Offline detection of change-points in the mean for stationary graph signals

This paper addresses the problem of segmenting a stream of graph signals: we aim to detect changes in the mean of the multivariate signal defined over the nodes of a known graph. We propose an offline algorithm that relies on the concept of graph signal stationarity and allows the convenient translation of the problem from the original vertex domain to the spectral domain (Graph Fourier Transform), where it is much easier to solve. Although the obtained spectral representation is sparse in real applications, to the best of our knowledge this property has not been much exploited in the existing related literature. Our main contribution is a change-point detection algorithm that adopts a model selection perspective, which takes into account the sparsity of the spectral representation and determines automatically the number of change-points. Our detector comes with a proof of a non-asymptotic oracle inequality, numerical experiments demonstrate the validity of our method.