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Conference Papers Year : 2016

Data driven estimation of Laplace-Beltrami operator

Frédéric Chazal
Ilaria Giulini
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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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Dates and versions

hal-01387021 , version 1 (25-10-2016)
hal-01387021 , version 2 (30-12-2016)

Identifiers

  • HAL Id : hal-01387021 , version 2

Cite

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. ⟨hal-01387021v2⟩
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