Coefficient Decomposition for Spectral Graph Convolution
This work addresses a domain-specific problem in graph neural networks by offering incremental architectural improvements for spectral graph convolutions.
The paper tackles the limited architectural exploration in spectral graph convolutional networks (SGCNs) by proposing a generalized spectral convolution form using a third-order tensor for polynomial coefficients, and introduces new convolutions (CoDeSGC-CP and -Tucker) via tensor decomposition, which achieve favorable performance improvements in experiments.
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.