Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30184
A New Approach to Polynomial Neural Networks based on Genetic Algorithm

Authors: S. Farzi

Abstract:

Recently, a lot of attention has been devoted to advanced techniques of system modeling. PNN(polynomial neural network) is a GMDH-type algorithm (Group Method of Data Handling) which is one of the useful method for modeling nonlinear systems but PNN performance depends strongly on the number of input variables and the order of polynomial which are determined by trial and error. In this paper, we introduce GPNN (genetic polynomial neural network) to improve the performance of PNN. GPNN determines the number of input variables and the order of all neurons with GA (genetic algorithm). We use GA to search between all possible values for the number of input variables and the order of polynomial. GPNN performance is obtained by two nonlinear systems. the quadratic equation and the time series Dow Jones stock index are two case studies for obtaining the GPNN performance.

Keywords: GMDH, GPNN, GA, PNN.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1331219

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1649

References:


[1] A.G. Ivahnenko, Polynomial theory of complex systems, IEEE Trans. Syst., Man Cybern.SMC-1,1971,pp.364-378.
[2] S.J. Farlow, The GMDH algorithm, in: S.J. Farlow (Ed.), Selforganizing Methods in Modeling: GMDH Type Algorithms, Marcel Dekker, New York, 1984, pp. 1-24.
[3] S.-K. Oh, D.-W. Kim, and B.-J. Park, "A study on the optimal design of polynomial neural networks structure," The Trans. of the Korean Institute of Electrical Engineers,2001, vol. 49d, no. 3, pp.365-396.
[4] G. Ivahnenko, "The group method of data handling: a rival of method of stochastic approximation," Soviet Automatic Control, 1968, vol.13, no. 3, pp. 43-55.
[5] D. E. Goldberg, "Genetic Algorithms in Search, Optimization & Machine Learning", Addison Wesley, 1989.
[6] B.-J. Park, S.-K. Oh, and W. Pedrycz, "The hybrid multi-layer inference architecture and algorithm of FPNN based on FNN and PNN," Joint 9th IFSA World Congress, 2001, pp. 1361-1366.
[7] S.-K. Oh, T.-C. Ahn, and W. Pedrycz, "A study on the selforganizing polynomial neural net works," Joint 9th IFSA World Congress, , 2001, pp.1690-1695.
[8] S.K. Oh, W.pedrycz, and B.J. Park, "polynomial neural networks architecture: Analysis and design," comput.Electr. Eng., ,2003, vol.29, no.6, pp.703-725.
[9] Oh S-K, Pedrycz W, Ahn T-C. "Self-organizing neural networks with fuzzy polynomial neurons". Appl Soft Comput 2002.
[10] Oh S-K, Pedrycz W. "The design of self-organizing polynomial neural networks". Inf Sci 2002, pp.237-258.
[11] Oh S-K, Pedrycz W. "Fuzzy polynomial neuron-based selforganizing neural networks". Int J Gen Syst 2003, pp.237-250.
[12] Oh S-K, Pedrycz W. "Self-organizing polynomial neural networks based on PNs or FPNs: analysis and design. Fuzzy Sets" Syst, 2004, pp.:163-198.
[13] Hayashi, H. Tanaka, "The Fuzzy GMDH algorithm by possibility models and its application," Fuzzy Sets and Systems 36, 1990, pp.245-258.
[14] S.-K. Oh, D.-W. Kim and B.-J. Park, "A study on the optimal design of polynomial neural networks structure," The Trans. of the Korean Institute of Electrical Engineers, 2000 (in Korean),vol. 49d, no. 3, pp. 145-156.
[15] G. Ivahnenko, "The group method of data handling: a rival of method of stochastic approximation," Soviet Automatic Control, 1968, vol.13, no. 3, pp. 43-55.
[16] D. E. Goldberg, Genetic Algorithms in Search, Optimization & Machine Learning, Addison -Wesley, 1989.
[17] M. Bishop, Neural Networks for Pattern Recognition, Oxford Univ. Press, 1995.
[18] B.-J. Park, W. Pedrycz, and S.-K. Oh "Fuzzy polynomial neural networks: hybrid architectures of fuzzy modeling," IEEE Trans. on Fuzzy Systems, October 2002, vol. 10, no. 5, pp. 607-621.