  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.
