Data driven estimation of Laplace-Beltrami operator

Frédéric Chazal; Ilaria Giulini; Bertrand Michel

Data driven estimation of Laplace-Beltrami operator

Frédéric Chazal ¹ Ilaria Giulini ¹ Bertrand Michel ²

1 DATASHAPE - Understanding the Shape of Data

CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France

2 LSTA - Laboratoire de Statistique Théorique et Appliquée

Abstract : Approximations of Laplace-Beltrami operators on manifolds through graph Lapla-cians have become popular tools in data analysis and machine learning. These discretized operators usually depend on bandwidth parameters whose tuning remains a theoretical and practical problem. In this paper, we address this problem for the unnormalized graph Laplacian by establishing an oracle inequality that opens the door to a well-founded data-driven procedure for the bandwidth selection. Our approach relies on recent results by Lacour and Massart [LM15] on the so-called Lepski's method.

Type de document :

Communication dans un congrès

30th Conference on Neural Information Processing Systems (NIPS 2016), Dec 2016, Barcelona, Spain. 30th Conference on Neural Information Processing Systems (NIPS 2016), Barcelona, Spain., 2016, 〈https://nips.cc/〉

Domaine :

Informatique [cs] / Géométrie algorithmique [cs.CG]

Mathématiques [math] / Statistiques [math.ST]

Informatique [cs] / Apprentissage [cs.LG]

Liste complète des métadonnées

https://hal.inria.fr/hal-01387021
Contributeur : Frédéric Chazal <>
Soumis le : vendredi 30 décembre 2016 - 10:22:32
Dernière modification le : mardi 11 décembre 2018 - 01:25:19

NIPS_vcorrect.pdf

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