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)


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.


Strong Principle Information Theoretical Approach Weak Principle Column Profile Weighted Average Operator 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. BAVAUD, F. (2000): An Information Theoretical approach to Factorial Correspondence Analysis. To appear in the proceedings of the 5th International Conference on the Statistical Analysis of Textual Data (JADT 2000)Google Scholar
  2. CRESSIE, N. and READ, T.R.C. (1984): Multinomial goodness-of-fit tests. J.R.Statist.Soc.B, 46, 440–464Google Scholar
  3. ESCOFIER, B. (1978): Analyse factorielle et distances répondant au principe d’équivalence distributionnelle. Revue de Statistique Appliquée, 26, 29–37Google Scholar
  4. FICHET, B. (1978): Note sur la métrique de l’analyse des correspondances. Statistique et Analyse de Données, 2, 87–93Google Scholar
  5. JARDINE,N. and SIBSON,R. (1971): Mathematical Taxonomy. Wiley, New York.Google Scholar
  6. KULLBACK, S. (1959): Information Theory and Statistics. Wiley, New York.Google Scholar
  7. LEBART, L. (1969): L’analyse statistique de la contiguïté. Publications de l’ISUP, XVIII, 81–112Google Scholar

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

Personalised recommendations