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.
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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/>
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https://hal.inria.fr/hal-01387021
Contributeur : Frédéric Chazal <>
Soumis le : vendredi 30 décembre 2016 - 10:22:32
Dernière modification le : jeudi 20 juillet 2017 - 09:27:16

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  • HAL Id : hal-01387021, version 2

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INSMI | UPMC | INRIA | LSTA | UNIV-PARIS-SACLAY | UNIV-PARIS13

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Frédéric Chazal, Ilaria Giulini, Bertrand Michel. Data driven estimation of Laplace-Beltrami operator. 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/>. <hal-01387021v2>

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