Locally Stationary Graph Processes
This work addresses the need for more flexible graph signal models in domains like network analysis, though it appears incremental by adapting classical concepts to graph settings.
The authors tackled the problem of modeling graph signals with varying local characteristics by proposing a locally stationary graph process (LSGP) model, which extends local stationarity to irregular graphs and achieves competitive accuracy in signal interpolation experiments.
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.