Diffusion Scattering Transforms on Graphs

Fernando Gama, Alejandro Ribeiro, Joan Bruna

Abstract:

Stability is a key aspect of data analysis. In many applications, the natural notion of stability is geometric, as illustrated for example in computer vision. Scattering transforms construct deep convolutional representations which are certified stable to input deformations. This stability to deformations can be interpreted as stability with respect to changes in the metric structure of the domain.

In this work, we show that scattering transforms can be generalized to non-Euclidean domains using diffusion wavelets, while preserving a notion of stability with respect to metric changes in the domain, measured with diffusion maps. The resulting representation is stable to metric perturbations of the domain while being able to capture ''high-frequency'' information, akin to the Euclidean Scattering.

Keywords: graph neural networks, deep learning, stability, scattering transforms, convolutional neural networks

TL;DR: Stability of scattering transform representations of graph data to deformations of the underlying graph support.