Shape-aware Graph Spectral Learning

Junjie Xu, Enyan Dai, Dongsheng Luo, Xiang Zhang, Suhang Wang

Primary Area: representation learning for computer vision, audio, language, and other modalities

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Keywords: Machine Learning, Graph Learning, Graph Neural Networks, Graph Spectral Learning

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TL;DR: NewtonNet, a spectral graph neural network, uses shape-ware regularization to tailor its filters based on the homophily or heterophily of graph data.

Abstract: Spectral Graph Neural Networks (GNNs) are gaining attention for their ability to surpass the limitations of message-passing GNNs. They rely on the supervision from the downstream task to learn spectral filters that capture the useful frequency information of the graph signal. However, some works empirically show that the preferred graph frequency is related to the graph homophily level. This relationship between graph frequency and graphs with homophily/heterophily has not been systematically analyzed and considered in existing spectral GNNs. To mitigate this gap, we conduct theoretical and empirical analyses which reveal that low-frequency importance is positively correlated with the homophily ratio, while high-frequency importance is negatively correlated. Motivated by this, we propose a shape-ware regularization on a Newton Interpolation-based spectral filter which can (i) learn arbitrary polynomial spectral filter and (ii) incorporate prior knowledge about the desired shape of the corresponding homophily level. Comprehensive experiments demonstrate that NewtonNet can achieve graph spectral filters with desired shapes and superior performance on both homophilous and heterophilous datasets. The code can be found at https://anonymous.4open.science/r/NewtonNet-8115.

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Submission Number: 3877