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The connection between regularization operators and support vector kernels.

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons84193

Schölkopf,  B
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons84096

Müller,  K-R
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Smola, A., Schölkopf, B., & Müller, K.-R. (1998). The connection between regularization operators and support vector kernels. Neural Networks, 11(4), 637-649. doi:10.1016/S0893-6080(98)00032-X.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-E865-0
Abstract
n this paper a correspondence is derived between regularization operators used in regularization networks and support vector kernels. We prove that the Green‘s Functions associated with regularization operators are suitable support vector kernels with equivalent regularization properties. Moreover, the paper provides an analysis of currently used support vector kernels in the view of regularization theory and corresponding operators associated with the classes of both polynomial kernels and translation invariant kernels. The latter are also analyzed on periodical domains. As a by-product we show that a large number of radial basis functions, namely conditionally positive definite functions, may be used as support vector kernels.