Séminaires : Séminaire Francilien de Géométrie Algorithmique et Combinatoire

Equipe(s) : co,
Responsables :Arnaud de Mesmay, Alfredo Hubard et Arnau Padrol
Email des responsables : arnau.padrol@imj-prg.fr
Salle :
Adresse :Big Blue Button
Description

Le Séminaire de Géométrie Algorithmique et Combinatoire vise à regrouper des exposés dans ce domaine au sens le plus large, et dans les disciplines connexes en mathématiques et informatique. Il est ouvert à tous les chercheurs et étudiants intéressés. Les exposés sont destinés à un public large.


Orateur(s) Eddie Aamari - LPSM, Paris Diderot,
Titre Estimating the reach of a manifold
Date07/11/2019
Horaire15:30 à 16:30
Diffusion
Résume

Various problems within computational geometry and manifold learning encode geometric regularity through the so-called reach, a generalized convexity parameter. The reach $\tau_M$ of a submanifold $M \subset \mathbb{R}^D$ is the maximal offset radius on which the projection onto $M$ is well defined. The quantity $\tau_M$ renders a certain minimal scale of $M$, giving bounds on both maximum curvature and possible bottleneck structures. In this talk, we will study the geometry of the reach through an approximation theory perspective. We present new geometric results on the reach of submanifolds without boundary. An estimator $\hat{\tau}_n$ of $\tau_M$ will be described, in an idealized i.i.d. framework where tangent spaces are known. The estimator $\hat{\tau}_n$ is showed to achieve uniform expected loss bounds over a $\mathcal{C}^3$-like model. Minimax upper and lower bounds are derived. We will conclude with an extension to a model in which tangent spaces are unknown.

Salle
AdresseBig Blue Button
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