Graph Neural Networks With Convolutional ARMA Filters

Popular graph neural networks implement convolution operations on graphs based on polynomial spectral filters. In this paper, we propose a novel graph convolutional layer inspired by the auto-regressive moving average (ARMA) filter that, compared to polynomial ones, provides a more flexible frequency response, is more robust to noise, and better captures the global graph structure. We propose a graph neural network implementation of the ARMA filter with a recursive and distributed formulation, obtaining a convolutional layer that is efficient to train, localized in the node space, and can be transferred to new graphs at test time. We perform a spectral analysis to study the filtering effect of the proposed ARMA layer and report experiments on four downstream tasks: semi-supervised node classification, graph signal classification, graph classification, and graph regression. Results show that the proposed ARMA layer brings significant improvements over graph neural networks based on polynomial filters.

Automated summary

This paper proposes a novel graph convolutional layer based on the auto-regressive moving average (ARMA) filter, which provides a more flexible frequency response, is more robust to noise, and better captures the global graph structure compared to polynomial filters. Experimental results show significant improvements of the proposed ARMA layer over graph neural networks based on polynomial filters.