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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.

 Author(s): Hein, M. and Maier, M. Book Title: AAAI-07 Journal: Proceedings of the Twenty-Second AAAI Conference on Artificial Intelligence (AAAI-07) Pages: 1646-1649 Year: 2007 Month: July Day: 0 Publisher: AAAI Press Department(s): Empirical Inference Bibtex Type: Conference Paper (inproceedings) Event Name: Twenty-Second AAAI Conference on Artificial Intelligence (AAAI-07) Event Place: Vancouver, BC, Canada Address: Menlo Park, CA, USA Digital: 0 Institution: Association for the Advancement of Artificial Intelligence Language: en Organization: Max-Planck-Gesellschaft School: Biologische Kybernetik Links: BibTex @inproceedings{4588, title = {Manifold Denoising as Preprocessing for Finding Natural Representations of Data}, author = {Hein, M. and Maier, M.}, journal = {Proceedings of the Twenty-Second AAAI Conference on Artificial Intelligence (AAAI-07)}, booktitle = {AAAI-07}, pages = {1646-1649}, publisher = {AAAI Press}, organization = {Max-Planck-Gesellschaft}, institution = {Association for the Advancement of Artificial Intelligence}, school = {Biologische Kybernetik}, address = {Menlo Park, CA, USA}, month = jul, year = {2007}, month_numeric = {7} }
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