[1806.08829] Diffusion Scattering Transforms on Graphs

Stability is a key aspect of data analysis. In many applications, the natural notion of stability is geometric, as illustrated for example in computer vision. Scattering transforms construct deep convolutional representations which are certified stable to input deformations. This stability to deformations can be interpreted as stability with respect to changes in the metric structure of the domain. In this work, we show that scattering transforms can be generalized to non-Euclidean domains using diffusion wavelets, while preserving a notion of stability with respect to metric changes in the domain, measured with diffusion maps. The resulting representation is stable to metric perturbations of the domain while being able to capture "high-frequency" information, akin to the Euclidean Scattering.

Submitted as a conference paper at ICLR 2019 D IFFUSION S CATTERING T RANSFORMS ON G RAPHS Fernando Gama Alejandro Ribeiro SEAS University of Pennsylvania SEAS University of Pennsylvania Joan Bruna Courant Institute of Mathematical Sciences New York…

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