基于主基底分析的变量筛选

王惠文; 仪 彬; 叶 明

基于主基底分析的变量筛选

北京航空航天大学经济管理学院, 北京 100191

基金项目: 国家自然科学基金资助项目(70771004,70521001,70531010)

详细信息

作者简介:
王惠文(1957-),女,辽宁大连人,教授,wanghw@vip.sina.com.

中图分类号: O 212
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- 被引次数: 0
出版历程
- 收稿日期: 2007-11-08
- 网络出版日期: 2008-11-30

Variable selection based on principal basis analysis

School of Economics and Management, Beijing University of Aeronautics and Astronautics, Beijing 100191, China

摘要

摘要: 利用Gram-Schmidt变换,提出一种主基底分析方法.解释并证明了Gram-Schmidt变换所删除的信息量.给出"主基底"的定义及构造方法,并提出"净信息含量比"的概念,用以测度所选基底包含的信息.该方法能在原始数据信息损失尽可能小的前提下,排除所有的冗余变量以及变量集合中的重叠信息,得到一个正交的主基底,从而更有效地对大规模变量集合中的信息进行筛选.多角度的理论分析指出,主基底在尽可能多地携带原始变量信息的同时,还可保证样本点间的相似性改变最小.实际案例分析说明了该方法的合理性和有效性.
- Gram-Schmidt变换 /
- 变量筛选 /
- 数据降维 /
- 主基底
Abstract: A principal basis analysis method based on Gram-Schmidt process was proposed.Information deleted by Gram-Schmidt process was explained and proved.Principal basis and introduced its construction method was defined.The concept of net information ratio was also put forward to measure the information retained in principal basis. This method selects information effectively from the large-scale variable set while excludes all the redundant variables and reduplicate information,on the promise that the loss of original information is minimized to obtain a mini-dimensional orthogonal basis. From different perspectives,the principal basis can not only retain original information to the utmost extent, but also ensure least similarity changes between elements. Case study was addressed to validate the rationality and effectiveness of this method.
- Gram-Schmidt process /
- variable selection /
- dimension reduction /
- principal basis

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参考文献(1)

[1] Wold S,Martens H,Wold H.The multivariate calibration problem in chemistry solved by the PLS method[M].Heidelberg:Springer-Verlag,1983 [2] Cook R D,Weisberg S. Sliced inverse regression for dimension reduction[J].Journal of the American Statistical Association,1991,86(414):328-332 [3] Yutaka Tanaka,Yoichi Mori.Principal component analysis based on a subset of variables:variable selection and sensitivity analysis[J].American Journal of Mathematical and Management Sciences,1997,17(1-2):61-89 [4] 王惠文,陈梅玲,Gilbert Saporta. 基于Gram-Schmidt过程的回归模型及其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) [5] Jain S K,Gunawarddena A D.Linear algebra:an interactive approach[M].Beijing: China Machine Press, 2003 [6] 王惠文.偏最小二乘回归方法及其应用[M].北京:国防工业出版社,1997:93-107 Wang Huiwen.Partial least-squares regression-method and applications[M].Beijing: National Defense Industry Press,1997:93-107(in Chinese)

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