, Volume 22, Issue 1–2, pp 211–231 | Cite as

On a Kernel-Based Method for Pattern Recognition, Regression, Approximation, and Operator Inversion

  • A. J. Smola
  • B. Schölkopf


We present a kernel-based framework for pattern recognition, regression estimation, function approximation, and multiple operator inversion. Adopting a regularization-theoretic framework, the above are formulated as constrained optimization problems. Previous approaches such as ridge regression, support vector methods, and regularization networks are included as special cases. We show connections between the cost function and some properties up to now believed to apply to support vector machines only. For appropriately chosen cost functions, the optimal solution of all the problems described above can be found by solving a simple quadratic programming problem.

Key words. Kernels, Support vector machines, Regularization, Inverse problems, Regression, Pattern Recognition. 


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Copyright information

© Springer-Verlag New York Inc. 1998

Authors and Affiliations

  • A. J. Smola
    • 1
  • B. Schölkopf
    • 2
  1. 1.GMD FIRST, Rudower Chaussee 5, 12489 Berlin, Germany.
  2. 2.Max Planck Institut für biologische Kybernetik, Spemannstrasse 38, 72076 Tübingen, Germany.

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