Simplify Functional Enrichment Results
2021-05-19
The simplifyEnrichment package clusters functional terms into groups by clustering the similarity matrix of the terms with a new proposed method “binary cut” which recursively applies partition around medoids (PAM) with two groups on the similarity matrix and in each iteration step, a score is assigned to decide whether the group of gene sets that corresponds to the current sub-matrix should be split or not. For more details of the method, please refer to the simplifyEnrichment paper.
Simplify GO enrichment results
The major use case for simplifyEnrichment is for simplying the GO enrichment results by clustering the corresponding semantic similarity matrix of the significant GO terms. To demonstrate the usage, we first generate a list of random GO IDs from the Biological Process (BP) ontology category:
simplifyEnrichment starts with the GO similarity matrix. Users can use their own similarity matrices or use the GO_similarity() function to calculate the semantic similarity matrix. The GO_similarity() function is simply a wrapper on GOSemSim::termSim(). The function accepts a vector of GO IDs. Note the GO terms should only belong to one same ontology (i.e., BP, CC or MF).
By default, GO_similarity() uses Rel method in GOSemSim::termSim(). Other methods to calculate GO similarities can be set by measure argument, e.g.:
With the similarity matrix mat, users can directly apply simplifyGO() function to perform the clustering as well as visualizing the results.
## Cluster 500 terms by 'binary_cut'... 43 clusters, used 1.914086 secs.
On the right side of the heatmap there are the word cloud annotations which summarize the functions with keywords in every GO cluster. Note there is no word cloud for the cluster that is merged from small clusters (size < 5).
The returned variable df is a data frame with GO IDs, GO terms and the cluster labels:
## id term cluster
## 1 GO:0003283 atrial septum development 1
## 2 GO:0022018 lateral ganglionic eminence cell proliferation 1
## 3 GO:0030032 lamellipodium assembly 2
## 4 GO:0061508 CDP phosphorylation 3
## 5 GO:1901222 regulation of NIK/NF-kappaB signaling 4
## 6 GO:0060164 regulation of timing of neuron differentiation 1
The size of GO clusters can be retrieved by:
##
## 5 7 8 10 12 13 17 18 21 22 24 25 26 27 28 29 30 31 32 33
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 34 35 36 37 38 39 40 41 42 43 20 23 9 16 19 15 14 11 2 6
## 1 1 1 1 1 1 1 1 1 1 2 2 3 5 5 6 10 12 37 45
## 4 1 3
## 97 114 132
Or split the data frame by the cluster labels:
plot argument can be set to FALSE in simplifyGO(), so that no plot is generated and only the data frame is returned.
If the aim is only to cluster GO terms, binary_cut() or cluster_terms() functions can be directly applied:
## [1] 1 1 2 3 4 1 2 3 1 3 5 6 1 3 1 3 6 7 3 3 4 8 4 4 1
## [26] 1 3 6 3 1 4 3 3 2 3 4 3 4 4 2 2 4 6 6 9 2 6 2 2 3
## [51] 3 4 2 2 4 6 3 3 4 3 4 3 3 3 10 3 1 11 3 1 6 4 6 3 12
## [76] 1 13 4 14 2 4 11 6 1 3 4 1 4 4 4 15 3 6 3 3 3 4 3 14 6
## [101] 3 4 16 6 1 2 2 2 11 4 3 3 3 17 1 4 1 3 6 3 1 3 1 3 4
## [126] 3 16 4 6 4 3 9 3 3 3 3 1 2 3 4 3 1 3 3 3 18 1 2 3 1
## [151] 3 19 1 3 4 1 1 1 1 4 3 20 15 2 3 1 1 1 1 1 21 4 1 4 6
## [176] 4 4 3 1 4 1 4 11 11 11 1 4 11 1 3 6 2 3 1 22 1 3 6 1 14
## [201] 1 3 4 4 4 2 4 6 3 3 1 3 1 6 3 4 4 11 4 1 1 23 1 24 6
## [226] 4 3 2 1 1 3 1 1 6 1 1 1 4 6 3 4 3 4 16 3 1 1 4 25 4
## [251] 4 4 1 1 26 4 4 4 6 4 1 3 3 3 2 19 4 3 4 27 4 4 2 6 3
## [276] 3 11 3 6 2 16 3 3 2 1 1 6 6 6 3 3 3 1 3 4 3 1 3 1 14
## [301] 15 28 2 20 1 3 1 1 1 4 1 3 3 4 1 19 29 4 4 4 1 4 6 4 30
## [326] 3 3 6 1 1 3 1 4 2 1 3 3 3 3 19 6 14 3 1 1 11 1 1 4 14
## [351] 6 11 3 3 4 3 3 2 1 14 1 1 4 1 2 31 1 1 4 1 3 4 3 1 3
## [376] 32 1 1 3 1 3 6 3 3 3 1 19 6 3 11 3 1 3 3 33 2 1 4 4 1
## [401] 6 1 4 2 15 6 4 2 3 4 4 4 14 3 3 4 4 1 1 3 6 2 3 2 1
## [426] 4 34 1 3 1 1 23 3 6 4 9 1 1 6 4 1 35 36 37 38 1 1 1 4 2
## [451] 1 14 15 4 3 14 3 3 6 2 1 15 16 3 4 3 3 4 3 3 4 1 39 6 4
## [476] 3 3 4 3 4 6 2 2 3 40 4 6 4 41 3 1 3 1 3 1 6 42 43 4 1
or
binary_cut() and cluster_terms() basically generate the same clusterings, but the labels of clusters might differ.
Simplify general functional enrichment results
Semantic measures can be used for the similarity of GO terms. However, there are still a lot of ontologies (e.g. MsigDB gene sets) that are only represented as a list of genes where the similarity between gene sets are mainly measured by gene overlap. simplifyEnrichment provides the term_similarity() and other related functions (term_similarity_from_enrichResult(), term_similarity_from_KEGG(), term_similarity_from_Reactome(), term_similarity_from_MSigDB() and term_similarity_from_gmt()) which calculate the similarity of terms by the gene overlapping, with methods of Jaccard coefficient, Dice coefficient, overlap coefficient and kappa coefficient.
The similarity can be calculated by providing:
- A list of gene sets where each gene set contains a vector of genes.
- A
enrichResult object which is normally from the ‘clusterProfiler’, ‘DOSE’, ‘meshes’ or ‘ReactomePA’ package.
- A list of KEGG/Reactome/MsigDB IDs. The gene set names can also be provided for MsigDB ontologies.
- A gmt file and the corresponding gene set IDs.
Once you have the similarity matrix, you can send it to simplifyEnrichment() function. But note, as we benchmarked in the manuscript, the clustering on the gene overlap similarity performs much worse than on the semantic similarity.
Comparing clustering methods
In the simplifyEnrichment package, there are also functions that compare clustering results from different methods. Here we still use previously generated variable mat which is the similarity matrix from the 500 random GO terms. Simply running compare_clustering_methods() function performs all supported methods (in all_clustering_methods()) excluding mclust, because mclust usually takes very long time to run. The function generates a figure with three panels:
- A heatmap of the similarity matrix with different clusterings as row annotations.
- A heatmap of the pair-wise concordance of the clustering from every two methods.
- Barplots of the difference scores for each method, the number of clusters (total clusters and the clusters with size >= 5) and the mean similarity of the terms that are in the same clusters (block mean).
In the barplots, the three metrics are defined as follows:
- Different score: This is the difference between the similarity values for the terms that belong to the same clusters and different clusters. For a similarity matrix \(M\), for term \(i\) and term \(j\) where \(i \ne j\), the similarity value \(x_{i,j}\) is saved to the vector \(\mathbf{x_1}\) only when term \(i\) and \(j\) are in a same cluster. \(x_{i,j}\) is saved to the vector \(\mathbf{x_2}\) when term \(i\) and \(j\) are not in the same cluster. The difference score measures the distribution difference between \(\mathbf{x_1}\) and \(\mathbf{x_2}\), calculated as the Kolmogorov-Smirnov statistic between the two distributions.
- Number of clusters: For each clustering, there are two numbers: the number of total clusters and the number of clusters with size >= 5 (only the big clusters).
- Block mean: Mean similarity values of the diagonal blocks in the similarity heatmap. Using the same convention as for the difference score, the block mean is the mean value of \(\mathbf{x_1}\).
## Cluster 500 terms by 'binary_cut'... 43 clusters, used 1.292667 secs.
## Cluster 500 terms by 'kmeans'... 15 clusters, used 5.466666 secs.
## Cluster 500 terms by 'dynamicTreeCut'... 58 clusters, used 0.2248063 secs.
## Cluster 500 terms by 'apcluster'... 39 clusters, used 1.05522 secs.
## Cluster 500 terms by 'hdbscan'... 13 clusters, used 0.2847941 secs.
## Cluster 500 terms by 'fast_greedy'... 29 clusters, used 0.1642258 secs.
## Cluster 500 terms by 'leading_eigen'... 30 clusters, used 0.4157999 secs.
## Cluster 500 terms by 'louvain'... 29 clusters, used 0.1897464 secs.
## Cluster 500 terms by 'walktrap'... 26 clusters, used 0.4785211 secs.
## Cluster 500 terms by 'MCL'... 28 clusters, used 4.439619 secs.
If plot_type argument is set to heatmap. There are heatmaps for the similarity matrix under different clusterings methods. The last panel is a table with the number of clusters.
## Cluster 500 terms by 'binary_cut'... 43 clusters, used 1.313843 secs.
## Cluster 500 terms by 'kmeans'... 16 clusters, used 5.596574 secs.
## Cluster 500 terms by 'dynamicTreeCut'... 58 clusters, used 0.229274 secs.
## Cluster 500 terms by 'apcluster'... 39 clusters, used 1.707315 secs.
## Cluster 500 terms by 'hdbscan'... 13 clusters, used 0.2676535 secs.
## Cluster 500 terms by 'fast_greedy'... 29 clusters, used 0.1445436 secs.
## Cluster 500 terms by 'leading_eigen'... 30 clusters, used 0.4241514 secs.
## Cluster 500 terms by 'louvain'... 29 clusters, used 0.1744215 secs.
## Cluster 500 terms by 'walktrap'... 26 clusters, used 0.4935129 secs.
## Cluster 500 terms by 'MCL'... 28 clusters, used 3.612622 secs.
Please note, the clustering methods might have randomness, which means, different runs of compare_clustering_methods() may generate different clusterings (slightly different). Thus, if users want to compare the plots between compare_clustering_methods(mat) and compare_clustering_methods(mat, plot_type = "heatmap"), they should set the same random seed before executing the function.
compare_clustering_methods() is simply a wrapper on cmp_make_clusters() and cmp_make_plot() functions where the former function performs clustering with different methods and the latter visualizes the results. To compare different plots, users can also use the following code without specifying the random seed.
Register new clustering methods
New clustering methods can be added by register_clustering_methods(), removed by remove_clustering_methods() and reset to the default methods by reset_clustering_methods(). All the supported methods can be retrieved by all_clustering_methods(). compare_clustering_methods() runs all the clustering methods in all_clustering_methods().
The new clustering methods should be as user-defined functions and sent to register_clustering_methods() as named arguments, e.g.:
The functions should accept at least one argument which is the input matrix (mat in above example). The second optional argument should always be ... so that parameters for the clustering function can be passed by control argument from cluster_terms() or simplifyGO(). If users forget to add ..., it is added internally.
Please note, the user-defined function should automatically identify the optimized number of clusters. The function should return a vector of cluster labels. Internally it is converted to numeric labels.
Examples
There are following examples which we did for the benchmarking in the manuscript:
Apply to multiple lists of GO IDs
It is always very common that users have multiple lists of GO enrichment results (e.g. from multiple groups of genes) and they want to compare the significant terms between different lists, e.g. to see which biological functions are more specific in a certain list. There is a function simplifyGOFromMultipleLists() in the package which helps this type of analysis.
The input data for simplifyGOFromMultipleLists() (with the argument lt) can have three types of formats:
- A list of numeric vectors of adjusted p-values where each vector has the GO IDs as names.
- A data frame. The column of the GO IDs can be specified with
go_id_column argument and the column of the adjusted p-values can be specified with padj_column argument. If the two columns are not specified, they are automatically identified. The GO ID column is found by checking whether a column contains all GO IDs. The adjusted p-value column is found by comparing the column names of the data frame to see whether it might be a column for adjusted p-values. These two columns are used to construct a numeric vector with GO IDs as names.
- A list of character vectors of GO IDs. In this case, each character vector is changed to a numeric vector where all values take 1 and the original GO IDs are used as names of the vector.
If the GO enrichment results is directly from upstream analysis, e.g. the package clusterProfiler or other similar packages, the results are most probably represented as a list of data frames, thus, we first demonstrate the usage on a list of data frames.
The function functional_enrichment() in cola package applies functional enrichment on different groups of signature genes from consensus clustering. The function internally uses clusterProfiler and returns a list of data frames:
## - 2076/4116 significant genes are taken from 3-group comparisons
## - on k-means group 1/4, 444 genes
## - 356/444 (80.2%) genes left after id mapping
## - gene set enrichment, GO:BP
## - on k-means group 2/4, 882 genes
## - 782/882 (88.7%) genes left after id mapping
## - gene set enrichment, GO:BP
## - on k-means group 3/4, 403 genes
## - 318/403 (78.9%) genes left after id mapping
## - gene set enrichment, GO:BP
## - on k-means group 4/4, 347 genes
## - 297/347 (85.6%) genes left after id mapping
## - gene set enrichment, GO:BP
## [1] "BP_km1" "BP_km2" "BP_km3" "BP_km4"
## ID Description GeneRatio BgRatio
## GO:0033993 GO:0033993 response to lipid 51/344 865/18862
## GO:0019725 GO:0019725 cellular homeostasis 47/344 937/18862
## GO:0009725 GO:0009725 response to hormone 44/344 876/18862
## GO:0044070 GO:0044070 regulation of anion transport 43/344 850/18862
## GO:0014070 GO:0014070 response to organic cyclic compound 44/344 907/18862
## GO:0055082 GO:0055082 cellular chemical homeostasis 41/344 811/18862
## pvalue p.adjust qvalue
## GO:0033993 1.104381e-13 4.686991e-10 3.726994e-10
## GO:0019725 2.941343e-10 6.241531e-07 4.963130e-07
## GO:0009725 1.112069e-09 1.500054e-06 1.192810e-06
## GO:0044070 1.413811e-09 1.500054e-06 1.192810e-06
## GO:0014070 3.222304e-09 2.552491e-06 2.029685e-06
## GO:0055082 3.608611e-09 2.552491e-06 2.029685e-06
By default, simplifyGOFromMultipleLists() automatically identifies the columns that contain GO IDs and adjusted p-values, so here we directly send lt to simplifyGOFromMultipleLists(). We additionally set padj_cutoff to 0.001 because under the default cutoff 0.01, there are too many GO IDs and to save the running time, we set a more strict cutoff.
## Use column 'ID' as `go_id_column`.
## Use column 'p.adjust' as `padj_column`.
## 838/6318 GO IDs left for clustering.
## Cluster 838 terms by 'binary_cut'... 33 clusters, used 1.288691 secs.
Next we demonstrate two other data types for simplifyGOFromMultipleLists(). Both usages are straightforward. The first is a list of numeric vectors:
And the second is a list of character vectors of GO IDs:
The process of this analysis is as follows. Let’s assume there are \(n\) GO lists, we first construct a global matrix where columns correspond to the \(n\) GO lists and rows correspond to the “union” of all GO IDs in the \(n\) lists. The value for the ith GO ID and in the jth list are taken from the corresponding numeric vector in lt. If the jth vector in lt does not contain the ith GO ID, the value defined by default argument is taken there (e.g. in most cases the numeric values are adjusted p-values, thus default is set to 1). Let’s call this matrix as \(M_0\).
Next step is to filter \(M_0\) so that we only take a subset of GO IDs of interest. We define a proper function via argument filter to remove GO IDs that are not important for the analysis. Function for filter is applied to every row in \(M_0\) and filter function needs to return a logical value to decide whether to keep or remove the current GO ID. For example, if the values in lt are adjusted p-values, the filter function can be set as function(x) any(x < padj_cutoff) so that the GO ID is kept as long as it is signfiicant in at least one list. After the filtering, let’s call the filtered matrix \(M_1\).
GO IDs in \(M_1\) (row names of \(M_1\)) are used for clustering. A heatmap of \(M_1\) is attached to the left of the GO similarity heatmap so that the group-specific (or list-specific) patterns can be easily observed and to corresponded to GO functions.
Argument heatmap_param controls several parameters for heatmap \(M_1\):
transform: A self-defined function to transform the data for heatmap visualization. The most typical case is to transform adjusted p-values by -log10(x).breaks: Break values for color interpolation.col: The corresponding values for breaks.labels: The corresponding labels for legend.name: Legend title.
Session Info
## R version 4.1.0 (2021-05-18)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 20.04.2 LTS
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## Matrix products: default
## BLAS: /home/biocbuild/bbs-3.13-bioc/R/lib/libRblas.so
## LAPACK: /home/biocbuild/bbs-3.13-bioc/R/lib/libRlapack.so
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## attached base packages:
## [1] stats4 grid parallel stats graphics grDevices utils
## [8] datasets methods base
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## other attached packages:
## [1] hu6800.db_3.2.3 org.Hs.eg.db_3.13.0 AnnotationDbi_1.54.0
## [4] IRanges_2.26.0 S4Vectors_0.30.0 Biobase_2.52.0
## [7] cola_1.8.0 simplifyEnrichment_1.2.0 BiocGenerics_0.38.0
## [10] knitr_1.33
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## loaded via a namespace (and not attached):
## [1] shadowtext_0.0.8 circlize_0.4.12 fastmatch_1.1-0
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