Simultaneous global and local clustering in multiplex networks with covariate information

TL;DR

This paper introduces HMPSBM, a Bayesian hierarchical model that detects both global and layer-specific communities in multiplex networks, incorporating covariate data and allowing for varying group structures across layers.

Contribution

The paper presents a novel hierarchical Bayesian model for multiplex networks that simultaneously infers global and local communities, integrating covariate information and enabling scalable inference.

Findings

Accurately recovers global and layer-specific clusters in simulations.

Effectively uncovers latent structures in real multiplex network data.

Scalable variational inference method for large networks.

Abstract

Understanding both global and layer-specific group structures is useful for uncovering complex patterns in networks with multiple interaction types. In this work, we introduce a new model, the hierarchical multiplex stochastic blockmodel (HMPSBM), that simultaneously detects communities within individual layers of a multiplex network while inferring a global node clustering across the layers. A stochastic blockmodel is assumed in each layer, with probabilities of layer-level group memberships determined by a node's global group assignment. Our model uses a Bayesian framework, employing a probit stick-breaking process to construct node-specific mixing proportions over a set of shared Griffiths-Engen-McCloseky (GEM) distributions. These proportions determine layer-level community assignment, allowing for an unknown and varying number of groups across layers, while incorporating nodal covariate information to inform the global clustering. We propose a scalable variational inference procedure with parallelisable updates for application to large networks. Extensive simulation studies demonstrate our model's ability to accurately recover both global and layer-level clusters in complicated settings, and applications to real data showcase the model's effectiveness in uncovering interesting latent network structure.