Quotient Dissimilarities, Euclidean Embeddability, and Huygens’ Weak Principle
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
KeywordsMutual Information Location Quotient Factorial Correspondence Analysis Weak Principle Column Profile
Unable to display preview. Download preview PDF.
- CRESSIE, N. and READ, T.R.C. (1984): Multinomial goodness-of-fit tests.J.R.Statist.Soc.B, 46,440–464.Google Scholar
- ESCOFIER, B. (1978): Analyse factorielle et distances répondant au principe d’équivalence distributionnelle. Revue de Statistique Appliquée, 26, 29–37Google Scholar
- LEBART, L. (1969): L’analyse statistique de la contiguïté. Publications de l’ISUP, XVIII, 81–112Google Scholar