A Mean-Field Variational Bayesian Approach to Detecting Overlapping Communities with Inner Roles using Poisson Link Generation

A novel model-based machine-learning approach is presented for the unsupervised and exploratory analysis of node affiliations to overlapping communities with roles in networks. At the heart of our approach is a new Bayesian probabilistic generative model of directed networks, that treats roles as abstract behavioral classes explaining node linking behavior. A generalized weighted instance of \emph{directed affiliation modeling} rules the strength of node participation in communities with whichever role through \emph{Gamma priors}. Moreover, link establishment between nodes is governed by a \emph{Poisson distribution}. The latter is parameterized so that, the stronger the affiliations of two nodes to common communities with respective roles, the more likely it is the formation of a connection. A coordinate-ascent algorithm is designed to implement mean-field variational inference for affiliation analysis and link prediction. A comparative experimentation on real-world networks demonstrates the superiority of our approach in community compactness, link prediction and scalability.