Abstract
In this paper, we introduce optimization methods of Polynomial Radial Basis Function Neural Network (pRBFNN). The connection weight of proposed pRBFNN is represented as four kinds of polynomials, unlike in most conventional RBFNN constructed with constant as connection weight. Input space in partitioned with the aid of kernel functions and each kernel function is used Gaussian type. Least Square Estimation (LSE) is used to estimate the coefficients of polynomial. Also, in order to design the optimized pRBFNN model, center value of each kernel function is determined based on C-Means clustering algorithm, the width of the RBF, the polynomial type in the each node, input variables are identified through Particle Swarm Optimization (PSO) algorithm. The performances of the NOx emission process of gas turbine power plant data and Automobile Miles per Gallon (MPG) data was applied to evaluate proposed model. We analyzed approximation and generalization of model.
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References
Frolov, A.A., Husek, D., Muraviev, I.P., Polyakov, P.Y.: A Boolean factor analysis by attractor neural network. IEEE Trans. Neural Netw. 3, 698–707 (2007)
Yuan, J.L., Fine, T.L.: Neural-network design for small training sets of high dimension. IEEE Trans. Neural Netw. 2, 266–280 (1998)
Park, J., Sandberg, I.: Universal approximation using radial-basis function networks. Neural Comput. 3, 246–257 (1991)
Chen, S., Billings, S.A.: Neural network for nonlinear dynamic system modeling and identification. Int. J. Control. 56, 319–346 (1992)
Xie, N., Leung, H.: Blind equalization using a predictive radial basis function neural network. IEEE Trans. Neural Netw. 16, 709–720 (2005)
Pedrycz, W.: Conditional Fuzzy Clustering in The Design of Radial Basis Function Neural Networks. IEEE Trans. Neural Network 9, 601–612 (1998)
Bezdek, J.C., Keller, J., Krisnapuram, R., Pal, N.R.: Fuzzy models and algorithms for pattern recognition and image processing. Kluwer Academic Publisher, Dordrecht (1999)
Tsekouras, G.E.: On the use of the weighted fuzzy c-means in fuzzy modeling. Advances in engineering Software 36, 287–300 (2005)
Kennedy, J., Eberhare, R.: Particle swarm optimization. In: IEEE Int. Conf. Neural Networks, pp. 1942–1948 (1995)
Oh, S.K., Pedrycz, W., Park, H.S.: Hybrid Identification in fuzzy-neural networks. Fuzzy Sets Syst. 138, 399–426 (2003)
Oh, S.K., Pedrycz, W., Park, H.S.: Rule-based multy-FNN Identification with the aid of evolutionary fuzzy granulation. J. Knowledge-Bases Syst. 17, 1–13 (2004)
Jang, J.R.: ANFIS: Adaptive-Network-Based Fuzzy Inference Systems. IEEE Trans. on Systems, Man and Cybernetics 23, 665–685 (1993)
Pedrycz, W., Kwak, K.C.: Linguistic Models as a Framework of User-Centric System Modeling. IEEE Trans. 36, 727–745 (2006)
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Kim, YH., Kim, HK., Oh, SK. (2010). Structural Design of Optimized Polynomial Radial Basis Function Neural Networks. In: Zhang, L., Lu, BL., Kwok, J. (eds) Advances in Neural Networks - ISNN 2010. ISNN 2010. Lecture Notes in Computer Science, vol 6063. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13278-0_32
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DOI: https://doi.org/10.1007/978-3-642-13278-0_32
Publisher Name: Springer, Berlin, Heidelberg
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