TY - JOUR
T1 - Stability of graph scattering transforms
AU - Gama, Fernando
AU - Bruna, Joan
AU - Ribeiro, Alejandro
N1 - Funding Information:
Joan Bruna is partially supported by the Alfred P. Sloan Foundation, NSF RI-1816753, NSF CAREER CIF 1845360, and Samsung Electronics.
Funding Information:
Fernando Gama and Alejandro Ribeiro are supported by NSF CCF 1717120, ARO W911NF1710438, ARL DCIST CRA W911NF-17-2-0181, ISTC-WAS and Intel DevCloud.
Publisher Copyright:
© 2019 Neural information processing systems foundation. All rights reserved.
PY - 2019
Y1 - 2019
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85089239305&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85089239305&partnerID=8YFLogxK
M3 - Conference article
AN - SCOPUS:85089239305
SN - 1049-5258
VL - 32
JO - Advances in Neural Information Processing Systems
JF - Advances in Neural Information Processing Systems
T2 - 33rd Annual Conference on Neural Information Processing Systems, NeurIPS 2019
Y2 - 8 December 2019 through 14 December 2019
ER -