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Quotient Dissimilarities, Euclidean Embeddability, and Huygens’ Weak Principle

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

Abstract

We introduce a broad class of categorical dissimilarities, the quotien­t dissimilarities, for which aggregation invariance is automatically satisfied. This class contains the chi-square, ratio, Kullback-Leibler and Hellinger dissimilarities, as well as presumably new “power” and “threshold” dissimilarity families. For a large sub-class of the latter, the product dissimilarities, we show that the Euclidean embeddability property on one hand and the weak Huygens’ principle on the other hand are mutually exclusive, the only exception being provided by the chi-square dissimilarity DX. Various suggestions are presented, aimed at generalizing Factorial Correspondence Analysis beyond the chi-square metric, by non-linear distortion of departures from independence. In particular, the central inertia appearing in one formulation precisely amounts to the mutual information of Information Theory. 1

Keywords

Mutual Information Location Quotient Factorial Correspondence Analysis Weak Principle Column Profile 
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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References

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • François Bavaud
    • 1
  1. 1.Section d’Informatique et de Méthodes MathématiquesFaculté des Lettres, Université de LausanneLausanne-DorignySchweiz

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