Coefficient Decomposition for Spectral Graph Convolution

TL;DR

This paper introduces a tensor-based coefficient decomposition framework for spectral graph convolutional networks, leading to novel convolution methods that improve performance on graph-structured data.

Contribution

It proposes a general spectral graph convolution formulation using a coefficient tensor and develops new convolutions via tensor decomposition methods CP and Tucker.

Findings

Proposed methods outperform existing spectral graph convolutions.

Tensor decomposition improves model expressivity and performance.

Extensive experiments validate the effectiveness of CoDeSGC-CP and -Tucker.

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.