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

TL;DR

This paper introduces a new method for detecting changes in graph topology over time by leveraging spectral signatures and prior information, improving detection accuracy in noisy data.

Contribution

It proposes a CUSUM-based algorithm that incorporates prior spectral information to enhance graph topology change-point detection from sequential graph signals.

Findings

Effective detection of topology changes demonstrated in experiments

Prior spectral information improves detection robustness

Method outperforms baseline approaches in noisy scenarios

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.