Selection of a subset of variables: minimisation of Procrustes loss between a subset and the full set

摘要

A statistical method to reduce a large set of variables to a smaller subset of variables was published by Krzanowski [Krzanowski, W. J. (1987). Selection of variables to preserve multivariate data structure, using principal components. Applied Statistics, 36(1), 22-33]. An application in the field of sensory science is presented in this paper. The method selects the subset from all possible subsets by matching the multidimensional configuration of objects of the subset to the full set of variables. To this end a Procrustes rotation is used and the subset which produces the lowest Procrustes loss in this matching is selected as the optimal subset. For two data sets the loss values of all possible subsets of all possible sizes are studied. It is concluded that considering the subsets corresponding to a range of lowest loss values should be considered instead of only the subset producing the lowest loss value. The method can easily be extended to include fitting methods other than Procrustes rotations and other optimality criteria than the Procrustes loss employed here.