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On the Eigenspectrum of the Gram Matrix and Its Relationship to the Operator Eigenspectrum

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Discovery Science (DS 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2534))

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Abstract

In this paper we analyze the relationships between the eigenvalues of the m × m Gram matrix K for a kernel k(·, ·) corresponding to a sample x1, … , xm drawn from a density p(x) and the eigenvalues of the corresponding continuous eigenproblem. We bound the differences between the two spectra and provide a performance bound on kernel PCA.

The full version of this paper is published in the Proceedings of the 13th International Conference on Algorithmic Learning Theory, Lecture Notes in Artificial Intelligence Vol. 2533

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Author information

Authors and Affiliations

  1. Department of Computer Science, Royal Holloway, University of London, Egham, TW20 0EX, Surrey, UK

    John Shawe-Taylor & Jaz Kandola

  2. Division of Informatics, University of Edinburgh, USA

    Chris Williams

  3. Department of Statistics, University of California at Davies, USA

    Nello Cristianini

Authors
  1. John Shawe-Taylor
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  2. Chris Williams
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  3. Nello Cristianini
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  4. Jaz Kandola
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Editor information

Editors and Affiliations

  1. Deutsches Forschungszentrum für Künstliche Intelligenz, Stuhlsatzenhausweg 3, 66123, Saarbrücken, Germany

    Steffen Lange

  2. National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, 101-8430, Tokyo, Japan

    Ken Satoh

  3. Department of Computer Science, University of Maryland, College Park, 20742, Maryland, MD, USA

    Carl H. Smith

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© 2002 Springer-Verlag Berlin Heidelberg

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Shawe-Taylor, J., Williams, C., Cristianini, N., Kandola, J. (2002). On the Eigenspectrum of the Gram Matrix and Its Relationship to the Operator Eigenspectrum. In: Lange, S., Satoh, K., Smith, C.H. (eds) Discovery Science. DS 2002. Lecture Notes in Computer Science, vol 2534. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36182-0_3

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  • DOI: https://doi.org/10.1007/3-540-36182-0_3

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00188-1

  • Online ISBN: 978-3-540-36182-4

  • eBook Packages: Springer Book Archive

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