From Regularization Operators to Support Vector Kernels

Part of Advances in Neural Information Processing Systems 10 (NIPS 1997)

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Alex Smola, Bernhard Schölkopf


We derive the correspondence between regularization operators used in Regularization Networks and Hilbert Schmidt Kernels appearing in Sup(cid:173) port Vector Machines. More specifica1ly, we prove that the Green's Func(cid:173) tions associated with regularization operators are suitable Support Vector Kernels with equivalent regularization properties. As a by-product we show that a large number of Radial Basis Functions namely condition(cid:173) ally positive definite functions may be used as Support Vector kernels.