Computer Engineering and Applications ›› 2013, Vol. 49 ›› Issue (15): 6-9.
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LI Liang, SUN Qin
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Published:
李 亮,孙 秦
Abstract: In order to construct approximation model for high dimensional problems, Least Squares Support Vector Machine(LS-SVM) is introduced into High Dimensional Model Representation(HDMR), and a modified approximation model construction method called SVM-HDMR for high dimensional nonlinear problems and corresponding adaptive sampling and model construction algorithm are proposed. This method transforms high dimensional problem into a series of low dimensional problems using Cut-HDMR, and then these low dimensional problems are solved using LS-SVM. The results of numerical examples show that the new method has good approximation quality and reduces computational expense dramatically, so it is more suitable for high dimensional problems.
Key words: approximation model, Least Squares Support Vector Machine(LS-SVM), Cut-High Dimensional Model Representation(HDMR), adaptive sampling
摘要: 为了构造高维下的近似模型,将最小二乘支持向量机(LS-SVM)引入切割高维模型表示(Cut-HDMR),提出了SVM-HDMR高维非线性近似模型构造法,给出了相应的自适应采样和模型构造算法。该方法利用Cut-HDMR将高维问题转化为一系列低维问题,用LS-SVM求解这些低维问题。数值算例的测试结果表明该方法具有较好的近似精度,且与传统近似方法相比极大地降低了计算成本,从而更适用于高维工程问题的求解。
关键词: 近似模型, 最小二乘支持向量机(LS-SVM), 切割高维模型表示(Cut-HDMR), 自适应采样
LI Liang, SUN Qin. SVM-HDMR approximation model construction method for high dimensional nonlinear problems[J]. Computer Engineering and Applications, 2013, 49(15): 6-9.
李 亮,孙 秦. SVM-HDMR高维非线性近似模型构造法[J]. 计算机工程与应用, 2013, 49(15): 6-9.
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http://cea.ceaj.org/EN/Y2013/V49/I15/6