DOI QR코드

DOI QR Code

K-Means-Based Polynomial-Radial Basis Function Neural Network Using Space Search Algorithm: Design and Comparative Studies

공간 탐색 최적화 알고리즘을 이용한 K-Means 클러스터링 기반 다항식 방사형 기저 함수 신경회로망: 설계 및 비교 해석

  • Received : 2011.05.20
  • Accepted : 2011.06.20
  • Published : 2011.08.01

Abstract

In this paper, we introduce an advanced architecture of K-Means clustering-based polynomial Radial Basis Function Neural Networks (p-RBFNNs) designed with the aid of SSOA (Space Search Optimization Algorithm) and develop a comprehensive design methodology supporting their construction. In order to design the optimized p-RBFNNs, a center value of each receptive field is determined by running the K-Means clustering algorithm and then the center value and the width of the corresponding receptive field are optimized through SSOA. The connections (weights) of the proposed p-RBFNNs are of functional character and are realized by considering three types of polynomials. In addition, a WLSE (Weighted Least Square Estimation) is used to estimate the coefficients of polynomials (serving as functional connections of the network) of each node from output node. Therefore, a local learning capability and an interpretability of the proposed model are improved. The proposed model is illustrated with the use of nonlinear function, NOx called Machine Learning dataset. A comparative analysis reveals that the proposed model exhibits higher accuracy and superb predictive capability in comparison to some previous models available in the literature.

Keywords

Acknowledgement

Grant : U-city 보안감시 기술협력센터

Supported by : 한국연구재단, 경기도

References

  1. L. Zhao, Y. Yang, and Y. Zeng, "Eliciting compact T-S fuzzy models using subtractive clustering and coevolutaionary particle swarm optimization," Neurocomputing, vol. 72, no. 10-12, pp. 2569-2575, June 2009. https://doi.org/10.1016/j.neucom.2008.11.001
  2. B. Niu, Y. Zhu, X. He, and H. Shen, "A multi-swarm optimizer based fuzzy modeling approach for dynamic systems processing," Neurocomputing, vol. 71, no. 7-9, pp. 1436-1448, March 2008. https://doi.org/10.1016/j.neucom.2007.05.010
  3. A. Kandal, L. Li, and Z. Cao, "Fuzzy inference and its application to control systems," Fuzzy Sets and Systems, vol. 48, no. 1, pp. 99-111, 1992. https://doi.org/10.1016/0165-0114(92)90254-2
  4. Z.-B. Xu, H. Q, J. Peng, and B. Zhang, "A comparative study of two modeling approaches in neural network," Neural Networks, vol. 17, no. 1, pp. 73-85, Jan. 2004. https://doi.org/10.1016/S0893-6080(03)00192-8
  5. L. Sanchez, I. Couso, and J. Casillas, "Genetic learning of fuzzy rules based on low quality data," Fuzzy Sets and Systems, vol. 160, no. 17, pp. 2524-2552, Sep. 2009. https://doi.org/10.1016/j.fss.2009.03.004
  6. S. Kiranyaz, T. Ince, A. Yildirim, and M. Gabbouj, "Evolutionary artificial neural networks by multi-dimensional particle swarm optimization," Neural Networks, vol. 22, no. 10, pp. 1448-1462, Dec. 2009. https://doi.org/10.1016/j.neunet.2009.05.013
  7. A. A. Frolov, D. Husek, I. P. Muraviev, and P. Y. Polyakov, "A boolean factor analysis by attractor neural network," IEEE Transactions Neural Networks, vol. 3, pp. 698-707, May 2007. https://doi.org/10.1109/TNN.2007.891664
  8. R. A. Aliev, B. G. Guirimov, B. Fazlollahi, and R. R. Aliev, "Evolutionary algorithm-based learning of fuzzy neural networks. part 2: recurrent fuzzy neural networks," Fuzzy Sets and Systems, vol. 160, no. 17, pp. 2553-2566, Sep. 2009. https://doi.org/10.1016/j.fss.2008.12.018
  9. S. B. Roh, S. K. Oh, and W. Pedrycz, "A fuzzy ensemble of parallel polynomial neural networks with information granules formed by fuzzy clustering," Knowledge-Based Systems, vol. 23, no. 3, pp. 202-219, April 2010. https://doi.org/10.1016/j.knosys.2009.12.002
  10. J. C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum, New York, 1981.
  11. S. P. Lloyd, "Least squares quantization in PCM," IEEE Transactions on Information Theory, vol. 28, no. 2, pp. 129-137, Mar. 1982. https://doi.org/10.1109/TIT.1982.1056489
  12. J. Wang, J. Liu, and L. Liu, "A mountain means clustering algorithm," 7th World Congress on Intelligent Control and Automation (WCICA 2008), pp. 5045-5049, 2008.
  13. N. R. Pal and D. Chakraborty, "Mountain and subtractive clustering method: Improvements and generalizations," International Journal of Intelligent Systems, vol. 15, no. 4, pp. 329-341, April 2000. https://doi.org/10.1002/(SICI)1098-111X(200004)15:4<329::AID-INT5>3.0.CO;2-9
  14. W. Shen, X. Guo, C. Wu, and D. Wu, "Forecasting stock indices using radial basis function neural networks optimized by artificial fish swarm optimization," Knowledge-Based Systems, vol. 24, no. 3 pp. 378-385, April 2011. https://doi.org/10.1016/j.knosys.2010.11.001
  15. A. Azadeh, M. Saberi, and S. M. Asadzadeh, "An adaptive network based fuzzy inference system-auto regression-analysis of variance algorithm for improvement of oil consumption estimation and policy making: The cases of Canada United Kingdom, and South Korea," Applied Mathematical Modelling, vol. 35, no. 2, pp. 581-593, Feb. 2011. https://doi.org/10.1016/j.apm.2010.06.001
  16. D. Wu, K. Warwick, Z. Ma, J. G. Burgess, S. Pan, and T. Z. Aziz, "Prediction of Parkinson's disease tremor onset using radial basis function neural networks," Expert Systems with Applications, vol. 37, no. 4, pp. 2923-2928, April 2010. https://doi.org/10.1016/j.eswa.2009.09.045
  17. J. Li and X. Liu, "Melt index prediction by RBF neural network optimized with an MPSO-SA hybrid algorithm," Neurocomputing, vol. 74, no. 5, pp. 735-740, Feb. 2011. https://doi.org/10.1016/j.neucom.2010.09.019
  18. O. Nelles and R. Isermann, "Basis function networks for interpolation of local linear models," Proceedings of IEEE Conference on Decision and Control, vol. 1, pp. 470-475, 1996. https://doi.org/10.1109/CDC.1996.574356
  19. S. K. Oh, W. Pedrycz, and H. S. Park, "Hybrid identification in fuzzy-neural networks," Fuzzy Set and Systems, vol. 138, no. 2, pp. 399-426, Sep. 2003. https://doi.org/10.1016/S0165-0114(02)00441-4
  20. S. K. Oh, W. Pedrycz, and H. S. Park, "Rule-based multi-FNN identification with the aid of evolutionary fuzzy granulation," Knowledge-Based systems, vol. 24, no. 1, pp. 1-13, Jan. 2004.
  21. B. S Kim, S. K. Park, B. H. Choi, E. T. Kim, H. J. Lee, and H. J. Kang, "Collision risk assessment for pedestrians' safety using neural network," Journal of Institute of Control Robotics and Systems (in Korean), vol. 17, no. 1, pp. 1-11, Jan. 2011. https://doi.org/10.5302/J.ICROS.2011.17.1.1
  22. K. S. Seo and B. Y. Hyun, "GPU implementation techniques of genetic algorithm and comparative studies," Journal of Institute of Control Robotics and Systems (in Korean), vol. 17, no. 32, pp. 328-335, Jan. 2011. https://doi.org/10.5302/J.ICROS.2011.17.4.328