Joint Modeling of Change-Point Identification and Dependent Dynamic Community Detection

: The field of dynamic network analysis has recently seen a surge of interest in community detection and evolution. However, existing methods for dynamic community detection do not consider dependencies between edges, which could lead to a loss of information when detecting community structures. In this study, we investigate the problem of identifying a change-point with abrupt changes in the community structure of a network. To do so, we propose an approximate likelihood approach for the change-point estimator and for identifying node membership that integrates marginal information and dependencies of network connectivities. We propose an expectation-maximization-type algorithm that maximizes the approximate likelihood jointly over change-point and community membership evolution. From a theoretical viewpoint, we establish estimation consistency under the regularity condition, and show that the proposed estimators achieve a higher convergence rate than those of their marginal likelihood counterparts, which do not incorporate dependencies between edges. We demonstrate the validity of the proposed method by applying it to the ADHD-200 data set to detect brain functional community changes over time.