Abstract
Algorithms which are operationnally efficient and which give a good partition of a finite set, produce solutions that are not necessarily optimum. The main aim of this paper is a synthetical study of properties of optimality in spaces formed by partitions of a finite set. We formalize and take for a model of that study a family of particularily efficient techniques of "clusters centers" type. The proposed algorithm operates on groups of points or "kernels"; these kernels adapt and evolve into interesting clusters.
After having developed the notion of "strong" and "weak" patterns, and the computer aspects, we illustrate the different results by an artificial example.
Institut de Recherche d'Informatique et d'Automatique.
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Bibliography
BALL G.H., 1970 — Classification Analysis — Technical Note, Stanford Research Institute. Menlo Park, California 94025 USA
BARBU M., 1968 — Partitions d'un ensemble fini: leur treillis M.S.H. no 22
BENZECRI J.P., 1971 — Algorithmes rapides d'agrégation.Sup.Class. no9 Laboratoire de Statistique Mathématique. Université de Paris-6
BENZECRI J.P., 1970 — Représentation Euclidienne d'un ensemble muni de masses et de distances. Université de Paris-6
BERGE C., 1967 — Théorie des graphes et ses applications — Dunod Ed. Paris.
'BOLSHEV L.N., 1969 — Cluster Analysis — I.S.I.R.S.S.'69
BONNER R.E., 1964 — On some clustering technics — IBM Journal of Research and Development
CORMACK R.M., 1971 — A review of Classification — The Journal of the Royal Statistical Society, Serie A, vol 134, Part 3
DIDAY E, BERGONTM, BARRE J, 1970–71–72 — Differentes notes sur la programmation de la Méthode des nuées dynamiques Note I.R.I.A., Rocquencourt 78.
DIDAY E, 1970 — La méthode des nuées dynamiques et la reconnaissance des formes. Cahiers de l'I.R.I.A., Rocquencourt 78
DIDAY E, 1971 — Une nouvelle méthode en classification automatique et reconnaissance des formes — Revue de Statistique appliquée, vol. XIX, no 2.
FISHER L, VAN NESS J.W. 1971 — Admissible Clustering Procedures. Biometrika, 58, 1, p. 91.
FREEMAN N, 1969 — Experiments in discrimination and classification. Pattern Recognition J.vol.1, no 3.
HALL D.J, HALL G.H, 1965 — Isodata a Novel Method of Data Analysis and Pattern Classification. Technical Report, 5R I Project 5533, Stanford Research Institute, Menlo Park, California U.S.A.
HILL D.R, 1967 — Mechanized Information Storage, retrieval and dissemination. Proceedings of the F.I.D/I.F.I.P. Joint Conference Rome.
JOHNSON S.C, 1967 — Hierarchical clustering schemes. Psychometrica 32, 241–45
LERMAN H, 1970 — Les bases de la classification automatique — Gauthiers-Villars, 1970
PICARD J, 1972 — Utilisation des méthodes d'analyse de données dans l'étude de courbes expérimentales. Thèse de 3è cycle Laboratoire de Statistique Mathématique Université Paris-6
ROMEDER J.M, 1969 — Methodes de discrimination. Thèse de 3è cycle Statistique Mathématique. Faculté des Sciences de Paris-6
ROUX M, 1968 — Un algorithme pour construire une hiérarchie particulière — Thèse de 3è cycle. Laboratoire de Statistique Mathématique, Université de Paris-6.
RUSPINI H.R, 1970 — Numerical Methods for fuzzy clustering. Information Science 2, p.319–350
SANDOR G, LENOIR P, KERBAOL M, 1971 — Une étude en ordinateur des corrélations entre les modifications des protéines sériques en pathologie humaine.C.R. Acad. Sc. Paris, t. 272, p. 331–334
SANDOR G, DIDAY E, LECHEVALLIER y, BARRE J, 1972 — Une étude informatique des corrélations entre les modifications des protéines sériques en pathologie humaine. C.R. Acad. Sc. Paris, t. 274, d.p. 464–467
SEBESTIEN G.S, 1966 — Automatic off-line Multivariate Data Analysis Proc. Fall Joint Computer Conference pp. 685–694
SOKHAL R.R, SNEATH P.H.R, 1963 — Numerical Tasconomy. W.H. Freeman & Co, San Francisco and London.
WATANABE M.S, 1971 — A unified view of clustering algorithms. IFIP Congress 71, Ijubiana, Booklet TA-2
ZADEH L.A, 1965 — Fuzzy sets. Inf. Control 8, pp. 338–353
ZAHN C.I, 1971 — Graph Theoretical methods for detecting and describing Gestalt Clusters. I.E.E.E. trans. on Computers, vol. C-20, no 1, January.
McQUEEN j, 1967 — Some Methods for Classification and Analysis of Multivariate Observations. 5th Berkeley Symposium on Mathematics, Statistics and probability, vol. 1, no 1, pp. 281–297
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Diday, E. (1973). The dynamic clusters method and optimization in non hierarchical-clustering. In: Conti, R., Ruberti, A. (eds) 5th Conference on Optimization Techniques Part I. Optimization Techniques 1973. Lecture Notes in Computer Science, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-06583-0_24
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DOI: https://doi.org/10.1007/3-540-06583-0_24
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