PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Hilbertian metrics and positive definite kernels on probability measures
Matthias Hein and Olivier Bousquet
In: AISTATS 2005, 6-8 Jan 2005, Barbados.

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 two image classification problems.

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EPrint Type:Conference or Workshop Item (Paper)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:591
Deposited By:Matthias Hein
Deposited On:27 December 2004