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Distance-Based Kernels for Real-Valued Data

  • Lluís Belanche
  • Jean Luis Vázquez
  • Miguel Vázquez
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)

Abstract

We consider distance-based similarity measures for real-valued vectors of interest in kernel-based machine learning algorithms. In particular, a truncated Euclidean similarity measure and a self-normalized similarity measure related to the Canberra distance. It is proved that they are positive semi-definite (p.s.d.), thus facilitating their use in kernel-based methods, like the Support Vector Machine, a very popular machine learning tool. These kernels may be better suited than standard kernels (like the RBF) in certain situations, that are described in the paper. Some rather general results concerning positivity properties are presented in detail as well as some interesting ways of proving the p.s.d. property.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Lluís Belanche
    • 1
  • Jean Luis Vázquez
    • 2
  • Miguel Vázquez
    • 3
  1. 1.Dept. de Llenguatges i Sistemes InformàticsUniversitÄt Politècnica de CatalunyaBarcelonaSpain
  2. 2.Departamento de MatemáticasUniversidad Autónoma de MadridMadridSpain
  3. 3.Dept. Sistemas Informáticos y ProgramaciónUniversidad Complutense de MadridMadridSpain

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