This paper addresses the problem of segmenting a stream of graph signals: we aim to detect changes in the mean of a multivariate signal defined over the nodes of a known graph. We propose an offline method 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 sufficiently exploited in the existing related literature. Our change-point detection method adopts a model selection approach that 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 performance of the proposed method.

翻译：本文针对图信号流的分割问题：我们旨在检测定义于已知图节点上的多变量信号均值变化。提出一种基于图信号平稳性概念的离线方法，该方法能够将原始顶点域的问题便捷地转换到谱域（图傅里叶变换），从而大幅简化问题求解。尽管实际应用中获得的谱表示具有稀疏性，但据我们所知，现有相关文献尚未充分利用这一特性。本文提出的变化点检测方法采用模型选择策略，兼顾谱表示的稀疏性并自动确定变化点数量。该检测器附带非渐近oracle不等式的理论证明。数值实验验证了所提方法的有效性。