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  Maximal Margin Classification for Metric Spaces

Hein, M., Bousquet, O., & Schölkopf, B. (2005). Maximal Margin Classification for Metric Spaces. Journal of Computer and System Sciences, 71(3), 333-359. doi:10.1016/j.jcss.2004.10.013.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-D3F9-2 Version Permalink: http://hdl.handle.net/21.11116/0000-0004-D77E-D
Genre: Journal Article

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 Creators:
Hein, M1, 2, Author              
Bousquet, O1, 2, Author              
Schölkopf, B1, 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 order to apply the maximum margin method in arbitrary metric spaces, we suggest to embed the metric space into a Banach or Hilbert space and to perform linear classification in this space. We propose several embeddings and recall that an isometric embedding in a Banach space is always possible while an isometric embedding in a Hilbert space is only possible for certain metric spaces. As a result, we obtain a general maximum margin classification algorithm for arbitrary metric spaces (whose solution is approximated by an algorithm of Graepel. Interestingly enough, the embedding approach, when applied to a metric which can be embedded into a Hilbert space, yields the SVM algorithm, which emphasizes the fact that its solution depends on the metric and not on the kernel. Furthermore we give upper bounds of the capacity of the function classes corresponding to both embeddings in terms of Rademacher averages. Finally we compare the capacities of these function classes directly.

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 Dates: 2005-10
 Publication Status: Published in print
 Pages: -
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 Table of Contents: -
 Rev. Method: -
 Identifiers: DOI: 10.1016/j.jcss.2004.10.013
BibTex Citekey: 2839
 Degree: -

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Title: Journal of Computer and System Sciences
Source Genre: Journal
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Publ. Info: Orlando, Fla. : Academic Press
Pages: - Volume / Issue: 71 (3) Sequence Number: - Start / End Page: 333 - 359 Identifier: ISSN: 0022-0000
CoNE: https://pure.mpg.de/cone/journals/resource/954922645032