Skip to main content
SpringerLink
Log in

Some Trends in the Classification of Variables

  • Conference paper
Data Science, Classification, and Related Methods

Summary

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • 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 

  • Bacelar-Nicolau, H. (1981) - Contribuiçóes no estudo dos coeficientes de comparaçdo em Andlise Classificatória - Duct. Thesis, FCL, Univ. de Lisboa.

    Google Scholar 

  • 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 

  • 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 

  • 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, 89–90

    Google Scholar 

  • 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, 63–74

    Google Scholar 

  • 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, 610–618

    Google Scholar 

  • Lance, G.N.; Williams, W.T. (1967)–A general theory of classificatory sorting strategies. Hierarchical systems. The Computer Journal, vol 9, no 4, 373–380

    Google Scholar 

  • 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 

  • 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 

  • Lerman, I.C. (1981) - Classification et Analyse Ordinale des Données. Dunod.

    Google Scholar 

  • Matusita, K. (1951) - On the Theory of Statistical Decision Functions. An. In. Stat. Math.,vol. I II, 1–30.

    Google Scholar 

  • Nicolau, F. Costa (1981) - Critérios de andlise classificatoria hiercírquica baseados na funçdo de distribuiçào - Doct. Thesis, FCL, Univ. de Lisboa.

    Google Scholar 

  • 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 

  • Nicolau, F. Costa (1983) - Cluster Analysis and Distribution Function,Meth. Oper. Res., vol. 45, Verlag Anton Hain, 431–433.

    Google Scholar 

  • Nicolau, F. Costa; Brito, M.P. (1989) - Improvment in NHMEAN method. Data Analysis, Learning Symbolic and Numerical Knowledge (ed. E. Diday) Nova Science Publishers

    Google Scholar 

  • Sibson, R. (1972) - Order invariant methods for Data Analysis in J.R.S.S., B, vol.34, n°.3, 31 1338.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences and Technology, Laboratory of Statistics and Actuarial Mathematics (LEMA), New University of Lisbon, Portugal

    F. Costa Nicolau

  2. Laboratory of Statistics and Data Analysis (LEAD), CEA / JNICT, University of Lisbon, Faculty of Psychology and Education, Portugal

    H. Bacelar-Nicolau

Authors
  1. F. Costa Nicolau
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. Bacelar-Nicolau
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106, Japan

    Chikio Hayashi , Noboru Ohsumi  & Yasumasa Baba ,  & 

  2. School of Management, Science University of Tokyo, 500 Shimokiyoku, Kuki, Saitama 346, Japan

    Keiji Yajima

  3. Institut für Statistik, Rheinisch-Westfälische Technische Hochschule (RWTH), D-52056, Aachen, Germany

    Hans-Hermann Bock

  4. Faculty of Environmental Science & Technology, Okayama University, 2-1-1 Tsushima-naka, Okayama 700, Japan

    Yutaka Tanaka

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer Japan

About this paper

Cite this paper

Nicolau, F.C., Bacelar-Nicolau, H. (1998). Some Trends in the Classification of Variables. In: Hayashi, C., Yajima, K., Bock, HH., Ohsumi, N., Tanaka, Y., Baba, Y. (eds) Data Science, Classification, and Related Methods. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Tokyo. https://doi.org/10.1007/978-4-431-65950-1_7

Download citation

  • DOI: https://doi.org/10.1007/978-4-431-65950-1_7

  • Publisher Name: Springer, Tokyo

  • Print ISBN: 978-4-431-70208-5

  • Online ISBN: 978-4-431-65950-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation