Nested stochastic block model for simultaneously clustering networks and nodes

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.

Bayesian community detection for networks with covariates

The increasing prevalence of network data in a vast variety of fields and the need to extract useful information out of them have spurred fast developments in related models and algorithms. Among the various learning tasks with network data, community detection, the discovery of node clusters or "communities," has arguably received the most attention in the scientific community. In many real-world applications, the network data often come with additional information in the form of node or edge covariates that should ideally be leveraged for inference. In this paper, we add to a limited literature on community detection for networks with covariates by proposing a Bayesian stochastic block model with a covariate-dependent random partition prior. Under our prior, the covariates are explicitly expressed in specifying the prior distribution on the cluster membership. Our model has the flexibility of modeling uncertainties of all the parameter estimates including the community membership. Importantly, and unlike the majority of existing methods, our model has the ability to learn the number of the communities via posterior inference without having to assume it to be known. Our model can be applied to community detection in both dense and sparse networks, with both categorical and continuous covariates, and our MCMC algorithm is very efficient with good mixing properties. We demonstrate the superior performance of our model over existing models in a comprehensive simulation study and an application to two real datasets.