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：平稳图过程模型常用于分析不规则网络拓扑上采集的数据集。现有方法大多采用全局有效的单一平稳过程模型来表示图信号，但在许多实际问题中，过程特性可能在不同图区域呈现局部变化。本研究提出一种局部平稳图过程模型，旨在将经典局部平稳性概念拓展至不规则图域。我们将整体过程表示为若干分量过程的组合，各分量对过程的贡献程度在整个图上平滑变化，以此表征局部平稳性。我们提出了一种从过程实现中计算LSGP模型的算法，并研究了用宽平稳过程对LSGP进行局部逼近的方法。信号插值实验表明，所提过程模型能够提供与现有最优方法相媲美的精确信号表示。