Data Driven Estimation of Laplace-Beltrami Operator
Abstract
Approximations of Laplace-Beltrami operators on manifolds through graph Laplacians 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 unormalized 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 (2015) on the so-called Lepski's method.
Cite
Text
Chazal et al. "Data Driven Estimation of Laplace-Beltrami Operator." Neural Information Processing Systems, 2016.Markdown
[Chazal et al. "Data Driven Estimation of Laplace-Beltrami Operator." Neural Information Processing Systems, 2016.](https://mlanthology.org/neurips/2016/chazal2016neurips-data/)BibTeX
@inproceedings{chazal2016neurips-data,
title = {{Data Driven Estimation of Laplace-Beltrami Operator}},
author = {Chazal, Frederic and Giulini, Ilaria and Michel, Bertrand},
booktitle = {Neural Information Processing Systems},
year = {2016},
pages = {3963-3971},
url = {https://mlanthology.org/neurips/2016/chazal2016neurips-data/}
}