Variable selection and interpretation in correlation principal components

Principal component analysis (PCA) is a dimension‐reducing tool that replaces the variables in a multivariate data set by a smaller number of derived variables. Dimension reduction is often undertaken to help in interpreting the data set but, as each principal component usually involves all the original variables, interpretation of a PCA can still be difficult. One way to overcome this difficulty is to select a subset of the original variables and use this subset to approximate the principal components. This article reviews a number of techniques for choosing subsets of the variables and examines their merits in terms of preserving the information in the PCA, and in aiding interpretation of the main sources of variation in the data. Copyright © 2005 John Wiley & Sons, Ltd.