Finding hypergraph communities: a Bayesian approach and variational solution

Data clustering, including problems such as finding network communities, can be put into a systematic framework by means of a Bayesian approach. Here we address the Bayesian formulation of the problem of finding hypergraph communities. We start by introducing a hypergraph generative model with a built-in group structure. Using a variational calculation we derive a variational Bayes algorithm, a generalized version of the expectation maximization algorithm with a built-in penalization for model complexity or bias. We demonstrate the good performance of the variational Bayes algorithm using test examples, including finding network communities. A MATLAB code implementing this algorithm is provided as supplementary material.