Nonparametric Multi-group Membership Model for Dynamic Networks

Statistical analysis of social networks and other relational data is becoming an increasingly important problem as the scope and availability of network data increases. Network data--such as the friendships in a social network--is often dynamic in a sense that relations between entities rise and decay over time. A fundamental problem in the analysis of such dynamic network data is to extract a summary of the common structure and the dynamics of the underlying relations between entities. Accurate models of structure and dynamics of network data have many applications. They allow us to predict missing relationships [20, 21, 23], recommend potential new relations [2], identify clusters and groups of nodes [1, 29], forecast future links [4, 9, 11, 24], and even predict group growth and longevity [15]. Here we present a new approach to modeling network dynamics by considering time-evolving interactions between groups of nodes as well as the arrival and departure dynamics of individual nodes to these groups. We develop a dynamic network model, Dynamic Multi-group Membership Graph Model, that identifies the birth and death of individual groups as well as the dynamics of node joining and leaving groups in order to explain changes in the underlying network linking structure. Our nonparametric model considers an infinite number of latent groups, where each node can belong to multiple groups simultaneously. We capture the evolution of individual node group memberships via a Factorial Hidden Markov model.