Spectral graph convolutional network (SGCN) is a kind of graph neural networks (GNN) based on graph signal filters, and has shown compelling expressivity for modeling graph-structured data. Most SGCNs adopt polynomial filters and learn the coefficients from the training data. Many of them focus on which polynomial basis leads to optimal expressive power and models' architecture is little discussed. In this paper, we propose a general form in terms of spectral graph convolution, where the coefficients of polynomial basis are stored in a third-order tensor. Then, we show that the convolution block in existing SGCNs can be derived by performing a certain coefficient decomposition operation on the coefficient tensor. Based on the generalized view, we develop novel spectral graph convolutions CoDeSGC-CP and -Tucker by tensor decomposition CP and Tucker on the coefficient tensor. Extensive experimental results demonstrate that the proposed convolutions achieve favorable performance improvements.

我们提出了一种基于谱图卷积的通用形式，其中多项式基的系数存储在一个三阶张量中，并通过在系数张量上执行某种系数分解操作来导出现有谱图卷积网络的卷积块。基于这个广义视角，我们开发了新颖的谱图卷积方法CoDeSGC-CP和-Tucker，通过在系数张量上进行CP分解和Tucker分解。广泛的实验结果表明，所提出的卷积方法取得了有利的性能改进。

谱图卷积的系数分解