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

Bo Wang, Lin Huang, Yuke Zhu, Anshul Kundaje, Serafim Batzoglou, Anna Goldenberg

Abstract: 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.