【标题】Principle Component Analysis

【作者】Herv ́ Abdi & Lynne J. Williams

【出版日期】2010
【文件格式】PDF
【文件大小】786.6 KB
【页数】47
【资料类别】主因素分析
【扫描版还是影印版】文字版
【是否缺页】否
【内容简介】
Principal component analysis (pca) is a multivariate 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 heterogenous
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.

【目录】
1 Introduction
2 Prerequisite notions and notations
3 Goals of PCA
4 Interpreting PCA
4.1 Contribution of an observation to a component
4.2 Squared Cosine of a component with an observation
4.3 Loading: correlation of a component and a variable
5 Statistical inference: Evaluating the quality of the model
5.1 Fixed Effect Model
5.2 Random Effect Model
5.3 How many components?
5.4 Bootstraped confidence intervals
6 Rotation
6.1 Orthogonal rotation
6.2 Oblique Rotations
6.3 When and why using rotations
7 Examples
7.1 Correlation PCA
7.2 Covariance PCA
8 Some extensions of PCA
8.1 Correspondence Analysis
8.2 Multiple factor analysis
9 Conclusion
References