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This paper analyzes the error characteristic of traditional support vector machine prediction algorithm, where the error series are smooth and regular. This is because a single prediction model is incapable of fitting chaotic system mapping function and omitting some deterministic component. On this basis, a prediction algorithm that consists of an iterative error correction and a least square support vector machine (LSSVM) is proposed. The algorithm creats multiple predictive models via the method of iterative error correction to approximate the chaotic system mapping function and obtain significant improvements of predictive performance. In addition, the optimal parameters of the prediction model are automatically obtained from the pattern search algorithm which is simple and effective. Experiment conducted on Lorenz time series and MackeyGlass time series indicates that the proposed algorithm has a much better performance than that recorded in the literature.
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Keywords:
- chaos time series prediction /
- least square support vector machine /
- iterative error correction /
- parameter composite optimization
[1] Chen D Y, Liu Y, Ma X Y 2012 Acta Phys. Sin. 61 100501 (in Chinese) [陈帝伊, 柳烨, 马孝义 2012 物理学报 61 100501]
[2] Han M, Xu M L 2013 Acta Phys. Sin. 62 120510 (in Chinese) [韩敏, 许美玲 2013 物理学报 62 120510]
[3] Song T, Li H 2012 Acta Phys. Sin. 61 080506 (in Chinese) [宋彤, 李菡 2012 物理学报 61 080506]
[4] Lei Z, Fengchun T, Shouqiong L, Lijun D, Xiongwei P, Xin Y 2013 Sensors and Actuators B: Chemical 182 71
[5] Rohitash C, Mengjie Z 2012 Neurocomputing 86 116
[6] Cheng-Jian L, Cheng-Hung C, Chin-Teng L 2009 IEEE Trans. Sys. Tem. Man Cyber. 39 55
[7] Ma Q L, Zheng Q L, Peng H, Tan J W 2009 Acta Phys. Sin. 58 1410 (in Chinese) [马千里, 郑启伦, 彭宏, 覃姜维 2009 物理学报 58 1410]
[8] Zhang C T, Ma Q L, Peng H 2010 Acta Phys. Sin. 59 7623 (in Chinese) [张春涛, 马千里, 彭宏 2010 物理学报 59 7623]
[9] Shi Z W, Han M 2007 IEEE Trans. Neural Netw. 18 359
[10] Chatzis S P, Demiris Y 2011 IEEE Trans. Neural Netw. 22 1435
[11] Zhang W Z, Long W, Jiao J J 2012 Acta Phys. Sin. 61 220506 (in Chinese) [张文专, 龙文, 焦建军 2012 物理学报 61 220506]
[12] Zhang J F, Hu S S 2008 Acta Phys. Sin. 57 2708 (in Chinese) [张军峰, 胡寿松 2008 物理学报 57 2708]
[13] Arash M, Majid A 2013 IEEE Trans. Neural Netw. 24 207
[14] Yu Y H, Song J D 2012 Acta Phys. Sin. 61 170516 (in Chinese) [于艳华, 宋俊德 2012 物理学报 61 170516]
[15] Vapnik V N, 1999 The Nature of Statistical Learning Theory (2nd Ed.) (New York, Springer) pp183-190
[16] Sapankevych N I, Sankar R 2009 IEEE Comput. Intell. Mag. 4 24
[17] Cai C Z, Fei J F, Wen Y F, Zhu X J, Xiao T T 2009 Acta Phys. Sin. 58 S008 (in Chinese) [蔡从中, 裴军芳, 温玉锋, 朱星键, 肖婷婷 2009 物理学报 58S008]
[18] Ligang Z, Kin K L, Lean Y 2009 Soft Comput. 13 149
[19] Chen M H, Ceckbum B, Reitich F 2005 J. Sci. Comput. 22 205
[20] Mirmomeni M, Lucas C, Araabi B N, Moshiri B, Bidar M R 2011 IET Signal Process. 5 515
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[1] Chen D Y, Liu Y, Ma X Y 2012 Acta Phys. Sin. 61 100501 (in Chinese) [陈帝伊, 柳烨, 马孝义 2012 物理学报 61 100501]
[2] Han M, Xu M L 2013 Acta Phys. Sin. 62 120510 (in Chinese) [韩敏, 许美玲 2013 物理学报 62 120510]
[3] Song T, Li H 2012 Acta Phys. Sin. 61 080506 (in Chinese) [宋彤, 李菡 2012 物理学报 61 080506]
[4] Lei Z, Fengchun T, Shouqiong L, Lijun D, Xiongwei P, Xin Y 2013 Sensors and Actuators B: Chemical 182 71
[5] Rohitash C, Mengjie Z 2012 Neurocomputing 86 116
[6] Cheng-Jian L, Cheng-Hung C, Chin-Teng L 2009 IEEE Trans. Sys. Tem. Man Cyber. 39 55
[7] Ma Q L, Zheng Q L, Peng H, Tan J W 2009 Acta Phys. Sin. 58 1410 (in Chinese) [马千里, 郑启伦, 彭宏, 覃姜维 2009 物理学报 58 1410]
[8] Zhang C T, Ma Q L, Peng H 2010 Acta Phys. Sin. 59 7623 (in Chinese) [张春涛, 马千里, 彭宏 2010 物理学报 59 7623]
[9] Shi Z W, Han M 2007 IEEE Trans. Neural Netw. 18 359
[10] Chatzis S P, Demiris Y 2011 IEEE Trans. Neural Netw. 22 1435
[11] Zhang W Z, Long W, Jiao J J 2012 Acta Phys. Sin. 61 220506 (in Chinese) [张文专, 龙文, 焦建军 2012 物理学报 61 220506]
[12] Zhang J F, Hu S S 2008 Acta Phys. Sin. 57 2708 (in Chinese) [张军峰, 胡寿松 2008 物理学报 57 2708]
[13] Arash M, Majid A 2013 IEEE Trans. Neural Netw. 24 207
[14] Yu Y H, Song J D 2012 Acta Phys. Sin. 61 170516 (in Chinese) [于艳华, 宋俊德 2012 物理学报 61 170516]
[15] Vapnik V N, 1999 The Nature of Statistical Learning Theory (2nd Ed.) (New York, Springer) pp183-190
[16] Sapankevych N I, Sankar R 2009 IEEE Comput. Intell. Mag. 4 24
[17] Cai C Z, Fei J F, Wen Y F, Zhu X J, Xiao T T 2009 Acta Phys. Sin. 58 S008 (in Chinese) [蔡从中, 裴军芳, 温玉锋, 朱星键, 肖婷婷 2009 物理学报 58S008]
[18] Ligang Z, Kin K L, Lean Y 2009 Soft Comput. 13 149
[19] Chen M H, Ceckbum B, Reitich F 2005 J. Sci. Comput. 22 205
[20] Mirmomeni M, Lucas C, Araabi B N, Moshiri B, Bidar M R 2011 IET Signal Process. 5 515
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