Work

Minimax estimation of distances on a surface and minimax manifold learning in the isometric-to-convex setting

Year: 2023

Type: article

Abstract: We start by considering the problem of estimating intrinsic distances on a smooth submanifold. We show that minimax optimality can be obtained via a reconstruction of the surface, and discuss the use of a particular mesh construction—the tangential Delaunay complex—for that purpose. We then turn to manifold learning and argue that a variant of Isomap where the distances are instead computed on a reconstructed surface is minimax optimal for the isometric variant of the problem.

Source: Information and Inference A Journal of the IMA

DOI: 10.1093/imaiai/iaad046

Authors: Ery Arias-Castro, Phong Alain Chau

Institution: University of California San Diego

Language: English

Topic: Topological and Geometric Data Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Award: Stable and Robust Graph Embedding, and Related Problems