Data granulation through optimization of similarity measure

• Autorzy: Bargiela A. , Pedrycz W. , Hirota K.
• Języki publikacji: EN

Abstrakty

EN

We introduce a logic-driven clustering in which prototypes are formed and evaluated in a sequential manner. The way of revealing a structure in data is realized by maximizing a certain performance index (objective function) that takes into consideration an overall level of matching and a similarity level between the prototypes. It is shown how the relevance of the prototypes translates into their granularity. The clustering method helps identify and quantify anisotropy of the feature space. We also show how each prototype is equipped with its own weight vector describing the anisotropy property and thus implying some ranking of the features in the data space.

Słowa kluczowe

EN

logic-based clustering; information granulation; t-norm; similarity index; granular prototypes; revelance; data mining; direct and inverse matching problem

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2002
• Tom: Vol. 12, no. 4
• Strony: 469--491
• Opis fizyczny: Bibliogr. 26 poz., rys., tab.

Twórcy

autor

Bargiela A.

• Department of Computing and Mathematics, The Nottingham Trent University, Nottingham NG1 4BU United Kingdom

autor

Pedrycz W.

• Department of Electrical & Computer Engineering, University of Alberta, Edmonton, Canada
• Systems Research Institute, Polish Academy of Sciences 01-447 Warsaw, Poland

autor

Hirota K.

• Department of Computational Intelligence and Systems Science, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology 4259 Nagatsuta, Midori-ku, Yokohama-city 226-8502, Japan

Bibliografia

• [1] M.R. Anderberg: Cluster Analysis for Applications. Academic Press, New York, 1973.
• [2] A. Bargiela: Interval and ellipsoidal uncertainty models. In: W. Pedrycz (Ed.) Granular Computing, Physica Verlag, Heidelberg, (2001), 23-57.
• [3] J.C. Bezdek: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, New York, 1981.
• [4] B. Bouchon-Meunier, M. Rifqi and S. Bothorel: Towards general measures of comparison of objects. Fuzzy Sets and Systems, 84(2), (1996), 143-153.
• [5] A. Di Nola, S. Sessa, W. Pedrycz and E. Sanchez: Fuzzy Relational Equations and Their Applications in Knowledge Engineering. Kluwer Academic Press, Dordrecht, 1989.
• [6] M. Delgado, F. Gomez-Skarmeta and F. Martin: A fuzzy clustering-based prototyping for fuzzy rule-based modeling. IEEE Trans. on Fuzzy Systems, 5(2), (1997), 223-233.
• [7] M.Delgado, A.F. Gomez-Skarmets and F. Martin: A methodology to model fuzzy systems using fuzzy clustering in a rapid-prototyping approach. Fuzzy Sets and Systems, 97(3), (1998), 287-302.
• [8] R.O. Duda, P.E. Hart and D.G. Stork: Pattern Classification. 2nd edition, J. Wiley, New York, 2001.
• [9] B. Gabrys and A. Bargiela: General fuzzy Min-Max neural network for clustering and classification. IEEE Trans. on Neural Networks, 11(3), (2000), 769-783.
• [10] F. Hoppner et al.: Fuzzy Cluster Analysis. J. Wiley, Chichester, 1999.
• [11] H. Ishibuchi, K. Nozaki, N. Yamamoto and H. Tanaka: Selecting fuzzy if-then rules for classification problems using genetic algorithms. IEEE Trans. On Fuzzy Systems, 3(3), (1995), 260-270.
• [12] A. Kandel: Fuzzy Mathematical Techniques with Applications. Addison-Wesley, Reading, 1986.
• [13] W. Pedrycz: Direct and inverse problem in comparison of fuzzy data. Fuzzy Sets and Systems, 34, (1990), 223-236.
• [14] W. Pedrycz: Neurocomputations in relational systems. IEEE Trans. on Pattern Analysis and Machine Intelligence, 13 (1991), 289-296.
• [15] W. Pedrycz and A. Rocha: Knowledge-based neural networks. IEEE Trans. On Fuzzy Systems, 1 (1993), 254-266.
• [16] W. Pedrycz: Computational Intelligence: An Introduction. CRC Press, Boca Raton, 1997.
• [17] W. Pedrycz: Conditional fuzzy clustering in the design of radial basis function neural networks. IEEE Trans. on Neural Networks, 9(4), (1998), 601-612.
• [18] W. Pedrycz and A.V. Vasilakos: Linguistic models and linguistic modeling. IEEE Trans. on Systems Man and Cybernetics, 29(6), (1999), 745-757.
• [19] W. Pedrycz and A. Bargiela: Granular clustering: a granular signature of data. IEEE Trans. on Systems, Man, and Cybernetics -B, (2002), to appear.
• [20] P.K. Simpson: Fuzzy Min-Max neural networks - Part1: Classification. IEEE Trans. on Neural Networks, 3(5), (1992), 776-786.
• [21] P.K. Simpson: Fuzzy Min-Max neural networks - Part2: Clustering. IEEE Trans. on Neural Networks, 4(1), (1993), 32-45.
• [22] T. Sudkamp: Similarity, interpolation, and fuzzy rule construction. Fuzzy Sets and Systems, 58(1), (1993), 73-86.
• [23] T.A. Sudkamp and R.J. Hammell II: Granularity and specificity in fuzzy function approximation. Proc. NAFIPS-98, (1998), 105-109.
• [24] L.A Zadeh: Fuzzy sets and information granularity. In: M.M. Gupta, R.K. Ragade, R.R. Yager, (Eds), Advances in Fuzzy Set Theory and Applications, North Holland, Amsterdam, (1979), 3-18.
• [25] L.A. Zadeh: Fuzzy logic = Computing with words. IEEE Trans. on Fuzzy Systems, 4(2), (1996), 103-111.
• [26] L.A. Zadeh: Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets and Systems, 90, (1997), 111-117.