Kalman Filter Driven Estimation of Community Structure in Time Varying Graphs

Abstract

Community detection is an NP-hard graph problem that has been the subject of decades of research. Moreover, efficient methods are needed for time-varying graphs. In this paper we propose and evaluate a method of approximating the latent block structure within a time-varying graph using a Kalman filter. The method described breaks a stream of graph updates into samples of sufficient size, each one forming a graph $G_{t}$, and has the desirable feature that it accurately updates its representation of the latent block structure using a relatively small amount of information: the prior $t-1$ predicted block structure and the current datastream sample $G_{t}$. This paper details the underlying system of linear equations, used here to represent community detection, that achieves 97 % accuracy estimating the latent block representation as the community structure changes. This is demonstrated for synthetic graphs generated by a hybrid mixed-model stochastic block model from the DARPAIMIT Graph Challenge with time-varying block structure.