Volume 2, Issue 4 p. 433-459
Overview

Principal component analysis

Hervé Abdi

Corresponding Author

Hervé Abdi

School of Behavioral and Brain Sciences, The University of Texas at Dallas, MS: GR4.1, Richardson, TX 75080-3021, USA

School of Behavioral and Brain Sciences, The University of Texas at Dallas, MS: GR4.1, Richardson, TX 75080-3021, USASearch for more papers by this author
Lynne J. Williams

Lynne J. Williams

Department of Psychology, University of Toronto Scarborough, Ontario, Canada

Search for more papers by this author
First published: 15 July 2010
Citations: 5,990

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.

This article is categorized under:

  • Statistical and Graphical Methods of Data Analysis > Multivariate Analysis
  • Statistical and Graphical Methods of Data Analysis > Dimension Reduction