A New Approach to Polynomial Neural Networks based on Genetic Algorithm
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.
[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.
[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.
@article{"International Journal of Information, Control and Computer Sciences:53043", author = "S. Farzi", title = "A New Approach to Polynomial Neural Networks based on Genetic Algorithm", 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.", volume = "2", number = "8", pages = "2619-8", }