Change Point Detection and Node Clustering for Time Series of Graphs

Abstract

Suppose an undirected graph is observed over time. Its structure (i.e., nodes and edges) remains the same but the measurements taken at the nodes may vary over time. This paper proposes a method that simultaneously performs the following two tasks: (i) it detects change points in the time domain, and (ii) for each time interval between any two consecutive detected change points, it partitions the nodes into different clusters of similar measurements. The method begins with recasting the problem into a model selection problem and employs the minimum description length principle to construct a selection criterion for which the best fitting model is defined as its minimizer. A practical algorithm is developed to (approximately) locate this minimizer. It is shown that the model selection criterion leads to statistically consistent estimates, while numerical experiments show that the method enjoys promising empirical properties. To the best of the authors’ knowledge, the proposed method is one of the first that performs simultaneous change point detection and node clustering for time series of graphs.