In this work we propose a novel approach for learning graph representation of the data using gradients obtained via backpropagation. Next we build a neural network architecture compatible with our optimization approach and motivated by graph filtering in the vertex domain. We demonstrate that the learned graph has richer structure than often used nearest neighbors graphs constructed based on features similarity. Our experiments demonstrate that we can improve prediction quality for several convolution on graphs architectures, while others appeared to be insensitive to the input graph.
Graph Optimization with signal filtering in the vertex domain. The paper investigates learning adjacency matrix of a graph with sparsely connected undirected graph with nonnegative edge weights uses a projected sub-gradient descent algorithm. Develops a novel scheme for backpropogating on the adjacency matrix of a neural network graph