Conference abstracts

Session A4 - Computational Geometry and Topology

July 11, 16:00 ~ 16:25 - Room B7

Estimating the Reach of a Manifold

Frédéric Chazal

INRIA, France   -   frederic.chazal@inria.fr

Various problems in manifold estimation, and topological and geometric inference make use of the so-called the reach (also known as the conditioning number or feature size)which is a measure of the regularity of the manifold. In this talk, we will investigate into the problem of how to estimate the reach of a manifold M from point clouds randomly sampled on M. We propose an estimator of the reach (in the framework where the tangent spaces of M are known) and we obtain upper and lower bounds on the minimax rates for estimating the reach.

Joint work with E. Aamari (Inria and Université Paris-Saclay, France), J. Kim (Carnegie Mellon University, USA), B. Michel (Ecole Centrale de Nantes, France), A. Rinaldo (Carnegie Mellon University, USA) and L. Wasserman (Carnegie Mellon University, USA).

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