Date: 2019-12-25 23:55:33 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 17931 rows and 61 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] 17931 61
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:hclust | 4 | 1.000 | 0.999 | 1.000 | ** | 2,3 |
| SD:mclust | 6 | 1.000 | 0.992 | 0.995 | ** | 3,4,5 |
| SD:NMF | 3 | 1.000 | 1.000 | 1.000 | ** | 2 |
| CV:hclust | 3 | 1.000 | 1.000 | 1.000 | ** | 2 |
| CV:pam | 3 | 1.000 | 0.995 | 0.998 | ** | 2 |
| CV:NMF | 5 | 1.000 | 0.985 | 0.988 | ** | 3,4 |
| MAD:hclust | 3 | 1.000 | 0.988 | 0.994 | ** | 2 |
| MAD:skmeans | 4 | 1.000 | 0.991 | 0.994 | ** | |
| MAD:pam | 2 | 1.000 | 1.000 | 1.000 | ** | |
| ATC:hclust | 2 | 1.000 | 0.998 | 0.999 | ** | |
| ATC:kmeans | 2 | 1.000 | 1.000 | 1.000 | ** | |
| ATC:pam | 2 | 1.000 | 1.000 | 1.000 | ** | |
| ATC:mclust | 2 | 1.000 | 1.000 | 1.000 | ** | |
| SD:pam | 6 | 0.969 | 0.930 | 0.962 | ** | 2,3,5 |
| CV:skmeans | 4 | 0.959 | 0.967 | 0.978 | ** | |
| SD:skmeans | 4 | 0.932 | 0.965 | 0.977 | * | 3 |
| MAD:mclust | 5 | 0.921 | 0.907 | 0.957 | * | |
| ATC:skmeans | 6 | 0.902 | 0.930 | 0.953 | * | 2 |
| CV:mclust | 4 | 0.893 | 0.922 | 0.961 | ||
| MAD:NMF | 4 | 0.881 | 0.888 | 0.952 | ||
| MAD:kmeans | 4 | 0.659 | 0.910 | 0.895 | ||
| ATC:NMF | 3 | 0.574 | 0.834 | 0.886 | ||
| SD:kmeans | 3 | 0.509 | 0.904 | 0.905 | ||
| CV:kmeans | 4 | 0.477 | 0.773 | 0.820 |
**: 1-PAC > 0.95, *: 1-PAC > 0.9
Cumulative distribution function curves of consensus matrix for all methods.
collect_plots(res_list, fun = plot_ecdf)
Consensus heatmaps for all methods. (What is a consensus heatmap?)
collect_plots(res_list, k = 2, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = consensus_heatmap, mc.cores = 4)
Membership heatmaps for all methods. (What is a membership heatmap?)
collect_plots(res_list, k = 2, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = membership_heatmap, mc.cores = 4)
Signature heatmaps for all methods. (What is a signature heatmap?)
Note in following heatmaps, rows are scaled.
collect_plots(res_list, k = 2, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 3, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 4, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 5, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 6, fun = get_signatures, mc.cores = 4)
The statistics used for measuring the stability of consensus partitioning. (How are they defined?)
get_stats(res_list, k = 2)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 2 1.000 1.000 1.000 0.154 0.847 0.847
#> CV:NMF 2 0.895 0.964 0.978 0.208 0.820 0.820
#> MAD:NMF 2 0.758 0.935 0.966 0.225 0.820 0.820
#> ATC:NMF 2 0.720 0.819 0.916 0.264 0.744 0.744
#> SD:skmeans 2 0.847 0.899 0.949 0.444 0.531 0.531
#> CV:skmeans 2 0.492 0.904 0.918 0.476 0.531 0.531
#> MAD:skmeans 2 0.515 0.716 0.876 0.506 0.498 0.498
#> ATC:skmeans 2 0.932 0.905 0.964 0.361 0.640 0.640
#> SD:mclust 2 0.716 0.918 0.937 0.335 0.591 0.591
#> CV:mclust 2 0.699 0.972 0.968 0.369 0.591 0.591
#> MAD:mclust 2 0.428 0.860 0.882 0.287 0.793 0.793
#> ATC:mclust 2 1.000 1.000 1.000 0.232 0.768 0.768
#> SD:kmeans 2 0.602 0.944 0.961 0.202 0.820 0.820
#> CV:kmeans 2 0.166 0.584 0.742 0.350 0.820 0.820
#> MAD:kmeans 2 0.163 0.486 0.774 0.354 0.744 0.744
#> ATC:kmeans 2 1.000 1.000 1.000 0.181 0.820 0.820
#> SD:pam 2 1.000 1.000 1.000 0.181 0.820 0.820
#> CV:pam 2 1.000 1.000 1.000 0.181 0.820 0.820
#> MAD:pam 2 1.000 1.000 1.000 0.181 0.820 0.820
#> ATC:pam 2 1.000 1.000 1.000 0.181 0.820 0.820
#> SD:hclust 2 1.000 0.988 0.995 0.163 0.847 0.847
#> CV:hclust 2 1.000 1.000 1.000 0.181 0.820 0.820
#> MAD:hclust 2 1.000 0.977 0.984 0.167 0.847 0.847
#> ATC:hclust 2 1.000 0.998 0.999 0.183 0.820 0.820
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 1.000 1.000 1.000 1.873 0.711 0.659
#> CV:NMF 3 0.920 0.942 0.975 1.229 0.727 0.669
#> MAD:NMF 3 0.722 0.798 0.917 1.459 0.560 0.476
#> ATC:NMF 3 0.574 0.834 0.886 0.909 0.779 0.710
#> SD:skmeans 3 0.932 0.970 0.971 0.501 0.694 0.475
#> CV:skmeans 3 0.754 0.860 0.929 0.414 0.694 0.475
#> MAD:skmeans 3 0.808 0.940 0.959 0.325 0.785 0.587
#> ATC:skmeans 3 0.859 0.881 0.954 0.762 0.643 0.473
#> SD:mclust 3 1.000 0.994 0.996 0.928 0.762 0.598
#> CV:mclust 3 0.530 0.740 0.777 0.563 0.738 0.556
#> MAD:mclust 3 0.727 0.836 0.921 1.237 0.484 0.379
#> ATC:mclust 3 0.864 0.894 0.943 1.569 0.627 0.515
#> SD:kmeans 3 0.509 0.904 0.905 1.332 0.736 0.677
#> CV:kmeans 3 0.249 0.562 0.676 0.577 0.588 0.497
#> MAD:kmeans 3 0.255 0.577 0.679 0.608 0.578 0.464
#> ATC:kmeans 3 0.478 0.254 0.571 1.796 0.587 0.496
#> SD:pam 3 1.000 1.000 1.000 1.459 0.736 0.677
#> CV:pam 3 1.000 0.995 0.998 1.443 0.727 0.669
#> MAD:pam 3 0.659 0.921 0.948 1.836 0.686 0.617
#> ATC:pam 3 0.505 0.852 0.915 1.803 0.672 0.600
#> SD:hclust 3 1.000 0.999 1.000 0.306 0.941 0.930
#> CV:hclust 3 1.000 1.000 1.000 1.459 0.736 0.677
#> MAD:hclust 3 1.000 0.988 0.994 1.655 0.711 0.659
#> ATC:hclust 3 0.812 0.845 0.937 0.760 0.942 0.929
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.780 0.903 0.953 0.53201 0.762 0.574
#> CV:NMF 4 0.926 0.900 0.963 0.50758 0.732 0.522
#> MAD:NMF 4 0.881 0.888 0.952 0.27196 0.747 0.477
#> ATC:NMF 4 0.569 0.753 0.832 0.35468 0.740 0.535
#> SD:skmeans 4 0.932 0.965 0.977 0.10191 0.896 0.698
#> CV:skmeans 4 0.959 0.967 0.978 0.10594 0.896 0.698
#> MAD:skmeans 4 1.000 0.991 0.994 0.10726 0.896 0.698
#> ATC:skmeans 4 0.811 0.905 0.953 0.08430 0.739 0.441
#> SD:mclust 4 1.000 0.997 0.998 0.05209 0.967 0.907
#> CV:mclust 4 0.893 0.922 0.961 0.19282 0.861 0.647
#> MAD:mclust 4 0.893 0.917 0.958 0.07325 0.967 0.907
#> ATC:mclust 4 0.893 0.906 0.964 0.15602 0.880 0.714
#> SD:kmeans 4 0.622 0.897 0.897 0.41352 0.738 0.528
#> CV:kmeans 4 0.477 0.773 0.820 0.21600 0.795 0.548
#> MAD:kmeans 4 0.659 0.910 0.895 0.21046 0.847 0.642
#> ATC:kmeans 4 0.574 0.735 0.852 0.35853 0.756 0.483
#> SD:pam 4 0.814 0.936 0.963 0.53077 0.770 0.587
#> CV:pam 4 0.669 0.766 0.902 0.53227 0.740 0.535
#> MAD:pam 4 0.841 0.852 0.933 0.35417 0.654 0.396
#> ATC:pam 4 0.725 0.855 0.921 0.36379 0.738 0.511
#> SD:hclust 4 1.000 0.999 1.000 1.13163 0.760 0.695
#> CV:hclust 4 0.694 0.860 0.851 0.30004 0.762 0.572
#> MAD:hclust 4 0.757 0.934 0.948 0.11870 0.989 0.980
#> ATC:hclust 4 0.805 0.828 0.938 0.00802 0.997 0.996
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.738 0.709 0.852 0.1267 0.831 0.532
#> CV:NMF 5 1.000 0.985 0.988 0.1368 0.859 0.559
#> MAD:NMF 5 0.706 0.753 0.858 0.1111 0.790 0.410
#> ATC:NMF 5 0.539 0.617 0.740 0.0925 0.854 0.561
#> SD:skmeans 5 0.836 0.847 0.902 0.0541 0.984 0.936
#> CV:skmeans 5 0.825 0.874 0.881 0.0619 0.959 0.841
#> MAD:skmeans 5 0.852 0.870 0.891 0.0498 0.984 0.936
#> ATC:skmeans 5 0.790 0.820 0.897 0.1002 0.837 0.545
#> SD:mclust 5 1.000 0.993 0.996 0.1500 0.896 0.676
#> CV:mclust 5 0.765 0.772 0.823 0.1218 0.934 0.796
#> MAD:mclust 5 0.921 0.907 0.957 0.1354 0.896 0.676
#> ATC:mclust 5 0.873 0.801 0.904 0.1184 0.902 0.693
#> SD:kmeans 5 0.639 0.790 0.818 0.1166 1.000 1.000
#> CV:kmeans 5 0.632 0.713 0.782 0.0975 1.000 1.000
#> MAD:kmeans 5 0.723 0.811 0.838 0.0932 1.000 1.000
#> ATC:kmeans 5 0.635 0.685 0.794 0.1011 1.000 1.000
#> SD:pam 5 0.949 0.927 0.967 0.1104 0.932 0.790
#> CV:pam 5 0.762 0.805 0.873 0.1115 0.793 0.453
#> MAD:pam 5 0.835 0.833 0.893 0.0795 0.818 0.506
#> ATC:pam 5 0.808 0.772 0.896 0.0943 0.860 0.603
#> SD:hclust 5 0.828 0.957 0.969 0.5588 0.738 0.521
#> CV:hclust 5 0.890 0.929 0.977 0.2144 0.891 0.695
#> MAD:hclust 5 0.893 0.959 0.983 0.4330 0.738 0.521
#> ATC:hclust 5 0.757 0.925 0.971 0.4417 0.784 0.715
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.682 0.689 0.794 0.05111 0.864 0.503
#> CV:NMF 6 0.802 0.632 0.823 0.03862 0.898 0.563
#> MAD:NMF 6 0.742 0.618 0.812 0.04792 0.987 0.936
#> ATC:NMF 6 0.558 0.583 0.709 0.06532 0.940 0.759
#> SD:skmeans 6 0.820 0.833 0.889 0.05751 0.959 0.830
#> CV:skmeans 6 0.842 0.813 0.868 0.04219 0.932 0.703
#> MAD:skmeans 6 0.831 0.866 0.882 0.04903 0.907 0.635
#> ATC:skmeans 6 0.902 0.930 0.953 0.06096 0.905 0.643
#> SD:mclust 6 1.000 0.992 0.995 0.02444 0.981 0.912
#> CV:mclust 6 0.825 0.829 0.880 0.07143 0.883 0.563
#> MAD:mclust 6 0.883 0.856 0.919 0.04875 0.907 0.620
#> ATC:mclust 6 0.892 0.804 0.869 0.02760 0.942 0.771
#> SD:kmeans 6 0.691 0.680 0.769 0.06725 0.923 0.739
#> CV:kmeans 6 0.664 0.616 0.722 0.06012 0.844 0.534
#> MAD:kmeans 6 0.728 0.594 0.679 0.05602 0.885 0.613
#> ATC:kmeans 6 0.693 0.702 0.730 0.05513 0.866 0.563
#> SD:pam 6 0.969 0.930 0.962 0.03493 0.975 0.904
#> CV:pam 6 0.797 0.686 0.862 0.04814 0.879 0.593
#> MAD:pam 6 0.832 0.805 0.876 0.05989 0.936 0.755
#> ATC:pam 6 0.820 0.821 0.879 0.03321 0.959 0.841
#> SD:hclust 6 0.816 0.918 0.970 0.00597 0.999 0.998
#> CV:hclust 6 0.886 0.898 0.960 0.02557 0.987 0.955
#> MAD:hclust 6 0.893 0.959 0.983 0.01599 0.989 0.960
#> ATC:hclust 6 0.658 0.731 0.819 0.43631 0.762 0.562
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 17931 rows and 61 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.988 0.995 0.16270 0.847 0.847
#> 3 3 1.000 0.999 1.000 0.30600 0.941 0.930
#> 4 4 1.000 0.999 1.000 1.13163 0.760 0.695
#> 5 5 0.828 0.957 0.969 0.55879 0.738 0.521
#> 6 6 0.816 0.918 0.970 0.00597 0.999 0.998
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
#> SRR1047813 1 0.000 0.994 1.000 0.000
#> SRR1047814 1 0.000 0.994 1.000 0.000
#> SRR1047815 1 0.000 0.994 1.000 0.000
#> SRR1047816 1 0.000 0.994 1.000 0.000
#> SRR1047817 1 0.000 0.994 1.000 0.000
#> SRR1047818 1 0.000 0.994 1.000 0.000
#> SRR1047819 1 0.000 0.994 1.000 0.000
#> SRR1047820 1 0.000 0.994 1.000 0.000
#> SRR1047821 1 0.000 0.994 1.000 0.000
#> SRR1047822 1 0.000 0.994 1.000 0.000
#> SRR1047823 1 0.000 0.994 1.000 0.000
#> SRR1047824 1 0.000 0.994 1.000 0.000
#> SRR1047825 1 0.000 0.994 1.000 0.000
#> SRR1047826 1 0.000 0.994 1.000 0.000
#> SRR1047827 1 0.000 0.994 1.000 0.000
#> SRR1047828 1 0.000 0.994 1.000 0.000
#> SRR1047829 1 0.000 0.994 1.000 0.000
#> SRR1047830 1 0.000 0.994 1.000 0.000
#> SRR1047831 1 0.000 0.994 1.000 0.000
#> SRR1047832 1 0.000 0.994 1.000 0.000
#> SRR1047833 2 0.000 1.000 0.000 1.000
#> SRR1047834 2 0.000 1.000 0.000 1.000
#> SRR1047835 2 0.000 1.000 0.000 1.000
#> SRR1047836 2 0.000 1.000 0.000 1.000
#> SRR1047837 2 0.000 1.000 0.000 1.000
#> SRR1047838 1 0.000 0.994 1.000 0.000
#> SRR1047839 1 0.000 0.994 1.000 0.000
#> SRR1047840 1 0.000 0.994 1.000 0.000
#> SRR1047841 1 0.000 0.994 1.000 0.000
#> SRR1047842 1 0.000 0.994 1.000 0.000
#> SRR1047843 1 0.000 0.994 1.000 0.000
#> SRR1047844 1 0.000 0.994 1.000 0.000
#> SRR1047845 1 0.000 0.994 1.000 0.000
#> SRR1047846 1 0.000 0.994 1.000 0.000
#> SRR1047847 1 0.000 0.994 1.000 0.000
#> SRR1047848 1 0.000 0.994 1.000 0.000
#> SRR1047849 1 0.000 0.994 1.000 0.000
#> SRR1047850 1 0.000 0.994 1.000 0.000
#> SRR1047851 1 0.000 0.994 1.000 0.000
#> SRR1047852 1 0.000 0.994 1.000 0.000
#> SRR1047853 1 0.000 0.994 1.000 0.000
#> SRR1047854 1 0.000 0.994 1.000 0.000
#> SRR1047855 1 0.000 0.994 1.000 0.000
#> SRR1047856 1 0.000 0.994 1.000 0.000
#> SRR1047857 1 0.000 0.994 1.000 0.000
#> SRR1047858 1 0.000 0.994 1.000 0.000
#> SRR1047859 1 0.000 0.994 1.000 0.000
#> SRR1047860 1 0.000 0.994 1.000 0.000
#> SRR1047861 1 0.000 0.994 1.000 0.000
#> SRR1047863 1 0.000 0.994 1.000 0.000
#> SRR1047864 1 0.634 0.813 0.840 0.160
#> SRR1047865 1 0.000 0.994 1.000 0.000
#> SRR1047866 1 0.000 0.994 1.000 0.000
#> SRR1047867 1 0.662 0.796 0.828 0.172
#> SRR1047868 1 0.000 0.994 1.000 0.000
#> SRR1047869 1 0.000 0.994 1.000 0.000
#> SRR1047870 1 0.000 0.994 1.000 0.000
#> SRR1047871 1 0.000 0.994 1.000 0.000
#> SRR1047872 1 0.000 0.994 1.000 0.000
#> SRR1047873 1 0.000 0.994 1.000 0.000
#> SRR1047874 1 0.000 0.994 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1047813 1 0.0000 1.000 1.000 0 0.000
#> SRR1047814 1 0.0000 1.000 1.000 0 0.000
#> SRR1047815 1 0.0000 1.000 1.000 0 0.000
#> SRR1047816 1 0.0000 1.000 1.000 0 0.000
#> SRR1047817 1 0.0000 1.000 1.000 0 0.000
#> SRR1047818 1 0.0000 1.000 1.000 0 0.000
#> SRR1047819 1 0.0000 1.000 1.000 0 0.000
#> SRR1047820 1 0.0000 1.000 1.000 0 0.000
#> SRR1047821 1 0.0000 1.000 1.000 0 0.000
#> SRR1047822 1 0.0000 1.000 1.000 0 0.000
#> SRR1047823 1 0.0000 1.000 1.000 0 0.000
#> SRR1047824 1 0.0000 1.000 1.000 0 0.000
#> SRR1047825 1 0.0000 1.000 1.000 0 0.000
#> SRR1047826 1 0.0000 1.000 1.000 0 0.000
#> SRR1047827 1 0.0000 1.000 1.000 0 0.000
#> SRR1047828 1 0.0000 1.000 1.000 0 0.000
#> SRR1047829 1 0.0000 1.000 1.000 0 0.000
#> SRR1047830 1 0.0000 1.000 1.000 0 0.000
#> SRR1047831 1 0.0000 1.000 1.000 0 0.000
#> SRR1047832 1 0.0000 1.000 1.000 0 0.000
#> SRR1047833 2 0.0000 1.000 0.000 1 0.000
#> SRR1047834 2 0.0000 1.000 0.000 1 0.000
#> SRR1047835 2 0.0000 1.000 0.000 1 0.000
#> SRR1047836 2 0.0000 1.000 0.000 1 0.000
#> SRR1047837 2 0.0000 1.000 0.000 1 0.000
#> SRR1047838 1 0.0000 1.000 1.000 0 0.000
#> SRR1047839 1 0.0000 1.000 1.000 0 0.000
#> SRR1047840 1 0.0000 1.000 1.000 0 0.000
#> SRR1047841 1 0.0000 1.000 1.000 0 0.000
#> SRR1047842 1 0.0000 1.000 1.000 0 0.000
#> SRR1047843 1 0.0000 1.000 1.000 0 0.000
#> SRR1047844 1 0.0000 1.000 1.000 0 0.000
#> SRR1047845 1 0.0000 1.000 1.000 0 0.000
#> SRR1047846 1 0.0000 1.000 1.000 0 0.000
#> SRR1047847 1 0.0000 1.000 1.000 0 0.000
#> SRR1047848 1 0.0000 1.000 1.000 0 0.000
#> SRR1047849 1 0.0000 1.000 1.000 0 0.000
#> SRR1047850 1 0.0000 1.000 1.000 0 0.000
#> SRR1047851 1 0.0000 1.000 1.000 0 0.000
#> SRR1047852 1 0.0000 1.000 1.000 0 0.000
#> SRR1047853 1 0.0000 1.000 1.000 0 0.000
#> SRR1047854 1 0.0000 1.000 1.000 0 0.000
#> SRR1047855 1 0.0000 1.000 1.000 0 0.000
#> SRR1047856 1 0.0000 1.000 1.000 0 0.000
#> SRR1047857 1 0.0000 1.000 1.000 0 0.000
#> SRR1047858 1 0.0000 1.000 1.000 0 0.000
#> SRR1047859 1 0.0000 1.000 1.000 0 0.000
#> SRR1047860 1 0.0000 1.000 1.000 0 0.000
#> SRR1047861 1 0.0000 1.000 1.000 0 0.000
#> SRR1047863 1 0.0000 1.000 1.000 0 0.000
#> SRR1047864 3 0.0592 0.966 0.012 0 0.988
#> SRR1047865 1 0.0000 1.000 1.000 0 0.000
#> SRR1047866 1 0.0000 1.000 1.000 0 0.000
#> SRR1047867 3 0.0000 0.966 0.000 0 1.000
#> SRR1047868 1 0.0000 1.000 1.000 0 0.000
#> SRR1047869 1 0.0000 1.000 1.000 0 0.000
#> SRR1047870 1 0.0000 1.000 1.000 0 0.000
#> SRR1047871 1 0.0000 1.000 1.000 0 0.000
#> SRR1047872 1 0.0000 1.000 1.000 0 0.000
#> SRR1047873 1 0.0000 1.000 1.000 0 0.000
#> SRR1047874 1 0.0000 1.000 1.000 0 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1047813 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047814 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047815 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047816 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047817 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047818 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047819 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047820 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047821 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047822 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047823 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047824 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047825 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047826 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047827 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047828 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047829 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047830 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047831 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047832 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047833 2 0.0000 1.000 0 1 0.000 0.000
#> SRR1047834 2 0.0000 1.000 0 1 0.000 0.000
#> SRR1047835 2 0.0000 1.000 0 1 0.000 0.000
#> SRR1047836 2 0.0000 1.000 0 1 0.000 0.000
#> SRR1047837 2 0.0000 1.000 0 1 0.000 0.000
#> SRR1047838 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047839 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047840 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047841 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047842 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047843 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047844 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047845 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047846 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047847 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047848 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047849 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047850 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047851 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047852 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047853 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047854 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047855 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047856 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047857 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047858 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047859 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047860 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047861 1 0.0000 1.000 1 0 0.000 0.000
#> SRR1047863 3 0.0000 1.000 0 0 1.000 0.000
#> SRR1047864 4 0.0469 0.984 0 0 0.012 0.988
#> SRR1047865 3 0.0000 1.000 0 0 1.000 0.000
#> SRR1047866 3 0.0000 1.000 0 0 1.000 0.000
#> SRR1047867 4 0.0000 0.984 0 0 0.000 1.000
#> SRR1047868 3 0.0000 1.000 0 0 1.000 0.000
#> SRR1047869 3 0.0000 1.000 0 0 1.000 0.000
#> SRR1047870 3 0.0000 1.000 0 0 1.000 0.000
#> SRR1047871 3 0.0000 1.000 0 0 1.000 0.000
#> SRR1047872 3 0.0000 1.000 0 0 1.000 0.000
#> SRR1047873 3 0.0000 1.000 0 0 1.000 0.000
#> SRR1047874 3 0.0000 1.000 0 0 1.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1047813 1 0.0000 0.923 1.000 0 0.000 0.000 0.00
#> SRR1047814 1 0.0000 0.923 1.000 0 0.000 0.000 0.00
#> SRR1047815 1 0.0000 0.923 1.000 0 0.000 0.000 0.00
#> SRR1047816 1 0.0000 0.923 1.000 0 0.000 0.000 0.00
#> SRR1047817 1 0.0000 0.923 1.000 0 0.000 0.000 0.00
#> SRR1047818 4 0.0404 0.982 0.012 0 0.000 0.988 0.00
#> SRR1047819 4 0.0404 0.982 0.012 0 0.000 0.988 0.00
#> SRR1047820 4 0.0404 0.982 0.012 0 0.000 0.988 0.00
#> SRR1047821 4 0.0404 0.982 0.012 0 0.000 0.988 0.00
#> SRR1047822 4 0.0404 0.982 0.012 0 0.000 0.988 0.00
#> SRR1047823 4 0.0404 0.982 0.012 0 0.000 0.988 0.00
#> SRR1047824 4 0.0404 0.982 0.012 0 0.000 0.988 0.00
#> SRR1047825 4 0.0404 0.982 0.012 0 0.000 0.988 0.00
#> SRR1047826 4 0.0404 0.982 0.012 0 0.000 0.988 0.00
#> SRR1047827 4 0.0404 0.982 0.012 0 0.000 0.988 0.00
#> SRR1047828 1 0.0000 0.923 1.000 0 0.000 0.000 0.00
#> SRR1047829 1 0.0000 0.923 1.000 0 0.000 0.000 0.00
#> SRR1047830 1 0.0000 0.923 1.000 0 0.000 0.000 0.00
#> SRR1047831 1 0.0000 0.923 1.000 0 0.000 0.000 0.00
#> SRR1047832 1 0.0000 0.923 1.000 0 0.000 0.000 0.00
#> SRR1047833 2 0.0000 1.000 0.000 1 0.000 0.000 0.00
#> SRR1047834 2 0.0000 1.000 0.000 1 0.000 0.000 0.00
#> SRR1047835 2 0.0000 1.000 0.000 1 0.000 0.000 0.00
#> SRR1047836 2 0.0000 1.000 0.000 1 0.000 0.000 0.00
#> SRR1047837 2 0.0000 1.000 0.000 1 0.000 0.000 0.00
#> SRR1047838 4 0.0963 0.982 0.036 0 0.000 0.964 0.00
#> SRR1047839 4 0.0963 0.982 0.036 0 0.000 0.964 0.00
#> SRR1047840 4 0.0963 0.982 0.036 0 0.000 0.964 0.00
#> SRR1047841 4 0.0963 0.982 0.036 0 0.000 0.964 0.00
#> SRR1047842 4 0.0963 0.982 0.036 0 0.000 0.964 0.00
#> SRR1047843 1 0.2516 0.878 0.860 0 0.000 0.140 0.00
#> SRR1047844 1 0.2516 0.878 0.860 0 0.000 0.140 0.00
#> SRR1047845 1 0.2516 0.878 0.860 0 0.000 0.140 0.00
#> SRR1047846 1 0.2516 0.878 0.860 0 0.000 0.140 0.00
#> SRR1047847 1 0.2516 0.878 0.860 0 0.000 0.140 0.00
#> SRR1047848 1 0.0404 0.924 0.988 0 0.000 0.012 0.00
#> SRR1047849 1 0.0404 0.924 0.988 0 0.000 0.012 0.00
#> SRR1047850 1 0.0404 0.924 0.988 0 0.000 0.012 0.00
#> SRR1047851 1 0.0404 0.924 0.988 0 0.000 0.012 0.00
#> SRR1047852 1 0.0404 0.924 0.988 0 0.000 0.012 0.00
#> SRR1047853 4 0.0963 0.982 0.036 0 0.000 0.964 0.00
#> SRR1047854 4 0.0963 0.982 0.036 0 0.000 0.964 0.00
#> SRR1047855 4 0.0963 0.982 0.036 0 0.000 0.964 0.00
#> SRR1047856 4 0.0963 0.982 0.036 0 0.000 0.964 0.00
#> SRR1047857 4 0.0963 0.982 0.036 0 0.000 0.964 0.00
#> SRR1047858 1 0.2516 0.878 0.860 0 0.000 0.140 0.00
#> SRR1047859 1 0.2516 0.878 0.860 0 0.000 0.140 0.00
#> SRR1047860 1 0.2516 0.878 0.860 0 0.000 0.140 0.00
#> SRR1047861 1 0.2516 0.878 0.860 0 0.000 0.140 0.00
#> SRR1047863 3 0.0000 1.000 0.000 0 1.000 0.000 0.00
#> SRR1047864 5 0.0693 0.986 0.000 0 0.008 0.012 0.98
#> SRR1047865 3 0.0000 1.000 0.000 0 1.000 0.000 0.00
#> SRR1047866 3 0.0000 1.000 0.000 0 1.000 0.000 0.00
#> SRR1047867 5 0.0000 0.986 0.000 0 0.000 0.000 1.00
#> SRR1047868 3 0.0000 1.000 0.000 0 1.000 0.000 0.00
#> SRR1047869 3 0.0000 1.000 0.000 0 1.000 0.000 0.00
#> SRR1047870 3 0.0000 1.000 0.000 0 1.000 0.000 0.00
#> SRR1047871 3 0.0000 1.000 0.000 0 1.000 0.000 0.00
#> SRR1047872 3 0.0000 1.000 0.000 0 1.000 0.000 0.00
#> SRR1047873 3 0.0000 1.000 0.000 0 1.000 0.000 0.00
#> SRR1047874 3 0.0000 1.000 0.000 0 1.000 0.000 0.00
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1047813 1 0.0000 0.919 1.000 0 0.00 0.000 0.00 0.00
#> SRR1047814 1 0.0000 0.919 1.000 0 0.00 0.000 0.00 0.00
#> SRR1047815 1 0.0000 0.919 1.000 0 0.00 0.000 0.00 0.00
#> SRR1047816 1 0.0000 0.919 1.000 0 0.00 0.000 0.00 0.00
#> SRR1047817 1 0.0000 0.919 1.000 0 0.00 0.000 0.00 0.00
#> SRR1047818 4 0.0000 0.982 0.000 0 0.00 1.000 0.00 0.00
#> SRR1047819 4 0.0000 0.982 0.000 0 0.00 1.000 0.00 0.00
#> SRR1047820 4 0.0000 0.982 0.000 0 0.00 1.000 0.00 0.00
#> SRR1047821 4 0.0000 0.982 0.000 0 0.00 1.000 0.00 0.00
#> SRR1047822 4 0.0000 0.982 0.000 0 0.00 1.000 0.00 0.00
#> SRR1047823 4 0.0000 0.982 0.000 0 0.00 1.000 0.00 0.00
#> SRR1047824 4 0.0000 0.982 0.000 0 0.00 1.000 0.00 0.00
#> SRR1047825 4 0.0000 0.982 0.000 0 0.00 1.000 0.00 0.00
#> SRR1047826 4 0.0000 0.982 0.000 0 0.00 1.000 0.00 0.00
#> SRR1047827 4 0.0000 0.982 0.000 0 0.00 1.000 0.00 0.00
#> SRR1047828 1 0.0000 0.919 1.000 0 0.00 0.000 0.00 0.00
#> SRR1047829 1 0.0000 0.919 1.000 0 0.00 0.000 0.00 0.00
#> SRR1047830 1 0.0000 0.919 1.000 0 0.00 0.000 0.00 0.00
#> SRR1047831 1 0.0000 0.919 1.000 0 0.00 0.000 0.00 0.00
#> SRR1047832 1 0.0000 0.919 1.000 0 0.00 0.000 0.00 0.00
#> SRR1047833 2 0.0000 1.000 0.000 1 0.00 0.000 0.00 0.00
#> SRR1047834 2 0.0000 1.000 0.000 1 0.00 0.000 0.00 0.00
#> SRR1047835 2 0.0000 1.000 0.000 1 0.00 0.000 0.00 0.00
#> SRR1047836 2 0.0000 1.000 0.000 1 0.00 0.000 0.00 0.00
#> SRR1047837 2 0.0000 1.000 0.000 1 0.00 0.000 0.00 0.00
#> SRR1047838 4 0.0632 0.982 0.024 0 0.00 0.976 0.00 0.00
#> SRR1047839 4 0.0632 0.982 0.024 0 0.00 0.976 0.00 0.00
#> SRR1047840 4 0.0632 0.982 0.024 0 0.00 0.976 0.00 0.00
#> SRR1047841 4 0.0632 0.982 0.024 0 0.00 0.976 0.00 0.00
#> SRR1047842 4 0.0632 0.982 0.024 0 0.00 0.976 0.00 0.00
#> SRR1047843 1 0.2300 0.871 0.856 0 0.00 0.144 0.00 0.00
#> SRR1047844 1 0.2300 0.871 0.856 0 0.00 0.144 0.00 0.00
#> SRR1047845 1 0.2300 0.871 0.856 0 0.00 0.144 0.00 0.00
#> SRR1047846 1 0.2300 0.871 0.856 0 0.00 0.144 0.00 0.00
#> SRR1047847 1 0.2300 0.871 0.856 0 0.00 0.144 0.00 0.00
#> SRR1047848 1 0.0363 0.921 0.988 0 0.00 0.012 0.00 0.00
#> SRR1047849 1 0.0363 0.921 0.988 0 0.00 0.012 0.00 0.00
#> SRR1047850 1 0.0363 0.921 0.988 0 0.00 0.012 0.00 0.00
#> SRR1047851 1 0.0363 0.921 0.988 0 0.00 0.012 0.00 0.00
#> SRR1047852 1 0.0363 0.921 0.988 0 0.00 0.012 0.00 0.00
#> SRR1047853 4 0.0632 0.982 0.024 0 0.00 0.976 0.00 0.00
#> SRR1047854 4 0.0632 0.982 0.024 0 0.00 0.976 0.00 0.00
#> SRR1047855 4 0.0632 0.982 0.024 0 0.00 0.976 0.00 0.00
#> SRR1047856 4 0.0632 0.982 0.024 0 0.00 0.976 0.00 0.00
#> SRR1047857 4 0.0632 0.982 0.024 0 0.00 0.976 0.00 0.00
#> SRR1047858 1 0.2300 0.871 0.856 0 0.00 0.144 0.00 0.00
#> SRR1047859 1 0.2300 0.871 0.856 0 0.00 0.144 0.00 0.00
#> SRR1047860 1 0.2300 0.871 0.856 0 0.00 0.144 0.00 0.00
#> SRR1047861 1 0.2300 0.871 0.856 0 0.00 0.144 0.00 0.00
#> SRR1047863 3 0.0000 0.981 0.000 0 1.00 0.000 0.00 0.00
#> SRR1047864 5 0.1267 0.000 0.000 0 0.00 0.000 0.94 0.06
#> SRR1047865 3 0.1267 0.954 0.000 0 0.94 0.000 0.06 0.00
#> SRR1047866 3 0.1267 0.954 0.000 0 0.94 0.000 0.06 0.00
#> SRR1047867 6 0.0000 0.000 0.000 0 0.00 0.000 0.00 1.00
#> SRR1047868 3 0.0000 0.981 0.000 0 1.00 0.000 0.00 0.00
#> SRR1047869 3 0.1267 0.954 0.000 0 0.94 0.000 0.06 0.00
#> SRR1047870 3 0.0000 0.981 0.000 0 1.00 0.000 0.00 0.00
#> SRR1047871 3 0.0000 0.981 0.000 0 1.00 0.000 0.00 0.00
#> SRR1047872 3 0.0000 0.981 0.000 0 1.00 0.000 0.00 0.00
#> SRR1047873 3 0.0000 0.981 0.000 0 1.00 0.000 0.00 0.00
#> SRR1047874 3 0.0000 0.981 0.000 0 1.00 0.000 0.00 0.00
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 17931 rows and 61 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 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 0.602 0.944 0.961 0.2023 0.820 0.820
#> 3 3 0.509 0.904 0.905 1.3317 0.736 0.677
#> 4 4 0.622 0.897 0.897 0.4135 0.738 0.528
#> 5 5 0.639 0.790 0.818 0.1166 1.000 1.000
#> 6 6 0.691 0.680 0.769 0.0673 0.923 0.739
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
#> SRR1047813 1 0.0376 0.965 0.996 0.004
#> SRR1047814 1 0.0376 0.965 0.996 0.004
#> SRR1047815 1 0.0376 0.965 0.996 0.004
#> SRR1047816 1 0.0376 0.965 0.996 0.004
#> SRR1047817 1 0.0376 0.965 0.996 0.004
#> SRR1047818 1 0.0000 0.965 1.000 0.000
#> SRR1047819 1 0.0000 0.965 1.000 0.000
#> SRR1047820 1 0.0000 0.965 1.000 0.000
#> SRR1047821 1 0.0000 0.965 1.000 0.000
#> SRR1047822 1 0.0000 0.965 1.000 0.000
#> SRR1047823 1 0.0376 0.965 0.996 0.004
#> SRR1047824 1 0.0376 0.965 0.996 0.004
#> SRR1047825 1 0.0376 0.965 0.996 0.004
#> SRR1047826 1 0.0376 0.965 0.996 0.004
#> SRR1047827 1 0.0376 0.965 0.996 0.004
#> SRR1047828 1 0.0376 0.965 0.996 0.004
#> SRR1047829 1 0.0376 0.965 0.996 0.004
#> SRR1047830 1 0.0376 0.965 0.996 0.004
#> SRR1047831 1 0.0376 0.965 0.996 0.004
#> SRR1047832 1 0.0376 0.965 0.996 0.004
#> SRR1047833 2 0.5842 0.969 0.140 0.860
#> SRR1047834 2 0.5842 0.969 0.140 0.860
#> SRR1047835 2 0.5842 0.969 0.140 0.860
#> SRR1047836 2 0.5842 0.969 0.140 0.860
#> SRR1047837 2 0.5842 0.969 0.140 0.860
#> SRR1047838 1 0.0000 0.965 1.000 0.000
#> SRR1047839 1 0.0000 0.965 1.000 0.000
#> SRR1047840 1 0.0000 0.965 1.000 0.000
#> SRR1047841 1 0.0000 0.965 1.000 0.000
#> SRR1047842 1 0.0000 0.965 1.000 0.000
#> SRR1047843 1 0.0672 0.961 0.992 0.008
#> SRR1047844 1 0.0672 0.961 0.992 0.008
#> SRR1047845 1 0.0672 0.961 0.992 0.008
#> SRR1047846 1 0.0672 0.961 0.992 0.008
#> SRR1047847 1 0.0672 0.961 0.992 0.008
#> SRR1047848 1 0.0376 0.965 0.996 0.004
#> SRR1047849 1 0.0376 0.965 0.996 0.004
#> SRR1047850 1 0.0376 0.965 0.996 0.004
#> SRR1047851 1 0.0376 0.965 0.996 0.004
#> SRR1047852 1 0.0376 0.965 0.996 0.004
#> SRR1047853 1 0.0000 0.965 1.000 0.000
#> SRR1047854 1 0.0000 0.965 1.000 0.000
#> SRR1047855 1 0.0000 0.965 1.000 0.000
#> SRR1047856 1 0.0000 0.965 1.000 0.000
#> SRR1047857 1 0.0000 0.965 1.000 0.000
#> SRR1047858 1 0.0000 0.965 1.000 0.000
#> SRR1047859 1 0.0000 0.965 1.000 0.000
#> SRR1047860 1 0.0000 0.965 1.000 0.000
#> SRR1047861 1 0.0000 0.965 1.000 0.000
#> SRR1047863 1 0.5842 0.861 0.860 0.140
#> SRR1047864 1 0.5842 0.861 0.860 0.140
#> SRR1047865 1 0.5842 0.861 0.860 0.140
#> SRR1047866 1 0.5842 0.861 0.860 0.140
#> SRR1047867 2 0.0672 0.855 0.008 0.992
#> SRR1047868 1 0.5842 0.861 0.860 0.140
#> SRR1047869 1 0.5842 0.861 0.860 0.140
#> SRR1047870 1 0.5842 0.861 0.860 0.140
#> SRR1047871 1 0.5842 0.861 0.860 0.140
#> SRR1047872 1 0.5842 0.861 0.860 0.140
#> SRR1047873 1 0.5842 0.861 0.860 0.140
#> SRR1047874 1 0.5842 0.861 0.860 0.140
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1047813 1 0.0892 0.884 0.980 0 0.020
#> SRR1047814 1 0.0892 0.884 0.980 0 0.020
#> SRR1047815 1 0.0892 0.884 0.980 0 0.020
#> SRR1047816 1 0.0892 0.884 0.980 0 0.020
#> SRR1047817 1 0.0892 0.884 0.980 0 0.020
#> SRR1047818 1 0.4887 0.859 0.772 0 0.228
#> SRR1047819 1 0.4887 0.859 0.772 0 0.228
#> SRR1047820 1 0.4887 0.859 0.772 0 0.228
#> SRR1047821 1 0.4887 0.859 0.772 0 0.228
#> SRR1047822 1 0.4887 0.859 0.772 0 0.228
#> SRR1047823 1 0.4399 0.870 0.812 0 0.188
#> SRR1047824 1 0.4399 0.870 0.812 0 0.188
#> SRR1047825 1 0.4399 0.870 0.812 0 0.188
#> SRR1047826 1 0.4399 0.870 0.812 0 0.188
#> SRR1047827 1 0.4399 0.870 0.812 0 0.188
#> SRR1047828 1 0.2165 0.895 0.936 0 0.064
#> SRR1047829 1 0.2165 0.895 0.936 0 0.064
#> SRR1047830 1 0.2165 0.895 0.936 0 0.064
#> SRR1047831 1 0.2165 0.895 0.936 0 0.064
#> SRR1047832 1 0.2165 0.895 0.936 0 0.064
#> SRR1047833 2 0.0000 1.000 0.000 1 0.000
#> SRR1047834 2 0.0000 1.000 0.000 1 0.000
#> SRR1047835 2 0.0000 1.000 0.000 1 0.000
#> SRR1047836 2 0.0000 1.000 0.000 1 0.000
#> SRR1047837 2 0.0000 1.000 0.000 1 0.000
#> SRR1047838 1 0.4887 0.859 0.772 0 0.228
#> SRR1047839 1 0.4887 0.859 0.772 0 0.228
#> SRR1047840 1 0.4887 0.859 0.772 0 0.228
#> SRR1047841 1 0.4887 0.859 0.772 0 0.228
#> SRR1047842 1 0.4887 0.859 0.772 0 0.228
#> SRR1047843 1 0.0747 0.892 0.984 0 0.016
#> SRR1047844 1 0.1529 0.889 0.960 0 0.040
#> SRR1047845 1 0.0747 0.892 0.984 0 0.016
#> SRR1047846 1 0.0747 0.892 0.984 0 0.016
#> SRR1047847 1 0.1529 0.889 0.960 0 0.040
#> SRR1047848 1 0.0747 0.885 0.984 0 0.016
#> SRR1047849 1 0.0747 0.885 0.984 0 0.016
#> SRR1047850 1 0.0747 0.885 0.984 0 0.016
#> SRR1047851 1 0.0747 0.885 0.984 0 0.016
#> SRR1047852 1 0.0747 0.885 0.984 0 0.016
#> SRR1047853 1 0.4002 0.873 0.840 0 0.160
#> SRR1047854 1 0.4002 0.873 0.840 0 0.160
#> SRR1047855 1 0.4002 0.873 0.840 0 0.160
#> SRR1047856 1 0.4002 0.873 0.840 0 0.160
#> SRR1047857 1 0.4002 0.873 0.840 0 0.160
#> SRR1047858 1 0.0747 0.892 0.984 0 0.016
#> SRR1047859 1 0.0747 0.892 0.984 0 0.016
#> SRR1047860 1 0.0747 0.892 0.984 0 0.016
#> SRR1047861 1 0.0747 0.892 0.984 0 0.016
#> SRR1047863 3 0.2878 0.968 0.096 0 0.904
#> SRR1047864 3 0.2625 0.958 0.084 0 0.916
#> SRR1047865 3 0.3879 0.922 0.152 0 0.848
#> SRR1047866 3 0.3686 0.909 0.140 0 0.860
#> SRR1047867 2 0.0000 1.000 0.000 1 0.000
#> SRR1047868 3 0.2878 0.968 0.096 0 0.904
#> SRR1047869 3 0.3879 0.922 0.152 0 0.848
#> SRR1047870 3 0.2878 0.968 0.096 0 0.904
#> SRR1047871 3 0.2878 0.968 0.096 0 0.904
#> SRR1047872 3 0.2878 0.968 0.096 0 0.904
#> SRR1047873 3 0.2878 0.968 0.096 0 0.904
#> SRR1047874 3 0.2878 0.968 0.096 0 0.904
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1047813 1 0.3674 0.884 0.848 0.000 0.036 0.116
#> SRR1047814 1 0.3674 0.884 0.848 0.000 0.036 0.116
#> SRR1047815 1 0.3674 0.884 0.848 0.000 0.036 0.116
#> SRR1047816 1 0.3674 0.884 0.848 0.000 0.036 0.116
#> SRR1047817 1 0.3674 0.884 0.848 0.000 0.036 0.116
#> SRR1047818 4 0.0376 0.932 0.004 0.000 0.004 0.992
#> SRR1047819 4 0.0376 0.932 0.004 0.000 0.004 0.992
#> SRR1047820 4 0.0376 0.932 0.004 0.000 0.004 0.992
#> SRR1047821 4 0.0376 0.932 0.004 0.000 0.004 0.992
#> SRR1047822 4 0.0376 0.932 0.004 0.000 0.004 0.992
#> SRR1047823 4 0.1452 0.920 0.036 0.000 0.008 0.956
#> SRR1047824 4 0.1452 0.920 0.036 0.000 0.008 0.956
#> SRR1047825 4 0.1452 0.920 0.036 0.000 0.008 0.956
#> SRR1047826 4 0.1452 0.920 0.036 0.000 0.008 0.956
#> SRR1047827 4 0.1452 0.920 0.036 0.000 0.008 0.956
#> SRR1047828 1 0.5339 0.678 0.624 0.000 0.020 0.356
#> SRR1047829 1 0.5339 0.678 0.624 0.000 0.020 0.356
#> SRR1047830 1 0.5339 0.678 0.624 0.000 0.020 0.356
#> SRR1047831 1 0.5339 0.678 0.624 0.000 0.020 0.356
#> SRR1047832 1 0.5339 0.678 0.624 0.000 0.020 0.356
#> SRR1047833 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> SRR1047834 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> SRR1047835 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> SRR1047836 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> SRR1047837 2 0.0000 0.985 0.000 1.000 0.000 0.000
#> SRR1047838 4 0.0000 0.931 0.000 0.000 0.000 1.000
#> SRR1047839 4 0.0000 0.931 0.000 0.000 0.000 1.000
#> SRR1047840 4 0.0000 0.931 0.000 0.000 0.000 1.000
#> SRR1047841 4 0.0000 0.931 0.000 0.000 0.000 1.000
#> SRR1047842 4 0.0000 0.931 0.000 0.000 0.000 1.000
#> SRR1047843 1 0.3831 0.886 0.792 0.000 0.004 0.204
#> SRR1047844 1 0.3831 0.886 0.792 0.000 0.004 0.204
#> SRR1047845 1 0.3831 0.886 0.792 0.000 0.004 0.204
#> SRR1047846 1 0.3831 0.886 0.792 0.000 0.004 0.204
#> SRR1047847 1 0.3831 0.886 0.792 0.000 0.004 0.204
#> SRR1047848 1 0.2814 0.895 0.868 0.000 0.000 0.132
#> SRR1047849 1 0.2814 0.895 0.868 0.000 0.000 0.132
#> SRR1047850 1 0.2814 0.895 0.868 0.000 0.000 0.132
#> SRR1047851 1 0.2814 0.895 0.868 0.000 0.000 0.132
#> SRR1047852 1 0.2814 0.895 0.868 0.000 0.000 0.132
#> SRR1047853 4 0.3024 0.807 0.148 0.000 0.000 0.852
#> SRR1047854 4 0.3024 0.807 0.148 0.000 0.000 0.852
#> SRR1047855 4 0.3024 0.807 0.148 0.000 0.000 0.852
#> SRR1047856 4 0.3024 0.807 0.148 0.000 0.000 0.852
#> SRR1047857 4 0.3024 0.807 0.148 0.000 0.000 0.852
#> SRR1047858 1 0.3356 0.893 0.824 0.000 0.000 0.176
#> SRR1047859 1 0.3356 0.893 0.824 0.000 0.000 0.176
#> SRR1047860 1 0.3356 0.893 0.824 0.000 0.000 0.176
#> SRR1047861 1 0.3356 0.893 0.824 0.000 0.000 0.176
#> SRR1047863 3 0.1584 0.978 0.012 0.000 0.952 0.036
#> SRR1047864 3 0.3552 0.886 0.128 0.000 0.848 0.024
#> SRR1047865 3 0.1488 0.961 0.032 0.000 0.956 0.012
#> SRR1047866 3 0.1174 0.963 0.020 0.000 0.968 0.012
#> SRR1047867 2 0.2589 0.921 0.116 0.884 0.000 0.000
#> SRR1047868 3 0.1584 0.978 0.012 0.000 0.952 0.036
#> SRR1047869 3 0.1488 0.961 0.032 0.000 0.956 0.012
#> SRR1047870 3 0.1584 0.978 0.012 0.000 0.952 0.036
#> SRR1047871 3 0.1584 0.978 0.012 0.000 0.952 0.036
#> SRR1047872 3 0.1584 0.978 0.012 0.000 0.952 0.036
#> SRR1047873 3 0.1584 0.978 0.012 0.000 0.952 0.036
#> SRR1047874 3 0.1584 0.978 0.012 0.000 0.952 0.036
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1047813 1 0.4397 0.689 0.564 0.000 0.004 0.000 NA
#> SRR1047814 1 0.4397 0.689 0.564 0.000 0.004 0.000 NA
#> SRR1047815 1 0.4397 0.689 0.564 0.000 0.004 0.000 NA
#> SRR1047816 1 0.4397 0.689 0.564 0.000 0.004 0.000 NA
#> SRR1047817 1 0.4397 0.689 0.564 0.000 0.004 0.000 NA
#> SRR1047818 4 0.1992 0.846 0.032 0.000 0.000 0.924 NA
#> SRR1047819 4 0.1992 0.846 0.032 0.000 0.000 0.924 NA
#> SRR1047820 4 0.1992 0.846 0.032 0.000 0.000 0.924 NA
#> SRR1047821 4 0.1992 0.846 0.032 0.000 0.000 0.924 NA
#> SRR1047822 4 0.1992 0.846 0.032 0.000 0.000 0.924 NA
#> SRR1047823 4 0.4739 0.753 0.056 0.000 0.008 0.724 NA
#> SRR1047824 4 0.4739 0.753 0.056 0.000 0.008 0.724 NA
#> SRR1047825 4 0.4739 0.753 0.056 0.000 0.008 0.724 NA
#> SRR1047826 4 0.4739 0.753 0.056 0.000 0.008 0.724 NA
#> SRR1047827 4 0.4739 0.753 0.056 0.000 0.008 0.724 NA
#> SRR1047828 1 0.6553 0.548 0.432 0.000 0.000 0.204 NA
#> SRR1047829 1 0.6553 0.548 0.432 0.000 0.000 0.204 NA
#> SRR1047830 1 0.6553 0.548 0.432 0.000 0.000 0.204 NA
#> SRR1047831 1 0.6553 0.548 0.432 0.000 0.000 0.204 NA
#> SRR1047832 1 0.6553 0.548 0.432 0.000 0.000 0.204 NA
#> SRR1047833 2 0.0162 0.964 0.000 0.996 0.000 0.004 NA
#> SRR1047834 2 0.0000 0.965 0.000 1.000 0.000 0.000 NA
#> SRR1047835 2 0.0000 0.965 0.000 1.000 0.000 0.000 NA
#> SRR1047836 2 0.0000 0.965 0.000 1.000 0.000 0.000 NA
#> SRR1047837 2 0.0000 0.965 0.000 1.000 0.000 0.000 NA
#> SRR1047838 4 0.2011 0.848 0.088 0.000 0.004 0.908 NA
#> SRR1047839 4 0.2011 0.848 0.088 0.000 0.004 0.908 NA
#> SRR1047840 4 0.2011 0.848 0.088 0.000 0.004 0.908 NA
#> SRR1047841 4 0.2011 0.848 0.088 0.000 0.004 0.908 NA
#> SRR1047842 4 0.2011 0.848 0.088 0.000 0.004 0.908 NA
#> SRR1047843 1 0.3427 0.689 0.844 0.000 0.004 0.096 NA
#> SRR1047844 1 0.3494 0.687 0.840 0.000 0.004 0.096 NA
#> SRR1047845 1 0.3427 0.689 0.844 0.000 0.004 0.096 NA
#> SRR1047846 1 0.3427 0.689 0.844 0.000 0.004 0.096 NA
#> SRR1047847 1 0.3494 0.687 0.840 0.000 0.004 0.096 NA
#> SRR1047848 1 0.3596 0.740 0.776 0.000 0.000 0.012 NA
#> SRR1047849 1 0.3596 0.740 0.776 0.000 0.000 0.012 NA
#> SRR1047850 1 0.3596 0.740 0.776 0.000 0.000 0.012 NA
#> SRR1047851 1 0.3596 0.740 0.776 0.000 0.000 0.012 NA
#> SRR1047852 1 0.3596 0.740 0.776 0.000 0.000 0.012 NA
#> SRR1047853 4 0.4272 0.755 0.196 0.000 0.000 0.752 NA
#> SRR1047854 4 0.4272 0.755 0.196 0.000 0.000 0.752 NA
#> SRR1047855 4 0.4272 0.755 0.196 0.000 0.000 0.752 NA
#> SRR1047856 4 0.4272 0.755 0.196 0.000 0.000 0.752 NA
#> SRR1047857 4 0.4272 0.755 0.196 0.000 0.000 0.752 NA
#> SRR1047858 1 0.1124 0.713 0.960 0.000 0.000 0.036 NA
#> SRR1047859 1 0.1124 0.713 0.960 0.000 0.000 0.036 NA
#> SRR1047860 1 0.1124 0.713 0.960 0.000 0.000 0.036 NA
#> SRR1047861 1 0.1124 0.713 0.960 0.000 0.000 0.036 NA
#> SRR1047863 3 0.0566 0.968 0.004 0.000 0.984 0.012 NA
#> SRR1047864 3 0.4070 0.744 0.004 0.000 0.728 0.012 NA
#> SRR1047865 3 0.1106 0.956 0.012 0.000 0.964 0.024 NA
#> SRR1047866 3 0.1106 0.956 0.012 0.000 0.964 0.024 NA
#> SRR1047867 2 0.3534 0.814 0.000 0.744 0.000 0.000 NA
#> SRR1047868 3 0.0566 0.968 0.004 0.000 0.984 0.012 NA
#> SRR1047869 3 0.1106 0.956 0.012 0.000 0.964 0.024 NA
#> SRR1047870 3 0.0566 0.968 0.004 0.000 0.984 0.012 NA
#> SRR1047871 3 0.0451 0.965 0.004 0.000 0.988 0.008 NA
#> SRR1047872 3 0.0566 0.968 0.004 0.000 0.984 0.012 NA
#> SRR1047873 3 0.0566 0.968 0.004 0.000 0.984 0.012 NA
#> SRR1047874 3 0.0566 0.968 0.004 0.000 0.984 0.012 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1047813 5 0.3489 0.425 0.288 0.000 0.000 0.004 0.708 NA
#> SRR1047814 5 0.3489 0.425 0.288 0.000 0.000 0.004 0.708 NA
#> SRR1047815 5 0.3489 0.425 0.288 0.000 0.000 0.004 0.708 NA
#> SRR1047816 5 0.3489 0.425 0.288 0.000 0.000 0.004 0.708 NA
#> SRR1047817 5 0.3489 0.425 0.288 0.000 0.000 0.004 0.708 NA
#> SRR1047818 4 0.2860 0.725 0.000 0.000 0.000 0.852 0.048 NA
#> SRR1047819 4 0.2860 0.725 0.000 0.000 0.000 0.852 0.048 NA
#> SRR1047820 4 0.2860 0.725 0.000 0.000 0.000 0.852 0.048 NA
#> SRR1047821 4 0.2860 0.725 0.000 0.000 0.000 0.852 0.048 NA
#> SRR1047822 4 0.2860 0.725 0.000 0.000 0.000 0.852 0.048 NA
#> SRR1047823 4 0.4402 0.599 0.020 0.000 0.000 0.564 0.004 NA
#> SRR1047824 4 0.4402 0.599 0.020 0.000 0.000 0.564 0.004 NA
#> SRR1047825 4 0.4402 0.599 0.020 0.000 0.000 0.564 0.004 NA
#> SRR1047826 4 0.4402 0.599 0.020 0.000 0.000 0.564 0.004 NA
#> SRR1047827 4 0.4402 0.599 0.020 0.000 0.000 0.564 0.004 NA
#> SRR1047828 5 0.7194 0.571 0.168 0.000 0.000 0.164 0.448 NA
#> SRR1047829 5 0.7194 0.571 0.168 0.000 0.000 0.164 0.448 NA
#> SRR1047830 5 0.7194 0.571 0.168 0.000 0.000 0.164 0.448 NA
#> SRR1047831 5 0.7194 0.571 0.168 0.000 0.000 0.164 0.448 NA
#> SRR1047832 5 0.7194 0.571 0.168 0.000 0.000 0.164 0.448 NA
#> SRR1047833 2 0.0260 0.947 0.000 0.992 0.000 0.000 0.008 NA
#> SRR1047834 2 0.0000 0.950 0.000 1.000 0.000 0.000 0.000 NA
#> SRR1047835 2 0.0000 0.950 0.000 1.000 0.000 0.000 0.000 NA
#> SRR1047836 2 0.0000 0.950 0.000 1.000 0.000 0.000 0.000 NA
#> SRR1047837 2 0.0000 0.950 0.000 1.000 0.000 0.000 0.000 NA
#> SRR1047838 4 0.2123 0.739 0.064 0.000 0.000 0.908 0.008 NA
#> SRR1047839 4 0.2036 0.738 0.064 0.000 0.000 0.912 0.008 NA
#> SRR1047840 4 0.2123 0.739 0.064 0.000 0.000 0.908 0.008 NA
#> SRR1047841 4 0.2123 0.739 0.064 0.000 0.000 0.908 0.008 NA
#> SRR1047842 4 0.2123 0.739 0.064 0.000 0.000 0.908 0.008 NA
#> SRR1047843 1 0.3013 0.604 0.864 0.000 0.000 0.064 0.028 NA
#> SRR1047844 1 0.3013 0.604 0.864 0.000 0.000 0.064 0.028 NA
#> SRR1047845 1 0.3013 0.604 0.864 0.000 0.000 0.064 0.028 NA
#> SRR1047846 1 0.3013 0.604 0.864 0.000 0.000 0.064 0.028 NA
#> SRR1047847 1 0.3013 0.604 0.864 0.000 0.000 0.064 0.028 NA
#> SRR1047848 1 0.4870 0.383 0.584 0.000 0.000 0.004 0.352 NA
#> SRR1047849 1 0.4870 0.383 0.584 0.000 0.000 0.004 0.352 NA
#> SRR1047850 1 0.4870 0.383 0.584 0.000 0.000 0.004 0.352 NA
#> SRR1047851 1 0.4870 0.383 0.584 0.000 0.000 0.004 0.352 NA
#> SRR1047852 1 0.4870 0.383 0.584 0.000 0.000 0.004 0.352 NA
#> SRR1047853 4 0.5218 0.597 0.212 0.000 0.000 0.668 0.052 NA
#> SRR1047854 4 0.5218 0.597 0.212 0.000 0.000 0.668 0.052 NA
#> SRR1047855 4 0.5218 0.597 0.212 0.000 0.000 0.668 0.052 NA
#> SRR1047856 4 0.5218 0.597 0.212 0.000 0.000 0.668 0.052 NA
#> SRR1047857 4 0.5218 0.597 0.212 0.000 0.000 0.668 0.052 NA
#> SRR1047858 1 0.2797 0.648 0.872 0.000 0.000 0.016 0.076 NA
#> SRR1047859 1 0.2797 0.648 0.872 0.000 0.000 0.016 0.076 NA
#> SRR1047860 1 0.2797 0.648 0.872 0.000 0.000 0.016 0.076 NA
#> SRR1047861 1 0.2797 0.648 0.872 0.000 0.000 0.016 0.076 NA
#> SRR1047863 3 0.0692 0.955 0.004 0.000 0.976 0.000 0.020 NA
#> SRR1047864 3 0.4886 0.642 0.004 0.000 0.652 0.000 0.100 NA
#> SRR1047865 3 0.0547 0.956 0.000 0.000 0.980 0.000 0.020 NA
#> SRR1047866 3 0.1075 0.948 0.000 0.000 0.952 0.000 0.048 NA
#> SRR1047867 2 0.4713 0.728 0.004 0.652 0.000 0.000 0.072 NA
#> SRR1047868 3 0.0000 0.960 0.000 0.000 1.000 0.000 0.000 NA
#> SRR1047869 3 0.0547 0.956 0.000 0.000 0.980 0.000 0.020 NA
#> SRR1047870 3 0.0692 0.955 0.004 0.000 0.976 0.000 0.020 NA
#> SRR1047871 3 0.0000 0.960 0.000 0.000 1.000 0.000 0.000 NA
#> SRR1047872 3 0.0000 0.960 0.000 0.000 1.000 0.000 0.000 NA
#> SRR1047873 3 0.0000 0.960 0.000 0.000 1.000 0.000 0.000 NA
#> SRR1047874 3 0.0000 0.960 0.000 0.000 1.000 0.000 0.000 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 17931 rows and 61 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 0.847 0.899 0.949 0.4442 0.531 0.531
#> 3 3 0.932 0.970 0.971 0.5009 0.694 0.475
#> 4 4 0.932 0.965 0.977 0.1019 0.896 0.698
#> 5 5 0.836 0.847 0.902 0.0541 0.984 0.936
#> 6 6 0.820 0.833 0.889 0.0575 0.959 0.830
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
#> SRR1047813 1 0.1633 0.976 0.976 0.024
#> SRR1047814 1 0.1633 0.976 0.976 0.024
#> SRR1047815 1 0.1633 0.976 0.976 0.024
#> SRR1047816 1 0.1633 0.976 0.976 0.024
#> SRR1047817 1 0.1633 0.976 0.976 0.024
#> SRR1047818 1 0.1184 0.984 0.984 0.016
#> SRR1047819 1 0.1184 0.984 0.984 0.016
#> SRR1047820 1 0.1184 0.984 0.984 0.016
#> SRR1047821 1 0.1184 0.984 0.984 0.016
#> SRR1047822 1 0.1414 0.981 0.980 0.020
#> SRR1047823 1 0.0938 0.983 0.988 0.012
#> SRR1047824 1 0.0938 0.983 0.988 0.012
#> SRR1047825 1 0.0938 0.983 0.988 0.012
#> SRR1047826 1 0.0938 0.983 0.988 0.012
#> SRR1047827 1 0.0938 0.983 0.988 0.012
#> SRR1047828 2 0.9954 0.293 0.460 0.540
#> SRR1047829 2 0.9635 0.449 0.388 0.612
#> SRR1047830 2 0.9954 0.293 0.460 0.540
#> SRR1047831 2 0.9954 0.293 0.460 0.540
#> SRR1047832 2 0.9954 0.293 0.460 0.540
#> SRR1047833 2 0.0672 0.872 0.008 0.992
#> SRR1047834 2 0.0672 0.872 0.008 0.992
#> SRR1047835 2 0.0672 0.872 0.008 0.992
#> SRR1047836 2 0.0672 0.872 0.008 0.992
#> SRR1047837 2 0.0672 0.872 0.008 0.992
#> SRR1047838 1 0.0672 0.986 0.992 0.008
#> SRR1047839 1 0.0672 0.986 0.992 0.008
#> SRR1047840 1 0.0672 0.986 0.992 0.008
#> SRR1047841 1 0.0672 0.986 0.992 0.008
#> SRR1047842 1 0.0672 0.986 0.992 0.008
#> SRR1047843 1 0.0672 0.986 0.992 0.008
#> SRR1047844 1 0.0672 0.986 0.992 0.008
#> SRR1047845 1 0.0672 0.986 0.992 0.008
#> SRR1047846 1 0.0672 0.986 0.992 0.008
#> SRR1047847 1 0.0672 0.986 0.992 0.008
#> SRR1047848 1 0.1633 0.976 0.976 0.024
#> SRR1047849 1 0.1633 0.976 0.976 0.024
#> SRR1047850 1 0.1633 0.976 0.976 0.024
#> SRR1047851 1 0.1633 0.976 0.976 0.024
#> SRR1047852 1 0.1633 0.976 0.976 0.024
#> SRR1047853 1 0.0672 0.986 0.992 0.008
#> SRR1047854 1 0.0672 0.986 0.992 0.008
#> SRR1047855 1 0.0672 0.986 0.992 0.008
#> SRR1047856 1 0.0672 0.986 0.992 0.008
#> SRR1047857 1 0.0672 0.986 0.992 0.008
#> SRR1047858 1 0.0000 0.986 1.000 0.000
#> SRR1047859 1 0.0000 0.986 1.000 0.000
#> SRR1047860 1 0.0000 0.986 1.000 0.000
#> SRR1047861 1 0.0000 0.986 1.000 0.000
#> SRR1047863 2 0.1843 0.877 0.028 0.972
#> SRR1047864 2 0.0672 0.875 0.008 0.992
#> SRR1047865 2 0.1843 0.877 0.028 0.972
#> SRR1047866 2 0.0938 0.875 0.012 0.988
#> SRR1047867 2 0.0000 0.874 0.000 1.000
#> SRR1047868 2 0.1843 0.877 0.028 0.972
#> SRR1047869 2 0.1843 0.877 0.028 0.972
#> SRR1047870 2 0.1633 0.876 0.024 0.976
#> SRR1047871 2 0.1843 0.877 0.028 0.972
#> SRR1047872 2 0.1843 0.877 0.028 0.972
#> SRR1047873 2 0.1843 0.877 0.028 0.972
#> SRR1047874 2 0.1843 0.877 0.028 0.972
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1047813 1 0.1163 0.977 0.972 0.028 0.000
#> SRR1047814 1 0.1163 0.977 0.972 0.028 0.000
#> SRR1047815 1 0.1163 0.977 0.972 0.028 0.000
#> SRR1047816 1 0.1163 0.977 0.972 0.028 0.000
#> SRR1047817 1 0.1163 0.977 0.972 0.028 0.000
#> SRR1047818 2 0.0000 0.993 0.000 1.000 0.000
#> SRR1047819 2 0.0000 0.993 0.000 1.000 0.000
#> SRR1047820 2 0.0000 0.993 0.000 1.000 0.000
#> SRR1047821 2 0.0000 0.993 0.000 1.000 0.000
#> SRR1047822 2 0.0000 0.993 0.000 1.000 0.000
#> SRR1047823 2 0.0892 0.982 0.020 0.980 0.000
#> SRR1047824 2 0.0892 0.982 0.020 0.980 0.000
#> SRR1047825 2 0.0892 0.982 0.020 0.980 0.000
#> SRR1047826 2 0.0892 0.982 0.020 0.980 0.000
#> SRR1047827 2 0.0892 0.982 0.020 0.980 0.000
#> SRR1047828 1 0.2537 0.909 0.920 0.000 0.080
#> SRR1047829 1 0.2537 0.909 0.920 0.000 0.080
#> SRR1047830 1 0.2537 0.909 0.920 0.000 0.080
#> SRR1047831 1 0.2537 0.909 0.920 0.000 0.080
#> SRR1047832 1 0.2537 0.909 0.920 0.000 0.080
#> SRR1047833 3 0.1163 0.956 0.028 0.000 0.972
#> SRR1047834 3 0.1163 0.956 0.028 0.000 0.972
#> SRR1047835 3 0.1163 0.956 0.028 0.000 0.972
#> SRR1047836 3 0.1163 0.956 0.028 0.000 0.972
#> SRR1047837 3 0.1163 0.956 0.028 0.000 0.972
#> SRR1047838 2 0.0000 0.993 0.000 1.000 0.000
#> SRR1047839 2 0.0000 0.993 0.000 1.000 0.000
#> SRR1047840 2 0.0000 0.993 0.000 1.000 0.000
#> SRR1047841 2 0.0000 0.993 0.000 1.000 0.000
#> SRR1047842 2 0.0000 0.993 0.000 1.000 0.000
#> SRR1047843 1 0.1163 0.977 0.972 0.028 0.000
#> SRR1047844 1 0.1163 0.977 0.972 0.028 0.000
#> SRR1047845 1 0.1163 0.977 0.972 0.028 0.000
#> SRR1047846 1 0.1163 0.977 0.972 0.028 0.000
#> SRR1047847 1 0.1163 0.977 0.972 0.028 0.000
#> SRR1047848 1 0.1163 0.977 0.972 0.028 0.000
#> SRR1047849 1 0.1163 0.977 0.972 0.028 0.000
#> SRR1047850 1 0.1163 0.977 0.972 0.028 0.000
#> SRR1047851 1 0.1163 0.977 0.972 0.028 0.000
#> SRR1047852 1 0.1163 0.977 0.972 0.028 0.000
#> SRR1047853 2 0.0237 0.991 0.004 0.996 0.000
#> SRR1047854 2 0.0237 0.991 0.004 0.996 0.000
#> SRR1047855 2 0.0237 0.991 0.004 0.996 0.000
#> SRR1047856 2 0.0237 0.991 0.004 0.996 0.000
#> SRR1047857 2 0.0237 0.991 0.004 0.996 0.000
#> SRR1047858 1 0.1163 0.977 0.972 0.028 0.000
#> SRR1047859 1 0.1163 0.977 0.972 0.028 0.000
#> SRR1047860 1 0.1163 0.977 0.972 0.028 0.000
#> SRR1047861 1 0.1163 0.977 0.972 0.028 0.000
#> SRR1047863 3 0.0892 0.961 0.000 0.020 0.980
#> SRR1047864 3 0.0000 0.960 0.000 0.000 1.000
#> SRR1047865 3 0.2636 0.955 0.048 0.020 0.932
#> SRR1047866 3 0.1529 0.958 0.040 0.000 0.960
#> SRR1047867 3 0.1163 0.956 0.028 0.000 0.972
#> SRR1047868 3 0.2689 0.957 0.036 0.032 0.932
#> SRR1047869 3 0.2636 0.955 0.048 0.020 0.932
#> SRR1047870 3 0.0892 0.961 0.000 0.020 0.980
#> SRR1047871 3 0.2663 0.956 0.044 0.024 0.932
#> SRR1047872 3 0.2689 0.957 0.036 0.032 0.932
#> SRR1047873 3 0.2689 0.957 0.036 0.032 0.932
#> SRR1047874 3 0.2689 0.957 0.036 0.032 0.932
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1047813 1 0.0188 0.998 0.996 0.004 0.000 0.000
#> SRR1047814 1 0.0188 0.998 0.996 0.004 0.000 0.000
#> SRR1047815 1 0.0188 0.998 0.996 0.004 0.000 0.000
#> SRR1047816 1 0.0188 0.998 0.996 0.004 0.000 0.000
#> SRR1047817 1 0.0188 0.998 0.996 0.004 0.000 0.000
#> SRR1047818 4 0.0000 0.989 0.000 0.000 0.000 1.000
#> SRR1047819 4 0.0000 0.989 0.000 0.000 0.000 1.000
#> SRR1047820 4 0.0000 0.989 0.000 0.000 0.000 1.000
#> SRR1047821 4 0.0000 0.989 0.000 0.000 0.000 1.000
#> SRR1047822 4 0.0000 0.989 0.000 0.000 0.000 1.000
#> SRR1047823 4 0.0000 0.989 0.000 0.000 0.000 1.000
#> SRR1047824 4 0.0000 0.989 0.000 0.000 0.000 1.000
#> SRR1047825 4 0.0000 0.989 0.000 0.000 0.000 1.000
#> SRR1047826 4 0.0000 0.989 0.000 0.000 0.000 1.000
#> SRR1047827 4 0.0000 0.989 0.000 0.000 0.000 1.000
#> SRR1047828 2 0.3837 0.824 0.224 0.776 0.000 0.000
#> SRR1047829 2 0.3837 0.824 0.224 0.776 0.000 0.000
#> SRR1047830 2 0.3837 0.824 0.224 0.776 0.000 0.000
#> SRR1047831 2 0.3837 0.824 0.224 0.776 0.000 0.000
#> SRR1047832 2 0.3837 0.824 0.224 0.776 0.000 0.000
#> SRR1047833 2 0.0188 0.860 0.000 0.996 0.004 0.000
#> SRR1047834 2 0.0188 0.860 0.000 0.996 0.004 0.000
#> SRR1047835 2 0.0188 0.860 0.000 0.996 0.004 0.000
#> SRR1047836 2 0.0188 0.860 0.000 0.996 0.004 0.000
#> SRR1047837 2 0.0188 0.860 0.000 0.996 0.004 0.000
#> SRR1047838 4 0.0000 0.989 0.000 0.000 0.000 1.000
#> SRR1047839 4 0.0000 0.989 0.000 0.000 0.000 1.000
#> SRR1047840 4 0.0000 0.989 0.000 0.000 0.000 1.000
#> SRR1047841 4 0.0000 0.989 0.000 0.000 0.000 1.000
#> SRR1047842 4 0.0000 0.989 0.000 0.000 0.000 1.000
#> SRR1047843 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> SRR1047844 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> SRR1047845 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> SRR1047846 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> SRR1047847 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> SRR1047848 1 0.0188 0.998 0.996 0.004 0.000 0.000
#> SRR1047849 1 0.0188 0.998 0.996 0.004 0.000 0.000
#> SRR1047850 1 0.0188 0.998 0.996 0.004 0.000 0.000
#> SRR1047851 1 0.0188 0.998 0.996 0.004 0.000 0.000
#> SRR1047852 1 0.0188 0.998 0.996 0.004 0.000 0.000
#> SRR1047853 4 0.1118 0.967 0.036 0.000 0.000 0.964
#> SRR1047854 4 0.1118 0.967 0.036 0.000 0.000 0.964
#> SRR1047855 4 0.1118 0.967 0.036 0.000 0.000 0.964
#> SRR1047856 4 0.1118 0.967 0.036 0.000 0.000 0.964
#> SRR1047857 4 0.1118 0.967 0.036 0.000 0.000 0.964
#> SRR1047858 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> SRR1047859 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> SRR1047860 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> SRR1047861 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> SRR1047863 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> SRR1047864 3 0.0707 0.981 0.000 0.020 0.980 0.000
#> SRR1047865 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> SRR1047866 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> SRR1047867 2 0.0188 0.860 0.000 0.996 0.004 0.000
#> SRR1047868 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> SRR1047869 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> SRR1047870 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> SRR1047871 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> SRR1047872 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> SRR1047873 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> SRR1047874 3 0.0000 0.998 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
#> SRR1047813 1 0.4201 0.615 0.592 0.000 0.000 0.000 0.408
#> SRR1047814 1 0.4201 0.615 0.592 0.000 0.000 0.000 0.408
#> SRR1047815 1 0.4201 0.615 0.592 0.000 0.000 0.000 0.408
#> SRR1047816 1 0.4201 0.615 0.592 0.000 0.000 0.000 0.408
#> SRR1047817 1 0.4201 0.615 0.592 0.000 0.000 0.000 0.408
#> SRR1047818 4 0.0000 0.893 0.000 0.000 0.000 1.000 0.000
#> SRR1047819 4 0.0000 0.893 0.000 0.000 0.000 1.000 0.000
#> SRR1047820 4 0.0000 0.893 0.000 0.000 0.000 1.000 0.000
#> SRR1047821 4 0.0000 0.893 0.000 0.000 0.000 1.000 0.000
#> SRR1047822 4 0.0000 0.893 0.000 0.000 0.000 1.000 0.000
#> SRR1047823 4 0.0162 0.893 0.000 0.000 0.000 0.996 0.004
#> SRR1047824 4 0.0162 0.893 0.000 0.000 0.000 0.996 0.004
#> SRR1047825 4 0.0162 0.893 0.000 0.000 0.000 0.996 0.004
#> SRR1047826 4 0.0162 0.893 0.000 0.000 0.000 0.996 0.004
#> SRR1047827 4 0.0162 0.893 0.000 0.000 0.000 0.996 0.004
#> SRR1047828 5 0.1502 1.000 0.004 0.056 0.000 0.000 0.940
#> SRR1047829 5 0.1502 1.000 0.004 0.056 0.000 0.000 0.940
#> SRR1047830 5 0.1502 1.000 0.004 0.056 0.000 0.000 0.940
#> SRR1047831 5 0.1502 1.000 0.004 0.056 0.000 0.000 0.940
#> SRR1047832 5 0.1502 1.000 0.004 0.056 0.000 0.000 0.940
#> SRR1047833 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047834 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047835 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047836 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047837 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047838 4 0.0404 0.892 0.000 0.000 0.000 0.988 0.012
#> SRR1047839 4 0.0404 0.892 0.000 0.000 0.000 0.988 0.012
#> SRR1047840 4 0.0404 0.892 0.000 0.000 0.000 0.988 0.012
#> SRR1047841 4 0.0404 0.892 0.000 0.000 0.000 0.988 0.012
#> SRR1047842 4 0.0404 0.892 0.000 0.000 0.000 0.988 0.012
#> SRR1047843 1 0.0510 0.745 0.984 0.000 0.000 0.000 0.016
#> SRR1047844 1 0.0510 0.745 0.984 0.000 0.000 0.000 0.016
#> SRR1047845 1 0.0510 0.745 0.984 0.000 0.000 0.000 0.016
#> SRR1047846 1 0.0510 0.745 0.984 0.000 0.000 0.000 0.016
#> SRR1047847 1 0.0510 0.745 0.984 0.000 0.000 0.000 0.016
#> SRR1047848 1 0.3752 0.716 0.708 0.000 0.000 0.000 0.292
#> SRR1047849 1 0.3752 0.716 0.708 0.000 0.000 0.000 0.292
#> SRR1047850 1 0.3752 0.716 0.708 0.000 0.000 0.000 0.292
#> SRR1047851 1 0.3752 0.716 0.708 0.000 0.000 0.000 0.292
#> SRR1047852 1 0.3752 0.716 0.708 0.000 0.000 0.000 0.292
#> SRR1047853 4 0.4840 0.653 0.320 0.000 0.000 0.640 0.040
#> SRR1047854 4 0.4840 0.653 0.320 0.000 0.000 0.640 0.040
#> SRR1047855 4 0.4840 0.653 0.320 0.000 0.000 0.640 0.040
#> SRR1047856 4 0.4840 0.653 0.320 0.000 0.000 0.640 0.040
#> SRR1047857 4 0.4840 0.653 0.320 0.000 0.000 0.640 0.040
#> SRR1047858 1 0.0290 0.752 0.992 0.000 0.000 0.000 0.008
#> SRR1047859 1 0.0290 0.752 0.992 0.000 0.000 0.000 0.008
#> SRR1047860 1 0.0290 0.752 0.992 0.000 0.000 0.000 0.008
#> SRR1047861 1 0.0290 0.752 0.992 0.000 0.000 0.000 0.008
#> SRR1047863 3 0.0000 0.983 0.000 0.000 1.000 0.000 0.000
#> SRR1047864 3 0.2813 0.798 0.000 0.168 0.832 0.000 0.000
#> SRR1047865 3 0.0000 0.983 0.000 0.000 1.000 0.000 0.000
#> SRR1047866 3 0.0000 0.983 0.000 0.000 1.000 0.000 0.000
#> SRR1047867 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047868 3 0.0000 0.983 0.000 0.000 1.000 0.000 0.000
#> SRR1047869 3 0.0000 0.983 0.000 0.000 1.000 0.000 0.000
#> SRR1047870 3 0.0000 0.983 0.000 0.000 1.000 0.000 0.000
#> SRR1047871 3 0.0000 0.983 0.000 0.000 1.000 0.000 0.000
#> SRR1047872 3 0.0000 0.983 0.000 0.000 1.000 0.000 0.000
#> SRR1047873 3 0.0000 0.983 0.000 0.000 1.000 0.000 0.000
#> SRR1047874 3 0.0000 0.983 0.000 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1047813 1 0.3190 0.634 0.772 0.000 0.00 0.000 0.220 0.008
#> SRR1047814 1 0.3190 0.634 0.772 0.000 0.00 0.000 0.220 0.008
#> SRR1047815 1 0.3190 0.634 0.772 0.000 0.00 0.000 0.220 0.008
#> SRR1047816 1 0.3190 0.634 0.772 0.000 0.00 0.000 0.220 0.008
#> SRR1047817 1 0.3190 0.634 0.772 0.000 0.00 0.000 0.220 0.008
#> SRR1047818 4 0.0405 0.883 0.000 0.000 0.00 0.988 0.008 0.004
#> SRR1047819 4 0.0405 0.883 0.000 0.000 0.00 0.988 0.008 0.004
#> SRR1047820 4 0.0405 0.883 0.000 0.000 0.00 0.988 0.008 0.004
#> SRR1047821 4 0.0405 0.883 0.000 0.000 0.00 0.988 0.008 0.004
#> SRR1047822 4 0.0405 0.883 0.000 0.000 0.00 0.988 0.008 0.004
#> SRR1047823 4 0.2009 0.862 0.008 0.000 0.00 0.904 0.004 0.084
#> SRR1047824 4 0.2009 0.862 0.008 0.000 0.00 0.904 0.004 0.084
#> SRR1047825 4 0.2009 0.862 0.008 0.000 0.00 0.904 0.004 0.084
#> SRR1047826 4 0.2009 0.862 0.008 0.000 0.00 0.904 0.004 0.084
#> SRR1047827 4 0.2009 0.862 0.008 0.000 0.00 0.904 0.004 0.084
#> SRR1047828 5 0.0520 1.000 0.008 0.008 0.00 0.000 0.984 0.000
#> SRR1047829 5 0.0520 1.000 0.008 0.008 0.00 0.000 0.984 0.000
#> SRR1047830 5 0.0520 1.000 0.008 0.008 0.00 0.000 0.984 0.000
#> SRR1047831 5 0.0520 1.000 0.008 0.008 0.00 0.000 0.984 0.000
#> SRR1047832 5 0.0520 1.000 0.008 0.008 0.00 0.000 0.984 0.000
#> SRR1047833 2 0.0000 1.000 0.000 1.000 0.00 0.000 0.000 0.000
#> SRR1047834 2 0.0000 1.000 0.000 1.000 0.00 0.000 0.000 0.000
#> SRR1047835 2 0.0000 1.000 0.000 1.000 0.00 0.000 0.000 0.000
#> SRR1047836 2 0.0000 1.000 0.000 1.000 0.00 0.000 0.000 0.000
#> SRR1047837 2 0.0000 1.000 0.000 1.000 0.00 0.000 0.000 0.000
#> SRR1047838 4 0.2597 0.803 0.000 0.000 0.00 0.824 0.000 0.176
#> SRR1047839 4 0.2597 0.803 0.000 0.000 0.00 0.824 0.000 0.176
#> SRR1047840 4 0.2597 0.803 0.000 0.000 0.00 0.824 0.000 0.176
#> SRR1047841 4 0.2597 0.803 0.000 0.000 0.00 0.824 0.000 0.176
#> SRR1047842 4 0.2597 0.803 0.000 0.000 0.00 0.824 0.000 0.176
#> SRR1047843 1 0.3997 0.359 0.508 0.000 0.00 0.000 0.004 0.488
#> SRR1047844 1 0.3999 0.342 0.500 0.000 0.00 0.000 0.004 0.496
#> SRR1047845 1 0.3997 0.359 0.508 0.000 0.00 0.000 0.004 0.488
#> SRR1047846 1 0.3997 0.359 0.508 0.000 0.00 0.000 0.004 0.488
#> SRR1047847 1 0.3999 0.342 0.500 0.000 0.00 0.000 0.004 0.496
#> SRR1047848 1 0.0547 0.737 0.980 0.000 0.00 0.000 0.020 0.000
#> SRR1047849 1 0.0547 0.737 0.980 0.000 0.00 0.000 0.020 0.000
#> SRR1047850 1 0.0547 0.737 0.980 0.000 0.00 0.000 0.020 0.000
#> SRR1047851 1 0.0547 0.737 0.980 0.000 0.00 0.000 0.020 0.000
#> SRR1047852 1 0.0547 0.737 0.980 0.000 0.00 0.000 0.020 0.000
#> SRR1047853 6 0.2003 1.000 0.000 0.000 0.00 0.116 0.000 0.884
#> SRR1047854 6 0.2003 1.000 0.000 0.000 0.00 0.116 0.000 0.884
#> SRR1047855 6 0.2003 1.000 0.000 0.000 0.00 0.116 0.000 0.884
#> SRR1047856 6 0.2003 1.000 0.000 0.000 0.00 0.116 0.000 0.884
#> SRR1047857 6 0.2003 1.000 0.000 0.000 0.00 0.116 0.000 0.884
#> SRR1047858 1 0.2320 0.717 0.864 0.000 0.00 0.000 0.004 0.132
#> SRR1047859 1 0.2320 0.717 0.864 0.000 0.00 0.000 0.004 0.132
#> SRR1047860 1 0.2320 0.717 0.864 0.000 0.00 0.000 0.004 0.132
#> SRR1047861 1 0.2320 0.717 0.864 0.000 0.00 0.000 0.004 0.132
#> SRR1047863 3 0.0000 0.981 0.000 0.000 1.00 0.000 0.000 0.000
#> SRR1047864 3 0.2631 0.780 0.000 0.180 0.82 0.000 0.000 0.000
#> SRR1047865 3 0.0000 0.981 0.000 0.000 1.00 0.000 0.000 0.000
#> SRR1047866 3 0.0000 0.981 0.000 0.000 1.00 0.000 0.000 0.000
#> SRR1047867 2 0.0000 1.000 0.000 1.000 0.00 0.000 0.000 0.000
#> SRR1047868 3 0.0000 0.981 0.000 0.000 1.00 0.000 0.000 0.000
#> SRR1047869 3 0.0000 0.981 0.000 0.000 1.00 0.000 0.000 0.000
#> SRR1047870 3 0.0000 0.981 0.000 0.000 1.00 0.000 0.000 0.000
#> SRR1047871 3 0.0000 0.981 0.000 0.000 1.00 0.000 0.000 0.000
#> SRR1047872 3 0.0000 0.981 0.000 0.000 1.00 0.000 0.000 0.000
#> SRR1047873 3 0.0000 0.981 0.000 0.000 1.00 0.000 0.000 0.000
#> SRR1047874 3 0.0000 0.981 0.000 0.000 1.00 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 17931 rows and 61 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.1811 0.820 0.820
#> 3 3 1.000 1.000 1.000 1.4586 0.736 0.677
#> 4 4 0.814 0.936 0.963 0.5308 0.770 0.587
#> 5 5 0.949 0.927 0.967 0.1104 0.932 0.790
#> 6 6 0.969 0.930 0.962 0.0349 0.975 0.904
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
#> SRR1047813 1 0 1 1 0
#> SRR1047814 1 0 1 1 0
#> SRR1047815 1 0 1 1 0
#> SRR1047816 1 0 1 1 0
#> SRR1047817 1 0 1 1 0
#> SRR1047818 1 0 1 1 0
#> SRR1047819 1 0 1 1 0
#> SRR1047820 1 0 1 1 0
#> SRR1047821 1 0 1 1 0
#> SRR1047822 1 0 1 1 0
#> SRR1047823 1 0 1 1 0
#> SRR1047824 1 0 1 1 0
#> SRR1047825 1 0 1 1 0
#> SRR1047826 1 0 1 1 0
#> SRR1047827 1 0 1 1 0
#> SRR1047828 1 0 1 1 0
#> SRR1047829 1 0 1 1 0
#> SRR1047830 1 0 1 1 0
#> SRR1047831 1 0 1 1 0
#> SRR1047832 1 0 1 1 0
#> SRR1047833 2 0 1 0 1
#> SRR1047834 2 0 1 0 1
#> SRR1047835 2 0 1 0 1
#> SRR1047836 2 0 1 0 1
#> SRR1047837 2 0 1 0 1
#> SRR1047838 1 0 1 1 0
#> SRR1047839 1 0 1 1 0
#> SRR1047840 1 0 1 1 0
#> SRR1047841 1 0 1 1 0
#> SRR1047842 1 0 1 1 0
#> SRR1047843 1 0 1 1 0
#> SRR1047844 1 0 1 1 0
#> SRR1047845 1 0 1 1 0
#> SRR1047846 1 0 1 1 0
#> SRR1047847 1 0 1 1 0
#> SRR1047848 1 0 1 1 0
#> SRR1047849 1 0 1 1 0
#> SRR1047850 1 0 1 1 0
#> SRR1047851 1 0 1 1 0
#> SRR1047852 1 0 1 1 0
#> SRR1047853 1 0 1 1 0
#> SRR1047854 1 0 1 1 0
#> SRR1047855 1 0 1 1 0
#> SRR1047856 1 0 1 1 0
#> SRR1047857 1 0 1 1 0
#> SRR1047858 1 0 1 1 0
#> SRR1047859 1 0 1 1 0
#> SRR1047860 1 0 1 1 0
#> SRR1047861 1 0 1 1 0
#> SRR1047863 1 0 1 1 0
#> SRR1047864 1 0 1 1 0
#> SRR1047865 1 0 1 1 0
#> SRR1047866 1 0 1 1 0
#> SRR1047867 2 0 1 0 1
#> SRR1047868 1 0 1 1 0
#> SRR1047869 1 0 1 1 0
#> SRR1047870 1 0 1 1 0
#> SRR1047871 1 0 1 1 0
#> SRR1047872 1 0 1 1 0
#> SRR1047873 1 0 1 1 0
#> SRR1047874 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1047813 1 0 1 1 0 0
#> SRR1047814 1 0 1 1 0 0
#> SRR1047815 1 0 1 1 0 0
#> SRR1047816 1 0 1 1 0 0
#> SRR1047817 1 0 1 1 0 0
#> SRR1047818 1 0 1 1 0 0
#> SRR1047819 1 0 1 1 0 0
#> SRR1047820 1 0 1 1 0 0
#> SRR1047821 1 0 1 1 0 0
#> SRR1047822 1 0 1 1 0 0
#> SRR1047823 1 0 1 1 0 0
#> SRR1047824 1 0 1 1 0 0
#> SRR1047825 1 0 1 1 0 0
#> SRR1047826 1 0 1 1 0 0
#> SRR1047827 1 0 1 1 0 0
#> SRR1047828 1 0 1 1 0 0
#> SRR1047829 1 0 1 1 0 0
#> SRR1047830 1 0 1 1 0 0
#> SRR1047831 1 0 1 1 0 0
#> SRR1047832 1 0 1 1 0 0
#> SRR1047833 2 0 1 0 1 0
#> SRR1047834 2 0 1 0 1 0
#> SRR1047835 2 0 1 0 1 0
#> SRR1047836 2 0 1 0 1 0
#> SRR1047837 2 0 1 0 1 0
#> SRR1047838 1 0 1 1 0 0
#> SRR1047839 1 0 1 1 0 0
#> SRR1047840 1 0 1 1 0 0
#> SRR1047841 1 0 1 1 0 0
#> SRR1047842 1 0 1 1 0 0
#> SRR1047843 1 0 1 1 0 0
#> SRR1047844 1 0 1 1 0 0
#> SRR1047845 1 0 1 1 0 0
#> SRR1047846 1 0 1 1 0 0
#> SRR1047847 1 0 1 1 0 0
#> SRR1047848 1 0 1 1 0 0
#> SRR1047849 1 0 1 1 0 0
#> SRR1047850 1 0 1 1 0 0
#> SRR1047851 1 0 1 1 0 0
#> SRR1047852 1 0 1 1 0 0
#> SRR1047853 1 0 1 1 0 0
#> SRR1047854 1 0 1 1 0 0
#> SRR1047855 1 0 1 1 0 0
#> SRR1047856 1 0 1 1 0 0
#> SRR1047857 1 0 1 1 0 0
#> SRR1047858 1 0 1 1 0 0
#> SRR1047859 1 0 1 1 0 0
#> SRR1047860 1 0 1 1 0 0
#> SRR1047861 1 0 1 1 0 0
#> SRR1047863 3 0 1 0 0 1
#> SRR1047864 3 0 1 0 0 1
#> SRR1047865 3 0 1 0 0 1
#> SRR1047866 3 0 1 0 0 1
#> SRR1047867 2 0 1 0 1 0
#> SRR1047868 3 0 1 0 0 1
#> SRR1047869 3 0 1 0 0 1
#> SRR1047870 3 0 1 0 0 1
#> SRR1047871 3 0 1 0 0 1
#> SRR1047872 3 0 1 0 0 1
#> SRR1047873 3 0 1 0 0 1
#> SRR1047874 3 0 1 0 0 1
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1047813 1 0.000 0.995 1.000 0 0 0.000
#> SRR1047814 1 0.000 0.995 1.000 0 0 0.000
#> SRR1047815 1 0.000 0.995 1.000 0 0 0.000
#> SRR1047816 1 0.000 0.995 1.000 0 0 0.000
#> SRR1047817 1 0.130 0.934 0.956 0 0 0.044
#> SRR1047818 4 0.000 0.911 0.000 0 0 1.000
#> SRR1047819 4 0.000 0.911 0.000 0 0 1.000
#> SRR1047820 4 0.000 0.911 0.000 0 0 1.000
#> SRR1047821 4 0.000 0.911 0.000 0 0 1.000
#> SRR1047822 4 0.000 0.911 0.000 0 0 1.000
#> SRR1047823 4 0.000 0.911 0.000 0 0 1.000
#> SRR1047824 4 0.000 0.911 0.000 0 0 1.000
#> SRR1047825 4 0.000 0.911 0.000 0 0 1.000
#> SRR1047826 4 0.000 0.911 0.000 0 0 1.000
#> SRR1047827 4 0.000 0.911 0.000 0 0 1.000
#> SRR1047828 4 0.387 0.794 0.228 0 0 0.772
#> SRR1047829 4 0.387 0.794 0.228 0 0 0.772
#> SRR1047830 4 0.387 0.794 0.228 0 0 0.772
#> SRR1047831 4 0.387 0.794 0.228 0 0 0.772
#> SRR1047832 4 0.387 0.794 0.228 0 0 0.772
#> SRR1047833 2 0.000 1.000 0.000 1 0 0.000
#> SRR1047834 2 0.000 1.000 0.000 1 0 0.000
#> SRR1047835 2 0.000 1.000 0.000 1 0 0.000
#> SRR1047836 2 0.000 1.000 0.000 1 0 0.000
#> SRR1047837 2 0.000 1.000 0.000 1 0 0.000
#> SRR1047838 4 0.000 0.911 0.000 0 0 1.000
#> SRR1047839 4 0.000 0.911 0.000 0 0 1.000
#> SRR1047840 4 0.000 0.911 0.000 0 0 1.000
#> SRR1047841 4 0.000 0.911 0.000 0 0 1.000
#> SRR1047842 4 0.000 0.911 0.000 0 0 1.000
#> SRR1047843 4 0.387 0.794 0.228 0 0 0.772
#> SRR1047844 4 0.353 0.820 0.192 0 0 0.808
#> SRR1047845 4 0.387 0.794 0.228 0 0 0.772
#> SRR1047846 4 0.387 0.794 0.228 0 0 0.772
#> SRR1047847 4 0.361 0.814 0.200 0 0 0.800
#> SRR1047848 1 0.000 0.995 1.000 0 0 0.000
#> SRR1047849 1 0.000 0.995 1.000 0 0 0.000
#> SRR1047850 1 0.000 0.995 1.000 0 0 0.000
#> SRR1047851 1 0.000 0.995 1.000 0 0 0.000
#> SRR1047852 1 0.000 0.995 1.000 0 0 0.000
#> SRR1047853 4 0.000 0.911 0.000 0 0 1.000
#> SRR1047854 4 0.000 0.911 0.000 0 0 1.000
#> SRR1047855 4 0.000 0.911 0.000 0 0 1.000
#> SRR1047856 4 0.000 0.911 0.000 0 0 1.000
#> SRR1047857 4 0.000 0.911 0.000 0 0 1.000
#> SRR1047858 1 0.000 0.995 1.000 0 0 0.000
#> SRR1047859 1 0.000 0.995 1.000 0 0 0.000
#> SRR1047860 1 0.000 0.995 1.000 0 0 0.000
#> SRR1047861 1 0.000 0.995 1.000 0 0 0.000
#> SRR1047863 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047864 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047865 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047866 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047867 2 0.000 1.000 0.000 1 0 0.000
#> SRR1047868 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047869 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047870 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047871 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047872 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047873 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047874 3 0.000 1.000 0.000 0 1 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1047813 1 0.0000 0.984 1.000 0 0 0.000 0.000
#> SRR1047814 1 0.0000 0.984 1.000 0 0 0.000 0.000
#> SRR1047815 1 0.0000 0.984 1.000 0 0 0.000 0.000
#> SRR1047816 1 0.0000 0.984 1.000 0 0 0.000 0.000
#> SRR1047817 1 0.2732 0.769 0.840 0 0 0.160 0.000
#> SRR1047818 4 0.4114 0.487 0.000 0 0 0.624 0.376
#> SRR1047819 4 0.4171 0.448 0.000 0 0 0.604 0.396
#> SRR1047820 4 0.4171 0.448 0.000 0 0 0.604 0.396
#> SRR1047821 4 0.4101 0.495 0.000 0 0 0.628 0.372
#> SRR1047822 4 0.3109 0.740 0.000 0 0 0.800 0.200
#> SRR1047823 5 0.0162 1.000 0.000 0 0 0.004 0.996
#> SRR1047824 5 0.0162 1.000 0.000 0 0 0.004 0.996
#> SRR1047825 5 0.0162 1.000 0.000 0 0 0.004 0.996
#> SRR1047826 5 0.0162 1.000 0.000 0 0 0.004 0.996
#> SRR1047827 5 0.0162 1.000 0.000 0 0 0.004 0.996
#> SRR1047828 4 0.0162 0.919 0.000 0 0 0.996 0.004
#> SRR1047829 4 0.0162 0.919 0.000 0 0 0.996 0.004
#> SRR1047830 4 0.0162 0.919 0.000 0 0 0.996 0.004
#> SRR1047831 4 0.0162 0.919 0.000 0 0 0.996 0.004
#> SRR1047832 4 0.0162 0.919 0.000 0 0 0.996 0.004
#> SRR1047833 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> SRR1047834 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> SRR1047835 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> SRR1047836 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> SRR1047837 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> SRR1047838 4 0.0162 0.919 0.000 0 0 0.996 0.004
#> SRR1047839 4 0.0162 0.919 0.000 0 0 0.996 0.004
#> SRR1047840 4 0.0162 0.919 0.000 0 0 0.996 0.004
#> SRR1047841 4 0.0162 0.919 0.000 0 0 0.996 0.004
#> SRR1047842 4 0.0162 0.919 0.000 0 0 0.996 0.004
#> SRR1047843 4 0.0162 0.919 0.004 0 0 0.996 0.000
#> SRR1047844 4 0.0162 0.919 0.004 0 0 0.996 0.000
#> SRR1047845 4 0.0162 0.919 0.004 0 0 0.996 0.000
#> SRR1047846 4 0.0162 0.919 0.004 0 0 0.996 0.000
#> SRR1047847 4 0.0162 0.919 0.004 0 0 0.996 0.000
#> SRR1047848 1 0.0000 0.984 1.000 0 0 0.000 0.000
#> SRR1047849 1 0.0000 0.984 1.000 0 0 0.000 0.000
#> SRR1047850 1 0.0000 0.984 1.000 0 0 0.000 0.000
#> SRR1047851 1 0.0000 0.984 1.000 0 0 0.000 0.000
#> SRR1047852 1 0.0000 0.984 1.000 0 0 0.000 0.000
#> SRR1047853 4 0.0000 0.920 0.000 0 0 1.000 0.000
#> SRR1047854 4 0.0000 0.920 0.000 0 0 1.000 0.000
#> SRR1047855 4 0.0000 0.920 0.000 0 0 1.000 0.000
#> SRR1047856 4 0.0000 0.920 0.000 0 0 1.000 0.000
#> SRR1047857 4 0.0000 0.920 0.000 0 0 1.000 0.000
#> SRR1047858 1 0.0000 0.984 1.000 0 0 0.000 0.000
#> SRR1047859 1 0.0000 0.984 1.000 0 0 0.000 0.000
#> SRR1047860 1 0.0000 0.984 1.000 0 0 0.000 0.000
#> SRR1047861 1 0.0000 0.984 1.000 0 0 0.000 0.000
#> SRR1047863 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> SRR1047864 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> SRR1047865 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> SRR1047866 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> SRR1047867 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> SRR1047868 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> SRR1047869 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> SRR1047870 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> SRR1047871 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> SRR1047872 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> SRR1047873 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> SRR1047874 3 0.0000 1.000 0.000 0 1 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1047813 6 0.1075 0.998 0.048 0 0.000 0.000 0.000 0.952
#> SRR1047814 6 0.1075 0.998 0.048 0 0.000 0.000 0.000 0.952
#> SRR1047815 6 0.1075 0.998 0.048 0 0.000 0.000 0.000 0.952
#> SRR1047816 6 0.1075 0.998 0.048 0 0.000 0.000 0.000 0.952
#> SRR1047817 6 0.1152 0.993 0.044 0 0.000 0.004 0.000 0.952
#> SRR1047818 4 0.3695 0.495 0.000 0 0.000 0.624 0.376 0.000
#> SRR1047819 4 0.3747 0.457 0.000 0 0.000 0.604 0.396 0.000
#> SRR1047820 4 0.3747 0.457 0.000 0 0.000 0.604 0.396 0.000
#> SRR1047821 4 0.3684 0.501 0.000 0 0.000 0.628 0.372 0.000
#> SRR1047822 4 0.2793 0.741 0.000 0 0.000 0.800 0.200 0.000
#> SRR1047823 5 0.0146 1.000 0.000 0 0.000 0.004 0.996 0.000
#> SRR1047824 5 0.0146 1.000 0.000 0 0.000 0.004 0.996 0.000
#> SRR1047825 5 0.0146 1.000 0.000 0 0.000 0.004 0.996 0.000
#> SRR1047826 5 0.0146 1.000 0.000 0 0.000 0.004 0.996 0.000
#> SRR1047827 5 0.0146 1.000 0.000 0 0.000 0.004 0.996 0.000
#> SRR1047828 4 0.1219 0.893 0.000 0 0.000 0.948 0.004 0.048
#> SRR1047829 4 0.1219 0.893 0.000 0 0.000 0.948 0.004 0.048
#> SRR1047830 4 0.1219 0.893 0.000 0 0.000 0.948 0.004 0.048
#> SRR1047831 4 0.1219 0.893 0.000 0 0.000 0.948 0.004 0.048
#> SRR1047832 4 0.1219 0.893 0.000 0 0.000 0.948 0.004 0.048
#> SRR1047833 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> SRR1047834 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> SRR1047835 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> SRR1047836 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> SRR1047837 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> SRR1047838 4 0.0146 0.910 0.000 0 0.000 0.996 0.004 0.000
#> SRR1047839 4 0.0146 0.910 0.000 0 0.000 0.996 0.004 0.000
#> SRR1047840 4 0.0146 0.910 0.000 0 0.000 0.996 0.004 0.000
#> SRR1047841 4 0.0146 0.910 0.000 0 0.000 0.996 0.004 0.000
#> SRR1047842 4 0.0146 0.910 0.000 0 0.000 0.996 0.004 0.000
#> SRR1047843 4 0.0146 0.910 0.004 0 0.000 0.996 0.000 0.000
#> SRR1047844 4 0.0146 0.910 0.004 0 0.000 0.996 0.000 0.000
#> SRR1047845 4 0.0146 0.910 0.004 0 0.000 0.996 0.000 0.000
#> SRR1047846 4 0.0146 0.910 0.004 0 0.000 0.996 0.000 0.000
#> SRR1047847 4 0.0146 0.910 0.004 0 0.000 0.996 0.000 0.000
#> SRR1047848 1 0.0000 1.000 1.000 0 0.000 0.000 0.000 0.000
#> SRR1047849 1 0.0000 1.000 1.000 0 0.000 0.000 0.000 0.000
#> SRR1047850 1 0.0000 1.000 1.000 0 0.000 0.000 0.000 0.000
#> SRR1047851 1 0.0000 1.000 1.000 0 0.000 0.000 0.000 0.000
#> SRR1047852 1 0.0000 1.000 1.000 0 0.000 0.000 0.000 0.000
#> SRR1047853 4 0.0000 0.911 0.000 0 0.000 1.000 0.000 0.000
#> SRR1047854 4 0.0000 0.911 0.000 0 0.000 1.000 0.000 0.000
#> SRR1047855 4 0.0000 0.911 0.000 0 0.000 1.000 0.000 0.000
#> SRR1047856 4 0.0000 0.911 0.000 0 0.000 1.000 0.000 0.000
#> SRR1047857 4 0.0000 0.911 0.000 0 0.000 1.000 0.000 0.000
#> SRR1047858 1 0.0000 1.000 1.000 0 0.000 0.000 0.000 0.000
#> SRR1047859 1 0.0000 1.000 1.000 0 0.000 0.000 0.000 0.000
#> SRR1047860 1 0.0000 1.000 1.000 0 0.000 0.000 0.000 0.000
#> SRR1047861 1 0.0000 1.000 1.000 0 0.000 0.000 0.000 0.000
#> SRR1047863 3 0.0000 1.000 0.000 0 1.000 0.000 0.000 0.000
#> SRR1047864 3 0.0146 0.996 0.000 0 0.996 0.000 0.000 0.004
#> SRR1047865 3 0.0000 1.000 0.000 0 1.000 0.000 0.000 0.000
#> SRR1047866 3 0.0000 1.000 0.000 0 1.000 0.000 0.000 0.000
#> SRR1047867 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> SRR1047868 3 0.0000 1.000 0.000 0 1.000 0.000 0.000 0.000
#> SRR1047869 3 0.0000 1.000 0.000 0 1.000 0.000 0.000 0.000
#> SRR1047870 3 0.0000 1.000 0.000 0 1.000 0.000 0.000 0.000
#> SRR1047871 3 0.0000 1.000 0.000 0 1.000 0.000 0.000 0.000
#> SRR1047872 3 0.0000 1.000 0.000 0 1.000 0.000 0.000 0.000
#> SRR1047873 3 0.0000 1.000 0.000 0 1.000 0.000 0.000 0.000
#> SRR1047874 3 0.0000 1.000 0.000 0 1.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 17931 rows and 61 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 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 0.716 0.918 0.937 0.3352 0.591 0.591
#> 3 3 1.000 0.994 0.996 0.9282 0.762 0.598
#> 4 4 1.000 0.997 0.998 0.0521 0.967 0.907
#> 5 5 1.000 0.993 0.996 0.1500 0.896 0.676
#> 6 6 1.000 0.992 0.995 0.0244 0.981 0.912
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
#> SRR1047813 1 0.0000 0.999 1.000 0.000
#> SRR1047814 1 0.0000 0.999 1.000 0.000
#> SRR1047815 1 0.0000 0.999 1.000 0.000
#> SRR1047816 1 0.0000 0.999 1.000 0.000
#> SRR1047817 1 0.0000 0.999 1.000 0.000
#> SRR1047818 1 0.0000 0.999 1.000 0.000
#> SRR1047819 1 0.0000 0.999 1.000 0.000
#> SRR1047820 1 0.0000 0.999 1.000 0.000
#> SRR1047821 1 0.0000 0.999 1.000 0.000
#> SRR1047822 1 0.0000 0.999 1.000 0.000
#> SRR1047823 1 0.0000 0.999 1.000 0.000
#> SRR1047824 1 0.0000 0.999 1.000 0.000
#> SRR1047825 1 0.0000 0.999 1.000 0.000
#> SRR1047826 1 0.0000 0.999 1.000 0.000
#> SRR1047827 1 0.0000 0.999 1.000 0.000
#> SRR1047828 1 0.0000 0.999 1.000 0.000
#> SRR1047829 1 0.0376 0.994 0.996 0.004
#> SRR1047830 1 0.0938 0.984 0.988 0.012
#> SRR1047831 1 0.1184 0.979 0.984 0.016
#> SRR1047832 1 0.1184 0.979 0.984 0.016
#> SRR1047833 2 0.0000 0.746 0.000 1.000
#> SRR1047834 2 0.0000 0.746 0.000 1.000
#> SRR1047835 2 0.0000 0.746 0.000 1.000
#> SRR1047836 2 0.0000 0.746 0.000 1.000
#> SRR1047837 2 0.0000 0.746 0.000 1.000
#> SRR1047838 1 0.0000 0.999 1.000 0.000
#> SRR1047839 1 0.0000 0.999 1.000 0.000
#> SRR1047840 1 0.0000 0.999 1.000 0.000
#> SRR1047841 1 0.0000 0.999 1.000 0.000
#> SRR1047842 1 0.0000 0.999 1.000 0.000
#> SRR1047843 1 0.0000 0.999 1.000 0.000
#> SRR1047844 1 0.0000 0.999 1.000 0.000
#> SRR1047845 1 0.0000 0.999 1.000 0.000
#> SRR1047846 1 0.0000 0.999 1.000 0.000
#> SRR1047847 1 0.0000 0.999 1.000 0.000
#> SRR1047848 1 0.0000 0.999 1.000 0.000
#> SRR1047849 1 0.0000 0.999 1.000 0.000
#> SRR1047850 1 0.0000 0.999 1.000 0.000
#> SRR1047851 1 0.0000 0.999 1.000 0.000
#> SRR1047852 1 0.0000 0.999 1.000 0.000
#> SRR1047853 1 0.0000 0.999 1.000 0.000
#> SRR1047854 1 0.0000 0.999 1.000 0.000
#> SRR1047855 1 0.0000 0.999 1.000 0.000
#> SRR1047856 1 0.0000 0.999 1.000 0.000
#> SRR1047857 1 0.0000 0.999 1.000 0.000
#> SRR1047858 1 0.0000 0.999 1.000 0.000
#> SRR1047859 1 0.0000 0.999 1.000 0.000
#> SRR1047860 1 0.0000 0.999 1.000 0.000
#> SRR1047861 1 0.0000 0.999 1.000 0.000
#> SRR1047863 2 0.9732 0.681 0.404 0.596
#> SRR1047864 2 0.0000 0.746 0.000 1.000
#> SRR1047865 2 0.6887 0.738 0.184 0.816
#> SRR1047866 2 0.9732 0.681 0.404 0.596
#> SRR1047867 2 0.0000 0.746 0.000 1.000
#> SRR1047868 2 0.9732 0.681 0.404 0.596
#> SRR1047869 2 0.9491 0.697 0.368 0.632
#> SRR1047870 2 0.9732 0.681 0.404 0.596
#> SRR1047871 2 0.9732 0.681 0.404 0.596
#> SRR1047872 2 0.9732 0.681 0.404 0.596
#> SRR1047873 2 0.9732 0.681 0.404 0.596
#> SRR1047874 2 0.9732 0.681 0.404 0.596
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1047813 1 0.0000 0.996 1.00 0.00 0.00
#> SRR1047814 1 0.0000 0.996 1.00 0.00 0.00
#> SRR1047815 1 0.0000 0.996 1.00 0.00 0.00
#> SRR1047816 1 0.0000 0.996 1.00 0.00 0.00
#> SRR1047817 1 0.0000 0.996 1.00 0.00 0.00
#> SRR1047818 2 0.0000 1.000 0.00 1.00 0.00
#> SRR1047819 2 0.0000 1.000 0.00 1.00 0.00
#> SRR1047820 2 0.0000 1.000 0.00 1.00 0.00
#> SRR1047821 2 0.0000 1.000 0.00 1.00 0.00
#> SRR1047822 2 0.0000 1.000 0.00 1.00 0.00
#> SRR1047823 2 0.0000 1.000 0.00 1.00 0.00
#> SRR1047824 2 0.0000 1.000 0.00 1.00 0.00
#> SRR1047825 2 0.0000 1.000 0.00 1.00 0.00
#> SRR1047826 2 0.0000 1.000 0.00 1.00 0.00
#> SRR1047827 2 0.0000 1.000 0.00 1.00 0.00
#> SRR1047828 1 0.0000 0.996 1.00 0.00 0.00
#> SRR1047829 1 0.0000 0.996 1.00 0.00 0.00
#> SRR1047830 1 0.0000 0.996 1.00 0.00 0.00
#> SRR1047831 1 0.0000 0.996 1.00 0.00 0.00
#> SRR1047832 1 0.0000 0.996 1.00 0.00 0.00
#> SRR1047833 3 0.0000 0.989 0.00 0.00 1.00
#> SRR1047834 3 0.0000 0.989 0.00 0.00 1.00
#> SRR1047835 3 0.0000 0.989 0.00 0.00 1.00
#> SRR1047836 3 0.0000 0.989 0.00 0.00 1.00
#> SRR1047837 3 0.0000 0.989 0.00 0.00 1.00
#> SRR1047838 2 0.0000 1.000 0.00 1.00 0.00
#> SRR1047839 2 0.0000 1.000 0.00 1.00 0.00
#> SRR1047840 2 0.0000 1.000 0.00 1.00 0.00
#> SRR1047841 2 0.0000 1.000 0.00 1.00 0.00
#> SRR1047842 2 0.0000 1.000 0.00 1.00 0.00
#> SRR1047843 1 0.0000 0.996 1.00 0.00 0.00
#> SRR1047844 1 0.0000 0.996 1.00 0.00 0.00
#> SRR1047845 1 0.0000 0.996 1.00 0.00 0.00
#> SRR1047846 1 0.0000 0.996 1.00 0.00 0.00
#> SRR1047847 1 0.0000 0.996 1.00 0.00 0.00
#> SRR1047848 1 0.0000 0.996 1.00 0.00 0.00
#> SRR1047849 1 0.0000 0.996 1.00 0.00 0.00
#> SRR1047850 1 0.0000 0.996 1.00 0.00 0.00
#> SRR1047851 1 0.0000 0.996 1.00 0.00 0.00
#> SRR1047852 1 0.0000 0.996 1.00 0.00 0.00
#> SRR1047853 1 0.0892 0.981 0.98 0.02 0.00
#> SRR1047854 1 0.0892 0.981 0.98 0.02 0.00
#> SRR1047855 1 0.0892 0.981 0.98 0.02 0.00
#> SRR1047856 1 0.0892 0.981 0.98 0.02 0.00
#> SRR1047857 1 0.0892 0.981 0.98 0.02 0.00
#> SRR1047858 1 0.0000 0.996 1.00 0.00 0.00
#> SRR1047859 1 0.0000 0.996 1.00 0.00 0.00
#> SRR1047860 1 0.0000 0.996 1.00 0.00 0.00
#> SRR1047861 1 0.0000 0.996 1.00 0.00 0.00
#> SRR1047863 3 0.0892 0.988 0.00 0.02 0.98
#> SRR1047864 3 0.0000 0.989 0.00 0.00 1.00
#> SRR1047865 3 0.0000 0.989 0.00 0.00 1.00
#> SRR1047866 3 0.0000 0.989 0.00 0.00 1.00
#> SRR1047867 3 0.0000 0.989 0.00 0.00 1.00
#> SRR1047868 3 0.0892 0.988 0.00 0.02 0.98
#> SRR1047869 3 0.0892 0.988 0.00 0.02 0.98
#> SRR1047870 3 0.0892 0.988 0.00 0.02 0.98
#> SRR1047871 3 0.0892 0.988 0.00 0.02 0.98
#> SRR1047872 3 0.0892 0.988 0.00 0.02 0.98
#> SRR1047873 3 0.0892 0.988 0.00 0.02 0.98
#> SRR1047874 3 0.0892 0.988 0.00 0.02 0.98
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1047813 1 0.0000 0.996 1.00 0 0 0.00
#> SRR1047814 1 0.0000 0.996 1.00 0 0 0.00
#> SRR1047815 1 0.0000 0.996 1.00 0 0 0.00
#> SRR1047816 1 0.0000 0.996 1.00 0 0 0.00
#> SRR1047817 1 0.0000 0.996 1.00 0 0 0.00
#> SRR1047818 4 0.0000 1.000 0.00 0 0 1.00
#> SRR1047819 4 0.0000 1.000 0.00 0 0 1.00
#> SRR1047820 4 0.0000 1.000 0.00 0 0 1.00
#> SRR1047821 4 0.0000 1.000 0.00 0 0 1.00
#> SRR1047822 4 0.0000 1.000 0.00 0 0 1.00
#> SRR1047823 4 0.0000 1.000 0.00 0 0 1.00
#> SRR1047824 4 0.0000 1.000 0.00 0 0 1.00
#> SRR1047825 4 0.0000 1.000 0.00 0 0 1.00
#> SRR1047826 4 0.0000 1.000 0.00 0 0 1.00
#> SRR1047827 4 0.0000 1.000 0.00 0 0 1.00
#> SRR1047828 1 0.0000 0.996 1.00 0 0 0.00
#> SRR1047829 1 0.0000 0.996 1.00 0 0 0.00
#> SRR1047830 1 0.0000 0.996 1.00 0 0 0.00
#> SRR1047831 1 0.0000 0.996 1.00 0 0 0.00
#> SRR1047832 1 0.0000 0.996 1.00 0 0 0.00
#> SRR1047833 2 0.0000 1.000 0.00 1 0 0.00
#> SRR1047834 2 0.0000 1.000 0.00 1 0 0.00
#> SRR1047835 2 0.0000 1.000 0.00 1 0 0.00
#> SRR1047836 2 0.0000 1.000 0.00 1 0 0.00
#> SRR1047837 2 0.0000 1.000 0.00 1 0 0.00
#> SRR1047838 4 0.0000 1.000 0.00 0 0 1.00
#> SRR1047839 4 0.0000 1.000 0.00 0 0 1.00
#> SRR1047840 4 0.0000 1.000 0.00 0 0 1.00
#> SRR1047841 4 0.0000 1.000 0.00 0 0 1.00
#> SRR1047842 4 0.0000 1.000 0.00 0 0 1.00
#> SRR1047843 1 0.0000 0.996 1.00 0 0 0.00
#> SRR1047844 1 0.0000 0.996 1.00 0 0 0.00
#> SRR1047845 1 0.0000 0.996 1.00 0 0 0.00
#> SRR1047846 1 0.0000 0.996 1.00 0 0 0.00
#> SRR1047847 1 0.0000 0.996 1.00 0 0 0.00
#> SRR1047848 1 0.0000 0.996 1.00 0 0 0.00
#> SRR1047849 1 0.0000 0.996 1.00 0 0 0.00
#> SRR1047850 1 0.0000 0.996 1.00 0 0 0.00
#> SRR1047851 1 0.0000 0.996 1.00 0 0 0.00
#> SRR1047852 1 0.0000 0.996 1.00 0 0 0.00
#> SRR1047853 1 0.0707 0.980 0.98 0 0 0.02
#> SRR1047854 1 0.0707 0.980 0.98 0 0 0.02
#> SRR1047855 1 0.0707 0.980 0.98 0 0 0.02
#> SRR1047856 1 0.0707 0.980 0.98 0 0 0.02
#> SRR1047857 1 0.0707 0.980 0.98 0 0 0.02
#> SRR1047858 1 0.0000 0.996 1.00 0 0 0.00
#> SRR1047859 1 0.0000 0.996 1.00 0 0 0.00
#> SRR1047860 1 0.0000 0.996 1.00 0 0 0.00
#> SRR1047861 1 0.0000 0.996 1.00 0 0 0.00
#> SRR1047863 3 0.0000 1.000 0.00 0 1 0.00
#> SRR1047864 3 0.0000 1.000 0.00 0 1 0.00
#> SRR1047865 3 0.0000 1.000 0.00 0 1 0.00
#> SRR1047866 3 0.0000 1.000 0.00 0 1 0.00
#> SRR1047867 3 0.0000 1.000 0.00 0 1 0.00
#> SRR1047868 3 0.0000 1.000 0.00 0 1 0.00
#> SRR1047869 3 0.0000 1.000 0.00 0 1 0.00
#> SRR1047870 3 0.0000 1.000 0.00 0 1 0.00
#> SRR1047871 3 0.0000 1.000 0.00 0 1 0.00
#> SRR1047872 3 0.0000 1.000 0.00 0 1 0.00
#> SRR1047873 3 0.0000 1.000 0.00 0 1 0.00
#> SRR1047874 3 0.0000 1.000 0.00 0 1 0.00
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1047813 1 0.0000 0.975 1.000 0 0 0.00 0.000
#> SRR1047814 1 0.0000 0.975 1.000 0 0 0.00 0.000
#> SRR1047815 1 0.0000 0.975 1.000 0 0 0.00 0.000
#> SRR1047816 1 0.0000 0.975 1.000 0 0 0.00 0.000
#> SRR1047817 1 0.0000 0.975 1.000 0 0 0.00 0.000
#> SRR1047818 4 0.0000 1.000 0.000 0 0 1.00 0.000
#> SRR1047819 4 0.0000 1.000 0.000 0 0 1.00 0.000
#> SRR1047820 4 0.0000 1.000 0.000 0 0 1.00 0.000
#> SRR1047821 4 0.0000 1.000 0.000 0 0 1.00 0.000
#> SRR1047822 4 0.0000 1.000 0.000 0 0 1.00 0.000
#> SRR1047823 4 0.0000 1.000 0.000 0 0 1.00 0.000
#> SRR1047824 4 0.0000 1.000 0.000 0 0 1.00 0.000
#> SRR1047825 4 0.0000 1.000 0.000 0 0 1.00 0.000
#> SRR1047826 4 0.0000 1.000 0.000 0 0 1.00 0.000
#> SRR1047827 4 0.0000 1.000 0.000 0 0 1.00 0.000
#> SRR1047828 5 0.0000 0.993 0.000 0 0 0.00 1.000
#> SRR1047829 5 0.0000 0.993 0.000 0 0 0.00 1.000
#> SRR1047830 5 0.0000 0.993 0.000 0 0 0.00 1.000
#> SRR1047831 5 0.0000 0.993 0.000 0 0 0.00 1.000
#> SRR1047832 5 0.0000 0.993 0.000 0 0 0.00 1.000
#> SRR1047833 2 0.0000 1.000 0.000 1 0 0.00 0.000
#> SRR1047834 2 0.0000 1.000 0.000 1 0 0.00 0.000
#> SRR1047835 2 0.0000 1.000 0.000 1 0 0.00 0.000
#> SRR1047836 2 0.0000 1.000 0.000 1 0 0.00 0.000
#> SRR1047837 2 0.0000 1.000 0.000 1 0 0.00 0.000
#> SRR1047838 4 0.0000 1.000 0.000 0 0 1.00 0.000
#> SRR1047839 4 0.0000 1.000 0.000 0 0 1.00 0.000
#> SRR1047840 4 0.0000 1.000 0.000 0 0 1.00 0.000
#> SRR1047841 4 0.0000 1.000 0.000 0 0 1.00 0.000
#> SRR1047842 4 0.0000 1.000 0.000 0 0 1.00 0.000
#> SRR1047843 5 0.0000 0.993 0.000 0 0 0.00 1.000
#> SRR1047844 5 0.0000 0.993 0.000 0 0 0.00 1.000
#> SRR1047845 5 0.0000 0.993 0.000 0 0 0.00 1.000
#> SRR1047846 5 0.0000 0.993 0.000 0 0 0.00 1.000
#> SRR1047847 5 0.0000 0.993 0.000 0 0 0.00 1.000
#> SRR1047848 1 0.0880 0.975 0.968 0 0 0.00 0.032
#> SRR1047849 1 0.0880 0.975 0.968 0 0 0.00 0.032
#> SRR1047850 1 0.0880 0.975 0.968 0 0 0.00 0.032
#> SRR1047851 1 0.0880 0.975 0.968 0 0 0.00 0.032
#> SRR1047852 1 0.0880 0.975 0.968 0 0 0.00 0.032
#> SRR1047853 5 0.0609 0.981 0.000 0 0 0.02 0.980
#> SRR1047854 5 0.0609 0.981 0.000 0 0 0.02 0.980
#> SRR1047855 5 0.0609 0.981 0.000 0 0 0.02 0.980
#> SRR1047856 5 0.0609 0.981 0.000 0 0 0.02 0.980
#> SRR1047857 5 0.0609 0.981 0.000 0 0 0.02 0.980
#> SRR1047858 5 0.0000 0.993 0.000 0 0 0.00 1.000
#> SRR1047859 5 0.0000 0.993 0.000 0 0 0.00 1.000
#> SRR1047860 5 0.0000 0.993 0.000 0 0 0.00 1.000
#> SRR1047861 5 0.0000 0.993 0.000 0 0 0.00 1.000
#> SRR1047863 3 0.0000 1.000 0.000 0 1 0.00 0.000
#> SRR1047864 3 0.0000 1.000 0.000 0 1 0.00 0.000
#> SRR1047865 3 0.0000 1.000 0.000 0 1 0.00 0.000
#> SRR1047866 3 0.0000 1.000 0.000 0 1 0.00 0.000
#> SRR1047867 3 0.0000 1.000 0.000 0 1 0.00 0.000
#> SRR1047868 3 0.0000 1.000 0.000 0 1 0.00 0.000
#> SRR1047869 3 0.0000 1.000 0.000 0 1 0.00 0.000
#> SRR1047870 3 0.0000 1.000 0.000 0 1 0.00 0.000
#> SRR1047871 3 0.0000 1.000 0.000 0 1 0.00 0.000
#> SRR1047872 3 0.0000 1.000 0.000 0 1 0.00 0.000
#> SRR1047873 3 0.0000 1.000 0.000 0 1 0.00 0.000
#> SRR1047874 3 0.0000 1.000 0.000 0 1 0.00 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1047813 1 0.0000 0.975 1.000 0 0.000 0.00 0.000 0.000
#> SRR1047814 1 0.0000 0.975 1.000 0 0.000 0.00 0.000 0.000
#> SRR1047815 1 0.0000 0.975 1.000 0 0.000 0.00 0.000 0.000
#> SRR1047816 1 0.0000 0.975 1.000 0 0.000 0.00 0.000 0.000
#> SRR1047817 1 0.0000 0.975 1.000 0 0.000 0.00 0.000 0.000
#> SRR1047818 4 0.0000 1.000 0.000 0 0.000 1.00 0.000 0.000
#> SRR1047819 4 0.0000 1.000 0.000 0 0.000 1.00 0.000 0.000
#> SRR1047820 4 0.0000 1.000 0.000 0 0.000 1.00 0.000 0.000
#> SRR1047821 4 0.0000 1.000 0.000 0 0.000 1.00 0.000 0.000
#> SRR1047822 4 0.0000 1.000 0.000 0 0.000 1.00 0.000 0.000
#> SRR1047823 4 0.0000 1.000 0.000 0 0.000 1.00 0.000 0.000
#> SRR1047824 4 0.0000 1.000 0.000 0 0.000 1.00 0.000 0.000
#> SRR1047825 4 0.0000 1.000 0.000 0 0.000 1.00 0.000 0.000
#> SRR1047826 4 0.0000 1.000 0.000 0 0.000 1.00 0.000 0.000
#> SRR1047827 4 0.0000 1.000 0.000 0 0.000 1.00 0.000 0.000
#> SRR1047828 5 0.0000 0.993 0.000 0 0.000 0.00 1.000 0.000
#> SRR1047829 5 0.0000 0.993 0.000 0 0.000 0.00 1.000 0.000
#> SRR1047830 5 0.0000 0.993 0.000 0 0.000 0.00 1.000 0.000
#> SRR1047831 5 0.0000 0.993 0.000 0 0.000 0.00 1.000 0.000
#> SRR1047832 5 0.0000 0.993 0.000 0 0.000 0.00 1.000 0.000
#> SRR1047833 2 0.0000 1.000 0.000 1 0.000 0.00 0.000 0.000
#> SRR1047834 2 0.0000 1.000 0.000 1 0.000 0.00 0.000 0.000
#> SRR1047835 2 0.0000 1.000 0.000 1 0.000 0.00 0.000 0.000
#> SRR1047836 2 0.0000 1.000 0.000 1 0.000 0.00 0.000 0.000
#> SRR1047837 2 0.0000 1.000 0.000 1 0.000 0.00 0.000 0.000
#> SRR1047838 4 0.0000 1.000 0.000 0 0.000 1.00 0.000 0.000
#> SRR1047839 4 0.0000 1.000 0.000 0 0.000 1.00 0.000 0.000
#> SRR1047840 4 0.0000 1.000 0.000 0 0.000 1.00 0.000 0.000
#> SRR1047841 4 0.0000 1.000 0.000 0 0.000 1.00 0.000 0.000
#> SRR1047842 4 0.0000 1.000 0.000 0 0.000 1.00 0.000 0.000
#> SRR1047843 5 0.0000 0.993 0.000 0 0.000 0.00 1.000 0.000
#> SRR1047844 5 0.0000 0.993 0.000 0 0.000 0.00 1.000 0.000
#> SRR1047845 5 0.0000 0.993 0.000 0 0.000 0.00 1.000 0.000
#> SRR1047846 5 0.0000 0.993 0.000 0 0.000 0.00 1.000 0.000
#> SRR1047847 5 0.0000 0.993 0.000 0 0.000 0.00 1.000 0.000
#> SRR1047848 1 0.0790 0.975 0.968 0 0.000 0.00 0.032 0.000
#> SRR1047849 1 0.0790 0.975 0.968 0 0.000 0.00 0.032 0.000
#> SRR1047850 1 0.0790 0.975 0.968 0 0.000 0.00 0.032 0.000
#> SRR1047851 1 0.0790 0.975 0.968 0 0.000 0.00 0.032 0.000
#> SRR1047852 1 0.0790 0.975 0.968 0 0.000 0.00 0.032 0.000
#> SRR1047853 5 0.0547 0.981 0.000 0 0.000 0.02 0.980 0.000
#> SRR1047854 5 0.0547 0.981 0.000 0 0.000 0.02 0.980 0.000
#> SRR1047855 5 0.0547 0.981 0.000 0 0.000 0.02 0.980 0.000
#> SRR1047856 5 0.0547 0.981 0.000 0 0.000 0.02 0.980 0.000
#> SRR1047857 5 0.0547 0.981 0.000 0 0.000 0.02 0.980 0.000
#> SRR1047858 5 0.0000 0.993 0.000 0 0.000 0.00 1.000 0.000
#> SRR1047859 5 0.0000 0.993 0.000 0 0.000 0.00 1.000 0.000
#> SRR1047860 5 0.0000 0.993 0.000 0 0.000 0.00 1.000 0.000
#> SRR1047861 5 0.0000 0.993 0.000 0 0.000 0.00 1.000 0.000
#> SRR1047863 3 0.0146 0.995 0.000 0 0.996 0.00 0.000 0.004
#> SRR1047864 6 0.0000 1.000 0.000 0 0.000 0.00 0.000 1.000
#> SRR1047865 6 0.0000 1.000 0.000 0 0.000 0.00 0.000 1.000
#> SRR1047866 6 0.0000 1.000 0.000 0 0.000 0.00 0.000 1.000
#> SRR1047867 6 0.0000 1.000 0.000 0 0.000 0.00 0.000 1.000
#> SRR1047868 3 0.0000 0.997 0.000 0 1.000 0.00 0.000 0.000
#> SRR1047869 6 0.0000 1.000 0.000 0 0.000 0.00 0.000 1.000
#> SRR1047870 3 0.0000 0.997 0.000 0 1.000 0.00 0.000 0.000
#> SRR1047871 3 0.0458 0.985 0.000 0 0.984 0.00 0.000 0.016
#> SRR1047872 3 0.0000 0.997 0.000 0 1.000 0.00 0.000 0.000
#> SRR1047873 3 0.0000 0.997 0.000 0 1.000 0.00 0.000 0.000
#> SRR1047874 3 0.0000 0.997 0.000 0 1.000 0.00 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 17931 rows and 61 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.1539 0.847 0.847
#> 3 3 1.000 1.000 1.000 1.8734 0.711 0.659
#> 4 4 0.780 0.903 0.953 0.5320 0.762 0.574
#> 5 5 0.738 0.709 0.852 0.1267 0.831 0.532
#> 6 6 0.682 0.689 0.794 0.0511 0.864 0.503
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
#> SRR1047813 1 0 1 1 0
#> SRR1047814 1 0 1 1 0
#> SRR1047815 1 0 1 1 0
#> SRR1047816 1 0 1 1 0
#> SRR1047817 1 0 1 1 0
#> SRR1047818 1 0 1 1 0
#> SRR1047819 1 0 1 1 0
#> SRR1047820 1 0 1 1 0
#> SRR1047821 1 0 1 1 0
#> SRR1047822 1 0 1 1 0
#> SRR1047823 1 0 1 1 0
#> SRR1047824 1 0 1 1 0
#> SRR1047825 1 0 1 1 0
#> SRR1047826 1 0 1 1 0
#> SRR1047827 1 0 1 1 0
#> SRR1047828 1 0 1 1 0
#> SRR1047829 1 0 1 1 0
#> SRR1047830 1 0 1 1 0
#> SRR1047831 1 0 1 1 0
#> SRR1047832 1 0 1 1 0
#> SRR1047833 2 0 1 0 1
#> SRR1047834 2 0 1 0 1
#> SRR1047835 2 0 1 0 1
#> SRR1047836 2 0 1 0 1
#> SRR1047837 2 0 1 0 1
#> SRR1047838 1 0 1 1 0
#> SRR1047839 1 0 1 1 0
#> SRR1047840 1 0 1 1 0
#> SRR1047841 1 0 1 1 0
#> SRR1047842 1 0 1 1 0
#> SRR1047843 1 0 1 1 0
#> SRR1047844 1 0 1 1 0
#> SRR1047845 1 0 1 1 0
#> SRR1047846 1 0 1 1 0
#> SRR1047847 1 0 1 1 0
#> SRR1047848 1 0 1 1 0
#> SRR1047849 1 0 1 1 0
#> SRR1047850 1 0 1 1 0
#> SRR1047851 1 0 1 1 0
#> SRR1047852 1 0 1 1 0
#> SRR1047853 1 0 1 1 0
#> SRR1047854 1 0 1 1 0
#> SRR1047855 1 0 1 1 0
#> SRR1047856 1 0 1 1 0
#> SRR1047857 1 0 1 1 0
#> SRR1047858 1 0 1 1 0
#> SRR1047859 1 0 1 1 0
#> SRR1047860 1 0 1 1 0
#> SRR1047861 1 0 1 1 0
#> SRR1047863 1 0 1 1 0
#> SRR1047864 1 0 1 1 0
#> SRR1047865 1 0 1 1 0
#> SRR1047866 1 0 1 1 0
#> SRR1047867 1 0 1 1 0
#> SRR1047868 1 0 1 1 0
#> SRR1047869 1 0 1 1 0
#> SRR1047870 1 0 1 1 0
#> SRR1047871 1 0 1 1 0
#> SRR1047872 1 0 1 1 0
#> SRR1047873 1 0 1 1 0
#> SRR1047874 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1047813 1 0 1 1 0 0
#> SRR1047814 1 0 1 1 0 0
#> SRR1047815 1 0 1 1 0 0
#> SRR1047816 1 0 1 1 0 0
#> SRR1047817 1 0 1 1 0 0
#> SRR1047818 1 0 1 1 0 0
#> SRR1047819 1 0 1 1 0 0
#> SRR1047820 1 0 1 1 0 0
#> SRR1047821 1 0 1 1 0 0
#> SRR1047822 1 0 1 1 0 0
#> SRR1047823 1 0 1 1 0 0
#> SRR1047824 1 0 1 1 0 0
#> SRR1047825 1 0 1 1 0 0
#> SRR1047826 1 0 1 1 0 0
#> SRR1047827 1 0 1 1 0 0
#> SRR1047828 1 0 1 1 0 0
#> SRR1047829 1 0 1 1 0 0
#> SRR1047830 1 0 1 1 0 0
#> SRR1047831 1 0 1 1 0 0
#> SRR1047832 1 0 1 1 0 0
#> SRR1047833 2 0 1 0 1 0
#> SRR1047834 2 0 1 0 1 0
#> SRR1047835 2 0 1 0 1 0
#> SRR1047836 2 0 1 0 1 0
#> SRR1047837 2 0 1 0 1 0
#> SRR1047838 1 0 1 1 0 0
#> SRR1047839 1 0 1 1 0 0
#> SRR1047840 1 0 1 1 0 0
#> SRR1047841 1 0 1 1 0 0
#> SRR1047842 1 0 1 1 0 0
#> SRR1047843 1 0 1 1 0 0
#> SRR1047844 1 0 1 1 0 0
#> SRR1047845 1 0 1 1 0 0
#> SRR1047846 1 0 1 1 0 0
#> SRR1047847 1 0 1 1 0 0
#> SRR1047848 1 0 1 1 0 0
#> SRR1047849 1 0 1 1 0 0
#> SRR1047850 1 0 1 1 0 0
#> SRR1047851 1 0 1 1 0 0
#> SRR1047852 1 0 1 1 0 0
#> SRR1047853 1 0 1 1 0 0
#> SRR1047854 1 0 1 1 0 0
#> SRR1047855 1 0 1 1 0 0
#> SRR1047856 1 0 1 1 0 0
#> SRR1047857 1 0 1 1 0 0
#> SRR1047858 1 0 1 1 0 0
#> SRR1047859 1 0 1 1 0 0
#> SRR1047860 1 0 1 1 0 0
#> SRR1047861 1 0 1 1 0 0
#> SRR1047863 3 0 1 0 0 1
#> SRR1047864 3 0 1 0 0 1
#> SRR1047865 3 0 1 0 0 1
#> SRR1047866 3 0 1 0 0 1
#> SRR1047867 3 0 1 0 0 1
#> SRR1047868 3 0 1 0 0 1
#> SRR1047869 3 0 1 0 0 1
#> SRR1047870 3 0 1 0 0 1
#> SRR1047871 3 0 1 0 0 1
#> SRR1047872 3 0 1 0 0 1
#> SRR1047873 3 0 1 0 0 1
#> SRR1047874 3 0 1 0 0 1
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1047813 1 0.000 0.921 1.000 0 0 0.000
#> SRR1047814 1 0.000 0.921 1.000 0 0 0.000
#> SRR1047815 1 0.000 0.921 1.000 0 0 0.000
#> SRR1047816 1 0.000 0.921 1.000 0 0 0.000
#> SRR1047817 1 0.000 0.921 1.000 0 0 0.000
#> SRR1047818 4 0.000 0.902 0.000 0 0 1.000
#> SRR1047819 4 0.000 0.902 0.000 0 0 1.000
#> SRR1047820 4 0.000 0.902 0.000 0 0 1.000
#> SRR1047821 4 0.000 0.902 0.000 0 0 1.000
#> SRR1047822 4 0.000 0.902 0.000 0 0 1.000
#> SRR1047823 4 0.349 0.765 0.188 0 0 0.812
#> SRR1047824 4 0.241 0.842 0.104 0 0 0.896
#> SRR1047825 4 0.407 0.686 0.252 0 0 0.748
#> SRR1047826 4 0.410 0.678 0.256 0 0 0.744
#> SRR1047827 4 0.265 0.830 0.120 0 0 0.880
#> SRR1047828 1 0.000 0.921 1.000 0 0 0.000
#> SRR1047829 1 0.000 0.921 1.000 0 0 0.000
#> SRR1047830 1 0.000 0.921 1.000 0 0 0.000
#> SRR1047831 1 0.000 0.921 1.000 0 0 0.000
#> SRR1047832 1 0.000 0.921 1.000 0 0 0.000
#> SRR1047833 2 0.000 1.000 0.000 1 0 0.000
#> SRR1047834 2 0.000 1.000 0.000 1 0 0.000
#> SRR1047835 2 0.000 1.000 0.000 1 0 0.000
#> SRR1047836 2 0.000 1.000 0.000 1 0 0.000
#> SRR1047837 2 0.000 1.000 0.000 1 0 0.000
#> SRR1047838 4 0.000 0.902 0.000 0 0 1.000
#> SRR1047839 4 0.000 0.902 0.000 0 0 1.000
#> SRR1047840 4 0.000 0.902 0.000 0 0 1.000
#> SRR1047841 4 0.000 0.902 0.000 0 0 1.000
#> SRR1047842 4 0.000 0.902 0.000 0 0 1.000
#> SRR1047843 1 0.000 0.921 1.000 0 0 0.000
#> SRR1047844 1 0.000 0.921 1.000 0 0 0.000
#> SRR1047845 1 0.000 0.921 1.000 0 0 0.000
#> SRR1047846 1 0.000 0.921 1.000 0 0 0.000
#> SRR1047847 1 0.000 0.921 1.000 0 0 0.000
#> SRR1047848 1 0.000 0.921 1.000 0 0 0.000
#> SRR1047849 1 0.000 0.921 1.000 0 0 0.000
#> SRR1047850 1 0.000 0.921 1.000 0 0 0.000
#> SRR1047851 1 0.000 0.921 1.000 0 0 0.000
#> SRR1047852 1 0.000 0.921 1.000 0 0 0.000
#> SRR1047853 1 0.349 0.795 0.812 0 0 0.188
#> SRR1047854 1 0.302 0.829 0.852 0 0 0.148
#> SRR1047855 1 0.281 0.841 0.868 0 0 0.132
#> SRR1047856 1 0.361 0.783 0.800 0 0 0.200
#> SRR1047857 1 0.413 0.706 0.740 0 0 0.260
#> SRR1047858 1 0.401 0.731 0.756 0 0 0.244
#> SRR1047859 1 0.410 0.714 0.744 0 0 0.256
#> SRR1047860 1 0.407 0.720 0.748 0 0 0.252
#> SRR1047861 1 0.407 0.720 0.748 0 0 0.252
#> SRR1047863 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047864 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047865 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047866 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047867 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047868 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047869 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047870 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047871 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047872 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047873 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047874 3 0.000 1.000 0.000 0 1 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1047813 5 0.4251 0.7661 0.316 0 0.000 0.012 0.672
#> SRR1047814 5 0.4270 0.7598 0.320 0 0.000 0.012 0.668
#> SRR1047815 5 0.4251 0.7661 0.316 0 0.000 0.012 0.672
#> SRR1047816 5 0.4251 0.7661 0.316 0 0.000 0.012 0.672
#> SRR1047817 5 0.4152 0.7739 0.296 0 0.000 0.012 0.692
#> SRR1047818 4 0.1341 0.9036 0.000 0 0.000 0.944 0.056
#> SRR1047819 4 0.1341 0.9020 0.000 0 0.000 0.944 0.056
#> SRR1047820 4 0.1197 0.9038 0.000 0 0.000 0.952 0.048
#> SRR1047821 4 0.1270 0.9032 0.000 0 0.000 0.948 0.052
#> SRR1047822 4 0.1341 0.8981 0.000 0 0.000 0.944 0.056
#> SRR1047823 1 0.5680 0.0200 0.492 0 0.000 0.428 0.080
#> SRR1047824 4 0.5399 0.0595 0.448 0 0.000 0.496 0.056
#> SRR1047825 1 0.5697 0.2077 0.548 0 0.000 0.360 0.092
#> SRR1047826 1 0.5663 0.2008 0.548 0 0.000 0.364 0.088
#> SRR1047827 1 0.5604 -0.0836 0.468 0 0.000 0.460 0.072
#> SRR1047828 1 0.4045 0.2657 0.644 0 0.000 0.000 0.356
#> SRR1047829 1 0.4455 0.1745 0.588 0 0.008 0.000 0.404
#> SRR1047830 1 0.4074 0.2782 0.636 0 0.000 0.000 0.364
#> SRR1047831 1 0.4074 0.2782 0.636 0 0.000 0.000 0.364
#> SRR1047832 1 0.4138 0.2392 0.616 0 0.000 0.000 0.384
#> SRR1047833 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> SRR1047834 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> SRR1047835 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> SRR1047836 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> SRR1047837 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> SRR1047838 4 0.1661 0.9000 0.024 0 0.000 0.940 0.036
#> SRR1047839 4 0.1638 0.8685 0.004 0 0.000 0.932 0.064
#> SRR1047840 4 0.1082 0.8929 0.028 0 0.000 0.964 0.008
#> SRR1047841 4 0.0912 0.8963 0.016 0 0.000 0.972 0.012
#> SRR1047842 4 0.1195 0.9021 0.012 0 0.000 0.960 0.028
#> SRR1047843 1 0.2966 0.5758 0.816 0 0.000 0.000 0.184
#> SRR1047844 1 0.5808 0.3417 0.576 0 0.100 0.004 0.320
#> SRR1047845 1 0.3242 0.5626 0.784 0 0.000 0.000 0.216
#> SRR1047846 1 0.3305 0.5576 0.776 0 0.000 0.000 0.224
#> SRR1047847 1 0.5203 0.3984 0.620 0 0.052 0.004 0.324
#> SRR1047848 1 0.0671 0.6561 0.980 0 0.000 0.004 0.016
#> SRR1047849 1 0.0671 0.6561 0.980 0 0.000 0.004 0.016
#> SRR1047850 1 0.0671 0.6561 0.980 0 0.000 0.004 0.016
#> SRR1047851 1 0.0671 0.6561 0.980 0 0.000 0.004 0.016
#> SRR1047852 1 0.0671 0.6561 0.980 0 0.000 0.004 0.016
#> SRR1047853 5 0.2423 0.7959 0.080 0 0.000 0.024 0.896
#> SRR1047854 5 0.2248 0.8015 0.088 0 0.000 0.012 0.900
#> SRR1047855 5 0.2361 0.8034 0.096 0 0.000 0.012 0.892
#> SRR1047856 5 0.2390 0.7964 0.084 0 0.000 0.020 0.896
#> SRR1047857 5 0.2423 0.7929 0.080 0 0.000 0.024 0.896
#> SRR1047858 1 0.0771 0.6574 0.976 0 0.000 0.004 0.020
#> SRR1047859 1 0.1205 0.6548 0.956 0 0.000 0.004 0.040
#> SRR1047860 1 0.1041 0.6565 0.964 0 0.000 0.004 0.032
#> SRR1047861 1 0.1124 0.6559 0.960 0 0.000 0.004 0.036
#> SRR1047863 3 0.0000 0.9693 0.000 0 1.000 0.000 0.000
#> SRR1047864 3 0.0000 0.9693 0.000 0 1.000 0.000 0.000
#> SRR1047865 3 0.1041 0.9524 0.004 0 0.964 0.000 0.032
#> SRR1047866 3 0.0000 0.9693 0.000 0 1.000 0.000 0.000
#> SRR1047867 3 0.0290 0.9672 0.000 0 0.992 0.000 0.008
#> SRR1047868 3 0.0162 0.9692 0.000 0 0.996 0.000 0.004
#> SRR1047869 3 0.2574 0.8881 0.012 0 0.876 0.000 0.112
#> SRR1047870 3 0.0000 0.9693 0.000 0 1.000 0.000 0.000
#> SRR1047871 3 0.0162 0.9692 0.000 0 0.996 0.000 0.004
#> SRR1047872 3 0.0566 0.9649 0.000 0 0.984 0.012 0.004
#> SRR1047873 3 0.1628 0.9416 0.000 0 0.936 0.008 0.056
#> SRR1047874 3 0.1956 0.9263 0.000 0 0.916 0.008 0.076
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1047813 5 0.3050 0.737 0.136 0 0.000 0.028 0.832 0.004
#> SRR1047814 5 0.3240 0.735 0.144 0 0.000 0.028 0.820 0.008
#> SRR1047815 5 0.3130 0.736 0.144 0 0.000 0.028 0.824 0.004
#> SRR1047816 5 0.3090 0.736 0.140 0 0.000 0.028 0.828 0.004
#> SRR1047817 5 0.2666 0.732 0.092 0 0.000 0.028 0.872 0.008
#> SRR1047818 4 0.2182 0.802 0.020 0 0.000 0.904 0.068 0.008
#> SRR1047819 4 0.1982 0.803 0.016 0 0.000 0.912 0.068 0.004
#> SRR1047820 4 0.2036 0.805 0.016 0 0.000 0.912 0.064 0.008
#> SRR1047821 4 0.1863 0.804 0.016 0 0.000 0.920 0.060 0.004
#> SRR1047822 4 0.1196 0.794 0.000 0 0.000 0.952 0.040 0.008
#> SRR1047823 4 0.5942 0.200 0.424 0 0.000 0.444 0.100 0.032
#> SRR1047824 4 0.5596 0.431 0.336 0 0.000 0.552 0.084 0.028
#> SRR1047825 1 0.5935 -0.223 0.460 0 0.000 0.408 0.100 0.032
#> SRR1047826 1 0.5937 -0.232 0.456 0 0.000 0.412 0.100 0.032
#> SRR1047827 4 0.5831 0.344 0.372 0 0.000 0.500 0.100 0.028
#> SRR1047828 5 0.5498 0.440 0.400 0 0.004 0.000 0.484 0.112
#> SRR1047829 5 0.6282 0.425 0.336 0 0.024 0.000 0.456 0.184
#> SRR1047830 5 0.5963 0.452 0.372 0 0.016 0.000 0.468 0.144
#> SRR1047831 5 0.5952 0.462 0.364 0 0.016 0.000 0.476 0.144
#> SRR1047832 5 0.6041 0.453 0.356 0 0.016 0.000 0.468 0.160
#> SRR1047833 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> SRR1047834 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> SRR1047835 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> SRR1047836 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> SRR1047837 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> SRR1047838 4 0.2209 0.801 0.072 0 0.000 0.900 0.024 0.004
#> SRR1047839 4 0.3488 0.688 0.032 0 0.000 0.804 0.012 0.152
#> SRR1047840 4 0.1728 0.801 0.064 0 0.000 0.924 0.004 0.008
#> SRR1047841 4 0.1951 0.797 0.060 0 0.000 0.916 0.004 0.020
#> SRR1047842 4 0.2002 0.799 0.056 0 0.000 0.916 0.008 0.020
#> SRR1047843 6 0.5710 0.749 0.372 0 0.000 0.012 0.120 0.496
#> SRR1047844 6 0.5977 0.841 0.228 0 0.036 0.020 0.104 0.612
#> SRR1047845 6 0.5435 0.865 0.316 0 0.000 0.012 0.104 0.568
#> SRR1047846 6 0.5491 0.868 0.308 0 0.000 0.016 0.104 0.572
#> SRR1047847 6 0.6035 0.839 0.224 0 0.032 0.028 0.104 0.612
#> SRR1047848 1 0.1218 0.658 0.956 0 0.000 0.004 0.028 0.012
#> SRR1047849 1 0.0508 0.671 0.984 0 0.000 0.004 0.012 0.000
#> SRR1047850 1 0.0653 0.669 0.980 0 0.000 0.004 0.012 0.004
#> SRR1047851 1 0.0508 0.671 0.984 0 0.000 0.004 0.012 0.000
#> SRR1047852 1 0.0508 0.671 0.984 0 0.000 0.004 0.012 0.000
#> SRR1047853 5 0.2854 0.690 0.024 0 0.000 0.068 0.872 0.036
#> SRR1047854 5 0.2701 0.710 0.044 0 0.000 0.044 0.884 0.028
#> SRR1047855 5 0.2701 0.710 0.044 0 0.000 0.044 0.884 0.028
#> SRR1047856 5 0.2883 0.683 0.020 0 0.000 0.076 0.868 0.036
#> SRR1047857 5 0.3139 0.657 0.012 0 0.000 0.084 0.848 0.056
#> SRR1047858 1 0.3477 0.597 0.808 0 0.000 0.004 0.132 0.056
#> SRR1047859 1 0.4493 0.474 0.720 0 0.000 0.004 0.144 0.132
#> SRR1047860 1 0.3576 0.592 0.800 0 0.000 0.004 0.136 0.060
#> SRR1047861 1 0.3795 0.577 0.784 0 0.000 0.004 0.136 0.076
#> SRR1047863 3 0.0865 0.866 0.000 0 0.964 0.000 0.000 0.036
#> SRR1047864 3 0.1387 0.842 0.000 0 0.932 0.000 0.000 0.068
#> SRR1047865 3 0.2810 0.813 0.004 0 0.832 0.000 0.008 0.156
#> SRR1047866 3 0.0508 0.860 0.004 0 0.984 0.000 0.000 0.012
#> SRR1047867 3 0.1556 0.837 0.000 0 0.920 0.000 0.000 0.080
#> SRR1047868 3 0.1204 0.863 0.000 0 0.944 0.000 0.000 0.056
#> SRR1047869 3 0.4670 0.460 0.004 0 0.548 0.000 0.036 0.412
#> SRR1047870 3 0.0937 0.852 0.000 0 0.960 0.000 0.000 0.040
#> SRR1047871 3 0.0790 0.866 0.000 0 0.968 0.000 0.000 0.032
#> SRR1047872 3 0.1542 0.864 0.000 0 0.936 0.008 0.004 0.052
#> SRR1047873 3 0.4318 0.709 0.004 0 0.700 0.012 0.028 0.256
#> SRR1047874 3 0.4495 0.681 0.004 0 0.676 0.012 0.032 0.276
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 17931 rows and 61 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.1811 0.820 0.820
#> 3 3 1.000 1.000 1.000 1.4586 0.736 0.677
#> 4 4 0.694 0.860 0.851 0.3000 0.762 0.572
#> 5 5 0.890 0.929 0.977 0.2144 0.891 0.695
#> 6 6 0.886 0.898 0.960 0.0256 0.987 0.955
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
#> SRR1047813 1 0 1 1 0
#> SRR1047814 1 0 1 1 0
#> SRR1047815 1 0 1 1 0
#> SRR1047816 1 0 1 1 0
#> SRR1047817 1 0 1 1 0
#> SRR1047818 1 0 1 1 0
#> SRR1047819 1 0 1 1 0
#> SRR1047820 1 0 1 1 0
#> SRR1047821 1 0 1 1 0
#> SRR1047822 1 0 1 1 0
#> SRR1047823 1 0 1 1 0
#> SRR1047824 1 0 1 1 0
#> SRR1047825 1 0 1 1 0
#> SRR1047826 1 0 1 1 0
#> SRR1047827 1 0 1 1 0
#> SRR1047828 1 0 1 1 0
#> SRR1047829 1 0 1 1 0
#> SRR1047830 1 0 1 1 0
#> SRR1047831 1 0 1 1 0
#> SRR1047832 1 0 1 1 0
#> SRR1047833 2 0 1 0 1
#> SRR1047834 2 0 1 0 1
#> SRR1047835 2 0 1 0 1
#> SRR1047836 2 0 1 0 1
#> SRR1047837 2 0 1 0 1
#> SRR1047838 1 0 1 1 0
#> SRR1047839 1 0 1 1 0
#> SRR1047840 1 0 1 1 0
#> SRR1047841 1 0 1 1 0
#> SRR1047842 1 0 1 1 0
#> SRR1047843 1 0 1 1 0
#> SRR1047844 1 0 1 1 0
#> SRR1047845 1 0 1 1 0
#> SRR1047846 1 0 1 1 0
#> SRR1047847 1 0 1 1 0
#> SRR1047848 1 0 1 1 0
#> SRR1047849 1 0 1 1 0
#> SRR1047850 1 0 1 1 0
#> SRR1047851 1 0 1 1 0
#> SRR1047852 1 0 1 1 0
#> SRR1047853 1 0 1 1 0
#> SRR1047854 1 0 1 1 0
#> SRR1047855 1 0 1 1 0
#> SRR1047856 1 0 1 1 0
#> SRR1047857 1 0 1 1 0
#> SRR1047858 1 0 1 1 0
#> SRR1047859 1 0 1 1 0
#> SRR1047860 1 0 1 1 0
#> SRR1047861 1 0 1 1 0
#> SRR1047863 1 0 1 1 0
#> SRR1047864 1 0 1 1 0
#> SRR1047865 1 0 1 1 0
#> SRR1047866 1 0 1 1 0
#> SRR1047867 2 0 1 0 1
#> SRR1047868 1 0 1 1 0
#> SRR1047869 1 0 1 1 0
#> SRR1047870 1 0 1 1 0
#> SRR1047871 1 0 1 1 0
#> SRR1047872 1 0 1 1 0
#> SRR1047873 1 0 1 1 0
#> SRR1047874 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1047813 1 0 1 1 0 0
#> SRR1047814 1 0 1 1 0 0
#> SRR1047815 1 0 1 1 0 0
#> SRR1047816 1 0 1 1 0 0
#> SRR1047817 1 0 1 1 0 0
#> SRR1047818 1 0 1 1 0 0
#> SRR1047819 1 0 1 1 0 0
#> SRR1047820 1 0 1 1 0 0
#> SRR1047821 1 0 1 1 0 0
#> SRR1047822 1 0 1 1 0 0
#> SRR1047823 1 0 1 1 0 0
#> SRR1047824 1 0 1 1 0 0
#> SRR1047825 1 0 1 1 0 0
#> SRR1047826 1 0 1 1 0 0
#> SRR1047827 1 0 1 1 0 0
#> SRR1047828 1 0 1 1 0 0
#> SRR1047829 1 0 1 1 0 0
#> SRR1047830 1 0 1 1 0 0
#> SRR1047831 1 0 1 1 0 0
#> SRR1047832 1 0 1 1 0 0
#> SRR1047833 2 0 1 0 1 0
#> SRR1047834 2 0 1 0 1 0
#> SRR1047835 2 0 1 0 1 0
#> SRR1047836 2 0 1 0 1 0
#> SRR1047837 2 0 1 0 1 0
#> SRR1047838 1 0 1 1 0 0
#> SRR1047839 1 0 1 1 0 0
#> SRR1047840 1 0 1 1 0 0
#> SRR1047841 1 0 1 1 0 0
#> SRR1047842 1 0 1 1 0 0
#> SRR1047843 1 0 1 1 0 0
#> SRR1047844 1 0 1 1 0 0
#> SRR1047845 1 0 1 1 0 0
#> SRR1047846 1 0 1 1 0 0
#> SRR1047847 1 0 1 1 0 0
#> SRR1047848 1 0 1 1 0 0
#> SRR1047849 1 0 1 1 0 0
#> SRR1047850 1 0 1 1 0 0
#> SRR1047851 1 0 1 1 0 0
#> SRR1047852 1 0 1 1 0 0
#> SRR1047853 1 0 1 1 0 0
#> SRR1047854 1 0 1 1 0 0
#> SRR1047855 1 0 1 1 0 0
#> SRR1047856 1 0 1 1 0 0
#> SRR1047857 1 0 1 1 0 0
#> SRR1047858 1 0 1 1 0 0
#> SRR1047859 1 0 1 1 0 0
#> SRR1047860 1 0 1 1 0 0
#> SRR1047861 1 0 1 1 0 0
#> SRR1047863 3 0 1 0 0 1
#> SRR1047864 3 0 1 0 0 1
#> SRR1047865 3 0 1 0 0 1
#> SRR1047866 3 0 1 0 0 1
#> SRR1047867 2 0 1 0 1 0
#> SRR1047868 3 0 1 0 0 1
#> SRR1047869 3 0 1 0 0 1
#> SRR1047870 3 0 1 0 0 1
#> SRR1047871 3 0 1 0 0 1
#> SRR1047872 3 0 1 0 0 1
#> SRR1047873 3 0 1 0 0 1
#> SRR1047874 3 0 1 0 0 1
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1047813 1 0.0000 0.88898 1.000 0.000 0 0.000
#> SRR1047814 1 0.0000 0.88898 1.000 0.000 0 0.000
#> SRR1047815 1 0.0000 0.88898 1.000 0.000 0 0.000
#> SRR1047816 1 0.0000 0.88898 1.000 0.000 0 0.000
#> SRR1047817 1 0.0000 0.88898 1.000 0.000 0 0.000
#> SRR1047818 4 0.4985 0.99043 0.468 0.000 0 0.532
#> SRR1047819 4 0.4985 0.99043 0.468 0.000 0 0.532
#> SRR1047820 4 0.4985 0.99043 0.468 0.000 0 0.532
#> SRR1047821 4 0.4985 0.99043 0.468 0.000 0 0.532
#> SRR1047822 4 0.4985 0.99043 0.468 0.000 0 0.532
#> SRR1047823 4 0.4985 0.99043 0.468 0.000 0 0.532
#> SRR1047824 4 0.4985 0.99043 0.468 0.000 0 0.532
#> SRR1047825 4 0.4985 0.99043 0.468 0.000 0 0.532
#> SRR1047826 4 0.4985 0.99043 0.468 0.000 0 0.532
#> SRR1047827 4 0.4985 0.99043 0.468 0.000 0 0.532
#> SRR1047828 1 0.0000 0.88898 1.000 0.000 0 0.000
#> SRR1047829 1 0.0000 0.88898 1.000 0.000 0 0.000
#> SRR1047830 1 0.0000 0.88898 1.000 0.000 0 0.000
#> SRR1047831 1 0.0000 0.88898 1.000 0.000 0 0.000
#> SRR1047832 1 0.0000 0.88898 1.000 0.000 0 0.000
#> SRR1047833 2 0.0000 0.94318 0.000 1.000 0 0.000
#> SRR1047834 2 0.0000 0.94318 0.000 1.000 0 0.000
#> SRR1047835 2 0.0000 0.94318 0.000 1.000 0 0.000
#> SRR1047836 2 0.0000 0.94318 0.000 1.000 0 0.000
#> SRR1047837 2 0.0000 0.94318 0.000 1.000 0 0.000
#> SRR1047838 4 0.4994 0.98049 0.480 0.000 0 0.520
#> SRR1047839 4 0.4994 0.98049 0.480 0.000 0 0.520
#> SRR1047840 4 0.4994 0.98049 0.480 0.000 0 0.520
#> SRR1047841 4 0.4994 0.98049 0.480 0.000 0 0.520
#> SRR1047842 4 0.4994 0.98049 0.480 0.000 0 0.520
#> SRR1047843 1 0.0469 0.88490 0.988 0.000 0 0.012
#> SRR1047844 1 0.0469 0.88490 0.988 0.000 0 0.012
#> SRR1047845 1 0.0469 0.88490 0.988 0.000 0 0.012
#> SRR1047846 1 0.0469 0.88490 0.988 0.000 0 0.012
#> SRR1047847 1 0.0469 0.88490 0.988 0.000 0 0.012
#> SRR1047848 1 0.0000 0.88898 1.000 0.000 0 0.000
#> SRR1047849 1 0.0000 0.88898 1.000 0.000 0 0.000
#> SRR1047850 1 0.0000 0.88898 1.000 0.000 0 0.000
#> SRR1047851 1 0.0000 0.88898 1.000 0.000 0 0.000
#> SRR1047852 1 0.0000 0.88898 1.000 0.000 0 0.000
#> SRR1047853 1 0.4331 -0.00914 0.712 0.000 0 0.288
#> SRR1047854 1 0.4331 -0.00914 0.712 0.000 0 0.288
#> SRR1047855 1 0.4331 -0.00914 0.712 0.000 0 0.288
#> SRR1047856 1 0.4331 -0.00914 0.712 0.000 0 0.288
#> SRR1047857 1 0.4331 -0.00914 0.712 0.000 0 0.288
#> SRR1047858 1 0.0469 0.88490 0.988 0.000 0 0.012
#> SRR1047859 1 0.0469 0.88490 0.988 0.000 0 0.012
#> SRR1047860 1 0.0469 0.88490 0.988 0.000 0 0.012
#> SRR1047861 1 0.0469 0.88490 0.988 0.000 0 0.012
#> SRR1047863 3 0.0000 1.00000 0.000 0.000 1 0.000
#> SRR1047864 3 0.0000 1.00000 0.000 0.000 1 0.000
#> SRR1047865 3 0.0000 1.00000 0.000 0.000 1 0.000
#> SRR1047866 3 0.0000 1.00000 0.000 0.000 1 0.000
#> SRR1047867 2 0.4985 0.68701 0.000 0.532 0 0.468
#> SRR1047868 3 0.0000 1.00000 0.000 0.000 1 0.000
#> SRR1047869 3 0.0000 1.00000 0.000 0.000 1 0.000
#> SRR1047870 3 0.0000 1.00000 0.000 0.000 1 0.000
#> SRR1047871 3 0.0000 1.00000 0.000 0.000 1 0.000
#> SRR1047872 3 0.0000 1.00000 0.000 0.000 1 0.000
#> SRR1047873 3 0.0000 1.00000 0.000 0.000 1 0.000
#> SRR1047874 3 0.0000 1.00000 0.000 0.000 1 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1047813 1 0.0000 0.994 1.000 0 0 0.000 0
#> SRR1047814 1 0.0000 0.994 1.000 0 0 0.000 0
#> SRR1047815 1 0.0000 0.994 1.000 0 0 0.000 0
#> SRR1047816 1 0.0000 0.994 1.000 0 0 0.000 0
#> SRR1047817 1 0.0000 0.994 1.000 0 0 0.000 0
#> SRR1047818 4 0.0000 0.896 0.000 0 0 1.000 0
#> SRR1047819 4 0.0000 0.896 0.000 0 0 1.000 0
#> SRR1047820 4 0.0000 0.896 0.000 0 0 1.000 0
#> SRR1047821 4 0.0000 0.896 0.000 0 0 1.000 0
#> SRR1047822 4 0.0000 0.896 0.000 0 0 1.000 0
#> SRR1047823 4 0.0000 0.896 0.000 0 0 1.000 0
#> SRR1047824 4 0.0000 0.896 0.000 0 0 1.000 0
#> SRR1047825 4 0.0000 0.896 0.000 0 0 1.000 0
#> SRR1047826 4 0.0000 0.896 0.000 0 0 1.000 0
#> SRR1047827 4 0.0000 0.896 0.000 0 0 1.000 0
#> SRR1047828 1 0.0000 0.994 1.000 0 0 0.000 0
#> SRR1047829 1 0.0000 0.994 1.000 0 0 0.000 0
#> SRR1047830 1 0.0000 0.994 1.000 0 0 0.000 0
#> SRR1047831 1 0.0000 0.994 1.000 0 0 0.000 0
#> SRR1047832 1 0.0000 0.994 1.000 0 0 0.000 0
#> SRR1047833 2 0.0000 1.000 0.000 1 0 0.000 0
#> SRR1047834 2 0.0000 1.000 0.000 1 0 0.000 0
#> SRR1047835 2 0.0000 1.000 0.000 1 0 0.000 0
#> SRR1047836 2 0.0000 1.000 0.000 1 0 0.000 0
#> SRR1047837 2 0.0000 1.000 0.000 1 0 0.000 0
#> SRR1047838 4 0.0404 0.895 0.012 0 0 0.988 0
#> SRR1047839 4 0.0404 0.895 0.012 0 0 0.988 0
#> SRR1047840 4 0.0404 0.895 0.012 0 0 0.988 0
#> SRR1047841 4 0.0404 0.895 0.012 0 0 0.988 0
#> SRR1047842 4 0.0404 0.895 0.012 0 0 0.988 0
#> SRR1047843 1 0.0404 0.990 0.988 0 0 0.012 0
#> SRR1047844 1 0.0404 0.990 0.988 0 0 0.012 0
#> SRR1047845 1 0.0404 0.990 0.988 0 0 0.012 0
#> SRR1047846 1 0.0404 0.990 0.988 0 0 0.012 0
#> SRR1047847 1 0.0404 0.990 0.988 0 0 0.012 0
#> SRR1047848 1 0.0000 0.994 1.000 0 0 0.000 0
#> SRR1047849 1 0.0000 0.994 1.000 0 0 0.000 0
#> SRR1047850 1 0.0000 0.994 1.000 0 0 0.000 0
#> SRR1047851 1 0.0000 0.994 1.000 0 0 0.000 0
#> SRR1047852 1 0.0000 0.994 1.000 0 0 0.000 0
#> SRR1047853 4 0.3480 0.684 0.248 0 0 0.752 0
#> SRR1047854 4 0.3480 0.684 0.248 0 0 0.752 0
#> SRR1047855 4 0.3480 0.684 0.248 0 0 0.752 0
#> SRR1047856 4 0.3480 0.684 0.248 0 0 0.752 0
#> SRR1047857 4 0.3480 0.684 0.248 0 0 0.752 0
#> SRR1047858 1 0.0404 0.990 0.988 0 0 0.012 0
#> SRR1047859 1 0.0404 0.990 0.988 0 0 0.012 0
#> SRR1047860 1 0.0404 0.990 0.988 0 0 0.012 0
#> SRR1047861 1 0.0404 0.990 0.988 0 0 0.012 0
#> SRR1047863 3 0.0000 1.000 0.000 0 1 0.000 0
#> SRR1047864 3 0.0000 1.000 0.000 0 1 0.000 0
#> SRR1047865 3 0.0000 1.000 0.000 0 1 0.000 0
#> SRR1047866 3 0.0000 1.000 0.000 0 1 0.000 0
#> SRR1047867 5 0.0000 0.000 0.000 0 0 0.000 1
#> SRR1047868 3 0.0000 1.000 0.000 0 1 0.000 0
#> SRR1047869 3 0.0000 1.000 0.000 0 1 0.000 0
#> SRR1047870 3 0.0000 1.000 0.000 0 1 0.000 0
#> SRR1047871 3 0.0000 1.000 0.000 0 1 0.000 0
#> SRR1047872 3 0.0000 1.000 0.000 0 1 0.000 0
#> SRR1047873 3 0.0000 1.000 0.000 0 1 0.000 0
#> SRR1047874 3 0.0000 1.000 0.000 0 1 0.000 0
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1047813 1 0.0547 9.82e-01 0.980 0 0.000 0.000 0.020 0
#> SRR1047814 1 0.0547 9.82e-01 0.980 0 0.000 0.000 0.020 0
#> SRR1047815 1 0.0547 9.82e-01 0.980 0 0.000 0.000 0.020 0
#> SRR1047816 1 0.0547 9.82e-01 0.980 0 0.000 0.000 0.020 0
#> SRR1047817 1 0.0547 9.82e-01 0.980 0 0.000 0.000 0.020 0
#> SRR1047818 4 0.0000 8.92e-01 0.000 0 0.000 1.000 0.000 0
#> SRR1047819 4 0.0000 8.92e-01 0.000 0 0.000 1.000 0.000 0
#> SRR1047820 4 0.0000 8.92e-01 0.000 0 0.000 1.000 0.000 0
#> SRR1047821 4 0.0000 8.92e-01 0.000 0 0.000 1.000 0.000 0
#> SRR1047822 4 0.0000 8.92e-01 0.000 0 0.000 1.000 0.000 0
#> SRR1047823 4 0.0000 8.92e-01 0.000 0 0.000 1.000 0.000 0
#> SRR1047824 4 0.0000 8.92e-01 0.000 0 0.000 1.000 0.000 0
#> SRR1047825 4 0.0000 8.92e-01 0.000 0 0.000 1.000 0.000 0
#> SRR1047826 4 0.0000 8.92e-01 0.000 0 0.000 1.000 0.000 0
#> SRR1047827 4 0.0000 8.92e-01 0.000 0 0.000 1.000 0.000 0
#> SRR1047828 1 0.0363 9.82e-01 0.988 0 0.000 0.000 0.012 0
#> SRR1047829 1 0.0363 9.82e-01 0.988 0 0.000 0.000 0.012 0
#> SRR1047830 1 0.0363 9.82e-01 0.988 0 0.000 0.000 0.012 0
#> SRR1047831 1 0.0363 9.82e-01 0.988 0 0.000 0.000 0.012 0
#> SRR1047832 1 0.0363 9.82e-01 0.988 0 0.000 0.000 0.012 0
#> SRR1047833 2 0.0000 1.00e+00 0.000 1 0.000 0.000 0.000 0
#> SRR1047834 2 0.0000 1.00e+00 0.000 1 0.000 0.000 0.000 0
#> SRR1047835 2 0.0000 1.00e+00 0.000 1 0.000 0.000 0.000 0
#> SRR1047836 2 0.0000 1.00e+00 0.000 1 0.000 0.000 0.000 0
#> SRR1047837 2 0.0000 1.00e+00 0.000 1 0.000 0.000 0.000 0
#> SRR1047838 4 0.0725 8.89e-01 0.012 0 0.000 0.976 0.012 0
#> SRR1047839 4 0.0725 8.89e-01 0.012 0 0.000 0.976 0.012 0
#> SRR1047840 4 0.0725 8.89e-01 0.012 0 0.000 0.976 0.012 0
#> SRR1047841 4 0.0725 8.89e-01 0.012 0 0.000 0.976 0.012 0
#> SRR1047842 4 0.0725 8.89e-01 0.012 0 0.000 0.976 0.012 0
#> SRR1047843 1 0.0458 9.80e-01 0.984 0 0.000 0.000 0.016 0
#> SRR1047844 1 0.0458 9.80e-01 0.984 0 0.000 0.000 0.016 0
#> SRR1047845 1 0.0458 9.80e-01 0.984 0 0.000 0.000 0.016 0
#> SRR1047846 1 0.0458 9.80e-01 0.984 0 0.000 0.000 0.016 0
#> SRR1047847 1 0.0458 9.80e-01 0.984 0 0.000 0.000 0.016 0
#> SRR1047848 1 0.0547 9.80e-01 0.980 0 0.000 0.000 0.020 0
#> SRR1047849 1 0.0547 9.80e-01 0.980 0 0.000 0.000 0.020 0
#> SRR1047850 1 0.0547 9.80e-01 0.980 0 0.000 0.000 0.020 0
#> SRR1047851 1 0.0547 9.80e-01 0.980 0 0.000 0.000 0.020 0
#> SRR1047852 1 0.0547 9.80e-01 0.980 0 0.000 0.000 0.020 0
#> SRR1047853 4 0.3534 6.82e-01 0.244 0 0.000 0.740 0.016 0
#> SRR1047854 4 0.3534 6.82e-01 0.244 0 0.000 0.740 0.016 0
#> SRR1047855 4 0.3534 6.82e-01 0.244 0 0.000 0.740 0.016 0
#> SRR1047856 4 0.3534 6.82e-01 0.244 0 0.000 0.740 0.016 0
#> SRR1047857 4 0.3534 6.82e-01 0.244 0 0.000 0.740 0.016 0
#> SRR1047858 1 0.0363 9.81e-01 0.988 0 0.000 0.000 0.012 0
#> SRR1047859 1 0.0363 9.81e-01 0.988 0 0.000 0.000 0.012 0
#> SRR1047860 1 0.0363 9.81e-01 0.988 0 0.000 0.000 0.012 0
#> SRR1047861 1 0.0363 9.81e-01 0.988 0 0.000 0.000 0.012 0
#> SRR1047863 3 0.0000 9.22e-01 0.000 0 1.000 0.000 0.000 0
#> SRR1047864 3 0.3862 -1.71e-08 0.000 0 0.524 0.000 0.476 0
#> SRR1047865 5 0.1075 1.00e+00 0.000 0 0.048 0.000 0.952 0
#> SRR1047866 5 0.1075 1.00e+00 0.000 0 0.048 0.000 0.952 0
#> SRR1047867 6 0.0000 0.00e+00 0.000 0 0.000 0.000 0.000 1
#> SRR1047868 3 0.0000 9.22e-01 0.000 0 1.000 0.000 0.000 0
#> SRR1047869 5 0.1075 1.00e+00 0.000 0 0.048 0.000 0.952 0
#> SRR1047870 3 0.0000 9.22e-01 0.000 0 1.000 0.000 0.000 0
#> SRR1047871 3 0.0000 9.22e-01 0.000 0 1.000 0.000 0.000 0
#> SRR1047872 3 0.0000 9.22e-01 0.000 0 1.000 0.000 0.000 0
#> SRR1047873 3 0.0000 9.22e-01 0.000 0 1.000 0.000 0.000 0
#> SRR1047874 3 0.0000 9.22e-01 0.000 0 1.000 0.000 0.000 0
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 17931 rows and 61 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.166 0.584 0.742 0.3499 0.820 0.820
#> 3 3 0.249 0.562 0.676 0.5773 0.588 0.497
#> 4 4 0.477 0.773 0.820 0.2160 0.795 0.548
#> 5 5 0.632 0.713 0.782 0.0975 1.000 1.000
#> 6 6 0.664 0.616 0.722 0.0601 0.844 0.534
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
#> SRR1047813 1 0.5737 0.615 0.864 0.136
#> SRR1047814 1 0.5737 0.615 0.864 0.136
#> SRR1047815 1 0.5737 0.615 0.864 0.136
#> SRR1047816 1 0.5737 0.615 0.864 0.136
#> SRR1047817 1 0.5737 0.615 0.864 0.136
#> SRR1047818 1 0.9087 0.474 0.676 0.324
#> SRR1047819 1 0.9087 0.474 0.676 0.324
#> SRR1047820 1 0.9087 0.474 0.676 0.324
#> SRR1047821 1 0.9087 0.474 0.676 0.324
#> SRR1047822 1 0.9087 0.474 0.676 0.324
#> SRR1047823 1 0.9580 0.422 0.620 0.380
#> SRR1047824 1 0.9580 0.422 0.620 0.380
#> SRR1047825 1 0.9580 0.422 0.620 0.380
#> SRR1047826 1 0.9580 0.422 0.620 0.380
#> SRR1047827 1 0.9580 0.422 0.620 0.380
#> SRR1047828 1 0.7139 0.630 0.804 0.196
#> SRR1047829 1 0.7139 0.630 0.804 0.196
#> SRR1047830 1 0.7139 0.630 0.804 0.196
#> SRR1047831 1 0.7139 0.630 0.804 0.196
#> SRR1047832 1 0.7139 0.630 0.804 0.196
#> SRR1047833 2 0.8016 0.904 0.244 0.756
#> SRR1047834 2 0.8016 0.904 0.244 0.756
#> SRR1047835 2 0.8016 0.904 0.244 0.756
#> SRR1047836 2 0.8016 0.904 0.244 0.756
#> SRR1047837 2 0.8016 0.904 0.244 0.756
#> SRR1047838 1 0.7299 0.632 0.796 0.204
#> SRR1047839 1 0.7299 0.632 0.796 0.204
#> SRR1047840 1 0.7299 0.632 0.796 0.204
#> SRR1047841 1 0.7299 0.632 0.796 0.204
#> SRR1047842 1 0.7299 0.632 0.796 0.204
#> SRR1047843 1 0.0376 0.678 0.996 0.004
#> SRR1047844 1 0.0376 0.678 0.996 0.004
#> SRR1047845 1 0.0376 0.678 0.996 0.004
#> SRR1047846 1 0.0376 0.678 0.996 0.004
#> SRR1047847 1 0.0376 0.678 0.996 0.004
#> SRR1047848 1 0.4431 0.642 0.908 0.092
#> SRR1047849 1 0.4431 0.642 0.908 0.092
#> SRR1047850 1 0.4431 0.642 0.908 0.092
#> SRR1047851 1 0.4431 0.642 0.908 0.092
#> SRR1047852 1 0.4431 0.642 0.908 0.092
#> SRR1047853 1 0.5842 0.663 0.860 0.140
#> SRR1047854 1 0.5842 0.663 0.860 0.140
#> SRR1047855 1 0.5842 0.663 0.860 0.140
#> SRR1047856 1 0.5842 0.663 0.860 0.140
#> SRR1047857 1 0.5842 0.663 0.860 0.140
#> SRR1047858 1 0.1184 0.677 0.984 0.016
#> SRR1047859 1 0.1184 0.677 0.984 0.016
#> SRR1047860 1 0.1184 0.677 0.984 0.016
#> SRR1047861 1 0.1184 0.677 0.984 0.016
#> SRR1047863 1 0.9922 0.351 0.552 0.448
#> SRR1047864 1 0.9933 0.346 0.548 0.452
#> SRR1047865 1 0.9323 0.383 0.652 0.348
#> SRR1047866 1 0.9323 0.383 0.652 0.348
#> SRR1047867 2 0.3114 0.608 0.056 0.944
#> SRR1047868 1 0.9922 0.351 0.552 0.448
#> SRR1047869 1 0.9323 0.383 0.652 0.348
#> SRR1047870 1 0.9922 0.351 0.552 0.448
#> SRR1047871 1 0.9922 0.351 0.552 0.448
#> SRR1047872 1 0.9850 0.373 0.572 0.428
#> SRR1047873 1 0.9850 0.373 0.572 0.428
#> SRR1047874 1 0.9833 0.375 0.576 0.424
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1047813 1 0.285 0.7617 0.924 0.056 0.020
#> SRR1047814 1 0.285 0.7617 0.924 0.056 0.020
#> SRR1047815 1 0.285 0.7617 0.924 0.056 0.020
#> SRR1047816 1 0.285 0.7617 0.924 0.056 0.020
#> SRR1047817 1 0.285 0.7617 0.924 0.056 0.020
#> SRR1047818 3 0.973 0.4912 0.292 0.260 0.448
#> SRR1047819 3 0.973 0.4912 0.292 0.260 0.448
#> SRR1047820 3 0.973 0.4912 0.292 0.260 0.448
#> SRR1047821 3 0.973 0.4912 0.292 0.260 0.448
#> SRR1047822 3 0.973 0.4912 0.292 0.260 0.448
#> SRR1047823 3 0.987 0.4611 0.324 0.268 0.408
#> SRR1047824 3 0.987 0.4611 0.324 0.268 0.408
#> SRR1047825 3 0.987 0.4611 0.324 0.268 0.408
#> SRR1047826 3 0.987 0.4611 0.324 0.268 0.408
#> SRR1047827 3 0.987 0.4611 0.324 0.268 0.408
#> SRR1047828 1 0.641 0.6844 0.764 0.144 0.092
#> SRR1047829 1 0.641 0.6844 0.764 0.144 0.092
#> SRR1047830 1 0.641 0.6844 0.764 0.144 0.092
#> SRR1047831 1 0.641 0.6844 0.764 0.144 0.092
#> SRR1047832 1 0.641 0.6844 0.764 0.144 0.092
#> SRR1047833 2 0.456 0.9127 0.064 0.860 0.076
#> SRR1047834 2 0.456 0.9127 0.064 0.860 0.076
#> SRR1047835 2 0.456 0.9127 0.064 0.860 0.076
#> SRR1047836 2 0.456 0.9127 0.064 0.860 0.076
#> SRR1047837 2 0.456 0.9127 0.064 0.860 0.076
#> SRR1047838 3 0.955 0.4337 0.352 0.200 0.448
#> SRR1047839 3 0.955 0.4337 0.352 0.200 0.448
#> SRR1047840 3 0.955 0.4337 0.352 0.200 0.448
#> SRR1047841 3 0.955 0.4337 0.352 0.200 0.448
#> SRR1047842 3 0.955 0.4337 0.352 0.200 0.448
#> SRR1047843 1 0.271 0.7632 0.912 0.000 0.088
#> SRR1047844 1 0.271 0.7632 0.912 0.000 0.088
#> SRR1047845 1 0.271 0.7632 0.912 0.000 0.088
#> SRR1047846 1 0.271 0.7632 0.912 0.000 0.088
#> SRR1047847 1 0.271 0.7632 0.912 0.000 0.088
#> SRR1047848 1 0.148 0.7805 0.968 0.012 0.020
#> SRR1047849 1 0.148 0.7805 0.968 0.012 0.020
#> SRR1047850 1 0.148 0.7805 0.968 0.012 0.020
#> SRR1047851 1 0.148 0.7805 0.968 0.012 0.020
#> SRR1047852 1 0.148 0.7805 0.968 0.012 0.020
#> SRR1047853 1 0.856 0.0452 0.528 0.104 0.368
#> SRR1047854 1 0.856 0.0452 0.528 0.104 0.368
#> SRR1047855 1 0.856 0.0452 0.528 0.104 0.368
#> SRR1047856 1 0.856 0.0452 0.528 0.104 0.368
#> SRR1047857 1 0.856 0.0452 0.528 0.104 0.368
#> SRR1047858 1 0.116 0.7815 0.972 0.000 0.028
#> SRR1047859 1 0.116 0.7815 0.972 0.000 0.028
#> SRR1047860 1 0.116 0.7815 0.972 0.000 0.028
#> SRR1047861 1 0.116 0.7815 0.972 0.000 0.028
#> SRR1047863 3 0.434 0.3654 0.136 0.016 0.848
#> SRR1047864 3 0.434 0.3654 0.136 0.016 0.848
#> SRR1047865 3 0.531 0.3275 0.192 0.020 0.788
#> SRR1047866 3 0.544 0.3200 0.192 0.024 0.784
#> SRR1047867 2 0.704 0.5413 0.020 0.536 0.444
#> SRR1047868 3 0.434 0.3654 0.136 0.016 0.848
#> SRR1047869 3 0.501 0.3280 0.204 0.008 0.788
#> SRR1047870 3 0.434 0.3654 0.136 0.016 0.848
#> SRR1047871 3 0.434 0.3654 0.136 0.016 0.848
#> SRR1047872 3 0.398 0.3788 0.144 0.004 0.852
#> SRR1047873 3 0.398 0.3788 0.144 0.004 0.852
#> SRR1047874 3 0.398 0.3788 0.144 0.004 0.852
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1047813 1 0.456 0.7728 0.820 0.084 0.084 0.012
#> SRR1047814 1 0.456 0.7728 0.820 0.084 0.084 0.012
#> SRR1047815 1 0.456 0.7728 0.820 0.084 0.084 0.012
#> SRR1047816 1 0.456 0.7728 0.820 0.084 0.084 0.012
#> SRR1047817 1 0.456 0.7728 0.820 0.084 0.084 0.012
#> SRR1047818 4 0.255 0.7755 0.056 0.004 0.024 0.916
#> SRR1047819 4 0.255 0.7755 0.056 0.004 0.024 0.916
#> SRR1047820 4 0.255 0.7755 0.056 0.004 0.024 0.916
#> SRR1047821 4 0.255 0.7755 0.056 0.004 0.024 0.916
#> SRR1047822 4 0.255 0.7755 0.056 0.004 0.024 0.916
#> SRR1047823 4 0.251 0.7417 0.052 0.020 0.008 0.920
#> SRR1047824 4 0.251 0.7417 0.052 0.020 0.008 0.920
#> SRR1047825 4 0.251 0.7417 0.052 0.020 0.008 0.920
#> SRR1047826 4 0.251 0.7417 0.052 0.020 0.008 0.920
#> SRR1047827 4 0.251 0.7417 0.052 0.020 0.008 0.920
#> SRR1047828 1 0.700 0.7043 0.668 0.064 0.092 0.176
#> SRR1047829 1 0.700 0.7043 0.668 0.064 0.092 0.176
#> SRR1047830 1 0.700 0.7043 0.668 0.064 0.092 0.176
#> SRR1047831 1 0.700 0.7043 0.668 0.064 0.092 0.176
#> SRR1047832 1 0.700 0.7043 0.668 0.064 0.092 0.176
#> SRR1047833 2 0.356 1.0000 0.016 0.864 0.016 0.104
#> SRR1047834 2 0.356 1.0000 0.016 0.864 0.016 0.104
#> SRR1047835 2 0.356 1.0000 0.016 0.864 0.016 0.104
#> SRR1047836 2 0.356 1.0000 0.016 0.864 0.016 0.104
#> SRR1047837 2 0.356 1.0000 0.016 0.864 0.016 0.104
#> SRR1047838 4 0.451 0.7699 0.176 0.004 0.032 0.788
#> SRR1047839 4 0.451 0.7699 0.176 0.004 0.032 0.788
#> SRR1047840 4 0.451 0.7699 0.176 0.004 0.032 0.788
#> SRR1047841 4 0.451 0.7699 0.176 0.004 0.032 0.788
#> SRR1047842 4 0.451 0.7699 0.176 0.004 0.032 0.788
#> SRR1047843 1 0.444 0.7728 0.808 0.004 0.048 0.140
#> SRR1047844 1 0.444 0.7728 0.808 0.004 0.048 0.140
#> SRR1047845 1 0.444 0.7728 0.808 0.004 0.048 0.140
#> SRR1047846 1 0.444 0.7728 0.808 0.004 0.048 0.140
#> SRR1047847 1 0.444 0.7728 0.808 0.004 0.048 0.140
#> SRR1047848 1 0.274 0.8123 0.908 0.020 0.008 0.064
#> SRR1047849 1 0.274 0.8123 0.908 0.020 0.008 0.064
#> SRR1047850 1 0.274 0.8123 0.908 0.020 0.008 0.064
#> SRR1047851 1 0.274 0.8123 0.908 0.020 0.008 0.064
#> SRR1047852 1 0.274 0.8123 0.908 0.020 0.008 0.064
#> SRR1047853 4 0.668 0.3941 0.404 0.004 0.076 0.516
#> SRR1047854 4 0.668 0.3941 0.404 0.004 0.076 0.516
#> SRR1047855 4 0.668 0.3941 0.404 0.004 0.076 0.516
#> SRR1047856 4 0.668 0.3941 0.404 0.004 0.076 0.516
#> SRR1047857 4 0.668 0.3941 0.404 0.004 0.076 0.516
#> SRR1047858 1 0.236 0.8193 0.920 0.012 0.004 0.064
#> SRR1047859 1 0.236 0.8193 0.920 0.012 0.004 0.064
#> SRR1047860 1 0.236 0.8193 0.920 0.012 0.004 0.064
#> SRR1047861 1 0.236 0.8193 0.920 0.012 0.004 0.064
#> SRR1047863 3 0.256 0.9268 0.020 0.000 0.908 0.072
#> SRR1047864 3 0.278 0.9235 0.016 0.008 0.904 0.072
#> SRR1047865 3 0.326 0.8965 0.056 0.008 0.888 0.048
#> SRR1047866 3 0.317 0.8947 0.052 0.008 0.892 0.048
#> SRR1047867 3 0.585 0.0564 0.000 0.456 0.512 0.032
#> SRR1047868 3 0.249 0.9270 0.020 0.000 0.912 0.068
#> SRR1047869 3 0.347 0.8974 0.056 0.012 0.880 0.052
#> SRR1047870 3 0.289 0.9251 0.020 0.008 0.900 0.072
#> SRR1047871 3 0.249 0.9270 0.020 0.000 0.912 0.068
#> SRR1047872 3 0.271 0.9243 0.016 0.004 0.904 0.076
#> SRR1047873 3 0.271 0.9243 0.016 0.004 0.904 0.076
#> SRR1047874 3 0.271 0.9243 0.016 0.004 0.904 0.076
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1047813 1 0.4600 0.65441 0.632 0.008 0.004 0.004 NA
#> SRR1047814 1 0.4600 0.65441 0.632 0.008 0.004 0.004 NA
#> SRR1047815 1 0.4600 0.65441 0.632 0.008 0.004 0.004 NA
#> SRR1047816 1 0.4600 0.65441 0.632 0.008 0.004 0.004 NA
#> SRR1047817 1 0.4600 0.65441 0.632 0.008 0.004 0.004 NA
#> SRR1047818 4 0.2607 0.73322 0.024 0.004 0.032 0.908 NA
#> SRR1047819 4 0.2607 0.73322 0.024 0.004 0.032 0.908 NA
#> SRR1047820 4 0.2607 0.73322 0.024 0.004 0.032 0.908 NA
#> SRR1047821 4 0.2607 0.73322 0.024 0.004 0.032 0.908 NA
#> SRR1047822 4 0.2607 0.73322 0.024 0.004 0.032 0.908 NA
#> SRR1047823 4 0.3512 0.67003 0.024 0.004 0.004 0.828 NA
#> SRR1047824 4 0.3512 0.67003 0.024 0.004 0.004 0.828 NA
#> SRR1047825 4 0.3512 0.67003 0.024 0.004 0.004 0.828 NA
#> SRR1047826 4 0.3512 0.67003 0.024 0.004 0.004 0.828 NA
#> SRR1047827 4 0.3512 0.67003 0.024 0.004 0.004 0.828 NA
#> SRR1047828 1 0.6958 0.61657 0.540 0.044 0.020 0.084 NA
#> SRR1047829 1 0.6958 0.61657 0.540 0.044 0.020 0.084 NA
#> SRR1047830 1 0.6958 0.61657 0.540 0.044 0.020 0.084 NA
#> SRR1047831 1 0.6958 0.61657 0.540 0.044 0.020 0.084 NA
#> SRR1047832 1 0.6958 0.61657 0.540 0.044 0.020 0.084 NA
#> SRR1047833 2 0.0703 0.99760 0.000 0.976 0.000 0.024 NA
#> SRR1047834 2 0.0609 0.99940 0.000 0.980 0.000 0.020 NA
#> SRR1047835 2 0.0609 0.99940 0.000 0.980 0.000 0.020 NA
#> SRR1047836 2 0.0609 0.99940 0.000 0.980 0.000 0.020 NA
#> SRR1047837 2 0.0609 0.99940 0.000 0.980 0.000 0.020 NA
#> SRR1047838 4 0.4769 0.72690 0.124 0.000 0.032 0.768 NA
#> SRR1047839 4 0.4769 0.72690 0.124 0.000 0.032 0.768 NA
#> SRR1047840 4 0.4769 0.72690 0.124 0.000 0.032 0.768 NA
#> SRR1047841 4 0.4769 0.72690 0.124 0.000 0.032 0.768 NA
#> SRR1047842 4 0.4769 0.72690 0.124 0.000 0.032 0.768 NA
#> SRR1047843 1 0.4711 0.63787 0.772 0.000 0.032 0.124 NA
#> SRR1047844 1 0.4711 0.63787 0.772 0.000 0.032 0.124 NA
#> SRR1047845 1 0.4711 0.63787 0.772 0.000 0.032 0.124 NA
#> SRR1047846 1 0.4711 0.63787 0.772 0.000 0.032 0.124 NA
#> SRR1047847 1 0.4711 0.63787 0.772 0.000 0.032 0.124 NA
#> SRR1047848 1 0.3814 0.69380 0.832 0.012 0.008 0.040 NA
#> SRR1047849 1 0.3814 0.69380 0.832 0.012 0.008 0.040 NA
#> SRR1047850 1 0.3814 0.69380 0.832 0.012 0.008 0.040 NA
#> SRR1047851 1 0.3814 0.69380 0.832 0.012 0.008 0.040 NA
#> SRR1047852 1 0.3814 0.69380 0.832 0.012 0.008 0.040 NA
#> SRR1047853 4 0.7107 0.38232 0.364 0.000 0.060 0.460 NA
#> SRR1047854 4 0.7107 0.38232 0.364 0.000 0.060 0.460 NA
#> SRR1047855 4 0.7107 0.38232 0.364 0.000 0.060 0.460 NA
#> SRR1047856 4 0.7107 0.38232 0.364 0.000 0.060 0.460 NA
#> SRR1047857 4 0.7107 0.38232 0.364 0.000 0.060 0.460 NA
#> SRR1047858 1 0.2838 0.69843 0.884 0.000 0.008 0.072 NA
#> SRR1047859 1 0.2838 0.69843 0.884 0.000 0.008 0.072 NA
#> SRR1047860 1 0.2838 0.69843 0.884 0.000 0.008 0.072 NA
#> SRR1047861 1 0.2838 0.69843 0.884 0.000 0.008 0.072 NA
#> SRR1047863 3 0.0727 0.92349 0.004 0.000 0.980 0.004 NA
#> SRR1047864 3 0.2330 0.88607 0.004 0.004 0.900 0.004 NA
#> SRR1047865 3 0.1369 0.92027 0.008 0.000 0.956 0.008 NA
#> SRR1047866 3 0.1186 0.92090 0.008 0.000 0.964 0.008 NA
#> SRR1047867 3 0.6495 0.00655 0.000 0.388 0.424 0.000 NA
#> SRR1047868 3 0.0486 0.92454 0.004 0.000 0.988 0.004 NA
#> SRR1047869 3 0.1369 0.92027 0.008 0.000 0.956 0.008 NA
#> SRR1047870 3 0.1604 0.91039 0.004 0.004 0.944 0.004 NA
#> SRR1047871 3 0.0486 0.92454 0.004 0.000 0.988 0.004 NA
#> SRR1047872 3 0.1314 0.92173 0.004 0.004 0.960 0.008 NA
#> SRR1047873 3 0.1314 0.92173 0.004 0.004 0.960 0.008 NA
#> SRR1047874 3 0.1314 0.92173 0.004 0.004 0.960 0.008 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1047813 5 0.3489 0.6986 0.288 0.000 0.000 0.004 0.708 NA
#> SRR1047814 5 0.3489 0.6986 0.288 0.000 0.000 0.004 0.708 NA
#> SRR1047815 5 0.3489 0.6986 0.288 0.000 0.000 0.004 0.708 NA
#> SRR1047816 5 0.3489 0.6986 0.288 0.000 0.000 0.004 0.708 NA
#> SRR1047817 5 0.3489 0.6986 0.288 0.000 0.000 0.004 0.708 NA
#> SRR1047818 4 0.2201 0.7579 0.016 0.000 0.008 0.916 0.036 NA
#> SRR1047819 4 0.2201 0.7579 0.016 0.000 0.008 0.916 0.036 NA
#> SRR1047820 4 0.2201 0.7579 0.016 0.000 0.008 0.916 0.036 NA
#> SRR1047821 4 0.2201 0.7579 0.016 0.000 0.008 0.916 0.036 NA
#> SRR1047822 4 0.2201 0.7579 0.016 0.000 0.008 0.916 0.036 NA
#> SRR1047823 4 0.3740 0.7164 0.012 0.000 0.000 0.728 0.008 NA
#> SRR1047824 4 0.3740 0.7164 0.012 0.000 0.000 0.728 0.008 NA
#> SRR1047825 4 0.3740 0.7164 0.012 0.000 0.000 0.728 0.008 NA
#> SRR1047826 4 0.3740 0.7164 0.012 0.000 0.000 0.728 0.008 NA
#> SRR1047827 4 0.3740 0.7164 0.012 0.000 0.000 0.728 0.008 NA
#> SRR1047828 5 0.7412 0.6863 0.348 0.020 0.024 0.072 0.428 NA
#> SRR1047829 5 0.7412 0.6863 0.348 0.020 0.024 0.072 0.428 NA
#> SRR1047830 5 0.7412 0.6863 0.348 0.020 0.024 0.072 0.428 NA
#> SRR1047831 5 0.7412 0.6863 0.348 0.020 0.024 0.072 0.428 NA
#> SRR1047832 5 0.7412 0.6863 0.348 0.020 0.024 0.072 0.428 NA
#> SRR1047833 2 0.0622 0.9957 0.000 0.980 0.000 0.012 0.008 NA
#> SRR1047834 2 0.0363 0.9983 0.000 0.988 0.000 0.012 0.000 NA
#> SRR1047835 2 0.0458 0.9974 0.000 0.984 0.000 0.016 0.000 NA
#> SRR1047836 2 0.0363 0.9983 0.000 0.988 0.000 0.012 0.000 NA
#> SRR1047837 2 0.0363 0.9983 0.000 0.988 0.000 0.012 0.000 NA
#> SRR1047838 4 0.5191 0.6313 0.188 0.000 0.008 0.692 0.052 NA
#> SRR1047839 4 0.5191 0.6313 0.188 0.000 0.008 0.692 0.052 NA
#> SRR1047840 4 0.5191 0.6313 0.188 0.000 0.008 0.692 0.052 NA
#> SRR1047841 4 0.5191 0.6313 0.188 0.000 0.008 0.692 0.052 NA
#> SRR1047842 4 0.5191 0.6313 0.188 0.000 0.008 0.692 0.052 NA
#> SRR1047843 1 0.3149 0.3924 0.856 0.000 0.008 0.080 0.044 NA
#> SRR1047844 1 0.3149 0.3924 0.856 0.000 0.008 0.080 0.044 NA
#> SRR1047845 1 0.3149 0.3924 0.856 0.000 0.008 0.080 0.044 NA
#> SRR1047846 1 0.3149 0.3924 0.856 0.000 0.008 0.080 0.044 NA
#> SRR1047847 1 0.3149 0.3924 0.856 0.000 0.008 0.080 0.044 NA
#> SRR1047848 1 0.6000 0.2820 0.552 0.000 0.000 0.024 0.208 NA
#> SRR1047849 1 0.6000 0.2820 0.552 0.000 0.000 0.024 0.208 NA
#> SRR1047850 1 0.6000 0.2820 0.552 0.000 0.000 0.024 0.208 NA
#> SRR1047851 1 0.6000 0.2820 0.552 0.000 0.000 0.024 0.208 NA
#> SRR1047852 1 0.6000 0.2820 0.552 0.000 0.000 0.024 0.208 NA
#> SRR1047853 1 0.6668 0.0632 0.416 0.000 0.020 0.412 0.096 NA
#> SRR1047854 1 0.6668 0.0632 0.416 0.000 0.020 0.412 0.096 NA
#> SRR1047855 1 0.6668 0.0632 0.416 0.000 0.020 0.412 0.096 NA
#> SRR1047856 1 0.6668 0.0632 0.416 0.000 0.020 0.412 0.096 NA
#> SRR1047857 1 0.6668 0.0632 0.416 0.000 0.020 0.412 0.096 NA
#> SRR1047858 1 0.3543 0.3895 0.812 0.000 0.000 0.012 0.124 NA
#> SRR1047859 1 0.3543 0.3895 0.812 0.000 0.000 0.012 0.124 NA
#> SRR1047860 1 0.3543 0.3895 0.812 0.000 0.000 0.012 0.124 NA
#> SRR1047861 1 0.3543 0.3895 0.812 0.000 0.000 0.012 0.124 NA
#> SRR1047863 3 0.0603 0.9005 0.000 0.000 0.980 0.000 0.004 NA
#> SRR1047864 3 0.2664 0.8418 0.000 0.000 0.848 0.000 0.016 NA
#> SRR1047865 3 0.2074 0.8866 0.004 0.000 0.912 0.000 0.048 NA
#> SRR1047866 3 0.1863 0.8872 0.000 0.000 0.920 0.000 0.044 NA
#> SRR1047867 3 0.6684 0.0831 0.000 0.292 0.380 0.000 0.032 NA
#> SRR1047868 3 0.0291 0.9017 0.000 0.000 0.992 0.000 0.004 NA
#> SRR1047869 3 0.2138 0.8861 0.004 0.000 0.908 0.000 0.052 NA
#> SRR1047870 3 0.1643 0.8826 0.000 0.000 0.924 0.000 0.008 NA
#> SRR1047871 3 0.0291 0.9017 0.000 0.000 0.992 0.000 0.004 NA
#> SRR1047872 3 0.1519 0.8978 0.004 0.008 0.948 0.004 0.028 NA
#> SRR1047873 3 0.1519 0.8978 0.004 0.008 0.948 0.004 0.028 NA
#> SRR1047874 3 0.1519 0.8978 0.004 0.008 0.948 0.004 0.028 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 17931 rows and 61 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.492 0.904 0.918 0.4757 0.531 0.531
#> 3 3 0.754 0.860 0.929 0.4140 0.694 0.475
#> 4 4 0.959 0.967 0.978 0.1059 0.896 0.698
#> 5 5 0.825 0.874 0.881 0.0619 0.959 0.841
#> 6 6 0.842 0.813 0.868 0.0422 0.932 0.703
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR1047813 1 0.184 0.898 0.972 0.028
#> SRR1047814 1 0.184 0.898 0.972 0.028
#> SRR1047815 1 0.184 0.898 0.972 0.028
#> SRR1047816 1 0.184 0.898 0.972 0.028
#> SRR1047817 1 0.184 0.898 0.972 0.028
#> SRR1047818 1 0.634 0.901 0.840 0.160
#> SRR1047819 1 0.634 0.901 0.840 0.160
#> SRR1047820 1 0.634 0.901 0.840 0.160
#> SRR1047821 1 0.634 0.901 0.840 0.160
#> SRR1047822 1 0.634 0.901 0.840 0.160
#> SRR1047823 1 0.295 0.903 0.948 0.052
#> SRR1047824 1 0.295 0.903 0.948 0.052
#> SRR1047825 1 0.295 0.903 0.948 0.052
#> SRR1047826 1 0.295 0.903 0.948 0.052
#> SRR1047827 1 0.295 0.903 0.948 0.052
#> SRR1047828 2 0.634 0.885 0.160 0.840
#> SRR1047829 2 0.634 0.885 0.160 0.840
#> SRR1047830 2 0.634 0.885 0.160 0.840
#> SRR1047831 2 0.634 0.885 0.160 0.840
#> SRR1047832 2 0.634 0.885 0.160 0.840
#> SRR1047833 2 0.506 0.902 0.112 0.888
#> SRR1047834 2 0.506 0.902 0.112 0.888
#> SRR1047835 2 0.506 0.902 0.112 0.888
#> SRR1047836 2 0.506 0.902 0.112 0.888
#> SRR1047837 2 0.506 0.902 0.112 0.888
#> SRR1047838 1 0.605 0.908 0.852 0.148
#> SRR1047839 1 0.605 0.908 0.852 0.148
#> SRR1047840 1 0.605 0.908 0.852 0.148
#> SRR1047841 1 0.605 0.908 0.852 0.148
#> SRR1047842 1 0.605 0.908 0.852 0.148
#> SRR1047843 1 0.506 0.908 0.888 0.112
#> SRR1047844 1 0.506 0.908 0.888 0.112
#> SRR1047845 1 0.506 0.908 0.888 0.112
#> SRR1047846 1 0.506 0.908 0.888 0.112
#> SRR1047847 1 0.506 0.908 0.888 0.112
#> SRR1047848 1 0.141 0.900 0.980 0.020
#> SRR1047849 1 0.141 0.900 0.980 0.020
#> SRR1047850 1 0.141 0.900 0.980 0.020
#> SRR1047851 1 0.141 0.900 0.980 0.020
#> SRR1047852 1 0.141 0.900 0.980 0.020
#> SRR1047853 1 0.605 0.908 0.852 0.148
#> SRR1047854 1 0.605 0.908 0.852 0.148
#> SRR1047855 1 0.605 0.908 0.852 0.148
#> SRR1047856 1 0.605 0.908 0.852 0.148
#> SRR1047857 1 0.605 0.908 0.852 0.148
#> SRR1047858 1 0.000 0.907 1.000 0.000
#> SRR1047859 1 0.000 0.907 1.000 0.000
#> SRR1047860 1 0.000 0.907 1.000 0.000
#> SRR1047861 1 0.000 0.907 1.000 0.000
#> SRR1047863 2 0.141 0.913 0.020 0.980
#> SRR1047864 2 0.141 0.913 0.020 0.980
#> SRR1047865 2 0.295 0.910 0.052 0.948
#> SRR1047866 2 0.295 0.910 0.052 0.948
#> SRR1047867 2 0.000 0.914 0.000 1.000
#> SRR1047868 2 0.141 0.913 0.020 0.980
#> SRR1047869 2 0.295 0.910 0.052 0.948
#> SRR1047870 2 0.141 0.913 0.020 0.980
#> SRR1047871 2 0.141 0.913 0.020 0.980
#> SRR1047872 2 0.141 0.913 0.020 0.980
#> SRR1047873 2 0.141 0.913 0.020 0.980
#> SRR1047874 2 0.141 0.913 0.020 0.980
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1047813 1 0.0237 0.883 0.996 0.000 0.004
#> SRR1047814 1 0.0237 0.883 0.996 0.000 0.004
#> SRR1047815 1 0.0237 0.883 0.996 0.000 0.004
#> SRR1047816 1 0.0237 0.883 0.996 0.000 0.004
#> SRR1047817 1 0.0237 0.883 0.996 0.000 0.004
#> SRR1047818 2 0.0000 0.954 0.000 1.000 0.000
#> SRR1047819 2 0.0000 0.954 0.000 1.000 0.000
#> SRR1047820 2 0.0000 0.954 0.000 1.000 0.000
#> SRR1047821 2 0.0000 0.954 0.000 1.000 0.000
#> SRR1047822 2 0.0000 0.954 0.000 1.000 0.000
#> SRR1047823 2 0.0000 0.954 0.000 1.000 0.000
#> SRR1047824 2 0.0000 0.954 0.000 1.000 0.000
#> SRR1047825 2 0.0000 0.954 0.000 1.000 0.000
#> SRR1047826 2 0.0000 0.954 0.000 1.000 0.000
#> SRR1047827 2 0.0000 0.954 0.000 1.000 0.000
#> SRR1047828 1 0.6410 0.351 0.576 0.004 0.420
#> SRR1047829 1 0.6410 0.351 0.576 0.004 0.420
#> SRR1047830 1 0.6410 0.351 0.576 0.004 0.420
#> SRR1047831 1 0.6410 0.351 0.576 0.004 0.420
#> SRR1047832 1 0.6410 0.351 0.576 0.004 0.420
#> SRR1047833 3 0.5467 0.827 0.032 0.176 0.792
#> SRR1047834 3 0.5467 0.827 0.032 0.176 0.792
#> SRR1047835 3 0.5467 0.827 0.032 0.176 0.792
#> SRR1047836 3 0.5467 0.827 0.032 0.176 0.792
#> SRR1047837 3 0.5467 0.827 0.032 0.176 0.792
#> SRR1047838 2 0.0237 0.953 0.004 0.996 0.000
#> SRR1047839 2 0.0237 0.953 0.004 0.996 0.000
#> SRR1047840 2 0.0237 0.953 0.004 0.996 0.000
#> SRR1047841 2 0.0237 0.953 0.004 0.996 0.000
#> SRR1047842 2 0.0237 0.953 0.004 0.996 0.000
#> SRR1047843 1 0.1453 0.879 0.968 0.008 0.024
#> SRR1047844 1 0.1453 0.879 0.968 0.008 0.024
#> SRR1047845 1 0.1453 0.879 0.968 0.008 0.024
#> SRR1047846 1 0.1453 0.879 0.968 0.008 0.024
#> SRR1047847 1 0.1453 0.879 0.968 0.008 0.024
#> SRR1047848 1 0.0592 0.887 0.988 0.012 0.000
#> SRR1047849 1 0.0592 0.887 0.988 0.012 0.000
#> SRR1047850 1 0.0592 0.887 0.988 0.012 0.000
#> SRR1047851 1 0.0592 0.887 0.988 0.012 0.000
#> SRR1047852 1 0.0592 0.887 0.988 0.012 0.000
#> SRR1047853 2 0.4390 0.854 0.012 0.840 0.148
#> SRR1047854 2 0.4390 0.854 0.012 0.840 0.148
#> SRR1047855 2 0.4390 0.854 0.012 0.840 0.148
#> SRR1047856 2 0.4390 0.854 0.012 0.840 0.148
#> SRR1047857 2 0.4390 0.854 0.012 0.840 0.148
#> SRR1047858 1 0.0592 0.887 0.988 0.012 0.000
#> SRR1047859 1 0.0592 0.887 0.988 0.012 0.000
#> SRR1047860 1 0.0592 0.887 0.988 0.012 0.000
#> SRR1047861 1 0.0592 0.887 0.988 0.012 0.000
#> SRR1047863 3 0.0237 0.932 0.004 0.000 0.996
#> SRR1047864 3 0.0237 0.932 0.004 0.000 0.996
#> SRR1047865 3 0.0237 0.932 0.004 0.000 0.996
#> SRR1047866 3 0.0237 0.932 0.004 0.000 0.996
#> SRR1047867 3 0.0237 0.928 0.004 0.000 0.996
#> SRR1047868 3 0.0237 0.932 0.004 0.000 0.996
#> SRR1047869 3 0.0237 0.932 0.004 0.000 0.996
#> SRR1047870 3 0.0237 0.932 0.004 0.000 0.996
#> SRR1047871 3 0.0237 0.932 0.004 0.000 0.996
#> SRR1047872 3 0.0237 0.932 0.004 0.000 0.996
#> SRR1047873 3 0.0237 0.932 0.004 0.000 0.996
#> SRR1047874 3 0.0237 0.932 0.004 0.000 0.996
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1047813 1 0.1792 0.945 0.932 0.068 0.000 0.000
#> SRR1047814 1 0.1792 0.945 0.932 0.068 0.000 0.000
#> SRR1047815 1 0.1792 0.945 0.932 0.068 0.000 0.000
#> SRR1047816 1 0.1792 0.945 0.932 0.068 0.000 0.000
#> SRR1047817 1 0.1792 0.945 0.932 0.068 0.000 0.000
#> SRR1047818 4 0.0188 0.963 0.000 0.004 0.000 0.996
#> SRR1047819 4 0.0188 0.963 0.000 0.004 0.000 0.996
#> SRR1047820 4 0.0188 0.963 0.000 0.004 0.000 0.996
#> SRR1047821 4 0.0188 0.963 0.000 0.004 0.000 0.996
#> SRR1047822 4 0.0188 0.963 0.000 0.004 0.000 0.996
#> SRR1047823 4 0.0188 0.963 0.000 0.004 0.000 0.996
#> SRR1047824 4 0.0188 0.963 0.000 0.004 0.000 0.996
#> SRR1047825 4 0.0188 0.963 0.000 0.004 0.000 0.996
#> SRR1047826 4 0.0188 0.963 0.000 0.004 0.000 0.996
#> SRR1047827 4 0.0188 0.963 0.000 0.004 0.000 0.996
#> SRR1047828 2 0.0707 0.978 0.020 0.980 0.000 0.000
#> SRR1047829 2 0.0707 0.978 0.020 0.980 0.000 0.000
#> SRR1047830 2 0.0707 0.978 0.020 0.980 0.000 0.000
#> SRR1047831 2 0.0707 0.978 0.020 0.980 0.000 0.000
#> SRR1047832 2 0.0707 0.978 0.020 0.980 0.000 0.000
#> SRR1047833 2 0.0188 0.979 0.000 0.996 0.000 0.004
#> SRR1047834 2 0.0188 0.979 0.000 0.996 0.000 0.004
#> SRR1047835 2 0.0188 0.979 0.000 0.996 0.000 0.004
#> SRR1047836 2 0.0188 0.979 0.000 0.996 0.000 0.004
#> SRR1047837 2 0.0188 0.979 0.000 0.996 0.000 0.004
#> SRR1047838 4 0.0000 0.963 0.000 0.000 0.000 1.000
#> SRR1047839 4 0.0000 0.963 0.000 0.000 0.000 1.000
#> SRR1047840 4 0.0000 0.963 0.000 0.000 0.000 1.000
#> SRR1047841 4 0.0000 0.963 0.000 0.000 0.000 1.000
#> SRR1047842 4 0.0000 0.963 0.000 0.000 0.000 1.000
#> SRR1047843 1 0.0188 0.978 0.996 0.000 0.000 0.004
#> SRR1047844 1 0.0188 0.978 0.996 0.000 0.000 0.004
#> SRR1047845 1 0.0188 0.978 0.996 0.000 0.000 0.004
#> SRR1047846 1 0.0188 0.978 0.996 0.000 0.000 0.004
#> SRR1047847 1 0.0188 0.978 0.996 0.000 0.000 0.004
#> SRR1047848 1 0.0188 0.979 0.996 0.004 0.000 0.000
#> SRR1047849 1 0.0188 0.979 0.996 0.004 0.000 0.000
#> SRR1047850 1 0.0188 0.979 0.996 0.004 0.000 0.000
#> SRR1047851 1 0.0188 0.979 0.996 0.004 0.000 0.000
#> SRR1047852 1 0.0188 0.979 0.996 0.004 0.000 0.000
#> SRR1047853 4 0.3670 0.884 0.044 0.004 0.092 0.860
#> SRR1047854 4 0.3670 0.884 0.044 0.004 0.092 0.860
#> SRR1047855 4 0.3670 0.884 0.044 0.004 0.092 0.860
#> SRR1047856 4 0.3670 0.884 0.044 0.004 0.092 0.860
#> SRR1047857 4 0.3670 0.884 0.044 0.004 0.092 0.860
#> SRR1047858 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> SRR1047859 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> SRR1047860 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> SRR1047861 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> SRR1047863 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR1047864 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR1047865 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR1047866 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR1047867 2 0.1867 0.912 0.000 0.928 0.072 0.000
#> SRR1047868 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR1047869 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR1047870 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR1047871 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR1047872 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR1047873 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR1047874 3 0.0000 1.000 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
#> SRR1047813 1 0.4232 0.676 0.676 0.012 0.000 0.000 0.312
#> SRR1047814 1 0.4232 0.676 0.676 0.012 0.000 0.000 0.312
#> SRR1047815 1 0.4232 0.676 0.676 0.012 0.000 0.000 0.312
#> SRR1047816 1 0.4232 0.676 0.676 0.012 0.000 0.000 0.312
#> SRR1047817 1 0.4232 0.676 0.676 0.012 0.000 0.000 0.312
#> SRR1047818 4 0.0000 0.924 0.000 0.000 0.000 1.000 0.000
#> SRR1047819 4 0.0000 0.924 0.000 0.000 0.000 1.000 0.000
#> SRR1047820 4 0.0000 0.924 0.000 0.000 0.000 1.000 0.000
#> SRR1047821 4 0.0000 0.924 0.000 0.000 0.000 1.000 0.000
#> SRR1047822 4 0.0000 0.924 0.000 0.000 0.000 1.000 0.000
#> SRR1047823 4 0.0671 0.918 0.000 0.004 0.000 0.980 0.016
#> SRR1047824 4 0.0671 0.918 0.000 0.004 0.000 0.980 0.016
#> SRR1047825 4 0.0671 0.918 0.000 0.004 0.000 0.980 0.016
#> SRR1047826 4 0.0671 0.918 0.000 0.004 0.000 0.980 0.016
#> SRR1047827 4 0.0671 0.918 0.000 0.004 0.000 0.980 0.016
#> SRR1047828 2 0.4360 0.810 0.020 0.680 0.000 0.000 0.300
#> SRR1047829 2 0.4360 0.810 0.020 0.680 0.000 0.000 0.300
#> SRR1047830 2 0.4360 0.810 0.020 0.680 0.000 0.000 0.300
#> SRR1047831 2 0.4360 0.810 0.020 0.680 0.000 0.000 0.300
#> SRR1047832 2 0.4360 0.810 0.020 0.680 0.000 0.000 0.300
#> SRR1047833 2 0.0324 0.842 0.000 0.992 0.004 0.004 0.000
#> SRR1047834 2 0.0324 0.842 0.000 0.992 0.004 0.004 0.000
#> SRR1047835 2 0.0324 0.842 0.000 0.992 0.004 0.004 0.000
#> SRR1047836 2 0.0324 0.842 0.000 0.992 0.004 0.004 0.000
#> SRR1047837 2 0.0324 0.842 0.000 0.992 0.004 0.004 0.000
#> SRR1047838 4 0.2230 0.848 0.000 0.000 0.000 0.884 0.116
#> SRR1047839 4 0.2230 0.848 0.000 0.000 0.000 0.884 0.116
#> SRR1047840 4 0.2230 0.848 0.000 0.000 0.000 0.884 0.116
#> SRR1047841 4 0.2230 0.848 0.000 0.000 0.000 0.884 0.116
#> SRR1047842 4 0.2230 0.848 0.000 0.000 0.000 0.884 0.116
#> SRR1047843 1 0.3109 0.771 0.800 0.000 0.000 0.000 0.200
#> SRR1047844 1 0.3109 0.771 0.800 0.000 0.000 0.000 0.200
#> SRR1047845 1 0.3109 0.771 0.800 0.000 0.000 0.000 0.200
#> SRR1047846 1 0.3109 0.771 0.800 0.000 0.000 0.000 0.200
#> SRR1047847 1 0.3109 0.771 0.800 0.000 0.000 0.000 0.200
#> SRR1047848 1 0.0162 0.842 0.996 0.000 0.000 0.000 0.004
#> SRR1047849 1 0.0162 0.842 0.996 0.000 0.000 0.000 0.004
#> SRR1047850 1 0.0162 0.842 0.996 0.000 0.000 0.000 0.004
#> SRR1047851 1 0.0162 0.842 0.996 0.000 0.000 0.000 0.004
#> SRR1047852 1 0.0162 0.842 0.996 0.000 0.000 0.000 0.004
#> SRR1047853 5 0.5124 1.000 0.004 0.000 0.048 0.320 0.628
#> SRR1047854 5 0.5124 1.000 0.004 0.000 0.048 0.320 0.628
#> SRR1047855 5 0.5124 1.000 0.004 0.000 0.048 0.320 0.628
#> SRR1047856 5 0.5124 1.000 0.004 0.000 0.048 0.320 0.628
#> SRR1047857 5 0.5124 1.000 0.004 0.000 0.048 0.320 0.628
#> SRR1047858 1 0.0963 0.841 0.964 0.000 0.000 0.000 0.036
#> SRR1047859 1 0.0963 0.841 0.964 0.000 0.000 0.000 0.036
#> SRR1047860 1 0.0963 0.841 0.964 0.000 0.000 0.000 0.036
#> SRR1047861 1 0.0963 0.841 0.964 0.000 0.000 0.000 0.036
#> SRR1047863 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047864 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047865 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047866 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047867 2 0.0510 0.836 0.000 0.984 0.016 0.000 0.000
#> SRR1047868 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047869 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047870 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047871 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047872 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047873 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047874 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1047813 5 0.4697 0.396 0.404 0.000 0.000 0.000 0.548 0.048
#> SRR1047814 5 0.4697 0.396 0.404 0.000 0.000 0.000 0.548 0.048
#> SRR1047815 5 0.4697 0.396 0.404 0.000 0.000 0.000 0.548 0.048
#> SRR1047816 5 0.4697 0.396 0.404 0.000 0.000 0.000 0.548 0.048
#> SRR1047817 5 0.4697 0.396 0.404 0.000 0.000 0.000 0.548 0.048
#> SRR1047818 4 0.1333 0.887 0.000 0.000 0.000 0.944 0.008 0.048
#> SRR1047819 4 0.1333 0.887 0.000 0.000 0.000 0.944 0.008 0.048
#> SRR1047820 4 0.1333 0.887 0.000 0.000 0.000 0.944 0.008 0.048
#> SRR1047821 4 0.1333 0.887 0.000 0.000 0.000 0.944 0.008 0.048
#> SRR1047822 4 0.1333 0.887 0.000 0.000 0.000 0.944 0.008 0.048
#> SRR1047823 4 0.0692 0.880 0.000 0.000 0.000 0.976 0.020 0.004
#> SRR1047824 4 0.0692 0.880 0.000 0.000 0.000 0.976 0.020 0.004
#> SRR1047825 4 0.0692 0.880 0.000 0.000 0.000 0.976 0.020 0.004
#> SRR1047826 4 0.0692 0.880 0.000 0.000 0.000 0.976 0.020 0.004
#> SRR1047827 4 0.0692 0.880 0.000 0.000 0.000 0.976 0.020 0.004
#> SRR1047828 5 0.3607 0.371 0.000 0.348 0.000 0.000 0.652 0.000
#> SRR1047829 5 0.3607 0.371 0.000 0.348 0.000 0.000 0.652 0.000
#> SRR1047830 5 0.3607 0.371 0.000 0.348 0.000 0.000 0.652 0.000
#> SRR1047831 5 0.3607 0.371 0.000 0.348 0.000 0.000 0.652 0.000
#> SRR1047832 5 0.3607 0.371 0.000 0.348 0.000 0.000 0.652 0.000
#> SRR1047833 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1047834 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1047835 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1047836 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1047837 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1047838 4 0.3572 0.794 0.000 0.000 0.000 0.764 0.032 0.204
#> SRR1047839 4 0.3572 0.794 0.000 0.000 0.000 0.764 0.032 0.204
#> SRR1047840 4 0.3572 0.794 0.000 0.000 0.000 0.764 0.032 0.204
#> SRR1047841 4 0.3572 0.794 0.000 0.000 0.000 0.764 0.032 0.204
#> SRR1047842 4 0.3572 0.794 0.000 0.000 0.000 0.764 0.032 0.204
#> SRR1047843 1 0.4226 0.741 0.736 0.000 0.000 0.000 0.112 0.152
#> SRR1047844 1 0.4261 0.737 0.732 0.000 0.000 0.000 0.112 0.156
#> SRR1047845 1 0.4226 0.741 0.736 0.000 0.000 0.000 0.112 0.152
#> SRR1047846 1 0.4226 0.741 0.736 0.000 0.000 0.000 0.112 0.152
#> SRR1047847 1 0.4261 0.737 0.732 0.000 0.000 0.000 0.112 0.156
#> SRR1047848 1 0.2051 0.799 0.896 0.000 0.000 0.004 0.096 0.004
#> SRR1047849 1 0.2051 0.799 0.896 0.000 0.000 0.004 0.096 0.004
#> SRR1047850 1 0.2051 0.799 0.896 0.000 0.000 0.004 0.096 0.004
#> SRR1047851 1 0.2051 0.799 0.896 0.000 0.000 0.004 0.096 0.004
#> SRR1047852 1 0.2051 0.799 0.896 0.000 0.000 0.004 0.096 0.004
#> SRR1047853 6 0.0858 1.000 0.000 0.000 0.004 0.028 0.000 0.968
#> SRR1047854 6 0.0858 1.000 0.000 0.000 0.004 0.028 0.000 0.968
#> SRR1047855 6 0.0858 1.000 0.000 0.000 0.004 0.028 0.000 0.968
#> SRR1047856 6 0.0858 1.000 0.000 0.000 0.004 0.028 0.000 0.968
#> SRR1047857 6 0.0858 1.000 0.000 0.000 0.004 0.028 0.000 0.968
#> SRR1047858 1 0.0363 0.820 0.988 0.000 0.000 0.000 0.012 0.000
#> SRR1047859 1 0.0363 0.820 0.988 0.000 0.000 0.000 0.012 0.000
#> SRR1047860 1 0.0363 0.820 0.988 0.000 0.000 0.000 0.012 0.000
#> SRR1047861 1 0.0363 0.820 0.988 0.000 0.000 0.000 0.012 0.000
#> SRR1047863 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047864 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047865 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047866 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047867 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1047868 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047869 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047870 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047871 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047872 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047873 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047874 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 17931 rows and 61 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 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 1.000 1.000 0.1811 0.820 0.820
#> 3 3 1.000 0.995 0.998 1.4432 0.727 0.669
#> 4 4 0.669 0.766 0.902 0.5323 0.740 0.535
#> 5 5 0.762 0.805 0.873 0.1115 0.793 0.453
#> 6 6 0.797 0.686 0.862 0.0481 0.879 0.593
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
#> SRR1047813 1 0 1 1 0
#> SRR1047814 1 0 1 1 0
#> SRR1047815 1 0 1 1 0
#> SRR1047816 1 0 1 1 0
#> SRR1047817 1 0 1 1 0
#> SRR1047818 1 0 1 1 0
#> SRR1047819 1 0 1 1 0
#> SRR1047820 1 0 1 1 0
#> SRR1047821 1 0 1 1 0
#> SRR1047822 1 0 1 1 0
#> SRR1047823 1 0 1 1 0
#> SRR1047824 1 0 1 1 0
#> SRR1047825 1 0 1 1 0
#> SRR1047826 1 0 1 1 0
#> SRR1047827 1 0 1 1 0
#> SRR1047828 1 0 1 1 0
#> SRR1047829 1 0 1 1 0
#> SRR1047830 1 0 1 1 0
#> SRR1047831 1 0 1 1 0
#> SRR1047832 1 0 1 1 0
#> SRR1047833 2 0 1 0 1
#> SRR1047834 2 0 1 0 1
#> SRR1047835 2 0 1 0 1
#> SRR1047836 2 0 1 0 1
#> SRR1047837 2 0 1 0 1
#> SRR1047838 1 0 1 1 0
#> SRR1047839 1 0 1 1 0
#> SRR1047840 1 0 1 1 0
#> SRR1047841 1 0 1 1 0
#> SRR1047842 1 0 1 1 0
#> SRR1047843 1 0 1 1 0
#> SRR1047844 1 0 1 1 0
#> SRR1047845 1 0 1 1 0
#> SRR1047846 1 0 1 1 0
#> SRR1047847 1 0 1 1 0
#> SRR1047848 1 0 1 1 0
#> SRR1047849 1 0 1 1 0
#> SRR1047850 1 0 1 1 0
#> SRR1047851 1 0 1 1 0
#> SRR1047852 1 0 1 1 0
#> SRR1047853 1 0 1 1 0
#> SRR1047854 1 0 1 1 0
#> SRR1047855 1 0 1 1 0
#> SRR1047856 1 0 1 1 0
#> SRR1047857 1 0 1 1 0
#> SRR1047858 1 0 1 1 0
#> SRR1047859 1 0 1 1 0
#> SRR1047860 1 0 1 1 0
#> SRR1047861 1 0 1 1 0
#> SRR1047863 1 0 1 1 0
#> SRR1047864 1 0 1 1 0
#> SRR1047865 1 0 1 1 0
#> SRR1047866 1 0 1 1 0
#> SRR1047867 2 0 1 0 1
#> SRR1047868 1 0 1 1 0
#> SRR1047869 1 0 1 1 0
#> SRR1047870 1 0 1 1 0
#> SRR1047871 1 0 1 1 0
#> SRR1047872 1 0 1 1 0
#> SRR1047873 1 0 1 1 0
#> SRR1047874 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1047813 1 0.000 1.000 1 0.000 0.000
#> SRR1047814 1 0.000 1.000 1 0.000 0.000
#> SRR1047815 1 0.000 1.000 1 0.000 0.000
#> SRR1047816 1 0.000 1.000 1 0.000 0.000
#> SRR1047817 1 0.000 1.000 1 0.000 0.000
#> SRR1047818 1 0.000 1.000 1 0.000 0.000
#> SRR1047819 1 0.000 1.000 1 0.000 0.000
#> SRR1047820 1 0.000 1.000 1 0.000 0.000
#> SRR1047821 1 0.000 1.000 1 0.000 0.000
#> SRR1047822 1 0.000 1.000 1 0.000 0.000
#> SRR1047823 1 0.000 1.000 1 0.000 0.000
#> SRR1047824 1 0.000 1.000 1 0.000 0.000
#> SRR1047825 1 0.000 1.000 1 0.000 0.000
#> SRR1047826 1 0.000 1.000 1 0.000 0.000
#> SRR1047827 1 0.000 1.000 1 0.000 0.000
#> SRR1047828 1 0.000 1.000 1 0.000 0.000
#> SRR1047829 1 0.000 1.000 1 0.000 0.000
#> SRR1047830 1 0.000 1.000 1 0.000 0.000
#> SRR1047831 1 0.000 1.000 1 0.000 0.000
#> SRR1047832 1 0.000 1.000 1 0.000 0.000
#> SRR1047833 2 0.000 1.000 0 1.000 0.000
#> SRR1047834 2 0.000 1.000 0 1.000 0.000
#> SRR1047835 2 0.000 1.000 0 1.000 0.000
#> SRR1047836 2 0.000 1.000 0 1.000 0.000
#> SRR1047837 2 0.000 1.000 0 1.000 0.000
#> SRR1047838 1 0.000 1.000 1 0.000 0.000
#> SRR1047839 1 0.000 1.000 1 0.000 0.000
#> SRR1047840 1 0.000 1.000 1 0.000 0.000
#> SRR1047841 1 0.000 1.000 1 0.000 0.000
#> SRR1047842 1 0.000 1.000 1 0.000 0.000
#> SRR1047843 1 0.000 1.000 1 0.000 0.000
#> SRR1047844 1 0.000 1.000 1 0.000 0.000
#> SRR1047845 1 0.000 1.000 1 0.000 0.000
#> SRR1047846 1 0.000 1.000 1 0.000 0.000
#> SRR1047847 1 0.000 1.000 1 0.000 0.000
#> SRR1047848 1 0.000 1.000 1 0.000 0.000
#> SRR1047849 1 0.000 1.000 1 0.000 0.000
#> SRR1047850 1 0.000 1.000 1 0.000 0.000
#> SRR1047851 1 0.000 1.000 1 0.000 0.000
#> SRR1047852 1 0.000 1.000 1 0.000 0.000
#> SRR1047853 1 0.000 1.000 1 0.000 0.000
#> SRR1047854 1 0.000 1.000 1 0.000 0.000
#> SRR1047855 1 0.000 1.000 1 0.000 0.000
#> SRR1047856 1 0.000 1.000 1 0.000 0.000
#> SRR1047857 1 0.000 1.000 1 0.000 0.000
#> SRR1047858 1 0.000 1.000 1 0.000 0.000
#> SRR1047859 1 0.000 1.000 1 0.000 0.000
#> SRR1047860 1 0.000 1.000 1 0.000 0.000
#> SRR1047861 1 0.000 1.000 1 0.000 0.000
#> SRR1047863 3 0.000 0.986 0 0.000 1.000
#> SRR1047864 3 0.000 0.986 0 0.000 1.000
#> SRR1047865 3 0.000 0.986 0 0.000 1.000
#> SRR1047866 3 0.000 0.986 0 0.000 1.000
#> SRR1047867 3 0.388 0.821 0 0.152 0.848
#> SRR1047868 3 0.000 0.986 0 0.000 1.000
#> SRR1047869 3 0.000 0.986 0 0.000 1.000
#> SRR1047870 3 0.000 0.986 0 0.000 1.000
#> SRR1047871 3 0.000 0.986 0 0.000 1.000
#> SRR1047872 3 0.000 0.986 0 0.000 1.000
#> SRR1047873 3 0.000 0.986 0 0.000 1.000
#> SRR1047874 3 0.000 0.986 0 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1047813 1 0.2921 0.7911 0.860 0.000 0.000 0.140
#> SRR1047814 1 0.2973 0.7913 0.856 0.000 0.000 0.144
#> SRR1047815 1 0.3024 0.7910 0.852 0.000 0.000 0.148
#> SRR1047816 1 0.3024 0.7911 0.852 0.000 0.000 0.148
#> SRR1047817 1 0.3688 0.7695 0.792 0.000 0.000 0.208
#> SRR1047818 4 0.0000 0.8535 0.000 0.000 0.000 1.000
#> SRR1047819 4 0.0000 0.8535 0.000 0.000 0.000 1.000
#> SRR1047820 4 0.0000 0.8535 0.000 0.000 0.000 1.000
#> SRR1047821 4 0.0000 0.8535 0.000 0.000 0.000 1.000
#> SRR1047822 4 0.0000 0.8535 0.000 0.000 0.000 1.000
#> SRR1047823 4 0.0000 0.8535 0.000 0.000 0.000 1.000
#> SRR1047824 4 0.0000 0.8535 0.000 0.000 0.000 1.000
#> SRR1047825 4 0.0000 0.8535 0.000 0.000 0.000 1.000
#> SRR1047826 4 0.0000 0.8535 0.000 0.000 0.000 1.000
#> SRR1047827 4 0.0000 0.8535 0.000 0.000 0.000 1.000
#> SRR1047828 1 0.3688 0.7695 0.792 0.000 0.000 0.208
#> SRR1047829 1 0.3688 0.7695 0.792 0.000 0.000 0.208
#> SRR1047830 1 0.3688 0.7695 0.792 0.000 0.000 0.208
#> SRR1047831 1 0.3688 0.7695 0.792 0.000 0.000 0.208
#> SRR1047832 1 0.3688 0.7695 0.792 0.000 0.000 0.208
#> SRR1047833 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> SRR1047834 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> SRR1047835 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> SRR1047836 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> SRR1047837 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> SRR1047838 4 0.0000 0.8535 0.000 0.000 0.000 1.000
#> SRR1047839 4 0.0000 0.8535 0.000 0.000 0.000 1.000
#> SRR1047840 4 0.0000 0.8535 0.000 0.000 0.000 1.000
#> SRR1047841 4 0.0000 0.8535 0.000 0.000 0.000 1.000
#> SRR1047842 4 0.0000 0.8535 0.000 0.000 0.000 1.000
#> SRR1047843 4 0.4948 0.0534 0.440 0.000 0.000 0.560
#> SRR1047844 4 0.4925 0.0837 0.428 0.000 0.000 0.572
#> SRR1047845 4 0.4925 0.0837 0.428 0.000 0.000 0.572
#> SRR1047846 4 0.4925 0.0837 0.428 0.000 0.000 0.572
#> SRR1047847 4 0.4925 0.0837 0.428 0.000 0.000 0.572
#> SRR1047848 1 0.0188 0.7282 0.996 0.000 0.000 0.004
#> SRR1047849 1 0.0707 0.7345 0.980 0.000 0.000 0.020
#> SRR1047850 1 0.0469 0.7326 0.988 0.000 0.000 0.012
#> SRR1047851 1 0.0336 0.7310 0.992 0.000 0.000 0.008
#> SRR1047852 1 0.0336 0.7310 0.992 0.000 0.000 0.008
#> SRR1047853 4 0.0469 0.8472 0.012 0.000 0.000 0.988
#> SRR1047854 4 0.2760 0.7428 0.128 0.000 0.000 0.872
#> SRR1047855 4 0.1867 0.8047 0.072 0.000 0.000 0.928
#> SRR1047856 4 0.1389 0.8242 0.048 0.000 0.000 0.952
#> SRR1047857 4 0.2149 0.7887 0.088 0.000 0.000 0.912
#> SRR1047858 1 0.4730 0.3644 0.636 0.000 0.000 0.364
#> SRR1047859 1 0.4790 0.3423 0.620 0.000 0.000 0.380
#> SRR1047860 1 0.4730 0.3644 0.636 0.000 0.000 0.364
#> SRR1047861 1 0.4730 0.3644 0.636 0.000 0.000 0.364
#> SRR1047863 3 0.0000 0.9860 0.000 0.000 1.000 0.000
#> SRR1047864 3 0.0000 0.9860 0.000 0.000 1.000 0.000
#> SRR1047865 3 0.0000 0.9860 0.000 0.000 1.000 0.000
#> SRR1047866 3 0.0000 0.9860 0.000 0.000 1.000 0.000
#> SRR1047867 3 0.3074 0.8208 0.000 0.152 0.848 0.000
#> SRR1047868 3 0.0000 0.9860 0.000 0.000 1.000 0.000
#> SRR1047869 3 0.0000 0.9860 0.000 0.000 1.000 0.000
#> SRR1047870 3 0.0000 0.9860 0.000 0.000 1.000 0.000
#> SRR1047871 3 0.0000 0.9860 0.000 0.000 1.000 0.000
#> SRR1047872 3 0.0000 0.9860 0.000 0.000 1.000 0.000
#> SRR1047873 3 0.0000 0.9860 0.000 0.000 1.000 0.000
#> SRR1047874 3 0.0000 0.9860 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
#> SRR1047813 5 0.4307 -0.05088 0.496 0.000 0.000 0.000 0.504
#> SRR1047814 1 0.4304 -0.04688 0.516 0.000 0.000 0.000 0.484
#> SRR1047815 5 0.4306 0.00767 0.492 0.000 0.000 0.000 0.508
#> SRR1047816 5 0.4307 -0.02529 0.500 0.000 0.000 0.000 0.500
#> SRR1047817 5 0.2813 0.70631 0.168 0.000 0.000 0.000 0.832
#> SRR1047818 4 0.1908 0.90396 0.000 0.000 0.000 0.908 0.092
#> SRR1047819 4 0.1410 0.93370 0.000 0.000 0.000 0.940 0.060
#> SRR1047820 4 0.1410 0.93370 0.000 0.000 0.000 0.940 0.060
#> SRR1047821 4 0.1908 0.90302 0.000 0.000 0.000 0.908 0.092
#> SRR1047822 5 0.3913 0.67656 0.000 0.000 0.000 0.324 0.676
#> SRR1047823 4 0.0000 0.94600 0.000 0.000 0.000 1.000 0.000
#> SRR1047824 4 0.0000 0.94600 0.000 0.000 0.000 1.000 0.000
#> SRR1047825 4 0.0000 0.94600 0.000 0.000 0.000 1.000 0.000
#> SRR1047826 4 0.0000 0.94600 0.000 0.000 0.000 1.000 0.000
#> SRR1047827 4 0.0000 0.94600 0.000 0.000 0.000 1.000 0.000
#> SRR1047828 5 0.0000 0.70722 0.000 0.000 0.000 0.000 1.000
#> SRR1047829 5 0.0000 0.70722 0.000 0.000 0.000 0.000 1.000
#> SRR1047830 5 0.0000 0.70722 0.000 0.000 0.000 0.000 1.000
#> SRR1047831 5 0.0290 0.70967 0.008 0.000 0.000 0.000 0.992
#> SRR1047832 5 0.0000 0.70722 0.000 0.000 0.000 0.000 1.000
#> SRR1047833 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000
#> SRR1047834 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000
#> SRR1047835 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000
#> SRR1047836 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000
#> SRR1047837 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000
#> SRR1047838 5 0.3774 0.71009 0.000 0.000 0.000 0.296 0.704
#> SRR1047839 5 0.3774 0.71009 0.000 0.000 0.000 0.296 0.704
#> SRR1047840 5 0.3774 0.71009 0.000 0.000 0.000 0.296 0.704
#> SRR1047841 5 0.3774 0.71009 0.000 0.000 0.000 0.296 0.704
#> SRR1047842 5 0.3774 0.71009 0.000 0.000 0.000 0.296 0.704
#> SRR1047843 5 0.4953 0.74290 0.216 0.000 0.000 0.088 0.696
#> SRR1047844 5 0.4893 0.74792 0.208 0.000 0.000 0.088 0.704
#> SRR1047845 5 0.4893 0.74792 0.208 0.000 0.000 0.088 0.704
#> SRR1047846 5 0.4871 0.74575 0.212 0.000 0.000 0.084 0.704
#> SRR1047847 5 0.4893 0.74792 0.208 0.000 0.000 0.088 0.704
#> SRR1047848 1 0.0000 0.92151 1.000 0.000 0.000 0.000 0.000
#> SRR1047849 1 0.0000 0.92151 1.000 0.000 0.000 0.000 0.000
#> SRR1047850 1 0.0000 0.92151 1.000 0.000 0.000 0.000 0.000
#> SRR1047851 1 0.0000 0.92151 1.000 0.000 0.000 0.000 0.000
#> SRR1047852 1 0.0000 0.92151 1.000 0.000 0.000 0.000 0.000
#> SRR1047853 5 0.4086 0.71892 0.012 0.000 0.000 0.284 0.704
#> SRR1047854 5 0.5038 0.76127 0.132 0.000 0.000 0.164 0.704
#> SRR1047855 5 0.4822 0.75181 0.076 0.000 0.000 0.220 0.704
#> SRR1047856 5 0.4629 0.74126 0.052 0.000 0.000 0.244 0.704
#> SRR1047857 5 0.4933 0.75718 0.096 0.000 0.000 0.200 0.704
#> SRR1047858 1 0.0000 0.92151 1.000 0.000 0.000 0.000 0.000
#> SRR1047859 1 0.1485 0.87208 0.948 0.000 0.000 0.020 0.032
#> SRR1047860 1 0.0162 0.91836 0.996 0.000 0.000 0.004 0.000
#> SRR1047861 1 0.0000 0.92151 1.000 0.000 0.000 0.000 0.000
#> SRR1047863 3 0.0000 0.98597 0.000 0.000 1.000 0.000 0.000
#> SRR1047864 3 0.0000 0.98597 0.000 0.000 1.000 0.000 0.000
#> SRR1047865 3 0.0000 0.98597 0.000 0.000 1.000 0.000 0.000
#> SRR1047866 3 0.0000 0.98597 0.000 0.000 1.000 0.000 0.000
#> SRR1047867 3 0.2648 0.82075 0.000 0.152 0.848 0.000 0.000
#> SRR1047868 3 0.0000 0.98597 0.000 0.000 1.000 0.000 0.000
#> SRR1047869 3 0.0000 0.98597 0.000 0.000 1.000 0.000 0.000
#> SRR1047870 3 0.0000 0.98597 0.000 0.000 1.000 0.000 0.000
#> SRR1047871 3 0.0000 0.98597 0.000 0.000 1.000 0.000 0.000
#> SRR1047872 3 0.0000 0.98597 0.000 0.000 1.000 0.000 0.000
#> SRR1047873 3 0.0000 0.98597 0.000 0.000 1.000 0.000 0.000
#> SRR1047874 3 0.0000 0.98597 0.000 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1047813 6 0.0146 1.000 0.004 0.000 0.000 0.000 0.000 0.996
#> SRR1047814 6 0.0146 1.000 0.004 0.000 0.000 0.000 0.000 0.996
#> SRR1047815 6 0.0146 1.000 0.004 0.000 0.000 0.000 0.000 0.996
#> SRR1047816 6 0.0146 1.000 0.004 0.000 0.000 0.000 0.000 0.996
#> SRR1047817 6 0.0146 1.000 0.004 0.000 0.000 0.000 0.000 0.996
#> SRR1047818 4 0.3843 -0.588 0.000 0.000 0.000 0.548 0.452 0.000
#> SRR1047819 4 0.3862 -0.636 0.000 0.000 0.000 0.524 0.476 0.000
#> SRR1047820 4 0.3854 -0.613 0.000 0.000 0.000 0.536 0.464 0.000
#> SRR1047821 4 0.3817 -0.545 0.000 0.000 0.000 0.568 0.432 0.000
#> SRR1047822 4 0.0363 0.568 0.000 0.000 0.000 0.988 0.012 0.000
#> SRR1047823 5 0.3828 0.745 0.000 0.000 0.000 0.440 0.560 0.000
#> SRR1047824 5 0.3828 0.745 0.000 0.000 0.000 0.440 0.560 0.000
#> SRR1047825 5 0.3828 0.745 0.000 0.000 0.000 0.440 0.560 0.000
#> SRR1047826 5 0.3828 0.745 0.000 0.000 0.000 0.440 0.560 0.000
#> SRR1047827 5 0.3828 0.745 0.000 0.000 0.000 0.440 0.560 0.000
#> SRR1047828 5 0.5722 -0.333 0.000 0.000 0.000 0.404 0.432 0.164
#> SRR1047829 4 0.4504 0.331 0.000 0.000 0.000 0.536 0.432 0.032
#> SRR1047830 4 0.4978 0.294 0.000 0.000 0.000 0.500 0.432 0.068
#> SRR1047831 4 0.4439 0.335 0.000 0.000 0.000 0.540 0.432 0.028
#> SRR1047832 4 0.4565 0.328 0.000 0.000 0.000 0.532 0.432 0.036
#> SRR1047833 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1047834 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1047835 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1047836 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1047837 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1047838 4 0.0000 0.579 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047839 4 0.0000 0.579 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047840 4 0.0000 0.579 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047841 4 0.0000 0.579 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047842 4 0.0000 0.579 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047843 4 0.3323 0.546 0.240 0.000 0.000 0.752 0.008 0.000
#> SRR1047844 4 0.3133 0.562 0.212 0.000 0.000 0.780 0.008 0.000
#> SRR1047845 4 0.3271 0.551 0.232 0.000 0.000 0.760 0.008 0.000
#> SRR1047846 4 0.3398 0.536 0.252 0.000 0.000 0.740 0.008 0.000
#> SRR1047847 4 0.3161 0.560 0.216 0.000 0.000 0.776 0.008 0.000
#> SRR1047848 1 0.0000 0.979 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1047849 1 0.0000 0.979 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1047850 1 0.0000 0.979 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1047851 1 0.0000 0.979 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1047852 1 0.0000 0.979 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1047853 4 0.0363 0.585 0.012 0.000 0.000 0.988 0.000 0.000
#> SRR1047854 4 0.2135 0.592 0.128 0.000 0.000 0.872 0.000 0.000
#> SRR1047855 4 0.1387 0.599 0.068 0.000 0.000 0.932 0.000 0.000
#> SRR1047856 4 0.1141 0.597 0.052 0.000 0.000 0.948 0.000 0.000
#> SRR1047857 4 0.1714 0.598 0.092 0.000 0.000 0.908 0.000 0.000
#> SRR1047858 1 0.0260 0.977 0.992 0.000 0.000 0.000 0.008 0.000
#> SRR1047859 1 0.1970 0.860 0.900 0.000 0.000 0.092 0.008 0.000
#> SRR1047860 1 0.0405 0.975 0.988 0.000 0.000 0.004 0.008 0.000
#> SRR1047861 1 0.0260 0.977 0.992 0.000 0.000 0.000 0.008 0.000
#> SRR1047863 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047864 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047865 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047866 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047867 3 0.2378 0.821 0.000 0.152 0.848 0.000 0.000 0.000
#> SRR1047868 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047869 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047870 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047871 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047872 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047873 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047874 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 17931 rows and 61 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.699 0.972 0.968 0.3685 0.591 0.591
#> 3 3 0.530 0.740 0.777 0.5634 0.738 0.556
#> 4 4 0.893 0.922 0.961 0.1928 0.861 0.647
#> 5 5 0.765 0.772 0.823 0.1218 0.934 0.796
#> 6 6 0.825 0.829 0.880 0.0714 0.883 0.563
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
#> SRR1047813 1 0.000 1.000 1.000 0.000
#> SRR1047814 1 0.000 1.000 1.000 0.000
#> SRR1047815 1 0.000 1.000 1.000 0.000
#> SRR1047816 1 0.000 1.000 1.000 0.000
#> SRR1047817 1 0.000 1.000 1.000 0.000
#> SRR1047818 1 0.000 1.000 1.000 0.000
#> SRR1047819 1 0.000 1.000 1.000 0.000
#> SRR1047820 1 0.000 1.000 1.000 0.000
#> SRR1047821 1 0.000 1.000 1.000 0.000
#> SRR1047822 1 0.000 1.000 1.000 0.000
#> SRR1047823 1 0.000 1.000 1.000 0.000
#> SRR1047824 1 0.000 1.000 1.000 0.000
#> SRR1047825 1 0.000 1.000 1.000 0.000
#> SRR1047826 1 0.000 1.000 1.000 0.000
#> SRR1047827 1 0.000 1.000 1.000 0.000
#> SRR1047828 1 0.000 1.000 1.000 0.000
#> SRR1047829 1 0.000 1.000 1.000 0.000
#> SRR1047830 1 0.000 1.000 1.000 0.000
#> SRR1047831 1 0.000 1.000 1.000 0.000
#> SRR1047832 1 0.000 1.000 1.000 0.000
#> SRR1047833 2 0.000 0.869 0.000 1.000
#> SRR1047834 2 0.000 0.869 0.000 1.000
#> SRR1047835 2 0.000 0.869 0.000 1.000
#> SRR1047836 2 0.000 0.869 0.000 1.000
#> SRR1047837 2 0.000 0.869 0.000 1.000
#> SRR1047838 1 0.000 1.000 1.000 0.000
#> SRR1047839 1 0.000 1.000 1.000 0.000
#> SRR1047840 1 0.000 1.000 1.000 0.000
#> SRR1047841 1 0.000 1.000 1.000 0.000
#> SRR1047842 1 0.000 1.000 1.000 0.000
#> SRR1047843 1 0.000 1.000 1.000 0.000
#> SRR1047844 1 0.000 1.000 1.000 0.000
#> SRR1047845 1 0.000 1.000 1.000 0.000
#> SRR1047846 1 0.000 1.000 1.000 0.000
#> SRR1047847 1 0.000 1.000 1.000 0.000
#> SRR1047848 1 0.000 1.000 1.000 0.000
#> SRR1047849 1 0.000 1.000 1.000 0.000
#> SRR1047850 1 0.000 1.000 1.000 0.000
#> SRR1047851 1 0.000 1.000 1.000 0.000
#> SRR1047852 1 0.000 1.000 1.000 0.000
#> SRR1047853 1 0.000 1.000 1.000 0.000
#> SRR1047854 1 0.000 1.000 1.000 0.000
#> SRR1047855 1 0.000 1.000 1.000 0.000
#> SRR1047856 1 0.000 1.000 1.000 0.000
#> SRR1047857 1 0.000 1.000 1.000 0.000
#> SRR1047858 1 0.000 1.000 1.000 0.000
#> SRR1047859 1 0.000 1.000 1.000 0.000
#> SRR1047860 1 0.000 1.000 1.000 0.000
#> SRR1047861 1 0.000 1.000 1.000 0.000
#> SRR1047863 2 0.680 0.917 0.180 0.820
#> SRR1047864 2 0.671 0.917 0.176 0.824
#> SRR1047865 2 0.680 0.917 0.180 0.820
#> SRR1047866 2 0.680 0.917 0.180 0.820
#> SRR1047867 2 0.000 0.869 0.000 1.000
#> SRR1047868 2 0.680 0.917 0.180 0.820
#> SRR1047869 2 0.680 0.917 0.180 0.820
#> SRR1047870 2 0.680 0.917 0.180 0.820
#> SRR1047871 2 0.680 0.917 0.180 0.820
#> SRR1047872 2 0.680 0.917 0.180 0.820
#> SRR1047873 2 0.680 0.917 0.180 0.820
#> SRR1047874 2 0.680 0.917 0.180 0.820
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1047813 1 0.5678 0.924 0.684 0.316 0.000
#> SRR1047814 1 0.5678 0.924 0.684 0.316 0.000
#> SRR1047815 1 0.5678 0.924 0.684 0.316 0.000
#> SRR1047816 1 0.5678 0.924 0.684 0.316 0.000
#> SRR1047817 1 0.5678 0.924 0.684 0.316 0.000
#> SRR1047818 2 0.0000 0.800 0.000 1.000 0.000
#> SRR1047819 2 0.0000 0.800 0.000 1.000 0.000
#> SRR1047820 2 0.0000 0.800 0.000 1.000 0.000
#> SRR1047821 2 0.0000 0.800 0.000 1.000 0.000
#> SRR1047822 2 0.0000 0.800 0.000 1.000 0.000
#> SRR1047823 2 0.0000 0.800 0.000 1.000 0.000
#> SRR1047824 2 0.0000 0.800 0.000 1.000 0.000
#> SRR1047825 2 0.0000 0.800 0.000 1.000 0.000
#> SRR1047826 2 0.0000 0.800 0.000 1.000 0.000
#> SRR1047827 2 0.0000 0.800 0.000 1.000 0.000
#> SRR1047828 1 0.5678 0.924 0.684 0.316 0.000
#> SRR1047829 1 0.5678 0.924 0.684 0.316 0.000
#> SRR1047830 1 0.5678 0.924 0.684 0.316 0.000
#> SRR1047831 1 0.5678 0.924 0.684 0.316 0.000
#> SRR1047832 1 0.5678 0.924 0.684 0.316 0.000
#> SRR1047833 3 0.0000 0.785 0.000 0.000 1.000
#> SRR1047834 3 0.0000 0.785 0.000 0.000 1.000
#> SRR1047835 3 0.0000 0.785 0.000 0.000 1.000
#> SRR1047836 3 0.0000 0.785 0.000 0.000 1.000
#> SRR1047837 3 0.0000 0.785 0.000 0.000 1.000
#> SRR1047838 2 0.0000 0.800 0.000 1.000 0.000
#> SRR1047839 2 0.0000 0.800 0.000 1.000 0.000
#> SRR1047840 2 0.0000 0.800 0.000 1.000 0.000
#> SRR1047841 2 0.0000 0.800 0.000 1.000 0.000
#> SRR1047842 2 0.0000 0.800 0.000 1.000 0.000
#> SRR1047843 1 0.6140 0.895 0.596 0.404 0.000
#> SRR1047844 1 0.6140 0.895 0.596 0.404 0.000
#> SRR1047845 1 0.6140 0.895 0.596 0.404 0.000
#> SRR1047846 1 0.6140 0.895 0.596 0.404 0.000
#> SRR1047847 1 0.6140 0.895 0.596 0.404 0.000
#> SRR1047848 1 0.5859 0.929 0.656 0.344 0.000
#> SRR1047849 1 0.5859 0.929 0.656 0.344 0.000
#> SRR1047850 1 0.5859 0.929 0.656 0.344 0.000
#> SRR1047851 1 0.5859 0.929 0.656 0.344 0.000
#> SRR1047852 1 0.5859 0.929 0.656 0.344 0.000
#> SRR1047853 2 0.6267 -0.474 0.452 0.548 0.000
#> SRR1047854 2 0.6267 -0.474 0.452 0.548 0.000
#> SRR1047855 2 0.6267 -0.474 0.452 0.548 0.000
#> SRR1047856 2 0.6267 -0.474 0.452 0.548 0.000
#> SRR1047857 2 0.6267 -0.474 0.452 0.548 0.000
#> SRR1047858 1 0.6140 0.895 0.596 0.404 0.000
#> SRR1047859 1 0.6140 0.895 0.596 0.404 0.000
#> SRR1047860 1 0.6140 0.895 0.596 0.404 0.000
#> SRR1047861 1 0.6140 0.895 0.596 0.404 0.000
#> SRR1047863 3 0.6786 0.816 0.448 0.012 0.540
#> SRR1047864 3 0.5678 0.828 0.316 0.000 0.684
#> SRR1047865 3 0.8882 0.777 0.316 0.144 0.540
#> SRR1047866 3 0.5678 0.828 0.316 0.000 0.684
#> SRR1047867 3 0.0237 0.784 0.004 0.000 0.996
#> SRR1047868 3 0.6280 0.814 0.460 0.000 0.540
#> SRR1047869 3 0.8930 0.775 0.316 0.148 0.536
#> SRR1047870 3 0.6280 0.814 0.460 0.000 0.540
#> SRR1047871 3 0.8720 0.790 0.336 0.124 0.540
#> SRR1047872 3 0.6495 0.813 0.460 0.004 0.536
#> SRR1047873 3 0.6495 0.813 0.460 0.004 0.536
#> SRR1047874 3 0.6495 0.813 0.460 0.004 0.536
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1047813 1 0.000 0.901 1.000 0 0 0.000
#> SRR1047814 1 0.000 0.901 1.000 0 0 0.000
#> SRR1047815 1 0.000 0.901 1.000 0 0 0.000
#> SRR1047816 1 0.000 0.901 1.000 0 0 0.000
#> SRR1047817 1 0.000 0.901 1.000 0 0 0.000
#> SRR1047818 4 0.000 1.000 0.000 0 0 1.000
#> SRR1047819 4 0.000 1.000 0.000 0 0 1.000
#> SRR1047820 4 0.000 1.000 0.000 0 0 1.000
#> SRR1047821 4 0.000 1.000 0.000 0 0 1.000
#> SRR1047822 4 0.000 1.000 0.000 0 0 1.000
#> SRR1047823 4 0.000 1.000 0.000 0 0 1.000
#> SRR1047824 4 0.000 1.000 0.000 0 0 1.000
#> SRR1047825 4 0.000 1.000 0.000 0 0 1.000
#> SRR1047826 4 0.000 1.000 0.000 0 0 1.000
#> SRR1047827 4 0.000 1.000 0.000 0 0 1.000
#> SRR1047828 1 0.000 0.901 1.000 0 0 0.000
#> SRR1047829 1 0.000 0.901 1.000 0 0 0.000
#> SRR1047830 1 0.000 0.901 1.000 0 0 0.000
#> SRR1047831 1 0.000 0.901 1.000 0 0 0.000
#> SRR1047832 1 0.000 0.901 1.000 0 0 0.000
#> SRR1047833 2 0.000 1.000 0.000 1 0 0.000
#> SRR1047834 2 0.000 1.000 0.000 1 0 0.000
#> SRR1047835 2 0.000 1.000 0.000 1 0 0.000
#> SRR1047836 2 0.000 1.000 0.000 1 0 0.000
#> SRR1047837 2 0.000 1.000 0.000 1 0 0.000
#> SRR1047838 4 0.000 1.000 0.000 0 0 1.000
#> SRR1047839 4 0.000 1.000 0.000 0 0 1.000
#> SRR1047840 4 0.000 1.000 0.000 0 0 1.000
#> SRR1047841 4 0.000 1.000 0.000 0 0 1.000
#> SRR1047842 4 0.000 1.000 0.000 0 0 1.000
#> SRR1047843 1 0.164 0.893 0.940 0 0 0.060
#> SRR1047844 1 0.164 0.893 0.940 0 0 0.060
#> SRR1047845 1 0.164 0.893 0.940 0 0 0.060
#> SRR1047846 1 0.164 0.893 0.940 0 0 0.060
#> SRR1047847 1 0.164 0.893 0.940 0 0 0.060
#> SRR1047848 1 0.000 0.901 1.000 0 0 0.000
#> SRR1047849 1 0.000 0.901 1.000 0 0 0.000
#> SRR1047850 1 0.000 0.901 1.000 0 0 0.000
#> SRR1047851 1 0.000 0.901 1.000 0 0 0.000
#> SRR1047852 1 0.000 0.901 1.000 0 0 0.000
#> SRR1047853 1 0.476 0.541 0.628 0 0 0.372
#> SRR1047854 1 0.476 0.541 0.628 0 0 0.372
#> SRR1047855 1 0.476 0.541 0.628 0 0 0.372
#> SRR1047856 1 0.476 0.541 0.628 0 0 0.372
#> SRR1047857 1 0.476 0.541 0.628 0 0 0.372
#> SRR1047858 1 0.164 0.893 0.940 0 0 0.060
#> SRR1047859 1 0.164 0.893 0.940 0 0 0.060
#> SRR1047860 1 0.164 0.893 0.940 0 0 0.060
#> SRR1047861 1 0.164 0.893 0.940 0 0 0.060
#> SRR1047863 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047864 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047865 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047866 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047867 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047868 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047869 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047870 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047871 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047872 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047873 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047874 3 0.000 1.000 0.000 0 1 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1047813 1 0.416 0.552 0.608 0 0.000 0.000 0.392
#> SRR1047814 1 0.416 0.552 0.608 0 0.000 0.000 0.392
#> SRR1047815 1 0.416 0.552 0.608 0 0.000 0.000 0.392
#> SRR1047816 1 0.416 0.552 0.608 0 0.000 0.000 0.392
#> SRR1047817 1 0.416 0.552 0.608 0 0.000 0.000 0.392
#> SRR1047818 4 0.000 0.821 0.000 0 0.000 1.000 0.000
#> SRR1047819 4 0.000 0.821 0.000 0 0.000 1.000 0.000
#> SRR1047820 4 0.000 0.821 0.000 0 0.000 1.000 0.000
#> SRR1047821 4 0.000 0.821 0.000 0 0.000 1.000 0.000
#> SRR1047822 4 0.000 0.821 0.000 0 0.000 1.000 0.000
#> SRR1047823 4 0.000 0.821 0.000 0 0.000 1.000 0.000
#> SRR1047824 4 0.000 0.821 0.000 0 0.000 1.000 0.000
#> SRR1047825 4 0.000 0.821 0.000 0 0.000 1.000 0.000
#> SRR1047826 4 0.000 0.821 0.000 0 0.000 1.000 0.000
#> SRR1047827 4 0.000 0.821 0.000 0 0.000 1.000 0.000
#> SRR1047828 1 0.491 0.617 0.588 0 0.032 0.000 0.380
#> SRR1047829 1 0.491 0.617 0.588 0 0.032 0.000 0.380
#> SRR1047830 1 0.491 0.617 0.588 0 0.032 0.000 0.380
#> SRR1047831 1 0.491 0.617 0.588 0 0.032 0.000 0.380
#> SRR1047832 1 0.491 0.617 0.588 0 0.032 0.000 0.380
#> SRR1047833 2 0.000 1.000 0.000 1 0.000 0.000 0.000
#> SRR1047834 2 0.000 1.000 0.000 1 0.000 0.000 0.000
#> SRR1047835 2 0.000 1.000 0.000 1 0.000 0.000 0.000
#> SRR1047836 2 0.000 1.000 0.000 1 0.000 0.000 0.000
#> SRR1047837 2 0.000 1.000 0.000 1 0.000 0.000 0.000
#> SRR1047838 4 0.417 0.481 0.000 0 0.000 0.604 0.396
#> SRR1047839 4 0.417 0.481 0.000 0 0.000 0.604 0.396
#> SRR1047840 4 0.417 0.481 0.000 0 0.000 0.604 0.396
#> SRR1047841 4 0.417 0.481 0.000 0 0.000 0.604 0.396
#> SRR1047842 4 0.417 0.481 0.000 0 0.000 0.604 0.396
#> SRR1047843 1 0.321 0.623 0.788 0 0.000 0.000 0.212
#> SRR1047844 1 0.321 0.623 0.788 0 0.000 0.000 0.212
#> SRR1047845 1 0.321 0.623 0.788 0 0.000 0.000 0.212
#> SRR1047846 1 0.321 0.623 0.788 0 0.000 0.000 0.212
#> SRR1047847 1 0.321 0.623 0.788 0 0.000 0.000 0.212
#> SRR1047848 1 0.247 0.603 0.864 0 0.000 0.000 0.136
#> SRR1047849 1 0.247 0.603 0.864 0 0.000 0.000 0.136
#> SRR1047850 1 0.247 0.603 0.864 0 0.000 0.000 0.136
#> SRR1047851 1 0.247 0.603 0.864 0 0.000 0.000 0.136
#> SRR1047852 1 0.247 0.603 0.864 0 0.000 0.000 0.136
#> SRR1047853 5 0.583 1.000 0.220 0 0.000 0.172 0.608
#> SRR1047854 5 0.583 1.000 0.220 0 0.000 0.172 0.608
#> SRR1047855 5 0.583 1.000 0.220 0 0.000 0.172 0.608
#> SRR1047856 5 0.583 1.000 0.220 0 0.000 0.172 0.608
#> SRR1047857 5 0.583 1.000 0.220 0 0.000 0.172 0.608
#> SRR1047858 1 0.314 0.627 0.796 0 0.000 0.000 0.204
#> SRR1047859 1 0.314 0.627 0.796 0 0.000 0.000 0.204
#> SRR1047860 1 0.314 0.627 0.796 0 0.000 0.000 0.204
#> SRR1047861 1 0.314 0.627 0.796 0 0.000 0.000 0.204
#> SRR1047863 3 0.000 1.000 0.000 0 1.000 0.000 0.000
#> SRR1047864 3 0.000 1.000 0.000 0 1.000 0.000 0.000
#> SRR1047865 3 0.000 1.000 0.000 0 1.000 0.000 0.000
#> SRR1047866 3 0.000 1.000 0.000 0 1.000 0.000 0.000
#> SRR1047867 3 0.000 1.000 0.000 0 1.000 0.000 0.000
#> SRR1047868 3 0.000 1.000 0.000 0 1.000 0.000 0.000
#> SRR1047869 3 0.000 1.000 0.000 0 1.000 0.000 0.000
#> SRR1047870 3 0.000 1.000 0.000 0 1.000 0.000 0.000
#> SRR1047871 3 0.000 1.000 0.000 0 1.000 0.000 0.000
#> SRR1047872 3 0.000 1.000 0.000 0 1.000 0.000 0.000
#> SRR1047873 3 0.000 1.000 0.000 0 1.000 0.000 0.000
#> SRR1047874 3 0.000 1.000 0.000 0 1.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1047813 1 0.000 0.792 1.000 0 0.000 0.000 0.000 0.000
#> SRR1047814 1 0.000 0.792 1.000 0 0.000 0.000 0.000 0.000
#> SRR1047815 1 0.000 0.792 1.000 0 0.000 0.000 0.000 0.000
#> SRR1047816 1 0.000 0.792 1.000 0 0.000 0.000 0.000 0.000
#> SRR1047817 1 0.000 0.792 1.000 0 0.000 0.000 0.000 0.000
#> SRR1047818 4 0.000 1.000 0.000 0 0.000 1.000 0.000 0.000
#> SRR1047819 4 0.000 1.000 0.000 0 0.000 1.000 0.000 0.000
#> SRR1047820 4 0.000 1.000 0.000 0 0.000 1.000 0.000 0.000
#> SRR1047821 4 0.000 1.000 0.000 0 0.000 1.000 0.000 0.000
#> SRR1047822 4 0.000 1.000 0.000 0 0.000 1.000 0.000 0.000
#> SRR1047823 4 0.000 1.000 0.000 0 0.000 1.000 0.000 0.000
#> SRR1047824 4 0.000 1.000 0.000 0 0.000 1.000 0.000 0.000
#> SRR1047825 4 0.000 1.000 0.000 0 0.000 1.000 0.000 0.000
#> SRR1047826 4 0.000 1.000 0.000 0 0.000 1.000 0.000 0.000
#> SRR1047827 4 0.000 1.000 0.000 0 0.000 1.000 0.000 0.000
#> SRR1047828 5 0.543 0.647 0.188 0 0.000 0.000 0.576 0.236
#> SRR1047829 5 0.543 0.647 0.188 0 0.000 0.000 0.576 0.236
#> SRR1047830 5 0.543 0.647 0.188 0 0.000 0.000 0.576 0.236
#> SRR1047831 5 0.543 0.647 0.188 0 0.000 0.000 0.576 0.236
#> SRR1047832 5 0.543 0.647 0.188 0 0.000 0.000 0.576 0.236
#> SRR1047833 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> SRR1047834 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> SRR1047835 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> SRR1047836 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> SRR1047837 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> SRR1047838 6 0.382 0.531 0.000 0 0.000 0.436 0.000 0.564
#> SRR1047839 6 0.382 0.531 0.000 0 0.000 0.436 0.000 0.564
#> SRR1047840 6 0.382 0.531 0.000 0 0.000 0.436 0.000 0.564
#> SRR1047841 6 0.382 0.531 0.000 0 0.000 0.436 0.000 0.564
#> SRR1047842 6 0.382 0.531 0.000 0 0.000 0.436 0.000 0.564
#> SRR1047843 5 0.000 0.816 0.000 0 0.000 0.000 1.000 0.000
#> SRR1047844 5 0.000 0.816 0.000 0 0.000 0.000 1.000 0.000
#> SRR1047845 5 0.000 0.816 0.000 0 0.000 0.000 1.000 0.000
#> SRR1047846 5 0.000 0.816 0.000 0 0.000 0.000 1.000 0.000
#> SRR1047847 5 0.000 0.816 0.000 0 0.000 0.000 1.000 0.000
#> SRR1047848 1 0.339 0.777 0.704 0 0.000 0.000 0.296 0.000
#> SRR1047849 1 0.339 0.777 0.704 0 0.000 0.000 0.296 0.000
#> SRR1047850 1 0.339 0.777 0.704 0 0.000 0.000 0.296 0.000
#> SRR1047851 1 0.339 0.777 0.704 0 0.000 0.000 0.296 0.000
#> SRR1047852 1 0.339 0.777 0.704 0 0.000 0.000 0.296 0.000
#> SRR1047853 6 0.276 0.630 0.000 0 0.000 0.000 0.196 0.804
#> SRR1047854 6 0.276 0.630 0.000 0 0.000 0.000 0.196 0.804
#> SRR1047855 6 0.276 0.630 0.000 0 0.000 0.000 0.196 0.804
#> SRR1047856 6 0.276 0.630 0.000 0 0.000 0.000 0.196 0.804
#> SRR1047857 6 0.276 0.630 0.000 0 0.000 0.000 0.196 0.804
#> SRR1047858 5 0.000 0.816 0.000 0 0.000 0.000 1.000 0.000
#> SRR1047859 5 0.000 0.816 0.000 0 0.000 0.000 1.000 0.000
#> SRR1047860 5 0.000 0.816 0.000 0 0.000 0.000 1.000 0.000
#> SRR1047861 5 0.000 0.816 0.000 0 0.000 0.000 1.000 0.000
#> SRR1047863 3 0.000 0.954 0.000 0 1.000 0.000 0.000 0.000
#> SRR1047864 3 0.200 0.935 0.000 0 0.884 0.000 0.000 0.116
#> SRR1047865 3 0.200 0.935 0.000 0 0.884 0.000 0.000 0.116
#> SRR1047866 3 0.200 0.935 0.000 0 0.884 0.000 0.000 0.116
#> SRR1047867 3 0.200 0.935 0.000 0 0.884 0.000 0.000 0.116
#> SRR1047868 3 0.000 0.954 0.000 0 1.000 0.000 0.000 0.000
#> SRR1047869 3 0.200 0.935 0.000 0 0.884 0.000 0.000 0.116
#> SRR1047870 3 0.000 0.954 0.000 0 1.000 0.000 0.000 0.000
#> SRR1047871 3 0.000 0.954 0.000 0 1.000 0.000 0.000 0.000
#> SRR1047872 3 0.000 0.954 0.000 0 1.000 0.000 0.000 0.000
#> SRR1047873 3 0.000 0.954 0.000 0 1.000 0.000 0.000 0.000
#> SRR1047874 3 0.000 0.954 0.000 0 1.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 17931 rows and 61 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 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 0.895 0.964 0.978 0.2084 0.820 0.820
#> 3 3 0.920 0.942 0.975 1.2291 0.727 0.669
#> 4 4 0.926 0.900 0.963 0.5076 0.732 0.522
#> 5 5 1.000 0.985 0.988 0.1368 0.859 0.559
#> 6 6 0.802 0.632 0.823 0.0386 0.898 0.563
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
#> attr(,"optional")
#> [1] 3 4
There is also optional best \(k\) = 3 4 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR1047813 1 0.0000 0.976 1.000 0.000
#> SRR1047814 1 0.0000 0.976 1.000 0.000
#> SRR1047815 1 0.0000 0.976 1.000 0.000
#> SRR1047816 1 0.0000 0.976 1.000 0.000
#> SRR1047817 1 0.0000 0.976 1.000 0.000
#> SRR1047818 1 0.0000 0.976 1.000 0.000
#> SRR1047819 1 0.0000 0.976 1.000 0.000
#> SRR1047820 1 0.0000 0.976 1.000 0.000
#> SRR1047821 1 0.0000 0.976 1.000 0.000
#> SRR1047822 1 0.0000 0.976 1.000 0.000
#> SRR1047823 1 0.0000 0.976 1.000 0.000
#> SRR1047824 1 0.0000 0.976 1.000 0.000
#> SRR1047825 1 0.0000 0.976 1.000 0.000
#> SRR1047826 1 0.0000 0.976 1.000 0.000
#> SRR1047827 1 0.0000 0.976 1.000 0.000
#> SRR1047828 1 0.2778 0.948 0.952 0.048
#> SRR1047829 1 0.6148 0.857 0.848 0.152
#> SRR1047830 1 0.5519 0.883 0.872 0.128
#> SRR1047831 1 0.4690 0.910 0.900 0.100
#> SRR1047832 1 0.5946 0.866 0.856 0.144
#> SRR1047833 2 0.0376 0.999 0.004 0.996
#> SRR1047834 2 0.0376 0.999 0.004 0.996
#> SRR1047835 2 0.0376 0.999 0.004 0.996
#> SRR1047836 2 0.0376 0.999 0.004 0.996
#> SRR1047837 2 0.0376 0.999 0.004 0.996
#> SRR1047838 1 0.0000 0.976 1.000 0.000
#> SRR1047839 1 0.0000 0.976 1.000 0.000
#> SRR1047840 1 0.0000 0.976 1.000 0.000
#> SRR1047841 1 0.0000 0.976 1.000 0.000
#> SRR1047842 1 0.0000 0.976 1.000 0.000
#> SRR1047843 1 0.0000 0.976 1.000 0.000
#> SRR1047844 1 0.0000 0.976 1.000 0.000
#> SRR1047845 1 0.0000 0.976 1.000 0.000
#> SRR1047846 1 0.0000 0.976 1.000 0.000
#> SRR1047847 1 0.0000 0.976 1.000 0.000
#> SRR1047848 1 0.0000 0.976 1.000 0.000
#> SRR1047849 1 0.0000 0.976 1.000 0.000
#> SRR1047850 1 0.0000 0.976 1.000 0.000
#> SRR1047851 1 0.0000 0.976 1.000 0.000
#> SRR1047852 1 0.0000 0.976 1.000 0.000
#> SRR1047853 1 0.0000 0.976 1.000 0.000
#> SRR1047854 1 0.0000 0.976 1.000 0.000
#> SRR1047855 1 0.0000 0.976 1.000 0.000
#> SRR1047856 1 0.0000 0.976 1.000 0.000
#> SRR1047857 1 0.0000 0.976 1.000 0.000
#> SRR1047858 1 0.0000 0.976 1.000 0.000
#> SRR1047859 1 0.0000 0.976 1.000 0.000
#> SRR1047860 1 0.0000 0.976 1.000 0.000
#> SRR1047861 1 0.0000 0.976 1.000 0.000
#> SRR1047863 1 0.4690 0.911 0.900 0.100
#> SRR1047864 1 0.4690 0.911 0.900 0.100
#> SRR1047865 1 0.4562 0.914 0.904 0.096
#> SRR1047866 1 0.4562 0.914 0.904 0.096
#> SRR1047867 2 0.0000 0.996 0.000 1.000
#> SRR1047868 1 0.4562 0.914 0.904 0.096
#> SRR1047869 1 0.0376 0.974 0.996 0.004
#> SRR1047870 1 0.4939 0.904 0.892 0.108
#> SRR1047871 1 0.4562 0.914 0.904 0.096
#> SRR1047872 1 0.1633 0.964 0.976 0.024
#> SRR1047873 1 0.0376 0.974 0.996 0.004
#> SRR1047874 1 0.1184 0.968 0.984 0.016
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1047813 1 0.000 0.972 1.000 0.000 0.00
#> SRR1047814 1 0.000 0.972 1.000 0.000 0.00
#> SRR1047815 1 0.000 0.972 1.000 0.000 0.00
#> SRR1047816 1 0.000 0.972 1.000 0.000 0.00
#> SRR1047817 1 0.000 0.972 1.000 0.000 0.00
#> SRR1047818 1 0.000 0.972 1.000 0.000 0.00
#> SRR1047819 1 0.000 0.972 1.000 0.000 0.00
#> SRR1047820 1 0.000 0.972 1.000 0.000 0.00
#> SRR1047821 1 0.000 0.972 1.000 0.000 0.00
#> SRR1047822 1 0.000 0.972 1.000 0.000 0.00
#> SRR1047823 1 0.000 0.972 1.000 0.000 0.00
#> SRR1047824 1 0.000 0.972 1.000 0.000 0.00
#> SRR1047825 1 0.000 0.972 1.000 0.000 0.00
#> SRR1047826 1 0.000 0.972 1.000 0.000 0.00
#> SRR1047827 1 0.000 0.972 1.000 0.000 0.00
#> SRR1047828 1 0.429 0.790 0.820 0.180 0.00
#> SRR1047829 1 0.571 0.571 0.680 0.320 0.00
#> SRR1047830 1 0.489 0.727 0.772 0.228 0.00
#> SRR1047831 1 0.455 0.765 0.800 0.200 0.00
#> SRR1047832 1 0.493 0.721 0.768 0.232 0.00
#> SRR1047833 2 0.000 1.000 0.000 1.000 0.00
#> SRR1047834 2 0.000 1.000 0.000 1.000 0.00
#> SRR1047835 2 0.000 1.000 0.000 1.000 0.00
#> SRR1047836 2 0.000 1.000 0.000 1.000 0.00
#> SRR1047837 2 0.000 1.000 0.000 1.000 0.00
#> SRR1047838 1 0.000 0.972 1.000 0.000 0.00
#> SRR1047839 1 0.000 0.972 1.000 0.000 0.00
#> SRR1047840 1 0.000 0.972 1.000 0.000 0.00
#> SRR1047841 1 0.000 0.972 1.000 0.000 0.00
#> SRR1047842 1 0.000 0.972 1.000 0.000 0.00
#> SRR1047843 1 0.000 0.972 1.000 0.000 0.00
#> SRR1047844 1 0.000 0.972 1.000 0.000 0.00
#> SRR1047845 1 0.000 0.972 1.000 0.000 0.00
#> SRR1047846 1 0.000 0.972 1.000 0.000 0.00
#> SRR1047847 1 0.000 0.972 1.000 0.000 0.00
#> SRR1047848 1 0.000 0.972 1.000 0.000 0.00
#> SRR1047849 1 0.000 0.972 1.000 0.000 0.00
#> SRR1047850 1 0.000 0.972 1.000 0.000 0.00
#> SRR1047851 1 0.000 0.972 1.000 0.000 0.00
#> SRR1047852 1 0.000 0.972 1.000 0.000 0.00
#> SRR1047853 1 0.000 0.972 1.000 0.000 0.00
#> SRR1047854 1 0.000 0.972 1.000 0.000 0.00
#> SRR1047855 1 0.000 0.972 1.000 0.000 0.00
#> SRR1047856 1 0.000 0.972 1.000 0.000 0.00
#> SRR1047857 1 0.000 0.972 1.000 0.000 0.00
#> SRR1047858 1 0.000 0.972 1.000 0.000 0.00
#> SRR1047859 1 0.000 0.972 1.000 0.000 0.00
#> SRR1047860 1 0.000 0.972 1.000 0.000 0.00
#> SRR1047861 1 0.000 0.972 1.000 0.000 0.00
#> SRR1047863 3 0.000 0.963 0.000 0.000 1.00
#> SRR1047864 3 0.000 0.963 0.000 0.000 1.00
#> SRR1047865 3 0.000 0.963 0.000 0.000 1.00
#> SRR1047866 3 0.000 0.963 0.000 0.000 1.00
#> SRR1047867 3 0.604 0.363 0.000 0.380 0.62
#> SRR1047868 3 0.000 0.963 0.000 0.000 1.00
#> SRR1047869 3 0.000 0.963 0.000 0.000 1.00
#> SRR1047870 3 0.000 0.963 0.000 0.000 1.00
#> SRR1047871 3 0.000 0.963 0.000 0.000 1.00
#> SRR1047872 3 0.000 0.963 0.000 0.000 1.00
#> SRR1047873 3 0.000 0.963 0.000 0.000 1.00
#> SRR1047874 3 0.000 0.963 0.000 0.000 1.00
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1047813 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> SRR1047814 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> SRR1047815 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> SRR1047816 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> SRR1047817 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> SRR1047818 4 0.0000 0.898 0.000 0.000 0.000 1.000
#> SRR1047819 4 0.0000 0.898 0.000 0.000 0.000 1.000
#> SRR1047820 4 0.0000 0.898 0.000 0.000 0.000 1.000
#> SRR1047821 4 0.0000 0.898 0.000 0.000 0.000 1.000
#> SRR1047822 4 0.0000 0.898 0.000 0.000 0.000 1.000
#> SRR1047823 4 0.0000 0.898 0.000 0.000 0.000 1.000
#> SRR1047824 4 0.0000 0.898 0.000 0.000 0.000 1.000
#> SRR1047825 4 0.0000 0.898 0.000 0.000 0.000 1.000
#> SRR1047826 4 0.0000 0.898 0.000 0.000 0.000 1.000
#> SRR1047827 4 0.0000 0.898 0.000 0.000 0.000 1.000
#> SRR1047828 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> SRR1047829 1 0.2589 0.857 0.884 0.116 0.000 0.000
#> SRR1047830 1 0.1118 0.940 0.964 0.036 0.000 0.000
#> SRR1047831 1 0.0336 0.963 0.992 0.008 0.000 0.000
#> SRR1047832 1 0.1716 0.914 0.936 0.064 0.000 0.000
#> SRR1047833 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> SRR1047834 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> SRR1047835 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> SRR1047836 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> SRR1047837 2 0.0000 0.945 0.000 1.000 0.000 0.000
#> SRR1047838 4 0.0000 0.898 0.000 0.000 0.000 1.000
#> SRR1047839 4 0.0000 0.898 0.000 0.000 0.000 1.000
#> SRR1047840 4 0.0000 0.898 0.000 0.000 0.000 1.000
#> SRR1047841 4 0.0000 0.898 0.000 0.000 0.000 1.000
#> SRR1047842 4 0.0000 0.898 0.000 0.000 0.000 1.000
#> SRR1047843 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> SRR1047844 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> SRR1047845 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> SRR1047846 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> SRR1047847 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> SRR1047848 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> SRR1047849 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> SRR1047850 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> SRR1047851 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> SRR1047852 1 0.0000 0.968 1.000 0.000 0.000 0.000
#> SRR1047853 4 0.4730 0.484 0.364 0.000 0.000 0.636
#> SRR1047854 4 0.4985 0.198 0.468 0.000 0.000 0.532
#> SRR1047855 1 0.4925 0.122 0.572 0.000 0.000 0.428
#> SRR1047856 4 0.3486 0.718 0.188 0.000 0.000 0.812
#> SRR1047857 4 0.4564 0.551 0.328 0.000 0.000 0.672
#> SRR1047858 1 0.0188 0.966 0.996 0.000 0.000 0.004
#> SRR1047859 1 0.0188 0.966 0.996 0.000 0.000 0.004
#> SRR1047860 1 0.0188 0.966 0.996 0.000 0.000 0.004
#> SRR1047861 1 0.0188 0.966 0.996 0.000 0.000 0.004
#> SRR1047863 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR1047864 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR1047865 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR1047866 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR1047867 2 0.4193 0.634 0.000 0.732 0.268 0.000
#> SRR1047868 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR1047869 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR1047870 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR1047871 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR1047872 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR1047873 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR1047874 3 0.0000 1.000 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
#> SRR1047813 5 0.0703 0.968 0.024 0.000 0.000 0.000 0.976
#> SRR1047814 5 0.0703 0.968 0.024 0.000 0.000 0.000 0.976
#> SRR1047815 5 0.0703 0.968 0.024 0.000 0.000 0.000 0.976
#> SRR1047816 5 0.0703 0.968 0.024 0.000 0.000 0.000 0.976
#> SRR1047817 5 0.0703 0.968 0.024 0.000 0.000 0.000 0.976
#> SRR1047818 4 0.0000 0.994 0.000 0.000 0.000 1.000 0.000
#> SRR1047819 4 0.0000 0.994 0.000 0.000 0.000 1.000 0.000
#> SRR1047820 4 0.0000 0.994 0.000 0.000 0.000 1.000 0.000
#> SRR1047821 4 0.0000 0.994 0.000 0.000 0.000 1.000 0.000
#> SRR1047822 4 0.0000 0.994 0.000 0.000 0.000 1.000 0.000
#> SRR1047823 4 0.0324 0.991 0.004 0.000 0.000 0.992 0.004
#> SRR1047824 4 0.0162 0.993 0.000 0.000 0.000 0.996 0.004
#> SRR1047825 4 0.0162 0.993 0.000 0.000 0.000 0.996 0.004
#> SRR1047826 4 0.0000 0.994 0.000 0.000 0.000 1.000 0.000
#> SRR1047827 4 0.0000 0.994 0.000 0.000 0.000 1.000 0.000
#> SRR1047828 5 0.1205 0.961 0.040 0.004 0.000 0.000 0.956
#> SRR1047829 5 0.1399 0.961 0.028 0.020 0.000 0.000 0.952
#> SRR1047830 5 0.1485 0.959 0.032 0.020 0.000 0.000 0.948
#> SRR1047831 5 0.1281 0.962 0.032 0.012 0.000 0.000 0.956
#> SRR1047832 5 0.1661 0.955 0.036 0.024 0.000 0.000 0.940
#> SRR1047833 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000
#> SRR1047834 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000
#> SRR1047835 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000
#> SRR1047836 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000
#> SRR1047837 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000
#> SRR1047838 4 0.0865 0.973 0.024 0.000 0.000 0.972 0.004
#> SRR1047839 4 0.0324 0.992 0.004 0.000 0.000 0.992 0.004
#> SRR1047840 4 0.0324 0.992 0.004 0.000 0.000 0.992 0.004
#> SRR1047841 4 0.0324 0.992 0.004 0.000 0.000 0.992 0.004
#> SRR1047842 4 0.0324 0.992 0.004 0.000 0.000 0.992 0.004
#> SRR1047843 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000
#> SRR1047844 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000
#> SRR1047845 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000
#> SRR1047846 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000
#> SRR1047847 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000
#> SRR1047848 1 0.0290 0.993 0.992 0.000 0.000 0.000 0.008
#> SRR1047849 1 0.0290 0.993 0.992 0.000 0.000 0.000 0.008
#> SRR1047850 1 0.0290 0.993 0.992 0.000 0.000 0.000 0.008
#> SRR1047851 1 0.0290 0.993 0.992 0.000 0.000 0.000 0.008
#> SRR1047852 1 0.0290 0.993 0.992 0.000 0.000 0.000 0.008
#> SRR1047853 5 0.0807 0.959 0.012 0.000 0.000 0.012 0.976
#> SRR1047854 5 0.0693 0.958 0.008 0.000 0.000 0.012 0.980
#> SRR1047855 5 0.0693 0.960 0.012 0.000 0.000 0.008 0.980
#> SRR1047856 5 0.2358 0.869 0.008 0.000 0.000 0.104 0.888
#> SRR1047857 5 0.1168 0.947 0.008 0.000 0.000 0.032 0.960
#> SRR1047858 1 0.0162 0.994 0.996 0.000 0.000 0.000 0.004
#> SRR1047859 1 0.0162 0.994 0.996 0.000 0.000 0.000 0.004
#> SRR1047860 1 0.0162 0.994 0.996 0.000 0.000 0.000 0.004
#> SRR1047861 1 0.0162 0.994 0.996 0.000 0.000 0.000 0.004
#> SRR1047863 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047864 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047865 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047866 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047867 2 0.0510 0.984 0.000 0.984 0.016 0.000 0.000
#> SRR1047868 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047869 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047870 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047871 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047872 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047873 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047874 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1047813 5 0.1007 0.7689 0.000 0.000 0.000 0.000 0.956 0.044
#> SRR1047814 5 0.1007 0.7689 0.000 0.000 0.000 0.000 0.956 0.044
#> SRR1047815 5 0.1007 0.7689 0.000 0.000 0.000 0.000 0.956 0.044
#> SRR1047816 5 0.1007 0.7689 0.000 0.000 0.000 0.000 0.956 0.044
#> SRR1047817 5 0.1007 0.7689 0.000 0.000 0.000 0.000 0.956 0.044
#> SRR1047818 4 0.2300 0.8931 0.000 0.000 0.000 0.856 0.000 0.144
#> SRR1047819 4 0.2178 0.8993 0.000 0.000 0.000 0.868 0.000 0.132
#> SRR1047820 4 0.2219 0.8978 0.000 0.000 0.000 0.864 0.000 0.136
#> SRR1047821 4 0.2178 0.8993 0.000 0.000 0.000 0.868 0.000 0.132
#> SRR1047822 4 0.2454 0.8793 0.000 0.000 0.000 0.840 0.000 0.160
#> SRR1047823 4 0.1307 0.8909 0.032 0.000 0.000 0.952 0.008 0.008
#> SRR1047824 4 0.0748 0.9009 0.016 0.000 0.000 0.976 0.004 0.004
#> SRR1047825 4 0.1116 0.8963 0.028 0.000 0.000 0.960 0.004 0.008
#> SRR1047826 4 0.1003 0.8986 0.028 0.000 0.000 0.964 0.004 0.004
#> SRR1047827 4 0.0951 0.8996 0.020 0.000 0.000 0.968 0.004 0.008
#> SRR1047828 5 0.4381 0.7416 0.036 0.000 0.000 0.072 0.760 0.132
#> SRR1047829 5 0.4088 0.7469 0.004 0.004 0.004 0.080 0.776 0.132
#> SRR1047830 5 0.4276 0.7469 0.020 0.004 0.000 0.076 0.768 0.132
#> SRR1047831 5 0.4114 0.7467 0.012 0.004 0.000 0.080 0.776 0.128
#> SRR1047832 5 0.4514 0.7422 0.032 0.004 0.000 0.080 0.756 0.128
#> SRR1047833 2 0.0000 0.9956 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1047834 2 0.0000 0.9956 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1047835 2 0.0000 0.9956 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1047836 2 0.0000 0.9956 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1047837 2 0.0000 0.9956 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1047838 6 0.4028 0.3655 0.024 0.000 0.000 0.308 0.000 0.668
#> SRR1047839 6 0.3547 0.3691 0.004 0.000 0.000 0.300 0.000 0.696
#> SRR1047840 6 0.3584 0.3583 0.004 0.000 0.000 0.308 0.000 0.688
#> SRR1047841 6 0.3448 0.3990 0.004 0.000 0.000 0.280 0.000 0.716
#> SRR1047842 6 0.3426 0.3986 0.004 0.000 0.000 0.276 0.000 0.720
#> SRR1047843 1 0.4109 0.3904 0.576 0.000 0.000 0.000 0.012 0.412
#> SRR1047844 6 0.4468 -0.3436 0.484 0.000 0.004 0.000 0.020 0.492
#> SRR1047845 1 0.4234 0.3404 0.544 0.000 0.000 0.000 0.016 0.440
#> SRR1047846 1 0.4076 0.4139 0.592 0.000 0.000 0.000 0.012 0.396
#> SRR1047847 1 0.4338 0.2167 0.492 0.000 0.000 0.000 0.020 0.488
#> SRR1047848 1 0.0000 0.6836 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1047849 1 0.0146 0.6832 0.996 0.000 0.000 0.000 0.000 0.004
#> SRR1047850 1 0.0000 0.6836 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1047851 1 0.0000 0.6836 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1047852 1 0.0146 0.6832 0.996 0.000 0.000 0.000 0.000 0.004
#> SRR1047853 6 0.4179 -0.0943 0.000 0.000 0.000 0.012 0.472 0.516
#> SRR1047854 5 0.3997 0.0808 0.000 0.000 0.000 0.004 0.508 0.488
#> SRR1047855 5 0.3996 0.0874 0.000 0.000 0.000 0.004 0.512 0.484
#> SRR1047856 6 0.4466 0.2179 0.000 0.000 0.000 0.044 0.336 0.620
#> SRR1047857 6 0.4026 0.1514 0.000 0.000 0.000 0.012 0.376 0.612
#> SRR1047858 6 0.4338 -0.2709 0.484 0.000 0.000 0.000 0.020 0.496
#> SRR1047859 6 0.4335 -0.2515 0.472 0.000 0.000 0.000 0.020 0.508
#> SRR1047860 6 0.4336 -0.2562 0.476 0.000 0.000 0.000 0.020 0.504
#> SRR1047861 6 0.4336 -0.2562 0.476 0.000 0.000 0.000 0.020 0.504
#> SRR1047863 3 0.0000 0.9644 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047864 3 0.0000 0.9644 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047865 3 0.0000 0.9644 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047866 3 0.0000 0.9644 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047867 2 0.0547 0.9779 0.000 0.980 0.020 0.000 0.000 0.000
#> SRR1047868 3 0.0000 0.9644 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047869 3 0.0000 0.9644 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047870 3 0.0000 0.9644 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047871 3 0.0000 0.9644 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047872 3 0.2823 0.7835 0.000 0.000 0.796 0.000 0.000 0.204
#> SRR1047873 3 0.2092 0.8687 0.000 0.000 0.876 0.000 0.000 0.124
#> SRR1047874 3 0.0363 0.9576 0.000 0.000 0.988 0.000 0.000 0.012
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 17931 rows and 61 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 1.000 0.977 0.984 0.167 0.847 0.847
#> 3 3 1.000 0.988 0.994 1.655 0.711 0.659
#> 4 4 0.757 0.934 0.948 0.119 0.989 0.980
#> 5 5 0.893 0.959 0.983 0.433 0.738 0.521
#> 6 6 0.893 0.959 0.983 0.016 0.989 0.960
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
#> SRR1047813 1 0.000 0.986 1.000 0.000
#> SRR1047814 1 0.000 0.986 1.000 0.000
#> SRR1047815 1 0.000 0.986 1.000 0.000
#> SRR1047816 1 0.000 0.986 1.000 0.000
#> SRR1047817 1 0.000 0.986 1.000 0.000
#> SRR1047818 1 0.000 0.986 1.000 0.000
#> SRR1047819 1 0.000 0.986 1.000 0.000
#> SRR1047820 1 0.000 0.986 1.000 0.000
#> SRR1047821 1 0.000 0.986 1.000 0.000
#> SRR1047822 1 0.000 0.986 1.000 0.000
#> SRR1047823 1 0.000 0.986 1.000 0.000
#> SRR1047824 1 0.000 0.986 1.000 0.000
#> SRR1047825 1 0.000 0.986 1.000 0.000
#> SRR1047826 1 0.000 0.986 1.000 0.000
#> SRR1047827 1 0.000 0.986 1.000 0.000
#> SRR1047828 1 0.000 0.986 1.000 0.000
#> SRR1047829 1 0.000 0.986 1.000 0.000
#> SRR1047830 1 0.000 0.986 1.000 0.000
#> SRR1047831 1 0.000 0.986 1.000 0.000
#> SRR1047832 1 0.000 0.986 1.000 0.000
#> SRR1047833 2 0.260 1.000 0.044 0.956
#> SRR1047834 2 0.260 1.000 0.044 0.956
#> SRR1047835 2 0.260 1.000 0.044 0.956
#> SRR1047836 2 0.260 1.000 0.044 0.956
#> SRR1047837 2 0.260 1.000 0.044 0.956
#> SRR1047838 1 0.000 0.986 1.000 0.000
#> SRR1047839 1 0.000 0.986 1.000 0.000
#> SRR1047840 1 0.000 0.986 1.000 0.000
#> SRR1047841 1 0.000 0.986 1.000 0.000
#> SRR1047842 1 0.000 0.986 1.000 0.000
#> SRR1047843 1 0.000 0.986 1.000 0.000
#> SRR1047844 1 0.000 0.986 1.000 0.000
#> SRR1047845 1 0.000 0.986 1.000 0.000
#> SRR1047846 1 0.000 0.986 1.000 0.000
#> SRR1047847 1 0.000 0.986 1.000 0.000
#> SRR1047848 1 0.000 0.986 1.000 0.000
#> SRR1047849 1 0.000 0.986 1.000 0.000
#> SRR1047850 1 0.000 0.986 1.000 0.000
#> SRR1047851 1 0.000 0.986 1.000 0.000
#> SRR1047852 1 0.000 0.986 1.000 0.000
#> SRR1047853 1 0.000 0.986 1.000 0.000
#> SRR1047854 1 0.000 0.986 1.000 0.000
#> SRR1047855 1 0.000 0.986 1.000 0.000
#> SRR1047856 1 0.000 0.986 1.000 0.000
#> SRR1047857 1 0.000 0.986 1.000 0.000
#> SRR1047858 1 0.000 0.986 1.000 0.000
#> SRR1047859 1 0.000 0.986 1.000 0.000
#> SRR1047860 1 0.000 0.986 1.000 0.000
#> SRR1047861 1 0.000 0.986 1.000 0.000
#> SRR1047863 1 0.260 0.957 0.956 0.044
#> SRR1047864 1 0.595 0.832 0.856 0.144
#> SRR1047865 1 0.260 0.957 0.956 0.044
#> SRR1047866 1 0.260 0.957 0.956 0.044
#> SRR1047867 1 0.595 0.832 0.856 0.144
#> SRR1047868 1 0.260 0.957 0.956 0.044
#> SRR1047869 1 0.260 0.957 0.956 0.044
#> SRR1047870 1 0.260 0.957 0.956 0.044
#> SRR1047871 1 0.260 0.957 0.956 0.044
#> SRR1047872 1 0.260 0.957 0.956 0.044
#> SRR1047873 1 0.260 0.957 0.956 0.044
#> SRR1047874 1 0.260 0.957 0.956 0.044
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1047813 1 0.000 1.000 1 0.00 0.00
#> SRR1047814 1 0.000 1.000 1 0.00 0.00
#> SRR1047815 1 0.000 1.000 1 0.00 0.00
#> SRR1047816 1 0.000 1.000 1 0.00 0.00
#> SRR1047817 1 0.000 1.000 1 0.00 0.00
#> SRR1047818 1 0.000 1.000 1 0.00 0.00
#> SRR1047819 1 0.000 1.000 1 0.00 0.00
#> SRR1047820 1 0.000 1.000 1 0.00 0.00
#> SRR1047821 1 0.000 1.000 1 0.00 0.00
#> SRR1047822 1 0.000 1.000 1 0.00 0.00
#> SRR1047823 1 0.000 1.000 1 0.00 0.00
#> SRR1047824 1 0.000 1.000 1 0.00 0.00
#> SRR1047825 1 0.000 1.000 1 0.00 0.00
#> SRR1047826 1 0.000 1.000 1 0.00 0.00
#> SRR1047827 1 0.000 1.000 1 0.00 0.00
#> SRR1047828 1 0.000 1.000 1 0.00 0.00
#> SRR1047829 1 0.000 1.000 1 0.00 0.00
#> SRR1047830 1 0.000 1.000 1 0.00 0.00
#> SRR1047831 1 0.000 1.000 1 0.00 0.00
#> SRR1047832 1 0.000 1.000 1 0.00 0.00
#> SRR1047833 2 0.000 1.000 0 1.00 0.00
#> SRR1047834 2 0.000 1.000 0 1.00 0.00
#> SRR1047835 2 0.000 1.000 0 1.00 0.00
#> SRR1047836 2 0.000 1.000 0 1.00 0.00
#> SRR1047837 2 0.000 1.000 0 1.00 0.00
#> SRR1047838 1 0.000 1.000 1 0.00 0.00
#> SRR1047839 1 0.000 1.000 1 0.00 0.00
#> SRR1047840 1 0.000 1.000 1 0.00 0.00
#> SRR1047841 1 0.000 1.000 1 0.00 0.00
#> SRR1047842 1 0.000 1.000 1 0.00 0.00
#> SRR1047843 1 0.000 1.000 1 0.00 0.00
#> SRR1047844 1 0.000 1.000 1 0.00 0.00
#> SRR1047845 1 0.000 1.000 1 0.00 0.00
#> SRR1047846 1 0.000 1.000 1 0.00 0.00
#> SRR1047847 1 0.000 1.000 1 0.00 0.00
#> SRR1047848 1 0.000 1.000 1 0.00 0.00
#> SRR1047849 1 0.000 1.000 1 0.00 0.00
#> SRR1047850 1 0.000 1.000 1 0.00 0.00
#> SRR1047851 1 0.000 1.000 1 0.00 0.00
#> SRR1047852 1 0.000 1.000 1 0.00 0.00
#> SRR1047853 1 0.000 1.000 1 0.00 0.00
#> SRR1047854 1 0.000 1.000 1 0.00 0.00
#> SRR1047855 1 0.000 1.000 1 0.00 0.00
#> SRR1047856 1 0.000 1.000 1 0.00 0.00
#> SRR1047857 1 0.000 1.000 1 0.00 0.00
#> SRR1047858 1 0.000 1.000 1 0.00 0.00
#> SRR1047859 1 0.000 1.000 1 0.00 0.00
#> SRR1047860 1 0.000 1.000 1 0.00 0.00
#> SRR1047861 1 0.000 1.000 1 0.00 0.00
#> SRR1047863 3 0.000 0.966 0 0.00 1.00
#> SRR1047864 3 0.429 0.800 0 0.18 0.82
#> SRR1047865 3 0.000 0.966 0 0.00 1.00
#> SRR1047866 3 0.000 0.966 0 0.00 1.00
#> SRR1047867 3 0.429 0.800 0 0.18 0.82
#> SRR1047868 3 0.000 0.966 0 0.00 1.00
#> SRR1047869 3 0.000 0.966 0 0.00 1.00
#> SRR1047870 3 0.000 0.966 0 0.00 1.00
#> SRR1047871 3 0.000 0.966 0 0.00 1.00
#> SRR1047872 3 0.000 0.966 0 0.00 1.00
#> SRR1047873 3 0.000 0.966 0 0.00 1.00
#> SRR1047874 3 0.000 0.966 0 0.00 1.00
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1047813 1 0.0000 0.934 1.000 0.00 0.000 0.000
#> SRR1047814 1 0.0000 0.934 1.000 0.00 0.000 0.000
#> SRR1047815 1 0.0000 0.934 1.000 0.00 0.000 0.000
#> SRR1047816 1 0.0000 0.934 1.000 0.00 0.000 0.000
#> SRR1047817 1 0.0000 0.934 1.000 0.00 0.000 0.000
#> SRR1047818 1 0.3583 0.864 0.816 0.18 0.000 0.004
#> SRR1047819 1 0.3583 0.864 0.816 0.18 0.000 0.004
#> SRR1047820 1 0.3583 0.864 0.816 0.18 0.000 0.004
#> SRR1047821 1 0.3583 0.864 0.816 0.18 0.000 0.004
#> SRR1047822 1 0.3583 0.864 0.816 0.18 0.000 0.004
#> SRR1047823 1 0.3583 0.864 0.816 0.18 0.000 0.004
#> SRR1047824 1 0.3583 0.864 0.816 0.18 0.000 0.004
#> SRR1047825 1 0.3583 0.864 0.816 0.18 0.000 0.004
#> SRR1047826 1 0.3583 0.864 0.816 0.18 0.000 0.004
#> SRR1047827 1 0.3583 0.864 0.816 0.18 0.000 0.004
#> SRR1047828 1 0.0000 0.934 1.000 0.00 0.000 0.000
#> SRR1047829 1 0.0000 0.934 1.000 0.00 0.000 0.000
#> SRR1047830 1 0.0000 0.934 1.000 0.00 0.000 0.000
#> SRR1047831 1 0.0000 0.934 1.000 0.00 0.000 0.000
#> SRR1047832 1 0.0000 0.934 1.000 0.00 0.000 0.000
#> SRR1047833 2 0.3400 1.000 0.000 0.82 0.000 0.180
#> SRR1047834 2 0.3400 1.000 0.000 0.82 0.000 0.180
#> SRR1047835 2 0.3400 1.000 0.000 0.82 0.000 0.180
#> SRR1047836 2 0.3400 1.000 0.000 0.82 0.000 0.180
#> SRR1047837 2 0.3400 1.000 0.000 0.82 0.000 0.180
#> SRR1047838 1 0.3583 0.864 0.816 0.18 0.000 0.004
#> SRR1047839 1 0.3583 0.864 0.816 0.18 0.000 0.004
#> SRR1047840 1 0.3583 0.864 0.816 0.18 0.000 0.004
#> SRR1047841 1 0.3583 0.864 0.816 0.18 0.000 0.004
#> SRR1047842 1 0.3583 0.864 0.816 0.18 0.000 0.004
#> SRR1047843 1 0.0000 0.934 1.000 0.00 0.000 0.000
#> SRR1047844 1 0.0000 0.934 1.000 0.00 0.000 0.000
#> SRR1047845 1 0.0000 0.934 1.000 0.00 0.000 0.000
#> SRR1047846 1 0.0000 0.934 1.000 0.00 0.000 0.000
#> SRR1047847 1 0.0000 0.934 1.000 0.00 0.000 0.000
#> SRR1047848 1 0.0000 0.934 1.000 0.00 0.000 0.000
#> SRR1047849 1 0.0000 0.934 1.000 0.00 0.000 0.000
#> SRR1047850 1 0.0000 0.934 1.000 0.00 0.000 0.000
#> SRR1047851 1 0.0000 0.934 1.000 0.00 0.000 0.000
#> SRR1047852 1 0.0000 0.934 1.000 0.00 0.000 0.000
#> SRR1047853 1 0.0000 0.934 1.000 0.00 0.000 0.000
#> SRR1047854 1 0.0000 0.934 1.000 0.00 0.000 0.000
#> SRR1047855 1 0.0000 0.934 1.000 0.00 0.000 0.000
#> SRR1047856 1 0.0000 0.934 1.000 0.00 0.000 0.000
#> SRR1047857 1 0.0000 0.934 1.000 0.00 0.000 0.000
#> SRR1047858 1 0.0000 0.934 1.000 0.00 0.000 0.000
#> SRR1047859 1 0.0000 0.934 1.000 0.00 0.000 0.000
#> SRR1047860 1 0.0000 0.934 1.000 0.00 0.000 0.000
#> SRR1047861 1 0.0000 0.934 1.000 0.00 0.000 0.000
#> SRR1047863 3 0.0592 0.987 0.000 0.00 0.984 0.016
#> SRR1047864 4 0.0188 1.000 0.000 0.00 0.004 0.996
#> SRR1047865 3 0.0000 0.995 0.000 0.00 1.000 0.000
#> SRR1047866 3 0.0000 0.995 0.000 0.00 1.000 0.000
#> SRR1047867 4 0.0188 1.000 0.000 0.00 0.004 0.996
#> SRR1047868 3 0.0000 0.995 0.000 0.00 1.000 0.000
#> SRR1047869 3 0.0000 0.995 0.000 0.00 1.000 0.000
#> SRR1047870 3 0.0592 0.987 0.000 0.00 0.984 0.016
#> SRR1047871 3 0.0592 0.987 0.000 0.00 0.984 0.016
#> SRR1047872 3 0.0000 0.995 0.000 0.00 1.000 0.000
#> SRR1047873 3 0.0000 0.995 0.000 0.00 1.000 0.000
#> SRR1047874 3 0.0000 0.995 0.000 0.00 1.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1047813 1 0.0000 1.000 1.0 0 0.000 0.0 0.000
#> SRR1047814 1 0.0000 1.000 1.0 0 0.000 0.0 0.000
#> SRR1047815 1 0.0000 1.000 1.0 0 0.000 0.0 0.000
#> SRR1047816 1 0.0000 1.000 1.0 0 0.000 0.0 0.000
#> SRR1047817 1 0.0000 1.000 1.0 0 0.000 0.0 0.000
#> SRR1047818 4 0.0000 0.922 0.0 0 0.000 1.0 0.000
#> SRR1047819 4 0.0000 0.922 0.0 0 0.000 1.0 0.000
#> SRR1047820 4 0.0000 0.922 0.0 0 0.000 1.0 0.000
#> SRR1047821 4 0.0000 0.922 0.0 0 0.000 1.0 0.000
#> SRR1047822 4 0.0000 0.922 0.0 0 0.000 1.0 0.000
#> SRR1047823 4 0.0000 0.922 0.0 0 0.000 1.0 0.000
#> SRR1047824 4 0.0000 0.922 0.0 0 0.000 1.0 0.000
#> SRR1047825 4 0.0000 0.922 0.0 0 0.000 1.0 0.000
#> SRR1047826 4 0.0000 0.922 0.0 0 0.000 1.0 0.000
#> SRR1047827 4 0.0000 0.922 0.0 0 0.000 1.0 0.000
#> SRR1047828 1 0.0000 1.000 1.0 0 0.000 0.0 0.000
#> SRR1047829 1 0.0000 1.000 1.0 0 0.000 0.0 0.000
#> SRR1047830 1 0.0000 1.000 1.0 0 0.000 0.0 0.000
#> SRR1047831 1 0.0000 1.000 1.0 0 0.000 0.0 0.000
#> SRR1047832 1 0.0000 1.000 1.0 0 0.000 0.0 0.000
#> SRR1047833 2 0.0000 1.000 0.0 1 0.000 0.0 0.000
#> SRR1047834 2 0.0000 1.000 0.0 1 0.000 0.0 0.000
#> SRR1047835 2 0.0000 1.000 0.0 1 0.000 0.0 0.000
#> SRR1047836 2 0.0000 1.000 0.0 1 0.000 0.0 0.000
#> SRR1047837 2 0.0000 1.000 0.0 1 0.000 0.0 0.000
#> SRR1047838 4 0.0000 0.922 0.0 0 0.000 1.0 0.000
#> SRR1047839 4 0.0000 0.922 0.0 0 0.000 1.0 0.000
#> SRR1047840 4 0.0000 0.922 0.0 0 0.000 1.0 0.000
#> SRR1047841 4 0.0000 0.922 0.0 0 0.000 1.0 0.000
#> SRR1047842 4 0.0000 0.922 0.0 0 0.000 1.0 0.000
#> SRR1047843 1 0.0000 1.000 1.0 0 0.000 0.0 0.000
#> SRR1047844 1 0.0000 1.000 1.0 0 0.000 0.0 0.000
#> SRR1047845 1 0.0000 1.000 1.0 0 0.000 0.0 0.000
#> SRR1047846 1 0.0000 1.000 1.0 0 0.000 0.0 0.000
#> SRR1047847 1 0.0000 1.000 1.0 0 0.000 0.0 0.000
#> SRR1047848 1 0.0000 1.000 1.0 0 0.000 0.0 0.000
#> SRR1047849 1 0.0000 1.000 1.0 0 0.000 0.0 0.000
#> SRR1047850 1 0.0000 1.000 1.0 0 0.000 0.0 0.000
#> SRR1047851 1 0.0000 1.000 1.0 0 0.000 0.0 0.000
#> SRR1047852 1 0.0000 1.000 1.0 0 0.000 0.0 0.000
#> SRR1047853 4 0.3109 0.750 0.2 0 0.000 0.8 0.000
#> SRR1047854 4 0.3109 0.750 0.2 0 0.000 0.8 0.000
#> SRR1047855 4 0.3109 0.750 0.2 0 0.000 0.8 0.000
#> SRR1047856 4 0.3109 0.750 0.2 0 0.000 0.8 0.000
#> SRR1047857 4 0.3109 0.750 0.2 0 0.000 0.8 0.000
#> SRR1047858 1 0.0000 1.000 1.0 0 0.000 0.0 0.000
#> SRR1047859 1 0.0000 1.000 1.0 0 0.000 0.0 0.000
#> SRR1047860 1 0.0000 1.000 1.0 0 0.000 0.0 0.000
#> SRR1047861 1 0.0000 1.000 1.0 0 0.000 0.0 0.000
#> SRR1047863 3 0.0510 0.987 0.0 0 0.984 0.0 0.016
#> SRR1047864 5 0.0000 1.000 0.0 0 0.000 0.0 1.000
#> SRR1047865 3 0.0162 0.993 0.0 0 0.996 0.0 0.004
#> SRR1047866 3 0.0162 0.993 0.0 0 0.996 0.0 0.004
#> SRR1047867 5 0.0000 1.000 0.0 0 0.000 0.0 1.000
#> SRR1047868 3 0.0000 0.993 0.0 0 1.000 0.0 0.000
#> SRR1047869 3 0.0162 0.993 0.0 0 0.996 0.0 0.004
#> SRR1047870 3 0.0510 0.987 0.0 0 0.984 0.0 0.016
#> SRR1047871 3 0.0510 0.987 0.0 0 0.984 0.0 0.016
#> SRR1047872 3 0.0000 0.993 0.0 0 1.000 0.0 0.000
#> SRR1047873 3 0.0000 0.993 0.0 0 1.000 0.0 0.000
#> SRR1047874 3 0.0000 0.993 0.0 0 1.000 0.0 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1047813 1 0.0000 1.000 1.0 0 0.000 0.0 0.000 0
#> SRR1047814 1 0.0000 1.000 1.0 0 0.000 0.0 0.000 0
#> SRR1047815 1 0.0000 1.000 1.0 0 0.000 0.0 0.000 0
#> SRR1047816 1 0.0000 1.000 1.0 0 0.000 0.0 0.000 0
#> SRR1047817 1 0.0000 1.000 1.0 0 0.000 0.0 0.000 0
#> SRR1047818 4 0.0000 0.922 0.0 0 0.000 1.0 0.000 0
#> SRR1047819 4 0.0000 0.922 0.0 0 0.000 1.0 0.000 0
#> SRR1047820 4 0.0000 0.922 0.0 0 0.000 1.0 0.000 0
#> SRR1047821 4 0.0000 0.922 0.0 0 0.000 1.0 0.000 0
#> SRR1047822 4 0.0000 0.922 0.0 0 0.000 1.0 0.000 0
#> SRR1047823 4 0.0000 0.922 0.0 0 0.000 1.0 0.000 0
#> SRR1047824 4 0.0000 0.922 0.0 0 0.000 1.0 0.000 0
#> SRR1047825 4 0.0000 0.922 0.0 0 0.000 1.0 0.000 0
#> SRR1047826 4 0.0000 0.922 0.0 0 0.000 1.0 0.000 0
#> SRR1047827 4 0.0000 0.922 0.0 0 0.000 1.0 0.000 0
#> SRR1047828 1 0.0000 1.000 1.0 0 0.000 0.0 0.000 0
#> SRR1047829 1 0.0000 1.000 1.0 0 0.000 0.0 0.000 0
#> SRR1047830 1 0.0000 1.000 1.0 0 0.000 0.0 0.000 0
#> SRR1047831 1 0.0000 1.000 1.0 0 0.000 0.0 0.000 0
#> SRR1047832 1 0.0000 1.000 1.0 0 0.000 0.0 0.000 0
#> SRR1047833 2 0.0000 1.000 0.0 1 0.000 0.0 0.000 0
#> SRR1047834 2 0.0000 1.000 0.0 1 0.000 0.0 0.000 0
#> SRR1047835 2 0.0000 1.000 0.0 1 0.000 0.0 0.000 0
#> SRR1047836 2 0.0000 1.000 0.0 1 0.000 0.0 0.000 0
#> SRR1047837 2 0.0000 1.000 0.0 1 0.000 0.0 0.000 0
#> SRR1047838 4 0.0000 0.922 0.0 0 0.000 1.0 0.000 0
#> SRR1047839 4 0.0000 0.922 0.0 0 0.000 1.0 0.000 0
#> SRR1047840 4 0.0000 0.922 0.0 0 0.000 1.0 0.000 0
#> SRR1047841 4 0.0000 0.922 0.0 0 0.000 1.0 0.000 0
#> SRR1047842 4 0.0000 0.922 0.0 0 0.000 1.0 0.000 0
#> SRR1047843 1 0.0000 1.000 1.0 0 0.000 0.0 0.000 0
#> SRR1047844 1 0.0000 1.000 1.0 0 0.000 0.0 0.000 0
#> SRR1047845 1 0.0000 1.000 1.0 0 0.000 0.0 0.000 0
#> SRR1047846 1 0.0000 1.000 1.0 0 0.000 0.0 0.000 0
#> SRR1047847 1 0.0000 1.000 1.0 0 0.000 0.0 0.000 0
#> SRR1047848 1 0.0000 1.000 1.0 0 0.000 0.0 0.000 0
#> SRR1047849 1 0.0000 1.000 1.0 0 0.000 0.0 0.000 0
#> SRR1047850 1 0.0000 1.000 1.0 0 0.000 0.0 0.000 0
#> SRR1047851 1 0.0000 1.000 1.0 0 0.000 0.0 0.000 0
#> SRR1047852 1 0.0000 1.000 1.0 0 0.000 0.0 0.000 0
#> SRR1047853 4 0.2793 0.750 0.2 0 0.000 0.8 0.000 0
#> SRR1047854 4 0.2793 0.750 0.2 0 0.000 0.8 0.000 0
#> SRR1047855 4 0.2793 0.750 0.2 0 0.000 0.8 0.000 0
#> SRR1047856 4 0.2793 0.750 0.2 0 0.000 0.8 0.000 0
#> SRR1047857 4 0.2793 0.750 0.2 0 0.000 0.8 0.000 0
#> SRR1047858 1 0.0000 1.000 1.0 0 0.000 0.0 0.000 0
#> SRR1047859 1 0.0000 1.000 1.0 0 0.000 0.0 0.000 0
#> SRR1047860 1 0.0000 1.000 1.0 0 0.000 0.0 0.000 0
#> SRR1047861 1 0.0000 1.000 1.0 0 0.000 0.0 0.000 0
#> SRR1047863 3 0.0458 0.989 0.0 0 0.984 0.0 0.016 0
#> SRR1047864 5 0.0000 1.000 0.0 0 0.000 0.0 1.000 0
#> SRR1047865 6 0.0000 1.000 0.0 0 0.000 0.0 0.000 1
#> SRR1047866 6 0.0000 1.000 0.0 0 0.000 0.0 0.000 1
#> SRR1047867 5 0.0000 1.000 0.0 0 0.000 0.0 1.000 0
#> SRR1047868 3 0.0000 0.992 0.0 0 1.000 0.0 0.000 0
#> SRR1047869 6 0.0000 1.000 0.0 0 0.000 0.0 0.000 1
#> SRR1047870 3 0.0458 0.989 0.0 0 0.984 0.0 0.016 0
#> SRR1047871 3 0.0458 0.989 0.0 0 0.984 0.0 0.016 0
#> SRR1047872 3 0.0000 0.992 0.0 0 1.000 0.0 0.000 0
#> SRR1047873 3 0.0000 0.992 0.0 0 1.000 0.0 0.000 0
#> SRR1047874 3 0.0000 0.992 0.0 0 1.000 0.0 0.000 0
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "kmeans"]
# you can also extract it by
# res = res_list["MAD:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 17931 rows and 61 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 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 0.163 0.486 0.774 0.3537 0.744 0.744
#> 3 3 0.255 0.577 0.679 0.6079 0.578 0.464
#> 4 4 0.659 0.910 0.895 0.2105 0.847 0.642
#> 5 5 0.723 0.811 0.838 0.0932 1.000 1.000
#> 6 6 0.728 0.594 0.679 0.0560 0.885 0.613
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
#> SRR1047813 1 0.469 0.5847 0.900 0.100
#> SRR1047814 1 0.469 0.5847 0.900 0.100
#> SRR1047815 1 0.469 0.5847 0.900 0.100
#> SRR1047816 1 0.469 0.5847 0.900 0.100
#> SRR1047817 1 0.469 0.5847 0.900 0.100
#> SRR1047818 1 0.936 0.5170 0.648 0.352
#> SRR1047819 1 0.936 0.5170 0.648 0.352
#> SRR1047820 1 0.936 0.5170 0.648 0.352
#> SRR1047821 1 0.936 0.5170 0.648 0.352
#> SRR1047822 1 0.936 0.5170 0.648 0.352
#> SRR1047823 1 0.895 0.5450 0.688 0.312
#> SRR1047824 1 0.895 0.5450 0.688 0.312
#> SRR1047825 1 0.895 0.5450 0.688 0.312
#> SRR1047826 1 0.895 0.5450 0.688 0.312
#> SRR1047827 1 0.895 0.5450 0.688 0.312
#> SRR1047828 1 0.634 0.6134 0.840 0.160
#> SRR1047829 1 0.634 0.6134 0.840 0.160
#> SRR1047830 1 0.634 0.6134 0.840 0.160
#> SRR1047831 1 0.634 0.6134 0.840 0.160
#> SRR1047832 1 0.634 0.6134 0.840 0.160
#> SRR1047833 2 0.827 0.6622 0.260 0.740
#> SRR1047834 2 0.827 0.6622 0.260 0.740
#> SRR1047835 2 0.827 0.6622 0.260 0.740
#> SRR1047836 2 0.827 0.6622 0.260 0.740
#> SRR1047837 2 0.827 0.6622 0.260 0.740
#> SRR1047838 1 0.866 0.5832 0.712 0.288
#> SRR1047839 1 0.866 0.5832 0.712 0.288
#> SRR1047840 1 0.866 0.5832 0.712 0.288
#> SRR1047841 1 0.866 0.5832 0.712 0.288
#> SRR1047842 1 0.866 0.5832 0.712 0.288
#> SRR1047843 1 0.278 0.6360 0.952 0.048
#> SRR1047844 1 0.295 0.6348 0.948 0.052
#> SRR1047845 1 0.278 0.6360 0.952 0.048
#> SRR1047846 1 0.278 0.6360 0.952 0.048
#> SRR1047847 1 0.295 0.6348 0.948 0.052
#> SRR1047848 1 0.388 0.6071 0.924 0.076
#> SRR1047849 1 0.388 0.6071 0.924 0.076
#> SRR1047850 1 0.388 0.6071 0.924 0.076
#> SRR1047851 1 0.388 0.6071 0.924 0.076
#> SRR1047852 1 0.388 0.6071 0.924 0.076
#> SRR1047853 1 0.745 0.6099 0.788 0.212
#> SRR1047854 1 0.745 0.6099 0.788 0.212
#> SRR1047855 1 0.745 0.6099 0.788 0.212
#> SRR1047856 1 0.745 0.6099 0.788 0.212
#> SRR1047857 1 0.745 0.6099 0.788 0.212
#> SRR1047858 1 0.000 0.6417 1.000 0.000
#> SRR1047859 1 0.000 0.6417 1.000 0.000
#> SRR1047860 1 0.000 0.6417 1.000 0.000
#> SRR1047861 1 0.000 0.6417 1.000 0.000
#> SRR1047863 1 1.000 -0.0895 0.508 0.492
#> SRR1047864 2 0.999 0.0379 0.480 0.520
#> SRR1047865 1 0.949 0.0689 0.632 0.368
#> SRR1047866 1 0.952 0.0641 0.628 0.372
#> SRR1047867 2 0.456 0.5579 0.096 0.904
#> SRR1047868 1 1.000 -0.0868 0.508 0.492
#> SRR1047869 1 0.949 0.0689 0.632 0.368
#> SRR1047870 2 1.000 -0.0301 0.496 0.504
#> SRR1047871 1 0.998 -0.0670 0.524 0.476
#> SRR1047872 2 1.000 -0.0350 0.500 0.500
#> SRR1047873 1 1.000 -0.0868 0.508 0.492
#> SRR1047874 1 1.000 -0.0868 0.508 0.492
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1047813 1 0.6742 0.7455 0.708 0.052 0.240
#> SRR1047814 1 0.6742 0.7455 0.708 0.052 0.240
#> SRR1047815 1 0.6742 0.7455 0.708 0.052 0.240
#> SRR1047816 1 0.6742 0.7455 0.708 0.052 0.240
#> SRR1047817 1 0.6742 0.7455 0.708 0.052 0.240
#> SRR1047818 3 0.0237 0.6718 0.000 0.004 0.996
#> SRR1047819 3 0.0237 0.6718 0.000 0.004 0.996
#> SRR1047820 3 0.0237 0.6718 0.000 0.004 0.996
#> SRR1047821 3 0.0237 0.6718 0.000 0.004 0.996
#> SRR1047822 3 0.0237 0.6718 0.000 0.004 0.996
#> SRR1047823 3 0.3845 0.5447 0.116 0.012 0.872
#> SRR1047824 3 0.3845 0.5447 0.116 0.012 0.872
#> SRR1047825 3 0.3845 0.5447 0.116 0.012 0.872
#> SRR1047826 3 0.3845 0.5447 0.116 0.012 0.872
#> SRR1047827 3 0.3845 0.5447 0.116 0.012 0.872
#> SRR1047828 1 0.7600 0.6885 0.600 0.056 0.344
#> SRR1047829 1 0.7600 0.6885 0.600 0.056 0.344
#> SRR1047830 1 0.7600 0.6885 0.600 0.056 0.344
#> SRR1047831 1 0.7600 0.6885 0.600 0.056 0.344
#> SRR1047832 1 0.7600 0.6885 0.600 0.056 0.344
#> SRR1047833 2 0.7319 0.8899 0.128 0.708 0.164
#> SRR1047834 2 0.7319 0.8899 0.128 0.708 0.164
#> SRR1047835 2 0.7319 0.8899 0.128 0.708 0.164
#> SRR1047836 2 0.7319 0.8899 0.128 0.708 0.164
#> SRR1047837 2 0.7319 0.8899 0.128 0.708 0.164
#> SRR1047838 3 0.0237 0.6704 0.004 0.000 0.996
#> SRR1047839 3 0.0000 0.6715 0.000 0.000 1.000
#> SRR1047840 3 0.0237 0.6704 0.004 0.000 0.996
#> SRR1047841 3 0.0237 0.6704 0.004 0.000 0.996
#> SRR1047842 3 0.0237 0.6704 0.004 0.000 0.996
#> SRR1047843 1 0.5835 0.7016 0.660 0.000 0.340
#> SRR1047844 1 0.6215 0.5876 0.572 0.000 0.428
#> SRR1047845 1 0.5835 0.7016 0.660 0.000 0.340
#> SRR1047846 1 0.5835 0.7016 0.660 0.000 0.340
#> SRR1047847 1 0.6215 0.5876 0.572 0.000 0.428
#> SRR1047848 1 0.6335 0.7482 0.724 0.036 0.240
#> SRR1047849 1 0.6335 0.7482 0.724 0.036 0.240
#> SRR1047850 1 0.6335 0.7482 0.724 0.036 0.240
#> SRR1047851 1 0.6335 0.7482 0.724 0.036 0.240
#> SRR1047852 1 0.6335 0.7482 0.724 0.036 0.240
#> SRR1047853 3 0.3918 0.5860 0.120 0.012 0.868
#> SRR1047854 3 0.3989 0.5831 0.124 0.012 0.864
#> SRR1047855 3 0.3989 0.5831 0.124 0.012 0.864
#> SRR1047856 3 0.3918 0.5860 0.120 0.012 0.868
#> SRR1047857 3 0.3918 0.5860 0.120 0.012 0.868
#> SRR1047858 1 0.5902 0.7146 0.680 0.004 0.316
#> SRR1047859 1 0.5902 0.7146 0.680 0.004 0.316
#> SRR1047860 1 0.5902 0.7146 0.680 0.004 0.316
#> SRR1047861 1 0.5902 0.7146 0.680 0.004 0.316
#> SRR1047863 3 0.9991 0.1934 0.332 0.316 0.352
#> SRR1047864 1 0.9736 -0.2149 0.436 0.324 0.240
#> SRR1047865 1 0.9248 -0.1044 0.516 0.296 0.188
#> SRR1047866 1 0.8776 -0.0523 0.560 0.296 0.144
#> SRR1047867 2 0.5659 0.4459 0.248 0.740 0.012
#> SRR1047868 3 0.9989 0.1969 0.328 0.316 0.356
#> SRR1047869 1 0.9248 -0.1044 0.516 0.296 0.188
#> SRR1047870 3 0.9986 0.1947 0.320 0.320 0.360
#> SRR1047871 3 0.9991 0.1934 0.332 0.316 0.352
#> SRR1047872 3 0.9989 0.1969 0.328 0.316 0.356
#> SRR1047873 3 0.9989 0.1969 0.328 0.316 0.356
#> SRR1047874 3 0.9989 0.1969 0.328 0.316 0.356
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1047813 1 0.2844 0.886 0.900 0.048 0.052 0.000
#> SRR1047814 1 0.2844 0.886 0.900 0.048 0.052 0.000
#> SRR1047815 1 0.2844 0.886 0.900 0.048 0.052 0.000
#> SRR1047816 1 0.2844 0.886 0.900 0.048 0.052 0.000
#> SRR1047817 1 0.2844 0.886 0.900 0.048 0.052 0.000
#> SRR1047818 4 0.1767 0.937 0.044 0.012 0.000 0.944
#> SRR1047819 4 0.1767 0.937 0.044 0.012 0.000 0.944
#> SRR1047820 4 0.1767 0.937 0.044 0.012 0.000 0.944
#> SRR1047821 4 0.1767 0.937 0.044 0.012 0.000 0.944
#> SRR1047822 4 0.1767 0.937 0.044 0.012 0.000 0.944
#> SRR1047823 4 0.4105 0.902 0.056 0.040 0.048 0.856
#> SRR1047824 4 0.4105 0.902 0.056 0.040 0.048 0.856
#> SRR1047825 4 0.4105 0.902 0.056 0.040 0.048 0.856
#> SRR1047826 4 0.4105 0.902 0.056 0.040 0.048 0.856
#> SRR1047827 4 0.4105 0.902 0.056 0.040 0.048 0.856
#> SRR1047828 1 0.4840 0.848 0.808 0.024 0.060 0.108
#> SRR1047829 1 0.4840 0.848 0.808 0.024 0.060 0.108
#> SRR1047830 1 0.4840 0.848 0.808 0.024 0.060 0.108
#> SRR1047831 1 0.4840 0.848 0.808 0.024 0.060 0.108
#> SRR1047832 1 0.4840 0.848 0.808 0.024 0.060 0.108
#> SRR1047833 2 0.3761 1.000 0.020 0.868 0.044 0.068
#> SRR1047834 2 0.3761 1.000 0.020 0.868 0.044 0.068
#> SRR1047835 2 0.3761 1.000 0.020 0.868 0.044 0.068
#> SRR1047836 2 0.3761 1.000 0.020 0.868 0.044 0.068
#> SRR1047837 2 0.3761 1.000 0.020 0.868 0.044 0.068
#> SRR1047838 4 0.1302 0.938 0.044 0.000 0.000 0.956
#> SRR1047839 4 0.1302 0.938 0.044 0.000 0.000 0.956
#> SRR1047840 4 0.1302 0.938 0.044 0.000 0.000 0.956
#> SRR1047841 4 0.1302 0.938 0.044 0.000 0.000 0.956
#> SRR1047842 4 0.1302 0.938 0.044 0.000 0.000 0.956
#> SRR1047843 1 0.3574 0.893 0.876 0.044 0.016 0.064
#> SRR1047844 1 0.3722 0.888 0.868 0.044 0.016 0.072
#> SRR1047845 1 0.3574 0.893 0.876 0.044 0.016 0.064
#> SRR1047846 1 0.3574 0.893 0.876 0.044 0.016 0.064
#> SRR1047847 1 0.3722 0.888 0.868 0.044 0.016 0.072
#> SRR1047848 1 0.0657 0.903 0.984 0.004 0.012 0.000
#> SRR1047849 1 0.0657 0.903 0.984 0.004 0.012 0.000
#> SRR1047850 1 0.0657 0.903 0.984 0.004 0.012 0.000
#> SRR1047851 1 0.0657 0.903 0.984 0.004 0.012 0.000
#> SRR1047852 1 0.0657 0.903 0.984 0.004 0.012 0.000
#> SRR1047853 4 0.3404 0.891 0.104 0.000 0.032 0.864
#> SRR1047854 4 0.3404 0.891 0.104 0.000 0.032 0.864
#> SRR1047855 4 0.3404 0.891 0.104 0.000 0.032 0.864
#> SRR1047856 4 0.3404 0.891 0.104 0.000 0.032 0.864
#> SRR1047857 4 0.3404 0.891 0.104 0.000 0.032 0.864
#> SRR1047858 1 0.2310 0.901 0.932 0.032 0.020 0.016
#> SRR1047859 1 0.2310 0.901 0.932 0.032 0.020 0.016
#> SRR1047860 1 0.2310 0.901 0.932 0.032 0.020 0.016
#> SRR1047861 1 0.2310 0.901 0.932 0.032 0.020 0.016
#> SRR1047863 3 0.2281 0.937 0.000 0.000 0.904 0.096
#> SRR1047864 3 0.3505 0.909 0.012 0.016 0.864 0.108
#> SRR1047865 3 0.3761 0.893 0.068 0.020 0.868 0.044
#> SRR1047866 3 0.4448 0.870 0.076 0.020 0.832 0.072
#> SRR1047867 3 0.3974 0.830 0.008 0.108 0.844 0.040
#> SRR1047868 3 0.2345 0.937 0.000 0.000 0.900 0.100
#> SRR1047869 3 0.3761 0.893 0.068 0.020 0.868 0.044
#> SRR1047870 3 0.2530 0.934 0.004 0.000 0.896 0.100
#> SRR1047871 3 0.2401 0.937 0.004 0.000 0.904 0.092
#> SRR1047872 3 0.2345 0.937 0.000 0.000 0.900 0.100
#> SRR1047873 3 0.2345 0.937 0.000 0.000 0.900 0.100
#> SRR1047874 3 0.2345 0.937 0.000 0.000 0.900 0.100
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1047813 1 0.4039 0.693 0.720 0.008 0.000 0.004 0.268
#> SRR1047814 1 0.4039 0.693 0.720 0.008 0.000 0.004 0.268
#> SRR1047815 1 0.4039 0.693 0.720 0.008 0.000 0.004 0.268
#> SRR1047816 1 0.4039 0.693 0.720 0.008 0.000 0.004 0.268
#> SRR1047817 1 0.4039 0.693 0.720 0.008 0.000 0.004 0.268
#> SRR1047818 4 0.1628 0.865 0.000 0.000 0.008 0.936 0.056
#> SRR1047819 4 0.1628 0.865 0.000 0.000 0.008 0.936 0.056
#> SRR1047820 4 0.1628 0.865 0.000 0.000 0.008 0.936 0.056
#> SRR1047821 4 0.1628 0.865 0.000 0.000 0.008 0.936 0.056
#> SRR1047822 4 0.1628 0.865 0.000 0.000 0.008 0.936 0.056
#> SRR1047823 4 0.3918 0.762 0.008 0.000 0.008 0.752 0.232
#> SRR1047824 4 0.3918 0.762 0.008 0.000 0.008 0.752 0.232
#> SRR1047825 4 0.3918 0.762 0.008 0.000 0.008 0.752 0.232
#> SRR1047826 4 0.3918 0.762 0.008 0.000 0.008 0.752 0.232
#> SRR1047827 4 0.3918 0.762 0.008 0.000 0.008 0.752 0.232
#> SRR1047828 1 0.6691 0.631 0.500 0.000 0.020 0.152 0.328
#> SRR1047829 1 0.6691 0.631 0.500 0.000 0.020 0.152 0.328
#> SRR1047830 1 0.6691 0.631 0.500 0.000 0.020 0.152 0.328
#> SRR1047831 1 0.6691 0.631 0.500 0.000 0.020 0.152 0.328
#> SRR1047832 1 0.6691 0.631 0.500 0.000 0.020 0.152 0.328
#> SRR1047833 2 0.0963 1.000 0.000 0.964 0.000 0.036 0.000
#> SRR1047834 2 0.0963 1.000 0.000 0.964 0.000 0.036 0.000
#> SRR1047835 2 0.0963 1.000 0.000 0.964 0.000 0.036 0.000
#> SRR1047836 2 0.0963 1.000 0.000 0.964 0.000 0.036 0.000
#> SRR1047837 2 0.0963 1.000 0.000 0.964 0.000 0.036 0.000
#> SRR1047838 4 0.0290 0.871 0.000 0.000 0.008 0.992 0.000
#> SRR1047839 4 0.0290 0.871 0.000 0.000 0.008 0.992 0.000
#> SRR1047840 4 0.0290 0.871 0.000 0.000 0.008 0.992 0.000
#> SRR1047841 4 0.0290 0.871 0.000 0.000 0.008 0.992 0.000
#> SRR1047842 4 0.0290 0.871 0.000 0.000 0.008 0.992 0.000
#> SRR1047843 1 0.5336 0.698 0.632 0.000 0.012 0.052 0.304
#> SRR1047844 1 0.5397 0.696 0.628 0.000 0.012 0.056 0.304
#> SRR1047845 1 0.5336 0.698 0.632 0.000 0.012 0.052 0.304
#> SRR1047846 1 0.5336 0.698 0.632 0.000 0.012 0.052 0.304
#> SRR1047847 1 0.5397 0.696 0.628 0.000 0.012 0.056 0.304
#> SRR1047848 1 0.0693 0.747 0.980 0.012 0.000 0.008 0.000
#> SRR1047849 1 0.0693 0.747 0.980 0.012 0.000 0.008 0.000
#> SRR1047850 1 0.0693 0.747 0.980 0.012 0.000 0.008 0.000
#> SRR1047851 1 0.0693 0.747 0.980 0.012 0.000 0.008 0.000
#> SRR1047852 1 0.0693 0.747 0.980 0.012 0.000 0.008 0.000
#> SRR1047853 4 0.3753 0.807 0.020 0.000 0.036 0.828 0.116
#> SRR1047854 4 0.3753 0.807 0.020 0.000 0.036 0.828 0.116
#> SRR1047855 4 0.3753 0.807 0.020 0.000 0.036 0.828 0.116
#> SRR1047856 4 0.3753 0.807 0.020 0.000 0.036 0.828 0.116
#> SRR1047857 4 0.3753 0.807 0.020 0.000 0.036 0.828 0.116
#> SRR1047858 1 0.3004 0.736 0.860 0.004 0.008 0.008 0.120
#> SRR1047859 1 0.3004 0.736 0.860 0.004 0.008 0.008 0.120
#> SRR1047860 1 0.3004 0.736 0.860 0.004 0.008 0.008 0.120
#> SRR1047861 1 0.3004 0.736 0.860 0.004 0.008 0.008 0.120
#> SRR1047863 3 0.0404 0.948 0.000 0.000 0.988 0.012 0.000
#> SRR1047864 3 0.2956 0.891 0.000 0.004 0.848 0.008 0.140
#> SRR1047865 3 0.2043 0.926 0.008 0.012 0.928 0.004 0.048
#> SRR1047866 3 0.3519 0.878 0.008 0.012 0.820 0.004 0.156
#> SRR1047867 3 0.3238 0.878 0.000 0.028 0.836 0.000 0.136
#> SRR1047868 3 0.0609 0.949 0.000 0.000 0.980 0.020 0.000
#> SRR1047869 3 0.2043 0.926 0.008 0.012 0.928 0.004 0.048
#> SRR1047870 3 0.0609 0.949 0.000 0.000 0.980 0.020 0.000
#> SRR1047871 3 0.0404 0.948 0.000 0.000 0.988 0.012 0.000
#> SRR1047872 3 0.0609 0.949 0.000 0.000 0.980 0.020 0.000
#> SRR1047873 3 0.0609 0.949 0.000 0.000 0.980 0.020 0.000
#> SRR1047874 3 0.0609 0.949 0.000 0.000 0.980 0.020 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1047813 5 0.4342 0.1066 0.308 0.008 0.000 0.000 0.656 0.028
#> SRR1047814 5 0.4342 0.1066 0.308 0.008 0.000 0.000 0.656 0.028
#> SRR1047815 5 0.4342 0.1066 0.308 0.008 0.000 0.000 0.656 0.028
#> SRR1047816 5 0.4342 0.1066 0.308 0.008 0.000 0.000 0.656 0.028
#> SRR1047817 5 0.4342 0.1066 0.308 0.008 0.000 0.000 0.656 0.028
#> SRR1047818 4 0.4693 0.4619 0.028 0.004 0.000 0.540 0.004 0.424
#> SRR1047819 4 0.4693 0.4619 0.028 0.004 0.000 0.540 0.004 0.424
#> SRR1047820 4 0.4693 0.4619 0.028 0.004 0.000 0.540 0.004 0.424
#> SRR1047821 4 0.4693 0.4619 0.028 0.004 0.000 0.540 0.004 0.424
#> SRR1047822 4 0.4693 0.4619 0.028 0.004 0.000 0.540 0.004 0.424
#> SRR1047823 4 0.0725 0.4180 0.012 0.000 0.000 0.976 0.012 0.000
#> SRR1047824 4 0.0260 0.4213 0.000 0.000 0.000 0.992 0.008 0.000
#> SRR1047825 4 0.0260 0.4213 0.000 0.000 0.000 0.992 0.008 0.000
#> SRR1047826 4 0.0260 0.4213 0.000 0.000 0.000 0.992 0.008 0.000
#> SRR1047827 4 0.0260 0.4213 0.000 0.000 0.000 0.992 0.008 0.000
#> SRR1047828 5 0.3488 0.4268 0.000 0.000 0.028 0.076 0.832 0.064
#> SRR1047829 5 0.3488 0.4268 0.000 0.000 0.028 0.076 0.832 0.064
#> SRR1047830 5 0.3488 0.4268 0.000 0.000 0.028 0.076 0.832 0.064
#> SRR1047831 5 0.3488 0.4268 0.000 0.000 0.028 0.076 0.832 0.064
#> SRR1047832 5 0.3488 0.4268 0.000 0.000 0.028 0.076 0.832 0.064
#> SRR1047833 2 0.0972 0.9976 0.000 0.964 0.000 0.028 0.008 0.000
#> SRR1047834 2 0.0858 0.9994 0.000 0.968 0.000 0.028 0.004 0.000
#> SRR1047835 2 0.0858 0.9994 0.000 0.968 0.000 0.028 0.004 0.000
#> SRR1047836 2 0.0858 0.9994 0.000 0.968 0.000 0.028 0.004 0.000
#> SRR1047837 2 0.0858 0.9994 0.000 0.968 0.000 0.028 0.004 0.000
#> SRR1047838 4 0.3937 0.4142 0.004 0.000 0.000 0.572 0.000 0.424
#> SRR1047839 4 0.3944 0.4076 0.004 0.000 0.000 0.568 0.000 0.428
#> SRR1047840 4 0.3937 0.4142 0.004 0.000 0.000 0.572 0.000 0.424
#> SRR1047841 4 0.3937 0.4142 0.004 0.000 0.000 0.572 0.000 0.424
#> SRR1047842 4 0.3937 0.4142 0.004 0.000 0.000 0.572 0.000 0.424
#> SRR1047843 5 0.6488 0.0821 0.352 0.000 0.000 0.020 0.372 0.256
#> SRR1047844 5 0.6488 0.0821 0.352 0.000 0.000 0.020 0.372 0.256
#> SRR1047845 5 0.6488 0.0821 0.352 0.000 0.000 0.020 0.372 0.256
#> SRR1047846 5 0.6488 0.0821 0.352 0.000 0.000 0.020 0.372 0.256
#> SRR1047847 5 0.6488 0.0821 0.352 0.000 0.000 0.020 0.372 0.256
#> SRR1047848 1 0.3707 0.7454 0.680 0.000 0.000 0.008 0.312 0.000
#> SRR1047849 1 0.3707 0.7454 0.680 0.000 0.000 0.008 0.312 0.000
#> SRR1047850 1 0.3707 0.7454 0.680 0.000 0.000 0.008 0.312 0.000
#> SRR1047851 1 0.3707 0.7454 0.680 0.000 0.000 0.008 0.312 0.000
#> SRR1047852 1 0.3707 0.7454 0.680 0.000 0.000 0.008 0.312 0.000
#> SRR1047853 6 0.6830 1.0000 0.024 0.000 0.032 0.356 0.160 0.428
#> SRR1047854 6 0.6830 1.0000 0.024 0.000 0.032 0.356 0.160 0.428
#> SRR1047855 6 0.6830 1.0000 0.024 0.000 0.032 0.356 0.160 0.428
#> SRR1047856 6 0.6830 1.0000 0.024 0.000 0.032 0.356 0.160 0.428
#> SRR1047857 6 0.6830 1.0000 0.024 0.000 0.032 0.356 0.160 0.428
#> SRR1047858 1 0.5572 0.6764 0.588 0.016 0.000 0.004 0.284 0.108
#> SRR1047859 1 0.5572 0.6764 0.588 0.016 0.000 0.004 0.284 0.108
#> SRR1047860 1 0.5572 0.6764 0.588 0.016 0.000 0.004 0.284 0.108
#> SRR1047861 1 0.5572 0.6764 0.588 0.016 0.000 0.004 0.284 0.108
#> SRR1047863 3 0.0405 0.8967 0.004 0.000 0.988 0.000 0.000 0.008
#> SRR1047864 3 0.5002 0.7672 0.076 0.000 0.692 0.000 0.040 0.192
#> SRR1047865 3 0.3506 0.8464 0.088 0.004 0.828 0.000 0.012 0.068
#> SRR1047866 3 0.5304 0.7585 0.136 0.004 0.656 0.000 0.016 0.188
#> SRR1047867 3 0.5002 0.7672 0.076 0.000 0.692 0.000 0.040 0.192
#> SRR1047868 3 0.0520 0.8976 0.008 0.000 0.984 0.000 0.000 0.008
#> SRR1047869 3 0.3506 0.8464 0.088 0.004 0.828 0.000 0.012 0.068
#> SRR1047870 3 0.0820 0.8958 0.012 0.000 0.972 0.000 0.000 0.016
#> SRR1047871 3 0.0000 0.8976 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047872 3 0.0520 0.8976 0.008 0.000 0.984 0.000 0.000 0.008
#> SRR1047873 3 0.0520 0.8976 0.008 0.000 0.984 0.000 0.000 0.008
#> SRR1047874 3 0.0520 0.8976 0.008 0.000 0.984 0.000 0.000 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 17931 rows and 61 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 0.515 0.716 0.876 0.5059 0.498 0.498
#> 3 3 0.808 0.940 0.959 0.3245 0.785 0.587
#> 4 4 1.000 0.991 0.994 0.1073 0.896 0.698
#> 5 5 0.852 0.870 0.891 0.0498 0.984 0.936
#> 6 6 0.831 0.866 0.882 0.0490 0.907 0.635
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
#> SRR1047813 1 0.000 0.864 1.000 0.000
#> SRR1047814 1 0.000 0.864 1.000 0.000
#> SRR1047815 1 0.000 0.864 1.000 0.000
#> SRR1047816 1 0.000 0.864 1.000 0.000
#> SRR1047817 1 0.000 0.864 1.000 0.000
#> SRR1047818 2 0.000 0.815 0.000 1.000
#> SRR1047819 2 0.000 0.815 0.000 1.000
#> SRR1047820 2 0.000 0.815 0.000 1.000
#> SRR1047821 2 0.000 0.815 0.000 1.000
#> SRR1047822 2 0.000 0.815 0.000 1.000
#> SRR1047823 2 0.992 0.401 0.448 0.552
#> SRR1047824 2 0.992 0.401 0.448 0.552
#> SRR1047825 2 0.992 0.401 0.448 0.552
#> SRR1047826 2 0.992 0.401 0.448 0.552
#> SRR1047827 2 0.992 0.401 0.448 0.552
#> SRR1047828 1 0.000 0.864 1.000 0.000
#> SRR1047829 1 0.000 0.864 1.000 0.000
#> SRR1047830 1 0.000 0.864 1.000 0.000
#> SRR1047831 1 0.000 0.864 1.000 0.000
#> SRR1047832 1 0.000 0.864 1.000 0.000
#> SRR1047833 2 0.969 0.487 0.396 0.604
#> SRR1047834 2 0.969 0.487 0.396 0.604
#> SRR1047835 2 0.969 0.487 0.396 0.604
#> SRR1047836 2 0.969 0.487 0.396 0.604
#> SRR1047837 2 0.969 0.487 0.396 0.604
#> SRR1047838 2 0.000 0.815 0.000 1.000
#> SRR1047839 2 0.000 0.815 0.000 1.000
#> SRR1047840 2 0.000 0.815 0.000 1.000
#> SRR1047841 2 0.000 0.815 0.000 1.000
#> SRR1047842 2 0.000 0.815 0.000 1.000
#> SRR1047843 1 0.689 0.717 0.816 0.184
#> SRR1047844 1 0.969 0.420 0.604 0.396
#> SRR1047845 1 0.689 0.717 0.816 0.184
#> SRR1047846 1 0.689 0.717 0.816 0.184
#> SRR1047847 1 0.969 0.420 0.604 0.396
#> SRR1047848 1 0.000 0.864 1.000 0.000
#> SRR1047849 1 0.000 0.864 1.000 0.000
#> SRR1047850 1 0.000 0.864 1.000 0.000
#> SRR1047851 1 0.000 0.864 1.000 0.000
#> SRR1047852 1 0.000 0.864 1.000 0.000
#> SRR1047853 2 0.000 0.815 0.000 1.000
#> SRR1047854 2 0.000 0.815 0.000 1.000
#> SRR1047855 2 0.000 0.815 0.000 1.000
#> SRR1047856 2 0.000 0.815 0.000 1.000
#> SRR1047857 2 0.000 0.815 0.000 1.000
#> SRR1047858 1 0.000 0.864 1.000 0.000
#> SRR1047859 1 0.000 0.864 1.000 0.000
#> SRR1047860 1 0.000 0.864 1.000 0.000
#> SRR1047861 1 0.000 0.864 1.000 0.000
#> SRR1047863 2 0.184 0.795 0.028 0.972
#> SRR1047864 2 0.767 0.567 0.224 0.776
#> SRR1047865 1 0.993 0.313 0.548 0.452
#> SRR1047866 1 0.992 0.320 0.552 0.448
#> SRR1047867 2 0.714 0.612 0.196 0.804
#> SRR1047868 2 0.000 0.815 0.000 1.000
#> SRR1047869 1 0.993 0.313 0.548 0.452
#> SRR1047870 2 0.000 0.815 0.000 1.000
#> SRR1047871 2 0.706 0.616 0.192 0.808
#> SRR1047872 2 0.000 0.815 0.000 1.000
#> SRR1047873 2 0.000 0.815 0.000 1.000
#> SRR1047874 2 0.000 0.815 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1047813 1 0.0000 0.958 1.000 0.000 0.000
#> SRR1047814 1 0.0000 0.958 1.000 0.000 0.000
#> SRR1047815 1 0.0000 0.958 1.000 0.000 0.000
#> SRR1047816 1 0.0000 0.958 1.000 0.000 0.000
#> SRR1047817 1 0.0000 0.958 1.000 0.000 0.000
#> SRR1047818 2 0.0000 0.986 0.000 1.000 0.000
#> SRR1047819 2 0.0000 0.986 0.000 1.000 0.000
#> SRR1047820 2 0.0000 0.986 0.000 1.000 0.000
#> SRR1047821 2 0.0000 0.986 0.000 1.000 0.000
#> SRR1047822 2 0.0000 0.986 0.000 1.000 0.000
#> SRR1047823 2 0.1411 0.964 0.036 0.964 0.000
#> SRR1047824 2 0.1411 0.964 0.036 0.964 0.000
#> SRR1047825 2 0.1411 0.964 0.036 0.964 0.000
#> SRR1047826 2 0.1411 0.964 0.036 0.964 0.000
#> SRR1047827 2 0.1411 0.964 0.036 0.964 0.000
#> SRR1047828 1 0.3619 0.875 0.864 0.000 0.136
#> SRR1047829 1 0.3619 0.875 0.864 0.000 0.136
#> SRR1047830 1 0.3619 0.875 0.864 0.000 0.136
#> SRR1047831 1 0.3619 0.875 0.864 0.000 0.136
#> SRR1047832 1 0.3619 0.875 0.864 0.000 0.136
#> SRR1047833 3 0.2339 0.907 0.048 0.012 0.940
#> SRR1047834 3 0.2339 0.907 0.048 0.012 0.940
#> SRR1047835 3 0.2339 0.907 0.048 0.012 0.940
#> SRR1047836 3 0.2339 0.907 0.048 0.012 0.940
#> SRR1047837 3 0.2339 0.907 0.048 0.012 0.940
#> SRR1047838 2 0.0000 0.986 0.000 1.000 0.000
#> SRR1047839 2 0.0000 0.986 0.000 1.000 0.000
#> SRR1047840 2 0.0000 0.986 0.000 1.000 0.000
#> SRR1047841 2 0.0000 0.986 0.000 1.000 0.000
#> SRR1047842 2 0.0000 0.986 0.000 1.000 0.000
#> SRR1047843 1 0.1753 0.934 0.952 0.000 0.048
#> SRR1047844 1 0.1989 0.932 0.948 0.004 0.048
#> SRR1047845 1 0.1753 0.934 0.952 0.000 0.048
#> SRR1047846 1 0.1753 0.934 0.952 0.000 0.048
#> SRR1047847 1 0.1989 0.932 0.948 0.004 0.048
#> SRR1047848 1 0.0000 0.958 1.000 0.000 0.000
#> SRR1047849 1 0.0000 0.958 1.000 0.000 0.000
#> SRR1047850 1 0.0000 0.958 1.000 0.000 0.000
#> SRR1047851 1 0.0000 0.958 1.000 0.000 0.000
#> SRR1047852 1 0.0000 0.958 1.000 0.000 0.000
#> SRR1047853 2 0.0424 0.983 0.000 0.992 0.008
#> SRR1047854 2 0.0424 0.983 0.000 0.992 0.008
#> SRR1047855 2 0.0424 0.983 0.000 0.992 0.008
#> SRR1047856 2 0.0424 0.983 0.000 0.992 0.008
#> SRR1047857 2 0.0424 0.983 0.000 0.992 0.008
#> SRR1047858 1 0.0000 0.958 1.000 0.000 0.000
#> SRR1047859 1 0.0000 0.958 1.000 0.000 0.000
#> SRR1047860 1 0.0000 0.958 1.000 0.000 0.000
#> SRR1047861 1 0.0000 0.958 1.000 0.000 0.000
#> SRR1047863 3 0.1643 0.920 0.000 0.044 0.956
#> SRR1047864 3 0.0000 0.916 0.000 0.000 1.000
#> SRR1047865 3 0.4335 0.882 0.100 0.036 0.864
#> SRR1047866 3 0.2959 0.883 0.100 0.000 0.900
#> SRR1047867 3 0.0000 0.916 0.000 0.000 1.000
#> SRR1047868 3 0.3619 0.877 0.000 0.136 0.864
#> SRR1047869 3 0.4335 0.882 0.100 0.036 0.864
#> SRR1047870 3 0.1643 0.920 0.000 0.044 0.956
#> SRR1047871 3 0.1643 0.920 0.000 0.044 0.956
#> SRR1047872 3 0.3619 0.877 0.000 0.136 0.864
#> SRR1047873 3 0.3619 0.877 0.000 0.136 0.864
#> SRR1047874 3 0.3619 0.877 0.000 0.136 0.864
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1047813 1 0.0336 0.991 0.992 0.008 0.000 0.000
#> SRR1047814 1 0.0336 0.991 0.992 0.008 0.000 0.000
#> SRR1047815 1 0.0336 0.991 0.992 0.008 0.000 0.000
#> SRR1047816 1 0.0336 0.991 0.992 0.008 0.000 0.000
#> SRR1047817 1 0.0336 0.991 0.992 0.008 0.000 0.000
#> SRR1047818 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> SRR1047819 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> SRR1047820 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> SRR1047821 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> SRR1047822 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> SRR1047823 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> SRR1047824 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> SRR1047825 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> SRR1047826 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> SRR1047827 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> SRR1047828 2 0.1211 0.972 0.040 0.960 0.000 0.000
#> SRR1047829 2 0.1211 0.972 0.040 0.960 0.000 0.000
#> SRR1047830 2 0.1211 0.972 0.040 0.960 0.000 0.000
#> SRR1047831 2 0.1211 0.972 0.040 0.960 0.000 0.000
#> SRR1047832 2 0.1211 0.972 0.040 0.960 0.000 0.000
#> SRR1047833 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> SRR1047834 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> SRR1047835 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> SRR1047836 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> SRR1047837 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> SRR1047838 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> SRR1047839 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> SRR1047840 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> SRR1047841 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> SRR1047842 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> SRR1047843 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> SRR1047844 1 0.1118 0.961 0.964 0.000 0.036 0.000
#> SRR1047845 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> SRR1047846 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> SRR1047847 1 0.1118 0.961 0.964 0.000 0.036 0.000
#> SRR1047848 1 0.0188 0.993 0.996 0.004 0.000 0.000
#> SRR1047849 1 0.0188 0.993 0.996 0.004 0.000 0.000
#> SRR1047850 1 0.0188 0.993 0.996 0.004 0.000 0.000
#> SRR1047851 1 0.0188 0.993 0.996 0.004 0.000 0.000
#> SRR1047852 1 0.0188 0.993 0.996 0.004 0.000 0.000
#> SRR1047853 4 0.0376 0.994 0.004 0.000 0.004 0.992
#> SRR1047854 4 0.0188 0.996 0.004 0.000 0.000 0.996
#> SRR1047855 4 0.0188 0.996 0.004 0.000 0.000 0.996
#> SRR1047856 4 0.0376 0.994 0.004 0.000 0.004 0.992
#> SRR1047857 4 0.0376 0.994 0.004 0.000 0.004 0.992
#> SRR1047858 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> SRR1047859 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> SRR1047860 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> SRR1047861 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> SRR1047863 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR1047864 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR1047865 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR1047866 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR1047867 2 0.0469 0.968 0.000 0.988 0.012 0.000
#> SRR1047868 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR1047869 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR1047870 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR1047871 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR1047872 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR1047873 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> SRR1047874 3 0.0000 1.000 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
#> SRR1047813 1 0.4294 0.424 0.532 0.000 0.000 0.000 0.468
#> SRR1047814 1 0.4294 0.424 0.532 0.000 0.000 0.000 0.468
#> SRR1047815 1 0.4294 0.424 0.532 0.000 0.000 0.000 0.468
#> SRR1047816 1 0.4294 0.424 0.532 0.000 0.000 0.000 0.468
#> SRR1047817 1 0.4294 0.424 0.532 0.000 0.000 0.000 0.468
#> SRR1047818 4 0.0000 0.928 0.000 0.000 0.000 1.000 0.000
#> SRR1047819 4 0.0000 0.928 0.000 0.000 0.000 1.000 0.000
#> SRR1047820 4 0.0000 0.928 0.000 0.000 0.000 1.000 0.000
#> SRR1047821 4 0.0000 0.928 0.000 0.000 0.000 1.000 0.000
#> SRR1047822 4 0.0000 0.928 0.000 0.000 0.000 1.000 0.000
#> SRR1047823 4 0.0963 0.917 0.000 0.000 0.000 0.964 0.036
#> SRR1047824 4 0.0963 0.917 0.000 0.000 0.000 0.964 0.036
#> SRR1047825 4 0.0963 0.917 0.000 0.000 0.000 0.964 0.036
#> SRR1047826 4 0.0963 0.917 0.000 0.000 0.000 0.964 0.036
#> SRR1047827 4 0.0963 0.917 0.000 0.000 0.000 0.964 0.036
#> SRR1047828 5 0.4270 1.000 0.012 0.320 0.000 0.000 0.668
#> SRR1047829 5 0.4270 1.000 0.012 0.320 0.000 0.000 0.668
#> SRR1047830 5 0.4270 1.000 0.012 0.320 0.000 0.000 0.668
#> SRR1047831 5 0.4270 1.000 0.012 0.320 0.000 0.000 0.668
#> SRR1047832 5 0.4270 1.000 0.012 0.320 0.000 0.000 0.668
#> SRR1047833 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047834 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047835 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047836 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047837 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047838 4 0.0000 0.928 0.000 0.000 0.000 1.000 0.000
#> SRR1047839 4 0.0000 0.928 0.000 0.000 0.000 1.000 0.000
#> SRR1047840 4 0.0000 0.928 0.000 0.000 0.000 1.000 0.000
#> SRR1047841 4 0.0000 0.928 0.000 0.000 0.000 1.000 0.000
#> SRR1047842 4 0.0000 0.928 0.000 0.000 0.000 1.000 0.000
#> SRR1047843 1 0.1341 0.795 0.944 0.000 0.000 0.000 0.056
#> SRR1047844 1 0.1341 0.795 0.944 0.000 0.000 0.000 0.056
#> SRR1047845 1 0.1341 0.795 0.944 0.000 0.000 0.000 0.056
#> SRR1047846 1 0.1341 0.795 0.944 0.000 0.000 0.000 0.056
#> SRR1047847 1 0.1341 0.795 0.944 0.000 0.000 0.000 0.056
#> SRR1047848 1 0.2127 0.798 0.892 0.000 0.000 0.000 0.108
#> SRR1047849 1 0.2127 0.798 0.892 0.000 0.000 0.000 0.108
#> SRR1047850 1 0.2127 0.798 0.892 0.000 0.000 0.000 0.108
#> SRR1047851 1 0.2127 0.798 0.892 0.000 0.000 0.000 0.108
#> SRR1047852 1 0.2127 0.798 0.892 0.000 0.000 0.000 0.108
#> SRR1047853 4 0.3715 0.787 0.000 0.000 0.004 0.736 0.260
#> SRR1047854 4 0.3715 0.787 0.000 0.000 0.004 0.736 0.260
#> SRR1047855 4 0.3715 0.787 0.000 0.000 0.004 0.736 0.260
#> SRR1047856 4 0.3715 0.787 0.000 0.000 0.004 0.736 0.260
#> SRR1047857 4 0.3715 0.787 0.000 0.000 0.004 0.736 0.260
#> SRR1047858 1 0.0000 0.808 1.000 0.000 0.000 0.000 0.000
#> SRR1047859 1 0.0000 0.808 1.000 0.000 0.000 0.000 0.000
#> SRR1047860 1 0.0000 0.808 1.000 0.000 0.000 0.000 0.000
#> SRR1047861 1 0.0000 0.808 1.000 0.000 0.000 0.000 0.000
#> SRR1047863 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> SRR1047864 3 0.0162 0.995 0.000 0.004 0.996 0.000 0.000
#> SRR1047865 3 0.0162 0.997 0.000 0.000 0.996 0.000 0.004
#> SRR1047866 3 0.0162 0.997 0.000 0.000 0.996 0.000 0.004
#> SRR1047867 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047868 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> SRR1047869 3 0.0162 0.997 0.000 0.000 0.996 0.000 0.004
#> SRR1047870 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> SRR1047871 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> SRR1047872 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> SRR1047873 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> SRR1047874 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1047813 5 0.4493 0.628 0.344 0.000 0.000 0.000 0.612 0.044
#> SRR1047814 5 0.4493 0.628 0.344 0.000 0.000 0.000 0.612 0.044
#> SRR1047815 5 0.4493 0.628 0.344 0.000 0.000 0.000 0.612 0.044
#> SRR1047816 5 0.4493 0.628 0.344 0.000 0.000 0.000 0.612 0.044
#> SRR1047817 5 0.4493 0.628 0.344 0.000 0.000 0.000 0.612 0.044
#> SRR1047818 4 0.0777 0.904 0.000 0.000 0.000 0.972 0.004 0.024
#> SRR1047819 4 0.0777 0.904 0.000 0.000 0.000 0.972 0.004 0.024
#> SRR1047820 4 0.0777 0.904 0.000 0.000 0.000 0.972 0.004 0.024
#> SRR1047821 4 0.0777 0.904 0.000 0.000 0.000 0.972 0.004 0.024
#> SRR1047822 4 0.0777 0.904 0.000 0.000 0.000 0.972 0.004 0.024
#> SRR1047823 4 0.2623 0.848 0.000 0.000 0.000 0.852 0.016 0.132
#> SRR1047824 4 0.2623 0.848 0.000 0.000 0.000 0.852 0.016 0.132
#> SRR1047825 4 0.2623 0.848 0.000 0.000 0.000 0.852 0.016 0.132
#> SRR1047826 4 0.2623 0.848 0.000 0.000 0.000 0.852 0.016 0.132
#> SRR1047827 4 0.2623 0.848 0.000 0.000 0.000 0.852 0.016 0.132
#> SRR1047828 5 0.1471 0.705 0.004 0.064 0.000 0.000 0.932 0.000
#> SRR1047829 5 0.1471 0.705 0.004 0.064 0.000 0.000 0.932 0.000
#> SRR1047830 5 0.1471 0.705 0.004 0.064 0.000 0.000 0.932 0.000
#> SRR1047831 5 0.1471 0.705 0.004 0.064 0.000 0.000 0.932 0.000
#> SRR1047832 5 0.1471 0.705 0.004 0.064 0.000 0.000 0.932 0.000
#> SRR1047833 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1047834 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1047835 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1047836 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1047837 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1047838 4 0.0146 0.912 0.000 0.000 0.000 0.996 0.000 0.004
#> SRR1047839 4 0.0146 0.912 0.000 0.000 0.000 0.996 0.000 0.004
#> SRR1047840 4 0.0146 0.912 0.000 0.000 0.000 0.996 0.000 0.004
#> SRR1047841 4 0.0146 0.912 0.000 0.000 0.000 0.996 0.000 0.004
#> SRR1047842 4 0.0146 0.912 0.000 0.000 0.000 0.996 0.000 0.004
#> SRR1047843 1 0.3168 0.775 0.804 0.000 0.000 0.000 0.024 0.172
#> SRR1047844 1 0.3168 0.775 0.804 0.000 0.000 0.000 0.024 0.172
#> SRR1047845 1 0.3168 0.775 0.804 0.000 0.000 0.000 0.024 0.172
#> SRR1047846 1 0.3168 0.775 0.804 0.000 0.000 0.000 0.024 0.172
#> SRR1047847 1 0.3168 0.775 0.804 0.000 0.000 0.000 0.024 0.172
#> SRR1047848 1 0.2909 0.744 0.836 0.000 0.000 0.000 0.136 0.028
#> SRR1047849 1 0.2909 0.744 0.836 0.000 0.000 0.000 0.136 0.028
#> SRR1047850 1 0.2909 0.744 0.836 0.000 0.000 0.000 0.136 0.028
#> SRR1047851 1 0.2909 0.744 0.836 0.000 0.000 0.000 0.136 0.028
#> SRR1047852 1 0.2909 0.744 0.836 0.000 0.000 0.000 0.136 0.028
#> SRR1047853 6 0.3426 1.000 0.000 0.000 0.004 0.276 0.000 0.720
#> SRR1047854 6 0.3426 1.000 0.000 0.000 0.004 0.276 0.000 0.720
#> SRR1047855 6 0.3426 1.000 0.000 0.000 0.004 0.276 0.000 0.720
#> SRR1047856 6 0.3426 1.000 0.000 0.000 0.004 0.276 0.000 0.720
#> SRR1047857 6 0.3426 1.000 0.000 0.000 0.004 0.276 0.000 0.720
#> SRR1047858 1 0.0146 0.819 0.996 0.000 0.000 0.000 0.004 0.000
#> SRR1047859 1 0.0146 0.819 0.996 0.000 0.000 0.000 0.004 0.000
#> SRR1047860 1 0.0146 0.819 0.996 0.000 0.000 0.000 0.004 0.000
#> SRR1047861 1 0.0146 0.819 0.996 0.000 0.000 0.000 0.004 0.000
#> SRR1047863 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047864 3 0.0146 0.996 0.000 0.004 0.996 0.000 0.000 0.000
#> SRR1047865 3 0.0146 0.997 0.000 0.000 0.996 0.000 0.000 0.004
#> SRR1047866 3 0.0146 0.997 0.000 0.000 0.996 0.000 0.000 0.004
#> SRR1047867 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1047868 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047869 3 0.0146 0.997 0.000 0.000 0.996 0.000 0.000 0.004
#> SRR1047870 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047871 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047872 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047873 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047874 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 17931 rows and 61 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.1811 0.820 0.820
#> 3 3 0.659 0.921 0.948 1.8355 0.686 0.617
#> 4 4 0.841 0.852 0.933 0.3542 0.654 0.396
#> 5 5 0.835 0.833 0.893 0.0795 0.818 0.506
#> 6 6 0.832 0.805 0.876 0.0599 0.936 0.755
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
#> SRR1047813 1 0 1 1 0
#> SRR1047814 1 0 1 1 0
#> SRR1047815 1 0 1 1 0
#> SRR1047816 1 0 1 1 0
#> SRR1047817 1 0 1 1 0
#> SRR1047818 1 0 1 1 0
#> SRR1047819 1 0 1 1 0
#> SRR1047820 1 0 1 1 0
#> SRR1047821 1 0 1 1 0
#> SRR1047822 1 0 1 1 0
#> SRR1047823 1 0 1 1 0
#> SRR1047824 1 0 1 1 0
#> SRR1047825 1 0 1 1 0
#> SRR1047826 1 0 1 1 0
#> SRR1047827 1 0 1 1 0
#> SRR1047828 1 0 1 1 0
#> SRR1047829 1 0 1 1 0
#> SRR1047830 1 0 1 1 0
#> SRR1047831 1 0 1 1 0
#> SRR1047832 1 0 1 1 0
#> SRR1047833 2 0 1 0 1
#> SRR1047834 2 0 1 0 1
#> SRR1047835 2 0 1 0 1
#> SRR1047836 2 0 1 0 1
#> SRR1047837 2 0 1 0 1
#> SRR1047838 1 0 1 1 0
#> SRR1047839 1 0 1 1 0
#> SRR1047840 1 0 1 1 0
#> SRR1047841 1 0 1 1 0
#> SRR1047842 1 0 1 1 0
#> SRR1047843 1 0 1 1 0
#> SRR1047844 1 0 1 1 0
#> SRR1047845 1 0 1 1 0
#> SRR1047846 1 0 1 1 0
#> SRR1047847 1 0 1 1 0
#> SRR1047848 1 0 1 1 0
#> SRR1047849 1 0 1 1 0
#> SRR1047850 1 0 1 1 0
#> SRR1047851 1 0 1 1 0
#> SRR1047852 1 0 1 1 0
#> SRR1047853 1 0 1 1 0
#> SRR1047854 1 0 1 1 0
#> SRR1047855 1 0 1 1 0
#> SRR1047856 1 0 1 1 0
#> SRR1047857 1 0 1 1 0
#> SRR1047858 1 0 1 1 0
#> SRR1047859 1 0 1 1 0
#> SRR1047860 1 0 1 1 0
#> SRR1047861 1 0 1 1 0
#> SRR1047863 1 0 1 1 0
#> SRR1047864 1 0 1 1 0
#> SRR1047865 1 0 1 1 0
#> SRR1047866 1 0 1 1 0
#> SRR1047867 2 0 1 0 1
#> SRR1047868 1 0 1 1 0
#> SRR1047869 1 0 1 1 0
#> SRR1047870 1 0 1 1 0
#> SRR1047871 1 0 1 1 0
#> SRR1047872 1 0 1 1 0
#> SRR1047873 1 0 1 1 0
#> SRR1047874 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1047813 3 0.000 1.000 0.0 0 1.0
#> SRR1047814 3 0.000 1.000 0.0 0 1.0
#> SRR1047815 3 0.000 1.000 0.0 0 1.0
#> SRR1047816 3 0.000 1.000 0.0 0 1.0
#> SRR1047817 3 0.000 1.000 0.0 0 1.0
#> SRR1047818 1 0.000 0.908 1.0 0 0.0
#> SRR1047819 1 0.000 0.908 1.0 0 0.0
#> SRR1047820 1 0.000 0.908 1.0 0 0.0
#> SRR1047821 1 0.000 0.908 1.0 0 0.0
#> SRR1047822 1 0.000 0.908 1.0 0 0.0
#> SRR1047823 1 0.000 0.908 1.0 0 0.0
#> SRR1047824 1 0.000 0.908 1.0 0 0.0
#> SRR1047825 1 0.000 0.908 1.0 0 0.0
#> SRR1047826 1 0.000 0.908 1.0 0 0.0
#> SRR1047827 1 0.000 0.908 1.0 0 0.0
#> SRR1047828 1 0.455 0.844 0.8 0 0.2
#> SRR1047829 1 0.455 0.844 0.8 0 0.2
#> SRR1047830 1 0.455 0.844 0.8 0 0.2
#> SRR1047831 1 0.455 0.844 0.8 0 0.2
#> SRR1047832 1 0.455 0.844 0.8 0 0.2
#> SRR1047833 2 0.000 1.000 0.0 1 0.0
#> SRR1047834 2 0.000 1.000 0.0 1 0.0
#> SRR1047835 2 0.000 1.000 0.0 1 0.0
#> SRR1047836 2 0.000 1.000 0.0 1 0.0
#> SRR1047837 2 0.000 1.000 0.0 1 0.0
#> SRR1047838 1 0.000 0.908 1.0 0 0.0
#> SRR1047839 1 0.000 0.908 1.0 0 0.0
#> SRR1047840 1 0.000 0.908 1.0 0 0.0
#> SRR1047841 1 0.000 0.908 1.0 0 0.0
#> SRR1047842 1 0.000 0.908 1.0 0 0.0
#> SRR1047843 1 0.455 0.844 0.8 0 0.2
#> SRR1047844 1 0.455 0.844 0.8 0 0.2
#> SRR1047845 1 0.455 0.844 0.8 0 0.2
#> SRR1047846 1 0.455 0.844 0.8 0 0.2
#> SRR1047847 1 0.455 0.844 0.8 0 0.2
#> SRR1047848 3 0.000 1.000 0.0 0 1.0
#> SRR1047849 3 0.000 1.000 0.0 0 1.0
#> SRR1047850 3 0.000 1.000 0.0 0 1.0
#> SRR1047851 3 0.000 1.000 0.0 0 1.0
#> SRR1047852 3 0.000 1.000 0.0 0 1.0
#> SRR1047853 1 0.000 0.908 1.0 0 0.0
#> SRR1047854 1 0.000 0.908 1.0 0 0.0
#> SRR1047855 1 0.000 0.908 1.0 0 0.0
#> SRR1047856 1 0.000 0.908 1.0 0 0.0
#> SRR1047857 1 0.000 0.908 1.0 0 0.0
#> SRR1047858 3 0.000 1.000 0.0 0 1.0
#> SRR1047859 3 0.000 1.000 0.0 0 1.0
#> SRR1047860 3 0.000 1.000 0.0 0 1.0
#> SRR1047861 3 0.000 1.000 0.0 0 1.0
#> SRR1047863 1 0.455 0.844 0.8 0 0.2
#> SRR1047864 1 0.455 0.844 0.8 0 0.2
#> SRR1047865 1 0.455 0.844 0.8 0 0.2
#> SRR1047866 1 0.455 0.844 0.8 0 0.2
#> SRR1047867 2 0.000 1.000 0.0 1 0.0
#> SRR1047868 1 0.000 0.908 1.0 0 0.0
#> SRR1047869 1 0.455 0.844 0.8 0 0.2
#> SRR1047870 1 0.000 0.908 1.0 0 0.0
#> SRR1047871 1 0.455 0.844 0.8 0 0.2
#> SRR1047872 1 0.000 0.908 1.0 0 0.0
#> SRR1047873 1 0.000 0.908 1.0 0 0.0
#> SRR1047874 1 0.000 0.908 1.0 0 0.0
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1047813 1 0.000 0.796 1.00 0 0.000 0.000
#> SRR1047814 1 0.000 0.796 1.00 0 0.000 0.000
#> SRR1047815 1 0.000 0.796 1.00 0 0.000 0.000
#> SRR1047816 1 0.000 0.796 1.00 0 0.000 0.000
#> SRR1047817 1 0.000 0.796 1.00 0 0.000 0.000
#> SRR1047818 4 0.000 0.946 0.00 0 0.000 1.000
#> SRR1047819 4 0.000 0.946 0.00 0 0.000 1.000
#> SRR1047820 4 0.000 0.946 0.00 0 0.000 1.000
#> SRR1047821 4 0.000 0.946 0.00 0 0.000 1.000
#> SRR1047822 4 0.000 0.946 0.00 0 0.000 1.000
#> SRR1047823 4 0.000 0.946 0.00 0 0.000 1.000
#> SRR1047824 4 0.000 0.946 0.00 0 0.000 1.000
#> SRR1047825 4 0.000 0.946 0.00 0 0.000 1.000
#> SRR1047826 4 0.000 0.946 0.00 0 0.000 1.000
#> SRR1047827 4 0.000 0.946 0.00 0 0.000 1.000
#> SRR1047828 1 0.479 0.566 0.62 0 0.000 0.380
#> SRR1047829 1 0.479 0.566 0.62 0 0.000 0.380
#> SRR1047830 1 0.479 0.566 0.62 0 0.000 0.380
#> SRR1047831 1 0.479 0.566 0.62 0 0.000 0.380
#> SRR1047832 1 0.479 0.566 0.62 0 0.000 0.380
#> SRR1047833 2 0.000 1.000 0.00 1 0.000 0.000
#> SRR1047834 2 0.000 1.000 0.00 1 0.000 0.000
#> SRR1047835 2 0.000 1.000 0.00 1 0.000 0.000
#> SRR1047836 2 0.000 1.000 0.00 1 0.000 0.000
#> SRR1047837 2 0.000 1.000 0.00 1 0.000 0.000
#> SRR1047838 4 0.000 0.946 0.00 0 0.000 1.000
#> SRR1047839 4 0.000 0.946 0.00 0 0.000 1.000
#> SRR1047840 4 0.000 0.946 0.00 0 0.000 1.000
#> SRR1047841 4 0.000 0.946 0.00 0 0.000 1.000
#> SRR1047842 4 0.000 0.946 0.00 0 0.000 1.000
#> SRR1047843 1 0.479 0.566 0.62 0 0.000 0.380
#> SRR1047844 4 0.760 0.116 0.20 0 0.376 0.424
#> SRR1047845 1 0.479 0.566 0.62 0 0.000 0.380
#> SRR1047846 1 0.479 0.566 0.62 0 0.000 0.380
#> SRR1047847 4 0.740 0.245 0.20 0 0.292 0.508
#> SRR1047848 1 0.000 0.796 1.00 0 0.000 0.000
#> SRR1047849 1 0.000 0.796 1.00 0 0.000 0.000
#> SRR1047850 1 0.000 0.796 1.00 0 0.000 0.000
#> SRR1047851 1 0.000 0.796 1.00 0 0.000 0.000
#> SRR1047852 1 0.000 0.796 1.00 0 0.000 0.000
#> SRR1047853 4 0.000 0.946 0.00 0 0.000 1.000
#> SRR1047854 4 0.000 0.946 0.00 0 0.000 1.000
#> SRR1047855 4 0.000 0.946 0.00 0 0.000 1.000
#> SRR1047856 4 0.000 0.946 0.00 0 0.000 1.000
#> SRR1047857 4 0.000 0.946 0.00 0 0.000 1.000
#> SRR1047858 1 0.000 0.796 1.00 0 0.000 0.000
#> SRR1047859 1 0.000 0.796 1.00 0 0.000 0.000
#> SRR1047860 1 0.000 0.796 1.00 0 0.000 0.000
#> SRR1047861 1 0.000 0.796 1.00 0 0.000 0.000
#> SRR1047863 3 0.000 1.000 0.00 0 1.000 0.000
#> SRR1047864 3 0.000 1.000 0.00 0 1.000 0.000
#> SRR1047865 3 0.000 1.000 0.00 0 1.000 0.000
#> SRR1047866 3 0.000 1.000 0.00 0 1.000 0.000
#> SRR1047867 3 0.000 1.000 0.00 0 1.000 0.000
#> SRR1047868 3 0.000 1.000 0.00 0 1.000 0.000
#> SRR1047869 3 0.000 1.000 0.00 0 1.000 0.000
#> SRR1047870 3 0.000 1.000 0.00 0 1.000 0.000
#> SRR1047871 3 0.000 1.000 0.00 0 1.000 0.000
#> SRR1047872 3 0.000 1.000 0.00 0 1.000 0.000
#> SRR1047873 3 0.000 1.000 0.00 0 1.000 0.000
#> SRR1047874 3 0.000 1.000 0.00 0 1.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1047813 1 0.2377 0.842 0.872 0 0.000 0.000 0.128
#> SRR1047814 1 0.0703 0.941 0.976 0 0.000 0.000 0.024
#> SRR1047815 1 0.0703 0.941 0.976 0 0.000 0.000 0.024
#> SRR1047816 1 0.0609 0.943 0.980 0 0.000 0.000 0.020
#> SRR1047817 1 0.4161 0.496 0.608 0 0.000 0.000 0.392
#> SRR1047818 4 0.0000 0.730 0.000 0 0.000 1.000 0.000
#> SRR1047819 4 0.0000 0.730 0.000 0 0.000 1.000 0.000
#> SRR1047820 4 0.0000 0.730 0.000 0 0.000 1.000 0.000
#> SRR1047821 4 0.0000 0.730 0.000 0 0.000 1.000 0.000
#> SRR1047822 4 0.0000 0.730 0.000 0 0.000 1.000 0.000
#> SRR1047823 5 0.4171 1.000 0.000 0 0.000 0.396 0.604
#> SRR1047824 5 0.4171 1.000 0.000 0 0.000 0.396 0.604
#> SRR1047825 5 0.4171 1.000 0.000 0 0.000 0.396 0.604
#> SRR1047826 5 0.4171 1.000 0.000 0 0.000 0.396 0.604
#> SRR1047827 5 0.4171 1.000 0.000 0 0.000 0.396 0.604
#> SRR1047828 4 0.4171 0.546 0.000 0 0.000 0.604 0.396
#> SRR1047829 4 0.4171 0.546 0.000 0 0.000 0.604 0.396
#> SRR1047830 4 0.4171 0.546 0.000 0 0.000 0.604 0.396
#> SRR1047831 4 0.4171 0.546 0.000 0 0.000 0.604 0.396
#> SRR1047832 4 0.4171 0.546 0.000 0 0.000 0.604 0.396
#> SRR1047833 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> SRR1047834 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> SRR1047835 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> SRR1047836 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> SRR1047837 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> SRR1047838 4 0.0000 0.730 0.000 0 0.000 1.000 0.000
#> SRR1047839 4 0.0000 0.730 0.000 0 0.000 1.000 0.000
#> SRR1047840 4 0.0000 0.730 0.000 0 0.000 1.000 0.000
#> SRR1047841 4 0.0000 0.730 0.000 0 0.000 1.000 0.000
#> SRR1047842 4 0.0000 0.730 0.000 0 0.000 1.000 0.000
#> SRR1047843 4 0.4171 0.474 0.396 0 0.000 0.604 0.000
#> SRR1047844 4 0.5998 0.498 0.200 0 0.192 0.604 0.004
#> SRR1047845 4 0.4171 0.474 0.396 0 0.000 0.604 0.000
#> SRR1047846 4 0.4171 0.474 0.396 0 0.000 0.604 0.000
#> SRR1047847 4 0.6084 0.499 0.200 0 0.188 0.604 0.008
#> SRR1047848 1 0.0000 0.951 1.000 0 0.000 0.000 0.000
#> SRR1047849 1 0.0000 0.951 1.000 0 0.000 0.000 0.000
#> SRR1047850 1 0.0000 0.951 1.000 0 0.000 0.000 0.000
#> SRR1047851 1 0.0000 0.951 1.000 0 0.000 0.000 0.000
#> SRR1047852 1 0.0000 0.951 1.000 0 0.000 0.000 0.000
#> SRR1047853 4 0.0000 0.730 0.000 0 0.000 1.000 0.000
#> SRR1047854 4 0.0000 0.730 0.000 0 0.000 1.000 0.000
#> SRR1047855 4 0.0000 0.730 0.000 0 0.000 1.000 0.000
#> SRR1047856 4 0.0000 0.730 0.000 0 0.000 1.000 0.000
#> SRR1047857 4 0.0000 0.730 0.000 0 0.000 1.000 0.000
#> SRR1047858 1 0.0000 0.951 1.000 0 0.000 0.000 0.000
#> SRR1047859 1 0.0000 0.951 1.000 0 0.000 0.000 0.000
#> SRR1047860 1 0.0000 0.951 1.000 0 0.000 0.000 0.000
#> SRR1047861 1 0.0000 0.951 1.000 0 0.000 0.000 0.000
#> SRR1047863 3 0.0000 0.999 0.000 0 1.000 0.000 0.000
#> SRR1047864 3 0.0000 0.999 0.000 0 1.000 0.000 0.000
#> SRR1047865 3 0.0000 0.999 0.000 0 1.000 0.000 0.000
#> SRR1047866 3 0.0000 0.999 0.000 0 1.000 0.000 0.000
#> SRR1047867 3 0.0404 0.987 0.000 0 0.988 0.000 0.012
#> SRR1047868 3 0.0000 0.999 0.000 0 1.000 0.000 0.000
#> SRR1047869 3 0.0000 0.999 0.000 0 1.000 0.000 0.000
#> SRR1047870 3 0.0000 0.999 0.000 0 1.000 0.000 0.000
#> SRR1047871 3 0.0000 0.999 0.000 0 1.000 0.000 0.000
#> SRR1047872 3 0.0000 0.999 0.000 0 1.000 0.000 0.000
#> SRR1047873 3 0.0000 0.999 0.000 0 1.000 0.000 0.000
#> SRR1047874 3 0.0000 0.999 0.000 0 1.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1047813 1 0.521 0.593 0.556 0.336 0.000 0.000 0.108 0.000
#> SRR1047814 1 0.521 0.593 0.556 0.336 0.000 0.000 0.108 0.000
#> SRR1047815 1 0.521 0.593 0.556 0.336 0.000 0.000 0.108 0.000
#> SRR1047816 1 0.521 0.593 0.556 0.336 0.000 0.000 0.108 0.000
#> SRR1047817 5 0.356 0.486 0.000 0.336 0.000 0.000 0.664 0.000
#> SRR1047818 4 0.000 0.737 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047819 4 0.000 0.737 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047820 4 0.000 0.737 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047821 4 0.000 0.737 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047822 4 0.000 0.737 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047823 6 0.381 1.000 0.000 0.000 0.000 0.428 0.000 0.572
#> SRR1047824 6 0.381 1.000 0.000 0.000 0.000 0.428 0.000 0.572
#> SRR1047825 6 0.381 1.000 0.000 0.000 0.000 0.428 0.000 0.572
#> SRR1047826 6 0.381 1.000 0.000 0.000 0.000 0.428 0.000 0.572
#> SRR1047827 6 0.381 1.000 0.000 0.000 0.000 0.428 0.000 0.572
#> SRR1047828 5 0.191 0.909 0.000 0.000 0.000 0.108 0.892 0.000
#> SRR1047829 5 0.191 0.909 0.000 0.000 0.000 0.108 0.892 0.000
#> SRR1047830 5 0.191 0.909 0.000 0.000 0.000 0.108 0.892 0.000
#> SRR1047831 5 0.191 0.909 0.000 0.000 0.000 0.108 0.892 0.000
#> SRR1047832 5 0.191 0.909 0.000 0.000 0.000 0.108 0.892 0.000
#> SRR1047833 2 0.356 1.000 0.000 0.664 0.000 0.000 0.000 0.336
#> SRR1047834 2 0.356 1.000 0.000 0.664 0.000 0.000 0.000 0.336
#> SRR1047835 2 0.356 1.000 0.000 0.664 0.000 0.000 0.000 0.336
#> SRR1047836 2 0.356 1.000 0.000 0.664 0.000 0.000 0.000 0.336
#> SRR1047837 2 0.356 1.000 0.000 0.664 0.000 0.000 0.000 0.336
#> SRR1047838 4 0.000 0.737 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047839 4 0.000 0.737 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047840 4 0.000 0.737 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047841 4 0.000 0.737 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047842 4 0.000 0.737 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047843 4 0.618 0.175 0.424 0.000 0.000 0.428 0.056 0.092
#> SRR1047844 4 0.744 0.278 0.200 0.000 0.184 0.484 0.040 0.092
#> SRR1047845 4 0.618 0.175 0.424 0.000 0.000 0.428 0.056 0.092
#> SRR1047846 4 0.618 0.175 0.424 0.000 0.000 0.428 0.056 0.092
#> SRR1047847 4 0.752 0.288 0.200 0.000 0.148 0.496 0.064 0.092
#> SRR1047848 1 0.000 0.845 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1047849 1 0.000 0.845 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1047850 1 0.000 0.845 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1047851 1 0.000 0.845 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1047852 1 0.000 0.845 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1047853 4 0.000 0.737 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047854 4 0.000 0.737 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047855 4 0.000 0.737 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047856 4 0.000 0.737 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047857 4 0.000 0.737 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047858 1 0.000 0.845 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1047859 1 0.079 0.821 0.968 0.000 0.000 0.000 0.000 0.032
#> SRR1047860 1 0.000 0.845 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1047861 1 0.000 0.845 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1047863 3 0.000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047864 3 0.000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047865 3 0.000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047866 3 0.000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047867 3 0.026 0.992 0.000 0.000 0.992 0.000 0.008 0.000
#> SRR1047868 3 0.000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047869 3 0.000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047870 3 0.000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047871 3 0.000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047872 3 0.000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047873 3 0.000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047874 3 0.000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 17931 rows and 61 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 0.428 0.860 0.882 0.2867 0.793 0.793
#> 3 3 0.727 0.836 0.921 1.2366 0.484 0.379
#> 4 4 0.893 0.917 0.958 0.0732 0.967 0.907
#> 5 5 0.921 0.907 0.957 0.1354 0.896 0.676
#> 6 6 0.883 0.856 0.919 0.0487 0.907 0.620
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
#> SRR1047813 1 0.0938 0.847 0.988 0.012
#> SRR1047814 1 0.0938 0.847 0.988 0.012
#> SRR1047815 1 0.0938 0.847 0.988 0.012
#> SRR1047816 1 0.0938 0.847 0.988 0.012
#> SRR1047817 1 0.0938 0.847 0.988 0.012
#> SRR1047818 1 0.7299 0.860 0.796 0.204
#> SRR1047819 1 0.7299 0.860 0.796 0.204
#> SRR1047820 1 0.7299 0.860 0.796 0.204
#> SRR1047821 1 0.7299 0.860 0.796 0.204
#> SRR1047822 1 0.7299 0.860 0.796 0.204
#> SRR1047823 1 0.7299 0.860 0.796 0.204
#> SRR1047824 1 0.7299 0.860 0.796 0.204
#> SRR1047825 1 0.7299 0.860 0.796 0.204
#> SRR1047826 1 0.7299 0.860 0.796 0.204
#> SRR1047827 1 0.7299 0.860 0.796 0.204
#> SRR1047828 1 0.4161 0.865 0.916 0.084
#> SRR1047829 1 0.9248 0.505 0.660 0.340
#> SRR1047830 1 0.4161 0.865 0.916 0.084
#> SRR1047831 1 0.4161 0.865 0.916 0.084
#> SRR1047832 1 0.5178 0.853 0.884 0.116
#> SRR1047833 2 0.0938 0.999 0.012 0.988
#> SRR1047834 2 0.0938 0.999 0.012 0.988
#> SRR1047835 2 0.0938 0.999 0.012 0.988
#> SRR1047836 2 0.0938 0.999 0.012 0.988
#> SRR1047837 2 0.0938 0.999 0.012 0.988
#> SRR1047838 1 0.7299 0.860 0.796 0.204
#> SRR1047839 1 0.7299 0.860 0.796 0.204
#> SRR1047840 1 0.7299 0.860 0.796 0.204
#> SRR1047841 1 0.7299 0.860 0.796 0.204
#> SRR1047842 1 0.7299 0.860 0.796 0.204
#> SRR1047843 1 0.2043 0.839 0.968 0.032
#> SRR1047844 1 0.0000 0.851 1.000 0.000
#> SRR1047845 1 0.1184 0.847 0.984 0.016
#> SRR1047846 1 0.0938 0.849 0.988 0.012
#> SRR1047847 1 0.0000 0.851 1.000 0.000
#> SRR1047848 1 0.0938 0.847 0.988 0.012
#> SRR1047849 1 0.0938 0.847 0.988 0.012
#> SRR1047850 1 0.0938 0.847 0.988 0.012
#> SRR1047851 1 0.0938 0.847 0.988 0.012
#> SRR1047852 1 0.0938 0.847 0.988 0.012
#> SRR1047853 1 0.4562 0.870 0.904 0.096
#> SRR1047854 1 0.5408 0.870 0.876 0.124
#> SRR1047855 1 0.4690 0.870 0.900 0.100
#> SRR1047856 1 0.4298 0.869 0.912 0.088
#> SRR1047857 1 0.4431 0.869 0.908 0.092
#> SRR1047858 1 0.1184 0.847 0.984 0.016
#> SRR1047859 1 0.1184 0.847 0.984 0.016
#> SRR1047860 1 0.1184 0.847 0.984 0.016
#> SRR1047861 1 0.1184 0.847 0.984 0.016
#> SRR1047863 1 0.8144 0.830 0.748 0.252
#> SRR1047864 2 0.1184 0.995 0.016 0.984
#> SRR1047865 1 0.8144 0.830 0.748 0.252
#> SRR1047866 1 0.8144 0.830 0.748 0.252
#> SRR1047867 2 0.0938 0.999 0.012 0.988
#> SRR1047868 1 0.8144 0.830 0.748 0.252
#> SRR1047869 1 0.9323 0.722 0.652 0.348
#> SRR1047870 1 0.8144 0.830 0.748 0.252
#> SRR1047871 1 0.8144 0.830 0.748 0.252
#> SRR1047872 1 0.8144 0.830 0.748 0.252
#> SRR1047873 1 0.8144 0.830 0.748 0.252
#> SRR1047874 1 0.8144 0.830 0.748 0.252
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1047813 1 0.000 0.909 1.000 0.000 0.000
#> SRR1047814 1 0.000 0.909 1.000 0.000 0.000
#> SRR1047815 1 0.000 0.909 1.000 0.000 0.000
#> SRR1047816 1 0.000 0.909 1.000 0.000 0.000
#> SRR1047817 1 0.000 0.909 1.000 0.000 0.000
#> SRR1047818 2 0.000 1.000 0.000 1.000 0.000
#> SRR1047819 2 0.000 1.000 0.000 1.000 0.000
#> SRR1047820 2 0.000 1.000 0.000 1.000 0.000
#> SRR1047821 2 0.000 1.000 0.000 1.000 0.000
#> SRR1047822 2 0.000 1.000 0.000 1.000 0.000
#> SRR1047823 2 0.000 1.000 0.000 1.000 0.000
#> SRR1047824 2 0.000 1.000 0.000 1.000 0.000
#> SRR1047825 2 0.000 1.000 0.000 1.000 0.000
#> SRR1047826 2 0.000 1.000 0.000 1.000 0.000
#> SRR1047827 2 0.000 1.000 0.000 1.000 0.000
#> SRR1047828 1 0.000 0.909 1.000 0.000 0.000
#> SRR1047829 1 0.000 0.909 1.000 0.000 0.000
#> SRR1047830 1 0.000 0.909 1.000 0.000 0.000
#> SRR1047831 1 0.000 0.909 1.000 0.000 0.000
#> SRR1047832 1 0.000 0.909 1.000 0.000 0.000
#> SRR1047833 3 0.000 0.823 0.000 0.000 1.000
#> SRR1047834 3 0.000 0.823 0.000 0.000 1.000
#> SRR1047835 3 0.000 0.823 0.000 0.000 1.000
#> SRR1047836 3 0.000 0.823 0.000 0.000 1.000
#> SRR1047837 3 0.000 0.823 0.000 0.000 1.000
#> SRR1047838 2 0.000 1.000 0.000 1.000 0.000
#> SRR1047839 2 0.000 1.000 0.000 1.000 0.000
#> SRR1047840 2 0.000 1.000 0.000 1.000 0.000
#> SRR1047841 2 0.000 1.000 0.000 1.000 0.000
#> SRR1047842 2 0.000 1.000 0.000 1.000 0.000
#> SRR1047843 1 0.000 0.909 1.000 0.000 0.000
#> SRR1047844 1 0.000 0.909 1.000 0.000 0.000
#> SRR1047845 1 0.000 0.909 1.000 0.000 0.000
#> SRR1047846 1 0.000 0.909 1.000 0.000 0.000
#> SRR1047847 1 0.000 0.909 1.000 0.000 0.000
#> SRR1047848 1 0.000 0.909 1.000 0.000 0.000
#> SRR1047849 1 0.000 0.909 1.000 0.000 0.000
#> SRR1047850 1 0.000 0.909 1.000 0.000 0.000
#> SRR1047851 1 0.000 0.909 1.000 0.000 0.000
#> SRR1047852 1 0.000 0.909 1.000 0.000 0.000
#> SRR1047853 1 0.618 0.372 0.584 0.416 0.000
#> SRR1047854 1 0.618 0.372 0.584 0.416 0.000
#> SRR1047855 1 0.618 0.372 0.584 0.416 0.000
#> SRR1047856 1 0.618 0.372 0.584 0.416 0.000
#> SRR1047857 1 0.618 0.372 0.584 0.416 0.000
#> SRR1047858 1 0.000 0.909 1.000 0.000 0.000
#> SRR1047859 1 0.000 0.909 1.000 0.000 0.000
#> SRR1047860 1 0.000 0.909 1.000 0.000 0.000
#> SRR1047861 1 0.000 0.909 1.000 0.000 0.000
#> SRR1047863 3 0.550 0.572 0.000 0.292 0.708
#> SRR1047864 3 0.000 0.823 0.000 0.000 1.000
#> SRR1047865 3 0.141 0.811 0.000 0.036 0.964
#> SRR1047866 3 0.000 0.823 0.000 0.000 1.000
#> SRR1047867 3 0.000 0.823 0.000 0.000 1.000
#> SRR1047868 3 0.852 0.630 0.280 0.132 0.588
#> SRR1047869 3 0.141 0.811 0.000 0.036 0.964
#> SRR1047870 3 0.569 0.654 0.288 0.004 0.708
#> SRR1047871 3 0.617 0.363 0.000 0.412 0.588
#> SRR1047872 3 0.846 0.626 0.288 0.124 0.588
#> SRR1047873 3 0.846 0.626 0.288 0.124 0.588
#> SRR1047874 3 0.846 0.626 0.288 0.124 0.588
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1047813 1 0.000 0.896 1.000 0 0.000 0.00
#> SRR1047814 1 0.000 0.896 1.000 0 0.000 0.00
#> SRR1047815 1 0.000 0.896 1.000 0 0.000 0.00
#> SRR1047816 1 0.000 0.896 1.000 0 0.000 0.00
#> SRR1047817 1 0.000 0.896 1.000 0 0.000 0.00
#> SRR1047818 4 0.000 1.000 0.000 0 0.000 1.00
#> SRR1047819 4 0.000 1.000 0.000 0 0.000 1.00
#> SRR1047820 4 0.000 1.000 0.000 0 0.000 1.00
#> SRR1047821 4 0.000 1.000 0.000 0 0.000 1.00
#> SRR1047822 4 0.000 1.000 0.000 0 0.000 1.00
#> SRR1047823 4 0.000 1.000 0.000 0 0.000 1.00
#> SRR1047824 4 0.000 1.000 0.000 0 0.000 1.00
#> SRR1047825 4 0.000 1.000 0.000 0 0.000 1.00
#> SRR1047826 4 0.000 1.000 0.000 0 0.000 1.00
#> SRR1047827 4 0.000 1.000 0.000 0 0.000 1.00
#> SRR1047828 1 0.112 0.903 0.964 0 0.036 0.00
#> SRR1047829 1 0.112 0.903 0.964 0 0.036 0.00
#> SRR1047830 1 0.112 0.903 0.964 0 0.036 0.00
#> SRR1047831 1 0.112 0.903 0.964 0 0.036 0.00
#> SRR1047832 1 0.112 0.903 0.964 0 0.036 0.00
#> SRR1047833 2 0.000 1.000 0.000 1 0.000 0.00
#> SRR1047834 2 0.000 1.000 0.000 1 0.000 0.00
#> SRR1047835 2 0.000 1.000 0.000 1 0.000 0.00
#> SRR1047836 2 0.000 1.000 0.000 1 0.000 0.00
#> SRR1047837 2 0.000 1.000 0.000 1 0.000 0.00
#> SRR1047838 4 0.000 1.000 0.000 0 0.000 1.00
#> SRR1047839 4 0.000 1.000 0.000 0 0.000 1.00
#> SRR1047840 4 0.000 1.000 0.000 0 0.000 1.00
#> SRR1047841 4 0.000 1.000 0.000 0 0.000 1.00
#> SRR1047842 4 0.000 1.000 0.000 0 0.000 1.00
#> SRR1047843 1 0.112 0.903 0.964 0 0.036 0.00
#> SRR1047844 1 0.112 0.903 0.964 0 0.036 0.00
#> SRR1047845 1 0.112 0.903 0.964 0 0.036 0.00
#> SRR1047846 1 0.112 0.903 0.964 0 0.036 0.00
#> SRR1047847 1 0.112 0.903 0.964 0 0.036 0.00
#> SRR1047848 1 0.000 0.896 1.000 0 0.000 0.00
#> SRR1047849 1 0.000 0.896 1.000 0 0.000 0.00
#> SRR1047850 1 0.000 0.896 1.000 0 0.000 0.00
#> SRR1047851 1 0.000 0.896 1.000 0 0.000 0.00
#> SRR1047852 1 0.000 0.896 1.000 0 0.000 0.00
#> SRR1047853 1 0.578 0.467 0.584 0 0.036 0.38
#> SRR1047854 1 0.578 0.467 0.584 0 0.036 0.38
#> SRR1047855 1 0.578 0.467 0.584 0 0.036 0.38
#> SRR1047856 1 0.578 0.467 0.584 0 0.036 0.38
#> SRR1047857 1 0.578 0.467 0.584 0 0.036 0.38
#> SRR1047858 1 0.112 0.903 0.964 0 0.036 0.00
#> SRR1047859 1 0.112 0.903 0.964 0 0.036 0.00
#> SRR1047860 1 0.112 0.903 0.964 0 0.036 0.00
#> SRR1047861 1 0.112 0.903 0.964 0 0.036 0.00
#> SRR1047863 3 0.000 1.000 0.000 0 1.000 0.00
#> SRR1047864 3 0.000 1.000 0.000 0 1.000 0.00
#> SRR1047865 3 0.000 1.000 0.000 0 1.000 0.00
#> SRR1047866 3 0.000 1.000 0.000 0 1.000 0.00
#> SRR1047867 3 0.000 1.000 0.000 0 1.000 0.00
#> SRR1047868 3 0.000 1.000 0.000 0 1.000 0.00
#> SRR1047869 3 0.000 1.000 0.000 0 1.000 0.00
#> SRR1047870 3 0.000 1.000 0.000 0 1.000 0.00
#> SRR1047871 3 0.000 1.000 0.000 0 1.000 0.00
#> SRR1047872 3 0.000 1.000 0.000 0 1.000 0.00
#> SRR1047873 3 0.000 1.000 0.000 0 1.000 0.00
#> SRR1047874 3 0.000 1.000 0.000 0 1.000 0.00
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1047813 1 0.000 1.000 1.00 0 0.00 0.000 0.000
#> SRR1047814 1 0.000 1.000 1.00 0 0.00 0.000 0.000
#> SRR1047815 1 0.000 1.000 1.00 0 0.00 0.000 0.000
#> SRR1047816 1 0.000 1.000 1.00 0 0.00 0.000 0.000
#> SRR1047817 1 0.000 1.000 1.00 0 0.00 0.000 0.000
#> SRR1047818 4 0.000 1.000 0.00 0 0.00 1.000 0.000
#> SRR1047819 4 0.000 1.000 0.00 0 0.00 1.000 0.000
#> SRR1047820 4 0.000 1.000 0.00 0 0.00 1.000 0.000
#> SRR1047821 4 0.000 1.000 0.00 0 0.00 1.000 0.000
#> SRR1047822 4 0.000 1.000 0.00 0 0.00 1.000 0.000
#> SRR1047823 4 0.000 1.000 0.00 0 0.00 1.000 0.000
#> SRR1047824 4 0.000 1.000 0.00 0 0.00 1.000 0.000
#> SRR1047825 4 0.000 1.000 0.00 0 0.00 1.000 0.000
#> SRR1047826 4 0.000 1.000 0.00 0 0.00 1.000 0.000
#> SRR1047827 4 0.000 1.000 0.00 0 0.00 1.000 0.000
#> SRR1047828 5 0.000 0.823 0.00 0 0.00 0.000 1.000
#> SRR1047829 5 0.000 0.823 0.00 0 0.00 0.000 1.000
#> SRR1047830 5 0.000 0.823 0.00 0 0.00 0.000 1.000
#> SRR1047831 5 0.000 0.823 0.00 0 0.00 0.000 1.000
#> SRR1047832 5 0.000 0.823 0.00 0 0.00 0.000 1.000
#> SRR1047833 2 0.000 1.000 0.00 1 0.00 0.000 0.000
#> SRR1047834 2 0.000 1.000 0.00 1 0.00 0.000 0.000
#> SRR1047835 2 0.000 1.000 0.00 1 0.00 0.000 0.000
#> SRR1047836 2 0.000 1.000 0.00 1 0.00 0.000 0.000
#> SRR1047837 2 0.000 1.000 0.00 1 0.00 0.000 0.000
#> SRR1047838 4 0.000 1.000 0.00 0 0.00 1.000 0.000
#> SRR1047839 4 0.000 1.000 0.00 0 0.00 1.000 0.000
#> SRR1047840 4 0.000 1.000 0.00 0 0.00 1.000 0.000
#> SRR1047841 4 0.000 1.000 0.00 0 0.00 1.000 0.000
#> SRR1047842 4 0.000 1.000 0.00 0 0.00 1.000 0.000
#> SRR1047843 5 0.104 0.831 0.04 0 0.00 0.000 0.960
#> SRR1047844 5 0.104 0.831 0.04 0 0.00 0.000 0.960
#> SRR1047845 5 0.104 0.831 0.04 0 0.00 0.000 0.960
#> SRR1047846 5 0.104 0.831 0.04 0 0.00 0.000 0.960
#> SRR1047847 5 0.104 0.831 0.04 0 0.00 0.000 0.960
#> SRR1047848 1 0.000 1.000 1.00 0 0.00 0.000 0.000
#> SRR1047849 1 0.000 1.000 1.00 0 0.00 0.000 0.000
#> SRR1047850 1 0.000 1.000 1.00 0 0.00 0.000 0.000
#> SRR1047851 1 0.000 1.000 1.00 0 0.00 0.000 0.000
#> SRR1047852 1 0.000 1.000 1.00 0 0.00 0.000 0.000
#> SRR1047853 5 0.422 0.425 0.00 0 0.00 0.416 0.584
#> SRR1047854 5 0.422 0.425 0.00 0 0.00 0.416 0.584
#> SRR1047855 5 0.422 0.425 0.00 0 0.00 0.416 0.584
#> SRR1047856 5 0.422 0.425 0.00 0 0.00 0.416 0.584
#> SRR1047857 5 0.422 0.425 0.00 0 0.00 0.416 0.584
#> SRR1047858 5 0.104 0.831 0.04 0 0.00 0.000 0.960
#> SRR1047859 5 0.104 0.831 0.04 0 0.00 0.000 0.960
#> SRR1047860 5 0.104 0.831 0.04 0 0.00 0.000 0.960
#> SRR1047861 5 0.104 0.831 0.04 0 0.00 0.000 0.960
#> SRR1047863 3 0.104 0.957 0.00 0 0.96 0.000 0.040
#> SRR1047864 3 0.000 0.978 0.00 0 1.00 0.000 0.000
#> SRR1047865 3 0.104 0.956 0.04 0 0.96 0.000 0.000
#> SRR1047866 3 0.104 0.956 0.04 0 0.96 0.000 0.000
#> SRR1047867 3 0.000 0.978 0.00 0 1.00 0.000 0.000
#> SRR1047868 3 0.104 0.957 0.00 0 0.96 0.000 0.040
#> SRR1047869 3 0.104 0.956 0.04 0 0.96 0.000 0.000
#> SRR1047870 3 0.000 0.978 0.00 0 1.00 0.000 0.000
#> SRR1047871 3 0.000 0.978 0.00 0 1.00 0.000 0.000
#> SRR1047872 3 0.000 0.978 0.00 0 1.00 0.000 0.000
#> SRR1047873 3 0.000 0.978 0.00 0 1.00 0.000 0.000
#> SRR1047874 3 0.000 0.978 0.00 0 1.00 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1047813 1 0.000 1.000 1 0 0 0.000 0.000 0.0
#> SRR1047814 1 0.000 1.000 1 0 0 0.000 0.000 0.0
#> SRR1047815 1 0.000 1.000 1 0 0 0.000 0.000 0.0
#> SRR1047816 1 0.000 1.000 1 0 0 0.000 0.000 0.0
#> SRR1047817 1 0.000 1.000 1 0 0 0.000 0.000 0.0
#> SRR1047818 4 0.000 0.681 0 0 0 1.000 0.000 0.0
#> SRR1047819 4 0.000 0.681 0 0 0 1.000 0.000 0.0
#> SRR1047820 4 0.000 0.681 0 0 0 1.000 0.000 0.0
#> SRR1047821 4 0.000 0.681 0 0 0 1.000 0.000 0.0
#> SRR1047822 4 0.000 0.681 0 0 0 1.000 0.000 0.0
#> SRR1047823 6 0.279 1.000 0 0 0 0.200 0.000 0.8
#> SRR1047824 6 0.279 1.000 0 0 0 0.200 0.000 0.8
#> SRR1047825 6 0.279 1.000 0 0 0 0.200 0.000 0.8
#> SRR1047826 6 0.279 1.000 0 0 0 0.200 0.000 0.8
#> SRR1047827 6 0.279 1.000 0 0 0 0.200 0.000 0.8
#> SRR1047828 5 0.279 0.842 0 0 0 0.000 0.800 0.2
#> SRR1047829 5 0.279 0.842 0 0 0 0.000 0.800 0.2
#> SRR1047830 5 0.279 0.842 0 0 0 0.000 0.800 0.2
#> SRR1047831 5 0.279 0.842 0 0 0 0.000 0.800 0.2
#> SRR1047832 5 0.279 0.842 0 0 0 0.000 0.800 0.2
#> SRR1047833 2 0.000 1.000 0 1 0 0.000 0.000 0.0
#> SRR1047834 2 0.000 1.000 0 1 0 0.000 0.000 0.0
#> SRR1047835 2 0.000 1.000 0 1 0 0.000 0.000 0.0
#> SRR1047836 2 0.000 1.000 0 1 0 0.000 0.000 0.0
#> SRR1047837 2 0.000 1.000 0 1 0 0.000 0.000 0.0
#> SRR1047838 4 0.000 0.681 0 0 0 1.000 0.000 0.0
#> SRR1047839 4 0.000 0.681 0 0 0 1.000 0.000 0.0
#> SRR1047840 4 0.000 0.681 0 0 0 1.000 0.000 0.0
#> SRR1047841 4 0.000 0.681 0 0 0 1.000 0.000 0.0
#> SRR1047842 4 0.000 0.681 0 0 0 1.000 0.000 0.0
#> SRR1047843 5 0.000 0.917 0 0 0 0.000 1.000 0.0
#> SRR1047844 5 0.000 0.917 0 0 0 0.000 1.000 0.0
#> SRR1047845 5 0.000 0.917 0 0 0 0.000 1.000 0.0
#> SRR1047846 5 0.000 0.917 0 0 0 0.000 1.000 0.0
#> SRR1047847 5 0.000 0.917 0 0 0 0.000 1.000 0.0
#> SRR1047848 1 0.000 1.000 1 0 0 0.000 0.000 0.0
#> SRR1047849 1 0.000 1.000 1 0 0 0.000 0.000 0.0
#> SRR1047850 1 0.000 1.000 1 0 0 0.000 0.000 0.0
#> SRR1047851 1 0.000 1.000 1 0 0 0.000 0.000 0.0
#> SRR1047852 1 0.000 1.000 1 0 0 0.000 0.000 0.0
#> SRR1047853 4 0.588 0.186 0 0 0 0.416 0.384 0.2
#> SRR1047854 4 0.588 0.186 0 0 0 0.416 0.384 0.2
#> SRR1047855 4 0.588 0.186 0 0 0 0.416 0.384 0.2
#> SRR1047856 4 0.588 0.186 0 0 0 0.416 0.384 0.2
#> SRR1047857 4 0.588 0.186 0 0 0 0.416 0.384 0.2
#> SRR1047858 5 0.000 0.917 0 0 0 0.000 1.000 0.0
#> SRR1047859 5 0.000 0.917 0 0 0 0.000 1.000 0.0
#> SRR1047860 5 0.000 0.917 0 0 0 0.000 1.000 0.0
#> SRR1047861 5 0.000 0.917 0 0 0 0.000 1.000 0.0
#> SRR1047863 3 0.000 1.000 0 0 1 0.000 0.000 0.0
#> SRR1047864 3 0.000 1.000 0 0 1 0.000 0.000 0.0
#> SRR1047865 3 0.000 1.000 0 0 1 0.000 0.000 0.0
#> SRR1047866 3 0.000 1.000 0 0 1 0.000 0.000 0.0
#> SRR1047867 3 0.000 1.000 0 0 1 0.000 0.000 0.0
#> SRR1047868 3 0.000 1.000 0 0 1 0.000 0.000 0.0
#> SRR1047869 3 0.000 1.000 0 0 1 0.000 0.000 0.0
#> SRR1047870 3 0.000 1.000 0 0 1 0.000 0.000 0.0
#> SRR1047871 3 0.000 1.000 0 0 1 0.000 0.000 0.0
#> SRR1047872 3 0.000 1.000 0 0 1 0.000 0.000 0.0
#> SRR1047873 3 0.000 1.000 0 0 1 0.000 0.000 0.0
#> SRR1047874 3 0.000 1.000 0 0 1 0.000 0.000 0.0
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 17931 rows and 61 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 0.758 0.935 0.966 0.2247 0.820 0.820
#> 3 3 0.722 0.798 0.917 1.4593 0.560 0.476
#> 4 4 0.881 0.888 0.952 0.2720 0.747 0.477
#> 5 5 0.706 0.753 0.858 0.1111 0.790 0.410
#> 6 6 0.742 0.618 0.812 0.0479 0.987 0.936
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
#> SRR1047813 1 0.0000 0.959 1.000 0.000
#> SRR1047814 1 0.0000 0.959 1.000 0.000
#> SRR1047815 1 0.0000 0.959 1.000 0.000
#> SRR1047816 1 0.0000 0.959 1.000 0.000
#> SRR1047817 1 0.0000 0.959 1.000 0.000
#> SRR1047818 1 0.7219 0.795 0.800 0.200
#> SRR1047819 1 0.7299 0.791 0.796 0.204
#> SRR1047820 1 0.7219 0.795 0.800 0.200
#> SRR1047821 1 0.7299 0.791 0.796 0.204
#> SRR1047822 1 0.7376 0.786 0.792 0.208
#> SRR1047823 1 0.7056 0.804 0.808 0.192
#> SRR1047824 1 0.7056 0.804 0.808 0.192
#> SRR1047825 1 0.7056 0.804 0.808 0.192
#> SRR1047826 1 0.7056 0.804 0.808 0.192
#> SRR1047827 1 0.7056 0.804 0.808 0.192
#> SRR1047828 1 0.0000 0.959 1.000 0.000
#> SRR1047829 1 0.0000 0.959 1.000 0.000
#> SRR1047830 1 0.0000 0.959 1.000 0.000
#> SRR1047831 1 0.0000 0.959 1.000 0.000
#> SRR1047832 1 0.0000 0.959 1.000 0.000
#> SRR1047833 2 0.0000 0.998 0.000 1.000
#> SRR1047834 2 0.0000 0.998 0.000 1.000
#> SRR1047835 2 0.0000 0.998 0.000 1.000
#> SRR1047836 2 0.0000 0.998 0.000 1.000
#> SRR1047837 2 0.0000 0.998 0.000 1.000
#> SRR1047838 1 0.0000 0.959 1.000 0.000
#> SRR1047839 1 0.0000 0.959 1.000 0.000
#> SRR1047840 1 0.0000 0.959 1.000 0.000
#> SRR1047841 1 0.0000 0.959 1.000 0.000
#> SRR1047842 1 0.0000 0.959 1.000 0.000
#> SRR1047843 1 0.0000 0.959 1.000 0.000
#> SRR1047844 1 0.0000 0.959 1.000 0.000
#> SRR1047845 1 0.0000 0.959 1.000 0.000
#> SRR1047846 1 0.0000 0.959 1.000 0.000
#> SRR1047847 1 0.0000 0.959 1.000 0.000
#> SRR1047848 1 0.0000 0.959 1.000 0.000
#> SRR1047849 1 0.0000 0.959 1.000 0.000
#> SRR1047850 1 0.0000 0.959 1.000 0.000
#> SRR1047851 1 0.0000 0.959 1.000 0.000
#> SRR1047852 1 0.0000 0.959 1.000 0.000
#> SRR1047853 1 0.0000 0.959 1.000 0.000
#> SRR1047854 1 0.0000 0.959 1.000 0.000
#> SRR1047855 1 0.0000 0.959 1.000 0.000
#> SRR1047856 1 0.0000 0.959 1.000 0.000
#> SRR1047857 1 0.0000 0.959 1.000 0.000
#> SRR1047858 1 0.0000 0.959 1.000 0.000
#> SRR1047859 1 0.0000 0.959 1.000 0.000
#> SRR1047860 1 0.0000 0.959 1.000 0.000
#> SRR1047861 1 0.0000 0.959 1.000 0.000
#> SRR1047863 1 0.0000 0.959 1.000 0.000
#> SRR1047864 1 0.0000 0.959 1.000 0.000
#> SRR1047865 1 0.0000 0.959 1.000 0.000
#> SRR1047866 1 0.0000 0.959 1.000 0.000
#> SRR1047867 2 0.0672 0.991 0.008 0.992
#> SRR1047868 1 0.0000 0.959 1.000 0.000
#> SRR1047869 1 0.0000 0.959 1.000 0.000
#> SRR1047870 1 0.5059 0.876 0.888 0.112
#> SRR1047871 1 0.0000 0.959 1.000 0.000
#> SRR1047872 1 0.0000 0.959 1.000 0.000
#> SRR1047873 1 0.0000 0.959 1.000 0.000
#> SRR1047874 1 0.0000 0.959 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1047813 1 0.0000 0.9655 1.000 0.000 0.000
#> SRR1047814 1 0.0000 0.9655 1.000 0.000 0.000
#> SRR1047815 1 0.0000 0.9655 1.000 0.000 0.000
#> SRR1047816 1 0.0000 0.9655 1.000 0.000 0.000
#> SRR1047817 1 0.0000 0.9655 1.000 0.000 0.000
#> SRR1047818 2 0.8470 0.3574 0.104 0.552 0.344
#> SRR1047819 2 0.7741 0.4365 0.376 0.568 0.056
#> SRR1047820 2 0.8087 0.4571 0.364 0.560 0.076
#> SRR1047821 2 0.8421 0.4310 0.116 0.584 0.300
#> SRR1047822 3 0.6126 0.1689 0.000 0.400 0.600
#> SRR1047823 1 0.1989 0.9323 0.948 0.048 0.004
#> SRR1047824 1 0.2496 0.9146 0.928 0.068 0.004
#> SRR1047825 1 0.1129 0.9523 0.976 0.020 0.004
#> SRR1047826 1 0.1399 0.9470 0.968 0.028 0.004
#> SRR1047827 1 0.2096 0.9291 0.944 0.052 0.004
#> SRR1047828 1 0.0000 0.9655 1.000 0.000 0.000
#> SRR1047829 1 0.0000 0.9655 1.000 0.000 0.000
#> SRR1047830 1 0.0000 0.9655 1.000 0.000 0.000
#> SRR1047831 1 0.0000 0.9655 1.000 0.000 0.000
#> SRR1047832 1 0.0000 0.9655 1.000 0.000 0.000
#> SRR1047833 2 0.0000 0.7269 0.000 1.000 0.000
#> SRR1047834 2 0.0000 0.7269 0.000 1.000 0.000
#> SRR1047835 2 0.0000 0.7269 0.000 1.000 0.000
#> SRR1047836 2 0.0000 0.7269 0.000 1.000 0.000
#> SRR1047837 2 0.0000 0.7269 0.000 1.000 0.000
#> SRR1047838 1 0.3918 0.8506 0.868 0.120 0.012
#> SRR1047839 3 0.8979 0.0836 0.420 0.128 0.452
#> SRR1047840 1 0.3695 0.8654 0.880 0.108 0.012
#> SRR1047841 1 0.4209 0.8359 0.856 0.128 0.016
#> SRR1047842 1 0.4277 0.8302 0.852 0.132 0.016
#> SRR1047843 1 0.0000 0.9655 1.000 0.000 0.000
#> SRR1047844 1 0.2878 0.8661 0.904 0.000 0.096
#> SRR1047845 1 0.0000 0.9655 1.000 0.000 0.000
#> SRR1047846 1 0.0000 0.9655 1.000 0.000 0.000
#> SRR1047847 1 0.2711 0.8766 0.912 0.000 0.088
#> SRR1047848 1 0.0000 0.9655 1.000 0.000 0.000
#> SRR1047849 1 0.0000 0.9655 1.000 0.000 0.000
#> SRR1047850 1 0.0000 0.9655 1.000 0.000 0.000
#> SRR1047851 1 0.0000 0.9655 1.000 0.000 0.000
#> SRR1047852 1 0.0000 0.9655 1.000 0.000 0.000
#> SRR1047853 3 0.6305 0.1808 0.484 0.000 0.516
#> SRR1047854 1 0.0424 0.9604 0.992 0.000 0.008
#> SRR1047855 1 0.0424 0.9604 0.992 0.000 0.008
#> SRR1047856 3 0.6140 0.3182 0.404 0.000 0.596
#> SRR1047857 3 0.5216 0.5052 0.260 0.000 0.740
#> SRR1047858 1 0.0000 0.9655 1.000 0.000 0.000
#> SRR1047859 1 0.0000 0.9655 1.000 0.000 0.000
#> SRR1047860 1 0.0000 0.9655 1.000 0.000 0.000
#> SRR1047861 1 0.0000 0.9655 1.000 0.000 0.000
#> SRR1047863 3 0.0237 0.7792 0.004 0.000 0.996
#> SRR1047864 3 0.0237 0.7792 0.004 0.000 0.996
#> SRR1047865 3 0.0237 0.7792 0.004 0.000 0.996
#> SRR1047866 3 0.0237 0.7792 0.004 0.000 0.996
#> SRR1047867 3 0.4702 0.5586 0.000 0.212 0.788
#> SRR1047868 3 0.0000 0.7774 0.000 0.000 1.000
#> SRR1047869 3 0.0237 0.7792 0.004 0.000 0.996
#> SRR1047870 3 0.0000 0.7774 0.000 0.000 1.000
#> SRR1047871 3 0.0237 0.7792 0.004 0.000 0.996
#> SRR1047872 3 0.0000 0.7774 0.000 0.000 1.000
#> SRR1047873 3 0.0000 0.7774 0.000 0.000 1.000
#> SRR1047874 3 0.0237 0.7792 0.004 0.000 0.996
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1047813 1 0.0000 0.930 1.000 0.000 0.000 0.000
#> SRR1047814 1 0.0000 0.930 1.000 0.000 0.000 0.000
#> SRR1047815 1 0.0000 0.930 1.000 0.000 0.000 0.000
#> SRR1047816 1 0.0000 0.930 1.000 0.000 0.000 0.000
#> SRR1047817 1 0.0000 0.930 1.000 0.000 0.000 0.000
#> SRR1047818 4 0.0000 0.910 0.000 0.000 0.000 1.000
#> SRR1047819 4 0.0000 0.910 0.000 0.000 0.000 1.000
#> SRR1047820 4 0.0000 0.910 0.000 0.000 0.000 1.000
#> SRR1047821 4 0.0000 0.910 0.000 0.000 0.000 1.000
#> SRR1047822 4 0.0188 0.908 0.000 0.000 0.004 0.996
#> SRR1047823 4 0.0707 0.905 0.020 0.000 0.000 0.980
#> SRR1047824 4 0.0592 0.907 0.016 0.000 0.000 0.984
#> SRR1047825 4 0.0921 0.901 0.028 0.000 0.000 0.972
#> SRR1047826 4 0.0921 0.901 0.028 0.000 0.000 0.972
#> SRR1047827 4 0.0592 0.907 0.016 0.000 0.000 0.984
#> SRR1047828 1 0.0336 0.927 0.992 0.008 0.000 0.000
#> SRR1047829 1 0.1022 0.913 0.968 0.032 0.000 0.000
#> SRR1047830 1 0.0336 0.927 0.992 0.008 0.000 0.000
#> SRR1047831 1 0.0336 0.927 0.992 0.008 0.000 0.000
#> SRR1047832 1 0.0592 0.922 0.984 0.016 0.000 0.000
#> SRR1047833 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> SRR1047834 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> SRR1047835 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> SRR1047836 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> SRR1047837 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> SRR1047838 4 0.0000 0.910 0.000 0.000 0.000 1.000
#> SRR1047839 4 0.0000 0.910 0.000 0.000 0.000 1.000
#> SRR1047840 4 0.0000 0.910 0.000 0.000 0.000 1.000
#> SRR1047841 4 0.0000 0.910 0.000 0.000 0.000 1.000
#> SRR1047842 4 0.0000 0.910 0.000 0.000 0.000 1.000
#> SRR1047843 1 0.0188 0.930 0.996 0.000 0.000 0.004
#> SRR1047844 1 0.2281 0.857 0.904 0.000 0.096 0.000
#> SRR1047845 1 0.0188 0.930 0.996 0.000 0.000 0.004
#> SRR1047846 1 0.0188 0.930 0.996 0.000 0.000 0.004
#> SRR1047847 1 0.2216 0.861 0.908 0.000 0.092 0.000
#> SRR1047848 1 0.0188 0.930 0.996 0.000 0.000 0.004
#> SRR1047849 1 0.0188 0.930 0.996 0.000 0.000 0.004
#> SRR1047850 1 0.0188 0.930 0.996 0.000 0.000 0.004
#> SRR1047851 1 0.0188 0.930 0.996 0.000 0.000 0.004
#> SRR1047852 1 0.0188 0.930 0.996 0.000 0.000 0.004
#> SRR1047853 4 0.4241 0.790 0.036 0.012 0.124 0.828
#> SRR1047854 4 0.5097 0.246 0.428 0.000 0.004 0.568
#> SRR1047855 4 0.5328 0.102 0.472 0.004 0.004 0.520
#> SRR1047856 4 0.3850 0.809 0.032 0.008 0.112 0.848
#> SRR1047857 4 0.1938 0.878 0.012 0.000 0.052 0.936
#> SRR1047858 1 0.4134 0.672 0.740 0.000 0.000 0.260
#> SRR1047859 1 0.4250 0.646 0.724 0.000 0.000 0.276
#> SRR1047860 1 0.4164 0.666 0.736 0.000 0.000 0.264
#> SRR1047861 1 0.4164 0.666 0.736 0.000 0.000 0.264
#> SRR1047863 3 0.0000 0.983 0.000 0.000 1.000 0.000
#> SRR1047864 3 0.0000 0.983 0.000 0.000 1.000 0.000
#> SRR1047865 3 0.0000 0.983 0.000 0.000 1.000 0.000
#> SRR1047866 3 0.0000 0.983 0.000 0.000 1.000 0.000
#> SRR1047867 3 0.2530 0.877 0.000 0.112 0.888 0.000
#> SRR1047868 3 0.0000 0.983 0.000 0.000 1.000 0.000
#> SRR1047869 3 0.0000 0.983 0.000 0.000 1.000 0.000
#> SRR1047870 3 0.0000 0.983 0.000 0.000 1.000 0.000
#> SRR1047871 3 0.0000 0.983 0.000 0.000 1.000 0.000
#> SRR1047872 3 0.1557 0.918 0.000 0.000 0.944 0.056
#> SRR1047873 3 0.0000 0.983 0.000 0.000 1.000 0.000
#> SRR1047874 3 0.0000 0.983 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
#> SRR1047813 5 0.3508 0.7564 0.252 0.000 0.000 0.000 0.748
#> SRR1047814 5 0.3508 0.7564 0.252 0.000 0.000 0.000 0.748
#> SRR1047815 5 0.3508 0.7564 0.252 0.000 0.000 0.000 0.748
#> SRR1047816 5 0.3508 0.7564 0.252 0.000 0.000 0.000 0.748
#> SRR1047817 5 0.3480 0.7570 0.248 0.000 0.000 0.000 0.752
#> SRR1047818 4 0.0404 0.8853 0.000 0.000 0.000 0.988 0.012
#> SRR1047819 4 0.0162 0.8847 0.000 0.000 0.000 0.996 0.004
#> SRR1047820 4 0.0000 0.8866 0.000 0.000 0.000 1.000 0.000
#> SRR1047821 4 0.0290 0.8870 0.000 0.000 0.000 0.992 0.008
#> SRR1047822 4 0.0703 0.8757 0.000 0.000 0.000 0.976 0.024
#> SRR1047823 1 0.5264 0.0323 0.500 0.016 0.000 0.464 0.020
#> SRR1047824 4 0.5181 0.1939 0.400 0.016 0.000 0.564 0.020
#> SRR1047825 1 0.5225 0.2750 0.576 0.016 0.000 0.384 0.024
#> SRR1047826 1 0.5292 0.1908 0.544 0.016 0.000 0.416 0.024
#> SRR1047827 4 0.5254 0.0278 0.448 0.016 0.000 0.516 0.020
#> SRR1047828 5 0.6452 0.6418 0.284 0.220 0.000 0.000 0.496
#> SRR1047829 5 0.6873 0.6134 0.228 0.268 0.016 0.000 0.488
#> SRR1047830 5 0.6467 0.6403 0.272 0.232 0.000 0.000 0.496
#> SRR1047831 5 0.6387 0.6549 0.272 0.216 0.000 0.000 0.512
#> SRR1047832 5 0.6477 0.6307 0.248 0.256 0.000 0.000 0.496
#> SRR1047833 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000
#> SRR1047834 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000
#> SRR1047835 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000
#> SRR1047836 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000
#> SRR1047837 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000
#> SRR1047838 4 0.0162 0.8878 0.000 0.000 0.000 0.996 0.004
#> SRR1047839 4 0.1121 0.8603 0.000 0.000 0.000 0.956 0.044
#> SRR1047840 4 0.0404 0.8789 0.000 0.000 0.000 0.988 0.012
#> SRR1047841 4 0.0162 0.8878 0.000 0.000 0.000 0.996 0.004
#> SRR1047842 4 0.0162 0.8878 0.000 0.000 0.000 0.996 0.004
#> SRR1047843 1 0.3165 0.7521 0.848 0.000 0.000 0.036 0.116
#> SRR1047844 3 0.5631 0.6126 0.200 0.000 0.684 0.040 0.076
#> SRR1047845 1 0.3099 0.7503 0.848 0.000 0.000 0.028 0.124
#> SRR1047846 1 0.2879 0.7666 0.868 0.000 0.000 0.032 0.100
#> SRR1047847 3 0.5715 0.6046 0.204 0.000 0.676 0.040 0.080
#> SRR1047848 1 0.0000 0.8277 1.000 0.000 0.000 0.000 0.000
#> SRR1047849 1 0.0000 0.8277 1.000 0.000 0.000 0.000 0.000
#> SRR1047850 1 0.0000 0.8277 1.000 0.000 0.000 0.000 0.000
#> SRR1047851 1 0.0000 0.8277 1.000 0.000 0.000 0.000 0.000
#> SRR1047852 1 0.0000 0.8277 1.000 0.000 0.000 0.000 0.000
#> SRR1047853 5 0.2929 0.6739 0.000 0.000 0.000 0.180 0.820
#> SRR1047854 5 0.3039 0.6899 0.012 0.000 0.000 0.152 0.836
#> SRR1047855 5 0.3098 0.6924 0.016 0.000 0.000 0.148 0.836
#> SRR1047856 5 0.3086 0.6738 0.000 0.000 0.004 0.180 0.816
#> SRR1047857 5 0.3305 0.6310 0.000 0.000 0.000 0.224 0.776
#> SRR1047858 1 0.0000 0.8277 1.000 0.000 0.000 0.000 0.000
#> SRR1047859 1 0.0798 0.8212 0.976 0.000 0.000 0.008 0.016
#> SRR1047860 1 0.0162 0.8272 0.996 0.000 0.000 0.000 0.004
#> SRR1047861 1 0.0324 0.8269 0.992 0.000 0.000 0.004 0.004
#> SRR1047863 3 0.0000 0.8973 0.000 0.000 1.000 0.000 0.000
#> SRR1047864 3 0.0162 0.8959 0.000 0.000 0.996 0.000 0.004
#> SRR1047865 3 0.0000 0.8973 0.000 0.000 1.000 0.000 0.000
#> SRR1047866 3 0.0000 0.8973 0.000 0.000 1.000 0.000 0.000
#> SRR1047867 3 0.4367 0.3755 0.000 0.372 0.620 0.000 0.008
#> SRR1047868 3 0.0000 0.8973 0.000 0.000 1.000 0.000 0.000
#> SRR1047869 3 0.0000 0.8973 0.000 0.000 1.000 0.000 0.000
#> SRR1047870 3 0.0000 0.8973 0.000 0.000 1.000 0.000 0.000
#> SRR1047871 3 0.0000 0.8973 0.000 0.000 1.000 0.000 0.000
#> SRR1047872 3 0.2561 0.7823 0.000 0.000 0.856 0.144 0.000
#> SRR1047873 3 0.0703 0.8845 0.000 0.000 0.976 0.024 0.000
#> SRR1047874 3 0.0162 0.8958 0.000 0.000 0.996 0.004 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1047813 5 0.0777 0.74523 0.024 0.000 0.000 0.000 0.972 0.004
#> SRR1047814 5 0.0891 0.74473 0.024 0.000 0.000 0.000 0.968 0.008
#> SRR1047815 5 0.0891 0.74473 0.024 0.000 0.000 0.000 0.968 0.008
#> SRR1047816 5 0.0632 0.74440 0.024 0.000 0.000 0.000 0.976 0.000
#> SRR1047817 5 0.1261 0.74060 0.024 0.000 0.000 0.000 0.952 0.024
#> SRR1047818 4 0.0405 0.86537 0.000 0.000 0.000 0.988 0.004 0.008
#> SRR1047819 4 0.0508 0.86456 0.000 0.000 0.000 0.984 0.004 0.012
#> SRR1047820 4 0.0508 0.86456 0.000 0.000 0.000 0.984 0.004 0.012
#> SRR1047821 4 0.0405 0.86537 0.000 0.000 0.000 0.988 0.004 0.008
#> SRR1047822 4 0.0858 0.86175 0.000 0.000 0.000 0.968 0.004 0.028
#> SRR1047823 1 0.6040 -0.00972 0.448 0.004 0.000 0.416 0.028 0.104
#> SRR1047824 4 0.5671 0.13443 0.372 0.004 0.000 0.512 0.012 0.100
#> SRR1047825 1 0.6036 0.09932 0.484 0.004 0.000 0.376 0.028 0.108
#> SRR1047826 1 0.6022 0.05948 0.472 0.004 0.000 0.392 0.028 0.104
#> SRR1047827 4 0.5834 0.00160 0.412 0.004 0.000 0.464 0.016 0.104
#> SRR1047828 5 0.6018 0.62055 0.108 0.124 0.000 0.000 0.620 0.148
#> SRR1047829 5 0.6373 0.60836 0.044 0.140 0.052 0.000 0.620 0.144
#> SRR1047830 5 0.5861 0.63143 0.084 0.124 0.000 0.000 0.632 0.160
#> SRR1047831 5 0.5693 0.64143 0.076 0.116 0.000 0.000 0.648 0.160
#> SRR1047832 5 0.6052 0.63329 0.068 0.120 0.016 0.000 0.636 0.160
#> SRR1047833 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1047834 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1047835 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1047836 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1047837 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1047838 4 0.0935 0.86372 0.004 0.000 0.000 0.964 0.000 0.032
#> SRR1047839 4 0.1843 0.82549 0.004 0.000 0.000 0.912 0.004 0.080
#> SRR1047840 4 0.0717 0.86531 0.008 0.000 0.000 0.976 0.000 0.016
#> SRR1047841 4 0.0937 0.86110 0.000 0.000 0.000 0.960 0.000 0.040
#> SRR1047842 4 0.0937 0.86110 0.000 0.000 0.000 0.960 0.000 0.040
#> SRR1047843 1 0.5104 -0.65251 0.496 0.000 0.004 0.004 0.056 0.440
#> SRR1047844 6 0.6518 0.96403 0.360 0.000 0.116 0.016 0.040 0.468
#> SRR1047845 1 0.5384 -0.68284 0.480 0.000 0.012 0.004 0.064 0.440
#> SRR1047846 1 0.5338 -0.67599 0.484 0.000 0.012 0.004 0.060 0.440
#> SRR1047847 6 0.6471 0.96351 0.368 0.000 0.100 0.020 0.040 0.472
#> SRR1047848 1 0.1092 0.45395 0.960 0.000 0.000 0.000 0.020 0.020
#> SRR1047849 1 0.0547 0.45962 0.980 0.000 0.000 0.000 0.020 0.000
#> SRR1047850 1 0.0547 0.45962 0.980 0.000 0.000 0.000 0.020 0.000
#> SRR1047851 1 0.0547 0.45962 0.980 0.000 0.000 0.000 0.020 0.000
#> SRR1047852 1 0.0547 0.45962 0.980 0.000 0.000 0.000 0.020 0.000
#> SRR1047853 5 0.4952 0.58983 0.008 0.000 0.000 0.132 0.672 0.188
#> SRR1047854 5 0.3635 0.68568 0.008 0.000 0.000 0.068 0.804 0.120
#> SRR1047855 5 0.3419 0.69341 0.008 0.000 0.000 0.056 0.820 0.116
#> SRR1047856 5 0.5156 0.56375 0.008 0.000 0.000 0.140 0.644 0.208
#> SRR1047857 5 0.5768 0.41228 0.008 0.000 0.000 0.168 0.532 0.292
#> SRR1047858 1 0.3736 0.40952 0.776 0.000 0.000 0.000 0.156 0.068
#> SRR1047859 1 0.4131 0.38488 0.744 0.000 0.000 0.000 0.156 0.100
#> SRR1047860 1 0.3842 0.40606 0.768 0.000 0.000 0.000 0.156 0.076
#> SRR1047861 1 0.3893 0.40309 0.764 0.000 0.000 0.000 0.156 0.080
#> SRR1047863 3 0.1714 0.88347 0.000 0.000 0.908 0.000 0.000 0.092
#> SRR1047864 3 0.1556 0.88379 0.000 0.000 0.920 0.000 0.000 0.080
#> SRR1047865 3 0.0146 0.90446 0.000 0.000 0.996 0.000 0.000 0.004
#> SRR1047866 3 0.0146 0.90446 0.000 0.000 0.996 0.000 0.000 0.004
#> SRR1047867 3 0.5480 0.49761 0.000 0.252 0.580 0.000 0.004 0.164
#> SRR1047868 3 0.0000 0.90431 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047869 3 0.1007 0.88945 0.000 0.000 0.956 0.000 0.000 0.044
#> SRR1047870 3 0.1610 0.88243 0.000 0.000 0.916 0.000 0.000 0.084
#> SRR1047871 3 0.0146 0.90442 0.000 0.000 0.996 0.000 0.000 0.004
#> SRR1047872 3 0.3154 0.74137 0.000 0.000 0.800 0.184 0.004 0.012
#> SRR1047873 3 0.1225 0.89114 0.000 0.000 0.952 0.036 0.000 0.012
#> SRR1047874 3 0.1575 0.88625 0.000 0.000 0.936 0.032 0.000 0.032
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 17931 rows and 61 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 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 0.998 0.999 0.18291 0.820 0.820
#> 3 3 0.812 0.845 0.937 0.75977 0.942 0.929
#> 4 4 0.805 0.828 0.938 0.00802 0.997 0.996
#> 5 5 0.757 0.925 0.971 0.44169 0.784 0.715
#> 6 6 0.658 0.731 0.819 0.43631 0.762 0.562
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
#> SRR1047813 1 0.000 0.999 1.000 0.000
#> SRR1047814 1 0.000 0.999 1.000 0.000
#> SRR1047815 1 0.000 0.999 1.000 0.000
#> SRR1047816 1 0.000 0.999 1.000 0.000
#> SRR1047817 1 0.000 0.999 1.000 0.000
#> SRR1047818 1 0.000 0.999 1.000 0.000
#> SRR1047819 1 0.000 0.999 1.000 0.000
#> SRR1047820 1 0.000 0.999 1.000 0.000
#> SRR1047821 1 0.000 0.999 1.000 0.000
#> SRR1047822 1 0.000 0.999 1.000 0.000
#> SRR1047823 1 0.000 0.999 1.000 0.000
#> SRR1047824 1 0.000 0.999 1.000 0.000
#> SRR1047825 1 0.000 0.999 1.000 0.000
#> SRR1047826 1 0.000 0.999 1.000 0.000
#> SRR1047827 1 0.000 0.999 1.000 0.000
#> SRR1047828 1 0.000 0.999 1.000 0.000
#> SRR1047829 1 0.000 0.999 1.000 0.000
#> SRR1047830 1 0.000 0.999 1.000 0.000
#> SRR1047831 1 0.000 0.999 1.000 0.000
#> SRR1047832 1 0.000 0.999 1.000 0.000
#> SRR1047833 2 0.000 1.000 0.000 1.000
#> SRR1047834 2 0.000 1.000 0.000 1.000
#> SRR1047835 2 0.000 1.000 0.000 1.000
#> SRR1047836 2 0.000 1.000 0.000 1.000
#> SRR1047837 2 0.000 1.000 0.000 1.000
#> SRR1047838 1 0.000 0.999 1.000 0.000
#> SRR1047839 1 0.000 0.999 1.000 0.000
#> SRR1047840 1 0.000 0.999 1.000 0.000
#> SRR1047841 1 0.000 0.999 1.000 0.000
#> SRR1047842 1 0.000 0.999 1.000 0.000
#> SRR1047843 1 0.000 0.999 1.000 0.000
#> SRR1047844 1 0.000 0.999 1.000 0.000
#> SRR1047845 1 0.000 0.999 1.000 0.000
#> SRR1047846 1 0.000 0.999 1.000 0.000
#> SRR1047847 1 0.000 0.999 1.000 0.000
#> SRR1047848 1 0.000 0.999 1.000 0.000
#> SRR1047849 1 0.000 0.999 1.000 0.000
#> SRR1047850 1 0.000 0.999 1.000 0.000
#> SRR1047851 1 0.000 0.999 1.000 0.000
#> SRR1047852 1 0.000 0.999 1.000 0.000
#> SRR1047853 1 0.000 0.999 1.000 0.000
#> SRR1047854 1 0.000 0.999 1.000 0.000
#> SRR1047855 1 0.000 0.999 1.000 0.000
#> SRR1047856 1 0.000 0.999 1.000 0.000
#> SRR1047857 1 0.000 0.999 1.000 0.000
#> SRR1047858 1 0.000 0.999 1.000 0.000
#> SRR1047859 1 0.000 0.999 1.000 0.000
#> SRR1047860 1 0.000 0.999 1.000 0.000
#> SRR1047861 1 0.000 0.999 1.000 0.000
#> SRR1047863 1 0.000 0.999 1.000 0.000
#> SRR1047864 1 0.358 0.927 0.932 0.068
#> SRR1047865 1 0.000 0.999 1.000 0.000
#> SRR1047866 1 0.000 0.999 1.000 0.000
#> SRR1047867 2 0.000 1.000 0.000 1.000
#> SRR1047868 1 0.000 0.999 1.000 0.000
#> SRR1047869 1 0.000 0.999 1.000 0.000
#> SRR1047870 1 0.000 0.999 1.000 0.000
#> SRR1047871 1 0.000 0.999 1.000 0.000
#> SRR1047872 1 0.000 0.999 1.000 0.000
#> SRR1047873 1 0.000 0.999 1.000 0.000
#> SRR1047874 1 0.000 0.999 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1047813 1 0.0000 0.920 1.000 0.000 0.000
#> SRR1047814 1 0.0000 0.920 1.000 0.000 0.000
#> SRR1047815 1 0.0000 0.920 1.000 0.000 0.000
#> SRR1047816 1 0.0000 0.920 1.000 0.000 0.000
#> SRR1047817 1 0.0000 0.920 1.000 0.000 0.000
#> SRR1047818 1 0.0892 0.907 0.980 0.000 0.020
#> SRR1047819 1 0.0892 0.907 0.980 0.000 0.020
#> SRR1047820 1 0.0892 0.907 0.980 0.000 0.020
#> SRR1047821 1 0.0892 0.907 0.980 0.000 0.020
#> SRR1047822 1 0.0892 0.907 0.980 0.000 0.020
#> SRR1047823 1 0.0000 0.920 1.000 0.000 0.000
#> SRR1047824 1 0.0000 0.920 1.000 0.000 0.000
#> SRR1047825 1 0.0000 0.920 1.000 0.000 0.000
#> SRR1047826 1 0.0000 0.920 1.000 0.000 0.000
#> SRR1047827 1 0.0000 0.920 1.000 0.000 0.000
#> SRR1047828 1 0.0000 0.920 1.000 0.000 0.000
#> SRR1047829 1 0.0000 0.920 1.000 0.000 0.000
#> SRR1047830 1 0.0000 0.920 1.000 0.000 0.000
#> SRR1047831 1 0.0000 0.920 1.000 0.000 0.000
#> SRR1047832 1 0.0000 0.920 1.000 0.000 0.000
#> SRR1047833 2 0.0000 0.988 0.000 1.000 0.000
#> SRR1047834 2 0.0000 0.988 0.000 1.000 0.000
#> SRR1047835 2 0.0000 0.988 0.000 1.000 0.000
#> SRR1047836 2 0.0000 0.988 0.000 1.000 0.000
#> SRR1047837 2 0.0000 0.988 0.000 1.000 0.000
#> SRR1047838 1 0.0000 0.920 1.000 0.000 0.000
#> SRR1047839 1 0.0000 0.920 1.000 0.000 0.000
#> SRR1047840 1 0.0000 0.920 1.000 0.000 0.000
#> SRR1047841 1 0.0000 0.920 1.000 0.000 0.000
#> SRR1047842 1 0.0000 0.920 1.000 0.000 0.000
#> SRR1047843 1 0.0000 0.920 1.000 0.000 0.000
#> SRR1047844 1 0.0000 0.920 1.000 0.000 0.000
#> SRR1047845 1 0.0000 0.920 1.000 0.000 0.000
#> SRR1047846 1 0.0000 0.920 1.000 0.000 0.000
#> SRR1047847 1 0.0000 0.920 1.000 0.000 0.000
#> SRR1047848 1 0.0000 0.920 1.000 0.000 0.000
#> SRR1047849 1 0.0000 0.920 1.000 0.000 0.000
#> SRR1047850 1 0.0000 0.920 1.000 0.000 0.000
#> SRR1047851 1 0.0000 0.920 1.000 0.000 0.000
#> SRR1047852 1 0.0000 0.920 1.000 0.000 0.000
#> SRR1047853 1 0.0000 0.920 1.000 0.000 0.000
#> SRR1047854 1 0.0000 0.920 1.000 0.000 0.000
#> SRR1047855 1 0.0000 0.920 1.000 0.000 0.000
#> SRR1047856 1 0.0000 0.920 1.000 0.000 0.000
#> SRR1047857 1 0.0000 0.920 1.000 0.000 0.000
#> SRR1047858 1 0.0000 0.920 1.000 0.000 0.000
#> SRR1047859 1 0.0000 0.920 1.000 0.000 0.000
#> SRR1047860 1 0.0000 0.920 1.000 0.000 0.000
#> SRR1047861 1 0.0000 0.920 1.000 0.000 0.000
#> SRR1047863 1 0.6168 0.379 0.588 0.000 0.412
#> SRR1047864 3 0.0000 0.830 0.000 0.000 1.000
#> SRR1047865 1 0.6154 0.389 0.592 0.000 0.408
#> SRR1047866 3 0.2261 0.838 0.068 0.000 0.932
#> SRR1047867 2 0.2261 0.940 0.000 0.932 0.068
#> SRR1047868 1 0.6111 0.415 0.604 0.000 0.396
#> SRR1047869 1 0.6126 0.406 0.600 0.000 0.400
#> SRR1047870 1 0.6168 0.379 0.588 0.000 0.412
#> SRR1047871 1 0.6111 0.415 0.604 0.000 0.396
#> SRR1047872 1 0.6154 0.389 0.592 0.000 0.408
#> SRR1047873 1 0.6111 0.415 0.604 0.000 0.396
#> SRR1047874 1 0.6111 0.415 0.604 0.000 0.396
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1047813 1 0.0000 0.920 1.000 0 0.000 0.000
#> SRR1047814 1 0.0000 0.920 1.000 0 0.000 0.000
#> SRR1047815 1 0.0000 0.920 1.000 0 0.000 0.000
#> SRR1047816 1 0.0000 0.920 1.000 0 0.000 0.000
#> SRR1047817 1 0.0000 0.920 1.000 0 0.000 0.000
#> SRR1047818 1 0.0707 0.907 0.980 0 0.000 0.020
#> SRR1047819 1 0.0707 0.907 0.980 0 0.000 0.020
#> SRR1047820 1 0.0707 0.907 0.980 0 0.000 0.020
#> SRR1047821 1 0.0707 0.907 0.980 0 0.000 0.020
#> SRR1047822 1 0.0707 0.907 0.980 0 0.000 0.020
#> SRR1047823 1 0.0000 0.920 1.000 0 0.000 0.000
#> SRR1047824 1 0.0000 0.920 1.000 0 0.000 0.000
#> SRR1047825 1 0.0000 0.920 1.000 0 0.000 0.000
#> SRR1047826 1 0.0000 0.920 1.000 0 0.000 0.000
#> SRR1047827 1 0.0000 0.920 1.000 0 0.000 0.000
#> SRR1047828 1 0.0000 0.920 1.000 0 0.000 0.000
#> SRR1047829 1 0.0000 0.920 1.000 0 0.000 0.000
#> SRR1047830 1 0.0000 0.920 1.000 0 0.000 0.000
#> SRR1047831 1 0.0000 0.920 1.000 0 0.000 0.000
#> SRR1047832 1 0.0000 0.920 1.000 0 0.000 0.000
#> SRR1047833 2 0.0000 1.000 0.000 1 0.000 0.000
#> SRR1047834 2 0.0000 1.000 0.000 1 0.000 0.000
#> SRR1047835 2 0.0000 1.000 0.000 1 0.000 0.000
#> SRR1047836 2 0.0000 1.000 0.000 1 0.000 0.000
#> SRR1047837 2 0.0000 1.000 0.000 1 0.000 0.000
#> SRR1047838 1 0.0000 0.920 1.000 0 0.000 0.000
#> SRR1047839 1 0.0000 0.920 1.000 0 0.000 0.000
#> SRR1047840 1 0.0000 0.920 1.000 0 0.000 0.000
#> SRR1047841 1 0.0000 0.920 1.000 0 0.000 0.000
#> SRR1047842 1 0.0000 0.920 1.000 0 0.000 0.000
#> SRR1047843 1 0.0000 0.920 1.000 0 0.000 0.000
#> SRR1047844 1 0.0000 0.920 1.000 0 0.000 0.000
#> SRR1047845 1 0.0000 0.920 1.000 0 0.000 0.000
#> SRR1047846 1 0.0000 0.920 1.000 0 0.000 0.000
#> SRR1047847 1 0.0000 0.920 1.000 0 0.000 0.000
#> SRR1047848 1 0.0000 0.920 1.000 0 0.000 0.000
#> SRR1047849 1 0.0000 0.920 1.000 0 0.000 0.000
#> SRR1047850 1 0.0000 0.920 1.000 0 0.000 0.000
#> SRR1047851 1 0.0000 0.920 1.000 0 0.000 0.000
#> SRR1047852 1 0.0000 0.920 1.000 0 0.000 0.000
#> SRR1047853 1 0.0000 0.920 1.000 0 0.000 0.000
#> SRR1047854 1 0.0000 0.920 1.000 0 0.000 0.000
#> SRR1047855 1 0.0000 0.920 1.000 0 0.000 0.000
#> SRR1047856 1 0.0000 0.920 1.000 0 0.000 0.000
#> SRR1047857 1 0.0000 0.920 1.000 0 0.000 0.000
#> SRR1047858 1 0.0000 0.920 1.000 0 0.000 0.000
#> SRR1047859 1 0.0000 0.920 1.000 0 0.000 0.000
#> SRR1047860 1 0.0000 0.920 1.000 0 0.000 0.000
#> SRR1047861 1 0.0000 0.920 1.000 0 0.000 0.000
#> SRR1047863 1 0.4888 0.379 0.588 0 0.000 0.412
#> SRR1047864 3 0.4888 0.758 0.000 0 0.588 0.412
#> SRR1047865 1 0.4877 0.389 0.592 0 0.000 0.408
#> SRR1047866 3 0.6407 0.776 0.068 0 0.520 0.412
#> SRR1047867 4 0.4888 0.000 0.000 0 0.412 0.588
#> SRR1047868 1 0.4843 0.415 0.604 0 0.000 0.396
#> SRR1047869 1 0.4855 0.406 0.600 0 0.000 0.400
#> SRR1047870 1 0.4888 0.379 0.588 0 0.000 0.412
#> SRR1047871 1 0.4843 0.415 0.604 0 0.000 0.396
#> SRR1047872 1 0.4877 0.389 0.592 0 0.000 0.408
#> SRR1047873 1 0.4843 0.415 0.604 0 0.000 0.396
#> SRR1047874 1 0.4843 0.415 0.604 0 0.000 0.396
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1047813 4 0.0000 0.966 0.00 0 0.000 1.000 0
#> SRR1047814 4 0.0000 0.966 0.00 0 0.000 1.000 0
#> SRR1047815 4 0.0000 0.966 0.00 0 0.000 1.000 0
#> SRR1047816 4 0.0000 0.966 0.00 0 0.000 1.000 0
#> SRR1047817 4 0.0000 0.966 0.00 0 0.000 1.000 0
#> SRR1047818 4 0.2605 0.854 0.00 0 0.148 0.852 0
#> SRR1047819 4 0.2605 0.854 0.00 0 0.148 0.852 0
#> SRR1047820 4 0.2605 0.854 0.00 0 0.148 0.852 0
#> SRR1047821 4 0.2605 0.854 0.00 0 0.148 0.852 0
#> SRR1047822 4 0.2605 0.854 0.00 0 0.148 0.852 0
#> SRR1047823 4 0.0000 0.966 0.00 0 0.000 1.000 0
#> SRR1047824 4 0.0000 0.966 0.00 0 0.000 1.000 0
#> SRR1047825 4 0.0000 0.966 0.00 0 0.000 1.000 0
#> SRR1047826 4 0.0000 0.966 0.00 0 0.000 1.000 0
#> SRR1047827 4 0.0000 0.966 0.00 0 0.000 1.000 0
#> SRR1047828 4 0.2230 0.885 0.00 0 0.116 0.884 0
#> SRR1047829 4 0.2230 0.885 0.00 0 0.116 0.884 0
#> SRR1047830 4 0.2230 0.885 0.00 0 0.116 0.884 0
#> SRR1047831 4 0.2230 0.885 0.00 0 0.116 0.884 0
#> SRR1047832 4 0.2230 0.885 0.00 0 0.116 0.884 0
#> SRR1047833 2 0.0000 1.000 0.00 1 0.000 0.000 0
#> SRR1047834 2 0.0000 1.000 0.00 1 0.000 0.000 0
#> SRR1047835 2 0.0000 1.000 0.00 1 0.000 0.000 0
#> SRR1047836 2 0.0000 1.000 0.00 1 0.000 0.000 0
#> SRR1047837 2 0.0000 1.000 0.00 1 0.000 0.000 0
#> SRR1047838 4 0.0000 0.966 0.00 0 0.000 1.000 0
#> SRR1047839 4 0.0000 0.966 0.00 0 0.000 1.000 0
#> SRR1047840 4 0.0000 0.966 0.00 0 0.000 1.000 0
#> SRR1047841 4 0.0000 0.966 0.00 0 0.000 1.000 0
#> SRR1047842 4 0.0000 0.966 0.00 0 0.000 1.000 0
#> SRR1047843 4 0.0000 0.966 0.00 0 0.000 1.000 0
#> SRR1047844 4 0.0000 0.966 0.00 0 0.000 1.000 0
#> SRR1047845 4 0.0000 0.966 0.00 0 0.000 1.000 0
#> SRR1047846 4 0.0000 0.966 0.00 0 0.000 1.000 0
#> SRR1047847 4 0.0000 0.966 0.00 0 0.000 1.000 0
#> SRR1047848 4 0.0000 0.966 0.00 0 0.000 1.000 0
#> SRR1047849 4 0.0000 0.966 0.00 0 0.000 1.000 0
#> SRR1047850 4 0.0000 0.966 0.00 0 0.000 1.000 0
#> SRR1047851 4 0.0000 0.966 0.00 0 0.000 1.000 0
#> SRR1047852 4 0.0000 0.966 0.00 0 0.000 1.000 0
#> SRR1047853 4 0.0000 0.966 0.00 0 0.000 1.000 0
#> SRR1047854 4 0.0000 0.966 0.00 0 0.000 1.000 0
#> SRR1047855 4 0.0000 0.966 0.00 0 0.000 1.000 0
#> SRR1047856 4 0.0000 0.966 0.00 0 0.000 1.000 0
#> SRR1047857 4 0.0000 0.966 0.00 0 0.000 1.000 0
#> SRR1047858 4 0.0000 0.966 0.00 0 0.000 1.000 0
#> SRR1047859 4 0.0000 0.966 0.00 0 0.000 1.000 0
#> SRR1047860 4 0.0000 0.966 0.00 0 0.000 1.000 0
#> SRR1047861 4 0.0000 0.966 0.00 0 0.000 1.000 0
#> SRR1047863 3 0.0000 0.886 0.00 0 1.000 0.000 0
#> SRR1047864 1 0.0000 0.884 1.00 0 0.000 0.000 0
#> SRR1047865 3 0.0162 0.892 0.00 0 0.996 0.004 0
#> SRR1047866 1 0.1732 0.885 0.92 0 0.080 0.000 0
#> SRR1047867 5 0.0000 0.000 0.00 0 0.000 0.000 1
#> SRR1047868 3 0.1671 0.914 0.00 0 0.924 0.076 0
#> SRR1047869 3 0.1608 0.914 0.00 0 0.928 0.072 0
#> SRR1047870 3 0.0000 0.886 0.00 0 1.000 0.000 0
#> SRR1047871 3 0.1671 0.914 0.00 0 0.924 0.076 0
#> SRR1047872 3 0.0162 0.892 0.00 0 0.996 0.004 0
#> SRR1047873 3 0.1671 0.914 0.00 0 0.924 0.076 0
#> SRR1047874 3 0.1671 0.914 0.00 0 0.924 0.076 0
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1047813 1 0.3747 1.000 0.604 0 0.000 0.396 0.000 0
#> SRR1047814 1 0.3747 1.000 0.604 0 0.000 0.396 0.000 0
#> SRR1047815 1 0.3747 1.000 0.604 0 0.000 0.396 0.000 0
#> SRR1047816 1 0.3747 1.000 0.604 0 0.000 0.396 0.000 0
#> SRR1047817 1 0.3747 1.000 0.604 0 0.000 0.396 0.000 0
#> SRR1047818 4 0.5391 0.501 0.244 0 0.176 0.580 0.000 0
#> SRR1047819 4 0.5391 0.501 0.244 0 0.176 0.580 0.000 0
#> SRR1047820 4 0.5391 0.501 0.244 0 0.176 0.580 0.000 0
#> SRR1047821 4 0.5391 0.501 0.244 0 0.176 0.580 0.000 0
#> SRR1047822 4 0.5391 0.501 0.244 0 0.176 0.580 0.000 0
#> SRR1047823 1 0.3747 1.000 0.604 0 0.000 0.396 0.000 0
#> SRR1047824 1 0.3747 1.000 0.604 0 0.000 0.396 0.000 0
#> SRR1047825 1 0.3747 1.000 0.604 0 0.000 0.396 0.000 0
#> SRR1047826 1 0.3747 1.000 0.604 0 0.000 0.396 0.000 0
#> SRR1047827 1 0.3747 1.000 0.604 0 0.000 0.396 0.000 0
#> SRR1047828 4 0.5186 0.538 0.232 0 0.156 0.612 0.000 0
#> SRR1047829 4 0.5186 0.538 0.232 0 0.156 0.612 0.000 0
#> SRR1047830 4 0.5186 0.538 0.232 0 0.156 0.612 0.000 0
#> SRR1047831 4 0.5186 0.538 0.232 0 0.156 0.612 0.000 0
#> SRR1047832 4 0.5186 0.538 0.232 0 0.156 0.612 0.000 0
#> SRR1047833 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0
#> SRR1047834 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0
#> SRR1047835 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0
#> SRR1047836 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0
#> SRR1047837 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0
#> SRR1047838 4 0.0000 0.677 0.000 0 0.000 1.000 0.000 0
#> SRR1047839 4 0.0000 0.677 0.000 0 0.000 1.000 0.000 0
#> SRR1047840 4 0.0000 0.677 0.000 0 0.000 1.000 0.000 0
#> SRR1047841 4 0.0000 0.677 0.000 0 0.000 1.000 0.000 0
#> SRR1047842 4 0.0000 0.677 0.000 0 0.000 1.000 0.000 0
#> SRR1047843 4 0.0000 0.677 0.000 0 0.000 1.000 0.000 0
#> SRR1047844 4 0.0000 0.677 0.000 0 0.000 1.000 0.000 0
#> SRR1047845 4 0.0000 0.677 0.000 0 0.000 1.000 0.000 0
#> SRR1047846 4 0.0000 0.677 0.000 0 0.000 1.000 0.000 0
#> SRR1047847 4 0.0000 0.677 0.000 0 0.000 1.000 0.000 0
#> SRR1047848 1 0.3747 1.000 0.604 0 0.000 0.396 0.000 0
#> SRR1047849 1 0.3747 1.000 0.604 0 0.000 0.396 0.000 0
#> SRR1047850 1 0.3747 1.000 0.604 0 0.000 0.396 0.000 0
#> SRR1047851 1 0.3747 1.000 0.604 0 0.000 0.396 0.000 0
#> SRR1047852 1 0.3747 1.000 0.604 0 0.000 0.396 0.000 0
#> SRR1047853 4 0.0000 0.677 0.000 0 0.000 1.000 0.000 0
#> SRR1047854 4 0.0000 0.677 0.000 0 0.000 1.000 0.000 0
#> SRR1047855 4 0.0000 0.677 0.000 0 0.000 1.000 0.000 0
#> SRR1047856 4 0.0000 0.677 0.000 0 0.000 1.000 0.000 0
#> SRR1047857 4 0.0000 0.677 0.000 0 0.000 1.000 0.000 0
#> SRR1047858 4 0.3428 -0.198 0.304 0 0.000 0.696 0.000 0
#> SRR1047859 4 0.3428 -0.198 0.304 0 0.000 0.696 0.000 0
#> SRR1047860 4 0.3428 -0.198 0.304 0 0.000 0.696 0.000 0
#> SRR1047861 4 0.3428 -0.198 0.304 0 0.000 0.696 0.000 0
#> SRR1047863 3 0.1152 0.927 0.044 0 0.952 0.000 0.004 0
#> SRR1047864 5 0.2092 0.805 0.124 0 0.000 0.000 0.876 0
#> SRR1047865 3 0.1007 0.930 0.044 0 0.956 0.000 0.000 0
#> SRR1047866 5 0.1765 0.806 0.052 0 0.024 0.000 0.924 0
#> SRR1047867 6 0.0000 0.000 0.000 0 0.000 0.000 0.000 1
#> SRR1047868 3 0.1257 0.939 0.020 0 0.952 0.028 0.000 0
#> SRR1047869 3 0.0632 0.939 0.000 0 0.976 0.024 0.000 0
#> SRR1047870 3 0.1152 0.927 0.044 0 0.952 0.000 0.004 0
#> SRR1047871 3 0.1257 0.939 0.020 0 0.952 0.028 0.000 0
#> SRR1047872 3 0.1007 0.930 0.044 0 0.956 0.000 0.000 0
#> SRR1047873 3 0.1257 0.939 0.020 0 0.952 0.028 0.000 0
#> SRR1047874 3 0.1257 0.939 0.020 0 0.952 0.028 0.000 0
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 17931 rows and 61 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 1.000 1.000 0.1811 0.820 0.820
#> 3 3 0.478 0.254 0.571 1.7964 0.587 0.496
#> 4 4 0.574 0.735 0.852 0.3585 0.756 0.483
#> 5 5 0.635 0.685 0.794 0.1011 1.000 1.000
#> 6 6 0.693 0.702 0.730 0.0551 0.866 0.563
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
#> SRR1047813 1 0 1 1 0
#> SRR1047814 1 0 1 1 0
#> SRR1047815 1 0 1 1 0
#> SRR1047816 1 0 1 1 0
#> SRR1047817 1 0 1 1 0
#> SRR1047818 1 0 1 1 0
#> SRR1047819 1 0 1 1 0
#> SRR1047820 1 0 1 1 0
#> SRR1047821 1 0 1 1 0
#> SRR1047822 1 0 1 1 0
#> SRR1047823 1 0 1 1 0
#> SRR1047824 1 0 1 1 0
#> SRR1047825 1 0 1 1 0
#> SRR1047826 1 0 1 1 0
#> SRR1047827 1 0 1 1 0
#> SRR1047828 1 0 1 1 0
#> SRR1047829 1 0 1 1 0
#> SRR1047830 1 0 1 1 0
#> SRR1047831 1 0 1 1 0
#> SRR1047832 1 0 1 1 0
#> SRR1047833 2 0 1 0 1
#> SRR1047834 2 0 1 0 1
#> SRR1047835 2 0 1 0 1
#> SRR1047836 2 0 1 0 1
#> SRR1047837 2 0 1 0 1
#> SRR1047838 1 0 1 1 0
#> SRR1047839 1 0 1 1 0
#> SRR1047840 1 0 1 1 0
#> SRR1047841 1 0 1 1 0
#> SRR1047842 1 0 1 1 0
#> SRR1047843 1 0 1 1 0
#> SRR1047844 1 0 1 1 0
#> SRR1047845 1 0 1 1 0
#> SRR1047846 1 0 1 1 0
#> SRR1047847 1 0 1 1 0
#> SRR1047848 1 0 1 1 0
#> SRR1047849 1 0 1 1 0
#> SRR1047850 1 0 1 1 0
#> SRR1047851 1 0 1 1 0
#> SRR1047852 1 0 1 1 0
#> SRR1047853 1 0 1 1 0
#> SRR1047854 1 0 1 1 0
#> SRR1047855 1 0 1 1 0
#> SRR1047856 1 0 1 1 0
#> SRR1047857 1 0 1 1 0
#> SRR1047858 1 0 1 1 0
#> SRR1047859 1 0 1 1 0
#> SRR1047860 1 0 1 1 0
#> SRR1047861 1 0 1 1 0
#> SRR1047863 1 0 1 1 0
#> SRR1047864 1 0 1 1 0
#> SRR1047865 1 0 1 1 0
#> SRR1047866 1 0 1 1 0
#> SRR1047867 2 0 1 0 1
#> SRR1047868 1 0 1 1 0
#> SRR1047869 1 0 1 1 0
#> SRR1047870 1 0 1 1 0
#> SRR1047871 1 0 1 1 0
#> SRR1047872 1 0 1 1 0
#> SRR1047873 1 0 1 1 0
#> SRR1047874 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1047813 1 0.622 0.1894 0.568 0.000 0.432
#> SRR1047814 1 0.622 0.1894 0.568 0.000 0.432
#> SRR1047815 1 0.622 0.1894 0.568 0.000 0.432
#> SRR1047816 1 0.622 0.1894 0.568 0.000 0.432
#> SRR1047817 1 0.627 0.1120 0.544 0.000 0.456
#> SRR1047818 1 0.319 0.2840 0.888 0.000 0.112
#> SRR1047819 1 0.319 0.2840 0.888 0.000 0.112
#> SRR1047820 1 0.319 0.2840 0.888 0.000 0.112
#> SRR1047821 1 0.319 0.2840 0.888 0.000 0.112
#> SRR1047822 1 0.312 0.2825 0.892 0.000 0.108
#> SRR1047823 1 0.622 0.1894 0.568 0.000 0.432
#> SRR1047824 1 0.622 0.1894 0.568 0.000 0.432
#> SRR1047825 1 0.622 0.1894 0.568 0.000 0.432
#> SRR1047826 1 0.622 0.1894 0.568 0.000 0.432
#> SRR1047827 1 0.622 0.1894 0.568 0.000 0.432
#> SRR1047828 1 0.000 0.3147 1.000 0.000 0.000
#> SRR1047829 1 0.000 0.3147 1.000 0.000 0.000
#> SRR1047830 1 0.000 0.3147 1.000 0.000 0.000
#> SRR1047831 1 0.000 0.3147 1.000 0.000 0.000
#> SRR1047832 1 0.000 0.3147 1.000 0.000 0.000
#> SRR1047833 2 0.000 0.9969 0.000 1.000 0.000
#> SRR1047834 2 0.000 0.9969 0.000 1.000 0.000
#> SRR1047835 2 0.000 0.9969 0.000 1.000 0.000
#> SRR1047836 2 0.000 0.9969 0.000 1.000 0.000
#> SRR1047837 2 0.000 0.9969 0.000 1.000 0.000
#> SRR1047838 3 0.627 0.2019 0.452 0.000 0.548
#> SRR1047839 3 0.627 0.2019 0.452 0.000 0.548
#> SRR1047840 3 0.627 0.2019 0.452 0.000 0.548
#> SRR1047841 3 0.627 0.2019 0.452 0.000 0.548
#> SRR1047842 3 0.627 0.2019 0.452 0.000 0.548
#> SRR1047843 3 0.627 0.2019 0.452 0.000 0.548
#> SRR1047844 3 0.627 0.2019 0.452 0.000 0.548
#> SRR1047845 3 0.627 0.2019 0.452 0.000 0.548
#> SRR1047846 3 0.627 0.2019 0.452 0.000 0.548
#> SRR1047847 3 0.627 0.2019 0.452 0.000 0.548
#> SRR1047848 1 0.621 0.1921 0.572 0.000 0.428
#> SRR1047849 1 0.621 0.1921 0.572 0.000 0.428
#> SRR1047850 1 0.621 0.1921 0.572 0.000 0.428
#> SRR1047851 1 0.621 0.1921 0.572 0.000 0.428
#> SRR1047852 1 0.621 0.1921 0.572 0.000 0.428
#> SRR1047853 3 0.627 0.2019 0.452 0.000 0.548
#> SRR1047854 3 0.627 0.2019 0.452 0.000 0.548
#> SRR1047855 3 0.627 0.2019 0.452 0.000 0.548
#> SRR1047856 3 0.627 0.2019 0.452 0.000 0.548
#> SRR1047857 3 0.627 0.2019 0.452 0.000 0.548
#> SRR1047858 3 0.627 0.2019 0.452 0.000 0.548
#> SRR1047859 3 0.627 0.2019 0.452 0.000 0.548
#> SRR1047860 3 0.627 0.2019 0.452 0.000 0.548
#> SRR1047861 3 0.627 0.2019 0.452 0.000 0.548
#> SRR1047863 3 0.631 0.0169 0.488 0.000 0.512
#> SRR1047864 1 0.627 -0.0783 0.548 0.000 0.452
#> SRR1047865 3 0.631 0.0169 0.488 0.000 0.512
#> SRR1047866 1 0.623 -0.0506 0.564 0.000 0.436
#> SRR1047867 2 0.129 0.9846 0.000 0.968 0.032
#> SRR1047868 3 0.631 0.0169 0.488 0.000 0.512
#> SRR1047869 3 0.630 0.0163 0.480 0.000 0.520
#> SRR1047870 1 0.630 -0.0656 0.516 0.000 0.484
#> SRR1047871 3 0.630 0.0163 0.480 0.000 0.520
#> SRR1047872 3 0.631 0.0169 0.488 0.000 0.512
#> SRR1047873 3 0.627 0.0184 0.456 0.000 0.544
#> SRR1047874 3 0.622 0.0128 0.432 0.000 0.568
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1047813 1 0.3356 0.749 0.824 0.0 0.000 0.176
#> SRR1047814 1 0.3356 0.749 0.824 0.0 0.000 0.176
#> SRR1047815 1 0.3356 0.749 0.824 0.0 0.000 0.176
#> SRR1047816 1 0.3356 0.749 0.824 0.0 0.000 0.176
#> SRR1047817 1 0.3356 0.749 0.824 0.0 0.000 0.176
#> SRR1047818 4 0.6465 0.329 0.080 0.0 0.364 0.556
#> SRR1047819 4 0.6465 0.329 0.080 0.0 0.364 0.556
#> SRR1047820 4 0.6465 0.329 0.080 0.0 0.364 0.556
#> SRR1047821 4 0.6465 0.329 0.080 0.0 0.364 0.556
#> SRR1047822 4 0.6465 0.329 0.080 0.0 0.364 0.556
#> SRR1047823 1 0.4866 0.507 0.596 0.0 0.000 0.404
#> SRR1047824 1 0.4866 0.507 0.596 0.0 0.000 0.404
#> SRR1047825 1 0.4866 0.507 0.596 0.0 0.000 0.404
#> SRR1047826 1 0.4866 0.507 0.596 0.0 0.000 0.404
#> SRR1047827 1 0.4866 0.507 0.596 0.0 0.000 0.404
#> SRR1047828 1 0.6015 0.513 0.652 0.0 0.268 0.080
#> SRR1047829 1 0.6280 0.426 0.604 0.0 0.316 0.080
#> SRR1047830 1 0.6015 0.513 0.652 0.0 0.268 0.080
#> SRR1047831 1 0.6015 0.513 0.652 0.0 0.268 0.080
#> SRR1047832 1 0.6015 0.513 0.652 0.0 0.268 0.080
#> SRR1047833 2 0.0000 0.987 0.000 1.0 0.000 0.000
#> SRR1047834 2 0.0000 0.987 0.000 1.0 0.000 0.000
#> SRR1047835 2 0.0000 0.987 0.000 1.0 0.000 0.000
#> SRR1047836 2 0.0000 0.987 0.000 1.0 0.000 0.000
#> SRR1047837 2 0.0000 0.987 0.000 1.0 0.000 0.000
#> SRR1047838 4 0.0817 0.827 0.024 0.0 0.000 0.976
#> SRR1047839 4 0.0188 0.829 0.004 0.0 0.000 0.996
#> SRR1047840 4 0.0817 0.827 0.024 0.0 0.000 0.976
#> SRR1047841 4 0.0817 0.827 0.024 0.0 0.000 0.976
#> SRR1047842 4 0.0817 0.827 0.024 0.0 0.000 0.976
#> SRR1047843 4 0.0921 0.825 0.028 0.0 0.000 0.972
#> SRR1047844 4 0.0188 0.829 0.004 0.0 0.000 0.996
#> SRR1047845 4 0.0921 0.825 0.028 0.0 0.000 0.972
#> SRR1047846 4 0.0921 0.825 0.028 0.0 0.000 0.972
#> SRR1047847 4 0.0188 0.829 0.004 0.0 0.000 0.996
#> SRR1047848 1 0.2216 0.750 0.908 0.0 0.000 0.092
#> SRR1047849 1 0.2216 0.750 0.908 0.0 0.000 0.092
#> SRR1047850 1 0.2216 0.750 0.908 0.0 0.000 0.092
#> SRR1047851 1 0.2216 0.750 0.908 0.0 0.000 0.092
#> SRR1047852 1 0.2216 0.750 0.908 0.0 0.000 0.092
#> SRR1047853 4 0.0336 0.825 0.000 0.0 0.008 0.992
#> SRR1047854 4 0.0000 0.828 0.000 0.0 0.000 1.000
#> SRR1047855 4 0.0000 0.828 0.000 0.0 0.000 1.000
#> SRR1047856 4 0.0336 0.825 0.000 0.0 0.008 0.992
#> SRR1047857 4 0.0336 0.825 0.000 0.0 0.008 0.992
#> SRR1047858 4 0.3123 0.685 0.156 0.0 0.000 0.844
#> SRR1047859 4 0.1867 0.786 0.072 0.0 0.000 0.928
#> SRR1047860 4 0.3123 0.685 0.156 0.0 0.000 0.844
#> SRR1047861 4 0.3123 0.685 0.156 0.0 0.000 0.844
#> SRR1047863 3 0.0707 0.918 0.000 0.0 0.980 0.020
#> SRR1047864 3 0.2345 0.842 0.100 0.0 0.900 0.000
#> SRR1047865 3 0.0707 0.918 0.000 0.0 0.980 0.020
#> SRR1047866 3 0.0817 0.892 0.024 0.0 0.976 0.000
#> SRR1047867 2 0.2706 0.932 0.080 0.9 0.020 0.000
#> SRR1047868 3 0.1118 0.916 0.000 0.0 0.964 0.036
#> SRR1047869 3 0.1118 0.916 0.000 0.0 0.964 0.036
#> SRR1047870 3 0.0707 0.918 0.000 0.0 0.980 0.020
#> SRR1047871 3 0.1211 0.915 0.000 0.0 0.960 0.040
#> SRR1047872 3 0.0707 0.918 0.000 0.0 0.980 0.020
#> SRR1047873 3 0.3837 0.730 0.000 0.0 0.776 0.224
#> SRR1047874 3 0.3975 0.710 0.000 0.0 0.760 0.240
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1047813 1 0.2209 0.689 0.912 0.000 0.000 0.032 NA
#> SRR1047814 1 0.2209 0.689 0.912 0.000 0.000 0.032 NA
#> SRR1047815 1 0.2209 0.689 0.912 0.000 0.000 0.032 NA
#> SRR1047816 1 0.2209 0.689 0.912 0.000 0.000 0.032 NA
#> SRR1047817 1 0.2209 0.689 0.912 0.000 0.000 0.032 NA
#> SRR1047818 4 0.7283 0.229 0.024 0.000 0.304 0.400 NA
#> SRR1047819 4 0.7283 0.229 0.024 0.000 0.304 0.400 NA
#> SRR1047820 4 0.7283 0.229 0.024 0.000 0.304 0.400 NA
#> SRR1047821 4 0.7283 0.229 0.024 0.000 0.304 0.400 NA
#> SRR1047822 4 0.7217 0.224 0.020 0.000 0.308 0.400 NA
#> SRR1047823 1 0.5854 0.502 0.600 0.000 0.000 0.240 NA
#> SRR1047824 1 0.5854 0.502 0.600 0.000 0.000 0.240 NA
#> SRR1047825 1 0.5854 0.502 0.600 0.000 0.000 0.240 NA
#> SRR1047826 1 0.5854 0.502 0.600 0.000 0.000 0.240 NA
#> SRR1047827 1 0.5854 0.502 0.600 0.000 0.000 0.240 NA
#> SRR1047828 1 0.6082 0.481 0.464 0.000 0.076 0.016 NA
#> SRR1047829 1 0.6250 0.456 0.448 0.000 0.092 0.016 NA
#> SRR1047830 1 0.6082 0.481 0.464 0.000 0.076 0.016 NA
#> SRR1047831 1 0.6082 0.481 0.464 0.000 0.076 0.016 NA
#> SRR1047832 1 0.6082 0.481 0.464 0.000 0.076 0.016 NA
#> SRR1047833 2 0.0000 0.974 0.000 1.000 0.000 0.000 NA
#> SRR1047834 2 0.0000 0.974 0.000 1.000 0.000 0.000 NA
#> SRR1047835 2 0.0000 0.974 0.000 1.000 0.000 0.000 NA
#> SRR1047836 2 0.0000 0.974 0.000 1.000 0.000 0.000 NA
#> SRR1047837 2 0.0000 0.974 0.000 1.000 0.000 0.000 NA
#> SRR1047838 4 0.0290 0.772 0.008 0.000 0.000 0.992 NA
#> SRR1047839 4 0.0609 0.772 0.000 0.000 0.000 0.980 NA
#> SRR1047840 4 0.0290 0.772 0.008 0.000 0.000 0.992 NA
#> SRR1047841 4 0.0290 0.772 0.008 0.000 0.000 0.992 NA
#> SRR1047842 4 0.0290 0.772 0.008 0.000 0.000 0.992 NA
#> SRR1047843 4 0.1774 0.763 0.016 0.000 0.000 0.932 NA
#> SRR1047844 4 0.1357 0.769 0.004 0.000 0.000 0.948 NA
#> SRR1047845 4 0.1774 0.763 0.016 0.000 0.000 0.932 NA
#> SRR1047846 4 0.1774 0.763 0.016 0.000 0.000 0.932 NA
#> SRR1047847 4 0.1357 0.769 0.004 0.000 0.000 0.948 NA
#> SRR1047848 1 0.2522 0.698 0.880 0.000 0.000 0.012 NA
#> SRR1047849 1 0.2522 0.698 0.880 0.000 0.000 0.012 NA
#> SRR1047850 1 0.2522 0.698 0.880 0.000 0.000 0.012 NA
#> SRR1047851 1 0.2522 0.698 0.880 0.000 0.000 0.012 NA
#> SRR1047852 1 0.2522 0.698 0.880 0.000 0.000 0.012 NA
#> SRR1047853 4 0.3339 0.744 0.000 0.000 0.048 0.840 NA
#> SRR1047854 4 0.3216 0.747 0.000 0.000 0.044 0.848 NA
#> SRR1047855 4 0.3216 0.747 0.000 0.000 0.044 0.848 NA
#> SRR1047856 4 0.3339 0.744 0.000 0.000 0.048 0.840 NA
#> SRR1047857 4 0.3339 0.744 0.000 0.000 0.048 0.840 NA
#> SRR1047858 4 0.4309 0.613 0.148 0.000 0.000 0.768 NA
#> SRR1047859 4 0.3536 0.684 0.084 0.000 0.000 0.832 NA
#> SRR1047860 4 0.4309 0.613 0.148 0.000 0.000 0.768 NA
#> SRR1047861 4 0.4309 0.613 0.148 0.000 0.000 0.768 NA
#> SRR1047863 3 0.1197 0.876 0.000 0.000 0.952 0.000 NA
#> SRR1047864 3 0.4276 0.631 0.004 0.000 0.616 0.000 NA
#> SRR1047865 3 0.1197 0.876 0.000 0.000 0.952 0.000 NA
#> SRR1047866 3 0.3177 0.772 0.000 0.000 0.792 0.000 NA
#> SRR1047867 2 0.3242 0.864 0.012 0.816 0.000 0.000 NA
#> SRR1047868 3 0.1357 0.873 0.000 0.000 0.948 0.004 NA
#> SRR1047869 3 0.1408 0.873 0.000 0.000 0.948 0.008 NA
#> SRR1047870 3 0.1478 0.872 0.000 0.000 0.936 0.000 NA
#> SRR1047871 3 0.1704 0.865 0.000 0.000 0.928 0.004 NA
#> SRR1047872 3 0.1043 0.878 0.000 0.000 0.960 0.000 NA
#> SRR1047873 3 0.3056 0.827 0.000 0.000 0.864 0.068 NA
#> SRR1047874 3 0.3517 0.795 0.000 0.000 0.832 0.100 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1047813 1 0.0547 0.698 0.980 0.000 0.000 0.020 0.000 0.000
#> SRR1047814 1 0.0547 0.698 0.980 0.000 0.000 0.020 0.000 0.000
#> SRR1047815 1 0.0547 0.698 0.980 0.000 0.000 0.020 0.000 0.000
#> SRR1047816 1 0.0547 0.698 0.980 0.000 0.000 0.020 0.000 0.000
#> SRR1047817 1 0.0547 0.698 0.980 0.000 0.000 0.020 0.000 0.000
#> SRR1047818 5 0.7621 0.441 0.004 0.000 0.220 0.268 0.352 0.156
#> SRR1047819 5 0.7621 0.441 0.004 0.000 0.220 0.268 0.352 0.156
#> SRR1047820 5 0.7621 0.441 0.004 0.000 0.220 0.268 0.352 0.156
#> SRR1047821 5 0.7621 0.441 0.004 0.000 0.220 0.268 0.352 0.156
#> SRR1047822 5 0.7621 0.441 0.004 0.000 0.220 0.268 0.352 0.156
#> SRR1047823 6 0.5935 1.000 0.424 0.000 0.000 0.124 0.020 0.432
#> SRR1047824 6 0.5935 1.000 0.424 0.000 0.000 0.124 0.020 0.432
#> SRR1047825 6 0.5935 1.000 0.424 0.000 0.000 0.124 0.020 0.432
#> SRR1047826 6 0.5935 1.000 0.424 0.000 0.000 0.124 0.020 0.432
#> SRR1047827 6 0.5935 1.000 0.424 0.000 0.000 0.124 0.020 0.432
#> SRR1047828 5 0.4308 0.259 0.300 0.000 0.028 0.008 0.664 0.000
#> SRR1047829 5 0.4359 0.263 0.296 0.000 0.032 0.008 0.664 0.000
#> SRR1047830 5 0.4308 0.259 0.300 0.000 0.028 0.008 0.664 0.000
#> SRR1047831 5 0.4308 0.259 0.300 0.000 0.028 0.008 0.664 0.000
#> SRR1047832 5 0.4308 0.259 0.300 0.000 0.028 0.008 0.664 0.000
#> SRR1047833 2 0.0405 0.949 0.004 0.988 0.000 0.000 0.008 0.000
#> SRR1047834 2 0.0260 0.950 0.000 0.992 0.000 0.000 0.008 0.000
#> SRR1047835 2 0.0146 0.951 0.000 0.996 0.000 0.000 0.004 0.000
#> SRR1047836 2 0.0146 0.951 0.000 0.996 0.004 0.000 0.000 0.000
#> SRR1047837 2 0.0146 0.950 0.000 0.996 0.000 0.000 0.004 0.000
#> SRR1047838 4 0.0291 0.776 0.004 0.000 0.000 0.992 0.000 0.004
#> SRR1047839 4 0.0891 0.766 0.000 0.000 0.000 0.968 0.008 0.024
#> SRR1047840 4 0.0291 0.776 0.004 0.000 0.000 0.992 0.000 0.004
#> SRR1047841 4 0.0291 0.776 0.004 0.000 0.000 0.992 0.000 0.004
#> SRR1047842 4 0.0291 0.776 0.004 0.000 0.000 0.992 0.000 0.004
#> SRR1047843 4 0.3633 0.742 0.020 0.000 0.000 0.812 0.052 0.116
#> SRR1047844 4 0.3112 0.754 0.004 0.000 0.000 0.840 0.052 0.104
#> SRR1047845 4 0.3633 0.742 0.020 0.000 0.000 0.812 0.052 0.116
#> SRR1047846 4 0.3633 0.742 0.020 0.000 0.000 0.812 0.052 0.116
#> SRR1047847 4 0.3112 0.754 0.004 0.000 0.000 0.840 0.052 0.104
#> SRR1047848 1 0.4338 0.727 0.716 0.000 0.000 0.004 0.208 0.072
#> SRR1047849 1 0.4444 0.729 0.700 0.000 0.000 0.004 0.224 0.072
#> SRR1047850 1 0.4444 0.729 0.700 0.000 0.000 0.004 0.224 0.072
#> SRR1047851 1 0.4444 0.729 0.700 0.000 0.000 0.004 0.224 0.072
#> SRR1047852 1 0.4444 0.729 0.700 0.000 0.000 0.004 0.224 0.072
#> SRR1047853 4 0.4709 0.627 0.000 0.000 0.060 0.744 0.104 0.092
#> SRR1047854 4 0.4709 0.627 0.000 0.000 0.060 0.744 0.104 0.092
#> SRR1047855 4 0.4709 0.627 0.000 0.000 0.060 0.744 0.104 0.092
#> SRR1047856 4 0.4709 0.627 0.000 0.000 0.060 0.744 0.104 0.092
#> SRR1047857 4 0.4709 0.627 0.000 0.000 0.060 0.744 0.104 0.092
#> SRR1047858 4 0.5167 0.526 0.096 0.000 0.000 0.664 0.028 0.212
#> SRR1047859 4 0.4674 0.589 0.056 0.000 0.000 0.704 0.028 0.212
#> SRR1047860 4 0.5167 0.526 0.096 0.000 0.000 0.664 0.028 0.212
#> SRR1047861 4 0.5167 0.526 0.096 0.000 0.000 0.664 0.028 0.212
#> SRR1047863 3 0.1924 0.859 0.000 0.000 0.920 0.004 0.048 0.028
#> SRR1047864 3 0.5940 0.433 0.000 0.000 0.456 0.000 0.296 0.248
#> SRR1047865 3 0.1924 0.859 0.000 0.000 0.920 0.004 0.048 0.028
#> SRR1047866 3 0.3833 0.713 0.000 0.000 0.736 0.004 0.232 0.028
#> SRR1047867 2 0.4503 0.752 0.000 0.684 0.000 0.000 0.084 0.232
#> SRR1047868 3 0.0922 0.856 0.000 0.000 0.968 0.004 0.024 0.004
#> SRR1047869 3 0.0806 0.858 0.000 0.000 0.972 0.008 0.020 0.000
#> SRR1047870 3 0.2113 0.854 0.000 0.000 0.908 0.004 0.060 0.028
#> SRR1047871 3 0.1116 0.853 0.000 0.000 0.960 0.004 0.028 0.008
#> SRR1047872 3 0.1636 0.861 0.000 0.000 0.936 0.004 0.036 0.024
#> SRR1047873 3 0.2085 0.822 0.000 0.000 0.912 0.056 0.024 0.008
#> SRR1047874 3 0.2377 0.803 0.000 0.000 0.892 0.076 0.024 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 17931 rows and 61 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.932 0.905 0.964 0.3610 0.640 0.640
#> 3 3 0.859 0.881 0.954 0.7619 0.643 0.473
#> 4 4 0.811 0.905 0.953 0.0843 0.739 0.441
#> 5 5 0.790 0.820 0.897 0.1002 0.837 0.545
#> 6 6 0.902 0.930 0.953 0.0610 0.905 0.643
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR1047813 1 0.000 0.971 1.000 0.000
#> SRR1047814 1 0.000 0.971 1.000 0.000
#> SRR1047815 1 0.000 0.971 1.000 0.000
#> SRR1047816 1 0.000 0.971 1.000 0.000
#> SRR1047817 1 0.000 0.971 1.000 0.000
#> SRR1047818 1 0.000 0.971 1.000 0.000
#> SRR1047819 1 0.000 0.971 1.000 0.000
#> SRR1047820 1 0.000 0.971 1.000 0.000
#> SRR1047821 1 0.000 0.971 1.000 0.000
#> SRR1047822 1 0.000 0.971 1.000 0.000
#> SRR1047823 1 0.000 0.971 1.000 0.000
#> SRR1047824 1 0.000 0.971 1.000 0.000
#> SRR1047825 1 0.000 0.971 1.000 0.000
#> SRR1047826 1 0.000 0.971 1.000 0.000
#> SRR1047827 1 0.000 0.971 1.000 0.000
#> SRR1047828 1 0.000 0.971 1.000 0.000
#> SRR1047829 1 0.000 0.971 1.000 0.000
#> SRR1047830 1 0.000 0.971 1.000 0.000
#> SRR1047831 1 0.000 0.971 1.000 0.000
#> SRR1047832 1 0.000 0.971 1.000 0.000
#> SRR1047833 2 0.000 0.921 0.000 1.000
#> SRR1047834 2 0.000 0.921 0.000 1.000
#> SRR1047835 2 0.000 0.921 0.000 1.000
#> SRR1047836 2 0.000 0.921 0.000 1.000
#> SRR1047837 2 0.000 0.921 0.000 1.000
#> SRR1047838 1 0.000 0.971 1.000 0.000
#> SRR1047839 1 0.000 0.971 1.000 0.000
#> SRR1047840 1 0.000 0.971 1.000 0.000
#> SRR1047841 1 0.000 0.971 1.000 0.000
#> SRR1047842 1 0.000 0.971 1.000 0.000
#> SRR1047843 1 0.000 0.971 1.000 0.000
#> SRR1047844 1 0.000 0.971 1.000 0.000
#> SRR1047845 1 0.000 0.971 1.000 0.000
#> SRR1047846 1 0.000 0.971 1.000 0.000
#> SRR1047847 1 0.000 0.971 1.000 0.000
#> SRR1047848 1 0.000 0.971 1.000 0.000
#> SRR1047849 1 0.000 0.971 1.000 0.000
#> SRR1047850 1 0.000 0.971 1.000 0.000
#> SRR1047851 1 0.000 0.971 1.000 0.000
#> SRR1047852 1 0.000 0.971 1.000 0.000
#> SRR1047853 1 0.000 0.971 1.000 0.000
#> SRR1047854 1 0.000 0.971 1.000 0.000
#> SRR1047855 1 0.000 0.971 1.000 0.000
#> SRR1047856 1 0.000 0.971 1.000 0.000
#> SRR1047857 1 0.000 0.971 1.000 0.000
#> SRR1047858 1 0.000 0.971 1.000 0.000
#> SRR1047859 1 0.000 0.971 1.000 0.000
#> SRR1047860 1 0.000 0.971 1.000 0.000
#> SRR1047861 1 0.000 0.971 1.000 0.000
#> SRR1047863 2 0.000 0.921 0.000 1.000
#> SRR1047864 2 0.000 0.921 0.000 1.000
#> SRR1047865 2 0.416 0.868 0.084 0.916
#> SRR1047866 2 0.000 0.921 0.000 1.000
#> SRR1047867 2 0.000 0.921 0.000 1.000
#> SRR1047868 2 0.971 0.372 0.400 0.600
#> SRR1047869 2 0.971 0.372 0.400 0.600
#> SRR1047870 2 0.000 0.921 0.000 1.000
#> SRR1047871 1 0.971 0.264 0.600 0.400
#> SRR1047872 2 0.416 0.868 0.084 0.916
#> SRR1047873 1 0.971 0.264 0.600 0.400
#> SRR1047874 1 0.971 0.264 0.600 0.400
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1047813 1 0.0000 0.903 1.000 0.000 0.000
#> SRR1047814 1 0.0000 0.903 1.000 0.000 0.000
#> SRR1047815 1 0.0000 0.903 1.000 0.000 0.000
#> SRR1047816 1 0.0000 0.903 1.000 0.000 0.000
#> SRR1047817 1 0.0000 0.903 1.000 0.000 0.000
#> SRR1047818 3 0.0000 0.973 0.000 0.000 1.000
#> SRR1047819 3 0.0000 0.973 0.000 0.000 1.000
#> SRR1047820 3 0.0000 0.973 0.000 0.000 1.000
#> SRR1047821 3 0.0000 0.973 0.000 0.000 1.000
#> SRR1047822 3 0.0000 0.973 0.000 0.000 1.000
#> SRR1047823 1 0.0592 0.898 0.988 0.000 0.012
#> SRR1047824 1 0.0592 0.898 0.988 0.000 0.012
#> SRR1047825 1 0.0592 0.898 0.988 0.000 0.012
#> SRR1047826 1 0.0592 0.898 0.988 0.000 0.012
#> SRR1047827 1 0.0592 0.898 0.988 0.000 0.012
#> SRR1047828 1 0.0000 0.903 1.000 0.000 0.000
#> SRR1047829 1 0.0000 0.903 1.000 0.000 0.000
#> SRR1047830 1 0.0000 0.903 1.000 0.000 0.000
#> SRR1047831 1 0.0000 0.903 1.000 0.000 0.000
#> SRR1047832 1 0.0000 0.903 1.000 0.000 0.000
#> SRR1047833 2 0.0000 0.954 0.000 1.000 0.000
#> SRR1047834 2 0.0000 0.954 0.000 1.000 0.000
#> SRR1047835 2 0.0000 0.954 0.000 1.000 0.000
#> SRR1047836 2 0.0000 0.954 0.000 1.000 0.000
#> SRR1047837 2 0.0000 0.954 0.000 1.000 0.000
#> SRR1047838 3 0.0000 0.973 0.000 0.000 1.000
#> SRR1047839 3 0.0000 0.973 0.000 0.000 1.000
#> SRR1047840 3 0.0000 0.973 0.000 0.000 1.000
#> SRR1047841 3 0.0000 0.973 0.000 0.000 1.000
#> SRR1047842 3 0.0000 0.973 0.000 0.000 1.000
#> SRR1047843 3 0.0000 0.973 0.000 0.000 1.000
#> SRR1047844 3 0.0000 0.973 0.000 0.000 1.000
#> SRR1047845 3 0.0000 0.973 0.000 0.000 1.000
#> SRR1047846 3 0.0000 0.973 0.000 0.000 1.000
#> SRR1047847 3 0.0000 0.973 0.000 0.000 1.000
#> SRR1047848 1 0.0000 0.903 1.000 0.000 0.000
#> SRR1047849 1 0.0000 0.903 1.000 0.000 0.000
#> SRR1047850 1 0.0000 0.903 1.000 0.000 0.000
#> SRR1047851 1 0.0000 0.903 1.000 0.000 0.000
#> SRR1047852 1 0.0000 0.903 1.000 0.000 0.000
#> SRR1047853 3 0.0000 0.973 0.000 0.000 1.000
#> SRR1047854 3 0.0000 0.973 0.000 0.000 1.000
#> SRR1047855 3 0.0000 0.973 0.000 0.000 1.000
#> SRR1047856 3 0.0000 0.973 0.000 0.000 1.000
#> SRR1047857 3 0.0000 0.973 0.000 0.000 1.000
#> SRR1047858 1 0.6204 0.346 0.576 0.000 0.424
#> SRR1047859 1 0.6260 0.281 0.552 0.000 0.448
#> SRR1047860 1 0.6204 0.346 0.576 0.000 0.424
#> SRR1047861 1 0.6204 0.346 0.576 0.000 0.424
#> SRR1047863 2 0.4555 0.751 0.000 0.800 0.200
#> SRR1047864 2 0.0000 0.954 0.000 1.000 0.000
#> SRR1047865 2 0.4555 0.751 0.000 0.800 0.200
#> SRR1047866 2 0.0000 0.954 0.000 1.000 0.000
#> SRR1047867 2 0.0000 0.954 0.000 1.000 0.000
#> SRR1047868 3 0.0237 0.970 0.000 0.004 0.996
#> SRR1047869 3 0.4555 0.734 0.000 0.200 0.800
#> SRR1047870 2 0.0000 0.954 0.000 1.000 0.000
#> SRR1047871 3 0.0237 0.970 0.000 0.004 0.996
#> SRR1047872 3 0.6215 0.230 0.000 0.428 0.572
#> SRR1047873 3 0.0237 0.970 0.000 0.004 0.996
#> SRR1047874 3 0.0237 0.970 0.000 0.004 0.996
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1047813 1 0.1389 0.959 0.952 0.000 0.000 0.048
#> SRR1047814 1 0.1389 0.959 0.952 0.000 0.000 0.048
#> SRR1047815 1 0.1389 0.959 0.952 0.000 0.000 0.048
#> SRR1047816 1 0.1389 0.959 0.952 0.000 0.000 0.048
#> SRR1047817 1 0.2868 0.845 0.864 0.000 0.000 0.136
#> SRR1047818 4 0.1022 0.903 0.000 0.000 0.032 0.968
#> SRR1047819 4 0.1022 0.903 0.000 0.000 0.032 0.968
#> SRR1047820 4 0.1022 0.903 0.000 0.000 0.032 0.968
#> SRR1047821 4 0.1022 0.903 0.000 0.000 0.032 0.968
#> SRR1047822 4 0.1118 0.900 0.000 0.000 0.036 0.964
#> SRR1047823 4 0.4356 0.652 0.292 0.000 0.000 0.708
#> SRR1047824 4 0.4356 0.652 0.292 0.000 0.000 0.708
#> SRR1047825 4 0.4356 0.652 0.292 0.000 0.000 0.708
#> SRR1047826 4 0.4356 0.652 0.292 0.000 0.000 0.708
#> SRR1047827 4 0.4356 0.652 0.292 0.000 0.000 0.708
#> SRR1047828 1 0.0188 0.955 0.996 0.000 0.004 0.000
#> SRR1047829 1 0.0188 0.955 0.996 0.000 0.004 0.000
#> SRR1047830 1 0.0188 0.955 0.996 0.000 0.004 0.000
#> SRR1047831 1 0.0188 0.955 0.996 0.000 0.004 0.000
#> SRR1047832 1 0.0188 0.955 0.996 0.000 0.004 0.000
#> SRR1047833 2 0.0000 0.940 0.000 1.000 0.000 0.000
#> SRR1047834 2 0.0000 0.940 0.000 1.000 0.000 0.000
#> SRR1047835 2 0.0000 0.940 0.000 1.000 0.000 0.000
#> SRR1047836 2 0.0000 0.940 0.000 1.000 0.000 0.000
#> SRR1047837 2 0.0000 0.940 0.000 1.000 0.000 0.000
#> SRR1047838 4 0.0000 0.921 0.000 0.000 0.000 1.000
#> SRR1047839 4 0.0000 0.921 0.000 0.000 0.000 1.000
#> SRR1047840 4 0.0000 0.921 0.000 0.000 0.000 1.000
#> SRR1047841 4 0.0000 0.921 0.000 0.000 0.000 1.000
#> SRR1047842 4 0.0000 0.921 0.000 0.000 0.000 1.000
#> SRR1047843 4 0.0000 0.921 0.000 0.000 0.000 1.000
#> SRR1047844 4 0.0000 0.921 0.000 0.000 0.000 1.000
#> SRR1047845 4 0.0000 0.921 0.000 0.000 0.000 1.000
#> SRR1047846 4 0.0000 0.921 0.000 0.000 0.000 1.000
#> SRR1047847 4 0.0000 0.921 0.000 0.000 0.000 1.000
#> SRR1047848 1 0.0921 0.967 0.972 0.000 0.000 0.028
#> SRR1047849 1 0.0921 0.967 0.972 0.000 0.000 0.028
#> SRR1047850 1 0.0921 0.967 0.972 0.000 0.000 0.028
#> SRR1047851 1 0.0921 0.967 0.972 0.000 0.000 0.028
#> SRR1047852 1 0.0921 0.967 0.972 0.000 0.000 0.028
#> SRR1047853 4 0.0000 0.921 0.000 0.000 0.000 1.000
#> SRR1047854 4 0.0000 0.921 0.000 0.000 0.000 1.000
#> SRR1047855 4 0.0000 0.921 0.000 0.000 0.000 1.000
#> SRR1047856 4 0.0000 0.921 0.000 0.000 0.000 1.000
#> SRR1047857 4 0.0000 0.921 0.000 0.000 0.000 1.000
#> SRR1047858 4 0.2469 0.859 0.108 0.000 0.000 0.892
#> SRR1047859 4 0.0188 0.919 0.004 0.000 0.000 0.996
#> SRR1047860 4 0.2469 0.859 0.108 0.000 0.000 0.892
#> SRR1047861 4 0.2469 0.859 0.108 0.000 0.000 0.892
#> SRR1047863 3 0.0188 0.995 0.000 0.004 0.996 0.000
#> SRR1047864 2 0.0000 0.940 0.000 1.000 0.000 0.000
#> SRR1047865 3 0.0188 0.995 0.000 0.004 0.996 0.000
#> SRR1047866 2 0.4877 0.309 0.000 0.592 0.408 0.000
#> SRR1047867 2 0.0000 0.940 0.000 1.000 0.000 0.000
#> SRR1047868 3 0.0188 0.998 0.000 0.000 0.996 0.004
#> SRR1047869 3 0.0188 0.998 0.000 0.000 0.996 0.004
#> SRR1047870 3 0.0188 0.995 0.000 0.004 0.996 0.000
#> SRR1047871 3 0.0188 0.998 0.000 0.000 0.996 0.004
#> SRR1047872 3 0.0188 0.998 0.000 0.000 0.996 0.004
#> SRR1047873 3 0.0188 0.998 0.000 0.000 0.996 0.004
#> SRR1047874 3 0.0188 0.998 0.000 0.000 0.996 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1047813 1 0.0510 0.7398 0.984 0.000 0.000 0.016 0.000
#> SRR1047814 1 0.0510 0.7398 0.984 0.000 0.000 0.016 0.000
#> SRR1047815 1 0.0510 0.7398 0.984 0.000 0.000 0.016 0.000
#> SRR1047816 1 0.0510 0.7398 0.984 0.000 0.000 0.016 0.000
#> SRR1047817 1 0.1478 0.7465 0.936 0.000 0.000 0.064 0.000
#> SRR1047818 4 0.3430 0.7823 0.000 0.000 0.004 0.776 0.220
#> SRR1047819 4 0.3430 0.7823 0.000 0.000 0.004 0.776 0.220
#> SRR1047820 4 0.3430 0.7823 0.000 0.000 0.004 0.776 0.220
#> SRR1047821 4 0.3430 0.7823 0.000 0.000 0.004 0.776 0.220
#> SRR1047822 4 0.3430 0.7823 0.000 0.000 0.004 0.776 0.220
#> SRR1047823 1 0.3586 0.7340 0.792 0.000 0.000 0.188 0.020
#> SRR1047824 1 0.3586 0.7340 0.792 0.000 0.000 0.188 0.020
#> SRR1047825 1 0.3586 0.7340 0.792 0.000 0.000 0.188 0.020
#> SRR1047826 1 0.3586 0.7340 0.792 0.000 0.000 0.188 0.020
#> SRR1047827 1 0.3586 0.7340 0.792 0.000 0.000 0.188 0.020
#> SRR1047828 5 0.3424 1.0000 0.240 0.000 0.000 0.000 0.760
#> SRR1047829 5 0.3424 1.0000 0.240 0.000 0.000 0.000 0.760
#> SRR1047830 5 0.3424 1.0000 0.240 0.000 0.000 0.000 0.760
#> SRR1047831 5 0.3424 1.0000 0.240 0.000 0.000 0.000 0.760
#> SRR1047832 5 0.3424 1.0000 0.240 0.000 0.000 0.000 0.760
#> SRR1047833 2 0.0000 0.9334 0.000 1.000 0.000 0.000 0.000
#> SRR1047834 2 0.0000 0.9334 0.000 1.000 0.000 0.000 0.000
#> SRR1047835 2 0.0000 0.9334 0.000 1.000 0.000 0.000 0.000
#> SRR1047836 2 0.0000 0.9334 0.000 1.000 0.000 0.000 0.000
#> SRR1047837 2 0.0000 0.9334 0.000 1.000 0.000 0.000 0.000
#> SRR1047838 4 0.0451 0.8991 0.008 0.000 0.000 0.988 0.004
#> SRR1047839 4 0.0798 0.9000 0.008 0.000 0.000 0.976 0.016
#> SRR1047840 4 0.0451 0.8991 0.008 0.000 0.000 0.988 0.004
#> SRR1047841 4 0.0451 0.8991 0.008 0.000 0.000 0.988 0.004
#> SRR1047842 4 0.0451 0.8991 0.008 0.000 0.000 0.988 0.004
#> SRR1047843 4 0.0451 0.8991 0.008 0.000 0.000 0.988 0.004
#> SRR1047844 4 0.0290 0.8997 0.008 0.000 0.000 0.992 0.000
#> SRR1047845 4 0.0451 0.8991 0.008 0.000 0.000 0.988 0.004
#> SRR1047846 4 0.0451 0.8991 0.008 0.000 0.000 0.988 0.004
#> SRR1047847 4 0.0290 0.8997 0.008 0.000 0.000 0.992 0.000
#> SRR1047848 1 0.1341 0.6950 0.944 0.000 0.000 0.000 0.056
#> SRR1047849 1 0.1341 0.6950 0.944 0.000 0.000 0.000 0.056
#> SRR1047850 1 0.1341 0.6950 0.944 0.000 0.000 0.000 0.056
#> SRR1047851 1 0.1341 0.6950 0.944 0.000 0.000 0.000 0.056
#> SRR1047852 1 0.1341 0.6950 0.944 0.000 0.000 0.000 0.056
#> SRR1047853 4 0.1251 0.8985 0.008 0.000 0.000 0.956 0.036
#> SRR1047854 4 0.1251 0.8985 0.008 0.000 0.000 0.956 0.036
#> SRR1047855 4 0.1251 0.8985 0.008 0.000 0.000 0.956 0.036
#> SRR1047856 4 0.1251 0.8985 0.008 0.000 0.000 0.956 0.036
#> SRR1047857 4 0.1251 0.8985 0.008 0.000 0.000 0.956 0.036
#> SRR1047858 1 0.4824 0.3429 0.512 0.000 0.000 0.468 0.020
#> SRR1047859 4 0.4752 -0.0735 0.412 0.000 0.000 0.568 0.020
#> SRR1047860 1 0.4824 0.3429 0.512 0.000 0.000 0.468 0.020
#> SRR1047861 1 0.4824 0.3429 0.512 0.000 0.000 0.468 0.020
#> SRR1047863 3 0.0162 0.9955 0.000 0.004 0.996 0.000 0.000
#> SRR1047864 2 0.0000 0.9334 0.000 1.000 0.000 0.000 0.000
#> SRR1047865 3 0.0162 0.9955 0.000 0.004 0.996 0.000 0.000
#> SRR1047866 2 0.4201 0.3082 0.000 0.592 0.408 0.000 0.000
#> SRR1047867 2 0.0000 0.9334 0.000 1.000 0.000 0.000 0.000
#> SRR1047868 3 0.0162 0.9978 0.000 0.000 0.996 0.004 0.000
#> SRR1047869 3 0.0162 0.9978 0.000 0.000 0.996 0.004 0.000
#> SRR1047870 3 0.0162 0.9955 0.000 0.004 0.996 0.000 0.000
#> SRR1047871 3 0.0162 0.9978 0.000 0.000 0.996 0.004 0.000
#> SRR1047872 3 0.0162 0.9978 0.000 0.000 0.996 0.004 0.000
#> SRR1047873 3 0.0162 0.9978 0.000 0.000 0.996 0.004 0.000
#> SRR1047874 3 0.0162 0.9978 0.000 0.000 0.996 0.004 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1047813 1 0.1152 0.921 0.952 0.000 0.000 0.000 0.044 0.004
#> SRR1047814 1 0.1152 0.921 0.952 0.000 0.000 0.000 0.044 0.004
#> SRR1047815 1 0.1152 0.921 0.952 0.000 0.000 0.000 0.044 0.004
#> SRR1047816 1 0.1152 0.921 0.952 0.000 0.000 0.000 0.044 0.004
#> SRR1047817 1 0.1152 0.921 0.952 0.000 0.000 0.000 0.044 0.004
#> SRR1047818 6 0.1501 1.000 0.000 0.000 0.000 0.076 0.000 0.924
#> SRR1047819 6 0.1501 1.000 0.000 0.000 0.000 0.076 0.000 0.924
#> SRR1047820 6 0.1501 1.000 0.000 0.000 0.000 0.076 0.000 0.924
#> SRR1047821 6 0.1501 1.000 0.000 0.000 0.000 0.076 0.000 0.924
#> SRR1047822 6 0.1501 1.000 0.000 0.000 0.000 0.076 0.000 0.924
#> SRR1047823 1 0.1713 0.889 0.928 0.000 0.000 0.028 0.000 0.044
#> SRR1047824 1 0.1713 0.889 0.928 0.000 0.000 0.028 0.000 0.044
#> SRR1047825 1 0.1713 0.889 0.928 0.000 0.000 0.028 0.000 0.044
#> SRR1047826 1 0.1713 0.889 0.928 0.000 0.000 0.028 0.000 0.044
#> SRR1047827 1 0.1713 0.889 0.928 0.000 0.000 0.028 0.000 0.044
#> SRR1047828 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1047829 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1047830 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1047831 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1047832 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1047833 2 0.0000 0.931 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1047834 2 0.0000 0.931 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1047835 2 0.0000 0.931 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1047836 2 0.0000 0.931 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1047837 2 0.0000 0.931 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1047838 4 0.0000 0.948 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047839 4 0.0000 0.948 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047840 4 0.0000 0.948 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047841 4 0.0000 0.948 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047842 4 0.0000 0.948 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047843 4 0.0000 0.948 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047844 4 0.0000 0.948 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047845 4 0.0000 0.948 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047846 4 0.0000 0.948 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047847 4 0.0000 0.948 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047848 1 0.2527 0.895 0.868 0.000 0.000 0.000 0.108 0.024
#> SRR1047849 1 0.2527 0.895 0.868 0.000 0.000 0.000 0.108 0.024
#> SRR1047850 1 0.2527 0.895 0.868 0.000 0.000 0.000 0.108 0.024
#> SRR1047851 1 0.2527 0.895 0.868 0.000 0.000 0.000 0.108 0.024
#> SRR1047852 1 0.2527 0.895 0.868 0.000 0.000 0.000 0.108 0.024
#> SRR1047853 4 0.0632 0.939 0.000 0.000 0.000 0.976 0.000 0.024
#> SRR1047854 4 0.0547 0.941 0.000 0.000 0.000 0.980 0.000 0.020
#> SRR1047855 4 0.0547 0.941 0.000 0.000 0.000 0.980 0.000 0.020
#> SRR1047856 4 0.0632 0.939 0.000 0.000 0.000 0.976 0.000 0.024
#> SRR1047857 4 0.0632 0.939 0.000 0.000 0.000 0.976 0.000 0.024
#> SRR1047858 4 0.3284 0.783 0.168 0.000 0.000 0.800 0.000 0.032
#> SRR1047859 4 0.2164 0.878 0.068 0.000 0.000 0.900 0.000 0.032
#> SRR1047860 4 0.3284 0.783 0.168 0.000 0.000 0.800 0.000 0.032
#> SRR1047861 4 0.3284 0.783 0.168 0.000 0.000 0.800 0.000 0.032
#> SRR1047863 3 0.0146 0.997 0.000 0.000 0.996 0.000 0.000 0.004
#> SRR1047864 2 0.0000 0.931 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1047865 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047866 2 0.3915 0.292 0.000 0.584 0.412 0.000 0.000 0.004
#> SRR1047867 2 0.0000 0.931 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1047868 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047869 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047870 3 0.0146 0.997 0.000 0.000 0.996 0.000 0.000 0.004
#> SRR1047871 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047872 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047873 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047874 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 17931 rows and 61 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.1811 0.820 0.820
#> 3 3 0.505 0.852 0.915 1.8028 0.672 0.600
#> 4 4 0.725 0.855 0.921 0.3638 0.738 0.511
#> 5 5 0.808 0.772 0.896 0.0943 0.860 0.603
#> 6 6 0.820 0.821 0.879 0.0332 0.959 0.841
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
#> SRR1047813 1 0 1 1 0
#> SRR1047814 1 0 1 1 0
#> SRR1047815 1 0 1 1 0
#> SRR1047816 1 0 1 1 0
#> SRR1047817 1 0 1 1 0
#> SRR1047818 1 0 1 1 0
#> SRR1047819 1 0 1 1 0
#> SRR1047820 1 0 1 1 0
#> SRR1047821 1 0 1 1 0
#> SRR1047822 1 0 1 1 0
#> SRR1047823 1 0 1 1 0
#> SRR1047824 1 0 1 1 0
#> SRR1047825 1 0 1 1 0
#> SRR1047826 1 0 1 1 0
#> SRR1047827 1 0 1 1 0
#> SRR1047828 1 0 1 1 0
#> SRR1047829 1 0 1 1 0
#> SRR1047830 1 0 1 1 0
#> SRR1047831 1 0 1 1 0
#> SRR1047832 1 0 1 1 0
#> SRR1047833 2 0 1 0 1
#> SRR1047834 2 0 1 0 1
#> SRR1047835 2 0 1 0 1
#> SRR1047836 2 0 1 0 1
#> SRR1047837 2 0 1 0 1
#> SRR1047838 1 0 1 1 0
#> SRR1047839 1 0 1 1 0
#> SRR1047840 1 0 1 1 0
#> SRR1047841 1 0 1 1 0
#> SRR1047842 1 0 1 1 0
#> SRR1047843 1 0 1 1 0
#> SRR1047844 1 0 1 1 0
#> SRR1047845 1 0 1 1 0
#> SRR1047846 1 0 1 1 0
#> SRR1047847 1 0 1 1 0
#> SRR1047848 1 0 1 1 0
#> SRR1047849 1 0 1 1 0
#> SRR1047850 1 0 1 1 0
#> SRR1047851 1 0 1 1 0
#> SRR1047852 1 0 1 1 0
#> SRR1047853 1 0 1 1 0
#> SRR1047854 1 0 1 1 0
#> SRR1047855 1 0 1 1 0
#> SRR1047856 1 0 1 1 0
#> SRR1047857 1 0 1 1 0
#> SRR1047858 1 0 1 1 0
#> SRR1047859 1 0 1 1 0
#> SRR1047860 1 0 1 1 0
#> SRR1047861 1 0 1 1 0
#> SRR1047863 1 0 1 1 0
#> SRR1047864 1 0 1 1 0
#> SRR1047865 1 0 1 1 0
#> SRR1047866 1 0 1 1 0
#> SRR1047867 2 0 1 0 1
#> SRR1047868 1 0 1 1 0
#> SRR1047869 1 0 1 1 0
#> SRR1047870 1 0 1 1 0
#> SRR1047871 1 0 1 1 0
#> SRR1047872 1 0 1 1 0
#> SRR1047873 1 0 1 1 0
#> SRR1047874 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1047813 1 0.400 0.786 0.840 0 0.160
#> SRR1047814 1 0.400 0.786 0.840 0 0.160
#> SRR1047815 1 0.400 0.786 0.840 0 0.160
#> SRR1047816 1 0.400 0.786 0.840 0 0.160
#> SRR1047817 1 0.000 0.908 1.000 0 0.000
#> SRR1047818 1 0.103 0.896 0.976 0 0.024
#> SRR1047819 1 0.103 0.896 0.976 0 0.024
#> SRR1047820 1 0.103 0.896 0.976 0 0.024
#> SRR1047821 1 0.103 0.896 0.976 0 0.024
#> SRR1047822 1 0.103 0.896 0.976 0 0.024
#> SRR1047823 1 0.375 0.803 0.856 0 0.144
#> SRR1047824 1 0.375 0.803 0.856 0 0.144
#> SRR1047825 1 0.375 0.803 0.856 0 0.144
#> SRR1047826 1 0.375 0.803 0.856 0 0.144
#> SRR1047827 1 0.375 0.803 0.856 0 0.144
#> SRR1047828 3 0.455 0.866 0.200 0 0.800
#> SRR1047829 3 0.455 0.866 0.200 0 0.800
#> SRR1047830 3 0.455 0.866 0.200 0 0.800
#> SRR1047831 3 0.455 0.866 0.200 0 0.800
#> SRR1047832 3 0.455 0.866 0.200 0 0.800
#> SRR1047833 2 0.000 1.000 0.000 1 0.000
#> SRR1047834 2 0.000 1.000 0.000 1 0.000
#> SRR1047835 2 0.000 1.000 0.000 1 0.000
#> SRR1047836 2 0.000 1.000 0.000 1 0.000
#> SRR1047837 2 0.000 1.000 0.000 1 0.000
#> SRR1047838 1 0.000 0.908 1.000 0 0.000
#> SRR1047839 1 0.000 0.908 1.000 0 0.000
#> SRR1047840 1 0.000 0.908 1.000 0 0.000
#> SRR1047841 1 0.000 0.908 1.000 0 0.000
#> SRR1047842 1 0.000 0.908 1.000 0 0.000
#> SRR1047843 1 0.000 0.908 1.000 0 0.000
#> SRR1047844 1 0.000 0.908 1.000 0 0.000
#> SRR1047845 1 0.000 0.908 1.000 0 0.000
#> SRR1047846 1 0.000 0.908 1.000 0 0.000
#> SRR1047847 1 0.000 0.908 1.000 0 0.000
#> SRR1047848 3 0.455 0.866 0.200 0 0.800
#> SRR1047849 3 0.455 0.866 0.200 0 0.800
#> SRR1047850 3 0.455 0.866 0.200 0 0.800
#> SRR1047851 3 0.455 0.866 0.200 0 0.800
#> SRR1047852 3 0.455 0.866 0.200 0 0.800
#> SRR1047853 1 0.000 0.908 1.000 0 0.000
#> SRR1047854 1 0.000 0.908 1.000 0 0.000
#> SRR1047855 1 0.000 0.908 1.000 0 0.000
#> SRR1047856 1 0.000 0.908 1.000 0 0.000
#> SRR1047857 1 0.000 0.908 1.000 0 0.000
#> SRR1047858 1 0.000 0.908 1.000 0 0.000
#> SRR1047859 1 0.000 0.908 1.000 0 0.000
#> SRR1047860 1 0.000 0.908 1.000 0 0.000
#> SRR1047861 1 0.000 0.908 1.000 0 0.000
#> SRR1047863 3 0.400 0.619 0.160 0 0.840
#> SRR1047864 3 0.000 0.687 0.000 0 1.000
#> SRR1047865 3 0.375 0.631 0.144 0 0.856
#> SRR1047866 3 0.000 0.687 0.000 0 1.000
#> SRR1047867 2 0.000 1.000 0.000 1 0.000
#> SRR1047868 1 0.460 0.725 0.796 0 0.204
#> SRR1047869 1 0.455 0.727 0.800 0 0.200
#> SRR1047870 3 0.375 0.631 0.144 0 0.856
#> SRR1047871 1 0.460 0.725 0.796 0 0.204
#> SRR1047872 1 0.536 0.643 0.724 0 0.276
#> SRR1047873 1 0.455 0.727 0.800 0 0.200
#> SRR1047874 1 0.455 0.727 0.800 0 0.200
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1047813 1 0.0188 0.887 0.996 0 0.000 0.004
#> SRR1047814 1 0.0188 0.887 0.996 0 0.000 0.004
#> SRR1047815 1 0.0188 0.887 0.996 0 0.000 0.004
#> SRR1047816 1 0.0188 0.887 0.996 0 0.000 0.004
#> SRR1047817 1 0.4040 0.646 0.752 0 0.000 0.248
#> SRR1047818 4 0.4290 0.777 0.036 0 0.164 0.800
#> SRR1047819 4 0.4568 0.799 0.124 0 0.076 0.800
#> SRR1047820 4 0.4591 0.798 0.116 0 0.084 0.800
#> SRR1047821 4 0.4139 0.771 0.024 0 0.176 0.800
#> SRR1047822 4 0.4746 0.509 0.000 0 0.368 0.632
#> SRR1047823 4 0.4040 0.744 0.248 0 0.000 0.752
#> SRR1047824 4 0.3942 0.756 0.236 0 0.000 0.764
#> SRR1047825 4 0.4866 0.497 0.404 0 0.000 0.596
#> SRR1047826 4 0.4454 0.670 0.308 0 0.000 0.692
#> SRR1047827 4 0.4008 0.748 0.244 0 0.000 0.756
#> SRR1047828 1 0.3569 0.824 0.804 0 0.196 0.000
#> SRR1047829 1 0.3764 0.802 0.784 0 0.216 0.000
#> SRR1047830 1 0.3569 0.824 0.804 0 0.196 0.000
#> SRR1047831 1 0.3569 0.824 0.804 0 0.196 0.000
#> SRR1047832 1 0.3569 0.824 0.804 0 0.196 0.000
#> SRR1047833 2 0.0000 1.000 0.000 1 0.000 0.000
#> SRR1047834 2 0.0000 1.000 0.000 1 0.000 0.000
#> SRR1047835 2 0.0000 1.000 0.000 1 0.000 0.000
#> SRR1047836 2 0.0000 1.000 0.000 1 0.000 0.000
#> SRR1047837 2 0.0000 1.000 0.000 1 0.000 0.000
#> SRR1047838 4 0.0000 0.900 0.000 0 0.000 1.000
#> SRR1047839 4 0.0000 0.900 0.000 0 0.000 1.000
#> SRR1047840 4 0.0000 0.900 0.000 0 0.000 1.000
#> SRR1047841 4 0.0000 0.900 0.000 0 0.000 1.000
#> SRR1047842 4 0.0000 0.900 0.000 0 0.000 1.000
#> SRR1047843 4 0.0000 0.900 0.000 0 0.000 1.000
#> SRR1047844 4 0.0000 0.900 0.000 0 0.000 1.000
#> SRR1047845 4 0.0000 0.900 0.000 0 0.000 1.000
#> SRR1047846 4 0.0000 0.900 0.000 0 0.000 1.000
#> SRR1047847 4 0.0000 0.900 0.000 0 0.000 1.000
#> SRR1047848 1 0.0000 0.887 1.000 0 0.000 0.000
#> SRR1047849 1 0.0592 0.891 0.984 0 0.016 0.000
#> SRR1047850 1 0.0592 0.891 0.984 0 0.016 0.000
#> SRR1047851 1 0.0592 0.891 0.984 0 0.016 0.000
#> SRR1047852 1 0.0592 0.891 0.984 0 0.016 0.000
#> SRR1047853 4 0.0000 0.900 0.000 0 0.000 1.000
#> SRR1047854 4 0.0000 0.900 0.000 0 0.000 1.000
#> SRR1047855 4 0.0000 0.900 0.000 0 0.000 1.000
#> SRR1047856 4 0.0000 0.900 0.000 0 0.000 1.000
#> SRR1047857 4 0.0000 0.900 0.000 0 0.000 1.000
#> SRR1047858 4 0.0000 0.900 0.000 0 0.000 1.000
#> SRR1047859 4 0.0000 0.900 0.000 0 0.000 1.000
#> SRR1047860 4 0.0000 0.900 0.000 0 0.000 1.000
#> SRR1047861 4 0.0000 0.900 0.000 0 0.000 1.000
#> SRR1047863 3 0.0000 0.865 0.000 0 1.000 0.000
#> SRR1047864 3 0.0188 0.863 0.004 0 0.996 0.000
#> SRR1047865 3 0.0000 0.865 0.000 0 1.000 0.000
#> SRR1047866 3 0.0188 0.863 0.004 0 0.996 0.000
#> SRR1047867 2 0.0000 1.000 0.000 1 0.000 0.000
#> SRR1047868 3 0.2647 0.849 0.000 0 0.880 0.120
#> SRR1047869 3 0.3172 0.831 0.000 0 0.840 0.160
#> SRR1047870 3 0.0000 0.865 0.000 0 1.000 0.000
#> SRR1047871 3 0.3172 0.831 0.000 0 0.840 0.160
#> SRR1047872 3 0.0707 0.865 0.000 0 0.980 0.020
#> SRR1047873 3 0.3801 0.771 0.000 0 0.780 0.220
#> SRR1047874 3 0.3837 0.768 0.000 0 0.776 0.224
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1047813 1 0.4182 0.429 0.600 0 0.000 0.000 0.400
#> SRR1047814 1 0.4182 0.429 0.600 0 0.000 0.000 0.400
#> SRR1047815 1 0.4182 0.429 0.600 0 0.000 0.000 0.400
#> SRR1047816 1 0.4182 0.429 0.600 0 0.000 0.000 0.400
#> SRR1047817 4 0.2127 0.833 0.108 0 0.000 0.892 0.000
#> SRR1047818 4 0.6012 0.632 0.040 0 0.124 0.660 0.176
#> SRR1047819 4 0.6176 0.621 0.100 0 0.080 0.664 0.156
#> SRR1047820 4 0.6300 0.603 0.096 0 0.080 0.648 0.176
#> SRR1047821 4 0.6024 0.615 0.032 0 0.124 0.648 0.196
#> SRR1047822 4 0.4166 0.536 0.000 0 0.348 0.648 0.004
#> SRR1047823 1 0.1732 0.702 0.920 0 0.000 0.080 0.000
#> SRR1047824 1 0.1732 0.702 0.920 0 0.000 0.080 0.000
#> SRR1047825 1 0.1732 0.702 0.920 0 0.000 0.080 0.000
#> SRR1047826 1 0.1732 0.702 0.920 0 0.000 0.080 0.000
#> SRR1047827 1 0.1732 0.702 0.920 0 0.000 0.080 0.000
#> SRR1047828 5 0.0000 0.721 0.000 0 0.000 0.000 1.000
#> SRR1047829 5 0.0510 0.710 0.000 0 0.000 0.016 0.984
#> SRR1047830 5 0.0000 0.721 0.000 0 0.000 0.000 1.000
#> SRR1047831 5 0.0000 0.721 0.000 0 0.000 0.000 1.000
#> SRR1047832 5 0.0000 0.721 0.000 0 0.000 0.000 1.000
#> SRR1047833 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> SRR1047834 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> SRR1047835 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> SRR1047836 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> SRR1047837 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> SRR1047838 4 0.0000 0.906 0.000 0 0.000 1.000 0.000
#> SRR1047839 4 0.0000 0.906 0.000 0 0.000 1.000 0.000
#> SRR1047840 4 0.0000 0.906 0.000 0 0.000 1.000 0.000
#> SRR1047841 4 0.0000 0.906 0.000 0 0.000 1.000 0.000
#> SRR1047842 4 0.0000 0.906 0.000 0 0.000 1.000 0.000
#> SRR1047843 4 0.0000 0.906 0.000 0 0.000 1.000 0.000
#> SRR1047844 4 0.0000 0.906 0.000 0 0.000 1.000 0.000
#> SRR1047845 4 0.0000 0.906 0.000 0 0.000 1.000 0.000
#> SRR1047846 4 0.0000 0.906 0.000 0 0.000 1.000 0.000
#> SRR1047847 4 0.0000 0.906 0.000 0 0.000 1.000 0.000
#> SRR1047848 5 0.4171 0.185 0.396 0 0.000 0.000 0.604
#> SRR1047849 5 0.3003 0.636 0.188 0 0.000 0.000 0.812
#> SRR1047850 5 0.3109 0.626 0.200 0 0.000 0.000 0.800
#> SRR1047851 5 0.3109 0.626 0.200 0 0.000 0.000 0.800
#> SRR1047852 5 0.3109 0.626 0.200 0 0.000 0.000 0.800
#> SRR1047853 4 0.0000 0.906 0.000 0 0.000 1.000 0.000
#> SRR1047854 4 0.0000 0.906 0.000 0 0.000 1.000 0.000
#> SRR1047855 4 0.0000 0.906 0.000 0 0.000 1.000 0.000
#> SRR1047856 4 0.0000 0.906 0.000 0 0.000 1.000 0.000
#> SRR1047857 4 0.0000 0.906 0.000 0 0.000 1.000 0.000
#> SRR1047858 4 0.3932 0.480 0.328 0 0.000 0.672 0.000
#> SRR1047859 4 0.0000 0.906 0.000 0 0.000 1.000 0.000
#> SRR1047860 4 0.0290 0.900 0.008 0 0.000 0.992 0.000
#> SRR1047861 4 0.0000 0.906 0.000 0 0.000 1.000 0.000
#> SRR1047863 3 0.0000 0.968 0.000 0 1.000 0.000 0.000
#> SRR1047864 5 0.4182 0.197 0.000 0 0.400 0.000 0.600
#> SRR1047865 3 0.0000 0.968 0.000 0 1.000 0.000 0.000
#> SRR1047866 5 0.4182 0.197 0.000 0 0.400 0.000 0.600
#> SRR1047867 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> SRR1047868 3 0.0000 0.968 0.000 0 1.000 0.000 0.000
#> SRR1047869 3 0.0404 0.961 0.000 0 0.988 0.012 0.000
#> SRR1047870 3 0.0162 0.966 0.000 0 0.996 0.000 0.004
#> SRR1047871 3 0.0000 0.968 0.000 0 1.000 0.000 0.000
#> SRR1047872 3 0.0000 0.968 0.000 0 1.000 0.000 0.000
#> SRR1047873 3 0.1732 0.896 0.000 0 0.920 0.080 0.000
#> SRR1047874 3 0.1732 0.896 0.000 0 0.920 0.080 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1047813 1 0.0000 0.639 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1047814 1 0.0000 0.639 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1047815 1 0.0000 0.639 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1047816 1 0.0000 0.639 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1047817 4 0.3528 0.574 0.296 0.000 0.004 0.700 0.000 0.000
#> SRR1047818 4 0.6011 0.524 0.024 0.000 0.088 0.564 0.024 0.300
#> SRR1047819 4 0.5992 0.517 0.056 0.000 0.072 0.564 0.008 0.300
#> SRR1047820 4 0.5992 0.517 0.056 0.000 0.072 0.564 0.008 0.300
#> SRR1047821 4 0.6008 0.525 0.020 0.000 0.088 0.564 0.028 0.300
#> SRR1047822 4 0.5466 0.518 0.000 0.000 0.136 0.560 0.004 0.300
#> SRR1047823 6 0.5160 1.000 0.332 0.000 0.000 0.104 0.000 0.564
#> SRR1047824 6 0.5160 1.000 0.332 0.000 0.000 0.104 0.000 0.564
#> SRR1047825 6 0.5160 1.000 0.332 0.000 0.000 0.104 0.000 0.564
#> SRR1047826 6 0.5160 1.000 0.332 0.000 0.000 0.104 0.000 0.564
#> SRR1047827 6 0.5160 1.000 0.332 0.000 0.000 0.104 0.000 0.564
#> SRR1047828 5 0.0000 0.896 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1047829 5 0.0000 0.896 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1047830 5 0.0000 0.896 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1047831 5 0.0000 0.896 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1047832 5 0.0000 0.896 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1047833 2 0.0000 0.981 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1047834 2 0.0000 0.981 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1047835 2 0.0000 0.981 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1047836 2 0.0000 0.981 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1047837 2 0.0000 0.981 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1047838 4 0.0000 0.874 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047839 4 0.0146 0.874 0.000 0.000 0.004 0.996 0.000 0.000
#> SRR1047840 4 0.0000 0.874 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1047841 4 0.0146 0.874 0.000 0.000 0.004 0.996 0.000 0.000
#> SRR1047842 4 0.0146 0.874 0.000 0.000 0.004 0.996 0.000 0.000
#> SRR1047843 4 0.0146 0.874 0.000 0.000 0.000 0.996 0.000 0.004
#> SRR1047844 4 0.0146 0.874 0.000 0.000 0.000 0.996 0.000 0.004
#> SRR1047845 4 0.0146 0.874 0.000 0.000 0.000 0.996 0.000 0.004
#> SRR1047846 4 0.0146 0.874 0.000 0.000 0.000 0.996 0.000 0.004
#> SRR1047847 4 0.0146 0.874 0.000 0.000 0.000 0.996 0.000 0.004
#> SRR1047848 1 0.1075 0.653 0.952 0.000 0.000 0.000 0.048 0.000
#> SRR1047849 1 0.3797 0.545 0.580 0.000 0.000 0.000 0.420 0.000
#> SRR1047850 1 0.3765 0.577 0.596 0.000 0.000 0.000 0.404 0.000
#> SRR1047851 1 0.3765 0.577 0.596 0.000 0.000 0.000 0.404 0.000
#> SRR1047852 1 0.3765 0.577 0.596 0.000 0.000 0.000 0.404 0.000
#> SRR1047853 4 0.0146 0.874 0.000 0.000 0.004 0.996 0.000 0.000
#> SRR1047854 4 0.0146 0.874 0.000 0.000 0.004 0.996 0.000 0.000
#> SRR1047855 4 0.0146 0.874 0.000 0.000 0.004 0.996 0.000 0.000
#> SRR1047856 4 0.0146 0.874 0.000 0.000 0.004 0.996 0.000 0.000
#> SRR1047857 4 0.0146 0.874 0.000 0.000 0.004 0.996 0.000 0.000
#> SRR1047858 4 0.3050 0.593 0.000 0.000 0.000 0.764 0.000 0.236
#> SRR1047859 4 0.0146 0.874 0.000 0.000 0.000 0.996 0.000 0.004
#> SRR1047860 4 0.0632 0.860 0.000 0.000 0.000 0.976 0.000 0.024
#> SRR1047861 4 0.0146 0.874 0.000 0.000 0.000 0.996 0.000 0.004
#> SRR1047863 3 0.0146 0.968 0.000 0.000 0.996 0.000 0.004 0.000
#> SRR1047864 5 0.1327 0.847 0.000 0.000 0.064 0.000 0.936 0.000
#> SRR1047865 3 0.0146 0.968 0.000 0.000 0.996 0.000 0.004 0.000
#> SRR1047866 5 0.3747 0.381 0.000 0.000 0.396 0.000 0.604 0.000
#> SRR1047867 2 0.2178 0.901 0.000 0.868 0.000 0.000 0.000 0.132
#> SRR1047868 3 0.0000 0.968 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047869 3 0.0363 0.964 0.000 0.000 0.988 0.012 0.000 0.000
#> SRR1047870 3 0.0260 0.966 0.000 0.000 0.992 0.000 0.008 0.000
#> SRR1047871 3 0.0146 0.968 0.000 0.000 0.996 0.004 0.000 0.000
#> SRR1047872 3 0.0000 0.968 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1047873 3 0.1387 0.909 0.000 0.000 0.932 0.068 0.000 0.000
#> SRR1047874 3 0.1387 0.909 0.000 0.000 0.932 0.068 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", "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 17931 rows and 61 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 1.000 1.000 0.2325 0.768 0.768
#> 3 3 0.864 0.894 0.943 1.5693 0.627 0.515
#> 4 4 0.893 0.906 0.964 0.1560 0.880 0.714
#> 5 5 0.873 0.801 0.904 0.1184 0.902 0.693
#> 6 6 0.892 0.804 0.869 0.0276 0.942 0.771
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
#> SRR1047813 1 0 1 1 0
#> SRR1047814 1 0 1 1 0
#> SRR1047815 1 0 1 1 0
#> SRR1047816 1 0 1 1 0
#> SRR1047817 1 0 1 1 0
#> SRR1047818 1 0 1 1 0
#> SRR1047819 1 0 1 1 0
#> SRR1047820 1 0 1 1 0
#> SRR1047821 1 0 1 1 0
#> SRR1047822 1 0 1 1 0
#> SRR1047823 1 0 1 1 0
#> SRR1047824 1 0 1 1 0
#> SRR1047825 1 0 1 1 0
#> SRR1047826 1 0 1 1 0
#> SRR1047827 1 0 1 1 0
#> SRR1047828 1 0 1 1 0
#> SRR1047829 1 0 1 1 0
#> SRR1047830 1 0 1 1 0
#> SRR1047831 1 0 1 1 0
#> SRR1047832 1 0 1 1 0
#> SRR1047833 2 0 1 0 1
#> SRR1047834 2 0 1 0 1
#> SRR1047835 2 0 1 0 1
#> SRR1047836 2 0 1 0 1
#> SRR1047837 2 0 1 0 1
#> SRR1047838 1 0 1 1 0
#> SRR1047839 1 0 1 1 0
#> SRR1047840 1 0 1 1 0
#> SRR1047841 1 0 1 1 0
#> SRR1047842 1 0 1 1 0
#> SRR1047843 1 0 1 1 0
#> SRR1047844 1 0 1 1 0
#> SRR1047845 1 0 1 1 0
#> SRR1047846 1 0 1 1 0
#> SRR1047847 1 0 1 1 0
#> SRR1047848 1 0 1 1 0
#> SRR1047849 1 0 1 1 0
#> SRR1047850 1 0 1 1 0
#> SRR1047851 1 0 1 1 0
#> SRR1047852 1 0 1 1 0
#> SRR1047853 1 0 1 1 0
#> SRR1047854 1 0 1 1 0
#> SRR1047855 1 0 1 1 0
#> SRR1047856 1 0 1 1 0
#> SRR1047857 1 0 1 1 0
#> SRR1047858 1 0 1 1 0
#> SRR1047859 1 0 1 1 0
#> SRR1047860 1 0 1 1 0
#> SRR1047861 1 0 1 1 0
#> SRR1047863 1 0 1 1 0
#> SRR1047864 2 0 1 0 1
#> SRR1047865 1 0 1 1 0
#> SRR1047866 2 0 1 0 1
#> SRR1047867 2 0 1 0 1
#> SRR1047868 1 0 1 1 0
#> SRR1047869 1 0 1 1 0
#> SRR1047870 1 0 1 1 0
#> SRR1047871 1 0 1 1 0
#> SRR1047872 1 0 1 1 0
#> SRR1047873 1 0 1 1 0
#> SRR1047874 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1047813 3 0.0000 0.897 0.000 0.000 1.000
#> SRR1047814 3 0.0000 0.897 0.000 0.000 1.000
#> SRR1047815 3 0.0000 0.897 0.000 0.000 1.000
#> SRR1047816 3 0.0000 0.897 0.000 0.000 1.000
#> SRR1047817 3 0.0000 0.897 0.000 0.000 1.000
#> SRR1047818 1 0.0892 0.939 0.980 0.000 0.020
#> SRR1047819 1 0.0892 0.939 0.980 0.000 0.020
#> SRR1047820 1 0.0892 0.939 0.980 0.000 0.020
#> SRR1047821 1 0.0892 0.939 0.980 0.000 0.020
#> SRR1047822 1 0.0892 0.939 0.980 0.000 0.020
#> SRR1047823 1 0.1289 0.935 0.968 0.000 0.032
#> SRR1047824 1 0.1289 0.935 0.968 0.000 0.032
#> SRR1047825 1 0.1289 0.935 0.968 0.000 0.032
#> SRR1047826 1 0.1289 0.935 0.968 0.000 0.032
#> SRR1047827 1 0.1289 0.935 0.968 0.000 0.032
#> SRR1047828 3 0.0000 0.897 0.000 0.000 1.000
#> SRR1047829 3 0.0000 0.897 0.000 0.000 1.000
#> SRR1047830 3 0.0000 0.897 0.000 0.000 1.000
#> SRR1047831 3 0.0000 0.897 0.000 0.000 1.000
#> SRR1047832 3 0.0000 0.897 0.000 0.000 1.000
#> SRR1047833 2 0.0000 1.000 0.000 1.000 0.000
#> SRR1047834 2 0.0000 1.000 0.000 1.000 0.000
#> SRR1047835 2 0.0000 1.000 0.000 1.000 0.000
#> SRR1047836 2 0.0000 1.000 0.000 1.000 0.000
#> SRR1047837 2 0.0000 1.000 0.000 1.000 0.000
#> SRR1047838 1 0.1289 0.953 0.968 0.000 0.032
#> SRR1047839 1 0.1529 0.950 0.960 0.000 0.040
#> SRR1047840 1 0.1289 0.953 0.968 0.000 0.032
#> SRR1047841 1 0.1289 0.953 0.968 0.000 0.032
#> SRR1047842 1 0.1289 0.953 0.968 0.000 0.032
#> SRR1047843 1 0.1411 0.952 0.964 0.000 0.036
#> SRR1047844 1 0.1411 0.952 0.964 0.000 0.036
#> SRR1047845 1 0.1411 0.952 0.964 0.000 0.036
#> SRR1047846 1 0.1411 0.952 0.964 0.000 0.036
#> SRR1047847 1 0.1411 0.952 0.964 0.000 0.036
#> SRR1047848 3 0.0000 0.897 0.000 0.000 1.000
#> SRR1047849 3 0.0000 0.897 0.000 0.000 1.000
#> SRR1047850 3 0.0000 0.897 0.000 0.000 1.000
#> SRR1047851 3 0.0000 0.897 0.000 0.000 1.000
#> SRR1047852 3 0.0000 0.897 0.000 0.000 1.000
#> SRR1047853 1 0.1289 0.953 0.968 0.000 0.032
#> SRR1047854 1 0.1289 0.953 0.968 0.000 0.032
#> SRR1047855 1 0.1289 0.953 0.968 0.000 0.032
#> SRR1047856 1 0.1289 0.953 0.968 0.000 0.032
#> SRR1047857 1 0.1289 0.953 0.968 0.000 0.032
#> SRR1047858 1 0.1643 0.949 0.956 0.000 0.044
#> SRR1047859 1 0.1643 0.949 0.956 0.000 0.044
#> SRR1047860 1 0.1643 0.949 0.956 0.000 0.044
#> SRR1047861 1 0.1643 0.949 0.956 0.000 0.044
#> SRR1047863 3 0.5325 0.748 0.248 0.004 0.748
#> SRR1047864 2 0.0000 1.000 0.000 1.000 0.000
#> SRR1047865 3 0.2860 0.856 0.084 0.004 0.912
#> SRR1047866 2 0.0000 1.000 0.000 1.000 0.000
#> SRR1047867 2 0.0000 1.000 0.000 1.000 0.000
#> SRR1047868 3 0.6505 0.274 0.468 0.004 0.528
#> SRR1047869 3 0.5325 0.748 0.248 0.004 0.748
#> SRR1047870 3 0.5325 0.748 0.248 0.004 0.748
#> SRR1047871 3 0.5325 0.748 0.248 0.004 0.748
#> SRR1047872 3 0.5325 0.748 0.248 0.004 0.748
#> SRR1047873 1 0.6008 0.390 0.664 0.004 0.332
#> SRR1047874 1 0.6104 0.343 0.648 0.004 0.348
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1047813 1 0.000 1.000 1.000 0 0 0.000
#> SRR1047814 1 0.000 1.000 1.000 0 0 0.000
#> SRR1047815 1 0.000 1.000 1.000 0 0 0.000
#> SRR1047816 1 0.000 1.000 1.000 0 0 0.000
#> SRR1047817 1 0.000 1.000 1.000 0 0 0.000
#> SRR1047818 4 0.000 0.905 0.000 0 0 1.000
#> SRR1047819 4 0.000 0.905 0.000 0 0 1.000
#> SRR1047820 4 0.000 0.905 0.000 0 0 1.000
#> SRR1047821 4 0.000 0.905 0.000 0 0 1.000
#> SRR1047822 4 0.000 0.905 0.000 0 0 1.000
#> SRR1047823 4 0.495 0.316 0.444 0 0 0.556
#> SRR1047824 4 0.495 0.316 0.444 0 0 0.556
#> SRR1047825 4 0.495 0.316 0.444 0 0 0.556
#> SRR1047826 4 0.495 0.316 0.444 0 0 0.556
#> SRR1047827 4 0.495 0.316 0.444 0 0 0.556
#> SRR1047828 1 0.000 1.000 1.000 0 0 0.000
#> SRR1047829 1 0.000 1.000 1.000 0 0 0.000
#> SRR1047830 1 0.000 1.000 1.000 0 0 0.000
#> SRR1047831 1 0.000 1.000 1.000 0 0 0.000
#> SRR1047832 1 0.000 1.000 1.000 0 0 0.000
#> SRR1047833 2 0.000 1.000 0.000 1 0 0.000
#> SRR1047834 2 0.000 1.000 0.000 1 0 0.000
#> SRR1047835 2 0.000 1.000 0.000 1 0 0.000
#> SRR1047836 2 0.000 1.000 0.000 1 0 0.000
#> SRR1047837 2 0.000 1.000 0.000 1 0 0.000
#> SRR1047838 4 0.000 0.905 0.000 0 0 1.000
#> SRR1047839 4 0.000 0.905 0.000 0 0 1.000
#> SRR1047840 4 0.000 0.905 0.000 0 0 1.000
#> SRR1047841 4 0.000 0.905 0.000 0 0 1.000
#> SRR1047842 4 0.000 0.905 0.000 0 0 1.000
#> SRR1047843 4 0.000 0.905 0.000 0 0 1.000
#> SRR1047844 4 0.000 0.905 0.000 0 0 1.000
#> SRR1047845 4 0.000 0.905 0.000 0 0 1.000
#> SRR1047846 4 0.000 0.905 0.000 0 0 1.000
#> SRR1047847 4 0.000 0.905 0.000 0 0 1.000
#> SRR1047848 1 0.000 1.000 1.000 0 0 0.000
#> SRR1047849 1 0.000 1.000 1.000 0 0 0.000
#> SRR1047850 1 0.000 1.000 1.000 0 0 0.000
#> SRR1047851 1 0.000 1.000 1.000 0 0 0.000
#> SRR1047852 1 0.000 1.000 1.000 0 0 0.000
#> SRR1047853 4 0.000 0.905 0.000 0 0 1.000
#> SRR1047854 4 0.000 0.905 0.000 0 0 1.000
#> SRR1047855 4 0.000 0.905 0.000 0 0 1.000
#> SRR1047856 4 0.000 0.905 0.000 0 0 1.000
#> SRR1047857 4 0.000 0.905 0.000 0 0 1.000
#> SRR1047858 4 0.000 0.905 0.000 0 0 1.000
#> SRR1047859 4 0.000 0.905 0.000 0 0 1.000
#> SRR1047860 4 0.000 0.905 0.000 0 0 1.000
#> SRR1047861 4 0.000 0.905 0.000 0 0 1.000
#> SRR1047863 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047864 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047865 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047866 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047867 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047868 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047869 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047870 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047871 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047872 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047873 3 0.000 1.000 0.000 0 1 0.000
#> SRR1047874 3 0.000 1.000 0.000 0 1 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1047813 1 0.000 0.790 1.00 0 0 0.000 0.000
#> SRR1047814 1 0.000 0.790 1.00 0 0 0.000 0.000
#> SRR1047815 1 0.000 0.790 1.00 0 0 0.000 0.000
#> SRR1047816 1 0.000 0.790 1.00 0 0 0.000 0.000
#> SRR1047817 1 0.477 0.629 0.56 0 0 0.020 0.420
#> SRR1047818 4 0.000 0.894 0.00 0 0 1.000 0.000
#> SRR1047819 4 0.000 0.894 0.00 0 0 1.000 0.000
#> SRR1047820 4 0.000 0.894 0.00 0 0 1.000 0.000
#> SRR1047821 4 0.000 0.894 0.00 0 0 1.000 0.000
#> SRR1047822 4 0.000 0.894 0.00 0 0 1.000 0.000
#> SRR1047823 5 0.000 0.652 0.00 0 0 0.000 1.000
#> SRR1047824 5 0.000 0.652 0.00 0 0 0.000 1.000
#> SRR1047825 5 0.000 0.652 0.00 0 0 0.000 1.000
#> SRR1047826 5 0.000 0.652 0.00 0 0 0.000 1.000
#> SRR1047827 5 0.000 0.652 0.00 0 0 0.000 1.000
#> SRR1047828 1 0.477 0.629 0.56 0 0 0.020 0.420
#> SRR1047829 1 0.477 0.629 0.56 0 0 0.020 0.420
#> SRR1047830 1 0.477 0.629 0.56 0 0 0.020 0.420
#> SRR1047831 1 0.477 0.629 0.56 0 0 0.020 0.420
#> SRR1047832 1 0.477 0.629 0.56 0 0 0.020 0.420
#> SRR1047833 2 0.000 1.000 0.00 1 0 0.000 0.000
#> SRR1047834 2 0.000 1.000 0.00 1 0 0.000 0.000
#> SRR1047835 2 0.000 1.000 0.00 1 0 0.000 0.000
#> SRR1047836 2 0.000 1.000 0.00 1 0 0.000 0.000
#> SRR1047837 2 0.000 1.000 0.00 1 0 0.000 0.000
#> SRR1047838 4 0.154 0.882 0.00 0 0 0.932 0.068
#> SRR1047839 4 0.148 0.884 0.00 0 0 0.936 0.064
#> SRR1047840 4 0.154 0.882 0.00 0 0 0.932 0.068
#> SRR1047841 4 0.154 0.882 0.00 0 0 0.932 0.068
#> SRR1047842 4 0.154 0.882 0.00 0 0 0.932 0.068
#> SRR1047843 4 0.402 0.399 0.00 0 0 0.652 0.348
#> SRR1047844 4 0.148 0.884 0.00 0 0 0.936 0.064
#> SRR1047845 4 0.402 0.399 0.00 0 0 0.652 0.348
#> SRR1047846 4 0.402 0.399 0.00 0 0 0.652 0.348
#> SRR1047847 4 0.148 0.884 0.00 0 0 0.936 0.064
#> SRR1047848 1 0.000 0.790 1.00 0 0 0.000 0.000
#> SRR1047849 1 0.000 0.790 1.00 0 0 0.000 0.000
#> SRR1047850 1 0.000 0.790 1.00 0 0 0.000 0.000
#> SRR1047851 1 0.000 0.790 1.00 0 0 0.000 0.000
#> SRR1047852 1 0.000 0.790 1.00 0 0 0.000 0.000
#> SRR1047853 4 0.000 0.894 0.00 0 0 1.000 0.000
#> SRR1047854 4 0.000 0.894 0.00 0 0 1.000 0.000
#> SRR1047855 4 0.000 0.894 0.00 0 0 1.000 0.000
#> SRR1047856 4 0.000 0.894 0.00 0 0 1.000 0.000
#> SRR1047857 4 0.000 0.894 0.00 0 0 1.000 0.000
#> SRR1047858 5 0.420 0.398 0.00 0 0 0.408 0.592
#> SRR1047859 5 0.430 0.192 0.00 0 0 0.476 0.524
#> SRR1047860 5 0.420 0.398 0.00 0 0 0.408 0.592
#> SRR1047861 5 0.420 0.398 0.00 0 0 0.408 0.592
#> SRR1047863 3 0.000 1.000 0.00 0 1 0.000 0.000
#> SRR1047864 3 0.000 1.000 0.00 0 1 0.000 0.000
#> SRR1047865 3 0.000 1.000 0.00 0 1 0.000 0.000
#> SRR1047866 3 0.000 1.000 0.00 0 1 0.000 0.000
#> SRR1047867 3 0.000 1.000 0.00 0 1 0.000 0.000
#> SRR1047868 3 0.000 1.000 0.00 0 1 0.000 0.000
#> SRR1047869 3 0.000 1.000 0.00 0 1 0.000 0.000
#> SRR1047870 3 0.000 1.000 0.00 0 1 0.000 0.000
#> SRR1047871 3 0.000 1.000 0.00 0 1 0.000 0.000
#> SRR1047872 3 0.000 1.000 0.00 0 1 0.000 0.000
#> SRR1047873 3 0.000 1.000 0.00 0 1 0.000 0.000
#> SRR1047874 3 0.000 1.000 0.00 0 1 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1047813 1 0.380 0.627 0.58 0 0.42 0.000 0.00 0.000
#> SRR1047814 1 0.380 0.627 0.58 0 0.42 0.000 0.00 0.000
#> SRR1047815 1 0.380 0.627 0.58 0 0.42 0.000 0.00 0.000
#> SRR1047816 1 0.380 0.627 0.58 0 0.42 0.000 0.00 0.000
#> SRR1047817 1 0.000 0.586 1.00 0 0.00 0.000 0.00 0.000
#> SRR1047818 4 0.000 0.963 0.00 0 0.00 1.000 0.00 0.000
#> SRR1047819 4 0.000 0.963 0.00 0 0.00 1.000 0.00 0.000
#> SRR1047820 4 0.000 0.963 0.00 0 0.00 1.000 0.00 0.000
#> SRR1047821 4 0.000 0.963 0.00 0 0.00 1.000 0.00 0.000
#> SRR1047822 4 0.000 0.963 0.00 0 0.00 1.000 0.00 0.000
#> SRR1047823 6 0.000 1.000 0.00 0 0.00 0.000 0.00 1.000
#> SRR1047824 6 0.000 1.000 0.00 0 0.00 0.000 0.00 1.000
#> SRR1047825 6 0.000 1.000 0.00 0 0.00 0.000 0.00 1.000
#> SRR1047826 6 0.000 1.000 0.00 0 0.00 0.000 0.00 1.000
#> SRR1047827 6 0.000 1.000 0.00 0 0.00 0.000 0.00 1.000
#> SRR1047828 1 0.000 0.586 1.00 0 0.00 0.000 0.00 0.000
#> SRR1047829 1 0.000 0.586 1.00 0 0.00 0.000 0.00 0.000
#> SRR1047830 1 0.000 0.586 1.00 0 0.00 0.000 0.00 0.000
#> SRR1047831 1 0.000 0.586 1.00 0 0.00 0.000 0.00 0.000
#> SRR1047832 1 0.000 0.586 1.00 0 0.00 0.000 0.00 0.000
#> SRR1047833 2 0.000 1.000 0.00 1 0.00 0.000 0.00 0.000
#> SRR1047834 2 0.000 1.000 0.00 1 0.00 0.000 0.00 0.000
#> SRR1047835 2 0.000 1.000 0.00 1 0.00 0.000 0.00 0.000
#> SRR1047836 2 0.000 1.000 0.00 1 0.00 0.000 0.00 0.000
#> SRR1047837 2 0.000 1.000 0.00 1 0.00 0.000 0.00 0.000
#> SRR1047838 4 0.000 0.963 0.00 0 0.00 1.000 0.00 0.000
#> SRR1047839 4 0.000 0.963 0.00 0 0.00 1.000 0.00 0.000
#> SRR1047840 4 0.000 0.963 0.00 0 0.00 1.000 0.00 0.000
#> SRR1047841 4 0.000 0.963 0.00 0 0.00 1.000 0.00 0.000
#> SRR1047842 4 0.000 0.963 0.00 0 0.00 1.000 0.00 0.000
#> SRR1047843 4 0.285 0.747 0.00 0 0.00 0.792 0.00 0.208
#> SRR1047844 4 0.000 0.963 0.00 0 0.00 1.000 0.00 0.000
#> SRR1047845 4 0.285 0.747 0.00 0 0.00 0.792 0.00 0.208
#> SRR1047846 4 0.285 0.747 0.00 0 0.00 0.792 0.00 0.208
#> SRR1047847 4 0.000 0.963 0.00 0 0.00 1.000 0.00 0.000
#> SRR1047848 1 0.380 0.627 0.58 0 0.42 0.000 0.00 0.000
#> SRR1047849 1 0.380 0.627 0.58 0 0.42 0.000 0.00 0.000
#> SRR1047850 1 0.380 0.627 0.58 0 0.42 0.000 0.00 0.000
#> SRR1047851 1 0.380 0.627 0.58 0 0.42 0.000 0.00 0.000
#> SRR1047852 1 0.380 0.627 0.58 0 0.42 0.000 0.00 0.000
#> SRR1047853 4 0.000 0.963 0.00 0 0.00 1.000 0.00 0.000
#> SRR1047854 4 0.000 0.963 0.00 0 0.00 1.000 0.00 0.000
#> SRR1047855 4 0.000 0.963 0.00 0 0.00 1.000 0.00 0.000
#> SRR1047856 4 0.000 0.963 0.00 0 0.00 1.000 0.00 0.000
#> SRR1047857 4 0.000 0.963 0.00 0 0.00 1.000 0.00 0.000
#> SRR1047858 1 0.591 -0.196 0.42 0 0.00 0.208 0.00 0.372
#> SRR1047859 1 0.599 -0.175 0.42 0 0.00 0.240 0.00 0.340
#> SRR1047860 1 0.591 -0.196 0.42 0 0.00 0.208 0.00 0.372
#> SRR1047861 1 0.591 -0.196 0.42 0 0.00 0.208 0.00 0.372
#> SRR1047863 3 0.380 1.000 0.00 0 0.58 0.000 0.42 0.000
#> SRR1047864 5 0.000 1.000 0.00 0 0.00 0.000 1.00 0.000
#> SRR1047865 3 0.380 1.000 0.00 0 0.58 0.000 0.42 0.000
#> SRR1047866 5 0.000 1.000 0.00 0 0.00 0.000 1.00 0.000
#> SRR1047867 5 0.000 1.000 0.00 0 0.00 0.000 1.00 0.000
#> SRR1047868 3 0.380 1.000 0.00 0 0.58 0.000 0.42 0.000
#> SRR1047869 3 0.380 1.000 0.00 0 0.58 0.000 0.42 0.000
#> SRR1047870 3 0.380 1.000 0.00 0 0.58 0.000 0.42 0.000
#> SRR1047871 3 0.380 1.000 0.00 0 0.58 0.000 0.42 0.000
#> SRR1047872 3 0.380 1.000 0.00 0 0.58 0.000 0.42 0.000
#> SRR1047873 3 0.380 1.000 0.00 0 0.58 0.000 0.42 0.000
#> SRR1047874 3 0.380 1.000 0.00 0 0.58 0.000 0.42 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 17931 rows and 61 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.720 0.819 0.916 0.2641 0.744 0.744
#> 3 3 0.574 0.834 0.886 0.9092 0.779 0.710
#> 4 4 0.569 0.753 0.832 0.3547 0.740 0.535
#> 5 5 0.539 0.617 0.740 0.0925 0.854 0.561
#> 6 6 0.558 0.583 0.709 0.0653 0.940 0.759
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
#> SRR1047813 1 0.3431 0.9022 0.936 0.064
#> SRR1047814 1 0.3431 0.9022 0.936 0.064
#> SRR1047815 1 0.3431 0.9022 0.936 0.064
#> SRR1047816 1 0.3431 0.9022 0.936 0.064
#> SRR1047817 1 0.2236 0.9157 0.964 0.036
#> SRR1047818 1 0.0672 0.9192 0.992 0.008
#> SRR1047819 1 0.0376 0.9205 0.996 0.004
#> SRR1047820 1 0.0376 0.9205 0.996 0.004
#> SRR1047821 1 0.0376 0.9205 0.996 0.004
#> SRR1047822 1 0.1184 0.9149 0.984 0.016
#> SRR1047823 1 0.3431 0.9022 0.936 0.064
#> SRR1047824 1 0.3274 0.9047 0.940 0.060
#> SRR1047825 1 0.3431 0.9022 0.936 0.064
#> SRR1047826 1 0.3431 0.9022 0.936 0.064
#> SRR1047827 1 0.3431 0.9022 0.936 0.064
#> SRR1047828 1 0.1414 0.9200 0.980 0.020
#> SRR1047829 1 0.0376 0.9205 0.996 0.004
#> SRR1047830 1 0.1414 0.9200 0.980 0.020
#> SRR1047831 1 0.0376 0.9213 0.996 0.004
#> SRR1047832 1 0.0376 0.9213 0.996 0.004
#> SRR1047833 2 0.0938 0.7399 0.012 0.988
#> SRR1047834 2 0.0938 0.7399 0.012 0.988
#> SRR1047835 2 0.0938 0.7399 0.012 0.988
#> SRR1047836 2 0.0938 0.7399 0.012 0.988
#> SRR1047837 2 0.0938 0.7399 0.012 0.988
#> SRR1047838 1 0.0000 0.9211 1.000 0.000
#> SRR1047839 1 0.0672 0.9192 0.992 0.008
#> SRR1047840 1 0.1184 0.9206 0.984 0.016
#> SRR1047841 1 0.0000 0.9211 1.000 0.000
#> SRR1047842 1 0.0000 0.9211 1.000 0.000
#> SRR1047843 1 0.0000 0.9211 1.000 0.000
#> SRR1047844 1 0.0672 0.9192 0.992 0.008
#> SRR1047845 1 0.0000 0.9211 1.000 0.000
#> SRR1047846 1 0.0000 0.9211 1.000 0.000
#> SRR1047847 1 0.0672 0.9192 0.992 0.008
#> SRR1047848 1 0.3431 0.9022 0.936 0.064
#> SRR1047849 1 0.3114 0.9070 0.944 0.056
#> SRR1047850 1 0.3114 0.9070 0.944 0.056
#> SRR1047851 1 0.3114 0.9070 0.944 0.056
#> SRR1047852 1 0.3114 0.9070 0.944 0.056
#> SRR1047853 1 0.1184 0.9149 0.984 0.016
#> SRR1047854 1 0.0672 0.9192 0.992 0.008
#> SRR1047855 1 0.0672 0.9192 0.992 0.008
#> SRR1047856 1 0.1184 0.9149 0.984 0.016
#> SRR1047857 1 0.1184 0.9149 0.984 0.016
#> SRR1047858 1 0.2043 0.9171 0.968 0.032
#> SRR1047859 1 0.1414 0.9200 0.980 0.020
#> SRR1047860 1 0.2043 0.9171 0.968 0.032
#> SRR1047861 1 0.2043 0.9171 0.968 0.032
#> SRR1047863 2 0.9998 0.3285 0.492 0.508
#> SRR1047864 2 0.9954 0.4090 0.460 0.540
#> SRR1047865 1 0.9815 -0.0587 0.580 0.420
#> SRR1047866 2 0.9998 0.3285 0.492 0.508
#> SRR1047867 2 0.9909 0.4375 0.444 0.556
#> SRR1047868 1 0.7376 0.6616 0.792 0.208
#> SRR1047869 1 0.6887 0.7072 0.816 0.184
#> SRR1047870 1 0.9087 0.3559 0.676 0.324
#> SRR1047871 1 0.5842 0.7792 0.860 0.140
#> SRR1047872 1 0.8207 0.5541 0.744 0.256
#> SRR1047873 1 0.5842 0.7792 0.860 0.140
#> SRR1047874 1 0.5842 0.7792 0.860 0.140
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1047813 1 0.1289 0.850 0.968 0.032 0.000
#> SRR1047814 1 0.1289 0.850 0.968 0.032 0.000
#> SRR1047815 1 0.1289 0.850 0.968 0.032 0.000
#> SRR1047816 1 0.1289 0.850 0.968 0.032 0.000
#> SRR1047817 1 0.1031 0.852 0.976 0.024 0.000
#> SRR1047818 1 0.6597 0.714 0.696 0.036 0.268
#> SRR1047819 1 0.4744 0.828 0.836 0.028 0.136
#> SRR1047820 1 0.5180 0.814 0.812 0.032 0.156
#> SRR1047821 1 0.6375 0.742 0.720 0.036 0.244
#> SRR1047822 1 0.7987 0.348 0.492 0.060 0.448
#> SRR1047823 1 0.0237 0.856 0.996 0.004 0.000
#> SRR1047824 1 0.0237 0.856 0.996 0.004 0.000
#> SRR1047825 1 0.0237 0.856 0.996 0.004 0.000
#> SRR1047826 1 0.0237 0.856 0.996 0.004 0.000
#> SRR1047827 1 0.0237 0.856 0.996 0.004 0.000
#> SRR1047828 1 0.3028 0.856 0.920 0.032 0.048
#> SRR1047829 1 0.5687 0.775 0.756 0.020 0.224
#> SRR1047830 1 0.3141 0.856 0.912 0.020 0.068
#> SRR1047831 1 0.3528 0.853 0.892 0.016 0.092
#> SRR1047832 1 0.3610 0.852 0.888 0.016 0.096
#> SRR1047833 2 0.1620 0.995 0.012 0.964 0.024
#> SRR1047834 2 0.1453 0.996 0.008 0.968 0.024
#> SRR1047835 2 0.1620 0.995 0.012 0.964 0.024
#> SRR1047836 2 0.1453 0.996 0.008 0.968 0.024
#> SRR1047837 2 0.1453 0.996 0.008 0.968 0.024
#> SRR1047838 1 0.3590 0.853 0.896 0.028 0.076
#> SRR1047839 1 0.6662 0.745 0.716 0.052 0.232
#> SRR1047840 1 0.3181 0.856 0.912 0.024 0.064
#> SRR1047841 1 0.3678 0.852 0.892 0.028 0.080
#> SRR1047842 1 0.3678 0.852 0.892 0.028 0.080
#> SRR1047843 1 0.3690 0.850 0.884 0.016 0.100
#> SRR1047844 1 0.7192 0.556 0.588 0.032 0.380
#> SRR1047845 1 0.3769 0.847 0.880 0.016 0.104
#> SRR1047846 1 0.3921 0.845 0.872 0.016 0.112
#> SRR1047847 1 0.7061 0.627 0.632 0.036 0.332
#> SRR1047848 1 0.1163 0.851 0.972 0.028 0.000
#> SRR1047849 1 0.1163 0.851 0.972 0.028 0.000
#> SRR1047850 1 0.0892 0.853 0.980 0.020 0.000
#> SRR1047851 1 0.1163 0.851 0.972 0.028 0.000
#> SRR1047852 1 0.1163 0.851 0.972 0.028 0.000
#> SRR1047853 1 0.7274 0.418 0.520 0.028 0.452
#> SRR1047854 1 0.6066 0.748 0.728 0.024 0.248
#> SRR1047855 1 0.5986 0.756 0.736 0.024 0.240
#> SRR1047856 1 0.7248 0.455 0.536 0.028 0.436
#> SRR1047857 1 0.7430 0.467 0.540 0.036 0.424
#> SRR1047858 1 0.0000 0.856 1.000 0.000 0.000
#> SRR1047859 1 0.1453 0.859 0.968 0.008 0.024
#> SRR1047860 1 0.0237 0.857 0.996 0.004 0.000
#> SRR1047861 1 0.0237 0.857 0.996 0.004 0.000
#> SRR1047863 3 0.2796 0.924 0.000 0.092 0.908
#> SRR1047864 3 0.2356 0.936 0.000 0.072 0.928
#> SRR1047865 3 0.1289 0.951 0.000 0.032 0.968
#> SRR1047866 3 0.2066 0.941 0.000 0.060 0.940
#> SRR1047867 3 0.2261 0.938 0.000 0.068 0.932
#> SRR1047868 3 0.1860 0.936 0.000 0.052 0.948
#> SRR1047869 3 0.0892 0.956 0.000 0.020 0.980
#> SRR1047870 3 0.1163 0.957 0.000 0.028 0.972
#> SRR1047871 3 0.0592 0.955 0.000 0.012 0.988
#> SRR1047872 3 0.1031 0.957 0.000 0.024 0.976
#> SRR1047873 3 0.2384 0.927 0.008 0.056 0.936
#> SRR1047874 3 0.1525 0.941 0.004 0.032 0.964
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1047813 1 0.1004 0.8257 0.972 0.000 0.024 0.004
#> SRR1047814 1 0.0779 0.8286 0.980 0.000 0.016 0.004
#> SRR1047815 1 0.0927 0.8282 0.976 0.000 0.016 0.008
#> SRR1047816 1 0.0927 0.8282 0.976 0.000 0.016 0.008
#> SRR1047817 1 0.1004 0.8277 0.972 0.000 0.004 0.024
#> SRR1047818 4 0.2075 0.7972 0.016 0.004 0.044 0.936
#> SRR1047819 4 0.1888 0.8038 0.044 0.000 0.016 0.940
#> SRR1047820 4 0.2007 0.8054 0.036 0.004 0.020 0.940
#> SRR1047821 4 0.1863 0.7961 0.012 0.004 0.040 0.944
#> SRR1047822 4 0.2597 0.7512 0.004 0.008 0.084 0.904
#> SRR1047823 1 0.4824 0.7276 0.744 0.004 0.024 0.228
#> SRR1047824 1 0.5243 0.6805 0.704 0.008 0.024 0.264
#> SRR1047825 1 0.4824 0.7276 0.744 0.004 0.024 0.228
#> SRR1047826 1 0.4824 0.7276 0.744 0.004 0.024 0.228
#> SRR1047827 1 0.4986 0.7050 0.724 0.004 0.024 0.248
#> SRR1047828 1 0.2988 0.7820 0.876 0.012 0.112 0.000
#> SRR1047829 1 0.4647 0.7441 0.796 0.012 0.156 0.036
#> SRR1047830 1 0.2928 0.7853 0.880 0.012 0.108 0.000
#> SRR1047831 1 0.2988 0.7831 0.876 0.012 0.112 0.000
#> SRR1047832 1 0.3289 0.7773 0.864 0.012 0.120 0.004
#> SRR1047833 2 0.0376 0.9954 0.004 0.992 0.000 0.004
#> SRR1047834 2 0.0188 0.9969 0.000 0.996 0.000 0.004
#> SRR1047835 2 0.0188 0.9969 0.000 0.996 0.000 0.004
#> SRR1047836 2 0.0376 0.9954 0.004 0.992 0.000 0.004
#> SRR1047837 2 0.0188 0.9969 0.000 0.996 0.000 0.004
#> SRR1047838 4 0.3157 0.7622 0.144 0.000 0.004 0.852
#> SRR1047839 4 0.1639 0.7960 0.008 0.004 0.036 0.952
#> SRR1047840 4 0.4319 0.6481 0.228 0.000 0.012 0.760
#> SRR1047841 4 0.2589 0.7844 0.116 0.000 0.000 0.884
#> SRR1047842 4 0.2647 0.7821 0.120 0.000 0.000 0.880
#> SRR1047843 1 0.5392 0.1992 0.528 0.000 0.012 0.460
#> SRR1047844 4 0.3256 0.7947 0.044 0.004 0.068 0.884
#> SRR1047845 4 0.5163 -0.0630 0.480 0.000 0.004 0.516
#> SRR1047846 4 0.5126 0.0973 0.444 0.000 0.004 0.552
#> SRR1047847 4 0.2549 0.7967 0.024 0.004 0.056 0.916
#> SRR1047848 1 0.1629 0.8211 0.952 0.024 0.024 0.000
#> SRR1047849 1 0.1297 0.8235 0.964 0.016 0.020 0.000
#> SRR1047850 1 0.0967 0.8278 0.976 0.016 0.004 0.004
#> SRR1047851 1 0.1059 0.8256 0.972 0.016 0.012 0.000
#> SRR1047852 1 0.1059 0.8256 0.972 0.016 0.012 0.000
#> SRR1047853 4 0.2926 0.7536 0.012 0.004 0.096 0.888
#> SRR1047854 4 0.3800 0.7939 0.112 0.004 0.036 0.848
#> SRR1047855 4 0.3706 0.7915 0.112 0.000 0.040 0.848
#> SRR1047856 4 0.2796 0.7497 0.008 0.004 0.096 0.892
#> SRR1047857 4 0.2715 0.7404 0.004 0.004 0.100 0.892
#> SRR1047858 1 0.3895 0.7626 0.804 0.000 0.012 0.184
#> SRR1047859 1 0.5026 0.6050 0.672 0.000 0.016 0.312
#> SRR1047860 1 0.4019 0.7560 0.792 0.000 0.012 0.196
#> SRR1047861 1 0.4253 0.7455 0.776 0.000 0.016 0.208
#> SRR1047863 3 0.5003 0.7726 0.000 0.016 0.676 0.308
#> SRR1047864 3 0.3312 0.6539 0.068 0.040 0.884 0.008
#> SRR1047865 3 0.2773 0.7957 0.004 0.000 0.880 0.116
#> SRR1047866 3 0.3238 0.6427 0.092 0.020 0.880 0.008
#> SRR1047867 3 0.3538 0.6645 0.024 0.096 0.868 0.012
#> SRR1047868 3 0.4836 0.7637 0.000 0.008 0.672 0.320
#> SRR1047869 3 0.3208 0.8167 0.004 0.000 0.848 0.148
#> SRR1047870 3 0.4086 0.8251 0.000 0.008 0.776 0.216
#> SRR1047871 3 0.3631 0.8239 0.004 0.004 0.824 0.168
#> SRR1047872 3 0.4089 0.8258 0.004 0.004 0.780 0.212
#> SRR1047873 3 0.5085 0.6913 0.000 0.008 0.616 0.376
#> SRR1047874 3 0.4917 0.7508 0.004 0.004 0.664 0.328
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1047813 1 0.5316 0.0227 0.520 0.004 0.032 0.004 0.440
#> SRR1047814 1 0.5396 0.0996 0.540 0.004 0.032 0.008 0.416
#> SRR1047815 1 0.5396 0.0956 0.540 0.004 0.032 0.008 0.416
#> SRR1047816 1 0.5419 0.0389 0.524 0.004 0.032 0.008 0.432
#> SRR1047817 1 0.5657 0.0666 0.516 0.008 0.024 0.020 0.432
#> SRR1047818 4 0.2707 0.7520 0.080 0.000 0.024 0.888 0.008
#> SRR1047819 4 0.3792 0.7402 0.180 0.000 0.020 0.792 0.008
#> SRR1047820 4 0.3678 0.7444 0.168 0.000 0.020 0.804 0.008
#> SRR1047821 4 0.2881 0.7519 0.092 0.000 0.024 0.876 0.008
#> SRR1047822 4 0.1787 0.7265 0.016 0.000 0.032 0.940 0.012
#> SRR1047823 1 0.1924 0.6215 0.924 0.000 0.004 0.064 0.008
#> SRR1047824 1 0.2237 0.6159 0.904 0.000 0.004 0.084 0.008
#> SRR1047825 1 0.2103 0.6201 0.920 0.000 0.004 0.056 0.020
#> SRR1047826 1 0.2005 0.6205 0.924 0.000 0.004 0.056 0.016
#> SRR1047827 1 0.1956 0.6196 0.916 0.000 0.000 0.076 0.008
#> SRR1047828 5 0.4445 0.8294 0.272 0.000 0.024 0.004 0.700
#> SRR1047829 5 0.4863 0.7331 0.176 0.000 0.064 0.020 0.740
#> SRR1047830 5 0.4260 0.8340 0.256 0.000 0.020 0.004 0.720
#> SRR1047831 5 0.4125 0.8258 0.236 0.000 0.020 0.004 0.740
#> SRR1047832 5 0.4155 0.8195 0.228 0.000 0.024 0.004 0.744
#> SRR1047833 2 0.0000 0.9944 0.000 1.000 0.000 0.000 0.000
#> SRR1047834 2 0.0162 0.9951 0.000 0.996 0.000 0.004 0.000
#> SRR1047835 2 0.0162 0.9953 0.000 0.996 0.004 0.000 0.000
#> SRR1047836 2 0.0162 0.9953 0.000 0.996 0.004 0.000 0.000
#> SRR1047837 2 0.0162 0.9951 0.000 0.996 0.000 0.004 0.000
#> SRR1047838 4 0.4387 0.5663 0.336 0.000 0.004 0.652 0.008
#> SRR1047839 4 0.0960 0.7330 0.008 0.000 0.016 0.972 0.004
#> SRR1047840 4 0.4658 0.1876 0.484 0.000 0.000 0.504 0.012
#> SRR1047841 4 0.3521 0.7063 0.232 0.000 0.000 0.764 0.004
#> SRR1047842 4 0.3671 0.6971 0.236 0.000 0.000 0.756 0.008
#> SRR1047843 1 0.5078 0.5310 0.692 0.000 0.024 0.244 0.040
#> SRR1047844 4 0.2256 0.7260 0.032 0.000 0.032 0.920 0.016
#> SRR1047845 1 0.5161 0.3413 0.620 0.000 0.020 0.336 0.024
#> SRR1047846 1 0.5322 0.2970 0.592 0.000 0.020 0.360 0.028
#> SRR1047847 4 0.2170 0.7202 0.020 0.000 0.036 0.924 0.020
#> SRR1047848 5 0.4252 0.7955 0.340 0.000 0.008 0.000 0.652
#> SRR1047849 5 0.4122 0.8377 0.304 0.000 0.004 0.004 0.688
#> SRR1047850 5 0.4299 0.8348 0.316 0.000 0.008 0.004 0.672
#> SRR1047851 5 0.4236 0.8279 0.328 0.000 0.004 0.004 0.664
#> SRR1047852 5 0.4218 0.8285 0.324 0.000 0.004 0.004 0.668
#> SRR1047853 4 0.2313 0.7367 0.032 0.000 0.040 0.916 0.012
#> SRR1047854 4 0.5190 0.6872 0.236 0.004 0.032 0.696 0.032
#> SRR1047855 4 0.5087 0.6825 0.244 0.004 0.028 0.696 0.028
#> SRR1047856 4 0.2140 0.7341 0.024 0.000 0.040 0.924 0.012
#> SRR1047857 4 0.1617 0.7366 0.020 0.000 0.020 0.948 0.012
#> SRR1047858 1 0.4295 0.5107 0.760 0.000 0.012 0.032 0.196
#> SRR1047859 1 0.4823 0.5766 0.744 0.000 0.008 0.120 0.128
#> SRR1047860 1 0.4220 0.5095 0.760 0.000 0.008 0.032 0.200
#> SRR1047861 1 0.4087 0.5459 0.784 0.000 0.008 0.040 0.168
#> SRR1047863 3 0.5235 0.4482 0.008 0.008 0.524 0.444 0.016
#> SRR1047864 3 0.4352 0.5833 0.020 0.012 0.732 0.000 0.236
#> SRR1047865 3 0.5317 0.7204 0.004 0.004 0.700 0.148 0.144
#> SRR1047866 3 0.5020 0.4409 0.016 0.012 0.564 0.000 0.408
#> SRR1047867 3 0.4583 0.5765 0.036 0.052 0.788 0.004 0.120
#> SRR1047868 3 0.4510 0.4625 0.000 0.008 0.560 0.432 0.000
#> SRR1047869 3 0.4855 0.7265 0.004 0.000 0.716 0.204 0.076
#> SRR1047870 3 0.4193 0.7355 0.012 0.008 0.784 0.172 0.024
#> SRR1047871 3 0.3995 0.7366 0.012 0.008 0.804 0.152 0.024
#> SRR1047872 3 0.4527 0.6849 0.000 0.004 0.696 0.272 0.028
#> SRR1047873 4 0.4876 0.1059 0.008 0.004 0.320 0.648 0.020
#> SRR1047874 4 0.4854 -0.1151 0.004 0.004 0.404 0.576 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1047813 5 0.6461 0.4092 0.240 0.000 0.008 0.016 0.464 NA
#> SRR1047814 5 0.6439 0.4166 0.228 0.000 0.008 0.016 0.468 NA
#> SRR1047815 5 0.6427 0.4188 0.228 0.000 0.008 0.016 0.472 NA
#> SRR1047816 5 0.6478 0.4196 0.220 0.000 0.008 0.020 0.472 NA
#> SRR1047817 5 0.7064 0.3640 0.180 0.000 0.008 0.072 0.420 NA
#> SRR1047818 4 0.3940 0.6326 0.104 0.000 0.016 0.804 0.012 NA
#> SRR1047819 4 0.4668 0.6276 0.152 0.000 0.012 0.740 0.020 NA
#> SRR1047820 4 0.4469 0.6283 0.136 0.000 0.012 0.760 0.020 NA
#> SRR1047821 4 0.4095 0.6299 0.108 0.000 0.012 0.792 0.016 NA
#> SRR1047822 4 0.3378 0.6221 0.056 0.000 0.024 0.848 0.008 NA
#> SRR1047823 1 0.1332 0.7323 0.952 0.000 0.000 0.008 0.028 NA
#> SRR1047824 1 0.1950 0.7272 0.924 0.000 0.000 0.032 0.028 NA
#> SRR1047825 1 0.1577 0.7314 0.940 0.000 0.000 0.008 0.036 NA
#> SRR1047826 1 0.1503 0.7321 0.944 0.000 0.000 0.008 0.032 NA
#> SRR1047827 1 0.1710 0.7325 0.936 0.000 0.000 0.020 0.028 NA
#> SRR1047828 5 0.3462 0.6013 0.120 0.000 0.012 0.020 0.828 NA
#> SRR1047829 5 0.4769 0.5440 0.084 0.000 0.016 0.076 0.760 NA
#> SRR1047830 5 0.3149 0.6001 0.100 0.000 0.012 0.020 0.852 NA
#> SRR1047831 5 0.3039 0.5973 0.100 0.000 0.012 0.024 0.856 NA
#> SRR1047832 5 0.3316 0.5901 0.100 0.000 0.012 0.020 0.844 NA
#> SRR1047833 2 0.0146 0.9938 0.000 0.996 0.000 0.000 0.004 NA
#> SRR1047834 2 0.0146 0.9969 0.000 0.996 0.000 0.004 0.000 NA
#> SRR1047835 2 0.0000 0.9942 0.000 1.000 0.000 0.000 0.000 NA
#> SRR1047836 2 0.0146 0.9969 0.000 0.996 0.000 0.004 0.000 NA
#> SRR1047837 2 0.0146 0.9969 0.000 0.996 0.000 0.004 0.000 NA
#> SRR1047838 4 0.5817 0.4747 0.280 0.004 0.004 0.568 0.012 NA
#> SRR1047839 4 0.3080 0.6163 0.036 0.000 0.036 0.860 0.000 NA
#> SRR1047840 4 0.6389 0.2170 0.372 0.004 0.004 0.440 0.020 NA
#> SRR1047841 4 0.5270 0.5895 0.208 0.004 0.016 0.664 0.004 NA
#> SRR1047842 4 0.5298 0.5956 0.200 0.004 0.020 0.668 0.004 NA
#> SRR1047843 1 0.5286 0.6114 0.680 0.000 0.004 0.184 0.044 NA
#> SRR1047844 4 0.4839 0.5514 0.048 0.000 0.060 0.724 0.004 NA
#> SRR1047845 1 0.5863 0.4494 0.592 0.000 0.008 0.264 0.036 NA
#> SRR1047846 1 0.5858 0.4176 0.572 0.000 0.004 0.284 0.032 NA
#> SRR1047847 4 0.4612 0.5639 0.040 0.000 0.048 0.744 0.008 NA
#> SRR1047848 5 0.4939 0.3935 0.380 0.000 0.004 0.000 0.556 NA
#> SRR1047849 5 0.4635 0.4778 0.336 0.000 0.000 0.000 0.608 NA
#> SRR1047850 5 0.4648 0.4756 0.340 0.000 0.000 0.000 0.604 NA
#> SRR1047851 5 0.4648 0.4756 0.340 0.000 0.000 0.000 0.604 NA
#> SRR1047852 5 0.4621 0.4793 0.332 0.000 0.000 0.000 0.612 NA
#> SRR1047853 4 0.5322 0.5886 0.032 0.000 0.040 0.696 0.052 NA
#> SRR1047854 4 0.7086 0.4493 0.144 0.004 0.016 0.484 0.076 NA
#> SRR1047855 4 0.7125 0.4411 0.148 0.004 0.016 0.476 0.076 NA
#> SRR1047856 4 0.5042 0.5952 0.036 0.000 0.032 0.720 0.044 NA
#> SRR1047857 4 0.4595 0.6070 0.028 0.000 0.036 0.760 0.036 NA
#> SRR1047858 1 0.4477 0.6357 0.740 0.000 0.000 0.016 0.124 NA
#> SRR1047859 1 0.4865 0.6843 0.732 0.000 0.000 0.068 0.100 NA
#> SRR1047860 1 0.4391 0.6408 0.748 0.000 0.000 0.016 0.128 NA
#> SRR1047861 1 0.4507 0.6562 0.748 0.000 0.000 0.028 0.116 NA
#> SRR1047863 3 0.4881 0.5707 0.000 0.000 0.604 0.324 0.004 NA
#> SRR1047864 3 0.3907 0.6073 0.000 0.000 0.764 0.000 0.152 NA
#> SRR1047865 3 0.5661 0.6963 0.004 0.000 0.660 0.104 0.072 NA
#> SRR1047866 3 0.6059 0.3072 0.004 0.000 0.464 0.012 0.368 NA
#> SRR1047867 3 0.4038 0.5673 0.008 0.020 0.764 0.000 0.024 NA
#> SRR1047868 3 0.4844 0.5600 0.000 0.000 0.608 0.312 0.000 NA
#> SRR1047869 3 0.5396 0.6918 0.004 0.000 0.664 0.152 0.028 NA
#> SRR1047870 3 0.3815 0.7108 0.000 0.004 0.800 0.132 0.020 NA
#> SRR1047871 3 0.2686 0.7165 0.000 0.000 0.868 0.100 0.008 NA
#> SRR1047872 3 0.5047 0.6729 0.004 0.000 0.672 0.208 0.012 NA
#> SRR1047873 4 0.5807 0.0218 0.004 0.000 0.284 0.516 0.000 NA
#> SRR1047874 4 0.5843 0.0330 0.008 0.000 0.308 0.512 0.000 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
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
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#> [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