Abstract
The paper addresses the problem of specifying differential weights for variables in the construction of a measure of dissimilarity. An assessor is required to provide subjective judgments of the pairwise dissimilarities within a training set of objects, and these dissimilarities are then modeled as a function of the recorded differences between the objects on each of the variables. The aim is to make explicit the relative importance that assessors attach to each of the variables, and thus obtain guidance on how these variables should be combined into a relevant dissimilarity matrix. The methodology is illustrated by application to some archaeological data.
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References
ANDERBERG, M. R. (1973),Cluster Analysis for Applications, New York: Academic Press.
ANDERSON, E. (1960) “A Semigraphical Method for the Analysis of Complex Problems,”Technometrics, 2, 387–391.
BERTIN, J. (1983),Semiology of Graphics: Diagrams, Networks, Maps (translated by W.J. Berg), Madison: University of Wisconsin Press.
CARROLL, J. D., and CHANG, J.-J. (1970), “Analysis of Individual Differences in Multidimensional Scaling Via an N-Way Generalization of ‘Eckhart-Young’ Decomposition,”Psychometrika, 35, 283–319.
CHERNOFF, H. (1973), “The Use of Faces to Represent Points in k-Dimensional Space Graphically,”Journal of the American Statistical Association, 68, 361–368.
DE SOETE, G., DESARBO, W. S., and CARROLL, J. D. (1985), “Optimal Variable Weighting for Hierarchical Clustering: An Alternating Least-Squares Algorithm,”Journal of Classification, 2, 173–192.
DESARBO, W. S., CARROLL, J. D., CLARK, L. A., and GREEN, P. E. (1984), “Synthesized Clustering: A Method for Amalgamating Alternative Clustering Bases with Differential Weighting of Variables,”Psychometrika, 49, 57–78.
DESARBO, W. S., and MAHAJAN, V. (1984), “Constrained Classification: The Use of A Priori Information in Cluster Analysis,”Psychometrika, 49, 187–215.
DIDAY, E., and MOREAU, J. V. (1984), “Learning Hierarchical Clustering from Examples — Application to the Adaptive Construction of Dissimilarity Indices,”Pattern Recognition Letters, 2, 365–378.
DIDAY, E., and SIMON, J. C. (1976), “Clustering Analysis,” inCommunication and Cybernetics 10: Digital Pattern Recognition, ed. K. S. Fu, Berlin: Springer-Verlag, 47–94.
DRAPER, N. R., and SMITH, H. (1981),Applied Regression Analysis (2nd ed.), New York: Wiley.
FOWLKES, E. B., GNANADESIKAN, R., and KETTENRING, J. R. (1988), “Variable Selection in Clustering,”Journal of Classification, 5, 205–228.
FRIEDMAN, J. H., and TUKEY, J. W. (1974), “A Projection Pursuit Algorithm for Exploratory Data Analysis,”IEEE Transactions on Computers, C-23, 881–890.
GORDON, A. D. (1981),Classification: Methods for the Exploratory Analysis of Multivariate Data, London: Chapman and Hall.
GOWER, J. C. (1971), “A General Coefficient of Similarity and Some of its Properties,”Biometrics, 27, 857–874.
GOWER, J. C. (1985), “Measures of Similarity, Dissimilarity, and Distance,” inEncyclopedia of Statistical Sciences, Volume 5, eds. S. Kotz, N. L. Johnson and C. B. Read, New York: Wiley, 397–405.
GOWER, J. C., and LEGENDRE, P. (1986), “Metric and Euclidean Properties of Dissimilarity Coefficients,”Journal of Classification, 3, 5–48.
GREEN, P. E., and DESARBO, W.S. (1978), “Additive Decomposition of Perceptions Data Via Conjoint Analysis,”Journal of Consumer Research, 5, 58–65.
HANSOHM, J., and TURULSKI, N. (1985), “Analysis of the Classification of Cetacea: Whales, Porpoises and Dolphins,” inData Analysis in Real Life Environment: Ins and Outs of Solving Problems, eds. J.-F. Marcotorchino, J.-M. Proth, and J. Janssen, Amsterdam: North-Holland, 55–67.
JAMBU, M. (1978),Classification Automatique pour L'Analyse des Données, Tome 1, Paris: Dunod.
JAMBU, M., and LEBEAUX, M.-O. (1983),Cluster Analysis and Data Analysis, Amsterdam: North Holland Publishing Company.
KLEINER, B., and HARTIGAN, J. A. (1981), “Representing Points in Many Dimensions by Trees and Castles,”Journal of the American Statistical Association, 76, 260–276.
KRUSKAL, J. B. (1964a), “Multidimensional Scaling by Optimizing Goodness of Fit to a Nonmetric Hypothesis,”Psychometrika, 29, 1–27.
KRUSKAL, J. B. (1964b), “Nonmetric Multidimensional Scaling: A Numerical Method,”Psychometrika, 27, 115–129.
KRUSKAL, J.B. (1972), “Linear Transformation of Multivariate Data to Reveal Clustering,” inMultidimensional Scaling. Theory and Applications in the Behavioral Sciences, Volume 1 Theory, eds. R. N. Shepard, A. K. Romney, and S. B. Nerlove, New York: Seminar Press, 179–191.
KRZANOWSKI, W. J. (1988),Principles of Multivariate Analysis. A User's Perspective, Oxford: Clarendon Press.
LACHENBRUCH, P. A. (1975),Discriminant Analysis, New York: Hafner.
LANCE, G. N., and WILLIAMS, W. T. (1967), “A General Theory of Classificatory Sorting Strategies I. Hierarchical Systems,”Computer Journal, 9, 373–380.
MILLIGAN, G. W. (1980), “An Examination of the Effect of Six Types of Error Perturbation on Fifteen Clustering Algorithms,”Psychometrika, 45, 325–342.
MILLIGAN, G. W., and COOPER, M. C. (1988), “A Study of Standardization of Variables in Cluster Analysis,”Journal of Classification, 5, 181–204.
SIBSON, R. (1972), “Order Invariant Methods for Data Analysis (with Discussion),”Journal of the Royal Statistical Society, Series B, 34, 311–349.
SNEATH, P. H. A., and SOKAL, R. R. (1973),Numerical Taxonomy, San Francisco: Freeman.
SNIJDERS, T. A. B., DORMAAR, M., VAN SCHUUR, W. H., DIJKMAN-CAES, C., and DRIESSEN, G. (1990), “Distribution of Some Similarity Coefficients for Dyadic Binary Data in the Case of Associated Attributes,”Journal of Classification, 7, 5–31.
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Gordon, A.D. Constructing dissimilarity measures. Journal of Classification 7, 257–269 (1990). https://doi.org/10.1007/BF01908719
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DOI: https://doi.org/10.1007/BF01908719