Locally Stationary Graph Processes

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.

Learning Graph ARMA Processes from Time-Vertex Spectra

The modeling of time-varying graph signals as stationary time-vertex stochastic processes permits the inference of missing signal values by efficiently employing the correlation patterns of the process across different graph nodes and time instants. In this study, we first propose an algorithm for computing graph autoregressive moving average (graph ARMA) processes based on learning the joint time-vertex power spectral density of the process from its incomplete realizations. Our solution relies on first roughly estimating the joint spectrum of the process from partially observed realizations and then refining this estimate by projecting it onto the spectrum manifold of the ARMA process. We then present a theoretical analysis of the sample complexity of learning graph ARMA processes. Experimental results show that the proposed approach achieves improvement in the time-vertex signal estimation performance in comparison with reference approaches in the literature.