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.

通过对频谱图神经网络的理论和实证分析，研究发现，低频滤波器与同质程度呈正相关关系，而高频滤波器呈负相关关系，为此引入了一种基于牛顿插值的形状感知正则化技术，使多项式频谱滤波器可以与所期望的同质程度对齐。大量实验证明了NewtonNet在同质和异质数据集上显示出优越性能。

通过牛顿插值学习用于频谱GNN的图滤波器