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.

翻译：谱图卷积网络（SGCN）是一类基于图信号滤波器的图神经网络，在建模图结构数据方面展现出显著的表达力。大多数SGCN采用多项式滤波器，并从训练数据中学习系数。其中许多研究侧重于哪种多项式基能产生最优的表达能力，而对模型架构的探讨较少。本文提出了一种谱图卷积的通用形式，其中多项式基的系数存储在三阶张量中。然后，我们证明了现有SGCN中的卷积模块可以通过对系数张量执行特定的系数分解操作推导得到。基于这一广义视角，我们利用张量分解中的CP分解和Tucker分解对系数张量进行处理，开发了新型谱图卷积CoDeSGC-CP和CoDeSGC-Tucker。大量实验结果表明，所提出的卷积方法在性能上取得了显著提升。