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快速Gram-Schmidt回归方法

王惠文 夏棒 孟洁

王惠文, 夏棒, 孟洁等 . 快速Gram-Schmidt回归方法[J]. 北京航空航天大学学报, 2013, 39(9): 1259-1262,1268.
引用本文: 王惠文, 夏棒, 孟洁等 . 快速Gram-Schmidt回归方法[J]. 北京航空航天大学学报, 2013, 39(9): 1259-1262,1268.
Wang Huiwen, Xia Bang, Meng Jieet al. Fast algorithm of Gram-Schmidt regression method[J]. Journal of Beijing University of Aeronautics and Astronautics, 2013, 39(9): 1259-1262,1268. (in Chinese)
Citation: Wang Huiwen, Xia Bang, Meng Jieet al. Fast algorithm of Gram-Schmidt regression method[J]. Journal of Beijing University of Aeronautics and Astronautics, 2013, 39(9): 1259-1262,1268. (in Chinese)

快速Gram-Schmidt回归方法

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

Fast algorithm of Gram-Schmidt regression method

  • 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.

     

  • [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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出版历程
  • 收稿日期:  2012-11-09
  • 网络出版日期:  2013-09-30

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