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Manifold Denoising

2007

Conference Paper

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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

Department(s): Empirical Inference
Bibtex Type: Conference Paper (inproceedings)

Event Name: Twentieth Annual Conference on Neural Information Processing Systems (NIPS 2006)
Event Place: Vancouver, BC, Canada

Address: Cambridge, MA, USA
Digital: 0
ISBN: 0-262-19568-2
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

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BibTex

@inproceedings{4249,
  title = {Manifold Denoising},
  author = {Hein, M. and Maier, M.},
  journal = {Advances in Neural Information Processing Systems 19: Proceedings of the 2006 Conference},
  booktitle = {Advances in Neural Information Processing Systems 19},
  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},
  month_numeric = {9}
}