Vicus: Exploiting local structures to improve network-based analysis of biological data

Biological networks entail important topological features and patterns critical to understanding interactions within complicated biological systems. Despite a great progress in understanding their structure, much more can be done to improve our inference and network analysis. Spectral methods play a key role in many network-based applications. Fundamental to spectral methods is the Laplacian, a matrix that captures the global structure of the network. Unfortunately, the Laplacian does not take into account intricacies of the network’s local structure and is sensitive to noise in the network. These two properties are fundamental to biological networks and cannot be ignored. We propose an alternative matrix Vicus. The Vicus matrix captures the local neighborhood structure of the network and thus is more effective at modeling biological interactions. We demonstrate the advantages of Vicus in the context of spectral methods by extensive empirical benchmarking on tasks such as single cell dimensionality reduction, protein module discovery and ranking genes for cancer subtyping. Our experiments show that using Vicus, spectral methods result in more accurate and robust performance in all of these tasks.Author summary: Networks are a representation of choice for many problems in biology and medicine including protein interactions, metabolic pathways, evolutionary biology, cancer subtyping and disease modeling to name a few. The key to much of network analysis lies in the spectrum decomposition represented by eigenvectors of the network Laplacian. While possessing many desirable algebraic properties, Laplacian lacks the power to capture fine-grained structure of the underlying network. Our novel matrix, Vicus, introduced in this work, takes advantage of the local structure of the network while preserving algebraic properties of the Laplacian. We show that using Vicus in spectral methods leads to superior performance across fundamental biological tasks such as dimensionality reduction in single cell analysis, identifying genes for cancer subtyping and identifying protein modules in a PPI network. We postulate, that in tasks where it is important to take into account local network information, spectral-based methods should be using Vicus matrix in place of Laplacian.