A comparison of procedures to select important variables for describing datasets

Procrustes rotation is a powerful technique to select a minimum number of variables to characterize sets of objects. Here, Procrustes rotation was investigated with regard to either data preprocessing (autoscaling and ‘minone’) or four different criteria to match the original and the reduced subspaces (i.e., for dropping out a vector from a data matrix). A well-known dataset which deals with morphologic descriptors of flying aphids was considered. In addition, a new procedure DROPCORA to look for variable selection was proposed and compared to the Procrustes one. It is based on evaluation of the correlation coefficients between vectors of matrix of variables. The number of selected variables was always equal to the number of important dimensions of the dataset. The variables selected in these ways differed and, so, robustness and multicollinearity were calculated. Considering both tests best results were obtained from the correlation matrix by procedure DROPCORA. Variable selection was also investigated by transforming vectors to Fourier coefficients.