Integrating overlapping community discovery and role analysis: Bayesian probabilistic generative modeling and mean-field variational inference

The joint modeling of community discovery and role analysis was shown useful to explain, predict and reason on network topology. Nonetheless, earlier research on the integration of both tasks suffers from major limitations. Foremost, a key aspect of role analysis, i.e., the strength of role-to-role interactions, is ignored. Moreover, two fundamental properties of networks are disregarded, i.e., heterogeneity in the connectivity structure of communities and the growing link probability with node involvement in common communities. Additionally, scalability with network size is limited. In this manuscript, we incrementally develop two new machine learning approaches to deal with the foresaid issues. The proposed approaches consist in performing inference under as many Bayesian generative models of networks with overlapping communities and roles. Under both models, nodes are associated with communities and roles through suitable affiliations, that are dichotomized for link directionality. The strength of such affiliations is captured through nonnegative latent random variables, drawn from Gamma priors. Besides, link establishment is explained by both models through Poisson distributions. In particular, under the second model, the parameterizing rate of the Poisson distribution also accommodates the strength of role-to-role interactions, as captured via latent mixed-membership stochastic blockmodeling. On sparse networks, the adoption of the Poisson distribution expedites model inference. On this point, mean-field variational inference is derived and implemented as a coordinate-ascent algorithm, for the exploratory and unsupervised analysis of node affiliations. Comparative experiments on several real-world networks demonstrate the superiority of the proposed approaches in community discovery, link prediction as well as scalability.