Department of Statistics & Data Science, UCLA

Principal Component Analysis (PCA from now on) is a multivariate data analysis technique used for many different purposes and in many different contexts. PCA is the basis for low rank least squares approximation of a data matrix, for finding linear combinations with maximum or minimum variance, for fitting bilinear biplot models, for computing factor analysis approximations, and for studying regression with errors in variables. It is closely related to simple correspondence analysis (CA) and multiple corre- spondence analysis (MCA), which are discussed in Chapters XX and YY of this book.

PCA is used wherever large and complicated multivariate data sets have to be reduced to a simpler form. We find PCA in microarray analysis, medical imaging, educational and psychological testing, survey analysis, large scale time series analysis, atmospheric sciences, high-energy physics, astronomy, and so on. Jolliffe [2002] is a comprehensive overview of the theory and applications of classical PCA.