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传统的滑动窗策略只是简单且机械地将最远的数据移出窗口, 而将最近的数据移进窗口. 针对这种遗忘策略存在的缺陷, 提出了过滤窗策略. 过滤窗采用"优胜劣汰"的选择机制, 将对模型贡献比较大的数据留在窗口当中. 将过滤窗和最小二乘支持向量回归机相结合, 提出了过滤窗最小二乘支持向量回归机. 与滑动窗最小二乘支持向量回归机相比较, 过滤窗最小二乘支持向量回归机具有较小的计算量, 需要较短的窗口长度就能达到和滑动窗最小二乘支持向量回归机几乎相同的预测精度, 而较短的窗口长度又预示着较少的计算量和较好的实时性. 混沌时间序列在线建模和预测的实例表明了过滤窗最小二乘支持向量回归机的有效性和可行性.When the traditional strategy of sliding window (SW) deals with the flowing data, the data far from current position are mechanically and briefly moved out of the window, and the nearest ones are moved into the window. To solve the shortcomings of this forgetting mechanism, the strategy of filtering window (FW) is proposed, in which adopted is the mechanism for selecting the superior and eliminating the inferior, thus resulting in the data making more contributions to the will-built model to be kept in the window. Merging the filtering window with least squares support vector regression (LSSVR) yields the filtering window based LSSVR (FW-LSSVR for short). As opposed to traditional sliding window based LSSVR (SW-LSSVR for short), FW-LSSVR cuts down the computational complexity, and needs smaller window size to obtain the almost same prediction accuracy, thus suggesting the less computational burden and better real time. The experimental results on classical chaotic time series demonstrate the effectiveness and feasibility of the proposed FW-LSSVR.
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Keywords:
- chaotic time series /
- support vector machine /
- sliding window /
- filtering window
[1] Zhang X, Wang H L 2011 Acta Phys. Sin. 60 080504 (in Chinese) [张弦, 王宏力 2011 物理学报 60 080504]
[2] Cai J W, Hu S S, Tao H F 2007 Acta Phys. Sin. 56 6820 (in Chinese) [蔡俊伟, 胡寿松, 陶洪峰 2007 物理学报 56 6820]
[3] Zhou Y D, Ma H, Lü W Y, Wang H Q 2007 Acta Phys. Sin. 56 6809 (in Chinese) [周永道, 马洪, 吕王勇, 王会琦 2007 物理学报 56 6809]
[4] Joshi B P, Kumar S 2012 Cybern. Syst. 43 34
[5] Mao J Q, Yao J, Ding H S 2009 Acta Phys. Sin. 58 2220 (in Chinese) [毛剑琴, 姚健, 丁海山 2009 物理学报 58 2220]
[6] 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]
[7] Li D, Han M Wang J 2012 IEEE Trans. Neural Netw. Learn. Syst. 23 787
[8] Song T, Li H 2012 Acta Phys. Sin. 61 080506 (in Chinese) [宋彤, 李菡 2012 物理学报 61 080506]
[9] Zhang L, Zhou W D, Chang P C, Yang J W, Li F Z 2013 Neurocomputing 99 411
[10] 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]
[11] Vapnik V N 1995 The Nature of Statistical Learning Theory (New York: Springer)
[12] Vapnik V N 1999 IEEE Trans. Neural Netw. 10 1045
[13] Ye M Y, Wang X D, Zhang H R 2005 Acta Phys. Sin. 54 2568 (in Chinese) [叶美盈, 汪晓东, 张浩然 2005 物理学报 54 2568]
[14] Zhang H R, Wang X D 2006 Chin. J. Comput. 29 400 (in Chinese) [张浩然, 汪晓东 2006 计算机学报 29 400]
[15] Fan Y G, Li P, Song Z H 2006 Control Decis. 21 1129 (in Chinese) [范玉刚, 李平, 宋执环 2006 控制与决策 21 1129]
[16] Suykens J A K, Vandewalle J 1999 Neural Process. Lett. 9 293
[17] Suykens J A K, van Gestel T, de Brabanter J, de Moor B, Vandewalle J 2002 Least Squares Support Vector Machines (Singapore: World Scientific)
[18] 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)]
[19] An S, Liu W, Venkatesh S 2007 Pattern Recognit. 40 2154
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[1] Zhang X, Wang H L 2011 Acta Phys. Sin. 60 080504 (in Chinese) [张弦, 王宏力 2011 物理学报 60 080504]
[2] Cai J W, Hu S S, Tao H F 2007 Acta Phys. Sin. 56 6820 (in Chinese) [蔡俊伟, 胡寿松, 陶洪峰 2007 物理学报 56 6820]
[3] Zhou Y D, Ma H, Lü W Y, Wang H Q 2007 Acta Phys. Sin. 56 6809 (in Chinese) [周永道, 马洪, 吕王勇, 王会琦 2007 物理学报 56 6809]
[4] Joshi B P, Kumar S 2012 Cybern. Syst. 43 34
[5] Mao J Q, Yao J, Ding H S 2009 Acta Phys. Sin. 58 2220 (in Chinese) [毛剑琴, 姚健, 丁海山 2009 物理学报 58 2220]
[6] 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]
[7] Li D, Han M Wang J 2012 IEEE Trans. Neural Netw. Learn. Syst. 23 787
[8] Song T, Li H 2012 Acta Phys. Sin. 61 080506 (in Chinese) [宋彤, 李菡 2012 物理学报 61 080506]
[9] Zhang L, Zhou W D, Chang P C, Yang J W, Li F Z 2013 Neurocomputing 99 411
[10] 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]
[11] Vapnik V N 1995 The Nature of Statistical Learning Theory (New York: Springer)
[12] Vapnik V N 1999 IEEE Trans. Neural Netw. 10 1045
[13] Ye M Y, Wang X D, Zhang H R 2005 Acta Phys. Sin. 54 2568 (in Chinese) [叶美盈, 汪晓东, 张浩然 2005 物理学报 54 2568]
[14] Zhang H R, Wang X D 2006 Chin. J. Comput. 29 400 (in Chinese) [张浩然, 汪晓东 2006 计算机学报 29 400]
[15] Fan Y G, Li P, Song Z H 2006 Control Decis. 21 1129 (in Chinese) [范玉刚, 李平, 宋执环 2006 控制与决策 21 1129]
[16] Suykens J A K, Vandewalle J 1999 Neural Process. Lett. 9 293
[17] Suykens J A K, van Gestel T, de Brabanter J, de Moor B, Vandewalle J 2002 Least Squares Support Vector Machines (Singapore: World Scientific)
[18] 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)]
[19] An S, Liu W, Venkatesh S 2007 Pattern Recognit. 40 2154
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