基于主基底分析的变量筛选  

Variable selection based on principal basis analysis

作　　者：王惠文[1] 仪彬[1] 叶明[1] 

机构地区：[1]北京航空航天大学经济管理学院,北京100191

出　　处：《北京航空航天大学学报》2008年第11期1288-1291,共4页Journal of Beijing University of Aeronautics and Astronautics

基　　金：国家自然科学基金资助项目(70771004;70521001;70531010)

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.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.

关 键 词：Gram—Schmidt变换 变量筛选 数据降维 主基底 

分 类 号：O212[理学—概率论与数理统计]