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Multivariate data approximation with preprocessing of data

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
An adaptive information system is constructed in order to approximate a set of multidimensional data. To get better approximation properties a pre-processing stage of data is proposed in which the set of points, forming the multidimensional data base and called a training set TRE, undergoes a clustering analysis. In the analysis two independent clustering algorithms are used; on each cluster a feed-forward neural network is trained and a membership function of a fuzzy set is constructed. The constructed system contains a module of two-conditional fuzzy rules consequent parts of which are of the functional type. Each rule is designed on a pair of clusters.
Rocznik
Strony
651--658
Opis fizyczny
Bibliogr. 30 poz., rys.
Twórcy
autor
autor
autor
  • Polish-Japanese Institute of Information Technology, Koszykowa 86, 02-008 Warszawa
Bibliografia
  • [1] M.R. Anderberg. Cluster Analysis for Applications. Probability and Mathematical Statistics, Academic Press, New York, 1973.
  • [2] J.J. Buckley, Y. Hayashi. Numerical relationships between neural networks, continuous functions, and fuzzy systems. Fuzzy Sets and Systems, 60: 1-8, 1993.
  • [3] G. Cybenko. Approximation by superpositions of sigmoidal function. Mathematics of Control, Signals, and Systems, 2: 303-314, 1989.
  • [4] K. Funahashi. On the approximate realization of continuous mapping by neural networks. Neural Networks, 2: 183-192, 1989.
  • [5] D.J. Hand. Discrimination and Classification. Wiley, Chichester, 1981.
  • [6] B. Goląbek, W. Kosiński, M. Weigl. Adaptation of learning rate via adaptation of weight vector in modified M-Delta networks. In: P.S. Szczepaniak, ed., Computational Intelligence and Applications, (Studies in Fuzziness and Soft Computing, Vol. 23), Physica-Verlag, c/o Springer-Verlag, 156-163, 1999.
  • [7] K. Hornik. Approximation capabilities of multilayer feedforward networks. Neural Networks, 4: 251-257, 1991.
  • [8] J. Jang, T.-C. Sun. Functional equivalence between radial basis function networks and fuzzy inference system. IEEE Transaction on Neural Networks, 4(1): 156-159, 1993.
  • [9] P. Kies, W. Kosinski, M. Weigl. Seed growing approach in clustering analysis. In Intelligent Information Systems. Proceedings of the Vl-th International Workshop on Intelligent Information Systems, Zakopane, 9-13 June, 1997, pp 7-15. Instytut Podstaw Informatyki PAN, Warszawa, 1997.
  • [10] R. Koleśnik, L. Koleśnik, W. Kosiński. Genetic operators for clustering analysis, In Intelligent Information Systems VIII, Proc. of the Workshop, Ustrori, Poland, 14-18 June, 1999, pp. 203-208. Instytut Podstaw Informatyki PAN, Warszawa, 1999.
  • [11] W. Kosiński. On fuzzy number calculus. Int. J. Appl. Math. Comput. Sci., 16(1): 51-57, 2006.
  • [12] W. Kosiński, B. Golenia. Double covering of data for multivariate approximation. Under preparation
  • [13] W. Kosinski, D. Kowalczyk, Adaptive decision support system using Web-users profile data, In: K.M. Węgrzyn-Wolska, P.S. Szczepaniak, eds., Advances in Intelligent Web Mastering, Proc. of 5th AWIV'2007, Fontainebleau, France, June 2007, ASC 43, pp. 180-185. Springer-Verlag, Berlin-Heidelberg, 2007.
  • [14] W. Kosiński, P. Prokopowicz. On Banach space of ordered fuzzy sets. In: O. Hryniewicz, J. Kacprzyk, D. Kuchta, eds., Issues in Soft Computing, Decisions and Operations Research, pp. 209-217. Akademicka Oficyna Wydawnicza EXIT, Warszawa, 2005.
  • [15] W. Kosiński, P. Prokopowicz, D. Ślęzak. Ordered fuzzy numbers. Bulletin of the Polish Academy of Sciences, Ser. Sci. Math., 51(3): 327-338, 2003.
  • [16] W. Kosiński, M. Weigl, P. Kies. Fuzzy domain covering of an inference system. In: Proceedings of the Third National Conference on Neural Networks and Their Applications, Kule n. Częstochowa, October 14-18, 1997, pp. 310-321. PNNS, Częstochowa, 1997.
  • [17] W. Kosiński, M. Weigl. General mapping approximation problems solving by neural networks and fuzzy inference systems. Systems Analysis Modelling Simulation, 30(1): 11-28, 1998.
  • [18] W. Kosiński, M. Weigl. Adaptive information systems for data approximation problems. In R. Hampel, M. Wagenknecht, N. Chaker, eds., Fuzzy Control Theory and Practice, pp. 109-120. Physica-Verlag, Springer-Verlag, Heidelberg-New York, 2000.
  • [19] W. Kosiński, M. Weigl, Z. Michalewicz. Evolutionary domain covering of an inference system for function approximation. In: V.W. Port, N. Saravanam, D. Waagen, A.E. Eiben, eds., Evolutionary Programming VII. Proceedings of the 7th International Conference, EP'98, San Diego, California, USA, March 25-27, 1998. NCS, vol. 1447, pp. 167-180, New York, 1998.
  • [20] W. Kosiński, M. Weigl, Z. Michalewicz, R. Kolesnik. Genetic algorithms for preprocessing of data for universal approximators. In: Intelligent Information Systems VII. Proceedings of the Workshop, Malbork, Poland, 15-19 June, 1998, pp. 320-331, Instytut Podstaw Informatyki PAN, Warszawa, 1998.
  • [21] D. Kowalczyk. An Adaptive Fuzzy Inference System as a Fuzzy Controller (in Polish: Rozmyty adaptacyjny system wnioskujący jako sterownik rozmyty). Master Thesis, WSP w Bydgoszczy, Wydzial Matematyki, Techniki i Nauk Przyrodniczych, Specjalność: Technika Komputerowa, Bydgoszcz, czerwiec 1999.
  • [22] H. Mhaskar, C. Micchelli. Approximation by superposition of a sigmoidal function and radial basis functions. Advances Applied Mathematics, 13: 350-373, 1992.
  • [23] H. Mhaskar, C. Micchelli. Dimension-independent bounds on the degree of approximation by neural network. IBM Journal of Research and Development, 38(3): 277-284, 1994.
  • [24] P. Prokopowicz. Algorithmization of Operations on Fuzzy Numbers and its Applications (in Polish: Algorytmizacja dzialań na liczbach rozmytych i jej zastosowania). Ph.D. Thesis, IPPT PAN, kwiecien 2005.
  • [25] F. Scarselli, A.Ch. Tsoi. Universal approximation using feedforward neural networks: A survey of some existing methods, and some new results. Neural Networks, 11(1): 15-37, 1998.
  • [26] H. Takagi, M. Sugeno. Fuzzy identification of systems and its applications to modeling and control. IEEE Trans.on Systems, Man and Cybernetics, 15: 116-132, 1985.
  • [27] M. Weigl, W. Kosiński. Fuzzy inference system and modified back-propagation network in approximation problems. Proceedings of the III-rd International Symposium on Intelligent Information Systems, Wigry n. Suwalki, June 1994, pp. 427-442. IPI PAN, Warszawa, 1994.
  • [28] M. Weigl. Neural Networks and Fuzzy Inference Systems in Approximation Problems (in Polish: Sieci neuronowei rozmyte systemy wnioskujące w problemach aproksymacji). Ph.D. Thesis, IPPT PAN, Warszawa, 1995.
  • [29] M. Weigl, W. Kosiński. Fuzzy reasoning in adaptive expert systems for approximation problems. In: Proceedings of the 3-th Zittau Fuzzy-Colloquy, Zittau, September 5-6, 1995. Wissenschaftliche Berichte, Heft 41, 163-174, 1995.
  • [30] M. Weigl, W. Kosinski. Approximation of multivariate functions by generalized adaptive fuzzy inference network. In: Proceedings of the 9-th International Symposium on Methodologies for Intelligent Systems ISMIS'96,Zakopane, June 1996, pp. 120-133. IPI PAN, Warszawa, 1996.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPB1-0031-0012
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