Stability of Graph Scattering Transforms
This work addresses the challenge of applying scattering transforms to irregular network data, making it useful for transfer learning, topology estimation, or time-varying graphs, but it is incremental as it extends existing methods to a new domain.
The authors tackled the problem of extending scattering transforms to network data by using multiresolution graph wavelets, proving that the resulting graph scattering transforms are stable to metric perturbations of the underlying network, which makes them robust to changes in network topology.
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.