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  Maximal Margin Classification for Metric Spaces

Hein, M., & Bousquet, O. (2004). Maximal Margin Classification for Metric Spaces. In B. Schölkopf, & M. Warmuth (Eds.), Learning Theory and Kernel Machines: 16th Annual Conference on Learning Theory and 7th Kernel Workshop, COLT/Kernel 2003, Washington, DC, USA, August 24-27, 2003 (pp. 72-86). Berlin, Germany: Springer.

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 Creators:
Hein, M1, 2, Author           
Bousquet, O1, 2, Author           
Affiliations:
1Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794              

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 Abstract: In this article we construct a maximal margin classification algorithm for arbitrary metric spaces. At first we show that the Support Vector Machine (SVM) is a maximal margin algorithm for the class of metric spaces where the negative squared distance is conditionally positive definite (CPD). This means that the metric space can be isometrically embedded into a Hilbert space, where one performs linear maximal margin separation. We will show that the solution only depends on the metric, but not on the kernel. Following the framework we develop for the SVM, we construct an algorithm for maximal margin classification in arbitrary metric spaces. The main difference compared with SVM is that we no longer embed isometrically into a Hilbert space, but a Banach space. We further give an estimate of the capacity of the function class involved in this algorithm via Rademacher averages. We recover an algorithm of Graepel et al. [6].

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 Dates: 2004-02
 Publication Status: Published in print
 Pages: -
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 Rev. Type: -
 Identifiers: DOI: 10.1007/978-3-540-45167-9_7
BibTex Citekey: 2263
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Title: 16th Annual Conference on Learning Theory and 7th Kernel Workshop (COLT/Kernel 2003)
Place of Event: Washington, DC, USA
Start-/End Date: 2003-08-24 - 2003-08-27

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Title: Learning Theory and Kernel Machines: 16th Annual Conference on Learning Theory and 7th Kernel Workshop, COLT/Kernel 2003, Washington, DC, USA, August 24-27, 2003
Source Genre: Proceedings
 Creator(s):
Schölkopf, B1, Editor           
Warmuth, MK, Editor
Affiliations:
1 Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497794            
Publ. Info: Berlin, Germany : Springer
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 72 - 86 Identifier: ISBN: 978-3-540-40720-1

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Title: Lecture Notes in Computer Science
Source Genre: Series
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Pages: - Volume / Issue: 2777 Sequence Number: - Start / End Page: - Identifier: -