, Volume 48, Issue 4, pp 621–626

A least squares algorithm for fitting additive trees to proximity data

  • Geert De Soete
Notes And Comments


A least squares algorithm for fitting additive trees to proximity data is described. The algorithm uses a penalty function to enforce the four point condition on the estimated path length distances. The algorithm is evaluated in a small Monte Carlo study. Finally, an illustrative application is presented.

Key words

tree structures clustering proximity data 


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References notes

  1. Carroll, J. D., & Pruzansky, S.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, August 1975.Google Scholar
  2. Furnas, G. W.The construction of random, terminally labeled, binary trees. Unpublished paper, Bell Laboratories, Murray Hill, New Jersey, 1981.Google Scholar


  1. Carroll, J. D. Spatial, nonspatial and hybrid models for scaling.Psychometrika, 1976,41, 439–463.Google Scholar
  2. Carroll, J. D., & Pruzansky, S. Discrete and hybrid scaling models. In E. D. Lantermann & H. Feger (Eds.),Similarity and choice. Bern: Huber, 1980.Google Scholar
  3. Cunningham, J. P. Free trees and bidirectional trees as representations of psychological distance.Journal of Mathematical Psychology, 1978,17, 165–188.Google Scholar
  4. Dobson, A. J. Unrooted trees for numerical taxonomy.Journal of Applied Probability, 1974,11, 32–42.Google Scholar
  5. Kuennapas, T., & Janson, A. J. Multidimensional similarity of letters.Perceptual & Motor Skills, 1969,28, 3–12.Google Scholar
  6. Powell, M. J. D. Restart procedures for the conjugate gradient method.Mathematical Programming, 1977,12, 241–254.Google Scholar
  7. Pruzansky, S., Tversky, A., & Carroll, J. D. Spatial versus tree representations of proximity data.Psychometrika, 1982,47, 3–24.Google Scholar
  8. Sattath, S., & Tversky, A. Additive similarity trees.Psychometrika, 1977,42, 319–345.Google Scholar

Copyright information

© The Psychometric Society 1983

Authors and Affiliations

  • Geert De Soete
    • 1
  1. 1.Department of PsychologyUniversity of GhentGhentBelgium

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