Linear functional organization of the omic embedding space

Abstract

Motivation We are increasingly accumulating complex omics data that capture different aspects of cellular functioning. A key challenge is to untangle their complexity and effectively mine them for new biomedical information. To decipher this new information, we introduce algorithms based on network embeddings. Such algorithms represent biological macromolecules as vectors in d-dimensional space, in which topologically similar molecules are embedded close in space and knowledge is extracted directly by vector operations. Recently, it has been shown that neural networks used to obtain vectorial representations (embeddings) are implicitly factorizing a mutual information matrix, called Positive Pointwise Mutual Information (PPMI) matrix. Thus, we propose the use of the PPMI matrix to represent the human protein-protein interaction (PPI) network and also introduce the Graphlet Degree Vector PPMI matrix of the PPI network to capture different topological (structural) similarities of the nodes in the molecular network. Results We generate the embeddings by decomposing these matrices with Non-Negative Matrix Tri-Factorization. We demonstrate that genes that are embedded close in these spaces have similar biological functions, so we can extract new biomedical knowledge directly by doing linear operations on their embedding vector representations. We exploit this property to predict new genes participating in protein complexes and to identify new cancer-related genes based on the cosine similarities between the vector representations of the genes. We validate 80% of our novel cancer-related gene predictions in the literature and also by patient survival curves that demonstrating that 93.3% of them have a potential clinical relevance as biomarkers of cancer. Availability Code and data are available online at https://gitlab.bsc.es/axenos/embedded-omics-data-geometry/ Supplementary information Supplementary data are available at Bioinformatics online.

The axes of biology: a novel axes-based network embedding paradigm to decipher the functional mechanisms of the cell

“…Following Xenos et. al [43] and Doria-Belenguer et. al [25], we use the Deepwalk closed formula by Qiu et.…”

“…This formula can be interpreted as a diffusion process that captures higher-order proximities between the nodes in the network; hence, the PPMI matrix is a richer representation than the adjacency matrix [43]. As demonstrated by Xenos et al [43] and Doria-Belenguer et al [25], the extra information encoded in PPMI matrices leads to embedding spaces that better functionally organize the vectorial representation of both genes and gene functions than those generated by using the adjacency matrix.…”

A functional analysis of omic network embedding spaces reveals key altered functions in cancer

“…We represent the tissue-specific PPI networks with their positive point-wise mutual information (PPMI) matrices, X , where each entry in the matrix contains information about how frequently two nodes co-occur in a random walk in the corresponding PPI network. Following Xenos et al (2021) , we use the DeepWalk closed formula by Perozzi et al (2014) with its default settings, which uses 10 iterations, to compute the PPMI matrix. This formula can be interpreted as a diffusion process that captures high-order proximities between the nodes in the network; hence, PPMI is a richer representation than the adjacency matrix ( Xenos et al 2021 ).…”

“…Following Xenos et al (2021) , we use the DeepWalk closed formula by Perozzi et al (2014) with its default settings, which uses 10 iterations, to compute the PPMI matrix. This formula can be interpreted as a diffusion process that captures high-order proximities between the nodes in the network; hence, PPMI is a richer representation than the adjacency matrix ( Xenos et al 2021 ). As a result of the extra information encoded in the PPMI, its corresponding embedding spaces better capture the functional organization of the cell than the ones generated by using the adjacency matrix (the details of this comparison are presented in Supplementary Section S1.2.1 ).…”

“…One of the advantages of NMTF over deep neural network-based ML approaches is that it requires way fewer parameters to tune, thanks to the careful modeling of the relationships between the data points that it takes as input. As shown by Xenos et al (2021) , the molecular network embedding space produced by NMTF can have valuable properties, e.g. orthonormality, that may lead to an easier interpretation and deeper scientific insight ( Isokääntä et al 2020 ).…”