Stability of Graph Scattering Transforms

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.

Submitted to Conference on Neural Information Processing Systems (NeurIPS 2019)

References in corpus (8)

• The Emerging Field of Signal Processing on Graphs: Extending High-Dimensional Data Analysis to Networks and Other Irregular Domains
• Geometric deep learning: going beyond Euclidean data
• Discrete Signal Processing on Graphs
• Convolutional Neural Network Architectures for Signals Supported on Graphs
• Diffusion Maps, Spectral Clustering and Eigenfunctions of Fokker-Planck operators
• Authorship Attribution through Function Word Adjacency Networks
• Diffusion Scattering Transforms on Graphs
• Geometric Scattering on Manifolds

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