Network topology change-point detection from graph signals with prior spectral signatures

Abstract: We consider the problem of sequential graph topology change-point detection from graph signals. We assume that signals on the nodes of the graph are regularized by the underlying graph structure via a graph filtering model, which we then leverage to distill the graph topology change-point detection problem to a subspace detection problem. We demonstrate how prior information on the spectral signature of the post-change graph can be incorporated to implicitly denoise the observed sequential data, thus leading to a natural CUSUM-based algorithm for change-point detection. Numerical experiments illustrate the performance of our proposed approach, particularly underscoring the benefits of (potentially noisy) prior information.