An Experimental Study of the Transferability of Spectral Graph Networks
This work is significant for researchers and practitioners in graph neural networks, as it challenges a long-held belief that has limited the application of spectral methods in multi-graph tasks, potentially broadening their utility.
This paper addresses the misconception that spectral graph convolutional networks cannot transfer filters between graphs of varying sizes and topologies. Through numerical experiments on two graph benchmarks, the authors demonstrate favorable performance of spectral graph networks in graph regression, graph classification, and node classification tasks, supporting high transferability.
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.