Some Trends in the Classification of Variables

  • F. Costa Nicolau
  • H. Bacelar-Nicolau
Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


In this paper we review a class of hierarchical clustering methods based on similarity coefficients and aggregation criteria which are associated to the integral transformation by the (probabilistic) distribution function of some suitable sample statistics. Some properties of those methods we have studied are remembered and/or derived here. Applications on either simulated or real data set have shown this approach performs better than the traditional one (using empirical clustering methods) in many situations. Moreover we define some “hybrid” criteria, which we generalise in order to get some mixed or parametric hierarchical clustering methods. Inside of such parametrical families we are able to find, among different criteria those better fitting to the initial similarities, and to search for stability and validity of those methods.


Similarity Coefficient Parametric Family Single Linkage Level Index Aggregation Criterion 
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. Bacelar-Nicolau, H. (1972) - Analyse d’un algorithme de classification automatique - Thèse de 3ème Cycle, Univ. ParisVl ( I.S.U.P. ), Nov. 1972.Google Scholar
  2. Bacelar-Nicolau, H. (1981) - Contribuiçóes no estudo dos coeficientes de comparaçdo em Andlise Classificatória - Duct. Thesis, FCL, Univ. de Lisboa.Google Scholar
  3. Bacelar-Nicolau, H. (1987)–On the distribution equivalence in cluster analysis, NATO ASI Series, vol F30, Patt. Recogn. Theory and Applic., P.A.Devijver( J.Kitler (eds), Springer-Verlag, 73–79.Google Scholar
  4. Bacelar-Nicolau, H. (1988) - Two Probabilistic Models for Classification of Variables in Frequency Tables. Classif. and Rel. Meth. of Data Analysis, H.H.Bock (ed.). North Holland,181186.Google Scholar
  5. Bacelar-Nicolau, H..(1989)–Sur l’équivalence distributionnelle entre coefficients d’association, Bulletin of the International Statistical Institute (ISI), 47th Session, Contributed Papers,Book 1, 89–90Google Scholar
  6. Bacelar-Nicolau, H.; Nicolau, F.C.(1993) - Classifying integer scale data by the affinity coefficient: a probabilistic approach: Proceedings of the Sixth Intern. Symp. on Applied Stochastic Models and Data Analysis (ASMDA). J.Jansen and C.H.Skiadas (ed), World Scientific, vol 1, 63–74Google Scholar
  7. Bacelar-Nicolau, H.;Nicolau,F.C. (1994)–Exploratory and confirmatory discrete multivariate analysis in a probabilistic approach for studying the regional distribution of AIDS in Angola. New App. in Classif. and Data Analysis, E.Diday, Y. Lechevallier, M. Shader (ed.), Springer-Verlag, 610–618Google Scholar
  8. Lance, G.N.; Williams, W.T. (1967)–A general theory of classificatory sorting strategies. Hierarchical systems. The Computer Journal, vol 9, no 4, 373–380Google Scholar
  9. Legendre, L.; Legendre, P. (1983) - Numerical Ecology. Elsevier Sc. Publ. I. C. LERMAN,I.C.(1970) - Sur l’Analyse des Données Préalable à une Classification Automatique,Rev. Math. et Sc.Hum., vol 32, 8ème année, 5–15.Google Scholar
  10. Lerman, I.C. (1973) - Etude distributionnelle de statistiques de proximité entre structures finies de même type, application à la classification automatique. Cahiers du BURO, Paris.Google Scholar
  11. Lerman, I.C. (1981) - Classification et Analyse Ordinale des Données. Dunod.Google Scholar
  12. Matusita, K. (1951) - On the Theory of Statistical Decision Functions. An. In. Stat. Math.,vol. I II, 1–30.Google Scholar
  13. Nicolau, F. Costa (1981) - Critérios de andlise classificatoria hiercírquica baseados na funçdo de distribuiçào - Doct. Thesis, FCL, Univ. de Lisboa.Google Scholar
  14. Nicolau, F. Costa; Bacelar-Nicolau, H. (1981) - Nouvelles méthods d’agrégation basées sur la fonction de répartition. Collection Séminaires INRIA de Classification et Perception par Ordinateur 1981, INRIA, Domaine de Voluceau-Rocquencourt, France.Google Scholar
  15. Nicolau, F. Costa (1983) - Cluster Analysis and Distribution Function,Meth. Oper. Res., vol. 45, Verlag Anton Hain, 431–433.Google Scholar
  16. Nicolau, F. Costa; Brito, M.P. (1989) - Improvment in NHMEAN method. Data Analysis, Learning Symbolic and Numerical Knowledge (ed. E. Diday) Nova Science PublishersGoogle Scholar
  17. Sibson, R. (1972) - Order invariant methods for Data Analysis in J.R.S.S., B, vol.34, n°.3, 31 1338.Google Scholar

Copyright information

© Springer Japan 1998

Authors and Affiliations

  • F. Costa Nicolau
    • 1
  • H. Bacelar-Nicolau
    • 2
  1. 1.Department of Mathematics, Faculty of Sciences and Technology, Laboratory of Statistics and Actuarial Mathematics (LEMA)New University of LisbonPortugal
  2. 2.Laboratory of Statistics and Data Analysis (LEAD), CEA / JNICTUniversity of Lisbon, Faculty of Psychology and EducationPortugal

Personalised recommendations