Constrained Spectral Clustering for Dynamic Community Detection

Abstract

Networks are useful representations of many systems with interacting entities, such as social, biological and physical systems. Characterizing the meso-scale organization, i.e. the community structure, is an important problem in network science. Community detection aims to partition the network into sets of nodes that are densely connected internally but sparsely connected to other dense sets of nodes. Current work on community detection mostly focuses on static networks. However, many real world networks are dynamic, i.e. their structure and properties change with time, requiring methods for dynamic community detection. In this paper, we propose a new stochastic block model (SBM) for modeling the evolution of community membership. Unlike existing SBMs, the proposed model allows each community to evolve at a different rate. This new model is used to derive a maximum a posteriori estimator for community detection, which can be written as a constrained spectral clustering problem. In particular, the transition probabilities for each community modify the graph adjacency matrix at each time point. This formulation provides a relationship between statistical network inference and spectral clustering for dynamic networks. The proposed method is evaluated on both simulated and real dynamic networks.

Community detection in complex networks: From statistical foundations to data science applications

“…Stochastic block model based community detection: This method is proposed as a temporal SBM in which interactions between nodes evolve and have certain time periods (Corneli et al, 2016;Karaaslanli & Aviyente, 2020;Pensky & Zhang, 2019). Time intervals are divided into subintervals of fixed identical duration.…”