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Conference Paper

Manifold Denoising

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons83958

Hein,  M
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons84070

Maier,  M
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Citation

Hein, M., & Maier, M. (2007). Manifold Denoising. Advances in Neural Information Processing Systems 19: Proceedings of the 2006 Conference, 561-568.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-CBF1-D
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.