Paper:
Language: English:
Genetically Optimized Multi-Layer Fuzzy Polynomial Neural Networks: Analysis and Design
Sung-Kwun Oh*, Witold Pedrycz**,***, and Ho-Sung Park****
*Department of Electrical Engineering, The University of Suwon, San 2-2, Wau-ri, Bongdam-eup, Hwaseong-si, Gyeonggi-do 445-743, South Korea
**Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB T6G 2G6, Canada
***Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland
****Department of Electrical Electronic and Information Engineering, Wonkwang University, 344-2, Shinyong-Dong, Iksan, Chon-Buk, 570-749, South Korea
Received: November 22, 2004
Accepted: June 20, 2005
Keywords: genetically optimized Fuzzy Polynomial Neural Networks (gFPNN), Fuzzy Polynomial Neuron, Multi-Layer Perceptron, Genetic Algorithms, Group Method of Data Handling, design procedure
Journal ref: Journal of Advanced Computational Intelligence and Intelligent Informatics, Vol.10, No.1 pp. 35-49, 2006
Abstract
In this study, we introduce a new category of neurofuzzy networks – Fuzzy Polynomial Neural Networks and develop a comprehensive design methodology involving mechanisms of genetic optimization, and genetic algorithms, in particular. The augmented genetically optimized FPNN (referred to as gFPNN) is a structurally optimized architecture which comes with a higher level of flexibility in comparison to the one we have encountered in the conventional FPNN. The GA-based design procedure being applied to each layer of FPNN leads to the selection of preferred nodes (or FPNs) available within the FPNN. In the sequel, two general optimization mechanisms are explored. First, the structural optimization is realized via GAs whereas for the ensuing detailed parametric optimization is carried out in the setting of a standard least square method-based learning. The performance of the gFPNN is quantified through experimentation where we use a number of modeling benchmarks – synthetic and experimental data already experimented with in fuzzy or neurofuzzy modeling.
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Reference
[1] V. Cherkassky, D. Gehring, and F. Mulier, “Comparison of adaptive methods for function estimation from samples,” IEEE Trans. Neural Networks, Vol.7, pp. 969-984, July, 1996.
[2] J. A. Dickerson, and B. Kosko, “Fuzzy function approximation with ellipsoidal rules,” IEEE Trans. Syst., Man, Cybernetics, Part B, Vol.26, pp. 542-560, Aug., 1996.
[3] A. G. Ivakhnenko, “Polynomial theory of complex systems,” IEEE Trans. on Systems, Man and Cybernetics, Vol.SMC-1, pp. 364-378, 1971.
[4] A. G. Ivakhnenko, G. A. Ivakhnenko, and J. A. Muller, “Selforganization of Neural Networks with Active Neurons,” Pattern Recognition and Image Analysis, Vol.4, No.2, pp. 185-196, 1994.
[5] S.-K. Oh, W. Pedrycz, and T.-C. Ahn, “Self-organizing neural networks with fuzzy polynomial neurons,” Applied Soft Computing, Vol.2, Issue 1F, pp. 1-10, Aug., 2002.
[6] S.-K. Oh, and W. Pedrycz, “Self-organizing Polynomial Neural Networks Based on PNs or FPNs: Analysis and Design,” Fuzzy Sets and Systems, 2003 (in press).
[7] S.-K. Oh, and W. Pedrycz, “Fuzzy Polynomial Neuron-Based Self-Organizing Neural Networks,” Int. J. of General Systems, Vol.32, No.3, pp. 237-250, May, 2003.
[8] W. Pedrycz, and M. Reformat, “Evolutionary Optimization of Fuzzy Models in Fuzzy Logic: A framework for the New Millennium,” V. Dimitrov, and V. Korotkich (eds.), “Studies in Fuzziness and Soft Computing,” Vol.8, Physica-Verlag, pp. 51-67, September, 1996.
[9] Z. Michalewicz, “Genetic Algorithms + Data Structures = Evolution Programs,” Springer-Verlag, Berlin Heidelberg, 1996.
[10] K. A. D. Jong, “Are Genetic Algorithms Function Optimizers?,” Parallel Problem Solving from Nature 2, R. Manner, and B. Manderick, eds., North-Holland, Amsterdam.
[11] L. X. Wang, and J. M. Mendel, “Generating fuzzy rules from numerical data with applications,” IEEE Trans. Systems, Man, Cybern., Vol.22, No.6, pp. 1414-1427, 1992.
[12] R. S. Crowder III, “Predicting the Mackey-Glass time series with cascade-correlation learning,” In D. Touretzky, G. Hinton, and T. Sejnowski, editors, Proceedings of the 1990 Connectionist Models Summer School, pp. 117-123, Carnegie Mellon University, 1990.
[13] J. S. R. Jang, “ANFIS: Adaptive-Network-Based Fuzzy Inference System,” IEEE Trans. System, Man, and Cybern., Vol.23, No.3, pp. 665-685, 1993.
[14] L. P. Maguire, B. Roche, T. M. McGinnity, and L. J. McDaid, “Predicting a chaotic time series using a fuzzy neural network,” Information Sciences, Vol.112, pp. 125-136, 1998.
[15] C. James Li, and T.-Y. Huang, “Automatic structure and parameter training methods for modeling of mechanical systems by recurrent neural networks,” Applied Mathematical Modeling, Vol.23, pp. 933-944, 1999.
[16] M. C. Mackey, and L. Glass, “Oscillation and chaos in physiological control systems,” Science, Vol.197, pp. 287-289, 1977.
[17] A. S. Lapedes, and R. Farber, “Non-linear Signal Processing Using Neural Networks: Prediction and System Modeling,” Technical Report LA-UR-87-2662, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, 1987.
[18] G. Vachtsevanos, V. Ramani, and T. W. Hwang, “Prediction of Gas Turbine NOx Emissions using Polynomial Neural Network,” Technical Report, Georgia Institute of Technology, Atlanta, 1995.
[19] S.-K. Oh, and T.-C. Ahn, “A thesis of emission pattern model about the atmosphere pollution material of a power plant,” Technical Report, Electrical Engineering & Science Research Institute, Korea, 1997 (in Korean).
[20] S.-K. Oh, W. Pedrycz, and H.-S. Park, “Hybrid Identification in Fuzzy-Neural Networks,” Fuzzy Sets and Systems, Vol.138, Issue 2, pp. 399-426, 2003.
[21] S.-K. Oh, W. Pedrycz, and H.-S. Park, “Rule-based Multi-FNN Identification with the Aid of Evolutionary Fuzzy Granulation,” Journal of Knowledge-Based Systems, Vol.17, No.1, pp. 1-13, 2004.
[22] S. Morihayashi, “The Forecasting and Test of Disaggregate Model,” Text of Infrastructure of Civil Engineering of Japan JSCE, Vol.15, 1984 (in Japanese).
[23] T. Akiyama, “Modeling of route choice behaviour using knowledge based techniques,” JSCE, Vol.11, pp. 65-72, 1993 (in Japanese).
[24] S.-K. Oh, S.-B. Rho, and G.-M. Nam, “Intelligence Modeling of Nonlinear Process System Using Fuzzy Neural Networks-based Structure,” Journal of Fuzzy Logic and Intelligent Systems, Vol.5, No.4, pp. 41-55, 1995 (in Korean).
[25] S.-K. Oh, and W. Pedrycz, “Fuzzy Identification by means of Auto-Tuning Algorithm and Its Application to Nonlinear Systems,” Fuzzy Sets and Systems, Vol.115, No.2, pp. 205-230, 2000.
[26] S.-K. Oh, K.-C. Yoon, and H.-K. Kim, “The Design of Optimal Fuzzy-Neural Networks Structure by Means of GA and an Aggregate Weighted Performance Index,” Journal of Control, Automation and Systems Engineering, Vol.6, No.3, pp. 273-283, 2000 (in Korean).
[27] B.-J. Park, W. Pedrycz, and S.-K. Oh, “Fuzzy Polynomial Neural Networks: Hybrid Architectures of Fuzzy Modeling,” IEEE Transactions on Fuzzy Systems, Vol.10, No.5, pp. 607-621, 2002.
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