The connection between regularization operators and support vector kernels

Alex J. Smola, Bernhard Schölkopf, Klaus Robert Müller

Research output: Contribution to journalArticlepeer-review

504 Citations (Scopus)


In 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.

Original languageEnglish
Pages (from-to)637-649
Number of pages13
JournalNeural Networks
Issue number4
Publication statusPublished - 1998 Jun


  • Conditionally positive definite functions
  • Green's functions
  • Mercer kernel
  • Polynomial kernels
  • Radial basis functions
  • Regularization networks
  • Ridge regression
  • Support vector machines

ASJC Scopus subject areas

  • Cognitive Neuroscience
  • Artificial Intelligence


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