Complex exponential graph convolutional networks

Graph convolutional networks based on spectral methods have recently achieved considerable success in processing non-Euclidean structured data such as graphs. In this paper, we propose the complex exponential graph convolutional network (CEGCN), which is a novel spectral convolutional architecture for performing deep learning on graphs. Specifically, we design a complex exponential polynomial filter with powerful expressive ability and whose zeros can be changed to prevent the over-smoothing issue. Furthermore, a CEGCN variant, called CEGCN-hp, combines the graph Fourier transform-based and high-pass filters to capture the high-frequency components in the graph spectral domain. We perform a spectral analysis to illustrate the motivation and expressive power of the proposed model. Experimental results show that our model matches or outperforms various state-of-the-art baselines on three downstream tasks: semi-supervised node classification, community detection, and graph classification. Our implementation is available online.1