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  Hilbertian Metrics and Positive Definite Kernels on Probability Measures

Hein, M., & Bousquet, O.(2004). Hilbertian Metrics and Positive Definite Kernels on Probability Measures (126). Tübingen, Germany: Max Planck Institute for Biological Cybernetics.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-D8B1-3 Version Permalink: http://hdl.handle.net/21.11116/0000-0002-8B22-B
Genre: Report

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MPIK-TR-126.pdf (Publisher version), 155KB
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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: We investigate the problem of defining Hilbertian metrics resp. positive definite kernels on probability measures, continuing previous work. This type of kernels has shown very good results in text classification and has a wide range of possible applications. In this paper we extend the two-parameter family of Hilbertian metrics of Topsoe such that it now includes all commonly used Hilbertian metrics on probability measures. This allows us to do model selection among these metrics in an elegant and unified way. Second we investigate further our approach to incorporate similarity information of the probability space into the kernel. The analysis provides a better understanding of these kernels and gives in some cases a more efficient way to compute them. Finally we compare all proposed kernels in two text and one image classification problem.

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 Dates: 2004-07
 Publication Status: Published in print
 Pages: 8
 Publishing info: Tübingen, Germany : Max Planck Institute for Biological Cybernetics
 Table of Contents: -
 Rev. Type: -
 Identifiers: Report Nr.: 126
BibTex Citekey: 2815
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Title: Max Planck Institute for Biological Cybernetics
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Pages: - Volume / Issue: 126 Sequence Number: - Start / End Page: - Identifier: -