Stationary graph process models are commonly used in the analysis and inference of data sets collected on irregular network topologies. While most of the existing methods represent graph signals with a single stationary process model that is globally valid on the entire graph, in many practical problems, the characteristics of the process may be subject to local variations in different regions of the graph. In this work, we propose a locally stationary graph process (LSGP) model that aims to extend the classical concept of local stationarity to irregular graph domains. We characterize local stationarity by expressing the overall process as the combination of a set of component processes such that the extent to which the process adheres to each component varies smoothly over the graph. We propose an algorithm for computing LSGP models from realizations of the process, and also study the approximation of LSGPs locally with WSS processes. Experiments on signal interpolation problems show that the proposed process model provides accurate signal representations competitive with the state of the art.

翻译：局部平稳图过程模型常用于分析不规则网络拓扑结构上收集的数据集并进行推断。尽管现有方法大多采用全局适用于整个图的单一平稳过程模型来表示图信号，但在许多实际问题中，过程的特性可能因图的不同区域而存在局部变化。本文提出了一种局部平稳图过程（LSGP）模型，旨在将经典的局部平稳性概念扩展到不规则图域。我们通过将整体过程表示为一系列分量过程的组合来刻画局部平稳性，使得过程对各分量的依从程度在图上是平滑变化的。我们提出了一种基于过程实现计算LSGP模型的算法，并研究了用WSS过程对LSGP进行局部近似的方法。在信号插值问题上的实验表明，所提出的过程模型能够提供与当前最先进技术相竞争的高精度信号表示。