Stability of Graph Scattering Transforms

TL;DR

This paper extends scattering transforms to graph data using multiresolution graph wavelets, demonstrating their stability to network topology perturbations, which enhances robustness for various graph-based applications.

Contribution

It introduces a novel graph scattering transform framework that is stable to metric perturbations of network topology, enabling robust analysis of irregular network data.

Findings

Graph scattering transforms are stable to network topology changes.

The method is applicable to transfer learning and time-varying graphs.

Provides theoretical guarantees of stability for graph data.

Abstract

Scattering transforms are non-trainable deep convolutional architectures that exploit the multi-scale resolution of a wavelet filter bank to obtain an appropriate representation of data. More importantly, they are proven invariant to translations, and stable to perturbations that are close to translations. This stability property dons the scattering transform with a robustness to small changes in the metric domain of the data. When considering network data, regular convolutions do not hold since the data domain presents an irregular structure given by the network topology. In this work, we extend scattering transforms to network data by using multiresolution graph wavelets, whose computation can be obtained by means of graph convolutions. Furthermore, we prove that the resulting graph scattering transforms are stable to metric perturbations of the underlying network. This renders graph scattering transforms robust to changes on the network topology, making it particularly useful for cases of transfer learning, topology estimation or time-varying graphs.