Stationary time-vertex signal processing
This addresses the challenge of efficiently processing high-dimensional graph-structured time series data, though it appears incremental as it builds on existing graph signal processing concepts.
The paper tackles the problem of regression with high-dimensional multivariate processes on graph topologies by introducing a new definition of time-vertex wide-sense stationarity (joint stationarity). This approach reduces estimation variance and recovery complexity, enabling reliable covariance learning from a single realization and solving MMSE recovery problems in near-linear computational time.
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.