|Table of Contents|

Gradient-enhanced Least Squares Support Vector Regression

《南京理工大学学报》(自然科学版)[ISSN:1005-9830/CN:32-1397/N]

Issue:
2011年01期
Page:
138-143
Research Field:
Publishing date:

Info

Title:
Gradient-enhanced Least Squares Support Vector Regression
Author(s):
ZHOU Xiao-jianMA Yi-zhongLIU Li-pingWANG Jian-jun
School of Economics and Management,NUST,Nanjing 210094,China
Keywords:
support vector machine least squares support vector regression gradient computer experiments
PACS:
TP18
DOI:
-
Abstract:
To solve the problem of the larger number of samples being required to improve the regression accuracy in the least squares support vector regressions( LS-SVR) ,a model of gradient-enhanced least squares support vector regression ( GE-LSS-VR) is proposed. After changing the objective functions and constraint conditions,the gradient is introduced into the model,and the decision function is reconstructed. Three benchmark functions are used to verify the model. Three commonly-used measurement criterions are used to compare the experimental results. The results show that the model presented here can achieve an ideal regression accuracy at the cost of smaller samples.

References:

[1] Jin R,Chen W,Simpson T W. Comparative studies of metamodeling techniques under multiple modeling criteria [J ]. Structural and Multidisciplinary Optimization,2001,23( 1) : 1-13.
[2] Smola J,Schlkopf B. A tutorial on support vector regression[J]. Statistics and Computing,2004,14( 3) : 199-222.
[3] 周晓剑,马义中,朱嘉钢. SMO 算法的简化及其在非 正定核条件下的应用[J]. 计算机研究与发展, 2010,47( 11) : 1962-1969.
[4] 周晓剑,马义中,朱嘉钢,等. 求解非半正定核Huber -支持向量回归机问题的序列最小最优化算法研究 [J]. 控制理论与应用,2010,27( 9) : 1178-1184.
[5] 周晓剑,马义中. 两种求解非正定核Laplace-SVR 的 SMO算法[J].控制与决策,2009,24( 11) : 1657-1662.
[6] 张玉珍,何新,王建宇,等. 一种基于SVM 的高效球 门检测方法[J]. 南京理工大学学报( 自然科学 版) ,2010,34( 1) : 13-18.
[7] Clarke S M,Griebsch J H,Simpson T W. Analysis of support vector regression for approximation of complex engineering analyses[J]. ASME Journal of Mechanical Design,2005,127( 11) : 1077-1087.
[8] Simpson T W,Toropov V,Balabanov V,et al. Design and analysis of computer experiments in multidisciplinary design optimization: A review of how we have come-or not[A]. Proceedings of 12th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference [C]. Colombia,British: AIAA,2008.
[9] Forrester A I J,Keane A J. Recent advances in surrogatebased optimization[J]. Progress in Aerospace Sciences, 2009,45: 50-79.
[10] Suykens J A K. Least squares support vector machines [M]. Singapore: World Scientific,2002.
[11] Sellar R S,Batill S M,Renaud J E. Concurrent subspace optimization using gradient-based neural network response surface mappings[A]. Proceedings of 6th AIAA/NASA/ USAF/ISSMO Symposium on Multidisciplinary Analysis and Optimization Conference[C]. Washington D C: AIAA,1996.
[12] Liu W,Batill S,Gradient-enhanced neural network response surface approximations[A]. Proceeding of 8th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization Conference[C]. Long Beach,CA: AIAA,2000.
[13] Keulen F V,Vervenne K. Gradient-enhanced response surface building[J]. Structural and Multidisciplinary Optimization,2004,27: 337-51.
[14] Kim C,Wang S,Choi K K. Efficient response surface modeling by using moving least-squares method and sensitivity[J]. AIAA Journal,2005,43( 11) : 2404-11.
[15] Chung H S,Alonso J J. Using gradients to construct cokriging approximation models for high-dimensional design optimization problems[A]. Proceeding of 40th AIAA Aerospace Sciences Meeting and Exhibit[C]. Reno,Nevada: AIAA,2002.
[16] Liu W,Batill S M. Gradient-enhanced response surface approximations using Kriging models[A]. Proceedings of 9th AIAA/ISSMO Symposium and Exhibit on Multidisciplinary Analysis and Optimization Conference [C]. Atlanta,GA: AIAA,2002.
[17] Barthelemy J,Hall L E. Automatic differentiation as a tool in engineering design[A]. Proceeding of 4th AIAA/NASA/USAF/ISSMO Symposium on Multidisciplinary Analysis and Optimization Conference [C]. Cleveland,Ohio: AIAA,1992.
[18] Giles M B,Pierce N A. An introduction to the adjoint approach to design [J]. Flow,Turbulence and Combustion,2000,65: 393-2000.

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Last Update: 2012-02-28