Graph Neural Networks with convolutional ARMA filters

Recent graph neural networks implement convolutional layers based on polynomial filters operating in the spectral domain. In this paper, we propose a novel graph convolutional layer based on auto-regressive moving average (ARMA) filters that, compared to the polynomial ones, provides a more flexible response thanks to a rich transfer function that accounts for the concept of state. We implement the ARMA filter with a recursive and distributed formulation, obtaining a convolutional layer that is efficient to train, is localized in the node space and can be applied to graphs with different topologies. In order to learn more abstract and compressed representations in deeper layers of the network, we alternate pooling operations based on node decimation to reduce the dimensionality of the node space with convolutions on coarsened versions of the original graph. We consider three major graph inference problems: semi-supervised node classification, graph classification, and graph signal classification. Results show that the proposed graph neural network with ARMA filters outperform those based on polynomial filters and sets the new state-of-the-art in several tasks.