Principal component analysis
Principal component analysis
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DOI：
10.1002/wics.101
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发表时间：
2010-07-01
影响因子：
3.2
通讯作者：
Williams, Lynne J.
中科院分区：
文献类型：
--
作者：
Abdi, Herve;Williams, Lynne J.
主成分分析(PCA)是一种分析数据表的多元技术，该表中的观测值由多个相互关联的数量因变量描述。它的目标是从表格中提取重要信息，将其表示为一组称为主成分的新的正交变量，并将观测值和变量的相似模式显示为地图上的点。主成分分析模型的质量可以使用交叉验证技术来评估，例如Bootstrap和jacksave。主成分分析可以概括为对应分析(CA)和多因素分析(MFA)，前者用于处理定性变量，后者用于处理不同类型的变量集。在数学上，主成分分析依赖于半正定矩阵的特征分解和矩形矩阵的奇异值分解。(C)2010年John Wiley父子公司
Principal component analysis (PCA) is amultivariate technique that analyzes a data table in which observations are described by several inter-correlated quantitative dependent variables. Its goal is to extract the important information from the table, to represent it as a set of new orthogonal variables called principal components, and to display the pattern of similarity of the observations and of the variables as points in maps. The quality of the PCA model can be evaluated using cross-validation techniques such as the bootstrap and the jackknife. PCA can be generalized as correspondence analysis (CA) in order to handle qualitative variables and as multiple factor analysis (MFA) in order to handle heterogeneous sets of variables. Mathematically, PCA depends upon the eigen-decomposition of positive semi-definite matrices and upon the singular value decomposition (SVD) of rectangular matrices. (C) 2010 John Wiley & Sons, Inc.