Modeling and change detection of dynamic network data by a network state space model

Dynamic network data are often encountered in social, biological, and engineering domains. There are two types of variability in dynamic network data: variability of natural evolution and variability due to assignable causes. The latter is the “change” referred to in this article. Accurate and timely change detection from dynamic network data is important. However, it has been infrequently studied, with most of the existing research having focused on community detection, prediction, and visualization. Change detection is a classic research area in Statistical Process Control (SPC), and various approaches have been developed for dynamic data in the form of univariate or multivariate time series but not in the form of networks. We propose a Network State Space Model (NSSM) to characterize the natural evolution of dynamic networks. For tractable parameter estimation of the NSSM, we develop an Expectation Propagation algorithm to produce an approximation for the observation equation of the NSSM and then use Expectation-Maximization integrated with Bayesian Optimal Smoothing to estimate the parameters. For change detection, we further propose a Singular Value Decomposition (SVD)-based method that integrates the NSSM with SPC. A realworld application on Enron dynamic email networks is presented, in which our method successfully detects two known changes.