Predicting the evolution of stationary graph signals

TL;DR

This paper introduces a graph-based prediction method for stationary time-vertex signals that leverages joint stationarity to improve accuracy and reduce complexity compared to traditional time-only models.

Contribution

It proposes a novel multivariate prediction approach using the joint stationarity framework for time-vertex processes, addressing the limitations of existing graph methods.

Findings

Achieves similar accuracy to joint mean-squared error estimators.

Outperforms purely time-based prediction methods.

Offers lower computational complexity.

Abstract

An emerging way of tackling the dimensionality issues arising in the modeling of a multivariate process is to assume that the inherent data structure can be captured by a graph. Nevertheless, though state-of-the-art graph-based methods have been successful for many learning tasks, they do not consider time-evolving signals and thus are not suitable for prediction. Based on the recently introduced joint stationarity framework for time-vertex processes, this letter considers multivariate models that exploit the graph topology so as to facilitate the prediction. The resulting method yields similar accuracy to the joint (time-graph) mean-squared error estimator but at lower complexity, and outperforms purely time-based methods.