On Properties of Additive Tree Algorithms

  • K. Wolf
  • P. O. Degens
Conference paper


There is a growing interest in methods used for analyzing dissimilarity measurements which occur in many fields of biology, medicine, psychology etc. These data may be analyzed by using some graph theoretical structures. We concentrate on a special graph: the additive tree. Different methods have been proposed for constructing additive trees for given dissimilarity data, but there is less knowledge concerning properties of these methods. We present some suggestions for analyzing properties of additive tree constructing methods which allow a preliminary rating of proposed methods.


Point Condition Additive Tree Special Graph Mental Demand Tree Hierarchy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Brölsch, J. (1983), Minimum-Quadrat-Schätzung von Evolutionsbäumen, in: Dahlberg, I. & Schader, M. (eds.), Automatisierung in der Klassifikation, Studien zur Klassifikation 13, 177–187Google Scholar
  2. Buneman, P. (1971), The recovery of trees from measure of dissimilarity, in: Hodson, F.R., Kendall, D.G. & Tautu, P. (eds.), Mathematics in the Archaeological and Historical Sciences, Edinburgh University Press, 387–395Google Scholar
  3. Day, W.H.E. (1987), Computational Complexity of Inferring Phytogenies from dissimilarity matrices, Preprint, (to appear in Bulletin of Mathematical Biology)Google Scholar
  4. Degens, P.O. (1983), Hierarchische Clusteranalyse. Approximation und Agglomeration, in: Dahlberg, I. & Schader, M. (eds.), Auto-matisierung in der Klassifikation, Studien zur Klassifikation 13, 189–202Google Scholar
  5. De Soete, G. (1983), A least squares algorithm for fitting additive trees to proximity data, Psychometrika, 48, 621–626CrossRefGoogle Scholar
  6. Fitch, W.M. & Margolish, E. (1967), Construction of Phylogenetic Trees, Science, 155, 279–284CrossRefGoogle Scholar
  7. Jardine, N. & Sibson, R. (1968), The construction of hierarchic and non-hierarchic classifications, Computer ournal, 11, 177–184MATHGoogle Scholar
  8. Patrinos, A.N. & Hakimi, S.L. (1972), The Distance Matrix of a graph and its Tree Realization, Quarterly of Applied Mathematics, 30, 255–269MathSciNetMATHGoogle Scholar
  9. Sattah, S. & Tversky, A. (1977), Additive Similarity Trees, Psychometrika, 42, 319–345CrossRefGoogle Scholar
  10. Vach, W. (1988), Schätzung bewerteter Bäume als Approximationsproblem, Diplomarbeit, Fachbereich Statistik, Universität DortmundGoogle Scholar
  11. Vach, W. (1989), Least Squares Approximation of Additive Tree Metrics, this volumeGoogle Scholar
  12. Wolf, K. (1989), Kritische Untersuchung einiger Verfahren zur Schätzung bewerteter Bäume, Diplomarbeit, Fachbereich Statistik, Universität DortmundGoogle Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1989

Authors and Affiliations

  • K. Wolf
    • 1
  • P. O. Degens
    • 1
  1. 1.Fachbereich StatistikUniversität DortmundGermany

Personalised recommendations