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International Conference on Algorithmic Learning Theory

ALT 2002: Algorithmic Learning Theory pp 23–40Cite as

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

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2533))

Abstract

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

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Author information

Authors and Affiliations

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

    John Shawe-Taylor & Chris Williams

  2. Division of Informatics, University of Edinburgh, Edinburgh

    Nello Cristianini

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

    Jaz Kandola

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. Dipartimento di Tecnologie dell’Informazione, Università degli Studi di Milano, via Bramante 65, 26013, Crema (CR), Italy

    Nicolò Cesa-Bianchi

  2. Department of Computer Science, Tokyo Institute of Technology, 2-12-1, Ohokayama Meguro Ward, 152-8552, Tokyo, Japan

    Masayuki Numao

  3. Institut für Theoretische Informatik, Universität zu Lübeck, Wallstr. 40, 23560, Lübeck, Germany

    Rüdiger Reischuk

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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: Cesa-Bianchi, N., Numao, M., Reischuk, R. (eds) Algorithmic Learning Theory. ALT 2002. Lecture Notes in Computer Science(), vol 2533. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36169-3_4

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  • DOI: https://doi.org/10.1007/3-540-36169-3_4

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00170-6

  • Online ISBN: 978-3-540-36169-5

  • eBook Packages: Springer Book Archive

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