRR949094 1 0.2814 0.923 0.868 0.000 0.0 0.132
#> SRR949096 1 0.2921 0.920 0.860 0.000 0.0 0.140
#> SRR949097 1 0.0000 0.941 1.000 0.000 0.0 0.000
#> SRR949098 2 0.0336 0.912 0.000 0.992 0.0 0.008
#> SRR949099 1 0.0000 0.941 1.000 0.000 0.0 0.000
#> SRR949101 3 0.4605 0.778 0.000 0.092 0.8 0.108
#> SRR949100 1 0.0000 0.941 1.000 0.000 0.0 0.000
#> SRR949102 4 0.4406 0.627 0.000 0.300 0.0 0.700
#> SRR949103 1 0.0000 0.941 1.000 0.000 0.0 0.000
#> SRR949104 2 0.0000 0.912 0.000 1.000 0.0 0.000
#> SRR949105 3 0.0000 0.981 0.000 0.000 1.0 0.000
#> SRR949106 3 0.0000 0.981 0.000 0.000 1.0 0.000
#> SRR949107 3 0.0000 0.981 0.000 0.000 1.0 0.000
#> SRR949108 1 0.1211 0.942 0.960 0.000 0.0 0.040
#> SRR949109 1 0.0000 0.941 1.000 0.000 0.0 0.000
#> SRR949110 1 0.0000 0.941 1.000 0.000 0.0 0.000
#> SRR949111 1 0.0000 0.941 1.000 0.000 0.0 0.000
#> SRR949112 1 0.1637 0.941 0.940 0.000 0.0 0.060
#> SRR949113 2 0.0000 0.912 0.000 1.000 0.0 0.000
#> SRR949114 3 0.0000 0.981 0.000 0.000 1.0 0.000
#> SRR949115 3 0.0000 0.981 0.000 0.000 1.0 0.000
#> SRR949116 3 0.0000 0.981 0.000 0.000 1.0 0.000
#> SRR949117 3 0.0000 0.981 0.000 0.000 1.0 0.000
#> SRR949118 3 0.0000 0.981 0.000 0.000 1.0 0.000
#> SRR949119 1 0.2921 0.920 0.860 0.000 0.0 0.140
#> SRR949120 1 0.2921 0.920 0.860 0.000 0.0 0.140
#> SRR949121 1 0.1940 0.938 0.924 0.000 0.0 0.076
#> SRR949122 1 0.1637 0.941 0.940 0.000 0.0 0.060
#> SRR949123 2 0.0336 0.912 0.000 0.992 0.0 0.008
#> SRR949124 2 0.0336 0.912 0.000 0.992 0.0 0.008
#> SRR949125 1 0.0000 0.941 1.000 0.000 0.0 0.000
#> SRR949126 1 0.0000 0.941 1.000 0.000 0.0 0.000
#> SRR949127 2 0.0000 0.912 0.000 1.000 0.0 0.000
#> SRR949128 2 0.0000 0.912 0.000 1.000 0.0 0.000
#> SRR949129 2 0.0000 0.912 0.000 1.000 0.0 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR949076 5 0.0703 0.844 0.000 0.024 0.000 0.000 0.976
#> SRR949078 5 0.4273 0.384 0.000 0.448 0.000 0.000 0.552
#> SRR949077 5 0.0609 0.839 0.020 0.000 0.000 0.000 0.980
#> SRR949079 1 0.4262 0.631 0.560 0.000 0.000 0.440 0.000
#> SRR949080 1 0.4262 0.631 0.560 0.000 0.000 0.440 0.000
#> SRR949081 5 0.1270 0.842 0.000 0.052 0.000 0.000 0.948
#> SRR949082 5 0.4242 0.432 0.000 0.428 0.000 0.000 0.572
#> SRR949083 5 0.0693 0.842 0.012 0.008 0.000 0.000 0.980
#> SRR949084 1 0.3670 0.818 0.820 0.000 0.000 0.112 0.068
#> SRR949085 2 0.0510 0.975 0.000 0.984 0.000 0.000 0.016
#> SRR949087 5 0.4294 0.784 0.152 0.080 0.000 0.000 0.768
#> SRR949088 5 0.4294 0.784 0.152 0.080 0.000 0.000 0.768
#> SRR949086 3 0.1952 0.927 0.084 0.000 0.912 0.000 0.004
#> SRR949089 2 0.0510 0.975 0.000 0.984 0.000 0.000 0.016
#> SRR949090 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> SRR949092 1 0.2929 0.878 0.820 0.000 0.000 0.180 0.000
#> SRR949093 1 0.2929 0.878 0.820 0.000 0.000 0.180 0.000
#> SRR949091 3 0.0000 0.966 0.000 0.000 1.000 0.000 0.000
#> SRR949095 5 0.1106 0.843 0.024 0.012 0.000 0.000 0.964
#> SRR949094 1 0.4268 0.624 0.556 0.000 0.000 0.444 0.000
#> SRR949096 1 0.3048 0.876 0.820 0.000 0.000 0.176 0.004
#> SRR949097 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> SRR949098 2 0.0510 0.975 0.000 0.984 0.000 0.000 0.016
#> SRR949099 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> SRR949101 3 0.4203 0.790 0.016 0.132 0.796 0.000 0.056
#> SRR949100 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> SRR949102 5 0.2020 0.824 0.000 0.100 0.000 0.000 0.900
#> SRR949103 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> SRR949104 2 0.0000 0.974 0.000 1.000 0.000 0.000 0.000
#> SRR949105 3 0.0000 0.966 0.000 0.000 1.000 0.000 0.000
#> SRR949106 3 0.0000 0.966 0.000 0.000 1.000 0.000 0.000
#> SRR949107 3 0.0000 0.966 0.000 0.000 1.000 0.000 0.000
#> SRR949108 1 0.3857 0.811 0.688 0.000 0.000 0.312 0.000
#> SRR949109 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> SRR949110 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> SRR949111 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> SRR949112 1 0.3366 0.854 0.768 0.000 0.000 0.232 0.000
#> SRR949113 2 0.0000 0.974 0.000 1.000 0.000 0.000 0.000
#> SRR949114 3 0.0404 0.964 0.012 0.000 0.988 0.000 0.000
#> SRR949115 3 0.0404 0.964 0.012 0.000 0.988 0.000 0.000
#> SRR949116 3 0.0404 0.964 0.012 0.000 0.988 0.000 0.000
#> SRR949117 3 0.1357 0.948 0.048 0.000 0.948 0.000 0.004
#> SRR949118 3 0.0671 0.961 0.016 0.000 0.980 0.000 0.004
#> SRR949119 1 0.3003 0.880 0.812 0.000 0.000 0.188 0.000
#> SRR949120 1 0.3003 0.880 0.812 0.000 0.000 0.188 0.000
#> SRR949121 1 0.3039 0.878 0.808 0.000 0.000 0.192 0.000
#> SRR949122 1 0.3395 0.861 0.764 0.000 0.000 0.236 0.000
#> SRR949123 2 0.0510 0.975 0.000 0.984 0.000 0.000 0.016
#> SRR949124 2 0.0510 0.975 0.000 0.984 0.000 0.000 0.016
#> SRR949125 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> SRR949126 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> SRR949127 2 0.1211 0.955 0.024 0.960 0.000 0.000 0.016
#> SRR949128 2 0.1211 0.955 0.024 0.960 0.000 0.000 0.016
#> SRR949129 2 0.1211 0.955 0.024 0.960 0.000 0.000 0.016
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR949076 5 0.1686 0.6694 0.000 0.064 0.000 0.000 0.924 0.012
#> SRR949078 2 0.3862 -0.1859 0.000 0.524 0.000 0.000 0.476 0.000
#> SRR949077 5 0.0622 0.6833 0.008 0.000 0.000 0.000 0.980 0.012
#> SRR949079 1 0.3695 0.6551 0.712 0.000 0.000 0.272 0.000 0.016
#> SRR949080 1 0.3695 0.6551 0.712 0.000 0.000 0.272 0.000 0.016
#> SRR949081 5 0.0632 0.6847 0.000 0.024 0.000 0.000 0.976 0.000
#> SRR949082 5 0.3869 -0.0125 0.000 0.500 0.000 0.000 0.500 0.000
#> SRR949083 5 0.0260 0.6813 0.008 0.000 0.000 0.000 0.992 0.000
#> SRR949084 1 0.1151 0.7434 0.956 0.000 0.000 0.012 0.032 0.000
#> SRR949085 2 0.0363 0.8518 0.000 0.988 0.000 0.000 0.012 0.000
#> SRR949087 6 0.4902 1.0000 0.000 0.060 0.000 0.000 0.460 0.480
#> SRR949088 6 0.4902 1.0000 0.000 0.060 0.000 0.000 0.460 0.480
#> SRR949086 3 0.3602 0.8027 0.032 0.000 0.760 0.000 0.000 0.208
#> SRR949089 2 0.0363 0.8518 0.000 0.988 0.000 0.000 0.012 0.000
#> SRR949090 4 0.0146 0.9941 0.000 0.000 0.000 0.996 0.000 0.004
#> SRR949092 1 0.3892 0.7545 0.740 0.000 0.000 0.048 0.000 0.212
#> SRR949093 1 0.3892 0.7545 0.740 0.000 0.000 0.048 0.000 0.212
#> SRR949091 3 0.0937 0.8947 0.000 0.000 0.960 0.000 0.000 0.040
#> SRR949095 5 0.0717 0.6667 0.008 0.000 0.000 0.000 0.976 0.016
#> SRR949094 1 0.3674 0.6597 0.716 0.000 0.000 0.268 0.000 0.016
#> SRR949096 1 0.1152 0.7648 0.952 0.000 0.000 0.044 0.004 0.000
#> SRR949097 4 0.0000 0.9960 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949098 2 0.0363 0.8518 0.000 0.988 0.000 0.000 0.012 0.000
#> SRR949099 4 0.0000 0.9960 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949101 3 0.5216 0.7247 0.028 0.136 0.708 0.000 0.020 0.108
#> SRR949100 4 0.0000 0.9960 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949102 5 0.2572 0.5918 0.000 0.136 0.000 0.000 0.852 0.012
#> SRR949103 4 0.0000 0.9960 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949104 2 0.1471 0.8402 0.004 0.932 0.000 0.000 0.000 0.064
#> SRR949105 3 0.0146 0.8978 0.000 0.000 0.996 0.000 0.000 0.004
#> SRR949106 3 0.0146 0.8978 0.000 0.000 0.996 0.000 0.000 0.004
#> SRR949107 3 0.0146 0.8978 0.000 0.000 0.996 0.000 0.000 0.004
#> SRR949108 1 0.5521 0.5208 0.488 0.000 0.000 0.376 0.000 0.136
#> SRR949109 4 0.0000 0.9960 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949110 4 0.0000 0.9960 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949111 4 0.0000 0.9960 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949112 1 0.5143 0.7063 0.612 0.000 0.000 0.140 0.000 0.248
#> SRR949113 2 0.1471 0.8402 0.004 0.932 0.000 0.000 0.000 0.064
#> SRR949114 3 0.1753 0.8749 0.004 0.000 0.912 0.000 0.000 0.084
#> SRR949115 3 0.1753 0.8749 0.004 0.000 0.912 0.000 0.000 0.084
#> SRR949116 3 0.1753 0.8749 0.004 0.000 0.912 0.000 0.000 0.084
#> SRR949117 3 0.2983 0.8517 0.032 0.000 0.832 0.000 0.000 0.136
#> SRR949118 3 0.2633 0.8656 0.032 0.000 0.864 0.000 0.000 0.104
#> SRR949119 1 0.1444 0.7717 0.928 0.000 0.000 0.072 0.000 0.000
#> SRR949120 1 0.1444 0.7717 0.928 0.000 0.000 0.072 0.000 0.000
#> SRR949121 1 0.4167 0.7452 0.708 0.000 0.000 0.056 0.000 0.236
#> SRR949122 1 0.5146 0.7078 0.616 0.000 0.000 0.148 0.000 0.236
#> SRR949123 2 0.0363 0.8518 0.000 0.988 0.000 0.000 0.012 0.000
#> SRR949124 2 0.0363 0.8518 0.000 0.988 0.000 0.000 0.012 0.000
#> SRR949125 4 0.0458 0.9863 0.000 0.000 0.000 0.984 0.000 0.016
#> SRR949126 4 0.0458 0.9863 0.000 0.000 0.000 0.984 0.000 0.016
#> SRR949127 2 0.2902 0.7770 0.004 0.800 0.000 0.000 0.000 0.196
#> SRR949128 2 0.2902 0.7770 0.004 0.800 0.000 0.000 0.000 0.196
#> SRR949129 2 0.2902 0.7770 0.004 0.800 0.000 0.000 0.000 0.196
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
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)
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 16816 rows and 54 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 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 0.779 0.826 0.937 0.3633 0.628 0.628
#> 3 3 0.456 0.523 0.753 0.7496 0.686 0.507
#> 4 4 0.766 0.848 0.873 0.0755 0.695 0.385
#> 5 5 0.824 0.798 0.916 0.1509 0.817 0.510
#> 6 6 0.859 0.793 0.911 0.0214 0.958 0.814
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
#> SRR949076 1 0.9661 0.2064 0.608 0.392
#> SRR949078 2 0.0000 0.8387 0.000 1.000
#> SRR949077 1 0.0000 0.9485 1.000 0.000
#> SRR949079 1 0.0000 0.9485 1.000 0.000
#> SRR949080 1 0.0000 0.9485 1.000 0.000
#> SRR949081 2 0.8955 0.5479 0.312 0.688
#> SRR949082 2 0.0000 0.8387 0.000 1.000
#> SRR949083 1 0.8555 0.5184 0.720 0.280
#> SRR949084 1 0.0000 0.9485 1.000 0.000
#> SRR949085 2 0.0000 0.8387 0.000 1.000
#> SRR949087 1 0.1184 0.9343 0.984 0.016
#> SRR949088 1 0.1414 0.9304 0.980 0.020
#> SRR949086 1 0.0000 0.9485 1.000 0.000
#> SRR949089 2 0.0000 0.8387 0.000 1.000
#> SRR949090 1 0.0000 0.9485 1.000 0.000
#> SRR949092 1 0.0000 0.9485 1.000 0.000
#> SRR949093 1 0.0000 0.9485 1.000 0.000
#> SRR949091 1 0.0000 0.9485 1.000 0.000
#> SRR949095 1 0.4690 0.8335 0.900 0.100
#> SRR949094 1 0.0000 0.9485 1.000 0.000
#> SRR949096 1 0.0000 0.9485 1.000 0.000
#> SRR949097 1 0.0000 0.9485 1.000 0.000
#> SRR949098 2 0.0000 0.8387 0.000 1.000
#> SRR949099 1 0.0000 0.9485 1.000 0.000
#> SRR949101 1 0.9850 0.0816 0.572 0.428
#> SRR949100 1 0.0938 0.9382 0.988 0.012
#> SRR949102 1 0.9850 0.0816 0.572 0.428
#> SRR949103 1 0.0000 0.9485 1.000 0.000
#> SRR949104 2 0.0000 0.8387 0.000 1.000
#> SRR949105 1 0.0000 0.9485 1.000 0.000
#> SRR949106 1 0.0000 0.9485 1.000 0.000
#> SRR949107 1 0.0000 0.9485 1.000 0.000
#> SRR949108 1 0.0000 0.9485 1.000 0.000
#> SRR949109 1 0.0000 0.9485 1.000 0.000
#> SRR949110 1 0.0000 0.9485 1.000 0.000
#> SRR949111 1 0.0000 0.9485 1.000 0.000
#> SRR949112 1 0.0000 0.9485 1.000 0.000
#> SRR949113 2 0.0000 0.8387 0.000 1.000
#> SRR949114 1 0.0000 0.9485 1.000 0.000
#> SRR949115 1 0.0000 0.9485 1.000 0.000
#> SRR949116 1 0.0000 0.9485 1.000 0.000
#> SRR949117 1 0.0000 0.9485 1.000 0.000
#> SRR949118 1 0.0000 0.9485 1.000 0.000
#> SRR949119 1 0.0000 0.9485 1.000 0.000
#> SRR949120 1 0.0000 0.9485 1.000 0.000
#> SRR949121 1 0.0000 0.9485 1.000 0.000
#> SRR949122 1 0.0000 0.9485 1.000 0.000
#> SRR949123 2 0.0000 0.8387 0.000 1.000
#> SRR949124 2 0.0000 0.8387 0.000 1.000
#> SRR949125 1 0.0000 0.9485 1.000 0.000
#> SRR949126 1 0.0000 0.9485 1.000 0.000
#> SRR949127 2 0.9977 0.2237 0.472 0.528
#> SRR949128 2 0.9977 0.2237 0.472 0.528
#> SRR949129 2 0.9977 0.2237 0.472 0.528
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR949076 1 0.304 0.6339 0.896 0.104 0.000
#> SRR949078 2 0.000 0.8522 0.000 1.000 0.000
#> SRR949077 1 0.000 0.7033 1.000 0.000 0.000
#> SRR949079 3 0.630 0.5546 0.472 0.000 0.528
#> SRR949080 3 0.630 0.5546 0.472 0.000 0.528
#> SRR949081 2 0.348 0.8029 0.128 0.872 0.000
#> SRR949082 2 0.327 0.8094 0.116 0.884 0.000
#> SRR949083 1 0.304 0.6339 0.896 0.104 0.000
#> SRR949084 1 0.000 0.7033 1.000 0.000 0.000
#> SRR949085 2 0.000 0.8522 0.000 1.000 0.000
#> SRR949087 1 0.429 0.5870 0.820 0.180 0.000
#> SRR949088 1 0.470 0.5575 0.788 0.212 0.000
#> SRR949086 1 0.625 0.2924 0.556 0.000 0.444
#> SRR949089 2 0.000 0.8522 0.000 1.000 0.000
#> SRR949090 3 0.630 0.5546 0.472 0.000 0.528
#> SRR949092 1 0.000 0.7033 1.000 0.000 0.000
#> SRR949093 1 0.000 0.7033 1.000 0.000 0.000
#> SRR949091 3 0.510 0.0803 0.248 0.000 0.752
#> SRR949095 1 0.000 0.7033 1.000 0.000 0.000
#> SRR949094 3 0.630 0.5546 0.472 0.000 0.528
#> SRR949096 1 0.000 0.7033 1.000 0.000 0.000
#> SRR949097 3 0.630 0.5546 0.472 0.000 0.528
#> SRR949098 2 0.000 0.8522 0.000 1.000 0.000
#> SRR949099 3 0.630 0.5546 0.472 0.000 0.528
#> SRR949101 1 0.630 0.2685 0.528 0.000 0.472
#> SRR949100 1 0.757 0.4523 0.684 0.200 0.116
#> SRR949102 2 0.576 0.6147 0.328 0.672 0.000
#> SRR949103 3 0.630 0.5546 0.472 0.000 0.528
#> SRR949104 2 0.000 0.8522 0.000 1.000 0.000
#> SRR949105 3 0.000 0.2868 0.000 0.000 1.000
#> SRR949106 3 0.455 0.1445 0.200 0.000 0.800
#> SRR949107 3 0.406 0.1791 0.164 0.000 0.836
#> SRR949108 3 0.630 0.5429 0.480 0.000 0.520
#> SRR949109 3 0.630 0.5546 0.472 0.000 0.528
#> SRR949110 3 0.630 0.5546 0.472 0.000 0.528
#> SRR949111 3 0.630 0.5546 0.472 0.000 0.528
#> SRR949112 1 0.000 0.7033 1.000 0.000 0.000
#> SRR949113 2 0.000 0.8522 0.000 1.000 0.000
#> SRR949114 3 0.615 -0.1524 0.408 0.000 0.592
#> SRR949115 3 0.615 -0.1524 0.408 0.000 0.592
#> SRR949116 3 0.615 -0.1524 0.408 0.000 0.592
#> SRR949117 1 0.630 0.2685 0.528 0.000 0.472
#> SRR949118 3 0.617 -0.1593 0.412 0.000 0.588
#> SRR949119 1 0.604 -0.2884 0.620 0.000 0.380
#> SRR949120 3 0.631 0.5301 0.488 0.000 0.512
#> SRR949121 1 0.000 0.7033 1.000 0.000 0.000
#> SRR949122 1 0.000 0.7033 1.000 0.000 0.000
#> SRR949123 2 0.000 0.8522 0.000 1.000 0.000
#> SRR949124 2 0.000 0.8522 0.000 1.000 0.000
#> SRR949125 3 0.630 0.5546 0.472 0.000 0.528
#> SRR949126 3 0.630 0.5546 0.472 0.000 0.528
#> SRR949127 2 0.608 0.5237 0.388 0.612 0.000
#> SRR949128 2 0.610 0.5161 0.392 0.608 0.000
#> SRR949129 2 0.576 0.6147 0.328 0.672 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR949076 1 0.5327 0.760 0.720 0.220 0.000 0.060
#> SRR949078 2 0.3726 0.765 0.000 0.788 0.000 0.212
#> SRR949077 1 0.5486 0.819 0.720 0.080 0.000 0.200
#> SRR949079 1 0.0188 0.832 0.996 0.000 0.000 0.004
#> SRR949080 1 0.0188 0.832 0.996 0.000 0.000 0.004
#> SRR949081 2 0.2814 0.833 0.000 0.868 0.000 0.132
#> SRR949082 2 0.3356 0.814 0.000 0.824 0.000 0.176
#> SRR949083 1 0.5647 0.813 0.720 0.116 0.000 0.164
#> SRR949084 1 0.5486 0.819 0.720 0.080 0.000 0.200
#> SRR949085 4 0.3610 1.000 0.000 0.200 0.000 0.800
#> SRR949087 1 0.7535 0.500 0.464 0.336 0.000 0.200
#> SRR949088 1 0.7586 0.440 0.436 0.364 0.000 0.200
#> SRR949086 3 0.3374 0.867 0.028 0.080 0.880 0.012
#> SRR949089 4 0.3610 1.000 0.000 0.200 0.000 0.800
#> SRR949090 1 0.0000 0.832 1.000 0.000 0.000 0.000
#> SRR949092 1 0.5288 0.823 0.732 0.068 0.000 0.200
#> SRR949093 1 0.5356 0.822 0.728 0.072 0.000 0.200
#> SRR949091 3 0.0000 0.961 0.000 0.000 1.000 0.000
#> SRR949095 1 0.5727 0.811 0.704 0.096 0.000 0.200
#> SRR949094 1 0.0000 0.832 1.000 0.000 0.000 0.000
#> SRR949096 1 0.5073 0.826 0.744 0.056 0.000 0.200
#> SRR949097 1 0.0000 0.832 1.000 0.000 0.000 0.000
#> SRR949098 4 0.3610 1.000 0.000 0.200 0.000 0.800
#> SRR949099 1 0.0000 0.832 1.000 0.000 0.000 0.000
#> SRR949101 3 0.2101 0.923 0.000 0.060 0.928 0.012
#> SRR949100 1 0.7346 0.606 0.520 0.280 0.000 0.200
#> SRR949102 2 0.2814 0.833 0.000 0.868 0.000 0.132
#> SRR949103 1 0.0000 0.832 1.000 0.000 0.000 0.000
#> SRR949104 2 0.2011 0.830 0.000 0.920 0.000 0.080
#> SRR949105 3 0.0000 0.961 0.000 0.000 1.000 0.000
#> SRR949106 3 0.0000 0.961 0.000 0.000 1.000 0.000
#> SRR949107 3 0.0000 0.961 0.000 0.000 1.000 0.000
#> SRR949108 1 0.0000 0.832 1.000 0.000 0.000 0.000
#> SRR949109 1 0.0000 0.832 1.000 0.000 0.000 0.000
#> SRR949110 1 0.0000 0.832 1.000 0.000 0.000 0.000
#> SRR949111 1 0.0000 0.832 1.000 0.000 0.000 0.000
#> SRR949112 1 0.5486 0.819 0.720 0.080 0.000 0.200
#> SRR949113 2 0.2011 0.830 0.000 0.920 0.000 0.080
#> SRR949114 3 0.0469 0.961 0.000 0.000 0.988 0.012
#> SRR949115 3 0.0469 0.961 0.000 0.000 0.988 0.012
#> SRR949116 3 0.0469 0.961 0.000 0.000 0.988 0.012
#> SRR949117 3 0.2706 0.890 0.000 0.080 0.900 0.020
#> SRR949118 3 0.0000 0.961 0.000 0.000 1.000 0.000
#> SRR949119 1 0.3486 0.833 0.812 0.000 0.000 0.188
#> SRR949120 1 0.3486 0.833 0.812 0.000 0.000 0.188
#> SRR949121 1 0.5486 0.819 0.720 0.080 0.000 0.200
#> SRR949122 1 0.5486 0.819 0.720 0.080 0.000 0.200
#> SRR949123 4 0.3610 1.000 0.000 0.200 0.000 0.800
#> SRR949124 4 0.3610 1.000 0.000 0.200 0.000 0.800
#> SRR949125 1 0.0000 0.832 1.000 0.000 0.000 0.000
#> SRR949126 1 0.0000 0.832 1.000 0.000 0.000 0.000
#> SRR949127 2 0.0000 0.853 0.000 1.000 0.000 0.000
#> SRR949128 2 0.0000 0.853 0.000 1.000 0.000 0.000
#> SRR949129 2 0.0000 0.853 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR949076 1 0.0404 0.8623 0.988 0.00 0.000 0.000 0.012
#> SRR949078 5 0.2280 0.7891 0.000 0.12 0.000 0.000 0.880
#> SRR949077 1 0.0000 0.8704 1.000 0.00 0.000 0.000 0.000
#> SRR949079 1 0.4161 0.5036 0.608 0.00 0.000 0.392 0.000
#> SRR949080 1 0.4150 0.5101 0.612 0.00 0.000 0.388 0.000
#> SRR949081 5 0.2280 0.7891 0.000 0.12 0.000 0.000 0.880
#> SRR949082 5 0.2280 0.7891 0.000 0.12 0.000 0.000 0.880
#> SRR949083 1 0.0000 0.8704 1.000 0.00 0.000 0.000 0.000
#> SRR949084 1 0.0000 0.8704 1.000 0.00 0.000 0.000 0.000
#> SRR949085 2 0.0000 1.0000 0.000 1.00 0.000 0.000 0.000
#> SRR949087 5 0.4305 0.0638 0.488 0.00 0.000 0.000 0.512
#> SRR949088 5 0.4297 0.1202 0.472 0.00 0.000 0.000 0.528
#> SRR949086 3 0.1544 0.8786 0.068 0.00 0.932 0.000 0.000
#> SRR949089 2 0.0000 1.0000 0.000 1.00 0.000 0.000 0.000
#> SRR949090 4 0.0000 0.9003 0.000 0.00 0.000 1.000 0.000
#> SRR949092 1 0.0000 0.8704 1.000 0.00 0.000 0.000 0.000
#> SRR949093 1 0.0000 0.8704 1.000 0.00 0.000 0.000 0.000
#> SRR949091 3 0.0000 0.9253 0.000 0.00 1.000 0.000 0.000
#> SRR949095 1 0.2966 0.6809 0.816 0.00 0.000 0.000 0.184
#> SRR949094 1 0.4171 0.4966 0.604 0.00 0.000 0.396 0.000
#> SRR949096 1 0.0000 0.8704 1.000 0.00 0.000 0.000 0.000
#> SRR949097 4 0.0000 0.9003 0.000 0.00 0.000 1.000 0.000
#> SRR949098 2 0.0000 1.0000 0.000 1.00 0.000 0.000 0.000
#> SRR949099 4 0.0000 0.9003 0.000 0.00 0.000 1.000 0.000
#> SRR949101 3 0.2280 0.8200 0.000 0.00 0.880 0.000 0.120
#> SRR949100 4 0.4171 0.3551 0.396 0.00 0.000 0.604 0.000
#> SRR949102 5 0.2280 0.7891 0.000 0.12 0.000 0.000 0.880
#> SRR949103 4 0.0000 0.9003 0.000 0.00 0.000 1.000 0.000
#> SRR949104 5 0.0000 0.8136 0.000 0.00 0.000 0.000 1.000
#> SRR949105 3 0.0000 0.9253 0.000 0.00 1.000 0.000 0.000
#> SRR949106 3 0.0000 0.9253 0.000 0.00 1.000 0.000 0.000
#> SRR949107 3 0.0000 0.9253 0.000 0.00 1.000 0.000 0.000
#> SRR949108 1 0.4126 0.5219 0.620 0.00 0.000 0.380 0.000
#> SRR949109 4 0.0000 0.9003 0.000 0.00 0.000 1.000 0.000
#> SRR949110 4 0.0000 0.9003 0.000 0.00 0.000 1.000 0.000
#> SRR949111 4 0.0000 0.9003 0.000 0.00 0.000 1.000 0.000
#> SRR949112 1 0.0000 0.8704 1.000 0.00 0.000 0.000 0.000
#> SRR949113 5 0.0000 0.8136 0.000 0.00 0.000 0.000 1.000
#> SRR949114 4 0.4171 0.2385 0.000 0.00 0.396 0.604 0.000
#> SRR949115 3 0.3003 0.7719 0.000 0.00 0.812 0.188 0.000
#> SRR949116 3 0.2605 0.8214 0.000 0.00 0.852 0.148 0.000
#> SRR949117 3 0.0703 0.9146 0.024 0.00 0.976 0.000 0.000
#> SRR949118 3 0.0000 0.9253 0.000 0.00 1.000 0.000 0.000
#> SRR949119 1 0.0000 0.8704 1.000 0.00 0.000 0.000 0.000
#> SRR949120 1 0.0000 0.8704 1.000 0.00 0.000 0.000 0.000
#> SRR949121 1 0.0000 0.8704 1.000 0.00 0.000 0.000 0.000
#> SRR949122 1 0.0000 0.8704 1.000 0.00 0.000 0.000 0.000
#> SRR949123 2 0.0000 1.0000 0.000 1.00 0.000 0.000 0.000
#> SRR949124 2 0.0000 1.0000 0.000 1.00 0.000 0.000 0.000
#> SRR949125 4 0.0000 0.9003 0.000 0.00 0.000 1.000 0.000
#> SRR949126 4 0.0000 0.9003 0.000 0.00 0.000 1.000 0.000
#> SRR949127 5 0.0000 0.8136 0.000 0.00 0.000 0.000 1.000
#> SRR949128 5 0.0000 0.8136 0.000 0.00 0.000 0.000 1.000
#> SRR949129 5 0.0000 0.8136 0.000 0.00 0.000 0.000 1.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR949076 1 0.0993 0.83101 0.964 0.00 0.000 0.000 0.012 0.024
#> SRR949078 5 0.2048 0.77694 0.000 0.12 0.000 0.000 0.880 0.000
#> SRR949077 1 0.0000 0.84732 1.000 0.00 0.000 0.000 0.000 0.000
#> SRR949079 1 0.3747 0.48541 0.604 0.00 0.000 0.396 0.000 0.000
#> SRR949080 1 0.3737 0.49209 0.608 0.00 0.000 0.392 0.000 0.000
#> SRR949081 5 0.2662 0.77206 0.000 0.12 0.000 0.000 0.856 0.024
#> SRR949082 5 0.2048 0.77694 0.000 0.12 0.000 0.000 0.880 0.000
#> SRR949083 1 0.0632 0.83716 0.976 0.00 0.000 0.000 0.000 0.024
#> SRR949084 1 0.0000 0.84732 1.000 0.00 0.000 0.000 0.000 0.000
#> SRR949085 2 0.0000 1.00000 0.000 1.00 0.000 0.000 0.000 0.000
#> SRR949087 5 0.4408 0.00473 0.488 0.00 0.000 0.000 0.488 0.024
#> SRR949088 5 0.4405 0.06534 0.472 0.00 0.000 0.000 0.504 0.024
#> SRR949086 1 0.4671 0.27814 0.532 0.00 0.044 0.000 0.000 0.424
#> SRR949089 2 0.0000 1.00000 0.000 1.00 0.000 0.000 0.000 0.000
#> SRR949090 4 0.0000 0.93979 0.000 0.00 0.000 1.000 0.000 0.000
#> SRR949092 1 0.0000 0.84732 1.000 0.00 0.000 0.000 0.000 0.000
#> SRR949093 1 0.0000 0.84732 1.000 0.00 0.000 0.000 0.000 0.000
#> SRR949091 3 0.1267 0.85084 0.000 0.00 0.940 0.000 0.000 0.060
#> SRR949095 1 0.3098 0.68433 0.812 0.00 0.000 0.000 0.164 0.024
#> SRR949094 1 0.3756 0.47832 0.600 0.00 0.000 0.400 0.000 0.000
#> SRR949096 1 0.0000 0.84732 1.000 0.00 0.000 0.000 0.000 0.000
#> SRR949097 4 0.0000 0.93979 0.000 0.00 0.000 1.000 0.000 0.000
#> SRR949098 2 0.0000 1.00000 0.000 1.00 0.000 0.000 0.000 0.000
#> SRR949099 4 0.0000 0.93979 0.000 0.00 0.000 1.000 0.000 0.000
#> SRR949101 3 0.4066 0.37690 0.000 0.00 0.596 0.000 0.012 0.392
#> SRR949100 4 0.3756 0.33551 0.400 0.00 0.000 0.600 0.000 0.000
#> SRR949102 5 0.2662 0.77206 0.000 0.12 0.000 0.000 0.856 0.024
#> SRR949103 4 0.0000 0.93979 0.000 0.00 0.000 1.000 0.000 0.000
#> SRR949104 5 0.0000 0.80330 0.000 0.00 0.000 0.000 1.000 0.000
#> SRR949105 3 0.0000 0.87800 0.000 0.00 1.000 0.000 0.000 0.000
#> SRR949106 3 0.0000 0.87800 0.000 0.00 1.000 0.000 0.000 0.000
#> SRR949107 3 0.0000 0.87800 0.000 0.00 1.000 0.000 0.000 0.000
#> SRR949108 1 0.3717 0.50452 0.616 0.00 0.000 0.384 0.000 0.000
#> SRR949109 4 0.0000 0.93979 0.000 0.00 0.000 1.000 0.000 0.000
#> SRR949110 4 0.0000 0.93979 0.000 0.00 0.000 1.000 0.000 0.000
#> SRR949111 4 0.0000 0.93979 0.000 0.00 0.000 1.000 0.000 0.000
#> SRR949112 1 0.0000 0.84732 1.000 0.00 0.000 0.000 0.000 0.000
#> SRR949113 5 0.0000 0.80330 0.000 0.00 0.000 0.000 1.000 0.000
#> SRR949114 6 0.0632 0.99054 0.000 0.00 0.024 0.000 0.000 0.976
#> SRR949115 6 0.0632 0.99054 0.000 0.00 0.024 0.000 0.000 0.976
#> SRR949116 6 0.0632 0.99054 0.000 0.00 0.024 0.000 0.000 0.976
#> SRR949117 6 0.0000 0.96225 0.000 0.00 0.000 0.000 0.000 1.000
#> SRR949118 6 0.0632 0.99054 0.000 0.00 0.024 0.000 0.000 0.976
#> SRR949119 1 0.0000 0.84732 1.000 0.00 0.000 0.000 0.000 0.000
#> SRR949120 1 0.0000 0.84732 1.000 0.00 0.000 0.000 0.000 0.000
#> SRR949121 1 0.0000 0.84732 1.000 0.00 0.000 0.000 0.000 0.000
#> SRR949122 1 0.0000 0.84732 1.000 0.00 0.000 0.000 0.000 0.000
#> SRR949123 2 0.0000 1.00000 0.000 1.00 0.000 0.000 0.000 0.000
#> SRR949124 2 0.0000 1.00000 0.000 1.00 0.000 0.000 0.000 0.000
#> SRR949125 4 0.0000 0.93979 0.000 0.00 0.000 1.000 0.000 0.000
#> SRR949126 4 0.0000 0.93979 0.000 0.00 0.000 1.000 0.000 0.000
#> SRR949127 5 0.0000 0.80330 0.000 0.00 0.000 0.000 1.000 0.000
#> SRR949128 5 0.0000 0.80330 0.000 0.00 0.000 0.000 1.000 0.000
#> SRR949129 5 0.0000 0.80330 0.000 0.00 0.000 0.000 1.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 16816 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.923 0.910 0.944 0.2984 0.693 0.693
#> 3 3 0.780 0.811 0.906 1.0584 0.499 0.360
#> 4 4 0.623 0.705 0.805 0.1325 0.895 0.731
#> 5 5 0.744 0.667 0.840 0.1148 0.814 0.467
#> 6 6 0.876 0.841 0.929 0.0532 0.939 0.731
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
#> SRR949076 1 0.0000 0.952 1.000 0.000
#> SRR949078 1 0.2778 0.958 0.952 0.048
#> SRR949077 1 0.2778 0.958 0.952 0.048
#> SRR949079 2 0.0000 0.867 0.000 1.000
#> SRR949080 2 0.0000 0.867 0.000 1.000
#> SRR949081 1 0.2778 0.958 0.952 0.048
#> SRR949082 1 0.2778 0.958 0.952 0.048
#> SRR949083 1 0.2778 0.958 0.952 0.048
#> SRR949084 2 0.2236 0.856 0.036 0.964
#> SRR949085 1 0.0000 0.952 1.000 0.000
#> SRR949087 1 0.2778 0.958 0.952 0.048
#> SRR949088 1 0.2778 0.958 0.952 0.048
#> SRR949086 1 0.0000 0.952 1.000 0.000
#> SRR949089 1 0.0000 0.952 1.000 0.000
#> SRR949090 1 0.4022 0.944 0.920 0.080
#> SRR949092 2 0.0376 0.867 0.004 0.996
#> SRR949093 2 0.0376 0.867 0.004 0.996
#> SRR949091 1 0.0000 0.952 1.000 0.000
#> SRR949095 1 0.2948 0.956 0.948 0.052
#> SRR949094 1 0.6887 0.825 0.816 0.184
#> SRR949096 2 0.9608 0.419 0.384 0.616
#> SRR949097 1 0.4022 0.944 0.920 0.080
#> SRR949098 1 0.0000 0.952 1.000 0.000
#> SRR949099 1 0.4022 0.944 0.920 0.080
#> SRR949101 1 0.0000 0.952 1.000 0.000
#> SRR949100 1 0.3114 0.955 0.944 0.056
#> SRR949102 1 0.0000 0.952 1.000 0.000
#> SRR949103 1 0.4022 0.944 0.920 0.080
#> SRR949104 1 0.2778 0.958 0.952 0.048
#> SRR949105 1 0.0000 0.952 1.000 0.000
#> SRR949106 1 0.0000 0.952 1.000 0.000
#> SRR949107 1 0.0000 0.952 1.000 0.000
#> SRR949108 2 0.8499 0.632 0.276 0.724
#> SRR949109 1 0.4022 0.944 0.920 0.080
#> SRR949110 1 0.4022 0.944 0.920 0.080
#> SRR949111 1 0.4022 0.944 0.920 0.080
#> SRR949112 1 0.4022 0.944 0.920 0.080
#> SRR949113 1 0.2778 0.958 0.952 0.048
#> SRR949114 1 0.0000 0.952 1.000 0.000
#> SRR949115 1 0.0000 0.952 1.000 0.000
#> SRR949116 1 0.0000 0.952 1.000 0.000
#> SRR949117 1 0.0000 0.952 1.000 0.000
#> SRR949118 1 0.0000 0.952 1.000 0.000
#> SRR949119 2 0.0000 0.867 0.000 1.000
#> SRR949120 2 0.0000 0.867 0.000 1.000
#> SRR949121 2 0.9661 0.405 0.392 0.608
#> SRR949122 1 0.4022 0.944 0.920 0.080
#> SRR949123 1 0.0000 0.952 1.000 0.000
#> SRR949124 1 0.0000 0.952 1.000 0.000
#> SRR949125 1 0.5946 0.877 0.856 0.144
#> SRR949126 1 0.5946 0.877 0.856 0.144
#> SRR949127 1 0.2778 0.958 0.952 0.048
#> SRR949128 1 0.2778 0.958 0.952 0.048
#> SRR949129 1 0.2778 0.958 0.952 0.048
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR949076 2 0.7685 0.520 0.384 0.564 0.052
#> SRR949078 2 0.0000 0.715 0.000 1.000 0.000
#> SRR949077 2 0.6235 0.465 0.436 0.564 0.000
#> SRR949079 1 0.0000 0.999 1.000 0.000 0.000
#> SRR949080 1 0.0000 0.999 1.000 0.000 0.000
#> SRR949081 2 0.7451 0.509 0.396 0.564 0.040
#> SRR949082 2 0.0000 0.715 0.000 1.000 0.000
#> SRR949083 2 0.6235 0.465 0.436 0.564 0.000
#> SRR949084 1 0.0000 0.999 1.000 0.000 0.000
#> SRR949085 2 0.0000 0.715 0.000 1.000 0.000
#> SRR949087 2 0.6302 0.375 0.480 0.520 0.000
#> SRR949088 2 0.6302 0.375 0.480 0.520 0.000
#> SRR949086 2 0.6307 0.186 0.000 0.512 0.488
#> SRR949089 2 0.0000 0.715 0.000 1.000 0.000
#> SRR949090 1 0.0000 0.999 1.000 0.000 0.000
#> SRR949092 1 0.0000 0.999 1.000 0.000 0.000
#> SRR949093 1 0.0000 0.999 1.000 0.000 0.000
#> SRR949091 3 0.0000 1.000 0.000 0.000 1.000
#> SRR949095 2 0.6235 0.465 0.436 0.564 0.000
#> SRR949094 1 0.0000 0.999 1.000 0.000 0.000
#> SRR949096 1 0.0000 0.999 1.000 0.000 0.000
#> SRR949097 1 0.0000 0.999 1.000 0.000 0.000
#> SRR949098 2 0.0000 0.715 0.000 1.000 0.000
#> SRR949099 1 0.0000 0.999 1.000 0.000 0.000
#> SRR949101 2 0.6307 0.186 0.000 0.512 0.488
#> SRR949100 1 0.0424 0.990 0.992 0.008 0.000
#> SRR949102 2 0.7685 0.520 0.384 0.564 0.052
#> SRR949103 1 0.0000 0.999 1.000 0.000 0.000
#> SRR949104 2 0.0000 0.715 0.000 1.000 0.000
#> SRR949105 3 0.0000 1.000 0.000 0.000 1.000
#> SRR949106 3 0.0000 1.000 0.000 0.000 1.000
#> SRR949107 3 0.0000 1.000 0.000 0.000 1.000
#> SRR949108 1 0.0000 0.999 1.000 0.000 0.000
#> SRR949109 1 0.0000 0.999 1.000 0.000 0.000
#> SRR949110 1 0.0000 0.999 1.000 0.000 0.000
#> SRR949111 1 0.0000 0.999 1.000 0.000 0.000
#> SRR949112 1 0.0424 0.990 0.992 0.008 0.000
#> SRR949113 2 0.0000 0.715 0.000 1.000 0.000
#> SRR949114 3 0.0000 1.000 0.000 0.000 1.000
#> SRR949115 3 0.0000 1.000 0.000 0.000 1.000
#> SRR949116 3 0.0000 1.000 0.000 0.000 1.000
#> SRR949117 2 0.6308 0.175 0.000 0.508 0.492
#> SRR949118 3 0.0000 1.000 0.000 0.000 1.000
#> SRR949119 1 0.0000 0.999 1.000 0.000 0.000
#> SRR949120 1 0.0000 0.999 1.000 0.000 0.000
#> SRR949121 1 0.0000 0.999 1.000 0.000 0.000
#> SRR949122 1 0.0000 0.999 1.000 0.000 0.000
#> SRR949123 2 0.0000 0.715 0.000 1.000 0.000
#> SRR949124 2 0.0000 0.715 0.000 1.000 0.000
#> SRR949125 1 0.0000 0.999 1.000 0.000 0.000
#> SRR949126 1 0.0000 0.999 1.000 0.000 0.000
#> SRR949127 2 0.0000 0.715 0.000 1.000 0.000
#> SRR949128 2 0.0000 0.715 0.000 1.000 0.000
#> SRR949129 2 0.0000 0.715 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR949076 2 0.4331 0.761 0.000 0.712 0.000 0.288
#> SRR949078 2 0.3610 0.777 0.000 0.800 0.000 0.200
#> SRR949077 2 0.4988 0.756 0.020 0.692 0.000 0.288
#> SRR949079 1 0.0000 0.726 1.000 0.000 0.000 0.000
#> SRR949080 1 0.0000 0.726 1.000 0.000 0.000 0.000
#> SRR949081 2 0.4331 0.761 0.000 0.712 0.000 0.288
#> SRR949082 2 0.3610 0.777 0.000 0.800 0.000 0.200
#> SRR949083 2 0.4331 0.761 0.000 0.712 0.000 0.288
#> SRR949084 1 0.3810 0.518 0.804 0.188 0.000 0.008
#> SRR949085 2 0.1940 0.782 0.000 0.924 0.000 0.076
#> SRR949087 2 0.5643 0.308 0.428 0.548 0.000 0.024
#> SRR949088 2 0.5643 0.308 0.428 0.548 0.000 0.024
#> SRR949086 2 0.4972 0.368 0.000 0.544 0.456 0.000
#> SRR949089 2 0.1557 0.763 0.000 0.944 0.000 0.056
#> SRR949090 4 0.4855 1.000 0.400 0.000 0.000 0.600
#> SRR949092 1 0.0000 0.726 1.000 0.000 0.000 0.000
#> SRR949093 1 0.0000 0.726 1.000 0.000 0.000 0.000
#> SRR949091 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR949095 2 0.5157 0.535 0.284 0.688 0.000 0.028
#> SRR949094 1 0.2401 0.644 0.904 0.092 0.000 0.004
#> SRR949096 1 0.1545 0.701 0.952 0.040 0.000 0.008
#> SRR949097 4 0.4855 1.000 0.400 0.000 0.000 0.600
#> SRR949098 2 0.1557 0.763 0.000 0.944 0.000 0.056
#> SRR949099 4 0.4855 1.000 0.400 0.000 0.000 0.600
#> SRR949101 2 0.4972 0.368 0.000 0.544 0.456 0.000
#> SRR949100 2 0.5138 0.324 0.392 0.600 0.000 0.008
#> SRR949102 2 0.4331 0.761 0.000 0.712 0.000 0.288
#> SRR949103 4 0.4855 1.000 0.400 0.000 0.000 0.600
#> SRR949104 2 0.0817 0.773 0.000 0.976 0.000 0.024
#> SRR949105 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR949106 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR949107 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR949108 1 0.2973 0.512 0.856 0.000 0.000 0.144
#> SRR949109 4 0.4855 1.000 0.400 0.000 0.000 0.600
#> SRR949110 4 0.4855 1.000 0.400 0.000 0.000 0.600
#> SRR949111 4 0.4855 1.000 0.400 0.000 0.000 0.600
#> SRR949112 1 0.5288 -0.111 0.520 0.472 0.000 0.008
#> SRR949113 2 0.0817 0.773 0.000 0.976 0.000 0.024
#> SRR949114 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR949115 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR949116 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR949117 2 0.4981 0.352 0.000 0.536 0.464 0.000
#> SRR949118 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR949119 1 0.0000 0.726 1.000 0.000 0.000 0.000
#> SRR949120 1 0.0000 0.726 1.000 0.000 0.000 0.000
#> SRR949121 1 0.0188 0.725 0.996 0.004 0.000 0.000
#> SRR949122 1 0.3610 0.487 0.800 0.200 0.000 0.000
#> SRR949123 2 0.3569 0.778 0.000 0.804 0.000 0.196
#> SRR949124 2 0.1557 0.763 0.000 0.944 0.000 0.056
#> SRR949125 1 0.4643 -0.181 0.656 0.000 0.000 0.344
#> SRR949126 1 0.4643 -0.181 0.656 0.000 0.000 0.344
#> SRR949127 2 0.1557 0.768 0.000 0.944 0.000 0.056
#> SRR949128 2 0.1557 0.768 0.000 0.944 0.000 0.056
#> SRR949129 2 0.1557 0.768 0.000 0.944 0.000 0.056
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR949076 5 0.0000 0.694 0.000 0.000 0.000 0.000 1.000
#> SRR949078 5 0.4278 -0.339 0.000 0.452 0.000 0.000 0.548
#> SRR949077 5 0.0000 0.694 0.000 0.000 0.000 0.000 1.000
#> SRR949079 1 0.0000 0.801 1.000 0.000 0.000 0.000 0.000
#> SRR949080 1 0.0000 0.801 1.000 0.000 0.000 0.000 0.000
#> SRR949081 5 0.0000 0.694 0.000 0.000 0.000 0.000 1.000
#> SRR949082 5 0.4242 -0.282 0.000 0.428 0.000 0.000 0.572
#> SRR949083 5 0.0000 0.694 0.000 0.000 0.000 0.000 1.000
#> SRR949084 1 0.1671 0.768 0.924 0.000 0.000 0.000 0.076
#> SRR949085 2 0.4235 0.469 0.000 0.576 0.000 0.000 0.424
#> SRR949087 1 0.6466 0.135 0.480 0.204 0.000 0.000 0.316
#> SRR949088 1 0.6455 0.148 0.484 0.204 0.000 0.000 0.312
#> SRR949086 3 0.4029 0.549 0.000 0.004 0.680 0.000 0.316
#> SRR949089 2 0.3636 0.678 0.000 0.728 0.000 0.000 0.272
#> SRR949090 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> SRR949092 1 0.0162 0.801 0.996 0.000 0.000 0.000 0.004
#> SRR949093 1 0.0162 0.801 0.996 0.000 0.000 0.000 0.004
#> SRR949091 3 0.0000 0.878 0.000 0.000 1.000 0.000 0.000
#> SRR949095 5 0.6038 0.185 0.240 0.184 0.000 0.000 0.576
#> SRR949094 1 0.1408 0.788 0.948 0.044 0.000 0.008 0.000
#> SRR949096 1 0.0162 0.801 0.996 0.000 0.000 0.000 0.004
#> SRR949097 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> SRR949098 2 0.3636 0.678 0.000 0.728 0.000 0.000 0.272
#> SRR949099 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> SRR949101 3 0.4009 0.556 0.000 0.004 0.684 0.000 0.312
#> SRR949100 1 0.8180 0.244 0.408 0.200 0.000 0.240 0.152
#> SRR949102 5 0.0000 0.694 0.000 0.000 0.000 0.000 1.000
#> SRR949103 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> SRR949104 2 0.3752 0.664 0.000 0.708 0.000 0.000 0.292
#> SRR949105 3 0.0000 0.878 0.000 0.000 1.000 0.000 0.000
#> SRR949106 3 0.0000 0.878 0.000 0.000 1.000 0.000 0.000
#> SRR949107 3 0.0000 0.878 0.000 0.000 1.000 0.000 0.000
#> SRR949108 1 0.0609 0.798 0.980 0.000 0.000 0.020 0.000
#> SRR949109 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> SRR949110 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> SRR949111 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> SRR949112 1 0.5135 0.600 0.696 0.200 0.000 0.004 0.100
#> SRR949113 2 0.3752 0.664 0.000 0.708 0.000 0.000 0.292
#> SRR949114 3 0.0000 0.878 0.000 0.000 1.000 0.000 0.000
#> SRR949115 3 0.0000 0.878 0.000 0.000 1.000 0.000 0.000
#> SRR949116 3 0.0000 0.878 0.000 0.000 1.000 0.000 0.000
#> SRR949117 3 0.3861 0.604 0.000 0.004 0.712 0.000 0.284
#> SRR949118 3 0.1197 0.849 0.000 0.000 0.952 0.000 0.048
#> SRR949119 1 0.0000 0.801 1.000 0.000 0.000 0.000 0.000
#> SRR949120 1 0.0000 0.801 1.000 0.000 0.000 0.000 0.000
#> SRR949121 1 0.0324 0.801 0.992 0.000 0.000 0.004 0.004
#> SRR949122 1 0.4814 0.631 0.724 0.192 0.000 0.004 0.080
#> SRR949123 2 0.4300 0.340 0.000 0.524 0.000 0.000 0.476
#> SRR949124 2 0.3966 0.621 0.000 0.664 0.000 0.000 0.336
#> SRR949125 1 0.4126 0.448 0.620 0.000 0.000 0.380 0.000
#> SRR949126 1 0.4126 0.448 0.620 0.000 0.000 0.380 0.000
#> SRR949127 2 0.1671 0.585 0.000 0.924 0.000 0.000 0.076
#> SRR949128 2 0.1671 0.585 0.000 0.924 0.000 0.000 0.076
#> SRR949129 2 0.1671 0.585 0.000 0.924 0.000 0.000 0.076
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR949076 5 0.0000 0.8568 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR949078 5 0.3706 0.4221 0.000 0.380 0.000 0.000 0.620 0.000
#> SRR949077 5 0.0000 0.8568 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR949079 1 0.0000 0.9236 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949080 1 0.0000 0.9236 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949081 5 0.0000 0.8568 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR949082 5 0.3695 0.4309 0.000 0.376 0.000 0.000 0.624 0.000
#> SRR949083 5 0.0000 0.8568 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR949084 1 0.2134 0.8867 0.904 0.000 0.044 0.000 0.052 0.000
#> SRR949085 2 0.0000 0.8372 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949087 1 0.3718 0.8091 0.784 0.000 0.132 0.000 0.084 0.000
#> SRR949088 1 0.3718 0.8091 0.784 0.000 0.132 0.000 0.084 0.000
#> SRR949086 3 0.1556 0.9221 0.000 0.000 0.920 0.000 0.080 0.000
#> SRR949089 2 0.0000 0.8372 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949090 4 0.0000 0.8699 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949092 1 0.0000 0.9236 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949093 1 0.0000 0.9236 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949091 3 0.0000 0.9686 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR949095 5 0.1141 0.8083 0.052 0.000 0.000 0.000 0.948 0.000
#> SRR949094 1 0.0000 0.9236 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949096 1 0.0000 0.9236 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949097 4 0.0000 0.8699 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949098 2 0.0000 0.8372 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949099 4 0.0000 0.8699 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949101 3 0.1556 0.9221 0.000 0.000 0.920 0.000 0.080 0.000
#> SRR949100 4 0.6510 0.0572 0.376 0.000 0.132 0.432 0.060 0.000
#> SRR949102 5 0.0000 0.8568 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR949103 4 0.0000 0.8699 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949104 2 0.4141 0.3793 0.000 0.556 0.000 0.000 0.012 0.432
#> SRR949105 3 0.0000 0.9686 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR949106 3 0.0000 0.9686 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR949107 3 0.0000 0.9686 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR949108 1 0.0000 0.9236 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949109 4 0.0000 0.8699 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949110 4 0.0000 0.8699 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949111 4 0.0000 0.8699 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR949112 1 0.3667 0.8116 0.788 0.000 0.132 0.000 0.080 0.000
#> SRR949113 2 0.4141 0.3793 0.000 0.556 0.000 0.000 0.012 0.432
#> SRR949114 3 0.0000 0.9686 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR949115 3 0.0000 0.9686 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR949116 3 0.0000 0.9686 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR949117 3 0.1556 0.9221 0.000 0.000 0.920 0.000 0.080 0.000
#> SRR949118 3 0.0458 0.9618 0.000 0.000 0.984 0.000 0.016 0.000
#> SRR949119 1 0.0000 0.9236 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949120 1 0.0000 0.9236 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR949121 1 0.1092 0.9112 0.960 0.000 0.020 0.000 0.020 0.000
#> SRR949122 1 0.3213 0.8314 0.820 0.000 0.132 0.000 0.048 0.000
#> SRR949123 2 0.0260 0.8319 0.000 0.992 0.000 0.000 0.008 0.000
#> SRR949124 2 0.0000 0.8372 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949125 4 0.2527 0.7445 0.168 0.000 0.000 0.832 0.000 0.000
#> SRR949126 4 0.2454 0.7524 0.160 0.000 0.000 0.840 0.000 0.000
#> SRR949127 6 0.0000 1.0000 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR949128 6 0.0000 1.0000 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR949129 6 0.0000 1.0000 0.000 0.000 0.000 0.000 0.000 1.000
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)
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 16816 rows and 54 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 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 0.969 0.988 0.3706 0.628 0.628
#> 3 3 0.947 0.922 0.970 0.7646 0.690 0.515
#> 4 4 0.809 0.844 0.926 0.1294 0.846 0.590
#> 5 5 0.715 0.584 0.804 0.0712 0.924 0.722
#> 6 6 0.664 0.618 0.789 0.0485 0.843 0.411
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
#> SRR949076 1 0.0000 0.993 1.000 0.000
#> SRR949078 2 0.0000 0.968 0.000 1.000
#> SRR949077 1 0.0000 0.993 1.000 0.000
#> SRR949079 1 0.0000 0.993 1.000 0.000
#> SRR949080 1 0.0000 0.993 1.000 0.000
#> SRR949081 2 0.9522 0.396 0.372 0.628
#> SRR949082 2 0.0000 0.968 0.000 1.000
#> SRR949083 1 0.0376 0.989 0.996 0.004
#> SRR949084 1 0.0000 0.993 1.000 0.000
#> SRR949085 2 0.0000 0.968 0.000 1.000
#> SRR949087 1 0.0000 0.993 1.000 0.000
#> SRR949088 1 0.0000 0.993 1.000 0.000
#> SRR949086 1 0.0000 0.993 1.000 0.000
#> SRR949089 2 0.0000 0.968 0.000 1.000
#> SRR949090 1 0.0000 0.993 1.000 0.000
#> SRR949092 1 0.0000 0.993 1.000 0.000
#> SRR949093 1 0.0000 0.993 1.000 0.000
#> SRR949091 1 0.0000 0.993 1.000 0.000
#> SRR949095 1 0.1633 0.969 0.976 0.024
#> SRR949094 1 0.0000 0.993 1.000 0.000
#> SRR949096 1 0.0000 0.993 1.000 0.000
#> SRR949097 1 0.0000 0.993 1.000 0.000
#> SRR949098 2 0.0000 0.968 0.000 1.000
#> SRR949099 1 0.0000 0.993 1.000 0.000
#> SRR949101 1 0.0000 0.993 1.000 0.000
#> SRR949100 1 0.0000 0.993 1.000 0.000
#> SRR949102 1 0.8144 0.648 0.748 0.252
#> SRR949103 1 0.0000 0.993 1.000 0.000
#> SRR949104 2 0.0000 0.968 0.000 1.000
#> SRR949105 1 0.0000 0.993 1.000 0.000
#> SRR949106 1 0.0000 0.993 1.000 0.000
#> SRR949107 1 0.0000 0.993 1.000 0.000
#> SRR949108 1 0.0000 0.993 1.000 0.000
#> SRR949109 1 0.0000 0.993 1.000 0.000
#> SRR949110 1 0.0000 0.993 1.000 0.000
#> SRR949111 1 0.0000 0.993 1.000 0.000
#> SRR949112 1 0.0000 0.993 1.000 0.000
#> SRR949113 2 0.0000 0.968 0.000 1.000
#> SRR949114 1 0.0000 0.993 1.000 0.000
#> SRR949115 1 0.0000 0.993 1.000 0.000
#> SRR949116 1 0.0000 0.993 1.000 0.000
#> SRR949117 1 0.0000 0.993 1.000 0.000
#> SRR949118 1 0.0000 0.993 1.000 0.000
#> SRR949119 1 0.0000 0.993 1.000 0.000
#> SRR949120 1 0.0000 0.993 1.000 0.000
#> SRR949121 1 0.0000 0.993 1.000 0.000
#> SRR949122 1 0.0000 0.993 1.000 0.000
#> SRR949123 2 0.0000 0.968 0.000 1.000
#> SRR949124 2 0.0000 0.968 0.000 1.000
#> SRR949125 1 0.0000 0.993 1.000 0.000
#> SRR949126 1 0.0000 0.993 1.000 0.000
#> SRR949127 2 0.0376 0.965 0.004 0.996
#> SRR949128 2 0.0376 0.965 0.004 0.996
#> SRR949129 2 0.0000 0.968 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR949076 1 0.0000 0.963 1.000 0.000 0.000
#> SRR949078 2 0.4121 0.801 0.168 0.832 0.000
#> SRR949077 1 0.0000 0.963 1.000 0.000 0.000
#> SRR949079 1 0.0000 0.963 1.000 0.000 0.000
#> SRR949080 1 0.0000 0.963 1.000 0.000 0.000
#> SRR949081 1 0.0000 0.963 1.000 0.000 0.000
#> SRR949082 2 0.5016 0.699 0.240 0.760 0.000
#> SRR949083 1 0.0000 0.963 1.000 0.000 0.000
#> SRR949084 1 0.0000 0.963 1.000 0.000 0.000
#> SRR949085 2 0.0000 0.961 0.000 1.000 0.000
#> SRR949087 1 0.0000 0.963 1.000 0.000 0.000
#> SRR949088 1 0.0000 0.963 1.000 0.000 0.000
#> SRR949086 3 0.0000 0.967 0.000 0.000 1.000
#> SRR949089 2 0.0000 0.961 0.000 1.000 0.000
#> SRR949090 3 0.0000 0.967 0.000 0.000 1.000
#> SRR949092 1 0.0000 0.963 1.000 0.000 0.000
#> SRR949093 1 0.0000 0.963 1.000 0.000 0.000
#> SRR949091 3 0.0000 0.967 0.000 0.000 1.000
#> SRR949095 1 0.0000 0.963 1.000 0.000 0.000
#> SRR949094 1 0.1964 0.910 0.944 0.000 0.056
#> SRR949096 1 0.0000 0.963 1.000 0.000 0.000
#> SRR949097 3 0.0000 0.967 0.000 0.000 1.000
#> SRR949098 2 0.0000 0.961 0.000 1.000 0.000
#> SRR949099 3 0.0000 0.967 0.000 0.000 1.000
#> SRR949101 3 0.0000 0.967 0.000 0.000 1.000
#> SRR949100 3 0.0424 0.959 0.008 0.000 0.992
#> SRR949102 1 0.0000 0.963 1.000 0.000 0.000
#> SRR949103 3 0.0000 0.967 0.000 0.000 1.000
#> SRR949104 2 0.0000 0.961 0.000 1.000 0.000
#> SRR949105 3 0.0000 0.967 0.000 0.000 1.000
#> SRR949106 3 0.0000 0.967 0.000 0.000 1.000
#> SRR949107 3 0.0000 0.967 0.000 0.000 1.000
#> SRR949108 3 0.6244 0.181 0.440 0.000 0.560
#> SRR949109 3 0.0000 0.967 0.000 0.000 1.000
#> SRR949110 3 0.0000 0.967 0.000 0.000 1.000
#> SRR949111 3 0.0000 0.967 0.000 0.000 1.000
#> SRR949112 3 0.4654 0.718 0.208 0.000 0.792
#> SRR949113 2 0.0000 0.961 0.000 1.000 0.000
#> SRR949114 3 0.0000 0.967 0.000 0.000 1.000
#> SRR949115 3 0.0000 0.967 0.000 0.000 1.000
#> SRR949116 3 0.0000 0.967 0.000 0.000 1.000
#> SRR949117 3 0.0000 0.967 0.000 0.000 1.000
#> SRR949118 3 0.0000 0.967 0.000 0.000 1.000
#> SRR949119 1 0.0000 0.963 1.000 0.000 0.000
#> SRR949120 1 0.0000 0.963 1.000 0.000 0.000
#> SRR949121 1 0.2878 0.866 0.904 0.000 0.096
#> SRR949122 1 0.6111 0.324 0.604 0.000 0.396
#> SRR949123 2 0.0000 0.961 0.000 1.000 0.000
#> SRR949124 2 0.0000 0.961 0.000 1.000 0.000
#> SRR949125 3 0.0000 0.967 0.000 0.000 1.000
#> SRR949126 3 0.0000 0.967 0.000 0.000 1.000
#> SRR949127 2 0.0000 0.961 0.000 1.000 0.000
#> SRR949128 2 0.0000 0.961 0.000 1.000 0.000
#> SRR949129 2 0.0000 0.961 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR949076 4 0.0000 0.950 0.000 0.000 0.000 1.000
#> SRR949078 2 0.4522 0.499 0.000 0.680 0.000 0.320
#> SRR949077 4 0.0000 0.950 0.000 0.000 0.000 1.000
#> SRR949079 4 0.1637 0.936 0.060 0.000 0.000 0.940
#> SRR949080 4 0.1557 0.938 0.056 0.000 0.000 0.944
#> SRR949081 4 0.0000 0.950 0.000 0.000 0.000 1.000
#> SRR949082 4 0.2760 0.844 0.000 0.128 0.000 0.872
#> SRR949083 4 0.0000 0.950 0.000 0.000 0.000 1.000
#> SRR949084 4 0.0188 0.950 0.004 0.000 0.000 0.996
#> SRR949085 2 0.0000 0.911 0.000 1.000 0.000 0.000
#> SRR949087 4 0.1022 0.945 0.032 0.000 0.000 0.968
#> SRR949088 4 0.1637 0.930 0.060 0.000 0.000 0.940
#> SRR949086 3 0.0000 0.929 0.000 0.000 1.000 0.000
#> SRR949089 2 0.0000 0.911 0.000 1.000 0.000 0.000
#> SRR949090 1 0.2589 0.776 0.884 0.000 0.116 0.000
#> SRR949092 4 0.1211 0.945 0.040 0.000 0.000 0.960
#> SRR949093 4 0.0592 0.950 0.016 0.000 0.000 0.984
#> SRR949091 3 0.0188 0.928 0.004 0.000 0.996 0.000
#> SRR949095 4 0.0188 0.950 0.004 0.000 0.000 0.996
#> SRR949094 4 0.1297 0.944 0.020 0.000 0.016 0.964
#> SRR949096 4 0.0336 0.950 0.008 0.000 0.000 0.992
#> SRR949097 1 0.0000 0.826 1.000 0.000 0.000 0.000
#> SRR949098 2 0.0000 0.911 0.000 1.000 0.000 0.000
#> SRR949099 1 0.0336 0.826 0.992 0.000 0.008 0.000
#> SRR949101 3 0.0000 0.929 0.000 0.000 1.000 0.000
#> SRR949100 1 0.0000 0.826 1.000 0.000 0.000 0.000
#> SRR949102 4 0.0188 0.949 0.000 0.000 0.004 0.996
#> SRR949103 1 0.1389 0.819 0.952 0.000 0.048 0.000
#> SRR949104 2 0.0000 0.911 0.000 1.000 0.000 0.000
#> SRR949105 3 0.0469 0.925 0.012 0.000 0.988 0.000
#> SRR949106 3 0.0336 0.927 0.008 0.000 0.992 0.000
#> SRR949107 3 0.0336 0.927 0.008 0.000 0.992 0.000
#> SRR949108 1 0.3958 0.751 0.824 0.000 0.032 0.144
#> SRR949109 3 0.4967 0.189 0.452 0.000 0.548 0.000
#> SRR949110 1 0.0000 0.826 1.000 0.000 0.000 0.000
#> SRR949111 1 0.1118 0.823 0.964 0.000 0.036 0.000
#> SRR949112 1 0.7890 0.206 0.380 0.000 0.312 0.308
#> SRR949113 2 0.0000 0.911 0.000 1.000 0.000 0.000
#> SRR949114 3 0.0000 0.929 0.000 0.000 1.000 0.000
#> SRR949115 3 0.0000 0.929 0.000 0.000 1.000 0.000
#> SRR949116 3 0.0000 0.929 0.000 0.000 1.000 0.000
#> SRR949117 3 0.0000 0.929 0.000 0.000 1.000 0.000
#> SRR949118 3 0.0000 0.929 0.000 0.000 1.000 0.000
#> SRR949119 4 0.2530 0.898 0.112 0.000 0.000 0.888
#> SRR949120 4 0.3649 0.785 0.204 0.000 0.000 0.796
#> SRR949121 4 0.3032 0.876 0.124 0.000 0.008 0.868
#> SRR949122 1 0.3933 0.696 0.792 0.000 0.008 0.200
#> SRR949123 2 0.0000 0.911 0.000 1.000 0.000 0.000
#> SRR949124 2 0.0000 0.911 0.000 1.000 0.000 0.000
#> SRR949125 3 0.3636 0.774 0.172 0.000 0.820 0.008
#> SRR949126 3 0.3356 0.776 0.176 0.000 0.824 0.000
#> SRR949127 1 0.4164 0.581 0.736 0.264 0.000 0.000
#> SRR949128 1 0.3907 0.628 0.768 0.232 0.000 0.000
#> SRR949129 2 0.4072 0.603 0.252 0.748 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR949076 5 0.4219 0.41845 0.000 0.000 0.000 0.416 0.584
#> SRR949078 2 0.4517 0.10420 0.000 0.556 0.000 0.008 0.436
#> SRR949077 5 0.3424 0.62554 0.000 0.000 0.000 0.240 0.760
#> SRR949079 5 0.6334 0.29081 0.360 0.000 0.012 0.120 0.508
#> SRR949080 5 0.6293 0.33512 0.328 0.000 0.008 0.136 0.528
#> SRR949081 5 0.0290 0.74844 0.000 0.000 0.000 0.008 0.992
#> SRR949082 5 0.1121 0.73876 0.000 0.044 0.000 0.000 0.956
#> SRR949083 5 0.0000 0.74848 0.000 0.000 0.000 0.000 1.000
#> SRR949084 5 0.0671 0.75078 0.016 0.000 0.000 0.004 0.980
#> SRR949085 2 0.0000 0.89022 0.000 1.000 0.000 0.000 0.000
#> SRR949087 5 0.1997 0.73087 0.000 0.000 0.040 0.036 0.924
#> SRR949088 5 0.2464 0.72603 0.012 0.000 0.048 0.032 0.908
#> SRR949086 3 0.1695 0.77493 0.008 0.000 0.940 0.044 0.008
#> SRR949089 2 0.0000 0.89022 0.000 1.000 0.000 0.000 0.000
#> SRR949090 1 0.4359 0.17395 0.584 0.000 0.412 0.004 0.000
#> SRR949092 5 0.2124 0.71690 0.096 0.000 0.000 0.004 0.900
#> SRR949093 5 0.1041 0.74801 0.032 0.000 0.000 0.004 0.964
#> SRR949091 3 0.1282 0.78554 0.004 0.000 0.952 0.044 0.000
#> SRR949095 5 0.0162 0.74841 0.000 0.000 0.000 0.004 0.996
#> SRR949094 5 0.6986 0.27854 0.248 0.000 0.028 0.220 0.504
#> SRR949096 5 0.0992 0.75089 0.024 0.000 0.000 0.008 0.968
#> SRR949097 1 0.0000 0.66984 1.000 0.000 0.000 0.000 0.000
#> SRR949098 2 0.0000 0.89022 0.000 1.000 0.000 0.000 0.000
#> SRR949099 1 0.0794 0.66769 0.972 0.000 0.028 0.000 0.000
#> SRR949101 3 0.0290 0.79578 0.000 0.000 0.992 0.008 0.000
#> SRR949100 1 0.0162 0.66947 0.996 0.000 0.000 0.004 0.000
#> SRR949102 5 0.4425 0.35542 0.000 0.000 0.004 0.452 0.544
#> SRR949103 1 0.0880 0.66660 0.968 0.000 0.032 0.000 0.000
#> SRR949104 2 0.0000 0.89022 0.000 1.000 0.000 0.000 0.000
#> SRR949105 3 0.0566 0.79345 0.012 0.000 0.984 0.004 0.000
#> SRR949106 3 0.0290 0.79339 0.008 0.000 0.992 0.000 0.000
#> SRR949107 3 0.0404 0.79139 0.012 0.000 0.988 0.000 0.000
#> SRR949108 1 0.3684 0.43737 0.720 0.000 0.000 0.280 0.000
#> SRR949109 1 0.4655 0.00642 0.512 0.000 0.476 0.012 0.000
#> SRR949110 1 0.0000 0.66984 1.000 0.000 0.000 0.000 0.000
#> SRR949111 1 0.1106 0.66450 0.964 0.000 0.024 0.012 0.000
#> SRR949112 4 0.3496 0.34997 0.200 0.000 0.012 0.788 0.000
#> SRR949113 2 0.0000 0.89022 0.000 1.000 0.000 0.000 0.000
#> SRR949114 3 0.4420 0.48027 0.004 0.000 0.548 0.448 0.000
#> SRR949115 3 0.4437 0.46079 0.004 0.000 0.532 0.464 0.000
#> SRR949116 3 0.4440 0.45548 0.004 0.000 0.528 0.468 0.000
#> SRR949117 3 0.0955 0.79563 0.004 0.000 0.968 0.028 0.000
#> SRR949118 3 0.2179 0.75632 0.000 0.000 0.888 0.112 0.000
#> SRR949119 4 0.6492 0.16923 0.348 0.000 0.000 0.456 0.196
#> SRR949120 1 0.5498 -0.16066 0.496 0.000 0.000 0.440 0.064
#> SRR949121 5 0.6655 -0.03435 0.296 0.000 0.000 0.260 0.444
#> SRR949122 1 0.4045 0.32947 0.644 0.000 0.000 0.356 0.000
#> SRR949123 2 0.1205 0.86306 0.000 0.956 0.004 0.040 0.000
#> SRR949124 2 0.0000 0.89022 0.000 1.000 0.000 0.000 0.000
#> SRR949125 4 0.6312 0.46457 0.156 0.000 0.392 0.452 0.000
#> SRR949126 4 0.6363 0.46797 0.164 0.000 0.392 0.444 0.000
#> SRR949127 1 0.3906 0.45719 0.704 0.292 0.000 0.004 0.000
#> SRR949128 1 0.3635 0.49888 0.748 0.248 0.000 0.004 0.000
#> SRR949129 2 0.3266 0.66696 0.200 0.796 0.000 0.004 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR949076 4 0.3151 0.6442 0.000 0.000 0.000 0.748 0.252 0.000
#> SRR949078 2 0.4693 0.5387 0.000 0.684 0.000 0.140 0.176 0.000
#> SRR949077 4 0.3774 0.4640 0.000 0.000 0.000 0.592 0.408 0.000
#> SRR949079 4 0.6919 0.5811 0.084 0.000 0.144 0.536 0.212 0.024
#> SRR949080 4 0.6816 0.6037 0.084 0.000 0.128 0.548 0.216 0.024
#> SRR949081 5 0.0858 0.8802 0.000 0.000 0.004 0.028 0.968 0.000
#> SRR949082 5 0.2006 0.8235 0.000 0.104 0.000 0.004 0.892 0.000
#> SRR949083 5 0.0603 0.8794 0.000 0.000 0.000 0.016 0.980 0.004
#> SRR949084 5 0.1944 0.8757 0.024 0.000 0.000 0.036 0.924 0.016
#> SRR949085 2 0.0000 0.9186 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949087 5 0.2747 0.8364 0.008 0.004 0.076 0.036 0.876 0.000
#> SRR949088 5 0.2879 0.8336 0.016 0.000 0.072 0.044 0.868 0.000
#> SRR949086 3 0.4988 0.3689 0.000 0.000 0.676 0.028 0.076 0.220
#> SRR949089 2 0.0000 0.9186 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949090 3 0.4949 0.5950 0.196 0.000 0.696 0.056 0.000 0.052
#> SRR949092 5 0.3726 0.7909 0.080 0.000 0.000 0.032 0.816 0.072
#> SRR949093 5 0.3329 0.8185 0.052 0.000 0.000 0.032 0.844 0.072
#> SRR949091 3 0.3039 0.6640 0.008 0.000 0.852 0.056 0.000 0.084
#> SRR949095 5 0.1082 0.8767 0.004 0.000 0.000 0.040 0.956 0.000
#> SRR949094 3 0.7853 0.0871 0.080 0.000 0.396 0.312 0.116 0.096
#> SRR949096 5 0.1924 0.8673 0.048 0.000 0.000 0.028 0.920 0.004
#> SRR949097 1 0.0922 0.6628 0.968 0.000 0.004 0.004 0.000 0.024
#> SRR949098 2 0.0000 0.9186 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949099 1 0.1340 0.6574 0.948 0.000 0.040 0.004 0.000 0.008
#> SRR949101 3 0.2506 0.6616 0.000 0.000 0.880 0.052 0.000 0.068
#> SRR949100 1 0.0692 0.6528 0.976 0.000 0.000 0.020 0.000 0.004
#> SRR949102 4 0.3590 0.6549 0.000 0.000 0.004 0.776 0.188 0.032
#> SRR949103 1 0.3355 0.6153 0.828 0.000 0.040 0.016 0.000 0.116
#> SRR949104 2 0.0146 0.9167 0.000 0.996 0.000 0.004 0.000 0.000
#> SRR949105 3 0.1219 0.6602 0.004 0.000 0.948 0.000 0.000 0.048
#> SRR949106 3 0.0865 0.6606 0.000 0.000 0.964 0.000 0.000 0.036
#> SRR949107 3 0.0865 0.6606 0.000 0.000 0.964 0.000 0.000 0.036
#> SRR949108 1 0.4744 0.4581 0.684 0.000 0.012 0.080 0.000 0.224
#> SRR949109 3 0.5579 0.5100 0.252 0.000 0.616 0.048 0.000 0.084
#> SRR949110 1 0.2113 0.6430 0.896 0.000 0.008 0.004 0.000 0.092
#> SRR949111 1 0.5456 -0.1255 0.496 0.000 0.420 0.036 0.000 0.048
#> SRR949112 6 0.3693 0.5991 0.120 0.000 0.000 0.092 0.000 0.788
#> SRR949113 2 0.0000 0.9186 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949114 6 0.1644 0.6816 0.000 0.000 0.076 0.004 0.000 0.920
#> SRR949115 6 0.1584 0.6867 0.000 0.000 0.064 0.008 0.000 0.928
#> SRR949116 6 0.1584 0.6867 0.000 0.000 0.064 0.008 0.000 0.928
#> SRR949117 3 0.4099 0.1564 0.000 0.000 0.612 0.016 0.000 0.372
#> SRR949118 6 0.4157 0.1455 0.000 0.000 0.444 0.012 0.000 0.544
#> SRR949119 4 0.5063 0.4997 0.276 0.000 0.000 0.640 0.044 0.040
#> SRR949120 4 0.4718 0.3919 0.340 0.000 0.000 0.608 0.008 0.044
#> SRR949121 6 0.5963 0.4680 0.132 0.000 0.004 0.048 0.212 0.604
#> SRR949122 6 0.5105 0.0604 0.428 0.000 0.004 0.068 0.000 0.500
#> SRR949123 2 0.2480 0.8309 0.000 0.872 0.000 0.024 0.000 0.104
#> SRR949124 2 0.0000 0.9186 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR949125 3 0.5900 0.5575 0.064 0.000 0.608 0.212 0.000 0.116
#> SRR949126 3 0.5889 0.5692 0.068 0.000 0.616 0.196 0.000 0.120
#> SRR949127 1 0.4263 0.0615 0.504 0.480 0.000 0.016 0.000 0.000
#> SRR949128 1 0.4184 0.2571 0.576 0.408 0.000 0.016 0.000 0.000
#> SRR949129 2 0.2404 0.8027 0.112 0.872 0.000 0.016 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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