Summary
The development of Symbolic Data Analysis comes from the need both to process more general data than classical techniques of Data Analysis do and to develop methods that yield easily interpretable results. In this paper we show how we may enlarge the domain of the data at the input and obtain an “explained” output of a clustering method by adopting notions of Symbolic Data Analysis. We start by recalling the definitions and properties of symbolic objects (Diday (1987b), Diday and Brito (1989)). We shall consider objects that take one and only one value per variable, objects that may present more than one value per variable, and objects such that the definition of a variable depends on the value taken by another one. We then compare notions defined on symbolic objects to similar notions present in the literature (Wille (1982), Ganter (1984), Duquenne (1986), Guénoche (1989)) and show how the former extend the latter. We then recall pyramidal clustering and the main properties of pyramids (Diday (1986)). Pyramids are halfway between hierarchies and lattices: they generalize the former by allowing the presence of non-disjoint clusters, however a pyramid does not present crossing in its graphical representation like lattices do. This intermediate situation led us to adopt pyramids to structure symbolic objects: they allow the definition of a structure on the objects representing inheritance without losing “too much” information, and they have a readable graphical representation. We present an algorithm of “symbolic pyramidal clustering”. This algorithm may apply to a data set of some kind of symbolic objects considering even the case of dependence between variables. As output it yields a pyramid whose clusters are represented by symbolic objects meeting a given property. The inheritance structure between the clusters will then allow for the generation of rules.
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References
BERTRAND, P. (1986), Etude de la Représentation Pyramidale, Thèse de 3ème cycle, Univ. Paris-IX Dauphine.
COHEN, P.R., and FEIGENBAUM, E.A. (1982), The handbook of Artificial intelligence, Vol. Ill, William Kauffman.
DIDAY, E. (1976), Selection Typologique de Paramètres, Rapport de Recherche 188, INRIA, Le Chesnay.
DIDAY, E. (1984), Une Représentation Visuelle des Classes Empiétantes: Les Pyramides, Rapport de Recherche 291, INRIA, Rocquencourt, Le Chesnay.
DIDAY, E. (1986), Orders and overlapping clusters by pyramids, in: Multidimensional Data Analysis Proc., eds. J. De Leeuw et al., DSWO Press, Leiden.
DIDAY, E. (1987a), The symbolic approach in clustering and related methods of data analysis: the basic choices, in: Classification and Related Methods of Data Analysis, ed. H.H. Bock, North-Holland, Amsterdam, 673–684.
DIDAY, E. (1987b), Introduction à l’approche symbolique en analyse des données, in: Actes des journées “Symboliques—Numériques” pour l’apprentissage de connaissances à partir d’observations, eds. E. Diday and Y. Kodratoff, CEREMADE–Univ. Paris IX-Dauphine, 21–56.
DIDAY, E. (1989), Introduction à l’approche symbolique en Analyse des Données, RA/RO, 23, 2.
DIDAY, E., and BRITO, P. (1989), Introduction to Symbolic Data Analysis, in: Conceptual and Numerical Analysis of Data, ed. O. Opitz, Springer, Berlin Heidelberg New York, 45–84.
DIDAY, E., GOVAERT, G., LECHEVALLIER, Y., and SIDI, J. (1980), Clustering in pattern recognition, in: Proc. of 5th Conf. Pattern Recognition Miami Beach FL., more complete in: Digital Image Processing, Proc. of the NATO Advanced Study Institute, ed. J.C. Simon.
DIDAY, E., and ROY, L. (1988), Generating rules by symbolic data analysis and application to soil feature recognition, in: Actes des Sèmes Journées Internationales “Les systèmes experts et leurs applications”, Avignon, 533–549.
DIDAY, E., and SIMON, J.C. (1976), Clustering Analysis, Communication and Cybernetics 10, Digital Pattern Recognition, ed. K.S. Fu, Springer Verlag, 47–94.
DURAND, C. (1988), Une aproximation de Robinson inferieur maximale, Rapport Interne, Univ. de Provence.
GANASCIA, J.G. (1987), Charade: apprentissage de bases de connaissances, in: Actes des journées “Symboliques—Numériques” pour l’apprentissage de (1 37 44 9980) connaissances à partir d’observations, eds. E. Diday and Y. Kodratoff, CEREMADE–Univ. Paris IX-Dauphine, 57–73.
GANASCIA, J.G. (1987), Apprentissage de connaissance par les cubes de Hilbert, Thèse d’Etat, Université d’Orsay.
GANTER, B. (1984), Two basic algorithms in concept analysis, FB4-Preprint 831, TH Darmstadt.
GASCUEL, O. (1987), Plage, un outil pour construire des systèmes d’apprentissage, AFCET-RFIA 6, Antibes, 863–880.
GUENOCHE, A. (1987), Propriétés caractéristiques d’une classe relativement à un contexte, in: Actes des journées “Symboliques—Numériques” pour l’apprentissage de connaissances à partir d’observations, eds. E. Diday and Y. Kodratoff, CEREMADE–Univ. Paris IX-Dauphine, 181–194.
GUÉNOCHE, A. (1989), Construction du treillis de Galois d’une relation binaire, à paraître dans: Mathématiques et Sciences Humaines, Paris.
GUIGUES, J.L., and DUQUENNE, V. (1986), Familles minimales d’implications informatives resultants d’un tableau binaire, Mathématiques et Sciences Humaines, 24, 95, 5–18.
HO TU, B., DIDAY, E., and SUMMA, M. (1987), Generating rules for expert system from observations, in: Les systèmes experts et leurs applications, 7ème journées internationales “Les systèmes experts et leurs applications”, EC2, Nanterre, France.
MATHEUS, C. (1987), Conceptual purpose: implications for representation and learning in machines and humans, Report No. UIUCDCS-R-87–1370, Univ. of Illinois, Urbana.
MICHALSKI, R. (1980), Knowledge aquisition through conceptual clustering: a theoretical framework and an algorithm for partitioning data into conjunctive concepts, Int. Journal of Policy Analysis and Information Systems, 4, 3.
MICHALSKI, R. (1983), Automated Construction of classifications: conceptual clustering versus numerical taxonomy, IEEE Trans. pattern analysis and Machine intelligence, PAMI-5, 4.
MICHALSKI, R., STEPP, R.E., and DIDAY, E. (1981), Recent advances in data analysis: clustering objects into classes characterized by conjunctive concepts, Progress in Pattern Recognition vol. 1, eds. L. Kanal and A. Rosenfeld.
MITCHELL, T.M., KELLER, R.M., and KEDAR-CABELLI, S.T. (1986), Explanation-based generalization—a unifying view, Machine Learning Journal, 1, 1.
QUINQUETON, J., and SALLANTIN, J. (1986), CALM: contestation for argumentative learning machine, in: Machine Learning, a Guide to current research, eds. R.S. Michalski, J. Carbonnel and T.M. Mitchell, Kluwer and sons.
RALAMBONDRAINY, H. (1987), GENREG: un générateur de règles à partir de données, in: Actes des journées “Symboliques—Numériques” pour l’apprentissage de connaissances à partir d’observations, eds. E. Diday and Y. Kodratoff, CEREMADE–Univ. Paris IX-Dauphine, 75–82.
UTGOFF, P.E. (1986), Shift of bias for inductive concept learning, in: Machine Learning, Vol. II, eds. R.S. Michalski, J. Carbonnel and T.M. Mitchell, Morgan Kaufmann Publishers, 107–148.
WILLE, R. (1982), Restructuring lattice theory: an approach based on hierarchies of concepts, in: Proceedings of the symposium on ordered sets, ed. I. Rival, Reidel, Dordrecht Boston, 445–470.
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Brito, P., Diday, E. (1990). Pyramidal Representation of Symbolic Objects. In: Schader, M., Gaul, W. (eds) Knowledge, Data and Computer-Assisted Decisions. NATO ASI Series, vol 61. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-84218-4_1
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DOI: https://doi.org/10.1007/978-3-642-84218-4_1
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