Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 425740, 11 pages
http://dx.doi.org/10.1155/2013/425740
Research Article

Review on Methods to Fix Number of Hidden Neurons in Neural Networks

Anna University, Regional Centre, Coimbatore 641047, India

Received 18 March 2013; Revised 16 May 2013; Accepted 26 May 2013

Academic Editor: Matjaz Perc

Copyright © 2013 K. Gnana Sheela and S. N. Deepa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. S. N. Sivanandam, S. Sumathi, and S. N. Deepa, Introduction to Neural Networks Using Matlab 6.0, Tata McGraw Hill, 1st edition, 2008.
  2. D. Hunter, H. Yu, M. S. Pukish III, J. Kolbusz, and B. M. Wilamowski, “Selection of proper neural network sizes and architectures: a comparative study,” IEEE Transactions on Industrial Informatics, vol. 8, no. 2, pp. 228–240, 2012. View at Publisher · View at Google Scholar · View at Scopus
  3. K. Jinchuan and L. Xinzhe, “Empirical analysis of optimal hidden neurons in neural network modeling for stock prediction,” in Proceedings of the Pacific-Asia Workshop on Computational Intelligence and Industrial Application, vol. 2, pp. 828–832, December 2008. View at Publisher · View at Google Scholar · View at Scopus
  4. B. Curry and P. H. Morgan, “Model selection in neural networks: some difficulties,” European Journal of Operational Research, vol. 170, no. 2, pp. 567–577, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  5. M. A. Sartori and P. J. Antsaklis, “A simple method to derive bounds on the size and to train multilayer neural networks,” IEEE Transactions on Neural Networks, vol. 2, no. 4, pp. 467–471, 1991. View at Publisher · View at Google Scholar · View at Scopus
  6. M. Arai, “Bounds on the number of hidden units in binary-valued three-layer neural networks,” Neural Networks, vol. 6, no. 6, pp. 855–860, 1993. View at Google Scholar · View at Scopus
  7. J. Y. Li, T. W. S. Chow, and Y. L. Yu, “Estimation theory and optimization algorithm for the number of hidden units in the higher-order feedforward neural network,” in Proceedings of the IEEE International Conference on Neural Networks, vol. 3, pp. 1229–1233, December 1995. View at Scopus
  8. M. Hagiwara, “A simple and effective method for removal of hidden units and weights,” Neurocomputing, vol. 6, no. 2, pp. 207–218, 1994. View at Publisher · View at Google Scholar · View at Scopus
  9. S. Tamura and M. Tateishi, “Capabilities of a four-layered feedforward neural network: four layers versus three,” IEEE Transactions on Neural Networks, vol. 8, no. 2, pp. 251–255, 1997. View at Publisher · View at Google Scholar · View at Scopus
  10. O. Fujita, “Statistical estimation of the number of hidden units for feedforward neural networks,” Neural Networks, vol. 11, no. 5, pp. 851–859, 1998. View at Publisher · View at Google Scholar · View at Scopus
  11. K. Keeni, K. Nakayama, and H. Shimodaira, “Estimation of initial weights and hidden units for fast learning of multi-layer neural networks for pattern classification,” in Proceedings of the International Joint Conference on Neural Networks (IJCNN '99), vol. 3, pp. 1652–1656, IEEE, July 1999. View at Publisher · View at Google Scholar · View at Scopus
  12. T. Onoda, “Neural network information criterion for the optimal number of hidden units,” in Proceedings of the 1995 IEEE International Conference on Neural Networks, vol. 1, pp. 275–280, December 1995. View at Publisher · View at Google Scholar · View at Scopus
  13. M. M. Islam and K. Murase, “A new algorithm to design compact two-hidden-layer artificial neural networks,” Neural Networks, vol. 14, no. 9, pp. 1265–1278, 2001. View at Publisher · View at Google Scholar · View at Scopus
  14. Z. Zhang, X. Ma, and Y. Yang, “Bounds on the number of hidden neurons in three-layer binary neural networks,” Neural Networks, vol. 16, no. 7, pp. 995–1002, 2003. View at Publisher · View at Google Scholar · View at Scopus
  15. G. B. Huang, “Learning capability and storage capacity of two-hidden-layer feedforward networks,” IEEE Transactions on Neural Networks, vol. 14, no. 2, pp. 274–281, 2003. View at Publisher · View at Google Scholar · View at Scopus
  16. B. Choi, J. H. Lee, and D. H. Kim, “Solving local minima problem with large number of hidden nodes on two-layered feed-forward artificial neural networks,” Neurocomputing, vol. 71, no. 16–18, pp. 3640–3643, 2008. View at Publisher · View at Google Scholar · View at Scopus
  17. N. Jiang, Z. Zhang, X. Ma, and J. Wang, “The lower bound on the number of hidden neurons in multi-valued multi-threshold neural networks,” in Proceedings of the 2nd International Symposium on Intelligent Information Technology Application (IITA '08), pp. 103–107, December 2008. View at Publisher · View at Google Scholar · View at Scopus
  18. S. Trenn, “Multilayer perceptrons: approximation order and necessary number of hidden units,” IEEE Transactions on Neural Networks, vol. 19, no. 5, pp. 836–844, 2008. View at Publisher · View at Google Scholar · View at Scopus
  19. S. Xu and L. Chen, “A novel approach for determining the optimal number of hidden layer neurons for FNN's and its application in data mining,” in Proceedings of the 5th International Conference on Information Technology and Applications (ICITA '08), pp. 683–686, June 2008. View at Scopus
  20. K. Shibata and Y. Ikeda, “Effect of number of hidden neurons on learning in large-scale layered neural networks,” in Proceedings of the ICROS-SICE International Joint Conference 2009 (ICCAS-SICE '09), pp. 5008–5013, August 2009. View at Scopus
  21. C. A. Doukim, J. A. Dargham, and A. Chekima, “Finding the number of hidden neurons for an MLP neural network using coarse to fine search technique,” in Proceedings of the 10th International Conference on Information Sciences, Signal Processing and Their Applications (ISSPA '10), pp. 606–609, May 2010. View at Publisher · View at Google Scholar · View at Scopus
  22. H. C. Yuan, F. L. Xiong, and X. Y. Huai, “A method for estimating the number of hidden neurons in feed-forward neural networks based on information entropy,” Computers and Electronics in Agriculture, vol. 40, no. 1–3, pp. 57–64, 2003. View at Publisher · View at Google Scholar · View at Scopus
  23. Y. K. Wu and J. S. Hong, “A literature review of wind forecasting technology in the world,” in Proceedings of the IEEE Lausanne Power Tech, pp. 504–509, July 2007. View at Publisher · View at Google Scholar · View at Scopus
  24. G. Panchal, A. Ganatra, Y. P. Kosta, and D. Panchal, “Behaviour analysis of multilayer perceptrons with multiple hidden neurons and hidden layers,” International Journal of Computer Theory and Engineeringvol, vol. 3, no. 2, pp. 332–337, 2011. View at Google Scholar
  25. K. Z. Mao and G. B. Huang, “Neuron selection for RBF neural network classifier based on data structure preserving criterion,” IEEE Transactions on Neural Networks, vol. 16, no. 6, pp. 1531–1540, 2005. View at Publisher · View at Google Scholar · View at Scopus
  26. R. Devi, B. S. Rani, and V. Prakash, “Role of hidden neurons in an elman recurrent neural network in classification of cavitation signals,” International Journal of Computer Applications, vol. 37, no. 7, pp. 9–13, 2012. View at Publisher · View at Google Scholar
  27. H. Beigy and M. R. Meybodi, “Backpropagation algorithm adaptation parameters using learning automata,” International Journal of Neural Systems, vol. 11, no. 3, pp. 219–228, 2001. View at Google Scholar · View at Scopus
  28. M. Han and J. Yin, “The hidden neurons selection of the wavelet networks using support vector machines and ridge regression,” Neurocomputing, vol. 72, no. 1–3, pp. 471–479, 2008. View at Publisher · View at Google Scholar · View at Scopus
  29. N. Murata, S. Yoshizawa, and S. I. Amari, “Network information criterion-determining the number of hidden units for an artificial neural network model,” IEEE Transactions on Neural Networks, vol. 5, no. 6, pp. 865–872, 1994. View at Publisher · View at Google Scholar · View at Scopus
  30. J. Sun, “Learning algorithm and hidden node selection scheme for local coupled feedforward neural network classifier,” Neurocomputing, vol. 79, pp. 158–163, 2012. View at Publisher · View at Google Scholar · View at Scopus
  31. X. Zeng and D. S. Yeung, “Hidden neuron pruning of multilayer perceptrons using a quantified sensitivity measure,” Neurocomputing, vol. 69, no. 7–9, pp. 825–837, 2006. View at Publisher · View at Google Scholar · View at Scopus
  32. X. Wang and Y. Huang, “Convergence study in extended Kalman filter-based training of recurrent neural networks,” IEEE Transactions on Neural Networks, vol. 22, no. 4, pp. 588–600, 2011. View at Publisher · View at Google Scholar · View at Scopus
  33. V. Kůrková, P. C. Kainen, and V. Kreinovich, “Estimates of the number of hidden units and variation with respect to half-spaces,” Neural Networks, vol. 10, no. 6, pp. 1061–1068, 1997. View at Publisher · View at Google Scholar · View at Scopus
  34. Y. Liu, J. A. Starzyk, and Z. Zhu, “Optimizing number of hidden neurons in neural networks,” in Proceedings of the IASTED International Conference on Artificial Intelligence and Applications (AIA '07), pp. 121–126, February 2007. View at Scopus
  35. Y. Lan, Y. C. Soh, and G. B. Huang, “Constructive hidden nodes selection of extreme learning machine for regression,” Neurocomputing, vol. 73, no. 16–18, pp. 3191–3199, 2010. View at Publisher · View at Google Scholar · View at Scopus
  36. J. Li, B. Zhang, C. Mao, G. Xie, Y. Li, and J. Lu, “Wind speed prediction based on the Elman recursion neural networks,” in Proceedings of the International Conference on Modelling, Identification and Control (ICMIC '10), pp. 728–732, July 2010. View at Scopus
  37. Q. Cao, B. T. Ewing, and M. A. Thompson, “Forecasting wind speed with recurrent neural networks,” European Journal of Operational Research, vol. 221, no. 1, pp. 148–154, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  38. W. M. Lin and C. M. Hong, “A new Elman neural network-based control algorithm for adjustable-pitch variable-speed wind-energy conversion systems,” IEEE Transactions on Power Electronics, vol. 26, no. 2, pp. 473–481, 2011. View at Publisher · View at Google Scholar · View at Scopus
  39. J. Zhang and A. J. Morris, “A sequential learning approach for single hidden layer neural networks,” Neural Networks, vol. 11, no. 1, pp. 65–80, 1998. View at Publisher · View at Google Scholar · View at Scopus
  40. B. S. Grewal, Higher Engineering Mathematics, Khanna Publishers, 40th edition, 2007.