Abstract
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.
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ARABIE, P., and CARROLL, J. D. (1980), “MAPCLUS: A Mathematical Programming Approach to Fitting the ADCLUS Model,”Psychometrika, 45, 211–235.
CARROLL, J. D., and ARABIE, P. (1983), “INDCLUS: An Individual Differences Generalization of the ADCLUS Model and the MAPCLUS Algorithm,”Psychometrika, 48, 157–169.
CARROLL, J. D., CLARK, L. A., and DeSARBO, W. S. (1984), “The Representation of Three-Way Proximities Data by Single and Multiple Tree Structure Models,”Journal of Classification, 1, 25–74.
CARROLL, J. D., and PRUZANSKY, S. (1975), “Fitting of Hierarchical Tree Structure (HTS) Models, Mixtures of HTS Models, and Hybrid Models, via Mathematical Programming and Alternating Least Squares,” Paper presented at the U.S.-Japan Seminar on Theory, Methods and Applications of Multidimensional Scaling and Related Techniques, San Diego, CA.
CARROLL, J. D., and PRUZANSKY, S. (1980), “Discrete and Hybrid Scaling Models,” inSimilarity and Choice, eds. E. D. Lantermann and H. Feger, Bern: Huber, 108–139.
COHEN, A., GNANADESIKAN, R., KETTENRING, J. R., and LANDWEHR, J. M. (1977), “Methodological Developments in Some Applications of Clustering,” inApplications of Statistics, ed. P. R. Krishnaiah, Amsterdam: North-Holland, 141–162.
De SOETE, G. (1983), “A Least Squares Algorithm for Fitting Additive Trees to Proximity Data,”Psychometrika, 48, 621–626.
De SOETE, G. (1984), “A Least Squares Algorithm for Fitting an Ultrametric Tree to a Dissimilarity Matrix,”Pattern Recognition Letters, 2, 133–137.
De SOETE, G., DeSARBO, W. S., FURNAS, G. W., and CARROLL, J. D. (1984), “The Estimation of Ultrametric and Path Length Trees from Rectangular Proximity Data,”Psychometrika, 49, 289–310.
FURNAS, G. W. (1981), “The Construction of Random, Terminally Labeled, Binary Trees,” Unpublished Memorandum, Bell Laboratories, Murray Hill, NJ.
GNANADESIKAN, R., KETTENRING, J. R., and LANDWEHR, J. M. (1977), “Interpreting and Assessing the Results of Cluster Analyses,”Bulletin of the International Statistical Institute, 47, 451–463.
HARTIGAN, J. A. (1967), “Representation of Similarity Matrices by Trees,”Journal of the American Statistical Association, 62, 1140–1158.
HARTIGAN, J. A. (1975),Clustering Algorithms, New York: Wiley.
JARDINE, C. J., JARDINE, N., and SIBSON, R. (1967), “The Structure and Construction of Taxonomic Hierarchies,”Mathematical Biosciences, 1, 173–179.
JARDINE, N., and SIBSON, R. (1971),Mathematical Taxonomy, London: Wiley.
JOHNSON, S. C. (1967), “Hierarchical Clustering Schemes,”Psychometrika, 32, 241–254.
POWELL, M. J. D. (1977), “Restart Procedures for the Conjugate Gradient Method,”Mathematical Programming, 12, 241–254.
SNEATH, P. H., and SOKAL, R. R. (1973),Numerical Taxonomy, San Francisco: Freeman.
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Geert De Soete is “Aangesteld Navorser” of the Belgian “National Fonds voor Wetenschappelijk Onderzoek.”
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De Soete, G. Ultrametric tree representations of incomplete dissimilarity data. Journal of Classification 1, 235–242 (1984). https://doi.org/10.1007/BF01890124
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DOI: https://doi.org/10.1007/BF01890124