Cross-spectral analysis of bivariate 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 the multivariate case. In this study, we define joint weak stationarity and introduce cross-spectral density and coherence for multivariate graph processes. We propose estimators for the cross-spectral density and investigate the theoretical properties of the proposed estimators. Furthermore, we demonstrate the effectiveness of these tools through numerical experiments, including simulation studies and a real data application. Finally, as an interesting extension, we discuss a robust spectral analysis of graph signals.

Contribution

We proposed a cross-spectral analysis tool for bivariate graph signals.

Code

To be uploaded.