### 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 provides 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.

Original language | English (US) |
---|---|

Journal | Advances in Neural Information Processing Systems |

Volume | 32 |

State | Published - 2019 |

Event | 33rd Annual Conference on Neural Information Processing Systems, NeurIPS 2019 - Vancouver, Canada Duration: Dec 8 2019 → Dec 14 2019 |

### ASJC Scopus subject areas

- Computer Networks and Communications
- Information Systems
- Signal Processing

## Fingerprint Dive into the research topics of 'Stability of graph scattering transforms'. Together they form a unique fingerprint.

## Cite this

*Advances in Neural Information Processing Systems*,

*32*.