Work

Geometric Wavelet Scattering Networks on Compact Riemannian Manifolds

Year: 2019

Type: article

Abstract: The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of convolutional neural networks. Inspired by recent interest in geometric deep learning, which aims to generalize convolutional neural networks to manifold and graph-structured domains, we define a geometric scattering transform on manifolds. Similar to the Euclidean scattering transform, the geometric scattering transform is based on a cascade of wavelet filters and pointwise nonlinearities. It is invariant to local isometries and stable to certain types of diffeomorphisms. Empirical results demonstrate its utility on several geometric learning tasks. Our results generalize the deformation stability and local translation invariance of Euclidean scattering, and demonstrate the importance of linking the used filter structures to the underlying geometry of the data.

Source: PubMed

DOI: 10.48550/arxiv.1905.10448

Authors: Perlmutter, Michael, Gao, Feng, Wolf, Guy, Hirn, Matthew

Institutions: Michigan State University, Yale University, Université de Montréal, Mila - Quebec Artificial Intelligence Institute

Language: English

Topic: Mathematical Analysis and Transform Methods

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Institute of General Medical Sciences, National Institute of Environmental Health Sciences

Awards: Finding emergent structure in multi-sample biological data with the dual geometry of cells and features , Environmental, Microbial and Mammalian Biomolecular Responses to AhR Ligands