Principal component analysis

TLDR: Principal component analysis (PCA) as discussed by the authors is a multivariate technique that analyzes a data table in which observations are described by several inter-correlated quantitative dependent variables, and 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 display the pattern of similarity of the observations and of the variables as points in maps.

Abstract: 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 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. Copyright © 2010 John Wiley & Sons, Inc.