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Foundations and Methods in Combinatorial and Statistical Data Analysis and Clustering pp 61–99Cite as

Two Methods of Non-hierarchical Clustering

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

Abstract

As mentioned in the Preface, the development provided in this book is dominated by the potential of applying ascendant agglomerative hierarchical clustering to all types of data. Nonetheless, the specific methodology devoted to non-hierarchical clustering is also very important. In these conditions, we shall describe in this chapter two mutually very different methods of non-hierarchical clustering. The first one, called “Central Partition” method, is due to S. Régnier (I.C.C. Bull. 4:175–191, 1965 [35], Revue Mathématiques et Sciences Humaines 22:13–29, 1983 [36], Revue Mathématiques et Sciences Humaines 22:31–44, 1983 [37]). The second method called “méthode des Nuées Dynamiques” or “Dynamic cluster method” is due to E. Diday and collaborators (Revue de Statistique Appliquée XIX(2):19–33, 1971 [10], J. Comput. Inf. Sci. 2(1):61–88, 1973 [11], Recherche Opérationnelle 10(6):75–1060, 1976 [16], R.A.I.R.O. Inf. Comput. Sci. 11(4):329–349, 1977 [13]). This approach corresponds to a vast generalization of the K-means method, initiated by Forgy (Biometrics, Biometric Society Meeting [17]) and Jancey (Aust. J. Bot. 14:127–130, 1966 [19]).

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References

  1. Anderberg, M.R.: Cluster Analysis for Applications. Academic Press, New York (1973)

    MATH  Google Scholar 

  2. Bock, H.-H.: On some significance tests in cluster analysis. J. Classif. 2, 77–108 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bock, H.-H.: Clustering methods: a history of \(k\)-means algorithms. In: Cucumel, G., Brito, P., Bertrand, P., de Carvalho, F. (eds.) Selected Contributions in Data Analysis and Classification, pp. 161–172. Springer, Berlin (2007)

    Chapter  Google Scholar 

  4. Celeux, G.: Étude exhaustive de l’algorithme de réallocation-recentrage dans un cas simple. R.A.I.R.O. Recherche opérationnelle/Operations Research 20(3), 229–243 (1986)

    MathSciNet  MATH  Google Scholar 

  5. Celeux, G.: Reconnaissance de mélanges de densités de probabilité et applications à la validation des résultats en classification, thèse de doctorat ès sciences. Ph.D. thesis, Université de Paris IX Dauphine, September 1987

    Google Scholar 

  6. Celeux, G., Govaert, G.: A classification EM algorithm for clustering and two stochastic versions. Comput. Stat. Data Anal. 14, 315–332 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  7. Charon, I., Denoeud, L., Guénoche, A., Hudry, O.: Maximum transfer distance between partitions. J. Classif. 23, 103–121 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  8. Charon, I., Denoeud, L., Hudry, O.: Maximum de la distance de transfert à une partition donnée. Revue Mathématiques et Sciences 179, 45–83 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  9. Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood estimation from incomplete data via the EM algorithm (with discussion). JRSS B. 39, 1–38 (1977)

    Google Scholar 

  10. Diday, E.: Une nouvelle méthode de classification automatique et reconnaissance des formes: la méthode des nuées dynamiques. Revue de Statistique Appliquée XIX(2), 19–33 (1971)

    Google Scholar 

  11. Diday, E.: The dynamic clusters method in nonhierarchical clustering. J. Comput. Inf. Sci. 2(1), 61–88 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  12. Diday, E. and Collaborators: Optimisation en Classification Automatique, vol. I, II. Institut National de Recherche en Informatique et en Automatique (INRIA), Le Chesnay (1979)

    Google Scholar 

  13. Diday, E., Govaert, G.: Classification automatique avec distances adaptatives. R.A.I.R.O. Inf. Comput. Sci. 11(4), 329–349 (1977)

    MathSciNet  MATH  Google Scholar 

  14. Diday, E., Schroeder, A.: The dynamic clusters method in pattern recognition. In: Rosenfeld, J.L. (ed.) Information Processing 74, pp. 691–697. North Holland, Amsterdam (1974)

    Google Scholar 

  15. Diday, E., Schroeder, A.: A new approach in mixed distribution detection. Research Report 52, INRIA, January 1974

    Google Scholar 

  16. Diday, E., Schroeder, A.: A new approach in mixed distribution detection. R.A.I.R.O. Recherche Opérationnelle 10(6), 75–1060 (1976)

    MathSciNet  MATH  Google Scholar 

  17. Forgy, E.W.: Cluster analysis of multivariate data: efficiency versus interpretability of classifications. In: Biometrics, Biometric Society Meeting, vol. 21, p. 768 (1965)

    Google Scholar 

  18. Jain, A.K.: Data clustering: 50 years beyond k-means. Pattern Recognit. Lett. 31, 651–666 (2010)

    Article  Google Scholar 

  19. Jancey, R.C.: Multidimensional group analysis. Aust. J. Bot. 14, 127–130 (1966)

    Article  Google Scholar 

  20. Lancaster, H.O.: The Chi-Squared Distribution. Wiley, New York (1969)

    MATH  Google Scholar 

  21. Lebart, L., Fenelon, J.-P.: Statistique et Informatique appliquées. Dunod, Paris (1973)

    Google Scholar 

  22. Leredde. H.: La méthode des pôles d’attraction; la méthode des pôles d’aggrégation: deux nouvelles familles d’algorithmes en classification automatique et sériation. Ph.D. thesis, Université de Paris, 6 Oct 1979

    Google Scholar 

  23. Lerman, I.C.: Les bases de la classification automatique. Gauthier-Villars, Paris (1970)

    MATH  Google Scholar 

  24. Lerman, I.C.: Analyse du phénomène de la sériation. Revue Mathématiques et Sciences Humaines 38 (1972)

    Google Scholar 

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

  26. Lerman, I.C.: Convergence optimale de l’algorithme de “réallocation-recentrage” dans le cas continu le plus simple. R.A.I.R.O. Recherche opérationnelle/Operations Research 20(1), 19–50 (1986)

    MathSciNet  MATH  Google Scholar 

  27. Lerman, I.C., Leredde, H.: La méthode des pôles d’attraction. In: IRIA (ed.): Analyse des Données et Informatique. IRIA (1977)

    Google Scholar 

  28. Loève, M.: Probability Theory. D. Van Nostrand Company, New Jersey (1963)

    MATH  Google Scholar 

  29. MacQueen, J.B.: Some methods for classification and analysis of multivariate observations. In: Proceedings of the 5th Berkeley Symposium on Mathematical Statistics and Probability, pp. 281–297. University of California Press, Berkeley (1967)

    Google Scholar 

  30. Marcotorchino, F.: Essai de Typologie Structurelle des Indices de Similarité Vectorielles par Unification Relationnelle. In: Benani, Y., Viennet, E. (eds.) RNTI A3, Revue des Nouvelles Technologies de l’Information, pp. 203–319. Cepaduès, Toulouse (2009)

    Google Scholar 

  31. Marcotorchino, F., Michaud, P.: Agrégation de similarités en classification automatique. Revue de Statistique Appliquée 2, 21–44 (1982)

    MathSciNet  MATH  Google Scholar 

  32. McLachlan, G., Krishnan, T.: The EM Algorithm and Extensions. Wiley, New York (1997)

    MATH  Google Scholar 

  33. Neveu, J.: Bases Mathématiques du Calcul des Probabilités. Masson, Paris (1964)

    MATH  Google Scholar 

  34. Pollard, D.: Strong consistency of \(k\)-means algorithm. Ann. Stat. 9(1), 135–140 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  35. Régnier, S.: Sur quelques aspects mathématiques des problèmes de la classification automatique. I.C.C. Bull. 4, 175–191 (1965)

    Google Scholar 

  36. Régnier, S.: Sur quelques aspects mathématiques des problèmes de la classification automatique. Revue Mathématiques et Sciences Humaines 22, 13–29 (1983)

    Google Scholar 

  37. Régnier, S.: Sur quelques aspects mathématiques des problèmes de la classification automatique. Revue Mathématiques et Sciences Humaines 22, 31–44 (1983)

    Google Scholar 

  38. Sclove, S.L.: Population mixture models and clustering algorithms. In: Commun. Stat. Theory Methods A6, 417–434 (1977)

    Google Scholar 

  39. Xu, R., Wunsh, D.: Survey of clustering algorithms. IEEE Trans. Neural Netw. 16(3), 645–678 (2005)

    Article  Google Scholar 

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  1. Department of Data Knowledge and Management, University of Rennes 1, IRISA, Rennes, Ille-et-Vilaine, France

    Israël César Lerman

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Lerman, I.C. (2016). Two Methods of Non-hierarchical Clustering. 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_2

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  • DOI: https://doi.org/10.1007/978-1-4471-6793-8_2

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