Learning Graph Filters for Spectral GNNs via Newton Interpolation
Junjie Xu Enyan Dai Dongsheng Luo Xiang Zhang Suhang Wang
Spectral Graph Neural Networks (GNNs) are gaining attention because they can
surpass the limitations of message-passing GNNs by learning spectral filters
that capture essential frequency information in graph data through task
supervision. However, previous research suggests that the choice of filter
frequency is tied to the graph's homophily level, a connection that hasn't been
thoroughly explored in existing spectral GNNs. To address this gap, the study
conducts both theoretical and empirical analyses, revealing that low-frequency
filters have a positive correlation with homophily, while high-frequency
filters have a negative correlation. This leads to the introduction of a
shape-aware regularization technique applied to a Newton Interpolation-based
spectral filter, enabling the customization of polynomial spectral filters that
align with desired homophily levels. Extensive experiments demonstrate that
NewtonNet successfully achieves the desired filter shapes and exhibits superior
performance on both homophilous and heterophilous datasets.