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 frequenc...

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Bibliographic Details
Published inIEEE transactions on pattern analysis and machine intelligence Vol. 44; no. 7; pp. 3496 - 3507
Main Authors Bianchi, Filippo Maria, Grattarola, Daniele, Livi, Lorenzo, Alippi, Cesare
Format Journal Article
LanguageEnglish
Published United States IEEE 01.07.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
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Summary: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.
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ISSN:0162-8828
1939-3539
2160-9292
DOI:10.1109/TPAMI.2021.3054830