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

The Korean Institute of Electrical Engineers (대한전기학회)
권호 표지
DOI QR코드

DOI QR Code

Structural Design of Radial Basis Function-based Polynomial Neural Networks by Using Multiobjective Particle Swarm Optimization

다중 목적 입자 군집 최적화 알고리즘 이용한 방사형 기저 함수 기반 다항식 신경회로망 구조 설계

  • Received : 2011.09.22
  • Accepted : 2011.11.16
  • Published : 2012.01.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we proposed a new architecture called radial basis function-based polynomial neural networks classifier that consists of heterogeneous neural networks such as radial basis function neural networks and polynomial neural networks. The underlying architecture of the proposed model equals to polynomial neural networks(PNNs) while polynomial neurons in PNNs are composed of Fuzzy-c means-based radial basis function neural networks(FCM-based RBFNNs) instead of the conventional polynomial function. We consider PNNs to find the optimal local models and use RBFNNs to cover the high dimensionality problems. Also, in the hidden layer of RBFNNs, FCM algorithm is used to produce some clusters based on the similarity of given dataset. The proposed model depends on some parameters such as the number of input variables in PNNs, the number of clusters and fuzzification coefficient in FCM and polynomial type in RBFNNs. A multiobjective particle swarm optimization using crowding distance (MoPSO-CD) is exploited in order to carry out both structural and parametric optimization of the proposed networks. MoPSO is introduced for not only the performance of model but also complexity and interpretability. The usefulness of the proposed model as a classifier is evaluated with the aid of some benchmark datasets such as iris and liver.

Keywords

References

  1. Y. W. Wong, K. P. Seng and L. M. Ang "Radial Basis Function Neural Network with Incremental Learning for Face Recognition," Systems Man, and Cybernetics, Part B: Cybernetics, IEEE Trans. on, Vol. 41, No.4, pp. 940-949, 2011. https://doi.org/10.1109/TSMCB.2010.2101591
  2. K. A. A. Aziz, R. A. Ramlee, S. S. Abdullah, and A.N. Jahari, "Face Detection Using Radial Basis Function Neural Networks with Variance Spread Value," International Conference of Soft Computing and Pattern Recognition 2009(SOCPAR'09), 399-403.
  3. M. Hou, X. Han, "Constructive Approximation to Multivariate Function by Decay RBF Neural Network," IEEE Trans. on Neural Networks, Vol. 21, No. 9, pp. 1517-1523, 2010. https://doi.org/10.1109/TNN.2010.2055888
  4. 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, 2010. https://doi.org/10.1016/j.knosys.2009.12.002
  5. C. A. Coello Coello, and M. S. Lechuga, "MOPSO: A Proposal for Multiple Objective Particle Swarm Optimization," Proceedings of the 2002 IEEE Congress on Evolutionary Computation, pp.12-17.
  6. I. Hayashi, and H. Tanaka, "The Fuzzy GMDH Algorithm by Possibility Models and Its Application," Fuzzy Sets and Systems, Vol. 36, pp. 245-258, 1990. https://doi.org/10.1016/0165-0114(90)90182-6
  7. J. C. Bezdek, R. Ehrlich, and W. Full "FCM: The Fuzzy C-Means Clustering Algorithm" Computers & Geosciences, Vol. 10, No. 2-3, pp. 191-203, 1984. https://doi.org/10.1016/0098-3004(84)90020-7
  8. C. R. Raquel and P. C. Naval Jr, "An Effective Use of Crowding Distance in Multiobjective Particle Swarm Optimization," Proc. Genetic and Evol. Comput. (GECCO 2005), pp. 257-264, 2005.
  9. M. H. Hassoun, "Fundamentals of Artificial Neural Networks," The MIT Press, Cambridge, MA, 1995.
  10. F. Klawounn, D. Nauck, and R. Kruse, "Generating Rules from Data by Fuzzy and Neuro-fuzzy Methods," in Poc. Fuzzy-Neuro-Systems (1999), pp. 223-230.
  11. J. R. Quinlan, "Improved Use of Continuous Attributes in C4.5," J. Artificial Intelligence Press 4 (1996), pp. 77-90.
  12. C. Z. Janikow, and M. Faifer, "Fuzzy Partitioning with FID 3.1," In proc. IEEE 18th Int. conf. North American Fuzzy Information Proceedings Society (1999), pp. 467-471.
  13. M. A. Tahir, A. Bouridane, and F. Kurugollu, "Simulatneous Feature Selection and Feature Weighting Using Hybrid Tabu Search/K-Nearest Neighbor Classifier," Pattern Recognition Letters, Vol. 28, pp. 438-446, 2007. https://doi.org/10.1016/j.patrec.2006.08.016
  14. R. O. Duda, P. E. Hart, "Pattern Classification and Science Analysis," New York: Wiley, 2002.
  15. Z. R. Young, "A Novel Radial Basis Function Neural Network for Discriminant Analysis," IEEE Trans. Neural Networks, Vol. 17, No. 3, pp. 604-612, 2006. https://doi.org/10.1109/TNN.2006.873282