  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.
