A continuum decorrelation of the variables; Application to multivariate regression

- A continuum standardization and decorrelation of the variables is introduced.
- Properties related to this new continuum standardization are investigated.
- This strategy of analysis is applied to a multivariate regression.
- Its link with continuum Power PLS regression and Redundancy analysis is shown.

A continuum standardization, called αM-standardization, of a dataset whereby the variances of the variables and their correlations are gradually shaded off is proposed. It is tightly connected to the Mahalanobis distance. After investigating its properties, it is used to set up a continuum approach to predict one data set from another. It turned out that this continuum strategy is tightly linked to an approach called PLS power regression [1,2]. It is also shown that this strategy of analysis is broad enough to encompass PLS regression and redundancy analysis. An illustration on the basis of a two case studies is outlined.