Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2014, Article ID 395686, 12 pages
http://dx.doi.org/10.1155/2014/395686
Research Article

RMSE-ELM: Recursive Model Based Selective Ensemble of Extreme Learning Machines for Robustness Improvement

1School of Information and Engineering, Ocean University of China, Shandong, Qingdao 266000, China
2School of Mechanical and Electrical Engineering, China Jiliang University, Zhejiang, Hangzhou 310018, China
3Department of Mechanical and Industrial Engineering and the Iowa Informatics Initiative, The University of Iowa, Iowa City, IA 52242-1527, USA
4Arcada University of Applied Sciences, 00550 Helsinki, Finland

Received 7 August 2014; Revised 14 September 2014; Accepted 22 September 2014; Published 9 October 2014

Academic Editor: Tao Chen

Copyright © 2014 Bo Han et al. 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. R. Salakhutdinov and G.-E. Hinton, “Deep boltzmann machine,” in Proceedings of the 12th International Conference on Artificial Intelligence and Statistics Proceedings (AISTATS '09), vol. 5, pp. 448–455, 2009.
  2. Y.-N. Chen, C.-C. Han, C.-T. Wang, B.-S. Jeng, and K.-C. Fan, “The application of a convolution neural network on face and license plate detection,” in Proceedings of the 18th International Conference on Pattern Recognition (ICPR '06), pp. 552–555, Hong Kong, August 2006. View at Publisher · View at Google Scholar · View at Scopus
  3. G. E. Hinton, S. Osindero, and Y. W. Teh, “A fast learning algorithm for deep belief nets,” Neural Computation, vol. 18, no. 7, pp. 1527–1554, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. Y. Bengio, “Learning deep architectures for AI,” Foundations and Trends in Machine Learning, vol. 2, no. 1, pp. 1–127, 2009. View at Publisher · View at Google Scholar
  5. G.-B. Huang, Q.-Y. Zhu, and C.-K. Siew, “Extreme learning machine: theory and applications,” Neurocomputing, vol. 70, no. 1–3, pp. 489–501, 2006. View at Publisher · View at Google Scholar · View at Scopus
  6. G. E. Hinton and R. R. Salakhutdinov, “Reducing the dimensionality of data with neural networks,” Science, vol. 313, no. 5786, pp. 504–507, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. R. Salakhutdinov and H. Larochelle, “Efficient learning of deep boltzmann machines,” in Proceedings of the International Conference on Artificial Intelligence and Statistics, 2010.
  8. G.-B. Huang, D.-H. Wang, and Y. Lan, “Extreme learning machines: a survey,” International Journal of Machine Learning and Cybernetics, vol. 2, no. 2, pp. 107–122, 2011. View at Publisher · View at Google Scholar · View at Scopus
  9. G.-B. Huang and C.-K. Slew, “Extreme learning machine: RBF network case,” in Proceedings of the 8th International Conference on Control, Automation, Robotics and Vision (ICARCV '04), pp. 1029–1036, December 2004. View at Scopus
  10. B. Frénay and M. Verleysen, “Parameter-insensitive kernel in extreme learning for non-linear support vector regression,” Neurocomputing, vol. 74, no. 16, pp. 2526–2531, 2011. View at Publisher · View at Google Scholar · View at Scopus
  11. G.-B. Huang, L. Chen, and C.-K. Siew, “Universal approximation using incremental constructive feedforward networks with random hidden nodes,” IEEE Transactions on Neural Networks, vol. 17, no. 4, pp. 879–892, 2006. View at Publisher · View at Google Scholar · View at Scopus
  12. C. Schüldt, I. Laptev, and B. Caputo, “Recognizing human actions: a local SVM approach,” in Proceedings of the 17th International Conference on Pattern Recognition (ICPR '04), vol. 3, pp. 32–36, August 2004. View at Publisher · View at Google Scholar · View at Scopus
  13. D. E. Rumelhart, G. E. Hinton, and R. J. Williams, “Learning representations by back-propagating errors,” Nature, vol. 323, no. 6088, pp. 533–536, 1986. View at Publisher · View at Google Scholar · View at Scopus
  14. N.-Y. Liang, G.-B. Huang, P. Saratchandran, and N. Sundararajan, “A fast and accurate online sequential learning algorithm for feedforward networks,” IEEE Transactions on Neural Networks, vol. 17, no. 6, pp. 1411–1423, 2006. View at Publisher · View at Google Scholar · View at Scopus
  15. Y. A. LeCun, L. Bottou, G. B. Orr, and K.-R. Müller, “Efficient backprop,” Lecture Notes in Computer Science, vol. 1524, pp. 9–50, 1998. View at Publisher · View at Google Scholar · View at Scopus
  16. G.-B. Huang, P. Saratchandran, and N. Sundararajan, “An efficient sequential learning algorithm for growing and pruning RBF (GAP-RBF) networks,” IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 34, no. 6, pp. 2284–2292, 2004. View at Publisher · View at Google Scholar · View at Scopus
  17. G.-B. Huang, P. Saratchandran, and N. Sundararajan, “A generalized growing and pruning RBF (GGAP-RBF) neural network for function approximation,” IEEE Transactions on Neural Networks, vol. 16, no. 1, pp. 57–67, 2005. View at Publisher · View at Google Scholar · View at Scopus
  18. G.-B. Huang, D. H. Wang, and Y. Lan, “Extreme learning machines: a survey,” International Journal of Machine Learning and Cybernetics, vol. 2, no. 2, pp. 107–122, 2011. View at Publisher · View at Google Scholar · View at Scopus
  19. H.-J. Rong, Y.-S. Ong, A.-H. Tan, and Z. Zhu, “A fast pruned-extreme learning machine for classification problem,” Neurocomputing, vol. 72, no. 1–3, pp. 359–366, 2008. View at Publisher · View at Google Scholar · View at Scopus
  20. Y. Miche, A. Sorjamaa, P. Bas, O. Simula, C. Jutten, and A. Lendasse, “OP-ELM: optimally pruned extreme learning machine,” IEEE Transactions on Neural Networks, vol. 21, no. 1, pp. 158–162, 2010. View at Publisher · View at Google Scholar · View at Scopus
  21. Y. Miche, A. Sorjamaa, and A. Lendasse, “OP-ELM: theory, experiments and a toolbox,” in Artificial Neural Networks—ICANN 2008, vol. 5163 of Lecture Notes in Computer Science, pp. 145–154, Springer, Berlin, Germany, 2008. View at Publisher · View at Google Scholar
  22. Y. Miche, P. Bas, C. Jutten, O. Simula, and A. Lendasse, “A methodology for building regression models using extreme learning machine: OP-ELM,” in Proceedings of the 16th European Symposium on Artificial Neural Networks—Advances in Computational Intelligence and Learning (ESANN '08), pp. 247–252, April 2008. View at Scopus
  23. L. K. Hansen and P. Salamon, “Neural network ensembles,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 12, no. 10, pp. 993–1001, 1990. View at Publisher · View at Google Scholar · View at Scopus
  24. A. Krogh and P. Sollich, Statistical Mechanics of Ensemble Learning, The American Physical Society, 1997.
  25. Z.-L. Sun, T.-M. Choi, K.-F. Au, and Y. Yu, “Sales forecasting using extreme learning machine with applications in fashion retailing,” Decision Support Systems, vol. 46, no. 1, pp. 411–419, 2008. View at Publisher · View at Google Scholar · View at Scopus
  26. Z.-H. Zhou, J.-X. Wu, Y. Jiang, and S.-F. Chen, “Genetic algorithm based selective neural network ensemble,” in Proceedings of the 17th International Joint Conference on Artificial Intelligence (IJCAI '01), pp. 797–802, Seattle, Wash, USA, August 2001. View at Scopus
  27. Y. Tang and B. Biondi, “Least-squares migration/inversion of blended data,” SEG Technical Program Expanded Abstracts, vol. 28, no. 1, pp. 2859–2863, 2009. View at Google Scholar · View at Scopus
  28. N. Li and Z.-H. Zhou, Selective Ensemble under Regularization Framework Multiple Classifier Systems, Springer, 2009.
  29. A. Asuncion and D.-J. Newman, “UCI machine learning repository,” 2007.
  30. G.-B. Huang, Q.-Y. Zhu, and C.-K. Siew, “Extreme learning machine: a new learning scheme of feedforward neural networks,” in Proceedings of the IEEE International Joint Conference on Neural Networks, vol. 2, pp. 985–990, July 2004. View at Publisher · View at Google Scholar · View at Scopus
  31. D. Serre, Matrices: Theory and Applications, vol. 216 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 2002. View at MathSciNet
  32. C.-R. Rao and S.-K. Mitra, Generalized Inverse of a Matrix and Its Applications, John Wiley & Sons, New York, NY, USA, 1972.
  33. H.-M. Van, Y. Miche, E. Oja et al., “Adaptive ensemble models of extreme learning machines for time series prediction,” in Proceedings of the 19th International Conference on Artificial Neural Networks (ICANN '09), vol. 5769 of Lecture Notes Computing Science, pp. 305–314, 2009.
  34. M. van Heeswijk, Y. Miche, E. Oja, and A. Lendasse, “GPU-accelerated and parallelized ELM ensembles for large-scale regression,” Neurocomputing, vol. 74, no. 16, pp. 2430–2437, 2011. View at Publisher · View at Google Scholar · View at Scopus
  35. Z.-H. Zhou, J. Wu, and W. Tang, “Ensembling neural networks: many could be better than all,” Artificial Intelligence, vol. 137, no. 1-2, pp. 239–263, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  36. L.-J. Zhao, T.-Y. Chai, and D.-C. Yuan, “Selective ensemble extreme learning machine modeling of effluent quality in wastewater treatment plants,” International Journal of Automation and Computing, vol. 9, no. 6, pp. 627–633, 2012. View at Publisher · View at Google Scholar · View at Scopus
  37. A. Asuncion and N. David, “UCI machine learning repository,” 2007.
  38. D. W. Opitz and J. W. Shavlik, “Generating accurate and diverse members of a neural-network ensemble,” in Advances in Neural Information Processing Systems, pp. 535–541, 1996. View at Google Scholar