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math.ST2017
Estimating the Reach of a Manifold
Eddie Aamari, Jisu Kim, Frédéric Chazal +3
Various problems in manifold estimation make use of a quantity called the reach, denoted by , which is a measure of the regularity of the manifold. This paper is the first in…
math.ST2017
Non-Asymptotic Rates for Manifold, Tangent Space, and Curvature Estimation
Eddie Aamari, Clément Levrard
Given an -sample drawn on a submanifold , we derive optimal rates for the estimation of tangent spaces , the second fundamental form , a…