Towards stationary time-vertex signal processing

TL;DR

This paper introduces a new concept of joint stationarity for time-varying graph signals, enabling scalable optimal processing methods that improve accuracy in real-world applications like weather data analysis.

Contribution

It proposes a novel definition of joint (time-vertex) stationarity that extends classical concepts and develops a Wiener optimization framework for joint signal processing on dynamic graphs.

Findings

Significant accuracy improvements in weather data reconstruction.

Scalable Wiener optimization framework for joint denoising and learning.

Validation on real-world data demonstrating effectiveness.

Abstract

Graph-based methods for signal processing have shown promise for the analysis of data exhibiting irregular structure, such as those found in social, transportation, and sensor networks. Yet, though these systems are often dynamic, state-of-the-art methods for signal processing on graphs ignore the dimension of time, treating successive graph signals independently or taking a global average. To address this shortcoming, this paper considers the statistical analysis of time-varying graph signals. We introduce a novel definition of joint (time-vertex) stationarity, which generalizes the classical definition of time stationarity and the more recent definition appropriate for graphs. Joint stationarity gives rise to a scalable Wiener optimization framework for joint denoising, semi-supervised learning, or more generally inversing a linear operator, that is provably optimal. Experimental results on real weather data demonstrate that taking into account graph and time dimensions jointly can yield significant accuracy improvements in the reconstruction effort.