Community Detection with Heterogeneous Block Covariance Model

TL;DR

This paper introduces the heterogeneous block covariance model (HBCM) for community detection in weighted networks with signed, continuous edges, providing a new approach that accounts for heterogeneity and offers consistent estimation.

Contribution

The paper proposes the HBCM, a novel covariance-based community detection model for weighted, signed networks, along with a variational EM algorithm for estimation and theoretical consistency guarantees.

Findings

HBCM accurately detects communities in simulated data.

HBCM successfully applied to biological and financial datasets.

The model outperforms traditional binary-edge community detection methods.

Abstract

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.