Skip to main content

Ordinal and Metrical Analysis of the Resemblance Notion

  • Chapter
  • First Online:
  • 1615 Accesses

Part of the book series: Advanced Information and Knowledge Processing ((AI&KP))

Abstract

The concept of resemblance between data units (objects, categories or attributes) is the most important element in Data Analysis and Machine Learning. In Chap. 3, the description of a set of objects \(\mathcal {O}\) (resp., categories \(\mathcal {C}\)) by a set of descriptive attributes \(\mathcal {A}\) is formalized and a mathematical representation of this description is established.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover 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

Learn about institutional subscriptions

Notes

  1. 1.

    \(F=P_{2}(E)=\{\{x,y\} | x \in E, y \in E, x \ne y\}\).

References

  1. Agrawal, T., Imielinski, T., Swami, A.N.: Mining association rules between sets of items in large databases. In: Proceedings of the 1993 ACM SIGMOD International Conference on Management of Data, pp. 207–216 (1993)

    Google Scholar 

  2. Batagelj, V., Bren, M.: Comparing resemblance measures. J. Classif. 12, 73–90 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bouchon-Meunier, B., Rifqi, M., Bothorel, S.: Towards general measures of comparison of objects. Fuzzy Sets Syst. 2, 143–153, 84 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  4. de la Vega. W.F.: Techniques de classification automatique utilisant un indice de ressemblance. Revue Francaise de Sociologie (1967)

    Google Scholar 

  5. Dice, L.R.: Measures of the amount of ecologic association between species. Ecology 26, 297–302 (1945)

    Google Scholar 

  6. Fowlkes, E.B., Mallows, C.L.: A method for comparing two hierarchical clusterings. J. Am. Stat. Assoc. J.A.S.A. 78, 553–569 (1983)

    Article  MATH  Google Scholar 

  7. Geng, L., Howard, J., Hamilton, J.: Choosing the right lens: Finding what is interesting in data mining. Studies in Computational Intelligence (SCI), vol. 43, pp. 3–24. Springer, New York (2007)

    Google Scholar 

  8. Giakoumakis, V., Monjardet, B.: Coefficients d ’ accord entre deux préordres totaux. Mathématiques et Sciences Humaines 98, 69–87 (1987)

    MATH  Google Scholar 

  9. Goodman, L.A., Kruskal, W.H.: Measures of association for cross classifications. J. Am. Stat. Assoc. 49, 732–764 (1954)

    MATH  Google Scholar 

  10. Gras, R.: Contribution à l’étude expérimentale et à l’analyse de certaines acquisitions cognitives et de certains objectifs didactiques en mathématiques. Ph.D. thesis, Thèse de doctorat d’état, Université de Rennes 1 (1979)

    Google Scholar 

  11. Guillet, F., Hamilton, H.J. (eds.): Quality measures in data mining. Studies in Computational Intelligence, vol. 43. Springer, New York (2007)

    Google Scholar 

  12. Hamann, V.: Merkmalbestand und verwandtschaftsbeziehungen der farinosae. Beitragzum System der Monokotyledonen 2, 639–768 (1961)

    Google Scholar 

  13. Jaccard, P.: Nouvelles recherches sur la distribution florale. Bulletin de la Société Vaudoise des Sciences Naturelles 44, 223–270 (1908)

    Google Scholar 

  14. Kendall, M.G.: Rank Correlation Methods. Charles Griffin, New York (1970). (1st edn in 1948)

    MATH  Google Scholar 

  15. Kulczynski, S.: Die pflanzenassoziationen der pieninen [in polish, german summary]. Bull. Inter. Acad. Pol. Sci. Lett. Cl. Sci. Math. Nat (Sci. Nat) 2, 57–203 (1927)

    Google Scholar 

  16. Lalich, S., Teytaud, O., Prudhomme, E.: Association rule interestingness: Measure and statistical validation. Studies in Computational Intelligence (SCI), vol. 43, pp. 251–275. Springer, New York (2007)

    Google Scholar 

  17. Lerman, I.C.: Indice de similarité et préordonnance associée. In: Barbut, M. (ed.) Ordres, Travaux du séminaire sur les ordres totaux finis. Aix-en-Provence, Mouton (1967)

    Google Scholar 

  18. Lerman, I.C.: Les Bases de la Classification Automatique. Gauthier-Villars, Paris (1970)

    MATH  Google Scholar 

  19. Lerman, I.C.: Sur l’analyse des données préalable à une classification automatique; proposition d’une nouvelle mesure de similarité. Mathématiques et Sciences Humaines 32, 5–15 (1970)

    MathSciNet  Google Scholar 

  20. Lerman, I.C.: Introduction à une méthode de classification automatique illustrée par la recherche d’une typolologie des personnages enfants à travers la littérature enfantine. Revue de Statistique Appliquée XXI(3), 23–49 (1973)

    MathSciNet  Google Scholar 

  21. Lerman, I.C.: Classification et analyse ordinale des données (1981). Dunod and http://www.brclasssoc.org.uk/books/index.html

  22. Lerman, I.C.: Comparing partitions (mathematical and statistical aspects). In: Bock, H.H. (ed.) Classification and Related Methods of Data Analysis, pp. 121–131. North-Holland, Amsterdam (1988)

    Google Scholar 

  23. Lesot, M.-J., Rifqi, M., Benhada, H.: Similarity measures for binary and numerical data. Int. J. Knowl. Eng. Soft Data Paradig. 1, 63–84 (2009)

    Article  Google Scholar 

  24. Loevinger, J.: A systematic approach to the construction and evaluation of tests of ability. Psychol. Monogr. 61, 1–49 (1947)

    Article  Google Scholar 

  25. Ochiai, A.: Zoogeographic studies on the soleoid fishes found in Japan and its neighbouring regions. Bull. Jpn. Soc. Sci. Fish. 22, 526–530 (1957)

    Article  Google Scholar 

  26. Pearson, K.: On the coefficient of racial likeness. Biometrika 18, 105–117 (1926)

    Google Scholar 

  27. Rand, W.M.: Objective criteria for the evaluation of clustering methods. J. Am. Stat. Assoc. J.A.S.A. 66, 846–850 (1971)

    Article  Google Scholar 

  28. Rogers, D.J., Tanimoto, T.T.: A computer program for classifying plants. Science 132, 1115–1118 (1960)

    Google Scholar 

  29. Russel, P.F., Rao, C.R.: On habitat and association of species of anopheline larvae in south-eastern madras. J. Malar. Inst. India T3, 153–178 (1940)

    Google Scholar 

  30. Schneider, J., Borlund, P.: Matrix comparison, part 1: Motivation and important issues for measuring the resemblance between proximity measures or ordination results. J. Am. Soc. Inf. Sci. Technol. 58(11), 1586–1595 (2007)

    Article  Google Scholar 

  31. Sokal, R.R., Michener, C.: A statistical method for evaluating systematic relationships. Univ. Kans. Sci. Bull. 38, 1409–1438 (1958)

    Google Scholar 

  32. Sokal, R.R., Sneath, P.H.A.: Principles of Numerical Taxonomy. W.H. Freeman, San Francisco (1963)

    Google Scholar 

  33. Sokal, R.R., Sneath, P.H.A.: Numerical Taxonomy. W.H. Freeman, San Francisco (1973)

    MATH  Google Scholar 

  34. Tan, P.-N., Kumar, V., Srivastava, J.: Selecting the right interestingness measure for association patterns. In: 8th ACM SIGKDD (ed.) Proceedings of the 8th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (2002)

    Google Scholar 

  35. Yule, G.U.: An introduction of the theory of statistics. Charles Griffin, London (1911)

    Book  MATH  Google Scholar 

  36. Yule, G.U.: On measuring association between attributes. J. Royal Statist. Soc. 75, 579–642 (1912)

    Google Scholar 

  37. Zighed, D.A., Abdesselam, R., Bounekkar, A.: Equivalence topologique entre mesures de proximité. In: Khenchaf, A., Poncelet, P. (eds.) Revue de l’Information et des Nouvelles Technologies, RNTI 20, EGC’2011, pp. 53–64. Hermann (2011)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Israël César Lerman .

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer-Verlag London

About this chapter

Cite this chapter

Lerman, I.C. (2016). Ordinal and Metrical Analysis of the Resemblance Notion . In: Foundations and Methods in Combinatorial and Statistical Data Analysis and Clustering. Advanced Information and Knowledge Processing. Springer, London. https://doi.org/10.1007/978-1-4471-6793-8_4

Download citation

  • DOI: https://doi.org/10.1007/978-1-4471-6793-8_4

  • Published:

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-6791-4

  • Online ISBN: 978-1-4471-6793-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics