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The connection between regularization operators and support vector kernels.

Alex J. Smola1, Bernhard Schölkopf, Klaus Robert Müller

  • 1GMD First, Rudower Chaussee 5, 12489, Berlin, Germany

Neural Networks : the Official Journal of the International Neural Network Society
|March 29, 2003
PubMed
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This study establishes a link between regularization operators and support vector kernels, proving Green's functions are effective kernels. This research enhances understanding of kernel methods in machine learning.

Area of Science:

  • Machine Learning
  • Kernel Methods
  • Regularization Theory

Background:

  • Support Vector Machines (SVMs) utilize kernel functions to map data into higher dimensions.
  • Regularization networks employ regularization operators to prevent overfitting and improve generalization.
  • A theoretical gap exists in understanding the direct relationship between these two concepts.

Purpose of the Study:

  • To derive a correspondence between regularization operators and support vector kernels.
  • To analyze existing support vector kernels through the lens of regularization theory.
  • To explore the applicability of radial basis functions as support vector kernels.

Main Methods:

  • Derivation of a mathematical correspondence between regularization operators and support vector kernels.

Related Experiment Videos

  • Analysis of polynomial and translation-invariant kernels using regularization theory.
  • Investigation of Green's functions as support vector kernels.
  • Examination of conditionally positive definite functions for kernel applications.

    • Main Results:

    • Green's functions associated with regularization operators are proven to be suitable support vector kernels with equivalent regularization properties.
    • Analysis of polynomial and translation-invariant kernels reveals their connections to regularization operators.
    • Conditional positive definite radial basis functions are identified as viable support vector kernels.

    Conclusions:

    • A strong theoretical link is established between regularization operators and support vector kernels.
    • The findings provide a new perspective on designing and understanding support vector kernels.
    • The study expands the repertoire of functions usable as support vector kernels, particularly radial basis functions.