Date: 2019-12-26 00:47:09 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 14626 rows and 51 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] 14626 51
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 | ||
|---|---|---|---|---|---|---|
| CV:hclust | 2 | 1.000 | 0.966 | 0.987 | ** | |
| CV:kmeans | 2 | 1.000 | 0.996 | 0.997 | ** | |
| CV:skmeans | 2 | 1.000 | 0.971 | 0.984 | ** | |
| CV:pam | 2 | 1.000 | 0.991 | 0.996 | ** | |
| CV:NMF | 2 | 1.000 | 0.971 | 0.990 | ** | |
| ATC:NMF | 2 | 0.910 | 0.903 | 0.960 | * | |
| ATC:pam | 5 | 0.909 | 0.876 | 0.950 | * | 2,4 |
| ATC:skmeans | 6 | 0.909 | 0.896 | 0.921 | * | 2 |
| SD:NMF | 3 | 0.869 | 0.902 | 0.959 | ||
| SD:pam | 4 | 0.822 | 0.880 | 0.949 | ||
| MAD:NMF | 3 | 0.793 | 0.858 | 0.923 | ||
| ATC:kmeans | 2 | 0.769 | 0.885 | 0.929 | ||
| MAD:pam | 2 | 0.764 | 0.879 | 0.949 | ||
| ATC:hclust | 5 | 0.702 | 0.660 | 0.771 | ||
| SD:kmeans | 5 | 0.660 | 0.746 | 0.792 | ||
| MAD:skmeans | 2 | 0.645 | 0.897 | 0.948 | ||
| SD:hclust | 4 | 0.580 | 0.698 | 0.862 | ||
| SD:skmeans | 2 | 0.546 | 0.774 | 0.893 | ||
| ATC:mclust | 4 | 0.490 | 0.699 | 0.801 | ||
| SD:mclust | 3 | 0.434 | 0.588 | 0.799 | ||
| CV:mclust | 3 | 0.401 | 0.603 | 0.741 | ||
| MAD:mclust | 5 | 0.382 | 0.581 | 0.724 | ||
| MAD:kmeans | 2 | 0.369 | 0.781 | 0.862 | ||
| MAD:hclust | 2 | 0.327 | 0.618 | 0.837 |
**: 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 0.437 0.768 0.879 0.377 0.655 0.655
#> CV:NMF 2 1.000 0.971 0.990 0.310 0.704 0.704
#> MAD:NMF 2 0.590 0.831 0.921 0.479 0.514 0.514
#> ATC:NMF 2 0.910 0.903 0.960 0.403 0.594 0.594
#> SD:skmeans 2 0.546 0.774 0.893 0.501 0.490 0.490
#> CV:skmeans 2 1.000 0.971 0.984 0.431 0.576 0.576
#> MAD:skmeans 2 0.645 0.897 0.948 0.509 0.490 0.490
#> ATC:skmeans 2 1.000 0.975 0.989 0.509 0.492 0.492
#> SD:mclust 2 0.759 0.938 0.964 0.331 0.678 0.678
#> CV:mclust 2 0.844 0.873 0.940 0.358 0.594 0.594
#> MAD:mclust 2 0.813 0.928 0.943 0.331 0.678 0.678
#> ATC:mclust 2 0.405 0.818 0.887 0.325 0.678 0.678
#> SD:kmeans 2 0.349 0.585 0.824 0.377 0.576 0.576
#> CV:kmeans 2 1.000 0.996 0.997 0.244 0.758 0.758
#> MAD:kmeans 2 0.369 0.781 0.862 0.470 0.492 0.492
#> ATC:kmeans 2 0.769 0.885 0.929 0.481 0.500 0.500
#> SD:pam 2 0.433 0.836 0.867 0.452 0.492 0.492
#> CV:pam 2 1.000 0.991 0.996 0.219 0.788 0.788
#> MAD:pam 2 0.764 0.879 0.949 0.503 0.500 0.500
#> ATC:pam 2 1.000 0.995 0.998 0.509 0.492 0.492
#> SD:hclust 2 0.301 0.590 0.775 0.332 0.758 0.758
#> CV:hclust 2 1.000 0.966 0.987 0.250 0.758 0.758
#> MAD:hclust 2 0.327 0.618 0.837 0.427 0.547 0.547
#> ATC:hclust 2 0.286 0.285 0.682 0.371 0.576 0.576
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.869 0.902 0.959 0.636 0.707 0.559
#> CV:NMF 3 0.779 0.812 0.929 1.057 0.655 0.509
#> MAD:NMF 3 0.793 0.858 0.923 0.283 0.800 0.636
#> ATC:NMF 3 0.571 0.817 0.901 0.467 0.802 0.669
#> SD:skmeans 3 0.541 0.725 0.847 0.314 0.791 0.604
#> CV:skmeans 3 0.679 0.838 0.891 0.560 0.721 0.527
#> MAD:skmeans 3 0.630 0.808 0.878 0.322 0.773 0.567
#> ATC:skmeans 3 0.881 0.934 0.962 0.311 0.711 0.479
#> SD:mclust 3 0.434 0.588 0.799 0.643 0.730 0.630
#> CV:mclust 3 0.401 0.603 0.741 0.589 0.755 0.588
#> MAD:mclust 3 0.254 0.352 0.729 0.609 0.768 0.683
#> ATC:mclust 3 0.365 0.574 0.730 0.698 0.773 0.675
#> SD:kmeans 3 0.458 0.682 0.835 0.541 0.774 0.635
#> CV:kmeans 3 0.441 0.592 0.812 1.383 0.624 0.504
#> MAD:kmeans 3 0.490 0.542 0.758 0.322 0.775 0.582
#> ATC:kmeans 3 0.526 0.624 0.818 0.292 0.818 0.658
#> SD:pam 3 0.715 0.846 0.934 0.320 0.704 0.507
#> CV:pam 3 0.528 0.723 0.885 1.708 0.613 0.508
#> MAD:pam 3 0.648 0.801 0.903 0.201 0.884 0.771
#> ATC:pam 3 0.779 0.893 0.934 0.224 0.901 0.799
#> SD:hclust 3 0.525 0.649 0.858 0.601 0.685 0.589
#> CV:hclust 3 0.433 0.746 0.794 0.595 0.961 0.948
#> MAD:hclust 3 0.398 0.573 0.789 0.344 0.886 0.792
#> ATC:hclust 3 0.466 0.641 0.806 0.547 0.784 0.626
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.671 0.752 0.887 0.1894 0.735 0.418
#> CV:NMF 4 0.775 0.688 0.876 0.1455 0.869 0.656
#> MAD:NMF 4 0.608 0.625 0.826 0.2007 0.751 0.438
#> ATC:NMF 4 0.531 0.642 0.807 0.1946 0.685 0.367
#> SD:skmeans 4 0.660 0.723 0.855 0.1394 0.795 0.490
#> CV:skmeans 4 0.625 0.541 0.753 0.1079 0.900 0.713
#> MAD:skmeans 4 0.678 0.760 0.875 0.1128 0.833 0.552
#> ATC:skmeans 4 0.874 0.912 0.958 0.1118 0.906 0.722
#> SD:mclust 4 0.497 0.518 0.746 0.1570 0.899 0.806
#> CV:mclust 4 0.337 0.460 0.672 0.1535 0.789 0.495
#> MAD:mclust 4 0.336 0.428 0.669 0.1908 0.703 0.507
#> ATC:mclust 4 0.490 0.699 0.801 0.2160 0.713 0.477
#> SD:kmeans 4 0.493 0.489 0.650 0.2117 0.824 0.622
#> CV:kmeans 4 0.499 0.649 0.778 0.2052 0.787 0.523
#> MAD:kmeans 4 0.504 0.638 0.727 0.1544 0.780 0.477
#> ATC:kmeans 4 0.647 0.838 0.874 0.1330 0.784 0.517
#> SD:pam 4 0.822 0.880 0.949 0.1541 0.815 0.596
#> CV:pam 4 0.516 0.660 0.808 0.1673 0.848 0.634
#> MAD:pam 4 0.807 0.853 0.942 0.1405 0.911 0.774
#> ATC:pam 4 0.957 0.925 0.971 0.1711 0.831 0.595
#> SD:hclust 4 0.580 0.698 0.862 0.1842 0.871 0.729
#> CV:hclust 4 0.377 0.778 0.818 0.0668 0.990 0.986
#> MAD:hclust 4 0.496 0.651 0.802 0.1439 0.867 0.705
#> ATC:hclust 4 0.583 0.603 0.769 0.1377 0.960 0.890
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.749 0.725 0.854 0.0816 0.856 0.531
#> CV:NMF 5 0.715 0.657 0.836 0.0737 0.934 0.768
#> MAD:NMF 5 0.738 0.753 0.857 0.0788 0.801 0.391
#> ATC:NMF 5 0.682 0.681 0.826 0.1021 0.841 0.508
#> SD:skmeans 5 0.711 0.731 0.839 0.0702 0.892 0.605
#> CV:skmeans 5 0.596 0.475 0.703 0.0701 0.865 0.556
#> MAD:skmeans 5 0.758 0.659 0.799 0.0670 0.912 0.674
#> ATC:skmeans 5 0.877 0.868 0.901 0.0560 0.929 0.740
#> SD:mclust 5 0.481 0.647 0.750 0.1220 0.736 0.454
#> CV:mclust 5 0.394 0.511 0.630 0.1028 0.869 0.628
#> MAD:mclust 5 0.382 0.581 0.724 0.1357 0.701 0.371
#> ATC:mclust 5 0.557 0.487 0.704 0.0812 0.769 0.414
#> SD:kmeans 5 0.660 0.746 0.792 0.0903 0.873 0.622
#> CV:kmeans 5 0.604 0.585 0.755 0.0859 0.920 0.747
#> MAD:kmeans 5 0.705 0.787 0.859 0.0844 0.896 0.641
#> ATC:kmeans 5 0.760 0.707 0.773 0.0832 0.993 0.976
#> SD:pam 5 0.870 0.876 0.946 0.1248 0.887 0.656
#> CV:pam 5 0.535 0.682 0.798 0.0514 0.918 0.745
#> MAD:pam 5 0.831 0.864 0.941 0.1220 0.893 0.665
#> ATC:pam 5 0.909 0.876 0.950 0.0449 0.965 0.873
#> SD:hclust 5 0.559 0.658 0.813 0.0882 0.984 0.954
#> CV:hclust 5 0.303 0.644 0.761 0.2433 0.845 0.784
#> MAD:hclust 5 0.539 0.648 0.720 0.1380 0.842 0.558
#> ATC:hclust 5 0.702 0.660 0.771 0.1119 0.934 0.806
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.799 0.689 0.857 0.0389 0.928 0.678
#> CV:NMF 6 0.764 0.707 0.794 0.0522 0.908 0.631
#> MAD:NMF 6 0.768 0.669 0.837 0.0365 0.920 0.648
#> ATC:NMF 6 0.658 0.529 0.772 0.0441 0.875 0.531
#> SD:skmeans 6 0.730 0.647 0.804 0.0407 0.955 0.776
#> CV:skmeans 6 0.644 0.518 0.686 0.0438 0.899 0.560
#> MAD:skmeans 6 0.717 0.645 0.791 0.0420 0.945 0.745
#> ATC:skmeans 6 0.909 0.896 0.921 0.0447 0.953 0.789
#> SD:mclust 6 0.624 0.677 0.779 0.0959 0.970 0.890
#> CV:mclust 6 0.549 0.421 0.629 0.0760 0.868 0.557
#> MAD:mclust 6 0.545 0.665 0.721 0.1019 0.864 0.564
#> ATC:mclust 6 0.696 0.706 0.823 0.1293 0.894 0.603
#> SD:kmeans 6 0.677 0.614 0.742 0.0571 0.915 0.666
#> CV:kmeans 6 0.676 0.634 0.731 0.0489 0.911 0.660
#> MAD:kmeans 6 0.798 0.744 0.801 0.0466 0.967 0.857
#> ATC:kmeans 6 0.787 0.827 0.863 0.0592 0.852 0.524
#> SD:pam 6 0.872 0.845 0.932 0.0307 0.975 0.889
#> CV:pam 6 0.621 0.578 0.809 0.0574 0.927 0.751
#> MAD:pam 6 0.806 0.740 0.881 0.0473 0.976 0.895
#> ATC:pam 6 0.934 0.906 0.954 0.0139 0.997 0.987
#> SD:hclust 6 0.574 0.392 0.764 0.0598 0.936 0.821
#> CV:hclust 6 0.357 0.538 0.741 0.1431 0.966 0.941
#> MAD:hclust 6 0.579 0.591 0.707 0.0364 0.920 0.692
#> ATC:hclust 6 0.736 0.550 0.746 0.0688 0.846 0.515
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 14626 rows and 51 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.301 0.590 0.775 0.3319 0.758 0.758
#> 3 3 0.525 0.649 0.858 0.6013 0.685 0.589
#> 4 4 0.580 0.698 0.862 0.1842 0.871 0.729
#> 5 5 0.559 0.658 0.813 0.0882 0.984 0.954
#> 6 6 0.574 0.392 0.764 0.0598 0.936 0.821
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
#> SRR1812752 1 0.9323 0.8356 0.652 0.348
#> SRR1812753 1 0.9323 0.8356 0.652 0.348
#> SRR1812751 1 0.9323 0.8356 0.652 0.348
#> SRR1812750 1 0.9323 0.8356 0.652 0.348
#> SRR1812748 2 0.9323 0.3765 0.348 0.652
#> SRR1812749 1 0.9323 0.8356 0.652 0.348
#> SRR1812746 1 0.9815 -0.0177 0.580 0.420
#> SRR1812745 2 0.9323 0.3765 0.348 0.652
#> SRR1812747 2 0.6973 0.6567 0.188 0.812
#> SRR1812744 2 0.8861 0.4258 0.304 0.696
#> SRR1812743 2 0.6247 0.5629 0.156 0.844
#> SRR1812742 2 0.6247 0.5629 0.156 0.844
#> SRR1812737 2 0.6973 0.6567 0.188 0.812
#> SRR1812735 2 0.6973 0.6567 0.188 0.812
#> SRR1812734 2 0.9209 0.3913 0.336 0.664
#> SRR1812733 2 0.7139 0.6568 0.196 0.804
#> SRR1812736 2 0.9323 0.3765 0.348 0.652
#> SRR1812732 2 0.6712 0.5545 0.176 0.824
#> SRR1812730 2 0.7950 0.6385 0.240 0.760
#> SRR1812731 2 0.2423 0.6407 0.040 0.960
#> SRR1812729 2 0.6973 0.6567 0.188 0.812
#> SRR1812727 2 0.9996 -0.0719 0.488 0.512
#> SRR1812726 2 0.6973 0.6567 0.188 0.812
#> SRR1812728 2 0.6531 0.6636 0.168 0.832
#> SRR1812724 2 0.4298 0.6143 0.088 0.912
#> SRR1812725 2 0.7950 0.6385 0.240 0.760
#> SRR1812723 2 0.6973 0.6567 0.188 0.812
#> SRR1812722 2 0.6973 0.6567 0.188 0.812
#> SRR1812721 2 0.5059 0.5962 0.112 0.888
#> SRR1812718 2 0.7056 0.6562 0.192 0.808
#> SRR1812717 2 0.3733 0.6239 0.072 0.928
#> SRR1812716 2 0.7950 0.6385 0.240 0.760
#> SRR1812715 2 0.6973 0.6567 0.188 0.812
#> SRR1812714 2 0.7056 0.6562 0.192 0.808
#> SRR1812719 2 0.9996 -0.0719 0.488 0.512
#> SRR1812713 2 0.7056 0.6562 0.192 0.808
#> SRR1812712 2 0.0672 0.6472 0.008 0.992
#> SRR1812711 2 0.6973 0.6567 0.188 0.812
#> SRR1812710 2 0.6973 0.6567 0.188 0.812
#> SRR1812709 2 0.0672 0.6472 0.008 0.992
#> SRR1812708 1 0.9460 0.8016 0.636 0.364
#> SRR1812707 2 0.6973 0.6567 0.188 0.812
#> SRR1812705 2 0.6973 0.6567 0.188 0.812
#> SRR1812706 2 0.3879 0.6277 0.076 0.924
#> SRR1812704 2 0.6623 0.6535 0.172 0.828
#> SRR1812703 2 0.7056 0.6562 0.192 0.808
#> SRR1812702 2 0.7950 0.6385 0.240 0.760
#> SRR1812741 2 0.5842 0.5768 0.140 0.860
#> SRR1812740 2 0.9323 0.3765 0.348 0.652
#> SRR1812739 2 0.2423 0.6407 0.040 0.960
#> SRR1812738 2 0.3733 0.6239 0.072 0.928
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1812752 1 0.0237 0.8882 0.996 0.004 0.000
#> SRR1812753 1 0.0237 0.8882 0.996 0.004 0.000
#> SRR1812751 1 0.0237 0.8882 0.996 0.004 0.000
#> SRR1812750 1 0.0237 0.8882 0.996 0.004 0.000
#> SRR1812748 3 0.0000 0.6132 0.000 0.000 1.000
#> SRR1812749 1 0.0237 0.8882 0.996 0.004 0.000
#> SRR1812746 3 0.4931 0.3931 0.232 0.000 0.768
#> SRR1812745 3 0.0000 0.6132 0.000 0.000 1.000
#> SRR1812747 2 0.0475 0.8443 0.004 0.992 0.004
#> SRR1812744 3 0.2384 0.6228 0.008 0.056 0.936
#> SRR1812743 3 0.6442 0.2164 0.004 0.432 0.564
#> SRR1812742 3 0.6359 0.2895 0.004 0.404 0.592
#> SRR1812737 2 0.0237 0.8453 0.004 0.996 0.000
#> SRR1812735 2 0.0237 0.8453 0.004 0.996 0.000
#> SRR1812734 3 0.1399 0.6222 0.004 0.028 0.968
#> SRR1812733 2 0.0661 0.8418 0.004 0.988 0.008
#> SRR1812736 3 0.0000 0.6132 0.000 0.000 1.000
#> SRR1812732 3 0.6359 0.2858 0.004 0.404 0.592
#> SRR1812730 2 0.2682 0.7975 0.004 0.920 0.076
#> SRR1812731 2 0.6189 0.3772 0.004 0.632 0.364
#> SRR1812729 2 0.0237 0.8453 0.004 0.996 0.000
#> SRR1812727 3 0.9865 0.1205 0.268 0.324 0.408
#> SRR1812726 2 0.0237 0.8453 0.004 0.996 0.000
#> SRR1812728 2 0.2200 0.8229 0.004 0.940 0.056
#> SRR1812724 2 0.6286 0.0517 0.000 0.536 0.464
#> SRR1812725 2 0.2682 0.7975 0.004 0.920 0.076
#> SRR1812723 2 0.0237 0.8453 0.004 0.996 0.000
#> SRR1812722 2 0.0237 0.8453 0.004 0.996 0.000
#> SRR1812721 2 0.6008 0.4586 0.004 0.664 0.332
#> SRR1812718 2 0.0237 0.8431 0.004 0.996 0.000
#> SRR1812717 2 0.5397 0.5608 0.000 0.720 0.280
#> SRR1812716 2 0.2682 0.7975 0.004 0.920 0.076
#> SRR1812715 2 0.0237 0.8453 0.004 0.996 0.000
#> SRR1812714 2 0.0237 0.8431 0.004 0.996 0.000
#> SRR1812719 3 0.9865 0.1205 0.268 0.324 0.408
#> SRR1812713 2 0.0237 0.8431 0.004 0.996 0.000
#> SRR1812712 2 0.4750 0.6565 0.000 0.784 0.216
#> SRR1812711 2 0.0237 0.8453 0.004 0.996 0.000
#> SRR1812710 2 0.0237 0.8453 0.004 0.996 0.000
#> SRR1812709 2 0.4750 0.6565 0.000 0.784 0.216
#> SRR1812708 1 0.6045 0.3473 0.620 0.380 0.000
#> SRR1812707 2 0.0237 0.8453 0.004 0.996 0.000
#> SRR1812705 2 0.0237 0.8453 0.004 0.996 0.000
#> SRR1812706 2 0.5815 0.5670 0.004 0.692 0.304
#> SRR1812704 2 0.4409 0.7386 0.004 0.824 0.172
#> SRR1812703 2 0.0237 0.8431 0.004 0.996 0.000
#> SRR1812702 2 0.2682 0.7975 0.004 0.920 0.076
#> SRR1812741 3 0.6295 0.1064 0.000 0.472 0.528
#> SRR1812740 3 0.0000 0.6132 0.000 0.000 1.000
#> SRR1812739 2 0.5988 0.3671 0.000 0.632 0.368
#> SRR1812738 2 0.6095 0.3027 0.000 0.608 0.392
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1812752 1 0.0000 0.868 1.000 0.000 0.000 0.000
#> SRR1812753 1 0.0000 0.868 1.000 0.000 0.000 0.000
#> SRR1812751 1 0.0000 0.868 1.000 0.000 0.000 0.000
#> SRR1812750 1 0.0000 0.868 1.000 0.000 0.000 0.000
#> SRR1812748 3 0.1389 0.771 0.000 0.000 0.952 0.048
#> SRR1812749 1 0.0000 0.868 1.000 0.000 0.000 0.000
#> SRR1812746 3 0.3837 0.589 0.224 0.000 0.776 0.000
#> SRR1812745 3 0.1211 0.771 0.000 0.000 0.960 0.040
#> SRR1812747 2 0.0524 0.856 0.000 0.988 0.004 0.008
#> SRR1812744 3 0.2730 0.736 0.000 0.016 0.896 0.088
#> SRR1812743 4 0.1297 0.596 0.000 0.016 0.020 0.964
#> SRR1812742 4 0.3659 0.523 0.000 0.024 0.136 0.840
#> SRR1812737 2 0.2868 0.773 0.000 0.864 0.000 0.136
#> SRR1812735 2 0.0469 0.856 0.000 0.988 0.000 0.012
#> SRR1812734 3 0.1118 0.759 0.000 0.000 0.964 0.036
#> SRR1812733 2 0.0336 0.855 0.000 0.992 0.008 0.000
#> SRR1812736 3 0.1389 0.771 0.000 0.000 0.952 0.048
#> SRR1812732 4 0.6310 0.640 0.000 0.188 0.152 0.660
#> SRR1812730 2 0.1940 0.815 0.000 0.924 0.076 0.000
#> SRR1812731 4 0.4761 0.569 0.000 0.372 0.000 0.628
#> SRR1812729 2 0.1474 0.836 0.000 0.948 0.000 0.052
#> SRR1812727 3 0.8677 0.218 0.260 0.288 0.412 0.040
#> SRR1812726 2 0.0336 0.856 0.000 0.992 0.000 0.008
#> SRR1812728 2 0.1807 0.834 0.000 0.940 0.052 0.008
#> SRR1812724 4 0.4008 0.730 0.000 0.244 0.000 0.756
#> SRR1812725 2 0.1940 0.815 0.000 0.924 0.076 0.000
#> SRR1812723 2 0.0336 0.856 0.000 0.992 0.000 0.008
#> SRR1812722 2 0.0469 0.856 0.000 0.988 0.000 0.012
#> SRR1812721 4 0.4761 0.518 0.000 0.372 0.000 0.628
#> SRR1812718 2 0.0000 0.855 0.000 1.000 0.000 0.000
#> SRR1812717 2 0.4817 0.194 0.000 0.612 0.000 0.388
#> SRR1812716 2 0.1940 0.815 0.000 0.924 0.076 0.000
#> SRR1812715 2 0.0469 0.856 0.000 0.988 0.000 0.012
#> SRR1812714 2 0.0592 0.850 0.000 0.984 0.000 0.016
#> SRR1812719 3 0.8677 0.218 0.260 0.288 0.412 0.040
#> SRR1812713 2 0.0469 0.855 0.000 0.988 0.000 0.012
#> SRR1812712 2 0.4356 0.470 0.000 0.708 0.000 0.292
#> SRR1812711 2 0.0336 0.856 0.000 0.992 0.000 0.008
#> SRR1812710 2 0.2868 0.773 0.000 0.864 0.000 0.136
#> SRR1812709 2 0.4356 0.470 0.000 0.708 0.000 0.292
#> SRR1812708 1 0.5592 0.288 0.608 0.368 0.008 0.016
#> SRR1812707 2 0.2868 0.773 0.000 0.864 0.000 0.136
#> SRR1812705 2 0.0336 0.856 0.000 0.992 0.000 0.008
#> SRR1812706 2 0.5693 0.506 0.000 0.688 0.072 0.240
#> SRR1812704 2 0.4301 0.732 0.000 0.816 0.064 0.120
#> SRR1812703 2 0.0592 0.850 0.000 0.984 0.000 0.016
#> SRR1812702 2 0.1940 0.815 0.000 0.924 0.076 0.000
#> SRR1812741 4 0.2530 0.694 0.000 0.112 0.000 0.888
#> SRR1812740 3 0.1389 0.771 0.000 0.000 0.952 0.048
#> SRR1812739 2 0.4994 -0.241 0.000 0.520 0.000 0.480
#> SRR1812738 4 0.4713 0.608 0.000 0.360 0.000 0.640
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1812752 1 0.0000 0.689 1.000 0.000 0.000 0.000 0.000
#> SRR1812753 1 0.0000 0.689 1.000 0.000 0.000 0.000 0.000
#> SRR1812751 1 0.4088 0.797 0.632 0.000 0.000 0.000 0.368
#> SRR1812750 1 0.4088 0.797 0.632 0.000 0.000 0.000 0.368
#> SRR1812748 3 0.0880 0.879 0.000 0.000 0.968 0.032 0.000
#> SRR1812749 1 0.4088 0.797 0.632 0.000 0.000 0.000 0.368
#> SRR1812746 3 0.4394 0.574 0.100 0.000 0.764 0.000 0.136
#> SRR1812745 3 0.0703 0.877 0.000 0.000 0.976 0.024 0.000
#> SRR1812747 2 0.1124 0.784 0.000 0.960 0.004 0.000 0.036
#> SRR1812744 3 0.3653 0.754 0.000 0.016 0.840 0.056 0.088
#> SRR1812743 4 0.1300 0.569 0.000 0.000 0.028 0.956 0.016
#> SRR1812742 4 0.3284 0.490 0.000 0.000 0.148 0.828 0.024
#> SRR1812737 2 0.2377 0.713 0.000 0.872 0.000 0.128 0.000
#> SRR1812735 2 0.0162 0.787 0.000 0.996 0.000 0.004 0.000
#> SRR1812734 3 0.2077 0.816 0.000 0.000 0.908 0.008 0.084
#> SRR1812733 2 0.1484 0.783 0.000 0.944 0.008 0.000 0.048
#> SRR1812736 3 0.0880 0.879 0.000 0.000 0.968 0.032 0.000
#> SRR1812732 4 0.5494 0.609 0.000 0.172 0.156 0.668 0.004
#> SRR1812730 2 0.4155 0.705 0.000 0.780 0.076 0.000 0.144
#> SRR1812731 4 0.4196 0.559 0.000 0.356 0.000 0.640 0.004
#> SRR1812729 2 0.1408 0.772 0.000 0.948 0.000 0.044 0.008
#> SRR1812727 5 0.6819 0.568 0.124 0.004 0.352 0.028 0.492
#> SRR1812726 2 0.0000 0.787 0.000 1.000 0.000 0.000 0.000
#> SRR1812728 2 0.4909 0.655 0.000 0.716 0.052 0.016 0.216
#> SRR1812724 4 0.3663 0.699 0.000 0.208 0.000 0.776 0.016
#> SRR1812725 2 0.4155 0.704 0.000 0.780 0.076 0.000 0.144
#> SRR1812723 2 0.0290 0.787 0.000 0.992 0.000 0.000 0.008
#> SRR1812722 2 0.0162 0.787 0.000 0.996 0.000 0.004 0.000
#> SRR1812721 4 0.5289 0.469 0.000 0.340 0.000 0.596 0.064
#> SRR1812718 2 0.1197 0.784 0.000 0.952 0.000 0.000 0.048
#> SRR1812717 2 0.4630 0.223 0.000 0.588 0.000 0.396 0.016
#> SRR1812716 2 0.4155 0.705 0.000 0.780 0.076 0.000 0.144
#> SRR1812715 2 0.0162 0.787 0.000 0.996 0.000 0.004 0.000
#> SRR1812714 2 0.3837 0.608 0.000 0.692 0.000 0.000 0.308
#> SRR1812719 5 0.6819 0.568 0.124 0.004 0.352 0.028 0.492
#> SRR1812713 2 0.1195 0.786 0.000 0.960 0.000 0.012 0.028
#> SRR1812712 2 0.4923 0.457 0.000 0.680 0.000 0.252 0.068
#> SRR1812711 2 0.0000 0.787 0.000 1.000 0.000 0.000 0.000
#> SRR1812710 2 0.2377 0.713 0.000 0.872 0.000 0.128 0.000
#> SRR1812709 2 0.4923 0.457 0.000 0.680 0.000 0.252 0.068
#> SRR1812708 5 0.3691 0.107 0.104 0.076 0.000 0.000 0.820
#> SRR1812707 2 0.2377 0.713 0.000 0.872 0.000 0.128 0.000
#> SRR1812705 2 0.0290 0.787 0.000 0.992 0.000 0.000 0.008
#> SRR1812706 2 0.7145 0.404 0.000 0.548 0.072 0.196 0.184
#> SRR1812704 2 0.5683 0.659 0.000 0.708 0.064 0.124 0.104
#> SRR1812703 2 0.3837 0.608 0.000 0.692 0.000 0.000 0.308
#> SRR1812702 2 0.4155 0.704 0.000 0.780 0.076 0.000 0.144
#> SRR1812741 4 0.1956 0.660 0.000 0.076 0.000 0.916 0.008
#> SRR1812740 3 0.0880 0.879 0.000 0.000 0.968 0.032 0.000
#> SRR1812739 2 0.4659 -0.203 0.000 0.500 0.000 0.488 0.012
#> SRR1812738 4 0.4384 0.594 0.000 0.324 0.000 0.660 0.016
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1812752 1 0.4871 0.57359 0.580 0.000 0.000 0.000 0.072 0.348
#> SRR1812753 1 0.4871 0.57359 0.580 0.000 0.000 0.000 0.072 0.348
#> SRR1812751 1 0.0000 0.70467 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812750 1 0.0000 0.70467 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812748 3 0.0000 0.84397 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1812749 1 0.0000 0.70467 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812746 3 0.4660 0.45370 0.024 0.000 0.644 0.000 0.304 0.028
#> SRR1812745 3 0.2300 0.73813 0.000 0.000 0.856 0.000 0.144 0.000
#> SRR1812747 2 0.2442 0.45610 0.000 0.852 0.004 0.000 0.000 0.144
#> SRR1812744 5 0.5818 0.16326 0.000 0.016 0.388 0.040 0.512 0.044
#> SRR1812743 4 0.2036 0.49503 0.000 0.000 0.048 0.916 0.008 0.028
#> SRR1812742 4 0.3604 0.39199 0.000 0.000 0.168 0.788 0.008 0.036
#> SRR1812737 2 0.2869 0.46618 0.000 0.832 0.000 0.148 0.000 0.020
#> SRR1812735 2 0.0405 0.56990 0.000 0.988 0.000 0.004 0.000 0.008
#> SRR1812734 5 0.4526 0.04515 0.000 0.000 0.456 0.000 0.512 0.032
#> SRR1812733 2 0.2700 0.46755 0.000 0.836 0.004 0.000 0.004 0.156
#> SRR1812736 3 0.0000 0.84397 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1812732 4 0.5617 0.57052 0.000 0.152 0.068 0.676 0.092 0.012
#> SRR1812730 2 0.4177 0.00966 0.000 0.668 0.008 0.000 0.020 0.304
#> SRR1812731 4 0.4031 0.52831 0.000 0.332 0.000 0.652 0.008 0.008
#> SRR1812729 2 0.2511 0.54084 0.000 0.880 0.000 0.064 0.000 0.056
#> SRR1812727 5 0.3309 0.50421 0.004 0.000 0.016 0.000 0.788 0.192
#> SRR1812726 2 0.0547 0.56409 0.000 0.980 0.000 0.000 0.000 0.020
#> SRR1812728 2 0.5548 -0.19899 0.000 0.608 0.008 0.004 0.184 0.196
#> SRR1812724 4 0.3536 0.63238 0.000 0.184 0.000 0.784 0.020 0.012
#> SRR1812725 2 0.4103 0.05250 0.000 0.684 0.008 0.000 0.020 0.288
#> SRR1812723 2 0.1204 0.54962 0.000 0.944 0.000 0.000 0.000 0.056
#> SRR1812722 2 0.0291 0.56939 0.000 0.992 0.000 0.004 0.000 0.004
#> SRR1812721 4 0.6011 0.19512 0.000 0.296 0.000 0.432 0.000 0.272
#> SRR1812718 2 0.2178 0.48728 0.000 0.868 0.000 0.000 0.000 0.132
#> SRR1812717 2 0.4943 -0.03657 0.000 0.544 0.000 0.404 0.020 0.032
#> SRR1812716 2 0.4177 0.00966 0.000 0.668 0.008 0.000 0.020 0.304
#> SRR1812715 2 0.0405 0.56990 0.000 0.988 0.000 0.004 0.000 0.008
#> SRR1812714 2 0.4774 0.03159 0.000 0.672 0.000 0.000 0.192 0.136
#> SRR1812719 5 0.3309 0.50421 0.004 0.000 0.016 0.000 0.788 0.192
#> SRR1812713 2 0.1500 0.55828 0.000 0.936 0.000 0.012 0.000 0.052
#> SRR1812712 2 0.4831 0.06501 0.000 0.636 0.000 0.096 0.000 0.268
#> SRR1812711 2 0.0363 0.56913 0.000 0.988 0.000 0.000 0.000 0.012
#> SRR1812710 2 0.2869 0.46618 0.000 0.832 0.000 0.148 0.000 0.020
#> SRR1812709 2 0.4831 0.06501 0.000 0.636 0.000 0.096 0.000 0.268
#> SRR1812708 1 0.6567 -0.02550 0.428 0.076 0.000 0.000 0.380 0.116
#> SRR1812707 2 0.2869 0.46618 0.000 0.832 0.000 0.148 0.000 0.020
#> SRR1812705 2 0.1267 0.54685 0.000 0.940 0.000 0.000 0.000 0.060
#> SRR1812706 6 0.4754 0.00000 0.000 0.432 0.004 0.012 0.020 0.532
#> SRR1812704 2 0.5632 -0.17991 0.000 0.592 0.004 0.124 0.016 0.264
#> SRR1812703 2 0.4774 0.03159 0.000 0.672 0.000 0.000 0.192 0.136
#> SRR1812702 2 0.4177 0.00788 0.000 0.668 0.008 0.000 0.020 0.304
#> SRR1812741 4 0.1921 0.58958 0.000 0.052 0.000 0.916 0.032 0.000
#> SRR1812740 3 0.0000 0.84397 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1812739 4 0.4336 0.17263 0.000 0.476 0.000 0.504 0.000 0.020
#> SRR1812738 4 0.4590 0.55430 0.000 0.288 0.000 0.660 0.028 0.024
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 14626 rows and 51 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 0.349 0.585 0.824 0.3769 0.576 0.576
#> 3 3 0.458 0.682 0.835 0.5410 0.774 0.635
#> 4 4 0.493 0.489 0.650 0.2117 0.824 0.622
#> 5 5 0.660 0.746 0.792 0.0903 0.873 0.622
#> 6 6 0.677 0.614 0.742 0.0571 0.915 0.666
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR1812752 1 0.2043 0.5276 0.968 0.032
#> SRR1812753 1 0.2043 0.5276 0.968 0.032
#> SRR1812751 1 0.9754 0.3627 0.592 0.408
#> SRR1812750 1 0.9795 0.3543 0.584 0.416
#> SRR1812748 1 0.9944 0.2466 0.544 0.456
#> SRR1812749 1 0.9754 0.3627 0.592 0.408
#> SRR1812746 1 0.2423 0.5317 0.960 0.040
#> SRR1812745 1 0.9944 0.2466 0.544 0.456
#> SRR1812747 2 0.0376 0.8150 0.004 0.996
#> SRR1812744 2 0.9732 0.2161 0.404 0.596
#> SRR1812743 2 0.9922 -0.0141 0.448 0.552
#> SRR1812742 1 0.9998 0.1741 0.508 0.492
#> SRR1812737 2 0.0000 0.8154 0.000 1.000
#> SRR1812735 2 0.0000 0.8154 0.000 1.000
#> SRR1812734 1 0.9944 0.2466 0.544 0.456
#> SRR1812733 2 0.8499 0.5527 0.276 0.724
#> SRR1812736 1 0.9944 0.2466 0.544 0.456
#> SRR1812732 2 0.8207 0.5771 0.256 0.744
#> SRR1812730 2 0.9815 0.1503 0.420 0.580
#> SRR1812731 2 0.0938 0.8117 0.012 0.988
#> SRR1812729 2 0.0000 0.8154 0.000 1.000
#> SRR1812727 1 0.2948 0.5331 0.948 0.052
#> SRR1812726 2 0.0000 0.8154 0.000 1.000
#> SRR1812728 2 0.8144 0.5874 0.252 0.748
#> SRR1812724 2 0.6623 0.6936 0.172 0.828
#> SRR1812725 2 0.3733 0.7781 0.072 0.928
#> SRR1812723 2 0.0000 0.8154 0.000 1.000
#> SRR1812722 2 0.0000 0.8154 0.000 1.000
#> SRR1812721 2 0.0376 0.8150 0.004 0.996
#> SRR1812718 2 0.0376 0.8150 0.004 0.996
#> SRR1812717 2 0.0000 0.8154 0.000 1.000
#> SRR1812716 2 0.8661 0.5252 0.288 0.712
#> SRR1812715 2 0.0000 0.8154 0.000 1.000
#> SRR1812714 2 0.0000 0.8154 0.000 1.000
#> SRR1812719 1 0.9635 0.3464 0.612 0.388
#> SRR1812713 2 0.1414 0.8077 0.020 0.980
#> SRR1812712 2 0.1414 0.8077 0.020 0.980
#> SRR1812711 2 0.0000 0.8154 0.000 1.000
#> SRR1812710 2 0.0000 0.8154 0.000 1.000
#> SRR1812709 2 0.0000 0.8154 0.000 1.000
#> SRR1812708 1 0.9833 0.3429 0.576 0.424
#> SRR1812707 2 0.0000 0.8154 0.000 1.000
#> SRR1812705 2 0.0376 0.8150 0.004 0.996
#> SRR1812706 2 0.8608 0.5329 0.284 0.716
#> SRR1812704 2 0.6343 0.7011 0.160 0.840
#> SRR1812703 2 0.0000 0.8154 0.000 1.000
#> SRR1812702 2 0.8661 0.5252 0.288 0.712
#> SRR1812741 2 0.9686 0.1450 0.396 0.604
#> SRR1812740 1 0.9944 0.2466 0.544 0.456
#> SRR1812739 2 0.1633 0.8077 0.024 0.976
#> SRR1812738 2 0.7139 0.6661 0.196 0.804
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1812752 1 0.3412 0.8079 0.876 0.000 0.124
#> SRR1812753 1 0.3412 0.8079 0.876 0.000 0.124
#> SRR1812751 1 0.2066 0.9087 0.940 0.060 0.000
#> SRR1812750 1 0.2066 0.9087 0.940 0.060 0.000
#> SRR1812748 3 0.1163 0.6983 0.028 0.000 0.972
#> SRR1812749 1 0.2066 0.9087 0.940 0.060 0.000
#> SRR1812746 3 0.3816 0.6023 0.148 0.000 0.852
#> SRR1812745 3 0.0592 0.7013 0.012 0.000 0.988
#> SRR1812747 2 0.5137 0.8027 0.104 0.832 0.064
#> SRR1812744 3 0.6195 0.5647 0.020 0.276 0.704
#> SRR1812743 2 0.8045 0.0631 0.064 0.504 0.432
#> SRR1812742 3 0.7015 0.5563 0.064 0.240 0.696
#> SRR1812737 2 0.2796 0.8153 0.092 0.908 0.000
#> SRR1812735 2 0.2796 0.8153 0.092 0.908 0.000
#> SRR1812734 3 0.0747 0.7010 0.016 0.000 0.984
#> SRR1812733 3 0.6688 0.4503 0.012 0.408 0.580
#> SRR1812736 3 0.1163 0.6983 0.028 0.000 0.972
#> SRR1812732 2 0.7029 0.1109 0.020 0.540 0.440
#> SRR1812730 3 0.4805 0.6880 0.012 0.176 0.812
#> SRR1812731 2 0.3369 0.7688 0.040 0.908 0.052
#> SRR1812729 2 0.4137 0.8162 0.096 0.872 0.032
#> SRR1812727 3 0.5171 0.5885 0.204 0.012 0.784
#> SRR1812726 2 0.4446 0.8132 0.112 0.856 0.032
#> SRR1812728 2 0.7278 -0.1744 0.028 0.516 0.456
#> SRR1812724 2 0.3237 0.7651 0.032 0.912 0.056
#> SRR1812725 2 0.6387 0.3899 0.020 0.680 0.300
#> SRR1812723 2 0.5137 0.7999 0.104 0.832 0.064
#> SRR1812722 2 0.4446 0.8132 0.112 0.856 0.032
#> SRR1812721 2 0.2229 0.7880 0.044 0.944 0.012
#> SRR1812718 2 0.5137 0.7999 0.104 0.832 0.064
#> SRR1812717 2 0.0000 0.8058 0.000 1.000 0.000
#> SRR1812716 3 0.7069 0.4431 0.024 0.408 0.568
#> SRR1812715 2 0.2796 0.8153 0.092 0.908 0.000
#> SRR1812714 2 0.4196 0.8142 0.112 0.864 0.024
#> SRR1812719 3 0.5138 0.6722 0.120 0.052 0.828
#> SRR1812713 2 0.0475 0.8034 0.004 0.992 0.004
#> SRR1812712 2 0.0475 0.8034 0.004 0.992 0.004
#> SRR1812711 2 0.4892 0.8083 0.112 0.840 0.048
#> SRR1812710 2 0.2796 0.8153 0.092 0.908 0.000
#> SRR1812709 2 0.0237 0.8047 0.004 0.996 0.000
#> SRR1812708 1 0.2261 0.9028 0.932 0.068 0.000
#> SRR1812707 2 0.2796 0.8153 0.092 0.908 0.000
#> SRR1812705 2 0.5304 0.7979 0.108 0.824 0.068
#> SRR1812706 3 0.7192 0.4311 0.028 0.412 0.560
#> SRR1812704 2 0.3213 0.7585 0.008 0.900 0.092
#> SRR1812703 2 0.4526 0.8116 0.104 0.856 0.040
#> SRR1812702 3 0.6777 0.5275 0.020 0.364 0.616
#> SRR1812741 2 0.7953 0.2236 0.068 0.564 0.368
#> SRR1812740 3 0.1163 0.6983 0.028 0.000 0.972
#> SRR1812739 2 0.2229 0.7854 0.012 0.944 0.044
#> SRR1812738 2 0.4953 0.6421 0.016 0.808 0.176
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1812752 1 0.1406 0.9039 0.960 0.000 0.024 0.016
#> SRR1812753 1 0.1406 0.9039 0.960 0.000 0.024 0.016
#> SRR1812751 1 0.1743 0.9396 0.940 0.056 0.000 0.004
#> SRR1812750 1 0.1743 0.9396 0.940 0.056 0.000 0.004
#> SRR1812748 3 0.4957 0.5744 0.012 0.000 0.668 0.320
#> SRR1812749 1 0.1743 0.9396 0.940 0.056 0.000 0.004
#> SRR1812746 3 0.6351 0.5150 0.080 0.000 0.588 0.332
#> SRR1812745 3 0.5038 0.5650 0.012 0.000 0.652 0.336
#> SRR1812747 2 0.5093 0.3787 0.012 0.640 0.000 0.348
#> SRR1812744 3 0.6478 0.1415 0.000 0.088 0.576 0.336
#> SRR1812743 3 0.7281 -0.0771 0.048 0.448 0.456 0.048
#> SRR1812742 3 0.6573 0.3852 0.048 0.180 0.692 0.080
#> SRR1812737 2 0.1211 0.5579 0.000 0.960 0.040 0.000
#> SRR1812735 2 0.1902 0.5407 0.004 0.932 0.000 0.064
#> SRR1812734 3 0.4978 0.5709 0.012 0.000 0.664 0.324
#> SRR1812733 4 0.3501 0.7384 0.000 0.132 0.020 0.848
#> SRR1812736 3 0.4978 0.5737 0.012 0.000 0.664 0.324
#> SRR1812732 3 0.6483 0.1586 0.000 0.312 0.592 0.096
#> SRR1812730 4 0.2441 0.6544 0.004 0.012 0.068 0.916
#> SRR1812731 2 0.6637 0.2681 0.000 0.572 0.324 0.104
#> SRR1812729 2 0.5040 0.3602 0.008 0.628 0.000 0.364
#> SRR1812727 4 0.5923 0.3311 0.128 0.000 0.176 0.696
#> SRR1812726 2 0.5093 0.3787 0.012 0.640 0.000 0.348
#> SRR1812728 4 0.2530 0.7545 0.000 0.100 0.004 0.896
#> SRR1812724 2 0.7038 0.2452 0.004 0.548 0.324 0.124
#> SRR1812725 4 0.4382 0.4160 0.000 0.296 0.000 0.704
#> SRR1812723 2 0.5300 0.2848 0.012 0.580 0.000 0.408
#> SRR1812722 2 0.5038 0.3874 0.012 0.652 0.000 0.336
#> SRR1812721 2 0.6820 0.3165 0.048 0.620 0.284 0.048
#> SRR1812718 2 0.5279 0.2993 0.012 0.588 0.000 0.400
#> SRR1812717 2 0.2844 0.5434 0.000 0.900 0.052 0.048
#> SRR1812716 4 0.2542 0.7623 0.000 0.084 0.012 0.904
#> SRR1812715 2 0.0188 0.5581 0.004 0.996 0.000 0.000
#> SRR1812714 2 0.5285 0.3737 0.012 0.632 0.004 0.352
#> SRR1812719 4 0.4595 0.4882 0.044 0.000 0.176 0.780
#> SRR1812713 2 0.5302 0.4822 0.004 0.752 0.080 0.164
#> SRR1812712 2 0.5736 0.4497 0.004 0.708 0.080 0.208
#> SRR1812711 2 0.5189 0.3454 0.012 0.616 0.000 0.372
#> SRR1812710 2 0.0188 0.5581 0.004 0.996 0.000 0.000
#> SRR1812709 2 0.4219 0.5162 0.004 0.832 0.088 0.076
#> SRR1812708 1 0.3791 0.8795 0.860 0.056 0.008 0.076
#> SRR1812707 2 0.0921 0.5588 0.000 0.972 0.028 0.000
#> SRR1812705 2 0.5244 0.3214 0.012 0.600 0.000 0.388
#> SRR1812706 4 0.2708 0.7624 0.004 0.076 0.016 0.904
#> SRR1812704 4 0.6446 0.2679 0.000 0.328 0.088 0.584
#> SRR1812703 2 0.5553 0.1831 0.012 0.532 0.004 0.452
#> SRR1812702 4 0.2473 0.7619 0.000 0.080 0.012 0.908
#> SRR1812741 2 0.7496 0.1340 0.048 0.512 0.372 0.068
#> SRR1812740 3 0.4978 0.5737 0.012 0.000 0.664 0.324
#> SRR1812739 2 0.5995 0.3786 0.000 0.660 0.256 0.084
#> SRR1812738 2 0.7671 0.1185 0.000 0.456 0.300 0.244
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1812752 1 0.2162 0.916 0.916 0.000 0.008 0.012 0.064
#> SRR1812753 1 0.2162 0.916 0.916 0.000 0.008 0.012 0.064
#> SRR1812751 1 0.0510 0.934 0.984 0.016 0.000 0.000 0.000
#> SRR1812750 1 0.0671 0.934 0.980 0.016 0.000 0.000 0.004
#> SRR1812748 3 0.1202 0.951 0.004 0.000 0.960 0.032 0.004
#> SRR1812749 1 0.0671 0.934 0.980 0.016 0.000 0.000 0.004
#> SRR1812746 3 0.2396 0.909 0.024 0.000 0.904 0.004 0.068
#> SRR1812745 3 0.0566 0.957 0.000 0.000 0.984 0.004 0.012
#> SRR1812747 2 0.2074 0.713 0.000 0.896 0.000 0.000 0.104
#> SRR1812744 4 0.6581 0.528 0.000 0.028 0.148 0.560 0.264
#> SRR1812743 4 0.2749 0.789 0.012 0.008 0.032 0.900 0.048
#> SRR1812742 4 0.5436 0.578 0.012 0.008 0.240 0.676 0.064
#> SRR1812737 2 0.3980 0.611 0.000 0.708 0.000 0.284 0.008
#> SRR1812735 2 0.2806 0.703 0.000 0.844 0.000 0.152 0.004
#> SRR1812734 3 0.1124 0.948 0.000 0.000 0.960 0.004 0.036
#> SRR1812733 5 0.5811 0.824 0.000 0.144 0.076 0.084 0.696
#> SRR1812736 3 0.0613 0.958 0.004 0.000 0.984 0.008 0.004
#> SRR1812732 4 0.3755 0.722 0.000 0.012 0.140 0.816 0.032
#> SRR1812730 5 0.5077 0.856 0.000 0.156 0.108 0.012 0.724
#> SRR1812731 4 0.1443 0.803 0.004 0.044 0.000 0.948 0.004
#> SRR1812729 2 0.1544 0.731 0.000 0.932 0.000 0.000 0.068
#> SRR1812727 5 0.4418 0.644 0.048 0.012 0.148 0.008 0.784
#> SRR1812726 2 0.1638 0.729 0.000 0.932 0.000 0.004 0.064
#> SRR1812728 5 0.4784 0.863 0.000 0.192 0.056 0.016 0.736
#> SRR1812724 4 0.1907 0.803 0.000 0.044 0.000 0.928 0.028
#> SRR1812725 5 0.4130 0.762 0.000 0.292 0.000 0.012 0.696
#> SRR1812723 2 0.2127 0.707 0.000 0.892 0.000 0.000 0.108
#> SRR1812722 2 0.1877 0.731 0.000 0.924 0.000 0.012 0.064
#> SRR1812721 4 0.4074 0.683 0.012 0.180 0.000 0.780 0.028
#> SRR1812718 2 0.2230 0.703 0.000 0.884 0.000 0.000 0.116
#> SRR1812717 2 0.4465 0.572 0.000 0.672 0.000 0.304 0.024
#> SRR1812716 5 0.5027 0.864 0.000 0.184 0.084 0.012 0.720
#> SRR1812715 2 0.3353 0.679 0.000 0.796 0.000 0.196 0.008
#> SRR1812714 2 0.2563 0.720 0.000 0.872 0.000 0.008 0.120
#> SRR1812719 5 0.3435 0.693 0.004 0.012 0.148 0.008 0.828
#> SRR1812713 2 0.6469 0.302 0.000 0.468 0.000 0.336 0.196
#> SRR1812712 2 0.6399 0.339 0.000 0.492 0.000 0.316 0.192
#> SRR1812711 2 0.1792 0.719 0.000 0.916 0.000 0.000 0.084
#> SRR1812710 2 0.3353 0.679 0.000 0.796 0.000 0.196 0.008
#> SRR1812709 2 0.5435 0.263 0.000 0.512 0.000 0.428 0.060
#> SRR1812708 1 0.4084 0.800 0.788 0.024 0.008 0.008 0.172
#> SRR1812707 2 0.3835 0.632 0.000 0.732 0.000 0.260 0.008
#> SRR1812705 2 0.2439 0.701 0.000 0.876 0.000 0.004 0.120
#> SRR1812706 5 0.4903 0.862 0.000 0.196 0.068 0.012 0.724
#> SRR1812704 5 0.4879 0.739 0.000 0.156 0.000 0.124 0.720
#> SRR1812703 2 0.3642 0.620 0.000 0.760 0.000 0.008 0.232
#> SRR1812702 5 0.5114 0.863 0.000 0.176 0.096 0.012 0.716
#> SRR1812741 4 0.1903 0.804 0.012 0.020 0.008 0.940 0.020
#> SRR1812740 3 0.1116 0.953 0.004 0.000 0.964 0.028 0.004
#> SRR1812739 4 0.4059 0.658 0.000 0.172 0.000 0.776 0.052
#> SRR1812738 4 0.3602 0.718 0.000 0.024 0.000 0.796 0.180
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1812752 1 0.2213 0.8632 0.888 0.000 0.008 0.000 0.004 0.100
#> SRR1812753 1 0.2213 0.8632 0.888 0.000 0.008 0.000 0.004 0.100
#> SRR1812751 1 0.0260 0.8888 0.992 0.008 0.000 0.000 0.000 0.000
#> SRR1812750 1 0.0260 0.8888 0.992 0.008 0.000 0.000 0.000 0.000
#> SRR1812748 3 0.0951 0.9292 0.000 0.000 0.968 0.004 0.008 0.020
#> SRR1812749 1 0.0260 0.8888 0.992 0.008 0.000 0.000 0.000 0.000
#> SRR1812746 3 0.2930 0.8792 0.000 0.000 0.840 0.000 0.036 0.124
#> SRR1812745 3 0.1633 0.9290 0.000 0.000 0.932 0.000 0.024 0.044
#> SRR1812747 2 0.2772 0.7756 0.000 0.816 0.000 0.000 0.180 0.004
#> SRR1812744 4 0.6516 -0.1420 0.000 0.016 0.052 0.436 0.092 0.404
#> SRR1812743 6 0.4165 0.5835 0.008 0.004 0.000 0.420 0.000 0.568
#> SRR1812742 6 0.6340 0.6448 0.008 0.000 0.160 0.276 0.032 0.524
#> SRR1812737 2 0.3955 0.3337 0.000 0.608 0.000 0.384 0.008 0.000
#> SRR1812735 2 0.2558 0.6901 0.000 0.840 0.000 0.156 0.004 0.000
#> SRR1812734 3 0.2250 0.9091 0.000 0.000 0.888 0.000 0.020 0.092
#> SRR1812733 5 0.4761 0.6377 0.000 0.036 0.028 0.220 0.704 0.012
#> SRR1812736 3 0.0508 0.9341 0.000 0.000 0.984 0.000 0.012 0.004
#> SRR1812732 4 0.4730 -0.3464 0.000 0.000 0.040 0.588 0.008 0.364
#> SRR1812730 5 0.2186 0.8471 0.000 0.036 0.048 0.000 0.908 0.008
#> SRR1812731 4 0.3606 -0.0275 0.000 0.004 0.000 0.724 0.008 0.264
#> SRR1812729 2 0.2404 0.7964 0.000 0.872 0.000 0.016 0.112 0.000
#> SRR1812727 5 0.5306 0.5947 0.016 0.008 0.060 0.008 0.640 0.268
#> SRR1812726 2 0.1610 0.7939 0.000 0.916 0.000 0.000 0.084 0.000
#> SRR1812728 5 0.2319 0.8412 0.000 0.060 0.008 0.008 0.904 0.020
#> SRR1812724 4 0.2851 0.2425 0.000 0.004 0.000 0.844 0.020 0.132
#> SRR1812725 5 0.2146 0.8086 0.000 0.116 0.000 0.004 0.880 0.000
#> SRR1812723 2 0.2730 0.7699 0.000 0.808 0.000 0.000 0.192 0.000
#> SRR1812722 2 0.2039 0.7935 0.000 0.904 0.000 0.020 0.076 0.000
#> SRR1812721 4 0.5457 0.1373 0.004 0.140 0.000 0.624 0.012 0.220
#> SRR1812718 2 0.2730 0.7699 0.000 0.808 0.000 0.000 0.192 0.000
#> SRR1812717 4 0.3923 0.1455 0.000 0.416 0.000 0.580 0.004 0.000
#> SRR1812716 5 0.2007 0.8482 0.000 0.036 0.044 0.000 0.916 0.004
#> SRR1812715 2 0.2772 0.6713 0.000 0.816 0.000 0.180 0.004 0.000
#> SRR1812714 2 0.2468 0.7613 0.000 0.888 0.000 0.004 0.048 0.060
#> SRR1812719 5 0.4758 0.6325 0.000 0.008 0.060 0.008 0.680 0.244
#> SRR1812713 4 0.5022 0.4321 0.000 0.204 0.000 0.640 0.156 0.000
#> SRR1812712 4 0.5126 0.4282 0.000 0.216 0.000 0.624 0.160 0.000
#> SRR1812711 2 0.1957 0.7922 0.000 0.888 0.000 0.000 0.112 0.000
#> SRR1812710 2 0.3052 0.6356 0.000 0.780 0.000 0.216 0.004 0.000
#> SRR1812709 4 0.4305 0.4349 0.000 0.260 0.000 0.684 0.056 0.000
#> SRR1812708 1 0.5762 0.5834 0.616 0.056 0.004 0.012 0.048 0.264
#> SRR1812707 2 0.3945 0.3442 0.000 0.612 0.000 0.380 0.008 0.000
#> SRR1812705 2 0.2871 0.7705 0.000 0.804 0.000 0.004 0.192 0.000
#> SRR1812706 5 0.2570 0.8429 0.000 0.064 0.024 0.024 0.888 0.000
#> SRR1812704 5 0.2881 0.8080 0.000 0.040 0.000 0.084 0.864 0.012
#> SRR1812703 2 0.3709 0.7181 0.000 0.808 0.000 0.016 0.100 0.076
#> SRR1812702 5 0.2007 0.8482 0.000 0.036 0.044 0.004 0.916 0.000
#> SRR1812741 4 0.4268 -0.4906 0.000 0.004 0.000 0.556 0.012 0.428
#> SRR1812740 3 0.0964 0.9304 0.000 0.000 0.968 0.004 0.012 0.016
#> SRR1812739 4 0.4235 0.3772 0.000 0.064 0.000 0.780 0.052 0.104
#> SRR1812738 4 0.4313 0.2735 0.000 0.000 0.000 0.728 0.124 0.148
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 14626 rows and 51 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.546 0.774 0.893 0.5006 0.490 0.490
#> 3 3 0.541 0.725 0.847 0.3137 0.791 0.604
#> 4 4 0.660 0.723 0.855 0.1394 0.795 0.490
#> 5 5 0.711 0.731 0.839 0.0702 0.892 0.605
#> 6 6 0.730 0.647 0.804 0.0407 0.955 0.776
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
#> SRR1812752 1 0.000 0.816 1.000 0.000
#> SRR1812753 1 0.000 0.816 1.000 0.000
#> SRR1812751 2 0.985 0.338 0.428 0.572
#> SRR1812750 2 0.985 0.338 0.428 0.572
#> SRR1812748 1 0.000 0.816 1.000 0.000
#> SRR1812749 2 0.985 0.338 0.428 0.572
#> SRR1812746 1 0.000 0.816 1.000 0.000
#> SRR1812745 1 0.000 0.816 1.000 0.000
#> SRR1812747 2 0.000 0.914 0.000 1.000
#> SRR1812744 1 0.000 0.816 1.000 0.000
#> SRR1812743 1 0.644 0.754 0.836 0.164
#> SRR1812742 1 0.000 0.816 1.000 0.000
#> SRR1812737 2 0.000 0.914 0.000 1.000
#> SRR1812735 2 0.000 0.914 0.000 1.000
#> SRR1812734 1 0.000 0.816 1.000 0.000
#> SRR1812733 1 0.985 0.508 0.572 0.428
#> SRR1812736 1 0.000 0.816 1.000 0.000
#> SRR1812732 1 0.295 0.799 0.948 0.052
#> SRR1812730 1 0.595 0.767 0.856 0.144
#> SRR1812731 2 0.000 0.914 0.000 1.000
#> SRR1812729 2 0.000 0.914 0.000 1.000
#> SRR1812727 1 0.000 0.816 1.000 0.000
#> SRR1812726 2 0.000 0.914 0.000 1.000
#> SRR1812728 1 0.921 0.622 0.664 0.336
#> SRR1812724 1 0.985 0.508 0.572 0.428
#> SRR1812725 1 0.985 0.508 0.572 0.428
#> SRR1812723 2 0.000 0.914 0.000 1.000
#> SRR1812722 2 0.000 0.914 0.000 1.000
#> SRR1812721 2 0.000 0.914 0.000 1.000
#> SRR1812718 2 0.000 0.914 0.000 1.000
#> SRR1812717 2 0.000 0.914 0.000 1.000
#> SRR1812716 1 0.932 0.609 0.652 0.348
#> SRR1812715 2 0.000 0.914 0.000 1.000
#> SRR1812714 2 0.000 0.914 0.000 1.000
#> SRR1812719 1 0.000 0.816 1.000 0.000
#> SRR1812713 2 0.000 0.914 0.000 1.000
#> SRR1812712 2 0.000 0.914 0.000 1.000
#> SRR1812711 2 0.000 0.914 0.000 1.000
#> SRR1812710 2 0.000 0.914 0.000 1.000
#> SRR1812709 2 0.000 0.914 0.000 1.000
#> SRR1812708 2 0.985 0.338 0.428 0.572
#> SRR1812707 2 0.000 0.914 0.000 1.000
#> SRR1812705 2 0.000 0.914 0.000 1.000
#> SRR1812706 1 0.952 0.583 0.628 0.372
#> SRR1812704 1 0.985 0.508 0.572 0.428
#> SRR1812703 2 0.000 0.914 0.000 1.000
#> SRR1812702 1 0.706 0.735 0.808 0.192
#> SRR1812741 1 0.000 0.816 1.000 0.000
#> SRR1812740 1 0.000 0.816 1.000 0.000
#> SRR1812739 2 0.000 0.914 0.000 1.000
#> SRR1812738 1 0.985 0.508 0.572 0.428
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1812752 1 0.2537 0.791 0.920 0.000 0.080
#> SRR1812753 1 0.2537 0.791 0.920 0.000 0.080
#> SRR1812751 1 0.2711 0.805 0.912 0.088 0.000
#> SRR1812750 1 0.2711 0.805 0.912 0.088 0.000
#> SRR1812748 3 0.5403 0.704 0.124 0.060 0.816
#> SRR1812749 1 0.2711 0.805 0.912 0.088 0.000
#> SRR1812746 1 0.6295 0.139 0.528 0.000 0.472
#> SRR1812745 3 0.2066 0.766 0.060 0.000 0.940
#> SRR1812747 2 0.5024 0.773 0.004 0.776 0.220
#> SRR1812744 3 0.6111 0.383 0.396 0.000 0.604
#> SRR1812743 3 0.9794 0.198 0.380 0.236 0.384
#> SRR1812742 3 0.6111 0.388 0.396 0.000 0.604
#> SRR1812737 2 0.1163 0.849 0.028 0.972 0.000
#> SRR1812735 2 0.1031 0.852 0.000 0.976 0.024
#> SRR1812734 3 0.4974 0.599 0.236 0.000 0.764
#> SRR1812733 3 0.1643 0.777 0.000 0.044 0.956
#> SRR1812736 3 0.2165 0.765 0.064 0.000 0.936
#> SRR1812732 3 0.9263 0.449 0.220 0.252 0.528
#> SRR1812730 3 0.0237 0.778 0.004 0.000 0.996
#> SRR1812731 2 0.5414 0.721 0.212 0.772 0.016
#> SRR1812729 2 0.2796 0.844 0.000 0.908 0.092
#> SRR1812727 1 0.4121 0.735 0.832 0.000 0.168
#> SRR1812726 2 0.3500 0.836 0.004 0.880 0.116
#> SRR1812728 3 0.0661 0.777 0.008 0.004 0.988
#> SRR1812724 2 0.7001 0.606 0.084 0.716 0.200
#> SRR1812725 3 0.0892 0.771 0.000 0.020 0.980
#> SRR1812723 2 0.5024 0.773 0.004 0.776 0.220
#> SRR1812722 2 0.3644 0.833 0.004 0.872 0.124
#> SRR1812721 2 0.5292 0.711 0.228 0.764 0.008
#> SRR1812718 2 0.5024 0.773 0.004 0.776 0.220
#> SRR1812717 2 0.2165 0.840 0.064 0.936 0.000
#> SRR1812716 3 0.0475 0.778 0.004 0.004 0.992
#> SRR1812715 2 0.0000 0.851 0.000 1.000 0.000
#> SRR1812714 2 0.4527 0.812 0.088 0.860 0.052
#> SRR1812719 1 0.5706 0.529 0.680 0.000 0.320
#> SRR1812713 2 0.2866 0.834 0.076 0.916 0.008
#> SRR1812712 2 0.2866 0.834 0.076 0.916 0.008
#> SRR1812711 2 0.4978 0.777 0.004 0.780 0.216
#> SRR1812710 2 0.0000 0.851 0.000 1.000 0.000
#> SRR1812709 2 0.2866 0.834 0.076 0.916 0.008
#> SRR1812708 1 0.2796 0.803 0.908 0.092 0.000
#> SRR1812707 2 0.1163 0.849 0.028 0.972 0.000
#> SRR1812705 2 0.5070 0.769 0.004 0.772 0.224
#> SRR1812706 3 0.0475 0.778 0.004 0.004 0.992
#> SRR1812704 3 0.6678 0.639 0.064 0.208 0.728
#> SRR1812703 2 0.4821 0.809 0.088 0.848 0.064
#> SRR1812702 3 0.0475 0.778 0.004 0.004 0.992
#> SRR1812741 1 0.3983 0.631 0.852 0.144 0.004
#> SRR1812740 3 0.2443 0.776 0.028 0.032 0.940
#> SRR1812739 2 0.3461 0.827 0.076 0.900 0.024
#> SRR1812738 3 0.7458 0.590 0.088 0.236 0.676
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1812752 1 0.0000 0.9760 1.000 0.000 0.000 0.000
#> SRR1812753 1 0.0000 0.9760 1.000 0.000 0.000 0.000
#> SRR1812751 1 0.0188 0.9767 0.996 0.004 0.000 0.000
#> SRR1812750 1 0.0188 0.9767 0.996 0.004 0.000 0.000
#> SRR1812748 3 0.1824 0.7593 0.004 0.000 0.936 0.060
#> SRR1812749 1 0.0188 0.9767 0.996 0.004 0.000 0.000
#> SRR1812746 3 0.5039 0.3291 0.404 0.000 0.592 0.004
#> SRR1812745 3 0.1398 0.7644 0.004 0.000 0.956 0.040
#> SRR1812747 2 0.0000 0.8527 0.000 1.000 0.000 0.000
#> SRR1812744 3 0.5464 0.5696 0.064 0.000 0.708 0.228
#> SRR1812743 4 0.3450 0.6815 0.008 0.000 0.156 0.836
#> SRR1812742 3 0.6058 0.3813 0.060 0.000 0.604 0.336
#> SRR1812737 4 0.4994 0.0276 0.000 0.480 0.000 0.520
#> SRR1812735 2 0.3486 0.7201 0.000 0.812 0.000 0.188
#> SRR1812734 3 0.1938 0.7611 0.012 0.000 0.936 0.052
#> SRR1812733 3 0.2174 0.7615 0.000 0.020 0.928 0.052
#> SRR1812736 3 0.1661 0.7626 0.004 0.000 0.944 0.052
#> SRR1812732 4 0.4456 0.5205 0.004 0.000 0.280 0.716
#> SRR1812730 3 0.4595 0.7534 0.000 0.184 0.776 0.040
#> SRR1812731 4 0.1854 0.7738 0.008 0.024 0.020 0.948
#> SRR1812729 2 0.1792 0.8325 0.000 0.932 0.000 0.068
#> SRR1812727 1 0.0336 0.9722 0.992 0.000 0.008 0.000
#> SRR1812726 2 0.0469 0.8553 0.000 0.988 0.000 0.012
#> SRR1812728 3 0.5572 0.7029 0.008 0.260 0.692 0.040
#> SRR1812724 4 0.0188 0.7726 0.000 0.000 0.004 0.996
#> SRR1812725 3 0.5695 0.6120 0.000 0.336 0.624 0.040
#> SRR1812723 2 0.0336 0.8487 0.000 0.992 0.008 0.000
#> SRR1812722 2 0.0592 0.8552 0.000 0.984 0.000 0.016
#> SRR1812721 4 0.1890 0.7685 0.008 0.056 0.000 0.936
#> SRR1812718 2 0.0188 0.8510 0.000 0.996 0.004 0.000
#> SRR1812717 4 0.4830 0.3250 0.000 0.392 0.000 0.608
#> SRR1812716 3 0.4868 0.7423 0.000 0.212 0.748 0.040
#> SRR1812715 2 0.4331 0.5780 0.000 0.712 0.000 0.288
#> SRR1812714 2 0.2214 0.8337 0.044 0.928 0.000 0.028
#> SRR1812719 1 0.2714 0.8511 0.884 0.000 0.112 0.004
#> SRR1812713 4 0.4553 0.6710 0.000 0.180 0.040 0.780
#> SRR1812712 4 0.4553 0.6710 0.000 0.180 0.040 0.780
#> SRR1812711 2 0.0336 0.8550 0.000 0.992 0.000 0.008
#> SRR1812710 2 0.4331 0.5780 0.000 0.712 0.000 0.288
#> SRR1812709 4 0.3306 0.7148 0.000 0.156 0.004 0.840
#> SRR1812708 1 0.0336 0.9739 0.992 0.008 0.000 0.000
#> SRR1812707 2 0.4999 -0.0466 0.000 0.508 0.000 0.492
#> SRR1812705 2 0.0336 0.8487 0.000 0.992 0.008 0.000
#> SRR1812706 3 0.5090 0.7310 0.000 0.228 0.728 0.044
#> SRR1812704 4 0.4964 0.5482 0.000 0.028 0.256 0.716
#> SRR1812703 2 0.1598 0.8497 0.020 0.956 0.004 0.020
#> SRR1812702 3 0.4755 0.7490 0.000 0.200 0.760 0.040
#> SRR1812741 4 0.3638 0.7115 0.120 0.000 0.032 0.848
#> SRR1812740 3 0.1661 0.7626 0.004 0.000 0.944 0.052
#> SRR1812739 4 0.1706 0.7749 0.000 0.036 0.016 0.948
#> SRR1812738 4 0.1389 0.7667 0.000 0.000 0.048 0.952
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1812752 1 0.0000 0.966 1.000 0.000 0.000 0.000 0.000
#> SRR1812753 1 0.0000 0.966 1.000 0.000 0.000 0.000 0.000
#> SRR1812751 1 0.0000 0.966 1.000 0.000 0.000 0.000 0.000
#> SRR1812750 1 0.0000 0.966 1.000 0.000 0.000 0.000 0.000
#> SRR1812748 3 0.3109 0.742 0.000 0.000 0.800 0.000 0.200
#> SRR1812749 1 0.0000 0.966 1.000 0.000 0.000 0.000 0.000
#> SRR1812746 3 0.6394 0.370 0.344 0.000 0.476 0.000 0.180
#> SRR1812745 3 0.3395 0.729 0.000 0.000 0.764 0.000 0.236
#> SRR1812747 2 0.2813 0.837 0.000 0.832 0.000 0.000 0.168
#> SRR1812744 3 0.1369 0.716 0.008 0.008 0.956 0.000 0.028
#> SRR1812743 3 0.4331 0.122 0.000 0.004 0.596 0.400 0.000
#> SRR1812742 3 0.3607 0.623 0.008 0.000 0.820 0.144 0.028
#> SRR1812737 4 0.4268 0.223 0.000 0.444 0.000 0.556 0.000
#> SRR1812735 2 0.2806 0.764 0.000 0.844 0.000 0.152 0.004
#> SRR1812734 3 0.3489 0.741 0.004 0.004 0.784 0.000 0.208
#> SRR1812733 5 0.3281 0.778 0.000 0.000 0.092 0.060 0.848
#> SRR1812736 3 0.3336 0.733 0.000 0.000 0.772 0.000 0.228
#> SRR1812732 3 0.1965 0.660 0.000 0.000 0.904 0.096 0.000
#> SRR1812730 5 0.0609 0.860 0.000 0.000 0.020 0.000 0.980
#> SRR1812731 4 0.3160 0.669 0.000 0.004 0.188 0.808 0.000
#> SRR1812729 2 0.1661 0.854 0.000 0.940 0.000 0.036 0.024
#> SRR1812727 1 0.0968 0.953 0.972 0.012 0.004 0.000 0.012
#> SRR1812726 2 0.0963 0.863 0.000 0.964 0.000 0.000 0.036
#> SRR1812728 5 0.2499 0.857 0.004 0.052 0.008 0.028 0.908
#> SRR1812724 4 0.1956 0.708 0.000 0.008 0.076 0.916 0.000
#> SRR1812725 5 0.2124 0.829 0.000 0.096 0.000 0.004 0.900
#> SRR1812723 2 0.2471 0.846 0.000 0.864 0.000 0.000 0.136
#> SRR1812722 2 0.0963 0.863 0.000 0.964 0.000 0.000 0.036
#> SRR1812721 4 0.2514 0.721 0.000 0.044 0.060 0.896 0.000
#> SRR1812718 2 0.2690 0.841 0.000 0.844 0.000 0.000 0.156
#> SRR1812717 4 0.3796 0.524 0.000 0.300 0.000 0.700 0.000
#> SRR1812716 5 0.0693 0.866 0.000 0.008 0.012 0.000 0.980
#> SRR1812715 2 0.3612 0.597 0.000 0.732 0.000 0.268 0.000
#> SRR1812714 2 0.0693 0.852 0.008 0.980 0.000 0.012 0.000
#> SRR1812719 1 0.3352 0.759 0.800 0.004 0.004 0.000 0.192
#> SRR1812713 4 0.3944 0.625 0.000 0.052 0.000 0.788 0.160
#> SRR1812712 4 0.4010 0.622 0.000 0.056 0.000 0.784 0.160
#> SRR1812711 2 0.1270 0.862 0.000 0.948 0.000 0.000 0.052
#> SRR1812710 2 0.3661 0.591 0.000 0.724 0.000 0.276 0.000
#> SRR1812709 4 0.1638 0.721 0.000 0.064 0.000 0.932 0.004
#> SRR1812708 1 0.0324 0.963 0.992 0.004 0.004 0.000 0.000
#> SRR1812707 4 0.4297 0.134 0.000 0.472 0.000 0.528 0.000
#> SRR1812705 2 0.2690 0.837 0.000 0.844 0.000 0.000 0.156
#> SRR1812706 5 0.2067 0.858 0.000 0.032 0.000 0.048 0.920
#> SRR1812704 5 0.4807 0.466 0.000 0.020 0.008 0.340 0.632
#> SRR1812703 2 0.2654 0.823 0.016 0.904 0.004 0.032 0.044
#> SRR1812702 5 0.0566 0.864 0.000 0.004 0.012 0.000 0.984
#> SRR1812741 4 0.5439 0.501 0.076 0.008 0.276 0.640 0.000
#> SRR1812740 3 0.3395 0.729 0.000 0.000 0.764 0.000 0.236
#> SRR1812739 4 0.3170 0.702 0.000 0.016 0.120 0.852 0.012
#> SRR1812738 4 0.4033 0.637 0.000 0.004 0.212 0.760 0.024
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1812752 1 0.0551 0.921 0.984 0.000 0.000 0.004 0.008 0.004
#> SRR1812753 1 0.0665 0.920 0.980 0.000 0.000 0.004 0.008 0.008
#> SRR1812751 1 0.0000 0.923 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812750 1 0.0000 0.923 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812748 3 0.1003 0.866 0.000 0.000 0.964 0.000 0.016 0.020
#> SRR1812749 1 0.0000 0.923 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812746 3 0.3633 0.599 0.252 0.000 0.732 0.000 0.012 0.004
#> SRR1812745 3 0.0937 0.863 0.000 0.000 0.960 0.000 0.040 0.000
#> SRR1812747 2 0.3745 0.775 0.000 0.796 0.000 0.028 0.144 0.032
#> SRR1812744 3 0.3954 0.608 0.008 0.008 0.764 0.012 0.012 0.196
#> SRR1812743 6 0.3125 0.613 0.000 0.000 0.084 0.080 0.000 0.836
#> SRR1812742 6 0.4490 0.356 0.000 0.000 0.372 0.008 0.024 0.596
#> SRR1812737 4 0.4344 0.275 0.000 0.336 0.000 0.628 0.000 0.036
#> SRR1812735 2 0.3652 0.628 0.000 0.720 0.000 0.264 0.000 0.016
#> SRR1812734 3 0.0653 0.852 0.000 0.004 0.980 0.000 0.004 0.012
#> SRR1812733 5 0.6557 0.454 0.000 0.000 0.264 0.156 0.508 0.072
#> SRR1812736 3 0.0972 0.868 0.000 0.000 0.964 0.000 0.028 0.008
#> SRR1812732 6 0.4274 0.242 0.000 0.000 0.432 0.012 0.004 0.552
#> SRR1812730 5 0.2714 0.806 0.000 0.004 0.136 0.000 0.848 0.012
#> SRR1812731 6 0.3482 0.325 0.000 0.000 0.000 0.316 0.000 0.684
#> SRR1812729 2 0.3394 0.779 0.000 0.832 0.000 0.104 0.036 0.028
#> SRR1812727 1 0.3164 0.857 0.868 0.004 0.028 0.008 0.048 0.044
#> SRR1812726 2 0.1622 0.794 0.000 0.940 0.000 0.016 0.028 0.016
#> SRR1812728 5 0.3195 0.790 0.000 0.048 0.044 0.004 0.860 0.044
#> SRR1812724 4 0.4338 -0.034 0.000 0.000 0.000 0.492 0.020 0.488
#> SRR1812725 5 0.3356 0.798 0.000 0.076 0.044 0.008 0.848 0.024
#> SRR1812723 2 0.2553 0.778 0.000 0.848 0.000 0.000 0.144 0.008
#> SRR1812722 2 0.2056 0.782 0.000 0.904 0.000 0.080 0.012 0.004
#> SRR1812721 4 0.4599 0.222 0.000 0.016 0.000 0.556 0.016 0.412
#> SRR1812718 2 0.3525 0.770 0.000 0.800 0.000 0.012 0.156 0.032
#> SRR1812717 4 0.4038 0.542 0.000 0.156 0.000 0.764 0.008 0.072
#> SRR1812716 5 0.2163 0.823 0.000 0.000 0.092 0.000 0.892 0.016
#> SRR1812715 2 0.4493 0.460 0.000 0.612 0.000 0.344 0.000 0.044
#> SRR1812714 2 0.2325 0.777 0.012 0.916 0.016 0.028 0.008 0.020
#> SRR1812719 1 0.5718 0.485 0.600 0.004 0.056 0.008 0.288 0.044
#> SRR1812713 4 0.2390 0.565 0.000 0.000 0.000 0.888 0.056 0.056
#> SRR1812712 4 0.2046 0.568 0.000 0.000 0.000 0.908 0.060 0.032
#> SRR1812711 2 0.1511 0.795 0.000 0.940 0.000 0.004 0.044 0.012
#> SRR1812710 2 0.4047 0.439 0.000 0.604 0.000 0.384 0.000 0.012
#> SRR1812709 4 0.2122 0.566 0.000 0.000 0.000 0.900 0.024 0.076
#> SRR1812708 1 0.0291 0.921 0.992 0.004 0.000 0.000 0.000 0.004
#> SRR1812707 4 0.4167 0.201 0.000 0.368 0.000 0.612 0.000 0.020
#> SRR1812705 2 0.3309 0.758 0.000 0.800 0.000 0.004 0.172 0.024
#> SRR1812706 5 0.3658 0.807 0.000 0.044 0.052 0.056 0.836 0.012
#> SRR1812704 5 0.4581 0.558 0.000 0.000 0.004 0.256 0.672 0.068
#> SRR1812703 2 0.4719 0.683 0.020 0.780 0.028 0.092 0.052 0.028
#> SRR1812702 5 0.2476 0.823 0.000 0.012 0.096 0.000 0.880 0.012
#> SRR1812741 6 0.3119 0.592 0.036 0.000 0.032 0.076 0.000 0.856
#> SRR1812740 3 0.1049 0.867 0.000 0.000 0.960 0.000 0.032 0.008
#> SRR1812739 4 0.4327 0.169 0.000 0.004 0.008 0.596 0.008 0.384
#> SRR1812738 6 0.4817 0.344 0.000 0.000 0.032 0.292 0.032 0.644
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 14626 rows and 51 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 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 0.433 0.836 0.867 0.4524 0.492 0.492
#> 3 3 0.715 0.846 0.934 0.3197 0.704 0.507
#> 4 4 0.822 0.880 0.949 0.1541 0.815 0.596
#> 5 5 0.870 0.876 0.946 0.1248 0.887 0.656
#> 6 6 0.872 0.845 0.932 0.0307 0.975 0.889
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
#> SRR1812752 1 0.722 0.7383 0.800 0.200
#> SRR1812753 1 0.722 0.7383 0.800 0.200
#> SRR1812751 2 0.541 0.5925 0.124 0.876
#> SRR1812750 2 0.184 0.6948 0.028 0.972
#> SRR1812748 1 0.000 0.8866 1.000 0.000
#> SRR1812749 1 0.855 0.7268 0.720 0.280
#> SRR1812746 1 0.722 0.7383 0.800 0.200
#> SRR1812745 1 0.000 0.8866 1.000 0.000
#> SRR1812747 2 0.722 0.9419 0.200 0.800
#> SRR1812744 1 0.358 0.8410 0.932 0.068
#> SRR1812743 2 0.722 0.9419 0.200 0.800
#> SRR1812742 2 0.722 0.9419 0.200 0.800
#> SRR1812737 2 0.722 0.9419 0.200 0.800
#> SRR1812735 2 0.722 0.9419 0.200 0.800
#> SRR1812734 1 0.000 0.8866 1.000 0.000
#> SRR1812733 1 0.000 0.8866 1.000 0.000
#> SRR1812736 1 0.000 0.8866 1.000 0.000
#> SRR1812732 2 0.722 0.9419 0.200 0.800
#> SRR1812730 1 0.000 0.8866 1.000 0.000
#> SRR1812731 2 0.722 0.9419 0.200 0.800
#> SRR1812729 2 0.722 0.9419 0.200 0.800
#> SRR1812727 1 0.000 0.8866 1.000 0.000
#> SRR1812726 1 0.416 0.8277 0.916 0.084
#> SRR1812728 1 0.000 0.8866 1.000 0.000
#> SRR1812724 2 0.722 0.9419 0.200 0.800
#> SRR1812725 1 0.000 0.8866 1.000 0.000
#> SRR1812723 1 0.402 0.8309 0.920 0.080
#> SRR1812722 2 0.722 0.9419 0.200 0.800
#> SRR1812721 1 0.697 0.6818 0.812 0.188
#> SRR1812718 2 0.722 0.9419 0.200 0.800
#> SRR1812717 2 0.722 0.9419 0.200 0.800
#> SRR1812716 1 0.000 0.8866 1.000 0.000
#> SRR1812715 2 0.722 0.9419 0.200 0.800
#> SRR1812714 2 0.722 0.9419 0.200 0.800
#> SRR1812719 1 0.000 0.8866 1.000 0.000
#> SRR1812713 2 0.833 0.8737 0.264 0.736
#> SRR1812712 1 0.971 -0.0634 0.600 0.400
#> SRR1812711 2 0.722 0.9419 0.200 0.800
#> SRR1812710 2 0.722 0.9419 0.200 0.800
#> SRR1812709 2 0.969 0.6378 0.396 0.604
#> SRR1812708 1 0.855 0.7268 0.720 0.280
#> SRR1812707 2 0.722 0.9419 0.200 0.800
#> SRR1812705 1 0.402 0.8309 0.920 0.080
#> SRR1812706 1 0.000 0.8866 1.000 0.000
#> SRR1812704 1 0.000 0.8866 1.000 0.000
#> SRR1812703 2 0.722 0.9419 0.200 0.800
#> SRR1812702 1 0.000 0.8866 1.000 0.000
#> SRR1812741 2 0.987 0.5501 0.432 0.568
#> SRR1812740 1 0.000 0.8866 1.000 0.000
#> SRR1812739 2 0.722 0.9419 0.200 0.800
#> SRR1812738 1 0.850 0.4907 0.724 0.276
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1812752 1 0.0000 1.000 1.000 0.000 0.000
#> SRR1812753 1 0.0000 1.000 1.000 0.000 0.000
#> SRR1812751 1 0.0000 1.000 1.000 0.000 0.000
#> SRR1812750 1 0.0000 1.000 1.000 0.000 0.000
#> SRR1812748 3 0.2959 0.833 0.000 0.100 0.900
#> SRR1812749 1 0.0000 1.000 1.000 0.000 0.000
#> SRR1812746 3 0.2878 0.851 0.096 0.000 0.904
#> SRR1812745 3 0.0000 0.950 0.000 0.000 1.000
#> SRR1812747 2 0.0000 0.881 0.000 1.000 0.000
#> SRR1812744 3 0.6168 0.125 0.000 0.412 0.588
#> SRR1812743 2 0.0000 0.881 0.000 1.000 0.000
#> SRR1812742 2 0.4555 0.759 0.000 0.800 0.200
#> SRR1812737 2 0.0000 0.881 0.000 1.000 0.000
#> SRR1812735 2 0.0000 0.881 0.000 1.000 0.000
#> SRR1812734 3 0.0000 0.950 0.000 0.000 1.000
#> SRR1812733 3 0.0000 0.950 0.000 0.000 1.000
#> SRR1812736 3 0.0000 0.950 0.000 0.000 1.000
#> SRR1812732 2 0.0000 0.881 0.000 1.000 0.000
#> SRR1812730 3 0.0000 0.950 0.000 0.000 1.000
#> SRR1812731 2 0.0000 0.881 0.000 1.000 0.000
#> SRR1812729 2 0.0747 0.877 0.000 0.984 0.016
#> SRR1812727 3 0.0000 0.950 0.000 0.000 1.000
#> SRR1812726 2 0.6154 0.426 0.000 0.592 0.408
#> SRR1812728 3 0.0000 0.950 0.000 0.000 1.000
#> SRR1812724 2 0.0000 0.881 0.000 1.000 0.000
#> SRR1812725 3 0.0000 0.950 0.000 0.000 1.000
#> SRR1812723 2 0.6180 0.407 0.000 0.584 0.416
#> SRR1812722 2 0.1753 0.864 0.000 0.952 0.048
#> SRR1812721 2 0.3116 0.823 0.000 0.892 0.108
#> SRR1812718 2 0.4178 0.786 0.000 0.828 0.172
#> SRR1812717 2 0.0000 0.881 0.000 1.000 0.000
#> SRR1812716 3 0.0000 0.950 0.000 0.000 1.000
#> SRR1812715 2 0.0000 0.881 0.000 1.000 0.000
#> SRR1812714 2 0.0000 0.881 0.000 1.000 0.000
#> SRR1812719 3 0.0000 0.950 0.000 0.000 1.000
#> SRR1812713 2 0.4887 0.668 0.000 0.772 0.228
#> SRR1812712 2 0.6062 0.354 0.000 0.616 0.384
#> SRR1812711 2 0.4504 0.763 0.000 0.804 0.196
#> SRR1812710 2 0.0000 0.881 0.000 1.000 0.000
#> SRR1812709 2 0.0000 0.881 0.000 1.000 0.000
#> SRR1812708 1 0.0000 1.000 1.000 0.000 0.000
#> SRR1812707 2 0.0000 0.881 0.000 1.000 0.000
#> SRR1812705 2 0.6154 0.426 0.000 0.592 0.408
#> SRR1812706 3 0.0000 0.950 0.000 0.000 1.000
#> SRR1812704 3 0.0000 0.950 0.000 0.000 1.000
#> SRR1812703 2 0.3551 0.818 0.000 0.868 0.132
#> SRR1812702 3 0.0000 0.950 0.000 0.000 1.000
#> SRR1812741 2 0.0000 0.881 0.000 1.000 0.000
#> SRR1812740 3 0.0000 0.950 0.000 0.000 1.000
#> SRR1812739 2 0.0000 0.881 0.000 1.000 0.000
#> SRR1812738 2 0.0892 0.875 0.000 0.980 0.020
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1812752 1 0.0000 1.000 1 0.000 0.000 0.000
#> SRR1812753 1 0.0000 1.000 1 0.000 0.000 0.000
#> SRR1812751 1 0.0000 1.000 1 0.000 0.000 0.000
#> SRR1812750 1 0.0000 1.000 1 0.000 0.000 0.000
#> SRR1812748 3 0.0000 1.000 0 0.000 1.000 0.000
#> SRR1812749 1 0.0000 1.000 1 0.000 0.000 0.000
#> SRR1812746 3 0.0000 1.000 0 0.000 1.000 0.000
#> SRR1812745 3 0.0000 1.000 0 0.000 1.000 0.000
#> SRR1812747 2 0.0000 0.908 0 1.000 0.000 0.000
#> SRR1812744 4 0.0469 0.920 0 0.012 0.000 0.988
#> SRR1812743 2 0.0000 0.908 0 1.000 0.000 0.000
#> SRR1812742 2 0.4701 0.729 0 0.780 0.164 0.056
#> SRR1812737 2 0.0000 0.908 0 1.000 0.000 0.000
#> SRR1812735 2 0.0000 0.908 0 1.000 0.000 0.000
#> SRR1812734 3 0.0000 1.000 0 0.000 1.000 0.000
#> SRR1812733 4 0.2973 0.798 0 0.000 0.144 0.856
#> SRR1812736 3 0.0000 1.000 0 0.000 1.000 0.000
#> SRR1812732 2 0.0000 0.908 0 1.000 0.000 0.000
#> SRR1812730 4 0.0000 0.929 0 0.000 0.000 1.000
#> SRR1812731 2 0.0000 0.908 0 1.000 0.000 0.000
#> SRR1812729 2 0.0592 0.902 0 0.984 0.000 0.016
#> SRR1812727 4 0.0000 0.929 0 0.000 0.000 1.000
#> SRR1812726 4 0.0188 0.926 0 0.004 0.000 0.996
#> SRR1812728 4 0.0000 0.929 0 0.000 0.000 1.000
#> SRR1812724 2 0.0000 0.908 0 1.000 0.000 0.000
#> SRR1812725 4 0.0000 0.929 0 0.000 0.000 1.000
#> SRR1812723 4 0.0000 0.929 0 0.000 0.000 1.000
#> SRR1812722 2 0.1389 0.884 0 0.952 0.000 0.048
#> SRR1812721 4 0.4454 0.551 0 0.308 0.000 0.692
#> SRR1812718 2 0.3311 0.785 0 0.828 0.000 0.172
#> SRR1812717 2 0.0000 0.908 0 1.000 0.000 0.000
#> SRR1812716 4 0.0000 0.929 0 0.000 0.000 1.000
#> SRR1812715 2 0.0000 0.908 0 1.000 0.000 0.000
#> SRR1812714 2 0.0000 0.908 0 1.000 0.000 0.000
#> SRR1812719 4 0.0000 0.929 0 0.000 0.000 1.000
#> SRR1812713 2 0.0469 0.902 0 0.988 0.000 0.012
#> SRR1812712 2 0.4843 0.323 0 0.604 0.000 0.396
#> SRR1812711 2 0.3569 0.756 0 0.804 0.000 0.196
#> SRR1812710 2 0.0000 0.908 0 1.000 0.000 0.000
#> SRR1812709 2 0.4072 0.647 0 0.748 0.000 0.252
#> SRR1812708 1 0.0000 1.000 1 0.000 0.000 0.000
#> SRR1812707 2 0.0000 0.908 0 1.000 0.000 0.000
#> SRR1812705 4 0.0000 0.929 0 0.000 0.000 1.000
#> SRR1812706 4 0.0000 0.929 0 0.000 0.000 1.000
#> SRR1812704 4 0.0000 0.929 0 0.000 0.000 1.000
#> SRR1812703 2 0.2814 0.823 0 0.868 0.000 0.132
#> SRR1812702 4 0.0000 0.929 0 0.000 0.000 1.000
#> SRR1812741 2 0.4356 0.575 0 0.708 0.000 0.292
#> SRR1812740 3 0.0000 1.000 0 0.000 1.000 0.000
#> SRR1812739 2 0.0000 0.908 0 1.000 0.000 0.000
#> SRR1812738 4 0.4843 0.344 0 0.396 0.000 0.604
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1812752 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> SRR1812753 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> SRR1812751 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> SRR1812750 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> SRR1812748 3 0.0000 1.000 0 0.000 1.000 0.000 0.000
#> SRR1812749 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> SRR1812746 3 0.0000 1.000 0 0.000 1.000 0.000 0.000
#> SRR1812745 3 0.0000 1.000 0 0.000 1.000 0.000 0.000
#> SRR1812747 2 0.0000 0.906 0 1.000 0.000 0.000 0.000
#> SRR1812744 5 0.0404 0.926 0 0.012 0.000 0.000 0.988
#> SRR1812743 2 0.0000 0.906 0 1.000 0.000 0.000 0.000
#> SRR1812742 2 0.4272 0.724 0 0.752 0.196 0.000 0.052
#> SRR1812737 2 0.3074 0.767 0 0.804 0.000 0.196 0.000
#> SRR1812735 2 0.0000 0.906 0 1.000 0.000 0.000 0.000
#> SRR1812734 3 0.0000 1.000 0 0.000 1.000 0.000 0.000
#> SRR1812733 4 0.0510 0.870 0 0.000 0.000 0.984 0.016
#> SRR1812736 3 0.0000 1.000 0 0.000 1.000 0.000 0.000
#> SRR1812732 2 0.0000 0.906 0 1.000 0.000 0.000 0.000
#> SRR1812730 5 0.0000 0.935 0 0.000 0.000 0.000 1.000
#> SRR1812731 2 0.0290 0.904 0 0.992 0.000 0.008 0.000
#> SRR1812729 2 0.1331 0.889 0 0.952 0.000 0.040 0.008
#> SRR1812727 5 0.0000 0.935 0 0.000 0.000 0.000 1.000
#> SRR1812726 5 0.0162 0.932 0 0.004 0.000 0.000 0.996
#> SRR1812728 5 0.0000 0.935 0 0.000 0.000 0.000 1.000
#> SRR1812724 4 0.4182 0.360 0 0.400 0.000 0.600 0.000
#> SRR1812725 5 0.0000 0.935 0 0.000 0.000 0.000 1.000
#> SRR1812723 5 0.0000 0.935 0 0.000 0.000 0.000 1.000
#> SRR1812722 2 0.1197 0.887 0 0.952 0.000 0.000 0.048
#> SRR1812721 4 0.0000 0.875 0 0.000 0.000 1.000 0.000
#> SRR1812718 2 0.2852 0.793 0 0.828 0.000 0.000 0.172
#> SRR1812717 2 0.0000 0.906 0 1.000 0.000 0.000 0.000
#> SRR1812716 5 0.0000 0.935 0 0.000 0.000 0.000 1.000
#> SRR1812715 2 0.0000 0.906 0 1.000 0.000 0.000 0.000
#> SRR1812714 2 0.0000 0.906 0 1.000 0.000 0.000 0.000
#> SRR1812719 5 0.0000 0.935 0 0.000 0.000 0.000 1.000
#> SRR1812713 4 0.0000 0.875 0 0.000 0.000 1.000 0.000
#> SRR1812712 4 0.0000 0.875 0 0.000 0.000 1.000 0.000
#> SRR1812711 2 0.3074 0.768 0 0.804 0.000 0.000 0.196
#> SRR1812710 2 0.0404 0.904 0 0.988 0.000 0.012 0.000
#> SRR1812709 4 0.0000 0.875 0 0.000 0.000 1.000 0.000
#> SRR1812708 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> SRR1812707 2 0.3109 0.763 0 0.800 0.000 0.200 0.000
#> SRR1812705 5 0.0000 0.935 0 0.000 0.000 0.000 1.000
#> SRR1812706 4 0.3561 0.617 0 0.000 0.000 0.740 0.260
#> SRR1812704 5 0.3424 0.652 0 0.000 0.000 0.240 0.760
#> SRR1812703 4 0.0404 0.872 0 0.000 0.000 0.988 0.012
#> SRR1812702 5 0.0000 0.935 0 0.000 0.000 0.000 1.000
#> SRR1812741 2 0.3752 0.547 0 0.708 0.000 0.000 0.292
#> SRR1812740 3 0.0000 1.000 0 0.000 1.000 0.000 0.000
#> SRR1812739 2 0.0000 0.906 0 1.000 0.000 0.000 0.000
#> SRR1812738 5 0.4171 0.354 0 0.396 0.000 0.000 0.604
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1812752 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> SRR1812753 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> SRR1812751 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> SRR1812750 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> SRR1812748 3 0.0632 0.965 0 0.000 0.976 0.000 0.000 0.024
#> SRR1812749 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> SRR1812746 3 0.1814 0.896 0 0.000 0.900 0.000 0.000 0.100
#> SRR1812745 3 0.0000 0.968 0 0.000 1.000 0.000 0.000 0.000
#> SRR1812747 2 0.1500 0.869 0 0.936 0.000 0.000 0.012 0.052
#> SRR1812744 5 0.1003 0.893 0 0.020 0.000 0.000 0.964 0.016
#> SRR1812743 6 0.2793 0.697 0 0.200 0.000 0.000 0.000 0.800
#> SRR1812742 6 0.3332 0.649 0 0.000 0.144 0.000 0.048 0.808
#> SRR1812737 2 0.2762 0.747 0 0.804 0.000 0.196 0.000 0.000
#> SRR1812735 2 0.0000 0.887 0 1.000 0.000 0.000 0.000 0.000
#> SRR1812734 3 0.0363 0.964 0 0.000 0.988 0.000 0.000 0.012
#> SRR1812733 4 0.0458 0.849 0 0.000 0.000 0.984 0.016 0.000
#> SRR1812736 3 0.0146 0.968 0 0.000 0.996 0.000 0.000 0.004
#> SRR1812732 2 0.0000 0.887 0 1.000 0.000 0.000 0.000 0.000
#> SRR1812730 5 0.0000 0.908 0 0.000 0.000 0.000 1.000 0.000
#> SRR1812731 2 0.0260 0.887 0 0.992 0.000 0.008 0.000 0.000
#> SRR1812729 2 0.2342 0.858 0 0.904 0.000 0.032 0.024 0.040
#> SRR1812727 5 0.0632 0.901 0 0.000 0.000 0.000 0.976 0.024
#> SRR1812726 5 0.1349 0.887 0 0.004 0.000 0.000 0.940 0.056
#> SRR1812728 5 0.0000 0.908 0 0.000 0.000 0.000 1.000 0.000
#> SRR1812724 4 0.3756 0.276 0 0.400 0.000 0.600 0.000 0.000
#> SRR1812725 5 0.0146 0.908 0 0.000 0.000 0.000 0.996 0.004
#> SRR1812723 5 0.1204 0.890 0 0.000 0.000 0.000 0.944 0.056
#> SRR1812722 2 0.1285 0.870 0 0.944 0.000 0.000 0.052 0.004
#> SRR1812721 4 0.0000 0.856 0 0.000 0.000 1.000 0.000 0.000
#> SRR1812718 2 0.3254 0.776 0 0.820 0.000 0.000 0.124 0.056
#> SRR1812717 2 0.0000 0.887 0 1.000 0.000 0.000 0.000 0.000
#> SRR1812716 5 0.0146 0.908 0 0.000 0.000 0.000 0.996 0.004
#> SRR1812715 2 0.0000 0.887 0 1.000 0.000 0.000 0.000 0.000
#> SRR1812714 2 0.0000 0.887 0 1.000 0.000 0.000 0.000 0.000
#> SRR1812719 5 0.0547 0.903 0 0.000 0.000 0.000 0.980 0.020
#> SRR1812713 4 0.0000 0.856 0 0.000 0.000 1.000 0.000 0.000
#> SRR1812712 4 0.0000 0.856 0 0.000 0.000 1.000 0.000 0.000
#> SRR1812711 2 0.3394 0.756 0 0.804 0.000 0.000 0.144 0.052
#> SRR1812710 2 0.0363 0.886 0 0.988 0.000 0.012 0.000 0.000
#> SRR1812709 4 0.0000 0.856 0 0.000 0.000 1.000 0.000 0.000
#> SRR1812708 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> SRR1812707 2 0.2793 0.742 0 0.800 0.000 0.200 0.000 0.000
#> SRR1812705 5 0.1204 0.890 0 0.000 0.000 0.000 0.944 0.056
#> SRR1812706 4 0.3470 0.555 0 0.000 0.000 0.740 0.248 0.012
#> SRR1812704 5 0.3076 0.655 0 0.000 0.000 0.240 0.760 0.000
#> SRR1812703 4 0.0363 0.852 0 0.000 0.000 0.988 0.012 0.000
#> SRR1812702 5 0.0000 0.908 0 0.000 0.000 0.000 1.000 0.000
#> SRR1812741 2 0.3371 0.477 0 0.708 0.000 0.000 0.292 0.000
#> SRR1812740 3 0.0632 0.965 0 0.000 0.976 0.000 0.000 0.024
#> SRR1812739 2 0.0000 0.887 0 1.000 0.000 0.000 0.000 0.000
#> SRR1812738 5 0.3747 0.330 0 0.396 0.000 0.000 0.604 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 14626 rows and 51 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 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 0.759 0.938 0.964 0.3308 0.678 0.678
#> 3 3 0.434 0.588 0.799 0.6428 0.730 0.630
#> 4 4 0.497 0.518 0.746 0.1570 0.899 0.806
#> 5 5 0.481 0.647 0.750 0.1220 0.736 0.454
#> 6 6 0.624 0.677 0.779 0.0959 0.970 0.890
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
#> SRR1812752 1 0.0000 0.940 1.000 0.000
#> SRR1812753 1 0.0000 0.940 1.000 0.000
#> SRR1812751 1 0.0000 0.940 1.000 0.000
#> SRR1812750 1 0.0000 0.940 1.000 0.000
#> SRR1812748 2 0.5408 0.887 0.124 0.876
#> SRR1812749 1 0.0000 0.940 1.000 0.000
#> SRR1812746 1 0.4431 0.912 0.908 0.092
#> SRR1812745 2 0.6247 0.852 0.156 0.844
#> SRR1812747 2 0.0000 0.964 0.000 1.000
#> SRR1812744 2 0.3274 0.934 0.060 0.940
#> SRR1812743 2 0.5178 0.894 0.116 0.884
#> SRR1812742 2 0.5408 0.887 0.124 0.876
#> SRR1812737 2 0.0000 0.964 0.000 1.000
#> SRR1812735 2 0.0000 0.964 0.000 1.000
#> SRR1812734 1 0.7453 0.757 0.788 0.212
#> SRR1812733 2 0.4562 0.910 0.096 0.904
#> SRR1812736 2 0.6623 0.832 0.172 0.828
#> SRR1812732 2 0.0376 0.963 0.004 0.996
#> SRR1812730 2 0.0672 0.962 0.008 0.992
#> SRR1812731 2 0.0376 0.963 0.004 0.996
#> SRR1812729 2 0.0000 0.964 0.000 1.000
#> SRR1812727 1 0.3431 0.928 0.936 0.064
#> SRR1812726 2 0.0000 0.964 0.000 1.000
#> SRR1812728 2 0.0000 0.964 0.000 1.000
#> SRR1812724 2 0.0376 0.963 0.004 0.996
#> SRR1812725 2 0.0000 0.964 0.000 1.000
#> SRR1812723 2 0.0000 0.964 0.000 1.000
#> SRR1812722 2 0.0000 0.964 0.000 1.000
#> SRR1812721 2 0.2423 0.946 0.040 0.960
#> SRR1812718 2 0.0000 0.964 0.000 1.000
#> SRR1812717 2 0.0000 0.964 0.000 1.000
#> SRR1812716 2 0.0376 0.963 0.004 0.996
#> SRR1812715 2 0.0000 0.964 0.000 1.000
#> SRR1812714 2 0.2603 0.944 0.044 0.956
#> SRR1812719 1 0.4690 0.905 0.900 0.100
#> SRR1812713 2 0.4939 0.899 0.108 0.892
#> SRR1812712 2 0.0000 0.964 0.000 1.000
#> SRR1812711 2 0.0000 0.964 0.000 1.000
#> SRR1812710 2 0.0000 0.964 0.000 1.000
#> SRR1812709 2 0.0000 0.964 0.000 1.000
#> SRR1812708 1 0.2236 0.937 0.964 0.036
#> SRR1812707 2 0.0000 0.964 0.000 1.000
#> SRR1812705 2 0.0000 0.964 0.000 1.000
#> SRR1812706 2 0.0376 0.963 0.004 0.996
#> SRR1812704 2 0.0000 0.964 0.000 1.000
#> SRR1812703 2 0.0000 0.964 0.000 1.000
#> SRR1812702 2 0.2423 0.946 0.040 0.960
#> SRR1812741 2 0.5408 0.887 0.124 0.876
#> SRR1812740 2 0.5408 0.887 0.124 0.876
#> SRR1812739 2 0.0000 0.964 0.000 1.000
#> SRR1812738 2 0.0000 0.964 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1812752 3 0.6309 -0.172 0.500 0.000 0.500
#> SRR1812753 3 0.6309 -0.172 0.500 0.000 0.500
#> SRR1812751 1 0.6309 -0.434 0.500 0.000 0.500
#> SRR1812750 3 0.6309 -0.172 0.500 0.000 0.500
#> SRR1812748 3 0.7983 0.362 0.264 0.104 0.632
#> SRR1812749 3 0.6309 -0.172 0.500 0.000 0.500
#> SRR1812746 3 0.0424 0.407 0.000 0.008 0.992
#> SRR1812745 3 0.8950 0.243 0.212 0.220 0.568
#> SRR1812747 2 0.0000 0.876 0.000 1.000 0.000
#> SRR1812744 1 0.9996 -0.302 0.348 0.328 0.324
#> SRR1812743 3 0.8995 0.173 0.372 0.136 0.492
#> SRR1812742 3 0.8853 0.310 0.252 0.176 0.572
#> SRR1812737 2 0.3941 0.845 0.156 0.844 0.000
#> SRR1812735 2 0.2537 0.860 0.080 0.920 0.000
#> SRR1812734 3 0.1453 0.410 0.024 0.008 0.968
#> SRR1812733 2 0.2527 0.866 0.020 0.936 0.044
#> SRR1812736 3 0.8113 0.367 0.212 0.144 0.644
#> SRR1812732 2 0.6228 0.527 0.372 0.624 0.004
#> SRR1812730 2 0.6056 0.640 0.032 0.744 0.224
#> SRR1812731 2 0.6652 0.773 0.172 0.744 0.084
#> SRR1812729 2 0.0000 0.876 0.000 1.000 0.000
#> SRR1812727 3 0.2599 0.396 0.016 0.052 0.932
#> SRR1812726 2 0.1015 0.872 0.008 0.980 0.012
#> SRR1812728 2 0.2269 0.871 0.040 0.944 0.016
#> SRR1812724 2 0.6138 0.797 0.172 0.768 0.060
#> SRR1812725 2 0.1289 0.875 0.032 0.968 0.000
#> SRR1812723 2 0.1774 0.866 0.024 0.960 0.016
#> SRR1812722 2 0.0237 0.876 0.004 0.996 0.000
#> SRR1812721 2 0.7657 0.635 0.116 0.676 0.208
#> SRR1812718 2 0.0237 0.876 0.004 0.996 0.000
#> SRR1812717 2 0.3116 0.859 0.108 0.892 0.000
#> SRR1812716 2 0.1525 0.874 0.032 0.964 0.004
#> SRR1812715 2 0.3941 0.845 0.156 0.844 0.000
#> SRR1812714 2 0.5731 0.807 0.108 0.804 0.088
#> SRR1812719 3 0.2599 0.396 0.016 0.052 0.932
#> SRR1812713 2 0.4121 0.837 0.168 0.832 0.000
#> SRR1812712 2 0.2711 0.865 0.088 0.912 0.000
#> SRR1812711 2 0.1905 0.865 0.028 0.956 0.016
#> SRR1812710 2 0.3941 0.845 0.156 0.844 0.000
#> SRR1812709 2 0.2711 0.863 0.088 0.912 0.000
#> SRR1812708 3 0.2651 0.383 0.060 0.012 0.928
#> SRR1812707 2 0.3941 0.845 0.156 0.844 0.000
#> SRR1812705 2 0.0592 0.874 0.012 0.988 0.000
#> SRR1812706 2 0.1525 0.874 0.032 0.964 0.004
#> SRR1812704 2 0.1529 0.878 0.040 0.960 0.000
#> SRR1812703 2 0.3434 0.838 0.032 0.904 0.064
#> SRR1812702 2 0.4662 0.784 0.032 0.844 0.124
#> SRR1812741 3 0.8107 0.241 0.424 0.068 0.508
#> SRR1812740 3 0.8399 0.351 0.220 0.160 0.620
#> SRR1812739 2 0.4178 0.834 0.172 0.828 0.000
#> SRR1812738 2 0.4121 0.837 0.168 0.832 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1812752 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> SRR1812753 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> SRR1812751 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> SRR1812750 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> SRR1812748 3 0.6832 0.4243 0.000 0.132 0.572 0.296
#> SRR1812749 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> SRR1812746 3 0.5364 0.4584 0.016 0.000 0.592 0.392
#> SRR1812745 3 0.7450 0.2326 0.000 0.228 0.508 0.264
#> SRR1812747 2 0.4830 0.6856 0.000 0.608 0.392 0.000
#> SRR1812744 4 0.6471 0.0501 0.000 0.416 0.072 0.512
#> SRR1812743 4 0.3266 0.4512 0.000 0.168 0.000 0.832
#> SRR1812742 4 0.3658 0.3888 0.000 0.020 0.144 0.836
#> SRR1812737 2 0.0188 0.5640 0.000 0.996 0.004 0.000
#> SRR1812735 2 0.2888 0.6105 0.000 0.872 0.124 0.004
#> SRR1812734 3 0.4804 0.4712 0.000 0.000 0.616 0.384
#> SRR1812733 2 0.5592 0.6565 0.000 0.572 0.404 0.024
#> SRR1812736 3 0.6120 0.4551 0.000 0.076 0.628 0.296
#> SRR1812732 2 0.4888 0.0170 0.000 0.588 0.000 0.412
#> SRR1812730 3 0.5543 -0.5299 0.000 0.424 0.556 0.020
#> SRR1812731 2 0.3688 0.3266 0.000 0.792 0.000 0.208
#> SRR1812729 2 0.4830 0.6860 0.000 0.608 0.392 0.000
#> SRR1812727 3 0.5626 0.4592 0.020 0.004 0.588 0.388
#> SRR1812726 2 0.4866 0.6836 0.000 0.596 0.404 0.000
#> SRR1812728 2 0.5643 0.6674 0.000 0.548 0.428 0.024
#> SRR1812724 2 0.3610 0.3402 0.000 0.800 0.000 0.200
#> SRR1812725 2 0.5161 0.6837 0.000 0.592 0.400 0.008
#> SRR1812723 2 0.4907 0.6770 0.000 0.580 0.420 0.000
#> SRR1812722 2 0.4843 0.6850 0.000 0.604 0.396 0.000
#> SRR1812721 2 0.4994 -0.3313 0.000 0.520 0.000 0.480
#> SRR1812718 2 0.4855 0.6844 0.000 0.600 0.400 0.000
#> SRR1812717 2 0.0000 0.5659 0.000 1.000 0.000 0.000
#> SRR1812716 2 0.5212 0.6760 0.000 0.572 0.420 0.008
#> SRR1812715 2 0.0188 0.5640 0.000 0.996 0.004 0.000
#> SRR1812714 2 0.7091 0.5179 0.000 0.568 0.224 0.208
#> SRR1812719 3 0.5441 0.4622 0.012 0.004 0.588 0.396
#> SRR1812713 2 0.3768 0.3518 0.000 0.808 0.008 0.184
#> SRR1812712 2 0.3448 0.6309 0.000 0.828 0.168 0.004
#> SRR1812711 2 0.4925 0.6716 0.000 0.572 0.428 0.000
#> SRR1812710 2 0.0188 0.5640 0.000 0.996 0.004 0.000
#> SRR1812709 2 0.0000 0.5659 0.000 1.000 0.000 0.000
#> SRR1812708 4 0.9419 -0.2249 0.196 0.120 0.316 0.368
#> SRR1812707 2 0.0188 0.5640 0.000 0.996 0.004 0.000
#> SRR1812705 2 0.4855 0.6844 0.000 0.600 0.400 0.000
#> SRR1812706 2 0.5203 0.6783 0.000 0.576 0.416 0.008
#> SRR1812704 2 0.5600 0.6804 0.000 0.596 0.376 0.028
#> SRR1812703 2 0.4888 0.6808 0.000 0.588 0.412 0.000
#> SRR1812702 2 0.5535 0.6621 0.000 0.560 0.420 0.020
#> SRR1812741 4 0.1716 0.4334 0.000 0.064 0.000 0.936
#> SRR1812740 3 0.6371 0.4576 0.000 0.092 0.608 0.300
#> SRR1812739 2 0.3356 0.3781 0.000 0.824 0.000 0.176
#> SRR1812738 2 0.3528 0.3539 0.000 0.808 0.000 0.192
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1812752 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000
#> SRR1812753 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000
#> SRR1812751 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000
#> SRR1812750 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000
#> SRR1812748 3 0.7878 0.3599 0.000 0.088 0.404 0.300 0.208
#> SRR1812749 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000
#> SRR1812746 3 0.0290 0.5884 0.000 0.000 0.992 0.000 0.008
#> SRR1812745 5 0.7635 -0.4198 0.000 0.104 0.376 0.124 0.396
#> SRR1812747 5 0.2852 0.7617 0.000 0.172 0.000 0.000 0.828
#> SRR1812744 5 0.3597 0.6539 0.000 0.008 0.116 0.044 0.832
#> SRR1812743 4 0.3055 0.7496 0.000 0.144 0.016 0.840 0.000
#> SRR1812742 4 0.5877 0.6444 0.000 0.056 0.092 0.680 0.172
#> SRR1812737 2 0.1851 0.6217 0.000 0.912 0.000 0.000 0.088
#> SRR1812735 2 0.2929 0.6126 0.000 0.820 0.000 0.000 0.180
#> SRR1812734 3 0.3051 0.5759 0.000 0.060 0.864 0.076 0.000
#> SRR1812733 5 0.4881 0.7402 0.000 0.124 0.032 0.084 0.760
#> SRR1812736 3 0.7616 0.3758 0.000 0.084 0.392 0.148 0.376
#> SRR1812732 2 0.7366 0.5670 0.000 0.376 0.028 0.264 0.332
#> SRR1812730 5 0.3667 0.7231 0.000 0.040 0.032 0.084 0.844
#> SRR1812731 2 0.6638 0.5526 0.000 0.440 0.000 0.320 0.240
#> SRR1812729 5 0.2813 0.7595 0.000 0.168 0.000 0.000 0.832
#> SRR1812727 3 0.1356 0.5890 0.012 0.000 0.956 0.004 0.028
#> SRR1812726 5 0.2471 0.7712 0.000 0.136 0.000 0.000 0.864
#> SRR1812728 5 0.1280 0.7676 0.000 0.024 0.008 0.008 0.960
#> SRR1812724 2 0.6636 0.6343 0.000 0.432 0.000 0.232 0.336
#> SRR1812725 5 0.4083 0.7580 0.000 0.132 0.000 0.080 0.788
#> SRR1812723 5 0.0963 0.7684 0.000 0.036 0.000 0.000 0.964
#> SRR1812722 5 0.3661 0.5686 0.000 0.276 0.000 0.000 0.724
#> SRR1812721 2 0.4321 0.0601 0.000 0.600 0.000 0.396 0.004
#> SRR1812718 5 0.2732 0.7731 0.000 0.160 0.000 0.000 0.840
#> SRR1812717 2 0.3966 0.5965 0.000 0.664 0.000 0.000 0.336
#> SRR1812716 5 0.4503 0.7496 0.000 0.140 0.008 0.084 0.768
#> SRR1812715 2 0.1851 0.6217 0.000 0.912 0.000 0.000 0.088
#> SRR1812714 5 0.1525 0.7642 0.000 0.036 0.012 0.004 0.948
#> SRR1812719 3 0.1356 0.5909 0.012 0.000 0.956 0.004 0.028
#> SRR1812713 2 0.5822 0.6542 0.000 0.548 0.000 0.108 0.344
#> SRR1812712 5 0.4171 0.2329 0.000 0.396 0.000 0.000 0.604
#> SRR1812711 5 0.0963 0.7684 0.000 0.036 0.000 0.000 0.964
#> SRR1812710 2 0.1851 0.6217 0.000 0.912 0.000 0.000 0.088
#> SRR1812709 2 0.3966 0.5965 0.000 0.664 0.000 0.000 0.336
#> SRR1812708 3 0.3662 0.3895 0.252 0.000 0.744 0.000 0.004
#> SRR1812707 2 0.1851 0.6217 0.000 0.912 0.000 0.000 0.088
#> SRR1812705 5 0.2813 0.7619 0.000 0.168 0.000 0.000 0.832
#> SRR1812706 5 0.4416 0.7557 0.000 0.132 0.008 0.084 0.776
#> SRR1812704 5 0.2852 0.7626 0.000 0.172 0.000 0.000 0.828
#> SRR1812703 5 0.0290 0.7669 0.000 0.008 0.000 0.000 0.992
#> SRR1812702 5 0.4820 0.7084 0.000 0.080 0.060 0.084 0.776
#> SRR1812741 4 0.4111 0.7843 0.000 0.120 0.092 0.788 0.000
#> SRR1812740 3 0.7469 0.4381 0.000 0.088 0.488 0.148 0.276
#> SRR1812739 2 0.6485 0.6336 0.000 0.460 0.000 0.196 0.344
#> SRR1812738 2 0.6244 0.6314 0.000 0.504 0.000 0.160 0.336
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1812752 1 0.0790 0.978 0.968 0.000 0.000 0.000 0.032 0.000
#> SRR1812753 1 0.0790 0.978 0.968 0.000 0.000 0.000 0.032 0.000
#> SRR1812751 1 0.0000 0.986 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812750 1 0.0000 0.986 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812748 3 0.3390 0.744 0.000 0.000 0.780 0.008 0.012 0.200
#> SRR1812749 1 0.0000 0.986 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812746 5 0.4700 0.789 0.040 0.032 0.016 0.000 0.732 0.180
#> SRR1812745 3 0.6098 0.371 0.000 0.380 0.428 0.000 0.012 0.180
#> SRR1812747 2 0.3290 0.708 0.000 0.776 0.016 0.208 0.000 0.000
#> SRR1812744 2 0.6656 0.445 0.000 0.492 0.048 0.172 0.008 0.280
#> SRR1812743 6 0.2831 0.741 0.000 0.000 0.000 0.024 0.136 0.840
#> SRR1812742 6 0.0603 0.835 0.000 0.016 0.004 0.000 0.000 0.980
#> SRR1812737 4 0.0000 0.782 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1812735 4 0.3136 0.643 0.000 0.188 0.016 0.796 0.000 0.000
#> SRR1812734 5 0.6117 0.418 0.000 0.024 0.280 0.000 0.516 0.180
#> SRR1812733 2 0.5054 0.405 0.000 0.696 0.064 0.000 0.060 0.180
#> SRR1812736 3 0.3419 0.750 0.000 0.016 0.792 0.000 0.012 0.180
#> SRR1812732 4 0.5492 0.495 0.000 0.028 0.000 0.576 0.080 0.316
#> SRR1812730 2 0.4167 0.519 0.000 0.708 0.236 0.000 0.056 0.000
#> SRR1812731 4 0.5031 0.691 0.000 0.028 0.000 0.688 0.180 0.104
#> SRR1812729 2 0.3261 0.710 0.000 0.780 0.016 0.204 0.000 0.000
#> SRR1812727 5 0.4455 0.797 0.052 0.032 0.000 0.000 0.736 0.180
#> SRR1812726 2 0.3201 0.709 0.000 0.780 0.012 0.208 0.000 0.000
#> SRR1812728 2 0.6097 0.650 0.000 0.584 0.188 0.172 0.056 0.000
#> SRR1812724 4 0.4988 0.694 0.000 0.028 0.000 0.692 0.180 0.100
#> SRR1812725 2 0.4239 0.565 0.000 0.736 0.196 0.012 0.056 0.000
#> SRR1812723 2 0.2854 0.711 0.000 0.792 0.000 0.208 0.000 0.000
#> SRR1812722 2 0.4129 0.342 0.000 0.564 0.012 0.424 0.000 0.000
#> SRR1812721 4 0.3862 0.223 0.000 0.000 0.004 0.608 0.000 0.388
#> SRR1812718 2 0.0865 0.658 0.000 0.964 0.000 0.036 0.000 0.000
#> SRR1812717 4 0.0790 0.780 0.000 0.032 0.000 0.968 0.000 0.000
#> SRR1812716 2 0.4142 0.523 0.000 0.712 0.232 0.000 0.056 0.000
#> SRR1812715 4 0.0000 0.782 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1812714 2 0.3341 0.710 0.000 0.776 0.012 0.208 0.004 0.000
#> SRR1812719 5 0.4455 0.797 0.052 0.032 0.000 0.000 0.736 0.180
#> SRR1812713 4 0.2883 0.623 0.000 0.212 0.000 0.788 0.000 0.000
#> SRR1812712 2 0.3668 0.423 0.000 0.668 0.004 0.328 0.000 0.000
#> SRR1812711 2 0.2854 0.711 0.000 0.792 0.000 0.208 0.000 0.000
#> SRR1812710 4 0.0000 0.782 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1812709 4 0.0790 0.780 0.000 0.032 0.000 0.968 0.000 0.000
#> SRR1812708 5 0.3330 0.532 0.284 0.000 0.000 0.000 0.716 0.000
#> SRR1812707 4 0.0000 0.782 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1812705 2 0.3240 0.684 0.000 0.752 0.004 0.244 0.000 0.000
#> SRR1812706 2 0.5076 0.572 0.000 0.672 0.224 0.048 0.056 0.000
#> SRR1812704 2 0.4656 0.617 0.000 0.660 0.016 0.280 0.000 0.044
#> SRR1812703 2 0.2915 0.715 0.000 0.808 0.008 0.184 0.000 0.000
#> SRR1812702 2 0.4494 0.514 0.000 0.708 0.220 0.000 0.056 0.016
#> SRR1812741 6 0.0000 0.838 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR1812740 3 0.3071 0.746 0.000 0.000 0.804 0.000 0.016 0.180
#> SRR1812739 4 0.6177 0.579 0.000 0.184 0.000 0.576 0.180 0.060
#> SRR1812738 4 0.4730 0.707 0.000 0.032 0.000 0.716 0.180 0.072
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 14626 rows and 51 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.437 0.768 0.879 0.3772 0.655 0.655
#> 3 3 0.869 0.902 0.959 0.6361 0.707 0.559
#> 4 4 0.671 0.752 0.887 0.1894 0.735 0.418
#> 5 5 0.749 0.725 0.854 0.0816 0.856 0.531
#> 6 6 0.799 0.689 0.857 0.0389 0.928 0.678
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
#> SRR1812752 1 0.5629 0.774 0.868 0.132
#> SRR1812753 1 0.2948 0.776 0.948 0.052
#> SRR1812751 1 0.8443 0.733 0.728 0.272
#> SRR1812750 1 0.9427 0.641 0.640 0.360
#> SRR1812748 2 0.9522 0.559 0.372 0.628
#> SRR1812749 1 0.8661 0.722 0.712 0.288
#> SRR1812746 1 0.0000 0.761 1.000 0.000
#> SRR1812745 2 0.9491 0.565 0.368 0.632
#> SRR1812747 2 0.0000 0.867 0.000 1.000
#> SRR1812744 2 0.9393 0.581 0.356 0.644
#> SRR1812743 2 0.6531 0.778 0.168 0.832
#> SRR1812742 2 0.9522 0.559 0.372 0.628
#> SRR1812737 2 0.0000 0.867 0.000 1.000
#> SRR1812735 2 0.0000 0.867 0.000 1.000
#> SRR1812734 1 0.6343 0.656 0.840 0.160
#> SRR1812733 2 0.6801 0.768 0.180 0.820
#> SRR1812736 2 0.9522 0.559 0.372 0.628
#> SRR1812732 2 0.6623 0.775 0.172 0.828
#> SRR1812730 2 0.9460 0.571 0.364 0.636
#> SRR1812731 2 0.0000 0.867 0.000 1.000
#> SRR1812729 2 0.0000 0.867 0.000 1.000
#> SRR1812727 1 0.0672 0.764 0.992 0.008
#> SRR1812726 2 0.0000 0.867 0.000 1.000
#> SRR1812728 2 0.2423 0.851 0.040 0.960
#> SRR1812724 2 0.0938 0.863 0.012 0.988
#> SRR1812725 2 0.3431 0.840 0.064 0.936
#> SRR1812723 2 0.0000 0.867 0.000 1.000
#> SRR1812722 2 0.0000 0.867 0.000 1.000
#> SRR1812721 2 0.0000 0.867 0.000 1.000
#> SRR1812718 2 0.0000 0.867 0.000 1.000
#> SRR1812717 2 0.0000 0.867 0.000 1.000
#> SRR1812716 2 0.8499 0.676 0.276 0.724
#> SRR1812715 2 0.0000 0.867 0.000 1.000
#> SRR1812714 2 0.0000 0.867 0.000 1.000
#> SRR1812719 1 0.0000 0.761 1.000 0.000
#> SRR1812713 2 0.0000 0.867 0.000 1.000
#> SRR1812712 2 0.0000 0.867 0.000 1.000
#> SRR1812711 2 0.0000 0.867 0.000 1.000
#> SRR1812710 2 0.0000 0.867 0.000 1.000
#> SRR1812709 2 0.0000 0.867 0.000 1.000
#> SRR1812708 1 0.9209 0.674 0.664 0.336
#> SRR1812707 2 0.0000 0.867 0.000 1.000
#> SRR1812705 2 0.0000 0.867 0.000 1.000
#> SRR1812706 2 0.5842 0.795 0.140 0.860
#> SRR1812704 2 0.0376 0.866 0.004 0.996
#> SRR1812703 2 0.0000 0.867 0.000 1.000
#> SRR1812702 2 0.9427 0.577 0.360 0.640
#> SRR1812741 1 0.9944 0.282 0.544 0.456
#> SRR1812740 2 0.9491 0.565 0.368 0.632
#> SRR1812739 2 0.0000 0.867 0.000 1.000
#> SRR1812738 2 0.4815 0.818 0.104 0.896
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1812752 1 0.0000 0.967 1.000 0.000 0.000
#> SRR1812753 1 0.0000 0.967 1.000 0.000 0.000
#> SRR1812751 1 0.0000 0.967 1.000 0.000 0.000
#> SRR1812750 1 0.0000 0.967 1.000 0.000 0.000
#> SRR1812748 3 0.0000 0.916 0.000 0.000 1.000
#> SRR1812749 1 0.0000 0.967 1.000 0.000 0.000
#> SRR1812746 1 0.5216 0.635 0.740 0.000 0.260
#> SRR1812745 3 0.0000 0.916 0.000 0.000 1.000
#> SRR1812747 2 0.0592 0.951 0.000 0.988 0.012
#> SRR1812744 3 0.0237 0.914 0.000 0.004 0.996
#> SRR1812743 3 0.5760 0.552 0.000 0.328 0.672
#> SRR1812742 3 0.0000 0.916 0.000 0.000 1.000
#> SRR1812737 2 0.0000 0.959 0.000 1.000 0.000
#> SRR1812735 2 0.0000 0.959 0.000 1.000 0.000
#> SRR1812734 3 0.0000 0.916 0.000 0.000 1.000
#> SRR1812733 3 0.3752 0.801 0.000 0.144 0.856
#> SRR1812736 3 0.0000 0.916 0.000 0.000 1.000
#> SRR1812732 3 0.2356 0.868 0.000 0.072 0.928
#> SRR1812730 3 0.0000 0.916 0.000 0.000 1.000
#> SRR1812731 2 0.0000 0.959 0.000 1.000 0.000
#> SRR1812729 2 0.0000 0.959 0.000 1.000 0.000
#> SRR1812727 1 0.0000 0.967 1.000 0.000 0.000
#> SRR1812726 2 0.0000 0.959 0.000 1.000 0.000
#> SRR1812728 2 0.5926 0.457 0.000 0.644 0.356
#> SRR1812724 2 0.0000 0.959 0.000 1.000 0.000
#> SRR1812725 2 0.5178 0.661 0.000 0.744 0.256
#> SRR1812723 2 0.0237 0.956 0.000 0.996 0.004
#> SRR1812722 2 0.0237 0.956 0.000 0.996 0.004
#> SRR1812721 2 0.0000 0.959 0.000 1.000 0.000
#> SRR1812718 2 0.0892 0.945 0.000 0.980 0.020
#> SRR1812717 2 0.0000 0.959 0.000 1.000 0.000
#> SRR1812716 3 0.0592 0.911 0.000 0.012 0.988
#> SRR1812715 2 0.0000 0.959 0.000 1.000 0.000
#> SRR1812714 2 0.0000 0.959 0.000 1.000 0.000
#> SRR1812719 1 0.0424 0.962 0.992 0.000 0.008
#> SRR1812713 2 0.0000 0.959 0.000 1.000 0.000
#> SRR1812712 2 0.0000 0.959 0.000 1.000 0.000
#> SRR1812711 2 0.0237 0.956 0.000 0.996 0.004
#> SRR1812710 2 0.0000 0.959 0.000 1.000 0.000
#> SRR1812709 2 0.0000 0.959 0.000 1.000 0.000
#> SRR1812708 1 0.0000 0.967 1.000 0.000 0.000
#> SRR1812707 2 0.0000 0.959 0.000 1.000 0.000
#> SRR1812705 2 0.2878 0.872 0.000 0.904 0.096
#> SRR1812706 3 0.5216 0.659 0.000 0.260 0.740
#> SRR1812704 2 0.0000 0.959 0.000 1.000 0.000
#> SRR1812703 2 0.0000 0.959 0.000 1.000 0.000
#> SRR1812702 3 0.0000 0.916 0.000 0.000 1.000
#> SRR1812741 1 0.0829 0.955 0.984 0.012 0.004
#> SRR1812740 3 0.0000 0.916 0.000 0.000 1.000
#> SRR1812739 2 0.0000 0.959 0.000 1.000 0.000
#> SRR1812738 2 0.5098 0.645 0.000 0.752 0.248
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1812752 1 0.0000 0.9190 1.000 0.000 0.000 0.000
#> SRR1812753 1 0.0000 0.9190 1.000 0.000 0.000 0.000
#> SRR1812751 1 0.0000 0.9190 1.000 0.000 0.000 0.000
#> SRR1812750 1 0.0000 0.9190 1.000 0.000 0.000 0.000
#> SRR1812748 3 0.0000 0.9002 0.000 0.000 1.000 0.000
#> SRR1812749 1 0.0000 0.9190 1.000 0.000 0.000 0.000
#> SRR1812746 1 0.5167 0.0737 0.508 0.004 0.488 0.000
#> SRR1812745 3 0.2704 0.7961 0.000 0.124 0.876 0.000
#> SRR1812747 2 0.4477 0.6025 0.000 0.688 0.000 0.312
#> SRR1812744 3 0.0524 0.8977 0.000 0.004 0.988 0.008
#> SRR1812743 4 0.3219 0.7045 0.000 0.000 0.164 0.836
#> SRR1812742 3 0.2760 0.8161 0.000 0.000 0.872 0.128
#> SRR1812737 4 0.0469 0.8572 0.000 0.012 0.000 0.988
#> SRR1812735 4 0.4304 0.5258 0.000 0.284 0.000 0.716
#> SRR1812734 3 0.0188 0.8991 0.000 0.004 0.996 0.000
#> SRR1812733 2 0.5579 0.5325 0.000 0.688 0.252 0.060
#> SRR1812736 3 0.0000 0.9002 0.000 0.000 1.000 0.000
#> SRR1812732 3 0.4382 0.5811 0.000 0.000 0.704 0.296
#> SRR1812730 2 0.2868 0.7257 0.000 0.864 0.136 0.000
#> SRR1812731 4 0.0000 0.8564 0.000 0.000 0.000 1.000
#> SRR1812729 2 0.3356 0.7609 0.000 0.824 0.000 0.176
#> SRR1812727 1 0.0000 0.9190 1.000 0.000 0.000 0.000
#> SRR1812726 2 0.4522 0.5909 0.000 0.680 0.000 0.320
#> SRR1812728 2 0.0188 0.8131 0.000 0.996 0.004 0.000
#> SRR1812724 4 0.0000 0.8564 0.000 0.000 0.000 1.000
#> SRR1812725 2 0.0000 0.8134 0.000 1.000 0.000 0.000
#> SRR1812723 2 0.2081 0.8073 0.000 0.916 0.000 0.084
#> SRR1812722 2 0.4746 0.5017 0.000 0.632 0.000 0.368
#> SRR1812721 4 0.0000 0.8564 0.000 0.000 0.000 1.000
#> SRR1812718 2 0.1474 0.8130 0.000 0.948 0.000 0.052
#> SRR1812717 4 0.0469 0.8572 0.000 0.012 0.000 0.988
#> SRR1812716 2 0.1716 0.7830 0.000 0.936 0.064 0.000
#> SRR1812715 4 0.0188 0.8571 0.000 0.004 0.000 0.996
#> SRR1812714 4 0.4933 0.0887 0.000 0.432 0.000 0.568
#> SRR1812719 1 0.3333 0.8111 0.872 0.088 0.040 0.000
#> SRR1812713 4 0.4356 0.5521 0.000 0.292 0.000 0.708
#> SRR1812712 2 0.4972 0.1441 0.000 0.544 0.000 0.456
#> SRR1812711 2 0.2814 0.7900 0.000 0.868 0.000 0.132
#> SRR1812710 4 0.1302 0.8449 0.000 0.044 0.000 0.956
#> SRR1812709 4 0.1557 0.8381 0.000 0.056 0.000 0.944
#> SRR1812708 1 0.0000 0.9190 1.000 0.000 0.000 0.000
#> SRR1812707 4 0.1474 0.8408 0.000 0.052 0.000 0.948
#> SRR1812705 2 0.2973 0.7839 0.000 0.856 0.000 0.144
#> SRR1812706 2 0.0336 0.8112 0.000 0.992 0.008 0.000
#> SRR1812704 2 0.2921 0.7655 0.000 0.860 0.000 0.140
#> SRR1812703 2 0.0000 0.8134 0.000 1.000 0.000 0.000
#> SRR1812702 2 0.1792 0.7805 0.000 0.932 0.068 0.000
#> SRR1812741 4 0.4669 0.6590 0.052 0.000 0.168 0.780
#> SRR1812740 3 0.0000 0.9002 0.000 0.000 1.000 0.000
#> SRR1812739 4 0.0000 0.8564 0.000 0.000 0.000 1.000
#> SRR1812738 4 0.3982 0.6447 0.000 0.004 0.220 0.776
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1812752 1 0.0000 0.94447 1.000 0.000 0.000 0.000 0.000
#> SRR1812753 1 0.0000 0.94447 1.000 0.000 0.000 0.000 0.000
#> SRR1812751 1 0.0000 0.94447 1.000 0.000 0.000 0.000 0.000
#> SRR1812750 1 0.0000 0.94447 1.000 0.000 0.000 0.000 0.000
#> SRR1812748 3 0.0162 0.82271 0.000 0.000 0.996 0.000 0.004
#> SRR1812749 1 0.0000 0.94447 1.000 0.000 0.000 0.000 0.000
#> SRR1812746 1 0.2519 0.85963 0.884 0.000 0.100 0.000 0.016
#> SRR1812745 5 0.4307 -0.19941 0.000 0.000 0.500 0.000 0.500
#> SRR1812747 2 0.2426 0.81899 0.000 0.900 0.000 0.036 0.064
#> SRR1812744 3 0.6031 0.60079 0.000 0.000 0.568 0.164 0.268
#> SRR1812743 4 0.4937 0.12189 0.000 0.000 0.428 0.544 0.028
#> SRR1812742 3 0.1731 0.81242 0.000 0.008 0.940 0.012 0.040
#> SRR1812737 4 0.0290 0.83869 0.000 0.008 0.000 0.992 0.000
#> SRR1812735 2 0.2248 0.79371 0.000 0.900 0.000 0.088 0.012
#> SRR1812734 3 0.3452 0.72931 0.000 0.000 0.756 0.000 0.244
#> SRR1812733 5 0.3232 0.65948 0.000 0.036 0.056 0.036 0.872
#> SRR1812736 3 0.0290 0.82249 0.000 0.000 0.992 0.000 0.008
#> SRR1812732 3 0.3910 0.62796 0.000 0.000 0.720 0.272 0.008
#> SRR1812730 5 0.3690 0.75621 0.000 0.200 0.020 0.000 0.780
#> SRR1812731 4 0.0000 0.83858 0.000 0.000 0.000 1.000 0.000
#> SRR1812729 2 0.2920 0.71887 0.000 0.852 0.000 0.016 0.132
#> SRR1812727 1 0.2339 0.88839 0.892 0.004 0.004 0.000 0.100
#> SRR1812726 2 0.1216 0.83246 0.000 0.960 0.000 0.020 0.020
#> SRR1812728 5 0.3913 0.70939 0.000 0.324 0.000 0.000 0.676
#> SRR1812724 4 0.0290 0.83906 0.000 0.000 0.000 0.992 0.008
#> SRR1812725 2 0.4304 -0.34364 0.000 0.516 0.000 0.000 0.484
#> SRR1812723 2 0.1768 0.81593 0.000 0.924 0.000 0.004 0.072
#> SRR1812722 2 0.0290 0.84253 0.000 0.992 0.000 0.008 0.000
#> SRR1812721 4 0.0000 0.83858 0.000 0.000 0.000 1.000 0.000
#> SRR1812718 2 0.0703 0.83943 0.000 0.976 0.000 0.000 0.024
#> SRR1812717 4 0.1310 0.83193 0.000 0.020 0.000 0.956 0.024
#> SRR1812716 5 0.3809 0.74887 0.000 0.256 0.008 0.000 0.736
#> SRR1812715 4 0.4088 0.54442 0.000 0.304 0.000 0.688 0.008
#> SRR1812714 2 0.4304 0.67141 0.012 0.792 0.000 0.104 0.092
#> SRR1812719 1 0.4011 0.78737 0.804 0.040 0.016 0.000 0.140
#> SRR1812713 4 0.2519 0.79424 0.000 0.016 0.000 0.884 0.100
#> SRR1812712 4 0.3550 0.72851 0.000 0.020 0.000 0.796 0.184
#> SRR1812711 2 0.0162 0.84179 0.000 0.996 0.000 0.004 0.000
#> SRR1812710 4 0.3913 0.52579 0.000 0.324 0.000 0.676 0.000
#> SRR1812709 4 0.0324 0.84002 0.000 0.004 0.000 0.992 0.004
#> SRR1812708 1 0.0794 0.93453 0.972 0.000 0.000 0.000 0.028
#> SRR1812707 4 0.0771 0.83702 0.000 0.020 0.000 0.976 0.004
#> SRR1812705 2 0.0865 0.83975 0.000 0.972 0.000 0.004 0.024
#> SRR1812706 5 0.3816 0.73404 0.000 0.304 0.000 0.000 0.696
#> SRR1812704 4 0.6304 -0.00922 0.000 0.156 0.000 0.460 0.384
#> SRR1812703 5 0.3274 0.68473 0.000 0.220 0.000 0.000 0.780
#> SRR1812702 5 0.3752 0.74392 0.000 0.292 0.000 0.000 0.708
#> SRR1812741 4 0.1651 0.82068 0.036 0.000 0.012 0.944 0.008
#> SRR1812740 3 0.1410 0.80777 0.000 0.000 0.940 0.000 0.060
#> SRR1812739 4 0.0566 0.83649 0.000 0.000 0.012 0.984 0.004
#> SRR1812738 4 0.0865 0.83758 0.000 0.004 0.000 0.972 0.024
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1812752 1 0.0000 0.8327 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812753 1 0.0000 0.8327 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812751 1 0.0000 0.8327 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812750 1 0.0000 0.8327 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812748 3 0.1196 0.6447 0.000 0.000 0.952 0.000 0.008 0.040
#> SRR1812749 1 0.0000 0.8327 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812746 1 0.4469 0.5260 0.700 0.004 0.076 0.000 0.000 0.220
#> SRR1812745 3 0.5887 -0.1637 0.000 0.004 0.428 0.000 0.172 0.396
#> SRR1812747 2 0.0508 0.7879 0.000 0.984 0.004 0.000 0.012 0.000
#> SRR1812744 6 0.2146 0.6613 0.000 0.004 0.116 0.000 0.000 0.880
#> SRR1812743 3 0.5108 0.1232 0.000 0.000 0.484 0.436 0.000 0.080
#> SRR1812742 3 0.2145 0.6232 0.000 0.012 0.904 0.004 0.004 0.076
#> SRR1812737 4 0.0146 0.9086 0.000 0.004 0.000 0.996 0.000 0.000
#> SRR1812735 2 0.0551 0.7879 0.000 0.984 0.004 0.008 0.004 0.000
#> SRR1812734 6 0.2482 0.6426 0.000 0.000 0.148 0.000 0.004 0.848
#> SRR1812733 6 0.4553 0.2669 0.000 0.000 0.020 0.008 0.452 0.520
#> SRR1812736 3 0.1370 0.6423 0.000 0.004 0.948 0.000 0.012 0.036
#> SRR1812732 3 0.3417 0.5826 0.000 0.000 0.796 0.160 0.000 0.044
#> SRR1812730 5 0.0436 0.8221 0.000 0.004 0.004 0.000 0.988 0.004
#> SRR1812731 4 0.0405 0.9059 0.000 0.000 0.008 0.988 0.000 0.004
#> SRR1812729 2 0.4325 0.0802 0.000 0.524 0.000 0.020 0.456 0.000
#> SRR1812727 1 0.4028 0.5125 0.668 0.000 0.000 0.000 0.024 0.308
#> SRR1812726 2 0.0405 0.7890 0.000 0.988 0.000 0.000 0.004 0.008
#> SRR1812728 5 0.1958 0.8516 0.000 0.100 0.000 0.000 0.896 0.004
#> SRR1812724 4 0.0551 0.9082 0.000 0.000 0.008 0.984 0.004 0.004
#> SRR1812725 5 0.3081 0.7599 0.000 0.220 0.004 0.000 0.776 0.000
#> SRR1812723 2 0.3756 0.3201 0.000 0.600 0.000 0.000 0.400 0.000
#> SRR1812722 2 0.1349 0.7799 0.000 0.940 0.000 0.004 0.056 0.000
#> SRR1812721 4 0.0146 0.9087 0.000 0.000 0.000 0.996 0.004 0.000
#> SRR1812718 2 0.0937 0.7871 0.000 0.960 0.000 0.000 0.040 0.000
#> SRR1812717 4 0.1267 0.8872 0.000 0.000 0.000 0.940 0.060 0.000
#> SRR1812716 5 0.0363 0.8308 0.000 0.012 0.000 0.000 0.988 0.000
#> SRR1812715 4 0.3878 0.5616 0.000 0.320 0.008 0.668 0.000 0.004
#> SRR1812714 2 0.3468 0.4569 0.004 0.712 0.000 0.000 0.000 0.284
#> SRR1812719 1 0.4531 0.2406 0.556 0.000 0.000 0.000 0.408 0.036
#> SRR1812713 4 0.1411 0.8857 0.000 0.000 0.000 0.936 0.060 0.004
#> SRR1812712 4 0.1524 0.8845 0.000 0.000 0.000 0.932 0.060 0.008
#> SRR1812711 2 0.0363 0.7909 0.000 0.988 0.000 0.000 0.012 0.000
#> SRR1812710 4 0.3607 0.5203 0.000 0.348 0.000 0.652 0.000 0.000
#> SRR1812709 4 0.0260 0.9089 0.000 0.000 0.000 0.992 0.008 0.000
#> SRR1812708 1 0.1806 0.7851 0.908 0.004 0.000 0.000 0.000 0.088
#> SRR1812707 4 0.0260 0.9089 0.000 0.000 0.000 0.992 0.008 0.000
#> SRR1812705 2 0.3371 0.5438 0.000 0.708 0.000 0.000 0.292 0.000
#> SRR1812706 5 0.4166 0.7791 0.000 0.196 0.000 0.000 0.728 0.076
#> SRR1812704 5 0.0937 0.8017 0.000 0.000 0.000 0.040 0.960 0.000
#> SRR1812703 6 0.2907 0.6371 0.000 0.020 0.000 0.000 0.152 0.828
#> SRR1812702 5 0.3172 0.8386 0.000 0.128 0.000 0.000 0.824 0.048
#> SRR1812741 4 0.1679 0.8807 0.036 0.000 0.012 0.936 0.000 0.016
#> SRR1812740 3 0.2730 0.5418 0.000 0.000 0.808 0.000 0.192 0.000
#> SRR1812739 4 0.0909 0.8995 0.000 0.000 0.012 0.968 0.000 0.020
#> SRR1812738 4 0.0405 0.9077 0.000 0.000 0.004 0.988 0.000 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 14626 rows and 51 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 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 0.966 0.987 0.2499 0.758 0.758
#> 3 3 0.433 0.746 0.794 0.5953 0.961 0.948
#> 4 4 0.377 0.778 0.818 0.0668 0.990 0.986
#> 5 5 0.303 0.644 0.761 0.2433 0.845 0.784
#> 6 6 0.357 0.538 0.741 0.1431 0.966 0.941
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
#> SRR1812752 1 0.000 0.9695 1.000 0.000
#> SRR1812753 1 0.000 0.9695 1.000 0.000
#> SRR1812751 1 0.000 0.9695 1.000 0.000
#> SRR1812750 1 0.000 0.9695 1.000 0.000
#> SRR1812748 2 0.000 0.9889 0.000 1.000
#> SRR1812749 1 0.000 0.9695 1.000 0.000
#> SRR1812746 2 0.995 0.0998 0.460 0.540
#> SRR1812745 2 0.000 0.9889 0.000 1.000
#> SRR1812747 2 0.000 0.9889 0.000 1.000
#> SRR1812744 2 0.000 0.9889 0.000 1.000
#> SRR1812743 2 0.000 0.9889 0.000 1.000
#> SRR1812742 2 0.000 0.9889 0.000 1.000
#> SRR1812737 2 0.000 0.9889 0.000 1.000
#> SRR1812735 2 0.000 0.9889 0.000 1.000
#> SRR1812734 2 0.000 0.9889 0.000 1.000
#> SRR1812733 2 0.000 0.9889 0.000 1.000
#> SRR1812736 2 0.000 0.9889 0.000 1.000
#> SRR1812732 2 0.000 0.9889 0.000 1.000
#> SRR1812730 2 0.000 0.9889 0.000 1.000
#> SRR1812731 2 0.000 0.9889 0.000 1.000
#> SRR1812729 2 0.000 0.9889 0.000 1.000
#> SRR1812727 2 0.000 0.9889 0.000 1.000
#> SRR1812726 2 0.000 0.9889 0.000 1.000
#> SRR1812728 2 0.000 0.9889 0.000 1.000
#> SRR1812724 2 0.000 0.9889 0.000 1.000
#> SRR1812725 2 0.000 0.9889 0.000 1.000
#> SRR1812723 2 0.000 0.9889 0.000 1.000
#> SRR1812722 2 0.000 0.9889 0.000 1.000
#> SRR1812721 2 0.000 0.9889 0.000 1.000
#> SRR1812718 2 0.000 0.9889 0.000 1.000
#> SRR1812717 2 0.000 0.9889 0.000 1.000
#> SRR1812716 2 0.000 0.9889 0.000 1.000
#> SRR1812715 2 0.000 0.9889 0.000 1.000
#> SRR1812714 2 0.000 0.9889 0.000 1.000
#> SRR1812719 2 0.000 0.9889 0.000 1.000
#> SRR1812713 2 0.000 0.9889 0.000 1.000
#> SRR1812712 2 0.000 0.9889 0.000 1.000
#> SRR1812711 2 0.000 0.9889 0.000 1.000
#> SRR1812710 2 0.000 0.9889 0.000 1.000
#> SRR1812709 2 0.000 0.9889 0.000 1.000
#> SRR1812708 1 0.260 0.9444 0.956 0.044
#> SRR1812707 2 0.000 0.9889 0.000 1.000
#> SRR1812705 2 0.000 0.9889 0.000 1.000
#> SRR1812706 2 0.000 0.9889 0.000 1.000
#> SRR1812704 2 0.000 0.9889 0.000 1.000
#> SRR1812703 2 0.000 0.9889 0.000 1.000
#> SRR1812702 2 0.000 0.9889 0.000 1.000
#> SRR1812741 1 0.574 0.8496 0.864 0.136
#> SRR1812740 2 0.000 0.9889 0.000 1.000
#> SRR1812739 2 0.000 0.9889 0.000 1.000
#> SRR1812738 2 0.000 0.9889 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1812752 1 0.6008 0.6120 0.628 0.000 0.372
#> SRR1812753 1 0.6008 0.6120 0.628 0.000 0.372
#> SRR1812751 1 0.6008 0.6120 0.628 0.000 0.372
#> SRR1812750 1 0.0000 0.5975 1.000 0.000 0.000
#> SRR1812748 2 0.5678 0.7317 0.000 0.684 0.316
#> SRR1812749 1 0.0000 0.5975 1.000 0.000 0.000
#> SRR1812746 3 0.8848 0.0489 0.372 0.124 0.504
#> SRR1812745 2 0.5621 0.7400 0.000 0.692 0.308
#> SRR1812747 2 0.1753 0.8495 0.000 0.952 0.048
#> SRR1812744 2 0.3340 0.8473 0.000 0.880 0.120
#> SRR1812743 2 0.2959 0.8121 0.000 0.900 0.100
#> SRR1812742 2 0.2959 0.8121 0.000 0.900 0.100
#> SRR1812737 2 0.2878 0.8148 0.000 0.904 0.096
#> SRR1812735 2 0.2165 0.8333 0.000 0.936 0.064
#> SRR1812734 2 0.5591 0.7361 0.000 0.696 0.304
#> SRR1812733 2 0.4235 0.8284 0.000 0.824 0.176
#> SRR1812736 2 0.5678 0.7317 0.000 0.684 0.316
#> SRR1812732 2 0.2959 0.8524 0.000 0.900 0.100
#> SRR1812730 2 0.5178 0.7835 0.000 0.744 0.256
#> SRR1812731 2 0.2878 0.8148 0.000 0.904 0.096
#> SRR1812729 2 0.1529 0.8563 0.000 0.960 0.040
#> SRR1812727 2 0.5497 0.7485 0.000 0.708 0.292
#> SRR1812726 2 0.1163 0.8469 0.000 0.972 0.028
#> SRR1812728 2 0.2261 0.8574 0.000 0.932 0.068
#> SRR1812724 2 0.2356 0.8557 0.000 0.928 0.072
#> SRR1812725 2 0.4452 0.8205 0.000 0.808 0.192
#> SRR1812723 2 0.0892 0.8507 0.000 0.980 0.020
#> SRR1812722 2 0.1964 0.8375 0.000 0.944 0.056
#> SRR1812721 2 0.2959 0.8121 0.000 0.900 0.100
#> SRR1812718 2 0.1031 0.8529 0.000 0.976 0.024
#> SRR1812717 2 0.1529 0.8565 0.000 0.960 0.040
#> SRR1812716 2 0.5178 0.7835 0.000 0.744 0.256
#> SRR1812715 2 0.2165 0.8333 0.000 0.936 0.064
#> SRR1812714 2 0.4702 0.8094 0.000 0.788 0.212
#> SRR1812719 2 0.5497 0.7485 0.000 0.708 0.292
#> SRR1812713 2 0.3267 0.8482 0.000 0.884 0.116
#> SRR1812712 2 0.2356 0.8557 0.000 0.928 0.072
#> SRR1812711 2 0.1163 0.8469 0.000 0.972 0.028
#> SRR1812710 2 0.2878 0.8148 0.000 0.904 0.096
#> SRR1812709 2 0.2356 0.8557 0.000 0.928 0.072
#> SRR1812708 1 0.3619 0.4740 0.864 0.000 0.136
#> SRR1812707 2 0.2878 0.8148 0.000 0.904 0.096
#> SRR1812705 2 0.0892 0.8507 0.000 0.980 0.020
#> SRR1812706 2 0.4931 0.7984 0.000 0.768 0.232
#> SRR1812704 2 0.2448 0.8570 0.000 0.924 0.076
#> SRR1812703 2 0.4702 0.8094 0.000 0.788 0.212
#> SRR1812702 2 0.5178 0.7835 0.000 0.744 0.256
#> SRR1812741 3 0.7043 -0.6169 0.400 0.024 0.576
#> SRR1812740 2 0.5678 0.7317 0.000 0.684 0.316
#> SRR1812739 2 0.3116 0.8519 0.000 0.892 0.108
#> SRR1812738 2 0.2356 0.8378 0.000 0.928 0.072
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1812752 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> SRR1812753 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> SRR1812751 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> SRR1812750 3 0.4925 0.4617 0.428 0.000 0.572 0.000
#> SRR1812748 4 0.4936 0.7297 0.000 0.372 0.004 0.624
#> SRR1812749 3 0.4925 0.4617 0.428 0.000 0.572 0.000
#> SRR1812746 3 0.6376 0.0798 0.000 0.432 0.504 0.064
#> SRR1812745 4 0.5007 0.7427 0.000 0.356 0.008 0.636
#> SRR1812747 4 0.2282 0.8504 0.000 0.024 0.052 0.924
#> SRR1812744 4 0.3606 0.8469 0.000 0.140 0.020 0.840
#> SRR1812743 4 0.3606 0.8035 0.000 0.020 0.140 0.840
#> SRR1812742 4 0.3606 0.8035 0.000 0.020 0.140 0.840
#> SRR1812737 4 0.2706 0.8258 0.000 0.020 0.080 0.900
#> SRR1812735 4 0.1970 0.8385 0.000 0.008 0.060 0.932
#> SRR1812734 4 0.5339 0.7191 0.000 0.356 0.020 0.624
#> SRR1812733 4 0.3969 0.8329 0.000 0.180 0.016 0.804
#> SRR1812736 4 0.4936 0.7297 0.000 0.372 0.004 0.624
#> SRR1812732 4 0.3335 0.8522 0.000 0.120 0.020 0.860
#> SRR1812730 4 0.4576 0.7958 0.000 0.260 0.012 0.728
#> SRR1812731 4 0.2706 0.8258 0.000 0.020 0.080 0.900
#> SRR1812729 4 0.1302 0.8577 0.000 0.044 0.000 0.956
#> SRR1812727 4 0.4955 0.7382 0.000 0.344 0.008 0.648
#> SRR1812726 4 0.0927 0.8488 0.000 0.008 0.016 0.976
#> SRR1812728 4 0.2048 0.8609 0.000 0.064 0.008 0.928
#> SRR1812724 4 0.2402 0.8563 0.000 0.076 0.012 0.912
#> SRR1812725 4 0.3893 0.8287 0.000 0.196 0.008 0.796
#> SRR1812723 4 0.0524 0.8521 0.000 0.004 0.008 0.988
#> SRR1812722 4 0.2489 0.8386 0.000 0.020 0.068 0.912
#> SRR1812721 4 0.3554 0.8057 0.000 0.020 0.136 0.844
#> SRR1812718 4 0.0657 0.8545 0.000 0.012 0.004 0.984
#> SRR1812717 4 0.1661 0.8571 0.000 0.052 0.004 0.944
#> SRR1812716 4 0.4576 0.7958 0.000 0.260 0.012 0.728
#> SRR1812715 4 0.1970 0.8385 0.000 0.008 0.060 0.932
#> SRR1812714 4 0.4194 0.8138 0.000 0.228 0.008 0.764
#> SRR1812719 4 0.4936 0.7422 0.000 0.340 0.008 0.652
#> SRR1812713 4 0.3166 0.8511 0.000 0.116 0.016 0.868
#> SRR1812712 4 0.2402 0.8563 0.000 0.076 0.012 0.912
#> SRR1812711 4 0.0927 0.8488 0.000 0.008 0.016 0.976
#> SRR1812710 4 0.2706 0.8258 0.000 0.020 0.080 0.900
#> SRR1812709 4 0.2402 0.8563 0.000 0.076 0.012 0.912
#> SRR1812708 3 0.4980 0.4733 0.304 0.016 0.680 0.000
#> SRR1812707 4 0.2706 0.8258 0.000 0.020 0.080 0.900
#> SRR1812705 4 0.0524 0.8521 0.000 0.004 0.008 0.988
#> SRR1812706 4 0.4353 0.8103 0.000 0.232 0.012 0.756
#> SRR1812704 4 0.2342 0.8582 0.000 0.080 0.008 0.912
#> SRR1812703 4 0.4194 0.8138 0.000 0.228 0.008 0.764
#> SRR1812702 4 0.4576 0.7958 0.000 0.260 0.012 0.728
#> SRR1812741 2 0.7149 0.0000 0.264 0.552 0.184 0.000
#> SRR1812740 4 0.4936 0.7297 0.000 0.372 0.004 0.624
#> SRR1812739 4 0.3108 0.8543 0.000 0.112 0.016 0.872
#> SRR1812738 4 0.2450 0.8448 0.000 0.016 0.072 0.912
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1812752 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> SRR1812753 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> SRR1812751 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> SRR1812750 3 0.304 0.904 0.192 0.000 0.808 0.000 0.000
#> SRR1812748 2 0.550 0.343 0.000 0.580 0.000 0.080 0.340
#> SRR1812749 3 0.304 0.904 0.192 0.000 0.808 0.000 0.000
#> SRR1812746 5 0.580 -0.322 0.000 0.008 0.372 0.076 0.544
#> SRR1812745 2 0.571 0.374 0.000 0.564 0.000 0.100 0.336
#> SRR1812747 2 0.271 0.743 0.000 0.880 0.000 0.088 0.032
#> SRR1812744 2 0.505 0.329 0.000 0.652 0.000 0.064 0.284
#> SRR1812743 2 0.346 0.670 0.000 0.792 0.000 0.196 0.012
#> SRR1812742 2 0.413 0.664 0.000 0.760 0.000 0.196 0.044
#> SRR1812737 2 0.247 0.711 0.000 0.864 0.000 0.136 0.000
#> SRR1812735 2 0.267 0.720 0.000 0.876 0.000 0.104 0.020
#> SRR1812734 5 0.391 0.640 0.000 0.240 0.000 0.016 0.744
#> SRR1812733 2 0.410 0.658 0.000 0.764 0.000 0.192 0.044
#> SRR1812736 2 0.560 0.307 0.000 0.544 0.000 0.080 0.376
#> SRR1812732 2 0.370 0.693 0.000 0.816 0.000 0.064 0.120
#> SRR1812730 2 0.524 0.570 0.000 0.680 0.000 0.132 0.188
#> SRR1812731 2 0.247 0.711 0.000 0.864 0.000 0.136 0.000
#> SRR1812729 2 0.170 0.741 0.000 0.932 0.000 0.060 0.008
#> SRR1812727 5 0.397 0.667 0.000 0.264 0.000 0.012 0.724
#> SRR1812726 2 0.311 0.658 0.000 0.852 0.000 0.036 0.112
#> SRR1812728 2 0.293 0.727 0.000 0.864 0.000 0.032 0.104
#> SRR1812724 2 0.257 0.728 0.000 0.880 0.000 0.104 0.016
#> SRR1812725 2 0.459 0.640 0.000 0.748 0.000 0.116 0.136
#> SRR1812723 2 0.201 0.738 0.000 0.920 0.000 0.020 0.060
#> SRR1812722 2 0.412 0.629 0.000 0.788 0.000 0.104 0.108
#> SRR1812721 2 0.353 0.670 0.000 0.792 0.000 0.192 0.016
#> SRR1812718 2 0.174 0.744 0.000 0.936 0.000 0.024 0.040
#> SRR1812717 2 0.194 0.736 0.000 0.920 0.000 0.068 0.012
#> SRR1812716 2 0.524 0.570 0.000 0.680 0.000 0.132 0.188
#> SRR1812715 2 0.267 0.720 0.000 0.876 0.000 0.104 0.020
#> SRR1812714 5 0.472 0.556 0.000 0.448 0.000 0.016 0.536
#> SRR1812719 5 0.443 0.617 0.000 0.360 0.000 0.012 0.628
#> SRR1812713 2 0.311 0.710 0.000 0.840 0.000 0.140 0.020
#> SRR1812712 2 0.247 0.727 0.000 0.884 0.000 0.104 0.012
#> SRR1812711 2 0.230 0.738 0.000 0.908 0.000 0.040 0.052
#> SRR1812710 2 0.247 0.711 0.000 0.864 0.000 0.136 0.000
#> SRR1812709 2 0.247 0.727 0.000 0.884 0.000 0.104 0.012
#> SRR1812708 3 0.500 0.803 0.140 0.000 0.720 0.004 0.136
#> SRR1812707 2 0.247 0.711 0.000 0.864 0.000 0.136 0.000
#> SRR1812705 2 0.201 0.738 0.000 0.920 0.000 0.020 0.060
#> SRR1812706 2 0.500 0.600 0.000 0.708 0.000 0.128 0.164
#> SRR1812704 2 0.267 0.733 0.000 0.876 0.000 0.104 0.020
#> SRR1812703 5 0.472 0.556 0.000 0.448 0.000 0.016 0.536
#> SRR1812702 2 0.524 0.570 0.000 0.680 0.000 0.132 0.188
#> SRR1812741 4 0.605 0.000 0.260 0.000 0.140 0.592 0.008
#> SRR1812740 2 0.559 0.318 0.000 0.548 0.000 0.080 0.372
#> SRR1812739 2 0.311 0.720 0.000 0.844 0.000 0.132 0.024
#> SRR1812738 2 0.254 0.726 0.000 0.868 0.000 0.128 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1812752 1 0.000 1.0000 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812753 1 0.000 1.0000 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812751 1 0.000 1.0000 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812750 4 0.176 0.9059 0.096 0.000 0.000 0.904 0.000 0.000
#> SRR1812748 2 0.664 0.0764 0.000 0.472 0.328 0.004 0.124 0.072
#> SRR1812749 4 0.176 0.9059 0.096 0.000 0.000 0.904 0.000 0.000
#> SRR1812746 3 0.584 -0.4480 0.000 0.000 0.632 0.160 0.132 0.076
#> SRR1812745 3 0.584 -0.4638 0.000 0.440 0.452 0.004 0.064 0.040
#> SRR1812747 2 0.410 0.6342 0.000 0.768 0.160 0.008 0.008 0.056
#> SRR1812744 2 0.620 0.2246 0.000 0.516 0.116 0.012 0.328 0.028
#> SRR1812743 2 0.528 0.5903 0.000 0.712 0.124 0.036 0.024 0.104
#> SRR1812742 2 0.579 0.5743 0.000 0.656 0.176 0.036 0.028 0.104
#> SRR1812737 2 0.342 0.6309 0.000 0.844 0.068 0.036 0.004 0.048
#> SRR1812735 2 0.370 0.6525 0.000 0.832 0.080 0.032 0.036 0.020
#> SRR1812734 5 0.271 0.6241 0.000 0.064 0.024 0.004 0.884 0.024
#> SRR1812733 2 0.514 0.5339 0.000 0.688 0.212 0.032 0.020 0.048
#> SRR1812736 2 0.674 -0.0418 0.000 0.408 0.388 0.004 0.128 0.072
#> SRR1812732 2 0.531 0.5705 0.000 0.688 0.152 0.012 0.120 0.028
#> SRR1812730 2 0.414 0.3349 0.000 0.556 0.432 0.000 0.012 0.000
#> SRR1812731 2 0.342 0.6309 0.000 0.844 0.068 0.036 0.004 0.048
#> SRR1812729 2 0.285 0.6573 0.000 0.876 0.068 0.028 0.024 0.004
#> SRR1812727 5 0.150 0.6588 0.000 0.076 0.000 0.000 0.924 0.000
#> SRR1812726 2 0.437 0.5881 0.000 0.740 0.052 0.012 0.188 0.008
#> SRR1812728 2 0.392 0.6090 0.000 0.748 0.192 0.000 0.060 0.000
#> SRR1812724 2 0.345 0.6354 0.000 0.828 0.116 0.036 0.008 0.012
#> SRR1812725 2 0.431 0.4665 0.000 0.624 0.344 0.000 0.032 0.000
#> SRR1812723 2 0.341 0.6426 0.000 0.808 0.128 0.000 0.064 0.000
#> SRR1812722 2 0.551 0.5625 0.000 0.680 0.056 0.020 0.180 0.064
#> SRR1812721 2 0.506 0.6039 0.000 0.736 0.100 0.036 0.028 0.100
#> SRR1812718 2 0.299 0.6494 0.000 0.828 0.144 0.000 0.028 0.000
#> SRR1812717 2 0.277 0.6472 0.000 0.880 0.068 0.032 0.008 0.012
#> SRR1812716 2 0.415 0.3299 0.000 0.552 0.436 0.000 0.012 0.000
#> SRR1812715 2 0.370 0.6525 0.000 0.832 0.080 0.032 0.036 0.020
#> SRR1812714 5 0.376 0.7275 0.000 0.256 0.012 0.008 0.724 0.000
#> SRR1812719 5 0.362 0.5565 0.000 0.244 0.020 0.000 0.736 0.000
#> SRR1812713 2 0.416 0.6032 0.000 0.788 0.120 0.036 0.008 0.048
#> SRR1812712 2 0.326 0.6322 0.000 0.844 0.100 0.036 0.008 0.012
#> SRR1812711 2 0.405 0.6468 0.000 0.780 0.144 0.012 0.056 0.008
#> SRR1812710 2 0.337 0.6325 0.000 0.848 0.064 0.036 0.004 0.048
#> SRR1812709 2 0.326 0.6322 0.000 0.844 0.100 0.036 0.008 0.012
#> SRR1812708 4 0.501 0.8031 0.092 0.000 0.140 0.712 0.056 0.000
#> SRR1812707 2 0.337 0.6325 0.000 0.848 0.064 0.036 0.004 0.048
#> SRR1812705 2 0.341 0.6426 0.000 0.808 0.128 0.000 0.064 0.000
#> SRR1812706 2 0.425 0.3804 0.000 0.580 0.400 0.000 0.020 0.000
#> SRR1812704 2 0.340 0.6474 0.000 0.832 0.116 0.028 0.012 0.012
#> SRR1812703 5 0.376 0.7275 0.000 0.256 0.012 0.008 0.724 0.000
#> SRR1812702 2 0.415 0.3299 0.000 0.552 0.436 0.000 0.012 0.000
#> SRR1812741 6 0.305 0.0000 0.236 0.000 0.000 0.000 0.000 0.764
#> SRR1812740 2 0.671 -0.0323 0.000 0.412 0.388 0.004 0.124 0.072
#> SRR1812739 2 0.427 0.6191 0.000 0.760 0.172 0.028 0.012 0.028
#> SRR1812738 2 0.328 0.6410 0.000 0.852 0.072 0.040 0.004 0.032
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 14626 rows and 51 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.996 0.997 0.2441 0.758 0.758
#> 3 3 0.441 0.592 0.812 1.3832 0.624 0.504
#> 4 4 0.499 0.649 0.778 0.2052 0.787 0.523
#> 5 5 0.604 0.585 0.755 0.0859 0.920 0.747
#> 6 6 0.676 0.634 0.731 0.0489 0.911 0.660
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
#> SRR1812752 1 0.0000 0.998 1.000 0.000
#> SRR1812753 1 0.0000 0.998 1.000 0.000
#> SRR1812751 1 0.0000 0.998 1.000 0.000
#> SRR1812750 1 0.0000 0.998 1.000 0.000
#> SRR1812748 2 0.0000 0.997 0.000 1.000
#> SRR1812749 1 0.0000 0.998 1.000 0.000
#> SRR1812746 2 0.2778 0.953 0.048 0.952
#> SRR1812745 2 0.0376 0.997 0.004 0.996
#> SRR1812747 2 0.0376 0.997 0.004 0.996
#> SRR1812744 2 0.0000 0.997 0.000 1.000
#> SRR1812743 2 0.0000 0.997 0.000 1.000
#> SRR1812742 2 0.0376 0.997 0.004 0.996
#> SRR1812737 2 0.0000 0.997 0.000 1.000
#> SRR1812735 2 0.0000 0.997 0.000 1.000
#> SRR1812734 2 0.0376 0.997 0.004 0.996
#> SRR1812733 2 0.0000 0.997 0.000 1.000
#> SRR1812736 2 0.0376 0.997 0.004 0.996
#> SRR1812732 2 0.0000 0.997 0.000 1.000
#> SRR1812730 2 0.0376 0.997 0.004 0.996
#> SRR1812731 2 0.0000 0.997 0.000 1.000
#> SRR1812729 2 0.0000 0.997 0.000 1.000
#> SRR1812727 2 0.0376 0.997 0.004 0.996
#> SRR1812726 2 0.0376 0.997 0.004 0.996
#> SRR1812728 2 0.0376 0.997 0.004 0.996
#> SRR1812724 2 0.0000 0.997 0.000 1.000
#> SRR1812725 2 0.0376 0.997 0.004 0.996
#> SRR1812723 2 0.0376 0.997 0.004 0.996
#> SRR1812722 2 0.0376 0.997 0.004 0.996
#> SRR1812721 2 0.0000 0.997 0.000 1.000
#> SRR1812718 2 0.0376 0.997 0.004 0.996
#> SRR1812717 2 0.0000 0.997 0.000 1.000
#> SRR1812716 2 0.0376 0.997 0.004 0.996
#> SRR1812715 2 0.0000 0.997 0.000 1.000
#> SRR1812714 2 0.0376 0.997 0.004 0.996
#> SRR1812719 2 0.0376 0.997 0.004 0.996
#> SRR1812713 2 0.0000 0.997 0.000 1.000
#> SRR1812712 2 0.0000 0.997 0.000 1.000
#> SRR1812711 2 0.0376 0.997 0.004 0.996
#> SRR1812710 2 0.0000 0.997 0.000 1.000
#> SRR1812709 2 0.0000 0.997 0.000 1.000
#> SRR1812708 1 0.0000 0.998 1.000 0.000
#> SRR1812707 2 0.0000 0.997 0.000 1.000
#> SRR1812705 2 0.0376 0.997 0.004 0.996
#> SRR1812706 2 0.0376 0.997 0.004 0.996
#> SRR1812704 2 0.0000 0.997 0.000 1.000
#> SRR1812703 2 0.0376 0.997 0.004 0.996
#> SRR1812702 2 0.0376 0.997 0.004 0.996
#> SRR1812741 1 0.0938 0.990 0.988 0.012
#> SRR1812740 2 0.0000 0.997 0.000 1.000
#> SRR1812739 2 0.0000 0.997 0.000 1.000
#> SRR1812738 2 0.0000 0.997 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1812752 1 0.0000 0.9178 1.000 0.000 0.000
#> SRR1812753 1 0.0000 0.9178 1.000 0.000 0.000
#> SRR1812751 1 0.0000 0.9178 1.000 0.000 0.000
#> SRR1812750 1 0.0747 0.9174 0.984 0.000 0.016
#> SRR1812748 3 0.6225 0.1460 0.000 0.432 0.568
#> SRR1812749 1 0.0747 0.9174 0.984 0.000 0.016
#> SRR1812746 3 0.1129 0.6032 0.004 0.020 0.976
#> SRR1812745 3 0.2537 0.6726 0.000 0.080 0.920
#> SRR1812747 3 0.6274 0.4344 0.000 0.456 0.544
#> SRR1812744 2 0.6192 0.2581 0.000 0.580 0.420
#> SRR1812743 2 0.1163 0.7899 0.000 0.972 0.028
#> SRR1812742 3 0.6302 0.3910 0.000 0.480 0.520
#> SRR1812737 2 0.0892 0.7908 0.000 0.980 0.020
#> SRR1812735 2 0.5859 0.0938 0.000 0.656 0.344
#> SRR1812734 3 0.5882 0.2394 0.000 0.348 0.652
#> SRR1812733 2 0.6291 -0.0796 0.000 0.532 0.468
#> SRR1812736 3 0.2537 0.6726 0.000 0.080 0.920
#> SRR1812732 2 0.3192 0.7170 0.000 0.888 0.112
#> SRR1812730 3 0.3686 0.6928 0.000 0.140 0.860
#> SRR1812731 2 0.0892 0.7908 0.000 0.980 0.020
#> SRR1812729 2 0.1163 0.7898 0.000 0.972 0.028
#> SRR1812727 3 0.6305 -0.0495 0.000 0.484 0.516
#> SRR1812726 2 0.6267 -0.2709 0.000 0.548 0.452
#> SRR1812728 3 0.4796 0.6685 0.000 0.220 0.780
#> SRR1812724 2 0.0592 0.7913 0.000 0.988 0.012
#> SRR1812725 3 0.4931 0.6614 0.000 0.232 0.768
#> SRR1812723 3 0.6307 0.3849 0.000 0.488 0.512
#> SRR1812722 2 0.6267 -0.2709 0.000 0.548 0.452
#> SRR1812721 2 0.0892 0.7908 0.000 0.980 0.020
#> SRR1812718 3 0.6307 0.3849 0.000 0.488 0.512
#> SRR1812717 2 0.0592 0.7913 0.000 0.988 0.012
#> SRR1812716 3 0.3686 0.6928 0.000 0.140 0.860
#> SRR1812715 2 0.0892 0.7908 0.000 0.980 0.020
#> SRR1812714 2 0.3116 0.7196 0.000 0.892 0.108
#> SRR1812719 3 0.1753 0.6508 0.000 0.048 0.952
#> SRR1812713 2 0.2356 0.7592 0.000 0.928 0.072
#> SRR1812712 2 0.2356 0.7592 0.000 0.928 0.072
#> SRR1812711 3 0.6308 0.3752 0.000 0.492 0.508
#> SRR1812710 2 0.0892 0.7908 0.000 0.980 0.020
#> SRR1812709 2 0.0592 0.7913 0.000 0.988 0.012
#> SRR1812708 1 0.1411 0.9108 0.964 0.000 0.036
#> SRR1812707 2 0.0892 0.7908 0.000 0.980 0.020
#> SRR1812705 3 0.6307 0.3849 0.000 0.488 0.512
#> SRR1812706 3 0.3816 0.6914 0.000 0.148 0.852
#> SRR1812704 2 0.2537 0.7693 0.000 0.920 0.080
#> SRR1812703 2 0.4750 0.6485 0.000 0.784 0.216
#> SRR1812702 3 0.3686 0.6928 0.000 0.140 0.860
#> SRR1812741 1 0.8257 0.3507 0.544 0.372 0.084
#> SRR1812740 3 0.3551 0.6902 0.000 0.132 0.868
#> SRR1812739 2 0.4002 0.6754 0.000 0.840 0.160
#> SRR1812738 2 0.0424 0.7909 0.000 0.992 0.008
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1812752 1 0.0000 0.94746 1.00 0.000 0.000 0.000
#> SRR1812753 1 0.0000 0.94746 1.00 0.000 0.000 0.000
#> SRR1812751 1 0.0000 0.94746 1.00 0.000 0.000 0.000
#> SRR1812750 1 0.2255 0.94248 0.92 0.012 0.068 0.000
#> SRR1812748 4 0.7902 -0.29224 0.00 0.296 0.352 0.352
#> SRR1812749 1 0.2255 0.94248 0.92 0.012 0.068 0.000
#> SRR1812746 3 0.4605 0.50056 0.00 0.336 0.664 0.000
#> SRR1812745 2 0.4707 0.52328 0.00 0.760 0.204 0.036
#> SRR1812747 2 0.5751 0.71854 0.00 0.712 0.164 0.124
#> SRR1812744 3 0.5131 0.60794 0.00 0.028 0.692 0.280
#> SRR1812743 4 0.4104 0.74093 0.00 0.028 0.164 0.808
#> SRR1812742 2 0.6193 0.68672 0.00 0.672 0.180 0.148
#> SRR1812737 4 0.3962 0.74740 0.00 0.028 0.152 0.820
#> SRR1812735 2 0.7253 0.38025 0.00 0.484 0.152 0.364
#> SRR1812734 3 0.4868 0.61867 0.00 0.212 0.748 0.040
#> SRR1812733 4 0.6187 0.39081 0.00 0.236 0.108 0.656
#> SRR1812736 2 0.4655 0.52051 0.00 0.760 0.208 0.032
#> SRR1812732 4 0.5466 -0.00562 0.00 0.016 0.436 0.548
#> SRR1812730 2 0.2830 0.66648 0.00 0.900 0.040 0.060
#> SRR1812731 4 0.3910 0.74596 0.00 0.024 0.156 0.820
#> SRR1812729 4 0.3052 0.68379 0.00 0.136 0.004 0.860
#> SRR1812727 3 0.5793 0.59124 0.00 0.324 0.628 0.048
#> SRR1812726 2 0.5993 0.70151 0.00 0.692 0.160 0.148
#> SRR1812728 2 0.2676 0.70690 0.00 0.896 0.012 0.092
#> SRR1812724 4 0.0657 0.75044 0.00 0.004 0.012 0.984
#> SRR1812725 2 0.3037 0.70112 0.00 0.880 0.020 0.100
#> SRR1812723 2 0.5758 0.71826 0.00 0.712 0.160 0.128
#> SRR1812722 2 0.5990 0.70291 0.00 0.692 0.164 0.144
#> SRR1812721 4 0.4105 0.74341 0.00 0.032 0.156 0.812
#> SRR1812718 2 0.5758 0.71830 0.00 0.712 0.160 0.128
#> SRR1812717 4 0.0376 0.75470 0.00 0.004 0.004 0.992
#> SRR1812716 2 0.2919 0.66652 0.00 0.896 0.044 0.060
#> SRR1812715 4 0.3913 0.74567 0.00 0.028 0.148 0.824
#> SRR1812714 3 0.6100 0.51686 0.00 0.072 0.624 0.304
#> SRR1812719 2 0.5510 0.06677 0.00 0.600 0.376 0.024
#> SRR1812713 4 0.1767 0.74463 0.00 0.044 0.012 0.944
#> SRR1812712 4 0.1635 0.74571 0.00 0.044 0.008 0.948
#> SRR1812711 2 0.5763 0.71636 0.00 0.712 0.156 0.132
#> SRR1812710 4 0.3913 0.74567 0.00 0.028 0.148 0.824
#> SRR1812709 4 0.0376 0.75470 0.00 0.004 0.004 0.992
#> SRR1812708 1 0.3707 0.88626 0.84 0.028 0.132 0.000
#> SRR1812707 4 0.3863 0.74758 0.00 0.028 0.144 0.828
#> SRR1812705 2 0.5758 0.71826 0.00 0.712 0.160 0.128
#> SRR1812706 2 0.1890 0.68141 0.00 0.936 0.008 0.056
#> SRR1812704 4 0.2647 0.69659 0.00 0.120 0.000 0.880
#> SRR1812703 3 0.7058 0.59562 0.00 0.168 0.560 0.272
#> SRR1812702 2 0.2919 0.66652 0.00 0.896 0.044 0.060
#> SRR1812741 3 0.7938 0.39350 0.18 0.020 0.488 0.312
#> SRR1812740 2 0.4595 0.55719 0.00 0.780 0.176 0.044
#> SRR1812739 4 0.3164 0.67158 0.00 0.064 0.052 0.884
#> SRR1812738 4 0.1297 0.75275 0.00 0.016 0.020 0.964
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1812752 1 0.000 0.8876 1.000 0.000 0.000 0.000 0.000
#> SRR1812753 1 0.000 0.8876 1.000 0.000 0.000 0.000 0.000
#> SRR1812751 1 0.000 0.8876 1.000 0.000 0.000 0.000 0.000
#> SRR1812750 1 0.330 0.8763 0.852 0.004 0.108 0.004 0.032
#> SRR1812748 3 0.614 0.2372 0.000 0.040 0.612 0.264 0.084
#> SRR1812749 1 0.330 0.8763 0.852 0.004 0.108 0.004 0.032
#> SRR1812746 3 0.385 0.1692 0.000 0.036 0.784 0.000 0.180
#> SRR1812745 3 0.473 0.4638 0.000 0.400 0.580 0.000 0.020
#> SRR1812747 2 0.258 0.6763 0.000 0.900 0.064 0.020 0.016
#> SRR1812744 5 0.345 0.7807 0.000 0.004 0.064 0.088 0.844
#> SRR1812743 4 0.476 0.6712 0.000 0.144 0.036 0.764 0.056
#> SRR1812742 2 0.469 0.5749 0.000 0.776 0.080 0.112 0.032
#> SRR1812737 4 0.432 0.6782 0.000 0.144 0.028 0.788 0.040
#> SRR1812735 2 0.591 0.3646 0.000 0.624 0.100 0.256 0.020
#> SRR1812734 5 0.374 0.7109 0.000 0.004 0.224 0.008 0.764
#> SRR1812733 4 0.701 0.4421 0.000 0.088 0.228 0.564 0.120
#> SRR1812736 3 0.477 0.4710 0.000 0.384 0.592 0.000 0.024
#> SRR1812732 4 0.566 0.0157 0.000 0.016 0.044 0.500 0.440
#> SRR1812730 2 0.521 0.2115 0.000 0.620 0.332 0.016 0.032
#> SRR1812731 4 0.461 0.6748 0.000 0.136 0.036 0.776 0.052
#> SRR1812729 4 0.556 0.6538 0.000 0.108 0.056 0.716 0.120
#> SRR1812727 5 0.389 0.7584 0.000 0.112 0.064 0.008 0.816
#> SRR1812726 2 0.173 0.6817 0.000 0.940 0.008 0.040 0.012
#> SRR1812728 2 0.306 0.6379 0.000 0.860 0.112 0.020 0.008
#> SRR1812724 4 0.387 0.6958 0.000 0.016 0.056 0.824 0.104
#> SRR1812725 2 0.355 0.5873 0.000 0.836 0.120 0.024 0.020
#> SRR1812723 2 0.147 0.6848 0.000 0.952 0.020 0.024 0.004
#> SRR1812722 2 0.277 0.6576 0.000 0.896 0.036 0.044 0.024
#> SRR1812721 4 0.495 0.6534 0.000 0.196 0.048 0.728 0.028
#> SRR1812718 2 0.226 0.6790 0.000 0.912 0.060 0.024 0.004
#> SRR1812717 4 0.360 0.6983 0.000 0.020 0.036 0.840 0.104
#> SRR1812716 2 0.503 0.2540 0.000 0.648 0.308 0.016 0.028
#> SRR1812715 4 0.493 0.6523 0.000 0.204 0.048 0.724 0.024
#> SRR1812714 5 0.400 0.7523 0.000 0.084 0.000 0.120 0.796
#> SRR1812719 2 0.618 0.1066 0.000 0.544 0.180 0.000 0.276
#> SRR1812713 4 0.446 0.6815 0.000 0.040 0.044 0.788 0.128
#> SRR1812712 4 0.453 0.6864 0.000 0.040 0.048 0.784 0.128
#> SRR1812711 2 0.243 0.6817 0.000 0.908 0.048 0.036 0.008
#> SRR1812710 4 0.456 0.6587 0.000 0.204 0.028 0.744 0.024
#> SRR1812709 4 0.330 0.7033 0.000 0.020 0.024 0.856 0.100
#> SRR1812708 1 0.584 0.6891 0.616 0.004 0.264 0.004 0.112
#> SRR1812707 4 0.440 0.6758 0.000 0.168 0.036 0.772 0.024
#> SRR1812705 2 0.146 0.6861 0.000 0.952 0.016 0.028 0.004
#> SRR1812706 2 0.462 0.4281 0.000 0.712 0.248 0.016 0.024
#> SRR1812704 4 0.497 0.6732 0.000 0.064 0.056 0.760 0.120
#> SRR1812703 5 0.274 0.7784 0.000 0.044 0.004 0.064 0.888
#> SRR1812702 2 0.505 0.2505 0.000 0.644 0.312 0.016 0.028
#> SRR1812741 4 0.806 -0.1363 0.096 0.000 0.300 0.364 0.240
#> SRR1812740 3 0.441 0.3339 0.000 0.440 0.556 0.000 0.004
#> SRR1812739 4 0.464 0.6647 0.000 0.024 0.072 0.772 0.132
#> SRR1812738 4 0.223 0.6951 0.000 0.008 0.020 0.916 0.056
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1812752 1 0.0000 0.837 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812753 1 0.0000 0.837 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812751 1 0.0000 0.837 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812750 1 0.4128 0.818 0.788 0.072 0.096 0.000 0.000 0.044
#> SRR1812748 3 0.5941 0.401 0.000 0.180 0.636 0.124 0.024 0.036
#> SRR1812749 1 0.4128 0.818 0.788 0.072 0.096 0.000 0.000 0.044
#> SRR1812746 3 0.3351 0.394 0.000 0.108 0.832 0.000 0.040 0.020
#> SRR1812745 3 0.3707 0.607 0.000 0.000 0.680 0.000 0.312 0.008
#> SRR1812747 5 0.3766 0.740 0.000 0.080 0.080 0.008 0.816 0.016
#> SRR1812744 6 0.4621 0.804 0.000 0.116 0.028 0.096 0.008 0.752
#> SRR1812743 2 0.4453 0.589 0.000 0.552 0.000 0.424 0.012 0.012
#> SRR1812742 5 0.5698 0.391 0.000 0.336 0.076 0.016 0.556 0.016
#> SRR1812737 2 0.4179 0.578 0.000 0.516 0.000 0.472 0.012 0.000
#> SRR1812735 2 0.6274 0.127 0.000 0.516 0.080 0.064 0.332 0.008
#> SRR1812734 6 0.3558 0.782 0.000 0.052 0.132 0.004 0.004 0.808
#> SRR1812733 4 0.4377 0.604 0.000 0.028 0.116 0.772 0.076 0.008
#> SRR1812736 3 0.3915 0.618 0.000 0.004 0.692 0.000 0.288 0.016
#> SRR1812732 2 0.5945 0.283 0.000 0.548 0.020 0.184 0.000 0.248
#> SRR1812730 5 0.4576 0.544 0.000 0.008 0.228 0.024 0.708 0.032
#> SRR1812731 2 0.4411 0.597 0.000 0.544 0.004 0.436 0.012 0.004
#> SRR1812729 4 0.2345 0.736 0.000 0.016 0.016 0.896 0.072 0.000
#> SRR1812727 6 0.1925 0.836 0.000 0.004 0.008 0.008 0.060 0.920
#> SRR1812726 5 0.2833 0.751 0.000 0.088 0.008 0.004 0.868 0.032
#> SRR1812728 5 0.1729 0.751 0.000 0.012 0.012 0.004 0.936 0.036
#> SRR1812724 4 0.1387 0.764 0.000 0.068 0.000 0.932 0.000 0.000
#> SRR1812725 5 0.1680 0.742 0.000 0.004 0.012 0.020 0.940 0.024
#> SRR1812723 5 0.1707 0.765 0.000 0.056 0.000 0.004 0.928 0.012
#> SRR1812722 5 0.3515 0.729 0.000 0.116 0.008 0.012 0.824 0.040
#> SRR1812721 2 0.4513 0.604 0.000 0.572 0.000 0.396 0.028 0.004
#> SRR1812718 5 0.3346 0.748 0.000 0.064 0.080 0.012 0.840 0.004
#> SRR1812717 4 0.1075 0.760 0.000 0.048 0.000 0.952 0.000 0.000
#> SRR1812716 5 0.3986 0.584 0.000 0.004 0.172 0.024 0.772 0.028
#> SRR1812715 2 0.4952 0.600 0.000 0.568 0.004 0.376 0.044 0.008
#> SRR1812714 6 0.3475 0.845 0.000 0.068 0.000 0.040 0.056 0.836
#> SRR1812719 5 0.4931 0.497 0.000 0.024 0.096 0.000 0.692 0.188
#> SRR1812713 4 0.0603 0.771 0.000 0.004 0.000 0.980 0.016 0.000
#> SRR1812712 4 0.2112 0.764 0.000 0.088 0.000 0.896 0.016 0.000
#> SRR1812711 5 0.3471 0.750 0.000 0.076 0.064 0.004 0.836 0.020
#> SRR1812710 2 0.4778 0.589 0.000 0.492 0.000 0.464 0.040 0.004
#> SRR1812709 4 0.2260 0.701 0.000 0.140 0.000 0.860 0.000 0.000
#> SRR1812708 1 0.7060 0.526 0.440 0.192 0.264 0.000 0.000 0.104
#> SRR1812707 2 0.4654 0.599 0.000 0.512 0.000 0.452 0.032 0.004
#> SRR1812705 5 0.1707 0.765 0.000 0.056 0.000 0.004 0.928 0.012
#> SRR1812706 5 0.4089 0.659 0.000 0.012 0.160 0.024 0.776 0.028
#> SRR1812704 4 0.2959 0.739 0.000 0.032 0.012 0.876 0.056 0.024
#> SRR1812703 6 0.3164 0.849 0.000 0.012 0.000 0.096 0.048 0.844
#> SRR1812702 5 0.3986 0.584 0.000 0.004 0.172 0.024 0.772 0.028
#> SRR1812741 2 0.7034 0.084 0.052 0.516 0.244 0.140 0.000 0.048
#> SRR1812740 3 0.4631 0.494 0.000 0.020 0.596 0.004 0.368 0.012
#> SRR1812739 4 0.3590 0.687 0.000 0.152 0.028 0.800 0.000 0.020
#> SRR1812738 4 0.3955 -0.142 0.000 0.340 0.004 0.648 0.000 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 14626 rows and 51 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.971 0.984 0.4312 0.576 0.576
#> 3 3 0.679 0.838 0.891 0.5598 0.721 0.527
#> 4 4 0.625 0.541 0.753 0.1079 0.900 0.713
#> 5 5 0.596 0.475 0.703 0.0701 0.865 0.556
#> 6 6 0.644 0.518 0.686 0.0438 0.899 0.560
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
#> SRR1812752 1 0.0000 0.991 1.000 0.000
#> SRR1812753 1 0.0000 0.991 1.000 0.000
#> SRR1812751 1 0.0000 0.991 1.000 0.000
#> SRR1812750 1 0.0000 0.991 1.000 0.000
#> SRR1812748 2 0.7528 0.735 0.216 0.784
#> SRR1812749 1 0.0000 0.991 1.000 0.000
#> SRR1812746 1 0.0672 0.988 0.992 0.008
#> SRR1812745 2 0.1633 0.968 0.024 0.976
#> SRR1812747 2 0.0376 0.981 0.004 0.996
#> SRR1812744 1 0.0938 0.988 0.988 0.012
#> SRR1812743 2 0.1843 0.967 0.028 0.972
#> SRR1812742 2 0.2778 0.952 0.048 0.952
#> SRR1812737 2 0.0672 0.980 0.008 0.992
#> SRR1812735 2 0.0672 0.980 0.008 0.992
#> SRR1812734 1 0.0672 0.988 0.992 0.008
#> SRR1812733 2 0.0000 0.981 0.000 1.000
#> SRR1812736 2 0.7602 0.733 0.220 0.780
#> SRR1812732 1 0.3274 0.942 0.940 0.060
#> SRR1812730 2 0.0376 0.981 0.004 0.996
#> SRR1812731 2 0.0672 0.980 0.008 0.992
#> SRR1812729 2 0.0000 0.981 0.000 1.000
#> SRR1812727 1 0.0000 0.991 1.000 0.000
#> SRR1812726 2 0.0938 0.980 0.012 0.988
#> SRR1812728 2 0.0376 0.981 0.004 0.996
#> SRR1812724 2 0.0000 0.981 0.000 1.000
#> SRR1812725 2 0.0376 0.981 0.004 0.996
#> SRR1812723 2 0.0672 0.981 0.008 0.992
#> SRR1812722 2 0.0938 0.980 0.012 0.988
#> SRR1812721 2 0.0672 0.980 0.008 0.992
#> SRR1812718 2 0.0376 0.981 0.004 0.996
#> SRR1812717 2 0.0376 0.981 0.004 0.996
#> SRR1812716 2 0.0376 0.981 0.004 0.996
#> SRR1812715 2 0.0672 0.980 0.008 0.992
#> SRR1812714 1 0.0376 0.990 0.996 0.004
#> SRR1812719 1 0.0376 0.990 0.996 0.004
#> SRR1812713 2 0.0000 0.981 0.000 1.000
#> SRR1812712 2 0.0000 0.981 0.000 1.000
#> SRR1812711 2 0.0938 0.980 0.012 0.988
#> SRR1812710 2 0.0672 0.980 0.008 0.992
#> SRR1812709 2 0.0000 0.981 0.000 1.000
#> SRR1812708 1 0.0000 0.991 1.000 0.000
#> SRR1812707 2 0.0672 0.980 0.008 0.992
#> SRR1812705 2 0.0938 0.980 0.012 0.988
#> SRR1812706 2 0.0376 0.981 0.004 0.996
#> SRR1812704 2 0.0000 0.981 0.000 1.000
#> SRR1812703 1 0.2043 0.971 0.968 0.032
#> SRR1812702 2 0.0376 0.981 0.004 0.996
#> SRR1812741 1 0.0376 0.990 0.996 0.004
#> SRR1812740 2 0.0000 0.981 0.000 1.000
#> SRR1812739 2 0.0000 0.981 0.000 1.000
#> SRR1812738 2 0.0376 0.981 0.004 0.996
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1812752 1 0.0000 0.967 1.000 0.000 0.000
#> SRR1812753 1 0.0000 0.967 1.000 0.000 0.000
#> SRR1812751 1 0.0000 0.967 1.000 0.000 0.000
#> SRR1812750 1 0.0000 0.967 1.000 0.000 0.000
#> SRR1812748 2 0.6111 0.629 0.000 0.604 0.396
#> SRR1812749 1 0.0000 0.967 1.000 0.000 0.000
#> SRR1812746 1 0.1031 0.957 0.976 0.000 0.024
#> SRR1812745 3 0.0000 0.827 0.000 0.000 1.000
#> SRR1812747 3 0.4654 0.826 0.000 0.208 0.792
#> SRR1812744 1 0.5554 0.806 0.812 0.076 0.112
#> SRR1812743 2 0.0000 0.836 0.000 1.000 0.000
#> SRR1812742 3 0.5016 0.813 0.000 0.240 0.760
#> SRR1812737 2 0.0000 0.836 0.000 1.000 0.000
#> SRR1812735 3 0.6305 0.444 0.000 0.484 0.516
#> SRR1812734 1 0.1753 0.941 0.952 0.000 0.048
#> SRR1812733 2 0.6286 0.500 0.000 0.536 0.464
#> SRR1812736 3 0.0000 0.827 0.000 0.000 1.000
#> SRR1812732 2 0.2446 0.846 0.012 0.936 0.052
#> SRR1812730 3 0.0000 0.827 0.000 0.000 1.000
#> SRR1812731 2 0.0000 0.836 0.000 1.000 0.000
#> SRR1812729 2 0.4002 0.834 0.000 0.840 0.160
#> SRR1812727 1 0.0000 0.967 1.000 0.000 0.000
#> SRR1812726 3 0.5431 0.780 0.000 0.284 0.716
#> SRR1812728 3 0.3030 0.834 0.004 0.092 0.904
#> SRR1812724 2 0.4654 0.816 0.000 0.792 0.208
#> SRR1812725 3 0.0424 0.828 0.000 0.008 0.992
#> SRR1812723 3 0.4887 0.819 0.000 0.228 0.772
#> SRR1812722 3 0.5754 0.766 0.004 0.296 0.700
#> SRR1812721 2 0.0000 0.836 0.000 1.000 0.000
#> SRR1812718 3 0.4654 0.826 0.000 0.208 0.792
#> SRR1812717 2 0.2625 0.851 0.000 0.916 0.084
#> SRR1812716 3 0.0000 0.827 0.000 0.000 1.000
#> SRR1812715 2 0.0000 0.836 0.000 1.000 0.000
#> SRR1812714 1 0.0237 0.965 0.996 0.004 0.000
#> SRR1812719 1 0.1031 0.953 0.976 0.000 0.024
#> SRR1812713 2 0.5016 0.799 0.000 0.760 0.240
#> SRR1812712 2 0.5016 0.799 0.000 0.760 0.240
#> SRR1812711 3 0.5016 0.813 0.000 0.240 0.760
#> SRR1812710 2 0.0000 0.836 0.000 1.000 0.000
#> SRR1812709 2 0.3619 0.843 0.000 0.864 0.136
#> SRR1812708 1 0.0000 0.967 1.000 0.000 0.000
#> SRR1812707 2 0.0000 0.836 0.000 1.000 0.000
#> SRR1812705 3 0.4974 0.816 0.000 0.236 0.764
#> SRR1812706 3 0.0000 0.827 0.000 0.000 1.000
#> SRR1812704 2 0.5291 0.782 0.000 0.732 0.268
#> SRR1812703 1 0.4261 0.846 0.848 0.012 0.140
#> SRR1812702 3 0.0000 0.827 0.000 0.000 1.000
#> SRR1812741 1 0.0000 0.967 1.000 0.000 0.000
#> SRR1812740 3 0.0000 0.827 0.000 0.000 1.000
#> SRR1812739 2 0.5016 0.799 0.000 0.760 0.240
#> SRR1812738 2 0.2537 0.851 0.000 0.920 0.080
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1812752 1 0.0000 0.8449 1.000 0.000 0.000 0.000
#> SRR1812753 1 0.0000 0.8449 1.000 0.000 0.000 0.000
#> SRR1812751 1 0.0000 0.8449 1.000 0.000 0.000 0.000
#> SRR1812750 1 0.0000 0.8449 1.000 0.000 0.000 0.000
#> SRR1812748 3 0.7541 -0.3146 0.000 0.388 0.424 0.188
#> SRR1812749 1 0.0000 0.8449 1.000 0.000 0.000 0.000
#> SRR1812746 1 0.4711 0.5934 0.740 0.024 0.236 0.000
#> SRR1812745 3 0.2271 0.5614 0.000 0.076 0.916 0.008
#> SRR1812747 3 0.4624 0.5904 0.000 0.340 0.660 0.000
#> SRR1812744 2 0.8943 0.2520 0.152 0.492 0.136 0.220
#> SRR1812743 4 0.4454 0.6862 0.000 0.308 0.000 0.692
#> SRR1812742 3 0.5396 0.4882 0.000 0.464 0.524 0.012
#> SRR1812737 4 0.4164 0.6995 0.000 0.264 0.000 0.736
#> SRR1812735 2 0.7559 -0.2914 0.000 0.460 0.336 0.204
#> SRR1812734 2 0.8007 0.0867 0.224 0.480 0.280 0.016
#> SRR1812733 4 0.6585 0.2543 0.000 0.104 0.312 0.584
#> SRR1812736 3 0.2198 0.5660 0.000 0.072 0.920 0.008
#> SRR1812732 2 0.6717 -0.0269 0.028 0.532 0.040 0.400
#> SRR1812730 3 0.0672 0.6149 0.000 0.008 0.984 0.008
#> SRR1812731 4 0.4193 0.7009 0.000 0.268 0.000 0.732
#> SRR1812729 4 0.4966 0.5790 0.000 0.156 0.076 0.768
#> SRR1812727 1 0.4643 0.5262 0.656 0.344 0.000 0.000
#> SRR1812726 3 0.5273 0.5023 0.000 0.456 0.536 0.008
#> SRR1812728 3 0.3710 0.6301 0.000 0.192 0.804 0.004
#> SRR1812724 4 0.1302 0.7229 0.000 0.044 0.000 0.956
#> SRR1812725 3 0.3636 0.6316 0.000 0.172 0.820 0.008
#> SRR1812723 3 0.4898 0.5463 0.000 0.416 0.584 0.000
#> SRR1812722 2 0.5512 -0.5595 0.000 0.496 0.488 0.016
#> SRR1812721 4 0.4761 0.6167 0.000 0.372 0.000 0.628
#> SRR1812718 3 0.4964 0.5694 0.000 0.380 0.616 0.004
#> SRR1812717 4 0.0592 0.7295 0.000 0.016 0.000 0.984
#> SRR1812716 3 0.0336 0.6190 0.000 0.000 0.992 0.008
#> SRR1812715 4 0.4643 0.6521 0.000 0.344 0.000 0.656
#> SRR1812714 1 0.6200 0.2819 0.504 0.444 0.000 0.052
#> SRR1812719 1 0.5318 0.6243 0.732 0.072 0.196 0.000
#> SRR1812713 4 0.1629 0.7161 0.000 0.024 0.024 0.952
#> SRR1812712 4 0.2036 0.7139 0.000 0.032 0.032 0.936
#> SRR1812711 3 0.5268 0.5072 0.000 0.452 0.540 0.008
#> SRR1812710 4 0.4564 0.6576 0.000 0.328 0.000 0.672
#> SRR1812709 4 0.1118 0.7321 0.000 0.036 0.000 0.964
#> SRR1812708 1 0.0000 0.8449 1.000 0.000 0.000 0.000
#> SRR1812707 4 0.4072 0.7048 0.000 0.252 0.000 0.748
#> SRR1812705 3 0.5097 0.5335 0.000 0.428 0.568 0.004
#> SRR1812706 3 0.1635 0.6287 0.000 0.044 0.948 0.008
#> SRR1812704 4 0.3224 0.6760 0.000 0.016 0.120 0.864
#> SRR1812703 2 0.8901 0.1339 0.244 0.440 0.068 0.248
#> SRR1812702 3 0.0336 0.6190 0.000 0.000 0.992 0.008
#> SRR1812741 1 0.0000 0.8449 1.000 0.000 0.000 0.000
#> SRR1812740 3 0.2124 0.5714 0.000 0.068 0.924 0.008
#> SRR1812739 4 0.4337 0.6006 0.000 0.140 0.052 0.808
#> SRR1812738 4 0.1902 0.7319 0.000 0.064 0.004 0.932
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1812752 1 0.000 0.8922 1.000 0.000 0.000 0.000 0.000
#> SRR1812753 1 0.000 0.8922 1.000 0.000 0.000 0.000 0.000
#> SRR1812751 1 0.000 0.8922 1.000 0.000 0.000 0.000 0.000
#> SRR1812750 1 0.000 0.8922 1.000 0.000 0.000 0.000 0.000
#> SRR1812748 3 0.650 0.2826 0.000 0.024 0.564 0.148 0.264
#> SRR1812749 1 0.000 0.8922 1.000 0.000 0.000 0.000 0.000
#> SRR1812746 1 0.452 0.5614 0.724 0.012 0.236 0.000 0.028
#> SRR1812745 2 0.670 0.3898 0.000 0.396 0.360 0.000 0.244
#> SRR1812747 2 0.511 0.6562 0.000 0.728 0.040 0.052 0.180
#> SRR1812744 3 0.477 0.4893 0.056 0.004 0.744 0.012 0.184
#> SRR1812743 4 0.220 0.5651 0.000 0.008 0.016 0.916 0.060
#> SRR1812742 2 0.659 0.4741 0.000 0.556 0.032 0.280 0.132
#> SRR1812737 4 0.189 0.5517 0.000 0.004 0.000 0.916 0.080
#> SRR1812735 4 0.614 0.1038 0.000 0.312 0.000 0.532 0.156
#> SRR1812734 3 0.181 0.5183 0.060 0.000 0.928 0.000 0.012
#> SRR1812733 5 0.576 0.3784 0.000 0.064 0.100 0.136 0.700
#> SRR1812736 3 0.676 -0.4319 0.000 0.336 0.392 0.000 0.272
#> SRR1812732 3 0.619 0.1605 0.004 0.000 0.496 0.376 0.124
#> SRR1812730 2 0.635 0.5409 0.000 0.524 0.232 0.000 0.244
#> SRR1812731 4 0.157 0.5620 0.000 0.000 0.004 0.936 0.060
#> SRR1812729 5 0.615 0.4708 0.000 0.156 0.004 0.276 0.564
#> SRR1812727 3 0.444 -0.0197 0.464 0.000 0.532 0.000 0.004
#> SRR1812726 2 0.366 0.6232 0.000 0.836 0.024 0.108 0.032
#> SRR1812728 2 0.358 0.6671 0.000 0.840 0.068 0.008 0.084
#> SRR1812724 4 0.475 -0.5775 0.000 0.000 0.016 0.492 0.492
#> SRR1812725 2 0.353 0.6672 0.000 0.832 0.072 0.000 0.096
#> SRR1812723 2 0.198 0.6580 0.000 0.928 0.004 0.044 0.024
#> SRR1812722 2 0.571 0.4772 0.000 0.668 0.048 0.224 0.060
#> SRR1812721 4 0.357 0.5251 0.000 0.092 0.004 0.836 0.068
#> SRR1812718 2 0.377 0.6644 0.000 0.812 0.008 0.036 0.144
#> SRR1812717 5 0.445 0.4988 0.000 0.000 0.004 0.492 0.504
#> SRR1812716 2 0.576 0.5824 0.000 0.620 0.192 0.000 0.188
#> SRR1812715 4 0.293 0.5453 0.000 0.068 0.000 0.872 0.060
#> SRR1812714 3 0.706 0.3774 0.244 0.040 0.588 0.060 0.068
#> SRR1812719 1 0.697 0.2889 0.540 0.124 0.272 0.000 0.064
#> SRR1812713 5 0.449 0.5503 0.000 0.000 0.008 0.420 0.572
#> SRR1812712 5 0.466 0.5187 0.000 0.000 0.012 0.484 0.504
#> SRR1812711 2 0.367 0.6461 0.000 0.828 0.004 0.100 0.068
#> SRR1812710 4 0.273 0.5695 0.000 0.060 0.000 0.884 0.056
#> SRR1812709 4 0.432 -0.3848 0.000 0.000 0.004 0.600 0.396
#> SRR1812708 1 0.000 0.8922 1.000 0.000 0.000 0.000 0.000
#> SRR1812707 4 0.177 0.5392 0.000 0.004 0.000 0.924 0.072
#> SRR1812705 2 0.224 0.6510 0.000 0.912 0.004 0.064 0.020
#> SRR1812706 2 0.576 0.6173 0.000 0.616 0.160 0.000 0.224
#> SRR1812704 5 0.599 0.5103 0.000 0.064 0.024 0.368 0.544
#> SRR1812703 3 0.676 0.3602 0.080 0.040 0.584 0.024 0.272
#> SRR1812702 2 0.567 0.5894 0.000 0.632 0.188 0.000 0.180
#> SRR1812741 1 0.029 0.8859 0.992 0.000 0.000 0.008 0.000
#> SRR1812740 2 0.678 0.3774 0.000 0.380 0.340 0.000 0.280
#> SRR1812739 5 0.614 0.4442 0.000 0.004 0.112 0.424 0.460
#> SRR1812738 4 0.464 -0.2690 0.000 0.000 0.016 0.584 0.400
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1812752 1 0.0000 0.8747 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812753 1 0.0000 0.8747 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812751 1 0.0000 0.8747 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812750 1 0.0000 0.8747 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812748 3 0.6573 -0.0541 0.000 0.000 0.512 0.080 0.260 0.148
#> SRR1812749 1 0.0000 0.8747 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812746 1 0.4478 0.5715 0.716 0.000 0.176 0.000 0.104 0.004
#> SRR1812745 3 0.5044 0.5341 0.000 0.220 0.656 0.004 0.116 0.004
#> SRR1812747 2 0.6047 0.3797 0.000 0.548 0.308 0.016 0.024 0.104
#> SRR1812744 5 0.4948 0.6339 0.012 0.000 0.104 0.088 0.740 0.056
#> SRR1812743 6 0.4550 0.5968 0.000 0.004 0.040 0.220 0.024 0.712
#> SRR1812742 2 0.6443 0.2871 0.000 0.428 0.228 0.000 0.024 0.320
#> SRR1812737 6 0.4154 0.6375 0.000 0.016 0.000 0.296 0.012 0.676
#> SRR1812735 6 0.7016 0.1802 0.000 0.268 0.184 0.036 0.036 0.476
#> SRR1812734 5 0.3056 0.6351 0.012 0.000 0.140 0.000 0.832 0.016
#> SRR1812733 4 0.6085 0.3956 0.000 0.032 0.316 0.540 0.012 0.100
#> SRR1812736 3 0.5487 0.5008 0.000 0.168 0.644 0.000 0.156 0.032
#> SRR1812732 5 0.7147 0.2646 0.000 0.000 0.136 0.144 0.404 0.316
#> SRR1812730 3 0.4433 0.4684 0.000 0.352 0.620 0.008 0.008 0.012
#> SRR1812731 6 0.3913 0.6374 0.000 0.008 0.012 0.240 0.008 0.732
#> SRR1812729 4 0.5733 0.4873 0.000 0.180 0.092 0.648 0.004 0.076
#> SRR1812727 5 0.3684 0.4736 0.300 0.000 0.004 0.000 0.692 0.004
#> SRR1812726 2 0.3528 0.5315 0.000 0.832 0.048 0.000 0.076 0.044
#> SRR1812728 2 0.4313 0.2533 0.000 0.708 0.240 0.000 0.036 0.016
#> SRR1812724 4 0.2971 0.6135 0.000 0.000 0.024 0.848 0.012 0.116
#> SRR1812725 2 0.3725 0.1230 0.000 0.676 0.316 0.000 0.000 0.008
#> SRR1812723 2 0.1531 0.5518 0.000 0.928 0.068 0.000 0.000 0.004
#> SRR1812722 2 0.5817 0.4311 0.000 0.624 0.076 0.000 0.100 0.200
#> SRR1812721 6 0.5765 0.5997 0.000 0.076 0.040 0.248 0.016 0.620
#> SRR1812718 2 0.4482 0.4242 0.000 0.664 0.288 0.000 0.012 0.036
#> SRR1812717 4 0.2703 0.5817 0.000 0.000 0.004 0.824 0.000 0.172
#> SRR1812716 3 0.4220 0.3663 0.000 0.468 0.520 0.008 0.000 0.004
#> SRR1812715 6 0.6388 0.5688 0.000 0.116 0.060 0.176 0.036 0.612
#> SRR1812714 5 0.4457 0.6744 0.092 0.024 0.008 0.044 0.792 0.040
#> SRR1812719 1 0.7686 -0.0880 0.380 0.180 0.128 0.000 0.292 0.020
#> SRR1812713 4 0.1563 0.6310 0.000 0.000 0.012 0.932 0.000 0.056
#> SRR1812712 4 0.2355 0.6164 0.000 0.000 0.004 0.876 0.008 0.112
#> SRR1812711 2 0.4183 0.5454 0.000 0.764 0.148 0.000 0.020 0.068
#> SRR1812710 6 0.4750 0.6555 0.000 0.064 0.000 0.260 0.012 0.664
#> SRR1812709 4 0.3388 0.5041 0.000 0.004 0.004 0.764 0.004 0.224
#> SRR1812708 1 0.0000 0.8747 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812707 6 0.4688 0.5855 0.000 0.020 0.012 0.352 0.008 0.608
#> SRR1812705 2 0.1462 0.5640 0.000 0.936 0.056 0.000 0.000 0.008
#> SRR1812706 3 0.4363 0.3273 0.000 0.400 0.580 0.004 0.008 0.008
#> SRR1812704 4 0.5821 0.4859 0.000 0.036 0.172 0.628 0.008 0.156
#> SRR1812703 5 0.4659 0.6189 0.040 0.008 0.028 0.176 0.740 0.008
#> SRR1812702 3 0.3982 0.3803 0.000 0.460 0.536 0.000 0.000 0.004
#> SRR1812741 1 0.0291 0.8698 0.992 0.000 0.000 0.000 0.004 0.004
#> SRR1812740 3 0.5303 0.5417 0.000 0.204 0.668 0.012 0.096 0.020
#> SRR1812739 4 0.5905 0.4950 0.000 0.000 0.116 0.632 0.104 0.148
#> SRR1812738 4 0.5643 0.0952 0.000 0.004 0.040 0.488 0.048 0.420
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 14626 rows and 51 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.991 0.996 0.2188 0.788 0.788
#> 3 3 0.528 0.723 0.885 1.7081 0.613 0.508
#> 4 4 0.516 0.660 0.808 0.1673 0.848 0.634
#> 5 5 0.535 0.682 0.798 0.0514 0.918 0.745
#> 6 6 0.621 0.578 0.809 0.0574 0.927 0.751
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
#> SRR1812752 1 0.000 1.000 1.000 0.000
#> SRR1812753 1 0.000 1.000 1.000 0.000
#> SRR1812751 1 0.000 1.000 1.000 0.000
#> SRR1812750 1 0.000 1.000 1.000 0.000
#> SRR1812748 2 0.000 0.995 0.000 1.000
#> SRR1812749 1 0.000 1.000 1.000 0.000
#> SRR1812746 2 0.000 0.995 0.000 1.000
#> SRR1812745 2 0.000 0.995 0.000 1.000
#> SRR1812747 2 0.000 0.995 0.000 1.000
#> SRR1812744 2 0.000 0.995 0.000 1.000
#> SRR1812743 2 0.000 0.995 0.000 1.000
#> SRR1812742 2 0.000 0.995 0.000 1.000
#> SRR1812737 2 0.000 0.995 0.000 1.000
#> SRR1812735 2 0.000 0.995 0.000 1.000
#> SRR1812734 2 0.000 0.995 0.000 1.000
#> SRR1812733 2 0.000 0.995 0.000 1.000
#> SRR1812736 2 0.000 0.995 0.000 1.000
#> SRR1812732 2 0.000 0.995 0.000 1.000
#> SRR1812730 2 0.000 0.995 0.000 1.000
#> SRR1812731 2 0.000 0.995 0.000 1.000
#> SRR1812729 2 0.000 0.995 0.000 1.000
#> SRR1812727 2 0.000 0.995 0.000 1.000
#> SRR1812726 2 0.000 0.995 0.000 1.000
#> SRR1812728 2 0.000 0.995 0.000 1.000
#> SRR1812724 2 0.000 0.995 0.000 1.000
#> SRR1812725 2 0.000 0.995 0.000 1.000
#> SRR1812723 2 0.000 0.995 0.000 1.000
#> SRR1812722 2 0.000 0.995 0.000 1.000
#> SRR1812721 2 0.000 0.995 0.000 1.000
#> SRR1812718 2 0.000 0.995 0.000 1.000
#> SRR1812717 2 0.000 0.995 0.000 1.000
#> SRR1812716 2 0.000 0.995 0.000 1.000
#> SRR1812715 2 0.000 0.995 0.000 1.000
#> SRR1812714 2 0.000 0.995 0.000 1.000
#> SRR1812719 2 0.000 0.995 0.000 1.000
#> SRR1812713 2 0.000 0.995 0.000 1.000
#> SRR1812712 2 0.000 0.995 0.000 1.000
#> SRR1812711 2 0.000 0.995 0.000 1.000
#> SRR1812710 2 0.000 0.995 0.000 1.000
#> SRR1812709 2 0.000 0.995 0.000 1.000
#> SRR1812708 1 0.000 1.000 1.000 0.000
#> SRR1812707 2 0.000 0.995 0.000 1.000
#> SRR1812705 2 0.000 0.995 0.000 1.000
#> SRR1812706 2 0.000 0.995 0.000 1.000
#> SRR1812704 2 0.000 0.995 0.000 1.000
#> SRR1812703 2 0.000 0.995 0.000 1.000
#> SRR1812702 2 0.000 0.995 0.000 1.000
#> SRR1812741 2 0.745 0.731 0.212 0.788
#> SRR1812740 2 0.000 0.995 0.000 1.000
#> SRR1812739 2 0.000 0.995 0.000 1.000
#> SRR1812738 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
#> SRR1812752 1 0.0000 1.0000 1.000 0.000 0.000
#> SRR1812753 1 0.0000 1.0000 1.000 0.000 0.000
#> SRR1812751 1 0.0000 1.0000 1.000 0.000 0.000
#> SRR1812750 1 0.0000 1.0000 1.000 0.000 0.000
#> SRR1812748 3 0.4002 0.7078 0.000 0.160 0.840
#> SRR1812749 1 0.0000 1.0000 1.000 0.000 0.000
#> SRR1812746 3 0.0237 0.8383 0.000 0.004 0.996
#> SRR1812745 3 0.0000 0.8402 0.000 0.000 1.000
#> SRR1812747 2 0.6295 0.1823 0.000 0.528 0.472
#> SRR1812744 2 0.6295 0.1478 0.000 0.528 0.472
#> SRR1812743 2 0.1529 0.8224 0.000 0.960 0.040
#> SRR1812742 2 0.6168 0.3563 0.000 0.588 0.412
#> SRR1812737 2 0.0000 0.8226 0.000 1.000 0.000
#> SRR1812735 2 0.4796 0.6950 0.000 0.780 0.220
#> SRR1812734 3 0.2959 0.7740 0.000 0.100 0.900
#> SRR1812733 3 0.4452 0.6664 0.000 0.192 0.808
#> SRR1812736 3 0.0000 0.8402 0.000 0.000 1.000
#> SRR1812732 2 0.1860 0.8186 0.000 0.948 0.052
#> SRR1812730 3 0.0000 0.8402 0.000 0.000 1.000
#> SRR1812731 2 0.2711 0.8085 0.000 0.912 0.088
#> SRR1812729 2 0.4178 0.7557 0.000 0.828 0.172
#> SRR1812727 3 0.5560 0.4863 0.000 0.300 0.700
#> SRR1812726 3 0.6180 0.1621 0.000 0.416 0.584
#> SRR1812728 3 0.0000 0.8402 0.000 0.000 1.000
#> SRR1812724 2 0.0000 0.8226 0.000 1.000 0.000
#> SRR1812725 3 0.0000 0.8402 0.000 0.000 1.000
#> SRR1812723 3 0.4654 0.6420 0.000 0.208 0.792
#> SRR1812722 2 0.6307 0.1140 0.000 0.512 0.488
#> SRR1812721 2 0.4178 0.7531 0.000 0.828 0.172
#> SRR1812718 2 0.6192 0.3369 0.000 0.580 0.420
#> SRR1812717 2 0.0000 0.8226 0.000 1.000 0.000
#> SRR1812716 3 0.0000 0.8402 0.000 0.000 1.000
#> SRR1812715 2 0.0000 0.8226 0.000 1.000 0.000
#> SRR1812714 2 0.3879 0.7583 0.000 0.848 0.152
#> SRR1812719 3 0.0000 0.8402 0.000 0.000 1.000
#> SRR1812713 2 0.0237 0.8222 0.000 0.996 0.004
#> SRR1812712 2 0.0000 0.8226 0.000 1.000 0.000
#> SRR1812711 3 0.6252 0.0599 0.000 0.444 0.556
#> SRR1812710 2 0.0747 0.8237 0.000 0.984 0.016
#> SRR1812709 2 0.0000 0.8226 0.000 1.000 0.000
#> SRR1812708 1 0.0000 1.0000 1.000 0.000 0.000
#> SRR1812707 2 0.1753 0.8209 0.000 0.952 0.048
#> SRR1812705 3 0.5882 0.3628 0.000 0.348 0.652
#> SRR1812706 3 0.0000 0.8402 0.000 0.000 1.000
#> SRR1812704 2 0.4750 0.6469 0.000 0.784 0.216
#> SRR1812703 2 0.4062 0.7182 0.000 0.836 0.164
#> SRR1812702 3 0.0000 0.8402 0.000 0.000 1.000
#> SRR1812741 2 0.0424 0.8215 0.008 0.992 0.000
#> SRR1812740 3 0.0000 0.8402 0.000 0.000 1.000
#> SRR1812739 2 0.0000 0.8226 0.000 1.000 0.000
#> SRR1812738 2 0.2537 0.8108 0.000 0.920 0.080
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1812752 1 0.0000 0.9138 1.000 0.000 0.000 0.000
#> SRR1812753 1 0.0000 0.9138 1.000 0.000 0.000 0.000
#> SRR1812751 1 0.0000 0.9138 1.000 0.000 0.000 0.000
#> SRR1812750 1 0.3726 0.9138 0.788 0.212 0.000 0.000
#> SRR1812748 3 0.2805 0.7262 0.000 0.012 0.888 0.100
#> SRR1812749 1 0.3726 0.9138 0.788 0.212 0.000 0.000
#> SRR1812746 3 0.2081 0.7624 0.000 0.084 0.916 0.000
#> SRR1812745 3 0.0469 0.7798 0.000 0.012 0.988 0.000
#> SRR1812747 2 0.6315 0.2837 0.000 0.540 0.396 0.064
#> SRR1812744 3 0.6660 -0.0359 0.000 0.084 0.464 0.452
#> SRR1812743 4 0.1211 0.8067 0.000 0.000 0.040 0.960
#> SRR1812742 2 0.5906 0.2394 0.000 0.528 0.436 0.036
#> SRR1812737 4 0.0000 0.7948 0.000 0.000 0.000 1.000
#> SRR1812735 2 0.6362 0.6471 0.000 0.656 0.176 0.168
#> SRR1812734 3 0.4633 0.6182 0.000 0.172 0.780 0.048
#> SRR1812733 3 0.2704 0.7118 0.000 0.000 0.876 0.124
#> SRR1812736 3 0.0707 0.7781 0.000 0.020 0.980 0.000
#> SRR1812732 2 0.5865 0.6507 0.000 0.612 0.048 0.340
#> SRR1812730 3 0.0000 0.7796 0.000 0.000 1.000 0.000
#> SRR1812731 4 0.2149 0.7891 0.000 0.000 0.088 0.912
#> SRR1812729 4 0.3142 0.7450 0.000 0.008 0.132 0.860
#> SRR1812727 3 0.5972 0.4590 0.000 0.068 0.640 0.292
#> SRR1812726 3 0.7259 0.2834 0.000 0.156 0.492 0.352
#> SRR1812728 3 0.1940 0.7672 0.000 0.076 0.924 0.000
#> SRR1812724 2 0.4967 0.5172 0.000 0.548 0.000 0.452
#> SRR1812725 3 0.1557 0.7652 0.000 0.056 0.944 0.000
#> SRR1812723 3 0.5655 0.6005 0.000 0.084 0.704 0.212
#> SRR1812722 2 0.5228 0.4456 0.000 0.664 0.312 0.024
#> SRR1812721 4 0.4589 0.6448 0.000 0.048 0.168 0.784
#> SRR1812718 4 0.6605 -0.0561 0.000 0.080 0.440 0.480
#> SRR1812717 2 0.4843 0.5990 0.000 0.604 0.000 0.396
#> SRR1812716 3 0.1118 0.7759 0.000 0.036 0.964 0.000
#> SRR1812715 2 0.4643 0.6410 0.000 0.656 0.000 0.344
#> SRR1812714 2 0.6167 0.6672 0.000 0.648 0.096 0.256
#> SRR1812719 3 0.1302 0.7734 0.000 0.044 0.956 0.000
#> SRR1812713 4 0.0188 0.7963 0.000 0.000 0.004 0.996
#> SRR1812712 4 0.2814 0.6720 0.000 0.132 0.000 0.868
#> SRR1812711 3 0.6510 0.2749 0.000 0.080 0.540 0.380
#> SRR1812710 4 0.0592 0.8029 0.000 0.000 0.016 0.984
#> SRR1812709 4 0.0000 0.7948 0.000 0.000 0.000 1.000
#> SRR1812708 1 0.3726 0.9138 0.788 0.212 0.000 0.000
#> SRR1812707 4 0.1389 0.8053 0.000 0.000 0.048 0.952
#> SRR1812705 3 0.6700 0.4264 0.000 0.112 0.572 0.316
#> SRR1812706 3 0.0469 0.7786 0.000 0.012 0.988 0.000
#> SRR1812704 4 0.3486 0.6384 0.000 0.000 0.188 0.812
#> SRR1812703 4 0.5816 0.4937 0.000 0.144 0.148 0.708
#> SRR1812702 3 0.0336 0.7799 0.000 0.008 0.992 0.000
#> SRR1812741 2 0.4643 0.6282 0.000 0.656 0.000 0.344
#> SRR1812740 3 0.0707 0.7781 0.000 0.020 0.980 0.000
#> SRR1812739 4 0.1118 0.7780 0.000 0.036 0.000 0.964
#> SRR1812738 4 0.2011 0.7932 0.000 0.000 0.080 0.920
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1812752 1 0.3707 1.0000 0.716 0.000 0.284 0.000 0.000
#> SRR1812753 1 0.3707 1.0000 0.716 0.000 0.284 0.000 0.000
#> SRR1812751 1 0.3707 1.0000 0.716 0.000 0.284 0.000 0.000
#> SRR1812750 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> SRR1812748 5 0.1885 0.7231 0.020 0.004 0.000 0.044 0.932
#> SRR1812749 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> SRR1812746 5 0.3610 0.7022 0.056 0.048 0.044 0.000 0.852
#> SRR1812745 5 0.0771 0.7378 0.020 0.004 0.000 0.000 0.976
#> SRR1812747 2 0.7205 -0.0997 0.156 0.416 0.000 0.044 0.384
#> SRR1812744 4 0.6274 0.0996 0.012 0.104 0.000 0.456 0.428
#> SRR1812743 4 0.0609 0.8336 0.000 0.000 0.000 0.980 0.020
#> SRR1812742 5 0.6302 0.1204 0.136 0.384 0.000 0.004 0.476
#> SRR1812737 4 0.0000 0.8300 0.000 0.000 0.000 1.000 0.000
#> SRR1812735 2 0.4096 0.6821 0.000 0.772 0.000 0.052 0.176
#> SRR1812734 5 0.4652 0.5662 0.056 0.188 0.000 0.012 0.744
#> SRR1812733 5 0.1764 0.7170 0.008 0.000 0.000 0.064 0.928
#> SRR1812736 5 0.1012 0.7359 0.020 0.012 0.000 0.000 0.968
#> SRR1812732 2 0.4527 0.7310 0.000 0.732 0.000 0.204 0.064
#> SRR1812730 5 0.0000 0.7392 0.000 0.000 0.000 0.000 1.000
#> SRR1812731 4 0.1341 0.8206 0.000 0.000 0.000 0.944 0.056
#> SRR1812729 4 0.2573 0.7714 0.016 0.000 0.000 0.880 0.104
#> SRR1812727 5 0.6689 0.3323 0.104 0.048 0.000 0.308 0.540
#> SRR1812726 5 0.7888 0.4394 0.264 0.112 0.000 0.184 0.440
#> SRR1812728 5 0.4552 0.6614 0.264 0.040 0.000 0.000 0.696
#> SRR1812724 2 0.4015 0.5858 0.000 0.652 0.000 0.348 0.000
#> SRR1812725 5 0.3940 0.6640 0.220 0.024 0.000 0.000 0.756
#> SRR1812723 5 0.6814 0.5662 0.264 0.048 0.000 0.136 0.552
#> SRR1812722 2 0.4325 0.5360 0.036 0.724 0.000 0.000 0.240
#> SRR1812721 4 0.4101 0.6218 0.000 0.048 0.000 0.768 0.184
#> SRR1812718 5 0.7338 0.4213 0.220 0.048 0.000 0.256 0.476
#> SRR1812717 2 0.3684 0.6662 0.000 0.720 0.000 0.280 0.000
#> SRR1812716 5 0.1661 0.7317 0.036 0.024 0.000 0.000 0.940
#> SRR1812715 2 0.3461 0.7108 0.000 0.772 0.000 0.224 0.004
#> SRR1812714 2 0.4361 0.7250 0.000 0.768 0.000 0.124 0.108
#> SRR1812719 5 0.2228 0.7241 0.048 0.040 0.000 0.000 0.912
#> SRR1812713 4 0.0000 0.8300 0.000 0.000 0.000 1.000 0.000
#> SRR1812712 4 0.2852 0.6720 0.000 0.172 0.000 0.828 0.000
#> SRR1812711 5 0.7061 0.4890 0.220 0.048 0.000 0.200 0.532
#> SRR1812710 4 0.0162 0.8317 0.000 0.000 0.000 0.996 0.004
#> SRR1812709 4 0.0000 0.8300 0.000 0.000 0.000 1.000 0.000
#> SRR1812708 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> SRR1812707 4 0.0510 0.8334 0.000 0.000 0.000 0.984 0.016
#> SRR1812705 5 0.7300 0.5256 0.264 0.072 0.000 0.156 0.508
#> SRR1812706 5 0.0404 0.7389 0.000 0.012 0.000 0.000 0.988
#> SRR1812704 4 0.2732 0.7141 0.000 0.000 0.000 0.840 0.160
#> SRR1812703 4 0.5664 0.4867 0.004 0.180 0.000 0.648 0.168
#> SRR1812702 5 0.0963 0.7406 0.036 0.000 0.000 0.000 0.964
#> SRR1812741 2 0.1851 0.6425 0.000 0.912 0.000 0.088 0.000
#> SRR1812740 5 0.1012 0.7359 0.020 0.012 0.000 0.000 0.968
#> SRR1812739 4 0.1121 0.8105 0.000 0.044 0.000 0.956 0.000
#> SRR1812738 4 0.1121 0.8268 0.000 0.000 0.000 0.956 0.044
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1812752 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.00
#> SRR1812753 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.00
#> SRR1812751 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.00
#> SRR1812750 6 0.0000 1.000 0 0.000 0.000 0.000 0.000 1.00
#> SRR1812748 5 0.1426 0.540 0 0.008 0.028 0.016 0.948 0.00
#> SRR1812749 6 0.0000 1.000 0 0.000 0.000 0.000 0.000 1.00
#> SRR1812746 5 0.3630 0.390 0 0.004 0.176 0.000 0.780 0.04
#> SRR1812745 5 0.0790 0.544 0 0.000 0.032 0.000 0.968 0.00
#> SRR1812747 5 0.6481 -0.329 0 0.360 0.252 0.020 0.368 0.00
#> SRR1812744 4 0.6403 0.115 0 0.152 0.040 0.412 0.396 0.00
#> SRR1812743 4 0.0260 0.836 0 0.000 0.000 0.992 0.008 0.00
#> SRR1812742 5 0.5918 -0.280 0 0.276 0.224 0.004 0.496 0.00
#> SRR1812737 4 0.0000 0.834 0 0.000 0.000 1.000 0.000 0.00
#> SRR1812735 2 0.2340 0.697 0 0.852 0.000 0.000 0.148 0.00
#> SRR1812734 5 0.5348 0.259 0 0.216 0.192 0.000 0.592 0.00
#> SRR1812733 5 0.1257 0.539 0 0.000 0.020 0.028 0.952 0.00
#> SRR1812736 5 0.1074 0.543 0 0.012 0.028 0.000 0.960 0.00
#> SRR1812732 2 0.2350 0.766 0 0.880 0.000 0.100 0.020 0.00
#> SRR1812730 5 0.0547 0.533 0 0.000 0.020 0.000 0.980 0.00
#> SRR1812731 4 0.1007 0.825 0 0.000 0.000 0.956 0.044 0.00
#> SRR1812729 4 0.2301 0.778 0 0.000 0.020 0.884 0.096 0.00
#> SRR1812727 5 0.7038 0.143 0 0.116 0.252 0.176 0.456 0.00
#> SRR1812726 3 0.4780 0.906 0 0.032 0.588 0.016 0.364 0.00
#> SRR1812728 3 0.3774 0.934 0 0.000 0.592 0.000 0.408 0.00
#> SRR1812724 2 0.3371 0.653 0 0.708 0.000 0.292 0.000 0.00
#> SRR1812725 5 0.4449 -0.594 0 0.028 0.440 0.000 0.532 0.00
#> SRR1812723 3 0.3899 0.940 0 0.000 0.592 0.004 0.404 0.00
#> SRR1812722 2 0.4983 0.418 0 0.644 0.148 0.000 0.208 0.00
#> SRR1812721 4 0.3807 0.629 0 0.052 0.000 0.756 0.192 0.00
#> SRR1812718 5 0.5278 -0.539 0 0.048 0.432 0.024 0.496 0.00
#> SRR1812717 2 0.2697 0.745 0 0.812 0.000 0.188 0.000 0.00
#> SRR1812716 5 0.2135 0.449 0 0.000 0.128 0.000 0.872 0.00
#> SRR1812715 2 0.2219 0.767 0 0.864 0.000 0.136 0.000 0.00
#> SRR1812714 2 0.1176 0.741 0 0.956 0.000 0.024 0.020 0.00
#> SRR1812719 5 0.2562 0.397 0 0.000 0.172 0.000 0.828 0.00
#> SRR1812713 4 0.0000 0.834 0 0.000 0.000 1.000 0.000 0.00
#> SRR1812712 4 0.2912 0.659 0 0.216 0.000 0.784 0.000 0.00
#> SRR1812711 5 0.5225 -0.540 0 0.044 0.432 0.024 0.500 0.00
#> SRR1812710 4 0.0146 0.835 0 0.000 0.000 0.996 0.004 0.00
#> SRR1812709 4 0.0363 0.831 0 0.012 0.000 0.988 0.000 0.00
#> SRR1812708 6 0.0000 1.000 0 0.000 0.000 0.000 0.000 1.00
#> SRR1812707 4 0.0146 0.835 0 0.000 0.000 0.996 0.004 0.00
#> SRR1812705 3 0.4343 0.939 0 0.020 0.592 0.004 0.384 0.00
#> SRR1812706 5 0.0622 0.538 0 0.012 0.008 0.000 0.980 0.00
#> SRR1812704 4 0.2932 0.723 0 0.016 0.000 0.820 0.164 0.00
#> SRR1812703 4 0.6040 0.416 0 0.288 0.036 0.540 0.136 0.00
#> SRR1812702 5 0.1444 0.481 0 0.000 0.072 0.000 0.928 0.00
#> SRR1812741 2 0.3547 0.579 0 0.668 0.332 0.000 0.000 0.00
#> SRR1812740 5 0.1074 0.545 0 0.012 0.028 0.000 0.960 0.00
#> SRR1812739 4 0.1663 0.795 0 0.088 0.000 0.912 0.000 0.00
#> SRR1812738 4 0.0547 0.833 0 0.000 0.000 0.980 0.020 0.00
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 14626 rows and 51 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 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 0.844 0.873 0.940 0.358 0.594 0.594
#> 3 3 0.401 0.603 0.741 0.589 0.755 0.588
#> 4 4 0.337 0.460 0.672 0.153 0.789 0.495
#> 5 5 0.394 0.511 0.630 0.103 0.869 0.628
#> 6 6 0.549 0.421 0.629 0.076 0.868 0.557
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
#> SRR1812752 1 0.0000 0.7883 1.000 0.000
#> SRR1812753 1 0.0000 0.7883 1.000 0.000
#> SRR1812751 1 0.0000 0.7883 1.000 0.000
#> SRR1812750 1 0.0000 0.7883 1.000 0.000
#> SRR1812748 2 0.2423 0.9357 0.040 0.960
#> SRR1812749 1 0.0000 0.7883 1.000 0.000
#> SRR1812746 1 0.9358 0.5968 0.648 0.352
#> SRR1812745 2 0.0376 0.9789 0.004 0.996
#> SRR1812747 2 0.0000 0.9825 0.000 1.000
#> SRR1812744 1 0.9944 0.4384 0.544 0.456
#> SRR1812743 2 0.0000 0.9825 0.000 1.000
#> SRR1812742 2 0.0000 0.9825 0.000 1.000
#> SRR1812737 2 0.0000 0.9825 0.000 1.000
#> SRR1812735 2 0.0000 0.9825 0.000 1.000
#> SRR1812734 1 0.9850 0.4993 0.572 0.428
#> SRR1812733 2 0.0376 0.9788 0.004 0.996
#> SRR1812736 2 0.0938 0.9707 0.012 0.988
#> SRR1812732 2 0.9732 -0.0121 0.404 0.596
#> SRR1812730 2 0.0000 0.9825 0.000 1.000
#> SRR1812731 2 0.0000 0.9825 0.000 1.000
#> SRR1812729 2 0.0000 0.9825 0.000 1.000
#> SRR1812727 1 0.1414 0.7837 0.980 0.020
#> SRR1812726 2 0.0000 0.9825 0.000 1.000
#> SRR1812728 2 0.0000 0.9825 0.000 1.000
#> SRR1812724 2 0.0000 0.9825 0.000 1.000
#> SRR1812725 2 0.0000 0.9825 0.000 1.000
#> SRR1812723 2 0.0000 0.9825 0.000 1.000
#> SRR1812722 2 0.0000 0.9825 0.000 1.000
#> SRR1812721 2 0.0000 0.9825 0.000 1.000
#> SRR1812718 2 0.0000 0.9825 0.000 1.000
#> SRR1812717 2 0.0000 0.9825 0.000 1.000
#> SRR1812716 2 0.0000 0.9825 0.000 1.000
#> SRR1812715 2 0.0000 0.9825 0.000 1.000
#> SRR1812714 1 0.9850 0.4993 0.572 0.428
#> SRR1812719 1 0.9608 0.5631 0.616 0.384
#> SRR1812713 2 0.1184 0.9659 0.016 0.984
#> SRR1812712 2 0.0000 0.9825 0.000 1.000
#> SRR1812711 2 0.0000 0.9825 0.000 1.000
#> SRR1812710 2 0.0000 0.9825 0.000 1.000
#> SRR1812709 2 0.0000 0.9825 0.000 1.000
#> SRR1812708 1 0.0000 0.7883 1.000 0.000
#> SRR1812707 2 0.0000 0.9825 0.000 1.000
#> SRR1812705 2 0.0000 0.9825 0.000 1.000
#> SRR1812706 2 0.0000 0.9825 0.000 1.000
#> SRR1812704 2 0.0000 0.9825 0.000 1.000
#> SRR1812703 1 0.9993 0.3636 0.516 0.484
#> SRR1812702 2 0.0000 0.9825 0.000 1.000
#> SRR1812741 1 0.0000 0.7883 1.000 0.000
#> SRR1812740 2 0.0000 0.9825 0.000 1.000
#> SRR1812739 2 0.0672 0.9750 0.008 0.992
#> SRR1812738 2 0.0000 0.9825 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1812752 1 0.0000 0.7641 1.000 0.000 0.000
#> SRR1812753 1 0.0000 0.7641 1.000 0.000 0.000
#> SRR1812751 1 0.0000 0.7641 1.000 0.000 0.000
#> SRR1812750 1 0.0000 0.7641 1.000 0.000 0.000
#> SRR1812748 2 0.5036 0.5874 0.048 0.832 0.120
#> SRR1812749 1 0.1163 0.7658 0.972 0.000 0.028
#> SRR1812746 1 0.6451 0.7086 0.560 0.004 0.436
#> SRR1812745 3 0.6244 0.7481 0.000 0.440 0.560
#> SRR1812747 2 0.6286 -0.6810 0.000 0.536 0.464
#> SRR1812744 1 0.9722 0.5567 0.444 0.312 0.244
#> SRR1812743 2 0.0424 0.7591 0.000 0.992 0.008
#> SRR1812742 3 0.5968 0.7642 0.000 0.364 0.636
#> SRR1812737 2 0.0424 0.7591 0.000 0.992 0.008
#> SRR1812735 2 0.4002 0.4941 0.000 0.840 0.160
#> SRR1812734 1 0.7262 0.7068 0.528 0.028 0.444
#> SRR1812733 2 0.4605 0.4878 0.000 0.796 0.204
#> SRR1812736 3 0.6460 0.7457 0.004 0.440 0.556
#> SRR1812732 2 0.8604 0.0993 0.312 0.564 0.124
#> SRR1812730 3 0.6291 0.7405 0.000 0.468 0.532
#> SRR1812731 2 0.0424 0.7591 0.000 0.992 0.008
#> SRR1812729 2 0.2448 0.6725 0.000 0.924 0.076
#> SRR1812727 1 0.8046 0.7090 0.536 0.068 0.396
#> SRR1812726 3 0.6209 0.7765 0.004 0.368 0.628
#> SRR1812728 3 0.6308 0.7163 0.000 0.492 0.508
#> SRR1812724 2 0.0000 0.7591 0.000 1.000 0.000
#> SRR1812725 2 0.6291 -0.6834 0.000 0.532 0.468
#> SRR1812723 3 0.5948 0.7719 0.000 0.360 0.640
#> SRR1812722 3 0.6667 0.7691 0.016 0.368 0.616
#> SRR1812721 2 0.0000 0.7591 0.000 1.000 0.000
#> SRR1812718 2 0.6252 -0.6411 0.000 0.556 0.444
#> SRR1812717 2 0.0592 0.7560 0.000 0.988 0.012
#> SRR1812716 3 0.6516 0.7282 0.004 0.480 0.516
#> SRR1812715 2 0.0424 0.7591 0.000 0.992 0.008
#> SRR1812714 1 0.8663 0.7101 0.524 0.112 0.364
#> SRR1812719 1 0.7276 0.7147 0.564 0.032 0.404
#> SRR1812713 2 0.1950 0.7161 0.008 0.952 0.040
#> SRR1812712 2 0.0237 0.7582 0.000 0.996 0.004
#> SRR1812711 3 0.5882 0.7649 0.000 0.348 0.652
#> SRR1812710 2 0.0424 0.7591 0.000 0.992 0.008
#> SRR1812709 2 0.0000 0.7591 0.000 1.000 0.000
#> SRR1812708 1 0.1163 0.7658 0.972 0.000 0.028
#> SRR1812707 2 0.0000 0.7591 0.000 1.000 0.000
#> SRR1812705 3 0.5988 0.7733 0.000 0.368 0.632
#> SRR1812706 3 0.6509 0.7256 0.004 0.472 0.524
#> SRR1812704 2 0.1411 0.7289 0.000 0.964 0.036
#> SRR1812703 1 0.9970 0.3562 0.356 0.296 0.348
#> SRR1812702 3 0.6516 0.7282 0.004 0.480 0.516
#> SRR1812741 1 0.8834 0.6964 0.580 0.196 0.224
#> SRR1812740 2 0.6345 -0.4052 0.004 0.596 0.400
#> SRR1812739 2 0.0661 0.7556 0.004 0.988 0.008
#> SRR1812738 2 0.0424 0.7587 0.000 0.992 0.008
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1812752 1 0.0000 0.90697 1.000 0.000 0.000 0.000
#> SRR1812753 1 0.0000 0.90697 1.000 0.000 0.000 0.000
#> SRR1812751 1 0.0000 0.90697 1.000 0.000 0.000 0.000
#> SRR1812750 1 0.2984 0.91113 0.888 0.084 0.028 0.000
#> SRR1812748 4 0.6124 0.19275 0.000 0.084 0.276 0.640
#> SRR1812749 1 0.2984 0.91113 0.888 0.084 0.028 0.000
#> SRR1812746 3 0.9673 -0.00856 0.260 0.180 0.372 0.188
#> SRR1812745 3 0.5695 0.57010 0.000 0.040 0.624 0.336
#> SRR1812747 3 0.7787 0.24532 0.000 0.244 0.384 0.372
#> SRR1812744 3 0.8877 -0.03373 0.044 0.312 0.324 0.320
#> SRR1812743 4 0.3710 0.66425 0.000 0.004 0.192 0.804
#> SRR1812742 3 0.7894 -0.18367 0.000 0.304 0.376 0.320
#> SRR1812737 4 0.3668 0.66309 0.000 0.004 0.188 0.808
#> SRR1812735 4 0.5062 0.21989 0.000 0.020 0.300 0.680
#> SRR1812734 2 0.7758 -0.05345 0.008 0.472 0.328 0.192
#> SRR1812733 4 0.5245 0.25769 0.004 0.016 0.320 0.660
#> SRR1812736 3 0.5954 0.56653 0.000 0.052 0.604 0.344
#> SRR1812732 4 0.7598 0.24961 0.028 0.232 0.164 0.576
#> SRR1812730 3 0.4730 0.57736 0.000 0.000 0.636 0.364
#> SRR1812731 4 0.3710 0.66425 0.000 0.004 0.192 0.804
#> SRR1812729 4 0.3612 0.59408 0.000 0.100 0.044 0.856
#> SRR1812727 2 0.8639 -0.03026 0.064 0.476 0.272 0.188
#> SRR1812726 2 0.7650 0.20485 0.000 0.424 0.364 0.212
#> SRR1812728 3 0.6930 0.46962 0.000 0.120 0.524 0.356
#> SRR1812724 4 0.1256 0.66263 0.000 0.008 0.028 0.964
#> SRR1812725 3 0.6819 0.50182 0.000 0.112 0.540 0.348
#> SRR1812723 2 0.7638 0.20726 0.000 0.420 0.372 0.208
#> SRR1812722 2 0.7762 0.20504 0.004 0.436 0.356 0.204
#> SRR1812721 4 0.3710 0.66718 0.000 0.004 0.192 0.804
#> SRR1812718 3 0.7782 0.27311 0.000 0.244 0.396 0.360
#> SRR1812717 4 0.2256 0.66485 0.000 0.056 0.020 0.924
#> SRR1812716 3 0.5093 0.58086 0.000 0.012 0.640 0.348
#> SRR1812715 4 0.3852 0.66403 0.000 0.008 0.192 0.800
#> SRR1812714 2 0.6879 0.01511 0.016 0.496 0.064 0.424
#> SRR1812719 3 0.9041 0.09064 0.108 0.240 0.464 0.188
#> SRR1812713 4 0.4775 0.51083 0.000 0.028 0.232 0.740
#> SRR1812712 4 0.3450 0.55545 0.000 0.008 0.156 0.836
#> SRR1812711 2 0.7654 0.20687 0.000 0.420 0.368 0.212
#> SRR1812710 4 0.3751 0.66498 0.000 0.004 0.196 0.800
#> SRR1812709 4 0.0000 0.67227 0.000 0.000 0.000 1.000
#> SRR1812708 1 0.2984 0.91060 0.888 0.084 0.028 0.000
#> SRR1812707 4 0.3710 0.66718 0.000 0.004 0.192 0.804
#> SRR1812705 2 0.7654 0.20687 0.000 0.420 0.368 0.212
#> SRR1812706 3 0.5592 0.55079 0.000 0.044 0.656 0.300
#> SRR1812704 4 0.3032 0.59158 0.000 0.008 0.124 0.868
#> SRR1812703 2 0.7170 0.04088 0.012 0.592 0.152 0.244
#> SRR1812702 3 0.5024 0.57933 0.000 0.008 0.632 0.360
#> SRR1812741 1 0.7026 0.72346 0.644 0.184 0.144 0.028
#> SRR1812740 3 0.5649 0.57082 0.000 0.036 0.620 0.344
#> SRR1812739 4 0.4617 0.45021 0.000 0.032 0.204 0.764
#> SRR1812738 4 0.0817 0.67343 0.000 0.024 0.000 0.976
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1812752 1 0.000 0.8599 1.000 0.000 NA 0.000 0.000
#> SRR1812753 1 0.000 0.8599 1.000 0.000 NA 0.000 0.000
#> SRR1812751 1 0.000 0.8599 1.000 0.000 NA 0.000 0.000
#> SRR1812750 1 0.452 0.8407 0.712 0.028 NA 0.000 0.008
#> SRR1812748 5 0.695 0.3972 0.000 0.056 NA 0.316 0.512
#> SRR1812749 1 0.452 0.8407 0.712 0.028 NA 0.000 0.008
#> SRR1812746 5 0.696 0.3226 0.092 0.040 NA 0.012 0.484
#> SRR1812745 5 0.523 0.4680 0.000 0.060 NA 0.112 0.744
#> SRR1812747 5 0.665 -0.3982 0.000 0.308 NA 0.144 0.524
#> SRR1812744 5 0.715 0.4318 0.000 0.164 NA 0.136 0.572
#> SRR1812743 4 0.495 0.6352 0.000 0.012 NA 0.616 0.020
#> SRR1812742 2 0.683 0.7634 0.000 0.508 NA 0.204 0.268
#> SRR1812737 4 0.502 0.6200 0.000 0.008 NA 0.556 0.020
#> SRR1812735 4 0.806 0.2347 0.000 0.136 NA 0.384 0.160
#> SRR1812734 5 0.642 0.4587 0.000 0.192 NA 0.020 0.584
#> SRR1812733 5 0.616 0.3198 0.000 0.028 NA 0.364 0.536
#> SRR1812736 5 0.548 0.4656 0.000 0.060 NA 0.140 0.720
#> SRR1812732 4 0.646 0.3330 0.000 0.144 NA 0.636 0.148
#> SRR1812730 5 0.450 0.3999 0.000 0.072 NA 0.136 0.776
#> SRR1812731 4 0.478 0.6349 0.000 0.004 NA 0.612 0.020
#> SRR1812729 4 0.709 0.0245 0.000 0.116 NA 0.468 0.356
#> SRR1812727 5 0.683 0.4542 0.024 0.228 NA 0.024 0.588
#> SRR1812726 2 0.604 0.8862 0.000 0.560 NA 0.156 0.284
#> SRR1812728 5 0.593 0.1246 0.000 0.200 NA 0.136 0.644
#> SRR1812724 4 0.121 0.6173 0.000 0.000 NA 0.960 0.024
#> SRR1812725 5 0.614 0.0411 0.000 0.212 NA 0.140 0.624
#> SRR1812723 2 0.606 0.8635 0.000 0.536 NA 0.140 0.324
#> SRR1812722 2 0.610 0.8773 0.000 0.552 NA 0.164 0.284
#> SRR1812721 4 0.511 0.6138 0.000 0.008 NA 0.544 0.024
#> SRR1812718 5 0.679 -0.4674 0.000 0.352 NA 0.148 0.476
#> SRR1812717 4 0.357 0.5625 0.000 0.076 NA 0.844 0.012
#> SRR1812716 5 0.413 0.4192 0.000 0.044 NA 0.144 0.796
#> SRR1812715 4 0.500 0.6203 0.000 0.004 NA 0.552 0.024
#> SRR1812714 5 0.742 0.3984 0.000 0.284 NA 0.128 0.492
#> SRR1812719 5 0.687 0.4552 0.052 0.120 NA 0.016 0.604
#> SRR1812713 4 0.321 0.5861 0.000 0.028 NA 0.872 0.060
#> SRR1812712 4 0.235 0.5993 0.000 0.000 NA 0.896 0.088
#> SRR1812711 2 0.591 0.8780 0.000 0.560 NA 0.128 0.312
#> SRR1812710 4 0.511 0.6177 0.000 0.008 NA 0.548 0.024
#> SRR1812709 4 0.121 0.6268 0.000 0.000 NA 0.960 0.016
#> SRR1812708 1 0.365 0.8605 0.816 0.028 NA 0.000 0.008
#> SRR1812707 4 0.518 0.6174 0.000 0.008 NA 0.544 0.028
#> SRR1812705 2 0.609 0.8726 0.000 0.524 NA 0.140 0.336
#> SRR1812706 5 0.458 0.4252 0.000 0.084 NA 0.120 0.776
#> SRR1812704 4 0.586 -0.0460 0.000 0.048 NA 0.508 0.420
#> SRR1812703 5 0.658 0.4049 0.000 0.312 NA 0.048 0.548
#> SRR1812702 5 0.400 0.4288 0.000 0.040 NA 0.148 0.800
#> SRR1812741 1 0.745 0.7042 0.520 0.208 NA 0.044 0.016
#> SRR1812740 5 0.519 0.4692 0.000 0.024 NA 0.184 0.716
#> SRR1812739 4 0.353 0.5766 0.000 0.016 NA 0.840 0.112
#> SRR1812738 4 0.074 0.6239 0.000 0.004 NA 0.980 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1812752 1 0.5503 7.24e-01 0.552 0.000 0.000 0.276 0.172 0.000
#> SRR1812753 1 0.5503 7.24e-01 0.552 0.000 0.000 0.276 0.172 0.000
#> SRR1812751 1 0.5503 7.24e-01 0.552 0.000 0.000 0.276 0.172 0.000
#> SRR1812750 1 0.1313 7.38e-01 0.952 0.000 0.028 0.004 0.000 0.016
#> SRR1812748 3 0.5795 3.61e-01 0.000 0.268 0.608 0.064 0.020 0.040
#> SRR1812749 1 0.1151 7.36e-01 0.956 0.000 0.032 0.000 0.000 0.012
#> SRR1812746 3 0.6025 3.55e-01 0.264 0.000 0.584 0.008 0.056 0.088
#> SRR1812745 3 0.6034 -1.76e-02 0.000 0.016 0.556 0.008 0.244 0.176
#> SRR1812747 5 0.6475 1.45e-01 0.000 0.076 0.092 0.008 0.512 0.312
#> SRR1812744 3 0.5302 4.37e-01 0.008 0.128 0.700 0.132 0.020 0.012
#> SRR1812743 2 0.2212 4.08e-01 0.000 0.880 0.000 0.112 0.000 0.008
#> SRR1812742 6 0.5466 6.78e-01 0.000 0.084 0.004 0.040 0.228 0.644
#> SRR1812737 2 0.1075 4.93e-01 0.000 0.952 0.000 0.048 0.000 0.000
#> SRR1812735 2 0.5825 1.45e-01 0.000 0.608 0.008 0.024 0.152 0.208
#> SRR1812734 3 0.0881 4.51e-01 0.000 0.000 0.972 0.008 0.008 0.012
#> SRR1812733 3 0.6837 2.65e-01 0.000 0.328 0.488 0.048 0.080 0.056
#> SRR1812736 3 0.5898 -1.22e-03 0.000 0.020 0.560 0.000 0.228 0.192
#> SRR1812732 4 0.5774 4.93e-01 0.000 0.216 0.248 0.532 0.000 0.004
#> SRR1812730 5 0.6497 4.28e-01 0.000 0.064 0.320 0.000 0.480 0.136
#> SRR1812731 2 0.2053 4.09e-01 0.000 0.888 0.000 0.108 0.000 0.004
#> SRR1812729 2 0.7856 1.11e-01 0.000 0.460 0.180 0.084 0.096 0.180
#> SRR1812727 3 0.4341 4.26e-01 0.040 0.000 0.796 0.032 0.076 0.056
#> SRR1812726 6 0.4340 8.00e-01 0.000 0.064 0.004 0.000 0.224 0.708
#> SRR1812728 5 0.6141 3.65e-01 0.000 0.052 0.148 0.000 0.564 0.236
#> SRR1812724 4 0.4513 7.54e-01 0.000 0.440 0.024 0.532 0.000 0.004
#> SRR1812725 5 0.6100 3.65e-01 0.000 0.068 0.136 0.000 0.588 0.208
#> SRR1812723 6 0.4787 7.36e-01 0.000 0.068 0.000 0.000 0.336 0.596
#> SRR1812722 6 0.4552 7.93e-01 0.000 0.064 0.004 0.004 0.236 0.692
#> SRR1812721 2 0.1138 5.12e-01 0.000 0.960 0.000 0.012 0.004 0.024
#> SRR1812718 5 0.6432 2.67e-02 0.000 0.072 0.088 0.004 0.448 0.388
#> SRR1812717 4 0.4460 6.83e-01 0.000 0.404 0.004 0.568 0.000 0.024
#> SRR1812716 5 0.5281 4.33e-01 0.000 0.060 0.324 0.000 0.588 0.028
#> SRR1812715 2 0.0508 5.08e-01 0.000 0.984 0.000 0.012 0.000 0.004
#> SRR1812714 3 0.6175 3.57e-01 0.012 0.032 0.668 0.084 0.100 0.104
#> SRR1812719 3 0.7681 2.75e-01 0.132 0.000 0.448 0.036 0.220 0.164
#> SRR1812713 4 0.5054 7.43e-01 0.000 0.400 0.036 0.544 0.004 0.016
#> SRR1812712 4 0.5298 7.24e-01 0.000 0.456 0.044 0.476 0.004 0.020
#> SRR1812711 6 0.4202 8.01e-01 0.000 0.064 0.000 0.000 0.224 0.712
#> SRR1812710 2 0.0603 5.14e-01 0.000 0.980 0.000 0.000 0.004 0.016
#> SRR1812709 2 0.4096 -7.56e-01 0.000 0.508 0.008 0.484 0.000 0.000
#> SRR1812708 1 0.1523 7.37e-01 0.940 0.000 0.044 0.008 0.000 0.008
#> SRR1812707 2 0.0665 5.13e-01 0.000 0.980 0.000 0.008 0.004 0.008
#> SRR1812705 6 0.4781 7.56e-01 0.000 0.072 0.000 0.000 0.320 0.608
#> SRR1812706 5 0.5886 3.81e-01 0.000 0.016 0.292 0.000 0.532 0.160
#> SRR1812704 2 0.8153 9.85e-05 0.000 0.396 0.252 0.152 0.104 0.096
#> SRR1812703 3 0.5398 2.90e-01 0.000 0.016 0.676 0.020 0.140 0.148
#> SRR1812702 5 0.5464 4.30e-01 0.000 0.072 0.336 0.000 0.564 0.028
#> SRR1812741 1 0.6339 5.55e-01 0.572 0.000 0.076 0.216 0.004 0.132
#> SRR1812740 3 0.6130 -7.67e-02 0.000 0.088 0.568 0.012 0.280 0.052
#> SRR1812739 2 0.5893 -6.65e-01 0.000 0.440 0.108 0.432 0.012 0.008
#> SRR1812738 4 0.4128 7.09e-01 0.000 0.488 0.004 0.504 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["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 14626 rows and 51 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.971 0.990 0.3096 0.704 0.704
#> 3 3 0.779 0.812 0.929 1.0570 0.655 0.509
#> 4 4 0.775 0.688 0.876 0.1455 0.869 0.656
#> 5 5 0.715 0.657 0.836 0.0737 0.934 0.768
#> 6 6 0.764 0.707 0.794 0.0522 0.908 0.631
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR1812752 1 0 1.0000 1.000 0.000
#> SRR1812753 1 0 1.0000 1.000 0.000
#> SRR1812751 1 0 1.0000 1.000 0.000
#> SRR1812750 1 0 1.0000 1.000 0.000
#> SRR1812748 2 0 0.9878 0.000 1.000
#> SRR1812749 1 0 1.0000 1.000 0.000
#> SRR1812746 1 0 1.0000 1.000 0.000
#> SRR1812745 2 0 0.9878 0.000 1.000
#> SRR1812747 2 0 0.9878 0.000 1.000
#> SRR1812744 2 0 0.9878 0.000 1.000
#> SRR1812743 2 0 0.9878 0.000 1.000
#> SRR1812742 2 0 0.9878 0.000 1.000
#> SRR1812737 2 0 0.9878 0.000 1.000
#> SRR1812735 2 0 0.9878 0.000 1.000
#> SRR1812734 2 0 0.9878 0.000 1.000
#> SRR1812733 2 0 0.9878 0.000 1.000
#> SRR1812736 2 0 0.9878 0.000 1.000
#> SRR1812732 2 0 0.9878 0.000 1.000
#> SRR1812730 2 0 0.9878 0.000 1.000
#> SRR1812731 2 0 0.9878 0.000 1.000
#> SRR1812729 2 0 0.9878 0.000 1.000
#> SRR1812727 1 0 1.0000 1.000 0.000
#> SRR1812726 2 0 0.9878 0.000 1.000
#> SRR1812728 2 0 0.9878 0.000 1.000
#> SRR1812724 2 0 0.9878 0.000 1.000
#> SRR1812725 2 0 0.9878 0.000 1.000
#> SRR1812723 2 0 0.9878 0.000 1.000
#> SRR1812722 2 0 0.9878 0.000 1.000
#> SRR1812721 2 0 0.9878 0.000 1.000
#> SRR1812718 2 0 0.9878 0.000 1.000
#> SRR1812717 2 0 0.9878 0.000 1.000
#> SRR1812716 2 0 0.9878 0.000 1.000
#> SRR1812715 2 0 0.9878 0.000 1.000
#> SRR1812714 2 0 0.9878 0.000 1.000
#> SRR1812719 2 1 0.0159 0.496 0.504
#> SRR1812713 2 0 0.9878 0.000 1.000
#> SRR1812712 2 0 0.9878 0.000 1.000
#> SRR1812711 2 0 0.9878 0.000 1.000
#> SRR1812710 2 0 0.9878 0.000 1.000
#> SRR1812709 2 0 0.9878 0.000 1.000
#> SRR1812708 1 0 1.0000 1.000 0.000
#> SRR1812707 2 0 0.9878 0.000 1.000
#> SRR1812705 2 0 0.9878 0.000 1.000
#> SRR1812706 2 0 0.9878 0.000 1.000
#> SRR1812704 2 0 0.9878 0.000 1.000
#> SRR1812703 2 0 0.9878 0.000 1.000
#> SRR1812702 2 0 0.9878 0.000 1.000
#> SRR1812741 1 0 1.0000 1.000 0.000
#> SRR1812740 2 0 0.9878 0.000 1.000
#> SRR1812739 2 0 0.9878 0.000 1.000
#> SRR1812738 2 0 0.9878 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1812752 1 0.0000 0.9364 1.000 0.000 0.000
#> SRR1812753 1 0.0000 0.9364 1.000 0.000 0.000
#> SRR1812751 1 0.0000 0.9364 1.000 0.000 0.000
#> SRR1812750 1 0.0000 0.9364 1.000 0.000 0.000
#> SRR1812748 2 0.6309 0.0354 0.000 0.500 0.500
#> SRR1812749 1 0.0000 0.9364 1.000 0.000 0.000
#> SRR1812746 1 0.6295 0.1016 0.528 0.000 0.472
#> SRR1812745 3 0.0000 0.8989 0.000 0.000 1.000
#> SRR1812747 3 0.0000 0.8989 0.000 0.000 1.000
#> SRR1812744 2 0.5404 0.6304 0.004 0.740 0.256
#> SRR1812743 2 0.0000 0.9091 0.000 1.000 0.000
#> SRR1812742 3 0.0000 0.8989 0.000 0.000 1.000
#> SRR1812737 2 0.0000 0.9091 0.000 1.000 0.000
#> SRR1812735 2 0.6154 0.2158 0.000 0.592 0.408
#> SRR1812734 3 0.2550 0.8504 0.012 0.056 0.932
#> SRR1812733 3 0.6154 0.2175 0.000 0.408 0.592
#> SRR1812736 3 0.0000 0.8989 0.000 0.000 1.000
#> SRR1812732 2 0.0000 0.9091 0.000 1.000 0.000
#> SRR1812730 3 0.0000 0.8989 0.000 0.000 1.000
#> SRR1812731 2 0.0000 0.9091 0.000 1.000 0.000
#> SRR1812729 2 0.0424 0.9044 0.000 0.992 0.008
#> SRR1812727 1 0.0000 0.9364 1.000 0.000 0.000
#> SRR1812726 3 0.5926 0.4657 0.000 0.356 0.644
#> SRR1812728 3 0.0000 0.8989 0.000 0.000 1.000
#> SRR1812724 2 0.0000 0.9091 0.000 1.000 0.000
#> SRR1812725 3 0.0000 0.8989 0.000 0.000 1.000
#> SRR1812723 3 0.0424 0.8954 0.000 0.008 0.992
#> SRR1812722 3 0.5465 0.6022 0.000 0.288 0.712
#> SRR1812721 2 0.0000 0.9091 0.000 1.000 0.000
#> SRR1812718 3 0.0237 0.8974 0.000 0.004 0.996
#> SRR1812717 2 0.0000 0.9091 0.000 1.000 0.000
#> SRR1812716 3 0.0000 0.8989 0.000 0.000 1.000
#> SRR1812715 2 0.0000 0.9091 0.000 1.000 0.000
#> SRR1812714 2 0.0000 0.9091 0.000 1.000 0.000
#> SRR1812719 3 0.1031 0.8827 0.024 0.000 0.976
#> SRR1812713 2 0.0000 0.9091 0.000 1.000 0.000
#> SRR1812712 2 0.0000 0.9091 0.000 1.000 0.000
#> SRR1812711 3 0.4002 0.7751 0.000 0.160 0.840
#> SRR1812710 2 0.0000 0.9091 0.000 1.000 0.000
#> SRR1812709 2 0.0000 0.9091 0.000 1.000 0.000
#> SRR1812708 1 0.0000 0.9364 1.000 0.000 0.000
#> SRR1812707 2 0.0000 0.9091 0.000 1.000 0.000
#> SRR1812705 3 0.4178 0.7635 0.000 0.172 0.828
#> SRR1812706 3 0.0000 0.8989 0.000 0.000 1.000
#> SRR1812704 2 0.1031 0.8935 0.000 0.976 0.024
#> SRR1812703 2 0.5988 0.4242 0.000 0.632 0.368
#> SRR1812702 3 0.0000 0.8989 0.000 0.000 1.000
#> SRR1812741 1 0.0424 0.9298 0.992 0.008 0.000
#> SRR1812740 3 0.0000 0.8989 0.000 0.000 1.000
#> SRR1812739 2 0.2165 0.8607 0.000 0.936 0.064
#> SRR1812738 2 0.0000 0.9091 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1812752 1 0.0000 0.8746 1.000 0.000 0.000 0.000
#> SRR1812753 1 0.0000 0.8746 1.000 0.000 0.000 0.000
#> SRR1812751 1 0.0000 0.8746 1.000 0.000 0.000 0.000
#> SRR1812750 1 0.0000 0.8746 1.000 0.000 0.000 0.000
#> SRR1812748 3 0.4343 0.4515 0.000 0.004 0.732 0.264
#> SRR1812749 1 0.0000 0.8746 1.000 0.000 0.000 0.000
#> SRR1812746 1 0.5366 0.2240 0.548 0.012 0.440 0.000
#> SRR1812745 2 0.5000 -0.1269 0.000 0.504 0.496 0.000
#> SRR1812747 2 0.0000 0.8611 0.000 1.000 0.000 0.000
#> SRR1812744 3 0.1557 0.4576 0.000 0.000 0.944 0.056
#> SRR1812743 4 0.0000 0.8886 0.000 0.000 0.000 1.000
#> SRR1812742 2 0.0469 0.8603 0.000 0.988 0.012 0.000
#> SRR1812737 4 0.0000 0.8886 0.000 0.000 0.000 1.000
#> SRR1812735 2 0.2011 0.7849 0.000 0.920 0.000 0.080
#> SRR1812734 3 0.0188 0.4569 0.000 0.004 0.996 0.000
#> SRR1812733 3 0.6324 0.2525 0.000 0.064 0.536 0.400
#> SRR1812736 3 0.4925 0.1694 0.000 0.428 0.572 0.000
#> SRR1812732 4 0.4730 0.4378 0.000 0.000 0.364 0.636
#> SRR1812730 2 0.3266 0.7342 0.000 0.832 0.168 0.000
#> SRR1812731 4 0.0000 0.8886 0.000 0.000 0.000 1.000
#> SRR1812729 4 0.4961 0.1396 0.000 0.448 0.000 0.552
#> SRR1812727 1 0.5132 0.3626 0.548 0.004 0.448 0.000
#> SRR1812726 2 0.1940 0.8088 0.000 0.924 0.076 0.000
#> SRR1812728 2 0.0336 0.8612 0.000 0.992 0.008 0.000
#> SRR1812724 4 0.0000 0.8886 0.000 0.000 0.000 1.000
#> SRR1812725 2 0.0336 0.8612 0.000 0.992 0.008 0.000
#> SRR1812723 2 0.0000 0.8611 0.000 1.000 0.000 0.000
#> SRR1812722 2 0.1792 0.8185 0.000 0.932 0.068 0.000
#> SRR1812721 4 0.0000 0.8886 0.000 0.000 0.000 1.000
#> SRR1812718 2 0.0188 0.8612 0.000 0.996 0.004 0.000
#> SRR1812717 4 0.0000 0.8886 0.000 0.000 0.000 1.000
#> SRR1812716 2 0.1211 0.8481 0.000 0.960 0.040 0.000
#> SRR1812715 4 0.0469 0.8815 0.000 0.012 0.000 0.988
#> SRR1812714 4 0.5483 0.2357 0.000 0.016 0.448 0.536
#> SRR1812719 2 0.6967 0.3240 0.176 0.580 0.244 0.000
#> SRR1812713 4 0.0000 0.8886 0.000 0.000 0.000 1.000
#> SRR1812712 4 0.0188 0.8862 0.000 0.000 0.004 0.996
#> SRR1812711 2 0.0000 0.8611 0.000 1.000 0.000 0.000
#> SRR1812710 4 0.0592 0.8785 0.000 0.016 0.000 0.984
#> SRR1812709 4 0.0000 0.8886 0.000 0.000 0.000 1.000
#> SRR1812708 1 0.0000 0.8746 1.000 0.000 0.000 0.000
#> SRR1812707 4 0.0000 0.8886 0.000 0.000 0.000 1.000
#> SRR1812705 2 0.0000 0.8611 0.000 1.000 0.000 0.000
#> SRR1812706 2 0.3266 0.7345 0.000 0.832 0.168 0.000
#> SRR1812704 4 0.0895 0.8710 0.000 0.020 0.004 0.976
#> SRR1812703 3 0.7117 0.0406 0.000 0.424 0.448 0.128
#> SRR1812702 2 0.2760 0.7809 0.000 0.872 0.128 0.000
#> SRR1812741 1 0.0707 0.8579 0.980 0.000 0.000 0.020
#> SRR1812740 3 0.4972 0.0995 0.000 0.456 0.544 0.000
#> SRR1812739 4 0.3486 0.6777 0.000 0.000 0.188 0.812
#> SRR1812738 4 0.0000 0.8886 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1812752 1 0.0000 0.927 1.000 0.000 0.000 0.000 0.000
#> SRR1812753 1 0.0000 0.927 1.000 0.000 0.000 0.000 0.000
#> SRR1812751 1 0.0000 0.927 1.000 0.000 0.000 0.000 0.000
#> SRR1812750 1 0.0162 0.926 0.996 0.000 0.004 0.000 0.000
#> SRR1812748 3 0.4547 0.315 0.000 0.000 0.704 0.044 0.252
#> SRR1812749 1 0.0000 0.927 1.000 0.000 0.000 0.000 0.000
#> SRR1812746 1 0.4812 0.369 0.600 0.000 0.372 0.000 0.028
#> SRR1812745 3 0.5937 0.431 0.000 0.300 0.564 0.000 0.136
#> SRR1812747 2 0.2929 0.655 0.000 0.840 0.152 0.000 0.008
#> SRR1812744 5 0.2488 0.706 0.000 0.000 0.124 0.004 0.872
#> SRR1812743 4 0.2645 0.815 0.000 0.000 0.068 0.888 0.044
#> SRR1812742 2 0.4522 0.569 0.000 0.744 0.176 0.000 0.080
#> SRR1812737 4 0.0162 0.862 0.000 0.000 0.000 0.996 0.004
#> SRR1812735 2 0.3832 0.636 0.000 0.824 0.104 0.060 0.012
#> SRR1812734 5 0.0794 0.745 0.000 0.000 0.028 0.000 0.972
#> SRR1812733 3 0.4737 0.163 0.000 0.016 0.600 0.380 0.004
#> SRR1812736 3 0.5264 0.503 0.000 0.128 0.676 0.000 0.196
#> SRR1812732 4 0.6825 -0.112 0.000 0.000 0.328 0.340 0.332
#> SRR1812730 2 0.4262 0.200 0.000 0.560 0.440 0.000 0.000
#> SRR1812731 4 0.0566 0.862 0.000 0.000 0.004 0.984 0.012
#> SRR1812729 4 0.5901 0.336 0.000 0.300 0.132 0.568 0.000
#> SRR1812727 5 0.3003 0.725 0.188 0.000 0.000 0.000 0.812
#> SRR1812726 2 0.3521 0.553 0.000 0.764 0.004 0.000 0.232
#> SRR1812728 2 0.0162 0.725 0.000 0.996 0.004 0.000 0.000
#> SRR1812724 4 0.0510 0.861 0.000 0.000 0.016 0.984 0.000
#> SRR1812725 2 0.0880 0.716 0.000 0.968 0.032 0.000 0.000
#> SRR1812723 2 0.0000 0.726 0.000 1.000 0.000 0.000 0.000
#> SRR1812722 2 0.2806 0.646 0.000 0.844 0.004 0.000 0.152
#> SRR1812721 4 0.0671 0.861 0.000 0.000 0.016 0.980 0.004
#> SRR1812718 2 0.0290 0.726 0.000 0.992 0.008 0.000 0.000
#> SRR1812717 4 0.0000 0.862 0.000 0.000 0.000 1.000 0.000
#> SRR1812716 2 0.4219 0.248 0.000 0.584 0.416 0.000 0.000
#> SRR1812715 4 0.4113 0.743 0.000 0.120 0.048 0.808 0.024
#> SRR1812714 5 0.3454 0.731 0.000 0.064 0.000 0.100 0.836
#> SRR1812719 5 0.6032 0.593 0.160 0.184 0.020 0.000 0.636
#> SRR1812713 4 0.1704 0.834 0.000 0.000 0.068 0.928 0.004
#> SRR1812712 4 0.1251 0.850 0.000 0.000 0.036 0.956 0.008
#> SRR1812711 2 0.0703 0.721 0.000 0.976 0.024 0.000 0.000
#> SRR1812710 4 0.1393 0.853 0.000 0.024 0.008 0.956 0.012
#> SRR1812709 4 0.0162 0.862 0.000 0.000 0.000 0.996 0.004
#> SRR1812708 1 0.0609 0.920 0.980 0.000 0.020 0.000 0.000
#> SRR1812707 4 0.0162 0.862 0.000 0.000 0.000 0.996 0.004
#> SRR1812705 2 0.0000 0.726 0.000 1.000 0.000 0.000 0.000
#> SRR1812706 2 0.4300 0.131 0.000 0.524 0.476 0.000 0.000
#> SRR1812704 4 0.3797 0.653 0.000 0.008 0.232 0.756 0.004
#> SRR1812703 5 0.4432 0.720 0.000 0.080 0.112 0.020 0.788
#> SRR1812702 2 0.4278 0.161 0.000 0.548 0.452 0.000 0.000
#> SRR1812741 1 0.1117 0.908 0.964 0.000 0.020 0.016 0.000
#> SRR1812740 3 0.5550 0.299 0.000 0.376 0.548 0.000 0.076
#> SRR1812739 4 0.3732 0.725 0.000 0.000 0.176 0.792 0.032
#> SRR1812738 4 0.0290 0.861 0.000 0.000 0.008 0.992 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1812752 1 0.0000 0.9226 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812753 1 0.0000 0.9226 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812751 1 0.0000 0.9226 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812750 1 0.1232 0.9199 0.956 0.000 0.016 0.000 0.024 0.004
#> SRR1812748 3 0.1932 0.6521 0.000 0.004 0.912 0.004 0.076 0.004
#> SRR1812749 1 0.0862 0.9208 0.972 0.000 0.016 0.000 0.008 0.004
#> SRR1812746 1 0.5207 0.5563 0.628 0.004 0.156 0.000 0.212 0.000
#> SRR1812745 3 0.5989 0.2683 0.000 0.248 0.432 0.000 0.320 0.000
#> SRR1812747 2 0.1958 0.7462 0.000 0.896 0.100 0.000 0.004 0.000
#> SRR1812744 6 0.2697 0.7966 0.000 0.000 0.188 0.000 0.000 0.812
#> SRR1812743 4 0.3917 0.6986 0.000 0.008 0.240 0.728 0.024 0.000
#> SRR1812742 2 0.3337 0.5210 0.000 0.736 0.260 0.000 0.004 0.000
#> SRR1812737 4 0.1082 0.8438 0.000 0.004 0.000 0.956 0.040 0.000
#> SRR1812735 2 0.2984 0.6931 0.000 0.860 0.064 0.064 0.012 0.000
#> SRR1812734 6 0.0547 0.9162 0.000 0.000 0.020 0.000 0.000 0.980
#> SRR1812733 5 0.3841 0.4409 0.000 0.000 0.032 0.244 0.724 0.000
#> SRR1812736 3 0.4650 0.6153 0.000 0.180 0.688 0.000 0.132 0.000
#> SRR1812732 3 0.2405 0.5729 0.000 0.000 0.880 0.100 0.004 0.016
#> SRR1812730 5 0.2902 0.5578 0.000 0.196 0.004 0.000 0.800 0.000
#> SRR1812731 4 0.1462 0.8404 0.000 0.000 0.056 0.936 0.008 0.000
#> SRR1812729 5 0.5202 0.0612 0.000 0.076 0.004 0.448 0.472 0.000
#> SRR1812727 6 0.0146 0.9193 0.000 0.000 0.004 0.000 0.000 0.996
#> SRR1812726 2 0.3566 0.7717 0.000 0.800 0.000 0.000 0.096 0.104
#> SRR1812728 2 0.3126 0.7428 0.000 0.752 0.000 0.000 0.248 0.000
#> SRR1812724 4 0.2488 0.8308 0.000 0.000 0.076 0.880 0.044 0.000
#> SRR1812725 2 0.3101 0.7456 0.000 0.756 0.000 0.000 0.244 0.000
#> SRR1812723 2 0.3023 0.7576 0.000 0.768 0.000 0.000 0.232 0.000
#> SRR1812722 2 0.2224 0.7809 0.000 0.904 0.012 0.000 0.020 0.064
#> SRR1812721 4 0.1838 0.8394 0.000 0.012 0.040 0.928 0.020 0.000
#> SRR1812718 2 0.1957 0.8080 0.000 0.888 0.000 0.000 0.112 0.000
#> SRR1812717 4 0.0632 0.8440 0.000 0.000 0.000 0.976 0.024 0.000
#> SRR1812716 5 0.3314 0.5469 0.000 0.224 0.012 0.000 0.764 0.000
#> SRR1812715 4 0.5764 0.2410 0.000 0.376 0.116 0.492 0.016 0.000
#> SRR1812714 6 0.0146 0.9191 0.000 0.000 0.000 0.000 0.004 0.996
#> SRR1812719 6 0.4081 0.7901 0.056 0.052 0.008 0.000 0.080 0.804
#> SRR1812713 4 0.2994 0.7002 0.000 0.000 0.004 0.788 0.208 0.000
#> SRR1812712 4 0.1663 0.8069 0.000 0.000 0.000 0.912 0.088 0.000
#> SRR1812711 2 0.1444 0.8037 0.000 0.928 0.000 0.000 0.072 0.000
#> SRR1812710 4 0.2122 0.8433 0.000 0.024 0.028 0.916 0.032 0.000
#> SRR1812709 4 0.0363 0.8458 0.000 0.000 0.000 0.988 0.012 0.000
#> SRR1812708 1 0.2206 0.9031 0.904 0.000 0.024 0.000 0.064 0.008
#> SRR1812707 4 0.0146 0.8461 0.000 0.000 0.000 0.996 0.004 0.000
#> SRR1812705 2 0.2527 0.7935 0.000 0.832 0.000 0.000 0.168 0.000
#> SRR1812706 5 0.3584 0.5008 0.000 0.308 0.004 0.000 0.688 0.000
#> SRR1812704 5 0.3706 0.3192 0.000 0.000 0.000 0.380 0.620 0.000
#> SRR1812703 6 0.0260 0.9183 0.000 0.000 0.000 0.000 0.008 0.992
#> SRR1812702 5 0.3231 0.5462 0.000 0.200 0.016 0.000 0.784 0.000
#> SRR1812741 1 0.1952 0.9011 0.920 0.000 0.016 0.012 0.052 0.000
#> SRR1812740 5 0.5199 0.0187 0.000 0.120 0.300 0.000 0.580 0.000
#> SRR1812739 4 0.3852 0.5779 0.000 0.000 0.324 0.664 0.012 0.000
#> SRR1812738 4 0.2506 0.8240 0.000 0.000 0.052 0.880 0.068 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", "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 14626 rows and 51 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 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 0.327 0.618 0.837 0.4268 0.547 0.547
#> 3 3 0.398 0.573 0.789 0.3440 0.886 0.792
#> 4 4 0.496 0.651 0.802 0.1439 0.867 0.705
#> 5 5 0.539 0.648 0.720 0.1380 0.842 0.558
#> 6 6 0.579 0.591 0.707 0.0364 0.920 0.692
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
#> SRR1812752 2 0.7674 0.651 0.224 0.776
#> SRR1812753 2 0.7674 0.651 0.224 0.776
#> SRR1812751 2 0.1184 0.806 0.016 0.984
#> SRR1812750 2 0.1184 0.806 0.016 0.984
#> SRR1812748 1 0.1184 0.720 0.984 0.016
#> SRR1812749 2 0.1184 0.806 0.016 0.984
#> SRR1812746 1 0.2043 0.723 0.968 0.032
#> SRR1812745 1 0.1184 0.720 0.984 0.016
#> SRR1812747 2 0.1633 0.803 0.024 0.976
#> SRR1812744 1 0.2778 0.721 0.952 0.048
#> SRR1812743 1 0.8267 0.656 0.740 0.260
#> SRR1812742 1 0.7883 0.674 0.764 0.236
#> SRR1812737 2 0.0000 0.815 0.000 1.000
#> SRR1812735 2 0.0000 0.815 0.000 1.000
#> SRR1812734 1 0.1414 0.720 0.980 0.020
#> SRR1812733 2 0.5946 0.737 0.144 0.856
#> SRR1812736 1 0.1184 0.720 0.984 0.016
#> SRR1812732 2 1.0000 -0.226 0.496 0.504
#> SRR1812730 2 0.8861 0.522 0.304 0.696
#> SRR1812731 2 0.9983 -0.195 0.476 0.524
#> SRR1812729 2 0.0000 0.815 0.000 1.000
#> SRR1812727 1 0.7219 0.686 0.800 0.200
#> SRR1812726 2 0.0000 0.815 0.000 1.000
#> SRR1812728 1 0.9087 0.580 0.676 0.324
#> SRR1812724 1 0.9996 0.256 0.512 0.488
#> SRR1812725 2 0.8909 0.516 0.308 0.692
#> SRR1812723 2 0.0000 0.815 0.000 1.000
#> SRR1812722 2 0.0000 0.815 0.000 1.000
#> SRR1812721 1 1.0000 0.242 0.504 0.496
#> SRR1812718 2 0.1843 0.803 0.028 0.972
#> SRR1812717 2 0.9996 -0.247 0.488 0.512
#> SRR1812716 2 0.8861 0.522 0.304 0.696
#> SRR1812715 2 0.0000 0.815 0.000 1.000
#> SRR1812714 2 0.0000 0.815 0.000 1.000
#> SRR1812719 1 0.7219 0.686 0.800 0.200
#> SRR1812713 2 0.4022 0.779 0.080 0.920
#> SRR1812712 2 0.7219 0.650 0.200 0.800
#> SRR1812711 2 0.0000 0.815 0.000 1.000
#> SRR1812710 2 0.0000 0.815 0.000 1.000
#> SRR1812709 2 0.7219 0.650 0.200 0.800
#> SRR1812708 2 0.0938 0.808 0.012 0.988
#> SRR1812707 2 0.0000 0.815 0.000 1.000
#> SRR1812705 2 0.0000 0.815 0.000 1.000
#> SRR1812706 1 0.9922 0.327 0.552 0.448
#> SRR1812704 2 0.8909 0.516 0.308 0.692
#> SRR1812703 2 0.0000 0.815 0.000 1.000
#> SRR1812702 2 0.8909 0.516 0.308 0.692
#> SRR1812741 1 0.9977 0.300 0.528 0.472
#> SRR1812740 1 0.1184 0.720 0.984 0.016
#> SRR1812739 2 0.9323 0.353 0.348 0.652
#> SRR1812738 1 0.9993 0.268 0.516 0.484
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1812752 1 0.4178 0.744 0.828 0.000 0.172
#> SRR1812753 1 0.4178 0.744 0.828 0.000 0.172
#> SRR1812751 1 0.4504 0.847 0.804 0.196 0.000
#> SRR1812750 1 0.4504 0.847 0.804 0.196 0.000
#> SRR1812748 3 0.0237 0.646 0.004 0.000 0.996
#> SRR1812749 1 0.4504 0.847 0.804 0.196 0.000
#> SRR1812746 3 0.0747 0.642 0.016 0.000 0.984
#> SRR1812745 3 0.0000 0.647 0.000 0.000 1.000
#> SRR1812747 2 0.1919 0.763 0.020 0.956 0.024
#> SRR1812744 3 0.2400 0.647 0.064 0.004 0.932
#> SRR1812743 3 0.7875 0.597 0.156 0.176 0.668
#> SRR1812742 3 0.7447 0.625 0.160 0.140 0.700
#> SRR1812737 2 0.1289 0.767 0.032 0.968 0.000
#> SRR1812735 2 0.1163 0.766 0.028 0.972 0.000
#> SRR1812734 3 0.0237 0.646 0.004 0.000 0.996
#> SRR1812733 2 0.5471 0.682 0.060 0.812 0.128
#> SRR1812736 3 0.0237 0.646 0.004 0.000 0.996
#> SRR1812732 2 0.9027 -0.175 0.132 0.440 0.428
#> SRR1812730 2 0.7396 0.494 0.060 0.644 0.296
#> SRR1812731 2 0.9224 -0.184 0.152 0.440 0.408
#> SRR1812729 2 0.1163 0.766 0.028 0.972 0.000
#> SRR1812727 3 0.5158 0.470 0.232 0.004 0.764
#> SRR1812726 2 0.1163 0.766 0.028 0.972 0.000
#> SRR1812728 3 0.7872 0.559 0.112 0.236 0.652
#> SRR1812724 3 0.9221 0.219 0.152 0.404 0.444
#> SRR1812725 2 0.7424 0.489 0.060 0.640 0.300
#> SRR1812723 2 0.1163 0.766 0.028 0.972 0.000
#> SRR1812722 2 0.1163 0.766 0.028 0.972 0.000
#> SRR1812721 3 0.9264 0.209 0.156 0.412 0.432
#> SRR1812718 2 0.2434 0.758 0.036 0.940 0.024
#> SRR1812717 2 0.9229 -0.228 0.152 0.428 0.420
#> SRR1812716 2 0.7396 0.494 0.060 0.644 0.296
#> SRR1812715 2 0.1163 0.766 0.028 0.972 0.000
#> SRR1812714 2 0.0592 0.763 0.012 0.988 0.000
#> SRR1812719 3 0.5158 0.470 0.232 0.004 0.764
#> SRR1812713 2 0.4194 0.714 0.064 0.876 0.060
#> SRR1812712 2 0.7273 0.562 0.156 0.712 0.132
#> SRR1812711 2 0.1163 0.766 0.028 0.972 0.000
#> SRR1812710 2 0.1289 0.767 0.032 0.968 0.000
#> SRR1812709 2 0.7273 0.562 0.156 0.712 0.132
#> SRR1812708 2 0.4178 0.574 0.172 0.828 0.000
#> SRR1812707 2 0.1289 0.767 0.032 0.968 0.000
#> SRR1812705 2 0.1399 0.765 0.028 0.968 0.004
#> SRR1812706 3 0.9130 0.296 0.152 0.356 0.492
#> SRR1812704 2 0.7564 0.483 0.068 0.636 0.296
#> SRR1812703 2 0.0424 0.763 0.008 0.992 0.000
#> SRR1812702 2 0.7424 0.489 0.060 0.640 0.300
#> SRR1812741 3 0.9202 0.258 0.152 0.388 0.460
#> SRR1812740 3 0.0237 0.646 0.004 0.000 0.996
#> SRR1812739 2 0.8520 0.314 0.132 0.588 0.280
#> SRR1812738 3 0.9217 0.230 0.152 0.400 0.448
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1812752 1 0.4387 0.697 0.804 0.000 0.144 0.052
#> SRR1812753 1 0.4387 0.697 0.804 0.000 0.144 0.052
#> SRR1812751 1 0.3837 0.832 0.776 0.224 0.000 0.000
#> SRR1812750 1 0.3837 0.832 0.776 0.224 0.000 0.000
#> SRR1812748 3 0.0779 0.858 0.004 0.000 0.980 0.016
#> SRR1812749 1 0.3837 0.832 0.776 0.224 0.000 0.000
#> SRR1812746 3 0.0895 0.854 0.020 0.000 0.976 0.004
#> SRR1812745 3 0.0188 0.858 0.000 0.000 0.996 0.004
#> SRR1812747 2 0.1022 0.741 0.032 0.968 0.000 0.000
#> SRR1812744 3 0.2611 0.796 0.008 0.000 0.896 0.096
#> SRR1812743 4 0.0712 0.471 0.004 0.004 0.008 0.984
#> SRR1812742 4 0.1847 0.444 0.004 0.004 0.052 0.940
#> SRR1812737 2 0.1118 0.727 0.000 0.964 0.000 0.036
#> SRR1812735 2 0.0000 0.742 0.000 1.000 0.000 0.000
#> SRR1812734 3 0.0336 0.857 0.000 0.000 0.992 0.008
#> SRR1812733 2 0.6791 0.571 0.184 0.676 0.092 0.048
#> SRR1812736 3 0.0376 0.859 0.004 0.000 0.992 0.004
#> SRR1812732 4 0.5598 0.709 0.028 0.332 0.004 0.636
#> SRR1812730 2 0.7928 0.410 0.184 0.528 0.260 0.028
#> SRR1812731 4 0.4819 0.733 0.000 0.344 0.004 0.652
#> SRR1812729 2 0.0188 0.741 0.000 0.996 0.000 0.004
#> SRR1812727 3 0.5540 0.673 0.208 0.004 0.720 0.068
#> SRR1812726 2 0.0000 0.742 0.000 1.000 0.000 0.000
#> SRR1812728 3 0.7629 0.473 0.088 0.220 0.608 0.084
#> SRR1812724 4 0.4923 0.767 0.004 0.304 0.008 0.684
#> SRR1812725 2 0.7861 0.409 0.184 0.528 0.264 0.024
#> SRR1812723 2 0.0000 0.742 0.000 1.000 0.000 0.000
#> SRR1812722 2 0.0000 0.742 0.000 1.000 0.000 0.000
#> SRR1812721 4 0.4872 0.720 0.004 0.356 0.000 0.640
#> SRR1812718 2 0.2589 0.712 0.116 0.884 0.000 0.000
#> SRR1812717 4 0.4776 0.709 0.000 0.376 0.000 0.624
#> SRR1812716 2 0.7928 0.410 0.184 0.528 0.260 0.028
#> SRR1812715 2 0.0000 0.742 0.000 1.000 0.000 0.000
#> SRR1812714 2 0.2125 0.729 0.076 0.920 0.004 0.000
#> SRR1812719 3 0.5540 0.673 0.208 0.004 0.720 0.068
#> SRR1812713 2 0.5640 0.623 0.184 0.740 0.032 0.044
#> SRR1812712 2 0.5649 0.300 0.052 0.664 0.000 0.284
#> SRR1812711 2 0.0000 0.742 0.000 1.000 0.000 0.000
#> SRR1812710 2 0.1118 0.727 0.000 0.964 0.000 0.036
#> SRR1812709 2 0.5649 0.300 0.052 0.664 0.000 0.284
#> SRR1812708 2 0.4122 0.595 0.236 0.760 0.004 0.000
#> SRR1812707 2 0.1118 0.727 0.000 0.964 0.000 0.036
#> SRR1812705 2 0.0469 0.742 0.000 0.988 0.000 0.012
#> SRR1812706 4 0.7729 0.450 0.004 0.328 0.208 0.460
#> SRR1812704 2 0.8469 0.384 0.168 0.528 0.224 0.080
#> SRR1812703 2 0.2053 0.730 0.072 0.924 0.004 0.000
#> SRR1812702 2 0.7861 0.409 0.184 0.528 0.264 0.024
#> SRR1812741 4 0.4509 0.766 0.000 0.288 0.004 0.708
#> SRR1812740 3 0.0779 0.858 0.004 0.000 0.980 0.016
#> SRR1812739 2 0.6178 -0.410 0.040 0.480 0.004 0.476
#> SRR1812738 4 0.4655 0.766 0.000 0.312 0.004 0.684
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1812752 1 0.0609 0.6943 0.980 0.000 0.000 0.000 0.020
#> SRR1812753 1 0.0609 0.6943 0.980 0.000 0.000 0.000 0.020
#> SRR1812751 1 0.4355 0.8167 0.732 0.224 0.000 0.000 0.044
#> SRR1812750 1 0.4355 0.8167 0.732 0.224 0.000 0.000 0.044
#> SRR1812748 3 0.2777 0.7261 0.000 0.000 0.864 0.016 0.120
#> SRR1812749 1 0.4355 0.8167 0.732 0.224 0.000 0.000 0.044
#> SRR1812746 3 0.0912 0.7619 0.012 0.000 0.972 0.000 0.016
#> SRR1812745 3 0.0290 0.7595 0.000 0.000 0.992 0.000 0.008
#> SRR1812747 2 0.1430 0.7623 0.000 0.944 0.000 0.004 0.052
#> SRR1812744 3 0.3178 0.7067 0.004 0.000 0.860 0.088 0.048
#> SRR1812743 4 0.3074 0.5006 0.000 0.000 0.000 0.804 0.196
#> SRR1812742 4 0.4150 0.4714 0.000 0.000 0.036 0.748 0.216
#> SRR1812737 2 0.3209 0.6415 0.000 0.812 0.000 0.180 0.008
#> SRR1812735 2 0.0510 0.7864 0.000 0.984 0.000 0.016 0.000
#> SRR1812734 3 0.1205 0.7519 0.004 0.000 0.956 0.000 0.040
#> SRR1812733 5 0.6362 0.5301 0.000 0.420 0.044 0.060 0.476
#> SRR1812736 3 0.2329 0.7291 0.000 0.000 0.876 0.000 0.124
#> SRR1812732 4 0.3574 0.7132 0.000 0.168 0.000 0.804 0.028
#> SRR1812730 5 0.6771 0.9112 0.000 0.264 0.184 0.024 0.528
#> SRR1812731 4 0.2929 0.7235 0.000 0.180 0.000 0.820 0.000
#> SRR1812729 2 0.1117 0.7847 0.000 0.964 0.000 0.020 0.016
#> SRR1812727 3 0.5671 0.4789 0.400 0.000 0.536 0.016 0.048
#> SRR1812726 2 0.0693 0.7863 0.000 0.980 0.000 0.012 0.008
#> SRR1812728 3 0.8259 0.2490 0.276 0.172 0.432 0.020 0.100
#> SRR1812724 4 0.2969 0.7312 0.000 0.128 0.000 0.852 0.020
#> SRR1812725 5 0.6692 0.9107 0.000 0.264 0.184 0.020 0.532
#> SRR1812723 2 0.0404 0.7783 0.000 0.988 0.000 0.000 0.012
#> SRR1812722 2 0.0510 0.7864 0.000 0.984 0.000 0.016 0.000
#> SRR1812721 4 0.5113 0.6904 0.008 0.208 0.000 0.700 0.084
#> SRR1812718 2 0.2732 0.6357 0.000 0.840 0.000 0.000 0.160
#> SRR1812717 4 0.3663 0.7148 0.000 0.208 0.000 0.776 0.016
#> SRR1812716 5 0.6771 0.9112 0.000 0.264 0.184 0.024 0.528
#> SRR1812715 2 0.0510 0.7864 0.000 0.984 0.000 0.016 0.000
#> SRR1812714 2 0.3635 0.4653 0.000 0.748 0.004 0.000 0.248
#> SRR1812719 3 0.5671 0.4789 0.400 0.000 0.536 0.016 0.048
#> SRR1812713 2 0.6526 0.0948 0.000 0.452 0.000 0.204 0.344
#> SRR1812712 4 0.6660 0.2747 0.000 0.384 0.000 0.388 0.228
#> SRR1812711 2 0.0880 0.7689 0.000 0.968 0.000 0.000 0.032
#> SRR1812710 2 0.3209 0.6415 0.000 0.812 0.000 0.180 0.008
#> SRR1812709 4 0.6660 0.2747 0.000 0.384 0.000 0.388 0.228
#> SRR1812708 2 0.6024 0.2661 0.152 0.588 0.004 0.000 0.256
#> SRR1812707 2 0.3209 0.6415 0.000 0.812 0.000 0.180 0.008
#> SRR1812705 2 0.0880 0.7695 0.000 0.968 0.000 0.000 0.032
#> SRR1812706 4 0.8502 -0.1939 0.008 0.176 0.168 0.368 0.280
#> SRR1812704 5 0.7484 0.8611 0.000 0.264 0.176 0.076 0.484
#> SRR1812703 2 0.3550 0.4821 0.000 0.760 0.004 0.000 0.236
#> SRR1812702 5 0.6692 0.9107 0.000 0.264 0.184 0.020 0.532
#> SRR1812741 4 0.2329 0.7270 0.000 0.124 0.000 0.876 0.000
#> SRR1812740 3 0.2777 0.7261 0.000 0.000 0.864 0.016 0.120
#> SRR1812739 4 0.5008 0.5615 0.000 0.300 0.000 0.644 0.056
#> SRR1812738 4 0.2909 0.7318 0.000 0.140 0.000 0.848 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1812752 1 0.2730 0.4367 0.808 0.000 0.000 0.000 0.000 0.192
#> SRR1812753 1 0.2730 0.4367 0.808 0.000 0.000 0.000 0.000 0.192
#> SRR1812751 1 0.2969 0.7366 0.776 0.224 0.000 0.000 0.000 0.000
#> SRR1812750 1 0.2969 0.7366 0.776 0.224 0.000 0.000 0.000 0.000
#> SRR1812748 3 0.0363 0.7043 0.000 0.000 0.988 0.012 0.000 0.000
#> SRR1812749 1 0.2969 0.7366 0.776 0.224 0.000 0.000 0.000 0.000
#> SRR1812746 3 0.4121 0.6910 0.004 0.000 0.736 0.000 0.060 0.200
#> SRR1812745 3 0.3992 0.6938 0.000 0.000 0.748 0.000 0.072 0.180
#> SRR1812747 2 0.1531 0.7018 0.000 0.928 0.000 0.004 0.068 0.000
#> SRR1812744 3 0.6553 0.3047 0.000 0.000 0.428 0.084 0.104 0.384
#> SRR1812743 4 0.3654 0.5168 0.000 0.000 0.004 0.792 0.144 0.060
#> SRR1812742 4 0.4511 0.4734 0.000 0.000 0.028 0.736 0.168 0.068
#> SRR1812737 2 0.2989 0.6143 0.000 0.812 0.000 0.176 0.008 0.004
#> SRR1812735 2 0.0146 0.7275 0.000 0.996 0.000 0.004 0.000 0.000
#> SRR1812734 3 0.5166 0.4466 0.000 0.000 0.524 0.000 0.092 0.384
#> SRR1812733 5 0.4753 0.4558 0.000 0.348 0.004 0.052 0.596 0.000
#> SRR1812736 3 0.0291 0.7052 0.000 0.000 0.992 0.000 0.004 0.004
#> SRR1812732 4 0.3481 0.7596 0.000 0.160 0.000 0.792 0.048 0.000
#> SRR1812730 5 0.3104 0.7547 0.000 0.204 0.004 0.004 0.788 0.000
#> SRR1812731 4 0.3088 0.7663 0.000 0.172 0.000 0.808 0.020 0.000
#> SRR1812729 2 0.1257 0.7260 0.000 0.952 0.000 0.020 0.028 0.000
#> SRR1812727 6 0.7641 1.0000 0.240 0.000 0.140 0.016 0.196 0.408
#> SRR1812726 2 0.0508 0.7267 0.000 0.984 0.000 0.000 0.012 0.004
#> SRR1812728 5 0.9191 -0.5469 0.220 0.144 0.128 0.024 0.276 0.208
#> SRR1812724 4 0.3054 0.7789 0.000 0.116 0.000 0.840 0.040 0.004
#> SRR1812725 5 0.2964 0.7543 0.000 0.204 0.004 0.000 0.792 0.000
#> SRR1812723 2 0.0790 0.7168 0.000 0.968 0.000 0.000 0.032 0.000
#> SRR1812722 2 0.0146 0.7275 0.000 0.996 0.000 0.004 0.000 0.000
#> SRR1812721 4 0.6762 0.4112 0.000 0.204 0.000 0.400 0.052 0.344
#> SRR1812718 2 0.2902 0.5783 0.000 0.800 0.000 0.004 0.196 0.000
#> SRR1812717 4 0.3849 0.7397 0.000 0.208 0.000 0.752 0.032 0.008
#> SRR1812716 5 0.3104 0.7547 0.000 0.204 0.004 0.004 0.788 0.000
#> SRR1812715 2 0.0146 0.7275 0.000 0.996 0.000 0.004 0.000 0.000
#> SRR1812714 2 0.4164 0.4359 0.004 0.708 0.004 0.000 0.252 0.032
#> SRR1812719 6 0.7641 1.0000 0.240 0.000 0.140 0.016 0.196 0.408
#> SRR1812713 2 0.6156 0.1033 0.000 0.408 0.000 0.192 0.388 0.012
#> SRR1812712 2 0.7495 0.0653 0.000 0.380 0.000 0.184 0.228 0.208
#> SRR1812711 2 0.1082 0.7119 0.000 0.956 0.000 0.000 0.040 0.004
#> SRR1812710 2 0.2989 0.6143 0.000 0.812 0.000 0.176 0.008 0.004
#> SRR1812709 2 0.7495 0.0653 0.000 0.380 0.000 0.184 0.228 0.208
#> SRR1812708 2 0.6171 0.2659 0.164 0.548 0.004 0.000 0.252 0.032
#> SRR1812707 2 0.2989 0.6143 0.000 0.812 0.000 0.176 0.008 0.004
#> SRR1812705 2 0.1285 0.7089 0.000 0.944 0.000 0.004 0.052 0.000
#> SRR1812706 5 0.6868 0.3022 0.000 0.144 0.004 0.080 0.440 0.332
#> SRR1812704 5 0.4232 0.7242 0.000 0.204 0.004 0.056 0.732 0.004
#> SRR1812703 2 0.3932 0.4506 0.000 0.720 0.004 0.000 0.248 0.028
#> SRR1812702 5 0.2964 0.7543 0.000 0.204 0.004 0.000 0.792 0.000
#> SRR1812741 4 0.2536 0.7763 0.000 0.116 0.000 0.864 0.020 0.000
#> SRR1812740 3 0.0363 0.7043 0.000 0.000 0.988 0.012 0.000 0.000
#> SRR1812739 4 0.4718 0.5451 0.000 0.292 0.000 0.632 0.076 0.000
#> SRR1812738 4 0.3010 0.7805 0.000 0.132 0.000 0.836 0.028 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["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 14626 rows and 51 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.369 0.781 0.862 0.4705 0.492 0.492
#> 3 3 0.490 0.542 0.758 0.3222 0.775 0.582
#> 4 4 0.504 0.638 0.727 0.1544 0.780 0.477
#> 5 5 0.705 0.787 0.859 0.0844 0.896 0.641
#> 6 6 0.798 0.744 0.801 0.0466 0.967 0.857
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
#> SRR1812752 1 0.000 0.755 1.000 0.000
#> SRR1812753 1 0.000 0.755 1.000 0.000
#> SRR1812751 2 0.913 0.574 0.328 0.672
#> SRR1812750 2 0.900 0.589 0.316 0.684
#> SRR1812748 1 0.605 0.836 0.852 0.148
#> SRR1812749 2 0.913 0.574 0.328 0.672
#> SRR1812746 1 0.204 0.777 0.968 0.032
#> SRR1812745 1 0.605 0.836 0.852 0.148
#> SRR1812747 2 0.000 0.884 0.000 1.000
#> SRR1812744 1 0.730 0.824 0.796 0.204
#> SRR1812743 1 0.936 0.711 0.648 0.352
#> SRR1812742 1 0.653 0.828 0.832 0.168
#> SRR1812737 2 0.000 0.884 0.000 1.000
#> SRR1812735 2 0.000 0.884 0.000 1.000
#> SRR1812734 1 0.204 0.777 0.968 0.032
#> SRR1812733 1 0.921 0.738 0.664 0.336
#> SRR1812736 1 0.605 0.836 0.852 0.148
#> SRR1812732 1 0.963 0.675 0.612 0.388
#> SRR1812730 1 0.662 0.837 0.828 0.172
#> SRR1812731 2 0.662 0.685 0.172 0.828
#> SRR1812729 2 0.000 0.884 0.000 1.000
#> SRR1812727 1 0.000 0.755 1.000 0.000
#> SRR1812726 2 0.000 0.884 0.000 1.000
#> SRR1812728 1 0.795 0.817 0.760 0.240
#> SRR1812724 1 0.975 0.640 0.592 0.408
#> SRR1812725 2 0.929 0.194 0.344 0.656
#> SRR1812723 2 0.000 0.884 0.000 1.000
#> SRR1812722 2 0.000 0.884 0.000 1.000
#> SRR1812721 2 0.833 0.515 0.264 0.736
#> SRR1812718 2 0.000 0.884 0.000 1.000
#> SRR1812717 2 0.000 0.884 0.000 1.000
#> SRR1812716 1 0.795 0.817 0.760 0.240
#> SRR1812715 2 0.000 0.884 0.000 1.000
#> SRR1812714 2 0.000 0.884 0.000 1.000
#> SRR1812719 1 0.184 0.775 0.972 0.028
#> SRR1812713 2 0.343 0.838 0.064 0.936
#> SRR1812712 2 0.343 0.838 0.064 0.936
#> SRR1812711 2 0.000 0.884 0.000 1.000
#> SRR1812710 2 0.000 0.884 0.000 1.000
#> SRR1812709 2 0.311 0.844 0.056 0.944
#> SRR1812708 2 0.895 0.587 0.312 0.688
#> SRR1812707 2 0.000 0.884 0.000 1.000
#> SRR1812705 2 0.000 0.884 0.000 1.000
#> SRR1812706 1 0.788 0.819 0.764 0.236
#> SRR1812704 1 0.943 0.713 0.640 0.360
#> SRR1812703 2 0.000 0.884 0.000 1.000
#> SRR1812702 1 0.689 0.835 0.816 0.184
#> SRR1812741 1 0.943 0.700 0.640 0.360
#> SRR1812740 1 0.605 0.836 0.852 0.148
#> SRR1812739 2 0.343 0.838 0.064 0.936
#> SRR1812738 1 0.943 0.713 0.640 0.360
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1812752 1 0.5465 0.203 0.712 0.000 0.288
#> SRR1812753 1 0.5465 0.203 0.712 0.000 0.288
#> SRR1812751 1 0.6783 0.412 0.588 0.396 0.016
#> SRR1812750 1 0.6783 0.412 0.588 0.396 0.016
#> SRR1812748 3 0.0424 0.684 0.008 0.000 0.992
#> SRR1812749 1 0.6783 0.412 0.588 0.396 0.016
#> SRR1812746 3 0.1411 0.669 0.036 0.000 0.964
#> SRR1812745 3 0.0000 0.684 0.000 0.000 1.000
#> SRR1812747 2 0.0000 0.774 0.000 1.000 0.000
#> SRR1812744 3 0.7970 0.522 0.300 0.088 0.612
#> SRR1812743 3 0.9808 0.102 0.368 0.240 0.392
#> SRR1812742 3 0.8261 0.472 0.260 0.124 0.616
#> SRR1812737 2 0.2165 0.767 0.064 0.936 0.000
#> SRR1812735 2 0.1411 0.775 0.036 0.964 0.000
#> SRR1812734 3 0.0237 0.683 0.004 0.000 0.996
#> SRR1812733 3 0.6668 0.625 0.264 0.040 0.696
#> SRR1812736 3 0.0237 0.683 0.004 0.000 0.996
#> SRR1812732 3 0.9894 0.106 0.324 0.276 0.400
#> SRR1812730 3 0.4249 0.689 0.108 0.028 0.864
#> SRR1812731 2 0.7533 0.457 0.392 0.564 0.044
#> SRR1812729 2 0.0592 0.773 0.012 0.988 0.000
#> SRR1812727 3 0.4702 0.613 0.212 0.000 0.788
#> SRR1812726 2 0.0000 0.774 0.000 1.000 0.000
#> SRR1812728 3 0.7523 0.638 0.260 0.080 0.660
#> SRR1812724 2 0.9544 0.154 0.388 0.420 0.192
#> SRR1812725 3 0.9766 0.218 0.236 0.348 0.416
#> SRR1812723 2 0.0237 0.773 0.004 0.996 0.000
#> SRR1812722 2 0.0000 0.774 0.000 1.000 0.000
#> SRR1812721 2 0.7004 0.438 0.428 0.552 0.020
#> SRR1812718 2 0.0747 0.771 0.016 0.984 0.000
#> SRR1812717 2 0.5560 0.625 0.300 0.700 0.000
#> SRR1812716 3 0.6728 0.661 0.184 0.080 0.736
#> SRR1812715 2 0.1529 0.774 0.040 0.960 0.000
#> SRR1812714 2 0.0237 0.773 0.004 0.996 0.000
#> SRR1812719 3 0.4291 0.659 0.180 0.000 0.820
#> SRR1812713 2 0.6501 0.594 0.316 0.664 0.020
#> SRR1812712 2 0.6445 0.595 0.308 0.672 0.020
#> SRR1812711 2 0.0237 0.773 0.004 0.996 0.000
#> SRR1812710 2 0.1411 0.775 0.036 0.964 0.000
#> SRR1812709 2 0.5956 0.602 0.324 0.672 0.004
#> SRR1812708 1 0.6659 0.312 0.532 0.460 0.008
#> SRR1812707 2 0.2066 0.769 0.060 0.940 0.000
#> SRR1812705 2 0.0237 0.773 0.004 0.996 0.000
#> SRR1812706 3 0.7186 0.650 0.224 0.080 0.696
#> SRR1812704 1 0.9942 -0.228 0.380 0.288 0.332
#> SRR1812703 2 0.1031 0.763 0.024 0.976 0.000
#> SRR1812702 3 0.6054 0.675 0.180 0.052 0.768
#> SRR1812741 1 0.9887 -0.180 0.396 0.268 0.336
#> SRR1812740 3 0.0424 0.684 0.008 0.000 0.992
#> SRR1812739 2 0.7442 0.557 0.316 0.628 0.056
#> SRR1812738 1 0.9857 -0.237 0.380 0.252 0.368
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1812752 1 0.2722 0.693286 0.904 0.000 0.064 0.032
#> SRR1812753 1 0.2722 0.693286 0.904 0.000 0.064 0.032
#> SRR1812751 1 0.3873 0.821533 0.772 0.228 0.000 0.000
#> SRR1812750 1 0.3873 0.821533 0.772 0.228 0.000 0.000
#> SRR1812748 3 0.1356 0.638793 0.008 0.000 0.960 0.032
#> SRR1812749 1 0.3873 0.821533 0.772 0.228 0.000 0.000
#> SRR1812746 3 0.0592 0.653523 0.016 0.000 0.984 0.000
#> SRR1812745 3 0.0336 0.657874 0.000 0.000 0.992 0.008
#> SRR1812747 2 0.0592 0.805068 0.000 0.984 0.000 0.016
#> SRR1812744 4 0.5284 0.442830 0.004 0.040 0.240 0.716
#> SRR1812743 4 0.5862 0.675832 0.152 0.044 0.060 0.744
#> SRR1812742 4 0.7959 0.341385 0.160 0.028 0.312 0.500
#> SRR1812737 2 0.3688 0.696738 0.000 0.792 0.000 0.208
#> SRR1812735 2 0.2814 0.757420 0.000 0.868 0.000 0.132
#> SRR1812734 3 0.0672 0.650393 0.008 0.000 0.984 0.008
#> SRR1812733 3 0.8228 0.499210 0.048 0.132 0.448 0.372
#> SRR1812736 3 0.0672 0.654073 0.008 0.000 0.984 0.008
#> SRR1812732 4 0.4971 0.699455 0.024 0.064 0.112 0.800
#> SRR1812730 3 0.8109 0.632758 0.068 0.120 0.540 0.272
#> SRR1812731 4 0.3903 0.737137 0.076 0.080 0.000 0.844
#> SRR1812729 2 0.0707 0.807537 0.000 0.980 0.000 0.020
#> SRR1812727 3 0.7695 0.578558 0.232 0.016 0.540 0.212
#> SRR1812726 2 0.0592 0.806901 0.000 0.984 0.000 0.016
#> SRR1812728 3 0.8580 0.587904 0.068 0.152 0.464 0.316
#> SRR1812724 4 0.2596 0.732576 0.024 0.068 0.000 0.908
#> SRR1812725 2 0.9178 -0.502710 0.068 0.316 0.308 0.308
#> SRR1812723 2 0.0469 0.800673 0.000 0.988 0.000 0.012
#> SRR1812722 2 0.0592 0.806901 0.000 0.984 0.000 0.016
#> SRR1812721 4 0.5332 0.701443 0.128 0.124 0.000 0.748
#> SRR1812718 2 0.0592 0.797689 0.000 0.984 0.000 0.016
#> SRR1812717 2 0.5168 -0.000888 0.004 0.504 0.000 0.492
#> SRR1812716 3 0.8538 0.606444 0.068 0.160 0.488 0.284
#> SRR1812715 2 0.3311 0.734578 0.000 0.828 0.000 0.172
#> SRR1812714 2 0.0779 0.805149 0.004 0.980 0.000 0.016
#> SRR1812719 3 0.7891 0.613488 0.132 0.048 0.552 0.268
#> SRR1812713 4 0.5577 0.447645 0.036 0.328 0.000 0.636
#> SRR1812712 4 0.5666 0.416329 0.036 0.348 0.000 0.616
#> SRR1812711 2 0.0336 0.801635 0.000 0.992 0.000 0.008
#> SRR1812710 2 0.3311 0.734578 0.000 0.828 0.000 0.172
#> SRR1812709 4 0.4220 0.618129 0.004 0.248 0.000 0.748
#> SRR1812708 1 0.5742 0.608192 0.596 0.368 0.000 0.036
#> SRR1812707 2 0.3688 0.696738 0.000 0.792 0.000 0.208
#> SRR1812705 2 0.0336 0.801635 0.000 0.992 0.000 0.008
#> SRR1812706 3 0.8544 0.598847 0.068 0.152 0.476 0.304
#> SRR1812704 4 0.6836 0.340056 0.060 0.088 0.172 0.680
#> SRR1812703 2 0.1022 0.785373 0.000 0.968 0.000 0.032
#> SRR1812702 3 0.8522 0.609344 0.068 0.160 0.492 0.280
#> SRR1812741 4 0.4625 0.704842 0.140 0.044 0.012 0.804
#> SRR1812740 3 0.0672 0.654073 0.008 0.000 0.984 0.008
#> SRR1812739 4 0.2589 0.730273 0.000 0.116 0.000 0.884
#> SRR1812738 4 0.1697 0.709161 0.004 0.028 0.016 0.952
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1812752 1 0.2158 0.8184 0.920 0.000 0.020 0.008 0.052
#> SRR1812753 1 0.2158 0.8184 0.920 0.000 0.020 0.008 0.052
#> SRR1812751 1 0.1908 0.8708 0.908 0.092 0.000 0.000 0.000
#> SRR1812750 1 0.1908 0.8708 0.908 0.092 0.000 0.000 0.000
#> SRR1812748 3 0.1117 0.9640 0.000 0.000 0.964 0.020 0.016
#> SRR1812749 1 0.1908 0.8708 0.908 0.092 0.000 0.000 0.000
#> SRR1812746 3 0.1364 0.9737 0.000 0.000 0.952 0.012 0.036
#> SRR1812745 3 0.1331 0.9768 0.000 0.000 0.952 0.008 0.040
#> SRR1812747 2 0.1121 0.8837 0.000 0.956 0.000 0.000 0.044
#> SRR1812744 4 0.4913 0.6967 0.004 0.004 0.076 0.724 0.192
#> SRR1812743 4 0.3386 0.7961 0.092 0.012 0.024 0.860 0.012
#> SRR1812742 4 0.5960 0.6318 0.092 0.012 0.196 0.672 0.028
#> SRR1812737 2 0.3556 0.8010 0.000 0.828 0.008 0.132 0.032
#> SRR1812735 2 0.1243 0.8788 0.000 0.960 0.004 0.028 0.008
#> SRR1812734 3 0.1168 0.9726 0.000 0.000 0.960 0.008 0.032
#> SRR1812733 5 0.3947 0.7777 0.000 0.020 0.072 0.084 0.824
#> SRR1812736 3 0.0880 0.9799 0.000 0.000 0.968 0.000 0.032
#> SRR1812732 4 0.2569 0.8274 0.004 0.016 0.044 0.908 0.028
#> SRR1812730 5 0.3246 0.7920 0.000 0.024 0.120 0.008 0.848
#> SRR1812731 4 0.1278 0.8326 0.004 0.020 0.000 0.960 0.016
#> SRR1812729 2 0.0609 0.8893 0.000 0.980 0.000 0.000 0.020
#> SRR1812727 5 0.4264 0.7227 0.056 0.004 0.084 0.040 0.816
#> SRR1812726 2 0.0798 0.8882 0.008 0.976 0.000 0.000 0.016
#> SRR1812728 5 0.3696 0.7983 0.000 0.032 0.076 0.048 0.844
#> SRR1812724 4 0.1484 0.8304 0.000 0.008 0.000 0.944 0.048
#> SRR1812725 5 0.3307 0.7583 0.000 0.116 0.024 0.012 0.848
#> SRR1812723 2 0.1357 0.8780 0.004 0.948 0.000 0.000 0.048
#> SRR1812722 2 0.0727 0.8890 0.000 0.980 0.004 0.004 0.012
#> SRR1812721 4 0.4120 0.7893 0.052 0.084 0.004 0.824 0.036
#> SRR1812718 2 0.1357 0.8780 0.004 0.948 0.000 0.000 0.048
#> SRR1812717 2 0.5256 0.4571 0.000 0.620 0.008 0.324 0.048
#> SRR1812716 5 0.3283 0.7942 0.000 0.028 0.116 0.008 0.848
#> SRR1812715 2 0.2349 0.8535 0.000 0.900 0.004 0.084 0.012
#> SRR1812714 2 0.1314 0.8838 0.008 0.960 0.004 0.004 0.024
#> SRR1812719 5 0.3291 0.7584 0.008 0.004 0.092 0.036 0.860
#> SRR1812713 5 0.6598 0.0289 0.000 0.184 0.004 0.368 0.444
#> SRR1812712 5 0.6615 0.0318 0.000 0.188 0.004 0.364 0.444
#> SRR1812711 2 0.0898 0.8880 0.008 0.972 0.000 0.000 0.020
#> SRR1812710 2 0.2390 0.8588 0.000 0.908 0.008 0.060 0.024
#> SRR1812709 4 0.5684 0.5753 0.000 0.196 0.004 0.644 0.156
#> SRR1812708 1 0.6205 0.6161 0.636 0.132 0.012 0.016 0.204
#> SRR1812707 2 0.3556 0.8010 0.000 0.828 0.008 0.132 0.032
#> SRR1812705 2 0.1357 0.8775 0.000 0.948 0.000 0.004 0.048
#> SRR1812706 5 0.3344 0.7976 0.000 0.028 0.104 0.016 0.852
#> SRR1812704 5 0.2825 0.7458 0.000 0.016 0.000 0.124 0.860
#> SRR1812703 2 0.3741 0.6739 0.004 0.768 0.004 0.004 0.220
#> SRR1812702 5 0.3283 0.7942 0.000 0.028 0.116 0.008 0.848
#> SRR1812741 4 0.2354 0.8224 0.052 0.012 0.008 0.916 0.012
#> SRR1812740 3 0.0880 0.9799 0.000 0.000 0.968 0.000 0.032
#> SRR1812739 4 0.3283 0.7823 0.000 0.028 0.000 0.832 0.140
#> SRR1812738 4 0.3121 0.7775 0.004 0.004 0.004 0.836 0.152
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1812752 1 0.3460 0.770 0.760 0.000 0.000 0.000 0.020 NA
#> SRR1812753 1 0.3460 0.770 0.760 0.000 0.000 0.000 0.020 NA
#> SRR1812751 1 0.0713 0.837 0.972 0.028 0.000 0.000 0.000 NA
#> SRR1812750 1 0.0713 0.837 0.972 0.028 0.000 0.000 0.000 NA
#> SRR1812748 3 0.0508 0.948 0.000 0.000 0.984 0.004 0.012 NA
#> SRR1812749 1 0.0713 0.837 0.972 0.028 0.000 0.000 0.000 NA
#> SRR1812746 3 0.2461 0.938 0.000 0.000 0.888 0.004 0.044 NA
#> SRR1812745 3 0.2401 0.939 0.000 0.000 0.892 0.004 0.044 NA
#> SRR1812747 2 0.1196 0.849 0.000 0.952 0.000 0.000 0.040 NA
#> SRR1812744 4 0.4230 0.628 0.000 0.008 0.008 0.764 0.076 NA
#> SRR1812743 4 0.4482 0.534 0.016 0.000 0.024 0.644 0.000 NA
#> SRR1812742 4 0.6003 0.429 0.016 0.000 0.164 0.496 0.000 NA
#> SRR1812737 2 0.4209 0.726 0.004 0.708 0.000 0.036 0.004 NA
#> SRR1812735 2 0.2737 0.815 0.004 0.832 0.000 0.004 0.000 NA
#> SRR1812734 3 0.2504 0.923 0.000 0.000 0.880 0.004 0.028 NA
#> SRR1812733 5 0.4218 0.657 0.000 0.004 0.032 0.192 0.748 NA
#> SRR1812736 3 0.0363 0.950 0.000 0.000 0.988 0.000 0.012 NA
#> SRR1812732 4 0.1340 0.677 0.000 0.004 0.008 0.948 0.000 NA
#> SRR1812730 5 0.1594 0.850 0.000 0.016 0.052 0.000 0.932 NA
#> SRR1812731 4 0.1757 0.684 0.000 0.000 0.000 0.916 0.008 NA
#> SRR1812729 2 0.0458 0.857 0.000 0.984 0.000 0.000 0.016 NA
#> SRR1812727 5 0.5514 0.579 0.052 0.000 0.028 0.020 0.616 NA
#> SRR1812726 2 0.0405 0.855 0.000 0.988 0.000 0.000 0.004 NA
#> SRR1812728 5 0.2934 0.839 0.000 0.016 0.024 0.040 0.880 NA
#> SRR1812724 4 0.3316 0.683 0.000 0.000 0.000 0.812 0.052 NA
#> SRR1812725 5 0.2114 0.824 0.000 0.076 0.012 0.000 0.904 NA
#> SRR1812723 2 0.1461 0.845 0.000 0.940 0.000 0.000 0.044 NA
#> SRR1812722 2 0.1493 0.850 0.004 0.936 0.000 0.000 0.004 NA
#> SRR1812721 4 0.5153 0.574 0.000 0.052 0.000 0.528 0.016 NA
#> SRR1812718 2 0.1528 0.844 0.000 0.936 0.000 0.000 0.048 NA
#> SRR1812717 2 0.6134 0.248 0.000 0.460 0.000 0.284 0.008 NA
#> SRR1812716 5 0.1528 0.851 0.000 0.016 0.048 0.000 0.936 NA
#> SRR1812715 2 0.2884 0.812 0.004 0.824 0.000 0.008 0.000 NA
#> SRR1812714 2 0.0363 0.855 0.000 0.988 0.000 0.000 0.000 NA
#> SRR1812719 5 0.4688 0.663 0.012 0.000 0.028 0.020 0.684 NA
#> SRR1812713 4 0.7266 0.304 0.000 0.092 0.000 0.336 0.284 NA
#> SRR1812712 4 0.7327 0.288 0.000 0.100 0.000 0.320 0.288 NA
#> SRR1812711 2 0.0820 0.853 0.000 0.972 0.000 0.000 0.012 NA
#> SRR1812710 2 0.3329 0.777 0.004 0.768 0.000 0.008 0.000 NA
#> SRR1812709 4 0.6501 0.534 0.000 0.112 0.000 0.504 0.088 NA
#> SRR1812708 1 0.6227 0.578 0.604 0.200 0.000 0.016 0.060 NA
#> SRR1812707 2 0.4209 0.726 0.004 0.708 0.000 0.036 0.004 NA
#> SRR1812705 2 0.1745 0.842 0.000 0.924 0.000 0.000 0.056 NA
#> SRR1812706 5 0.3059 0.829 0.000 0.016 0.032 0.016 0.868 NA
#> SRR1812704 5 0.2240 0.820 0.000 0.008 0.000 0.056 0.904 NA
#> SRR1812703 2 0.1921 0.827 0.000 0.916 0.000 0.000 0.052 NA
#> SRR1812702 5 0.1929 0.849 0.000 0.016 0.048 0.004 0.924 NA
#> SRR1812741 4 0.2378 0.649 0.000 0.000 0.000 0.848 0.000 NA
#> SRR1812740 3 0.0363 0.950 0.000 0.000 0.988 0.000 0.012 NA
#> SRR1812739 4 0.3074 0.680 0.000 0.016 0.000 0.856 0.060 NA
#> SRR1812738 4 0.1951 0.684 0.000 0.000 0.000 0.908 0.076 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", "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 14626 rows and 51 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 0.645 0.897 0.948 0.509 0.490 0.490
#> 3 3 0.630 0.808 0.878 0.322 0.773 0.567
#> 4 4 0.678 0.760 0.875 0.113 0.833 0.552
#> 5 5 0.758 0.659 0.799 0.067 0.912 0.674
#> 6 6 0.717 0.645 0.791 0.042 0.945 0.745
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR1812752 1 0.000 0.929 1.000 0.000
#> SRR1812753 1 0.000 0.929 1.000 0.000
#> SRR1812751 2 0.722 0.769 0.200 0.800
#> SRR1812750 2 0.722 0.769 0.200 0.800
#> SRR1812748 1 0.000 0.929 1.000 0.000
#> SRR1812749 2 0.722 0.769 0.200 0.800
#> SRR1812746 1 0.000 0.929 1.000 0.000
#> SRR1812745 1 0.000 0.929 1.000 0.000
#> SRR1812747 2 0.000 0.948 0.000 1.000
#> SRR1812744 1 0.000 0.929 1.000 0.000
#> SRR1812743 1 0.706 0.810 0.808 0.192
#> SRR1812742 1 0.000 0.929 1.000 0.000
#> SRR1812737 2 0.000 0.948 0.000 1.000
#> SRR1812735 2 0.000 0.948 0.000 1.000
#> SRR1812734 1 0.000 0.929 1.000 0.000
#> SRR1812733 1 0.644 0.832 0.836 0.164
#> SRR1812736 1 0.000 0.929 1.000 0.000
#> SRR1812732 1 0.706 0.810 0.808 0.192
#> SRR1812730 1 0.000 0.929 1.000 0.000
#> SRR1812731 2 0.430 0.868 0.088 0.912
#> SRR1812729 2 0.000 0.948 0.000 1.000
#> SRR1812727 1 0.000 0.929 1.000 0.000
#> SRR1812726 2 0.000 0.948 0.000 1.000
#> SRR1812728 1 0.000 0.929 1.000 0.000
#> SRR1812724 1 0.722 0.802 0.800 0.200
#> SRR1812725 1 0.697 0.742 0.812 0.188
#> SRR1812723 2 0.000 0.948 0.000 1.000
#> SRR1812722 2 0.000 0.948 0.000 1.000
#> SRR1812721 2 0.821 0.617 0.256 0.744
#> SRR1812718 2 0.000 0.948 0.000 1.000
#> SRR1812717 2 0.000 0.948 0.000 1.000
#> SRR1812716 1 0.000 0.929 1.000 0.000
#> SRR1812715 2 0.000 0.948 0.000 1.000
#> SRR1812714 2 0.000 0.948 0.000 1.000
#> SRR1812719 1 0.000 0.929 1.000 0.000
#> SRR1812713 2 0.000 0.948 0.000 1.000
#> SRR1812712 2 0.000 0.948 0.000 1.000
#> SRR1812711 2 0.000 0.948 0.000 1.000
#> SRR1812710 2 0.000 0.948 0.000 1.000
#> SRR1812709 2 0.000 0.948 0.000 1.000
#> SRR1812708 2 0.722 0.769 0.200 0.800
#> SRR1812707 2 0.000 0.948 0.000 1.000
#> SRR1812705 2 0.000 0.948 0.000 1.000
#> SRR1812706 1 0.000 0.929 1.000 0.000
#> SRR1812704 1 0.714 0.806 0.804 0.196
#> SRR1812703 2 0.000 0.948 0.000 1.000
#> SRR1812702 1 0.000 0.929 1.000 0.000
#> SRR1812741 1 0.706 0.810 0.808 0.192
#> SRR1812740 1 0.000 0.929 1.000 0.000
#> SRR1812739 2 0.000 0.948 0.000 1.000
#> SRR1812738 1 0.722 0.802 0.800 0.200
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1812752 3 0.3879 0.824 0.152 0.000 0.848
#> SRR1812753 3 0.3879 0.824 0.152 0.000 0.848
#> SRR1812751 2 0.3921 0.834 0.080 0.884 0.036
#> SRR1812750 2 0.3921 0.834 0.080 0.884 0.036
#> SRR1812748 3 0.0424 0.886 0.008 0.000 0.992
#> SRR1812749 2 0.3921 0.834 0.080 0.884 0.036
#> SRR1812746 3 0.1289 0.881 0.032 0.000 0.968
#> SRR1812745 3 0.0592 0.886 0.012 0.000 0.988
#> SRR1812747 2 0.0000 0.887 0.000 1.000 0.000
#> SRR1812744 3 0.5882 0.511 0.348 0.000 0.652
#> SRR1812743 1 0.3116 0.841 0.892 0.000 0.108
#> SRR1812742 3 0.5733 0.561 0.324 0.000 0.676
#> SRR1812737 2 0.6008 0.404 0.372 0.628 0.000
#> SRR1812735 2 0.3619 0.795 0.136 0.864 0.000
#> SRR1812734 3 0.1031 0.884 0.024 0.000 0.976
#> SRR1812733 3 0.3755 0.849 0.120 0.008 0.872
#> SRR1812736 3 0.0424 0.886 0.008 0.000 0.992
#> SRR1812732 1 0.3551 0.840 0.868 0.000 0.132
#> SRR1812730 3 0.3310 0.870 0.064 0.028 0.908
#> SRR1812731 1 0.3896 0.854 0.888 0.052 0.060
#> SRR1812729 2 0.0000 0.887 0.000 1.000 0.000
#> SRR1812727 3 0.2448 0.869 0.076 0.000 0.924
#> SRR1812726 2 0.0000 0.887 0.000 1.000 0.000
#> SRR1812728 3 0.3590 0.870 0.076 0.028 0.896
#> SRR1812724 1 0.2903 0.859 0.924 0.028 0.048
#> SRR1812725 3 0.6004 0.761 0.064 0.156 0.780
#> SRR1812723 2 0.0000 0.887 0.000 1.000 0.000
#> SRR1812722 2 0.0000 0.887 0.000 1.000 0.000
#> SRR1812721 1 0.2301 0.859 0.936 0.060 0.004
#> SRR1812718 2 0.0000 0.887 0.000 1.000 0.000
#> SRR1812717 1 0.6026 0.404 0.624 0.376 0.000
#> SRR1812716 3 0.3310 0.870 0.064 0.028 0.908
#> SRR1812715 2 0.4702 0.711 0.212 0.788 0.000
#> SRR1812714 2 0.0424 0.884 0.008 0.992 0.000
#> SRR1812719 3 0.2261 0.872 0.068 0.000 0.932
#> SRR1812713 1 0.5075 0.837 0.836 0.096 0.068
#> SRR1812712 1 0.5085 0.837 0.836 0.092 0.072
#> SRR1812711 2 0.0000 0.887 0.000 1.000 0.000
#> SRR1812710 2 0.4346 0.747 0.184 0.816 0.000
#> SRR1812709 1 0.2878 0.849 0.904 0.096 0.000
#> SRR1812708 2 0.3832 0.836 0.076 0.888 0.036
#> SRR1812707 2 0.6008 0.404 0.372 0.628 0.000
#> SRR1812705 2 0.0000 0.887 0.000 1.000 0.000
#> SRR1812706 3 0.3310 0.870 0.064 0.028 0.908
#> SRR1812704 1 0.6307 0.506 0.660 0.012 0.328
#> SRR1812703 2 0.0000 0.887 0.000 1.000 0.000
#> SRR1812702 3 0.3310 0.870 0.064 0.028 0.908
#> SRR1812741 1 0.2448 0.835 0.924 0.000 0.076
#> SRR1812740 3 0.0424 0.886 0.008 0.000 0.992
#> SRR1812739 1 0.3769 0.847 0.880 0.104 0.016
#> SRR1812738 1 0.3551 0.840 0.868 0.000 0.132
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1812752 1 0.0937 0.8079 0.976 0.000 0.012 0.012
#> SRR1812753 1 0.0937 0.8079 0.976 0.000 0.012 0.012
#> SRR1812751 1 0.2589 0.8360 0.884 0.116 0.000 0.000
#> SRR1812750 1 0.2589 0.8360 0.884 0.116 0.000 0.000
#> SRR1812748 3 0.3392 0.8876 0.072 0.000 0.872 0.056
#> SRR1812749 1 0.2589 0.8360 0.884 0.116 0.000 0.000
#> SRR1812746 3 0.3710 0.8040 0.192 0.000 0.804 0.004
#> SRR1812745 3 0.2466 0.9039 0.056 0.000 0.916 0.028
#> SRR1812747 2 0.0804 0.8966 0.012 0.980 0.008 0.000
#> SRR1812744 4 0.7781 0.0748 0.248 0.000 0.344 0.408
#> SRR1812743 4 0.2101 0.7646 0.060 0.000 0.012 0.928
#> SRR1812742 4 0.7918 0.0243 0.332 0.000 0.316 0.352
#> SRR1812737 2 0.3942 0.7021 0.000 0.764 0.000 0.236
#> SRR1812735 2 0.0707 0.8934 0.000 0.980 0.000 0.020
#> SRR1812734 3 0.3616 0.8726 0.112 0.000 0.852 0.036
#> SRR1812733 3 0.1510 0.8998 0.016 0.000 0.956 0.028
#> SRR1812736 3 0.2965 0.8961 0.072 0.000 0.892 0.036
#> SRR1812732 4 0.2944 0.7524 0.044 0.004 0.052 0.900
#> SRR1812730 3 0.0927 0.9089 0.008 0.016 0.976 0.000
#> SRR1812731 4 0.0895 0.7770 0.020 0.004 0.000 0.976
#> SRR1812729 2 0.0672 0.8984 0.008 0.984 0.000 0.008
#> SRR1812727 1 0.2530 0.7731 0.888 0.000 0.112 0.000
#> SRR1812726 2 0.0336 0.8983 0.008 0.992 0.000 0.000
#> SRR1812728 3 0.1884 0.9051 0.020 0.016 0.948 0.016
#> SRR1812724 4 0.1271 0.7767 0.012 0.008 0.012 0.968
#> SRR1812725 3 0.3166 0.8127 0.016 0.116 0.868 0.000
#> SRR1812723 2 0.0927 0.8928 0.008 0.976 0.016 0.000
#> SRR1812722 2 0.0000 0.8987 0.000 1.000 0.000 0.000
#> SRR1812721 4 0.2529 0.7681 0.024 0.048 0.008 0.920
#> SRR1812718 2 0.0804 0.8966 0.012 0.980 0.008 0.000
#> SRR1812717 2 0.5334 0.1118 0.004 0.508 0.004 0.484
#> SRR1812716 3 0.0779 0.9073 0.004 0.016 0.980 0.000
#> SRR1812715 2 0.2469 0.8428 0.000 0.892 0.000 0.108
#> SRR1812714 2 0.0707 0.8950 0.020 0.980 0.000 0.000
#> SRR1812719 1 0.4989 -0.0249 0.528 0.000 0.472 0.000
#> SRR1812713 4 0.5787 0.6451 0.016 0.168 0.084 0.732
#> SRR1812712 4 0.5940 0.6754 0.016 0.124 0.132 0.728
#> SRR1812711 2 0.0524 0.8977 0.008 0.988 0.004 0.000
#> SRR1812710 2 0.2216 0.8549 0.000 0.908 0.000 0.092
#> SRR1812709 4 0.3345 0.7246 0.012 0.124 0.004 0.860
#> SRR1812708 1 0.2589 0.8334 0.884 0.116 0.000 0.000
#> SRR1812707 2 0.3873 0.7129 0.000 0.772 0.000 0.228
#> SRR1812705 2 0.1042 0.8899 0.008 0.972 0.020 0.000
#> SRR1812706 3 0.1762 0.9001 0.012 0.016 0.952 0.020
#> SRR1812704 4 0.5408 0.1582 0.012 0.000 0.488 0.500
#> SRR1812703 2 0.0592 0.8984 0.016 0.984 0.000 0.000
#> SRR1812702 3 0.0779 0.9075 0.004 0.016 0.980 0.000
#> SRR1812741 4 0.1489 0.7724 0.044 0.000 0.004 0.952
#> SRR1812740 3 0.2816 0.8993 0.064 0.000 0.900 0.036
#> SRR1812739 4 0.1262 0.7783 0.008 0.016 0.008 0.968
#> SRR1812738 4 0.0937 0.7775 0.012 0.000 0.012 0.976
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1812752 1 0.1278 0.8793 0.960 0.000 0.020 0.004 0.016
#> SRR1812753 1 0.1372 0.8781 0.956 0.000 0.024 0.004 0.016
#> SRR1812751 1 0.0703 0.8889 0.976 0.024 0.000 0.000 0.000
#> SRR1812750 1 0.0703 0.8889 0.976 0.024 0.000 0.000 0.000
#> SRR1812748 3 0.1205 0.8324 0.004 0.000 0.956 0.040 0.000
#> SRR1812749 1 0.0609 0.8894 0.980 0.020 0.000 0.000 0.000
#> SRR1812746 3 0.2522 0.7473 0.108 0.000 0.880 0.000 0.012
#> SRR1812745 3 0.0510 0.8327 0.000 0.000 0.984 0.000 0.016
#> SRR1812747 2 0.0771 0.8870 0.004 0.976 0.000 0.000 0.020
#> SRR1812744 3 0.5646 0.2883 0.016 0.000 0.616 0.300 0.068
#> SRR1812743 4 0.3497 0.6439 0.012 0.000 0.140 0.828 0.020
#> SRR1812742 4 0.5751 0.0755 0.044 0.000 0.448 0.488 0.020
#> SRR1812737 2 0.5136 0.6527 0.000 0.688 0.000 0.196 0.116
#> SRR1812735 2 0.1211 0.8790 0.000 0.960 0.000 0.016 0.024
#> SRR1812734 3 0.1153 0.8417 0.024 0.000 0.964 0.004 0.008
#> SRR1812733 5 0.5032 0.4361 0.000 0.000 0.448 0.032 0.520
#> SRR1812736 3 0.0162 0.8440 0.004 0.000 0.996 0.000 0.000
#> SRR1812732 4 0.4961 0.1078 0.000 0.000 0.448 0.524 0.028
#> SRR1812730 5 0.4235 0.5525 0.000 0.000 0.424 0.000 0.576
#> SRR1812731 4 0.1267 0.6983 0.012 0.000 0.004 0.960 0.024
#> SRR1812729 2 0.0451 0.8870 0.004 0.988 0.000 0.000 0.008
#> SRR1812727 1 0.3693 0.8046 0.828 0.000 0.080 0.004 0.088
#> SRR1812726 2 0.0566 0.8866 0.012 0.984 0.000 0.000 0.004
#> SRR1812728 5 0.4852 0.5401 0.016 0.000 0.380 0.008 0.596
#> SRR1812724 4 0.3196 0.6270 0.004 0.000 0.000 0.804 0.192
#> SRR1812725 5 0.5309 0.5476 0.000 0.060 0.364 0.000 0.576
#> SRR1812723 2 0.0898 0.8855 0.008 0.972 0.000 0.000 0.020
#> SRR1812722 2 0.0162 0.8864 0.000 0.996 0.000 0.000 0.004
#> SRR1812721 4 0.4645 0.5451 0.012 0.016 0.000 0.672 0.300
#> SRR1812718 2 0.0992 0.8846 0.008 0.968 0.000 0.000 0.024
#> SRR1812717 2 0.6170 0.3443 0.000 0.524 0.000 0.320 0.156
#> SRR1812716 5 0.4210 0.5624 0.000 0.000 0.412 0.000 0.588
#> SRR1812715 2 0.2813 0.8370 0.000 0.876 0.000 0.084 0.040
#> SRR1812714 2 0.1484 0.8713 0.048 0.944 0.000 0.000 0.008
#> SRR1812719 1 0.6304 0.3191 0.532 0.000 0.248 0.000 0.220
#> SRR1812713 5 0.5078 -0.2727 0.004 0.028 0.000 0.424 0.544
#> SRR1812712 5 0.5137 -0.2640 0.004 0.032 0.000 0.416 0.548
#> SRR1812711 2 0.0807 0.8861 0.012 0.976 0.000 0.000 0.012
#> SRR1812710 2 0.2863 0.8388 0.000 0.876 0.000 0.064 0.060
#> SRR1812709 4 0.4999 0.4802 0.004 0.032 0.000 0.604 0.360
#> SRR1812708 1 0.0992 0.8867 0.968 0.024 0.000 0.000 0.008
#> SRR1812707 2 0.5039 0.6683 0.000 0.700 0.000 0.184 0.116
#> SRR1812705 2 0.0963 0.8797 0.000 0.964 0.000 0.000 0.036
#> SRR1812706 5 0.3920 0.5657 0.004 0.000 0.268 0.004 0.724
#> SRR1812704 5 0.3526 0.4540 0.000 0.000 0.072 0.096 0.832
#> SRR1812703 2 0.2438 0.8487 0.060 0.900 0.000 0.000 0.040
#> SRR1812702 5 0.4227 0.5571 0.000 0.000 0.420 0.000 0.580
#> SRR1812741 4 0.2069 0.7003 0.012 0.000 0.052 0.924 0.012
#> SRR1812740 3 0.0566 0.8396 0.004 0.000 0.984 0.000 0.012
#> SRR1812739 4 0.2784 0.6798 0.000 0.004 0.016 0.872 0.108
#> SRR1812738 4 0.3086 0.6940 0.004 0.000 0.092 0.864 0.040
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1812752 1 0.2832 0.8615 0.884 0.000 0.016 0.016 0.044 0.040
#> SRR1812753 1 0.2987 0.8582 0.876 0.000 0.020 0.016 0.044 0.044
#> SRR1812751 1 0.0000 0.8917 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812750 1 0.0000 0.8917 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812748 3 0.1204 0.8572 0.000 0.000 0.944 0.000 0.000 0.056
#> SRR1812749 1 0.0000 0.8917 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812746 3 0.2009 0.8053 0.068 0.000 0.908 0.000 0.024 0.000
#> SRR1812745 3 0.1152 0.8468 0.000 0.000 0.952 0.004 0.044 0.000
#> SRR1812747 2 0.2221 0.8009 0.004 0.908 0.000 0.040 0.044 0.004
#> SRR1812744 3 0.5124 0.3436 0.008 0.000 0.628 0.044 0.024 0.296
#> SRR1812743 6 0.1857 0.6517 0.000 0.000 0.044 0.028 0.004 0.924
#> SRR1812742 6 0.4438 0.3903 0.004 0.000 0.332 0.012 0.016 0.636
#> SRR1812737 2 0.4713 0.4379 0.000 0.560 0.000 0.400 0.028 0.012
#> SRR1812735 2 0.3485 0.7393 0.000 0.784 0.000 0.184 0.028 0.004
#> SRR1812734 3 0.0820 0.8634 0.000 0.000 0.972 0.000 0.016 0.012
#> SRR1812733 5 0.6203 0.4000 0.000 0.000 0.336 0.140 0.488 0.036
#> SRR1812736 3 0.0622 0.8684 0.000 0.000 0.980 0.000 0.008 0.012
#> SRR1812732 6 0.4536 0.4566 0.000 0.000 0.300 0.036 0.012 0.652
#> SRR1812730 5 0.3151 0.7107 0.000 0.000 0.252 0.000 0.748 0.000
#> SRR1812731 6 0.2793 0.5661 0.000 0.000 0.000 0.200 0.000 0.800
#> SRR1812729 2 0.1719 0.8019 0.000 0.932 0.000 0.032 0.032 0.004
#> SRR1812727 1 0.6429 0.5225 0.584 0.000 0.128 0.048 0.212 0.028
#> SRR1812726 2 0.1957 0.7856 0.048 0.920 0.000 0.008 0.024 0.000
#> SRR1812728 5 0.4387 0.6793 0.004 0.008 0.132 0.060 0.772 0.024
#> SRR1812724 6 0.4395 0.1576 0.000 0.000 0.000 0.404 0.028 0.568
#> SRR1812725 5 0.4489 0.6941 0.000 0.072 0.140 0.024 0.756 0.008
#> SRR1812723 2 0.1464 0.7944 0.016 0.944 0.000 0.004 0.036 0.000
#> SRR1812722 2 0.2176 0.7905 0.000 0.896 0.000 0.080 0.024 0.000
#> SRR1812721 4 0.4223 0.3123 0.000 0.004 0.000 0.612 0.016 0.368
#> SRR1812718 2 0.2577 0.7806 0.024 0.888 0.000 0.008 0.072 0.008
#> SRR1812717 4 0.5715 -0.1436 0.000 0.396 0.000 0.492 0.028 0.084
#> SRR1812716 5 0.3259 0.7251 0.000 0.000 0.216 0.012 0.772 0.000
#> SRR1812715 2 0.4430 0.6813 0.000 0.708 0.000 0.232 0.032 0.028
#> SRR1812714 2 0.3997 0.7255 0.128 0.796 0.000 0.040 0.024 0.012
#> SRR1812719 5 0.7163 0.0477 0.328 0.000 0.192 0.048 0.408 0.024
#> SRR1812713 4 0.3690 0.5994 0.000 0.012 0.000 0.804 0.116 0.068
#> SRR1812712 4 0.3368 0.5996 0.000 0.004 0.000 0.820 0.116 0.060
#> SRR1812711 2 0.1116 0.7937 0.028 0.960 0.000 0.004 0.008 0.000
#> SRR1812710 2 0.3907 0.6703 0.000 0.704 0.000 0.268 0.028 0.000
#> SRR1812709 4 0.3071 0.5486 0.000 0.000 0.000 0.804 0.016 0.180
#> SRR1812708 1 0.1007 0.8793 0.968 0.004 0.000 0.004 0.016 0.008
#> SRR1812707 2 0.4554 0.4541 0.000 0.568 0.000 0.400 0.024 0.008
#> SRR1812705 2 0.1982 0.7975 0.000 0.912 0.000 0.016 0.068 0.004
#> SRR1812706 5 0.4348 0.6908 0.000 0.000 0.124 0.152 0.724 0.000
#> SRR1812704 5 0.4828 0.5616 0.000 0.000 0.036 0.184 0.708 0.072
#> SRR1812703 2 0.5460 0.6248 0.112 0.712 0.008 0.096 0.056 0.016
#> SRR1812702 5 0.3314 0.7193 0.000 0.000 0.224 0.012 0.764 0.000
#> SRR1812741 6 0.1442 0.6448 0.000 0.000 0.004 0.040 0.012 0.944
#> SRR1812740 3 0.1092 0.8646 0.000 0.000 0.960 0.000 0.020 0.020
#> SRR1812739 6 0.4814 0.3405 0.000 0.004 0.020 0.416 0.016 0.544
#> SRR1812738 6 0.4029 0.6137 0.000 0.000 0.028 0.160 0.040 0.772
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 14626 rows and 51 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 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 0.764 0.879 0.949 0.5027 0.500 0.500
#> 3 3 0.648 0.801 0.903 0.2011 0.884 0.771
#> 4 4 0.807 0.853 0.942 0.1405 0.911 0.774
#> 5 5 0.831 0.864 0.941 0.1220 0.893 0.665
#> 6 6 0.806 0.740 0.881 0.0473 0.976 0.895
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
#> SRR1812752 1 0.0000 0.936 1.000 0.000
#> SRR1812753 1 0.0000 0.936 1.000 0.000
#> SRR1812751 2 0.5294 0.841 0.120 0.880
#> SRR1812750 2 0.2423 0.923 0.040 0.960
#> SRR1812748 1 0.0000 0.936 1.000 0.000
#> SRR1812749 1 0.2236 0.911 0.964 0.036
#> SRR1812746 1 0.0000 0.936 1.000 0.000
#> SRR1812745 1 0.0000 0.936 1.000 0.000
#> SRR1812747 2 0.0000 0.951 0.000 1.000
#> SRR1812744 1 0.0000 0.936 1.000 0.000
#> SRR1812743 2 0.3114 0.907 0.056 0.944
#> SRR1812742 2 0.9323 0.460 0.348 0.652
#> SRR1812737 2 0.0000 0.951 0.000 1.000
#> SRR1812735 2 0.0000 0.951 0.000 1.000
#> SRR1812734 1 0.0000 0.936 1.000 0.000
#> SRR1812733 1 0.0000 0.936 1.000 0.000
#> SRR1812736 1 0.0000 0.936 1.000 0.000
#> SRR1812732 2 0.0000 0.951 0.000 1.000
#> SRR1812730 1 0.0000 0.936 1.000 0.000
#> SRR1812731 2 0.0000 0.951 0.000 1.000
#> SRR1812729 2 0.0000 0.951 0.000 1.000
#> SRR1812727 1 0.0000 0.936 1.000 0.000
#> SRR1812726 1 0.5178 0.835 0.884 0.116
#> SRR1812728 1 0.0000 0.936 1.000 0.000
#> SRR1812724 2 0.0000 0.951 0.000 1.000
#> SRR1812725 1 0.0000 0.936 1.000 0.000
#> SRR1812723 1 0.0000 0.936 1.000 0.000
#> SRR1812722 2 0.0000 0.951 0.000 1.000
#> SRR1812721 1 0.0376 0.934 0.996 0.004
#> SRR1812718 2 0.1184 0.942 0.016 0.984
#> SRR1812717 2 0.0000 0.951 0.000 1.000
#> SRR1812716 1 0.0000 0.936 1.000 0.000
#> SRR1812715 2 0.0000 0.951 0.000 1.000
#> SRR1812714 2 0.0000 0.951 0.000 1.000
#> SRR1812719 1 0.0000 0.936 1.000 0.000
#> SRR1812713 2 0.9209 0.452 0.336 0.664
#> SRR1812712 1 0.9393 0.473 0.644 0.356
#> SRR1812711 2 0.1414 0.939 0.020 0.980
#> SRR1812710 2 0.0000 0.951 0.000 1.000
#> SRR1812709 1 0.9710 0.370 0.600 0.400
#> SRR1812708 1 0.0000 0.936 1.000 0.000
#> SRR1812707 2 0.0000 0.951 0.000 1.000
#> SRR1812705 1 0.5737 0.812 0.864 0.136
#> SRR1812706 1 0.0000 0.936 1.000 0.000
#> SRR1812704 1 0.0000 0.936 1.000 0.000
#> SRR1812703 2 0.0000 0.951 0.000 1.000
#> SRR1812702 1 0.0000 0.936 1.000 0.000
#> SRR1812741 1 0.9686 0.380 0.604 0.396
#> SRR1812740 1 0.0000 0.936 1.000 0.000
#> SRR1812739 2 0.0000 0.951 0.000 1.000
#> SRR1812738 1 0.7139 0.744 0.804 0.196
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1812752 1 0.4555 0.822 0.800 0.000 0.200
#> SRR1812753 1 0.4555 0.822 0.800 0.000 0.200
#> SRR1812751 1 0.4555 0.723 0.800 0.200 0.000
#> SRR1812750 1 0.4555 0.723 0.800 0.200 0.000
#> SRR1812748 3 0.4555 0.749 0.200 0.000 0.800
#> SRR1812749 1 0.5413 0.829 0.800 0.036 0.164
#> SRR1812746 3 0.4555 0.749 0.200 0.000 0.800
#> SRR1812745 3 0.4555 0.749 0.200 0.000 0.800
#> SRR1812747 2 0.0000 0.942 0.000 1.000 0.000
#> SRR1812744 3 0.0000 0.838 0.000 0.000 1.000
#> SRR1812743 2 0.1964 0.880 0.000 0.944 0.056
#> SRR1812742 2 0.5882 0.385 0.000 0.652 0.348
#> SRR1812737 2 0.0000 0.942 0.000 1.000 0.000
#> SRR1812735 2 0.0000 0.942 0.000 1.000 0.000
#> SRR1812734 3 0.4555 0.749 0.200 0.000 0.800
#> SRR1812733 3 0.0000 0.838 0.000 0.000 1.000
#> SRR1812736 3 0.4555 0.749 0.200 0.000 0.800
#> SRR1812732 2 0.0000 0.942 0.000 1.000 0.000
#> SRR1812730 3 0.0000 0.838 0.000 0.000 1.000
#> SRR1812731 2 0.0000 0.942 0.000 1.000 0.000
#> SRR1812729 2 0.0000 0.942 0.000 1.000 0.000
#> SRR1812727 3 0.0000 0.838 0.000 0.000 1.000
#> SRR1812726 3 0.3267 0.754 0.000 0.116 0.884
#> SRR1812728 3 0.0000 0.838 0.000 0.000 1.000
#> SRR1812724 2 0.0000 0.942 0.000 1.000 0.000
#> SRR1812725 3 0.0000 0.838 0.000 0.000 1.000
#> SRR1812723 3 0.0000 0.838 0.000 0.000 1.000
#> SRR1812722 2 0.0000 0.942 0.000 1.000 0.000
#> SRR1812721 3 0.0237 0.836 0.000 0.004 0.996
#> SRR1812718 2 0.0747 0.928 0.000 0.984 0.016
#> SRR1812717 2 0.0000 0.942 0.000 1.000 0.000
#> SRR1812716 3 0.0000 0.838 0.000 0.000 1.000
#> SRR1812715 2 0.0000 0.942 0.000 1.000 0.000
#> SRR1812714 2 0.0000 0.942 0.000 1.000 0.000
#> SRR1812719 3 0.0000 0.838 0.000 0.000 1.000
#> SRR1812713 2 0.5810 0.425 0.000 0.664 0.336
#> SRR1812712 3 0.5926 0.404 0.000 0.356 0.644
#> SRR1812711 2 0.0892 0.923 0.000 0.980 0.020
#> SRR1812710 2 0.0000 0.942 0.000 1.000 0.000
#> SRR1812709 3 0.6126 0.332 0.000 0.400 0.600
#> SRR1812708 1 0.5859 0.633 0.656 0.000 0.344
#> SRR1812707 2 0.0000 0.942 0.000 1.000 0.000
#> SRR1812705 3 0.3619 0.746 0.000 0.136 0.864
#> SRR1812706 3 0.0000 0.838 0.000 0.000 1.000
#> SRR1812704 3 0.0000 0.838 0.000 0.000 1.000
#> SRR1812703 2 0.0000 0.942 0.000 1.000 0.000
#> SRR1812702 3 0.0000 0.838 0.000 0.000 1.000
#> SRR1812741 3 0.6111 0.339 0.000 0.396 0.604
#> SRR1812740 3 0.4555 0.749 0.200 0.000 0.800
#> SRR1812739 2 0.0000 0.942 0.000 1.000 0.000
#> SRR1812738 3 0.4504 0.643 0.000 0.196 0.804
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1812752 1 0.0000 0.900 1.000 0.000 0.000 0.000
#> SRR1812753 1 0.0000 0.900 1.000 0.000 0.000 0.000
#> SRR1812751 1 0.0000 0.900 1.000 0.000 0.000 0.000
#> SRR1812750 1 0.0000 0.900 1.000 0.000 0.000 0.000
#> SRR1812748 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR1812749 1 0.0000 0.900 1.000 0.000 0.000 0.000
#> SRR1812746 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR1812745 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR1812747 2 0.0000 0.951 0.000 1.000 0.000 0.000
#> SRR1812744 4 0.0000 0.864 0.000 0.000 0.000 1.000
#> SRR1812743 2 0.1557 0.897 0.000 0.944 0.000 0.056
#> SRR1812742 2 0.5764 0.459 0.000 0.644 0.052 0.304
#> SRR1812737 2 0.0000 0.951 0.000 1.000 0.000 0.000
#> SRR1812735 2 0.0000 0.951 0.000 1.000 0.000 0.000
#> SRR1812734 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR1812733 4 0.3649 0.700 0.000 0.000 0.204 0.796
#> SRR1812736 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR1812732 2 0.0000 0.951 0.000 1.000 0.000 0.000
#> SRR1812730 4 0.0000 0.864 0.000 0.000 0.000 1.000
#> SRR1812731 2 0.0000 0.951 0.000 1.000 0.000 0.000
#> SRR1812729 2 0.0000 0.951 0.000 1.000 0.000 0.000
#> SRR1812727 4 0.0000 0.864 0.000 0.000 0.000 1.000
#> SRR1812726 4 0.2589 0.777 0.000 0.116 0.000 0.884
#> SRR1812728 4 0.0000 0.864 0.000 0.000 0.000 1.000
#> SRR1812724 2 0.0000 0.951 0.000 1.000 0.000 0.000
#> SRR1812725 4 0.0000 0.864 0.000 0.000 0.000 1.000
#> SRR1812723 4 0.0000 0.864 0.000 0.000 0.000 1.000
#> SRR1812722 2 0.0000 0.951 0.000 1.000 0.000 0.000
#> SRR1812721 4 0.0188 0.863 0.000 0.004 0.000 0.996
#> SRR1812718 2 0.0592 0.938 0.000 0.984 0.000 0.016
#> SRR1812717 2 0.0000 0.951 0.000 1.000 0.000 0.000
#> SRR1812716 4 0.0000 0.864 0.000 0.000 0.000 1.000
#> SRR1812715 2 0.0000 0.951 0.000 1.000 0.000 0.000
#> SRR1812714 2 0.0000 0.951 0.000 1.000 0.000 0.000
#> SRR1812719 4 0.0000 0.864 0.000 0.000 0.000 1.000
#> SRR1812713 2 0.4605 0.406 0.000 0.664 0.000 0.336
#> SRR1812712 4 0.4697 0.509 0.000 0.356 0.000 0.644
#> SRR1812711 2 0.0707 0.935 0.000 0.980 0.000 0.020
#> SRR1812710 2 0.0000 0.951 0.000 1.000 0.000 0.000
#> SRR1812709 4 0.4855 0.416 0.000 0.400 0.000 0.600
#> SRR1812708 1 0.4643 0.425 0.656 0.000 0.000 0.344
#> SRR1812707 2 0.0000 0.951 0.000 1.000 0.000 0.000
#> SRR1812705 4 0.2868 0.754 0.000 0.136 0.000 0.864
#> SRR1812706 4 0.0000 0.864 0.000 0.000 0.000 1.000
#> SRR1812704 4 0.0000 0.864 0.000 0.000 0.000 1.000
#> SRR1812703 2 0.0000 0.951 0.000 1.000 0.000 0.000
#> SRR1812702 4 0.0000 0.864 0.000 0.000 0.000 1.000
#> SRR1812741 4 0.4843 0.425 0.000 0.396 0.000 0.604
#> SRR1812740 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR1812739 2 0.0000 0.951 0.000 1.000 0.000 0.000
#> SRR1812738 4 0.3569 0.714 0.000 0.196 0.000 0.804
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1812752 1 0.0000 0.912 1.000 0.000 0.000 0.000 0.000
#> SRR1812753 1 0.0000 0.912 1.000 0.000 0.000 0.000 0.000
#> SRR1812751 1 0.0000 0.912 1.000 0.000 0.000 0.000 0.000
#> SRR1812750 1 0.0000 0.912 1.000 0.000 0.000 0.000 0.000
#> SRR1812748 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> SRR1812749 1 0.0000 0.912 1.000 0.000 0.000 0.000 0.000
#> SRR1812746 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> SRR1812745 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> SRR1812747 2 0.0000 0.937 0.000 1.000 0.000 0.000 0.000
#> SRR1812744 5 0.0000 0.908 0.000 0.000 0.000 0.000 1.000
#> SRR1812743 2 0.1341 0.893 0.000 0.944 0.000 0.000 0.056
#> SRR1812742 2 0.5068 0.489 0.000 0.640 0.060 0.000 0.300
#> SRR1812737 2 0.2230 0.860 0.000 0.884 0.000 0.116 0.000
#> SRR1812735 2 0.0000 0.937 0.000 1.000 0.000 0.000 0.000
#> SRR1812734 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> SRR1812733 4 0.3090 0.796 0.000 0.000 0.088 0.860 0.052
#> SRR1812736 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> SRR1812732 2 0.0000 0.937 0.000 1.000 0.000 0.000 0.000
#> SRR1812730 5 0.0000 0.908 0.000 0.000 0.000 0.000 1.000
#> SRR1812731 2 0.2471 0.843 0.000 0.864 0.000 0.136 0.000
#> SRR1812729 2 0.0000 0.937 0.000 1.000 0.000 0.000 0.000
#> SRR1812727 5 0.0000 0.908 0.000 0.000 0.000 0.000 1.000
#> SRR1812726 5 0.3317 0.781 0.000 0.116 0.000 0.044 0.840
#> SRR1812728 5 0.0000 0.908 0.000 0.000 0.000 0.000 1.000
#> SRR1812724 4 0.3274 0.706 0.000 0.220 0.000 0.780 0.000
#> SRR1812725 5 0.0000 0.908 0.000 0.000 0.000 0.000 1.000
#> SRR1812723 5 0.0000 0.908 0.000 0.000 0.000 0.000 1.000
#> SRR1812722 2 0.0000 0.937 0.000 1.000 0.000 0.000 0.000
#> SRR1812721 4 0.0510 0.847 0.000 0.000 0.000 0.984 0.016
#> SRR1812718 2 0.0510 0.930 0.000 0.984 0.000 0.000 0.016
#> SRR1812717 2 0.0000 0.937 0.000 1.000 0.000 0.000 0.000
#> SRR1812716 5 0.0000 0.908 0.000 0.000 0.000 0.000 1.000
#> SRR1812715 2 0.0000 0.937 0.000 1.000 0.000 0.000 0.000
#> SRR1812714 2 0.0000 0.937 0.000 1.000 0.000 0.000 0.000
#> SRR1812719 5 0.0000 0.908 0.000 0.000 0.000 0.000 1.000
#> SRR1812713 4 0.0000 0.852 0.000 0.000 0.000 1.000 0.000
#> SRR1812712 4 0.0000 0.852 0.000 0.000 0.000 1.000 0.000
#> SRR1812711 2 0.0798 0.927 0.000 0.976 0.000 0.008 0.016
#> SRR1812710 2 0.0000 0.937 0.000 1.000 0.000 0.000 0.000
#> SRR1812709 4 0.0000 0.852 0.000 0.000 0.000 1.000 0.000
#> SRR1812708 1 0.3999 0.459 0.656 0.000 0.000 0.000 0.344
#> SRR1812707 2 0.3210 0.760 0.000 0.788 0.000 0.212 0.000
#> SRR1812705 5 0.2471 0.787 0.000 0.136 0.000 0.000 0.864
#> SRR1812706 4 0.3983 0.519 0.000 0.000 0.000 0.660 0.340
#> SRR1812704 5 0.0510 0.898 0.000 0.000 0.000 0.016 0.984
#> SRR1812703 4 0.2329 0.796 0.000 0.124 0.000 0.876 0.000
#> SRR1812702 5 0.0000 0.908 0.000 0.000 0.000 0.000 1.000
#> SRR1812741 5 0.4171 0.385 0.000 0.396 0.000 0.000 0.604
#> SRR1812740 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> SRR1812739 2 0.0290 0.934 0.000 0.992 0.000 0.008 0.000
#> SRR1812738 5 0.3074 0.719 0.000 0.196 0.000 0.000 0.804
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1812752 1 0.0000 0.894 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812753 1 0.0000 0.894 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812751 1 0.0000 0.894 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812750 1 0.0000 0.894 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812748 3 0.3747 0.997 0.000 0.000 0.604 0.000 0.000 0.396
#> SRR1812749 1 0.0000 0.894 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812746 3 0.3737 0.999 0.000 0.000 0.608 0.000 0.000 0.392
#> SRR1812745 3 0.3737 0.999 0.000 0.000 0.608 0.000 0.000 0.392
#> SRR1812747 2 0.3634 0.570 0.000 0.644 0.356 0.000 0.000 0.000
#> SRR1812744 5 0.0000 0.802 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1812743 6 0.3747 0.491 0.000 0.396 0.000 0.000 0.000 0.604
#> SRR1812742 6 0.4764 0.529 0.000 0.108 0.000 0.000 0.232 0.660
#> SRR1812737 2 0.2260 0.731 0.000 0.860 0.000 0.140 0.000 0.000
#> SRR1812735 2 0.0000 0.802 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1812734 3 0.3737 0.999 0.000 0.000 0.608 0.000 0.000 0.392
#> SRR1812733 4 0.3396 0.733 0.000 0.000 0.000 0.812 0.072 0.116
#> SRR1812736 3 0.3737 0.999 0.000 0.000 0.608 0.000 0.000 0.392
#> SRR1812732 2 0.0000 0.802 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1812730 5 0.0000 0.802 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1812731 2 0.2664 0.701 0.000 0.816 0.000 0.184 0.000 0.000
#> SRR1812729 2 0.2762 0.693 0.000 0.804 0.196 0.000 0.000 0.000
#> SRR1812727 5 0.0000 0.802 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1812726 5 0.5391 0.339 0.000 0.116 0.392 0.000 0.492 0.000
#> SRR1812728 5 0.0000 0.802 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1812724 4 0.3076 0.587 0.000 0.240 0.000 0.760 0.000 0.000
#> SRR1812725 5 0.0000 0.802 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1812723 5 0.3737 0.495 0.000 0.000 0.392 0.000 0.608 0.000
#> SRR1812722 2 0.0146 0.802 0.000 0.996 0.004 0.000 0.000 0.000
#> SRR1812721 4 0.0458 0.813 0.000 0.000 0.000 0.984 0.016 0.000
#> SRR1812718 2 0.3737 0.543 0.000 0.608 0.392 0.000 0.000 0.000
#> SRR1812717 2 0.0000 0.802 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1812716 5 0.0000 0.802 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1812715 2 0.0000 0.802 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1812714 2 0.0713 0.796 0.000 0.972 0.028 0.000 0.000 0.000
#> SRR1812719 5 0.0000 0.802 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1812713 4 0.0000 0.819 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1812712 4 0.0000 0.819 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1812711 2 0.3872 0.538 0.000 0.604 0.392 0.000 0.004 0.000
#> SRR1812710 2 0.0000 0.802 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1812709 4 0.0000 0.819 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1812708 1 0.3833 0.397 0.648 0.000 0.008 0.000 0.344 0.000
#> SRR1812707 2 0.3076 0.642 0.000 0.760 0.000 0.240 0.000 0.000
#> SRR1812705 5 0.5502 0.333 0.000 0.136 0.364 0.000 0.500 0.000
#> SRR1812706 4 0.3592 0.477 0.000 0.000 0.000 0.656 0.344 0.000
#> SRR1812704 5 0.0363 0.795 0.000 0.000 0.000 0.012 0.988 0.000
#> SRR1812703 4 0.3062 0.727 0.000 0.024 0.160 0.816 0.000 0.000
#> SRR1812702 5 0.0000 0.802 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1812741 5 0.3747 0.275 0.000 0.396 0.000 0.000 0.604 0.000
#> SRR1812740 3 0.3747 0.997 0.000 0.000 0.604 0.000 0.000 0.396
#> SRR1812739 2 0.0260 0.801 0.000 0.992 0.000 0.008 0.000 0.000
#> SRR1812738 5 0.2762 0.613 0.000 0.196 0.000 0.000 0.804 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 14626 rows and 51 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.813 0.928 0.943 0.331 0.678 0.678
#> 3 3 0.254 0.352 0.729 0.609 0.768 0.683
#> 4 4 0.336 0.428 0.669 0.191 0.703 0.507
#> 5 5 0.382 0.581 0.724 0.136 0.701 0.371
#> 6 6 0.545 0.665 0.721 0.102 0.864 0.564
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
#> SRR1812752 1 0.3733 0.944 0.928 0.072
#> SRR1812753 1 0.3733 0.944 0.928 0.072
#> SRR1812751 1 0.3733 0.944 0.928 0.072
#> SRR1812750 1 0.3733 0.944 0.928 0.072
#> SRR1812748 2 0.0376 0.949 0.004 0.996
#> SRR1812749 1 0.3733 0.944 0.928 0.072
#> SRR1812746 1 0.5294 0.934 0.880 0.120
#> SRR1812745 2 0.5946 0.813 0.144 0.856
#> SRR1812747 2 0.3733 0.935 0.072 0.928
#> SRR1812744 2 0.0376 0.949 0.004 0.996
#> SRR1812743 2 0.0376 0.949 0.004 0.996
#> SRR1812742 2 0.0938 0.946 0.012 0.988
#> SRR1812737 2 0.3733 0.935 0.072 0.928
#> SRR1812735 2 0.3733 0.935 0.072 0.928
#> SRR1812734 1 0.8909 0.685 0.692 0.308
#> SRR1812733 2 0.0376 0.949 0.004 0.996
#> SRR1812736 2 0.6148 0.801 0.152 0.848
#> SRR1812732 2 0.0376 0.949 0.004 0.996
#> SRR1812730 2 0.3431 0.909 0.064 0.936
#> SRR1812731 2 0.0376 0.949 0.004 0.996
#> SRR1812729 2 0.3733 0.935 0.072 0.928
#> SRR1812727 1 0.4939 0.941 0.892 0.108
#> SRR1812726 2 0.3733 0.935 0.072 0.928
#> SRR1812728 2 0.0376 0.949 0.004 0.996
#> SRR1812724 2 0.0376 0.949 0.004 0.996
#> SRR1812725 2 0.2948 0.918 0.052 0.948
#> SRR1812723 2 0.4022 0.934 0.080 0.920
#> SRR1812722 2 0.3733 0.935 0.072 0.928
#> SRR1812721 2 0.0376 0.949 0.004 0.996
#> SRR1812718 2 0.2423 0.944 0.040 0.960
#> SRR1812717 2 0.3733 0.935 0.072 0.928
#> SRR1812716 2 0.3733 0.901 0.072 0.928
#> SRR1812715 2 0.3733 0.935 0.072 0.928
#> SRR1812714 2 0.4690 0.922 0.100 0.900
#> SRR1812719 1 0.6623 0.887 0.828 0.172
#> SRR1812713 2 0.0376 0.949 0.004 0.996
#> SRR1812712 2 0.0000 0.949 0.000 1.000
#> SRR1812711 2 0.3733 0.935 0.072 0.928
#> SRR1812710 2 0.3733 0.935 0.072 0.928
#> SRR1812709 2 0.3584 0.937 0.068 0.932
#> SRR1812708 1 0.4939 0.941 0.892 0.108
#> SRR1812707 2 0.3733 0.935 0.072 0.928
#> SRR1812705 2 0.3879 0.935 0.076 0.924
#> SRR1812706 2 0.3431 0.908 0.064 0.936
#> SRR1812704 2 0.0376 0.949 0.004 0.996
#> SRR1812703 2 0.0376 0.949 0.004 0.996
#> SRR1812702 2 0.1414 0.941 0.020 0.980
#> SRR1812741 2 0.0376 0.949 0.004 0.996
#> SRR1812740 2 0.0376 0.949 0.004 0.996
#> SRR1812739 2 0.2043 0.945 0.032 0.968
#> SRR1812738 2 0.0376 0.949 0.004 0.996
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1812752 1 0.0892 0.8065 0.980 0.020 0.000
#> SRR1812753 1 0.0892 0.8065 0.980 0.020 0.000
#> SRR1812751 1 0.0892 0.8065 0.980 0.020 0.000
#> SRR1812750 1 0.0892 0.8065 0.980 0.020 0.000
#> SRR1812748 3 0.7536 0.3894 0.064 0.304 0.632
#> SRR1812749 1 0.0892 0.8065 0.980 0.020 0.000
#> SRR1812746 1 0.9550 0.3945 0.408 0.192 0.400
#> SRR1812745 2 0.8286 0.1842 0.104 0.588 0.308
#> SRR1812747 2 0.0892 0.4967 0.020 0.980 0.000
#> SRR1812744 2 0.4963 0.3518 0.008 0.792 0.200
#> SRR1812743 3 0.6819 0.6149 0.028 0.328 0.644
#> SRR1812742 3 0.7389 0.5519 0.036 0.408 0.556
#> SRR1812737 2 0.5621 0.1503 0.000 0.692 0.308
#> SRR1812735 2 0.5431 0.1906 0.000 0.716 0.284
#> SRR1812734 2 0.9492 -0.0919 0.184 0.416 0.400
#> SRR1812733 2 0.4808 0.4593 0.008 0.804 0.188
#> SRR1812736 2 0.8964 0.0375 0.160 0.544 0.296
#> SRR1812732 2 0.6286 -0.2274 0.000 0.536 0.464
#> SRR1812730 2 0.6379 0.2542 0.008 0.624 0.368
#> SRR1812731 2 0.7278 -0.2976 0.028 0.516 0.456
#> SRR1812729 2 0.0892 0.4967 0.020 0.980 0.000
#> SRR1812727 1 0.8703 0.5816 0.588 0.168 0.244
#> SRR1812726 2 0.1781 0.4967 0.020 0.960 0.020
#> SRR1812728 2 0.4121 0.4665 0.000 0.832 0.168
#> SRR1812724 2 0.5948 0.0928 0.000 0.640 0.360
#> SRR1812725 2 0.2772 0.4810 0.004 0.916 0.080
#> SRR1812723 2 0.3502 0.4788 0.020 0.896 0.084
#> SRR1812722 2 0.1129 0.4954 0.020 0.976 0.004
#> SRR1812721 3 0.7268 0.4502 0.028 0.448 0.524
#> SRR1812718 2 0.1453 0.4990 0.024 0.968 0.008
#> SRR1812717 2 0.5733 0.1372 0.000 0.676 0.324
#> SRR1812716 2 0.4521 0.4331 0.004 0.816 0.180
#> SRR1812715 2 0.5650 0.1454 0.000 0.688 0.312
#> SRR1812714 2 0.5708 0.3690 0.028 0.768 0.204
#> SRR1812719 2 0.9642 -0.1043 0.208 0.416 0.376
#> SRR1812713 2 0.6260 0.0728 0.000 0.552 0.448
#> SRR1812712 2 0.5016 0.3244 0.000 0.760 0.240
#> SRR1812711 2 0.3752 0.4712 0.020 0.884 0.096
#> SRR1812710 2 0.5650 0.1454 0.000 0.688 0.312
#> SRR1812709 2 0.5706 0.1407 0.000 0.680 0.320
#> SRR1812708 1 0.8072 0.5947 0.652 0.184 0.164
#> SRR1812707 2 0.5650 0.1454 0.000 0.688 0.312
#> SRR1812705 2 0.1129 0.4954 0.020 0.976 0.004
#> SRR1812706 2 0.4293 0.4471 0.004 0.832 0.164
#> SRR1812704 2 0.4654 0.3411 0.000 0.792 0.208
#> SRR1812703 2 0.2772 0.4860 0.004 0.916 0.080
#> SRR1812702 2 0.5201 0.3418 0.004 0.760 0.236
#> SRR1812741 3 0.6819 0.6149 0.028 0.328 0.644
#> SRR1812740 3 0.8206 0.1838 0.072 0.448 0.480
#> SRR1812739 2 0.5948 0.0928 0.000 0.640 0.360
#> SRR1812738 2 0.6008 0.0610 0.000 0.628 0.372
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1812752 1 0.1211 0.96291 0.960 0.000 0.000 0.040
#> SRR1812753 1 0.1211 0.96291 0.960 0.000 0.000 0.040
#> SRR1812751 1 0.0000 0.97552 1.000 0.000 0.000 0.000
#> SRR1812750 1 0.0000 0.97552 1.000 0.000 0.000 0.000
#> SRR1812748 3 0.4755 0.38706 0.000 0.200 0.760 0.040
#> SRR1812749 1 0.0000 0.97552 1.000 0.000 0.000 0.000
#> SRR1812746 3 0.0779 0.53779 0.016 0.004 0.980 0.000
#> SRR1812745 3 0.3877 0.57213 0.000 0.048 0.840 0.112
#> SRR1812747 2 0.8217 0.41905 0.040 0.448 0.148 0.364
#> SRR1812744 2 0.7900 0.17499 0.000 0.368 0.300 0.332
#> SRR1812743 4 0.4817 0.62637 0.000 0.388 0.000 0.612
#> SRR1812742 4 0.5511 0.53118 0.000 0.196 0.084 0.720
#> SRR1812737 2 0.0188 0.37190 0.000 0.996 0.004 0.000
#> SRR1812735 2 0.2647 0.39347 0.000 0.880 0.000 0.120
#> SRR1812734 3 0.1585 0.55945 0.004 0.004 0.952 0.040
#> SRR1812733 4 0.7910 -0.43247 0.000 0.320 0.316 0.364
#> SRR1812736 3 0.3217 0.56629 0.000 0.012 0.860 0.128
#> SRR1812732 2 0.5962 0.35413 0.000 0.692 0.128 0.180
#> SRR1812730 3 0.5448 0.51367 0.000 0.056 0.700 0.244
#> SRR1812731 2 0.6248 0.30112 0.000 0.660 0.128 0.212
#> SRR1812729 2 0.8223 0.41602 0.040 0.444 0.148 0.368
#> SRR1812727 3 0.2530 0.47971 0.112 0.000 0.888 0.000
#> SRR1812726 2 0.8254 0.41025 0.040 0.440 0.152 0.368
#> SRR1812728 3 0.7825 0.10790 0.000 0.304 0.412 0.284
#> SRR1812724 2 0.6011 0.35491 0.000 0.688 0.132 0.180
#> SRR1812725 3 0.7818 0.05485 0.000 0.332 0.404 0.264
#> SRR1812723 2 0.8613 0.35669 0.040 0.432 0.252 0.276
#> SRR1812722 2 0.7184 0.42430 0.000 0.492 0.144 0.364
#> SRR1812721 4 0.4866 0.62081 0.000 0.404 0.000 0.596
#> SRR1812718 2 0.8580 0.36404 0.040 0.440 0.244 0.276
#> SRR1812717 2 0.3196 0.48440 0.000 0.856 0.136 0.008
#> SRR1812716 3 0.7802 0.12160 0.000 0.304 0.420 0.276
#> SRR1812715 2 0.0000 0.36654 0.000 1.000 0.000 0.000
#> SRR1812714 2 0.8593 0.38298 0.040 0.436 0.244 0.280
#> SRR1812719 3 0.0336 0.54121 0.008 0.000 0.992 0.000
#> SRR1812713 2 0.7082 0.35454 0.036 0.648 0.140 0.176
#> SRR1812712 2 0.6906 0.43118 0.000 0.580 0.156 0.264
#> SRR1812711 2 0.8602 0.35813 0.040 0.436 0.260 0.264
#> SRR1812710 2 0.0000 0.36654 0.000 1.000 0.000 0.000
#> SRR1812709 2 0.3088 0.48322 0.000 0.864 0.128 0.008
#> SRR1812708 3 0.8182 0.00188 0.208 0.340 0.432 0.020
#> SRR1812707 2 0.0000 0.36654 0.000 1.000 0.000 0.000
#> SRR1812705 2 0.7571 0.36685 0.000 0.484 0.244 0.272
#> SRR1812706 3 0.7790 0.12602 0.000 0.304 0.424 0.272
#> SRR1812704 2 0.7244 0.39371 0.000 0.488 0.152 0.360
#> SRR1812703 2 0.8595 0.36995 0.040 0.432 0.236 0.292
#> SRR1812702 3 0.7746 0.15989 0.000 0.288 0.440 0.272
#> SRR1812741 4 0.5807 0.63045 0.000 0.344 0.044 0.612
#> SRR1812740 3 0.4996 0.50585 0.000 0.056 0.752 0.192
#> SRR1812739 2 0.6025 0.36285 0.000 0.688 0.140 0.172
#> SRR1812738 2 0.5962 0.35413 0.000 0.692 0.128 0.180
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1812752 1 0.1478 0.945 0.936 0.000 0.000 0.000 0.064
#> SRR1812753 1 0.1638 0.943 0.932 0.000 0.004 0.000 0.064
#> SRR1812751 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000
#> SRR1812750 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000
#> SRR1812748 2 0.8338 0.359 0.000 0.348 0.184 0.172 0.296
#> SRR1812749 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000
#> SRR1812746 5 0.3392 0.832 0.004 0.084 0.000 0.064 0.848
#> SRR1812745 2 0.6063 0.421 0.000 0.540 0.144 0.000 0.316
#> SRR1812747 2 0.2648 0.545 0.000 0.848 0.000 0.152 0.000
#> SRR1812744 2 0.7024 0.522 0.000 0.536 0.048 0.184 0.232
#> SRR1812743 3 0.2690 0.721 0.000 0.000 0.844 0.156 0.000
#> SRR1812742 3 0.5556 0.389 0.000 0.152 0.660 0.004 0.184
#> SRR1812737 4 0.0000 0.679 0.000 0.000 0.000 1.000 0.000
#> SRR1812735 4 0.0963 0.668 0.000 0.036 0.000 0.964 0.000
#> SRR1812734 5 0.3234 0.831 0.000 0.084 0.000 0.064 0.852
#> SRR1812733 2 0.6462 0.463 0.000 0.548 0.176 0.012 0.264
#> SRR1812736 2 0.7894 0.420 0.000 0.400 0.144 0.124 0.332
#> SRR1812732 4 0.5931 0.626 0.000 0.088 0.220 0.652 0.040
#> SRR1812730 2 0.7104 0.474 0.000 0.496 0.144 0.052 0.308
#> SRR1812731 4 0.6116 0.599 0.000 0.084 0.272 0.608 0.036
#> SRR1812729 2 0.3398 0.422 0.000 0.780 0.000 0.216 0.004
#> SRR1812727 5 0.2349 0.830 0.012 0.084 0.004 0.000 0.900
#> SRR1812726 2 0.4787 0.494 0.000 0.712 0.000 0.208 0.080
#> SRR1812728 2 0.7131 0.541 0.000 0.536 0.060 0.184 0.220
#> SRR1812724 4 0.6079 0.616 0.000 0.084 0.252 0.624 0.040
#> SRR1812725 2 0.6265 0.487 0.000 0.596 0.172 0.016 0.216
#> SRR1812723 2 0.2818 0.552 0.000 0.856 0.000 0.132 0.012
#> SRR1812722 2 0.4449 -0.109 0.000 0.512 0.000 0.484 0.004
#> SRR1812721 4 0.4306 -0.227 0.000 0.000 0.492 0.508 0.000
#> SRR1812718 2 0.2214 0.538 0.000 0.916 0.004 0.028 0.052
#> SRR1812717 4 0.3928 0.684 0.000 0.152 0.008 0.800 0.040
#> SRR1812716 2 0.6296 0.485 0.000 0.592 0.176 0.016 0.216
#> SRR1812715 4 0.0000 0.679 0.000 0.000 0.000 1.000 0.000
#> SRR1812714 2 0.5091 0.473 0.000 0.692 0.000 0.196 0.112
#> SRR1812719 5 0.1792 0.830 0.000 0.084 0.000 0.000 0.916
#> SRR1812713 4 0.5437 0.576 0.000 0.296 0.024 0.636 0.044
#> SRR1812712 4 0.5379 0.375 0.000 0.460 0.004 0.492 0.044
#> SRR1812711 2 0.4901 0.495 0.000 0.708 0.000 0.196 0.096
#> SRR1812710 4 0.0000 0.679 0.000 0.000 0.000 1.000 0.000
#> SRR1812709 4 0.3154 0.691 0.000 0.088 0.008 0.864 0.040
#> SRR1812708 5 0.6823 0.535 0.228 0.132 0.000 0.064 0.576
#> SRR1812707 4 0.0000 0.679 0.000 0.000 0.000 1.000 0.000
#> SRR1812705 2 0.3596 0.541 0.000 0.776 0.000 0.212 0.012
#> SRR1812706 2 0.7442 0.525 0.000 0.516 0.176 0.092 0.216
#> SRR1812704 2 0.6866 0.539 0.000 0.564 0.048 0.196 0.192
#> SRR1812703 2 0.1981 0.547 0.000 0.924 0.000 0.028 0.048
#> SRR1812702 2 0.6571 0.464 0.000 0.540 0.176 0.016 0.268
#> SRR1812741 3 0.3081 0.726 0.000 0.000 0.832 0.156 0.012
#> SRR1812740 2 0.8193 0.412 0.000 0.384 0.156 0.172 0.288
#> SRR1812739 4 0.6941 0.557 0.000 0.244 0.172 0.540 0.044
#> SRR1812738 4 0.5695 0.647 0.000 0.088 0.188 0.684 0.040
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1812752 1 0.0458 0.987 0.984 0.000 0.016 0.000 0.000 0.000
#> SRR1812753 1 0.0458 0.987 0.984 0.000 0.016 0.000 0.000 0.000
#> SRR1812751 1 0.0000 0.990 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812750 1 0.0000 0.990 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812748 5 0.7455 0.301 0.000 0.220 0.104 0.032 0.472 0.172
#> SRR1812749 1 0.0146 0.988 0.996 0.004 0.000 0.000 0.000 0.000
#> SRR1812746 3 0.2631 0.829 0.000 0.004 0.856 0.012 0.128 0.000
#> SRR1812745 5 0.4533 0.703 0.000 0.048 0.092 0.104 0.756 0.000
#> SRR1812747 2 0.3835 0.706 0.000 0.684 0.000 0.300 0.016 0.000
#> SRR1812744 2 0.7728 0.560 0.000 0.428 0.160 0.268 0.056 0.088
#> SRR1812743 6 0.0260 0.720 0.000 0.000 0.000 0.008 0.000 0.992
#> SRR1812742 6 0.3277 0.613 0.000 0.084 0.092 0.000 0.000 0.824
#> SRR1812737 4 0.1495 0.758 0.000 0.020 0.020 0.948 0.004 0.008
#> SRR1812735 4 0.3048 0.614 0.000 0.152 0.020 0.824 0.004 0.000
#> SRR1812734 3 0.2631 0.829 0.000 0.004 0.856 0.012 0.128 0.000
#> SRR1812733 5 0.5111 0.604 0.000 0.220 0.064 0.020 0.680 0.016
#> SRR1812736 5 0.5144 0.453 0.000 0.220 0.120 0.012 0.648 0.000
#> SRR1812732 4 0.5571 0.590 0.000 0.004 0.088 0.656 0.060 0.192
#> SRR1812730 5 0.3821 0.690 0.000 0.068 0.092 0.032 0.808 0.000
#> SRR1812731 4 0.3840 0.582 0.000 0.000 0.000 0.696 0.020 0.284
#> SRR1812729 2 0.4065 0.702 0.000 0.672 0.000 0.300 0.028 0.000
#> SRR1812727 3 0.1448 0.828 0.012 0.000 0.948 0.016 0.024 0.000
#> SRR1812726 2 0.3050 0.708 0.000 0.764 0.000 0.236 0.000 0.000
#> SRR1812728 2 0.7534 0.599 0.000 0.404 0.108 0.268 0.204 0.016
#> SRR1812724 4 0.4276 0.700 0.000 0.008 0.092 0.788 0.068 0.044
#> SRR1812725 5 0.4535 0.569 0.000 0.152 0.000 0.144 0.704 0.000
#> SRR1812723 2 0.4771 0.710 0.000 0.664 0.000 0.220 0.116 0.000
#> SRR1812722 2 0.4620 0.509 0.000 0.532 0.000 0.428 0.000 0.040
#> SRR1812721 6 0.4322 0.118 0.000 0.000 0.000 0.452 0.020 0.528
#> SRR1812718 2 0.4511 0.356 0.000 0.620 0.000 0.048 0.332 0.000
#> SRR1812717 4 0.2203 0.760 0.000 0.016 0.004 0.896 0.084 0.000
#> SRR1812716 5 0.3856 0.668 0.000 0.068 0.000 0.132 0.788 0.012
#> SRR1812715 4 0.1321 0.760 0.000 0.024 0.020 0.952 0.004 0.000
#> SRR1812714 2 0.4489 0.702 0.000 0.704 0.040 0.232 0.000 0.024
#> SRR1812719 3 0.1168 0.827 0.000 0.000 0.956 0.016 0.028 0.000
#> SRR1812713 4 0.5186 0.463 0.000 0.004 0.088 0.596 0.308 0.004
#> SRR1812712 2 0.7300 0.146 0.000 0.360 0.088 0.236 0.312 0.004
#> SRR1812711 2 0.4740 0.710 0.000 0.664 0.000 0.228 0.108 0.000
#> SRR1812710 4 0.1592 0.756 0.000 0.032 0.020 0.940 0.000 0.008
#> SRR1812709 4 0.2058 0.762 0.000 0.008 0.000 0.908 0.072 0.012
#> SRR1812708 3 0.4386 0.685 0.092 0.164 0.736 0.004 0.000 0.004
#> SRR1812707 4 0.1237 0.760 0.000 0.020 0.020 0.956 0.004 0.000
#> SRR1812705 2 0.6302 0.678 0.000 0.516 0.000 0.304 0.116 0.064
#> SRR1812706 5 0.4255 0.677 0.000 0.068 0.020 0.120 0.780 0.012
#> SRR1812704 2 0.6383 0.562 0.000 0.480 0.108 0.352 0.056 0.004
#> SRR1812703 2 0.4030 0.690 0.000 0.756 0.000 0.140 0.104 0.000
#> SRR1812702 5 0.4776 0.699 0.000 0.072 0.052 0.112 0.752 0.012
#> SRR1812741 6 0.0260 0.720 0.000 0.000 0.000 0.008 0.000 0.992
#> SRR1812740 5 0.5770 0.393 0.000 0.328 0.104 0.028 0.540 0.000
#> SRR1812739 4 0.5683 0.465 0.000 0.004 0.088 0.572 0.308 0.028
#> SRR1812738 4 0.2974 0.744 0.000 0.004 0.044 0.872 0.052 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["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 14626 rows and 51 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 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 0.590 0.831 0.921 0.4790 0.514 0.514
#> 3 3 0.793 0.858 0.923 0.2825 0.800 0.636
#> 4 4 0.608 0.625 0.826 0.2007 0.751 0.438
#> 5 5 0.738 0.753 0.857 0.0788 0.801 0.391
#> 6 6 0.768 0.669 0.837 0.0365 0.920 0.648
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
#> SRR1812752 1 0.163 0.875 0.976 0.024
#> SRR1812753 1 0.000 0.878 1.000 0.000
#> SRR1812751 2 0.722 0.741 0.200 0.800
#> SRR1812750 2 0.722 0.741 0.200 0.800
#> SRR1812748 1 0.295 0.881 0.948 0.052
#> SRR1812749 2 0.722 0.741 0.200 0.800
#> SRR1812746 1 0.000 0.878 1.000 0.000
#> SRR1812745 1 0.000 0.878 1.000 0.000
#> SRR1812747 2 0.000 0.924 0.000 1.000
#> SRR1812744 1 0.494 0.864 0.892 0.108
#> SRR1812743 1 0.999 0.222 0.516 0.484
#> SRR1812742 1 0.295 0.865 0.948 0.052
#> SRR1812737 2 0.000 0.924 0.000 1.000
#> SRR1812735 2 0.000 0.924 0.000 1.000
#> SRR1812734 1 0.000 0.878 1.000 0.000
#> SRR1812733 1 0.722 0.801 0.800 0.200
#> SRR1812736 1 0.000 0.878 1.000 0.000
#> SRR1812732 2 0.997 -0.103 0.468 0.532
#> SRR1812730 1 0.260 0.882 0.956 0.044
#> SRR1812731 2 0.000 0.924 0.000 1.000
#> SRR1812729 2 0.000 0.924 0.000 1.000
#> SRR1812727 1 0.000 0.878 1.000 0.000
#> SRR1812726 2 0.000 0.924 0.000 1.000
#> SRR1812728 1 0.881 0.678 0.700 0.300
#> SRR1812724 2 0.118 0.912 0.016 0.984
#> SRR1812725 2 0.767 0.651 0.224 0.776
#> SRR1812723 2 0.000 0.924 0.000 1.000
#> SRR1812722 2 0.000 0.924 0.000 1.000
#> SRR1812721 2 0.000 0.924 0.000 1.000
#> SRR1812718 2 0.000 0.924 0.000 1.000
#> SRR1812717 2 0.000 0.924 0.000 1.000
#> SRR1812716 1 0.714 0.805 0.804 0.196
#> SRR1812715 2 0.000 0.924 0.000 1.000
#> SRR1812714 2 0.000 0.924 0.000 1.000
#> SRR1812719 1 0.000 0.878 1.000 0.000
#> SRR1812713 2 0.000 0.924 0.000 1.000
#> SRR1812712 2 0.000 0.924 0.000 1.000
#> SRR1812711 2 0.000 0.924 0.000 1.000
#> SRR1812710 2 0.000 0.924 0.000 1.000
#> SRR1812709 2 0.000 0.924 0.000 1.000
#> SRR1812708 2 0.722 0.741 0.200 0.800
#> SRR1812707 2 0.000 0.924 0.000 1.000
#> SRR1812705 2 0.000 0.924 0.000 1.000
#> SRR1812706 1 0.738 0.795 0.792 0.208
#> SRR1812704 2 0.456 0.836 0.096 0.904
#> SRR1812703 2 0.000 0.924 0.000 1.000
#> SRR1812702 1 0.327 0.879 0.940 0.060
#> SRR1812741 2 0.881 0.491 0.300 0.700
#> SRR1812740 1 0.584 0.845 0.860 0.140
#> SRR1812739 2 0.000 0.924 0.000 1.000
#> SRR1812738 1 0.781 0.771 0.768 0.232
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1812752 1 0.0237 0.916 0.996 0.000 0.004
#> SRR1812753 1 0.0237 0.916 0.996 0.000 0.004
#> SRR1812751 1 0.2448 0.938 0.924 0.076 0.000
#> SRR1812750 1 0.2625 0.933 0.916 0.084 0.000
#> SRR1812748 3 0.2356 0.837 0.072 0.000 0.928
#> SRR1812749 1 0.2448 0.938 0.924 0.076 0.000
#> SRR1812746 3 0.2959 0.826 0.100 0.000 0.900
#> SRR1812745 3 0.0592 0.843 0.012 0.000 0.988
#> SRR1812747 2 0.0000 0.956 0.000 1.000 0.000
#> SRR1812744 3 0.1989 0.844 0.048 0.004 0.948
#> SRR1812743 3 0.8334 0.205 0.080 0.440 0.480
#> SRR1812742 3 0.4346 0.769 0.184 0.000 0.816
#> SRR1812737 2 0.0237 0.954 0.004 0.996 0.000
#> SRR1812735 2 0.0000 0.956 0.000 1.000 0.000
#> SRR1812734 3 0.2448 0.836 0.076 0.000 0.924
#> SRR1812733 3 0.2096 0.827 0.004 0.052 0.944
#> SRR1812736 3 0.2356 0.837 0.072 0.000 0.928
#> SRR1812732 3 0.6082 0.598 0.012 0.296 0.692
#> SRR1812730 3 0.0237 0.842 0.004 0.000 0.996
#> SRR1812731 2 0.0475 0.954 0.004 0.992 0.004
#> SRR1812729 2 0.0000 0.956 0.000 1.000 0.000
#> SRR1812727 1 0.1643 0.889 0.956 0.000 0.044
#> SRR1812726 2 0.0237 0.954 0.004 0.996 0.000
#> SRR1812728 3 0.1647 0.834 0.004 0.036 0.960
#> SRR1812724 2 0.2772 0.906 0.004 0.916 0.080
#> SRR1812725 2 0.6330 0.313 0.004 0.600 0.396
#> SRR1812723 2 0.0000 0.956 0.000 1.000 0.000
#> SRR1812722 2 0.0000 0.956 0.000 1.000 0.000
#> SRR1812721 2 0.0475 0.954 0.004 0.992 0.004
#> SRR1812718 2 0.0237 0.955 0.000 0.996 0.004
#> SRR1812717 2 0.0829 0.951 0.004 0.984 0.012
#> SRR1812716 3 0.0475 0.841 0.004 0.004 0.992
#> SRR1812715 2 0.0000 0.956 0.000 1.000 0.000
#> SRR1812714 2 0.2796 0.877 0.092 0.908 0.000
#> SRR1812719 3 0.4796 0.734 0.220 0.000 0.780
#> SRR1812713 2 0.2682 0.909 0.004 0.920 0.076
#> SRR1812712 2 0.2590 0.912 0.004 0.924 0.072
#> SRR1812711 2 0.0592 0.949 0.012 0.988 0.000
#> SRR1812710 2 0.0237 0.954 0.004 0.996 0.000
#> SRR1812709 2 0.0475 0.954 0.004 0.992 0.004
#> SRR1812708 1 0.2959 0.918 0.900 0.100 0.000
#> SRR1812707 2 0.0000 0.956 0.000 1.000 0.000
#> SRR1812705 2 0.0000 0.956 0.000 1.000 0.000
#> SRR1812706 3 0.3983 0.756 0.004 0.144 0.852
#> SRR1812704 2 0.3272 0.883 0.004 0.892 0.104
#> SRR1812703 2 0.1620 0.941 0.024 0.964 0.012
#> SRR1812702 3 0.0237 0.842 0.000 0.004 0.996
#> SRR1812741 3 0.8603 0.590 0.232 0.168 0.600
#> SRR1812740 3 0.1643 0.843 0.044 0.000 0.956
#> SRR1812739 2 0.1267 0.945 0.004 0.972 0.024
#> SRR1812738 3 0.5158 0.668 0.004 0.232 0.764
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1812752 1 0.1022 0.8559 0.968 0.000 0.032 0.000
#> SRR1812753 1 0.2011 0.8192 0.920 0.000 0.080 0.000
#> SRR1812751 1 0.0000 0.8652 1.000 0.000 0.000 0.000
#> SRR1812750 1 0.0000 0.8652 1.000 0.000 0.000 0.000
#> SRR1812748 3 0.0921 0.7283 0.000 0.000 0.972 0.028
#> SRR1812749 1 0.0000 0.8652 1.000 0.000 0.000 0.000
#> SRR1812746 3 0.6497 0.3943 0.100 0.000 0.596 0.304
#> SRR1812745 3 0.5000 0.0342 0.000 0.000 0.500 0.500
#> SRR1812747 2 0.4891 0.5782 0.012 0.680 0.000 0.308
#> SRR1812744 3 0.1637 0.7215 0.000 0.000 0.940 0.060
#> SRR1812743 3 0.4977 0.2818 0.000 0.460 0.540 0.000
#> SRR1812742 3 0.1661 0.7002 0.004 0.052 0.944 0.000
#> SRR1812737 2 0.0188 0.7988 0.000 0.996 0.000 0.004
#> SRR1812735 2 0.3024 0.7435 0.000 0.852 0.000 0.148
#> SRR1812734 3 0.1302 0.7302 0.000 0.000 0.956 0.044
#> SRR1812733 4 0.4040 0.5029 0.000 0.000 0.248 0.752
#> SRR1812736 3 0.1211 0.7303 0.000 0.000 0.960 0.040
#> SRR1812732 3 0.4790 0.4348 0.000 0.380 0.620 0.000
#> SRR1812730 4 0.2469 0.6908 0.000 0.000 0.108 0.892
#> SRR1812731 2 0.0921 0.7887 0.000 0.972 0.028 0.000
#> SRR1812729 2 0.5007 0.4987 0.008 0.636 0.000 0.356
#> SRR1812727 1 0.0817 0.8596 0.976 0.000 0.024 0.000
#> SRR1812726 2 0.5592 0.5521 0.044 0.656 0.000 0.300
#> SRR1812728 4 0.1389 0.7300 0.000 0.000 0.048 0.952
#> SRR1812724 2 0.0921 0.7887 0.000 0.972 0.028 0.000
#> SRR1812725 4 0.0657 0.7347 0.000 0.012 0.004 0.984
#> SRR1812723 4 0.6238 0.3589 0.084 0.296 0.000 0.620
#> SRR1812722 2 0.4606 0.6319 0.012 0.724 0.000 0.264
#> SRR1812721 2 0.0817 0.7914 0.000 0.976 0.024 0.000
#> SRR1812718 4 0.3707 0.6701 0.028 0.132 0.000 0.840
#> SRR1812717 2 0.0336 0.7991 0.000 0.992 0.000 0.008
#> SRR1812716 4 0.1867 0.7189 0.000 0.000 0.072 0.928
#> SRR1812715 2 0.0592 0.7949 0.000 0.984 0.016 0.000
#> SRR1812714 1 0.6229 0.4883 0.664 0.204 0.000 0.132
#> SRR1812719 1 0.7205 0.2125 0.504 0.000 0.152 0.344
#> SRR1812713 2 0.3266 0.7081 0.000 0.832 0.000 0.168
#> SRR1812712 4 0.4989 0.1066 0.000 0.472 0.000 0.528
#> SRR1812711 4 0.7685 0.1730 0.256 0.288 0.000 0.456
#> SRR1812710 2 0.1398 0.7969 0.004 0.956 0.000 0.040
#> SRR1812709 2 0.1302 0.7962 0.000 0.956 0.000 0.044
#> SRR1812708 1 0.0336 0.8634 0.992 0.000 0.000 0.008
#> SRR1812707 2 0.1389 0.7953 0.000 0.952 0.000 0.048
#> SRR1812705 2 0.5921 0.2284 0.036 0.516 0.000 0.448
#> SRR1812706 4 0.0921 0.7345 0.000 0.000 0.028 0.972
#> SRR1812704 4 0.5113 0.5904 0.000 0.252 0.036 0.712
#> SRR1812703 4 0.2943 0.7119 0.076 0.032 0.000 0.892
#> SRR1812702 4 0.2011 0.7139 0.000 0.000 0.080 0.920
#> SRR1812741 3 0.4761 0.4542 0.000 0.372 0.628 0.000
#> SRR1812740 3 0.1389 0.7302 0.000 0.000 0.952 0.048
#> SRR1812739 2 0.0817 0.7914 0.000 0.976 0.024 0.000
#> SRR1812738 2 0.5132 -0.0907 0.000 0.548 0.448 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1812752 1 0.0162 0.888 0.996 0.004 0.000 0.000 0.000
#> SRR1812753 1 0.1074 0.883 0.968 0.016 0.012 0.000 0.004
#> SRR1812751 1 0.0880 0.889 0.968 0.032 0.000 0.000 0.000
#> SRR1812750 1 0.1965 0.851 0.904 0.096 0.000 0.000 0.000
#> SRR1812748 3 0.0898 0.798 0.000 0.000 0.972 0.008 0.020
#> SRR1812749 1 0.0880 0.889 0.968 0.032 0.000 0.000 0.000
#> SRR1812746 1 0.6944 0.302 0.532 0.040 0.252 0.000 0.176
#> SRR1812745 5 0.4808 0.248 0.000 0.032 0.348 0.000 0.620
#> SRR1812747 2 0.1830 0.886 0.000 0.924 0.000 0.068 0.008
#> SRR1812744 3 0.8583 0.432 0.200 0.044 0.436 0.096 0.224
#> SRR1812743 4 0.4980 0.238 0.000 0.020 0.396 0.576 0.008
#> SRR1812742 3 0.1653 0.785 0.000 0.028 0.944 0.024 0.004
#> SRR1812737 4 0.0794 0.818 0.000 0.028 0.000 0.972 0.000
#> SRR1812735 2 0.2377 0.852 0.000 0.872 0.000 0.128 0.000
#> SRR1812734 3 0.5281 0.624 0.024 0.040 0.680 0.004 0.252
#> SRR1812733 5 0.1851 0.791 0.004 0.024 0.024 0.008 0.940
#> SRR1812736 3 0.0671 0.796 0.000 0.004 0.980 0.000 0.016
#> SRR1812732 3 0.4134 0.563 0.000 0.004 0.704 0.284 0.008
#> SRR1812730 5 0.2326 0.874 0.004 0.072 0.012 0.004 0.908
#> SRR1812731 4 0.0162 0.817 0.000 0.004 0.000 0.996 0.000
#> SRR1812729 2 0.4313 0.772 0.000 0.760 0.000 0.068 0.172
#> SRR1812727 1 0.1173 0.883 0.964 0.020 0.004 0.000 0.012
#> SRR1812726 2 0.2177 0.885 0.004 0.908 0.000 0.080 0.008
#> SRR1812728 5 0.2284 0.878 0.004 0.096 0.000 0.004 0.896
#> SRR1812724 4 0.0671 0.818 0.000 0.004 0.000 0.980 0.016
#> SRR1812725 5 0.3300 0.783 0.000 0.204 0.000 0.004 0.792
#> SRR1812723 2 0.3556 0.806 0.004 0.808 0.000 0.020 0.168
#> SRR1812722 2 0.2046 0.890 0.000 0.916 0.000 0.068 0.016
#> SRR1812721 4 0.0794 0.817 0.000 0.028 0.000 0.972 0.000
#> SRR1812718 2 0.2069 0.878 0.000 0.912 0.000 0.012 0.076
#> SRR1812717 4 0.1818 0.811 0.000 0.024 0.000 0.932 0.044
#> SRR1812716 5 0.2286 0.872 0.000 0.108 0.000 0.004 0.888
#> SRR1812715 4 0.3816 0.521 0.000 0.304 0.000 0.696 0.000
#> SRR1812714 2 0.3734 0.748 0.168 0.796 0.000 0.036 0.000
#> SRR1812719 1 0.2959 0.813 0.864 0.016 0.008 0.000 0.112
#> SRR1812713 4 0.3013 0.740 0.000 0.008 0.000 0.832 0.160
#> SRR1812712 4 0.4532 0.634 0.004 0.036 0.000 0.712 0.248
#> SRR1812711 2 0.2086 0.883 0.028 0.928 0.000 0.016 0.028
#> SRR1812710 4 0.4182 0.313 0.000 0.400 0.000 0.600 0.000
#> SRR1812709 4 0.0693 0.820 0.000 0.012 0.000 0.980 0.008
#> SRR1812708 1 0.1704 0.880 0.928 0.068 0.000 0.000 0.004
#> SRR1812707 4 0.1205 0.815 0.000 0.040 0.000 0.956 0.004
#> SRR1812705 2 0.2462 0.860 0.000 0.880 0.000 0.008 0.112
#> SRR1812706 5 0.2068 0.879 0.000 0.092 0.000 0.004 0.904
#> SRR1812704 4 0.5624 0.241 0.004 0.064 0.000 0.512 0.420
#> SRR1812703 5 0.2678 0.865 0.016 0.100 0.000 0.004 0.880
#> SRR1812702 5 0.2293 0.877 0.000 0.084 0.016 0.000 0.900
#> SRR1812741 4 0.2312 0.784 0.008 0.012 0.056 0.916 0.008
#> SRR1812740 3 0.1310 0.791 0.000 0.020 0.956 0.000 0.024
#> SRR1812739 4 0.0798 0.816 0.000 0.008 0.016 0.976 0.000
#> SRR1812738 4 0.1597 0.807 0.000 0.008 0.024 0.948 0.020
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1812752 1 0.0000 0.873 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812753 1 0.0964 0.869 0.968 0.000 0.012 0.000 0.004 0.016
#> SRR1812751 1 0.1148 0.874 0.960 0.020 0.016 0.000 0.000 0.004
#> SRR1812750 1 0.2680 0.809 0.856 0.124 0.016 0.000 0.000 0.004
#> SRR1812748 6 0.3564 0.638 0.000 0.000 0.264 0.000 0.012 0.724
#> SRR1812749 1 0.1485 0.871 0.944 0.028 0.024 0.000 0.000 0.004
#> SRR1812746 3 0.4712 0.490 0.292 0.000 0.648 0.000 0.016 0.044
#> SRR1812745 3 0.4204 0.612 0.000 0.000 0.740 0.000 0.128 0.132
#> SRR1812747 2 0.0508 0.782 0.000 0.984 0.000 0.000 0.012 0.004
#> SRR1812744 3 0.1991 0.651 0.012 0.000 0.920 0.024 0.000 0.044
#> SRR1812743 4 0.3995 0.110 0.000 0.000 0.004 0.516 0.000 0.480
#> SRR1812742 6 0.0912 0.621 0.000 0.012 0.004 0.008 0.004 0.972
#> SRR1812737 4 0.0777 0.857 0.000 0.024 0.004 0.972 0.000 0.000
#> SRR1812735 2 0.1261 0.777 0.000 0.956 0.004 0.028 0.004 0.008
#> SRR1812734 3 0.1663 0.653 0.000 0.000 0.912 0.000 0.000 0.088
#> SRR1812733 3 0.3595 0.548 0.000 0.000 0.704 0.008 0.288 0.000
#> SRR1812736 6 0.3314 0.638 0.000 0.000 0.256 0.000 0.004 0.740
#> SRR1812732 6 0.6054 0.276 0.000 0.000 0.328 0.268 0.000 0.404
#> SRR1812730 5 0.0692 0.780 0.000 0.000 0.020 0.000 0.976 0.004
#> SRR1812731 4 0.0551 0.858 0.000 0.004 0.004 0.984 0.000 0.008
#> SRR1812729 5 0.4455 0.277 0.000 0.388 0.008 0.020 0.584 0.000
#> SRR1812727 1 0.1870 0.863 0.928 0.004 0.044 0.000 0.012 0.012
#> SRR1812726 2 0.1605 0.777 0.000 0.936 0.044 0.004 0.016 0.000
#> SRR1812728 5 0.1931 0.782 0.016 0.020 0.032 0.004 0.928 0.000
#> SRR1812724 4 0.0964 0.860 0.000 0.000 0.004 0.968 0.016 0.012
#> SRR1812725 5 0.2118 0.764 0.000 0.104 0.008 0.000 0.888 0.000
#> SRR1812723 2 0.3950 0.172 0.000 0.564 0.004 0.000 0.432 0.000
#> SRR1812722 2 0.1788 0.775 0.000 0.928 0.004 0.012 0.052 0.004
#> SRR1812721 4 0.0405 0.861 0.000 0.004 0.000 0.988 0.008 0.000
#> SRR1812718 2 0.1663 0.756 0.000 0.912 0.000 0.000 0.088 0.000
#> SRR1812717 4 0.3053 0.747 0.000 0.004 0.012 0.812 0.172 0.000
#> SRR1812716 5 0.0951 0.783 0.000 0.020 0.004 0.000 0.968 0.008
#> SRR1812715 2 0.4227 -0.127 0.000 0.496 0.004 0.492 0.000 0.008
#> SRR1812714 2 0.2564 0.737 0.044 0.892 0.052 0.004 0.004 0.004
#> SRR1812719 1 0.3836 0.697 0.764 0.000 0.040 0.000 0.188 0.008
#> SRR1812713 4 0.1970 0.824 0.000 0.000 0.008 0.900 0.092 0.000
#> SRR1812712 4 0.3065 0.763 0.000 0.000 0.028 0.820 0.152 0.000
#> SRR1812711 2 0.0405 0.781 0.000 0.988 0.004 0.000 0.008 0.000
#> SRR1812710 4 0.3866 0.031 0.000 0.484 0.000 0.516 0.000 0.000
#> SRR1812709 4 0.0508 0.860 0.000 0.000 0.004 0.984 0.012 0.000
#> SRR1812708 1 0.3971 0.663 0.704 0.024 0.268 0.000 0.000 0.004
#> SRR1812707 4 0.0603 0.860 0.000 0.016 0.000 0.980 0.004 0.000
#> SRR1812705 2 0.3699 0.423 0.000 0.660 0.004 0.000 0.336 0.000
#> SRR1812706 5 0.2573 0.755 0.000 0.024 0.112 0.000 0.864 0.000
#> SRR1812704 5 0.2151 0.744 0.008 0.000 0.016 0.072 0.904 0.000
#> SRR1812703 5 0.5638 0.314 0.028 0.076 0.400 0.000 0.496 0.000
#> SRR1812702 5 0.3629 0.596 0.000 0.016 0.260 0.000 0.724 0.000
#> SRR1812741 4 0.0820 0.856 0.016 0.000 0.000 0.972 0.000 0.012
#> SRR1812740 6 0.3214 0.627 0.004 0.000 0.080 0.000 0.080 0.836
#> SRR1812739 4 0.1524 0.831 0.000 0.000 0.060 0.932 0.000 0.008
#> SRR1812738 4 0.0665 0.860 0.000 0.000 0.008 0.980 0.008 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 14626 rows and 51 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 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 0.286 0.285 0.682 0.3708 0.576 0.576
#> 3 3 0.466 0.641 0.806 0.5473 0.784 0.626
#> 4 4 0.583 0.603 0.769 0.1377 0.960 0.890
#> 5 5 0.702 0.660 0.771 0.1119 0.934 0.806
#> 6 6 0.736 0.550 0.746 0.0688 0.846 0.515
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
#> SRR1812752 2 0.978 -0.00421 0.412 0.588
#> SRR1812753 2 0.978 -0.00421 0.412 0.588
#> SRR1812751 2 0.000 0.27977 0.000 1.000
#> SRR1812750 2 0.000 0.27977 0.000 1.000
#> SRR1812748 1 0.000 0.49735 1.000 0.000
#> SRR1812749 2 0.000 0.27977 0.000 1.000
#> SRR1812746 1 0.000 0.49735 1.000 0.000
#> SRR1812745 1 0.000 0.49735 1.000 0.000
#> SRR1812747 2 0.961 0.37721 0.384 0.616
#> SRR1812744 2 0.994 0.23941 0.456 0.544
#> SRR1812743 2 0.978 -0.00421 0.412 0.588
#> SRR1812742 2 0.978 -0.00421 0.412 0.588
#> SRR1812737 2 0.939 0.42095 0.356 0.644
#> SRR1812735 2 0.939 0.42095 0.356 0.644
#> SRR1812734 1 0.000 0.49735 1.000 0.000
#> SRR1812733 2 0.991 0.27632 0.444 0.556
#> SRR1812736 1 0.000 0.49735 1.000 0.000
#> SRR1812732 2 0.994 0.23941 0.456 0.544
#> SRR1812730 1 0.904 0.39032 0.680 0.320
#> SRR1812731 2 0.574 0.23471 0.136 0.864
#> SRR1812729 2 0.939 0.42095 0.356 0.644
#> SRR1812727 1 0.904 0.39032 0.680 0.320
#> SRR1812726 2 0.939 0.42095 0.356 0.644
#> SRR1812728 1 1.000 -0.08994 0.508 0.492
#> SRR1812724 1 1.000 -0.08994 0.508 0.492
#> SRR1812725 2 0.991 0.27632 0.444 0.556
#> SRR1812723 2 0.939 0.42095 0.356 0.644
#> SRR1812722 2 0.939 0.42095 0.356 0.644
#> SRR1812721 2 0.978 -0.00421 0.412 0.588
#> SRR1812718 2 0.961 0.37721 0.384 0.616
#> SRR1812717 2 0.943 0.41541 0.360 0.640
#> SRR1812716 1 0.983 0.14301 0.576 0.424
#> SRR1812715 2 0.939 0.42095 0.356 0.644
#> SRR1812714 2 0.932 0.41645 0.348 0.652
#> SRR1812719 1 0.904 0.39032 0.680 0.320
#> SRR1812713 2 0.991 0.27632 0.444 0.556
#> SRR1812712 2 0.991 0.27632 0.444 0.556
#> SRR1812711 2 0.939 0.42095 0.356 0.644
#> SRR1812710 2 0.939 0.42095 0.356 0.644
#> SRR1812709 2 0.574 0.23471 0.136 0.864
#> SRR1812708 2 0.000 0.27977 0.000 1.000
#> SRR1812707 2 0.939 0.42095 0.356 0.644
#> SRR1812705 2 0.939 0.42095 0.356 0.644
#> SRR1812706 1 0.904 0.39032 0.680 0.320
#> SRR1812704 1 1.000 -0.08994 0.508 0.492
#> SRR1812703 2 0.991 0.27632 0.444 0.556
#> SRR1812702 2 0.991 0.27632 0.444 0.556
#> SRR1812741 2 0.978 -0.00421 0.412 0.588
#> SRR1812740 1 0.000 0.49735 1.000 0.000
#> SRR1812739 2 0.985 0.30728 0.428 0.572
#> SRR1812738 1 1.000 -0.08994 0.508 0.492
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1812752 1 0.3192 0.65604 0.888 0.000 0.112
#> SRR1812753 1 0.3192 0.65604 0.888 0.000 0.112
#> SRR1812751 1 0.6244 0.45560 0.560 0.440 0.000
#> SRR1812750 1 0.6244 0.45560 0.560 0.440 0.000
#> SRR1812748 3 0.1529 0.54147 0.040 0.000 0.960
#> SRR1812749 1 0.6244 0.45560 0.560 0.440 0.000
#> SRR1812746 3 0.1529 0.54147 0.040 0.000 0.960
#> SRR1812745 3 0.1529 0.54147 0.040 0.000 0.960
#> SRR1812747 2 0.1163 0.83894 0.000 0.972 0.028
#> SRR1812744 2 0.6728 0.70955 0.124 0.748 0.128
#> SRR1812743 1 0.3192 0.65604 0.888 0.000 0.112
#> SRR1812742 1 0.3192 0.65604 0.888 0.000 0.112
#> SRR1812737 2 0.0000 0.84809 0.000 1.000 0.000
#> SRR1812735 2 0.0000 0.84809 0.000 1.000 0.000
#> SRR1812734 3 0.1529 0.54147 0.040 0.000 0.960
#> SRR1812733 2 0.6526 0.72500 0.112 0.760 0.128
#> SRR1812736 3 0.1529 0.54147 0.040 0.000 0.960
#> SRR1812732 2 0.6728 0.70955 0.124 0.748 0.128
#> SRR1812730 3 0.6200 0.63096 0.012 0.312 0.676
#> SRR1812731 1 0.8665 -0.00632 0.508 0.384 0.108
#> SRR1812729 2 0.0000 0.84809 0.000 1.000 0.000
#> SRR1812727 3 0.6200 0.63096 0.012 0.312 0.676
#> SRR1812726 2 0.0000 0.84809 0.000 1.000 0.000
#> SRR1812728 3 0.8848 0.46099 0.124 0.372 0.504
#> SRR1812724 3 0.8848 0.46099 0.124 0.372 0.504
#> SRR1812725 2 0.6526 0.72500 0.112 0.760 0.128
#> SRR1812723 2 0.0000 0.84809 0.000 1.000 0.000
#> SRR1812722 2 0.0000 0.84809 0.000 1.000 0.000
#> SRR1812721 1 0.3192 0.65604 0.888 0.000 0.112
#> SRR1812718 2 0.1163 0.83894 0.000 0.972 0.028
#> SRR1812717 2 0.0237 0.84727 0.000 0.996 0.004
#> SRR1812716 3 0.7867 0.54859 0.068 0.348 0.584
#> SRR1812715 2 0.0000 0.84809 0.000 1.000 0.000
#> SRR1812714 2 0.0424 0.84251 0.008 0.992 0.000
#> SRR1812719 3 0.6200 0.63096 0.012 0.312 0.676
#> SRR1812713 2 0.6526 0.72500 0.112 0.760 0.128
#> SRR1812712 2 0.6526 0.72500 0.112 0.760 0.128
#> SRR1812711 2 0.0000 0.84809 0.000 1.000 0.000
#> SRR1812710 2 0.0000 0.84809 0.000 1.000 0.000
#> SRR1812709 1 0.8665 -0.00632 0.508 0.384 0.108
#> SRR1812708 2 0.6941 0.02567 0.464 0.520 0.016
#> SRR1812707 2 0.0000 0.84809 0.000 1.000 0.000
#> SRR1812705 2 0.0000 0.84809 0.000 1.000 0.000
#> SRR1812706 3 0.6200 0.63096 0.012 0.312 0.676
#> SRR1812704 3 0.8848 0.46099 0.124 0.372 0.504
#> SRR1812703 2 0.5874 0.74946 0.088 0.796 0.116
#> SRR1812702 2 0.6526 0.72500 0.112 0.760 0.128
#> SRR1812741 1 0.3192 0.65604 0.888 0.000 0.112
#> SRR1812740 3 0.1529 0.54147 0.040 0.000 0.960
#> SRR1812739 2 0.6255 0.73965 0.112 0.776 0.112
#> SRR1812738 3 0.8848 0.46099 0.124 0.372 0.504
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1812752 4 0.0000 0.7518 0.000 0.000 0.000 1.000
#> SRR1812753 4 0.0000 0.7518 0.000 0.000 0.000 1.000
#> SRR1812751 1 0.4925 0.8149 0.572 0.428 0.000 0.000
#> SRR1812750 1 0.4925 0.8149 0.572 0.428 0.000 0.000
#> SRR1812748 3 0.0000 0.5441 0.000 0.000 1.000 0.000
#> SRR1812749 1 0.4925 0.8149 0.572 0.428 0.000 0.000
#> SRR1812746 3 0.0000 0.5441 0.000 0.000 1.000 0.000
#> SRR1812745 3 0.0000 0.5441 0.000 0.000 1.000 0.000
#> SRR1812747 2 0.1867 0.6515 0.072 0.928 0.000 0.000
#> SRR1812744 2 0.5320 0.5405 0.416 0.572 0.000 0.012
#> SRR1812743 4 0.0000 0.7518 0.000 0.000 0.000 1.000
#> SRR1812742 4 0.0000 0.7518 0.000 0.000 0.000 1.000
#> SRR1812737 2 0.0000 0.6639 0.000 1.000 0.000 0.000
#> SRR1812735 2 0.0000 0.6639 0.000 1.000 0.000 0.000
#> SRR1812734 3 0.0000 0.5441 0.000 0.000 1.000 0.000
#> SRR1812733 2 0.4925 0.5479 0.428 0.572 0.000 0.000
#> SRR1812736 3 0.0000 0.5441 0.000 0.000 1.000 0.000
#> SRR1812732 2 0.5320 0.5405 0.416 0.572 0.000 0.012
#> SRR1812730 3 0.7405 0.6495 0.236 0.184 0.568 0.012
#> SRR1812731 4 0.7666 0.0367 0.392 0.212 0.000 0.396
#> SRR1812729 2 0.0000 0.6639 0.000 1.000 0.000 0.000
#> SRR1812727 3 0.7405 0.6495 0.236 0.184 0.568 0.012
#> SRR1812726 2 0.0000 0.6639 0.000 1.000 0.000 0.000
#> SRR1812728 3 0.7999 0.5430 0.392 0.200 0.396 0.012
#> SRR1812724 3 0.7999 0.5430 0.392 0.200 0.396 0.012
#> SRR1812725 2 0.4925 0.5479 0.428 0.572 0.000 0.000
#> SRR1812723 2 0.0000 0.6639 0.000 1.000 0.000 0.000
#> SRR1812722 2 0.0000 0.6639 0.000 1.000 0.000 0.000
#> SRR1812721 4 0.0000 0.7518 0.000 0.000 0.000 1.000
#> SRR1812718 2 0.1867 0.6515 0.072 0.928 0.000 0.000
#> SRR1812717 2 0.0592 0.6633 0.016 0.984 0.000 0.000
#> SRR1812716 3 0.7442 0.6055 0.340 0.184 0.476 0.000
#> SRR1812715 2 0.0000 0.6639 0.000 1.000 0.000 0.000
#> SRR1812714 2 0.0707 0.6334 0.020 0.980 0.000 0.000
#> SRR1812719 3 0.7405 0.6495 0.236 0.184 0.568 0.012
#> SRR1812713 2 0.4925 0.5479 0.428 0.572 0.000 0.000
#> SRR1812712 2 0.4925 0.5479 0.428 0.572 0.000 0.000
#> SRR1812711 2 0.0000 0.6639 0.000 1.000 0.000 0.000
#> SRR1812710 2 0.0000 0.6639 0.000 1.000 0.000 0.000
#> SRR1812709 4 0.7666 0.0367 0.392 0.212 0.000 0.396
#> SRR1812708 1 0.4855 0.2183 0.600 0.400 0.000 0.000
#> SRR1812707 2 0.0000 0.6639 0.000 1.000 0.000 0.000
#> SRR1812705 2 0.0000 0.6639 0.000 1.000 0.000 0.000
#> SRR1812706 3 0.7405 0.6495 0.236 0.184 0.568 0.012
#> SRR1812704 3 0.7999 0.5430 0.392 0.200 0.396 0.012
#> SRR1812703 2 0.4830 0.5633 0.392 0.608 0.000 0.000
#> SRR1812702 2 0.4925 0.5479 0.428 0.572 0.000 0.000
#> SRR1812741 4 0.0000 0.7518 0.000 0.000 0.000 1.000
#> SRR1812740 3 0.0000 0.5441 0.000 0.000 1.000 0.000
#> SRR1812739 2 0.4855 0.5603 0.400 0.600 0.000 0.000
#> SRR1812738 3 0.7999 0.5430 0.392 0.200 0.396 0.012
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1812752 4 0.0000 0.7345 0.000 0.000 0.000 1.000 0.000
#> SRR1812753 4 0.0000 0.7345 0.000 0.000 0.000 1.000 0.000
#> SRR1812751 1 0.0404 0.8378 0.988 0.000 0.000 0.000 0.012
#> SRR1812750 1 0.0404 0.8378 0.988 0.000 0.000 0.000 0.012
#> SRR1812748 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> SRR1812749 1 0.0404 0.8378 0.988 0.000 0.000 0.000 0.012
#> SRR1812746 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> SRR1812745 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> SRR1812747 2 0.3966 0.6395 0.336 0.664 0.000 0.000 0.000
#> SRR1812744 2 0.4219 0.0282 0.000 0.584 0.000 0.000 0.416
#> SRR1812743 4 0.4015 0.8664 0.000 0.000 0.000 0.652 0.348
#> SRR1812742 4 0.4015 0.8664 0.000 0.000 0.000 0.652 0.348
#> SRR1812737 2 0.4235 0.6528 0.424 0.576 0.000 0.000 0.000
#> SRR1812735 2 0.4235 0.6528 0.424 0.576 0.000 0.000 0.000
#> SRR1812734 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> SRR1812733 2 0.0963 0.4909 0.000 0.964 0.000 0.000 0.036
#> SRR1812736 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> SRR1812732 2 0.4219 0.0282 0.000 0.584 0.000 0.000 0.416
#> SRR1812730 5 0.4249 0.6321 0.000 0.000 0.432 0.000 0.568
#> SRR1812731 5 0.3109 0.2829 0.000 0.200 0.000 0.000 0.800
#> SRR1812729 2 0.4201 0.6555 0.408 0.592 0.000 0.000 0.000
#> SRR1812727 5 0.4249 0.6321 0.000 0.000 0.432 0.000 0.568
#> SRR1812726 2 0.4235 0.6528 0.424 0.576 0.000 0.000 0.000
#> SRR1812728 5 0.6189 0.7027 0.000 0.140 0.384 0.000 0.476
#> SRR1812724 5 0.6189 0.7027 0.000 0.140 0.384 0.000 0.476
#> SRR1812725 2 0.0963 0.4909 0.000 0.964 0.000 0.000 0.036
#> SRR1812723 2 0.4201 0.6555 0.408 0.592 0.000 0.000 0.000
#> SRR1812722 2 0.4201 0.6555 0.408 0.592 0.000 0.000 0.000
#> SRR1812721 4 0.4138 0.8594 0.000 0.000 0.000 0.616 0.384
#> SRR1812718 2 0.4066 0.6359 0.324 0.672 0.000 0.000 0.004
#> SRR1812717 2 0.4150 0.6553 0.388 0.612 0.000 0.000 0.000
#> SRR1812716 5 0.5790 0.6745 0.000 0.092 0.408 0.000 0.500
#> SRR1812715 2 0.4235 0.6528 0.424 0.576 0.000 0.000 0.000
#> SRR1812714 2 0.4397 0.6285 0.432 0.564 0.000 0.000 0.004
#> SRR1812719 5 0.4249 0.6321 0.000 0.000 0.432 0.000 0.568
#> SRR1812713 2 0.0963 0.4909 0.000 0.964 0.000 0.000 0.036
#> SRR1812712 2 0.0963 0.4909 0.000 0.964 0.000 0.000 0.036
#> SRR1812711 2 0.4210 0.6551 0.412 0.588 0.000 0.000 0.000
#> SRR1812710 2 0.4235 0.6528 0.424 0.576 0.000 0.000 0.000
#> SRR1812709 5 0.3109 0.2829 0.000 0.200 0.000 0.000 0.800
#> SRR1812708 1 0.5010 0.3562 0.572 0.392 0.000 0.000 0.036
#> SRR1812707 2 0.4235 0.6528 0.424 0.576 0.000 0.000 0.000
#> SRR1812705 2 0.4201 0.6555 0.408 0.592 0.000 0.000 0.000
#> SRR1812706 5 0.4249 0.6321 0.000 0.000 0.432 0.000 0.568
#> SRR1812704 5 0.6189 0.7027 0.000 0.140 0.384 0.000 0.476
#> SRR1812703 2 0.0693 0.5038 0.012 0.980 0.000 0.000 0.008
#> SRR1812702 2 0.0963 0.4909 0.000 0.964 0.000 0.000 0.036
#> SRR1812741 4 0.4138 0.8594 0.000 0.000 0.000 0.616 0.384
#> SRR1812740 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> SRR1812739 2 0.1750 0.5023 0.028 0.936 0.000 0.000 0.036
#> SRR1812738 5 0.6189 0.7027 0.000 0.140 0.384 0.000 0.476
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1812752 6 0.0000 0.6940 0.000 0.000 0 0.000 0.000 1.000
#> SRR1812753 6 0.0000 0.6940 0.000 0.000 0 0.000 0.000 1.000
#> SRR1812751 1 0.0865 0.8056 0.964 0.036 0 0.000 0.000 0.000
#> SRR1812750 1 0.0865 0.8056 0.964 0.036 0 0.000 0.000 0.000
#> SRR1812748 3 0.0000 1.0000 0.000 0.000 1 0.000 0.000 0.000
#> SRR1812749 1 0.0865 0.8056 0.964 0.036 0 0.000 0.000 0.000
#> SRR1812746 3 0.0000 1.0000 0.000 0.000 1 0.000 0.000 0.000
#> SRR1812745 3 0.0000 1.0000 0.000 0.000 1 0.000 0.000 0.000
#> SRR1812747 2 0.1700 0.8303 0.024 0.928 0 0.000 0.048 0.000
#> SRR1812744 4 0.4252 0.1269 0.024 0.372 0 0.604 0.000 0.000
#> SRR1812743 6 0.3607 0.8490 0.000 0.000 0 0.348 0.000 0.652
#> SRR1812742 6 0.3607 0.8490 0.000 0.000 0 0.348 0.000 0.652
#> SRR1812737 2 0.0458 0.8736 0.016 0.984 0 0.000 0.000 0.000
#> SRR1812735 2 0.0458 0.8736 0.016 0.984 0 0.000 0.000 0.000
#> SRR1812734 3 0.0000 1.0000 0.000 0.000 1 0.000 0.000 0.000
#> SRR1812733 5 0.6472 0.1130 0.024 0.360 0 0.224 0.392 0.000
#> SRR1812736 3 0.0000 1.0000 0.000 0.000 1 0.000 0.000 0.000
#> SRR1812732 4 0.4252 0.1269 0.024 0.372 0 0.604 0.000 0.000
#> SRR1812730 5 0.4037 -0.2888 0.012 0.000 0 0.380 0.608 0.000
#> SRR1812731 4 0.0363 0.3850 0.000 0.012 0 0.988 0.000 0.000
#> SRR1812729 2 0.0000 0.8730 0.000 1.000 0 0.000 0.000 0.000
#> SRR1812727 5 0.4037 -0.2888 0.012 0.000 0 0.380 0.608 0.000
#> SRR1812726 2 0.0547 0.8722 0.020 0.980 0 0.000 0.000 0.000
#> SRR1812728 4 0.3817 0.4715 0.000 0.000 0 0.568 0.432 0.000
#> SRR1812724 4 0.3817 0.4715 0.000 0.000 0 0.568 0.432 0.000
#> SRR1812725 5 0.6472 0.1130 0.024 0.360 0 0.224 0.392 0.000
#> SRR1812723 2 0.0000 0.8730 0.000 1.000 0 0.000 0.000 0.000
#> SRR1812722 2 0.0000 0.8730 0.000 1.000 0 0.000 0.000 0.000
#> SRR1812721 6 0.3717 0.8410 0.000 0.000 0 0.384 0.000 0.616
#> SRR1812718 2 0.3502 0.7095 0.024 0.800 0 0.016 0.160 0.000
#> SRR1812717 2 0.2377 0.7789 0.004 0.868 0 0.004 0.124 0.000
#> SRR1812716 5 0.3851 -0.4412 0.000 0.000 0 0.460 0.540 0.000
#> SRR1812715 2 0.0458 0.8736 0.016 0.984 0 0.000 0.000 0.000
#> SRR1812714 2 0.1951 0.8267 0.076 0.908 0 0.016 0.000 0.000
#> SRR1812719 5 0.4037 -0.2888 0.012 0.000 0 0.380 0.608 0.000
#> SRR1812713 5 0.6472 0.1130 0.024 0.360 0 0.224 0.392 0.000
#> SRR1812712 5 0.6472 0.1130 0.024 0.360 0 0.224 0.392 0.000
#> SRR1812711 2 0.0146 0.8734 0.004 0.996 0 0.000 0.000 0.000
#> SRR1812710 2 0.0458 0.8736 0.016 0.984 0 0.000 0.000 0.000
#> SRR1812709 4 0.0363 0.3850 0.000 0.012 0 0.988 0.000 0.000
#> SRR1812708 1 0.7019 0.3831 0.480 0.208 0 0.168 0.144 0.000
#> SRR1812707 2 0.0458 0.8736 0.016 0.984 0 0.000 0.000 0.000
#> SRR1812705 2 0.0000 0.8730 0.000 1.000 0 0.000 0.000 0.000
#> SRR1812706 5 0.4037 -0.2888 0.012 0.000 0 0.380 0.608 0.000
#> SRR1812704 4 0.3817 0.4715 0.000 0.000 0 0.568 0.432 0.000
#> SRR1812703 2 0.6351 -0.0627 0.024 0.436 0 0.196 0.344 0.000
#> SRR1812702 5 0.6472 0.1130 0.024 0.360 0 0.224 0.392 0.000
#> SRR1812741 6 0.3717 0.8410 0.000 0.000 0 0.384 0.000 0.616
#> SRR1812740 3 0.0000 1.0000 0.000 0.000 1 0.000 0.000 0.000
#> SRR1812739 2 0.6435 -0.0854 0.024 0.428 0 0.224 0.324 0.000
#> SRR1812738 4 0.3817 0.4715 0.000 0.000 0 0.568 0.432 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", "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 14626 rows and 51 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.769 0.885 0.929 0.4807 0.500 0.500
#> 3 3 0.526 0.624 0.818 0.2922 0.818 0.658
#> 4 4 0.647 0.838 0.874 0.1330 0.784 0.517
#> 5 5 0.760 0.707 0.773 0.0832 0.993 0.976
#> 6 6 0.787 0.827 0.863 0.0592 0.852 0.524
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
#> SRR1812752 1 0.373 0.867 0.928 0.072
#> SRR1812753 1 0.373 0.867 0.928 0.072
#> SRR1812751 2 0.443 0.861 0.092 0.908
#> SRR1812750 2 0.443 0.861 0.092 0.908
#> SRR1812748 1 0.443 0.917 0.908 0.092
#> SRR1812749 2 0.000 0.948 0.000 1.000
#> SRR1812746 1 0.443 0.917 0.908 0.092
#> SRR1812745 1 0.443 0.917 0.908 0.092
#> SRR1812747 2 0.000 0.948 0.000 1.000
#> SRR1812744 1 0.662 0.851 0.828 0.172
#> SRR1812743 1 0.373 0.867 0.928 0.072
#> SRR1812742 1 0.373 0.867 0.928 0.072
#> SRR1812737 2 0.000 0.948 0.000 1.000
#> SRR1812735 2 0.000 0.948 0.000 1.000
#> SRR1812734 1 0.443 0.917 0.908 0.092
#> SRR1812733 2 0.373 0.903 0.072 0.928
#> SRR1812736 1 0.443 0.917 0.908 0.092
#> SRR1812732 1 0.958 0.492 0.620 0.380
#> SRR1812730 1 0.443 0.917 0.908 0.092
#> SRR1812731 2 0.802 0.601 0.244 0.756
#> SRR1812729 2 0.000 0.948 0.000 1.000
#> SRR1812727 1 0.000 0.873 1.000 0.000
#> SRR1812726 2 0.000 0.948 0.000 1.000
#> SRR1812728 1 0.456 0.916 0.904 0.096
#> SRR1812724 1 0.456 0.916 0.904 0.096
#> SRR1812725 2 0.358 0.906 0.068 0.932
#> SRR1812723 2 0.000 0.948 0.000 1.000
#> SRR1812722 2 0.000 0.948 0.000 1.000
#> SRR1812721 1 0.373 0.867 0.928 0.072
#> SRR1812718 2 0.000 0.948 0.000 1.000
#> SRR1812717 2 0.000 0.948 0.000 1.000
#> SRR1812716 2 0.963 0.299 0.388 0.612
#> SRR1812715 2 0.000 0.948 0.000 1.000
#> SRR1812714 2 0.000 0.948 0.000 1.000
#> SRR1812719 1 0.443 0.917 0.908 0.092
#> SRR1812713 2 0.358 0.906 0.068 0.932
#> SRR1812712 2 0.358 0.906 0.068 0.932
#> SRR1812711 2 0.000 0.948 0.000 1.000
#> SRR1812710 2 0.000 0.948 0.000 1.000
#> SRR1812709 2 0.000 0.948 0.000 1.000
#> SRR1812708 2 0.000 0.948 0.000 1.000
#> SRR1812707 2 0.000 0.948 0.000 1.000
#> SRR1812705 2 0.000 0.948 0.000 1.000
#> SRR1812706 1 0.443 0.917 0.908 0.092
#> SRR1812704 1 0.876 0.672 0.704 0.296
#> SRR1812703 2 0.118 0.939 0.016 0.984
#> SRR1812702 2 0.388 0.901 0.076 0.924
#> SRR1812741 1 0.373 0.867 0.928 0.072
#> SRR1812740 1 0.443 0.917 0.908 0.092
#> SRR1812739 2 0.327 0.912 0.060 0.940
#> SRR1812738 1 0.456 0.916 0.904 0.096
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1812752 1 0.1170 0.8465 0.976 0.008 0.016
#> SRR1812753 1 0.1170 0.8465 0.976 0.008 0.016
#> SRR1812751 2 0.3454 0.7732 0.104 0.888 0.008
#> SRR1812750 2 0.3454 0.7732 0.104 0.888 0.008
#> SRR1812748 3 0.6045 0.0486 0.380 0.000 0.620
#> SRR1812749 2 0.2384 0.8129 0.056 0.936 0.008
#> SRR1812746 3 0.2356 0.5560 0.072 0.000 0.928
#> SRR1812745 3 0.2356 0.5560 0.072 0.000 0.928
#> SRR1812747 2 0.0424 0.8504 0.000 0.992 0.008
#> SRR1812744 3 0.6979 0.6077 0.140 0.128 0.732
#> SRR1812743 1 0.2680 0.8756 0.924 0.008 0.068
#> SRR1812742 1 0.2680 0.8756 0.924 0.008 0.068
#> SRR1812737 2 0.0000 0.8516 0.000 1.000 0.000
#> SRR1812735 2 0.0000 0.8516 0.000 1.000 0.000
#> SRR1812734 3 0.5988 0.0764 0.368 0.000 0.632
#> SRR1812733 3 0.5397 0.5164 0.000 0.280 0.720
#> SRR1812736 3 0.6045 0.0486 0.380 0.000 0.620
#> SRR1812732 3 0.7278 0.6014 0.136 0.152 0.712
#> SRR1812730 3 0.2066 0.5622 0.060 0.000 0.940
#> SRR1812731 2 0.9700 -0.0640 0.224 0.428 0.348
#> SRR1812729 2 0.0424 0.8504 0.000 0.992 0.008
#> SRR1812727 1 0.4291 0.7429 0.820 0.000 0.180
#> SRR1812726 2 0.0000 0.8516 0.000 1.000 0.000
#> SRR1812728 3 0.7003 0.5478 0.248 0.060 0.692
#> SRR1812724 3 0.7372 0.5741 0.220 0.092 0.688
#> SRR1812725 2 0.6215 0.3145 0.000 0.572 0.428
#> SRR1812723 2 0.0424 0.8504 0.000 0.992 0.008
#> SRR1812722 2 0.0000 0.8516 0.000 1.000 0.000
#> SRR1812721 1 0.2680 0.8756 0.924 0.008 0.068
#> SRR1812718 2 0.0424 0.8504 0.000 0.992 0.008
#> SRR1812717 2 0.0424 0.8504 0.000 0.992 0.008
#> SRR1812716 3 0.6232 0.5831 0.040 0.220 0.740
#> SRR1812715 2 0.0000 0.8516 0.000 1.000 0.000
#> SRR1812714 2 0.0000 0.8516 0.000 1.000 0.000
#> SRR1812719 1 0.6235 0.1516 0.564 0.000 0.436
#> SRR1812713 2 0.6215 0.3145 0.000 0.572 0.428
#> SRR1812712 2 0.6215 0.3145 0.000 0.572 0.428
#> SRR1812711 2 0.0000 0.8516 0.000 1.000 0.000
#> SRR1812710 2 0.0000 0.8516 0.000 1.000 0.000
#> SRR1812709 2 0.9252 0.0779 0.160 0.468 0.372
#> SRR1812708 2 0.0424 0.8504 0.000 0.992 0.008
#> SRR1812707 2 0.0000 0.8516 0.000 1.000 0.000
#> SRR1812705 2 0.0000 0.8516 0.000 1.000 0.000
#> SRR1812706 3 0.4555 0.5448 0.200 0.000 0.800
#> SRR1812704 3 0.7635 0.5751 0.212 0.112 0.676
#> SRR1812703 2 0.2796 0.7937 0.000 0.908 0.092
#> SRR1812702 3 0.5291 0.5352 0.000 0.268 0.732
#> SRR1812741 1 0.2680 0.8756 0.924 0.008 0.068
#> SRR1812740 3 0.6045 0.0486 0.380 0.000 0.620
#> SRR1812739 2 0.6008 0.4313 0.000 0.628 0.372
#> SRR1812738 3 0.7372 0.5741 0.220 0.092 0.688
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1812752 1 0.2973 0.854 0.884 0.000 0.096 0.020
#> SRR1812753 1 0.2973 0.854 0.884 0.000 0.096 0.020
#> SRR1812751 2 0.6320 0.711 0.080 0.700 0.188 0.032
#> SRR1812750 2 0.6320 0.711 0.080 0.700 0.188 0.032
#> SRR1812748 3 0.4656 0.862 0.160 0.000 0.784 0.056
#> SRR1812749 2 0.6320 0.711 0.080 0.700 0.188 0.032
#> SRR1812746 3 0.4262 0.755 0.008 0.000 0.756 0.236
#> SRR1812745 3 0.4360 0.746 0.008 0.000 0.744 0.248
#> SRR1812747 2 0.1302 0.908 0.000 0.956 0.000 0.044
#> SRR1812744 4 0.1953 0.831 0.012 0.032 0.012 0.944
#> SRR1812743 1 0.3286 0.909 0.876 0.000 0.044 0.080
#> SRR1812742 1 0.3286 0.909 0.876 0.000 0.044 0.080
#> SRR1812737 2 0.0188 0.929 0.000 0.996 0.004 0.000
#> SRR1812735 2 0.0188 0.929 0.000 0.996 0.004 0.000
#> SRR1812734 3 0.4656 0.862 0.160 0.000 0.784 0.056
#> SRR1812733 4 0.3370 0.808 0.000 0.080 0.048 0.872
#> SRR1812736 3 0.4656 0.862 0.160 0.000 0.784 0.056
#> SRR1812732 4 0.1953 0.831 0.012 0.032 0.012 0.944
#> SRR1812730 4 0.3636 0.724 0.008 0.000 0.172 0.820
#> SRR1812731 4 0.5058 0.783 0.128 0.104 0.000 0.768
#> SRR1812729 2 0.0921 0.917 0.000 0.972 0.000 0.028
#> SRR1812727 1 0.3542 0.858 0.852 0.000 0.028 0.120
#> SRR1812726 2 0.0188 0.929 0.000 0.996 0.004 0.000
#> SRR1812728 4 0.3617 0.801 0.124 0.012 0.012 0.852
#> SRR1812724 4 0.3676 0.812 0.112 0.020 0.012 0.856
#> SRR1812725 4 0.3672 0.784 0.000 0.164 0.012 0.824
#> SRR1812723 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> SRR1812722 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> SRR1812721 1 0.2149 0.899 0.912 0.000 0.000 0.088
#> SRR1812718 2 0.1302 0.908 0.000 0.956 0.000 0.044
#> SRR1812717 2 0.0817 0.919 0.000 0.976 0.000 0.024
#> SRR1812716 4 0.3392 0.807 0.000 0.072 0.056 0.872
#> SRR1812715 2 0.0188 0.929 0.000 0.996 0.004 0.000
#> SRR1812714 2 0.0188 0.929 0.000 0.996 0.004 0.000
#> SRR1812719 4 0.5639 0.458 0.324 0.000 0.040 0.636
#> SRR1812713 4 0.3672 0.784 0.000 0.164 0.012 0.824
#> SRR1812712 4 0.3672 0.784 0.000 0.164 0.012 0.824
#> SRR1812711 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> SRR1812710 2 0.0188 0.929 0.000 0.996 0.004 0.000
#> SRR1812709 4 0.4784 0.805 0.100 0.112 0.000 0.788
#> SRR1812708 2 0.3707 0.847 0.004 0.852 0.112 0.032
#> SRR1812707 2 0.0188 0.929 0.000 0.996 0.004 0.000
#> SRR1812705 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> SRR1812706 4 0.4070 0.783 0.132 0.000 0.044 0.824
#> SRR1812704 4 0.3672 0.821 0.092 0.032 0.012 0.864
#> SRR1812703 2 0.3895 0.750 0.000 0.804 0.012 0.184
#> SRR1812702 4 0.3392 0.807 0.000 0.072 0.056 0.872
#> SRR1812741 1 0.2149 0.899 0.912 0.000 0.000 0.088
#> SRR1812740 3 0.4656 0.862 0.160 0.000 0.784 0.056
#> SRR1812739 4 0.3672 0.784 0.000 0.164 0.012 0.824
#> SRR1812738 4 0.3444 0.813 0.104 0.016 0.012 0.868
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1812752 4 0.1605 0.806 0.004 0.000 0.040 0.944 0.012
#> SRR1812753 4 0.1605 0.806 0.004 0.000 0.040 0.944 0.012
#> SRR1812751 2 0.5457 0.450 0.000 0.480 0.460 0.060 0.000
#> SRR1812750 2 0.5457 0.450 0.000 0.480 0.460 0.060 0.000
#> SRR1812748 3 0.5300 1.000 0.468 0.000 0.492 0.032 0.008
#> SRR1812749 2 0.5547 0.457 0.004 0.484 0.456 0.056 0.000
#> SRR1812746 1 0.4849 0.620 0.548 0.000 0.432 0.004 0.016
#> SRR1812745 1 0.4849 0.620 0.548 0.000 0.432 0.004 0.016
#> SRR1812747 2 0.2891 0.739 0.176 0.824 0.000 0.000 0.000
#> SRR1812744 5 0.2621 0.739 0.112 0.004 0.000 0.008 0.876
#> SRR1812743 4 0.2179 0.869 0.000 0.000 0.004 0.896 0.100
#> SRR1812742 4 0.2179 0.869 0.000 0.000 0.004 0.896 0.100
#> SRR1812737 2 0.0609 0.831 0.000 0.980 0.020 0.000 0.000
#> SRR1812735 2 0.0510 0.832 0.000 0.984 0.016 0.000 0.000
#> SRR1812734 1 0.5299 -0.556 0.496 0.000 0.464 0.032 0.008
#> SRR1812733 5 0.4594 0.654 0.484 0.004 0.004 0.000 0.508
#> SRR1812736 3 0.5300 1.000 0.468 0.000 0.492 0.032 0.008
#> SRR1812732 5 0.2621 0.739 0.112 0.004 0.000 0.008 0.876
#> SRR1812730 5 0.3622 0.704 0.124 0.000 0.056 0.000 0.820
#> SRR1812731 5 0.2492 0.684 0.020 0.008 0.000 0.072 0.900
#> SRR1812729 2 0.1671 0.808 0.076 0.924 0.000 0.000 0.000
#> SRR1812727 4 0.4538 0.467 0.000 0.000 0.008 0.540 0.452
#> SRR1812726 2 0.0324 0.833 0.004 0.992 0.004 0.000 0.000
#> SRR1812728 5 0.0566 0.722 0.000 0.000 0.004 0.012 0.984
#> SRR1812724 5 0.0324 0.730 0.000 0.004 0.000 0.004 0.992
#> SRR1812725 5 0.4894 0.658 0.456 0.024 0.000 0.000 0.520
#> SRR1812723 2 0.0703 0.828 0.024 0.976 0.000 0.000 0.000
#> SRR1812722 2 0.0404 0.833 0.000 0.988 0.012 0.000 0.000
#> SRR1812721 4 0.2280 0.868 0.000 0.000 0.000 0.880 0.120
#> SRR1812718 2 0.3838 0.652 0.280 0.716 0.000 0.000 0.004
#> SRR1812717 2 0.1608 0.809 0.072 0.928 0.000 0.000 0.000
#> SRR1812716 5 0.4572 0.665 0.452 0.004 0.004 0.000 0.540
#> SRR1812715 2 0.0510 0.832 0.000 0.984 0.016 0.000 0.000
#> SRR1812714 2 0.0324 0.833 0.004 0.992 0.004 0.000 0.000
#> SRR1812719 5 0.2321 0.666 0.024 0.000 0.008 0.056 0.912
#> SRR1812713 5 0.4894 0.658 0.456 0.024 0.000 0.000 0.520
#> SRR1812712 5 0.4894 0.658 0.456 0.024 0.000 0.000 0.520
#> SRR1812711 2 0.0404 0.831 0.012 0.988 0.000 0.000 0.000
#> SRR1812710 2 0.0609 0.831 0.000 0.980 0.020 0.000 0.000
#> SRR1812709 5 0.1059 0.732 0.020 0.008 0.000 0.004 0.968
#> SRR1812708 2 0.6587 0.487 0.156 0.488 0.344 0.000 0.012
#> SRR1812707 2 0.0290 0.833 0.000 0.992 0.008 0.000 0.000
#> SRR1812705 2 0.0290 0.831 0.008 0.992 0.000 0.000 0.000
#> SRR1812706 5 0.1116 0.720 0.028 0.000 0.004 0.004 0.964
#> SRR1812704 5 0.0486 0.730 0.004 0.004 0.000 0.004 0.988
#> SRR1812703 2 0.5232 0.350 0.456 0.500 0.000 0.000 0.044
#> SRR1812702 5 0.4594 0.654 0.484 0.004 0.004 0.000 0.508
#> SRR1812741 4 0.2329 0.868 0.000 0.000 0.000 0.876 0.124
#> SRR1812740 3 0.5300 1.000 0.468 0.000 0.492 0.032 0.008
#> SRR1812739 5 0.4968 0.656 0.456 0.028 0.000 0.000 0.516
#> SRR1812738 5 0.0648 0.728 0.004 0.004 0.004 0.004 0.984
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1812752 6 0.2509 0.842 0.088 0.000 0.000 0.036 0.000 0.876
#> SRR1812753 6 0.2509 0.842 0.088 0.000 0.000 0.036 0.000 0.876
#> SRR1812751 1 0.4251 0.859 0.624 0.348 0.000 0.000 0.000 0.028
#> SRR1812750 1 0.4251 0.859 0.624 0.348 0.000 0.000 0.000 0.028
#> SRR1812748 3 0.0146 0.921 0.000 0.000 0.996 0.000 0.000 0.004
#> SRR1812749 1 0.4180 0.858 0.628 0.348 0.000 0.000 0.000 0.024
#> SRR1812746 3 0.3395 0.887 0.136 0.000 0.812 0.048 0.004 0.000
#> SRR1812745 3 0.3395 0.887 0.136 0.000 0.812 0.048 0.004 0.000
#> SRR1812747 2 0.3776 0.653 0.052 0.760 0.000 0.188 0.000 0.000
#> SRR1812744 5 0.3645 0.757 0.064 0.000 0.000 0.152 0.784 0.000
#> SRR1812743 6 0.2060 0.916 0.016 0.000 0.000 0.000 0.084 0.900
#> SRR1812742 6 0.2060 0.916 0.016 0.000 0.000 0.000 0.084 0.900
#> SRR1812737 2 0.0260 0.853 0.008 0.992 0.000 0.000 0.000 0.000
#> SRR1812735 2 0.0260 0.853 0.008 0.992 0.000 0.000 0.000 0.000
#> SRR1812734 3 0.2203 0.914 0.084 0.000 0.896 0.016 0.000 0.004
#> SRR1812733 4 0.2839 0.911 0.044 0.000 0.004 0.860 0.092 0.000
#> SRR1812736 3 0.0146 0.921 0.000 0.000 0.996 0.000 0.000 0.004
#> SRR1812732 5 0.3645 0.757 0.064 0.000 0.000 0.152 0.784 0.000
#> SRR1812730 5 0.5694 0.518 0.188 0.000 0.012 0.224 0.576 0.000
#> SRR1812731 5 0.3549 0.776 0.020 0.032 0.000 0.020 0.836 0.092
#> SRR1812729 2 0.2908 0.771 0.048 0.848 0.000 0.104 0.000 0.000
#> SRR1812727 5 0.3777 0.727 0.084 0.000 0.000 0.004 0.788 0.124
#> SRR1812726 2 0.0632 0.852 0.000 0.976 0.000 0.024 0.000 0.000
#> SRR1812728 5 0.1745 0.855 0.068 0.000 0.000 0.012 0.920 0.000
#> SRR1812724 5 0.0937 0.865 0.000 0.000 0.000 0.040 0.960 0.000
#> SRR1812725 4 0.1957 0.923 0.000 0.000 0.000 0.888 0.112 0.000
#> SRR1812723 2 0.2660 0.789 0.048 0.868 0.000 0.084 0.000 0.000
#> SRR1812722 2 0.0260 0.853 0.008 0.992 0.000 0.000 0.000 0.000
#> SRR1812721 6 0.1806 0.916 0.004 0.000 0.000 0.000 0.088 0.908
#> SRR1812718 2 0.4853 0.112 0.056 0.488 0.000 0.456 0.000 0.000
#> SRR1812717 2 0.3113 0.765 0.048 0.856 0.000 0.072 0.024 0.000
#> SRR1812716 4 0.3049 0.902 0.048 0.000 0.004 0.844 0.104 0.000
#> SRR1812715 2 0.0260 0.853 0.008 0.992 0.000 0.000 0.000 0.000
#> SRR1812714 2 0.1010 0.846 0.004 0.960 0.000 0.036 0.000 0.000
#> SRR1812719 5 0.2056 0.845 0.080 0.000 0.000 0.012 0.904 0.004
#> SRR1812713 4 0.1957 0.923 0.000 0.000 0.000 0.888 0.112 0.000
#> SRR1812712 4 0.1957 0.923 0.000 0.000 0.000 0.888 0.112 0.000
#> SRR1812711 2 0.0790 0.851 0.000 0.968 0.000 0.032 0.000 0.000
#> SRR1812710 2 0.0260 0.853 0.008 0.992 0.000 0.000 0.000 0.000
#> SRR1812709 5 0.1549 0.857 0.020 0.000 0.000 0.044 0.936 0.000
#> SRR1812708 1 0.6057 0.557 0.484 0.268 0.000 0.240 0.008 0.000
#> SRR1812707 2 0.0000 0.854 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1812705 2 0.0692 0.852 0.020 0.976 0.000 0.004 0.000 0.000
#> SRR1812706 5 0.2376 0.852 0.068 0.000 0.000 0.044 0.888 0.000
#> SRR1812704 5 0.0865 0.865 0.000 0.000 0.000 0.036 0.964 0.000
#> SRR1812703 4 0.2839 0.718 0.044 0.092 0.000 0.860 0.004 0.000
#> SRR1812702 4 0.2839 0.911 0.044 0.000 0.004 0.860 0.092 0.000
#> SRR1812741 6 0.2062 0.915 0.008 0.000 0.000 0.004 0.088 0.900
#> SRR1812740 3 0.0146 0.921 0.000 0.000 0.996 0.000 0.000 0.004
#> SRR1812739 4 0.2979 0.895 0.044 0.000 0.000 0.840 0.116 0.000
#> SRR1812738 5 0.0777 0.865 0.004 0.000 0.000 0.024 0.972 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", "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 14626 rows and 51 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 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.975 0.989 0.5088 0.492 0.492
#> 3 3 0.881 0.934 0.962 0.3112 0.711 0.479
#> 4 4 0.874 0.912 0.958 0.1118 0.906 0.722
#> 5 5 0.877 0.868 0.901 0.0560 0.929 0.740
#> 6 6 0.909 0.896 0.921 0.0447 0.953 0.789
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR1812752 1 0.000 0.988 1.000 0.000
#> SRR1812753 1 0.000 0.988 1.000 0.000
#> SRR1812751 2 0.000 0.988 0.000 1.000
#> SRR1812750 2 0.000 0.988 0.000 1.000
#> SRR1812748 1 0.000 0.988 1.000 0.000
#> SRR1812749 2 0.000 0.988 0.000 1.000
#> SRR1812746 1 0.000 0.988 1.000 0.000
#> SRR1812745 1 0.000 0.988 1.000 0.000
#> SRR1812747 2 0.000 0.988 0.000 1.000
#> SRR1812744 1 0.000 0.988 1.000 0.000
#> SRR1812743 1 0.000 0.988 1.000 0.000
#> SRR1812742 1 0.000 0.988 1.000 0.000
#> SRR1812737 2 0.000 0.988 0.000 1.000
#> SRR1812735 2 0.000 0.988 0.000 1.000
#> SRR1812734 1 0.000 0.988 1.000 0.000
#> SRR1812733 2 0.000 0.988 0.000 1.000
#> SRR1812736 1 0.000 0.988 1.000 0.000
#> SRR1812732 1 0.000 0.988 1.000 0.000
#> SRR1812730 1 0.000 0.988 1.000 0.000
#> SRR1812731 1 0.781 0.694 0.768 0.232
#> SRR1812729 2 0.000 0.988 0.000 1.000
#> SRR1812727 1 0.000 0.988 1.000 0.000
#> SRR1812726 2 0.000 0.988 0.000 1.000
#> SRR1812728 1 0.000 0.988 1.000 0.000
#> SRR1812724 1 0.000 0.988 1.000 0.000
#> SRR1812725 2 0.000 0.988 0.000 1.000
#> SRR1812723 2 0.000 0.988 0.000 1.000
#> SRR1812722 2 0.000 0.988 0.000 1.000
#> SRR1812721 1 0.000 0.988 1.000 0.000
#> SRR1812718 2 0.000 0.988 0.000 1.000
#> SRR1812717 2 0.000 0.988 0.000 1.000
#> SRR1812716 1 0.224 0.954 0.964 0.036
#> SRR1812715 2 0.000 0.988 0.000 1.000
#> SRR1812714 2 0.000 0.988 0.000 1.000
#> SRR1812719 1 0.000 0.988 1.000 0.000
#> SRR1812713 2 0.000 0.988 0.000 1.000
#> SRR1812712 2 0.000 0.988 0.000 1.000
#> SRR1812711 2 0.000 0.988 0.000 1.000
#> SRR1812710 2 0.000 0.988 0.000 1.000
#> SRR1812709 2 0.260 0.946 0.044 0.956
#> SRR1812708 2 0.000 0.988 0.000 1.000
#> SRR1812707 2 0.000 0.988 0.000 1.000
#> SRR1812705 2 0.000 0.988 0.000 1.000
#> SRR1812706 1 0.000 0.988 1.000 0.000
#> SRR1812704 1 0.000 0.988 1.000 0.000
#> SRR1812703 2 0.000 0.988 0.000 1.000
#> SRR1812702 2 0.808 0.667 0.248 0.752
#> SRR1812741 1 0.000 0.988 1.000 0.000
#> SRR1812740 1 0.000 0.988 1.000 0.000
#> SRR1812739 2 0.000 0.988 0.000 1.000
#> SRR1812738 1 0.000 0.988 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1812752 1 0.000 0.977 1.000 0.000 0.000
#> SRR1812753 1 0.000 0.977 1.000 0.000 0.000
#> SRR1812751 2 0.000 0.996 0.000 1.000 0.000
#> SRR1812750 2 0.000 0.996 0.000 1.000 0.000
#> SRR1812748 3 0.304 0.881 0.104 0.000 0.896
#> SRR1812749 2 0.000 0.996 0.000 1.000 0.000
#> SRR1812746 3 0.164 0.903 0.044 0.000 0.956
#> SRR1812745 3 0.153 0.902 0.040 0.000 0.960
#> SRR1812747 2 0.000 0.996 0.000 1.000 0.000
#> SRR1812744 3 0.164 0.903 0.044 0.000 0.956
#> SRR1812743 1 0.000 0.977 1.000 0.000 0.000
#> SRR1812742 1 0.000 0.977 1.000 0.000 0.000
#> SRR1812737 2 0.000 0.996 0.000 1.000 0.000
#> SRR1812735 2 0.000 0.996 0.000 1.000 0.000
#> SRR1812734 3 0.304 0.881 0.104 0.000 0.896
#> SRR1812733 3 0.000 0.893 0.000 0.000 1.000
#> SRR1812736 3 0.304 0.881 0.104 0.000 0.896
#> SRR1812732 3 0.164 0.903 0.044 0.000 0.956
#> SRR1812730 3 0.164 0.903 0.044 0.000 0.956
#> SRR1812731 1 0.164 0.932 0.956 0.044 0.000
#> SRR1812729 2 0.000 0.996 0.000 1.000 0.000
#> SRR1812727 1 0.000 0.977 1.000 0.000 0.000
#> SRR1812726 2 0.000 0.996 0.000 1.000 0.000
#> SRR1812728 1 0.000 0.977 1.000 0.000 0.000
#> SRR1812724 1 0.103 0.956 0.976 0.000 0.024
#> SRR1812725 3 0.394 0.800 0.000 0.156 0.844
#> SRR1812723 2 0.000 0.996 0.000 1.000 0.000
#> SRR1812722 2 0.000 0.996 0.000 1.000 0.000
#> SRR1812721 1 0.000 0.977 1.000 0.000 0.000
#> SRR1812718 2 0.000 0.996 0.000 1.000 0.000
#> SRR1812717 2 0.000 0.996 0.000 1.000 0.000
#> SRR1812716 3 0.000 0.893 0.000 0.000 1.000
#> SRR1812715 2 0.000 0.996 0.000 1.000 0.000
#> SRR1812714 2 0.000 0.996 0.000 1.000 0.000
#> SRR1812719 1 0.000 0.977 1.000 0.000 0.000
#> SRR1812713 3 0.394 0.800 0.000 0.156 0.844
#> SRR1812712 3 0.254 0.857 0.000 0.080 0.920
#> SRR1812711 2 0.000 0.996 0.000 1.000 0.000
#> SRR1812710 2 0.000 0.996 0.000 1.000 0.000
#> SRR1812709 1 0.435 0.769 0.816 0.184 0.000
#> SRR1812708 2 0.000 0.996 0.000 1.000 0.000
#> SRR1812707 2 0.000 0.996 0.000 1.000 0.000
#> SRR1812705 2 0.000 0.996 0.000 1.000 0.000
#> SRR1812706 3 0.475 0.761 0.216 0.000 0.784
#> SRR1812704 1 0.000 0.977 1.000 0.000 0.000
#> SRR1812703 2 0.245 0.921 0.000 0.924 0.076
#> SRR1812702 3 0.000 0.893 0.000 0.000 1.000
#> SRR1812741 1 0.000 0.977 1.000 0.000 0.000
#> SRR1812740 3 0.304 0.881 0.104 0.000 0.896
#> SRR1812739 3 0.590 0.475 0.000 0.352 0.648
#> SRR1812738 1 0.000 0.977 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1812752 1 0.0336 0.9019 0.992 0.000 0.000 0.008
#> SRR1812753 1 0.0336 0.9019 0.992 0.000 0.000 0.008
#> SRR1812751 2 0.0336 0.9842 0.000 0.992 0.000 0.008
#> SRR1812750 2 0.0336 0.9842 0.000 0.992 0.000 0.008
#> SRR1812748 3 0.0000 0.9734 0.000 0.000 1.000 0.000
#> SRR1812749 2 0.0336 0.9842 0.000 0.992 0.000 0.008
#> SRR1812746 3 0.0000 0.9734 0.000 0.000 1.000 0.000
#> SRR1812745 3 0.0469 0.9684 0.000 0.000 0.988 0.012
#> SRR1812747 2 0.0707 0.9712 0.000 0.980 0.000 0.020
#> SRR1812744 3 0.0469 0.9684 0.000 0.000 0.988 0.012
#> SRR1812743 1 0.0000 0.9038 1.000 0.000 0.000 0.000
#> SRR1812742 1 0.0000 0.9038 1.000 0.000 0.000 0.000
#> SRR1812737 2 0.0000 0.9887 0.000 1.000 0.000 0.000
#> SRR1812735 2 0.0000 0.9887 0.000 1.000 0.000 0.000
#> SRR1812734 3 0.0000 0.9734 0.000 0.000 1.000 0.000
#> SRR1812733 4 0.0336 0.9240 0.000 0.000 0.008 0.992
#> SRR1812736 3 0.0000 0.9734 0.000 0.000 1.000 0.000
#> SRR1812732 3 0.0469 0.9684 0.000 0.000 0.988 0.012
#> SRR1812730 3 0.0000 0.9734 0.000 0.000 1.000 0.000
#> SRR1812731 1 0.0000 0.9038 1.000 0.000 0.000 0.000
#> SRR1812729 2 0.0000 0.9887 0.000 1.000 0.000 0.000
#> SRR1812727 1 0.2530 0.8720 0.888 0.000 0.112 0.000
#> SRR1812726 2 0.0000 0.9887 0.000 1.000 0.000 0.000
#> SRR1812728 1 0.2589 0.8699 0.884 0.000 0.116 0.000
#> SRR1812724 1 0.2593 0.8725 0.892 0.000 0.104 0.004
#> SRR1812725 4 0.0336 0.9240 0.000 0.000 0.008 0.992
#> SRR1812723 2 0.0000 0.9887 0.000 1.000 0.000 0.000
#> SRR1812722 2 0.0000 0.9887 0.000 1.000 0.000 0.000
#> SRR1812721 1 0.0000 0.9038 1.000 0.000 0.000 0.000
#> SRR1812718 4 0.4985 0.0979 0.000 0.468 0.000 0.532
#> SRR1812717 2 0.0000 0.9887 0.000 1.000 0.000 0.000
#> SRR1812716 4 0.0592 0.9181 0.000 0.000 0.016 0.984
#> SRR1812715 2 0.0000 0.9887 0.000 1.000 0.000 0.000
#> SRR1812714 2 0.0000 0.9887 0.000 1.000 0.000 0.000
#> SRR1812719 1 0.4356 0.6756 0.708 0.000 0.292 0.000
#> SRR1812713 4 0.0336 0.9240 0.000 0.000 0.008 0.992
#> SRR1812712 4 0.0336 0.9240 0.000 0.000 0.008 0.992
#> SRR1812711 2 0.0000 0.9887 0.000 1.000 0.000 0.000
#> SRR1812710 2 0.0000 0.9887 0.000 1.000 0.000 0.000
#> SRR1812709 1 0.2345 0.8251 0.900 0.100 0.000 0.000
#> SRR1812708 2 0.2921 0.8321 0.000 0.860 0.000 0.140
#> SRR1812707 2 0.0000 0.9887 0.000 1.000 0.000 0.000
#> SRR1812705 2 0.0000 0.9887 0.000 1.000 0.000 0.000
#> SRR1812706 3 0.3448 0.7586 0.168 0.000 0.828 0.004
#> SRR1812704 1 0.3554 0.8496 0.844 0.000 0.136 0.020
#> SRR1812703 4 0.0469 0.9163 0.000 0.012 0.000 0.988
#> SRR1812702 4 0.0336 0.9240 0.000 0.000 0.008 0.992
#> SRR1812741 1 0.0000 0.9038 1.000 0.000 0.000 0.000
#> SRR1812740 3 0.0000 0.9734 0.000 0.000 1.000 0.000
#> SRR1812739 4 0.0376 0.9221 0.000 0.004 0.004 0.992
#> SRR1812738 1 0.4608 0.6550 0.692 0.000 0.304 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1812752 1 0.3366 0.842 0.768 0.000 0.000 0.000 0.232
#> SRR1812753 1 0.3480 0.861 0.752 0.000 0.000 0.000 0.248
#> SRR1812751 2 0.3837 0.717 0.308 0.692 0.000 0.000 0.000
#> SRR1812750 2 0.3837 0.717 0.308 0.692 0.000 0.000 0.000
#> SRR1812748 3 0.0162 0.992 0.000 0.000 0.996 0.000 0.004
#> SRR1812749 2 0.3837 0.717 0.308 0.692 0.000 0.000 0.000
#> SRR1812746 3 0.0162 0.992 0.000 0.000 0.996 0.000 0.004
#> SRR1812745 3 0.0324 0.990 0.000 0.000 0.992 0.004 0.004
#> SRR1812747 2 0.0963 0.883 0.000 0.964 0.000 0.036 0.000
#> SRR1812744 3 0.0566 0.981 0.012 0.000 0.984 0.004 0.000
#> SRR1812743 1 0.3949 0.929 0.668 0.000 0.000 0.000 0.332
#> SRR1812742 1 0.3949 0.929 0.668 0.000 0.000 0.000 0.332
#> SRR1812737 2 0.0000 0.906 0.000 1.000 0.000 0.000 0.000
#> SRR1812735 2 0.0000 0.906 0.000 1.000 0.000 0.000 0.000
#> SRR1812734 3 0.0162 0.992 0.000 0.000 0.996 0.000 0.004
#> SRR1812733 4 0.0000 0.994 0.000 0.000 0.000 1.000 0.000
#> SRR1812736 3 0.0162 0.992 0.000 0.000 0.996 0.000 0.004
#> SRR1812732 3 0.1179 0.966 0.016 0.000 0.964 0.004 0.016
#> SRR1812730 3 0.0162 0.992 0.000 0.000 0.996 0.000 0.004
#> SRR1812731 1 0.3983 0.899 0.660 0.000 0.000 0.000 0.340
#> SRR1812729 2 0.0000 0.906 0.000 1.000 0.000 0.000 0.000
#> SRR1812727 5 0.2712 0.740 0.088 0.000 0.032 0.000 0.880
#> SRR1812726 2 0.0000 0.906 0.000 1.000 0.000 0.000 0.000
#> SRR1812728 5 0.1403 0.779 0.024 0.000 0.024 0.000 0.952
#> SRR1812724 5 0.1907 0.759 0.028 0.000 0.044 0.000 0.928
#> SRR1812725 4 0.0000 0.994 0.000 0.000 0.000 1.000 0.000
#> SRR1812723 2 0.0000 0.906 0.000 1.000 0.000 0.000 0.000
#> SRR1812722 2 0.0000 0.906 0.000 1.000 0.000 0.000 0.000
#> SRR1812721 1 0.3966 0.928 0.664 0.000 0.000 0.000 0.336
#> SRR1812718 2 0.4278 0.220 0.000 0.548 0.000 0.452 0.000
#> SRR1812717 2 0.0000 0.906 0.000 1.000 0.000 0.000 0.000
#> SRR1812716 4 0.0880 0.965 0.000 0.000 0.032 0.968 0.000
#> SRR1812715 2 0.0000 0.906 0.000 1.000 0.000 0.000 0.000
#> SRR1812714 2 0.0290 0.902 0.008 0.992 0.000 0.000 0.000
#> SRR1812719 5 0.2864 0.773 0.024 0.000 0.112 0.000 0.864
#> SRR1812713 4 0.0000 0.994 0.000 0.000 0.000 1.000 0.000
#> SRR1812712 4 0.0162 0.992 0.000 0.000 0.000 0.996 0.004
#> SRR1812711 2 0.0000 0.906 0.000 1.000 0.000 0.000 0.000
#> SRR1812710 2 0.0000 0.906 0.000 1.000 0.000 0.000 0.000
#> SRR1812709 5 0.3745 0.485 0.196 0.024 0.000 0.000 0.780
#> SRR1812708 2 0.5393 0.641 0.312 0.608 0.000 0.080 0.000
#> SRR1812707 2 0.0000 0.906 0.000 1.000 0.000 0.000 0.000
#> SRR1812705 2 0.0000 0.906 0.000 1.000 0.000 0.000 0.000
#> SRR1812706 5 0.4182 0.400 0.000 0.000 0.400 0.000 0.600
#> SRR1812704 5 0.1012 0.779 0.012 0.000 0.020 0.000 0.968
#> SRR1812703 4 0.0000 0.994 0.000 0.000 0.000 1.000 0.000
#> SRR1812702 4 0.0000 0.994 0.000 0.000 0.000 1.000 0.000
#> SRR1812741 1 0.3966 0.928 0.664 0.000 0.000 0.000 0.336
#> SRR1812740 3 0.0162 0.992 0.000 0.000 0.996 0.000 0.004
#> SRR1812739 4 0.0162 0.992 0.004 0.000 0.000 0.996 0.000
#> SRR1812738 5 0.2915 0.765 0.024 0.000 0.116 0.000 0.860
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1812752 6 0.1720 0.940 0.040 0.000 0.000 0.000 0.032 0.928
#> SRR1812753 6 0.1418 0.950 0.024 0.000 0.000 0.000 0.032 0.944
#> SRR1812751 1 0.3126 0.968 0.752 0.248 0.000 0.000 0.000 0.000
#> SRR1812750 1 0.3126 0.968 0.752 0.248 0.000 0.000 0.000 0.000
#> SRR1812748 3 0.0363 0.955 0.000 0.000 0.988 0.000 0.012 0.000
#> SRR1812749 1 0.3126 0.968 0.752 0.248 0.000 0.000 0.000 0.000
#> SRR1812746 3 0.0146 0.954 0.000 0.000 0.996 0.000 0.004 0.000
#> SRR1812745 3 0.0291 0.953 0.000 0.000 0.992 0.004 0.004 0.000
#> SRR1812747 2 0.1401 0.897 0.020 0.948 0.000 0.028 0.004 0.000
#> SRR1812744 3 0.2839 0.868 0.092 0.000 0.860 0.000 0.044 0.004
#> SRR1812743 6 0.0000 0.961 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR1812742 6 0.0000 0.961 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR1812737 2 0.0000 0.937 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1812735 2 0.0000 0.937 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1812734 3 0.0260 0.955 0.000 0.000 0.992 0.000 0.008 0.000
#> SRR1812733 4 0.0000 0.976 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1812736 3 0.0363 0.955 0.000 0.000 0.988 0.000 0.012 0.000
#> SRR1812732 3 0.3633 0.826 0.124 0.000 0.808 0.000 0.052 0.016
#> SRR1812730 3 0.0837 0.947 0.004 0.000 0.972 0.004 0.020 0.000
#> SRR1812731 6 0.1462 0.923 0.056 0.000 0.000 0.000 0.008 0.936
#> SRR1812729 2 0.0603 0.927 0.016 0.980 0.000 0.000 0.004 0.000
#> SRR1812727 5 0.3394 0.745 0.000 0.000 0.024 0.000 0.776 0.200
#> SRR1812726 2 0.0603 0.925 0.016 0.980 0.000 0.000 0.004 0.000
#> SRR1812728 5 0.2106 0.827 0.000 0.000 0.032 0.000 0.904 0.064
#> SRR1812724 5 0.4486 0.735 0.052 0.000 0.032 0.000 0.732 0.184
#> SRR1812725 4 0.0000 0.976 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1812723 2 0.0603 0.927 0.016 0.980 0.000 0.000 0.004 0.000
#> SRR1812722 2 0.0000 0.937 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1812721 6 0.0603 0.960 0.004 0.000 0.000 0.000 0.016 0.980
#> SRR1812718 2 0.4481 0.188 0.024 0.556 0.000 0.416 0.004 0.000
#> SRR1812717 2 0.0146 0.936 0.004 0.996 0.000 0.000 0.000 0.000
#> SRR1812716 4 0.1219 0.941 0.004 0.000 0.048 0.948 0.000 0.000
#> SRR1812715 2 0.0000 0.937 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1812714 2 0.1700 0.849 0.080 0.916 0.000 0.000 0.004 0.000
#> SRR1812719 5 0.2527 0.825 0.000 0.000 0.084 0.000 0.876 0.040
#> SRR1812713 4 0.0146 0.975 0.004 0.000 0.000 0.996 0.000 0.000
#> SRR1812712 4 0.1257 0.955 0.028 0.000 0.000 0.952 0.020 0.000
#> SRR1812711 2 0.0146 0.936 0.000 0.996 0.000 0.000 0.004 0.000
#> SRR1812710 2 0.0000 0.937 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1812709 5 0.5457 0.600 0.160 0.012 0.000 0.000 0.612 0.216
#> SRR1812708 1 0.3122 0.900 0.804 0.176 0.000 0.020 0.000 0.000
#> SRR1812707 2 0.0000 0.937 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1812705 2 0.0000 0.937 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1812706 5 0.3586 0.661 0.012 0.000 0.268 0.000 0.720 0.000
#> SRR1812704 5 0.1528 0.823 0.012 0.000 0.016 0.000 0.944 0.028
#> SRR1812703 4 0.0458 0.970 0.016 0.000 0.000 0.984 0.000 0.000
#> SRR1812702 4 0.0000 0.976 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1812741 6 0.0790 0.958 0.000 0.000 0.000 0.000 0.032 0.968
#> SRR1812740 3 0.0363 0.955 0.000 0.000 0.988 0.000 0.012 0.000
#> SRR1812739 4 0.1549 0.949 0.044 0.000 0.000 0.936 0.020 0.000
#> SRR1812738 5 0.3149 0.814 0.020 0.000 0.076 0.000 0.852 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["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 14626 rows and 51 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 1.000 0.995 0.998 0.5086 0.492 0.492
#> 3 3 0.779 0.893 0.934 0.2242 0.901 0.799
#> 4 4 0.957 0.925 0.971 0.1711 0.831 0.595
#> 5 5 0.909 0.876 0.950 0.0449 0.965 0.873
#> 6 6 0.934 0.906 0.954 0.0139 0.997 0.987
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
#> SRR1812752 1 0.000 0.998 1.000 0.000
#> SRR1812753 1 0.000 0.998 1.000 0.000
#> SRR1812751 2 0.000 0.997 0.000 1.000
#> SRR1812750 2 0.000 0.997 0.000 1.000
#> SRR1812748 1 0.000 0.998 1.000 0.000
#> SRR1812749 2 0.000 0.997 0.000 1.000
#> SRR1812746 1 0.000 0.998 1.000 0.000
#> SRR1812745 1 0.000 0.998 1.000 0.000
#> SRR1812747 2 0.000 0.997 0.000 1.000
#> SRR1812744 1 0.000 0.998 1.000 0.000
#> SRR1812743 1 0.000 0.998 1.000 0.000
#> SRR1812742 1 0.000 0.998 1.000 0.000
#> SRR1812737 2 0.000 0.997 0.000 1.000
#> SRR1812735 2 0.000 0.997 0.000 1.000
#> SRR1812734 1 0.000 0.998 1.000 0.000
#> SRR1812733 2 0.388 0.917 0.076 0.924
#> SRR1812736 1 0.000 0.998 1.000 0.000
#> SRR1812732 1 0.000 0.998 1.000 0.000
#> SRR1812730 1 0.000 0.998 1.000 0.000
#> SRR1812731 1 0.000 0.998 1.000 0.000
#> SRR1812729 2 0.000 0.997 0.000 1.000
#> SRR1812727 1 0.000 0.998 1.000 0.000
#> SRR1812726 2 0.000 0.997 0.000 1.000
#> SRR1812728 1 0.000 0.998 1.000 0.000
#> SRR1812724 1 0.000 0.998 1.000 0.000
#> SRR1812725 2 0.000 0.997 0.000 1.000
#> SRR1812723 2 0.000 0.997 0.000 1.000
#> SRR1812722 2 0.000 0.997 0.000 1.000
#> SRR1812721 1 0.000 0.998 1.000 0.000
#> SRR1812718 2 0.000 0.997 0.000 1.000
#> SRR1812717 2 0.000 0.997 0.000 1.000
#> SRR1812716 1 0.000 0.998 1.000 0.000
#> SRR1812715 2 0.000 0.997 0.000 1.000
#> SRR1812714 2 0.000 0.997 0.000 1.000
#> SRR1812719 1 0.000 0.998 1.000 0.000
#> SRR1812713 2 0.000 0.997 0.000 1.000
#> SRR1812712 1 0.242 0.958 0.960 0.040
#> SRR1812711 2 0.000 0.997 0.000 1.000
#> SRR1812710 2 0.000 0.997 0.000 1.000
#> SRR1812709 1 0.000 0.998 1.000 0.000
#> SRR1812708 2 0.000 0.997 0.000 1.000
#> SRR1812707 2 0.000 0.997 0.000 1.000
#> SRR1812705 2 0.000 0.997 0.000 1.000
#> SRR1812706 1 0.000 0.998 1.000 0.000
#> SRR1812704 1 0.000 0.998 1.000 0.000
#> SRR1812703 2 0.000 0.997 0.000 1.000
#> SRR1812702 1 0.000 0.998 1.000 0.000
#> SRR1812741 1 0.000 0.998 1.000 0.000
#> SRR1812740 1 0.000 0.998 1.000 0.000
#> SRR1812739 2 0.000 0.997 0.000 1.000
#> SRR1812738 1 0.000 0.998 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1812752 1 0.0000 0.887 1.000 0.000 0.000
#> SRR1812753 1 0.0000 0.887 1.000 0.000 0.000
#> SRR1812751 2 0.0000 0.948 0.000 1.000 0.000
#> SRR1812750 2 0.0000 0.948 0.000 1.000 0.000
#> SRR1812748 3 0.3879 0.924 0.152 0.000 0.848
#> SRR1812749 2 0.0000 0.948 0.000 1.000 0.000
#> SRR1812746 3 0.0592 0.849 0.012 0.000 0.988
#> SRR1812745 3 0.0000 0.837 0.000 0.000 1.000
#> SRR1812747 2 0.0000 0.948 0.000 1.000 0.000
#> SRR1812744 1 0.3879 0.874 0.848 0.000 0.152
#> SRR1812743 1 0.0000 0.887 1.000 0.000 0.000
#> SRR1812742 1 0.0000 0.887 1.000 0.000 0.000
#> SRR1812737 2 0.0000 0.948 0.000 1.000 0.000
#> SRR1812735 2 0.0000 0.948 0.000 1.000 0.000
#> SRR1812734 3 0.3879 0.924 0.152 0.000 0.848
#> SRR1812733 2 0.5639 0.735 0.016 0.752 0.232
#> SRR1812736 3 0.3879 0.924 0.152 0.000 0.848
#> SRR1812732 1 0.3879 0.874 0.848 0.000 0.152
#> SRR1812730 1 0.4931 0.824 0.768 0.000 0.232
#> SRR1812731 1 0.3879 0.874 0.848 0.000 0.152
#> SRR1812729 2 0.0000 0.948 0.000 1.000 0.000
#> SRR1812727 1 0.0000 0.887 1.000 0.000 0.000
#> SRR1812726 2 0.0000 0.948 0.000 1.000 0.000
#> SRR1812728 1 0.0000 0.887 1.000 0.000 0.000
#> SRR1812724 1 0.3879 0.874 0.848 0.000 0.152
#> SRR1812725 2 0.4750 0.774 0.000 0.784 0.216
#> SRR1812723 2 0.0000 0.948 0.000 1.000 0.000
#> SRR1812722 2 0.0000 0.948 0.000 1.000 0.000
#> SRR1812721 1 0.0000 0.887 1.000 0.000 0.000
#> SRR1812718 2 0.0000 0.948 0.000 1.000 0.000
#> SRR1812717 2 0.0000 0.948 0.000 1.000 0.000
#> SRR1812716 1 0.4931 0.824 0.768 0.000 0.232
#> SRR1812715 2 0.0000 0.948 0.000 1.000 0.000
#> SRR1812714 2 0.0000 0.948 0.000 1.000 0.000
#> SRR1812719 1 0.0000 0.887 1.000 0.000 0.000
#> SRR1812713 2 0.4931 0.755 0.000 0.768 0.232
#> SRR1812712 1 0.6361 0.781 0.728 0.040 0.232
#> SRR1812711 2 0.0000 0.948 0.000 1.000 0.000
#> SRR1812710 2 0.0000 0.948 0.000 1.000 0.000
#> SRR1812709 1 0.3879 0.874 0.848 0.000 0.152
#> SRR1812708 2 0.2796 0.886 0.000 0.908 0.092
#> SRR1812707 2 0.0000 0.948 0.000 1.000 0.000
#> SRR1812705 2 0.0000 0.948 0.000 1.000 0.000
#> SRR1812706 1 0.0000 0.887 1.000 0.000 0.000
#> SRR1812704 1 0.3879 0.874 0.848 0.000 0.152
#> SRR1812703 2 0.3879 0.836 0.000 0.848 0.152
#> SRR1812702 1 0.4931 0.824 0.768 0.000 0.232
#> SRR1812741 1 0.0000 0.887 1.000 0.000 0.000
#> SRR1812740 3 0.3879 0.924 0.152 0.000 0.848
#> SRR1812739 2 0.3879 0.836 0.000 0.848 0.152
#> SRR1812738 1 0.1860 0.887 0.948 0.000 0.052
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1812752 1 0.0000 0.981 1.000 0.000 0.000 0.000
#> SRR1812753 1 0.0000 0.981 1.000 0.000 0.000 0.000
#> SRR1812751 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> SRR1812750 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> SRR1812748 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> SRR1812749 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> SRR1812746 3 0.0188 0.996 0.000 0.000 0.996 0.004
#> SRR1812745 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> SRR1812747 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> SRR1812744 4 0.4830 0.393 0.392 0.000 0.000 0.608
#> SRR1812743 1 0.0000 0.981 1.000 0.000 0.000 0.000
#> SRR1812742 1 0.0000 0.981 1.000 0.000 0.000 0.000
#> SRR1812737 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> SRR1812735 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> SRR1812734 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> SRR1812733 4 0.0000 0.903 0.000 0.000 0.000 1.000
#> SRR1812736 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> SRR1812732 4 0.0592 0.892 0.016 0.000 0.000 0.984
#> SRR1812730 4 0.4746 0.434 0.368 0.000 0.000 0.632
#> SRR1812731 1 0.0000 0.981 1.000 0.000 0.000 0.000
#> SRR1812729 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> SRR1812727 1 0.0000 0.981 1.000 0.000 0.000 0.000
#> SRR1812726 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> SRR1812728 1 0.0000 0.981 1.000 0.000 0.000 0.000
#> SRR1812724 1 0.4008 0.639 0.756 0.000 0.000 0.244
#> SRR1812725 4 0.0000 0.903 0.000 0.000 0.000 1.000
#> SRR1812723 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> SRR1812722 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> SRR1812721 1 0.0000 0.981 1.000 0.000 0.000 0.000
#> SRR1812718 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> SRR1812717 2 0.4331 0.598 0.000 0.712 0.000 0.288
#> SRR1812716 4 0.0000 0.903 0.000 0.000 0.000 1.000
#> SRR1812715 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> SRR1812714 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> SRR1812719 1 0.0000 0.981 1.000 0.000 0.000 0.000
#> SRR1812713 4 0.0000 0.903 0.000 0.000 0.000 1.000
#> SRR1812712 4 0.0000 0.903 0.000 0.000 0.000 1.000
#> SRR1812711 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> SRR1812710 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> SRR1812709 1 0.0000 0.981 1.000 0.000 0.000 0.000
#> SRR1812708 2 0.3444 0.777 0.000 0.816 0.000 0.184
#> SRR1812707 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> SRR1812705 2 0.0000 0.972 0.000 1.000 0.000 0.000
#> SRR1812706 1 0.0000 0.981 1.000 0.000 0.000 0.000
#> SRR1812704 1 0.0000 0.981 1.000 0.000 0.000 0.000
#> SRR1812703 4 0.0000 0.903 0.000 0.000 0.000 1.000
#> SRR1812702 4 0.0000 0.903 0.000 0.000 0.000 1.000
#> SRR1812741 1 0.0000 0.981 1.000 0.000 0.000 0.000
#> SRR1812740 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> SRR1812739 4 0.0000 0.903 0.000 0.000 0.000 1.000
#> SRR1812738 1 0.0000 0.981 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1812752 1 0.0000 0.644 1.000 0.000 0.000 0.000 0.000
#> SRR1812753 1 0.0000 0.644 1.000 0.000 0.000 0.000 0.000
#> SRR1812751 2 0.2891 0.792 0.176 0.824 0.000 0.000 0.000
#> SRR1812750 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> SRR1812748 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> SRR1812749 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> SRR1812746 3 0.0162 0.994 0.000 0.000 0.996 0.000 0.004
#> SRR1812745 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> SRR1812747 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> SRR1812744 5 0.4161 0.385 0.000 0.000 0.000 0.392 0.608
#> SRR1812743 1 0.3999 0.567 0.656 0.000 0.000 0.344 0.000
#> SRR1812742 1 0.4307 0.279 0.504 0.000 0.000 0.496 0.000
#> SRR1812737 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> SRR1812735 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> SRR1812734 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> SRR1812733 5 0.0000 0.903 0.000 0.000 0.000 0.000 1.000
#> SRR1812736 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> SRR1812732 5 0.0510 0.891 0.000 0.000 0.000 0.016 0.984
#> SRR1812730 5 0.4088 0.437 0.000 0.000 0.000 0.368 0.632
#> SRR1812731 4 0.0000 0.955 0.000 0.000 0.000 1.000 0.000
#> SRR1812729 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> SRR1812727 4 0.0000 0.955 0.000 0.000 0.000 1.000 0.000
#> SRR1812726 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> SRR1812728 4 0.0000 0.955 0.000 0.000 0.000 1.000 0.000
#> SRR1812724 4 0.3452 0.561 0.000 0.000 0.000 0.756 0.244
#> SRR1812725 5 0.0000 0.903 0.000 0.000 0.000 0.000 1.000
#> SRR1812723 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> SRR1812722 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> SRR1812721 4 0.0000 0.955 0.000 0.000 0.000 1.000 0.000
#> SRR1812718 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> SRR1812717 2 0.3730 0.602 0.000 0.712 0.000 0.000 0.288
#> SRR1812716 5 0.0000 0.903 0.000 0.000 0.000 0.000 1.000
#> SRR1812715 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> SRR1812714 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> SRR1812719 4 0.0000 0.955 0.000 0.000 0.000 1.000 0.000
#> SRR1812713 5 0.0000 0.903 0.000 0.000 0.000 0.000 1.000
#> SRR1812712 5 0.0000 0.903 0.000 0.000 0.000 0.000 1.000
#> SRR1812711 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> SRR1812710 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> SRR1812709 4 0.0000 0.955 0.000 0.000 0.000 1.000 0.000
#> SRR1812708 2 0.2966 0.763 0.000 0.816 0.000 0.000 0.184
#> SRR1812707 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> SRR1812705 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> SRR1812706 4 0.0000 0.955 0.000 0.000 0.000 1.000 0.000
#> SRR1812704 4 0.0000 0.955 0.000 0.000 0.000 1.000 0.000
#> SRR1812703 5 0.0000 0.903 0.000 0.000 0.000 0.000 1.000
#> SRR1812702 5 0.0000 0.903 0.000 0.000 0.000 0.000 1.000
#> SRR1812741 4 0.0880 0.917 0.032 0.000 0.000 0.968 0.000
#> SRR1812740 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000
#> SRR1812739 5 0.0000 0.903 0.000 0.000 0.000 0.000 1.000
#> SRR1812738 4 0.0000 0.955 0.000 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1812752 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812753 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1812751 2 0.2597 0.779 0.176 0.824 0.000 0.000 0.000 0.000
#> SRR1812750 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1812748 3 0.0000 0.936 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1812749 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1812746 3 0.2632 0.864 0.000 0.000 0.832 0.004 0.000 0.164
#> SRR1812745 3 0.2491 0.866 0.000 0.000 0.836 0.000 0.000 0.164
#> SRR1812747 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1812744 4 0.3737 0.371 0.000 0.000 0.000 0.608 0.392 0.000
#> SRR1812743 6 0.2491 1.000 0.164 0.000 0.000 0.000 0.000 0.836
#> SRR1812742 6 0.2491 1.000 0.164 0.000 0.000 0.000 0.000 0.836
#> SRR1812737 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1812735 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1812734 3 0.0000 0.936 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1812733 4 0.0000 0.907 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1812736 3 0.0000 0.936 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1812732 4 0.0458 0.894 0.000 0.000 0.000 0.984 0.016 0.000
#> SRR1812730 4 0.5083 0.511 0.000 0.000 0.000 0.632 0.204 0.164
#> SRR1812731 5 0.0000 0.965 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1812729 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1812727 5 0.0000 0.965 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1812726 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1812728 5 0.0000 0.965 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1812724 5 0.3101 0.640 0.000 0.000 0.000 0.244 0.756 0.000
#> SRR1812725 4 0.0000 0.907 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1812723 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1812722 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1812721 5 0.0000 0.965 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1812718 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1812717 2 0.3351 0.582 0.000 0.712 0.000 0.288 0.000 0.000
#> SRR1812716 4 0.0000 0.907 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1812715 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1812714 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1812719 5 0.0000 0.965 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1812713 4 0.0000 0.907 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1812712 4 0.0000 0.907 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1812711 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1812710 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1812709 5 0.0000 0.965 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1812708 2 0.2664 0.751 0.000 0.816 0.000 0.184 0.000 0.000
#> SRR1812707 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1812705 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1812706 5 0.0000 0.965 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1812704 5 0.0000 0.965 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1812703 4 0.0000 0.907 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1812702 4 0.0000 0.907 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1812741 5 0.0790 0.936 0.032 0.000 0.000 0.000 0.968 0.000
#> SRR1812740 3 0.0000 0.936 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1812739 4 0.0000 0.907 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1812738 5 0.0000 0.965 0.000 0.000 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 14626 rows and 51 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.405 0.818 0.887 0.3247 0.678 0.678
#> 3 3 0.365 0.574 0.730 0.6980 0.773 0.675
#> 4 4 0.490 0.699 0.801 0.2160 0.713 0.477
#> 5 5 0.557 0.487 0.704 0.0812 0.769 0.414
#> 6 6 0.696 0.706 0.823 0.1293 0.894 0.603
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
#> SRR1812752 1 0.7139 0.755 0.804 0.196
#> SRR1812753 1 0.7139 0.755 0.804 0.196
#> SRR1812751 1 0.1184 0.717 0.984 0.016
#> SRR1812750 1 0.2043 0.724 0.968 0.032
#> SRR1812748 2 0.5059 0.763 0.112 0.888
#> SRR1812749 1 0.1184 0.717 0.984 0.016
#> SRR1812746 1 0.9977 0.577 0.528 0.472
#> SRR1812745 2 0.2948 0.844 0.052 0.948
#> SRR1812747 2 0.6148 0.835 0.152 0.848
#> SRR1812744 2 0.0000 0.889 0.000 1.000
#> SRR1812743 2 0.0376 0.887 0.004 0.996
#> SRR1812742 2 0.0376 0.887 0.004 0.996
#> SRR1812737 2 0.7139 0.810 0.196 0.804
#> SRR1812735 2 0.7139 0.810 0.196 0.804
#> SRR1812734 1 0.9977 0.577 0.528 0.472
#> SRR1812733 2 0.0000 0.889 0.000 1.000
#> SRR1812736 2 0.5408 0.743 0.124 0.876
#> SRR1812732 2 0.0000 0.889 0.000 1.000
#> SRR1812730 2 0.0376 0.887 0.004 0.996
#> SRR1812731 2 0.0000 0.889 0.000 1.000
#> SRR1812729 2 0.6973 0.816 0.188 0.812
#> SRR1812727 1 0.9977 0.577 0.528 0.472
#> SRR1812726 2 0.6801 0.821 0.180 0.820
#> SRR1812728 2 0.0000 0.889 0.000 1.000
#> SRR1812724 2 0.0000 0.889 0.000 1.000
#> SRR1812725 2 0.0000 0.889 0.000 1.000
#> SRR1812723 2 0.6973 0.816 0.188 0.812
#> SRR1812722 2 0.6801 0.820 0.180 0.820
#> SRR1812721 2 0.0376 0.887 0.004 0.996
#> SRR1812718 2 0.6148 0.835 0.152 0.848
#> SRR1812717 2 0.4815 0.859 0.104 0.896
#> SRR1812716 2 0.0000 0.889 0.000 1.000
#> SRR1812715 2 0.7139 0.810 0.196 0.804
#> SRR1812714 2 0.7139 0.810 0.196 0.804
#> SRR1812719 1 0.9977 0.577 0.528 0.472
#> SRR1812713 2 0.0000 0.889 0.000 1.000
#> SRR1812712 2 0.0000 0.889 0.000 1.000
#> SRR1812711 2 0.7139 0.810 0.196 0.804
#> SRR1812710 2 0.7139 0.810 0.196 0.804
#> SRR1812709 2 0.0000 0.889 0.000 1.000
#> SRR1812708 1 0.6623 0.758 0.828 0.172
#> SRR1812707 2 0.7139 0.810 0.196 0.804
#> SRR1812705 2 0.7139 0.810 0.196 0.804
#> SRR1812706 2 0.0000 0.889 0.000 1.000
#> SRR1812704 2 0.0000 0.889 0.000 1.000
#> SRR1812703 2 0.3584 0.871 0.068 0.932
#> SRR1812702 2 0.0000 0.889 0.000 1.000
#> SRR1812741 2 0.0376 0.887 0.004 0.996
#> SRR1812740 2 0.3114 0.839 0.056 0.944
#> SRR1812739 2 0.1633 0.885 0.024 0.976
#> SRR1812738 2 0.0000 0.889 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1812752 1 0.7184 0.558 0.504 0.024 0.472
#> SRR1812753 1 0.6521 0.551 0.504 0.004 0.492
#> SRR1812751 1 0.6228 0.725 0.624 0.004 0.372
#> SRR1812750 1 0.6330 0.726 0.600 0.004 0.396
#> SRR1812748 3 0.3686 0.302 0.000 0.140 0.860
#> SRR1812749 1 0.6314 0.727 0.604 0.004 0.392
#> SRR1812746 3 0.1453 0.205 0.008 0.024 0.968
#> SRR1812745 3 0.6505 0.181 0.004 0.468 0.528
#> SRR1812747 2 0.4796 0.716 0.220 0.780 0.000
#> SRR1812744 2 0.0661 0.723 0.008 0.988 0.004
#> SRR1812743 3 0.8743 0.289 0.108 0.440 0.452
#> SRR1812742 3 0.8737 0.306 0.108 0.428 0.464
#> SRR1812737 2 0.6302 0.588 0.480 0.520 0.000
#> SRR1812735 2 0.6302 0.588 0.480 0.520 0.000
#> SRR1812734 3 0.1031 0.193 0.000 0.024 0.976
#> SRR1812733 2 0.2313 0.726 0.032 0.944 0.024
#> SRR1812736 3 0.3686 0.302 0.000 0.140 0.860
#> SRR1812732 2 0.1636 0.729 0.016 0.964 0.020
#> SRR1812730 2 0.1989 0.700 0.004 0.948 0.048
#> SRR1812731 2 0.0237 0.726 0.004 0.996 0.000
#> SRR1812729 2 0.4796 0.716 0.220 0.780 0.000
#> SRR1812727 3 0.4589 0.284 0.008 0.172 0.820
#> SRR1812726 2 0.6468 0.612 0.444 0.552 0.004
#> SRR1812728 2 0.2486 0.681 0.008 0.932 0.060
#> SRR1812724 2 0.1399 0.709 0.004 0.968 0.028
#> SRR1812725 2 0.1163 0.737 0.028 0.972 0.000
#> SRR1812723 2 0.5785 0.672 0.332 0.668 0.000
#> SRR1812722 2 0.6260 0.612 0.448 0.552 0.000
#> SRR1812721 2 0.8311 -0.109 0.112 0.596 0.292
#> SRR1812718 2 0.4796 0.716 0.220 0.780 0.000
#> SRR1812717 2 0.4702 0.718 0.212 0.788 0.000
#> SRR1812716 2 0.0000 0.728 0.000 1.000 0.000
#> SRR1812715 2 0.6302 0.588 0.480 0.520 0.000
#> SRR1812714 2 0.6633 0.609 0.444 0.548 0.008
#> SRR1812719 3 0.4409 0.281 0.004 0.172 0.824
#> SRR1812713 2 0.2443 0.725 0.032 0.940 0.028
#> SRR1812712 2 0.1163 0.737 0.028 0.972 0.000
#> SRR1812711 2 0.6468 0.612 0.444 0.552 0.004
#> SRR1812710 2 0.6302 0.588 0.480 0.520 0.000
#> SRR1812709 2 0.0892 0.735 0.020 0.980 0.000
#> SRR1812708 1 0.8929 0.583 0.460 0.124 0.416
#> SRR1812707 2 0.6302 0.588 0.480 0.520 0.000
#> SRR1812705 2 0.6235 0.618 0.436 0.564 0.000
#> SRR1812706 2 0.1267 0.719 0.004 0.972 0.024
#> SRR1812704 2 0.0000 0.728 0.000 1.000 0.000
#> SRR1812703 2 0.4682 0.721 0.192 0.804 0.004
#> SRR1812702 2 0.2187 0.728 0.028 0.948 0.024
#> SRR1812741 3 0.8768 0.314 0.112 0.408 0.480
#> SRR1812740 3 0.3686 0.302 0.000 0.140 0.860
#> SRR1812739 2 0.1289 0.737 0.032 0.968 0.000
#> SRR1812738 2 0.0424 0.724 0.008 0.992 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1812752 1 0.4134 0.649 0.740 0.000 0.260 0.000
#> SRR1812753 1 0.4134 0.649 0.740 0.000 0.260 0.000
#> SRR1812751 1 0.4059 0.827 0.788 0.200 0.012 0.000
#> SRR1812750 1 0.4356 0.825 0.780 0.200 0.016 0.004
#> SRR1812748 4 0.6112 0.427 0.248 0.000 0.096 0.656
#> SRR1812749 1 0.4114 0.827 0.788 0.200 0.008 0.004
#> SRR1812746 3 0.6796 0.590 0.252 0.000 0.596 0.152
#> SRR1812745 2 0.8637 0.260 0.208 0.492 0.068 0.232
#> SRR1812747 2 0.1661 0.814 0.004 0.944 0.000 0.052
#> SRR1812744 4 0.4336 0.756 0.000 0.128 0.060 0.812
#> SRR1812743 3 0.1474 0.797 0.000 0.000 0.948 0.052
#> SRR1812742 3 0.1474 0.797 0.000 0.000 0.948 0.052
#> SRR1812737 2 0.2457 0.749 0.008 0.912 0.004 0.076
#> SRR1812735 2 0.2125 0.757 0.000 0.920 0.004 0.076
#> SRR1812734 4 0.7479 0.102 0.252 0.000 0.244 0.504
#> SRR1812733 2 0.5711 0.605 0.012 0.656 0.028 0.304
#> SRR1812736 4 0.6112 0.427 0.248 0.000 0.096 0.656
#> SRR1812732 4 0.3610 0.753 0.000 0.200 0.000 0.800
#> SRR1812730 4 0.4631 0.754 0.008 0.144 0.048 0.800
#> SRR1812731 4 0.3982 0.737 0.000 0.220 0.004 0.776
#> SRR1812729 2 0.1576 0.814 0.004 0.948 0.000 0.048
#> SRR1812727 3 0.4072 0.770 0.052 0.000 0.828 0.120
#> SRR1812726 2 0.1356 0.812 0.008 0.960 0.000 0.032
#> SRR1812728 4 0.4746 0.688 0.004 0.064 0.140 0.792
#> SRR1812724 4 0.4701 0.760 0.000 0.164 0.056 0.780
#> SRR1812725 2 0.4744 0.652 0.012 0.704 0.000 0.284
#> SRR1812723 2 0.1118 0.814 0.000 0.964 0.000 0.036
#> SRR1812722 2 0.0817 0.793 0.000 0.976 0.000 0.024
#> SRR1812721 3 0.1792 0.797 0.000 0.000 0.932 0.068
#> SRR1812718 2 0.1824 0.812 0.004 0.936 0.000 0.060
#> SRR1812717 2 0.2654 0.797 0.000 0.888 0.004 0.108
#> SRR1812716 2 0.5337 0.390 0.012 0.564 0.000 0.424
#> SRR1812715 2 0.2125 0.757 0.000 0.920 0.004 0.076
#> SRR1812714 2 0.1968 0.812 0.008 0.940 0.008 0.044
#> SRR1812719 3 0.5673 0.603 0.052 0.000 0.660 0.288
#> SRR1812713 2 0.5392 0.664 0.016 0.708 0.024 0.252
#> SRR1812712 2 0.4584 0.640 0.004 0.696 0.000 0.300
#> SRR1812711 2 0.1356 0.812 0.008 0.960 0.000 0.032
#> SRR1812710 2 0.1978 0.763 0.000 0.928 0.004 0.068
#> SRR1812709 4 0.3801 0.736 0.000 0.220 0.000 0.780
#> SRR1812708 1 0.6083 0.767 0.708 0.204 0.048 0.040
#> SRR1812707 2 0.2197 0.757 0.000 0.916 0.004 0.080
#> SRR1812705 2 0.1824 0.801 0.000 0.936 0.004 0.060
#> SRR1812706 4 0.3626 0.762 0.000 0.184 0.004 0.812
#> SRR1812704 4 0.4079 0.765 0.000 0.180 0.020 0.800
#> SRR1812703 2 0.3047 0.791 0.012 0.872 0.000 0.116
#> SRR1812702 2 0.5233 0.597 0.020 0.648 0.000 0.332
#> SRR1812741 3 0.2101 0.796 0.012 0.000 0.928 0.060
#> SRR1812740 4 0.6112 0.427 0.248 0.000 0.096 0.656
#> SRR1812739 2 0.4535 0.650 0.004 0.704 0.000 0.292
#> SRR1812738 4 0.4415 0.759 0.000 0.140 0.056 0.804
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1812752 1 0.4465 0.4715 0.736 0.000 0.060 0.204 0.000
#> SRR1812753 1 0.4624 0.4919 0.740 0.000 0.096 0.164 0.000
#> SRR1812751 1 0.4779 0.7190 0.716 0.200 0.084 0.000 0.000
#> SRR1812750 1 0.5086 0.7144 0.700 0.200 0.096 0.004 0.000
#> SRR1812748 3 0.0963 0.7209 0.000 0.000 0.964 0.000 0.036
#> SRR1812749 1 0.4617 0.7160 0.736 0.196 0.064 0.000 0.004
#> SRR1812746 3 0.0404 0.7088 0.012 0.000 0.988 0.000 0.000
#> SRR1812745 3 0.4866 0.3792 0.028 0.000 0.580 0.000 0.392
#> SRR1812747 2 0.4989 0.6546 0.056 0.648 0.000 0.000 0.296
#> SRR1812744 5 0.0771 0.5636 0.000 0.000 0.004 0.020 0.976
#> SRR1812743 4 0.3003 0.6978 0.188 0.000 0.000 0.812 0.000
#> SRR1812742 4 0.3003 0.6978 0.188 0.000 0.000 0.812 0.000
#> SRR1812737 2 0.0324 0.6203 0.004 0.992 0.000 0.000 0.004
#> SRR1812735 2 0.0324 0.6203 0.004 0.992 0.000 0.000 0.004
#> SRR1812734 3 0.0162 0.7087 0.004 0.000 0.996 0.000 0.000
#> SRR1812733 5 0.6001 -0.0959 0.068 0.400 0.004 0.012 0.516
#> SRR1812736 3 0.0963 0.7209 0.000 0.000 0.964 0.000 0.036
#> SRR1812732 5 0.1270 0.5658 0.000 0.052 0.000 0.000 0.948
#> SRR1812730 5 0.2833 0.4074 0.004 0.004 0.140 0.000 0.852
#> SRR1812731 5 0.1774 0.5674 0.000 0.052 0.000 0.016 0.932
#> SRR1812729 2 0.5142 0.6146 0.052 0.600 0.000 0.000 0.348
#> SRR1812727 3 0.5838 0.1505 0.008 0.000 0.496 0.424 0.072
#> SRR1812726 2 0.4240 0.6812 0.008 0.684 0.004 0.000 0.304
#> SRR1812728 5 0.4876 0.4603 0.004 0.040 0.012 0.232 0.712
#> SRR1812724 5 0.2673 0.5698 0.000 0.044 0.004 0.060 0.892
#> SRR1812725 5 0.5425 -0.1233 0.060 0.420 0.000 0.000 0.520
#> SRR1812723 2 0.5080 0.6197 0.048 0.604 0.000 0.000 0.348
#> SRR1812722 2 0.3395 0.6942 0.000 0.764 0.000 0.000 0.236
#> SRR1812721 4 0.0000 0.6701 0.000 0.000 0.000 1.000 0.000
#> SRR1812718 2 0.5328 0.5973 0.064 0.584 0.000 0.000 0.352
#> SRR1812717 2 0.3913 0.6720 0.000 0.676 0.000 0.000 0.324
#> SRR1812716 5 0.3051 0.4914 0.060 0.076 0.000 0.000 0.864
#> SRR1812715 2 0.0324 0.6203 0.004 0.992 0.000 0.000 0.004
#> SRR1812714 2 0.4858 0.6899 0.052 0.688 0.004 0.000 0.256
#> SRR1812719 3 0.6016 0.1629 0.012 0.000 0.496 0.412 0.080
#> SRR1812713 5 0.5425 -0.1330 0.060 0.420 0.000 0.000 0.520
#> SRR1812712 5 0.5467 -0.1025 0.064 0.412 0.000 0.000 0.524
#> SRR1812711 2 0.4858 0.6899 0.052 0.688 0.004 0.000 0.256
#> SRR1812710 2 0.0324 0.6203 0.004 0.992 0.000 0.000 0.004
#> SRR1812709 5 0.3936 0.5466 0.004 0.052 0.000 0.144 0.800
#> SRR1812708 1 0.5848 0.5191 0.644 0.012 0.160 0.000 0.184
#> SRR1812707 2 0.1357 0.6220 0.004 0.948 0.000 0.000 0.048
#> SRR1812705 2 0.3816 0.6846 0.000 0.696 0.000 0.000 0.304
#> SRR1812706 5 0.3595 0.5160 0.004 0.008 0.004 0.188 0.796
#> SRR1812704 5 0.3994 0.5435 0.004 0.044 0.004 0.148 0.800
#> SRR1812703 5 0.5579 -0.1422 0.072 0.420 0.000 0.000 0.508
#> SRR1812702 5 0.5499 -0.0871 0.068 0.400 0.000 0.000 0.532
#> SRR1812741 4 0.4047 0.1975 0.004 0.000 0.320 0.676 0.000
#> SRR1812740 3 0.1043 0.7194 0.000 0.000 0.960 0.000 0.040
#> SRR1812739 5 0.5420 -0.1171 0.060 0.416 0.000 0.000 0.524
#> SRR1812738 5 0.4195 0.5316 0.004 0.044 0.004 0.168 0.780
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1812752 6 0.3390 0.654 0.296 0.000 0.000 0.000 0.000 0.704
#> SRR1812753 6 0.3528 0.653 0.296 0.000 0.000 0.000 0.004 0.700
#> SRR1812751 1 0.0858 0.889 0.968 0.028 0.000 0.004 0.000 0.000
#> SRR1812750 1 0.0858 0.889 0.968 0.028 0.000 0.004 0.000 0.000
#> SRR1812748 3 0.0000 0.845 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1812749 1 0.0972 0.886 0.964 0.028 0.000 0.008 0.000 0.000
#> SRR1812746 3 0.1155 0.839 0.036 0.004 0.956 0.000 0.004 0.000
#> SRR1812745 5 0.5692 0.298 0.008 0.004 0.400 0.108 0.480 0.000
#> SRR1812747 2 0.5422 0.549 0.160 0.564 0.000 0.276 0.000 0.000
#> SRR1812744 5 0.2838 0.750 0.000 0.004 0.000 0.188 0.808 0.000
#> SRR1812743 6 0.0000 0.726 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR1812742 6 0.0000 0.726 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR1812737 2 0.2872 0.747 0.140 0.836 0.000 0.024 0.000 0.000
#> SRR1812735 2 0.3062 0.738 0.160 0.816 0.000 0.024 0.000 0.000
#> SRR1812734 3 0.0858 0.841 0.028 0.004 0.968 0.000 0.000 0.000
#> SRR1812733 4 0.1908 0.836 0.000 0.096 0.004 0.900 0.000 0.000
#> SRR1812736 3 0.0000 0.845 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1812732 5 0.3583 0.734 0.004 0.008 0.000 0.260 0.728 0.000
#> SRR1812730 5 0.5764 0.594 0.008 0.004 0.196 0.220 0.572 0.000
#> SRR1812731 5 0.4616 0.735 0.016 0.120 0.000 0.124 0.736 0.004
#> SRR1812729 2 0.2768 0.695 0.012 0.832 0.000 0.156 0.000 0.000
#> SRR1812727 3 0.5571 0.472 0.220 0.000 0.552 0.000 0.228 0.000
#> SRR1812726 2 0.1268 0.754 0.008 0.952 0.000 0.036 0.004 0.000
#> SRR1812728 5 0.0436 0.791 0.004 0.004 0.004 0.000 0.988 0.000
#> SRR1812724 5 0.2706 0.788 0.000 0.008 0.000 0.160 0.832 0.000
#> SRR1812725 4 0.1387 0.848 0.000 0.068 0.000 0.932 0.000 0.000
#> SRR1812723 2 0.1802 0.745 0.012 0.916 0.000 0.072 0.000 0.000
#> SRR1812722 2 0.2896 0.742 0.160 0.824 0.000 0.016 0.000 0.000
#> SRR1812721 6 0.2632 0.675 0.004 0.000 0.000 0.000 0.164 0.832
#> SRR1812718 2 0.3895 0.522 0.016 0.696 0.000 0.284 0.004 0.000
#> SRR1812717 2 0.3867 0.439 0.012 0.660 0.000 0.328 0.000 0.000
#> SRR1812716 4 0.3547 0.263 0.000 0.004 0.000 0.696 0.300 0.000
#> SRR1812715 2 0.2558 0.741 0.156 0.840 0.000 0.004 0.000 0.000
#> SRR1812714 2 0.2629 0.761 0.040 0.868 0.000 0.092 0.000 0.000
#> SRR1812719 3 0.4967 0.601 0.132 0.000 0.640 0.000 0.228 0.000
#> SRR1812713 4 0.2300 0.810 0.000 0.144 0.000 0.856 0.000 0.000
#> SRR1812712 4 0.2231 0.841 0.004 0.068 0.000 0.900 0.028 0.000
#> SRR1812711 2 0.3297 0.765 0.112 0.820 0.000 0.068 0.000 0.000
#> SRR1812710 2 0.2558 0.742 0.156 0.840 0.000 0.004 0.000 0.000
#> SRR1812709 5 0.1897 0.806 0.004 0.004 0.000 0.084 0.908 0.000
#> SRR1812708 1 0.3264 0.669 0.796 0.184 0.000 0.012 0.008 0.000
#> SRR1812707 2 0.0858 0.755 0.004 0.968 0.000 0.028 0.000 0.000
#> SRR1812705 2 0.3512 0.511 0.008 0.720 0.000 0.272 0.000 0.000
#> SRR1812706 5 0.1457 0.802 0.004 0.004 0.016 0.028 0.948 0.000
#> SRR1812704 5 0.1897 0.806 0.004 0.004 0.000 0.084 0.908 0.000
#> SRR1812703 2 0.3997 0.042 0.004 0.508 0.000 0.488 0.000 0.000
#> SRR1812702 4 0.0603 0.819 0.000 0.016 0.004 0.980 0.000 0.000
#> SRR1812741 6 0.6195 0.583 0.224 0.000 0.052 0.000 0.164 0.560
#> SRR1812740 3 0.0000 0.845 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1812739 4 0.2743 0.780 0.008 0.164 0.000 0.828 0.000 0.000
#> SRR1812738 5 0.0777 0.804 0.000 0.004 0.000 0.024 0.972 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", "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 14626 rows and 51 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.910 0.903 0.960 0.4034 0.594 0.594
#> 3 3 0.571 0.817 0.901 0.4672 0.802 0.669
#> 4 4 0.531 0.642 0.807 0.1946 0.685 0.367
#> 5 5 0.682 0.681 0.826 0.1021 0.841 0.508
#> 6 6 0.658 0.529 0.772 0.0441 0.875 0.531
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
#> SRR1812752 2 0.0000 0.9667 0.000 1.000
#> SRR1812753 2 0.0672 0.9612 0.008 0.992
#> SRR1812751 2 0.0000 0.9667 0.000 1.000
#> SRR1812750 2 0.0000 0.9667 0.000 1.000
#> SRR1812748 1 0.0000 0.9214 1.000 0.000
#> SRR1812749 2 0.0000 0.9667 0.000 1.000
#> SRR1812746 1 0.0000 0.9214 1.000 0.000
#> SRR1812745 1 0.0000 0.9214 1.000 0.000
#> SRR1812747 2 0.0000 0.9667 0.000 1.000
#> SRR1812744 1 0.9988 0.0848 0.520 0.480
#> SRR1812743 2 0.0000 0.9667 0.000 1.000
#> SRR1812742 2 0.0000 0.9667 0.000 1.000
#> SRR1812737 2 0.0000 0.9667 0.000 1.000
#> SRR1812735 2 0.0000 0.9667 0.000 1.000
#> SRR1812734 1 0.0000 0.9214 1.000 0.000
#> SRR1812733 1 0.4161 0.8793 0.916 0.084
#> SRR1812736 1 0.0000 0.9214 1.000 0.000
#> SRR1812732 2 0.8763 0.5582 0.296 0.704
#> SRR1812730 1 0.0000 0.9214 1.000 0.000
#> SRR1812731 2 0.0000 0.9667 0.000 1.000
#> SRR1812729 2 0.0000 0.9667 0.000 1.000
#> SRR1812727 1 0.6973 0.7732 0.812 0.188
#> SRR1812726 2 0.0000 0.9667 0.000 1.000
#> SRR1812728 2 0.3879 0.9045 0.076 0.924
#> SRR1812724 2 0.4562 0.8826 0.096 0.904
#> SRR1812725 2 0.3733 0.9086 0.072 0.928
#> SRR1812723 2 0.0000 0.9667 0.000 1.000
#> SRR1812722 2 0.0000 0.9667 0.000 1.000
#> SRR1812721 2 0.0000 0.9667 0.000 1.000
#> SRR1812718 2 0.0000 0.9667 0.000 1.000
#> SRR1812717 2 0.0000 0.9667 0.000 1.000
#> SRR1812716 1 0.6048 0.8216 0.852 0.148
#> SRR1812715 2 0.0000 0.9667 0.000 1.000
#> SRR1812714 2 0.0000 0.9667 0.000 1.000
#> SRR1812719 1 0.1414 0.9160 0.980 0.020
#> SRR1812713 2 0.2948 0.9277 0.052 0.948
#> SRR1812712 2 0.2043 0.9443 0.032 0.968
#> SRR1812711 2 0.0000 0.9667 0.000 1.000
#> SRR1812710 2 0.0000 0.9667 0.000 1.000
#> SRR1812709 2 0.0000 0.9667 0.000 1.000
#> SRR1812708 2 0.0000 0.9667 0.000 1.000
#> SRR1812707 2 0.0000 0.9667 0.000 1.000
#> SRR1812705 2 0.0000 0.9667 0.000 1.000
#> SRR1812706 1 0.0000 0.9214 1.000 0.000
#> SRR1812704 2 0.1843 0.9474 0.028 0.972
#> SRR1812703 2 0.0000 0.9667 0.000 1.000
#> SRR1812702 1 0.2423 0.9073 0.960 0.040
#> SRR1812741 2 0.0000 0.9667 0.000 1.000
#> SRR1812740 1 0.0000 0.9214 1.000 0.000
#> SRR1812739 2 0.0672 0.9618 0.008 0.992
#> SRR1812738 2 0.9833 0.2068 0.424 0.576
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1812752 1 0.0000 0.8757 1.000 0.000 0.000
#> SRR1812753 1 0.0000 0.8757 1.000 0.000 0.000
#> SRR1812751 1 0.3192 0.8184 0.888 0.112 0.000
#> SRR1812750 1 0.4062 0.7708 0.836 0.164 0.000
#> SRR1812748 3 0.0000 0.8592 0.000 0.000 1.000
#> SRR1812749 1 0.5621 0.4993 0.692 0.308 0.000
#> SRR1812746 3 0.0424 0.8625 0.000 0.008 0.992
#> SRR1812745 3 0.0424 0.8625 0.000 0.008 0.992
#> SRR1812747 2 0.0424 0.8714 0.008 0.992 0.000
#> SRR1812744 3 0.6062 0.5431 0.000 0.384 0.616
#> SRR1812743 1 0.0000 0.8757 1.000 0.000 0.000
#> SRR1812742 1 0.0000 0.8757 1.000 0.000 0.000
#> SRR1812737 2 0.3816 0.8504 0.148 0.852 0.000
#> SRR1812735 2 0.3816 0.8504 0.148 0.852 0.000
#> SRR1812734 3 0.0000 0.8592 0.000 0.000 1.000
#> SRR1812733 3 0.4235 0.8518 0.000 0.176 0.824
#> SRR1812736 3 0.0000 0.8592 0.000 0.000 1.000
#> SRR1812732 2 0.9013 0.4246 0.152 0.524 0.324
#> SRR1812730 3 0.3816 0.8701 0.000 0.148 0.852
#> SRR1812731 2 0.4235 0.8311 0.176 0.824 0.000
#> SRR1812729 2 0.0237 0.8711 0.004 0.996 0.000
#> SRR1812727 1 0.3816 0.7199 0.852 0.000 0.148
#> SRR1812726 2 0.3752 0.8525 0.144 0.856 0.000
#> SRR1812728 2 0.2711 0.8009 0.000 0.912 0.088
#> SRR1812724 2 0.1529 0.8451 0.000 0.960 0.040
#> SRR1812725 2 0.0237 0.8689 0.000 0.996 0.004
#> SRR1812723 2 0.0000 0.8704 0.000 1.000 0.000
#> SRR1812722 2 0.3816 0.8504 0.148 0.852 0.000
#> SRR1812721 2 0.4178 0.8327 0.172 0.828 0.000
#> SRR1812718 2 0.0000 0.8704 0.000 1.000 0.000
#> SRR1812717 2 0.3412 0.8598 0.124 0.876 0.000
#> SRR1812716 3 0.4555 0.8281 0.000 0.200 0.800
#> SRR1812715 2 0.3816 0.8504 0.148 0.852 0.000
#> SRR1812714 2 0.3752 0.8525 0.144 0.856 0.000
#> SRR1812719 3 0.3752 0.8709 0.000 0.144 0.856
#> SRR1812713 2 0.0000 0.8704 0.000 1.000 0.000
#> SRR1812712 2 0.0000 0.8704 0.000 1.000 0.000
#> SRR1812711 2 0.3412 0.8598 0.124 0.876 0.000
#> SRR1812710 2 0.3816 0.8504 0.148 0.852 0.000
#> SRR1812709 2 0.0000 0.8704 0.000 1.000 0.000
#> SRR1812708 2 0.0747 0.8651 0.016 0.984 0.000
#> SRR1812707 2 0.3816 0.8504 0.148 0.852 0.000
#> SRR1812705 2 0.3551 0.8572 0.132 0.868 0.000
#> SRR1812706 3 0.3816 0.8701 0.000 0.148 0.852
#> SRR1812704 2 0.0237 0.8689 0.000 0.996 0.004
#> SRR1812703 2 0.0000 0.8704 0.000 1.000 0.000
#> SRR1812702 3 0.3879 0.8685 0.000 0.152 0.848
#> SRR1812741 1 0.0000 0.8757 1.000 0.000 0.000
#> SRR1812740 3 0.0000 0.8592 0.000 0.000 1.000
#> SRR1812739 2 0.0000 0.8704 0.000 1.000 0.000
#> SRR1812738 2 0.6168 0.0662 0.000 0.588 0.412
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1812752 1 0.1398 0.7661 0.956 0.040 0.004 0.000
#> SRR1812753 1 0.1305 0.7654 0.960 0.036 0.004 0.000
#> SRR1812751 1 0.3710 0.7438 0.804 0.192 0.000 0.004
#> SRR1812750 1 0.4343 0.6850 0.732 0.264 0.000 0.004
#> SRR1812748 3 0.3486 0.7827 0.000 0.000 0.812 0.188
#> SRR1812749 1 0.3710 0.7438 0.804 0.192 0.000 0.004
#> SRR1812746 3 0.4855 0.6278 0.000 0.000 0.600 0.400
#> SRR1812745 3 0.4624 0.7082 0.000 0.000 0.660 0.340
#> SRR1812747 2 0.1637 0.7863 0.000 0.940 0.000 0.060
#> SRR1812744 4 0.5793 0.0847 0.012 0.036 0.288 0.664
#> SRR1812743 2 0.7205 0.4002 0.172 0.532 0.296 0.000
#> SRR1812742 2 0.7172 0.4048 0.168 0.536 0.296 0.000
#> SRR1812737 2 0.0188 0.8145 0.004 0.996 0.000 0.000
#> SRR1812735 2 0.0188 0.8146 0.000 0.996 0.004 0.000
#> SRR1812734 3 0.3726 0.7810 0.000 0.000 0.788 0.212
#> SRR1812733 4 0.0927 0.6846 0.000 0.016 0.008 0.976
#> SRR1812736 3 0.3486 0.7827 0.000 0.000 0.812 0.188
#> SRR1812732 3 0.6603 -0.2350 0.052 0.436 0.500 0.012
#> SRR1812730 4 0.2345 0.5776 0.000 0.000 0.100 0.900
#> SRR1812731 2 0.6066 0.5962 0.116 0.692 0.188 0.004
#> SRR1812729 2 0.4509 0.3937 0.004 0.708 0.000 0.288
#> SRR1812727 1 0.1109 0.7499 0.968 0.004 0.028 0.000
#> SRR1812726 2 0.0779 0.8135 0.016 0.980 0.000 0.004
#> SRR1812728 4 0.4307 0.7712 0.024 0.192 0.000 0.784
#> SRR1812724 2 0.5700 0.5870 0.036 0.724 0.032 0.208
#> SRR1812725 4 0.3569 0.7739 0.000 0.196 0.000 0.804
#> SRR1812723 2 0.5165 -0.3130 0.004 0.512 0.000 0.484
#> SRR1812722 2 0.0524 0.8149 0.004 0.988 0.000 0.008
#> SRR1812721 2 0.6014 0.6073 0.112 0.696 0.188 0.004
#> SRR1812718 4 0.4800 0.6433 0.004 0.340 0.000 0.656
#> SRR1812717 2 0.1743 0.7888 0.004 0.940 0.000 0.056
#> SRR1812716 4 0.1936 0.6764 0.000 0.028 0.032 0.940
#> SRR1812715 2 0.0707 0.8080 0.000 0.980 0.020 0.000
#> SRR1812714 2 0.0895 0.8129 0.004 0.976 0.000 0.020
#> SRR1812719 1 0.5756 0.3667 0.592 0.000 0.036 0.372
#> SRR1812713 4 0.3569 0.7739 0.000 0.196 0.000 0.804
#> SRR1812712 4 0.3569 0.7739 0.000 0.196 0.000 0.804
#> SRR1812711 2 0.0779 0.8126 0.004 0.980 0.000 0.016
#> SRR1812710 2 0.0188 0.8145 0.004 0.996 0.000 0.000
#> SRR1812709 4 0.5376 0.5111 0.016 0.396 0.000 0.588
#> SRR1812708 1 0.7351 0.2826 0.524 0.212 0.000 0.264
#> SRR1812707 2 0.0000 0.8151 0.000 1.000 0.000 0.000
#> SRR1812705 2 0.0817 0.8095 0.000 0.976 0.000 0.024
#> SRR1812706 4 0.0336 0.6688 0.000 0.000 0.008 0.992
#> SRR1812704 4 0.4175 0.7636 0.012 0.212 0.000 0.776
#> SRR1812703 4 0.4454 0.6823 0.000 0.308 0.000 0.692
#> SRR1812702 4 0.0524 0.6787 0.000 0.008 0.004 0.988
#> SRR1812741 1 0.1182 0.7539 0.968 0.016 0.016 0.000
#> SRR1812740 3 0.3486 0.7827 0.000 0.000 0.812 0.188
#> SRR1812739 4 0.5320 0.4670 0.012 0.416 0.000 0.572
#> SRR1812738 4 0.5241 0.7191 0.040 0.140 0.040 0.780
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1812752 1 0.1168 0.70805 0.960 0.008 0.000 0.032 0.000
#> SRR1812753 1 0.1082 0.70379 0.964 0.000 0.008 0.028 0.000
#> SRR1812751 1 0.3074 0.66304 0.804 0.196 0.000 0.000 0.000
#> SRR1812750 2 0.4437 -0.00448 0.464 0.532 0.000 0.004 0.000
#> SRR1812748 3 0.0324 0.73161 0.004 0.000 0.992 0.004 0.000
#> SRR1812749 1 0.3305 0.63800 0.776 0.224 0.000 0.000 0.000
#> SRR1812746 3 0.4249 0.73958 0.000 0.000 0.688 0.016 0.296
#> SRR1812745 3 0.3551 0.77933 0.000 0.000 0.772 0.008 0.220
#> SRR1812747 2 0.1012 0.87388 0.000 0.968 0.000 0.020 0.012
#> SRR1812744 5 0.5991 0.40919 0.008 0.000 0.172 0.204 0.616
#> SRR1812743 4 0.5548 0.71043 0.056 0.096 0.132 0.716 0.000
#> SRR1812742 4 0.5846 0.70237 0.060 0.156 0.096 0.688 0.000
#> SRR1812737 2 0.0162 0.88063 0.000 0.996 0.000 0.004 0.000
#> SRR1812735 2 0.0290 0.88066 0.000 0.992 0.000 0.008 0.000
#> SRR1812734 3 0.2843 0.78108 0.000 0.000 0.848 0.008 0.144
#> SRR1812733 5 0.2813 0.61596 0.000 0.000 0.108 0.024 0.868
#> SRR1812736 3 0.0290 0.73192 0.000 0.000 0.992 0.008 0.000
#> SRR1812732 4 0.6147 0.58183 0.004 0.188 0.228 0.580 0.000
#> SRR1812730 3 0.4238 0.66498 0.000 0.000 0.628 0.004 0.368
#> SRR1812731 4 0.2932 0.74307 0.032 0.104 0.000 0.864 0.000
#> SRR1812729 2 0.1830 0.84276 0.000 0.924 0.000 0.008 0.068
#> SRR1812727 1 0.0898 0.69849 0.972 0.000 0.000 0.020 0.008
#> SRR1812726 2 0.1341 0.84915 0.000 0.944 0.000 0.056 0.000
#> SRR1812728 5 0.4563 0.69219 0.028 0.016 0.000 0.228 0.728
#> SRR1812724 4 0.3777 0.62297 0.004 0.040 0.008 0.824 0.124
#> SRR1812725 5 0.1377 0.72894 0.000 0.020 0.004 0.020 0.956
#> SRR1812723 2 0.1800 0.85374 0.000 0.932 0.000 0.020 0.048
#> SRR1812722 2 0.0566 0.87972 0.000 0.984 0.000 0.012 0.004
#> SRR1812721 4 0.3110 0.71825 0.028 0.112 0.000 0.856 0.004
#> SRR1812718 5 0.4873 0.44970 0.000 0.312 0.000 0.044 0.644
#> SRR1812717 2 0.6036 0.33568 0.000 0.564 0.000 0.160 0.276
#> SRR1812716 3 0.4764 0.53100 0.000 0.004 0.548 0.012 0.436
#> SRR1812715 2 0.0290 0.88066 0.000 0.992 0.000 0.008 0.000
#> SRR1812714 2 0.0324 0.88001 0.004 0.992 0.000 0.004 0.000
#> SRR1812719 5 0.5525 0.51004 0.288 0.000 0.000 0.100 0.612
#> SRR1812713 5 0.0960 0.72091 0.000 0.004 0.016 0.008 0.972
#> SRR1812712 5 0.0324 0.72618 0.000 0.000 0.004 0.004 0.992
#> SRR1812711 2 0.0162 0.88051 0.000 0.996 0.000 0.004 0.000
#> SRR1812710 2 0.0162 0.88063 0.000 0.996 0.000 0.004 0.000
#> SRR1812709 5 0.5081 0.64483 0.020 0.032 0.000 0.284 0.664
#> SRR1812708 1 0.5832 -0.05129 0.468 0.044 0.000 0.024 0.464
#> SRR1812707 2 0.0290 0.88010 0.000 0.992 0.000 0.008 0.000
#> SRR1812705 2 0.0865 0.87618 0.000 0.972 0.000 0.024 0.004
#> SRR1812706 5 0.0451 0.72322 0.000 0.000 0.008 0.004 0.988
#> SRR1812704 5 0.4605 0.68858 0.020 0.016 0.004 0.236 0.724
#> SRR1812703 2 0.4774 0.56961 0.000 0.684 0.012 0.028 0.276
#> SRR1812702 5 0.0807 0.71668 0.000 0.000 0.012 0.012 0.976
#> SRR1812741 4 0.4047 0.49896 0.320 0.000 0.000 0.676 0.004
#> SRR1812740 3 0.0000 0.73512 0.000 0.000 1.000 0.000 0.000
#> SRR1812739 5 0.5230 0.63593 0.028 0.028 0.000 0.296 0.648
#> SRR1812738 5 0.5227 0.60305 0.032 0.000 0.016 0.336 0.616
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1812752 1 0.0146 0.6626 0.996 0.000 0.000 0.000 0.000 0.004
#> SRR1812753 1 0.0363 0.6602 0.988 0.000 0.000 0.000 0.000 0.012
#> SRR1812751 1 0.3273 0.6068 0.776 0.212 0.000 0.004 0.008 0.000
#> SRR1812750 2 0.4091 0.3352 0.340 0.644 0.000 0.004 0.008 0.004
#> SRR1812748 3 0.1049 0.7250 0.000 0.000 0.960 0.000 0.008 0.032
#> SRR1812749 1 0.4105 0.4301 0.640 0.344 0.000 0.004 0.008 0.004
#> SRR1812746 5 0.4749 0.1665 0.000 0.004 0.384 0.036 0.572 0.004
#> SRR1812745 5 0.4184 -0.0953 0.000 0.000 0.488 0.000 0.500 0.012
#> SRR1812747 2 0.1223 0.8051 0.012 0.960 0.000 0.008 0.004 0.016
#> SRR1812744 6 0.7528 0.2174 0.000 0.004 0.236 0.168 0.196 0.396
#> SRR1812743 6 0.1078 0.6879 0.012 0.016 0.008 0.000 0.000 0.964
#> SRR1812742 6 0.1875 0.6897 0.020 0.032 0.020 0.000 0.000 0.928
#> SRR1812737 2 0.0993 0.8047 0.012 0.964 0.000 0.000 0.000 0.024
#> SRR1812735 2 0.1053 0.8081 0.000 0.964 0.000 0.004 0.012 0.020
#> SRR1812734 3 0.3518 0.4929 0.000 0.000 0.732 0.000 0.256 0.012
#> SRR1812733 5 0.1321 0.6377 0.000 0.000 0.020 0.024 0.952 0.004
#> SRR1812736 3 0.1552 0.7266 0.000 0.000 0.940 0.004 0.020 0.036
#> SRR1812732 6 0.3592 0.5890 0.000 0.020 0.240 0.000 0.000 0.740
#> SRR1812730 3 0.4654 0.1688 0.000 0.012 0.564 0.008 0.404 0.012
#> SRR1812731 6 0.2558 0.5740 0.004 0.000 0.000 0.156 0.000 0.840
#> SRR1812729 2 0.3539 0.6926 0.000 0.768 0.000 0.008 0.208 0.016
#> SRR1812727 1 0.2488 0.5985 0.864 0.000 0.004 0.124 0.000 0.008
#> SRR1812726 2 0.2455 0.7518 0.012 0.872 0.000 0.112 0.000 0.004
#> SRR1812728 4 0.1814 0.6263 0.000 0.000 0.000 0.900 0.100 0.000
#> SRR1812724 4 0.5846 0.4987 0.000 0.008 0.012 0.580 0.228 0.172
#> SRR1812725 5 0.4062 0.5135 0.000 0.044 0.024 0.128 0.792 0.012
#> SRR1812723 2 0.1390 0.8035 0.000 0.948 0.000 0.004 0.032 0.016
#> SRR1812722 2 0.2765 0.7555 0.000 0.848 0.000 0.004 0.132 0.016
#> SRR1812721 4 0.4218 0.2543 0.004 0.012 0.000 0.584 0.000 0.400
#> SRR1812718 2 0.5675 0.4014 0.000 0.584 0.016 0.108 0.284 0.008
#> SRR1812717 2 0.7361 -0.0742 0.000 0.348 0.000 0.256 0.284 0.112
#> SRR1812716 5 0.5578 -0.1175 0.000 0.036 0.440 0.028 0.480 0.016
#> SRR1812715 2 0.0993 0.8076 0.012 0.964 0.000 0.000 0.000 0.024
#> SRR1812714 2 0.1406 0.7984 0.016 0.952 0.000 0.004 0.008 0.020
#> SRR1812719 4 0.5977 0.1877 0.152 0.000 0.008 0.512 0.320 0.008
#> SRR1812713 5 0.2289 0.6135 0.000 0.020 0.024 0.036 0.912 0.008
#> SRR1812712 5 0.2445 0.6162 0.000 0.000 0.008 0.120 0.868 0.004
#> SRR1812711 2 0.0508 0.8079 0.012 0.984 0.000 0.000 0.000 0.004
#> SRR1812710 2 0.0622 0.8071 0.012 0.980 0.000 0.000 0.000 0.008
#> SRR1812709 4 0.2001 0.6239 0.000 0.000 0.000 0.912 0.048 0.040
#> SRR1812708 5 0.6945 0.0989 0.236 0.032 0.012 0.280 0.436 0.004
#> SRR1812707 2 0.0603 0.8096 0.000 0.980 0.000 0.000 0.004 0.016
#> SRR1812705 2 0.2288 0.7865 0.000 0.896 0.000 0.004 0.072 0.028
#> SRR1812706 5 0.2182 0.6286 0.000 0.000 0.020 0.068 0.904 0.008
#> SRR1812704 4 0.3584 0.5583 0.000 0.000 0.004 0.740 0.244 0.012
#> SRR1812703 2 0.4265 0.4526 0.000 0.596 0.000 0.004 0.384 0.016
#> SRR1812702 5 0.1843 0.6256 0.000 0.004 0.004 0.080 0.912 0.000
#> SRR1812741 1 0.6041 -0.0813 0.400 0.000 0.000 0.344 0.000 0.256
#> SRR1812740 3 0.1285 0.7308 0.000 0.000 0.944 0.000 0.052 0.004
#> SRR1812739 4 0.6067 0.1001 0.000 0.004 0.000 0.456 0.264 0.276
#> SRR1812738 4 0.3107 0.6075 0.000 0.000 0.000 0.832 0.052 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.
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