## Introduction

Modern high-throughput experiments enable researchers to determine the association between each individual gene and a phenotype. Currently, gene set enrichment analysis (GSEA) is used to interpret which biological processes are associated with the phenotype of interest1. Gene sets are collections of genes that share a common characteristic (e.g., biological function). Overrepresentation of gene sets in the top associated genes can be used to identify which biological processes are driving the phenotype. Although gene sets are continuously updated, they are still far from complete. This can bias and hamper the interpretation of high-throughput experiments2.

A strategy to reduce this limitation is to extend gene sets by providing a gene set membership likelihood for every gene. This can be accomplished by comparing gene co-expression patterns within a guilt-by-association (GBA) strategy. For example, if there are 50 genes that are known to be involved in DNA repair, a gene that is strongly co-expressed with these 50 is likely to be involved in DNA repair as well. A potential limitation arises when a gene is involved in multiple biological processes3. Each biological process is the result of the coordinated expression of multiple genes, which together represent a transcriptional footprint. One of these biological processes might have a transcriptional footprint that dominates the observed gene expression profile and therefore overshadows the other biological processes with more subtle transcriptional footprints4. Therefore, relying on co-expression may bias GBA predictions for genes involved in multiple biological processes towards those biological processes with dominant transcriptional footprints.

A strategy to overcome this limitation is to first apply principal component analysis (PCA) to the gene expression input data. Applying PCA results in a smaller set of new variables called principal components (PCs). These PCs capture most of the variance of the original input data. In the context of gene expression data, PCs are referred to as transcriptional components (TCs). Both dominant and more subtle transcriptional footprints of biological processes can be captured by PCA-TCs4. Using PCA-TCs in a GBA strategy improves gene set membership predictions compared to regular gene to gene co-expression patterns5. However, two or more PCA-TCs may still possess a mutual nonlinear correlation. This correlation reflects the transcriptional footprint of a biological process that is partially captured in multiple PCA-TCs. Segregating nonlinear correlations into individual TCs may further improve gene set membership predictions. Independent component analysis (ICA) can enable the estimation of ICA-TCs that capture strong and subtle transcriptional footprints while minimizing their mutual nonlinear correlation6.

In this study, we utilize three large messenger RNA (mRNA) expression datasets originating from microarray and RNA-sequencing (RNA-seq) platforms, and 16 gene set collections in a GBA strategy using ICA-TCs to infer gene set memberships for up to 58,433 individual genes. We show that using ICA-TCs (1) provides more confident functionality predictions, (2) improves predictions when new members are added to the gene sets, and (3) is less affected by gene multifunctionality in comparison with PCA-TCs.

## Results

### Data acquisition

To generate our human microarray input dataset, all publicly available unprocessed microarray expression data generated with the Affymetrix HG-U133 Plus 2.0 platform were downloaded from the Gene Expression Omnibus (GEO)7. After preprocessing and quality control, a total of 106,462 samples were included for further analysis. The R package “jetset” (version 3.4.0) served to obtain one-to-one mapping between genes and the most representative probe sets on the Affymetrix HG-U133 Plus 2.0 platform and resulted in unique expression measurements for 19,635 genes (R jetset package v3.4.0)8. Gene set collections (n = 16) were retrieved from The Human Phenotype Ontology (The Monarch Initiative), the Mammalian Phenotypes (Mouse Genome Database), and 14 collections from the Molecular Signatures Database v6.29,10,11. These gene set collections contain 23,372 gene sets in total.

### Consensus ICA captures the variance of the input dataset

Consensus ICA (c-ICA) was performed on the input dataset to calculate ICA-TCs (Fig. 1). In ICA, a preprocessing technique called whitening is applied to make the estimation more time efficient by reducing the dimensionality of the input dataset. Whitening was achieved with PCA on the covariance matrix between the genes and resulted in 817 PCs that captured 90% of the total variance in gene expression observed in the human microarray input dataset. Subsequently, using these 817 PCs as input for c-ICA, we obtained 523 ICA-TCs with a credibility index >0.5.

### Framework for generating predictions using ICA-TCs

The c-ICA method provides a mixing matrix (MM) together with the ICA-TCs. In the MM each column corresponds to an ICA-TC and each row corresponds to a gene. Each weight in the MM describes the effect of a latent transcriptional regulating factor on the expression level of a gene. The vector of weights of an individual gene in the MM is referred to as the transcriptional regulatory “barcode.” For each of the 23,372 gene sets, an average transcriptional regulatory barcode was calculated by taking the mean vector of weights in the MM of genes that are members of the gene set. Next, the distance correlations between the transcriptional regulatory barcode of all combinations of genes and gene sets were calculated12. A strong positive correlation indicates that the transcriptional regulation of an individual gene is similar to the average transcriptional regulation of members of the gene set. Gene sets that capture biological processes with highly co-regulated genes generate consistent regulatory barcodes. Therefore, genes with strong correlation have a high likelihood of belonging in those gene sets even if they are not currently members. For example, BRCA2 is a DNA repair protein with a strong co-regulation with the cell cycle KEGG (Kyoto Encyclopedia of Genes and Genomes) gene set (prediction score = 15.53). Even though BRCA2 does not directly regulate the cell cycle, progression through the G2–M checkpoint depends on the successful repair of all DNA damaged during replication. Therefore, when viewed through co-regulation BRCA2 participates in two biological processes, namely, DNA repair and cell cycle progression.

A permutation strategy in combination with a Gaussian kernel density estimator enabled the construction of a null distribution for each gene-to-gene set combination. The permutation tests determined the significance of the distance correlation without assuming an underlying shape for the null distribution of each method. Resulting p values were transformed to a Z-score, hereafter referred to as prediction score (see Supplementary Notes). The prediction scores obtained using the human microarray dataset are made available on a portal at http://genetica-network.com. This interface allows users to rank the scores of all genes that predict membership to a particular gene set (gene set perspective) or the scores of all gene sets that predict membership of a particular gene (gene perspective).

### Using ICA-TCs results in stronger predictions than PCA-TCs

Data-driven Expression Prioritized Integration for Complex Traits (DEPICT) and the more recent GeneNetwork Assisted Diagnostic Optimization (GADO) are two successful methods that utilize gene functional predictions obtained with a PCA-TC-based GBA method5,13. DEPICT and GADO use predictions for biological interpretation of genome-wide association studies and to improve the discovery of disease-causing genes from exome sequencing, respectively (Table 1). A comparison between the predictions obtained with a GBA method using ICA-TCs and PCA-TCs was performed. To ensure a fair comparison, the whitened matrix that was used to run c-ICA served as input for the PCA-TC-based method. Using the whitened matrix as input ensures that both methods have the same amount of variance in the expression data available for generating TCs.

First, genes that were already assigned to gene sets were analyzed. A gene is expected to get a high prediction score for a gene set of which it is currently a member. For each gene set, a median prediction score for the subset of current member genes was calculated as well as for the subset of genes that are not assigned to any gene set in that collection (nonmember genes) (Supplementary Data 1). Median prediction scores of member genes were higher compared with nonmember genes in both the PCA-TC- and the ICA-TC-based method. However, ICA-TC-based predictions outperformed PCA-TC by obtaining higher median prediction scores for current member genes in all gene set collections (area under the curves (AUCs) calculated from two-sided Mann–Whitney U test range 0.7–0.99; Fig. 2). Moreover, median prediction scores for nonmember genes were also higher for ICA-TC- than PCA-TC-based predictions (AUCs all >0.99). These results indicate that the ICA-TC-based method provides predictions with higher confidence than the PCA-TC-based method.

To explore if a subset of gene sets is better predicted with the PCA-TC-based method the differences between gene set prediction scores of both PCA and ICA methods were calculated (delta). Gene sets with deltas higher than zero were defined as ICA-improved and below zero as PCA-improved gene sets. We observed that 811/23,413 (3.4%) gene sets belonged to the PCA-improved subset (Supplementary Fig. 1). Gene sets belonging to the PCA-improved subset had fewer members (median = 23) than the ICA-improved subset (median = 57).

### ICA-TCs outperform PCA-TCs in predicting future ontologies

The predictive power of the PCA-TC- and ICA-TC-based GBA prediction strategies was further evaluated by generating predictions using a previous version of three Gene Ontology (GO) gene set collections (Molecular Signatures Database C5 v3.0). Genes that are not members in v3.0 are expected to obtain high prediction scores if they got added as members to those gene sets in later version updates. In addition, such a gene would be expected to have an equal or higher prediction score when predictions are generated using the newer gene set versions with updated membership information. This would indicate the capacity of the method to predict future gene set memberships and to improve predictions when updated gene set membership information is available.

Genes that were added as member of a gene set after v3.0 are referred to as updated member genes. Median prediction scores for these updated member genes were calculated with the ICA-TC- and PCA-TC-based method (Fig. 3). This was done independently with v3.0 and v6.2 as input for the transcriptional barcode generation step. Only gene sets that got new genes added in between v3.0 and v6.2 were included in this analysis. Prediction scores for the updated member genes with v3.0 barcodes were higher for ICA-TC- compared to the PCA-TC-based method (AUC ranging from 0.90 to 0.96). This indicates that the ICA-TC-based method outperforms the PCA-TC method at predicting future gene memberships in the GO gene set collection.

Surprisingly, for the PCA-TC-based method, scores of the updated member genes were lower when using v6.2 barcodes than when using v3.0 barcodes as input (AUC ranging from 0.19 to 0.34). In contrast, using v6.2 as input did improve prediction scores when applying ICA-TC-based method (AUCs ranging from 0.65 to 0.71). This indicates that the ICA-TC- but not the PCA-TC-based method is able to improve predictions when updated membership information is available for the GO gene set collections.

### Gene membership frequencies do not drive prediction scores

Previously, it was shown that multifunctionality, rather than association, can be a main driver of functional predictions when using GBA methodology14. Here, the degree of multifunctionality of a gene is defined as a function of the number of gene sets of which it is currently a member14. The degree of multifunctionality of a gene might have a strong correlation with the gene set prediction scores of that gene. This would indicate that the likelihood of a gene being a member of the gene set, as expressed by the prediction score, can largely be explained by the degree of multifunctionality and not by the predictions obtained with the GBA strategy.

Per gene set collection, the degree of multifunctionality was calculated for all genes (see “Methods”). The associations between the degree of multifunctionality and the prediction scores (Fig. 4 and Supplementary Data 2) were lower for the ICA-TC-based method than the PCA-TC-based method (AUCs range 0.03–0.47). This means that ICA-TC-based predictions are less driven by the membership frequencies of a gene and therefore are relying more on the GBA strategy. The predictions of some gene set collections showed on average higher association with multifunctionality. The most affected gene set collections were either constructed based on predicted targets of transcriptional regulators (microRNA and transcription factor targets) or obtained from signatures of published perturbation experiments (Chemical and Genetic Perturbations and Immune signatures). In conclusion, the association between the degree of multifunctionality and prediction scores is very limited for most gene sets for both the ICA-TC and PCA-TC method.

### Mouse and human prediction scores are correlated

In addition, ICA-TC-based gene function predictions were generated for mouse microarray samples (GPL1261 platform; n = 25,585; genes = 18,425) for 16 gene set collections (n = 23,128). We correlated the prediction scores between the unique ortholog mapping genes (n = 14, 589) between human and mouse microarray datasets for every matching gene set collection to investigate the concordance between prediction scores (Supplementary Fig. 2). A subset of 10,974/14,589 (75.2%) mouse genes have a correlation >0.3 to their human orthologs based on their prediction scores for at least one of the gene set collections. GO Cellular Component and Cancer Modules gene set collections showed the highest median Spearman correlations (0.155 and 0.154, respectively). The low correlating gene predictions across species could be explained by the smaller number of samples (n = 25, 585) and the more limited sample heterogeneity available in the mouse dataset compared to the human microarray dataset (n = 106,462). These results show that many genes may be similarly regulated in both species. The mouse prediction scores have been made available at http://www.genetica-network.com.

### Current gene sets do not capture all co-regulation clusters

When using a GBA strategy with mRNA profiles, high prediction scores for a biological process depend on three factors. First, the existence of at least one gene set that covers that process. Second, if such a gene set contains all relevant genes involved in that biological process. Third, the degree of co-regulation among the genes of that biological process as reflected by possessing similar transcriptional regulatory barcodes. The existence of co-regulated biological processes that are underrepresented in current gene set collections was evaluated with the human microarray-based prediction scores. Hierarchical clustering was applied to the transcriptional regulatory barcodes of individual genes (see “Methods” for details), which resulted in 173 clusters of co-regulated genes (Supplementary Data 3). The size of the clusters ranged between 10 and 389, which is similar to the size range 23,372 gene sets used in our ICA-TC-based GBA method.

For each cluster, the similarity among transcriptional regulatory barcodes was defined as the median pairwise correlation between gene members. This is referred to as the cluster transcriptional similarity score. In addition, for each member gene, the maximum prediction score obtained in any of the 23,372 gene sets in our framework was obtained. Then, a median per cluster was calculated, referred to as cluster predictability score. A correlation (R = 0.59) was observed between the cluster transcriptional similarity and cluster predictability scores of the 173 clusters (Fig. 5). This confirms that our method provides higher prediction scores for the biological processes that are well represented in a gene set and involves genes that are highly co-regulated. However, some clusters were observed with a low predictability score and high transcriptional similarity score. These clusters may represent co-regulated biological processes that are underrepresented or completely missing in current gene set collections. In general, the member genes of these clusters tended to be of unknown functionality, such as open-reading frames (ORFs) or uncharacterized loci (LOC). In addition, a pan-collection multifunctionality score was calculated using the gene set frequencies of all 16 gene set collections for each gene. The low multifunctionality scores of the genes belonging to these clusters reflect their low frequency of gene set memberships across all 16 gene set collections. Taken together, these results indicate that patterns of co-regulation can point towards sets of genes that participate in the same biological process even when that biological process is not well characterized in current gene set collections.

### GENETICA predicts co-functionality of uncharacterized genes

Genes that encode uncharacterized proteins are referred to as chromosome ORFs (Corfs) or uncharacterized LOCs. Compared to the PCA-TC-based method, the ICA-TC-based method generated higher prediction scores for both Corfs and LOCs with the Hallmark gene set collection (AUC calculated with two-sided Mann–Whitney U test 0.76; Fig. 6a). Hierarchical clustering of the ICA-TC-based prediction scores of 835 Corfs and LOCs based on the Hallmark gene set collection resulted in 116 clusters when using a height cutoff of 0.8. Cluster 17 was captured from 28 Corfs and LOCs that were predicted to be members of the DNA repair Hallmark gene set (Fig. 6b). Out of the 28 uncharacterized genes in this cluster, seven have been recently implicated in DNA repair based on experimental work (Fig. 6b and Supplementary Data 4). Cluster 84 consisted of Corfs predicted to be involved in estrogen receptor signaling and response (Fig. 6b). In this cluster, C6orf141 has recently been suggested to be estrogen receptor alpha regulated in breast cancer cells15 (Supplementary Data 4). These results show that GENETICA can predict the functionality of uncharacterized genes.

### GENETICA shows co-functionality in essentiality screen hits

We developed a visualization tool capable of constructing networks of genes based on predicted co-functionality in one gene set collection (see “Methods” for details). Genes are clustered together in the co-functionality network based on how similar their prediction scores are for the gene sets in the selected collection. Co-functionality networks can be explored for an input list of genes to a maximum of 300.

As an example, we used the results of a recent study, in which multiple CRISPR-based genetic screens were performed in RPE-1 cells treated with different DNA-damaging agents16. Each screen uncovered genes that are essential for cell survival in the context of specific DNA damage-inducing agents. Overall, 840 genes were found essential for survival in the context of at least one DNA-damaging agent. Out of these 840 genes, only 334 genes were assigned to a DNA repair gene set at the time of the analysis. For the 506 genes that are currently not assigned to DNA repair pathways, the ICA-TC-based method generated higher prediction scores than the PCA-TC-based method for the “GO DNA REPAIR” gene set (Fig. 7).

Next, we constructed a co-functionality network with all 840 essential genes based on the GO Biological Process collection. We observed a large cluster containing 114 genes with high pairwise co-functionality (R > 0.7). A high prediction score (Z-score 12) was observed in this cluster for the DNA repair gene set (Supplementary Fig. 3). Some genes in the cluster (n = 32) were not members of a DNA repair gene set in the original analysis, but are nevertheless known to participate in DNA repair. In other cases, these genes participate in biological processes that are indirectly associated with the cellular response to DNA damage and repair such as cell cycle regulation and nucleotide metabolism or by regulating components of the DNA damage response pathway. Less direct associations include the protein kinase C-interacting cousin of thioredoxin PICOT, which has only been recently shown to regulate the phosphorylation and activation of CHK1, CHK2, and H2AX17. The ubiquitin conjugase UBE2S has also been recently shown to bind to components of nonhomologous end joining18. Finally, some genes are still underexplored in the context of the cellular response to DNA repair (GLMN, CFAP20, C1ORF112, SAMD1), but have a high prediction score for DNA repair, which makes them candidates for further study.

In addition, we investigated three genome-wide CRISPR screens that aimed to capture genes involved in the inflammatory response to bacterial lipopolysaccharide (LPS)19, lysosomal accumulation20, and viral entry21.

A co-functionality network was built using all 111 hit genes of the response to bacterial LPS CRISPR screen performed on dendritic cells (Fig. 8a)19. Two clusters were observed. The first cluster showed high prediction scores for Immunological Signatures gene sets defining the response to TREM-1, a receptor involved in amplifying the cellular response to LPS, and gene sets defining the response to Francisella tularensis, a pathogen that produces LPS (Fig. 8a). In contrast, the second cluster showed a high prediction score for an Immunological Signatures gene set defining reactive oxygen species-induced genes within dendritic cells (Fig. 8a). These results show the possibility to use a co-functionality network to identify distinct biological processes that are related to the phenotype under investigation in a CRISPR screen.

In the genome-wide CRISPR-knockout screen identifying 16 genes essential for lysosomal integrity, a network was built with GO Biological Process and KEGG gene set collections20. The ICA-TC-based prediction scores of the 16 genes for KEGG lysosome gene set ranged from 0.8 to 2.6, indicating that the ICA-TC method did not confidently predict these genes to play a role in lysosome-related processes (Fig. 8b). Reassuringly, the ICA-TC-based method still generated higher prediction scores than the PCA-TC method for the KEGG lysosome gene set. This suggests that this particular CRISPR screen identified genes that have unique expression patterns that are incompatible within a GBA strategy.

The third genome-wide screen, studying genes involved in Ebola virus infection prioritized 13 genes21. Within the original publication, GNPTAB, a gene encoding a protein normally involved in the production of mannose-6-phosphate, was subsequently validated. Concordantly, GNPTAB showed the highest ICA-TC-based prediction score (prediction score = 6.4) for negative regulation of viral transcription by the host in the GO biological Process gene set collection (Fig. 8c). The other 12 genes showed prediction scores ranging from 0.7 to 2.6 for the respective gene set, demonstrating how ICA-TC-based prediction scores can be used to prioritize genes for further validation.

### Using RNA-seq data improves only ICA-TC-based predictions

RNA-seq experiments measure more genes and have a higher dynamic range of measurement than mRNA microarray experiments. However, the amount and diversity of publicly available microarray experiments still surpasses publicly available RNA-seq experiments. To evaluate whether RNA-seq profiles may improve upon the prediction scores generated using microarray data, the ICA-TC and PCA-TC-based methods were applied to a large set of publicly available RNA-seq samples (n = 29,138) (See Supplementary Notes). Using RNA-seq data did not improve the average prediction scores in most gene set collections when applying the PCA-TC-based method (AUC range: 0.12–0.41, p values < 2.6 × 10−4)(Fig. 9a). By contrast, average prediction scores improved in most gene set collections when applying the ICA-TC-based method (AUC range: 0.54–0.95, p values < 2.04 × 10−2) (Fig. 9b). The PCA-TC method had comparable multifunctionality associations when using RNA-seq and microarray input data for most gene set collections and improved in the case of the Oncogenic Signatures collection (AUC 0.21, p value 7.08 × 10−22) (Fig. 9c). Predictions obtained using the ICA-TC-based method had a lower association to multifunctionality for the microRNA Targets gene set collection when using RNA-seq data as input in comparison with microarray data (AUC 0.12, p value 5.1 × 10−40) (Fig. 9d). Predictions obtained using the ICA-TC-based method had a higher association to multifunctionality for the Immunological signatures gene set collection when using RNA-seq data as input (AUC 0.59, p value 6.6 × 10−58). The subset of gene set median prediction scores improved by microarray data in comparison to RNA-seq data when using ICA-TC-based method was 14.83%. These results show that the ICA-TC-based method can leverage RNA-seq profiles to improve the predictions in some gene set collections. The prediction scores based on the RNA-seq dataset have also been made available at http://genetica-network.com.

## Discussion

In this study, we utilized three large expression profile datasets generated with RNA-seq and microarray technologies, and 16 gene set collections in a GBA strategy using c-ICA to predict functional annotations. We show that our ICA-TC-based GBA strategy outperforms a currently successful method, which uses PCA-TCs in a GBA strategy. In comparison to PCA-TC-, our ICA-TC-based method (1) provides more confident functionality predictions for known and unknown gene-to-gene set combinations, (2) provides improved predictions when new knowledge is added to gene set collections, and (3) is less biased by gene multifunctionality.

Many genes do not yet have a defined function. Therefore, gene function prediction methods remain an important tool for researchers. The critical assessment of functional annotation is a famous benchmark of methods that use protein sequence data to predict gene functions via gene sets22. Other data such as gene cross-species homology, protein–protein interaction, mRNA transcription, essentiality, and semantics can also be used to predict gene functions5,13,23,24,25,26. One limitation of using mRNA expression data is that some information about the gene function can only be found at the protein level using expression, interaction, or sequence data. One advantage of mRNA expression data is the greater amount of publicly available profiles in comparison to protein experiment data.

New methods such as embeddings and neural networks can identify complex relationships from protein and mRNA expression data, which serve to improve gene function predictions.

For example, autoencoders are a neural network architecture currently used to infer a latent representation of the mRNA transcription patterns obtained from both bulk and single-cell samples27,28. This representation can be used as a regulatory barcode to generate gene function prediction scores within a GBA strategy. Convolutional neural networks and deep neural networks have also been used to directly improve gene function prediction from the protein sequences29,30. The recently developed embedding technique Uniform Manifold Approximation Projection has also been utilized to predict novel protein interactions when processing mRNA expression of different gene knockout experiments31.

In our framework, the prediction score is a Z-score obtained from a p value. This p value represents the significance level for the association between the transcriptional regulatory barcode of an individual gene and the average barcode of a gene set. We do not assume a shape for the underlying null distribution to calculate the parametric p values due to several reasons. The number of genes used to generate an average transcriptional regulatory barcode differs between gene sets (range 10–500). In addition, the association statistics used in the PCA-TC and ICA-TC-based method also differ (Pearson versus distance correlation). Finally, in the ICA-TC-based method, the average transcriptional regulatory barcode is generated by taking the mean vector of MM weights of member genes. The PCA-TC-based method instead calculates a vector of T statistics resulting from the per TC Welch T tests comparing member genes against nonmember genes5. Therefore, we utilized a permutation strategy to calculate a null distribution for each gene to gene set combination, which was then applied to calculate the p values. This enabled the generation of comparable prediction scores (Z-scores), which allow the comparison between our ICA-TC-based method and the PCA-TC-based method that is used by DEPICT and GADO5,13.

Prediction scores obtained with the ICA-TC-based method suggest that the majority of genes participate to a small degree in most biological processes. This observation is also in line with a recent report that shows how complex traits are associated with every gene in the genome to a small degree in the context of genome-wide association studies32. The PCA-TC-based method did not generate similarly high prediction scores for all genes. This suggests that the ICA-TC-based method is able to use more information than the PCA-TC method from the same input expression dataset.

Predicted gene functions can be used to find commonalities in the functional annotations of a group of genes without the bias to well-studied gene sets that can occur with conventional GSEA. These predictions can also enable the prioritization of genes that may be more likely to participate in a biological process from a list of candidate genes obtained as the result of an experiment. Finally, our unbiased clustering could be used to direct the future updates of gene set collections and the efforts for functional characterization of understudied co-regulated genes.

## Methods

### Data acquisition

We downloaded the following 14 gene set collections from the Broad Institute Molecular Signatures Database v6.2 (Hallmark, Chemical and Genetic Perturbations, BIOCARTA, KEGG, REACTOME, microRNA Targets, Transcription Factor Targets, Cancer Gene Neighborhoods, Cancer Modules, Oncogenic Signatures, Immunological Signatures, GO-Cellular Component, GO-Molecular Function, GO-Biological Process). In addition, we obtained two gene set collections from other sources: The Mammalian Phenotypes and Human Phenotype Ontology. We discarded from further analysis gene sets that contained <10 or >500 genes. Publicly available raw microarray expression data (CEL files) were collected from GEO. All available samples hybridized to Affymetrix HG-U133 Plus 2.0 (GPL570) were included (April 2018).

### Quality control and preprocessing

To identify samples that have been uploaded to GEO multiple times, we generated an MD5 hash for each individual CEL file, after which duplicate CEL files were removed. Aggregation of raw expression data was performed according to the robust multi-array average algorithm with RMAExpress (version 1.1.0). As a quality control measure, PCA was applied on the sample correlation matrix. The first PC nearly always discriminates a platform-specific signature. Low-quality samples that did not strongly correlate with this component were discarded (Pearson R < 0.8). As multiple probe sets can target a single gene on Affymetrix gene expression microarrays, we utilized The R package “jetset” (version 3.4.0) to obtain one-to-one mapping between genes and the “best” probe sets for expression data generated with Affymetrix HG-U133 Plus 2.0 platform.

### PC analysis

We performed PCA on the covariance matrix using the princomp function (R version 3.4.3) between the genes to whiten the observed variables (gene expression patterns) and reduce the dimensionality of the input data used for the c-ICA analysis. After whitening, the dimensionality was reduced from 19,635 genes to 817 whitened variables (referred in this manuscript as PCA-TCs) that explained 90% of the original variance observed in our original input dataset.

### Consensus-independent component analysis

The FastICA algorithm utilized the whitened variables obtained by PCA to calculate independent components using the FastICA R package (version 1.2.0). The number of expected components to extract was the same as the number of withered variables (n = 817). To ensure that we would capture reproducible independent components, we performed 25 runs of FastICA and only retained independent components that have an equivalent component in at least 13 runs of FastICA (Pearson R > 0.98). A total of 523 consensus-independent components (referred in this manuscript as ICA-TCs) met this requirement. A mixing matrix was recalculated using these 523 ICA-TCs by performing a matrix multiplication against the inverse of the input dataset.

### Gene prediction scores

The likelihood for an individual gene to be part of a biological pathway (e.g., gene set) is described by a prediction score. This will result in a vector of n prediction scores (e.g., functional likelihood vector) for each individual gene for each of the n gene sets in a collection. The absolute Pearson correlation between the vectors of prediction scores of two genes represents their co-functionality. A high co-functionality correlation indicates that two individual genes have similar predicted biological functions. Prediction scores were calculated using the mixing matrix and each of the 16 gene set collections was used as input using the AnalyzerTool desktop app (version 5.0).

### Co-functionality network

Genes are plotted as nodes and their co-functionality correlation as edges in the network visualization. Only nodes with at least one correlation higher than the threshold will be shown. Selecting a group of nodes shows their average prediction scores for gene sets of the selected gene set collection.

### Gene multifunctionality score calculation

We calculate gene multifunctionality scores for each gene set collection as described in ref. 14. A gene multifunctionality score is a weighted sum of the number of gene sets that have that gene as a member. The weight of each membership is corrected by the size of each gene set as follows:

$$\,{\text{Score}}\,({G}_{A})=\mathop{\sum}\limits_{i| {G}_{A}\in {C}_{i}}\frac{1}{{N}_{{\mathrm{in}}_{i}}\times {N}_{{\mathrm{out}}_{i}}}$$

Where GA is a gene, Ci is a gene set in the collection that has GA as a member, $${N}_{{\mathrm{in}}_{i}}$$ is the number of genes that belong to Ci and $${N}_{{\mathrm{out}}_{i}}$$ is the complementary set of genes that do not belong to Ci. Distance correlations were calculated using the dcor2d function from the energy R package (version 1.7).

### Hierarchical clustering of regulatory barcodes

Using the “hclust” function, we performed a hierarchical clustering using the “ward.D2” method over an input distance matrix generated from the c-ICA mixing matrix using dcor2d (1 − correlation) (R version 3.4.3, hclust version 3.4.3, energy 1.7). Note that the mixing matrix is an output of the c-ICA and is not generated using gene sets. Clusters were generated by cutting the dendrogram at a height (h = 2.5), which guaranteed the size of every cluster to be within the range 10–500 genes, which is the same size range used for gene sets. This resulted in 173 clusters of sizes 13 to 389 with a mean of 115.

Uncharacterized genes were defined as genes with the “C*orf*” or the “LOC*” glob pattern in their gene symbol. For these 835 genes, the ICA-TC-based prediction scores were selected for all 50 Hallmark gene sets. The resulting data frame was clustered hierarchically, both for genes and gene sets, using the “ward.D2” method and (1 − correlation) as the distance measurement (R version 3.4.3, hclust version 3.4.3). To obtain clusters of uncharacterized genes, the gene dendrogram resulting from clustering was cut off at a height of 0.8.

### RNA-seq-based prediction scores

The sample subset processed in the manuscript by Deelen et al.13 was downloaded and quality controlled. Pseudocounts were obtained using kallisto and gene-level counts were calculated using DESeq233,34. After quality control, 58,433 genes and 29,138 samples remained (see Supplementary Notes). In total, 85% of the variance of this dataset was explained by 2711 PCs, which were used for calculating PCA-TC-based prediction scores. These same 2711 PCs were used as input for the consensus ICA method that generated 1373 ICs (with credibility index of 0.5), which were used to generate the ICA-TC-based prediction scores.

### Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.