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Manifold Denoising as Preprocessing for Finding Natural Representations of Data

2007

Conference Paper

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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

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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}
}