Nested stochastic block model for simultaneously clustering networks and nodes

TL;DR

The paper introduces the nested stochastic block model (NSBM), a Bayesian approach that simultaneously clusters multiple networks and their communities, handling unlabeled, heterogeneous, and varying-sized networks with automatic model selection.

Contribution

It presents a novel Bayesian nested Dirichlet process prior for joint network and community clustering, with efficient MCMC algorithms for inference, addressing challenges in analyzing unlabeled and diverse networks.

Findings

Accurate estimation of dual clustering structures demonstrated in simulations.

Successful application to social network datasets with anonymized and varying node counts.

Model outperforms previous methods limited to single networks or labeled data.

Abstract

We introduce the nested stochastic block model (NSBM) to cluster a collection of networks while simultaneously detecting communities within each network. NSBM has several appealing features including the ability to work on unlabeled networks with potentially different node sets, the flexibility to model heterogeneous communities, and the means to automatically select the number of classes for the networks and the number of communities within each network. This is accomplished via a Bayesian model, with a novel application of the nested Dirichlet process (NDP) as a prior to jointly model the between-network and within-network clusters. The dependency introduced by the network data creates nontrivial challenges for the NDP, especially in the development of efficient samplers. For posterior inference, we propose several Markov chain Monte Carlo algorithms including a standard Gibbs sampler, a collapsed Gibbs sampler, and two blocked Gibbs samplers that ultimately return two levels of clustering labels from both within and across the networks. Extensive simulation studies are carried out which demonstrate that the model provides very accurate estimates of both levels of the clustering structure. We also apply our model to two social network datasets that cannot be analyzed using any previous method in the literature due to the anonymity of the nodes and the varying number of nodes in each network.