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Conference Paper

Manifold Denoising as Preprocessing for Finding Natural Representations of Data

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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 as Preprocessing for Finding Natural Representations of Data. Proceedings of the Twenty-Second AAAI Conference on Artificial Intelligence (AAAI-07), 1646-1649.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-CCBF-8
Abstract
A natural representation of data are the parameters which generated the data. If the parameter space is continuous we can regard it as a manifold. In practice we usually do not know this manifold but we just have some representation of the data, often in a very high-dimensional feature space. Since the number of internal parameters does not change with the representation, the data will effectively lie on a low-dimensional submanifold in feature space. Due to measurement errors this data is usually corrupted by noise which particularly in high-dimensional feature spaces makes it almost impossible to find the manifold structure. This paper reviews a method called Manifold Denoising which projects the data onto the submanifold using a diffusion process on a graph generated by the data. We will demonstrate that the method is capable of dealing with non-trival high-dimensional noise. Moreover we will show that using the method as a preprocessing step one can significantly improve the results of a semi-supervised learning algorithm.