Metric and Euclidean properties of dissimilarity coefficients

We assemble here properties of certain dissimilarity coefficients and are specially concerned with their metric and Euclidean status. No attempt is made to be exhaustive as far as coefficients are concerned, but certain mathematical results that we have found useful are presented and should help establish similar properties for other coefficients. The response to different types of data is investigated, leading to guidance on the choice of an appropriate coefficient.The authors wish to thank the referees, one of whom did a magnificent job in painstakingly checking the detailed algebra and detecting several slips.     

Ultrametric tree representations of incomplete dissimilarity data

The least squares algorithm for fitting ultrametric trees to proximity data originally proposed by Carroll and Pruzansky and further elaborated by De Soete is extended to handle missing data. A Monte Carlo evaluation reveals that the algorithm is capable of recovering an ultrametric tree underlying an incomplete set of error-perturbed dissimilarities quite well.Geert De Soete is Aangesteld Navorser of the Belgian National Fonds voor Wetenschappelijk Onderzoek.     

Comparing resemblance measures

In the paper some types of equivalences over resemblance measures and some basic results about them are given. Based on induced partial orderings on the set of unordered pairs of units a dissimilarity between two resemblance measures over finite sets of units can be defined. As an example, using this dissimilarity standard association coefficients between binary vectors are compared both theoretically and computationally.Extended version of the paper presented at DISTANCIA'92, June 22–26, 1992, Rennes, France. This work was supported in part by the Ministry for Science and Technology of Slovenia, J2-6191-101-94. We would like to thank the editor and two anonymous referees for numerous remarks and suggestions that significantly improved the presentation of the material.