An Experimental Study of the Transferability of Spectral Graph Networks

TL;DR

This paper demonstrates that spectral graph convolutional networks are highly transferable across graphs of varying sizes and structures, challenging misconceptions and supporting their use in diverse graph learning tasks.

Contribution

The study provides empirical evidence of spectral filter transferability across different graphs, emphasizing its stability and practical effectiveness.

Findings

Spectral graph networks perform well on multiple graph tasks.

Spectral filters are stable under graph perturbations.

Transferability is validated across various graph benchmarks.

Abstract

Spectral graph convolutional networks are generalizations of standard convolutional networks for graph-structured data using the Laplacian operator. A common misconception is the instability of spectral filters, i.e. the impossibility to transfer spectral filters between graphs of variable size and topology. This misbelief has limited the development of spectral networks for multi-graph tasks in favor of spatial graph networks. However, recent works have proved the stability of spectral filters under graph perturbation. Our work complements and emphasizes further the high quality of spectral transferability by benchmarking spectral graph networks on tasks involving graphs of different size and connectivity. Numerical experiments exhibit favorable performance on graph regression, graph classification, and node classification problems on two graph benchmarks. The implementation of our experiments is available on GitHub for reproducibility.