Improving the Generalization Ability of Neuro-Fuzzy Systems by e-Insensitive Learning

• Autorzy: Łęski J.
• Języki publikacji: EN

Abstrakty

EN

A new learning method tolerant of imprecision is introduced and used in neuro-fuzzy modelling. The proposed method makes it possible to dispose of an intrinsic inconsistency of neuro-fuzzy modelling, where zero-tolerance learning is used to obtain a fuzzy model tolerant of imprecision. This new method can be called e-insensitive learning, where, in order to fit the fuzzy model to real data, the e-insensitive loss function is used. e-insensitive learning leads to a model with minimal Vapnik-Chervonenkis dimension, which results in an improved generalization ability of this system. Another advantage of the proposed method is its robustness against outliers. This paper introduces two approaches to solving e-insensitive learning problem. The first approach leads to a quadratic programming problem with bound constraints and one linear equality constraint. The second approach leads to a problem of solving a system of linear inequalities. Two computationally efficient numerical methods for e-insensitive learning are proposed. Finally, examples are given to demonstrate the validity of the introduced methods.

Słowa kluczowe

EN

fuzzy systems; neural networks; tolerant learning; generalization control; robust methods

PL

system rozmyty; sieć neuronowa; metoda odporna

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2002
• Tom: Vol. 12, no 3
• Strony: 437--447
• Opis fizyczny: Bibliogr. 29 poz., rys., tab., wykr.

Twórcy

autor

Łęski J.

• Institute of Electronics Silesian University of Technology Akademicka 16, 44-100 Gliwice, Poland,

Bibliografia

• [1] Bezdek J.C. (1982): Pattern Recognition with Fuzzy Objective Function Algorithms. - New York: Plenum Press.
• [2] Box G.E.P. and Jenkins G.M. (1976): Time Series Analysis. Forecasting and Control. - San Francisco: Holden-Day.
• [3] Cauwenberghs G. and Poggio T. (2001): Incremental and decremental support vector machine learning. - Proc. IEEE Neural Information Processing Systems Conference, Cambridge MA: MIT Press, Vol. 13, pp. 175-181.
• [4] Chen J.-Q., Xi Y.-G. and Zhang Z.-J. (1998): A clustering algorithm for fuzzy model identification. - Fuzzy Sets Syst., Vol. 98, No. 3, pp. 319-329.
• [5] Czogała E. and Łęski J. (2001): Fuzzy and Neuro-Fuzzy Intelligent Systems. - Heidelberg: Physica-Verlag, Springer-Verlag Comp.
• [6] Gantmacher F.R. (1959): The Theory of Matrices. - New York: Chelsea Publ.
• [7] Haykin S. (1999): Neural Networks. A Comprehensive Foundation. - Upper Saddle River: Prentice-Hall.
• [8] Ho Y.-C. and Kashyap R.L. (1965): An algorithm for linear inequalities and its applications. - IEEE Trans. Elec. Comp., Vol. 14, No. 5, pp. 683-688.
• [9] Ho Y.-C. and Kashyap R.L. (1966): A class of iterative procedures for linear inequalities. - SIAM J. Contr., Vol. 4, No. 2, pp. 112-115.
• [10] Huber P.J. (1981): Robust Statistics. - New York: Wiley.
• [11] Jang J.-S.R., Sun C.-T. and Mizutani E. (1997): Neuro-Fuzzy and Soft Computing. A Computational Approach to Learning and Machine Intelligence. - Upper Saddle River: Prentice-Hall.
• [12] Joachims T. (1999): Making large-scale support vector machine learning practical, In: Advances in Kernel Methods - Support Vector Learning (B. Schölkopf, J.C. Burges and A.J. Smola, Eds.). - New York: MIT Press.
• [13] Łęski J. (2001): An ε-insensitive approach to fuzzy clustering. - Int. J. Appl. Math. Comp. Sci., Vol. 11, No. 4, pp. 993-1007.
• [14] Osuna E., Freund R. and Girosi F. (1997): An improved training algorithm for support vector machines. - Proc. IEEE Workshop Neural Networks for Signal Processing, Breckenridge, Colorado, pp. 276-285.
• [15] Pedrycz W. (1984): An identification algorithm in fuzzy relational systems. - Fuzzy Sets Syst., Vol. 13, No. 1, pp. 153-167.
• [16] Platt J. (1999): Sequential minimal optimization: A fast algorithm for training support vector machines, In: Advances in Kernel Methods - Support Vector Learning (B. Schölkopf, J.C. Burges and A.J. Smola, Eds.). - New York: MIT Press.
• [17] Rutkowska D. (2001): Neuro-Fuzzy Architectures and Hybrid Learning. - Heidelberg: Physica-Verlag, Springer-Verlag Comp.
• [18] Rutkowska D. and Hayashi Y. (1999): Neuro-fuzzy systems approaches. - Int. J. Adv. Comp. Intell., Vol. 3, No. 3, pp. 177-185.
• [19] Rutkowska D. and Nowicki R. (2000): Implication-based neuro-fuzzy architectures. - Int. J. Appl. Math. Comp. Sci., Vol. 10, No. 4, pp. 675-701.
• [20] Setnes M. (2000): Supervised fuzzy clustering for rule extraction. - IEEE Trans. Fuzzy Syst., Vol. 8, No. 4, pp. 416-424.
• [21] Sugeno M. and Kang G.T. (1988): Structure identification of fuzzy model. - Fuzzy Sets Syst., Vol. 28, No. 1, pp. 15-33.
• [22] Takagi H. and Sugeno M. (1985): Fuzzy identification of systems and its application to modeling and control. - IEEE Trans. Syst. Man Cybern., Vol. 15, No. 1, pp. 116-132.
• [23] Vapnik V. (1998): Statistical Learning Theory. - New York: Wiley.
• [24] Vapnik V. (1999): An overview of statistical learning theory. - IEEE Trans. Neural Netw., Vol. 10, No. 5, pp. 988-999.
• [25] Wang L.-X. (1998): A Course in Fuzzy Systems and Control. - New York: Prentice-Hall.
• [26] Weigend A.S., Huberman B.A. and Rumelhart D.E. (1990): Predicting the future: A connectionist approach. - Int. J. Neural Syst., Vol. 1, No. 2, pp. 193-209.
• [27] Yen J., Wang L. and Gillespie C.W. (1998): Improving the interpretability of TSK fuzzy models by combining global learning and local learning. - IEEE Trans. Fuzzy Syst., Vol. 6, No. 4, pp. 530-537.
• [28] Zadeh L.A. (1964): Fuzzy sets. - Inf. Contr., Vol. 8, No. 4, pp. 338-353.
• [29] Zadeh L.A. (1973): Outline of a new approach to the analysis of complex systems and decision processes. - IEEE Trans. Syst. Man Cybern., Vol. 3, No. 1, pp. 28-44.