Community Detection with Heterogeneous Block Covariance Model
This addresses the limitation of existing methods that only handle binary edges, offering a solution for domains like biology and finance where edge weights are continuous and signed.
The authors tackled the problem of community detection in networks with continuous, signed edge weights by introducing the heterogeneous block covariance model (HBCM), which provides provable consistent membership estimates and shows promising performance in simulations and real-world datasets like single-cell RNA-seq and stock prices.
Community detection is the task of clustering objects based on their pairwise relationships. Most of the model-based community detection methods, such as the stochastic block model and its variants, are designed for networks with binary (yes/no) edges. In many practical scenarios, edges often possess continuous weights, spanning positive and negative values, which reflect varying levels of connectivity. To address this challenge, we introduce the heterogeneous block covariance model (HBCM) that defines a community structure within the covariance matrix, where edges have signed and continuous weights. Furthermore, it takes into account the heterogeneity of objects when forming connections with other objects within a community. A novel variational expectation-maximization algorithm is proposed to estimate the group membership. The HBCM provides provable consistent estimates of memberships, and its promising performance is observed in numerical simulations with different setups. The model is applied to a single-cell RNA-seq dataset of a mouse embryo and a stock price dataset. Supplementary materials for this article are available online.