The Manifold Scattering Transform for High-Dimensional Point Cloud Data
Abstract
The manifold scattering transform is a deep feature extractor for data defined on a Riemannian manifold. It is one of the first examples of extending convolutional neural network-like operators to general manifolds. The initial work on this model focused primarily on its theoretical stability and invariance properties but did not provide methods for its numerical implementation except in the case of two-dimensional surfaces with predefined meshes. In this work, we present practical schemes, based on the theory of diffusion maps, for implementing the manifold scattering transform to datasets arising in naturalistic systems, such as single cell genetics, where the data is a high-dimensional point cloud modeled as lying on a low-dimensional manifold. We show that our methods are effective for signal classification and manifold classification tasks.
Cite
@article{arxiv.2206.10078,
title = {The Manifold Scattering Transform for High-Dimensional Point Cloud Data},
author = {Joyce Chew and Holly R. Steach and Siddharth Viswanath and Hau-Tieng Wu and Matthew Hirn and Deanna Needell and Smita Krishnaswamy and Michael Perlmutter},
journal= {arXiv preprint arXiv:2206.10078},
year = {2024}
}
Comments
Accepted for publication in the TAG in DS Workshop at ICML. For subsequent theoretical guarantees, please see Section 6 of arXiv:2208.08561