We consider the problem of denoising a noisily sampled submanifold $M$ in $R^d$, where the submanifold $M$ is a priori unknown and we are only given a noisy point sample. The presented denoising algorithm is based on a graph-based diffusion process of the point sample. We analyze this diffusion process using recent results about the convergence of graph Laplacians. In the experiments we show that our method is capable of dealing with non-trivial high-dimensional noise. Moreover using the denoising algorithm as pre-processing method we can improve the results of a semi-supervised learning algorithm.
| Author(s): | Hein, M. and Maier, M. |
| Book Title: | Advances in Neural Information Processing Systems 19 |
| Journal: | Advances in Neural Information Processing Systems 19: Proceedings of the 2006 Conference |
| Pages: | 561-568 |
| Year: | 2007 |
| Month: | September |
| Day: | 0 |
| Editors: | Sch{\"o}lkopf, B. , J. Platt, T. Hofmann |
| Publisher: | MIT Press |
| Bibtex Type: | Conference Paper (inproceedings) |
| Address: | Cambridge, MA, USA |
| Event Name: | Twentieth Annual Conference on Neural Information Processing Systems (NIPS 2006) |
| Event Place: | Vancouver, BC, Canada |
| Digital: | 0 |
| Electronic Archiving: | grant_archive |
| ISBN: | 0-262-19568-2 |
| Language: | en |
| Organization: | Max-Planck-Gesellschaft |
| School: | Biologische Kybernetik |
| Links: | |
BibTex
@inproceedings{4249,
title = {Manifold Denoising},
journal = {Advances in Neural Information Processing Systems 19: Proceedings of the 2006 Conference},
booktitle = {Advances in Neural Information Processing Systems 19},
abstract = {We consider the problem of denoising a noisily sampled submanifold $M$ in $R^d$, where the submanifold $M$
is a priori unknown and we are only given a noisy point sample. The presented denoising algorithm is based
on a graph-based diffusion process of the point sample. We analyze this diffusion process using recent results about
the convergence of graph Laplacians. In the experiments we show that our method is capable of dealing with
non-trivial high-dimensional noise. Moreover using the denoising algorithm as pre-processing method we
can improve the results of a semi-supervised learning algorithm.},
pages = {561-568},
editors = {Sch{\"o}lkopf, B. , J. Platt, T. Hofmann},
publisher = {MIT Press},
organization = {Max-Planck-Gesellschaft},
school = {Biologische Kybernetik},
address = {Cambridge, MA, USA},
month = sep,
year = {2007},
slug = {4249},
author = {Hein, M. and Maier, M.},
month_numeric = {9}
}