Simultaneous global and local clustering in multiplex networks with covariate information.

Music City Center 

We introduce a new model that simultaneously detects communities within individual layers of a multiplex network while inferring a global node clustering across the layers. A Stochastic Block Model (SBM) 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 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.

Multiplex networks

Community detection

Dirichlet process

Stochastic block model

Variational inference 

Royal Statistical Society