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International Conference on Algorithmic Learning Theory

ALT 2002: Algorithmic Learning Theory pp 128–138Cite as

On the Smallest Possible Dimension and the Largest Possible Margin of Linear Arrangements Representing Given Concept Classes Uniform Distribution

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

Abstract

This paper discusses theoretical limitations of classification systems that are based on feature maps and use a separating hyper-plane in the feature space. In particular, we study the embeddability of a given concept class into a class of Euclidean half spaces of low dimension, or of arbitrarily large dimension but realizing a large margin. New bounds on the smallest possible dimension or on the largest possible margin are presented. In addition, we present new results on the rigidity of matrices and briefly mention applications in complexity and learning theory.

This work has been supported in part by the ESPRIT Working Group in Neural, Computational Learning II, NeuroCOLT2, No. 27150 and by the Deutsche Forschungsgemeinschaft Grant SI 498/4-1.

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Author information

Authors and Affiliations

  1. Fakultät für Mathematik, Ruhr-Universität Bochum, D-44780, Bochum, Germany

    Jürgen Forster & Hans Ulrich Simon

Authors
  1. Jürgen Forster
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  2. Hans Ulrich Simon
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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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Forster, J., Simon, H.U. (2002). On the Smallest Possible Dimension and the Largest Possible Margin of Linear Arrangements Representing Given Concept Classes Uniform Distribution. 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_12

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  • DOI: https://doi.org/10.1007/3-540-36169-3_12

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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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