Learning Local Receptive Fields and their Weight Sharing Scheme on Graphs
This work addresses the challenge of applying convolutional operations to non-Euclidean domains like graphs, which is important for graph neural network researchers.
The authors tackled the problem of extending convolutional layer properties to graph-structured data by proposing a layer formulation that learns both filter weights and weight sharing schemes. They demonstrated comparable performance to convolutional filters on image datasets.
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.