Date: 2019-12-26 00:56:30 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 14198 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] 14198 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 | ||
|---|---|---|---|---|---|---|
| SD:pam | 6 | 1.000 | 0.952 | 0.977 | ** | 2,3 |
| CV:hclust | 2 | 1.000 | 0.961 | 0.985 | ** | |
| CV:kmeans | 2 | 1.000 | 1.000 | 1.000 | ** | |
| CV:pam | 2 | 1.000 | 0.972 | 0.989 | ** | |
| ATC:kmeans | 2 | 1.000 | 0.991 | 0.996 | ** | |
| ATC:skmeans | 4 | 1.000 | 0.990 | 0.997 | ** | 2,3 |
| ATC:pam | 4 | 1.000 | 0.990 | 0.996 | ** | 2,3 |
| ATC:mclust | 2 | 1.000 | 0.990 | 0.988 | ** | |
| CV:NMF | 4 | 0.998 | 0.951 | 0.976 | ** | 2,3 |
| MAD:skmeans | 4 | 0.963 | 0.956 | 0.973 | ** | 2,3 |
| ATC:hclust | 6 | 0.951 | 0.923 | 0.960 | ** | 2,3,4,5 |
| MAD:pam | 6 | 0.946 | 0.858 | 0.922 | * | 2,3,5 |
| SD:skmeans | 4 | 0.941 | 0.954 | 0.973 | * | |
| CV:mclust | 6 | 0.938 | 0.923 | 0.949 | * | 3,4,5 |
| SD:mclust | 5 | 0.934 | 0.924 | 0.958 | * | |
| CV:skmeans | 3 | 0.931 | 0.970 | 0.984 | * | 2 |
| MAD:kmeans | 3 | 0.920 | 0.887 | 0.948 | * | |
| SD:NMF | 4 | 0.912 | 0.862 | 0.943 | * | 3 |
| MAD:NMF | 4 | 0.906 | 0.842 | 0.934 | * | 2 |
| MAD:mclust | 5 | 0.903 | 0.827 | 0.933 | * | |
| SD:hclust | 3 | 0.843 | 0.925 | 0.962 | ||
| MAD:hclust | 3 | 0.838 | 0.924 | 0.961 | ||
| SD:kmeans | 2 | 0.776 | 0.847 | 0.934 | ||
| ATC:NMF | 2 | 0.754 | 0.842 | 0.932 |
**: 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 0.794 0.944 0.957 0.479 0.523 0.523
#> CV:NMF 2 1.000 0.997 0.999 0.423 0.576 0.576
#> MAD:NMF 2 1.000 0.986 0.993 0.468 0.534 0.534
#> ATC:NMF 2 0.754 0.842 0.932 0.491 0.500 0.500
#> SD:skmeans 2 0.885 0.954 0.979 0.509 0.490 0.490
#> CV:skmeans 2 1.000 0.992 0.996 0.496 0.506 0.506
#> MAD:skmeans 2 1.000 0.986 0.994 0.510 0.490 0.490
#> ATC:skmeans 2 1.000 1.000 1.000 0.510 0.490 0.490
#> SD:mclust 2 0.447 0.862 0.917 0.438 0.534 0.534
#> CV:mclust 2 0.510 0.949 0.954 0.381 0.633 0.633
#> MAD:mclust 2 0.442 0.802 0.834 0.435 0.534 0.534
#> ATC:mclust 2 1.000 0.990 0.988 0.325 0.678 0.678
#> SD:kmeans 2 0.776 0.847 0.934 0.493 0.490 0.490
#> CV:kmeans 2 1.000 1.000 1.000 0.440 0.561 0.561
#> MAD:kmeans 2 0.810 0.939 0.967 0.503 0.490 0.490
#> ATC:kmeans 2 1.000 0.991 0.996 0.475 0.523 0.523
#> SD:pam 2 0.920 0.955 0.981 0.503 0.495 0.495
#> CV:pam 2 1.000 0.972 0.989 0.446 0.547 0.547
#> MAD:pam 2 1.000 0.972 0.988 0.509 0.492 0.492
#> ATC:pam 2 1.000 0.960 0.985 0.466 0.534 0.534
#> SD:hclust 2 0.655 0.904 0.938 0.489 0.492 0.492
#> CV:hclust 2 1.000 0.961 0.985 0.426 0.576 0.576
#> MAD:hclust 2 0.624 0.915 0.941 0.489 0.492 0.492
#> ATC:hclust 2 1.000 1.000 1.000 0.509 0.492 0.492
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 1.000 0.950 0.978 0.416 0.773 0.576
#> CV:NMF 3 0.918 0.909 0.962 0.587 0.753 0.571
#> MAD:NMF 3 0.826 0.876 0.929 0.435 0.787 0.601
#> ATC:NMF 3 0.467 0.688 0.819 0.316 0.747 0.550
#> SD:skmeans 3 0.797 0.888 0.928 0.185 0.918 0.832
#> CV:skmeans 3 0.931 0.970 0.984 0.265 0.848 0.706
#> MAD:skmeans 3 0.994 0.965 0.975 0.169 0.918 0.832
#> ATC:skmeans 3 1.000 1.000 1.000 0.175 0.911 0.818
#> SD:mclust 3 0.764 0.826 0.918 0.513 0.767 0.575
#> CV:mclust 3 1.000 0.974 0.972 0.698 0.718 0.554
#> MAD:mclust 3 0.592 0.740 0.873 0.469 0.661 0.440
#> ATC:mclust 3 0.515 0.937 0.930 0.549 0.835 0.757
#> SD:kmeans 3 0.887 0.770 0.900 0.344 0.829 0.662
#> CV:kmeans 3 0.646 0.867 0.895 0.418 0.762 0.583
#> MAD:kmeans 3 0.920 0.887 0.948 0.323 0.729 0.501
#> ATC:kmeans 3 0.755 0.922 0.925 0.353 0.777 0.594
#> SD:pam 3 0.971 0.939 0.976 0.344 0.704 0.469
#> CV:pam 3 0.741 0.818 0.926 0.470 0.755 0.571
#> MAD:pam 3 1.000 0.963 0.986 0.329 0.708 0.474
#> ATC:pam 3 1.000 0.920 0.973 0.418 0.749 0.552
#> SD:hclust 3 0.843 0.925 0.962 0.343 0.862 0.719
#> CV:hclust 3 0.639 0.777 0.851 0.378 0.784 0.626
#> MAD:hclust 3 0.838 0.924 0.961 0.345 0.859 0.713
#> ATC:hclust 3 1.000 0.998 0.999 0.277 0.859 0.713
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.912 0.862 0.943 0.1051 0.909 0.726
#> CV:NMF 4 0.998 0.951 0.976 0.1336 0.852 0.585
#> MAD:NMF 4 0.906 0.842 0.934 0.1167 0.855 0.592
#> ATC:NMF 4 0.717 0.791 0.873 0.1639 0.867 0.641
#> SD:skmeans 4 0.941 0.954 0.973 0.1557 0.867 0.684
#> CV:skmeans 4 0.842 0.857 0.907 0.0761 0.947 0.862
#> MAD:skmeans 4 0.963 0.956 0.973 0.1733 0.867 0.684
#> ATC:skmeans 4 1.000 0.990 0.997 0.0378 0.973 0.932
#> SD:mclust 4 0.886 0.906 0.963 0.0976 0.915 0.752
#> CV:mclust 4 0.965 0.925 0.954 0.1589 0.890 0.687
#> MAD:mclust 4 0.738 0.800 0.864 0.1162 0.881 0.670
#> ATC:mclust 4 0.714 0.740 0.805 0.2876 0.852 0.716
#> SD:kmeans 4 0.747 0.790 0.825 0.0970 0.859 0.653
#> CV:kmeans 4 0.781 0.765 0.842 0.1408 0.953 0.864
#> MAD:kmeans 4 0.736 0.785 0.783 0.0956 0.935 0.801
#> ATC:kmeans 4 0.804 0.857 0.901 0.1393 0.915 0.758
#> SD:pam 4 0.848 0.836 0.894 0.0844 0.905 0.726
#> CV:pam 4 0.790 0.868 0.936 0.0664 0.835 0.583
#> MAD:pam 4 0.863 0.752 0.838 0.0867 0.898 0.700
#> ATC:pam 4 1.000 0.990 0.996 0.1053 0.861 0.627
#> SD:hclust 4 0.749 0.890 0.911 0.0869 0.950 0.858
#> CV:hclust 4 0.820 0.858 0.935 0.1555 0.938 0.832
#> MAD:hclust 4 0.787 0.829 0.850 0.1139 0.915 0.758
#> ATC:hclust 4 1.000 0.987 0.991 0.1500 0.900 0.714
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.842 0.809 0.887 0.0501 0.917 0.687
#> CV:NMF 5 0.871 0.818 0.905 0.0454 0.950 0.793
#> MAD:NMF 5 0.895 0.874 0.922 0.0584 0.915 0.677
#> ATC:NMF 5 0.679 0.676 0.796 0.0551 0.922 0.697
#> SD:skmeans 5 0.790 0.704 0.858 0.0798 0.954 0.848
#> CV:skmeans 5 0.842 0.876 0.897 0.0566 0.895 0.690
#> MAD:skmeans 5 0.821 0.823 0.901 0.0675 0.952 0.844
#> ATC:skmeans 5 0.869 0.919 0.952 0.0453 0.998 0.996
#> SD:mclust 5 0.934 0.924 0.958 0.1062 0.882 0.593
#> CV:mclust 5 0.933 0.914 0.945 0.0349 0.973 0.886
#> MAD:mclust 5 0.903 0.827 0.933 0.0964 0.908 0.674
#> ATC:mclust 5 0.824 0.813 0.893 0.1904 0.812 0.522
#> SD:kmeans 5 0.729 0.787 0.761 0.0701 0.893 0.667
#> CV:kmeans 5 0.738 0.790 0.838 0.0721 0.889 0.655
#> MAD:kmeans 5 0.735 0.695 0.771 0.0660 0.949 0.824
#> ATC:kmeans 5 0.747 0.755 0.826 0.0639 0.965 0.870
#> SD:pam 5 0.891 0.948 0.949 0.0675 0.922 0.726
#> CV:pam 5 0.868 0.855 0.925 0.0810 0.929 0.753
#> MAD:pam 5 1.000 0.996 0.998 0.0724 0.885 0.605
#> ATC:pam 5 0.881 0.936 0.900 0.0762 0.934 0.757
#> SD:hclust 5 0.780 0.848 0.852 0.0938 0.915 0.721
#> CV:hclust 5 0.824 0.785 0.888 0.0570 0.954 0.862
#> MAD:hclust 5 0.790 0.784 0.755 0.0543 0.973 0.897
#> ATC:hclust 5 0.904 0.942 0.931 0.0412 0.973 0.890
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.844 0.798 0.872 0.03000 1.000 1.000
#> CV:NMF 6 0.896 0.749 0.882 0.03071 0.979 0.895
#> MAD:NMF 6 0.871 0.770 0.877 0.02615 0.996 0.980
#> ATC:NMF 6 0.699 0.623 0.769 0.02581 0.986 0.932
#> SD:skmeans 6 0.814 0.663 0.848 0.04264 0.915 0.697
#> CV:skmeans 6 0.933 0.968 0.970 0.05886 0.992 0.968
#> MAD:skmeans 6 0.804 0.707 0.850 0.04444 0.969 0.883
#> ATC:skmeans 6 0.869 0.527 0.785 0.06709 0.895 0.721
#> SD:mclust 6 0.871 0.862 0.905 0.02671 0.970 0.846
#> CV:mclust 6 0.938 0.923 0.949 0.00892 0.940 0.760
#> MAD:mclust 6 0.852 0.760 0.882 0.05343 0.956 0.786
#> ATC:mclust 6 0.890 0.852 0.924 0.07619 0.926 0.679
#> SD:kmeans 6 0.815 0.791 0.774 0.04344 0.940 0.729
#> CV:kmeans 6 0.793 0.668 0.781 0.05680 0.965 0.852
#> MAD:kmeans 6 0.818 0.665 0.756 0.04682 0.878 0.555
#> ATC:kmeans 6 0.800 0.737 0.805 0.04858 0.936 0.730
#> SD:pam 6 1.000 0.952 0.977 0.05406 0.962 0.827
#> CV:pam 6 0.881 0.851 0.901 0.02937 0.947 0.780
#> MAD:pam 6 0.946 0.858 0.922 0.04741 0.962 0.823
#> ATC:pam 6 0.887 0.896 0.919 0.05736 0.961 0.809
#> SD:hclust 6 0.809 0.812 0.841 0.02831 0.958 0.814
#> CV:hclust 6 0.823 0.784 0.877 0.03130 0.947 0.830
#> MAD:hclust 6 0.821 0.786 0.820 0.04086 0.938 0.745
#> ATC:hclust 6 0.951 0.923 0.960 0.04540 0.965 0.845
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 14198 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 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 0.655 0.904 0.938 0.4889 0.492 0.492
#> 3 3 0.843 0.925 0.962 0.3433 0.862 0.719
#> 4 4 0.749 0.890 0.911 0.0869 0.950 0.858
#> 5 5 0.780 0.848 0.852 0.0938 0.915 0.721
#> 6 6 0.809 0.812 0.841 0.0283 0.958 0.814
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 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
#> SRR2936906 1 0.000 0.866 1.000 0.000
#> SRR2936909 1 0.000 0.866 1.000 0.000
#> SRR2936918 1 0.000 0.866 1.000 0.000
#> SRR2936917 2 0.000 1.000 0.000 1.000
#> SRR2936916 1 0.866 0.751 0.712 0.288
#> SRR2936915 1 0.866 0.751 0.712 0.288
#> SRR2936914 2 0.000 1.000 0.000 1.000
#> SRR2936913 2 0.000 1.000 0.000 1.000
#> SRR2936912 1 0.000 0.866 1.000 0.000
#> SRR2936910 1 0.000 0.866 1.000 0.000
#> SRR2936911 2 0.000 1.000 0.000 1.000
#> SRR2936907 2 0.000 1.000 0.000 1.000
#> SRR2936908 2 0.000 1.000 0.000 1.000
#> SRR2936904 1 0.866 0.751 0.712 0.288
#> SRR2936905 2 0.000 1.000 0.000 1.000
#> SRR2936903 1 0.000 0.866 1.000 0.000
#> SRR2936901 1 0.866 0.751 0.712 0.288
#> SRR2936902 2 0.000 1.000 0.000 1.000
#> SRR2936900 1 0.000 0.866 1.000 0.000
#> SRR2936898 1 0.866 0.751 0.712 0.288
#> SRR2936899 1 0.866 0.751 0.712 0.288
#> SRR2936897 1 0.000 0.866 1.000 0.000
#> SRR2936896 2 0.000 1.000 0.000 1.000
#> SRR2936894 1 0.000 0.866 1.000 0.000
#> SRR2936893 2 0.000 1.000 0.000 1.000
#> SRR2936895 2 0.000 1.000 0.000 1.000
#> SRR2936892 2 0.000 1.000 0.000 1.000
#> SRR2936891 1 0.000 0.866 1.000 0.000
#> SRR2936890 2 0.000 1.000 0.000 1.000
#> SRR2936886 1 0.866 0.751 0.712 0.288
#> SRR2936885 1 0.000 0.866 1.000 0.000
#> SRR2936888 1 0.000 0.866 1.000 0.000
#> SRR2936889 2 0.000 1.000 0.000 1.000
#> SRR2936887 1 0.866 0.751 0.712 0.288
#> SRR2936884 2 0.000 1.000 0.000 1.000
#> SRR2936883 2 0.000 1.000 0.000 1.000
#> SRR2936881 2 0.000 1.000 0.000 1.000
#> SRR2936882 1 0.000 0.866 1.000 0.000
#> SRR2936880 2 0.000 1.000 0.000 1.000
#> SRR2936878 2 0.000 1.000 0.000 1.000
#> SRR2936879 1 0.866 0.751 0.712 0.288
#> SRR2936875 2 0.000 1.000 0.000 1.000
#> SRR2936877 2 0.000 1.000 0.000 1.000
#> SRR2936876 1 0.000 0.866 1.000 0.000
#> SRR2936873 1 0.000 0.866 1.000 0.000
#> SRR2936872 2 0.000 1.000 0.000 1.000
#> SRR2936871 2 0.000 1.000 0.000 1.000
#> SRR2936874 2 0.000 1.000 0.000 1.000
#> SRR2936870 1 0.000 0.866 1.000 0.000
#> SRR2936869 1 0.866 0.751 0.712 0.288
#> SRR2936868 1 0.866 0.751 0.712 0.288
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR2936906 1 0.000 0.987 1.0 0.000 0.000
#> SRR2936909 1 0.000 0.987 1.0 0.000 0.000
#> SRR2936918 1 0.000 0.987 1.0 0.000 0.000
#> SRR2936917 2 0.000 0.919 0.0 1.000 0.000
#> SRR2936916 3 0.000 1.000 0.0 0.000 1.000
#> SRR2936915 3 0.000 1.000 0.0 0.000 1.000
#> SRR2936914 2 0.000 0.919 0.0 1.000 0.000
#> SRR2936913 2 0.000 0.919 0.0 1.000 0.000
#> SRR2936912 1 0.000 0.987 1.0 0.000 0.000
#> SRR2936910 1 0.000 0.987 1.0 0.000 0.000
#> SRR2936911 2 0.000 0.919 0.0 1.000 0.000
#> SRR2936907 2 0.000 0.919 0.0 1.000 0.000
#> SRR2936908 2 0.000 0.919 0.0 1.000 0.000
#> SRR2936904 3 0.000 1.000 0.0 0.000 1.000
#> SRR2936905 2 0.000 0.919 0.0 1.000 0.000
#> SRR2936903 1 0.000 0.987 1.0 0.000 0.000
#> SRR2936901 3 0.000 1.000 0.0 0.000 1.000
#> SRR2936902 2 0.546 0.684 0.0 0.712 0.288
#> SRR2936900 1 0.000 0.987 1.0 0.000 0.000
#> SRR2936898 3 0.000 1.000 0.0 0.000 1.000
#> SRR2936899 3 0.000 1.000 0.0 0.000 1.000
#> SRR2936897 1 0.000 0.987 1.0 0.000 0.000
#> SRR2936896 2 0.000 0.919 0.0 1.000 0.000
#> SRR2936894 1 0.000 0.987 1.0 0.000 0.000
#> SRR2936893 2 0.000 0.919 0.0 1.000 0.000
#> SRR2936895 2 0.546 0.684 0.0 0.712 0.288
#> SRR2936892 2 0.000 0.919 0.0 1.000 0.000
#> SRR2936891 1 0.000 0.987 1.0 0.000 0.000
#> SRR2936890 2 0.000 0.919 0.0 1.000 0.000
#> SRR2936886 3 0.000 1.000 0.0 0.000 1.000
#> SRR2936885 1 0.000 0.987 1.0 0.000 0.000
#> SRR2936888 1 0.000 0.987 1.0 0.000 0.000
#> SRR2936889 2 0.000 0.919 0.0 1.000 0.000
#> SRR2936887 3 0.000 1.000 0.0 0.000 1.000
#> SRR2936884 2 0.546 0.684 0.0 0.712 0.288
#> SRR2936883 2 0.546 0.684 0.0 0.712 0.288
#> SRR2936881 2 0.546 0.684 0.0 0.712 0.288
#> SRR2936882 1 0.000 0.987 1.0 0.000 0.000
#> SRR2936880 2 0.546 0.684 0.0 0.712 0.288
#> SRR2936878 2 0.000 0.919 0.0 1.000 0.000
#> SRR2936879 3 0.000 1.000 0.0 0.000 1.000
#> SRR2936875 2 0.000 0.919 0.0 1.000 0.000
#> SRR2936877 2 0.000 0.919 0.0 1.000 0.000
#> SRR2936876 1 0.455 0.754 0.8 0.000 0.200
#> SRR2936873 1 0.000 0.987 1.0 0.000 0.000
#> SRR2936872 2 0.000 0.919 0.0 1.000 0.000
#> SRR2936871 2 0.000 0.919 0.0 1.000 0.000
#> SRR2936874 2 0.000 0.919 0.0 1.000 0.000
#> SRR2936870 1 0.000 0.987 1.0 0.000 0.000
#> SRR2936869 3 0.000 1.000 0.0 0.000 1.000
#> SRR2936868 3 0.000 1.000 0.0 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR2936906 1 0.3610 1.000 0.800 0.000 0.000 0.2
#> SRR2936909 4 0.0000 0.954 0.000 0.000 0.000 1.0
#> SRR2936918 1 0.3610 1.000 0.800 0.000 0.000 0.2
#> SRR2936917 2 0.3610 0.787 0.200 0.800 0.000 0.0
#> SRR2936916 3 0.0000 1.000 0.000 0.000 1.000 0.0
#> SRR2936915 3 0.0000 1.000 0.000 0.000 1.000 0.0
#> SRR2936914 2 0.3610 0.787 0.200 0.800 0.000 0.0
#> SRR2936913 2 0.3610 0.787 0.200 0.800 0.000 0.0
#> SRR2936912 4 0.0000 0.954 0.000 0.000 0.000 1.0
#> SRR2936910 1 0.3610 1.000 0.800 0.000 0.000 0.2
#> SRR2936911 2 0.3610 0.787 0.200 0.800 0.000 0.0
#> SRR2936907 2 0.0000 0.864 0.000 1.000 0.000 0.0
#> SRR2936908 2 0.0000 0.864 0.000 1.000 0.000 0.0
#> SRR2936904 3 0.0000 1.000 0.000 0.000 1.000 0.0
#> SRR2936905 2 0.0000 0.864 0.000 1.000 0.000 0.0
#> SRR2936903 4 0.0000 0.954 0.000 0.000 0.000 1.0
#> SRR2936901 3 0.0000 1.000 0.000 0.000 1.000 0.0
#> SRR2936902 2 0.4331 0.653 0.000 0.712 0.288 0.0
#> SRR2936900 4 0.0000 0.954 0.000 0.000 0.000 1.0
#> SRR2936898 3 0.0000 1.000 0.000 0.000 1.000 0.0
#> SRR2936899 3 0.0000 1.000 0.000 0.000 1.000 0.0
#> SRR2936897 4 0.0000 0.954 0.000 0.000 0.000 1.0
#> SRR2936896 2 0.0188 0.863 0.004 0.996 0.000 0.0
#> SRR2936894 1 0.3610 1.000 0.800 0.000 0.000 0.2
#> SRR2936893 2 0.0000 0.864 0.000 1.000 0.000 0.0
#> SRR2936895 2 0.4331 0.653 0.000 0.712 0.288 0.0
#> SRR2936892 2 0.0000 0.864 0.000 1.000 0.000 0.0
#> SRR2936891 1 0.3610 1.000 0.800 0.000 0.000 0.2
#> SRR2936890 2 0.0000 0.864 0.000 1.000 0.000 0.0
#> SRR2936886 3 0.0000 1.000 0.000 0.000 1.000 0.0
#> SRR2936885 4 0.0000 0.954 0.000 0.000 0.000 1.0
#> SRR2936888 1 0.3610 1.000 0.800 0.000 0.000 0.2
#> SRR2936889 2 0.0000 0.864 0.000 1.000 0.000 0.0
#> SRR2936887 3 0.0000 1.000 0.000 0.000 1.000 0.0
#> SRR2936884 2 0.4331 0.653 0.000 0.712 0.288 0.0
#> SRR2936883 2 0.4331 0.653 0.000 0.712 0.288 0.0
#> SRR2936881 2 0.4331 0.653 0.000 0.712 0.288 0.0
#> SRR2936882 4 0.0000 0.954 0.000 0.000 0.000 1.0
#> SRR2936880 2 0.4331 0.653 0.000 0.712 0.288 0.0
#> SRR2936878 2 0.3610 0.787 0.200 0.800 0.000 0.0
#> SRR2936879 3 0.0000 1.000 0.000 0.000 1.000 0.0
#> SRR2936875 2 0.0000 0.864 0.000 1.000 0.000 0.0
#> SRR2936877 2 0.3610 0.787 0.200 0.800 0.000 0.0
#> SRR2936876 4 0.3610 0.699 0.000 0.000 0.200 0.8
#> SRR2936873 1 0.3610 1.000 0.800 0.000 0.000 0.2
#> SRR2936872 2 0.0000 0.864 0.000 1.000 0.000 0.0
#> SRR2936871 2 0.0000 0.864 0.000 1.000 0.000 0.0
#> SRR2936874 2 0.0000 0.864 0.000 1.000 0.000 0.0
#> SRR2936870 1 0.3610 1.000 0.800 0.000 0.000 0.2
#> SRR2936869 3 0.0000 1.000 0.000 0.000 1.000 0.0
#> SRR2936868 3 0.0000 1.000 0.000 0.000 1.000 0.0
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR2936906 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000
#> SRR2936909 3 0.3074 0.9586 0.196 0.000 0.804 0.000 0.000
#> SRR2936918 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000
#> SRR2936917 5 0.3730 1.0000 0.000 0.288 0.000 0.000 0.712
#> SRR2936916 4 0.4951 0.8046 0.000 0.000 0.196 0.704 0.100
#> SRR2936915 4 0.4951 0.8046 0.000 0.000 0.196 0.704 0.100
#> SRR2936914 5 0.3730 1.0000 0.000 0.288 0.000 0.000 0.712
#> SRR2936913 5 0.3730 1.0000 0.000 0.288 0.000 0.000 0.712
#> SRR2936912 3 0.3074 0.9586 0.196 0.000 0.804 0.000 0.000
#> SRR2936910 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000
#> SRR2936911 5 0.3730 1.0000 0.000 0.288 0.000 0.000 0.712
#> SRR2936907 2 0.0000 0.8209 0.000 1.000 0.000 0.000 0.000
#> SRR2936908 2 0.0000 0.8209 0.000 1.000 0.000 0.000 0.000
#> SRR2936904 4 0.0000 0.7982 0.000 0.000 0.000 1.000 0.000
#> SRR2936905 2 0.0000 0.8209 0.000 1.000 0.000 0.000 0.000
#> SRR2936903 3 0.3074 0.9586 0.196 0.000 0.804 0.000 0.000
#> SRR2936901 4 0.6333 0.7301 0.000 0.000 0.196 0.516 0.288
#> SRR2936902 2 0.3730 0.6965 0.000 0.712 0.000 0.000 0.288
#> SRR2936900 3 0.3074 0.9586 0.196 0.000 0.804 0.000 0.000
#> SRR2936898 4 0.6333 0.7301 0.000 0.000 0.196 0.516 0.288
#> SRR2936899 4 0.6333 0.7301 0.000 0.000 0.196 0.516 0.288
#> SRR2936897 3 0.3074 0.9586 0.196 0.000 0.804 0.000 0.000
#> SRR2936896 2 0.3876 0.0877 0.000 0.684 0.000 0.000 0.316
#> SRR2936894 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000
#> SRR2936893 2 0.0000 0.8209 0.000 1.000 0.000 0.000 0.000
#> SRR2936895 2 0.4886 0.6411 0.000 0.712 0.000 0.188 0.100
#> SRR2936892 2 0.0000 0.8209 0.000 1.000 0.000 0.000 0.000
#> SRR2936891 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000
#> SRR2936890 2 0.0000 0.8209 0.000 1.000 0.000 0.000 0.000
#> SRR2936886 4 0.0000 0.7982 0.000 0.000 0.000 1.000 0.000
#> SRR2936885 3 0.3074 0.9586 0.196 0.000 0.804 0.000 0.000
#> SRR2936888 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000
#> SRR2936889 2 0.0000 0.8209 0.000 1.000 0.000 0.000 0.000
#> SRR2936887 4 0.0000 0.7982 0.000 0.000 0.000 1.000 0.000
#> SRR2936884 2 0.3730 0.6965 0.000 0.712 0.000 0.000 0.288
#> SRR2936883 2 0.3730 0.6965 0.000 0.712 0.000 0.000 0.288
#> SRR2936881 2 0.3730 0.6965 0.000 0.712 0.000 0.000 0.288
#> SRR2936882 3 0.3074 0.9586 0.196 0.000 0.804 0.000 0.000
#> SRR2936880 2 0.3730 0.6965 0.000 0.712 0.000 0.000 0.288
#> SRR2936878 5 0.3730 1.0000 0.000 0.288 0.000 0.000 0.712
#> SRR2936879 4 0.4951 0.8046 0.000 0.000 0.196 0.704 0.100
#> SRR2936875 2 0.0000 0.8209 0.000 1.000 0.000 0.000 0.000
#> SRR2936877 5 0.3730 1.0000 0.000 0.288 0.000 0.000 0.712
#> SRR2936876 3 0.0162 0.7174 0.000 0.000 0.996 0.004 0.000
#> SRR2936873 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000
#> SRR2936872 2 0.0000 0.8209 0.000 1.000 0.000 0.000 0.000
#> SRR2936871 2 0.0000 0.8209 0.000 1.000 0.000 0.000 0.000
#> SRR2936874 2 0.0000 0.8209 0.000 1.000 0.000 0.000 0.000
#> SRR2936870 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000
#> SRR2936869 4 0.0000 0.7982 0.000 0.000 0.000 1.000 0.000
#> SRR2936868 4 0.0000 0.7982 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
#> SRR2936906 1 0.000 0.9687 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936909 6 0.000 0.7161 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR2936918 1 0.000 0.9687 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936917 5 0.000 0.9064 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936916 3 0.181 0.7721 0.000 0.100 0.900 0.000 0.000 0.000
#> SRR2936915 3 0.181 0.7721 0.000 0.100 0.900 0.000 0.000 0.000
#> SRR2936914 5 0.000 0.9064 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936913 5 0.000 0.9064 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936912 6 0.000 0.7161 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR2936910 1 0.000 0.9687 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936911 5 0.000 0.9064 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936907 2 0.335 0.8243 0.000 0.712 0.000 0.000 0.288 0.000
#> SRR2936908 2 0.335 0.8243 0.000 0.712 0.000 0.000 0.288 0.000
#> SRR2936904 4 0.387 1.0000 0.000 0.000 0.492 0.508 0.000 0.000
#> SRR2936905 2 0.335 0.8243 0.000 0.712 0.000 0.000 0.288 0.000
#> SRR2936903 6 0.387 0.7409 0.000 0.000 0.000 0.492 0.000 0.508
#> SRR2936901 3 0.335 0.8111 0.000 0.288 0.712 0.000 0.000 0.000
#> SRR2936902 2 0.000 0.6965 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936900 6 0.387 0.7409 0.000 0.000 0.000 0.492 0.000 0.508
#> SRR2936898 3 0.335 0.8111 0.000 0.288 0.712 0.000 0.000 0.000
#> SRR2936899 3 0.335 0.8111 0.000 0.288 0.712 0.000 0.000 0.000
#> SRR2936897 6 0.000 0.7161 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR2936896 5 0.375 -0.0877 0.000 0.396 0.000 0.000 0.604 0.000
#> SRR2936894 1 0.000 0.9687 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936893 2 0.335 0.8243 0.000 0.712 0.000 0.000 0.288 0.000
#> SRR2936895 2 0.270 0.6325 0.000 0.812 0.188 0.000 0.000 0.000
#> SRR2936892 2 0.335 0.8243 0.000 0.712 0.000 0.000 0.288 0.000
#> SRR2936891 1 0.000 0.9687 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936890 2 0.335 0.8243 0.000 0.712 0.000 0.000 0.288 0.000
#> SRR2936886 4 0.387 1.0000 0.000 0.000 0.492 0.508 0.000 0.000
#> SRR2936885 6 0.387 0.7409 0.000 0.000 0.000 0.492 0.000 0.508
#> SRR2936888 1 0.000 0.9687 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936889 2 0.335 0.8243 0.000 0.712 0.000 0.000 0.288 0.000
#> SRR2936887 4 0.387 1.0000 0.000 0.000 0.492 0.508 0.000 0.000
#> SRR2936884 2 0.000 0.6965 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936883 2 0.000 0.6965 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936881 2 0.000 0.6965 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936882 6 0.387 0.7409 0.000 0.000 0.000 0.492 0.000 0.508
#> SRR2936880 2 0.000 0.6965 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936878 5 0.000 0.9064 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936879 3 0.181 0.7721 0.000 0.100 0.900 0.000 0.000 0.000
#> SRR2936875 2 0.335 0.8243 0.000 0.712 0.000 0.000 0.288 0.000
#> SRR2936877 5 0.000 0.9064 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936876 6 0.279 0.4960 0.000 0.000 0.200 0.000 0.000 0.800
#> SRR2936873 1 0.276 0.7335 0.804 0.000 0.000 0.000 0.000 0.196
#> SRR2936872 2 0.335 0.8243 0.000 0.712 0.000 0.000 0.288 0.000
#> SRR2936871 2 0.335 0.8243 0.000 0.712 0.000 0.000 0.288 0.000
#> SRR2936874 2 0.335 0.8243 0.000 0.712 0.000 0.000 0.288 0.000
#> SRR2936870 1 0.000 0.9687 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936869 4 0.387 1.0000 0.000 0.000 0.492 0.508 0.000 0.000
#> SRR2936868 4 0.387 1.0000 0.000 0.000 0.492 0.508 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
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 14198 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 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 0.776 0.847 0.934 0.4929 0.490 0.490
#> 3 3 0.887 0.770 0.900 0.3436 0.829 0.662
#> 4 4 0.747 0.790 0.825 0.0970 0.859 0.653
#> 5 5 0.729 0.787 0.761 0.0701 0.893 0.667
#> 6 6 0.815 0.791 0.774 0.0434 0.940 0.729
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
#> SRR2936906 1 0.000 0.8691 1.000 0.000
#> SRR2936909 1 0.000 0.8691 1.000 0.000
#> SRR2936918 1 0.000 0.8691 1.000 0.000
#> SRR2936917 2 0.000 0.9788 0.000 1.000
#> SRR2936916 2 0.000 0.9788 0.000 1.000
#> SRR2936915 1 0.993 0.3553 0.548 0.452
#> SRR2936914 2 0.000 0.9788 0.000 1.000
#> SRR2936913 2 0.000 0.9788 0.000 1.000
#> SRR2936912 1 0.000 0.8691 1.000 0.000
#> SRR2936910 1 0.000 0.8691 1.000 0.000
#> SRR2936911 2 0.000 0.9788 0.000 1.000
#> SRR2936907 2 0.000 0.9788 0.000 1.000
#> SRR2936908 2 0.000 0.9788 0.000 1.000
#> SRR2936904 1 0.311 0.8394 0.944 0.056
#> SRR2936905 2 0.000 0.9788 0.000 1.000
#> SRR2936903 1 0.000 0.8691 1.000 0.000
#> SRR2936901 1 0.204 0.8537 0.968 0.032
#> SRR2936902 2 0.000 0.9788 0.000 1.000
#> SRR2936900 1 0.000 0.8691 1.000 0.000
#> SRR2936898 1 0.900 0.5996 0.684 0.316
#> SRR2936899 1 0.993 0.3553 0.548 0.452
#> SRR2936897 1 0.000 0.8691 1.000 0.000
#> SRR2936896 2 0.000 0.9788 0.000 1.000
#> SRR2936894 1 0.000 0.8691 1.000 0.000
#> SRR2936893 2 0.000 0.9788 0.000 1.000
#> SRR2936895 2 0.000 0.9788 0.000 1.000
#> SRR2936892 2 0.000 0.9788 0.000 1.000
#> SRR2936891 1 0.000 0.8691 1.000 0.000
#> SRR2936890 2 0.000 0.9788 0.000 1.000
#> SRR2936886 1 0.958 0.5075 0.620 0.380
#> SRR2936885 1 0.000 0.8691 1.000 0.000
#> SRR2936888 1 0.000 0.8691 1.000 0.000
#> SRR2936889 2 0.000 0.9788 0.000 1.000
#> SRR2936887 1 0.958 0.5075 0.620 0.380
#> SRR2936884 2 0.000 0.9788 0.000 1.000
#> SRR2936883 2 0.000 0.9788 0.000 1.000
#> SRR2936881 2 0.000 0.9788 0.000 1.000
#> SRR2936882 1 0.000 0.8691 1.000 0.000
#> SRR2936880 2 0.000 0.9788 0.000 1.000
#> SRR2936878 2 0.000 0.9788 0.000 1.000
#> SRR2936879 1 0.996 0.3231 0.536 0.464
#> SRR2936875 2 0.000 0.9788 0.000 1.000
#> SRR2936877 2 0.000 0.9788 0.000 1.000
#> SRR2936876 1 0.000 0.8691 1.000 0.000
#> SRR2936873 1 0.000 0.8691 1.000 0.000
#> SRR2936872 2 0.000 0.9788 0.000 1.000
#> SRR2936871 2 0.000 0.9788 0.000 1.000
#> SRR2936874 2 0.000 0.9788 0.000 1.000
#> SRR2936870 1 0.000 0.8691 1.000 0.000
#> SRR2936869 2 0.988 -0.0328 0.436 0.564
#> SRR2936868 1 0.958 0.5075 0.620 0.380
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR2936906 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936909 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936918 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936917 2 0.6307 0.781 0.000 0.512 0.488
#> SRR2936916 3 0.6309 0.949 0.000 0.496 0.504
#> SRR2936915 3 0.6308 0.953 0.000 0.492 0.508
#> SRR2936914 2 0.6307 0.781 0.000 0.512 0.488
#> SRR2936913 2 0.6307 0.781 0.000 0.512 0.488
#> SRR2936912 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936910 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936911 2 0.6307 0.781 0.000 0.512 0.488
#> SRR2936907 2 0.6307 0.781 0.000 0.512 0.488
#> SRR2936908 2 0.6111 0.796 0.000 0.604 0.396
#> SRR2936904 3 0.8466 0.854 0.092 0.400 0.508
#> SRR2936905 2 0.6111 0.796 0.000 0.604 0.396
#> SRR2936903 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936901 3 0.6520 0.950 0.004 0.488 0.508
#> SRR2936902 2 0.4399 -0.298 0.000 0.812 0.188
#> SRR2936900 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936898 3 0.6308 0.953 0.000 0.492 0.508
#> SRR2936899 3 0.6308 0.953 0.000 0.492 0.508
#> SRR2936897 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936896 2 0.6307 0.781 0.000 0.512 0.488
#> SRR2936894 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936893 2 0.6111 0.796 0.000 0.604 0.396
#> SRR2936895 2 0.3619 -0.144 0.000 0.864 0.136
#> SRR2936892 2 0.6111 0.796 0.000 0.604 0.396
#> SRR2936891 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936890 2 0.6111 0.796 0.000 0.604 0.396
#> SRR2936886 3 0.6308 0.953 0.000 0.492 0.508
#> SRR2936885 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936888 1 0.0237 0.997 0.996 0.000 0.004
#> SRR2936889 2 0.6111 0.796 0.000 0.604 0.396
#> SRR2936887 3 0.6308 0.953 0.000 0.492 0.508
#> SRR2936884 2 0.0000 0.256 0.000 1.000 0.000
#> SRR2936883 2 0.4399 -0.298 0.000 0.812 0.188
#> SRR2936881 2 0.4399 -0.298 0.000 0.812 0.188
#> SRR2936882 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936880 2 0.3619 -0.144 0.000 0.864 0.136
#> SRR2936878 2 0.6307 0.781 0.000 0.512 0.488
#> SRR2936879 3 0.6308 0.953 0.000 0.492 0.508
#> SRR2936875 2 0.6111 0.796 0.000 0.604 0.396
#> SRR2936877 2 0.6307 0.781 0.000 0.512 0.488
#> SRR2936876 3 0.9387 0.610 0.272 0.220 0.508
#> SRR2936873 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936872 2 0.6111 0.796 0.000 0.604 0.396
#> SRR2936871 2 0.6111 0.796 0.000 0.604 0.396
#> SRR2936874 2 0.6111 0.796 0.000 0.604 0.396
#> SRR2936870 1 0.0237 0.997 0.996 0.000 0.004
#> SRR2936869 3 0.6308 0.953 0.000 0.492 0.508
#> SRR2936868 3 0.6308 0.953 0.000 0.492 0.508
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR2936906 1 0.0000 0.929 1.000 0.000 0.000 NA
#> SRR2936909 1 0.2081 0.921 0.916 0.000 0.000 NA
#> SRR2936918 1 0.0000 0.929 1.000 0.000 0.000 NA
#> SRR2936917 2 0.4643 0.748 0.000 0.656 0.000 NA
#> SRR2936916 3 0.4245 0.725 0.000 0.116 0.820 NA
#> SRR2936915 3 0.1716 0.745 0.000 0.000 0.936 NA
#> SRR2936914 2 0.4643 0.748 0.000 0.656 0.000 NA
#> SRR2936913 2 0.4643 0.748 0.000 0.656 0.000 NA
#> SRR2936912 1 0.2081 0.921 0.916 0.000 0.000 NA
#> SRR2936910 1 0.0000 0.929 1.000 0.000 0.000 NA
#> SRR2936911 2 0.4643 0.748 0.000 0.656 0.000 NA
#> SRR2936907 2 0.1211 0.848 0.000 0.960 0.000 NA
#> SRR2936908 2 0.0707 0.858 0.000 0.980 0.020 NA
#> SRR2936904 3 0.5513 0.646 0.004 0.016 0.596 NA
#> SRR2936905 2 0.0779 0.858 0.000 0.980 0.016 NA
#> SRR2936903 1 0.3764 0.877 0.784 0.000 0.000 NA
#> SRR2936901 3 0.2081 0.733 0.000 0.000 0.916 NA
#> SRR2936902 3 0.4903 0.648 0.000 0.248 0.724 NA
#> SRR2936900 1 0.3764 0.877 0.784 0.000 0.000 NA
#> SRR2936898 3 0.0469 0.746 0.000 0.000 0.988 NA
#> SRR2936899 3 0.0469 0.746 0.000 0.000 0.988 NA
#> SRR2936897 1 0.2530 0.914 0.888 0.000 0.000 NA
#> SRR2936896 2 0.2589 0.828 0.000 0.884 0.000 NA
#> SRR2936894 1 0.0000 0.929 1.000 0.000 0.000 NA
#> SRR2936893 2 0.0707 0.858 0.000 0.980 0.020 NA
#> SRR2936895 3 0.5055 0.640 0.000 0.256 0.712 NA
#> SRR2936892 2 0.0707 0.858 0.000 0.980 0.020 NA
#> SRR2936891 1 0.0000 0.929 1.000 0.000 0.000 NA
#> SRR2936890 2 0.0707 0.858 0.000 0.980 0.020 NA
#> SRR2936886 3 0.5746 0.657 0.000 0.040 0.612 NA
#> SRR2936885 1 0.3764 0.877 0.784 0.000 0.000 NA
#> SRR2936888 1 0.1637 0.905 0.940 0.000 0.000 NA
#> SRR2936889 2 0.0707 0.858 0.000 0.980 0.020 NA
#> SRR2936887 3 0.5746 0.657 0.000 0.040 0.612 NA
#> SRR2936884 3 0.5478 0.511 0.000 0.344 0.628 NA
#> SRR2936883 3 0.4903 0.648 0.000 0.248 0.724 NA
#> SRR2936881 3 0.4903 0.648 0.000 0.248 0.724 NA
#> SRR2936882 1 0.3764 0.877 0.784 0.000 0.000 NA
#> SRR2936880 3 0.4964 0.639 0.000 0.256 0.716 NA
#> SRR2936878 2 0.4643 0.748 0.000 0.656 0.000 NA
#> SRR2936879 3 0.1716 0.745 0.000 0.000 0.936 NA
#> SRR2936875 2 0.0707 0.858 0.000 0.980 0.020 NA
#> SRR2936877 2 0.4643 0.748 0.000 0.656 0.000 NA
#> SRR2936876 3 0.6386 0.470 0.212 0.000 0.648 NA
#> SRR2936873 1 0.0000 0.929 1.000 0.000 0.000 NA
#> SRR2936872 2 0.0779 0.858 0.000 0.980 0.016 NA
#> SRR2936871 2 0.0707 0.858 0.000 0.980 0.020 NA
#> SRR2936874 2 0.0707 0.858 0.000 0.980 0.020 NA
#> SRR2936870 1 0.1637 0.905 0.940 0.000 0.000 NA
#> SRR2936869 3 0.5746 0.657 0.000 0.040 0.612 NA
#> SRR2936868 3 0.5746 0.657 0.000 0.040 0.612 NA
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR2936906 1 0.4262 0.8410 0.560 0.000 0.000 0.440 0.000
#> SRR2936909 1 0.4572 0.8197 0.684 0.000 0.000 0.280 0.036
#> SRR2936918 1 0.4262 0.8410 0.560 0.000 0.000 0.440 0.000
#> SRR2936917 5 0.4161 1.0000 0.000 0.392 0.000 0.000 0.608
#> SRR2936916 3 0.5089 0.6727 0.000 0.072 0.756 0.068 0.104
#> SRR2936915 3 0.5422 0.4219 0.000 0.004 0.668 0.208 0.120
#> SRR2936914 5 0.4161 1.0000 0.000 0.392 0.000 0.000 0.608
#> SRR2936913 5 0.4161 1.0000 0.000 0.392 0.000 0.000 0.608
#> SRR2936912 1 0.4594 0.8207 0.680 0.000 0.000 0.284 0.036
#> SRR2936910 1 0.4262 0.8410 0.560 0.000 0.000 0.440 0.000
#> SRR2936911 5 0.4161 1.0000 0.000 0.392 0.000 0.000 0.608
#> SRR2936907 2 0.0510 0.9069 0.000 0.984 0.000 0.000 0.016
#> SRR2936908 2 0.0290 0.9243 0.000 0.992 0.008 0.000 0.000
#> SRR2936904 4 0.6715 0.8948 0.016 0.000 0.204 0.520 0.260
#> SRR2936905 2 0.0162 0.9226 0.000 0.996 0.000 0.000 0.004
#> SRR2936903 1 0.1393 0.6564 0.956 0.000 0.012 0.008 0.024
#> SRR2936901 3 0.4189 0.6362 0.060 0.000 0.816 0.080 0.044
#> SRR2936902 3 0.2230 0.7393 0.000 0.116 0.884 0.000 0.000
#> SRR2936900 1 0.0404 0.6863 0.988 0.000 0.012 0.000 0.000
#> SRR2936898 3 0.2989 0.6585 0.000 0.004 0.872 0.080 0.044
#> SRR2936899 3 0.2989 0.6585 0.000 0.004 0.872 0.080 0.044
#> SRR2936897 1 0.4210 0.8017 0.740 0.000 0.000 0.224 0.036
#> SRR2936896 2 0.4227 -0.5269 0.000 0.580 0.000 0.000 0.420
#> SRR2936894 1 0.4262 0.8410 0.560 0.000 0.000 0.440 0.000
#> SRR2936893 2 0.0290 0.9243 0.000 0.992 0.008 0.000 0.000
#> SRR2936895 3 0.2818 0.7333 0.000 0.128 0.860 0.008 0.004
#> SRR2936892 2 0.0290 0.9243 0.000 0.992 0.008 0.000 0.000
#> SRR2936891 1 0.4262 0.8410 0.560 0.000 0.000 0.440 0.000
#> SRR2936890 2 0.0000 0.9249 0.000 1.000 0.000 0.000 0.000
#> SRR2936886 4 0.6606 0.9734 0.000 0.008 0.268 0.512 0.212
#> SRR2936885 1 0.0404 0.6863 0.988 0.000 0.012 0.000 0.000
#> SRR2936888 1 0.5680 0.8036 0.492 0.000 0.000 0.428 0.080
#> SRR2936889 2 0.0000 0.9249 0.000 1.000 0.000 0.000 0.000
#> SRR2936887 4 0.6606 0.9734 0.000 0.008 0.268 0.512 0.212
#> SRR2936884 3 0.2648 0.7112 0.000 0.152 0.848 0.000 0.000
#> SRR2936883 3 0.2230 0.7393 0.000 0.116 0.884 0.000 0.000
#> SRR2936881 3 0.2230 0.7393 0.000 0.116 0.884 0.000 0.000
#> SRR2936882 1 0.0404 0.6863 0.988 0.000 0.012 0.000 0.000
#> SRR2936880 3 0.2377 0.7330 0.000 0.128 0.872 0.000 0.000
#> SRR2936878 5 0.4161 1.0000 0.000 0.392 0.000 0.000 0.608
#> SRR2936879 3 0.5422 0.4219 0.000 0.004 0.668 0.208 0.120
#> SRR2936875 2 0.0290 0.9243 0.000 0.992 0.008 0.000 0.000
#> SRR2936877 5 0.4161 1.0000 0.000 0.392 0.000 0.000 0.608
#> SRR2936876 3 0.8239 0.0562 0.272 0.000 0.376 0.212 0.140
#> SRR2936873 1 0.4262 0.8410 0.560 0.000 0.000 0.440 0.000
#> SRR2936872 2 0.0162 0.9226 0.000 0.996 0.000 0.000 0.004
#> SRR2936871 2 0.0000 0.9249 0.000 1.000 0.000 0.000 0.000
#> SRR2936874 2 0.0290 0.9243 0.000 0.992 0.008 0.000 0.000
#> SRR2936870 1 0.5680 0.8036 0.492 0.000 0.000 0.428 0.080
#> SRR2936869 4 0.6606 0.9734 0.000 0.008 0.268 0.512 0.212
#> SRR2936868 4 0.6606 0.9734 0.000 0.008 0.268 0.512 0.212
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR2936906 1 0.0260 0.8229 0.992 0.000 0.000 0.000 0.008 0.000
#> SRR2936909 1 0.4955 0.5164 0.712 0.000 0.020 0.016 0.076 0.176
#> SRR2936918 1 0.0000 0.8222 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936917 5 0.3482 0.9676 0.000 0.316 0.000 0.000 0.684 0.000
#> SRR2936916 3 0.7284 0.5626 0.000 0.040 0.484 0.072 0.156 0.248
#> SRR2936915 3 0.7377 0.4533 0.000 0.004 0.404 0.148 0.160 0.284
#> SRR2936914 5 0.3482 0.9676 0.000 0.316 0.000 0.000 0.684 0.000
#> SRR2936913 5 0.3482 0.9676 0.000 0.316 0.000 0.000 0.684 0.000
#> SRR2936912 1 0.4955 0.5164 0.712 0.000 0.020 0.016 0.076 0.176
#> SRR2936910 1 0.0000 0.8222 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936911 5 0.3482 0.9676 0.000 0.316 0.000 0.000 0.684 0.000
#> SRR2936907 2 0.0405 0.9670 0.000 0.988 0.000 0.000 0.004 0.008
#> SRR2936908 2 0.0935 0.9717 0.000 0.964 0.000 0.004 0.000 0.032
#> SRR2936904 4 0.3772 0.8214 0.000 0.000 0.032 0.812 0.088 0.068
#> SRR2936905 2 0.0146 0.9733 0.000 0.996 0.000 0.000 0.000 0.004
#> SRR2936903 6 0.3221 0.5967 0.264 0.000 0.000 0.000 0.000 0.736
#> SRR2936901 3 0.4897 0.6935 0.000 0.000 0.672 0.040 0.044 0.244
#> SRR2936902 3 0.1349 0.7582 0.000 0.056 0.940 0.004 0.000 0.000
#> SRR2936900 6 0.3695 0.6277 0.376 0.000 0.000 0.000 0.000 0.624
#> SRR2936898 3 0.4917 0.7077 0.000 0.008 0.700 0.040 0.044 0.208
#> SRR2936899 3 0.4917 0.7077 0.000 0.008 0.700 0.040 0.044 0.208
#> SRR2936897 1 0.5185 0.4444 0.680 0.000 0.020 0.016 0.076 0.208
#> SRR2936896 5 0.4234 0.7721 0.000 0.440 0.000 0.000 0.544 0.016
#> SRR2936894 1 0.0260 0.8229 0.992 0.000 0.000 0.000 0.008 0.000
#> SRR2936893 2 0.0935 0.9717 0.000 0.964 0.000 0.004 0.000 0.032
#> SRR2936895 3 0.1707 0.7547 0.000 0.056 0.928 0.012 0.000 0.004
#> SRR2936892 2 0.0935 0.9717 0.000 0.964 0.000 0.004 0.000 0.032
#> SRR2936891 1 0.0260 0.8229 0.992 0.000 0.000 0.000 0.008 0.000
#> SRR2936890 2 0.0000 0.9749 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936886 4 0.1141 0.9581 0.000 0.000 0.052 0.948 0.000 0.000
#> SRR2936885 6 0.3695 0.6277 0.376 0.000 0.000 0.000 0.000 0.624
#> SRR2936888 1 0.3339 0.7282 0.856 0.000 0.024 0.024 0.064 0.032
#> SRR2936889 2 0.0000 0.9749 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936887 4 0.1141 0.9581 0.000 0.000 0.052 0.948 0.000 0.000
#> SRR2936884 3 0.1555 0.7540 0.000 0.060 0.932 0.004 0.000 0.004
#> SRR2936883 3 0.1349 0.7582 0.000 0.056 0.940 0.004 0.000 0.000
#> SRR2936881 3 0.1349 0.7582 0.000 0.056 0.940 0.004 0.000 0.000
#> SRR2936882 6 0.3695 0.6277 0.376 0.000 0.000 0.000 0.000 0.624
#> SRR2936880 3 0.1349 0.7582 0.000 0.056 0.940 0.004 0.000 0.000
#> SRR2936878 5 0.3482 0.9676 0.000 0.316 0.000 0.000 0.684 0.000
#> SRR2936879 3 0.7450 0.4626 0.000 0.008 0.404 0.148 0.156 0.284
#> SRR2936875 2 0.0935 0.9717 0.000 0.964 0.000 0.004 0.000 0.032
#> SRR2936877 5 0.3619 0.9654 0.000 0.316 0.000 0.000 0.680 0.004
#> SRR2936876 6 0.7775 -0.0525 0.076 0.000 0.140 0.096 0.232 0.456
#> SRR2936873 1 0.0260 0.8229 0.992 0.000 0.000 0.000 0.008 0.000
#> SRR2936872 2 0.0146 0.9733 0.000 0.996 0.000 0.000 0.000 0.004
#> SRR2936871 2 0.0000 0.9749 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936874 2 0.0935 0.9717 0.000 0.964 0.000 0.004 0.000 0.032
#> SRR2936870 1 0.3339 0.7282 0.856 0.000 0.024 0.024 0.064 0.032
#> SRR2936869 4 0.1141 0.9581 0.000 0.000 0.052 0.948 0.000 0.000
#> SRR2936868 4 0.1141 0.9581 0.000 0.000 0.052 0.948 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
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 14198 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 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 0.885 0.954 0.979 0.5087 0.490 0.490
#> 3 3 0.797 0.888 0.928 0.1851 0.918 0.832
#> 4 4 0.941 0.954 0.973 0.1557 0.867 0.684
#> 5 5 0.790 0.704 0.858 0.0798 0.954 0.848
#> 6 6 0.814 0.663 0.848 0.0426 0.915 0.697
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
#> SRR2936906 1 0.000 0.958 1.000 0.000
#> SRR2936909 1 0.000 0.958 1.000 0.000
#> SRR2936918 1 0.000 0.958 1.000 0.000
#> SRR2936917 2 0.000 0.997 0.000 1.000
#> SRR2936916 2 0.311 0.937 0.056 0.944
#> SRR2936915 1 0.000 0.958 1.000 0.000
#> SRR2936914 2 0.000 0.997 0.000 1.000
#> SRR2936913 2 0.000 0.997 0.000 1.000
#> SRR2936912 1 0.000 0.958 1.000 0.000
#> SRR2936910 1 0.000 0.958 1.000 0.000
#> SRR2936911 2 0.000 0.997 0.000 1.000
#> SRR2936907 2 0.000 0.997 0.000 1.000
#> SRR2936908 2 0.000 0.997 0.000 1.000
#> SRR2936904 1 0.000 0.958 1.000 0.000
#> SRR2936905 2 0.000 0.997 0.000 1.000
#> SRR2936903 1 0.000 0.958 1.000 0.000
#> SRR2936901 1 0.000 0.958 1.000 0.000
#> SRR2936902 2 0.000 0.997 0.000 1.000
#> SRR2936900 1 0.000 0.958 1.000 0.000
#> SRR2936898 1 0.000 0.958 1.000 0.000
#> SRR2936899 1 0.000 0.958 1.000 0.000
#> SRR2936897 1 0.000 0.958 1.000 0.000
#> SRR2936896 2 0.000 0.997 0.000 1.000
#> SRR2936894 1 0.000 0.958 1.000 0.000
#> SRR2936893 2 0.000 0.997 0.000 1.000
#> SRR2936895 2 0.000 0.997 0.000 1.000
#> SRR2936892 2 0.000 0.997 0.000 1.000
#> SRR2936891 1 0.000 0.958 1.000 0.000
#> SRR2936890 2 0.000 0.997 0.000 1.000
#> SRR2936886 1 0.722 0.770 0.800 0.200
#> SRR2936885 1 0.000 0.958 1.000 0.000
#> SRR2936888 1 0.000 0.958 1.000 0.000
#> SRR2936889 2 0.000 0.997 0.000 1.000
#> SRR2936887 1 0.722 0.770 0.800 0.200
#> SRR2936884 2 0.000 0.997 0.000 1.000
#> SRR2936883 2 0.000 0.997 0.000 1.000
#> SRR2936881 2 0.000 0.997 0.000 1.000
#> SRR2936882 1 0.000 0.958 1.000 0.000
#> SRR2936880 2 0.000 0.997 0.000 1.000
#> SRR2936878 2 0.000 0.997 0.000 1.000
#> SRR2936879 1 0.184 0.937 0.972 0.028
#> SRR2936875 2 0.000 0.997 0.000 1.000
#> SRR2936877 2 0.000 0.997 0.000 1.000
#> SRR2936876 1 0.000 0.958 1.000 0.000
#> SRR2936873 1 0.000 0.958 1.000 0.000
#> SRR2936872 2 0.000 0.997 0.000 1.000
#> SRR2936871 2 0.000 0.997 0.000 1.000
#> SRR2936874 2 0.000 0.997 0.000 1.000
#> SRR2936870 1 0.000 0.958 1.000 0.000
#> SRR2936869 1 0.971 0.393 0.600 0.400
#> SRR2936868 1 0.722 0.770 0.800 0.200
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR2936906 1 0.0000 0.951 1.000 0.000 0.000
#> SRR2936909 1 0.0000 0.951 1.000 0.000 0.000
#> SRR2936918 1 0.0000 0.951 1.000 0.000 0.000
#> SRR2936917 2 0.0000 0.925 0.000 1.000 0.000
#> SRR2936916 2 0.2711 0.830 0.088 0.912 0.000
#> SRR2936915 1 0.0000 0.951 1.000 0.000 0.000
#> SRR2936914 2 0.0000 0.925 0.000 1.000 0.000
#> SRR2936913 2 0.0000 0.925 0.000 1.000 0.000
#> SRR2936912 1 0.0000 0.951 1.000 0.000 0.000
#> SRR2936910 1 0.0000 0.951 1.000 0.000 0.000
#> SRR2936911 2 0.0000 0.925 0.000 1.000 0.000
#> SRR2936907 2 0.0000 0.925 0.000 1.000 0.000
#> SRR2936908 2 0.0000 0.925 0.000 1.000 0.000
#> SRR2936904 3 0.5363 0.641 0.276 0.000 0.724
#> SRR2936905 2 0.0000 0.925 0.000 1.000 0.000
#> SRR2936903 1 0.0000 0.951 1.000 0.000 0.000
#> SRR2936901 1 0.5363 0.666 0.724 0.000 0.276
#> SRR2936902 2 0.5363 0.694 0.000 0.724 0.276
#> SRR2936900 1 0.0000 0.951 1.000 0.000 0.000
#> SRR2936898 1 0.5363 0.666 0.724 0.000 0.276
#> SRR2936899 1 0.5363 0.666 0.724 0.000 0.276
#> SRR2936897 1 0.0000 0.951 1.000 0.000 0.000
#> SRR2936896 2 0.0000 0.925 0.000 1.000 0.000
#> SRR2936894 1 0.0000 0.951 1.000 0.000 0.000
#> SRR2936893 2 0.0000 0.925 0.000 1.000 0.000
#> SRR2936895 2 0.0000 0.925 0.000 1.000 0.000
#> SRR2936892 2 0.0000 0.925 0.000 1.000 0.000
#> SRR2936891 1 0.0000 0.951 1.000 0.000 0.000
#> SRR2936890 2 0.0000 0.925 0.000 1.000 0.000
#> SRR2936886 3 0.6841 0.922 0.076 0.200 0.724
#> SRR2936885 1 0.0000 0.951 1.000 0.000 0.000
#> SRR2936888 1 0.0000 0.951 1.000 0.000 0.000
#> SRR2936889 2 0.0000 0.925 0.000 1.000 0.000
#> SRR2936887 3 0.6841 0.922 0.076 0.200 0.724
#> SRR2936884 2 0.5363 0.694 0.000 0.724 0.276
#> SRR2936883 2 0.5363 0.694 0.000 0.724 0.276
#> SRR2936881 2 0.5363 0.694 0.000 0.724 0.276
#> SRR2936882 1 0.0000 0.951 1.000 0.000 0.000
#> SRR2936880 2 0.5363 0.694 0.000 0.724 0.276
#> SRR2936878 2 0.0000 0.925 0.000 1.000 0.000
#> SRR2936879 1 0.0237 0.947 0.996 0.004 0.000
#> SRR2936875 2 0.0000 0.925 0.000 1.000 0.000
#> SRR2936877 2 0.0000 0.925 0.000 1.000 0.000
#> SRR2936876 1 0.0000 0.951 1.000 0.000 0.000
#> SRR2936873 1 0.0000 0.951 1.000 0.000 0.000
#> SRR2936872 2 0.0000 0.925 0.000 1.000 0.000
#> SRR2936871 2 0.0000 0.925 0.000 1.000 0.000
#> SRR2936874 2 0.0000 0.925 0.000 1.000 0.000
#> SRR2936870 1 0.0000 0.951 1.000 0.000 0.000
#> SRR2936869 3 0.6804 0.917 0.072 0.204 0.724
#> SRR2936868 3 0.6841 0.922 0.076 0.200 0.724
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR2936906 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> SRR2936909 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> SRR2936918 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> SRR2936917 2 0.1302 0.973 0.000 0.956 0.044 0.000
#> SRR2936916 2 0.1807 0.963 0.008 0.940 0.052 0.000
#> SRR2936915 1 0.0336 0.982 0.992 0.000 0.008 0.000
#> SRR2936914 2 0.1302 0.973 0.000 0.956 0.044 0.000
#> SRR2936913 2 0.1302 0.973 0.000 0.956 0.044 0.000
#> SRR2936912 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> SRR2936910 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> SRR2936911 2 0.1302 0.973 0.000 0.956 0.044 0.000
#> SRR2936907 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> SRR2936908 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> SRR2936904 4 0.4103 0.639 0.256 0.000 0.000 0.744
#> SRR2936905 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> SRR2936903 1 0.1557 0.951 0.944 0.000 0.056 0.000
#> SRR2936901 3 0.1557 0.876 0.056 0.000 0.944 0.000
#> SRR2936902 3 0.1716 0.927 0.000 0.064 0.936 0.000
#> SRR2936900 1 0.1474 0.954 0.948 0.000 0.052 0.000
#> SRR2936898 3 0.1557 0.876 0.056 0.000 0.944 0.000
#> SRR2936899 3 0.1557 0.876 0.056 0.000 0.944 0.000
#> SRR2936897 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> SRR2936896 2 0.1302 0.973 0.000 0.956 0.044 0.000
#> SRR2936894 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> SRR2936893 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> SRR2936895 2 0.1389 0.970 0.000 0.952 0.048 0.000
#> SRR2936892 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> SRR2936891 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> SRR2936890 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> SRR2936886 4 0.0000 0.911 0.000 0.000 0.000 1.000
#> SRR2936885 1 0.1474 0.954 0.948 0.000 0.052 0.000
#> SRR2936888 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> SRR2936889 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> SRR2936887 4 0.0000 0.911 0.000 0.000 0.000 1.000
#> SRR2936884 3 0.1792 0.923 0.000 0.068 0.932 0.000
#> SRR2936883 3 0.1716 0.927 0.000 0.064 0.936 0.000
#> SRR2936881 3 0.1716 0.927 0.000 0.064 0.936 0.000
#> SRR2936882 1 0.1474 0.954 0.948 0.000 0.052 0.000
#> SRR2936880 3 0.1716 0.927 0.000 0.064 0.936 0.000
#> SRR2936878 2 0.1302 0.973 0.000 0.956 0.044 0.000
#> SRR2936879 1 0.0336 0.982 0.992 0.000 0.008 0.000
#> SRR2936875 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> SRR2936877 2 0.1302 0.973 0.000 0.956 0.044 0.000
#> SRR2936876 1 0.0336 0.982 0.992 0.000 0.008 0.000
#> SRR2936873 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> SRR2936872 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> SRR2936871 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> SRR2936874 2 0.0000 0.978 0.000 1.000 0.000 0.000
#> SRR2936870 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> SRR2936869 4 0.0000 0.911 0.000 0.000 0.000 1.000
#> SRR2936868 4 0.0000 0.911 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
#> SRR2936906 1 0.0000 0.8535 1.000 0.000 0.000 0.000 0.000
#> SRR2936909 1 0.0000 0.8535 1.000 0.000 0.000 0.000 0.000
#> SRR2936918 1 0.0000 0.8535 1.000 0.000 0.000 0.000 0.000
#> SRR2936917 2 0.4451 0.6355 0.000 0.644 0.340 0.000 0.016
#> SRR2936916 3 0.7324 0.2351 0.036 0.224 0.436 0.000 0.304
#> SRR2936915 1 0.3816 0.5588 0.696 0.000 0.000 0.000 0.304
#> SRR2936914 2 0.4451 0.6355 0.000 0.644 0.340 0.000 0.016
#> SRR2936913 2 0.4451 0.6355 0.000 0.644 0.340 0.000 0.016
#> SRR2936912 1 0.0000 0.8535 1.000 0.000 0.000 0.000 0.000
#> SRR2936910 1 0.0000 0.8535 1.000 0.000 0.000 0.000 0.000
#> SRR2936911 2 0.4451 0.6355 0.000 0.644 0.340 0.000 0.016
#> SRR2936907 2 0.0000 0.7973 0.000 1.000 0.000 0.000 0.000
#> SRR2936908 2 0.0000 0.7973 0.000 1.000 0.000 0.000 0.000
#> SRR2936904 4 0.3966 0.4768 0.336 0.000 0.000 0.664 0.000
#> SRR2936905 2 0.0000 0.7973 0.000 1.000 0.000 0.000 0.000
#> SRR2936903 5 0.4249 0.0436 0.432 0.000 0.000 0.000 0.568
#> SRR2936901 5 0.4029 0.7273 0.004 0.000 0.316 0.000 0.680
#> SRR2936902 3 0.0510 0.8531 0.000 0.000 0.984 0.000 0.016
#> SRR2936900 1 0.4297 0.0104 0.528 0.000 0.000 0.000 0.472
#> SRR2936898 5 0.4029 0.7273 0.004 0.000 0.316 0.000 0.680
#> SRR2936899 5 0.4029 0.7273 0.004 0.000 0.316 0.000 0.680
#> SRR2936897 1 0.0000 0.8535 1.000 0.000 0.000 0.000 0.000
#> SRR2936896 2 0.4451 0.6355 0.000 0.644 0.340 0.000 0.016
#> SRR2936894 1 0.0000 0.8535 1.000 0.000 0.000 0.000 0.000
#> SRR2936893 2 0.0000 0.7973 0.000 1.000 0.000 0.000 0.000
#> SRR2936895 2 0.4723 0.4299 0.000 0.536 0.448 0.000 0.016
#> SRR2936892 2 0.0000 0.7973 0.000 1.000 0.000 0.000 0.000
#> SRR2936891 1 0.0000 0.8535 1.000 0.000 0.000 0.000 0.000
#> SRR2936890 2 0.0000 0.7973 0.000 1.000 0.000 0.000 0.000
#> SRR2936886 4 0.0000 0.8818 0.000 0.000 0.000 1.000 0.000
#> SRR2936885 1 0.4291 0.0373 0.536 0.000 0.000 0.000 0.464
#> SRR2936888 1 0.0000 0.8535 1.000 0.000 0.000 0.000 0.000
#> SRR2936889 2 0.0000 0.7973 0.000 1.000 0.000 0.000 0.000
#> SRR2936887 4 0.0000 0.8818 0.000 0.000 0.000 1.000 0.000
#> SRR2936884 3 0.0000 0.8426 0.000 0.000 1.000 0.000 0.000
#> SRR2936883 3 0.0510 0.8531 0.000 0.000 0.984 0.000 0.016
#> SRR2936881 3 0.0510 0.8531 0.000 0.000 0.984 0.000 0.016
#> SRR2936882 1 0.4297 0.0104 0.528 0.000 0.000 0.000 0.472
#> SRR2936880 3 0.0510 0.8531 0.000 0.000 0.984 0.000 0.016
#> SRR2936878 2 0.4451 0.6355 0.000 0.644 0.340 0.000 0.016
#> SRR2936879 1 0.2929 0.7035 0.820 0.000 0.000 0.000 0.180
#> SRR2936875 2 0.0000 0.7973 0.000 1.000 0.000 0.000 0.000
#> SRR2936877 2 0.4451 0.6355 0.000 0.644 0.340 0.000 0.016
#> SRR2936876 1 0.0794 0.8356 0.972 0.000 0.000 0.000 0.028
#> SRR2936873 1 0.0000 0.8535 1.000 0.000 0.000 0.000 0.000
#> SRR2936872 2 0.0000 0.7973 0.000 1.000 0.000 0.000 0.000
#> SRR2936871 2 0.0000 0.7973 0.000 1.000 0.000 0.000 0.000
#> SRR2936874 2 0.0000 0.7973 0.000 1.000 0.000 0.000 0.000
#> SRR2936870 1 0.0000 0.8535 1.000 0.000 0.000 0.000 0.000
#> SRR2936869 4 0.0000 0.8818 0.000 0.000 0.000 1.000 0.000
#> SRR2936868 4 0.0000 0.8818 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
#> SRR2936906 1 0.0000 0.955 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936909 1 0.0000 0.955 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936918 1 0.0000 0.955 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936917 2 0.5558 0.458 0.000 0.524 0.316 0.000 0.160 0.000
#> SRR2936916 5 0.3659 -0.217 0.000 0.000 0.364 0.000 0.636 0.000
#> SRR2936915 5 0.2491 0.383 0.164 0.000 0.000 0.000 0.836 0.000
#> SRR2936914 2 0.5558 0.458 0.000 0.524 0.316 0.000 0.160 0.000
#> SRR2936913 2 0.5558 0.458 0.000 0.524 0.316 0.000 0.160 0.000
#> SRR2936912 1 0.0000 0.955 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936910 1 0.0000 0.955 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936911 2 0.5558 0.458 0.000 0.524 0.316 0.000 0.160 0.000
#> SRR2936907 2 0.0000 0.760 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936908 2 0.0000 0.760 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936904 4 0.3810 0.180 0.428 0.000 0.000 0.572 0.000 0.000
#> SRR2936905 2 0.0000 0.760 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936903 6 0.3706 0.624 0.380 0.000 0.000 0.000 0.000 0.620
#> SRR2936901 6 0.0000 0.547 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR2936902 3 0.0865 0.802 0.000 0.000 0.964 0.000 0.000 0.036
#> SRR2936900 6 0.3854 0.568 0.464 0.000 0.000 0.000 0.000 0.536
#> SRR2936898 6 0.0000 0.547 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR2936899 6 0.0000 0.547 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR2936897 1 0.0000 0.955 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936896 2 0.5558 0.458 0.000 0.524 0.316 0.000 0.160 0.000
#> SRR2936894 1 0.0000 0.955 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936893 2 0.0000 0.760 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936895 3 0.5678 -0.220 0.000 0.376 0.464 0.000 0.160 0.000
#> SRR2936892 2 0.0000 0.760 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936891 1 0.0000 0.955 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936890 2 0.0000 0.760 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936886 4 0.0000 0.837 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR2936885 6 0.3862 0.547 0.476 0.000 0.000 0.000 0.000 0.524
#> SRR2936888 1 0.0000 0.955 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936889 2 0.0000 0.760 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936887 4 0.0000 0.837 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR2936884 3 0.0000 0.772 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936883 3 0.0865 0.802 0.000 0.000 0.964 0.000 0.000 0.036
#> SRR2936881 3 0.0865 0.802 0.000 0.000 0.964 0.000 0.000 0.036
#> SRR2936882 6 0.3857 0.562 0.468 0.000 0.000 0.000 0.000 0.532
#> SRR2936880 3 0.0865 0.802 0.000 0.000 0.964 0.000 0.000 0.036
#> SRR2936878 2 0.5558 0.458 0.000 0.524 0.316 0.000 0.160 0.000
#> SRR2936879 5 0.3823 0.131 0.436 0.000 0.000 0.000 0.564 0.000
#> SRR2936875 2 0.0000 0.760 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936877 2 0.5558 0.458 0.000 0.524 0.316 0.000 0.160 0.000
#> SRR2936876 1 0.3647 0.199 0.640 0.000 0.000 0.000 0.360 0.000
#> SRR2936873 1 0.0000 0.955 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936872 2 0.0000 0.760 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936871 2 0.0000 0.760 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936874 2 0.0000 0.760 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936870 1 0.0000 0.955 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936869 4 0.0000 0.837 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR2936868 4 0.0000 0.837 0.000 0.000 0.000 1.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 14198 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 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 0.920 0.955 0.981 0.5025 0.495 0.495
#> 3 3 0.971 0.939 0.976 0.3440 0.704 0.469
#> 4 4 0.848 0.836 0.894 0.0844 0.905 0.726
#> 5 5 0.891 0.948 0.949 0.0675 0.922 0.726
#> 6 6 1.000 0.952 0.977 0.0541 0.962 0.827
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR2936906 1 0.000 0.963 1.000 0.000
#> SRR2936909 1 0.000 0.963 1.000 0.000
#> SRR2936918 1 0.000 0.963 1.000 0.000
#> SRR2936917 2 0.000 0.992 0.000 1.000
#> SRR2936916 2 0.000 0.992 0.000 1.000
#> SRR2936915 2 0.000 0.992 0.000 1.000
#> SRR2936914 2 0.000 0.992 0.000 1.000
#> SRR2936913 2 0.000 0.992 0.000 1.000
#> SRR2936912 1 0.000 0.963 1.000 0.000
#> SRR2936910 1 0.000 0.963 1.000 0.000
#> SRR2936911 2 0.000 0.992 0.000 1.000
#> SRR2936907 2 0.000 0.992 0.000 1.000
#> SRR2936908 2 0.000 0.992 0.000 1.000
#> SRR2936904 1 0.000 0.963 1.000 0.000
#> SRR2936905 2 0.000 0.992 0.000 1.000
#> SRR2936903 1 0.000 0.963 1.000 0.000
#> SRR2936901 1 0.000 0.963 1.000 0.000
#> SRR2936902 2 0.000 0.992 0.000 1.000
#> SRR2936900 1 0.000 0.963 1.000 0.000
#> SRR2936898 1 0.000 0.963 1.000 0.000
#> SRR2936899 1 0.000 0.963 1.000 0.000
#> SRR2936897 1 0.000 0.963 1.000 0.000
#> SRR2936896 2 0.000 0.992 0.000 1.000
#> SRR2936894 1 0.000 0.963 1.000 0.000
#> SRR2936893 2 0.000 0.992 0.000 1.000
#> SRR2936895 2 0.000 0.992 0.000 1.000
#> SRR2936892 2 0.000 0.992 0.000 1.000
#> SRR2936891 1 0.000 0.963 1.000 0.000
#> SRR2936890 2 0.000 0.992 0.000 1.000
#> SRR2936886 1 0.722 0.759 0.800 0.200
#> SRR2936885 1 0.000 0.963 1.000 0.000
#> SRR2936888 1 0.000 0.963 1.000 0.000
#> SRR2936889 2 0.000 0.992 0.000 1.000
#> SRR2936887 1 0.722 0.759 0.800 0.200
#> SRR2936884 2 0.000 0.992 0.000 1.000
#> SRR2936883 2 0.000 0.992 0.000 1.000
#> SRR2936881 2 0.000 0.992 0.000 1.000
#> SRR2936882 1 0.000 0.963 1.000 0.000
#> SRR2936880 2 0.000 0.992 0.000 1.000
#> SRR2936878 2 0.000 0.992 0.000 1.000
#> SRR2936879 2 0.722 0.739 0.200 0.800
#> SRR2936875 2 0.000 0.992 0.000 1.000
#> SRR2936877 2 0.000 0.992 0.000 1.000
#> SRR2936876 1 0.000 0.963 1.000 0.000
#> SRR2936873 1 0.000 0.963 1.000 0.000
#> SRR2936872 2 0.000 0.992 0.000 1.000
#> SRR2936871 2 0.000 0.992 0.000 1.000
#> SRR2936874 2 0.000 0.992 0.000 1.000
#> SRR2936870 1 0.000 0.963 1.000 0.000
#> SRR2936869 2 0.000 0.992 0.000 1.000
#> SRR2936868 1 0.963 0.408 0.612 0.388
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR2936906 1 0.0000 0.998 1.000 0.000 0.000
#> SRR2936909 1 0.0000 0.998 1.000 0.000 0.000
#> SRR2936918 1 0.0000 0.998 1.000 0.000 0.000
#> SRR2936917 2 0.0000 0.981 0.000 1.000 0.000
#> SRR2936916 3 0.0000 0.944 0.000 0.000 1.000
#> SRR2936915 3 0.0000 0.944 0.000 0.000 1.000
#> SRR2936914 2 0.0000 0.981 0.000 1.000 0.000
#> SRR2936913 2 0.0000 0.981 0.000 1.000 0.000
#> SRR2936912 1 0.0000 0.998 1.000 0.000 0.000
#> SRR2936910 1 0.0000 0.998 1.000 0.000 0.000
#> SRR2936911 2 0.0000 0.981 0.000 1.000 0.000
#> SRR2936907 2 0.0000 0.981 0.000 1.000 0.000
#> SRR2936908 2 0.0000 0.981 0.000 1.000 0.000
#> SRR2936904 3 0.0000 0.944 0.000 0.000 1.000
#> SRR2936905 2 0.0000 0.981 0.000 1.000 0.000
#> SRR2936903 3 0.0000 0.944 0.000 0.000 1.000
#> SRR2936901 3 0.0000 0.944 0.000 0.000 1.000
#> SRR2936902 3 0.0000 0.944 0.000 0.000 1.000
#> SRR2936900 1 0.0000 0.998 1.000 0.000 0.000
#> SRR2936898 3 0.0000 0.944 0.000 0.000 1.000
#> SRR2936899 3 0.0000 0.944 0.000 0.000 1.000
#> SRR2936897 1 0.0000 0.998 1.000 0.000 0.000
#> SRR2936896 2 0.0000 0.981 0.000 1.000 0.000
#> SRR2936894 1 0.0000 0.998 1.000 0.000 0.000
#> SRR2936893 2 0.0000 0.981 0.000 1.000 0.000
#> SRR2936895 3 0.5431 0.581 0.000 0.284 0.716
#> SRR2936892 2 0.0000 0.981 0.000 1.000 0.000
#> SRR2936891 1 0.0000 0.998 1.000 0.000 0.000
#> SRR2936890 2 0.0000 0.981 0.000 1.000 0.000
#> SRR2936886 3 0.0000 0.944 0.000 0.000 1.000
#> SRR2936885 1 0.1163 0.969 0.972 0.000 0.028
#> SRR2936888 1 0.0000 0.998 1.000 0.000 0.000
#> SRR2936889 2 0.0000 0.981 0.000 1.000 0.000
#> SRR2936887 3 0.0000 0.944 0.000 0.000 1.000
#> SRR2936884 2 0.5760 0.497 0.000 0.672 0.328
#> SRR2936883 3 0.0000 0.944 0.000 0.000 1.000
#> SRR2936881 3 0.0000 0.944 0.000 0.000 1.000
#> SRR2936882 1 0.0000 0.998 1.000 0.000 0.000
#> SRR2936880 3 0.0000 0.944 0.000 0.000 1.000
#> SRR2936878 2 0.0000 0.981 0.000 1.000 0.000
#> SRR2936879 3 0.0000 0.944 0.000 0.000 1.000
#> SRR2936875 2 0.0000 0.981 0.000 1.000 0.000
#> SRR2936877 2 0.0000 0.981 0.000 1.000 0.000
#> SRR2936876 3 0.6126 0.332 0.400 0.000 0.600
#> SRR2936873 1 0.0000 0.998 1.000 0.000 0.000
#> SRR2936872 2 0.0000 0.981 0.000 1.000 0.000
#> SRR2936871 2 0.0000 0.981 0.000 1.000 0.000
#> SRR2936874 2 0.0000 0.981 0.000 1.000 0.000
#> SRR2936870 1 0.0000 0.998 1.000 0.000 0.000
#> SRR2936869 3 0.4555 0.735 0.000 0.200 0.800
#> SRR2936868 3 0.0237 0.941 0.000 0.004 0.996
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR2936906 1 0.000 0.9711 1.000 0.000 0.000 0.000
#> SRR2936909 1 0.000 0.9711 1.000 0.000 0.000 0.000
#> SRR2936918 1 0.000 0.9711 1.000 0.000 0.000 0.000
#> SRR2936917 2 0.464 0.7553 0.000 0.656 0.000 0.344
#> SRR2936916 3 0.000 0.8030 0.000 0.000 1.000 0.000
#> SRR2936915 3 0.387 0.3355 0.000 0.000 0.772 0.228
#> SRR2936914 2 0.464 0.7553 0.000 0.656 0.000 0.344
#> SRR2936913 2 0.464 0.7553 0.000 0.656 0.000 0.344
#> SRR2936912 1 0.000 0.9711 1.000 0.000 0.000 0.000
#> SRR2936910 1 0.000 0.9711 1.000 0.000 0.000 0.000
#> SRR2936911 2 0.464 0.7553 0.000 0.656 0.000 0.344
#> SRR2936907 2 0.000 0.8823 0.000 1.000 0.000 0.000
#> SRR2936908 2 0.000 0.8823 0.000 1.000 0.000 0.000
#> SRR2936904 4 0.464 0.9979 0.000 0.000 0.344 0.656
#> SRR2936905 2 0.000 0.8823 0.000 1.000 0.000 0.000
#> SRR2936903 3 0.497 0.0325 0.456 0.000 0.544 0.000
#> SRR2936901 3 0.000 0.8030 0.000 0.000 1.000 0.000
#> SRR2936902 3 0.000 0.8030 0.000 0.000 1.000 0.000
#> SRR2936900 1 0.000 0.9711 1.000 0.000 0.000 0.000
#> SRR2936898 3 0.000 0.8030 0.000 0.000 1.000 0.000
#> SRR2936899 3 0.000 0.8030 0.000 0.000 1.000 0.000
#> SRR2936897 1 0.000 0.9711 1.000 0.000 0.000 0.000
#> SRR2936896 2 0.172 0.8637 0.000 0.936 0.000 0.064
#> SRR2936894 1 0.000 0.9711 1.000 0.000 0.000 0.000
#> SRR2936893 2 0.000 0.8823 0.000 1.000 0.000 0.000
#> SRR2936895 3 0.344 0.5759 0.000 0.184 0.816 0.000
#> SRR2936892 2 0.000 0.8823 0.000 1.000 0.000 0.000
#> SRR2936891 1 0.000 0.9711 1.000 0.000 0.000 0.000
#> SRR2936890 2 0.000 0.8823 0.000 1.000 0.000 0.000
#> SRR2936886 4 0.464 0.9979 0.000 0.000 0.344 0.656
#> SRR2936885 1 0.000 0.9711 1.000 0.000 0.000 0.000
#> SRR2936888 1 0.000 0.9711 1.000 0.000 0.000 0.000
#> SRR2936889 2 0.000 0.8823 0.000 1.000 0.000 0.000
#> SRR2936887 4 0.464 0.9979 0.000 0.000 0.344 0.656
#> SRR2936884 3 0.464 0.3731 0.000 0.344 0.656 0.000
#> SRR2936883 3 0.000 0.8030 0.000 0.000 1.000 0.000
#> SRR2936881 3 0.000 0.8030 0.000 0.000 1.000 0.000
#> SRR2936882 1 0.000 0.9711 1.000 0.000 0.000 0.000
#> SRR2936880 3 0.000 0.8030 0.000 0.000 1.000 0.000
#> SRR2936878 2 0.464 0.7553 0.000 0.656 0.000 0.344
#> SRR2936879 3 0.000 0.8030 0.000 0.000 1.000 0.000
#> SRR2936875 2 0.000 0.8823 0.000 1.000 0.000 0.000
#> SRR2936877 2 0.464 0.7553 0.000 0.656 0.000 0.344
#> SRR2936876 1 0.456 0.3985 0.672 0.000 0.328 0.000
#> SRR2936873 1 0.000 0.9711 1.000 0.000 0.000 0.000
#> SRR2936872 2 0.000 0.8823 0.000 1.000 0.000 0.000
#> SRR2936871 2 0.000 0.8823 0.000 1.000 0.000 0.000
#> SRR2936874 2 0.000 0.8823 0.000 1.000 0.000 0.000
#> SRR2936870 1 0.000 0.9711 1.000 0.000 0.000 0.000
#> SRR2936869 4 0.480 0.9917 0.000 0.004 0.340 0.656
#> SRR2936868 4 0.464 0.9979 0.000 0.000 0.344 0.656
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR2936906 1 0.000 0.951 1.0 0.000 0.000 0.000 0.000
#> SRR2936909 1 0.000 0.951 1.0 0.000 0.000 0.000 0.000
#> SRR2936918 1 0.000 0.951 1.0 0.000 0.000 0.000 0.000
#> SRR2936917 5 0.311 1.000 0.0 0.200 0.000 0.000 0.800
#> SRR2936916 3 0.000 0.968 0.0 0.000 1.000 0.000 0.000
#> SRR2936915 3 0.340 0.700 0.0 0.000 0.764 0.236 0.000
#> SRR2936914 5 0.311 1.000 0.0 0.200 0.000 0.000 0.800
#> SRR2936913 5 0.311 1.000 0.0 0.200 0.000 0.000 0.800
#> SRR2936912 1 0.000 0.951 1.0 0.000 0.000 0.000 0.000
#> SRR2936910 1 0.000 0.951 1.0 0.000 0.000 0.000 0.000
#> SRR2936911 5 0.311 1.000 0.0 0.200 0.000 0.000 0.800
#> SRR2936907 2 0.000 0.973 0.0 1.000 0.000 0.000 0.000
#> SRR2936908 2 0.000 0.973 0.0 1.000 0.000 0.000 0.000
#> SRR2936904 4 0.000 1.000 0.0 0.000 0.000 1.000 0.000
#> SRR2936905 2 0.000 0.973 0.0 1.000 0.000 0.000 0.000
#> SRR2936903 1 0.311 0.842 0.8 0.000 0.000 0.000 0.200
#> SRR2936901 3 0.223 0.872 0.0 0.000 0.884 0.000 0.116
#> SRR2936902 3 0.000 0.968 0.0 0.000 1.000 0.000 0.000
#> SRR2936900 1 0.311 0.842 0.8 0.000 0.000 0.000 0.200
#> SRR2936898 3 0.000 0.968 0.0 0.000 1.000 0.000 0.000
#> SRR2936899 3 0.000 0.968 0.0 0.000 1.000 0.000 0.000
#> SRR2936897 1 0.000 0.951 1.0 0.000 0.000 0.000 0.000
#> SRR2936896 2 0.337 0.592 0.0 0.768 0.000 0.000 0.232
#> SRR2936894 1 0.000 0.951 1.0 0.000 0.000 0.000 0.000
#> SRR2936893 2 0.000 0.973 0.0 1.000 0.000 0.000 0.000
#> SRR2936895 3 0.000 0.968 0.0 0.000 1.000 0.000 0.000
#> SRR2936892 2 0.000 0.973 0.0 1.000 0.000 0.000 0.000
#> SRR2936891 1 0.000 0.951 1.0 0.000 0.000 0.000 0.000
#> SRR2936890 2 0.000 0.973 0.0 1.000 0.000 0.000 0.000
#> SRR2936886 4 0.000 1.000 0.0 0.000 0.000 1.000 0.000
#> SRR2936885 1 0.311 0.842 0.8 0.000 0.000 0.000 0.200
#> SRR2936888 1 0.000 0.951 1.0 0.000 0.000 0.000 0.000
#> SRR2936889 2 0.000 0.973 0.0 1.000 0.000 0.000 0.000
#> SRR2936887 4 0.000 1.000 0.0 0.000 0.000 1.000 0.000
#> SRR2936884 3 0.000 0.968 0.0 0.000 1.000 0.000 0.000
#> SRR2936883 3 0.000 0.968 0.0 0.000 1.000 0.000 0.000
#> SRR2936881 3 0.000 0.968 0.0 0.000 1.000 0.000 0.000
#> SRR2936882 1 0.311 0.842 0.8 0.000 0.000 0.000 0.200
#> SRR2936880 3 0.000 0.968 0.0 0.000 1.000 0.000 0.000
#> SRR2936878 5 0.311 1.000 0.0 0.200 0.000 0.000 0.800
#> SRR2936879 3 0.000 0.968 0.0 0.000 1.000 0.000 0.000
#> SRR2936875 2 0.000 0.973 0.0 1.000 0.000 0.000 0.000
#> SRR2936877 5 0.311 1.000 0.0 0.200 0.000 0.000 0.800
#> SRR2936876 1 0.000 0.951 1.0 0.000 0.000 0.000 0.000
#> SRR2936873 1 0.000 0.951 1.0 0.000 0.000 0.000 0.000
#> SRR2936872 2 0.000 0.973 0.0 1.000 0.000 0.000 0.000
#> SRR2936871 2 0.000 0.973 0.0 1.000 0.000 0.000 0.000
#> SRR2936874 2 0.000 0.973 0.0 1.000 0.000 0.000 0.000
#> SRR2936870 1 0.000 0.951 1.0 0.000 0.000 0.000 0.000
#> SRR2936869 4 0.000 1.000 0.0 0.000 0.000 1.000 0.000
#> SRR2936868 4 0.000 1.000 0.0 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
#> SRR2936906 1 0.000 0.995 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936909 1 0.000 0.995 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936918 1 0.000 0.995 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936917 5 0.000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936916 3 0.000 0.950 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936915 3 0.405 0.679 0.000 0.000 0.716 0.236 0.000 0.048
#> SRR2936914 5 0.000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936913 5 0.000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936912 1 0.000 0.995 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936910 1 0.000 0.995 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936911 5 0.000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936907 2 0.000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936908 2 0.000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936904 4 0.000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR2936905 2 0.000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936903 6 0.000 0.926 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR2936901 3 0.249 0.839 0.000 0.000 0.836 0.000 0.000 0.164
#> SRR2936902 3 0.000 0.950 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936900 6 0.107 0.976 0.048 0.000 0.000 0.000 0.000 0.952
#> SRR2936898 3 0.107 0.936 0.000 0.000 0.952 0.000 0.000 0.048
#> SRR2936899 3 0.107 0.936 0.000 0.000 0.952 0.000 0.000 0.048
#> SRR2936897 1 0.000 0.995 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936896 2 0.378 0.299 0.000 0.588 0.000 0.000 0.412 0.000
#> SRR2936894 1 0.000 0.995 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936893 2 0.000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936895 3 0.000 0.950 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936892 2 0.000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936891 1 0.000 0.995 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936890 2 0.000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936886 4 0.000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR2936885 6 0.107 0.976 0.048 0.000 0.000 0.000 0.000 0.952
#> SRR2936888 1 0.000 0.995 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936889 2 0.000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936887 4 0.000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR2936884 3 0.000 0.950 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936883 3 0.000 0.950 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936881 3 0.000 0.950 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936882 6 0.107 0.976 0.048 0.000 0.000 0.000 0.000 0.952
#> SRR2936880 3 0.000 0.950 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936878 5 0.000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936879 3 0.107 0.936 0.000 0.000 0.952 0.000 0.000 0.048
#> SRR2936875 2 0.000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936877 5 0.000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936876 1 0.107 0.941 0.952 0.000 0.000 0.000 0.000 0.048
#> SRR2936873 1 0.000 0.995 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936872 2 0.000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936871 2 0.000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936874 2 0.000 0.959 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936870 1 0.000 0.995 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936869 4 0.000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR2936868 4 0.000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 14198 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 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 0.447 0.862 0.917 0.4377 0.534 0.534
#> 3 3 0.764 0.826 0.918 0.5132 0.767 0.575
#> 4 4 0.886 0.906 0.963 0.0976 0.915 0.752
#> 5 5 0.934 0.924 0.958 0.1062 0.882 0.593
#> 6 6 0.871 0.862 0.905 0.0267 0.970 0.846
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
#> SRR2936906 2 0.634 0.879 0.160 0.840
#> SRR2936909 2 0.634 0.879 0.160 0.840
#> SRR2936918 2 0.634 0.879 0.160 0.840
#> SRR2936917 2 0.000 0.903 0.000 1.000
#> SRR2936916 2 0.625 0.880 0.156 0.844
#> SRR2936915 2 0.625 0.880 0.156 0.844
#> SRR2936914 2 0.000 0.903 0.000 1.000
#> SRR2936913 2 0.000 0.903 0.000 1.000
#> SRR2936912 2 0.634 0.879 0.160 0.840
#> SRR2936910 2 0.634 0.879 0.160 0.840
#> SRR2936911 2 0.000 0.903 0.000 1.000
#> SRR2936907 2 0.000 0.903 0.000 1.000
#> SRR2936908 2 0.000 0.903 0.000 1.000
#> SRR2936904 2 0.625 0.880 0.156 0.844
#> SRR2936905 2 0.000 0.903 0.000 1.000
#> SRR2936903 1 0.000 0.878 1.000 0.000
#> SRR2936901 1 0.000 0.878 1.000 0.000
#> SRR2936902 1 0.000 0.878 1.000 0.000
#> SRR2936900 1 0.000 0.878 1.000 0.000
#> SRR2936898 1 0.000 0.878 1.000 0.000
#> SRR2936899 1 0.000 0.878 1.000 0.000
#> SRR2936897 2 0.644 0.876 0.164 0.836
#> SRR2936896 2 0.430 0.893 0.088 0.912
#> SRR2936894 2 0.634 0.879 0.160 0.840
#> SRR2936893 2 0.000 0.903 0.000 1.000
#> SRR2936895 2 0.644 0.876 0.164 0.836
#> SRR2936892 2 0.000 0.903 0.000 1.000
#> SRR2936891 2 0.634 0.879 0.160 0.840
#> SRR2936890 2 0.000 0.903 0.000 1.000
#> SRR2936886 1 0.866 0.662 0.712 0.288
#> SRR2936885 1 0.000 0.878 1.000 0.000
#> SRR2936888 1 0.866 0.662 0.712 0.288
#> SRR2936889 2 0.000 0.903 0.000 1.000
#> SRR2936887 1 0.866 0.662 0.712 0.288
#> SRR2936884 1 0.000 0.878 1.000 0.000
#> SRR2936883 1 0.000 0.878 1.000 0.000
#> SRR2936881 1 0.000 0.878 1.000 0.000
#> SRR2936882 1 0.000 0.878 1.000 0.000
#> SRR2936880 1 0.000 0.878 1.000 0.000
#> SRR2936878 2 0.000 0.903 0.000 1.000
#> SRR2936879 2 0.634 0.878 0.160 0.840
#> SRR2936875 2 0.000 0.903 0.000 1.000
#> SRR2936877 2 0.000 0.903 0.000 1.000
#> SRR2936876 2 0.634 0.879 0.160 0.840
#> SRR2936873 2 0.634 0.879 0.160 0.840
#> SRR2936872 2 0.000 0.903 0.000 1.000
#> SRR2936871 2 0.000 0.903 0.000 1.000
#> SRR2936874 2 0.000 0.903 0.000 1.000
#> SRR2936870 1 0.866 0.662 0.712 0.288
#> SRR2936869 1 0.866 0.662 0.712 0.288
#> SRR2936868 1 0.866 0.662 0.712 0.288
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR2936906 1 0.000 0.910 1.000 0.000 0.000
#> SRR2936909 1 0.000 0.910 1.000 0.000 0.000
#> SRR2936918 1 0.000 0.910 1.000 0.000 0.000
#> SRR2936917 2 0.196 0.900 0.056 0.944 0.000
#> SRR2936916 1 0.599 0.402 0.632 0.368 0.000
#> SRR2936915 1 0.327 0.821 0.884 0.116 0.000
#> SRR2936914 2 0.216 0.894 0.064 0.936 0.000
#> SRR2936913 2 0.000 0.935 0.000 1.000 0.000
#> SRR2936912 1 0.000 0.910 1.000 0.000 0.000
#> SRR2936910 1 0.000 0.910 1.000 0.000 0.000
#> SRR2936911 2 0.000 0.935 0.000 1.000 0.000
#> SRR2936907 2 0.000 0.935 0.000 1.000 0.000
#> SRR2936908 2 0.000 0.935 0.000 1.000 0.000
#> SRR2936904 3 0.972 0.106 0.220 0.384 0.396
#> SRR2936905 2 0.000 0.935 0.000 1.000 0.000
#> SRR2936903 3 0.000 0.871 0.000 0.000 1.000
#> SRR2936901 3 0.000 0.871 0.000 0.000 1.000
#> SRR2936902 3 0.000 0.871 0.000 0.000 1.000
#> SRR2936900 3 0.000 0.871 0.000 0.000 1.000
#> SRR2936898 3 0.000 0.871 0.000 0.000 1.000
#> SRR2936899 3 0.000 0.871 0.000 0.000 1.000
#> SRR2936897 1 0.000 0.910 1.000 0.000 0.000
#> SRR2936896 2 0.369 0.828 0.140 0.860 0.000
#> SRR2936894 1 0.000 0.910 1.000 0.000 0.000
#> SRR2936893 2 0.000 0.935 0.000 1.000 0.000
#> SRR2936895 2 0.929 0.140 0.168 0.476 0.356
#> SRR2936892 2 0.000 0.935 0.000 1.000 0.000
#> SRR2936891 1 0.000 0.910 1.000 0.000 0.000
#> SRR2936890 2 0.000 0.935 0.000 1.000 0.000
#> SRR2936886 3 0.597 0.746 0.216 0.032 0.752
#> SRR2936885 3 0.000 0.871 0.000 0.000 1.000
#> SRR2936888 3 0.665 0.665 0.288 0.032 0.680
#> SRR2936889 2 0.000 0.935 0.000 1.000 0.000
#> SRR2936887 3 0.597 0.746 0.216 0.032 0.752
#> SRR2936884 3 0.000 0.871 0.000 0.000 1.000
#> SRR2936883 3 0.000 0.871 0.000 0.000 1.000
#> SRR2936881 3 0.000 0.871 0.000 0.000 1.000
#> SRR2936882 3 0.000 0.871 0.000 0.000 1.000
#> SRR2936880 3 0.000 0.871 0.000 0.000 1.000
#> SRR2936878 2 0.348 0.842 0.128 0.872 0.000
#> SRR2936879 1 0.613 0.319 0.600 0.400 0.000
#> SRR2936875 2 0.000 0.935 0.000 1.000 0.000
#> SRR2936877 2 0.348 0.842 0.128 0.872 0.000
#> SRR2936876 1 0.000 0.910 1.000 0.000 0.000
#> SRR2936873 1 0.000 0.910 1.000 0.000 0.000
#> SRR2936872 2 0.000 0.935 0.000 1.000 0.000
#> SRR2936871 2 0.000 0.935 0.000 1.000 0.000
#> SRR2936874 2 0.000 0.935 0.000 1.000 0.000
#> SRR2936870 3 0.665 0.665 0.288 0.032 0.680
#> SRR2936869 3 0.597 0.746 0.216 0.032 0.752
#> SRR2936868 3 0.597 0.746 0.216 0.032 0.752
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR2936906 1 0.0000 0.9092 1.000 0.000 0 0.000
#> SRR2936909 1 0.0000 0.9092 1.000 0.000 0 0.000
#> SRR2936918 1 0.0000 0.9092 1.000 0.000 0 0.000
#> SRR2936917 2 0.0000 0.9371 0.000 1.000 0 0.000
#> SRR2936916 1 0.4522 0.5370 0.680 0.320 0 0.000
#> SRR2936915 1 0.0336 0.9034 0.992 0.008 0 0.000
#> SRR2936914 2 0.0000 0.9371 0.000 1.000 0 0.000
#> SRR2936913 2 0.0000 0.9371 0.000 1.000 0 0.000
#> SRR2936912 1 0.0000 0.9092 1.000 0.000 0 0.000
#> SRR2936910 1 0.0000 0.9092 1.000 0.000 0 0.000
#> SRR2936911 2 0.0000 0.9371 0.000 1.000 0 0.000
#> SRR2936907 2 0.0000 0.9371 0.000 1.000 0 0.000
#> SRR2936908 2 0.0000 0.9371 0.000 1.000 0 0.000
#> SRR2936904 2 0.5167 0.0289 0.004 0.508 0 0.488
#> SRR2936905 2 0.0000 0.9371 0.000 1.000 0 0.000
#> SRR2936903 3 0.0000 1.0000 0.000 0.000 1 0.000
#> SRR2936901 3 0.0000 1.0000 0.000 0.000 1 0.000
#> SRR2936902 3 0.0000 1.0000 0.000 0.000 1 0.000
#> SRR2936900 3 0.0000 1.0000 0.000 0.000 1 0.000
#> SRR2936898 3 0.0000 1.0000 0.000 0.000 1 0.000
#> SRR2936899 3 0.0000 1.0000 0.000 0.000 1 0.000
#> SRR2936897 1 0.2868 0.7935 0.864 0.136 0 0.000
#> SRR2936896 2 0.3172 0.8005 0.160 0.840 0 0.000
#> SRR2936894 1 0.0000 0.9092 1.000 0.000 0 0.000
#> SRR2936893 2 0.0000 0.9371 0.000 1.000 0 0.000
#> SRR2936895 2 0.3172 0.8005 0.160 0.840 0 0.000
#> SRR2936892 2 0.0000 0.9371 0.000 1.000 0 0.000
#> SRR2936891 1 0.0000 0.9092 1.000 0.000 0 0.000
#> SRR2936890 2 0.0000 0.9371 0.000 1.000 0 0.000
#> SRR2936886 4 0.0000 1.0000 0.000 0.000 0 1.000
#> SRR2936885 3 0.0000 1.0000 0.000 0.000 1 0.000
#> SRR2936888 4 0.0000 1.0000 0.000 0.000 0 1.000
#> SRR2936889 2 0.0000 0.9371 0.000 1.000 0 0.000
#> SRR2936887 4 0.0000 1.0000 0.000 0.000 0 1.000
#> SRR2936884 3 0.0000 1.0000 0.000 0.000 1 0.000
#> SRR2936883 3 0.0000 1.0000 0.000 0.000 1 0.000
#> SRR2936881 3 0.0000 1.0000 0.000 0.000 1 0.000
#> SRR2936882 3 0.0000 1.0000 0.000 0.000 1 0.000
#> SRR2936880 3 0.0000 1.0000 0.000 0.000 1 0.000
#> SRR2936878 2 0.2868 0.8272 0.136 0.864 0 0.000
#> SRR2936879 1 0.4679 0.4692 0.648 0.352 0 0.000
#> SRR2936875 2 0.0000 0.9371 0.000 1.000 0 0.000
#> SRR2936877 2 0.2868 0.8272 0.136 0.864 0 0.000
#> SRR2936876 1 0.0000 0.9092 1.000 0.000 0 0.000
#> SRR2936873 1 0.0000 0.9092 1.000 0.000 0 0.000
#> SRR2936872 2 0.0000 0.9371 0.000 1.000 0 0.000
#> SRR2936871 2 0.0000 0.9371 0.000 1.000 0 0.000
#> SRR2936874 2 0.0000 0.9371 0.000 1.000 0 0.000
#> SRR2936870 4 0.0000 1.0000 0.000 0.000 0 1.000
#> SRR2936869 4 0.0000 1.0000 0.000 0.000 0 1.000
#> SRR2936868 4 0.0000 1.0000 0.000 0.000 0 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR2936906 1 0.0000 0.965 1.000 0.000 0 0.000 0.000
#> SRR2936909 1 0.0794 0.966 0.972 0.000 0 0.000 0.028
#> SRR2936918 1 0.0880 0.965 0.968 0.000 0 0.000 0.032
#> SRR2936917 5 0.2471 0.807 0.000 0.136 0 0.000 0.864
#> SRR2936916 5 0.4392 0.388 0.380 0.008 0 0.000 0.612
#> SRR2936915 1 0.0880 0.965 0.968 0.000 0 0.000 0.032
#> SRR2936914 5 0.2471 0.807 0.000 0.136 0 0.000 0.864
#> SRR2936913 5 0.3109 0.765 0.000 0.200 0 0.000 0.800
#> SRR2936912 1 0.0162 0.965 0.996 0.000 0 0.000 0.004
#> SRR2936910 1 0.0000 0.965 1.000 0.000 0 0.000 0.000
#> SRR2936911 5 0.3109 0.765 0.000 0.200 0 0.000 0.800
#> SRR2936907 2 0.0000 1.000 0.000 1.000 0 0.000 0.000
#> SRR2936908 2 0.0000 1.000 0.000 1.000 0 0.000 0.000
#> SRR2936904 4 0.5404 0.707 0.072 0.116 0 0.732 0.080
#> SRR2936905 2 0.0000 1.000 0.000 1.000 0 0.000 0.000
#> SRR2936903 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> SRR2936901 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> SRR2936902 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> SRR2936900 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> SRR2936898 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> SRR2936899 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> SRR2936897 1 0.3109 0.791 0.800 0.000 0 0.000 0.200
#> SRR2936896 5 0.0609 0.822 0.000 0.020 0 0.000 0.980
#> SRR2936894 1 0.0000 0.965 1.000 0.000 0 0.000 0.000
#> SRR2936893 2 0.0000 1.000 0.000 1.000 0 0.000 0.000
#> SRR2936895 5 0.0609 0.822 0.000 0.020 0 0.000 0.980
#> SRR2936892 2 0.0000 1.000 0.000 1.000 0 0.000 0.000
#> SRR2936891 1 0.0000 0.965 1.000 0.000 0 0.000 0.000
#> SRR2936890 2 0.0000 1.000 0.000 1.000 0 0.000 0.000
#> SRR2936886 4 0.0000 0.959 0.000 0.000 0 1.000 0.000
#> SRR2936885 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> SRR2936888 4 0.0000 0.959 0.000 0.000 0 1.000 0.000
#> SRR2936889 2 0.0000 1.000 0.000 1.000 0 0.000 0.000
#> SRR2936887 4 0.0000 0.959 0.000 0.000 0 1.000 0.000
#> SRR2936884 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> SRR2936883 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> SRR2936881 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> SRR2936882 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> SRR2936880 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> SRR2936878 5 0.0609 0.822 0.000 0.020 0 0.000 0.980
#> SRR2936879 5 0.4570 0.419 0.348 0.020 0 0.000 0.632
#> SRR2936875 2 0.0000 1.000 0.000 1.000 0 0.000 0.000
#> SRR2936877 5 0.0609 0.822 0.000 0.020 0 0.000 0.980
#> SRR2936876 1 0.0880 0.965 0.968 0.000 0 0.000 0.032
#> SRR2936873 1 0.0794 0.966 0.972 0.000 0 0.000 0.028
#> SRR2936872 2 0.0000 1.000 0.000 1.000 0 0.000 0.000
#> SRR2936871 2 0.0000 1.000 0.000 1.000 0 0.000 0.000
#> SRR2936874 2 0.0000 1.000 0.000 1.000 0 0.000 0.000
#> SRR2936870 4 0.0000 0.959 0.000 0.000 0 1.000 0.000
#> SRR2936869 4 0.0000 0.959 0.000 0.000 0 1.000 0.000
#> SRR2936868 4 0.0000 0.959 0.000 0.000 0 1.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR2936906 1 0.0000 0.892 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936909 1 0.2436 0.809 0.880 0.000 0.000 0.000 0.032 0.088
#> SRR2936918 1 0.1088 0.883 0.960 0.000 0.000 0.000 0.016 0.024
#> SRR2936917 5 0.2416 0.819 0.000 0.156 0.000 0.000 0.844 0.000
#> SRR2936916 6 0.5499 0.625 0.116 0.100 0.000 0.000 0.108 0.676
#> SRR2936915 6 0.4523 0.329 0.452 0.000 0.000 0.000 0.032 0.516
#> SRR2936914 5 0.2416 0.819 0.000 0.156 0.000 0.000 0.844 0.000
#> SRR2936913 5 0.2793 0.793 0.000 0.200 0.000 0.000 0.800 0.000
#> SRR2936912 1 0.0000 0.892 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936910 1 0.0000 0.892 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936911 5 0.2793 0.793 0.000 0.200 0.000 0.000 0.800 0.000
#> SRR2936907 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936908 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936904 4 0.5565 0.527 0.004 0.188 0.000 0.644 0.032 0.132
#> SRR2936905 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936903 3 0.2362 0.922 0.000 0.000 0.860 0.000 0.004 0.136
#> SRR2936901 3 0.1610 0.938 0.000 0.000 0.916 0.000 0.000 0.084
#> SRR2936902 3 0.0937 0.945 0.000 0.000 0.960 0.000 0.000 0.040
#> SRR2936900 3 0.2362 0.922 0.000 0.000 0.860 0.000 0.004 0.136
#> SRR2936898 3 0.0000 0.948 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936899 3 0.0000 0.948 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936897 6 0.4316 0.578 0.312 0.000 0.000 0.000 0.040 0.648
#> SRR2936896 5 0.2234 0.742 0.000 0.004 0.000 0.000 0.872 0.124
#> SRR2936894 1 0.1921 0.851 0.916 0.000 0.000 0.000 0.032 0.052
#> SRR2936893 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936895 5 0.2668 0.699 0.000 0.004 0.000 0.000 0.828 0.168
#> SRR2936892 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936891 1 0.0458 0.890 0.984 0.000 0.000 0.000 0.016 0.000
#> SRR2936890 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936886 4 0.0000 0.921 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR2936885 3 0.2320 0.923 0.000 0.000 0.864 0.000 0.004 0.132
#> SRR2936888 4 0.1204 0.908 0.000 0.000 0.000 0.944 0.000 0.056
#> SRR2936889 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936887 4 0.0000 0.921 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR2936884 3 0.0000 0.948 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936883 3 0.0000 0.948 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936881 3 0.0000 0.948 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936882 3 0.2362 0.922 0.000 0.000 0.860 0.000 0.004 0.136
#> SRR2936880 3 0.0000 0.948 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936878 5 0.0146 0.798 0.000 0.004 0.000 0.000 0.996 0.000
#> SRR2936879 6 0.3732 0.620 0.076 0.000 0.000 0.000 0.144 0.780
#> SRR2936875 2 0.0146 0.995 0.004 0.996 0.000 0.000 0.000 0.000
#> SRR2936877 5 0.0146 0.798 0.000 0.004 0.000 0.000 0.996 0.000
#> SRR2936876 1 0.4186 0.284 0.656 0.000 0.000 0.000 0.032 0.312
#> SRR2936873 1 0.0000 0.892 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936872 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936871 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936874 2 0.0146 0.995 0.004 0.996 0.000 0.000 0.000 0.000
#> SRR2936870 4 0.1204 0.908 0.000 0.000 0.000 0.944 0.000 0.056
#> SRR2936869 4 0.0000 0.921 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR2936868 4 0.0000 0.921 0.000 0.000 0.000 1.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 14198 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 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 0.794 0.944 0.957 0.4788 0.523 0.523
#> 3 3 1.000 0.950 0.978 0.4160 0.773 0.576
#> 4 4 0.912 0.862 0.943 0.1051 0.909 0.726
#> 5 5 0.842 0.809 0.887 0.0501 0.917 0.687
#> 6 6 0.844 0.798 0.872 0.0300 1.000 1.000
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 3
There is also optional best \(k\) = 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR2936906 1 0.4690 0.929 0.900 0.100
#> SRR2936909 1 0.4562 0.932 0.904 0.096
#> SRR2936918 1 0.4562 0.932 0.904 0.096
#> SRR2936917 1 0.0672 0.936 0.992 0.008
#> SRR2936916 1 0.4431 0.932 0.908 0.092
#> SRR2936915 1 0.5519 0.910 0.872 0.128
#> SRR2936914 2 0.7056 0.792 0.192 0.808
#> SRR2936913 2 0.0000 0.988 0.000 1.000
#> SRR2936912 1 0.4562 0.932 0.904 0.096
#> SRR2936910 1 0.4562 0.932 0.904 0.096
#> SRR2936911 2 0.0938 0.978 0.012 0.988
#> SRR2936907 2 0.0000 0.988 0.000 1.000
#> SRR2936908 2 0.0000 0.988 0.000 1.000
#> SRR2936904 2 0.1843 0.963 0.028 0.972
#> SRR2936905 2 0.0000 0.988 0.000 1.000
#> SRR2936903 1 0.0000 0.934 1.000 0.000
#> SRR2936901 1 0.0672 0.934 0.992 0.008
#> SRR2936902 1 0.1843 0.931 0.972 0.028
#> SRR2936900 1 0.0000 0.934 1.000 0.000
#> SRR2936898 1 0.0672 0.934 0.992 0.008
#> SRR2936899 1 0.1633 0.932 0.976 0.024
#> SRR2936897 1 0.4562 0.932 0.904 0.096
#> SRR2936896 1 0.6343 0.808 0.840 0.160
#> SRR2936894 1 0.4562 0.932 0.904 0.096
#> SRR2936893 2 0.0000 0.988 0.000 1.000
#> SRR2936895 1 0.0376 0.935 0.996 0.004
#> SRR2936892 2 0.0000 0.988 0.000 1.000
#> SRR2936891 1 0.4562 0.932 0.904 0.096
#> SRR2936890 2 0.0000 0.988 0.000 1.000
#> SRR2936886 2 0.0000 0.988 0.000 1.000
#> SRR2936885 1 0.0000 0.934 1.000 0.000
#> SRR2936888 1 0.6148 0.887 0.848 0.152
#> SRR2936889 2 0.0000 0.988 0.000 1.000
#> SRR2936887 2 0.0000 0.988 0.000 1.000
#> SRR2936884 1 0.1843 0.931 0.972 0.028
#> SRR2936883 1 0.1843 0.931 0.972 0.028
#> SRR2936881 1 0.1633 0.932 0.976 0.024
#> SRR2936882 1 0.0000 0.934 1.000 0.000
#> SRR2936880 1 0.1414 0.933 0.980 0.020
#> SRR2936878 1 0.1843 0.931 0.972 0.028
#> SRR2936879 1 0.4431 0.932 0.908 0.092
#> SRR2936875 2 0.0000 0.988 0.000 1.000
#> SRR2936877 1 0.0672 0.934 0.992 0.008
#> SRR2936876 1 0.4562 0.932 0.904 0.096
#> SRR2936873 1 0.4562 0.932 0.904 0.096
#> SRR2936872 2 0.0000 0.988 0.000 1.000
#> SRR2936871 2 0.0000 0.988 0.000 1.000
#> SRR2936874 2 0.0000 0.988 0.000 1.000
#> SRR2936870 1 0.6343 0.879 0.840 0.160
#> SRR2936869 2 0.0000 0.988 0.000 1.000
#> SRR2936868 2 0.0000 0.988 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR2936906 1 0.0000 0.999 1.000 0.000 0.000
#> SRR2936909 1 0.0000 0.999 1.000 0.000 0.000
#> SRR2936918 1 0.0000 0.999 1.000 0.000 0.000
#> SRR2936917 3 0.4796 0.721 0.220 0.000 0.780
#> SRR2936916 1 0.0000 0.999 1.000 0.000 0.000
#> SRR2936915 1 0.0237 0.995 0.996 0.004 0.000
#> SRR2936914 3 0.5363 0.605 0.000 0.276 0.724
#> SRR2936913 2 0.0424 0.995 0.000 0.992 0.008
#> SRR2936912 1 0.0000 0.999 1.000 0.000 0.000
#> SRR2936910 1 0.0000 0.999 1.000 0.000 0.000
#> SRR2936911 2 0.0424 0.995 0.000 0.992 0.008
#> SRR2936907 2 0.0000 0.998 0.000 1.000 0.000
#> SRR2936908 2 0.0000 0.998 0.000 1.000 0.000
#> SRR2936904 2 0.0000 0.998 0.000 1.000 0.000
#> SRR2936905 2 0.0000 0.998 0.000 1.000 0.000
#> SRR2936903 3 0.0424 0.938 0.008 0.000 0.992
#> SRR2936901 3 0.0424 0.938 0.008 0.000 0.992
#> SRR2936902 3 0.0424 0.938 0.008 0.000 0.992
#> SRR2936900 3 0.1031 0.929 0.024 0.000 0.976
#> SRR2936898 3 0.0237 0.937 0.004 0.000 0.996
#> SRR2936899 3 0.0237 0.937 0.004 0.000 0.996
#> SRR2936897 1 0.0000 0.999 1.000 0.000 0.000
#> SRR2936896 3 0.0000 0.935 0.000 0.000 1.000
#> SRR2936894 1 0.0000 0.999 1.000 0.000 0.000
#> SRR2936893 2 0.0000 0.998 0.000 1.000 0.000
#> SRR2936895 3 0.6295 0.142 0.472 0.000 0.528
#> SRR2936892 2 0.0000 0.998 0.000 1.000 0.000
#> SRR2936891 1 0.0000 0.999 1.000 0.000 0.000
#> SRR2936890 2 0.0000 0.998 0.000 1.000 0.000
#> SRR2936886 2 0.0424 0.995 0.000 0.992 0.008
#> SRR2936885 3 0.0592 0.936 0.012 0.000 0.988
#> SRR2936888 1 0.0237 0.996 0.996 0.000 0.004
#> SRR2936889 2 0.0000 0.998 0.000 1.000 0.000
#> SRR2936887 2 0.0424 0.995 0.000 0.992 0.008
#> SRR2936884 3 0.0000 0.935 0.000 0.000 1.000
#> SRR2936883 3 0.0000 0.935 0.000 0.000 1.000
#> SRR2936881 3 0.0424 0.938 0.008 0.000 0.992
#> SRR2936882 3 0.0747 0.934 0.016 0.000 0.984
#> SRR2936880 3 0.0424 0.938 0.008 0.000 0.992
#> SRR2936878 3 0.0424 0.938 0.008 0.000 0.992
#> SRR2936879 1 0.0000 0.999 1.000 0.000 0.000
#> SRR2936875 2 0.0000 0.998 0.000 1.000 0.000
#> SRR2936877 3 0.0424 0.938 0.008 0.000 0.992
#> SRR2936876 1 0.0000 0.999 1.000 0.000 0.000
#> SRR2936873 1 0.0000 0.999 1.000 0.000 0.000
#> SRR2936872 2 0.0000 0.998 0.000 1.000 0.000
#> SRR2936871 2 0.0000 0.998 0.000 1.000 0.000
#> SRR2936874 2 0.0000 0.998 0.000 1.000 0.000
#> SRR2936870 1 0.0237 0.996 0.996 0.000 0.004
#> SRR2936869 2 0.0424 0.995 0.000 0.992 0.008
#> SRR2936868 2 0.0424 0.995 0.000 0.992 0.008
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR2936906 1 0.0000 0.9221 1.000 0.000 0.000 0.000
#> SRR2936909 1 0.0188 0.9213 0.996 0.000 0.000 0.004
#> SRR2936918 1 0.0188 0.9211 0.996 0.000 0.000 0.004
#> SRR2936917 3 0.5594 0.6387 0.100 0.180 0.720 0.000
#> SRR2936916 1 0.0000 0.9221 1.000 0.000 0.000 0.000
#> SRR2936915 1 0.0188 0.9213 0.996 0.000 0.000 0.004
#> SRR2936914 4 0.4998 0.0378 0.000 0.000 0.488 0.512
#> SRR2936913 4 0.0336 0.8422 0.000 0.008 0.000 0.992
#> SRR2936912 1 0.0188 0.9211 0.996 0.000 0.000 0.004
#> SRR2936910 1 0.0188 0.9211 0.996 0.000 0.000 0.004
#> SRR2936911 4 0.0336 0.8422 0.000 0.008 0.000 0.992
#> SRR2936907 2 0.0817 0.9555 0.000 0.976 0.000 0.024
#> SRR2936908 2 0.0469 0.9602 0.000 0.988 0.000 0.012
#> SRR2936904 2 0.0336 0.9606 0.000 0.992 0.000 0.008
#> SRR2936905 2 0.0000 0.9604 0.000 1.000 0.000 0.000
#> SRR2936903 3 0.0000 0.9700 0.000 0.000 1.000 0.000
#> SRR2936901 3 0.0000 0.9700 0.000 0.000 1.000 0.000
#> SRR2936902 3 0.0000 0.9700 0.000 0.000 1.000 0.000
#> SRR2936900 3 0.1792 0.8999 0.068 0.000 0.932 0.000
#> SRR2936898 3 0.0000 0.9700 0.000 0.000 1.000 0.000
#> SRR2936899 3 0.0000 0.9700 0.000 0.000 1.000 0.000
#> SRR2936897 1 0.0000 0.9221 1.000 0.000 0.000 0.000
#> SRR2936896 3 0.1022 0.9442 0.000 0.000 0.968 0.032
#> SRR2936894 1 0.0000 0.9221 1.000 0.000 0.000 0.000
#> SRR2936893 2 0.3764 0.7664 0.000 0.784 0.000 0.216
#> SRR2936895 4 0.7542 0.2568 0.312 0.000 0.212 0.476
#> SRR2936892 2 0.2345 0.9015 0.000 0.900 0.000 0.100
#> SRR2936891 1 0.0000 0.9221 1.000 0.000 0.000 0.000
#> SRR2936890 2 0.0469 0.9602 0.000 0.988 0.000 0.012
#> SRR2936886 4 0.0336 0.8422 0.000 0.008 0.000 0.992
#> SRR2936885 3 0.0707 0.9546 0.000 0.000 0.980 0.020
#> SRR2936888 1 0.4977 0.1893 0.540 0.000 0.000 0.460
#> SRR2936889 2 0.1940 0.9247 0.000 0.924 0.000 0.076
#> SRR2936887 4 0.0336 0.8422 0.000 0.008 0.000 0.992
#> SRR2936884 3 0.0000 0.9700 0.000 0.000 1.000 0.000
#> SRR2936883 3 0.0000 0.9700 0.000 0.000 1.000 0.000
#> SRR2936881 3 0.0000 0.9700 0.000 0.000 1.000 0.000
#> SRR2936882 3 0.0000 0.9700 0.000 0.000 1.000 0.000
#> SRR2936880 3 0.0000 0.9700 0.000 0.000 1.000 0.000
#> SRR2936878 3 0.0000 0.9700 0.000 0.000 1.000 0.000
#> SRR2936879 1 0.0657 0.9140 0.984 0.012 0.000 0.004
#> SRR2936875 2 0.0000 0.9604 0.000 1.000 0.000 0.000
#> SRR2936877 3 0.0000 0.9700 0.000 0.000 1.000 0.000
#> SRR2936876 1 0.1004 0.9042 0.972 0.024 0.000 0.004
#> SRR2936873 1 0.0188 0.9213 0.996 0.000 0.000 0.004
#> SRR2936872 2 0.0000 0.9604 0.000 1.000 0.000 0.000
#> SRR2936871 2 0.0000 0.9604 0.000 1.000 0.000 0.000
#> SRR2936874 2 0.0000 0.9604 0.000 1.000 0.000 0.000
#> SRR2936870 1 0.4989 0.1548 0.528 0.000 0.000 0.472
#> SRR2936869 4 0.0592 0.8386 0.000 0.016 0.000 0.984
#> SRR2936868 4 0.0592 0.8386 0.000 0.016 0.000 0.984
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR2936906 1 0.0932 0.972 0.972 0.000 0.020 0.004 0.004
#> SRR2936909 1 0.0451 0.973 0.988 0.000 0.000 0.004 0.008
#> SRR2936918 1 0.0693 0.976 0.980 0.000 0.012 0.000 0.008
#> SRR2936917 5 0.3556 0.635 0.036 0.012 0.116 0.000 0.836
#> SRR2936916 1 0.0880 0.962 0.968 0.000 0.000 0.000 0.032
#> SRR2936915 1 0.0510 0.970 0.984 0.000 0.000 0.000 0.016
#> SRR2936914 5 0.4968 0.650 0.000 0.000 0.152 0.136 0.712
#> SRR2936913 5 0.4367 0.138 0.000 0.008 0.000 0.372 0.620
#> SRR2936912 1 0.0162 0.975 0.996 0.000 0.000 0.000 0.004
#> SRR2936910 1 0.0290 0.973 0.992 0.000 0.000 0.000 0.008
#> SRR2936911 4 0.4109 0.449 0.000 0.012 0.000 0.700 0.288
#> SRR2936907 2 0.0579 0.968 0.000 0.984 0.000 0.008 0.008
#> SRR2936908 2 0.0162 0.970 0.000 0.996 0.000 0.004 0.000
#> SRR2936904 2 0.0451 0.968 0.008 0.988 0.000 0.004 0.000
#> SRR2936905 2 0.0290 0.970 0.000 0.992 0.000 0.000 0.008
#> SRR2936903 3 0.2416 0.826 0.060 0.000 0.908 0.016 0.016
#> SRR2936901 3 0.0912 0.852 0.016 0.000 0.972 0.000 0.012
#> SRR2936902 3 0.1043 0.835 0.000 0.000 0.960 0.000 0.040
#> SRR2936900 3 0.4347 0.606 0.256 0.000 0.716 0.004 0.024
#> SRR2936898 3 0.1483 0.848 0.012 0.000 0.952 0.028 0.008
#> SRR2936899 3 0.1356 0.849 0.012 0.000 0.956 0.028 0.004
#> SRR2936897 1 0.1026 0.970 0.968 0.000 0.024 0.004 0.004
#> SRR2936896 5 0.6527 0.621 0.000 0.004 0.328 0.184 0.484
#> SRR2936894 1 0.0865 0.971 0.972 0.000 0.024 0.000 0.004
#> SRR2936893 2 0.2389 0.891 0.000 0.880 0.000 0.116 0.004
#> SRR2936895 4 0.6608 0.488 0.280 0.000 0.024 0.544 0.152
#> SRR2936892 2 0.1502 0.944 0.000 0.940 0.000 0.056 0.004
#> SRR2936891 1 0.0671 0.974 0.980 0.000 0.016 0.000 0.004
#> SRR2936890 2 0.0162 0.970 0.000 0.996 0.000 0.004 0.000
#> SRR2936886 4 0.0807 0.662 0.000 0.012 0.012 0.976 0.000
#> SRR2936885 3 0.4478 0.730 0.084 0.000 0.788 0.104 0.024
#> SRR2936888 4 0.5407 0.383 0.424 0.000 0.004 0.524 0.048
#> SRR2936889 2 0.1638 0.938 0.000 0.932 0.000 0.064 0.004
#> SRR2936887 4 0.1074 0.663 0.000 0.016 0.012 0.968 0.004
#> SRR2936884 3 0.1282 0.829 0.000 0.000 0.952 0.004 0.044
#> SRR2936883 3 0.1300 0.842 0.000 0.000 0.956 0.016 0.028
#> SRR2936881 3 0.0880 0.841 0.000 0.000 0.968 0.000 0.032
#> SRR2936882 3 0.4095 0.656 0.220 0.000 0.752 0.004 0.024
#> SRR2936880 3 0.1124 0.842 0.004 0.000 0.960 0.000 0.036
#> SRR2936878 5 0.4030 0.637 0.000 0.000 0.352 0.000 0.648
#> SRR2936879 1 0.1790 0.951 0.940 0.004 0.036 0.004 0.016
#> SRR2936875 2 0.0579 0.967 0.000 0.984 0.000 0.008 0.008
#> SRR2936877 5 0.4383 0.537 0.000 0.000 0.424 0.004 0.572
#> SRR2936876 1 0.1235 0.963 0.964 0.012 0.004 0.004 0.016
#> SRR2936873 1 0.0404 0.976 0.988 0.000 0.012 0.000 0.000
#> SRR2936872 2 0.0579 0.967 0.000 0.984 0.000 0.008 0.008
#> SRR2936871 2 0.0162 0.970 0.000 0.996 0.000 0.000 0.004
#> SRR2936874 2 0.0579 0.967 0.000 0.984 0.000 0.008 0.008
#> SRR2936870 4 0.5447 0.440 0.396 0.000 0.012 0.552 0.040
#> SRR2936869 4 0.1173 0.662 0.000 0.020 0.012 0.964 0.004
#> SRR2936868 4 0.1299 0.661 0.000 0.020 0.012 0.960 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR2936906 1 0.0405 0.911 0.988 0.000 0.000 0.004 0.000 0.008
#> SRR2936909 1 0.1007 0.906 0.956 0.000 0.000 0.000 0.000 0.044
#> SRR2936918 1 0.1501 0.884 0.924 0.000 0.000 0.000 0.000 0.076
#> SRR2936917 5 0.3300 0.610 0.020 0.004 0.008 0.000 0.816 0.152
#> SRR2936916 1 0.3134 0.802 0.820 0.000 0.000 0.000 0.036 0.144
#> SRR2936915 1 0.1444 0.889 0.928 0.000 0.000 0.000 0.000 0.072
#> SRR2936914 5 0.1737 0.642 0.000 0.000 0.020 0.040 0.932 0.008
#> SRR2936913 5 0.4974 0.432 0.000 0.008 0.000 0.220 0.660 0.112
#> SRR2936912 1 0.1152 0.909 0.952 0.000 0.000 0.004 0.000 0.044
#> SRR2936910 1 0.0603 0.910 0.980 0.000 0.000 0.004 0.000 0.016
#> SRR2936911 4 0.5112 0.468 0.000 0.008 0.000 0.648 0.132 0.212
#> SRR2936907 2 0.1124 0.956 0.000 0.956 0.000 0.036 0.000 0.008
#> SRR2936908 2 0.0363 0.963 0.000 0.988 0.000 0.012 0.000 0.000
#> SRR2936904 2 0.0717 0.963 0.000 0.976 0.000 0.016 0.000 0.008
#> SRR2936905 2 0.0146 0.962 0.000 0.996 0.000 0.004 0.000 0.000
#> SRR2936903 3 0.1789 0.911 0.032 0.000 0.924 0.000 0.000 0.044
#> SRR2936901 3 0.0520 0.935 0.008 0.000 0.984 0.000 0.000 0.008
#> SRR2936902 3 0.0260 0.935 0.000 0.000 0.992 0.000 0.008 0.000
#> SRR2936900 3 0.3316 0.800 0.136 0.000 0.812 0.000 0.000 0.052
#> SRR2936898 3 0.0436 0.937 0.004 0.000 0.988 0.004 0.004 0.000
#> SRR2936899 3 0.0436 0.937 0.004 0.000 0.988 0.004 0.004 0.000
#> SRR2936897 1 0.2225 0.885 0.892 0.000 0.008 0.008 0.000 0.092
#> SRR2936896 5 0.7482 0.145 0.012 0.000 0.084 0.260 0.336 0.308
#> SRR2936894 1 0.0692 0.912 0.976 0.000 0.000 0.004 0.000 0.020
#> SRR2936893 2 0.1588 0.937 0.000 0.924 0.000 0.072 0.000 0.004
#> SRR2936895 4 0.7466 0.195 0.136 0.000 0.012 0.372 0.144 0.336
#> SRR2936892 2 0.1349 0.948 0.000 0.940 0.000 0.056 0.000 0.004
#> SRR2936891 1 0.0508 0.911 0.984 0.000 0.000 0.004 0.000 0.012
#> SRR2936890 2 0.0692 0.961 0.000 0.976 0.000 0.020 0.000 0.004
#> SRR2936886 4 0.0862 0.643 0.000 0.016 0.000 0.972 0.004 0.008
#> SRR2936885 3 0.3046 0.882 0.036 0.000 0.868 0.036 0.004 0.056
#> SRR2936888 4 0.5973 0.451 0.292 0.000 0.000 0.496 0.008 0.204
#> SRR2936889 2 0.2170 0.904 0.000 0.888 0.000 0.100 0.000 0.012
#> SRR2936887 4 0.0603 0.641 0.000 0.016 0.000 0.980 0.004 0.000
#> SRR2936884 3 0.1262 0.921 0.000 0.000 0.956 0.008 0.020 0.016
#> SRR2936883 3 0.0551 0.934 0.000 0.000 0.984 0.004 0.008 0.004
#> SRR2936881 3 0.0260 0.935 0.000 0.000 0.992 0.000 0.008 0.000
#> SRR2936882 3 0.3049 0.841 0.104 0.000 0.844 0.004 0.000 0.048
#> SRR2936880 3 0.0260 0.935 0.000 0.000 0.992 0.000 0.008 0.000
#> SRR2936878 5 0.3470 0.635 0.000 0.000 0.152 0.000 0.796 0.052
#> SRR2936879 1 0.4320 0.700 0.692 0.028 0.004 0.004 0.004 0.268
#> SRR2936875 2 0.1219 0.938 0.000 0.948 0.000 0.004 0.000 0.048
#> SRR2936877 5 0.6352 0.523 0.020 0.012 0.180 0.000 0.512 0.276
#> SRR2936876 1 0.3481 0.762 0.756 0.012 0.000 0.000 0.004 0.228
#> SRR2936873 1 0.0547 0.911 0.980 0.000 0.000 0.000 0.000 0.020
#> SRR2936872 2 0.0692 0.953 0.000 0.976 0.000 0.004 0.000 0.020
#> SRR2936871 2 0.0146 0.960 0.000 0.996 0.000 0.000 0.000 0.004
#> SRR2936874 2 0.0865 0.948 0.000 0.964 0.000 0.000 0.000 0.036
#> SRR2936870 4 0.5832 0.458 0.292 0.000 0.000 0.508 0.004 0.196
#> SRR2936869 4 0.2085 0.624 0.000 0.056 0.000 0.912 0.008 0.024
#> SRR2936868 4 0.1682 0.630 0.000 0.052 0.000 0.928 0.000 0.020
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 14198 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 0.961 0.985 0.4257 0.576 0.576
#> 3 3 0.639 0.777 0.851 0.3784 0.784 0.626
#> 4 4 0.820 0.858 0.935 0.1555 0.938 0.832
#> 5 5 0.824 0.785 0.888 0.0570 0.954 0.862
#> 6 6 0.823 0.784 0.877 0.0313 0.947 0.830
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
#> SRR2936906 1 0.000 0.976 1.000 0.000
#> SRR2936909 1 0.000 0.976 1.000 0.000
#> SRR2936918 1 0.000 0.976 1.000 0.000
#> SRR2936917 2 0.000 0.987 0.000 1.000
#> SRR2936916 2 0.000 0.987 0.000 1.000
#> SRR2936915 2 0.000 0.987 0.000 1.000
#> SRR2936914 2 0.000 0.987 0.000 1.000
#> SRR2936913 2 0.000 0.987 0.000 1.000
#> SRR2936912 1 0.000 0.976 1.000 0.000
#> SRR2936910 1 0.000 0.976 1.000 0.000
#> SRR2936911 2 0.000 0.987 0.000 1.000
#> SRR2936907 2 0.000 0.987 0.000 1.000
#> SRR2936908 2 0.000 0.987 0.000 1.000
#> SRR2936904 2 0.000 0.987 0.000 1.000
#> SRR2936905 2 0.000 0.987 0.000 1.000
#> SRR2936903 1 0.000 0.976 1.000 0.000
#> SRR2936901 2 0.966 0.340 0.392 0.608
#> SRR2936902 2 0.000 0.987 0.000 1.000
#> SRR2936900 1 0.000 0.976 1.000 0.000
#> SRR2936898 2 0.000 0.987 0.000 1.000
#> SRR2936899 2 0.000 0.987 0.000 1.000
#> SRR2936897 1 0.909 0.512 0.676 0.324
#> SRR2936896 2 0.000 0.987 0.000 1.000
#> SRR2936894 1 0.000 0.976 1.000 0.000
#> SRR2936893 2 0.000 0.987 0.000 1.000
#> SRR2936895 2 0.000 0.987 0.000 1.000
#> SRR2936892 2 0.000 0.987 0.000 1.000
#> SRR2936891 1 0.000 0.976 1.000 0.000
#> SRR2936890 2 0.000 0.987 0.000 1.000
#> SRR2936886 2 0.000 0.987 0.000 1.000
#> SRR2936885 1 0.000 0.976 1.000 0.000
#> SRR2936888 1 0.000 0.976 1.000 0.000
#> SRR2936889 2 0.000 0.987 0.000 1.000
#> SRR2936887 2 0.000 0.987 0.000 1.000
#> SRR2936884 2 0.000 0.987 0.000 1.000
#> SRR2936883 2 0.000 0.987 0.000 1.000
#> SRR2936881 2 0.000 0.987 0.000 1.000
#> SRR2936882 1 0.000 0.976 1.000 0.000
#> SRR2936880 2 0.000 0.987 0.000 1.000
#> SRR2936878 2 0.000 0.987 0.000 1.000
#> SRR2936879 2 0.000 0.987 0.000 1.000
#> SRR2936875 2 0.000 0.987 0.000 1.000
#> SRR2936877 2 0.000 0.987 0.000 1.000
#> SRR2936876 2 0.295 0.934 0.052 0.948
#> SRR2936873 1 0.000 0.976 1.000 0.000
#> SRR2936872 2 0.000 0.987 0.000 1.000
#> SRR2936871 2 0.000 0.987 0.000 1.000
#> SRR2936874 2 0.000 0.987 0.000 1.000
#> SRR2936870 1 0.000 0.976 1.000 0.000
#> SRR2936869 2 0.000 0.987 0.000 1.000
#> SRR2936868 2 0.000 0.987 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR2936906 1 0.000 0.896 1.000 0.000 0.000
#> SRR2936909 1 0.000 0.896 1.000 0.000 0.000
#> SRR2936918 1 0.000 0.896 1.000 0.000 0.000
#> SRR2936917 2 0.000 0.871 0.000 1.000 0.000
#> SRR2936916 3 0.617 0.871 0.000 0.412 0.588
#> SRR2936915 3 0.617 0.871 0.000 0.412 0.588
#> SRR2936914 2 0.000 0.871 0.000 1.000 0.000
#> SRR2936913 2 0.000 0.871 0.000 1.000 0.000
#> SRR2936912 1 0.000 0.896 1.000 0.000 0.000
#> SRR2936910 1 0.000 0.896 1.000 0.000 0.000
#> SRR2936911 2 0.000 0.871 0.000 1.000 0.000
#> SRR2936907 2 0.000 0.871 0.000 1.000 0.000
#> SRR2936908 2 0.000 0.871 0.000 1.000 0.000
#> SRR2936904 2 0.624 -0.449 0.000 0.560 0.440
#> SRR2936905 2 0.000 0.871 0.000 1.000 0.000
#> SRR2936903 1 0.595 0.760 0.640 0.000 0.360
#> SRR2936901 3 0.000 0.336 0.000 0.000 1.000
#> SRR2936902 3 0.610 0.899 0.000 0.392 0.608
#> SRR2936900 1 0.595 0.760 0.640 0.000 0.360
#> SRR2936898 3 0.610 0.899 0.000 0.392 0.608
#> SRR2936899 3 0.610 0.899 0.000 0.392 0.608
#> SRR2936897 1 0.839 0.457 0.624 0.172 0.204
#> SRR2936896 2 0.000 0.871 0.000 1.000 0.000
#> SRR2936894 1 0.000 0.896 1.000 0.000 0.000
#> SRR2936893 2 0.000 0.871 0.000 1.000 0.000
#> SRR2936895 2 0.455 0.598 0.000 0.800 0.200
#> SRR2936892 2 0.000 0.871 0.000 1.000 0.000
#> SRR2936891 1 0.000 0.896 1.000 0.000 0.000
#> SRR2936890 2 0.000 0.871 0.000 1.000 0.000
#> SRR2936886 2 0.455 0.598 0.000 0.800 0.200
#> SRR2936885 1 0.595 0.760 0.640 0.000 0.360
#> SRR2936888 1 0.000 0.896 1.000 0.000 0.000
#> SRR2936889 2 0.000 0.871 0.000 1.000 0.000
#> SRR2936887 2 0.455 0.598 0.000 0.800 0.200
#> SRR2936884 3 0.610 0.899 0.000 0.392 0.608
#> SRR2936883 3 0.610 0.899 0.000 0.392 0.608
#> SRR2936881 3 0.610 0.899 0.000 0.392 0.608
#> SRR2936882 1 0.595 0.760 0.640 0.000 0.360
#> SRR2936880 3 0.610 0.899 0.000 0.392 0.608
#> SRR2936878 2 0.000 0.871 0.000 1.000 0.000
#> SRR2936879 2 0.610 -0.237 0.000 0.608 0.392
#> SRR2936875 2 0.000 0.871 0.000 1.000 0.000
#> SRR2936877 2 0.000 0.871 0.000 1.000 0.000
#> SRR2936876 3 0.595 0.840 0.000 0.360 0.640
#> SRR2936873 1 0.000 0.896 1.000 0.000 0.000
#> SRR2936872 2 0.000 0.871 0.000 1.000 0.000
#> SRR2936871 2 0.000 0.871 0.000 1.000 0.000
#> SRR2936874 2 0.000 0.871 0.000 1.000 0.000
#> SRR2936870 1 0.000 0.896 1.000 0.000 0.000
#> SRR2936869 2 0.455 0.598 0.000 0.800 0.200
#> SRR2936868 2 0.455 0.598 0.000 0.800 0.200
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR2936906 1 0.000 0.957 1.000 0.000 0.000 0.00
#> SRR2936909 1 0.000 0.957 1.000 0.000 0.000 0.00
#> SRR2936918 1 0.000 0.957 1.000 0.000 0.000 0.00
#> SRR2936917 2 0.000 0.923 0.000 1.000 0.000 0.00
#> SRR2936916 3 0.276 0.837 0.000 0.128 0.872 0.00
#> SRR2936915 3 0.276 0.837 0.000 0.128 0.872 0.00
#> SRR2936914 2 0.000 0.923 0.000 1.000 0.000 0.00
#> SRR2936913 2 0.000 0.923 0.000 1.000 0.000 0.00
#> SRR2936912 1 0.000 0.957 1.000 0.000 0.000 0.00
#> SRR2936910 1 0.000 0.957 1.000 0.000 0.000 0.00
#> SRR2936911 2 0.000 0.923 0.000 1.000 0.000 0.00
#> SRR2936907 2 0.000 0.923 0.000 1.000 0.000 0.00
#> SRR2936908 2 0.000 0.923 0.000 1.000 0.000 0.00
#> SRR2936904 3 0.496 0.184 0.000 0.448 0.552 0.00
#> SRR2936905 2 0.000 0.923 0.000 1.000 0.000 0.00
#> SRR2936903 4 0.000 1.000 0.000 0.000 0.000 1.00
#> SRR2936901 3 0.462 0.397 0.000 0.000 0.660 0.34
#> SRR2936902 3 0.147 0.880 0.000 0.052 0.948 0.00
#> SRR2936900 4 0.000 1.000 0.000 0.000 0.000 1.00
#> SRR2936898 3 0.147 0.880 0.000 0.052 0.948 0.00
#> SRR2936899 3 0.147 0.880 0.000 0.052 0.948 0.00
#> SRR2936897 1 0.478 0.473 0.624 0.000 0.376 0.00
#> SRR2936896 2 0.000 0.923 0.000 1.000 0.000 0.00
#> SRR2936894 1 0.000 0.957 1.000 0.000 0.000 0.00
#> SRR2936893 2 0.000 0.923 0.000 1.000 0.000 0.00
#> SRR2936895 2 0.365 0.743 0.000 0.796 0.204 0.00
#> SRR2936892 2 0.000 0.923 0.000 1.000 0.000 0.00
#> SRR2936891 1 0.000 0.957 1.000 0.000 0.000 0.00
#> SRR2936890 2 0.000 0.923 0.000 1.000 0.000 0.00
#> SRR2936886 2 0.365 0.743 0.000 0.796 0.204 0.00
#> SRR2936885 4 0.000 1.000 0.000 0.000 0.000 1.00
#> SRR2936888 1 0.000 0.957 1.000 0.000 0.000 0.00
#> SRR2936889 2 0.000 0.923 0.000 1.000 0.000 0.00
#> SRR2936887 2 0.365 0.743 0.000 0.796 0.204 0.00
#> SRR2936884 3 0.147 0.880 0.000 0.052 0.948 0.00
#> SRR2936883 3 0.147 0.880 0.000 0.052 0.948 0.00
#> SRR2936881 3 0.147 0.880 0.000 0.052 0.948 0.00
#> SRR2936882 4 0.000 1.000 0.000 0.000 0.000 1.00
#> SRR2936880 3 0.147 0.880 0.000 0.052 0.948 0.00
#> SRR2936878 2 0.000 0.923 0.000 1.000 0.000 0.00
#> SRR2936879 2 0.495 0.154 0.000 0.556 0.444 0.00
#> SRR2936875 2 0.000 0.923 0.000 1.000 0.000 0.00
#> SRR2936877 2 0.000 0.923 0.000 1.000 0.000 0.00
#> SRR2936876 3 0.194 0.833 0.000 0.076 0.924 0.00
#> SRR2936873 1 0.000 0.957 1.000 0.000 0.000 0.00
#> SRR2936872 2 0.000 0.923 0.000 1.000 0.000 0.00
#> SRR2936871 2 0.000 0.923 0.000 1.000 0.000 0.00
#> SRR2936874 2 0.000 0.923 0.000 1.000 0.000 0.00
#> SRR2936870 1 0.000 0.957 1.000 0.000 0.000 0.00
#> SRR2936869 2 0.365 0.743 0.000 0.796 0.204 0.00
#> SRR2936868 2 0.365 0.743 0.000 0.796 0.204 0.00
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR2936906 1 0.281 0.8913 0.832 0.000 0.000 0.00 0.168
#> SRR2936909 1 0.000 0.8674 1.000 0.000 0.000 0.00 0.000
#> SRR2936918 1 0.289 0.8898 0.824 0.000 0.000 0.00 0.176
#> SRR2936917 2 0.000 0.8804 0.000 1.000 0.000 0.00 0.000
#> SRR2936916 5 0.538 0.9494 0.000 0.064 0.368 0.00 0.568
#> SRR2936915 5 0.538 0.9494 0.000 0.064 0.368 0.00 0.568
#> SRR2936914 2 0.000 0.8804 0.000 1.000 0.000 0.00 0.000
#> SRR2936913 2 0.000 0.8804 0.000 1.000 0.000 0.00 0.000
#> SRR2936912 1 0.000 0.8674 1.000 0.000 0.000 0.00 0.000
#> SRR2936910 1 0.273 0.8915 0.840 0.000 0.000 0.00 0.160
#> SRR2936911 2 0.000 0.8804 0.000 1.000 0.000 0.00 0.000
#> SRR2936907 2 0.000 0.8804 0.000 1.000 0.000 0.00 0.000
#> SRR2936908 2 0.000 0.8804 0.000 1.000 0.000 0.00 0.000
#> SRR2936904 2 0.672 -0.3528 0.000 0.384 0.368 0.00 0.248
#> SRR2936905 2 0.000 0.8804 0.000 1.000 0.000 0.00 0.000
#> SRR2936903 4 0.000 1.0000 0.000 0.000 0.000 1.00 0.000
#> SRR2936901 3 0.672 0.1048 0.000 0.000 0.404 0.34 0.256
#> SRR2936902 3 0.000 0.7608 0.000 0.000 1.000 0.00 0.000
#> SRR2936900 4 0.000 1.0000 0.000 0.000 0.000 1.00 0.000
#> SRR2936898 3 0.314 0.6660 0.000 0.000 0.796 0.00 0.204
#> SRR2936899 3 0.314 0.6660 0.000 0.000 0.796 0.00 0.204
#> SRR2936897 1 0.411 0.3994 0.624 0.000 0.000 0.00 0.376
#> SRR2936896 2 0.000 0.8804 0.000 1.000 0.000 0.00 0.000
#> SRR2936894 1 0.289 0.8898 0.824 0.000 0.000 0.00 0.176
#> SRR2936893 2 0.000 0.8804 0.000 1.000 0.000 0.00 0.000
#> SRR2936895 2 0.353 0.6491 0.000 0.744 0.256 0.00 0.000
#> SRR2936892 2 0.000 0.8804 0.000 1.000 0.000 0.00 0.000
#> SRR2936891 1 0.289 0.8898 0.824 0.000 0.000 0.00 0.176
#> SRR2936890 2 0.000 0.8804 0.000 1.000 0.000 0.00 0.000
#> SRR2936886 2 0.353 0.6491 0.000 0.744 0.256 0.00 0.000
#> SRR2936885 4 0.000 1.0000 0.000 0.000 0.000 1.00 0.000
#> SRR2936888 1 0.000 0.8674 1.000 0.000 0.000 0.00 0.000
#> SRR2936889 2 0.000 0.8804 0.000 1.000 0.000 0.00 0.000
#> SRR2936887 2 0.353 0.6491 0.000 0.744 0.256 0.00 0.000
#> SRR2936884 3 0.000 0.7608 0.000 0.000 1.000 0.00 0.000
#> SRR2936883 3 0.000 0.7608 0.000 0.000 1.000 0.00 0.000
#> SRR2936881 3 0.000 0.7608 0.000 0.000 1.000 0.00 0.000
#> SRR2936882 4 0.000 1.0000 0.000 0.000 0.000 1.00 0.000
#> SRR2936880 3 0.000 0.7608 0.000 0.000 1.000 0.00 0.000
#> SRR2936878 2 0.000 0.8804 0.000 1.000 0.000 0.00 0.000
#> SRR2936879 2 0.645 0.0409 0.000 0.492 0.296 0.00 0.212
#> SRR2936875 2 0.000 0.8804 0.000 1.000 0.000 0.00 0.000
#> SRR2936877 2 0.000 0.8804 0.000 1.000 0.000 0.00 0.000
#> SRR2936876 5 0.520 0.9009 0.000 0.064 0.316 0.00 0.620
#> SRR2936873 1 0.281 0.8913 0.832 0.000 0.000 0.00 0.168
#> SRR2936872 2 0.000 0.8804 0.000 1.000 0.000 0.00 0.000
#> SRR2936871 2 0.000 0.8804 0.000 1.000 0.000 0.00 0.000
#> SRR2936874 2 0.000 0.8804 0.000 1.000 0.000 0.00 0.000
#> SRR2936870 1 0.000 0.8674 1.000 0.000 0.000 0.00 0.000
#> SRR2936869 2 0.353 0.6491 0.000 0.744 0.256 0.00 0.000
#> SRR2936868 2 0.353 0.6491 0.000 0.744 0.256 0.00 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR2936906 1 0.372 0.825 0.616 0.000 0.000 0.000 0.384 0.000
#> SRR2936909 5 0.000 0.860 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936918 1 0.291 0.900 0.784 0.000 0.000 0.000 0.216 0.000
#> SRR2936917 2 0.000 0.904 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936916 4 0.353 0.536 0.000 0.000 0.328 0.672 0.000 0.000
#> SRR2936915 4 0.353 0.536 0.000 0.000 0.328 0.672 0.000 0.000
#> SRR2936914 2 0.000 0.904 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936913 2 0.000 0.904 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936912 5 0.000 0.860 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936910 1 0.331 0.890 0.720 0.000 0.000 0.000 0.280 0.000
#> SRR2936911 2 0.000 0.904 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936907 2 0.000 0.904 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936908 2 0.000 0.904 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936904 4 0.625 0.260 0.004 0.320 0.324 0.352 0.000 0.000
#> SRR2936905 2 0.000 0.904 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936903 6 0.000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR2936901 4 0.765 -0.198 0.212 0.000 0.260 0.320 0.000 0.208
#> SRR2936902 3 0.000 0.873 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936900 6 0.000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR2936898 3 0.282 0.697 0.000 0.000 0.796 0.204 0.000 0.000
#> SRR2936899 3 0.282 0.697 0.000 0.000 0.796 0.204 0.000 0.000
#> SRR2936897 5 0.441 0.465 0.040 0.000 0.000 0.336 0.624 0.000
#> SRR2936896 2 0.000 0.904 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936894 1 0.291 0.900 0.784 0.000 0.000 0.000 0.216 0.000
#> SRR2936893 2 0.000 0.904 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936895 2 0.379 0.668 0.000 0.744 0.216 0.040 0.000 0.000
#> SRR2936892 2 0.000 0.904 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936891 1 0.291 0.900 0.784 0.000 0.000 0.000 0.216 0.000
#> SRR2936890 2 0.000 0.904 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936886 2 0.379 0.668 0.000 0.744 0.216 0.040 0.000 0.000
#> SRR2936885 6 0.000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR2936888 5 0.000 0.860 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936889 2 0.000 0.904 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936887 2 0.379 0.668 0.000 0.744 0.216 0.040 0.000 0.000
#> SRR2936884 3 0.000 0.873 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936883 3 0.000 0.873 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936881 3 0.000 0.873 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936882 6 0.000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR2936880 3 0.000 0.873 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936878 2 0.000 0.904 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936879 2 0.601 -0.169 0.000 0.428 0.256 0.316 0.000 0.000
#> SRR2936875 2 0.000 0.904 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936877 2 0.000 0.904 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936876 4 0.433 0.515 0.040 0.000 0.316 0.644 0.000 0.000
#> SRR2936873 1 0.372 0.825 0.616 0.000 0.000 0.000 0.384 0.000
#> SRR2936872 2 0.000 0.904 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936871 2 0.000 0.904 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936874 2 0.000 0.904 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936870 5 0.000 0.860 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936869 2 0.379 0.668 0.000 0.744 0.216 0.040 0.000 0.000
#> SRR2936868 2 0.379 0.668 0.000 0.744 0.216 0.040 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 14198 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 1.000 1.000 0.4398 0.561 0.561
#> 3 3 0.646 0.867 0.895 0.4176 0.762 0.583
#> 4 4 0.781 0.765 0.842 0.1408 0.953 0.864
#> 5 5 0.738 0.790 0.838 0.0721 0.889 0.655
#> 6 6 0.793 0.668 0.781 0.0568 0.965 0.852
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
#> SRR2936906 1 0 1 1 0
#> SRR2936909 1 0 1 1 0
#> SRR2936918 1 0 1 1 0
#> SRR2936917 2 0 1 0 1
#> SRR2936916 2 0 1 0 1
#> SRR2936915 2 0 1 0 1
#> SRR2936914 2 0 1 0 1
#> SRR2936913 2 0 1 0 1
#> SRR2936912 1 0 1 1 0
#> SRR2936910 1 0 1 1 0
#> SRR2936911 2 0 1 0 1
#> SRR2936907 2 0 1 0 1
#> SRR2936908 2 0 1 0 1
#> SRR2936904 2 0 1 0 1
#> SRR2936905 2 0 1 0 1
#> SRR2936903 1 0 1 1 0
#> SRR2936901 1 0 1 1 0
#> SRR2936902 2 0 1 0 1
#> SRR2936900 1 0 1 1 0
#> SRR2936898 2 0 1 0 1
#> SRR2936899 2 0 1 0 1
#> SRR2936897 1 0 1 1 0
#> SRR2936896 2 0 1 0 1
#> SRR2936894 1 0 1 1 0
#> SRR2936893 2 0 1 0 1
#> SRR2936895 2 0 1 0 1
#> SRR2936892 2 0 1 0 1
#> SRR2936891 1 0 1 1 0
#> SRR2936890 2 0 1 0 1
#> SRR2936886 2 0 1 0 1
#> SRR2936885 1 0 1 1 0
#> SRR2936888 1 0 1 1 0
#> SRR2936889 2 0 1 0 1
#> SRR2936887 2 0 1 0 1
#> SRR2936884 2 0 1 0 1
#> SRR2936883 2 0 1 0 1
#> SRR2936881 2 0 1 0 1
#> SRR2936882 1 0 1 1 0
#> SRR2936880 2 0 1 0 1
#> SRR2936878 2 0 1 0 1
#> SRR2936879 2 0 1 0 1
#> SRR2936875 2 0 1 0 1
#> SRR2936877 2 0 1 0 1
#> SRR2936876 2 0 1 0 1
#> SRR2936873 1 0 1 1 0
#> SRR2936872 2 0 1 0 1
#> SRR2936871 2 0 1 0 1
#> SRR2936874 2 0 1 0 1
#> SRR2936870 1 0 1 1 0
#> SRR2936869 2 0 1 0 1
#> SRR2936868 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR2936906 1 0.0000 0.932 1.000 0.000 0.000
#> SRR2936909 1 0.0237 0.932 0.996 0.000 0.004
#> SRR2936918 1 0.0000 0.932 1.000 0.000 0.000
#> SRR2936917 2 0.0000 0.920 0.000 1.000 0.000
#> SRR2936916 3 0.5291 0.897 0.000 0.268 0.732
#> SRR2936915 3 0.5291 0.897 0.000 0.268 0.732
#> SRR2936914 2 0.0000 0.920 0.000 1.000 0.000
#> SRR2936913 2 0.0000 0.920 0.000 1.000 0.000
#> SRR2936912 1 0.0237 0.932 0.996 0.000 0.004
#> SRR2936910 1 0.0000 0.932 1.000 0.000 0.000
#> SRR2936911 2 0.0000 0.920 0.000 1.000 0.000
#> SRR2936907 2 0.0000 0.920 0.000 1.000 0.000
#> SRR2936908 2 0.0000 0.920 0.000 1.000 0.000
#> SRR2936904 3 0.5968 0.739 0.000 0.364 0.636
#> SRR2936905 2 0.0000 0.920 0.000 1.000 0.000
#> SRR2936903 1 0.5291 0.821 0.732 0.000 0.268
#> SRR2936901 3 0.0237 0.655 0.004 0.000 0.996
#> SRR2936902 3 0.4605 0.911 0.000 0.204 0.796
#> SRR2936900 1 0.5254 0.821 0.736 0.000 0.264
#> SRR2936898 3 0.4504 0.905 0.000 0.196 0.804
#> SRR2936899 3 0.4504 0.905 0.000 0.196 0.804
#> SRR2936897 1 0.2959 0.870 0.900 0.000 0.100
#> SRR2936896 2 0.0000 0.920 0.000 1.000 0.000
#> SRR2936894 1 0.0000 0.932 1.000 0.000 0.000
#> SRR2936893 2 0.0000 0.920 0.000 1.000 0.000
#> SRR2936895 2 0.5363 0.523 0.000 0.724 0.276
#> SRR2936892 2 0.0000 0.920 0.000 1.000 0.000
#> SRR2936891 1 0.0000 0.932 1.000 0.000 0.000
#> SRR2936890 2 0.0000 0.920 0.000 1.000 0.000
#> SRR2936886 2 0.5363 0.523 0.000 0.724 0.276
#> SRR2936885 1 0.5291 0.821 0.732 0.000 0.268
#> SRR2936888 1 0.0424 0.931 0.992 0.000 0.008
#> SRR2936889 2 0.0000 0.920 0.000 1.000 0.000
#> SRR2936887 2 0.5363 0.523 0.000 0.724 0.276
#> SRR2936884 3 0.5327 0.893 0.000 0.272 0.728
#> SRR2936883 3 0.4654 0.912 0.000 0.208 0.792
#> SRR2936881 3 0.4654 0.912 0.000 0.208 0.792
#> SRR2936882 1 0.5254 0.821 0.736 0.000 0.264
#> SRR2936880 3 0.4654 0.912 0.000 0.208 0.792
#> SRR2936878 2 0.0000 0.920 0.000 1.000 0.000
#> SRR2936879 3 0.5327 0.893 0.000 0.272 0.728
#> SRR2936875 2 0.0000 0.920 0.000 1.000 0.000
#> SRR2936877 2 0.0000 0.920 0.000 1.000 0.000
#> SRR2936876 3 0.5178 0.900 0.000 0.256 0.744
#> SRR2936873 1 0.0237 0.932 0.996 0.000 0.004
#> SRR2936872 2 0.0000 0.920 0.000 1.000 0.000
#> SRR2936871 2 0.0000 0.920 0.000 1.000 0.000
#> SRR2936874 2 0.0000 0.920 0.000 1.000 0.000
#> SRR2936870 1 0.0424 0.931 0.992 0.000 0.008
#> SRR2936869 2 0.3879 0.746 0.000 0.848 0.152
#> SRR2936868 2 0.5363 0.523 0.000 0.724 0.276
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR2936906 1 0.0707 0.961 0.980 0.000 0.020 0.000
#> SRR2936909 1 0.0524 0.958 0.988 0.000 0.008 0.004
#> SRR2936918 1 0.0707 0.961 0.980 0.000 0.020 0.000
#> SRR2936917 2 0.1637 0.851 0.000 0.940 0.000 0.060
#> SRR2936916 3 0.5897 0.698 0.000 0.044 0.588 0.368
#> SRR2936915 3 0.5897 0.698 0.000 0.044 0.588 0.368
#> SRR2936914 2 0.1637 0.851 0.000 0.940 0.000 0.060
#> SRR2936913 2 0.1637 0.851 0.000 0.940 0.000 0.060
#> SRR2936912 1 0.0524 0.958 0.988 0.000 0.008 0.004
#> SRR2936910 1 0.0707 0.961 0.980 0.000 0.020 0.000
#> SRR2936911 2 0.1637 0.851 0.000 0.940 0.000 0.060
#> SRR2936907 2 0.1637 0.851 0.000 0.940 0.000 0.060
#> SRR2936908 2 0.0000 0.859 0.000 1.000 0.000 0.000
#> SRR2936904 3 0.7688 0.488 0.000 0.220 0.416 0.364
#> SRR2936905 2 0.0000 0.859 0.000 1.000 0.000 0.000
#> SRR2936903 4 0.4941 0.760 0.436 0.000 0.000 0.564
#> SRR2936901 4 0.4933 0.134 0.000 0.000 0.432 0.568
#> SRR2936902 3 0.1022 0.790 0.000 0.032 0.968 0.000
#> SRR2936900 4 0.4941 0.760 0.436 0.000 0.000 0.564
#> SRR2936898 3 0.1356 0.787 0.000 0.032 0.960 0.008
#> SRR2936899 3 0.1356 0.787 0.000 0.032 0.960 0.008
#> SRR2936897 1 0.3088 0.809 0.888 0.000 0.052 0.060
#> SRR2936896 2 0.1637 0.851 0.000 0.940 0.000 0.060
#> SRR2936894 1 0.0707 0.961 0.980 0.000 0.020 0.000
#> SRR2936893 2 0.0000 0.859 0.000 1.000 0.000 0.000
#> SRR2936895 2 0.7397 0.233 0.000 0.508 0.200 0.292
#> SRR2936892 2 0.0000 0.859 0.000 1.000 0.000 0.000
#> SRR2936891 1 0.0707 0.961 0.980 0.000 0.020 0.000
#> SRR2936890 2 0.0000 0.859 0.000 1.000 0.000 0.000
#> SRR2936886 2 0.7588 0.155 0.000 0.468 0.220 0.312
#> SRR2936885 4 0.4941 0.760 0.436 0.000 0.000 0.564
#> SRR2936888 1 0.0657 0.957 0.984 0.000 0.012 0.004
#> SRR2936889 2 0.0000 0.859 0.000 1.000 0.000 0.000
#> SRR2936887 2 0.7588 0.155 0.000 0.468 0.220 0.312
#> SRR2936884 3 0.1022 0.790 0.000 0.032 0.968 0.000
#> SRR2936883 3 0.1022 0.790 0.000 0.032 0.968 0.000
#> SRR2936881 3 0.1022 0.790 0.000 0.032 0.968 0.000
#> SRR2936882 4 0.4941 0.760 0.436 0.000 0.000 0.564
#> SRR2936880 3 0.1022 0.790 0.000 0.032 0.968 0.000
#> SRR2936878 2 0.1637 0.851 0.000 0.940 0.000 0.060
#> SRR2936879 3 0.5954 0.701 0.000 0.052 0.604 0.344
#> SRR2936875 2 0.0000 0.859 0.000 1.000 0.000 0.000
#> SRR2936877 2 0.1637 0.851 0.000 0.940 0.000 0.060
#> SRR2936876 3 0.6035 0.682 0.020 0.020 0.588 0.372
#> SRR2936873 1 0.0188 0.960 0.996 0.000 0.000 0.004
#> SRR2936872 2 0.0000 0.859 0.000 1.000 0.000 0.000
#> SRR2936871 2 0.0000 0.859 0.000 1.000 0.000 0.000
#> SRR2936874 2 0.0000 0.859 0.000 1.000 0.000 0.000
#> SRR2936870 1 0.0657 0.957 0.984 0.000 0.012 0.004
#> SRR2936869 2 0.5910 0.538 0.000 0.672 0.084 0.244
#> SRR2936868 2 0.7588 0.155 0.000 0.468 0.220 0.312
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR2936906 1 0.1410 0.867 0.940 0.000 0.000 0.060 0.000
#> SRR2936909 1 0.2511 0.821 0.892 0.000 0.000 0.080 0.028
#> SRR2936918 1 0.1410 0.867 0.940 0.000 0.000 0.060 0.000
#> SRR2936917 2 0.4031 0.821 0.000 0.772 0.000 0.044 0.184
#> SRR2936916 4 0.3909 0.625 0.000 0.000 0.216 0.760 0.024
#> SRR2936915 4 0.3909 0.625 0.000 0.000 0.216 0.760 0.024
#> SRR2936914 2 0.4031 0.821 0.000 0.772 0.000 0.044 0.184
#> SRR2936913 2 0.4031 0.821 0.000 0.772 0.000 0.044 0.184
#> SRR2936912 1 0.1704 0.845 0.928 0.000 0.000 0.068 0.004
#> SRR2936910 1 0.1410 0.867 0.940 0.000 0.000 0.060 0.000
#> SRR2936911 2 0.4031 0.821 0.000 0.772 0.000 0.044 0.184
#> SRR2936907 2 0.3958 0.821 0.000 0.776 0.000 0.040 0.184
#> SRR2936908 2 0.0000 0.854 0.000 1.000 0.000 0.000 0.000
#> SRR2936904 4 0.3991 0.656 0.000 0.048 0.172 0.780 0.000
#> SRR2936905 2 0.0000 0.854 0.000 1.000 0.000 0.000 0.000
#> SRR2936903 5 0.3774 0.993 0.296 0.000 0.000 0.000 0.704
#> SRR2936901 3 0.4268 0.478 0.000 0.000 0.648 0.008 0.344
#> SRR2936902 3 0.0162 0.939 0.000 0.000 0.996 0.004 0.000
#> SRR2936900 5 0.4152 0.993 0.296 0.000 0.000 0.012 0.692
#> SRR2936898 3 0.0162 0.936 0.000 0.000 0.996 0.004 0.000
#> SRR2936899 3 0.0162 0.936 0.000 0.000 0.996 0.004 0.000
#> SRR2936897 1 0.5109 0.353 0.580 0.000 0.008 0.384 0.028
#> SRR2936896 2 0.4031 0.821 0.000 0.772 0.000 0.044 0.184
#> SRR2936894 1 0.1410 0.867 0.940 0.000 0.000 0.060 0.000
#> SRR2936893 2 0.0000 0.854 0.000 1.000 0.000 0.000 0.000
#> SRR2936895 4 0.7298 0.505 0.000 0.388 0.104 0.424 0.084
#> SRR2936892 2 0.0000 0.854 0.000 1.000 0.000 0.000 0.000
#> SRR2936891 1 0.1410 0.867 0.940 0.000 0.000 0.060 0.000
#> SRR2936890 2 0.0000 0.854 0.000 1.000 0.000 0.000 0.000
#> SRR2936886 4 0.7219 0.590 0.000 0.332 0.104 0.480 0.084
#> SRR2936885 5 0.3774 0.993 0.296 0.000 0.000 0.000 0.704
#> SRR2936888 1 0.1478 0.850 0.936 0.000 0.000 0.064 0.000
#> SRR2936889 2 0.0000 0.854 0.000 1.000 0.000 0.000 0.000
#> SRR2936887 4 0.7219 0.590 0.000 0.332 0.104 0.480 0.084
#> SRR2936884 3 0.0162 0.939 0.000 0.000 0.996 0.004 0.000
#> SRR2936883 3 0.0162 0.939 0.000 0.000 0.996 0.004 0.000
#> SRR2936881 3 0.0162 0.939 0.000 0.000 0.996 0.004 0.000
#> SRR2936882 5 0.4152 0.993 0.296 0.000 0.000 0.012 0.692
#> SRR2936880 3 0.0162 0.939 0.000 0.000 0.996 0.004 0.000
#> SRR2936878 2 0.4031 0.821 0.000 0.772 0.000 0.044 0.184
#> SRR2936879 4 0.3521 0.627 0.000 0.004 0.232 0.764 0.000
#> SRR2936875 2 0.0000 0.854 0.000 1.000 0.000 0.000 0.000
#> SRR2936877 2 0.4031 0.821 0.000 0.772 0.000 0.044 0.184
#> SRR2936876 4 0.3687 0.611 0.000 0.000 0.180 0.792 0.028
#> SRR2936873 1 0.0955 0.859 0.968 0.000 0.000 0.028 0.004
#> SRR2936872 2 0.0000 0.854 0.000 1.000 0.000 0.000 0.000
#> SRR2936871 2 0.0000 0.854 0.000 1.000 0.000 0.000 0.000
#> SRR2936874 2 0.0000 0.854 0.000 1.000 0.000 0.000 0.000
#> SRR2936870 1 0.1478 0.850 0.936 0.000 0.000 0.064 0.000
#> SRR2936869 2 0.6476 -0.159 0.000 0.544 0.044 0.328 0.084
#> SRR2936868 4 0.7219 0.590 0.000 0.332 0.104 0.480 0.084
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR2936906 1 0.0000 0.8846 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936909 1 0.4344 0.7798 0.716 0.000 0.000 0.096 0.188 0.000
#> SRR2936918 1 0.0146 0.8843 0.996 0.000 0.000 0.004 0.000 0.000
#> SRR2936917 2 0.0000 0.6407 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936916 4 0.1141 0.4877 0.000 0.000 0.052 0.948 0.000 0.000
#> SRR2936915 4 0.1141 0.4877 0.000 0.000 0.052 0.948 0.000 0.000
#> SRR2936914 2 0.0000 0.6407 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936913 2 0.0000 0.6407 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936912 1 0.3516 0.8398 0.788 0.000 0.000 0.048 0.164 0.000
#> SRR2936910 1 0.0146 0.8843 0.996 0.000 0.000 0.004 0.000 0.000
#> SRR2936911 2 0.0000 0.6407 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936907 2 0.0000 0.6407 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936908 2 0.3838 0.6961 0.000 0.552 0.000 0.000 0.000 0.448
#> SRR2936904 4 0.4102 0.3918 0.000 0.004 0.048 0.752 0.188 0.008
#> SRR2936905 2 0.3838 0.6961 0.000 0.552 0.000 0.000 0.000 0.448
#> SRR2936903 6 0.5559 0.9894 0.176 0.000 0.000 0.000 0.284 0.540
#> SRR2936901 3 0.4428 0.6215 0.000 0.000 0.696 0.000 0.084 0.220
#> SRR2936902 3 0.0146 0.9505 0.000 0.000 0.996 0.000 0.004 0.000
#> SRR2936900 6 0.5625 0.9894 0.176 0.000 0.000 0.000 0.304 0.520
#> SRR2936898 3 0.0713 0.9421 0.000 0.000 0.972 0.000 0.028 0.000
#> SRR2936899 3 0.0713 0.9421 0.000 0.000 0.972 0.000 0.028 0.000
#> SRR2936897 4 0.5514 -0.0284 0.272 0.000 0.000 0.552 0.176 0.000
#> SRR2936896 2 0.0146 0.6378 0.000 0.996 0.000 0.000 0.000 0.004
#> SRR2936894 1 0.0000 0.8846 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936893 2 0.3838 0.6961 0.000 0.552 0.000 0.000 0.000 0.448
#> SRR2936895 5 0.8097 0.7032 0.000 0.116 0.060 0.288 0.360 0.176
#> SRR2936892 2 0.3838 0.6961 0.000 0.552 0.000 0.000 0.000 0.448
#> SRR2936891 1 0.0000 0.8846 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936890 2 0.3838 0.6961 0.000 0.552 0.000 0.000 0.000 0.448
#> SRR2936886 4 0.7013 -0.5068 0.000 0.108 0.048 0.404 0.396 0.044
#> SRR2936885 6 0.5559 0.9894 0.176 0.000 0.000 0.000 0.284 0.540
#> SRR2936888 1 0.2814 0.8593 0.820 0.000 0.000 0.008 0.172 0.000
#> SRR2936889 2 0.3838 0.6961 0.000 0.552 0.000 0.000 0.000 0.448
#> SRR2936887 4 0.7013 -0.5068 0.000 0.108 0.048 0.404 0.396 0.044
#> SRR2936884 3 0.0146 0.9505 0.000 0.000 0.996 0.000 0.004 0.000
#> SRR2936883 3 0.0146 0.9505 0.000 0.000 0.996 0.000 0.004 0.000
#> SRR2936881 3 0.0000 0.9504 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936882 6 0.5625 0.9894 0.176 0.000 0.000 0.000 0.304 0.520
#> SRR2936880 3 0.0000 0.9504 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936878 2 0.0000 0.6407 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936879 4 0.3063 0.4523 0.000 0.000 0.068 0.840 0.092 0.000
#> SRR2936875 2 0.3843 0.6930 0.000 0.548 0.000 0.000 0.000 0.452
#> SRR2936877 2 0.0000 0.6407 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936876 4 0.1625 0.4494 0.000 0.000 0.012 0.928 0.060 0.000
#> SRR2936873 1 0.3088 0.8573 0.832 0.000 0.000 0.048 0.120 0.000
#> SRR2936872 2 0.3838 0.6961 0.000 0.552 0.000 0.000 0.000 0.448
#> SRR2936871 2 0.3838 0.6961 0.000 0.552 0.000 0.000 0.000 0.448
#> SRR2936874 2 0.3843 0.6930 0.000 0.548 0.000 0.000 0.000 0.452
#> SRR2936870 1 0.2814 0.8593 0.820 0.000 0.000 0.008 0.172 0.000
#> SRR2936869 5 0.7667 0.7258 0.000 0.152 0.016 0.264 0.396 0.172
#> SRR2936868 4 0.7013 -0.5068 0.000 0.108 0.048 0.404 0.396 0.044
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 14198 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 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.992 0.996 0.4957 0.506 0.506
#> 3 3 0.931 0.970 0.984 0.2646 0.848 0.706
#> 4 4 0.842 0.857 0.907 0.0761 0.947 0.862
#> 5 5 0.842 0.876 0.897 0.0566 0.895 0.690
#> 6 6 0.933 0.968 0.970 0.0589 0.992 0.968
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR2936906 1 0.0000 1.000 1.000 0.000
#> SRR2936909 1 0.0000 1.000 1.000 0.000
#> SRR2936918 1 0.0000 1.000 1.000 0.000
#> SRR2936917 2 0.0000 0.994 0.000 1.000
#> SRR2936916 1 0.0000 1.000 1.000 0.000
#> SRR2936915 1 0.0000 1.000 1.000 0.000
#> SRR2936914 2 0.0000 0.994 0.000 1.000
#> SRR2936913 2 0.0000 0.994 0.000 1.000
#> SRR2936912 1 0.0000 1.000 1.000 0.000
#> SRR2936910 1 0.0000 1.000 1.000 0.000
#> SRR2936911 2 0.0000 0.994 0.000 1.000
#> SRR2936907 2 0.0000 0.994 0.000 1.000
#> SRR2936908 2 0.0000 0.994 0.000 1.000
#> SRR2936904 2 0.0000 0.994 0.000 1.000
#> SRR2936905 2 0.0000 0.994 0.000 1.000
#> SRR2936903 1 0.0000 1.000 1.000 0.000
#> SRR2936901 1 0.0000 1.000 1.000 0.000
#> SRR2936902 2 0.6801 0.780 0.180 0.820
#> SRR2936900 1 0.0000 1.000 1.000 0.000
#> SRR2936898 1 0.0000 1.000 1.000 0.000
#> SRR2936899 1 0.0376 0.996 0.996 0.004
#> SRR2936897 1 0.0000 1.000 1.000 0.000
#> SRR2936896 2 0.0000 0.994 0.000 1.000
#> SRR2936894 1 0.0000 1.000 1.000 0.000
#> SRR2936893 2 0.0000 0.994 0.000 1.000
#> SRR2936895 2 0.0000 0.994 0.000 1.000
#> SRR2936892 2 0.0000 0.994 0.000 1.000
#> SRR2936891 1 0.0000 1.000 1.000 0.000
#> SRR2936890 2 0.0000 0.994 0.000 1.000
#> SRR2936886 2 0.0000 0.994 0.000 1.000
#> SRR2936885 1 0.0000 1.000 1.000 0.000
#> SRR2936888 1 0.0000 1.000 1.000 0.000
#> SRR2936889 2 0.0000 0.994 0.000 1.000
#> SRR2936887 2 0.0000 0.994 0.000 1.000
#> SRR2936884 2 0.0000 0.994 0.000 1.000
#> SRR2936883 2 0.0000 0.994 0.000 1.000
#> SRR2936881 2 0.0000 0.994 0.000 1.000
#> SRR2936882 1 0.0000 1.000 1.000 0.000
#> SRR2936880 2 0.0000 0.994 0.000 1.000
#> SRR2936878 2 0.0000 0.994 0.000 1.000
#> SRR2936879 2 0.0000 0.994 0.000 1.000
#> SRR2936875 2 0.0000 0.994 0.000 1.000
#> SRR2936877 2 0.0000 0.994 0.000 1.000
#> SRR2936876 1 0.0000 1.000 1.000 0.000
#> SRR2936873 1 0.0000 1.000 1.000 0.000
#> SRR2936872 2 0.0000 0.994 0.000 1.000
#> SRR2936871 2 0.0000 0.994 0.000 1.000
#> SRR2936874 2 0.0000 0.994 0.000 1.000
#> SRR2936870 1 0.0000 1.000 1.000 0.000
#> SRR2936869 2 0.0000 0.994 0.000 1.000
#> SRR2936868 2 0.0000 0.994 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR2936906 1 0.000 0.950 1.0 0 0.0
#> SRR2936909 1 0.000 0.950 1.0 0 0.0
#> SRR2936918 1 0.000 0.950 1.0 0 0.0
#> SRR2936917 2 0.000 1.000 0.0 1 0.0
#> SRR2936916 1 0.000 0.950 1.0 0 0.0
#> SRR2936915 1 0.000 0.950 1.0 0 0.0
#> SRR2936914 2 0.000 1.000 0.0 1 0.0
#> SRR2936913 2 0.000 1.000 0.0 1 0.0
#> SRR2936912 1 0.000 0.950 1.0 0 0.0
#> SRR2936910 1 0.000 0.950 1.0 0 0.0
#> SRR2936911 2 0.000 1.000 0.0 1 0.0
#> SRR2936907 2 0.000 1.000 0.0 1 0.0
#> SRR2936908 2 0.000 1.000 0.0 1 0.0
#> SRR2936904 2 0.000 1.000 0.0 1 0.0
#> SRR2936905 2 0.000 1.000 0.0 1 0.0
#> SRR2936903 1 0.455 0.794 0.8 0 0.2
#> SRR2936901 3 0.000 1.000 0.0 0 1.0
#> SRR2936902 3 0.000 1.000 0.0 0 1.0
#> SRR2936900 1 0.455 0.794 0.8 0 0.2
#> SRR2936898 3 0.000 1.000 0.0 0 1.0
#> SRR2936899 3 0.000 1.000 0.0 0 1.0
#> SRR2936897 1 0.000 0.950 1.0 0 0.0
#> SRR2936896 2 0.000 1.000 0.0 1 0.0
#> SRR2936894 1 0.000 0.950 1.0 0 0.0
#> SRR2936893 2 0.000 1.000 0.0 1 0.0
#> SRR2936895 2 0.000 1.000 0.0 1 0.0
#> SRR2936892 2 0.000 1.000 0.0 1 0.0
#> SRR2936891 1 0.000 0.950 1.0 0 0.0
#> SRR2936890 2 0.000 1.000 0.0 1 0.0
#> SRR2936886 2 0.000 1.000 0.0 1 0.0
#> SRR2936885 1 0.455 0.794 0.8 0 0.2
#> SRR2936888 1 0.000 0.950 1.0 0 0.0
#> SRR2936889 2 0.000 1.000 0.0 1 0.0
#> SRR2936887 2 0.000 1.000 0.0 1 0.0
#> SRR2936884 3 0.000 1.000 0.0 0 1.0
#> SRR2936883 3 0.000 1.000 0.0 0 1.0
#> SRR2936881 3 0.000 1.000 0.0 0 1.0
#> SRR2936882 1 0.455 0.794 0.8 0 0.2
#> SRR2936880 3 0.000 1.000 0.0 0 1.0
#> SRR2936878 2 0.000 1.000 0.0 1 0.0
#> SRR2936879 2 0.000 1.000 0.0 1 0.0
#> SRR2936875 2 0.000 1.000 0.0 1 0.0
#> SRR2936877 2 0.000 1.000 0.0 1 0.0
#> SRR2936876 1 0.000 0.950 1.0 0 0.0
#> SRR2936873 1 0.000 0.950 1.0 0 0.0
#> SRR2936872 2 0.000 1.000 0.0 1 0.0
#> SRR2936871 2 0.000 1.000 0.0 1 0.0
#> SRR2936874 2 0.000 1.000 0.0 1 0.0
#> SRR2936870 1 0.000 0.950 1.0 0 0.0
#> SRR2936869 2 0.000 1.000 0.0 1 0.0
#> SRR2936868 2 0.000 1.000 0.0 1 0.0
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR2936906 1 0.000 0.8938 1.000 0.000 0.000 0.000
#> SRR2936909 1 0.000 0.8938 1.000 0.000 0.000 0.000
#> SRR2936918 1 0.000 0.8938 1.000 0.000 0.000 0.000
#> SRR2936917 2 0.000 0.9524 0.000 1.000 0.000 0.000
#> SRR2936916 1 0.498 0.3197 0.540 0.000 0.000 0.460
#> SRR2936915 1 0.497 0.3296 0.548 0.000 0.000 0.452
#> SRR2936914 2 0.000 0.9524 0.000 1.000 0.000 0.000
#> SRR2936913 2 0.000 0.9524 0.000 1.000 0.000 0.000
#> SRR2936912 1 0.000 0.8938 1.000 0.000 0.000 0.000
#> SRR2936910 1 0.000 0.8938 1.000 0.000 0.000 0.000
#> SRR2936911 2 0.000 0.9524 0.000 1.000 0.000 0.000
#> SRR2936907 2 0.000 0.9524 0.000 1.000 0.000 0.000
#> SRR2936908 2 0.000 0.9524 0.000 1.000 0.000 0.000
#> SRR2936904 2 0.462 0.6600 0.000 0.660 0.000 0.340
#> SRR2936905 2 0.000 0.9524 0.000 1.000 0.000 0.000
#> SRR2936903 4 0.647 0.8030 0.416 0.000 0.072 0.512
#> SRR2936901 4 0.517 -0.0964 0.004 0.000 0.484 0.512
#> SRR2936902 3 0.000 0.9443 0.000 0.000 1.000 0.000
#> SRR2936900 4 0.647 0.8030 0.416 0.000 0.072 0.512
#> SRR2936898 3 0.000 0.9443 0.000 0.000 1.000 0.000
#> SRR2936899 3 0.000 0.9443 0.000 0.000 1.000 0.000
#> SRR2936897 1 0.000 0.8938 1.000 0.000 0.000 0.000
#> SRR2936896 2 0.000 0.9524 0.000 1.000 0.000 0.000
#> SRR2936894 1 0.000 0.8938 1.000 0.000 0.000 0.000
#> SRR2936893 2 0.000 0.9524 0.000 1.000 0.000 0.000
#> SRR2936895 2 0.000 0.9524 0.000 1.000 0.000 0.000
#> SRR2936892 2 0.000 0.9524 0.000 1.000 0.000 0.000
#> SRR2936891 1 0.000 0.8938 1.000 0.000 0.000 0.000
#> SRR2936890 2 0.000 0.9524 0.000 1.000 0.000 0.000
#> SRR2936886 2 0.373 0.8021 0.000 0.788 0.000 0.212
#> SRR2936885 4 0.647 0.8030 0.416 0.000 0.072 0.512
#> SRR2936888 1 0.000 0.8938 1.000 0.000 0.000 0.000
#> SRR2936889 2 0.000 0.9524 0.000 1.000 0.000 0.000
#> SRR2936887 2 0.373 0.8021 0.000 0.788 0.000 0.212
#> SRR2936884 3 0.353 0.6565 0.000 0.192 0.808 0.000
#> SRR2936883 3 0.000 0.9443 0.000 0.000 1.000 0.000
#> SRR2936881 3 0.000 0.9443 0.000 0.000 1.000 0.000
#> SRR2936882 4 0.647 0.8030 0.416 0.000 0.072 0.512
#> SRR2936880 3 0.000 0.9443 0.000 0.000 1.000 0.000
#> SRR2936878 2 0.000 0.9524 0.000 1.000 0.000 0.000
#> SRR2936879 2 0.000 0.9524 0.000 1.000 0.000 0.000
#> SRR2936875 2 0.000 0.9524 0.000 1.000 0.000 0.000
#> SRR2936877 2 0.000 0.9524 0.000 1.000 0.000 0.000
#> SRR2936876 1 0.000 0.8938 1.000 0.000 0.000 0.000
#> SRR2936873 1 0.000 0.8938 1.000 0.000 0.000 0.000
#> SRR2936872 2 0.000 0.9524 0.000 1.000 0.000 0.000
#> SRR2936871 2 0.000 0.9524 0.000 1.000 0.000 0.000
#> SRR2936874 2 0.000 0.9524 0.000 1.000 0.000 0.000
#> SRR2936870 1 0.000 0.8938 1.000 0.000 0.000 0.000
#> SRR2936869 2 0.373 0.8021 0.000 0.788 0.000 0.212
#> SRR2936868 2 0.373 0.8021 0.000 0.788 0.000 0.212
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR2936906 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000
#> SRR2936909 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000
#> SRR2936918 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000
#> SRR2936917 2 0.0000 0.9981 0.000 1.000 0.000 0.000 0.000
#> SRR2936916 4 0.6552 -0.0904 0.248 0.000 0.000 0.476 0.276
#> SRR2936915 4 0.6552 -0.0904 0.248 0.000 0.000 0.476 0.276
#> SRR2936914 2 0.0000 0.9981 0.000 1.000 0.000 0.000 0.000
#> SRR2936913 2 0.0000 0.9981 0.000 1.000 0.000 0.000 0.000
#> SRR2936912 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000
#> SRR2936910 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000
#> SRR2936911 2 0.0000 0.9981 0.000 1.000 0.000 0.000 0.000
#> SRR2936907 2 0.0000 0.9981 0.000 1.000 0.000 0.000 0.000
#> SRR2936908 2 0.0000 0.9981 0.000 1.000 0.000 0.000 0.000
#> SRR2936904 4 0.4321 0.5051 0.000 0.396 0.000 0.600 0.004
#> SRR2936905 2 0.0000 0.9981 0.000 1.000 0.000 0.000 0.000
#> SRR2936903 5 0.3885 0.8941 0.268 0.000 0.008 0.000 0.724
#> SRR2936901 5 0.3661 0.4854 0.000 0.000 0.276 0.000 0.724
#> SRR2936902 3 0.0162 0.9452 0.000 0.000 0.996 0.004 0.000
#> SRR2936900 5 0.3885 0.8941 0.268 0.000 0.008 0.000 0.724
#> SRR2936898 3 0.0000 0.9462 0.000 0.000 1.000 0.000 0.000
#> SRR2936899 3 0.0000 0.9462 0.000 0.000 1.000 0.000 0.000
#> SRR2936897 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000
#> SRR2936896 2 0.0000 0.9981 0.000 1.000 0.000 0.000 0.000
#> SRR2936894 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000
#> SRR2936893 2 0.0000 0.9981 0.000 1.000 0.000 0.000 0.000
#> SRR2936895 2 0.0404 0.9812 0.000 0.988 0.000 0.012 0.000
#> SRR2936892 2 0.0000 0.9981 0.000 1.000 0.000 0.000 0.000
#> SRR2936891 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000
#> SRR2936890 2 0.0000 0.9981 0.000 1.000 0.000 0.000 0.000
#> SRR2936886 4 0.4306 0.4996 0.000 0.492 0.000 0.508 0.000
#> SRR2936885 5 0.3885 0.8941 0.268 0.000 0.008 0.000 0.724
#> SRR2936888 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000
#> SRR2936889 2 0.0000 0.9981 0.000 1.000 0.000 0.000 0.000
#> SRR2936887 4 0.4306 0.4996 0.000 0.492 0.000 0.508 0.000
#> SRR2936884 3 0.3196 0.6740 0.000 0.192 0.804 0.004 0.000
#> SRR2936883 3 0.0162 0.9452 0.000 0.000 0.996 0.004 0.000
#> SRR2936881 3 0.0000 0.9462 0.000 0.000 1.000 0.000 0.000
#> SRR2936882 5 0.3885 0.8941 0.268 0.000 0.008 0.000 0.724
#> SRR2936880 3 0.0000 0.9462 0.000 0.000 1.000 0.000 0.000
#> SRR2936878 2 0.0000 0.9981 0.000 1.000 0.000 0.000 0.000
#> SRR2936879 2 0.0404 0.9812 0.000 0.988 0.000 0.012 0.000
#> SRR2936875 2 0.0000 0.9981 0.000 1.000 0.000 0.000 0.000
#> SRR2936877 2 0.0000 0.9981 0.000 1.000 0.000 0.000 0.000
#> SRR2936876 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000
#> SRR2936873 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000
#> SRR2936872 2 0.0000 0.9981 0.000 1.000 0.000 0.000 0.000
#> SRR2936871 2 0.0000 0.9981 0.000 1.000 0.000 0.000 0.000
#> SRR2936874 2 0.0000 0.9981 0.000 1.000 0.000 0.000 0.000
#> SRR2936870 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000
#> SRR2936869 4 0.4306 0.4996 0.000 0.492 0.000 0.508 0.000
#> SRR2936868 4 0.4306 0.4996 0.000 0.492 0.000 0.508 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR2936906 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936909 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936918 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936917 2 0.0000 0.990 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936916 5 0.0547 1.000 0.020 0.000 0.000 0.000 0.980 0.000
#> SRR2936915 5 0.0547 1.000 0.020 0.000 0.000 0.000 0.980 0.000
#> SRR2936914 2 0.0000 0.990 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936913 2 0.0000 0.990 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936912 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936910 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936911 2 0.0000 0.990 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936907 2 0.0000 0.990 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936908 2 0.0000 0.990 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936904 4 0.4524 0.553 0.000 0.100 0.000 0.760 0.076 0.064
#> SRR2936905 2 0.0000 0.990 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936903 6 0.1327 0.966 0.064 0.000 0.000 0.000 0.000 0.936
#> SRR2936901 6 0.1327 0.875 0.000 0.000 0.064 0.000 0.000 0.936
#> SRR2936902 3 0.0260 0.980 0.000 0.000 0.992 0.008 0.000 0.000
#> SRR2936900 6 0.1387 0.968 0.068 0.000 0.000 0.000 0.000 0.932
#> SRR2936898 3 0.0260 0.980 0.000 0.000 0.992 0.000 0.000 0.008
#> SRR2936899 3 0.0260 0.980 0.000 0.000 0.992 0.000 0.000 0.008
#> SRR2936897 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936896 2 0.0000 0.990 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936894 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936893 2 0.0000 0.990 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936895 2 0.0937 0.947 0.000 0.960 0.000 0.040 0.000 0.000
#> SRR2936892 2 0.0000 0.990 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936891 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936890 2 0.0000 0.990 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936886 4 0.2527 0.911 0.000 0.168 0.000 0.832 0.000 0.000
#> SRR2936885 6 0.1387 0.968 0.068 0.000 0.000 0.000 0.000 0.932
#> SRR2936888 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936889 2 0.0000 0.990 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936887 4 0.2527 0.911 0.000 0.168 0.000 0.832 0.000 0.000
#> SRR2936884 3 0.1265 0.919 0.000 0.044 0.948 0.008 0.000 0.000
#> SRR2936883 3 0.0260 0.980 0.000 0.000 0.992 0.008 0.000 0.000
#> SRR2936881 3 0.0000 0.982 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936882 6 0.1387 0.968 0.068 0.000 0.000 0.000 0.000 0.932
#> SRR2936880 3 0.0000 0.982 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936878 2 0.0000 0.990 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936879 2 0.2686 0.846 0.000 0.876 0.000 0.080 0.012 0.032
#> SRR2936875 2 0.0000 0.990 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936877 2 0.0000 0.990 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936876 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936873 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936872 2 0.0000 0.990 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936871 2 0.0000 0.990 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936874 2 0.0000 0.990 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936870 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936869 4 0.2527 0.911 0.000 0.168 0.000 0.832 0.000 0.000
#> SRR2936868 4 0.2527 0.911 0.000 0.168 0.000 0.832 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
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 14198 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 0.972 0.989 0.4460 0.547 0.547
#> 3 3 0.741 0.818 0.926 0.4702 0.755 0.571
#> 4 4 0.790 0.868 0.936 0.0664 0.835 0.583
#> 5 5 0.868 0.855 0.925 0.0810 0.929 0.753
#> 6 6 0.881 0.851 0.901 0.0294 0.947 0.780
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
#> SRR2936906 1 0.000 0.965 1.000 0.000
#> SRR2936909 1 0.000 0.965 1.000 0.000
#> SRR2936918 1 0.000 0.965 1.000 0.000
#> SRR2936917 2 0.000 1.000 0.000 1.000
#> SRR2936916 2 0.000 1.000 0.000 1.000
#> SRR2936915 2 0.000 1.000 0.000 1.000
#> SRR2936914 2 0.000 1.000 0.000 1.000
#> SRR2936913 2 0.000 1.000 0.000 1.000
#> SRR2936912 1 0.000 0.965 1.000 0.000
#> SRR2936910 1 0.000 0.965 1.000 0.000
#> SRR2936911 2 0.000 1.000 0.000 1.000
#> SRR2936907 2 0.000 1.000 0.000 1.000
#> SRR2936908 2 0.000 1.000 0.000 1.000
#> SRR2936904 2 0.000 1.000 0.000 1.000
#> SRR2936905 2 0.000 1.000 0.000 1.000
#> SRR2936903 1 0.000 0.965 1.000 0.000
#> SRR2936901 1 0.482 0.866 0.896 0.104
#> SRR2936902 2 0.000 1.000 0.000 1.000
#> SRR2936900 1 0.000 0.965 1.000 0.000
#> SRR2936898 2 0.000 1.000 0.000 1.000
#> SRR2936899 2 0.000 1.000 0.000 1.000
#> SRR2936897 1 0.000 0.965 1.000 0.000
#> SRR2936896 2 0.000 1.000 0.000 1.000
#> SRR2936894 1 0.000 0.965 1.000 0.000
#> SRR2936893 2 0.000 1.000 0.000 1.000
#> SRR2936895 2 0.000 1.000 0.000 1.000
#> SRR2936892 2 0.000 1.000 0.000 1.000
#> SRR2936891 1 0.000 0.965 1.000 0.000
#> SRR2936890 2 0.000 1.000 0.000 1.000
#> SRR2936886 2 0.000 1.000 0.000 1.000
#> SRR2936885 1 0.000 0.965 1.000 0.000
#> SRR2936888 1 0.000 0.965 1.000 0.000
#> SRR2936889 2 0.000 1.000 0.000 1.000
#> SRR2936887 2 0.000 1.000 0.000 1.000
#> SRR2936884 2 0.000 1.000 0.000 1.000
#> SRR2936883 2 0.000 1.000 0.000 1.000
#> SRR2936881 2 0.000 1.000 0.000 1.000
#> SRR2936882 1 0.000 0.965 1.000 0.000
#> SRR2936880 2 0.000 1.000 0.000 1.000
#> SRR2936878 2 0.000 1.000 0.000 1.000
#> SRR2936879 2 0.000 1.000 0.000 1.000
#> SRR2936875 2 0.000 1.000 0.000 1.000
#> SRR2936877 2 0.000 1.000 0.000 1.000
#> SRR2936876 1 0.991 0.218 0.556 0.444
#> SRR2936873 1 0.000 0.965 1.000 0.000
#> SRR2936872 2 0.000 1.000 0.000 1.000
#> SRR2936871 2 0.000 1.000 0.000 1.000
#> SRR2936874 2 0.000 1.000 0.000 1.000
#> SRR2936870 1 0.000 0.965 1.000 0.000
#> SRR2936869 2 0.000 1.000 0.000 1.000
#> SRR2936868 2 0.000 1.000 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR2936906 1 0.0000 0.962 1.000 0.00 0.000
#> SRR2936909 1 0.0000 0.962 1.000 0.00 0.000
#> SRR2936918 1 0.0000 0.962 1.000 0.00 0.000
#> SRR2936917 2 0.0000 0.885 0.000 1.00 0.000
#> SRR2936916 3 0.4555 0.708 0.000 0.20 0.800
#> SRR2936915 3 0.4555 0.708 0.000 0.20 0.800
#> SRR2936914 2 0.0000 0.885 0.000 1.00 0.000
#> SRR2936913 2 0.0000 0.885 0.000 1.00 0.000
#> SRR2936912 1 0.0000 0.962 1.000 0.00 0.000
#> SRR2936910 1 0.0000 0.962 1.000 0.00 0.000
#> SRR2936911 2 0.0000 0.885 0.000 1.00 0.000
#> SRR2936907 2 0.0000 0.885 0.000 1.00 0.000
#> SRR2936908 2 0.0000 0.885 0.000 1.00 0.000
#> SRR2936904 2 0.6192 0.370 0.000 0.58 0.420
#> SRR2936905 2 0.0000 0.885 0.000 1.00 0.000
#> SRR2936903 3 0.6192 0.109 0.420 0.00 0.580
#> SRR2936901 3 0.0000 0.895 0.000 0.00 1.000
#> SRR2936902 3 0.0000 0.895 0.000 0.00 1.000
#> SRR2936900 1 0.0592 0.955 0.988 0.00 0.012
#> SRR2936898 3 0.0000 0.895 0.000 0.00 1.000
#> SRR2936899 3 0.0000 0.895 0.000 0.00 1.000
#> SRR2936897 1 0.4887 0.656 0.772 0.00 0.228
#> SRR2936896 2 0.0000 0.885 0.000 1.00 0.000
#> SRR2936894 1 0.0000 0.962 1.000 0.00 0.000
#> SRR2936893 2 0.0000 0.885 0.000 1.00 0.000
#> SRR2936895 2 0.6192 0.370 0.000 0.58 0.420
#> SRR2936892 2 0.0000 0.885 0.000 1.00 0.000
#> SRR2936891 1 0.0000 0.962 1.000 0.00 0.000
#> SRR2936890 2 0.0000 0.885 0.000 1.00 0.000
#> SRR2936886 2 0.6192 0.370 0.000 0.58 0.420
#> SRR2936885 1 0.4555 0.757 0.800 0.00 0.200
#> SRR2936888 1 0.0000 0.962 1.000 0.00 0.000
#> SRR2936889 2 0.0000 0.885 0.000 1.00 0.000
#> SRR2936887 2 0.6192 0.370 0.000 0.58 0.420
#> SRR2936884 3 0.0000 0.895 0.000 0.00 1.000
#> SRR2936883 3 0.0000 0.895 0.000 0.00 1.000
#> SRR2936881 3 0.0000 0.895 0.000 0.00 1.000
#> SRR2936882 1 0.0237 0.960 0.996 0.00 0.004
#> SRR2936880 3 0.0000 0.895 0.000 0.00 1.000
#> SRR2936878 2 0.0000 0.885 0.000 1.00 0.000
#> SRR2936879 3 0.4555 0.708 0.000 0.20 0.800
#> SRR2936875 2 0.0000 0.885 0.000 1.00 0.000
#> SRR2936877 2 0.0000 0.885 0.000 1.00 0.000
#> SRR2936876 3 0.0000 0.895 0.000 0.00 1.000
#> SRR2936873 1 0.0000 0.962 1.000 0.00 0.000
#> SRR2936872 2 0.0000 0.885 0.000 1.00 0.000
#> SRR2936871 2 0.0000 0.885 0.000 1.00 0.000
#> SRR2936874 2 0.0000 0.885 0.000 1.00 0.000
#> SRR2936870 1 0.0000 0.962 1.000 0.00 0.000
#> SRR2936869 2 0.4555 0.706 0.000 0.80 0.200
#> SRR2936868 2 0.6192 0.370 0.000 0.58 0.420
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR2936906 1 0.000 0.946 1.000 0.0 0.000 0.00
#> SRR2936909 1 0.000 0.946 1.000 0.0 0.000 0.00
#> SRR2936918 1 0.000 0.946 1.000 0.0 0.000 0.00
#> SRR2936917 2 0.000 0.986 0.000 1.0 0.000 0.00
#> SRR2936916 3 0.361 0.752 0.000 0.2 0.800 0.00
#> SRR2936915 3 0.361 0.752 0.000 0.2 0.800 0.00
#> SRR2936914 2 0.000 0.986 0.000 1.0 0.000 0.00
#> SRR2936913 2 0.000 0.986 0.000 1.0 0.000 0.00
#> SRR2936912 1 0.000 0.946 1.000 0.0 0.000 0.00
#> SRR2936910 1 0.000 0.946 1.000 0.0 0.000 0.00
#> SRR2936911 2 0.000 0.986 0.000 1.0 0.000 0.00
#> SRR2936907 2 0.000 0.986 0.000 1.0 0.000 0.00
#> SRR2936908 2 0.000 0.986 0.000 1.0 0.000 0.00
#> SRR2936904 3 0.485 0.584 0.000 0.4 0.600 0.00
#> SRR2936905 2 0.000 0.986 0.000 1.0 0.000 0.00
#> SRR2936903 4 0.000 0.991 0.000 0.0 0.000 1.00
#> SRR2936901 4 0.121 0.962 0.000 0.0 0.040 0.96
#> SRR2936902 3 0.000 0.757 0.000 0.0 1.000 0.00
#> SRR2936900 4 0.000 0.991 0.000 0.0 0.000 1.00
#> SRR2936898 3 0.000 0.757 0.000 0.0 1.000 0.00
#> SRR2936899 3 0.000 0.757 0.000 0.0 1.000 0.00
#> SRR2936897 1 0.488 0.255 0.592 0.0 0.408 0.00
#> SRR2936896 2 0.000 0.986 0.000 1.0 0.000 0.00
#> SRR2936894 1 0.000 0.946 1.000 0.0 0.000 0.00
#> SRR2936893 2 0.000 0.986 0.000 1.0 0.000 0.00
#> SRR2936895 3 0.485 0.584 0.000 0.4 0.600 0.00
#> SRR2936892 2 0.000 0.986 0.000 1.0 0.000 0.00
#> SRR2936891 1 0.000 0.946 1.000 0.0 0.000 0.00
#> SRR2936890 2 0.000 0.986 0.000 1.0 0.000 0.00
#> SRR2936886 3 0.485 0.584 0.000 0.4 0.600 0.00
#> SRR2936885 4 0.000 0.991 0.000 0.0 0.000 1.00
#> SRR2936888 1 0.000 0.946 1.000 0.0 0.000 0.00
#> SRR2936889 2 0.000 0.986 0.000 1.0 0.000 0.00
#> SRR2936887 3 0.485 0.584 0.000 0.4 0.600 0.00
#> SRR2936884 3 0.000 0.757 0.000 0.0 1.000 0.00
#> SRR2936883 3 0.000 0.757 0.000 0.0 1.000 0.00
#> SRR2936881 3 0.000 0.757 0.000 0.0 1.000 0.00
#> SRR2936882 4 0.000 0.991 0.000 0.0 0.000 1.00
#> SRR2936880 3 0.000 0.757 0.000 0.0 1.000 0.00
#> SRR2936878 2 0.000 0.986 0.000 1.0 0.000 0.00
#> SRR2936879 3 0.361 0.752 0.000 0.2 0.800 0.00
#> SRR2936875 2 0.000 0.986 0.000 1.0 0.000 0.00
#> SRR2936877 2 0.000 0.986 0.000 1.0 0.000 0.00
#> SRR2936876 3 0.000 0.757 0.000 0.0 1.000 0.00
#> SRR2936873 1 0.000 0.946 1.000 0.0 0.000 0.00
#> SRR2936872 2 0.000 0.986 0.000 1.0 0.000 0.00
#> SRR2936871 2 0.000 0.986 0.000 1.0 0.000 0.00
#> SRR2936874 2 0.000 0.986 0.000 1.0 0.000 0.00
#> SRR2936870 1 0.000 0.946 1.000 0.0 0.000 0.00
#> SRR2936869 2 0.361 0.661 0.000 0.8 0.200 0.00
#> SRR2936868 3 0.485 0.584 0.000 0.4 0.600 0.00
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR2936906 1 0.000 0.9549 1.000 0.000 0.000 0.000 0.000
#> SRR2936909 1 0.120 0.9181 0.952 0.000 0.000 0.048 0.000
#> SRR2936918 1 0.000 0.9549 1.000 0.000 0.000 0.000 0.000
#> SRR2936917 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> SRR2936916 4 0.000 0.5067 0.000 0.000 0.000 1.000 0.000
#> SRR2936915 4 0.000 0.5067 0.000 0.000 0.000 1.000 0.000
#> SRR2936914 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> SRR2936913 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> SRR2936912 1 0.000 0.9549 1.000 0.000 0.000 0.000 0.000
#> SRR2936910 1 0.000 0.9549 1.000 0.000 0.000 0.000 0.000
#> SRR2936911 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> SRR2936907 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> SRR2936908 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> SRR2936904 4 0.281 0.6379 0.000 0.168 0.000 0.832 0.000
#> SRR2936905 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> SRR2936903 5 0.000 0.8657 0.000 0.000 0.000 0.000 1.000
#> SRR2936901 5 0.431 -0.0254 0.000 0.000 0.492 0.000 0.508
#> SRR2936902 3 0.000 0.9344 0.000 0.000 1.000 0.000 0.000
#> SRR2936900 5 0.000 0.8657 0.000 0.000 0.000 0.000 1.000
#> SRR2936898 3 0.000 0.9344 0.000 0.000 1.000 0.000 0.000
#> SRR2936899 3 0.000 0.9344 0.000 0.000 1.000 0.000 0.000
#> SRR2936897 1 0.417 0.5089 0.604 0.000 0.000 0.396 0.000
#> SRR2936896 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> SRR2936894 1 0.000 0.9549 1.000 0.000 0.000 0.000 0.000
#> SRR2936893 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> SRR2936895 4 0.655 0.5447 0.000 0.384 0.200 0.416 0.000
#> SRR2936892 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> SRR2936891 1 0.000 0.9549 1.000 0.000 0.000 0.000 0.000
#> SRR2936890 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> SRR2936886 4 0.414 0.6615 0.000 0.384 0.000 0.616 0.000
#> SRR2936885 5 0.000 0.8657 0.000 0.000 0.000 0.000 1.000
#> SRR2936888 1 0.000 0.9549 1.000 0.000 0.000 0.000 0.000
#> SRR2936889 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> SRR2936887 4 0.414 0.6615 0.000 0.384 0.000 0.616 0.000
#> SRR2936884 3 0.000 0.9344 0.000 0.000 1.000 0.000 0.000
#> SRR2936883 3 0.000 0.9344 0.000 0.000 1.000 0.000 0.000
#> SRR2936881 3 0.000 0.9344 0.000 0.000 1.000 0.000 0.000
#> SRR2936882 5 0.000 0.8657 0.000 0.000 0.000 0.000 1.000
#> SRR2936880 3 0.000 0.9344 0.000 0.000 1.000 0.000 0.000
#> SRR2936878 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> SRR2936879 4 0.314 0.3203 0.000 0.000 0.204 0.796 0.000
#> SRR2936875 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> SRR2936877 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> SRR2936876 3 0.418 0.4674 0.000 0.000 0.600 0.400 0.000
#> SRR2936873 1 0.000 0.9549 1.000 0.000 0.000 0.000 0.000
#> SRR2936872 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> SRR2936871 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> SRR2936874 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> SRR2936870 1 0.000 0.9549 1.000 0.000 0.000 0.000 0.000
#> SRR2936869 4 0.417 0.6444 0.000 0.396 0.000 0.604 0.000
#> SRR2936868 4 0.415 0.6569 0.000 0.388 0.000 0.612 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR2936906 1 0.0000 0.8398 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936909 1 0.3123 0.8105 0.824 0.000 0.000 0.136 0.040 0.000
#> SRR2936918 1 0.0000 0.8398 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936917 2 0.0000 0.9453 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936916 5 0.0000 0.8767 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936915 5 0.0000 0.8767 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936914 2 0.0000 0.9453 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936913 2 0.0000 0.9453 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936912 1 0.3804 0.7067 0.576 0.000 0.000 0.424 0.000 0.000
#> SRR2936910 1 0.2260 0.8217 0.860 0.000 0.000 0.140 0.000 0.000
#> SRR2936911 2 0.0000 0.9453 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936907 2 0.0000 0.9453 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936908 2 0.0000 0.9453 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936904 5 0.3370 0.5893 0.000 0.148 0.000 0.048 0.804 0.000
#> SRR2936905 2 0.0000 0.9453 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936903 6 0.0000 0.8586 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR2936901 6 0.3868 0.0261 0.000 0.000 0.492 0.000 0.000 0.508
#> SRR2936902 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936900 6 0.0000 0.8586 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR2936898 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936899 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936897 5 0.2219 0.7914 0.000 0.000 0.000 0.136 0.864 0.000
#> SRR2936896 2 0.0000 0.9453 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936894 1 0.0000 0.8398 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936893 2 0.0000 0.9453 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936895 2 0.7308 -0.7615 0.000 0.352 0.200 0.328 0.120 0.000
#> SRR2936892 2 0.0000 0.9453 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936891 1 0.0000 0.8398 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936890 2 0.0000 0.9453 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936886 4 0.5353 0.9951 0.000 0.352 0.000 0.528 0.120 0.000
#> SRR2936885 6 0.0000 0.8586 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR2936888 1 0.3860 0.6800 0.528 0.000 0.000 0.472 0.000 0.000
#> SRR2936889 2 0.0000 0.9453 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936887 4 0.5353 0.9951 0.000 0.352 0.000 0.528 0.120 0.000
#> SRR2936884 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936883 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936881 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936882 6 0.0000 0.8586 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR2936880 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936878 2 0.0000 0.9453 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936879 5 0.0146 0.8755 0.000 0.000 0.000 0.004 0.996 0.000
#> SRR2936875 2 0.0000 0.9453 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936877 2 0.0000 0.9453 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936876 5 0.2003 0.7939 0.000 0.000 0.116 0.000 0.884 0.000
#> SRR2936873 1 0.0000 0.8398 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936872 2 0.0000 0.9453 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936871 2 0.0000 0.9453 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936874 2 0.0000 0.9453 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936870 1 0.3860 0.6800 0.528 0.000 0.000 0.472 0.000 0.000
#> SRR2936869 4 0.5329 0.9951 0.000 0.356 0.000 0.528 0.116 0.000
#> SRR2936868 4 0.5329 0.9951 0.000 0.356 0.000 0.528 0.116 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "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 14198 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 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 0.510 0.949 0.954 0.38089 0.633 0.633
#> 3 3 1.000 0.974 0.972 0.69779 0.718 0.554
#> 4 4 0.965 0.925 0.954 0.15892 0.890 0.687
#> 5 5 0.933 0.914 0.945 0.03491 0.973 0.886
#> 6 6 0.938 0.923 0.949 0.00892 0.940 0.760
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] 3 4 5
There is also optional best \(k\) = 3 4 5 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR2936906 2 0.482 0.940 0.104 0.896
#> SRR2936909 2 0.482 0.940 0.104 0.896
#> SRR2936918 2 0.482 0.940 0.104 0.896
#> SRR2936917 2 0.000 0.935 0.000 1.000
#> SRR2936916 2 0.482 0.940 0.104 0.896
#> SRR2936915 2 0.482 0.940 0.104 0.896
#> SRR2936914 2 0.000 0.935 0.000 1.000
#> SRR2936913 2 0.000 0.935 0.000 1.000
#> SRR2936912 2 0.482 0.940 0.104 0.896
#> SRR2936910 2 0.482 0.940 0.104 0.896
#> SRR2936911 2 0.000 0.935 0.000 1.000
#> SRR2936907 2 0.000 0.935 0.000 1.000
#> SRR2936908 2 0.000 0.935 0.000 1.000
#> SRR2936904 2 0.482 0.940 0.104 0.896
#> SRR2936905 2 0.000 0.935 0.000 1.000
#> SRR2936903 1 0.000 1.000 1.000 0.000
#> SRR2936901 1 0.000 1.000 1.000 0.000
#> SRR2936902 1 0.000 1.000 1.000 0.000
#> SRR2936900 1 0.000 1.000 1.000 0.000
#> SRR2936898 1 0.000 1.000 1.000 0.000
#> SRR2936899 1 0.000 1.000 1.000 0.000
#> SRR2936897 2 0.482 0.940 0.104 0.896
#> SRR2936896 2 0.000 0.935 0.000 1.000
#> SRR2936894 2 0.482 0.940 0.104 0.896
#> SRR2936893 2 0.000 0.935 0.000 1.000
#> SRR2936895 2 0.814 0.770 0.252 0.748
#> SRR2936892 2 0.000 0.935 0.000 1.000
#> SRR2936891 2 0.482 0.940 0.104 0.896
#> SRR2936890 2 0.000 0.935 0.000 1.000
#> SRR2936886 2 0.482 0.940 0.104 0.896
#> SRR2936885 1 0.000 1.000 1.000 0.000
#> SRR2936888 2 0.482 0.940 0.104 0.896
#> SRR2936889 2 0.000 0.935 0.000 1.000
#> SRR2936887 2 0.482 0.940 0.104 0.896
#> SRR2936884 1 0.000 1.000 1.000 0.000
#> SRR2936883 1 0.000 1.000 1.000 0.000
#> SRR2936881 1 0.000 1.000 1.000 0.000
#> SRR2936882 1 0.000 1.000 1.000 0.000
#> SRR2936880 1 0.000 1.000 1.000 0.000
#> SRR2936878 2 0.000 0.935 0.000 1.000
#> SRR2936879 2 0.482 0.940 0.104 0.896
#> SRR2936875 2 0.000 0.935 0.000 1.000
#> SRR2936877 2 0.000 0.935 0.000 1.000
#> SRR2936876 2 0.482 0.940 0.104 0.896
#> SRR2936873 2 0.482 0.940 0.104 0.896
#> SRR2936872 2 0.000 0.935 0.000 1.000
#> SRR2936871 2 0.000 0.935 0.000 1.000
#> SRR2936874 2 0.000 0.935 0.000 1.000
#> SRR2936870 2 0.482 0.940 0.104 0.896
#> SRR2936869 2 0.482 0.940 0.104 0.896
#> SRR2936868 2 0.482 0.940 0.104 0.896
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR2936906 1 0.2651 0.972 0.928 0.012 0.060
#> SRR2936909 1 0.2651 0.972 0.928 0.012 0.060
#> SRR2936918 1 0.2651 0.972 0.928 0.012 0.060
#> SRR2936917 2 0.0000 0.986 0.000 1.000 0.000
#> SRR2936916 1 0.2651 0.972 0.928 0.012 0.060
#> SRR2936915 1 0.2301 0.970 0.936 0.004 0.060
#> SRR2936914 2 0.0237 0.983 0.004 0.996 0.000
#> SRR2936913 2 0.3816 0.849 0.148 0.852 0.000
#> SRR2936912 1 0.2301 0.970 0.936 0.004 0.060
#> SRR2936910 1 0.2301 0.970 0.936 0.004 0.060
#> SRR2936911 2 0.2066 0.942 0.060 0.940 0.000
#> SRR2936907 2 0.0000 0.986 0.000 1.000 0.000
#> SRR2936908 2 0.0000 0.986 0.000 1.000 0.000
#> SRR2936904 1 0.2651 0.972 0.928 0.012 0.060
#> SRR2936905 2 0.0000 0.986 0.000 1.000 0.000
#> SRR2936903 3 0.0000 1.000 0.000 0.000 1.000
#> SRR2936901 3 0.0000 1.000 0.000 0.000 1.000
#> SRR2936902 3 0.0000 1.000 0.000 0.000 1.000
#> SRR2936900 3 0.0000 1.000 0.000 0.000 1.000
#> SRR2936898 3 0.0000 1.000 0.000 0.000 1.000
#> SRR2936899 3 0.0000 1.000 0.000 0.000 1.000
#> SRR2936897 1 0.2651 0.972 0.928 0.012 0.060
#> SRR2936896 1 0.1031 0.941 0.976 0.024 0.000
#> SRR2936894 1 0.2651 0.972 0.928 0.012 0.060
#> SRR2936893 2 0.0000 0.986 0.000 1.000 0.000
#> SRR2936895 1 0.0424 0.949 0.992 0.008 0.000
#> SRR2936892 2 0.0000 0.986 0.000 1.000 0.000
#> SRR2936891 1 0.2651 0.972 0.928 0.012 0.060
#> SRR2936890 2 0.0000 0.986 0.000 1.000 0.000
#> SRR2936886 1 0.0237 0.948 0.996 0.000 0.004
#> SRR2936885 3 0.0000 1.000 0.000 0.000 1.000
#> SRR2936888 1 0.2165 0.968 0.936 0.000 0.064
#> SRR2936889 2 0.0000 0.986 0.000 1.000 0.000
#> SRR2936887 1 0.0237 0.948 0.996 0.000 0.004
#> SRR2936884 3 0.0000 1.000 0.000 0.000 1.000
#> SRR2936883 3 0.0000 1.000 0.000 0.000 1.000
#> SRR2936881 3 0.0000 1.000 0.000 0.000 1.000
#> SRR2936882 3 0.0000 1.000 0.000 0.000 1.000
#> SRR2936880 3 0.0000 1.000 0.000 0.000 1.000
#> SRR2936878 1 0.1411 0.937 0.964 0.036 0.000
#> SRR2936879 1 0.2651 0.972 0.928 0.012 0.060
#> SRR2936875 2 0.0000 0.986 0.000 1.000 0.000
#> SRR2936877 1 0.1289 0.936 0.968 0.032 0.000
#> SRR2936876 1 0.2301 0.970 0.936 0.004 0.060
#> SRR2936873 1 0.2651 0.972 0.928 0.012 0.060
#> SRR2936872 2 0.0000 0.986 0.000 1.000 0.000
#> SRR2936871 2 0.0000 0.986 0.000 1.000 0.000
#> SRR2936874 2 0.0000 0.986 0.000 1.000 0.000
#> SRR2936870 1 0.2165 0.968 0.936 0.000 0.064
#> SRR2936869 1 0.0237 0.948 0.996 0.000 0.004
#> SRR2936868 1 0.0237 0.948 0.996 0.000 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR2936906 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> SRR2936909 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> SRR2936918 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> SRR2936917 2 0.0000 0.971 0.000 1.000 0.000 0.000
#> SRR2936916 1 0.0188 0.996 0.996 0.004 0.000 0.000
#> SRR2936915 1 0.0188 0.996 0.996 0.004 0.000 0.000
#> SRR2936914 2 0.0000 0.971 0.000 1.000 0.000 0.000
#> SRR2936913 2 0.4564 0.502 0.000 0.672 0.000 0.328
#> SRR2936912 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> SRR2936910 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> SRR2936911 2 0.1474 0.925 0.000 0.948 0.000 0.052
#> SRR2936907 2 0.0000 0.971 0.000 1.000 0.000 0.000
#> SRR2936908 2 0.0000 0.971 0.000 1.000 0.000 0.000
#> SRR2936904 1 0.0188 0.996 0.996 0.004 0.000 0.000
#> SRR2936905 2 0.0000 0.971 0.000 1.000 0.000 0.000
#> SRR2936903 3 0.0707 0.988 0.000 0.000 0.980 0.020
#> SRR2936901 3 0.0707 0.988 0.000 0.000 0.980 0.020
#> SRR2936902 3 0.0188 0.991 0.000 0.000 0.996 0.004
#> SRR2936900 3 0.0707 0.988 0.000 0.000 0.980 0.020
#> SRR2936898 3 0.0188 0.991 0.000 0.000 0.996 0.004
#> SRR2936899 3 0.0188 0.991 0.000 0.000 0.996 0.004
#> SRR2936897 1 0.0188 0.996 0.996 0.004 0.000 0.000
#> SRR2936896 4 0.5174 0.619 0.368 0.012 0.000 0.620
#> SRR2936894 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> SRR2936893 2 0.0000 0.971 0.000 1.000 0.000 0.000
#> SRR2936895 4 0.4790 0.606 0.380 0.000 0.000 0.620
#> SRR2936892 2 0.0000 0.971 0.000 1.000 0.000 0.000
#> SRR2936891 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> SRR2936890 2 0.0000 0.971 0.000 1.000 0.000 0.000
#> SRR2936886 4 0.0707 0.806 0.020 0.000 0.000 0.980
#> SRR2936885 3 0.0707 0.988 0.000 0.000 0.980 0.020
#> SRR2936888 4 0.2216 0.789 0.092 0.000 0.000 0.908
#> SRR2936889 2 0.0000 0.971 0.000 1.000 0.000 0.000
#> SRR2936887 4 0.0707 0.806 0.020 0.000 0.000 0.980
#> SRR2936884 3 0.0188 0.991 0.000 0.000 0.996 0.004
#> SRR2936883 3 0.0188 0.991 0.000 0.000 0.996 0.004
#> SRR2936881 3 0.0188 0.991 0.000 0.000 0.996 0.004
#> SRR2936882 3 0.0707 0.988 0.000 0.000 0.980 0.020
#> SRR2936880 3 0.0188 0.991 0.000 0.000 0.996 0.004
#> SRR2936878 4 0.5615 0.625 0.356 0.032 0.000 0.612
#> SRR2936879 1 0.0188 0.996 0.996 0.004 0.000 0.000
#> SRR2936875 2 0.0000 0.971 0.000 1.000 0.000 0.000
#> SRR2936877 4 0.5527 0.628 0.356 0.028 0.000 0.616
#> SRR2936876 1 0.0188 0.996 0.996 0.004 0.000 0.000
#> SRR2936873 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> SRR2936872 2 0.0000 0.971 0.000 1.000 0.000 0.000
#> SRR2936871 2 0.0000 0.971 0.000 1.000 0.000 0.000
#> SRR2936874 2 0.0000 0.971 0.000 1.000 0.000 0.000
#> SRR2936870 4 0.2216 0.789 0.092 0.000 0.000 0.908
#> SRR2936869 4 0.0707 0.806 0.020 0.000 0.000 0.980
#> SRR2936868 4 0.0707 0.806 0.020 0.000 0.000 0.980
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR2936906 1 0.0162 0.988 0.996 0.000 0.000 0.004 0.000
#> SRR2936909 1 0.0000 0.991 1.000 0.000 0.000 0.000 0.000
#> SRR2936918 1 0.0000 0.991 1.000 0.000 0.000 0.000 0.000
#> SRR2936917 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> SRR2936916 1 0.0000 0.991 1.000 0.000 0.000 0.000 0.000
#> SRR2936915 1 0.0290 0.985 0.992 0.000 0.000 0.008 0.000
#> SRR2936914 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> SRR2936913 2 0.3177 0.728 0.000 0.792 0.000 0.208 0.000
#> SRR2936912 1 0.0290 0.985 0.992 0.000 0.000 0.008 0.000
#> SRR2936910 1 0.0000 0.991 1.000 0.000 0.000 0.000 0.000
#> SRR2936911 2 0.1410 0.925 0.000 0.940 0.000 0.060 0.000
#> SRR2936907 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> SRR2936908 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> SRR2936904 1 0.0000 0.991 1.000 0.000 0.000 0.000 0.000
#> SRR2936905 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> SRR2936903 5 0.1732 1.000 0.000 0.000 0.080 0.000 0.920
#> SRR2936901 5 0.1732 1.000 0.000 0.000 0.080 0.000 0.920
#> SRR2936902 3 0.1608 0.915 0.000 0.000 0.928 0.000 0.072
#> SRR2936900 5 0.1732 1.000 0.000 0.000 0.080 0.000 0.920
#> SRR2936898 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000
#> SRR2936899 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000
#> SRR2936897 1 0.0000 0.991 1.000 0.000 0.000 0.000 0.000
#> SRR2936896 4 0.5509 0.569 0.360 0.076 0.000 0.564 0.000
#> SRR2936894 1 0.0000 0.991 1.000 0.000 0.000 0.000 0.000
#> SRR2936893 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> SRR2936895 4 0.4060 0.572 0.360 0.000 0.000 0.640 0.000
#> SRR2936892 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> SRR2936891 1 0.0000 0.991 1.000 0.000 0.000 0.000 0.000
#> SRR2936890 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> SRR2936886 4 0.0000 0.732 0.000 0.000 0.000 1.000 0.000
#> SRR2936885 5 0.1732 1.000 0.000 0.000 0.080 0.000 0.920
#> SRR2936888 4 0.3239 0.704 0.068 0.000 0.000 0.852 0.080
#> SRR2936889 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> SRR2936887 4 0.0000 0.732 0.000 0.000 0.000 1.000 0.000
#> SRR2936884 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000
#> SRR2936883 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000
#> SRR2936881 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000
#> SRR2936882 5 0.1732 1.000 0.000 0.000 0.080 0.000 0.920
#> SRR2936880 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000
#> SRR2936878 4 0.5583 0.577 0.352 0.084 0.000 0.564 0.000
#> SRR2936879 1 0.1608 0.898 0.928 0.000 0.000 0.072 0.000
#> SRR2936875 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> SRR2936877 4 0.5583 0.577 0.352 0.084 0.000 0.564 0.000
#> SRR2936876 1 0.0000 0.991 1.000 0.000 0.000 0.000 0.000
#> SRR2936873 1 0.0000 0.991 1.000 0.000 0.000 0.000 0.000
#> SRR2936872 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> SRR2936871 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> SRR2936874 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> SRR2936870 4 0.3239 0.704 0.068 0.000 0.000 0.852 0.080
#> SRR2936869 4 0.0000 0.732 0.000 0.000 0.000 1.000 0.000
#> SRR2936868 4 0.0000 0.732 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
#> SRR2936906 1 0.1267 0.916 0.940 0.000 0.000 0.000 0.060 0.000
#> SRR2936909 1 0.0713 0.921 0.972 0.000 0.000 0.000 0.028 0.000
#> SRR2936918 1 0.0790 0.919 0.968 0.000 0.000 0.000 0.032 0.000
#> SRR2936917 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936916 1 0.1863 0.885 0.896 0.000 0.000 0.000 0.104 0.000
#> SRR2936915 1 0.1863 0.885 0.896 0.000 0.000 0.000 0.104 0.000
#> SRR2936914 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936913 2 0.1610 0.906 0.000 0.916 0.000 0.084 0.000 0.000
#> SRR2936912 1 0.0790 0.919 0.968 0.000 0.000 0.000 0.032 0.000
#> SRR2936910 1 0.0713 0.920 0.972 0.000 0.000 0.000 0.028 0.000
#> SRR2936911 2 0.1267 0.924 0.000 0.940 0.000 0.060 0.000 0.000
#> SRR2936907 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936908 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936904 1 0.1863 0.885 0.896 0.000 0.000 0.000 0.104 0.000
#> SRR2936905 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936903 6 0.0000 0.999 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR2936901 6 0.0146 0.995 0.000 0.000 0.004 0.000 0.000 0.996
#> SRR2936902 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936900 6 0.0000 0.999 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR2936898 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936899 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936897 1 0.1610 0.894 0.916 0.000 0.000 0.000 0.084 0.000
#> SRR2936896 2 0.4523 0.742 0.048 0.756 0.000 0.084 0.112 0.000
#> SRR2936894 1 0.1267 0.916 0.940 0.000 0.000 0.000 0.060 0.000
#> SRR2936893 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936895 4 0.5574 0.438 0.048 0.164 0.000 0.648 0.140 0.000
#> SRR2936892 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936891 1 0.1267 0.916 0.940 0.000 0.000 0.000 0.060 0.000
#> SRR2936890 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936886 4 0.0000 0.851 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR2936885 6 0.0000 0.999 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR2936888 5 0.2793 1.000 0.000 0.000 0.000 0.200 0.800 0.000
#> SRR2936889 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936887 4 0.0000 0.851 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR2936884 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936883 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936881 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936882 6 0.0000 0.999 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR2936880 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936878 2 0.3059 0.861 0.020 0.856 0.000 0.084 0.040 0.000
#> SRR2936879 1 0.4599 0.632 0.696 0.164 0.000 0.000 0.140 0.000
#> SRR2936875 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936877 2 0.3059 0.861 0.020 0.856 0.000 0.084 0.040 0.000
#> SRR2936876 1 0.0937 0.920 0.960 0.000 0.000 0.000 0.040 0.000
#> SRR2936873 1 0.0713 0.921 0.972 0.000 0.000 0.000 0.028 0.000
#> SRR2936872 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936871 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936874 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936870 5 0.2793 1.000 0.000 0.000 0.000 0.200 0.800 0.000
#> SRR2936869 4 0.0000 0.851 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR2936868 4 0.0000 0.851 0.000 0.000 0.000 1.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 14198 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.997 0.999 0.4232 0.576 0.576
#> 3 3 0.918 0.909 0.962 0.5867 0.753 0.571
#> 4 4 0.998 0.951 0.976 0.1336 0.852 0.585
#> 5 5 0.871 0.818 0.905 0.0454 0.950 0.793
#> 6 6 0.896 0.749 0.882 0.0307 0.979 0.895
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR2936906 2 0.0000 1.000 0.000 1.000
#> SRR2936909 2 0.0000 1.000 0.000 1.000
#> SRR2936918 2 0.0000 1.000 0.000 1.000
#> SRR2936917 2 0.0000 1.000 0.000 1.000
#> SRR2936916 2 0.0000 1.000 0.000 1.000
#> SRR2936915 2 0.0000 1.000 0.000 1.000
#> SRR2936914 2 0.0000 1.000 0.000 1.000
#> SRR2936913 2 0.0000 1.000 0.000 1.000
#> SRR2936912 2 0.0000 1.000 0.000 1.000
#> SRR2936910 2 0.0000 1.000 0.000 1.000
#> SRR2936911 2 0.0000 1.000 0.000 1.000
#> SRR2936907 2 0.0000 1.000 0.000 1.000
#> SRR2936908 2 0.0000 1.000 0.000 1.000
#> SRR2936904 2 0.0000 1.000 0.000 1.000
#> SRR2936905 2 0.0000 1.000 0.000 1.000
#> SRR2936903 1 0.0000 0.995 1.000 0.000
#> SRR2936901 1 0.0000 0.995 1.000 0.000
#> SRR2936902 1 0.0000 0.995 1.000 0.000
#> SRR2936900 1 0.0000 0.995 1.000 0.000
#> SRR2936898 1 0.0000 0.995 1.000 0.000
#> SRR2936899 1 0.0000 0.995 1.000 0.000
#> SRR2936897 2 0.0000 1.000 0.000 1.000
#> SRR2936896 1 0.3431 0.932 0.936 0.064
#> SRR2936894 2 0.0000 1.000 0.000 1.000
#> SRR2936893 2 0.0000 1.000 0.000 1.000
#> SRR2936895 2 0.0938 0.988 0.012 0.988
#> SRR2936892 2 0.0000 1.000 0.000 1.000
#> SRR2936891 2 0.0000 1.000 0.000 1.000
#> SRR2936890 2 0.0000 1.000 0.000 1.000
#> SRR2936886 2 0.0000 1.000 0.000 1.000
#> SRR2936885 1 0.0000 0.995 1.000 0.000
#> SRR2936888 2 0.0000 1.000 0.000 1.000
#> SRR2936889 2 0.0000 1.000 0.000 1.000
#> SRR2936887 2 0.0000 1.000 0.000 1.000
#> SRR2936884 1 0.0000 0.995 1.000 0.000
#> SRR2936883 1 0.0000 0.995 1.000 0.000
#> SRR2936881 1 0.0000 0.995 1.000 0.000
#> SRR2936882 1 0.0000 0.995 1.000 0.000
#> SRR2936880 1 0.0000 0.995 1.000 0.000
#> SRR2936878 1 0.0000 0.995 1.000 0.000
#> SRR2936879 2 0.0000 1.000 0.000 1.000
#> SRR2936875 2 0.0000 1.000 0.000 1.000
#> SRR2936877 1 0.0000 0.995 1.000 0.000
#> SRR2936876 2 0.0000 1.000 0.000 1.000
#> SRR2936873 2 0.0000 1.000 0.000 1.000
#> SRR2936872 2 0.0000 1.000 0.000 1.000
#> SRR2936871 2 0.0000 1.000 0.000 1.000
#> SRR2936874 2 0.0000 1.000 0.000 1.000
#> SRR2936870 2 0.0000 1.000 0.000 1.000
#> SRR2936869 2 0.0000 1.000 0.000 1.000
#> SRR2936868 2 0.0000 1.000 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR2936906 1 0.0237 0.933 0.996 0.004 0.000
#> SRR2936909 1 0.0237 0.933 0.996 0.004 0.000
#> SRR2936918 1 0.0237 0.933 0.996 0.004 0.000
#> SRR2936917 1 0.5591 0.584 0.696 0.304 0.000
#> SRR2936916 1 0.0237 0.933 0.996 0.004 0.000
#> SRR2936915 1 0.0237 0.933 0.996 0.004 0.000
#> SRR2936914 2 0.0424 0.948 0.008 0.992 0.000
#> SRR2936913 1 0.1411 0.908 0.964 0.036 0.000
#> SRR2936912 1 0.0237 0.933 0.996 0.004 0.000
#> SRR2936910 1 0.0237 0.933 0.996 0.004 0.000
#> SRR2936911 1 0.5327 0.635 0.728 0.272 0.000
#> SRR2936907 2 0.0000 0.953 0.000 1.000 0.000
#> SRR2936908 2 0.0000 0.953 0.000 1.000 0.000
#> SRR2936904 2 0.0000 0.953 0.000 1.000 0.000
#> SRR2936905 2 0.0000 0.953 0.000 1.000 0.000
#> SRR2936903 3 0.0000 0.994 0.000 0.000 1.000
#> SRR2936901 3 0.0000 0.994 0.000 0.000 1.000
#> SRR2936902 3 0.0000 0.994 0.000 0.000 1.000
#> SRR2936900 3 0.0000 0.994 0.000 0.000 1.000
#> SRR2936898 3 0.0000 0.994 0.000 0.000 1.000
#> SRR2936899 3 0.0000 0.994 0.000 0.000 1.000
#> SRR2936897 1 0.0237 0.933 0.996 0.004 0.000
#> SRR2936896 3 0.2537 0.910 0.080 0.000 0.920
#> SRR2936894 1 0.0237 0.933 0.996 0.004 0.000
#> SRR2936893 2 0.0000 0.953 0.000 1.000 0.000
#> SRR2936895 1 0.0424 0.927 0.992 0.000 0.008
#> SRR2936892 2 0.0000 0.953 0.000 1.000 0.000
#> SRR2936891 1 0.0237 0.933 0.996 0.004 0.000
#> SRR2936890 2 0.0000 0.953 0.000 1.000 0.000
#> SRR2936886 1 0.5138 0.649 0.748 0.252 0.000
#> SRR2936885 3 0.0000 0.994 0.000 0.000 1.000
#> SRR2936888 1 0.0000 0.931 1.000 0.000 0.000
#> SRR2936889 2 0.0000 0.953 0.000 1.000 0.000
#> SRR2936887 1 0.5859 0.469 0.656 0.344 0.000
#> SRR2936884 3 0.0000 0.994 0.000 0.000 1.000
#> SRR2936883 3 0.0000 0.994 0.000 0.000 1.000
#> SRR2936881 3 0.0000 0.994 0.000 0.000 1.000
#> SRR2936882 3 0.0000 0.994 0.000 0.000 1.000
#> SRR2936880 3 0.0000 0.994 0.000 0.000 1.000
#> SRR2936878 3 0.0237 0.990 0.000 0.004 0.996
#> SRR2936879 1 0.0237 0.933 0.996 0.004 0.000
#> SRR2936875 2 0.0000 0.953 0.000 1.000 0.000
#> SRR2936877 3 0.0000 0.994 0.000 0.000 1.000
#> SRR2936876 1 0.0237 0.933 0.996 0.004 0.000
#> SRR2936873 1 0.0237 0.933 0.996 0.004 0.000
#> SRR2936872 2 0.0000 0.953 0.000 1.000 0.000
#> SRR2936871 2 0.0000 0.953 0.000 1.000 0.000
#> SRR2936874 2 0.0000 0.953 0.000 1.000 0.000
#> SRR2936870 1 0.0000 0.931 1.000 0.000 0.000
#> SRR2936869 2 0.4235 0.761 0.176 0.824 0.000
#> SRR2936868 2 0.6204 0.220 0.424 0.576 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR2936906 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> SRR2936909 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> SRR2936918 1 0.0188 0.996 0.996 0.000 0.000 0.004
#> SRR2936917 4 0.7202 0.203 0.396 0.140 0.000 0.464
#> SRR2936916 1 0.0336 0.995 0.992 0.000 0.000 0.008
#> SRR2936915 1 0.0336 0.995 0.992 0.000 0.000 0.008
#> SRR2936914 4 0.0817 0.890 0.000 0.024 0.000 0.976
#> SRR2936913 4 0.0376 0.899 0.004 0.004 0.000 0.992
#> SRR2936912 1 0.0336 0.995 0.992 0.000 0.000 0.008
#> SRR2936910 1 0.0336 0.995 0.992 0.000 0.000 0.008
#> SRR2936911 4 0.0376 0.899 0.004 0.004 0.000 0.992
#> SRR2936907 2 0.0188 0.998 0.000 0.996 0.000 0.004
#> SRR2936908 2 0.0188 0.998 0.000 0.996 0.000 0.004
#> SRR2936904 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> SRR2936905 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> SRR2936903 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> SRR2936901 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> SRR2936902 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> SRR2936900 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> SRR2936898 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> SRR2936899 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> SRR2936897 1 0.0188 0.996 0.996 0.000 0.000 0.004
#> SRR2936896 4 0.4454 0.549 0.000 0.000 0.308 0.692
#> SRR2936894 1 0.0188 0.996 0.996 0.000 0.000 0.004
#> SRR2936893 2 0.0188 0.998 0.000 0.996 0.000 0.004
#> SRR2936895 4 0.2345 0.855 0.100 0.000 0.000 0.900
#> SRR2936892 2 0.0188 0.998 0.000 0.996 0.000 0.004
#> SRR2936891 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> SRR2936890 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> SRR2936886 4 0.0188 0.899 0.004 0.000 0.000 0.996
#> SRR2936885 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> SRR2936888 4 0.2149 0.865 0.088 0.000 0.000 0.912
#> SRR2936889 2 0.0188 0.998 0.000 0.996 0.000 0.004
#> SRR2936887 4 0.0188 0.899 0.000 0.004 0.000 0.996
#> SRR2936884 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> SRR2936883 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> SRR2936881 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> SRR2936882 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> SRR2936880 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> SRR2936878 3 0.0336 0.991 0.000 0.008 0.992 0.000
#> SRR2936879 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> SRR2936875 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> SRR2936877 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> SRR2936876 1 0.0188 0.994 0.996 0.000 0.000 0.004
#> SRR2936873 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> SRR2936872 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> SRR2936871 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> SRR2936874 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> SRR2936870 4 0.2011 0.870 0.080 0.000 0.000 0.920
#> SRR2936869 4 0.0336 0.898 0.000 0.008 0.000 0.992
#> SRR2936868 4 0.0188 0.899 0.000 0.004 0.000 0.996
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR2936906 1 0.0609 0.92894 0.980 0.000 0.000 0.000 0.020
#> SRR2936909 1 0.0162 0.93138 0.996 0.000 0.000 0.000 0.004
#> SRR2936918 1 0.2280 0.87281 0.880 0.000 0.000 0.000 0.120
#> SRR2936917 5 0.7279 0.23003 0.096 0.148 0.000 0.216 0.540
#> SRR2936916 1 0.3612 0.74431 0.764 0.000 0.000 0.008 0.228
#> SRR2936915 1 0.2230 0.87327 0.884 0.000 0.000 0.000 0.116
#> SRR2936914 4 0.5492 0.07127 0.000 0.064 0.000 0.504 0.432
#> SRR2936913 4 0.4206 0.49219 0.000 0.016 0.000 0.696 0.288
#> SRR2936912 1 0.0162 0.93056 0.996 0.000 0.000 0.000 0.004
#> SRR2936910 1 0.0000 0.93110 1.000 0.000 0.000 0.000 0.000
#> SRR2936911 5 0.5083 0.00719 0.004 0.028 0.000 0.428 0.540
#> SRR2936907 2 0.0404 0.98012 0.000 0.988 0.000 0.000 0.012
#> SRR2936908 2 0.0000 0.98453 0.000 1.000 0.000 0.000 0.000
#> SRR2936904 2 0.2536 0.87380 0.004 0.868 0.000 0.000 0.128
#> SRR2936905 2 0.0000 0.98453 0.000 1.000 0.000 0.000 0.000
#> SRR2936903 3 0.0290 0.95392 0.000 0.000 0.992 0.000 0.008
#> SRR2936901 3 0.0000 0.95590 0.000 0.000 1.000 0.000 0.000
#> SRR2936902 3 0.0000 0.95590 0.000 0.000 1.000 0.000 0.000
#> SRR2936900 3 0.0963 0.93714 0.000 0.000 0.964 0.000 0.036
#> SRR2936898 3 0.3274 0.67213 0.000 0.000 0.780 0.000 0.220
#> SRR2936899 3 0.1544 0.90200 0.000 0.000 0.932 0.000 0.068
#> SRR2936897 1 0.0703 0.92291 0.976 0.000 0.000 0.000 0.024
#> SRR2936896 5 0.6628 0.55230 0.040 0.004 0.208 0.148 0.600
#> SRR2936894 1 0.0162 0.93149 0.996 0.000 0.000 0.000 0.004
#> SRR2936893 2 0.0162 0.98418 0.000 0.996 0.000 0.000 0.004
#> SRR2936895 5 0.6256 0.35522 0.188 0.000 0.004 0.248 0.560
#> SRR2936892 2 0.0000 0.98453 0.000 1.000 0.000 0.000 0.000
#> SRR2936891 1 0.0404 0.93082 0.988 0.000 0.000 0.000 0.012
#> SRR2936890 2 0.0290 0.98273 0.000 0.992 0.000 0.000 0.008
#> SRR2936886 4 0.0000 0.83033 0.000 0.000 0.000 1.000 0.000
#> SRR2936885 3 0.0510 0.95062 0.000 0.000 0.984 0.000 0.016
#> SRR2936888 4 0.1557 0.79233 0.052 0.000 0.000 0.940 0.008
#> SRR2936889 2 0.0290 0.98273 0.000 0.992 0.000 0.000 0.008
#> SRR2936887 4 0.0000 0.83033 0.000 0.000 0.000 1.000 0.000
#> SRR2936884 3 0.0000 0.95590 0.000 0.000 1.000 0.000 0.000
#> SRR2936883 3 0.0000 0.95590 0.000 0.000 1.000 0.000 0.000
#> SRR2936881 3 0.0510 0.94942 0.000 0.000 0.984 0.000 0.016
#> SRR2936882 3 0.0794 0.94323 0.000 0.000 0.972 0.000 0.028
#> SRR2936880 3 0.0404 0.95156 0.000 0.000 0.988 0.000 0.012
#> SRR2936878 5 0.4674 0.50967 0.000 0.024 0.316 0.004 0.656
#> SRR2936879 1 0.3561 0.63639 0.740 0.000 0.000 0.000 0.260
#> SRR2936875 2 0.0290 0.98058 0.000 0.992 0.000 0.000 0.008
#> SRR2936877 5 0.4219 0.32735 0.000 0.000 0.416 0.000 0.584
#> SRR2936876 1 0.0510 0.92761 0.984 0.000 0.000 0.000 0.016
#> SRR2936873 1 0.0290 0.93110 0.992 0.000 0.000 0.000 0.008
#> SRR2936872 2 0.0162 0.98418 0.000 0.996 0.000 0.000 0.004
#> SRR2936871 2 0.0000 0.98453 0.000 1.000 0.000 0.000 0.000
#> SRR2936874 2 0.0290 0.98058 0.000 0.992 0.000 0.000 0.008
#> SRR2936870 4 0.1408 0.79981 0.044 0.000 0.000 0.948 0.008
#> SRR2936869 4 0.0000 0.83033 0.000 0.000 0.000 1.000 0.000
#> SRR2936868 4 0.0000 0.83033 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
#> SRR2936906 1 0.0622 0.8713 0.980 0.000 0.000 0.000 0.012 0.008
#> SRR2936909 1 0.0146 0.8761 0.996 0.000 0.000 0.000 0.004 0.000
#> SRR2936918 1 0.2431 0.7787 0.860 0.000 0.000 0.000 0.008 0.132
#> SRR2936917 6 0.6386 0.3416 0.016 0.100 0.000 0.064 0.256 0.564
#> SRR2936916 6 0.5020 -0.0145 0.436 0.000 0.000 0.004 0.060 0.500
#> SRR2936915 1 0.3802 0.4684 0.676 0.000 0.000 0.000 0.012 0.312
#> SRR2936914 6 0.6860 0.2512 0.000 0.064 0.000 0.220 0.284 0.432
#> SRR2936913 4 0.6349 -0.3631 0.000 0.024 0.000 0.400 0.188 0.388
#> SRR2936912 1 0.0891 0.8721 0.968 0.000 0.000 0.000 0.024 0.008
#> SRR2936910 1 0.0622 0.8757 0.980 0.000 0.000 0.000 0.012 0.008
#> SRR2936911 5 0.6627 -0.2415 0.004 0.036 0.000 0.216 0.460 0.284
#> SRR2936907 2 0.0260 0.9494 0.000 0.992 0.000 0.000 0.000 0.008
#> SRR2936908 2 0.0000 0.9539 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936904 2 0.4693 0.3971 0.012 0.532 0.000 0.000 0.024 0.432
#> SRR2936905 2 0.0146 0.9530 0.000 0.996 0.000 0.000 0.000 0.004
#> SRR2936903 3 0.0260 0.9290 0.000 0.000 0.992 0.000 0.008 0.000
#> SRR2936901 3 0.0000 0.9306 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936902 3 0.0508 0.9314 0.000 0.000 0.984 0.000 0.012 0.004
#> SRR2936900 3 0.0603 0.9250 0.000 0.000 0.980 0.000 0.016 0.004
#> SRR2936898 3 0.3817 0.2451 0.000 0.000 0.568 0.000 0.432 0.000
#> SRR2936899 3 0.1910 0.8603 0.000 0.000 0.892 0.000 0.108 0.000
#> SRR2936897 1 0.1829 0.8416 0.920 0.000 0.000 0.000 0.056 0.024
#> SRR2936896 5 0.2434 0.7173 0.032 0.000 0.056 0.016 0.896 0.000
#> SRR2936894 1 0.0291 0.8762 0.992 0.000 0.000 0.000 0.004 0.004
#> SRR2936893 2 0.0000 0.9539 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936895 5 0.2608 0.6595 0.080 0.000 0.000 0.048 0.872 0.000
#> SRR2936892 2 0.0000 0.9539 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936891 1 0.0520 0.8738 0.984 0.000 0.000 0.000 0.008 0.008
#> SRR2936890 2 0.0146 0.9522 0.000 0.996 0.000 0.000 0.000 0.004
#> SRR2936886 4 0.0000 0.8536 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR2936885 3 0.0508 0.9268 0.000 0.000 0.984 0.000 0.012 0.004
#> SRR2936888 4 0.1924 0.8022 0.048 0.000 0.000 0.920 0.004 0.028
#> SRR2936889 2 0.0000 0.9539 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936887 4 0.0000 0.8536 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR2936884 3 0.0692 0.9302 0.000 0.000 0.976 0.000 0.020 0.004
#> SRR2936883 3 0.0603 0.9310 0.000 0.000 0.980 0.000 0.016 0.004
#> SRR2936881 3 0.0790 0.9263 0.000 0.000 0.968 0.000 0.032 0.000
#> SRR2936882 3 0.0603 0.9250 0.000 0.000 0.980 0.000 0.016 0.004
#> SRR2936880 3 0.0790 0.9263 0.000 0.000 0.968 0.000 0.032 0.000
#> SRR2936878 5 0.3228 0.6830 0.004 0.012 0.080 0.000 0.848 0.056
#> SRR2936879 1 0.4646 0.0897 0.500 0.000 0.000 0.000 0.460 0.040
#> SRR2936875 2 0.0603 0.9427 0.004 0.980 0.000 0.000 0.000 0.016
#> SRR2936877 5 0.2346 0.6895 0.008 0.000 0.124 0.000 0.868 0.000
#> SRR2936876 1 0.1138 0.8646 0.960 0.004 0.000 0.000 0.024 0.012
#> SRR2936873 1 0.0000 0.8757 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936872 2 0.0000 0.9539 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936871 2 0.0146 0.9527 0.000 0.996 0.000 0.000 0.000 0.004
#> SRR2936874 2 0.0692 0.9401 0.004 0.976 0.000 0.000 0.000 0.020
#> SRR2936870 4 0.1401 0.8298 0.020 0.000 0.000 0.948 0.004 0.028
#> SRR2936869 4 0.0260 0.8501 0.000 0.000 0.000 0.992 0.000 0.008
#> SRR2936868 4 0.0000 0.8536 0.000 0.000 0.000 1.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 14198 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 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 0.624 0.915 0.941 0.4885 0.492 0.492
#> 3 3 0.838 0.924 0.961 0.3447 0.859 0.713
#> 4 4 0.787 0.829 0.850 0.1139 0.915 0.758
#> 5 5 0.790 0.784 0.755 0.0543 0.973 0.897
#> 6 6 0.821 0.786 0.820 0.0409 0.938 0.745
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
#> SRR2936906 1 0.0000 0.877 1.000 0.000
#> SRR2936909 1 0.0000 0.877 1.000 0.000
#> SRR2936918 1 0.0000 0.877 1.000 0.000
#> SRR2936917 2 0.0000 0.996 0.000 1.000
#> SRR2936916 1 0.8144 0.801 0.748 0.252
#> SRR2936915 1 0.8144 0.801 0.748 0.252
#> SRR2936914 2 0.0000 0.996 0.000 1.000
#> SRR2936913 2 0.0000 0.996 0.000 1.000
#> SRR2936912 1 0.0000 0.877 1.000 0.000
#> SRR2936910 1 0.0000 0.877 1.000 0.000
#> SRR2936911 2 0.0000 0.996 0.000 1.000
#> SRR2936907 2 0.0000 0.996 0.000 1.000
#> SRR2936908 2 0.0000 0.996 0.000 1.000
#> SRR2936904 1 0.8144 0.801 0.748 0.252
#> SRR2936905 2 0.0000 0.996 0.000 1.000
#> SRR2936903 1 0.0000 0.877 1.000 0.000
#> SRR2936901 1 0.8144 0.801 0.748 0.252
#> SRR2936902 2 0.0938 0.989 0.012 0.988
#> SRR2936900 1 0.0000 0.877 1.000 0.000
#> SRR2936898 1 0.8144 0.801 0.748 0.252
#> SRR2936899 1 0.8144 0.801 0.748 0.252
#> SRR2936897 1 0.0000 0.877 1.000 0.000
#> SRR2936896 2 0.0000 0.996 0.000 1.000
#> SRR2936894 1 0.0000 0.877 1.000 0.000
#> SRR2936893 2 0.0000 0.996 0.000 1.000
#> SRR2936895 2 0.0938 0.989 0.012 0.988
#> SRR2936892 2 0.0000 0.996 0.000 1.000
#> SRR2936891 1 0.0000 0.877 1.000 0.000
#> SRR2936890 2 0.0000 0.996 0.000 1.000
#> SRR2936886 1 0.8144 0.801 0.748 0.252
#> SRR2936885 1 0.0000 0.877 1.000 0.000
#> SRR2936888 1 0.0000 0.877 1.000 0.000
#> SRR2936889 2 0.0000 0.996 0.000 1.000
#> SRR2936887 1 0.8144 0.801 0.748 0.252
#> SRR2936884 2 0.0938 0.989 0.012 0.988
#> SRR2936883 2 0.0938 0.989 0.012 0.988
#> SRR2936881 2 0.0938 0.989 0.012 0.988
#> SRR2936882 1 0.0000 0.877 1.000 0.000
#> SRR2936880 2 0.0938 0.989 0.012 0.988
#> SRR2936878 2 0.0000 0.996 0.000 1.000
#> SRR2936879 1 0.8144 0.801 0.748 0.252
#> SRR2936875 2 0.0000 0.996 0.000 1.000
#> SRR2936877 2 0.0000 0.996 0.000 1.000
#> SRR2936876 1 0.6048 0.840 0.852 0.148
#> SRR2936873 1 0.0000 0.877 1.000 0.000
#> SRR2936872 2 0.0000 0.996 0.000 1.000
#> SRR2936871 2 0.0000 0.996 0.000 1.000
#> SRR2936874 2 0.0000 0.996 0.000 1.000
#> SRR2936870 1 0.0000 0.877 1.000 0.000
#> SRR2936869 1 0.8144 0.801 0.748 0.252
#> SRR2936868 1 0.8144 0.801 0.748 0.252
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR2936906 1 0.000 0.983 1.000 0.000 0.000
#> SRR2936909 1 0.245 0.928 0.924 0.000 0.076
#> SRR2936918 1 0.000 0.983 1.000 0.000 0.000
#> SRR2936917 2 0.000 0.926 0.000 1.000 0.000
#> SRR2936916 3 0.000 0.981 0.000 0.000 1.000
#> SRR2936915 3 0.000 0.981 0.000 0.000 1.000
#> SRR2936914 2 0.000 0.926 0.000 1.000 0.000
#> SRR2936913 2 0.000 0.926 0.000 1.000 0.000
#> SRR2936912 1 0.245 0.928 0.924 0.000 0.076
#> SRR2936910 1 0.000 0.983 1.000 0.000 0.000
#> SRR2936911 2 0.000 0.926 0.000 1.000 0.000
#> SRR2936907 2 0.000 0.926 0.000 1.000 0.000
#> SRR2936908 2 0.000 0.926 0.000 1.000 0.000
#> SRR2936904 3 0.000 0.981 0.000 0.000 1.000
#> SRR2936905 2 0.000 0.926 0.000 1.000 0.000
#> SRR2936903 1 0.000 0.983 1.000 0.000 0.000
#> SRR2936901 3 0.000 0.981 0.000 0.000 1.000
#> SRR2936902 2 0.525 0.720 0.000 0.736 0.264
#> SRR2936900 1 0.000 0.983 1.000 0.000 0.000
#> SRR2936898 3 0.000 0.981 0.000 0.000 1.000
#> SRR2936899 3 0.000 0.981 0.000 0.000 1.000
#> SRR2936897 1 0.245 0.928 0.924 0.000 0.076
#> SRR2936896 2 0.000 0.926 0.000 1.000 0.000
#> SRR2936894 1 0.000 0.983 1.000 0.000 0.000
#> SRR2936893 2 0.000 0.926 0.000 1.000 0.000
#> SRR2936895 2 0.525 0.720 0.000 0.736 0.264
#> SRR2936892 2 0.000 0.926 0.000 1.000 0.000
#> SRR2936891 1 0.000 0.983 1.000 0.000 0.000
#> SRR2936890 2 0.000 0.926 0.000 1.000 0.000
#> SRR2936886 3 0.000 0.981 0.000 0.000 1.000
#> SRR2936885 1 0.000 0.983 1.000 0.000 0.000
#> SRR2936888 1 0.000 0.983 1.000 0.000 0.000
#> SRR2936889 2 0.000 0.926 0.000 1.000 0.000
#> SRR2936887 3 0.000 0.981 0.000 0.000 1.000
#> SRR2936884 2 0.525 0.720 0.000 0.736 0.264
#> SRR2936883 2 0.525 0.720 0.000 0.736 0.264
#> SRR2936881 2 0.525 0.720 0.000 0.736 0.264
#> SRR2936882 1 0.000 0.983 1.000 0.000 0.000
#> SRR2936880 2 0.525 0.720 0.000 0.736 0.264
#> SRR2936878 2 0.000 0.926 0.000 1.000 0.000
#> SRR2936879 3 0.000 0.981 0.000 0.000 1.000
#> SRR2936875 2 0.000 0.926 0.000 1.000 0.000
#> SRR2936877 2 0.000 0.926 0.000 1.000 0.000
#> SRR2936876 3 0.445 0.747 0.192 0.000 0.808
#> SRR2936873 1 0.000 0.983 1.000 0.000 0.000
#> SRR2936872 2 0.000 0.926 0.000 1.000 0.000
#> SRR2936871 2 0.000 0.926 0.000 1.000 0.000
#> SRR2936874 2 0.000 0.926 0.000 1.000 0.000
#> SRR2936870 1 0.000 0.983 1.000 0.000 0.000
#> SRR2936869 3 0.000 0.981 0.000 0.000 1.000
#> SRR2936868 3 0.000 0.981 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR2936906 1 0.3528 0.907 0.808 0.000 0.000 0.192
#> SRR2936909 1 0.1940 0.846 0.924 0.000 0.076 0.000
#> SRR2936918 1 0.3528 0.907 0.808 0.000 0.000 0.192
#> SRR2936917 4 0.4998 1.000 0.000 0.488 0.000 0.512
#> SRR2936916 3 0.0469 0.962 0.000 0.000 0.988 0.012
#> SRR2936915 3 0.0469 0.962 0.000 0.000 0.988 0.012
#> SRR2936914 4 0.4998 1.000 0.000 0.488 0.000 0.512
#> SRR2936913 4 0.4998 1.000 0.000 0.488 0.000 0.512
#> SRR2936912 1 0.1940 0.846 0.924 0.000 0.076 0.000
#> SRR2936910 1 0.3528 0.907 0.808 0.000 0.000 0.192
#> SRR2936911 4 0.4998 1.000 0.000 0.488 0.000 0.512
#> SRR2936907 2 0.0000 0.708 0.000 1.000 0.000 0.000
#> SRR2936908 2 0.0000 0.708 0.000 1.000 0.000 0.000
#> SRR2936904 3 0.0336 0.963 0.000 0.000 0.992 0.008
#> SRR2936905 2 0.0000 0.708 0.000 1.000 0.000 0.000
#> SRR2936903 1 0.0000 0.886 1.000 0.000 0.000 0.000
#> SRR2936901 3 0.1637 0.944 0.000 0.000 0.940 0.060
#> SRR2936902 2 0.6508 0.554 0.000 0.600 0.104 0.296
#> SRR2936900 1 0.0000 0.886 1.000 0.000 0.000 0.000
#> SRR2936898 3 0.1637 0.944 0.000 0.000 0.940 0.060
#> SRR2936899 3 0.1637 0.944 0.000 0.000 0.940 0.060
#> SRR2936897 1 0.1940 0.846 0.924 0.000 0.076 0.000
#> SRR2936896 2 0.1940 0.547 0.000 0.924 0.000 0.076
#> SRR2936894 1 0.3528 0.907 0.808 0.000 0.000 0.192
#> SRR2936893 2 0.0000 0.708 0.000 1.000 0.000 0.000
#> SRR2936895 2 0.6756 0.539 0.000 0.600 0.148 0.252
#> SRR2936892 2 0.0000 0.708 0.000 1.000 0.000 0.000
#> SRR2936891 1 0.3528 0.907 0.808 0.000 0.000 0.192
#> SRR2936890 2 0.0000 0.708 0.000 1.000 0.000 0.000
#> SRR2936886 3 0.0336 0.963 0.000 0.000 0.992 0.008
#> SRR2936885 1 0.0000 0.886 1.000 0.000 0.000 0.000
#> SRR2936888 1 0.3528 0.907 0.808 0.000 0.000 0.192
#> SRR2936889 2 0.0000 0.708 0.000 1.000 0.000 0.000
#> SRR2936887 3 0.0336 0.963 0.000 0.000 0.992 0.008
#> SRR2936884 2 0.6508 0.554 0.000 0.600 0.104 0.296
#> SRR2936883 2 0.6508 0.554 0.000 0.600 0.104 0.296
#> SRR2936881 2 0.6508 0.554 0.000 0.600 0.104 0.296
#> SRR2936882 1 0.0000 0.886 1.000 0.000 0.000 0.000
#> SRR2936880 2 0.6508 0.554 0.000 0.600 0.104 0.296
#> SRR2936878 4 0.4998 1.000 0.000 0.488 0.000 0.512
#> SRR2936879 3 0.0469 0.962 0.000 0.000 0.988 0.012
#> SRR2936875 2 0.0000 0.708 0.000 1.000 0.000 0.000
#> SRR2936877 4 0.4998 1.000 0.000 0.488 0.000 0.512
#> SRR2936876 3 0.3528 0.782 0.192 0.000 0.808 0.000
#> SRR2936873 1 0.3528 0.907 0.808 0.000 0.000 0.192
#> SRR2936872 2 0.0000 0.708 0.000 1.000 0.000 0.000
#> SRR2936871 2 0.0000 0.708 0.000 1.000 0.000 0.000
#> SRR2936874 2 0.0000 0.708 0.000 1.000 0.000 0.000
#> SRR2936870 1 0.3528 0.907 0.808 0.000 0.000 0.192
#> SRR2936869 3 0.0336 0.963 0.000 0.000 0.992 0.008
#> SRR2936868 3 0.0336 0.963 0.000 0.000 0.992 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR2936906 1 0.427 0.772 0.552 0.000 0.000 0.000 0.448
#> SRR2936909 1 0.188 0.686 0.924 0.000 0.000 0.064 0.012
#> SRR2936918 1 0.427 0.772 0.552 0.000 0.000 0.000 0.448
#> SRR2936917 5 0.624 1.000 0.000 0.400 0.000 0.144 0.456
#> SRR2936916 3 0.134 0.857 0.000 0.000 0.944 0.056 0.000
#> SRR2936915 3 0.134 0.857 0.000 0.000 0.944 0.056 0.000
#> SRR2936914 5 0.624 1.000 0.000 0.400 0.000 0.144 0.456
#> SRR2936913 5 0.624 1.000 0.000 0.400 0.000 0.144 0.456
#> SRR2936912 1 0.188 0.686 0.924 0.000 0.000 0.064 0.012
#> SRR2936910 1 0.427 0.772 0.552 0.000 0.000 0.000 0.448
#> SRR2936911 5 0.624 1.000 0.000 0.400 0.000 0.144 0.456
#> SRR2936907 2 0.000 0.744 0.000 1.000 0.000 0.000 0.000
#> SRR2936908 2 0.000 0.744 0.000 1.000 0.000 0.000 0.000
#> SRR2936904 4 0.406 1.000 0.000 0.000 0.360 0.640 0.000
#> SRR2936905 2 0.000 0.744 0.000 1.000 0.000 0.000 0.000
#> SRR2936903 1 0.000 0.725 1.000 0.000 0.000 0.000 0.000
#> SRR2936901 3 0.000 0.862 0.000 0.000 1.000 0.000 0.000
#> SRR2936902 2 0.682 0.597 0.000 0.600 0.164 0.152 0.084
#> SRR2936900 1 0.000 0.725 1.000 0.000 0.000 0.000 0.000
#> SRR2936898 3 0.000 0.862 0.000 0.000 1.000 0.000 0.000
#> SRR2936899 3 0.000 0.862 0.000 0.000 1.000 0.000 0.000
#> SRR2936897 1 0.188 0.686 0.924 0.000 0.000 0.064 0.012
#> SRR2936896 2 0.327 0.421 0.000 0.844 0.000 0.112 0.044
#> SRR2936894 1 0.427 0.772 0.552 0.000 0.000 0.000 0.448
#> SRR2936893 2 0.000 0.744 0.000 1.000 0.000 0.000 0.000
#> SRR2936895 2 0.674 0.584 0.000 0.600 0.112 0.204 0.084
#> SRR2936892 2 0.000 0.744 0.000 1.000 0.000 0.000 0.000
#> SRR2936891 1 0.427 0.772 0.552 0.000 0.000 0.000 0.448
#> SRR2936890 2 0.000 0.744 0.000 1.000 0.000 0.000 0.000
#> SRR2936886 4 0.406 1.000 0.000 0.000 0.360 0.640 0.000
#> SRR2936885 1 0.000 0.725 1.000 0.000 0.000 0.000 0.000
#> SRR2936888 1 0.427 0.772 0.552 0.000 0.000 0.000 0.448
#> SRR2936889 2 0.000 0.744 0.000 1.000 0.000 0.000 0.000
#> SRR2936887 4 0.406 1.000 0.000 0.000 0.360 0.640 0.000
#> SRR2936884 2 0.682 0.597 0.000 0.600 0.164 0.152 0.084
#> SRR2936883 2 0.682 0.597 0.000 0.600 0.164 0.152 0.084
#> SRR2936881 2 0.682 0.597 0.000 0.600 0.164 0.152 0.084
#> SRR2936882 1 0.000 0.725 1.000 0.000 0.000 0.000 0.000
#> SRR2936880 2 0.682 0.597 0.000 0.600 0.164 0.152 0.084
#> SRR2936878 5 0.624 1.000 0.000 0.400 0.000 0.144 0.456
#> SRR2936879 3 0.134 0.857 0.000 0.000 0.944 0.056 0.000
#> SRR2936875 2 0.000 0.744 0.000 1.000 0.000 0.000 0.000
#> SRR2936877 5 0.624 1.000 0.000 0.400 0.000 0.144 0.456
#> SRR2936876 3 0.544 0.501 0.192 0.000 0.684 0.112 0.012
#> SRR2936873 1 0.427 0.772 0.552 0.000 0.000 0.000 0.448
#> SRR2936872 2 0.000 0.744 0.000 1.000 0.000 0.000 0.000
#> SRR2936871 2 0.000 0.744 0.000 1.000 0.000 0.000 0.000
#> SRR2936874 2 0.000 0.744 0.000 1.000 0.000 0.000 0.000
#> SRR2936870 1 0.427 0.772 0.552 0.000 0.000 0.000 0.448
#> SRR2936869 4 0.406 1.000 0.000 0.000 0.360 0.640 0.000
#> SRR2936868 4 0.406 1.000 0.000 0.000 0.360 0.640 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR2936906 1 0.000 0.938 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936909 6 0.436 0.843 0.000 0.108 0.008 0.144 0.000 0.740
#> SRR2936918 1 0.000 0.938 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936917 5 0.000 0.884 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936916 3 0.026 0.898 0.000 0.000 0.992 0.008 0.000 0.000
#> SRR2936915 3 0.026 0.898 0.000 0.000 0.992 0.008 0.000 0.000
#> SRR2936914 5 0.000 0.884 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936913 5 0.000 0.884 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936912 6 0.436 0.843 0.000 0.108 0.008 0.144 0.000 0.740
#> SRR2936910 1 0.000 0.938 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936911 5 0.000 0.884 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936907 2 0.376 0.714 0.000 0.600 0.000 0.000 0.400 0.000
#> SRR2936908 2 0.376 0.714 0.000 0.600 0.000 0.000 0.400 0.000
#> SRR2936904 4 0.238 0.946 0.000 0.000 0.152 0.848 0.000 0.000
#> SRR2936905 2 0.376 0.714 0.000 0.600 0.000 0.000 0.400 0.000
#> SRR2936903 6 0.026 0.885 0.008 0.000 0.000 0.000 0.000 0.992
#> SRR2936901 3 0.120 0.901 0.000 0.056 0.944 0.000 0.000 0.000
#> SRR2936902 2 0.191 0.588 0.000 0.892 0.108 0.000 0.000 0.000
#> SRR2936900 6 0.026 0.885 0.008 0.000 0.000 0.000 0.000 0.992
#> SRR2936898 3 0.120 0.901 0.000 0.056 0.944 0.000 0.000 0.000
#> SRR2936899 3 0.120 0.901 0.000 0.056 0.944 0.000 0.000 0.000
#> SRR2936897 6 0.436 0.843 0.000 0.108 0.008 0.144 0.000 0.740
#> SRR2936896 5 0.383 -0.421 0.000 0.444 0.000 0.000 0.556 0.000
#> SRR2936894 1 0.000 0.938 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936893 2 0.376 0.714 0.000 0.600 0.000 0.000 0.400 0.000
#> SRR2936895 2 0.263 0.573 0.000 0.840 0.152 0.008 0.000 0.000
#> SRR2936892 2 0.376 0.714 0.000 0.600 0.000 0.000 0.400 0.000
#> SRR2936891 1 0.000 0.938 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936890 2 0.376 0.714 0.000 0.600 0.000 0.000 0.400 0.000
#> SRR2936886 4 0.270 0.987 0.000 0.000 0.188 0.812 0.000 0.000
#> SRR2936885 6 0.026 0.885 0.008 0.000 0.000 0.000 0.000 0.992
#> SRR2936888 1 0.000 0.938 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936889 2 0.376 0.714 0.000 0.600 0.000 0.000 0.400 0.000
#> SRR2936887 4 0.270 0.987 0.000 0.000 0.188 0.812 0.000 0.000
#> SRR2936884 2 0.191 0.588 0.000 0.892 0.108 0.000 0.000 0.000
#> SRR2936883 2 0.191 0.588 0.000 0.892 0.108 0.000 0.000 0.000
#> SRR2936881 2 0.191 0.588 0.000 0.892 0.108 0.000 0.000 0.000
#> SRR2936882 6 0.026 0.885 0.008 0.000 0.000 0.000 0.000 0.992
#> SRR2936880 2 0.191 0.588 0.000 0.892 0.108 0.000 0.000 0.000
#> SRR2936878 5 0.000 0.884 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936879 3 0.026 0.898 0.000 0.000 0.992 0.008 0.000 0.000
#> SRR2936875 2 0.376 0.714 0.000 0.600 0.000 0.000 0.400 0.000
#> SRR2936877 5 0.000 0.884 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936876 3 0.472 0.627 0.000 0.108 0.696 0.188 0.000 0.008
#> SRR2936873 1 0.374 0.294 0.608 0.000 0.000 0.000 0.000 0.392
#> SRR2936872 2 0.376 0.714 0.000 0.600 0.000 0.000 0.400 0.000
#> SRR2936871 2 0.376 0.714 0.000 0.600 0.000 0.000 0.400 0.000
#> SRR2936874 2 0.376 0.714 0.000 0.600 0.000 0.000 0.400 0.000
#> SRR2936870 1 0.000 0.938 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936869 4 0.270 0.987 0.000 0.000 0.188 0.812 0.000 0.000
#> SRR2936868 4 0.270 0.987 0.000 0.000 0.188 0.812 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
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 14198 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 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 0.810 0.939 0.967 0.5032 0.490 0.490
#> 3 3 0.920 0.887 0.948 0.3234 0.729 0.501
#> 4 4 0.736 0.785 0.783 0.0956 0.935 0.801
#> 5 5 0.735 0.695 0.771 0.0660 0.949 0.824
#> 6 6 0.818 0.665 0.756 0.0468 0.878 0.555
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
#> SRR2936906 1 0.0000 0.931 1.000 0.000
#> SRR2936909 1 0.0000 0.931 1.000 0.000
#> SRR2936918 1 0.0000 0.931 1.000 0.000
#> SRR2936917 2 0.0000 1.000 0.000 1.000
#> SRR2936916 2 0.0672 0.991 0.008 0.992
#> SRR2936915 1 0.7376 0.794 0.792 0.208
#> SRR2936914 2 0.0000 1.000 0.000 1.000
#> SRR2936913 2 0.0000 1.000 0.000 1.000
#> SRR2936912 1 0.0000 0.931 1.000 0.000
#> SRR2936910 1 0.0000 0.931 1.000 0.000
#> SRR2936911 2 0.0000 1.000 0.000 1.000
#> SRR2936907 2 0.0000 1.000 0.000 1.000
#> SRR2936908 2 0.0000 1.000 0.000 1.000
#> SRR2936904 1 0.4161 0.890 0.916 0.084
#> SRR2936905 2 0.0000 1.000 0.000 1.000
#> SRR2936903 1 0.0000 0.931 1.000 0.000
#> SRR2936901 1 0.0000 0.931 1.000 0.000
#> SRR2936902 2 0.0000 1.000 0.000 1.000
#> SRR2936900 1 0.0000 0.931 1.000 0.000
#> SRR2936898 1 0.2948 0.908 0.948 0.052
#> SRR2936899 1 0.4939 0.875 0.892 0.108
#> SRR2936897 1 0.0000 0.931 1.000 0.000
#> SRR2936896 2 0.0000 1.000 0.000 1.000
#> SRR2936894 1 0.0000 0.931 1.000 0.000
#> SRR2936893 2 0.0000 1.000 0.000 1.000
#> SRR2936895 2 0.0000 1.000 0.000 1.000
#> SRR2936892 2 0.0000 1.000 0.000 1.000
#> SRR2936891 1 0.0000 0.931 1.000 0.000
#> SRR2936890 2 0.0000 1.000 0.000 1.000
#> SRR2936886 1 0.7219 0.802 0.800 0.200
#> SRR2936885 1 0.0000 0.931 1.000 0.000
#> SRR2936888 1 0.0000 0.931 1.000 0.000
#> SRR2936889 2 0.0000 1.000 0.000 1.000
#> SRR2936887 1 0.7219 0.802 0.800 0.200
#> SRR2936884 2 0.0000 1.000 0.000 1.000
#> SRR2936883 2 0.0000 1.000 0.000 1.000
#> SRR2936881 2 0.0000 1.000 0.000 1.000
#> SRR2936882 1 0.0000 0.931 1.000 0.000
#> SRR2936880 2 0.0000 1.000 0.000 1.000
#> SRR2936878 2 0.0000 1.000 0.000 1.000
#> SRR2936879 1 0.7376 0.794 0.792 0.208
#> SRR2936875 2 0.0000 1.000 0.000 1.000
#> SRR2936877 2 0.0000 1.000 0.000 1.000
#> SRR2936876 1 0.0000 0.931 1.000 0.000
#> SRR2936873 1 0.0000 0.931 1.000 0.000
#> SRR2936872 2 0.0000 1.000 0.000 1.000
#> SRR2936871 2 0.0000 1.000 0.000 1.000
#> SRR2936874 2 0.0000 1.000 0.000 1.000
#> SRR2936870 1 0.0000 0.931 1.000 0.000
#> SRR2936869 1 0.9754 0.435 0.592 0.408
#> SRR2936868 1 0.7745 0.769 0.772 0.228
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR2936906 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936909 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936918 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936917 2 0.0237 0.947 0.000 0.996 0.004
#> SRR2936916 3 0.0000 0.871 0.000 0.000 1.000
#> SRR2936915 3 0.0237 0.873 0.004 0.000 0.996
#> SRR2936914 2 0.0237 0.947 0.000 0.996 0.004
#> SRR2936913 2 0.0237 0.947 0.000 0.996 0.004
#> SRR2936912 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936910 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936911 2 0.0237 0.947 0.000 0.996 0.004
#> SRR2936907 2 0.0000 0.947 0.000 1.000 0.000
#> SRR2936908 2 0.1411 0.953 0.000 0.964 0.036
#> SRR2936904 3 0.1529 0.841 0.040 0.000 0.960
#> SRR2936905 2 0.1411 0.953 0.000 0.964 0.036
#> SRR2936903 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936901 3 0.0237 0.873 0.004 0.000 0.996
#> SRR2936902 3 0.5591 0.609 0.000 0.304 0.696
#> SRR2936900 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936898 3 0.0237 0.873 0.004 0.000 0.996
#> SRR2936899 3 0.0237 0.873 0.004 0.000 0.996
#> SRR2936897 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936896 2 0.0237 0.947 0.000 0.996 0.004
#> SRR2936894 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936893 2 0.1411 0.953 0.000 0.964 0.036
#> SRR2936895 3 0.6180 0.382 0.000 0.416 0.584
#> SRR2936892 2 0.1411 0.953 0.000 0.964 0.036
#> SRR2936891 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936890 2 0.1411 0.953 0.000 0.964 0.036
#> SRR2936886 3 0.0237 0.873 0.004 0.000 0.996
#> SRR2936885 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936888 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936889 2 0.1411 0.953 0.000 0.964 0.036
#> SRR2936887 3 0.0237 0.873 0.004 0.000 0.996
#> SRR2936884 2 0.6204 0.123 0.000 0.576 0.424
#> SRR2936883 3 0.5591 0.609 0.000 0.304 0.696
#> SRR2936881 3 0.5591 0.609 0.000 0.304 0.696
#> SRR2936882 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936880 3 0.6180 0.382 0.000 0.416 0.584
#> SRR2936878 2 0.0237 0.947 0.000 0.996 0.004
#> SRR2936879 3 0.0237 0.873 0.004 0.000 0.996
#> SRR2936875 2 0.1411 0.953 0.000 0.964 0.036
#> SRR2936877 2 0.0237 0.947 0.000 0.996 0.004
#> SRR2936876 3 0.0237 0.873 0.004 0.000 0.996
#> SRR2936873 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936872 2 0.1411 0.953 0.000 0.964 0.036
#> SRR2936871 2 0.1411 0.953 0.000 0.964 0.036
#> SRR2936874 2 0.1411 0.953 0.000 0.964 0.036
#> SRR2936870 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936869 3 0.0237 0.871 0.000 0.004 0.996
#> SRR2936868 3 0.0237 0.873 0.004 0.000 0.996
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR2936906 1 0.0000 0.923 1.000 0.000 0.000 0.000
#> SRR2936909 1 0.2868 0.908 0.864 0.000 0.136 0.000
#> SRR2936918 1 0.0000 0.923 1.000 0.000 0.000 0.000
#> SRR2936917 2 0.0000 0.698 0.000 1.000 0.000 0.000
#> SRR2936916 4 0.4972 -0.112 0.000 0.000 0.456 0.544
#> SRR2936915 4 0.3569 0.669 0.000 0.000 0.196 0.804
#> SRR2936914 2 0.0000 0.698 0.000 1.000 0.000 0.000
#> SRR2936913 2 0.0000 0.698 0.000 1.000 0.000 0.000
#> SRR2936912 1 0.2760 0.910 0.872 0.000 0.128 0.000
#> SRR2936910 1 0.0000 0.923 1.000 0.000 0.000 0.000
#> SRR2936911 2 0.0000 0.698 0.000 1.000 0.000 0.000
#> SRR2936907 2 0.4624 0.832 0.000 0.660 0.340 0.000
#> SRR2936908 2 0.4905 0.839 0.000 0.632 0.364 0.004
#> SRR2936904 4 0.0895 0.682 0.004 0.000 0.020 0.976
#> SRR2936905 2 0.4905 0.839 0.000 0.632 0.364 0.004
#> SRR2936903 1 0.3975 0.874 0.760 0.000 0.240 0.000
#> SRR2936901 4 0.4866 0.488 0.000 0.000 0.404 0.596
#> SRR2936902 3 0.6249 0.916 0.000 0.072 0.592 0.336
#> SRR2936900 1 0.3975 0.874 0.760 0.000 0.240 0.000
#> SRR2936898 4 0.4605 0.514 0.000 0.000 0.336 0.664
#> SRR2936899 4 0.4605 0.514 0.000 0.000 0.336 0.664
#> SRR2936897 1 0.3024 0.906 0.852 0.000 0.148 0.000
#> SRR2936896 2 0.4643 0.831 0.000 0.656 0.344 0.000
#> SRR2936894 1 0.0000 0.923 1.000 0.000 0.000 0.000
#> SRR2936893 2 0.4905 0.839 0.000 0.632 0.364 0.004
#> SRR2936895 3 0.6412 0.917 0.000 0.088 0.592 0.320
#> SRR2936892 2 0.4905 0.839 0.000 0.632 0.364 0.004
#> SRR2936891 1 0.0000 0.923 1.000 0.000 0.000 0.000
#> SRR2936890 2 0.4905 0.839 0.000 0.632 0.364 0.004
#> SRR2936886 4 0.0336 0.697 0.000 0.000 0.008 0.992
#> SRR2936885 1 0.3975 0.874 0.760 0.000 0.240 0.000
#> SRR2936888 1 0.0336 0.921 0.992 0.000 0.008 0.000
#> SRR2936889 2 0.4905 0.839 0.000 0.632 0.364 0.004
#> SRR2936887 4 0.0336 0.697 0.000 0.000 0.008 0.992
#> SRR2936884 3 0.6233 0.739 0.000 0.124 0.660 0.216
#> SRR2936883 3 0.6249 0.916 0.000 0.072 0.592 0.336
#> SRR2936881 3 0.6249 0.916 0.000 0.072 0.592 0.336
#> SRR2936882 1 0.3975 0.874 0.760 0.000 0.240 0.000
#> SRR2936880 3 0.6412 0.917 0.000 0.088 0.592 0.320
#> SRR2936878 2 0.0000 0.698 0.000 1.000 0.000 0.000
#> SRR2936879 4 0.3873 0.648 0.000 0.000 0.228 0.772
#> SRR2936875 2 0.4905 0.839 0.000 0.632 0.364 0.004
#> SRR2936877 2 0.0000 0.698 0.000 1.000 0.000 0.000
#> SRR2936876 4 0.4072 0.658 0.000 0.000 0.252 0.748
#> SRR2936873 1 0.0000 0.923 1.000 0.000 0.000 0.000
#> SRR2936872 2 0.4905 0.839 0.000 0.632 0.364 0.004
#> SRR2936871 2 0.4905 0.839 0.000 0.632 0.364 0.004
#> SRR2936874 2 0.4905 0.839 0.000 0.632 0.364 0.004
#> SRR2936870 1 0.0336 0.921 0.992 0.000 0.008 0.000
#> SRR2936869 4 0.0336 0.697 0.000 0.000 0.008 0.992
#> SRR2936868 4 0.0336 0.697 0.000 0.000 0.008 0.992
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR2936906 1 0.4697 0.7943 0.648 0.000 0.000 0.032 NA
#> SRR2936909 1 0.1329 0.7478 0.956 0.000 0.004 0.032 NA
#> SRR2936918 1 0.4623 0.7954 0.664 0.000 0.000 0.032 NA
#> SRR2936917 2 0.0404 0.6121 0.000 0.988 0.012 0.000 NA
#> SRR2936916 3 0.4573 0.5763 0.000 0.000 0.744 0.164 NA
#> SRR2936915 4 0.6047 0.1740 0.000 0.000 0.400 0.480 NA
#> SRR2936914 2 0.0404 0.6121 0.000 0.988 0.012 0.000 NA
#> SRR2936913 2 0.0404 0.6121 0.000 0.988 0.012 0.000 NA
#> SRR2936912 1 0.1026 0.7514 0.968 0.000 0.004 0.024 NA
#> SRR2936910 1 0.4623 0.7954 0.664 0.000 0.000 0.032 NA
#> SRR2936911 2 0.0404 0.6121 0.000 0.988 0.012 0.000 NA
#> SRR2936907 2 0.5597 0.7997 0.000 0.488 0.072 0.000 NA
#> SRR2936908 2 0.5733 0.8012 0.000 0.476 0.084 0.000 NA
#> SRR2936904 4 0.3359 0.7815 0.000 0.000 0.108 0.840 NA
#> SRR2936905 2 0.5733 0.8012 0.000 0.476 0.084 0.000 NA
#> SRR2936903 1 0.3862 0.6897 0.824 0.000 0.012 0.072 NA
#> SRR2936901 3 0.5375 0.4328 0.000 0.000 0.604 0.320 NA
#> SRR2936902 3 0.0865 0.7374 0.000 0.024 0.972 0.000 NA
#> SRR2936900 1 0.3689 0.6970 0.836 0.000 0.012 0.068 NA
#> SRR2936898 3 0.5139 0.4540 0.000 0.000 0.648 0.280 NA
#> SRR2936899 3 0.5139 0.4540 0.000 0.000 0.648 0.280 NA
#> SRR2936897 1 0.1329 0.7478 0.956 0.000 0.004 0.032 NA
#> SRR2936896 2 0.5613 0.7368 0.000 0.648 0.096 0.012 NA
#> SRR2936894 1 0.4697 0.7943 0.648 0.000 0.000 0.032 NA
#> SRR2936893 2 0.6075 0.8002 0.000 0.476 0.084 0.012 NA
#> SRR2936895 3 0.0865 0.7374 0.000 0.024 0.972 0.000 NA
#> SRR2936892 2 0.6077 0.7988 0.000 0.472 0.084 0.012 NA
#> SRR2936891 1 0.4697 0.7943 0.648 0.000 0.000 0.032 NA
#> SRR2936890 2 0.5733 0.8012 0.000 0.476 0.084 0.000 NA
#> SRR2936886 4 0.2471 0.8137 0.000 0.000 0.136 0.864 NA
#> SRR2936885 1 0.3515 0.7018 0.844 0.000 0.008 0.064 NA
#> SRR2936888 1 0.5102 0.7860 0.620 0.000 0.008 0.036 NA
#> SRR2936889 2 0.5733 0.8012 0.000 0.476 0.084 0.000 NA
#> SRR2936887 4 0.2471 0.8137 0.000 0.000 0.136 0.864 NA
#> SRR2936884 3 0.1493 0.7113 0.000 0.028 0.948 0.000 NA
#> SRR2936883 3 0.0865 0.7374 0.000 0.024 0.972 0.000 NA
#> SRR2936881 3 0.0865 0.7374 0.000 0.024 0.972 0.000 NA
#> SRR2936882 1 0.3626 0.6997 0.840 0.000 0.012 0.064 NA
#> SRR2936880 3 0.0865 0.7374 0.000 0.024 0.972 0.000 NA
#> SRR2936878 2 0.0404 0.6121 0.000 0.988 0.012 0.000 NA
#> SRR2936879 3 0.6024 -0.0802 0.000 0.000 0.472 0.412 NA
#> SRR2936875 2 0.6075 0.8002 0.000 0.476 0.084 0.012 NA
#> SRR2936877 2 0.0404 0.6121 0.000 0.988 0.012 0.000 NA
#> SRR2936876 4 0.7689 0.4228 0.184 0.000 0.196 0.496 NA
#> SRR2936873 1 0.4623 0.7954 0.664 0.000 0.000 0.032 NA
#> SRR2936872 2 0.5733 0.8012 0.000 0.476 0.084 0.000 NA
#> SRR2936871 2 0.5733 0.8012 0.000 0.476 0.084 0.000 NA
#> SRR2936874 2 0.6077 0.7988 0.000 0.472 0.084 0.012 NA
#> SRR2936870 1 0.5102 0.7860 0.620 0.000 0.008 0.036 NA
#> SRR2936869 4 0.2471 0.8137 0.000 0.000 0.136 0.864 NA
#> SRR2936868 4 0.2471 0.8137 0.000 0.000 0.136 0.864 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR2936906 1 0.0000 0.8178 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936909 1 0.5615 0.4143 0.584 0.088 0.008 0.020 0.000 0.300
#> SRR2936918 1 0.0146 0.8179 0.996 0.004 0.000 0.000 0.000 0.000
#> SRR2936917 5 0.0000 0.8923 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936916 3 0.6070 0.4057 0.000 0.016 0.460 0.164 0.000 0.360
#> SRR2936915 6 0.5976 -0.2471 0.000 0.000 0.228 0.364 0.000 0.408
#> SRR2936914 5 0.0000 0.8923 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936913 5 0.0000 0.8923 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936912 1 0.5537 0.4183 0.588 0.088 0.008 0.016 0.000 0.300
#> SRR2936910 1 0.0291 0.8174 0.992 0.004 0.004 0.000 0.000 0.000
#> SRR2936911 5 0.0000 0.8923 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936907 2 0.3595 0.9459 0.000 0.704 0.000 0.000 0.288 0.008
#> SRR2936908 2 0.4593 0.9466 0.000 0.660 0.008 0.000 0.280 0.052
#> SRR2936904 4 0.2826 0.8542 0.000 0.000 0.028 0.844 0.000 0.128
#> SRR2936905 2 0.3468 0.9551 0.000 0.712 0.004 0.000 0.284 0.000
#> SRR2936903 6 0.6070 0.0937 0.344 0.224 0.004 0.000 0.000 0.428
#> SRR2936901 3 0.6175 0.5084 0.000 0.028 0.508 0.172 0.000 0.292
#> SRR2936902 3 0.1088 0.7598 0.000 0.024 0.960 0.000 0.016 0.000
#> SRR2936900 6 0.5995 0.0540 0.388 0.196 0.004 0.000 0.000 0.412
#> SRR2936898 3 0.6092 0.5239 0.000 0.028 0.532 0.172 0.000 0.268
#> SRR2936899 3 0.6092 0.5239 0.000 0.028 0.532 0.172 0.000 0.268
#> SRR2936897 1 0.5739 0.3759 0.564 0.096 0.008 0.020 0.000 0.312
#> SRR2936896 5 0.5112 -0.2709 0.000 0.392 0.000 0.008 0.536 0.064
#> SRR2936894 1 0.0000 0.8178 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936893 2 0.4944 0.9436 0.000 0.644 0.008 0.008 0.280 0.060
#> SRR2936895 3 0.1232 0.7584 0.000 0.024 0.956 0.000 0.016 0.004
#> SRR2936892 2 0.4944 0.9436 0.000 0.644 0.008 0.008 0.280 0.060
#> SRR2936891 1 0.0000 0.8178 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936890 2 0.3468 0.9551 0.000 0.712 0.004 0.000 0.284 0.000
#> SRR2936886 4 0.0865 0.9656 0.000 0.000 0.036 0.964 0.000 0.000
#> SRR2936885 6 0.5995 0.0540 0.388 0.196 0.004 0.000 0.000 0.412
#> SRR2936888 1 0.2146 0.7795 0.908 0.060 0.024 0.008 0.000 0.000
#> SRR2936889 2 0.3468 0.9551 0.000 0.712 0.004 0.000 0.284 0.000
#> SRR2936887 4 0.0865 0.9656 0.000 0.000 0.036 0.964 0.000 0.000
#> SRR2936884 3 0.1464 0.7476 0.000 0.036 0.944 0.000 0.016 0.004
#> SRR2936883 3 0.1088 0.7598 0.000 0.024 0.960 0.000 0.016 0.000
#> SRR2936881 3 0.1088 0.7598 0.000 0.024 0.960 0.000 0.016 0.000
#> SRR2936882 6 0.5995 0.0540 0.388 0.196 0.004 0.000 0.000 0.412
#> SRR2936880 3 0.1088 0.7598 0.000 0.024 0.960 0.000 0.016 0.000
#> SRR2936878 5 0.0000 0.8923 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936879 6 0.6087 -0.3059 0.000 0.000 0.292 0.316 0.000 0.392
#> SRR2936875 2 0.4944 0.9436 0.000 0.644 0.008 0.008 0.280 0.060
#> SRR2936877 5 0.1007 0.8664 0.000 0.000 0.000 0.000 0.956 0.044
#> SRR2936876 6 0.4580 -0.2009 0.000 0.000 0.052 0.336 0.000 0.612
#> SRR2936873 1 0.0291 0.8174 0.992 0.004 0.004 0.000 0.000 0.000
#> SRR2936872 2 0.3468 0.9551 0.000 0.712 0.004 0.000 0.284 0.000
#> SRR2936871 2 0.3468 0.9551 0.000 0.712 0.004 0.000 0.284 0.000
#> SRR2936874 2 0.4944 0.9436 0.000 0.644 0.008 0.008 0.280 0.060
#> SRR2936870 1 0.2146 0.7795 0.908 0.060 0.024 0.008 0.000 0.000
#> SRR2936869 4 0.0865 0.9656 0.000 0.000 0.036 0.964 0.000 0.000
#> SRR2936868 4 0.0865 0.9656 0.000 0.000 0.036 0.964 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
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 14198 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.986 0.994 0.5103 0.490 0.490
#> 3 3 0.994 0.965 0.975 0.1693 0.918 0.832
#> 4 4 0.963 0.956 0.973 0.1733 0.867 0.684
#> 5 5 0.821 0.823 0.901 0.0675 0.952 0.844
#> 6 6 0.804 0.707 0.850 0.0444 0.969 0.883
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR2936906 1 0.000 0.990 1.00 0.00
#> SRR2936909 1 0.000 0.990 1.00 0.00
#> SRR2936918 1 0.000 0.990 1.00 0.00
#> SRR2936917 2 0.000 0.998 0.00 1.00
#> SRR2936916 2 0.242 0.958 0.04 0.96
#> SRR2936915 1 0.000 0.990 1.00 0.00
#> SRR2936914 2 0.000 0.998 0.00 1.00
#> SRR2936913 2 0.000 0.998 0.00 1.00
#> SRR2936912 1 0.000 0.990 1.00 0.00
#> SRR2936910 1 0.000 0.990 1.00 0.00
#> SRR2936911 2 0.000 0.998 0.00 1.00
#> SRR2936907 2 0.000 0.998 0.00 1.00
#> SRR2936908 2 0.000 0.998 0.00 1.00
#> SRR2936904 1 0.000 0.990 1.00 0.00
#> SRR2936905 2 0.000 0.998 0.00 1.00
#> SRR2936903 1 0.000 0.990 1.00 0.00
#> SRR2936901 1 0.000 0.990 1.00 0.00
#> SRR2936902 2 0.000 0.998 0.00 1.00
#> SRR2936900 1 0.000 0.990 1.00 0.00
#> SRR2936898 1 0.000 0.990 1.00 0.00
#> SRR2936899 1 0.000 0.990 1.00 0.00
#> SRR2936897 1 0.000 0.990 1.00 0.00
#> SRR2936896 2 0.000 0.998 0.00 1.00
#> SRR2936894 1 0.000 0.990 1.00 0.00
#> SRR2936893 2 0.000 0.998 0.00 1.00
#> SRR2936895 2 0.000 0.998 0.00 1.00
#> SRR2936892 2 0.000 0.998 0.00 1.00
#> SRR2936891 1 0.000 0.990 1.00 0.00
#> SRR2936890 2 0.000 0.998 0.00 1.00
#> SRR2936886 1 0.000 0.990 1.00 0.00
#> SRR2936885 1 0.000 0.990 1.00 0.00
#> SRR2936888 1 0.000 0.990 1.00 0.00
#> SRR2936889 2 0.000 0.998 0.00 1.00
#> SRR2936887 1 0.000 0.990 1.00 0.00
#> SRR2936884 2 0.000 0.998 0.00 1.00
#> SRR2936883 2 0.000 0.998 0.00 1.00
#> SRR2936881 2 0.000 0.998 0.00 1.00
#> SRR2936882 1 0.000 0.990 1.00 0.00
#> SRR2936880 2 0.000 0.998 0.00 1.00
#> SRR2936878 2 0.000 0.998 0.00 1.00
#> SRR2936879 1 0.000 0.990 1.00 0.00
#> SRR2936875 2 0.000 0.998 0.00 1.00
#> SRR2936877 2 0.000 0.998 0.00 1.00
#> SRR2936876 1 0.000 0.990 1.00 0.00
#> SRR2936873 1 0.000 0.990 1.00 0.00
#> SRR2936872 2 0.000 0.998 0.00 1.00
#> SRR2936871 2 0.000 0.998 0.00 1.00
#> SRR2936874 2 0.000 0.998 0.00 1.00
#> SRR2936870 1 0.000 0.990 1.00 0.00
#> SRR2936869 1 0.827 0.650 0.74 0.26
#> SRR2936868 1 0.000 0.990 1.00 0.00
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR2936906 1 0.000 0.983 1.000 0.000 0.000
#> SRR2936909 1 0.000 0.983 1.000 0.000 0.000
#> SRR2936918 1 0.000 0.983 1.000 0.000 0.000
#> SRR2936917 2 0.000 0.975 0.000 1.000 0.000
#> SRR2936916 2 0.382 0.797 0.148 0.852 0.000
#> SRR2936915 1 0.175 0.938 0.952 0.000 0.048
#> SRR2936914 2 0.000 0.975 0.000 1.000 0.000
#> SRR2936913 2 0.000 0.975 0.000 1.000 0.000
#> SRR2936912 1 0.000 0.983 1.000 0.000 0.000
#> SRR2936910 1 0.000 0.983 1.000 0.000 0.000
#> SRR2936911 2 0.000 0.975 0.000 1.000 0.000
#> SRR2936907 2 0.000 0.975 0.000 1.000 0.000
#> SRR2936908 2 0.000 0.975 0.000 1.000 0.000
#> SRR2936904 3 0.263 0.986 0.084 0.000 0.916
#> SRR2936905 2 0.000 0.975 0.000 1.000 0.000
#> SRR2936903 1 0.000 0.983 1.000 0.000 0.000
#> SRR2936901 1 0.263 0.908 0.916 0.000 0.084
#> SRR2936902 2 0.263 0.924 0.000 0.916 0.084
#> SRR2936900 1 0.000 0.983 1.000 0.000 0.000
#> SRR2936898 1 0.263 0.908 0.916 0.000 0.084
#> SRR2936899 1 0.263 0.908 0.916 0.000 0.084
#> SRR2936897 1 0.000 0.983 1.000 0.000 0.000
#> SRR2936896 2 0.000 0.975 0.000 1.000 0.000
#> SRR2936894 1 0.000 0.983 1.000 0.000 0.000
#> SRR2936893 2 0.000 0.975 0.000 1.000 0.000
#> SRR2936895 2 0.000 0.975 0.000 1.000 0.000
#> SRR2936892 2 0.000 0.975 0.000 1.000 0.000
#> SRR2936891 1 0.000 0.983 1.000 0.000 0.000
#> SRR2936890 2 0.000 0.975 0.000 1.000 0.000
#> SRR2936886 3 0.263 0.986 0.084 0.000 0.916
#> SRR2936885 1 0.000 0.983 1.000 0.000 0.000
#> SRR2936888 1 0.000 0.983 1.000 0.000 0.000
#> SRR2936889 2 0.000 0.975 0.000 1.000 0.000
#> SRR2936887 3 0.263 0.986 0.084 0.000 0.916
#> SRR2936884 2 0.263 0.924 0.000 0.916 0.084
#> SRR2936883 2 0.263 0.924 0.000 0.916 0.084
#> SRR2936881 2 0.263 0.924 0.000 0.916 0.084
#> SRR2936882 1 0.000 0.983 1.000 0.000 0.000
#> SRR2936880 2 0.263 0.924 0.000 0.916 0.084
#> SRR2936878 2 0.000 0.975 0.000 1.000 0.000
#> SRR2936879 1 0.000 0.983 1.000 0.000 0.000
#> SRR2936875 2 0.000 0.975 0.000 1.000 0.000
#> SRR2936877 2 0.000 0.975 0.000 1.000 0.000
#> SRR2936876 1 0.000 0.983 1.000 0.000 0.000
#> SRR2936873 1 0.000 0.983 1.000 0.000 0.000
#> SRR2936872 2 0.000 0.975 0.000 1.000 0.000
#> SRR2936871 2 0.000 0.975 0.000 1.000 0.000
#> SRR2936874 2 0.000 0.975 0.000 1.000 0.000
#> SRR2936870 1 0.000 0.983 1.000 0.000 0.000
#> SRR2936869 3 0.315 0.945 0.044 0.040 0.916
#> SRR2936868 3 0.263 0.986 0.084 0.000 0.916
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR2936906 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> SRR2936909 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> SRR2936918 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> SRR2936917 2 0.1637 0.950 0.000 0.940 0.060 0.000
#> SRR2936916 2 0.5507 0.711 0.156 0.732 0.112 0.000
#> SRR2936915 1 0.1059 0.975 0.972 0.000 0.016 0.012
#> SRR2936914 2 0.1637 0.950 0.000 0.940 0.060 0.000
#> SRR2936913 2 0.1637 0.950 0.000 0.940 0.060 0.000
#> SRR2936912 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> SRR2936910 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> SRR2936911 2 0.1637 0.950 0.000 0.940 0.060 0.000
#> SRR2936907 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> SRR2936908 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> SRR2936904 4 0.0921 0.962 0.028 0.000 0.000 0.972
#> SRR2936905 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> SRR2936903 1 0.0188 0.995 0.996 0.000 0.004 0.000
#> SRR2936901 3 0.2469 0.864 0.108 0.000 0.892 0.000
#> SRR2936902 3 0.0707 0.912 0.000 0.020 0.980 0.000
#> SRR2936900 1 0.0188 0.995 0.996 0.000 0.004 0.000
#> SRR2936898 3 0.2408 0.868 0.104 0.000 0.896 0.000
#> SRR2936899 3 0.2408 0.868 0.104 0.000 0.896 0.000
#> SRR2936897 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> SRR2936896 2 0.1637 0.950 0.000 0.940 0.060 0.000
#> SRR2936894 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> SRR2936893 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> SRR2936895 2 0.2149 0.930 0.000 0.912 0.088 0.000
#> SRR2936892 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> SRR2936891 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> SRR2936890 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> SRR2936886 4 0.0000 0.991 0.000 0.000 0.000 1.000
#> SRR2936885 1 0.0188 0.995 0.996 0.000 0.004 0.000
#> SRR2936888 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> SRR2936889 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> SRR2936887 4 0.0000 0.991 0.000 0.000 0.000 1.000
#> SRR2936884 3 0.2149 0.841 0.000 0.088 0.912 0.000
#> SRR2936883 3 0.0707 0.912 0.000 0.020 0.980 0.000
#> SRR2936881 3 0.0707 0.912 0.000 0.020 0.980 0.000
#> SRR2936882 1 0.0188 0.995 0.996 0.000 0.004 0.000
#> SRR2936880 3 0.0707 0.912 0.000 0.020 0.980 0.000
#> SRR2936878 2 0.1637 0.950 0.000 0.940 0.060 0.000
#> SRR2936879 1 0.0469 0.989 0.988 0.000 0.012 0.000
#> SRR2936875 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> SRR2936877 2 0.1637 0.950 0.000 0.940 0.060 0.000
#> SRR2936876 1 0.0469 0.989 0.988 0.000 0.012 0.000
#> SRR2936873 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> SRR2936872 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> SRR2936871 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> SRR2936874 2 0.0000 0.960 0.000 1.000 0.000 0.000
#> SRR2936870 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> SRR2936869 4 0.0000 0.991 0.000 0.000 0.000 1.000
#> SRR2936868 4 0.0000 0.991 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
#> SRR2936906 1 0.0000 0.896 1.000 0.000 0.000 0.000 0.000
#> SRR2936909 1 0.0000 0.896 1.000 0.000 0.000 0.000 0.000
#> SRR2936918 1 0.0000 0.896 1.000 0.000 0.000 0.000 0.000
#> SRR2936917 2 0.3661 0.725 0.000 0.724 0.276 0.000 0.000
#> SRR2936916 3 0.6094 0.585 0.100 0.064 0.664 0.000 0.172
#> SRR2936915 1 0.3521 0.707 0.764 0.000 0.000 0.004 0.232
#> SRR2936914 2 0.3661 0.725 0.000 0.724 0.276 0.000 0.000
#> SRR2936913 2 0.3661 0.725 0.000 0.724 0.276 0.000 0.000
#> SRR2936912 1 0.0000 0.896 1.000 0.000 0.000 0.000 0.000
#> SRR2936910 1 0.0000 0.896 1.000 0.000 0.000 0.000 0.000
#> SRR2936911 2 0.3661 0.725 0.000 0.724 0.276 0.000 0.000
#> SRR2936907 2 0.0000 0.858 0.000 1.000 0.000 0.000 0.000
#> SRR2936908 2 0.0000 0.858 0.000 1.000 0.000 0.000 0.000
#> SRR2936904 4 0.1965 0.858 0.096 0.000 0.000 0.904 0.000
#> SRR2936905 2 0.0000 0.858 0.000 1.000 0.000 0.000 0.000
#> SRR2936903 1 0.4045 0.519 0.644 0.000 0.000 0.000 0.356
#> SRR2936901 5 0.4101 0.957 0.048 0.000 0.184 0.000 0.768
#> SRR2936902 3 0.0290 0.825 0.000 0.000 0.992 0.000 0.008
#> SRR2936900 1 0.3612 0.667 0.732 0.000 0.000 0.000 0.268
#> SRR2936898 5 0.3845 0.978 0.024 0.000 0.208 0.000 0.768
#> SRR2936899 5 0.3845 0.978 0.024 0.000 0.208 0.000 0.768
#> SRR2936897 1 0.0000 0.896 1.000 0.000 0.000 0.000 0.000
#> SRR2936896 2 0.3661 0.725 0.000 0.724 0.276 0.000 0.000
#> SRR2936894 1 0.0000 0.896 1.000 0.000 0.000 0.000 0.000
#> SRR2936893 2 0.0000 0.858 0.000 1.000 0.000 0.000 0.000
#> SRR2936895 3 0.3895 0.389 0.000 0.320 0.680 0.000 0.000
#> SRR2936892 2 0.0000 0.858 0.000 1.000 0.000 0.000 0.000
#> SRR2936891 1 0.0000 0.896 1.000 0.000 0.000 0.000 0.000
#> SRR2936890 2 0.0000 0.858 0.000 1.000 0.000 0.000 0.000
#> SRR2936886 4 0.0162 0.966 0.004 0.000 0.000 0.996 0.000
#> SRR2936885 1 0.3586 0.671 0.736 0.000 0.000 0.000 0.264
#> SRR2936888 1 0.0000 0.896 1.000 0.000 0.000 0.000 0.000
#> SRR2936889 2 0.0000 0.858 0.000 1.000 0.000 0.000 0.000
#> SRR2936887 4 0.0162 0.966 0.004 0.000 0.000 0.996 0.000
#> SRR2936884 3 0.0162 0.820 0.000 0.004 0.996 0.000 0.000
#> SRR2936883 3 0.0290 0.825 0.000 0.000 0.992 0.000 0.008
#> SRR2936881 3 0.0290 0.825 0.000 0.000 0.992 0.000 0.008
#> SRR2936882 1 0.3612 0.667 0.732 0.000 0.000 0.000 0.268
#> SRR2936880 3 0.0290 0.825 0.000 0.000 0.992 0.000 0.008
#> SRR2936878 2 0.3661 0.725 0.000 0.724 0.276 0.000 0.000
#> SRR2936879 1 0.2629 0.806 0.860 0.000 0.000 0.004 0.136
#> SRR2936875 2 0.0000 0.858 0.000 1.000 0.000 0.000 0.000
#> SRR2936877 2 0.3661 0.725 0.000 0.724 0.276 0.000 0.000
#> SRR2936876 1 0.1892 0.847 0.916 0.000 0.000 0.004 0.080
#> SRR2936873 1 0.0000 0.896 1.000 0.000 0.000 0.000 0.000
#> SRR2936872 2 0.0000 0.858 0.000 1.000 0.000 0.000 0.000
#> SRR2936871 2 0.0000 0.858 0.000 1.000 0.000 0.000 0.000
#> SRR2936874 2 0.0000 0.858 0.000 1.000 0.000 0.000 0.000
#> SRR2936870 1 0.0000 0.896 1.000 0.000 0.000 0.000 0.000
#> SRR2936869 4 0.0162 0.966 0.004 0.000 0.000 0.996 0.000
#> SRR2936868 4 0.0162 0.966 0.004 0.000 0.000 0.996 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR2936906 1 0.0000 0.826 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936909 1 0.0000 0.826 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936918 1 0.0000 0.826 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936917 2 0.5288 0.600 0.000 0.592 0.252 0.000 0.000 0.156
#> SRR2936916 6 0.4095 -0.454 0.000 0.008 0.480 0.000 0.000 0.512
#> SRR2936915 6 0.2527 0.304 0.168 0.000 0.000 0.000 0.000 0.832
#> SRR2936914 2 0.5288 0.600 0.000 0.592 0.252 0.000 0.000 0.156
#> SRR2936913 2 0.5288 0.600 0.000 0.592 0.252 0.000 0.000 0.156
#> SRR2936912 1 0.0000 0.826 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936910 1 0.0000 0.826 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936911 2 0.5288 0.600 0.000 0.592 0.252 0.000 0.000 0.156
#> SRR2936907 2 0.0000 0.803 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936908 2 0.0000 0.803 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936904 4 0.3030 0.712 0.168 0.000 0.000 0.816 0.008 0.008
#> SRR2936905 2 0.0000 0.803 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936903 1 0.3797 0.383 0.580 0.000 0.000 0.000 0.420 0.000
#> SRR2936901 5 0.0363 1.000 0.000 0.000 0.012 0.000 0.988 0.000
#> SRR2936902 3 0.0458 0.882 0.000 0.000 0.984 0.000 0.016 0.000
#> SRR2936900 1 0.3547 0.549 0.668 0.000 0.000 0.000 0.332 0.000
#> SRR2936898 5 0.0363 1.000 0.000 0.000 0.012 0.000 0.988 0.000
#> SRR2936899 5 0.0363 1.000 0.000 0.000 0.012 0.000 0.988 0.000
#> SRR2936897 1 0.0000 0.826 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936896 2 0.5288 0.600 0.000 0.592 0.252 0.000 0.000 0.156
#> SRR2936894 1 0.0000 0.826 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936893 2 0.0000 0.803 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936895 3 0.4915 0.403 0.000 0.188 0.656 0.000 0.000 0.156
#> SRR2936892 2 0.0000 0.803 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936891 1 0.0000 0.826 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936890 2 0.0000 0.803 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936886 4 0.0000 0.936 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR2936885 1 0.3499 0.565 0.680 0.000 0.000 0.000 0.320 0.000
#> SRR2936888 1 0.0000 0.826 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936889 2 0.0000 0.803 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936887 4 0.0000 0.936 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR2936884 3 0.0260 0.875 0.000 0.000 0.992 0.000 0.008 0.000
#> SRR2936883 3 0.0458 0.882 0.000 0.000 0.984 0.000 0.016 0.000
#> SRR2936881 3 0.0458 0.882 0.000 0.000 0.984 0.000 0.016 0.000
#> SRR2936882 1 0.3547 0.549 0.668 0.000 0.000 0.000 0.332 0.000
#> SRR2936880 3 0.0458 0.882 0.000 0.000 0.984 0.000 0.016 0.000
#> SRR2936878 2 0.5288 0.600 0.000 0.592 0.252 0.000 0.000 0.156
#> SRR2936879 6 0.4161 0.101 0.448 0.000 0.000 0.000 0.012 0.540
#> SRR2936875 2 0.0000 0.803 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936877 2 0.5288 0.600 0.000 0.592 0.252 0.000 0.000 0.156
#> SRR2936876 1 0.4184 -0.310 0.500 0.000 0.000 0.000 0.012 0.488
#> SRR2936873 1 0.0000 0.826 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936872 2 0.0000 0.803 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936871 2 0.0000 0.803 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936874 2 0.0000 0.803 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936870 1 0.0000 0.826 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936869 4 0.0000 0.936 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR2936868 4 0.0000 0.936 0.000 0.000 0.000 1.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 14198 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 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 0.972 0.988 0.5089 0.492 0.492
#> 3 3 1.000 0.963 0.986 0.3287 0.708 0.474
#> 4 4 0.863 0.752 0.838 0.0867 0.898 0.700
#> 5 5 1.000 0.996 0.998 0.0724 0.885 0.605
#> 6 6 0.946 0.858 0.922 0.0474 0.962 0.823
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 3 5
There is also optional best \(k\) = 2 3 5 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR2936906 1 0.000 0.990 1.000 0.000
#> SRR2936909 1 0.000 0.990 1.000 0.000
#> SRR2936918 1 0.000 0.990 1.000 0.000
#> SRR2936917 2 0.000 0.984 0.000 1.000
#> SRR2936916 2 0.000 0.984 0.000 1.000
#> SRR2936915 1 0.204 0.959 0.968 0.032
#> SRR2936914 2 0.000 0.984 0.000 1.000
#> SRR2936913 2 0.000 0.984 0.000 1.000
#> SRR2936912 1 0.000 0.990 1.000 0.000
#> SRR2936910 1 0.000 0.990 1.000 0.000
#> SRR2936911 2 0.000 0.984 0.000 1.000
#> SRR2936907 2 0.000 0.984 0.000 1.000
#> SRR2936908 2 0.000 0.984 0.000 1.000
#> SRR2936904 1 0.000 0.990 1.000 0.000
#> SRR2936905 2 0.000 0.984 0.000 1.000
#> SRR2936903 1 0.000 0.990 1.000 0.000
#> SRR2936901 1 0.000 0.990 1.000 0.000
#> SRR2936902 2 0.000 0.984 0.000 1.000
#> SRR2936900 1 0.000 0.990 1.000 0.000
#> SRR2936898 1 0.000 0.990 1.000 0.000
#> SRR2936899 1 0.000 0.990 1.000 0.000
#> SRR2936897 1 0.000 0.990 1.000 0.000
#> SRR2936896 2 0.000 0.984 0.000 1.000
#> SRR2936894 1 0.000 0.990 1.000 0.000
#> SRR2936893 2 0.000 0.984 0.000 1.000
#> SRR2936895 2 0.000 0.984 0.000 1.000
#> SRR2936892 2 0.000 0.984 0.000 1.000
#> SRR2936891 1 0.000 0.990 1.000 0.000
#> SRR2936890 2 0.000 0.984 0.000 1.000
#> SRR2936886 1 0.000 0.990 1.000 0.000
#> SRR2936885 1 0.000 0.990 1.000 0.000
#> SRR2936888 1 0.000 0.990 1.000 0.000
#> SRR2936889 2 0.000 0.984 0.000 1.000
#> SRR2936887 1 0.000 0.990 1.000 0.000
#> SRR2936884 2 0.000 0.984 0.000 1.000
#> SRR2936883 2 0.000 0.984 0.000 1.000
#> SRR2936881 2 0.000 0.984 0.000 1.000
#> SRR2936882 1 0.000 0.990 1.000 0.000
#> SRR2936880 2 0.000 0.984 0.000 1.000
#> SRR2936878 2 0.000 0.984 0.000 1.000
#> SRR2936879 2 0.722 0.750 0.200 0.800
#> SRR2936875 2 0.000 0.984 0.000 1.000
#> SRR2936877 2 0.000 0.984 0.000 1.000
#> SRR2936876 1 0.000 0.990 1.000 0.000
#> SRR2936873 1 0.000 0.990 1.000 0.000
#> SRR2936872 2 0.000 0.984 0.000 1.000
#> SRR2936871 2 0.000 0.984 0.000 1.000
#> SRR2936874 2 0.000 0.984 0.000 1.000
#> SRR2936870 1 0.000 0.990 1.000 0.000
#> SRR2936869 2 0.722 0.748 0.200 0.800
#> SRR2936868 1 0.722 0.745 0.800 0.200
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR2936906 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936909 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936918 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936917 2 0.0000 0.988 0.000 1.000 0.000
#> SRR2936916 3 0.0000 0.968 0.000 0.000 1.000
#> SRR2936915 3 0.0000 0.968 0.000 0.000 1.000
#> SRR2936914 2 0.0000 0.988 0.000 1.000 0.000
#> SRR2936913 2 0.0000 0.988 0.000 1.000 0.000
#> SRR2936912 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936910 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936911 2 0.0000 0.988 0.000 1.000 0.000
#> SRR2936907 2 0.0000 0.988 0.000 1.000 0.000
#> SRR2936908 2 0.0000 0.988 0.000 1.000 0.000
#> SRR2936904 3 0.2356 0.901 0.072 0.000 0.928
#> SRR2936905 2 0.0000 0.988 0.000 1.000 0.000
#> SRR2936903 3 0.6267 0.173 0.452 0.000 0.548
#> SRR2936901 3 0.0000 0.968 0.000 0.000 1.000
#> SRR2936902 3 0.0000 0.968 0.000 0.000 1.000
#> SRR2936900 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936898 3 0.0000 0.968 0.000 0.000 1.000
#> SRR2936899 3 0.0000 0.968 0.000 0.000 1.000
#> SRR2936897 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936896 2 0.0000 0.988 0.000 1.000 0.000
#> SRR2936894 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936893 2 0.0000 0.988 0.000 1.000 0.000
#> SRR2936895 3 0.0237 0.965 0.000 0.004 0.996
#> SRR2936892 2 0.0000 0.988 0.000 1.000 0.000
#> SRR2936891 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936890 2 0.0000 0.988 0.000 1.000 0.000
#> SRR2936886 3 0.0000 0.968 0.000 0.000 1.000
#> SRR2936885 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936888 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936889 2 0.0000 0.988 0.000 1.000 0.000
#> SRR2936887 3 0.0000 0.968 0.000 0.000 1.000
#> SRR2936884 2 0.4555 0.749 0.000 0.800 0.200
#> SRR2936883 3 0.0000 0.968 0.000 0.000 1.000
#> SRR2936881 3 0.0000 0.968 0.000 0.000 1.000
#> SRR2936882 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936880 3 0.0000 0.968 0.000 0.000 1.000
#> SRR2936878 2 0.0000 0.988 0.000 1.000 0.000
#> SRR2936879 3 0.0000 0.968 0.000 0.000 1.000
#> SRR2936875 2 0.0000 0.988 0.000 1.000 0.000
#> SRR2936877 2 0.0000 0.988 0.000 1.000 0.000
#> SRR2936876 3 0.0000 0.968 0.000 0.000 1.000
#> SRR2936873 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936872 2 0.0000 0.988 0.000 1.000 0.000
#> SRR2936871 2 0.0000 0.988 0.000 1.000 0.000
#> SRR2936874 2 0.0000 0.988 0.000 1.000 0.000
#> SRR2936870 1 0.0000 1.000 1.000 0.000 0.000
#> SRR2936869 3 0.0000 0.968 0.000 0.000 1.000
#> SRR2936868 3 0.0000 0.968 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR2936906 1 0.497 1.000 0.548 0.000 0.000 0.452
#> SRR2936909 1 0.497 1.000 0.548 0.000 0.000 0.452
#> SRR2936918 1 0.497 1.000 0.548 0.000 0.000 0.452
#> SRR2936917 4 0.497 0.722 0.452 0.000 0.000 0.548
#> SRR2936916 3 0.497 0.794 0.000 0.452 0.548 0.000
#> SRR2936915 3 0.000 0.686 0.000 0.000 1.000 0.000
#> SRR2936914 4 0.497 0.722 0.452 0.000 0.000 0.548
#> SRR2936913 4 0.497 0.722 0.452 0.000 0.000 0.548
#> SRR2936912 1 0.497 1.000 0.548 0.000 0.000 0.452
#> SRR2936910 1 0.497 1.000 0.548 0.000 0.000 0.452
#> SRR2936911 4 0.497 0.722 0.452 0.000 0.000 0.548
#> SRR2936907 2 0.497 0.806 0.452 0.548 0.000 0.000
#> SRR2936908 2 0.497 0.806 0.452 0.548 0.000 0.000
#> SRR2936904 3 0.147 0.646 0.052 0.000 0.948 0.000
#> SRR2936905 2 0.497 0.806 0.452 0.548 0.000 0.000
#> SRR2936903 4 0.769 -0.616 0.252 0.000 0.296 0.452
#> SRR2936901 3 0.497 0.794 0.000 0.452 0.548 0.000
#> SRR2936902 3 0.497 0.794 0.000 0.452 0.548 0.000
#> SRR2936900 1 0.497 1.000 0.548 0.000 0.000 0.452
#> SRR2936898 3 0.497 0.794 0.000 0.452 0.548 0.000
#> SRR2936899 3 0.497 0.794 0.000 0.452 0.548 0.000
#> SRR2936897 1 0.497 1.000 0.548 0.000 0.000 0.452
#> SRR2936896 2 0.497 0.806 0.452 0.548 0.000 0.000
#> SRR2936894 1 0.497 1.000 0.548 0.000 0.000 0.452
#> SRR2936893 2 0.497 0.806 0.452 0.548 0.000 0.000
#> SRR2936895 2 0.494 -0.718 0.000 0.564 0.436 0.000
#> SRR2936892 2 0.497 0.806 0.452 0.548 0.000 0.000
#> SRR2936891 1 0.497 1.000 0.548 0.000 0.000 0.452
#> SRR2936890 2 0.497 0.806 0.452 0.548 0.000 0.000
#> SRR2936886 3 0.000 0.686 0.000 0.000 1.000 0.000
#> SRR2936885 1 0.497 1.000 0.548 0.000 0.000 0.452
#> SRR2936888 1 0.497 1.000 0.548 0.000 0.000 0.452
#> SRR2936889 2 0.497 0.806 0.452 0.548 0.000 0.000
#> SRR2936887 3 0.000 0.686 0.000 0.000 1.000 0.000
#> SRR2936884 2 0.000 0.220 0.000 1.000 0.000 0.000
#> SRR2936883 3 0.497 0.794 0.000 0.452 0.548 0.000
#> SRR2936881 3 0.497 0.794 0.000 0.452 0.548 0.000
#> SRR2936882 1 0.497 1.000 0.548 0.000 0.000 0.452
#> SRR2936880 3 0.497 0.794 0.000 0.452 0.548 0.000
#> SRR2936878 4 0.497 0.722 0.452 0.000 0.000 0.548
#> SRR2936879 3 0.497 0.794 0.000 0.452 0.548 0.000
#> SRR2936875 2 0.497 0.806 0.452 0.548 0.000 0.000
#> SRR2936877 4 0.497 0.722 0.452 0.000 0.000 0.548
#> SRR2936876 3 0.497 0.255 0.000 0.000 0.548 0.452
#> SRR2936873 1 0.497 1.000 0.548 0.000 0.000 0.452
#> SRR2936872 2 0.497 0.806 0.452 0.548 0.000 0.000
#> SRR2936871 2 0.497 0.806 0.452 0.548 0.000 0.000
#> SRR2936874 2 0.497 0.806 0.452 0.548 0.000 0.000
#> SRR2936870 1 0.497 1.000 0.548 0.000 0.000 0.452
#> SRR2936869 3 0.000 0.686 0.000 0.000 1.000 0.000
#> SRR2936868 3 0.000 0.686 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR2936906 1 0.000 1.000 1 0.000 0 0 0.000
#> SRR2936909 1 0.000 1.000 1 0.000 0 0 0.000
#> SRR2936918 1 0.000 1.000 1 0.000 0 0 0.000
#> SRR2936917 5 0.000 1.000 0 0.000 0 0 1.000
#> SRR2936916 3 0.000 1.000 0 0.000 1 0 0.000
#> SRR2936915 4 0.000 1.000 0 0.000 0 1 0.000
#> SRR2936914 5 0.000 1.000 0 0.000 0 0 1.000
#> SRR2936913 5 0.000 1.000 0 0.000 0 0 1.000
#> SRR2936912 1 0.000 1.000 1 0.000 0 0 0.000
#> SRR2936910 1 0.000 1.000 1 0.000 0 0 0.000
#> SRR2936911 5 0.000 1.000 0 0.000 0 0 1.000
#> SRR2936907 2 0.000 0.991 0 1.000 0 0 0.000
#> SRR2936908 2 0.000 0.991 0 1.000 0 0 0.000
#> SRR2936904 4 0.000 1.000 0 0.000 0 1 0.000
#> SRR2936905 2 0.000 0.991 0 1.000 0 0 0.000
#> SRR2936903 1 0.000 1.000 1 0.000 0 0 0.000
#> SRR2936901 3 0.000 1.000 0 0.000 1 0 0.000
#> SRR2936902 3 0.000 1.000 0 0.000 1 0 0.000
#> SRR2936900 1 0.000 1.000 1 0.000 0 0 0.000
#> SRR2936898 3 0.000 1.000 0 0.000 1 0 0.000
#> SRR2936899 3 0.000 1.000 0 0.000 1 0 0.000
#> SRR2936897 1 0.000 1.000 1 0.000 0 0 0.000
#> SRR2936896 2 0.196 0.894 0 0.904 0 0 0.096
#> SRR2936894 1 0.000 1.000 1 0.000 0 0 0.000
#> SRR2936893 2 0.000 0.991 0 1.000 0 0 0.000
#> SRR2936895 3 0.000 1.000 0 0.000 1 0 0.000
#> SRR2936892 2 0.000 0.991 0 1.000 0 0 0.000
#> SRR2936891 1 0.000 1.000 1 0.000 0 0 0.000
#> SRR2936890 2 0.000 0.991 0 1.000 0 0 0.000
#> SRR2936886 4 0.000 1.000 0 0.000 0 1 0.000
#> SRR2936885 1 0.000 1.000 1 0.000 0 0 0.000
#> SRR2936888 1 0.000 1.000 1 0.000 0 0 0.000
#> SRR2936889 2 0.000 0.991 0 1.000 0 0 0.000
#> SRR2936887 4 0.000 1.000 0 0.000 0 1 0.000
#> SRR2936884 3 0.000 1.000 0 0.000 1 0 0.000
#> SRR2936883 3 0.000 1.000 0 0.000 1 0 0.000
#> SRR2936881 3 0.000 1.000 0 0.000 1 0 0.000
#> SRR2936882 1 0.000 1.000 1 0.000 0 0 0.000
#> SRR2936880 3 0.000 1.000 0 0.000 1 0 0.000
#> SRR2936878 5 0.000 1.000 0 0.000 0 0 1.000
#> SRR2936879 3 0.000 1.000 0 0.000 1 0 0.000
#> SRR2936875 2 0.000 0.991 0 1.000 0 0 0.000
#> SRR2936877 5 0.000 1.000 0 0.000 0 0 1.000
#> SRR2936876 1 0.000 1.000 1 0.000 0 0 0.000
#> SRR2936873 1 0.000 1.000 1 0.000 0 0 0.000
#> SRR2936872 2 0.000 0.991 0 1.000 0 0 0.000
#> SRR2936871 2 0.000 0.991 0 1.000 0 0 0.000
#> SRR2936874 2 0.000 0.991 0 1.000 0 0 0.000
#> SRR2936870 1 0.000 1.000 1 0.000 0 0 0.000
#> SRR2936869 4 0.000 1.000 0 0.000 0 1 0.000
#> SRR2936868 4 0.000 1.000 0 0.000 0 1 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR2936906 1 0.000 0.9296 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936909 1 0.000 0.9296 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936918 1 0.000 0.9296 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936917 5 0.000 1.0000 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936916 3 0.381 0.8184 0.000 0.000 0.572 0.000 0.000 0.428
#> SRR2936915 4 0.381 0.4402 0.000 0.000 0.428 0.572 0.000 0.000
#> SRR2936914 5 0.000 1.0000 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936913 5 0.000 1.0000 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936912 1 0.000 0.9296 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936910 1 0.000 0.9296 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936911 5 0.000 1.0000 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936907 2 0.000 0.9909 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936908 2 0.000 0.9909 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936904 4 0.000 0.9060 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR2936905 2 0.000 0.9909 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936903 6 0.381 0.2594 0.000 0.000 0.428 0.000 0.000 0.572
#> SRR2936901 3 0.026 0.6309 0.000 0.000 0.992 0.000 0.000 0.008
#> SRR2936902 3 0.381 0.8184 0.000 0.000 0.572 0.000 0.000 0.428
#> SRR2936900 6 0.381 0.7131 0.428 0.000 0.000 0.000 0.000 0.572
#> SRR2936898 3 0.000 0.6390 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936899 3 0.000 0.6390 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936897 1 0.000 0.9296 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936896 2 0.176 0.8938 0.000 0.904 0.000 0.000 0.096 0.000
#> SRR2936894 1 0.000 0.9296 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936893 2 0.000 0.9909 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936895 3 0.381 0.8184 0.000 0.000 0.572 0.000 0.000 0.428
#> SRR2936892 2 0.000 0.9909 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936891 1 0.000 0.9296 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936890 2 0.000 0.9909 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936886 4 0.000 0.9060 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR2936885 6 0.381 0.7131 0.428 0.000 0.000 0.000 0.000 0.572
#> SRR2936888 1 0.000 0.9296 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936889 2 0.000 0.9909 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936887 4 0.000 0.9060 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR2936884 3 0.381 0.8184 0.000 0.000 0.572 0.000 0.000 0.428
#> SRR2936883 3 0.381 0.8184 0.000 0.000 0.572 0.000 0.000 0.428
#> SRR2936881 3 0.381 0.8184 0.000 0.000 0.572 0.000 0.000 0.428
#> SRR2936882 6 0.381 0.7131 0.428 0.000 0.000 0.000 0.000 0.572
#> SRR2936880 3 0.381 0.8184 0.000 0.000 0.572 0.000 0.000 0.428
#> SRR2936878 5 0.000 1.0000 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936879 3 0.000 0.6390 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936875 2 0.000 0.9909 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936877 5 0.000 1.0000 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936876 1 0.406 0.0995 0.552 0.000 0.440 0.000 0.000 0.008
#> SRR2936873 1 0.000 0.9296 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936872 2 0.000 0.9909 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936871 2 0.000 0.9909 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936874 2 0.000 0.9909 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936870 1 0.000 0.9296 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936869 4 0.000 0.9060 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR2936868 4 0.000 0.9060 0.000 0.000 0.000 1.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 14198 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 0.442 0.802 0.834 0.4352 0.534 0.534
#> 3 3 0.592 0.740 0.873 0.4687 0.661 0.440
#> 4 4 0.738 0.800 0.864 0.1162 0.881 0.670
#> 5 5 0.903 0.827 0.933 0.0964 0.908 0.674
#> 6 6 0.852 0.760 0.882 0.0534 0.956 0.786
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
#> SRR2936906 2 0.000 0.729 0.000 1.000
#> SRR2936909 2 0.000 0.729 0.000 1.000
#> SRR2936918 2 0.000 0.729 0.000 1.000
#> SRR2936917 2 0.680 0.737 0.180 0.820
#> SRR2936916 2 0.278 0.687 0.048 0.952
#> SRR2936915 2 0.000 0.729 0.000 1.000
#> SRR2936914 2 0.680 0.737 0.180 0.820
#> SRR2936913 2 0.680 0.737 0.180 0.820
#> SRR2936912 2 0.000 0.729 0.000 1.000
#> SRR2936910 2 0.000 0.729 0.000 1.000
#> SRR2936911 2 0.680 0.737 0.180 0.820
#> SRR2936907 2 0.963 0.687 0.388 0.612
#> SRR2936908 2 0.963 0.687 0.388 0.612
#> SRR2936904 2 0.000 0.729 0.000 1.000
#> SRR2936905 2 0.963 0.687 0.388 0.612
#> SRR2936903 1 0.963 0.974 0.612 0.388
#> SRR2936901 1 0.963 0.974 0.612 0.388
#> SRR2936902 1 0.963 0.974 0.612 0.388
#> SRR2936900 1 0.963 0.974 0.612 0.388
#> SRR2936898 1 0.963 0.974 0.612 0.388
#> SRR2936899 1 0.963 0.974 0.612 0.388
#> SRR2936897 2 0.000 0.729 0.000 1.000
#> SRR2936896 2 0.278 0.687 0.048 0.952
#> SRR2936894 2 0.000 0.729 0.000 1.000
#> SRR2936893 2 0.963 0.687 0.388 0.612
#> SRR2936895 2 0.295 0.682 0.052 0.948
#> SRR2936892 2 0.963 0.687 0.388 0.612
#> SRR2936891 2 0.000 0.729 0.000 1.000
#> SRR2936890 2 0.963 0.687 0.388 0.612
#> SRR2936886 1 0.988 0.946 0.564 0.436
#> SRR2936885 1 0.963 0.974 0.612 0.388
#> SRR2936888 1 0.988 0.946 0.564 0.436
#> SRR2936889 2 0.963 0.687 0.388 0.612
#> SRR2936887 1 0.988 0.946 0.564 0.436
#> SRR2936884 1 0.963 0.974 0.612 0.388
#> SRR2936883 1 0.963 0.974 0.612 0.388
#> SRR2936881 1 0.963 0.974 0.612 0.388
#> SRR2936882 1 0.963 0.974 0.612 0.388
#> SRR2936880 1 0.963 0.974 0.612 0.388
#> SRR2936878 2 0.680 0.737 0.180 0.820
#> SRR2936879 2 0.000 0.729 0.000 1.000
#> SRR2936875 2 0.963 0.687 0.388 0.612
#> SRR2936877 2 0.680 0.737 0.180 0.820
#> SRR2936876 2 0.000 0.729 0.000 1.000
#> SRR2936873 2 0.000 0.729 0.000 1.000
#> SRR2936872 2 0.963 0.687 0.388 0.612
#> SRR2936871 2 0.963 0.687 0.388 0.612
#> SRR2936874 2 0.963 0.687 0.388 0.612
#> SRR2936870 1 0.988 0.946 0.564 0.436
#> SRR2936869 1 0.988 0.946 0.564 0.436
#> SRR2936868 1 0.988 0.946 0.564 0.436
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR2936906 1 0.0000 0.797 1.000 0.000 0.000
#> SRR2936909 1 0.0829 0.797 0.984 0.004 0.012
#> SRR2936918 1 0.0000 0.797 1.000 0.000 0.000
#> SRR2936917 2 0.6421 0.394 0.424 0.572 0.004
#> SRR2936916 1 0.5115 0.646 0.796 0.188 0.016
#> SRR2936915 1 0.5008 0.657 0.804 0.180 0.016
#> SRR2936914 2 0.6421 0.394 0.424 0.572 0.004
#> SRR2936913 2 0.6421 0.394 0.424 0.572 0.004
#> SRR2936912 1 0.0000 0.797 1.000 0.000 0.000
#> SRR2936910 1 0.0000 0.797 1.000 0.000 0.000
#> SRR2936911 2 0.6421 0.394 0.424 0.572 0.004
#> SRR2936907 2 0.0000 0.769 0.000 1.000 0.000
#> SRR2936908 2 0.0000 0.769 0.000 1.000 0.000
#> SRR2936904 1 0.5115 0.646 0.796 0.188 0.016
#> SRR2936905 2 0.0000 0.769 0.000 1.000 0.000
#> SRR2936903 3 0.0000 0.985 0.000 0.000 1.000
#> SRR2936901 3 0.0000 0.985 0.000 0.000 1.000
#> SRR2936902 3 0.0000 0.985 0.000 0.000 1.000
#> SRR2936900 3 0.3412 0.820 0.124 0.000 0.876
#> SRR2936898 3 0.0000 0.985 0.000 0.000 1.000
#> SRR2936899 3 0.0000 0.985 0.000 0.000 1.000
#> SRR2936897 1 0.0592 0.798 0.988 0.000 0.012
#> SRR2936896 2 0.6683 0.173 0.492 0.500 0.008
#> SRR2936894 1 0.0000 0.797 1.000 0.000 0.000
#> SRR2936893 2 0.0000 0.769 0.000 1.000 0.000
#> SRR2936895 1 0.8380 0.611 0.600 0.124 0.276
#> SRR2936892 2 0.0000 0.769 0.000 1.000 0.000
#> SRR2936891 1 0.0000 0.797 1.000 0.000 0.000
#> SRR2936890 2 0.0000 0.769 0.000 1.000 0.000
#> SRR2936886 1 0.5785 0.651 0.668 0.000 0.332
#> SRR2936885 3 0.0592 0.975 0.012 0.000 0.988
#> SRR2936888 1 0.5785 0.651 0.668 0.000 0.332
#> SRR2936889 2 0.0000 0.769 0.000 1.000 0.000
#> SRR2936887 1 0.5785 0.651 0.668 0.000 0.332
#> SRR2936884 3 0.0000 0.985 0.000 0.000 1.000
#> SRR2936883 3 0.0000 0.985 0.000 0.000 1.000
#> SRR2936881 3 0.0000 0.985 0.000 0.000 1.000
#> SRR2936882 3 0.0000 0.985 0.000 0.000 1.000
#> SRR2936880 3 0.0000 0.985 0.000 0.000 1.000
#> SRR2936878 2 0.6421 0.394 0.424 0.572 0.004
#> SRR2936879 1 0.5115 0.646 0.796 0.188 0.016
#> SRR2936875 2 0.0000 0.769 0.000 1.000 0.000
#> SRR2936877 2 0.6421 0.394 0.424 0.572 0.004
#> SRR2936876 1 0.0983 0.797 0.980 0.004 0.016
#> SRR2936873 1 0.0000 0.797 1.000 0.000 0.000
#> SRR2936872 2 0.0000 0.769 0.000 1.000 0.000
#> SRR2936871 2 0.0000 0.769 0.000 1.000 0.000
#> SRR2936874 2 0.0000 0.769 0.000 1.000 0.000
#> SRR2936870 1 0.5785 0.651 0.668 0.000 0.332
#> SRR2936869 1 0.5785 0.651 0.668 0.000 0.332
#> SRR2936868 1 0.5785 0.651 0.668 0.000 0.332
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR2936906 1 0.4804 0.8841 0.616 0.000 0.000 0.384
#> SRR2936909 1 0.5112 0.8809 0.608 0.008 0.000 0.384
#> SRR2936918 1 0.4804 0.8841 0.616 0.000 0.000 0.384
#> SRR2936917 2 0.4830 0.7180 0.392 0.608 0.000 0.000
#> SRR2936916 1 0.7071 0.7835 0.504 0.112 0.004 0.380
#> SRR2936915 1 0.7877 0.5011 0.392 0.224 0.004 0.380
#> SRR2936914 2 0.4830 0.7180 0.392 0.608 0.000 0.000
#> SRR2936913 2 0.4830 0.7180 0.392 0.608 0.000 0.000
#> SRR2936912 1 0.4804 0.8841 0.616 0.000 0.000 0.384
#> SRR2936910 1 0.4804 0.8841 0.616 0.000 0.000 0.384
#> SRR2936911 2 0.4830 0.7180 0.392 0.608 0.000 0.000
#> SRR2936907 2 0.0000 0.8397 0.000 1.000 0.000 0.000
#> SRR2936908 2 0.0000 0.8397 0.000 1.000 0.000 0.000
#> SRR2936904 2 0.7005 -0.0394 0.104 0.500 0.004 0.392
#> SRR2936905 2 0.0000 0.8397 0.000 1.000 0.000 0.000
#> SRR2936903 3 0.1389 0.8567 0.000 0.000 0.952 0.048
#> SRR2936901 3 0.0000 0.8888 0.000 0.000 1.000 0.000
#> SRR2936902 3 0.0000 0.8888 0.000 0.000 1.000 0.000
#> SRR2936900 3 0.5613 0.1728 0.028 0.000 0.592 0.380
#> SRR2936898 3 0.0000 0.8888 0.000 0.000 1.000 0.000
#> SRR2936899 3 0.0000 0.8888 0.000 0.000 1.000 0.000
#> SRR2936897 1 0.4804 0.8841 0.616 0.000 0.000 0.384
#> SRR2936896 1 0.7504 0.6978 0.460 0.160 0.004 0.376
#> SRR2936894 1 0.4804 0.8841 0.616 0.000 0.000 0.384
#> SRR2936893 2 0.0000 0.8397 0.000 1.000 0.000 0.000
#> SRR2936895 1 0.7310 0.7458 0.480 0.136 0.004 0.380
#> SRR2936892 2 0.0000 0.8397 0.000 1.000 0.000 0.000
#> SRR2936891 1 0.4804 0.8841 0.616 0.000 0.000 0.384
#> SRR2936890 2 0.0000 0.8397 0.000 1.000 0.000 0.000
#> SRR2936886 4 0.0188 0.9735 0.000 0.000 0.004 0.996
#> SRR2936885 3 0.5428 0.1952 0.020 0.000 0.600 0.380
#> SRR2936888 4 0.1305 0.9441 0.036 0.000 0.004 0.960
#> SRR2936889 2 0.0000 0.8397 0.000 1.000 0.000 0.000
#> SRR2936887 4 0.0188 0.9735 0.000 0.000 0.004 0.996
#> SRR2936884 3 0.0000 0.8888 0.000 0.000 1.000 0.000
#> SRR2936883 3 0.0000 0.8888 0.000 0.000 1.000 0.000
#> SRR2936881 3 0.0000 0.8888 0.000 0.000 1.000 0.000
#> SRR2936882 3 0.1389 0.8567 0.000 0.000 0.952 0.048
#> SRR2936880 3 0.0000 0.8888 0.000 0.000 1.000 0.000
#> SRR2936878 2 0.4830 0.7180 0.392 0.608 0.000 0.000
#> SRR2936879 1 0.7027 0.7866 0.508 0.108 0.004 0.380
#> SRR2936875 2 0.0336 0.8355 0.008 0.992 0.000 0.000
#> SRR2936877 2 0.4855 0.7132 0.400 0.600 0.000 0.000
#> SRR2936876 1 0.5272 0.8787 0.608 0.008 0.004 0.380
#> SRR2936873 1 0.4804 0.8841 0.616 0.000 0.000 0.384
#> SRR2936872 2 0.0000 0.8397 0.000 1.000 0.000 0.000
#> SRR2936871 2 0.0000 0.8397 0.000 1.000 0.000 0.000
#> SRR2936874 2 0.0336 0.8355 0.008 0.992 0.000 0.000
#> SRR2936870 4 0.1305 0.9441 0.036 0.000 0.004 0.960
#> SRR2936869 4 0.0188 0.9735 0.000 0.000 0.004 0.996
#> SRR2936868 4 0.0188 0.9735 0.000 0.000 0.004 0.996
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR2936906 1 0.0000 0.9141 1.000 0.000 0.000 0.000 0.000
#> SRR2936909 1 0.1331 0.9025 0.952 0.008 0.000 0.000 0.040
#> SRR2936918 1 0.0000 0.9141 1.000 0.000 0.000 0.000 0.000
#> SRR2936917 5 0.0162 0.9043 0.000 0.004 0.000 0.000 0.996
#> SRR2936916 1 0.2561 0.8200 0.856 0.000 0.000 0.000 0.144
#> SRR2936915 1 0.1568 0.8983 0.944 0.020 0.000 0.000 0.036
#> SRR2936914 5 0.0162 0.9043 0.000 0.004 0.000 0.000 0.996
#> SRR2936913 5 0.0162 0.9043 0.000 0.004 0.000 0.000 0.996
#> SRR2936912 1 0.0000 0.9141 1.000 0.000 0.000 0.000 0.000
#> SRR2936910 1 0.0000 0.9141 1.000 0.000 0.000 0.000 0.000
#> SRR2936911 5 0.0162 0.9043 0.000 0.004 0.000 0.000 0.996
#> SRR2936907 2 0.0000 0.9460 0.000 1.000 0.000 0.000 0.000
#> SRR2936908 2 0.0000 0.9460 0.000 1.000 0.000 0.000 0.000
#> SRR2936904 1 0.3086 0.8454 0.876 0.020 0.000 0.068 0.036
#> SRR2936905 2 0.0000 0.9460 0.000 1.000 0.000 0.000 0.000
#> SRR2936903 3 0.0963 0.9086 0.036 0.000 0.964 0.000 0.000
#> SRR2936901 3 0.0000 0.9235 0.000 0.000 1.000 0.000 0.000
#> SRR2936902 3 0.0000 0.9235 0.000 0.000 1.000 0.000 0.000
#> SRR2936900 3 0.4201 0.2830 0.408 0.000 0.592 0.000 0.000
#> SRR2936898 3 0.0000 0.9235 0.000 0.000 1.000 0.000 0.000
#> SRR2936899 3 0.1197 0.9004 0.048 0.000 0.952 0.000 0.000
#> SRR2936897 1 0.0000 0.9141 1.000 0.000 0.000 0.000 0.000
#> SRR2936896 5 0.4161 0.2013 0.392 0.000 0.000 0.000 0.608
#> SRR2936894 1 0.0000 0.9141 1.000 0.000 0.000 0.000 0.000
#> SRR2936893 2 0.0000 0.9460 0.000 1.000 0.000 0.000 0.000
#> SRR2936895 1 0.6003 -0.0414 0.444 0.000 0.112 0.000 0.444
#> SRR2936892 2 0.0000 0.9460 0.000 1.000 0.000 0.000 0.000
#> SRR2936891 1 0.0000 0.9141 1.000 0.000 0.000 0.000 0.000
#> SRR2936890 2 0.0000 0.9460 0.000 1.000 0.000 0.000 0.000
#> SRR2936886 4 0.0000 0.7623 0.000 0.000 0.000 1.000 0.000
#> SRR2936885 3 0.1908 0.8632 0.092 0.000 0.908 0.000 0.000
#> SRR2936888 4 0.4367 0.3451 0.416 0.000 0.004 0.580 0.000
#> SRR2936889 2 0.0000 0.9460 0.000 1.000 0.000 0.000 0.000
#> SRR2936887 4 0.0000 0.7623 0.000 0.000 0.000 1.000 0.000
#> SRR2936884 3 0.0000 0.9235 0.000 0.000 1.000 0.000 0.000
#> SRR2936883 3 0.0000 0.9235 0.000 0.000 1.000 0.000 0.000
#> SRR2936881 3 0.0000 0.9235 0.000 0.000 1.000 0.000 0.000
#> SRR2936882 3 0.1341 0.8976 0.056 0.000 0.944 0.000 0.000
#> SRR2936880 3 0.0000 0.9235 0.000 0.000 1.000 0.000 0.000
#> SRR2936878 5 0.0162 0.9043 0.000 0.004 0.000 0.000 0.996
#> SRR2936879 1 0.1965 0.8669 0.904 0.000 0.000 0.000 0.096
#> SRR2936875 2 0.3210 0.7311 0.212 0.788 0.000 0.000 0.000
#> SRR2936877 5 0.0162 0.9043 0.000 0.004 0.000 0.000 0.996
#> SRR2936876 1 0.1331 0.9025 0.952 0.008 0.000 0.000 0.040
#> SRR2936873 1 0.0000 0.9141 1.000 0.000 0.000 0.000 0.000
#> SRR2936872 2 0.0000 0.9460 0.000 1.000 0.000 0.000 0.000
#> SRR2936871 2 0.0000 0.9460 0.000 1.000 0.000 0.000 0.000
#> SRR2936874 2 0.3210 0.7311 0.212 0.788 0.000 0.000 0.000
#> SRR2936870 4 0.4367 0.3451 0.416 0.000 0.004 0.580 0.000
#> SRR2936869 4 0.0000 0.7623 0.000 0.000 0.000 1.000 0.000
#> SRR2936868 4 0.0000 0.7623 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
#> SRR2936906 1 0.000 0.949 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936909 3 0.381 0.142 0.368 0.004 0.628 0.000 0.000 0.000
#> SRR2936918 1 0.000 0.949 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936917 5 0.000 0.919 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936916 3 0.522 0.447 0.112 0.000 0.560 0.000 0.328 0.000
#> SRR2936915 3 0.529 0.502 0.116 0.340 0.544 0.000 0.000 0.000
#> SRR2936914 5 0.000 0.919 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936913 5 0.000 0.919 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936912 1 0.000 0.949 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936910 1 0.000 0.949 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936911 5 0.000 0.919 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936907 2 0.000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936908 2 0.000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936904 3 0.582 0.471 0.084 0.328 0.544 0.044 0.000 0.000
#> SRR2936905 2 0.000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936903 6 0.373 0.487 0.000 0.000 0.388 0.000 0.000 0.612
#> SRR2936901 6 0.000 0.814 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR2936902 6 0.000 0.814 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR2936900 6 0.380 0.462 0.000 0.000 0.420 0.000 0.000 0.580
#> SRR2936898 6 0.000 0.814 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR2936899 6 0.000 0.814 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR2936897 1 0.302 0.517 0.768 0.000 0.232 0.000 0.000 0.000
#> SRR2936896 5 0.356 0.263 0.000 0.000 0.336 0.000 0.664 0.000
#> SRR2936894 1 0.000 0.949 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936893 2 0.000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936895 3 0.564 0.207 0.000 0.000 0.464 0.000 0.384 0.152
#> SRR2936892 2 0.000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936891 1 0.000 0.949 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936890 2 0.000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936886 4 0.000 0.774 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR2936885 6 0.380 0.462 0.000 0.000 0.420 0.000 0.000 0.580
#> SRR2936888 4 0.384 0.336 0.000 0.000 0.448 0.552 0.000 0.000
#> SRR2936889 2 0.000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936887 4 0.000 0.774 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR2936884 6 0.000 0.814 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR2936883 6 0.000 0.814 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR2936881 6 0.000 0.814 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR2936882 6 0.380 0.462 0.000 0.000 0.420 0.000 0.000 0.580
#> SRR2936880 6 0.000 0.814 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR2936878 5 0.000 0.919 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936879 3 0.545 0.524 0.284 0.000 0.556 0.000 0.160 0.000
#> SRR2936875 2 0.079 0.959 0.032 0.968 0.000 0.000 0.000 0.000
#> SRR2936877 5 0.000 0.919 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936876 3 0.215 0.517 0.116 0.004 0.880 0.000 0.000 0.000
#> SRR2936873 1 0.000 0.949 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936872 2 0.000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936871 2 0.000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936874 2 0.079 0.959 0.032 0.968 0.000 0.000 0.000 0.000
#> SRR2936870 4 0.384 0.336 0.000 0.000 0.448 0.552 0.000 0.000
#> SRR2936869 4 0.000 0.774 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR2936868 4 0.000 0.774 0.000 0.000 0.000 1.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 14198 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.986 0.993 0.4682 0.534 0.534
#> 3 3 0.826 0.876 0.929 0.4351 0.787 0.601
#> 4 4 0.906 0.842 0.934 0.1167 0.855 0.592
#> 5 5 0.895 0.874 0.922 0.0584 0.915 0.677
#> 6 6 0.871 0.770 0.877 0.0262 0.996 0.980
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR2936906 1 0.0000 0.992 1.000 0.000
#> SRR2936909 1 0.0000 0.992 1.000 0.000
#> SRR2936918 1 0.0000 0.992 1.000 0.000
#> SRR2936917 1 0.0000 0.992 1.000 0.000
#> SRR2936916 1 0.0000 0.992 1.000 0.000
#> SRR2936915 1 0.7219 0.751 0.800 0.200
#> SRR2936914 1 0.1414 0.974 0.980 0.020
#> SRR2936913 2 0.3879 0.916 0.076 0.924
#> SRR2936912 1 0.0000 0.992 1.000 0.000
#> SRR2936910 1 0.0000 0.992 1.000 0.000
#> SRR2936911 2 0.0000 0.995 0.000 1.000
#> SRR2936907 2 0.0000 0.995 0.000 1.000
#> SRR2936908 2 0.0000 0.995 0.000 1.000
#> SRR2936904 2 0.0000 0.995 0.000 1.000
#> SRR2936905 2 0.0000 0.995 0.000 1.000
#> SRR2936903 1 0.0000 0.992 1.000 0.000
#> SRR2936901 1 0.0000 0.992 1.000 0.000
#> SRR2936902 1 0.0000 0.992 1.000 0.000
#> SRR2936900 1 0.0000 0.992 1.000 0.000
#> SRR2936898 1 0.0000 0.992 1.000 0.000
#> SRR2936899 1 0.0000 0.992 1.000 0.000
#> SRR2936897 1 0.0000 0.992 1.000 0.000
#> SRR2936896 1 0.0376 0.989 0.996 0.004
#> SRR2936894 1 0.0000 0.992 1.000 0.000
#> SRR2936893 2 0.0000 0.995 0.000 1.000
#> SRR2936895 1 0.0000 0.992 1.000 0.000
#> SRR2936892 2 0.0000 0.995 0.000 1.000
#> SRR2936891 1 0.0000 0.992 1.000 0.000
#> SRR2936890 2 0.0000 0.995 0.000 1.000
#> SRR2936886 2 0.0000 0.995 0.000 1.000
#> SRR2936885 1 0.0000 0.992 1.000 0.000
#> SRR2936888 1 0.0000 0.992 1.000 0.000
#> SRR2936889 2 0.0000 0.995 0.000 1.000
#> SRR2936887 2 0.0000 0.995 0.000 1.000
#> SRR2936884 1 0.0000 0.992 1.000 0.000
#> SRR2936883 1 0.0000 0.992 1.000 0.000
#> SRR2936881 1 0.0000 0.992 1.000 0.000
#> SRR2936882 1 0.0000 0.992 1.000 0.000
#> SRR2936880 1 0.0000 0.992 1.000 0.000
#> SRR2936878 1 0.0000 0.992 1.000 0.000
#> SRR2936879 1 0.2043 0.963 0.968 0.032
#> SRR2936875 2 0.0000 0.995 0.000 1.000
#> SRR2936877 1 0.0000 0.992 1.000 0.000
#> SRR2936876 1 0.0000 0.992 1.000 0.000
#> SRR2936873 1 0.0000 0.992 1.000 0.000
#> SRR2936872 2 0.0000 0.995 0.000 1.000
#> SRR2936871 2 0.0000 0.995 0.000 1.000
#> SRR2936874 2 0.0000 0.995 0.000 1.000
#> SRR2936870 1 0.0000 0.992 1.000 0.000
#> SRR2936869 2 0.0000 0.995 0.000 1.000
#> SRR2936868 2 0.0000 0.995 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR2936906 1 0.1163 0.957 0.972 0.000 0.028
#> SRR2936909 1 0.1163 0.957 0.972 0.000 0.028
#> SRR2936918 1 0.1031 0.956 0.976 0.000 0.024
#> SRR2936917 3 0.1163 0.922 0.028 0.000 0.972
#> SRR2936916 1 0.1163 0.957 0.972 0.000 0.028
#> SRR2936915 1 0.1919 0.942 0.956 0.020 0.024
#> SRR2936914 3 0.2056 0.880 0.024 0.024 0.952
#> SRR2936913 2 0.8129 0.647 0.244 0.632 0.124
#> SRR2936912 1 0.1031 0.956 0.976 0.000 0.024
#> SRR2936910 1 0.1031 0.956 0.976 0.000 0.024
#> SRR2936911 2 0.6079 0.769 0.216 0.748 0.036
#> SRR2936907 2 0.0000 0.923 0.000 1.000 0.000
#> SRR2936908 2 0.0000 0.923 0.000 1.000 0.000
#> SRR2936904 2 0.0000 0.923 0.000 1.000 0.000
#> SRR2936905 2 0.0000 0.923 0.000 1.000 0.000
#> SRR2936903 3 0.1529 0.918 0.040 0.000 0.960
#> SRR2936901 3 0.1163 0.922 0.028 0.000 0.972
#> SRR2936902 3 0.1031 0.922 0.024 0.000 0.976
#> SRR2936900 3 0.5621 0.616 0.308 0.000 0.692
#> SRR2936898 3 0.1529 0.917 0.040 0.000 0.960
#> SRR2936899 3 0.1031 0.922 0.024 0.000 0.976
#> SRR2936897 1 0.1163 0.957 0.972 0.000 0.028
#> SRR2936896 3 0.1860 0.891 0.052 0.000 0.948
#> SRR2936894 1 0.1163 0.957 0.972 0.000 0.028
#> SRR2936893 2 0.0000 0.923 0.000 1.000 0.000
#> SRR2936895 1 0.6252 0.150 0.556 0.000 0.444
#> SRR2936892 2 0.0000 0.923 0.000 1.000 0.000
#> SRR2936891 1 0.1163 0.957 0.972 0.000 0.028
#> SRR2936890 2 0.0000 0.923 0.000 1.000 0.000
#> SRR2936886 2 0.6148 0.740 0.244 0.728 0.028
#> SRR2936885 3 0.5810 0.563 0.336 0.000 0.664
#> SRR2936888 1 0.0892 0.921 0.980 0.000 0.020
#> SRR2936889 2 0.0000 0.923 0.000 1.000 0.000
#> SRR2936887 2 0.5894 0.769 0.220 0.752 0.028
#> SRR2936884 3 0.0000 0.910 0.000 0.000 1.000
#> SRR2936883 3 0.0000 0.910 0.000 0.000 1.000
#> SRR2936881 3 0.1031 0.922 0.024 0.000 0.976
#> SRR2936882 3 0.5733 0.587 0.324 0.000 0.676
#> SRR2936880 3 0.1163 0.922 0.028 0.000 0.972
#> SRR2936878 3 0.1031 0.922 0.024 0.000 0.976
#> SRR2936879 1 0.1711 0.951 0.960 0.008 0.032
#> SRR2936875 2 0.0000 0.923 0.000 1.000 0.000
#> SRR2936877 3 0.1163 0.922 0.028 0.000 0.972
#> SRR2936876 1 0.1163 0.957 0.972 0.000 0.028
#> SRR2936873 1 0.1163 0.957 0.972 0.000 0.028
#> SRR2936872 2 0.0000 0.923 0.000 1.000 0.000
#> SRR2936871 2 0.0000 0.923 0.000 1.000 0.000
#> SRR2936874 2 0.0000 0.923 0.000 1.000 0.000
#> SRR2936870 1 0.0892 0.921 0.980 0.000 0.020
#> SRR2936869 2 0.4015 0.870 0.096 0.876 0.028
#> SRR2936868 2 0.4609 0.850 0.128 0.844 0.028
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR2936906 1 0.0000 0.915 1.000 0.000 0.000 0.000
#> SRR2936909 1 0.0188 0.914 0.996 0.000 0.000 0.004
#> SRR2936918 1 0.0000 0.915 1.000 0.000 0.000 0.000
#> SRR2936917 3 0.0672 0.924 0.008 0.008 0.984 0.000
#> SRR2936916 1 0.0000 0.915 1.000 0.000 0.000 0.000
#> SRR2936915 1 0.0188 0.914 0.996 0.000 0.000 0.004
#> SRR2936914 3 0.2408 0.876 0.000 0.000 0.896 0.104
#> SRR2936913 4 0.0336 0.810 0.000 0.008 0.000 0.992
#> SRR2936912 1 0.0000 0.915 1.000 0.000 0.000 0.000
#> SRR2936910 1 0.0000 0.915 1.000 0.000 0.000 0.000
#> SRR2936911 4 0.0188 0.810 0.000 0.004 0.000 0.996
#> SRR2936907 2 0.0336 0.989 0.000 0.992 0.000 0.008
#> SRR2936908 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> SRR2936904 2 0.0188 0.990 0.000 0.996 0.000 0.004
#> SRR2936905 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> SRR2936903 3 0.0188 0.929 0.004 0.000 0.996 0.000
#> SRR2936901 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> SRR2936902 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> SRR2936900 1 0.4855 0.348 0.600 0.000 0.400 0.000
#> SRR2936898 3 0.2081 0.895 0.000 0.000 0.916 0.084
#> SRR2936899 3 0.1474 0.916 0.000 0.000 0.948 0.052
#> SRR2936897 1 0.0000 0.915 1.000 0.000 0.000 0.000
#> SRR2936896 3 0.3486 0.791 0.000 0.000 0.812 0.188
#> SRR2936894 1 0.0000 0.915 1.000 0.000 0.000 0.000
#> SRR2936893 2 0.1118 0.970 0.000 0.964 0.000 0.036
#> SRR2936895 4 0.5793 0.325 0.048 0.000 0.324 0.628
#> SRR2936892 2 0.0592 0.985 0.000 0.984 0.000 0.016
#> SRR2936891 1 0.0000 0.915 1.000 0.000 0.000 0.000
#> SRR2936890 2 0.0188 0.990 0.000 0.996 0.000 0.004
#> SRR2936886 4 0.0188 0.810 0.000 0.004 0.000 0.996
#> SRR2936885 3 0.6052 0.317 0.048 0.000 0.556 0.396
#> SRR2936888 4 0.4981 0.245 0.464 0.000 0.000 0.536
#> SRR2936889 2 0.1302 0.964 0.000 0.956 0.000 0.044
#> SRR2936887 4 0.0188 0.810 0.000 0.004 0.000 0.996
#> SRR2936884 3 0.0817 0.926 0.000 0.000 0.976 0.024
#> SRR2936883 3 0.1211 0.922 0.000 0.000 0.960 0.040
#> SRR2936881 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> SRR2936882 1 0.5493 0.163 0.528 0.000 0.456 0.016
#> SRR2936880 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> SRR2936878 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> SRR2936879 1 0.0188 0.914 0.996 0.000 0.000 0.004
#> SRR2936875 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> SRR2936877 3 0.0469 0.925 0.012 0.000 0.988 0.000
#> SRR2936876 1 0.0657 0.904 0.984 0.012 0.000 0.004
#> SRR2936873 1 0.0188 0.914 0.996 0.000 0.000 0.004
#> SRR2936872 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> SRR2936871 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> SRR2936874 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> SRR2936870 4 0.4985 0.235 0.468 0.000 0.000 0.532
#> SRR2936869 4 0.1211 0.799 0.000 0.040 0.000 0.960
#> SRR2936868 4 0.1118 0.802 0.000 0.036 0.000 0.964
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR2936906 1 0.0609 0.973 0.980 0.000 0.020 0.000 0.000
#> SRR2936909 1 0.0794 0.974 0.972 0.000 0.028 0.000 0.000
#> SRR2936918 1 0.0854 0.969 0.976 0.000 0.012 0.008 0.004
#> SRR2936917 5 0.1571 0.897 0.004 0.000 0.060 0.000 0.936
#> SRR2936916 1 0.0912 0.950 0.972 0.000 0.000 0.016 0.012
#> SRR2936915 1 0.0613 0.961 0.984 0.004 0.000 0.008 0.004
#> SRR2936914 5 0.1357 0.893 0.000 0.000 0.048 0.004 0.948
#> SRR2936913 5 0.4029 0.569 0.024 0.000 0.000 0.232 0.744
#> SRR2936912 1 0.0451 0.966 0.988 0.000 0.004 0.008 0.000
#> SRR2936910 1 0.0451 0.966 0.988 0.000 0.004 0.008 0.000
#> SRR2936911 4 0.4937 0.273 0.024 0.004 0.000 0.580 0.392
#> SRR2936907 2 0.0290 0.983 0.000 0.992 0.000 0.008 0.000
#> SRR2936908 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000
#> SRR2936904 2 0.0162 0.983 0.000 0.996 0.000 0.000 0.004
#> SRR2936905 2 0.0162 0.985 0.000 0.996 0.000 0.000 0.004
#> SRR2936903 3 0.1430 0.895 0.052 0.000 0.944 0.004 0.000
#> SRR2936901 3 0.0865 0.905 0.024 0.000 0.972 0.000 0.004
#> SRR2936902 3 0.1341 0.894 0.000 0.000 0.944 0.000 0.056
#> SRR2936900 3 0.2852 0.797 0.172 0.000 0.828 0.000 0.000
#> SRR2936898 3 0.1282 0.901 0.004 0.000 0.952 0.044 0.000
#> SRR2936899 3 0.1197 0.899 0.000 0.000 0.952 0.048 0.000
#> SRR2936897 1 0.1043 0.969 0.960 0.000 0.040 0.000 0.000
#> SRR2936896 5 0.2927 0.871 0.000 0.000 0.060 0.068 0.872
#> SRR2936894 1 0.0963 0.971 0.964 0.000 0.036 0.000 0.000
#> SRR2936893 2 0.1502 0.955 0.000 0.940 0.000 0.056 0.004
#> SRR2936895 4 0.5543 0.635 0.108 0.000 0.052 0.716 0.124
#> SRR2936892 2 0.0794 0.974 0.000 0.972 0.000 0.028 0.000
#> SRR2936891 1 0.0880 0.973 0.968 0.000 0.032 0.000 0.000
#> SRR2936890 2 0.0510 0.980 0.000 0.984 0.000 0.016 0.000
#> SRR2936886 4 0.0955 0.730 0.000 0.004 0.028 0.968 0.000
#> SRR2936885 3 0.3238 0.832 0.028 0.000 0.836 0.136 0.000
#> SRR2936888 4 0.4866 0.453 0.396 0.000 0.004 0.580 0.020
#> SRR2936889 2 0.1410 0.952 0.000 0.940 0.000 0.060 0.000
#> SRR2936887 4 0.1116 0.730 0.000 0.004 0.028 0.964 0.004
#> SRR2936884 3 0.2230 0.881 0.000 0.000 0.912 0.044 0.044
#> SRR2936883 3 0.2260 0.881 0.000 0.000 0.908 0.064 0.028
#> SRR2936881 3 0.1043 0.900 0.000 0.000 0.960 0.000 0.040
#> SRR2936882 3 0.2732 0.811 0.160 0.000 0.840 0.000 0.000
#> SRR2936880 3 0.1357 0.897 0.004 0.000 0.948 0.000 0.048
#> SRR2936878 5 0.1792 0.894 0.000 0.000 0.084 0.000 0.916
#> SRR2936879 1 0.1522 0.960 0.944 0.012 0.044 0.000 0.000
#> SRR2936875 2 0.0162 0.985 0.000 0.996 0.000 0.000 0.004
#> SRR2936877 5 0.2179 0.881 0.000 0.000 0.100 0.004 0.896
#> SRR2936876 1 0.1728 0.956 0.940 0.020 0.036 0.004 0.000
#> SRR2936873 1 0.0794 0.974 0.972 0.000 0.028 0.000 0.000
#> SRR2936872 2 0.0162 0.985 0.000 0.996 0.000 0.000 0.004
#> SRR2936871 2 0.0162 0.985 0.000 0.996 0.000 0.000 0.004
#> SRR2936874 2 0.0162 0.985 0.000 0.996 0.000 0.000 0.004
#> SRR2936870 4 0.4852 0.483 0.380 0.000 0.008 0.596 0.016
#> SRR2936869 4 0.1124 0.729 0.000 0.004 0.036 0.960 0.000
#> SRR2936868 4 0.1205 0.727 0.000 0.004 0.040 0.956 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR2936906 1 0.1196 0.902 0.952 0.000 0.008 0.000 0.000 0.040
#> SRR2936909 1 0.1387 0.894 0.932 0.000 0.000 0.000 0.000 0.068
#> SRR2936918 1 0.2624 0.854 0.844 0.000 0.004 0.004 0.000 0.148
#> SRR2936917 5 0.0858 0.792 0.000 0.000 0.004 0.000 0.968 0.028
#> SRR2936916 1 0.3806 0.777 0.752 0.000 0.000 0.008 0.028 0.212
#> SRR2936915 1 0.2553 0.855 0.848 0.000 0.000 0.008 0.000 0.144
#> SRR2936914 5 0.0665 0.794 0.000 0.000 0.004 0.008 0.980 0.008
#> SRR2936913 5 0.2608 0.723 0.000 0.000 0.000 0.048 0.872 0.080
#> SRR2936912 1 0.0790 0.903 0.968 0.000 0.000 0.000 0.000 0.032
#> SRR2936910 1 0.1411 0.902 0.936 0.000 0.004 0.000 0.000 0.060
#> SRR2936911 4 0.5635 -0.212 0.004 0.000 0.000 0.528 0.152 0.316
#> SRR2936907 2 0.0935 0.963 0.000 0.964 0.000 0.032 0.000 0.004
#> SRR2936908 2 0.0508 0.966 0.000 0.984 0.000 0.012 0.000 0.004
#> SRR2936904 2 0.0891 0.963 0.000 0.968 0.000 0.024 0.000 0.008
#> SRR2936905 2 0.0000 0.965 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936903 3 0.1003 0.942 0.020 0.000 0.964 0.000 0.000 0.016
#> SRR2936901 3 0.0862 0.948 0.016 0.000 0.972 0.000 0.004 0.008
#> SRR2936902 3 0.0603 0.948 0.000 0.000 0.980 0.000 0.016 0.004
#> SRR2936900 3 0.2586 0.863 0.100 0.000 0.868 0.000 0.000 0.032
#> SRR2936898 3 0.1218 0.946 0.004 0.000 0.956 0.012 0.000 0.028
#> SRR2936899 3 0.0972 0.945 0.000 0.000 0.964 0.008 0.000 0.028
#> SRR2936897 1 0.1588 0.889 0.924 0.000 0.004 0.000 0.000 0.072
#> SRR2936896 6 0.7440 0.000 0.020 0.012 0.036 0.336 0.256 0.340
#> SRR2936894 1 0.0717 0.903 0.976 0.000 0.008 0.000 0.000 0.016
#> SRR2936893 2 0.1524 0.951 0.000 0.932 0.000 0.060 0.000 0.008
#> SRR2936895 4 0.6344 -0.352 0.096 0.000 0.008 0.436 0.048 0.412
#> SRR2936892 2 0.1644 0.941 0.000 0.920 0.000 0.076 0.000 0.004
#> SRR2936891 1 0.1049 0.904 0.960 0.000 0.008 0.000 0.000 0.032
#> SRR2936890 2 0.0632 0.965 0.000 0.976 0.000 0.024 0.000 0.000
#> SRR2936886 4 0.1015 0.478 0.000 0.012 0.004 0.968 0.004 0.012
#> SRR2936885 3 0.2307 0.917 0.016 0.000 0.904 0.048 0.000 0.032
#> SRR2936888 4 0.6088 0.235 0.244 0.000 0.000 0.440 0.004 0.312
#> SRR2936889 2 0.1858 0.925 0.000 0.904 0.000 0.092 0.000 0.004
#> SRR2936887 4 0.1015 0.473 0.000 0.012 0.004 0.968 0.004 0.012
#> SRR2936884 3 0.1262 0.940 0.000 0.000 0.956 0.008 0.020 0.016
#> SRR2936883 3 0.0767 0.947 0.000 0.000 0.976 0.008 0.012 0.004
#> SRR2936881 3 0.1138 0.947 0.004 0.000 0.960 0.000 0.012 0.024
#> SRR2936882 3 0.2122 0.895 0.076 0.000 0.900 0.000 0.000 0.024
#> SRR2936880 3 0.1138 0.947 0.004 0.000 0.960 0.000 0.012 0.024
#> SRR2936878 5 0.2474 0.753 0.000 0.000 0.040 0.000 0.880 0.080
#> SRR2936879 1 0.3620 0.765 0.772 0.044 0.000 0.000 0.000 0.184
#> SRR2936875 2 0.0865 0.951 0.000 0.964 0.000 0.000 0.000 0.036
#> SRR2936877 5 0.5378 0.428 0.032 0.000 0.072 0.000 0.604 0.292
#> SRR2936876 1 0.2703 0.825 0.824 0.004 0.000 0.000 0.000 0.172
#> SRR2936873 1 0.0692 0.903 0.976 0.000 0.004 0.000 0.000 0.020
#> SRR2936872 2 0.0363 0.962 0.000 0.988 0.000 0.000 0.000 0.012
#> SRR2936871 2 0.0146 0.964 0.000 0.996 0.000 0.000 0.000 0.004
#> SRR2936874 2 0.0972 0.959 0.000 0.964 0.000 0.008 0.000 0.028
#> SRR2936870 4 0.5997 0.257 0.224 0.000 0.000 0.468 0.004 0.304
#> SRR2936869 4 0.1578 0.478 0.000 0.048 0.004 0.936 0.000 0.012
#> SRR2936868 4 0.1605 0.480 0.000 0.044 0.004 0.936 0.000 0.016
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 14198 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 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5087 0.492 0.492
#> 3 3 1.000 0.998 0.999 0.2771 0.859 0.713
#> 4 4 1.000 0.987 0.991 0.1500 0.900 0.714
#> 5 5 0.904 0.942 0.931 0.0412 0.973 0.890
#> 6 6 0.951 0.923 0.960 0.0454 0.965 0.845
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 3 4 5
There is also optional best \(k\) = 2 3 4 5 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR2936906 1 0 1 1 0
#> SRR2936909 1 0 1 1 0
#> SRR2936918 1 0 1 1 0
#> SRR2936917 2 0 1 0 1
#> SRR2936916 1 0 1 1 0
#> SRR2936915 1 0 1 1 0
#> SRR2936914 2 0 1 0 1
#> SRR2936913 2 0 1 0 1
#> SRR2936912 1 0 1 1 0
#> SRR2936910 1 0 1 1 0
#> SRR2936911 2 0 1 0 1
#> SRR2936907 2 0 1 0 1
#> SRR2936908 2 0 1 0 1
#> SRR2936904 1 0 1 1 0
#> SRR2936905 2 0 1 0 1
#> SRR2936903 1 0 1 1 0
#> SRR2936901 1 0 1 1 0
#> SRR2936902 2 0 1 0 1
#> SRR2936900 1 0 1 1 0
#> SRR2936898 1 0 1 1 0
#> SRR2936899 1 0 1 1 0
#> SRR2936897 1 0 1 1 0
#> SRR2936896 2 0 1 0 1
#> SRR2936894 1 0 1 1 0
#> SRR2936893 2 0 1 0 1
#> SRR2936895 2 0 1 0 1
#> SRR2936892 2 0 1 0 1
#> SRR2936891 1 0 1 1 0
#> SRR2936890 2 0 1 0 1
#> SRR2936886 1 0 1 1 0
#> SRR2936885 1 0 1 1 0
#> SRR2936888 1 0 1 1 0
#> SRR2936889 2 0 1 0 1
#> SRR2936887 1 0 1 1 0
#> SRR2936884 2 0 1 0 1
#> SRR2936883 2 0 1 0 1
#> SRR2936881 2 0 1 0 1
#> SRR2936882 1 0 1 1 0
#> SRR2936880 2 0 1 0 1
#> SRR2936878 2 0 1 0 1
#> SRR2936879 1 0 1 1 0
#> SRR2936875 2 0 1 0 1
#> SRR2936877 2 0 1 0 1
#> SRR2936876 1 0 1 1 0
#> SRR2936873 1 0 1 1 0
#> SRR2936872 2 0 1 0 1
#> SRR2936871 2 0 1 0 1
#> SRR2936874 2 0 1 0 1
#> SRR2936870 1 0 1 1 0
#> SRR2936869 1 0 1 1 0
#> SRR2936868 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR2936906 1 0.0000 0.995 1.000 0 0.000
#> SRR2936909 1 0.0747 0.987 0.984 0 0.016
#> SRR2936918 1 0.0000 0.995 1.000 0 0.000
#> SRR2936917 2 0.0000 1.000 0.000 1 0.000
#> SRR2936916 3 0.0000 1.000 0.000 0 1.000
#> SRR2936915 3 0.0000 1.000 0.000 0 1.000
#> SRR2936914 2 0.0000 1.000 0.000 1 0.000
#> SRR2936913 2 0.0000 1.000 0.000 1 0.000
#> SRR2936912 1 0.0747 0.987 0.984 0 0.016
#> SRR2936910 1 0.0000 0.995 1.000 0 0.000
#> SRR2936911 2 0.0000 1.000 0.000 1 0.000
#> SRR2936907 2 0.0000 1.000 0.000 1 0.000
#> SRR2936908 2 0.0000 1.000 0.000 1 0.000
#> SRR2936904 3 0.0000 1.000 0.000 0 1.000
#> SRR2936905 2 0.0000 1.000 0.000 1 0.000
#> SRR2936903 1 0.0747 0.987 0.984 0 0.016
#> SRR2936901 3 0.0000 1.000 0.000 0 1.000
#> SRR2936902 2 0.0000 1.000 0.000 1 0.000
#> SRR2936900 1 0.0000 0.995 1.000 0 0.000
#> SRR2936898 3 0.0000 1.000 0.000 0 1.000
#> SRR2936899 3 0.0000 1.000 0.000 0 1.000
#> SRR2936897 1 0.0747 0.987 0.984 0 0.016
#> SRR2936896 2 0.0000 1.000 0.000 1 0.000
#> SRR2936894 1 0.0000 0.995 1.000 0 0.000
#> SRR2936893 2 0.0000 1.000 0.000 1 0.000
#> SRR2936895 2 0.0000 1.000 0.000 1 0.000
#> SRR2936892 2 0.0000 1.000 0.000 1 0.000
#> SRR2936891 1 0.0000 0.995 1.000 0 0.000
#> SRR2936890 2 0.0000 1.000 0.000 1 0.000
#> SRR2936886 3 0.0000 1.000 0.000 0 1.000
#> SRR2936885 1 0.0000 0.995 1.000 0 0.000
#> SRR2936888 1 0.0000 0.995 1.000 0 0.000
#> SRR2936889 2 0.0000 1.000 0.000 1 0.000
#> SRR2936887 3 0.0000 1.000 0.000 0 1.000
#> SRR2936884 2 0.0000 1.000 0.000 1 0.000
#> SRR2936883 2 0.0000 1.000 0.000 1 0.000
#> SRR2936881 2 0.0000 1.000 0.000 1 0.000
#> SRR2936882 1 0.0000 0.995 1.000 0 0.000
#> SRR2936880 2 0.0000 1.000 0.000 1 0.000
#> SRR2936878 2 0.0000 1.000 0.000 1 0.000
#> SRR2936879 3 0.0000 1.000 0.000 0 1.000
#> SRR2936875 2 0.0000 1.000 0.000 1 0.000
#> SRR2936877 2 0.0000 1.000 0.000 1 0.000
#> SRR2936876 3 0.0000 1.000 0.000 0 1.000
#> SRR2936873 1 0.0000 0.995 1.000 0 0.000
#> SRR2936872 2 0.0000 1.000 0.000 1 0.000
#> SRR2936871 2 0.0000 1.000 0.000 1 0.000
#> SRR2936874 2 0.0000 1.000 0.000 1 0.000
#> SRR2936870 1 0.0000 0.995 1.000 0 0.000
#> SRR2936869 3 0.0000 1.000 0.000 0 1.000
#> SRR2936868 3 0.0000 1.000 0.000 0 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR2936906 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> SRR2936909 1 0.0592 0.989 0.984 0.000 0.000 0.016
#> SRR2936918 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> SRR2936917 4 0.0592 0.959 0.000 0.016 0.000 0.984
#> SRR2936916 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> SRR2936915 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> SRR2936914 4 0.0592 0.959 0.000 0.016 0.000 0.984
#> SRR2936913 4 0.0592 0.959 0.000 0.016 0.000 0.984
#> SRR2936912 1 0.0592 0.989 0.984 0.000 0.000 0.016
#> SRR2936910 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> SRR2936911 4 0.0592 0.959 0.000 0.016 0.000 0.984
#> SRR2936907 4 0.2973 0.872 0.000 0.144 0.000 0.856
#> SRR2936908 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> SRR2936904 3 0.0592 0.987 0.000 0.000 0.984 0.016
#> SRR2936905 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> SRR2936903 1 0.0592 0.989 0.984 0.000 0.000 0.016
#> SRR2936901 3 0.0188 0.995 0.000 0.000 0.996 0.004
#> SRR2936902 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> SRR2936900 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> SRR2936898 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> SRR2936899 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> SRR2936897 1 0.0592 0.989 0.984 0.000 0.000 0.016
#> SRR2936896 4 0.2973 0.872 0.000 0.144 0.000 0.856
#> SRR2936894 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> SRR2936893 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> SRR2936895 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> SRR2936892 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> SRR2936891 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> SRR2936890 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> SRR2936886 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> SRR2936885 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> SRR2936888 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> SRR2936889 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> SRR2936887 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> SRR2936884 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> SRR2936883 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> SRR2936881 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> SRR2936882 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> SRR2936880 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> SRR2936878 4 0.0592 0.959 0.000 0.016 0.000 0.984
#> SRR2936879 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> SRR2936875 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> SRR2936877 4 0.0592 0.959 0.000 0.016 0.000 0.984
#> SRR2936876 3 0.0592 0.987 0.000 0.000 0.984 0.016
#> SRR2936873 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> SRR2936872 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> SRR2936871 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> SRR2936874 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> SRR2936870 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> SRR2936869 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> SRR2936868 3 0.0000 0.997 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR2936906 1 0.0162 0.910 0.996 0.000 0.004 0.000 0.000
#> SRR2936909 1 0.3983 0.735 0.660 0.000 0.340 0.000 0.000
#> SRR2936918 1 0.0000 0.910 1.000 0.000 0.000 0.000 0.000
#> SRR2936917 5 0.0000 0.949 0.000 0.000 0.000 0.000 1.000
#> SRR2936916 3 0.4045 0.995 0.000 0.000 0.644 0.356 0.000
#> SRR2936915 3 0.4088 0.981 0.000 0.000 0.632 0.368 0.000
#> SRR2936914 5 0.0000 0.949 0.000 0.000 0.000 0.000 1.000
#> SRR2936913 5 0.0000 0.949 0.000 0.000 0.000 0.000 1.000
#> SRR2936912 1 0.3983 0.735 0.660 0.000 0.340 0.000 0.000
#> SRR2936910 1 0.0000 0.910 1.000 0.000 0.000 0.000 0.000
#> SRR2936911 5 0.0000 0.949 0.000 0.000 0.000 0.000 1.000
#> SRR2936907 5 0.2424 0.844 0.000 0.132 0.000 0.000 0.868
#> SRR2936908 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936904 4 0.0794 0.958 0.000 0.000 0.028 0.972 0.000
#> SRR2936905 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936903 1 0.3983 0.735 0.660 0.000 0.340 0.000 0.000
#> SRR2936901 4 0.0963 0.940 0.000 0.000 0.036 0.964 0.000
#> SRR2936902 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936900 1 0.0404 0.909 0.988 0.000 0.012 0.000 0.000
#> SRR2936898 3 0.4045 0.995 0.000 0.000 0.644 0.356 0.000
#> SRR2936899 3 0.4045 0.995 0.000 0.000 0.644 0.356 0.000
#> SRR2936897 1 0.3983 0.735 0.660 0.000 0.340 0.000 0.000
#> SRR2936896 5 0.2424 0.844 0.000 0.132 0.000 0.000 0.868
#> SRR2936894 1 0.0162 0.910 0.996 0.000 0.004 0.000 0.000
#> SRR2936893 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936895 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936892 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936891 1 0.0162 0.910 0.996 0.000 0.004 0.000 0.000
#> SRR2936890 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936886 4 0.0000 0.976 0.000 0.000 0.000 1.000 0.000
#> SRR2936885 1 0.0404 0.909 0.988 0.000 0.012 0.000 0.000
#> SRR2936888 1 0.0162 0.910 0.996 0.000 0.004 0.000 0.000
#> SRR2936889 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936887 4 0.0000 0.976 0.000 0.000 0.000 1.000 0.000
#> SRR2936884 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936883 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936881 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936882 1 0.0404 0.909 0.988 0.000 0.012 0.000 0.000
#> SRR2936880 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936878 5 0.0000 0.949 0.000 0.000 0.000 0.000 1.000
#> SRR2936879 3 0.4045 0.995 0.000 0.000 0.644 0.356 0.000
#> SRR2936875 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936877 5 0.0000 0.949 0.000 0.000 0.000 0.000 1.000
#> SRR2936876 4 0.0794 0.958 0.000 0.000 0.028 0.972 0.000
#> SRR2936873 1 0.0162 0.910 0.996 0.000 0.004 0.000 0.000
#> SRR2936872 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936871 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936874 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936870 1 0.0162 0.910 0.996 0.000 0.004 0.000 0.000
#> SRR2936869 4 0.0000 0.976 0.000 0.000 0.000 1.000 0.000
#> SRR2936868 4 0.0000 0.976 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
#> SRR2936906 1 0.0000 0.822 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936909 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR2936918 1 0.0363 0.821 0.988 0.000 0.000 0.000 0.000 0.012
#> SRR2936917 5 0.0000 0.947 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936916 3 0.0000 0.993 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936915 3 0.0632 0.973 0.000 0.000 0.976 0.024 0.000 0.000
#> SRR2936914 5 0.0000 0.947 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936913 5 0.0000 0.947 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936912 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR2936910 1 0.0363 0.821 0.988 0.000 0.000 0.000 0.000 0.012
#> SRR2936911 5 0.0000 0.947 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936907 5 0.2178 0.836 0.000 0.132 0.000 0.000 0.868 0.000
#> SRR2936908 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936904 4 0.0000 0.972 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR2936905 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936903 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR2936901 4 0.1204 0.961 0.000 0.000 0.056 0.944 0.000 0.000
#> SRR2936902 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936900 1 0.3765 0.529 0.596 0.000 0.000 0.000 0.000 0.404
#> SRR2936898 3 0.0000 0.993 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936899 3 0.0000 0.993 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936897 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR2936896 5 0.2178 0.836 0.000 0.132 0.000 0.000 0.868 0.000
#> SRR2936894 1 0.0000 0.822 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936893 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936895 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936892 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936891 1 0.0000 0.822 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936890 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936886 4 0.0713 0.985 0.000 0.000 0.028 0.972 0.000 0.000
#> SRR2936885 1 0.3765 0.529 0.596 0.000 0.000 0.000 0.000 0.404
#> SRR2936888 1 0.0000 0.822 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936889 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936887 4 0.0713 0.985 0.000 0.000 0.028 0.972 0.000 0.000
#> SRR2936884 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936883 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936881 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936882 1 0.3765 0.529 0.596 0.000 0.000 0.000 0.000 0.404
#> SRR2936880 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936878 5 0.0000 0.947 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936879 3 0.0000 0.993 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936875 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936877 5 0.0000 0.947 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936876 4 0.0363 0.972 0.000 0.000 0.000 0.988 0.000 0.012
#> SRR2936873 1 0.3547 0.610 0.668 0.000 0.000 0.000 0.000 0.332
#> SRR2936872 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936871 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936874 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936870 1 0.0000 0.822 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936869 4 0.0713 0.985 0.000 0.000 0.028 0.972 0.000 0.000
#> SRR2936868 4 0.0713 0.985 0.000 0.000 0.028 0.972 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
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 14198 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 1.000 0.991 0.996 0.4750 0.523 0.523
#> 3 3 0.755 0.922 0.925 0.3533 0.777 0.594
#> 4 4 0.804 0.857 0.901 0.1393 0.915 0.758
#> 5 5 0.747 0.755 0.826 0.0639 0.965 0.870
#> 6 6 0.800 0.737 0.805 0.0486 0.936 0.730
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
#> SRR2936906 1 0.000 0.988 1.000 0.000
#> SRR2936909 1 0.000 0.988 1.000 0.000
#> SRR2936918 1 0.000 0.988 1.000 0.000
#> SRR2936917 2 0.000 1.000 0.000 1.000
#> SRR2936916 2 0.000 1.000 0.000 1.000
#> SRR2936915 2 0.000 1.000 0.000 1.000
#> SRR2936914 2 0.000 1.000 0.000 1.000
#> SRR2936913 2 0.000 1.000 0.000 1.000
#> SRR2936912 1 0.000 0.988 1.000 0.000
#> SRR2936910 1 0.000 0.988 1.000 0.000
#> SRR2936911 2 0.000 1.000 0.000 1.000
#> SRR2936907 2 0.000 1.000 0.000 1.000
#> SRR2936908 2 0.000 1.000 0.000 1.000
#> SRR2936904 1 0.000 0.988 1.000 0.000
#> SRR2936905 2 0.000 1.000 0.000 1.000
#> SRR2936903 1 0.000 0.988 1.000 0.000
#> SRR2936901 1 0.343 0.930 0.936 0.064
#> SRR2936902 2 0.000 1.000 0.000 1.000
#> SRR2936900 1 0.000 0.988 1.000 0.000
#> SRR2936898 2 0.000 1.000 0.000 1.000
#> SRR2936899 2 0.000 1.000 0.000 1.000
#> SRR2936897 1 0.000 0.988 1.000 0.000
#> SRR2936896 2 0.000 1.000 0.000 1.000
#> SRR2936894 1 0.000 0.988 1.000 0.000
#> SRR2936893 2 0.000 1.000 0.000 1.000
#> SRR2936895 2 0.000 1.000 0.000 1.000
#> SRR2936892 2 0.000 1.000 0.000 1.000
#> SRR2936891 1 0.000 0.988 1.000 0.000
#> SRR2936890 2 0.000 1.000 0.000 1.000
#> SRR2936886 2 0.000 1.000 0.000 1.000
#> SRR2936885 1 0.000 0.988 1.000 0.000
#> SRR2936888 1 0.000 0.988 1.000 0.000
#> SRR2936889 2 0.000 1.000 0.000 1.000
#> SRR2936887 2 0.000 1.000 0.000 1.000
#> SRR2936884 2 0.000 1.000 0.000 1.000
#> SRR2936883 2 0.000 1.000 0.000 1.000
#> SRR2936881 2 0.000 1.000 0.000 1.000
#> SRR2936882 1 0.000 0.988 1.000 0.000
#> SRR2936880 2 0.000 1.000 0.000 1.000
#> SRR2936878 2 0.000 1.000 0.000 1.000
#> SRR2936879 2 0.000 1.000 0.000 1.000
#> SRR2936875 2 0.000 1.000 0.000 1.000
#> SRR2936877 2 0.000 1.000 0.000 1.000
#> SRR2936876 1 0.000 0.988 1.000 0.000
#> SRR2936873 1 0.000 0.988 1.000 0.000
#> SRR2936872 2 0.000 1.000 0.000 1.000
#> SRR2936871 2 0.000 1.000 0.000 1.000
#> SRR2936874 2 0.000 1.000 0.000 1.000
#> SRR2936870 1 0.000 0.988 1.000 0.000
#> SRR2936869 2 0.000 1.000 0.000 1.000
#> SRR2936868 1 0.605 0.832 0.852 0.148
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR2936906 1 0.00 1.000 1.000 0.000 0.000
#> SRR2936909 1 0.00 1.000 1.000 0.000 0.000
#> SRR2936918 1 0.00 1.000 1.000 0.000 0.000
#> SRR2936917 2 0.47 0.828 0.000 0.788 0.212
#> SRR2936916 3 0.47 0.947 0.000 0.212 0.788
#> SRR2936915 3 0.47 0.947 0.000 0.212 0.788
#> SRR2936914 2 0.47 0.828 0.000 0.788 0.212
#> SRR2936913 2 0.47 0.828 0.000 0.788 0.212
#> SRR2936912 1 0.00 1.000 1.000 0.000 0.000
#> SRR2936910 1 0.00 1.000 1.000 0.000 0.000
#> SRR2936911 2 0.47 0.828 0.000 0.788 0.212
#> SRR2936907 2 0.47 0.828 0.000 0.788 0.212
#> SRR2936908 2 0.00 0.911 0.000 1.000 0.000
#> SRR2936904 3 0.47 0.691 0.212 0.000 0.788
#> SRR2936905 2 0.00 0.911 0.000 1.000 0.000
#> SRR2936903 1 0.00 1.000 1.000 0.000 0.000
#> SRR2936901 3 0.47 0.947 0.000 0.212 0.788
#> SRR2936902 2 0.00 0.911 0.000 1.000 0.000
#> SRR2936900 1 0.00 1.000 1.000 0.000 0.000
#> SRR2936898 3 0.47 0.947 0.000 0.212 0.788
#> SRR2936899 3 0.47 0.947 0.000 0.212 0.788
#> SRR2936897 1 0.00 1.000 1.000 0.000 0.000
#> SRR2936896 2 0.47 0.828 0.000 0.788 0.212
#> SRR2936894 1 0.00 1.000 1.000 0.000 0.000
#> SRR2936893 2 0.00 0.911 0.000 1.000 0.000
#> SRR2936895 2 0.00 0.911 0.000 1.000 0.000
#> SRR2936892 2 0.00 0.911 0.000 1.000 0.000
#> SRR2936891 1 0.00 1.000 1.000 0.000 0.000
#> SRR2936890 2 0.00 0.911 0.000 1.000 0.000
#> SRR2936886 3 0.47 0.947 0.000 0.212 0.788
#> SRR2936885 1 0.00 1.000 1.000 0.000 0.000
#> SRR2936888 1 0.00 1.000 1.000 0.000 0.000
#> SRR2936889 2 0.00 0.911 0.000 1.000 0.000
#> SRR2936887 3 0.47 0.947 0.000 0.212 0.788
#> SRR2936884 2 0.00 0.911 0.000 1.000 0.000
#> SRR2936883 2 0.00 0.911 0.000 1.000 0.000
#> SRR2936881 2 0.00 0.911 0.000 1.000 0.000
#> SRR2936882 1 0.00 1.000 1.000 0.000 0.000
#> SRR2936880 2 0.00 0.911 0.000 1.000 0.000
#> SRR2936878 2 0.47 0.828 0.000 0.788 0.212
#> SRR2936879 3 0.47 0.947 0.000 0.212 0.788
#> SRR2936875 2 0.00 0.911 0.000 1.000 0.000
#> SRR2936877 2 0.47 0.828 0.000 0.788 0.212
#> SRR2936876 3 0.47 0.691 0.212 0.000 0.788
#> SRR2936873 1 0.00 1.000 1.000 0.000 0.000
#> SRR2936872 2 0.00 0.911 0.000 1.000 0.000
#> SRR2936871 2 0.00 0.911 0.000 1.000 0.000
#> SRR2936874 2 0.00 0.911 0.000 1.000 0.000
#> SRR2936870 1 0.00 1.000 1.000 0.000 0.000
#> SRR2936869 3 0.47 0.947 0.000 0.212 0.788
#> SRR2936868 3 0.47 0.947 0.000 0.212 0.788
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR2936906 1 0.0921 0.913 0.972 0.000 0.000 0.028
#> SRR2936909 1 0.4193 0.829 0.732 0.000 0.000 0.268
#> SRR2936918 1 0.0921 0.913 0.972 0.000 0.000 0.028
#> SRR2936917 4 0.4406 1.000 0.000 0.300 0.000 0.700
#> SRR2936916 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> SRR2936915 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> SRR2936914 4 0.4406 1.000 0.000 0.300 0.000 0.700
#> SRR2936913 4 0.4406 1.000 0.000 0.300 0.000 0.700
#> SRR2936912 1 0.4193 0.829 0.732 0.000 0.000 0.268
#> SRR2936910 1 0.1211 0.914 0.960 0.000 0.000 0.040
#> SRR2936911 4 0.4406 1.000 0.000 0.300 0.000 0.700
#> SRR2936907 2 0.4941 -0.365 0.000 0.564 0.000 0.436
#> SRR2936908 2 0.0000 0.877 0.000 1.000 0.000 0.000
#> SRR2936904 3 0.3074 0.867 0.000 0.000 0.848 0.152
#> SRR2936905 2 0.0000 0.877 0.000 1.000 0.000 0.000
#> SRR2936903 1 0.4222 0.826 0.728 0.000 0.000 0.272
#> SRR2936901 3 0.0921 0.955 0.000 0.000 0.972 0.028
#> SRR2936902 2 0.2469 0.797 0.000 0.892 0.108 0.000
#> SRR2936900 1 0.1022 0.915 0.968 0.000 0.000 0.032
#> SRR2936898 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> SRR2936899 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> SRR2936897 1 0.4222 0.826 0.728 0.000 0.000 0.272
#> SRR2936896 2 0.4941 -0.365 0.000 0.564 0.000 0.436
#> SRR2936894 1 0.0921 0.913 0.972 0.000 0.000 0.028
#> SRR2936893 2 0.0000 0.877 0.000 1.000 0.000 0.000
#> SRR2936895 2 0.0592 0.873 0.000 0.984 0.016 0.000
#> SRR2936892 2 0.0817 0.869 0.000 0.976 0.024 0.000
#> SRR2936891 1 0.0921 0.913 0.972 0.000 0.000 0.028
#> SRR2936890 2 0.0000 0.877 0.000 1.000 0.000 0.000
#> SRR2936886 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> SRR2936885 1 0.2011 0.908 0.920 0.000 0.000 0.080
#> SRR2936888 1 0.0921 0.913 0.972 0.000 0.000 0.028
#> SRR2936889 2 0.0000 0.877 0.000 1.000 0.000 0.000
#> SRR2936887 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> SRR2936884 2 0.0000 0.877 0.000 1.000 0.000 0.000
#> SRR2936883 2 0.2469 0.797 0.000 0.892 0.108 0.000
#> SRR2936881 2 0.2469 0.797 0.000 0.892 0.108 0.000
#> SRR2936882 1 0.1022 0.915 0.968 0.000 0.000 0.032
#> SRR2936880 2 0.0817 0.869 0.000 0.976 0.024 0.000
#> SRR2936878 4 0.4406 1.000 0.000 0.300 0.000 0.700
#> SRR2936879 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> SRR2936875 2 0.0000 0.877 0.000 1.000 0.000 0.000
#> SRR2936877 4 0.4406 1.000 0.000 0.300 0.000 0.700
#> SRR2936876 3 0.3400 0.845 0.000 0.000 0.820 0.180
#> SRR2936873 1 0.2011 0.908 0.920 0.000 0.000 0.080
#> SRR2936872 2 0.0000 0.877 0.000 1.000 0.000 0.000
#> SRR2936871 2 0.0000 0.877 0.000 1.000 0.000 0.000
#> SRR2936874 2 0.2011 0.825 0.000 0.920 0.080 0.000
#> SRR2936870 1 0.0921 0.913 0.972 0.000 0.000 0.028
#> SRR2936869 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> SRR2936868 3 0.0817 0.957 0.000 0.000 0.976 0.024
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR2936906 1 0.000 0.7103 1.000 0.000 0.000 0.000 0.000
#> SRR2936909 3 0.420 0.9855 0.408 0.000 0.592 0.000 0.000
#> SRR2936918 1 0.191 0.6922 0.908 0.000 0.000 0.000 0.092
#> SRR2936917 5 0.256 0.9980 0.000 0.144 0.000 0.000 0.856
#> SRR2936916 4 0.388 0.6171 0.000 0.000 0.316 0.684 0.000
#> SRR2936915 4 0.029 0.8944 0.000 0.000 0.008 0.992 0.000
#> SRR2936914 5 0.256 0.9980 0.000 0.144 0.000 0.000 0.856
#> SRR2936913 5 0.256 0.9980 0.000 0.144 0.000 0.000 0.856
#> SRR2936912 3 0.420 0.9855 0.408 0.000 0.592 0.000 0.000
#> SRR2936910 1 0.446 0.5766 0.756 0.000 0.152 0.000 0.092
#> SRR2936911 5 0.256 0.9980 0.000 0.144 0.000 0.000 0.856
#> SRR2936907 2 0.457 -0.0828 0.000 0.580 0.012 0.000 0.408
#> SRR2936908 2 0.000 0.8003 0.000 1.000 0.000 0.000 0.000
#> SRR2936904 4 0.434 0.7182 0.000 0.000 0.296 0.684 0.020
#> SRR2936905 2 0.000 0.8003 0.000 1.000 0.000 0.000 0.000
#> SRR2936903 3 0.483 0.9561 0.408 0.000 0.568 0.000 0.024
#> SRR2936901 4 0.112 0.8916 0.000 0.000 0.016 0.964 0.020
#> SRR2936902 2 0.448 0.6969 0.000 0.668 0.308 0.024 0.000
#> SRR2936900 1 0.510 0.5015 0.692 0.000 0.192 0.000 0.116
#> SRR2936898 4 0.029 0.8944 0.000 0.000 0.008 0.992 0.000
#> SRR2936899 4 0.029 0.8944 0.000 0.000 0.008 0.992 0.000
#> SRR2936897 3 0.420 0.9855 0.408 0.000 0.592 0.000 0.000
#> SRR2936896 2 0.457 -0.0828 0.000 0.580 0.012 0.000 0.408
#> SRR2936894 1 0.000 0.7103 1.000 0.000 0.000 0.000 0.000
#> SRR2936893 2 0.000 0.8003 0.000 1.000 0.000 0.000 0.000
#> SRR2936895 2 0.384 0.7092 0.000 0.692 0.308 0.000 0.000
#> SRR2936892 2 0.134 0.7923 0.000 0.944 0.056 0.000 0.000
#> SRR2936891 1 0.000 0.7103 1.000 0.000 0.000 0.000 0.000
#> SRR2936890 2 0.000 0.8003 0.000 1.000 0.000 0.000 0.000
#> SRR2936886 4 0.173 0.8909 0.000 0.000 0.080 0.920 0.000
#> SRR2936885 1 0.551 0.3484 0.632 0.000 0.252 0.000 0.116
#> SRR2936888 1 0.029 0.7088 0.992 0.000 0.000 0.000 0.008
#> SRR2936889 2 0.000 0.8003 0.000 1.000 0.000 0.000 0.000
#> SRR2936887 4 0.173 0.8909 0.000 0.000 0.080 0.920 0.000
#> SRR2936884 2 0.293 0.7569 0.000 0.820 0.180 0.000 0.000
#> SRR2936883 2 0.448 0.6969 0.000 0.668 0.308 0.024 0.000
#> SRR2936881 2 0.448 0.6969 0.000 0.668 0.308 0.024 0.000
#> SRR2936882 1 0.510 0.5015 0.692 0.000 0.192 0.000 0.116
#> SRR2936880 2 0.384 0.7092 0.000 0.692 0.308 0.000 0.000
#> SRR2936878 5 0.256 0.9980 0.000 0.144 0.000 0.000 0.856
#> SRR2936879 4 0.029 0.8944 0.000 0.000 0.008 0.992 0.000
#> SRR2936875 2 0.000 0.8003 0.000 1.000 0.000 0.000 0.000
#> SRR2936877 5 0.295 0.9899 0.000 0.144 0.012 0.000 0.844
#> SRR2936876 4 0.432 0.6584 0.000 0.000 0.292 0.688 0.020
#> SRR2936873 1 0.535 0.3414 0.636 0.000 0.272 0.000 0.092
#> SRR2936872 2 0.000 0.8003 0.000 1.000 0.000 0.000 0.000
#> SRR2936871 2 0.000 0.8003 0.000 1.000 0.000 0.000 0.000
#> SRR2936874 2 0.344 0.7572 0.000 0.808 0.172 0.020 0.000
#> SRR2936870 1 0.029 0.7088 0.992 0.000 0.000 0.000 0.008
#> SRR2936869 4 0.148 0.8915 0.000 0.000 0.064 0.936 0.000
#> SRR2936868 4 0.173 0.8909 0.000 0.000 0.080 0.920 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR2936906 1 0.0146 0.748 0.996 0.000 0.004 0.000 0.000 0.000
#> SRR2936909 6 0.3351 0.991 0.288 0.000 0.000 0.000 0.000 0.712
#> SRR2936918 1 0.2480 0.735 0.872 0.000 0.104 0.000 0.024 0.000
#> SRR2936917 5 0.0937 0.992 0.000 0.040 0.000 0.000 0.960 0.000
#> SRR2936916 3 0.4205 0.102 0.000 0.000 0.564 0.420 0.000 0.016
#> SRR2936915 4 0.0717 0.849 0.000 0.000 0.016 0.976 0.000 0.008
#> SRR2936914 5 0.0937 0.992 0.000 0.040 0.000 0.000 0.960 0.000
#> SRR2936913 5 0.1082 0.992 0.000 0.040 0.000 0.000 0.956 0.004
#> SRR2936912 6 0.3351 0.991 0.288 0.000 0.000 0.000 0.000 0.712
#> SRR2936910 1 0.4587 0.665 0.736 0.000 0.104 0.000 0.024 0.136
#> SRR2936911 5 0.1082 0.992 0.000 0.040 0.000 0.000 0.956 0.004
#> SRR2936907 2 0.5134 0.402 0.000 0.628 0.008 0.000 0.256 0.108
#> SRR2936908 2 0.1588 0.745 0.000 0.924 0.004 0.000 0.000 0.072
#> SRR2936904 4 0.5326 0.714 0.000 0.000 0.172 0.612 0.004 0.212
#> SRR2936905 2 0.0000 0.761 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936903 6 0.3859 0.972 0.288 0.000 0.020 0.000 0.000 0.692
#> SRR2936901 4 0.1949 0.836 0.000 0.000 0.088 0.904 0.004 0.004
#> SRR2936902 3 0.4046 0.788 0.000 0.368 0.620 0.004 0.000 0.008
#> SRR2936900 1 0.4734 0.627 0.680 0.000 0.152 0.000 0.000 0.168
#> SRR2936898 4 0.1124 0.844 0.000 0.000 0.036 0.956 0.000 0.008
#> SRR2936899 4 0.1124 0.844 0.000 0.000 0.036 0.956 0.000 0.008
#> SRR2936897 6 0.3351 0.991 0.288 0.000 0.000 0.000 0.000 0.712
#> SRR2936896 2 0.5211 0.394 0.000 0.620 0.008 0.000 0.256 0.116
#> SRR2936894 1 0.0146 0.748 0.996 0.000 0.004 0.000 0.000 0.000
#> SRR2936893 2 0.1588 0.745 0.000 0.924 0.004 0.000 0.000 0.072
#> SRR2936895 3 0.4437 0.742 0.000 0.392 0.576 0.000 0.000 0.032
#> SRR2936892 2 0.3017 0.658 0.000 0.844 0.084 0.000 0.000 0.072
#> SRR2936891 1 0.0146 0.748 0.996 0.000 0.004 0.000 0.000 0.000
#> SRR2936890 2 0.0000 0.761 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936886 4 0.3215 0.851 0.000 0.000 0.100 0.828 0.000 0.072
#> SRR2936885 1 0.5177 0.516 0.612 0.000 0.152 0.000 0.000 0.236
#> SRR2936888 1 0.0725 0.744 0.976 0.000 0.012 0.000 0.012 0.000
#> SRR2936889 2 0.0000 0.761 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936887 4 0.3215 0.851 0.000 0.000 0.100 0.828 0.000 0.072
#> SRR2936884 2 0.4333 -0.266 0.000 0.596 0.376 0.000 0.000 0.028
#> SRR2936883 3 0.4046 0.788 0.000 0.368 0.620 0.004 0.000 0.008
#> SRR2936881 3 0.3807 0.788 0.000 0.368 0.628 0.004 0.000 0.000
#> SRR2936882 1 0.4734 0.627 0.680 0.000 0.152 0.000 0.000 0.168
#> SRR2936880 3 0.3975 0.763 0.000 0.392 0.600 0.000 0.000 0.008
#> SRR2936878 5 0.0937 0.992 0.000 0.040 0.000 0.000 0.960 0.000
#> SRR2936879 4 0.1124 0.844 0.000 0.000 0.036 0.956 0.000 0.008
#> SRR2936875 2 0.1588 0.745 0.000 0.924 0.004 0.000 0.000 0.072
#> SRR2936877 5 0.2051 0.966 0.000 0.040 0.008 0.000 0.916 0.036
#> SRR2936876 4 0.5037 0.543 0.000 0.000 0.088 0.604 0.004 0.304
#> SRR2936873 1 0.5426 0.510 0.616 0.000 0.104 0.000 0.024 0.256
#> SRR2936872 2 0.0000 0.761 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936871 2 0.0000 0.761 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936874 2 0.4586 0.222 0.000 0.660 0.264 0.000 0.000 0.076
#> SRR2936870 1 0.0725 0.744 0.976 0.000 0.012 0.000 0.012 0.000
#> SRR2936869 4 0.3063 0.851 0.000 0.000 0.092 0.840 0.000 0.068
#> SRR2936868 4 0.3352 0.849 0.000 0.000 0.112 0.816 0.000 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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
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 14198 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5103 0.490 0.490
#> 3 3 1.000 1.000 1.000 0.1751 0.911 0.818
#> 4 4 1.000 0.990 0.997 0.0378 0.973 0.932
#> 5 5 0.869 0.919 0.952 0.0453 0.998 0.996
#> 6 6 0.869 0.527 0.785 0.0671 0.895 0.721
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR2936906 1 0.0000 1.000 1.000 0.000
#> SRR2936909 1 0.0000 1.000 1.000 0.000
#> SRR2936918 1 0.0000 1.000 1.000 0.000
#> SRR2936917 2 0.0000 1.000 0.000 1.000
#> SRR2936916 2 0.0000 1.000 0.000 1.000
#> SRR2936915 1 0.0000 1.000 1.000 0.000
#> SRR2936914 2 0.0000 1.000 0.000 1.000
#> SRR2936913 2 0.0000 1.000 0.000 1.000
#> SRR2936912 1 0.0000 1.000 1.000 0.000
#> SRR2936910 1 0.0000 1.000 1.000 0.000
#> SRR2936911 2 0.0000 1.000 0.000 1.000
#> SRR2936907 2 0.0000 1.000 0.000 1.000
#> SRR2936908 2 0.0000 1.000 0.000 1.000
#> SRR2936904 1 0.0000 1.000 1.000 0.000
#> SRR2936905 2 0.0000 1.000 0.000 1.000
#> SRR2936903 1 0.0000 1.000 1.000 0.000
#> SRR2936901 1 0.0000 1.000 1.000 0.000
#> SRR2936902 2 0.0000 1.000 0.000 1.000
#> SRR2936900 1 0.0000 1.000 1.000 0.000
#> SRR2936898 1 0.0376 0.996 0.996 0.004
#> SRR2936899 1 0.0000 1.000 1.000 0.000
#> SRR2936897 1 0.0000 1.000 1.000 0.000
#> SRR2936896 2 0.0000 1.000 0.000 1.000
#> SRR2936894 1 0.0000 1.000 1.000 0.000
#> SRR2936893 2 0.0000 1.000 0.000 1.000
#> SRR2936895 2 0.0000 1.000 0.000 1.000
#> SRR2936892 2 0.0000 1.000 0.000 1.000
#> SRR2936891 1 0.0000 1.000 1.000 0.000
#> SRR2936890 2 0.0000 1.000 0.000 1.000
#> SRR2936886 1 0.0000 1.000 1.000 0.000
#> SRR2936885 1 0.0000 1.000 1.000 0.000
#> SRR2936888 1 0.0000 1.000 1.000 0.000
#> SRR2936889 2 0.0000 1.000 0.000 1.000
#> SRR2936887 1 0.0000 1.000 1.000 0.000
#> SRR2936884 2 0.0000 1.000 0.000 1.000
#> SRR2936883 2 0.0000 1.000 0.000 1.000
#> SRR2936881 2 0.0000 1.000 0.000 1.000
#> SRR2936882 1 0.0000 1.000 1.000 0.000
#> SRR2936880 2 0.0000 1.000 0.000 1.000
#> SRR2936878 2 0.0000 1.000 0.000 1.000
#> SRR2936879 2 0.0000 1.000 0.000 1.000
#> SRR2936875 2 0.0000 1.000 0.000 1.000
#> SRR2936877 2 0.0000 1.000 0.000 1.000
#> SRR2936876 1 0.0000 1.000 1.000 0.000
#> SRR2936873 1 0.0000 1.000 1.000 0.000
#> SRR2936872 2 0.0000 1.000 0.000 1.000
#> SRR2936871 2 0.0000 1.000 0.000 1.000
#> SRR2936874 2 0.0000 1.000 0.000 1.000
#> SRR2936870 1 0.0000 1.000 1.000 0.000
#> SRR2936869 1 0.0000 1.000 1.000 0.000
#> SRR2936868 1 0.0000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR2936906 1 0 1 1 0 0
#> SRR2936909 1 0 1 1 0 0
#> SRR2936918 1 0 1 1 0 0
#> SRR2936917 2 0 1 0 1 0
#> SRR2936916 2 0 1 0 1 0
#> SRR2936915 1 0 1 1 0 0
#> SRR2936914 2 0 1 0 1 0
#> SRR2936913 2 0 1 0 1 0
#> SRR2936912 1 0 1 1 0 0
#> SRR2936910 1 0 1 1 0 0
#> SRR2936911 2 0 1 0 1 0
#> SRR2936907 2 0 1 0 1 0
#> SRR2936908 2 0 1 0 1 0
#> SRR2936904 1 0 1 1 0 0
#> SRR2936905 2 0 1 0 1 0
#> SRR2936903 1 0 1 1 0 0
#> SRR2936901 1 0 1 1 0 0
#> SRR2936902 2 0 1 0 1 0
#> SRR2936900 1 0 1 1 0 0
#> SRR2936898 3 0 1 0 0 1
#> SRR2936899 3 0 1 0 0 1
#> SRR2936897 1 0 1 1 0 0
#> SRR2936896 2 0 1 0 1 0
#> SRR2936894 1 0 1 1 0 0
#> SRR2936893 2 0 1 0 1 0
#> SRR2936895 2 0 1 0 1 0
#> SRR2936892 2 0 1 0 1 0
#> SRR2936891 1 0 1 1 0 0
#> SRR2936890 2 0 1 0 1 0
#> SRR2936886 3 0 1 0 0 1
#> SRR2936885 1 0 1 1 0 0
#> SRR2936888 1 0 1 1 0 0
#> SRR2936889 2 0 1 0 1 0
#> SRR2936887 3 0 1 0 0 1
#> SRR2936884 2 0 1 0 1 0
#> SRR2936883 2 0 1 0 1 0
#> SRR2936881 2 0 1 0 1 0
#> SRR2936882 1 0 1 1 0 0
#> SRR2936880 2 0 1 0 1 0
#> SRR2936878 2 0 1 0 1 0
#> SRR2936879 2 0 1 0 1 0
#> SRR2936875 2 0 1 0 1 0
#> SRR2936877 2 0 1 0 1 0
#> SRR2936876 1 0 1 1 0 0
#> SRR2936873 1 0 1 1 0 0
#> SRR2936872 2 0 1 0 1 0
#> SRR2936871 2 0 1 0 1 0
#> SRR2936874 2 0 1 0 1 0
#> SRR2936870 1 0 1 1 0 0
#> SRR2936869 3 0 1 0 0 1
#> SRR2936868 3 0 1 0 0 1
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR2936906 1 0.0000 1.000 1 0.000 0.000 0.000
#> SRR2936909 1 0.0000 1.000 1 0.000 0.000 0.000
#> SRR2936918 1 0.0000 1.000 1 0.000 0.000 0.000
#> SRR2936917 2 0.0000 0.998 0 1.000 0.000 0.000
#> SRR2936916 2 0.0000 0.998 0 1.000 0.000 0.000
#> SRR2936915 1 0.0000 1.000 1 0.000 0.000 0.000
#> SRR2936914 2 0.0000 0.998 0 1.000 0.000 0.000
#> SRR2936913 2 0.0000 0.998 0 1.000 0.000 0.000
#> SRR2936912 1 0.0000 1.000 1 0.000 0.000 0.000
#> SRR2936910 1 0.0000 1.000 1 0.000 0.000 0.000
#> SRR2936911 2 0.0000 0.998 0 1.000 0.000 0.000
#> SRR2936907 2 0.0188 0.998 0 0.996 0.004 0.000
#> SRR2936908 2 0.0188 0.998 0 0.996 0.004 0.000
#> SRR2936904 1 0.0000 1.000 1 0.000 0.000 0.000
#> SRR2936905 2 0.0188 0.998 0 0.996 0.004 0.000
#> SRR2936903 1 0.0000 1.000 1 0.000 0.000 0.000
#> SRR2936901 1 0.0000 1.000 1 0.000 0.000 0.000
#> SRR2936902 2 0.0000 0.998 0 1.000 0.000 0.000
#> SRR2936900 1 0.0000 1.000 1 0.000 0.000 0.000
#> SRR2936898 3 0.0188 0.888 0 0.000 0.996 0.004
#> SRR2936899 3 0.0188 0.888 0 0.000 0.996 0.004
#> SRR2936897 1 0.0000 1.000 1 0.000 0.000 0.000
#> SRR2936896 2 0.0000 0.998 0 1.000 0.000 0.000
#> SRR2936894 1 0.0000 1.000 1 0.000 0.000 0.000
#> SRR2936893 2 0.0188 0.998 0 0.996 0.004 0.000
#> SRR2936895 2 0.0000 0.998 0 1.000 0.000 0.000
#> SRR2936892 2 0.0188 0.998 0 0.996 0.004 0.000
#> SRR2936891 1 0.0000 1.000 1 0.000 0.000 0.000
#> SRR2936890 2 0.0188 0.998 0 0.996 0.004 0.000
#> SRR2936886 4 0.0000 1.000 0 0.000 0.000 1.000
#> SRR2936885 1 0.0000 1.000 1 0.000 0.000 0.000
#> SRR2936888 1 0.0000 1.000 1 0.000 0.000 0.000
#> SRR2936889 2 0.0188 0.998 0 0.996 0.004 0.000
#> SRR2936887 4 0.0000 1.000 0 0.000 0.000 1.000
#> SRR2936884 2 0.0000 0.998 0 1.000 0.000 0.000
#> SRR2936883 2 0.0000 0.998 0 1.000 0.000 0.000
#> SRR2936881 2 0.0000 0.998 0 1.000 0.000 0.000
#> SRR2936882 1 0.0000 1.000 1 0.000 0.000 0.000
#> SRR2936880 2 0.0000 0.998 0 1.000 0.000 0.000
#> SRR2936878 2 0.0000 0.998 0 1.000 0.000 0.000
#> SRR2936879 3 0.2469 0.778 0 0.108 0.892 0.000
#> SRR2936875 2 0.0188 0.998 0 0.996 0.004 0.000
#> SRR2936877 2 0.0000 0.998 0 1.000 0.000 0.000
#> SRR2936876 1 0.0000 1.000 1 0.000 0.000 0.000
#> SRR2936873 1 0.0000 1.000 1 0.000 0.000 0.000
#> SRR2936872 2 0.0188 0.998 0 0.996 0.004 0.000
#> SRR2936871 2 0.0188 0.998 0 0.996 0.004 0.000
#> SRR2936874 2 0.0188 0.998 0 0.996 0.004 0.000
#> SRR2936870 1 0.0000 1.000 1 0.000 0.000 0.000
#> SRR2936869 4 0.0000 1.000 0 0.000 0.000 1.000
#> SRR2936868 4 0.0000 1.000 0 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
#> SRR2936906 1 0.0000 0.988 1.000 0.000 0.000 0 0.000
#> SRR2936909 1 0.0000 0.988 1.000 0.000 0.000 0 0.000
#> SRR2936918 1 0.0000 0.988 1.000 0.000 0.000 0 0.000
#> SRR2936917 2 0.0000 0.906 0.000 1.000 0.000 0 0.000
#> SRR2936916 2 0.0290 0.904 0.000 0.992 0.000 0 0.008
#> SRR2936915 1 0.3242 0.725 0.784 0.000 0.000 0 0.216
#> SRR2936914 2 0.0000 0.906 0.000 1.000 0.000 0 0.000
#> SRR2936913 2 0.0000 0.906 0.000 1.000 0.000 0 0.000
#> SRR2936912 1 0.0000 0.988 1.000 0.000 0.000 0 0.000
#> SRR2936910 1 0.0000 0.988 1.000 0.000 0.000 0 0.000
#> SRR2936911 2 0.0000 0.906 0.000 1.000 0.000 0 0.000
#> SRR2936907 2 0.2966 0.879 0.000 0.816 0.000 0 0.184
#> SRR2936908 2 0.2966 0.879 0.000 0.816 0.000 0 0.184
#> SRR2936904 1 0.0000 0.988 1.000 0.000 0.000 0 0.000
#> SRR2936905 2 0.2966 0.879 0.000 0.816 0.000 0 0.184
#> SRR2936903 1 0.0000 0.988 1.000 0.000 0.000 0 0.000
#> SRR2936901 1 0.0000 0.988 1.000 0.000 0.000 0 0.000
#> SRR2936902 2 0.0290 0.904 0.000 0.992 0.000 0 0.008
#> SRR2936900 1 0.0000 0.988 1.000 0.000 0.000 0 0.000
#> SRR2936898 3 0.0000 1.000 0.000 0.000 1.000 0 0.000
#> SRR2936899 3 0.0000 1.000 0.000 0.000 1.000 0 0.000
#> SRR2936897 1 0.0000 0.988 1.000 0.000 0.000 0 0.000
#> SRR2936896 2 0.0000 0.906 0.000 1.000 0.000 0 0.000
#> SRR2936894 1 0.0000 0.988 1.000 0.000 0.000 0 0.000
#> SRR2936893 2 0.2966 0.879 0.000 0.816 0.000 0 0.184
#> SRR2936895 2 0.0162 0.905 0.000 0.996 0.000 0 0.004
#> SRR2936892 2 0.2966 0.879 0.000 0.816 0.000 0 0.184
#> SRR2936891 1 0.0000 0.988 1.000 0.000 0.000 0 0.000
#> SRR2936890 2 0.2966 0.879 0.000 0.816 0.000 0 0.184
#> SRR2936886 4 0.0000 1.000 0.000 0.000 0.000 1 0.000
#> SRR2936885 1 0.0000 0.988 1.000 0.000 0.000 0 0.000
#> SRR2936888 1 0.0000 0.988 1.000 0.000 0.000 0 0.000
#> SRR2936889 2 0.2966 0.879 0.000 0.816 0.000 0 0.184
#> SRR2936887 4 0.0000 1.000 0.000 0.000 0.000 1 0.000
#> SRR2936884 2 0.0290 0.904 0.000 0.992 0.000 0 0.008
#> SRR2936883 2 0.0290 0.904 0.000 0.992 0.000 0 0.008
#> SRR2936881 2 0.0290 0.904 0.000 0.992 0.000 0 0.008
#> SRR2936882 1 0.0000 0.988 1.000 0.000 0.000 0 0.000
#> SRR2936880 2 0.0290 0.904 0.000 0.992 0.000 0 0.008
#> SRR2936878 2 0.0000 0.906 0.000 1.000 0.000 0 0.000
#> SRR2936879 5 0.2843 0.000 0.000 0.008 0.144 0 0.848
#> SRR2936875 2 0.2966 0.879 0.000 0.816 0.000 0 0.184
#> SRR2936877 2 0.0000 0.906 0.000 1.000 0.000 0 0.000
#> SRR2936876 1 0.0000 0.988 1.000 0.000 0.000 0 0.000
#> SRR2936873 1 0.0000 0.988 1.000 0.000 0.000 0 0.000
#> SRR2936872 2 0.2966 0.879 0.000 0.816 0.000 0 0.184
#> SRR2936871 2 0.2966 0.879 0.000 0.816 0.000 0 0.184
#> SRR2936874 2 0.2966 0.879 0.000 0.816 0.000 0 0.184
#> SRR2936870 1 0.0000 0.988 1.000 0.000 0.000 0 0.000
#> SRR2936869 4 0.0000 1.000 0.000 0.000 0.000 1 0.000
#> SRR2936868 4 0.0000 1.000 0.000 0.000 0.000 1 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR2936906 1 0.0000 1.000 1.000 0.000 0.000 0 0.000 0.000
#> SRR2936909 1 0.0000 1.000 1.000 0.000 0.000 0 0.000 0.000
#> SRR2936918 1 0.0000 1.000 1.000 0.000 0.000 0 0.000 0.000
#> SRR2936917 2 0.3868 -0.961 0.000 0.508 0.492 0 0.000 0.000
#> SRR2936916 3 0.3868 1.000 0.000 0.496 0.504 0 0.000 0.000
#> SRR2936915 5 0.5171 -0.117 0.416 0.000 0.000 0 0.496 0.088
#> SRR2936914 2 0.3868 -0.961 0.000 0.508 0.492 0 0.000 0.000
#> SRR2936913 2 0.3868 -0.961 0.000 0.508 0.492 0 0.000 0.000
#> SRR2936912 1 0.0000 1.000 1.000 0.000 0.000 0 0.000 0.000
#> SRR2936910 1 0.0000 1.000 1.000 0.000 0.000 0 0.000 0.000
#> SRR2936911 2 0.3868 -0.961 0.000 0.508 0.492 0 0.000 0.000
#> SRR2936907 2 0.0000 0.560 0.000 1.000 0.000 0 0.000 0.000
#> SRR2936908 2 0.0000 0.560 0.000 1.000 0.000 0 0.000 0.000
#> SRR2936904 1 0.0146 0.995 0.996 0.000 0.000 0 0.004 0.000
#> SRR2936905 2 0.0000 0.560 0.000 1.000 0.000 0 0.000 0.000
#> SRR2936903 1 0.0000 1.000 1.000 0.000 0.000 0 0.000 0.000
#> SRR2936901 1 0.0000 1.000 1.000 0.000 0.000 0 0.000 0.000
#> SRR2936902 3 0.3868 1.000 0.000 0.496 0.504 0 0.000 0.000
#> SRR2936900 1 0.0000 1.000 1.000 0.000 0.000 0 0.000 0.000
#> SRR2936898 5 0.3868 0.286 0.000 0.000 0.496 0 0.504 0.000
#> SRR2936899 5 0.3868 0.286 0.000 0.000 0.496 0 0.504 0.000
#> SRR2936897 1 0.0000 1.000 1.000 0.000 0.000 0 0.000 0.000
#> SRR2936896 2 0.3868 -0.961 0.000 0.508 0.492 0 0.000 0.000
#> SRR2936894 1 0.0000 1.000 1.000 0.000 0.000 0 0.000 0.000
#> SRR2936893 2 0.0000 0.560 0.000 1.000 0.000 0 0.000 0.000
#> SRR2936895 2 0.3869 -0.987 0.000 0.500 0.500 0 0.000 0.000
#> SRR2936892 2 0.0000 0.560 0.000 1.000 0.000 0 0.000 0.000
#> SRR2936891 1 0.0000 1.000 1.000 0.000 0.000 0 0.000 0.000
#> SRR2936890 2 0.0000 0.560 0.000 1.000 0.000 0 0.000 0.000
#> SRR2936886 4 0.0000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> SRR2936885 1 0.0000 1.000 1.000 0.000 0.000 0 0.000 0.000
#> SRR2936888 1 0.0000 1.000 1.000 0.000 0.000 0 0.000 0.000
#> SRR2936889 2 0.0000 0.560 0.000 1.000 0.000 0 0.000 0.000
#> SRR2936887 4 0.0000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> SRR2936884 3 0.3868 1.000 0.000 0.496 0.504 0 0.000 0.000
#> SRR2936883 3 0.3868 1.000 0.000 0.496 0.504 0 0.000 0.000
#> SRR2936881 3 0.3868 1.000 0.000 0.496 0.504 0 0.000 0.000
#> SRR2936882 1 0.0000 1.000 1.000 0.000 0.000 0 0.000 0.000
#> SRR2936880 3 0.3868 1.000 0.000 0.496 0.504 0 0.000 0.000
#> SRR2936878 2 0.3868 -0.961 0.000 0.508 0.492 0 0.000 0.000
#> SRR2936879 6 0.0000 0.000 0.000 0.000 0.000 0 0.000 1.000
#> SRR2936875 2 0.0000 0.560 0.000 1.000 0.000 0 0.000 0.000
#> SRR2936877 2 0.3868 -0.961 0.000 0.508 0.492 0 0.000 0.000
#> SRR2936876 1 0.0000 1.000 1.000 0.000 0.000 0 0.000 0.000
#> SRR2936873 1 0.0000 1.000 1.000 0.000 0.000 0 0.000 0.000
#> SRR2936872 2 0.0000 0.560 0.000 1.000 0.000 0 0.000 0.000
#> SRR2936871 2 0.0000 0.560 0.000 1.000 0.000 0 0.000 0.000
#> SRR2936874 2 0.0000 0.560 0.000 1.000 0.000 0 0.000 0.000
#> SRR2936870 1 0.0000 1.000 1.000 0.000 0.000 0 0.000 0.000
#> SRR2936869 4 0.0000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> SRR2936868 4 0.0000 1.000 0.000 0.000 0.000 1 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
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 14198 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.960 0.985 0.4658 0.534 0.534
#> 3 3 1.000 0.920 0.973 0.4181 0.749 0.552
#> 4 4 1.000 0.990 0.996 0.1053 0.861 0.627
#> 5 5 0.881 0.936 0.900 0.0762 0.934 0.757
#> 6 6 0.887 0.896 0.919 0.0574 0.961 0.809
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR2936906 1 0.000 0.977 1.000 0.000
#> SRR2936909 1 0.000 0.977 1.000 0.000
#> SRR2936918 1 0.000 0.977 1.000 0.000
#> SRR2936917 2 0.000 0.988 0.000 1.000
#> SRR2936916 2 0.000 0.988 0.000 1.000
#> SRR2936915 2 0.000 0.988 0.000 1.000
#> SRR2936914 2 0.000 0.988 0.000 1.000
#> SRR2936913 2 0.000 0.988 0.000 1.000
#> SRR2936912 1 0.000 0.977 1.000 0.000
#> SRR2936910 1 0.000 0.977 1.000 0.000
#> SRR2936911 2 0.000 0.988 0.000 1.000
#> SRR2936907 2 0.000 0.988 0.000 1.000
#> SRR2936908 2 0.000 0.988 0.000 1.000
#> SRR2936904 1 0.000 0.977 1.000 0.000
#> SRR2936905 2 0.000 0.988 0.000 1.000
#> SRR2936903 1 0.000 0.977 1.000 0.000
#> SRR2936901 1 0.958 0.370 0.620 0.380
#> SRR2936902 2 0.000 0.988 0.000 1.000
#> SRR2936900 1 0.000 0.977 1.000 0.000
#> SRR2936898 2 0.000 0.988 0.000 1.000
#> SRR2936899 2 0.000 0.988 0.000 1.000
#> SRR2936897 1 0.000 0.977 1.000 0.000
#> SRR2936896 2 0.000 0.988 0.000 1.000
#> SRR2936894 1 0.000 0.977 1.000 0.000
#> SRR2936893 2 0.000 0.988 0.000 1.000
#> SRR2936895 2 0.000 0.988 0.000 1.000
#> SRR2936892 2 0.000 0.988 0.000 1.000
#> SRR2936891 1 0.000 0.977 1.000 0.000
#> SRR2936890 2 0.000 0.988 0.000 1.000
#> SRR2936886 2 0.000 0.988 0.000 1.000
#> SRR2936885 1 0.000 0.977 1.000 0.000
#> SRR2936888 1 0.000 0.977 1.000 0.000
#> SRR2936889 2 0.000 0.988 0.000 1.000
#> SRR2936887 2 0.000 0.988 0.000 1.000
#> SRR2936884 2 0.000 0.988 0.000 1.000
#> SRR2936883 2 0.000 0.988 0.000 1.000
#> SRR2936881 2 0.000 0.988 0.000 1.000
#> SRR2936882 1 0.000 0.977 1.000 0.000
#> SRR2936880 2 0.000 0.988 0.000 1.000
#> SRR2936878 2 0.000 0.988 0.000 1.000
#> SRR2936879 2 0.000 0.988 0.000 1.000
#> SRR2936875 2 0.000 0.988 0.000 1.000
#> SRR2936877 2 0.000 0.988 0.000 1.000
#> SRR2936876 1 0.000 0.977 1.000 0.000
#> SRR2936873 1 0.000 0.977 1.000 0.000
#> SRR2936872 2 0.000 0.988 0.000 1.000
#> SRR2936871 2 0.000 0.988 0.000 1.000
#> SRR2936874 2 0.000 0.988 0.000 1.000
#> SRR2936870 1 0.000 0.977 1.000 0.000
#> SRR2936869 2 0.000 0.988 0.000 1.000
#> SRR2936868 2 0.955 0.371 0.376 0.624
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR2936906 1 0.000 1.0000 1 0.000 0.000
#> SRR2936909 1 0.000 1.0000 1 0.000 0.000
#> SRR2936918 1 0.000 1.0000 1 0.000 0.000
#> SRR2936917 2 0.000 0.9764 0 1.000 0.000
#> SRR2936916 3 0.000 0.9180 0 0.000 1.000
#> SRR2936915 3 0.000 0.9180 0 0.000 1.000
#> SRR2936914 2 0.000 0.9764 0 1.000 0.000
#> SRR2936913 2 0.000 0.9764 0 1.000 0.000
#> SRR2936912 1 0.000 1.0000 1 0.000 0.000
#> SRR2936910 1 0.000 1.0000 1 0.000 0.000
#> SRR2936911 2 0.000 0.9764 0 1.000 0.000
#> SRR2936907 2 0.000 0.9764 0 1.000 0.000
#> SRR2936908 2 0.000 0.9764 0 1.000 0.000
#> SRR2936904 3 0.000 0.9180 0 0.000 1.000
#> SRR2936905 2 0.000 0.9764 0 1.000 0.000
#> SRR2936903 1 0.000 1.0000 1 0.000 0.000
#> SRR2936901 3 0.000 0.9180 0 0.000 1.000
#> SRR2936902 3 0.629 0.1495 0 0.468 0.532
#> SRR2936900 1 0.000 1.0000 1 0.000 0.000
#> SRR2936898 3 0.000 0.9180 0 0.000 1.000
#> SRR2936899 3 0.000 0.9180 0 0.000 1.000
#> SRR2936897 1 0.000 1.0000 1 0.000 0.000
#> SRR2936896 2 0.000 0.9764 0 1.000 0.000
#> SRR2936894 1 0.000 1.0000 1 0.000 0.000
#> SRR2936893 2 0.000 0.9764 0 1.000 0.000
#> SRR2936895 2 0.000 0.9764 0 1.000 0.000
#> SRR2936892 2 0.000 0.9764 0 1.000 0.000
#> SRR2936891 1 0.000 1.0000 1 0.000 0.000
#> SRR2936890 2 0.000 0.9764 0 1.000 0.000
#> SRR2936886 3 0.000 0.9180 0 0.000 1.000
#> SRR2936885 1 0.000 1.0000 1 0.000 0.000
#> SRR2936888 1 0.000 1.0000 1 0.000 0.000
#> SRR2936889 2 0.000 0.9764 0 1.000 0.000
#> SRR2936887 3 0.000 0.9180 0 0.000 1.000
#> SRR2936884 2 0.000 0.9764 0 1.000 0.000
#> SRR2936883 2 0.625 0.0789 0 0.556 0.444
#> SRR2936881 3 0.629 0.1495 0 0.468 0.532
#> SRR2936882 1 0.000 1.0000 1 0.000 0.000
#> SRR2936880 2 0.000 0.9764 0 1.000 0.000
#> SRR2936878 2 0.000 0.9764 0 1.000 0.000
#> SRR2936879 3 0.000 0.9180 0 0.000 1.000
#> SRR2936875 2 0.000 0.9764 0 1.000 0.000
#> SRR2936877 2 0.000 0.9764 0 1.000 0.000
#> SRR2936876 3 0.000 0.9180 0 0.000 1.000
#> SRR2936873 1 0.000 1.0000 1 0.000 0.000
#> SRR2936872 2 0.000 0.9764 0 1.000 0.000
#> SRR2936871 2 0.000 0.9764 0 1.000 0.000
#> SRR2936874 2 0.000 0.9764 0 1.000 0.000
#> SRR2936870 1 0.000 1.0000 1 0.000 0.000
#> SRR2936869 3 0.000 0.9180 0 0.000 1.000
#> SRR2936868 3 0.000 0.9180 0 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR2936906 1 0.000 1.000 1 0.000 0.000 0
#> SRR2936909 1 0.000 1.000 1 0.000 0.000 0
#> SRR2936918 1 0.000 1.000 1 0.000 0.000 0
#> SRR2936917 4 0.000 1.000 0 0.000 0.000 1
#> SRR2936916 2 0.373 0.731 0 0.788 0.212 0
#> SRR2936915 3 0.000 1.000 0 0.000 1.000 0
#> SRR2936914 4 0.000 1.000 0 0.000 0.000 1
#> SRR2936913 4 0.000 1.000 0 0.000 0.000 1
#> SRR2936912 1 0.000 1.000 1 0.000 0.000 0
#> SRR2936910 1 0.000 1.000 1 0.000 0.000 0
#> SRR2936911 4 0.000 1.000 0 0.000 0.000 1
#> SRR2936907 2 0.000 0.987 0 1.000 0.000 0
#> SRR2936908 2 0.000 0.987 0 1.000 0.000 0
#> SRR2936904 3 0.000 1.000 0 0.000 1.000 0
#> SRR2936905 2 0.000 0.987 0 1.000 0.000 0
#> SRR2936903 1 0.000 1.000 1 0.000 0.000 0
#> SRR2936901 3 0.000 1.000 0 0.000 1.000 0
#> SRR2936902 2 0.000 0.987 0 1.000 0.000 0
#> SRR2936900 1 0.000 1.000 1 0.000 0.000 0
#> SRR2936898 3 0.000 1.000 0 0.000 1.000 0
#> SRR2936899 3 0.000 1.000 0 0.000 1.000 0
#> SRR2936897 1 0.000 1.000 1 0.000 0.000 0
#> SRR2936896 2 0.000 0.987 0 1.000 0.000 0
#> SRR2936894 1 0.000 1.000 1 0.000 0.000 0
#> SRR2936893 2 0.000 0.987 0 1.000 0.000 0
#> SRR2936895 2 0.000 0.987 0 1.000 0.000 0
#> SRR2936892 2 0.000 0.987 0 1.000 0.000 0
#> SRR2936891 1 0.000 1.000 1 0.000 0.000 0
#> SRR2936890 2 0.000 0.987 0 1.000 0.000 0
#> SRR2936886 3 0.000 1.000 0 0.000 1.000 0
#> SRR2936885 1 0.000 1.000 1 0.000 0.000 0
#> SRR2936888 1 0.000 1.000 1 0.000 0.000 0
#> SRR2936889 2 0.000 0.987 0 1.000 0.000 0
#> SRR2936887 3 0.000 1.000 0 0.000 1.000 0
#> SRR2936884 2 0.000 0.987 0 1.000 0.000 0
#> SRR2936883 2 0.000 0.987 0 1.000 0.000 0
#> SRR2936881 2 0.000 0.987 0 1.000 0.000 0
#> SRR2936882 1 0.000 1.000 1 0.000 0.000 0
#> SRR2936880 2 0.000 0.987 0 1.000 0.000 0
#> SRR2936878 4 0.000 1.000 0 0.000 0.000 1
#> SRR2936879 3 0.000 1.000 0 0.000 1.000 0
#> SRR2936875 2 0.000 0.987 0 1.000 0.000 0
#> SRR2936877 4 0.000 1.000 0 0.000 0.000 1
#> SRR2936876 3 0.000 1.000 0 0.000 1.000 0
#> SRR2936873 1 0.000 1.000 1 0.000 0.000 0
#> SRR2936872 2 0.000 0.987 0 1.000 0.000 0
#> SRR2936871 2 0.000 0.987 0 1.000 0.000 0
#> SRR2936874 2 0.000 0.987 0 1.000 0.000 0
#> SRR2936870 1 0.000 1.000 1 0.000 0.000 0
#> SRR2936869 3 0.000 1.000 0 0.000 1.000 0
#> SRR2936868 3 0.000 1.000 0 0.000 1.000 0
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR2936906 1 0.0000 0.801 1.000 0.000 0.000 0.000 0
#> SRR2936909 1 0.4182 0.835 0.600 0.000 0.400 0.000 0
#> SRR2936918 1 0.3143 0.857 0.796 0.000 0.204 0.000 0
#> SRR2936917 5 0.0000 1.000 0.000 0.000 0.000 0.000 1
#> SRR2936916 3 0.5844 0.716 0.000 0.244 0.600 0.156 0
#> SRR2936915 4 0.0000 0.994 0.000 0.000 0.000 1.000 0
#> SRR2936914 5 0.0000 1.000 0.000 0.000 0.000 0.000 1
#> SRR2936913 5 0.0000 1.000 0.000 0.000 0.000 0.000 1
#> SRR2936912 1 0.4182 0.835 0.600 0.000 0.400 0.000 0
#> SRR2936910 1 0.4088 0.843 0.632 0.000 0.368 0.000 0
#> SRR2936911 5 0.0000 1.000 0.000 0.000 0.000 0.000 1
#> SRR2936907 2 0.0000 1.000 0.000 1.000 0.000 0.000 0
#> SRR2936908 2 0.0000 1.000 0.000 1.000 0.000 0.000 0
#> SRR2936904 4 0.0880 0.972 0.000 0.000 0.032 0.968 0
#> SRR2936905 2 0.0000 1.000 0.000 1.000 0.000 0.000 0
#> SRR2936903 1 0.4182 0.835 0.600 0.000 0.400 0.000 0
#> SRR2936901 4 0.0000 0.994 0.000 0.000 0.000 1.000 0
#> SRR2936902 3 0.4182 0.946 0.000 0.400 0.600 0.000 0
#> SRR2936900 1 0.3143 0.857 0.796 0.000 0.204 0.000 0
#> SRR2936898 4 0.0000 0.994 0.000 0.000 0.000 1.000 0
#> SRR2936899 4 0.0000 0.994 0.000 0.000 0.000 1.000 0
#> SRR2936897 1 0.4182 0.835 0.600 0.000 0.400 0.000 0
#> SRR2936896 2 0.0000 1.000 0.000 1.000 0.000 0.000 0
#> SRR2936894 1 0.0000 0.801 1.000 0.000 0.000 0.000 0
#> SRR2936893 2 0.0000 1.000 0.000 1.000 0.000 0.000 0
#> SRR2936895 3 0.4182 0.946 0.000 0.400 0.600 0.000 0
#> SRR2936892 2 0.0000 1.000 0.000 1.000 0.000 0.000 0
#> SRR2936891 1 0.0000 0.801 1.000 0.000 0.000 0.000 0
#> SRR2936890 2 0.0000 1.000 0.000 1.000 0.000 0.000 0
#> SRR2936886 4 0.0000 0.994 0.000 0.000 0.000 1.000 0
#> SRR2936885 1 0.3612 0.856 0.732 0.000 0.268 0.000 0
#> SRR2936888 1 0.0000 0.801 1.000 0.000 0.000 0.000 0
#> SRR2936889 2 0.0000 1.000 0.000 1.000 0.000 0.000 0
#> SRR2936887 4 0.0000 0.994 0.000 0.000 0.000 1.000 0
#> SRR2936884 3 0.4182 0.946 0.000 0.400 0.600 0.000 0
#> SRR2936883 3 0.4182 0.946 0.000 0.400 0.600 0.000 0
#> SRR2936881 3 0.4182 0.946 0.000 0.400 0.600 0.000 0
#> SRR2936882 1 0.3143 0.857 0.796 0.000 0.204 0.000 0
#> SRR2936880 3 0.4182 0.946 0.000 0.400 0.600 0.000 0
#> SRR2936878 5 0.0000 1.000 0.000 0.000 0.000 0.000 1
#> SRR2936879 4 0.0000 0.994 0.000 0.000 0.000 1.000 0
#> SRR2936875 2 0.0000 1.000 0.000 1.000 0.000 0.000 0
#> SRR2936877 5 0.0000 1.000 0.000 0.000 0.000 0.000 1
#> SRR2936876 4 0.0963 0.968 0.000 0.000 0.036 0.964 0
#> SRR2936873 1 0.4101 0.843 0.628 0.000 0.372 0.000 0
#> SRR2936872 2 0.0000 1.000 0.000 1.000 0.000 0.000 0
#> SRR2936871 2 0.0000 1.000 0.000 1.000 0.000 0.000 0
#> SRR2936874 2 0.0000 1.000 0.000 1.000 0.000 0.000 0
#> SRR2936870 1 0.0000 0.801 1.000 0.000 0.000 0.000 0
#> SRR2936869 4 0.0000 0.994 0.000 0.000 0.000 1.000 0
#> SRR2936868 4 0.0000 0.994 0.000 0.000 0.000 1.000 0
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR2936906 1 0.000 1.000 1.000 0.0 0.0 0.000 0 0.000
#> SRR2936909 6 0.279 0.794 0.200 0.0 0.0 0.000 0 0.800
#> SRR2936918 6 0.387 0.685 0.488 0.0 0.0 0.000 0 0.512
#> SRR2936917 5 0.000 1.000 0.000 0.0 0.0 0.000 1 0.000
#> SRR2936916 3 0.000 0.920 0.000 0.0 1.0 0.000 0 0.000
#> SRR2936915 4 0.279 0.899 0.000 0.0 0.0 0.800 0 0.200
#> SRR2936914 5 0.000 1.000 0.000 0.0 0.0 0.000 1 0.000
#> SRR2936913 5 0.000 1.000 0.000 0.0 0.0 0.000 1 0.000
#> SRR2936912 6 0.279 0.794 0.200 0.0 0.0 0.000 0 0.800
#> SRR2936910 6 0.352 0.804 0.324 0.0 0.0 0.000 0 0.676
#> SRR2936911 5 0.000 1.000 0.000 0.0 0.0 0.000 1 0.000
#> SRR2936907 2 0.000 0.980 0.000 1.0 0.0 0.000 0 0.000
#> SRR2936908 2 0.000 0.980 0.000 1.0 0.0 0.000 0 0.000
#> SRR2936904 4 0.150 0.848 0.000 0.0 0.0 0.924 0 0.076
#> SRR2936905 2 0.000 0.980 0.000 1.0 0.0 0.000 0 0.000
#> SRR2936903 6 0.279 0.794 0.200 0.0 0.0 0.000 0 0.800
#> SRR2936901 4 0.279 0.899 0.000 0.0 0.0 0.800 0 0.200
#> SRR2936902 3 0.000 0.920 0.000 0.0 1.0 0.000 0 0.000
#> SRR2936900 6 0.387 0.685 0.488 0.0 0.0 0.000 0 0.512
#> SRR2936898 4 0.279 0.899 0.000 0.0 0.0 0.800 0 0.200
#> SRR2936899 4 0.279 0.899 0.000 0.0 0.0 0.800 0 0.200
#> SRR2936897 6 0.279 0.794 0.200 0.0 0.0 0.000 0 0.800
#> SRR2936896 2 0.000 0.980 0.000 1.0 0.0 0.000 0 0.000
#> SRR2936894 1 0.000 1.000 1.000 0.0 0.0 0.000 0 0.000
#> SRR2936893 2 0.000 0.980 0.000 1.0 0.0 0.000 0 0.000
#> SRR2936895 3 0.000 0.920 0.000 0.0 1.0 0.000 0 0.000
#> SRR2936892 2 0.000 0.980 0.000 1.0 0.0 0.000 0 0.000
#> SRR2936891 1 0.000 1.000 1.000 0.0 0.0 0.000 0 0.000
#> SRR2936890 2 0.000 0.980 0.000 1.0 0.0 0.000 0 0.000
#> SRR2936886 4 0.000 0.884 0.000 0.0 0.0 1.000 0 0.000
#> SRR2936885 6 0.377 0.761 0.408 0.0 0.0 0.000 0 0.592
#> SRR2936888 1 0.000 1.000 1.000 0.0 0.0 0.000 0 0.000
#> SRR2936889 2 0.000 0.980 0.000 1.0 0.0 0.000 0 0.000
#> SRR2936887 4 0.000 0.884 0.000 0.0 0.0 1.000 0 0.000
#> SRR2936884 3 0.376 0.338 0.000 0.4 0.6 0.000 0 0.000
#> SRR2936883 3 0.000 0.920 0.000 0.0 1.0 0.000 0 0.000
#> SRR2936881 3 0.000 0.920 0.000 0.0 1.0 0.000 0 0.000
#> SRR2936882 6 0.387 0.685 0.488 0.0 0.0 0.000 0 0.512
#> SRR2936880 3 0.000 0.920 0.000 0.0 1.0 0.000 0 0.000
#> SRR2936878 5 0.000 1.000 0.000 0.0 0.0 0.000 1 0.000
#> SRR2936879 4 0.279 0.899 0.000 0.0 0.0 0.800 0 0.200
#> SRR2936875 2 0.000 0.980 0.000 1.0 0.0 0.000 0 0.000
#> SRR2936877 5 0.000 1.000 0.000 0.0 0.0 0.000 1 0.000
#> SRR2936876 4 0.353 0.825 0.000 0.0 0.0 0.672 0 0.328
#> SRR2936873 6 0.350 0.805 0.320 0.0 0.0 0.000 0 0.680
#> SRR2936872 2 0.000 0.980 0.000 1.0 0.0 0.000 0 0.000
#> SRR2936871 2 0.000 0.980 0.000 1.0 0.0 0.000 0 0.000
#> SRR2936874 2 0.279 0.729 0.000 0.8 0.2 0.000 0 0.000
#> SRR2936870 1 0.000 1.000 1.000 0.0 0.0 0.000 0 0.000
#> SRR2936869 4 0.000 0.884 0.000 0.0 0.0 1.000 0 0.000
#> SRR2936868 4 0.000 0.884 0.000 0.0 0.0 1.000 0 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 14198 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 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.990 0.988 0.3250 0.678 0.678
#> 3 3 0.515 0.937 0.930 0.5492 0.835 0.757
#> 4 4 0.714 0.740 0.805 0.2876 0.852 0.716
#> 5 5 0.824 0.813 0.893 0.1904 0.812 0.522
#> 6 6 0.890 0.852 0.924 0.0762 0.926 0.679
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
#> SRR2936906 1 0.0000 0.991 1.000 0.000
#> SRR2936909 1 0.0000 0.991 1.000 0.000
#> SRR2936918 1 0.0000 0.991 1.000 0.000
#> SRR2936917 1 0.2236 0.978 0.964 0.036
#> SRR2936916 1 0.0672 0.989 0.992 0.008
#> SRR2936915 1 0.0376 0.990 0.996 0.004
#> SRR2936914 1 0.2236 0.978 0.964 0.036
#> SRR2936913 1 0.2236 0.978 0.964 0.036
#> SRR2936912 1 0.0000 0.991 1.000 0.000
#> SRR2936910 1 0.0000 0.991 1.000 0.000
#> SRR2936911 1 0.2236 0.978 0.964 0.036
#> SRR2936907 2 0.1184 1.000 0.016 0.984
#> SRR2936908 2 0.1184 1.000 0.016 0.984
#> SRR2936904 1 0.0938 0.988 0.988 0.012
#> SRR2936905 2 0.1184 1.000 0.016 0.984
#> SRR2936903 1 0.0000 0.991 1.000 0.000
#> SRR2936901 1 0.0000 0.991 1.000 0.000
#> SRR2936902 1 0.0000 0.991 1.000 0.000
#> SRR2936900 1 0.0000 0.991 1.000 0.000
#> SRR2936898 1 0.0376 0.990 0.996 0.004
#> SRR2936899 1 0.0672 0.989 0.992 0.008
#> SRR2936897 1 0.0000 0.991 1.000 0.000
#> SRR2936896 1 0.1633 0.984 0.976 0.024
#> SRR2936894 1 0.0000 0.991 1.000 0.000
#> SRR2936893 2 0.1184 1.000 0.016 0.984
#> SRR2936895 1 0.0672 0.989 0.992 0.008
#> SRR2936892 1 0.2043 0.978 0.968 0.032
#> SRR2936891 1 0.0000 0.991 1.000 0.000
#> SRR2936890 2 0.1184 1.000 0.016 0.984
#> SRR2936886 1 0.0938 0.988 0.988 0.012
#> SRR2936885 1 0.0000 0.991 1.000 0.000
#> SRR2936888 1 0.0000 0.991 1.000 0.000
#> SRR2936889 2 0.1184 1.000 0.016 0.984
#> SRR2936887 1 0.0938 0.988 0.988 0.012
#> SRR2936884 1 0.1184 0.986 0.984 0.016
#> SRR2936883 1 0.1184 0.986 0.984 0.016
#> SRR2936881 1 0.0938 0.988 0.988 0.012
#> SRR2936882 1 0.0000 0.991 1.000 0.000
#> SRR2936880 1 0.1184 0.986 0.984 0.016
#> SRR2936878 1 0.2236 0.978 0.964 0.036
#> SRR2936879 1 0.0376 0.990 0.996 0.004
#> SRR2936875 2 0.1184 1.000 0.016 0.984
#> SRR2936877 1 0.2236 0.978 0.964 0.036
#> SRR2936876 1 0.0000 0.991 1.000 0.000
#> SRR2936873 1 0.0000 0.991 1.000 0.000
#> SRR2936872 2 0.1184 1.000 0.016 0.984
#> SRR2936871 2 0.1184 1.000 0.016 0.984
#> SRR2936874 2 0.1184 1.000 0.016 0.984
#> SRR2936870 1 0.0000 0.991 1.000 0.000
#> SRR2936869 1 0.0938 0.988 0.988 0.012
#> SRR2936868 1 0.0938 0.988 0.988 0.012
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR2936906 1 0.3482 0.917 0.872 0.128 0.000
#> SRR2936909 1 0.0000 0.908 1.000 0.000 0.000
#> SRR2936918 1 0.3482 0.917 0.872 0.128 0.000
#> SRR2936917 3 0.3482 1.000 0.128 0.000 0.872
#> SRR2936916 1 0.0000 0.908 1.000 0.000 0.000
#> SRR2936915 1 0.3482 0.917 0.872 0.128 0.000
#> SRR2936914 3 0.3482 1.000 0.128 0.000 0.872
#> SRR2936913 3 0.3482 1.000 0.128 0.000 0.872
#> SRR2936912 1 0.3482 0.917 0.872 0.128 0.000
#> SRR2936910 1 0.3482 0.917 0.872 0.128 0.000
#> SRR2936911 3 0.3482 1.000 0.128 0.000 0.872
#> SRR2936907 2 0.0000 1.000 0.000 1.000 0.000
#> SRR2936908 2 0.0000 1.000 0.000 1.000 0.000
#> SRR2936904 1 0.3482 0.917 0.872 0.128 0.000
#> SRR2936905 2 0.0000 1.000 0.000 1.000 0.000
#> SRR2936903 1 0.0000 0.908 1.000 0.000 0.000
#> SRR2936901 1 0.0000 0.908 1.000 0.000 0.000
#> SRR2936902 1 0.0000 0.908 1.000 0.000 0.000
#> SRR2936900 1 0.0000 0.908 1.000 0.000 0.000
#> SRR2936898 1 0.3482 0.917 0.872 0.128 0.000
#> SRR2936899 1 0.3482 0.917 0.872 0.128 0.000
#> SRR2936897 1 0.3482 0.917 0.872 0.128 0.000
#> SRR2936896 1 0.0000 0.908 1.000 0.000 0.000
#> SRR2936894 1 0.3482 0.917 0.872 0.128 0.000
#> SRR2936893 2 0.0000 1.000 0.000 1.000 0.000
#> SRR2936895 1 0.0000 0.908 1.000 0.000 0.000
#> SRR2936892 1 0.4002 0.896 0.840 0.160 0.000
#> SRR2936891 1 0.3482 0.917 0.872 0.128 0.000
#> SRR2936890 2 0.0000 1.000 0.000 1.000 0.000
#> SRR2936886 1 0.3482 0.895 0.872 0.000 0.128
#> SRR2936885 1 0.3482 0.917 0.872 0.128 0.000
#> SRR2936888 1 0.3482 0.895 0.872 0.000 0.128
#> SRR2936889 2 0.0000 1.000 0.000 1.000 0.000
#> SRR2936887 1 0.3482 0.895 0.872 0.000 0.128
#> SRR2936884 1 0.0892 0.902 0.980 0.020 0.000
#> SRR2936883 1 0.1289 0.907 0.968 0.032 0.000
#> SRR2936881 1 0.0892 0.902 0.980 0.020 0.000
#> SRR2936882 1 0.0000 0.908 1.000 0.000 0.000
#> SRR2936880 1 0.0892 0.902 0.980 0.020 0.000
#> SRR2936878 3 0.3482 1.000 0.128 0.000 0.872
#> SRR2936879 1 0.3482 0.917 0.872 0.128 0.000
#> SRR2936875 2 0.0000 1.000 0.000 1.000 0.000
#> SRR2936877 3 0.3482 1.000 0.128 0.000 0.872
#> SRR2936876 1 0.0000 0.908 1.000 0.000 0.000
#> SRR2936873 1 0.3482 0.917 0.872 0.128 0.000
#> SRR2936872 2 0.0000 1.000 0.000 1.000 0.000
#> SRR2936871 2 0.0000 1.000 0.000 1.000 0.000
#> SRR2936874 2 0.0000 1.000 0.000 1.000 0.000
#> SRR2936870 1 0.3482 0.895 0.872 0.000 0.128
#> SRR2936869 1 0.3482 0.895 0.872 0.000 0.128
#> SRR2936868 1 0.3482 0.895 0.872 0.000 0.128
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR2936906 1 0.0000 0.6539 1.000 0.000 0.000 0.000
#> SRR2936909 1 0.4406 0.7121 0.700 0.000 0.000 0.300
#> SRR2936918 1 0.0000 0.6539 1.000 0.000 0.000 0.000
#> SRR2936917 3 0.4543 1.0000 0.000 0.000 0.676 0.324
#> SRR2936916 1 0.6423 0.6449 0.544 0.008 0.052 0.396
#> SRR2936915 1 0.5476 0.6846 0.584 0.020 0.000 0.396
#> SRR2936914 3 0.4543 1.0000 0.000 0.000 0.676 0.324
#> SRR2936913 3 0.4543 1.0000 0.000 0.000 0.676 0.324
#> SRR2936912 1 0.0469 0.6548 0.988 0.000 0.012 0.000
#> SRR2936910 1 0.0469 0.6548 0.988 0.000 0.012 0.000
#> SRR2936911 3 0.4543 1.0000 0.000 0.000 0.676 0.324
#> SRR2936907 2 0.0000 0.9864 0.000 1.000 0.000 0.000
#> SRR2936908 2 0.0000 0.9864 0.000 1.000 0.000 0.000
#> SRR2936904 1 0.8932 0.0715 0.496 0.132 0.208 0.164
#> SRR2936905 2 0.0000 0.9864 0.000 1.000 0.000 0.000
#> SRR2936903 1 0.4564 0.7090 0.672 0.000 0.000 0.328
#> SRR2936901 1 0.4543 0.7095 0.676 0.000 0.000 0.324
#> SRR2936902 1 0.5268 0.6879 0.592 0.012 0.000 0.396
#> SRR2936900 1 0.0188 0.6516 0.996 0.000 0.000 0.004
#> SRR2936898 1 0.5268 0.6858 0.592 0.000 0.012 0.396
#> SRR2936899 1 0.5476 0.6846 0.584 0.020 0.000 0.396
#> SRR2936897 1 0.4522 0.7104 0.680 0.000 0.000 0.320
#> SRR2936896 4 0.7716 -0.5655 0.380 0.000 0.224 0.396
#> SRR2936894 1 0.0469 0.6548 0.988 0.000 0.012 0.000
#> SRR2936893 2 0.0000 0.9864 0.000 1.000 0.000 0.000
#> SRR2936895 1 0.6121 0.6495 0.552 0.000 0.052 0.396
#> SRR2936892 2 0.2081 0.8607 0.084 0.916 0.000 0.000
#> SRR2936891 1 0.0469 0.6548 0.988 0.000 0.012 0.000
#> SRR2936890 2 0.0000 0.9864 0.000 1.000 0.000 0.000
#> SRR2936886 4 0.6258 0.7061 0.076 0.000 0.324 0.600
#> SRR2936885 1 0.4543 0.7095 0.676 0.000 0.000 0.324
#> SRR2936888 1 0.0000 0.6539 1.000 0.000 0.000 0.000
#> SRR2936889 2 0.0000 0.9864 0.000 1.000 0.000 0.000
#> SRR2936887 4 0.6258 0.7061 0.076 0.000 0.324 0.600
#> SRR2936884 1 0.7089 0.6198 0.516 0.040 0.048 0.396
#> SRR2936883 1 0.6575 0.6484 0.540 0.048 0.016 0.396
#> SRR2936881 1 0.7089 0.6198 0.516 0.040 0.048 0.396
#> SRR2936882 1 0.0188 0.6516 0.996 0.000 0.000 0.004
#> SRR2936880 1 0.7089 0.6198 0.516 0.040 0.048 0.396
#> SRR2936878 3 0.4543 1.0000 0.000 0.000 0.676 0.324
#> SRR2936879 1 0.5268 0.6879 0.592 0.012 0.000 0.396
#> SRR2936875 2 0.0188 0.9829 0.000 0.996 0.000 0.004
#> SRR2936877 3 0.4543 1.0000 0.000 0.000 0.676 0.324
#> SRR2936876 1 0.4543 0.7095 0.676 0.000 0.000 0.324
#> SRR2936873 1 0.0000 0.6539 1.000 0.000 0.000 0.000
#> SRR2936872 2 0.0000 0.9864 0.000 1.000 0.000 0.000
#> SRR2936871 2 0.0000 0.9864 0.000 1.000 0.000 0.000
#> SRR2936874 2 0.0000 0.9864 0.000 1.000 0.000 0.000
#> SRR2936870 1 0.0000 0.6539 1.000 0.000 0.000 0.000
#> SRR2936869 4 0.6258 0.7061 0.076 0.000 0.324 0.600
#> SRR2936868 4 0.6258 0.7061 0.076 0.000 0.324 0.600
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR2936906 1 0.0162 0.801 0.996 0.000 0.004 0.000 0.000
#> SRR2936909 1 0.4341 0.577 0.592 0.000 0.404 0.000 0.004
#> SRR2936918 1 0.0162 0.801 0.996 0.000 0.004 0.000 0.000
#> SRR2936917 5 0.1478 1.000 0.000 0.000 0.064 0.000 0.936
#> SRR2936916 3 0.3291 0.833 0.000 0.040 0.840 0.000 0.120
#> SRR2936915 3 0.1965 0.849 0.024 0.052 0.924 0.000 0.000
#> SRR2936914 5 0.1478 1.000 0.000 0.000 0.064 0.000 0.936
#> SRR2936913 5 0.1478 1.000 0.000 0.000 0.064 0.000 0.936
#> SRR2936912 1 0.0162 0.801 0.996 0.000 0.004 0.000 0.000
#> SRR2936910 1 0.0162 0.801 0.996 0.000 0.004 0.000 0.000
#> SRR2936911 5 0.1478 1.000 0.000 0.000 0.064 0.000 0.936
#> SRR2936907 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> SRR2936908 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> SRR2936904 4 0.6274 -0.039 0.420 0.016 0.072 0.484 0.008
#> SRR2936905 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> SRR2936903 1 0.5973 0.572 0.552 0.000 0.360 0.024 0.064
#> SRR2936901 3 0.5461 -0.256 0.408 0.000 0.528 0.000 0.064
#> SRR2936902 3 0.2260 0.758 0.028 0.000 0.908 0.000 0.064
#> SRR2936900 1 0.4582 0.729 0.764 0.000 0.164 0.024 0.048
#> SRR2936898 3 0.1830 0.854 0.004 0.052 0.932 0.000 0.012
#> SRR2936899 3 0.1670 0.852 0.012 0.052 0.936 0.000 0.000
#> SRR2936897 1 0.4182 0.570 0.600 0.000 0.400 0.000 0.000
#> SRR2936896 3 0.3010 0.790 0.004 0.000 0.824 0.000 0.172
#> SRR2936894 1 0.0162 0.801 0.996 0.000 0.004 0.000 0.000
#> SRR2936893 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> SRR2936895 3 0.3495 0.797 0.028 0.000 0.812 0.000 0.160
#> SRR2936892 2 0.1502 0.936 0.000 0.940 0.004 0.056 0.000
#> SRR2936891 1 0.0162 0.801 0.996 0.000 0.004 0.000 0.000
#> SRR2936890 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> SRR2936886 4 0.0703 0.839 0.024 0.000 0.000 0.976 0.000
#> SRR2936885 1 0.3586 0.674 0.736 0.000 0.264 0.000 0.000
#> SRR2936888 1 0.0865 0.790 0.972 0.000 0.004 0.024 0.000
#> SRR2936889 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> SRR2936887 4 0.0703 0.839 0.024 0.000 0.000 0.976 0.000
#> SRR2936884 3 0.3226 0.842 0.000 0.060 0.852 0.000 0.088
#> SRR2936883 3 0.1638 0.851 0.000 0.064 0.932 0.000 0.004
#> SRR2936881 3 0.3359 0.838 0.000 0.052 0.840 0.000 0.108
#> SRR2936882 1 0.4582 0.729 0.764 0.000 0.164 0.024 0.048
#> SRR2936880 3 0.3359 0.838 0.000 0.052 0.840 0.000 0.108
#> SRR2936878 5 0.1478 1.000 0.000 0.000 0.064 0.000 0.936
#> SRR2936879 3 0.1597 0.852 0.012 0.048 0.940 0.000 0.000
#> SRR2936875 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> SRR2936877 5 0.1478 1.000 0.000 0.000 0.064 0.000 0.936
#> SRR2936876 1 0.4497 0.545 0.568 0.000 0.424 0.000 0.008
#> SRR2936873 1 0.0162 0.801 0.996 0.000 0.004 0.000 0.000
#> SRR2936872 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> SRR2936871 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> SRR2936874 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> SRR2936870 1 0.0865 0.790 0.972 0.000 0.004 0.024 0.000
#> SRR2936869 4 0.0703 0.839 0.024 0.000 0.000 0.976 0.000
#> SRR2936868 4 0.0703 0.839 0.024 0.000 0.000 0.976 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR2936906 1 0.0458 0.9327 0.984 0.000 0.000 0.000 0.000 0.016
#> SRR2936909 6 0.2877 0.6671 0.168 0.000 0.012 0.000 0.000 0.820
#> SRR2936918 1 0.1204 0.8959 0.944 0.000 0.000 0.000 0.000 0.056
#> SRR2936917 5 0.0000 0.9989 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936916 3 0.0000 0.8913 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936915 3 0.0363 0.8900 0.000 0.000 0.988 0.000 0.000 0.012
#> SRR2936914 5 0.0000 0.9989 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936913 5 0.0000 0.9989 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936912 1 0.0146 0.9360 0.996 0.000 0.000 0.000 0.000 0.004
#> SRR2936910 1 0.0146 0.9360 0.996 0.000 0.000 0.000 0.000 0.004
#> SRR2936911 5 0.0000 0.9989 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936907 2 0.0000 0.9948 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936908 2 0.0000 0.9948 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936904 6 0.5761 0.0287 0.000 0.172 0.000 0.396 0.000 0.432
#> SRR2936905 2 0.0000 0.9948 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936903 6 0.0000 0.6691 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR2936901 6 0.3737 0.2652 0.000 0.000 0.392 0.000 0.000 0.608
#> SRR2936902 3 0.3404 0.7153 0.000 0.000 0.760 0.000 0.016 0.224
#> SRR2936900 6 0.1007 0.6865 0.044 0.000 0.000 0.000 0.000 0.956
#> SRR2936898 3 0.0000 0.8913 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936899 3 0.0363 0.8900 0.000 0.000 0.988 0.000 0.000 0.012
#> SRR2936897 6 0.4047 0.4212 0.384 0.000 0.012 0.000 0.000 0.604
#> SRR2936896 3 0.3515 0.6351 0.000 0.000 0.676 0.000 0.324 0.000
#> SRR2936894 1 0.0000 0.9355 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936893 2 0.0000 0.9948 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936895 3 0.2996 0.7676 0.000 0.000 0.772 0.000 0.228 0.000
#> SRR2936892 2 0.0937 0.9573 0.000 0.960 0.000 0.040 0.000 0.000
#> SRR2936891 1 0.0000 0.9355 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR2936890 2 0.0000 0.9948 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936886 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR2936885 6 0.3748 0.5550 0.300 0.000 0.012 0.000 0.000 0.688
#> SRR2936888 1 0.2562 0.8032 0.828 0.000 0.000 0.172 0.000 0.000
#> SRR2936889 2 0.0000 0.9948 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936887 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR2936884 3 0.2697 0.8068 0.000 0.000 0.812 0.000 0.188 0.000
#> SRR2936883 3 0.1663 0.8645 0.000 0.000 0.912 0.000 0.088 0.000
#> SRR2936881 3 0.0000 0.8913 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936882 6 0.1007 0.6865 0.044 0.000 0.000 0.000 0.000 0.956
#> SRR2936880 3 0.0000 0.8913 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR2936878 5 0.0000 0.9989 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR2936879 3 0.0363 0.8900 0.000 0.000 0.988 0.000 0.000 0.012
#> SRR2936875 2 0.0260 0.9869 0.000 0.992 0.008 0.000 0.000 0.000
#> SRR2936877 5 0.0146 0.9944 0.000 0.000 0.004 0.000 0.996 0.000
#> SRR2936876 6 0.3563 0.4393 0.000 0.000 0.336 0.000 0.000 0.664
#> SRR2936873 1 0.0363 0.9334 0.988 0.000 0.000 0.000 0.000 0.012
#> SRR2936872 2 0.0000 0.9948 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936871 2 0.0000 0.9948 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936874 2 0.0000 0.9948 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR2936870 1 0.2562 0.8032 0.828 0.000 0.000 0.172 0.000 0.000
#> SRR2936869 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR2936868 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 14198 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 0.754 0.842 0.932 0.4912 0.500 0.500
#> 3 3 0.467 0.688 0.819 0.3161 0.747 0.550
#> 4 4 0.717 0.791 0.873 0.1639 0.867 0.641
#> 5 5 0.679 0.676 0.796 0.0551 0.922 0.697
#> 6 6 0.699 0.623 0.769 0.0258 0.986 0.932
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
#> SRR2936906 1 0.0000 0.917 1.000 0.000
#> SRR2936909 1 0.1184 0.915 0.984 0.016
#> SRR2936918 1 0.0000 0.917 1.000 0.000
#> SRR2936917 1 0.0000 0.917 1.000 0.000
#> SRR2936916 1 0.0000 0.917 1.000 0.000
#> SRR2936915 1 0.9552 0.443 0.624 0.376
#> SRR2936914 1 0.0000 0.917 1.000 0.000
#> SRR2936913 1 0.9286 0.521 0.656 0.344
#> SRR2936912 1 0.0000 0.917 1.000 0.000
#> SRR2936910 1 0.0000 0.917 1.000 0.000
#> SRR2936911 2 0.2948 0.893 0.052 0.948
#> SRR2936907 2 0.0000 0.926 0.000 1.000
#> SRR2936908 2 0.0000 0.926 0.000 1.000
#> SRR2936904 2 0.0000 0.926 0.000 1.000
#> SRR2936905 2 0.0000 0.926 0.000 1.000
#> SRR2936903 1 0.2603 0.904 0.956 0.044
#> SRR2936901 1 0.6148 0.814 0.848 0.152
#> SRR2936902 2 0.9754 0.265 0.408 0.592
#> SRR2936900 1 0.0938 0.916 0.988 0.012
#> SRR2936898 1 0.3274 0.895 0.940 0.060
#> SRR2936899 1 0.9286 0.517 0.656 0.344
#> SRR2936897 1 0.2423 0.906 0.960 0.040
#> SRR2936896 2 0.0376 0.924 0.004 0.996
#> SRR2936894 1 0.0000 0.917 1.000 0.000
#> SRR2936893 2 0.0000 0.926 0.000 1.000
#> SRR2936895 1 0.4431 0.871 0.908 0.092
#> SRR2936892 2 0.0000 0.926 0.000 1.000
#> SRR2936891 1 0.0000 0.917 1.000 0.000
#> SRR2936890 2 0.0000 0.926 0.000 1.000
#> SRR2936886 2 0.2778 0.896 0.048 0.952
#> SRR2936885 1 0.2778 0.902 0.952 0.048
#> SRR2936888 1 0.0000 0.917 1.000 0.000
#> SRR2936889 2 0.0000 0.926 0.000 1.000
#> SRR2936887 2 0.2236 0.905 0.036 0.964
#> SRR2936884 2 0.9833 0.214 0.424 0.576
#> SRR2936883 1 0.9635 0.413 0.612 0.388
#> SRR2936881 1 0.1633 0.912 0.976 0.024
#> SRR2936882 1 0.0000 0.917 1.000 0.000
#> SRR2936880 1 0.0938 0.916 0.988 0.012
#> SRR2936878 1 0.0000 0.917 1.000 0.000
#> SRR2936879 2 0.8955 0.518 0.312 0.688
#> SRR2936875 2 0.0000 0.926 0.000 1.000
#> SRR2936877 2 0.3431 0.882 0.064 0.936
#> SRR2936876 1 0.6438 0.801 0.836 0.164
#> SRR2936873 1 0.0000 0.917 1.000 0.000
#> SRR2936872 2 0.0000 0.926 0.000 1.000
#> SRR2936871 2 0.0000 0.926 0.000 1.000
#> SRR2936874 2 0.0000 0.926 0.000 1.000
#> SRR2936870 1 0.0000 0.917 1.000 0.000
#> SRR2936869 2 0.0000 0.926 0.000 1.000
#> SRR2936868 2 0.0000 0.926 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR2936906 1 0.5431 0.7004 0.716 0.000 0.284
#> SRR2936909 1 0.3851 0.7579 0.860 0.004 0.136
#> SRR2936918 1 0.4504 0.7418 0.804 0.000 0.196
#> SRR2936917 1 0.3193 0.7630 0.896 0.004 0.100
#> SRR2936916 1 0.3941 0.7526 0.844 0.000 0.156
#> SRR2936915 1 0.8345 0.6115 0.628 0.200 0.172
#> SRR2936914 3 0.6189 -0.0365 0.364 0.004 0.632
#> SRR2936913 3 0.3644 0.7209 0.004 0.124 0.872
#> SRR2936912 1 0.6095 0.5852 0.608 0.000 0.392
#> SRR2936910 1 0.5785 0.6581 0.668 0.000 0.332
#> SRR2936911 3 0.3551 0.7219 0.000 0.132 0.868
#> SRR2936907 2 0.0237 0.9185 0.000 0.996 0.004
#> SRR2936908 2 0.0237 0.9185 0.000 0.996 0.004
#> SRR2936904 2 0.1585 0.9043 0.008 0.964 0.028
#> SRR2936905 2 0.0000 0.9185 0.000 1.000 0.000
#> SRR2936903 1 0.2152 0.7510 0.948 0.016 0.036
#> SRR2936901 1 0.4790 0.7062 0.848 0.096 0.056
#> SRR2936902 1 0.7890 0.1268 0.512 0.432 0.056
#> SRR2936900 1 0.1877 0.7527 0.956 0.012 0.032
#> SRR2936898 1 0.5291 0.6947 0.732 0.000 0.268
#> SRR2936899 1 0.7603 0.6138 0.688 0.172 0.140
#> SRR2936897 1 0.5650 0.6791 0.688 0.000 0.312
#> SRR2936896 3 0.6274 0.3428 0.000 0.456 0.544
#> SRR2936894 1 0.4750 0.7385 0.784 0.000 0.216
#> SRR2936893 2 0.1411 0.8991 0.000 0.964 0.036
#> SRR2936895 3 0.1482 0.6765 0.020 0.012 0.968
#> SRR2936892 2 0.1031 0.9085 0.000 0.976 0.024
#> SRR2936891 1 0.5835 0.6532 0.660 0.000 0.340
#> SRR2936890 2 0.0424 0.9179 0.000 0.992 0.008
#> SRR2936886 3 0.4291 0.7072 0.000 0.180 0.820
#> SRR2936885 1 0.4834 0.7465 0.792 0.004 0.204
#> SRR2936888 3 0.3038 0.5992 0.104 0.000 0.896
#> SRR2936889 2 0.1163 0.9078 0.000 0.972 0.028
#> SRR2936887 3 0.4605 0.6926 0.000 0.204 0.796
#> SRR2936884 1 0.8631 0.3057 0.520 0.372 0.108
#> SRR2936883 1 0.7949 0.5291 0.640 0.252 0.108
#> SRR2936881 1 0.3415 0.7427 0.900 0.020 0.080
#> SRR2936882 1 0.1585 0.7541 0.964 0.008 0.028
#> SRR2936880 1 0.3370 0.7425 0.904 0.024 0.072
#> SRR2936878 1 0.2590 0.7623 0.924 0.004 0.072
#> SRR2936879 2 0.8511 0.2986 0.244 0.604 0.152
#> SRR2936875 2 0.0424 0.9155 0.008 0.992 0.000
#> SRR2936877 2 0.5268 0.6531 0.212 0.776 0.012
#> SRR2936876 1 0.4768 0.7383 0.848 0.100 0.052
#> SRR2936873 1 0.4750 0.7357 0.784 0.000 0.216
#> SRR2936872 2 0.0661 0.9129 0.008 0.988 0.004
#> SRR2936871 2 0.0000 0.9185 0.000 1.000 0.000
#> SRR2936874 2 0.0237 0.9176 0.004 0.996 0.000
#> SRR2936870 3 0.3686 0.5535 0.140 0.000 0.860
#> SRR2936869 3 0.6225 0.4028 0.000 0.432 0.568
#> SRR2936868 3 0.6095 0.4794 0.000 0.392 0.608
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR2936906 1 0.1042 0.916 0.972 0.000 0.008 0.020
#> SRR2936909 1 0.1526 0.907 0.960 0.016 0.012 0.012
#> SRR2936918 1 0.0895 0.915 0.976 0.000 0.020 0.004
#> SRR2936917 1 0.3428 0.798 0.844 0.000 0.144 0.012
#> SRR2936916 1 0.1398 0.905 0.956 0.000 0.040 0.004
#> SRR2936915 1 0.4599 0.743 0.792 0.168 0.012 0.028
#> SRR2936914 4 0.7464 0.411 0.296 0.000 0.208 0.496
#> SRR2936913 4 0.4084 0.770 0.036 0.044 0.064 0.856
#> SRR2936912 1 0.2300 0.897 0.920 0.000 0.016 0.064
#> SRR2936910 1 0.1584 0.913 0.952 0.000 0.012 0.036
#> SRR2936911 4 0.1284 0.779 0.024 0.012 0.000 0.964
#> SRR2936907 2 0.0927 0.926 0.000 0.976 0.016 0.008
#> SRR2936908 2 0.0336 0.929 0.000 0.992 0.008 0.000
#> SRR2936904 2 0.0859 0.921 0.004 0.980 0.008 0.008
#> SRR2936905 2 0.0188 0.929 0.000 0.996 0.004 0.000
#> SRR2936903 3 0.2528 0.788 0.080 0.004 0.908 0.008
#> SRR2936901 3 0.2019 0.801 0.032 0.024 0.940 0.004
#> SRR2936902 3 0.2222 0.793 0.000 0.060 0.924 0.016
#> SRR2936900 3 0.5488 0.501 0.340 0.012 0.636 0.012
#> SRR2936898 3 0.3632 0.764 0.008 0.004 0.832 0.156
#> SRR2936899 3 0.3384 0.784 0.000 0.024 0.860 0.116
#> SRR2936897 1 0.1722 0.908 0.944 0.000 0.008 0.048
#> SRR2936896 4 0.6311 0.644 0.008 0.212 0.108 0.672
#> SRR2936894 1 0.1584 0.915 0.952 0.000 0.036 0.012
#> SRR2936893 2 0.1406 0.920 0.000 0.960 0.016 0.024
#> SRR2936895 4 0.2821 0.757 0.020 0.004 0.076 0.900
#> SRR2936892 2 0.1297 0.921 0.000 0.964 0.016 0.020
#> SRR2936891 1 0.2060 0.906 0.932 0.000 0.016 0.052
#> SRR2936890 2 0.0927 0.926 0.000 0.976 0.016 0.008
#> SRR2936886 4 0.2291 0.785 0.016 0.036 0.016 0.932
#> SRR2936885 3 0.4718 0.745 0.092 0.000 0.792 0.116
#> SRR2936888 4 0.4635 0.620 0.268 0.000 0.012 0.720
#> SRR2936889 2 0.1411 0.920 0.000 0.960 0.020 0.020
#> SRR2936887 4 0.2141 0.785 0.012 0.040 0.012 0.936
#> SRR2936884 3 0.3616 0.779 0.000 0.036 0.852 0.112
#> SRR2936883 3 0.3404 0.786 0.000 0.032 0.864 0.104
#> SRR2936881 3 0.2140 0.808 0.008 0.008 0.932 0.052
#> SRR2936882 3 0.4690 0.612 0.276 0.000 0.712 0.012
#> SRR2936880 3 0.2271 0.808 0.008 0.012 0.928 0.052
#> SRR2936878 3 0.5345 0.289 0.428 0.000 0.560 0.012
#> SRR2936879 2 0.6149 0.340 0.356 0.596 0.016 0.032
#> SRR2936875 2 0.0524 0.923 0.008 0.988 0.004 0.000
#> SRR2936877 2 0.4990 0.726 0.060 0.784 0.144 0.012
#> SRR2936876 1 0.4765 0.754 0.788 0.164 0.032 0.016
#> SRR2936873 1 0.0804 0.917 0.980 0.000 0.012 0.008
#> SRR2936872 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> SRR2936871 2 0.0188 0.929 0.000 0.996 0.004 0.000
#> SRR2936874 2 0.0000 0.928 0.000 1.000 0.000 0.000
#> SRR2936870 4 0.4868 0.569 0.304 0.000 0.012 0.684
#> SRR2936869 4 0.4900 0.671 0.000 0.236 0.032 0.732
#> SRR2936868 4 0.4645 0.711 0.008 0.204 0.020 0.768
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR2936906 1 0.1568 0.7294 0.944 0.000 0.000 0.020 0.036
#> SRR2936909 1 0.3944 0.6431 0.720 0.004 0.004 0.000 0.272
#> SRR2936918 1 0.2347 0.6824 0.912 0.000 0.016 0.016 0.056
#> SRR2936917 1 0.5087 0.5317 0.740 0.004 0.108 0.016 0.132
#> SRR2936916 1 0.1153 0.7086 0.964 0.000 0.008 0.004 0.024
#> SRR2936915 1 0.3728 0.6632 0.840 0.092 0.004 0.016 0.048
#> SRR2936914 1 0.7683 0.1674 0.504 0.004 0.172 0.216 0.104
#> SRR2936913 4 0.6845 0.5497 0.084 0.104 0.100 0.660 0.052
#> SRR2936912 1 0.4821 0.6394 0.680 0.000 0.004 0.044 0.272
#> SRR2936910 1 0.3438 0.7196 0.808 0.000 0.000 0.020 0.172
#> SRR2936911 4 0.3691 0.4709 0.008 0.008 0.008 0.804 0.172
#> SRR2936907 2 0.0727 0.9618 0.000 0.980 0.012 0.004 0.004
#> SRR2936908 2 0.0451 0.9618 0.000 0.988 0.000 0.004 0.008
#> SRR2936904 2 0.2156 0.9290 0.004 0.924 0.004 0.036 0.032
#> SRR2936905 2 0.0290 0.9623 0.000 0.992 0.000 0.008 0.000
#> SRR2936903 3 0.2909 0.7911 0.028 0.008 0.892 0.016 0.056
#> SRR2936901 3 0.1794 0.8053 0.008 0.012 0.944 0.012 0.024
#> SRR2936902 3 0.1836 0.8017 0.000 0.040 0.936 0.008 0.016
#> SRR2936900 3 0.5683 0.5353 0.256 0.004 0.640 0.008 0.092
#> SRR2936898 3 0.4539 0.7554 0.008 0.000 0.768 0.100 0.124
#> SRR2936899 3 0.4085 0.7776 0.004 0.008 0.812 0.084 0.092
#> SRR2936897 1 0.5181 0.4420 0.564 0.004 0.004 0.028 0.400
#> SRR2936896 5 0.6843 0.3435 0.000 0.108 0.060 0.292 0.540
#> SRR2936894 1 0.3365 0.7159 0.808 0.000 0.008 0.004 0.180
#> SRR2936893 2 0.1299 0.9586 0.000 0.960 0.012 0.020 0.008
#> SRR2936895 5 0.5458 0.0772 0.000 0.000 0.060 0.464 0.476
#> SRR2936892 2 0.1211 0.9546 0.000 0.960 0.016 0.024 0.000
#> SRR2936891 1 0.2850 0.7299 0.872 0.000 0.000 0.036 0.092
#> SRR2936890 2 0.0912 0.9590 0.000 0.972 0.012 0.016 0.000
#> SRR2936886 4 0.2346 0.6229 0.008 0.052 0.016 0.916 0.008
#> SRR2936885 3 0.5388 0.7108 0.088 0.008 0.748 0.072 0.084
#> SRR2936888 4 0.5688 0.4333 0.296 0.000 0.008 0.608 0.088
#> SRR2936889 2 0.1560 0.9481 0.000 0.948 0.020 0.028 0.004
#> SRR2936887 4 0.2220 0.6232 0.008 0.052 0.016 0.920 0.004
#> SRR2936884 3 0.2988 0.7972 0.000 0.024 0.880 0.072 0.024
#> SRR2936883 3 0.2770 0.8041 0.004 0.020 0.896 0.060 0.020
#> SRR2936881 3 0.3366 0.7745 0.000 0.000 0.828 0.032 0.140
#> SRR2936882 3 0.5042 0.6459 0.180 0.000 0.716 0.008 0.096
#> SRR2936880 3 0.3810 0.7561 0.000 0.000 0.792 0.040 0.168
#> SRR2936878 5 0.6810 0.1883 0.180 0.004 0.356 0.008 0.452
#> SRR2936879 5 0.6045 0.5249 0.116 0.200 0.004 0.028 0.652
#> SRR2936875 2 0.2249 0.8827 0.000 0.896 0.008 0.000 0.096
#> SRR2936877 5 0.5819 0.5764 0.060 0.128 0.104 0.004 0.704
#> SRR2936876 5 0.6104 0.3581 0.256 0.148 0.008 0.000 0.588
#> SRR2936873 1 0.3910 0.6776 0.740 0.000 0.004 0.008 0.248
#> SRR2936872 2 0.0290 0.9604 0.000 0.992 0.000 0.000 0.008
#> SRR2936871 2 0.0510 0.9579 0.000 0.984 0.000 0.000 0.016
#> SRR2936874 2 0.1124 0.9460 0.000 0.960 0.004 0.000 0.036
#> SRR2936870 4 0.5839 0.3153 0.368 0.000 0.008 0.544 0.080
#> SRR2936869 4 0.5247 0.4888 0.004 0.320 0.024 0.632 0.020
#> SRR2936868 4 0.5054 0.5233 0.004 0.280 0.024 0.672 0.020
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR2936906 1 0.1769 0.658 0.924 0.000 0.000 0.012 0.004 NA
#> SRR2936909 1 0.3665 0.498 0.728 0.000 0.000 0.000 0.252 NA
#> SRR2936918 1 0.3541 0.608 0.748 0.000 0.000 0.020 0.000 NA
#> SRR2936917 1 0.4860 0.446 0.516 0.000 0.040 0.000 0.008 NA
#> SRR2936916 1 0.4329 0.549 0.624 0.000 0.004 0.012 0.008 NA
#> SRR2936915 1 0.5363 0.576 0.688 0.060 0.000 0.012 0.064 NA
#> SRR2936914 1 0.7586 0.178 0.392 0.000 0.116 0.172 0.020 NA
#> SRR2936913 4 0.6733 0.391 0.048 0.044 0.024 0.536 0.044 NA
#> SRR2936912 1 0.3534 0.585 0.796 0.000 0.000 0.036 0.160 NA
#> SRR2936910 1 0.2563 0.655 0.892 0.000 0.000 0.036 0.044 NA
#> SRR2936911 4 0.6141 0.207 0.012 0.000 0.040 0.596 0.192 NA
#> SRR2936907 2 0.0551 0.911 0.000 0.984 0.004 0.004 0.000 NA
#> SRR2936908 2 0.0582 0.910 0.000 0.984 0.004 0.004 0.004 NA
#> SRR2936904 2 0.6510 0.439 0.012 0.548 0.012 0.052 0.092 NA
#> SRR2936905 2 0.1570 0.899 0.000 0.944 0.004 0.008 0.016 NA
#> SRR2936903 3 0.3272 0.829 0.044 0.004 0.852 0.004 0.016 NA
#> SRR2936901 3 0.2026 0.847 0.008 0.004 0.916 0.000 0.012 NA
#> SRR2936902 3 0.2112 0.848 0.000 0.028 0.916 0.000 0.020 NA
#> SRR2936900 3 0.5452 0.668 0.192 0.004 0.648 0.000 0.024 NA
#> SRR2936898 3 0.2886 0.828 0.004 0.000 0.876 0.028 0.060 NA
#> SRR2936899 3 0.2687 0.832 0.004 0.000 0.888 0.028 0.052 NA
#> SRR2936897 1 0.4783 0.403 0.640 0.000 0.000 0.032 0.300 NA
#> SRR2936896 5 0.6635 0.365 0.008 0.040 0.076 0.236 0.580 NA
#> SRR2936894 1 0.1484 0.655 0.944 0.000 0.004 0.008 0.040 NA
#> SRR2936893 2 0.1490 0.904 0.000 0.948 0.004 0.024 0.016 NA
#> SRR2936895 5 0.6954 0.123 0.016 0.000 0.080 0.376 0.416 NA
#> SRR2936892 2 0.1894 0.891 0.000 0.928 0.004 0.040 0.016 NA
#> SRR2936891 1 0.3161 0.644 0.852 0.000 0.004 0.032 0.020 NA
#> SRR2936890 2 0.0748 0.909 0.000 0.976 0.004 0.016 0.000 NA
#> SRR2936886 4 0.2295 0.555 0.016 0.072 0.000 0.900 0.004 NA
#> SRR2936885 3 0.5964 0.710 0.104 0.004 0.672 0.072 0.028 NA
#> SRR2936888 4 0.5964 0.317 0.324 0.000 0.000 0.532 0.044 NA
#> SRR2936889 2 0.2427 0.874 0.000 0.900 0.004 0.056 0.020 NA
#> SRR2936887 4 0.3203 0.559 0.028 0.088 0.004 0.856 0.016 NA
#> SRR2936884 3 0.2290 0.844 0.000 0.012 0.912 0.040 0.016 NA
#> SRR2936883 3 0.1722 0.847 0.000 0.004 0.936 0.036 0.008 NA
#> SRR2936881 3 0.1816 0.844 0.004 0.000 0.928 0.004 0.048 NA
#> SRR2936882 3 0.4735 0.747 0.144 0.000 0.724 0.000 0.028 NA
#> SRR2936880 3 0.2256 0.840 0.004 0.000 0.908 0.008 0.048 NA
#> SRR2936878 1 0.7334 -0.170 0.336 0.004 0.268 0.008 0.324 NA
#> SRR2936879 5 0.5025 0.523 0.192 0.104 0.004 0.016 0.684 NA
#> SRR2936875 2 0.1814 0.874 0.000 0.900 0.000 0.000 0.100 NA
#> SRR2936877 5 0.5009 0.556 0.108 0.096 0.048 0.008 0.736 NA
#> SRR2936876 5 0.5201 0.172 0.392 0.064 0.000 0.000 0.532 NA
#> SRR2936873 1 0.2799 0.615 0.852 0.000 0.000 0.012 0.124 NA
#> SRR2936872 2 0.0508 0.911 0.000 0.984 0.000 0.000 0.004 NA
#> SRR2936871 2 0.2150 0.883 0.000 0.912 0.004 0.004 0.036 NA
#> SRR2936874 2 0.1845 0.890 0.000 0.916 0.004 0.000 0.072 NA
#> SRR2936870 4 0.6050 0.125 0.412 0.000 0.000 0.448 0.040 NA
#> SRR2936869 4 0.4119 0.493 0.000 0.280 0.004 0.692 0.016 NA
#> SRR2936868 4 0.4088 0.502 0.004 0.268 0.004 0.704 0.016 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.
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