论文标题
静态图形信号中平均值中更改点的离线检测
Offline detection of change-points in the mean for stationary graph signals
论文作者
论文摘要
本文解决了分割图形信号流的问题：我们旨在检测已知图的节点上定义的多元信号的变化。我们提出了一种离线方法，该方法依赖于图形信号平稳性的概念，并允许问题从原始顶点域到频谱域（图形傅立叶变换）的方便翻译，在此更容易求解。尽管所获得的光谱表示在实际应用中很少，但据我们所知，该属性在现有相关文献中尚未得到充分利用。我们的更改点检测方法采用了一种模型选择方法，该方法考虑了光谱表示的稀疏性并自动确定变更点的数量。我们的探测器提供了非肿瘤甲骨文不平等的证明。数值实验证明了该方法的性能。
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.
