Learning local receptive fields and their weight sharing scheme on graphs

We propose a simple and generic layer formulation that extends the properties of convolutional layers to any domain that can be 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 in the same fashion as for images. 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.