摘要： 主成分分析和奇异值分解都可以用于代数空间降维的线性投影分析,该文详细分析了这两种代数方法并给出了用于代数空间降维分析时二者之间的联系,并得到了在正定的实对称矩阵条件下主成分分析和奇异值分解是等价的这一结论。
关键词:
主成分分析,
奇异值分解,
降维,
特征抽取,
正定对称矩阵
Abstract: Principal component analysis(PCA) and Singular value decomposition(SVD) are two algebra methods used in linear projection analysis to reduce the dimensions in algebra space.The paper analyses the two methods in detail and deduces the relation of PCA to SVD when they are used in dimension reduction.Through the research this paper arrives at a conclusion that PCA and SVD are equivalent in the condition of being applied to positively definite symmetric matrices.
中图分类号:
张志佳,黄莎白,史泽林,王东署. 基于线性投影的代数空间降维分析[J]. , 2005, 31(21): 35-37.
ZHANG Zhijia1,2,HUANG Shabai1,SHI Zelin1,WANG Dongshu3. Linear Projection Based Dimension Reduction Analysis in Algebra Space[J]. , 2005, 31(21): 35-37.