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Hilbertian Metrics on Probability Measures and their Application in SVM's

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons83958

Hein,  H
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons84035

Lal,  TN
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons83824

Bousquet,  O
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Citation

Hein, H., Lal, T., & Bousquet, O. (2004). Hilbertian Metrics on Probability Measures and their Application in SVM's. In Pattern Recognition, Proceedings of th 26th DAGM Symposium (pp. 270-277).


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-F399-5
Abstract
The goal of this article is to investigate the field of Hilbertian metrics on probability measures. Since they are very versatile and can therefore be applied in various problems they are of great interest in kernel methods. Quit recently Topsoe and Fuglede introduced a family of Hilbertian metrics on probability measures. We give basic properties of the Hilbertian metrics of this family and other used metrics in the literature. Then we propose an extension of the considered metrics which incorporates structural information of the probability space into the Hilbertian metric. Finally we compare all proposed metrics in an image and text classification problem using histogram data.