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.

翻译：我们提出图规范相干分析（gCChA），这是一种将典型相关分析扩展到图频域中多元图信号的新框架。该方法解决了图数据固有特征——离散性、有限性和不规则性——带来的挑战。它通过识别能最大化相干性的规范图信号对，实现了从谱视角探索两组图信号之间的关联关系。该框架揭示了这些关联关系如何随图结构尺度的变化而演变。我们通过对G20国家经济与能源数据集以及USPS手写数字数据集的应用，验证了该方法的实用价值。