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  Distance-based classification with Lipschitz functions

von Luxburg, U., & Bousquet, O. (2003). Distance-based classification with Lipschitz functions. 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. 314-328). Berlin, Germany: Springer.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-DD9A-8 Version Permalink: http://hdl.handle.net/21.11116/0000-0005-7162-D
Genre: Conference Paper

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 Creators:
von Luxburg, U1, 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: The goal of this article is to develop a framework for large margin classification in metric spaces. We want to find a generalization of linear decision functions for metric spaces and define a corresponding notion of margin such that the decision function separates the training points with a large margin. It will turn out that using Lipschitz functions as decision functions, the inverse of the Lipschitz constant can be interpreted as the size of a margin. In order to construct a clean mathematical setup we isometrically embed the given metric space into a Banach space and the space of Lipschitz functions into its dual space. Our approach leads to a general large margin algorithm for classification in metric spaces. To analyze this algorithm, we first prove a representer theorem. It states that there exists a solution which can be expressed as linear combination of distances to sets of training points. Then we analyze the Rademacher complexity of some Lipschitz function classes. The generality of the Lipschitz approach can be seen from the fact that several well-known algorithms are special cases of the Lipschitz algorithm, among them the support vector machine, the linear programming machine, and the 1-nearest neighbor classifier.

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 Dates: 2003-08
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: BibTex Citekey: 2261
DOI: 10.1007/978-3-540-45167-9_24
 Degree: -

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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: 314 - 328 Identifier: ISBN: 978-3-540-40720-1

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