Cross-Spectral Analysis of Bivariate Graph Signals

TL;DR

This paper introduces a novel cross-spectral analysis framework for multivariate graph signals, extending spectral analysis tools to understand relationships between multiple quantities on graphs, with theoretical and empirical validation.

Contribution

It defines joint weak stationarity for multivariate graph processes and proposes estimators for cross-spectral density and coherence, including robustness considerations.

Findings

Proposed estimators are effective in simulations and real data.

The framework extends spectral analysis to multivariate graph signals.

Robust analysis methods handle outliers in graph signals.

Abstract

With the advancements in technology and monitoring tools, we often encounter multivariate graph signals, which can be seen as the realizations of multivariate graph processes, and revealing the relationship between their constituent quantities is one of the important problems. To address this issue, we propose a cross-spectral analysis tool for bivariate graph signals. The main goal of this study is to extend the scope of spectral analysis of graph signals to multivariate graph signals. In this study, we define joint weak stationarity graph processes and introduce graph cross-spectral density and coherence for multivariate graph processes. We propose several estimators for the cross-spectral density and investigate the theoretical properties of the proposed estimators. Furthermore, we demonstrate the effectiveness of the proposed estimators through numerical experiments, including simulation studies and a real data application. Finally, as an interesting extension, we discuss robust spectral analysis of graph signals in the presence of outliers.