A continuum standardization of the variables. Application to principal components analysis and PLS-regression

• A continuum standardization of the variables is introduced.
• We discuss properties related to this standardization.
• We investigate its effect on principal component analysis and PLS-regression.

A continuum standardization of the variables is proposed. It consists of dividing each variable by its standard deviation to the power α, where α is a scalar between 0 and 1. The non-standardized dataset and the standardized datasets appear as the two extreme points of this continuum and the Pareto standardization is its mid-point. Properties related to this standardization are discussed. Application to principal components analysis and PLS-regression is outlined and illustrated on the basis of real datasets.