Date: 2021-07-26 10:23:01 CEST, cola version: 1.9.4
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First the variable is renamed to res_rh.
res_rh = rh
The partition hierarchy and all available functions which can be applied to res_rh object.
res_rh
#> A 'HierarchicalPartition' object with 'ATC:skmeans' method.
#> On a matrix with 9856 rows and 367 columns.
#> Performed in total 1650 partitions.
#> There are 7 groups under the following parameters:
#> - min_samples: 6
#> - mean_silhouette_cutoff: 0.9
#> - min_n_signatures: 203 (signatures are selected based on:)
#> - fdr_cutoff: 0.05
#> - group_diff (scaled values): 0.5
#>
#> Hierarchy of the partition:
#> 0, 367 cols
#> |-- 01, 129 cols, 1046 signatures
#> | |-- 011, 44 cols, 33 signatures (c)
#> | |-- 012, 45 cols, 8 signatures (c)
#> | `-- 013, 40 cols, 44 signatures (c)
#> |-- 02, 112 cols, 597 signatures
#> | |-- 021, 64 cols, 26 signatures (c)
#> | `-- 022, 48 cols, 177 signatures (c)
#> `-- 03, 126 cols, 329 signatures
#> |-- 031, 64 cols, 5 signatures (c)
#> `-- 032, 62 cols, 5 signatures (c)
#> Stop reason:
#> c) There were too few signatures.
#>
#> Following methods can be applied to this 'HierarchicalPartition' object:
#> [1] "all_leaves" "all_nodes" "cola_report" "collect_classes"
#> [5] "colnames" "compare_signatures" "dimension_reduction" "functional_enrichment"
#> [9] "get_anno_col" "get_anno" "get_children_nodes" "get_classes"
#> [13] "get_matrix" "get_signatures" "is_leaf_node" "max_depth"
#> [17] "merge_node" "ncol" "node_info" "node_level"
#> [21] "nrow" "rownames" "show" "split_node"
#> [25] "suggest_best_k" "test_to_known_factors" "top_rows_heatmap" "top_rows_overlap"
#>
#> You can get result for a single node by e.g. object["01"]
The call of hierarchical_partition() was:
#> hierarchical_partition(data = lt$mat, anno = lt$anno, subset = 500, cores = 4)
Dimension of the input matrix:
mat = get_matrix(res_rh)
dim(mat)
#> [1] 9856 367
All the methods that were tried:
res_rh@param$combination_method
#> [[1]]
#> [1] "ATC" "skmeans"
The density distribution for each sample is visualized as one column in the following heatmap. The clustering is based on the distance which is the Kolmogorov-Smirnov statistic between two distributions.
library(ComplexHeatmap)
densityHeatmap(mat, top_annotation = HeatmapAnnotation(df = get_anno(res_rh),
col = get_anno_col(res_rh)), ylab = "value", cluster_columns = TRUE, show_column_names = FALSE,
mc.cores = 1)
Some values about the hierarchy:
all_nodes(res_rh)
#> [1] "0" "01" "011" "012" "013" "02" "021" "022" "03" "031" "032"
all_leaves(res_rh)
#> [1] "011" "012" "013" "021" "022" "031" "032"
node_info(res_rh)
#> id best_method depth best_k n_columns n_signatures p_signatures is_leaf
#> 1 0 ATC:skmeans 1 3 367 4074 0.413352 FALSE
#> 2 01 ATC:skmeans 2 3 129 1046 0.106128 FALSE
#> 3 011 ATC:skmeans 3 2 44 33 0.003348 TRUE
#> 4 012 ATC:skmeans 3 2 45 8 0.000812 TRUE
#> 5 013 ATC:skmeans 3 2 40 44 0.004464 TRUE
#> 6 02 ATC:skmeans 2 2 112 597 0.060572 FALSE
#> 7 021 ATC:skmeans 3 2 64 26 0.002638 TRUE
#> 8 022 ATC:skmeans 3 3 48 177 0.017959 TRUE
#> 9 03 ATC:skmeans 2 2 126 329 0.033381 FALSE
#> 10 031 ATC:skmeans 3 2 64 5 0.000507 TRUE
#> 11 032 ATC:skmeans 3 2 62 5 0.000507 TRUE
In the output from node_info(), there are the following columns:
id: The node id.best_method: The best method selected.depth: Depth of the node in the hierarchy.best_k: Best number of groups of the partition on that node.n_columns: Number of columns in the submatrix.n_signatures: Number of signatures with the best_k.p_signatures: Proportion of hte signatures in total number of rows in the matrix.is_leaf: Whether the node is a leaf.Labels of nodes are encoded in a special way. The number of digits correspond to the depth of the node in the hierarchy and the value of the digits correspond to the index of the subgroup in the current node, E.g. a label of “012” means the node is the second subgroup of the partition which is the first subgroup of the root node.
Following table shows the best k (number of partitions) for each node in the
partition hierarchy. Clicking on the node name in the table goes to the
corresponding section for the partitioning on that node.
The cola vignette explains the definition of the metrics used for determining the best number of partitions.
suggest_best_k(res_rh)
| Node | Best method | Is leaf | Best k | 1-PAC | Mean silhouette | Concordance | #samples | |
|---|---|---|---|---|---|---|---|---|
| Node0 | ATC:skmeans | 4 | 0.98 | 0.95 | 0.96 | 367 | ** | |
| Node01 | ATC:skmeans | 3 | 1.00 | 0.98 | 0.99 | 129 | ** | |
| Node011-leaf | ATC:skmeans | ✓ (c) | 2 | 0.95 | 0.96 | 0.98 | 44 | ** |
| Node012-leaf | ATC:skmeans | ✓ (c) | 2 | 0.91 | 0.92 | 0.97 | 45 | * |
| Node013-leaf | ATC:skmeans | ✓ (c) | 2 | 0.95 | 0.96 | 0.98 | 40 | * |
| Node02 | ATC:skmeans | 2 | 1.00 | 0.97 | 0.99 | 112 | ** | |
| Node021-leaf | ATC:skmeans | ✓ (c) | 2 | 1.00 | 0.97 | 0.99 | 64 | ** |
| Node022-leaf | ATC:skmeans | ✓ (c) | 3 | 1.00 | 0.99 | 0.99 | 48 | ** |
| Node03 | ATC:skmeans | 2 | 1.00 | 0.97 | 0.99 | 126 | ** | |
| Node031-leaf | ATC:skmeans | ✓ (c) | 2 | 1.00 | 0.94 | 0.98 | 64 | ** |
| Node032-leaf | ATC:skmeans | ✓ (c) | 2 | 0.93 | 0.94 | 0.98 | 62 | * |
Stop reason: c) There were too few signatures.
**: 1-PAC > 0.95, *: 1-PAC > 0.9
The nodes of the hierarchy can be merged by setting the merge_node parameters. Here we
control the hierarchy with the min_n_signatures parameter. The value of min_n_signatures is
from node_info().
collect_classes(res_rh, merge_node = merge_node_param(min_n_signatures = 329))
collect_classes(res_rh, merge_node = merge_node_param(min_n_signatures = 597))
collect_classes(res_rh, merge_node = merge_node_param(min_n_signatures = 1046))
collect_classes(res_rh, merge_node = merge_node_param(min_n_signatures = 4074))
Following shows the table of the partitions (You need to click the show/hide code output link to see it).
get_classes(res_rh, merge_node = merge_node_param(min_n_signatures = 329))
#> O10-A1 O10-A11 O10-A12 O10-A3 O10-A4 O10-A5 O10-A7 O10-A8 O10-A9 O10-B1 O10-B10 O10-B11
#> "022" "031" "022" "012" "021" "032" "032" "032" "013" "011" "032" "032"
#> O10-B12 O10-B2 O10-B5 O10-B6 O10-B7 O10-B9 O10-C10 O10-C11 O10-C12 O10-C2 O10-C4 O10-C5
#> "013" "032" "032" "031" "032" "032" "032" "013" "032" "013" "022" "032"
#> O10-C6 O10-C9 O10-D1 O10-D11 O10-D12 O10-D2 O10-D3 O10-D5 O10-D6 O10-D8 O10-D9 O10-E1
#> "032" "032" "032" "032" "032" "012" "021" "032" "032" "013" "032" "032"
#> O10-E11 O10-E12 O10-E6 O10-E8 O10-E9 O10-F1 O10-F11 O10-F12 O10-F2 O10-F4 O10-F5 O10-F6
#> "032" "032" "032" "012" "013" "031" "031" "032" "013" "012" "031" "021"
#> O10-F8 O10-F9 O10-G1 O10-G12 O10-G2 O10-G3 O10-G4 O10-G5 O10-G7 O10-H1 O10-H4 O10-H5
#> "012" "032" "011" "011" "011" "011" "011" "011" "011" "011" "011" "011"
#> O10-H6 O10-H7 O12-A1 O12-A12 O12-A2 O12-A3 O12-B1 O12-B12 O12-C1 O12-D1 O12-D2 O12-E1
#> "011" "011" "021" "021" "012" "021" "022" "031" "022" "022" "011" "011"
#> O12-E12 O12-F12 O12-F2 O12-G2 O12-H1 O12-H2 O7-A3 O7-A5 O7-A7 O7-A8 O7-A9 O7-B1
#> "021" "031" "021" "022" "021" "022" "032" "022" "022" "021" "031" "021"
#> O7-B11 O7-B12 O7-B6 O7-B7 O7-B8 O7-B9 O7-C1 O7-C11 O7-C2 O7-C3 O7-C6 O7-C7
#> "032" "022" "032" "032" "022" "021" "031" "032" "022" "022" "021" "032"
#> O7-D1 O7-D11 O7-D12 O7-D2 O7-D3 O7-D4 O7-D5 O7-E10 O7-E11 O7-E5 O7-E6 O7-F1
#> "021" "021" "021" "021" "012" "031" "013" "032" "032" "021" "022" "021"
#> O7-F10 O7-F11 O7-F2 O7-F3 O7-F4 O7-F7 O7-F9 O7-G12 O7-G3 O7-G9 O7-H3 O7-H4
#> "022" "021" "031" "031" "021" "032" "032" "022" "011" "022" "021" "022"
#> O7-H8 O8-A2 O8-A3 O8-A5 O8-A8 O8-A9 O8-B1 O8-B2 O8-B4 O8-B6 O8-B7 O8-B9
#> "022" "031" "032" "022" "032" "021" "022" "031" "032" "032" "032" "032"
#> O8-C11 O8-C12 O8-C2 O8-C3 O8-C4 O8-C5 O8-C6 O8-C8 O8-D3 O8-D5 O8-D6 O8-D9
#> "031" "032" "021" "031" "031" "032" "032" "032" "031" "031" "031" "031"
#> O8-E1 O8-E11 O8-E2 O8-E3 O8-E5 O8-E7 O8-E9 O8-F10 O8-F11 O8-F12 O8-F2 O8-F3
#> "012" "032" "031" "021" "031" "022" "032" "011" "032" "032" "022" "032"
#> O8-F6 O8-F8 O8-F9 O8-G1 O8-G12 O8-G5 O8-G9 O8-H1 O8-H11 O8-H2 O8-H6 O9-A10
#> "022" "021" "011" "031" "032" "032" "011" "011" "022" "021" "012" "031"
#> O9-A12 O9-A2 O9-A3 O9-A5 O9-A6 O9-A8 O9-A9 O9-B10 O9-B11 O9-B12 O9-B2 O9-B3
#> "022" "013" "022" "021" "021" "031" "013" "013" "013" "031" "031" "013"
#> O9-B5 O9-B6 O9-B7 O9-B8 O9-C10 O9-C2 O9-C3 O9-C4 O9-C5 O9-C6 O9-C9 O9-D1
#> "021" "031" "031" "021" "013" "031" "013" "031" "013" "031" "013" "013"
#> O9-D10 O9-D11 O9-D12 O9-D2 O9-D5 O9-D6 O9-D7 O9-D8 O9-E1 O9-E10 O9-E11 O9-E12
#> "011" "013" "031" "021" "012" "031" "022" "022" "022" "013" "011" "031"
#> O9-E2 O9-E4 O9-E5 O9-E7 O9-E8 O9-E9 O9-F1 O9-F10 O9-F12 O9-F2 O9-F4 O9-F5
#> "021" "031" "013" "013" "011" "013" "021" "013" "013" "013" "021" "021"
#> O9-F9 O9-G10 O9-G12 O9-G2 O9-G3 O9-G4 O9-G6 O9-G7 O9-G9 O9-H12 O9-H3 O9-H5
#> "031" "011" "013" "013" "031" "011" "013" "031" "021" "022" "013" "022"
#> O9-H9 S37-A1 S37-A10 S37-A2 S37-A3 S37-A4 S37-A5 S37-A6 S37-A7 S37-A8 S37-A9 S37-B1
#> "011" "012" "012" "022" "012" "031" "021" "021" "031" "022" "011" "013"
#> S37-B10 S37-B11 S37-B12 S37-B2 S37-B3 S37-B4 S37-B5 S37-B6 S37-B7 S37-B9 S37-C10 S37-C12
#> "012" "021" "022" "012" "031" "013" "031" "031" "012" "031" "012" "022"
#> S37-C3 S37-C4 S37-C6 S37-C7 S37-C8 S37-C9 S37-D10 S37-D11 S37-D12 S37-D2 S37-D4 S37-D6
#> "012" "011" "012" "012" "021" "011" "012" "031" "021" "012" "012" "012"
#> S37-D8 S37-D9 S37-E1 S37-E10 S37-E11 S37-E2 S37-E3 S37-E5 S37-E6 S37-E7 S37-E8 S37-E9
#> "012" "031" "012" "031" "012" "012" "012" "031" "013" "021" "021" "012"
#> S37-F1 S37-F10 S37-F12 S37-F2 S37-F3 S37-F5 S37-F7 S37-F9 S37-G1 S37-G10 S37-G12 S37-G2
#> "011" "011" "013" "012" "013" "011" "012" "012" "012" "012" "012" "022"
#> S37-G3 S37-G4 S37-G5 S37-G6 S37-G7 S37-G8 S37-H2 S37-H4 S37-H7 S37-H8 S37-H9 S38-A1
#> "012" "022" "031" "012" "012" "031" "011" "031" "012" "011" "011" "011"
#> S38-A10 S38-A12 S38-A2 S38-A3 S38-A5 S38-A9 S38-B10 S38-B11 S38-B2 S38-B6 S38-B7 S38-B8
#> "011" "022" "021" "031" "021" "021" "032" "013" "021" "011" "021" "021"
#> S38-B9 S38-C1 S38-C10 S38-C11 S38-C3 S38-C4 S38-C5 S38-C6 S38-C7 S38-C9 S38-D1 S38-D10
#> "022" "032" "032" "032" "021" "012" "032" "031" "031" "022" "021" "032"
#> S38-D11 S38-D12 S38-D2 S38-D4 S38-D5 S38-D6 S38-D7 S38-D8 S38-D9 S38-E1 S38-E2 S38-E3
#> "032" "011" "013" "031" "021" "021" "031" "011" "012" "021" "031" "031"
#> S38-E4 S38-E5 S38-E6 S38-E7 S38-E8 S38-E9 S38-F10 S38-F11 S38-F2 S38-F3 S38-F5 S38-F6
#> "021" "022" "022" "021" "031" "022" "013" "012" "021" "011" "022" "021"
#> S38-F7 S38-F8 S38-F9 S38-G10 S38-G12 S38-G4 S38-G5 S38-G6 S38-G7 S38-G8 S38-G9 S38-H1
#> "031" "021" "013" "011" "011" "021" "021" "022" "032" "031" "032" "011"
#> S38-H11 S38-H2 S38-H3 S38-H4 S38-H5 S38-H6 S38-H8
#> "013" "021" "031" "012" "022" "021" "012"
get_classes(res_rh, merge_node = merge_node_param(min_n_signatures = 597))
#> O10-A1 O10-A11 O10-A12 O10-A3 O10-A4 O10-A5 O10-A7 O10-A8 O10-A9 O10-B1 O10-B10 O10-B11
#> "022" "03" "022" "012" "021" "03" "03" "03" "013" "011" "03" "03"
#> O10-B12 O10-B2 O10-B5 O10-B6 O10-B7 O10-B9 O10-C10 O10-C11 O10-C12 O10-C2 O10-C4 O10-C5
#> "013" "03" "03" "03" "03" "03" "03" "013" "03" "013" "022" "03"
#> O10-C6 O10-C9 O10-D1 O10-D11 O10-D12 O10-D2 O10-D3 O10-D5 O10-D6 O10-D8 O10-D9 O10-E1
#> "03" "03" "03" "03" "03" "012" "021" "03" "03" "013" "03" "03"
#> O10-E11 O10-E12 O10-E6 O10-E8 O10-E9 O10-F1 O10-F11 O10-F12 O10-F2 O10-F4 O10-F5 O10-F6
#> "03" "03" "03" "012" "013" "03" "03" "03" "013" "012" "03" "021"
#> O10-F8 O10-F9 O10-G1 O10-G12 O10-G2 O10-G3 O10-G4 O10-G5 O10-G7 O10-H1 O10-H4 O10-H5
#> "012" "03" "011" "011" "011" "011" "011" "011" "011" "011" "011" "011"
#> O10-H6 O10-H7 O12-A1 O12-A12 O12-A2 O12-A3 O12-B1 O12-B12 O12-C1 O12-D1 O12-D2 O12-E1
#> "011" "011" "021" "021" "012" "021" "022" "03" "022" "022" "011" "011"
#> O12-E12 O12-F12 O12-F2 O12-G2 O12-H1 O12-H2 O7-A3 O7-A5 O7-A7 O7-A8 O7-A9 O7-B1
#> "021" "03" "021" "022" "021" "022" "03" "022" "022" "021" "03" "021"
#> O7-B11 O7-B12 O7-B6 O7-B7 O7-B8 O7-B9 O7-C1 O7-C11 O7-C2 O7-C3 O7-C6 O7-C7
#> "03" "022" "03" "03" "022" "021" "03" "03" "022" "022" "021" "03"
#> O7-D1 O7-D11 O7-D12 O7-D2 O7-D3 O7-D4 O7-D5 O7-E10 O7-E11 O7-E5 O7-E6 O7-F1
#> "021" "021" "021" "021" "012" "03" "013" "03" "03" "021" "022" "021"
#> O7-F10 O7-F11 O7-F2 O7-F3 O7-F4 O7-F7 O7-F9 O7-G12 O7-G3 O7-G9 O7-H3 O7-H4
#> "022" "021" "03" "03" "021" "03" "03" "022" "011" "022" "021" "022"
#> O7-H8 O8-A2 O8-A3 O8-A5 O8-A8 O8-A9 O8-B1 O8-B2 O8-B4 O8-B6 O8-B7 O8-B9
#> "022" "03" "03" "022" "03" "021" "022" "03" "03" "03" "03" "03"
#> O8-C11 O8-C12 O8-C2 O8-C3 O8-C4 O8-C5 O8-C6 O8-C8 O8-D3 O8-D5 O8-D6 O8-D9
#> "03" "03" "021" "03" "03" "03" "03" "03" "03" "03" "03" "03"
#> O8-E1 O8-E11 O8-E2 O8-E3 O8-E5 O8-E7 O8-E9 O8-F10 O8-F11 O8-F12 O8-F2 O8-F3
#> "012" "03" "03" "021" "03" "022" "03" "011" "03" "03" "022" "03"
#> O8-F6 O8-F8 O8-F9 O8-G1 O8-G12 O8-G5 O8-G9 O8-H1 O8-H11 O8-H2 O8-H6 O9-A10
#> "022" "021" "011" "03" "03" "03" "011" "011" "022" "021" "012" "03"
#> O9-A12 O9-A2 O9-A3 O9-A5 O9-A6 O9-A8 O9-A9 O9-B10 O9-B11 O9-B12 O9-B2 O9-B3
#> "022" "013" "022" "021" "021" "03" "013" "013" "013" "03" "03" "013"
#> O9-B5 O9-B6 O9-B7 O9-B8 O9-C10 O9-C2 O9-C3 O9-C4 O9-C5 O9-C6 O9-C9 O9-D1
#> "021" "03" "03" "021" "013" "03" "013" "03" "013" "03" "013" "013"
#> O9-D10 O9-D11 O9-D12 O9-D2 O9-D5 O9-D6 O9-D7 O9-D8 O9-E1 O9-E10 O9-E11 O9-E12
#> "011" "013" "03" "021" "012" "03" "022" "022" "022" "013" "011" "03"
#> O9-E2 O9-E4 O9-E5 O9-E7 O9-E8 O9-E9 O9-F1 O9-F10 O9-F12 O9-F2 O9-F4 O9-F5
#> "021" "03" "013" "013" "011" "013" "021" "013" "013" "013" "021" "021"
#> O9-F9 O9-G10 O9-G12 O9-G2 O9-G3 O9-G4 O9-G6 O9-G7 O9-G9 O9-H12 O9-H3 O9-H5
#> "03" "011" "013" "013" "03" "011" "013" "03" "021" "022" "013" "022"
#> O9-H9 S37-A1 S37-A10 S37-A2 S37-A3 S37-A4 S37-A5 S37-A6 S37-A7 S37-A8 S37-A9 S37-B1
#> "011" "012" "012" "022" "012" "03" "021" "021" "03" "022" "011" "013"
#> S37-B10 S37-B11 S37-B12 S37-B2 S37-B3 S37-B4 S37-B5 S37-B6 S37-B7 S37-B9 S37-C10 S37-C12
#> "012" "021" "022" "012" "03" "013" "03" "03" "012" "03" "012" "022"
#> S37-C3 S37-C4 S37-C6 S37-C7 S37-C8 S37-C9 S37-D10 S37-D11 S37-D12 S37-D2 S37-D4 S37-D6
#> "012" "011" "012" "012" "021" "011" "012" "03" "021" "012" "012" "012"
#> S37-D8 S37-D9 S37-E1 S37-E10 S37-E11 S37-E2 S37-E3 S37-E5 S37-E6 S37-E7 S37-E8 S37-E9
#> "012" "03" "012" "03" "012" "012" "012" "03" "013" "021" "021" "012"
#> S37-F1 S37-F10 S37-F12 S37-F2 S37-F3 S37-F5 S37-F7 S37-F9 S37-G1 S37-G10 S37-G12 S37-G2
#> "011" "011" "013" "012" "013" "011" "012" "012" "012" "012" "012" "022"
#> S37-G3 S37-G4 S37-G5 S37-G6 S37-G7 S37-G8 S37-H2 S37-H4 S37-H7 S37-H8 S37-H9 S38-A1
#> "012" "022" "03" "012" "012" "03" "011" "03" "012" "011" "011" "011"
#> S38-A10 S38-A12 S38-A2 S38-A3 S38-A5 S38-A9 S38-B10 S38-B11 S38-B2 S38-B6 S38-B7 S38-B8
#> "011" "022" "021" "03" "021" "021" "03" "013" "021" "011" "021" "021"
#> S38-B9 S38-C1 S38-C10 S38-C11 S38-C3 S38-C4 S38-C5 S38-C6 S38-C7 S38-C9 S38-D1 S38-D10
#> "022" "03" "03" "03" "021" "012" "03" "03" "03" "022" "021" "03"
#> S38-D11 S38-D12 S38-D2 S38-D4 S38-D5 S38-D6 S38-D7 S38-D8 S38-D9 S38-E1 S38-E2 S38-E3
#> "03" "011" "013" "03" "021" "021" "03" "011" "012" "021" "03" "03"
#> S38-E4 S38-E5 S38-E6 S38-E7 S38-E8 S38-E9 S38-F10 S38-F11 S38-F2 S38-F3 S38-F5 S38-F6
#> "021" "022" "022" "021" "03" "022" "013" "012" "021" "011" "022" "021"
#> S38-F7 S38-F8 S38-F9 S38-G10 S38-G12 S38-G4 S38-G5 S38-G6 S38-G7 S38-G8 S38-G9 S38-H1
#> "03" "021" "013" "011" "011" "021" "021" "022" "03" "03" "03" "011"
#> S38-H11 S38-H2 S38-H3 S38-H4 S38-H5 S38-H6 S38-H8
#> "013" "021" "03" "012" "022" "021" "012"
get_classes(res_rh, merge_node = merge_node_param(min_n_signatures = 1046))
#> O10-A1 O10-A11 O10-A12 O10-A3 O10-A4 O10-A5 O10-A7 O10-A8 O10-A9 O10-B1 O10-B10 O10-B11
#> "02" "03" "02" "012" "02" "03" "03" "03" "013" "011" "03" "03"
#> O10-B12 O10-B2 O10-B5 O10-B6 O10-B7 O10-B9 O10-C10 O10-C11 O10-C12 O10-C2 O10-C4 O10-C5
#> "013" "03" "03" "03" "03" "03" "03" "013" "03" "013" "02" "03"
#> O10-C6 O10-C9 O10-D1 O10-D11 O10-D12 O10-D2 O10-D3 O10-D5 O10-D6 O10-D8 O10-D9 O10-E1
#> "03" "03" "03" "03" "03" "012" "02" "03" "03" "013" "03" "03"
#> O10-E11 O10-E12 O10-E6 O10-E8 O10-E9 O10-F1 O10-F11 O10-F12 O10-F2 O10-F4 O10-F5 O10-F6
#> "03" "03" "03" "012" "013" "03" "03" "03" "013" "012" "03" "02"
#> O10-F8 O10-F9 O10-G1 O10-G12 O10-G2 O10-G3 O10-G4 O10-G5 O10-G7 O10-H1 O10-H4 O10-H5
#> "012" "03" "011" "011" "011" "011" "011" "011" "011" "011" "011" "011"
#> O10-H6 O10-H7 O12-A1 O12-A12 O12-A2 O12-A3 O12-B1 O12-B12 O12-C1 O12-D1 O12-D2 O12-E1
#> "011" "011" "02" "02" "012" "02" "02" "03" "02" "02" "011" "011"
#> O12-E12 O12-F12 O12-F2 O12-G2 O12-H1 O12-H2 O7-A3 O7-A5 O7-A7 O7-A8 O7-A9 O7-B1
#> "02" "03" "02" "02" "02" "02" "03" "02" "02" "02" "03" "02"
#> O7-B11 O7-B12 O7-B6 O7-B7 O7-B8 O7-B9 O7-C1 O7-C11 O7-C2 O7-C3 O7-C6 O7-C7
#> "03" "02" "03" "03" "02" "02" "03" "03" "02" "02" "02" "03"
#> O7-D1 O7-D11 O7-D12 O7-D2 O7-D3 O7-D4 O7-D5 O7-E10 O7-E11 O7-E5 O7-E6 O7-F1
#> "02" "02" "02" "02" "012" "03" "013" "03" "03" "02" "02" "02"
#> O7-F10 O7-F11 O7-F2 O7-F3 O7-F4 O7-F7 O7-F9 O7-G12 O7-G3 O7-G9 O7-H3 O7-H4
#> "02" "02" "03" "03" "02" "03" "03" "02" "011" "02" "02" "02"
#> O7-H8 O8-A2 O8-A3 O8-A5 O8-A8 O8-A9 O8-B1 O8-B2 O8-B4 O8-B6 O8-B7 O8-B9
#> "02" "03" "03" "02" "03" "02" "02" "03" "03" "03" "03" "03"
#> O8-C11 O8-C12 O8-C2 O8-C3 O8-C4 O8-C5 O8-C6 O8-C8 O8-D3 O8-D5 O8-D6 O8-D9
#> "03" "03" "02" "03" "03" "03" "03" "03" "03" "03" "03" "03"
#> O8-E1 O8-E11 O8-E2 O8-E3 O8-E5 O8-E7 O8-E9 O8-F10 O8-F11 O8-F12 O8-F2 O8-F3
#> "012" "03" "03" "02" "03" "02" "03" "011" "03" "03" "02" "03"
#> O8-F6 O8-F8 O8-F9 O8-G1 O8-G12 O8-G5 O8-G9 O8-H1 O8-H11 O8-H2 O8-H6 O9-A10
#> "02" "02" "011" "03" "03" "03" "011" "011" "02" "02" "012" "03"
#> O9-A12 O9-A2 O9-A3 O9-A5 O9-A6 O9-A8 O9-A9 O9-B10 O9-B11 O9-B12 O9-B2 O9-B3
#> "02" "013" "02" "02" "02" "03" "013" "013" "013" "03" "03" "013"
#> O9-B5 O9-B6 O9-B7 O9-B8 O9-C10 O9-C2 O9-C3 O9-C4 O9-C5 O9-C6 O9-C9 O9-D1
#> "02" "03" "03" "02" "013" "03" "013" "03" "013" "03" "013" "013"
#> O9-D10 O9-D11 O9-D12 O9-D2 O9-D5 O9-D6 O9-D7 O9-D8 O9-E1 O9-E10 O9-E11 O9-E12
#> "011" "013" "03" "02" "012" "03" "02" "02" "02" "013" "011" "03"
#> O9-E2 O9-E4 O9-E5 O9-E7 O9-E8 O9-E9 O9-F1 O9-F10 O9-F12 O9-F2 O9-F4 O9-F5
#> "02" "03" "013" "013" "011" "013" "02" "013" "013" "013" "02" "02"
#> O9-F9 O9-G10 O9-G12 O9-G2 O9-G3 O9-G4 O9-G6 O9-G7 O9-G9 O9-H12 O9-H3 O9-H5
#> "03" "011" "013" "013" "03" "011" "013" "03" "02" "02" "013" "02"
#> O9-H9 S37-A1 S37-A10 S37-A2 S37-A3 S37-A4 S37-A5 S37-A6 S37-A7 S37-A8 S37-A9 S37-B1
#> "011" "012" "012" "02" "012" "03" "02" "02" "03" "02" "011" "013"
#> S37-B10 S37-B11 S37-B12 S37-B2 S37-B3 S37-B4 S37-B5 S37-B6 S37-B7 S37-B9 S37-C10 S37-C12
#> "012" "02" "02" "012" "03" "013" "03" "03" "012" "03" "012" "02"
#> S37-C3 S37-C4 S37-C6 S37-C7 S37-C8 S37-C9 S37-D10 S37-D11 S37-D12 S37-D2 S37-D4 S37-D6
#> "012" "011" "012" "012" "02" "011" "012" "03" "02" "012" "012" "012"
#> S37-D8 S37-D9 S37-E1 S37-E10 S37-E11 S37-E2 S37-E3 S37-E5 S37-E6 S37-E7 S37-E8 S37-E9
#> "012" "03" "012" "03" "012" "012" "012" "03" "013" "02" "02" "012"
#> S37-F1 S37-F10 S37-F12 S37-F2 S37-F3 S37-F5 S37-F7 S37-F9 S37-G1 S37-G10 S37-G12 S37-G2
#> "011" "011" "013" "012" "013" "011" "012" "012" "012" "012" "012" "02"
#> S37-G3 S37-G4 S37-G5 S37-G6 S37-G7 S37-G8 S37-H2 S37-H4 S37-H7 S37-H8 S37-H9 S38-A1
#> "012" "02" "03" "012" "012" "03" "011" "03" "012" "011" "011" "011"
#> S38-A10 S38-A12 S38-A2 S38-A3 S38-A5 S38-A9 S38-B10 S38-B11 S38-B2 S38-B6 S38-B7 S38-B8
#> "011" "02" "02" "03" "02" "02" "03" "013" "02" "011" "02" "02"
#> S38-B9 S38-C1 S38-C10 S38-C11 S38-C3 S38-C4 S38-C5 S38-C6 S38-C7 S38-C9 S38-D1 S38-D10
#> "02" "03" "03" "03" "02" "012" "03" "03" "03" "02" "02" "03"
#> S38-D11 S38-D12 S38-D2 S38-D4 S38-D5 S38-D6 S38-D7 S38-D8 S38-D9 S38-E1 S38-E2 S38-E3
#> "03" "011" "013" "03" "02" "02" "03" "011" "012" "02" "03" "03"
#> S38-E4 S38-E5 S38-E6 S38-E7 S38-E8 S38-E9 S38-F10 S38-F11 S38-F2 S38-F3 S38-F5 S38-F6
#> "02" "02" "02" "02" "03" "02" "013" "012" "02" "011" "02" "02"
#> S38-F7 S38-F8 S38-F9 S38-G10 S38-G12 S38-G4 S38-G5 S38-G6 S38-G7 S38-G8 S38-G9 S38-H1
#> "03" "02" "013" "011" "011" "02" "02" "02" "03" "03" "03" "011"
#> S38-H11 S38-H2 S38-H3 S38-H4 S38-H5 S38-H6 S38-H8
#> "013" "02" "03" "012" "02" "02" "012"
get_classes(res_rh, merge_node = merge_node_param(min_n_signatures = 4074))
#> O10-A1 O10-A11 O10-A12 O10-A3 O10-A4 O10-A5 O10-A7 O10-A8 O10-A9 O10-B1 O10-B10 O10-B11
#> "02" "03" "02" "01" "02" "03" "03" "03" "01" "01" "03" "03"
#> O10-B12 O10-B2 O10-B5 O10-B6 O10-B7 O10-B9 O10-C10 O10-C11 O10-C12 O10-C2 O10-C4 O10-C5
#> "01" "03" "03" "03" "03" "03" "03" "01" "03" "01" "02" "03"
#> O10-C6 O10-C9 O10-D1 O10-D11 O10-D12 O10-D2 O10-D3 O10-D5 O10-D6 O10-D8 O10-D9 O10-E1
#> "03" "03" "03" "03" "03" "01" "02" "03" "03" "01" "03" "03"
#> O10-E11 O10-E12 O10-E6 O10-E8 O10-E9 O10-F1 O10-F11 O10-F12 O10-F2 O10-F4 O10-F5 O10-F6
#> "03" "03" "03" "01" "01" "03" "03" "03" "01" "01" "03" "02"
#> O10-F8 O10-F9 O10-G1 O10-G12 O10-G2 O10-G3 O10-G4 O10-G5 O10-G7 O10-H1 O10-H4 O10-H5
#> "01" "03" "01" "01" "01" "01" "01" "01" "01" "01" "01" "01"
#> O10-H6 O10-H7 O12-A1 O12-A12 O12-A2 O12-A3 O12-B1 O12-B12 O12-C1 O12-D1 O12-D2 O12-E1
#> "01" "01" "02" "02" "01" "02" "02" "03" "02" "02" "01" "01"
#> O12-E12 O12-F12 O12-F2 O12-G2 O12-H1 O12-H2 O7-A3 O7-A5 O7-A7 O7-A8 O7-A9 O7-B1
#> "02" "03" "02" "02" "02" "02" "03" "02" "02" "02" "03" "02"
#> O7-B11 O7-B12 O7-B6 O7-B7 O7-B8 O7-B9 O7-C1 O7-C11 O7-C2 O7-C3 O7-C6 O7-C7
#> "03" "02" "03" "03" "02" "02" "03" "03" "02" "02" "02" "03"
#> O7-D1 O7-D11 O7-D12 O7-D2 O7-D3 O7-D4 O7-D5 O7-E10 O7-E11 O7-E5 O7-E6 O7-F1
#> "02" "02" "02" "02" "01" "03" "01" "03" "03" "02" "02" "02"
#> O7-F10 O7-F11 O7-F2 O7-F3 O7-F4 O7-F7 O7-F9 O7-G12 O7-G3 O7-G9 O7-H3 O7-H4
#> "02" "02" "03" "03" "02" "03" "03" "02" "01" "02" "02" "02"
#> O7-H8 O8-A2 O8-A3 O8-A5 O8-A8 O8-A9 O8-B1 O8-B2 O8-B4 O8-B6 O8-B7 O8-B9
#> "02" "03" "03" "02" "03" "02" "02" "03" "03" "03" "03" "03"
#> O8-C11 O8-C12 O8-C2 O8-C3 O8-C4 O8-C5 O8-C6 O8-C8 O8-D3 O8-D5 O8-D6 O8-D9
#> "03" "03" "02" "03" "03" "03" "03" "03" "03" "03" "03" "03"
#> O8-E1 O8-E11 O8-E2 O8-E3 O8-E5 O8-E7 O8-E9 O8-F10 O8-F11 O8-F12 O8-F2 O8-F3
#> "01" "03" "03" "02" "03" "02" "03" "01" "03" "03" "02" "03"
#> O8-F6 O8-F8 O8-F9 O8-G1 O8-G12 O8-G5 O8-G9 O8-H1 O8-H11 O8-H2 O8-H6 O9-A10
#> "02" "02" "01" "03" "03" "03" "01" "01" "02" "02" "01" "03"
#> O9-A12 O9-A2 O9-A3 O9-A5 O9-A6 O9-A8 O9-A9 O9-B10 O9-B11 O9-B12 O9-B2 O9-B3
#> "02" "01" "02" "02" "02" "03" "01" "01" "01" "03" "03" "01"
#> O9-B5 O9-B6 O9-B7 O9-B8 O9-C10 O9-C2 O9-C3 O9-C4 O9-C5 O9-C6 O9-C9 O9-D1
#> "02" "03" "03" "02" "01" "03" "01" "03" "01" "03" "01" "01"
#> O9-D10 O9-D11 O9-D12 O9-D2 O9-D5 O9-D6 O9-D7 O9-D8 O9-E1 O9-E10 O9-E11 O9-E12
#> "01" "01" "03" "02" "01" "03" "02" "02" "02" "01" "01" "03"
#> O9-E2 O9-E4 O9-E5 O9-E7 O9-E8 O9-E9 O9-F1 O9-F10 O9-F12 O9-F2 O9-F4 O9-F5
#> "02" "03" "01" "01" "01" "01" "02" "01" "01" "01" "02" "02"
#> O9-F9 O9-G10 O9-G12 O9-G2 O9-G3 O9-G4 O9-G6 O9-G7 O9-G9 O9-H12 O9-H3 O9-H5
#> "03" "01" "01" "01" "03" "01" "01" "03" "02" "02" "01" "02"
#> O9-H9 S37-A1 S37-A10 S37-A2 S37-A3 S37-A4 S37-A5 S37-A6 S37-A7 S37-A8 S37-A9 S37-B1
#> "01" "01" "01" "02" "01" "03" "02" "02" "03" "02" "01" "01"
#> S37-B10 S37-B11 S37-B12 S37-B2 S37-B3 S37-B4 S37-B5 S37-B6 S37-B7 S37-B9 S37-C10 S37-C12
#> "01" "02" "02" "01" "03" "01" "03" "03" "01" "03" "01" "02"
#> S37-C3 S37-C4 S37-C6 S37-C7 S37-C8 S37-C9 S37-D10 S37-D11 S37-D12 S37-D2 S37-D4 S37-D6
#> "01" "01" "01" "01" "02" "01" "01" "03" "02" "01" "01" "01"
#> S37-D8 S37-D9 S37-E1 S37-E10 S37-E11 S37-E2 S37-E3 S37-E5 S37-E6 S37-E7 S37-E8 S37-E9
#> "01" "03" "01" "03" "01" "01" "01" "03" "01" "02" "02" "01"
#> S37-F1 S37-F10 S37-F12 S37-F2 S37-F3 S37-F5 S37-F7 S37-F9 S37-G1 S37-G10 S37-G12 S37-G2
#> "01" "01" "01" "01" "01" "01" "01" "01" "01" "01" "01" "02"
#> S37-G3 S37-G4 S37-G5 S37-G6 S37-G7 S37-G8 S37-H2 S37-H4 S37-H7 S37-H8 S37-H9 S38-A1
#> "01" "02" "03" "01" "01" "03" "01" "03" "01" "01" "01" "01"
#> S38-A10 S38-A12 S38-A2 S38-A3 S38-A5 S38-A9 S38-B10 S38-B11 S38-B2 S38-B6 S38-B7 S38-B8
#> "01" "02" "02" "03" "02" "02" "03" "01" "02" "01" "02" "02"
#> S38-B9 S38-C1 S38-C10 S38-C11 S38-C3 S38-C4 S38-C5 S38-C6 S38-C7 S38-C9 S38-D1 S38-D10
#> "02" "03" "03" "03" "02" "01" "03" "03" "03" "02" "02" "03"
#> S38-D11 S38-D12 S38-D2 S38-D4 S38-D5 S38-D6 S38-D7 S38-D8 S38-D9 S38-E1 S38-E2 S38-E3
#> "03" "01" "01" "03" "02" "02" "03" "01" "01" "02" "03" "03"
#> S38-E4 S38-E5 S38-E6 S38-E7 S38-E8 S38-E9 S38-F10 S38-F11 S38-F2 S38-F3 S38-F5 S38-F6
#> "02" "02" "02" "02" "03" "02" "01" "01" "02" "01" "02" "02"
#> S38-F7 S38-F8 S38-F9 S38-G10 S38-G12 S38-G4 S38-G5 S38-G6 S38-G7 S38-G8 S38-G9 S38-H1
#> "03" "02" "01" "01" "01" "02" "02" "02" "03" "03" "03" "01"
#> S38-H11 S38-H2 S38-H3 S38-H4 S38-H5 S38-H6 S38-H8
#> "01" "02" "03" "01" "02" "02" "01"
Heatmaps of the top rows:
top_rows_heatmap(res_rh)
Top rows on each node:
top_rows_overlap(res_rh, method = "upset")
UMAP plot which shows how samples are separated.
par(mfrow = c(1, 2))
dimension_reduction(res_rh, merge_node = merge_node_param(min_n_signatures = 329),
method = "UMAP", top_value_method = "SD", top_n = 1000, scale_rows = FALSE)
dimension_reduction(res_rh, merge_node = merge_node_param(min_n_signatures = 329),
method = "UMAP", top_value_method = "ATC", top_n = 1000, scale_rows = TRUE)
par(mfrow = c(1, 2))
dimension_reduction(res_rh, merge_node = merge_node_param(min_n_signatures = 597),
method = "UMAP", top_value_method = "SD", top_n = 1000, scale_rows = FALSE)
dimension_reduction(res_rh, merge_node = merge_node_param(min_n_signatures = 597),
method = "UMAP", top_value_method = "ATC", top_n = 1000, scale_rows = TRUE)
par(mfrow = c(1, 2))
dimension_reduction(res_rh, merge_node = merge_node_param(min_n_signatures = 1046),
method = "UMAP", top_value_method = "SD", top_n = 1000, scale_rows = FALSE)
dimension_reduction(res_rh, merge_node = merge_node_param(min_n_signatures = 1046),
method = "UMAP", top_value_method = "ATC", top_n = 1000, scale_rows = TRUE)
par(mfrow = c(1, 2))
dimension_reduction(res_rh, merge_node = merge_node_param(min_n_signatures = 4074),
method = "UMAP", top_value_method = "SD", top_n = 1000, scale_rows = FALSE)
dimension_reduction(res_rh, merge_node = merge_node_param(min_n_signatures = 4074),
method = "UMAP", top_value_method = "ATC", top_n = 1000, scale_rows = TRUE)
Signatures on the heatmap are the union of all signatures found on every node on the hierarchy. The number of k-means on rows are automatically selected by the function.
get_signatures(res_rh, merge_node = merge_node_param(min_n_signatures = 329))
get_signatures(res_rh, merge_node = merge_node_param(min_n_signatures = 597))
get_signatures(res_rh, merge_node = merge_node_param(min_n_signatures = 1046))
get_signatures(res_rh, merge_node = merge_node_param(min_n_signatures = 4074))
Compare signatures from different nodes:
compare_signatures(res_rh, verbose = FALSE)
If there are too many signatures, top_signatures = ... can be set to only show the
signatures with the highest FDRs. Note it only works on every node and the final signatures
are the union of all signatures of all nodes.
# code only for demonstration
# e.g. to show the top 500 most significant rows on each node.
tb = get_signature(res_rh, top_signatures = 500)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res_rh, merge_node = merge_node_param(min_n_signatures = 329))
#> Age Inferred.Cell.Type
#> class 6.34e-09 1.03e-117
test_to_known_factors(res_rh, merge_node = merge_node_param(min_n_signatures = 597))
#> Age Inferred.Cell.Type
#> class 5.21e-08 2.42e-119
test_to_known_factors(res_rh, merge_node = merge_node_param(min_n_signatures = 1046))
#> Age Inferred.Cell.Type
#> class 2.87e-08 2.67e-119
test_to_known_factors(res_rh, merge_node = merge_node_param(min_n_signatures = 4074))
#> Age Inferred.Cell.Type
#> class 0.000943 1.49e-80
Child nodes: Node01 , Node02 , Node03 .
The object with results only for a single top-value method and a single partitioning method can be extracted as:
res = res_rh["0"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4.
#> On a matrix with 9277 rows and 367 columns.
#> Top rows (928) are extracted by 'ATC' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 150 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_partitions"
#> [7] "compare_signatures" "consensus_heatmap" "dimension_reduction"
#> [10] "functional_enrichment" "get_anno_col" "get_anno"
#> [13] "get_classes" "get_consensus" "get_matrix"
#> [16] "get_membership" "get_param" "get_signatures"
#> [19] "get_stats" "is_best_k" "is_stable_k"
#> [22] "membership_heatmap" "ncol" "nrow"
#> [25] "plot_ecdf" "predict_classes" "rownames"
#> [28] "select_partition_number" "show" "suggest_best_k"
#> [31] "test_to_known_factors" "top_rows_heatmap"
collect_plots() function collects all the plots made from res for all k (number of subgroups)
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, higher 1-PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.987 0.995 0.4332 0.566 0.566
#> 3 3 1.000 0.977 0.990 0.5409 0.751 0.567
#> 4 4 0.978 0.946 0.960 0.0779 0.943 0.829
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 is 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 subgroup
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
#> O10-A1 2 0.000 0.990 0.00 1.00
#> O10-A11 1 0.000 0.997 1.00 0.00
#> O10-A12 2 0.000 0.990 0.00 1.00
#> O10-A3 1 0.000 0.997 1.00 0.00
#> O10-A4 2 0.000 0.990 0.00 1.00
#> O10-A5 1 0.000 0.997 1.00 0.00
#> O10-A7 1 0.000 0.997 1.00 0.00
#> O10-A8 1 0.000 0.997 1.00 0.00
#> O10-A9 1 0.000 0.997 1.00 0.00
#> O10-B1 1 0.000 0.997 1.00 0.00
#> O10-B10 1 0.000 0.997 1.00 0.00
#> O10-B11 1 0.000 0.997 1.00 0.00
#> O10-B12 1 0.000 0.997 1.00 0.00
#> O10-B2 1 0.000 0.997 1.00 0.00
#> O10-B5 1 0.000 0.997 1.00 0.00
#> O10-B6 1 0.000 0.997 1.00 0.00
#> O10-B7 1 0.000 0.997 1.00 0.00
#> O10-B9 1 0.000 0.997 1.00 0.00
#> O10-C10 1 0.000 0.997 1.00 0.00
#> O10-C11 1 0.000 0.997 1.00 0.00
#> O10-C12 1 0.000 0.997 1.00 0.00
#> O10-C2 1 0.000 0.997 1.00 0.00
#> O10-C4 2 0.000 0.990 0.00 1.00
#> O10-C5 1 0.000 0.997 1.00 0.00
#> O10-C6 1 0.000 0.997 1.00 0.00
#> O10-C9 1 0.000 0.997 1.00 0.00
#> O10-D1 2 0.855 0.617 0.28 0.72
#> O10-D11 1 0.000 0.997 1.00 0.00
#> O10-D12 1 0.000 0.997 1.00 0.00
#> O10-D2 1 0.000 0.997 1.00 0.00
#> O10-D3 2 0.000 0.990 0.00 1.00
#> O10-D5 1 0.000 0.997 1.00 0.00
#> O10-D6 1 0.000 0.997 1.00 0.00
#> O10-D8 1 0.000 0.997 1.00 0.00
#> O10-D9 1 0.000 0.997 1.00 0.00
#> O10-E1 1 0.000 0.997 1.00 0.00
#> O10-E11 1 0.000 0.997 1.00 0.00
#> O10-E12 1 0.000 0.997 1.00 0.00
#> O10-E6 1 0.000 0.997 1.00 0.00
#> O10-E8 1 0.000 0.997 1.00 0.00
#> O10-E9 1 0.000 0.997 1.00 0.00
#> O10-F1 1 0.000 0.997 1.00 0.00
#> O10-F11 1 0.000 0.997 1.00 0.00
#> O10-F12 1 0.000 0.997 1.00 0.00
#> O10-F2 1 0.000 0.997 1.00 0.00
#> O10-F4 1 0.000 0.997 1.00 0.00
#> O10-F5 1 0.000 0.997 1.00 0.00
#> O10-F6 2 0.000 0.990 0.00 1.00
#> O10-F8 1 0.000 0.997 1.00 0.00
#> O10-F9 1 0.000 0.997 1.00 0.00
#> O10-G1 1 0.000 0.997 1.00 0.00
#> O10-G12 1 0.000 0.997 1.00 0.00
#> O10-G2 1 0.000 0.997 1.00 0.00
#> O10-G3 1 0.925 0.479 0.66 0.34
#> O10-G4 1 0.000 0.997 1.00 0.00
#> O10-G5 1 0.000 0.997 1.00 0.00
#> O10-G7 1 0.000 0.997 1.00 0.00
#> O10-H1 1 0.000 0.997 1.00 0.00
#> O10-H4 1 0.000 0.997 1.00 0.00
#> O10-H5 1 0.000 0.997 1.00 0.00
#> O10-H6 1 0.000 0.997 1.00 0.00
#> O10-H7 1 0.000 0.997 1.00 0.00
#> O12-A1 2 0.000 0.990 0.00 1.00
#> O12-A12 2 0.000 0.990 0.00 1.00
#> O12-A2 1 0.000 0.997 1.00 0.00
#> O12-A3 2 0.000 0.990 0.00 1.00
#> O12-B1 2 0.000 0.990 0.00 1.00
#> O12-B12 1 0.000 0.997 1.00 0.00
#> O12-C1 2 0.000 0.990 0.00 1.00
#> O12-D1 2 0.000 0.990 0.00 1.00
#> O12-D2 1 0.000 0.997 1.00 0.00
#> O12-E1 1 0.000 0.997 1.00 0.00
#> O12-E12 2 0.000 0.990 0.00 1.00
#> O12-F12 1 0.000 0.997 1.00 0.00
#> O12-F2 2 0.000 0.990 0.00 1.00
#> O12-G2 2 0.000 0.990 0.00 1.00
#> O12-H1 2 0.000 0.990 0.00 1.00
#> O12-H2 2 0.000 0.990 0.00 1.00
#> O7-A3 1 0.000 0.997 1.00 0.00
#> O7-A5 2 0.000 0.990 0.00 1.00
#> O7-A7 2 0.000 0.990 0.00 1.00
#> O7-A8 2 0.000 0.990 0.00 1.00
#> O7-A9 1 0.000 0.997 1.00 0.00
#> O7-B1 2 0.000 0.990 0.00 1.00
#> O7-B11 1 0.000 0.997 1.00 0.00
#> O7-B12 2 0.000 0.990 0.00 1.00
#> O7-B6 1 0.000 0.997 1.00 0.00
#> O7-B7 1 0.000 0.997 1.00 0.00
#> O7-B8 2 0.000 0.990 0.00 1.00
#> O7-B9 2 0.000 0.990 0.00 1.00
#> O7-C1 1 0.000 0.997 1.00 0.00
#> O7-C11 1 0.000 0.997 1.00 0.00
#> O7-C2 2 0.000 0.990 0.00 1.00
#> O7-C3 2 0.000 0.990 0.00 1.00
#> O7-C6 2 0.000 0.990 0.00 1.00
#> O7-C7 1 0.000 0.997 1.00 0.00
#> O7-D1 2 0.000 0.990 0.00 1.00
#> O7-D11 2 0.000 0.990 0.00 1.00
#> O7-D12 2 0.000 0.990 0.00 1.00
#> O7-D2 2 0.000 0.990 0.00 1.00
#> O7-D3 1 0.000 0.997 1.00 0.00
#> O7-D4 1 0.000 0.997 1.00 0.00
#> O7-D5 1 0.000 0.997 1.00 0.00
#> O7-E10 1 0.000 0.997 1.00 0.00
#> O7-E11 1 0.327 0.934 0.94 0.06
#> O7-E5 2 0.000 0.990 0.00 1.00
#> O7-E6 2 0.000 0.990 0.00 1.00
#> O7-F1 2 0.000 0.990 0.00 1.00
#> O7-F10 2 0.000 0.990 0.00 1.00
#> O7-F11 2 0.000 0.990 0.00 1.00
#> O7-F2 1 0.000 0.997 1.00 0.00
#> O7-F3 1 0.000 0.997 1.00 0.00
#> O7-F4 2 0.000 0.990 0.00 1.00
#> O7-F7 1 0.000 0.997 1.00 0.00
#> O7-F9 1 0.000 0.997 1.00 0.00
#> O7-G12 2 0.000 0.990 0.00 1.00
#> O7-G3 1 0.000 0.997 1.00 0.00
#> O7-G9 2 0.000 0.990 0.00 1.00
#> O7-H3 2 0.000 0.990 0.00 1.00
#> O7-H4 2 0.000 0.990 0.00 1.00
#> O7-H8 2 0.000 0.990 0.00 1.00
#> O8-A2 1 0.000 0.997 1.00 0.00
#> O8-A3 1 0.000 0.997 1.00 0.00
#> O8-A5 2 0.000 0.990 0.00 1.00
#> O8-A8 1 0.000 0.997 1.00 0.00
#> O8-A9 2 0.000 0.990 0.00 1.00
#> O8-B1 2 0.000 0.990 0.00 1.00
#> O8-B2 1 0.000 0.997 1.00 0.00
#> O8-B4 1 0.000 0.997 1.00 0.00
#> O8-B6 1 0.000 0.997 1.00 0.00
#> O8-B7 1 0.000 0.997 1.00 0.00
#> O8-B9 1 0.000 0.997 1.00 0.00
#> O8-C11 1 0.000 0.997 1.00 0.00
#> O8-C12 1 0.000 0.997 1.00 0.00
#> O8-C2 2 0.000 0.990 0.00 1.00
#> O8-C3 1 0.000 0.997 1.00 0.00
#> O8-C4 1 0.000 0.997 1.00 0.00
#> O8-C5 1 0.141 0.977 0.98 0.02
#> O8-C6 1 0.000 0.997 1.00 0.00
#> O8-C8 1 0.000 0.997 1.00 0.00
#> O8-D3 1 0.000 0.997 1.00 0.00
#> O8-D5 1 0.000 0.997 1.00 0.00
#> O8-D6 1 0.000 0.997 1.00 0.00
#> O8-D9 1 0.000 0.997 1.00 0.00
#> O8-E1 1 0.000 0.997 1.00 0.00
#> O8-E11 1 0.000 0.997 1.00 0.00
#> O8-E2 1 0.000 0.997 1.00 0.00
#> O8-E3 2 0.000 0.990 0.00 1.00
#> O8-E5 1 0.000 0.997 1.00 0.00
#> O8-E7 2 0.000 0.990 0.00 1.00
#> O8-E9 1 0.000 0.997 1.00 0.00
#> O8-F10 1 0.000 0.997 1.00 0.00
#> O8-F11 1 0.000 0.997 1.00 0.00
#> O8-F12 1 0.000 0.997 1.00 0.00
#> O8-F2 2 0.000 0.990 0.00 1.00
#> O8-F3 1 0.000 0.997 1.00 0.00
#> O8-F6 2 0.000 0.990 0.00 1.00
#> O8-F8 2 0.000 0.990 0.00 1.00
#> O8-F9 1 0.000 0.997 1.00 0.00
#> O8-G1 1 0.000 0.997 1.00 0.00
#> O8-G12 1 0.000 0.997 1.00 0.00
#> O8-G5 1 0.000 0.997 1.00 0.00
#> O8-G9 1 0.000 0.997 1.00 0.00
#> O8-H1 1 0.000 0.997 1.00 0.00
#> O8-H11 2 0.000 0.990 0.00 1.00
#> O8-H2 2 0.000 0.990 0.00 1.00
#> O8-H6 1 0.000 0.997 1.00 0.00
#> O9-A10 1 0.000 0.997 1.00 0.00
#> O9-A12 2 0.000 0.990 0.00 1.00
#> O9-A2 1 0.000 0.997 1.00 0.00
#> O9-A3 2 0.000 0.990 0.00 1.00
#> O9-A5 2 0.000 0.990 0.00 1.00
#> O9-A6 2 0.000 0.990 0.00 1.00
#> O9-A8 1 0.000 0.997 1.00 0.00
#> O9-A9 1 0.000 0.997 1.00 0.00
#> O9-B10 1 0.000 0.997 1.00 0.00
#> O9-B11 1 0.000 0.997 1.00 0.00
#> O9-B12 1 0.000 0.997 1.00 0.00
#> O9-B2 1 0.000 0.997 1.00 0.00
#> O9-B3 1 0.000 0.997 1.00 0.00
#> O9-B5 2 0.000 0.990 0.00 1.00
#> O9-B6 1 0.000 0.997 1.00 0.00
#> O9-B7 1 0.000 0.997 1.00 0.00
#> O9-B8 2 0.000 0.990 0.00 1.00
#> O9-C10 1 0.000 0.997 1.00 0.00
#> O9-C2 1 0.000 0.997 1.00 0.00
#> O9-C3 1 0.000 0.997 1.00 0.00
#> O9-C4 1 0.141 0.977 0.98 0.02
#> O9-C5 1 0.000 0.997 1.00 0.00
#> O9-C6 1 0.000 0.997 1.00 0.00
#> O9-C9 1 0.000 0.997 1.00 0.00
#> O9-D1 1 0.000 0.997 1.00 0.00
#> O9-D10 1 0.000 0.997 1.00 0.00
#> O9-D11 1 0.000 0.997 1.00 0.00
#> O9-D12 2 0.925 0.492 0.34 0.66
#> O9-D2 2 0.000 0.990 0.00 1.00
#> O9-D5 1 0.000 0.997 1.00 0.00
#> O9-D6 1 0.000 0.997 1.00 0.00
#> O9-D7 2 0.000 0.990 0.00 1.00
#> O9-D8 2 0.000 0.990 0.00 1.00
#> O9-E1 2 0.000 0.990 0.00 1.00
#> O9-E10 1 0.000 0.997 1.00 0.00
#> O9-E11 1 0.000 0.997 1.00 0.00
#> O9-E12 1 0.000 0.997 1.00 0.00
#> O9-E2 2 0.000 0.990 0.00 1.00
#> O9-E4 1 0.000 0.997 1.00 0.00
#> O9-E5 1 0.000 0.997 1.00 0.00
#> O9-E7 1 0.000 0.997 1.00 0.00
#> O9-E8 1 0.000 0.997 1.00 0.00
#> O9-E9 1 0.000 0.997 1.00 0.00
#> O9-F1 2 0.000 0.990 0.00 1.00
#> O9-F10 1 0.000 0.997 1.00 0.00
#> O9-F12 1 0.000 0.997 1.00 0.00
#> O9-F2 1 0.000 0.997 1.00 0.00
#> O9-F4 2 0.000 0.990 0.00 1.00
#> O9-F5 2 0.000 0.990 0.00 1.00
#> O9-F9 1 0.000 0.997 1.00 0.00
#> O9-G10 1 0.000 0.997 1.00 0.00
#> O9-G12 1 0.000 0.997 1.00 0.00
#> O9-G2 1 0.000 0.997 1.00 0.00
#> O9-G3 1 0.000 0.997 1.00 0.00
#> O9-G4 1 0.000 0.997 1.00 0.00
#> O9-G6 1 0.000 0.997 1.00 0.00
#> O9-G7 1 0.000 0.997 1.00 0.00
#> O9-G9 2 0.000 0.990 0.00 1.00
#> O9-H12 2 0.000 0.990 0.00 1.00
#> O9-H3 1 0.000 0.997 1.00 0.00
#> O9-H5 2 0.000 0.990 0.00 1.00
#> O9-H9 1 0.000 0.997 1.00 0.00
#> S37-A1 1 0.000 0.997 1.00 0.00
#> S37-A10 1 0.000 0.997 1.00 0.00
#> S37-A2 2 0.000 0.990 0.00 1.00
#> S37-A3 1 0.000 0.997 1.00 0.00
#> S37-A4 1 0.000 0.997 1.00 0.00
#> S37-A5 2 0.000 0.990 0.00 1.00
#> S37-A6 2 0.000 0.990 0.00 1.00
#> S37-A7 1 0.000 0.997 1.00 0.00
#> S37-A8 2 0.000 0.990 0.00 1.00
#> S37-A9 1 0.000 0.997 1.00 0.00
#> S37-B1 1 0.000 0.997 1.00 0.00
#> S37-B10 1 0.000 0.997 1.00 0.00
#> S37-B11 2 0.000 0.990 0.00 1.00
#> S37-B12 2 0.000 0.990 0.00 1.00
#> S37-B2 1 0.000 0.997 1.00 0.00
#> S37-B3 1 0.000 0.997 1.00 0.00
#> S37-B4 1 0.000 0.997 1.00 0.00
#> S37-B5 1 0.000 0.997 1.00 0.00
#> S37-B6 1 0.000 0.997 1.00 0.00
#> S37-B7 1 0.000 0.997 1.00 0.00
#> S37-B9 1 0.000 0.997 1.00 0.00
#> S37-C10 1 0.000 0.997 1.00 0.00
#> S37-C12 2 0.000 0.990 0.00 1.00
#> S37-C3 1 0.000 0.997 1.00 0.00
#> S37-C4 1 0.000 0.997 1.00 0.00
#> S37-C6 1 0.000 0.997 1.00 0.00
#> S37-C7 1 0.000 0.997 1.00 0.00
#> S37-C8 2 0.000 0.990 0.00 1.00
#> S37-C9 1 0.000 0.997 1.00 0.00
#> S37-D10 1 0.000 0.997 1.00 0.00
#> S37-D11 1 0.000 0.997 1.00 0.00
#> S37-D12 2 0.000 0.990 0.00 1.00
#> S37-D2 1 0.000 0.997 1.00 0.00
#> S37-D4 1 0.000 0.997 1.00 0.00
#> S37-D6 1 0.000 0.997 1.00 0.00
#> S37-D8 1 0.000 0.997 1.00 0.00
#> S37-D9 1 0.000 0.997 1.00 0.00
#> S37-E1 1 0.000 0.997 1.00 0.00
#> S37-E10 1 0.000 0.997 1.00 0.00
#> S37-E11 1 0.000 0.997 1.00 0.00
#> S37-E2 1 0.000 0.997 1.00 0.00
#> S37-E3 1 0.000 0.997 1.00 0.00
#> S37-E5 1 0.000 0.997 1.00 0.00
#> S37-E6 1 0.000 0.997 1.00 0.00
#> S37-E7 2 0.000 0.990 0.00 1.00
#> S37-E8 2 0.000 0.990 0.00 1.00
#> S37-E9 1 0.000 0.997 1.00 0.00
#> S37-F1 1 0.000 0.997 1.00 0.00
#> S37-F10 1 0.000 0.997 1.00 0.00
#> S37-F12 1 0.000 0.997 1.00 0.00
#> S37-F2 1 0.000 0.997 1.00 0.00
#> S37-F3 1 0.000 0.997 1.00 0.00
#> S37-F5 1 0.000 0.997 1.00 0.00
#> S37-F7 1 0.000 0.997 1.00 0.00
#> S37-F9 1 0.000 0.997 1.00 0.00
#> S37-G1 1 0.000 0.997 1.00 0.00
#> S37-G10 1 0.000 0.997 1.00 0.00
#> S37-G12 1 0.000 0.997 1.00 0.00
#> S37-G2 2 0.000 0.990 0.00 1.00
#> S37-G3 2 0.722 0.751 0.20 0.80
#> S37-G4 2 0.000 0.990 0.00 1.00
#> S37-G5 1 0.000 0.997 1.00 0.00
#> S37-G6 1 0.000 0.997 1.00 0.00
#> S37-G7 1 0.000 0.997 1.00 0.00
#> S37-G8 1 0.000 0.997 1.00 0.00
#> S37-H2 1 0.000 0.997 1.00 0.00
#> S37-H4 1 0.000 0.997 1.00 0.00
#> S37-H7 1 0.000 0.997 1.00 0.00
#> S37-H8 1 0.000 0.997 1.00 0.00
#> S37-H9 1 0.000 0.997 1.00 0.00
#> S38-A1 1 0.000 0.997 1.00 0.00
#> S38-A10 1 0.000 0.997 1.00 0.00
#> S38-A12 2 0.000 0.990 0.00 1.00
#> S38-A2 2 0.000 0.990 0.00 1.00
#> S38-A3 1 0.000 0.997 1.00 0.00
#> S38-A5 2 0.000 0.990 0.00 1.00
#> S38-A9 2 0.000 0.990 0.00 1.00
#> S38-B10 1 0.000 0.997 1.00 0.00
#> S38-B11 1 0.000 0.997 1.00 0.00
#> S38-B2 2 0.000 0.990 0.00 1.00
#> S38-B6 1 0.000 0.997 1.00 0.00
#> S38-B7 2 0.000 0.990 0.00 1.00
#> S38-B8 2 0.000 0.990 0.00 1.00
#> S38-B9 2 0.000 0.990 0.00 1.00
#> S38-C1 1 0.904 0.524 0.68 0.32
#> S38-C10 1 0.000 0.997 1.00 0.00
#> S38-C11 1 0.000 0.997 1.00 0.00
#> S38-C3 2 0.000 0.990 0.00 1.00
#> S38-C4 1 0.000 0.997 1.00 0.00
#> S38-C5 1 0.000 0.997 1.00 0.00
#> S38-C6 1 0.000 0.997 1.00 0.00
#> S38-C7 1 0.000 0.997 1.00 0.00
#> S38-C9 2 0.000 0.990 0.00 1.00
#> S38-D1 2 0.000 0.990 0.00 1.00
#> S38-D10 1 0.000 0.997 1.00 0.00
#> S38-D11 1 0.000 0.997 1.00 0.00
#> S38-D12 1 0.000 0.997 1.00 0.00
#> S38-D2 1 0.000 0.997 1.00 0.00
#> S38-D4 2 0.958 0.394 0.38 0.62
#> S38-D5 2 0.000 0.990 0.00 1.00
#> S38-D6 2 0.000 0.990 0.00 1.00
#> S38-D7 1 0.000 0.997 1.00 0.00
#> S38-D8 1 0.000 0.997 1.00 0.00
#> S38-D9 1 0.000 0.997 1.00 0.00
#> S38-E1 2 0.000 0.990 0.00 1.00
#> S38-E2 1 0.000 0.997 1.00 0.00
#> S38-E3 1 0.000 0.997 1.00 0.00
#> S38-E4 2 0.000 0.990 0.00 1.00
#> S38-E5 2 0.000 0.990 0.00 1.00
#> S38-E6 2 0.000 0.990 0.00 1.00
#> S38-E7 2 0.000 0.990 0.00 1.00
#> S38-E8 1 0.000 0.997 1.00 0.00
#> S38-E9 2 0.000 0.990 0.00 1.00
#> S38-F10 1 0.000 0.997 1.00 0.00
#> S38-F11 1 0.000 0.997 1.00 0.00
#> S38-F2 2 0.000 0.990 0.00 1.00
#> S38-F3 1 0.000 0.997 1.00 0.00
#> S38-F5 2 0.000 0.990 0.00 1.00
#> S38-F6 2 0.000 0.990 0.00 1.00
#> S38-F7 1 0.000 0.997 1.00 0.00
#> S38-F8 2 0.000 0.990 0.00 1.00
#> S38-F9 1 0.000 0.997 1.00 0.00
#> S38-G10 1 0.000 0.997 1.00 0.00
#> S38-G12 1 0.000 0.997 1.00 0.00
#> S38-G4 2 0.000 0.990 0.00 1.00
#> S38-G5 2 0.000 0.990 0.00 1.00
#> S38-G6 2 0.000 0.990 0.00 1.00
#> S38-G7 1 0.000 0.997 1.00 0.00
#> S38-G8 1 0.000 0.997 1.00 0.00
#> S38-G9 1 0.000 0.997 1.00 0.00
#> S38-H1 1 0.000 0.997 1.00 0.00
#> S38-H11 1 0.000 0.997 1.00 0.00
#> S38-H2 2 0.000 0.990 0.00 1.00
#> S38-H3 1 0.000 0.997 1.00 0.00
#> S38-H4 1 0.000 0.997 1.00 0.00
#> S38-H5 2 0.000 0.990 0.00 1.00
#> S38-H6 2 0.000 0.990 0.00 1.00
#> S38-H8 1 0.000 0.997 1.00 0.00
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> O10-A1 2 0.0000 1.000 0.00 1.00 0.00
#> O10-A11 3 0.0000 0.981 0.00 0.00 1.00
#> O10-A12 2 0.0000 1.000 0.00 1.00 0.00
#> O10-A3 1 0.1529 0.950 0.96 0.00 0.04
#> O10-A4 2 0.0000 1.000 0.00 1.00 0.00
#> O10-A5 3 0.0000 0.981 0.00 0.00 1.00
#> O10-A7 3 0.0000 0.981 0.00 0.00 1.00
#> O10-A8 3 0.0000 0.981 0.00 0.00 1.00
#> O10-A9 1 0.4555 0.750 0.80 0.00 0.20
#> O10-B1 1 0.0000 0.989 1.00 0.00 0.00
#> O10-B10 3 0.0000 0.981 0.00 0.00 1.00
#> O10-B11 3 0.0000 0.981 0.00 0.00 1.00
#> O10-B12 1 0.0000 0.989 1.00 0.00 0.00
#> O10-B2 3 0.0000 0.981 0.00 0.00 1.00
#> O10-B5 3 0.0000 0.981 0.00 0.00 1.00
#> O10-B6 3 0.0000 0.981 0.00 0.00 1.00
#> O10-B7 3 0.0000 0.981 0.00 0.00 1.00
#> O10-B9 3 0.0000 0.981 0.00 0.00 1.00
#> O10-C10 3 0.0000 0.981 0.00 0.00 1.00
#> O10-C11 1 0.0000 0.989 1.00 0.00 0.00
#> O10-C12 3 0.0000 0.981 0.00 0.00 1.00
#> O10-C2 1 0.0000 0.989 1.00 0.00 0.00
#> O10-C4 2 0.0000 1.000 0.00 1.00 0.00
#> O10-C5 3 0.0000 0.981 0.00 0.00 1.00
#> O10-C6 3 0.0000 0.981 0.00 0.00 1.00
#> O10-C9 3 0.0000 0.981 0.00 0.00 1.00
#> O10-D1 3 0.0000 0.981 0.00 0.00 1.00
#> O10-D11 3 0.0892 0.965 0.02 0.00 0.98
#> O10-D12 3 0.0000 0.981 0.00 0.00 1.00
#> O10-D2 1 0.5216 0.646 0.74 0.00 0.26
#> O10-D3 2 0.0000 1.000 0.00 1.00 0.00
#> O10-D5 3 0.0000 0.981 0.00 0.00 1.00
#> O10-D6 3 0.0000 0.981 0.00 0.00 1.00
#> O10-D8 1 0.0000 0.989 1.00 0.00 0.00
#> O10-D9 3 0.0000 0.981 0.00 0.00 1.00
#> O10-E1 3 0.0000 0.981 0.00 0.00 1.00
#> O10-E11 3 0.0000 0.981 0.00 0.00 1.00
#> O10-E12 3 0.0000 0.981 0.00 0.00 1.00
#> O10-E6 3 0.0000 0.981 0.00 0.00 1.00
#> O10-E8 1 0.0000 0.989 1.00 0.00 0.00
#> O10-E9 1 0.0000 0.989 1.00 0.00 0.00
#> O10-F1 3 0.0000 0.981 0.00 0.00 1.00
#> O10-F11 3 0.0000 0.981 0.00 0.00 1.00
#> O10-F12 3 0.0892 0.965 0.02 0.00 0.98
#> O10-F2 1 0.0000 0.989 1.00 0.00 0.00
#> O10-F4 1 0.0000 0.989 1.00 0.00 0.00
#> O10-F5 3 0.1529 0.948 0.04 0.00 0.96
#> O10-F6 2 0.0000 1.000 0.00 1.00 0.00
#> O10-F8 1 0.3686 0.834 0.86 0.00 0.14
#> O10-F9 3 0.0000 0.981 0.00 0.00 1.00
#> O10-G1 1 0.0000 0.989 1.00 0.00 0.00
#> O10-G12 1 0.0000 0.989 1.00 0.00 0.00
#> O10-G2 1 0.0000 0.989 1.00 0.00 0.00
#> O10-G3 1 0.0000 0.989 1.00 0.00 0.00
#> O10-G4 1 0.0000 0.989 1.00 0.00 0.00
#> O10-G5 1 0.0000 0.989 1.00 0.00 0.00
#> O10-G7 1 0.0000 0.989 1.00 0.00 0.00
#> O10-H1 1 0.0000 0.989 1.00 0.00 0.00
#> O10-H4 1 0.0000 0.989 1.00 0.00 0.00
#> O10-H5 1 0.0000 0.989 1.00 0.00 0.00
#> O10-H6 1 0.0000 0.989 1.00 0.00 0.00
#> O10-H7 1 0.0000 0.989 1.00 0.00 0.00
#> O12-A1 2 0.0000 1.000 0.00 1.00 0.00
#> O12-A12 2 0.0000 1.000 0.00 1.00 0.00
#> O12-A2 1 0.0000 0.989 1.00 0.00 0.00
#> O12-A3 2 0.0000 1.000 0.00 1.00 0.00
#> O12-B1 2 0.0000 1.000 0.00 1.00 0.00
#> O12-B12 3 0.0000 0.981 0.00 0.00 1.00
#> O12-C1 2 0.0000 1.000 0.00 1.00 0.00
#> O12-D1 2 0.0000 1.000 0.00 1.00 0.00
#> O12-D2 1 0.0000 0.989 1.00 0.00 0.00
#> O12-E1 1 0.0000 0.989 1.00 0.00 0.00
#> O12-E12 2 0.0000 1.000 0.00 1.00 0.00
#> O12-F12 3 0.0000 0.981 0.00 0.00 1.00
#> O12-F2 2 0.0000 1.000 0.00 1.00 0.00
#> O12-G2 2 0.0000 1.000 0.00 1.00 0.00
#> O12-H1 2 0.0000 1.000 0.00 1.00 0.00
#> O12-H2 2 0.0000 1.000 0.00 1.00 0.00
#> O7-A3 3 0.0000 0.981 0.00 0.00 1.00
#> O7-A5 2 0.0000 1.000 0.00 1.00 0.00
#> O7-A7 2 0.0000 1.000 0.00 1.00 0.00
#> O7-A8 2 0.0000 1.000 0.00 1.00 0.00
#> O7-A9 3 0.0000 0.981 0.00 0.00 1.00
#> O7-B1 2 0.0000 1.000 0.00 1.00 0.00
#> O7-B11 3 0.0000 0.981 0.00 0.00 1.00
#> O7-B12 2 0.0000 1.000 0.00 1.00 0.00
#> O7-B6 3 0.0000 0.981 0.00 0.00 1.00
#> O7-B7 3 0.0000 0.981 0.00 0.00 1.00
#> O7-B8 2 0.0000 1.000 0.00 1.00 0.00
#> O7-B9 2 0.0000 1.000 0.00 1.00 0.00
#> O7-C1 3 0.0000 0.981 0.00 0.00 1.00
#> O7-C11 3 0.0000 0.981 0.00 0.00 1.00
#> O7-C2 2 0.0000 1.000 0.00 1.00 0.00
#> O7-C3 2 0.0000 1.000 0.00 1.00 0.00
#> O7-C6 2 0.0000 1.000 0.00 1.00 0.00
#> O7-C7 3 0.0000 0.981 0.00 0.00 1.00
#> O7-D1 2 0.0000 1.000 0.00 1.00 0.00
#> O7-D11 2 0.0000 1.000 0.00 1.00 0.00
#> O7-D12 2 0.0000 1.000 0.00 1.00 0.00
#> O7-D2 2 0.0000 1.000 0.00 1.00 0.00
#> O7-D3 1 0.0000 0.989 1.00 0.00 0.00
#> O7-D4 3 0.0000 0.981 0.00 0.00 1.00
#> O7-D5 1 0.0000 0.989 1.00 0.00 0.00
#> O7-E10 3 0.0000 0.981 0.00 0.00 1.00
#> O7-E11 3 0.0000 0.981 0.00 0.00 1.00
#> O7-E5 2 0.0000 1.000 0.00 1.00 0.00
#> O7-E6 2 0.0000 1.000 0.00 1.00 0.00
#> O7-F1 2 0.0000 1.000 0.00 1.00 0.00
#> O7-F10 2 0.0000 1.000 0.00 1.00 0.00
#> O7-F11 2 0.0000 1.000 0.00 1.00 0.00
#> O7-F2 3 0.0000 0.981 0.00 0.00 1.00
#> O7-F3 3 0.0000 0.981 0.00 0.00 1.00
#> O7-F4 2 0.0000 1.000 0.00 1.00 0.00
#> O7-F7 3 0.0000 0.981 0.00 0.00 1.00
#> O7-F9 3 0.0000 0.981 0.00 0.00 1.00
#> O7-G12 2 0.0000 1.000 0.00 1.00 0.00
#> O7-G3 1 0.0000 0.989 1.00 0.00 0.00
#> O7-G9 2 0.0000 1.000 0.00 1.00 0.00
#> O7-H3 2 0.0000 1.000 0.00 1.00 0.00
#> O7-H4 2 0.0000 1.000 0.00 1.00 0.00
#> O7-H8 2 0.0000 1.000 0.00 1.00 0.00
#> O8-A2 3 0.0000 0.981 0.00 0.00 1.00
#> O8-A3 3 0.0000 0.981 0.00 0.00 1.00
#> O8-A5 2 0.0000 1.000 0.00 1.00 0.00
#> O8-A8 3 0.0000 0.981 0.00 0.00 1.00
#> O8-A9 2 0.0000 1.000 0.00 1.00 0.00
#> O8-B1 2 0.0000 1.000 0.00 1.00 0.00
#> O8-B2 3 0.0000 0.981 0.00 0.00 1.00
#> O8-B4 3 0.0000 0.981 0.00 0.00 1.00
#> O8-B6 3 0.0000 0.981 0.00 0.00 1.00
#> O8-B7 3 0.0000 0.981 0.00 0.00 1.00
#> O8-B9 3 0.0000 0.981 0.00 0.00 1.00
#> O8-C11 3 0.0000 0.981 0.00 0.00 1.00
#> O8-C12 3 0.0000 0.981 0.00 0.00 1.00
#> O8-C2 2 0.0000 1.000 0.00 1.00 0.00
#> O8-C3 3 0.0000 0.981 0.00 0.00 1.00
#> O8-C4 3 0.0000 0.981 0.00 0.00 1.00
#> O8-C5 3 0.0000 0.981 0.00 0.00 1.00
#> O8-C6 3 0.0000 0.981 0.00 0.00 1.00
#> O8-C8 3 0.0000 0.981 0.00 0.00 1.00
#> O8-D3 3 0.0000 0.981 0.00 0.00 1.00
#> O8-D5 3 0.0000 0.981 0.00 0.00 1.00
#> O8-D6 3 0.4291 0.789 0.18 0.00 0.82
#> O8-D9 3 0.0000 0.981 0.00 0.00 1.00
#> O8-E1 1 0.4796 0.716 0.78 0.00 0.22
#> O8-E11 3 0.0000 0.981 0.00 0.00 1.00
#> O8-E2 3 0.0000 0.981 0.00 0.00 1.00
#> O8-E3 2 0.0000 1.000 0.00 1.00 0.00
#> O8-E5 3 0.0000 0.981 0.00 0.00 1.00
#> O8-E7 2 0.0000 1.000 0.00 1.00 0.00
#> O8-E9 3 0.0000 0.981 0.00 0.00 1.00
#> O8-F10 1 0.0000 0.989 1.00 0.00 0.00
#> O8-F11 3 0.0000 0.981 0.00 0.00 1.00
#> O8-F12 3 0.0000 0.981 0.00 0.00 1.00
#> O8-F2 2 0.0000 1.000 0.00 1.00 0.00
#> O8-F3 3 0.0000 0.981 0.00 0.00 1.00
#> O8-F6 2 0.0000 1.000 0.00 1.00 0.00
#> O8-F8 2 0.0000 1.000 0.00 1.00 0.00
#> O8-F9 1 0.0000 0.989 1.00 0.00 0.00
#> O8-G1 3 0.2959 0.890 0.10 0.00 0.90
#> O8-G12 3 0.0000 0.981 0.00 0.00 1.00
#> O8-G5 3 0.0000 0.981 0.00 0.00 1.00
#> O8-G9 1 0.0000 0.989 1.00 0.00 0.00
#> O8-H1 1 0.0000 0.989 1.00 0.00 0.00
#> O8-H11 2 0.0000 1.000 0.00 1.00 0.00
#> O8-H2 2 0.0000 1.000 0.00 1.00 0.00
#> O8-H6 1 0.0000 0.989 1.00 0.00 0.00
#> O9-A10 3 0.0000 0.981 0.00 0.00 1.00
#> O9-A12 2 0.0000 1.000 0.00 1.00 0.00
#> O9-A2 1 0.0000 0.989 1.00 0.00 0.00
#> O9-A3 2 0.0000 1.000 0.00 1.00 0.00
#> O9-A5 2 0.0000 1.000 0.00 1.00 0.00
#> O9-A6 2 0.0000 1.000 0.00 1.00 0.00
#> O9-A8 3 0.0000 0.981 0.00 0.00 1.00
#> O9-A9 1 0.0000 0.989 1.00 0.00 0.00
#> O9-B10 1 0.0000 0.989 1.00 0.00 0.00
#> O9-B11 1 0.0000 0.989 1.00 0.00 0.00
#> O9-B12 3 0.0000 0.981 0.00 0.00 1.00
#> O9-B2 3 0.0000 0.981 0.00 0.00 1.00
#> O9-B3 1 0.0000 0.989 1.00 0.00 0.00
#> O9-B5 2 0.0000 1.000 0.00 1.00 0.00
#> O9-B6 3 0.0000 0.981 0.00 0.00 1.00
#> O9-B7 3 0.0000 0.981 0.00 0.00 1.00
#> O9-B8 2 0.0000 1.000 0.00 1.00 0.00
#> O9-C10 1 0.0000 0.989 1.00 0.00 0.00
#> O9-C2 3 0.3340 0.867 0.12 0.00 0.88
#> O9-C3 1 0.0000 0.989 1.00 0.00 0.00
#> O9-C4 3 0.0000 0.981 0.00 0.00 1.00
#> O9-C5 1 0.0000 0.989 1.00 0.00 0.00
#> O9-C6 3 0.0000 0.981 0.00 0.00 1.00
#> O9-C9 1 0.0000 0.989 1.00 0.00 0.00
#> O9-D1 1 0.0000 0.989 1.00 0.00 0.00
#> O9-D10 1 0.0000 0.989 1.00 0.00 0.00
#> O9-D11 1 0.0000 0.989 1.00 0.00 0.00
#> O9-D12 3 0.1529 0.946 0.00 0.04 0.96
#> O9-D2 2 0.0000 1.000 0.00 1.00 0.00
#> O9-D5 1 0.0000 0.989 1.00 0.00 0.00
#> O9-D6 3 0.0000 0.981 0.00 0.00 1.00
#> O9-D7 2 0.0000 1.000 0.00 1.00 0.00
#> O9-D8 2 0.0000 1.000 0.00 1.00 0.00
#> O9-E1 2 0.0000 1.000 0.00 1.00 0.00
#> O9-E10 1 0.0000 0.989 1.00 0.00 0.00
#> O9-E11 1 0.0000 0.989 1.00 0.00 0.00
#> O9-E12 3 0.0000 0.981 0.00 0.00 1.00
#> O9-E2 2 0.0000 1.000 0.00 1.00 0.00
#> O9-E4 3 0.0000 0.981 0.00 0.00 1.00
#> O9-E5 1 0.0000 0.989 1.00 0.00 0.00
#> O9-E7 1 0.0000 0.989 1.00 0.00 0.00
#> O9-E8 1 0.0000 0.989 1.00 0.00 0.00
#> O9-E9 1 0.0000 0.989 1.00 0.00 0.00
#> O9-F1 2 0.0000 1.000 0.00 1.00 0.00
#> O9-F10 1 0.0000 0.989 1.00 0.00 0.00
#> O9-F12 1 0.0000 0.989 1.00 0.00 0.00
#> O9-F2 1 0.0000 0.989 1.00 0.00 0.00
#> O9-F4 2 0.0000 1.000 0.00 1.00 0.00
#> O9-F5 2 0.0000 1.000 0.00 1.00 0.00
#> O9-F9 3 0.0000 0.981 0.00 0.00 1.00
#> O9-G10 1 0.0000 0.989 1.00 0.00 0.00
#> O9-G12 1 0.0000 0.989 1.00 0.00 0.00
#> O9-G2 1 0.0000 0.989 1.00 0.00 0.00
#> O9-G3 3 0.5560 0.587 0.30 0.00 0.70
#> O9-G4 1 0.0000 0.989 1.00 0.00 0.00
#> O9-G6 1 0.0000 0.989 1.00 0.00 0.00
#> O9-G7 3 0.0000 0.981 0.00 0.00 1.00
#> O9-G9 2 0.0000 1.000 0.00 1.00 0.00
#> O9-H12 2 0.0000 1.000 0.00 1.00 0.00
#> O9-H3 1 0.0000 0.989 1.00 0.00 0.00
#> O9-H5 2 0.0000 1.000 0.00 1.00 0.00
#> O9-H9 1 0.0000 0.989 1.00 0.00 0.00
#> S37-A1 1 0.0000 0.989 1.00 0.00 0.00
#> S37-A10 1 0.0000 0.989 1.00 0.00 0.00
#> S37-A2 2 0.0000 1.000 0.00 1.00 0.00
#> S37-A3 1 0.0892 0.970 0.98 0.00 0.02
#> S37-A4 3 0.0000 0.981 0.00 0.00 1.00
#> S37-A5 2 0.0000 1.000 0.00 1.00 0.00
#> S37-A6 2 0.0000 1.000 0.00 1.00 0.00
#> S37-A7 3 0.0000 0.981 0.00 0.00 1.00
#> S37-A8 2 0.0000 1.000 0.00 1.00 0.00
#> S37-A9 1 0.0000 0.989 1.00 0.00 0.00
#> S37-B1 1 0.0000 0.989 1.00 0.00 0.00
#> S37-B10 1 0.0000 0.989 1.00 0.00 0.00
#> S37-B11 2 0.0000 1.000 0.00 1.00 0.00
#> S37-B12 2 0.0000 1.000 0.00 1.00 0.00
#> S37-B2 1 0.0000 0.989 1.00 0.00 0.00
#> S37-B3 3 0.5397 0.627 0.28 0.00 0.72
#> S37-B4 1 0.0000 0.989 1.00 0.00 0.00
#> S37-B5 3 0.0000 0.981 0.00 0.00 1.00
#> S37-B6 3 0.0000 0.981 0.00 0.00 1.00
#> S37-B7 1 0.0000 0.989 1.00 0.00 0.00
#> S37-B9 3 0.0000 0.981 0.00 0.00 1.00
#> S37-C10 1 0.0000 0.989 1.00 0.00 0.00
#> S37-C12 2 0.0000 1.000 0.00 1.00 0.00
#> S37-C3 1 0.0000 0.989 1.00 0.00 0.00
#> S37-C4 1 0.0000 0.989 1.00 0.00 0.00
#> S37-C6 1 0.6126 0.321 0.60 0.00 0.40
#> S37-C7 1 0.0000 0.989 1.00 0.00 0.00
#> S37-C8 2 0.0000 1.000 0.00 1.00 0.00
#> S37-C9 1 0.0000 0.989 1.00 0.00 0.00
#> S37-D10 1 0.0000 0.989 1.00 0.00 0.00
#> S37-D11 3 0.0000 0.981 0.00 0.00 1.00
#> S37-D12 2 0.0000 1.000 0.00 1.00 0.00
#> S37-D2 1 0.0000 0.989 1.00 0.00 0.00
#> S37-D4 1 0.0000 0.989 1.00 0.00 0.00
#> S37-D6 1 0.0000 0.989 1.00 0.00 0.00
#> S37-D8 1 0.0000 0.989 1.00 0.00 0.00
#> S37-D9 3 0.4291 0.789 0.18 0.00 0.82
#> S37-E1 1 0.0000 0.989 1.00 0.00 0.00
#> S37-E10 3 0.5397 0.625 0.28 0.00 0.72
#> S37-E11 1 0.0000 0.989 1.00 0.00 0.00
#> S37-E2 1 0.0000 0.989 1.00 0.00 0.00
#> S37-E3 1 0.0000 0.989 1.00 0.00 0.00
#> S37-E5 3 0.1529 0.948 0.04 0.00 0.96
#> S37-E6 1 0.0000 0.989 1.00 0.00 0.00
#> S37-E7 2 0.0000 1.000 0.00 1.00 0.00
#> S37-E8 2 0.0000 1.000 0.00 1.00 0.00
#> S37-E9 1 0.0000 0.989 1.00 0.00 0.00
#> S37-F1 1 0.0000 0.989 1.00 0.00 0.00
#> S37-F10 1 0.0000 0.989 1.00 0.00 0.00
#> S37-F12 1 0.0000 0.989 1.00 0.00 0.00
#> S37-F2 1 0.0892 0.970 0.98 0.00 0.02
#> S37-F3 1 0.0000 0.989 1.00 0.00 0.00
#> S37-F5 1 0.0000 0.989 1.00 0.00 0.00
#> S37-F7 1 0.0000 0.989 1.00 0.00 0.00
#> S37-F9 1 0.0000 0.989 1.00 0.00 0.00
#> S37-G1 1 0.2959 0.885 0.90 0.00 0.10
#> S37-G10 1 0.0000 0.989 1.00 0.00 0.00
#> S37-G12 1 0.0000 0.989 1.00 0.00 0.00
#> S37-G2 2 0.0000 1.000 0.00 1.00 0.00
#> S37-G3 1 0.0000 0.989 1.00 0.00 0.00
#> S37-G4 2 0.0000 1.000 0.00 1.00 0.00
#> S37-G5 3 0.0000 0.981 0.00 0.00 1.00
#> S37-G6 1 0.0000 0.989 1.00 0.00 0.00
#> S37-G7 1 0.0000 0.989 1.00 0.00 0.00
#> S37-G8 3 0.0000 0.981 0.00 0.00 1.00
#> S37-H2 1 0.0000 0.989 1.00 0.00 0.00
#> S37-H4 3 0.2959 0.889 0.10 0.00 0.90
#> S37-H7 1 0.0000 0.989 1.00 0.00 0.00
#> S37-H8 1 0.0000 0.989 1.00 0.00 0.00
#> S37-H9 1 0.0000 0.989 1.00 0.00 0.00
#> S38-A1 1 0.0000 0.989 1.00 0.00 0.00
#> S38-A10 1 0.0000 0.989 1.00 0.00 0.00
#> S38-A12 2 0.0000 1.000 0.00 1.00 0.00
#> S38-A2 2 0.0000 1.000 0.00 1.00 0.00
#> S38-A3 3 0.1529 0.948 0.04 0.00 0.96
#> S38-A5 2 0.0000 1.000 0.00 1.00 0.00
#> S38-A9 2 0.0000 1.000 0.00 1.00 0.00
#> S38-B10 3 0.0000 0.981 0.00 0.00 1.00
#> S38-B11 1 0.0000 0.989 1.00 0.00 0.00
#> S38-B2 2 0.0000 1.000 0.00 1.00 0.00
#> S38-B6 1 0.0000 0.989 1.00 0.00 0.00
#> S38-B7 2 0.0000 1.000 0.00 1.00 0.00
#> S38-B8 2 0.0000 1.000 0.00 1.00 0.00
#> S38-B9 2 0.0000 1.000 0.00 1.00 0.00
#> S38-C1 3 0.2066 0.927 0.00 0.06 0.94
#> S38-C10 3 0.0000 0.981 0.00 0.00 1.00
#> S38-C11 3 0.2959 0.889 0.10 0.00 0.90
#> S38-C3 2 0.0000 1.000 0.00 1.00 0.00
#> S38-C4 1 0.0000 0.989 1.00 0.00 0.00
#> S38-C5 3 0.0000 0.981 0.00 0.00 1.00
#> S38-C6 3 0.0000 0.981 0.00 0.00 1.00
#> S38-C7 3 0.0000 0.981 0.00 0.00 1.00
#> S38-C9 2 0.0000 1.000 0.00 1.00 0.00
#> S38-D1 2 0.0000 1.000 0.00 1.00 0.00
#> S38-D10 3 0.2959 0.889 0.10 0.00 0.90
#> S38-D11 3 0.0000 0.981 0.00 0.00 1.00
#> S38-D12 1 0.0000 0.989 1.00 0.00 0.00
#> S38-D2 1 0.0000 0.989 1.00 0.00 0.00
#> S38-D4 3 0.4291 0.780 0.00 0.18 0.82
#> S38-D5 2 0.0000 1.000 0.00 1.00 0.00
#> S38-D6 2 0.0000 1.000 0.00 1.00 0.00
#> S38-D7 3 0.4291 0.789 0.18 0.00 0.82
#> S38-D8 1 0.0000 0.989 1.00 0.00 0.00
#> S38-D9 1 0.0000 0.989 1.00 0.00 0.00
#> S38-E1 2 0.0000 1.000 0.00 1.00 0.00
#> S38-E2 3 0.0000 0.981 0.00 0.00 1.00
#> S38-E3 3 0.0892 0.965 0.02 0.00 0.98
#> S38-E4 2 0.0000 1.000 0.00 1.00 0.00
#> S38-E5 2 0.0000 1.000 0.00 1.00 0.00
#> S38-E6 2 0.0000 1.000 0.00 1.00 0.00
#> S38-E7 2 0.1529 0.958 0.00 0.96 0.04
#> S38-E8 3 0.0000 0.981 0.00 0.00 1.00
#> S38-E9 2 0.0000 1.000 0.00 1.00 0.00
#> S38-F10 1 0.0000 0.989 1.00 0.00 0.00
#> S38-F11 1 0.0000 0.989 1.00 0.00 0.00
#> S38-F2 2 0.0000 1.000 0.00 1.00 0.00
#> S38-F3 1 0.0000 0.989 1.00 0.00 0.00
#> S38-F5 2 0.0000 1.000 0.00 1.00 0.00
#> S38-F6 2 0.0000 1.000 0.00 1.00 0.00
#> S38-F7 3 0.0000 0.981 0.00 0.00 1.00
#> S38-F8 2 0.0000 1.000 0.00 1.00 0.00
#> S38-F9 1 0.0000 0.989 1.00 0.00 0.00
#> S38-G10 1 0.0000 0.989 1.00 0.00 0.00
#> S38-G12 1 0.0000 0.989 1.00 0.00 0.00
#> S38-G4 2 0.0000 1.000 0.00 1.00 0.00
#> S38-G5 2 0.0000 1.000 0.00 1.00 0.00
#> S38-G6 2 0.0000 1.000 0.00 1.00 0.00
#> S38-G7 3 0.0000 0.981 0.00 0.00 1.00
#> S38-G8 3 0.0000 0.981 0.00 0.00 1.00
#> S38-G9 3 0.0000 0.981 0.00 0.00 1.00
#> S38-H1 1 0.0000 0.989 1.00 0.00 0.00
#> S38-H11 1 0.0000 0.989 1.00 0.00 0.00
#> S38-H2 2 0.0000 1.000 0.00 1.00 0.00
#> S38-H3 3 0.0000 0.981 0.00 0.00 1.00
#> S38-H4 1 0.0000 0.989 1.00 0.00 0.00
#> S38-H5 2 0.0000 1.000 0.00 1.00 0.00
#> S38-H6 2 0.0000 1.000 0.00 1.00 0.00
#> S38-H8 1 0.0000 0.989 1.00 0.00 0.00
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> O10-A1 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> O10-A11 3 0.1411 0.945 0.02 0.00 0.96 0.02
#> O10-A12 4 0.2011 0.975 0.00 0.08 0.00 0.92
#> O10-A3 1 0.1411 0.937 0.96 0.00 0.02 0.02
#> O10-A4 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> O10-A5 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O10-A7 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O10-A8 3 0.1913 0.937 0.04 0.00 0.94 0.02
#> O10-A9 1 0.4936 0.563 0.70 0.00 0.28 0.02
#> O10-B1 1 0.0000 0.963 1.00 0.00 0.00 0.00
#> O10-B10 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O10-B11 3 0.1913 0.937 0.04 0.00 0.94 0.02
#> O10-B12 1 0.0000 0.963 1.00 0.00 0.00 0.00
#> O10-B2 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O10-B5 3 0.0707 0.951 0.00 0.00 0.98 0.02
#> O10-B6 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O10-B7 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O10-B9 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O10-C10 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O10-C11 1 0.0000 0.963 1.00 0.00 0.00 0.00
#> O10-C12 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O10-C2 1 0.0000 0.963 1.00 0.00 0.00 0.00
#> O10-C4 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> O10-C5 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O10-C6 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O10-C9 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O10-D1 3 0.4790 0.366 0.00 0.38 0.62 0.00
#> O10-D11 3 0.2335 0.925 0.06 0.00 0.92 0.02
#> O10-D12 3 0.1913 0.937 0.04 0.00 0.94 0.02
#> O10-D2 1 0.4642 0.640 0.74 0.00 0.24 0.02
#> O10-D3 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> O10-D5 3 0.0707 0.951 0.00 0.00 0.98 0.02
#> O10-D6 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O10-D8 1 0.0000 0.963 1.00 0.00 0.00 0.00
#> O10-D9 3 0.1411 0.945 0.02 0.00 0.96 0.02
#> O10-E1 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O10-E11 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O10-E12 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O10-E6 3 0.0707 0.951 0.00 0.00 0.98 0.02
#> O10-E8 1 0.0000 0.963 1.00 0.00 0.00 0.00
#> O10-E9 1 0.0707 0.952 0.98 0.00 0.00 0.02
#> O10-F1 3 0.0707 0.951 0.00 0.00 0.98 0.02
#> O10-F11 3 0.0707 0.951 0.00 0.00 0.98 0.02
#> O10-F12 3 0.2335 0.925 0.06 0.00 0.92 0.02
#> O10-F2 1 0.0000 0.963 1.00 0.00 0.00 0.00
#> O10-F4 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> O10-F5 3 0.2706 0.909 0.08 0.00 0.90 0.02
#> O10-F6 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> O10-F8 1 0.3606 0.801 0.84 0.00 0.14 0.02
#> O10-F9 3 0.1913 0.937 0.04 0.00 0.94 0.02
#> O10-G1 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> O10-G12 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> O10-G2 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> O10-G3 1 0.5713 0.475 0.62 0.34 0.00 0.04
#> O10-G4 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> O10-G5 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> O10-G7 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> O10-H1 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> O10-H4 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> O10-H5 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> O10-H6 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> O10-H7 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> O12-A1 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> O12-A12 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> O12-A2 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> O12-A3 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> O12-B1 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> O12-B12 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O12-C1 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> O12-D1 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> O12-D2 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> O12-E1 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> O12-E12 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> O12-F12 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O12-F2 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> O12-G2 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> O12-H1 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> O12-H2 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> O7-A3 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O7-A5 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> O7-A7 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> O7-A8 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> O7-A9 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O7-B1 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> O7-B11 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O7-B12 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> O7-B6 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O7-B7 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O7-B8 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> O7-B9 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> O7-C1 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O7-C11 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O7-C2 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> O7-C3 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> O7-C6 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> O7-C7 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O7-D1 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> O7-D11 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> O7-D12 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> O7-D2 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> O7-D3 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> O7-D4 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O7-D5 1 0.0000 0.963 1.00 0.00 0.00 0.00
#> O7-E10 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O7-E11 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O7-E5 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> O7-E6 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> O7-F1 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> O7-F10 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> O7-F11 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> O7-F2 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O7-F3 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O7-F4 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> O7-F7 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O7-F9 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O7-G12 4 0.2011 0.975 0.00 0.08 0.00 0.92
#> O7-G3 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> O7-G9 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> O7-H3 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> O7-H4 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> O7-H8 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> O8-A2 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O8-A3 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O8-A5 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> O8-A8 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O8-A9 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> O8-B1 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> O8-B2 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O8-B4 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O8-B6 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O8-B7 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O8-B9 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O8-C11 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O8-C12 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O8-C2 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> O8-C3 3 0.0707 0.951 0.00 0.00 0.98 0.02
#> O8-C4 3 0.0707 0.951 0.00 0.00 0.98 0.02
#> O8-C5 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O8-C6 3 0.1913 0.937 0.04 0.00 0.94 0.02
#> O8-C8 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O8-D3 3 0.0707 0.951 0.00 0.00 0.98 0.02
#> O8-D5 3 0.0707 0.951 0.00 0.00 0.98 0.02
#> O8-D6 3 0.4472 0.752 0.22 0.00 0.76 0.02
#> O8-D9 3 0.1913 0.937 0.04 0.00 0.94 0.02
#> O8-E1 1 0.4642 0.642 0.74 0.00 0.24 0.02
#> O8-E11 3 0.1913 0.937 0.04 0.00 0.94 0.02
#> O8-E2 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O8-E3 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> O8-E5 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O8-E7 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> O8-E9 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O8-F10 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> O8-F11 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O8-F12 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O8-F2 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> O8-F3 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O8-F6 4 0.2011 0.975 0.00 0.08 0.00 0.92
#> O8-F8 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> O8-F9 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> O8-G1 3 0.3606 0.849 0.14 0.00 0.84 0.02
#> O8-G12 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O8-G5 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O8-G9 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> O8-H1 1 0.0707 0.964 0.98 0.00 0.00 0.02
#> O8-H11 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> O8-H2 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> O8-H6 1 0.0707 0.964 0.98 0.00 0.00 0.02
#> O9-A10 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O9-A12 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> O9-A2 1 0.0707 0.952 0.98 0.00 0.00 0.02
#> O9-A3 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> O9-A5 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> O9-A6 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> O9-A8 3 0.1411 0.945 0.02 0.00 0.96 0.02
#> O9-A9 1 0.0707 0.952 0.98 0.00 0.00 0.02
#> O9-B10 1 0.0707 0.952 0.98 0.00 0.00 0.02
#> O9-B11 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> O9-B12 3 0.0707 0.951 0.00 0.00 0.98 0.02
#> O9-B2 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O9-B3 1 0.0707 0.952 0.98 0.00 0.00 0.02
#> O9-B5 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> O9-B6 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O9-B7 3 0.1913 0.937 0.04 0.00 0.94 0.02
#> O9-B8 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> O9-C10 1 0.0707 0.964 0.98 0.00 0.00 0.02
#> O9-C2 3 0.3335 0.871 0.12 0.00 0.86 0.02
#> O9-C3 1 0.0000 0.963 1.00 0.00 0.00 0.00
#> O9-C4 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O9-C5 1 0.0000 0.963 1.00 0.00 0.00 0.00
#> O9-C6 3 0.2335 0.925 0.06 0.00 0.92 0.02
#> O9-C9 1 0.0707 0.964 0.98 0.00 0.00 0.02
#> O9-D1 1 0.0000 0.963 1.00 0.00 0.00 0.00
#> O9-D10 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> O9-D11 1 0.0000 0.963 1.00 0.00 0.00 0.00
#> O9-D12 2 0.4277 0.625 0.00 0.72 0.28 0.00
#> O9-D2 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> O9-D5 1 0.0000 0.963 1.00 0.00 0.00 0.00
#> O9-D6 3 0.0707 0.951 0.00 0.00 0.98 0.02
#> O9-D7 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> O9-D8 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> O9-E1 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> O9-E10 1 0.0707 0.952 0.98 0.00 0.00 0.02
#> O9-E11 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> O9-E12 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O9-E2 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> O9-E4 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O9-E5 1 0.0707 0.964 0.98 0.00 0.00 0.02
#> O9-E7 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> O9-E8 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> O9-E9 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> O9-F1 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> O9-F10 1 0.0707 0.952 0.98 0.00 0.00 0.02
#> O9-F12 1 0.0000 0.963 1.00 0.00 0.00 0.00
#> O9-F2 1 0.0707 0.964 0.98 0.00 0.00 0.02
#> O9-F4 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> O9-F5 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> O9-F9 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> O9-G10 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> O9-G12 1 0.0000 0.963 1.00 0.00 0.00 0.00
#> O9-G2 1 0.0707 0.952 0.98 0.00 0.00 0.02
#> O9-G3 3 0.5271 0.535 0.34 0.00 0.64 0.02
#> O9-G4 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> O9-G6 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> O9-G7 3 0.1913 0.937 0.04 0.00 0.94 0.02
#> O9-G9 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> O9-H12 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> O9-H3 1 0.0000 0.963 1.00 0.00 0.00 0.00
#> O9-H5 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> O9-H9 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> S37-A1 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> S37-A10 1 0.0707 0.964 0.98 0.00 0.00 0.02
#> S37-A2 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> S37-A3 1 0.0707 0.952 0.98 0.00 0.00 0.02
#> S37-A4 3 0.2335 0.926 0.06 0.00 0.92 0.02
#> S37-A5 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> S37-A6 4 0.2345 0.955 0.00 0.10 0.00 0.90
#> S37-A7 3 0.1411 0.945 0.02 0.00 0.96 0.02
#> S37-A8 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> S37-A9 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> S37-B1 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> S37-B10 1 0.0000 0.963 1.00 0.00 0.00 0.00
#> S37-B11 4 0.2011 0.975 0.00 0.08 0.00 0.92
#> S37-B12 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> S37-B2 1 0.0000 0.963 1.00 0.00 0.00 0.00
#> S37-B3 3 0.5062 0.619 0.30 0.00 0.68 0.02
#> S37-B4 1 0.0707 0.964 0.98 0.00 0.00 0.02
#> S37-B5 3 0.1913 0.937 0.04 0.00 0.94 0.02
#> S37-B6 3 0.1913 0.937 0.04 0.00 0.94 0.02
#> S37-B7 1 0.0707 0.964 0.98 0.00 0.00 0.02
#> S37-B9 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> S37-C10 1 0.0000 0.963 1.00 0.00 0.00 0.00
#> S37-C12 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> S37-C3 1 0.0000 0.963 1.00 0.00 0.00 0.00
#> S37-C4 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> S37-C6 1 0.5173 0.466 0.66 0.00 0.32 0.02
#> S37-C7 1 0.0000 0.963 1.00 0.00 0.00 0.00
#> S37-C8 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> S37-C9 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> S37-D10 1 0.0000 0.963 1.00 0.00 0.00 0.00
#> S37-D11 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> S37-D12 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> S37-D2 1 0.0707 0.964 0.98 0.00 0.00 0.02
#> S37-D4 1 0.0707 0.952 0.98 0.00 0.00 0.02
#> S37-D6 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> S37-D8 1 0.0000 0.963 1.00 0.00 0.00 0.00
#> S37-D9 3 0.4284 0.776 0.20 0.00 0.78 0.02
#> S37-E1 1 0.0707 0.952 0.98 0.00 0.00 0.02
#> S37-E10 3 0.5355 0.488 0.36 0.00 0.62 0.02
#> S37-E11 1 0.0000 0.963 1.00 0.00 0.00 0.00
#> S37-E2 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> S37-E3 1 0.0000 0.963 1.00 0.00 0.00 0.00
#> S37-E5 3 0.3853 0.827 0.16 0.00 0.82 0.02
#> S37-E6 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> S37-E7 4 0.4134 0.735 0.00 0.26 0.00 0.74
#> S37-E8 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> S37-E9 1 0.0707 0.964 0.98 0.00 0.00 0.02
#> S37-F1 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> S37-F10 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> S37-F12 1 0.0000 0.963 1.00 0.00 0.00 0.00
#> S37-F2 1 0.1411 0.937 0.96 0.00 0.02 0.02
#> S37-F3 1 0.0000 0.963 1.00 0.00 0.00 0.00
#> S37-F5 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> S37-F7 1 0.0000 0.963 1.00 0.00 0.00 0.00
#> S37-F9 1 0.0000 0.963 1.00 0.00 0.00 0.00
#> S37-G1 1 0.3335 0.826 0.86 0.00 0.12 0.02
#> S37-G10 1 0.0000 0.963 1.00 0.00 0.00 0.00
#> S37-G12 1 0.0707 0.952 0.98 0.00 0.00 0.02
#> S37-G2 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> S37-G3 4 0.0707 0.917 0.02 0.00 0.00 0.98
#> S37-G4 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> S37-G5 3 0.1913 0.937 0.04 0.00 0.94 0.02
#> S37-G6 1 0.0000 0.963 1.00 0.00 0.00 0.00
#> S37-G7 1 0.0000 0.963 1.00 0.00 0.00 0.00
#> S37-G8 3 0.1411 0.945 0.02 0.00 0.96 0.02
#> S37-H2 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> S37-H4 3 0.3335 0.871 0.12 0.00 0.86 0.02
#> S37-H7 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> S37-H8 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> S37-H9 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> S38-A1 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> S38-A10 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> S38-A12 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> S38-A2 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> S38-A3 3 0.2706 0.909 0.08 0.00 0.90 0.02
#> S38-A5 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> S38-A9 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> S38-B10 3 0.1913 0.937 0.04 0.00 0.94 0.02
#> S38-B11 1 0.1411 0.937 0.96 0.00 0.02 0.02
#> S38-B2 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> S38-B6 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> S38-B7 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> S38-B8 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> S38-B9 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> S38-C1 2 0.4907 0.293 0.00 0.58 0.42 0.00
#> S38-C10 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> S38-C11 3 0.3853 0.827 0.16 0.00 0.82 0.02
#> S38-C3 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> S38-C4 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> S38-C5 3 0.1913 0.937 0.04 0.00 0.94 0.02
#> S38-C6 3 0.1913 0.937 0.04 0.00 0.94 0.02
#> S38-C7 3 0.1913 0.937 0.04 0.00 0.94 0.02
#> S38-C9 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> S38-D1 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> S38-D10 3 0.4079 0.803 0.18 0.00 0.80 0.02
#> S38-D11 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> S38-D12 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> S38-D2 1 0.0000 0.963 1.00 0.00 0.00 0.00
#> S38-D4 2 0.2345 0.865 0.00 0.90 0.10 0.00
#> S38-D5 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> S38-D6 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> S38-D7 3 0.4936 0.654 0.28 0.00 0.70 0.02
#> S38-D8 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> S38-D9 1 0.0000 0.963 1.00 0.00 0.00 0.00
#> S38-E1 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> S38-E2 3 0.1913 0.937 0.04 0.00 0.94 0.02
#> S38-E3 3 0.3853 0.827 0.16 0.00 0.82 0.02
#> S38-E4 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> S38-E5 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> S38-E6 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> S38-E7 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> S38-E8 3 0.1913 0.937 0.04 0.00 0.94 0.02
#> S38-E9 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> S38-F10 1 0.0000 0.963 1.00 0.00 0.00 0.00
#> S38-F11 1 0.0707 0.952 0.98 0.00 0.00 0.02
#> S38-F2 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> S38-F3 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> S38-F5 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> S38-F6 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> S38-F7 3 0.1913 0.937 0.04 0.00 0.94 0.02
#> S38-F8 4 0.2011 0.975 0.00 0.08 0.00 0.92
#> S38-F9 1 0.0000 0.963 1.00 0.00 0.00 0.00
#> S38-G10 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> S38-G12 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> S38-G4 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> S38-G5 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> S38-G6 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> S38-G7 3 0.1913 0.937 0.04 0.00 0.94 0.02
#> S38-G8 3 0.0000 0.954 0.00 0.00 1.00 0.00
#> S38-G9 3 0.1913 0.937 0.04 0.00 0.94 0.02
#> S38-H1 1 0.1211 0.963 0.96 0.00 0.00 0.04
#> S38-H11 1 0.0707 0.952 0.98 0.00 0.00 0.02
#> S38-H2 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> S38-H3 3 0.0707 0.951 0.00 0.00 0.98 0.02
#> S38-H4 1 0.0000 0.963 1.00 0.00 0.00 0.00
#> S38-H5 4 0.1637 0.992 0.00 0.06 0.00 0.94
#> S38-H6 2 0.0000 0.983 0.00 1.00 0.00 0.00
#> S38-H8 1 0.0000 0.963 1.00 0.00 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)
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)
As soon as the classes for columns are determined, the signatures that are significantly different between subgroups can be looked for. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
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)
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 (which is done by automatically selecting number of clusters).If there are too many signatures, top_signatures = ... can be set to only show the
signatures with the highest FDRs:
# code only for demonstration
# e.g. to show the top 500 most significant rows
tb = get_signature(res, k = ..., top_signatures = 500)
If the signatures are defined as these which are uniquely high in current group, diff_method argument
can be set to "uniquely_high_in_one_group":
# code only for demonstration
tb = get_signature(res, k = ..., diff_method = "uniquely_high_in_one_group")
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")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n_sample Age(p-value) Inferred.Cell.Type(p-value) k
#> ATC:skmeans 364 1.00000 4.93e-66 2
#> ATC:skmeans 366 0.00122 1.47e-80 3
#> ATC:skmeans 362 0.00174 1.36e-79 4
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.
Parent node: Node0. Child nodes: Node011-leaf , Node012-leaf , Node013-leaf , Node021-leaf , Node022-leaf , Node031-leaf , Node032-leaf .
The object with results only for a single top-value method and a single partitioning method can be extracted as:
res = res_rh["01"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4.
#> On a matrix with 9180 rows and 129 columns.
#> Top rows (578) are extracted by 'ATC' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 150 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_partitions"
#> [7] "compare_signatures" "consensus_heatmap" "dimension_reduction"
#> [10] "functional_enrichment" "get_anno_col" "get_anno"
#> [13] "get_classes" "get_consensus" "get_matrix"
#> [16] "get_membership" "get_param" "get_signatures"
#> [19] "get_stats" "is_best_k" "is_stable_k"
#> [22] "membership_heatmap" "ncol" "nrow"
#> [25] "plot_ecdf" "predict_classes" "rownames"
#> [28] "select_partition_number" "show" "suggest_best_k"
#> [31] "test_to_known_factors" "top_rows_heatmap"
collect_plots() function collects all the plots made from res for all k (number of subgroups)
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, higher 1-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 1.00 0.976 0.990 0.4796 0.518 0.518
#> 3 3 1.00 0.981 0.992 0.3993 0.744 0.536
#> 4 4 0.79 0.758 0.871 0.0882 0.984 0.953
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 is 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 subgroup
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
#> O10-A3 2 0.000 0.996 0.00 1.00
#> O10-A9 2 0.000 0.996 0.00 1.00
#> O10-B1 1 0.000 0.979 1.00 0.00
#> O10-B12 2 0.000 0.996 0.00 1.00
#> O10-C11 2 0.000 0.996 0.00 1.00
#> O10-C2 2 0.000 0.996 0.00 1.00
#> O10-D2 2 0.000 0.996 0.00 1.00
#> O10-D8 2 0.000 0.996 0.00 1.00
#> O10-E8 2 0.000 0.996 0.00 1.00
#> O10-E9 2 0.000 0.996 0.00 1.00
#> O10-F2 2 0.000 0.996 0.00 1.00
#> O10-F4 1 0.680 0.786 0.82 0.18
#> O10-F8 2 0.000 0.996 0.00 1.00
#> O10-G1 1 0.000 0.979 1.00 0.00
#> O10-G12 1 0.000 0.979 1.00 0.00
#> O10-G2 1 0.000 0.979 1.00 0.00
#> O10-G3 1 0.000 0.979 1.00 0.00
#> O10-G4 1 0.000 0.979 1.00 0.00
#> O10-G5 1 0.000 0.979 1.00 0.00
#> O10-G7 1 0.000 0.979 1.00 0.00
#> O10-H1 1 0.000 0.979 1.00 0.00
#> O10-H4 1 0.000 0.979 1.00 0.00
#> O10-H5 1 0.000 0.979 1.00 0.00
#> O10-H6 1 0.000 0.979 1.00 0.00
#> O10-H7 1 0.000 0.979 1.00 0.00
#> O12-A2 1 0.000 0.979 1.00 0.00
#> O12-D2 1 0.000 0.979 1.00 0.00
#> O12-E1 1 0.000 0.979 1.00 0.00
#> O7-D3 2 0.827 0.639 0.26 0.74
#> O7-D5 2 0.000 0.996 0.00 1.00
#> O7-G3 1 0.000 0.979 1.00 0.00
#> O8-E1 2 0.000 0.996 0.00 1.00
#> O8-F10 1 0.000 0.979 1.00 0.00
#> O8-F9 1 0.000 0.979 1.00 0.00
#> O8-G9 1 0.000 0.979 1.00 0.00
#> O8-H1 1 0.000 0.979 1.00 0.00
#> O8-H6 2 0.000 0.996 0.00 1.00
#> O9-A2 2 0.000 0.996 0.00 1.00
#> O9-A9 2 0.000 0.996 0.00 1.00
#> O9-B10 2 0.000 0.996 0.00 1.00
#> O9-B11 2 0.000 0.996 0.00 1.00
#> O9-B3 2 0.000 0.996 0.00 1.00
#> O9-C10 2 0.000 0.996 0.00 1.00
#> O9-C3 2 0.000 0.996 0.00 1.00
#> O9-C5 2 0.000 0.996 0.00 1.00
#> O9-C9 2 0.000 0.996 0.00 1.00
#> O9-D1 1 0.242 0.944 0.96 0.04
#> O9-D10 1 0.000 0.979 1.00 0.00
#> O9-D11 2 0.000 0.996 0.00 1.00
#> O9-D5 2 0.000 0.996 0.00 1.00
#> O9-E10 2 0.000 0.996 0.00 1.00
#> O9-E11 1 0.000 0.979 1.00 0.00
#> O9-E5 2 0.000 0.996 0.00 1.00
#> O9-E7 2 0.000 0.996 0.00 1.00
#> O9-E8 1 0.000 0.979 1.00 0.00
#> O9-E9 2 0.000 0.996 0.00 1.00
#> O9-F10 2 0.000 0.996 0.00 1.00
#> O9-F12 2 0.000 0.996 0.00 1.00
#> O9-F2 2 0.000 0.996 0.00 1.00
#> O9-G10 1 0.000 0.979 1.00 0.00
#> O9-G12 2 0.000 0.996 0.00 1.00
#> O9-G2 2 0.000 0.996 0.00 1.00
#> O9-G4 1 0.000 0.979 1.00 0.00
#> O9-G6 2 0.000 0.996 0.00 1.00
#> O9-H3 1 0.943 0.456 0.64 0.36
#> O9-H9 1 0.000 0.979 1.00 0.00
#> S37-A1 2 0.000 0.996 0.00 1.00
#> S37-A10 2 0.000 0.996 0.00 1.00
#> S37-A3 2 0.000 0.996 0.00 1.00
#> S37-A9 1 0.000 0.979 1.00 0.00
#> S37-B1 1 0.722 0.757 0.80 0.20
#> S37-B10 2 0.000 0.996 0.00 1.00
#> S37-B2 2 0.000 0.996 0.00 1.00
#> S37-B4 2 0.000 0.996 0.00 1.00
#> S37-B7 2 0.000 0.996 0.00 1.00
#> S37-C10 2 0.000 0.996 0.00 1.00
#> S37-C3 2 0.000 0.996 0.00 1.00
#> S37-C4 1 0.000 0.979 1.00 0.00
#> S37-C6 2 0.000 0.996 0.00 1.00
#> S37-C7 2 0.000 0.996 0.00 1.00
#> S37-C9 1 0.000 0.979 1.00 0.00
#> S37-D10 2 0.000 0.996 0.00 1.00
#> S37-D2 2 0.141 0.976 0.02 0.98
#> S37-D4 2 0.000 0.996 0.00 1.00
#> S37-D6 2 0.000 0.996 0.00 1.00
#> S37-D8 2 0.000 0.996 0.00 1.00
#> S37-E1 2 0.000 0.996 0.00 1.00
#> S37-E11 2 0.000 0.996 0.00 1.00
#> S37-E2 1 0.827 0.661 0.74 0.26
#> S37-E3 2 0.000 0.996 0.00 1.00
#> S37-E6 2 0.000 0.996 0.00 1.00
#> S37-E9 2 0.000 0.996 0.00 1.00
#> S37-F1 1 0.000 0.979 1.00 0.00
#> S37-F10 1 0.000 0.979 1.00 0.00
#> S37-F12 2 0.000 0.996 0.00 1.00
#> S37-F2 2 0.000 0.996 0.00 1.00
#> S37-F3 2 0.000 0.996 0.00 1.00
#> S37-F5 1 0.000 0.979 1.00 0.00
#> S37-F7 2 0.000 0.996 0.00 1.00
#> S37-F9 2 0.000 0.996 0.00 1.00
#> S37-G1 2 0.000 0.996 0.00 1.00
#> S37-G10 2 0.000 0.996 0.00 1.00
#> S37-G12 2 0.000 0.996 0.00 1.00
#> S37-G3 2 0.000 0.996 0.00 1.00
#> S37-G6 2 0.000 0.996 0.00 1.00
#> S37-G7 2 0.000 0.996 0.00 1.00
#> S37-H2 1 0.000 0.979 1.00 0.00
#> S37-H7 1 0.141 0.962 0.98 0.02
#> S37-H8 1 0.000 0.979 1.00 0.00
#> S37-H9 1 0.000 0.979 1.00 0.00
#> S38-A1 1 0.000 0.979 1.00 0.00
#> S38-A10 1 0.000 0.979 1.00 0.00
#> S38-B11 2 0.000 0.996 0.00 1.00
#> S38-B6 1 0.000 0.979 1.00 0.00
#> S38-C4 2 0.000 0.996 0.00 1.00
#> S38-D12 1 0.000 0.979 1.00 0.00
#> S38-D2 2 0.000 0.996 0.00 1.00
#> S38-D8 1 0.000 0.979 1.00 0.00
#> S38-D9 2 0.000 0.996 0.00 1.00
#> S38-F10 2 0.000 0.996 0.00 1.00
#> S38-F11 2 0.000 0.996 0.00 1.00
#> S38-F3 1 0.000 0.979 1.00 0.00
#> S38-F9 2 0.000 0.996 0.00 1.00
#> S38-G10 1 0.000 0.979 1.00 0.00
#> S38-G12 1 0.000 0.979 1.00 0.00
#> S38-H1 1 0.000 0.979 1.00 0.00
#> S38-H11 2 0.000 0.996 0.00 1.00
#> S38-H4 2 0.000 0.996 0.00 1.00
#> S38-H8 2 0.000 0.996 0.00 1.00
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> O10-A3 2 0.0000 0.993 0.00 1.00 0.00
#> O10-A9 3 0.0000 0.988 0.00 0.00 1.00
#> O10-B1 1 0.4291 0.776 0.82 0.00 0.18
#> O10-B12 3 0.0000 0.988 0.00 0.00 1.00
#> O10-C11 3 0.0000 0.988 0.00 0.00 1.00
#> O10-C2 3 0.0000 0.988 0.00 0.00 1.00
#> O10-D2 2 0.0000 0.993 0.00 1.00 0.00
#> O10-D8 3 0.0000 0.988 0.00 0.00 1.00
#> O10-E8 2 0.0000 0.993 0.00 1.00 0.00
#> O10-E9 3 0.0000 0.988 0.00 0.00 1.00
#> O10-F2 3 0.0000 0.988 0.00 0.00 1.00
#> O10-F4 2 0.0000 0.993 0.00 1.00 0.00
#> O10-F8 2 0.0000 0.993 0.00 1.00 0.00
#> O10-G1 1 0.0000 0.996 1.00 0.00 0.00
#> O10-G12 1 0.0000 0.996 1.00 0.00 0.00
#> O10-G2 1 0.0000 0.996 1.00 0.00 0.00
#> O10-G3 1 0.0000 0.996 1.00 0.00 0.00
#> O10-G4 1 0.0000 0.996 1.00 0.00 0.00
#> O10-G5 1 0.0000 0.996 1.00 0.00 0.00
#> O10-G7 1 0.0000 0.996 1.00 0.00 0.00
#> O10-H1 1 0.0000 0.996 1.00 0.00 0.00
#> O10-H4 1 0.0000 0.996 1.00 0.00 0.00
#> O10-H5 1 0.0000 0.996 1.00 0.00 0.00
#> O10-H6 1 0.0000 0.996 1.00 0.00 0.00
#> O10-H7 1 0.0000 0.996 1.00 0.00 0.00
#> O12-A2 2 0.4002 0.810 0.16 0.84 0.00
#> O12-D2 1 0.0000 0.996 1.00 0.00 0.00
#> O12-E1 1 0.0000 0.996 1.00 0.00 0.00
#> O7-D3 2 0.5334 0.811 0.06 0.82 0.12
#> O7-D5 3 0.0000 0.988 0.00 0.00 1.00
#> O7-G3 1 0.0000 0.996 1.00 0.00 0.00
#> O8-E1 2 0.0000 0.993 0.00 1.00 0.00
#> O8-F10 1 0.0000 0.996 1.00 0.00 0.00
#> O8-F9 1 0.0000 0.996 1.00 0.00 0.00
#> O8-G9 1 0.0000 0.996 1.00 0.00 0.00
#> O8-H1 1 0.0000 0.996 1.00 0.00 0.00
#> O8-H6 2 0.0000 0.993 0.00 1.00 0.00
#> O9-A2 3 0.0000 0.988 0.00 0.00 1.00
#> O9-A9 3 0.0000 0.988 0.00 0.00 1.00
#> O9-B10 3 0.0000 0.988 0.00 0.00 1.00
#> O9-B11 3 0.0000 0.988 0.00 0.00 1.00
#> O9-B3 3 0.0000 0.988 0.00 0.00 1.00
#> O9-C10 3 0.0000 0.988 0.00 0.00 1.00
#> O9-C3 3 0.0000 0.988 0.00 0.00 1.00
#> O9-C5 3 0.0000 0.988 0.00 0.00 1.00
#> O9-C9 3 0.0000 0.988 0.00 0.00 1.00
#> O9-D1 3 0.6280 0.139 0.46 0.00 0.54
#> O9-D10 1 0.0000 0.996 1.00 0.00 0.00
#> O9-D11 3 0.0000 0.988 0.00 0.00 1.00
#> O9-D5 2 0.0000 0.993 0.00 1.00 0.00
#> O9-E10 3 0.0000 0.988 0.00 0.00 1.00
#> O9-E11 1 0.0000 0.996 1.00 0.00 0.00
#> O9-E5 3 0.0000 0.988 0.00 0.00 1.00
#> O9-E7 3 0.0000 0.988 0.00 0.00 1.00
#> O9-E8 1 0.0000 0.996 1.00 0.00 0.00
#> O9-E9 3 0.0000 0.988 0.00 0.00 1.00
#> O9-F10 3 0.0000 0.988 0.00 0.00 1.00
#> O9-F12 3 0.0000 0.988 0.00 0.00 1.00
#> O9-F2 3 0.0000 0.988 0.00 0.00 1.00
#> O9-G10 1 0.0000 0.996 1.00 0.00 0.00
#> O9-G12 3 0.0000 0.988 0.00 0.00 1.00
#> O9-G2 3 0.0000 0.988 0.00 0.00 1.00
#> O9-G4 1 0.0000 0.996 1.00 0.00 0.00
#> O9-G6 3 0.0000 0.988 0.00 0.00 1.00
#> O9-H3 3 0.0000 0.988 0.00 0.00 1.00
#> O9-H9 1 0.0000 0.996 1.00 0.00 0.00
#> S37-A1 2 0.0000 0.993 0.00 1.00 0.00
#> S37-A10 2 0.0000 0.993 0.00 1.00 0.00
#> S37-A3 2 0.0000 0.993 0.00 1.00 0.00
#> S37-A9 1 0.0000 0.996 1.00 0.00 0.00
#> S37-B1 3 0.0892 0.968 0.02 0.00 0.98
#> S37-B10 2 0.0000 0.993 0.00 1.00 0.00
#> S37-B2 2 0.0000 0.993 0.00 1.00 0.00
#> S37-B4 3 0.0000 0.988 0.00 0.00 1.00
#> S37-B7 2 0.0000 0.993 0.00 1.00 0.00
#> S37-C10 2 0.0000 0.993 0.00 1.00 0.00
#> S37-C3 2 0.0000 0.993 0.00 1.00 0.00
#> S37-C4 1 0.0000 0.996 1.00 0.00 0.00
#> S37-C6 2 0.0000 0.993 0.00 1.00 0.00
#> S37-C7 2 0.0000 0.993 0.00 1.00 0.00
#> S37-C9 1 0.0000 0.996 1.00 0.00 0.00
#> S37-D10 2 0.0000 0.993 0.00 1.00 0.00
#> S37-D2 2 0.0000 0.993 0.00 1.00 0.00
#> S37-D4 2 0.0000 0.993 0.00 1.00 0.00
#> S37-D6 2 0.0000 0.993 0.00 1.00 0.00
#> S37-D8 2 0.0000 0.993 0.00 1.00 0.00
#> S37-E1 2 0.0000 0.993 0.00 1.00 0.00
#> S37-E11 2 0.0000 0.993 0.00 1.00 0.00
#> S37-E2 2 0.0000 0.993 0.00 1.00 0.00
#> S37-E3 2 0.0000 0.993 0.00 1.00 0.00
#> S37-E6 3 0.0000 0.988 0.00 0.00 1.00
#> S37-E9 2 0.0000 0.993 0.00 1.00 0.00
#> S37-F1 1 0.0000 0.996 1.00 0.00 0.00
#> S37-F10 1 0.0000 0.996 1.00 0.00 0.00
#> S37-F12 3 0.0000 0.988 0.00 0.00 1.00
#> S37-F2 2 0.0000 0.993 0.00 1.00 0.00
#> S37-F3 3 0.0000 0.988 0.00 0.00 1.00
#> S37-F5 1 0.0000 0.996 1.00 0.00 0.00
#> S37-F7 2 0.0000 0.993 0.00 1.00 0.00
#> S37-F9 2 0.0000 0.993 0.00 1.00 0.00
#> S37-G1 2 0.0000 0.993 0.00 1.00 0.00
#> S37-G10 2 0.0000 0.993 0.00 1.00 0.00
#> S37-G12 2 0.0000 0.993 0.00 1.00 0.00
#> S37-G3 2 0.0000 0.993 0.00 1.00 0.00
#> S37-G6 2 0.0000 0.993 0.00 1.00 0.00
#> S37-G7 2 0.0000 0.993 0.00 1.00 0.00
#> S37-H2 1 0.0000 0.996 1.00 0.00 0.00
#> S37-H7 2 0.0000 0.993 0.00 1.00 0.00
#> S37-H8 1 0.0000 0.996 1.00 0.00 0.00
#> S37-H9 1 0.0000 0.996 1.00 0.00 0.00
#> S38-A1 1 0.0000 0.996 1.00 0.00 0.00
#> S38-A10 1 0.0000 0.996 1.00 0.00 0.00
#> S38-B11 3 0.0000 0.988 0.00 0.00 1.00
#> S38-B6 1 0.0000 0.996 1.00 0.00 0.00
#> S38-C4 2 0.0000 0.993 0.00 1.00 0.00
#> S38-D12 1 0.0000 0.996 1.00 0.00 0.00
#> S38-D2 3 0.0000 0.988 0.00 0.00 1.00
#> S38-D8 1 0.0000 0.996 1.00 0.00 0.00
#> S38-D9 2 0.0000 0.993 0.00 1.00 0.00
#> S38-F10 3 0.0000 0.988 0.00 0.00 1.00
#> S38-F11 2 0.0000 0.993 0.00 1.00 0.00
#> S38-F3 1 0.0000 0.996 1.00 0.00 0.00
#> S38-F9 3 0.0000 0.988 0.00 0.00 1.00
#> S38-G10 1 0.0000 0.996 1.00 0.00 0.00
#> S38-G12 1 0.0000 0.996 1.00 0.00 0.00
#> S38-H1 1 0.0000 0.996 1.00 0.00 0.00
#> S38-H11 3 0.0000 0.988 0.00 0.00 1.00
#> S38-H4 2 0.0000 0.993 0.00 1.00 0.00
#> S38-H8 2 0.0000 0.993 0.00 1.00 0.00
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> O10-A3 2 0.4855 0.474 0.00 0.60 0.00 0.40
#> O10-A9 3 0.4855 0.578 0.00 0.00 0.60 0.40
#> O10-B1 4 0.6262 0.597 0.06 0.00 0.40 0.54
#> O10-B12 3 0.4907 0.560 0.00 0.00 0.58 0.42
#> O10-C11 3 0.4907 0.560 0.00 0.00 0.58 0.42
#> O10-C2 3 0.4907 0.560 0.00 0.00 0.58 0.42
#> O10-D2 2 0.4855 0.448 0.00 0.60 0.00 0.40
#> O10-D8 3 0.4907 0.560 0.00 0.00 0.58 0.42
#> O10-E8 2 0.4790 0.478 0.00 0.62 0.00 0.38
#> O10-E9 3 0.4907 0.560 0.00 0.00 0.58 0.42
#> O10-F2 3 0.0000 0.778 0.00 0.00 1.00 0.00
#> O10-F4 2 0.2345 0.820 0.00 0.90 0.00 0.10
#> O10-F8 2 0.2647 0.782 0.00 0.88 0.00 0.12
#> O10-G1 1 0.2921 0.852 0.86 0.00 0.00 0.14
#> O10-G12 1 0.4134 0.743 0.74 0.00 0.00 0.26
#> O10-G2 1 0.4134 0.743 0.74 0.00 0.00 0.26
#> O10-G3 1 0.2921 0.853 0.86 0.00 0.00 0.14
#> O10-G4 1 0.2011 0.884 0.92 0.00 0.00 0.08
#> O10-G5 1 0.4134 0.743 0.74 0.00 0.00 0.26
#> O10-G7 1 0.4134 0.743 0.74 0.00 0.00 0.26
#> O10-H1 1 0.3172 0.838 0.84 0.00 0.00 0.16
#> O10-H4 1 0.3172 0.838 0.84 0.00 0.00 0.16
#> O10-H5 1 0.3172 0.838 0.84 0.00 0.00 0.16
#> O10-H6 1 0.0000 0.909 1.00 0.00 0.00 0.00
#> O10-H7 1 0.1637 0.893 0.94 0.00 0.00 0.06
#> O12-A2 2 0.4977 0.179 0.00 0.54 0.00 0.46
#> O12-D2 1 0.0000 0.909 1.00 0.00 0.00 0.00
#> O12-E1 1 0.1637 0.894 0.94 0.00 0.00 0.06
#> O7-D3 4 0.7010 0.107 0.02 0.34 0.08 0.56
#> O7-D5 3 0.0707 0.781 0.00 0.00 0.98 0.02
#> O7-G3 1 0.0000 0.909 1.00 0.00 0.00 0.00
#> O8-E1 2 0.0000 0.849 0.00 1.00 0.00 0.00
#> O8-F10 1 0.0000 0.909 1.00 0.00 0.00 0.00
#> O8-F9 1 0.0000 0.909 1.00 0.00 0.00 0.00
#> O8-G9 1 0.0000 0.909 1.00 0.00 0.00 0.00
#> O8-H1 1 0.4977 0.431 0.54 0.00 0.00 0.46
#> O8-H6 2 0.4277 0.680 0.00 0.72 0.00 0.28
#> O9-A2 3 0.0000 0.778 0.00 0.00 1.00 0.00
#> O9-A9 3 0.0000 0.778 0.00 0.00 1.00 0.00
#> O9-B10 3 0.0000 0.778 0.00 0.00 1.00 0.00
#> O9-B11 3 0.1637 0.752 0.00 0.00 0.94 0.06
#> O9-B3 3 0.3975 0.395 0.00 0.00 0.76 0.24
#> O9-C10 3 0.0707 0.781 0.00 0.00 0.98 0.02
#> O9-C3 3 0.0000 0.778 0.00 0.00 1.00 0.00
#> O9-C5 3 0.0000 0.778 0.00 0.00 1.00 0.00
#> O9-C9 3 0.3172 0.735 0.00 0.00 0.84 0.16
#> O9-D1 4 0.6262 0.598 0.06 0.00 0.40 0.54
#> O9-D10 1 0.2647 0.851 0.88 0.00 0.00 0.12
#> O9-D11 3 0.0000 0.778 0.00 0.00 1.00 0.00
#> O9-D5 2 0.0707 0.848 0.00 0.98 0.00 0.02
#> O9-E10 3 0.0000 0.778 0.00 0.00 1.00 0.00
#> O9-E11 1 0.2647 0.850 0.88 0.00 0.00 0.12
#> O9-E5 3 0.0000 0.778 0.00 0.00 1.00 0.00
#> O9-E7 3 0.0707 0.765 0.00 0.00 0.98 0.02
#> O9-E8 1 0.1637 0.890 0.94 0.00 0.00 0.06
#> O9-E9 3 0.2011 0.771 0.00 0.00 0.92 0.08
#> O9-F10 3 0.0707 0.781 0.00 0.00 0.98 0.02
#> O9-F12 3 0.3610 0.713 0.00 0.00 0.80 0.20
#> O9-F2 3 0.0000 0.778 0.00 0.00 1.00 0.00
#> O9-G10 1 0.3172 0.838 0.84 0.00 0.00 0.16
#> O9-G12 3 0.1211 0.779 0.00 0.00 0.96 0.04
#> O9-G2 3 0.0000 0.778 0.00 0.00 1.00 0.00
#> O9-G4 1 0.4332 0.776 0.80 0.00 0.04 0.16
#> O9-G6 3 0.0707 0.781 0.00 0.00 0.98 0.02
#> O9-H3 3 0.4472 0.407 0.02 0.00 0.76 0.22
#> O9-H9 1 0.0000 0.909 1.00 0.00 0.00 0.00
#> S37-A1 2 0.0707 0.847 0.00 0.98 0.00 0.02
#> S37-A10 2 0.2011 0.835 0.00 0.92 0.00 0.08
#> S37-A3 2 0.0000 0.849 0.00 1.00 0.00 0.00
#> S37-A9 1 0.0000 0.909 1.00 0.00 0.00 0.00
#> S37-B1 3 0.3335 0.681 0.02 0.00 0.86 0.12
#> S37-B10 2 0.1211 0.844 0.00 0.96 0.00 0.04
#> S37-B2 2 0.2647 0.809 0.00 0.88 0.00 0.12
#> S37-B4 3 0.2921 0.730 0.00 0.00 0.86 0.14
#> S37-B7 2 0.2345 0.825 0.00 0.90 0.00 0.10
#> S37-C10 2 0.0707 0.847 0.00 0.98 0.00 0.02
#> S37-C3 2 0.0000 0.849 0.00 1.00 0.00 0.00
#> S37-C4 1 0.0000 0.909 1.00 0.00 0.00 0.00
#> S37-C6 2 0.2345 0.823 0.00 0.90 0.00 0.10
#> S37-C7 2 0.1211 0.844 0.00 0.96 0.00 0.04
#> S37-C9 1 0.0000 0.909 1.00 0.00 0.00 0.00
#> S37-D10 2 0.0000 0.849 0.00 1.00 0.00 0.00
#> S37-D2 2 0.3975 0.674 0.00 0.76 0.00 0.24
#> S37-D4 2 0.0000 0.849 0.00 1.00 0.00 0.00
#> S37-D6 2 0.1637 0.840 0.00 0.94 0.00 0.06
#> S37-D8 2 0.2647 0.808 0.00 0.88 0.00 0.12
#> S37-E1 2 0.2011 0.837 0.00 0.92 0.00 0.08
#> S37-E11 2 0.0000 0.849 0.00 1.00 0.00 0.00
#> S37-E2 2 0.1637 0.841 0.00 0.94 0.00 0.06
#> S37-E3 2 0.1211 0.838 0.00 0.96 0.00 0.04
#> S37-E6 3 0.2011 0.770 0.00 0.00 0.92 0.08
#> S37-E9 2 0.0707 0.847 0.00 0.98 0.00 0.02
#> S37-F1 1 0.0707 0.901 0.98 0.00 0.00 0.02
#> S37-F10 1 0.2345 0.853 0.90 0.00 0.00 0.10
#> S37-F12 3 0.0707 0.781 0.00 0.00 0.98 0.02
#> S37-F2 2 0.0000 0.849 0.00 1.00 0.00 0.00
#> S37-F3 3 0.0707 0.779 0.00 0.00 0.98 0.02
#> S37-F5 1 0.1637 0.884 0.94 0.00 0.00 0.06
#> S37-F7 2 0.3172 0.774 0.00 0.84 0.00 0.16
#> S37-F9 2 0.2011 0.834 0.00 0.92 0.00 0.08
#> S37-G1 2 0.1211 0.839 0.00 0.96 0.00 0.04
#> S37-G10 2 0.0707 0.845 0.00 0.98 0.00 0.02
#> S37-G12 2 0.0000 0.849 0.00 1.00 0.00 0.00
#> S37-G3 2 0.5957 0.330 0.00 0.54 0.04 0.42
#> S37-G6 2 0.0707 0.845 0.00 0.98 0.00 0.02
#> S37-G7 2 0.2345 0.824 0.00 0.90 0.00 0.10
#> S37-H2 1 0.6323 0.263 0.50 0.06 0.00 0.44
#> S37-H7 2 0.2921 0.793 0.00 0.86 0.00 0.14
#> S37-H8 1 0.0000 0.909 1.00 0.00 0.00 0.00
#> S37-H9 1 0.0000 0.909 1.00 0.00 0.00 0.00
#> S38-A1 1 0.0000 0.909 1.00 0.00 0.00 0.00
#> S38-A10 1 0.0000 0.909 1.00 0.00 0.00 0.00
#> S38-B11 3 0.4522 0.630 0.00 0.00 0.68 0.32
#> S38-B6 1 0.0000 0.909 1.00 0.00 0.00 0.00
#> S38-C4 2 0.4907 0.414 0.00 0.58 0.00 0.42
#> S38-D12 1 0.0000 0.909 1.00 0.00 0.00 0.00
#> S38-D2 3 0.4713 0.609 0.00 0.00 0.64 0.36
#> S38-D8 1 0.0000 0.909 1.00 0.00 0.00 0.00
#> S38-D9 2 0.4855 0.448 0.00 0.60 0.00 0.40
#> S38-F10 3 0.4855 0.578 0.00 0.00 0.60 0.40
#> S38-F11 2 0.4790 0.478 0.00 0.62 0.00 0.38
#> S38-F3 1 0.0000 0.909 1.00 0.00 0.00 0.00
#> S38-F9 3 0.4907 0.560 0.00 0.00 0.58 0.42
#> S38-G10 1 0.0000 0.909 1.00 0.00 0.00 0.00
#> S38-G12 1 0.0000 0.909 1.00 0.00 0.00 0.00
#> S38-H1 1 0.0000 0.909 1.00 0.00 0.00 0.00
#> S38-H11 3 0.4855 0.578 0.00 0.00 0.60 0.40
#> S38-H4 2 0.1211 0.846 0.00 0.96 0.00 0.04
#> S38-H8 2 0.0707 0.845 0.00 0.98 0.00 0.02
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)
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)
As soon as the classes for columns are determined, the signatures that are significantly different between subgroups can be looked for. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
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)
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 (which is done by automatically selecting number of clusters).If there are too many signatures, top_signatures = ... can be set to only show the
signatures with the highest FDRs:
# code only for demonstration
# e.g. to show the top 500 most significant rows
tb = get_signature(res, k = ..., top_signatures = 500)
If the signatures are defined as these which are uniquely high in current group, diff_method argument
can be set to "uniquely_high_in_one_group":
# code only for demonstration
tb = get_signature(res, k = ..., diff_method = "uniquely_high_in_one_group")
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")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n_sample Age(p-value) Inferred.Cell.Type(p-value) k
#> ATC:skmeans 128 2.60e-01 4.38e-03 2
#> ATC:skmeans 128 4.61e-06 1.88e-19 3
#> ATC:skmeans 116 1.53e-06 4.78e-18 4
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.
Parent node: Node0. Child nodes: Node011-leaf , Node012-leaf , Node013-leaf , Node021-leaf , Node022-leaf , Node031-leaf , Node032-leaf .
The object with results only for a single top-value method and a single partitioning method can be extracted as:
res = res_rh["02"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4.
#> On a matrix with 9164 rows and 112 columns.
#> Top rows (877) are extracted by 'ATC' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 150 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_partitions"
#> [7] "compare_signatures" "consensus_heatmap" "dimension_reduction"
#> [10] "functional_enrichment" "get_anno_col" "get_anno"
#> [13] "get_classes" "get_consensus" "get_matrix"
#> [16] "get_membership" "get_param" "get_signatures"
#> [19] "get_stats" "is_best_k" "is_stable_k"
#> [22] "membership_heatmap" "ncol" "nrow"
#> [25] "plot_ecdf" "predict_classes" "rownames"
#> [28] "select_partition_number" "show" "suggest_best_k"
#> [31] "test_to_known_factors" "top_rows_heatmap"
collect_plots() function collects all the plots made from res for all k (number of subgroups)
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, higher 1-PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.972 0.988 0.498 0.506 0.506
#> 3 3 0.711 0.822 0.899 0.289 0.819 0.653
#> 4 4 0.759 0.805 0.908 0.137 0.847 0.613
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following is 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 subgroup
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
#> O10-A1 2 0.000 1.000 0.00 1.00
#> O10-A12 2 0.000 1.000 0.00 1.00
#> O10-A4 1 0.000 0.980 1.00 0.00
#> O10-C4 2 0.000 1.000 0.00 1.00
#> O10-D3 1 0.000 0.980 1.00 0.00
#> O10-F6 1 0.000 0.980 1.00 0.00
#> O12-A1 1 0.000 0.980 1.00 0.00
#> O12-A12 1 0.000 0.980 1.00 0.00
#> O12-A3 1 0.000 0.980 1.00 0.00
#> O12-B1 2 0.000 1.000 0.00 1.00
#> O12-C1 2 0.000 1.000 0.00 1.00
#> O12-D1 2 0.141 0.979 0.02 0.98
#> O12-E12 1 0.327 0.924 0.94 0.06
#> O12-F2 1 0.000 0.980 1.00 0.00
#> O12-G2 2 0.000 1.000 0.00 1.00
#> O12-H1 1 0.995 0.159 0.54 0.46
#> O12-H2 2 0.000 1.000 0.00 1.00
#> O7-A5 2 0.000 1.000 0.00 1.00
#> O7-A7 2 0.000 1.000 0.00 1.00
#> O7-A8 1 0.000 0.980 1.00 0.00
#> O7-B1 1 0.000 0.980 1.00 0.00
#> O7-B12 2 0.000 1.000 0.00 1.00
#> O7-B8 2 0.000 1.000 0.00 1.00
#> O7-B9 1 0.000 0.980 1.00 0.00
#> O7-C2 2 0.000 1.000 0.00 1.00
#> O7-C3 2 0.000 1.000 0.00 1.00
#> O7-C6 1 0.881 0.586 0.70 0.30
#> O7-D1 1 0.000 0.980 1.00 0.00
#> O7-D11 1 0.000 0.980 1.00 0.00
#> O7-D12 1 0.242 0.944 0.96 0.04
#> O7-D2 1 0.000 0.980 1.00 0.00
#> O7-E5 1 0.000 0.980 1.00 0.00
#> O7-E6 2 0.000 1.000 0.00 1.00
#> O7-F1 1 0.000 0.980 1.00 0.00
#> O7-F10 2 0.000 1.000 0.00 1.00
#> O7-F11 1 0.000 0.980 1.00 0.00
#> O7-F4 1 0.000 0.980 1.00 0.00
#> O7-G12 2 0.000 1.000 0.00 1.00
#> O7-G9 2 0.000 1.000 0.00 1.00
#> O7-H3 1 0.000 0.980 1.00 0.00
#> O7-H4 2 0.000 1.000 0.00 1.00
#> O7-H8 2 0.000 1.000 0.00 1.00
#> O8-A5 2 0.000 1.000 0.00 1.00
#> O8-A9 1 0.000 0.980 1.00 0.00
#> O8-B1 2 0.000 1.000 0.00 1.00
#> O8-C2 1 0.000 0.980 1.00 0.00
#> O8-E3 1 0.000 0.980 1.00 0.00
#> O8-E7 2 0.000 1.000 0.00 1.00
#> O8-F2 2 0.000 1.000 0.00 1.00
#> O8-F6 2 0.000 1.000 0.00 1.00
#> O8-F8 1 0.000 0.980 1.00 0.00
#> O8-H11 2 0.000 1.000 0.00 1.00
#> O8-H2 1 0.904 0.546 0.68 0.32
#> O9-A12 2 0.000 1.000 0.00 1.00
#> O9-A3 2 0.000 1.000 0.00 1.00
#> O9-A5 1 0.000 0.980 1.00 0.00
#> O9-A6 1 0.000 0.980 1.00 0.00
#> O9-B5 1 0.469 0.881 0.90 0.10
#> O9-B8 1 0.000 0.980 1.00 0.00
#> O9-D2 1 0.000 0.980 1.00 0.00
#> O9-D7 2 0.000 1.000 0.00 1.00
#> O9-D8 2 0.000 1.000 0.00 1.00
#> O9-E1 2 0.000 1.000 0.00 1.00
#> O9-E2 1 0.000 0.980 1.00 0.00
#> O9-F1 1 0.000 0.980 1.00 0.00
#> O9-F4 1 0.000 0.980 1.00 0.00
#> O9-F5 1 0.000 0.980 1.00 0.00
#> O9-G9 1 0.000 0.980 1.00 0.00
#> O9-H12 2 0.000 1.000 0.00 1.00
#> O9-H5 2 0.000 1.000 0.00 1.00
#> S37-A2 2 0.000 1.000 0.00 1.00
#> S37-A5 1 0.000 0.980 1.00 0.00
#> S37-A6 1 0.000 0.980 1.00 0.00
#> S37-A8 2 0.000 1.000 0.00 1.00
#> S37-B11 1 0.000 0.980 1.00 0.00
#> S37-B12 2 0.000 1.000 0.00 1.00
#> S37-C12 2 0.000 1.000 0.00 1.00
#> S37-C8 1 0.000 0.980 1.00 0.00
#> S37-D12 1 0.000 0.980 1.00 0.00
#> S37-E7 1 0.000 0.980 1.00 0.00
#> S37-E8 1 0.000 0.980 1.00 0.00
#> S37-G2 2 0.000 1.000 0.00 1.00
#> S37-G4 2 0.000 1.000 0.00 1.00
#> S38-A12 2 0.000 1.000 0.00 1.00
#> S38-A2 1 0.000 0.980 1.00 0.00
#> S38-A5 1 0.000 0.980 1.00 0.00
#> S38-A9 1 0.000 0.980 1.00 0.00
#> S38-B2 1 0.000 0.980 1.00 0.00
#> S38-B7 1 0.000 0.980 1.00 0.00
#> S38-B8 1 0.000 0.980 1.00 0.00
#> S38-B9 2 0.000 1.000 0.00 1.00
#> S38-C3 1 0.000 0.980 1.00 0.00
#> S38-C9 2 0.000 1.000 0.00 1.00
#> S38-D1 1 0.000 0.980 1.00 0.00
#> S38-D5 1 0.000 0.980 1.00 0.00
#> S38-D6 1 0.000 0.980 1.00 0.00
#> S38-E1 1 0.000 0.980 1.00 0.00
#> S38-E4 1 0.000 0.980 1.00 0.00
#> S38-E5 2 0.000 1.000 0.00 1.00
#> S38-E6 2 0.000 1.000 0.00 1.00
#> S38-E7 1 0.000 0.980 1.00 0.00
#> S38-E9 2 0.000 1.000 0.00 1.00
#> S38-F2 1 0.000 0.980 1.00 0.00
#> S38-F5 2 0.000 1.000 0.00 1.00
#> S38-F6 1 0.000 0.980 1.00 0.00
#> S38-F8 1 0.000 0.980 1.00 0.00
#> S38-G4 1 0.000 0.980 1.00 0.00
#> S38-G5 1 0.000 0.980 1.00 0.00
#> S38-G6 2 0.000 1.000 0.00 1.00
#> S38-H2 1 0.000 0.980 1.00 0.00
#> S38-H5 2 0.000 1.000 0.00 1.00
#> S38-H6 1 0.000 0.980 1.00 0.00
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> O10-A1 3 0.0892 0.7458 0.00 0.02 0.98
#> O10-A12 3 0.2537 0.6988 0.00 0.08 0.92
#> O10-A4 1 0.0000 0.9404 1.00 0.00 0.00
#> O10-C4 2 0.2959 0.8623 0.00 0.90 0.10
#> O10-D3 1 0.0000 0.9404 1.00 0.00 0.00
#> O10-F6 1 0.0000 0.9404 1.00 0.00 0.00
#> O12-A1 1 0.0000 0.9404 1.00 0.00 0.00
#> O12-A12 1 0.0000 0.9404 1.00 0.00 0.00
#> O12-A3 3 0.4002 0.7621 0.16 0.00 0.84
#> O12-B1 2 0.0000 0.8567 0.00 1.00 0.00
#> O12-C1 2 0.0000 0.8567 0.00 1.00 0.00
#> O12-D1 2 0.3686 0.6969 0.14 0.86 0.00
#> O12-E12 1 0.4796 0.6878 0.78 0.22 0.00
#> O12-F2 1 0.0000 0.9404 1.00 0.00 0.00
#> O12-G2 2 0.0000 0.8567 0.00 1.00 0.00
#> O12-H1 1 0.5560 0.5660 0.70 0.30 0.00
#> O12-H2 2 0.5706 0.7607 0.00 0.68 0.32
#> O7-A5 2 0.5216 0.8285 0.00 0.74 0.26
#> O7-A7 2 0.5216 0.8285 0.00 0.74 0.26
#> O7-A8 3 0.5560 0.6345 0.30 0.00 0.70
#> O7-B1 3 0.4796 0.7224 0.22 0.00 0.78
#> O7-B12 2 0.5216 0.8285 0.00 0.74 0.26
#> O7-B8 2 0.5216 0.8285 0.00 0.74 0.26
#> O7-B9 3 0.3340 0.7782 0.12 0.00 0.88
#> O7-C2 2 0.5216 0.8285 0.00 0.74 0.26
#> O7-C3 2 0.5216 0.8285 0.00 0.74 0.26
#> O7-C6 3 0.0000 0.7563 0.00 0.00 1.00
#> O7-D1 1 0.0000 0.9404 1.00 0.00 0.00
#> O7-D11 3 0.2959 0.7775 0.10 0.00 0.90
#> O7-D12 3 0.0000 0.7563 0.00 0.00 1.00
#> O7-D2 1 0.2959 0.8723 0.90 0.00 0.10
#> O7-E5 1 0.5397 0.5866 0.72 0.00 0.28
#> O7-E6 2 0.2537 0.8617 0.00 0.92 0.08
#> O7-F1 1 0.0000 0.9404 1.00 0.00 0.00
#> O7-F10 2 0.5216 0.8285 0.00 0.74 0.26
#> O7-F11 1 0.0000 0.9404 1.00 0.00 0.00
#> O7-F4 3 0.5397 0.6647 0.28 0.00 0.72
#> O7-G12 3 0.2537 0.6988 0.00 0.08 0.92
#> O7-G9 2 0.5216 0.8285 0.00 0.74 0.26
#> O7-H3 1 0.3340 0.8500 0.88 0.00 0.12
#> O7-H4 2 0.1529 0.8612 0.00 0.96 0.04
#> O7-H8 2 0.5216 0.8285 0.00 0.74 0.26
#> O8-A5 2 0.0000 0.8567 0.00 1.00 0.00
#> O8-A9 1 0.2066 0.9079 0.94 0.00 0.06
#> O8-B1 2 0.0000 0.8567 0.00 1.00 0.00
#> O8-C2 1 0.0000 0.9404 1.00 0.00 0.00
#> O8-E3 1 0.1529 0.9200 0.96 0.00 0.04
#> O8-E7 2 0.5216 0.8285 0.00 0.74 0.26
#> O8-F2 2 0.2537 0.8629 0.00 0.92 0.08
#> O8-F6 3 0.2066 0.7167 0.00 0.06 0.94
#> O8-F8 3 0.5216 0.6872 0.26 0.00 0.74
#> O8-H11 2 0.4002 0.8569 0.00 0.84 0.16
#> O8-H2 3 0.0000 0.7563 0.00 0.00 1.00
#> O9-A12 2 0.4002 0.8569 0.00 0.84 0.16
#> O9-A3 2 0.0000 0.8567 0.00 1.00 0.00
#> O9-A5 1 0.0000 0.9404 1.00 0.00 0.00
#> O9-A6 1 0.2066 0.9079 0.94 0.00 0.06
#> O9-B5 3 0.0000 0.7563 0.00 0.00 1.00
#> O9-B8 1 0.0000 0.9404 1.00 0.00 0.00
#> O9-D2 1 0.0000 0.9404 1.00 0.00 0.00
#> O9-D7 2 0.0000 0.8567 0.00 1.00 0.00
#> O9-D8 2 0.0000 0.8567 0.00 1.00 0.00
#> O9-E1 2 0.0000 0.8567 0.00 1.00 0.00
#> O9-E2 1 0.0000 0.9404 1.00 0.00 0.00
#> O9-F1 1 0.4796 0.6852 0.78 0.22 0.00
#> O9-F4 1 0.0000 0.9404 1.00 0.00 0.00
#> O9-F5 1 0.1529 0.9211 0.96 0.00 0.04
#> O9-G9 1 0.0000 0.9404 1.00 0.00 0.00
#> O9-H12 2 0.5216 0.8285 0.00 0.74 0.26
#> O9-H5 2 0.0000 0.8567 0.00 1.00 0.00
#> S37-A2 2 0.0000 0.8567 0.00 1.00 0.00
#> S37-A5 1 0.2537 0.8918 0.92 0.00 0.08
#> S37-A6 1 0.0000 0.9404 1.00 0.00 0.00
#> S37-A8 2 0.0000 0.8567 0.00 1.00 0.00
#> S37-B11 1 0.4551 0.7883 0.84 0.02 0.14
#> S37-B12 2 0.4291 0.8531 0.00 0.82 0.18
#> S37-C12 2 0.3340 0.8617 0.00 0.88 0.12
#> S37-C8 1 0.0000 0.9404 1.00 0.00 0.00
#> S37-D12 1 0.2537 0.8918 0.92 0.00 0.08
#> S37-E7 1 0.0000 0.9404 1.00 0.00 0.00
#> S37-E8 1 0.0000 0.9404 1.00 0.00 0.00
#> S37-G2 2 0.0000 0.8567 0.00 1.00 0.00
#> S37-G4 2 0.0000 0.8567 0.00 1.00 0.00
#> S38-A12 2 0.5216 0.8285 0.00 0.74 0.26
#> S38-A2 1 0.0000 0.9404 1.00 0.00 0.00
#> S38-A5 1 0.1529 0.9209 0.96 0.00 0.04
#> S38-A9 1 0.0892 0.9314 0.98 0.00 0.02
#> S38-B2 1 0.2066 0.9079 0.94 0.00 0.06
#> S38-B7 3 0.5216 0.6872 0.26 0.00 0.74
#> S38-B8 1 0.6302 -0.0649 0.52 0.00 0.48
#> S38-B9 3 0.6309 -0.4318 0.00 0.50 0.50
#> S38-C3 1 0.2066 0.9079 0.94 0.00 0.06
#> S38-C9 3 0.2537 0.6988 0.00 0.08 0.92
#> S38-D1 1 0.0000 0.9404 1.00 0.00 0.00
#> S38-D5 1 0.0000 0.9404 1.00 0.00 0.00
#> S38-D6 1 0.0000 0.9404 1.00 0.00 0.00
#> S38-E1 1 0.0000 0.9404 1.00 0.00 0.00
#> S38-E4 1 0.0000 0.9404 1.00 0.00 0.00
#> S38-E5 2 0.4796 0.8417 0.00 0.78 0.22
#> S38-E6 2 0.5216 0.8285 0.00 0.74 0.26
#> S38-E7 1 0.0000 0.9404 1.00 0.00 0.00
#> S38-E9 2 0.0000 0.8567 0.00 1.00 0.00
#> S38-F2 1 0.0000 0.9404 1.00 0.00 0.00
#> S38-F5 2 0.0000 0.8567 0.00 1.00 0.00
#> S38-F6 3 0.5216 0.6872 0.26 0.00 0.74
#> S38-F8 3 0.5835 0.5793 0.34 0.00 0.66
#> S38-G4 3 0.5397 0.6647 0.28 0.00 0.72
#> S38-G5 1 0.0000 0.9404 1.00 0.00 0.00
#> S38-G6 2 0.5216 0.8285 0.00 0.74 0.26
#> S38-H2 1 0.0892 0.9314 0.98 0.00 0.02
#> S38-H5 3 0.4291 0.5481 0.00 0.18 0.82
#> S38-H6 1 0.0000 0.9404 1.00 0.00 0.00
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> O10-A1 3 0.5860 0.266 0.00 0.38 0.58 0.04
#> O10-A12 2 0.3606 0.784 0.00 0.84 0.14 0.02
#> O10-A4 1 0.0000 0.904 1.00 0.00 0.00 0.00
#> O10-C4 2 0.3610 0.730 0.00 0.80 0.00 0.20
#> O10-D3 1 0.0000 0.904 1.00 0.00 0.00 0.00
#> O10-F6 1 0.0000 0.904 1.00 0.00 0.00 0.00
#> O12-A1 1 0.0000 0.904 1.00 0.00 0.00 0.00
#> O12-A12 1 0.0707 0.897 0.98 0.00 0.02 0.00
#> O12-A3 3 0.0707 0.897 0.00 0.00 0.98 0.02
#> O12-B1 4 0.3975 0.663 0.00 0.24 0.00 0.76
#> O12-C1 4 0.0707 0.885 0.00 0.02 0.00 0.98
#> O12-D1 4 0.0707 0.873 0.02 0.00 0.00 0.98
#> O12-E12 4 0.4977 0.120 0.46 0.00 0.00 0.54
#> O12-F2 1 0.0000 0.904 1.00 0.00 0.00 0.00
#> O12-G2 4 0.2921 0.794 0.00 0.14 0.00 0.86
#> O12-H1 4 0.0707 0.873 0.02 0.00 0.00 0.98
#> O12-H2 2 0.0707 0.884 0.00 0.98 0.02 0.00
#> O7-A5 2 0.0000 0.891 0.00 1.00 0.00 0.00
#> O7-A7 2 0.0000 0.891 0.00 1.00 0.00 0.00
#> O7-A8 3 0.1211 0.879 0.04 0.00 0.96 0.00
#> O7-B1 3 0.0000 0.899 0.00 0.00 1.00 0.00
#> O7-B12 2 0.0000 0.891 0.00 1.00 0.00 0.00
#> O7-B8 2 0.0000 0.891 0.00 1.00 0.00 0.00
#> O7-B9 3 0.0000 0.899 0.00 0.00 1.00 0.00
#> O7-C2 2 0.0000 0.891 0.00 1.00 0.00 0.00
#> O7-C3 2 0.0000 0.891 0.00 1.00 0.00 0.00
#> O7-C6 3 0.0707 0.897 0.00 0.00 0.98 0.02
#> O7-D1 1 0.0000 0.904 1.00 0.00 0.00 0.00
#> O7-D11 3 0.0707 0.897 0.00 0.00 0.98 0.02
#> O7-D12 3 0.0000 0.899 0.00 0.00 1.00 0.00
#> O7-D2 1 0.4994 0.218 0.52 0.00 0.48 0.00
#> O7-E5 3 0.3975 0.625 0.24 0.00 0.76 0.00
#> O7-E6 4 0.4713 0.425 0.00 0.36 0.00 0.64
#> O7-F1 1 0.0000 0.904 1.00 0.00 0.00 0.00
#> O7-F10 2 0.0000 0.891 0.00 1.00 0.00 0.00
#> O7-F11 1 0.2647 0.843 0.88 0.00 0.12 0.00
#> O7-F4 3 0.0707 0.891 0.02 0.00 0.98 0.00
#> O7-G12 2 0.3037 0.823 0.00 0.88 0.10 0.02
#> O7-G9 2 0.0000 0.891 0.00 1.00 0.00 0.00
#> O7-H3 1 0.4907 0.408 0.58 0.00 0.42 0.00
#> O7-H4 2 0.4948 0.228 0.00 0.56 0.00 0.44
#> O7-H8 2 0.0000 0.891 0.00 1.00 0.00 0.00
#> O8-A5 4 0.1211 0.881 0.00 0.04 0.00 0.96
#> O8-A9 1 0.3975 0.737 0.76 0.00 0.24 0.00
#> O8-B1 4 0.1211 0.881 0.00 0.04 0.00 0.96
#> O8-C2 1 0.0000 0.904 1.00 0.00 0.00 0.00
#> O8-E3 1 0.3801 0.750 0.78 0.00 0.22 0.00
#> O8-E7 2 0.0000 0.891 0.00 1.00 0.00 0.00
#> O8-F2 2 0.4134 0.639 0.00 0.74 0.00 0.26
#> O8-F6 2 0.5487 0.328 0.00 0.58 0.40 0.02
#> O8-F8 3 0.0000 0.899 0.00 0.00 1.00 0.00
#> O8-H11 2 0.1637 0.862 0.00 0.94 0.00 0.06
#> O8-H2 3 0.0707 0.897 0.00 0.00 0.98 0.02
#> O9-A12 2 0.2647 0.816 0.00 0.88 0.00 0.12
#> O9-A3 4 0.0707 0.885 0.00 0.02 0.00 0.98
#> O9-A5 1 0.0000 0.904 1.00 0.00 0.00 0.00
#> O9-A6 1 0.4134 0.711 0.74 0.00 0.26 0.00
#> O9-B5 3 0.0707 0.897 0.00 0.00 0.98 0.02
#> O9-B8 1 0.0707 0.897 0.98 0.00 0.02 0.00
#> O9-D2 1 0.0707 0.897 0.98 0.00 0.02 0.00
#> O9-D7 2 0.4855 0.348 0.00 0.60 0.00 0.40
#> O9-D8 2 0.4790 0.404 0.00 0.62 0.00 0.38
#> O9-E1 4 0.0707 0.885 0.00 0.02 0.00 0.98
#> O9-E2 1 0.0000 0.904 1.00 0.00 0.00 0.00
#> O9-F1 4 0.2921 0.762 0.14 0.00 0.00 0.86
#> O9-F4 1 0.0000 0.904 1.00 0.00 0.00 0.00
#> O9-F5 1 0.3400 0.796 0.82 0.00 0.18 0.00
#> O9-G9 1 0.0000 0.904 1.00 0.00 0.00 0.00
#> O9-H12 2 0.0000 0.891 0.00 1.00 0.00 0.00
#> O9-H5 4 0.0707 0.885 0.00 0.02 0.00 0.98
#> S37-A2 4 0.0707 0.885 0.00 0.02 0.00 0.98
#> S37-A5 1 0.3975 0.731 0.76 0.00 0.24 0.00
#> S37-A6 1 0.0000 0.904 1.00 0.00 0.00 0.00
#> S37-A8 4 0.0707 0.885 0.00 0.02 0.00 0.98
#> S37-B11 1 0.4894 0.722 0.78 0.00 0.12 0.10
#> S37-B12 2 0.1637 0.863 0.00 0.94 0.00 0.06
#> S37-C12 2 0.2011 0.848 0.00 0.92 0.00 0.08
#> S37-C8 1 0.0000 0.904 1.00 0.00 0.00 0.00
#> S37-D12 1 0.4790 0.483 0.62 0.00 0.38 0.00
#> S37-E7 1 0.0000 0.904 1.00 0.00 0.00 0.00
#> S37-E8 1 0.0000 0.904 1.00 0.00 0.00 0.00
#> S37-G2 4 0.4522 0.517 0.00 0.32 0.00 0.68
#> S37-G4 4 0.0707 0.885 0.00 0.02 0.00 0.98
#> S38-A12 2 0.0000 0.891 0.00 1.00 0.00 0.00
#> S38-A2 1 0.0000 0.904 1.00 0.00 0.00 0.00
#> S38-A5 1 0.4624 0.568 0.66 0.00 0.34 0.00
#> S38-A9 1 0.3172 0.813 0.84 0.00 0.16 0.00
#> S38-B2 1 0.4277 0.673 0.72 0.00 0.28 0.00
#> S38-B7 3 0.0000 0.899 0.00 0.00 1.00 0.00
#> S38-B8 3 0.3801 0.669 0.22 0.00 0.78 0.00
#> S38-B9 2 0.0707 0.882 0.00 0.98 0.00 0.02
#> S38-C3 1 0.3975 0.735 0.76 0.00 0.24 0.00
#> S38-C9 2 0.3335 0.805 0.00 0.86 0.12 0.02
#> S38-D1 1 0.0000 0.904 1.00 0.00 0.00 0.00
#> S38-D5 1 0.0000 0.904 1.00 0.00 0.00 0.00
#> S38-D6 1 0.0000 0.904 1.00 0.00 0.00 0.00
#> S38-E1 1 0.0707 0.897 0.98 0.00 0.02 0.00
#> S38-E4 1 0.0000 0.904 1.00 0.00 0.00 0.00
#> S38-E5 2 0.0000 0.891 0.00 1.00 0.00 0.00
#> S38-E6 2 0.0000 0.891 0.00 1.00 0.00 0.00
#> S38-E7 1 0.0000 0.904 1.00 0.00 0.00 0.00
#> S38-E9 4 0.1211 0.881 0.00 0.04 0.00 0.96
#> S38-F2 1 0.0000 0.904 1.00 0.00 0.00 0.00
#> S38-F5 4 0.1211 0.881 0.00 0.04 0.00 0.96
#> S38-F6 3 0.0707 0.897 0.00 0.00 0.98 0.02
#> S38-F8 3 0.4936 0.604 0.28 0.00 0.70 0.02
#> S38-G4 3 0.1637 0.867 0.06 0.00 0.94 0.00
#> S38-G5 1 0.0000 0.904 1.00 0.00 0.00 0.00
#> S38-G6 2 0.0000 0.891 0.00 1.00 0.00 0.00
#> S38-H2 1 0.2011 0.868 0.92 0.00 0.08 0.00
#> S38-H5 2 0.1913 0.864 0.00 0.94 0.04 0.02
#> S38-H6 1 0.0000 0.904 1.00 0.00 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)
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)
As soon as the classes for columns are determined, the signatures that are significantly different between subgroups can be looked for. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
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)
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 (which is done by automatically selecting number of clusters).If there are too many signatures, top_signatures = ... can be set to only show the
signatures with the highest FDRs:
# code only for demonstration
# e.g. to show the top 500 most significant rows
tb = get_signature(res, k = ..., top_signatures = 500)
If the signatures are defined as these which are uniquely high in current group, diff_method argument
can be set to "uniquely_high_in_one_group":
# code only for demonstration
tb = get_signature(res, k = ..., diff_method = "uniquely_high_in_one_group")
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")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n_sample Age(p-value) Inferred.Cell.Type(p-value) k
#> ATC:skmeans 111 0.293 6.16e-03 2
#> ATC:skmeans 110 0.192 1.33e-03 3
#> ATC:skmeans 102 0.309 4.29e-08 4
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.
Parent node: Node0. Child nodes: Node011-leaf , Node012-leaf , Node013-leaf , Node021-leaf , Node022-leaf , Node031-leaf , Node032-leaf .
The object with results only for a single top-value method and a single partitioning method can be extracted as:
res = res_rh["03"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4.
#> On a matrix with 9177 rows and 126 columns.
#> Top rows (644) are extracted by 'ATC' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 150 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_partitions"
#> [7] "compare_signatures" "consensus_heatmap" "dimension_reduction"
#> [10] "functional_enrichment" "get_anno_col" "get_anno"
#> [13] "get_classes" "get_consensus" "get_matrix"
#> [16] "get_membership" "get_param" "get_signatures"
#> [19] "get_stats" "is_best_k" "is_stable_k"
#> [22] "membership_heatmap" "ncol" "nrow"
#> [25] "plot_ecdf" "predict_classes" "rownames"
#> [28] "select_partition_number" "show" "suggest_best_k"
#> [31] "test_to_known_factors" "top_rows_heatmap"
collect_plots() function collects all the plots made from res for all k (number of subgroups)
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, higher 1-PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.999 0.968 0.986 0.504 0.496 0.496
#> 3 3 0.848 0.867 0.940 0.251 0.851 0.707
#> 4 4 0.698 0.763 0.888 0.127 0.890 0.720
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following is 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 subgroup
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
#> O10-A11 1 0.000 0.981 1.00 0.00
#> O10-A5 2 0.000 0.990 0.00 1.00
#> O10-A7 2 0.000 0.990 0.00 1.00
#> O10-A8 2 0.000 0.990 0.00 1.00
#> O10-B10 2 0.000 0.990 0.00 1.00
#> O10-B11 2 0.000 0.990 0.00 1.00
#> O10-B2 2 0.000 0.990 0.00 1.00
#> O10-B5 2 0.000 0.990 0.00 1.00
#> O10-B6 1 0.327 0.924 0.94 0.06
#> O10-B7 2 0.000 0.990 0.00 1.00
#> O10-B9 2 0.000 0.990 0.00 1.00
#> O10-C10 2 0.000 0.990 0.00 1.00
#> O10-C12 2 0.000 0.990 0.00 1.00
#> O10-C5 2 0.000 0.990 0.00 1.00
#> O10-C6 2 0.000 0.990 0.00 1.00
#> O10-C9 2 0.000 0.990 0.00 1.00
#> O10-D1 2 0.000 0.990 0.00 1.00
#> O10-D11 2 0.000 0.990 0.00 1.00
#> O10-D12 2 0.000 0.990 0.00 1.00
#> O10-D5 2 0.000 0.990 0.00 1.00
#> O10-D6 2 0.000 0.990 0.00 1.00
#> O10-D9 2 0.000 0.990 0.00 1.00
#> O10-E1 2 0.000 0.990 0.00 1.00
#> O10-E11 2 0.000 0.990 0.00 1.00
#> O10-E12 2 0.000 0.990 0.00 1.00
#> O10-E6 2 0.000 0.990 0.00 1.00
#> O10-F1 1 0.000 0.981 1.00 0.00
#> O10-F11 1 0.000 0.981 1.00 0.00
#> O10-F12 2 0.141 0.973 0.02 0.98
#> O10-F5 1 0.000 0.981 1.00 0.00
#> O10-F9 2 0.000 0.990 0.00 1.00
#> O12-B12 1 0.000 0.981 1.00 0.00
#> O12-F12 1 0.000 0.981 1.00 0.00
#> O7-A3 2 0.000 0.990 0.00 1.00
#> O7-A9 1 0.000 0.981 1.00 0.00
#> O7-B11 2 0.000 0.990 0.00 1.00
#> O7-B6 2 0.000 0.990 0.00 1.00
#> O7-B7 2 0.000 0.990 0.00 1.00
#> O7-C1 1 0.000 0.981 1.00 0.00
#> O7-C11 2 0.000 0.990 0.00 1.00
#> O7-C7 2 0.000 0.990 0.00 1.00
#> O7-D4 1 0.000 0.981 1.00 0.00
#> O7-E10 2 0.000 0.990 0.00 1.00
#> O7-E11 2 0.000 0.990 0.00 1.00
#> O7-F2 1 0.000 0.981 1.00 0.00
#> O7-F3 1 0.000 0.981 1.00 0.00
#> O7-F7 2 0.000 0.990 0.00 1.00
#> O7-F9 2 0.000 0.990 0.00 1.00
#> O8-A2 1 0.000 0.981 1.00 0.00
#> O8-A3 2 0.827 0.649 0.26 0.74
#> O8-A8 2 0.242 0.955 0.04 0.96
#> O8-B2 1 0.000 0.981 1.00 0.00
#> O8-B4 2 0.000 0.990 0.00 1.00
#> O8-B6 2 0.327 0.935 0.06 0.94
#> O8-B7 2 0.000 0.990 0.00 1.00
#> O8-B9 2 0.000 0.990 0.00 1.00
#> O8-C11 1 0.904 0.543 0.68 0.32
#> O8-C12 2 0.000 0.990 0.00 1.00
#> O8-C3 1 0.827 0.662 0.74 0.26
#> O8-C4 1 0.000 0.981 1.00 0.00
#> O8-C5 2 0.000 0.990 0.00 1.00
#> O8-C6 2 0.141 0.973 0.02 0.98
#> O8-C8 2 0.000 0.990 0.00 1.00
#> O8-D3 1 0.000 0.981 1.00 0.00
#> O8-D5 1 0.000 0.981 1.00 0.00
#> O8-D6 1 0.000 0.981 1.00 0.00
#> O8-D9 1 0.000 0.981 1.00 0.00
#> O8-E11 2 0.242 0.955 0.04 0.96
#> O8-E2 1 0.000 0.981 1.00 0.00
#> O8-E5 1 0.000 0.981 1.00 0.00
#> O8-E9 2 0.000 0.990 0.00 1.00
#> O8-F11 2 0.000 0.990 0.00 1.00
#> O8-F12 2 0.000 0.990 0.00 1.00
#> O8-F3 2 0.000 0.990 0.00 1.00
#> O8-G1 1 0.000 0.981 1.00 0.00
#> O8-G12 2 0.000 0.990 0.00 1.00
#> O8-G5 2 0.000 0.990 0.00 1.00
#> O9-A10 1 0.000 0.981 1.00 0.00
#> O9-A8 1 0.000 0.981 1.00 0.00
#> O9-B12 1 0.000 0.981 1.00 0.00
#> O9-B2 1 0.000 0.981 1.00 0.00
#> O9-B6 1 0.000 0.981 1.00 0.00
#> O9-B7 1 0.000 0.981 1.00 0.00
#> O9-C2 1 0.000 0.981 1.00 0.00
#> O9-C4 1 0.000 0.981 1.00 0.00
#> O9-C6 1 0.000 0.981 1.00 0.00
#> O9-D12 1 0.000 0.981 1.00 0.00
#> O9-D6 1 0.000 0.981 1.00 0.00
#> O9-E12 1 0.000 0.981 1.00 0.00
#> O9-E4 1 0.000 0.981 1.00 0.00
#> O9-F9 1 0.000 0.981 1.00 0.00
#> O9-G3 1 0.000 0.981 1.00 0.00
#> O9-G7 1 0.000 0.981 1.00 0.00
#> S37-A4 1 0.000 0.981 1.00 0.00
#> S37-A7 1 0.000 0.981 1.00 0.00
#> S37-B3 1 0.000 0.981 1.00 0.00
#> S37-B5 1 0.000 0.981 1.00 0.00
#> S37-B6 1 0.000 0.981 1.00 0.00
#> S37-B9 1 0.000 0.981 1.00 0.00
#> S37-D11 1 0.000 0.981 1.00 0.00
#> S37-D9 1 0.000 0.981 1.00 0.00
#> S37-E10 1 0.000 0.981 1.00 0.00
#> S37-E5 1 0.000 0.981 1.00 0.00
#> S37-G5 1 0.000 0.981 1.00 0.00
#> S37-G8 1 0.000 0.981 1.00 0.00
#> S37-H4 1 0.000 0.981 1.00 0.00
#> S38-A3 1 0.000 0.981 1.00 0.00
#> S38-B10 2 0.327 0.934 0.06 0.94
#> S38-C1 2 0.469 0.889 0.10 0.90
#> S38-C10 2 0.000 0.990 0.00 1.00
#> S38-C11 2 0.000 0.990 0.00 1.00
#> S38-C5 2 0.000 0.990 0.00 1.00
#> S38-C6 1 0.000 0.981 1.00 0.00
#> S38-C7 1 0.000 0.981 1.00 0.00
#> S38-D10 2 0.000 0.990 0.00 1.00
#> S38-D11 2 0.000 0.990 0.00 1.00
#> S38-D4 1 0.000 0.981 1.00 0.00
#> S38-D7 1 0.000 0.981 1.00 0.00
#> S38-E2 1 0.000 0.981 1.00 0.00
#> S38-E3 1 0.855 0.622 0.72 0.28
#> S38-E8 1 0.000 0.981 1.00 0.00
#> S38-F7 1 0.827 0.661 0.74 0.26
#> S38-G7 2 0.000 0.990 0.00 1.00
#> S38-G8 1 0.000 0.981 1.00 0.00
#> S38-G9 2 0.000 0.990 0.00 1.00
#> S38-H3 1 0.000 0.981 1.00 0.00
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> O10-A11 1 0.1529 0.925 0.96 0.00 0.04
#> O10-A5 2 0.5016 0.679 0.00 0.76 0.24
#> O10-A7 2 0.0000 0.939 0.00 1.00 0.00
#> O10-A8 2 0.0000 0.939 0.00 1.00 0.00
#> O10-B10 2 0.0000 0.939 0.00 1.00 0.00
#> O10-B11 2 0.0000 0.939 0.00 1.00 0.00
#> O10-B2 2 0.0000 0.939 0.00 1.00 0.00
#> O10-B5 2 0.0000 0.939 0.00 1.00 0.00
#> O10-B6 1 0.5948 0.445 0.64 0.36 0.00
#> O10-B7 2 0.0892 0.927 0.00 0.98 0.02
#> O10-B9 2 0.0000 0.939 0.00 1.00 0.00
#> O10-C10 2 0.0000 0.939 0.00 1.00 0.00
#> O10-C12 2 0.0000 0.939 0.00 1.00 0.00
#> O10-C5 2 0.0000 0.939 0.00 1.00 0.00
#> O10-C6 2 0.0000 0.939 0.00 1.00 0.00
#> O10-C9 2 0.0000 0.939 0.00 1.00 0.00
#> O10-D1 2 0.0000 0.939 0.00 1.00 0.00
#> O10-D11 2 0.0000 0.939 0.00 1.00 0.00
#> O10-D12 2 0.0000 0.939 0.00 1.00 0.00
#> O10-D5 2 0.3340 0.838 0.00 0.88 0.12
#> O10-D6 2 0.0892 0.927 0.00 0.98 0.02
#> O10-D9 2 0.0000 0.939 0.00 1.00 0.00
#> O10-E1 2 0.0892 0.927 0.00 0.98 0.02
#> O10-E11 2 0.0000 0.939 0.00 1.00 0.00
#> O10-E12 2 0.0000 0.939 0.00 1.00 0.00
#> O10-E6 2 0.0000 0.939 0.00 1.00 0.00
#> O10-F1 1 0.0000 0.951 1.00 0.00 0.00
#> O10-F11 1 0.0000 0.951 1.00 0.00 0.00
#> O10-F12 2 0.4555 0.735 0.00 0.80 0.20
#> O10-F5 1 0.0000 0.951 1.00 0.00 0.00
#> O10-F9 3 0.2537 0.858 0.00 0.08 0.92
#> O12-B12 1 0.0000 0.951 1.00 0.00 0.00
#> O12-F12 1 0.0000 0.951 1.00 0.00 0.00
#> O7-A3 2 0.3572 0.871 0.04 0.90 0.06
#> O7-A9 1 0.0892 0.941 0.98 0.00 0.02
#> O7-B11 2 0.0000 0.939 0.00 1.00 0.00
#> O7-B6 2 0.5216 0.631 0.00 0.74 0.26
#> O7-B7 3 0.5835 0.524 0.00 0.34 0.66
#> O7-C1 1 0.0892 0.941 0.98 0.00 0.02
#> O7-C11 2 0.0000 0.939 0.00 1.00 0.00
#> O7-C7 2 0.1529 0.920 0.00 0.96 0.04
#> O7-D4 1 0.0000 0.951 1.00 0.00 0.00
#> O7-E10 3 0.6302 0.124 0.00 0.48 0.52
#> O7-E11 2 0.0000 0.939 0.00 1.00 0.00
#> O7-F2 1 0.5397 0.613 0.72 0.00 0.28
#> O7-F3 1 0.0892 0.941 0.98 0.00 0.02
#> O7-F7 2 0.0892 0.927 0.00 0.98 0.02
#> O7-F9 2 0.2959 0.860 0.00 0.90 0.10
#> O8-A2 3 0.6244 0.158 0.44 0.00 0.56
#> O8-A3 3 0.0892 0.880 0.00 0.02 0.98
#> O8-A8 3 0.0892 0.880 0.00 0.02 0.98
#> O8-B2 1 0.4555 0.747 0.80 0.00 0.20
#> O8-B4 3 0.2959 0.845 0.00 0.10 0.90
#> O8-B6 3 0.6229 0.631 0.02 0.28 0.70
#> O8-B7 3 0.0892 0.880 0.00 0.02 0.98
#> O8-B9 2 0.0000 0.939 0.00 1.00 0.00
#> O8-C11 3 0.0892 0.869 0.02 0.00 0.98
#> O8-C12 3 0.2066 0.866 0.00 0.06 0.94
#> O8-C3 1 0.9593 -0.160 0.42 0.20 0.38
#> O8-C4 1 0.4291 0.773 0.82 0.00 0.18
#> O8-C5 3 0.0892 0.880 0.00 0.02 0.98
#> O8-C6 3 0.0892 0.880 0.00 0.02 0.98
#> O8-C8 3 0.5016 0.709 0.00 0.24 0.76
#> O8-D3 3 0.0892 0.869 0.02 0.00 0.98
#> O8-D5 3 0.0892 0.869 0.02 0.00 0.98
#> O8-D6 1 0.2537 0.890 0.92 0.00 0.08
#> O8-D9 1 0.0892 0.939 0.98 0.00 0.02
#> O8-E11 3 0.1529 0.875 0.00 0.04 0.96
#> O8-E2 1 0.0892 0.940 0.98 0.00 0.02
#> O8-E5 1 0.2066 0.909 0.94 0.00 0.06
#> O8-E9 3 0.0892 0.880 0.00 0.02 0.98
#> O8-F11 2 0.6045 0.357 0.00 0.62 0.38
#> O8-F12 3 0.0892 0.880 0.00 0.02 0.98
#> O8-F3 3 0.4291 0.773 0.00 0.18 0.82
#> O8-G1 1 0.0000 0.951 1.00 0.00 0.00
#> O8-G12 3 0.0892 0.880 0.00 0.02 0.98
#> O8-G5 2 0.5016 0.673 0.00 0.76 0.24
#> O9-A10 1 0.0000 0.951 1.00 0.00 0.00
#> O9-A8 1 0.0000 0.951 1.00 0.00 0.00
#> O9-B12 1 0.0000 0.951 1.00 0.00 0.00
#> O9-B2 1 0.0000 0.951 1.00 0.00 0.00
#> O9-B6 1 0.0000 0.951 1.00 0.00 0.00
#> O9-B7 1 0.0000 0.951 1.00 0.00 0.00
#> O9-C2 1 0.0000 0.951 1.00 0.00 0.00
#> O9-C4 1 0.0892 0.941 0.98 0.00 0.02
#> O9-C6 1 0.0000 0.951 1.00 0.00 0.00
#> O9-D12 1 0.0892 0.941 0.98 0.00 0.02
#> O9-D6 1 0.0000 0.951 1.00 0.00 0.00
#> O9-E12 1 0.0000 0.951 1.00 0.00 0.00
#> O9-E4 1 0.0892 0.941 0.98 0.00 0.02
#> O9-F9 1 0.0000 0.951 1.00 0.00 0.00
#> O9-G3 1 0.0000 0.951 1.00 0.00 0.00
#> O9-G7 1 0.0000 0.951 1.00 0.00 0.00
#> S37-A4 1 0.0000 0.951 1.00 0.00 0.00
#> S37-A7 1 0.1529 0.925 0.96 0.00 0.04
#> S37-B3 1 0.0000 0.951 1.00 0.00 0.00
#> S37-B5 1 0.1529 0.925 0.96 0.00 0.04
#> S37-B6 1 0.0000 0.951 1.00 0.00 0.00
#> S37-B9 1 0.0000 0.951 1.00 0.00 0.00
#> S37-D11 1 0.0000 0.951 1.00 0.00 0.00
#> S37-D9 1 0.0000 0.951 1.00 0.00 0.00
#> S37-E10 1 0.0000 0.951 1.00 0.00 0.00
#> S37-E5 1 0.0000 0.951 1.00 0.00 0.00
#> S37-G5 1 0.0000 0.951 1.00 0.00 0.00
#> S37-G8 1 0.0000 0.951 1.00 0.00 0.00
#> S37-H4 1 0.0000 0.951 1.00 0.00 0.00
#> S38-A3 1 0.0000 0.951 1.00 0.00 0.00
#> S38-B10 2 0.2414 0.894 0.04 0.94 0.02
#> S38-C1 2 0.7884 0.490 0.10 0.64 0.26
#> S38-C10 2 0.2066 0.909 0.00 0.94 0.06
#> S38-C11 2 0.0000 0.939 0.00 1.00 0.00
#> S38-C5 2 0.0000 0.939 0.00 1.00 0.00
#> S38-C6 1 0.0000 0.951 1.00 0.00 0.00
#> S38-C7 1 0.0000 0.951 1.00 0.00 0.00
#> S38-D10 2 0.0000 0.939 0.00 1.00 0.00
#> S38-D11 2 0.0892 0.927 0.00 0.98 0.02
#> S38-D4 1 0.0892 0.941 0.98 0.00 0.02
#> S38-D7 1 0.0000 0.951 1.00 0.00 0.00
#> S38-E2 1 0.3340 0.826 0.88 0.12 0.00
#> S38-E3 2 0.4551 0.758 0.14 0.84 0.02
#> S38-E8 1 0.0000 0.951 1.00 0.00 0.00
#> S38-F7 1 0.7464 0.268 0.56 0.40 0.04
#> S38-G7 2 0.0892 0.927 0.00 0.98 0.02
#> S38-G8 1 0.0000 0.951 1.00 0.00 0.00
#> S38-G9 2 0.0000 0.939 0.00 1.00 0.00
#> S38-H3 1 0.0892 0.941 0.98 0.00 0.02
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> O10-A11 1 0.1637 0.8735 0.94 0.00 0.06 0.00
#> O10-A5 2 0.2706 0.8385 0.00 0.90 0.08 0.02
#> O10-A7 2 0.2411 0.8593 0.00 0.92 0.04 0.04
#> O10-A8 2 0.1211 0.8719 0.00 0.96 0.00 0.04
#> O10-B10 2 0.0707 0.8783 0.00 0.98 0.00 0.02
#> O10-B11 2 0.0000 0.8833 0.00 1.00 0.00 0.00
#> O10-B2 2 0.0000 0.8833 0.00 1.00 0.00 0.00
#> O10-B5 2 0.0000 0.8833 0.00 1.00 0.00 0.00
#> O10-B6 1 0.7004 0.2275 0.58 0.22 0.00 0.20
#> O10-B7 2 0.0000 0.8833 0.00 1.00 0.00 0.00
#> O10-B9 2 0.0000 0.8833 0.00 1.00 0.00 0.00
#> O10-C10 2 0.0707 0.8766 0.00 0.98 0.02 0.00
#> O10-C12 2 0.0000 0.8833 0.00 1.00 0.00 0.00
#> O10-C5 2 0.0000 0.8833 0.00 1.00 0.00 0.00
#> O10-C6 2 0.0000 0.8833 0.00 1.00 0.00 0.00
#> O10-C9 2 0.0000 0.8833 0.00 1.00 0.00 0.00
#> O10-D1 2 0.0000 0.8833 0.00 1.00 0.00 0.00
#> O10-D11 2 0.0000 0.8833 0.00 1.00 0.00 0.00
#> O10-D12 2 0.0000 0.8833 0.00 1.00 0.00 0.00
#> O10-D5 2 0.2647 0.8140 0.00 0.88 0.12 0.00
#> O10-D6 2 0.1211 0.8703 0.00 0.96 0.04 0.00
#> O10-D9 2 0.0707 0.8783 0.00 0.98 0.00 0.02
#> O10-E1 2 0.2345 0.8425 0.00 0.90 0.00 0.10
#> O10-E11 2 0.0000 0.8833 0.00 1.00 0.00 0.00
#> O10-E12 2 0.0000 0.8833 0.00 1.00 0.00 0.00
#> O10-E6 2 0.0000 0.8833 0.00 1.00 0.00 0.00
#> O10-F1 1 0.0000 0.9035 1.00 0.00 0.00 0.00
#> O10-F11 1 0.0707 0.8999 0.98 0.00 0.00 0.02
#> O10-F12 2 0.3972 0.8012 0.00 0.84 0.08 0.08
#> O10-F5 1 0.0707 0.8958 0.98 0.00 0.00 0.02
#> O10-F9 3 0.5677 0.6731 0.00 0.14 0.72 0.14
#> O12-B12 1 0.0707 0.8999 0.98 0.00 0.00 0.02
#> O12-F12 1 0.0707 0.8999 0.98 0.00 0.00 0.02
#> O7-A3 4 0.1411 0.7027 0.00 0.02 0.02 0.96
#> O7-A9 4 0.4797 0.6797 0.26 0.00 0.02 0.72
#> O7-B11 2 0.0000 0.8833 0.00 1.00 0.00 0.00
#> O7-B6 2 0.2921 0.7982 0.00 0.86 0.14 0.00
#> O7-B7 2 0.6336 -0.0826 0.00 0.48 0.46 0.06
#> O7-C1 4 0.0707 0.7183 0.02 0.00 0.00 0.98
#> O7-C11 2 0.0707 0.8783 0.00 0.98 0.00 0.02
#> O7-C7 2 0.5570 0.3024 0.00 0.54 0.02 0.44
#> O7-D4 1 0.2345 0.8428 0.90 0.00 0.00 0.10
#> O7-E10 3 0.7310 0.3307 0.00 0.36 0.48 0.16
#> O7-E11 2 0.0000 0.8833 0.00 1.00 0.00 0.00
#> O7-F2 1 0.5661 0.5697 0.70 0.00 0.22 0.08
#> O7-F3 4 0.4642 0.6901 0.24 0.00 0.02 0.74
#> O7-F7 2 0.3400 0.7845 0.00 0.82 0.00 0.18
#> O7-F9 2 0.2345 0.8317 0.00 0.90 0.10 0.00
#> O8-A2 3 0.6714 0.1640 0.36 0.00 0.54 0.10
#> O8-A3 3 0.0000 0.8155 0.00 0.00 1.00 0.00
#> O8-A8 3 0.0000 0.8155 0.00 0.00 1.00 0.00
#> O8-B2 1 0.4642 0.6397 0.74 0.00 0.24 0.02
#> O8-B4 3 0.3801 0.7038 0.00 0.22 0.78 0.00
#> O8-B6 3 0.7168 0.5399 0.04 0.28 0.60 0.08
#> O8-B7 3 0.0000 0.8155 0.00 0.00 1.00 0.00
#> O8-B9 2 0.0000 0.8833 0.00 1.00 0.00 0.00
#> O8-C11 3 0.1411 0.8026 0.02 0.00 0.96 0.02
#> O8-C12 3 0.2345 0.7908 0.00 0.10 0.90 0.00
#> O8-C3 1 0.7664 0.3133 0.58 0.14 0.24 0.04
#> O8-C4 1 0.5327 0.6176 0.72 0.00 0.22 0.06
#> O8-C5 3 0.0000 0.8155 0.00 0.00 1.00 0.00
#> O8-C6 3 0.5291 0.6916 0.00 0.08 0.74 0.18
#> O8-C8 3 0.4936 0.6289 0.00 0.28 0.70 0.02
#> O8-D3 3 0.0707 0.8081 0.02 0.00 0.98 0.00
#> O8-D5 3 0.0000 0.8155 0.00 0.00 1.00 0.00
#> O8-D6 1 0.2011 0.8580 0.92 0.00 0.08 0.00
#> O8-D9 1 0.3247 0.8344 0.88 0.00 0.06 0.06
#> O8-E11 3 0.3522 0.7945 0.02 0.06 0.88 0.04
#> O8-E2 1 0.1913 0.8784 0.94 0.00 0.04 0.02
#> O8-E5 1 0.2011 0.8550 0.92 0.00 0.08 0.00
#> O8-E9 3 0.0707 0.8176 0.00 0.02 0.98 0.00
#> O8-F11 2 0.3400 0.7482 0.00 0.82 0.18 0.00
#> O8-F12 3 0.1637 0.8106 0.00 0.06 0.94 0.00
#> O8-F3 2 0.5606 -0.0443 0.00 0.50 0.48 0.02
#> O8-G1 1 0.0000 0.9035 1.00 0.00 0.00 0.00
#> O8-G12 3 0.0707 0.8176 0.00 0.02 0.98 0.00
#> O8-G5 2 0.4949 0.6970 0.00 0.76 0.18 0.06
#> O9-A10 1 0.0707 0.8999 0.98 0.00 0.00 0.02
#> O9-A8 1 0.0000 0.9035 1.00 0.00 0.00 0.00
#> O9-B12 1 0.2011 0.8563 0.92 0.00 0.00 0.08
#> O9-B2 1 0.0707 0.8999 0.98 0.00 0.00 0.02
#> O9-B6 1 0.0000 0.9035 1.00 0.00 0.00 0.00
#> O9-B7 1 0.1637 0.8711 0.94 0.00 0.00 0.06
#> O9-C2 1 0.0000 0.9035 1.00 0.00 0.00 0.00
#> O9-C4 4 0.5606 0.2056 0.48 0.00 0.02 0.50
#> O9-C6 1 0.0000 0.9035 1.00 0.00 0.00 0.00
#> O9-D12 1 0.4994 -0.1250 0.52 0.00 0.00 0.48
#> O9-D6 1 0.0000 0.9035 1.00 0.00 0.00 0.00
#> O9-E12 1 0.0000 0.9035 1.00 0.00 0.00 0.00
#> O9-E4 4 0.4936 0.6589 0.28 0.00 0.02 0.70
#> O9-F9 1 0.0000 0.9035 1.00 0.00 0.00 0.00
#> O9-G3 1 0.0000 0.9035 1.00 0.00 0.00 0.00
#> O9-G7 1 0.0000 0.9035 1.00 0.00 0.00 0.00
#> S37-A4 1 0.4277 0.5654 0.72 0.00 0.00 0.28
#> S37-A7 1 0.2011 0.8586 0.92 0.00 0.08 0.00
#> S37-B3 1 0.0000 0.9035 1.00 0.00 0.00 0.00
#> S37-B5 1 0.2706 0.8566 0.90 0.00 0.02 0.08
#> S37-B6 1 0.0000 0.9035 1.00 0.00 0.00 0.00
#> S37-B9 1 0.0707 0.8999 0.98 0.00 0.00 0.02
#> S37-D11 1 0.0000 0.9035 1.00 0.00 0.00 0.00
#> S37-D9 1 0.0000 0.9035 1.00 0.00 0.00 0.00
#> S37-E10 1 0.0707 0.8999 0.98 0.00 0.00 0.02
#> S37-E5 1 0.0000 0.9035 1.00 0.00 0.00 0.00
#> S37-G5 1 0.0707 0.8999 0.98 0.00 0.00 0.02
#> S37-G8 1 0.0000 0.9035 1.00 0.00 0.00 0.00
#> S37-H4 1 0.0707 0.8999 0.98 0.00 0.00 0.02
#> S38-A3 1 0.2647 0.8113 0.88 0.00 0.00 0.12
#> S38-B10 4 0.3606 0.6117 0.00 0.14 0.02 0.84
#> S38-C1 4 0.0707 0.7046 0.00 0.00 0.02 0.98
#> S38-C10 2 0.4977 0.2800 0.00 0.54 0.00 0.46
#> S38-C11 2 0.4284 0.7448 0.00 0.78 0.02 0.20
#> S38-C5 2 0.1211 0.8711 0.00 0.96 0.00 0.04
#> S38-C6 1 0.0000 0.9035 1.00 0.00 0.00 0.00
#> S38-C7 4 0.4522 0.5813 0.32 0.00 0.00 0.68
#> S38-D10 2 0.4406 0.6406 0.00 0.70 0.00 0.30
#> S38-D11 4 0.2345 0.6556 0.00 0.10 0.00 0.90
#> S38-D4 4 0.2706 0.7334 0.08 0.00 0.02 0.90
#> S38-D7 1 0.3801 0.6707 0.78 0.00 0.00 0.22
#> S38-E2 4 0.3400 0.7058 0.18 0.00 0.00 0.82
#> S38-E3 4 0.0000 0.7056 0.00 0.00 0.00 1.00
#> S38-E8 1 0.0707 0.8999 0.98 0.00 0.00 0.02
#> S38-F7 4 0.7896 0.4518 0.30 0.18 0.02 0.50
#> S38-G7 2 0.4855 0.4669 0.00 0.60 0.00 0.40
#> S38-G8 1 0.0000 0.9035 1.00 0.00 0.00 0.00
#> S38-G9 2 0.2647 0.8299 0.00 0.88 0.00 0.12
#> S38-H3 4 0.2921 0.7349 0.14 0.00 0.00 0.86
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)
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)
As soon as the classes for columns are determined, the signatures that are significantly different between subgroups can be looked for. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
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)
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 (which is done by automatically selecting number of clusters).If there are too many signatures, top_signatures = ... can be set to only show the
signatures with the highest FDRs:
# code only for demonstration
# e.g. to show the top 500 most significant rows
tb = get_signature(res, k = ..., top_signatures = 500)
If the signatures are defined as these which are uniquely high in current group, diff_method argument
can be set to "uniquely_high_in_one_group":
# code only for demonstration
tb = get_signature(res, k = ..., diff_method = "uniquely_high_in_one_group")
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")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n_sample Age(p-value) Inferred.Cell.Type(p-value) k
#> ATC:skmeans 126 6.32e-03 1.53e-01 2
#> ATC:skmeans 119 1.93e-03 1.07e-01 3
#> ATC:skmeans 114 3.72e-05 2.01e-06 4
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 4.1.0 (2021-05-18)
#> Platform: x86_64-pc-linux-gnu (64-bit)
#> Running under: CentOS Linux 7 (Core)
#>
#> Matrix products: default
#> BLAS/LAPACK: /usr/lib64/libopenblas-r0.3.3.so
#>
#> locale:
#> [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C LC_TIME=en_US.UTF-8
#> [4] LC_COLLATE=en_US.UTF-8 LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
#> [7] LC_PAPER=en_US.UTF-8 LC_NAME=C LC_ADDRESS=C
#> [10] LC_TELEPHONE=C LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
#>
#> attached base packages:
#> [1] grid parallel stats4 stats graphics grDevices utils datasets methods
#> [10] base
#>
#> other attached packages:
#> [1] genefilter_1.74.0 ComplexHeatmap_2.8.0 markdown_1.1
#> [4] knitr_1.33 scRNAseq_2.6.1 SingleCellExperiment_1.14.1
#> [7] SummarizedExperiment_1.22.0 Biobase_2.52.0 GenomicRanges_1.44.0
#> [10] GenomeInfoDb_1.28.1 IRanges_2.26.0 S4Vectors_0.30.0
#> [13] BiocGenerics_0.38.0 MatrixGenerics_1.4.0 matrixStats_0.59.0
#> [16] cola_1.9.4
#>
#> loaded via a namespace (and not attached):
#> [1] circlize_0.4.13 AnnotationHub_3.0.1 BiocFileCache_2.0.0
#> [4] lazyeval_0.2.2 polylabelr_0.2.0 splines_4.1.0
#> [7] Polychrome_1.3.1 BiocParallel_1.26.1 ggplot2_3.3.5
#> [10] digest_0.6.27 foreach_1.5.1 ensembldb_2.16.3
#> [13] htmltools_0.5.1.1 viridis_0.6.1 fansi_0.5.0
#> [16] magrittr_2.0.1 memoise_2.0.0 cluster_2.1.2
#> [19] doParallel_1.0.16 Biostrings_2.60.1 annotate_1.70.0
#> [22] askpass_1.1 prettyunits_1.1.1 colorspace_2.0-2
#> [25] blob_1.2.1 rappdirs_0.3.3 xfun_0.24
#> [28] dplyr_1.0.7 crayon_1.4.1 RCurl_1.98-1.3
#> [31] microbenchmark_1.4-7 jsonlite_1.7.2 impute_1.66.0
#> [34] brew_1.0-6 survival_3.2-11 iterators_1.0.13
#> [37] glue_1.4.2 polyclip_1.10-0 gtable_0.3.0
#> [40] zlibbioc_1.38.0 XVector_0.32.0 GetoptLong_1.0.5
#> [43] DelayedArray_0.18.0 shape_1.4.6 scales_1.1.1
#> [46] data.tree_1.0.0 DBI_1.1.1 Rcpp_1.0.7
#> [49] viridisLite_0.4.0 xtable_1.8-4 progress_1.2.2
#> [52] clue_0.3-59 reticulate_1.20 bit_4.0.4
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#> [61] XML_3.99-0.6 dbplyr_2.1.1 utf8_1.2.1
#> [64] tidyselect_1.1.1 rlang_0.4.11 later_1.2.0
#> [67] AnnotationDbi_1.54.1 munsell_0.5.0 BiocVersion_3.13.1
#> [70] tools_4.1.0 cachem_1.0.5 generics_0.1.0
#> [73] RSQLite_2.2.7 ExperimentHub_2.0.0 evaluate_0.14
#> [76] stringr_1.4.0 fastmap_1.1.0 yaml_2.2.1
#> [79] bit64_4.0.5 purrr_0.3.4 dendextend_1.15.1
#> [82] KEGGREST_1.32.0 AnnotationFilter_1.16.0 mime_0.11
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#> [97] GenomicFeatures_1.44.0 RSpectra_0.16-0 lattice_0.20-44
#> [100] ProtGenerics_1.24.0 Matrix_1.3-4 vctrs_0.3.8
#> [103] pillar_1.6.1 lifecycle_1.0.0 BiocManager_1.30.16
#> [106] eulerr_6.1.0 GlobalOptions_0.1.2 bitops_1.0-7
#> [109] irlba_2.3.3 httpuv_1.6.1 rtracklayer_1.52.0
#> [112] R6_2.5.0 BiocIO_1.2.0 promises_1.2.0.1
#> [115] gridExtra_2.3 codetools_0.2-18 assertthat_0.2.1
#> [118] openssl_1.4.4 rjson_0.2.20 GenomicAlignments_1.28.0
#> [121] Rsamtools_2.8.0 GenomeInfoDbData_1.2.6 hms_1.1.0
#> [124] skmeans_0.2-13 Cairo_1.5-12.2 scatterplot3d_0.3-41
#> [127] shiny_1.6.0 restfulr_0.0.13