Non-Asymptotic Rates for Manifold, Tangent Space, and Curvature Estimation

Eddie Aamari, Clément Levrard

Given an $n$-sample drawn on a submanifold $M\subset {\mathbb{R}}^D$, we derive optimal rates for the estimation of tangent spaces $T\_XM$, the second fundamental form $II\_X^M$, a…