MOTIVATION: Combining omics and images can lead to a more comprehensive clustering of individuals than classic single-view approaches. Among the various approaches for multi-view clustering, nonnegative matrix tri-factorization (NMTF) and nonnegative Tucker decomposition (NTD) are advantageous in learning low-rank embeddings with promising interpretability. Besides, there is a need to handle unwanted drivers of clusterings (i.e. confounders). RESULTS: In this work, we introduce a novel multi-view clustering method based on NMTF and NTD, named INMTD, which integrates omics and 3D imaging data to derive unconfounded subgroups of individuals. According to the adjusted Rand index, INMTD outperformed other clustering methods on a synthetic dataset with known clusters. In the application to real-life facial-genomic data, INMTD generated biologically relevant embeddings for individuals, genetics, and facial morphology. By removing confounded embedding vectors, we derived an unconfounded clustering with better internal and external quality; the genetic and facial annotations of each derived subgroup highlighted distinctive characteristics. In conclusion, INMTD can effectively integrate omics data and 3D images for unconfounded clustering with biologically meaningful interpretation. AVAILABILITY AND IMPLEMENTATION: INMTD is freely available at https://github.com/ZuqiLi/INMTD.

MOTIVATION: Spatial Analysis of Functional Enrichment (SAFE) is a popular tool for biologists to investigate the functional organization of biological networks via highly intuitive 2D functional maps. To create these maps, SAFE uses Spring embedding to project a given network into a 2D space in which nodes connected in the network are near each other in space. However, many biological networks are scale-free, containing highly connected hub nodes. Because Spring embedding fails to separate hub nodes, it provides uninformative embeddings that resemble a 'hairball'. In addition, Spring embedding only captures direct node connectivity in the network and does not consider higher-order node wiring patterns, which are best captured by graphlets, small, connected, nonisomorphic, induced subgraphs. The scale-free structure of biological networks is hypothesized to stem from an underlying low-dimensional hyperbolic geometry, which novel hyperbolic embedding methods try to uncover. These include coalescent embedding, which projects a network onto a 2D disk. RESULTS: To better capture the functional organization of scale-free biological networks, whilst also going beyond simple direct connectivity patterns, we introduce Graphlet Coalescent (GraCoal) embedding, which embeds nodes nearby on a disk if they frequently co-occur on a given graphlet together. We use GraCoal to extend SAFE-based network analysis. Through SAFE-enabled enrichment analysis, we show that GraCoal outperforms graphlet-based Spring embedding in capturing the functional organization of the genetic interaction networks of fruit fly, budding yeast, fission yeast and Escherichia coli. We show that depending on the underlying graphlet, GraCoal embeddings capture different topology-function relationships. We show that triangle-based GraCoal embedding captures functional redundancies between paralogs. AVAILABILITY AND IMPLEMENTATION: https://gitlab.bsc.es/swindels/gracoal_embedding.

MOTIVATION: Cancer is a genetic disease in which accumulated mutations of driver genes induce a functional reorganization of the cell by reprogramming cellular pathways. Current approaches identify cancer pathways as those most internally perturbed by gene expression changes. However, driver genes characteristically perform hub roles between pathways. Therefore, we hypothesize that cancer pathways should be identified by changes in their pathway-pathway relationships. RESULTS: To learn an embedding space that captures the relationships between pathways in a healthy cell, we propose pathway-driven non-negative matrix tri-factorization. In this space, we determine condition-specific (i.e. diseased and healthy) embeddings of pathways and genes. Based on these embeddings, we define our 'NMTF centrality' to measure a pathway's or gene's functional importance, and our 'moving distance', to measure the change in its functional relationships. We combine both measures to predict 15 genes and pathways involved in four major cancers, predicting 60 gene-cancer associations in total, covering 28 unique genes. To further exploit driver genes' tendency to perform hub roles, we model our network data using graphlet adjacency, which considers nodes adjacent if their interaction patterns form specific shapes (e.g. paths or triangles). We find that the predicted genes rewire pathway-pathway interactions in the immune system and provide literary evidence that many are druggable (15/28) and implicated in the associated cancers (47/60). We predict six druggable cancer-specific drug targets. AVAILABILITY AND IMPLEMENTATION: The code and data are available at: https://gitlab.bsc.es/swindels/pathway_driven_nmtf. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Laplacian matrices capture the global structure of networks and are widely used to study biological networks. However, the local structure of the network around a node can also capture biological information. Local wiring patterns are typically quantified by counting how often a node touches different graphlets (small, connected, induced sub-graphs). Currently available graphlet-based methods do not consider whether nodes are in the same network neighbourhood. To combine graphlet-based topological information and membership of nodes to the same network neighbourhood, we generalize the Laplacian to the Graphlet Laplacian, by considering a pair of nodes to be 'adjacent' if they simultaneously touch a given graphlet. RESULTS: We utilize Graphlet Laplacians to generalize spectral embedding, spectral clustering and network diffusion. Applying Graphlet Laplacian-based spectral embedding, we visually demonstrate that Graphlet Laplacians capture biological functions. This result is quantified by applying Graphlet Laplacian-based spectral clustering, which uncovers clusters enriched in biological functions dependent on the underlying graphlet. We explain the complementarity of biological functions captured by different Graphlet Laplacians by showing that they capture different local topologies. Finally, diffusing pan-cancer gene mutation scores based on different Graphlet Laplacians, we find complementary sets of cancer-related genes. Hence, we demonstrate that Graphlet Laplacians capture topology-function and topology-disease relationships in biological networks. AVAILABILITY AND IMPLEMENTATION: http://www0.cs.ucl.ac.uk/staff/natasa/graphlet-laplacian/index.html. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.