Manifold Denoising

Hein, M; Maier, M

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Manifold Denoising

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

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

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https://papers.nips.cc/paper/2997-manifold-denoising.pdf
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Citation

Hein, M., & Maier, M. (2007). Manifold Denoising. In B. Schölkopf, J. Platt, & T. Hoffman (Eds.), Advances in Neural Information Processing Systems 19 (pp. 561-568). Cambridge, MA, USA: MIT Press.

Cite as: https://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.