Year: 2022
Type: article
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.
Source: PubMed
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G328145712, Graduate Research Fellowship Program (GRFP), G5355037660, Tensors, Topics, Truth, and Time: Methods for Real Tensor Applications, CAREER: Understanding Invariant Convolutional Neural Networks through Many Particle Physics, Collaborative Research: Fast, Low-Memory Embeddings for Tensor Data with Applications, Finding emergent structure in multi-sample biological data with the dual geometry of cells and features , CAREER: Deep representation learning for exploration and inference in biomedical data, Human and Translational Immunology Training Program
OpenAlex ID: W4376132686