Locally Stationary Graph Processes

TL;DR

This paper introduces a locally stationary graph process model that captures local variations in graph signals, extending classical stationarity concepts to irregular graph domains for improved data analysis.

Contribution

It proposes a novel LSGP model, an algorithm for its computation, and demonstrates its effectiveness in signal interpolation tasks.

Findings

Accurate signal representations comparable to state-of-the-art methods.

Effective modeling of local variations in graph signals.

Enhanced analysis of data on irregular network topologies.

Abstract

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.