Combining a popularity-productivity stochastic block model with a discriminative content model for detecting general structures

Latent community discovery that combines links and contents of a text-associated network, has drawn more attention with the advance of social medias. Most of the previous studies aim at detecting densely connected communities, and are not able to identify general structures, e.g., bipartite structure. Several variants based on stochastic block model are more flexible for exploring general structures by introducing link probabilities between communities. However, neither can these variants identify degree distributions of real networks due to lacking of modeling the differences among nodes, nor can they be suitable for discovering communities in text-associated networks due to ignoring the contents of nodes. In this paper, we propose a popularity-productivity stochastic block (PPSB) model by introducing two random variables, popularity and productivity, to model the differences among nodes in receiving links and producing links, respectively. The new model has the flexibility of existing stochastic block models in discovering general community structures, and inherits the richness of previous models that also exploit popularity and productivity in modeling the real scale-free networks with power law degree distributions. To incorporate contents in text-associated networks, we propose a PPSB-DC model which combines the PPSB model with a discriminative model that models the community memberships of nodes by their contents. We then develop EM algorithms for inferring the parameters in the two models. Experiments on synthetic and real networks have demonstrated that the proposed models can yield better performances than previous models, especially on networks with general structures.