NeurIPS 2016poster12 citations
Data driven estimation of Laplace-Beltrami operator
Frederic Chazal, Ilaria Giulini, Bertrand Michel
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.
BibTeX
@inproceedings{NIPS2016_dd055f53,
author = {Chazal, Frederic and Giulini, Ilaria and Michel, Bertrand},
booktitle = {Advances in Neural Information Processing Systems},
editor = {D. Lee and M. Sugiyama and U. Luxburg and I. Guyon and R. Garnett},
pages = {},
publisher = {Curran Associates, Inc.},
title = {Data driven estimation of Laplace-Beltrami operator},
url = {https://proceedings.neurips.cc/paper_files/paper/2016/file/dd055f53a45702fe05e449c30ac80df9-Paper.pdf},
volume = {29},
year = {2016}
}