Procrustes rotation as a diagnostic tool for projection pursuit analysis

Abstract

Projection pursuit (PP) is an effective exploratory data analysis tool because it optimizes the projection of high dimensional data using distributional characteristics rather than variance or distance metrics. The recent development of fast and simple PP algorithms based on minimization of kurtosis for clustering data has made this powerful tool more accessible, but under conditions where the sample-to-variable ratio is small, PP fails due to opportunistic overfitting of random correlations to limiting distributional targets. Therefore, some kind of variable compression or data regularization is required in these cases. However, this introduces an additional parameter whose optimization is manually time consuming and subject to bias. The present work describes the use of Procrustes analysis as diagnostic tool that can be used to evaluate the results of PP analysis in an efficient manner. Through Procrustes rotation, the similarity of different PP projections can be examined in an automated fashion with “Procrustes maps” to establish regions of stable projections as a function of the parameter to be optimized. The application of this diagnostic is demonstrated using principal components analysis to compress FTIR spectra from ink samples of ten different brands of pen, and also in conjunction with regularized PP for soybean disease classification.