Data driven estimation of Laplace-Beltrami operator
Computational Geometry
2017-01-02 v1 Machine Learning
Statistics Theory
Statistics Theory
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.
Cite
@article{arxiv.1612.09434,
title = {Data driven estimation of Laplace-Beltrami operator},
author = {Frédéric Chazal and Ilaria Giulini and Bertrand Michel},
journal= {arXiv preprint arXiv:1612.09434},
year = {2017}
}