The Manifold Scattering Transform for High-Dimensional Point Cloud Data

The manifold scattering transform is a multiscalefeature extractor for data defined on a Riemannianmanifold. The initial work on this model focusedprimarily on its theoretical stability and invarianceproperties but did not provide methods forits numerical implementation except in the case oftwo-dimensional surfaces with predefined meshes.In this work, we present practical schemes, basedon the theory of diffusion maps, for implementingthe manifold scattering transform to datasets arisingin, e.g., single cell genetics, where the datais a high-dimensional point cloud modeled as lyingon a low-dimensional manifold. We will thenshow that our methods are effective for signalclassification and manifold classification tasks.