Network topology change-point detection from graph signals with prior spectral signatures
This work addresses change-point detection in network structures for applications like sensor networks or social media analysis, but it is incremental as it builds on existing graph signal processing and CUSUM methods.
The paper tackles the problem of detecting changes in graph topology from sequential graph signals by reducing it to a subspace detection problem and incorporating prior spectral information to denoise data, resulting in a CUSUM-based algorithm that shows improved performance in numerical experiments.
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.