Procrustes rotation in analytical chemistry, a tutorial

Most analytical chemists are well acquainted with collecting multivariate data and analyzing them by basic tools provided in standard chemometric software. But sometimes this is not enough to extract the desired information. Two typical cases are when data sets need to be compared or when a subset of the measured variables shall be ranked. Both these cases can be addressed by so-called Procrustes rotation and its generalized forms. Procrustes rotation is conceptually a rather simple procedure, and it is available in some chemometric software. In this tutorial, we present the basics of Procrustes rotation, we exemplify its application on some selected examples and, finally, we review the literature. The goal is to make this very powerful technique more popular and accessible to the broader chemometric community.