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Journal of Classification

, Volume 12, Issue 1, pp 73–90 | Cite as

Comparing resemblance measures

  • Vladimir Batagelj
  • Matevz Bren
Article

Abstract

In the paper some types of equivalences over resemblance measures and some basic results about them are given. Based on induced partial orderings on the set of unordered pairs of units a dissimilarity between two resemblance measures over finite sets of units can be defined. As an example, using this dissimilarity standard association coefficients between binary vectors are compared both theoretically and computationally.

Key Words

Dissimilarity spaces Metric spaces Association coefficients Profile measures of resemblance 

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References

  1. ANDERBERG, M. R. (1973),Cluster Analysis for Applications, New York: Academic Press.Google Scholar
  2. BANDELT, H.-J. (1990), “Recognition of Tree Metrics,”SIAM Journal on Discrete Mathematics, 3/1, 1–6.Google Scholar
  3. BATAGELJ, J. (1989), “Similarity Measures Between Structured Objects,” inProceedings MATH/CHEM/COMP/1988, Dubrovnik, Yugoslavia 20–25 June 1988, Studies in Physical and Theoretical Chemistry. Vol 63, Ed., A. Graovac, Amsterdam: Elsevier, 25–40.Google Scholar
  4. BATAGELJ, V. (1992),CLUSE/TV-Clustering Programs, Manual, Ljubljana.Google Scholar
  5. BATAGELJ, V., PISANSKI, T., and SIMOES-PEREIRA, J. M. S. (1990), “An Algorithm for Tree-Realizability of Distance Matrices,”International journal of Computer Mathematics, 34, 171–176.Google Scholar
  6. BAULIEU, F. B. (1989), “A Classification of Presence/Absence Based Dissimilarity Coefficients,”Journal of Classification, 6, 233–246.Google Scholar
  7. BENINEL, F. (1987),Problemes de representations spheriques des tableaux de dissimilarite, Thesis, Université de Rennes I, (in French).Google Scholar
  8. DIEUDONNÉ, J. (1960),Foundation of Modern Analysis, New York: Academic Press.Google Scholar
  9. GORDON, A. D. (1981),Classification, London: Chapman and Hall.Google Scholar
  10. GOWER, J. C., and LEGENDRE, P. (1986), “Metric and Euclidean Properties of Dissimilarity Coefficients,”Journal of Classification, 3, 5–48.Google Scholar
  11. GOWER, J. C. (1971), “A General Coefficient of Similarity and Some of Its Properties,”Biometrics 27, 857–871.Google Scholar
  12. HUBÁLEK, Z. (1982), “Coefficients of Association and Similarity, Based on Binary (Presence-Absence) Data: An Evaluation,”Biological Review, 57, 669–689.Google Scholar
  13. JAMBU, M., and LEBEAUX, M.-O. (1983),Cluster Analysis and Data Analysis, Amsterdam: North-Holland.Google Scholar
  14. JOLY, S., and LE CALVE, G. (1986), “Etude des puissances d'une distance,”Statistique et Analyse de Données, 11/3, 30–50.Google Scholar
  15. KAUFMANN, A. (1975),Introduction a la théorie des sous-ensembles flous, Vol. III, Paris: Masson, 153–155.Google Scholar
  16. KRANTZ, D. H., LUCE, R. D., SUPPES, P., and TVERSKY, A. (1971),Foundations of Measurement, Vol. I, New York: Academic Press.Google Scholar
  17. KRUSKAL, J. B. (1983), “An Overview of Sequence Comparison: Time Warps, String Edits and Macro-Molecules,”SIAM Review, 25/2, 201–237.Google Scholar
  18. LERMAN, I. C. (1971),Indice de similarité et préordonnance associée, Ordres, Travaux de séminaire sur les ordres totaux finis, Aix-en-Provence, 1967, Paris: Mouton.Google Scholar
  19. LIEBETRAU, A. M. (1983),Measure of Association, Newbury Park, CA: Sage Publications.Google Scholar
  20. SNEATH, P. H. A., and SOKAL, R. R. (1973),Numerical Taxonomy, San Francisco: W. H. Freeman.Google Scholar
  21. SPÄTH, H. (1977),Cluster Analyse Algorithmen zur Objekt-Klassifizierung und Datenreduction, München: R. Oldenbourg.Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Vladimir Batagelj
    • 1
  • Matevz Bren
    • 2
  1. 1.Department of MathematicsUniversity of LjubljanaLjubljanaSlovenia
  2. 2.FOV KranjUniversity of MariborKranjSlovenia

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