Abstract
This paper considers the task of constructing fuzzy prototypes for numerical data in order to characterize the data subgroups obtained after a clustering step. The proposed solution is motivated by the will of describing prototypes with a richer representation than point-based methods, and also to provide a characterization of the groups that catches not only the common features of the data pertaining to a group, but also their specificity. It transposes a method that has been designed for fuzzy data to numerical data, based on a prior computation of typicality degrees that are defined according to concepts used in cognitive science and psychology. The paper discusses the construction of prototypes and how their desirable semantics and properties can guide the selection of the various operators involved in the construction process.
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References
N. Aladenise and B. Bouchon-Meunier. Acquisition de connaissances imparfaites: mise en évidence d’une fonction d’appartenance. Revue Internationale de systémique, 11(1):109–127, 1997.
M. Detyniecki. Mathematical aggregation operators and their application to video querying. PhD thesis, Université de Paris VI, 2000.
V. Eude, B. Bouchon-Meunier, and E. Collain. Choix d’opérateurs d’agrégation pour l’évaluation de structures hierarchisees. In Proc. of IPMU’98, pages 778–785, Paris, France, 1998.
R.A. Fisher. The use of multiple measurements in taxonomic problems. Annals of Eugenics, 7:170–188, 1936.
M. Friedman, M. Ming, and A. Kandel. On the theory of typicality. Int. Journal of Uncertainty, Fuzzyness and Knowledge-Based Systems, 3(2):127–142, 1995.
A. Gyenesei. Fuzzy partitioning of quantitative attribute domains by a cluster goodness index. Technical Report 368, Turku Centre for Computer Science, 2000.
T.P. Hong and C.Y. Lee. Induction of fuzzy rules and membership functions from training examples. Fuzzy Sets and Systems, 84(1):33–47, 1996.
F. Höppner, F. Klawonn, R. Kruse, and T. Runkler. Fuzzy Cluster Analysis, Methods for classification, data analysis and image recognition. Wiley, 2000.
A. Jain, M. Murty, and P. Flynn. Data clustering: a review. ACM Computing survey, 31(3):264–323, 1999.
A. Kelman and R. Yager. On the application of a class of mica operators. Int. Journal of Uncertainty, Fuzzyness and Knowledge-Based Systems, 7:113–126, 1995.
M.J. Lesot and B. Bouchon-Meunier. Descriptive concept extraction with exceptions by hybrid clustering. In FuzzIEEE04, Budapest, Hungary, 2004.
C. Marsala and B. Bouchon-Meunier. Fuzzy partitioning using mathematical morphology in a learning scheme. In Proc. of the 5th IEEE Int. Conf. on Fuzzy Systems, volume 2, New Orleans, USA, 1996.
S. Medasani, J. Kim, and R. Krishnapuram. An overview of membership function generation techniques for pattern recognition. Int. Journal of Approximate Reasoning, 19(3–4):391–417, 1998.
N. Pal, K. Pal, and J. Bezdek. A mixed c-means clustering model. In FuzzIEEE97, pages 11–21, 1997.
M. Rifqi. Constructing prototypes from large databases. In Proc. of IPMU’96, Granada, Spain, 1996.
M. Rifqi. Mesures de comparaison, typicalité et classification d’objets flous: théorie et pratique. PhD thesis, Université de Paris VI, 1996.
M. Rifqi, V. Berger, and B. Bouchon-Meunier. Discrimination power of measures of comparison. Fuzzy sets and systems, 110:189–196, 2000.
E. Rosch. Principles of categorization. In E. Rosch and B. Lloyd, editors, Cognition and categorization, pages 27–48. Lawrence Erlbaum associates, 1978.
W. Silvert. Symmetric summation: a class of operations on fuzzy sets. IEEE Transactions on Systems, Man and Cybernetics, 9:659–667, 1979.
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Lesot, MJ., Mouillet, L., Bouchon-Meunier, B. (2005). Fuzzy Prototypes Based on Typicality Degrees. In: Reusch, B. (eds) Computational Intelligence, Theory and Applications. Advances in Soft Computing, vol 33. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-31182-3_11
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DOI: https://doi.org/10.1007/3-540-31182-3_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22807-3
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