Convolution Neural Network (CNN) has gained tremendous success in computer vision tasks with its outstanding ability to capture the local latent features. Recently, there has been an increasing interest in extending convolution operations to the non-Euclidean geometry. Although various types of convolution operations have been proposed for graphs or manifolds, their connections with traditional convolution over grid-structured data are not well-understood. In this paper, we show that depthwise separable convolution can be successfully generalized for the unification of both graph-based and grid-based convolution methods. Based on this insight we propose a novel Depthwise Separable Graph Convolution (DSGC) approach which is compatible with the tradition convolution network and subsumes existing convolution methods as special cases. It is equipped with the combined strengths in model expressiveness, compatibility (relatively small number of parameters), modularity and computational efficiency in training. Extensive experiments show the outstanding performance of DSGC in comparison with strong baselines on multi-domain benchmark datasets.
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