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Considering a regularized extreme learning machine (RELM) with randomly generated hidden nodes, an add-delete mechanism is proposed to determine the number of hidden nodes adaptively, where the extent of contribution to the objective function of RELM is treated as the criterion for judging each hidden node, that is, the large the better, and vice versa. As a result, the better hidden nodes are kept. On the contrary, the so-called worse hidden nodes are deleted. Naturally, the hidden nodes of RELM are selected optimally. In contrast to the other method only with the add mechanism, the proposed one has some advantages in the number of hidden nodes, generalization performance, and the real time. The experimental results on classical chaotic time series demonstrate the effectiveness and feasibility of the proposed add-delete mechanism for RELM.
[1] Li D C, Han M 2011 Acta Phys. Sin. 60 108903 (in Chinese) [李德才, 韩敏 2011 60 108903]
[2] Li H, Yang Z, Zhang Y M, Wen B C 2011 Acta Phys. Sin. 60 070512 (in Chinese) [李鹤, 杨周, 张义民, 闻邦椿 2011 60 070512]
[3] Ma Q L, Zheng Q L, Peng H, Qin J W 2009 Acta Phys. Sin. 58 1410 (in Chinese) [马千里, 郑启伦, 彭宏, 覃姜维 2009 58 1410]
[4] Zhang S, Liu H X, Gao D T, Du S D 2003 Chin. Phys. B 12 594
[5] Zhang J S, Xiao X C 2000 Chin. Phys. Lett. 17 88
[6] Huang G B, Zhu Q Y, Siew C K 2004 Proceedings of IEEE International Conference on Neural Networks Budapest, Hungary, July 25–29, 2004 p985
[7] Huang G B, Chen L, Siew C K 2006 IEEE Trans. Neural Netw. 17 879
[8] Huang G B, Zhou H M, Ding X J, Zhang R 2012 IEEE Trans. Syst. Man Cybern. B Cybern. 42 513
[9] Wang X Y, Han M 2012 Acta Phys. Sin. 61 080507 (in Chinese) [王新迎, 韩敏 2012 61 080507]
[10] Gao G Y, Jiang G P 2012 Acta Phys. Sin. 61 040506 (in Chinese) [高光勇, 蒋国平 2012 61 040506]
[11] Zhang X, Wang H L 2011 Acta Phys. Sin. 60 080504 (in Chinese) [张弦, 王宏力 2011 60 080504]
[12] Deng W Y, Zheng Q H, Chen L 2009 Proceedings of 2009 IEEE Symposium on Computational Intelligence and Data Mining Nashville, TN, United states, March 30 – April 2, 2009 p389
[13] Zhang X, Wang H L 2011 Acta Phys. Sin. 60 110201 (in Chinese) [张弦, 王宏力 2011 60 110201]
[14] Duda R O, Hart P E, Stork D G 2001 Pattern Classification (New York: John Wiley & Sons, Inc.)
[15] Zhang X D 2004 Matrix Analysis and Applications (Beijing: Tsinghua University Press) (in Chinese) [张贤达 2004 矩阵分析与应用 (北京: 清华大学出版社)]
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[1] Li D C, Han M 2011 Acta Phys. Sin. 60 108903 (in Chinese) [李德才, 韩敏 2011 60 108903]
[2] Li H, Yang Z, Zhang Y M, Wen B C 2011 Acta Phys. Sin. 60 070512 (in Chinese) [李鹤, 杨周, 张义民, 闻邦椿 2011 60 070512]
[3] Ma Q L, Zheng Q L, Peng H, Qin J W 2009 Acta Phys. Sin. 58 1410 (in Chinese) [马千里, 郑启伦, 彭宏, 覃姜维 2009 58 1410]
[4] Zhang S, Liu H X, Gao D T, Du S D 2003 Chin. Phys. B 12 594
[5] Zhang J S, Xiao X C 2000 Chin. Phys. Lett. 17 88
[6] Huang G B, Zhu Q Y, Siew C K 2004 Proceedings of IEEE International Conference on Neural Networks Budapest, Hungary, July 25–29, 2004 p985
[7] Huang G B, Chen L, Siew C K 2006 IEEE Trans. Neural Netw. 17 879
[8] Huang G B, Zhou H M, Ding X J, Zhang R 2012 IEEE Trans. Syst. Man Cybern. B Cybern. 42 513
[9] Wang X Y, Han M 2012 Acta Phys. Sin. 61 080507 (in Chinese) [王新迎, 韩敏 2012 61 080507]
[10] Gao G Y, Jiang G P 2012 Acta Phys. Sin. 61 040506 (in Chinese) [高光勇, 蒋国平 2012 61 040506]
[11] Zhang X, Wang H L 2011 Acta Phys. Sin. 60 080504 (in Chinese) [张弦, 王宏力 2011 60 080504]
[12] Deng W Y, Zheng Q H, Chen L 2009 Proceedings of 2009 IEEE Symposium on Computational Intelligence and Data Mining Nashville, TN, United states, March 30 – April 2, 2009 p389
[13] Zhang X, Wang H L 2011 Acta Phys. Sin. 60 110201 (in Chinese) [张弦, 王宏力 2011 60 110201]
[14] Duda R O, Hart P E, Stork D G 2001 Pattern Classification (New York: John Wiley & Sons, Inc.)
[15] Zhang X D 2004 Matrix Analysis and Applications (Beijing: Tsinghua University Press) (in Chinese) [张贤达 2004 矩阵分析与应用 (北京: 清华大学出版社)]
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