Graph Canonical Coherence Analysis

TL;DR

Graph canonical coherence analysis (gCChA) extends canonical correlation analysis to multivariate graph signals, revealing relationships across different graph structures and scales, with applications in economics, energy, and image datasets.

Contribution

This paper introduces gCChA, a novel spectral framework for analyzing relationships between multivariate graph signals, addressing challenges of graph discreteness, finiteness, and irregularity.

Findings

Successfully applied to G20 economic and energy data.

Effectively analyzed USPS handwritten digit dataset.

Revealed multi-scale relationships between graph signals.

Abstract

We propose graph canonical coherence analysis (gCChA), a novel framework that extends canonical correlation analysis to multivariate graph signals in the graph frequency domain. The proposed method addresses challenges posed by the inherent features of graphs: discreteness, finiteness, and irregularity. It identifies pairs of canonical graph signals that maximize their coherence, enabling the exploration of relationships between two sets of graph signals from a spectral perspective. This framework shows how these relationships change across different structural scales of the graph. We demonstrate the usefulness of this method through applications to economic and energy datasets of G20 countries and the USPS handwritten digit dataset.