对主成分分析法三个问题的剖析  

Dissection to Three Typical Issues of Principal Component Analysis

作　　者：许淑娜[1] 李长坡[1] 

机构地区：[1]许昌学院城市与环境学院,许昌461000

出　　处：《数学理论与应用》2011年第4期116-121,共6页Mathematical Theory and Applications

摘　　要：从主成分分析法的基本原理入手,针对教学过程中学生对主成分分析法感到费解的三个问题进行了逐一剖析:1.为什么主成分系数是经标准差标准化后原始变量的协方差矩阵的特征向量?2.特征向量正负号如何选取?对进一步的研究如计算综合得分和聚类分析有何影响?3.主成分载荷值是如何得来的?同时指出有些教材在计算主成分得分时混淆了主成分载荷和特征向量的概念,以致造成错误的结果.Starting from the basic principles of Principal Component Analysis （ PCA）, dissected the three issues which always puzzling students in the process of teaching one by one. The first one is, why the principal component coefficients is the eigenvectors of the covariance matrix of normalized original variables？ And the second one, How to select the sign of eigenvectors？ What is the impact on further studies such as the calculation of composite scores and cluster analysis？ The third one, How the principal component loading values come from？ Besides, confusion of the concept of principal component loading and eigenvectors in the process of calculating the principal component scores from some materials was pointed out, which would cause erroneous results.

关 键 词：主成分分析法 特征值 特征向量 主成分载荷 主成分得分 

分 类 号：O212.4[理学—概率论与数理统计]