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arXiv · 1612.09434

Data driven estimation of Laplace-Beltrami operator

Frédéric Chazal·Ilaria Giulini·Bertrand Michel
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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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BibTeXRIS

Frédéric Chazal, Ilaria Giulini, Bertrand Michel. 2016-12-30. Data driven estimation of Laplace-Beltrami operator. https://arxiv.org/abs/1612.09434

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