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Graph Convolutional Neural Networks (GCNNs) extend classical CNNs to graphdata domain, such as brain networks, social networks and 3D point clouds. It iscritical to identify an appropriate graph for the subsequent graph convolution.Existing methods manually construct or learn one fixed graph for all the layersof a GCNN. In order to adapt to the underlying structure of node features indifferent layers, we propose dynamic learning of graphs and node featuresjointly in GCNNs. In particular, we cast the graph optimization problem asdistance metric learning to capture pairwise similarities of features in eachlayer. We deploy the Mahalanobis distance metric and further decompose themetric matrix into a low-dimensional matrix, which converts graph learning tothe optimization of a low-dimensional matrix for efficient implementation.Extensive experiments on point clouds and citation network datasets demonstratethe superiority of the proposed method in terms of both accuracies androbustness.

Joint Learning of Graph Representation and Node Features in Graph Convolutional Neural Networks