主方差分析方法

The Method of Principal Variance Analysis

该文提出一种对高维随机向量 X=( x1 ,x2 ,… ,xp)′p× 1 进行降维处理的实用方法 ,其基本思想是利用矩阵的扫描运算 ,构造 X的很少几个综合指标 (称为主方差变量 )以反映 X的统计特性。给出了该方法的理论依据和直观解释以及算法。特别指出 ,当变量 X多重相关性突出时 ,该文方法显著地优于主成分分析方法。

A practical method that reduces the dimensions of a high dimensional random vector X=(x 1,x 2,…,x p)′ p×1 is put forward.Its fundamental idea is, with the sweep operation of matrix, to structure a few synthetical indexes(called principal variance variables) of X to depict X's statistical feature. The theoretical foundation, audio-visual explanation and algorithm of the method are given. The method is markedly superior to of principal component analysis especially when X has serious multi-correlation.