Stationary time-vertex signal processing

TL;DR

This paper introduces a new concept of joint stationarity for time-vertex signals, enabling efficient covariance estimation and signal recovery in high-dimensional graph-structured data.

Contribution

It proposes a novel definition of joint stationarity that extends beyond product graphs, reducing estimation variance and computational complexity for multivariate processes.

Findings

Reliable covariance learning from a single realization

Nearly linear time MMSE recovery algorithms

Improved accuracy in high-dimensional process recovery

Abstract

This paper considers regression tasks involving high-dimensional multivariate processes whose structure is dependent on some {known} graph topology. We put forth a new definition of time-vertex wide-sense stationarity, or joint stationarity for short, that goes beyond product graphs. Joint stationarity helps by reducing the estimation variance and recovery complexity. In particular, for any jointly stationary process (a) one reliably learns the covariance structure from as little as a single realization of the process, and (b) solves MMSE recovery problems, such as interpolation and denoising, in computational time nearly linear on the number of edges and timesteps. Experiments with three datasets suggest that joint stationarity can yield accuracy improvements in the recovery of high-dimensional processes evolving over a graph, even when the latter is only approximately known, or the process is not strictly stationary.