PLS has been extensively studied in the past, but several issues about its theoretical foundation are still open. In this study, we draw an alternative formulation of PLS2 based on gradient descent method. A new algorithm to solve the least squares problem called "gradient descent" PLS2 is introduced. The "latent variable" language is not used in its formulation. Well-defined elements of linear algebra are used and the method is developed within the non-linear programming field, rather than statistical modelling. The new algorithm is equivalent to the standard "eigenvalue" PLS2 algorithm. The use of "gradient descent" PLS2 to solve linear regression problems is discussed and two data sets, one simulated and one real, are investigated to show the behaviour of the algorithm.
NSTL
Elsevier
