Abstract
We generalize the scattering transform to graphs and consequently construct a convolutional neural network on graphs. We show that under certain conditions, any feature generated by such a network is approximately invariant to permutations and stable to signal and graph manipulations. Numerical results demonstrate competitive performance on relevant datasets.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1046-1074 |
| Number of pages | 29 |
| Journal | Applied and Computational Harmonic Analysis |
| Volume | 49 |
| Issue number | 3 |
| DOIs | |
| State | Published - Nov 2020 |
Bibliographical note
Funding Information:This research was partially supported by NSF awards DMS-14-18386 , DMS-18-21266 and DMS-18-30418 , where the latter award is jointly funded by NGA and NSF. We thank the anonymous reviewer for helpful feedback and Charles K. Chui for the professional handling of the manuscript. We also thank Radu Balan, Addison Bohannon and Maneesh Singh for helpful references and Loren Anderson, Vahan Huroyan and Tyler Maunu for commenting on an earlier version of this manuscript.
Funding Information:
This research was partially supported by NSF awards DMS-14-18386, DMS-18-21266 and DMS-18-30418, where the latter award is jointly funded by NGA and NSF. We thank the anonymous reviewer for helpful feedback and Charles K. Chui for the professional handling of the manuscript. We also thank Radu Balan, Addison Bohannon and Maneesh Singh for helpful references and Loren Anderson, Vahan Huroyan and Tyler Maunu for commenting on an earlier version of this manuscript.
Keywords
- Feature learning
- Graph convolution
- Graph neural networks
- Permutation invariance
- Scattering transform
- Spectral graph theory
- Wavelets