Bridging the Gap Between Spectral and Spatial Domains in Graph Neural Networks

TL;DR

This paper unifies spectral and spatial graph convolutional neural networks, providing a theoretical framework, designing new spectral convolutions, and introducing a parameter-efficient depthwise approach, with experiments confirming transferability and effectiveness.

Contribution

It introduces a general framework linking spectral and spatial graph convolutions, enabling new spectral designs and a depthwise separable convolution extension for GNNs.

Findings

Spectral and spatial convolutions are theoretically equivalent.

New spectral convolutions with custom frequency profiles improve performance.

Depthwise separable GNNs reduce parameters while maintaining capacity.

Abstract

This paper aims at revisiting Graph Convolutional Neural Networks by bridging the gap between spectral and spatial design of graph convolutions. We theoretically demonstrate some equivalence of the graph convolution process regardless it is designed in the spatial or the spectral domain. The obtained general framework allows to lead a spectral analysis of the most popular ConvGNNs, explaining their performance and showing their limits. Moreover, the proposed framework is used to design new convolutions in spectral domain with a custom frequency profile while applying them in the spatial domain. We also propose a generalization of the depthwise separable convolution framework for graph convolutional networks, what allows to decrease the total number of trainable parameters by keeping the capacity of the model. To the best of our knowledge, such a framework has never been used in the GNNs literature. Our proposals are evaluated on both transductive and inductive graph learning problems. Obtained results show the relevance of the proposed method and provide one of the first experimental evidence of transferability of spectral filter coefficients from one graph to another. Our source codes are publicly available at: https://github.com/balcilar/Spectral-Designed-Graph-Convolutions