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