Denoising and dimension reduction in feature space

Mikio L. Braun, Joachim Buhmann, Klaus Robert Müller

Research output: Chapter in Book/Report/Conference proceedingConference contribution

11 Citations (Scopus)

Abstract

We show that the relevant information about a classification problem in feature space is contained up to negligible error in a finite number of leading kernel PCA components if the kernel matches the underlying learning problem. Thus, kernels not only transform data sets such that good generalization can be achieved even by linear discriminant functions, but this transformation is also performed in a manner which makes economic use of feature space dimensions. In the best case, kernels provide efficient implicit representations of the data to perform classification. Practically, we propose an algorithm which enables us to recover the subspace and dimensionality relevant for good classification. Our algorithm can therefore be applied (1) to analyze the interplay of data set and kernel in a geometric fashion, (2) to help in model selection, and to (3) de-noise in feature space in order to yield better classification results.

Original languageEnglish
Title of host publicationAdvances in Neural Information Processing Systems 19 - Proceedings of the 2006 Conference
Pages185-192
Number of pages8
Publication statusPublished - 2007
Externally publishedYes
Event20th Annual Conference on Neural Information Processing Systems, NIPS 2006 - Vancouver, BC, Canada
Duration: 2006 Dec 42006 Dec 7

Publication series

NameAdvances in Neural Information Processing Systems
ISSN (Print)1049-5258

Other

Other20th Annual Conference on Neural Information Processing Systems, NIPS 2006
CountryCanada
CityVancouver, BC
Period06/12/406/12/7

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

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  • Cite this

    Braun, M. L., Buhmann, J., & Müller, K. R. (2007). Denoising and dimension reduction in feature space. In Advances in Neural Information Processing Systems 19 - Proceedings of the 2006 Conference (pp. 185-192). (Advances in Neural Information Processing Systems).