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/〉
https://hal.inria.fr/hal-01387021
Contributeur : Frédéric Chazal
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Soumis le : vendredi 30 décembre 2016 - 10:22:32
Dernière modification le : mercredi 21 mars 2018 - 18:58:22
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〉