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On Not Making Dissimilarities Euclidean

  • Elzbieta Pękalska
  • Robert P. W. Duin
  • Simon Günter
  • Horst Bunke
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3138)

Abstract

Non-metric dissimilarity measures may arise in practice e.g. when objects represented by sensory measurements or by structural descriptions are compared. It is an open issue whether such non-metric measures should be corrected in some way to be metric or even Euclidean. The reason for such corrections is the fact that pairwise metric distances are interpreted in metric spaces, while Euclidean distances can be embedded into Euclidean spaces. Hence, traditional learning methods can be used.

The k-nearest neighbor rule is usually applied to dissimilarities. In our earlier study [2,3], we proposed some alternative approaches to general dissimilarity representations (DRs). They rely either on an embedding to a pseudo-Euclidean space and building classifiers there or on constructing classifiers on the representation directly. In this paper, we investigate ways of correcting DRs to make them more Euclidean (metric) either by adding a proper constant or by some concave transformations. Classification experiments conducted on five dissimilarity data sets indicate that non-metric dissimilarity measures can be more beneficial than their corrected Euclidean or metric counterparts. The discriminating power of the measure itself is more important than its Euclidean (or metric) properties.

Keywords

Euclidean Space Average Error Negative Eigenvalue Handwritten Digit Deformable Template 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Elzbieta Pękalska
    • 1
  • Robert P. W. Duin
    • 1
  • Simon Günter
    • 2
  • Horst Bunke
    • 2
  1. 1.ICT Group, Faculty of Electrical Engineering, Mathematics and Computer SciencesDelft University of TechnologyThe Netherlands
  2. 2.Department of Computer ScienceUniversity of BernSwitzerland

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