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

Graph Convolutional Networks (GCNs) have shown to be effective in handling unordered data like point cloud and meshes. In this work we propose novel approaches for graph convolution, pooling and unpooling, taking inspiration from finite-elements and algebraic multigrid frameworks. We form a parameterized convolution kernel based on discretized differential operators, leveraging the graph mass, gradient and Laplacian. This way, the parameterization does not depend on the graph structure, only on the meaning of the network convolutions as differential operators. To allow hierarchical representations of the input, we propose pooling and unpooling operations that are based on algebraic multigrid methods. To motivate and explain our method, we compare it to standard Convolutional Neural Networks, and show their similarities and relations in the case of a regular grid. Our proposed method is demonstrated in various experiments like classification and segmentation, achieving on par or better than state of the art results. We also analyze the computational cost of our method compared to other GCNs.