Learning Local Receptive Fields and their Weight Sharing Scheme on Graphs

To achieve state-of-the-art results on challenges in vision, Convolutional Neural Networks learn stationary filters that take advantage of the underlying image structure. Our purpose is to propose an efficient layer formulation that extends this property to any domain described by a graph. Namely, we use the support of its adjacency matrix to design learnable weight sharing filters able to exploit the underlying structure of signals. The proposed formulation makes it possible to learn the weights of the filter as well as a scheme that controls how they are shared across the graph. We perform validation experiments with image datasets and show that these filters offer performances comparable with convolutional ones.