Diffusion Scattering Transforms on Graphs

TL;DR

This paper extends scattering transforms to non-Euclidean domains using diffusion wavelets, ensuring stability to metric perturbations while capturing high-frequency information, thus broadening their applicability beyond Euclidean spaces.

Contribution

It introduces a generalized scattering transform on graphs based on diffusion wavelets that maintains stability under metric changes, a novel extension of Euclidean scattering methods.

Findings

The proposed method is stable to metric perturbations in graph domains.

It effectively captures high-frequency information in non-Euclidean settings.

The approach generalizes Euclidean scattering transforms to graphs using diffusion wavelets.

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.