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In order to solve the hidden-layer neuron determination problem of regularized extreme learning machine (RELM) applied to chaotic time series prediction, a new algorithm based on Cholesky factorization is proposed. First, an RELM-based prediction model with one hidden-layer neuron is constructed and then a new hidden-layer neuron is added to the prediction model in each training step until the generalization performance of the prediction model reaches its peak value. Thus, the optimal network structure of the prediction model is determined. In the training procedure, Cholesky factorization is used to calculate the output weights of RELM. Experiments on chaotic time series prediction indicate that the algorithm can be effectively used to determine the optimal network strueture of RELM, and the prediction model trained by the algorithm has excellent performance in prediction accuracy and computational cost.
[1] Muhammad A F, Zolfaghari S 2010 Neurocomputing 73 2540
[2] Vairappan C, Tamura H, Gao S C 2009 Neurocomputing 72 1870
[3] [4] [5] Han M, Wang Y 2009 Expert. Syst. Appl. 36 1280
[6] Lee C C, Chiang Y C, Shih C Y, Tsai C L 2009 Expert. Syst. Appl. 36 4717
[7] [8] Mirzaee H 2009 Chaos Soliton Fract. 41 2681
[9] [10] [11] Hanias M P, Karras D A 2009 ENG Appl. Artif. Intel. 22 32
[12] [13] Xiu C B, Xu M 2010 Acta Phys. Sin. 59 7650(in Chinese)[修春波、徐 勐 2010 59 7650]
[14] [15] 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]
[16] [17] Zhang J F, Hu S S 2007 Acta Phys. Sin. 56 713(in Chinese)[张军峰、胡寿松 2007 56 713]
[18] Li J, Liu J H 2005 Acta Phys. Sin. 54 4569(in Chinese)[李 军、刘君华 2005 54 4569]
[19] [20] Huang G B, Zhu Q Y, Siew C K 2006 Neurocomputing 70 489
[21] [22] Feng G, Huang G B, Lin Q P, Gay R 2009 IEEE Neural 20 1352
[23] [24] [25] Huang G B, Chen L 2008 Neurocomputing 71 3460
[26] Liu N, Wang H 2010 IEEE Signal Pro. Let. 17 754
[27] [28] [29] Lan Y, Soh C Y, Huang G B 2010 Neurocomputing 73 3191
[30] Malathi V, Marimuthu N S, Baskar S 2010 Neurocomputing 73 2160
[31] [32] [33] Deng W Y, Zheng Q H, Chen L, Xu X B 2010 Chin. J. Comp. 33 279 (in Chinese)[邓万宇、郑庆华、陈 琳、许学斌 2010 计算机学报 33 279]
[34] Zhang X D 2005 Matrix Analysis and Applications (Beijing: Tsinghua University Press) p64 (in Chinese) [张贤达 2005 矩阵分析与应用(北京: 清华大学出版社) 第64页]
[35] -
[1] Muhammad A F, Zolfaghari S 2010 Neurocomputing 73 2540
[2] Vairappan C, Tamura H, Gao S C 2009 Neurocomputing 72 1870
[3] [4] [5] Han M, Wang Y 2009 Expert. Syst. Appl. 36 1280
[6] Lee C C, Chiang Y C, Shih C Y, Tsai C L 2009 Expert. Syst. Appl. 36 4717
[7] [8] Mirzaee H 2009 Chaos Soliton Fract. 41 2681
[9] [10] [11] Hanias M P, Karras D A 2009 ENG Appl. Artif. Intel. 22 32
[12] [13] Xiu C B, Xu M 2010 Acta Phys. Sin. 59 7650(in Chinese)[修春波、徐 勐 2010 59 7650]
[14] [15] 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]
[16] [17] Zhang J F, Hu S S 2007 Acta Phys. Sin. 56 713(in Chinese)[张军峰、胡寿松 2007 56 713]
[18] Li J, Liu J H 2005 Acta Phys. Sin. 54 4569(in Chinese)[李 军、刘君华 2005 54 4569]
[19] [20] Huang G B, Zhu Q Y, Siew C K 2006 Neurocomputing 70 489
[21] [22] Feng G, Huang G B, Lin Q P, Gay R 2009 IEEE Neural 20 1352
[23] [24] [25] Huang G B, Chen L 2008 Neurocomputing 71 3460
[26] Liu N, Wang H 2010 IEEE Signal Pro. Let. 17 754
[27] [28] [29] Lan Y, Soh C Y, Huang G B 2010 Neurocomputing 73 3191
[30] Malathi V, Marimuthu N S, Baskar S 2010 Neurocomputing 73 2160
[31] [32] [33] Deng W Y, Zheng Q H, Chen L, Xu X B 2010 Chin. J. Comp. 33 279 (in Chinese)[邓万宇、郑庆华、陈 琳、许学斌 2010 计算机学报 33 279]
[34] Zhang X D 2005 Matrix Analysis and Applications (Beijing: Tsinghua University Press) p64 (in Chinese) [张贤达 2005 矩阵分析与应用(北京: 清华大学出版社) 第64页]
[35]
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