Geometric Scattering on Measure Spaces

arXiv preprint, 2022

Recommended citation: Chew, J.A.; Hirn, M.; Krishnaswamy, S.; Needell, D.; Perlmutter, M.; Steach, H.R.; Viswanath, S.; Wu, H.-T. Geometric Scattering on Measure Spaces. Submitted for publication, 2022. Online access

We introduce a unified framework for geometric scattering on generic measure spaces and propose a new criterion to ensure that the scattering transform enjoys stability and invariance properties. We also propose two schemes for approximating the scattering transform using point cloud data sampled from an underlying manifold. We demonstrate the flexibility and utility of our methods on three-dimensional images, directed graphs, and high-dimensional single cell data.