The Transactions of The Korean Institute of Electrical Engineers (전기학회논문지)

The Korean Institute of Electrical Engineers (대한전기학회)
권호 표지

The Design of Polynomial RBF Neural Network by Means of Fuzzy Inference System and Its Optimization

퍼지추론 기반 다항식 RBF 뉴럴 네트워크의 설계 및 최적화

  • Published : 2009.02.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this study, Polynomial Radial Basis Function Neural Network(pRBFNN) based on Fuzzy Inference System is designed and its parameters such as learning rate, momentum coefficient, and distributed weight (width of RBF) are optimized by means of Particle Swarm Optimization. The proposed model can be expressed as three functional module that consists of condition part, conclusion part, and inference part in the viewpoint of fuzzy rule formed in 'If-then'. In the condition part of pRBFNN as a fuzzy rule, input space is partitioned by defining kernel functions (RBFs). Here, the structure of kernel functions, namely, RBF is generated from HCM clustering algorithm. We use Gaussian type and Inverse multiquadratic type as a RBF. Besides these types of RBF, Conic RBF is also proposed and used as a kernel function. Also, in order to reflect the characteristic of dataset when partitioning input space, we consider the width of RBF defined by standard deviation of dataset. In the conclusion part, the connection weights of pRBFNN are represented as a polynomial which is the extended structure of the general RBF neural network with constant as a connection weights. Finally, the output of model is decided by the fuzzy inference of the inference part of pRBFNN. In order to evaluate the proposed model, nonlinear function with 2 inputs, waster water dataset and gas furnace time series dataset are used and the results of pRBFNN are compared with some previous models. Approximation as well as generalization abilities are discussed with these results.

Keywords

References

  1. M. L. Kothari, S. Madnani, and R. Segal, 'Orthogonal Least Square Learning Algorithm Based Radial Basis Function Network Adaptive Power System Stabilizer', Proceeding of IEEE SMC, Vol. 1, pp. 542-547, 1997 https://doi.org/10.1109/ICSMC.1997.625808
  2. J.S Roger Jang, C.T. Sun, 'Functional equivalence between radial basis function networks and fuzzy inference systems', IEEE Trans. Neural Networks, Vol. 4, No.1, pp. 156-158, 1993 https://doi.org/10.1109/72.182710
  3. J. C. Bezdek, 'Pattern Recognition with Fuzzy Objective Function Algorithms', Plenum Press, New York, 1981
  4. K. Z. Mao, 'RBF Neural Network Center Selection Based on Fisher Ratio Class Separability Measure', IEEE Trans. Neural Network, Vol. 13, No.5, pp.1211-1217, 2002 https://doi.org/10.1109/TNN.2002.1031953
  5. A. C. Micchelli, 'Interpolation of scattered data:Distance matrices and conditionally positive definite functions', Construct. Approx, Vol. 2, pp. 11-22, 1986 https://doi.org/10.1007/BF01893414
  6. M. J. D. Powell, 'Radial basis functions for multivariable interpolation: A review', in Proc. IMA Conf. Algorithms for the Approximation of Functions and Data, Shrivenham, U.K., 1985
  7. D. S. Broomhead and D. Lowe, 'Multivariable functional interpolation and adaptive networks', Complex Syst., Vol. 2, pp. 321-355, 1988
  8. Richard O. Duda, Peter E. Hart, David G. Stork, 'Pattern Classification; Second Edition', John Wiley&Sons, INC., 2000
  9. R. C. Eberhard, P. Simpson, R. Dobbins, 'Computional Intelligence PC Tools', Boston: Academic Press Professional, 1996
  10. A. Staiano. J. Tagliaferri, W. Pedrycz, 'Improving RBF networks performance in regression tasks by means of a supervised fuzzy clusering Automatic structure and parameter', Neurocomputing, Vol. 69, pp. 1570-1581, 2006 https://doi.org/10.1016/j.neucom.2005.06.014
  11. S.-K. Oh, W. Pedryz, B. - J, Park, 'Hybrid Identification of Fuzzy Rule-Based Models', International Journal of Intelligent System, Vol. 17, pp. 77-103, 2002 https://doi.org/10.1002/int.1004
  12. Y. Shi, R. C. Eberhart, 'Extracting Rules from Fuzzy Neural Network by Particle Swarm Optimization', Proceedings of the IEEE International Conference on Evolutionary Computation, 1998
  13. F. Behloul, B.P.F. Lelieveldt, A. Boudraa, J,H.C. Reiber, 'Optimal design of radial basis function neural networks for fuzzy-rule extraction in high dimensional data', The Journal of the Pattern Recognition Society, Vol. 35, pp. 659-675, 2002 https://doi.org/10.1016/S0031-3203(01)00033-4
  14. S.-K. Oh and W. Pedrycz, 'Identification of Fuzzy Systems by means of an Auto-Tuning Algorithm and Its Application to Nonlinear Systems', Fuzzy Sets and Syst., Vol. 115, No.2, pp. 205-230, 2000 https://doi.org/10.1016/S0165-0114(98)00174-2
  15. T. Tagaki and M. sugeno, 'Fuzzy identification of system and its applications to modeling and control', IEEE Trans. Syst. Cybem., Vol. SMC-15, No.1, pp. 116-132, 1985 https://doi.org/10.1109/TSMC.1985.6313399
  16. W. Pderyca and G. Vukovich, 'Granular neural networks', Neurocumputing, Vol. 36, pp. 205-224, 2001 https://doi.org/10.1016/S0925-2312(00)00342-8
  17. George E. Tsekouras, 'On the use of the weighted fuzzy c-means in fuzzy modeling', Advances in Engineering Software, Vol. 36, pp. 287-300, 2005 https://doi.org/10.1016/j.advengsoft.2004.12.001
  18. S. -K. Oh and W. Pedryz, 'Identification of Fuzzy Systems by means of an Auto-Tuning Algorithms and Its Application to Nonlinear Systems', Fuzzy Sets and Systs, Vol. 115, No.2, pp. 205-230, 2000 https://doi.org/10.1016/S0165-0114(98)00174-2
  19. B. - J, Park, W. Pedrycz and S. -K. Oh, 'Identification of fuzzy models with the aid of evolutionary data granulation', Vol. 148, No.5, pp. 406-418, 2001 https://doi.org/10.1049/ip-cta:20010677
  20. 오성권, 프로그램에 의한 컴퓨터지능(퍼지, 신경회로망 및 진화 알고리즘을 중심으로), 내하출판사, 2002