Continuum redundancy-PLS regression: A simple continuum approach

The relationships between two data sets are investigated. The aim is to predict one data set from the other. New formulations of Redundancy Analysis and Partial Least Square Regression (PLS) are discussed, clearly showing the connexions between these two popular methods. Moreover, it is shown that the Redundancy Analysis and PLS regression are the two end points of a continuum approach. Properties related to this continuum approach are discussed, showing how the multicolinearity problem is handled. The interest of the general strategy of analysis is illustrated on the basis of a data set pertaining to epidemiology.