Selection of Variables to Preserve Multivariate Data Structure, Using Principal Components

A common objective in exploratory multivariate analysis is to identify a subset of the variables which conveys the main features of the whole sample. Analysis of a well-known multivariate data set shows that methods currently available for selecting variables in principal component analysis may not lead to an appropriate subset. A new selection method, based on Procrustes Analysis, is proposed and shown to lead to a better subset for the data first analysed. Some supporting Monte Carlo results are presented, and implications for other multivariate techniques are briefly discussed.