快速Gram-Schmidt回归方法

王惠文; 夏棒; 孟洁

快速Gram-Schmidt回归方法

1.
北京航空航天大学经济管理学院, 北京 100191
2. 中央财经大学统计学院, 北京 102206

基金项目: 国家自然科学基金资助项目(71031001,71001110)

详细信息

作者简介:
王惠文(1957-),女,河北玉田人,教授,wanghw@vip.sina.com.

中图分类号: O212
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- 被引次数: 0
出版历程
- 收稿日期: 2012-11-09
- 网络出版日期: 2013-09-30

Fast algorithm of Gram-Schmidt regression method

1.
School of Economics and Management, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
2. School of Statistics, Central University of Finance and Economics, Beijing 102206, China

摘要

摘要: 提出一种快速的变量筛选与回归建模方法.该方法将在建模过程中,一方面筛选出对因变量有最佳解释作用的信息;另一方面基于Gram-Schmidt正交变换,识别和检验模型中的冗余变量,以便能够及时和成批量地删除所有冗余信息.仿真分析指出,在自变量数量巨大,同时变量之间的多重相关程度又非常高的情形下,与经典的逐步回归相比,该方法的计算速度更快,建模过程更加简洁有效.
- Gram-Schmidt正交变换 /
- 冗余变量 /
- 变量筛选 /
- 快速建模
Abstract: A new multiple linear regression method was proposed which can screen the variables fast. In the modeling process, not only can it screen variables containing best information to explain the dependent variable, but also distinguish and test redundant variables in the model based on Gram-Schmidt orthogonal transformation, so as to timely strike out all the redundant information in quantity. The simulation analysis shows that compared to classic stepwise regression this new method has a higher arithmetic speed and the modeling process is briefer and more efficient, when the variables appear in a large quantity and have a pretty serious server multicollinearity at the same time.
- Gram-Schmidt orthogonal transformation /
- redundant variables /
- variable selection /
- fast modeling

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参考文献(1)

[1] Björck Å.Solving linear least squares problems by Gram-Schmidt orthogonalization[J].BIT,1967,7:1-21 [2] Chen S,Billings S A,Luo W.Orthogonal least squares methods and their application to non-linear system identification[J].International Journal of Control,1989,50(5):1873-1896 [3] Cristianini N,Shawe-Taylor J,Lodhi H.Latent semantic kernels[J].Journal of Intelligent Information Systems,2002,18(2/3):127-152 [4] Mao K Z.Orthogonal forward selection and backward elimination algorithms for feature subset selection[J].IEEE Transactions on Systems,Man,and Cybernetics,Part B:Cybernetics,2004,34(1): 629-634 [5] He Yunhui.Modified generalized discriminant analysis using kernel Gram-Schmidt orthogonalization in difference space for face recognition[C]//Proceedings-2009 2nd International Workshop on Knowledge Discovery and Data Mining,WKKD 2009.Piscataway,NJ:IEEE Computer Society,2009:36-39 [6] Su Chaoton, Hsiao Yuhsiang.Multiclass MTS for simultaneous feature selection and classification[C]//IEEE Transactions on Knowledge and Data Engineering.Piscataway,NJ:IEEE Computer Society,2009:192-205 [7] Bian Yiwen. A Gram-Schmidt process based approach for improving DEA discrimination in the presence of large dimensionality of data set[J].Expert Systems with Applications:An International Journal,2012,39(3):3793-3799 [8] 王惠文,陈梅玲,Gilbert Saporta.Gram-Schmidt回归及在刀具磨损预报中的应用[J].北京航空航天大学学报,2008,34(6): 729-733 Wang Huiwen,Chen Meiling,Gilbert Saporta.Gram-Schmidt regression and application in cutting tool abrasion prediction[J].Journal of Beijing University of Aeronautics and Astronautics,2008,34(6):729-733(in Chinese) [9] Wang Huiwen,Yi Bin,Ye Ming.Unsupervised dimension reduction method based on Gram-Schmidt process[C]//Proceedings of IASC 2008.Tokyo:Japanese Society of Computational Statistics,2008:1659-1667 [10] 王惠文,仪彬,叶明.基于主基底分析的变量筛选[J].北京航空航天大学学报,2008,34(11):1288-1291 Wang Huiwen,Yi Bin,Ye Ming.Variable selection based on principal basis analysis[J].Journal of Beijing University of Aeronautics and Astronautics,2008,34(11):1288-1291(in Chinese)

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