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Classification with Invariant Distance Substitution Kernels

  • Bernard Haasdonk
  • Hans Burkhardt
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)

Abstract

Kernel methods offer a flexible toolbox for pattern analysis and machine learning. A general class of kernel functions which incorporates known pattern invariances are invariant distance substitution (IDS) kernels. Instances such as tangent distance or dynamic time-warping kernels have demonstrated the real world applicability. This motivates the demand for investigating the elementary properties of the general IDS-kernels. In this paper we formally state and demonstrate their invariance properties, in particular the adjustability of the invariance in two conceptionally different ways. We characterize the definiteness of the kernels. We apply the kernels in different classification methods, which demonstrates various benefits of invariance.

Keywords

Kernel Method Optical Character Recognition Kernel Principal Component Analysis Total Invariance Transformation Knowledge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. HAASDONK, B. (2005): Transformation Knowledge in Pattern Analysis with Kernel Methods - Distance and Integration Kernels. PhD thesis, University of Freiburg.Google Scholar
  2. HAASDONK, B. and BAHLMANN, B. (2004): Learning with distance substitution kernels. In: Proc. of 26th DAGM-Symposium. Springer, 220-227.Google Scholar
  3. HAASDONK, B. and BURKHARDT, H. (2007): Invariant kernels for pattern analysis and machine learning. Machine Learning, 68, 35-61.CrossRefGoogle Scholar
  4. SCHÖLKOPF, B. and SMOLA, A. J. (2002): Learning with Kernels: Support Vector Ma-chines, Regularization, Optimization and Beyond. MIT Press.Google Scholar
  5. SHAWE-TAYLOR, J. and CRISTIANINI, N. (2004): Kernel Methods for Pattern Analysis. Cambridge University Press.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Bernard Haasdonk
    • 1
  • Hans Burkhardt
    • 2
  1. 1.Institute of MathematicsUniversity of FreiburgFreiburgGermany
  2. 2.Institute of Computer ScienceUniversity of FreiburgFreiburgGermany

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