Regularized-Generalized Partial Least Squares Discriminant Analysis

Linear Discriminant Analysis leads to unstable models and poor predictions in the presence of quasi collinearity among variables or in situations where the number of variables is large with respect to the samples. Partial Least Squares Discriminant Analysis (PLS-DA) was than proposed to overcome the multicollinearity problem and defined as a straightforward extension of the PLS regression. Generalized PLS-DA (GPLS-DA) and “Between” PLS-DA (B-PLS-DA) are two suitable extension of PLS-DA. A simple regularization procedure is proposed to cope with the problems of quasi collinearity or multicollinearity. It is shown that the GPLS-DA and Between PLS- DA are the two end points of a continuum approach.