A Kernel Approach to Metric Multidimensional Scaling

  • Andrew Webb
Conference paper

DOI: 10.1007/3-540-70659-3_47

Part of the Lecture Notes in Computer Science book series (LNCS, volume 2396)
Cite this paper as:
Webb A. (2002) A Kernel Approach to Metric Multidimensional Scaling. In: Caelli T., Amin A., Duin R.P.W., de Ridder D., Kamel M. (eds) Structural, Syntactic, and Statistical Pattern Recognition. SSPR /SPR 2002. Lecture Notes in Computer Science, vol 2396. Springer, Berlin, Heidelberg

Abstract

The solution for the parameters of a nonlinear mapping in a metric multidimensional scaling by transformation, in which a stress criterion is optimised, satisfies a nonlinear eigenvector equation, which may be solved iteratively. This can be cast in a kernel-based framework in which the configuration of training samples in the transformation space may be found iteratively by successive linear projections, without the need for gradient calculations. A new data sample can be projected using knowledge of the kernel and the final configuration of data points.

Keywords

multidimensional scaling kernel representation nonlinear feature extraction 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Andrew Webb
    • 1
  1. 1.QinetiQMalvern

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