Abstract
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.
Abstract (translated)
光谱图卷积神经网络（SGCN）是一种基于图信号滤波器的图神经网络（GNN），在建模图形数据方面表现出强大的表现力。大多数SGCN采用多项式滤波器并从训练数据中学习系数。许多关注于哪个多项式基带来最优的表现力，模型的架构讨论较少。在本文中，我们提出了一种关于谱图卷积的一般形式，其中多项式基的系数存储在第三维张量中。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某种系数分解操作来推导出来。基于扩展观点，我们在系数张量上开发了新的光谱图卷积CDeSGC-CP和-Tucker。大量实验结果表明，与传统的卷积方法相比，所提出的卷积方法实现了显著的性能改进。
URL
https://arxiv.org/abs/2405.03296
