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On a Class of Aggregation-invariant Dissimilarities Obeying the Weak Huygens’ Principle

  • F. Bavaud
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)

Abstract

We propose a complete characterization of a certain class of aggregation-invariant dissimilarities between row (or column) profiles. This class (for which row and column dispersions coincide) contains the chi-square, ratio, Kullback-Leibler, Hellinger, Cressie-Read dissimilarities, as well as a presumably new “type s” class of dissimilarities. Distinguishing between two forms of Huygens’ principle from Classical Mechanics, we show “type s” dissimilarities to satisfy the weak Huygens’ principle; the strong Huygens’ principle however holds for a single member of the class, namely the chi-square dissimilarity. Extending the concept of dissimilarity to “type s” divergences restores the strong principle.

Keywords

Strong Principle Information Theoretical Approach Weak Principle Column Profile Weighted Average Operator 
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Copyright information

© Springer-Verlag Berlin · Heidelberg 2000

Authors and Affiliations

  • F. Bavaud
    • 1
  1. 1.Section d’Informatique et de Méthodes Mathématiques, Faculté des LettresUniversité de LausanneLausanne-DorignySwitzerland

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