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Kernels, Associated Structures and Generalizations

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

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

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MPIK-TR-127.pdf
(Publisher version), 177KB

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Citation

Hein, M., & Bousquet, O.(2004). Kernels, Associated Structures and Generalizations (127). Tübingen, Germany: Max Planck Institute for Biological Cybernetics.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-D8B3-0
Abstract
This paper gives a survey of results in the mathematical literature on positive definite kernels and their associated structures. We concentrate on properties which seem potentially relevant for Machine Learning and try to clarify some results that have been misused in the literature. Moreover we consider different lines of generalizations of positive definite kernels. Namely we deal with operator-valued kernels and present the general framework of Hilbertian subspaces of Schwartz which we use to introduce kernels which are distributions. Finally indefinite kernels and their associated reproducing kernel spaces are considered.