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Graph Convolutional Networks (GCNs) have shown to be effective in handlingunordered data like point clouds and meshes. In this work we propose novelapproaches for graph convolution, pooling and unpooling, inspired from finitedifferences and algebraic multigrid frameworks. We form a parameterizedconvolution kernel based on discretized differential operators, leveraging thegraph mass, gradient and Laplacian. This way, the parameterization does notdepend on the graph structure, only on the meaning of the network convolutionsas differential operators. To allow hierarchical representations of the input,we propose pooling and unpooling operations that are based on algebraicmultigrid methods, which are mainly used to solve partial differentialequations on unstructured grids. To motivate and explain our method, we compareit to standard convolutional neural networks, and show their similarities andrelations in the case of a regular grid. Our proposed method is demonstrated invarious experiments like classification and part-segmentation, achieving on paror better than state of the art results. We also analyze the computational costof our method compared to other GCNs.

DiffGCN: Graph Convolutional Networks via Differential Operators and Algebraic Multigrid Pooling