Overlapping communities and roles in networks with node attributes: Probabilistic graphical modeling, Bayesian formulation and variational inference

Community and role discovery are key tasks in network analysis. The former unveils the organization of a network, whereas the latter highlights the social functions of nodes. The integration of community discovery and role analysis has been investigated, to gain a deeper understanding of topology, i.e., the social functions fulfilled by nodes to pursue community purposes. However, hitherto, node attributes and behavioral role patterns have been ignored in the combination of both tasks. In this manuscript, we study the seamless integration of community discovery and behavioral role analysis, in the domain of networks with node attributes. In particular, we focus on unifying the two tasks, by explicitly harnessing node attributes and behavioral role patterns in a principled manner. To this end, we propose two Bayesian probabilistic generative models of networks, whose novelty consists in the interrelationship of overlapping communities, roles, their behavioral patterns and node attributes. The devised models allow for a variety of exploratory, descriptive and predictive tasks. These are carried out through mean-field variational inference, which is in turn mathematically derived and implemented into a coordinate-ascent algorithm. A wide spectrum of experiments is designed, to validate the devised models against three classes of state-of-the-art competitors using various real-world benchmark data sets from different social networking services. Our models are found to be more accurate in community detection, link prediction and attribute prediction. Notably, the gain in accuracy is robust to perturbations in the form of noise or lack of observations in either network structure or node attributes. Beside accuracy, scalability is also comparatively investigated. Finally, a qualitative demonstration of the tasks enabled by our models is developed, in which node roles are intuitively explained through an unprecedented visual representation.