Metric and Euclidean Properties of Diss imilari ty 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. R6sum~: Ce travail pr6sente quelques propri6t6s de certains coefficients de ressemblance et en particulier leur capacit6 de produire des matrices de distance m&riques et euclidiennes. Sans pr&endre ~tre exhaustifs dans cette revue de coefficients, nous pr6sentons certains r6sultats math6matiques que nous croyons int6ressants et qui pourraient ~tre 6tablis pour d'autres coefficients. Finalement, nous analysons la r6ponse des mesures de ressemblance face ~ diff6rents types de donn6es, ce qui permet de formuler des recommandations quant au choix d 'un coefficient.

[1]  J. Gower A General Coefficient of Similarity and Some of Its Properties , 1971 .

[2]  John C. Ogilvie,et al.  Evaluation of hierarchical grouping techniques; a preliminary study , 1972, Comput. J..

[3]  William M. Rand,et al.  Objective Criteria for the Evaluation of Clustering Methods , 1971 .

[4]  R. Sibson Studies in the Robustness of Multidimensional Scaling: Perturbational Analysis of Classical Scaling , 1979 .

[5]  Francis Cailliez,et al.  The analytical solution of the additive constant problem , 1983 .

[6]  J. Lingoes Some boundary conditions for a monotone analysis of symmetric matrices , 1971 .

[7]  Louis Legendre,et al.  Succession of Species within a Community: Chronological Clustering, with Applications to Marine and Freshwater Zooplankton , 1985, The American Naturalist.

[8]  Robin Sibson,et al.  Some Observations on a Paper by Lance and Williams , 1971, Comput. J..

[9]  George F. Estabrook,et al.  A General Method of Taxonomic Description for a Computed Similarity Measure , 1966 .

[10]  Robert F. Ling,et al.  Cluster analysis algorithms for data reduction and classification of objects , 1981 .

[11]  P. Legendre,et al.  Partitioning ordered variables into discrete states for discriminant analysis of ecological classifications , 1983 .

[12]  Nathaniel E. Helwig,et al.  An Introduction to Linear Algebra , 2006 .

[13]  G. N. Lance,et al.  Group-Size Depencence: A Rationale for Choice Between Numerical Classifications , 1971, Comput. J..

[14]  John C. Gower,et al.  Measures of Similarity, Dissimilarity and Distance , 1985 .

[15]  John C. Gower Distance matrices and their Euclidean approximation , 1983 .

[16]  L. Hubert Approximate Evaluation Techniques for the Single-Link and Complete-Link Hierarchical Clustering Procedures , 1974 .

[17]  J. V. Ness,et al.  Admissible clustering procedures , 1971 .

[18]  D. Faith Distance Methods and the Approximation of Most-Parsimonious Trees , 1985 .

[19]  G. N. Lance,et al.  Controversy Concerning the Criteria for Taxonometric Strategies , 1971, Computer/law journal.

[20]  F. Baker Stability of Two Hierarchical Grouping Techniques Case I: Sensitivity to Data Errors , 1974 .

[21]  H. Wolda,et al.  Similarity indices, sample size and diversity , 1981, Oecologia.

[22]  Roger K. Blashfield,et al.  Mixture model tests of cluster analysis: Accuracy of four agglomerative hierarchical methods. , 1976 .

[23]  J. Gower Euclidean Distance Geometry , 1982 .

[24]  Robin Sibson,et al.  The Construction of Hierarchic and Non-Hierarchic Classifications , 1968, Comput. J..

[25]  J. Gower Multivariate analysis : Ordination, multidimensional scaling and allied topics , 1984 .

[26]  L. J. Hajdu Graphical comparison of resemblance measures in phytosociology , 1981, Vegetatio.

[27]  P. Jaccard,et al.  Etude comparative de la distribution florale dans une portion des Alpes et des Jura , 1901 .